diff --git a/README.md b/README.md
index 4ce110c89..972e6bf9c 100644
--- a/README.md
+++ b/README.md
@@ -1,4 +1,5 @@
# Braket Tutorials GitHub
+
Welcome to the primary repository for Amazon Braket tutorials. We provide tutorials on quantum computing, using Amazon Braket. We provide examples for quantum circuits and Analog Hamiltonian Simulation. We cover canonical routines, such as the Quantum Fourier Transform (QFT), as well as hybrid quantum algorithms, such as the Variational Quantum Eigensolver (VQE).
The examples in this repository are structured as follows:
@@ -14,285 +15,299 @@ The examples in this repository are structured as follows:
- [Qiskit with Braket](#qiskit)
---
+
## I'm new to quantum
- * [**Getting started**](examples/getting_started/0_Getting_started/0_Getting_started.ipynb)
+- [**Getting started**](examples/getting_started/0_Getting_started/0_Getting_started.ipynb)
- A hello-world tutorial that shows you how to build a simple circuit and run it on a local simulator.
+ A hello-world tutorial that shows you how to build a simple circuit and run it on a local simulator.
- * [**Running quantum circuits on simulators**](examples/getting_started/1_Running_quantum_circuits_on_simulators/1_Running_quantum_circuits_on_simulators.ipynb)
+- [**Running quantum circuits on simulators**](examples/getting_started/1_Running_quantum_circuits_on_simulators/1_Running_quantum_circuits_on_simulators.ipynb)
- This tutorial prepares a paradigmatic example for a multi-qubit entangled state, the so-called GHZ state (named after the three physicists Greenberger, Horne, and Zeilinger). The GHZ state is extremely non-classical, and therefore very sensitive to decoherence. For this reason, it is often used as a performance benchmark for today's hardware. Moreover, in many quantum information protocols it is used as a resource for quantum error correction, quantum communication, and quantum metrology.
+ This tutorial prepares a paradigmatic example for a multi-qubit entangled state, the so-called GHZ state (named after the three physicists Greenberger, Horne, and Zeilinger). The GHZ state is extremely non-classical, and therefore very sensitive to decoherence. For this reason, it is often used as a performance benchmark for today's hardware. Moreover, in many quantum information protocols it is used as a resource for quantum error correction, quantum communication, and quantum metrology.
- * [**Running quantum circuits on QPU devices**](examples/getting_started/2_Running_quantum_circuits_on_QPU_devices/2_Running_quantum_circuits_on_QPU_devices.ipynb)
+- [**Running quantum circuits on QPU devices**](examples/getting_started/2_Running_quantum_circuits_on_QPU_devices/2_Running_quantum_circuits_on_QPU_devices.ipynb)
- This tutorial prepares a maximally-entangled Bell state between two qubits, for classical simulators and for QPUs. For classical devices, we can run the circuit on a local simulator or a cloud-based on-demand simulator. For the quantum devices, we run the circuit on the superconducting machine from Rigetti, and on the ion-trap machine provided by IonQ. As shown, one can swap between different devices seamlessly, without any modifications to the circuit definition, by re-defining the device object. We also show how to recover results using the unique Amazon resource identifier (ARN) associated with every quantum task. This tool is useful if you must deal with potential delays, which can occur if your quantum task sits in the queue awaiting execution.
+ This tutorial prepares a maximally-entangled Bell state between two qubits, for classical simulators and for QPUs. For classical devices, we can run the circuit on a local simulator or a cloud-based on-demand simulator. For the quantum devices, we run the circuit on the superconducting machine from Rigetti, and on the ion-trap machine provided by IonQ. As shown, one can swap between different devices seamlessly, without any modifications to the circuit definition, by re-defining the device object. We also show how to recover results using the unique Amazon resource identifier (ARN) associated with every quantum task. This tool is useful if you must deal with potential delays, which can occur if your quantum task sits in the queue awaiting execution.
- * [**Deep Dive into the anatomy of quantum circuits**](examples/getting_started/3_Deep_dive_into_the_anatomy_of_quantum_circuits/3_Deep_dive_into_the_anatomy_of_quantum_circuits.ipynb)
+- [**Deep Dive into the anatomy of quantum circuits**](examples/getting_started/3_Deep_dive_into_the_anatomy_of_quantum_circuits/3_Deep_dive_into_the_anatomy_of_quantum_circuits.ipynb)
- This tutorial discusses in detail the anatomy of quantum circuits in the Amazon Braket SDK. Specifically, you'll learn how to build (parameterized) circuits and display them graphically, and how to append circuits to each other. We discuss the associated circuit depth and circuit size. Finally we show how to execute the circuit on a device of our choice (defining a quantum task). We then learn how to track, log, recover, or cancel such a _quantum task_ efficiently.
+ This tutorial discusses in detail the anatomy of quantum circuits in the Amazon Braket SDK. Specifically, you'll learn how to build (parameterized) circuits and display them graphically, and how to append circuits to each other. We discuss the associated circuit depth and circuit size. Finally we show how to execute the circuit on a device of our choice (defining a quantum task). We then learn how to track, log, recover, or cancel such a _quantum task_ efficiently.
- * [**Superdense coding**](examples/getting_started/4_Superdense_coding/4_Superdense_coding.ipynb)
+- [**Superdense coding**](examples/getting_started/4_Superdense_coding/4_Superdense_coding.ipynb)
- This tutorial constructs an implementation of the _superdense coding_ protocol, by means of the Amazon Braket SDK. Superdense coding is a method of transmitting two classical bits by sending only one qubit. Starting with a pair of entanged qubits, the sender (_aka_ Alice) applies a certain quantum gate to their qubit and sends the result to the receiver (_aka_ Bob), who is then able to decode the full two-bit message.
+ This tutorial constructs an implementation of the _superdense coding_ protocol, by means of the Amazon Braket SDK. Superdense coding is a method of transmitting two classical bits by sending only one qubit. Starting with a pair of entanged qubits, the sender (_aka_ Alice) applies a certain quantum gate to their qubit and sends the result to the receiver (_aka_ Bob), who is then able to decode the full two-bit message.
----
-## Advanced circuits and algorithms
+---
- * [**Grover**](examples/advanced_circuits_algorithms/Grover/Grover.ipynb)
+## Advanced circuits and algorithms
- This tutorial provides a step-by-step walkthrough explaining Grover's quantum algorithm. We show how to build the corresponding quantum circuit with simple modular building blocks, by means of the Amazon Braket SDK. Specifically, we demonstrate how to build custom gates that are not part of the basic gate set provided by the SDK. A custom gate can used as a core quantum gate by registering it as a subroutine.
+- [**Grover**](examples/advanced_circuits_algorithms/Grover/Grover.ipynb)
- * [**Quantum Amplitude Amplification**](examples/advanced_circuits_algorithms/Quantum_Amplitude_Amplification/Quantum_Amplitude_Amplification.ipynb)
+ This tutorial provides a step-by-step walkthrough explaining Grover's quantum algorithm. We show how to build the corresponding quantum circuit with simple modular building blocks, by means of the Amazon Braket SDK. Specifically, we demonstrate how to build custom gates that are not part of the basic gate set provided by the SDK. A custom gate can used as a core quantum gate by registering it as a subroutine.
- This tutorial provides a detailed discussion and implementation of the Quantum Amplitude Amplification (QAA) algorithm, using the Amazon Braket SDK. QAA is a routine in quantum computing which generalizes the idea behind Grover's famous search algorithm, with applications across many quantum algorithms. In short, QAA uses an iterative approach to systematically increase the probability of finding one or multiple target states in a given search space. In a quantum computer, QAA can be used to obtain a quadratic speedup over several classical algorithms.
+- [**Quantum Amplitude Amplification**](examples/advanced_circuits_algorithms/Quantum_Amplitude_Amplification/Quantum_Amplitude_Amplification.ipynb)
- * [**Quantum Fourier Transform**](examples/advanced_circuits_algorithms/Quantum_Fourier_Transform/Quantum_Fourier_Transform.ipynb)
+ This tutorial provides a detailed discussion and implementation of the Quantum Amplitude Amplification (QAA) algorithm, using the Amazon Braket SDK. QAA is a routine in quantum computing which generalizes the idea behind Grover's famous search algorithm, with applications across many quantum algorithms. In short, QAA uses an iterative approach to systematically increase the probability of finding one or multiple target states in a given search space. In a quantum computer, QAA can be used to obtain a quadratic speedup over several classical algorithms.
- This tutorial provides a detailed implementation of the Quantum Fourier Transform (QFT) and the inverse QFT, using the Amazon Braket SDK. We provide two different implementations: with and without recursion. The QFT is an important subroutine to many quantum algorithms, most famously Shor's algorithm for factoring, and the quantum phase estimation (QPE) algorithm for estimating the eigenvalues of a unitary operator. The QFT can be performed efficiently on a quantum computer, using only O(n2) single-qubit Hadamard gates and two-qubit controlled phase shift gates, where 𝑛 is the number of qubits. We first review the basics of the quantum Fourier transform, and its relationship to the discrete (classical) Fourier transform. We then implement the QFT in code two ways: recursively and non-recursively. This notebook also showcases the Amazon Braket `circuit.subroutine` functionality, which allows one to define custom methods and add them to the Circuit class.
+- [**Quantum Fourier Transform**](examples/advanced_circuits_algorithms/Quantum_Fourier_Transform/Quantum_Fourier_Transform.ipynb)
- * [**Quantum Phase Estimation**](examples/advanced_circuits_algorithms/Quantum_Phase_Estimation/Quantum_Phase_Estimation.ipynb)
+ This tutorial provides a detailed implementation of the Quantum Fourier Transform (QFT) and the inverse QFT, using the Amazon Braket SDK. We provide two different implementations: with and without recursion. The QFT is an important subroutine to many quantum algorithms, most famously Shor's algorithm for factoring, and the quantum phase estimation (QPE) algorithm for estimating the eigenvalues of a unitary operator. The QFT can be performed efficiently on a quantum computer, using only O(n2) single-qubit Hadamard gates and two-qubit controlled phase shift gates, where 𝑛 is the number of qubits. We first review the basics of the quantum Fourier transform, and its relationship to the discrete (classical) Fourier transform. We then implement the QFT in code two ways: recursively and non-recursively. This notebook also showcases the Amazon Braket `circuit.subroutine` functionality, which allows one to define custom methods and add them to the Circuit class.
- This tutorial provides a detailed implementation of the Quantum Phase Estimation (QPE) algorithm, through the Amazon Braket SDK. The QPE algorithm is designed to estimate the eigenvalues of a unitary operator 𝑈; it is a very important subroutine to many quantum algorithms, most famously Shor's algorithm for factoring, and the HHL algorithm (named after the physicists Harrow, Hassidim and Lloyd) for solving linear systems of equations on a quantum computer. Moreover, eigenvalue problems can be found across many disciplines and application areas, including (for example) principal component analysis (PCA) as used in machine learning, or in the solution of differential equations as relevant across mathematics, physics, engineering and chemistry. We first review the basics of the QPE algorithm. We then implement the QPE algorithm in code using the Amazon Braket SDK, and we illustrate the application of the algorithm with simple examples. This notebook also showcases the Amazon Braket `circuit.subroutine` functionality, which allows you to use custom-built gates as if they were any other built-in gates. This tutorial is set up to run on the local simulator or the on-demand simulator. Changing between these devices requires changing only one line of code, as demonstrated below in cell.
+- [**Quantum Phase Estimation**](examples/advanced_circuits_algorithms/Quantum_Phase_Estimation/Quantum_Phase_Estimation.ipynb)
- * [**Randomness Generation**](examples/advanced_circuits_algorithms/Randomness/Randomness_Generation.ipynb)
+ This tutorial provides a detailed implementation of the Quantum Phase Estimation (QPE) algorithm, through the Amazon Braket SDK. The QPE algorithm is designed to estimate the eigenvalues of a unitary operator 𝑈; it is a very important subroutine to many quantum algorithms, most famously Shor's algorithm for factoring, and the HHL algorithm (named after the physicists Harrow, Hassidim and Lloyd) for solving linear systems of equations on a quantum computer. Moreover, eigenvalue problems can be found across many disciplines and application areas, including (for example) principal component analysis (PCA) as used in machine learning, or in the solution of differential equations as relevant across mathematics, physics, engineering and chemistry. We first review the basics of the QPE algorithm. We then implement the QPE algorithm in code using the Amazon Braket SDK, and we illustrate the application of the algorithm with simple examples. This notebook also showcases the Amazon Braket `circuit.subroutine` functionality, which allows you to use custom-built gates as if they were any other built-in gates. This tutorial is set up to run on the local simulator or the on-demand simulator. Changing between these devices requires changing only one line of code, as demonstrated below in cell.
- This tutorial provides a detailed implementation of a Quantum Random Number Generator (QRNG). It shows how to use two separate quantum processor units (QPUs) from different suppliers in Amazon Braket to supply two streams of weakly random bits. We then show how to generate physically secure randomness from these two weak sources by means of classical post-processing based on randomness extractors.
+- [**Randomness Generation**](examples/advanced_circuits_algorithms/Randomness/Randomness_Generation.ipynb)
- * [**Simon's Algorithm**](examples/advanced_circuits_algorithms/Simons_Algorithm/Simons_Algorithm.ipynb)
+ This tutorial provides a detailed implementation of a Quantum Random Number Generator (QRNG). It shows how to use two separate quantum processor units (QPUs) from different suppliers in Amazon Braket to supply two streams of weakly random bits. We then show how to generate physically secure randomness from these two weak sources by means of classical post-processing based on randomness extractors.
- This tutorial provides a detailed implementation of Simon’s algorithm, which shows the first example of an exponential speedup over the best known classical algorithm by using a quantum computer to solve a particular problem. Originally published in 1994, Simon’s algorithm was a precursor to Shor’s well-known factoring algorithm, and it served as inspiration for many of the seminal works in quantum computation that followed.
+- [**Simon's Algorithm**](examples/advanced_circuits_algorithms/Simons_Algorithm/Simons_Algorithm.ipynb)
+ This tutorial provides a detailed implementation of Simon’s algorithm, which shows the first example of an exponential speedup over the best known classical algorithm by using a quantum computer to solve a particular problem. Originally published in 1994, Simon’s algorithm was a precursor to Shor’s well-known factoring algorithm, and it served as inspiration for many of the seminal works in quantum computation that followed.
---
-## Hybrid quantum algorithms
- * [**QAOA**](examples/hybrid_quantum_algorithms/QAOA/QAOA_braket.ipynb)
+## Hybrid quantum algorithms
+
+- [**QAOA**](examples/hybrid_quantum_algorithms/QAOA/QAOA_braket.ipynb)
- This tutorial shows how to (approximately) solve binary combinatorial optimization problems, using the Quantum Approximate Optimization Algorithm (QAOA). The QAOA algorithm belongs to the class of _hybrid quantum algorithms_ (leveraging classical and quantum computers), which are widely believed to be the working horse for the current NISQ (noisy intermediate-scale quantum) era. In this NISQ era, QAOA is also an emerging approach for benchmarking quantum devices. It is a prime candidate for demonstrating a practical quantum speed-up on near-term NISQ device. To validate our approach, we benchmark our results with exact results as obtained from classical QUBO solvers.
+ This tutorial shows how to (approximately) solve binary combinatorial optimization problems, using the Quantum Approximate Optimization Algorithm (QAOA). The QAOA algorithm belongs to the class of _hybrid quantum algorithms_ (leveraging classical and quantum computers), which are widely believed to be the working horse for the current NISQ (noisy intermediate-scale quantum) era. In this NISQ era, QAOA is also an emerging approach for benchmarking quantum devices. It is a prime candidate for demonstrating a practical quantum speed-up on near-term NISQ device. To validate our approach, we benchmark our results with exact results as obtained from classical QUBO solvers.
- * [**VQE Chemistry**](examples/hybrid_quantum_algorithms/VQE_Chemistry/VQE_chemistry_braket.ipynb)
+- [**VQE Chemistry**](examples/hybrid_quantum_algorithms/VQE_Chemistry/VQE_chemistry_braket.ipynb)
- This tutorial shows how to implement the Variational Quantum Eigensolver (VQE) algorithm in Amazon Braket SDK to compute the potential energy surface (PES) for the Hydrogen molecule.
+ This tutorial shows how to implement the Variational Quantum Eigensolver (VQE) algorithm in Amazon Braket SDK to compute the potential energy surface (PES) for the Hydrogen molecule.
- * [**VQE Transverse Ising**](examples/hybrid_quantum_algorithms/VQE_Transverse_Ising/VQE_Transverse_Ising_Model.ipynb)
+- [**VQE Transverse Ising**](examples/hybrid_quantum_algorithms/VQE_Transverse_Ising/VQE_Transverse_Ising_Model.ipynb)
- This tutorial shows how to solve for the ground state of the Transverse Ising Model, which is arguably one of the most prominent, canonical quantum spin systems, using the variational quantum eigenvalue solver (VQE). The VQE algorithm belongs to the class of _hybrid quantum algorithms_ (leveraging classical andquantum computers), which are widely believed to be the working horse for the current NISQ (noisy intermediate-scale quantum) era. To validate our approach, we benchmark our results with exact results as obtained from a Jordan-Wigner transformation.
+ This tutorial shows how to solve for the ground state of the Transverse Ising Model, which is arguably one of the most prominent, canonical quantum spin systems, using the variational quantum eigenvalue solver (VQE). The VQE algorithm belongs to the class of _hybrid quantum algorithms_ (leveraging classical andquantum computers), which are widely believed to be the working horse for the current NISQ (noisy intermediate-scale quantum) era. To validate our approach, we benchmark our results with exact results as obtained from a Jordan-Wigner transformation.
---
+
## Quantum machine learning and optimization with PennyLane
- * [**Combining PennyLane with Amazon Braket**](examples/pennylane/0_Getting_started/0_Getting_started.ipynb)
- This tutorial shows you how to construct circuits and evaluate their gradients in PennyLane with execution performed using Amazon Braket.
+- [**Combining PennyLane with Amazon Braket**](examples/pennylane/0_Getting_started/0_Getting_started.ipynb)
- * [**Computing gradients in parallel with PennyLane-Braket**](examples/pennylane/1_Parallelized_optimization_of_quantum_circuits/1_Parallelized_optimization_of_quantum_circuits.ipynb)
+ This tutorial shows you how to construct circuits and evaluate their gradients in PennyLane with execution performed using Amazon Braket.
- In this tutorial, we explore how to speed up training of quantum circuits by using parallel execution on Amazon Braket. We begin by discussing why quantum circuit training involving gradients requires multiple device executions and motivate how the Braket SV1 simulator can be used to overcome this. The tutorial benchmarks SV1 against a local simulator, showing that SV1 outperforms the local simulator for both executions and gradient calculations. This illustrates how parallel capabilities can be combined between PennyLane and SV1.
+- [**Computing gradients in parallel with PennyLane-Braket**](examples/pennylane/1_Parallelized_optimization_of_quantum_circuits/1_Parallelized_optimization_of_quantum_circuits.ipynb)
- * [**Graph optimization with QAOA**](examples/pennylane/2_Graph_optimization_with_QAOA/2_Graph_optimization_with_QAOA.ipynb)
+ In this tutorial, we explore how to speed up training of quantum circuits by using parallel execution on Amazon Braket. We begin by discussing why quantum circuit training involving gradients requires multiple device executions and motivate how the Braket SV1 simulator can be used to overcome this. The tutorial benchmarks SV1 against a local simulator, showing that SV1 outperforms the local simulator for both executions and gradient calculations. This illustrates how parallel capabilities can be combined between PennyLane and SV1.
- In this tutorial we dig deeper into how quantum circuit training can be applied to a problem of practical relevance in graph optimization. We show how easy it is to train a QAOA circuit in PennyLane to solve the maximum clique problem on a simple example graph. The tutorial then extends to a more difficult 20-node graph and uses the parallel capabilities of the Amazon Braket SV1 simulator to speed up gradient calculations and hence train the quantum circuit faster, using around 1-2 minutes per iteration.
+- [**Graph optimization with QAOA**](examples/pennylane/2_Graph_optimization_with_QAOA/2_Graph_optimization_with_QAOA.ipynb)
- * [**Hydrogen geometry with VQE**](examples/pennylane/3_Hydrogen_Molecule_geometry_with_VQE/3_Hydrogen_Molecule_geometry_with_VQE.ipynb)
+ In this tutorial we dig deeper into how quantum circuit training can be applied to a problem of practical relevance in graph optimization. We show how easy it is to train a QAOA circuit in PennyLane to solve the maximum clique problem on a simple example graph. The tutorial then extends to a more difficult 20-node graph and uses the parallel capabilities of the Amazon Braket SV1 simulator to speed up gradient calculations and hence train the quantum circuit faster, using around 1-2 minutes per iteration.
- In this tutorial, we see how PennyLane and Amazon Braket can be combined to solve an important problem in quantum chemistry. The ground state energy of molecular hydrogen is calculated by optimizing a VQE circuit using the local Braket simulator. This tutorial highlights how qubit-wise commuting observables can be measured together in PennyLane and Braket, making optimization more efficient.
+- [**Hydrogen geometry with VQE**](examples/pennylane/3_Hydrogen_Molecule_geometry_with_VQE/3_Hydrogen_Molecule_geometry_with_VQE.ipynb)
- * [**Simulation of Noisy Circuits with PennyLane-Braket**](examples/pennylane/4_Simulation_of_noisy_quantum_circuits_on_Amazon_Braket_with_PennyLane/4_Simulation_of_noisy_quantum_circuits_on_Amazon_Braket_with_PennyLane.ipynb)
+ In this tutorial, we see how PennyLane and Amazon Braket can be combined to solve an important problem in quantum chemistry. The ground state energy of molecular hydrogen is calculated by optimizing a VQE circuit using the local Braket simulator. This tutorial highlights how qubit-wise commuting observables can be measured together in PennyLane and Braket, making optimization more efficient.
- In this tutorial, we explore the impact of noise on quantum hybrid algorithms and overview of noise simulation on Amazon Braket with PennyLane. The tutorial shows how to use PennyLane to simulate the noisy circuits, on either the local or Braket on-demand noise simulator, and covers the basic concepts of noise channels, using PennyLane to compute cost functions of noisy circuits and optimize them.
+- [**Simulation of Noisy Circuits with PennyLane-Braket**](examples/pennylane/4_Simulation_of_noisy_quantum_circuits_on_Amazon_Braket_with_PennyLane/4_Simulation_of_noisy_quantum_circuits_on_Amazon_Braket_with_PennyLane.ipynb)
- * [**Tracking Resource Usage**](examples/pennylane/5_Tracking_resource_usage/5_Tracking_resource_usage.ipynb)
+ In this tutorial, we explore the impact of noise on quantum hybrid algorithms and overview of noise simulation on Amazon Braket with PennyLane. The tutorial shows how to use PennyLane to simulate the noisy circuits, on either the local or Braket on-demand noise simulator, and covers the basic concepts of noise channels, using PennyLane to compute cost functions of noisy circuits and optimize them.
- In this tutorial, we see how to use the PennyLane device tracker feature with Amazon Braket. The PennyLane device resource tracker keeps a record of the usage of a device, such as numbers of circuit evaluations and shots. Amazon Braket extends this information with quantum task IDs and simulator duration to allow further tracking. The device tracker can be combined with additional logic to monitor and limit resource usage on devices.
+- [**Tracking Resource Usage**](examples/pennylane/5_Tracking_resource_usage/5_Tracking_resource_usage.ipynb)
- * [**Adjoint Gradient Computation**](examples/pennylane/6_Adjoint_gradient_computation/6_Adjoint_gradient_computation.ipynb)
+ In this tutorial, we see how to use the PennyLane device tracker feature with Amazon Braket. The PennyLane device resource tracker keeps a record of the usage of a device, such as numbers of circuit evaluations and shots. Amazon Braket extends this information with quantum task IDs and simulator duration to allow further tracking. The device tracker can be combined with additional logic to monitor and limit resource usage on devices.
- In this tutorial, we will show you how to compute gradients of free parameters in a quantum circuit using PennyLane and Amazon Braket. Adjoint differentiation is a technique used to compute gradients of parametrized quantum circuits. It can be used when shots=0 and is available on Amazon Braket’s on-demand state vector simulator, SV1. The adjoint differentiation method allows you to compute the gradient of a circuit with P parameters in only 1+1 circuit executions (one forward and one backward pass, similar to backpropagation), as opposed to the parameter-shift or finite-difference methods, both of which require 2P circuit executions for every gradient calculation. The adjoint method can lower the cost of running variational quantum workflows, especially for circuits with a large number of parameters.
+- [**Adjoint Gradient Computation**](examples/pennylane/6_Adjoint_gradient_computation/6_Adjoint_gradient_computation.ipynb)
+
+ In this tutorial, we will show you how to compute gradients of free parameters in a quantum circuit using PennyLane and Amazon Braket. Adjoint differentiation is a technique used to compute gradients of parametrized quantum circuits. It can be used when shots=0 and is available on Amazon Braket’s on-demand state vector simulator, SV1. The adjoint differentiation method allows you to compute the gradient of a circuit with P parameters in only 1+1 circuit executions (one forward and one backward pass, similar to backpropagation), as opposed to the parameter-shift or finite-difference methods, both of which require 2P circuit executions for every gradient calculation. The adjoint method can lower the cost of running variational quantum workflows, especially for circuits with a large number of parameters.
---
+
## Amazon Braket features
+
This folder contains examples that illustrate the usage of individual features of Amazon Braket
-* [**Getting notifications when a quantum task completes**](examples/braket_features/Getting_notifications_when_a_quantum_task_completes/Getting_notifications_when_a_quantum_task_completes.ipynb)
+- [**Getting notifications when a quantum task completes**](examples/braket_features/Getting_notifications_when_a_quantum_task_completes/Getting_notifications_when_a_quantum_task_completes.ipynb)
- This tutorial illustrates how Amazon Braket integrates with Amazon EventBridge for event-based processing. In the tutorial, you will learn how to configure Amazon Braket and Amazon Eventbridge to receive text notification about quantum task completions on your phone. Of course, EventBridge also allows you to build full, event-driven applications based on events emitted by Amazon Braket.
+ This tutorial illustrates how Amazon Braket integrates with Amazon EventBridge for event-based processing. In the tutorial, you will learn how to configure Amazon Braket and Amazon Eventbridge to receive text notification about quantum task completions on your phone. Of course, EventBridge also allows you to build full, event-driven applications based on events emitted by Amazon Braket.
-* [**Noise Models on Amazon Braket**](examples/braket_features/Noise_models/Noise_models_on_Amazon_Braket.ipynb)
+- [**Noise Models on Amazon Braket**](examples/braket_features/Noise_models/Noise_models_on_Amazon_Braket.ipynb)
- This tutorial shows how to create noise models containing different types of noise and instructions for how to apply the noise to a circuit. A noise model encapsulates the assumptions on quantum noise channels and how they act on a given circuit. Simulating this noisy circuit gives information about much the noise impacts the results of the quantum computation. By incrementally adjusting the noise model, the impact of noise can be understood on a variety of quantum algorithms.
+ This tutorial shows how to create noise models containing different types of noise and instructions for how to apply the noise to a circuit. A noise model encapsulates the assumptions on quantum noise channels and how they act on a given circuit. Simulating this noisy circuit gives information about much the noise impacts the results of the quantum computation. By incrementally adjusting the noise model, the impact of noise can be understood on a variety of quantum algorithms.
-* [**Noise Models on Rigetti's Aspen device**](examples/braket_features/Noise_models/Noise_models_on_Rigetti.ipynb)
+- [**Noise Models on Rigetti's device**](examples/braket_features/Noise_models/Noise_models_on_Rigetti.ipynb)
- This tutorial builds on the previous noise model tutorial to show how to construct a noise model from device calibration data for a Rigetti quantum processing unit (QPU). We compare the measurement outcomes of circuits run on a noisy simulator with the same circuits run on a QPU, to show that simulating circuits with noise models more closely mimics the QPU.
+ This tutorial builds on the previous noise model tutorial to show how to construct a noise model from device calibration data for a Rigetti quantum processing unit (QPU). We compare the measurement outcomes of circuits run on a noisy simulator with the same circuits run on a QPU, to show that simulating circuits with noise models more closely mimics the QPU.
-* [**Allocating Qubits on QPU Devices**](examples/braket_features/Allocating_Qubits_on_QPU_Devices.ipynb)
+- [**Allocating Qubits on QPU Devices**](examples/braket_features/Allocating_Qubits_on_QPU_Devices.ipynb)
- This tutorial explains how you can use the Amazon Braket SDK to allocate the qubit selection for your circuits manually, when running on QPUs.
+ This tutorial explains how you can use the Amazon Braket SDK to allocate the qubit selection for your circuits manually, when running on QPUs.
-* [**Error Mitigation**](examples/braket_features/Error_Mitigation_on_Amazon_Braket.ipynb)
+- [**Error Mitigation**](examples/braket_features/Error_Mitigation_on_Amazon_Braket.ipynb)
- This tutorial explains how to get started with using error mitigation on IonQ’s Aria QPU. You’ll learn how Aria’s two built-in error mitigation techniques work, how to switch between them, and the performance difference you can expect to see with and without these techniques for some problems.
-
-* [**Getting Devices and Checking Device Properties**](examples/braket_features/Getting_Devices_and_Checking_Device_Properties.ipynb)
+ This tutorial explains how to get started with using error mitigation on IonQ’s Aria QPU. You’ll learn how Aria’s two built-in error mitigation techniques work, how to switch between them, and the performance difference you can expect to see with and without these techniques for some problems.
- This example shows how to interact with the Amazon Braket GetDevice API to retrieve Amazon Braket devices (such as simulators and QPUs) programmatically, and how to gain access to their properties.
+- [**Getting Devices and Checking Device Properties**](examples/braket_features/Getting_Devices_and_Checking_Device_Properties.ipynb)
-* [**Getting Started with OpenQASM on Braket**](examples/braket_features/Getting_Started_with_OpenQASM_on_Braket.ipynb)
+ This example shows how to interact with the Amazon Braket GetDevice API to retrieve Amazon Braket devices (such as simulators and QPUs) programmatically, and how to gain access to their properties.
- This tutorial demonstrates how to submit OpenQASM quantum tasks to various devices on Braket and introduce some OpenQASM features available on Braket. OpenQASM is a popular, open source, human-readable and hardware-agnostic quantum circuit description language.
+- [**Getting Started with OpenQASM on Braket**](examples/braket_features/Getting_Started_with_OpenQASM_on_Braket.ipynb)
-* [**IonQ Native Gates**](examples/braket_features/IonQ_Native_Gates.ipynb)
+ This tutorial demonstrates how to submit OpenQASM quantum tasks to various devices on Braket and introduce some OpenQASM features available on Braket. OpenQASM is a popular, open source, human-readable and hardware-agnostic quantum circuit description language.
- This tutorial goes into details of IonQ’s native gates and their functionalities, enabling us to realize direct control over the quantum operations on the computer without compiler optimizations or error mitigation. It will discuss the native gates available on IonQ, their mathematical representations, and how they can be used for applications such as the quantum Fourier transform (QFT).
+- [**IonQ Native Gates**](examples/braket_features/IonQ_Native_Gates.ipynb)
-* [**Advanced OpenQASM programs using the Local Simulator**](examples/braket_features/Simulating_Advanced_OpenQASM_Programs_with_the_Local_Simulator.ipynb)
+ This tutorial goes into details of IonQ’s native gates and their functionalities, enabling us to realize direct control over the quantum operations on the computer without compiler optimizations or error mitigation. It will discuss the native gates available on IonQ, their mathematical representations, and how they can be used for applications such as the quantum Fourier transform (QFT).
- This notebook serves as a reference of OpenQASM features supported by Braket with the LocalSimulator.
+- [**Advanced OpenQASM programs using the Local Simulator**](examples/braket_features/Simulating_Advanced_OpenQASM_Programs_with_the_Local_Simulator.ipynb)
-* [**Using the tensor network simulator TN1**](examples/braket_features/Using_the_tensor_network_simulator_TN1.ipynb)
+ This notebook serves as a reference of OpenQASM features supported by Braket with the LocalSimulator.
- This notebook introduces the Amazon Braket on-demand tensor network simulator, TN1. You will learn about how TN1 works, how to use it, and which problems are best suited to run on TN1.
+- [**Using the tensor network simulator TN1**](examples/braket_features/Using_the_tensor_network_simulator_TN1.ipynb)
-* [**Simulating noise on Amazon Braket**](examples/braket_features/Simulating_Noise_On_Amazon_Braket.ipynb)
+ This notebook introduces the Amazon Braket on-demand tensor network simulator, TN1. You will learn about how TN1 works, how to use it, and which problems are best suited to run on TN1.
- This notebook provides a detailed overview of noise simulation on Amazon Braket. You will learn how to define noise channels, apply noise to new or existing circuits, and run those circuits on the Amazon Braket noise simulators.
+- [**Simulating noise on Amazon Braket**](examples/braket_features/Simulating_Noise_On_Amazon_Braket.ipynb)
-* [**TN1 and Hayden-Preskill circuits**](examples/braket_features/TN1_demo_local_vs_non-local_random_circuits.ipynb)
+ This notebook provides a detailed overview of noise simulation on Amazon Braket. You will learn how to define noise channels, apply noise to new or existing circuits, and run those circuits on the Amazon Braket noise simulators.
- This tutorial dives into showing the degree to which the tensor network simulator is capable of detecting a hidden local structure in a quantum circuit by working with Hayden-Preskill circuits, which are a class of unstructured, random quantum circuits.
+- [**TN1 and Hayden-Preskill circuits**](examples/braket_features/TN1_demo_local_vs_non-local_random_circuits.ipynb)
-* [**Adjoint Gradient Result Type**](examples/braket_features/Using_The_Adjoint_Gradient_Result_Type.ipynb)
+ This tutorial dives into showing the degree to which the tensor network simulator is capable of detecting a hidden local structure in a quantum circuit by working with Hayden-Preskill circuits, which are a class of unstructured, random quantum circuits.
- This tutorial introduces the AdjointGradient result type, discusses what a gradient is and how to compute one on a quantum circuit, explains how they can be used to accelerate your workflows, and shows an example of gradients in action on a hybrid quantum algorithm.
+- [**Adjoint Gradient Result Type**](examples/braket_features/Using_The_Adjoint_Gradient_Result_Type.ipynb)
-* [**Verbatim Compilation**](examples/braket_features/Verbatim_Compilation.ipynb)
+ This tutorial introduces the AdjointGradient result type, discusses what a gradient is and how to compute one on a quantum circuit, explains how they can be used to accelerate your workflows, and shows an example of gradients in action on a hybrid quantum algorithm.
- This tutorial explains how to use _verbatim compilation_ to run your circuits exactly as defined without any modification during the compilation process that's usually done behind-the-scenes when you run your circuits.
+- [**Verbatim Compilation**](examples/braket_features/Verbatim_Compilation.ipynb)
-* [**IQM Garnet Native Gates**](examples/braket_features/IQM_Garnet_Native_Gates.ipynb)
+ This tutorial explains how to use _verbatim compilation_ to run your circuits exactly as defined without any modification during the compilation process that's usually done behind-the-scenes when you run your circuits.
- This tutorial explores the functionality of the native gates of IQM Garnet.
+- [**IQM Garnet Native Gates**](examples/braket_features/IQM_Garnet_Native_Gates.ipynb)
-* [**Using the experimental local simulator**](examples/braket_features/Using_the_experimental_local_simulator.ipynb)
+ This tutorial explores the functionality of the native gates of IQM Garnet.
- This tutorial serves as an introduction to the experimental v2 local simulator for Amazon Braket. This tutorial explains how to use the v2 local simulator and the performance difference you can expect to see.
+- [**Using the experimental local simulator**](examples/braket_features/Using_the_experimental_local_simulator.ipynb)
+
+ This tutorial serves as an introduction to the experimental v2 local simulator for Amazon Braket. This tutorial explains how to use the v2 local simulator and the performance difference you can expect to see.
---
+
## Amazon Braket Hybrid Jobs
+
This folder contains examples that illustrate the use of Amazon Braket Hybrid Jobs (Braket Jobs for short).
-* [**Getting started with Amazon Braket Hybrid Jobs**](examples/hybrid_jobs/0_Creating_your_first_Hybrid_Job/0_Creating_your_first_Hybrid_Job.ipynb)
+- [**Getting started with Amazon Braket Hybrid Jobs**](examples/hybrid_jobs/0_Creating_your_first_Hybrid_Job/0_Creating_your_first_Hybrid_Job.ipynb)
- This notebook provides a demonstration of running a simple Braket Hybrid Job. You will learn how to create a Braket Hybrid Job using the Braket SDK or the Braket console, how to set the output S3 folder for a hybrid job, and how to retrieve results. You will also learn how to specify the Braket device to run your hybrid job on simulators or QPUs. Finally, you will learn how to use local mode to quickly debug your code.
+ This notebook provides a demonstration of running a simple Braket Hybrid Job. You will learn how to create a Braket Hybrid Job using the Braket SDK or the Braket console, how to set the output S3 folder for a hybrid job, and how to retrieve results. You will also learn how to specify the Braket device to run your hybrid job on simulators or QPUs. Finally, you will learn how to use local mode to quickly debug your code.
-* [**Quantum machine learning in Amazon Braket Hybrid Jobs**](examples/hybrid_jobs/1_Quantum_machine_learning_in_Amazon_Braket_Hybrid_Jobs/Quantum_machine_learning_in_Amazon_Braket_Hybrid_Jobs.ipynb)
+- [**Quantum machine learning in Amazon Braket Hybrid Jobs**](examples/hybrid_jobs/1_Quantum_machine_learning_in_Amazon_Braket_Hybrid_Jobs/Quantum_machine_learning_in_Amazon_Braket_Hybrid_Jobs.ipynb)
- This notebook shows a typical quantum machine learning workflow using Braket Hybrid Jobs. In the process, you will learn how to upload input data, how to set up hyperparameters for your hybrid job, and how to retrieve and plot metrics. Finally, you will see how to run multiple Braket Hybrid Jobs in parallel with different sets of hyperparameters.
+ This notebook shows a typical quantum machine learning workflow using Braket Hybrid Jobs. In the process, you will learn how to upload input data, how to set up hyperparameters for your hybrid job, and how to retrieve and plot metrics. Finally, you will see how to run multiple Braket Hybrid Jobs in parallel with different sets of hyperparameters.
-* [**QAOA with Amazon Braket Hybrid Jobs and PennyLane**](examples/hybrid_jobs/2_Using_PennyLane_with_Braket_Hybrid_Jobs/Using_PennyLane_with_Braket_Hybrid_Jobs.ipynb)
+- [**QAOA with Amazon Braket Hybrid Jobs and PennyLane**](examples/hybrid_jobs/2_Using_PennyLane_with_Braket_Hybrid_Jobs/Using_PennyLane_with_Braket_Hybrid_Jobs.ipynb)
- This notebook shows how to run the QAOA algorithm with PennyLane (similar to a [previous notebook](examples/pennylane/2_Graph_optimization_with_QAOA/2_Graph_optimization_with_QAOA.ipynb)), but this time using Braket Hybrid Jobs. In the process, you will learn how to select a container image that supports PennyLane, and how to use checkpoints to save and load training progress of a hybrid job.
+ This notebook shows how to run the QAOA algorithm with PennyLane (similar to a [previous notebook](examples/pennylane/2_Graph_optimization_with_QAOA/2_Graph_optimization_with_QAOA.ipynb)), but this time using Braket Hybrid Jobs. In the process, you will learn how to select a container image that supports PennyLane, and how to use checkpoints to save and load training progress of a hybrid job.
-* [**Bring your own containers to Braket Hybrid Jobs**](examples/hybrid_jobs/3_Bring_your_own_container/bring_your_own_container.ipynb)
+- [**Bring your own containers to Braket Hybrid Jobs**](examples/hybrid_jobs/3_Bring_your_own_container/bring_your_own_container.ipynb)
- This notebook demonstrates the use of the Bring-Your-Own-Container (BYOC) functionality of Braket Hybrid Jobs. While Amazon Braket has pre-configured environments which support most use cases of Braket Hybrid Jobs, BYOC enables you to define fully customizable environments using Docker containers. You will learn how to use BYOC, including preparing a Dockerfile, creating a private Amazon Elastic Container Registry (ECR), building the container, and submitting a Braket Hybrid Job using the custom container.
+ This notebook demonstrates the use of the Bring-Your-Own-Container (BYOC) functionality of Braket Hybrid Jobs. While Amazon Braket has pre-configured environments which support most use cases of Braket Hybrid Jobs, BYOC enables you to define fully customizable environments using Docker containers. You will learn how to use BYOC, including preparing a Dockerfile, creating a private Amazon Elastic Container Registry (ECR), building the container, and submitting a Braket Hybrid Job using the custom container.
-* [**Embedded simulators in Braket Hybrid Jobs**](examples/hybrid_jobs/4_Embedded_simulators_in_Braket_Hybrid_Jobs/Embedded_simulators_in_Braket_Hybrid_Jobs.ipynb)
+- [**Embedded simulators in Braket Hybrid Jobs**](examples/hybrid_jobs/4_Embedded_simulators_in_Braket_Hybrid_Jobs/Embedded_simulators_in_Braket_Hybrid_Jobs.ipynb)
- This notebook shows how to use embedded simulators in Braket Hybrid Jobs. An embedded simulator is a local simulator that runs completely within a hybrid job instance, i.e., the compute resource that is running your algorithm script. In contrast, on-demand simulators, such as SV1, DM1, or TN1, calculate the results of a quantum circuit on dedicated compute infrastructure on-demand by Amazon Braket. Hybrid workloads usually consist of iterations of quantum circuit executions and variational parameter optimizations. By using embedded simulators, we keep all computations in the same environment. This allows the optimization algorithm to access advanced features supported by the embedded simulator.
+ This notebook shows how to use embedded simulators in Braket Hybrid Jobs. An embedded simulator is a local simulator that runs completely within a hybrid job instance, i.e., the compute resource that is running your algorithm script. In contrast, on-demand simulators, such as SV1, DM1, or TN1, calculate the results of a quantum circuit on dedicated compute infrastructure on-demand by Amazon Braket. Hybrid workloads usually consist of iterations of quantum circuit executions and variational parameter optimizations. By using embedded simulators, we keep all computations in the same environment. This allows the optimization algorithm to access advanced features supported by the embedded simulator.
-* [**Parallelize training for Quantum Machine Learning**](examples/hybrid_jobs/5_Parallelize_training_for_QML/Parallelize_training_for_QML.ipynb)
+- [**Parallelize training for Quantum Machine Learning**](examples/hybrid_jobs/5_Parallelize_training_for_QML/Parallelize_training_for_QML.ipynb)
- This notebook introduces using data parallelism for Quantum Machine Learning (QML) workloads.
+ This notebook introduces using data parallelism for Quantum Machine Learning (QML) workloads.
-* [**QN-SPSA optimizer using an Embedded Simulator**](examples/hybrid_jobs/6_QNSPSA_optimizer_with_embedded_simulator/qnspsa_with_embedded_simulator.ipynb)
+- [**QN-SPSA optimizer using an Embedded Simulator**](examples/hybrid_jobs/6_QNSPSA_optimizer_with_embedded_simulator/qnspsa_with_embedded_simulator.ipynb)
- This notebook demonstrates how to implement and benchmark the QN-SPSA optimizer, a novel quantum optimization algorithm.
+ This notebook demonstrates how to implement and benchmark the QN-SPSA optimizer, a novel quantum optimization algorithm.
-* [**Running Jupyter notebooks as a Hybrid Job**](examples/hybrid_jobs/7_Running_notebooks_as_hybrid_jobs/Running_notebooks_as_hybrid_jobs.ipynb)
+- [**Running Jupyter notebooks as a Hybrid Job**](examples/hybrid_jobs/7_Running_notebooks_as_hybrid_jobs/Running_notebooks_as_hybrid_jobs.ipynb)
- This tutorial is a step-by-step guide for running a Jupyter notebook as a Hybrid Job.
+ This tutorial is a step-by-step guide for running a Jupyter notebook as a Hybrid Job.
-* [**Creating Hybrid Job Scripts**](examples/hybrid_jobs/8_Creating_Hybrid_Job_Scripts/Creating_your_first_Hybrid_Job.ipynb)
+- [**Creating Hybrid Job Scripts**](examples/hybrid_jobs/8_Creating_Hybrid_Job_Scripts/Creating_your_first_Hybrid_Job.ipynb)
- This notebook shows an alternate way to create a Hybrid Job without using a @hybrid_job decorator. The demonstrated method may be useful in some circumstances, such as using older versions of Python.
+ This notebook shows an alternate way to create a Hybrid Job without using a @hybrid_job decorator. The demonstrated method may be useful in some circumstances, such as using older versions of Python.
---
+
## Pulse Control
-* [**Bringup Experiments**](examples/pulse_control/1_Bringup_experiments.ipynb)
+- [**Bringup Experiments**](examples/pulse_control/1_Bringup_experiments.ipynb)
- This tutorial introduces common pulse sequences and calibrating pulses via Rabi spectroscopy.
+ This tutorial introduces common pulse sequences and calibrating pulses via Rabi spectroscopy.
-* [**Native Gate Calibrations**](examples/pulse_control/2_Native_gate_calibrations.ipynb)
+- [**Native Gate Calibrations**](examples/pulse_control/2_Native_gate_calibrations.ipynb)
- This tutorial shows how to retrieve the calibrations of native gates for Rigetti's Ankaa devices and submit a circuit with custom gate calibrations.
+ This tutorial shows how to retrieve the calibrations of native gates for Rigetti's Ankaa devices and submit a circuit with custom gate calibrations.
-* [**Bell pair with pulses (Rigetti)**](examples/pulse_control/3_Bell_pair_with_pulses_Rigetti.ipynb)
+- [**Bell pair with pulses (Rigetti)**](examples/pulse_control/3_Bell_pair_with_pulses_Rigetti.ipynb)
- This tutorial shows creating a Bell state with cross-resonance pulses on Rigetti's Ankaa device.
+ This tutorial shows creating a Bell state with cross-resonance pulses on Rigetti's Ankaa device.
-* [**Build single qubit gates**](examples/pulse_control/4_Build_single_qubit_gates.ipynb)
+- [**Build single qubit gates**](examples/pulse_control/4_Build_single_qubit_gates.ipynb)
- This tutorial describes a method to create any single-qubit gate with pulses.
+ This tutorial describes a method to create any single-qubit gate with pulses.
---
+
## Analog Hamiltonian Simulation
-* [**Intruction to Analog Hamiltonian Simulation**](examples/analog_hamiltonian_simulation/00_Introduction_of_Analog_Hamiltonian_Simulation_with_Rydberg_Atoms.ipynb)
+- [**Intruction to Analog Hamiltonian Simulation**](examples/analog_hamiltonian_simulation/00_Introduction_of_Analog_Hamiltonian_Simulation_with_Rydberg_Atoms.ipynb)
- This tutorial provides an introduction to Analog Hamiltonian Simulation (AHS), a quantum computing paradigm different from gate-based computing. AHS uses a well-controlled quantum system and tunes its parameters to mimic the dynamics of another quantum system, the one we aim to study.
+ This tutorial provides an introduction to Analog Hamiltonian Simulation (AHS), a quantum computing paradigm different from gate-based computing. AHS uses a well-controlled quantum system and tunes its parameters to mimic the dynamics of another quantum system, the one we aim to study.
-* [**Intruction to Aquila**](examples/analog_hamiltonian_simulation/01_Introduction_to_Aquila.ipynb)
+- [**Intruction to Aquila**](examples/analog_hamiltonian_simulation/01_Introduction_to_Aquila.ipynb)
- This tutorial illustrates how to run an AHS program on QuEra’s Aquila, a Rydberg based QPU, via Amazon Braket.
+ This tutorial illustrates how to run an AHS program on QuEra’s Aquila, a Rydberg based QPU, via Amazon Braket.
-* [**Ordered Phases in Rydberg Systems**](examples/analog_hamiltonian_simulation/02_Ordered_phases_in_Rydberg_systems.ipynb)
+- [**Ordered Phases in Rydberg Systems**](examples/analog_hamiltonian_simulation/02_Ordered_phases_in_Rydberg_systems.ipynb)
- This tutorial shows how to prepare ordered phases in Rydberg systems, focusing on the 1D phase and the 2D checkerboard phase. It uses an adiabatic time-evolution to prepare these many-body ground states.
+ This tutorial shows how to prepare ordered phases in Rydberg systems, focusing on the 1D phase and the 2D checkerboard phase. It uses an adiabatic time-evolution to prepare these many-body ground states.
-* [**Parallel Tasks on Aquila**](examples/analog_hamiltonian_simulation/03_Parallel_tasks_on_Aquila.ipynb)
+- [**Parallel Tasks on Aquila**](examples/analog_hamiltonian_simulation/03_Parallel_tasks_on_Aquila.ipynb)
- This tutorial builds on the previous notebook tutorial to use a checkerboard preparation that takes advantage of the full area.
+ This tutorial builds on the previous notebook tutorial to use a checkerboard preparation that takes advantage of the full area.
-* [**Maximum Independent Sets**](examples/analog_hamiltonian_simulation/04_Maximum_Independent_Sets_with_Analog_Hamiltonian_Simulation.ipynb)
+- [**Maximum Independent Sets**](examples/analog_hamiltonian_simulation/04_Maximum_Independent_Sets_with_Analog_Hamiltonian_Simulation.ipynb)
- This tutorial demonstrates how to set up a unit disk graph and solve for its maximum independent set using the Amazon Braket analog Hamiltonian simulation (AHS) local simulator.
+ This tutorial demonstrates how to set up a unit disk graph and solve for its maximum independent set using the Amazon Braket analog Hamiltonian simulation (AHS) local simulator.
-* [**Running on Local Simulator**](examples/analog_hamiltonian_simulation/05_Running_Analog_Hamiltonian_Simulation_with_local_simulator.ipynb)
+- [**Running on Local Simulator**](examples/analog_hamiltonian_simulation/05_Running_Analog_Hamiltonian_Simulation_with_local_simulator.ipynb)
- This tutorial shows how to test and debug an analog Hamiltonian simulation (AHS) program on the local simulator before submitting it to a QPU. It introduces several features of the local simulator that will be useful to streamline this testing process.
+ This tutorial shows how to test and debug an analog Hamiltonian simulation (AHS) program on the local simulator before submitting it to a QPU. It introduces several features of the local simulator that will be useful to streamline this testing process.
-* [**Simulation with PennyLane**](examples/analog_hamiltonian_simulation/06_Analog_Hamiltonian_simulation_with_PennyLane.ipynb)
+- [**Simulation with PennyLane**](examples/analog_hamiltonian_simulation/06_Analog_Hamiltonian_simulation_with_PennyLane.ipynb)
- This tutorial shows how to run analog Hamiltonian simulation (AHS) on Braket’s Rydberg atom devices leveraging quantum machine learning techniques from PennyLane.
+ This tutorial shows how to run analog Hamiltonian simulation (AHS) on Braket’s Rydberg atom devices leveraging quantum machine learning techniques from PennyLane.
-* [**Simulating lattice gauge theory with Rydberg atoms**](examples/analog_hamiltonian_simulation/07_Simulating_Lattice_Gauge_Theory_with_Rydberg_Atoms.ipynb)
+- [**Simulating lattice gauge theory with Rydberg atoms**](examples/analog_hamiltonian_simulation/07_Simulating_Lattice_Gauge_Theory_with_Rydberg_Atoms.ipynb)
- This tutorial shows how to prepare a specific initial state, using local detuning, to simulate the dynamics of a lattice gauge theory.
+ This tutorial shows how to prepare a specific initial state, using local detuning, to simulate the dynamics of a lattice gauge theory.
-* [**Maximum weight independent set**](examples/analog_hamiltonian_simulation/08_Maximum_Weight_Independent_Set.ipynb)
+- [**Maximum weight independent set**](examples/analog_hamiltonian_simulation/08_Maximum_Weight_Independent_Set.ipynb)
This tutorial generalizes the approach to solve the maximum weight independent set (MWIS) problem.
-* [**Noisy quantum dynamics**](examples/analog_hamiltonian_simulation/09_Noisy_quantum_dynamics_for_Rydberg_atom_arrays.ipynb)
+- [**Noisy quantum dynamics**](examples/analog_hamiltonian_simulation/09_Noisy_quantum_dynamics_for_Rydberg_atom_arrays.ipynb)
This tutorial shows how to run noise simulation on Braket’s Rydberg atom devices
-
+
---
-## Qiskit with Braket
-* [**Getting started with Qiskit on Amazon Braket**](examples/qiskit/0_Getting_Started.ipynb)
+## Qiskit with Braket
- This tutorial shows how you can run your Qiskit code on Amazon Braket computing services.
+- [**Getting started with Qiskit on Amazon Braket**](examples/qiskit/0_Getting_Started.ipynb)
+ This tutorial shows how you can run your Qiskit code on Amazon Braket computing services.
---
+
## Still can't find what you're looking for?
-Braket provides other libraries, tools, algorithms, experimental features, and more to help with your quantum computing journey. You can, for example, search all of our repositories for the [Bernstein Vazirani](https://github.com/search?q=org%3Aamazon-braket+Bernstein&type=code) algorithm or more [experimental features](https://github.com/search?q=org%3Aamazon-braket+experimental+features&type=code).
+
+Braket provides other libraries, tools, algorithms, experimental features, and more to help with your quantum computing journey. You can, for example, search all of our repositories for the [Bernstein Vazirani](https://github.com/search?q=org%3Aamazon-braket+Bernstein&type=code) algorithm or more [experimental features](https://github.com/search?q=org%3Aamazon-braket+experimental+features&type=code).
---
+
## Creating a conda environment
+
To install the dependencies required for running the notebook examples in this repository you can create a conda environment with below commands.
```bash
@@ -300,11 +315,13 @@ conda env create -n -f environment.yml
```
Activate the conda environment using:
+
```bash
conda activate
```
To remove the conda environment use:
+
```bash
conda deactivate
```
@@ -320,16 +337,17 @@ export AWS_PROFILE=YOUR_PROFILE_NAME
```
---
+
## Support
### Issues and Bug Reports
-If you encounter bugs or face issues while using the examples, please let us know by posting
+If you encounter bugs or face issues while using the examples, please let us know by posting
the issue on our [Github issue tracker](https://github.com/amazon-braket/amazon-braket-examples/issues/).
For other issues or general questions, please ask on the [Quantum Computing Stack Exchange](https://quantumcomputing.stackexchange.com/questions/ask) and add the tag [amazon-braket](https://quantumcomputing.stackexchange.com/questions/tagged/amazon-braket).
### Feedback and Feature Requests
If you have feedback or features that you would like to see on Amazon Braket, we would love to hear from you!
-[Github issues](https://github.com/amazon-braket/amazon-braket-examples/issues/) is our preferred mechanism for collecting feedback and feature requests, allowing other users
-to engage in the conversation, and +1 issues to help drive priority.
+[Github issues](https://github.com/amazon-braket/amazon-braket-examples/issues/) is our preferred mechanism for collecting feedback and feature requests, allowing other users
+to engage in the conversation, and +1 issues to help drive priority.
diff --git a/examples/braket_features/Allocating_Qubits_on_QPU_Devices.ipynb b/examples/braket_features/Allocating_Qubits_on_QPU_Devices.ipynb
index 69ffdee35..6439d2cad 100644
--- a/examples/braket_features/Allocating_Qubits_on_QPU_Devices.ipynb
+++ b/examples/braket_features/Allocating_Qubits_on_QPU_Devices.ipynb
@@ -1,541 +1,427 @@
{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Allocating Qubits on QPU Devices"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [],
- "source": [
- "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
- "from braket.tracking import Tracker\n",
- "t = Tracker().start()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This notebook demonstrates how you can specify explicitly which qubits to use when you run a quantum circuit on QPU devices from Rigetti.\n",
- "\n",
- "When you submit a circuit for execution on a QPU, Amazon Braket performs a series of compilation steps: it maps the _abstract qubits_ in your circuit to _physical qubits_ in the device; it synthesizes gates into the native gate set of the device; it optimizes the circuit to reduce the number of gates; and finally, it translates the gates into executable pulses.\n",
- "\n",
- "This section shows how the first step, called qubit allocation, works for the Rigetti Aspen-M-3 device."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {},
- "outputs": [],
- "source": [
- "# general imports\n",
- "from braket.aws import AwsDevice\n",
- "from braket.circuits import Circuit\n",
- "from braket.devices import Devices\n",
- "import numpy as np\n",
- "import random"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "pycharm": {
- "name": "#%% md\n"
- }
- },
- "source": [
- "## Automatic qubit allocation\n",
- "\n",
- "Qubit allocation for Rigetti devices on Amazon Braket utilizes [the Quil Compilers](https://pyquil-docs.rigetti.com/en/latest/compiler.html#the-quil-compiler)'s _rewiring_ strategies. By default, when you submit a circuit on Amazon Braket to a Rigetti device, the circuit is rewired according to the [PARTIAL](https://pyquil-docs.rigetti.com/en/latest/compiler.html#partial) rewiring strategy. Specifically, the compiler starts with an empty mapping from logical to physical qubits. Taking into account the latest calibration data of the device, the compiler fills in the mapping with the goal, sequentially, to maximize the overall fidelity of the circuit.\n",
- "\n",
- "The example that follows shows how to create a GHZ state on qubits that are not physically connected. After the quantum task is completed, you can obtain a list of the actual gates executed on the device, by viewing the result metadata.\n",
- "\n",
- "First, instantiate the Rigetti Aspen-M-3 device and retrieve its connectivity graph, which shows the qubits that are directly connected on the chip."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {
- "pycharm": {
- "name": "#%%\n"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "the connectivity of Aspen-M-3 is: {'0': ['1', '7'], '1': ['0', '16', '2'], '10': ['11', '113', '17'], '100': ['101', '107'], '101': ['100', '102', '116'], '102': ['101', '103', '115'], '103': ['102', '104'], '104': ['103', '105', '7'], '105': ['104', '106'], '106': ['105', '107'], '107': ['100', '106'], '11': ['10', '12', '26'], '110': ['111', '117'], '111': ['110', '112', '126'], '112': ['111', '113'], '113': ['10', '112', '114'], '114': ['113', '115', '17'], '115': ['102', '114', '116'], '116': ['101', '115', '117'], '117': ['110', '116'], '12': ['11', '13', '25'], '120': ['121', '127'], '121': ['120', '122', '136'], '122': ['121', '123', '135'], '123': ['122', '124', '20'], '124': ['123', '125', '27'], '125': ['124', '126'], '126': ['111', '125', '127'], '127': ['120', '126'], '13': ['12', '14'], '130': ['131', '137'], '131': ['130', '132', '146'], '132': ['131', '133', '145'], '133': ['132', '134', '30'], '134': ['133', '135', '37'], '135': ['122', '134', '136'], '136': ['121', '135', '137'], '137': ['130', '136'], '14': ['13', '15'], '140': ['141', '147'], '141': ['140', '142'], '142': ['141', '143'], '143': ['142', '144', '40'], '144': ['143', '145', '47'], '145': ['132', '144', '146'], '146': ['131', '145', '147'], '147': ['140', '146'], '15': ['14', '16', '2'], '16': ['1', '15', '17'], '17': ['10', '16', '114'], '2': ['1', '15', '3'], '20': ['123', '21', '27'], '21': ['20', '22', '36'], '22': ['21', '23', '35'], '23': ['22', '24'], '24': ['23', '25'], '25': ['12', '24', '26'], '26': ['11', '25', '27'], '27': ['20', '26', '124'], '3': ['2', '4'], '30': ['133', '31', '37'], '31': ['30', '32', '46'], '32': ['31', '33', '45'], '33': ['32', '34'], '34': ['33', '35'], '35': ['22', '34', '36'], '36': ['21', '35', '37'], '37': ['30', '36', '134'], '4': ['3', '5'], '40': ['143', '41', '47'], '41': ['40', '42'], '42': ['41', '43'], '43': ['42', '44'], '44': ['43', '45'], '45': ['32', '44', '46'], '46': ['31', '45', '47'], '47': ['40', '46', '144'], '5': ['4', '6'], '6': ['5', '7'], '7': ['0', '6', '104']}\n"
- ]
- }
- ],
- "source": [
- "device = AwsDevice(Devices.Rigetti.AspenM3)\n",
- "\n",
- "connectivity_graph = device.properties.paradigm.connectivity.connectivityGraph\n",
- "print(f\"the connectivity of {device.name} is: {connectivity_graph}\")"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "pycharm": {
- "name": "#%% md\n"
- }
- },
- "source": [
- "Next, create a GHZ circuit with three qubits 0, 2, 4, and run it on the Aspen-M-3 device. Notice that none of these qubits are connected on the Aspen-M-3 connectivity graph."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {
- "pycharm": {
- "name": "#%%\n"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : |0|1|2|\n",
- " \n",
- "q0 : -H-C-C-\n",
- " | | \n",
- "q2 : ---X-|-\n",
- " | \n",
- "q4 : -----X-\n",
- "\n",
- "T : |0|1|2|\n"
- ]
- }
- ],
- "source": [
- "# create a GHZ state with non-neighboring qubits\n",
- "circuit = Circuit()\n",
- "circuit.h(0).cnot(0,2).cnot(0,4)\n",
- "print(circuit)\n",
- "\n",
- "rigetti_rewiring = device.run(circuit, shots=10)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Status of task: CREATED\n"
- ]
- }
- ],
- "source": [
- "print(\"Status of quantum task:\", rigetti_rewiring.state())"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "pycharm": {
- "name": "#%% md\n"
- }
- },
- "source": [
- "To verify the final qubit allocation, retrieve the compiled program that was executed:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {
- "pycharm": {
- "name": "#%%\n"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Measurement counts: Counter({'001': 4, '111': 3, '000': 2, '101': 1})\n",
- "The compiled circuit is:\n",
- " DECLARE ro BIT[3]\n",
- "PRAGMA INITIAL_REWIRING \"PARTIAL\"\n",
- "RESET\n",
- "RZ(-pi/2) 12\n",
- "RX(-pi/2) 12\n",
- "RZ(pi) 13\n",
- "XY(pi) 12 13\n",
- "RZ(pi/2) 12\n",
- "RX(pi/2) 12\n",
- "RZ(-pi/2) 12\n",
- "XY(pi) 12 13\n",
- "RZ(pi/2) 25\n",
- "RX(-pi/2) 25\n",
- "CZ 25 12\n",
- "RZ(pi) 12\n",
- "RX(-pi/2) 13\n",
- "RX(pi/2) 25\n",
- "RZ(-pi/2) 25\n",
- "MEASURE 25 ro[2]\n",
- "MEASURE 13 ro[1]\n",
- "MEASURE 12 ro[0]\n"
- ]
- }
- ],
- "source": [
- "result = rigetti_rewiring.result()\n",
- "counts = result.measurement_counts\n",
- "print(\"Measurement counts:\", counts)\n",
- "print(\"The compiled circuit is:\\n\", result.additional_metadata.rigettiMetadata.compiledProgram)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "pycharm": {
- "name": "#%% md\n"
- }
- },
- "source": [
- "Notice that the PARTIAL rewiring was applied. The qubits 0, 2, 4 in the original circuit were mapped to three other qubits in the Rigetti device, and the gates were compiled into native gates."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## User-defined qubit allocation"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In Amazon Braket, you can choose to prescribe a qubit mapping manually, and prevent further rewiring for Rigetti devices. To enable manual mapping, set `disable_qubit_rewiring=True` when submitting the quantum task to run.\n",
- "\n",
- "If all the gates in the circuit satisfy the topological constraints of the device, Amazon Braket maps abstract qubit $i$ in the circuit to the physical qubit $i$ in the device, and maps qubit pair $(i, j)$ to the connection $(i, j)$ in the device. On the other hand, Amazon Braket raises an exception if a specified qubit or qubit pair do not exist in the device connectivity graph."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "metadata": {
- "pycharm": {
- "name": "#%%\n"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : | 0 |1|\n",
- " \n",
- "q0 : -Rz(1.57)-C-\n",
- " | \n",
- "q1 : ----------X-\n",
- " \n",
- "q3 : -X----------\n",
- "\n",
- "T : | 0 |1|\n"
- ]
- }
- ],
- "source": [
- "# create a random state with neighboring qubits\n",
- "q1=random.choice(list(connectivity_graph))\n",
- "q2=int(connectivity_graph[q1][0])\n",
- "q1=int(q1)\n",
- "\n",
- "circuit = Circuit()\n",
- "circuit.rz(0,np.pi/2).cnot(q1,q2).x(7)\n",
- "print(circuit)\n",
- "rigetti_task = device.run(circuit, shots=10, disable_qubit_rewiring=True)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Status of task: COMPLETED\n"
- ]
- }
- ],
- "source": [
- "print(\"Status of quantum task:\", rigetti_task.state())"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Measurement counts: Counter({'011': 6, '001': 2, '101': 1, '000': 1})\n",
- "The compiled circuit is:\n",
- " DECLARE ro BIT[3]\n",
- "PRAGMA INITIAL_REWIRING \"NAIVE\"\n",
- "RESET\n",
- "RZ(pi) 1\n",
- "RX(-pi/2) 1\n",
- "XY(pi) 0 1\n",
- "RZ(-pi/2) 0\n",
- "RX(pi/2) 0\n",
- "RZ(pi/2) 0\n",
- "XY(pi) 0 1\n",
- "RX(pi) 3\n",
- "MEASURE 3 ro[2]\n",
- "MEASURE 1 ro[1]\n",
- "MEASURE 0 ro[0]\n"
- ]
- }
- ],
- "source": [
- "result = rigetti_task.result()\n",
- "counts = result.measurement_counts\n",
- "print(\"Measurement counts:\", counts)\n",
- "print(\"The compiled circuit is:\\n\", result.additional_metadata.rigettiMetadata.compiledProgram)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "pycharm": {
- "name": "#%% md\n"
- }
- },
- "source": [
- "The qubits in the original circuit followed a one-to-one mapping to the physical qubits in the device. Other compilation steps, such as gate synthesis and circuit optimization, are still performed. These steps allow the circuit to run successfully and improve the overall fidelity."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Using the qubits with the highest two-qubit gate fidelity\n",
- "\n",
- "Additionally, the device properties include calibration data, which you can use to find the qubits and qubit pairs with the highest fidelities for particular gates.\n",
- "\n",
- "The following function finds the qubit pair that has the highest two-qubit fidelity of an input gate, which can be any of the gates native to the Rigetti device, namely CPHASE, XY or CZ."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {
- "pycharm": {
- "name": "#%%\n"
- }
- },
- "outputs": [],
- "source": [
- "def find_qubit_pair(gate):\n",
- " \"Function to find the qubit pair that has the highest gate fidelity of a particular gate\"\n",
- " \n",
- " # check whether the input gate is a string\n",
- " if not isinstance(gate, str):\n",
- " raise ValueError('The input gate must be a string type.') \n",
- " \n",
- " # check whether the input gate is a native gate\n",
- " gate_list = ['CPHASE', 'CZ', 'XY']\n",
- " if gate not in gate_list:\n",
- " raise ValueError('The input gate must be either CPHASE, CZ or XY.')\n",
- " \n",
- " # load all calibration data from device.properties\n",
- " calibration_2Q = device.properties.provider.specs['2Q']\n",
- " highest_fidelity = 0\n",
- "\n",
- " # iterate through all calibration data to find the highest fidelity\n",
- " for pair in calibration_2Q.keys():\n",
- " \n",
- " # if the particular gate type is supported by the qubit pair\n",
- " if ('f'+ gate) in calibration_2Q[pair].keys(): \n",
- " \n",
- " if calibration_2Q[pair]['f'+ gate] > highest_fidelity:\n",
- " \n",
- " # update the highest_fidelity and the best_pair\n",
- " highest_fidelity = calibration_2Q[pair]['f'+ gate]\n",
- " best_pair = pair\n",
- "\n",
- " # generate the two qubits as integers \n",
- " q1 = best_pair[0]\n",
- " i = 1\n",
- " while best_pair[i] is not '-':\n",
- " q1 += best_pair[i]\n",
- " i += 1\n",
- "\n",
- " q1 = int(q1)\n",
- " q2 = int(best_pair[i+1:])\n",
- " \n",
- " return q1, q2, highest_fidelity"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "pycharm": {
- "name": "#%% md\n"
- }
- },
- "source": [
- "The example in the following code applies a native two-qubit gate on the qubit pair that has the highest fidelity of that gate. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {
- "pycharm": {
- "name": "#%%\n"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "The highest fidelity for CZ gate is: 0.9794230141816626\n",
- "And the corresponding qubit pair is: qubit 21 and qubit 36\n",
- "T : |0|\n",
- " \n",
- "q21 : -C-\n",
- " | \n",
- "q36 : -Z-\n",
- "\n",
- "T : |0|\n"
- ]
- }
- ],
- "source": [
- "# the gate must be either 'CZ', 'CPHASE' or 'XY'\n",
- "gate = 'CZ'\n",
- "# find the qubit pair with the highest gate fidelity\n",
- "q1, q2, highest_fidelity = find_qubit_pair(gate)\n",
- "print('The highest fidelity for '+gate+' gate is:', highest_fidelity)\n",
- "print(f'And the corresponding qubit pair is: qubit {q1} and qubit {q2}')\n",
- "\n",
- "# create a circuit with the gate applied to the discovered qubit pair.\n",
- "# note that CPHASE in Rigetti corresponds to cphaseshift in Braket\n",
- "circuit = Circuit()\n",
- "circuit.cz(q1,q2)\n",
- "print(circuit)\n",
- "rigetti_task = device.run(circuit, shots=1000, disable_qubit_rewiring=True)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Measurement counts: Counter({'00': 910, '01': 55, '10': 33, '11': 2})\n",
- "The compiled circuit is:\n",
- " DECLARE ro BIT[2]\n",
- "PRAGMA INITIAL_REWIRING \"NAIVE\"\n",
- "RESET\n",
- "CZ 21 36\n",
- "MEASURE 21 ro[1]\n",
- "MEASURE 36 ro[0]\n"
- ]
- }
- ],
- "source": [
- "print(\"Status of quantum task:\", rigetti_task.state())"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The qubits in the original circuit followed a one-to-one mapping to the physical qubits in the device. Since only native gates were used, the actual gates executed are the same as the gates in the original circuit."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "pycharm": {
- "name": "#%% md\n"
- }
- },
- "source": [
- "
\n",
- "Note: The IonQ device does not support manual allocation. For circuits submitted to the IonQ device, qubits are allocated automatically.\n",
- "
"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Task Summary\n",
- "{'arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3': {'shots': 1020, 'tasks': {'QUEUED': 1, 'CREATED': 2}}}\n",
- "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
- "Estimated cost to run this example: 1.26 USD\n"
- ]
- }
- ],
- "source": [
- "print(\"Quantum Task Summary\")\n",
- "print(t.quantum_tasks_statistics())\n",
- "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n",
- "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.2f} USD\")"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "conda_braket",
- "language": "python",
- "name": "conda_braket"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.8.10"
- },
- "vscode": {
- "interpreter": {
- "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2"
- }
- }
- },
- "nbformat": 4,
- "nbformat_minor": 4
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Allocating Qubits on QPU Devices"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
+ "from braket.tracking import Tracker\n",
+ "t = Tracker().start()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This notebook demonstrates how you can specify explicitly which qubits to use when you run a quantum circuit on QPU devices from Rigetti.\n",
+ "\n",
+ "When you submit a circuit for execution on a QPU, Amazon Braket performs a series of compilation steps: it maps the _abstract qubits_ in your circuit to _physical qubits_ in the device; it synthesizes gates into the native gate set of the device; it optimizes the circuit to reduce the number of gates; and finally, it translates the gates into executable pulses.\n",
+ "\n",
+ "This section shows how the first step, called qubit allocation, works for the Rigetti Ankaa 2 device."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# general imports\n",
+ "from braket.aws import AwsDevice\n",
+ "from braket.circuits import Circuit\n",
+ "from braket.devices import Devices\n",
+ "import numpy as np\n",
+ "import random"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "pycharm": {
+ "name": "#%% md\n"
+ }
+ },
+ "source": [
+ "## Automatic qubit allocation\n",
+ "\n",
+ "Qubit allocation for Rigetti devices on Amazon Braket utilizes [the Quil Compilers](https://pyquil-docs.rigetti.com/en/latest/compiler.html#the-quil-compiler)'s _rewiring_ strategies. By default, when you submit a circuit on Amazon Braket to a Rigetti device, the circuit is rewired according to the [PARTIAL](https://pyquil-docs.rigetti.com/en/latest/compiler.html#partial) rewiring strategy. Specifically, the compiler starts with an empty mapping from logical to physical qubits. Taking into account the latest calibration data of the device, the compiler fills in the mapping with the goal, sequentially, to maximize the overall fidelity of the circuit.\n",
+ "\n",
+ "The example that follows shows how to create a GHZ state on qubits that are not physically connected. After the quantum task is completed, you can obtain a list of the actual gates executed on the device, by viewing the result metadata.\n",
+ "\n",
+ "First, instantiate the Rigetti Ankaa 2 device and retrieve its connectivity graph, which shows the qubits that are directly connected on the chip."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "pycharm": {
+ "name": "#%%\n"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the connectivity of Ankaa-2 is: {'0': ['1', '7'], '1': ['0', '2', '8'], '2': ['1', '3', '9'], '3': ['2', '4', '10'], '4': ['3', '5', '11'], '5': ['4', '6', '12'], '6': ['5', '13'], '7': ['0', '8', '14'], '8': ['1', '7', '9', '15'], '9': ['2', '8', '10', '16'], '10': ['3', '9', '11', '17'], '11': ['4', '10', '12', '18'], '12': ['5', '11', '13', '19'], '13': ['6', '12', '20'], '14': ['7', '15', '21'], '15': ['8', '14', '22'], '16': ['9', '17', '23'], '17': ['10', '16', '18', '24'], '18': ['11', '17', '19', '25'], '19': ['12', '18', '20', '26'], '20': ['13', '19', '27'], '21': ['14', '22', '28'], '22': ['15', '21', '23', '29'], '23': ['16', '22', '24', '30'], '24': ['17', '23', '25', '31'], '25': ['18', '24', '26', '32'], '26': ['19', '25', '33'], '27': ['20', '34'], '28': ['21', '29', '35'], '29': ['22', '28', '30', '36'], '30': ['23', '29', '31', '37'], '31': ['24', '30', '32', '38'], '32': ['25', '31', '33', '39'], '33': ['26', '32', '34', '40'], '34': ['27', '33', '41'], '35': ['28', '36', '42'], '36': ['29', '35', '37', '43'], '37': ['30', '36', '38', '44'], '38': ['31', '37', '39', '45'], '39': ['32', '38', '40', '46'], '40': ['33', '39', '41', '47'], '41': ['34', '40', '48'], '42': ['35', '43', '49'], '43': ['36', '42', '44', '50'], '44': ['37', '43', '45', '51'], '45': ['38', '44', '46', '52'], '46': ['39', '45', '47', '53'], '47': ['40', '46', '48', '54'], '48': ['41', '47', '55'], '49': ['42', '56'], '50': ['43', '51', '57'], '51': ['44', '50', '52', '58'], '52': ['45', '51', '53', '59'], '53': ['46', '52', '54'], '54': ['47', '53', '55', '61'], '55': ['48', '54', '62'], '56': ['49', '57', '63'], '57': ['50', '56', '58', '64'], '58': ['51', '57', '59', '65'], '59': ['52', '58', '60', '66'], '60': ['59'], '61': ['54', '62', '68'], '62': ['55', '61', '69'], '63': ['56', '64', '70'], '64': ['57', '63', '65', '71'], '65': ['58', '64', '66', '72'], '66': ['59', '65', '67'], '67': ['66', '68', '74'], '68': ['61', '67', '69', '75'], '69': ['62', '68', '76'], '70': ['63', '71', '77'], '71': ['64', '70', '72', '78'], '72': ['65', '71', '73', '79'], '73': ['72', '74', '80'], '74': ['67', '73', '75', '81'], '75': ['68', '74', '76', '82'], '76': ['69', '75', '83'], '77': ['70', '78'], '78': ['71', '77', '79'], '79': ['72', '78', '80'], '80': ['73', '79', '81'], '81': ['74', '80', '82'], '82': ['75', '81', '83'], '83': ['76', '82']}\n"
+ ]
+ }
+ ],
+ "source": [
+ "device = AwsDevice(Devices.Rigetti.Ankaa2)\n",
+ "\n",
+ "connectivity_graph = device.properties.paradigm.connectivity.connectivityGraph\n",
+ "print(f\"the connectivity of {device.name} is: {connectivity_graph}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "pycharm": {
+ "name": "#%% md\n"
+ }
+ },
+ "source": [
+ "Next, create a GHZ circuit with three qubits 0, 2, 4, and run it on the Ankaa 2 device. Notice that none of these qubits are connected on the Ankaa 2 connectivity graph."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "pycharm": {
+ "name": "#%%\n"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "T : │ 0 │ 1 │ 2 │\n",
+ " ┌───┐ \n",
+ "q0 : ─┤ H ├───●─────●───\n",
+ " └───┘ │ │ \n",
+ " ┌─┴─┐ │ \n",
+ "q2 : ───────┤ X ├───┼───\n",
+ " └───┘ │ \n",
+ " ┌─┴─┐ \n",
+ "q4 : ─────────────┤ X ├─\n",
+ " └───┘ \n",
+ "T : │ 0 │ 1 │ 2 │\n"
+ ]
+ }
+ ],
+ "source": [
+ "# create a GHZ state with non-neighboring qubits\n",
+ "circuit = Circuit()\n",
+ "circuit.h(0).cnot(0,2).cnot(0,4)\n",
+ "print(circuit)\n",
+ "\n",
+ "rigetti_rewiring = device.run(circuit, shots=10)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Status of quantum task: QUEUED\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Status of quantum task:\", rigetti_rewiring.state())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "pycharm": {
+ "name": "#%% md\n"
+ }
+ },
+ "source": [
+ "To verify the final qubit allocation, retrieve the compiled program that was executed:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "pycharm": {
+ "name": "#%%\n"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "result = rigetti_rewiring.result()\n",
+ "counts = result.measurement_counts\n",
+ "print(\"Measurement counts:\", counts)\n",
+ "print(\"The compiled circuit is:\\n\", result.additional_metadata.rigettiMetadata.compiledProgram)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "pycharm": {
+ "name": "#%% md\n"
+ }
+ },
+ "source": [
+ "Notice that the PARTIAL rewiring was applied. The qubits 0, 2, 4 in the original circuit were mapped to three other qubits in the Rigetti device, and the gates were compiled into native gates."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## User-defined qubit allocation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In Amazon Braket, you can choose to prescribe a qubit mapping manually, and prevent further rewiring for Rigetti devices. To enable manual mapping, set `disable_qubit_rewiring=True` when submitting the quantum task to run.\n",
+ "\n",
+ "If all the gates in the circuit satisfy the topological constraints of the device, Amazon Braket maps abstract qubit $i$ in the circuit to the physical qubit $i$ in the device, and maps qubit pair $(i, j)$ to the connection $(i, j)$ in the device. On the other hand, Amazon Braket raises an exception if a specified qubit or qubit pair do not exist in the device connectivity graph."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "pycharm": {
+ "name": "#%%\n"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# create a random state with neighboring qubits\n",
+ "q1=random.choice(list(connectivity_graph))\n",
+ "q2=int(connectivity_graph[q1][0])\n",
+ "q1=int(q1)\n",
+ "\n",
+ "circuit = Circuit()\n",
+ "circuit.rz(0,np.pi/2).cnot(q1,q2).x(7)\n",
+ "print(circuit)\n",
+ "rigetti_task = device.run(circuit, shots=10, disable_qubit_rewiring=True)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "print(\"Status of quantum task:\", rigetti_task.state())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "result = rigetti_task.result()\n",
+ "counts = result.measurement_counts\n",
+ "print(\"Measurement counts:\", counts)\n",
+ "print(\"The compiled circuit is:\\n\", result.additional_metadata.rigettiMetadata.compiledProgram)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "pycharm": {
+ "name": "#%% md\n"
+ }
+ },
+ "source": [
+ "The qubits in the original circuit followed a one-to-one mapping to the physical qubits in the device. Other compilation steps, such as gate synthesis and circuit optimization, are still performed. These steps allow the circuit to run successfully and improve the overall fidelity."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Using the qubits with the highest two-qubit gate fidelity\n",
+ "\n",
+ "Additionally, the device properties include calibration data, which you can use to find the qubits and qubit pairs with the highest fidelities for particular gates.\n",
+ "\n",
+ "The following function finds the qubit pair that has the highest two-qubit fidelity of an input gate, which can be any of the gates native to the Rigetti device. First, you can access the native gates as follows:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "native_gates = device.properties.paradigm.nativeGateSet\n",
+ "gates_uppercase = [gate.upper() for gate in native_gates]\n",
+ "gates_uppercase"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "metadata": {
+ "pycharm": {
+ "name": "#%%\n"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def find_qubit_pair(gate):\n",
+ " \"Function to find the qubit pair that has the highest gate fidelity of a particular gate\"\n",
+ " \n",
+ " # check whether the input gate is a string\n",
+ " if not isinstance(gate, str):\n",
+ " raise ValueError('The input gate must be a string type.') \n",
+ " \n",
+ " # check whether the input gate is a native gate\n",
+ " gate_list = gates_uppercase\n",
+ " if gate not in gate_list:\n",
+ " raise ValueError(f'The input gate must be one of {gates_uppercase}.')\n",
+ " \n",
+ " # load all calibration data from device.properties\n",
+ " calibration_2Q = device.properties.provider.specs['2Q']\n",
+ " highest_fidelity = 0\n",
+ "\n",
+ " # iterate through all calibration data to find the highest fidelity\n",
+ " for pair in calibration_2Q.keys():\n",
+ " # if the particular gate type is supported by the qubit pair\n",
+ " if ('f'+ gate) in calibration_2Q[pair].keys(): \n",
+ " if calibration_2Q[pair]['f'+ gate] > highest_fidelity: \n",
+ " # update the highest_fidelity and the best_pair\n",
+ " highest_fidelity = calibration_2Q[pair]['f'+ gate]\n",
+ " best_pair = pair\n",
+ "\n",
+ " # generate the two qubits as integers \n",
+ " q1 = best_pair[0]\n",
+ " i = 1\n",
+ " while best_pair[i] != '-':\n",
+ " q1 += best_pair[i]\n",
+ " i += 1\n",
+ "\n",
+ " q1 = int(q1)\n",
+ " q2 = int(best_pair[i+1:])\n",
+ " \n",
+ " return q1, q2, highest_fidelity"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "pycharm": {
+ "name": "#%% md\n"
+ }
+ },
+ "source": [
+ "The example in the following code applies a native two-qubit gate on the qubit pair that has the highest fidelity of that gate. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "pycharm": {
+ "name": "#%%\n"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# the gate must be a native gate\n",
+ "gate = 'ISWAP'\n",
+ "# find the qubit pair with the highest gate fidelity\n",
+ "q1, q2, highest_fidelity = find_qubit_pair(gate)\n",
+ "print('The highest fidelity for '+gate+' gate is:', highest_fidelity)\n",
+ "print(f'And the corresponding qubit pair is: qubit {q1} and qubit {q2}')\n",
+ "\n",
+ "# create a circuit with the gate applied to the discovered qubit pair.\n",
+ "# note that CPHASE in Rigetti corresponds to cphaseshift in Braket\n",
+ "circuit = Circuit()\n",
+ "circuit.cz(q1,q2)\n",
+ "print(circuit)\n",
+ "rigetti_task = device.run(circuit, shots=1000, disable_qubit_rewiring=True)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "print(\"Status of quantum task:\", rigetti_task.state())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The qubits in the original circuit followed a one-to-one mapping to the physical qubits in the device. Since only native gates were used, the actual gates executed are the same as the gates in the original circuit."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "pycharm": {
+ "name": "#%% md\n"
+ }
+ },
+ "source": [
+ "
\n",
+ "Note: The IonQ device does not support manual allocation. For circuits submitted to the IonQ device, qubits are allocated automatically.\n",
+ "
\n",
+ " Note: This section and the next verbatim box section uses the Rigetti Ankaa 2 device. When you run this notebook, make sure the device is currently available. You can find QPU availability windows on the Devices page in the Amazon Braket Console\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import networkx as nx\n",
+ "# access and visualize the device topology\n",
+ "print(rigetti.properties.paradigm.connectivity.connectivityGraph)\n",
+ "nx.draw_kamada_kawai(rigetti.topology_graph, with_labels=True, font_color=\"white\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9fa09f83a0747394",
+ "metadata": {},
+ "source": [
+ "Now we can submit a quantum task of the above program with verbatim box."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "id": "b5e7c89c1c9f8879",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-11-21T08:32:56.299544Z",
+ "start_time": "2023-11-21T08:32:56.297194Z"
+ },
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "DECLARE ro BIT[2]\n",
+ "PRAGMA INITIAL_REWIRING \"NAIVE\"\n",
+ "RESET\n",
+ "RX(pi) 0\n",
+ "RX(pi) 0\n",
+ "CZ 0 1\n",
+ "MEASURE 1 ro[1]\n",
+ "MEASURE 0 ro[0]\n"
+ ]
+ }
+ ],
+ "source": [
+ "verbatim_task = rigetti.run(OpenQASMProgram(source=program_with_verbatim_box), shots = 10)\n",
+ "verbatim_result = verbatim_task.result()\n",
+ "meta = verbatim_result.additional_metadata.rigettiMetadata\n",
+ "print(meta.compiledProgram)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "bcd27bc239db889d",
+ "metadata": {},
+ "source": [
+ "As shown above, the two consecutive `rx` $\\pi$-rotation gates did not get optimized and we confirm that our program was indeed executed verbatim."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b4768a96f7b1b3b6",
+ "metadata": {},
+ "source": [
+ "## Requesting Result Types with OpenQASM\n",
+ "\n",
+ "Braket provides [a rich library of result types](https://docs.aws.amazon.com/braket/latest/developerguide/braket-result-types.html) for circuit executions. With OpenQASM, requesting different result types for our quantum tasks is easier than ever using the `result` pragma. Next, we give an example of requesting result types for our Bell state program submitted to SV1. Before doing that, let's see what result types are supported on SV1:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "id": "b17d21060cda7fa7",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-11-21T08:32:56.304110Z",
+ "start_time": "2023-11-21T08:32:56.300283Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "name='Sample' observables=['x', 'y', 'z', 'h', 'i', 'hermitian'] minShots=1 maxShots=100000\n",
+ "name='Expectation' observables=['x', 'y', 'z', 'h', 'i', 'hermitian'] minShots=0 maxShots=100000\n",
+ "name='Variance' observables=['x', 'y', 'z', 'h', 'i', 'hermitian'] minShots=0 maxShots=100000\n",
+ "name='Probability' observables=None minShots=1 maxShots=100000\n",
+ "name='Amplitude' observables=None minShots=0 maxShots=0\n",
+ "name='AdjointGradient' observables=['x', 'y', 'z', 'h', 'i'] minShots=0 maxShots=0\n"
+ ]
+ }
+ ],
+ "source": [
+ "# print the result types supported by SV1\n",
+ "for iter in sv1.properties.action['braket.ir.openqasm.program'].supportedResultTypes:\n",
+ " print(iter)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "bbc02495939691c9",
+ "metadata": {},
+ "source": [
+ "With knowing the supported result types on SV1, we choose to request the `Expectation` of $X \\otimes Z$ observable on `q[0]` and `q[1]` and the `Amplitude` result type for a `shots=0` quantum task of our bell program:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "id": "6e3b521b7356b4bd",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-11-21T08:32:56.305634Z",
+ "start_time": "2023-11-21T08:32:56.302835Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "bell_with_result_type = \"\"\"\n",
+ "OPENQASM 3;\n",
+ "\n",
+ "qubit[2] q;\n",
+ "\n",
+ "#pragma braket result expectation x(q[0]) @ z(q[1])\n",
+ "#pragma braket result amplitude \"00\", \"11\"\n",
+ "h q[0];\n",
+ "cnot q[0], q[1];\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6435b34ab2525039",
+ "metadata": {},
+ "source": [
+ "The location of the `result` pragma is very flexible as long as it's after the qubit register definition (if you use physical qubits, you can put `result` pragmas anywhere after the program header).\n",
+ "\n",
+ "We can submit the above program and receive the results for our requested result types."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "id": "a42b0ebc71b59136",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-11-21T08:32:59.113501Z",
+ "start_time": "2023-11-21T08:32:56.306452Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0.0, {'00': (0.7071067811865475+0j), '11': (0.7071067811865475+0j)}]\n"
+ ]
+ }
+ ],
+ "source": [
+ "bell_result_types_task = sv1.run(OpenQASMProgram(source=bell_with_result_type), shots = 0)\n",
+ "bell_result = bell_result_types_task.result()\n",
+ "values = bell_result.values\n",
+ "print(values)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "38675f5678613895",
+ "metadata": {},
+ "source": [
+ "At last, we want to remind our Braket OpenQASM users that there are two requirements when requesting result types:\n",
+ "1. For `shots=0` quantum tasks, requesting non-simultaneously measurable result types is allowed, but for `shots>0` quantum tasks, it is not allowed. For example, we can write the following OpenQASM program in a `shots=0` quantum task but not in a `shots>0` quantum task, since the two result types are not simultaneously measurable:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "id": "45277f89209faec7",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-11-21T08:32:59.115339Z",
+ "start_time": "2023-11-21T08:32:59.112696Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "program_with_non_simultaneously_measurable_result_types = \"\"\"\n",
+ "OPENQASM 3;\n",
+ "\n",
+ "qubit[2] q;\n",
+ "\n",
+ "h q[0];\n",
+ "cnot q[0], q[1];\n",
+ "\n",
+ "#pragma braket result expectation x(q[0]) @ z(q[1])\n",
+ "#pragma braket result expectation hermitian([[0, -1im], [1im, 0]]) q[0]\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a9af8819fba31a90",
+ "metadata": {},
+ "source": [
+ "2. Do not use measurement instructions and request result types in the same OpenQASM program, otherwise a validation error will be raised. Since measurement instructions are basically equivalent to `#pragma braket result sample z(qubit)`, we encourage users to adapt a consistent style of requesting result types in the same program."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "db79ad324a5f6478",
+ "metadata": {
+ "collapsed": false
+ },
+ "source": [
+ "Circuits constructed with `from_ir` will have the correct result types:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "id": "f3c438da3a351153",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-11-21T08:32:59.127212Z",
+ "start_time": "2023-11-21T08:32:59.124909Z"
+ },
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "bell_with_result_type:\n",
+ "T : |0|1| Result Types |\n",
+ " \n",
+ "q0 : -H-C-Expectation(X@Z)-\n",
+ " | | \n",
+ "q1 : ---X-Expectation(X@Z)-\n",
+ "\n",
+ "T : |0|1| Result Types |\n",
+ "\n",
+ "Additional result types: Amplitude(00,11)\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"bell_with_result_type:\")\n",
+ "print(Circuit.from_ir(bell_with_result_type))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c371de3097c0598a",
+ "metadata": {
+ "collapsed": false
+ },
+ "source": [
+ "## Advanced OpenQASM features\n",
+ "\n",
+ "OpenQASM has features beyond what is natively supported by the `Circuit` class. You can run OpenQASM tasks directly on the Local Simulator or use Circuit.from_ir to convert an OpenQASM program to a Circuit object, which is supported by all circuit-based Braket devices. The following OpenQASM program is a GHZ state written with classical control flow and subroutines:\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "id": "5acb72003cd0a0f5",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-12-04T04:04:08.355878Z",
+ "start_time": "2023-12-04T04:04:08.353679Z"
+ },
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "ghz_with_advanced_features = \"\"\"\n",
+ "OPENQASM 3.0;\n",
+ "\n",
+ "def ghz(int[32] n) {\n",
+ " h q[0];\n",
+ " for int i in [0:n - 1] {\n",
+ " cnot q[i], q[i + 1];\n",
+ " }\n",
+ "}\n",
+ "\n",
+ "int[32] n = 5;\n",
+ "bit[n + 1] c;\n",
+ "qubit[n + 1] q;\n",
+ "\n",
+ "ghz(n);\n",
+ "\n",
+ "c = measure q;\n",
+ "\"\"\"\n",
+ "qasm_program = OpenQASMProgram(source=ghz_with_advanced_features)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f5d32bd10c64543",
+ "metadata": {
+ "collapsed": false
+ },
+ "source": [
+ "The local simulator supports these features:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "id": "c82bee530da348f6",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-12-04T04:04:13.932270Z",
+ "start_time": "2023-12-04T04:04:13.863203Z"
+ },
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "Counter({'000000': 480, '111111': 520})"
+ ]
+ },
+ "execution_count": 36,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from braket.devices import LocalSimulator\n",
+ "LocalSimulator().run(qasm_program, shots=1000).result().measurement_counts"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "96fca192b4f51797",
+ "metadata": {
+ "collapsed": false
+ },
+ "source": [
+ "but SV1 does not. However, `from_ir` will \"unroll\" the subroutine and loop to create a `Circuit` object that _can_ run on SV1:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 37,
+ "id": "b0886dfc74978bfa",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-12-04T04:04:19.974386Z",
+ "start_time": "2023-12-04T04:04:16.705969Z"
+ },
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "T : |0|1|2|3|4|5|\n",
+ " \n",
+ "q0 : -H-C---------\n",
+ " | \n",
+ "q1 : ---X-C-------\n",
+ " | \n",
+ "q2 : -----X-C-----\n",
+ " | \n",
+ "q3 : -------X-C---\n",
+ " | \n",
+ "q4 : ---------X-C-\n",
+ " | \n",
+ "q5 : -----------X-\n",
+ "\n",
+ "T : |0|1|2|3|4|5|\n",
+ "Counter({'000000': 503, '111111': 497})\n"
+ ]
+ }
+ ],
+ "source": [
+ "circuit = Circuit.from_ir(qasm_program)\n",
+ "print(circuit)\n",
+ "print(sv1.run(circuit, shots=1000).result().measurement_counts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a329fa3df47ffee4",
+ "metadata": {
+ "collapsed": false
+ },
+ "source": [
+ "For an in-depth exploration of advanced OpenQASM features, see [Simulating Advanced OpenQASM Programs with the Local Simulator](https://github.com/amazon-braket/amazon-braket-examples/blob/main/examples/braket_features/Simulating_Advanced_OpenQASM_Programs_with_the_Local_Simulator.ipynb)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9e4c7a48a2b83ce1",
+ "metadata": {},
+ "source": [
+ "# Conclusion\n",
+ "\n",
+ "In this notebook, you learned how to submit OpenQASM quantum tasks and use OpenQASM features on Braket. Hope you enjoyed it! You can find more information about OpenQASM3.0 in its [live specification](https://openqasm.com/), and you can learn more about OpenQASM support on Braket in the [Amazon Braket documentation](https://docs.aws.amazon.com/braket/latest/developerguide/)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "id": "3f5bc3dfad520f14",
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-11-21T08:32:59.624204Z",
+ "start_time": "2023-11-21T08:32:59.127772Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Quantum Task Summary\n",
+ "{'arn:aws:braket:::device/quantum-simulator/amazon/sv1': {'shots': 120, 'tasks': {'CREATED': 1, 'COMPLETED': 3}, 'execution_duration': datetime.timedelta(microseconds=20000), 'billed_execution_duration': datetime.timedelta(seconds=9)}, 'arn:aws:braket:::device/quantum-simulator/amazon/dm1': {'shots': 30, 'tasks': {'COMPLETED': 3}, 'execution_duration': datetime.timedelta(microseconds=12000), 'billed_execution_duration': datetime.timedelta(seconds=9)}}\n",
+ "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
+ "Estimated cost to run this example: 0.02 USD\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Quantum Task Summary\")\n",
+ "print(t.quantum_tasks_statistics())\n",
+ "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n",
+ "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.2f} USD\")"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.6"
+ }
},
- "scrolled": false
- },
- "outputs": [],
- "source": [
- "from braket.ir.openqasm import Program as OpenQASMProgram\n",
- "\n",
- "bell_program = OpenQASMProgram(source=bell_qasm)\n",
- "bell_task = sv1.run(\n",
- " bell_program, \n",
- " shots=100, \n",
- ")"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "ba9729ce6ab2bf91",
- "metadata": {},
- "source": [
- "### Submit OpenQASM 3.0 programs using the AWS Command Line Interface\n",
- "\n",
- "Alternatively, if you like the command line experience or you are not a Python user, you can also choose to use the [AWS Command Line Interface (CLI)](https://aws.amazon.com/cli/) to submit our Bell state program. Before doing that we have to make sure we have [AWS CLI installed](https://docs.aws.amazon.com/cli/latest/userguide/getting-started-install.html). The following code saves the `bell_qasm` string to a file named `bell.qasm`:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "id": "61362f489016dd1f",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:41.407834Z",
- "start_time": "2023-11-21T08:32:41.403524Z"
- }
- },
- "outputs": [],
- "source": [
- "with open(\"bell.qasm\", \"w\") as f:\n",
- " f.write(bell_qasm)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "5c4be932b51fd2ac",
- "metadata": {},
- "source": [
- "Then we can use the command below to submit the quantum task via AWS CLI. Remember to replace the placeholder \\\"amazon-braket-my-bucket\\\" with your own bucket name.\n",
- " \n",
- " aws braket create-quantum-task \\\n",
- " --region \"us-west-1\" \\\n",
- " --device-arn \"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\" \\\n",
- " --shots 100 \\\n",
- " --action '{\n",
- " \"braketSchemaHeader\": {\n",
- " \"name\": \"braket.ir.openqasm.program\", \n",
- " \"version\": \"1\"\n",
- " },\n",
- " \"source\": $(cat bell.qasm)\n",
- " }'"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "68222e9240c91d58",
- "metadata": {
- "collapsed": false
- },
- "source": [
- "## Convert OpenQASM 3.0 programs to circuits\n",
- "\n",
- "You can convert OpenQASM programs into Braket `Circuit` objects if you want to programmatically change your program."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "id": "96417df481e2f5d",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:41.420933Z",
- "start_time": "2023-11-21T08:32:41.407658Z"
- },
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : |0|1|\n",
- " \n",
- "q0 : -H-C-\n",
- " | \n",
- "q1 : ---X-\n",
- "\n",
- "T : |0|1|\n"
- ]
- }
- ],
- "source": [
- "from braket.circuits import Circuit\n",
- "print(Circuit.from_ir(bell_qasm))"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "4fec44c2bb4680df",
- "metadata": {},
- "source": [
- "## Figure out what OpenQASM features are supported on each device\n",
- "\n",
- "Different devices on Braket support different subsets of OpenQASM features. To see what are the supported OpenQASM features on each device, we can simply check the device capability for OpenQASM actions. As an example, we can take a look at the `action` field in the device capability of SV1 simulator:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "id": "78a5c9f03581cea4",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:41.425542Z",
- "start_time": "2023-11-21T08:32:41.422663Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "['ccnot',\n",
- " 'cnot',\n",
- " 'cphaseshift',\n",
- " 'cphaseshift00',\n",
- " 'cphaseshift01',\n",
- " 'cphaseshift10',\n",
- " 'cswap',\n",
- " 'cy',\n",
- " 'cz',\n",
- " 'ecr',\n",
- " 'h',\n",
- " 'i',\n",
- " 'iswap',\n",
- " 'pswap',\n",
- " 'phaseshift',\n",
- " 'rx',\n",
- " 'ry',\n",
- " 'rz',\n",
- " 's',\n",
- " 'si',\n",
- " 'swap',\n",
- " 't',\n",
- " 'ti',\n",
- " 'v',\n",
- " 'vi',\n",
- " 'x',\n",
- " 'xx',\n",
- " 'xy',\n",
- " 'y',\n",
- " 'yy',\n",
- " 'z',\n",
- " 'zz',\n",
- " 'gpi',\n",
- " 'gpi2',\n",
- " 'ms']"
- ]
- },
- "execution_count": 9,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# supportedOperations\n",
- "sv1.properties.action['braket.ir.openqasm.program'].supportedOperations"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "id": "85fbc40dc254813e",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:41.463833Z",
- "start_time": "2023-11-21T08:32:41.425725Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "['braket_unitary_matrix',\n",
- " 'braket_basis_rotation',\n",
- " 'braket_result_type_sample',\n",
- " 'braket_result_type_expectation',\n",
- " 'braket_result_type_variance',\n",
- " 'braket_result_type_probability',\n",
- " 'braket_result_type_amplitude',\n",
- " 'braket_result_type_adjoint_gradient']"
- ]
- },
- "execution_count": 10,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# supportedPragmas\n",
- "sv1.properties.action['braket.ir.openqasm.program'].supportedPragmas"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "id": "1fa721d9960f5412",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:41.464559Z",
- "start_time": "2023-11-21T08:32:41.429030Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "['braket_result_type_state_vector',\n",
- " 'braket_result_type_density_matrix',\n",
- " 'braket_noise_amplitude_damping',\n",
- " 'braket_noise_bit_flip',\n",
- " 'braket_noise_depolarizing',\n",
- " 'braket_noise_kraus',\n",
- " 'braket_noise_pauli_channel',\n",
- " 'braket_noise_generalized_amplitude_damping',\n",
- " 'braket_noise_phase_flip',\n",
- " 'braket_noise_phase_damping',\n",
- " 'braket_noise_two_qubit_dephasing',\n",
- " 'braket_noise_two_qubit_depolarizing']"
- ]
- },
- "execution_count": 11,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# forbiddenPragmas\n",
- "sv1.properties.action['braket.ir.openqasm.program'].forbiddenPragmas"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "8190bb8089c7db3f",
- "metadata": {},
- "source": [
- "The SV1 OpenQASM `action` field lists supported/forbidden OpenQASM features on the device, including `supportedPragmas`, `forbiddenPragmas`, `maximumQubitArrays`, `maximumClassicalArrays`, `requiresAllQubitsMeasurement`, `supportedResultTypes`, etc. The names are self-evident, but readers are encouraged to visit the [Amazon Braket developer guide](https://docs.aws.amazon.com/braket/latest/developerguide/braket-using.html) for full information of what these fields mean."
- ]
- },
- {
- "cell_type": "markdown",
- "id": "ee537a4601e4c244",
- "metadata": {},
- "source": [
- "# OpenQASM features on Braket\n",
- "\n",
- "Braket supports many useful OpenQASM features, either through the OpenQASM program syntax or Braket-specific pragmas. We will walk through some of these features in this section.\n",
- "\n",
- "## Simulating Noise with OpenQASM\n",
- "\n",
- "With the fully on-demand, high-performance, density-matrix simulator [DM1](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html#braket-simulator-dm1), you can easily investigate the effects of realistic noise on your quantum programs. Now, we show how to use OpenQASM programs to leverage the circuit-level noise simulation capability of DM1.\n",
- "\n",
- "To simulate noise, we have to be able to specify different noise channels. Although syntax for noise channels is not available in the OpenQASM language, Braket uses the `pragma` statement to extend OpenQASM for defining noise channels. Here is an example of an OpenQASM program that prepares a noisy 3-qubit [GHZ state](https://en.wikipedia.org/wiki/Greenberger%E2%80%93Horne%E2%80%93Zeilinger_state):"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "id": "4d8a62cfc51a18b",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:41.464621Z",
- "start_time": "2023-11-21T08:32:41.431447Z"
- }
- },
- "outputs": [],
- "source": [
- "noisy_ghz3_program = \"\"\"\n",
- "// noisy_ghz3.qasm\n",
- "// Prepare a 3 noisy qubit GHZ state\n",
- "OPENQASM 3;\n",
- "\n",
- "qubit[3] q;\n",
- "bit[3] c;\n",
- "\n",
- "h q[0];\n",
- "#pragma braket noise depolarizing(0.1) q[0]\n",
- "cnot q[0], q[1];\n",
- "#pragma braket noise depolarizing(0.1) q[0]\n",
- "#pragma braket noise depolarizing(0.1) q[1]\n",
- "cnot q[1], q[2];\n",
- "#pragma braket noise depolarizing(0.1) q[0]\n",
- "#pragma braket noise depolarizing(0.1) q[1]\n",
- "\n",
- "c = measure q;\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "id": "3a988726bb4c39e8",
- "metadata": {},
- "source": [
- "In the example above, we inserted the depolarizing noise channel with probability of 0.1 after each gate in the circuit. The `noisy_ghz3_program` is equivalent to the following program in the Braket SDK:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "id": "647e3717ccbba672",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:41.464801Z",
- "start_time": "2023-11-21T08:32:41.434396Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "Circuit('instructions': [Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(0)]), 'control': QubitSet([]), 'control_state': (), 'power': 1), Instruction('operator': Depolarizing(0.1), 'target': QubitSet([Qubit(0)]), 'control': QubitSet([]), 'control_state': (), 'power': 1), Instruction('operator': CNot('qubit_count': 2), 'target': QubitSet([Qubit(0), Qubit(1)]), 'control': QubitSet([]), 'control_state': (), 'power': 1), Instruction('operator': Depolarizing(0.1), 'target': QubitSet([Qubit(0)]), 'control': QubitSet([]), 'control_state': (), 'power': 1), Instruction('operator': Depolarizing(0.1), 'target': QubitSet([Qubit(1)]), 'control': QubitSet([]), 'control_state': (), 'power': 1), Instruction('operator': CNot('qubit_count': 2), 'target': QubitSet([Qubit(1), Qubit(2)]), 'control': QubitSet([]), 'control_state': (), 'power': 1), Instruction('operator': Depolarizing(0.1), 'target': QubitSet([Qubit(1)]), 'control': QubitSet([]), 'control_state': (), 'power': 1), Instruction('operator': Depolarizing(0.1), 'target': QubitSet([Qubit(2)]), 'control': QubitSet([]), 'control_state': (), 'power': 1)])"
- ]
- },
- "execution_count": 13,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from braket.circuits import Circuit, noises\n",
- "\n",
- "noisy_ghz3_circ = Circuit().h(0).cnot(0, 1).cnot(1, 2)\n",
- "noise = noises.Depolarizing(probability=0.1)\n",
- "noisy_ghz3_circ.apply_gate_noise(noise)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "1db047fbac6a26bb",
- "metadata": {},
- "source": [
- "To see if `noisy_ghz3_program` and `noisy_ghz3_circ` are indeed the same, we can run both circuits and compare the results:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "id": "4c57de26c172aa5",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:42.963722Z",
- "start_time": "2023-11-21T08:32:41.441098Z"
- }
- },
- "outputs": [],
- "source": [
- "dm1 = AwsDevice(Devices.Amazon.DM1)\n",
- "\n",
- "noisy_ghz3_circ_task = dm1.run(noisy_ghz3_circ, shots = 10)\n",
- "noisy_ghz3_program_task = dm1.run(OpenQASMProgram(source=noisy_ghz3_program), shots = 10)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "id": "75984e0e95dc4afb",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:45.959888Z",
- "start_time": "2023-11-21T08:32:42.975561Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "sdk measurement results: Counter({'111': 5, '000': 4, '100': 1})\n",
- "openqasm measurement results: Counter({'000': 5, '111': 4, '100': 1})\n"
- ]
- }
- ],
- "source": [
- "sdk_result = noisy_ghz3_circ_task.result()\n",
- "openqasm_result = noisy_ghz3_program_task.result()\n",
- "sdk_measurement = sdk_result.measurement_counts\n",
- "openqasm_measurement = openqasm_result.measurement_counts\n",
- "print('sdk measurement results:', sdk_measurement)\n",
- "print('openqasm measurement results:', openqasm_measurement)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "f2720672ca96b104",
- "metadata": {},
- "source": [
- "As expected, the measurement counts of the two are very close.\n",
- "\n",
- "In addition to depolarizing noises, we can simulate more complicated noise types with Braket, e.g., `pauli_channel`, `amplitude_damping`, etc. Check the [Amazon Braket developer guide](https://docs.aws.amazon.com/braket/latest/developerguide/braket-using.html) for a complete list of noise channels supported on Braket. Here we give another example of general noise channels defined by the Kraus representation."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "id": "f3231a7767d20640",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:45.971122Z",
- "start_time": "2023-11-21T08:32:45.960859Z"
- }
- },
- "outputs": [],
- "source": [
- "noisy_program_with_kraus_operators = \"\"\"\n",
- "// noisy_program_with_kraus_operators\n",
- "OPENQASM 3;\n",
- "\n",
- "qubit[2] q;\n",
- "bit[2] c;\n",
- "\n",
- "h q[0];\n",
- "#pragma braket noise kraus([[0.9486833, 0], [0, 0.9486833]], [[0, 0.31622777], [0.31622777, 0]]) q[0]\n",
- "cnot q[0], q[1];\n",
- "\n",
- "c = measure q;\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "id": "ebac8bbb6d45341d",
- "metadata": {},
- "source": [
- "We inserted a single qubit noise channel defined by two 2x2 complex Kraus operators in the example above on qubit `q[0]`. Braket will validate if the Kraus operators indeed form a Completely-Positive and Trace-Preserving (CPTP) map."
- ]
- },
- {
- "cell_type": "markdown",
- "id": "ffa5e09c2ceab140",
- "metadata": {
- "collapsed": false
- },
- "source": [
- "The `from_ir` method supports noise operations, including general Kraus operators."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "id": "69c7ae1c396ac705",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:46.004276Z",
- "start_time": "2023-11-21T08:32:45.977541Z"
- },
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "noisy_ghz3_program:\n",
- "T : | 0 | 1 | 2 |\n",
- " \n",
- "q0 : -H-DEPO(0.1)-C-DEPO(0.1)-DEPO(0.1)-------------\n",
- " | \n",
- "q1 : -------------X-DEPO(0.1)-----------C-DEPO(0.1)-\n",
- " | \n",
- "q2 : -----------------------------------X-----------\n",
- "\n",
- "T : | 0 | 1 | 2 |\n",
- "\n",
- "noisy_program_with_kraus_operators:\n",
- "T : | 0 |1|\n",
- " \n",
- "q0 : -H-KR-C-\n",
- " | \n",
- "q1 : ------X-\n",
- "\n",
- "T : | 0 |1|\n",
- "\n",
- "Kraus operators:\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "[array([[0.9486833+0.j, 0. +0.j],\n",
- " [0. +0.j, 0.9486833+0.j]]),\n",
- " array([[0. +0.j, 0.31622777+0.j],\n",
- " [0.31622777+0.j, 0. +0.j]])]"
- ]
- },
- "execution_count": 16,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "print(\"noisy_ghz3_program:\")\n",
- "print(Circuit.from_ir(noisy_ghz3_program))\n",
- "print()\n",
- "print(\"noisy_program_with_kraus_operators:\")\n",
- "circuit_kraus = Circuit.from_ir(noisy_program_with_kraus_operators)\n",
- "print(circuit_kraus)\n",
- "print()\n",
- "print(\"Kraus operators:\")\n",
- "circuit_kraus.instructions[1].operator.to_matrix()"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "a6b1ce4e1900550",
- "metadata": {},
- "source": [
- "## Submitting parametrized quantum tasks with OpenQASM\n",
- "\n",
- "The on-demand [SV1 simulator](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html#braket-simulator-sv1) and [DM1 simulator](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html#braket-simulator-dm1) support submitting OpenQASM programs with free parameters. You can set the value of the parameter when you submit the quantum task, like so:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "id": "71245a134d32fa26",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:46.007177Z",
- "start_time": "2023-11-21T08:32:46.003030Z"
- }
- },
- "outputs": [],
- "source": [
- "parameter_qasm = \"\"\"\n",
- "OPENQASM 3.0;\n",
- "input float alpha;\n",
- "\n",
- "bit[2] b;\n",
- "qubit[2] q;\n",
- "\n",
- "h q[0];\n",
- "h q[1];\n",
- "rx(alpha) q[0];\n",
- "rx(alpha) q[1];\n",
- "b[0] = measure q[0];\n",
- "b[1] = measure q[1];\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "id": "bec130ddc2409db5",
- "metadata": {},
- "source": [
- "The `input float alpha` line indicates that we have an input parameter of type `float` named `alpha`. We can specify a value for `alpha` when we submit the quantum task using the optional `inputs` argument to `run`. `input` should be a `dict` of `string`-`float` pairs."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 19,
- "id": "b831353ac6cfab2a",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:48.743543Z",
- "start_time": "2023-11-21T08:32:46.007096Z"
- },
- "scrolled": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Counter({'00': 4, '01': 3, '11': 3})\n"
- ]
- }
- ],
- "source": [
- "input_dict = {'alpha': 0.1}\n",
- "param_sv1_task = sv1.run(OpenQASMProgram(source=parameter_qasm), shots = 10, inputs=input_dict)\n",
- "param_sv1_result = param_sv1_task.result()\n",
- "print(param_sv1_result.measurement_counts)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "eb90a29d1debc7b4",
- "metadata": {},
- "source": [
- "Similarly, we can specify values for parametrized noise operations:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 20,
- "id": "94f2688b3380c621",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:48.746739Z",
- "start_time": "2023-11-21T08:32:48.743876Z"
- }
- },
- "outputs": [],
- "source": [
- "parameter_noise_qasm = \"\"\"\n",
- "OPENQASM 3.0;\n",
- "input float beta;\n",
- "input float alpha;\n",
- "bit[2] b;\n",
- "qubit[2] q;\n",
- "h q[0];\n",
- "h q[1];\n",
- "rx(alpha) q[0];\n",
- "rx(alpha) q[1];\n",
- "#pragma braket noise bit_flip(beta) q[0]\n",
- "b[0] = measure q[0];\n",
- "b[1] = measure q[1];\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "id": "101d366dca84ddb2",
- "metadata": {},
- "source": [
- "We can see there are now two `input` lines, one for each free parameter."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 21,
- "id": "a0aa8a773b16dc22",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:51.579287Z",
- "start_time": "2023-11-21T08:32:48.747668Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Counter({'00': 3, '01': 3, '11': 2, '10': 2})\n"
- ]
- }
- ],
- "source": [
- "noise_input_dict = {'alpha': 0.1, 'beta': 0.2}\n",
- "param_dm1_task = dm1.run(OpenQASMProgram(source=parameter_qasm), shots = 10, inputs=noise_input_dict)\n",
- "param_dm1_result = param_dm1_task.result()\n",
- "print(param_dm1_result.measurement_counts)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "7e60112ddc974a94",
- "metadata": {},
- "source": [
- "## Simulating arbitrary unitaries with OpenQASM\n",
- "\n",
- "The on-demand [SV1 simulator](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html#braket-simulator-sv1) allows us to simulate arbitrary unitary gates in a circuit. With OpenQASM, we can use the `unitary` pramga to insert these arbitrary unitary gates: "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 22,
- "id": "ffc32efec9315f0",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:51.589214Z",
- "start_time": "2023-11-21T08:32:51.579008Z"
- }
- },
- "outputs": [],
- "source": [
- "program_with_unitary = \"\"\"\n",
- "// noisy_program_with_kraus_operators\n",
- "OPENQASM 3;\n",
- "\n",
- "qubit q;\n",
- "bit c;\n",
- "\n",
- "#pragma braket unitary([[0, -1im], [1im, 0]]) q\n",
- "c = measure q;\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "id": "8c190474a6e28563",
- "metadata": {},
- "source": [
- "The `1im` in the `unitary` pragma is the OpenQASM notation of the imaginary number $i$, thus, we were simply using the pragma to perform a Pauli Y gate. We can check it by submitting the above program to SV1."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 23,
- "id": "6d687471d81b2367",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:54.390589Z",
- "start_time": "2023-11-21T08:32:51.586164Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Counter({'1': 10})\n"
- ]
- }
- ],
- "source": [
- "unitary_task = sv1.run(OpenQASMProgram(source=program_with_unitary), shots = 10)\n",
- "unitary_result = unitary_task.result()\n",
- "print(unitary_result.measurement_counts)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "76f2897ec744dafb",
- "metadata": {},
- "source": [
- "As expected, the Pauli Y gate flipped the initial 0 state to the 1 state."
- ]
- },
- {
- "cell_type": "markdown",
- "id": "111ead44155005a8",
- "metadata": {
- "collapsed": false
- },
- "source": [
- "`from_ir` will reconstruct the unitary:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "id": "7b631be4b6785b90",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:54.403015Z",
- "start_time": "2023-11-21T08:32:54.398210Z"
- },
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([[0.+0.j, 0.-1.j],\n",
- " [0.+1.j, 0.+0.j]])"
- ]
- },
- "execution_count": 24,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "Circuit.from_ir(program_with_unitary).instructions[0].operator.to_matrix()"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "ce9caf39",
- "metadata": {},
- "source": [
- "## Measuring specific qubits with OpenQASM\n",
- "\n",
- "The Local State Vector Simulator and Local Density Matrix Simulator support submitting OpenQASM programs where a subset of the circuit's qubits can be measured, which is often called partial measurement. For example, you can create a two-qubit circuit and only measure the first qubit like so:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "id": "d33a0cb6",
- "metadata": {},
- "outputs": [],
- "source": [
- "partial_measure_qasm = \"\"\"\n",
- "OPENQASM 3.0;\n",
- "bit[1] b;\n",
- "qubit[2] q;\n",
- "h q[0];\n",
- "cnot q[0], q[1];\n",
- "b[0] = measure q[0];\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "id": "81247da3",
- "metadata": {},
- "source": [
- "We can see that there are two qubits, `q[0]` and `q[1]` but we are only measuring qubit 0 here: `b[0] = measure q[0]`.\n",
- "\n",
- "Now we can run this on the local state vector simulator"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 27,
- "id": "d747fcb4",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Counter({'0': 7, '1': 3})\n",
- "Measured qubits: [0]\n"
- ]
- }
- ],
- "source": [
- "from braket.devices import LocalSimulator\n",
- "\n",
- "local_sim = LocalSimulator()\n",
- "partial_measure_local_sim_task = local_sim.run(OpenQASMProgram(source=partial_measure_qasm), shots = 10)\n",
- "partial_measure_local_sim_result = partial_measure_local_sim_task.result()\n",
- "print(partial_measure_local_sim_result.measurement_counts)\n",
- "print(\"Measured qubits: \", partial_measure_local_sim_result.measured_qubits)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "923c3cd7",
- "metadata": {},
- "source": [
- "As expected, only the targeted qubits were measured. \n",
- "\n",
- "The OpenQASM program `partial_measure_qasm` is equivalent to the following `Circuit`:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 43,
- "id": "5b4e6ae6",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Counter({'0': 7, '1': 3})\n",
- "Measured qubits: [0]\n"
- ]
- }
- ],
- "source": [
- "partial_measure = Circuit().h(0).cnot(0, 1).measure(0)\n",
- "partial_measure_task = local_sim.run(partial_measure, shots=10)\n",
- "partial_measure_result = partial_measure_task.result()\n",
- "print(partial_measure_result.measurement_counts)\n",
- "print(\"Measured qubits: \", partial_measure_result.measured_qubits)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "49b97636",
- "metadata": {},
- "source": [
- "We can check whether a device supports partial measurement by inspecting the `requiresAllQubitsMeasurement` field in its action properties; if it is `False`, then partial measurement is supported."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "id": "74a715eb",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "False"
- ]
- },
- "execution_count": 15,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "AwsDevice(Devices.Rigetti.AspenM3).properties.action['braket.ir.openqasm.program'].requiresAllQubitsMeasurement"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "a6a94ac1",
- "metadata": {},
- "source": [
- "Here, `requiresAllQubitsMeasurement` is `False`, which indicates that not all qubits must be measured."
- ]
- },
- {
- "cell_type": "markdown",
- "id": "8996e0c59741a66f",
- "metadata": {},
- "source": [
- "## Qubit Rewiring with OpenQASM\n",
- "\n",
- "Amazon Braket supports the [physical qubit notation within OpenQASM](https://openqasm.com/language/types.html#physical-qubits) on Rigetti devices. When using physical qubits, you have to ensure that the qubits are indeed connected on the selected device. Alternatively, if qubit registers are used instead, the `PARTIAL` rewiring strategy is enabled by default on Rigetti devices. The following example shows how to use physical qubit notation in an OpenQASM program:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "id": "144cc3e458a21b2d",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:54.410178Z",
- "start_time": "2023-11-21T08:32:54.402877Z"
- }
- },
- "outputs": [],
- "source": [
- "ghz_program_with_physical_qubits = \"\"\"\n",
- "// Prepare a GHZ state\n",
- "OPENQASM 3;\n",
- "\n",
- "bit[3] ro;\n",
- "h $0;\n",
- "cnot $0, $1;\n",
- "cnot $1, $2;\n",
- "ro[0] = measure $0;\n",
- "ro[1] = measure $1;\n",
- "ro[2] = measure $2;\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "id": "3f01e6dc44e0e226",
- "metadata": {},
- "source": [
- "We can run the above program on the Rigetti Aspen-M-3 device,"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "id": "768b980b78c4d451",
- "metadata": {
- "ExecuteTime": {
- "end_time": "2023-11-21T08:32:55.489511Z",
- "start_time": "2023-11-21T08:32:54.414005Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Measured qubits: [0, 1, 2]\n"
- ]
- }
- ],
- "source": [
- "# choose the quantum device\n",
- "aspen_m = AwsDevice(Devices.Rigetti.AspenM3)\n",
- "\n",
- "ghz_program_with_physical_qubits_task = aspen_m.run(OpenQASMProgram(source=ghz_program_with_physical_qubits), shots = 10)\n",
- "measured_qubits = ghz_program_with_physical_qubits_task.result().measured_qubits\n",
- "print(\"Measured qubits:\", measured_qubits)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "5a5597dc7843d541",
- "metadata": {},
- "source": [
- "As we can see, physical qubits 0, 1 and 2 are indeed being used and measured."
- ]
- },
- {
- "cell_type": "markdown",
- "id": "25cb2ccc4337dc1e",
- "metadata": {},
- "source": [
- "
\n",
- " Note: This section and the next verbatim box section uses the Rigetti Aspen-M-3 device. When you run this notebook, make sure the device is currently available. You can find QPU availability windows on the Devices page in the Amazon Braket Console\n",
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "276d680f-887d-4929-bcaa-e276a6303496",
- "metadata": {},
- "source": [
- "We can programmatically access all the calibration data with the Braket SDK. First we load the AwsDevice using the ARN for Rigetti Aspen-M-3."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "id": "a55ea9d5-05f3-4da5-a305-a391e914d012",
- "metadata": {},
- "outputs": [],
- "source": [
- "aspen_m = AwsDevice(Devices.Rigetti.AspenM3)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "a8a42ae1-51ac-4bf1-bd6a-81ffd982b5f8",
- "metadata": {},
- "source": [
- "The properties dictionary contains keys \"provider\" and \"specs\", with \"1Q\" and \"2Q\" keys for the one- and two-qubit calibration data. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "id": "153b5b63-8205-4a7e-bb18-0305ef428f36",
- "metadata": {},
- "outputs": [],
- "source": [
- "aspen_m_specs = aspen_m.properties.dict()[\"provider\"][\"specs\"]\n",
- "\n",
- "one_qubit_data = aspen_m_specs[\"1Q\"]\n",
- "two_qubit_data = aspen_m_specs[\"2Q\"]"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "661cca17-01fa-40be-bd3e-741bacc74ce4",
- "metadata": {},
- "source": [
- "The keys of the \"1Q\" dictionary is the qubit number. \n",
- "For Aspen-M-3, there are 79 qubits indexed by the first digit representing the octagon (0 to 4, and 10 to 14)\n",
- "and the second representing the qubit in that octagon (0 to 7). We can get all qubit indices with `one_qubit_data.keys()` or with `aspen_m.topology_graph.nodes`.\n",
- "\n",
- "The keys of the \"2Q\" dictionary are the connected qubit pairs separated by a hyphen. \n",
- "For example, if qubit 0 and 1 are connected the key is \"0-1\".\n",
- "\n",
- "\n",
- "#### One-qubit noise \n",
- "\n",
- "Let's look at the one qubit calibration data for qubit 0."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "id": "8d4ecc35-f4dc-49d8-b6ff-adaee560ac4b",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{'T1': 2.4443429874176914e-05,\n",
- " 'T2': 1.627681336532139e-05,\n",
- " 'f1QRB': 0.9985669301541129,\n",
- " 'f1QRB_std_err': 0.0004092835114091019,\n",
- " 'f1Q_simultaneous_RB': 0.9977676229871197,\n",
- " 'f1Q_simultaneous_RB_std_err': 0.00021522363993495725,\n",
- " 'fActiveReset': 0.9905000000000002,\n",
- " 'fRO': 0.9795}"
- ]
- },
- "execution_count": 4,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "one_qubit_data[\"0\"]"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "4b676762-e642-4a98-89e3-86d79367071a",
- "metadata": {},
- "source": [
- "For each qubit, there are various metrics of the quality:\n",
- "\n",
- "- **T1**: Thermal relaxation time is related to the time it takes for the excited state, |1⟩, to decay into the ground state, |0⟩. The probability of remaining in the excited state is $p(|1⟩)\\sim e^{-t/T_1}$\n",
- "\n",
- "- **T2**: The dephasing time, is the decay constant for the scale for a |+⟩ state to decohere into the completely mixed state. $p(|+⟩)\\sim e^{-t/T_2}$ \n",
- "\n",
- "- **Fidelity (RB)**: Single-qubit randomized benchmarking fidelities. RB fidelity quantifies the average gate fidelity where the average is over all Clifford gates. RB describes an *effective* noise model with gate-independent depolarizing noise on each Clifford gate.\n",
- "\n",
- "- **Fidelity (sRB)**: Single-qubit simultaneous randomized benchmarking fidelities. These are extracted by running single-qubit RB on all qubits simultaneously. Note that we expect the sRB fidelity to be lower than standard RB fidelity due to non-local crosstalk type noise on the device. \n",
- "\n",
- "- **Active reset fidelity**: Single-qubit active reset fidelities represents the accuracy to which qubits are reinitalized into the ground state |0⟩.\n",
- "\n",
- "- **Readout fidelity**: Single-qubit readout fidelities describes the probability of a bit flip error before readout in the computational basis. The readout fidelity is related to the probability of correctly measuring the ground state and excited states respectively, e.g. $f_{RO} =\\frac{p(0|0)+p(1|1)}{2}$"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "296708a3-771e-42b4-9ba8-f3db1a02970b",
- "metadata": {},
- "source": [
- "Now that we know how to extract and use the calibration data, we can build a simple noise model. For every qubit we will add:\n",
- "- amplitude dampening noise with probability $p= 1-e^{-t/T_1}$ for every gate\n",
- "- phase dampening noise with probability $p= 0.5(1-e^{-t/T_2})$ for every gate\n",
- "- depolarizing noise with probability $p=1-f_{sRB}$ (from simultaneous RB fidelity) for every gate\n",
- "- readout bit flip noise with probability $p=1-f_{RO}$ to measurements \n",
- "\n",
- "Technically, the sRB fidelity already includes effects from $T_1$/$T_2$, however to be explicit we add these as separate terms. In a sense, this model might overestimate the noise on the QPU. \n",
- "\n",
- "For the dampening noises, we first need the gate times to model $T_1$ and $T_2$ errors.\n",
- "From the Braket Aspen-M-3 device page: \"These gates offer fast (40ns and 180ns) 1Q and 2Q gate times.\""
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "id": "cd27adfb-f7d6-4583-b854-794e38152c90",
- "metadata": {},
- "outputs": [],
- "source": [
- "# median 1q and 2q gate times\n",
- "gate_time_1_qubit = 40e-9\n",
- "gate_time_2_qubit = 240e-09"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "5769f2f4-de1c-4b47-9e4e-fd8d39b9e975",
- "metadata": {},
- "source": [
- "To create the noise model, we iterate over all qubits keys in `one_qubit_data`"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "id": "508070bc-b1d2-4737-a2fc-d7711e419996",
- "metadata": {},
- "outputs": [],
- "source": [
- "noise_model = NoiseModel()\n",
- "\n",
- "# Single-qubit noise\n",
- "for q, data in one_qubit_data.items(): # iterate over qubits\n",
- "\n",
- " # T1 dampening\n",
- " t1 = data[\"T1\"]\n",
- " damping_prob = 1 - np.exp(-(gate_time_1_qubit / t1))\n",
- " noise_model.add_noise(AmplitudeDamping(damping_prob), GateCriteria(qubits=int(q)))\n",
- "\n",
- " # T2 phase flip\n",
- " t2 = data[\"T2\"]\n",
- " dephasing_prob = 0.5 * (1 - np.exp(-(gate_time_1_qubit / t2)))\n",
- " noise_model.add_noise(PhaseDamping(dephasing_prob), GateCriteria(qubits=int(q)))\n",
- "\n",
- " # 1q RB depolarizing rate from simultaneous RB\n",
- " depolar_rate = 1 - data[\"f1Q_simultaneous_RB\"]\n",
- " noise_model.add_noise(Depolarizing(depolar_rate), GateCriteria(qubits=int(q)))\n",
- "\n",
- " # 1q RB readout\n",
- " readout_value = 1 - data[\"fRO\"]\n",
- " noise_model.add_noise(BitFlip(readout_value), ObservableCriteria(qubits=int(q)))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "id": "9d20d24c-17e2-4bba-b317-fb2d156bedb0",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Number of terms in noise model is: 320\n",
- "Number of parameters in noise model is: 320\n"
- ]
- }
- ],
- "source": [
- "num_params = sum(len(item.noise.parameters) for item in noise_model.instructions)\n",
- "print(f\"Number of terms in noise model is: {len(noise_model.instructions)}\")\n",
- "print(f\"Number of parameters in noise model is: {num_params}\")"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "790c62f7-776a-4e4c-9405-7b7a14eee5b0",
- "metadata": {},
- "source": [
- "#### Two-qubit noise \n",
- "Next we consider adding two-qubit noise to the model. \n",
- "\n",
- "Let's first look at the data provided in the Aspen-M-3 device calibration data. On the first connect, \"0-1\", the properties are:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "id": "626cbe56-3649-48eb-a2a1-f669eb790b47",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{'fCPHASE': 0.8991973184700036,\n",
- " 'fCPHASE_std_err': 0.019391126441846068,\n",
- " 'fCZ': 0.9406104552003762,\n",
- " 'fCZ_std_err': 0.011069113247524152,\n",
- " 'fXY': 0.8365560014004874,\n",
- " 'fXY_std_err': 0.014585224789608713}"
- ]
- },
- "execution_count": 8,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "two_qubit_data[\"0-1\"]"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "4bcd3be4-a6e4-4cf3-841e-1a451e01803a",
- "metadata": {},
- "source": [
- "Here, we see the fidelity per gate (CPhase, CZ, or XY) and the associated standard error. \n",
- "\n",
- "Next we loop over the entries in the `two_qubit_data` dictionary and add two-qubit depolarizing noise to the model. Notice that Aspen-M-3 has symmetric connections (\"0-1\" and \"1-0\") so we need to add noise in both directions."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "id": "80f57550-6549-46b6-9a6d-ff7f0f03e90d",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Two-qubit noise\n",
- "for pair, data in two_qubit_data.items(): # iterate over qubit connections\n",
- "\n",
- " # parse strings \"0-1\" to integers [0, 1]\n",
- " q0, q1 = (int(s) for s in pair.split(\"-\"))\n",
- "\n",
- " if \"fCPHASE\" in data:\n",
- " phase_rate = 1 - data[\"fCPHASE\"]\n",
- " noise_model.add_noise(\n",
- " TwoQubitDepolarizing(phase_rate),\n",
- " GateCriteria(\n",
- " Gate.CPhaseShift, [(q0, q1), (q1, q0)]\n",
- " ), # symmetric connections\n",
- " )\n",
- "\n",
- " if \"fXY\" in data:\n",
- " xy_rate = 1 - data[\"fXY\"]\n",
- " noise_model.add_noise(\n",
- " TwoQubitDepolarizing(xy_rate), GateCriteria(Gate.XY, [(q0, q1), (q1, q0)])\n",
- " )\n",
- "\n",
- " if \"fCZ\" in data:\n",
- " cz_rate = 1 - data[\"fCZ\"]\n",
- " noise_model.add_noise(\n",
- " TwoQubitDepolarizing(cz_rate), GateCriteria(Gate.CZ, [(q0, q1), (q1, q0)])\n",
- " )"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "id": "82376d08-84bc-4249-9c8d-d7aacdb73113",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Number of terms in noise model is: 612\n",
- "Number of parameters in noise model is: 612\n"
- ]
- }
- ],
- "source": [
- "num_params = sum(len(item.noise.parameters) for item in noise_model.instructions)\n",
- "print(f\"Number of terms in noise model is: {len(noise_model.instructions)}\")\n",
- "print(f\"Number of parameters in noise model is: {num_params}\")"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "5913a8a2-a9de-4e32-a35d-c48191891b1f",
- "metadata": {},
- "source": [
- "### Compare circuits run on device vs simulator with a noise model\n",
- "\n",
- "Let's just look at the first 5 qubits. Note that to ensure the noise model applied T1 and T2 noise during the time between gate, we manually add identity gates to each moment."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "id": "6fabbd05-b480-43c6-b43a-d396d81bd687",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : | 0 | 1 |2|\n",
- " \n",
- "q0 : -Rx(0.50)-Rx(3.14)-C-\n",
- " | \n",
- "q1 : -Rz(0.50)-Rx(3.14)-Z-\n",
- " \n",
- "q2 : -Rz(0.50)-Rx(3.14)---\n",
- "\n",
- "T : | 0 | 1 |2|\n"
- ]
- }
- ],
- "source": [
- "np.random.seed(42)\n",
- "\n",
- "circ = Circuit().rx(0, 0.5).rz(1, 0.5).rz(2, 0.5).rx(0, np.pi).rx(1, np.pi).rx(2, np.pi).cz(0, 1)\n",
- "print(circ)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "id": "e2af07ed-33de-4709-9e7c-5e3c3caaa751",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : | 0 | 1 | 2 |\n",
- " \n",
- "q0 : -Rx(0.50)-AD(0.0016)--PD(0.0012)-DEPO(0.0022)-Rx(3.14)-AD(0.0016)--PD(0.0012)-DEPO(0.0022)-C-DEPO(0.059)-\n",
- " | | \n",
- "q1 : -Rz(0.50)-AD(0.00086)-PD(0.0015)-DEPO(0.025)--Rx(3.14)-AD(0.00086)-PD(0.0015)-DEPO(0.025)--Z-DEPO(0.059)-\n",
- " \n",
- "q2 : -Rz(0.50)-AD(0.0018)--PD(0.0011)-DEPO(0.0041)-Rx(3.14)-AD(0.0018)--PD(0.0011)-DEPO(0.0041)---------------\n",
- "\n",
- "T : | 0 | 1 | 2 |\n"
- ]
- }
- ],
- "source": [
- "noisy_circ = noise_model.apply(circ)\n",
- "\n",
- "print(noisy_circ)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "id": "9304dcf1-a1e8-4e41-a6b5-769841f4eefe",
- "metadata": {},
- "outputs": [],
- "source": [
- "simulator = LocalSimulator() # noise free simulator\n",
- "task = simulator.run(circ, shots=100_000)\n",
- "free_probs = task.result().measurement_probabilities"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "id": "0e1d9cfe-03d6-406b-b4ab-89166a907681",
- "metadata": {},
- "outputs": [],
- "source": [
- "noisy_simulator = LocalSimulator(\"braket_dm\")\n",
- "noisy_task = noisy_simulator.run(noisy_circ, shots=100_000)\n",
- "noisy_probs = noisy_task.result().measurement_probabilities"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "b3f370bd-a8b3-4d5b-a724-da549fc4c81f",
- "metadata": {},
- "source": [
- "
\n",
- "Note: The below section runs tasks on the Rigetti Aspen-M-3 device. When you run this notebook, make sure the device is currently available. You can find QPU availability windows on the Devices page in the Amazon Braket Console.\n",
- "
\n",
- "\n",
- "
\n",
- "Note: Running the circuit below will result in charges on your AWS account.\n",
- "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "276d680f-887d-4929-bcaa-e276a6303496",
+ "metadata": {},
+ "source": [
+ "We can programmatically access all the calibration data with the Braket SDK. First we load the AwsDevice using the ARN for Rigetti Ankaa 2."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "a55ea9d5-05f3-4da5-a305-a391e914d012",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rigetti = AwsDevice(Devices.Rigetti.Ankaa2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a8a42ae1-51ac-4bf1-bd6a-81ffd982b5f8",
+ "metadata": {},
+ "source": [
+ "The properties dictionary contains keys \"provider\" and \"specs\", with \"1Q\" and \"2Q\" keys for the one- and two-qubit calibration data. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "153b5b63-8205-4a7e-bb18-0305ef428f36",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rigetti_specs = rigetti.properties.dict()[\"provider\"][\"specs\"]\n",
+ "\n",
+ "one_qubit_data = rigetti_specs[\"1Q\"]\n",
+ "two_qubit_data = rigetti_specs[\"2Q\"]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "661cca17-01fa-40be-bd3e-741bacc74ce4",
+ "metadata": {},
+ "source": [
+ "The keys of the \"1Q\" dictionary is the qubit number. \n",
+ "For Ankaa 2, there are 79 qubits indexed by the first digit representing the octagon (0 to 4, and 10 to 14)\n",
+ "and the second representing the qubit in that octagon (0 to 7). We can get all qubit indices with `one_qubit_data.keys()` or with `rigetti.topology_graph.nodes`.\n",
+ "\n",
+ "The keys of the \"2Q\" dictionary are the connected qubit pairs separated by a hyphen. \n",
+ "For example, if qubit 0 and 1 are connected the key is \"0-1\".\n",
+ "\n",
+ "\n",
+ "#### One-qubit noise \n",
+ "\n",
+ "Let's look at the one qubit calibration data for qubit 0."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "8d4ecc35-f4dc-49d8-b6ff-adaee560ac4b",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'fRO': 0.938,\n",
+ " 'f1QRB': 0.9989513243443735,\n",
+ " 'f1QRB_std_err': 3.143256529775241e-05,\n",
+ " 'f1Q_simultaneous_RB': 0.9980020320287597,\n",
+ " 'f1Q_simultaneous_RB_std_err': 6.0290055170609306e-05,\n",
+ " 'T1': 9.640008015307057e-06,\n",
+ " 'T2': 1.5283124633776463e-05}"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "one_qubit_data[\"0\"]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4b676762-e642-4a98-89e3-86d79367071a",
+ "metadata": {},
+ "source": [
+ "For each qubit, there are various metrics of the quality:\n",
+ "\n",
+ "- **T1**: Thermal relaxation time is related to the time it takes for the excited state, |1⟩, to decay into the ground state, |0⟩. The probability of remaining in the excited state is $p(|1⟩)\\sim e^{-t/T_1}$\n",
+ "\n",
+ "- **T2**: The dephasing time, is the decay constant for the scale for a |+⟩ state to decohere into the completely mixed state. $p(|+⟩)\\sim e^{-t/T_2}$ \n",
+ "\n",
+ "- **Fidelity (RB)**: Single-qubit randomized benchmarking fidelities. RB fidelity quantifies the average gate fidelity where the average is over all Clifford gates. RB describes an *effective* noise model with gate-independent depolarizing noise on each Clifford gate.\n",
+ "\n",
+ "- **Fidelity (sRB)**: Single-qubit simultaneous randomized benchmarking fidelities. These are extracted by running single-qubit RB on all qubits simultaneously. Note that we expect the sRB fidelity to be lower than standard RB fidelity due to non-local crosstalk type noise on the device. \n",
+ "\n",
+ "- **Active reset fidelity**: Single-qubit active reset fidelities represents the accuracy to which qubits are reinitalized into the ground state |0⟩.\n",
+ "\n",
+ "- **Readout fidelity**: Single-qubit readout fidelities describes the probability of a bit flip error before readout in the computational basis. The readout fidelity is related to the probability of correctly measuring the ground state and excited states respectively, e.g. $f_{RO} =\\frac{p(0|0)+p(1|1)}{2}$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "296708a3-771e-42b4-9ba8-f3db1a02970b",
+ "metadata": {},
+ "source": [
+ "Now that we know how to extract and use the calibration data, we can build a simple noise model. For every qubit we will add:\n",
+ "- amplitude dampening noise with probability $p= 1-e^{-t/T_1}$ for every gate\n",
+ "- phase dampening noise with probability $p= 0.5(1-e^{-t/T_2})$ for every gate\n",
+ "- depolarizing noise with probability $p=1-f_{sRB}$ (from simultaneous RB fidelity) for every gate\n",
+ "- readout bit flip noise with probability $p=1-f_{RO}$ to measurements \n",
+ "\n",
+ "Technically, the sRB fidelity already includes effects from $T_1$/$T_2$, however to be explicit we add these as separate terms. In a sense, this model might overestimate the noise on the QPU. \n",
+ "\n",
+ "For the dampening noises, we first need the gate times to model $T_1$ and $T_2$ errors.\n",
+ "From the Braket Ankaa 2 device page: \"These gates offer fast (40ns and 180ns) 1Q and 2Q gate times.\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "cd27adfb-f7d6-4583-b854-794e38152c90",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# median 1q and 2q gate times\n",
+ "gate_time_1_qubit = 40e-9\n",
+ "gate_time_2_qubit = 240e-09"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 37,
+ "id": "cd7f87ac",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "x = rigetti.properties.standardized.twoQubitProperties"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5769f2f4-de1c-4b47-9e4e-fd8d39b9e975",
+ "metadata": {},
+ "source": [
+ "To create the noise model, we iterate over all qubits keys in `one_qubit_data`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 46,
+ "id": "c01c05ff",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "dict"
+ ]
+ },
+ "execution_count": 46,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "type(rigetti.properties.standardized.oneQubitProperties)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 44,
+ "id": "7442cd27",
+ "metadata": {},
+ "outputs": [
+ {
+ "ename": "ValueError",
+ "evalue": "not enough values to unpack (expected 2, got 1)",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+ "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
+ "Cell \u001b[0;32mIn[44], line 4\u001b[0m\n\u001b[1;32m 1\u001b[0m noise_model \u001b[38;5;241m=\u001b[39m NoiseModel()\n\u001b[1;32m 3\u001b[0m \u001b[38;5;66;03m# Readout Noise Model\u001b[39;00m\n\u001b[0;32m----> 4\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m q, data \u001b[38;5;129;01min\u001b[39;00m rigetti\u001b[38;5;241m.\u001b[39mproperties\u001b[38;5;241m.\u001b[39mstandardized\u001b[38;5;241m.\u001b[39moneQubitProperties:\n\u001b[1;32m 5\u001b[0m \u001b[38;5;28mprint\u001b[39m(q)\n\u001b[1;32m 6\u001b[0m \u001b[38;5;66;03m# readout_value = 1 - data.oneQubitFidelity[2] # readout\u001b[39;00m\n\u001b[1;32m 7\u001b[0m \u001b[38;5;66;03m# noise_model.add_noise(\u001b[39;00m\n\u001b[1;32m 8\u001b[0m \u001b[38;5;66;03m# BitFlip(readout_value), ObservableCriteria(Observable.Z, qubits=int(q))\u001b[39;00m\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[38;5;66;03m# Depolarizing(probability=depolarizing_rate), GateCriteria(qubits=q)\u001b[39;00m\n\u001b[1;32m 13\u001b[0m \u001b[38;5;66;03m# )\u001b[39;00m\n",
+ "\u001b[0;31mValueError\u001b[0m: not enough values to unpack (expected 2, got 1)"
+ ]
+ }
+ ],
+ "source": [
+ "noise_model = NoiseModel()\n",
+ "\n",
+ "# Readout Noise Model\n",
+ "for q, data in rigetti.properties.standardized.oneQubitProperties:\n",
+ " print(q)\n",
+ " # readout_value = 1 - data.oneQubitFidelity[2] # readout\n",
+ " # noise_model.add_noise(\n",
+ " # BitFlip(readout_value), ObservableCriteria(Observable.Z, qubits=int(q))\n",
+ " # )\n",
+ " # depolarizing_rate = 1 - data.oneQubitFidelity[1] # SIMULTANEOUS_RANDOMIZED_BENCHMARKING\n",
+ " # noise_model.add_noise(\n",
+ " # Depolarizing(probability=depolarizing_rate), GateCriteria(qubits=q)\n",
+ " # )"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "508070bc-b1d2-4737-a2fc-d7711e419996",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0\n",
+ "1\n",
+ "2\n",
+ "3\n",
+ "4\n",
+ "5\n",
+ "6\n",
+ "7\n",
+ "8\n",
+ "9\n",
+ "10\n",
+ "11\n",
+ "12\n",
+ "13\n",
+ "14\n",
+ "15\n",
+ "16\n",
+ "17\n",
+ "18\n",
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+ "74\n"
+ ]
+ },
+ {
+ "ename": "KeyError",
+ "evalue": "'T2'",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+ "\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)",
+ "Cell \u001b[0;32mIn[10], line 13\u001b[0m\n\u001b[1;32m 11\u001b[0m \u001b[38;5;66;03m# T2 phase flip\u001b[39;00m\n\u001b[1;32m 12\u001b[0m \u001b[38;5;28mprint\u001b[39m(q)\n\u001b[0;32m---> 13\u001b[0m t2 \u001b[38;5;241m=\u001b[39m \u001b[43mdata\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mT2\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m]\u001b[49m\n\u001b[1;32m 14\u001b[0m dephasing_prob \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0.5\u001b[39m \u001b[38;5;241m*\u001b[39m (\u001b[38;5;241m1\u001b[39m \u001b[38;5;241m-\u001b[39m np\u001b[38;5;241m.\u001b[39mexp(\u001b[38;5;241m-\u001b[39m(gate_time_1_qubit \u001b[38;5;241m/\u001b[39m t2)))\n\u001b[1;32m 15\u001b[0m noise_model\u001b[38;5;241m.\u001b[39madd_noise(PhaseDamping(dephasing_prob), GateCriteria(qubits\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mint\u001b[39m(q)))\n",
+ "\u001b[0;31mKeyError\u001b[0m: 'T2'"
+ ]
+ }
+ ],
+ "source": [
+ "noise_model = NoiseModel()\n",
+ "\n",
+ "# Single-qubit noise\n",
+ "for q, data in one_qubit_data.items(): # iterate over qubits\n",
+ "\n",
+ " # T1 dampening\n",
+ " t1 = data[\"T1\"]\n",
+ " damping_prob = 1 - np.exp(-(gate_time_1_qubit / t1))\n",
+ " noise_model.add_noise(AmplitudeDamping(damping_prob), GateCriteria(qubits=int(q)))\n",
+ "\n",
+ " # T2 phase flip\n",
+ " t2 = data[\"T2\"]\n",
+ " dephasing_prob = 0.5 * (1 - np.exp(-(gate_time_1_qubit / t2)))\n",
+ " noise_model.add_noise(PhaseDamping(dephasing_prob), GateCriteria(qubits=int(q)))\n",
+ "\n",
+ " # 1q RB depolarizing rate from simultaneous RB\n",
+ " depolar_rate = 1 - data[\"f1Q_simultaneous_RB\"]\n",
+ " noise_model.add_noise(Depolarizing(depolar_rate), GateCriteria(qubits=int(q)))\n",
+ "\n",
+ " # 1q RB readout\n",
+ " readout_value = 1 - data[\"fRO\"]\n",
+ " noise_model.add_noise(BitFlip(readout_value), ObservableCriteria(qubits=int(q)))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9d20d24c-17e2-4bba-b317-fb2d156bedb0",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "num_params = sum(len(item.noise.parameters) for item in noise_model.instructions)\n",
+ "print(f\"Number of terms in noise model is: {len(noise_model.instructions)}\")\n",
+ "print(f\"Number of parameters in noise model is: {num_params}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "790c62f7-776a-4e4c-9405-7b7a14eee5b0",
+ "metadata": {},
+ "source": [
+ "#### Two-qubit noise \n",
+ "Next we consider adding two-qubit noise to the model. \n",
+ "\n",
+ "Let's first look at the data provided in the Ankaa 2 device calibration data. On the first connect, \"0-1\", the properties are:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "626cbe56-3649-48eb-a2a1-f669eb790b47",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "two_qubit_data[\"0-1\"]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4bcd3be4-a6e4-4cf3-841e-1a451e01803a",
+ "metadata": {},
+ "source": [
+ "Here, we see the fidelity per gate (ISWAP or CZ) and the associated standard error. \n",
+ "\n",
+ "Next we loop over the entries in the `two_qubit_data` dictionary and add two-qubit depolarizing noise to the model. Notice that Ankaa 2 has symmetric connections (\"0-1\" and \"1-0\") so we need to add noise in both directions."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "80f57550-6549-46b6-9a6d-ff7f0f03e90d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Two-qubit noise\n",
+ "for pair, data in two_qubit_data.items(): # iterate over qubit connections\n",
+ "\n",
+ " # parse strings \"0-1\" to integers [0, 1]\n",
+ " q0, q1 = (int(s) for s in pair.split(\"-\"))\n",
+ "\n",
+ " if \"fCPHASE\" in data:\n",
+ " phase_rate = 1 - data[\"fCPHASE\"]\n",
+ " noise_model.add_noise(\n",
+ " TwoQubitDepolarizing(phase_rate),\n",
+ " GateCriteria(\n",
+ " Gate.CPhaseShift, [(q0, q1), (q1, q0)]\n",
+ " ), # symmetric connections\n",
+ " )\n",
+ "\n",
+ " if \"fXY\" in data:\n",
+ " xy_rate = 1 - data[\"fXY\"]\n",
+ " noise_model.add_noise(\n",
+ " TwoQubitDepolarizing(xy_rate), GateCriteria(Gate.XY, [(q0, q1), (q1, q0)])\n",
+ " )\n",
+ "\n",
+ " if \"fCZ\" in data:\n",
+ " cz_rate = 1 - data[\"fCZ\"]\n",
+ " noise_model.add_noise(\n",
+ " TwoQubitDepolarizing(cz_rate), GateCriteria(Gate.CZ, [(q0, q1), (q1, q0)])\n",
+ " )"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "82376d08-84bc-4249-9c8d-d7aacdb73113",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "num_params = sum(len(item.noise.parameters) for item in noise_model.instructions)\n",
+ "print(f\"Number of terms in noise model is: {len(noise_model.instructions)}\")\n",
+ "print(f\"Number of parameters in noise model is: {num_params}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5913a8a2-a9de-4e32-a35d-c48191891b1f",
+ "metadata": {},
+ "source": [
+ "### Compare circuits run on device vs simulator with a noise model\n",
+ "\n",
+ "Let's just look at the first 5 qubits. Note that to ensure the noise model applied T1 and T2 noise during the time between gate, we manually add identity gates to each moment."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "6fabbd05-b480-43c6-b43a-d396d81bd687",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "np.random.seed(42)\n",
+ "\n",
+ "circ = Circuit().rx(0, 0.5).rz(1, 0.5).rz(2, 0.5).rx(0, np.pi).rx(1, np.pi).rx(2, np.pi).cz(0, 1)\n",
+ "print(circ)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "e2af07ed-33de-4709-9e7c-5e3c3caaa751",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "noisy_circ = noise_model.apply(circ)\n",
+ "\n",
+ "print(noisy_circ)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "id": "9304dcf1-a1e8-4e41-a6b5-769841f4eefe",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "simulator = LocalSimulator() # noise free simulator\n",
+ "task = simulator.run(circ, shots=100_000)\n",
+ "free_probs = task.result().measurement_probabilities"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "id": "0e1d9cfe-03d6-406b-b4ab-89166a907681",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "noisy_simulator = LocalSimulator(\"braket_dm\")\n",
+ "noisy_task = noisy_simulator.run(noisy_circ, shots=100_000)\n",
+ "noisy_probs = noisy_task.result().measurement_probabilities"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b3f370bd-a8b3-4d5b-a724-da549fc4c81f",
+ "metadata": {},
+ "source": [
+ "
\n",
+ "Note: The below section runs tasks on the Rigetti Ankaa 2 device. When you run this notebook, make sure the device is currently available. You can find QPU availability windows on the Devices page in the Amazon Braket Console.\n",
+ "
\n",
+ "\n",
+ "
\n",
+ "Note: Running the circuit below will result in charges on your AWS account.\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "c8f4664a-0527-46fb-87f2-2a0c85f0bd79",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rigetti_task = rigetti.run(circ, shots=100_000, disable_qubit_rewiring=True)\n",
+ "rigetti_result = rigetti_task.result()\n",
+ "rigetti_probs = rigetti_result.measurement_probabilities"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "1676a45c-5ef8-49cc-b227-69f69fa2004a",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "free_sim = pd.DataFrame.from_dict(free_probs, orient=\"index\").rename(\n",
+ " columns={0: \"free_sim\"}\n",
+ ")\n",
+ "noisy_sim = pd.DataFrame.from_dict(noisy_probs, orient=\"index\").rename(\n",
+ " columns={0: \"noisy_sim\"}\n",
+ ")\n",
+ "Ankaam = pd.DataFrame.from_dict(rigetti_probs, orient=\"index\").rename(\n",
+ " columns={0: \"Ankaa-m\"}\n",
+ ")\n",
+ "df = Ankaam.join(noisy_sim).join(free_sim)\n",
+ "df"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "472e6850-2603-4174-bf92-b04eb0c38c2f",
+ "metadata": {},
+ "source": [
+ "We can compute the fidelity between the free simulation and Rigetti, as well as the noisy simulation and Rigetti. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5b7d1740-cb46-433e-8c2b-7e8b7c10fb4e",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def fidelity(p, q):\n",
+ " return np.sum(np.sqrt(p * q))\n",
+ "\n",
+ "\n",
+ "f_free_Ankaa = fidelity(df[\"free_sim\"], df[\"Ankaa-m\"])\n",
+ "f_noisy_Ankaa = fidelity(df[\"noisy_sim\"], df[\"Ankaa-m\"])\n",
+ "\n",
+ "print(f\"\\nTotal fidelity between Ankaa-M and noise-free simulator is {f_free_Ankaa}\")\n",
+ "print(f\"\\nTotal fidelity between Ankaa-M and noisy simulator is {f_noisy_Ankaa}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "fd4d88b7-015e-445b-ba26-1bdbc6a2bd16",
+ "metadata": {},
+ "source": [
+ "To better visualize, we can also plot the output probability distributions from each circuit:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9329ed72-2f30-4383-b48f-0d50e1a5dd11",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "%matplotlib inline\n",
+ "\n",
+ "df.plot.bar(\n",
+ " title=\"Comparing noise-free simulator, noisy simulator, and Ankaa-M\",\n",
+ " figsize=(12, 6),\n",
+ ")\n",
+ "\n",
+ "text = f\"f_free_Ankaa = {f_free_Ankaa:.3f} \\nf_noise_model_Ankaa = {f_noisy_Ankaa:.3f}\"\n",
+ "plt.text(1, 0.5, text, fontsize=14)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "aa8ffab8-e062-4c33-9c9d-4a312cd76b63",
+ "metadata": {},
+ "source": [
+ "We confirm that the simulator with a noise model is closer to the distribution produced by Ankaa 2."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c4571a5e-2f8d-4767-b28e-a527d2490830",
+ "metadata": {},
+ "source": [
+ "### Smaller, reduced noise models\n",
+ "\n",
+ "The full Rigetti Ankaa 2 noise model contains due to non-uniform qubit noise. We can obtain simpler, smaller noise models by coarse graining the model above.\n",
+ "\n",
+ "Here, we consider taking the average over all qubits for the $T_1$, $T_2$, depolarizing, and readout depolarizing rates. This is a substantially smaller noise model, but may be less accurate. \n",
+ "\n",
+ "We use the `from_filter` function to extract all instructions with amplitude dampening noise in the model. We then compute the mean of the error probabilities. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "id": "eac8479f-4b29-42d8-a15a-ba10aae82d3f",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "avg_t1 = np.mean(\n",
+ " [\n",
+ " n.noise.parameters\n",
+ " for n in noise_model.from_filter(noise=AmplitudeDamping).instructions\n",
+ " ]\n",
+ ")\n",
+ "avg_t2 = np.mean(\n",
+ " [\n",
+ " n.noise.parameters\n",
+ " for n in noise_model.from_filter(noise=PhaseDamping).instructions\n",
+ " ]\n",
+ ")\n",
+ "avg_depo = np.mean(\n",
+ " [\n",
+ " n.noise.parameters\n",
+ " for n in noise_model.from_filter(noise=Depolarizing).instructions\n",
+ " ]\n",
+ ")\n",
+ "avg_readout = np.mean(\n",
+ " [n.noise.parameters for n in noise_model.from_filter(noise=BitFlip).instructions]\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d1a64cae-226c-45d2-9af3-4b5b7a36c7a4",
+ "metadata": {},
+ "source": [
+ "Now we construct a new noise model with the mean values above:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "e49eb24c-5f24-4084-9d4c-c2e7e82fc259",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "simple_noise_model = NoiseModel()\n",
+ "simple_noise_model.add_noise(AmplitudeDamping(avg_t1), GateCriteria())\n",
+ "simple_noise_model.add_noise(PhaseDamping(avg_t2), GateCriteria())\n",
+ "simple_noise_model.add_noise(Depolarizing(avg_depo), GateCriteria())\n",
+ "simple_noise_model.add_noise(BitFlip(avg_readout), ObservableCriteria())\n",
+ "\n",
+ "print(simple_noise_model)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b44bbbd1-fb65-4b8f-8dfa-0ea5aa7979b2",
+ "metadata": {},
+ "source": [
+ "We can see the resultant circuits contain qubit-independent noise:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "c83e96f6-54b0-445b-bcdd-8a7a16691b62",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "simple_noisy_circ = simple_noise_model.apply(circ)\n",
+ "print(simple_noisy_circ)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e2c20b79-cbf2-4897-80b3-452c78d56a03",
+ "metadata": {},
+ "source": [
+ "We run the circuit on a noisy simulator below"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "id": "a1bb19e8-6824-4a50-b9fb-ae06c14359b6",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "simple_noisy_task = noisy_simulator.run(simple_noisy_circ, shots=100_000)\n",
+ "simple_noisy_probs = simple_noisy_task.result().measurement_probabilities"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "76418e5c-be5b-4b3a-8916-c0f56f003cd7",
+ "metadata": {},
+ "source": [
+ "and add it to the previous dataframe"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "b4d27a95-612d-4dea-9f6a-98d4525b0a70",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "simple_noisy_sim = pd.DataFrame.from_dict(simple_noisy_probs, orient=\"index\").rename(\n",
+ " columns={0: \"simple_noisy_sim\"}\n",
+ ")\n",
+ "df = df.join(simple_noisy_sim)\n",
+ "df"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b1699bc2-712f-4a99-b9d6-0a0920114a13",
+ "metadata": {},
+ "source": [
+ "We compute the fidelity between the simple noise model and the QPU:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "d7710e0b-29ac-4968-aa00-e23cb8b32269",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "f_simple = fidelity(df[\"simple_noisy_sim\"], df[\"Ankaa-m\"])\n",
+ "\n",
+ "print(f\"\\nTotal fidelity between Ankaa-M and full noise model is: {f_noisy_Ankaa}\")\n",
+ "print(f\"\\nTotal fidelity between Ankaa-M and simple noise model is: {f_simple}\")\n",
+ "print(f\"\\nTotal fidelity between Ankaa-M and noise-free is: {f_free_Ankaa}\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "e36e19d0-664a-4cb4-a2e3-0061cd60a6c1",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "df.plot.bar(title=\"Comparing simulators and Ankaa-M\", figsize=(12, 6))\n",
+ "text = f\"f_free = {f_free_Ankaa:.3f} \\nf_simple_noise_model = {f_simple:.3f} \\nf_noise_model = {f_noisy_Ankaa:.3f}\"\n",
+ "plt.text(1, 0.5, text, fontsize=14)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6da72e22-a594-41e7-a4e2-cb82cfe0726a",
+ "metadata": {},
+ "source": [
+ "We see that compared to the full noise model, the simple model is less accurate, however, it is still a significant improvement over the noise-free case and has far fewer parameters in the model. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b2c6b2ba-cb54-43f6-9a89-e29066b5192a",
+ "metadata": {},
+ "source": [
+ "## Summary\n",
+ "\n",
+ "In this notebook, we showed how to construct a noise model for Rigetti Ankaa 2 based only on the available calibration data.\n",
+ "We used a coarse assumption of gate-independent single-qubit depolarizing noise and gate-dependant two-qubit noise. Our qubit-dependent model could be improved in many ways. We could add gate-dependence noise, or change the depolarizing channel to Pauli channels. "
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "braket",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.10.11"
+ },
+ "toc-autonumbering": false,
+ "toc-showcode": false,
+ "toc-showmarkdowntxt": false,
+ "toc-showtags": true
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
}
diff --git a/examples/braket_features/Verbatim_Compilation.ipynb b/examples/braket_features/Verbatim_Compilation.ipynb
index bb1e821c6..50e1833e2 100644
--- a/examples/braket_features/Verbatim_Compilation.ipynb
+++ b/examples/braket_features/Verbatim_Compilation.ipynb
@@ -1,956 +1,956 @@
{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Verbatim compilation"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [],
- "source": [
- "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
- "from braket.tracking import Tracker\n",
- "t = Tracker().start()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Usually, when you run a circuit on a QPU, behind the scenes, Amazon Braket will do a series of compilation steps to optimize your circuit and map the abstract circuit to the physical qubits on the QPU. However, in many situations, such as for error mitigation or benchmarking experiments, researchers require full control of the qubits and the gates that are being applied. In a [previous notebook](https://github.com/amazon-braket/amazon-braket-examples/blob/main/examples/braket_features/Allocating_Qubits_on_QPU_Devices.ipynb), we showed you how to manually allocate the qubits of your circuit, i.e., how you can exactly define which logical qubit maps to which physical qubit. In this notebook, you will learn how to use _verbatim compilation_ to run your circuits exactly as defined without any modification during the compilation process.\n",
- "\n",
- "### Table of contents:\n",
- "\n",
- "* [Recap: Running circuits on Amazon Braket](#Recap)\n",
- "* [Using verbatim compilation to run circuits without further compilation](#Verbatim)\n",
- "* [Programming verbatim circuits onto the Rigetti device](#Rigetti)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Recap: Running circuits on Amazon Braket "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Let us begin with importing the usual dependencies. Verbatim compilation is supported by all Rigetti devices, and we will use the Ankaa-2 device for this demonstration."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {},
- "outputs": [],
- "source": [
- "# general imports\n",
- "from braket.aws import AwsDevice\n",
- "from braket.circuits import Circuit\n",
- "from braket.devices import Devices\n",
- "from math import pi\n",
- "import networkx as nx\n",
- "%matplotlib inline"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "When you run a circuit on Amazon Braket, different compilation and optimization steps occur before the circuit is executed on the selected QPU. First, the gates of your circuit are decomposed into the _native gates_ of the QPU. Let's first remember what the native gates of the Ankaa-2 device are:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "The native gates for the Ankaa-2 device are:\n",
- "rx\n",
- "rz\n",
- "cz\n",
- "iswap\n"
- ]
- }
- ],
- "source": [
- "# set up the Rigetti Ankaa-2 device\n",
- "device = AwsDevice(Devices.Rigetti.Ankaa2)\n",
- "\n",
- "# list the native gate set\n",
- "print(\"The native gates for the\", device.name, \"device are:\")\n",
- "for gate in device.properties.paradigm.nativeGateSet:\n",
- " print(gate)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "If we create a circuit with gates that are not part of that list, the gates will automatically be decomposed into a gate set that can be executed on the device."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "
\n",
- " Note: This notebook uses the Rigetti Ankaa-2 device. When you run this notebook, make sure the device is currently available. You can find QPU availability windows on the Devices page in the Amazon Braket Console\n",
- "
"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "scrolled": true
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : │ 0 │ 1 │\n",
- " ┌───┐ \n",
- "q0 : ─┤ H ├───●───\n",
- " └───┘ │ \n",
- " ┌─┴─┐ \n",
- "q1 : ───────┤ X ├─\n",
- " └───┘ \n",
- "T : │ 0 │ 1 │\n",
- "Counter({'11': 475, '00': 450, '10': 56, '01': 19})\n"
- ]
- }
- ],
- "source": [
- "bell = Circuit().h(0).cnot(0,1)\n",
- "print(bell)\n",
- "result = device.run(bell, shots=1000).result()\n",
- "print(result.measurement_counts)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Let's have a look at the circuit that was actually executed. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "PRAGMA INITIAL_REWIRING \"NAIVE\"\n",
- "DECLARE ro BIT[2]\n",
- "PRAGMA PRESERVE_BLOCK\n",
- "RX(1.5707963267948966) 5\n",
- "RZ(3.141592653589793) 5\n",
- "ISWAP 5 6\n",
- "RZ(1.5707963267948966) 5\n",
- "RX(1.5707963267948966) 5\n",
- "RZ(4.71238898038469) 5\n",
- "ISWAP 5 6\n",
- "RZ(3.141592653589793) 6\n",
- "RX(1.5707963267948966) 6\n",
- "PRAGMA END_PRESERVE_BLOCK\n",
- "MEASURE 5 ro[0]\n",
- "MEASURE 6 ro[1]\n"
- ]
- }
- ],
- "source": [
- "meta = result.additional_metadata.rigettiMetadata\n",
- "print(meta.compiledProgram)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "As you can see, the original gates, `h` and `cnot`, were decomposed into the native `rz`, `rx`, and `iswap`. You will also note that the abstract qubit indices 0 and 1 (which were chosen as an example) were remapped to qubits that actually exist on the device, in this case, 5 and 6, respectively. At the time when you run this notebook, you might see a different remapping, as the compiler takes into account the latest calibration of the device and tries to map to the qubits that yield the best results. \n",
- "\n",
- "The compiler further performs circuit optimizations to minimize the number of operations, e.g., by removing redundant gates. Let's have a look at a single-qubit circuit containing two subsequent `x` gates:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [],
- "source": [
- "identity = Circuit().x(0).x(0)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Of course, if you do the math, two consecutive `x` gates just cancel each other out, and we are left with an empty circuit after compilation."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "PRAGMA INITIAL_REWIRING \"NAIVE\"\n",
- "DECLARE ro BIT[1]\n",
- "PRAGMA PRESERVE_BLOCK\n",
- "PRAGMA END_PRESERVE_BLOCK\n",
- "MEASURE 0 ro[0]\n",
- "Counter({'0': 985, '1': 15})\n"
- ]
- }
- ],
- "source": [
- "result = device.run(identity, shots=1000).result()\n",
- "compiled_program = result.additional_metadata.rigettiMetadata.compiledProgram\n",
- "print(compiled_program)\n",
- "print(result.measurement_counts)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Using verbatim compilation to run circuits without further compilation "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In some cases, however, you may need to run circuits exactly as defined, without any further modifications by the compiler. For instance, if you want to benchmark device performance you may want to control exactly which gates are executed on the hardware. Similarly, [certain error mitigation protocols](https://arxiv.org/pdf/2005.10921.pdf) require insertion of additional, redundant operations that would normally be removed by the compiler but are essential for the protocol to work. To prevent circuits (or parts of circuits) from further compiler optimizations, you can use the `add_verbatim_box` function in the Amazon Braket SDK."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "
\n",
- " Note:add_verbatim_box is currently supported on Rigetti, IonQ, and IQM devices.\n",
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "When you define a (sub-)circuit in a verbatim box, you need to make sure that everything inside the verbatim box can be executed on the device _exactly_ as you defined it. This means that\n",
- "1. The circuit can only use qubit indices that exist on the device\n",
- "2. All gates of the circuit have to be part of the native gate set of the device\n",
- "3. All multi-qubit gates have to be between qubits that are connected according to the connectivity graph of the device "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Getting started with a minimal example\n",
- "Let's have a look at the simple example from before of an identify circuit. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {},
- "outputs": [],
- "source": [
- "identity = Circuit().rx(0,pi).rx(0,pi)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Here, we have chosen the Rigetti-native `rx` gate, which is identical to `x` if we choose the angle to be $\\pi$. Next, we wrap this circuit in a verbatim box to prevent the compiler from collapsing the two gates. You can see the circuit diagram indicates the start and end of the verbatim box."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : │ 0 │ 1 │ 2 │ 3 │\n",
- " ┌──────────┐ ┌──────────┐ \n",
- "q0 : ───StartVerbatim───┤ Rx(3.14) ├─┤ Rx(3.14) ├───EndVerbatim───\n",
- " └──────────┘ └──────────┘ \n",
- "T : │ 0 │ 1 │ 2 │ 3 │\n"
- ]
- }
- ],
- "source": [
- "circ = Circuit().add_verbatim_box(identity)\n",
- "print(circ)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "When we run the circuit, both gates will be executed on the device."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "
\n",
- " Note: To run a circuit that contains a verbatim box the disable_qubit_rewiring flag must be set to True \n",
- "
"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "PRAGMA INITIAL_REWIRING \"NAIVE\"\n",
- "DECLARE ro BIT[1]\n",
- "PRAGMA PRESERVE_BLOCK\n",
- "RX(3.141592653589793) 0\n",
- "RX(3.141592653589793) 0\n",
- "PRAGMA END_PRESERVE_BLOCK\n",
- "MEASURE 0 ro[0]\n",
- "Counter({'0': 975, '1': 25})\n"
- ]
- }
- ],
- "source": [
- "result = device.run(circ, shots=1000, disable_qubit_rewiring=True).result()\n",
- "compiled_program = result.additional_metadata.rigettiMetadata.compiledProgram\n",
- "print(compiled_program)\n",
- "print(result.measurement_counts)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Programming verbatim circuits onto the Rigetti device "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "As we have mentioned above, to build circuits with multi-qubit gates, you need to take into consideration the connectivity graph of the device. When a circuit contains a verbatim box, automatic qubit rewiring has to be disables, and you have manually allocate the qubits on the device that you want to use for your circuit.\n",
- "You can access the connectivity graph on the [device detail page](https://console.aws.amazon.com/braket/home?region=us-west-1#/devices/arn:aws:braket:us-west-2::device/qpu/rigetti/Aspen-M-3) in the Amazon Braket Console, or by using the code below."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "{'0': ['1', '7'], '1': ['0', '2', '8'], '2': ['1', '3', '9'], '3': ['2', '4', '10'], '4': ['3', '5', '11'], '5': ['4', '6', '12'], '6': ['5', '13'], '7': ['0', '8', '14'], '8': ['1', '7', '9', '15'], '9': ['2', '8', '10', '16'], '10': ['3', '9', '11', '17'], '11': ['4', '10', '12', '18'], '12': ['5', '11', '13', '19'], '13': ['6', '12', '20'], '14': ['7', '15', '21'], '15': ['8', '14', '22'], '16': ['9', '17', '23'], '17': ['10', '16', '18', '24'], '18': ['11', '17', '19', '25'], '19': ['12', '18', '20', '26'], '20': ['13', '19', '27'], '21': ['14', '22', '28'], '22': ['15', '21', '23', '29'], '23': ['16', '22', '24', '30'], '24': ['17', '23', '25', '31'], '25': ['18', '24', '26', '32'], '26': ['19', '25', '33'], '27': ['20', '34'], '28': ['21', '29', '35'], '29': ['22', '28', '30', '36'], '30': ['23', '29', '31', '37'], '31': ['24', '30', '32', '38'], '32': ['25', '31', '33', '39'], '33': ['26', '32', '34', '40'], '34': ['27', '33', '41'], '35': ['28', '36', '42'], '36': ['29', '35', '37', '43'], '37': ['30', '36', '38', '44'], '38': ['31', '37', '39', '45'], '39': ['32', '38', '40', '46'], '40': ['33', '39', '41', '47'], '41': ['34', '40', '48'], '42': ['35', '43', '49'], '43': ['36', '42', '44', '50'], '44': ['37', '43', '45', '51'], '45': ['38', '44', '46', '52'], '46': ['39', '45', '47', '53'], '47': ['40', '46', '48', '54'], '48': ['41', '47', '55'], '49': ['42', '56'], '50': ['43', '51', '57'], '51': ['44', '50', '52', '58'], '52': ['45', '51', '53', '59'], '53': ['46', '52', '54'], '54': ['47', '53', '55', '61'], '55': ['48', '54', '62'], '56': ['49', '57', '63'], '57': ['50', '56', '58', '64'], '58': ['51', '57', '59', '65'], '59': ['52', '58', '60', '66'], '60': ['59'], '61': ['54', '62', '68'], '62': ['55', '61', '69'], '63': ['56', '64', '70'], '64': ['57', '63', '65', '71'], '65': ['58', '64', '66', '72'], '66': ['59', '65', '67'], '67': ['66', '68', '74'], '68': ['61', '67', '69', '75'], '69': ['62', '68', '76'], '70': ['63', '71', '77'], '71': ['64', '70', '72', '78'], '72': ['65', '71', '73', '79'], '73': ['72', '74', '80'], '74': ['67', '73', '75', '81'], '75': ['68', '74', '76', '82'], '76': ['69', '75', '83'], '77': ['70', '78'], '78': ['71', '77', '79'], '79': ['72', '78', '80'], '80': ['73', '79', '81'], '81': ['74', '80', '82'], '82': ['75', '81', '83'], '83': ['76', '82']}\n"
- ]
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Verbatim compilation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
+ "from braket.tracking import Tracker\n",
+ "t = Tracker().start()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Usually, when you run a circuit on a QPU, behind the scenes, Amazon Braket will do a series of compilation steps to optimize your circuit and map the abstract circuit to the physical qubits on the QPU. However, in many situations, such as for error mitigation or benchmarking experiments, researchers require full control of the qubits and the gates that are being applied. In a [previous notebook](https://github.com/amazon-braket/amazon-braket-examples/blob/main/examples/braket_features/Allocating_Qubits_on_QPU_Devices.ipynb), we showed you how to manually allocate the qubits of your circuit, i.e., how you can exactly define which logical qubit maps to which physical qubit. In this notebook, you will learn how to use _verbatim compilation_ to run your circuits exactly as defined without any modification during the compilation process.\n",
+ "\n",
+ "### Table of contents:\n",
+ "\n",
+ "* [Recap: Running circuits on Amazon Braket](#Recap)\n",
+ "* [Using verbatim compilation to run circuits without further compilation](#Verbatim)\n",
+ "* [Programming verbatim circuits onto the Rigetti device](#Rigetti)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Recap: Running circuits on Amazon Braket "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let us begin with importing the usual dependencies. Verbatim compilation is supported by all Rigetti devices, and we will use the Ankaa-2 device for this demonstration."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# general imports\n",
+ "from braket.aws import AwsDevice\n",
+ "from braket.circuits import Circuit\n",
+ "from braket.devices import Devices\n",
+ "from math import pi\n",
+ "import networkx as nx\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "When you run a circuit on Amazon Braket, different compilation and optimization steps occur before the circuit is executed on the selected QPU. First, the gates of your circuit are decomposed into the _native gates_ of the QPU. Let's first remember what the native gates of the Ankaa-2 device are:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The native gates for the Ankaa-2 device are:\n",
+ "rx\n",
+ "rz\n",
+ "cz\n",
+ "iswap\n"
+ ]
+ }
+ ],
+ "source": [
+ "# set up the Rigetti Ankaa-2 device\n",
+ "device = AwsDevice(Devices.Rigetti.Ankaa2)\n",
+ "\n",
+ "# list the native gate set\n",
+ "print(\"The native gates for the\", device.name, \"device are:\")\n",
+ "for gate in device.properties.paradigm.nativeGateSet:\n",
+ " print(gate)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If we create a circuit with gates that are not part of that list, the gates will automatically be decomposed into a gate set that can be executed on the device."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
\n",
+ " Note: This notebook uses the Rigetti Ankaa-2 device. When you run this notebook, make sure the device is currently available. You can find QPU availability windows on the Devices page in the Amazon Braket Console\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "T : │ 0 │ 1 │\n",
+ " ┌───┐ \n",
+ "q0 : ─┤ H ├───●───\n",
+ " └───┘ │ \n",
+ " ┌─┴─┐ \n",
+ "q1 : ───────┤ X ├─\n",
+ " └───┘ \n",
+ "T : │ 0 │ 1 │\n",
+ "Counter({'11': 475, '00': 450, '10': 56, '01': 19})\n"
+ ]
+ }
+ ],
+ "source": [
+ "bell = Circuit().h(0).cnot(0,1)\n",
+ "print(bell)\n",
+ "result = device.run(bell, shots=1000).result()\n",
+ "print(result.measurement_counts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's have a look at the circuit that was actually executed. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "PRAGMA INITIAL_REWIRING \"NAIVE\"\n",
+ "DECLARE ro BIT[2]\n",
+ "PRAGMA PRESERVE_BLOCK\n",
+ "RX(1.5707963267948966) 5\n",
+ "RZ(3.141592653589793) 5\n",
+ "ISWAP 5 6\n",
+ "RZ(1.5707963267948966) 5\n",
+ "RX(1.5707963267948966) 5\n",
+ "RZ(4.71238898038469) 5\n",
+ "ISWAP 5 6\n",
+ "RZ(3.141592653589793) 6\n",
+ "RX(1.5707963267948966) 6\n",
+ "PRAGMA END_PRESERVE_BLOCK\n",
+ "MEASURE 5 ro[0]\n",
+ "MEASURE 6 ro[1]\n"
+ ]
+ }
+ ],
+ "source": [
+ "meta = result.additional_metadata.rigettiMetadata\n",
+ "print(meta.compiledProgram)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As you can see, the original gates, `h` and `cnot`, were decomposed into the native `rz`, `rx`, and `iswap`. You will also note that the abstract qubit indices 0 and 1 (which were chosen as an example) were remapped to qubits that actually exist on the device, in this case, 5 and 6, respectively. At the time when you run this notebook, you might see a different remapping, as the compiler takes into account the latest calibration of the device and tries to map to the qubits that yield the best results. \n",
+ "\n",
+ "The compiler further performs circuit optimizations to minimize the number of operations, e.g., by removing redundant gates. Let's have a look at a single-qubit circuit containing two subsequent `x` gates:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "identity = Circuit().x(0).x(0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Of course, if you do the math, two consecutive `x` gates just cancel each other out, and we are left with an empty circuit after compilation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "PRAGMA INITIAL_REWIRING \"NAIVE\"\n",
+ "DECLARE ro BIT[1]\n",
+ "PRAGMA PRESERVE_BLOCK\n",
+ "PRAGMA END_PRESERVE_BLOCK\n",
+ "MEASURE 0 ro[0]\n",
+ "Counter({'0': 985, '1': 15})\n"
+ ]
+ }
+ ],
+ "source": [
+ "result = device.run(identity, shots=1000).result()\n",
+ "compiled_program = result.additional_metadata.rigettiMetadata.compiledProgram\n",
+ "print(compiled_program)\n",
+ "print(result.measurement_counts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Using verbatim compilation to run circuits without further compilation "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In some cases, however, you may need to run circuits exactly as defined, without any further modifications by the compiler. For instance, if you want to benchmark device performance you may want to control exactly which gates are executed on the hardware. Similarly, [certain error mitigation protocols](https://arxiv.org/pdf/2005.10921.pdf) require insertion of additional, redundant operations that would normally be removed by the compiler but are essential for the protocol to work. To prevent circuits (or parts of circuits) from further compiler optimizations, you can use the `add_verbatim_box` function in the Amazon Braket SDK."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
\n",
+ " Note:add_verbatim_box is currently supported on Rigetti, IonQ, and IQM devices.\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "When you define a (sub-)circuit in a verbatim box, you need to make sure that everything inside the verbatim box can be executed on the device _exactly_ as you defined it. This means that\n",
+ "1. The circuit can only use qubit indices that exist on the device\n",
+ "2. All gates of the circuit have to be part of the native gate set of the device\n",
+ "3. All multi-qubit gates have to be between qubits that are connected according to the connectivity graph of the device "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Getting started with a minimal example\n",
+ "Let's have a look at the simple example from before of an identify circuit. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "identity = Circuit().rx(0,pi).rx(0,pi)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here, we have chosen the Rigetti-native `rx` gate, which is identical to `x` if we choose the angle to be $\\pi$. Next, we wrap this circuit in a verbatim box to prevent the compiler from collapsing the two gates. You can see the circuit diagram indicates the start and end of the verbatim box."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "T : │ 0 │ 1 │ 2 │ 3 │\n",
+ " ┌──────────┐ ┌──────────┐ \n",
+ "q0 : ───StartVerbatim───┤ Rx(3.14) ├─┤ Rx(3.14) ├───EndVerbatim───\n",
+ " └──────────┘ └──────────┘ \n",
+ "T : │ 0 │ 1 │ 2 │ 3 │\n"
+ ]
+ }
+ ],
+ "source": [
+ "circ = Circuit().add_verbatim_box(identity)\n",
+ "print(circ)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "When we run the circuit, both gates will be executed on the device."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
\n",
+ " Note: To run a circuit that contains a verbatim box the disable_qubit_rewiring flag must be set to True \n",
+ "
\n",
+ " Note: At the time when you run this notebook the fidelity numbers may be different as QPU devices are periodically recalibrated\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "After selecting the qubits and validating their gate fidelities, you can now construct a circuit and run it. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "T : │ 0 │ 1 │ 2 │ 3 │ 4 │ 5 │\n",
+ " ┌───────┐ ┌───────┐ ┌──────────┐ ┌───────┐ \n",
+ "q10 : ───StartVerbatim───┤ ISWAP ├─┤ ISWAP ├─┤ Rx(3.14) ├─┤ ISWAP ├───EndVerbatim───\n",
+ " ║ └───┬───┘ └───┬───┘ └──────────┘ └───┬───┘ ║ \n",
+ " ║ ┌───┴───┐ │ ┌───┴───┐ ║ \n",
+ "q11 : ─────────║─────────┤ ISWAP ├─────┼──────────────────┤ ISWAP ├────────║────────\n",
+ " ║ └───────┘ │ └───────┘ ║ \n",
+ " ║ ┌───┴───┐ ║ \n",
+ "q17 : ─────────╨───────────────────┤ ISWAP ├───────────────────────────────╨────────\n",
+ " └───────┘ \n",
+ "T : │ 0 │ 1 │ 2 │ 3 │ 4 │ 5 │\n"
+ ]
+ }
+ ],
+ "source": [
+ "circ = Circuit().iswap(10, 11).iswap(10, 17).rx(10, pi).iswap(10, 11)\n",
+ "verbatim_circ = Circuit().add_verbatim_box(circ)\n",
+ "print(verbatim_circ)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "PRAGMA INITIAL_REWIRING \"NAIVE\"\n",
+ "DECLARE ro BIT[3]\n",
+ "PRAGMA PRESERVE_BLOCK\n",
+ "ISWAP 10 11\n",
+ "ISWAP 10 17\n",
+ "RX(3.141592653589793) 10\n",
+ "ISWAP 10 11\n",
+ "PRAGMA END_PRESERVE_BLOCK\n",
+ "MEASURE 10 ro[0]\n",
+ "MEASURE 11 ro[1]\n",
+ "MEASURE 17 ro[2]\n",
+ "Counter({'010': 811, '000': 115, '100': 52, '110': 14, '011': 6, '001': 1, '111': 1})\n"
+ ]
+ }
+ ],
+ "source": [
+ "result = rigetti.run(verbatim_circ, shots=1000, disable_qubit_rewiring=True).result()\n",
+ "compiled_program = result.additional_metadata.rigettiMetadata.compiledProgram\n",
+ "print(compiled_program)\n",
+ "print(result.measurement_counts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As expected, the program is faithfully executed exactly as it was defined."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Defining verbatim subcircuits "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In some situations, you might only be interested in executing parts of your circuits verbatim, and have the compiler nativize and optimize the rest. The next example demonstrates how to do this. Let's get started by defining the subcircuit we want to execute verbatim."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "verbatim_subcirc = Circuit().rx(10,pi).rx(10,pi)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next, define the part of the circuit you want to compiler to process, so you don't have to worry about nativizing gates. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "subcirc1 = Circuit().cnot(10,11).cnot(10,17)\n",
+ "subcirc2 = Circuit().cnot(10,17).cnot(10,11)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Finally, put everything together"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "T : │ 0 │ 1 │ 2 │ 3 │ 4 │ 5 │ 6 │ 7 │\n",
+ " ┌──────────┐ ┌──────────┐ \n",
+ "q10 : ───●─────●─────StartVerbatim───┤ Rx(3.14) ├─┤ Rx(3.14) ├───EndVerbatim─────●─────●───\n",
+ " │ │ ║ └──────────┘ └──────────┘ ║ │ │ \n",
+ " ┌─┴─┐ │ ║ ║ │ ┌─┴─┐ \n",
+ "q11 : ─┤ X ├───┼───────────║──────────────────────────────────────────║──────────┼───┤ X ├─\n",
+ " └───┘ │ ║ ║ │ └───┘ \n",
+ " ┌─┴─┐ ║ ║ ┌─┴─┐ \n",
+ "q17 : ───────┤ X ├─────────╨──────────────────────────────────────────╨────────┤ X ├───────\n",
+ " └───┘ └───┘ \n",
+ "T : │ 0 │ 1 │ 2 │ 3 │ 4 │ 5 │ 6 │ 7 │\n"
+ ]
+ }
+ ],
+ "source": [
+ "circ = subcirc1.add_verbatim_box(verbatim_subcirc).add_circuit(subcirc2)\n",
+ "print(circ)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "PRAGMA INITIAL_REWIRING \"NAIVE\"\n",
+ "DECLARE ro BIT[3]\n",
+ "PRAGMA PRESERVE_BLOCK\n",
+ "RX(1.5707963267948966) 10\n",
+ "RZ(4.71238898038469) 10\n",
+ "ISWAP 10 11\n",
+ "RZ(1.5707963267948966) 10\n",
+ "RZ(3.141592653589793) 11\n",
+ "ISWAP 10 17\n",
+ "RX(1.5707963267948966) 11\n",
+ "RZ(1.5707963267948966) 10\n",
+ "RX(1.5707963267948966) 10\n",
+ "RZ(4.71238898038469) 10\n",
+ "ISWAP 10 17\n",
+ "RX(3.141592653589793) 10\n",
+ "RX(3.141592653589793) 10\n",
+ "RZ(3.141592653589793) 17\n",
+ "RZ(1.5707963267948966) 10\n",
+ "RX(1.5707963267948966) 17\n",
+ "ISWAP 10 17\n",
+ "RZ(1.5707963267948966) 10\n",
+ "RX(1.5707963267948966) 10\n",
+ "RZ(4.71238898038469) 10\n",
+ "ISWAP 10 17\n",
+ "RZ(1.5707963267948966) 10\n",
+ "RZ(3.141592653589793) 17\n",
+ "ISWAP 10 11\n",
+ "RX(1.5707963267948966) 17\n",
+ "RZ(1.5707963267948966) 10\n",
+ "RX(1.5707963267948966) 10\n",
+ "RZ(4.71238898038469) 10\n",
+ "ISWAP 10 11\n",
+ "RZ(3.141592653589793) 11\n",
+ "RX(1.5707963267948966) 11\n",
+ "PRAGMA END_PRESERVE_BLOCK\n",
+ "MEASURE 17 ro[2]\n",
+ "MEASURE 10 ro[0]\n",
+ "MEASURE 11 ro[1]\n",
+ "Counter({'000': 583, '001': 207, '010': 60, '100': 53, '110': 29, '011': 29, '111': 22, '101': 17})\n"
+ ]
+ }
+ ],
+ "source": [
+ "result = rigetti.run(circ, shots=1000, disable_qubit_rewiring=True).result()\n",
+ "compiled_program = result.additional_metadata.rigettiMetadata.compiledProgram\n",
+ "print(compiled_program)\n",
+ "print(result.measurement_counts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Inspecting the compiled program, you can see that the `cnot` gates were nativized, however, the two `rx` gates in the middle of the circuit remain unaltered, and were not removed by the compiler. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Programming verbatim circuits onto the IonQ device"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "IonQ also supports verbatim compilation. Because qubits in the IonQ device have all-to-all connection, there is no restriction in qubit connectivity; all qubit pairs are available for 2-qubit gates. Because there is no circuit optimization or gate decomposition in verbatim compilation, all gates in the circuit must be native gates. Let's look at IonQ's native gate set."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The native gates for the Aria 1 device are:\n",
+ "GPI\n",
+ "GPI2\n",
+ "MS\n"
+ ]
+ }
+ ],
+ "source": [
+ "# set up the IonQ Aria 1 device\n",
+ "ionq_device = AwsDevice(Devices.IonQ.Aria1)\n",
+ "\n",
+ "# list the native gate set\n",
+ "print(\"The native gates for the\", ionq_device.name, \"device are:\")\n",
+ "for gate in ionq_device.properties.paradigm.nativeGateSet:\n",
+ " print(gate)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In `device.property`, you can see `fullyConnected=True`, showing that qubits are fully connected. This manifests as the device having a complete topology graph."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "fullyConnected=True connectivityGraph={}\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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OABwcHODs7AyFQoGMjAxcvaq/cYkAoFAoYO7zNiSth+qtzKSj/0PmrRN6K2/9+vUQBAF79uzBsWPH9Fau3L4WnEcuK/vA51gYyXB8ckek5eSj59LgMo8/Mqk9GjqXfzIRY+zl4ZVyGKuk5WfCMGNfKPJUmgqPI1NrCHkqDWbsC8XyM6VP1NBoNPjyyy8xfPhwqFSqciX5joyMxIMHD4qdsV1ZmtRY5Dy6Dmj00+KpRRo1ch/dgCYlVm9lNmrUCKdOncL169dx+vRp/Pzzz2I6JX1JTU1FTNBvaJAfXrChsr/N//+8lKBfkBV6Uk+1KxAZGQl3d3eMHDkStra2eitXkMordV56rgqn7yXAy8kChuWY6FXR7AKMsZeHWygZq4SdV6IwY1+o3spb2M+72GTO2dnZGDZsGPbu3au3a1WFzNIBTqNXQpAZ6LWb99nmT5GTqL/WSS1BECAIgl7WqS6Nc4cBkLX6qGA4QAXGVAogqPOVyAzaiJSrR6qxhvpl7uYF68E/Vurcb99vBP9WNVFv9jHklREwVraFMiMjA5GRkXj8+DEePXoEa2tr+Pv7V6q+jLHy4cEpjFVQacmcK6u4ZM5Pnz5Fr169cPPmzUqV+e2334KI8NVXX+mrmlClxcPozmEoffrrpTxBEJB8Yo3eg0lLS0ukpaWJk0mqW2zwbshunYW130QY12oG0qhLHWuq3Z/96AaSj6+oljGT77//PtLS0hAaGorExLLT+1SELCel1OTuJbEwkqFrfXvciU0rM5gUALjbFM19CRSshPT48WOdR0REBMLDwxEZGVlkuU1nZ2f4+/tDrVbj5MmT6N69u7isJ2NMPzigZKyCykrm3NDJApO7eaKJqwIWRnLEpubg4M0nWBscgdz84r9En0/mfPPmTfTs2RMJCQmVbl3r0qUL1q9fX6lzSyKVShF2fDNqSgyBxu8WdNdWoqVSG4ykBP2CjJt/6LWO2vL79++PMWPGwMzMDNevX8ehQ4dw4oT+xic+T5UWj4RdcyC3cYVZ054wrt0CMisnnaBLuwJOTsRVZNw4qtcxo89bunQpXF1dodFocO3aNbRt27bSyzc+L+XZUxiXktwdAP430AexqTm49SQNKVlKuNuaYkz72rA1M8S03WX/SLKQKnFo326kpKSIQWNYWBgiIyORkvLPLHFBEMR1zov78SCTyfDBBx8AAHbt2gV/f38MHz4cGzdu1PswCMb+zbjLm7EKCIvPQI8lJSfMrmNvht8/aY+IZ5lY8edDJGcp0aqWNT7pUgdn7idgzJZrpZZ/ckpH3LschP79+yMvL0/f1dcbMzMzoHZbOPT6BPlqDQRp+X+bkkYNUquQcmK1XiegvGyFV+OxsLBAeno6Ppv+BVb88hs8POvhYdh9qFLiINHk623mfVmkUmm1XcvObyKMG79VYkvs+E4e6N3YCa5WJjAxkCI1Jx9XH6dgZVA4bsWkFXuOSKNGeqFZ/xKJpEqtzX/++Sc6deoEPz8/BAYGgojw8ccfY9WqVXpf652xfysOKBmrgHmH7mBLSGSJk3Cm9qiLSV090fHHM4hKzha3f/d+IwxuVRON5/+B9NziW4kkIBhEhuD+jm/0UleJRIKuXbtiwoQJ6Nevn17KLMzExAQqI0vY+k2C3K1xubt5cx5dr7ZuXqlUikaNGiEqKkqnFQsAjIyMMHLkSNy9exdnzpzR+7WLY2tri8TEREgkErGlWV/LQJZGGyRpr+Pi4gJnZ2dcvnxZb9d4nWb9z58/H5mZmVi0aJHOa//pp59iyZIlHFQypgfc3s9YBZy5n1DqjG5tV3hGru4Sgum5Kqg1hHx1yedqICDL0l0v9QSAgIAAbNiwAbm5+lkT+nnZ2dlQJschdvssxK4bj4zrR5CfHFskWCIi5CfHIuP6EcStn4CEXXOqLc+il5cXAgMD0blzZ3GMnPa/ubm52LhxY7W9HsXRjl0sPGyhuoPJWrVqYfr06di7dy8CAwPh4+ODmJgYvQaTAGCkTK2eWf9qFZR6TO4OAD169MCPP/5Y5LVfunQpZs6c+ULG2TL2puMWSsbKKTNPBe95f6C0PxgXhTGOfNoB58IT8f2xuwVd3rVtsORDH+y9EYP5h/8u9RpEhOifB4DyX1zQo2+C3Ahya2dAIkPTJt64fOoImjVuiGvXSu/u17fatWtj8eLF6NOnDzIzM7Fw4UKsXr1a7xNU/s18u/jhabMxkMgMKjWW9nlEBEGjwpO14/T2o6Nz586YNm0aevfuXeIx8+bNw9y5c/VyPcb+rbiFkrFyikzKKjWYBICY1Bz0W3Ue9RzMEfx5V9yZ74eNw32x93rZwSTw/xMMrJz0U+H/Z2lpiUGDBum1zOJoJzhQfi6U8RFQxj1Awv3roPzcFx5MAoBarUZ+fkFLsVKpxJkzZ5CYmAiZTIaWLVu+8Pq8CB07dizSfaudtFIds5qvnDmOhrl39BJMAgV1TfpjpV5bsBUKBQYMGFDqMfPmzcMPP/ygl+tl5alwJzYNN6JScCc2DVl5+pkIxdirjmd5M1ZO5Umy7KIwxvphvkjMzMO4rdeQnKWEj6sCn3StAxMDGb7Yd6vMMiqbNLo4x44dg5+fHwAgPj6+WscOFjcb/dGjR9V2vec1bdoUmzdvhouLC8aNG4d9+/ahf//+MDU1RU5ODjQaDTp27IiDBw9CoVDg6dOn8PT0RGZm5gurY3U7e/YsDA0NYWpqiuTkZABAv379sH37dhgYGKB169YICQnR6zWPr5iDev0mI7duj0rP+teelxL0i94nauXm5iInp+w14r/44gsYGRnh008/rfA1wuIzsC0kCmfuJyAqOVvnh6cAwM3aBF3q2cO/lRs8HcwrXD5jrwMOKBkrJ4NyrOzxhV99mBnK0GtpMHLyC8aWXX6cjJRsJX7s3wT7bsQg5FFyqWWQOr/U/RXRs2dPvZX1qjMxMYGLiwusra3x22+/4eLFi+jRoweysrIAAKampvDz84OFhQU0Gg0mT578RgWT1tbWCAwMRPPmzQEUBPO9e/fG3r17YWpqCgsLCzHI1Lf7+/4Hs8Z3YfP2eBCECs36F0BQq5TIv7QN6Rf36b1ux48fL/exkydPhpGREcaOHVuu46OTszFrfyiCwxMhlQjFjq8mAJHJ2dgSEonNFx+jQx1bfNfXWyfnLGNvAu7yZqyc3G1MUVbbSwMnC4QnZIrBpNbNmFQAQN0yWie0eQr1wdDQED179oSxsTGAgskplpZv3rrINWrUQKdOnXD+/Hk4ODjgv//9Lz788EO0bdsW2dnZGDNmDKZNmwYiwqxZs2BqagobGxv89ttv8PHxQbdu3V72U6gSV1dXDBkyBMnJyejUqROuXLkClUqFQ4cOia3GKpUKycnJMDMzQ/369aulHpm3AvFk7TjkRhW0wlNZk3WooG45j29CFrgAT8/rP5gMCAio8Dnjxo3DL7/8UuZxO69EofviIFyISAKAMpdf1e6/EJGE7ouDsPNKVIXrxtirjFsoGSsnU0MZ3KxNEFkoHdDz4jNyUdfBHCYGUmQr//lCbeZmBQB4mlb6ZBtVSpzeJuTI5XIcO3YMgiBg5MiR6NWrF3bt2oXjx48jIyNDL9d42SwsLNC3b1+4u7ujWbNmWLlypTi5ombNmjh9+jRq164NjUaDESNGYMKECTh79qw40/v27dt6S/b9MvTv3x+7d+8GAHTv3h0BAQFo2bKlmJpIKpWiTZs2+PTTT7Fjxw4cOnQI9+7dq5a6CIIAVVo8kvf+F4KlU6nJ3TVp8cgKvwzb1LuIvBpcbWl7KpPLlYgQEBAAQ0PDEsceLz8ThkWBDypVJ7WGoNYQZuwLRWJmHj7p4lmpchh71fAsb/ZGIyKkpaVBLpeLj6p8eU3cGIQjD9IBofjG/e5e9lg7pAX+iknFhnOPkJylRFM3BSZ0roPY1By8syy4xNRBpFEjo1AyZ/bivIjckNVBoVBg06ZNWLZsGc6dOwelUinua9asGUJCQiCTFbQbaDQajB49Gps2barWOsnlcuTn56NDhw4IDg6GIDcqCCqlcgikhjLpCQS1strXV68qiUSCPXv2oG/fvjrbd16Jwox9oXq7zsJ+3hjo66a38hh7WTigZG8ktVqNW7duYefOnUVmb0okEsjlcshkMvFROOCUy+UwMDCAXC6HoaEhDAwMEB8fj6ioKOQb25SZzLlNbRuM7+SB+o7mMDeSIzYtB6fuJmBlUDhSs0sfH/l0w0TkPYus8vMv7Pkk128Ke3t7PHv2rFzPS5tYXBAE2NnZAShovcrNzX2lVyQqiUQigaGhoc5kk1q1aiEgIAATJ05Ejx49cP36dXh4eODs2bNYsGAB1q9fj9zcXJibm8PBwQHh4eHVWkcjIyPk5ubCysqqSJL5F6F79+44efJklcqQyWQ4ePAgevXqBaBgzGT3xUFlrkNeEYYyCU5O6cRjKtlrj8dQsjfSzJkz0axZs2JbIzUaDfLy8pCVlYW0tDQkJSXh6dOniI6ORkREBO7fv4/Q0FBcv34dFy9eRFBQEO7du4fs7Gw4m0mQ8+hGqcmcL0YkYdimy2i54BS85h5Ht5+D8N2xu6UGk6RRQx1zW6/B5Mcff4y0tDRoNBr8/PPPEAQBUqkUQ4cOxfDhw1/71DkJCQk6waSJiQk+++wz7N69G/Hx8SAiLFq0CEDBPTc2NkZ4eDji4+MRHx+P1NRUdOnSBQDQvHlzeHl5vZTnURkajabIzGVDQ0PExsYiNDQUBw8exIgRI/Dw4UPUqFEDy5cvh5mZGZYtW4b09HRcvnwZJibVG8BohxW8jGCyYcOG5RoHWRaVSoV3330XO3bsAADM2h8qLl5QHgNbuOLxgndwZ97bJV9DQ5i1X38tnoy9LNxCyd44e/fuRf/+/QEArVu3RlxcHKKiovTWQtdzwBDccesLQY/JnCUaFWL0mMwZKGhdcXd3R35+PiIjI2FlZYWLFy+iXr16AIDY2Fh4enoiO7vkMaGvKicnJ8TFxUEqlWLq1KkICwvD/v37YWVlhfPnz8PLywvnz59Hjx49kJOTg5o1ayIyMhISiQT/+c9/sHDhQvTr1w8HDx5Ex44dERQUBAC4fv06+vbti6ioN2/ChEwmg7GxMQwMDKBWq5Gamvqyq/Ra8RsYgLu1Pij38Q4WhjjxWSdkK9UwN5Kh4bw/Sj3+5JSOqGPPKYXY64tbKNkb5d69exg6dKjYMnnp0iXk5eXpLZgUBAHHdm9FnfQbek3mnKjnZM6urq6oW7cuwsPDERlZ0OqZlpYGPz8/DBkyBNu3b4eXlxeys7MxYMCA12b2t3aGclxcHFxcXBAdHY2FCxdi3759WLJkCVJTU+Ht7Y3BgwejQ4cOyM/Px86dO/H48WOcO3cOdnZ2WLRoEUxMTHDw4EG0atVKJzenubk5njx5AnNzc7Rq1eplPc0iBEFA+/bt4e3tDQBYs2YN8vLyEB0djWvXrmHgwIEA/kkuXxyVSoXs7Gykpqa+0cGko6OjOG5UX0xMTPC30rrsmeuFfPu+N0IeJeNc+LMyj5VKBGy99Ob9iGH/LhxQsjdGRkYG+vTpA6VSqRNAPn36VG/XICKYmJjg9LpvkHp2i7itkoUBQLUkc3Z0dBSTig8bNgxffvklmjZtimfPnmHbtm3w9/dHeno6FAoFNBoNVq9ejcaNG+u1DvokCAJcXV1x7949mJiYwMTEBDExMThy5Ih4zOTJk3H+/HkAwI4dOyCXy/H333+LwVa7du0QFxeHRo0aieMmFQqF2DWrTXyu0Whw6tQpXLp0CXFxcWjduvULfra63nvvPWg0GgQHB+PSpUswNzfHhAkT8OTJE7i4uACAOB5So9HAwMAAZ8+ehVqtxpEjRzB48GC4uroCKBhbrFarIZFI0KhRI4wePRoeHh4v7bnpW82aNbFp0yY8fPgQFhYWeitXEASo7OtBkJRvtaH3fWqgVS1rzD54u1zHqzWEMw8SqlJFxl467vJmbwQiwoABA3DgwAGo1eVvRagqs8Zvwa7nRKg1VKFkziANNKp8pJxYrfdgUksQBCxcuBDTp08Xt6Wnp6NWrVpITk6Gu7s7kpOTkZ6eXi3Xrw6DBg3CL7/8gtTUVHh6eiI9PR1btmzBkCFDkIfCf60AACAASURBVJiYiBYtWiAyMhKGhobIy8tDkyZNcOHCBXG84Pjx47F69WrUrVsXpqamuHHjBgwNDbF48WKcOnUKe/fuFcff7tq1C5cuXUJMTMwLf54GBgbYuHEjhg8fDkdHR506nD9/Hh06dIC1tTVsbW1x//59AAUBs6urK3bu3IkGDRogNDQUEokEZ8+eRf/+/fHs2TPxdREEARKJ5IX+rbzOBANjuE75rVwZImxMDXBiSif8fPIBtl6KxKL+jdGzkVOZXd4CgNvz3oapIWfzY68nbqFkb4TFixdj7969L+wLUvvF4qKMQvKWKTDNii3YQaXP/tR2meU8/gtx6ydUazBJRPj8889hY2ODkSNH4v79+6hXrx6Sk5OxcOFCPHr0CGlpabhy5QocHR2rpR76JJFIkJGRgfnz5+PSpUu4cOECTE1NMWzYMMyfPx+urq6IjIzEZ599huzsbAwcOBA3b96Es7Mz7ty5gylTpmD16tXw9PTEnTt3cP36dezcuRNSqRQTJkzA3r17IZVK8f3332PAgAHYs2eP2DVsbW2NmJgY5OTkVPu66J07d0ZYWBj8/f0xYsQIPHnyBFu2bBH3P336FObm5khKSsL9+/fh5+eHyMhInDt3Djt27MCIESPw999/w8fHB2+//TY6deqE5ORkzJw5E7m5udi1axekUinUajXk8oJlPvXdRfwyaIdtGBgYYODAgWJCf32QKRzLnW7s6/caIeJZJrZeqtgEOwLwOCmrErVj7NXAASV77QUFBem0wr0I2ob9iIgIpMVGoLv0LmLXjUdj41RQerzYnV34+PzkWGRcP4In68YhYdccyJXV0zLo4OCA3NxcPHz4EEOHDoVGo8GmTZtQv359PH36FLVr18bVq1fh7OwMqVQKX19fvQ4L0CdtV7eZmRk0Gg2OHDmC7777Du+99x4aNWqEnJwcEBHmzZuH3Nxc9O3bF126dEF6ejp27tyJFStWICMjA97e3liyZAnc3d1x4cIFrF27Fm+99RYmTpyoMylJrVbD0dERP/30E5KSksTu7kOHDqFGjRowMjLCjh074ODgALlcrjNT2sjISKxzeclkMvj4+GDz5s2wtbUFAPz555+oWbMmXFxcYGFhAQMDA0yZMgVr166Fo6Mj+vfvj6ysLLFLd9SoUXBz+yeP4aZNm9C8eXOEhoYiMDAQzZo1Q0xMDL777jsAwIcffoj58+cDAPLz8+Ht7Y3c3Fzs37+/MrfolWBoaIhu3brhyy+/hEqlwu7du8X7oQ9yw/IFp34NHdHNyx4zKjlrW6nHdESMvWjc5c1ea0+ePEHjxo2Rmpr6UhMla5M5GxsbIycnRyeZM6nzdVbAsbGxQVJSUrXVxcvLC/369UN8fDzu3r2LyMjIcnXbalfT6dChA2xtbWFpaQmNRoMhQ4Zg7doXk2xdm7sQKJiAc+HCBVhZFawy1KRJE9y6dQsLFiyAqakprl27hoMHD5Y4wUQqlcLCwgJqtVrs1te2zGnZ2dkhMzMTOTk5WLx4MZYsWYLIyEgoFAosXLgQH3/8MXx8fHDjxg3xnEePHqF27dro27cv9uzZgxUrVmD+/PniPe3fvz9kMhliY2Mhk8lw+vRp8VyZTIa3334bFy9ehEwmQ3z8PxOxdu3ahUGDBuHjjz/GkydPcOrUqSKpgQwMDDB8+HAsWbIESqUSTk5O0Gg0iI6Ohr29PcLCwtC7d288ePBAfK6FZ7EDwPDhw/Hrr7/CzMwM7u7uuH37Ntzc3HD48GE0b978tV45qLrI7WvBeeSyUo8xMZAiaFpn7L8Ri+VnwsTtX7/XCN29HNDm+1PIV1ORZVkLOzKpPRo6vx4T5Bgrghh7CTJz8+n2k1S6HplMt5+kUmZufoXLyMvLo5YtW5JMJiMU9Bi9Mg9TU9Mi25ycnF5KXQRB0Pl/iURCFhYWJJVKxW01atSgzZs3k1qtJiKiWbNmEQBauHAhERGlpKTQ8OHDSS6XFymvKg9tHTw9Pcne3p4AiHWzs7PTud8pKSlkbGxMcrmcbt26Ra6urgSA2rZtSzdu3CADAwOSSCQUEBBAPj4+ZGZmVuq1LS0tSaFQEABq2rQpHTx4kFJSUmjBggUkl8vF486fP69Tj4CAAAJA165d09murX9xDw8PD53jfX19SSaT6ZyvVqvJwMCAPDw8KD8/n6ZPn06GhoZFymratKl4rw4fPiy+fqNGjRLvzeDBgyk/P5/8/PwIAPXo0YPS0tLIy8uLAFCDBg0oIyODiIimTJmiU36NGjVe+t9PRd/bgiBQnTp1yNbWVud9ra+HsbmC3L44TDVn/F7io933p8r8zPrjdlyJ57vP+L1Sn4OMvSq4hZK9MGHxGdgWEoUz9xMQlZyNwm88AYCbtQm61LOHfys3eDqUnY/tk08+wcqVK9+4FWCq4q233kKtWrVw/PhxMV2Qlq+vL6ZOnYoBAwZAIpFg2bJl+PTTT2FqaoqcnBxoNBrI5XK0atUKISEhMDMzQ3Jysnj+7du34e3tDX9/fzg5OWHDhg2VSlptZmaGvLw8NG7cGBs3bkSTJk0AFHQVjx07FitXrsSUKVOwdOlSLF++HBMnThTPPXbsGHr16iWOEZ02bRpGjx6NzZs3Y//+/eIElcK0E1zq1auH8ePH4+rVq5BKpTAzM0NaWlqR46VSKYyNjZGZmQmgYOzm4MGDsWzZMigUCtja2kKtVovPXTukYMyYMSW+F0ePHo1169aJ/z9mzBisX78ecXFxOuNXO3TogHPnzokt3gqFAjNnzgQRYcaMGbC3t0diYqJ4r9q0aYP09HT89ddfAApmOf/+++9o1KgRNBoNkpOT8c477+Dy5cviakFNmzZF9+7dkZqaivT0dCQlJeH06dNiC7+lpSUEQXilUwsJgoCTJ0+ia9euWLVqFSZMmABra2s8fPgQCoUCISEh6N27NxITE/V2zZqfbALM7ErcbyiToKmrosj28Z090KqWDUZsuozkbCUexGcWX76NCYKmddFbfRl70TigZNUuOjkbs/aHIjg8EVKJAHUpK01o93eoY4vv+nqXuBzZ1q1bMXTo0Oqq8mvJzs4ODRs2xKVLl8Ru48IcHR3x7bffYuTIkQgLC4OXlxfMzMzE8ZNLly7F+vXrERZW0F1nYGAAPz8/zJ49Gy1atMCHH36I3bt34/z581i0aBEOHTokdh+7ublh0qRJ2LRpExQKBeLi4vDo0SMoFIoigYmNjQ3ee+891KhRAz///DOysrIgCALCwsLEFDYqlQoWFhaQyWRITU0V8yt+8803mD17NgDA1NQUKpVKTAEkk8lgb2+PuLg4AAARwcrKCuHh4bC2thavv3btWowfPx4ajQZSqRRRUVFISEhAcHAwrl+/jvv37+PKlSvFdv1qA1kLCwvUrVsXT58+RVxcnPg6WFhYYNmyZRgyZAhCQkIQEBAgBrnNmzfH2rVr0axZM2zZsgXDhg3Dxo0bERAQgISEBIwcORJHjx4FEcHAwAD9+vWDl5eXmDdy69atUKlU8PX1RXR0NJ49e1akjtrXqTLDPwoPB9AmP39VZ4G7ubkhMjISKpUKISEh+P777/H7779DJpPB2toaqampOuua64NV97GwaPYOUM7UQVrlmeUtlQgY2qom5vVpWNVqMvbScEDJqtXOK1GYe+gOVBoqNZB8nlQiQCYRML9PQwzyddPZd+vWLbRs2fK1XIP5RTAzM4O5uTni4uIwcOBArF+/Hp9++im2bdsGpVIJhUIBlUqFrKwshISEwNfXVzw3IyMDVlZWMDIygqWlJWJjC2avKxQKscVOrVaDiFC7dm3MnTsXw4cPx4gRI7Bp0yaxnK5duyIoKEgMSG7fvo1169Zh6dKlYlCmpR03OWfOHMydO7dI8DhixAjIZDJs3769yKo+Li4u6N27N4YNG4Y2bdoAAGbNmoUFCxYAAM6cOYPOnTsXeY3q1q0rBs7Dhg3TWabvxIkTeOutt9C7d28cPHgQN2/exKRJk8Qcl6XRtnwaGRnByMgIgiDg8ePHOsGaRCKBVCpFfn7p67qX5PmUP9qWRy2JRAJnZ2c0bdoU9+7dQ1hYGAwMDGBjY4O4uDj4+flh+fLlMDc3R5MmTfD06VMsXLgQn3/+OZRKJbp164Zz584BAN555x2kpaWJ//+y2dnZIT8/X/yRUVzgLAgCGjZsCGtra5w9e1Yv15VIJDC0qwn7gNLHURanvGmDeKUc9rrjgJJVm+VnwrAo8EGVy5n2Vl180sUTAJCamgofHx9ER0dXaRKOTCZ7oyYfWFlZoVOnTggODhYnh7Rv3x7BwcHiMUqlEjNnzsSSJUug0Wggk8kwbdo0fP3112LaGG26nIMHD6JPnz6IjIzE5MmTcfjwYfH1lkql6NevH1avXo1jx45hyJAhWL9+PUaNGiVe6/mAEvgn6bZ2m4eHBywtLXH37l2dySc2NjYwNTVFdnZ2kS5LExMTjBkzBn369IGfnx9kMhmePn0qznjetWsXPvroIxgaGkKpVEIul+Pw4cMwMzPDs2fPkJSUhK1bt+L06dOoVasWkpKSkJ6eDhMTE9SrVw95eXm4f/8+1Gq1GHgrlUrk5+dXeWjF84F0YZaWlujWrRu8vb2xa9cu3Lt3D9u3b4enpyfs7e1hb28PIyMj2Nvb49mzgpVXrKyssG3bNvTs2RMA8PPPP2Pq1KlFJh7Z2tri2rVrcHFxgY+PD0JDQxEQEIATJ04gJiYG8+bNw9y5c8Xjg4KCxCDcwMAAR48ehZGRETp16vRKtFjKZDJoNBoxEX23bt3Qrl07tGnTBj/88APmz58PFxcXHDt2TFxZSB8UCgVM3/kC0hoNyp3gvDxIrYJxRjSm+Mjh6+sLR0dH2NnZiSmdGHtdcEDJqsXOK1GYsa9yqTOKs7CfNwY0d0GPHj10Zs2yglnFu3fvBlAwhvLEiX9yW/bq1Qu7d+8W09vs2LEDgwcPhqOjI3JycpCWlgZDQ0OMGDECM2bMgIeHB2rXro2wsDCcO3cO48ePx+3b/6z20bp1a4SGhiIrqyBfnrm5OTIyMhAREYFatWqJxz0fUJ47dw4ffPABEhISIAgCzp49i/bt20OlUuHAgQMYNmxYkRnNz3N0dESTJk2QnZ2NrKwsxMXFIS4uDjKZDGZmZsjJyalyq7U2GDMwMIBcLkdubq74HLT7bGxskJqaCrVaDVdXV8yaNQsbNmzA1atX8eTJE9jb20MikSA0NBT79u3Df//7Xzg5OUEqleLZs2fF1tHExARubm5ikL19+3aMHTsWa9asAVDwY2DIkCHifa5VqxbCw8OLLLX4/vvv4+DBg+IPpsLBZe3atTF8+HBs2bJFXFlnxowZYmsuAGRmZsLR0RF5eXlYs2YNxo0bB5VKhVmzZmHhwoWwsrKCIAhISHjxq7pMmDABP/74I0xMTBAVFQUPDw8YGhoiISFBfH/fu3cPw4cPx+XLl6ulDnWbtUVu12mAVF6h9FAlISJISI2YNR8XWXrV0tIS9vb2cHZ2hrOzMxwdHeHg4AAHBwedf9vb278ReUTZ648DSqZ30cnZ6L44CHnF5FRr4mKJqT3qoVlNKwgAbsWkYdGJ+7gWWfrkDkOZAIOTP+L2pT/1Vs83oZVSO3mjXbt2sLa2xuHDh9G5c2ds27YNvXv3FleC+d///od3330X7u7uOq16q1atwrx588RAj4gwZ84cbN26FRERERAEAV27dsWFCxegUCgQGxsLlUqFPXv24KeffsLVq1fFujg4OKBx48ZwcXHB77//jmfPnqF169a4c+cOMjIyAPzTPVtaa115CIIAuVwOjUYDlUoFExMTZGdnQxAENG/eHHZ2drCwsEBiYiJOnToFuVyO2bNnY8GCBcjLy8PRo0fh6+sLhUIBiUSCDRs2YOzYsUVavU1NTfH2229j7ty5mDt3Lg4cOIDHjx/Dzs4OAwYMwNGjR8VubrVaLT5PrYcPH6JOnTro168fbt26hfDwcAiCgBYtWuDJkyeIjY0t9bWQSqUwNDQU823a2NiIgWlsbGyRhPRLly7F5MmTAQDz58/HnDlzcOLECSxYsADnzp0r0s0+ffp0/PDDD+L/t2zZEleuXMGmTZswYsQIREVFoWXLlmJ6o+3bt6NXr17Ytm0b5s+fX22BpbGxMSwtLZGUlKRTZ0EQ0LRpU/zwww94/PgxRo8eDQcHB9jY2ODhw4disK59TbV/H/rk3s0f5PuR3spLOvq/Mhc40A6TIKIin1mCIIjBp6GhIczMzHD+/Hm9BLyMVQQHlEzvhm4IwYWIpCJjJhu7WGL32Db4KyYVG849ggDg404eaOhkgY/WX8L1qJJnlZJGjbyoW0jYNUdvs7p79eqFkJCQas0JWZ3mzJmDmTNnom/fvjh+/DgAwMfHB9euXRNbrjZv3owJEyYgJydHbK0aP3487O3tkZKSgrS0NKSnp+POnTt48EB3eIJcLhe7jvU9wQEoCJbMzc3h7OyMunXr4sCBA3B2dsakSZPwyy+/4N69e7C2tsZ//vMffPXVV/D19YWtrS2uXr0qdvsWJpFIEBQUhPbt2+ts37ZtG4YMGSI+/xUrVmDChAkACrrh161bhxUrViA09J8WdQcHB2zduhXdu3cXt5mbm8PMzEyc9APotrxKpVIEBQWhXbt24v6ffvoJ06ZNE+v37rvvYvXq1XB0dBSXgYyIiMDq1auxfPlyZGdnw8jICGZmZkhMTNTJy1kchUIBR0dH1K5dGxEREbh37544a9/CwgLx8fEwMDAAUDDRyd3dHU+ePNEpw8XFBStXrsTNmzcxe/Zs9O7dG4cPHxb3JyQkwMHBAQDg5OSECxcu4MmTJ/jf//6H3bt3w9HREQkJCVXOA+vs7IyxY8di3rx54nKaAHD37l20atWqSLBemEQigaenJ7p27Yphw4ahdevWGDdunNjCq2/W7T+CeXt/EFHlAjciQBCQGvQr8PcfxWYbqIrdu3ejf//+ei2TsbJwQMn0Kiw+Az2WFD8Q/pcAXzRwskCHH88gN7/gy8fUQIqz07vgUWIW+q+5WGb5T9aNgypJf2srlzSw/1Unk8ng6emJvLw8xMXF6XQXSyQSEJFeAm8jIyNIJBJkZ2ejQ4cOsLGxgYWFBSwtLaFQKPDtt9/C3d0dy5Ytg6WlJfbs2YNNmzYV+wVpZ2eHmjVr4urVq5g7dy7mzZuns9/LywthYWGwtbVFfHw8unTpgsDAQMhkMtSuXRuRkZGIj4+Hra0tlEol9uzZg9WrV+uMEwUKJiU1aNAAPXv2REBAAGrWrIlBgwZh165dkMlkiIuLQ3BwMH788UdxNrcgCBAEAVKpFPXr10doaCjq1q2LkJAQKBQKnD17Fp06dcInn3yCZct0J2bk5ubqLPPn5+eHrl27YuHCheKPlQYNGuDixYviWE8A2LlzJz766COsWbNGbB394Ycf8P333+u8fn5+fti7dy+MjIxw+/ZtBAcHY86cOUhOToaDgwNSU1OLdKNrW+hMTEzQpUsXNGzYELt378ajR48wYsQIrFmzBj///DO++uornXGRcrkcZ86cga+vLy5fvowLFy5gyZIliIuLE9cBf55MJoOVlRXs7Ozg4OCAM2fOoG3btsjMzMS9e/fg4OCA6OhosV5SqRTe3t5wc3PDwYMHcfnyZdSqVQu2trbIzc2FiYkJmjdvjpCQEBw/fhzbt2/HyZMndZLAl8TJyQmtW7dG165d8ddff+HXX3/Vewulllnjt2DrNwEaCBUaU0lqVcEP5PNbkHDpgN7rJQgC7OzsEBYWpvN+Y6zaVWOOS/YvNPfgbao960ixiXszcvPp0F9Pimw/GhpLREQtvj1RauLgmp8fJKvuY/WWrLhfv37k6OhIKJRg+3V6CIIgJuCWyWTk7OwsJnp2c3OjDz74gAICAqhv374EFCTytrGxIQBkbm5O7777rk4C9ho1alBeXh4REV2+fJmaNWsm7pPL5XTp0iWdex0XF0cAqFmzZtSqVatik7kXTsxtaWlJAwcOJAD03nvvFXnvjBo1Sjx29uzZOvvOnDlDAMjPz0/cdvnyZZLJZCSTycTk3HZ2duTm5kYSiaRIHZ6/x4IgUP369WnJkiViIvfvvvuOiIhGjx5NQEGC+suXL4sJwuPi4orUOzAwkADQzJkzxfeT9p4MHTqUAND06dOLnJecnEwAaNiwYeK24OBgsrOz06mnVCql/v37U1JSknjc33//TQDIy8uLTExMCAANGDCAli9fTgEBAdS2bVsyMDAo9n0jlUpJoVBQvXr1xATr5Xm/2dnZUa1atXSSiTdo0EDnOW3dupUA0Pr163W2Ozg4kJmZmfh+bdeuHS1evJgA0Pbt24mIKD8/n3bt2kUWFhZFrm1qakpGRkYEgM6ePUtEROvXr9d5vbXv0+fvcXX+bcssHch+4H+p5ozfye3zg2V+ftWc8Ts5DPyaZJYO1frZIJFI6NNPPy3ynmOsOnFAyfSq4w+nS/xAzc1X0Z5r0UW2H7gRQ0REQzZcKv0Decbv5Dp+vd4+dLVfNHZ2dq9NQLl27VrSaDTUq1cvcVvdunUpP79ghY34+Hhyc3MjANS6dWtKSEgQV5eJi4ujnJwc8vX11XkNbGxsSBAEioyMLHI/V61apXN9d3d3GjBgADVt2lTny1sQBDHQsLW1pebNm5NEIiEioujoaBozZowYzGqvO2nSJIqPjyeif1bmAQpWlSmOt7c3CYJAERERdPPmTZLL5SSVSik4OJiIiLp06UIAaPHixaRWq+nkyZP0/vvvF/s6CoJAAQEBdPXqVVIqlWRoaEgKhUJcKYiI6JdffiGpVEqCIJBMJiNXV9di6zV16lQCIAZwRkZGYpBWq1YtAooPKImI5HI5NW3alLKyssSgVSqV0owZM+jDDz8kAOTs7CzW+e233xbvk4eHhxg8bN26tUjZOTk5OsGZ9gfF80FXeR79+vUT71V0dLRYbp06dcT3HhHRxx9/TAAoJiZGpy4ODg7k4OBAKSkp1KlTJ7HeQMGPHwcHhyIrMNWuXZu+++47evLkCRERXbt2jQBQ+/btxXLz8vJoxIgROj8gJBIJeXp6UosWLXTec/p+FP6xJLdxJavuY8l57NoiK+q4fXGYms89RFbdx9KkL7/R+eypzocgCEVWc2KsOnFAyfQmIzef3EsJBm8/SaXwhAxyn/nPttqzjtDjxEwiIpq043qZAaXbF4dJkBtV2wdwdX/IV+XRo0cP8bX+4osvxO09e/bUuQ9qtZp69+6t88W1fv16GjRokBjo2NjYiAEJAKpfv36x91TbSunh4aHzpQ1AbDGqX78+AQUtct9++y0RFQR32oCysNDQULFF7fkvZkdHR/Ly8iKJRCK2lBZ28+ZNAkA+Pj5kaGhIEomETp48Ke7Py8sjS0tLkkgkNHjwYJ2WPmNjY+rbty8NGzaMbG1ti73v7du3p6CgIJ2g8vbt22J969Wrp7MvLS2Nhg4dKp5vbW1NS5cuJbVaTXl5eWJrLABq3LixzrlaTk5OZGJiIr4GzZs3F1tBb9++TQDI39+fTp06JS6bqL2W9t/u7u4UHBxM33//PQ0aNIiaNWtGDg4OxbZQyuVysrOzoyZNmtAHH3wgvk9cXV3FQNPKyoqMjY2LfQ9KJBKytbXVaY22t7cXg9xWrVqRVCot8jwdHBzIzs6Oli1bRt27dydzc3Odci0sLKhLly60ZMkSio+PJ4lEQo0bNy5STqtWrQgoaEnW/mjRvveef1+1adOGTp8+Td27d6/Wv8siraJyI5Lb1yIDp7rUqIMfCXIjmjRpks7f44t4SKVSatq0KalUqmL/thnTNw4omd7cfpJaajA4bfdfRET068XH1PK7E9R6wUnacTmS8lUFX7QTt10rM6CsOeN3ktvX0tuHrpWVFS1atIjUajV99dVXBBS07D3/5fQyH46OjuL6ysePH6e5c+eKQUCbNm0IAH3wwQdF7oe2xa7ww9XVlXbu3CkeUzi4cnNzo02bNtGYMWPI09NTpyvUwMCA6tevTyNHjqQePXoU6SZt3769TpdsSQElEYktcdu2bSvyZaxd7/ynn34q9tzC3fBHjx4Vt2dlZdHs2bN1ukC1AVXDhg2LlDN79mwCUOx631KplGrWrEn+/v505MgRat++vbjPw8OD7t69S3369BGDGalUSsbGxsXWV7vWNgBSKBQ6dX7w4IEYlJuamurcFy1ra2tSKBSUl5dHwcHBOut1lxbg2NnZiUGbpaUlAaC+ffvqlB0eHk5SqZTMzc0pJyeH4uLiyNzcnARBoO3bt5O3tzcBoPnz51PPnj3Fckp6mJqaklQqJQMDA/riiy9o48aNNGfOHOrQoUOROtvZ2ZGfn5/O+2jAgAHiD4lmzZoV+WERGBhILVu2FI8XBIEaN25Ma9euJbVaTTk5OWRubk4SiYTq1q2rcz0Hh+rtYn7+8Sr9OF2xYkWx703G9I0DSqY31yOTywwGFxz9mzJy/+kiu/o4mVaeCSMiog9WnS9XQGngVFcvH7SmpqY0f/58Wr58OX399dckCAJZW1tTTEwM5ebm0rRp017qF4FEIqENGzaQRqOhuLg4ksvl4hewk5MTZWVlkVqtphYtWhBQ0JKltWvXriLlPT9ucdu2bQQUtHA9H1gZGhqKXeeffPKJznk3b94U92kfFhYWNH/+fLEVrrSAUhvMabuT582bR7t27SJfX1+dVtDWrVvTnj17xPMiIyPFAMzV1ZXy8/Np2bJl1KBBA/EL3NDQkGrXri1+qZuYmFBGRkax9Sh8f/fs2UMPHz6kr776ilq0aFFkPKhUKiUXFxedbZ6ennT06FEyMjIqMpZQKzw8nABQhw4dxHvXvn17GjZsmE7Qce/ePTFoXLBggdjSWLhb9fmA5fkhB99++y1lZ2cTEdGAAQMIKGilU6vV1KRJEwIgBq1qtZqcnJxIEAS6cOGCzmtsPmKlfwAAIABJREFUamoq1u2tt97SeT5qtZr8/f0r/Z728fGhqVOn0r59+ygpKYlatGhBUqlUbH01NTWlrVu30saNGwkATZkyhd5//32d+6FtPS3cOq21YcMGnesV94PhRT7KOz61Oh+mpqbFjv1lTN84oGR6U1YLpfbh+eVR6rH4T2r7/SmqOeN32nbpMWXm5lPdr46+8BbKV/FhbW1NgiCQvb29zus7bNgwAgqCm7S0NHG7Wq2mxo0bE1AQNGqDB6Bg0kZgYCC5u7sTUDAu7f333xdbPAt/6TRs2FDsSjU1NSUPDw8SBIGysrKIiEipVIrduNoxky1btqQvv/xS/MI3Njamzz77jDp16lRiQKktQyqVFgkK8vPziwSrhoaG1KlTJzGQqFmzplgHbTna4FOj0ZBarRaDrZkzZ5b4fo2PjxevUb9+/SJdg7GxsfTRRx+VeJ+8vLzEMab9+/cv9hragHL69OmUlJSk020tl8vF+1BcV6hcLicrKysCII5ZlEqltGXLFrH8uLg4cnV1Fc+pUaOG2KLatGlTMcBPS0vTGUurvQczZswoUueIiAjxtd22bVuR/fXq1SOZTEY3b96kbt26FRv0WltbU/Pmzalbt27Upk2bIsMlnn/UqVOHGjVqJL4Oz7eGOjo60pQpUygxMVHsEi881jYwMLBIq2SvXr2IiOjp06di1/6/8SGVSmngwIEl/h0wpi8cUDK9ySxjDGVxjzYLTlJatpLWBz8s1/H6HEPZoUMHunz5sti117dvX5o9ezZNmjSJhg0bJrZIeXh4UO3atUscV6bPh6WlJXl7e4tdt23atKEJEyboTNgAQMOHD6fw8HCx9e348eNFxszNnDmTNm/eTL179yZ7e3udfdqAq23btuKkB60VK1aIQYKRkRHFxcXRzp07xaCxXr16dPbsWQJA48aNI6KCoPann34SA1JtQFK4dTAvL4/atm0r1qF79+7Fvo+0M4Xnzp1LX331VZHgt/BzWLFihc6kECKigIAAAiDOAI+Oji72Om+99RYBEIMNb29vnXGOp0+f1rnnrVq1opkzZ1KrVq2KdGmamJhQt27daNmyZRQfH09nz56lBQsW0DvvvCO+jqV1gyoUCurfvz998803dOrUKcrJyRFfV+19tba2pgcPHhR5Hjk5OSSXy8nQ0FC8hkQioZ9//lnn+fzxxx8E/NP96+3tXezrsm/fPrGMwuNUr1y5QmPHjtW5v9rXuVatWkVacE1NTWngwIF09+5dcVKOWq2m0NBQWrFiBY0aNYrq1KkjllHSa1OzZk3q1asXff7552LLprYFdurUqWJALZFIqFevXhQdHS3+Te/evZvWrFkjtmy/Ci2GL+sRGBhY7P1mTF84oGR6Vdos7x6L/6SfT9ynEZsu0+B1F+nr3+9Q4v+xd+VhVVXr+9v77DPC4TAPIqOADCoq5iyK85SziTgPOaWmpqSYmiNZmkNpWdrNNMX0dkPTvCSSac4TSmY4p4gTIgIiHA7v749z1+pszgGta/dXxvc863lgn73XXmvttfd61ze8X/5jnL6ei7DZ3zwVoPQe/fEz+8DWr1+fL5AxMTGyfuTk5EAURfj5+fFjq1evfua+UYIgcMBgZ2fHtUjP+j4KhQIGg0EGLEVRxIIFC7BmzRps27YN+/btw7lz55CTk4MVK1ZY1aFWq7k/1po1a0BE2Lx5s9Uc+PTTT3mfFAoFevTogaNHj3J/zU6dOkGn0yEoKMjmHGIaRl9fX3Tr1k3WhvKarvbt28vMecxnMSQkBHv27AGRGZCUD4i5dOkSiIgHfjAzblRUFLZu3cq1oOy5lI+Az8vLQ3BwsOw5Ps1zcHV1xcyZM7Fnzx4MGzaMX2cwGKyA8Z07d2Ta2rS0tArfOxZpTmQGp2xDoNfrMWvWLN5/Sy13bm6uzbo8PT0hSRI++OADmZ+oZT+8vb0xduxYGZXU8OHDQWR2kbA1z7VarexZFRcXy6L7iczAu3bt2mjevPkTtZqWdYeFheGzzz7DvXv3AAC5ubkyzalOp8PGjRtx48YNKw3436GIooiAgAC+UamSKvkjpApQVskzlcp4KFstScPhS/dwv7AYj42luHy3ACtSMxE66+nA5LPmobQsCoUCzs7OiIiIQPfu3TlY2LRpE8aMGWMVPDJw4ECcPHkSmzZtwttvvw0iQqtWrWRBFszPjWlFLLUjb731Fv7973+joKCA06EMHTpUNpbx8fGyBXHr1q3YunUr5s+fb3NRtbWIaLVaaLVaqFQq7rP434yTo6MjfHx8eMBHo0aN0KFDB/Tp0wcjRozAlClTMH/+fAQHB0MQBCuewKlTpwIAgoKCYGdnZzV/srKyMHr0aCtNUosWLThtzblz59C7d2/Z776+vpgyZQrUajVUKhXu3LkDABzcjBgxQnYfFi189uxZfswy4EehUCAqKgpEZgDcr18/1K9fH+7u7hXyOxoMBvj6+qJatWo2ffdCQkIwZ84cXL16ld/zwoULHKxZBuakpaXxucQ4MZkJ15ZMmzaNz4OioiKYTCbMmTOHPyeNRoPx48fLIvt3797NrzeZTNi5cycPerE1T/r37w9vb2+oVCqbEesNGjSAJEkAgNTUVN7+mjVryupzdnaGh4eHDDDa29tj586dsvpMJpPsnKZNm6JTp05PpD0SRVH2jJRKJZKSkjjYXLVq1R/yDfmzF+av/Ful4LERGVkPcPLafWRkPUDBY+OTL6qSv6VUZcqpkmcqlWXKeRbyLDPl6PV6ys/Pp06dOlFOTg5dv36d7t+/bzMbCNGvWXW8vLxo3bp11KJFC7K3t6clS5bQtGnTaNeuXdS2bVvKz88nOzs7cnFxIR8fH0pKSqKYmBjKzc0lPz8/unbtGl25coX8/f153U5OTiSKoiwN5D//+U+ePu3KlStERDRs2DDav3+/LLsJEZGnpyfdv3+fjEYj7d27lwYMGEA3b96kBQsW0MyZM/l5RqOR9Ho9qVQqMhgMdOPGDQoICKBp06ZRQUEB5ebm0o8//kjbt28nInPmlICAALp37x7dv3+fiMyZUUwmEwEghUJBZWVlvzkrD8vkotfreb7loqIim7nVmzVrRm3btiVnZ2dycXEhFxcXcnNzo/fee4/Wr19PYWFhdOXKFZ6i0Nvbm+Lj42ncuHEkSRKFhITQhQsXaOfOndS5c2c6efIkRUVFUfPmzenbb7+lV199lT777DNZikNb+bWVSiU5OjqSt7c3BQUFUd26dWnFihVUUFBARqORTCYTLV68mF599VUaPHgwbdmyhV9rb29Pjx494lmZtFot1axZk9q1a0dpaWl04sQJUqlUVFxcTNWqVaPs7GxSKBSUlJREvXv3purVq1Nubi4VFhZajc+bb75Jc+fOJYPBQHl5eZSQkEALFy4kInNqyVWrVtHcuXP53GLpFwVBoA4dOtDJkyfp5s2bsv5GRUXxTEO3b9+mFi1akCiKZDQaKSYmhvbu3WvVDjc3N1IoFHTr1i0iMqdsbNCgAV2/fp0UCgVvj+V9vLy8KD8/nzQajc10mjExMfTdd9+Rq6sr3bt3j4iIVCoVvfbaa/TGG2+Qs7MzabVa2rdvHx04cICSk5MpNTWVTCbTf50v/nkUSZLo3LlzFBwcXOl5F27n0+dHfqG0n+/QL/cfkeUoCkTk66yjmJruNKCRLwV76P/QNlfJX0j+36BslTy3ErvmAPxe3/6bfCmf6Ds57St4xC545rv2OXPmADBrQz799FPUrVvXpsbDxcXFZuCEJElcY9KlSxfMmjULu3btwsOHD2FnZwdvb29IkgRBEJCYmIitW7eCyJrKIy4uDkSEjIwMAMCuXbtkZOHlNUZ6vZ6br99++21uGp47dy4AID8/n/++ZMkSfp8xY8aAiPDxxx/DZDKhT58+IDJrHo8fPy4jTG/Xrp1ME3Xjxg3Z+Dg4OMj6UFhYiKtXr+Lo0aOoVasWP89gMGDEiBF48cUXeZCJ5diW//9ZmvtVKpWMMsbT07NSU6pCoZBpwDw9PbF3794KTYVqtRq1a9fGxYsXOYk2myehoaFITU0FkTkox2QyITU1FcOGDUONGjWstLD+/v5cq0dEGD16NMrKygAAU6ZMAZG1H1xiYiJvZ0FBAZycnKBWq614PC3pi8oXBwcHNGvWjPuUls9SBJg1puy5fPDBBzbHggVHMTl27Bi6dOkiG28/Pz8sXrwYSUlJaNKkieydeuGFF5CUlMTnXH5+voxD0s7Ojj+bkJAQZGZmcqqv2bNnIzo6mr+TCxYsAGAO8mLE8MwHWJKkCqPnn/ciSRJiYmL4vCovv+QUYuBac4KJiixNrLDfB649jF9yCm3WVyV/L6nSUFbJM5P8/Hxat24dLfvoM6Ius0hQKIkE4b+uFwAJJiNlfTyWSvOenM/3t4goilwzVP5VEEWRJk2aRO+88w6JokihoaF06dIl+uGHH+jgwYN08uRJ+vnnn+nkyZM2NWtMBEGgpk2bUuvWralOnTrUt29fGjBgAG3cuJGf8/PPP1NoaCgFBwdTSUkJXbt2zaoepVJJw4cPp/fff58kSaKSkhLy8PCgvLw8AkANGjSgY8eO8fMfPHhAQUFBlJOTQ6tWraLBgweTk5MTubq6UnZ2Nj/vvffeo1dffZX3X61WU2lpKZWUlJAoilbt+Pzzz2ngwIFERBQaGkq7du2igIAA/vvFixcpLCyMSktLqVu3bvSvf/2La3c3b95MixcvprNnz/Lz1Wo1TZkyhRYtWkQlJSUUGhpKV65c4drcs2fPUmlpKd29e5fu3btH9+7do9zcXMrNzaXvvvuOTp8+TURm7YuLiwsVFhZSUVGRlRb394parSZJkkilUpFarSa1Wk06nY7UajWdPn2avLy8qGHDhrR//36uxdXpdPT++++TTqej2NhYmjBhAi1fvtxqPI8cOUJz586lb775xua9NRoNLVmyhPr27UseHh7Upk0b2rNnDxERrVixgiZNmkRubm508eJFcnBwoHXr1tHIkSNp2LBhVL9+fUpOTqYTJ05Qbm4ur9Pe3p5MJhPP/+7r60spKSlUr149kiSJHjx4YPO5u7m50b1790ij0dCZM2dkWq4bN26Qj48P9e/fnyRJoh07dtCDBw+IyKwxvnPnDhmNRpIkiTZv3sw176WlpRQTE0MHDhzgdTFNcE5ODtfoOjs7U05ODpWUlNCQIUMoKSmJBEGgYcOG0caNG6mkpISIzNrs7du3k7OzM6/v3//+N3Xs2JGIiOLi4ujzzz8nIrO2NDIykjIyMiqfAM+hbNq0ifr37y87lnTsF5qz/UcqLQOZyp4eFihEgSRRoLndIij2Bd9n3dQq+QtJFaCskt8lRqORMjIy6OjRo3TkyBH64YcfKDMzk4iIFAoFNYqbTFnerZ7Z/XJ2raCCM98+s/qIzO2sCHTo9Xp69913aejQoSRJEhUUFJCDgwM1adKEfvjhB9m5BoOBnJyc6NKlS3Ty5ElKS0ujt99+m5sYVSoVX/DK30OhUHBzL1s8ywszZY4YMYLWrl0r+2337t3UqVMnIiLKy8sjBwcH2e/37t2j4OBgevDgATVo0ICOHz9OX375JfXs2ZOIiC5dukRdu3al8+fPy6574YUX6OjRozbbc+XKFQoMDKQaNWrQpUuXSBAEGj16NK1atYq2bdtGAwYMoNLSUhIEgcrKyig1NZUWLVpEBw4coJKSEhIEgSIiIigjI4Pc3d0pJyeHTCYTeXh4EBHR7du36dVXX6UXX3yR2rZtS5MnT6Z3332XSkpK6PDhw/TDDz9Qeno6ZWZm0i+//CJzE2DCQImXlxeVlpbSjRs36OHDh7LfR44cSX379qW7d+9STk4O3b9/nx48eEAPHjygLVu2UH5+PhGZ3RHc3d2pqKiIHj9+TCUlJbxUtpGoSERRJEmSSJIkUiqVBIC3zdnZmTQaDT18+JAKCwtlmxxRFAkALViwgIqKimjBggXk7OxMFy9eJKPRSJ9++il9/fXXdODAAdl1bJ6PGDGCli9fTvb29kRE9MMPP1CrVq1kfYiPj6fFixdbtfnWrVvk5eVF9erVo9OnT5NWq6Vz586Rn58f3bt3j/r16yczgzs7O1OPHj1o9uzZ5OfnR56enlRSUkKPHz+moqIimjhxIq1YsYKIft2gzJ8/n/7xj3/Q5cuXeT0ajYYMBgPdvn2bbt++Te7u7kREdObMGerYsaNsY9SjRw/617/+JWv3Bx98QOPHjyeY4wWofv36dOLECSIiGj58OP3jH//gLhd/J9FqtXTz5k1ydHQkIqL30y7QkpTM/7reqe1DaHxM5eb0Knl+pQpQVskTBQBdvXqVg8eDBw/S6dOnqbi4mARBIIVCIVuUmDaqx8wP6JTJhwj4fZrK/1yXu289PTy09Rn2yCze3t4UFxdHcXFx9NJLL9GFCxeISO4/JwgCeXh4kMFgoJ9//pk+//xziouL43WUlZWRJEnUtm1bSklJoQsXLlDjxo3p/v37pFAoKDg4mH766ScyGo20atUq2rhxI1/QniRKpZLq1atHHTp0oNWrV9ODBw/o/v37HDSWlZVRQEAA/fLLL0RE1L17d/rqq6+s6rl16xYFBwdTQUEBubm50Z07d6isrIzGjRtHH330EQGgvn370vvvv0/h4eGUk5NDPj4+dP78edLpdFb1rV69ml555RXatm0bBQQEUI8ePej69eukVqupuLiYtFot+fn50fnz58nOzo77/QUGBtLw4cPptddeI41GQ3q9ntzd3Sk9PZ0mTJhAn376KRERH0+9Xk/btm0jQRC4Rrb8+ADgc69Jkya0aNEiaty4MWk0GiIi+uWXX2jUqFGUkpJi05/OxcWFevbsSXPmzKHq1asTEdHjx49Jp9NR/fr1qbS0lNLT02nYsGH0ySefyK7t27cvbdu2jYiI3N3daf369RQQEEB3796lHTt20JIlS/gmITIyksLCwig/P58KCgqooKCAHj16RDdv3qS8vDxeJ9MO/x6/1PKiVCrJzs6OHjx4QM7OzhQVFUV6vZ4cHBzI0dGRHB0dqbS0lBYuXCi7V82aNemDDz6gmJgYfmzChAn0/vvv0/79++nmzZsUGxtLSqWSPD09+fwjIurSpQstWLCA6tatK2uLp6cnERFlZGRQgwYN6Nq1a/TCCy/Q999/T0ePHqWWLVvycyMiImjBggW0d+9e+uKLL+j27dt8bAYPHkwJCQmUkJBAmzdvJqJf31dBEOjGjRtUrVo1Kisro4EDB9LmzZvJwcGBfvjhB5o1axZ99dVXNHv2bLp37x6tXr2awsLCKCMjg7Zv3069e/eucFP3PIqHhwcdP36cDmSX0fQvzz75gqeUxb1qU78qTeXfUqoAZZVwyc3Npd69e9PEiRNJq9XSkSNH6PDhw3T48GFuMnva3bzBYKCHDx9SUIchZKzdncoEkQRR8fSNKTNRmamUcr/98JlrJpl4eXmRp6cnnT59mgCQnZ0dFRUVUXZ2NgmCQJ999hlt376dzpw5w813RGbTX/369alXr14UGhpKLVu2pBkzZlBkZCQNHDiQTCYTvfXWWzR79mxSqVTk4OAgC3pggPuNN96goUOH0sOHD6lPnz5cMyMIAjk7O1NhYaEsUIT95uTkRF5eXvTw4UO6fv06vfjii3T9+nU6ffo0rV+/ngYPHmzV15YtW9L335uDpRISEjhA9fHxoeTkZKpXrx4REdWoUYOuXLlCAPhCXKtWLVldAwYMoE2bNnGN6OPHj6lGjRp08+ZNIpJrfj09PSk2NpZmzpxJrq6uRERUUlJChw4doj59+lBubi7VqlWLMjIyKjVRh4eHU0REBNWtW5eaNm1KjRs3ppUrV9Lrr79OHTt2pJMnT1Jubi49ePCAdDod/fjjjzRq1Cg6ePAgERGFhYVRdnY2FRQUEADSaDT04osv0jfffMMBXfXq1WngwIGk0WjozTffpA0bNlBcXBzVqlWLfvrpJxo3bhytWrWKHj16RH369OFm6vj4eEpMTLQyE1+5coUaNGhA9+/fp4CAALp48SI/p6ysjDp06EB79uwhd3d3UigU9OjRI9k8IyIqKCigu3fv0rvvvkurVq2qFGSKokharZZ0Oh3dv39fNp6/N3hKoVCQUqnk89BgMNCjR49k3wAnJycyGo306NEjSkhIICcnJx485eHhQe7u7tSwYUMSBIFu3bpFZWVl1KtXL0pOTubvApHZTeDgwYMUGRkpa8OFCxcoPDycB4JZ3nfPnj0UGBhITZo0ofPnz5MgCDRz5kz64osvKDMzk+rUqUOHDh0inU7HA+ru3LlDRERBQUH0008/kSRJREQ0ZcoUWrZs2W8an/+VsA1S+e/B7xWVSmWu086FXIesIBNZuziEeznQ1PY1qaannlzsVPTYaKLL9wrps0PX6KvTWRXWrZZE2jO5Jfk4W29Gq+T5lipAWSVERJSSkkLx8fGUnp7Oj/3eRchS3NzcKLdEJOeOr5A2oD4JBAJVoq0sMxGJCiq6cpLu7171zH0miYjmzZtHO3fupCNHjvBjLi4ulJOTQ7179+ZaJyb3798nFxcXCgkJIT8/Pzp58qSVmdXZ2Znu379PoiiSwWCgBw8e8HFzcHCgWrVqUdeuXWnIkCH0zjvv0PLly+nzzz+nxMREmQ+Xg4MDmUwmKigoICIik8lEp06dogMHDtDs2bMpPz+f3N3dKTc3t0JgHxwcTGFhYVSnTh1q3LgxVa9enerWrUtBQUF0+fJlKisrI1EUad68ebII8IcPH5LBYKAWLVpwvz8ioo8//piGDx/Oz4uMjKTz589TcXExHT16lKKjoyuMjF+0aBGdPn2aLly4QFlZWZW229HRkdq1a0eRkZF0+fJl2rp1Kzc7h4WF0cmTJ/nCmpGRQZGRkeTo6Ei3b9+mr776ivr27Uvt27enW7du0ZkzZ4iIqEGDBrRmzRo6fPgwvfLKKzRx4kQKDw+nMWPGULNmzejAgQN05MgRmjdvHqWlpXG/QiKid955hyZOnEiiKFJYWBhdvHiR2rRpQwcOHKDi4mKSJIlrACuSn376icLDw4nIDFiPHTtGZWVl9MILL9DNmzcpOjqaUlNTqUOHDpSWlkalpaUkiiIdP36c1q9fT3v37qWLFy/adJno2rUrffLJJ7R582ZKTk6m06dPcx9OS5k5cyZNnTqVmzdLSkrozp07dOfOHbp06RL169ePWxmio6PJ29ubvv/+e8rKqhg0CP+xOPzWb4MgCNwVovxxURSpbt26ZG9vT/b29uTg4EAGg4EcHR3pyy+/5C417FwGmENCQmj06NGUmJjII8GJiHr27Elffvml7D5jx46lDz/8kARBoIcPH3Lz/4ULFyg0NJR0Oh15eHjQpUuXflO//kjR6XT06NGjZ16vVqslr7hFVOocQIJCsvq9cYAzvRhZjY5dzaXbDx+TVqWgHnWrUbdIb1qS8jO9n3bRZr0KUaCmgS60YUSjZ97mKvmTyx8Z8VMlfx3p2bPnHxpdWK9ePShdfDD0vZ2oNuojmxlwqo36CE5tR0Fyqf6HtoXxDUqShAEDBvDoUCJzNHW9evXw6aef8mhTxvG3a9cuPl63b9/GwIEDK+TEc3BwgEKhQEBAgNVYlydzZpHNu3btwoQJE0Bkm8T64MGDIDLngtZoNFCpVEhJScGyZcswePBghIaGPvUYCIKAefPmyVI4snYlJycDAI4fP875FC05Mh0dHeHg4CAjSRcEAQ4ODnB0dKwwjaC7uzvq1q2Lvn37YuHChZxfkcg6zzgTSzJ5SZIQGxuLu3fvwsXFBaIo4syZMwCAnTt3yqKmY2JicPHiRQDmCH69Xg+tVsvJw1lE89tvvy273+bNm62eTVRUFBITE2V8ops2bYJSqURkZGSl7xVLvfjCCy/wcWD1sLSQJpMJsbGxIDLnKLfsh0qlQmhoKLp27QpBEPhvLCORk5OTbF4WFBRg7dq1/HfLYjAY0Lx5c7z11luc05NlCfr666/h6OgIURRx/vx5HDx4EO3bt7d6ll26dJFFvK9cuVL2jp89exapqanYsmULVq9ejQULFmDq1KnQarWQJEnGD2lnZ8fJ7i37+7SE5k9T7O3tERkZiebNm3NuWfbOBgYG4sMPP8SWLVvg5OQEQRCQkpKC0tJSbNu27Yl8l390+SPvr1AoENYo5ncxbpy8dh83ch898bwLtx9W+m5UyfMnVYCySgAAixcv/p98JFlKtPmJb0PpHgA73wgo3QMgKDX/0w+4j48PX1Q//ticfadVq1aoW7cuX9CUSiVatmwJV1dXaDQaLF68GC1atLDKM0xEcHd3x6hRo9CjRw9Ur15dtijqdDpERUWhc+fOcHNz48c9PDyg1WohCAK++uorAL/ml+7QoYPN52RJvr1t2zar3xkgHTp0KI4fP84zoxARJ1q3tbg4OztDkiSIoog33ngDX3/9NfLy8mTZWjQaTaV0K5agkQEFBgbj4uKsMsE0adIERGQTdFsKozZi9C+svP7669i4cSNPzcju1bp1a9n1c+bMMc+5+fP5MaPRCGdnZ4iiKCM3nzVrFh/bjz/+mM9XVthzZeB7wIABlbbdMpf3Sy+9xOtp1aoV4uLi4OfnJwNtkiShTp06mDp1Km/Xnj17IIoi1Go1Tp06BUEQ0KBBAyxYsIADzOjoaJ75hoG8Bg0agMicOrRnz56oVq2ajJJJp9OByJy95+rVqzzlouU5Pj4+fPPCztfpdJg2bRp/ntOnTweROY+7ZapNwAyWlyxZwutUKpUYOnQoHj78FWzk5OTwXOUREREcsO7fv59vWlj2H3t7e7z11luIj4/H6NGjERsbi44dO9okkv+rFh8fHwiCgOvXr6O4uJinmXyWJTw8HNW7T4ZvfPJvBpR7frqFazmFT6QUmpOcUem7USXPn1QByipBaWkp/P39/6cfzf+vnLos5zGReQGcMmUKHBwcZNw9591MAAAgAElEQVR9jx8/xowZM6w4E4nMi62XlxeioqI4uHBxcbEaU5PJBLVaDQcHhydyL27ZskV2LVvEbcnQoUNBZNZMVSQhISEgIpnmNTY2lmtcTSYTNm7cyDWjoaGhNvv6pGJnZ4c33ngD3333nRVPY0xMDERRRGZmJm+Pvb0972v37t15Pe3atat0fqanp4OIMHjwYM7HWH4uDRo0CHl5eYiIiIAgCDwbjdFohEajgcFgsMrukp6eDkEQ4OrqysGRv78/1Go1ALPW09HREURm7V75XNVEZmBZmTBAyTgqbeUAb9CgAWbMmAEiQq9evWTXHzhwgHNjpqenAwBq1aoFhUIBo9GInJwcNG/enM/tqVOnQhRFGAwGFBcXo0WLFiAiHDt2jD/77du3IzY2tsKMP0Rm8H7jxg2cO3cOROYsOSaTCYmJiXxMVCoVRo4ciWXLlvHrvL29UVRUBKPRiISEBM79yPpanh+TSVJSEj/PYDCgZcuW/F157bXXZFrc8+fP8+tycnJ49p/69etz3k9LPk/L9+78+fPIz8/Hjz/+yLNZsf4mJCRg3LhxGDBgAB83e3t7BAcHy/rxRxWNRoPg4GCuzXZ3d8eECRMwa9YsPh7PorDc696jP34qAOk/wwwQ681PwcyvzqKk1IQZX5554nXR7+yt9N2okudPqgBlleCLL774wz+Wf4bi4+OD0tJSmEwmLF68WAaiatasicmTJ6Nu3brQarVW11ouvuxvtmh17NjRakyNRqMsJ7dWq0Xfvn0xfPhwBAYGyupWKpWoWbMmRo8ejYMHD/KUizt27JDVuX//ftn9LfMoW8pHH30kq79ly5Z4/Pgx0tLSsHDhQvTt2xd169blwKB8USgUNs3W5YsoinB2dkZ4eDi6deuGmTNnYseOHcjLy+OAksl7773HgTwb90aNGkGv18vypVckTk5OMBgMMkBm+Xe9evVw9OhRnDp1CkSEZs2aAQBeeeUVEBE+/PBDm/UuWGAmy+/SpQvu3bsHIjMQZ4BCkiQsWrSIn5+Tk4Nx48bJxsHJyQnDhg3j+b4LCwuxbt06dO7c2Uqbrdfr0aRJEwQEBIDIDGSysrIAABqNBqGhofxeR48ehSRJkCSJA0I2lkRygvEdO3ZwLR/RrznWr127xnNdMyksLMTYsWOtQIadnZ1ssyNJEq/ziy++kI3bmjVrOGE8ew5sXPR6PZ+jDg4OmDdvHjw8PODh4VHh883NzQURyXKo+/r64vr16/ycjIwMEJm13YDZBYRpTceOHcvPY5rZgwcPol27dlbztlatWrh69Sp27tzJj5XPax4WFgZBEGQ53FlueCKSWRr+m8Lar1QqodGYrTTP0uRfUZE09vB9fcdTAcqNh39NFfrYWIqZ/3oymPSb/jX8p39dlabxbyZVgPJvLmVlZYiMjPyffMT+v4vBYOD+ZidOnOBgw7IIggB/f38MHToUe/bsgYeHB+zt7QGYc0jb8k1r1KgRcnJyAABFRUUYM2YMB0+iKGLu3LlcO5aTkyMDshMnTkStWrVkpmT2LDw8PJCSkgKTyYTCwkLY29tDoVDg0KFDEAQBISEhsmd55coVrg2ULR42tMEqlQru7u4ICgqSZeOxBEDVqlXD1KlTkZOTg/Xr11uBTBcXF1SrVs2mNogVS7C5ZcsWWW7v6dOnIywsrEJtLJPHjx/L+qXVajFnzhyYTCacP38e0dHRvA8hISEICwsDEeHQoUOQJKlSIAOA569mfpWsny1atODPtaJriOTasIqy/Pj5+VmBFmY2V6lU2L17N/z8/KDX6wEAp06dglKphEKhwIEDB2TXGY1GiKKIOnXqyI736NFDds/+/fvDaDRyP8nx48dzDS47p2nTplb+uqmpqTbnjCRJCAoKwvDhw5GWlgaTyVShr6Eoili+fDmv80mA8vLly7LxZIB01KhRsvNcXFzg6OiId999F4IgQKFQYNOmTbJzMjMzQUTcVcPBwQFHjhxBp06dZH23/Ob17t2bX5+SkgIiQteuXWX1Ll26lD9jSZKwZs0azJs3DzqdDs7OzlxTKggCnxMVmeIHDhyIGzduAADs7Ozg6elpsw+1atVCeno6z4T1rIrSPeCpTdxNEveg63v7MeQfR7Dh0FWUmsqwYOe5p7o2I+tBhc+8Sp4/qQKUf3NhJqLnvTRr1qzCxd7d3R0dOnSAl5cXXxDatWuH77//HkSEnj174uzZsxxs9evXDydOnLAKgrHU8Li5ufGACiZ5eXlcs9G6dWsQkcx/7/z585g+fTrq169vtfCxBXbkyJHYs2cPB02BgYFwc3OrdEPg7u6Ol156CYsWLcK+ffu4eTonJweTJ0+WgUgHBwcMGzaMm4wBYMSIEbx/gYGBUKlUPLViaGgo8vLyYDKZcPz4caxYsQKDBw/mmq2KwCbrH2v3P//5Tzx4IF988vLyMGjQIBm4cXNzszJdA0BWVpZVmj+m/bHla2ophYWFMq20o6Mjdu7cWeH5t2/f5uD+SfOOtWfatGk269q5cyd/tkxrmZGRAbVaDVEUkZqaavO6+vXrQxRFbkLeuHEjiMyaWks3A7Vazesl+k8wxn/mTps2bSrso6U2rkePHpg6dSoiIyNlz1MURXh7e1f4XgUGBvJnVRGgNJlMGDt2rMzHsri4GLm5uTyIJjIyEoWF5tR+zOWDyKwZtjR/WwqbnxqNRqblNJlMMr9iyxIbG4vi4mL4+vpCoVBYbSZCQ0OhUCjw7bffcp9WpjVt3749ysrKcPfuXdy+fRvt27eHIAgoLi5GVlYWHj16xH1UWfH29kZGRgbfCFy+fBmAecNw8+ZNvml58803ucb8WRWVV8jvToO74dBVlJSaUG9+ylMF8FTJ30eqAOXfXNq0afNUC+PzUiyBjCiKcHV1lY3Hd999h/DwcNk1Y8eOhUKhgCiKshzcXbp0AdGvwQ+WpU6dOjJAWVhYyLVzixcvxq5du0Akz7PNpKioCMOGDeOLzpOClVif1Go1Ro4ciX379sHNzQ2SJMHLywuCIHAtV1FRERYtWsS1KQxksHq0Wi0HkwUFBTwoJSQkBHl5eTAYDPDx8QHw6+Jub2+P48ePy/pgafI2mUw8V7ler0fDhg3h5eVlc94pFAoYDAaZZof9rVAorPKHl5fc3Fx+L9an8nnTLaW4uBj9+vWT3b988NDVq1cxe/ZsNGzY0MqXzt3dnfdj48aNMBqNiIiIsOqXm5sbPvnkE5tg+Pr163wzQ0Tc7GkZvV1ePvnkEz5/srKyoFQqodPpkJeXh/3796N9+/YyIM6A7caNG1GjRg2Ioojs7OxKx5K5Zrz00kuy45cvX8a4ceNsat/c3NxkGniNRoMDBw7YBJS7d+/m5/r4+KBevXoyNwlLv0mDwYB9+/ZxP1YnJ6cK86snJyfz+/v7+1v9zt69ynxImzZtKntWhYWFEASB5yrftWsXRFHk7+awYcOwa9cufPbZZ1i2bBkfu8GDB6NHjx5o06YNGjduzJ/v/+c3UKFQ/CYNZfkydetpAED3VQeqNJRVIpMqQPk3FuZv9rwXvV6PhIQETiOzY8cO/lF3dXXl1DPlx8YS8IiiiLVr1/Lfz58/L9PWhISEYNeuXdi4caMsYIeI0KRJEx6U8eabbwL41WcsPDyc+zS6ublVuNgIgoCIiAhERkbC39+fa98sF+727dvjww8/xJIlS0BkNqdfuXIFCoUCarUatWrVkmmCYmJikJKSAjc3N+j1emzduhWCIMDOzg7ffvst1zLGxcXBZDLBZDJBEARZFPUnn3xiE2xbAkoWBezv728VlMHMi2yMK4siZ8Xf3x8vvvgiEhISsH37divNJgCrIAYHBweZ6wEAbNq0iQNES3/Sbt26YerUqVb+tKIows/Pj1NsDRkyBIAZcLJofabtbd++PYxGoxV7giRJaNGihZUGtDwQ/fjjjyt9d00mEyRJQs2aNbkGMjo6Gnq9ntfh5+eH+Ph4tG3blh9j49unT59K6wcg08Ky9h47dkzGNMC09M2aNUOzZs1kfpzli8FgAGCe++z5SJLEo+8nTpwIIkJmZqasHatWrZLVo9VquRtKeUlJSYEoitBoNOjQoQOIfqXBys/Px4kTJ6BWqyFJEt59913ExcVVGiCoVqvh5OTE5wHzaa1IK1tREUVRdh8XFxeb73rjxo0xePBgTJw4EbNnz0ZkZCSIyKYv6O8tGo0GntX9ntqHsnzZduI6Sk1lT9RQVvlQ/v2kClD+jSU2Nvb/Ldr6f1EYCCMiVK9enWtkcnNzIYqiLMozNjZWppk6evQor0en0/HzvL29ZUE1KpUKR48etRrb4uJi7gNn2SaVSlWpT2O9evXQr18/LFq0CD4+Pvx3S9C7Zs0aGZiVJMmKz4/ITMHi7+8vA7f169fHhg0bOLBivloMYDDTKRs/y2CWM2fOgMjafFveHcBkMnFA+eabb/Lxt6VRYiDVsj9qtRrbtm2DyWTi7AMxMTGoW7cuX5zL95VRH4WHh6NNmzb8uRGZ/eMYcNRqtRg5ciSvS61W4/XXX4dWq7Wql/kMDhs2DKmpqXzM2BhZbjA++OADft3gwYP5cRblPWXKFLz99tvcjMva0rVrVxw7dgxZWVky7adKparU7A4AUVFRVuPg5uaGcePGWWkf9+3bJwPHe/bsqbTuffv2gciseVOpVFCpVDIfwebNm+Onn37C8uXLQfQraAPM79eKFSvQunXrSrVxjRo1wr179/h1//rXv0BEWL58OXJycnDu3Dns27cPAwcOlF3H5lqjRo3QokUL1K9fH6GhoTxIiI3tf6MJZAwI5Y8HBQWhadOmaN++PXr37s19qiVJwsKFC7F582Z8++23aNKkCQRBQElJiWxcGzduDIVCwf+fO3eu1T2qVauGzz77DADw8OFDKBSKZx5lHhERgepj11UKCD8/cg1r9l3CuM9P4KU1BzF6w3FsP20OIPvgu4tVUd5VYiVVgPJvKpcvX/7Nu+y/UqlWrRoeP34M4FdicrVajT179nAH95SUFCtam6SkJKSnp3PQ9+KLLwIAtmzZIvuos8WqU6dO2Lt3LxYsWIA+ffo8UdPIiiRJPLKzIioVpv1hVDKXL1/m/m86nQ4bNmzA1KlTQURYunQpioqKZFRBloU963bt2vFgAAAYNGgQiIhT0gwZMoRfo9frZQv+O++8AyKyaYotLCzk2pTg4GA0b96c39PT05P7wFlKWloa7w+RWTvDAmMEQeDmdqYJBAAvLy/odDqYTCacPHkSK1aswJAhQ9C4cWN4e3tX6LPp5OQENzc32ZwvH80uCAKCg4M5TY9l3y1l9OjRICIenc2eAdssiKLIA10seSiZ5ObmYtq0aZw/07IolUp4e3tzTeL06dNl987Pz0dCQoJss0Fk3hCdO3fOZnuZWIJeInNku63nAgAdO3YEEWHNmjVcu05E6Ny5s8wnkXEkHj58GHv27EFSUhJWrVqF+fPnY8qUKRgxYoSMAN9WEUURCoXid32PFAoFVCqVTLPt6emJmjVrol69etzNpGHDhnwTUatWLXz44YfYtm0bvvvuO/z444+4c+eOTOtvZ2eHXbt2ITc3l2tOWXF0dMSgQYNw+fJlBAcHc9O5wWDAnTt3AID7UJaXMWPGgIhkY7hnzx7+vbFkhrB8b5910el0CO6XUCkP5dStp3H48j3cy3+MklITHjwqwaFL9/Bq0qkngskqHsq/p1QByr+pvPLKK8+176S3t7cMqCUnJ8tAnmWwDCCntbFcVJKSkrjfliAIcHd3t0lszgrTNLLFi8hsQmVtuX79Ol5++WXZIs345hjROvAr2ToRoW7duhgzZgxfXPr06cPrM5lMPAuJpU+bt7c3pk2bhg0bNqBv375W4IWRrTOOxvz8fO47GhYWxsGji4sLj07u3bs3iKhC3zUAePnll2ULoZubmywbDwBs27aN08MIggB7e3uoVCr++4kTJ3jwEssgxGTSpEkgogqDVZgbR506dbBixQq+WXiauR4dHY2EhAQefW1JtWMpjRo1gkKhQHFxMZo2bQoisw9gdnY2Tp48yTXTBw8etAkoLSU9Pd3Kl08QBIwcOZKDoebNm2Pp0qUIDQ2V+cuyv5+GdqmsrIxnwiH61cQvSRK6dOmCiRMnYsiQIejZsyfatm1rBWTY/wxs/zesEE96FiyCnc3nwMBAfPHFFzhw4AAyMzNlRN/p6ek4ceIEN0WXp9IqLi6GWq2GXq/nHLK2/FgZof2MGTNk7WvRogVeffVVEBHWrVuHESNGyJgemJsDczNxdnbG/fv3bQLKW7ducXAaHh6O4OBgGAwGm2NpacX4vWD7ScU1sNbv9qN8mlKVKefvJ1WA8i8uBY+NyMh6gJPX7iMj68FT+azcuXPnqXzV/opFq9Vy5/eQkBCZGfvatWscVL7wwguyhaWoqAitWrV6qnuoVCpuPmSLgVarxfTp0znPJQOUzG/MlrDUg5amSH9/f0yePBkKhQL29vYyXj4fHx+cOHECgDnSeMKECTIzH1sIExMTbd6PEXmrVCr4+fnZXMjCwsK4tpItkh4eHsjPz0doaOgTKX4AeSSuJYfjxx9/zNurUCjQt29f5OTk8KAYpi0rKCjgEfOsT61atUJubi7PJFQRGToDxR06dLDKrMP6MmLECMyePRutW7d+4nugVqsRHh6Orl27IiEhAcnJyXB1dYWzszN3M+jUqZNsLh0+fJgDnK+++gpEtgFlXl4er2PFihVIT0+XPU8iaw2Vt7c3OnbsyAEh06rVrFkTgYGB8PLygrOzM+zt7bmv4H8DRpRKJZycnGRBVOHh4WjdujW6d+8OpVIJe3t7zJo1C++++y7Wr1+PnTt34ujRo3j//fe5Vt/Sh7BPnz4wmUyYM2cO9/lUKpVcO2x5f0mSEBkZialTp+LHH3/kY2fpU8g0zfv27bM5J5iFQhAE7kdtKYz83tHRESaTiZOsW1okJEmSXZOenm5F08Q2ifb29lyDHBwcDAcHB5vvmk6ng6+vL1q0aIFRo0bxzFFEZt/uixcv4s0335T5xT6rwrS61Qe+Bb/fkS3nSdrJgWttc+RWyfMtVYDyLyiZtx5iTnIGot/eC38bjtDRb+/FnOQMZN6yvUOcPXv2c8k7GRQUxDV3zLQUERHBF/sTJ07wjylbJFjKwYrqFAQBLVu2RGJiIvbv38/rZyZBo9Eo++ir1WoZaCqvCbUURs2SmJiItLQ0tG3bVqZFtQQ7nTt3RmFhIebOnSvLamRvb48+ffrw+7u7u1c6dxITE0FkBkEspaHlwmwJJGrWrMkj2KtVq8YBbmXy6aefcgDB6oqIiOBaXZVKhZdffllmai3vh8cyhXz66ae4e/cu1wIqlUq888478PX15cC2sLAQa9euRefOna2I2jUajQxMvf7661btZbQvllpnPz8/dO3alc+TyqKBXV1d0aFDB4wePRqJiYnYsGEDPvroI4wePRqCIPBxCAgIQHR0NKKiohAaGgpfX19Zik+1Wv27LAaWec4dHBzg5uaG6tWrIzg4GHXq1EHTpk3Rtm1bKBQKSJKEV199lbt8tGnTBl9//TWnsGKFtYuZb5lcvnwZCoUCer0eRUVF3P81JiZGdl52djafNyqVCitXroSHhwfc3d253+egQYMAmDXsK1eulGns2Vxs06YNgoKCrHKbh4WFcSorViqjQGrWrBm/1pZ2kpG8WwZCMS2oJf+jr68v0tPTcevWLWzZsoVvhPR6fYXPzhI0jh49Gh999BEkSULdunWt2nH16lUQEd8UiaKIiIiI35XF6mmKi4sLPINqwXfql/D7nQE6tkrIG7vwS45tV4oqeb6lClD+heSXnEIMXHuY7wKftEv0m/41Bq49LHu5CwoK/pAd75+h9O/fH0VFRUhNTcX8+fO5do8tpk+7OLOFYNKkSXxxLe9vFhAQYBVp+t577/H7MNLl4ODgCp9ncXExiAjdu3fnxywpb8q3jbVPpVKhbdu2MkJqxlnXtm3bJ84jpsFlfXNwcOBayVOnTuHVV1+1IltnxdPTk5Otl5ekpCRuwmbaFkvS9AkTJlhR8gDmiHkiwqRJkzB//nwQWZNKJycnW3FblqetYf2ZMmUKD35hvqZ6vR5arRZZWVk4e/YsUlNTsWXLFh6xPGzYMPTq1UtmzmRAkqVn/G/zRTM+URYRzsbez8/PyvSpUqnQrFkzzJ49G8OHD5fRChGZQSjL/67VajmVky157bXXQERYtmwZP+bp6QlJkjBgwAC+ibGc/+WJtpmsWbMGRGZanbNnz4KIMHXqVP57QkICB1ft27fnub0ZbZDJZOK+sSNHjuTXWR5npVu3bjy46MiRI3jllVcQFhZmBfDZuPn6+lqRxzMycjYfLNsKmH1SJUmy6m9WVpZsg1KeVcGyqNVq+Pn5oXnz5mjdurVscyJJEpo2bSoLWvL09LRK15qVlYX58+fb9L3W6XTo2rUr9y9+lsXe3h51e497phrKpKPXUCV/T6kClH8R2Xz0GkLe2PVEIGkLWIa8sQub//OSM/+w56kw2hpbv1n6nBERatSowTWNzN+PFScnJ67ZHD9+PACzzyMzX2s0GqxZswaAeREvn6mGffDr1Kkjy/vctWtX3Lx50+ZztazHMieyTqdDSEiIzcjj9u3bY//+/byOu3fvcvOwQqGw8lksL9nZ2TJAwxZ9W5KZmYnp06fbzEfu4+ODl156CV9++SW2bdsGQRCg0+kQGxvL63d0dESjRo1AZDbt//DDDzbvI4oiJ3R3c3NDYWEhrl+/jpSUFAwbNgwhISE2Aa6zszMCAwO5ibE81RMLkvkt88mWidiSXJ7IrA3v0qUL+vfvj1GjRmHo0KHo1q0bmjZtipCQELi6utpsL+M/JSIOctlvnp6eGD9+PIjMG5jywvwxLYtGo+Fm81u3blldU1RUBJVKJQMwd+/e5c+E3XfdunUAIOPkZG4G5YXR8XTu3BlE5iCtgwcPcp9PNzc3q+w7ljyURqMRNWvWBBFhwoQJyM7O5j6+TDvH+iQIAlq1aiUzVV+/fl02buVBmKenJ+Li4rBq1SqIoggnJycUFxfDxcUFKpWK+wBnZ2fzjU9kZGSl5mmtVgtvb29+X8YxS0Q2N1dsM2u5kdVoNOjUqRNq164NURQxY8YMREVF2QSr0dHRWLt2LZ/XjRo14hrMP6J0jX/PvGb8Xk3lf65zbNoPr7/+eoWE81XyfEsVoPwLyHt7M5/JznHGxu+ey8hupVLJI3hFUcTMmTNl5unu3bvzc7Ozs2ULmCWAaNWqFQeF5WlXNmzYwD/8bCGx1Cwy01irVq34MbVaLdP+tGzZ0opjj2k6e/XqZdUeloOZ0abExMTIfCr1ej369euH5s2bg4h4XmrLNHLl5dixYzLfsIqCFMrLokWL+DWurq48D3dFz4QBu/Hjx2PQoEEyihsPDw8EBgaiWrVqcHFx+a815uUBAMvgEhERgYYNG3J/P5Z9Jj4+HkuXLuWBGN26dcOVK1dQUFAg6/Pdu3dlz4Xo1zzklgFUlQmjZWJjUhm4VSgUcHJy4sB8xowZSE5O5qCOPWdGhaXVaq0I0fv37y9bzJk/68aNG3H16lVZwA3zr7TsS9OmTTmBN6vz7bfflvXJaDTKNLmdOnXi4z5lyhSb86k8sbnRaOT0W2xM4uPjUVRUBCKzn+XBgwdRp04dfp8GDRrg22+/5QE2a9euhSAIaNq0Ka5cuYIXX3zR5rjq9XoEBQXxTV5FmwydTgc/Pz9unn7rrbf4by1atOBtX716tSy1Kov2txRLbWKNGjUwbNgwmxpuURTh7++PgQMHYteuXcjKygIRoWPHjgDMmlvmAvJHl3p9xsNv2pfwe337bwST2+Hz2j9RveVLsvrq1KmDJUuWyCLaq+T5lipA+SeXzUevPVNzhE/Ll/7y0d2WPJBffPEFHysWAFHeb9Eyc4alGUulUiEpKQlGo1HmR+bl5WXzWRQXF8v8Dhs1agSTycT9rZo0aSJbTO3s7BAaGopDhw7Jor6joqJw7NgxAJDR5rDi6+uLWbNmcc2hyWTiQQuAWbMyduxYHglNZAYjY8eOhb+/PwRBsJkFZeXKlVxDJkkSXxTr1auH6dOnY8yYMejfvz+6dOmCli1bIioqCmFhYfD39+fn/jdzpzxlj4uLC9zd3a18H1nR6/WoXbs2Xn75ZWzYsAG7d+/GiRMncP36dc5vWb49CxYsqPBdYsEWzH+PbTSuXavYRJeUlGQTfCxZsuSpgPi5c+dARFYE6V26dMHBgwdx6tQprFy5EkOHDkWTJk0qTGXIjjHzJwsgkySJ++VZXufu7o6RI0dCFEV4eHjINJIRERHYt28fTy3aoUMHPs8YWTpgfm+Y+dbf31+WJjQ9PV3WvsjIyEqBg61MOQzQE5n5S5loNBqEh4fz/zMyMrgfLSvMdB0SEgJJkrBp0yZMmTKF8z8+aS4aDAY+7zZu3GjzWbKgOQboli5dyn8rLCzk80KhUCA+Pl5WB3NBKc8IIUmSbC6wZzV+/HgO7KtXrw61Wo3OnTtXSIP1RxXJ4IFWc7f9xx+/cm0l+z141ApIBg+b9TE+z+bNm+PDDz+skIqrSp4PqQKUf2L5JacQIW/senaA8vUd8J36JdQu1Z65prJXr17c+f6P+NCp1Wr06NEDly9f5tQxRIStW7fKxozl6Z00aRI/Zgm8WLFlUuzfvz//CFZGKs3SIhL96mdXv359q0WJAUom586d4wECtkrNmjU5EDSZTLh79y4yMjKQlpbGTYSzZs3CtGnT8PLLL+Oll17i2r3yz1MUReh0OqhUqt8VgMVMvDqdDgaDgQO3kJAQrqWzrJflAF+yZAlGjBhhUxvj6OiIunXrVkrSPGDAAKSlpT0RrBUWFlpdq1AokJCQUOl1LBgmJycHdnZ2FW4eAGDcuHEgMoPBDRs2WI2jnZ0dZsyYYeUXajKZsJ+/yD4AACAASURBVH79equc7JbjcPfu3Qrv27VrVxARjh8/jpUrV/JoYkEQKoxKZ/dp2LAhQkNDrUALkXkjc/r0adm9ateuDUEQcPnyZR5QZamRNJlMGDFiBPfhjYuLQ2Zmpiw9aWRkZKVjDsgBZWlpKc/e4+bmxnkqGSOAr6+vVYrN8+fPW5mGK/qGWbomGAwGLF++HEePHsXy5cs5V6plcXZ2RuvWrbFy5UqZid/V1RUODg4oLi6Gk5MTRFHkXJ9GoxFEZl9SZp5Xq9WoVq2abJOjVqs5cK1ZsyZMJhPy8vJAZHaF6du3r0xDr9PpZPOsevXqmD59Ok+p+b8CmEpXX/RJ3IJqoz6yuY5UG/URnNqOgtLVx+pbUNH3hL2jnTt3xueff843zKmpqYiIiLCy3lTJX0+qAOWfWAauPYzAhJ0In/0NPvjuIvZl3sG9fDNZ97Jvf7YJGjuv/B77L9xFwWMj8h6V4Juz2Wi+OPXXc+KT4RW38Jl+fAICArBnzx7Mnz+fg43KUrA9bdFqtZg0aRI3w+Xn5/MMHt7e3pAkySqq2WQycb+j9957zyZ1DJF1fmIAXOvDFqTypNJMmNnQMgVdo0aNsG/fPqSkpGDTpk147733oFQq4ezsjGHDhqF79+4ICAioNGL49/j7WS5cGo3GKvjIMjOPo6MjRowYwc3mS5cuxfr166FUKqFUKnHx4sUKgZy9vT0CAwOtzJBExLN6WArLlPPNN98gOjq60qAGyzHftm3bE9+L9PR0memfyEx+zhZ2T09PKz5CJiyynvnOTZw40eqcoqIibqIPCAhATk4OAPA0igaDAQsWLODaJ7VajTFjxiA5ORmtWrWSuTmwjQCRWQvH0gha8nuWl3nz5oGIsG/fPhiNRu7OcfLkSQDmOX769GmsXLkS/fv3r3ROlS8uLi4YNWoUB7QssKZx48Y8Zagtov3MzEwEBQVZ1cfec8usQbaEAcqsrCxupm/ZsiWMRiPy8/M5qBw0aBB/f4OCguDg4GATOJbXTDs7O+Pnn3/GtWvXIEkS7Ozs+ObSzs5Ols3K8pk0b97cinjdwcGBv9vdunUDYGaIYP69jx8/5s/IFo8kC7Sy5KFkvqmNGzeGyWSCSqVCnTp1cPv2bYwfP95mJLdWq8WqVav4huXQoUM288Q/y1Ke6J+IMGPWm1C6B2DsG4uhdA+Ak5vnM+Eh1Wg0iI6O5t+nOXPmVDqHquTPL1WA8k8qmbcechDY7K1U5D0qweFL97DpiNk8ZwtQtl6ahodFJTh8+R6G/OMIRm04jvPZD5H9oMgq76raze93fxCepnh4eCAqKgq9evXii/dXX32FsLAwuLq6yoCPWq2Gl5cX5s2bh+rVq8NgMODWrVsoKysDYCbCJjKTDtvZ2UGSJFy9epUHMKxevVo2duvWrbPZJkdHRxw7dox/lFu3bo3169dj2bJleOONNyCKIuzt7dGhQwe+SOt0OgQGBsLb2/uZ+PtZlvIgS5IkhISEoFu3bhgwYADGjRuHhIQELFmyBJ988gmUSiU8PT1x6dIl5Ofn89zcV69elfWfUeGU12a88MILSEpK4lGpTJhLQEUURyaTyaq9los8o2wxmUzYvn074uLirDRpWq0WkZGRmDx5MpYtW4a+ffvK/PBYcXNzw4wZM2xqK4xGI2JjY/n9mVlRrVbzXONTpkzhi123bt1skrBbuhmU94U8d+4cX9x79eolA9i//PILv44FZ82YMcMK0AUEBGDRokUoKiri5tIaNWrweljksbu7u82AqMOHD4PIrI1mfoHz5s2z+WzYuFv6CVuW0NBQeHt7V5i5yc7OTqbN9PPzw/37963ukZKSYvN5jR49WvZOViQeHh5wdHTkY9WwYUO0b9+eB8LYAo0ajQY+Pj78mh49eiAzM5M/k8LCQm6WJjK7SDCQz4KCNmzYwInBV65cCQD47LPPQEQyLWhxcTGSkpLQq1cvq02oTqdDQECAFbURm9eNGjXC3LlzcfToUdSrVw9Ev5p6LYU9o+bNm0Ov18tAGaP/Sk9Px9atW2XvD8tNzuZ9y5Yt/6e+8Oze5ZkGnnVxdHR8KutElfx5pQpQ/kllTnKGzYjuuvP+DcA2oNyRnoV7+Y8RMWc3P9b0rVQUG02y3Ku+8cnw7jb5mX4MFi9ejPj4eBDJ6UkAIDo6GqIoAgAOHDgg+5C2bt1adm5MTAwEQYDJZMLDhw9x4cIF7N+/H5Ik8Z1t586dMXbsWMTGxvLo5qioKCtz039TLGl6iMzBGN7e3jItjUajQffu3TFkyBB07dqVLwJ6vR6+vr6yBcHSTMwCFxjYUCqVcHBwkKVwW7hwodWHleWovnv3LtLS0kD0q/N+ebEMeBg6dCgHn6xN/v7+skhclnKxvMZu48aNMpeBmJgYbkbfvXs3B+eWmVvYfYnMoOjKlSs228i0NhVp2DQaDWrXro1JkyZh8eLF3FQeEhKCzMxMbpKuXr26rN7r169zLapGo7HSnh0/fpzft3xfGfhYvny5VXsZZQ7rq6UW3tHRkW82RFFEp06dZGkwyxObL1y4kC/S5dMfMgBfq1YtEJk3AhWJyWTC0qVLbYK9qKgoq3OPHz+OPn36VOi3yopCoYCjoyNCQkJ43QqFAtOnT0d+fj6n4REEgQeNVa9eHSaTCTdv3kRSUhImT57MQWNF75idnR38/PwQHR2NIUOGyMDtggUL+Hs0a9asCsdg5cqVvD7Wzvj4eK7ZO3fuHO9vnz59ZOb6n376yaq+/Px8aLVaKBSKCl0M2HfmzJkzVtdv2rSJz//Q0FBcvHgRRqMRq1evtnIFKU//xWTOnDkgIivXBZVKhfbt22PUqFHP9Pv9ZyrVq1d/6qC3KvlzSRWg/JNK9Nt7bZq0KwKUgQk78ai4FBsPX7W6Zt/Pd3Dpbr7sWLVRHz3Tj8D169d5arjNmzdjzZo1WLRoEeLj46HT6XgkNjuffaiZj5GdnR1UKtUz2XlrNBqZNsHOzg4dOnRAnz59MGLECEyZMgVz5szhpq5evXqhTp06EATBygw5f/58CIIApVKJ5ORkzJw5k3/oLbVfaWlpaN26tZUpSK/X8x2+ZeCCJd9iUFAQ7OzsYDQaMX36dA6cdDodpk6dyhfGlJQUEBEmT54Mf39/iKJo5YtnMpnQs2dPfv+AgAD+W2FhoQzoEpk1I71790Z6ejr/LTU1VUY2zfq0atUqrumylX7SxcUFiYmJyM7O5ibvimTLli0gItSuXRvFxcVciy2KIrZv347Ro0fzgAvLe7i7u2P06NHYs2cPT3FYkZl2/fr1XKsaHh7Oge2OHTt4fSzQhOXn1ul0Ns3lOTk5VgFUgiBg0KBBMs1cSkqKzKTKAIStTDksKMXX19eq/WwO2NnZ2dRiGo1GJCQk8PM0Gg3Py85KXFxcheMPmIHTnDlzZO4DkiTB398fkZGRFbqtWOZAf5r31fKdGDhwINauXYvMzExugbCU7OxsPmZso1FR2krLsWD3cHV15eDRkkS/qKhI5qLCgnzq16+Pu3fvYunSpWjVqpUV0HZxcUG7du3w/vvvY8eOHRg0aJBVnxnZ+rhx47hpnfmIWs4VNnaWoPLnn3+W9YURvVtuEAYOHIisrCyrZ/U8FkEQULt27UrTu1bJn1eqAOWfUPIfG60y4DwJUMYsSQMAzPzqrNU1H+67CJOpTBbg4/v6DgjK/20EoeVHgy2EzPwaGhqK+vXrc41XZGQkRo0ahfj4eJ7/lojQt29fnDt3Drdv38b06dNlZtgJEyaguLgY7777Lj/GtEmnTp2yGufi4mIEBATwNlVk8k1NTbUyHy9atAhnz55F7969ZQuEv78/xo8fL/vwq1QqmZ/hqVOnuD+W0WhEly5dQEQcOJpMJixevJhrNVUqFUaMGIHCwkLodDq+2PTv31/WzpycHK6ZjIqK4jyBu3fv5vUqlUoEBQXZTN1YfjFVq9WIjo62qf1ydnZGmzZtsHLlSuTk5PDMKAMGDACASgHl7du3oVKpoNFoZACeAXyNRoPU1FRMnz6dAxc/Pz+EhYVZaYyYVnDUqFE2TWXFxcU8B7koihg3bhxatGjBr69duzaPwA8KCpK1p6ioCImJiVa+g927d+f+ebGxsVb3ZFH/lnPT3d1d5sfHhKUFDAwMlD1/BqTLa6+KioowduxYPg4ODg6YO3cu73t58veoqKgnLs6MqoeNkWVfFQoF2rVrh8aNG8PNza1C07llYUThjRs35u+5Uql8YhYnJpcvX+Z1derU6Ynn5+TkcMDGNmxr1qyxmeaTzReFQmEVHCYIAjw9PTmfpmWqR0th1gHGrBAeHi7TsltyjVoWrVaLHTt2wGQy8Rzz9erVAwCrVJRsoy1Jkmxev/nmm/yd+KuzddgqOp3OpstFlfw1pApQ/gklI+tBhZHaFQHKnqvNhNHjN52wumbxN2azToOF38qOK90DntmHgAGK3r17Y926dUhOTsY///lP1KhRQ3be0KFDeT+JrEERW9wYlyLjvBNFEWq1Gt7e3lYLKgNk48ePl+XXdXR0REZGBjc528rSUlRUxIFbRfmhgV81iqxYam88PDwwYcIE3L59GyaTCePGjbPSYjRo0ADZ2dmyiNGMjAwAwNy5c0FE+P77763uu3btWr7AKRQK2d+WptL9+/dz8xgjZc/JyYFCoeBZVDZu3Agia2qdjIwMmVatsjJ69GgrEy1gXhCZmXnkyJGVAkpmAt21a5fsOANplgulm5ubVY7mo0eP8pzk5el4fHx80LdvX3z55Zey533s2DEZ2byXl5csd3K/fv24H+batWsRGRkpS43YqlUr6PV6WVQ4M0lbMg2wPrCo/3//+9+y8QsJCUFKSoqsPxMmTACROQrYaDT+H3vfHR5Vlb9/7p2emfTeG2mQ0FKAQIBQIkUxtKVJUVqICU1BQKQIC6uCoAgiAoIgYouw1BVQWRABRRcEZUOWHwj5YmQRYzYbs+Pw/v6Y/ZzcM/dOAgh89fvk8zznUTJzy5x77jnv+ZT35ekHjDHuubx+/TqGDh3KgWZgYCBWrFih6lsCJHv37uUcmr6+vrw62dXKy8s5u0FDhXQGgwFRUVHo2LEjDAYDAgICcPbsWZw8eRILFiwQNiTuijZ8fHyQnJyM3r17Y8aMGXj//fcFAOGqmCNJUr2MCwCEQhVXzsx3333XbWEeNZvNhnfeeYePF09Pz3rBLylcKeezb775Bj169NBM35AkCT4+PnxO6NChAy5evMg/T05OFtSfnnrqKfzyyy949tlnwZhTgvSzzz7j3Ll+fn7Yt28fAGDSpEl3bA7/LTR3lGeN9vuwRkD5G7QvLv5w24Dy0TfqAZQLRUBpDE28YxNBYmIidDodX5SLi4tVi4qrN4cxNaAEnDx05C0kVY558+YJSeGuCypV+DLGeKh206ZNAMAn5ry8PM3+VlKJLF68WPW50uOpbH369BGKR/7yl79wb15ERATMZjMSExM5ybFOp+M63EuWLOHHHTlyBIwxzJkzx+2YKCkpETS8rVYrD7U+99xzkCQJer0eb731lnAcAZzNmzcjMzMTkiRxQHjq1ClOG3Mzz1ipdaxlDoeDk76Hh4drAkrSTVbK7pG99NJLqmvm5eWpPI/keT1w4AAAcA9jZmamUDRFHqc+ffpg06ZNqKmp4d5KZQsICMCOHTvQoUMHDthIuWfjxo38+rIso3379vw+rl+/DrPZDKPRiIqKCq68pNSPJ3WbCRMmoHfv3vydiIyMxNatW/m56FjybNN43rp1q+q4LVu2aPa/MpTft29fAE6ddCL879GjB7p3716vIgy1jIwMFBQUYObMmcjJyRGKQmjzofU+KSm9GGNYsGABXnrpJZjNZhgMBkRERGhSGul0Onh7e/PrkPeQ8nX379+v+Zsff/xxPo8Qh+bJkycxefJkpKWluaXZiYuLEyILO3bsAODM8abn5c5ok0DvuhKIBwYGYsKECbxwZs6cOcjKyqqXKosxp0dy2bJlwlivra2FLMscqMuyjKKiIuE7xBrwf6VJkoTVq1e77ftG+21bI6D8DdrteChvNeQdPWMnzKFqGpA7MSFo/b/FYkHLli2RnZ3N8xkZc3plnn76abz00kvYunUr9u/fj9DQUNhsNqxatQqMOb0aysXP1ZN46NAhHoqLj4+HTqdTFWoQ/6PrZEX5V02bNuU5nsuXL0dtbS2WLl0qhISJmsdgMHAA9+677+LHH38UiKbnz58PQOSh/Oijj/gCZjAYcOTIEX4PVIThrsBG+T3XynBabPz8/DQro2tqamAwGODv78/JxFNSUlRgIiAgAEOHDsWOHTtQW1vLqWpcC23S09OxadMmt5WYdrtdCBErjSh7YmNjVce/8sor3Lvj7++P//f//h8PTYeHh3PpygsXLkCSJDRr1owfu2XLFjDmBC+AU+FmyZIl6NSpkyqM35Cme2JiIpYsWaLKaaQwLHl/yXbu3Ck8h8TERMEzSoCS8gCvX7/OwQ8BkJUrVwKoC5VLkoT169er7mvPnj1ux0Z5eTlX2aHx6Q40KgthqGqeMSd4o0IiuiellZSUIDs7WzhnRkYGtmzZAofDAbvdztV8lHNAYWGhitjc4XDg1KlTeOmll/Dwww8jOzu7QfqjqKgowbO5a9cu3odjx45VgUeDwYDExESMHTsWU6Y4ixAHDx7MoymM1aUG6HQ6XL16lW9WtNRvAGfeqdKzTa1v376CFzgvL09V5X3lyhXMmjXLrSZ8dHQ01q5dyzd8Gzdu5O9f06ZNhVxdh8PBi9oaouT6PTVZltGtWze347zRftvWCCh/g/av28ihpKKcTZ+qi3I+/nuFqign+i7kUConyoCAAGGCt9lsMJlMKkWPW2lKfr/w8HDEx8fzEDCFQOm7Q4cOxfLly7Fp0ybs3r0bhw8fhs1mg06nw/nz53lfr1ixAow5qYeI7JrOp5zkNmzYAMApp5iamoqDBw8KXhvGnNyGyiIZJaAsKyvjZOG0IN9///3497//DaCO57E+I+47Kg5R5rOlpqbi8OHDwvePHz+OwsJCzRxIxpz5h4sXL9YEh0RdQ61Pnz68cImu3blzZ1X4FnB6ViglYfbs2QCAyspKWCwWGAwGYbE+f/4892oSqXPbtm3550888QQYc4L5Dz74gG8MlDmxytxQLfvpp5/w8ssvIzc3t97xVR9gI0+QFk8mhWg9PT1VQNQVUJJp5UJqEfDbbDYcO3YMgBM0btmyBZMnT0b37t05T6M7T2NwcDA6deqEgoICvPjii9z72aJFC1RXV+PJJ5/kz7NFixaoqqqC3W6HxWKBl5eX200DqRTFxsYK44HGY15eHueSVGpy+/r6uu1fUqq6//77edoBY87UAWUI/GZaQkICPvzwQ35uh8MBLy8vWCwWDvbLysrQuXNnlXoTpdUozW6344UXXkBKSorw/by8PJ4Ko9zgAGpAWVZWxhksGHNufOurtKdnSv9VRmOuX7/O00ZatmyJ6upqVUHW77np9Xr8+OOPbsdKo/12rRFQ/kbtVqu8iTbo+59+RtM5e/jf2i3ej5/tv2DVR+eE74YXvHpXJoM2bdrg+++/5/x5RqMRfn5+mr+RMSdQOX78OHbv3o3XX38dU6ZMEXbcVqsVGRkZaNOmDdLS0jjgU6q3/JqJS1l9qfUdnU6H/Px8FBYW8vBaZmYmVqxYIXgvExIS8PPPPwu/jwClw+FAaGgoJEnCkSNHcOnSJR5mN5vNWLNmDRITE2GxWNyOB+VCT4stY84cLuVC5enpiZCQEMET5/rbmjdvLnhIXa26upoDdWpU+VxTU4NFixYJubFWqxX5+fkCyFNS5ixcuJBX2G7evBmAc5EvKCjg9z1gwADU1tYiICBAJdG3Y8cOATwrAafr9SorK1WfXb16FUOHDhV+j81mQ1RUlIpbUK/Xo02bNliwYIEgJUjHu56f6F2oj11Ds+4ApfK5zpo1y+340+v1mqCRCttiYmLQqVMnvlk7c+YMrly5AsbUBS1Krxb1uyzLMBgMQsU1bVzI0+5qyiKy6upqVd9arVb06NGDF77Mnj2bf9a5c2dVH5IWuNIzRUo0vXv3RklJiSCNqmxGoxGenp6a9D5EfUTPuEOHDnj//fc5UT3g9BrS76FGijZbt25FZmamUATTrl07rqDjOjZIDhKoA5Rffvml4BFt3rw53/jRfHIzlduUbjFhwgSeMjBu3Dh+PQqP3405/X+jvfHGG5pjr9F+29YIKH+j5spDOXL9MRRs/hyPv+OUTttxshwFmz9HwebPkfTUbk5sXvWzHUf/8U+MXH8M417/DN9cqVQRm0dN3w7fbneex8xisSAhIYEDrYSEBOj1el7J6GqM1eVQfvDBB7zykZorjx4AfPHFF3zRYswJLsgrRGFnxhh27dqFffv2cdWa+fPnY8qUKdzb4efnp/IQUOFPQ2HRhiZ+o9HI70+n03GAHBwcjI4dO6JXr14YPHgwOnfuzK9FC+L+/fvxzTff4IcffhA8RFTp3qdPHw4GzGYzhgwZwlU5lPeh1+uRlZUl6J67LkJaVlNTw4tX5s2bx/tIKwR67do1TJ06Vcht9fX1xcMPP8w1lZWgm/L69uzZwwuhIiMjceLECX7O9PR06PV61bVIAYUxpyfYtcCKyNlnzpwJwAmKFyxYwKv4lY101Mmqq6vdAjoPDw+0bt2aVzgrbdGiRWDMqcxz7tw5GAwGeHh4CDQ/WoBS6WlMS0trEAgQaCwoKMDatWtRVlYm3AflCCuVnShX0fXZ9unTh5+XxowrF6zD4eD5jFqFbE2aNIGHhwcA4LHHHuNjsaSkBBMnTlRtRgIDA+Hv7883BQaDgecQE8VVhw4d+D1u2rRJuE/l/KK8b9cUESW369ChQ5Gdnc0LWVwbgc3k5GT06tWLKyO5NkmSkJqailWrVvG+cNUadzgc/DqHDh0CAAFE0phVaqEDwO7du8GYM5/atbhmxIgRnGxdy5NpMpmQmZmJp556CufPnxeOvxXlpN9i0+l0vCiz0X5f1ggof6OmVMqJnrETl35QV9aStf9TnbRi7/9KL1bX2lFZ8x/sPX0FORrezjutlJOSkoLo6Gi3C7OXlxcSEhKQl5eHqVOnYuvWrWDMyQdH4TFZlrnSBGNOehZXI8oOxpx8jGTffPMNGGM8fKosniC7ePEiHn74YdUCft9993Gvxf79+7nXxmKxQJIkvPvuu7h69argdQsMDMSUKVO4rraysCcmJgZJSUm8GIIWJqPRyImzb6VvG/q+LMvw8vJCSkoK8vPzVYsocUaazWaYTCZNzkbA6eWgwh8CJ+Q90el0KiCjtPPnz2PkyJEqCTnKC2TMWYFLfajX63nOo9IeeeQRMKZWsCHJTTp/SEiI4EEEnOkIfn5+QqGREnzLsuxWd3rWrFlgzBlyVeZyRkVFqbSZ09LS+O8IDAzkHjdSYElPT+egcdSoUWDMmWPZUCFM69atMWHCBDzyyCNC+DskJMQt0bPD4YDVaoXVahU2IERHRGH8tWvX8hSN5s2bY+fOnUKI2tVWr14NxtQ5o4DT8x4XF8dzCSMjI1X3V1ZWhuHDhwubM1mW0a9fP144RZuu6OhodO/eXSiso+/LsowlS5bwVBK6L8aYZuU6gTQC8Eo1rVOnTmHlypV45JFHkJ2d7bZAyPUesrOz8e677+Kf//wn15AfMGCAcN0LFy5Ap9PBbDYLXK95eXm4ePGi5rMjRguiy1IW7TFWp0BFGuuMOT3rvXv3RnR0tGos6fV66PV6WCwWngv6e21ms5mnAzXa78caAeVv2EjL212Bzu20qGnbED3quTv68lM1r7LK9ZtvvuGyaAkJCYiOjobVanULjmw2G0/4NxgMMJlMSExMFPpj4cKFQqEI0e4A4CHVs2fPom3btmCM4eTJk7h+/Toef/xxgTpEGS6nynTAWeGp0+lgMBhw6tQplJWVwWw2Q5IkwXv6wgsvaD6vw4cP8wWqsLCQeyZd+RYBJxCorKxEaWkpDh8+LFTHms1m9OjRA1lZWZp5ddTnjDkB0+2AVCVo9vLy4kU7jDmBVNu2bdGtWzfIssx/h81mw7Jly7B582bs3bsXJ06cwKVLl1QA9fPPP9eUqaPWvn17IeyoNFo8N27cKPw9Li4OsiyjoqKCh1CNRiN2796Nbdu2cb136pNWrVpxYN20aVOuw02Sia7mcDhgs9ng4eGByspKTkyt0+kwe/ZsXjGelJQkAEyqwg0PD0d4eHi9oeuoqCjExMRwwGo0GjmY0KqgV9IHMeYEGMr8XwBcnUrJGgA4vceMOT1jRKtjsViEfqU0DMacObiuBOrBwcHQ6/UCTRSFogmM9u7du16pPLvdrkmCr9X8/f2Rl5eHVatWobKykoOiX375hZ+LxpUkSbBYLJpyjxaLBREREaiuroZer1elUABONaWxY8dqjtPg4GC3hTPUX4GBgejVqxeeeOIJlJSUYNmyZSoqMdeiHFcjhR/GnGk0BMp37NjBr2Oz2XgEwGQyCZyiDoeDjxGlktj/lfbnP/+53v5rtN+eNQLK37B9e61aVZn9q8DkEzsQM30b9N7Bd/zlJ29DaGgon/QKCgrAWB3ZsMPhwNNPPy1M1qTX645Ww8vLC/Hx8Xzi9/T05N5NoiH69NNPwZhTFhAAzp49yxdsOo+Hhwf69OmDzz//HECdPrjZbAbgLGChHb4yJEoKKrSI+vj41PvMlOTi1Fz5Ft0dR/fjro+7dOkiANPAwEB4eXlh8eLFgjrIoEGDcPDgQezatQsvv/yysBBS69ChA7KyspCamorY2FjuSTIYDDCbzbcV9qfKd7PZXO/iZjab0bZtWxQWFmL27NlYunQpNmzYgB07dvDK3ZEjR/LfWVJSAsacXJFkS5YsUTEKkGdo0KBBfIyNGDECANC0aVPodDoOTrRs+fLlYIxh6tSpAIAPP/xQ8LgGBwdzAHgzbejQC/ez/wAAIABJREFUodi3bx8Yc1ZD02bDarVixowZvKDDHXn3V199BcbUhPNZWVk4efIkamtr3eYoUyEKHdOvXz8B+JeXl4Mxp4zpsGHD+Lt18uRJ/h16R5SKO1SQw5hTbrUhu3TpEvcS1teMRqOK8oquRWFkyrVcvHgx3n77bZ5HevnyZeE4+h5pZ1MhVWVlJWbMmCHwkXp7e2PYsGFo3bo1LxwiL35JSYnARep6v+7eAZpvGGN477338M9//lO4v7Nnz3ImBALGrnblyhXhHaTrKUH/4sWL+ZxLoP/48eNu5SJ/T02v1wucxY32+7BGQPkbtzePX7yjHkpb8+53/OV3rSKm3Dmi+6msrMSUKVOEBXXmzJlgrC6Hkhad/v3749VXX+Vh8IZIiRMSEvjkPXz4cDRr1kwIBbVo0UIT0JHsHWPOsCzJ+H3yiZPP8+jRozwXjBQrGHNWZzZkDodDUODRCs1duXIFixYtQvv27VWE0kr5OGquBRJ2u50TidMCNm3aNFXOG4GWrVu3YsWKFTzcKEkShg0bhuvXr/M0AyWIA8DB0IIFC3D58mW+CE6cOBEvvvgi5s+fj8mTJ2PUqFHo168funfvjnbt2qF58+YqQHo7XlTlAs0YEyibXL/n6+uLQYMGCZ7bESNGoKSkBPv374ckSZxs3NUuX76MN954A5MnT+bAwWaz1RuebteuHSZMmIB169ahrKwMpaWlmDlzJtLT091uCqxWK6+qP3nyJCRJgr+/v2aeIgDcuHEDkiShU6dOXH9aS9nI1Zu7b98+4Z3UAn6kg04FIq+88goPMSu9pUqJT6Vi1apVqzTvmfqhdevWmnQ29Lf4+Hi88soraNGihfA8acMIAJ988gkYY5g7dy5efdVZRKgsyKIUAy8vLyHkfujQIX6+6OhoLFmyRIgwUEiYCs1ImSgxMZF7yIkn9fz58zxKkJaWplLEYcwJNlNTU9GuXbt6cza9vb2Fd71jx47o2LEjJElSjUvXDRO13r17A6jb/ChTLsjIo9mtWzecOXMGjz322E17iX9Lzdvb2+27Qfavn+04Xf4jvrj4A06X/4h//Vz/9xvt7lojoPwd2IoPS7mH8baA5H+P82o38K69/JGRkSgvL8fzzz+Pzp07q3LpGHPuOvPz87mXjTEnoDxw4ACf/GlinTNnDp+sGWOYPn06SktLsXbtWhQUFAiKMVr3QxO/xWLBlClTsHXrVoGuhkKPtABIkoQPP/xQKFyQZRmTJ0+Gw+HguZuSJGlK6CmN+BaVi8myZcvw1FNPISMjQ/DGEgVSv379EBYWBrPZDIfDge7dReAfExODr776CtXV1Rg7dqywsFEluZbFx8fDYDAIn2uF0fv06aM6dsaMGWCM8aIZVyJvd0aLHWNOOUMlP+aFCxf4xkIJjmhRpipWs9mMgQMHciDg6o0k6cabkQK8nUbqSvHx8arcPoPBgMcffxxfffUVV0dS2tWrV1W638p7Dw4O5sDYtUDI1by9vREZGSnwe44ePVooQIuLi8P27dtRWVnJqZH0ej1mzpwJSZKQnZ2tOi+FdZX25Zdf8g0HeXZp3BMgoWdHv/lvf/sbLy5SesZ0Oh1iY2MxfPhw7NmzB8HBwRyA+fn5Cd7SmpoazJs3T8hnNBgMnCmCitdsNptKpWnNmjVgzLmhoDQKh8MhbCyoPzp06IDt27er+mLTpk1gjOFPf/oTAPDUBQJqtbW1nF9TC+R16tRJyC8mzzJjDC+++CJGjx7Nc6rdjTebzYakpCT06NGDMyj4+vri448/VgFzem/8/PxUqTTEt2mxWITfQKFxqvL/vTQl/RNZ6Xc/Ye720+j47Icqer2YGTvR8dkPMXf7aZR+95PWK9Vod9EaAeVv3ChPxtY8D3Ez/oyo6dtvCUzGzNiBqMfeQ3C7/Lv20hsMBkF+7vvvv+fVm4w5wZ1rThJ5V9LS0mCxWKDX64Uii4cffpgv7K6LwGeffYauXbsK54uMjET//v0xZswYdOzY0W2BkCzL/F6URRJGoxEvvviiULjw7bff8mtS+I9yD//2t79pPi/iW6TwuSvgkWUZ0dHRnERcCUZIKo/AMnkzlJXd9N/g4GC88sorCA0NhdVq1byX69evgzGnJ0Rp5MFxBbadOnUSwF+3bt1U3hMqekhISFBd78qVKzyXlc6pZaWlpbxIpqSkBNOnTxc8O/RMlNXjNpuN67i72o8//qjKhQsICEBISIhbbyFV43t4eMBms8HLywteXl4NKprU11yJ4JXN398f0dHRnHxc+ZnVakVaWhqKi4tx6NAhXL58Gf/5z38AOOUdTSYTACewoSIpAtrZ2dmqca7kQ01KSlLpQRNJe79+/VR9WVVVxXMuU1JScOLECf48unfvjtDQUK5IoxzbRCI+btw4HqJWmpLf1ZULVmnbt293+8zefvttzWMoF9HLy0tQO2LMudl69dVX683zzMjIgCRJPFWHFIeof65du4aBAwcKz23SpEk4cuSIECXIyMjg1FnEE9m1a1devETV7Q6HA1999RVWrlyJHj16gDEmqAQpm06ng6enp+a4GjVqlPC7qHAtMjISf/7zn8GYk1nh+vXrggTr119/jb59+/4uQuNKKqlvr1XjobVHOe9yfeseff7Q2qP49pr7gtZGu7PWCCh/o3bjxg1Bbs9oNKJpZg7Chi3m1D/1gsn/fh465I/wDou7ay+8MixoNptVC7tyQvj555+xefNmPPjggwJYYMyZcN6mTRvMmTNHUNugSsfz589j+PDhQiiYJtmHHnpIsw+rqqqg1+sREBDAPZsdO3ZsULM4ODgY3bt3x5QpU7BlyxaUl5fzkPwbb7zB6YWU4IZIxLUm6djYWH7N5s2ba2phA+BFTIw5vVCMMbRq1YovOsp+JgBPYUiSIVQaeRi1vDIEqnNycnDkyBGhSj09PR2ff/45oqOjBb491/tUytPNnDlTADaRkZFutbwBp344Vb0fPHgQdrsdTz/9tCZFSkpKCgdIly5dwubNmzFp0iR069bNbYiRMSdQo7zK0NBQrF+/vt5KdbK9e/eCMSeQV3qb33zzTezYsQNr1qwRyLZjYmKEkKLJZEJoaKhAn0P5pbf7nplMJnh6enIdeHr3CHC6jo8HHngAr732Gt+YLVmyhFfNUuW5kjfU1VwLgrTuJzU1FRMnTsQXX3xRb38SrZEkSdi3bx8kSUJYWJhbkOdwODBlyhRNEBUaGoqpU6dyb+SXX36J/Px8AdwqvfcPP/xwvfdmt9uh0+mQmpoq/D0hIQGSJAnk55SGQ/+mNJTTp08jOztbGK+utEG5ubmaHKmkC96hQwcOKIcNG4ZVq1Zh9OjRnAXDHciWJAkRERHIy8uDwWCALMsCqJUkiUc7XEUIiE9z2bJlv2kOyy+//BJvHr+IxNm7b7lINW7WLiTO3o03j2tX2jfanbVGQPkbsxs3bmDnzp3CzpexupBTixYt4B2VjNSR8xFZuE4VBo96YgdaPrUNvt3GYXjRtLv+sl+/fh1HjhzRBIiM1Z+4T98NCwtDZGSkKqwpSRJMJpMQcvTz88Po0aNx8eJFgbvRnZF2tLK6V6mu06FDB+G65KVy52lKSEjg4EuWZYSFhamAgqenJ4qKigRNciWptLe3t4qTTpnT2a9fPxUnZ3JyMg4cOIAXXniBL5iZmZk8vOYqRwkAUVFRvOhIaVSswJizwIPs66+/5ko01D9RUVGq45U5oi+++CLvTwKprVq1Qm5ubr2AEnB6mgmE0oLmSp1ysy0pKQmFhYVYunQpHxfp6elcaUcLVNdnycnJgsdR2U9kr776qvDsk5KSVJ7r9957D4w5cwfPnz8PnU4Hm82G69ev49KlSzhx4gT27t2L9evXY/jw4UhKStLMPaTim5CQkDtWzWsymWC1WuHr64uQkBBER0cjIiJCJXXq2tLS0nD48GGUlpaisrKyXu8fKVFJkoTAwEAAdZXpVFTnzihvkjGnd69ly5ZC3yjvMTQ0VJBEbNOmDSc1r89I3vXFF1/kf/v666+FDUNycjL279/Pi8PmzZvHw87dunXjhV4XL17Efffdp+ovWZY1q9HJCAyTlKuWlZSUCHPS/fffL9ATuTYilVfOm0R/BtQVLioL3ajIh+ZBX19fmM1mnmqhtSGy2WyYPHkyp227k83T0xMpKSkI6TrqjtQPrPhQLU3baHfWGgHlPbYbN25o7lRv3LiBDz74gBPzuls0qEiFchSNHp5o2j4PlogUDCt6ApLBzPNo7nYzGAx8106L7gcffIAxY8YIXpPg4GBMnDgR33//Pf+9J06c4Iuaw+HA7t27OVAKCgpSTV6yLCM+Ph7FxcU4ceIElixZwj+777773Pa33W6H2WyGt7c3L4ag42jCDQ8Px7FjxxAUFCTktZ07dw5r167FuHHj+P24A5rKKulJkyZhy5YtsFgsHFCSrVy5ErIsQ6fTYcOGDbDb7Tzvja6v9Eakp6cLxN+A0/Oal5fHx4mXl5cKOFZUVIAxNcfgH/7wBzDmLG4g8EiV72SXLl0Scjijo6OFlAbAyTOoDMOPGzeO0xBRLp87QHnw4EHk5OSonrG7fEiz2czpm5QLGWNOcK6kjwIgPGMKbd+qvfbaa8I9KInJ//znP/NKfkmSEBsby9/XLl26CO83EZvT75AkSTMk7Gp2ux0lJSUq77RWI3lLu92OiooKnDx5EqNGjVJxLA4fPpyPm8DAQDRv3hzBwcGqvr2dRqFsSiPw8fHh+Zg03g0GA3r27IlBgwbx+WvIkCFYvXo13nnnHXz00Uc4ffo0rl69ioqKCphMJt6vNDe48/K2aNECa9eu5ZvP8PBwPtbPnDnjtp+JWN5ut+Po0aOCp5767+9//zuAumhAaWkp7HY7z2MNDQ1FeXk5amtr0b9/f8378/X1VQFvh8PBK9IZY26957t374Ysy7BYLDylRKfT4fjx47h27ZqgtPPggw9i9OjRaN++vTA3u86l9K7l5ORg+vTpHGwqi7koN3vLli1gzKlyRWTr/fv3v6teTZrTYrsNu6NFqVsbPZV31RoB5T22DRs2QK/X4/nnn+dyZwcPHuSL+616HyjMwRjjYZZ7zUdmNBqxaNEi4XdmZmZClmX0799f2CnHxMRgzpw53OPaq1cvTiqtXNSMRiMPn48dOxbJyckqqg5JkuDh4QGj0Vivl4S8f7NmzRLOodfrMXfuXP69s2fPQpZleHt74/XXX0ffvn0RFhYm3JfVakVWVhaKi4u55FpDE6uXlxeaNGmC7t27Y/LkyVi4cKHAUcmYMxSulDNkjOHTTz+tdyx9+OGHgvf22Wef5Z/R4vfRRx/xv40YMQKMOT2IDocDFy9ehCRJguoHGeVKtmjRgo+noKAgvPLKK3j11VcF0JuamsoBFoXVCFBu3rwZEydORNu2bW8qPzEjI4Pzmep0OuGeHA4H1qxZoyr+yM7OVnkg/fz8+PckSUJJSUm9fam0L7/8UgVud+/ejQ0bNnBPvCzLyM/P58VJV69e5R4yo9GIpUuXAqgDlHQvVKV7KybLMnJycvDWW2/Vu9GcNGmSKoy9cuVKDr6JFocxNRWRj48PMjIy+HPt378/HA4HHA4HLl++jKSkJP7dgQMHYvHixZg+fTrGjx+PwYMHo1evXujYsSPS09ORnJwsjEslsP21wFX5HjZv3hxNmjThwFU5JhhjfP647777UF5erqoYJrnC+Ph4nvOozCX++uuv+ZgEgA4dOqg2STR3kQ44Y07e05ycHEiShDFjxgh52lTlX1FRwQEfPQutOYyEFkwmE7755hue/yxJEgwGA9566y1IkgQvLy/eD1TAd+bMGd4nTZs25WH09u3b1/sclPOZzWbjUR6STSXLyMiAXq/Hzp07NYswb7fRvSW2zkb04yW3X4yq0RJn727MqbyL1ggo77GNHz+evzBt27blJNx3AgTeayD5wAMPYNiwYRyk+fj48AkzMDAQQUFB/HcfOHAAXbt2VYFC5eQlSRIyMjLwxhtvcM5KxhgOHjzIz3Pq1ClN4CxJEmJiYvDQQw9h9+7dwuRMpNXK6yoLF6qrq/Hqq6+iZ8+equ95e3ujTZs2fCF1NaWKxcKFCwE4QcTatWu5akVMTEy9YXTlbyAgowxF1WcOh4NTwNAzqampURXrEJ9ms2bNhL4h8mjXtAHSGabKcvJA0nUMBgM2btwoeNDCw8MRHx+vWuBdn3dYWBhGjRqF1157Df/4xz8AOKU3aeGkKnvXKuRPP/2UA/GxY8di2bJlPDTNmBOc9+zZE0eOHOHgmRZyxkRlJXd25swZGI1GyLKMjRs38nPQgmkwGDBy5EjNKAMAvP/++zxfNi4ujgNz5fNVsg3cjPn6+go0Rr6+vqiqqsLhw4cxYsQI1YaGCmRGjBiBRx99FDk5OarnYDAY0KlTJ04ivnnzZk7ttHz5cs37UKaK1Md0QCDHarXyQrvg4GCBYLyqqoqHtMPCwrB+/XosWbIEM2fOFHgileMmODgYAQEBwnt0u6T+er1e1W8eHh5ISkpCmzZt0LVrV+Tn53Pe0UceeYSnw+zevRvHjx/HhQsXUFZWJsh79urVC0CdljcgErIzxgTP62OPPcY3vERjROYqtEBms9mE4i5JknD69Gk4HA6MGTOG/52AalZWFhhjOHbsGADnhokxJ02Yw+HA6dOn8fLLL/MNstVq1czZlCQJ3t7eSEpKQs+ePZGamgrGnIpFDSkO3WpLTk5G9KjnnEIcGsBw8JpP8dZn36KsogrVtXZc+bEGH5y5gt4v/rXBnMqH1or93Gh3zhoB5T02Aie/90bFMoBzwpw2bRpf7D08PCBJkmbembtwfFRUlIrY+OjRo2CM4amnnuJ/cyVzptA5qZwoJ7/w8HAMGDAAixcvFhadjIwMLF++HF26dFFxaCo1vin/k0I+a9asUf2eF154gR+rpC4BnJWtriHvsrIyIcxVX3P1bFKBkJYpw17kKSEqINL5TUxMVHlprl27xivPlZabmwtJknDjxg1cvHgRXbp0ual79vDwgLe3tyo8PXToUKGCXMuUCiHkeSdbtmwZD6u6ekoqKysxa9YsIcRHGwNS16F8M6X2u6udO3eOV5/v3LmTe58Yc4LSSZMmuT1WaXa7HaNGjRL6QJZlzhQQFxfX4DnIjh07xsO8sixDkiTVGLh8+TL/vQkJCQ0u7kou0pycHJ7ba7VaVaBGaUq5P0mShLxDsu3bt2uq2LgCSjIqPuvduzdycnKETWKLFi2wYcMGeHp6IiYmRjhu3rx5vF9yc3M59U+fPn3w0UcfYeDAgcLmVafTIS4uDt26dUNiYqIQOjebzfDz8+NhVi2weStNp9Px88fGxqJp06Zo2bKlCvjSHElz4pgxY3Du3Dn89NNPboUWgDo2CKrG1+v1Qri8tLSUg3KdTodVq1ZBkiQkJSUJx7uG2GlzvGHDBgDASy+9JNxvQEAAIiMj7zh41Oq/hIyO9QLDnaf+B5+UXcWT75/CH145goLNn+PExR/wn18cGLzm0wY9lecqGimF7oY1Asp7aCdPnvw/JY/Vs2dPoWLZ4XBg0aJF3EMjyzLGjh2LL774AkOGDNGUMwsKClJ5mXr06IHDhw/D4XCAMYYePXrwa9ACRJMe4JTlo7B3eXk5Fi5ciOzsbLfyaa7X79WrF9atW8d/S21tLby9vSHLMkpLS1WKP2R///vfeYiccjqVRMOugLK2tlZIpDcajSgqKsKKFSs4WKDPmjVr5tazKcsyPD09BbA5YMAAMOasvKYxFhsby+89NjbWLRgipZRHH30UEydORNeuXesdpx4eHvD19VV9xxVAMcZw5MiRW3pH0tPT+aLCGMP58+c5BZWvry/Onj1b7/Hl5eUYP368EIILCgpCYWEhzx/09/dXLaYXLlzgG6GePXuqKqebNGlyS78DcBZ3ELDQ6/V47733+PMYO3ZsvcfW1NQIxVPU8vPz+XdKS0sxY8YMtG7dWuVRioiIQM+ePdGvXz+0atVKAFeSJCEoKEhgOzAajdi3b1+992Q2m7n0JD3rAQMGcI/33r17IcsyzGazavOgBSiPHz+O3r17q4rxZFkWaIWSk5M1i8uUaQY05lwZFFz5XF3HZ5s2ber9zXa7XSi06dChAyZNmsQ3rxaLBZ07d8Z9992nOed4e3tzGrHbmWOJc9VqtcLHxwfBwcFCASSBO1mWMXToUEyfPh2LFi3iXLP0HtGz3r17N2w2mxA9IqO59cqVK277r2/fvjwV4uOPPwZj7LaK6Bpqvt3G1ctk0nrBB6q/pczZg+9/qsGhc1cb9FLO3X5a9fsb7ddbI6C8B3b27FkMGjTojuUP/W810tj29/fnyeEmkwkvv/yy8HvXrl3LFyl356IFm5RyqqqqMHv2bAFweXl5Qa/XIzw8HIDTE6XT6fi/yebPnw/GGPdwnj9/Hv3792+wv/38/NC9e3esXLlSFcI8fvw4J6HOysrSzOcjvV4K/5FedEhICKqrqzmgrK2tFWhYSB9aGXomTyu1yZMnC9crKyvDunXrMGHCBHTq1Ommw+jU1+fOncOlS5ewadMmDhrdhaddOS8lSULfvn2FRd7hcGgm/ev1emzcuPGmqrxdjXI6lepI5C1OT08XdIwbMqVkptKjQufT6/Wc17C8vJzndxLQCAgIwAsvvMDBF2MMO3bsuKXfU1xczK9L583KyuLe5L1792oet379en7PaWlpWLhwIX8O48ePV1EFEYk40efIsqw6N23OJElCu3btNCvJGXMW0Gn9zpqaGjDmzK189NFHwVgdjU58fDy2b9/OC6Bci6SAOkD5j3/8Q0X/RaTnNN5clX9oQ+FuQ6R81nFxccL1KU9SOT6VqRtBQUFYsGCBWyovwMnnSucgwnqdTodZs2Zpfn/u3Ln8/Dt37kR5eTmnt6KxNG7cOHz99deYP3++IDQQFhYmgN2cnBy0bt3aGQKOjkZwcLCwEbhdTyp5kb29vREYGIjIyEg+prKzs3HfffdhwIABGDVqFAfDlPceEhKCjz/+mMtDKvNrf22jMRA2fs1t5Uh+UnYVZd9XNfi9js+pCdMb7ddbI6C8y/bTTz/9Lghkb6YRVcb48eMBOEPBtBAnJSXh1KlTmDt3rlB8YTabNZUeSEuYAKXSysvLUVBQIEy0gYGBPFfJdcE7duwYGHMCB62+Tk5OxsqVK8FYXTi+S5cuKsUYb29vdOzYEc8++ywqKip4bhNRFymNFrk5c+YIfyf94YiICFgsFnh5eQmevJ49e2om3//xj38EY4wXM1C19M1YWVkZ1q9ff8uJ8QaDAYGBgcjOzuY0KXPnzuVyjbS4UK4p4CwS6NKli7CQpaWloaCgQCiCoRyvWzHK9fvss894mJ4xJyfnrVpQUBAfh71798bBgwfRvXt31fhIT08XvEcRERHYsmULgDqQP3XqVOh0OoSFhd309UlhhsDxxIkT0a1bNzDmBCNUtat8xhcuXOBhTIvFglmzZmH8+PGaSj2JiYkYP348l04kI35PWZaFgizyJjHGsHr1au5l7NevHzp37qyS5pNlGWlpaVi1ahV++uknngv63HPPCcwJSjCn0+k0uS2vXr0KDw8PYcwo6b8A8Opob29v1fHEY6kFwEmz3Gw2Y8SIEZzqadCgQRg2bJiquIpSdUJDQ4WcZUmSkJaWhtWrV2u+n0oN94yMDMGLp2Xkaad+YYxhxowZcDgcfNOsfD6uxX8pKSma1ekOh0PgXiXwTOFqm80GPz8/yLKMFStW4LnnnsOsWbPw4IMPCv3fpEkTNG3aFLGxsQgNDRVSf25XJvVONcloua1CnNS5e1H57/9gz1dXGvxuzIydjTKNd8EaAeU9sD/96U+qkObvrSkXXWX1cXV1tTB58klBkvDxxx8DqFOyUDYiAtYClEqj3D1lKCkkJATp6elITEx06wWlECCRb1Oe2Lp168CYk8cNcHowlGTrrrl/BIYjIiL4PW3evBmMOaultYxI0F37zx1fpt1uh4eHBzw9PeFwOPhvstlsKsogANzTWFxcjK5duyIuLs5tIYzFYhE8dHq9/qZpYjp37ozLly/j5MmT6Nu3r6pK21UKr7a2VvWddu3aaXqsXI34NLOysvDMM88I9+fv76+SmKvPqLJ6wIABCA8Ph4eHB//M4XDgnXfe4drY1GRZVnmcFi1aBMacBUtE5q5MtXBnVVVVsFqt0Ov1vCqXaIcOHDggFGg0adIEDocDRUVF/De7gi/luK+PjJyMqtR1Oh1POXDlR7TZbKrcvKqqKjz//PMCITs1AuJTp07F1atXuReusLBQyKtctmwZAKdHc+HChbz6n1q/fv1w8uRJ4bpffPEFD+0yxgTmBaCOBmr69Omq30qFe3TMJ598IoxBX19fPv8QaKLUh86dO8PhcODNN99EZmYmB356vR7t2rVDSUkJzp49yyvAGXPmn96M0TWopaSkcPWjixcvQq/Xw2q1oqqqCgCEHGVln7Vo0UKYb4cMGQLGnEVCjIlcnqtXr+bHkXSm0qqrq4V7uv/++4X3V6fTqVIA/v3vfwt54q1ateLAncbqnVpjqBmCYm/LO1nyxWX85xdHg4U51E6X/3hTz7LRbt4aAeU9sk8++eSuJzPfrXb//ffjf/7nfwSuxenTp6NNmzYCMTUtCJIkwcfHB4AzfEfnefLJJ3HixAkBgHp7e9ebZ0eLujvvm9FoRMuWLXnfWq1WTr8zatQofh4vLy/uZUxJSYEkSdw7ojS73Y5t27Zh0KBBqpCu2WxGs2bNeJ6YqwexrKyMF7MojwsPD6/XozF58mQwVkeu3Lx5c8FLkJSUxEGjVmK/zWZDXFwcOnXqJPSrEoQp881IAo48m+PHjxc8MO6aTqdDREQED6tq8SlSqoBrzhiRYbsz4v8jTk4/Pz8EBQXxjUFQUBBffBsyqvA+efIkL3ggOqPPPvtMkId0bSaTCXmDewIgAAAgAElEQVR5eTh06BDPYaytrUVtbS1MJhN8fX0bvD6xEGzcuJGDWyWPJQFId/fg4eGB1q1bY+bMmVztyGw2IyQk5KZ+P1BXzENFHWazmb+rBoOhQe93TU0Nxo4d6zb3z2q1CkBy8+bN/B11zc3s0qULfH19NYtyamtrufrP6dOnVVyw1F8UVVCa3W7nUYDS0lLh3QsICOD3npWVhbCwMJhMJkHRZteuXarzLV++HMnJyZrzDI1FAs3uzG63874IDg7m72VgYCAvVCKPYmZmJsrLy7mndN68eQCc+bFKlZ6EhAReJEaqPgEBASqPLs2D/v7+qmdMClCM1XnOzWYz1qxZg0uXLoGxuuiT0qgokYDuhg0bUFpaqipovBPNaDQiKCXrlsHkCwecObtPbf/qpo/54uIP9T7HRrt1awSU99Ao/+b31GRZxvfff88l6FyBR9OmTfHSSy/x6mECgIwxITTjqphTWloqnCchIYHT/Wzfvh2DBw9GVFSUKmG/ZcuWmDZtGpYvX46srCwVwCJQq9y5Hz9+HIw5qygBJ6hgzEnq25ApaYFcF1eTyYRmzZph8ODBgscrOTlZCCE2bdpUM4x28eJFrFu3jhMNx8XFuS0k0uv1iImJQW5uLoqKirBhwwaVHjLlkjLG3FaDb9u2jS/4sbGxWLp0Kb9mbGysKkRoNBoRHByMiIgITR5JSZLg6emJ+Ph4dOvWDZMmTUJ+fp1uvCvIjo+PV6UskBePvGBt2rRBbW0tcnJyIMsyzyEMCwurN9eNzM/PjwO/q1evgjGnZ0WZ60W/85lnnuEV5JIkCeFlqioniU0Cd/WpP9EzoAp7ApRTpkzBxo0b0adPH00PIGPOghtl4ZfD4YDVaoXVakXLli1hMBga/O2u/arT6YSUC0pbUbIR1Gd2ux2zZs0Squ8TExP5eZR95TpuVq1axce9uypvSgMg3k7igvXx8RFyJr28vLgWNRlxrSrzrpUbl6qqKn5+ur8dO3bwZ+9OsnX79u38HXGlJtPpdPDw8HDLe3vp0iXh+dK8uHDhQh5if//99wEA999/vzDuGRMZLQDgypUr6NOnj9C/xDZBRTSuOdxEuE653GTkBbVYLLBarVi8eDG/Nv3e3r17q7hFKdVI6Vkn/t87vd54eHggtnXOLYHJ5/c5ieef2fvNLR3X6KG889YIKO+RKUOZv5emJORVhuDCw8N5iLV9+/bCxH/hwgVhwabFXMto4XXnMbLZbFw5iDEmaGcrCxfCwsIEqUJJktCtWzcecidPk9IjSdxsrhKIrkaTtrKopm/fvigoKNAsSlHy5BkMBg7WAgICkJuby0GjVsiZPI0UYnv00Udx6tQpnt+YmJjoNvS7detW4Vz1eVHsdjtPAaD+cs3T0+IapEr27OxsrF+/HoWFhejcuXO9BUJmsxnx8fHo0KED4uLi6pLuw8Lw+uuvA4BQhKMsRlIqk8yePRuMOcFDfdQ9p06dAmNOVRgAePvttwUvel5eHl/wSYsZAI4cOcLDdyNGjBC4PRlzepfGjRsHDw8PWK1WTUBx4sQJSJJTYvCHH37Ayy+/LOjSK/uE+qFZs2ZCv6WmpvJxOnPmTDDmBLDkdb1ZIEimpOmaMWMG91I9/vjjt3Qek8mE4ODgW/JKSZKE/v3748svv9QElJTX7LqxW758ORhjgkeyadOmMJlM/N979uwRrtWuXTu37/KBAwf4fdO8RO8lbTIB5+aDPJgGg4ELBVA6hhL4eXh4oLCwUIg87Nq1i8/xNNZd74O8nI899hgqKir4syfvo5LRAoCKBF0ZaqaIQ2hoKPLy8iDLMmRZRkJCAt/QUvHN7aw9BKBpI22xWLjnVa/Xo2XLlnecBk+SJCSkpN50DiWByef3/f2WwGRjDuXdsUZAeY9MKcH2e2iJiYnCjpQxZ5jru+++A+Cc6IjUOjAwkHvLlF4yxupAaXR0NE6ePMlJxLUk5QwGA58wKfeJuChpMXEtXKCcNmXOknLRs9ls0Ol0XEfY9Xm0aNGi3ueWmZkJvV4vEFQ/+eSTnCpDkiS0bt0anTt3vqniK6vViri4OOTm5nISYtdij/Pnz4MxhqKiIv43yuGzWq0qoKfU+fXz84NOp9NUvyGbOXOmZo5eSkoKdu3axf+tDDGfOXMGsizD19e3XkBHYXSll4YKoRrqm0mTJgkeOtJOplQAIluPj49X8WmSDRw4EIw5wSJ50+na69at4xXWM2fOVB177do1HtZr2bIlGHOCnSFDhghhXMacfJbK/ikvL+cbHK181ujoaMyZM4ePG09PT67eQ8CK3jdZllFYWAiDwcA9rUQCTgVDN2PDhw8X7sFiseD8+fOwWCxCTnBDRrl3PXv21KQyYswp+Qc4ybgLCgqETQI1nU6HcePG4dChQygrK+OyoVrV+xQmXrFihfBct2zZItDUpKWl1auTTUbFO3RcdnY234QWFRVhwYIFHDh17txZ2LhRzvTatWtx5swZlRc/OjqabxwMBgNeeuklpKenc67OefPmYfLkyRg1ahR69eqlOU8oGRWU6me32kjD29fXl0cU9Ho99zImJCRgyJAhMBqN0Ol0+OMf/4i1a9cK0SQfHx/s2bOH/36l9CJQt9GjlKLbpURy17y8vBBd9FqDoHDJB04KsRcOlN5yiLyxyvvuWCOgvEe2bdu2O/rS3Yvm5eWFwYMHo3fv3mBMXYQBOKuTKWfuscce4xMjKTycPn1a4IpzbcHBwVixYgWfwGtqalBUVMR38jSxGgwGFBUV8X/37duXL0SkrNKpUyfodDo0a9YMFRUVKCoqEnIvAwICMG7cOFy+fBlAXbitPm3lwMBABAQEwGQyqUCRu4nUYrGopO2oGY1G9O/fH++88w7vV8rvU5osy2jfvr3wt40bN/LcSgJZpPNLHoiCggKeCuD6rJYtW6ZaDFu2bInBgwfz45XeYkobsNvtCAwMhCRJmkVCWqYMcxORN4HNwsJCdOjQwS3XJYXRlYvg5s2bcenSJZ57SDrDSnM4HMJzMplMGD9+PK5cuQLG6gq16lPMcTgcnNOTsbqiLsCZB+26ETKbzSqAEBISgj59+uD111/H6dOnwZgz7YHC6iNHjlQB4q5du4IxJ6hWgrHHHnsMAOrNcXO1yspKngdIBNdEW2a1WnlI9GYUeyoqKriakrLl5uZi/fr1QgFJx44dBXB37tw5wVOm9ax79OiBPXv2qJ5lTU0NvL29odPpUFpaynW5lXPCrYBiQL3ZNRqNQoqJxWLBkCFDUFRUhOHDh+PBBx8U2CCioqIQFhbGgdqdKrKkcUnjIysrC126dMGDDz7I5yjiut2wYQN27tyJo0ePori4WEXQ7rrZo/xsugZtgqg4cdy4cQAAf39/hISE4OmnnxaA9Y8//sgB5bp16/CXv/wFc+fO5f1WnyrWr2mh909EdD08lAt2OivgPzpbgfyVh1WtPjDZyEN596wRUN4jW7hw4R3fyd3NNmDAAH7vyrCdVsjxo48+0gQHrmTL9B2TycRzE91VeTscDl7RKEw0oaGCh448F9nZ2XA4HMjIyIAkSRxskueyX79+Ql5jREQEiouLIUkS4uPjAThzGjdu3Iji4mJ06dJFVaGqbJIkIS4uDm3btuWAomvXrsLCSDyURLbuSs1CfdK7d29s2LBB8NT4+fkhNDRU1S+nT5/m5+nYsSMkSYLJZELHjh3BGMPly5fxxhtvgDGnFOTnn3+OXr16CR4PkshUXu+nn37iixdjzsWV8mcfeOABMCaGiBsy4qGk0LGSyPvKlSuCvF6rVq34Ik30PNHR0W5zNpVhy+LiYrz22msYO3Ysfw46nQ4zZszgoE2ZbnIzgAyok6SUZRmvv/66QCLuCsqpmUwmbNq0SRgDq1at4p/Hx8cLaRtKq62thY+PD2RZxrFjxwSw0rVrV87B2hAR94kTJ/hiP3LkSLRt25ZvLt544w1IksRD+4WFhZrnqK6uxty5cwX1JeX7u379euH7y5YtE77Xpk0bHn6ura3l8rKyLOPo0aMc7CrnQ1mWERERgYEDB+Ldd9+F3W7n0QllX0RGRvJ85cGDB6OgoABDhgxB79690alTJ6SnpyMlJQUxMTEICQnhnjqtDeHNNOV74+XlhcDAQERERPC+oP96e3vD399fdY0nn3wSn3/+OS5fvoza2lrU1NTwsd+tWze+GVcWAtH8WlVVBQ8PD+j1epWoAhltlqgZDAaMGDFCKMgZN24cGGNc/IEsNDQUer0eVVVVkGUZ2dnZ+Ne//oW33npLeD8bCpdrvae/plksFhj8I+sFhZ/+45/1vgcNeSgblXLujjUCyntkgwcP/lVyXne7BQcH4+2331bxpDkcDhgMBiQkJGiGHL/++mtBuUHZwsPD0b9/f2zdupVPkqtWrRI8OkrlD1dThmGUE+bw4cNRWVnJ88rS09P5REkSbIsXLwbgVPdQJvOXlJTwKuqG+sQ1Ib9nz54oKyvjIDY/Px96vR6SJPF8K6VpSS+Sd4gWddcdvr+/P7p168arqbWsurpaoDL561//CovFwgnfy8rKeD6V8tyBgYGCJrCWKQtqGKur7MzIyKj3OFdTEps3adIEjDlVOvbv38+fv8lkgslk4mNjxYoVPJdTr9dj2LBhCAsLg5eXF1577TWesxkbG1vv5iwyMhJdu3bFxIkT8frrr/MUCcYYNm3adFP3T5yYrgCBJPyI2uezzz7j6i7KBTgnJ0cACbm5uQ1ek3IwqX82b97Mc9RILUVL4YRs1apV/LmvX78eDoeDgxUyJeuCMg3Ebrdj5cqV3JNKz6d79+5C/61atUrz2nQc5fsy5ty0TZ06VdhMK3MAW7Vqhfj4eHh7e7sF6bfSyFNP8p9BQUGIiopCUlISWrVqJRQSKfPDlecoKipCRUWF4EEOCgpSpcwoZTmVGy3qRyXIon7ct28fD9dTysXBgwd5qgTNN0TsTmwYrkTvSrt+/bowtmnOlGUZDz74IK5cuSJo0rds2RI//fQT9u7di8GDB4OxunzShgB3y5YtsWTJEnz66aew2+08JeVW+W9vpqWlpSFo0NP1eilvpzVqed9dawSU98jupJrAnWxUcKPMGbp06RLnSSPVm0WLFgGo40EzmUyqRUBZAe7n56eStyOrrq7metaSJHHCX6UNHTpUmFwYY+jVqxefMGnycw190iIaHBzMqyi9vb3dFsK4VpFHRUWhbdu2wm8zm83CAuNwODggNJlMbulwtAClw+FA8+bN+UQMOD0Rr7zyCnr06KEiW/f09EROTg4nWwfAdX6VCz9jznC1Frg3m831LkpKy87OhiRJArG4LMsCufnNmBJQfvfddzAajQLtFG0GtNRGNm/eLHhIGBPl4K5evcqJsGkhpuvpdDq3z5r6isAmhdEBZ0X0uHHjkJiYKDx7pbJKfHw8TyOgnFryfB09ehTV1dVYsGCBkO5A9zFy5Mib6rfHHnsMjDm9PmTvvfeesPFw9XIqvfleXl7cO0jvLlVQkym9ppMnT0ZycrJAAURUN/n5+ZzGiTFnykhERAQCAwPh5eXl9CT9inw/k8nE8/1CQkIQFRWlylV111asWIGzZ8/i+vXrbiuuXU0JfPR6PV555RUATtYH5XtTUFAgHKfX65GZmcn/PW3aNOH5Ul650vLy8iBJEubNm6eSJkxISBC4Wa9evSp4g61WK+bMmQPG6nJT3ZlyA7hz504AzuIgZXRFSRdVX5/GxcVh2LBhWLJkCY4ePQq73Q6HwyHQkQ0bNoz/ffv27XdFdpHmnC59BiLysfcQfRsk5+5a4uzd+PZaw0wRjXZ71ggo74HV1tb+JjW8R44cib/85S9grI7mhIx2tRS2TkpKchv6mDBhAqqrq/lOt3Xr1jyUQ3KIWkaLCmNOD+nhw4dx5swZYTLcunUrbty4AUmSuJeHQrDUfHx8EBER4RZIUCFMly5dUFxcjI0bNwq5XmPHjhV+q2tTcuLV1NQIPJqenp5uJQG1ACUADigZ0yYgrq2t5cTFPj4+wm+yWCw812rLli1Cbhl9TrmHjDmLq+oronG1kJAQ+Pv7w+FwCJXfZrMZ69atu+nzKAGlw+FAamoqX9zOnz8PDw8P2Gy2esHA7t27OTiTJAlt2rRB+/bteX/ExMTwZ9GqVSswJlaJE0NAbGwscnNzb8oLJkkS/P39IcsyL5ZyB9hovBcXFwNwAn3Kf/T19UV+fr7Qh/7+/hgzZozb8CVQl0vJWJ1nqqamBmVlZQLIzsjIwJNPPomxY8dysGmz2ZCeno7U1FTExcVxAG+z2WA2m4VNyO00UmEJDQ1FXFwcmjVrhszMTOTm5qJPnz68qGjs2LFYunQpXnjhBbRr1051TQKNPXr0gMPhwLVr1zBw4EA+RwYFBWH16tUAnJutZcuWaYJWHx8fdOzYEUuWLKl3w+NwOASWBsa0i/GmT5/OP09KSkJlZSUPKY8ZMwa1tbVo3749GHN6X7dv3w7GnKFrVyNASdenAiAlF3FAQADGjx+P8vJyOBwO1bwWFBRU7/tx7tw5SJLEgbKHhwf8/f3deu+VrBNxcXE4evQoDh48yD//8UdtGh3KoVTmw94LkQ5JktC9YO4d9VBuPa7mHm60O2eNgPIeGCXm/283ZThKWeWanJzMib7379+PUaNGcXJwaiaTCU2bNkVRUZFQtJCUlASHw8Fz+Bhj2LZtGw4dOsQnT1pwXY0xZ7HAtGnTNBeM0aNHY+PGjSgqKuJ8evWBAqPRiMzMTCH/jfIj3dmlS5eECvGIiAgMGTJECMtbrVb07dsXJSUlfPLu16+fW9oTMi1ASZyLXbp04SBLK6/v22+/BWNObwmRrZNXt75G/RMREQGj0YioqKiGhqdgBoMBrVq1wqhRo8AY49Xa1B/NmjW7qapaApTl5eUcZBG4Isqm5cuXN3geqjp39RgTFx8AIffz+++/BwB0794djDlBi91ux7vvvssrt5VNr9fDZrPB29tbsxpdybNJUQZJkjBs2DD+HfLm0ZgbMWIE/vrXv2Lbtm2cl9Xf31/YkBmNRoSEhCApKYnn+92sd85dIz5Ti8XCQaZer0eTJk2QkJDAGQBcj/P09MTatWuxd+9enDhxApcuXUJVVZVAizV06NAGnxWxEzRv3lz4e1VVlXBdX19f7tlSvmfR0dF45513NM/9wQcf8O/98Y9/dKts1bZtW8yfPx/ffvstAGdIWen1f+ONN9C8eXPIsqzJFHD27FkhP5LCwkuWLOHnUcqn0pg6d+6ccB4ClA6Hg3+HqqJLS0sxdOhQ4XlHRkZi5syZwhgZPnw4qqqqsGfPHsydOxf5+flIS0urFzQGBwcjMzOTexrJm6rcZFI4Pi8vDwD4Rrq0tJTfP7Fx9OzZ023hTXh4OE6dOsWp4u50o+t2GLfACQh/pafypQ/FZ9Rod94aAeWvtH/9bMfp8h/xxcUfcLr8R01uK6KduBtNp9Npeg5pUiwsLMT69ev5ZM9YnV7uL7/8gm3btvHFV9koJ4/+feLECdTU1PAq4Li4OL6jpsWBQt5USXj16lX+WUZGhsqTx5jTM+pardhQM5lMmDBhAl5//XVcuHBBVUmekpLCf//TTz+t+dy+/vpr7m1grI6yZfHixZxvkUiMXYmos7KyOFegKzGz0rQAZXx8PCRJwpUrV2C327nnYuLEiarjdTod2rZtCwBYs2aNALrJk6YFQmRZxujRo3n+HYXKG7Jr166BMcYJkJOSknDhwgVIkoSUlBSuXy7LMoqKiur1nlCVN43NWbNmweFw8L7U0mx2tcOHDwv5e6mpqQIoTE5OxoEDBwCAA4t+/frxDQVVrrqCRA8PD8yfPx8nT57EmTNn8NFHH+Gdd97B6tWrsWjRIp4q4evrCz8/P5hMprua/yzLMqxWKwfNycnJfLPh4eGBhx9+GFOnTsUTTzwBxpzVt8qxGxcXx4E0GckN5uTkCF7SoKAgzp+oTCuJjIzEzz//DMCZB0hRAnrHV65ceVNjiDZnSuYEAoOyLGPKlCmqqnh3OchKU3rSlB5Bu92O999/nytbKZ+TMoxvNBrh7+8PoC7kT5RErnblyhWVqhlJ51LqDxk5C7KyslT9QF51xkShBaUdOXIE3bt3v+kcUpPJhNDQUD4+IiIicOzYMS6F6RoRSktL4+D54sWLuO+++4T3ITMzkwO3qKgodOnSRcU1SgB0xIgRuH79Oqqqqvhz1ul0GDBgwF2LwFH6UnjHPyD2ie2IusWcyrhZu5A4e3ejZ/IeWSOgvA0r/e4nzN1+Gh2f/RAxLgM4ZsZOdHz2Q8zdfhql3zkryejlv9NhAiLCpn+bzWZ0794dhw8fxueffw7GGM9PpHAFTZTBwcHC/dDkW1hYyD1QLVq04AUHXl5e/Bz9+/fnYILya/R6PZo1ayaQDwPOcA/pCJtMJmRlZdWrCOPqyXjuuedw4cIF7l11VX9Q2sWLF/lETueg0BnZ0aNHucwfY86CnhMnTsDhcPDQIIWRqPJx/Pjx/N6U9x0WFoapU6fC29sbsiyrcttcASWFyJQV9LW1tfwZumoVe3t7w2g0CgtwWFgYli5dysPYyhym4OBgzUpyb29vjBkzBgcPHqwXBFJoS6/Xw2g08jAiUeUcOHAAx48f5xsNPz8/t/rklBNmNBoFiTvKfbRYLG5TBXbs2ME95BRei42Nxd/+9jfs27cPL774oqA6Rf3jLkeWPNu3w7JAx1NRzK14EU0mE9+opKSkYNWqVYJ3d8eOHcjJyRHuy2q1YuPGjXA4HCguLgZjDA8//DA/Rq/XCxKHVEGt0+kwd+5cVFVVYdasWcI5if7r7NmzQj+fPXsWjDFePBQXF4eamhruiS0uLuY0Ta6qTO6soqJCiAxUVlbyOcfHx0d491xBuqtKjNKUpPiMMezdu1fzew6HA48++qjmBkCWZaSmpnL6MZIw1LJvv/1WVb2cl5en6dWkAi5laowy6pGfn889jXPmzEF+fj5SU1Pr9TQqm6+vLz7++GPh2rSxp2daXV0NSZL4BhRwpkoQT67Srl69yinLtFpQUBB69eqFdevWobq6WsVDCTg3exRpuBdt5MiR0PuEIPvJLf9dZ+v3VtLnmdM3NuZM3kNrBJS3YN9eq8ZDa4/ynU9DO6PoGTvxwPN/gclfVHK5k41Ajk6nE+7V4XDwxUKL1oEqUZ955hl89913XAqRVG1qa2shyzJatWoleDKUYUqHwyGEk2RZhs1mQ25uLmJjY93mNJrNZqFwoWnTpjh9+jTXS/b29uZhdUmSBO/j1q1bG3xOFRUVwvVCQkIwceJEXhktSRI6d+4shHiAOiUYxpwJ7ozVeS6bNGnCVUo+++wz9OnTR+XFsFqtAth1BZRKmg6l1dTU8PBicXExhg0bJgBD6sPXXnuNH3P69GkO2iRJwrZt2/hnb731lluPgU6nQ0xMDIYNG4Zdu3YJAJOAM2MM7733Hv/71atXIcsyYmJi+N/mzp3Lr5Gbm8tpSqqqqjjIYcyp2LNs2TLMmTMH48aN47m1jDlDWmlpaYiPj0d4eLhbtZ3baZLk1JMPDQ1FbGwsmjZtioyMDA6WWrdujcLCQsyaNQtLlizB+vXrsX37dhw5coSnb2iBb6Jgce1T6rMNGzagqKiIvwNUvOV6b56enjyvt6ioSLURMBgM6Ny5MwfvO3bswLVr1zhQat26NQfke/fu1byOt7d3vfrpQJ0eNJFVk0eZaJ7at2/Pc2Fv1iiv9/333+e5rUri7k6dOvF3b+XKlYJHLDg4WKUGRNXEf/jDH/gGw2KxqLSqS0tL+Txrs9m4t46eZ1xcnCqa06RJE4wdOxaHDh3CjRs3+Llqa2sF8EvznJKQnuzixYuQJAmJiYnYvXs35syZwz2O7jYy5GnMzMzEQw89xMUGaHNUXFysqp5u06YN9u/fz+mUXJkDkpOTodfr+bh99tlnwRjjEaqnnnoKGRkZ9dL8BAQEqMY9AcrnnntORfIfGRl5T4AljZ8pU6bA4B+JkS/uRNi4NRqKOjsQUfAqUh6aA1uYk13iiSeecCuE0Gh31hoB5U3am8cvInH27gaBpKpN347oae+jWZ9xnFj4Tr5oYWFhyMjIgMFgwLVr17Bs2TLk5uZqUjm0bNkSK1asUFHpkFGo85NPPsHSpUvBGOOTMS1kw4cPx6OPPorc3FzNRcx1waSK2k2bNuG9995TFb4oJ0VarNeuXQsA+PLLL1W/Q1l04c6oupU8bcrjk5OT3RZFUKhTp9Nx2TtayNx59nbt2oWOHTsKHpGWLVtiw4YNsFgsHFASkbBWvmRFRQXGjx8vnMPf31/IYyVFILvdjmHDhgnAa+HChapzlpaWCgv1xx9/jNmzZyM9PV01BgMDA9GuXTsOkJs1a4bCwkIMGzYMDzzwADp37szPFRQUhNDQUPj5+d20Ak59TafTqTgCfXx8kJ6ejq5duyI/P58v5mFhYYK3VpLqJCOVAJr6UUlKTqZFpeNq5EF3NdJKpns5fvw4Xn31VX49LUofUmQaO3asADbdSXBSeNYVhCjTByg3780330RGRgb/7a7nupkiKqUeNPWlt7c3H+/0rG/FqqqqoNfrVaFto9Holkx98+bNwrvapUsX/t2QkBC+EfPz8+ObUSqscTgcGD16NP/9Q4cOFQCEzWYTZB9PnTrFve7KcaPT6RAbG4sHH3xQyBukKE1BQQEHimFhYejZsyf3NLp7D5SgcenSpTh27JgK3FAqiCRJPD1q2rRpuHHjhmYVNV1r3759wnloQ7x27VqcPn2az53K5yDLMqKjozF06FDs3LkTzz//vOq8JpMJ06dPh91uR0VFhSolKjAwEAUFBcKzpPntbjZKO2CM8fSbxUuehyEoFl6xzWEObYLg8CgeRVIWsWVlZd20l73Rbt8aAeVN2IoPb13aSWj/3UXljF94x18y0hZ2/XtwcLAAUJKSkvjvoRC0a27dlV61rScAACAASURBVCtXOG2IFvWJVjMajejatatAQq6VwF9TU6PiOGSMYeDAgQDqFiElmTdx5plMJr7Aenl5udWzJmvZsqXgCZNlGSkpKRwweXh48AmTjIjWXcnMn3nmmZsaIw6HQ5BjpOMtFguvVlZyLlZXV2P+/PnCguHh4cEn/0WLFgm5S9euXcPy5cv5bwgMDOS8eqNHj8agQYPQq1cv5OTkoHXr1khOTkZkZKSwYBoMBq60c6sTuZJHMDAwEJGRkUhISECLFi2QmJgojLW0tDTExsZCkiS8+eab2L9/Pz744ANIksTHYXV1tbC5MJvNmDRpEmpra/H3v/8dM2bMQKtWrYRNiyRJnPy6pKQEdrudk7gzxjhXqvKY9PR01QKuJPvWMovFgsTERP7vyspKgTrFdVNz8uRJQV1EaQQop02b5nbsUHHJmDFj/j97bx4eVZV1D59bc6UyV+YAGZhCIIyBhEnmMRDEiEGQMaLMAiICQiOCiLQIgraiNIKAgCPIII3QgNKIwYgKTUdETERExYgx5ouxvL2+P6r3zj11byUB6f75dmc/z3kgNdy6wxnW2XvttWus927UmjZtimeeeQaqqqKoqIiBmbY0qT+jhAoCH6RBS9qulKR1LbZ27VqJEzhixAjurzWZbzEDiiqQlE/r1q1htVpZC/a2225j725CQoKunjclwU2ZMkV6na6tSZMmOH/+PObPn4927doZ8tGrC0ubzWbExsaiTZs2kuh+SEgIZ3nXZBSNIZ6xVtHi0qVLsFqtsNvthioU4eHhyMvLwxtvvCFFGLStUaNGyMvLw5EjR3Qb49zcXP5MTfN9RkaGoWTVY4895rcy2L+r0TkalfA1cnSYTCYEBATUWoe2zq7P6gBlDbYtv/iGyhZ0HXv/v22Q5eTkYMeOHaisrJQyX4UQUnWZbdu28cJfU3ia6sD26tWLJ3G3280JKxS+JY8mZRNqeV8bNmxgINSiRQtcuHCBJ1Eqz0jH3rVrFwBvmIU8nZcvX0ZJSYmkp2YE9FRVxQMPPMDnTpM7he9UVcWyZct48rPZbJgwYQIKCwtZd1Nb/9iXRlCTUWULs9nMnh9tCwkJQcuWLaWQEYXvIiMjERkZ+ZtKmfny/UJDQyUxZxKeHjBgAHJzczFhwgTcd999ePDBB3khdTgcOp4gia2Tt9pX3Hru3Lk8adPvEEeXjADZ22+/jcmTJ0teE4fDgSlTpjAHV3v/k5OTuS+TWL3WSD8wMTERv/zyCz/npUuXcn+m50EAcseOHRDCuPJPZWUlhKgS3F+1apUEMp5++mnDZ3/p0iX+TEpKCodjawKU5JEy0qlUVVXi4tX07AMDA3mDEhwczP0/LS2Nk8iMjK5v0KBBAKqqT5HskpG0ldG5Pvjgg7r+GxQUBFVVER0dXStACXi9/kYlQk+ePMnj89NPP+XPmM1mvxs/UkbQ6pgC3rFKFXeysrLQokULwxrbRi0xMRGjRo3ieYS81bQZTUxMRJ8+fWoFKGku1soYhYSESBEk6iPaggzx8fFITk72myyWnp4OIfRJOr5G111eXs70Hn9Ny0f3eDyYN28eb3qdTieXvV24cOF1z2HX2q4nGWj48OGSRNIvv/yCZ555BhMnTqy1pmmdGVsdoKzGvigpR5MF+5D6hzfx9JHzOHruW3xX5s2EXPXWJzqwmPP037Atvxgff/kDfvb8CgDovPyQ5Kmsf++rCIpNvKGDKjIyUqqqQpmZ5HVwOBx+QaNWFqVXr15cyUUIgfHjx+vuCYEHIYSUkEEAsby8nBMmRo0axck0TqdTV7LNd1IgIv9rr73G9ADtQtiyZUtYLBbJI/Hxxx+jsrIS06dPl3bwAwcOhKqqCAoKMgxFrlu3ThJiF0JwWJdCJiaTCUOHDkXv3r2RmZmJtLQ0NGrUCPHx8YiIiEBwcDAcDsdvEnemesLh4eGIiYlBQkKC32MlJibioYcewvr169kbsWDBAvz4448S/8vXCCCQDuHDDz8sva/lPObl5QGoXmxdCIHOnTtj2bJlnMUaFxeHS5cu4ezZs1Ko/tVXX8XZs2f5/pK3x+FwICoqSrpWq9WKpk2b4u6775a4fwTyhg4dKp33ggUL+LqMEnyoHrS2n91666349ttvYbPZuMa41g4ePAghvFwtug4CXDk5OX7vMQCMGzeOfyswMBDvv/9+jYAyIiICNptNd/4fffSRLnFNe6/q168v9Xen04mwsLBqs4WDg4PRvXt3TJ06FZs2bUJxcbEkRXX06FH+fa0molaiydd8x15gYCBzewkML1u27JoAJeCV8yJwqgV6tEHS3gt/WrBlZWWw2WwICgrCkCFDqk2EoXnRZrPh1ltvxeOPP85qAZ9++ilWrVol1bmnZuQ1jIiIkHQo/dlXX33FMk9aPqhvcqOqqtIY1Ta73Y4mTZqgYcOGutC22Wz2m/hGxw0ICIDNZtMBM5vNhn/+85945ZVXJJWAPn36YNSoUfxbISEhWLp0KVRVRb169RASEsIg+ffazGYzIiMjsWPHDmzbtk2KEv34Y11Jxt9idYCyGrtj/Qkkz9+LzssPofT/+wUnPvsOL77nBThGgPLxtz7Bxe/Lsf/MZRw/7601KgHKuXvQYM4uROU+dEMHiM1m40xYfzs2LWicPn06T45awKZdEIXQ1+z1/Yw2QSY1NRUOhwOAd5HRLuQ333yz4cRGiw4tDllZWdi7dy977bScl59++gnZ2dkQQuDFF1+UdC+pWa1WXlCbNWuG5ORknvApnHw94s4UPnc4HAgKCoLb7UZcXBwaNmyIFi1aICMjg/l+o0ePlsj82tagQQO0b99e4oXGxMRg5syZKCkpker83n777dJ5kjwOWXVaer728ccf83MgcEii0qSTSMDfX4i0srISW7ZsMaz4ZDab0b59eyxatIj7kxZUVle1Ji0tjUFCdeFZp9Mp0TbovIWonpZQVlbGx6f7Tgk7QggdfUIrbq0o3nKbiqIgJiamRu9FRUUFe4fNZjNMJhMefPBBCGEMKFevXg0hBGbNmgUA+OGHHzBnzhxpAbfZbBg1ahTOnz+Pzz//nMc3ebT279+P7t27S0BSURQsX76cOZvt2rWr1pNDzyc8PJzBZlFREfdFo7KRVPqUftftdnMCFn2HNnQBAQGIioq6JkDp8XjgcDj4vCMjI6WCAkJ4tXTp9+rXr18jaKREmA4dOmDUqFF4/PHHpflg6NCh0jNu06aNrvzpkSNHGKx16dLFcLNF51sToKQx8pe//EV6nTbngwcPRlxcnG78NGvWjDcCZrNZStYjJQlqlFi5ceNGvrajR4+iT58+kue9efPmeOqpp1BaWsoh48GDBwOoSsrRgmeLxYIFCxZI592lSxfp/etZy/5fNO39/e676muE11n1Vgco/di5r380DFm3fsg7+I0AZeK8qv8v3evlmvgCSmoWd70bPjC02bNa8XGjBSE/Px9CeCtAlJWVsd4fcWlIOkdru3fvhhBenqHT6YTNZuNQUnBwMBo0aIC33nqLF24CigMHDsTy5ctx//334+6778bw4cN59+9PhuV6+X7UnE4ngoOD+VyCgoLQqlUrdOrUCX379kVOTo5UlUQIYSi5061bt1r3mcLCQuTm5urCfk6nU5fZferUKQwdOlTiv9Lzo9CZ9tq1maWUge8rB1KdhYWFISwsTKr2QR5at9vNGwWjMnJaU1VVym5PS0tDgwYNdJ5GIy+r2WxGu3btMG/ePCnDvqysDC6XCxaLhQWpfY087AAYRBBoq6kSUGlpKYfzpk+fzqFOIbyeVSqD9/rrrzOAIZmikJAQmM1mnSKAPyMh6dmzZ0v96d5779Xdx8DAQAQEBODRRx/VqUAoimKYbPXss89yX/E9Hgnta/tTly5dsHv3bgDAwoUL+fpo3AUFBTHftbrxFBERgalTp2Lt2rXo06cPP9+4uDiu6FNYWAiTyYSQkBB+JqSHGRAQcE2AcubMmRBCYM2aNVKpw5qaFjTSRuKtt94y3Hhp9YGXLFmie5+qAvnaX/7yF5hMJjgcDtx5550QwgsgjTaSgYGByMjIwOLFi6XNOyUg3n333ZKIuG/UJCQkBF26dOH5UlEUvr8nT55kL7aWYkRar1OnTkXr1q0lKop2XFLBAV8NXNKjFULgwQcflLRfY2JiJJ55q1atcOLECSxatIj7UEZGBkpLS5mf+X+pffXVV7Xuo3WmtzpA6ccW7TpjmNFdHaDUtuoAZYM5uxA1YMoNHQg0UaSlpXGpLwpnG2V0A2BtSQI1Xbp04TAVkeHT0tLQv39/dOjQgSeMuLg4qQzX9er7af/W7n4VRUFKSgq6dOmCAQMG4LbbbsOECRN0ZQbj4uLwpz/9CcuXL5fCPU8++aR0nSRQrTWtBIvL5UJBQQEAoKCgQKoQIoTXI+rPLl++jEmTJkmeisjISMmT66uF6Wv79u3TSRA5HA4sX76cr1lRFOzbtw9AVTankQfZn1Ht7I8++ggAMGvWLP6t5557Dunp6TqQYmSzZ8/m7w0dOhQVFRXYuHEjBg0aZKgs4Ns/IyMjJT4v2eHDhyGE14tr5AmkRLInn3wSQgjWCW3dunWtrr+kpIS9ks899xxOnTqlS56i/1O4kegf/gSwjUxVVbhcLrhcLpSVlbHGY2hoKHtDVVVlbzs1s9nMlAu3243z58/7/Q26juXLl0uv0zPdt28fHnvsMQmkOp1OZGVlYf/+/ewBVRQFq1atAlDlmd2wYQNXp7JarToQ4ttHk5OT0aNHD0yePBnBwcFQFEXSYwTAvxcZGen3mn788Ufs27cPCxcuZI3E6n7bZDLpKBOKovDmQFVV2Gw2JCUlGf7exIkTIUQVnYG8xFozmUzo3Lmz4fe1nsDY2FiOwGh1PIXwAkrtOTqdTqlKkK+IeHh4OMukUSKStk+RV5uSv0pLS7mPNW/enDPhhfB6cO+++25DbqTD4eCNlVYn1vf+aNv999/P7587d06iR2nHEBV5uHr1qt9yvb/XVh3XuM5qtjpA6cduWvHXa/ZQ1hZQJszdg4Spz9/wwRAYGIiePXvyBENeHyG8Hgmn0/mb+H40CYaFhSEmJoZ3x1ow6Ha7MXr0aMydOxePPvoonnzySV4A58yZg9LSUgYM9J3WrVvDYrHAYrHg/vvvh8lkgslkkuSDKEFACK+3w1dfjxJihPAuznPnzuX37rjjDgghOAO0tLSUJ7p69erpvIdUbk0bYmvcuDEDurKyMixcuJAzYoXwenpyc3M5C/Lq1av8XvPmzf32M1VVGbwL4fXuJSYm8jPS/msymXDw4EGd3lxtjLh8JKpO2ZEkxeF0Og25pmSVlZXo1KkThPCCIyOuni+vjQBbUFCQbtPhcrkwduxYSWydtBCpRJ3WiC8phNdrs2TJEgjhBYe1tW+++YY9c5s3b2aQ6tvq1avHC3fPnj1rfXwy0v+bO3cu33caO23atJHuRcuWLfH4449zX8rMzKzR4zpp0iQI4QVQ2qzm+Ph4BAQESJ8tLS3F3LlzJQkVIbyLP20kGzZsyNqG2ix1i8WCZs2acYIHjb2cnBz07NmzWukjKrrQo0cP3qSSyP3ChQsxZMgQNG/eXOLV+utPJpMJw4YNw759+9irJoSAx+Ph5BDtHHTPPfdg+/btEEJg0aJF0v0oLy9nbcyGDRuipKQEAQEBiI+Plz5HlcWmTp1q+Ay0lAuXy4Uvv/yS31NVVaIYhIaGon///jrvo3be7tWrF44fP87HUBQFN910E4Aq3vpjjz0GwFuFSgiBJ554gj9PpUCNMpyDg4MxYsQInDt3Dt9//z1mz54t3ceQkBCMGTMGFy5cQH5+Pt8f36YVNq+oqGDpHt/Wvn175Ofn33CJvP9EGzRokN+a5nVWs9UBSgMr+9mjq4BzwwHl/bththvrOP6Wpp3cXS4XA6ekpCS0aNECHTp0QM+ePaUFpmHDhnj88cc5PJWRkYHPP/+cJ00Cc77lw86ePSstBn/4wx8M76c25Kj19tD3LBYLzGYzT6gFBQUMVrVhw44dOyIkJAQxMTGGvyGE16NK3sKYmBgcO3YMn3zyCYTw1g0vKChgMOTPe5GWlsZeKgJRdF+11+twONCvXz+pzBzZkCFDpAl+9uzZus94PB6JL0ceP8AL4FauXCnJeWhbx44dDc+9OqMs8nXr1vExiouLeaELDg7Gr7/+Kn3nypUrmDt3rt9FPzQ0lD0iJpMJAwYMwMWLF3nRM5vNnHBw+vRp3HnnnbpsWq3YOvXLN954QzoPyt632Wz46quvuLzmtWZlXrx4kQXUtUkfO3bs0FUPcTqdNYI7fxYWFga73Y6XXnqJ7w0dl67/qaeewuHDhxkMzZw5s1bHpmMqirf8psfjwcWLFyGEl4fszyZMmKA7F/ptAoFWqxWqqrKYOLWMjAwOdfrqe27evBlCeJPk7r77brRq1QqhoaE1ZuAqioKAgAAkJydj6NChWLVqFctL0WeysrIkeSdVVRkMud1urjzkLyNem9195swZnk+GDRvGfYfCyVpdRaIPvPLKK7r7SJSLyMhIpiAEBwczXeTChQuSF1h7PjSOhg0bhgkTJiAlJUXy4pGUkc1mQ0REBCoqKtiTSUYcdZPJhE8++QQejwerVq2SFB2oHThwwG9/aNSokeQZ951faNNG/YWkl0hjVwivakdRURFKS0t54659vps2bcL+/ft/c536/1QzmUyoV68e/va3v/m9b3Xm3+oApYGdufSDX6B4wwDl3D2wRiXdsIFA4cpNmzZBiKpsXfK0kByPb4gkLCwMoaGhAKo8RIcPH+Z7QRNBbGwsT8AejwdjxozRTZZUqs/IfEOOVN+XBrH2N1977TXJ++dyudjzZ0SUB4D58+dDCIGdO3dCVVXMnj1bSvZxu92SFyMsLMwvGAkJCUG9evWgqiqDL98WFBSENWvWGB7jyy+/5IoeTZs25WonvvWNacF1OBy6MKHWzGYzZ8nS79vtdvY61NYoM5wqGtFCTVqEQnh5lffeey8yMzMNJWCGDBmCzZs3Y82aNZIHKTc3V6pwQn3szjvvNDyXDRs2MLByOBy6kL8Q3qSAHTt2sMyPEAK9evXiMnMZGRm1vnayiooKCXiYzWbeoOzbt49fo/fdbjdWr159TcC1qKhISlCgPjx27FgeT3a7HUuWLGHKiG/1lershx9+gBCCOXsDBw7kEKXWy6U1Gh8JCQmorKzExx9/jJycHEMvkva5N2/enEGbx+PhDc7NN9+MhQsXSvfSKPJB2fw0V7hcLsTFxdVYFclsNuOWW27Bxo0bpXKVQJU+rRBeAKatEqX1pmqP8+STTzIn25fCcOzYMQghA2WqDuZbjefpp5+GEN7QNFEYKPGKRPp9ryU7O1uiH2glgshOnz6NWbNmIS0tTUf/EcIL8Pbt28f9kDjw2qQiivJof9s3cUZrwcHBcLvdEsVH+wwbNmyoC9nTvOx0OnXC+b78aupLDz74IKsn/F9oxM32JxFWZ/6tDlAa2AfF3/9HAKUt9saVYzSZTFi8eDECAgJgsViwZ88efPjhh3j77bchhFeMWev5I927sWPHQgiBU6dOITY2Fi6Xi+9DeXk5T5AUKn399dd5UUxOTsaZM2eYBF6TALI25KgVwqW6vM899xwfiyReSPImKCgIp06dYi6gb3m2hIQEXR3xixcvMqFcu3iZzWbdIqU1SkjyXRwmTZqEsrIyTJ06lSf9oKAgLFq0SAIcpLnocDiQkpKCoqIiLpF5+fJlrkgkhCw4789iYmLgdrsBwDBsFh0djalTp+qE6n2tuLiYv0Pg9pNPPpHC39rjUl+xWq04dOgQ6zuSl4cWr759++p+i96rzsOnFbs3mUwYN24cli5daphJTp+JiorCokWLIITAtm3barx3WtN6Vho3bix5hoqKiiR+6AMPPIBp06ZJcjgLFy70CyxLSkowa9Ys1sWkPkf9jrK8b7nlFuma3G73dVXwsNlsaNWqFcvJBAUFISgoyPCzDz3kVZWIj483VFs4dOgQbwB82z333IPs7GwOT/ujy4SHh3P29KpVq3Dy5EnJ2x0dHc2ATlupqqioCOvXr5c2kL7jlf4ODAxEUlISRw1atmzJz5AiACQVRHOWNoHEZDJJ4FNrvvJidGytPf/889wXxo0bp/Mu0m+MGjVKAra5ublMKaDratiwoU4kXGu+HFtts9vt0nMIDg7GunXrOEyflZXFSZYWi0UHigGv+Dx932Kx4Pbbb2eAfODAAfTo0cOvBFVmZqauH5WUlEjKDj/++CMWLlyok776v9BoQ1ldMYI6M7Y6QGlg/xc9lNfSLBYLy9+Q14s8FRERESx/Q+DO4XDAZDKxd8JXWJyyVYWofkcMeEGedhKmeuJasfG8vDyJ10jl7UwmE4dVtIkyV65cgRACvXv31v1eaWkpXwe1ZcuW6T53+vRp5OTkSBykxMRELF68GJcvX4bZbEZcXBx/XlVVacJ0OByYNm0aPvzwQwghuMQhlfh77rnndM/BKPveyDp16gSTycS8zFatWsFkMsFqtaJv377SpJ2YmIgHH3zQsAoMeV1MJpNORFwIr/ehV69ekpcjISEBX331Fe69914GYy6XC3PnzoXH40Hz5s2hKIoE0IlDWNtKIfn5+VIY8+DBg8wJo+MYhcx69uyJtWvX1sh5Ki4ulvRQiZt75swZXjSzsrJYP1W7MVJVFYsWLWKvncPhwNSpU1FRUYGKigosW7ZMWkgDAgIwZMgQFBQUsCoCLU7ffPMNi8/T606ns8Z620YWFxeHsLAwlJeXc58dMGCA7nP0LKKjo/HTTz9J7129ehVjx4411FL0bVarFXFxccjIyMCIESMkKsrkyZNrPN/o6GhO2iJuIOANLVM/pDmIvPVFRUXYvHkzpk+fjl69eiE5OVni5vo2u92Obt268bnFxMSgRYsWPK/Q5zIyMnQVdXJyciCEwGeffQbAm/gUHx8PVVVx6NAhQ5kyu92O1NRUTJ06Ffn5+fjjH//I97pnz55QFIXFx4OCgmA2m1FYWIjRo0fzZmPMmDGGGejajP01a9ZgwIAB1WqMtmnTBl27dpXuH817AQEBKCgogKqqWLJkiTSW2rRp41erUlVVSXdY27RZ8cePH+c+SBv4U6dOAfAm72jnk9/C3/9Pta5du+Ldd9+tsU/Xmd7qAKWB/fQf4FA2uH83TDZ9mO96m9lshtPphMPhwKZNm7B69WosWrQI06ZN40FsNpuRlpaGtLQ0NGzYEPHx8TVWR7ie5na7kZSUhNTUVKSnp6N79+4YPHgwRo4cyR5G3+ZwODB9+nS/Hq2PPvpICsVRBiRQJTGiFVoHgJMnT/IipSWaK4qCSZMmobi4GBMmTJDuAYGzrVu3SscieRBfrURVVbF69WrdfSwoKGBAeebMGV1JR98SfdXZ5MmT+ZqF8GZl7tu3j6VLzp8/j8OHD6N3795SvefmzZtj1qxZyMvLkzxn1BdSUlIwceJENGnShGkE586dk7zH0dHRvCCEhYXh0Ucflbx0p06dghACnTp14vvhcrl4A3AtppW10T4vuufa8KpvaC8kJIQ3J+SpVVUV99xzD/f/IUOG6BZPOn9t803SomOtWbPGcLxYrVZ0796dPe1aI5HvSZMmScLYc+bMwfbt2zlkSQkXtbWuXbvy/aXkoujoaOnZECc6ODgYs2fPZk9jWFiYISiz2+0MNvyFr/v3749jx47h1Vdf5ddXrFhR4/kSZYP42Hv27OEwsMvlYjDWvn37Wl1/eHg4goKCMH36dPTo0cOQMqHtK4mJiWjfvr1EG2nRogV76mkjOHr0aM7gttlsuvuQmpqK++67z693kXiHBJIpQiSElzNLdvbsWZ4TgoODdZ7T119/XXcdMTExmDFjBq5cuYKSkhKsWrWKQaTv/NunTx9MmSIriRAgdblcnKHtj2P5448/6qqtUeEF+ttmsyElJYU3SS+++CJTmZYvX46ioiIEBARAURS8/vrr2Lx5M9N/fq/t0UcfrbZIRJ1Vb3WA0o/5ZnmP2fAeJm55H7Nf/hAAsPujS5i45X1M3PI+mi7ch4S5e9BmyQF+7ZUCb1jngdc/xsQt7+O2dcdlQDn5zzd0INACofUcXr16lTOIq6tdTFmjFO4+ffo08+x8yeWzZ8/GrFmzMH78eOTk5KBDhw68mNFkQwkP15tV7q+EYP369SXA1LdvX+Tm5nKYf9myZVi3bh1eeeUV3HPPPSw78tBDD0FRFJ7kfTMhQ0JCMHLkSJw7d471O32BR2VlpY4c72t/+MMf+JgEqMijoiiKFNYj+Z7aGHEIw8LCWDweAHbu3MmJDcXFxVBVFXv37kXXrl39ynUQxUHrzXW73YiJiZEADnl26FqqAw0Udv3oo49YM7Bhw4bXDCgBLy2CwnX0nInvSVw1Ibyc4MrKSrz44ou4+eabuR42ve9wOBh0RkdH48SJE35/U6tHaqQ7CHg1WLt06aIDsoqiICsrS1faj+zll1+GEELyIhOfGfACeEqKyM7OrjVX85577oEQAufOnZMq5NSrVw+pqamG2b5CyPxQq9WKgQMHIj8/n3+XNE6F8IK7qVOn8t9GoI28gWvWrKn2fAlQUoIcteHDh6OyspI9W59++mmtrr99+/a60qiPPPKI4TXHxMRU69k0mUyGHnCr1crzp8PhqDU1QVv+9dFHH+X/G31/5cqVPFbT09MxZcoUCXRRCJ08p0am5SdGR0f7FVsXwsuJ9Xg8TDUx2sCvXr2az6lDhw7MGxXC68EliS9tCwwMxMiRI7kqVr9+/VgBQFsAAwBHAn6PzWhTWGe1tzpA6cd8dSgvfm8MxoAqL2TuOmNCPAC8+9l3VYByzi6E97773zYoHA4HIiMjeSEgr4pvVRAy2kXHxMTA4/FIXhiTyYRp06bh+PHjEEIfpqUd+ZEjRwBUeUV8PXCffvqptBhrdSwVReHa0rm5uZgukwAAIABJREFUuRgwYAC6du2Ktm3bIiUlBQkJCYiOjkZoaOi/RYrC4XCgRYsW6NSpE3vXxo8fj1mzZmHJkiV46qmnsH37dhbqXbhwoWGYqnHjxlAUBS+88IIUZnc4HAxaUlJSYDKZODu3NqaVIOrXrx+/7vF4WHvQd7EMCAhA27Zt0bdvXylUZrfbuVwkmclk4vPVgv/ExETWwbTZbNizZ4/h+V24cIFBqM1mQ3h4OHr06HFdgPLUqVOsf6gFRS1btuTkCX811j0eD7Zt22aY7ep0OtG6dWvMmTMH//jHP6TvaXmNJpOJw6H5+fnIysqSgFSTJk3w2GOPobKyEvv27ZM2bN26ddMlSRUWFkrnYeQRqqioYM9dQkKCYXJbaWkp9uzZgwceeADZ2dk6GSBtI9BoNptx2223YdmyZejTpw+/HhUVVW3CAS34lFBVVFTEIN/hcOjGIPW9P/7xj36PSeNXGyqnCi/0XI0oK/6MMtZ9gbwWuA8dOhQ2mw0Oh4M514WFhcjLy0NCQkKN+rk0bhRFwe23347nn38en3/+ea3OT+vJo/uVmZmp+1xlZSUeeughqY/RczKZTH43OL5GdKScnBxcuXIFN998s9+NPG2uLRaLpLtYWFjI9I2goCDOcKdKOUJ46QJXrlyRIh7Z2dl+I12+ER0C2H369DEsJPH/uvmqS9TZtVkdoPRj/irl3Kh2Iyvl0MSYlZWFrKwsv3pntCDUq1cPHTt2xLhx47B27VqWS3E4HGjZsiV/liQhyChkV1hYyK8NGjQIQggJHJFkzOrVq3Hx4kVd6ITkh4TwAiSqiuMvQ9XX0tPTufwZHXPHjh148803GRjFxsbqeEfaJImkpCROFPBdGK+lEZeRfkf7f99mNpuRm5vL4LJly5Z488038f777+OLL77Azz//7PeaaXGYN28eBg0ahOjoaN35ms1mzJs3T9LEmzZtGoQQGDFiBBYuXCgtdE6nU6rlTC01NVXKuj9w4AB7d7X6nlrThqM3bdp0XYDyzJkzHGb861//Co/HI1EkyGtKCUq+5utZuXz5Mg4ePIixY8eiYcOGEoAg/hv1X7qX5NXWApP4+Hjcf//9hskNgJdDpq2S0q5dOxQUFODSpUuSt0ib8GZkRGmwWCzo1KkTUlNTER4ebii/Q9dJfe2BBx7AoUOH+BoDAgKQn5+P/v37c99p0KABXnrppRqfA/GUR48eLb2+fv16Pn5ISAgOHTqE3Nxc6V653W4sXLhQioaUlJRI42P+/PlQFAWNGjUC4AVDJpPJr5fXyEiqiMT9tSLyNpuNM5eTkpL43vsK77vdbvTu3RuPPfYYRowYUetIijZBqHv37pg8eTKef/55yQPZp08f/nxiYiInEn3wwQdQVRUbN25EmzZt+DctFgtatGih40MbKVoYGckIac8zOTmZAdyECROwc+dOHfWG5n2tdNCoUaOk+ZwAJVEUaC4YOnQoTCYT7HY7zp49i9OnT0s14OkaFi9ejPLyco58hYeHw+Px4OzZs787TqWRTFSd1d7qAGU1RrW8bySQbDBnF6Jzl1x3ScHqmqqqHLINDQ3F2bNnUVJSgmeeeQZCeL0fzZo1Q1hYWI0acZ07d8batWvx4YcfcjjsH//4By+YZI0bN9aJKVdWVuokZ4Twgq/Q0FBJ2Pz222/HiRMnWPKCKtZUZ3l5eRBC4OjRo3wfe/Xqxbv8uLg4KeTrdDrx3HPPQVVVzJs3D0LIYcc33nhD2i1nZGSgvLwcRUVFyM/Px969e7Fp0yasWrWKwXFqaipuvvlm9OrVCxkZGTpvR033t6YFy2KxwGazwWazGXpSLBYL3G432rZti/HjxzMwDAgIwNatW/Huu+9i69atEEJffebcuXP8PLTHjIyM9MupunTpEofiunTpovOukoA3eQ+vFVCeO3eOk7/efPNN6b2PP/5YOlffkqD+PCtGduLECUyaNAkpKSnVJjkIIXDbbbdJGck12dmzZ7mspb926NAh7N69mz2N1YFGi8XCiTCjR4/G6tWr8f777/OzpGxfqkCjrd6iTbhKSUnR8Yurs1GjRvH3tEZRCjq2yWTCjBkzoKoqXn75Zd3mjAA79V+r1cpREpqnSM6IVCRqa5SIN27cOJw6dUqab3JyctCxY0fdPQ0ICEBWVhY2bNhgSP+prKzUhfXHjRsHj8eD4uJibNmyhROEGjZsaBhGVxSFoxxCVEWHqH8GBARwv6NKTxs2bOBnStng2qbVxzQyrawWnQMVYQD0GewkLSeE4KiK9vt2ux3NmzfHtGnTUFBQwIBSCxZpY6Llcp86dUrS1e3Zs6c0D1OWv3aOX7lyJb+/adMmv7q7/6lWXVW0OqvZ6gBlNfZFSTmaLNh348Dk/buRMPs1WMNi/y2DQVsa0beElFEZsZKSEmlA+x5H2xwOB+Lj45lrdO+99+LDDz+Ey+VCw4YN+ZgnTpwwrGlLIT1tZRMhvIASAI4ePcq8Sd8MTF/buHEjhKjiJxnxBRs0aCDx78hIAF2baQp4ky5IjFwIr0fPX0g6PDwcNpuN+UcLFy7k77ndbhw6dAgAeOFITk5GZWUlzp8/j27duunu78yZMzFz5kwMHz4cLVq0qFYU2mq1wmKx/CZeqpFWnvacAgIC0KZNG8ycORPLly/Hs88+i1dffRVHjhxhT0tkZKTkvdZWzXjllVeuCVBqyftaoK+106dPS+ebkZGBr776CmPHjmXPs69npTorLy+v1pNP9+Tmm2/G3r17r0mHksKxtWkOh0MHGl9//XUGIgMHDvT723T+d911F/bv3y954OkZVadv6s8oEqEoilRSkDKVL1y4gBMnTnDYMyIiAocPH5aeo68MkNlsRkhICF/Ljz/+yP3YYrHgxx9/vObzJMBtNF8pioL4+HjO7qdmVIRAa9p+TJQLu92OSZMm+c2G/uKLLySwWVO/MplMSEpKwl133aXzbFKSy/Hjx1n5wGq16kLHAPDOO+9IXOdWrVpxVn9aWhp/jjLYqZynr4QRJYUdP36cN1vaOVU719C8pN2g7Ny5U7o+kkV77733oKoqtm/fLm3YzWYzMjMz8dprr+GVV16Rzh8Avv76a0Ox9f9EM7rPdVZ7qwOUNdi2/OIb6qEMbNnnhg8Cf+AjMDAQHTp0wKJFixAaGqrj4xw6dEhKcqHJCwC+//577Nq1i0Os5Nk0AjLECdTKj7Rp04bDN40aNYLFYtFVuBGiClAC3tAqhVC0YXVfu3z5MoQQhl5Qi8WC/fv3Iz4+HoqiGC4gDRs25IogWlu+fDmEEOyJCwwMxI4dO3Tfpx3+mDFjJBA6ZcoUPiZpJVosFt1CdOXKFdx6663SvdRO4IqiIDY2FkOGDMGWLVs4kUYIoePoqaqKK1eu4MyZMzh8+DDL7dCxb7rpJgwbNgz9+/dH48aN/fLGbDbbdXnNjWq5m0wm9vR07twZ/fv3x7Bhw5CXl4d7770XS5cuZV7q9u3b4XQ6oShKtbqSWg1N30Z6qDWZqqp45plnJJChKAp69eoFt9vN3qUFCxZwqFT7ufj4eOTk5GD79u24cuUKdu/ejfnz52Pw4MFITU2VsuP93SshvNn6JOPizyorK7mmc/369Q01Rgl0ktedWteuXRnsEbf5WsztdjMAeOSRRwCAhdp9uZcPPPAAzz99+vTByZMnpX7duXNnKQnDbrejT58+OHr0KOu1duvWrdbnRgLgWmqOtkVEROg2AMeOHeO5yWq1+k1O/Pvf/y6VqgW88j1EW/DVazSyixcvGo4xX++tkWeTztHtdmPy5Ml47LHHpO+mpaWhuLgYu3bt4tA1bRQjIiL4HIjrTfSUjz76CEJUURiIkkRznBBVZSh97/XEiRMN1xez2YyRI0di3759KC8vZwBotVoZJJK00Pr16yGEl4ayZs0aNGvWTLp+7f/Pnz/PddgTEhIwfvx4vp90HkaZ7TeqPfvss7Xui3WmtzpAWQtb+9dzv90zOXcPgjsO+02h0Jraiy++CI/Hg127dmH48OFo0KCBDgC2bt0aM2bM4Mxc7UDNyMiAEKLGqh3EuSTpidp6y3r06IE1a9bg1KlTUFUVQsiAEvBm01Jtad+syKtXr+rq0ArhFVU+e/YsNm/eLN1fo3KHQFUikW/2oTbzcc2aNezJa9eunY7f5cvH0soYETClSjlkhYWFuP/++9GmTRvDjFmr1YpRo0bpMi/dbjd/vqZsWqBqwXA4HCgvL8eqVat0O/7ExERejLT6moAXeL3wwgto3bo1P1tFUVCvXj1kZ2fjrrvuQs+ePfk98sTGxMTwedIiQWGua+nHxEt1Op0IDg5GRESEVKfd9/Mulwt33nknnnjiCWzZsgX79+9HQUEBLl68iMrKSrz22mvo2LEjL0x0PmFhYezRtNlsDNBoE0Liz2azGaGhodX2c63ETExMDFauXCnVe9aKcCuKgmXLltXK60lJVw6Hgz3fZL7n07VrVw6PFhcXw2KxwOVy6fQnazKTyYTMzEzOciZgYyRgD3gz8ykCQY24qMTFjYqKgsvlQmJiou7eEXgzMi1FwZ9ywZtvvslRAn90h5KSEg7Hulwu3Sbv008/lTbEvtzF7du3My/TZDJh4MCBUii6pKREkqiiNm7cOPbkU4lHIbycb/Js3nPPPejdu3e1a4Pve4qioF+/fiwvpNUCVVWVVQ+Ilx4WFobg4GApg5zC4qTyERAQIPHYtWVBhRBYuXIlFixY4Nd7SPx1AqmDBg1CUVER90MtkC8rK5Puh3YcUXU3qsP+yy+/YPbs2ZLT41rmk2tpTz75pN++WGc1Wx2grKVtyy9GkwX7rplTmXj/G2gw+zUEte73bwWTiqLoFhzAO7kcPHiQOTzaCU+70CcmJqKsrAyKouhC4772ww8/6MIgI0eOxA8//IDvvvuOJ96EhARJ9NmoOZ1OdOzYEWPHjmWw+fLLL7O36MKFC3j00Uc5m5YmHfq/b6UZmoyEELjlllsMF21/pfuaNm0Kp9PJf5eVlbHGHyW8FBUVSWEmOk/6Hfr9yMhIOBwOhIWF6UTEzWYzkpOTMWbMGLz11ltSMgFN7HPmzIHH42HeKoWtfOup+1pBQQEDcu0zJj6mEN7KHaqqIjU1FUJ4OZH+jLx6LVq0kI7Vq1cvvPrqq5J4cmVlJTweDxwOBwNJrZWVlXG4dOvWrQwSBw4ciKlTp2LUqFEYMmQIevbsiQ4dOqB58+ZITk72G9a8nqbtt1FRUUhISOCMaS3gNPo9q9WKyMhI1K9fXwLP2paUlMRi65GRkXzM++67j4Xg6bMBAQH8enW2c+dOznxfunQp1q5dq5O5MeJIEjWkQ4cO1R5fa1SGc/LkycwHVRQF4eHh+OWXXwy/c+nSJUk3VAivV9ViscBsNuNvf/sbywYBXgBK3lftvZgwYQK2b99ebRLVbbfdxvedKioVFxcjKSkJdru9WpCuqiorADgcDtaS1Ibqx4wZw7+pTUwjO3DggFTJKTExURfeT05ORseOHQ2F/ckr61uFZ8uWLRDCK+sFeD2dW7Zs4bFU06a9Xr16nCC0YcMGHDlyBGazGUFBQSgtLZXKK4aEhOh47y+++CKP2ZUrV2Lp0qUcfSCd3y1btgDwzp9WqxVut5s3YUYgz+l08sb76NGjumcREhICh8OBixcvSvedWl5enrSRj4qKqpUI/29pCxcu9Nt/6qxmqwOU12BflJTjjvUnWPqnWjD5r/ejch9Cq849/20DICoqSgJYLpcLOTk5Oh4ilV+jgd6vXz+dVp3FYuGF6/Dhw7rJWVVVPPjgg7pQM+08VVVlPTmaGAmQCeHlNe7cuZPD6DQRGQFt3wnUZDJxAop2sdeGgL/55hsGTsTjTE5O1oVyAK80itlslq4xMDAQiYmJus8eOXJEIpsL4a1lTCFOKsl377338rlqr4kEgCdOnIi//e1vuuOXlJTAbrdzBiyFG202GwPyM2fOwG63S9woX6usrERoaCgURdH1CfIYaXfglBBR24o95eXlWLx4sRQO1j6LiIgIfPbZZxKn1MhKS0v5ftbG46oV0dZ6hqmU4PHjx/k++YbgXS4XGjVqhBYtWiA+Pv6GZpX6A56+Y0oIL+1j4sSJXGPearWynIzVasXo0aMNBdXJLly44FdbsrqQMY2zpUuX1nifgapa1Tt27GANTSEEPvzwQ91nVVXFfffdx/d04MCBKC0txahRo/jekBc8LCyMAaWqqggICEBgYCDWrFljeA8tFgvS0tIwZ84cBn5r167lsbVx40Zs374dQgg8/vjjEMLL3avJPB4PA1KTyYS1a9eyXuKOHTt44yaEsUdWVVU899xzuuQRAjpNmjQB4FU9MAKU//znP5mOoK3I5Ha7YbPZ2HPq8Xgwb948SQN05syZqKysZI1d+m0CjrXp22lpaXA6nRLvnaywsFCibURERODChQuclEOAEqhSjxCiKjpDYutGiTWUUf/UU0+htLQUS5cuhRBVXkgAqFevnsTr1K4bCxYsgMViqZGfer2NNpUtW7aU7slPP3tw5tIP+KD4e5y59AN++rl2HO3/VasDlNdoBw8ehNVdH20nPIKEKc8j4V/hbG14O2X2doT1vgv9bxv7b+n81GiXm56eDovFgmnTpkkafG63G+PGjWMtQSG8WX3kEaFBu3r1auYlaRdjs9mMhIQEDB8+HIMHD2YvW2BgoFSSC/BOtCRyTmHszz77jCcxqvZC2naAzKG8evUqFi1ahPr161+TN+q2227DmjVr8MEHH7Csxe7duwFUVZgxKm+3atUqCFGVJEQheK3Oo/aZ+4Z5BgwYwBO4w+GQzpmAn8ViQVJSUq36FWXoksd13bp10rMcNmwY4uLiEBoaavj9H374QdK+jIiIwNq1a9n7qSgK3nvvPek7lJBlBKJrsm+//VbqV9QURcHTTz/NgNrX+1ZWVsbnqRXhN7LKykpJI/L222+HqqoICgpiD90tt9yCyZMn6wC/ttyd7zmaTCbEx8cjMzMTo0ePZk7WZ599xvW8t2/fjo8//hiHDh3C9u3bOcPV5XJh9OjRuOWWW3jxtVgsSE5ORv369dkz/VvGNW0IAgICEBwcXG0VGOIvP/zww3j66afx0ksv4a9//StOnz6Nb7/9FpWVlYiMjISiKFwOrzojDu7Vq1cZjBr1uXfeeYcX96ioKN34OnPmjI6HGh4ejq1bt/qNWrjdbjRq1IjnGUVRkJKSgpUrV3JWeEhICPNlSZ+VOJq1FaX2TfASwpthDHiTYhwOBxo0aCAVEfAVtjeZTGjXrh1WrFjB854QXi7igQMH/AJK6tc0X4wYMYLnotmzZ6OiogKTJk3ie0CeP1/KzTfffMPznclkwurVqwF4PZtbt27F+PHja6yjTRSEbt26YdKkSVi5cqUE2Bo0aIArV67oAKWqqrxhN+KiA+DQuqIo6NOnj6HYutlsxvLly5kfTGOPrmnnzp3o16+fLrrzW8aW0VijMTxy5Eg4HA4cP3MBi3adwU0r/qqrmJc4dw9uWvFXLNp1Bue+vvZEsv92qwOU12D5+fk8wEl3L7Z+IoITUmGPawprVBIUq0OnxfXvaoqioGfPnkhLS5M4P+fOncOIESMkjwYNxPT0dABVfMFmzZpJ11hRUeG9rthYtGnTxrDE3dChQ7Fjxw4+5sqVK7nW7dChQ/lYxNMkbymFrYm7I4QXwA0aNEhaNBs3bowVK1agsrKSa9rSwA8NDZW0FI0mKQILY8eOxZgxYziUoy1vRxVBWrduDQB47733IIRci7y0tJQzFs1mM2699VYMHDiw2sQWrQdSW8u7NkZhn2nTpgHwhq9p4tf+zhdffMHf+eqrr3jhp3PYunUrysrKODRP4Kt169bS5E/kfZPJ5LfkZXXWpEkTTnwaOXKkdJ70vCZNmsSfr6io4IVm8eLF1R5706ZN3H9NJhNCQkJw9epV7Nq1y2/pQKMWExOD0aNHY968eRy69QW5nTt35oz0kpISCGHs7SLPa1xcHAPYfv366RZUSshasmQJV4Zp2rSp5IGhFh0djQ4dOqBjx47SeA0MDJQiAYqicIb/b5kzHA4HgoODERkZiXr16qFx48Zo1aoVOnXqhL59+7KeIeko0mL+0ksv4YMPPsC5c+c46mAymTBnzhy/Yeby8nLk5OT4zcLWlsr09dDt3LkTnTt31tU9X79+vfR7pPuqparUxrRedCG8Gcbl5eUICgpCQkICb5jT09N1wvYrV66UxguNs7Zt2/Im0263+wWUAKSqTxaLBU6nE7m5ufx8IyMj8dRTT2HDhg0Qogrwao240jTuGjVqhLNnz2LGjBl8HoMHD2b+r5azmJycjEaNGvn1bPoCZ5rnVVVlrj1dt9bLCHiTDrXPrV69eqioqEBlZSW2bt1qqIUZGBgolSYVQkheVK1H9EY3Kv4wYsI0xI18BAlz99RIbaP371h/Al+U+C968r9mdYCylvbuu+9KCyZNtEYT/L9DY9K3JScn6yQxqJzflStXGMxZLBakpKRIk6K2ysa3336ru1atV0sIrwfi1ltvRefOnQ1LlGkHJtkHH3wAIYTEx6SQtN1ux/Dhw6XvxsfH47777tNlUB49epTvsdPpRFlZmQSgRowYweETp9OJlJSUanU27XY7OnTogLFjxyIuLg4mkwkVFRV8DOJNrVixgo/h+4z97fx9pZquFVCqqsp8rMOHD7OEyeeff67zkrZt2xbp6ek6uZ+Kigp89NFH/JxGjhwJAHy/MzIyeEFu0aKFtCm4Ftu3bx+E8Ib+tbZ//36dh65x48ZYvnw5X9u8efP8Hvfjjz/mxA3yvtVmPOTm5rKnWlVVnDhxgpO33G43goODoSiKYcnL2NhYqaRmYmIibDabYU1f2ogZLaQAmENKEjmkz3nfffcB8D7jQ4cO8SKtfX42mw3x8fESH81qtWLZsmUAvPI02jlI+7ljx45h165d2LBhAx577DHMnz8fkydPxsiRI5Gdnc1eQZfLheTkZL7mwMBALlN5PfOWxWKBw+FAUFAQwsLCmBdXU/j1rrvuwt69e5Gfn4+ioiL8+c/eUrTjxo3je3nixAkG2dpNhM1mQ48ePXDw4EH24g8YMKD6DqsxLeVCCC9oFKJq4xUTEyPNc/Xq1cPcuXMNhe2p1Kg20jJ8+HA+18jISPzpT3/SfY887b73pX79+lKyIClaaCM79H2bzYakpCR4PB7WDqUWExPD5UZPnTrFmyl6X7vxXbx4MYTwbpqzs7PRu3dvNGrUqFrPuNPp5BKvVqtVUuWg9UMIweoAiYmJqKysZP5lZGSkLoFU2/+o/7Rq1QqFhYW48847r7lv1qbFxsbCZDJh0PRlqH/vq0i4/41rypFInr8XTRbsw7Z8ee7/X7U6QFkLO3bsGAICAn5Xqv5U2/Xjjz+WFhltycUePXpIk6BRqKldu3bYvHkzVFXFZ599JklKREREcPhYa99//z2Hk30XofDwcPTq1YvDmpTheOXKFcyYMUNXbis5OVkHxMgeeeQR5sTdfvvtPAE4nU7ExsbCarWiVatWcLlcsFgsOhHqq1ev4o033sD8+fMxYMCAakORdB1GPLWwsDD06NEDq1atQklJCQO9BQsWSJ/LycmRvCfXCiiBKtkRl8uFgIAA5p0BwN69eyGEDHAJvCiKghMnTmD9+vVcR3zdunXSsQkMEecuJCQE8fHxMJvN13ye9erVg9lsNpRQUVVVAoLaPhIVFYVnnnkGO3fuxPz581mSirif/p6LdqGhvrV//37s3r0bQuiTs8i0nqjk5GRDUGC1WiU+G33n1VdflT5HHFkC4SkpKfj111+lz9C4oHvvCyi19yg0NBR2ux1vv/027rjjDr8cSSG8CW60wJvNZjRq1AjFxcU89tu3b19jco8/6R+tmUwm5t+uW7cO+/btg9VqlSq63HTTTRg6dCi6dOmC+vXrc0JLTc+uts2XgxwSEoLExESkpKQgLi7OcBwPGzYM69evx86dO3Hs2DGcO3cOP/74o25T8NNPP3H/WbJkCQIDA2E2m9nrRs3tdiMoKMhvSBfwrgskJ+X7GaqGRY6H4OBgLF26lD9XWFio89T5E3e3WCxo37699BrxWxctWoSysjKpMg/93s6dO/nzpGxBz0RVVXg8Hi7UEB0dbTgPnz9/nvuldmMfHBysWw+1/GUKcbdo0QLjxo2DEN6N5YgRIyCEXmEDqFJVoPO5EX2pphYVFYXWI+d6AaIPfe1a29q/ntNd0/+a1QHKf9nXX3+N1NRU5OXl4eDBg/j111/x66+/YseOHbXacf+n29ixY3kBSU9Ph9lslrgmMTExOpHo8ePH6waTEQm6RYsWMJlM1SaAUEKHdgHo16+fjitDtaPpb5fLJUlX+MoGAd7Fliq/EDEckMHB1KlTERMTwwuPUUjIyKZPn87npS0XWF0jUffMzEwMGzaMJ0zSzHz22Wf5s+Hh4Vxt5noAJSBXsiA5kIMHDzJnSggvoV8r1RIWFsaLWFBQED744APDY/fv3x9CCOZ4de/eHZmZmVAUxa8+n69R2TutN8nXrkUrTquB6XQ6MWzYMGRmZkr9uXnz5njqqafg8XhYV2/OnDkAwAsWUQW0RiFDAl4kS0JGIW5tmUFSO+jUqRMAY01I8pikpaUxSCgrK4PFYpE2Af4AJVClz6cdM2lpadi0aRPuvfdeSWrId2EdNWoUVFVlTzGN+eoq+2jFyWlDqjWqoCSEV2xfVVVJpL13796YO3cu0tPTdfQG0ujcsWOHIX3CN3mQWmpqKqZPn468vDwGvNpKMtHR0YiMjERISAicTqcEbmvbKDFI69ElUOQvktGiRQsGWzNmzMCRI0fw97//Hd999x1UVUV5eTmDUV95M6AqKYeSa+h+2e12XWIJSXIJYZxlHBUVxdWQyDp16gRFUbBixQq+r+3bt8fXX3+NlStX8rV27NiRa8Nr54uXXnqJk4O6desmQed/AAAgAElEQVRW7WZEOx/ZbDZJE/XLL79kmgRl+teUrGa32zFx4kSsX78en376KR8rLS0NJpOJx97ly5dhNptrleV+va3JgHE3VGd6+/+4p7IOUP7LaOKngeB2u3Xaar+XRiHB4OBgvPTSS5wcYDKZMH78eAwdOpQnytjYWK53SwkO5FHYu3evFJ6gFhAQwJ5Ef9UhtJmKFK668847oaqqTqNR2wIDA9G+fXsOG/fu3Vs67uXLl3ly7dSpk25xIv6kVu5l8ODBNT7f4uJiPPjgg8jIyKjWU5mcnIwTJ06wZ5NEq/2F0SlMSddM/adbt24cgr8eo0UnOzubQ8WUqd24cWMA4CxXbejMYrHgz3/+c7XHJv1QIbyJAHSchx56qFbnRny3y5cvG4rf+1ukXS4XMjIy0LZtW10SDfVrLZ2APEl5eXnS76uqyoLk9Df1C63Ui1aLsby8HK+88grfq4YNG+If//gHJxxoKzgBXn6oxWLBuXPn/FatoQSWdu3aQVVVphVotRD9AcrDhw+zbJMQXjBgVCHq6tWrPL6N+i2NQ/rXZrNJZfd87fjx41AUBXFxcTqvGoHH+Ph47N27l++V7/M0m81ITEzEyJEja11FiJ5306ZN8fzzz/N8RfPNCy+8INX8TktL8zv3+N5bIbzeYl8OasuWLXHLLbdg4MCB6Ny5swRUb9RcbDabGZySpFTjxo25H/ft2xc5OTno27evYQiZPpeTk8MUjYcffli6zg4dOnBJU8Db37UAOTAwEC+//LL0ndLSUo42WSwWLF68GD/99JPu9+fPn1/jsyPvLa0JDodDGmckZG42m2GxWNjTmZSUBJvNhhkzZqBPnz5+5wVFUfjZBQYGMkD95JNPeHze6OZwOGAJif5XmNvYM5n6hzfx9JHzOHruW3xX9jMAYNVbn1QLKJss2Pc/zamsA5T/sl9++eV354U0aiTRsHLlSt0A1ZbCKysrw7hx43jS8eU+ajX3+vbti+LiYpSUlGDmzJm8OAnh3cmPHTtWOjYtPCaTiRcT4udod6bt2rXDli1b8Msvv2DXrl24/fbbDcXWW7Zsifvuuw/r169nr5Q/UXLia2m/TyXFtFZYWIg5c+boRMRNJhPq16+PrKwsHRfSN0HJ6Jja43Tt2pVrMfvrO4qiIDMzE2PGjMETTzxRY4UUMm1Y22QyITc3FyUlJWjQoAGCg4Nx+fJl5qOS9yMpKYm/FxERgTVr1hjyALUArEuXLszHMpISoUQYAo0EdI08EOTJ7dixoxSy0t7ntm3boqKiAmvWrPHLP05JSUFBQQEL6H/55Ze68woODkaDBg34by1VoKysDKqqsvaeVgOP+GbkRSGvr69nj8p6ksdk+fLlhs+Jso87dOjAJfW05gsoX3vtNd4QKorC2bLDhg3THbusrIzv96pVq6CqKmev1zRXDRw40K/HmRJOcnNz+bWSkhKJo+g7VyiKt5LL0aNHr6kMJRnNQ/n5+QCq5IkCAgIYKGv7VPfu3Ws8JnmmhaiKdOTn5+uS/KKjo3XqFe3bt8f27dv5Wgjc22w2lJWVITs7m8+JPIHESyVptLCwMKSnpyM1NRVJSUkSL/W3riUWiwVBQUFwu90Mtpo2bYoOHTpItKGmTZtiwYIFWLVqFV544QXs27ePeakVFRU4cOAAz82+BSH27NlT4z0ePXo0f37z5s147bXXuD9opaioz2hlwOgeUi10RVF4HWrTpg22bNnCYNMfV5o20b/lXvo2s9mM6OhoROU+hAbVyP91Xn4Ipf/fLzjx2Xd48T0vSK4JUCbP34s71p+o/cD4L7M6QKkxbbLK77W9//77KC4u5oQc7WAzShKorKzEjBkzDI916623cjjE186fP68bzHFxcVJYo0GDBobcRJPJVG15MkpM8HeN9evXx9SpU3V1iKlm7Jw5c6RF76mnnkJBQQGmTZumExEnSZexY8fi4MGDUmlE34nKH4glo0XHZDLpZFKAKo/V4MGDa/Ru+9ZwfuKJJ3Dy5EksWbKEASItZqGhoeyp7dWrFxRFkfhXJpMJ69evB+ANa06dOpWfSVBQEBYtWqQDAVo5nuHDh7Pgdt++fWv0NJIovFaM3vf4tOjdfPPNOHnyJIQQvGj4gtHg4GBkZ2dj6NChOu92YGCgYV9KTU2F3W6XXqPQXHp6Oi+EM2fONHyWZ86cke6hlm8GQOII+4oy+5o2ScxXDJsAZb9+/djjajabkZOTw2OvYcOGMJlM+Prrr/l75eXlvLGjpJznnnsOQnjB5c8//4zp06dLYy8xMVG3cSQqxJo1a6T7SPNHt27dDLnVJDROY9C3HvS12NmzZ3ksao3kcrSeRUVRGEST/qQ/c7vdCA0Nhc1m09Fzjh07pssaFsLrffXNFAeqqA9CCH4u69at4746ZswYAF7JIZPJZKgWoDVtuUmLxYJhw4bh9OnTOHnyJLZs2QJFURAUFCTpPlqtVmRkZPC4c7vdiI+P5w3Z9Urm+As/OxwOpKamon379ujevTsGDx6MkSNHYvLkyZg/fz57JgmQrly5kosTEE2jf//+zM+kv8moUtShQ4eYzlBQUMDlarX6qU2bNoXFYoGqqrhw4QL3A3+SQ7+lmUwmWN31rymU3fqhv3j7bA2Aktqn3/xvSgrVAUqNaUOBv8fmy03Jzs5GRUWFxK2Lj49nLwDgBW/aKjPUbDYbJk6cWG1Yiao9HD16FNnZ2X4lS+rXr4/58+dzWMs3ROnPhJDJ1yS4qwWLFosFjRs3Rl5enrQIaic63+siEXFtGTGy/Px83qmHh4fj4MGD7PG0Wq2G1YYAYNu2bfwb/j5TUVHBJfwAwOl0csKMEF6vy7x58ziMHh4eXu0i0aZNG85A7dChA1RVlfQ/hfCCMaPMZVVVsXDhQl6MHA4HBg0ahNmzZyMrK8tvGTv6LHkax44di7Vr1+LDDz/EnDlzIETN+pHaBAHA6xXUVuqglpaWZviMCgoKdJVUGjVqhEceeYSBNXFZfb1w5BURQtSKbqDlAmZmZuLixYu8GSC+Xk3JLhcuXOBjDBw4UHoGlAVMfXP8+PE6AfN33nkHQlTRP37++We+X1pOHZXC1NJAVFWVAKHD4cCdd97J1Vx8wYTFYvHLy6T/7927V3eNxFslYHUtRptQGhfac9cqSmzatEmKjhC1w8jOnDkDIbwqD/Hx8QgNDUVhYSFyc3OlCAZ5RjMzM6VSolarFTfddBPTA0iH1rff5Ofn8+sjRozgmu/+xtySJUskUD9p0iTdHEvcTCrxefToUWkT3LZtW76G9evXS5ER8g6mpaXB4/Hgq6++wocffoi33noL27Ztw9q1a7F48WLMnDkT48aNQ05ODm666Sa/5QopS/t6eKm+f9NclpycjLZt2/Jzp41bbGwsHnnkEaxbt469vJ06dWLvJXGWAe+Gx2w2w+PxYOzYsdd0brVpkf2nVOud/C2AMnn+XizadeYaR8l/h9UBSo35Zsr9XprFYmFuCb3Wt29fDmeSsPnUqVN5YhgyZAhmz54t1Q+mElpCVCUCWCwWDB8+3NALRJmE9913n1+PG4Xt1q9fz96S2lZeEUJIE6l2kj59+jQnJtRGKDouLs6Qg0ZWUVHBWc4mkwnTpk1jLwV5Mii8uWTJEum75K0Vwhv2qc4IQKxcuZKTcgoLCxnUa/lO5eXlyMvL48ne4XDwAuub6UpNO/GHhoZi+fLleP/996GqKr7//nvs3LkTc+fORVZWFpo1ayYBWt9mNpuRmZnJCyDRAYyssrISdrsdYWFh1V4/eevod9u1a6cDLLNmzWKv1N133214HEow2rZtG7p16ybx31q3bs18RV8Vgm+//ZZ/yx/w15rFYkHr1q0ldQMaP2vWrIEQXg94dUYSXdSPbr75ZsydO1cCq+np6dVqfVLoW5v9S0lHgF43VWukNjBr1iz2AlssFkMQX1OrrupOaGioJK9UGzt+/DiE8AI4bbLSlStXmHZBG7z69eujoqJCSvjr0KGDYQUhev7vvPOOBEJpbrv77rsZ0GjLlf7888+6Uq4BAQHsQWvZsiWEEJg+fTp/R1tqVQh94kxlZSVmzpzJYXaXy4WkpCRDHcpPP/0UQnjlcLRGgF1LD6GxTv8GBgZixYoVteqTZLt37+axQ/2KPN00HrXzrqqqrPkYGxuLF198kZM5s7KyMGHCBOTm5mLAgAHo3LmzNLYJBJNSwPWEqqmKlJYfeqNrd9vtdjSYsuHf6qG86Y9/rdXz+W+zOkD5L3v11Vf/I/qRv6WZzWbMnj2bPXVNmzZFaWkp0tPTWdj87NmzUhiFBlB5eTn+9Kc/8WuXLl3C9u3bOeHDZDJhwIABzCUrLy/HH/7wB+k4iqJg6NChzF166KGH0KZNG2nioMGvLYloZAcOHODvUDlF0ibzeDx4+eWXceuttyI+Pr7Wz6V58+aGi/aGDRt4sm/RooXEBwXAE218fDwD7b59+0JVVRQVFTEo9639bWSqqsLlcsHlcumSctasWcPHIrFhIbzJJxSyJoI70Rd++OEHvPrqq9V6FP01q9WKqKgoZGZmYty4cRg1apQUPoqIiMDXX3+NyspKKfyrzeIkI97s888/7/faiU9Imo++fZdKsr3zzju4evUqL+okKq01u90uVfBRVRWbNm2SxKPpmWk9ahRqVBQFYWFh1YK4b775BkJ4Perbt2/XHffEiRM1qh2cOnUKQng9LWVlZdL9DQkJYakhoyxvrZHHjTZPWkADVIWHn332Wd13jxw5AiG8EYv+/fsb6hsK4QWL33zzDZcJ9Sdo3bp1a8yePVsXciZKR3UbN19r3LgxFEVBREQEA8qjR4/ydc6YMQMA2PudnJwMj8fD95Xmr7Vr1/Ixy8rKYLfbdeffv39/PmcqtOCrk6q177//HrNnz5a4hTR2haiiL6xbt076ncDAQBQUFKCsrAxjx47lOS88PByPPfYYVFX1WymHqupQtR+tderUCUJ4uY2+G3i73Q632y157moyimbY7XYcOHAACQkJCAoKAlAlvk+NsvrpdRIjB2BYehEAq2Ro7wFtYqgqE20ce/TogXPnzuHYsWPYuXMn1q9fj0cffVS691lZWejevTvS09N5HF+vPmp1rX5So2uWCLpWQJk4d8//ZJnGOkAJYMeOHb/LhBwtiGjatKlUfisvL48nwJSUFFitVuTm5rJXS7vTJa3HtLQ0HpwEYAAvuKMQmRDGWozBwcHsKejZsycURWEPX3l5uW7gK4qCQYMGSeF3Mi1Q7datGyoqKljbUSshQ7/bqVMnSWroxIkTuHz5MpYtW2YotB4VFYWBAwdixYoVzHt0Op1+s58DAgIYcH711VcseRMTEyNVa6mOF6o18iKQqDxZUVGRzhOWk5MjfZfkQLZt28aexpSUFMmT69tHSFQ6NDQUTqfTsC9rOZvaxUpRFPTo0QNnzpxhMNShQwfpnEpLS2E2mxEXF2d4vR999JHOG6alR/To0QNXr17F5cuXYTKZOPlHVVWu1hMSEsJA5bXXXoMQctUirVVWVvI9puZ0OhkUjxo1ius7+6oIaI04l1QNyel04u2338aUKVP4HtakdtC8eXMoioKsrCwee/TvuHHjqpUN0hrVtxbCGASlpqZKteepbnKPHj10G0iqmzxp0iSd1mFaWhqHG7WKFvR+bGys9OxsNhtSU1MxZcoU3uzcdttt1V4L2Z49eyCEt3pWdHQ0oqOjJW1ZbTY8UCXp1bRpU3g8Hp4TCHxGRkZK4X2TyYR+/fph+fLlEMLLLQWqIk3XInZOfUDL4VUUBVOmTMH777/Pfz/99NPcN+j+xcbGYuPGjdLxjAAlcYm7du1qeA6ff/65lLiilRPSnlO7du2qvZZffvmFPa7x8fG4dOkSAHAEBPDO2YqiSFEv6n8xMTHSBs8IUD7zzDMQoqpwRXFxsURfat68OYCqZCyjTSrg9VTTd7TSXQA4unGjE3MSWnW+ZjmgawWUCXP34MylH6p9Tv+N9j8PKLdu3fq780z6hjop/OmbCLJp0ybdQEtISMDLL7/MCzV5hehzFL7RcqFeeeUVZGZm6o6l5ShqNf7q16+P4OBg/nvKlCkQQuCZZ57B1atXdZNgaGgoRo0ahcLCQgZU5EUx8rylpKSwiDhQJRMjhF7m4p577oEQ3mQlWjx9QyRWqxXdu3fH2rVrdaDQ4/FACMGcPfKY+Jb6qk5z0choYWratClOnz7NYVEhvNp7Dz/8MN8Du92OhIQEnei79vn7Xk9AQEC12balpaXYs2cPHnjgAWRnZ9eKs6ndSEydOpWPTwkZ2vBycXEx8vLypD5iNpsxfPhwyetAmpxk5MXUJsE89dRT3Mc3btyILl26QFEUQxFyrYWGhiI2NhZz5syRZIhCQkIwatQoBs7+woNablZycjL3N8C7uGtlfYxAFMktUWvQoAFeeuklqKrKHhby6lUHKFVV5co5QujVBmjxr1evHjp16iRtohRFQXR0NMxmM6KiogyB7/Hjx3VVtShMPHDgQFy6dInHFyUGnThxApMnT0azZs0MOZfjx4/H4cOHq+2DJJpfWlqK6OhoPk5ERITf5J677roLQniBb0lJCUwmk467TcehSEN5eTmE8GbKE4e2trQbskaNGsHlcgHwep0pXO7byPNJrWvXrob3wAhQNmvWDIqi+C3ksHnzZh7rCQkJrG9ZUFAgrVEul4vLIPpaUVERbwy1ZUGppK62NG6zZs1gMpl083WPHj0kmoEvoLxw4QLMZjOCgoKk/ubxeKQ8BC1/WBsp+Omnn/DZZ5/h3Xff5eRA2hSlpqbijjvuQHZ2tqGk3Y1o4Y3b/kcA5QfF31fT4/477X8aUBYWFv4uPZPa1rBhQ+Tn58NiscBisXDW5dmzZ9G5c2fps926dYOqqtixYwdPyoB3cSDwQmK8TZo0Qd++fdnzpSgKUlNTsXbtWpw5c0ZK9KGQFZndbucdKHkno6Ki+P2LFy9yJnJeXp7Og6Jtdrsd/fv3x7p163D58mWueqOddElE2shD9vrrr0MIr1yFluQvhBdYdOrUSSckHBISgi5duuDRRx9lb9jDDz+MgIAAxMXFoaSkRJdtXBu9Nq2R1p52ISDJI3+gjhbO9PR0PPnkk3j77bclj0xUVJQEDK5HvgWo4jnOnTsX2dnZSE5O9ntOtHhTucwePXpIYV16PykpiT1KpHNI9bG1RuLfsbGx0usnT56UsturS8ggS0tLg81mQ3l5OVwuF8sraUEueTjee+896btnz57la/atcKQ1rWh9WloaiouLdWOvUaNGOHjwoPQ9j8fDmzlaXI1M/f/Ze/PoqKrse/y+mlOVeSITScjAEAgBAoEkzPPUKPMkkxEkyBAGMSA0oCioIAgyKZMNKjSIIIJ0CyKiiCKtCI00goJ0vuk0xhjpdLqM1fv3R61zct9QCSj057fQs9ZdSqrq1av77nDuOfvs7fFwqnPw4MH8bLZu3YpHH30UmZmZqgOSTCL+xz/+kVOfycnJ7BBp7f333+fokbzeKYrCDj8dAlq0aGF4jXPnzmHWrFm6Qjiz2YyEhASMGDEC+/fv537cunUrhPDCCUpKSvh7jbhltUYRRnnuxMbG4tFHH1VRLsnCDXa7nR3tnJycW54bTqcTKSkpqr/J1fvaNaugoIDnYv369XUHVa1DSRCfvn376r772rVrjN0kDXAt/dSyZcv4+2k8uFwuzJ07l8fA66+/DqvVqqP0AaqlUp9++mn+G8EoZDlRwvKSAEBZWRl/97Rp07B+/XreS+655x4MGzYMffr0Qfv27ZGZmYlGjRoZQi4In34re9+dCvRYI+v9FqG8Q/ardijdbjfmz5/POEJfVcz/q2b0/VQJePz4cSaOlZ29zMxMVbqauAgdDodqkWvQoIHhBE1ISMDvf/973YlUURS4XC4ujhDC69DRRkG8eSSlJaevrl69yvdUW0GNlsD46NGjEMKLxfF4PKxlK4QwpDi6ceMGhPA6BfK9CqGOKrrdbrzyyivo378/YmJidH2RlpbGmD5yJmmhpchd586dddil0tJSvP7666r0tFyMITc/Pz+OMo0bNw7PP/88zpw5gytXrvCGIoTA2rVr8eGHH/L3UhXmxYsXUVZWxuOkJgLrmqxBgwbw8/PT/f3q1atcVU6tpoimLMdH/1+vXj18+eWX6NSpk6FDCQAPPvgghFDDLgBvVJUiZ3Xq1DEsxpCN5DjpnuXrnTlzBgMGDFDxEdarVw+PP/44Nm/erIKG1GZaWT659ejRw+fn3G43QzXatGlj+B6K2Hfs2BEzZsxQRUWp/wlO8uabb/p0lHr37g0hhGp8VlRU8N9NJhMefvhhuN1u3fgkWUfqKyO1FrKrV69CCC+UYP78+WjVqpVONScmJgZWqxUWiwX79+/nNcDpdPq87tmzZzFw4EAdNyxpm1Mx0LFjx1RjLycnB9evX+e5QiTzt2KUpejTp4/q7zIdDjWtDCU56i6XSwXv0TqUxL8rR8E9Hg+mT5/O1+vbty8qKyt5XMtr6rVr11RjYvz48exA2+12Xj9sNhuWLVuGnTt3Yu3atVi8eLEKd5+Tk4Pc3Fw0a9bMkP2DnuGt7l1msxk2mw1Op1OFD5efY69evTBkyBCMHz8es2bNwiOPPAIhBJo1a4Z33nkHf/nLX3gvpoI0yjzQ329HU6wOxP+Gobwj9qt2KMn++9//4tSpUz6B6ne60QS2Wq14+umnVVgWskOHDqlwhK1ateLCFyrKoY1aCG+VMQAUFRXpJBep2Ww2PPfcc6q+oOIkl8vFUUI63coLDfHomUwmxMbGGpKIy5+xWCxcPHH48GHGLNF70tPTsWHDBng8HubNHD16NKexk5KSfD4/2RHPyspCcXExpxxJulBrHo8H+/btY25A7XOPioqC1WqFw+FAcXExQwXsdjuSk5MRHBx807xwXbt2rXWTq6qq0tFCmUwm/h0yYTCRbt9qxS2Zv7+/LgIimxFxtslkQk5ODhYsWIB58+b53Iy0zz0rKwujR4/GihUrcOrUKfz0009cMR4cHKzrFxnfGRAQYEjPQiZr/8p0PVqjDVobnVMURYcXNTK56lj+vNlsrlWukopthBAq9oAPP/yQcafyM7darRzhWbBgAcrKyiCEb9wd2aJFiyBE9QF0/fr1nH1o3rw54+hIenPevHmq9UT+bkVRdBywskVHR+uiocXFxViyZAlyc3MN8b4WiwWBgYGq/rp27RrGjx+vwnDWqVMHU6ZMQUlJCaevyZlYtmwZevToASEE/va3v3F6Ve6/mylW0Ro5qaQUtW/fPp0DQ9kOIbwH2+XLlxse0mfMmAFA7VAS5RhhBH/88Uf88Y9/5INrUFAQCgoKsHDhQhQUFOC+++6Doiiw2WzIzs5G06ZNDdXHfi4vJcn0ys8pNjaWDwaJiYno3bs3R4Op0eEnKSkJf/vb3/D9998brmsej0eFAxXCm9LWPhvieqUxC3hT8zQvBg0a5FOt6Zc0h8OB2AdfvCnHcMzmjzBx+yeYteszAMD+M0WYuP0TTNz+CRrMP/hblbfGfnMoNfa/JDfX0opQRJEmoaIoWLJkCd+TyWRCq1atoCgK/Pz8GIdEDmV+fr5uEsvfl52djQsXLvBEpu9PSUnBhQsXcODAAb62Vp/W5XIhMjJSFUkz2jSSk5MxduxYHDp0iFPNwcHBvKHJRveUmZmpOvVri3CE0EvjAd60pZwSlk/0csqRFnkjS0xMREBAAK5du+azOtaohYWFIScnB2PHjsXAgQMZ/2i1WjF69GiUl5fD5XJxCkouqDKyNWvWQAihw7oJoadyoYiKENXKSTdrxLdnFFk7ePAgOnTo4DNCQTRF2shN3759UVJSggMHDmDevHno168fH4qMou4Oh4MjUc2bN2dn8z//+Q/MZjMaN26MDRs2wGQywWQyGT57wEuJIoTXya/NkZD7Va4QJv47LbE54I3Uy+uBn58fioqK2CkTQqBbt241RlKpKIc279DQUFWfKIqCxo0bY8qUKfjkk08AeDdVq9WKiIgIdmbl9K6RffDBBxDCi3Um2IfL5cIrr7zC76FqZeL783g8qrSu7HDb7XafhUhUPPPOO/pNk1gOZL5HbeGcw+FQOTNBQUEYMWKEITMEVRKbTCa4XC7Y7XYVtRWRZFN79dVXa+wnI5s/fz6E8DrZWgqiDRs28DOoV68ehPAeEOfNm4fJkydj6NChSElJ0eG2aQ7dyppi1EwmExwOh2pPkO+RHK2QkBAVBrpp06Z46aWX8NFHH+Hrr79GXFycCve+Z88edlqF8BY0VVVV6Xg2z549q4K4WK3WWosTidCcMgd073Xq1FFBmSIiImC32zFjxgx0794dqampCAwMvONBHUVRkDJ0zk3xUF77zveBMXfpEcPP/MZD+ZuxzZ49+46lvmlipaamciifFlvil/voo48ghLpYxWw2Y+TIkTyRaTFwOp2cpqSFRbuw1alTB9HR0bDZbHyaJIzl6tWr+TRM77fZbLhw4QL3h8fjwbFjx2pMOZjNZgwdOpSxUVeuXFFJ9GkJjcmEqJZMc7vdWLFiheGpX64oB7wO1ZgxYzjKVKdOHUOKDrfbzVx3c+fORWlpKfbs2YNHHnkEvXv3vinQd506dRAUFGR4Qo6MjOR0nsPhwNSpU1X4MJfLxd9PutO+TFbWaNmypUrDNjQ0VFfc4nQ6eZxqX6vJaHxRWvPUqVMqB1AIdXopKyuLo87a4oyIiAhDYnIAqpR3eXk5Dhw4gPnz56Nfv35o3LhxjXrvgYGByMrKQu/evdnxGDlypOr6VVVVjOfzhfsjO3v2rIojr6ioiKX/oqOjebw5HA706tULM2bM4PlpsVgwYsQIrvy/fv06AgMDYbfbecPURvqrqqqwd+9eDB06VOegCCG4P9PT031GrilKHxISAofDUetzlQ8ZQgjVfAS8RUZUSKGNqvbq1YvnWc0FPt0AACAASURBVL9+/VScnw8//LDOWSe6pe7du+vugw6rQnijqlVVVXC73TXKEQYGBqJt27ZYunSpSi2ITFsIQ+lQohpKTEzk3yCEFz6wc+dOpqYpLCzExIkTMWLECPTp0wcdOnRgvF9CQsJtiX754o2lsRUZGYkGDRpwH9SpUwezZs3CqlWrsH37dhw6dAinT5/GtWvX4Ha7UVVVBYfDgaCgIK6EJo1rAHj00Uf5O2SFr0OHDjEkSlEUtG/fHhcvXoTdbkdaWhoAcODA4XDg4sWLMJvN/JqREpBWT5tgBkb2008/wel0wt/fnzMR2vXc6XQarvG0XrZv3x7jxo1TiTL80uejbQFxqbeMo7yV9ptSzm8GQA3Cv5NNURRMmjQJHo+HsX/Hjx9XRRVpgerWrZvuPmmSOxwO1YSj1OSOHTtUlaNE7wCA02i0SRN9ihDeqMa8efMwcuRIJCYm6hZJRVFgt9sZvD1jxgze2K1WKzp37syYr0WLFmHGjBkQQmDlypW63yBEtUMpG+kyazed4cOHY82aNeyEJyUlcbGAEF5uN63TWL9+fZ8RN+o3WuQ7d+6M1157jV/fvHmz6r7OnTuHgoICnTOkKIphYQJROhFNiy9uzsOHD/O1iHA9MjISiqJg/Pjx3BedOnXiyufk5GT4+fnBarXCz8+v1opossWLF0MIb4RSHmsxMTGYNWsWvvvOW5lIfXLt2jVcvnzZcFG32WyYMGGCYdq3Jgwl2cqVKyGEt/J0/vz5/FxDQkJ86nxHRUUhKyuLHTW73a4r8JFt69atMJvNMJlMzEaQkpKCMWPGQAiBb7/9FuXl5ZgzZ46uyj4lJYUjNQT7oGKchQsXAvCS/9PG53Q6ERERoRpv5Kjn5OTgzJkz7JTHxcXVCIMgh0KI2g8jBw8e5GdpNpuZA5DM4/Ewn6uRZChhhen7HnroIY7G0XN+4IEHVM85Pj5e5+gSTZAQXqdv27ZtquwD9d/rr7+OoqIiPP3002jbtq1uPlksFoSGhiI5ORmtWrVCs2bNVOMvICDgFx36qXJce43g4GCG2DgcDgwcOBB5eXmYOXMmFixYoIqqHjt2DCUlJYaR8YkTJ/r8bpvNVqs4AhlxQtKYo2jsqFGjeL2ljJKWW/fjjz/WVap37doVhw8fhslkgt1uZ87OrKwsKIrCz5cgNSSjSEVSubm5nPa2WCwMESguLsaOHTswY8YMPow6HI4aI400Lx599FH87W9/M5wLRLN0p1rMyCVIuAW1nJtpv2l5/2Yqkzf3O9XMZrMqpUxAd7mNGDECVVVVjNvZsGEDv//IkSPo0qWLztkbO3asbmLSomKz2VRYFavVioyMDJw4cYIr8LRgfT8/P7Rs2RLz5s3DpUuXeMMl/Fx2djZfb+vWrarP5+bmMokynVi19yaEsUNJDhjJ68mbHbUGDRpgypQp6N27N6fHjRxHPz8/BvYL4S20OXv2LDweDzsJQlSnjsvLy/laspWXl2PkyJG8CYWFhfHmY7FYdHrEMTExMJvNiI6OxmeffQYhvJFHrdHiLYRXpg2o3uCJ3Pz69etMa2S1WrFs2TIutti2bRuE8KaOa7LS0lJMnz5dtSmGhoZi3Lhxus3o0KFD/J5PP/0Uq1evVm0OGzduxPr16zkKbTabMWTIEFXBwc04lIBXj9lms6G8vBwmk0n1O+TIZm1QFHIss7KyMGrUKKxYsQK/+93vIIS38IYwgYQzDgsLg9VqhdvtVmliO51ONG/eXIXri4yMxOTJk7nvAgMDsX79evTs2dNQZ5j4FktKSlQ8lARJob6szbGgZ37fffcZvl5WVsbRO4vFgrCwMMNiKyqc81VpTkVa169fZ9xcixYtmKCeDowmkwlZWVlYunQpR2y7dOmCgQMHqvgujQ6ht3P9lHHZOTk56N27N4YNGwaz2YzQ0FAMGDCA53tycjLeffddlJWVwePxoLKyEvn5+apnSYWOxBagZZkgI9UfIbwVzzWZEXRFTls3btwYa9eurRGqIWMRHQ6HSv41MTER169fx65du3jtJlEK2S5cuKAr9LJYLCpsMgUn5Mpw2ndkdbVJkyZhxowZukOCUaNI44QJE3jN3LNnD4qKini9NiJoLy8vx5o1a9C1a1dDPuTbOYackfGIn/naLZOc19TqzzuIb0prxlXfzfabQ6kxWZf3TrarV6/ixo0bGDNmjKG0FKWrKioqmGqme/fuKqetXr16KmoSI2xL3bp1ueJSURQ8+eST2LJli2EqIjAwEK1bt+bohMViwaJFi/haxCHocrmgKAo7xW63mxegsLAwTvMqioIuXbowH5mWekcIvUNJqZzf/e53iIqK4uKHmvqSXg8NDcX999+PNWvWsNNIVl5ezk7C6tWrOQoohFdhhIw4F4XwSkEWFxejb9++vIDGxcWpCH4XLlwIIbyO3tatW7kwQYsbo2f86KOPoqKiQoVfo3SZx+NhB9Eojbt3716+LkWk3n//feZy0xKBV1ZW4sknn1ThTKk/tVEs7ZihsSGPN9L9lTlRd+3axc/bZDKhZ8+e+Oabb27aody+fTuEqMZb+SKfB4CNGzfyc7DZbNizZw9v3A0bNtThE+X7lp1NGgeyxFtoaCieffZZ1Zg5d+4cBg8erKs8lltYWBi6deuGNWvW4MMPP+S5ExgYiL1797JDSdmC1NRUfP311zyHdu7c6fP3UsGYw+HQbbxLlizhe2/bti1KS0vRp08fCCFw4sQJHDhwAC+99BJHYkNDQzF69Gjce++96NKlC1q3bo309HQkJyczcXRAQIDhuvBzmslkgr+/PxITE9G4cWNYLBZYrVb069cPI0eOxKRJkzB37lwsW7YMmzdvxhtvvIEPP/wQly9fxo0bN+DxePDOO+9g3LhxSElJMXRgxo8fr6qsJjw0APz73/9Wza9JkyZh6NChPD4iIiKwZs0auN1uCOGN/pGKjTYzIRupz9QGQ6AMDjViiNi5cyeysrJUJPht2rTRkbyTER4xJiaG53xsbKxqnNKaERgYaIjVlp1CavHx8Tz2PB4PrFYrEhMTsWPHDkyfPp3FK4yeLcGt5HnRokULLqKScbtAtTQowbrkQrWwsDAUFhaiXbt2ugwBOf2LFi26Y7jKxv3G39YI5Y6PjTlGfy32m0OpMaq2vRODV24JCQk8SWJiYlj5hlIYgDf1+8ADD6ick8jISEydOhXXr1/HqVOnVCoCERERqgIBotxp1KgRK7AY3cvkyZNV0SXAy5tGkYnY2Fh88sknnKIUojod8tVXXzHerFevXrzQHT9+XKWBazabOSJERpvh7Nmz0bt3b3ZMamqtW7dGXl4epk2bhuzsbBWuz2azYfXq1T5P/aWlpbwoyyk9uufi4mIoisJpm/DwcBXu1RdNz+HDh3nxk6NAfn5+iIyMROfOnXUFUvTMqKIxJycHf//735m03FcKu6qqCmPHjuX7Sk9Ph9vtZhzpyZMn8eKLL6Jp06Yq9oBOnTrhz3/+M1wuFyvVGBk5ePJBRQjBeN1Tp05xulDezA8fPqzCpFJ062aM+sBkMtWYBvZ4PKqI4PDhwxkLuWPHDgBeuiDa6NLT03HPPfegcePGPp1NIbzYNHI2n332WRw4cACLFi3SkYhrW8OGDbFmzRrdeHvmmWfY2ZPTjomJiTz+z549y8UWc+fOxaZNm/D0009jzpw5yM/P11FWhYSEoF69eggLC1Ntrj+H349SvnJxFLEXpKeno02bNroq/oYNG2LlypUoLCysUSP8nnvu0a0lAFgp5+eaLAygbRaLBSkpKcylKT+PN954QxWVj4iI4LECVGekqPhHSx1kZITHXbt2re6169ev8+Ga+oMOSxRVBLzzeNWqVUx2LoTXSe3Ro4cqkyRjUmkdNZICJX3u4OBgfPvtt6rXSGPebDZj+/btyM7O5u80m82GcBYt24QQXk7Rixcv4r///S9f+6uvvlJFQH0xT9A1L1y4wPuCtjgtOjoa9957L7Zv3w6324309HTY7XYA4Hl+J1rzkYVeh/AXRiqff+fLWsfO3W6/OZQGJhPH3qlBLIQ3HUPqI7Lz4nA4VFXOQUFBXLQhF7EQSLtJkyY86SMjI7F48WK0a9dOV0QRHh6uOwXWFBHyeDyYNGkS35cc6bp+/Tr27Nmjinwa2bvvvqvanChyUVPUsVmzZqqNfNKkSbxgavW0ichdW8TUunVr7Nq1S+eglJSUqAqY5MpHwrLKPJ8EC6jNiouL+Znl5uYy358svUhpaiMHwOl08sa3a9euWr/v/Pnz/NmAgABWGJH7OTMzE9u3b+c+8MW3J5vc71Q8YrfbVRCNDz74gA8I2kjnJ598osLuZmRk4MMPP6zxt+zduxdCeJ2mmozofwoKCphtgA4G+fn5ePHFF7kyXIaIAN6NzyjqQoUPvpwyk8mEoKAgxvmZTCb4+fmporiK4pWwa9iwIVq0aIGGDRtyZkB7rV9C7izPmcDAQDRt2hQ5OTno0aMHBg0axBGi9u3bY82aNYwzXbVqFYqLiw0PWh9//DGE8EbOtXbixAlV2nHDhg067Wu5ydXXWvslDqXH41FJYcp0NllZWcjIyFA5RQQ5kQ8foaGhfI0ePXrwwZsijrQ+3gzt0J/+9Cd+nrKk4OOPP647tJCR8pafn5/KYQS8XLoyHzLN6aFDh6qc4e7duyMuLg7BwcGG90U0WiEhIXjxxRcxffp0lXN7M+OsV69euHjxIuM35TVfq+UtmxyRzcjI4PT7hQsXMHv2bMNxHx8fj44dO3Kfadk4goKC4O/vr2P8uBMtoFkPJBW+gfiH994yZrL+vIO/+sgk2a/eofzXf6pwruh7/OXqdzhX9D1uVP4Im82G8PBwnsy3kwNLbqRdvHz5ct4k6DU/Pz/06dMHJ09WA3wbN24MIbwOB4GjFyxYwETdRhuY2WzGyy+/rKrAln/P1KlTa+0j7SlUCMGbu8PhwN69e/Haa69xpLFBgwa18jRS37Zs2RJnz55lLNh9993HjoyiKCp8HzlkRs5r165defNMS0vjBcxut6Nbt244duwYgGoaErq32NhYANXKHtSIsFju/9rM4/FwtWlERAT8/PxUDiXRkwjhxRO53W4u4tDihVwuF1q1aoX58+frMI5kVJSj7dvk5GRDNZLjx49DCKGCMZCVlpayc2YymTB+/HjuQy1tEQC88847OnC/bEQGLkd433rrLcPfQRyKiqIY4sAAb2pdCK90KBkpKAlRDQFwuVzYuXMnDh8+jB07dqCwsFC1IQUGBrKjdacyEXRo0qbKbTYbcnNzMXToUEyYMAGzZ89GQUEBzGYzFEXBc889h/Pnz6O0tBQRERF82KHCNiG8hx1fxV1ECdWtWzdMnjwZQtQuGUpFWkePHjV8vbi42LBoRv6vPM9TUlKYb1a2X+JQ0mHJZrOhuLiYsYxyShTwyugKoWe6EMKbBerduzePcbvdjueff54PkYqi4Ny5m6d6oTUqNTUVp0+f5qhtSEgIr2XaCP3OnTv5AP7UU08ZXre4uBj5+fkqKVEa11RwqSgKioqK8Oqrr2L69Ono1q0bUlJSaoymm81mtG/fHhMnTsTGjRvx5ZfeaFpVVRXmzJmjUqkaMWIEFEVBZGQkPB4P45d94UZJGa1BgwaMrdWOC22Tx2VJSQn3X1ZWFp544glVEMLPzw/9+vXjPe9OtISEBFiC6iBhzDNIKHyzVkqhpLkHkFD4Ju7bePJXjZnU2q/Sobz4jx+wYN85tH/6HSQaDJaYB1/AsKdfgzU83hBcfbta8+bNuQCFNiL6f6MF57vvvoPNZlNFRuTrxcfHc9qRFoF7772XP19UVAR/f38oisIbjhDGDprWiLpC23wVwtStWxc5OTnIy8vD2rVrcfbsWZY5JI1fIbwOKTmntKjRRqGtbjfiSSOjSANFzOjUL6fR6TtbtmypivDJi3fbtm1x7do1VqYwkkqrzZ588knuF8I7kaNJv2379u0oLS2FEIKjbRSxHj58uAoSQX2akZGBvLw89OnTRxVpjomJ0cEFjKrqKerwwQcfqP7++OOPc9+YTCa8+eabrHwRGRlpWOgBAG+99Rbz5Gm1mQlDWVRUpMOgvvzyy6isrOQUelRUFL8eHx+PqVOnYsyYMejfvz+6du2KFi1aMEVUdHQ0wsLCEBAQoOLn+6UtMDAQCQkJSEtLQ8uWLdGxY0f07dsXI0aM4MhRr169eMMMCAjwSSdlND9ktoGBAweqHP5PP/2UsaknTpzAxYsXIYQXRyxHexVFUUXEjCwgIIAPQwkJCbUS6hPOUI7MeTwebN68Gc2aNfOJXYuJiUFRURFHsBo3box+/frx+2NjY1VFRz/XoZRZF+QxRmlcmrsPPPCAyglp164djh8/jiVLlqBt27Y1OltCqCUJb8YITy4/m/z8fBQXF6u4I7X25ZdfMoa3b9++hs/n/PnzhmwfNY0xmXJHFgegZlT8KJvH49HBHAYMGIAbN24w84nFYlGNP6KUI6yv0X06HA6sWbOG13hq8iGZxpv8jGgcydrjf/nLX27LXK+ptW3bFtawugjrPhFx+Rt1afD4R/Yjd8nbWLDv3K+WGqgm+1U5lN+UVuC+jSdVJwyf7ZE3kFD4JjJnboElqI7PNM/tav379+dIjZ+fH5xOJzweD06fPo0pU6YgLS1Np0BRr149jBs3DvXr14fVauXfScTDQlRH2EpKSnjC0kJPmxhtliUlJdi9ezdmz56NXr163VSkMSYmBvfffz87jbVtYMnJyTCZTLh8+bJqw6X2u9/9juldjhw5ovv8uXPndDxpQLVW7tKlS3WfKS4uVqVuaKHT/ha5ah3w6hvXJBdXk5GEpBCCI1W5ubkoLy/nCDjRHVmtVthsNp2z4PF4cPToUQwfPlwHVaAFXn7GR44cUVUnaws+yKmlZyRHVqg/8vPzVbrxM2fOhBACW7ZswYkTJ7Bv3z5s3rwZy5Ytw9y5c/maVFzQqlUrNG7cmK8XGhoKf39/1UHoVprWqQ4LC0NsbCySk5N5LMnvr1Onjs/qUNKgDw8Ph8ViAQDm4QsKCjKM6l65coWrcsmCgoJU3Ko//PADDh48iPnz5+Oee+7Racf7+l05OTlYvnw5PvroI5w4cYL7XQuN6NmzJzMS1CT1CIDhGhaLxWe0V7bU1FQe4wcOHED79u1VPJTNmzfH1q1b8dVXX6kif1u2bAEAjv6SClB5eTlGjRqlYkNYuXIlIiMjb9mhPHDgAH+fHOkHqiEfiYmJOkypLxWosrIyrFq1Cl26dNFFXW02Gzp16oRVq1bVStwNVBfLUKM1lZR8SIDCyNxuN2NCY2NjsX79ehQUFKBbt258GLiZFh0djXnz5unS9EVFRfysCO+5evXqWn/TkSNH+NqyQo3soMbGxhpSyimKV+1sxowZnHmbO3cuv0fL+XvlyhUcPHhQN9602QOKdu/ateu2yi/ebAsKi4QrrgFs0fWR3XswFKujVtWqX7P9ahzKVz++ivrzDtbuSGpa/MN7Ue+RfQho1uOODFiLxcISdFSlSdWG8kJps9mY3oP+NnnyZADVSjmykfPZpEkTXL9+nRfQZ599lp1GOkX7chgp0pidna26F1oMqWgnPDzcZ8pMa5R2JW4zbXO5XHC5XD6jYkA11Y68uVK1phyRJRs9ejSE8EaEp06dapgSE0LgpZdeUn2OqiMPHz58U79NazKuMzo6mh0WSmHK2D2t81dRUYFFixap8GL+/v7o1KkThg0bhkaNGqmeG6kUDR8+XKU93bRpUzz22GOYPXs2swX07NlTFZU1wgpTRPDnjGc/Pz++t7p16yI1NRUZGRnIyclB586dVY4gvW/mzJnYvHkzj1nqK4qk5+Xlqfpn7dq1jJf0RVDvcDjQvHlzPPLII/jiiy/4syEhIYiJieF/E/asY8eOumdIGDQZK0rRFqNU/x/+8AcI4Y14lpSUMD5Uu/ka3a92XLpcLqxbt44dhvT0dBW7gpFRZEurk+7LHA4HnE6nal1JTU3FU089xc9g3759fG9yFIlomYSoruAlq6ysxJQpU/hgQVG0m9XZJr5E6rd169apXl+7di3fk6JUK76Eh4frZCGN7KuvvuIxaBSFDQwMRG5uLpYsWaKqnL527ZoKLyhzwZ45c4YdK1l6saioCK+88go7jbWlpxVF4THdunVrTk/LEbrQ0FBVpXirVq2wY8cOFBcX87VlRSdZrMKX0Tyw2WwAgN27d/s8HLlcLmRmZrID7AuGUVxczEVJ2t/oa7wdO3aMn0n79u35HiwWy/+JUymPCfr/P/zhD7X256/RfhUO5ep3Lv6i6i0Skg/MHnJHBmrr1q11uqk06aZNm8YnPqKHmTt3Lqc4jxw5onMoSYZNu2j52sjq1q3LEViLxYJNmzapFn5ycIXwqjJQ9XjPnj1Vp9Du3bvXKENHJld/C+FNM3g8HixevFilaDJx4kSf8m9G/Jx+fn5o0KCB6n2EvwoLC1NxDVJkTrvYJSQksAwZpfm7du16S+MNqMYFCiH4hB8WFoZLly7B4/GoIqQdO3bEjh078Nxzz6Fv376qKCMVfCQnJ6N+/fqoW7cuIiMjERQUdFsUJBwOh654KzU1Fe3atUOvXr0wdOhQLqJ64oknsH79euzatQtHjx7FuXPncP36dXg8HibHJ0eqNtqgn376CfPnz1cVok2dOpX1md9//32OmCQmJvJ4rKysrLHil/rEz8/PZzGVyWTSRRlIW16GCpw5cwZCeA9QslF0TJtG3LlzJxRFgb+/P0uNyjyUJ06cQK9evQyfW2JiYo1FgHa7nQ8B4eHhHNmUo1NEYSWE8IlXBbzO1OjRo1VR79jYWDz88MO66BxRftntdhw+fBj/+Mc/GAdIn23YsCFMJpNhhNfj8WDBggWq5zx58mT85z//8Xl/x48fZ8hFcnIy8xXSGkHrGjmU9evXV2VghBC1sgXIGadly5bhqaeeUlFIEWUZvcfpdDKTghCC4RBCCCxZsgRCVCtJZWdns4OudVbJsU5MTESHDh3Qo0cP1XtSU1NRVlaGYcOGQQi9I0hjPykpCT/99BPWrVuHJk2a6NZ2KnChdHSjRo1q7BOK1NO9ELTI13jctGkT3n//fQhRO/H+V199pVM7EsLLm2wUDfZ4PKoDr6IoyMvLQ0VFBb744gsIIWpU2vpfNFIZ+s3Udtc7lK9+fPW28kxF5w68IwOUQNchISG4fPkyc4uNHTsWQDWdC0UCPvvsM5jNZlgsFnbCqOrb6PomkwnZ2dnIy8vDunXrcO7cOY6UERh97969rL7w2GOPobKykrFK1IjwNy4ujqOI8inUZrNh1apVPp/HypUrVZGYoKAg1evjx49XLRgWiwXDhg3TLTwyPydFbOrVqwd/f39+DxFJUwsODsZTTz3FyiHBwcGoW7cuzGYz4wvl/mrZsiUTb1+7dg2nT5/GoUOHsH37djz33HNYsGCBDu/XunVrVTGGyWRi8uSfOzbMZjPsdjtcLhdCQkIQFRWFxMREjmKEhITwBjdy5Ejk5OQgLi7O54ZgsViwZs0aAF6sqYyfPHTokO6ZUTHRa6+9VuNcI63okJAQ5Obm1spD+Y9//ANCeEnqyYmmfkpMTGR5yaVLl6Jnz54qR1vbP0JURzFffvllLnRZsWKF6jsJn6gtMHC73QgODobJZOJNvKaIYFhYmGrs7tu3j4urZHyY7FDKtmfPHuTk5OiyA+SUUNRtypQpuPfee9GkSROfv99ut/Nr9PmRI0eqnM3r16+joKCAHQwhqtOaBQUFut8nc8vGxcWponQ7duzQba5CGON2ySIjI+Hv7696zqNGjdLRY3300Uec+n///fehKAoyMzMxY8YMdtJcLhfmzJmDqqoqVo956623VKleUnExMnLW6KBMB/aysjJ06NCB7+/xxx/H/v370aVLF926ajKZfGY6ZCq3Dh06ID8/H5s2bdLhjAEvfZS8XvTo0QMejwdBQUEIDw/XvZ94krVzq7i4WAf18Pf3h8Ph4PvMyMjQcfM+//zzhuwHBAFYsWIFYyiffPJJFeaf9goj7ksSUpDHm7aFhISo7ufHH3/EzJkzVUWZhOsMDQ3FxYsXcf369TsmjXyra3LTpk1rPBj9Gu2udii/Ka1A/XkHb5szGf/IfsTPfA2OsNtLY/DGG28wpUvv3r35/mNiYmAymTBu3DhOQQYGBvp0GuvWrYvc3FzYbDY+UdOGLYRXuk82kkpbvnw5/03W4ZYnLmFmyChyIXMzyjJ0qampqtP1hQsXmNtQXvi0p1u5unXHjh0qjsLevXvj73//O7+XNhwqfCH80kcffaRKjbhcLvTu3RsPPfQQ7rvvPvTr109VFe/v74/o6GjeYG9Ho2dksViQlJSEJk2aoFGjRjUS9NatWxczZ87EpUuXDOUMjSwgIACJiYmGr5WXl9cYxYyMjFRRq+zbt8/wOjdu3ICiKCr5Tl+2atUq1WZTkxGVyrvvvgvAmy6uaQOiRptfUFAQFi9eDI/HA7PZjKysLL72hQsX+FBy77338sZF97d3717d/Zw+fZqrWwkD6wuzeP/990MIgU8++QSHDh3iQgxt1MKXQwkAly9f5rmpbcSq4HK58M033/BnCNMZHx+PBQsW4N5770Xjxo19Hh7MZrPKabXZbOjQoQNOnTrFhyitHKMvblnZaNPv3Lkzj+maJDDlopxt27Yx9tJkMqFfv34oLi7WFSdRxFUWLli2bJnqfsrKymA2mxEXFwcA+OMf/8i/1egZE1tAeno6OnXqBEVRVNcrKirC7NmzGTL0c2AfW7duVaW8fdmWLVs4Krhy5UqWWKQ5qYV5kBHUiOZNRUUFz5unnnoKJSUlmDJligqPSQeN6Oho5ObmGmKyk5KSsGHDBgQEBCAiIoK/j5R0iDZo2bJlus/t27cPlZWVWLx4sUo1yeVyoX///jzvTCYTc7DS67t27UJeXh7fvVpdmwAAIABJREFUI8E2aG9Yvnw573/y+kkY9P/L5nA4sG/fPmzcuBHTp09H165dkZqaekuMAXeT3dUO5X0bTyJp7gGk/f4trHv3Eo5d/Ce+veE9Uax4+28qZ7HenDfx2Jt/xbt/K8H/+/7f+Lf7J3xZcgNrj36J9IWHqp3K2fsQOfSx2zoomzdvzrgsinwYOR42m42dxgceeADr1q1jKgU6sZ4+fZonqhDV6jSEWSRCcsCrJiGEwKBBg1T9Jmt700Jep04d1YmZKpS1TmpVVRVGjhzJC8DYsWMxZswY/veIESNUFcn+/v44fvw49uzZg8cffxxCeFNoEydOxPDhw9GnTx8muKXPWK1WBAQEcFT3l/Y/LaBxcXGcClMUBa1bt9Zt+DabDa1atcL69evx6aefoqioCG63G2+99RYviNTnWh7KCxcucERFbpmZmTcFFTCyhg0b+lTtOHbsGG8ctDHKESJtRCM0NBSdO3c2LEyoX78+LBbLTWHgZDnJmhzjqKgoOJ1OLF68GDk5OT4dei2FSmRkpI5UOiIiQrUJAt70uJZUmqJTvvqbnCyn0wmTycRE1Fq7cuUKhPDCNYg+yWgTMXIoPR4PJk6cyM9k8ODBcLvd7Oxom9lsVhWoUdEO/Y2ob1asWMFFX0apVu116W+ZmZkYOXIkli1bhqVLl9bKLUvZEz8/PyiKgq1bt/L3jRw50vAzRlXeBw4c4AgUrQ+KouD1119neI8Q3kKrmtRrxo0bByG8Dg8dzAlfK0fcS0pKYLPZYLfb8cILLzCUIyUlBQEBATWuJaGhoZgwYYIu0ti/f/8a15Zx48bhnXfe0c0bumdZFhQAZs+ezZ99+eWXDX8v4Yrj4uJQWVnJjB6kL0/2+eef85qlvS+Xy4U+ffowcbqMgSXJWzocaR1KoBqjn5qaqhtbspACGUFZhPAqupWUlOg+V6dOHWzatAmffvophBAoLCwE4N3T5IMvjfd77rkHzzzzzC9e/29XkyPWMmb712R3rUN58R8/sBOYu/QIyv/9I05e/havfORN2Wodyka/fws/VP6Il09ewcTtn2DohhN47M2/oqzCjb/94wddpNMSVrO28M9tdrtd5TRSJMCXnq/H4+FI4unTp1UOi5YolnAscuGKw+FAWloa/5u0jp1Op0qC0WQyIS0tDUeOHMHOnTuxdu1ahISEwGQy4f7778fgwYPRs2dPtG3bFs2bN9fR3tB1fk6fEJ7K4XCooi12ux3169c3jML5+flh5cqV2LlzJ9555x2cPXsW//znP+HxeFRUJNOnT9f16YEDB6AoXsWir776CqmpqbBYLJgyZYoqghYaGoq8vDyuqrfZbCoOPpfLhZSUFOTn5xtqPgtRnR77uQ4lbWgyfu1f//oXR2vNZrMKtkCYNrkfu3fvjt69e+sA+IGBgWjbti2WLFmCuXPnQoibB6MTJjg2NlaFg7106RLmzp2rw9EqioK4uDh06dIFiqLwM5XHkMVi8cnfR3J2RiaTSterV4/VN3wZRVi02EmtUaTIiOBd/r1CVDuUb731FkdO69ati9OnT/N7qShv3bp17OzLm25ISAjy8vLw2WefwWQyISEhgQspGjdujJycHNUc0xLb37hxA4cOHeLIJm2ARvPSarUiKioKLVu2ZGfz5MmTTN1ls9nw17/+FWazGYGBgVizZg1/Ni0tTTeea6INIuyp0fxo1KhRjc8A8B4cbDYbV967XC5ER0ezY9yiRQuWmDT6DhnTOHz4cI7s+fv7Y/Xq1Swq4XQ6deTeRC8mhEBpaSnmzJnD807+DnpegwYN4uxJw4YNDRWx5OioEWcsEasLUR3NLCwsxBdffIHZs2ejWbNmqiIrIbx0XF27djUsBrJaraqD09mzZyGEwKhRowDoHUoqnvPVnyEhIVi+fDmPO4/Hw8wWQni5gokPWB5/BDOgA+mBAwdYCpdwlPKepN0P/v/SEhMTVWpCvya7ax3KBfvOGVZ0N3vsTwCMI5QZj/1J9/6J2z8BAEzb8Wn132fvQ2i3B2/rIKQNVj7JElWIEMYVqGT0WZm7bMiQIYz3W7VqFRYuXIipU6fypK5Tpw6ys7M5NRkTE8OTU5tauNlGFeNWq9Xw87RQOp1OFS9ZUFAQXnzxRbhcLgQEBODChQv4/vvvfUbDLly4YAjypmaz2XxKFwLVJ3wjjWSy3bt3M4Ceoga0oF66dAkjR45UpY1MJhPy8/NRVlbGHJjyghsQEIBevXpxFCYoKAgrVqzg92gVgG7WaPGlSMyaNWu4nzMzMxnfRIv2wYMHUVpaqsJt2Ww2hj243W7s2LEDAwYMYMJ8uW+dTifmz5+Pr7/+usb7kkmIAwICVFRC8mbUq1cvHDx4EB6PR4VjlPlfrVarKlKclpamYxUg7K0RnguoJpWm8VaTyZAPGWIhG8meCiGwfv16n9cih3LKlCk8Zmnj1JrT6eTq86qqKiaYNhrjWoeB+rRBgwZchVwbbMLpdCI1NRVut5sjuUFBQejVqxfS09MRFhbm8xDodDrRsmVLLjjLyMjgzAE9c9nJ9uVQXrlypUZYRk1YyL///e94+eWXUVBQwFkPLbWaPD+FEIiKikJ+fj5L+Q0dOhSA1+nJy8vj/h4xYoRqbdiwYQPfZ7NmzbjoaufOnRBCqA4z8tj/+uuv8fvf/x5ZWVm6ZxYTE4P+/fvj1VdfVVU4C+HFztM47Nq1q+peiNGCWmhoqOp3E+MDzRmtMAIVoGnpljIzM7Ft2zZ4PB6EhoaychU5lAsXLuTouHYs3rhxA263GwUFBdxP/v7+mDt3LmNuiW2DWsOGDWE2mxEVFYVDhw7xQYv6if6blpbGOGaPx8NOpvwbbkeB4u1oFosFs2bNqnHe3c121zqU7Z9+xxAH6cuh9NWyl3gpY5566wvV32MffPG2DkRKxTz77LOYN28eHnjgAS4soPR1SkoKkpKSEBMToyJ3/rnfaeQ4ulwupKWlsbOUnZ2tqoROSUnBxo0bsX//fq7ClbFrixYt4k2oU6dOKC8vR1lZGdq2bcvXeOSRRwB49V0pkkWVkqNHj6712e7fv1/HKym3pKSkGj9PuMzaCN23b9/OVbva3/nNN99wtFKuINc2l8uF48ePo6qqSpW6HTFiBACvvB1tYmPGjKn1t2uNKpHHjx/PHIQul0ulVwxURz0cDgdH1oTwpknJCUhKSsJf//pX1ec8Hg/279+PESNG6IoQHA4HMjIyMGvWLE73njhxAg8++KChw5OSkoLx48fj+PHjLAMqm0ziLTeKSl69epWxaTR2qFCI0rA1pUa//PJLvqYvUmkqLCJKHLnCnOzzzz9XHZpkGInWyKGk9+bm5hpqXZOmtDarcPbsWRUDhMPhYK4+aiaTCZ06deIo04oVKyCEb0wsUC3D2blzZ4ZB/O53vzPsE4pszp8/n9ekmrTRZejCwIEDcfLkSUMeyj179qgc5tatW+PMmTO4evWqavyEh4ejd+/e6Nq1K5KTk2tMTyuKwo7JCy+8gNdee40PytHR0fz79u3bByG8hUT79+/n9S4hIQGff/65YZ9VVFRwFNlkMmHWrFkIDw/neyF6MbfbzX1DOHJZFrR///5o27atDscYGRnJa8TXX3+NqqoqLhKKjo7G7t27kZeXx1h0amazGQ0bNkR+fr6K2aBNmzY+o/YUha1Xrx42btyIjIwMfhZWq5Vff+ONNwzlG7Ozs1FeXo5nn30WQqix8B6PB4sWLfJJjeRyufiwQYWTL7zwAjweD0aNGqUa11poS1VVlWEwYfbs2TeFv/5ftPfee8/nvLvb7a50KG/8p8pQAefnOJQz//gZACDvpY91BTqK9X9zKpKVcQIDAxEeHo64uDikpKSgadOmOixcdnY2Fi5ciFWrVmH79u04dOgQTp8+jWvXrsHtdsPj8TDoXy5eIfJbAv5TKpyiPwQaj4qKYtLkBg0awGKx4KOPPmKgfWhoqAo/A4AjTuQcE+5n8ODBsFqt7PAYVUKSvfTSS4xxNJlMuOeee1BcXIznn39e12dUxaw1Ot1rwfi+jNI7tBl4PB4cOHCAcUkDBw5Eq1atfKZe7HY7XnrpJT7ZUzRZxtjIBM7Nmze/6YIcoNoxoDZ8+HBd1JV+s9Zha9u2LV9DxrmOGjXKMHJLwPpp06bh/vvvZ0qXmsbu1KlTWVUkLS0NHo8HFy5cgBDV0aFDhw7pIAFmsxnbt29nXlL5WV2/fh2DBg3i746KimInqiapwXPnzkEIwQ5ZfHy8TvmD6JiqqqoMOTC/+OIL2O12mEwmHD58WMV2oLWzZ8/yeLXZbHjjjTd83htJhxphNktKSpCdna3rH3njpf+2aNGCD2dGcA4yOgySvvjNKMVQOleGHdy4cQP79+9XHahkHlJti4qKQnJysmrNSklJwbPPPotp06aha9euhhRq8nxKTExEx44dMWnSJGzevJnXDIrWk8Px7rvv4ocffuC1xWq1ssJWQUEBzzd6zRecQmsffPCBquCF1IZkZS/igo2MjMTIkSMhhD5qC6jJ1uWDnhDeCF+dOnV0h1XZCbfZbMxjrLU6deqoCPjJDh06xH0pRDXutbKyEk888YROdYtahw4d4OfnB39/f9X3UX8///zzqu/Zv3+/jgLNarUiMjKS31NVVQWHw4GgoCBMmzaNxzL9RhlmIBeMduvWTQXR+b/kp9Q+s5vRg79b7a50KM8Vfe/TQbwVhzLrybfxzx8q8dm1MiTO0b9ujax3WwYhLU5JSUk4cuQIaxQPHDiQfxOlUYy49SiCRg6B2Wyu0TEDvBNZPkE+9NBD/Bo5joTvkvFpRCFDeEFZMUJRFEyaNEm3uFHKeNiwYfB4PMjPz+cFIy4ujjdumfKHzOPxYMWKFbwwWa1WjB49mlPar776KhRFQUBAAC5duqTayAIDA/HYY4+p7mfixIkQwotfu1lbu3YtX5PSRYqicBRCURQ0adIEa9euZb68jRs36tKV/v7+cDqdhou8nOINCgq6qSpBObJiNpt1cpRktIFoIwZEAUV2/vx5jvwGBAToaIIqKys5XV+3bl1VlIiojbSOREpKCsaNG8eYzmbNmjHc4emnn+aDhbyJhISEcGSHdO6NqqRv3Lihqg4VwptG9HVQoGsdOHCAHQqHw8Hpc9K1nj9/Pn+GikYOHjyIy5cvcyEKYWVpbMtsB1VVVTqpudrSYHa7HQkJCfzviooKLFiwQLW5u1wulSNGspgBAQHYuHGjTioxKCjIkAYKqI4G2+12HD9+vMZ7A7yHErvdzmlQrf3lL3/h5xcfHw/AS2VTk3Poq9F1kpOT8eCDD2LdunUYMmSIqgp4yZIlhs85JCSEI+nz5s1j/PCcOXNU2vPyfXXo0OGm1HFkI1wgXYP4XMlkjKAQXoxrTTjpqqoqPPLII/xMausjOoA9+uijEMI422KxWJCZman62/fff89k7EVFRSz7OmbMGCxcuLDG50XrnTw/AO+6EBgYyPuOfPCnZzlgwADODAkh0KdPH4YNyKlw2gt79OihghkkJiby9xOulPpLHjcbN27k3/R/0fz8/G55LN1Ndlc6lH+5+t0vdiibLvoTzv+/cvzzh/+g7VNHDN9ji65/WwYhpZTr1q2LkydPQlEUREVF6egsiJdLNqrepolLFdbaz8v2r3/9ix0YmqR0XQJky5g+bQXtoUOHeNGTNbmN+PqI2ke70ROfmryAWq1WFZB73rx57CwT8bVcfEIpM6fTyc4RSQWazWaOhvr5+aGgoAClpaV8vwQ4v1mbNm2a7rklJiZi0aJFPiOKLpcLSUlJHAWiz5nNZvTr109VkEH9npCQwIcCrXIPWWlpKTv9dOKvqdCE+EaF8EYF6f+1mt5kK1as4M0yKSkJPXr00BE9u1wutGnTBosWLdI5pufOnePNwyj1LTdyROW5oCWzDw0Nhc1m80ly73a7VRQiTqcTjzzyiC5SQJFSus6ePXu4cOOxxx5j50wep3JlMDmTe/bs4de/++47CFGNcd65c6eKOuvtt9+GEMYOMdnrr78OIbyFFWvWrFHRANlsNnTt2pWd3uLiYh02V4jqCt/KykosWbJE5Vg6nU7cc889OH36NCorK1WR6tq0wckoS1ETpICoxITwamknJyersLra5u/vj8TERNSrVw9xcXEIDg42TKPb7XZERUWhRYsWaNSoETuMTqcTDz/8sOo5U0aBxq4Q1XrQBw8eVPWdoiiqg8CtGFEaPfzww6r+nDBhAgDoyPdlXXPAe2DYvHkz+vTpoyJMp37JycnBk08+ia+//poxzUZ906BBAy5YlPvhn//8J4TQR+wJX7tjxw5UVVVh9erVKsdYHm9UoEmHL7nFxMRg1qxZ7DydOHFCtQ9ZrVaMGTMGGRkZKtJ7raMt4/4tFgtfZ968edxPMg3RoEGDeH6WlZXp7isoKAhnz56tEWN/J5vJZMKAAQN+K8q5m+yXRijTFx7C53//HqX/cqPHymM+33e7IpS+NlqHw4GAgACEhYWxrjRtVJ07d+bTnIxtW716NYYM8Sr69OrVS+fsfP755xypGjFiBCoqKvizixYt4tOd7BxqOf6uXr2qkrsjnWbtBl5ZWakjH5dNCK+KjLz5PfTQQ5g0aRKfTAMCArBw4UKdcyxXYl++fJn/TipBQgi0aNECy5Yt41SSvGjLCju+7Nq1axg/frxq0aONrLaiFABMzC2EwNGjR1n3Wk7VhISEYMyYMbhy5QrjTLdu3crOsJaLbvHixXxNiqwQzYeRY1tVVcVOXUFBAeLj49lhDQgIUDlpN27cwPr169GjRw8dibbdbkf79u15bD3zzDM1/nZZKefKlSuYP38+QyLkJm9mkyZNMrwW0VjVlM4GvJs4RVDp2hMmTOB+SUtL01EsffXVV6p0+3PPPae7LhE7CyHwyiuv6F5PSkqC1WrlaJjdbmf4SE08lGRURSzLUWZlZWHnzp26cU8R5H79+uk2Mvn5p6enw2q1YtasWSpVGJoDDofDMCNgZD/88AMsFgtiYmJw7do1bN++HVOnTkWXLl0Y02hUPEQFf0brm68Ue1FREYTw4pUXLlyI/v3711ogJIQXZzlkyBA888wzqrEbGRnJBV80T6hpVbVu1uQ0LT0f2ZGV5/fq1at5HVi8eDG6du2qm1shISHo2LEjzGazT05ZcsS6du3qMwJnNpuRkZGBmTNncuZIPgAQU0N2djbjK2ns0KFOxvBSBTvBAoTwFkn169dPFSkPCQlRzeOUlBS43W5UVVVxgR0Z9VPPnj1VY4NgKITXPHr0qIpcPyIigvGlEREROHbsGBcw0dqwZs0aPrz/Xxfp3Mz+cjfaXelQ/usXYCjJmSyrcKP3c+/5dCZvJ4ZS67A0aNAAbdq0QXp6OlJSUhAbG4vw8PAaT/u1NUqH07+dTicrrmgX6qioKEycOBGFhYWYN28ehPBiVt577z2MHTuWN74+ffpwClgIPQ8aRdF8VcEK4cX8+fn56bjSwsLCeFPWGun82u12Hd+Xx+NRLep0T88995zq+j169DCMzpSXl6OwsFCViqVG/GdCeKPJRlJzstGCTUokLpcLUVFRALxO1pgxY1QSYnTP9evXR1lZGadb09PTceLECY76hYSEqCIrhB/cv3+/ri/IWbHZbFxtOWrUKE7j16tXDx07dtSNwbCwMHTv3h1Tp05lhzwmJgYnT56ExWKpdTMmh9LtdmPatGm8wGv1x7V9HBkZiV69emHjxo0qByk2NhZms7nGdBIB/K9evYr169dzf5rNZgwZMgT+/v6cjpVNjnTExsaqKsWvX7+uKp6ggjLZ5IKzHj16qFKbvhzK48ePo3v37qpxn5aWhlWrVvnEYFHE6MEHHwRQHTWUaVcoEkYpd4KGrFy5Uufcmc1mzJgxQ1ckpHUafUlCUsEgjaFJkybp5llgYCAef/xxREREqL5/yJAhhhkUeoa+ouc3btzAn//8Z3Y2Y2NjayQfDw8PZ1EGIbwZgCeeeIL7i9Kut2IE0dGua3IkjVpubq6u/yIiItCzZ0+88MILPFaoWtyIJogODzLTB63LiqJgyZIlhvNLCG/wYdKkSYbp4UaNGvF4c7vdjEOk6CDgFdegMSrDHSorK9GnTx9d39N9vPLKK0xpJRfWHD9+nN/r7++PZ599Fm3bttVd5+LFi4bk+nPmzFGxkdDn+vXrB8DLvkD7U3Z2Nt577z00btz4lvbK29FsNtuvktz8rnQogZ9X5U3O5Pf//hF9Vx+vMSUeM+GF2zb4goODedIGBATU+Lvy8vL4c5mZmXC73Yx7GTVqFHbs2IE1a9bg0UcfZf7Ivn37qopZ4uPjVZrQP5ccnCJdWtxWfHw8LwbBwcHo1asXhgwZgvHjx2PWrFl44oknmLbD12SPiIhgJQjZSOfXarX6rMakTS4yMhKKouD06dN8wpdxPIqioEuXLrhw4QKWL1+O+vXr8wJFnIVCeCNOR44cYUUWcrCSkpJ8bv579+7lhQWopgOZPHmy7r3EHyqf+qOjo7F48WIVRYYQAhMnTtRtxKQtLUcXPB4Pp7dMJhMaN26MsLAwmEwmtG7dWkciHhUVhb59+2Lr1q261LLH48HUqVP5OZMTXBMmjFJOsj7y8uXLudBAdqSPHTvmszCByNZJk13mUNUaOcxydGDXrl0qHGJYWJhKeQYAV5ZScQXpVpeVlfH9PP/880yjRM7OiRMnVJWljRs31t2T7FCeP38egwcPVvU9RasWLFjg83cB1TjY5ORkw3uX52BGRgbjQXfv3q3ilj1x4gROnjyp+4zFYjEkwJZfJ6dxy5YtqqwA4HXKhw8frjokUATP7Xbzd82aNYvHJelWyxYZGVnrGmhku3fvNizMqE3pxmQyYeDAgXj66adx4sSJWgsqKioqYLFYdBXrZ86c8QnvCAkJ4bXEV5SdouvaLANFVdu0aaOb95QZEqI6Yj169Gh8/PHHfJjS/n6TyYSMjAzs379fd72KigreJxYvXgwAmD59On/24Ycfxvfff4+RI0fycw4PD8eqVauwdetWNG/eXPV9fn5+MJlMjCu///77VQILcl9fu3aNx4XcjLChf/rTn/g6WpUmKswiJ75x48b44Ycf+HD+v2xG68HdbnetQ6nloRyz+SNM3P4JZu3yVm3vP1OEids/wcTtn6DB/IOoP+8gPv2mDB7Pf7HgjXO4d837qtZOclDjZ+9DSNcJd2wgdunSBQUFBXj55Zd1J2hSWDCbzbwg0OTRbvC0CdGmnpaWhh9++EHXV3Tald+7YsUKfPHFF4zRpMWpTZs2ePDBBzFs2DD07t0b7du3R2ZmpirtLm9MWvzgrTaz2YywsDDExcWpooatW7fGwIEDMW7cOBQUFGDRokVYvXo1XnnlFcTGxsLhcODdd99lLW0hBJo2bcqVj8eOHdNFIc1mM9q2bYvdu3dzqqVu3bqqiFXr1q2hKAoX9zRo0EC3CZWWlqqUJABwUco//vGPGsetL7UU6v9NmzYZfk5RFHTo0AGA1wEkfkCCJsjPwGQyIS4uDgMGDGC1oZs5TV+5ckVFSE5RAdlKSkpw77338nuio6OxdetWANXRCW2kffDgwaprVFRUYOPGjYZk60J4YRJPPvmkjnOSIo1G+Nj169errpGbm4vz58+jtLSUD1mAl05GxujRXAC86XGz2Qx/f3/07NmT+3LGjBk+lYQIgiE7GxEREZg0aRKKi4vRqlUrKIriEx8KeKPmVEhhxLNJ2FDqb3mjlXHECQkJNyUvGhYWhvvvvx+XLl3iqLxWnpGsqKgIffr04e+rW7cuK14J4XVwaDN3Op38OYquOp1OnDx5EkC18y0XI96qUfRQbu3bt8f169c5skmRRC07BjXCbGZmZmLEiBEqZ5MivytXrsTDDz+MZs2a6YpoZNodGktt27Zlp1KL2yRxCllVC6g+LLRo0cIwmpuUlAQ/Pz+GkpCDSVK98romhPfQKI9DGvfDhw/Hvn374PF4cOPGDZ5zy5YtY2y3EN7UNz3nuLg4Q/iH2+1WBT2oD8gBTUxMREhIiE7Vikz7LCIiIlQRzrNnz8Jms8FsNmPBggWq37N//36YTCaEhoayYpt27v2vWlxcHMaOHfurw1LetQ6lrJSTUPgmrn3nm4old+kR5C494vN1ANj1yTeq690JpRxfvF3kFFHqjRawefPmcYpXCP2jJG1cIYSumEc20i02mUy4fPky3wdNSCG8xRK+SKOBapyb/BtkSTHAm67au3evTs7Q5XJh0qRJGDlyJBcoBQcHq3Aw8qL9c51UX1Qm2mIT6rOUlBQsX74cL730Eg4cOICPP/6YqXMef/xx3hTT09NVCz6lme12O28SDofjpivL5aikFqoghLfSXGvBwcGIjIxEQUGBz43SbDbjzTffVN3rp59+CkVREB4eftN0Fxs3buRrNmnSBFevXsVXX32Fzp07qzB6iqLWMiYqFWoTJkxg3GFN/KNEti7Lt8nPq1WrVky2brVaVTJyZEuXLoUQ3kijXERBDtbbb7/N7/3iiy9440xJScFPP/3Er8lzIiMjg+mzSAJuy5YtuHHjBubOnauKhttsNgwbNgznz5/na1VVVcFsNtcayWjWrBmEEHj11Vd1r127dg3btm3TcVUaPX9/f3/Uq1ePI3mLFi1SEUZv27YNmZmZKiynEF5YhNYuXryI9u3b8/Nu0KCBiiqMqn7pu/38/HRRvW3btjGv5XPPPYcxY8ZACOGTraA2u3jxos+1oWnTpsyQkZuby/hegosEBQWhsLAQAwYMQHp6OsLDw29J2UtRFBQWFqJRo0Ywm83o1q0bFEVBWVmZitCeNN/lyOymTZsghNeBI6OIfJMmTXwWVxIV2XfffWeYbg8NDWUWApkn8sqVK1iwYAGysrJUhzsqnuzTpw//XUshlJqairfeeqvWZ5GVlQUhhI67Njg4GGFhYTp+TLfbzYdgut+JEyfyuh8YGIgej6QuAAAgAElEQVRp06YxZReNNcrOyE2mZiJe2f9F27BhA06dOoV//etftfbP3Wp3rUMJVGt53wzf5M22+Nn7EDV88W0fjN26dWMQc9OmTXHp0iVs2rQJ+fn56NChg44EV14E6P+7du3KkU2q9DSZTFx04ItChNLPFKV57733VNcNDg6uta/plK0lJKYN68iRI6pCHsJXCqHG7ADgyuiSkhLs3LlT5SBpK58rKytx9epVnDp1CgcPHsS2bduYfLh///6cxtQ2s9kMp9MJf3//ny3hJTt7JpMJwcHBfK8EJXA6nbxQNmvWDHPmzMHTTz+NjRs3Yu/evXj//fdx8eJFlJeX46effsKsWbNUFb4VFRVwu91YtmyZisxdURRkZWWhf//+OgddCG/0Zfz48aqqbkpjaY0iSn379q31OZP5qqJMT0/H8ePHVUU5QDUlDzVK3Xo8Ho56jh8/vtbvJWdw3bp1rAuvhWyYzWbMnDlTFXWlqCnhXi9evKhycGmjrKysZEeQHK+YmBh8+OGHuuIZuTCpoqICiqLAbrernOp27dpBCOOiHIqaGhUCkVEhRatWrW6qEEa7JlCTsZ3k+PtyVGi8yYc4Pz8/9OnTB1u3blVJeTZv3hwff/yx7hpaNZOIiAhDpZzz588z/MFqtdaqYuTLbty4wZkRRVFUmthyX6WkpCA4OBihoaH8WeLtjI6ORkVFBTweD959913k5eUZcq366ne73c6OGB1U3n//fVRVVeHgwYMqnHJKSgp/P0X+aGySlGv9+vV9HvKqqqq4yE8e9/K/Bw0aBJPJhJCQkBrx3sXFxVi6dKkh2brcbiVyLBcepaen4+zZs8jLy1NBWiIiIlBQUICPPvpI9f7w8HAoioKrV6+iqqoKhYWFqn3lnnvuUc1j7X0GBQVh//79+O9//8uZpDvZFEVBr169VAfPX6vd1Q7lN6UVOg3uX9Qe2Y/4WXtgCapz2wdlQkICJkyYgNTUVNXiAlRzP8bHx8PtduPSpUtcbSufAI0WOtKpJbzjiy++qJKT83g8vNAlJyer0iW0QN1sNSQ5PJmZmXjyySf5OwlPqSgKevbsyTQzdI9amUTCG/bo0QOXLl1SbWyK4tV0rYmU/NSpUxDCG5UwwocabeBEC2S329G2bVv+XGhoKCZOnIg1a9bg8ccfx4wZMxg316lTJ+Tm5vIiLPNS/tIqQxnLWadOHdStW5epVYzeL//O5s2b469//Su+/fZbdmjkilQjI6d3y5YtN/WsCaukXchJLYQcSo/Hw+lhGlPa1G1VVRU7xVOnTq3xe4kUXebX83g8OHr0KPLy8nT9brPZ0KhRIwQHB+uolaiYpl27drqo3OzZswFUk3lTGzRoECoqKhAaGgqTyYRnnnkGLVu2VG3mbdq0YQ7Pmqq8iVLlxx9/xDfffINt27apnEZf8ooUaezUqRMeeughbN26lQ9ucuUupeFlzsnVq1cjPj4egYGBNfYzzaHs7GwUFhaqVJ6E8DoDf/rTnww/Kx8S6DBrNpt9anlXVlay0IK/v7+hklBNRtW9QnjTujS2AgMDee04dOgQ+vXrx++zWq1MmO3xeDBs2DC+T3kuORwONG3alNO4TZo0QWlpKa91KSkpmD9/PgYMGICmTZvqKrjlcSgr4dB6Xl5ezkEEoJrXNCkpSecEejwe7NixQyekEBcXh927dwNQc+ZSlb1MT1abHT58uEa8IWGaV65cie+++073+dOnT3MK3mQywWw2w8/PT7XG0+FSCxWgKCtlQNq1awfAG4Un6Ab912q1Yty4cfj0009V13jiiSd4T/xfFuN89tlntzBi7167qx1KAHj146u3NULp37TbHRmQ2skVGhqKUaNGYezYsRCi+vQsG53sHQ4HrFYrysvLGacTGhqKdu3aITEx0bBK02QyISAggE+McnonMTERZ8+exXvvvcd/qy3NcfXqVV6ICwsLsWHDBpXzk5qaqtooKFXvC4BPPJmUOt27d69Kho5OobKVlZVh1qxZOmm6uLg4vPbaa/xv2aH+z3/+w+mZhIQEViq5ceMGxo4dqyoqWbZsGTweD9544w3+nWQULVAUhbVzXS4XGjZsCJvNhqSkJJSWluL8+fM4duwYdu/ejQ0bNmDRokX8zBRFQVJSEnJzc1UA9V+CQZWvYbVa4efnh6CgIERERKBu3bpITU1FRkYGWrduzenCwYMHY8aMGXjsscfw/PPP49VXX8Xbb7+NM2fOYMuWLar0qt1uZ1og2uS6dOnCThptLjIUQisLCQA//vgjbyjkzPkySn0T9k62KVOmQAiBPXv2YPLkyUhLS1NheknnmCKWrVq1AgB8++23KnxheHg48vPzdQ78vHnzcOTIER4z1Jo0acL4OpmdQHYoZaeRfoNRipaqp2VuWdlpNDKZW1aex0J4U6I7duxQrQNyhMzIGjZsCEVRsHbtWlWxS1xcnKqgKioqClOnTlUp/MgFWSEhIQwTkDGUWpMj6X5+fj4xm7JdvHiR5Ubp98pGz54qmgHg66+/1vW1dq7YbDYUFhaqCo8IU71161bOQuTn5xveF0EUhPDCCsjZDA8P16WAqQUEBPBBNSgoCEeOHOHo5NGjR9GlSxdVBJaEFITwVkHLJkcB4+LiamWjANTFayaTiXk0s7OzVXuTVtEqMDAQubm5eOyxx3TZoN27d7MOuAxDuX79OoSoxnebTCbV/tOkSRMeu++++y7PSzoAbNq0SSezSHvPqlWrUFZWpsqA3ekWExPzq8NK+rK73qEEgNXvXPzFkcmEwjcR2nb4bR+MISEhHC24ePEiCgsLDRe62NhYDB48GLt37+aF5r777oMQ3lObxWLhDeP+++837AcqDGnRogU6duzoU2KLlGdo8aDUrpEjAHidQ0oTyhukzWbDfffdx6+1bt2aFzfSXqaTudZIGk4IgZ07d6pee+qpp3hhzs7OxoIFC1T6tk6nkyMNJpOJHVlyNAcNGsT9TYtvv379DCN4brcb06dP52iRy+XCnDlzYLfbVRQ0cvqUFniXy8VVk0Z0IGvXruXFunnz5li1ahX69eunIxG32WyGJOJnzpzRFVnI0RUZH9WxY0e0bNkSaWlpqFevHqKjoxEaGgp/f3/Y7fZbwotpm91uR0BAgEqlRG4pKSn8exo1aoSVK1di27ZtOHjwIE6dOoWrV6+isrJSlW6uqeqZSP7r16+ve40ODrIMHB1eEhMT0axZM8PCBIoyjxs3Dnl5ear+79ixo4rMnxo5m/S8CbISFxeHKVOmoHPnziocpVELDw9Hp06dMHnyZJXT+P+x9+bhUVTZ+3h19ZakOxshC4TsQAISlrBvYd9VCIsEFwQEwbAliAgIQgQREARBEAQRBAEFUVQYhCA6ICIoEEFkIrLnh5iJTD6ZGNtM+f7+6O853NtVnYTNmZE5z3OfR0N3ddWtu5x7znvelzScPeXsjMyTW9YTq0rYy99++03iYvQW6f/444953CmK2wlPT0+XcH8nTpxAv379pDEWFxfHh4IePXqwAsrx48d5XHpT5QkICEBoaCg2b97MZPMiplA0TdMwfPhwfkfER+uZ6aBiJVr3mjZt6hWnbrPZkJWVxQcSMd2cm5sLRZFFB4wKUshWrVrF1zWykpISvPnmm7o1t6J55nA40KVLF+Tk5PC9kXiCaCKjh6K4i6y8KaetXLlSotcaOHAgCgsLmfEiPz8fixcv5nt48sknGdPcr18/HbcsHVxF7mGCP0ydOhWAOyJNn4+NjUVBQQE0TUNYWBiv2Z7Pvnr1at29v/vuu7rP0ppAAhd/RDNi7rhb7a5wKAF3pLL2tJ03jKmMfup9RD35LqLbp9+xARkYGChFH0TdXl9fXzRt2lRyHEgJx9OZMJvNXFFrZJqmsbNy+PBhPnUrisKLUFpaGtq3b2/IT0m/7e/vj4SEBHTu3Bnjx4/n06D4+bFjx/Kip2ka01qEhITg+++/5xSrZ4Uv4K4UFhd+T/1bTdOwdOlSKeKiqiratWvHFZT0PA8//DB/LzQ0lKNo48ePr3Dj8vzNWbNm8X3RBnDhwgUmEe7ZsyenmNPS0uBwODjCKgK18/LyOK2kqqqu6jkoKAjt2rXD/PnzERAQoFPBEE2ULVMUd7p179696NSpk7RJidKQ5Rnht/r164cvv/wSw4YN44iMqqqoU6cO0tPT0adPH8bSValSBQkJCYiMjGTA/e2YF1arFVWqVEG1atUQFxeHunXromnTpmjfvj1HKHr16oWpU6diwYIFWLNmDTZt2gRFUXDfffcxZvDLL7+EolzH6lK1eVxcnI5Y33Neej4LjXF/f38MGTKE56CInRTnCvVdVFQUO43nzp1DUlKSYVU4cL1QxKj4ytNWr17NmzDxIpIKFTmEYtHPhx9+CEW5Tv0kRvo1TcPs2bOlA+GoUaPKrUAHYDjekpOTGZs7YMAATgU7nU5dpuXw4cNQlOsY2vIOejt27GDnPyYmhh0asSDo2rVrWLp0qXTIpEaHgpkzZ6KwsBCapuHZZ5/l9+jj48OpUiqIEZkNRFlQb1ZeoaRo5KiJ/ZaUlCStBxaLxSvGm6qdTSYTBg0ahHnz5mHbtm3SZ0jm1mKxYMuWLXx/zz//vCQAMHLkSH4vO3bs4DUMAEcZqVFfi1Q/VqsVzZo10zFn+Pj4IDk5GX5+fjCZTHjnnXd47NlsNund+vn5oVatWnC5XMwVKl6nR48ekvQwVcHTvkL/3axZM6+R4NvVxHcmFvTd7XbXOJSAG1P58OpDiJn8UYWOZdxkd1QyfOCsO4KZVBSFq/SoVatWDVlZWZzmttvtUiqpoKAACxYsQLt27QyxdK1atcLy5ct1J3XRPCshTSYTdu3axfQmYmSoYcOGsFqtOHPmDKZNm8aRyurVq0spObHRRI6Ojsb48eOxYcMGqRKWFjf67qBBg6T7Kyws5AWHcJi0Ie7cuROpqan8G6qqIj4+Xtq0jx49CgC8mf7jH//ga5vNZqSkpEhykZVJrXnasmXLuP/pOYiqQqTsod9JSkpCQUEBXnzxRV06XlHcUaquXbsavjuqUjRSkaFoSmJiIlfImkwmHDlyBFevXuXrR0dHSxjBli1bSvKBnkZ4Rtp8fX19MWHCBMPUmdPpZLL2srIydO7cmTdCz4V3165dOH78OHbv3s3Ex9nZ2cjKysLQoUPRr18/dO3aFc2bN+e+o/R8YGAgU+fcLG8qRfHp+9WrV+doZUBAwC1FaRXFHS0nmh1K2xthKKmAp0WLFrr+PH36NBd4VZSqpHfudDp1ODkRt6oo1zlKSYbz1KlTmDt3Ls+l6tWrS/jTevXqVbrqH7geDaxVq5YOU6qqKgIDA/kw1rJlS+m7dNgUo++lpaUSFCUvL48xr1arFS+88AKzLAwZMgTz5s3zWlQSGxvLh3QqsvE0TdPw8ssvs2NC41aEdzRt2rRC55qMntWbLCsAPogaOStdunRBXl6e9PmSkhLk5OQgOzsb/fr1Q/369cvlDqU53KlTJx7bDRs25PXS4XBg8uTJuvdMIgK0FpFDSRkrVVXxwAMP8Dy69957+TlpfL344ot47LHHUKtWLcN55XQ6paK9srIyKIr7ACFSF5lMJgQHB0uR/oCAAD64E5Z10qRJusK/O9FEJ5z+uzKQgrvF7iqHkizvx//DjO0nkfqiEfn5h4gc+RpqDpzC1EB36rRDRMxPPvkk+vTpo8M6BgYGel3ASEvWW6Mo14IFC9gpdblcOqJsEZiuKDIeh6JDZCKpeKdOnaSNvXXr1hzZ9LZI+vv7Mzk0/b137958/aKiIgatL1myBMB17JK4cNaqVQvz58/niaxpGkaNGsXXFTFMVNl+5coVKIp8kvUmc1ZZE+/JZDKhZ8+euHz5MjRN4yIDWtTFvlBVFampqVi3bl2lNqiIiAhYLBaJZ5R0k0VydRF2QBXJiqLghx9+QFlZGRYvXszYOEVxO9TdunVjp/qXX37ByJEjpfE+derUcot5CIv4xRdfsLPcrl07tGvXDqqqShXBAQEB5Tqyoomk4iIPnWh08JozZw727duHLVu2YMWKFVyMQVXutBE2bNiQI9d2u/22RVJpHoiYUbvdjtatW/PGV69ePUyYMAGzZs1irNm0adOQm5uLH3/8kQ8jIhm/NysuLubxVadOHcMDZEFBAR8c6f6mTp2Kdu3aMZ1TcXGxRINEa53Vaq204wRcjxQ1btyYx0pZWRlefvll3cGX5rdIWO1wOKR1RjRPHenU1FTk5ubiwQcf5HknzsFq1aohLS0NGzduhMvlgslkQvv27VFaWspFKlWrVi33edavX69L5aanp1e6P4DrGPBZs2bp/o2q6D3HX9u2bfHII4/w342kcz2NnKgdO3ZIOtkhISHlOpt+fn5o1KgR0tPTMW/ePBw4cAAul4vp30TJV3IoCWJFLTg4WIoYAm5n1NfXV3efaWlphvdhNpuRkJDAsIRnn31WIleng8r27duRn5+PkSNHShhRGl+jR49mppHbMae9NZvNhujoaNhsNixbtgwmqw++OH0JRy/8jJP5/8A/f638IezPaHelQynaG+s3whoWh7EzF8IaFofQajXueLicGuGNiJtu69atvDGJEcT69etj1apVvFgfOnSI/33EiBEMbk5NTcX69esNcXiUelUUhYtAFOU6aTOgx+Ooqoo2bdrw/1+4cEHi8KOF7/3335f6lApUPv/8c7zxxhvIyMhA+/btERcXZ1ggRJWrdL2UlBS0bt1aSnubzWY89dRT5UrvnT17VqImUpTrkSLx9Nq3b1+ObpCM3c0YOSrp6elSn3pG0MSqeW/UPeUZpbFoUxOr/n/99Vf+HG3slDKjceRpRUVFOp5EMWocFhbG6ipUzODNvvrqK+mZCSfVoUMHafz16tWLN7jmzZvjp59+qvC5RdlDUZOYrLS0FDabTaKAASA5TRcuXEB4eDgsFgs6duxYoRNpt9tRt25dPPzww5g2bRpWrlyJ1atXY/bs2ejZsyeio6PLXR/ECOrNRlJVVYWvry8CAgJQtWpVREZGombNmkhOTkZycjI/Q3x8PMaNG4cZM2Zg8eLF2LBhA/7yl7/gq6++wsWLF5kJwmQysYPk7++PgIAA9O3bl69DmRGK1jqdTh3MxJsNHz4ciqLnYiUjPWgjbFz37t3ZgTGq7j927JgOg+rpMFSvXh3p6enYvn27YUQ1MDAQNWrUAHBd9aUyfLBGLAbt27f3ikX0NBKEEOmxPHk+qWVnZ8NkMiE0NBRlZWXIz8+XdOG9HaiA63ABetdEqL5582acO3dOx7FL84mwoN7GoOhsPvvss1AURUr9E1ZSPPiQDnvPnj35byUlJXzAT0hI4AMWRaVr1KhhyGZQt25dbN++HUVFRbBYLNKBgw7LrVq1kijlYmJidMU6t7MRtGvhqrcQ3PlxNJz2PqL/X30FtdjJHyF1/ieYsf0k8n7Ui4j82e2udygpjSJiP252I6hsM5lMEr6nffv2WLVqFYPLz549y1in8PBwvh+LxSI5LkRWTmTgiqJI+J6ysjK89tprXrnF6LoUxatVqxZXYlKqbty4cTh58qSE6xQXeTHCSEYYNaM0LcmwiY4fEf566y9a+JKTkzFu3Dgpje5ptPjRd5xOJ5YsWcILq+jQkUPvjZ+zPCOnrrLjJTIy0pBmo7JG3JzES2hU9U+8hiLJsaqqXp3wS5cuoUOHDrp7DQ0NxRNPPIG+fftCURRkZWV5vS9RZUlUAKF0JWG8SktLUVRUxNrvpHRRkV25coV5BI0KIShSm56ejjFjxqBjx45eCy+8tbCwMKxevbrcSKynuVwuZGdnG/4WOZxt27Zl0YDMzEycP38ee/bsgaK4YQqLFi3C9OnTMXbsWF6H/P390bx5c9SrVw/x8fGoXr06QkJC4O/vf0vRFyN4isViQVRUFJo2bcoRZfFz9evXx2uvvYYPP/wQhw4dwtmzZ6UxJ0IuykuPU8QpPDwcV65cYedHbEOHDmW6n4MHDxriH8X7VhSl3MIYsnr16jFdFDk8VqvV67vWNI15bAmeIx6iFcUt8lCRwy1GC9u0acNjwmQySVmc1157DYAxF+zGjRv5AJ6YmGjozFJmSVVV2Gw2Lrpq37699C5Hjx7N31mwYAE/29q1a5GTk4NZs2ZxVJWgJeWNJ7q+xWLhviAddsp4nDx5kveeAQMGsAxnUFAQr5mkakXjX5w/1F/kND7++OOM8SYhBOKhjI2N1WWCblej+xkw9AnEDFngdh4nbS8XMkeQuodXH8LFwvKjzH8mu6sdypMnT96RAVhRo5RLaGio5IyYTCYpJUjqKpQi8SzeSElJwaFDh9CkSRNeZImfT9M0TJgwQcK5FBcXY8OGDTxJxBMqVeoqilvhZunSpVAURaIMadq0KY4dO8Y8kYriTp2I2Ccy0mz2tAULFkBRrnONeZ4oHQ4HunbtiuzsbI5sVlSNnpCQgE6dOmHMmDGwWCzw9/dHcXGx7gQuYnYAt7NCVDrl4U4Bt4TeyJEjkZiYqNvYVVXF448/zgvpe++9J/02/TdF727GxD4PCwsz1NE+f/48f6ZVq1a8oYjydoAbp9emTRv+d1I5MdKapnv3pI0qKytj6hvC3lGkXdM0Cedar1496bs5OTmctqpevbohMbZoFy5c4ChGjx490LFjR8THx+vmA40Jup+aNWsiIyMDiqLoNMIVxR0xETHKN2snTpzQpUg9W2hoKJ588knmMxQpry5dugSLxQI/Pz/D9/r7779zijcgIICVZFwuF/Lz83Hs2DEdLjUzMxNDhgzhFLPnXPDx8UFAQEClnIeKmp+fH4KDgxEREYGYmBgkJSWhcePGSE1NRa9evSRM7rx587Bq1SqpoKK8Fh8fj4yMDBw6dAgul4v72dfXF1evXq3w3RC/ZHFxMUdDFUXB9OnTdZ+9evUqH5bp4E6OGFEhieOoTp062Ldvn+46x44d00mGJiQkYM6cOdi2bRtj0W02m/Q9wl6LhZUul4ufwWQyYcSIETpnmNb4l156SYrY1a1bF7t374bdbkdwcLD0nQMHDvCcysjIgKZpcDgccDgcfP3c3Fwp0BISEmI45xTleoZDVVWkp6djwIABfEARabQAN1clrT0NGjSQ1guqmP7xxx8xb948tG3bVndoU1UV3bp1w6pVq7gCf9KkSfj2229vaRwbNepb/4bdEfXku4h9+oMbKuqNn7oDtaftxKbD+j3yz2h3tUNJg/52D8KKms1mg8vlYn5Cz3tISkrC3r17GVfy3XffcdSpQYMGhhPMZDLxgrRixQpOx0ZEREg4F0o5kCwiaYMTSNrofhs1asSn45KSEqYposif0+nUaY5TdMuTOy8xMZGdDPE3aIHxloKmaEh2djbWrl0rpdGdTqdhha3RsxABMJkRT5qmafj4448xePBgxMfHS5uxzWZjh/KNN95g/rzTp0/D5XJJfHqK4t5sxX594IEHbmqsLlu2jK9RXnSEPkMLbevWrTlKmJmZKeFLU1JSvDpzn332Gbp27SrhsJKSkrBkyRKcPXuWU2udOnXCN998A0VxU9YAQO/evaU+MKK+0TQNY8eO5b5JS0vD3/72N6xbt44jjeQ0Gr1Lp9OJ+Ph4dOzYkVNRxAtYUlICRXFHLYw2QLPZjL17y5davRnbuHGj7l4pe2A0xzMyMvDFF1/wgcnonoqKitghS05ONnQ4vdn+/fslFSWK+pEjQdExl8sFu92OoKAglJWVoaCgACdPnkRWVhZv9BERERg5ciSGDx/OKUebzYYGDRogMTER0dHRCAsLY7UosQL5VjZzp9OJGjVqoHbt2sw5KRaYDRgwALNnz8by5cvx9ttvY+/evThx4gSuXr0KTdNYKvW9995jZ96IOeGTTz7hg0hmZiYCAwOlz2iaxnRM999/P7p168bPFhMTg1dffRVDhgyRODrpHinlnpOTw5FEmjuiFRcX89rqeUjPzc3lw31QUBBnAyZOnKjrN6vVKq0RlNWYN2+edM3CwkLeV2g+E9euSJ1FOPYNGzYwTjExMRE5OTmMwRUhWkb7XXh4OFJSUpCeno65c+cy/tlqtXJktDyVJIpM0vN7/kZ0dLSE175dLTg4GFVTH5LoA2+2Lf0kz+vz/VnsrnUoT548eVsIo2+00QJNJ0lKGxAfn7hQ0SQnh2b06NEoLCyEorhVWi5duoQRI0YYYmFUVcWUKVN0z6wo18mcySilQwUWRs1sNiMuLo6LWlatWgUAWLNmDS8GYrTn6NGjUBR3BSYAbN++XeLHE/t+1KhR+Pnnn7lir2HDhrp0bllZGePKjNJVFJEMCAhAenq61CfeHBKKbNKimpCQgKioKGnz9/PzQ0pKCiZPnoy8vDwmr6aq3RMnTkBR3I4bpaeIw41S+9euXWNwuaK4o7DLli2r9FglrV9yjoyqg4Hr3J02m40LvlauXIlVq1ZJz9SmTZsKqU9Eo1SWZ+vfvz+/i5CQEAQGBnIUiKKcZrNZ2rjPnz/PTmOHDh10/S2+M9FpHDt2LObOnQubzQZVVVmRhyw4OBg2mw3jxo2TKumNBANupHr5Ru3HH380VEnq1q0b8zs6HA5dwURAQACGDh2KnJwc7tMjR47wmBo6dGil7+GDDz7gMS2OfZp/hw4d4kPpm2++yfJ0NKdFKykp4RQwYaoVxRhyYWQul0uinalozQ0ODkZsbKyuD291raaooDiPAgICUL9+fY5KmkwmdOjQgeE93bt3x4YNG7Br1y58/fXXuHjxItPkDBkyBGfOnJGI1Wm9ePTRR9G2bVuYTCZOfX/wwQdc0EjRWZHqiIwgElFRUYbr3Jw5c/hA61kA2b59ex3uHXA7w06nE35+frpraprG677J5CayF2mZTpw4we+PCjhbtGgBk8nE73/Lli18D3RPNWrUwDPPPIP+/fujQYMGCA0NrTASHhkZiblz52L//v26ymkKlhDVUElJCXZ5hewAACAASURBVNasWcN8rXeihYaGIjL1gdsqjLL5Tx6pvCscyl9//ZWJk0tLS3Hw4ME7Xg1m1IYNG8YgdtHh2b59u3S/hYWFGDBggLSIDh8+HMD1E6mYgmzSpIlUzSlO7uzsbJ74FJ0S6Sg0TcPcuXOl71WrVg2BgYGIjIzE999/j6lTp6Jx48bSgkAEzv379+dnqlKlioTXczqdsFqtus3hkUce4YU5Li5OuhfCVwUGBkpazACQnZ0NRXFzyHkapYVGjx7NpOZU0U4OWevWrSWlB2+bFOnftm7dGuPGjcP69etx8eJFXjjFFG5+fj6/SwLQkzawzWZDUlISf/bq1atSXwQEBGDWrFnlYvcIouDv748rV65wtMAoSkmRLovFwk4gOVcmk4mdCFLtuRHzpLiivrPb7ejcuTPT1JDUGkXDyCn0FkWmf09KSpKkPo1gFICbxJvgGvv370dpaSleeOEFKcXo5+cHHx8f2O12aU7caWeSrKyszNCpJOf2k08+AQC8+uqrPE48ydYp0mUymQwLkoxs7dq1/L7NZjPS0tJw9epVTnuLRVr5+fn8TlRVZeonb3bgwAE+JBDVmJGVlJRg9erV6NmzJ1esi32QlJSEOXPmID8/XyoEU1UVf/3rX3X9uHz5cklCz2KxoHPnzvjss89w8uRJPuA2atQIa9aswcKFCzFt2jSMGTMGjzzyCEfLqehPVVVUq1at3IjazTTxOqqq8rsWuX5VVcX48eMRHBwMu92OL7/8EufOndM55hSNe/TRRw37eNmyZdJaTGl4OtyPHTtW9x3iNp04caLu3yhyS81sNkvRTE+Hkg6rzz33HH9GHO9paWle17RffvkFe/fuxaxZsyqkPKLIJo1pmuMippswlJ4qUbfa7HY7HOExiJ64TVd4Q63Os3/B6wfO4seiUvz627/wbf4/MGbj1+U6lLWn7fxTYyr/9A6leHr6d7ePPvqIFWI8J/CkSZN4EopE4OJCFRQUxOkastOnT/Pi5XQ68frrr8NkMsFut0tSXYQJIrJkTdMwffp0Pq2LnyVFiHbt2vHvHD9+nDnBsrOz0bJlSx2xOi34nkTs4eHhmDp1KmJjY2Gz2fi0qSh6HkoAWLp0KVchingiTdMM01U//fSTRBDucDhw5MgRnDp1CoqiMNaP5M/E+1VVFcnJyVyZbjabOVXqbbOJjY1Fhw4dkJKSIn2GoAW1atWC1WqFn5+f5FAC7sOCyGWmKO4UZFZWlu5UvnXrVphMbhk+crDOnz8vcXN6jnN6z+ScWSwWPPjgg+zoE6awsvJ2gHtjFzfGPXv24NSpU+jdu7fhGPBs/v7+UqTxzTffZHlK0UpLS9kBUFUV48aNM9yYDh8+rDs8Wa1Wjl5+8803EpaMrvdH8sVduHBB+n2KviuK2+EdP348z1HCApKEpSfek7hf+/Tpw3Q4ZJqmYeHChfwdq9WKIUOGSKnxZs2aSQcAsvPnz/M48cxmeBrJ/Pn4+HDfd+/eHfn5+ViyZAk6deqku29R95kcv7Zt26KkpIQPlCJUhyATnrZw4UIoivsgJEblnE4n+vXrx6nO6tWr66A3gDt6Xb16dZjNZjRv3hzA9cyKorgj9r/99hsAYMyYMVAUt6zqrl27sGHDBixevBj333+/bu1QFPehsGbNmkzqX5GTVF6jNU8kyQ8KCkJsbCySkpJQo0YNXSBE/H8SS1i6dCmKiop0c4fuT6SEKioq0jnDiuIugCHzdCg1TYPNZuMKdjroi/tURdhk4msV2xdffIG9e/cyXVCDBg10EAJxvoeHh0v0bLe7VX/ohXKLbz7L+wn/+OU3TNn2DdJf+wIbv3Sv0WM3HS0XU/nwar1k7J/F/vQO5b8rte3ZaOKLyiYmkwl//etfOWoWHh6Ojz76iCNNzZo1w4EDB6Ao7hMYRTFUVcXEiRMxZMgQ6aRNThbhU958801s3rxZ0h02m81Mo6Io7s1+xowZ0DSNF1NaVIgMuaysDFWqVIGqqrqo4d///ndkZ2cbFiXQ4tq4cWPeYClKRmkWI4cScDsNlO4TOdEoqiPKXRGZtqK4o1s//PADE8B73hORiC9ZsoTT0CaTCcOHD8fLL78MRVEkR/rs2bNYu3YtO4Hh4eGGNBf0jmnDi4iIkBZd0UQloPT0dENn4KOPPpKq/kUj51fE3JFsmZji9fHxMeQTrIy8HeB2OBYsWMDPW95m6W2OeYs0lmeHDh3iqERISAg/54cffog2bdpIm6jJZMJzzz0HTdOwfft2r/dX2Sjf7TSSURVbnTp1JNaFzp07c4Tq2rVrHNlt2LAhzp49y4UJnkwNoaGhiI+Pl8jnMzMzDZ1mosiiRr9H5PcUpfQWdRRhLadOncKUKVMM6b/CwsLQo0cPrFq1Sof1DA8Ph9lshtlslsbR999/DwAchfTEOJ86dYojtvRsV69exdixYxkSRM9Pc8gzldygQQOO6I0cORJ79uyR5gk59CUlJbBarQgNDQXgVoxp27YtjzfiVSX+WJrrns64pmns3Ilt+/btuO+++6Aobu7h2bNnc6FW//790a1bN7Ru3RoNGzaUDiC3UjRFTqrNZuN+9/HxQXR0NAcO6NmIB5MwipGRkXjzzTeZyeHVV19lJ5XWVoIAKYqCbdu24ZVXXuF5641dgrIddA16d56wDnHf+frrr7F3716uYg8ODkZoaOgdyzQ6qtcsN9L46BtfAtA7j5/l/YQr/yhF3JTyU9/fX/1zUgr96R1KwF188+9IcSuK2wH55ptvkJ+fLy2Aqqoyf56maZg4caIUdREpdwIDA1G1alVOY4rpBYfDgaSkJFitVv488fOFhIQAAG+0nmBmi8WCrl27SpEqsYiBKlGpOGj+/Pn8uZKSEsyYMUMXMRArOkUScbElJiaioKCAFyRvVlRUxBil5ORkli8MCwuDxWJBSUkJy4QpittZ9JSopGY2mw2dq9zcXHbgAwMDUb9+fSiKzM85evRoKIo7VU/OnKqqGDlyJN544w2MGTOGSZONFn+qRhejdIsXL2Y5srfffhtvvPEGO1E0Dmw2myHWkUirY2Nj4XK5JOofEZtLFf9GJsrbNWrUCE888QQ6dOjgtchJUdyHD/pOdHQ01q9fj/PnzzPFFTk9FBGmVqNGDUyZMqXCSnpPmzZtmiGnY61atfDiiy/i448/5iKHVatWSREykbZFjOj/0eZ5/3Xr1mU1EXJqzGYzOnXqxBurt8K0a9euYdGiRTp5O9pgO3TogMWLF+voqTyzIiRHSn20bt06hgd4Vi3TIUtVVSnqS9kKinDWqlVLp+wiWtWqVXlMEVenyHFaWFgIHx8fKWJbVlaG0NBQmEzeid7z8vLw4IMP6hzuNm3a8HgTydupWNBqtTLUp2vXrgDAxN0pKSnSodFTSIGstLSU34UnDEekwRGhAna7HQ6Hw2s/idcW1Y78/f0xc+ZM5Obm8t7x008/4bvvvsNf//pXyUG2Wq3o2LEj0tPT0bNnT6SmpqJx48YSrOR274cmkwk1atRArVq1eB2zWq24//77MXToUGRmZiI7O5sj0/fccw+OHTsGm83Ga6eiuAnayYz2HcAt4GA2m3Ht2jWmqLvdlEE1B05BdDnRyY1fXkDxr2U6xb2xm9xKbWnLPy83SjljuxyY+bPYXeFQ/jujlFS8kZ+fr0vD1a1bl++RcHfiJkjavIQPDA4OliocRefPZDJJuDjCWmZnZ0uTLTIyEqtXr8b06dMlSiB/f38MHDhQKsC4fPkyS/+1bt0aZWVlWLZsGe655x4phdalSxdpI5o0aRIUxZ1+pUXaW/+HhIQgOzsbFy9eNHx3v//+O28IRJlCm5xRWrNGjRoYMGAAtm7dirKyMsbWeFPiEPufnEGqTj19+jRycnKgKO70HZ3wU1JSdKk16reIiAjY7XacO3cONpsNQUFB6NChQ7kVy/S9jh07SnyfJpMJnTp1wrlz53T3Syd10dGaP38+NE3jTYNO/OfPn8fatWsxevRoyWk0ug9yfKlQwWq1YtOmTdJvU/p75cqVkiNA1d4ih2CPHj34AGQymZCYmIiFCxeWm34+c+YMHnnkEZ2TYDab8cILL0iffffdd6X3P2zYMN0zecOi/REmRs9F3HRYWBg0TcM777wjHfQaNGhgyLF67do1PPjgg+wIhIaGYuHChVizZg169eqlo6kJCAhAq1atMGfOHC4co3GsqiqOHDkCRXHDQAA31Q1hU9PT06WoHr27mJgYDBo0CNu3b+dIlSetzfDhw6VUq6ZpuggpHeBeeukl6RnpYJKYmAjguiRjdnZ2pfr6iy++0PGq1q5dW6cOFh4ezpFzOkB6YoQjIyMxadKkcoUUAPfBmqjPCHd4/vx5npck+uDr6yvN1W7duhlG74uKivDQQw/xe6a1e8KECSgrK0NISAhUVcWJEyek71HqNygoiL9jtE7R2iyunyILSHFxMc6cOYODBw9i5MiRUjFT586d8dBDD6Fdu3Y8lunffH19UaVKFTidTkNd+xtpdrudn8FqtSIhIQH16tVD8+bNpTUyLi6OOU4rou26kebn54fo0WvKjTB+feFnHLt4Tff3zi99CgCY/G5uud9PffGTSo3p/za7KxxKwL0B3y6ptco2OuU+++yznOIUZb2Id5KiXlWrVsUPP/yADRs28GRPSkrCX/7yF+m67dq144Vu69atEv6RFirSBBY3GJF4muzKlSt44oknpGIVakSZ4+vri2bNmnH/mc1mNGvWDO+8845X8DUBy0Ui9sDAQLhcLmzbtk1Hr0P91ahRI0yePFmKzB0/ftyQgJtacHAwdu3aZXgvlJLxVhkt2rVr15hvjhYW0Rl3OBxeyZSJNFlRrtOBUPTY086dO4e1a9dizJgxaNGiRaXGUkBAAAYNGoRXXnkFXbt21WEIMzMz2WkUi4SMCmFE7s5x48ZxJMDHxwc5OTl8T1FRUYZcfyUlJfD394fZbObUHqUqa9SowZuQyPv5/vvvo1WrVlL6sHHjxkxFUlBQgHHjxkm8pFWqVMFjjz2GCxcuYOvWrRzpSUhIwHfffYcFCxZITo+vr6+hPjJRZP07TEzDk6whzaGNGzeyJJ3T6ZTmSuvWrXHq1Cnk5+ejV69e/L6joqK8jkGXy4W3334b/fr1Q2RkpOGmTlATctY3b96MjIwM1KlTRwcloPukd1SeeUb6d+zYgZ07d7KzTFE1cnxMJpPhoYLgOuSIN2nS5Ib7XDxIerY6derA5XKhoKAAmZmZuixK9+7dbximIUrGPvfcc3xYowIoABKZu/ieW7VqhW+//RZXrlzBvffey++5Ro0aeOutt6BpGkdBqUrf81AFXNdSb926NUpKSiRM+KRJk3Dp0iUuyhTHRUpKSrnPduTIEV4D27VrhxUrVrDqkYhfNOozSpVHRUWxUx8XF4d169Zh8eLFmDFjBkczq1evzu9M3M+qVKkCf39/+Pj4VCiAcbua3RHgtRCH2g8Fxfj0b1d1f2/y/B4AwLy/fFfu92Mnf/SnlGm8axzKP5LEvHr16vj73/+OoqIiKQ1HtBy0WIoObqtWraQF1uVycRRKbJ4ksYC7yttsNkv6zWKrbEHCqVOnDFUsqNWtWxdLly6tdKUsyfdRo+pWMkVRMHDgQOzevduQ89FzQxSrQsVmVOBBNmPGDCiKLAdWke3cuVOXQhk4cGCFfUi4MsJweXMoPe3kyZOSYzR9+nSm1YmMjLzpRTQmJoadxvXr15e7UW7dulXq+549e5brRBC2l/qGjHC4DodDRyQPuCNWK1euRHJysuG7dDgc6Nu3L5N3i1ZWVqYjxPb398f777+Pt99+m//mGbm+EQWc222kOCW2p556SkqpNm7cmOEYR44c0SmzKIo70najik6apmHHjh06vW6jZrPZUKdOHaSlpUmp6RuhlwJkWhta4+bMmYPw8HCEh4ezsEFkZKTXexb10G+Ed9PTRDUrb83hcLDTK8rO3qgVFhZKkeZ69epJDiVFiYnM/Ouvv5YUzqjVqlVLd/AXI56elG9kFHkUlcv279+vi1z36tVLEkkgMYLyjEQoqDmdTuTm5jLFEamrGZnIk5mYmKibi3TAmTx5MgBIgQZPnXDRDh48KN2TEQzkZps1LK5C+p8fCoqx77R3h3JuBQ5lzOSPcDL/HxX2/X+bqcr/7LYbgHL/3WQy6T5n9J2KruN5TW+fv5Hr/P777+Ve/3Zcy/O6v//+u+G1b+S3yrv+zZjnb1fmWW7F6PdUVVUAcJ/cjuv+/vvvFV7vVn7rRvuYfqu88eqtvz3/bjSX/husvLnvbS24mWe8kXFEv0Gfvx1zx9s1yrv2rf4+2Z2es55W0Xru+dnbOWa99ZVnH/zRa6r4+0bf81wLxPu7kfd3W/vSbK3wM//4pUwJ8rPp/h7ka/1///5bhdf47V9/7Pj8Q+xOear/afbvSHlTpGTGjBlSyptwH5TyJvyOt5T3rl27pOumpqZyynvLli1SioBSNnl5eVJky9/fXwI8k+Xn52PUqFHlprx9fHx0Ke+mTZti8+bNN5Xy3rp1q2H0lUjEp0yZIgH8c3NzWQPaqJFyRHkp75YtW1Y4RgoLC1lJSFHcKVTPAqi33nrL8Ls3kvI+e/Ys3njjDWRkZEgV+OW1gIAAPPjgg1i2bBm6d++uG8uZmZlMGF5RylskDB8zZgy6dOkCRXGnvPfs2cMYpfJS3sTrR0VTW7ZsASCnvMUIzbZt29CyZUsp5d2kSRNs3LiRU96ZmZm6lPfQoUM55U2pxJo1a+L06dO6lLePj48Oi6wo/96U9wcffMD3YbFYOPKtqio2bdrERSJOp5ML3EwmE9q2bYvTp08jPz/fMBVqZC6XC5s3b0ZaWhqqV69uGAEmWiYx5T1mzBjUrVtXxzNLc339+vWVSnmLSi4Vpby9ZU0o5U1j8mZT3p5KXNSSkpLgcrnw97//HVlZWToqoNuZ8ha3VzHzIxYyErThypUruP/++7nfIyMjGWrgmfKeM2eO7h4o5d2mTRuUlJRIvLCTJ0/G5cuX0ahRIx5f9Ps3kvJOTU3FypUrK53yJoWe6Ohovr+4uDi88cYbrGMvprzpnYn7WXBwsJTy/iNqIfwia1cYXXzLS1HOmI3u4rHyinL+zBHKu8Kh/E8pyvEshPAsyhHvsTJFOSJ1x40U5axatQrPPPOMVJRDCjPEU6goCvLz87kop1WrVkw0TOkcmvydO3c2LMqJj4/nFGV5RTmzZs0yLEQA3CkwUcf4m2++YZ1xb0U5/fv3x5YtW264KIecHSJAPnXqFKvPVKlShfuxUaNGXotyqlWrBrvdjrNnz3JRTnkSkdQiIiLQqVMnHaayc+fOhil9cshFx3LevHnQNI3HiFiUUxlJQ9HZpKIci8Wiw+xRUc5rr72Ga9eulVuU0717d6koJykpCYsWLWLePyM7e/YsBg8erGMlUFVVt5mKRTlms9mwKIfUmv4d5q0oJzw8HJqm4e233650UY5YrFG1alUsWLAAq1atYhJx8ZkDAgLQunVrvPDCC5LGMa0hX3/9NRRFX5SjqioeeughNGzYUKL3UVUV0dHRSE9P1xXlUJrSZNJrTWuapoO+3KminIMHD+oYBmrXri2pVCmKuyCK5hQV5ZAakLhOPvXUUxUW5fzzn/+sdFGOON+6d+9u+J6LiorwyCOP6IpysrKyuCjHZDLpICFGRTmNGzfGlStXpM89/fTTfA+eRTm///47ioqKkJeXhwMHDmDEiBHSPXfq1AkPPvggUlNTdQfaO1WUQ9RrycnJaNGiBTp16sQH3vj4eIZH3NainMDgCjGUj65x0waNfksmMt93+mqlaIP+h6H8L7b/FNogcdH3pA168sknpUlIusSAnjZIdBCdTuct0QZ169ZNog0SnVRP2iBRPaGkpATZ2dk62iCKWNntdh3RMbXK0gZdu3aNr1e/fn2JNshqtepog0JCQm6JNigoKMiQNoh0xAcPHszRZFVVMWLECLz++uvIyMioFG2QWAjz8ssvM23QO++8gzVr1vDGJFbQV4Y2SIzeik52ZWmDUlJSMHr06ErpZxPRcHR0NNatW2dIG+TJ/xkVFYWpU6feVtqgefPmMW2Q3W7H6tWrvdIGiWTef7RVhjaI1F/o3ZVHG7RgwQLDzTM4OBgdO3bEkiVLdE5QZWiDSHv7008/lb4r0gZ5HmCDgoIk2iDilDQycoTISSiPNohIsStDG3T69GkMGjSIM0DU2rZtWyFtEBVwedIGNW7cWEcbNG/evHJpgzydXqINImEC+m+73Q6n0+m1n8Rri5XnxBcs0gb9+OOP+Pbbb/Hpp59KmRSiDRo4cCB69OiBtm3bIiUl5Y7SBtE8r127NkcdbTYbevfujWHDhmHChAmYNWsW0wbVq1cPubm5t0wb9Pnnn+v2xNvRYseuqzDC+FneT7hW4sLT7+Yi/bUv8Nb/IzYft9k7sfn/qrz/y+0/hdicHA1PYvPPPvvMK7F506ZNmWerXr16vGioqoqnnnoKQ4cOrZDYfNOmTZIyjclkQkREBN+Pv78/pk+fDk3TmG+RrmlEbO5JV1FQUICZM2dyGl9sFOFo0qQJLl68CEW5TmxOqbcbJTYnxQ6R2FxUXUhMTMTZs2fx0ksv6aIViuJ2Ort06YLFixfz5kKRlSVLlkBR3KkdMkpPk7MUFhZmKKtHizSl+ClSWbNmTd2zeRKbk5NmtVoxdOhQFBcXY8eOHTdEbB4aGgpVVaV7s9vtt0xs/tJLL/Hm6m3RFqlFPJu3yHN55o3Y3JNomlp2djY0TcP777/vdf79pxCbJyUlSXRIXbp04Xd07do1rppv0KABfvjhB7zwwgto06aNzmGqWrUqEhIS+J34+Phg3LhxlSI2/+WXXwC4x6FIbP3xxx8bPocnsfnUqVMNic1DQ0PRvXt3vPbaa3z4IxOJzcVxdObMGQA3Tmw+ZswY6YBO495msxkSm9OYGTlyJHJycgyJzX/55RdYrVaEhYUBcI+31NRUXitVVUWjRo2wdu3aConNxSg9tffff5+JzSdMmIDnnnsOEyZMwNChQ9GvXz907doVrVq1QoMGDViLXVxHb6Z5IzaPiYlBbGysVM2fmpqKwYMH83pUo0YNbNiwgYubVqxYUSGxOWWPQkJCvB4gb4bY/KuvvkJOTg5XixOx+Z2CsYV2yyhXJSdmslt6cc2Bs7haVIpfy/6FU/9fUYXSi//jofwvt/9U6UVxAyacy++//w7AvSCRwyV+jqQXfX19+fny8vJ4cXQ4HHj99dc5aiNiUWiBInyfpmmYMWMGR/TERYsWGlExJjc3lzEtM2bMQIsWLbxKLzZr1kzaAMPDwzF58mTExsbCarVKuMGKpBfXrVvHf/cmvUgRO2/Si7RwNWjQQIcVNZJejImJgcPhKFd6sWPHjmjcuLEUOfviiy8AXJde9PX1NZRepEixKL04YcIEnTOwbdu2G5ZepPdMG6jFYsGgQYNuWXpRJGrOycm5IelFSqN36NABY8aMwdq1a71KL1KaU1VVZGZmGmL3vvzyS+53sSKZUrbffPONzuH5o6UXz58/L/2+6CA4HA5kZWXpiLzPnz+PadOmeZVeTEtLw6ZNm3TSi4sWLWL6G6vVisGDB+P//u+6EkezZs24vzylF+nvNyO92KNHD1y5cgVLly5F586ddRQ8RLa+aNEixhiS9KJIYUPVzhVJL8bFxfFhW1Hch2FRejEyMvKmpBdbt27NfUrzY9KkSdi5cyfWr1+Pl156Cb179zbEmVPmITIyUuKqvZlGa56n9GJcXBzq1KmDqKgo3WFKXH8om7Ns2TLD6vgbkV4Uo+QVSS/OmjVLuqegoCAJfmVk3qQXc3Jy8Nxzz6Ffv36oX7++LqtGjaQXRZ3329msIVEVOoa30v6nlPNfbL/++itKS0u5HTx48JbkrG62DRkyBMOHD5c2QkW5nlomKywsRP/+/aXPjBgxAsB1bORf/vIX/nyTJk0YKC3+XlxcHGbNmsVSa7SIiwUvmqZh/vz50veqVauGgIAAREZGIi8vD5MnT0ZKSooOtB8VFYUBAwbg8ccfh6K4cYZius3pdLJjJV7/4Ycf5tRyXFycdC+EDQwMDNTJPJJmrKcqBXAdZzp27FjGQFIE8vXXX4eiuHGgIgjfm8NIEZE2bdpg/Pjx2LBhAy5evIitW7dCUdzRYrL8/HypCGb58uVcGGKz2SSH8urVq1JkJDAwELNnzy634OGtt97ilPmVK1cYv3js2DHdZyliYjabGR5BkWNVVdnJj4+Pr3DB9zQx/Sb2m91uR9euXSWH3MfHhyNt5Ez6+/uXi9kU03GJiYleCyNyc3OZgHv//v0oLS3FvHnzdDJ85KyJcyI4OLjSlFe3YmVlZYZRbHr3RJ9FTprdbpc+T+OP/ruy0dV169bx+zabzejduzeuXr3KjpDIDZqfn89Ot6qqiIiIKPfaBw4ckPgVvVEYlZSUMNl6eHi47p0nJSXh+eefx6VLlyReQVVV8dlnn+n6cdmyZVLxh9lsRteuXfHZZ5/h5MmTktrT6tWrsWDBAkydOhUZGRl46KGH+IBCRWSqqqJatWpSZud2rO2eThm969atW0t/z8rKQnBwMOx2Ow4fPozz589zxJiMChq9EfK/+uqr0lpMfUBO8tixY3XfWbRoERRFwcSJE3X/9thjj0nP4ikg4OlQbt68GYriLkAiE9f4Pn36eF3TfvnlF+Tk5Oiw/UbNZrMhPDycxzRFpLOysvh6eXl5UBTFK+/ozTabzYaIQc+Xq5ZzM+1/Wt5/Uvt3pcJpIRAl8iwWC44cOYILFy6ga9eufF+0SdKpNCMjA4WFhVAUBR06dMClS5cwfPhww7C/qqrM7SU+s6LoucyI944cMKNmNpsRHx/PDhlxaorpMMI+AcDRo0ehKNcLIrZv3y6pwIgb/eOPP46ff/6Z9WsbNWrETjAZbdIBAQGGaJ4WEAAAIABJREFUi1VJSQksFgsCAgIwcODAClMhTqcTCQkJ6Ny5M0ePatasiaioKOneiGz96aefZryWolwvtiJ+uVatWvEGTc6UqqpISkrCtWvXJLUOh8OB5cuXV3qsUh9TNNAbSTsVENlsNl70V65cidWrV0vP1KZNG/ztb3+r1G9rmoZRo0YZ9mH//v35XYSEhCAwMBDr1q2T7tVsNktO3Pnz57F+/XqMHTsWHTt2RHR0tCHPJjmbcXFxHNkkNSNVVZGTkyPdZ3BwMKxWK7KysiT4heemdaedyh9//NFQ67179+7M1uBwOHSRrICAAAwdOhR79+7lPj1y5AiPKc90YHn24Ycf8lwS1ziqEj506JDEOkHvl+a0aCUlJRJumFgQqlWrppujRvbbb7/xWPS8H6P1Nzg4GDExMV5hJTfbRFgGOcYBAQFo0KABFyeaTCZ07NiRD209evTAxo0bsXv3bhw7dgyXL19mDOCQIUPw/fffc1SQmp+fHwYPHow2bdrAZDIxTvWDDz6A2WyG1WrlQkXP1DwA5naMjo42XOdEnk8Rv64o7kyMyWRCmzZtpO9omgan0wk/Pz/dNT2zYa+++ipDMmJiYpCbm6tzKJs3bw6TycTvX+SAJcgPya1SpLFq1aoVBnFq1KiBefPm4cCBA7psAmW1bDYbNE1DSUkJVq9eLQlR3O4WFlcH0RO3VVigcyOt9rSduFhY8bz5b7W71qEE3MU6fwTzvmez2WxwuVyw2WyIj4+HqqrS4lqnTh3s3buXQcnfffcdOz0NGjTQ4alIKpCwkitWrOCoREREhJTapA2BqFSGDh0KRblORG10v40aNWKsU0lJCRwOBywWC15++WUpeiYaOaee+L/ExEROMxv91qhRowzfFRXGZGdnY82aNcjIyED79u0RGxtbbnrac1N59913pevSYtmgQQP+m6Zp2LNnDx599FEd2brdbucFfc2aNVzhevr0aUmGjpqPj490bw888MBNjVWKZimKcXSSjD6Tm5sLRXFHSGh8ZGVlMXUIvdfDhw8bXuezzz5Dly5dpE0gKSkJr7zyCs6ePcsFRB07duTfopQlbVDUXnnlFd31NU3DmDFjeMz17dsXeXl5WL9+PcaNG8cFQuVFNsnZpIMKjZ2SkhLecI1S8qqqSvjT22UbNmzQ/Ralcz3nVp06dZCRkYGDBw+yY2B0T0VFRUhMTISiuCPjN0L0feDAASQlJfFvEq6PHF5yIF0uF+x2O4KCglBWVoarV6/ixIkTyMzM5PdfrVo1PP7443jsscdYQMFms6F+/fqoXbs2oqKiEBYWhsDAQPj5+emiwzfTVFWFv78/oqKikJiYyM6bSF82cOBAzJkzBytWrMCWLVuwb98+nDx5EgUFBdA0jXHR7733HkfiAgICYLfbJaaBffv2sRObmZmJwMBACVqjaRo75Pfdd5908I+NjcXKlSsxdOhQHVzBbDYziXtOTg5rzyvKdfgRWXFxMa+tnhH6Y8eOSbRMRH4uEodTs1qt0hpB9D1iUSXgzoTRvkLBC5JvFSu8aX4RjZHFYkFiYiL27NnDDBzi3DTa7yIiItC4cWMMGjQI8+bN433HYrFwtiowMNDrWCbBBHp+z9+Ijo5m6MPtbKEt+tzWCOXmwzdGSfXfZne1Q/lHqueIrWrVqgCuF1KIk3Hbtm18fz4+PoiKioLL5cL8+fN1uLDGjRvj0KFDaNKkCTs5VNlLleN0/V69eqG4uBhvvvkmLzrib9tsNt58v/rqKwZXi5ilJk2a4OjRo5LSgq+vr2F60ul0Ijw8XPd3Usog9QUxVakobse2S5cumDlzJp544gm0a9dOojcy2nAo0jh27FhYrVb4+/ujuLhYhzcym83SveTn53NKvqIK5M8//xyjRo3iinrP644YMQL79+/n4hDRCaV+njp16g2PUTKKXCiKO/Vj5FiIuL1WrVrx7zocDhw6dD3Ncvr0abRt25YX/9q1a2P37t04efIk+vfvL9Fb0XOIEAvAHTEmOUzaiL/77jsA7rFHfWQymSSIAODeWGnjjYyMrJAn8sKFC+wE9erVC506dUJCQoJXZ5PuJyEhgaNvRowDCQkJUlT9Zu3EiRMV0paEhoZi4sSJ7NSIMBcah35+fl4dRqpU9vf3Z8oYl8uFS5cu4euvv8auXbuwYcMGLFmyBDNnzsT48ePx6KOPckbBcy7Y7XbGY98q/MfPzw/BwcGIiIhAbGws6tSpgyZNmqBdu3a499572SG22+2YP38+Vq9erVM88tbi4+PxxBNP4NChQ3C5XBx99vX1NeRI9TQ64BUXF3P0XFEUTJs2TffZq1ev8lpDkTYq/qNIGEERFMVdsS/SpZEdO3ZMR+MUHx+P2bNn47333uN5KTJzAOCAwNq1a/lvnrRMI0eO1EUZ6XqLFi2SWB7q1q2L3bt3w263Izg4WPrOgQMHeE5lZGRA0zQ4HA44HA6+fm5urqRAExISYliMJe4nqqpi0KBBGDhwIAdKlixZIv32kSNHeN42aNCAnVRFUTB69GgA7kj/3Llz0aZNG92hUFVVdO/eHatXr+bD7KRJkyR6rNvVzGYzAlo+gJjJH91ypPKVT7yzIPxZ7K52KIHr9A7Eu0cT93YPTKPNjP67Q4cOWLVqlVTVS1Qs4eHhvGBQFTHdX61atQC4MZT0N5FmpqysDCtXrvQKbKY0EOGhatWqxTJaJBk3btw4nDx5ktNAnn3Vp08fXZ9SZXpGRobu31wuF1OGiJO2vD4npyY5ORmZmZl46623vFYPk9Qi9ZnT6eQiH0VRMGvWLP4snc5vVNIOkGXdKlNpWL169RvGLYoWFxcHVVXxzDPPQFGMU47EGSqOLVVVvXLpXbp0yRAcHxYWhtGjRzN/H1X7V9QPomQcpaiob0pLS1FUVMQURxaLBTNmzKjwufPz89lxNNKwfuqpp6Ao7ujouHHj0KlTJ07ZVXYeh4aGYuXKlTck0ehyuTBjxgwdtyw9m6K4C1DoIJCZmYmzZ89i9+7dUBQ3TnThwoWYNm0axowZw1g7f39/NGvWDPfccw/i4+NRrVo15ve7FaoXo2ihxWJBVFQUmjVrhvbt2+vmYYMGDbB69Wrs2LGD8X7imCOsX2JiYrkwAnICw8PDkZ+fbyhqMHToUHYQDx48yLARo0b94E3TXLR69epxIRKJD1gsFq/vWtM03HvvvTx+zGazLvLVtGnTcrMEACTaqrZt20oFkuIhfeXKlQCuF7bce++9fI2NGzeyA5eUlMRZIs/7pfdrs9l4znbs2FF6l+SoAe5DPUGt1q1bh927dyM7O5uJxX18fCo8ZLRv356vQX1BuG3KiH377bc8Fwke43K5EBQUxPf2yCOPAIBU9OepKS/SadGYGzx4MIDrGMqYmJhbKogqr1mtVjjrd0Xc0+9XWPlthJmsPW3nnz4ySXbXO5SU8qQJHRoa+ocU7IiV16SnSlW9nos/Ley0CB46dIgn5IgRI9g5a9euHdatW4f77rsPEREROqJ0uq6oXrN48WLuC4fDIenZqqoq4XEuXLgg6c/SxCfyXjIq0Pj888/x+uuvc6SR0tNG/UGgeUVxR1nbtm0rpfbNZjMmTpxYLtHwmTNnOBpCbdKkSQCA559/nv+WlpbGxVHeOP8qYwQrGDhwoIRn8nx/YuGBCGSvrFExUHp6OoDrTlxUVBR+/fVX/hxFfaiPqQjB04qKijBlyhTpYCCqUISGhjIZtUi+b2RfffWV9IwUhaXoJbVevXrxgt+iRYtKRQYLCgp4QxKjNmTEt0p8rmSEJQPcYzY8PBwWiwWdOnWq0Pm32+2oU6cOHnroIUyZMgWvvvoqVq1ahVmzZqF79+6Iiooqd33wLDS5mbVBVVX4+voiICAAoaGhqFGjBmrVqoX69eujfv36/Azx8fHIzMzEzJkzsWTJErz11lv4+OOPcfToUVy+fJnVWVRV5QhqQEAAAgIC0K9fP75OREQExo8fzxErp9NZocNERpRE9erVM3TSLl26JI1F8Tl79OjBGZNx48bpvnv8+HFddsKz7yMjI5Geno7333/f0KkNDAxEjRo1AABZWVk8byoyz0JFRXEf/H/44YdK9Qsp/VAltKZp2LBhg44ZQlHcMB6TyYTQ0FCUlZUhPz+foSl2u50FLozs8OHDUBSFnXTK+GzevBnnzp2T9gCHw8FrKjnL3sZgSkoKBg0ahPnz52PmzJn8jsX9y2q1Svyg5LD37NmT//bLL7/wsyQkJLDjSLCYyMhIQ7zsPffcgw8++ABFRUWwWCySMAXtdy1btpQisrGxsZLS1u1uLTr1QtjA59zRygocS1LQeXj1oT81ZtLT7nqH8ug338IaFoelmz6CNSwOr73hJvkVMX53iuvqnXfegaIoePLJJ9G7d2+d8ktQUJAhjyBwPRLnrZFCy8KFC3nzdrlcOtUIkQqCFnmyKlWqSBN5//79MJvNsFgs6NKli9QvLVu2ZKfR2yZJlePi38UIZ1FRETtpL7/8MgBw5EYsrqhZsybmzp3LwG1S46DFU8QJUvTxypUrUBRFqvKOiYm5pbEjnohNJhN69uyJ/Px8aJomRWA9C0NUVUVqairz2VVkERERsFgsUjpUVCOijZQ2X88I8A8//ICysjIsWrQISUlJ3E8+Pj7o0aMHK2WUlpZi1KhR0nNNmTKl3Mhdnz59oCiKxB2ZmpqKdu3aQVVVKboTEBCA9957r1J9e+3aNU5Te9tQiW919uzZ2Lt3L95++20sX76cMXLDhw/HgAEDeEw1aNCAo2W3A+PnuT6IjpvdbkebNm04VZqcnIyJEydi9uzZHAGbPn06Tpw4gZ9++gn/+te/oGkawsLCyiXyBtxYO6JLSUpKMoRrEJWWyP4wdepUydkuLi7Gww8/LDkdVqsVFoulUuOSjA4yKSkpPFZovImcm+L8mzt3Ln/f4XB4VbKiiBS1tm3b4vjx4wwB8CzyqVatGvr06YMNGzbA5XLBZDKhffv2KC0tZQJtghx5szfffFPHq1ueAIOR0f4hZkTIXC4XXnrpJd2+0rZtWzz88MP89549e1ZY+DR79mwoipsQXIyKVkRhRDK3Dz74IObPn4/PP/8cLpeLYQEi9y8FXYj4XfwNT+qxyMhIidaOTCxK9Jw7NWvWZKnIZ599lvt+9uzZvF9t374dly9fxogRIyTYAf336NGjpdT5nWpWqxXR9Zqharcn0GDae7o0eOxkN2n5jO0n/7TUQOXZXelQ5v34f5ix/SRS539icLr4ENVHvoYH5m2BNaT8aMStNorkUatWrRomTJjAG6WPj48UySkoKMCLL76I1NRUXWGOorgLMFasWFEucP/777+XKh4p5U2KA2IasmHDhrBarThz5gyeeeYZ/l61atW8RhppQsfExCAzMxMbN27E5cuXAbhP/XQypk3Oc6EuLCzkReL555+XOBd37typIxqOj49nRzwqKgpHjx4FcN3ZEyOaZrMZjRs35gXbx8cH+/fvv+Hx88orr+g2yipVqqCsrAyapjEWip4xKSkJhYWFWLhwoSEBPJGtL1u2TOccrFixAopiDB8QU46PPvooX+/IkSMoKCjgdyxWrlssFrRq1apcx07EvCmKG6+WlZVlyOPodDqZcqasrIwjM0bzZteuXTh69KgO75eZmYkhQ4agb9++6NKlC5o2bcrvKDAwEKGhoRLe72YdQavVKhWf0eanKG5n91Y3I5KGU5TrLAAEHaH/B9xFQyaTybBa//Tp01BVFUFBQRXyZtI7dzqdOgeUNmhqBFsglZ5vv/2Wq+YVxQ3JEKvT69Wrd0PV8BQhq1Wrli4KZzabERgYyFi4li1bSt8lah8Ri11aWsrzKDY2Fnl5eRzdslgsmDNnDkdHBw8ejPnz5yM1NVU3L+n7JGlas2ZNHZYa0PN50tzxxJBX1tGm9bk8h5CUejybyWRCly5dJHo3wD1uKD3dt29fJCcnV5jmtdvt6NSpE4/tRo0a8Xrp5+eHSZMm6d5zZGQkzGYzr0XkUIr0U4SRVBR39oGe88knn4SiuAuAhg0bhpo1axrOK6fTKWVPysrKoCgK7r//fhQXF0sY1KCgIAnLGRgYyAc1gvdMmjSJnes72ei9Wq1WBAYGwmT1wbHzf8fRCz/jZP4//pRyijdid5VDebGwBA+vPiSFpL22pz9AzOSPEDbwOdhDqnstDLkdLTAwUCJ6Ful1fH190aRJE52kYEREhA6sbDabDVODZJqmcSr88OHDEi6SHJ0+ffpwpNFbZDYgIAA1a9ZEly5dkJmZyVFEceEYM2aMVCFJUZmQkBB8//33vFkMGDBAd5+ikoyi6KuaNU3DK6+8Ijm1FPUjHB89D8nMAZCUFcaNG8dp3hdffLHCsaNpGrKzs6WUEW2CtDH07NmTq+jT0tLgcDi4ylt08s+cOSNRC3m+R1ow582bB39/fx2Ru2h0+KDWokUL5OTk6DBUycnJlcIJjh8/HoqioF+/fjh06BAee+wxia8wKSkJAwcORO/evTkSXKVKFcTHx6N69eoICQm5bRF9SmdXq1YN8fHxuOeee9CsWTN06NCBU1u9evXCtGnTsHDhQqxdu5YpTO677z7u8y+//BKKcr0QgzC+cXFxhilI8T14PouoMDVs2DAeD57V/DRGxMNORkYG3njjDZw9exZJSUlesXyLFy+GorhxcBUZUUKpqspUVGfPnpXuVYQtEDabDm2BgYFcIKRpGh/iqP9HjhxZYZRs7969huONYEQDBgzgyKTT6dRdj9K2xLX7t7/9jaPTvXv3lvpox44djAmPjo7miLBIwVNUVIRly5YZ4jDpkDRjxgwUFhZC0zRMnz6dsbA+Pj4c/aU0vkieHRwcbCiHKhplexSl/O2V3rMnw4cn1MfHx8dwTtntdsa9UqTRUy2KMjcWi4VViDRNw5w5cySBhREjRvB7ITnbtLQ0ANcdSmrU15cvX2ZuY6vViqZNm0qOH+1f9evXZ5nZLVu2SMpg4rv18/NDrVq14HK5dM6hj48PevbsyeIRAKTCLpFUv3nz5nc8Uim+sz179pT7nu8mu2scyk2HL6D2tJ0VO5IeLfqp9xH39HY4G3S77XqhiuLejAMCAgC4F1JKZXpuTpGRkRg4cCC2bdvGzgWlIIhqoiLOOopapKSkVFg9HRAQwJsARSbfeecdw+tqmsZ4PDHFZrPZ8NBDD/Ei06JFC466kGJQ/fr1Da+5Z88evp/NmzdL/zZ37lzeLFu2bIkZM2ZIm4evry9HQVVV5WIYSsn269cPgKxnfd999xlu7i6XC5mZmRy9cTgcmDp1Knx8fBAdHc2fI0oRRbmOIXI4HOzYemr9Am4qIBpTDRs2xNKlS9G7d2+JeJn6sXnz5pg5c6YUxTl27JiuKET8nvhv7dq1Q+PGjVGnTh3GGgUHB8PhcPDGdLNjmCqGq1SpYhiZFGXo6tatiyVLlmDDhg3YtWsXvv76a1y6dAkulwulpaU8jsor2MnPz4fJZELt2rV1//buu+9CUWSqItrgY2NjUb9+fQmzZTKZEBUVxZGtIUOGYNiwYVI/dujQAbt379ZhvWhD7t69OwB3lEVVVdSoUYMLhCo6iIaEhKB9+/aSswlcl7ZbunSp134g++abb9gJGTRokDQWFUXBpk2b+P5EyMvw4cMNxzwVDlH0i+h5xKKy3Nxc9O3bVzrUxcfHc8SoR48eLDN7/PhxXhO8ZQQIL7pp0yZ2krzJgnrS2lBlv2d0n56VUsHNmzc3jGDSs06YMIHpacRCI6okJgUxs9mMt956y+v7WLVqFV/XyIj8/UbnGTFgfPLJJ3xvnrh3AOxkU59XrVrVsKAHcBfyEe7SbDZjwIABKCwsRO3atWEymZCfn8+Or6K44VkulwubNm1CWlqaLuNC2Eqz2Yxz584BuJ7upgNdaWkpfz42NpYpnsLCwgwFOhTFzQriaVu3btWtW7QmEF72j2iiDPDdbneFQ7n0k7xbKvcnnETVdg/fsUHpmboIDg7G4MGDMWzYMCiKcVUvnfSoKq+oqIgLboKDg9G6dWuWEfT8PXIayaEST3SxsbE4ceIEPv30U/5bRZXQFy5c4IXg6aefxsqVKyWsS82aNaUNiTZ5p9NpeD3CIFHk57333kNubi6noMTICtm1a9fw1FNP6Ra5yMhIdjQUReEUPOBWUaINOCYmhiEGxcXFePTRR9lBqlKlChYuXAhN0/DBBx9AURSJOJ6cdZPJxNFmh8OBxMRE5hstKCjAyZMnsW/fPmzZsgUrVqzAzJkz+Z2ZTCbExcWhVatWzM0mbgy30kwmE2w2G/z8/BAYGIiwsDBERUWhdu3aaNiwIVq0aME0Hw888ACefPJJzJ49G8uWLcPmzZuRk5ODEydOYO3atVJRl91ux/nz5zF9+nRe3Dt37sy0RHSYEDdyzwMC4Hbc6bpUSOXNSKNdpEIiI77Sd999FxkZGUhKSpLmlsViQc2aNZGWlgZFuU7yX1BQIEWKQ0NDkZGRIY1hRXHjHvft2yc5bQTLIHoX0QkUU94XL17Ehg0bMH78eC5a8uSgpeuJ3KoPPvig5Gwa2T//+U9pzNA8VhQFP//8MzZv3szrgMlkMtSYF42wtsuXL5eIv2vUqCGxRkRERCAzM1OC5lA60mq1Ijg4mPGOxCBhZNR3iuI+EH7++efl3h/ghu+IRXiemOi6deuyjCEpVp07d07X1579b7PZMHnyZKm/KZuzdu1ajjp748wVZSVnzpyJtLQ0JCcnIyQkxGvkLCAggA+8gYGB2LdvHzuN+/btQ+fOnaVK8XvuuQfLli2Dosi4dwASRRbRzlVkW7du5bWV4BiK4qYfE+ePiEGn+27Tpg1mzZrFOuXUtm7dytHNhg0b8m8VFBRAURTGeauqKvVLcnIyj91PP/2U5yXh/VevXq0rvqE1csmSJbh27ZqU5bvTrXr16iybfLfbn96h3HT4wm0lJg1v2eeODMqYmBiMHDkStWvX1ukOUwEOVfV+//33fPoWI0JGNCl+fn58srZYLHj99dclvVtN03iDiIuLw2OPPcbXEaXwKmMUiWrcuDHmzJnDFesi9qZbt24cZaN79IwskCPbrVs3nDlzRhdR8hZZITty5AgUxV2EYeSMUcGPaJmZmVAUtwPbpk0b/l6VKlUwcuRILF26FNnZ2cjKyuITfYcOHdCqVSuODtGiKHIh3mrz9fVFREQEoqOjERUVheDgYMP3LD5nSkoKvvvuO/z888+MOwsMDCy3z4jmpzzIhGjz5s3T3UNgYCCTc3fo0AGqqkLTNAkrrKoqrFarRIRfVlbGpNVG1b6inT59mscYmaZp2Lt3L4YOHarrd5vNhjp16iAoKEjSsQauU5W0bt2a+4/GPDm1Tz/9tHS9fv36oaSkBFWqVIHJZMLChQslzKeiuCNhlF40wlCS0fj87bffJGezc+fOSEhI0BXp0dhyOByIjY3lyOaaNWu4+lgsEKpVqxYsFgsrYdntdixbtgzR0dGcFfFmNIdatmyJSZMm6XS6Q0ND8fHHHxt+V9M0rgimuW82mw15aQF3xIoI2J1O5w3Tay1fvpzfX0REBK9vVJylKO4D8b333itxQIoFiaSAZTabpXfp4+OD5ORk5g+tV68eCgsLORKbkJCAZ555hp1GI75T6vvw8HDJIYuOjkZRURFUVeVMDY23uLg4nSOoaRrefvttNGvWTLrHyMhIHm+iAAIVIZVX4OVpe/fu1an/iK1KlSro1KkTO26e9vXXX/MhkvrSk+eX0tmeQRRiPSGO4rZt2wJwMwXQYYjmhM1mw7Bhw3Ds2DHpGrNnz+Y9UaxKv9Pt+PHjNzBi/7z2p3YoLxaWoPa0naj77F/w6qdn8FneT/h7sZtmZdGev+mcxRkfnMTRCz+j8J8u/Fr2L1y+9gs+OJ6Pzi99ypHK6Inb4Fu1xm0biOQcdOnShVNm9evXR15eHlavXo1Ro0Z5LcLxbF27dkVWVhY2bdqEefPmcfqAFnUjqS/geuEHpXD/+te/Sk5LeQoGZFRhJ26CoaGhfMrfu3evVHks4jc9SYaJc7GgoABvv/22VCywbt066bOlpaU4f/48Dh8+jB07dmDdunUsFZeWloZevXrp+poWOz8/PzidTq8Ypcq8O7om6S/T8wcGBkJVVfj5+bGz1qhRI0ydOhULFizAmjVrsH37dhw8eBBnzpxBcXExNE3DU089JW16JSUlTGxPCy79dvPmzdG3b19JDYWan58fVznT34wqToHrC7zIgVeReZM8q1evHvbv388OJZlnAYJIp0ILf2UonMg5Wr58OQYNGoSYmBjdoYEopkQteKpGp006Ly+P34uiuFNlu3btktLuFJmrXr06Dh48yJrS9Hsi9vaf//wnFEXGUlKlt6IYO5Q074wOOGTTpk2DorgjqaKzaUTqbjTOqXXv3p0xpYR39HbAoPEmQnx8fX1x7733Yu3atfwOFMUdeTKKFItVvbQGGTmUp06d4gOt1WpFUFCQ174oz4qLi9lBUVWV+UkVxe2kity9wcHBEtUUjU3KAmmahv3792P48OFcxFNR/9L7pmgardcHDx5EWVkZdu7cKUV2xQhxo0aNpCAC4Zhr167tFTtdVlbGBzXPAAC1/v37V6rA68qVK5gzZw5at25d7j5DUKHKmHgASU5OxokTJ3RKQqGhocjKysKXX34pfT4kJAQmkwkXLlxAWVkZnn76aZ1WuDiPPe8zMDAQO3bswO+////sfXl4FVW2/ak739yMZB4gkIE5IcwkgMwgEAYRBEEmAQUEZZYZUQahQQIIDYJANzwEQSQyiIpPEdQoIk+hEVGByIsh0iEdY0zHy+31++O+vVOnqm4SFPu9H7q/73xibt26VadOnbPO3muv/S+fZWPvZFMUBT179sStW7eq3T93q93VgPKhrTlImHsEbZ99G8U//Yycb/6O3R95vWNGgDLr+Jd47q0vMe6vp/H/TqT+AAAgAElEQVTA5g8wY99/4evvS/DjP93otOod1p+KHPzMbzIwjcrE0QQZGBjIYUOa6BcsWFApAfzs2bO8WzPim5GR+LLJZMI333zDk8qwYcN4smrevLmuvKLatDWchRBSWb9//etf+OGHH/Dqq6/qAJDL5cKECRMwdOhQ1rmk0md0jPrfRmHC6jRfoFHLO6Q+S0pKwnPPPYedO3fi6NGjOH36NFcQeuaZZ1jLMiUlRVqcCTjb7XYOtVHVo+qYejE2uk+jZI3g4GBERERg2rRpPjPwzWYzXnvtNelaz549K2ngVcfIg0D3npubi8uXL6NLly6SJBHJ05BpuX3jxo1jWSESKjay8vJy7N692xDEulwutGzZEgsWLMDVq1dhtVql8BrZs88+CyG84WitlJEQ8mbrwoULDBqTkpKkhUItnZKamopvv/0WAPCnP/0JQghs374dJSUlmD9/vsSftNlsGDx4MGvOAl5QYDabWcXAl1EIlbiQart27Rp27dolyXUZ1RJXezYJMD/11FPs2fR4PPjLX/6CZs2a6by1Wo4e4F3ISYKI5hc1LSYwMFAC+k6nUwcod+7cyXzJtWvXctZ6dTUwja7JKIQthDdaQfJY5JEGgDVr1vB8M2fOnGqFp33NHbNmzUKDBg1gNpvRrVs3KIqCmzdvcqIeeewcDofk3XvxxRchhJA4o6QD26hRI5/AnzbON2/elGgo1GrUqMEeT3WZxytXrmDBggVo2bKlNFcoioKYmBhkZmYy/1qd5S6EF5CrCxj4Mkq61Hohg4ODOXFPbeXl5dL80LlzZzz66KP8/aCgIEydOhV2ux0mk4nf1wsXLujuW+2RpWIP/462adMmfPzxx/jxxx+r7J+71e5aQHnp+g+GIeu0p71hGiNAadQ6r34XAJB1XOZhWkLvnJdS27p06cKeRnV4GgCHXiicCIAnBa1c0LFjxyBERVi8QYMGhpp15AVRH/vcc8/hb3/7G7p27SpNOK1bt8a4ceMwePBg9OzZE+3bt0ezZs2k0Lv6378U/FEzm80ICwtDzZo1JSHuNm3aYODAgXj44Ycxbdo0PP3008z3i4uLg8PhwIkTJxiMC+EFAJGRkQgNDcU777yj08Q0m83IyMjA/v372YMaFxcnAenWrVtDURSe8I2qhBQWFjLop2pGVJf9+vXrlY5bylL2tXht27bN8HuKoqBDhw4AvOCAvG8E3rV6fbGxsZyJriiK5M3zZVevXpXCSEZVkgoKCpifKITX60NhdMqu1iYSaTP9S0tLsWXLFvTs2VNXwk4IgVatWmH58uW6DU5RURGEqKi+oTbyBtL9t2vXDhcuXEBhYSFMJhN757Ozs3n8krd5zZo1ALzZ02azGf7+/ryYm0wmTJ06FXXr1jXM2v7www8hhAzywsPDMX78eOTl5aFly5ZQFKVSOZri4mKWTPruu+90n6sTbYiHR8+b+trpdHJt86rex9DQUIwePRpfffUVyyBp9QbJ8vLypFByXFwcnn76aT7XiBEjOGFOzaEkyR+Xy4WPPvoIQAU94HY8YVojDq26tW/fHt9//z2OHTuGRYsWMfgyAt5CeDeCUVFRaNGiBYYNG4ZVq1YhJycHbrebQ+Nr167FrFmz0LRpU12yps1mkxJd6Brod7WAjKI7tPkko6Smpk2bGoJKkkwjzjjxRdW0JSEqqDiRkZG6jXl8fDyGDh2KQ4cOwePxSJI9q1evxueff87HkyeVnrNRYlJ5eTnX6Vb3h1pOLiQkBOHh4YbPT/ssIiIi8Oc//5k/P3/+PGw2G8xmMxYtWiQ9w8OHD3OkyO12M3f3TtGPbqfFxsZi5MiRvztu5V0LKBdlnzfM6L5dQEnHr37zYsXfZ2UjpOsjd2zwhYSE8E4sICCg0vsiQCmE12tYXl7Ou8jhw4fjpZdewvPPP4958+Zx1Y7evXvzpGMymRichYeHc2j2l1w3ZTxqw+Px8fEcZg8ODkavXr0wePBgPPLII5g1axaWLVvGO0eS5NAucuHh4Thx4oTu/klc3Wq1ck1jrVHmY3h4OHOIKNNTW2Kza9euuHTpEtasWYN69epJHjZaAOx2O44fPw6PxwOz2cxhG7WouNZIvsNmswEA1z83ygg8ffo0+vbtK9EFoqOjsXTpUgwYMEC6XqNavrRLV5dI9Hg87NkymUxo1KgRatSoAZPJhNatW+tCW5GRkejduze2b9+uAzcejweTJ0+WeKVaKSStkVdGndS0atUquFwuRERESMkuJ0+eRFZWFjp37qzjoBFn65FHvO+bEYgl27NnD4SoKGcHAC+//LLkKQwNDdWV7ST5EUoqoOetFlffsGEDYmJioCgKe7o++OADKTnAqKqQmkN54cIFDB48WPLiU6hv4cKFPu8LqMi8JqoAGS2a6nc4LS2NJXv279/PYT8/Pz988MEHDHK1oIMAifYdp887dOiACRMm4MUXX9RlDRcVFWHo0KGSV494u1RuVQiBGTNmcPJQcnKyjocXERFR5RxoZPv27ZPebWpVzW0mkwn333+/BBors9LSUlgsFp239fPPP2dwo+3DkJAQ9iD7UuBo06YNFEXRJV4SZaVNmza6914NZEnLc8SIEfj4448ZFGqvxWw2o0mTJjhy5IjufKWlpbwhWbJkCQA5W3rmzJkoLi7GQw89xM85LCwMa9euxbZt25CWlib9ntPphMlkYn1eNdAl3V6ya9eu6ZLK1NehtjfeeEOiGtF8CVRwu8nJ0rhxY/zwww+VlvL8rVpVkYe70e5aQGksWl49QFlnzmEkzzuKzqvfwRvn8/H9D/9Em+XHpWNix2+5YwNPW2u7bt26aN26NVJSUpCYmIjY2FiEhoYa1g2ubqMEGfXLHh0djTp16uhCO1FRUZgwYQLmzJnD3svu3bvj5MmTGD16NJ+nV69enHErhF4ah/QpfVU6EcIrc0LeF/U1hIaGYu3atYY78+PHj8NkMsFut0shRKAie5wmVJKfUUtfCOHllBmV/ysuLsbcuXMNFyeqQy2El1+nLntoZOSdmDJlCgAv0CUR8MuXL2PEiBHSs6drrlu3LoqKingSTE1NxQcffMDAKDg4WPJyUNhOm/Xu8XiY92e1WhlwDR8+HH/+858hhJf836lTJ102c2hoKLp27YpJkybxZ7Gxsfjoo49gsViqTNQiDqVWdklNOzAKKUZERKBXr17YunWrtLiS2HJlpTeplnBubi42bdrE/WmxWDBkyBAEBARIUk/qZ04LlNYjrS7/KIRXwUBr6jrE3bt312mOCqHnUJ48eRI9eshSZPXr10dWVpZPUEPA8JFHHgEAplxQn5rNZk40IU8aRSSysrIMwcWMGTN0STDXrl3Df/zHf2DKlCno2rWrlB2unVMojE5gc+3atdIxgYGBWLx4McLCwqTvDx482PDdpmfoK8u7pKSEPY0kW1OZxzUsLAx16tThPoqPj2ewbbFYKqXx+DKSFlJ7zgBIHGdq7du311FQwsPD0aNHD2zevJnHCkUmjOTFCCx27NiR/0bzsqIoWLZsGY8jLa0nOTkZjz32GGbPnq17durxVl5ezvPLggUL+HdiYmKkTSFZWVkZMjMzdX1P17F7926mB5E+KgAuoCGE13u+evVqXifU7dKlS+yUuPfee+HxePCvf/0Ls2fP5ntU0xv69u0LwLs5p/UpPT0d7733Hs+B/85mt9urFfW52+yuBJQl/3SjdhUex8oA5T9/ruBMff19CTqvftdQSkix/naudOLaBAQEIDQ0FDExMezBqlu3Lrp06cLeETUY27BhA9fw7dmzJ3766Sepb7SadaWlpfzdxYsX8y5R7YEwm81o1aoV//+1a9ekl5TK2GkXwrKyMgQEBMBsNhtKngjhTTZQA93HHnsMkyZN4jBFQEAAFi5cqFt8jh49CpPJBIfDIV2resJq1qwZ/vSnPzEgUk9+ai+WL8vLy8Ojjz6qA1tOp5M11iozp9PJoOnEiRMcJqWJUgiv92LUqFG4evUqA5O//OUvvAiNHTtWOueSJUv4nPfccw+KiorYi2EkQO12uxnMTZkyhZNYSFBd7Y0sKSnB5s2bce+99+rkQex2O9q3b89jqyoxeHVSzuXLlzF37lzDKkHqsWtUDQio4Of68u6QkZdHzTUeP34890vDhg3hcDik71y+fFm6V6MEGbWu4O7du3WfJyQkwGq1StnUJB1UWZY3GdES1MCwZcuW2LNnj27cU3axVqLFZDJJz5+qqEybNo29Tup3wOFwwOVyVdqfZD/88AMsFgtiYmJ0YDMpKUnHl1Q/W19gb+XKlYa/RfWgW7VqhUWLFqF///7V4jSGhYVhyJAhWLVqlfQ8IyIi2EtKY5daddUrtOZ2u+FwOBAYGMjPh3iQQlTU0xbCq4dK88DSpUvRrVs3XcZ8SEgIlyr1VQ6WIixdu3aVygKrm8ViQZMmTTBjxgwsX74cQgiJIjN37lwI4QVa6enp0nijCNn06dP5eKrDri5lu3jxYvTp00eKpqgjbEJ4ecfl5eVSkikZ6W/27NlTGhs0Rolq9M4776C8vJzBZnh4OD/X8PBwvPfeexz1EcKrH7thwwae24y87f/OVp315W60uxJQns/7R5Uh7MoAZa9176H/hlN4fM+n+OxaEb7/oYwzvdXNGqEnQv+SRgTmWrVqIScnB4rirYSjXkxIzJk4eWTq+q1CVCTSaL+vNrVmHU3SlLRz7tw5COGVPiELDw+XOC/Hjh3jCYS+73A4DEHjBx98wGRv9fVQNQ9agGkBomM8Hg8WLlzI4UGHw4FJkyZJXsEDBw5AUbzVSEiKiErLURa3EBWlAwsLC3kSNeLZVWbamsJCeL0dixYt8llJxOVycca6NsO8X79+Enmc+j0+Pp6pBNqMdrLCwkIGn1arFeHh4TpJHLWpw1ZqvT8K3WptzZo1/HwTExPRs2dPndi6y+VC69atsWjRIklsHfDynEg6pCr+EoVa6f+NyttRXWJfPMPy8nJ+7nRtc+bM0W1wiGtI5zlw4ABXS3r66afhdDoREBAgjdOCggLYbDbY7Xau9kESLQBw8+ZNCFHhPdq7dy9HEpKTkzlUXRmgJHrEnDlzsHHjRjRu3Jj72mazoUuXLizHlJ+fLz0Hej+eeuopAN5N3LJlyySA53K50L9/f5w5cwZlZWWc+CaEQEFBgc/rUhtxHn1xeAFgxowZfN4OHTogKSnJZ6KhEF4PVa1atVC7dm3ExMQgKCjIEDTa7XZER0ezML+a46otHagWDCfwTRVfqAKMWhC9OgkmRvbUU0/xc1UneZE2Jek4UiPPMVlZWRl27NiBzMxMREZG6hIDMzIysGTJEly5coVFxI2KBpDOqraa1vfffw8h9JuwJk2aQAjBm5UNGzZIYFA93ognTlnn6hYbG4uZM2dyxOCDDz6Q+tZqtWLEiBFITU2VMti165V6s26xWPg8pPxRWloqJRwNGjSI30/iTKt/NygoCOfPn/epQvFbN6JQ/N64k2R3JaD8NPfmrwKU6tZw4ev4/od/4s2/5es+s0X71uu6nUahuYSEBBw/fpzFzAcMGMD3RELIRiCAFjACLmaz2WdlBDK32y1N9o899hh/RrtCAjykewYACxYs4InnyJEjkhyMoiiYMGGCDshS9Z8hQ4bA4/Fg/PjxPAHUrFmTifRGIucejwdr167lXb3FYsHw4cM5lPfSSy9BURT4+/vj66+/lkI+QUFBeOaZZ6TrobBhXFxcpf2jNhIQFqIi7K0oCk/waqFh4gtt2bJFt0MOCAiAy+VCaGio7jfUXofg4GD87W9/q/K6jhw5wt44s9nsk1NKyVla3qQWCF64cIHDdgEBAXjllVekz8vKytgDWKtWLV29ZsrAVP9GUlISxowZw8LvaWlpHI5duXKljtNKiwyVt1u1ahUv3ForKSnB6NGjpQUxNjbW50Zq9erVEELgyJEjku7oO++8A6BCPkkd8iPawdGjR3H58mU4nU4oioIjR44AqBjbamDidrsxdOhQKSSn9vwYmd1ul7xTpaWleOqpp6TsbZfLJSUhREZGwul0IjAwEFu2bNHprgYFBfksSKD2plannn15eTnsdjtCQkIMP//000/5XolWkJ+fr8sSrk6j8yQmJuKRRx7Bxo0bMWjQIH7OwcHBWLFiheFzDgkJ4fdy/vz5DPZmz57NnquLFy9K10We/tsxt9stjTuHwyFt6rTAqWHDhpVyjt1uN4elq1ORjaIc8+bNgxACy5Yt052TNEjV9o9//IMpRnl5eTzvjBw5EosXLzbMFqdGYF8r81ZWVobAwEBed3bu3MkJj/Qs77vvPqksY2ZmJiecUvKREIKjbkQJoA1pnTp1+LkSLUCrEasoCrZu3fpv1Z/UNqfTedtj6W6yuxJQ/loPpbblfPN3fFVQ8pt5KKs7wSqKgoCAAISFhSE2NhaJiYlISUnRCSBTOcKsrCxJ8iY3NxdlZWUSt05dBWPdunUAvFVvFEXhJAPyTlA4IioqihMb6tWrB4vFgtOnT/OEERISolvIaOKiUC4BiUGDBsFqtfLkXBkQVk9UJpMJffv2RX5+Pp5//nldn23YsMHwHOXl5Xy/VdW1BiokckwmE8xmMzweD44cOcLXe//99+uEhtXN4XBg586dHO6mfvjiiy/4N8hzIoQ3TF9Zxq/W3G639HtDhgzReebontX6gUIItGvXjs8xYsQIBkAjRoww5PGtW7cOQng9FqNHj0ZCQoLPpAcas5MnT2YZJJJAIXHywYMHA/ACXm02t8lkwq5du+ByueByuaRndePGDdx///3c59HR0XxtlYXFz58/Ly1a8fHxkofO4/GwXJXb7cbEiRMhhMCYMWP4mIsXLzJwPn78OOLi4uB0Og1/79y5czxebTYbsrOzfV4bqSkY8XoLCgok3VYh9EoK9N/mzZuzRNLUqVN9/t7bb7/N31EUBStWrPB5LNmcOXMghJCOLSkpQXZ2tuSJpmQMo3ERHR2N5ORkiVeYmJiIrKwsTJkyBd26dasU1NhsNuZsjh8/Hlu3bsVXX30FoCIhg7xT7777Ln744QcGaBaLBefOnQNQUciA3gmr1Yrly5dX2QcAcOrUKSmsTfSDbt268THkoYyIiODEqYCAAJ0kUlFREdauXWuYkObv74+oqCidl1+9HthsNgQHBxvOZaRooTXaYFK/DBs2DIAXGC5ZssRnudAOHTrA6XTq3kfqb+2ce+TIEYl+QJvwiIgIPkZNH5g6dSqPG7pHPz8/9u7m5uZyv3ft2lWiDlFk59eutb+2+fv7V1t+7W60uxJQ/vgrOZTa44tKy/HWheu/KYfSarXCbrdjzZo1WLBgAcaNG8cZ1DT5JicnS0k6AQEBv0oSwUizzc/PDw0bNmTPV3p6ugREkpKSsGXLFmRnZ3O9bTW/cvHixbyT7dixI4qKilBUVCQRrymxQYiK8nC0CFamR0h25MgRqT60ttWpU6fS7xPwNdrVq23Xrl08SSiKouOREjChkKzRtbhcLpw8eRJut1tKTBg6dCiACkqAEF4vwe0a1RkeO3Ysl6FzuVy68oY0Tux2u8ThWrNmDXuqExMTDZOcsrOzMWTIEF3Izel0Ii0tDTNnzmQC+ocffojx48cbSrIkJSVh7NixOHHiBGrUqKETzNcCXmrEt7t69Srr+9FzPnjwIICK2vCVhWTVIsh9+/Y1XIRJfYBAQu3atXXHnTt3jqVLhKio5W1kxKGkhTIjIwN///vfdccdP34cQsiZ+vRbam8aJdOp+8dkMqFTp04MRilJqzIASxuRzp0783jIzMw07JOSkhIcPXoU8+fP5zmpRo0aPjmN6uTBgQMHIicnBxEREbrM6FdffVUCnq1atcJ//dd/ITc3V5rXwsPDkZmZiW7duvnkbKpBFgGzzZs3Y//+/VImMN1fdnY2hBDIysrCoUOHeL6Lj4/36ekvLS2V5KJmzpyJ8PBwPj/REsrLy7lvyNO+ZcsW5vf179/fUEQ8IiKCAdiVK1fgdrsZrEVFReHAgQMYN26cLmPZbDajfv36GD9+vBTBatOmjU7vkYyAWZ06dfDCCy8gNTVVolnQ59nZ2YZJM23atEFxcTF7/dU6lx6PB0899ZRPkXSXy8XAmpKwtmzZAo/HI+m8mkwmKaGHxi3VuVe3WbNm6d6L/6323nvv+Xzv7na7KwEloM/yHrntI4zf9Qlm7POWSDr0WR7G7/oE43d9gnoLjqLxomM4+20RFh86j1HbP8aQFz7E3AOf46uCEpSWu5G5/qR0vphHXrijg5Dkc9QT+tGjR/lzdYaf1sjFr85GHTRoEN58803Otlu8eDGmTJnCE1ZUVBQyMjKYOB8bGyuVDqyOqK+2UbidknS0n9OO2M/PD0OGDOG/BwcHY/PmzfDz80NAQAAuXLiAmzdv+vQgXrx4kWVpjJrNZjPU2ySjLE2Hw+GzusH+/fsZzFNYk3bKX331FYYOHSpRBkwmEyZOnIji4mKUlJRg4cKFOq5bjx49GMQHBgbyZCyEzFm9HSOvDHmEN2zYwP3crFkzzmKl53n06FEUFhZK126z2VhrkUTE77vvPh1vkp7dokWLuF65L+vUqRN/NzAwECkpKboSmkJ4wRhJmJSXlyM4OBiKokgSIlarVarZ3KhRI52kFHnRfWXt7t27l/ugqspP6uxwrQ4s2enTp/kefKkYABWAcvLkybwQWiwWw6pFpCkIQNI8NGq+NBTr1q3LfeeL26v+veTkZJSXlzOPOzAwEPfeey8aN25caSIMCcrT91JTU2G1WhlMar1xkZGRhpVyrl69Wumm2CjrmSwvLw8vvfQSJ5up5xhtI/AfFRWF8ePHM42FvOQejwdjx47lZ6r19G/atImvs2nTpjwuXn75ZT4/GdGTFEXB5cuXWURc+8xiY2MxYMAA7NmzhzmGlGgycuRIHofdunWT5imKOFCrUaOGdN9msxkJCQlcQlGbQEi0HfUcTd7tXbt2wePxICQkhOkNVI/7qaeekiqPUXM4HCgpKUF5eTkef/xx7id/f3/Mnz9fUpdQf69evXowmUyIiorC66+/znxK6ieKvDVo0ID5+R6PR5JSo+f6v6E1adQsFgtmzJhR6Xt3N9tdCyi1OpTXbvqeXNs++zaS5x3F7o9ycen6Dyj5pxs/3/Igr+gnvPLpNXTRJOTUusM6lOpmt9tRs2ZNZGRkYMyYMfyikEdLaySKK4SX89ivXz8+lzbkRbtdtZafw+GQ9PPUmnXkPTSbzTCZTGjYsCHeeecd7Nu3D5s2bUJISAhMJhPGjh2rEzqvXbu2DlRWlvVZWTOZTEw8V5/Tbrejbt26hpOJw+HAmjVrsGfPHhw/fhyff/45rl+/jlu3buGVV17h47QeIQA4dOgQFEWB0+nE5cuXkZycDKvViscee0wKdYWGhmLs2LFMWideKZnL5UJSUhImTpwohWfUjUB4ZfyqyoxExNWl1X788UfmLJrNZilL0+PxYNGiRVI/duvWDT179tRdY1BQENq1a4cVK1YwV+uvf/1rta6Lxk5cXJwUwv/6668xb948neYcbWpISJsWSPV1WiwWn9nBap6v1mgD4XQ6UadOnUoTmIAK+ZeqQD4tgFar1Wd1F22W97Fjx/h7NWvWlBKzaLHeuHGjoVRPSEgIxo4di88//5wzggkYNWzYEG3btpUAYPPmzbFz507emJGnccGCBejfvz97nI1Ao9VqRXR0NFq2bInhw4dj9erV+Pjjj+F2uxEaGgqbzYbz58/DbDYjMDCQZaiE8AJ+7Xj2BSgBL9j3NS9oxb6NrKysDDabjcO7LpcL0dHRfF/NmzdHUlKSz99wuVyIj4/HPffcgyFDhvA77nK5kJWVxVn4fn5+OjFvyoQWQqCwsJB5kFoKDD2vQYMGMfitV6+e4caX5jNFUQwB9RtvvMHnJdA5e/ZsXLx4EU8++SSaNm0qgVdFUVCzZk106dLF0GtotVolqgWJmVPiIgFK2lBT4pOv/gwJCcGaNWukBEubzcbOjPXr13OhB/X4s1gsWLJkCW+SDx8+zIl0iqJg9OjRPK9QMp9RotL/dqtdu/YfSTl3m/mqlHOn2p2slJOWloahQ4dCCC9ICQ4ONuTkacHmhg0bWAeSJFrOnDkDISrCTnPmzAEAdOvWDUJ45RrIfvrpJwjhDUup7a9//av0u6GhoYiMjERYWBgfU1hYCCEEOnXqJH2XEhJoEnj44YcxatQo9swNHTpUCuH5+/vj1KlTOHjwIJYuXcqLCJVizMzMRGpqqrQDt1qtCAoKgsvl+kU1uLVNzUslaRsKcas9Y0J4QWPLli2xadMmnDlzBteuXUN5ebmU+U597nK5pAXxiy++kKrIUGvatOkvBpT169fXSeGQvffee+y1VgsK04Ss9ZiQiPj69et1xHJflWCMjBYEISr3kkVFRcHPzw9Lly5FRkaGzxCZFuiGh4frQmFaJQLACzQojF67dm38/e9/Z8+4r/5etGgRhPCCB5PJ5DML+sqVKxBCoG3btuyVN9KdM5IN8ng8mDBhAj+TgQMHory8HPv37ze8f4vFwolDQEXJPQqxEghfvXo1iouLDSMERos/HdOiRQsGjStWrODM96VLlxreO9ELKEFpx44dfK6HHnrI8DtGgFJLXSGt3AMHDkjlR6OiovDiiy8anhcAV2bZtWsXh/IpvKzmcqsz9rds2QJ/f3+YzWYkJyf7lD5Svxvjxo3D1q1bcenSJT6n+n026uMxY8bgnXfe0b03dM3+/v44ffo0/11dg1ybGU722GOPQQivh7OsrIwpPJTpT0bA0Mhr63K50KtXLw45q8uVkgwZ3acWUAIVoNcIqFutVnTs2FEqZ6rWKy4qKkJBQYHumiIiIrB161acPXsWQnhBMuBd09RzAI33fv36ccnT/wtNDW7VHPnfk921gBKoqOV9J4FkrZkHETlkyR0diNnZ2bh16xaE8IqFk1HIkRXeHiQAACAASURBVCoMUIatLxAVFxfHYWyn0ykJZQuhB3+HDx/mhYjs6tWrUsiPzh0fHy95gGjiU2e3aiVTvvzyS/7s4sWLzP1RE/LV3BvACwwCAwMBeCufUPKOyWRCr169pBDkqVOn2LPl8Xh41/vJJ59IxHKXy4XevXtj0qRJGD58OPr16ydlafv7+yMmJsYnoKluU0+s6nrICQkJaNSoEerXr1/pohUbG4upU6fi0qVLVYYryQICAlC7dm3Dz4qLiyvNGI2IiJAmal+cu5KSEiiKgrZt21Z5PSRsbbVaeZPjyyi7/913veVNd+zYIVWeqaqfAwMDsWTJEq5gpOa4Xrx4kT2B9913Hy/olLxD3Eu1URg7IiKC69v36NHD8NpJieGTTz7BsWPHWBNVDTaAynUoL1++rKtrT61hw4ZMuaB64YD3/VQUBbVq1cKCBQvQr18/PtboPFQ/Wr3odejQAadPn2bwrC2rePnyZZ2otNZoM6KmNlC43sjUgFKbXNevXz/k5+fj7NmzsFqtMJvNeP/991mah64/JCREl91dVFQEs9nMqg0Ugvb1jPft2wchvMlxdO1aebYnn3yyWpnWvtr27dvRvXt3KIqi+3217dixg6M/a9as4cQrmn/VyWBqo00h0T5KS0v5vXn22WdRUFCASZMmSYlutNmNjo5G+/btdcU0hPDyKTdt2gR/f39pc6YFlKS8QC0xMRGHDh1iySqSaxLCuzHr378/v3cmkwnnzp1jQOpyubBv3z6MHTtWyuIXwsvvpd+j9U89f6plqv63mt1ux2uvvYYXX3wR06ZNQ7du3VC3bt3fpag5cJcDym8LS1F3/tE7ByafPIRaMw7AEhR5xwcmeUSCg4PxzTffsBdg1KhRACoSRGgnSWEvi8XCQMiXZ5Mm5fT0dPZsnjt3jvUJafAfPHiQw9LPPPOM5OGhRlIz6uzW/Px8Ps5ms3G2uJGtW7dO2slp+WzEhaNJxWKx4MEHH9R5zEpLS9nDQPyaOnXqSNJDtPumFhwcjOXLl8Pj8SA2NhbBwcGoWbMmzGYzFi5cqOuvli1bIiwsDDabDXl5eTh79izzUtetW8e81FGjRmHAgAHo1q0b2rRpIyUlUC3xXxqaoZC43W6Hy+VCSEgIoqKiEB8fz2AkODgYvXv3xoMPPoihQ4ciIyNDV6dc3axWKwtvl5SUSFnCRjIzJBWllRHSGiW0hISEoF27dlUCyuvXr0MIb+iPFkkav7Vr14afnx/MZjNWrFiBnj176sTWqdHG5+GHHwbgfVcoeYS4oWSUmPPEE09Ifyf+pslk4kSKlJQU5sFpLTQ0VBq72dnZTJNQ80t9AcoDBw4gPT1dt8FQAxmbzYbJkyejX79+aNy4sS4LWP0d6htalIcPHy5xAAsLCzF16lQpcYF4tFTJSdsflIwRGxsrcVOJE0eNwEFWVpbPZx0ZGclFGmgMjhgxQhfy/fjjj2GxWGCxWHjD2KxZM0yfPp1BrMvlwuzZs+F2u5nic/ToUeTl5fF79vTTT/u8FvJSU717yvwuKipiWhDxXLOzs9GlSxfdczKZTD7faTXwueeeezgb/dKlS7pQ6Pnz5yU+MwH4oKAgKSJE9s033/Dvqy0/P1+n9uHv7w+Hw8HX2aRJEwk8FxcXY8OGDejatatuQ2Kz2dCxY0esXr2a3+slS5awjiU9Q0VRDHnLhYWFOlF9bQsJCZGu5+eff8aMGTP4PhRFYQ92jRo1cOnSJdy4ceMX8fvvdDObzUhNTa2yWtrvze5qQAkAL32ce0c9lP6p3e744GzdurWkN6dujz/+OD7//HMAYDLynDlz2AP39ttvo0WLFrBarXzPJA6r9bj58mLExcVxqNdsNmPr1q3Si966dWs+dsaMGfjuu+948pszZw6DgB49elQrdEsJSNTatWsHj8eDp59+msEYaVr6ktCh3by6IoHT6dRVvyBx3tDQUJ6o/Pz8OEykBczx8fFcjuzGjRsQwitRcbv29NNP8zlJSDo0NBRff/01PB6PBBw6deqEvXv3YsOGDejbt69OaiMoKAhJSUmoV68eatWqhYiICAQHB98RIrrD4dBlqCclJaFdu3a49957MWjQIPj7+8NkMmHJkiXYuHEj9u7di7fffhvnzp1DQUEBPB4PV7MJDAxEQUGBVCnHyNxuN+bNm8dj0uFwYMqUKRwa++CDDzjzOT4+nsdjWVkZ0tPTfd4P9avD4fAp3G4ymdC+fXvpb5SooAZFJDbfpk0b6Viqnf7ggw9Kf3/55ZfZq0iedDWgPHXqFHr06GH43OLj4ystraoGjWFhYVizZg1zGsnIoyeEwOuvv+6z7y9fvoyRI0dKXqqYmBjMmDFDt3GjhDSqb379+nUdF5o872oeL5nH4+ENCT2Xxx9/vNKF+OTJkzCbzbBarUhMTITZbGZ916VLlzKNg8ZtcnIyCgoKpPmuMmqGx+ORqjatWrUKzz77LAOv0NBQREVFSffo5+cn/Y02cEII1uKl60lPT2fwa0Q9UHM2yZNJn1N9cwK9tLkhIzmihIQEuN1ubNiwAY0aNdLN7cSfJ89lgwYNKu2TS5cuMU2AxlhlfPcXX3yRq5Jpo0xau3LlimFm9siRIw01Gz0ej24OfPjhh1FaWoovvvgCQghd9bJ/d3M6nbpoxB/2OwCUALD+Py/9OiD55CHEzz6MwPRBd3xgms1mBAUFwePxMCmfds7qychms6FevXrSYjR58mQA0AFKALywpqSk4MaNG/wCrl69GgcOHMCTTz7JSS6+vJpOpxNxcXE6TwpNauQxCQ8P57BlVXby5EkIIZjTqW0ulwv+/v7w8/PzeQ7i6KnDkZT5qE44IiPh3CZNmmDq1Kk+PQvahBPy4B4/frxa96Y1NVCLjo7mBZequlBGsxAC+/btk75bWlqKp59+WtLkc7lc6NixIx544AFd+NxisSAxMRHDhg3j8SOEN/t2yZIlmD17NpfB1Hr7jICMtrpPdRtxM2lMxcXFITk5GampqUhPT0fnzp0l/Ur677Rp07h8XaNGjbivKKGGvI9kf/7zn/kafYWNHQ4H0tLSMGvWLInTFBISIoVnqeawkZICbVzUSTcEJLQSS0AF/5iANVXBqYzqQE07Ll0uFzZt2sSgsTKPKRmBxK1bt/o8Rm0OhwN+fn6SdyspKQnLly9n0Jednc3XpgZt6gRANQcP8AJ/dQlVup/qcHABr4wSRWCE0NfN3rhxI1+T2lsYFhZWrZKSly9flmpCa5+FOiFN7YG7du0a0tLSpDnSarXCz88Pn332GSsUqEPe3333Hfbs2YNp06ahe/fuzNn0NQ7UY7pVq1b48ssv4fF48Omnn/IxNWrUkEontmrVCnv37kV+fj6fW534ogWmRkbvAa0lL7/8ss9kQj8/PzRv3pzD6r7AlTp6pZ1ftOONnAcnTpzgzzt06MBJUmaz2adG5r+jqZ9ZdZMTf2/2uwCUgNdTWXf+0dvmVNZ+8jXUnP4KanZ44DcdrP3792evFk3yHo8HZ86cweOPP45GjRrpeD116tTBqFGjOGGCTF0mMCcnBwCkHTyV9CO+khBe7ub333/PYLNXr16oX79+pWF0IbxAafTo0diwYQM+//zzKheMxMREmEwmDt1oW2ZmJpPOKelAbefOnYPJZEKNGjUk7wyVuHv22Wd138nPz5d4PUIYE9W1niiqn/5LjDh4QlQAtoyMDE6aCAsLYw6QzWaDzWbTJYB4PB4cP34cQ4YMkSShqNFi++GHHwLwilWrw6JakNqzZ08IUeG9OXPmDHNUaeGfOHEihxxPnz6N6dOnQwiBHTt2ICcnB4cOHcKOHTuwevVqzJ8/X9Lly8jIQKtWrdC4cWM+X2hoKPz9/X9xbV31d5xOJ9e1T0hI4LGkPj4yMlLi6Kqb1WpFw4YNERYWxu/LpUuXeFNn5GEjzmKjRo34b0FBQZJgdElJCY4cOcKcRrUSgK9mMpnQtm1b9jSeOnUKFosFVqtV6lMhvMDg9ddf539XZsSXtlgsXHygMktOTuYxfvToUXTo0EECamlpadi2bRuuXLkiAd7t27cDqNB0pRBzcXExHnroIR6boaGhWLduXaVZ3r7syJEj/Py1kQfyElNtehorJpPJpw7tzZs3kZWVhc6dO+s4hDabDZ06dTJMSDMySiCktnPnTgBgENeyZUufHMry8nKO+sTGxmLz5s0MNqszdqhFRUVh/vz5unGbl5fHm1kKpxPFpTKjiID6ewRW6e+xsbEYPnw46tSpI60LiqIgJSUFU6ZMYR1PdfSqQYMG0vt89epVvP7667rxRiFyOo5UM/bv3/+Lqi792hYcHMxrBclBaaMbf1iF/W4AJeDlVD60NQfxsw9XCSzrzPZ6JRMefu434UwK4d3Vq+vAql9Qo8oVhYWFsNls/LJpF9OaNWvyzpYmerXHLi8vj0W6yfMjhKhWhQjK6lY3LUmaGnk2MzIyJLB54MABCOENr6n1wygrnIAAgRF15QkALFmiKIpOfJjkOsiTVFJSgvnz50s7WvrNli1b8oIkhJxF3LZtW+Tm5rIcSGZm5m2PsyVLlvAzooQhAgk0Oe3evZv7lKrnJCcns4i4trQhiYiPHTsWmZmZEsCMiYnR7dyN+GyUhPH+++/rrpcAgMlkwpEjRzhzOTw83GclmNdff52TUbQVjijknZeXh969e/O91KxZE7t370Z5eTmuXbuGM2fOICoqij+Pj4/X8VKJMqAoCqKjoxEWFobAwEDJE/prW2BgIGrXro0GDRqgefPm6NChA4c1CXT36NGDa6j7+/sjKCioSs8jjYO6devqsrrJ1MkoH374IfM8+/Tpo/PufP/995WOvYCAAAYlaqqAL8vMzIQQQtqceTwe7NixA02bNq204k1eXh5v1Bo3bow+ffrw8bGxsVJW8C8BlAB4zhBCrqJF8yZxMseNGycpMrRr1w7vvfceli1bZigirm2+5Kh8GcnZqJ/z+PHjcf36dZhMJs6A19pXX33F1+xLXP/ChQtSSLeqMa4oCvz8/DiMTtqg6qalZ2jN4/HoBNMHDBiAkpISvPCCV3PZYrFI8kL/+te/cPLkSQ6rG3EbHQ4HNmzYoNNUVfOMabypnxHds3r9Untof6tGvGGr1YqQkBA0bdkGne8fgejG6Rg/ewkUqwPXr1+/rbHye7LfFaAku3T9ByzKPo97/vSfuoo6tWcfRuyjLyCmzxPwi07w+aLciUbcyOeeew5CCGnX7HQ60atXL/YwAhXcw/379/NuaeHChcwHUodYCeyZzWbs2rWLF7CrV69K9/P4449X2V+XL1/mHSY1AoEOhwPZ2dl49dVXMXv2bPTu3btank0CVs2bN8fnn3/OQuUPPfQQ848URZEmHgJlRhVuiFielZWFBg0a8OJtt9vRvXt3rl5ANXbVIVkAzAGkRouyuv+rMo/Hw/qPBMTUskHqxJ8DBw6gvLwc4eHhUBRFx6vz9/dHq1atKhURVxPu1S0hIcHQ20Z0AyNtu8LCQg6vk7aoOrFAa2+//TbXRjYK/ZIHRg2ofNWVXrx4MV+7L68aSeo0btyY/zZmzBj+HgFsyhp9++23sXfvXsybN0+qIRwYGChJQ/0W77XJZIK/v7+OSmCz2ZCRkYEHHngA48aNw4wZM/DEE09ICUTnz5/HjRs3GDQDYC8x9aOv8KLH44EQ3o0YRSkqK0UJVNQvV8sSqS0/P1/nzVPrBqrfJSG8myK18gPZLwWUAPDII4/wu/zdd98xR5zmOxrPlLhoNF/HxsaiV69ePMbtdjs2bNggiXzfTmYuzVHJycmSpz8kJEQquqA2EtdXFMUngP3uu+8wfvx4qZoVjWvyalMijFEYvbJs//bt2+PRRx/Fli1bOIxONcTVuqcPPfQQqx14PB5+f3ytFdeuXYOiKKhXrx5vuLTjQtvU47KgoID7r3Xr1li2bJkEbp1OJzIzMyXpoTvdaEMeHx8Pa2hNxPWbivoz9zLdTU1/u2flf2JR9nlcuv5DtcfL78V+l4BSbT/+043zef/Ap7k3cT7vH/jxn26eqCojyd+JlpCQwFItYWFhvIA7HA5pEQwKCmJARzvN8vJy9pA0btyYX96IiAgsXboU99xzjy7ZghYp9d8q03fT6uWpw8Y3btzAgQMHeIL0VcbwxIkTktYcLbaVTTZNmjSRrnPChAnYsmULTzjaa9yzZ490r2azGW3atMH+/ft115Ofn8/9bLVaedEGKuopqzl5qampPpM7tOelzOp27dqhvLxcp0NJgNho0nc4HAyyX3755Sp/j+pSC+ENT1HykbqfmzVrhr/+9a/sBSGNPrU0ldbU/U4g12az4ZtvvuFjTp06xUkTWk/x6dOnJa9aWlpalaCceIbBwcGVHkeJClOmTGGvLiWz0RihxAJ1shbg3RR16dJF1/cOhwNBQUE+F2JKiiKPkdls5vdTXe4vODiYvZv169dHzZo1dWCfgOPtzBHq49VAKTAwEKmpqcjIyED37t1x//33o2/fvhDCuwFYv349hw/Xrl2LvLw8wxrDH3/8MYQQmDdvnu6z999/X9IqfeGFFzBz5kyfCgK0OTOyXwMoPR4Pv7NBQUESr7hVq1ZITU3VVWGKiYmRIg8hISFSdSZKHqTIhqIoCAsLq1YdZqLXKIoi0VSeeeYZHZglU4vrnzx5UjpfSUkJ5s2bJ0UZAgMDMWTIEIma0717d8TFxfl8T4gDGRISgu3bt2PatGlS2cTKxp66by5evMiJVOq525cuJgAp+zstLY03hhcvXsTs2bMNf7tmzZro0KED95m2yERgYCD8/f0rVay4U81sNmPK/CWIGPwMFy+pLIJJEc6Htubg28LqSbz9Hux3Dyi15na7q0Wg/7VNXUkmOjpa8rZQiPHatWsYN26cFN6MjIzE5MmTUVBQwLp5dJ6IiAgpyzo/Px9CVFTR8DWhPPbYYygsLJT64Y033mA+XlxcHD755BNkZWXxd6h+sS/Nuvfee0/K5qYQqtpzJoQXfJFn01emu7q1bt0ao0ePxhNPPIHWrVtLi7bNZsOGDRt8LgqFhYXsbVEvSnTN+fn5UBSFuTrkPaSJ1cjzAgBvvfUWT/yzZs3iv/v5+SEiIgKdOnXScSDVIWAhvPxKkj3x8/PzmS3vdrsxcuRIPk9qairKy8sRGRkJRVGQk5ODrVu3okmTJnztpD34xhtvwOVyITEx0ef4J805bfjL6XQiNzcXp0+fZo7lxx9/zN87fvw4A3ECYVXJBpFRH5jN5iqzc9UgYejQoVyhhWqXf/bZZ8z/aty4Mfr27YtGjRpVWns6KCgIrVq1wogRI7BmzRocO3YMS5YsqVRsXQgvL2zjxo268bZy5Uoel2pKS3x8PI//8+fPMwiaN28etm/fjlWrVmHu3LmYOHEiC2aT5ygkJAQJCQlS7WgaR78EpFosFjgcDu4ru92OxMREpKSkoHXr1rrnX79+faxZswZPPvmktNnVtr59+0phUbJfAyiBiuxmo2axWJCcnMyeZ/XzOHjwoLTZDA8Px0svvcSfE2+QIhe9e/eu8lqoz7Ti+oB3jlGDuH79+unE9QHve0xVeNRKB/fee6+kCzpx4kTpuZnNZqSkpOh+lzbcwcHBurmcxiBFq9q0acO/SRskozGi3jAJ4dXFvHjxovSOaqNXNWrUMOwz+vzixYtcKli74YqKikK/fv2wc+dOlJWVISUlhatabdy48bbG+O20rl27IiK9P2rPOohaMw/eVo5FwtwjqDv/KF76OLfKcfN7sD8ApcYuX778mw1cdcvNzUVJSQlGjRplGLakhYf0Fk0mE3r27Cl5TWvXri1N/EZkcvKUqD2JO3bsMExKCQgIQKtWrRhsWSwWKTxK1SsCAgKkbFO1Zl1oaCjvtBVFQdeuXVl6ZO7cudK1CaHn9syfPx9CeLmLxK2rikNEQKFGjRoYPXo0nn/+eXz22Wc6AWQKI61fvx4ej4czFPv06aO7RyEEPvvsM+Tn56Nv374+uWEk1WK1WrF9+3YsW7bMEIjQM54/fz5KS0vh8XjYo0T36PF4WH+0efPmumd58OBBPi95zE6dOsVyUgsWLJCONxIapg3Ip59+6vMdqFmzJt+verzZbDZYLBaYzWZe9Pbt28fPm8botWvXqpQNIqMwJfEkK/OYb926VaIyvPLKK7w4kZalEWi02WyIiYlh0EjjwGaz8XOpUaMGVq9eLY2Z8+fPY+DAgT6TfGi8d+3aFevXr8epU6d4UxQYGIjs7GyWDaL7S05OxpUrV+ByuaAoii5xSm3kYXQ4HDrQqpa5adu2LQoLC1klIicnB0ePHsXOnTu5IkuNGjUwcuRI3HfffejatSvatGmDlJQUrnRCeqkOh+OOUAEoEhEfH4+GDRtywlFmZiaGDh2KCRMmYM6cOVi5ciW2bt2K7OxsvP/++/jqq6/www8/4NatWzh+/DhGjx5tmHwlhMAjjzwibWpq166NgIAAAN55k/rDZDJh0qRJePDBB3l8hIWFYf369awO0a9fP04+2bZtm89nQh5NX7xiMrXHTgivtI7b7caePXvQsmVLKUM7PT0dBw4cMDzP8uXLIYSXJ03vfExMjDROac4gZQGtkVqFutWqVYsjIR6PB1arFbVr18bevXsxbdo0Q2++uvn5+UlzQ7NmzXg+2717t/T7NKeTEoA6uhIaGoq5c+finnvuMUyUEsJLafitnDzNmjVDYPoDrDP9a9Rg1v/nHzJCfwBKjakz3X6rphbjBoDc3FzdMQ8++CDcbjfLlmzZsoWPf+edd9C1a1fd4jly5EjdwkN1nG02m7TztVqtaNKkCT744AP2cmhD/CQNMXfuXHz99dfsZSMQm56ezufbtm2btPC2a9eONQpp8tF6n+g+tUayHFQCTAh9Vna9evUwefJk9O7dmz0mRhOg0+lETEwM91X//v0ZbB49epSPe/TRRwF4s1TpXGorLi7G8OHDpexVNfDW1s6NjY2F2WxGTEwMlxJr0aKF7l7VpcMmTJgAAOjfvz+EEFi0aBEA4MaNG+yhsdlsWL16NYfPaTFp2rRppeOahIbV/RgSEoJRo0bpOJoU0hPCm+S0fv16CdRv27YNmzZtkioqDRkyRPKMVBdQUl3o4uJimEwm6T6Ki4tx6NAhzJ8/v1KvmBBe0BUTE4PWrVtjxIgRyMrK4gVOXd6OhPPDwsJgtVpRXl6OKVOm8PPz8/NDWlqalC1PUQHqO39/f2zevNmw/jkdv3z5chQUFEg6lORtosWRMoN9Gb37VFNZa1oh7tDQUEOgQ3xno2o9AFCvXj04nU7cuHGDAXHz5s11mxeTyYQ2bdpg5cqV/LvdunXDwIEDpU2LdgN4JwCq+hz0b4vFgoyMDPTs2RODBw+G2WxGjRo10L9/f35PExMT8c4776CwsBAejwdlZWWYOHEiP8vAwED2cJaWlsLlcsFisXABB7URd1MIYzF4tRElw+geFEVB48aNsWnTpio98vQMnE6nJCgfHx+PGzducB10l8tlyD++cOGCjv9usVgkqgpFJZYsWcJ/o7GnBqOPPfYYpk2bhubNm1cJ8GrVqoX27dtj3LhxPB5eeeUV5OXlcQib9EXVVlxcjI0bN6J79+6VbuTuxHhyOByo0TLzjupU7/mdeyr/AJQao4y237qRcLfH4+HapO+99560S6NJUZvtDFRMAg6HQwpZ0I73pZdekrhs6rJ5RUVFEEJg2LBhALwlwOg4Pz8/LFy40FAagq7bbrfzDnzq1Km84FitVnTu3JmFjxcvXsyai0ZZx0IYA8pr167pwHJQUBCGDh2KjRs38iRbp04dnD9/nuV3zp8/j8LCQhw8eJDD6PXq1fO5oFG/qTXPqDSbEHpPxblz5/D4448bli2rVasWhg0bhiNHjvAiQRxKAsi+kinUm5hJkyax91RRFIwbN477onPnzlxZJDExEX5+flxmU1txxJc988wzEMJLT1BnkkZHR2P69Om4efMmAHCfXLt2DV9//bWhR9tut2P8+PGGZSKrAyjXrFkDIbwgf/78+RKAMfJKK4qCqKgotG7dmr13drsd0dHRPn9DXd6O5KiSkpKYNvD3v/8dxcXFePLJJ3Ve5aSkJE6co80HeeKpbvK+fft44XO5XPzc1O+TEN7N19mzZ9nrUrNmzUrBhNvt5vFZlbD+0aNHJY6nWjMTAFeGUhRFV2YRqNjA0DOeNGmSRAmx2WwYN26c9Jxr1aqlqyF/5MgR/s6sWbOwa9cuHfjIyMjAgQMHkJ+fj5UrV6Jdu3Y6kWqLxYIaNWogKSkJLVu2RNOmTaU5LigoSIrq3C5gJd1K7RwTHBzMwNhut+P+++/Hww8/jGnTpmHRokXSO/Duu+8iPz/fkF6j5TOrm81mq7aGIaky0Jgj3U8auzSWtNWZACAnJ0fSy6RxRPqe6mS6Vq1aQVEUfr7PPvsszxFARSJj27ZtOTGGKgkBXqrQ3r17MX36dKYLkcaxr36g92Lu3Lm6MDrZ6dOnb+u53m6rUasu4me++qs9k+pWd/7R3zWn8g9AqbFZs2b95qWdkpKS2LNBXj8KBxBJXs37sVgsGDp0KIe09+/fz7vS3NxctGjRgl9eCm3TdyMiIhAdHQ2bzcYv7d69eyGEN/Q7bNgw6Xi73S6J4JI0BE0URpO32WzGkCFDpExy8l4pilIpr0adZLR69WpJXkW9AKgnHLfbjVGjRjHPhzKytVZeXs7XPW/ePB3Y1O7ctY3O7at+emRkJHu2HA4HJk+eLHFEqSKGEFVXk1BfS/PmzXnDIIQXYL311lvS8X5+fjxO33zzzUrPrbacnBwI4Q29A14tyn79+knC1sRpFMKb9ECfaZO8IiIifCYsqQGl2tPYt29fNGzYsNJKF0FBQWjdujV69+7Ni7jWS+d2u9mLWJV39vz58wwWFUVBXl4ecy/V1U8cDgd69eqFadOm8ftJpT8pe/XGjRsIinF2DQAAIABJREFUDAyE3W73WW701q1bLP+krshCjcZMSkqKT1A5ZcoUfvZa4GZklHBFbdCgQdJYvHLlCsxmM/z9/XUbAFImMJlM6NOnj6QLOGvWLB1oKigogBBe3qHW1Jy/du3awe12c4KaL+AXFBSE9u3b60TEycgbSo14ykSlqVOnDmusCuHVC9y/fz9efPFF/OlPf2Je6rBhwzhbuEWLFmjYsCFq1659R6Sn1CLs2jmE3hX15jY8PBzTpk1DVlYWdu7ciaNHj+L06dPIzc1FWVkZbyiCgoK4Ypeal0xhZCG81cvIjh07xhEkRVHQoUMHXLp0CXa7HQ0bNgTg3YCoa8+bzWb+zEjnVz0XCeHdFBjxZAHv2KeIVHl5Ob+/2k2WEdj08/Njz+aoUaM4YvZr6qr7ai6XC0ljs1Br5kEMeeFD7D39Lb4uKEFpuRv5/yjDm3/LR+9171UKHnMue/mwOz64InEqH9pafWWQu83+AJQa+3dklFFTh5hbtGjBgFH9sq1YsYIXeJPJxBpjTqeTw+ZUKUc9mdNipP7/9PR0XLx4kY8joJCcnIyLFy/iyJEjrKGmzuoFvOAoMjISqampPu/HbDYjISEBI0eOxNGjR3lRDgkJ4VJ0ahPCKyau9mJYLBa0bdtW9xzUIX+yixcvSlmI6qxut9vNn02fPt3n8ybe1bVr16rUqlO30NBQpKenY+TIkRgwYABvDKxWK4YPH47i4mK4XK5K692qbcOGDRBCGPZvp06dpGPV4IHC5NU1kpYxEsg+duwYOnTo4HPhDwkJwcqVK9nLSa13797Iz8/HoUOHMHfuXPTt25fHltFi7XA4eOw3a9YMWVlZOHPmDMrLy2E2m9GoUSNs2rSJM7Z9VX05dOgQn6+q7FziWmoXKEVR0LZtW1ZbUNvu3bslcO10OpGXl8cATAgvqKqs3CiFvAmMh4aGSsBDURQ0bNgQkyZN4rD8Tz/9BKvVivDwcMydOxdCCMPrUxuVwZs8eTInR7lcLonvS9GXjIwMAJCqc9G1qJ+Rr7KnJElkJDVEFBetkoL2+aufQWBgIB588EHDai5UUctsNsPlcsHhcKBmzZr8ubpajxBCSriprlFG84IFC3QbgM2bN2PevHkQoiKRr1u3bliwYAEmT56MIUOGIDk5WceDp/tX1+n+JaF/8iaqw+Xq+tg0loKDg6UQcWpqKrZv344PP/wQ33zzDeLi4iRFiwMHDkBRFB6Xa9asYZ1fk8nE9c3PnTsn0TqsVmuVwu9UipI2XNQXUVFREpUgLCwMdrsd06dPR48ePVC3bt1qabv+2qYoChq06cwg8PDn3+H9r29g3quf44HNH2D8rk9wJvcmfr7lwZAXPjQEkwuyz+F6sff9UANKal8V/D4lhf4AlPB64T7++GNMmzbt35Lh7atZrVasWLGCPRjqUN6xY8ckHlmLFi04hEqAUh1qWb16NQBvOGLs2LE+f2/t2rVSX9BEQ95PoCKUpZ4Q77//fty4cQMmkwkxMTGYPXs2mjVrJnEJ1d+xWCw4fPgwAC9HT60pRuXKXnjhBXg8HjzxxBMQQmDEiBFISPBqgSYkJPh8fmo5lpYtWyI/P58X1YkTJxp+59atWzh48CB7N7WTfVRUFIeTr1+/zoDEbrcjKSnJZ1jWqHXp0qVKgWm32y1lVgrhXUTJc6mudEEhKV+e36rM39/fZzUR+lx7b8SfW7hwIebOnavLAjZaCIUQEqfxzJkz8Hg87LkIDg7W9QslrwjhBRpaWSK1kUyKEJVLIZGoshEPr1WrVlX2FwEKbTObzYbhfrWpExAoRAh4PcXq5DU6xmKxMAhZuHAh01Oqqs5BWp4kSbNp0yYOE6elpfGGjsDwggULdJs2q9XKCXcEbo0sOjpaV97wu+++44Q0I4+SxWJBYGCg1F95eXl49NFHpTKgERERmDRpEgoKCtCnTx8IUaERuGrVKq5Ec+nSJa4Pre6/6sj+aO3EiRMQoqLaz2uvvaZTnAgMDGRe4Y0bN7Bq1SquSqRuJH2jLr340ksv8XwGAD///DNeeeUVps4EBQVh2rRpWLx4MaZOnYrhw4cz2MvIyECTJk3YG68dK78kw58UN9TPKTY2lgEpeXy1lWlI+7hOnTr44osvcPPmTcN5zePx6FQtgoODdc+GKChqGaWysjJe5wYOHMibkTsZNXQ6najR7VGWBmr2zJs6QNhg4ev4/ocynPzqhu6zts++jZJ/uvHIX73viBZQJsw9gkXZ1dc0vZvsdw0oy8vLsWDBAp6wfutQd1XNKNubXraTJ0/CbDbDYrFIFSGaNWsm6SbWrl0bVqsVDodD2kmqv6NutWrVwoIFCyQvy+7duxlUkvCvEN7sQuJbDho0CEAF4V/tHczNzeXf0wJMbUtNTZU8Ie+++y6EqOCYkfSREMZVQkpKSiCEF+CSjiQ1df3n8vJy7Nq1C/3790d0dLRuIm7YsCGDJJq8iVtG3jbK1FTbzZs3kZ2djTlz5iAzMxMNGjTwqV/qcDgQGxuL9PR0jBo1CuvWrcPZs2dx5coVicS/ceNGfPjhh/y7VEXl0qVLKCoq4nHqS8aoKqMkDK1dvXpVkrkRovIa1OrNAgHQOnXq4Ouvv66UQ0kbH63nsbi4mKtuREZGVur5AyqAIoFQ9fk+++wz3HfffRL3rk6dOliyZAlefPFFvl5/f/8q+4tE2o1aZaUQy8vL2eOlLetJRov0Pffcg+nTp0tSW0IIfucVRcFrr73mc2NCSVrq8VlaWiqVcZwxYwaHn9W/ER8fD6fTye8qJYMZGSUQdu3aFfPnz0eLFi2k81FCGnEUDx06xM+gsjKm586dw8CBA3XvDp2LNk8E/mjsUYY7vSvNmjWrdr1wMvL4ayWDtJ54ehfV0RTakLpcLinjXA0oAS/n1Gw2S4lrHo9HcmL07t0bpaWlPK7VcypV7qLfHTt2LIMtu93OkQ1K2tu3bx82bdqEZcuWYebMmfx527Zt0a5dOzRt2tQQEKtl6G6nmUwm2Gw2+Pn5GXoZY2Njce+992LQoEEYM2YMpk+fjieffBJCeHWHjx8/jk8++YQjAkRrIO/ona7hHfPoC1XyId//+ga+/r5E9/cTl77H6+fyET/b6yAx8lDe86f/vK0xeLfY7xpQXrx48X/VI1mdlpCQgJycHKm+MuDN3lNXJRDCm1Ti8XiYI0l6ZTk5Oez1cLlcMJvNSE5ORo8ePXiyVxQFDRo0wLp163D+/HndZBMeHs79ZrfbubZxaWkprFYrIiIi+HOqnJCYmIjRo0cb1qGmZrfb0aNHD2zatAnXr183zLIkD2tMTIzuGb766qsQQmDdunXweDzSdQcFBaFNmza6TFw1Z+uVV16BEAJLly6Fn58fYmJiUFhYKGX5CmEs/FyZbdu2TVr4hPACysDAQJ+eTQKKzZs3x7p163DixAn20Arh9d6ogeftLpxkBDJmzZqFPn36ICEhwec1UUjM4XDgwQcfRJcuXZgfq/48Pj6eJZcIVGgz5QHvBsBisegSaU6fPi1V60hOTq7yPlJSUmCz2Tg712w2Y9CgQdKzI6+v1uN24cIFvucBAwb47MvNmzfzuVJTU3Ht2jVcvHhRqoaSlJSE48ePS99TUy6E8J1h7fF42PM1cOBALoX4l7/8BQsWLODog/p+YmNjMWDAAOzZswc///wzAG+SltZrSHbq1CkGPur5TlEU5t8S8G3WrJnhOc6dO4dp06bp3guTyYT4+HhdQhptPMeMGYOCggL+3fT0dMMqTmqjJBD1uxMTEyOJfxPAJrPb7TzHpaen3/a74efnh6SkJOlv9CyM5qwpU6Zw1KJu3bq6pDgtoHzrrbcghHEp12vXrnGSI3kNtREEtRoEjQd/f3/Mnz+fNxEHDx5kio06YxuoSCpTV+hRJ8Wpxzi911lZWSguLsbq1ashhDcB84UXXmAg279/fwwdOhSZmZno0KED81LVYX71OPklyVO/dv00aorNWWUiTuNFx1D8088MHKnN2v8Zin/6GS2XvlUpoKw9+zB+/Ofte8v/f7ffNaAEKrxxv8XAvWMvwP+EKbQJEDt27NBde61atbB3714MHjyYFzv15EyAZOTIkXye/fv3Iz09XfcCqxePyZMn8/E1a9aU+DgUuti4cSOKiop0Ei/BwcEYMWIELl26xB5PmnS0iR5CeCWBnnvuORYB9ng8fP1aLUsKj3/00UcMvrSeZqvVio4dO+L555/XTfzknUhPT4cQFXIgkydPls5RVQk7rRF/tV69ejh//jyDBiG8gthLliyRPAy1a9f2maiifS42mw1Op7PSRbOoqAivvfYa5s6di8zMTE6EqSxMr07MmTx5Mp+fgKKax5ebm4uxY8dKJeJIPkjN8dKWW6QayAcPHuS/rV+/nrU4d+zYgXbt2kFRlCoz14ODgxEdHY2ZM2dKYdOgoCCMGDGC+cZGAtQAJIH4hIQEyXt05coVNGzYkD8fPHiw7vtqGRf1u+fxeJiq8NBDD0EI34AS8I5vtSJDgwYNpM9LS0shhLfAgLYutaJ4S+SZTCZEREQYhuDff/99neeTAGSvXr2Ql5fH7xfVKc7JycGECRNQv3593TuqKArGjBmDEydOVDoGSTqruLgYEREREo9UW/udjGSdUlJSUFhYCEVRGCSpx78QAleuXJH6Z9CgQSwVpeUdV2VJSUkMyM+ePctya9rWsWNH6Vruuecewz7QAkoAXBL222+/NbyGnTt3SjXtiSN/5swZ6RpcLhfWrFlj+LvqhMju3bvzMWVlZRBC4L777pOux2w266gPnTt31kWshKiolHP58mWYzWYEBARI0SW32800BCEEJ00JIaRNRGlpKa5cuYKPPvqINXQp/N+oUSMMHz4c/fr1qzJp8pe2sOS0Kr2TBz79b/x8yyMl5rRa9haKf/oZs1/5jP8GGAPK+NmHcT7vH5WMuLvTfveAEgBefvnl/5OeSvVEXrduXSmxgyrr+Pv7o0GDBryYE5hS7xITExPx7bffIiUlhSdDdXjwzTfflDx7fn5+OqAaGBjIk0znzp2hKApPVqWlpTo+j6Io6Nu3ryEXi+QwhPB6VcvKynhisdls0nkCAgKQnp4u1V/OyclBXl4eli5dargbjoyMRO/evbFq1SpeSJ1Op0/BYj8/PwZT3333HXt+IyMjJa9ZVWR0shUrVkAIL5BVl17Mzc1liShq999/v/RdAp579+5lMNigQQOfmY7EewsODkZQUBCcTqfhWKZwe5s2bSSeoqIo6Ny5My5cuMCgTMsrLC4uZk1NI/vss890ISk1qO/YsSOKioq47CVV6vF4PKw1GhQUxLWUyetMmehaKy8v5z6m5nQ6eUMxfPhw9qpUJrlD9dtpk0Nl8SZOnMh9GBwcDJPJ5NOrRuOrT58+utrWDz/8sKRDWZlRMosQXs+P1ho2bChVErp58yaysrLQuXNn3UakRo0a6NKlC8aPH6/jAqampjJYovdMvSmIioqSnh1lB0+aNInrqT/wwAOV3gvZ4cOHIYQXxFClnOXLl3OlHq2oOyX71KtXD263m6sFURQlPDychdiF8G60unfvzpziNWvWAKjwcJLsTXWMxoBaEkxRFEyaNAmffvop///GjRt1FWSioqJ0gvxGgJJkcHzxYa9cucJzLZ1fC/YURTEseqA2t9vNHvSYmBjmzzocDp6PSktLoSiKFD2iuS4qKkramGgBJeDl6ApRIUeXm5srRS4ogkXeVCPBdQCcwS5EBceUrHnz5hyCv1Prs6IoqN28Y6Vgcu3b3tyEBdnnpL+/deE6cr75u/Q3wDeg/DT3ZqXP6W60PwDl/9grr7zyf95TaTabMX36dKk6SHFxMYfFAOBvf/ubboGhsKC6fFVeXh727NkjZZD36tUL//3f/w3AO+FQFRj1y9i/f3+uvrF48WKkpaVJLztNIL40F8nU4tkkAUS1dN1uN/bv34+BAwciLi6u2pNJo0aNOASoth07djA/rFGjRjrNNgIisbGxHB7v0aMHPB4Prl69ymCuOgkcHo8HLpcLLpcLfn5+EqBct24dbxLU3sLIyEjOYqdFm3hsRUVF2Ldvn6Ent6pGmcKtW7fGqFGjMGzYMMmTFx4ejoKCApSXl0u6g0aTP3mOKqsiQuAwMDBQ9y6ZzWbW+Dt58iSKiorYe56WlqbzrJHXVt2vO3bsQNOmTaXxEBsbiyNHjvBx5NVQFAUhISGVhldJ/mbMmDHYs2ePdN64uDjk5OTAZDIZlrojI9H6jIwM/PjjjxK9gpIthKgaUJ47dw5CVIAndUQAqAhPvvDCC7rvEu+4b9++6Nmzp0+1gg4dOqCgoAC3bt3CjBkzDL3VFosFaWlpmDlzJusUkg0bNgxCCM4Aro4lJyfzu02lF0+cOMH3+fjjjwOokABKSEiA2+3mfhXCC2rVSWklJSWw2+26eaFHjx68KSGpISNwTnbz5k1Mnz5dyuym91aIiix2Ne1BCO8m/syZMygpKcHo0aOld3rlypXweDyGgBIAV+Oh61QbbSYPHz4sbfqoD0JDQ5GSkmIoCG5kVNXHbrfjzTffRHx8PFcSUm/qhfAmE3k8Hv57XFwcex+NACVQAdzV1d5oPSEtVJp3O3bsiC+//BInT57EgQMHsGXLFixfvlzq+169eqFDhw5o3rw55wX8ksSjqlp8k7Y+weRzb30JAFhx7Avp7+N3fYKfb3nQb8MppDx1jBsA/MdHuUh56hgS/6e+9x8eyj8MQIVExf+1ZrVa4e/vLwFFdTIAAcrHHnuMJ9n+/ftj1qxZPNmZTCbWtiMwQS/sgw8+aOh9I5HvGTNmcPhQ2xRFQVpaGrZt28YTcXXDTeoF9P+x993xUVX522f6TCa9F1LpJYFAQkfp0jtSpIjSCWxESmDRiKAUQak2siwIKqhLWaQIRhZxEYKC0SwbUdggyyJiFrIxxnH27vP+Mb/vl3vm3klRfH++7+b7+ZyPmJm55dxzz3nOtzyPEEKq6KWcLdJzra6PYmJi8Mknn/g8V2VlJXs8SIqNvD1UiEL5dupqXMBD/UKTmvek6m3z58+HEJ4qeyI2V9Mb+fv7c7J9RUUFJk+ezJOxzWbjYiZfkpPqRTQ4OBirV6/GuXPnoCgKbt26hf3792vC3L4AuclkQrt27RiAGI1G1KtXT/e+qDI7JCSkyvunkGNQUBAMBoPEkUotOzubxwopFHkbeXJ37dqFe+65R+JGTE9P58KFAwcOSL/75ptv+Dz5+flVXisAmM1mpKenS6wDQnjA2fr16yGEwObNm6s8BqkYkedvyJAhWLRokVSskpGRUSW4pRy64uJi3uCoQajL5YLRaGS+WrURJ+EjjzzC3kaTySRRHtW03XPPPT6vMTg4uNbMAqQuY7FYJC3vmzdvchUxgYr4+HhUVlZi0aJFfD3t2rXTLc4aPXo0hPBsTtQpFkJ4VJCmTp3Kz2P06NH8u8rKSqxYsULKb/Xz8+OoBOUQEtAFZMopITzV92pzuVyYO3cugyen08meYW8jj7X3cywsLOTfer/rahnU1atX12hMkh04cIDXANo0eot3qDcIiqJwuk9UVBReffVVPPTQQxDCA/gmT56MkSNHok+fPujUqZMmmkTXa7Vaf5JXkSrQ1XmiesWqP6fZ/YN0cygJTD577HPNZ8/9z2dV2ZRXztblUP5vX8CvybwXlV9ro5d4wIABqKyslMLV9erVk8LMiqLoUrxYLBbMmDHDJ9ccAHTo0AEGgwEnTpzAgAEDfFbB16tXDzk5OZxz+fDDD9eov4UQUpjEbrcjJSVF8sZZLBY0bNgQkydP5sme8nS8CwTo+40bN8a0adN0SbfPnj3LYaTQ0FC8++67XFlqNpt9ghAqdBLCN1CprKyE1WpFWFgYAHDFIwHVrl27YuHChRzGri6nsXXr1uypaNu2LRRFYa8DNV/UOm63G0uWLJHIgQcNGoQFCxZgwIABVXo81eHxiRMnYsOGDTh37hxXZa5atarK50qeCyEEX4seuElNTcWf//xn3WdEOa3UGjZsiFWrVjEoI2+ot2eTAK0QQvIO+zJ1VXGHDh1w9epV9iJR7l513qDLly/zMdT0RYqiSHlkFosFkyZN0gCkkydPQog74fkffviBUwjU+uwUDVADU0VRpMItu92OKVOm8MbE27tjsVgkXkMhtDm6ao8vGXkM1bnXNTUCdvReqK9d7VHevn07V/nTM/dlRMc0duxYxMXFITg4GMXFxRg9erTkoSUw0q5dO7Rs2VLix7z33ntx+PBhvha9cXPmzBn++7hx4xAWFgaDwaD7zimKguXLl0th5GnTpuH777+XvkdsFKRadOLECWnT3KZNGwZnW7duRXFxsXQ/BoMBqamp+PHHH/H3v/8d586dwzvvvINXX30VGzZswNKlS5GdnY1JkyZh2LBh6NKli09QRuCttuDPe1xRnr8QnhSrNm3a8HOn8RkTE4NVq1Zhy5YtvIHq2LEjV7ATPyoAyRP74IMP1uraatLipudJgHHNUQ8H6vr8i7qey04r8zHqpVOaBgBHiq5j1Eun0OrJd+qqvP+3L+DXZNXpBf8a2kcffYSrV68yuFJPBCQHpzaXy8WFK94TAHFJ6hl55bzDi2pvXkJCAvr166ehBjIajVXmGyqKUqVmenx8PGbPnq3Jv9y/fz+EEJLnVQjPbv3cuXOYM2cOWrRoIU3ORLY+YcIEHD16lL2Subm5GjBXXViSijRMJpOuhB2FBAcMGKAJWXk3NWgjCqGPP/4YTz31FHspqO+DgoIYRPTo0YMr6Ok5qMm/9bSKly5dqkngp0IbITweHMoFvO+++2pUwNOuXTtMnDgR69evZw+p2mhRHTJkCOeOqXP11C0wMBADBw7E4MGDNTls/v7+umOpWbNmsNls0t+osjgjIwMTJkyAEL41l4uKiqQwv7pICACysrL4Gk6cOFHluFCTg3uTfZNHqk+fPuxJM5lMGDZsGL979evXh9Fo5IIYwOO9pu8//fTTAIAtW7ZACE+u4A8//ICsrCzJw5+UlKQJd4eGhqJnz57YuHGjVOREXreuXbtKOtzUHA4HJk+ezO8gjRdfxTRV2YULFyCEZ8OmNgrje9MOUUW6d8jd28LCwhAcHAyr1apJS/jggw84B08CEnFx2Lp1q2a8lpaW8nfouVCeoBB3gHRRUZFGSUbP1AUlZrMZI0aMQGFhIQoKCrBjxw4IITj3mb5nsVjQtm1bfu/Cw8MRGxvLm56fqujjzW+rnoOaN2+Otm3bolu3bhg0aBDGjRuHWbNm4be//S173um9ffbZZ1FeXo7Lly9zhKtv374SvZI6b5UIzvPz89kDTMpcQngcA2SNGzeG2WyGoii4dOkShPBE0Xr27Klh6fi5zWQyIaTnVOahXPb2XwAAx4tvYMjmDzStqnxLoI6HUm11gPJ/7Mcff/xVFuZ4NwoRrlmzRjPBUFUg4MkzUue2eC805G00GAzo1asXSkpKcPPmTWRnZ0teAofDgUmTJkl5h8QjqJZEpHC8ug/btGmDHTt2wOVyYd++fRg1ahQSEhI0/dyyZUssWLAAW7duZSCklhNTm1plhZreIldcXMxk6+rqZaPRiPj4ePTr10/Dx1edR0vtKTAajejcuTN7Gn2NHSIEV/NO1oTSRO1RMBqNGDlyJEpLS5GQkIDAwEBcv36dyYmpP5KTk/m5RkRESHlnalMUhT1gnTt3hqIosFqtXCyjNnW1+MCBA30SwdMCRSCZvieEDBjatGmDyspKbNiwwadUXZMmTXD27FkGapTXq7bAwEAkJCTw/5P+u9PpRHl5ORRFYa+oGhC63W6WGzUYDOzJu3r1qnR8KvohupMVK1bo9iUBrbZt28JoNGroXryLcvbt28dAlgj9hbjD66q28vJy9uBTVS9V11Y3VxGnoZ6Rl1tduU4V1fQcvecKg8EAu92O48eP/yS6KhrPZ86cAQDO53Y6nbryfGqw4csol1uIOxKuBQUF6N+/v7TJjYqKksaa0WhERkYGXnvtNb4X2iySEoyaMshgMGDVqlXIycnB9OnTWSM7JCREknCMjo5GaGioJDP5U/P/iAg+PDyc568mTZqgXbt2Eght3LgxlixZgvXr12Pnzp04fPgwOx1cLheOHj3KkRzvAh8SmqjKaGMmhMCOHTuwZ88eHg+00QHAG3y1UAZFC9xuN65cuQKDwcDrUHp6Onbs2IHf/OY36NmzJ4PWqjyfd6uZTCbENE5nAPjhpW+r7IPaAsrEnDqlnP96o4lfXflIoa9fW6Pco8DAQLzxxhsM5gwGAyZNmoTBgwfzSxgTE4Nt27YBAFdSUxX3oUOHdKkZnE4nh2p95X2R9yQ9PR2/+93vIITA5MmToShKlTrN/v7+yMzMZBDUq1cv6bjXr19nIKDHWUf3npiYyB7lgQMHVvt8r1y5gqVLl6J9+/aaBVPdkpOTcerUKQ1ZuS+PndVqRVxcnOaeu3btqinKqY0RkBg0aJCko240Gpkvj2hr1ADbbDZrKk69TZ3aMW/ePD4OKYVUZ2FhYbBarbh+/boENps1a4bQ0FCfC4Cfnx/atm2LVq1a6XorSQaT/p82NpMnT5bOTzRSpI+uBshqD+GVK1cYZFZUVOCtt97ivmrQoAGKi4u54MBb2rNRo0Ywm824ePEiX2u/fv0kMEUe6YyMDCiKwnl9akJqX1XeJ06ckKh8MjIydItdbt26xQBCb9xS/iG9j1artUrC+1OnTsFgMCA2NlYDDKnwigqdfHnGiHty7NixOHDgQI0AJhWDNW7cmDlaCRT7+flhx44dKC0tZeCZmppaZTqOum/puOqNo7+/P9LS0jB06FD07dsXHTt2lPJw79ZcbDKZOLUlMjIS8fHxaNSoEY/j++67DyNGjMB9992nK/JAfTxixAiNR5qMvJZktLFQ5xl6V8yXlZXxe242m/HEE0/gu+++4/P6omHTM/JUUtSzKNonAAAgAElEQVSBNhZkVEhIJPzEIZycnAyr1cqg0de8QCIadC/ErHDx4kXs3Lnzrj0rdbPb7Ygc9SQS5u+rlkKoNq1Oy7vOAABff/01mjVrhsmTJyM/Px///ve/8e9//xu7d++G3W7/1XkvJ02axCGXjIwMmEwmKdQbFRWlCeNRcjW1iIgI3R10ixYtOE/Hl5HGME0kJpMJvXv31oQnbDabtBA6nU6pso88C2pTFIXJt8PDw9nzSsUHQniqYKOjo3mSItBcnRE1CRGq13TyIYWb+++/X+L+s9lsUpJ7aGgok0VTUU5tjUK3QtyRjszPz5fUjtLT06WwekhICOdmBQQE4Ny5c7rHpnumKtSuXbuiffv2MBgM1coIklHIripuTm/SffUi5t3UVFF2ux0jR45E+/btpbSGZs2aYdOmTXC73VzAQGoa5KlSF1KQEXihBYsIm8ko1KmmLCkvL4fBYOCcLpfLxTmd8fHxuHHjBpPtp6WlMaD67rvvWD2FrCraoLy8PH4P6T5TU1Oxbds2zJ07F2lpaT5zXcePHw9FUZiwWggPqPT2tKqtsrISAQEBMJlMUjSD7OLFi3ys7OxsKIoiybl2794dixYtQmZmpq46DpGt621CIyMjdfP4mjVrhjlz5mDSpEno1KkThBAS8IuOjkZERAQCAwPhcDh+cr4fFXvQOKNNsxrkqMdnamoqv09z587F+++/L8kNVlRUVNmX9H653W7k5ORwf9lsNilvnM5Lm2N1zqy679TCEoCnItxgMGD16tU8RjIyMvD1119jzZo13IcdOnTgEL66sHL37t0MYO+5554qw/dEr0Xvj5oF4urVq8zqQJ5bXyF29Zowc+ZMbN26VYouUd6kEJ58ymvXrvHa8kusv+agKCTO31styXltWqMlh/BVac3m0f8frQ5Q1sA++OADXW7G/81GL+Knn34q7cwjIyP5pezatauUN6WubKTWpk0b7Ny5E4qi4PLly5LUYnh4uKaKFvAswjNmzNC9rrCwMPTs2RPR0dEwGAwcKi8tLcUjjzwihWuE8CRsq1Vx1KbmrKOq3tjYWPj5+SEmJgYWiwVpaWnw8/OD2WzWLKZU9bxo0SL06dOnSs8kPVs92cTg4GB07doVa9euxc2bN7la/LHHHpO+N2LECMlb81MA5VdffcVeNafTKYET0lRXL8x2u529yadPn0ZeXh7ztr344ovSsb1zl4KCglCvXj2YTKZaXyf9Ti+/UVEUn/mSkZGRePnll7F//3789re/xaBBgzhnU+/90guBUTj90KFDOHDgAITweKj0TL0JqV+/vm7FsMViQXp6Ov8/Pdc//OEP0vceffRRCHHHY9ekSRP8+9//lr4zc+ZMCCG4730BSkVREBwcDJvNhvfffx9jx46V3mPvlpiYyJ+bTCY0aNAAV65c4b+1bdu22uIhAvkvvPCCz+8QkTjdw6FDhyTqFrPZjM6dO2PIkCHo0qUL4uPjfc6N1QELX408Xer3Lzk5GU2bNkVcXJzue3z//fdj69at2L9/P06dOoUvv/xS91lXVFSw53v58uXw9/eH0WjUyGuGhoYiICCA8/r07IMPPmAw7f0dYimgTX5QUBCeeuop/t7nn3+uyV0dMWKE7nnMZjMyMzOlvxEDR25uLsrLy6VCOCE80Su1Q4HyHOl5KIoCt9vNzCaRkZEaOjXAM37VErBCeNKgSPPd+3nTd+gdTU1N5aKahg0bslTvrl27NOfauHEjH0udMqM3D9ytFtt5xF31UO4q0F/L/lusDlDW0D788ENpV04Tha88sF9i8KtbSkqKRGehrjy8efMme1TMZjOaNGkiTcLqils9fWziAKNdYVRUFIYNG4aOHTv65LgTQg5fExkwEd8CHt4/q9UKq9XKAJFf7NhYzJs3TwNQTpw4wX3scDhQXl4u5TeNGTOGJ0uHw4HGjRtXWVBit9uZlzEuLg5GoxGVlZVYvnw5hLgTMl21ahUfw5sLTQ90GgwGDTCuLaD0Dt0ScL18+TLeffddKazepk0bZGZmStfl5+eHyspKFBYW8nMaO3YsFEVh5aR27drxotaiRQvu27Vr19b4OoE7Um7ePH9HjhzRhPYaNmyI1atXc+h+0aJFPo/7l7/8hSlXjEYje++qe6dGjRqFdevW4aOPPoKiKDh9+jR7YEJDQxl0Ez+e2mJiYiQ6nKSkJNhsNvznP//RfJdAuRAeHlZvc7vdDPIVRdEASipIUxe3qecU0q6mv1ksFjz11FMAPJsN9RyknntOnjyJ/fv343e/+x2eeeYZLF68GDNnzsQDDzyAgQMHMnhxOp1ITk7me/b394fNZvtJfH+02SNJUepnX+T66jZ9+nQcOnQIZ8+exZUrVzhtRu31Pn36NIMZ9YbDarWie/fuePfdd9nb17dv32pG7B0rKyuT+FhJpYjemejoaKlSOy4uDgsWLNDdPBFNGEVa/vnPf2LUqFF8rZGRkbpKTYqi6M6l8fHxEti6fv06hNBP+7BarUhOTobb7WZFJmrR0dE4fdoTej1//jzzstLnanaFpUuXQggPkB8wYAB69OiB+vXrV7kB9/Pzw7333sua7Z9/fodWh9YPmv+F8KQSuVwufP/998yP63a7sXfvXowaNQrx8fHSmKG5Nz09HcXFxRwRuNstNjYWwZ1GIzHn7Z/tqdz03hc1HoP/v1odoKyFFRQU8GRPO8KYmBhNccfAgQN/kcGv13r06IHU1FQmNgc8xSNjxoyRFnZ6QTMyMgDcyaf0lnmrrKyEwWBAdHQ0WrVqpQFmgYGBGDZsGN544w0JjOgRCVPuDeWGEX0R0ZII4ckxGjRokOSdUVPEbN68mRcvITw7fW9VFnUjKbEOHTpg0qRJePDBB2EymWAwGLBmzRq+Nm9eP6IHUauzlJWVcdjLaDRixIgR6N+/v08KDovFIlV/1xZQ0k6eQrckueY9vtSe2OvXr2PQoEHSYrtz506Ul5ezzKY6EV7tSSGQWVWubFXWqFEjGAwGnDx5EmPHjtWEQYUQmDFjBn+/srKSCwP0wJjaXnnlFR4TRqMRgYGBuH37Ng4cOIDQ0NAag5/o6GiMHz8eCxcuhMFgQHBwsMaT16lTJxiNRgB3QuDdu3fXXBN5O2NjYxnoquXtyIgcetmyZfj8888hhEfpivTN1dcXFRWFtm3bokOHDpocQHU+qcFgkPj5fmpzOBwICgpCREQE5/u1atUKHTt2xH333cfAm1IjaOP81ltvobCwEJcvX+bPjEYj5s+f79ODV1FRwVKbeq1z585YsWIFbty4wXm5lDe5b98+dOzYUQIZpHalPp/FYoHFYoHD4ahyPPl6ltSIXD8gIACJiYlcuJSRkSHNow0bNsSaNWuk94U29mrSfaJm8mUE4oTwbAwcDgfGjBkjFdVt2rSJUza2b9+uOUa3bt2k+aFhw4a4cOECHnnkEb6O/v37IygoiIUr6JwpKSmoX7++rqeR5jJ6xpRa8+yzz0JRFJ7XKQeYRBjIbt68Ka0bRJLucrmwc+dOieZKPd7V8qNCCElbnVgXfonWu3dvBLXuh+SF+7nyuzY5k42WHPqv90yS1QHKWhrR3dCuv2ef/hg0cSaademHBpldYbDYOVeRPEy/VLNarQDuEJtnZWVJ+TlhYWGYPHky5/3RpEMLKv3tueeewyOPPILU1FTJ62EymZCUlIQxY8Zg8ODBvGP19/eX+PUAz46ZwkZEJEz8fKmpqRwiV3NUCiHv7B977DHEx8fXylNy//33Y+PGjfjkk0+Yj5PC9BR+dDgcGpofoiyhYgzioVMTxpPl5+drQrj9+vXjSdM7x9Zms3FfqtVeqrI//vGPEOJO6PbFF1+UnuWoUaM8u+ngYN3fl5WVSdX5YWFh2LBhA/eJwWBAQUGB9BuSJ0xMTKzRNartxo0bumDBYDDgpZde4r7xBm/qkOPq1aurPIfL5dLQGymKgoCAAAbJw4YNQ1ZWluRxooUwMDDQJzl8bGws2rVrhwkTJrBM3aVLlzBv3jwIIfDaa6+hsLAQ7777Lnbt2sWbRKfTiQkTJmDYsGGcvmE2m5GSkoL4+HhEREToFl/UplG+n9PpRHBwcJXpNgaDAaGhoXj66afx0ksv4a233sKf/vQn/OUvf8G3334Ll8vFudJVEf+TUaGRutJZb8ydPHmSx2dkZCROnjwpff7ZZ59pZB9DQkLw+uuv66beCOHxJNevX59zAqni/9lnn5UkOmmDeuvWLQghuLDQWzfelxUWFmr6kwAbRXMSEhJgt9v5NwcOHECXLl14fjQajWjdujVWrlwpFW82aNAA7777rk+lHBrXdP6xY8fyXDRv3jwN7RcBO7XsLuB5/+jdNhqN2LBhAwBPTuPOnTvx0EMP6UZS1M3f3x/Jycno2rUrZs6cieeee04KNSckJODmzZsapRxFUThf0ldKgFoq1xf1j9FoxOrVqznHk949+mzfvn3o3bu3hgbu57xbvprZbMaIidMQM+YpBorVAcnEnLcxLu/0f3XOpLfVAcqfYIMnTEPDUYvRdP5uJHq5yRMWHkDc9Dw0HLUY90/x8D9SeOuXaBEREZLXwt/fHyNGjNBUjD755JP8HT8/P/Tq1Uuz8NFu32Aw4E9/+pNmolAUBUuXLtWEaqiYQz3RPPjggwAgFb4kJCRgz549yMnJYUoYi8WiO0noVZa2bt0aDz30kLQYqCUev/nmG6bSITqWlJQUlJaWap5h06ZNJW1kwENyrQcAjx8/rgGUQ4YM4bAYJdLThGg0GjVhSyJb1yPyLi0thc1mg9VqxeLFi/m4NpuNF9+ioiIGqr7M5XLxb9XFHE6nk/Mq1VRCv/3tbyFEzZWNSI5TDRTUzyI8PByXLl3iHERfC6o65EgLYVW2Z88eCXTQv+Pi4vD999/jz3/+s0TFo94U+fn5oUGDBkhNTUVsbOxdTe6vSY4gjYOGDRtixowZmD9/PiuJkEfSbDZj4sSJ+O6773z2weXLlyUPpvq8VanbEChcvnx59Q8YwAsvvAAhPEUbb7zxBp9DL1WAiNupT/v27YuysjKmZVI/j9DQUM4HJt1yPz8/bNy4UbcPzWYzWrRogXnz5jEf5ebNm1lBatu2bcxOQBsjPa+yt7ndbsnzvXHjRvj7+8NgMGDXrl3SBqZ3796695yXl6cBxbTZbtSoEQB9LW/6vZohg8zbQ+t2u7F48WLuW4fDgezsbLhcLsyZM0fqM6KSqslGPDU1FQ6HQ5cirLi4WMpxp4JIPelFUtMR4g6VXWlpKZ599lndDUNYWBh69+6N559/HmVlZZxipPZuqnmg1feSmJiIxx57DCaTSZNbebcaRU7S0tJw8et/IXd/Ee555j0keQHJpP8hLc/dX/RfSw1UldUBylrYV6UVGJd32gMcq3ONL/wjEnPeRuaCVxAUm+JTZeZuNm9SZcAzgR07dkyXvFjdkpKSuLpVnfeoZ7dv39ZMaGPHjsWtW7fw7bffco5mQkKCRB6t1xwOB4enN27ciMLCQrz55ptMJXHp0iWsXr1aUvtR71hpAidbt24dfzZ8+HDd3XNFRQUMBgPatWsn/b1x48ZS6Eyd7G4ymbB48WKUlJRwKJkmPqfTyeeh80dERLBUYVVk6++88w7nHBEIdDqdyMnJgdvtxl//+le+FyFkGTk9+/jjj5kzUD0xE2AVwsN5qCgKc+917tzZ5/Hcbjeef/55NG/eXAqr9+zZE3v27OEJ3ul0wuVycQ4hVWaq7bvvvsOlS5fw4Ycf4tVXX+WFvV+/fpzvN2jQIHTr1g2ZmZlo3rw5UlJSEBMTc9fyktXvYWRkJJKSkni8qj1jvsKA4eHhiI+PR1RUlG6OWXJyMjZv3oyysjJERETw+ebPnw+32y1RBfn5+WHBggXVFtPs2bOHN3rLly/Hxo0bpRw/IQQzC6iN2AJqokFPVlJSAiE87AKU/2Y0GhESEoIff/xR9zfXrl3TbJrj4+NhNpthMplw6tQpREVFMaC8ceOGRgnJz88PU6dOxe7duzFp0iQ0aNBAelZWqxVNmzbFyJEjud/pvbly5QpT1FRFYaQoCntV7XY7/vrXv/I9kxd44sSJVc6nR44ckZTJkpKSNCk4SUlJzJzgbZQaRNElMqLHoY341atXsWPHDtYsr24jFB8fj27dumHWrFnYtm0bjh8/zkCzrKyMxzhxQXqnCLz22mucGvTcc8/h6aef5s3AI488AiHuAMqKigpYLBaEhobyRlsvFcPhcPAG0FscQFEUBAUFwW6348qVKxg/frzm91OmTJE8szSn3o15wFfzrrL/7gc3iq7dxrkr/0TRtdv/lXKKtbE6QFlDe73gChotOVStK1wPWCbM24M+s5bx5PxLvQyvvvpqlYnOQnh2xdnZ2dKETt5ACt3s2bOnyr4g7yLxnNX0nrp3745NmzahsLCQQ8zetEEHDhyAwWCAw+HQ0HHcunUL8+fP1xD0hoaG4sKFC9ixY4fk2fRFjk5FPN6VhkOGDIEQAi6XCxs3buTJKyMjQxNy8q5Wnz59On9GpNhCyNXHFy9e1CVbp2axWDB+/HhNPmNYWBh/vyYePXoudrsdFRUVWLduncbDSl5Gk8mE2NhY6feKomD79u1IS0vjZ0vUJoMGDcLUqVPRtWtXScZOCE++Inm9CZDRIlWbcUweXofDgcDAQERERHCemJ432+l0YurUqdi4cSNee+01HD16FOfPn8e1a9eYVL9jx45SuFIIIeVTkmSmEILDt1R1ajKZOA/N1zWrtYujo6OxZs0aVgoRQnCeM/XNihUrasTfOHfuXH6W3pKf3tfTpUsXXLt2DYDMwVmV51PPjEYjOnTowLKna9asgRD6HjvAAxD1lKEMBgODssjISDidTi7MUreAgACf13L69GnMnDkTTZs29UmhdPDgQfaKqzlA1VZaWspecafTqeG4/PLLL2G326VqdrXt2rWLQZnRaET//v25r+n46txFag8++CBXT/ft25f//sYbb+Crr77Cjh07MGfOHPTo0YPHtt774j3uDQYDevfuzephRC8G3PGCGgwGlp8NCQlBYGCg5AUkvtLp06dDCA+oV8vVHj9+XNo0rV27FosXL9aVvKVxL8SdosUBAwZouGDJysvLpf5Qz4G0KSfv5Y8//ohHH32U++Vua3ur26ZNm3yOxTqr3uoAZQ1s43v6+p41B5WesHi3rFW/yEvga6Hz9/dHu3bt8MQTTyA4OBgxMTHSfR0/fpwnaTU4ADwT5N69ezk83aRJEyac1Tt/eHi4NPmkp6fzxFK/fn2YzWZER0dL5xdCBpRHjx5lbsfi4mKfz4MqH9VFC9TMZjMOHTrEoNM7twvwSN1ZLBbNgr5y5UoIcYcsWo8wGLjDyzZhwgQGoTSp0zGfeOIJvh7vxevmzZtSaE0I2etKRVGDBg3CK6+8InlN1CF+wLN43LhxA5999hny8/OZloOeU5cuXTBy5Ej06dOHybr1xooaENV27HkTRhuNRgaWnTt3Rt++fXH//fdjypQpmDdvHp566im88MILePPNN/Hmm28yWH799dd9PvMrV674vIbk5GQUFVUvdaYoCl566SXJw2w0GtGtWzfWaHY6nVi8eLEm/4/oYYYPH47du3ejtLQUBw8exJIlSzBo0CA0b97cJ/WRd5s2bRrOnj2roRxSm8vl4uIH4r70NgLAixYtko7fpUsXXtz/9Kc/VdsvesclDygpBPmiHFq8eDGDnd69e+PMmTPSJqRjx46SeILNZkPv3r1x4sQJ9tbVRBWHrKioCPPmzWMtaO85kKjO1O/2Bx98IOUk+uJbvXDhAs+HgYGBADybCsr/M5vNHInxZVevXq02hUfPA66OKoSFhWHWrFkcyqffpqWl4cqVK9i/fz8XthDHplonnYrtcnJyANzRYSeuVSrmoTmO5mjv1KDCwkJMmzbN5/2MHz8ehw8fRkVFBYNMi8XCROfLli0DcIdvtW3btli3bh2aNGki3b/6319++SUURYHNZkNiYiImTZrEcxb9lzznv0R7+eWXazwW60xrdYCyGnu94Mpd5alK6jH2F6MVouPGxsbib3/7m3QfRqNRE8ouLS1l74PecdTN4XCgXr16nD/56KOPorCwEE6nU8rHOX36NOdRqht5MF566SX+rhB3AOWJEye4GEFPMURtFMojT6DejjUhIYEBgnoBuX37NoTQ5p0piiJRwjzwwAM+Q5GhoaGwWq344YcfAEDiowwLC8O7774LADwBJiUlweVy4eLFi1wAou7r7OxsZGdnY/To0WjRogWCg4N9Jp8TTcdPJXf2JprXe+Z+fn5o06YN5s6di1WrViEvLw979+7F+++/j44dO0IIT0hfzVunLkDbs2cPunXrpgl5+zJ1yHH//v263/nss8+k623fvj2+/vprTJo0iRfoqp6Zt1VWVmoIpvX6ZOjQoTh06FCt5AbJ41PdOyWEx/MYGxuLtm3bYvz48Xjuueewd+9eXqD79+/v89x0/VOnTsWRI0c0QCUiIoK1uGtjakoj2gypSdEvXbqE06dPM2gNDw/H8ePHUVJSAofDAYPBoAkDk5eX7uVf//oXj2Oz2Yx//av2+Whms1kSSfDu79jYWIlaTQj9DabaiP2C3gMh7hBx+1LuIU/j7Nmz0b1792q1p00mE5KTkzF9+nRs27ZNisQQ2Prwww8519JisehWeZ88eVLaHLVs2RKrV6+GEELKtfbWYT99+rQ0Jg0GD0H6qVOnMH36dDRu3FiaU9VzEf2b5jhAznEWQjBgPXPmDBRFweuvvy6laJhMJnTo0AF79uzBH/7wB+n6AY/IiC8v6C/daiqQUWf6Vgcoq7CvSivQaMmhuwcoFx5AwqN/gD0s7hd5GRRF4WrI4OBgFBUVobS0lBPtExMT2dNYXbVcp06dsGnTJnz66ae8CFA+X5s2bbiPGjZsCD8/P6nfXC6XboWh0WiUFhUhPIDy9OnTMJvNsFgs+Pjjj6t9Lg8//DCE8HhfaFLs2bMnLwCxsbFSeMzPzw8vvfQSFEVhb44auOzfv1+a8Nq3b4+Kigr87W9/w+nTp3HgwAFs27YNa9euZcLiZs2aYfDgwejevTvatm2r8fz9nGpEyl2y2WzMEej9HbPZjLCwMLRu3RoPP/wwU4I4nU689tprOHPmDCfTJyQkSKCEqGy8QU54eDiOHTum2+fXrl3jxbtLly4a4PbFF1/wfQOoFaCk31O1vHe1bmFhoQSgQ0JCpM+Li4u5EMCXV5nsww8/xPTp09GkSZNq85pHjhzpk3Rfz4qKihhw+2r5+fkcoh08eDCaN2+O0NBQn8/YG2wWFBRw31N+Hamo7N+/X8qZpX83btxYAgDVGeWzeZPFk2wjefuMRiMeeeQRKIqCt956S+OFa968OQYOHMj3ZrFY2AtGDAGkuOWL1NuX3bx5E0J4eCvPnz8vRStGjhyJTp06afrU4XCgX79+yMvL0/VSulwuzWbroYceYi3qV155hUFjSkqKT3JvIkund0oIwTnsfn5+kke/ZcuWyMvL4/eTwJ66eafbeNvu3bs110DUbAAQEBCAyMhI/v/f//73/N2GDRtq7sFms6FFixaYM2cOzp07x/MIaXML4SnaAjx8tEajEXa7HefPn5fAdPfu3aW8ZBof6gIv8sIK4QFz6lz5/4322muv1Woc1plsdYCyChuXdxopiw+i2eOH8cKfvsSJi9/g23KPV+q5Y59XCyBPX/aIzkvi8Qv2I2r08rv6EtDE2a9fP/Tr169Kzwt5Gjt27IiHHnoImzdv5pxIdXW0EB6eMbUXijwX6nA0VZGqAQbtUNetW4erV6+yGgM1KiwRwkPTQ163Dz/8sEbPJSMjg6s96Zi7du3CoUOHuEgkOjoa/fr185lvk5SUJKkK0aRX276nkC9NnETcrvddk8mEMWPGMCht2bIl3nnnHZw7dw5///vfq+SCpGtbtGgRBg0axEpE3sdfuHChxFNJUpMPPPAAlixZInmOHA4H+vTpo7nOpk2bSgUJR48eZRBBYTRvUyt1bN++vdaAEvCQmhNIeu+99+B2u6VkffI2qcN7alu/fj33fWZmJq5fv45jx47hwQcfREqKXBhns9nQvHlzHr/qvjQajRJAqYrYGvAALfV7k5GRgY8//hjXrl2T3kWn01nl/ZPModlsRqdOnaoEm/Q86H4XLVqEY8eO8Xj28/NDQUEB+vbty+AmISGBgUBVRiTZajlKwBO6pOMHBQUhPz8fI0eOlPhHw8PDkZubKwE2tUa32WzG4sWLYTAYmGewQYMGMBqN1QIntZH859atWwF4cvIotG6z2TjfkYoCnU6nxusVGhqKHj16YPXq1RgzZoxPr78v0JiSkoJu3bohKysL27Ztk6JC6jkvOTmZNxrnzp3jHOXWrVvzOamqXb0RT0pKkviFqzLiD1Vfb3JyMkdxpkyZgj179ugWSfr5+Uk51uPGjZPmcwKUBPZo7A0ZMoRTlC5cuIBPP/1Uw8GcnJyMZcuWoaKiAkVFRTAajQgNDYXb7caFCxd+dZLGvnJw66xmVgcofdjFr//FILDTynyUff8jTl/6Fq+d8XgsqgOUj+3/DF+XeUIkEqD8n2YJj//FXgqHw8Fa07QACyF8Lojvv/8+hPCQtLvdbmniNRqNyMrKwp///GcIoaWYoQIXytXasGEDhPAU7Kjtiy++kBZGtUfQYDBg1KhRmDJlCu6//3706dMHnTt3Rnp6Oho3boyEhARERkYyJ98v0V+pqano1KkTU+xMnjwZ8+bNw/Lly/H8889j9+7dGD16NIQQePzxx3Xz32i3v337donewm63M0E66XGHhYXVODxLfHtCyDyZbrebKzC9w51+fn5IT09Hz549pX632+2w2+3SQmU0Gvl6jUYjHycxMZE93larFW+//bbu9V2+fBkGgwEtWrSA1WpFaGjoTwKUgCffi/Sa1bRWLVu2xAcffD20aBAAACAASURBVAAh7nhBvc3tduP111/XpRZxOBxIT0/HggULmIaGTB3mNBgMnHJRUFCAAQMGaIitV69eDZfLhYMHD7Jn1GDw6KKrtYkBj/dUfR3vvPOO5rorKys5JSQpKYl5+dRWVlaGQ4cOsWeTNgZVFXAYjUaMHDkSy5cvR69evXg+8KXeQkbAjDhjS0pKmBHA4XBoiPbpGqpSW4qKikJwcLBUzEbhRXquPXv29Pl7b5syZQqE0Hrv1IBsyJAhsFqtsNvt7BktLi7Gww8/jMTExGqLO9TetQceeEADGqsydfERbU7at2+v+Z7L5cKyZct0RSgMBoMm792X0TgcPnw4bt68icGDB1fJXUqRj6+++oqP4e3pJ3BFgFIIj9LWzZs3ORwvhMdz6Utq1TuETAC3V69eGqaCX0P74x//WKP+rjN9qwOUPix3f5FuRXerJz0LQlWAstPKfJT/4MbUVzz5S96AMmHBftQb/MhdfRFo8li1ahXfw61bt6QQgq9kdCIdJw9KUVER5x96S989+uijyM7OxqRJkzB8+HCuDI+KiuJJVE1NQeCgtvdC+X5OpxMhISGIjo5GQkKCNMn37t0bo0ePZi3vlStXYsuWLdizZw+ys7N5UX3iiSc4LEOLovp8gYGBGDt2LC5evMihOO98KZfLBZvNJkn0eZs6l5KoPigsZjAYpEWGZDJrYhTSCgkJkciW9+7dC4PBAD8/P1y5cgWKouDQoUPo0qWLTy/phAkTNIt3WFgYoqOjsXv3bgaf3oUrVZGQqxWRiPC+fv36PwlQ3rhxg8ELNX9/f+bApL/t37+flTcGDx6soRZyOBx8L5GRkSxDp2fkMRZC+FzADx48KBFbq8fqgAEDfHrXiMtRDXTU6Raff/45b+AGDx5c41zN3/zGw3F78eJFBAcHMziqV68emjdvrgF91NQeeYvFgr59++LMmTO8uSEFKSE8RRSzZs2SuBC9751AgZrfVM+INsgbYI8aNQoul4vzrr2LznxZZmamZmOxYsUK3XuOjo5mrkm9z4kE3/vvFouFKYJsNptms+DLKIwvhOCcRiGEhrUC8IR81V712bNnSywWRqMRDzzwQJXnJrENmoeryuFs3rw53G63xGjhbevWrZOu6cUXX5TuIT8/X3PcgIAAjB8/HhcuXIAQno2vmt9TbeoirV9bqyk5fp3pWx2g9GH3rH5PFyzWBFCeuPgNDn92HYk5Ho+OnocyfkbeXS3OMZlMsNvtsNls2LZtG5577jk89thjyMrKkihcUlNT0aJFC9SvXx+xsbFc3apeJGpzXvq+2rMVHh6OlJQUNG/eHJmZmejWrRsGDRqEcePGsbyg9+/tdjuysrJ8hn0LCwulMKSapoe8dN55YmfPnuWFNT09XTrnzJkzcfXqVUybNk1SWaGFX03iC4C1ZL133Iqi4LnnntOE0+jcTZo0wYULFzRyY7WpbCXFHwqJHjx4UMpd+vLLL5Gfn48ePXpIgJuIoadMmSJ5FITwhNiIbL1hw4bssSSAQt+LiYnhYwYHB2PlypUS6KEK0o4dO3J/kJdXj4evKiPyYiFkMYDf//73AOSwujewCwoKwj333IPVq1dzRbSiKMjOzmZANGjQIM1Gga5f3fQKRBRFwbp163SLBSwWC+655x4cPnxY8zvaRMyYMUO6pwULFuD111/XlQWtiXXp0oUBO4kHREVFSc+GaI8CAgKwYMECDB48GC1atPApXWmz2RhY6eUA2+129O3bF6dOnZKKKapTPALuAMrMzEwew+StdzqdDLwyMzNrdP+hoaEICAhAVlYWunXrVqU6kdlsRnJyMjIzM6UUhNTUVC7SUVdCHzhwgPvDezPctGlTzJs3D3/5y190r4skFSmH9cSJE/xbNeguKiriOSEwMBD79u2TjkN0QOrnFB0djTlz5uDmzZv49ttvsXbtWq6+V7fw8HD07t1bIh+ncUr9fe+990IIff5SwJNCQGF7uga104DukTZ/JpMJr776Ko4ePQohBFauXCkV2+3Zswfbt2/3WUT1a2krV67Ef/7znxqNwTrTWh2g1LHyH9wahvyaAsoFbxWi7PsfkfnUsSoBZcLCAzBYtNW2/zeaxWJBYGAgwsPDOTxIQCo8PBxDhw7FxIkTGYTQZE3eTrPZLHlC/f39ORTtTQzrbVevXpVCTZ06dcLq1asREhICITxhpkmTJqG8vJx/s2XLFvb4UX6XOnmaEvT1QmZlZWUaMPX0009rvvfZZ59hxIgRUkg9MTERubm5uH79uoav0e12Y8mSJdxvdrsdc+bMQWFhIYTwFC6ptbxffvllzQLhnRbgy0jTmELfLVu25NzNXr16Sd6o5ORkLF26VNcbTZRCBDa9SYITExPRvXt3aRFNTEzE9evXMX/+fO4bNSE3EZ6rc23VXpmaWEFBAT+jsLAw5OfnswQgXa8eRVSPHj2YRLwq++qrrzjH0W63Iy8vD4BnUSdg2r9/f/acqBVMFEXBY489xue32+2YPXs2KisrUVlZiRUrVkjKIH5+fhg0aBA++ugjBiZCeIjNb9y4wYsv/d1ut+uqJ1VnsbGxCAkJQUVFBT+Xvn37ar73zDPPMBhQv1OAh/HgoYce0q3615szYmJi0LZtW4wZM0by6Kn12n1ZVFQUg3E1w8Lzzz/P45DGMVWml5SUYPv27cjKyuJCmKo8jTabDV27dmWvaVRUFHva1R779u3ba5gkqBL60qVLADw8s3FxcVAUBcePH2cApm5Etj5z5kwUFBTwuI+KikL37t1hMBiQkpLC49dkMqG4uBjjx4/nqMWDDz6om/qyefNmPs+mTZvQt2/fKkP06enpTMNE/UdV+E6nEx9//DEURcHy5culUHOrVq18Vq8risKa5t5Nrbx06tQpHoPkaabCm4sXL0qbv/8bAh8/t3Xp0qXG+fx1JlsdoNSxomu3fXofqwKUbZ8+hrLvf0TOHwr5b4A+oEzMeRuWyKpVZGrTDAYDli1bxuHfw4cP49NPP+X8pOzsbHz88ccMgCZOnAgA7DE8f/48YmJipMKB77//nhcbqsLct28fLyYpKSkoKirSlRLTs+vXr/PCrJ7UyLOTl5fHk6DJZMLw4cM5BB0QEIDz589zyNabMy0xMRE2m03629WrVzV8dUJ4vKlqAORtQnjCy96Aa/r06SgvL5e0dgMCAvDEE09IniFafOx2O5o0aYKSkhKYTCb4+/vj+vXrUojVW+lHz6Kjo7kQRS8/MCoqCnPmzME333xT5XHUXI7kmbl48SITDHsXKNFYsVgsyM/Ph6IoePrppyUNayH0Ca/ps6oKjSorK5mqyWg04qGHHsKyZcskJRLvMR4VFYXc3FwIUTVvpZ5t376dN0cNGjSQQMaVK1ckLeHFixcjKyuLx39AQAByc3N9hqRLS0sxb948yQOjBj7z588HIOdrCuEB0Hqh0OrMarWiZcuWnG4QEBDgkyCc8pzj4uJ0wcO7777LqjPeLTs7mz2bYWFhPgFBaGgoMjMzMW7cODz77LNSNTrgGbfkjVUXjZWUlGDLli0amqGqCmHIK5eWlsbPkEQMysvL+W8jRoyQilBIH1rPvCuh6dhqI7oyp9OJSZMm6ZKtU4haTfQ+atQoDVVPgwYNWKlHz9QV1d4RJHUFvxAeD+eLL76Iy5cvQwjP5og8h2azWXfDpQasZrMZo0eP5hz7d955B127dvUJYNu1a6cZR6WlpZIa2+3bt6UN9/9LjeZBemfrrOZWByh17NyVf/4kQHnswtc4felb6W+Ab0BpjdFfOH/qSwDcId2mhHpSHaC8rbKyMvbENGvWDCEhIQgODgZwpyJYXeFL4DEmJoYXU7fbjQcffFBTCKJXTED27bffMhDJy8vDsWPHpEn4vffe4+/u2bNHCq04nU4mrk5PT9etfKS8pb1790JRFMydO5c9bQMGDGDidbrekJAQn+AgKCgI9erVYyJsvf4OCAjwmTf297//nfumSZMmiIuLg8FgkDjwjh49yhOX3W5HQUGBz74zm82IioqSwnU2mw0PPPBAjXPOgDtVxEajkfMSAeBvf/sbHzcyMhLz589H+/btNV5Bf39/DBo0CNu3b8eGDRu4f00mE0aOHCmBfAIokydP1r2WrVu3Mii32+26IcuBAwcy+Tk9tx49eviUzqyJuVwuqbKd9IEBDwUKLbD0eVhYGDZs2FArHsqSkhIN36jT6cTEiRN5gbXZbFi+fDlTRFWnTqU24lIlb1C/fv2Y+1KtdKI2ej8SExPhcrlQWFiIYcOG6eZaqr2PaqYHt9vN3tihQ4fi8ccf53C7d7+px2lERAQ/Pz8/P8TGxup6GtX/bzabMXz4cLzyyiuazd/WrVv5exaLRcpJ9VbsoY3ppk2bGNB6q03RplvtaSVvvjcYo3zC0NBQBmC0waG0I71xrM5lJ75FtRUWFiI7OxupqanSMahPOnbsiCNHjvA4PHPmDPeTulLcO1VhyZIlPsdRYGAgwsLCJDCv/n2DBg00gJDmZbvdjt/97nfS8RRF0dx/YGAgli5dqpt3+WttJBvrTeJfZ9VbHaDUsZ/ioZy+8yP8+G8Fgzd/gNQnjnADgFfPXEHqE0dQ36vIxxZdtb72T2nqSdnf35930ElJSVJOo1qCq379+lizZg3Wr18PITzJ+JcuXcJTTz0FIQTnPXnrSP/1r3+VFpHHH39ctz9v3brFVYBqEKZePEwmEz744AMAkDyp6ny+9u3bIzAwUKO4A3iAshAerwUlpUdHR+PUqVPMuzhq1Ch8/PHHvPNOTk7Wvd7U1FT2dnrnKHlTz/Tu3VuXLJk8bxQK0pOBdLvdUv7m0KFDeefvcrmwZs0anxrsHTp00L32qiwiIgIBAQHYsmULH6OkpISBamBgoKZ6/ebNm1i0aJFPz1RwcDCHMg0GA/r06YOvvvqKqaNMJhMvyoWFhXj44Yc1nl+TyYSkpCSMGzeOx6V3teWSJUsghCfMeO3aNTRt2hQmk6lWQA/weK0JRBFgttlseOONN5jLk5qfn1+VHtaqjDzcRPqsXqjp/jdv3izJ2z3yyCM1OjYV+ghxhy3g6tWrEMLjnfJlVBmtTmlQa77TfKEoCvbu3Sv1Rbt27TjnTy3zB9zRoU5MTMTUqVORlpZWI65bKihLTk7GkCFDsHbtWrzzzjvSd/r16yelb5CsoBCe9BwCm4qiaOjJhJCrwIuKing+GTFiBI8deu5qKUXy4OnRyNAmPSIigjecgYGBnLtbUlLC77V3Dia9R8OHD8eUKVM0JOJUCGS1WhEeHq5bDOhyuVgK9OLFi3C73Vi3bh1Hd9RNj1WAjArnKN3I+3k/+eST0j3MmjULgOzppw3H7du3pTQVer7bt2/H4cOHdYuefo3NaDQiPj7e58aszqq2OkCpY9/9hBzK5459Xu1xp7xyViI5v9s5lP7+/ujZsyd7IJ1OJ09gP7fqmv5ts9m46lqdP0ifh4aGYsKECVi4cCFWrlyJDRs28GRCXH5qYnMhPJ4Ws9kMs9mMhQsXcr4kccydP3+eq8mF8Cz0BD7JysvLGbwZjUYsWrSIP6O8S8qbUofF6tWrp/FCED2QupCnYcOGrH1bXl6O3NxcDTXIyJEjmZJGTfXTvHlzn2NCURTJe2G1WpGYmCjJGNJ/jUYj8vPzmZS7NmDqyy+/5IUUAHvpqHjGz89PCvl5m8vlYi694OBgXYCpHldq76a/v7/m+xQ2PHnyJN8HecgffPBBzfkJUArhSZegMO6WLVtq3AfXr1/nsbhz507Ju6Zu8fHxDBq8abJqYpRLl5OTw/1O707r1q0lAJGamoq1a9cyb2L79u2rBbHkjVRTHAFAXFycRmTg1q1bWLBggVQ5TO8QvS8NGjRAQUEBhJDzes1mM5o2bcobSvrdsGHD0K1bNyQnJ/v0NAYEBCAlJQXdu3fnfrZYLDh06BAef/xxDBkypNowunrsDx8+HG+//TaDSYPBALfbDbfbjZycHGkOys7Oxq5duyDEHT1ossrKSi6OIrlBPz8/xMXFSd+j8HFWVpbuMyCZVuqTv//97/yZoigSmA4ODkafPn0kT633vN2jRw8JxBgMBs41pTzGZ555BsAdnl+1p5U8qnq0aoGBgRg9ejSKi4vxz3/+E48++qiUVx4cHMya4wUFBVLxmLqpCxV/+OEHDd0W/btt27YoKCjwyTTwa24DBw6sNie7znxbHaD0YbWt8u60Mh+jXjqlaQBwpOg6Rr10Cq2efIe/X2/6lrv6ItAL3aJFCyiKgkaNGvHEHh8fr3uPAQEBCAwM5EmoU6dOPPlTHltaWhr69u2L9u3b8zni4uJ4p28wGHxS1NSmqUOeFCru1KkT+vTpg5EjR+Lhhx/G/fffL/0mJiYGGzduxFNPPSVdw6ZNm6T7DAkJ0dD9lJaW8oJFSeuApzJc7b0VoupcvevXr2PmzJlSODoiIkLS337xxRerHGuHDh3ShHxtNhtWrVrFurxCCAa0JJdJgLsmRrmnRFf06KOP8nFffvllZGRkwGw2V3scdZ7h4MGDUVlZie3bt2PAgAG6ng7vFhERoRveP378OITQqvqQ0bgkzxFVKrdq1apG919aWiqlXJw/f15DM6Tue+BOLqx3iLQqoyp3p9OJ8vJyrmQODg7mEKla5pOuwWw2s6c3LCysSpoYug91YRwAzJ07l8fJ6tWrpY2Kw+HAgAEDcOTIEckr/uyzzwIA0z1t3boV27ZtQ1ZWFm8+fW1AHQ4Hg8asrCzeRHjLPdL5qtqwlJeX4/Dhw3j88cclsnlf5yaFIO/PKTVGURRYrVafUQiiSiNv8dy5czXf0ZOrJaMqbJqH1BKV9MyFEJJqjhCCPbJ0bj2ydcqLJSYL9Zjy3uiUlZVxekmLFi1QXl7Ox8zJycH06dN1OSIdDgfnWapVdbz7R90WLlzIn1+8eFFTqETvEPGR3r59WxON+LW32ihj1ZnW6gClD/PmoZy49Qym7/wI8978BABwoPAapu/8CNN3foTGj/mWZwT0eShDek696y8D7fT9/f25alE9+aiNPBKTJ09GeXk5q5DQImQwGDQSd1S1Wr9+fTgcDlitVg4pBQYGIiEhAceOHWNgQYtl//79sWrVKp7gxo4dy+o8vkIhVquVc55q2w8GgwEOhwOBgYG8+AYEBCAtLQ0dOnRAz549MXToUKk4xte11Ibep7i4GKNHj9Ycx+FwaCpsz58/jyFDhkgeBXp+FOZWL0R79+7l3xJXYOvWrWt8bSEhIQgJCZE8jVFRUTAYDAgLC+PirOrUShRFkcBXixYtEB8fL12r1WrVBQImkwmtW7dGTk6OlPtZXl7O3nQ10bLayBsGAM899xwfz2AwVOvRU6dczJkzR+LBi42NZRCyb98+9iwlJyfj3LlzCAoKgslkqnGu6vz58yGEJ8VBPQ68Ux4URYG/vz8cDgeeeeYZTSGSwWCQKmnJKMTqDf4VRcGmTZs080GXLl0YMCxZsoTvj64tICAAycnJ1b5nERERmDNnDjZt2oTevXvz842JiWEqreLiYpZXpWdCaTR+fn6cq1oTIyqw9evXS5uY6prNZkNMTAwyMzO5gO3o0aO6ldRqwu4nn3xS83loaKguL+mRI0eYsovSCMLDwyW1JGoBAQFo3749nnzySakYifKZp06dioqKCuTl5emqnAUGBqJTp05SOgb1r5oWbdKkSXxsuu9Zs2YxIwSNKbXnlLyUc+bMke6vtLSUv/PEE09IkZrIyEip0KlVq1Y4ffo0cnNzeQy1a9cOZWVlGgfA/wvtH//4R43HaJ1prQ5Q+jC1Uk5iztu4+k99UnAA6LQyv1aAMjHnbZjD6t21l8BqtTJFha/wEVVIdu/eHbNnz+ZJQr0jmzRpkvQbPQ+Y+jtqwtpmzZox6Tbl+ND3yJPlbUIIaXEaMGAADh48KPErkn333Xdc+bhr1y6myFA3i8XC4cTmzZsjJSWFQ2FOpxN2ux1ms/kncW2azWbY7XYEBAQgLCwMsbGxzLXZtm1bdO/eHYMHD8b48eMlUnB1i4+PR+vWrTU8j3PnzkVpaSkqKyvZOzp69GjpOvPz86W+S0tLg9ForJHazqeffgohPMoh5C3q27cvFEVhMmhaDL15NsmIRFztfaFmMpnQtm1bPPHEEzye1LmfVdG8tGjRghdAX+cGAIfDIWlLq0msvT11aisvL+fjqzc69G9v9aiFCxfydwwGA1fAe3M86lllZSWsVivzcBKpvhD6FaMEtsg7VlZWhpycHImY2mq14oEHHsAXX3yBv/3tbwwIqLDjyJEjuPfee6UwusFgwKpVq7B161bMmjULbdq0qTKfkd6/0NBQzJkzBzt27MCVK1d4LOrRW5WVlWHixIl83tDQUKxduxbPPvsshPBsYhVFQUBAAKdT1AZQut1uOBwOvu6IiAhNwc2iRYtYCzohIQFDhgxBamqqzzC6Gmw+8MADWLNmjbRpHTJkiPSM9QoAjx8/zsCsU6dOkrdX3egZVmX0jniTaROzxeDBg7mgT33sJk2aSMwMxNMKyJ5TeratW7fG9u3b+d5OnDiB3r17S97DZs2aYePGjSgrK+NN7sCBAwHcAd7qtAKz2awp+OnUqZP0eW3XsV9D+/bbb2s8RutMa3WAsgojLW9fYPGntIT5+xAz5qm7+hKEh4dLEx8BL1o0KTTlK99JDTa7du3Kn6l3vWS04AohE4nTJFhRUcEhmAkTJjC4cjgcGoCqnvQMBgPq168PwFPlrVaAIUtLS4PZbGawmpSUhM8++wwulwu/+c1vpAmvb9++cLvdGjoQshdffFGjKEGLA4XujEYjhg0bhl69eqFDhw5IS0tDw4YNUa9ePYSHh/+svFQ6vrcaUGJios/FPzExEUuXLsWWLVswdarHw/3b3/4Wt2/frhLskHwiLZ7ePJwUYhPiDjtAeXk5XnzxRdx33326yhudO3fGihUr+LexsbG4du2ahsT9D3/4A6tnqHWpbTabJA8qxJ2ChKlTp0o5si6XC0J4ipbURspEZrNZd8NSWVkpgXeqRv/mm29gtVqRkpKi+Q2pjsydO5crmimdYvjw4T77GJA3W/7+/vjoo484h9IXBUl4eDisVqvm+j/55BNNha26r+rVqyeNd4fDgZCQkCq5CoOCgtC9e3cJNKo9XydOnODzU9hZCE9KhC9zuVzIzs7ma/H39+eqYSKif/rpp5nYvKZ29epVvn91OotaIpT+FhAQoPv8y8vLmXO3OrBJ86LVasWIESOwZs0aBm0XL17E2rVrJU8dNb2q7rCwMPTu3btaYv/r16/DYrHA4XBIeXvNmzeXKNAURUGHDh10n6nNZkODBg2QnJwsAUTa0PjimCSjSJP3nEPFWW+++SbPiwaDAffddx8mTJjA5woMDMSTTz4JRVFQr149BAUFcf7qr7WZTCZERkbijTfewK5duySPq56oQZ3V3OoAZRX2VWkFGi3xHc6uNZhceABJC/bBHKTlErwbbejQodi1axdcLpekKiKEkKTnXn/9dQjh8UpVRxhsNpsZbBIwIWDg5+fHoVzyFCQlJUGIO8AE8PC3qasCL1++zADUYrHgwoULfGyiAHnttdc4B/TatWsoLS3lSc9iseh6pRRFkYo3aHGdMmUKf64m9rVarZg2bRqKi4thNpvhdDo515AmntpYeXk5e1Uefvhh3QW9ZcuWGg1b8uBERkb+7GpIk8kEq9UKPz8/BAcHSyE0IjSnvFTSK8/NzeVF22azaeiCwsLC0KtXL86Z8taBJkoadWgtOjpakl6k377//vsSv6MQd1SSvMnWTSYTkpOTWQd9xYoVmj6nsF1SUhKHWRVFwbJlyyQVpylTpnC1MElZLl26VHM8Aq9DhgwBIMvQCSF8Uolcu3aNv9OkSRMGCNUBSvL+EC+s2hRF0bzHvhq9K/T+BQUF8fhPTU2tMjeM7m/AgAEA7mwOqRBuwoQJPn+rvtalS5dqxq/T6YSiKLUClAcPHtSAvvT0dJw9exbjx4+HEAJffPEF35/ZbNYdGwAYFHqHMsvLyzmHcMCAARq6nqpacnIyxo0bx5uVuLg4nD17ljdSSUlJ6NWrV42UomguVlMJBQUFSXnvVEWflpbGc2BcXBxSUlJ8bmTbtGkDIQR2795d5fnpnauoqPCpx03vkToX3O12Y/HixRxydzgcMBqNaN68uTQH/9Ltp2zkx4wZg9u3b/O9/Pjjj3jppZcwffr0WrNG1JlsdYCyGnu94Mpd9VD6p2mpLX5O8/Pz0yWP9fb+qMOFVOBANBdk//jHPyCExwug9ux4802qm9VqRffu3TFmzBj+29ixYzX9WFlZiaFDh2p+P3LkSACeCd5sNks5S0QkbLPZpNwv7zClt5EngRYck8mEJk2aSOHvnJwcKVxM5/KWSKwqnKo2RVF4Mfd+PocPH2YaGQI9FRUVWLZsmbQ7djqdvLg//fTTPFlPmDABt27dwvr16xmYR0REsLdm8uTJGD16NPr374977rkHbdq0QdOmTTXezp+al0qqPDQWIiIiUK9ePTRs2BBpaWlo1KiRNNbS0tK4L0iO7ciRIxDiDpF7ZWWlBlTOmTMHLpcLFy9exKJFi9C6dWspx9RgMKBevXoYOXIk3nrrLbjdbrz66qv8eaNGjfDoo49KOZ4ZGRmatAAqMPOlbe9wOCTC+X/961+S5z47O1v6/ieffML97J2vXB2gBMA65A8//DC6du3qs3pa3dSfNWrUCM8//zzcbjdKSkp4DNntdmzfvr3KcVtSUgIhBBdykHexTZs2UBQFFoulWsECb9u4caMEwseMGcPjtTpTF6EJcSenmwpUWrVqBYvFwhvQkSNH8gYtMTGRi87ITp48CSHuUN6Q0b01atQIX3zxBRYtWoQ2bdroFhhWFb41mUyIjo7mOUfNqiFEzZZXAvCLFy+GoigwGAw8jq5duwaLxQKbzaZb4BIWFobJkydjFlNgGgAAIABJREFU//79XEjjPW7q16+PSZMm4b333tMAJupvtdqTr3HXtm1bzjdW9+PatWtrVJB3Nxtdo96GS4/T1mQywc/PTyOpW2d31+oAZQ1s43sXfx6QXHgAiTlvI6jD/XedSqFevXrIyMiAxWLBP//5T6xfvx7du3fX1Rxu1aoVNmzYAJvNplv53b17dwjhIUcmjyPlKhJgmDBhAkuh6VFU0MuuDqNnZWVh+/bt2LNnj2ZSVC/AFMYlabzz589rJirvxVzP8vLyIIQHUHovEE2aNJGS49VGYT6iHaLfjBw50ufO9eDBg6yrTN9PT0/H9u3b4efnx9KLRMY8bdo0zTFu3ryJGTNmSMcICwuTwC3lF7rdbpZuo8/0ijcuXrwojYETJ05g8eLFaNOmjea5RUREoGPHjpIXedasWRg3bhwGDRqEbt268bEiIyMRExOD0NBQOJ3On61HbzabNcofQUFBaNOmDeelUsg9NjZW8zz1+P7oWN58iYBnATSbzfxc9Iw89t6mlpSMiYlBQUEBXn75ZT6fXmoFAcopU6bg97//PWbOnMmgUa//SAnFVw4gfUdRFOzatQuZmZkMZr2PVRMWAPKknzlzhvsyODiYxzs969oYbQ6933XiENWznTt3Ss+2R48e/N3o6GiYzWauYKbNLnn1FEXB5MmT+f5Hjx4tbSL8/f0lMFtYWMhARN3PJpMJKSkpGDJkiMZLbzQaMX36dN5YxcXFoV+/fhxG9/UeREdHIyMjg3M2P/zwQ80GR1EUREdHw2AwsDeSNiB6m1Q617Fjx6TjEPtDXl4eioqK+J1Vb9yMRiMSExMxZswY/PGPf+ScV+9xRhvuGzduaEBbeHg4pk2bJj1L4rb9JZvasUHOCbp+yluOiopiBwtRcQnhAcM/RZGqzmpndYCyhvZ6wRU0WnKo1jmVyYveRvyjf0BKr3G/yEtGqife4VlFUSCEB0DpeTCtVivnwX399ddM/k3eCKokTk9PZ44zIQTWrVsnnUMdUjUajXA6ndWG0e12u+QBbdq0KedC2mw2BAcHc5W6wWDgqmQhaia3R5rJ6kk9OztbqmC/9957NZW7pHsshMDbb7/Nk6cQdzjrAE+F/IABAzQ7YafTKXm91FregGdxpoVRbepinDlz5mD8+PEaD7E3QCgqKmLvpsFgkCTldu/e7TMPk8LI48ePx6FDhySgTJWnQghJueXmzZswGo1ISkriv+Xm5vI5evTowSHeiooKKd9r/fr1WL9+PXJzc/n4tCgHBAQgNTUVDRo0QFxcHAICAn42QFWPxeDgYERHRyMpKQnNmjVDRkYGV1Onp6djxowZWLRoEVavXo28vDzs27cPH3zwAavc6BU8qftIfS4hPPmiW7dulUCj3qaLwtP169dHjx49MHv2bE0ahMViQbdu3Zg/8sCBAxLVVXp6Oo+1I0eO+OQf1CPdV1t4eDiCgoIwe/ZsnheEuKNw1KlTJyl1oSZG1b379u1jzx09V+JXpHdv8+bN0qYxOjpaI6tKJOv3338/37933iHg2UTR83U6nVw0SJvi5ORkTY5pw4YNMW3aNA2vrcvlYiUiIe4U2QQEBGhUja5cuQKDwYDGjRvjyJEjyM3N5fNYLBafmwM12MzJyZEo2LKysjSb6fbt2yM/P59lHL294d78tLQB2rp1K0pKSpCbm4vMzMwqnRrh4eGazTOlZTzzzDMYO3aslNYQFxcn8ZT+0k1NjSWEgF9gCCyRyVi4+gXYoutjw/MvISAgAO3ateP5edGiRTUqXqyzn291gLIW9lVpBcblnUZiztvVAkv6fFzeaTTL7CJNqner0aJE/2+329GzZ0+cPHkSH330EYTwcJEpisIAhV4y2hF7L4ozZsxg9QminKAFkI4xbNgwnnRosjabzWjWrJlGT1udB2az2dC+fXsGm3r3pAZCISEhWLNmDUpKSri4JyoqymeosqSkhHOX6BjeHJCnT5+WFoo2bdrg7NmzTONit9tZPYLALBFJkx63ejKdO3cuq1YQqTmZN6CkCkwiFwc8CxcBw5ycHOn3QUFBsFqtkochNjYWa9as4dC52oPhKwczODgYU6ZMkUjE9YwWDvIukZQmkaDn5+ejoKCA9arDwsKkwiy1Eem71WqVeO5oo2C3230WDBw8eJBDcPQsk5KS8Omnn+Ldd9/Fpk2bJOofWoT13i+qyFUzANSm0e8pLzUwMLDG77HNZuMNSdOmTfHCCy9IMoIHDhxA586dJcDh7++PHTt2QFEUZGVlQQi5OM5kMjHQCAoK4jxHs9mM3NxclJeXY8mSJdIxAwICMGrUKI12dHFxMYQQXESXkpKCyspK/v/Zs2fzNdTUu3Pjxg0YjUYueCorK+M5JygoSHr3vPPffCltAR6vsbrfvSujyRRFwaxZs3Rz64xGI1JTUzF79mwYjUa0aNHC5/muXLmiAen33XefLjChDYiaf1Pt1Rs8eDDKy8vxzjvvIDc3F0OHDq2yQMi7hYSE4L333pPOTeTjxcXFAMBypO3bt+fv+KIXu3nzpkYVSt0iIyPRt29f5OXloaKigucFdbj41KlTktjEL90mTpwIo9GIp556CkEJTXDf4jzETtuChP+J/t1pBxA77WWMWLEblrB4XX7ROvvlrA5Q/gS7+PW/kLu/CPc8855GUScp523c88x7yN1fhC9ueCrG1Hled7vRYue9oBIwmzlzJn73u9+x8oMQHs8F4Jl89+/f7zMPRa2u8fHHH6OyspKTvVNSUjhETKCGvJXkgbt58yZ/lpmZqQEQQnioKebMmVMrmgmbzYbp06dj27ZtKCkpwWeffSZVKjdr1ozvX49fDgAuXLggySpSQvqK/8Peu4dVVW3v43OvfWWzud/lLgIi4h0VLyCKd1LxknfNkySpmZqZeiw1yfKWhtnRRNM0szITNSrTzFIzyUwlMzJ/kREZh8iIQ5zd8v39sb9juuZea6OZeezzMJ5nPuVm7bXnWmuuOccc4x3v++STPHVEhUfOkmYdOnTgRQ5UMEJkvkpzdigBoEmTJpAkCeXl5bDb7TyiopXK1+v1fIFQplbpWfv6+mo6kFSE0qFDBzCmxsq6MuKfIyWOpk2b4ptvvoFOp0OzZs0waNAgfv5p06bV65ymp6cLEZe5c+fy1B5jDufienbkyBHOj8qYg/NSyfWXkJDA6ZTo3gwZMoQvln5+fqqNE43thQsXori4GF988QUOHz6MnTt3Yv369XjyySf5uPb19YWvry/MZvNNgf9vtFFknxze+Ph4JCYmgjEHBveee+7BjBkzOMdlWlqaELVv3Lgxd/7J8vLywJgDsqKs0g8ICMD999+P8vJyIfMQERGB3377DYADVkEbVWKMWLt27Q2NIZpLnHXr6TqnT5+uiQUkFRhXRlhIxhy4OTK73Y7XX38dw4YNU/GhKovEjEYj/Pz8AADPPfccGBNlYJX2/fffqwp0CHv8xBNPCMcWFxeDMUdKVes+0Ds4fPhwzd86evQoMjIyblgcgiKb9F6Ehobio48+wmOPPQbG1EU4SUlJnF5Ma8OdnJzM55CIiAj06NFDBZeiiObYsWNRVVWF6upqLnNJzAnXk9m82WY0GhEcHIzQ0FCMuHcKQkc/ybmc64eZ7UHknH0Ynf8Rvq10TfnXYLfWGhzKP2m//mZHcdnP+LT0JxSX/Yxff1PvYGnS+V83JT+iUpowPj4eOp0OpaWlOHjwICZMmICYmBhh4jGZTEhISMDkyZM5iJwxh9Mhy7LAC7l792588MEHPDLxwAMPaN47xhx4p1mzZmlGfe69915s3boVDzzwAPR6PY80ubo+k8mEdu3a8cpOJRWRK7t06ZIgwRceHo7hw4cLi567uzsGDx6M3bt38+hQVlYW1qxZA8YYunbtqnluLYfyyJEjYMyRJiangQoOnPtFf7Pb7di1axePFF5vAqaFxmQyISIiot7rdzYqwiClH6qipvvRvHlzIcrmytLT0yFJEsrKynhEk6J1FNlYtWrVdc/z5ptvCtfFmCO6uX79en6MkqD+xx9/BHBtQe/Tpw93Oig65rzxstls8PLygtVqdSkjGBMTwzk4dTodl/NkzOG0EaZLp9Nh7NixOHLkCAoKCjhfpp+fn3AN5Bg0bdoU0dHRCAkJ4Wnvm81kSJIk8KUy5tgUxcTEIDY2Fr6+vpoLv81mQ35+PgoLC1FUVITS0lJcuXKFF+gwpl1o52xff/01GHMUZSmturpalXmgjabFYuHXGxERgVdffVXz3EqN79zcXAwYMEC1WfDw8EBKSgoWL17McdKHDx8WHOpt27bVy+H6xRdf8L7q9Xouw7pixQp+nj59+vDNFI0pZ2Ujog2SZZkfQ5Ki58+fx8iRI4XNYHh4OObNmyeMkTFjxuDXX3/FO++8g4ULF/LIpr+/v8sNOKXRR40aheXLl3NSeGUmgxzE3r17AwB3npUQICXZuivmibCwMJw5c4YXdt3qRpCpu+++G4EpgxA1e/f1HUmNTGHc/EK8fKJBAed2WINDeRusrq7ujiR6HT9+PK++HTBggNBnZYU1Y46oiatddE5ODmpqang6uHXr1pwMvD7aCuX5g4ODcezYMZw7d05I47/88su4evWqUPl41113Cb/v7e2NiIgIlxg8d3d3REdHIz09HVOnTuWRTTJSu3BFG6KUClRGaWnSc5W61XIoAQeUQPkMtMYLcRp6e3urJAIJnL59+3aVGoXVahUWj7i4uOsqySgtODgYvr6+Knysm5sbNm7ceMPnIYcScETCaTOj1+tx8eJFzk5QX5SzsLBQwJJ27NgRXbp0EdLg9CwoBaiM9BK2KyoqCt26dRMq1V29E6QcJEkSZxyQZZlXw3p6enL9bBrvtGEqKiriUX0fHx8MHDhQoGLx8/NDdna2y6IwQHSOqUK7trYWFy9eFDIG7du3x/z583HffffxBd/d3R3t2rVDUlISYmJi+Jzj4eHBSf3/TKTVZrNx9Zjo6GiOS+3WrRsyMzP5tWZnZ2PFihVYvXo1OnTooLrf1F8i16+srMTw4cN5fwMDAzk9U3V1NZ5++mnNfnt7eyMtLQ0rV65URWiVJsuySrRBSdNDRvKTNN9duXIF5eXlYMyBKa2rq+NZjdDQUOzZsweMMWRkZKjOpeShlGWZb0aUc0xAQABycnJQVlYGWZYF7k/6e33vR0lJCR9r9PzrczaNRiMfs9HR0Th27BgOHz7M/66k0lEapbzpud1q6FZ97+K4cePgmXI3p937M8Wxa967MbWrBrt5a3Aob5NpKYzcCY1UdpRUPJcuXeK8jFQxTWTYRA+kRWNBNDY02bvSI66pqRGibcpoKZkyAkTpnb59+/JoFzWKkJLJssypPGiC9vLy0nQ2dTq1VnBERARSUlIE59lsNgvRDFmWOb7KbDa7LHzQcihlWeZpW5K2rI9E3NPTE6mpqVi+fDmPvhUVFQmKP9TXNm3a8Iiist0IfQxZp06deEqbvi9JUr0LtpYpHcoffvgBJpOJL3RGo5Hzfc6bN0/13W3btgnOE2OiJGRFRQWGDh3Kr1+v1yMtLQ2SJEGv19dbfW42m5GRkYHp06fjpZde4s7dkSNHMGnSJMTHxwtRIiX2MiYmhuN3KXJKFerHjx9HTU0NFi1aJDjBNL4oOnU9o4iS1Wrln73++utC1bEzVleWZZ6+Vjq89O46wzFID50xR5FDQkKCUDQTFBSEbt26YfDgwZz5gTFHhDk8PBwBAQHw8vL6U6T+BIdwd3eHt7c3goKCEB4efsM8rGvWrMG5c+dQWVl5w9yBhIum50pR7hMnTgiwFueMgcFgQHJyMv83OZ50rh9++EH1WxQhX7BgAccTU4uNjRWeYUVFhXCMu7s7FixYAMYc+Mv6jGAojDkKtwAHNlfJEEER1+ul1Rs3bswjm8eOHYPdbldln8aMGcM/37t3r2YV+q1oer0effr0ga1Fr1tK27ejIVL5l1qDQ3mbbMSIEX8pDuvPtsDAQLzyyiuQZZmnug4dOsT52mJjY/liFxMTwx2sc+fOaToxjDkKSLKysvDyyy/zKNnatWsFR9RZ/URpzs4jLQTjx4/HlStXuFPSpk0bvqhs3boVjF0jwbZYLAJF0htvvIGkpKTrYn4Id6X8rE+fPrhw4QLnwBs4cCB37JYtW6bqv5ZDSXyG5JC6IhEPCwtTyb6R1dTUCLxxhw8f5phXALh48aKms+zv76/i6XM25QJFz5oxJiyoN2JKh5L6WlhYiAMHDvDnT5uSuro6yLKMvLw8HuUyGAwYO3YsGjVqBA8PD2zatAn3338/0tLSEBUVVW/EPzIykjuN27Zt4wTWjDFs3br1hvpPhRbOjilVyROR88cff6y61yaTCampqULhkJZ8obOdPHlSwJ2++OKLHB5AzpcWNRHZunXruELKxo0bNSmSNm7cyPsUEBDAP7fb7XjuueeQmJgobFQyMjKE++cKS0nHKDGv4eHheOihh7BkyRL+vOjcVqsVbdq0QePGjeHl5XVLMjjEl+rm5gYvLy8EBAQgPDwccXFxaNWqlRBxV4okKM8xZcoUjm8mCwwMFO4VcI3MnzGRIN9ut2PNmjVCJbXZbEavXr1w4MAB7oBRAd7hw4d51JLGEI1Rir7Xtxmsqqriv7NlyxY+Z0qShEGDBuHy5cvYsmULP6Z169b45ZdfsH//fh4coKjl9SKPLVu2xLJly3D06FEOw2GM3XIOSp1O51BF8wrCiHUf4pWiUly4XI2aOjvKf67F/s/L0T/vA8FRXLCnGJ+W/oTKX+vwm/13fFf1H+z5rAwZT78vHBc3v7ABU/kXWoNDeZssNzf3jkx7a73MjImVyMrilYiICFUK9dChQ5oOmjOtDh1jNpt5Sn3kyJGa90uWZY5fUjbi/yOjlG9KSgpkWUa7du2g0+l4GpoiBVlZWSrM0rRp0yBJEsdZlpaWYuvWrZg2bRp69OghpN617lN0dDQ6dOjAHaTu3bsL0RJyKMvKyrB48WIVNQzdk8zMTGzevFlInVNq0dmKi4v5eSgqZzabeRThu+++40Vgubm5OHnyJPr37y88Hy8vLyxZskT4vStXrgjpVnKYKioqeGHG4sWLb3i8k0NJFfKkVgQ4JOeIJokWOVqA9Xo9GjVqhMjISE16EyXJus1mw7Rp07BlyxZMmjSJPweDwYDZs2dzp0CWZe6kafGAahnhcCVJwosvvsjJ1l2RXzPmiAS/9NJLwhigAhDGHBEg5+giWV1dHby9vSFJEk6cOCEs7hkZGbhy5Qr0ej06dOhQb79PnjzJHYTx48cLJO40Lui91OLpBBwbloULF6qiTzR/EU8smTOXYceOHXmUtK6ujjvFkiTho48+4lXkyvlQkiSEh4fj7rvvxq5du2C32zk9jrKFh4dz53XkyJG4//77MWrUKGRmZqJbt25o164dmjVrxnGpvr6+sNlsgjjCH2nEcsGYI/rr7++P0NBQfi4lrMDf31/llM2bNw+ffPIJvv32W/z2228CRVhGRgaHBtE9YYzx+bW6uhpWqxUGg8ElTIJS8tSUG24ygvSQnCKZksZMkiR06tQJNTU1eO211wQOx+tFNl3xEd9so/EZMX4Z9p0uw9ELFfjnG2dw9/pjyNn2CU6W/oT//i5jxPMfcUdx9YEv8fS7XyL7xSLcvf4YZr32GS78WI1ff7MjfcUhAVM5Jv+41q1ssFtgDQ7lbbLdu3ff0pfudjRPT08MHz6cp45tNpuKsic3N5dPig8//DCfUA0GA4xGIz7//HOhAtu5BQUFIS8vj6fca2trMXnyZL5rV6aoyAFkzCGNRw7RwIEDwZjDwdLr9UhMTMTly5cxefJkIf3oTMhLFdr1cfUFBATA399fRb5N16i1q6cIidb1klbwzp070b9/fzDGsH//ftXvSpKEzp07C59t2bKFV5tShWphYSEkSeKTfk5ODtq3b6+pBOMsI6jT6dCyZUsMHz6cO2mERWTMUTAFOKIuAQEB0Ol0OHXq1A2Nd6ryZoxxCpkLFy4gPz8f999/P7p06eJygZckCZ6enjxtFxcXh+3bt+PSpUucxsYZ6gA4HEflczKZTMjOzuaLLo2pGTNmuOy3LMuc2ogxB40W2ZEjR4QCLnrWztAPglts3ryZF+RR5I9wYc4FIeTMz5gxQ4jME8E1FWndiEN85coVHh0l52X48OHQ6XRwd3fnVfxKGIEru3z5sgrbx5iDCSA/P19QekpLSxOwySUlJddNYffr1w/vvPOO6lnW1tbC09MTer0eJSUlgoIOjZuwsLDr9l9pixYtEuYUk8kk0IBZLBaMGjUKDzzwAMaNG4dBgwahR48eHIYSGRmJRo0a8Y2Okmj7jzTn7yjnOp1Oh+TkZKSnp2PAgAF8XHh6emL58uV44YUXsGfPHhw7dgxTpkwRnHKlEhfZ9OnThd8gBg6KVN93330AwBkRFi1axM+Znp6On3/+mWMo8/Pz8e6772LRokX8vv1ZqVhXzT8mCZFz9qHN4v2qtHXCY2/hx19q8eFXFfWmt7uvfB8AsPqAWpiEGFga7NZag0N5m4wUM/4uLT4+nlflUnN3d+eLkCzLHAcZEBDAeepo0nZuJItG1YMUAVI2ZfrJ19cXa9aswYkTJ/hkCTi4Jimt5ubmxsm+ldRHStoLDw8P6PV6+Pv7C8/jq6++AmPa4HylJScnw2AwcCJdxhjmz5/Pozc6nQ6tWrVCamqqJh2Kc6MCoW7duuHee++FTqdDo0aNhN8kiqepU6fyz0jRxN3dXYjQAo7NCi1SVMnbrFkzl9c0d+5czYUwISGBYwMZY/j111/5d86dO8f5Oesr8iGnUQmD0Kqe1mrTp0/Hd999x89FKbW8vDwA0IRcOBvBERYtWsRTnPTbL7zwAn9uWrjdyspK7sRSZW7Xrl0xYsQI1cLZsWNHgaC+rKyML9pai2xkZCQeffRR7oApCbKJLYDS/ZIkYcqUKTCbzRxnS0ok27dvd3nvnY10r6m5ubnh4sWLcHNz+0POWE1NDRhzYJidIRHUqKiPsKhaMBi9Xs9JxC9cuAC9Xg9PT0/NojbSfqeNEz3X7du3C05sUlLSDbEOyLIsPJdOnTpxoYNp06Zh8eLF3JFKS0sTMOWkXpOfn4+zZ8+q0uSRkZE8i2M0GrFmzRqerl6zZg0WLVqEGTNmYMKECejfv7/mPKHEsN4sLpXusbu7O3x8fLjjazQa+T2LjY3FiBEjYDKZIEkScnNzsWHDBmET4+3tLfB8OvNQEr6aCgpvdebNy8sLUUMerrei++iFClz4sbpeh7LV4+8AAFbuP6+q/F5QIEpINtitsQaH8jYZRU9u5Yv3Vzea1EgDmj4PCwvj2L8uXboIDgZRSCgnXVdOG2MOHKIyKqZsVLVK/1amCzdt2sRTIyEhISot2l69euH99x07VIpgEnckAJ6Gc9amdTZy5AivyZgjOjpp0iQhLURNmfYyGo38PgUEBKB79+6IiYm5bjU6LXRTpkzBmTNneIV0XFycSh2EbMeOHcK56qPksdvtKs1k52IgnU6nclxJjrNz58480piWlsbT066itU2aNEFqaiqio6P5MaGhoRwrplzMlFXatHCVlJRg/vz5YEwbcqG0M2fOgDEHZx4AvPbaa3zsSpKEnj178gIMJfbt6NGjfDyNHz+e6yIr78+kSZNgtVrh7u6uWQhCGMiAgABUVVVh3bp1HIupbEqqHCU+kTGHg0TjlOQ/ly5dysefs4rM9WzGjBn83HPmzOGsDrNmzfpD5zGbzQgKCvpDeDmdTodhw4bhs88+Q1BQkErLm+AAzrRbq1atAmMOCAmZs2gCXQc1ZZrd2Q4ePMg3mUq4BGMiFKOyshKdO3fmxy1duhTAtTGlnL+tViumTp0qcLwWFhbyDACNded+0KbjoYcewuXLl/k4IExmnz59hO/IsoyKigo+19CcbLVaORdpo0aN0Lt3b46fjYuLEyiorFbrDfNcaq0B9P5YrVae8TEYDGjVqhXn2bxVTa/XIy4uDhFTNrl0FJsveBtX/vNfvHW2XFOZLvafhei+8hDeKS7Hj7/8ho5PHlAdl7r8vRsZ9g32B63BobyNRryDf6cmSRJ+/PFHHDhwAIwxAdjOmCOqlZeXxyNGS5Ys4X9TVurS5ExGlBfUYmNjuRTgnj17MHLkSERGRqo0mlu2bImZM2di5cqVmpJfNHEqiYQpyklyckVFRZoLmZYR1pMmO+Vvmc1mNG/eHCNHjhSebXx8vJDyTkhI0HRASktLsWnTJh6VIGdT6zkYDAZOfzN58mRs2rRJpV7y+OOP8+NdYa52797NIzWNGzfGypUrBSoR5+iLyWRCYGAgQkNDXWIaPT090aRJE/Ts2RPTp08XolgXLlxAt27d+MLZpEkTQTkHuEZaTYtt+/btUVdXxzXSc3NzwZhj4XSlkqQ0X19fHtmrqKgAY46IoxKnRte5dOlSrFy5kqcblTQ/pJJDG5k5c+aAMaZZgEVGEXqK2FFmYsaMGdi6dSsGDhyoSbbOmGNz9e233/JzkXqTu7s7WrVq5bJIy5V98MEH0Ov1wjtETAw36pja7XYhom00GhEXFycwOtA4cB43//rXv/i413IoAbUwwPnz57lspnLj4OnpKRTXAdc2HMoK6aSkJC6jqMQFU//37t3Lnz1tOpxtz549/D1UvvPkXFmtVpeV5ZcuXRKiszQvLl68mL/nJJNKUAKlo/roo48K5ysvL0dmZqZwf6k6nTa7pNCzdOlSMMZ44V9wcLDwvlDFvtlshtVqxdKlS/lv03yVmZmJnJwcjBw5Ev3790daWhqPbirfjT/jpNbXrFYrouMS6qUI2vXpd/jv77KqMCdyzj789t/f+fVe+LEa3Ve+r3mOqDn7NDmjG+zPWYNDeZvsyJEjqiKVv0vLzMzE999/L+jTzpkzBx07dhSiP8oJhhb0F154gX82f/58FBUVCTyO3t5AzQFEAAAgAElEQVTeOHbsmMv79sQTT/DzafXNZDKhVatWHBju7u7Oo5VKqhYC1APgNCnKiCUZVS/efffdqgikxWJB8+bNIUkSLBaLKlp48eJFdO/eXeUshIaG1otXoygSpXaJeJnO07RpU5eRTcLFRUdHC/Qenp6egtNQUVHBsaxGoxErV65ESUkJ8vPzkZ2drdooaDW9Xs+rz3U6HY4ePaq6FioocU6DtWjRot7nTNyc5AD4+voiMDCQvzOBgYEqDXRXRtG806dP83tLONWTJ08K48+5mc1m9O7dGx9++CGPbNfV1XGdeRrX9RlF1Tdv3swdSsJCAtfkAV31wc3NDa1bt8acOXO4E2uxWBAcHHxD1w84JEYNBgMMBgOKiopgNpuF99dVpJustrYWEydOdIlzVY5FnU6HrVu3cqfEy8tLwCmmp6dzaiBnq6urg4+PDyRJQnFxMQIDA6HT6XDy5Enhful0OiFiCTjeVTc3N3h6euLChQvCu6eUNezQoQMaNWoEi8Ui6Mw7b2zsdjtWrVqFpk2bqt4zk8nEna/rEfLb7XYeEQ0KCuLvZUBAAE/P00Y1OTkZZWVlfO5csGABAMeGOy0tjfcjNjaWRzFJMpJ02JVG74ufn5/qGSujuuT0WiwWbNiwoV6MLqW8ybHcvHkzSkpKVIo6t6KZzWYExrVx6Uw+c9DBJflowVnNv/fL+wCD1h7BtB2f4vSlKvz4S62q0ptacZk272aD3bw1OJS3wZ588knBQfg7NuXCcvz4tSq5mpoaVcqaoj2HDh0CcE0GTtkoteSqypuMCgiUlYRBQUFo165dvWTrNPkTpxyleImbLzMzE4Bj4XQVOfLw8OC/q4yOEKaqdevWmn1+4IEHNO+fK91ru90Oq9UKDw8PoSLZZrMJCyvZpUuXsG3bNkybNg0ZGRn1ptHd3NyEjQwpqTgfq4XZ6tatG8rKynDmzBkMGTJEFaG02WyCk1dXV6c6plOnTteFFQCihN3y5cuF/vn5+QmYtusZOXFDhw5FaGiowOkoyzJeeeUVgdKH7ss///lP4TwUbT9w4AAmTpzIF9PrWXV1Ndzd3WEwGHj0lRzKAwcOCJGe2NhYyLIsjBmr1arpyAUFBeHTTz+97u+fOnUKRqMRer2eO/HOxUTu7u6C9jQA/PLLL1ixYoUq+qh8n2bNmoV///vfnCfx/vvvF/pKzlZtbS2eeOIJFVPCoEGDVIVdn376qUCXRE4V2enTp8EYw+zZs1XXSlF5+s6HH34ozBU+Pj5YvXo1GLuGraZ70a1bN8iyjJdeegnt2rXj74DBYECnTp2we/dulJSUcAgKjfkbMWc528TERB6tLC0t5Ty/9P7QPMcYEzgkW7ZsKWzEiOqHopNUOAc4aKPoe+PGjVP1ibCw1O666y4Bv6rFIlBTU4NnnnlG6M/YsWMF+qdbuc4wxmAKidN0AJ9+90sAwNK3v7ghzslmj72FH3/5Dfs/V6fGI+fsw6elP93Qs2ywG7cGh/Ivtl9++eVvh5101Qh7RrvY7du3cweiadOmOHPmDBYuXCg4FRaLRRWZDQoKQllZGRjTdijLysowadIkoSgoMDCQT7RE4EtGKWyr1aqpdhMfH88LH0hpJj09XVV0RMobK1asQEVFBcftmc1mVVEPSe3Nnz9f+HzhwoVgzIEzpeiJcsFVyrYpjZwX6pObmxt++eXGKhEp0qisaL+RZjAYEBAQgI4dO3Kc5sKFC3mKmTEHHZOS1PzgwYPo0aOHcE1JSUm47777BOfe19eX81DeqBHesKioCA8++CA/1z/+8Y8/dB7AwR1Iqfz+/fvj0KFDyMjIUL2L7dq1U+GDX3rpJQCOaCZjDvJvojO6UTt06BAYYxwfSlRUjDGOdXNzcxOiSM4FZ3PnzkVOTo4K30pp5+zsbHz44Ye4evUqP0dxcTHHPNOGDgDef/99/v1169ZxtoCsrCykpaWpCokkSULLli2xbt06VFdX86K05cuXw263w2KxwMvLi1PS0HjSYgGorKyE1WoVNi2+vr6YMGECzxIMHjwYjGlrvC9btgyMMaFQhEyWZXh5ecFisXBHR6fTYcSIERg7dqwKwtGjRw8A4JtHGrM6nQ5JSUlYv3695vupjOC3bdv2uhXyyig4ja85c+ZAlmWe+VA+H+cipmbNmmlSTMmyLECJaLO2adMmMHZNzUiSJKxZswZLly7FnDlzMGDAAOH+N2nSBAkJCYiKikJwcLCQAaKx8b9aZ4yB0S6dyaff/fIPEZkf//rf+OqydvFOQ4Ty1luDQ3kb7Pz585qcin+3RtEtPz8/tG7dGow5HMZ169YJ10tRQOfJXDlJ0cJODmV1dTXmzZsnpJk9PT1hMBh4RSpx8RGBNxnh1kjm8eLFixg6dOh1KyV9fX3Rq1cvPPfcc6r0EKVug4KC0KFDB+j1euHvJE2oLF4h3WbCLhEPZV1dHe655x5hwp43b56wcJHzQs2Z2oacxpycHKSmptZbCOPczGYzLly4wCOb06dPrzeyqUxl0n8HDRqEr7/+Wrh+raIkg8GAF198USA2v1ErLS3lVe90Plro2rZt61LiUssmTZrEz6Hc0CiLCkg3uqysjEdaaMz4+/vzyAw5E84bmeuZs9oQY470K1WaazlIgFhwlpSUhMWLF/Pz5OTkICkpSdg46fV6REVFYeDAgRyO4HxuWZb5s+zYsaMmHpbGrtZ11tbWgjGGIUOG8HQ9URLFxMRg37590Ov1MJlMmhFpwlBevHgR48aNEzY/QUFBwrvqHAWmzZurYiziOmXMEd1T/n5dXZ1wbr1eL8xLgYGByM3NrXdsVVVV8XeBItt6vV6TKQAAj94yxrBv3z6UlZVxJ5DGUnZ2NoqLi7FgwQJhYxsaGsp/Kzk5GV26dEHr1q0RHx+PiIgIBAYGCs7/zXBr0ni0Wq3w8vJCYGAgIiIi+JzcuXNn9OnTB8OGDcOECRM4dIAgDSEhIfjggw9w+fJl6PX6W6oCp9PpoDNaBAzliv3nAQDPHFTT/1yvyruqpg7vnvuhAUN5m6zBobyNdubMmZueAO7E1q9fPwH0LcsycnNzOaBdkiRMmjQJp0+fxqhRowTON+WErsQsWSwW9O3bF0ePHuWLoLLykVI9ykWncePGnLT30qVLWLx4MVJSUjR/T+v3+/btiw0bNvBrqaurg5eXFyRJQklJCV+wnAtdqIDAy8sLK1asAGMOnBQ5p85KOXV1dUIBgdlsxuTJk5GXl6dyfhMTE106jVQIExsbi169emHGjBmc4D0nJ4ePsejoaF6tHBUV5XJBHj16NBhzVJWTs0nncIXZJNybc7/oePobFUjcqFFkh75/8eJFHr3y8fFxSQxOdunSJWRnZwsRl6CgIEyZMoUXgPj5+alkQb/55hvuVPbr108VySTy+z9i586d44uxXq/H66+/zh3d6/FJ1tbWalL0DBo0iB/z1VdfYd68eWjbtq3gNOt0OoSFhaFPnz7IyspC69atheixJEkIDAwUCsfMZjPefffdevtksVgQFxcnRLDuvvtuvjHav38/xxeXlIi6yVpFOUVFRcjMzBTGGKkOKTcvTZs2hcViUfVHiQum61JSXQGiNrrzWGWMXZco3m63C+nrTp064cEHH+T322KxoFu3bujVq5fmnOPp6cklKm9mjiXhAnrngoODhWgm9UOv12P06NF45JFH8NRTT/GoNo0/ckILCwths9k0FZdoblVGX+mdoTZkyBDIsgxZlnkU3lla8la0RpOeR+ScfVi873MAwKHzlzFo7RFVo6rvU99WYdHeYtzzwgmMeP4jzNt1Bl/9P3WdzDUfNlR53yZrcChvs91qmoX/VaPUEeCYdGfNmsUnN3KC2rdvr7r+hx56SPN8kZGRPMJIRkoZyspHKo7w9fUFAHzyySdgzJHqUeJ5JElCWFgYhg0bhqVLlwqLVrt27ZCXl4cePXqogOW+vr48ekLyjQRKf/7551XXQ/gs+u5PP13D5Tg7lFevXkVJSQn69et3QwuJs9O4Y8cOTsrubM6OKmPXKo2J3Dg2NlbF31hZWQlJkhAZGSl8TsTkV69eRWlpqWph0WpEUaIsyqBnM3LkSJw/f16z72R79+7l3yEuPrJVq1bxqmviwyO7cuUK5s6dK6jv0MIuSRIuX77Mo6kpKSkuHesLFy7AYrFAkiTs27cPjz76KD+fyWTCtGnT6qUsIrPb7Rg3bpxwD/R6PV599VUwdo3o/UbsxIkT3CkgJ8h5DHz33Xc84hgXF3fd4j+l1F5qairHF1utVgEf7WzOrAvEEam0goIC6HQ6uLm5CfyQrqq8yYnJzMxEamqqsOFu2bIlNm3aBJvNhqioKOF7Cxcu5Pele/fuXHL1rrvuwrvvvoshQ4YITrTRaETjxo2RkZGBuLg4oWjMzc0Nvr6+8PDwgMVicSlYcKNNr9fz8zdu3BiJiYma1GiSJKFDhw68cCw7Oxtff/01qqur+XOnoiqlUcSW4BEGg0HYIJ0/f56/C3q9HuvWrYNOp0N8fDyAa/AC500VFQrRZv3ZZ58V+hsQEMChPH/l2mI0GtF46COImF2Aj77+t8vxCACRcxw0Qds/LkXJD7+g+jc7/vu7jLKq/+D1Ty+hh0ZBTgMP5V9nDQ7lbbZJkybxySolJYXvsP+OkcvMzEyMHDmST9w+Pj5YunQpZFlGQECAsAs+cOAAunfvriqiUS5QkiShbdu22LZtG2RZ5oD7w4cP8/OcPn2aV9Eq7xlJIY4dOxZvvfWWkE6WZVmV4uvYsSPHBhLZer9+/TQjDMRZOWzYMNXzVNIKLV68GLIso6SkBBs2bIBer4ebm9sfSk/TQqSkParPZFkWOBMHDhyI2tpahISEwN3dnR9HUdbExETh3pBz61wwRCTiZ8+eRU1NDbKzs4Uoi9FoxObNm4Vij7CwMDRp0sQl9RE940aNGmH8+PHYuHEjX9SU0S2KzDkXQHz00Ud80zBx4kSsXLkS8fHx/L66ubmhX79+OH78uMAbSv2eOXPmde/nuXPnYDabIUmSoIGs5DEcN26cyyrpXbt28WhQTEyMUFlLtDE3olCjNB8fH9hsNv6ueHt748qVKzhy5AjGjBmjGldGoxHx8fEYP348pk6dyknCnY9JTU3F2rVrceXKFWzbto1HHlevXq3ZD8JQM8ZUHKVKe+2113gkm6L6Sofy6tWr+OWXX/D888+DMUcKNT8/H8uWLcOcOXOEjYFy3AQFBcHPz0+43pspdiT5TucIu9VqRdOmTdGxY0dkZGQgKyuLFyhNnDgRnp6ecHd3x1tvvcXlFC9cuCAQrffr1w+AoyiHeCiVVd+MOaKaNHc99NBDfOPi7MwfOXKEp+hPnz7NP7fZbPDx8REgKWfPnoUsy1wsQafT8Sg90avRMzt16hQYc/CtyrKMs2fPYu3atbzgx93dXROLTnROTZs2Rb9+/Tju+osvvrjlxTnx7dP+UHr7j7YGpZy/xhocyttsmzdvhsFgwKpVqziY/oMPPuBVz3/UsVTupildeLudU5PJxKN5ZMnJydDr9Rg8eLDgzEVHR2PBggU83davXz/885//FBZdWvBoEp44cSLi4+M1MZnEh1af0YQ9b9484RwGg0GoKKUUtqenJ7Zu3YrBgwejUaNGwoLl7u6Otm3bYvLkyTyyc71FTRlpnDlzJp544gk+ASuxcspqUsZYvTQ7APDee+8J+CslPyLh995771pqZ/z48WDMwckoyzLHLGqp6lARRosWLfh4CgoKwvr167FhwwZhwWnevDkvmCLHlCKc27dvx/Tp05GSkuISt6ds7dq144UezhhMWZaxfv16IR2t1+vRuXNnFBQUCMf6+vry43Q6HVeluRH77LPPVGOtsLAQW7Zs4fhOSZIwcOBA/PDDDwCAH3/8kWcfTCYTnn76aQDXKs6pL/3797/hfpBJkoQuXbpgx44dLt/t0NBQTJ8+XXA8AGDt2rWCVCA5Gc40XN7e3mjbti1/roMHD+apzdLSUmFsDhs2DEuWLMHDDz+M7OxsDB8+HH379kXXrl3Rpk0bNG3aVMVZ6Px+/9lms9nQokULzQ0M3SPqQ58+fVBeXq6KzhO+MiYmBnFxcbx/qampKCkpwblz5/iYBIAuXbqoxiRR+RgMBv6MExISuHLOvffeKwhE0IZbGTWnjIhWMdDBgwd52vvcuXOcNYA2J+S8e3h48I1MVFQUzp49i88//5zfk2bNmmHt2rX4xz/+gU6dOtX7HJSOtoeHB9+wOmcGqKBtz549f4jw/nqNfj/6HysRWY9azs20Bi3vv9YaHMrbbFevXtWMbly9ehXvvvsu3026WjgIP0MvsNFoRFJSEgwGAyZPngzGmKCO8Vc2vV6PiIgI/u/k5GS89dZbuPfee4VIZHBwMB588EGhWpiKUMxmM2RZxttvv82/ExgYqOIxpIl/2rRp+PTTTzlmkTEHDYgrU1akyrLMKUgYY3yhbdSoET7++GNeZFNUVARZlvHll19iw4YNyM7OdokppKbk+KP0tJubm5DyBhwye0SQvHnzZtjtdk44TNEQZUqpbdu2qpRXdXU1T0GTfJ0zxuzy5ctgjKFXr17C5+QEd+jQgSttOFMTlZaWCtizyMhI7Ny5Uzjm66+/FvCS2dnZMBgMvHK5vqKcw4cPIzU1VfWMSQ7O+d5aLBZVxIScCC8vL1URiPIZEz/qHzUlfypjIo/k3r17OR2OTqdDVFQU73ePHj2E91spuUrXUJ92PJndbsfOnTu5vGl9jeiO7HY7ysvLcerUKYwfP151z8aMGYOePXuCMUfRUVJSEoKCgnia/8/MBQRHMJlMcHd3h7e3N3dwaLwbjUb069cPI0aM4PPXqFGjsH79euzcuROHDx/GuXPnUFlZicuXL8NsNvMxQu+XlsyfTueQP920aRN3IkNDQ/lY//zzz13e56SkJEiSBLvdjuPHj3PJTeV7SHhQpXKT3W7nkd+QkBCUlZWhrq4OQ4cO1bw/Pj4+mtrzSviLcwqarLCwkEfvqRhSr9ejqKgIlZWVfA6m4jlyGrUivfRdup9du3bFI488gl27duHf//63EElt2rQpZFkWpBfr6urw8ssvIysr6y+tBPf09IQtOBKRD+9CZD0k53+0xc0vxLeV1xdHaLCbswaH8g6zq1ev4s0330SLFi1ULxhjjuiSh4cH0tLSEBISAp3RgsiWndGkQwZmLFoJb/8gbNy4EYwx7mD+la2qqgpHjhxR0V6Qc+iskKM0OrZRo0YIDw9XpbIYczicStoUJd0IRQTqKyag3bUS/6jk2aPIsPI+16c9HRsbyyd1nU6H0NBQ1SJns9kwefJkWCwW7lDKssz1iLWcoMcee4x/f/DgwTxiopzcDxw4gNWrV/N72759e87f2LNnT9W1R0REaBYzEGE3nYOsuLiYO5l0fREREarvy7LMK5WfeeYZ/uzJyWvTps0NVXmfPHlSIManxe5mQP7x8fHIycnBypUr+bho06YNJwZ/44036u2Ls5GqDvUvOTlZdcyGDRuEZx8fH6+izdm5cycYc0TpLl68CL1eD5vNhsrKSpSWlqKoqAiFhYXYuHEjRo0ahdjYWM30oclkgq+vL4KCgm6ZdrLZbOY0MyEhIYiKikJ4eDh8fHzqzXIkJSXh2LFjuHDhwnXJ5omuiyQpAWD27NlgTORQ1LL169cL19+yZUsVTpr+Pzg4WCjQ6dChA7y9veHn51fvb5D8I4kKAA7Yg3L+pXePtOUXLlzIq7V79uyJ3393qLOUlpbyVLfyfkmSVK/eOD1Pg8GA1157TfOYN954Qzhn//79NVkWqNE4U86b5DQCjmwMYyK0Rqly5unpCR8fH5jNZr550hp3NpsNM2bMwBdffHFLxqSyeXp6Iq7vPbc0QrnjhFrMosFunTU4lHeoXb16FW+88QbH55jNZiQmJsLX1xfTFyxFQJ/JaD5np1qi6pG9iJ3xEhLHLkTm6GxYrVYVx9ytbMpJnfgalROqsnintrYWL774IgYMGCDgsei7HTt2xGOPPSboH6enpwOAJt0I/c6YMWM072F1dTX0ej38/PywYcMGTJo0CV27dq0X48eYI1JI6ekdO3agvLwcU6dOBWMML730kpCCIjtx4gQmT56syTkaHR3Nf7Nly5Yu5QOVnH7/+Mc/wJiDPL1v377CPbVYLDxiSFGTgwcPqs5HzpRzOhgAX2y6dOmCY8eOCQtou3btcPLkSURGRsLT01P1XSL5njx5Mv9s3rx5ghMSHh5er0Op5Es8fPgw7HY7Fi9erMml2bRpU676U1ZWxtPoPXv2rHdRdXd3538PDg5Gfn4+vvrqK5d9IiPc44ABA7jkKGMM27dvR0FBAdatWydIbUZGRgr9NpvNCAkJEca4JEl/yhG0WCzw8PCAn58ff+ckSUKLFi1UkUg3NzcMHDgQmzdv5uPo6aef5tQ4RGGlxRlJRvAIV43mowceeECTfF9plE3Q6XTYv38/p4ZyJV8oyzKmT5+uualr1KgRZs2axcfDqVOnkJWVJWRElO/ghAkT6u2b3W6HXq/n6jNklOLv3r07v98U8aN+kRZ8cXGxoMDTrFkzjvOm1q1bN/z8s5r3sK6ujr+HFBEdNWqUkJ4OCwtzyWVMFf29e/fmuFAiv4+NjYVOp+NV6u+8847w2/7+/vD09OTSozczLv9qvkqdTod5L6klFm+mPfve9d/9Bvtz1uBQ3uEmyzJfAGY8mougEbmInLMPEdfBlkT9P0ez49yX4OYf9pfIZFEzGo1CSrSiogJDhgzhf6c0mPI7tAAnJSXBzc0NBoNBoOWZMGECXzSdHaKioiJV1XFYWBgGDx6MiRMnomvXroiMjNSMskiSJKRLabEwGo149tln+eKclJQkSDNSpImwS85YNbIrV65wpRNnzjv6/cjISIwcORIFBQXCokrVl4TTo43AXXfdpZrAAwMDsX79elXxjdKqqqrAGENqaqrw+eHDh8EYE56JTqdDt27dBIcrIyMDOp1O6CNhK2NjY1W/V15erpI11LKSkhKeZt21axdmzZolcE/SM1ESONtsNgwdOlST4/DKlSsCZo8xR0o3ODjY5UJMqXA3NzfYbDZ4enryooubXSzrw9L6+flxx9P5GHd3d7Ro0QIPPvggjh49iu+//57j/Zo3bw6z2QxApJ0i7r+UlBTVOFcWnMXHx8NgMAjP8OLFi2DMEQl3turqajRr1gyMORyjTz/9lD+PjIwMBAcHw2AwoGnTpqoirdjYWGRnZ+ODDz5QOYtKHKckSSoderKCggLNghDGGOcNdTZS4vL09ETXrl2FfsXHx7skKydr164ddDodd7iJbYDuT2VlJYYPHy48t+nTp+PIkSO8MIUxRxSbnHSSf+3RoweP+huNRixfvhyyLOPMmTN49tlneVEbkbM7XzNBWrTG1YQJE4Trovc6LCwMe/bsAWMMWVlZqKqqgl6v52pf586dQ1ZWlsv7fCe1jIwMAMDLJ0oRN78Qjee9+Ycxk3HzCxsik7fJGhzKv4kNemg5Ih56HZGP7PljO7PZBYh8+A20GvLXpr/DwsJw6dIlrFixAmlpaZqRJoPBgEGDBnEZPcYcxOYHDx4EY45ID02QlAKmxeGhhx7C+fPn8fzzz2PSpEk8be0q6kOTpZubG2bOnIlXXnlFqK6NioqC2WwWiiwOHjyI2tpanhKWJAkPPvggZFnmfSSMZX327rvvqhaF1atX49FHH0VycrLKaWnUqBGysrIQEhLCMaXO0m3R0dEoLi5GTU0NJk2aJERkCOukZTExMTAajcLftXS777rrLtV3KcJJEaiqqipYLBaYTCZcvnzZ5fUrpdpiYmIEuqBvvvlG0Oem40wmE5KSkpCTkwM3NzeYzWYMHTqUO07OXIXkDN4sv9/1miRJ8PHxQUxMjEpRyWAw4OGHH0ZxcTEqKipU976iokIl7ajse3BwMO93fdXSAODl5YXw8HDY7XbupNx7771C5Xbjxo1RUFCAK1eucDyuwWDAnDlzoNPp0KlTJ9V5g4KCVFX0p06d4pstku4jrkEqoqP3iq6Z9NJdka2PGTMGhYWFCAwM5I6pr6+vQL9UW1uLBQsWCNhho9HI38O0tDQYDAbYbDZVdJ/S4j4+PjxqSdrfynFDcopa0XqiHHrqqacAAKGhodDr9RwLW1dXp4LGKFu3bt0E/KMSw/vMM89gwoQJmvrgyubh4cGrpyk66u3tjffff18FgaDIt6+vr0qSlPDzbm5uwjVQxJn4av8uTVlU+G1lDcbkH+eO4vUcycg5+zAm/3gDZvI2WoND+TewNe+V8HT2TYX7/9/3UnOe+EteeufoEC2a3t7ekCQJV65cwcyZMwWeSnJWSCmHtIwHDx6M559/nqeXlMoRWk2JORs3bhwSExOFNHyLFi1QWFiouqdKjsHhw4dz7WMi4j5+/DjHBnp7e/MoUJMmTa77vGRZFqhEvvjiC9Ux5eXlePLJJ9GlSxeBYJoxR3TN2SF//PHHhe/b7Xa0bNmS/91qtWLWrFmqSlZSWdm+fTvy8vK4w6DT6TB27FhUVVVxTKiz/i85xosXL8alS5c4lmrq1Kl45plnsGDBAkybNg3jx49HVlYWMjIyuIyjs6Ov1+tvqvBD+ezd3NxgMpk0x4OPjw9GjBgh/G38+PHYvXs33wy0bt1a0/EuKyvDyy+/jBkzZnBHz8PDw2V/dTodOnTogJycHOTn56OkpARffvkl5syZgzZt2riM/FitVjzxxBOcqkWSJPj5+ameGdnVq1d55JgcVKUTTmNky5YtwvcOHDggZCTIUVIa4atpvK9bt45LQubn5/PjqOCooqKC85kyxrB27VrNPl+4cIGTrWthQWkOiI6Oxrp169CiRQvhmXl4ePBI5NGjR8GYQ6d7w4YNYMwRfSUjWidPT09hg6OshI6MjMTTTz8t0EuReAKxKMiyDIPBgLi4OKNHgPcAACAASURBVE4DNnHiRACOaC5huFu0aCFINSqzG82bN0fHjh2FqLrz+Pf29hbe9dTUVHTp0kWVBQAcMAGtcU4sAcR/qxRSIKN5KyMjA8XFxZg5c+YflmW9E5qXl5fmu1Hywy9YUFCM1OXvIco5MzfHQVq+oKC4gRrof2ANDuUdbi+fKL2loOSu42f/JS8/Rd1CQkJ46shZYUaWZSxevFil9R0eHu6Sx4wodyhK5OHhgVdeeQWMXQP1f/TRR2DsGt6SAOfKKJ6bmxsyMzN5dJFS2FS04opIWCnhZzQaNbWGlVZZWckpdKhpObRa36P+uLrH6enpQkQiICAAHh4eWLp0qVD1P2zYMBw6dAh79+7FunXrNM/VpUsXJCcnIzExEdHR0UJhwM2SO+t0Ov79+oo63Nzc0KlTJ0ydOhWPPvooVq1ahS1btuDNN9/kKfXx48fz66RiCGUBgTPuS6fTcbzk8OHDOUaUnORmzZpBr9fzAgoto0Wa+CoPHjwo0KEEBwcLBV3Xa6NGjcI777wDxhy4VBrjVqsVjzzyCNdM79u3r2Z/zp49yxdW5Xk7dOiA06dPo66ujhfrOJssywJWOCsrS5AXLCsr4789atQo/q4poRz0jtCmDwDnhmWMqajCtOzSpUuCBKWrZjabVQUpCxcuBGPXquL79u0LxhiWLFmCV155BTqdDjabTUX0TscRATjBcYgA31neddSoUWjdujV0Oh28vb1hNptRV1eHXbt2CU6jsr/OfLrKcUjPmDFHMRhFTsnOnz/Po5BEAu9s5eXlwqaMfk9ZBLV06VI+Lilye+LECZd9+zs1g8GAe+6557rj69ff7Cgu+xmflv6E4rKfG+QU/8fW4FDewfZtZQ3i5hei2WNv4V/vX8Dhkh/x7+rfAACr3v1S5Sy+9sm3mue5cLmaRyrDH3od0UntbunLT8UX9913HxhzYK8+//xzroLRpEkTRERE1Et+a7PZ0LlzZ168YDKZEBcXJ1zHkiVLOGkvY0zA05ESxfnz53m159mzZ1FVVYWHH35YiBx4eXlxh0eJL3MmEiblFJ1OJ1RduyJ+PnLkCI/ATJkyRZBnc05NybKMqqoqnD9/Hh9++KGw6FosFvTu3RvJyckICAjQlD9UVkcrpfD+yDMzGo1wc3ODp6cn/P39+QLm7++PlJQU9OzZE5Ik8Q2AzWbDM888g+3bt2P//v04deoUp0tRWlFRkSpqrWydOnXi1abORhEi56hb48aNueoNcf+ZTCYUFhZi9+7dAreeJElo3bo1hzMkJCTgqaeeAmMM69ev1/xdWZa52tLPP//MaZP0ej2PZgcHB3PpQboWvV4PHx8fhIWFISwszCUEw2g0IjIyElFRUQLFFEW/tFSYlPrvjDkiTs7VwlQxvWLFCuFz2qCkpKRwRRU3NzdBslTJsZqUlKSq2KaKcmWa2W63874z5uCRrQ+faLfbVQ4xjWHnz/z8/JCRkcHJ1olShzYBdrtdIDa3Wq2a1dNubm4ICwtDTU0NDAaDpkLPd999h/vuu08FZ2DMUZTnaq5SYpj79++POXPm4I033sDq1auF4keKJNdnhP1kzLHhoCjr3r17+e94eHjwiKPZbBY2BbIs81S2Up3H1f39u7U9e/bUe/8a7M6zBofyDrYx+cfReN6b6PzUQVz5z39x/Ot/Y/vHDnCxK4fyP3W/q/RO+6w+zI+JmF2AwOGP3zLqEWoJCQmIiIhwGZny8vJCXFwcevfujYceeohHGTt16sR51MgRoO8MHDhQdU8I08WYg2+TjGgrKDXYuXNn1XdLS0sFomFqvXr14g4OEQmbTCbuTO7atQuXL18Wqs/9/f3x4IMPYtasWZg4caJQJR0VFYW4uDghLUa4v5tJ+17vO0TGnpCQgMGDB6v452hBN5vNMJlMLuUD6+rqeKp+9uzZAMDpgfR6vctCCkC7Cp8xEbO1dOlSdOvWDYw5HPnFixerzkNVyc4YzQ8++ACMXeNfDQkJUWmrm0wm+Pj4ICkpSXAuGWP8WbZs2VKz/+SkZmZmcmfJz89PNaYtFguSkpL4dShTji+++CIYc3CHfv/999ixYwcvLiNexvqeZZs2bZCTk4Px48cLVFnBwcECh6vSSAXK3d1dcOwefvhhMMbw1ltvAQDy8/MFEv29e/fy63TmKgWu0elMnTpV9Td3d3c0btyYF5uEh4ernteFCxcwevRoYZ6RJAmDBw/mkVPaqERGRqJXr17CNdPxkiRh2bJl/Pz/+te/+N+1dN0pwk28ocTOsHbtWnz22WdYs2YNJkyYgJSUlBuSEdTr9ejSpQt27dqFyspK1NTUgDGGoUOHCr/7zTffQK/Xw2KxCLRXPXv2dEkZVFtbC8auOZ+SJPH3jbFrBSlKTlSr1Yp+/fqpZDAZczj5xAV7I/Kud3KzWCyC89xgfw9rcCjvUCv54RfNlHWrxx3UD64cyl9/s99Q6tvgp016+2ea1WpFXFwcTws2adKEO4laxti1dNq7777LCzCotW3bVvWdTz/9VFiMOnTowB0kWuQZY9i3bx/eeecdbNu2DXl5eVi4cCGmT5/OozW+vr4qdQeiA/ozhR56vR5ms5n3T6/X82hHcHAw0tLS0L9/f4wcORLp6el8waVq5Pfeew9ffvklfv75Z8FBoAjmgAEDuLNkNpsxatQozcXFYDCgffv2qvT7fffdV++4q62t5Q7pggULuIP47LPPqo6trKzE9OnTBXocX19f3HvvvUhJSYEkSQLmLysrC4CDlofufXh4uEA707ZtWxgMBtVvlZaWcseuU6dOKmxVQUEBGGOYO3cuv47c3FzV9TPGVEVVFMlyNabbtm3LyfaVRlHP4OBglJSUwGAwwGq1CpE+IjZXEqOTszlz5ky0bNnyuspWkZGRSE1NxaRJk7BhwwaUlJRwlS0AWL58ORhjmDNnDv+MnCXnZ6vkIKXWvXt34ThZljlZvhaGrUmTJrBarQCuSXRaLBbs2rULDzzwgAoWEBAQAF9fXyEySxFVYjbo0qUL7+O2bds0+0nOH43/Pn36qPpNdD0jR45ESkrKdTGNCQkJ6N+/v4qdgJpOp0NiYiLWrl3L74XFYhHUpWRZ5lhvSs+TQAW1jh074uzZs0J/yfldsWIFHnzwQeH4e+65h5OIa+EfzWYz2rdvj8ceewzffPON8P1bHSy43U2v12PIkCGqcddgd741OJR3qC0oKNasZLslDuXsAgT2nfKXTAbt27fH5cuXMWDAADDGXGK8AIdDmZmZiY8//hj79u3D5s2bMWPGDCHdRFKH7du3R/PmzbmjpiyUUS4yN9oI76esAtU6jqIqU6dO5enF9u3bY+3atcLCGRsbi99++024Pnd3d16BHRISAp1Oh2PHjqG0tJRHNC0WC/Lz8xEXF6eJpSKz2+08PU0ayIw5MIJKR5pSZMrrcb62pKQkXoyhZTU1NSqeUNIZ1nLU3N3dkZWVJfAaKquQc3NzOSRh69atAK5pkNP9Hzp0KOrq6uDv769KURYUFAhOvrIwgyw1NRWMMU0VqoqKCowePVq4HuKo1KrgTklJQW5uLr777jt+DsIZOp9/wYIFfBFkTK2JruVQOj/XuXPnunQqDQaDZmSTtLLJ2SROz7Nnz+LSpUtgTI3NVJLrKyO4RqNRcFAJJ7lw4ULNPvfv3x+MMdjtdtTU1HANaGo2mw19+/blcIn58+fzv6Wnp6vuIUXTlJy1lFrv168fdu/eLSg3KZvJZILNZtOkhyI4Aj3jrl27oqCgQMA0lpeXq6J58fHxkGUZr776Ktq3b8+fjV6vR8eOHeHn5yfws9LYmDVrFv+MCM5PnTqF9u3ba7575IzfCJE/yW9OnjyZO9bKzWFdXd3/iTQ3tZdeeklz7DXYnW0NDuUdaqnL3rupCOXv8lX8+Estfpev4vuf/4PNx/4/tFj0jvpcU1+45ZOAUpnB399fKDBxd3eH2Wy+KbyfcvGgxTAsLAxNmjTh+CJKKdOxo0ePRl5eHrZt24a3334bx44dg7u7u4oDj5Q8nnvuOVRUVAh8ecrJ/IUXXgAAmM1mNG/eHIcPH+bXR4t9SkqKkJokhxJwSBUSPpPOfdddd/G0js1mQ+PGjesdE1SxTWl9paPYvHlzHD16VDj+xIkTmDp1qksOUpvNhtzcXE0M3PHjx4VjBwwYIKSSTSYT0tPTVQ4U4FjcaIGfP38+gGv8nEajUSiiuHjxIr8eUihSOozkxJvNZuzfv5/TtyidV1mWYTQaXVbgX7lyBWvXrkV6enq94+vtt992ee/Xrl0LxphKghIA5yL09PRUwQlcOZS1tbXIycnh98nLy0uTzslms3Fnvry8nEc2e/XqhdjY2HrT6EFBQTyyuXr1ag4tadWqFWpqajB//nz+PFu0aIHq6mph4+IKG0mUXtHR0fz7RqORO/09e/bkkUFy5khH3JUR3VH//v0hyzLy8/PBmKMyX8n1WF+jvjRp0kSgm6GIq5ubG48ylpSUIC0tTXjPKbsQGhoq9M1utyMvLw/NmjUTju/Zsyd/JxMTE4XvkENJdvHiRXTv3p1/Pzo6WhNbquyLcm5Zs2YNP1dVVRUv6iGhhLFjx97y+fx/1QwGgyYJfIPd+dbgUN6BVv2bXUWHcCMO5eN7P8fjez/H6PzjGJ1/HHkHS1BTZ8dXl6uR8NhbKiohg8X9lk8GysVNWUBjtVrRqlUrdO7cGX369OGRkvj4eOTm5mLt2rV45ZVXcPDgQYSEhMBms3EcF9EPKSdypX344Yd8MYuJiYFer0dYWJhwDDki69atEz632+2QJAmJiYkcw7V69WrU1dVh1apVQqSONKWJusZgMGDnzp24cuWKgA0kBQ2lQ3no0CHurBqNRnz00Ue8D7IsgzF1Cs/ZCC+nvN+UOvb19eWaw0qrra2F0WjkCit+fn4qaiXGHHjBESNGoKCgAHV1dfxeKI+TJAlt27bFtm3bXDobdrtd0LlWGqnOREVFqb6/fv167lz5+fnh4sWL6NKlCxhzUEd9//33ABxYNUpDkpHWMGEyKyoqsHz5cqSmpqrShddLB8bGxmLZsmUqx5DIwJ0xhfv27QNj13CqcXFxQprY2aGsqqrCiBEjeD8CAwPx3HPPAQDXgdbpdNi0aZOqX4SH1LLy8nL4+Phw4n2dTufS2bRarTyyqYwuGo1GjhPWogXatWsXhzJQP5OTk7Fjxw7Isgy73S7gjGnMTJ06FUFBQULkWZZlfPbZZ8jLy8M999yDlJSU61YnR0ZGIjMzE3PnzkVBQQEKCwuh0+ng7++P++67T4WHJLL1iRMncsqjESNGCOlt2hTq9XpUVFTwaKVz5ThZdXW1IE9KbeDAgQKm09mhpGf0z3/+U9h4K1tUVBQ2btzIi6C2bNnC589mzZoJWExZljFixAgwxlye7+/YJEni2NEG+/tZg0N5B1px2c8u09X1OZRabdLWTwAAj+/9XPU3U5AaX3azrUmTJtDr9ZBlGbIsY9q0aarFTEn7AogYSqUpNbBJSWLBggWCXri/v7+wa1emLqnCmNKry5YtA2PaxQcABD5HLe3xp59+mi+gyusZMGCA4MTt37+fRwNDQ0NhsVgQFxeHnj178kWLQPfKqtxjx46BMYbHHnvM5ZjYuXOnkBpzd3fnSj7EWWcwGLBjxw7he+PGjQNjDh7K5ORk6HQ6vmCdOXNGpRlfX9OqRFaaLMtcAzs0NFRTepH4D4nnT2nPPvus6jd79eqlcj5p0Se5yVatWoExh1KJcnHV6XQICQnBwIEDsW3bNtTW1goKTsrx8uabb6Jr167c0SPs7+bNm/nvS5IkFHv99NNPAtE7UUwlJiby75BDmZOTg379+vF3IiIiQnhWJGdJz5gc+pdffhmZmZmC/J+rdCApvDB2Da+6atUqfi/69u17Q5FNxhxVx5MmTcLs2bPRpUsX7uzrdDr+jLXeJ2csYG5uLvLy8jgVFb0Xzr9H6Wn6G22cDAYDJEnSjIQD19LGI0eOhMFgQHx8vEuydWWLiYkRxsq+ffsAOJgaGGO4//77NX8PAKeConddGWkMCAhATk4Oh2BoiRloNbPZjFWrVgljnYp26PySJGHKlCnCMRQ5/7/SdDqdatPfYH8fa3Ao70D7tPSnW+ZQRs3dh19/s2Pv6TK1QxkSd8smAgLDDxkyBPn5+XjjjTfw2muvcXUPakp+QVoIlEaTKIGy7XY7fH19ecFMo0aNBM1sT09P7mBMmTKFc8/RRFxcXAxJkuDr66tZYFBbW8ujfM6RT6VRaouaMvIVGBiIqVOn4vLly5BlGVOmTFEt1snJySgvL0ddXR18fHwgSRKnPVq0aBEYY/jggw9Uv7thwwYeJdXr9dypdqZzUVIWkcZ2ZWWlILm2bds2vsgrrbi4WKBFqq9lZ2drapHLssyd04kTJyI9Pd2lljel65z5Ocn5Vd67gIAAHD58WDiO0vFEe0THSpKE8PBwDB8+HLt37xaed1FRkVCgERISIugvDxs2jG+GNm3ahFatWgkchGlpabDZbAgJCeHnpAIvZRqcroFI1Mn5oBYfH4/9+/cL10OVyE2bNoXdbhd0tClSWlVVJVRN+/v7Iy8vT8A+AuDUNW+99RZ/F3x8fDTJ9QFH1IyilEraG61mMBgQHh7OHW9/f3+cO3cOJ0+exOOPPy68E64woT4+PkhISBAijT/99JMwjpQpbp1OhzfffFOz72RKXfVly5YJf3vttddcFuZQs9lsePXVV/l48fDwQGBgoMvfI/1txq5phX/xxRfo27evZpRVkiR4eXnxDWlqaipKS0v53xMSErjja7PZMH/+fPz+++98I7x582YUFRXxYjlfX18+hpwd+P8LTalo1mB/L2twKO9Au5URyqi5+1BTZ0fBZ9+p/mYMjP6fTBiSJPHCG7PZjIiICMTHx6N169Z8cWjRogWys7Mxa9YsrqLDGON6zuXl5Zg7d66w8586dSpPVdNnlJ7W0t6uq6vjEUOKvGjZgQMHVKD/JUuW4OzZsxg6dKgQ6YiKisKUKVME8mSTySTwKp46dQo6nQ4BAQGw2+1CkQPgWFSffPJJvkCbTCZMnDgRNTU1sFqtPDLi7IwrSdXbtm3LCZ5p8VFiDS9fvoypU6cKuD1nTJfJZEJqaqomBtPHxwfdu3fH6tWrUVFRwTcUo0ePBoB6HcrLly9zWiYlPyf1xWKx4ODBg0KxSkREBBISElTPgShocnJyNNPwdXV13LGi9CtFjxhzFElQhLNJkyZCf2pra7F06VLuAFMbMGAAxowZA8aukesrjaiSlMVlgYGBmjKLFGGLiYkRnj85jocOHRKOr62txZQpU4QN1YIFC/i1k1NIDkrbtm2vS79Cmzi6R8pr1ev16NmzJzp27IiAgIAbYkAwGAzcYad7YDAY6nXSlEbwAsZck74rrbKykjtrRCW1fv16Pp70ej2GDRuGyspK/q4aDAZV1FCn0yEoKIhv4LR044Fr1GWSJCEnJwcJCQmCI+lKFcrNzQ179+6FLMt8TLVq1QqA45kvWrSIPz+z2cwLD5XjeuHChfzcf/dqbq1mtVqFDUaD/b2swaG8A+3Xm8RQarXJLzkoWRbuKRY+j3hkL3RG16osf7SVlZVxvdodO3bg+eefx1NPPYVHHnkEVquVLyh0PC2IFosFPj4+vGjnVlQqms1mIQXu7u6OXr16YciQIZgwYQJmzJiBBQsW8LRiVlYWj645E5AvWrSI49IKCgp4xaqbm5uwUB86dAgZGRmqhcTDw4Nfa4sWLXiamiKemZmZaNKkCdzd3WG32zF79mxBUeXhhx/mjsb+/fvBmIN/Mzo6mkviKU2WZU7FwpgD/E9WU1PDCzOo2Ww2DB06FKdPn+ZO8KFDh7BmzRp+D+mannvuOb6IaRUU+Pn5YcmSJfj+++/rdSgBcB7SpKQk1NXVcTJ6nU6HgoICZGdnIy4uTrVoBgUFIScnBwcPHuRymZIkaXJrbtmyhUcwExMTOQZNmRomp4HS1VarlRfBKK2yshLNmjUT+kLylcoir/379wvRXnJ4taq8iTA9IiJC1X8aA+7u7irCccARuZ8/fz53kCwWi6qSnZx7V1ZdXY1HH31UgFIYjUZERUWhRYsWLotGlCTaN8Krqjxm9OjReP7553H+/HmXMph0TfTeKKuntcxut/N5w9/fn/fbZDLxiHpNTY3AcUvR6TZt2qCyshKrVq1Cenq6ikqMyNbz8vKwZ88ejBkzRjVHmUwmNGvWDFOnTuWbhoyMDNVYoXun3IB++eWXqutZs2aNIAwwevRofPfdd6pn9X+x6XQ6JCUlNXBQ/k2twaG8Q825ynv8po+Rs+0TzHrtMwDA3tNlyNn2CXK2fYL4RwvR6amDKPr/KvFYQTHGb/oY4zZ9jLWHvkLtf3/H+fJf0PRRsSgn/P6Nt3QSePLJJzmZ8qpVq8RrSU3lzgWp0dB3SS6RLD09nWvbVldX4+uvv8bRo0dhMBj49/r164fJkydj5MiRXCmmXbt2aNSo0XU5/f7INdEiQBWqoaGhvOCEMcciPmDAAIwbNw6ZmZl8AfTw8BAIiiVJ4tFGSZIwffp0yLLMuepMJhM8PDx4lMPb2xtLlixRLbhEnVJRUcGjJK4KeShSKUkSxo8fj8TERGEhjI6OFqJflGadNm2acJ5t27bxjQDpShuNRkiShMLCQh5Rdt4MkBMxf/58l4Tow4cPB2NqWTvl/U1KSsKMGTOwbNkyHlGKi4tDSUkJpkxxUF85V+WWlpbytCnRMimtqKiI99n5WomFwHkMA46oFz0vnU4nOFze3t7cUZAkCf369ROok5wdyieeeAKMMTRq1EgFIaAiLUqpJycna94/OnbVqlWaUWRnHldZlnHixAkMGTKk3gpjxq5hGuPj47lzI0kS5syZg+rqakE6kKK14eHhkGUZ5eXleOWVVzBz5kz07t1bFeFVNqvVioiICHTt2hXjxo0TMI+5ubl8A0RsAVr2zDPPCGPOYDBg9uzZfCNWXFzM379hw4YJGwMtKEB1dTWXD9WiI6L7wxhTcUvSOKK+JCQk4Ouvv4Ysy1i3bp2qgKZHjx4cC6w0oqNyVuwxmUzo3bs3VyX7v9jCwsLw448/unzeDXbnWoNDeYeaMw/lpZ/UuDWyzk8dRNLCt/HW2XJ8W1mD/9T9jt/sv+Primr86/0LaL7gbRUPpW/PnL90UggMDESbNm0wePBgHn16/fXX0bRpU/j6+gqRJ7PZjODgYCxatAhhYWHw8vJCeXk5x4eRpjCluA0GA7755huOPaMqWbKNG7WdZS+v/5+96w6L6ljf39m+LOzSq1IFERUFjAUr9ha7othQY6Im4RpjJRJMNBpjLNFgLsbkaiwR9XqtxO71YsVuiGIJsYQgEkRERFiX9/fH/mbcs7ugSTD3JtnveeYRd0+ZMzN75p1vvu99dTh9+jQHQR06dMCaNWuwZMkSJCUlQSKRwN7eHl27duXgTqPRICgoCD4+PnB1dX1mnNkvKeZbbjKZDCEhIejZsyfi4uIwfvx4zJgxAx999BFWrlwJmUwGT09PXL9+HSUlJWjQoAEEQbAAbFlZWSAS64ILgoCmTZti48aNUCqV8PPz48czUvCqtvwZwGGTm7mHhvEHGgwG7NixA3FxcRYTsUqlQnh4OCZOnIiPP/4YAwYMsAqC3NzckJiYiOvXr1vUQ6/X83g/lmHMrs3iHydOnMgn8969e1v1dDCaIiJLRZ7s7Gzuperbt68I1N+6dYufxyQcp02bZhE35+/vjw8++ABlZWW8jqaURgsXLuS/EWveRxYjmpSUhJdffhlEhPfff99q37B2Z7yv5iU0NBTe3t5Vbo9qNBpRHKqfn5+Flx4QJ5yZlnHjxvHfJPO+WzMPDw84OjryxUPTpk052KwqQUilUqF27dr8nN69e4s8m6WlpRgzZgwfjzqdjgNHtlhavXo1XySwJD4m72nKJVleXo7169ejb9++XLLTtI0CAwOtyomq1Wo0bdoUycnJOHnyJA+fYM9jaoysvVWrVnBwcBA9s0ajQb9+/XD+/HmkpaWJxpREIuG/ZUEQ0Lp161+luPVrC/stm3PT1nRxdHTEv//972qlPG32v202QPk/alUp5dRUqUmlnICAABw4cABz5szhk7E1dYfnLWyCUKvVeOutt7hOc0lJCQ4fPgwio1dKKpVaxGUZDAa+dbt06dIqA/LNM86Bp0o7bAIzVR4xtY4dO0IQBBH9SPPmzZGRkYH9+/djw4YNSElJgVwu58oxffr0QWBgYJUeD3bfXztRsJhEc+CgVCpF29Tx8fF82+zjjz/GP/7xD84hePXq1Spf5own89ixY6KseCJL3W3gqad5z549aN26dbU67qz+RNZ5Hs3t22+/tdj6GzlyJN+i9/LysrptDTwNG2BbnuYeWcAYU8j6NiAggIcVzJ8/n7fj7NmzRfFu48ePx44dOxATE8PHjyAIIvWn2NhYnpXr4uJiFbgBT4nFDx8+DL1ez/Xcz549C8A4xs+ePYulS5di8ODBz6TbMS2urq4YN24cf6aLFy/y8RsVFQVBEKyC8OzsbJF3nhW2pW/uBTY3RhuUm5vLE8vatm0LvV6PkpISHn4yYsQI7pUMDg6GTqez+psw/8zZ2RmXL1/GzZs3eXwk42bUaDSi+FXTPmnZsqWF5KNOp+P936tXLwDAmTNneNzz48ePeciKabINK1qtlj8DM0aT1rx5cxgMBigUCoSHh+Pu3btISEiw2Gpn7z9ThZ7jx4+LEpBeRDHd4WFtzHhH2b+Mnuq33kOlUqFt27b8/ZScnFztGLLZ/77ZAOX/sDEt75oEkkYt79k1rqrQt29fLFmyxEJ2raaKUqlE79698f3333NOOSLCpk2bRG3GsmxNdb7N1VCIrAf7M++XRCKpNrOU6TMTPQVCLKvX1Ex5KAHgu+++s8phx0pISAjnvzMYDCgsLMSlT6p1kgAAIABJREFUS5dw+PBhTtWSnJyMqVOn4rXXXkNsbCyf0M37kyU+MQWVX9reTEFFrVbzSV0QBAQHB4u2700n0fj4eHz88ccYNWqUVW48JycnREREVEuhEhcXh/379z/TS8E0lU2LIAh45513qj3P19cXEokEhYWF0Gg0oqxtc2MecLVajVWrVlmAGI1Gg8TERAv2AIPBgDVr1iAqKsoqGHJ0dKxSmxsAevbsCSJCZmYmPvnkE+7ZEgShShocdp9mzZohNDTUqkZ1ZGSkiBAeACerz8nJ4Z4700xpg8GA0aNH8xCQoUOH4vr16yJgEx4eXm2bAxDxUOr1ek6l5ebmxgHd3LlzeR+Zeg8B4MqVKxaLkqreYaYAW6fTYfHixThx4gQWL15ssRgiMoLRDh06YNmyZSKQz3YkTJkZGNckU/KJjo7m9VepVBbeYKVSycMLmAJPcXExiIyhO+ZJfUx8gf3fx8cHU6dOxf3795GRkfFM7fGaKhKJhCty7fhmL+TuAfj7pt2QuwegVbsOvP1ZXZ/1jmHvD6lUih49emD9+vV4+PAhAODgwYOoX7++VR5dm/2xzAYo/4ftVmEpQmam1xyYnLYDvpO3QOni/cJeRL9HMZX9S0tL4+21detWEFlu3W7fvp0fb+oJkMvlWL9+PfR6vUhFpSqQUV5eLuIxbNasGQwGA8/qZd4HZgxQHj9+XDSRRUVFcf1qBhRNi6+vL9555x2+Hcqys4ODgwEYExfGjRsn8qxIpVJMmDAB/v7+EATBKvVGSkoKBwYymYx7SyMiIjBjxgyMHz8ecXFx6NmzJ9q1a4cmTZogLCwMAQEB/FjTyfLXyF2yv2UyGVxcXODu7l6lN9vBwQH169fHK6+8gtWrVyM9PR2nTp3CzZs3LSQP2fXNKZFMbcOGDSAiDB8+HMDTLcjqtmrT0tKsTpYLFy58rq25S5cugUgc3iCVStG9e3ccO3YMZ86cwSeffIKRI0eiefPmXBO6qrbTaDR4+eWX+XiVSqVYsWKFSEaUyJi8NHbsWEgkEnh4ePCwEyIjSfahQ4e4t79Lly58nDEuR8AYCsHAUEBAgChe8MKFC6L6mSacWTNzYnPgaVISEWHQoEH8c3Ot7KysLBHFE9HTmNSQkBBIpVJs2LABkydP5rsZzxqLjo6OfNx99dVXVvuScYOysIVFixbx70pLS0Vgavr06SIKJya3aB6rKpVKLUChh4cHpx0DjDrsSqUSPXr0sDj299jqXrFiBeQutTFgXhq8X1sBv+k7LOYR79dWoP/cDZC71BaNLfPCgGTr1q2RmpqKn3/++Zm/GZv9cc0GKP/H7evMmzXqobRv1PmFv5B+7yKXy+Hq6spXzDNnzsThw4d55iwDDkRGjrP8/HzO6WY6WcfExKBz5878OFNbs2YN95AwENi7d2/+PbtHu3bt+GdKpVK0/dmuXTuLVXhgYCA0Gg1XSTGdNBiVEcvejYmJEWVpa7VaDB48mCvKzJkzB0RPOTyt2alTp0TgxtPT87mA0dy5c/k5rq6uaNq0abUKHaxN33zzTYwYMUIUHuDp6cnjUl1cXLiX9dcW80lWIpHAx8cH9evXx0svvYSYmBj06tWLJw5NnToVH3/8MQc0vXr1wvfff889Jszy8/NFvKZET8mszWMvq7KrV6+K6lUdIJBKpXB2doYgCLCzs0NiYiK2b9/OZehYP7OkErVaLYprUygUiIuLE42x+Ph4EBHWrl2LGzduoFOnThb69abeUgbImjVrxn9b5tyOjBuW3ZfxwJomnJmbOaAsLy/nC0MG2KdMmcIpjAYMGIAjR46IOClfeukl7Nu3T7TNLggCoqOjkZOTwz275kWr1SI4OJiHwlQVWsIShFq1aoWxY8di3rx5/LvWrVvzuqekpPAFlkQisbp4Y+8RIiMlVFVee0EQ4O/vj6FDh2LXrl1ch50l2xkMBk7J9aJL27ZtUadRM4S9vtw4X0zbXv188v/fh/9tBWQ6D9E7lcgoC7lw4UL8+OOPz/Vbsdkf32yA8g9gyw5erREw+enBa0hMTPxdXk6/Z5FKpVVuubCJg00AgYGBHGyaZ0o6OTlx+hgmsXf79m3uXVSpVFwtRq1WIyQkRNRPTNWnYcOGotjNl19+mUsHmpvpdUz5M9nn5hOfTCZDly5dcOTIEX6NgoICnu0ulUpRXFxc7XjKy8sTJTJYSwxhlp2djWnTplnEeJmTiG/evBmCIECtVmPIkCGi6zNwYmdnZ6E3zowp07A4tdLSUuTm5mLfvn0YM2YM6tata3W718XFBUFBQRxom44Dpp3+S7061jxcUqlUtJVap04ddO/eHYMHD8bYsWMxcuRI9OzZE82bN0dwcDBcXV2txsuachQ6ODiIPFAeHh5cSahHjx4WbXTt2jWL66nVah7ScefOHYtzysrKoFAo4OLiIhovpl4lT09PHgPJMu+JjIsja3GebJwzIJmeno7jx4/z2EhXV1cL/kzzLW8Wx5iQkIC8vDwORljCFEuAEQQBMTExoiSt27dvi9rNnCXAy8sLQ4cOxfLlyzlDQ3l5OVxcXKBQKHiMaH5+Pvd8Nm7cGCEhIVXGbNrZ2cHLy4uPQaVSyZ/BGoBm49G0biqVCt27d+dhBomJiYiKirIaAtK2bVt8/vnnHAQ3b94cP/zwwwt7h06dOhX24Z0RMG0bfKds/WU7X1O2InDaNtg36gKpVIoZM2ZYpUOy2Z/fbIDyD2JfZ95EyMz0XxxTGZi4CyEz07Eh07gd9fDhwxrNVP5fKoMHD0ZZWRkOHTqEOXPm8MQNmUz2XITMpkDCzs4Of/vb3/jk0rNnTzx69Ij3R0BAAOzt7fn/DQYDli5dyr0+LF7IHHSaGlPcMPV0xsXFVVk3Vj+FQmFBN8JA2/Po4DIwYQpsGPH7mTNnkJCQgPr161sFRF5eXlXGOG7YsAGCIMDe3t7iHoIg4PXXX7eqVpSdnQ0iwsSJE0X8nKa2bds2C9Juc88mu9fbb7/NqWrs7OywZs0aODg4QKVSIS8vD1lZWTh06BA2bdrEPadjxoxBv379RJ43U7lBV1dX2Nvb/6bYY0EQoFAooFarRYDbz8/PAsgoFApER0dj5syZiI+Pt8iwlcvl2Lp1KwDjooSpIVmzt99+G0RiOi9PT09IpVKMGDGCA2XTZ/P09LR6LUadFB0djW+//RZEYp7IxMREDuo7derEFysMUBoMBk6HNHbsWH6eqdISq0vv3r259+/kyZOYMGECQkNDLZKQ2P2sZaizjHo2Hsw5LUtKSjh7gqnl5eWJQjGqSypj4gwtW7ZETEyM6P0qk8nQsmVLbNu2TdT2pgAfMIaxzJkzx+p7Sq1Wo0ePHiKvZ00VBwcHtGrVCq5th/Ht7F8bTuU3fScW7bkEm/11zQYo/0B2q7AUw1ae4EDxWUDSb/pODFt5ArcKxZRD77777u9KO/F7lcDAQL7NbU1X+cyZM3yyZi97FxeXasGmIAho27Yt5s6dK9pG79q1K4iM6jbJyckc3CgUCp6YJJVKq6TiAYwKPESEefPm4cCBA+jQoYOFR4P93b17d5SWlmL27NkICHiqcKTRaNC/f3/u5XiWGgnbuu7WrZuFrrWpd0+hUCA0NJTHj/n4+MDBwUFEN2TNWGKH6fhq0KCBVdUfZkuWLAER8UmX3XPVqlUoKCjgXiS5XI4FCxbA19cXKpUKgDGW7csvv0SPHj0svKgqlUoEkqZOnWpRX0axZBrr5uvri549e/JxUl0WtZubG7p164Zx48bho48+wrp167By5Uq89tprokVAYGAg2rZti6ioKNSrVw9+fn68jRQKBZRK5a9KnjLdvtZqtXB1dYWPjw/q1KmDhg0bokWLFujQoQMkEglkMhkSEhL41nCHDh14ZrrpNVm9zLkAc3JyIJVK4eDggLKyMhgMBu5BNLW8vDwRx+rSpUs5oIyMjATR0zhWxqNpTskjkUjQvn17BAUFWSS5hIWF8fhGVhh1lTVjoQIKhcLqQmj8+PEgEmvVs6xsRttEZASsFy5cQH5+PjZt2sST+Ozt7avsO7VaLdpGT01NhVQq5Qo55u1LZPTSsvCd+vXr/ybGjOqKi4sLvLy84Nmyf42GVTHnhc3+emYDlH9Au3rnAZK3ZaHNgoMWijr+03eizYKDSN6WhWv5D6yeX1BQUC19zR+5qNVq7h0LCQkRecRu3Lgh4sEznVzKysosJtaqikKhsOBkVKvVmDFjBudDZKoc5tmqpsYmRVPgGBAQgEmTJnFFDVN6nFq1avFknoKCAiQkJIiy6tmkxrJlze3cuXO8/qaAxrSEhYXh4sWLAICPP/4YRMat2JKSEoSGhnIgV52ZZsHPmzePf75y5UqRLvmAAQNQWFjIt1kZyCwpKeHZruyZYmJicP/+feTn54Ooat11Fl/YtWtXqwku7u7uGDVqFJKSkhATE/PM3wFLEOnVqxfeeecd7NixA66urnBycuJbzV27dhWNpRMnTkAmk0Emk/FEMWtKOcXFxTyx6pNPPsG5c+dEalKm44v97ePjg27dunGQwcZhvXr1EBgYCG9vbx6XymikfotXVSaTwcnJCV5eXrwv6tWrx+NS5XI5NBoNZs6ciYULF2LVqlXYsWMHTpw4gU8//ZQvdEzDUphuelJSEo8rlMvlVYZ4NG7cGFOmTOEZ1oBYiYZd21zznRkTXBAEoUp+U5VKBZ1OB4PBwJO3TL2SMplMdM758+fRp08fUV0ZKLa3t+db1c/aRjcFm6ZhCG5ubrh+/bposVqThS1iPALD4DflX7/aM2mthMxMt3Bi2OyvYTZA+Qe3h4/1yMq9j7M37yEr9z4ePrbcUrRmr7/+eo2pyvwvltq1a4vk7LZt2yby/pl7DpctW2YBLjQaDdLS0kTB5u7u7tWqjCgUCri7u3OCYyJj0gery+3bt/HKK6+IPDLu7u5ISEgQJUd8/vnn/PtGjRphwoQJHBj079+fX89gMHDgYFovHx8fTJ48GatWrcKAAQMs+Dg1Gg2ioqKgUqmg1WpRUlLCqWBCQ0OxYMECPkmymEwm6VidLNrYsWNF93F1dbWI6dyyZYtIQ12j0UAul/Pvz5w5w8GaIAjYvXs3/45RRllTFwGegubw8HAsWbKEb3U+z1hv27Yt3nnnHbzzzjsgMgIna9asWTNIpVKUl5dzGqhatWohLy8PZ8+ehVwuh0wmw7Fjx3D9+nUQWQeUgBGYWPOAjh07loPvVq1aYfHixdxzRWT01DGQ4uvrW2V/MKusrBQBGwZIZTIZevXqhYkTJyI+Ph79+vXjlD6mxVSF5rfwpT5PX0ilUjRq1IiDzYCAAKSlpSEjIwPZ2dmiBLYLFy7gzJkzvM3N+UfLy8uhVCrh4OAAQRDg5eVl1UvJErSmT58uerY2bdrwMffFF19g1KhRFgTvWq2WL76cnZ1RVFSEzp07QxAE0T3y8/ORkJAAIuPOSXVg0/Sz37ooqKq4uLggcPQiDP77EaSduoXr+SUoLdcj734Z9n6Xhx5L/8NBYsCMnXh/53f495V8/HT/ER6VP8G1/BIsP3QNDWeJhTMCE3dh2ErrPLA2+3ObDVD+RS0nJ+dPue3NipeXFx4/fgzgqYdCqVRi//79XFVk9+7dyM7O5qDD3t4eaWlpuHDhAt9m69GjByorK7FhwwZR8DwDp127dsWhQ4cwd+5cDBw4EI0bN4a7u/szYzYZmbhKpeL1NDcW9N+vXz/eZ8wDx2IDJ0+eDCIjpUlZWRlat25t9X5sQurcuTPnugTAyZ9ZDCWTYGTtUVhYyI9lIDM9Pd2irqWlpTwGLjg4WFQPT09PC3lBwKh/biqD16xZMw5mBEHg1xs5ciQ/x8vLC3Z2djAYDDh9+jQWL16MESNGoFmzZvD29q6Sp9HZ2RkeHh4W8pDmNEjBwcGcg7MqihMWTsHakY0vhULBJUKZt8waoCwqKsLkyZMtFFkYePDx8eGLmxkzZojuXVJSgpkzZ1possfGxoo8eNbs73//u+icnj17Vrk4YCEdqampIh7Xbt264fbt2/w4Bu5OnjyJAwcOIC0tDcuXL8ecOXMwefJkvPLKKxZeV/PCst9/DWhiyVKm/e7p6Ym6desiIiKCe/CbNGnCk+saNGiA5cuXIy0tDQcPHsS3336LO3fuiBJ9NBoN0tPTUVRUhDfffFN0T0dHR4wYMQI5OTkIDg7mCwKdTscXhdYAJQCMG2dUKDNtw3379vH3BZP1NP3Nvoii0WgQ1qID/KbvxM6LP+Ho9QK886+LGJR6DOPWnsaZm/dQ8cSAwSuOw2/6TtR79xs8KKvAuhM3MG7tacSmHsP7O79DUWk5rtx5YJXerqodMpv9ec0GKP/CNnjw4Col2f4shQEW5kECjBO6VCqFRqPhL+24uDjR9jjTeyYi0URTq1YtkWKIQqGwqspSXl4OmUxmAdoZ6DCvp1wuh7u7OyIiIjBw4EDMnTuXe0YFQeCADwBWrFghmkBZLKj5NRs0aMB5KdlnkZGRWL16NffSMFqbAQMGADDqELNjJRKJSNaSqaqYe9u+/fZbnogwePBgGAwGxMTEQCKRYNasWSAyekytgRcm62j6PEqlEps2bcKTJ0+4JzMmJsZC1s60MMqd+vXr8+1QtmXZr18/vhhQq9V49dVXeUiCUqnE1KlToVarLUCNTCZDUFAQ4uPjRYlIrI1M1WFMwdqIESP45wxQvvXWW5g/f75I19rOzg69evXCqVOnkJubK6KVUSgU1ZLrAxBRMbHi5uaG8ePHW1DZHD58WDSO9+/fX+21MzIyQEQYPXo0FAoFFAqFqO4tW7bEpUuXLOJfAeDevXtYvHgxYmJiqn2/NG3aVOSV/9e//gUiwpIlS1BUVITs7GxkZGRwsQJWmCe+RYsWorhU08QltVr9ixSEzItp/KtpCQoKQosWLdCpUyf069eP/+5kMhlmz56NdevWYc+ePXz7uqKiQtSuzZs3h1Qq5f9/7733LO7h4+ODNWvWAAAePHgAiURSrRjAr3m2hg0bwrP7m/Cdug2Rs/dagMF6736Duw/KkHGtgHsoG72/x+K4cWtPAwD+tuGchZcyeVtWtWPMZn8+swHKv7Cx7cE/e9FqtZgxYwaPn9q+fTv3CLi6uvKYQfO2MSfN/uKLL/j32dnZIhAUHByM9PR0fPXVV4iMjBSBnujoaD7xzJo1C4AR1BIZt74GDhyIiIgIuLu7VzkJCoKA+vXrIzw8HP7+/hYTjFqtRpcuXZCamsozWxMSEvDDDz9AIpFAqVRyuhIiI4Bt164d9uzZAzc3Nzg4OGDTpk18C3rv3r0cJA4ZMoTHhgqCgPbt2/N2+PLLL7mHKSUlhX/OACUATJ8+HUTGpAbTMAQA2L17t+gZq4tpZHUPCAhAr169MHPmTOzcudMqTVLbtm1F5zK5RNPtTlOvs2m4QK9evTBlyhQ0btxYBMIkEgl8fX05NyXznN64cYMfx67TqVMn6PV6fPjhh6J6yOVytGnTxsLLq9frRRrjz5IyNCUhZ0labdu2FcXb+fr6YsqUKejQoQP/jI0vtoCozkyTTRi4PXXqlAjIMk7W6OhoREdHV8kgIQgCdDodAOPYZzKnMpmM65Sz7WBzrlYmV2k61k0ZFkxt7969XPua0Rtt374dgNG7e+7cOZ4AtWTJEgwbNqza3QSVSgUnJyfev2xr/deQ+puCa2dnZ6v3bdasGYYPH4433ngDSUlJ3Etv2oe/tTD+UiNpedWxkEevF+D63ZJqj2kxz7gwmf/NZYvv2iw4+MwxZrM/l9kA5V/cOnTo8KeOpWQvc/O/mQfC1dVV1B7m27BEhPHjx3P+wGXLlvFje/ToASLiqhimpVGjRjxTGjBuCTMPyvz585Geng4io562uZWVlfHEllq1aj0X5RHR0wzqQ4cOwdXVFXK5HF5eXhAEgfNWlpWVYd68eahTpw4/z3SiU6vVuHHjBgAjxRSb0EJCQlBUVASdTscpahhptr29PU6fPi16BlNA+eTJE54R6+DggKZNm4qSPEyLTCaDo6OjCBgxz51UKq02yQkwghV2L9bPpkDX3MrLyzF48GB+vEQisaA2unHjBpKTk62Subu7u/PnYKpLjBbH/LhVq1ZZjd+7ffu2BUG5RCKxGlrA7Msvv+TjJzc3l8tkFhcXIyMjA126dBH1K1vgrF27FkFBQVUScpsaA6oDBw4UfZ6Tk4Px48dbtAXjEDXNSlapVDhy5IhVpZw9e/bwzPxatWohIiKCjxnACJpZwpZOp0NGRgb32js6Ola5Xb9t2zb+O7cWX8p+e9boktjf0dHRor4qLS2FIAho3rw5AGDXrl0QBIH/NkeNGoXdu3dj7dq1+OSTTzhpe3x8PPr27YuOHTtytoL/9q6QXC6HoFBXm4jTIHk3ih9V4Jtv86oFlG9vPA8AGLM60+I7/+k7nzum32Z/DrMByr+4HThw4L/6cvu9SqtWraqMTXJ3d0fnzp35pC4IAjp37owjR46AyKhTnpWVxb1PAwcOxJkzZ3iMIyv29vZ84nZ1dRUBSkCc1csyyk3l7LKzszF16lRO8G0KBtjk9+qrr+LAgQPcmxUUFAR3d/dq42Hd3NwwcOBAzJkzB4cOHeITcWFhISZNmiQCAEyTm4FK4Gk2ukaj4TKMpgk8xcXFePLkCU6dOoXFixdj+PDhHBBWFdNo3hdbtmyx8DQWFxdjxIgRIkDt5uZmFZTl5uaie/fuonZgW96bN2+u9jdQWloq8kTqdLpqt5vz8/OrpYoxLaw+VSXl7Nq1i/ctA3BZWVk86aaq5CPmBWceX7YNHxERgatXryIkJIS3v6lUKaOyIiKRp9ncGKUVEaFPnz6YNGkSwsPDRf0plUpRq1atKr11gYGBvK+sAUrACBpNE87kcjnKy8tRVFTEt9gbN27MY3BNY3ydnJyQnZ1ttf5MYUelUoniFQ0GA48bNi9DhgxBeXk5fH19IZVKRfHDgFEmVSqVci+oUqnktFOdO3dGZWUlCgoKkJ+fz2Moy8vLkZubi0ePHmHLli2i+/n4+CArK4tni7PfnF6vR35+PueWfe+999CmTZsafR/K3QOqBYpbzv6IiicGUWKOeWk6dx/uPijD+dtF8J9h/Zis3PtVjjGb/fnMBij/4lZZWYnGjRv/qRN0TIHCN998A8CYSfzGG29YHCMIAvz8/DBy5Ejs27cP7u7ufHvt0qVLFlyHREYVCzb5lJWVYfz48SJptlmzZvGJtbCwUJQl+sYbb1iQiDOg4uHhwWP3SktLOYg5duwYBEGwIE3/4YcfOMg1neSteThZzKapp5JtS7L/e3l5YdKkSSgsLMTq1astxoiLi0uViTDs/vXr10fv3r2RlJSEzZs3izxx06dPR7169Z5JRfT48WMOkIiMXtSkpCQYDAZkZ2ejdevW/H5169blYPvkyZOQyWRWgYypMQ8zI45m7d+qVSsLUMGM8Syy+pg/t3nx8/OzuNaMGTNAZIzj3L17N/z8/ODg4ADAqJUtl8shlUpFqkiAEXBIJBKEh4eLPjelsREEgccFM97JhIQENGjQQFTHFi1aWKjaHDhwoErvcXBwMMaMGYPDhw/DYDBg06ZNVseXRCLBkiVL+DWrApTMGAcjaw/TBZSpubi4wNHREYsXL+biAevXrxcdw+KCWeKSg4MDTpw4gS5dulj1RhKJ5Ur37t0LIktyfRZKwjyTK1aswPvvvw87Ozuu2MS+r4p8n5WhQ4dySUKNRmNBrM6eISwsDOfOnatSVvLXFoVXSJVA8ZMDxpCDpG3fVnlM+Ht7cOmnYtx98Bit5h+o8rizN+9V2ec2+/OZDVDaDBs3bvxdAN1/u/j6+kKv18NgMODDDz8UeeZCQ0Px1ltvISIiQgQQ+AvYJLaR/c2OY7q7pqbX60WxVkqlEv3798eoUaNEHiN2vdDQUIwbNw7Hjh3D1KlTQUTYsWOH6JoZGRlcbYXICJismSnlEJGR+qSsrAyHDx/G3LlzERsbi4iICKvgmIGB51lgyGQyngjDQOOuXbtQXFws2vIGxLRMDFCzLeRnkaUDgJOTE7RabZWAIDIyEpmZmTwuuGXLlgCM9FhEhL///e9Wr8v0z3v06IGff/4ZREbdZuYRkslkIl7PgoICnqnLirOzM0aPHo2bN42EztWRrWu1WrRo0YInG3l7e/NscZVKJfJoZ2Zmcj7LzMxMUVsSET777DP+2Y4dO0Txi19//TUA4ObNmxAEQUSBVFpayiUeTftSo9GIgCQjSycibNy4UdRuqampPHub9QMjCLe3t+d9rdVq8d5778Hd3b1aQMliik15V2vXri3yLjJvYFxcHADg2LFj3As9btw4fhzTvj569KiIr5KVhg0b4ocffsCuXbv4Z+YKO4yiifUpIPbasp2G31pYDC9jfLCWyPciisqrjlUAuGifUTJx/m7LmEhWGs7ajYs/3kfhw3J0WXK4Wk+nzUP51zIboLSZKJv29yr/rTgiuVzOAZmdnR3efvttODo6QqlU8u3DsrIyq/rVbPL08vJCZGQkn0idnZ0t2tRgMHD+O/PrmHt/NmzYIDq3du3aVXrtWGylk5NTlf3JvHmm22SDBg3iXlK9Xo+vvvqKZzWHhoZWCS6fNRkmJiaKttGZMUBpTsvEgEnv3r35daoiKWd24cIFEBmzpydNmmR1LA0bNgzFxcWoX78+BEEQbR+aklab2rlz53gcLYub9Pf3h1KpBGCMtWOLDp1OJ+IjZSUxMbHaurMsb1NtatPz7ezsEBUVhWnTpoHoKUUUsyNHjnBNcpbp36BBA0ilUuj1ehQWFqJly5Z8bE+ePBkSiQQ6nQ7l5eWcvunUqVMAjL/1bdu2YfDgwdVmQXt5eeH27du4dOkSiJ4mZs2dO5d7sRUKBcaOHSvSoGfZ/Hq9HjNnzhTFWarVaoukLGaMTJy1NUvakUgkmDRpEgwGA491Nd3mLiws5J72fBC7AAAgAElEQVTBiIgIDvqsec0lEgkuXbqEBw8eICsrS5TY5u3tjRkzZmD8+PGIi4vj7WZvb4/g4OBqpRdrqqhUKoSEhHCPuYeHBxISEpCcnGyRZPZb34H+wXUtYigZmFy078ozwWRRaTm6f1L1drgthvKvaTZAaTMAsMhGfVGFJSzMmzcPRCTa6n3e5JOaKLVr10Z+fj6Apx69tm3bolGjRtxDwDKhXV1doVQqsWDBArRp08aqFJqbmxvGjh2L3r17Wyi0aDQaNGnSBC+//LLIs+Hh4cF1nbds2QIAXAmmS5cuVvuJSdcRETZt2mTxPdvGHzlyJDIzM0WUK6ZJBKaFeRoZYXVSUhLS09NRXFyMgoICrvqhUqmqjIlk7eXm5obGjRuLuAuJjFt85skuLEnB39+/2rHJuA69vLxE15w2bRrWrl0rolcisowNTE5OBhFh9uzZ/DO9Xg8nJydIJBJkZT2lN2EE15s3b0ZqaiqPxWOFjQ1Gfj506NBq627KQ8kSTIgI7dq1w9ChQ+Hv72/hFWzYsCEmTZrE42sPHDjAY/YYCG7SpAnmzJnDF2Zt27blXrZPPvkERMS35QMDA9GnTx+eoMXuxUCSq6srbty4wWP8TI+pVasW34Jmx9vZ2WHq1Km8P1kWv1qttuAbZdKKpjGSI0aMwIMHTzkKCwsL+dZwgwYN+OLkyJEj3Auq0+mgUCig0Wgwd+5cTJkyBWPHjkVsbCy6dOlSo7Q6/+3CxvOtW7dQXl4uInKvqRIWFgbfCV9y8PfxXiNI/+TA1WeCyfuPKtBzWUa1YNKW5f3XNBugtBkAcCqUF1UYh+CePXtARNiyYxdUXnWQuHAFXIMbw9HV44Xe37Qw2hOZTIahQ4eKSLgFQbDgamTE1aZZt/n5+Rg+fHiVIFir1UIikSAgIMCirRMTE0X3YyAlPT2dkyibx7UBxi0+IuN2rkqlglwux+7du7Fo0SIMHz6cJ1s8b5kzZ44oEYbVa+vWrQCA06dPcw9TfHw8P06n00Gr1YoIqwVBgFarhZOTU5U8mwxsDhgwAHPmzBHpMffq1cvquDSljJHJZBgyZAgKCgrg4uIi4udMT0/n9xUEAe3ateM0UQaDAVqtFmq1moMgFi/50Ucfie6XlpYmqrdEIkFUVBTmz5/PgZ9cLsf69eshl8vRqFGjan9XDFAycMcI7YmMMaSsfgxs+vr6itqPhUN0796dtwHR07ABJycnkZLQw4cPsWLFCgs1FyIjKGvdujXmz5/PF1MsNm/Xrl1wdHTkXmUWc2hOndW9e3eRN3rp0qX8+4iICFy4cAH79+/Hhg0bkJKSgtmzZ2PSpEl8O9fUK6rRaCwWHr9Vhce8ODg4oHHjxmjdujX3lLP2DwoKQmpqKjZt2sQ99Pv27cOTJ0+wefPm38RjWRPlRS6wZTIZ6gyaAd+p2zB753cAgEPZ+eiTcsSi+E03yimeu1UEg6ESyduzLI5p/dFBGw+lzWyA0mZG27t3r0gukMi4Nftb1RpMPXJKd3/0eHcVao1bCb/p5pQVO+Dz2ufw6zcZcpfaL/RF/f7771tQ/bCJzTQ4n1lhYSGIjFyTHTt2tEoiziZwQRDg7OwsajcHBwdER0djzpw5yM3N5VJu69ats/CAabVaaDQafm+9Xo/MzEwsWrSIe3E8PDyqnWzq1q3LYxrT09P5lnGdOnV4vaRSKebMmSN6zuLiYhAZYwhTUlJ4LOWXX34pOi48PBwKhQKAMc6vOu7IefPmITY2FpGRkVXybLI6OTo6YsCAAZg9ezbi4+NFCQ1hYWEiIJOVlQWJRAJnZ2fo9XoeB9ypUyeuiEJkXDycOXOGA9OEhAROQs7iLI8dO4Zu3bpZeF8XLlyI8vJy6PV6nrzUsWNH/rxM7rI6Y1vGRE/J9XNzc7lKTuvWraHX69G+fXsIgsAXMadOncKbb76JsLCwKtv35ZdfRn5+PicRrypsISkpSbRwKCsrw82bN3Hq1CmkpaXx5BZWn9jYWJGKjzWAVxXx97OK6QLK2udNmjRBu3bt0LNnT8TFxWH8+PFITEwUMSqYcjoKgoC6deti0aJFFr/Lvn37WvQHi/MUBAElJSX886tXr0IikcDe3p5n2/+vFGsx3b+1CIIAjbcxjvL499YVoZj5Td+Jlh9aZxtgtun0LQsPpU0p569nAgCQzWxGREVFRTRgwAB68803yc7Ojk6ePEknTpyg48ePU1FRERERyeVy0uv1z7yWTqejBw8eUL169cixVh363vklUvlHECoNJEikVZ4nEAgkkOTuVbr9z/n0pDi/xp7P3Ly9vcnT05POnz9PlZWVZGdnR2VlZXTnzh0iIlq9ejXt2LGDLl68SMXFxfw8Nzc3ioqKon79+lFoaCi1adOGZsyYQY0aNaJhw4aRwWCgefPmUXJyMikUCtLpdPTTTz9RZWUlERFJJBKqrKykxMREGj16NBUXF9OgQYPo+++/N7aBIJCTkxOVlpZSeXm5uH0EgZydncnLy4uKi4vp9u3b1LNnT/rxxx/p/PnztHr1ahoxYoTFs7Zr144OHz5MRETvvPMOLV++nIqKiqh27dq0bds2ioiIICKiOnXqUE5ODgEgrVZLR48epQYNGoiuNXToUFq/fj0VFxeTVqulx48fU1BQEP30009ERCSTyejJkydEROTp6UmDBg2ipKQkcnV1JSKiiooKOnHiBPXv35/u3btHjRo1om+//ZafY83CwsIoLCyMGjduTC1atKDo6GhaunQpTZs2jbp27Upnz56loqIiun//PtnZ2dHly5dp7NixdPToUSIiCg0Npby8PCotLaXKykpSq9XUs2dP+uabb+jBgwdERFS7dm0aNmwYKZVKmjVrFq1Zs4bi4uKoQYMGdPnyZZowYQKlpKTQo0ePaODAgZSenk5ERFOmTKEPP/yQJBKJqM4//PADRUZG0v379ykgIICuX7/Oj6msrKRu3brR3r17yd3dnaRSKT169Iju378vusbDhw8pPz+fFi1aRJ999hlV97qWSqWkVqtJpVLRvXv3+Hhj31VWVlZ7vjWTSCSkUCiovLycAJCjoyM9evSIKioq+DFOTk6k1+uptLSUZs6cSc7OzuTs7Eyurq7k7u5O7u7u1KRJE5JIJHTnzh2qrKykvn370vbt2/lvgYjIzs6Ojh07Ro0aNRLV4dq1a1SvXj2L+js5OdH+/fspICCAWrRoQVeuXCFBECgpKYk2bNhAV69epYYNG9KJEyfIzs6OKisrycvLi+7evUtEREFBQZSdnU0ymYyIiCZNmkSLFy/+Re3ze5lSqaTKysrnevc+jykUClKr1WTXYyopfcMJJNTIdYmIpBKBogNdaM2YZjV2TZv9McwGKG32TANAN2/epMzMTDp58iQdP36czp49S+Xl5SQIAkkkEjIYDPx4Nkm8++67tHj7SXLtMoEMlSBBKnv+e1YaSEKge/v+Tg/O7X4Rj0Xe3t4UFxdHw4cPpwEDBtC1a9eIyAja2M9CEATy9PQkrVZLV65cofXr19OQIUP4NSorK0kmk1HHjh1p7969dO3aNWrevDndu3ePpFIp1alTh7Kzs6miooI+++wzWrNmDZ05c+a56ieXyykyMpK6dOlCn376Kd2/f5+KiopIq9XyewcGBtLNmzeJiKh37960detWi+vcuXOHgoOD6eHDh+Tu7k75+flUWVlJr7/+OqWmphIAGjBgAKWkpFBYWBgVFhZS7dq1KTs7m+zs7Cyut3z5cnr99ddp8+bNFBAQQH369KHbt2+TUqmk8vJyUqvV5OvrS1euXCGNRkOlpaVERBQQEECjR4+mt99+m9RqNTk4OJC7uztduHCB3njjDVq9ejURGQFpp06dyN7enjZv3kyCIJBMJhOBGNY+ADgQbdasGc2dO5eio6NJpVIREdGtW7fotddeoz179lgFUy4uLtSvXz969913qVatWkRE9PjxY7Kzs6PIyEh68uQJXbhwgUaPHk1ffPGF6NyBAwfS5s2bici4yFi9ejX5+/tTQUEB7dy5kxYuXMjBUnh4OIWFhdGDBw/o4cOHVFpaSqWlpZSXl8cXK4IgkFwuJ4PB8KvAn7kpFArSaDRUVFREzs7O1KRJE3JwcCCtVkuOjo7k6OhIBoOB3n//fdF5oaGhlJKSQu3bt+efvfnmm/Tpp5/S4cOH6c6dOxQbG0tyuZy8vb35+CMi6t69O33wwQfUuHFj0TU9PT2JiCgrK4uaNGlCN2/epKZNm9Lhw4cpMzOT2rZty48NCwujDz74gA4cOEAbN27kAFClUtGIESMoMTGREhMT6euvvyYAot9rbm4ueXt7U2VlJQ0fPpzWr1/PF0ZJSUm0detWSk5OpoKCAlq+fDmFhobSd999R1u3bqWBAweKQPif3Tw8PGj7waM0/OurVP6k5p5bKZPQ/rfaUm1ny3eHzf7cZgOUNvtV9uTJE8rKyuIg8+jRo3TlyhUiMgKCrl270pEie9K1HsZf+r/YACJBIPW1/ZT9zyU1/ARiT5q52dvb05IlS2jkyJEkk8no4cOHpNVqqUWLFtzrxUyn05GTkxNdv36dzp49S//+97/po48+osLCQiIiDrTMTavVklQqpYqKCiorK6tyMtPpdFRcXExjxoyhlStXir775ptvqHv37kRE3GNoaj///DMFBwfT/fv36aWXXqJTp07Rli1bqG/fvkRk9KL16NGDLl++LDrvpZdeoszMTKv1+eGHHygwMJCCgoLo+++/J0EQaNy4cfTpp5/S5s2baejQobxdAdDBgwdp7ty5lJGRQRUVFSQIAtWvX5+ysrLIzc2N7t27RwaDgYOOO3fuUEJCAvXq1Ys6duxIb731Fi1atIgqKiooMzOTjhw5QhcuXKCrV6/S7du3qaCgwKKOcrmcHB0dydPTkwwGA/3444/cE8m+HzVqFA0aNIh+/vlnKiwspHv37lFRUREVFxfTxo0bqaSkhIiMnjA3NzcqKyuj8vJyKi8vJ71eTxUVFdV6Va0ZW4BJpVKSyWSkUCiIiLhn0tnZmVQqFT148IBKS0tFoFIikRAAmjdvHpWWltLs2bPJ0dGRcnJySK/Xc4/6kSNHROexcT5q1ChaunQp2dvbExHRkSNHKCYmRvQMkydPpgULFljU+86dO+Tl5UURERF0/vx5UqvVdOnSJfLz86N79+5RbGws7d+/nx/v5OREffr0oeTkZPLz8yNPT08+zh8/fkwTJ07k3sB169bRsGHDaPbs2fSPf/yDcnJy+HVUKhXpdDrKz8+n/Px8cnd3JyKiixcvUteuXSkvL48fa21BlZqaShMmTCAYw7soMjKSL+heeeUV+uKLL5571+XPZGq1mn766SdydHSkDadu0fQt39bYtef3a0ixL/nW2PVs9scxG6C0WY1ZSUkJffnll7R48WIq9WhEmvav1tzFM9fRzYNf19z1/t/Mt/RMTRAE+tvf/kYLFy4kiURCoaGhdP36dTpy5AgdO3aMzp07R1euXKGzZ8+KPLTmJggCtWzZktq3b0/h4eE0YMAAGjp0KK1du5Yfc+XKFQoNDaXg4GDS6/V048YNi+vI5XIaOXIkffbZZ9xj5+HhQcXFxQSAoqKi6PTp0/z4+/fvU506daiwsJBSUlJoxIgR5OTkRK6urqKJeNmyZZSQkMD/r1QqSa/Xk16vt9jGJXoKAIiI6tWrR7t27aKAgAD+/fXr16levXr05MkT6tmzJ23bto17rdPS0ujDDz+kixcviu731ltv0bx586iiooLq1atHOTk55OfnRzdv3qTz58+TwWCggoICC/B3+PBhunDhAhEZt3VdXV3p4cOH1QL0X2pKpZKDP6VSSSqVim8tnzt3jry9valZs2b0n//8hy8i7Ozs6LPPPiOVSkWxsbGUkJBAixcvtmjPEydO0HvvvUe7d1v3wqtUKlq0aBH179+fPDw8qEOHDhy4ffLJJzRx4kRyc3Oj69evk1arpS+++IJeeeUVio+Pp5deeon+9a9/0dmzZ+nevXv8mhqNhiorK6msrIyIiPz8/GjPnj0UERFBMpmM7t+/b7Xf3d3dqaCggFQqFWVlZVFQUBD/7scff6TatWvTkCFDSC6X0/bt2zlI9vb2prt379KTJ09IJpPRhg0bqH///kRkXJi2a9eOjh49yj2NCoWCHB0dqaCggP8mnZ2dqbCwkCoqKmjEiBGUlpZGgiDQmDFjaPXq1RwQRkdH044dO8jZ2ZnXbffu3dStWzciIoqLi6N169YRkdHDHx4eTt99991zjYM/k5nvtHx66Bp9vPfqb77ulM516fWYOr/5Ojb7g9qLD9O02V/NLt3Kh//UrdVqxf6iMm0Har/9T6hdLXkAf2tJSkoCYMy0Xb16NSIiIiyOYckfVamHsESTnj174t1330V6ejpKSkqg0Wjg4+PDCc7nzZuHTZs2gYgs9KXj4uJARJzChukNswQG8wQIrVbLE54WLFiAXr16gYgwa9YsAEBJSQnPwjbVC2dJCampqTAYDOjfvz+IjAkxZ86c4frkRMYEF1Puxtu3b4sSXswTUkpLS5GTk4MTJ05waUZW19GjR6Nnz54WlEvmCRoSiaRGteUVCoWIbsjLy6vaLGKpVCrKsvbw8MCBAweq1I1WKpVo2LAhrl27xpNCWP3r1q3LpU2nTJkCg8GA/fv3Iz4+HkFBQRbZ8AEBAaLEoPHjx/P7MP7NvXv3iu7P6L48PT3x8OFDC05VZqYk3uZFq9UiOjqak4Cz34SpmUq0pqamWm0LqVTKta4BY2JRz549Re3t6+uLefPm4euvv0bz5s1Ffd20aVOkpaXxMVdSUoJOnTrx7+3s7PhvrW7durh+/TpmzpzJ68y4GmUyGaeI0uv1vP8ZtZBMJquW/urPXGQyGWJiYlBZWWnRf19n3kTIzHQEJu76Re/nwMRdCJmZjg2ZNy2uabO/ltkApc1q3IatPIHAxF0Ie/cbfPbv6zh89S5+LnkMAFhcBWluUOIuvL/zO1zOK0ZZxRMUP6rA6Rv30Hf5UeMxU7fBPfb9Gn25MhWQrl274qWXXoKXl1e1Gcts8vP09MQ333zDs0QXLFgAIiPtT0VFBQoLC/H48WNoNBqEhobi/PnzHGwwObgffvhB1GaOjo4WBOmm2r83btzAjRs30L59ewvAJQgCPD09+WR78OBBnqVrnsmt1+s54bqPjw8HMikpKZg/fz6mT5/OwSmbgEJCQkQ0NKYKQL+WCYCdo9Vq4eLiAgcHBxHAMgUh0dHReO+997B06VKsW7cOe/bswdmzZxEfHw8iQr169UT9VqtWLSxdupRTBDG6GKbPfebMGRAZpRXLysowbtw4C4Bh7ZkY9VGjRo3Qv39/zJ49G66urlCr1bxNFixYgPLyck7CzYqDg4PomdRqNRo3boypU6eiSZMmEASBP4O3tzfPZGY65D4+PrCzs7P6e2M8m4xw3JRsnfFAmmZAM+5LuVxulTeVyJgdn5iYiO+//56Tq7P+iYmJsVoPV1dXkRpOfn4+5zCVSqVWx4qXlxc0Gg1cXFysXpMRnJvSCykUCkyfPh2lpaVQKpXQ6XQ4d+4cPv30U3Tu3LnaBclvZa34oxe5XI6rV69abWsAuFVYimErT3Cg+Cwg6Td9J4atPIFbhaVVXtNmfx2zAUqb1ahdvfOAv3BafngAxY8qcOL7n7H+pHH1ag1QBszYif2X76D4UQXm776M2NRjiP9HJhbuzcbQ/3+5sSJzqXkvJZERJLm4uKBBgwbo06cPByHr16/HhAkTLGh64uLicObMGaxbtw4fffQRiIzk0gyY2NnZcZlENhGbXuPDDz/Enj178PDhQw5wTLkeAXAJRna9tLQ0pKWl4b333nuuiVIikUCtVkOtVkOhUNQIv5+TkxN8fX05GG/evDm6du2KgQMH4pVXXsHkyZMxZ84crtZjTkY+efJkAECdOnVE9EjMcnNzMW7cOAvvXcuWLZGXlwfASMXTr18/0fd+fn6YMmUKJ+FmPItMYnDMmDGi+zRr1gxExMnDAYi801KplJPId+/eHYMHD0ZkZCQ8PDyq5CfUarXw9fWFl5eXSCGGlbp162LWrFlcxQcw0tUwAKTRaLhq0qFDh/hYYnyd3bt3r/J3x8aKIAgoKyuDwWBAUlISr4dKpcKbb77JVWWIxN5Og8GA9PR03i7WxtOQIUPg4+MDhUJhoToEGCUPZTIZAKNHk9W/bt26ouu5uLjAw8ND9Jm9vT0H/MyYZrnpGOjatesz+RmlUqmoj+RyOTZu3Mi11E25Tf9KRRAEvoPxLLt65wGSt2WhzYKD8LeigNNmwUEkb8uyUQPZTGQ2QGmzGrXkbVlWV7aN398DwDqgfG9HFp4YKjmJbpVl6ja4dhlfYy/YyMhIvPbaayCy9LoUFhZCIpGIdKaXL19e4zq7pp4pjUYDtVpd4+TObJLV6XQiMnKJRIK5c+fi888/x5YtW5CRkYHs7GwUFRVxtRXTolQq+VZ9amoqiJ5qRpvaqlWr+IQulUrRt29fZGZm8i36rl27Qq1Wo06dOlbHkMFggFwuh6+vL/r06SOqg3m7dOnShQNNwKhpTWQEMUyGz9/f3wIA5eTkgIgQHh4OABg6dCiICE2aNMHmzZtFUqQajUak6QwYOTsZN6W1elVVXFxcMGPGDOzduxfx8fEcVOl0OlRUVIjucffuXZG2tTWye2Zvv/02P06n0/Ex5eDggOTkZP78w4YN4/1irl/NzNPTE1KpFCkpKSJPtOlz+Pj4YNy4cTh+/Dg/b/To0SAirp9uPs7VarWor8rLy7nikOkYq1+/PqKjo5/b08i0ytesWcNBY1FRkQhU2tnZYe3atfjxxx/5LsFfqTCRhapCN6qzh4/1yMq9j7M37yEr975NTtFmVZoNUNqsRq2NmWLC8wDKW4WlOHb95+eK16k17vMae8m2bNkSJ0+e5HKQffv2xcyZM/HGG29g+PDhXAItKCgIgYGBL4Rg2Lw4OjoiPDyce/ZatGiB119/HV27dhVN7CNHjkROTg7fdt+9e7eF52b69OlYvXo1Xn75ZXh4iJWI2GQbHR2N3NxcUR9++umn/HuVSoW8vDxs2LCBx6CFhITg8OHDICKMGzcOgBEEfvzxxyKCdyISkUeXl5dz3WkiI0m4NVu7di2ICO+++y4SExP51rx5kcvlWLZsmYWkI9M7Z9u65s/HjKnlsLjR8PBwEfA8ePCgqM+bNm2KqVOnomnTplY1uTt27IiUlBQUFBQgIyMD8+fP59dmEpvV9TvbRt+/fz+f+A0GA+8LZ2dnq9uVZWVlPJbXFAAuWbJE9Dy7d+8GEfFFRcOGDa22Cwu1YMT2+/fvB2BUTho3bpyof9m9/P39LfrJ3t4egwcPxuXLl+Hh4QEPDw8YDAZcuHABy5Ytw6hRozgor87r6O/vjx49emD69OnYunUrCgsLMXDgQBAZPd4MIEokEnTr1g23b9/mggGbNm1Camoq95ZaU3H6q5R9+/ZZ7W+b2aymzAYobVZjVvJYb7E98ixA2XyecbL68mgOPj14DXcfPIb+iQFX7jzApI3nLK7jO20HBPmfO6De2dkZEolEFI8GgOtyS6VSkfKJwWDgE2jv3r1Fikf16tXD7t27uacrKCgIffv25WCZFTs7O9SvX58DQnt7e66sw/SZKyoqeGwgU0pp2rQpEhMTOdhUq9V466230LZtW0gkEqvjhF1DKpVysMJMr9dzgMBAi0qlQrt27Ti4Y8/CvIJSqRTNmjXDxo0bYTAYRCBsxowZVY5XpptORAgNDcWTJ09E3+fm5oqe17yfwsLCuKd2wIABVu9hquVdWFgokseUy+W8H6x54+RyOe8PFmIgkUiwevVqfv28vDxRX/r4+HAp0YiICA4oi4uLufc7Ly+PSz1OmzbNap3Z865du9bi+7p160Imk+HChQvo0KGD1bhjR0dHREZGon379mjevHmVHlx2nzp16qBBgwa8HcyTtzw9PTFx4kQUFBQgPz8fEokEQUFBvE579+4VqekQEbp168bbyDTZ7K9WpFIpYmNjq/wd2MxmNWU2QGmzGrOs3PtVeharApR9Uo4AAIrLKnDlzgOMX3saw744gZ0XfwIATPvnBYtryd1rRhpNo9Fg9uzZSElJwQcffAAi45bkTz/9hMePH4u2Ef8bRRAErFy5EpWVlcjLy4NcLuceFk9PT5SWlsJgMHBt8qFDh/K+MNekJjKCTVNbt24diIxJOeYxf0qlkidUTJgwQXTehQsXLLYNtVotZs+ezQFMTExMlYAyKSkJRE+Te2bNmoUNGzagSZMmImDVokUL/POf/+Tn3bx5k4PK2rVrQ6/XIyUlBfXr1+fARKlUIjAwkLefRqMReUlNbfLkyfxemzZtwvfff4/ExERERUXBzs7OYlI2B+F16tTBrl27oFKpEBYWZvUeDFC2bt2a913r1q1F291EhOzsbJSXl+PIkSOYP38+Bg8ejKioqGqzkU29eoIg4IMPPsCjR48AAIMGDQKRMcbVYDDw7HwWo2kwGODl5QVBEHD06FFRG5s+e+fOnUXPYzAYOCPBr0lwady4MaZMmcI9jU2aNIFEIuFAW6PRYP369fjyyy9BRHjrrbfQt29fvmAheipFaL4YAYAVK1aI7mdvb8/rWdNhJM/7G/5vvkNYG5iGGtjMZi/KbIDSZjVmZ2/e+8WAsu9y42T2WP8E0R8eEH138cf7yC16ZHEthVdIjb1sdTodPvroI57EwCbh32N7+3mLt7c3BzO7d+/GrFmzQGTMZm7RogWIrHvIWIas6cRWu3ZtDioAiLTW/f39sWrVKrz66qsICQkRARa5XI66deti1KhR6Nixo9WkGRa/BlQPKNn2/bp16yxAEctOX7RokdVzWaKMIAiiJI7S0lIkJyeLkoCY58wa2GN0M9aSZ9gW7rBhw5Ceno5WrVrx7+rUqYPLly+jd+/eHKBIJFbf/2oAACAASURBVBKoVCqr9d2+fTs/19HREenp6fy769ev83Gm0WisxqM6OzvD0dGRg82xY8c+E6TI5XK4urpyryb711zbOicnB1KpFA4ODigrK0Nubi4HYOvXr+ehIMnJyejSpQu/TnXAhSXETJ8+HatWrcKsWbPQpk0bizq7ublZZGTHxsZyuqPIyEhIJBIR/dH+/fvRvHlz0Xhp2LAhp8AqKyvj2fQsKYwV09jhv1oxpyizmc1elNkApc1qzH6NhzLm40MAgEs/FVuc8+nBawCAyNl7X4iH0rz8L3gTqium3qLp06fzz82zfw0GA9/iYxP2ypUrMWTIEA4EXVxcEBDwtB1DQ0Ot9inLfA4ODrbw8DDvWb169UBk9Dh+8MEHAKoGlBcuXLDw/jHg5+npiXr16lkACdNziQiNGjWCUqkUxfcBxhhNnU4HQRAwdOhQEYiws7ND7969MXz4cBEFDdFTz1WrVq3wn//8RxR3mJWVxesbGhoq+q64uBgjRozg48bFxYXHLZaXl3MvIauztcxoLy8v2NnZ8TaIjIzkMZ9ZWVkgMnqeDxw4INouN6Vx8vPz457NIUOGICoqSkQjZVoY2AwPD0f//v3RvXt3EBkXGgzcOzk5VekZlUgkcHV1FXkM3d3dcevWLQDG7HmpVGrxnB4eHnBzc0NKSgo6deoEBwcH0XUdHBzQrl07LFq0iG9ps4QpU2NZ6PPmzUNUVBTvO5lMZrEIjI6OxsGDB3ms7Isq1cV/sgXQm2++Kfo9/h5FKpUiIiLCIpTDZjZ7UWYDlDarMXv4K2IoAxN3obRcbxVQphwyAsrG7+95ITGUbDJyd3f/XV/0v6WkpqaisrKSAwEiY5IMS0wx5f5r0aIF8vPzRbFzZWVlaNq0qWjSYRyF5pnMAPDZZ5+J7h8QEIDY2FhERkaKAAuLqSQyAis22QNGQvRXXnlFxIUolUqRkJCAgoICAEBiYiL/LjAw0Or4atiwIQRBQE5ODi5evAi5XA6pVIqMjAwARhBLRBzU7du3zyJL3LS+o0ePxunTp1FRUQGVSgVHR0cR6Fu9ejXnTpTL5ahdu7bVerHQCNNEJgbc2fb7lClTrJ4rl8sRERGB0tJSdOvWjbfN1KlTeeIJ89oKgoAuXbrwfmIUQBKJxGqsI/PYsWfW6XRwcXF5Ju2OtdK3b1/cvXuX9ye7bnBwsCgpirEm/Pjjj6K6sKScoqIitGnThj8nkZGb1ZxGiLXdnDlzOMA+ffo0iIzAn1l5eTni4+NFix1BEBAUFISoqCgR8K7pYq0dZTIZ7HROGPr6NHiENUPyks8hV9tj8+bNICLuGf89Fq+CIODMmTNWx53NbPYizAYobVaj9muyvLee+xHlegNamm15Z+Xexw8/PxR95v3qihp74fbv3x+enp58Un7RL/iaLhKJhE9qMpmME2KzSbpfv36Ij4/noEqn04mSbl5++WWRt9Db25t7BjMzM0W8jHK5HJmZmaK+zsvLA5HRC9O8eXMLrxMRiTxdOp0OQ4YMAZFlPCcAzrfIJl5TO3ToEIiMlEPMTp06BZlMBplMhokTJ4LIuJVau3ZtUX+yOpj3sSAICA0NxeLFizmgnTt3LgBgzJgxIDJuRWdmZvJtemuxaHv37gWRMQGIjSfWJ8OHDweRdUB57949EBFGjBjBP8vIyLDYnpVKpRg4cKAopODSpUsgMnpNWR/269cPS5cuRXx8PFq0aFElX6ZUKoWTkxNCQ0PRtGnT515Mubq6IiAgQASGzMMJWIb+ypUrRZ97eHjA3t6ej9dWrVph8eLFIDJyvQLGhKxNmzbxrXXT+9jZ2fF+/M9//gMA+Pzzzy3YC8xBniAIv8ti0b9RCzh3fA3hiVssFcKm7UDdt79G0KDpGDT2b79aDOCXvhsSEhIsxpzNbPYizablbbMatVnbv6M1J2+SodI4rNqFuJFaISV7pYwWDGhEOy/+RLu+NepIH7pylx7rK8nX2Y52vNGKfi4ppyUHrlJJ+RMa3MSXOod50Otfn6Vvsu4QEREqDVRydhcV7V9RY/VlGtN/NJPL5RQSEkJlZWWUl5fHdZmJjJrWlZWVFtrkv8ZUKhVJJBJ69OgRtWrVilxcXEir1ZJOpyNHR0f64IMPyN/fn5YuXUo6nY7++c9/0ldffUVFRUUW13JzcyM/Pz86ffo0JScn06xZs0Tf16tXj65evUru7u50584dateuHe3bt49kMhkFBgbSzZs3KT8/n1xdXamiooI2bdpEqamplJGRIbqOvb091a9fn7p160ajRo0iX19fio2NpY0bN5JMJqO8vDw6evQoffTRR5SZmUlPnjzh2tVSqZSCg4Pp0qVLFBISQqdOnSKtVksZGRnUpk0beuONN2jZsmWi+z1+/JjUajX/f7du3ahDhw40b948ru0dFhZGx48fJ61Wy4/bsGEDDRkyhFJTU+nVV1+lyspKmj9/Ps2fP5+Ki4v5cZ07d6Z//etfpFKp6OLFi5SRkUGzZs2ie/fucS33x48f/1979x0dVbk1cPh3pqX3HkISAqGFHkAICU2KgKIUJUoRBMGGiiLKVYFrQYqIwr0iH4pSLCgoEcul92YoSugBQgBpIUA6aXO+P+IcGBJImyDgftaatWDmtJlMMnv2+757W12TpS+2o6MjHTt2pEGDBixatIikpCQGDRrEnDlzmDZtGm+++aZVH3qj0cjatWtp0aIF8fHxbNmyhenTp3PmzBns7e2LnQfAYDDg7u6Or68vvr6+rFu3jqioKDIzMzl48KDWO15VVRRFQa/X07BhQ4KDg4mLi2P79u2EhYXh7e3NlStXcHR0JDIyku3bt7N8+XK+/vprVq5cydmzZ0t8j177nAMCAmjVqhWdO3dmx44dLFiwgLy8vJvuVxntuvfmsHskpuDGqOZCFJ3+xhubC0GnJydpFxf/919cdHmkpaVVyd8fX19fEhMTrd5vQlS5vzWcFXedazvlhLz2k3ry4o1bcl2bkew8fZ266sBZNT0nT83JK1B3Jl9Uh3zxW/EV3t7VbfYtvkePHsXm091Jt3Hjxqk5OTlq165dtfuuLRWjqkVFxi1zyyyZmqefflqdMGGC+uKLL6qDBw9We/fuXWwRA39le1xcXG6Y6Srv7fqsjKXYer169bR2jwEBAerEiRO1+YIeHh5aZ6DIyEj1vvvus1pIdO1Np9Np2atrWbJmlgzltYsUCgsL1dmzZ2tllyw3Pz+/YnX7nJ2dVX9/f6v7rs0o6vV6ddOmTVaPT5s2zer6evbsqWU5LTUdjx07po4ePVrLNNrb22vvy9IWh3l4eKj16tVTe/ToYbVSWlEUbTGPRX5+fok1PatXr67++OOP6ttvv61CUU/6a11bXikgIEBNSkpSN2/erJUeKq0/ellvgYGB2oKzBQsWaOffv39/iYunrn9v1a5dW33qqafULVu2qKqqqk8++WSV/e6ZTCb1/ucnqtVfXqKGvPpjmWroXtugIWT09+o9j41SoXiJJFvcvvvuuxv+3RWiqkiGUtjcwM+2s+VYqpaltAW9Asr5RI5+Nsp2x9TrrbIzdyKTyUReXh7R0dG4u7vz008/0b59exYuXMj999/P77//jr29PR999BEPPPAAISEhGAwGzp49i6urK7NmzWL8+PGkpKRoWa1x48axcOFCjh07hqIodOjQga1bt+Lu7s7p06cpKChgyZIlvP/+++zYsQMoyg75+fnRqFEjgoKCWLZsGSkpKbRu3Zp9+/aRnp4OXM0IVzYzrCgKRqORwsJCCgsLcXR0JDs7G0VRaNasGT4+Pri4uHDx4kVWr16N0WjkjTfeYNKkSVy5coWff/6ZFi1a4OnpiU6n47PPPuPJJ58sltV1cnKiS5cuTJgwgfHjx7N06VKOHz+Oj48Pffv25ddff0Wv1+Ps7ExhYSEZGRlW+x89epRatWrRp08f9uzZQ2JiIgCRkZGcPn2aM2fOaK97SfR6Pfb29mRnZ6OqKp6enuj1elJSUjhz5gz+/v5W28+cOZPnn38eQLvmlStXMnHiRDZv3kx+fr7V9q+88gpTpkzR/t+yZUvi4+P5/PPPGTx4MMnJybRs2ZLz588D8NVXX9GtWzcWLlzI22+/rd1va3Z2dri7u3Px4kWra9bpdDRt2pQpU6aQlJTEsGHD8PX1xcfHhyNHjpCbmwtczdBafj9sqWbNmpia9iS71r2gqqAo5T/IX/uFpu1h/ax/lbq5Xq/Xfmeu/5ulKIqWIbazs8PZ2ZlNmzahVOS6hKgECSiFzZ28mE2n6evJLbDdUI6dQceKF2J4ot+DrFmzxmbHvRv07duX7777DoCuXbuyYsUK7bEePXrw7bff4ujoCBQFBP3798ff35/s7GzS09Oxs7NjyJAhvPbaa4SFhREWFkZiYiKbNm3imWeeISEhQTteq1at2LNnD9nZ2QC4uLiQkZHB0aNHCQsL07br2LEj69ev1z78Nm/eTJ8+fTh37hwAGzduJDo6moKCAuLi4hgwYECJw6nXCggIoFGjRuTk5JCVlcWZM2c4ffo0BoMBFxcXsrOziwUU5WUwGCgoKMBkMmEymcjJydGeg+ULiJeXF5cvX6awsJCgoCDGjh3L3Llz2blzJydPnsTf3x+dTscff/zBDz/8wNtvv01AQAA6nY6UlJQSAxxHR0dCQkKoWbMmbm5ufPnllwwfPpzZs2cDkJeXx6BBg1i0aBEANWrU4MiRI9pQvcVDDz1EXFyc9jyu/dJUs2ZNBg8ezBdffMHRo0cBePXVV5k0aZK2f2ZmJv7+/uTm5jJ79myeeuopCgoKeP3115k0aRIeHh4oilJlgeTNPPvss0yZMgVHR0dOnDhBzZo1sbOz4/z589r7+9ChQzz++ONs3769wu+Bm6lfvz4Zvg3RtRpos2MGnV7P5vlTre5TFAU3Nzd8fX0JDAwkMDAQf39//Pz88PPzs/q3j48PBoPBZtcjREVJQCmqxDfxJ3jt+4TSNyyjyb0b0q9FMJcvX6ZJkyacPHmyUhkuo9FYLFtzJ3N3d6ddu3Zs3LiRixcvAhAdHW01vzAvL4/XXnuNjz76CLPZjMFg4JVXXuGtt97SPpAefvhhFi9eTFxcHD179iQ5OZnnn3+en376SXu9DQYDvXr14pNPPuHXX39lwIABfPrppwwdOlQ71/UBJYDZbMZkMmn3hYWF4ebmxqFDh7QAVVEUvLy8cHJyIicnp1jg4ujoyNChQ+nZsyfdu3e3yrYCfPvtt8TGxmrz/YxGIz///DMuLi6kpKSQmprKggULWL16NTVq1ODixYukpaXh6OhIvXr1uHLlCgcPHqSwsBAPDw/y8/PJy8sjPz/fJsHJjYIcNzc3q7mOhw8f5ssvvyQ8PBxfX1/8/Pywt7fHx8eHCxcuAEU/c0vGEOCDDz7g5ZdfLpZ59/LyYteuXQQFBdG4cWP27t3L0KFDWb58OadOnSo2n3X9+vW0b98eKMqA//LLL9jb29OuXbvbIqNvMBgwm82YzWZiYmK49957iYqKok2bNkyaNIm3336b6tWr88svv9CwYUObndfd3R29my9OD08iqrY/vZoGERnsQYC7Pek5BST8eZmPViey93S6tk/zEA/6RgYREehGbT9n7Ax6oiev4dTlv+Y8qyrmgjyqJ8xjUO/utGzZEn9/fwkSxR1JAkpRZf6zNpH3Vxyu9HFe6VKHZzvU0v6/Z88eWrZsqWWjhDUXFxdcXFw4ffo0/fr149NPP2XkyJF8+eWX5Ofn4+7uTmFhIZmZmWzfvp0WLVpo+2ZmZuLm5oaDgwOurq6cOVO0gMrDw4OMjAxUVdUW/NSoUYN///vfDBo0iMGDB/P5559rx7k+oExISGDOnDnMnDmz2HC3JfgbP34848aN07Ju77zzDm+++SZDhgzBYDDw5ZdfaoGnRVBQED169GDQoEFERUUB8K9//Yv33nsPgHXr1tGuXbtir1GdOnU4fLjovTlo0CDmzZunPbZy5Uq6dOnC/fffT1xcHLt372bkyJFs3bq11NfeMvzt4OCAvb09iqKQlJRkFeTpdDoMBkOFh2IVRUGn01kdD9BeU71eT0BAAM2aNePAgQMkJiZiZ2eHh4cHZ8+e5b777mPGjBm4uLjQpEkTzp07x6RJk3j11VfJy8ujY8eObN68GSjKcF++fFn7/9/N29ub/Px80tLSbjhlRVEU6tevj5eXFxs2bLDJeS0/M88+47Cr3pD/DmiBh6ORXxLOkHg+E08nE0/GhNGwmhuD5v7G1mNFi7FeuDechyOD2Hc6HVd7I61relkHlIBOgTY1vVkw9B6bXKsQfxcJKEWV+ib+BON/3EeBWS3XnEq9TsGgU3irZwT9WgQXe3zhwoUMHGi7Yae7gbe3Nw0bNmTr1q0lDh8HBAQwceJEBg8eTGJiIvXq1cPJyUkbhv7www/57LPPOHLkCFCUnerWrRvjxo2jWbNmPPLII3z33Xds3ryZadOmERcXp32gBwcH89xzz/H555/j4eHBmTNnSEpKwsPDo9iKb29vbx566CGqVavG+++/T1ZWFoqicPjwYWrVKvriUFBQgKurK0ajkUuXLhULMqFoNXd+fr72xUKv1+Pn56cFwaqq4uHhwZEjR/D09NTOP3v2bJ5++mlUVUWv13PixAnOnj3Lpk2b2LVrF4cOHWLHjh0UFBQUew0twbCrqyt169bVht0tr4OrqyszZsxg4MCBbN26laFDh3Lo0CEAmjdvzuzZs2nWrBkLFixg0KBBzJ07lyFDhnD+/HmGDRvGTz/9pM3969u3L/Xq1ePSpUukpaUxf/58CgoKaNmyJcnJyVy4cKHYNV4fXJbHtQGaJZN8O2QkSxIcHExycjIFBQXEx8fz3nvvsWzZMgwGgzYlwdZfOO18Q/F/4j8AeDmZSM2y/kLgaNKzfnR7Dp3LZMBn24Gi6ZWWT9gnY8J4vXu9YgGlxapRbanl62LTaxbiVtKVvokQFRfbIphVo9oRFeYFFAWKN2N5PCrMi1Wj2pUYTAIMGDCAZ599ViaeX+PChQvo9XoGDhxISEhIscerVauGnZ0dZrOZ8PBwPvjgA9LT0/H29sbJyYmxY8eSnJxMTEwMRqMRJycnli5dSrNmzQAYN24cAB9//DE1atTAxeXqh9+JEycYM2YMBw4cYMuWLSQlJQGUWD4oJyeHefPmsWzZMi3zpaoqtWvX1srnvPzyy+Tk5PDee+9ZzROMjIwEirJQmZmZPPfccxw+fJixY8dSq1YtTp8+jVpUXxdFUbh06RIBAQEsWLCA3377jebNm/PUU09pc9QKCwupVq0akZGRvPDCC8ybN4/4+Hjs7e21c+p0OgYNGsSlS5e0OZQ6nY7t27dz4sQJ8vLymDt3LoqikJ6ezuDBg9Hr9URHR2vB5LBhw4iPj9deS0vmzDJc7evry48//qhlWVVV5auvvmLatGn4+PhQq1Yt8vPz8fHxIT4+nrNnz6IoCu3ataNJkybatVavXp3du3ejqiqFhYWkpqbSsmVL7TUDaNq0KWPGjGHEiBHExsbSuXNnq4ynu7s7Tk5Ot20wCfDnn3+yZs0aDAYDv//+O8uWLcPT05OUlBTOnj3L+vXr8fb2tuk5/aP7opqLXpPrg0mA7LxCEs9nEuB29b1T1nSNXqewcNsJm1ynEH+bW7KWXAi1qKTQ+Li9atupa4p11Al97Se17dQ16vi4vWriufQyHS83N7dchZlv5e3a1nSW2/VFmG/F7doONpabTqdTXVxcrF63atWqqfPmzdNKDlkKfU+ePFlV1aIi3IMGDapQl5Wb3SzlZmrVqqWV33Fzc1P1er3q4+Nj9fO+dOmS1vUnISHBqiPQ7t27VaPRqCqKog4ePFht0qTJTUvN6HQ61d3dXSvZ0rRpU/XHH39UL126pE6cONGqV/nmzZutrmPIkCEqUKwLyc36RdesWVONj4/Xtm3RooVqMBis9i8sLFRNJpNas2ZNNT8/Xx0zZkyxkk06nU5t2rSp9rNatmyZCkUda4YNG6b9rGNjY9X8/HytIHuXLl3UjIwMtX79+ioUtctMS0tTVVVVR40aZXUOS2eeO+lm6Y7j5eVVJX8P7O3t1cARc25aDqjB+P+padl56q8JZ0p8/J2f96uqqhZr4GC5tZ26pkx/94S4XcmQt/hbZOUWcDw1i7wCMyaDjlAvJ5zsyj8J/c8//6RRo0Zcvnz5by1QbllVaylfczOenp7awpmqUL9+fXr37s25c+c4cOAAycnJnDx5stT9hgwZQvfu3Wnbti3e3t64ublhNpt59NFH+eyzz6rseq/l4ODAlStXUFWVunXrsnnzZm24unHjxuzZs4eJEyfi5OTEzp07iYuLsyoCfi29Xq9lIS3bXD/vztvbm6ysLHJycpg+fTrTp0/nxIkTuLu7M2XKFIYPH06TJk3YvXu3tk9ycjKhoaH06tWLxYsXM3PmTN5++22tiPkjjzwCwOnTpzGZTFZVCYxGI126dGHLli0YjUZtugHAokWLiI2NZcSIEZw6dYo1a9ZYFay37P/444/z0UcfceXKFapVq4bZbObkyZNaMesHHniAQ4cOac+1bdu2rF+/XjvG448/zvz583F2diY0NJS9e/cSHBzMsmXLaNGiRZUWAr9TKSYHqo/69qYjItMfacL9jQLo9fFmq4U5FqUNeSvA3gldK/R3UIjbwt8c0ApRaevWrfvbWidaMlkjR45UAXXq1KlqtWrV1Af7PKJ6hzdR3cIaq0bfGiX2H7+2LaEtb76+vmpubq565MgRdcCAAaqbm5vV42FhYWq/fv1uWpD6VvQaLstNURS1evXqN8w2Xp+N6tWrl7ps2TL18uXLqqqq6syZM1WdTqc9n5CQEDUlJUWdNWuW2qVLlxIL2wcEBKjvv/++mpKSonbq1EkFihUs9/X1VY1Go1Um2lKEvDyvncFgUBs3bqzOnTvXqtc5FGWNX3rpJdVoNKpeXl7qnDlztNaOer1ea1G4ePHiYr8TkZGR2nGaNWtWrGXkxIkTtccbNmyoFhQUqD/88MPf/vOu6M3Ozk7t3bu3+vrrr6s6nU7LQNvq+E5BdW6anfxo9WFVVVX1zbiEG25TWobS0m5WiDuVzKEUd7x27doxderU0jesArVq1cLV1ZXExETaPxjLvL3ZODwymd9rDcSpzzu4P/IugU/MJPil76j21Bx8uz2L0as6QKl1Fyvq/Pnz2NvbU6tWLRYuXIher2fo0KEcPHgQf39/jh07RpMmTbTFJL/99ht+fn5Wx1Bvk4ELVVU5efIkmZmZ6PV67r//fl5//XWWLVvG/v37tZXUEyZMwN7enh9++IGVK1fi4uLCI488wsiRI3FxcSEhIYFRo0aRnJxMVFQUw4YNY/ny5cycOVOrYQhFGcyzZ88yevRofHx8tJXdDzzwAKdOneLKlSvExsaSkpJCfn4+WVlZ2r6WbGJ5XruCggL++OMPnnjiCS3D2b59e5KTkzl16hRpaWnk5+czffp0hg0bxpkzZ1i8eDFOTk5asfg5c+Zw4sTV+XdDhgxh586dNGzYkK5du2olg8aOHQsUlVayzIc1Go0kJCRgb29Pr169KvIjui3k5uayZs0a3n33XQwGA3379rXp71d+4Y1/pi/cG87zHcOZsvwg87cmV+o8eTas3SvErSZD3uKuoKoqDz/8MEuXLr1liwksw19DnhvNT+ddcKjRrNR+voqqoioKLll/cnD+OArSzt1wW1tc3+TJk3nllVe0+9LT07X6i6GhoaSmphbr7nI769evH/Pnz+fixYvUrl2bjIwMFi5cSP/+/blw4QLNmzcnOTkZOzs7cnNzadKkCZs3b9aCxqeffppPPvmE2rVr4+joyO+//46dnR3Tp09n9erVLFmyhNdee43mzZuzaNEitm3bVqbpArZmMpn47LPPGDx4MP7+/pw6dUp7bPPmzcTExODp6YmPjw8HDx4EICoqimrVqvHdd98RERHBnj170Ol0bNiwgb59+5KSkqJ1jrm+9JC4OaNvDQKfmFns/hfuDWdUp9pMX3WYj1Yn3vQYpQ15A/w8MpqIQDebXLMQt5oElOKukZGRQWRkJMeOHavSD0oHBwdycnIwGAzY1++IR+cRKHo9iq7sc59UcyE6VHI2zuP8tqU2zwi2aNGCvXv3kpOTw4ABAwgODmb58uUcOHDAao6nh4cH9957L3379uWdd95h7969Nr0OWwoJCSE5OVkLDrOzs4sVVN+6dSvR0dGYzWbs7OxISEggPDxce9xsNmvFvQHuu+8+lixZgqOjI2azmWrVqnHu3DmtPufZs2fp3bt3mWpQVpWePXsSFxcHFD1nPz8/cnJySExMpEaNGuzatYsRI0ZobTBNJhOrV68mKiqKX375ha+++opNmzZZBcY6nY6IiAhatWrF2rVrtVJRd7qwsDA+/vhjIiIiiIiI0LK4leXk7onXiHlWcyhHdqzFy53rMGNNIh+sLL3ersyhFHc7CSjFXeXgwYNERkaSk5OjBWn+/v6cPXvWpueJjY1l9Vkjjq36aSVqysuyn+vx9SR8Y9sh++rVq+Pi4sL+/fu1+/R6PcHBwURHR9O9e3eGDx9ORkYGffv2ZcWKFTb78K1K9erV48CBA0BRUfPt27cTGBgIFNXRfOmll9DpdPTr14+vv/4avV7PwoUL6devn1X7R0sGs2XLlmzdulUrTWSpz+ng4EBERATbt2//257rtXQ6HVFRUaSlpZGQkMDs2bMZNGgQ58+f5/z580ydOpVvv/221HaDBoNBKyl0t/L39y+xRmdlODo64j3kvyguPgAMi67BGz3qs+7Q+RIzk7tPXgbA08nEPTWKFpV1qudHn2ZBvLE0gdSsPC5m5bE96erivBAvR9aP7mCzaxbiVpOAUtx1vv/+e/r06QMU9Z4+c+YMJ06csFkWsFevXqxKysHzvudscjwAzyO/snvxf212PCiadA8qSgAAHiZJREFUHxcaGkp+fj7Hjx/H3d2dbdu2UadOHaBoFXJ4eHipq9JvR4GBgZw+fRq9Xs9LL73E4cOHiYuLw8PDg61bt1KnTh22bNlCp06dyMnJITg4mBMnTqDT6Rg9ejTvvfceffr0YenSpVaroHft2sVDDz30twxzVzWDwYCDgwMmkwmz2VxijVBxY81HTCbVoz5mFL55shWt/qqtW5LQsT8D0KqGJ98Mb13iNtuOpRI7ZxtQVIdy4D0hTOgZYfsLF+IWkYBS3JXGjBnD1KlTefXVV5k8ebLNjhsSEsKfl69QbfgsHO3tef7e2tQPdCUiwBUvZzs+XHWYD6/LWBx/r8cNj3f0fCYdP1gHhXnkfv8m547tv+G25TV8+HCmTp2Kq6srH374IaNGjUKn0/HYY4+h0+k4cOAAO3bsuG0W4FSWo6Mjw4YNo02bNrRt2xZ/f3+mTZvG6NGjgaKpCnv37iUsLEzbp1u3bvzvf/+jWbNmZGdna/MR70T16tWjY8eOPPLII9SqVYuxY8cyf/587XEvLy/Gjx/Ps88+S1paGkFBQXfkl4myaNCgAStWrNCy15WhKApfffUVkR160PlD27RyLIl0yhF3OgkoxV2psLCQhIQEvv76a6ZMmWL1mF6vx2g0YjAYtJvRaLS6mUwmjEYjdnZ2mEwmzp07R3JyMtnZ2VQfOBkloC7VPZ355fkYDpxJ59iFLB5tGVxiQNm0unux62tS3Z3xD0Tw8bojTFl+CNVcSG7yHlK+G2/zepqW4fi77Vfd19eX8+fPl2lbS8tERVHw8fFBVVXy8vLIycm5I+suWt6z19apDA0NZciQITzzzDN06dKF3bt3U7NmTTZs2MCkSZOYM2cOV65cwcXFBV9fX44ePVql12jp0e7u7s7ly5er9FzX0+l0dOjQgdWrV1fqOAaDgbi4OLp37w7AwM+2s+VYarnayJZGr1OICvOSXt7ijicBpbirqapKWlqaFiAaDIZKtWtctmEHI38tvjLbw9HI7je7lBhQlmRqn0b0aRZEhw/WkZx6NUv055ynKEg9dZM9y6+0eXXizn2N3N3d+eKLL5g5cyYbN260Co6bNm3Ktm3bMJlMQNGCpGHDhvH5559X6TVZivy3adNGa61pYXmdry8wfzvS6XQsXrzYqpzSyYvZdJq+nlwblvexM+hYNaod1T0dS99YiNuY1KEUdzVFUXB3d8fR0RGj0Vjp3t87LzuU2o+8NE4mPd0bBrA96aJVMKmaC3Fp2r1Sx76Ws7Oz9u8hQ4bw/fff069fP9zdi2dM71Rubm6MHDmSadOm8dJLL2nBE0BwcDBHjhzRFqHs37+fdu3aWe2v1xeVeLoTg0mAzp078+CDD7Jq1Spmz56tvb8VRWH37t04OjrSunVrvvzySx588MEqDyYt5wa0YFIx2mP0rYEpoDZG3xro7RxxdXUFoG7dulV6Lf3796/QfpZh7utrc1b3dOTfNp7n+FbPCAkmxV1B6hMIUQ5rD52v9HDXA40DcbIz8M2OE1b3Kzo9DmHNucT/Ver4Fvn5+XTr1o1169bx+eefM2/ePFxdXW/58GNVSktL44cffiAsLIwNGzZgMBj497//zf79+1m0aBHh4eEMHToUNzc3Zs2aRXZ2Ng4ODtjZ2XH58mUaNGiAh4cH69at+7ufSoV89913BAcH065dOxYuXIiTkxNr166ladOmzJo1i48//pht27axbVvR4g9nZ2eCgoKqdK5ofn4+Rq/quDTrgVN4SxQXH+svcqqKPucSNXPPYEjail1SEoGBgSQlJdn8Wq79glFWiqLwxRdf0K9fvxIfj20RzIXMXN5fUXqpoNK80qUO/VoEV/o4QtwOZMhbiDLKzC2g4YTllPQLU54h7x+ejiLMx5mWE1cVGzpTVZWTHzyMmm/bLjp36pBueURHRxMXF6f1/t66dSudO3fWutk4OTnxxhtvMGbMGAAee+wxFi1a9Lddr615eHiwcuVKIiMjAUhKSqJHjx4cOHAAo9GIq6ur1o2nqjSL6cypwJiyFflHRUUhyJBB/Mcv4aYvICUlpUqvryxmz57N8OHDS93um/gTjP9xHwVmtVxfMvU6BYNO4a2eERJMiruKDHkLUUbJqVklBpPlEe7rTNNgD5b+/meJ87AURcHgEVDJs1z166+/oqoqZrOZDh3u7hp3GRkZnDp1itTUVB5++GFiYmLIysrC2dkZnU5HVlYWv/zyC+np6eh0Oj788EOcnJz+7su2mUuXLtG8eXPs7Ozw8vIiLCyMAwcO0LdvXzIzM7lw4QItW7asknM3adKE2t2GkNrqGRxCGgPcNJgEUCnKWp7KcyRg6H8x1m1fJdfWrVu3Mm/70UcflSmYhKJM5apR7Yj6q3xQaVNhLI9HhXmxalQ7CSbFXUcCSiHKyBZ9dvu1KOrjvSj+xnUOFb2x0uex6NatG25ubsTGxrJ27VqbHbckJc1PDQ0NrdJzXuuPP/6gcePGeHt7s3jxYoKCgli8eDEZGRmkpKQQHR3Nxo0b8fb2pmXLlgQEBFj14r4bxMTEUFBQwMWLVwtmW3p/GwwGfvvtN5uf88knn+SEcz1yG/dB1RmglECyGJ0eVWfE2OZxXFs/YvPrs7e3x97evtTtJk+ezPPPP1+uY1f3dGTB0HtY+WJbBt4TQoiXI9f/FigUFS0feE8Iq0a1ZcHQe2TOpLgryRxKIcrIZKjc9y+jXqFXk2rsOXWZ/Wdu3JVGLcyv1Hmul56efkuGdq8dUreU6QkKCuL48eNERkayc+fOKr+Ga+l0OozGouDcZDLRtm1bDh48yIULF4iPj7+l13KrbNy4scT7bdk15lpt2rTh6+3JeHUvCsQquujNsp9Hu0HUCPDij+9n2ewaL126xOLFi7n//vtvuM2ECRO0qRAVEe7nwoSeEUwggqzcAo6nZpFXYMZk0BHq5STtFMU/gmQohSijUC+nYtmH8uhUzw8vZzu+3XHj7KSqqhRcOlOJs1w1bNgwTp48yddff22T45WVYrRH7x2CKaA22w//iWK014JJy6rqqhIREcH58+fp3bs3ycnJPPjggxgMBlxcXJg4cSKZmZm0adOmSq/h7xYaGsprr73G0qVLWbFiBY0bN66S87i4uLB97xG8uj5tu/m5qsrFGp1wCwwrfdsyWrdunTavtiSvvvoq48aNs9n5nOwMRAS60TTYg4hANwkmxT+GvNOFKCMnOwPBno4kX7xa6qd9bR8cTHqc//rQqOXrTLcG/kDRivAr+VeHyfs1r05OXiFxv5++4Tn02RdttiBn7ty5JCUl8eyzz9rkeNdzcnLiypUrODk5Ed68LSdMITjXbkmhg6dVpkpVVQounyXnaDyZu3+lMLXq2hru37+fTp06cfLkSS3IsdQ7tLOzY/DgwVov8FvBy8uL1NRULWN7Kxw/fpxJkyZZLcQKCgoiICDAppnZjIwMwp74NwWKjqia3vRqWo3IYA8C3O1Jzykg4c/LfLQ6kb2nrbPxEYGujO1Wj6bV3Sk0q2w5msq7v+zn5KUcUBR0egN2MYNhke2CvJUrV/LKK68wbdo0q5/DCy+8wHvvvVfpcmJCCFnlLUS5TPhxHwu2J2urOjeN6UCQR8nzoaInr+HU5aJOJgFu9mwa05Glv//Jy9/9UeL2ln6+LfTH6dOnD7m5uVXzJGzAycmJrKws3v1oNh9tOVemVb2oZlB0mE/v4+yyD8m3USb2duTi4kJGRgajR4/m/fffJyIign379gHc0uCyKguIuwSF4zlgOgD/fawZHo5Gfkk4Q+L5TDydTDwZE0bDam4MmvsbW48VrS6v6ePE0mfasP9MOrPWH8XOoOelTrVxczDSfeZGLmZdLcx+bZF/na5oMK2ir9u6deto164d9913HytWrEBVVZ566ik+/vhjCSaFsBEJKIUoh8RzGbekn++ePXu47777OHfuXIU/RLds2cLcuXP59NNPbXZ9lgClRo0aODXqTEb4faA3gFL22TOKaqawIJ829qf55t2RNru2azk7O9O1a1dGjBiBi4sLO3bsYNmyZaxYsaJKzncjitEeg0cAit6IWphPwaUzNi8JdSMnTpygevWiRWA7d+6kVatWNp1L6dFpOC7NeqDo9Hg5mUjNsm5h6WjSs350ew6dy2TAZ9sB+M+jTWkd5kW799eRmVt0LdXcHVj7cnvmbk5i0v/+qo+pmmnilE5suJ5Lly5x/Phxjh8/TmJiIsePH+fSpUvaeRRF0brzlPRxptfreeaZZ5gxYwZfffUV/fv3Z/DgwXz22WdaoCqEqDwZ8haiHML9XIip5V1l/Xxr+boA0KhRI3bt2kWPHj34/fffKxRUrlmzhuBg25YmKSwsJCIigjMejTDX64mqquXO8KiKDp3BxNbCGjR//HV2zp9o8xqZBoOBJUuWsGTJEpsetyyMXtVxbtoNh5rNMbgHlDD8f4Yrx3aSsesX8qtw+H/kyJGkpaWRkJBg8/qTXl5e2NdqqWWkrw8mAbLzCkk8n0mAW9EKa71O4d66fny/+5QWTAL8eTmHbcdS6RLhdzWgVHRccggkNrbkUldZWVkkJydrgebx48c5duwYR44cITk52ap4f2FhIUuWLGHGjBnExsbi5eVFp06dJJgUwsYkoBSinCb2akin6ettGlAadAoTezW0us/f359NmzYxcODACgVGb7zxhq0uz0qyvhpe0UUt7So8XPjXfikBrfGP6k1q/DKrPtSVZQkoKjtUWhrLPMWAgABydI749HiBPM8wbXi/pO2NHoGYIgNwiXyAUPsrbJ7+LIbcNK5csW3mMi4uzqbHu9aVAhUnN7+bbuNiZ6BBoBtbjhYFsyGejjiY9Bw4m1Fs2wNn04mu5Y2dQafVZz2Rmk1WbkGJi1qcnJyoX78+9evXL/HcmZmZWsCZlJSEh4cHUPR+6Nq1a7meqxCibOQrmhDldCv7+To4OPDtt9/y+uuvl+t4EyZMYNasWRVqPXcjer0eg5ufzVf1Glv3x+zoadOMUcOGDdm3bx+FhYUUFhayYcOGKstIjRo1igzfRngO+IBct78ywqVMAbAU9U7KNhI0YjbOjbvY/LoURWHcuHGsXbuWxYsX4+3tbbNj59m5lfpl4q0HG+Bg0vOftUWdo9wdi96LadnFvzikZeej0ym4OlytwaoCx1MrVifU2dmZiIgIevTowXPPPVfhnt5CiLKTDKUQFXAr+/nqdDreeecd6tSpwxNPPIHZbC414xYcHExwcLBNs35ms5laj/yLXEWHs52BkR3DqR/oSkSAK17OdjdsOxnbojr97wkh1MuRArPK4bMZfLLhGGsPnS/KVOr0eHcbydmvyxc030xCQgLt27cnMDAQDw8PMjMzbZ6l9PDwwNnZmcUHMvHqNpICVUXRly9jq+j0qKqKU4fheAaGcPiHmTa7PlVVCQoK4siRIyxZsoQLFy7Y7NilFd9/qXNtejWtxrgf9xZb5X3T7yLXPWaLZgJCiFtDAkohKui5DuF4O9vdsn6+AwcOJDQ0lJ49e5KRkXHD1budOnWif//+XL58WVusYAsNo7uQ5lUTBfBwNPFYy2AOnElnxf5zPNqy5OcwqlNtXrg3nIXbkpn8v4PYGXQ8HhXK54NbMGLhTpbvO4ui02MX0hiDV5C2qtcWUlJSqqw3tIuLC+np6fhF9San4YNA5Yf/c+t0xbNFEhfjf7LVZZa5jWB5OdrfOPP9wr3hPN8xnCnLDzJ/a7J2/+W/MpPuTsX3dXM0YjarpF+xLupf2WYCQohbR35bhaiEW93PNyYmhh07dlCjRo0bFgmPiYnBZDIRHx9vs2DSycmJi571Uc1FQeypyzk0emsF/eZsY8rygzfc75HmQfyWdJE34vay6cgFVh88z5Pzd5Cek0/fZtW07VRzIZ4tH7TJtVqud+zYsSxcuJB3332XOnXq2OzY8FcNxkYtya7Xw2bD/6qq4tR2CIZS5iaWh52dHTExMYwbN47WrVvb5Jgmk4nBfXtQLJ1IUTA5qlNtpq86zMfrjlo9lnwxm5y8Qur6uRTbr66/C8cvZln1t1coaiYghLgzSEApRCXd6n6+NWvWJD4+nrZt21plxRRFwWg0Eh0dDcDChQsr+IyKVklbGI1GTCYTZv96N68zWYKCQpWMXOusU26BmdyCQuvgQafHGNLEZjUBs7KycHd3JygoiO7du5OWlmaT414rrXY3+Gv4/7X76jL/iZbsfL0Tx9/rwYv3hpe4z+CoUFaPaseht+/jt7H38s6DDXC1L3qtlb+KenveZ7tC9Hl5eSxZsoThw4dz5kzF634qioJOp+PNN98kMzOT6VMmEeJpHeyN7FiLUZ1qM2NNIh+VMPWh0Kyy+uA5ukb442S6+j4KdLOnVZgXy/eetdo+2MtRuswIcQeR31YhbORW9vN1d3dn+fLlPPfcc/zf//2fdv8HH3xAx44dAbQahKXR64vm8ZnNZkwmEy1atKBt27ZERUXRunVrvLy8yMwtoOGE5SXkpG7u8y1J/KtbPR5pXp3/7T2DnVHPiLZhuNgb+XzLcevrcPMHgx3YqE7jq6++apPjXM/BwQGTTwgONZoBZR/+f717PZ5oU4M5G4+x6cgFwn2dGdW5No2C3Og9awsFZhV0ehxqNLPZ8L+qqvj5+VUqi6rT6QgJCeHrr7/mnnvu0e7vUMdXK/I/LLoGL3euw7pD51l78DxNq7tbHWP3yaJV99NXHSbu2WjmPt7ir8LmOkZ1rs2lrHzmbErSttfrFDrU9q3wNQshbj0JKIWoApZ+vlXJaDTyySefUK9ePV566SVUVaVdu3ba456eniV2SjEajeTnF2UNvb29adeuHdHR0URFRdGkSZMSV4Ynp2aVO5gEmLv5OFfyzbzdM4IpfRoBcCk7j6Hz4tmZfMlqW0VRMHgEkH8+qaRDlYteryc6Opr09HTS09M5evRo6TuVgaIouLq6kle7rdYZyDL8D+DhaCwxoPRztWNIVCjztx3Xai1uOnKB1Kw8ZsQ2pW9kEN/EF9WkVM2FuEXeT+qKT2xyza1bt6ZJkya4uroyadKkMu9n6egzYsQIpk6dipOTdUay/z3BfLH1OFDUpx6gfR1f2tcpHgiGjv0ZgKMpWcT+31Ze61aPj/s3o8CssvVoKsN/2WnVJafQrDKglW1rqAohqpYElELcwRRF4cUXXyQ8PJxly5YREXG1nNG6desoLCzUFuYoikK9evVo3749UVFRtGnThpCQkDINM1d0te3DkUGMv78+87Yms+7weUx6Hb2bVWPOoOY8tXAnGxKtVx7rDLYpc1RYWMj8+fMJDg7mjz/+oEmTJjY5rqqqnDt3jsCHmpdr+L9pdQ8Meh3rDlkvElp94BwA3Rr4awGlotNjF9rMJtcLEBsby8iRI1m+fHmZA0q9Xo+npycLFiy4Yd3Ga4v8x87ZVubr2Xs6XeucU+K5ryvyL4S4M0hAKcRdoEePHvTo0cPqvrp165Kfn09MTAxt2rThnnvuwdXVtULHr8hqW1d7A2/1bMA3O04y8dcD2v3rDqfwzZOtePehhsRMXWu1T2hwEIfPHLbJQhdLsGzr+pOKyQGDe0C59rG8ftcH5gVmFbNZpa6/9c/F4BGAYrS3SZtGZ2dnAFq1akV4eDiJicXnN1pYCrX37t2bTz75BE9Pz5se+1YV+RdC3P5kUY4Qd6kPP/yQ1atXM2HCBDp37lzhYBKKVtuWd7lMTR9nHEx69py6XOyxPafSqO7piOM1izMUYOe6/3HixAkGDhwIUOFg0NnZmV69enHvvfcSGRlZoWOURFEU3KrVLPfiocRzRd1hIkM8rO5vFuyBTqfg7mhd11FRFN6aPov+/ftrQ803WtVfGkv7TTc3N9q3b3/D7QwGA87Oznz11Vd8++23pQaTcGuL/Ashbm8SUAohSuVkZyC4nB/y59KLsmtNq3sUe6xpsDuXs/PIzrs6v9OyqjcoKIj58+ezc+dO2rRpA5S/xqPZbOb7779n5cqV5Zo3WBLLuQMDA3niiScY/MSwch/jwNkMth9LZXjbMLo38MfV3kCzYA/e7dWAgkJzicW+ezzwIAsXLuTChQvExcURGxurBZfXrsIvzYYNG7R/+/j43HC7mJgY9u/fz6OPPlr2J0ZR6azRXWqXa58bKa3IvxDi9iUBpRCiTDrU8bWqs9m+tg/dGvhrCzJq+TrTrYE/3Rr4Y2/UcTrtCr/uPcOjLYMZd399YsK9ubeuLx8/1owWoZ58Wsqq3mbNmrF+/XqWLl1KaGhouYLKsLAwbdi8sLCwQuWIdDodJpOJoUOHsm/fPv78808+/fRThj0xuNzHAnjmq13sTL7Ex/0j2TO+K18/eQ/L955l/5l0zqYXH9q2DJPb29vTs2dPq+CyX79+ZQ4ur61F+uyzz1K79tXgT6/XYzKZmDFjBqtWrSIoKKhCz+25DuFM6t0QO4Ou1Fqs19PrFOwMOib3bsizHWpV6PxCiL+fotqsKa8Q4m6WeC6Dzh9ezXZtGtOBII+Ss5bRk9dw6nIOdgYdg1qH0rtpNYI8HCgwqyRdyGLe1uPE/X7aap9Vo9recCFGXl4en3zyCePGjSMjI6PUNoozZ87kueeeA4oW0tjb25epDaVlZbO3tzcvvPACI0aMKJbVy8otoMENSih5OBrZ/WaXG7ahBPByMuHjYsefl3K4UlDIrjc68+ves4xZskfbRgH2Tuh601JTV65cYcWKFXz77bcsXbqUrKysEjsj7dq1i6ZNm2r/HzJkCPPmzQOgUaNGfPPNN9StW7eUV6ZsTl7M5l8/JLDxyAX0OuWmcystj8fU8mZir4YyzC3EHU4W5QghyuTaVb2FZpXoKWtL3Se3wMycjceYs/HYDbcpy6pek8nE888/z8CBA3nnnXeYMWMGwA07AWVmZmr/Tk1NLTWYtJRXqlevHq+88gqxsbHY2dmVuK1l+D/5YvZNj3kjqVl5pP5VImdwVCiOJgPzth632qYsRb0tmcuePXuWGFxantORI0esAsrGjRuj0+n417/+xZtvvonRePO+3OVhKfKfeC6DL7efYO3h85xIzbYKvpW/nl+H2r4MaBUsq7mFuEtIhlIIUWYnL2bTafp6qy43lWVn0LFqVLtyZaiOHj3KmDFj+P7774vV2nRycuLHH3/UCrynpKQQHBxMbm5usdXjln27d+/O6NGjad++fZmGxyf8uE8r6g1Fw/8OJj3Odgam9m3MT3tO83NCUWeatYfOcyXfTGyLokLzyanZuDoYaV/bh37NqzN1xSFmrb9aJ1OvUxh4TwgTKrjY5drg8tdff+WLL77ggQce0B7Py8sjNTWVgIDyrVSvqKou8i+EuD1IQCmEKJdv4k/w2vcJNjve5N4NK7wQY/PmzTz//PPs2rVLK3nTtGlTdu3aZbXdU089xdy5c7WC7pb5kUOGDOHFF1+0mldYFhUZ/n+0RXWeaFODah4OmFXYdzqNTzcmsfKvWpTXutnwvxBC3I7ka6IQolxiWwRzITOX91ccrvSxKruqt02bNsTHx7No0SJGjx7N6dOnSyyPlJmZqQWTfn5+jBo1iieffLJMpXFKUpHh/6/jT/L1X8XLb0SKegsh7lSSoRRCVMg38ScY/+M+CsxquQpb63UKBp3CWz0jbFoiJicnh08++YSwsDAefPBBq8cmTZrEDz/8wAsvvMDDDz9sk3mDt8vwvxBC3A4koBRCVNg/fVXv7TT8L4QQfycJKIUQlfZPXtX7n7WJNhv+lzqMQog7lQSUQgib+ieu6r3dhv+FEOJWk4BSCCFs4J8+/C+E+GeTgFIIIWzonzz8L4T455KAUgghqsg/cfhfCPHPJAGlEEIIIYSoFN3ffQFCCCGEEOLOJgGlEEIIIYSoFAkohRBCCCFEpUhAKYQQQgghKkUCSiGEEEIIUSkSUAohhBBCiEqRgFIIIYQQQlSKBJRCCCGEEKJSJKAUQgghhBCVIgGlEEIIIYSoFAkohRBCCCFEpUhAKYQQQgghKkUCSiGEEEIIUSkSUAohhBBCiEqRgFIIIYQQQlSKBJRCCCGEEKJSJKAUQgghhBCVIgGlEEIIIYSoFAkohRBCCCFEpUhAKYQQQgghKkUCSiGEEEIIUSkSUAohhBBCiEqRgFIIIYQQQlSKBJRCCCGEEKJSJKAUQgghhBCVIgGlEEIIIYSoFAkohRBCCCFEpUhAKYQQQgghKkUCSiGEEEIIUSkSUAohhBBCiEqRgFIIIYQQQlSKBJRCCCGEEKJSJKAUQgghhBCVIgGlEEIIIYSoFAkohRBCCCFEpUhAKYQQQgghKkUCSiGEEEIIUSn/DwHkEnJdsbrjAAAAAElFTkSuQmCC",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# access and visualize the device topology\n",
+ "print(ionq_device.properties.paradigm.connectivity)\n",
+ "nx.draw_kamada_kawai(ionq_device.topology_graph, with_labels=True, font_color=\"white\", arrows=True, arrowsize=30)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "With this information, you can write a circuit to run verbatim on an IonQ device. IonQ currently only supports verbatim compilation for the entire circuit, so every instruction in the circuit will need to be enclosed in a verbatim box. In other words, you cannot have any gates outside of the verbatim box. As well, note that IonQ native gates cannot be used outside of a verbatim box. To learn more about IonQ native gates and the best practice of using them, see the [Amazon Braket Developer Guide](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html?tag=local002-20#braket-qpu-partner-ionq) and [IonQ's documentation page](https://ionq.com/docs/getting-started-with-native-gates). "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "T : | 0 | 1 | 2 | 3 |\n",
+ " \n",
+ "q0 : -StartVerbatim-GPi(3.13)-MS(0.10, 0.20, 0.30)-EndVerbatim-\n",
+ " | | | \n",
+ "q1 : -*************-----------MS(0.10, 0.20, 0.30)-***********-\n",
+ "\n",
+ "T : | 0 | 1 | 2 | 3 |\n"
+ ]
+ }
+ ],
+ "source": [
+ "circ = Circuit().gpi(0,pi).ms(0, 1, 0.1, 0.2, 0.3)\n",
+ "verbatim_circ = Circuit().add_verbatim_box(circ)\n",
+ "print(verbatim_circ)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Counter({'10': 9, '01': 1})\n"
+ ]
+ }
+ ],
+ "source": [
+ "task = ionq_device.run(verbatim_circ, shots=10)\n",
+ "print(task.result().measurement_counts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Programming verbatim circuits onto the IQM device"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The native gates of IQM Garnet are PRx and CZ. Use these gates in verbatim circuits when submiting to IQM Garnet. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The native gates for the Garnet device are:\n",
+ "cz\n",
+ "prx\n"
+ ]
+ }
+ ],
+ "source": [
+ "# set up the IQM Garnet device\n",
+ "iqm_device = AwsDevice(Devices.IQM.Garnet)\n",
+ "\n",
+ "# list the native gate set\n",
+ "print(\"The native gates for the\", iqm_device.name, \"device are:\")\n",
+ "for gate in iqm_device.properties.paradigm.nativeGateSet:\n",
+ " print(gate)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The native gates need to be programmed on the physical edegs of the device. Let's take a look at the topology of IQM Garnet, shown in the figure below. The topology is a square lattice. The edges are bi-directional where a two-qubit gate can apply on (i,j) and (j,i) where i and j are indices of two qubits. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "fullyConnected=False connectivityGraph={'1': ['2', '4'], '2': ['5'], '3': ['4', '8'], '4': ['5', '9'], '5': ['6'], '6': ['7'], '8': ['9'], '10': ['11', '15', '5', '9'], '11': ['12', '16', '6'], '12': ['17', '7'], '13': ['14', '8'], '14': ['15', '18', '9'], '15': ['16', '19'], '16': ['17', '20'], '18': ['19'], '19': ['20']}\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# access and visualize the device topology\n",
+ "print(iqm_device.properties.paradigm.connectivity)\n",
+ "\n",
+ "nx.draw_networkx(\n",
+ " iqm_device.topology_graph,\n",
+ " pos={\n",
+ " 1: (-1,2), 2: (0,2),\n",
+ " 3: (-2,1), 4: (-1,1), 5: (0,1), 6: (1,1), 7: (2,1),\n",
+ " 8: (-2,0), 9: (-1,0), 10: (0,0), 11: (1,0), 12: (2,0),\n",
+ " 13: (-2,-1), 14: (-1,-1), 15: (0,-1), 16: (1,-1), 17: (2,-1),\n",
+ " 18: (-1,-2), 19: (0,-2), 20: (1,-2),\n",
+ " },\n",
+ " arrows=False,\n",
+ " with_labels=True,\n",
+ " font_color=\"white\", \n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now, let's compose a verbatim circuit to IQM Garnet. The circuit below creates a Bell state. With verbatim compilation, you have control in preparing a quantum state. There is no gate optimization and you can experiment with different ways to create the quantum state."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "T : │ 0 │ 1 │ 2 │ 3 │ 4 │\n",
+ " ┌──────────────┐ \n",
+ "q1 : ───StartVerbatim───┤ PRx(1.57, 0) ├───●───────────────────────EndVerbatim───\n",
+ " ║ └──────────────┘ │ ║ \n",
+ " ║ ┌──────────────┐ ┌─┴─┐ ┌───────────────┐ ║ \n",
+ "q2 : ─────────╨─────────┤ PRx(1.57, 0) ├─┤ Z ├─┤ PRx(-1.57, 0) ├────────╨────────\n",
+ " └──────────────┘ └───┘ └───────────────┘ \n",
+ "T : │ 0 │ 1 │ 2 │ 3 │ 4 │\n"
+ ]
+ }
+ ],
+ "source": [
+ "circ = Circuit().prx(1, pi/2, 0).prx(2, pi/2, 0).cz(1,2).prx(2, -pi*0.5, 0)\n",
+ "verbatim_circ = Circuit().add_verbatim_box(circ)\n",
+ "print(verbatim_circ)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Conclusion \n",
+ "This notebook introduced the basic functionality of verbatim compilation of Amazon Braket, that allows you to run circuits or subcircuits to be executed exactly as defined without any compiler modifications. You can find further information in the [Amazon Braket documentation](https://docs.aws.amazon.com/braket/). "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Task Summary\n",
+ "{'arn:aws:braket:us-west-1::device/qpu/rigetti/Ankaa-2': {'shots': 5000, 'tasks': {'COMPLETED': 5}}, 'arn:aws:braket:us-east-1::device/qpu/ionq/Harmony': {'shots': 10, 'tasks': {'COMPLETED': 1}}}\n",
+ "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
+ "Estimated cost to run this example: 6.400 USD\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Quantum Task Summary\")\n",
+ "print(t.quantum_tasks_statistics())\n",
+ "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n",
+ "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.3f} USD\")"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.10.10"
+ },
+ "vscode": {
+ "interpreter": {
+ "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2"
+ }
+ }
},
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# set up the Rigetti Ankaa-2 device\n",
- "rigetti = AwsDevice(Devices.Rigetti.Ankaa2)\n",
- "\n",
- "# access and visualize the device topology\n",
- "# note that device topology can change day-to-day based on edge fidelity data\n",
- "print(rigetti.properties.paradigm.connectivity.connectivityGraph)\n",
- "nx.draw_kamada_kawai(rigetti.topology_graph, with_labels=True, font_color=\"white\")"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "From the connectivity graph, you can see that qubits 11, 10, and 17 are connected in a line, and with the code in the next cell you can access their respective 2-qubit gate fidelities to make sure you have selected a high-quality qubit subset. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "{'fISWAP': 0.947781142837921, 'fISWAP_std_err': 0.00880368328462963}\n",
- "{'fISWAP': 0.5, 'fISWAP_std_err': 1.0}\n"
- ]
- }
- ],
- "source": [
- "print(rigetti.properties.provider.specs[\"2Q\"][\"10-11\"])\n",
- "print(rigetti.properties.provider.specs[\"2Q\"][\"10-17\"])"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "
\n",
- " Note: At the time when you run this notebook the fidelity numbers may be different as QPU devices are periodically recalibrated\n",
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "After selecting the qubits and validating their gate fidelities, you can now construct a circuit and run it. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : │ 0 │ 1 │ 2 │ 3 │ 4 │ 5 │\n",
- " ┌───────┐ ┌───────┐ ┌──────────┐ ┌───────┐ \n",
- "q10 : ───StartVerbatim───┤ ISWAP ├─┤ ISWAP ├─┤ Rx(3.14) ├─┤ ISWAP ├───EndVerbatim───\n",
- " ║ └───┬───┘ └───┬───┘ └──────────┘ └───┬───┘ ║ \n",
- " ║ ┌───┴───┐ │ ┌───┴───┐ ║ \n",
- "q11 : ─────────║─────────┤ ISWAP ├─────┼──────────────────┤ ISWAP ├────────║────────\n",
- " ║ └───────┘ │ └───────┘ ║ \n",
- " ║ ┌───┴───┐ ║ \n",
- "q17 : ─────────╨───────────────────┤ ISWAP ├───────────────────────────────╨────────\n",
- " └───────┘ \n",
- "T : │ 0 │ 1 │ 2 │ 3 │ 4 │ 5 │\n"
- ]
- }
- ],
- "source": [
- "circ = Circuit().iswap(10, 11).iswap(10, 17).rx(10, pi).iswap(10, 11)\n",
- "verbatim_circ = Circuit().add_verbatim_box(circ)\n",
- "print(verbatim_circ)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "PRAGMA INITIAL_REWIRING \"NAIVE\"\n",
- "DECLARE ro BIT[3]\n",
- "PRAGMA PRESERVE_BLOCK\n",
- "ISWAP 10 11\n",
- "ISWAP 10 17\n",
- "RX(3.141592653589793) 10\n",
- "ISWAP 10 11\n",
- "PRAGMA END_PRESERVE_BLOCK\n",
- "MEASURE 10 ro[0]\n",
- "MEASURE 11 ro[1]\n",
- "MEASURE 17 ro[2]\n",
- "Counter({'010': 811, '000': 115, '100': 52, '110': 14, '011': 6, '001': 1, '111': 1})\n"
- ]
- }
- ],
- "source": [
- "result = rigetti.run(verbatim_circ, shots=1000, disable_qubit_rewiring=True).result()\n",
- "compiled_program = result.additional_metadata.rigettiMetadata.compiledProgram\n",
- "print(compiled_program)\n",
- "print(result.measurement_counts)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "As expected, the program is faithfully executed exactly as it was defined."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Defining verbatim subcircuits "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In some situations, you might only be interested in executing parts of your circuits verbatim, and have the compiler nativize and optimize the rest. The next example demonstrates how to do this. Let's get started by defining the subcircuit we want to execute verbatim."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {},
- "outputs": [],
- "source": [
- "verbatim_subcirc = Circuit().rx(10,pi).rx(10,pi)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Next, define the part of the circuit you want to compiler to process, so you don't have to worry about nativizing gates. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {},
- "outputs": [],
- "source": [
- "subcirc1 = Circuit().cnot(10,11).cnot(10,17)\n",
- "subcirc2 = Circuit().cnot(10,17).cnot(10,11)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Finally, put everything together"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : │ 0 │ 1 │ 2 │ 3 │ 4 │ 5 │ 6 │ 7 │\n",
- " ┌──────────┐ ┌──────────┐ \n",
- "q10 : ───●─────●─────StartVerbatim───┤ Rx(3.14) ├─┤ Rx(3.14) ├───EndVerbatim─────●─────●───\n",
- " │ │ ║ └──────────┘ └──────────┘ ║ │ │ \n",
- " ┌─┴─┐ │ ║ ║ │ ┌─┴─┐ \n",
- "q11 : ─┤ X ├───┼───────────║──────────────────────────────────────────║──────────┼───┤ X ├─\n",
- " └───┘ │ ║ ║ │ └───┘ \n",
- " ┌─┴─┐ ║ ║ ┌─┴─┐ \n",
- "q17 : ───────┤ X ├─────────╨──────────────────────────────────────────╨────────┤ X ├───────\n",
- " └───┘ └───┘ \n",
- "T : │ 0 │ 1 │ 2 │ 3 │ 4 │ 5 │ 6 │ 7 │\n"
- ]
- }
- ],
- "source": [
- "circ = subcirc1.add_verbatim_box(verbatim_subcirc).add_circuit(subcirc2)\n",
- "print(circ)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "PRAGMA INITIAL_REWIRING \"NAIVE\"\n",
- "DECLARE ro BIT[3]\n",
- "PRAGMA PRESERVE_BLOCK\n",
- "RX(1.5707963267948966) 10\n",
- "RZ(4.71238898038469) 10\n",
- "ISWAP 10 11\n",
- "RZ(1.5707963267948966) 10\n",
- "RZ(3.141592653589793) 11\n",
- "ISWAP 10 17\n",
- "RX(1.5707963267948966) 11\n",
- "RZ(1.5707963267948966) 10\n",
- "RX(1.5707963267948966) 10\n",
- "RZ(4.71238898038469) 10\n",
- "ISWAP 10 17\n",
- "RX(3.141592653589793) 10\n",
- "RX(3.141592653589793) 10\n",
- "RZ(3.141592653589793) 17\n",
- "RZ(1.5707963267948966) 10\n",
- "RX(1.5707963267948966) 17\n",
- "ISWAP 10 17\n",
- "RZ(1.5707963267948966) 10\n",
- "RX(1.5707963267948966) 10\n",
- "RZ(4.71238898038469) 10\n",
- "ISWAP 10 17\n",
- "RZ(1.5707963267948966) 10\n",
- "RZ(3.141592653589793) 17\n",
- "ISWAP 10 11\n",
- "RX(1.5707963267948966) 17\n",
- "RZ(1.5707963267948966) 10\n",
- "RX(1.5707963267948966) 10\n",
- "RZ(4.71238898038469) 10\n",
- "ISWAP 10 11\n",
- "RZ(3.141592653589793) 11\n",
- "RX(1.5707963267948966) 11\n",
- "PRAGMA END_PRESERVE_BLOCK\n",
- "MEASURE 17 ro[2]\n",
- "MEASURE 10 ro[0]\n",
- "MEASURE 11 ro[1]\n",
- "Counter({'000': 583, '001': 207, '010': 60, '100': 53, '110': 29, '011': 29, '111': 22, '101': 17})\n"
- ]
- }
- ],
- "source": [
- "result = rigetti.run(circ, shots=1000, disable_qubit_rewiring=True).result()\n",
- "compiled_program = result.additional_metadata.rigettiMetadata.compiledProgram\n",
- "print(compiled_program)\n",
- "print(result.measurement_counts)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Inspecting the compiled program, you can see that the `cnot` gates were nativized, however, the two `rx` gates in the middle of the circuit remain unaltered, and were not removed by the compiler. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Programming verbatim circuits onto the IonQ device"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "IonQ also supports verbatim compilation. Because qubits in the IonQ device have all-to-all connection, there is no restriction in qubit connectivity; all qubit pairs are available for 2-qubit gates. Because there is no circuit optimization or gate decomposition in verbatim compilation, all gates in the circuit must be native gates. Let's look at IonQ's native gate set."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 23,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "The native gates for the Aria 1 device are:\n",
- "GPI\n",
- "GPI2\n",
- "MS\n"
- ]
- }
- ],
- "source": [
- "# set up the IonQ Aria 1 device\n",
- "ionq_device = AwsDevice(Devices.IonQ.Aria1)\n",
- "\n",
- "# list the native gate set\n",
- "print(\"The native gates for the\", ionq_device.name, \"device are:\")\n",
- "for gate in ionq_device.properties.paradigm.nativeGateSet:\n",
- " print(gate)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In `device.property`, you can see `fullyConnected=True`, showing that qubits are fully connected. This manifests as the device having a complete topology graph."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "fullyConnected=True connectivityGraph={}\n"
- ]
- },
- {
- "data": {
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",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# access and visualize the device topology\n",
- "print(ionq_device.properties.paradigm.connectivity)\n",
- "nx.draw_kamada_kawai(ionq_device.topology_graph, with_labels=True, font_color=\"white\", arrows=True, arrowsize=30)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "With this information, you can write a circuit to run verbatim on an IonQ device. IonQ currently only supports verbatim compilation for the entire circuit, so every instruction in the circuit will need to be enclosed in a verbatim box. In other words, you cannot have any gates outside of the verbatim box. As well, note that IonQ native gates cannot be used outside of a verbatim box. To learn more about IonQ native gates and the best practice of using them, see the [Amazon Braket Developer Guide](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html?tag=local002-20#braket-qpu-partner-ionq) and [IonQ's documentation page](https://ionq.com/docs/getting-started-with-native-gates). "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : | 0 | 1 | 2 | 3 |\n",
- " \n",
- "q0 : -StartVerbatim-GPi(3.13)-MS(0.10, 0.20, 0.30)-EndVerbatim-\n",
- " | | | \n",
- "q1 : -*************-----------MS(0.10, 0.20, 0.30)-***********-\n",
- "\n",
- "T : | 0 | 1 | 2 | 3 |\n"
- ]
- }
- ],
- "source": [
- "circ = Circuit().gpi(0,pi).ms(0, 1, 0.1, 0.2, 0.3)\n",
- "verbatim_circ = Circuit().add_verbatim_box(circ)\n",
- "print(verbatim_circ)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 26,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Counter({'10': 9, '01': 1})\n"
- ]
- }
- ],
- "source": [
- "task = ionq_device.run(verbatim_circ, shots=10)\n",
- "print(task.result().measurement_counts)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Programming verbatim circuits onto the IQM device"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The native gates of IQM Garnet are PRx and CZ. Use these gates in verbatim circuits when submiting to IQM Garnet. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "The native gates for the Garnet device are:\n",
- "cz\n",
- "prx\n"
- ]
- }
- ],
- "source": [
- "# set up the IQM Garnet device\n",
- "iqm_device = AwsDevice(Devices.IQM.Garnet)\n",
- "\n",
- "# list the native gate set\n",
- "print(\"The native gates for the\", iqm_device.name, \"device are:\")\n",
- "for gate in iqm_device.properties.paradigm.nativeGateSet:\n",
- " print(gate)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The native gates need to be programmed on the physical edegs of the device. Let's take a look at the topology of IQM Garnet, shown in the figure below. The topology is a square lattice. The edges are bi-directional where a two-qubit gate can apply on (i,j) and (j,i) where i and j are indices of two qubits. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "fullyConnected=False connectivityGraph={'1': ['2', '4'], '2': ['5'], '3': ['4', '8'], '4': ['5', '9'], '5': ['6'], '6': ['7'], '8': ['9'], '10': ['11', '15', '5', '9'], '11': ['12', '16', '6'], '12': ['17', '7'], '13': ['14', '8'], '14': ['15', '18', '9'], '15': ['16', '19'], '16': ['17', '20'], '18': ['19'], '19': ['20']}\n"
- ]
- },
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# access and visualize the device topology\n",
- "print(iqm_device.properties.paradigm.connectivity)\n",
- "\n",
- "nx.draw_networkx(\n",
- " iqm_device.topology_graph,\n",
- " pos={\n",
- " 1: (-1,2), 2: (0,2),\n",
- " 3: (-2,1), 4: (-1,1), 5: (0,1), 6: (1,1), 7: (2,1),\n",
- " 8: (-2,0), 9: (-1,0), 10: (0,0), 11: (1,0), 12: (2,0),\n",
- " 13: (-2,-1), 14: (-1,-1), 15: (0,-1), 16: (1,-1), 17: (2,-1),\n",
- " 18: (-1,-2), 19: (0,-2), 20: (1,-2),\n",
- " },\n",
- " arrows=False,\n",
- " with_labels=True,\n",
- " font_color=\"white\", \n",
- ")"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now, let's compose a verbatim circuit to IQM Garnet. The circuit below creates a Bell state. With verbatim compilation, you have control in preparing a quantum state. There is no gate optimization and you can experiment with different ways to create the quantum state."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : │ 0 │ 1 │ 2 │ 3 │ 4 │\n",
- " ┌──────────────┐ \n",
- "q1 : ───StartVerbatim───┤ PRx(1.57, 0) ├───●───────────────────────EndVerbatim───\n",
- " ║ └──────────────┘ │ ║ \n",
- " ║ ┌──────────────┐ ┌─┴─┐ ┌───────────────┐ ║ \n",
- "q2 : ─────────╨─────────┤ PRx(1.57, 0) ├─┤ Z ├─┤ PRx(-1.57, 0) ├────────╨────────\n",
- " └──────────────┘ └───┘ └───────────────┘ \n",
- "T : │ 0 │ 1 │ 2 │ 3 │ 4 │\n"
- ]
- }
- ],
- "source": [
- "circ = Circuit().prx(1, pi/2, 0).prx(2, pi/2, 0).cz(1,2).prx(2, -pi*0.5, 0)\n",
- "verbatim_circ = Circuit().add_verbatim_box(circ)\n",
- "print(verbatim_circ)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Conclusion \n",
- "This notebook introduced the basic functionality of verbatim compilation of Amazon Braket, that allows you to run circuits or subcircuits to be executed exactly as defined without any compiler modifications. You can find further information in the [Amazon Braket documentation](https://docs.aws.amazon.com/braket/). "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 27,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Task Summary\n",
- "{'arn:aws:braket:us-west-1::device/qpu/rigetti/Ankaa-2': {'shots': 5000, 'tasks': {'COMPLETED': 5}}, 'arn:aws:braket:us-east-1::device/qpu/ionq/Harmony': {'shots': 10, 'tasks': {'COMPLETED': 1}}}\n",
- "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
- "Estimated cost to run this example: 6.400 USD\n"
- ]
- }
- ],
- "source": [
- "print(\"Quantum Task Summary\")\n",
- "print(t.quantum_tasks_statistics())\n",
- "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n",
- "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.3f} USD\")"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Python 3 (ipykernel)",
- "language": "python",
- "name": "python3"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.10.10"
- },
- "vscode": {
- "interpreter": {
- "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2"
- }
- }
- },
- "nbformat": 4,
- "nbformat_minor": 4
+ "nbformat": 4,
+ "nbformat_minor": 4
}
diff --git a/examples/hybrid_jobs/0_Creating_your_first_Hybrid_Job/0_Creating_your_first_Hybrid_Job.ipynb b/examples/hybrid_jobs/0_Creating_your_first_Hybrid_Job/0_Creating_your_first_Hybrid_Job.ipynb
index 29470f399..842668156 100644
--- a/examples/hybrid_jobs/0_Creating_your_first_Hybrid_Job/0_Creating_your_first_Hybrid_Job.ipynb
+++ b/examples/hybrid_jobs/0_Creating_your_first_Hybrid_Job/0_Creating_your_first_Hybrid_Job.ipynb
@@ -1,644 +1,644 @@
{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Creating your first Hybrid Job\n",
- "\n",
- "\n",
- "This tutorial provides an introduction to running hybrid quantum-classical algorithms using\n",
- "PennyLane on Amazon Braket . With Amazon Braket, you gain access to both real quantum devices and\n",
- "scalable classical compute, enabling you to push the boundaries of your algorithm.\n",
- "\n",
- "In this tutorial, we'll walk through how to create your first hybrid quantum-classical algorithms on AWS.\n",
- "With a single line of code, we'll see how to scale from PennyLane simulators on your laptop to running full-scale experiments on AWS that leverage both powerful classical compute and quantum devices.\n",
- "You'll gain understanding of the hybrid jobs queue, including QPU priority queuing, and learn how to scale classical resources for resource-intensive tasks. \n",
- "We hope these tools will empower you to start experimenting today with hybrid quantum algorithms!\n",
- "\n",
- "\n",
- "\n",
- "## Amazon Braket Hybrid Jobs\n",
- "\n",
- "Amazon Braket Hybrid Jobs offers a way for you to run hybrid quantum-classical algorithms that\n",
- "require both classical resources and quantum processing units (QPUs). Hybrid Jobs is designed to\n",
- "spin up the requested classical compute, run your algorithm, and release the instances after\n",
- "completion so you only pay for what you use. This workflow is ideal for long-running iterative\n",
- "algorithms involving both classical and quantum resources. Simply package up your code into a single\n",
- "function, create a hybrid job with a single line of code, and Braket will schedule it to run as soon\n",
- "as possible without interruption.\n",
- "\n",
- "Hybrid jobs have a separate queue from quantum tasks, so once your algorithm starts running, it will\n",
- "not be interrupted by variations in the quantum task queue. This helps your long-running algorithms\n",
- "run efficiently and predictably. Any quantum tasks created from a running hybrid job will be run\n",
- "before any other quantum tasks in the queue. This is particularly beneficial for iterative hybrid\n",
- "algorithms where subsequent tasks depend on the outcomes of prior quantum tasks. Examples of such\n",
- "algorithms include the Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum\n",
- "Eigensolver (VQE), or Quantum Machine Learning (QML). You can also monitor your algorithm's progress in near-real\n",
- "time, enabling you to keep track of costs, budget, or custom metrics such as training loss or\n",
- "expectation values.\n",
- "\n",
- "Importantly, on specific QPUs, running your algorithm in Hybrid Jobs benefits from [parametric compilation](https://docs.aws.amazon.com/braket/latest/developerguide/braket-jobs-parametric-compilation.html). \n",
- "This reduces the overhead associated with the computationally expensive compilation step by compiling a circuit only once and not for every iteration in your hybrid algorithm. \n",
- "This reduces the total runtime for many variational algorithms by up to 10x.\n",
- "For long-running hybrid jobs, Braket automatically uses the updated calibration data from the hardware provider when compiling your circuit to ensure the highest quality results.\n",
- "\n",
- "## Getting started with PennyLane\n",
- "\n",
- "\n",
- "Let’s setup an algorithm that makes use of both classical and quantum resources. We adapt the [PennyLane qubit rotation tutorial](https://pennylane.ai/qml/demos/tutorial_qubit_rotation).\n",
- "\n",
- "First, we define a quantum simulator to run the algorithm on. In this example, we will use the Braket local simulator before moving onto a QPU."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [],
- "source": [
- "import pennylane as qml\n",
- "from pennylane import numpy as np\n",
- "\n",
- "device = qml.device(\"braket.local.qubit\", wires=1)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now we define a circuit with two rotation gates and measure the expectation value in the $Z$-basis"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {},
- "outputs": [],
- "source": [
- "@qml.qnode(device)\n",
- "def circuit(params):\n",
- " qml.RX(params[0], wires=0)\n",
- " qml.RY(params[1], wires=0)\n",
- " return qml.expval(qml.PauliZ(0))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Finally, we create a classical-quantum loop that uses gradient descent to minimize the expectation value.\n",
- "\n",
- "We add the ``log_metric`` function from Braket to record the training progress (see [metrics\n",
- "documentation](https://amazon-braket-sdk-python.readthedocs.io/en/stable/_apidoc/braket.jobs.metrics.html)).\n",
- "When running on AWS, ``log_metric`` records the metrics in [Amazon CloudWatch](https://aws.amazon.com/cloudwatch/), which is accessible\n",
- "through the Braket console page or the Braket SDK. When running locally on your laptop,\n",
- "``log_metric`` prints the iteration numbers.\n",
- "\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {},
- "outputs": [],
- "source": [
- "from braket.jobs.metrics import log_metric\n",
- "\n",
- "\n",
- "def qubit_rotation(num_steps=10, stepsize=0.5):\n",
- " opt = qml.GradientDescentOptimizer(stepsize=stepsize)\n",
- " params = np.array([0.5, 0.75])\n",
- "\n",
- " for i in range(num_steps):\n",
- " # update the circuit parameters\n",
- " params = opt.step(circuit, params)\n",
- " expval = circuit(params)\n",
- "\n",
- " log_metric(metric_name=\"expval\", iteration_number=i, value=expval)\n",
- "\n",
- " return params"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "To run the entire algorithm, we call the `qubit_rotation`` function to see that it runs correctly."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Metrics - timestamp=1700084056.91118; expval=0.38894534132396147; iteration_number=0;\n",
- "Metrics - timestamp=1700084056.9852457; expval=0.12290715413453956; iteration_number=1;\n",
- "Metrics - timestamp=1700084057.0590365; expval=-0.09181374013482171; iteration_number=2;\n",
- "Metrics - timestamp=1700084057.128326; expval=-0.2936094099948542; iteration_number=3;\n",
- "Metrics - timestamp=1700084057.1863492; expval=-0.5344079938678078; iteration_number=4;\n"
- ]
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Creating your first Hybrid Job\n",
+ "\n",
+ "\n",
+ "This tutorial provides an introduction to running hybrid quantum-classical algorithms using\n",
+ "PennyLane on Amazon Braket . With Amazon Braket, you gain access to both real quantum devices and\n",
+ "scalable classical compute, enabling you to push the boundaries of your algorithm.\n",
+ "\n",
+ "In this tutorial, we'll walk through how to create your first hybrid quantum-classical algorithms on AWS.\n",
+ "With a single line of code, we'll see how to scale from PennyLane simulators on your laptop to running full-scale experiments on AWS that leverage both powerful classical compute and quantum devices.\n",
+ "You'll gain understanding of the hybrid jobs queue, including QPU priority queuing, and learn how to scale classical resources for resource-intensive tasks. \n",
+ "We hope these tools will empower you to start experimenting today with hybrid quantum algorithms!\n",
+ "\n",
+ "\n",
+ "\n",
+ "## Amazon Braket Hybrid Jobs\n",
+ "\n",
+ "Amazon Braket Hybrid Jobs offers a way for you to run hybrid quantum-classical algorithms that\n",
+ "require both classical resources and quantum processing units (QPUs). Hybrid Jobs is designed to\n",
+ "spin up the requested classical compute, run your algorithm, and release the instances after\n",
+ "completion so you only pay for what you use. This workflow is ideal for long-running iterative\n",
+ "algorithms involving both classical and quantum resources. Simply package up your code into a single\n",
+ "function, create a hybrid job with a single line of code, and Braket will schedule it to run as soon\n",
+ "as possible without interruption.\n",
+ "\n",
+ "Hybrid jobs have a separate queue from quantum tasks, so once your algorithm starts running, it will\n",
+ "not be interrupted by variations in the quantum task queue. This helps your long-running algorithms\n",
+ "run efficiently and predictably. Any quantum tasks created from a running hybrid job will be run\n",
+ "before any other quantum tasks in the queue. This is particularly beneficial for iterative hybrid\n",
+ "algorithms where subsequent tasks depend on the outcomes of prior quantum tasks. Examples of such\n",
+ "algorithms include the Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum\n",
+ "Eigensolver (VQE), or Quantum Machine Learning (QML). You can also monitor your algorithm's progress in near-real\n",
+ "time, enabling you to keep track of costs, budget, or custom metrics such as training loss or\n",
+ "expectation values.\n",
+ "\n",
+ "Importantly, on specific QPUs, running your algorithm in Hybrid Jobs benefits from [parametric compilation](https://docs.aws.amazon.com/braket/latest/developerguide/braket-jobs-parametric-compilation.html). \n",
+ "This reduces the overhead associated with the computationally expensive compilation step by compiling a circuit only once and not for every iteration in your hybrid algorithm. \n",
+ "This reduces the total runtime for many variational algorithms by up to 10x.\n",
+ "For long-running hybrid jobs, Braket automatically uses the updated calibration data from the hardware provider when compiling your circuit to ensure the highest quality results.\n",
+ "\n",
+ "## Getting started with PennyLane\n",
+ "\n",
+ "\n",
+ "Let’s setup an algorithm that makes use of both classical and quantum resources. We adapt the [PennyLane qubit rotation tutorial](https://pennylane.ai/qml/demos/tutorial_qubit_rotation).\n",
+ "\n",
+ "First, we define a quantum simulator to run the algorithm on. In this example, we will use the Braket local simulator before moving onto a QPU."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import pennylane as qml\n",
+ "from pennylane import numpy as np\n",
+ "\n",
+ "device = qml.device(\"braket.local.qubit\", wires=1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we define a circuit with two rotation gates and measure the expectation value in the $Z$-basis"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "@qml.qnode(device)\n",
+ "def circuit(params):\n",
+ " qml.RX(params[0], wires=0)\n",
+ " qml.RY(params[1], wires=0)\n",
+ " return qml.expval(qml.PauliZ(0))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Finally, we create a classical-quantum loop that uses gradient descent to minimize the expectation value.\n",
+ "\n",
+ "We add the ``log_metric`` function from Braket to record the training progress (see [metrics\n",
+ "documentation](https://amazon-braket-sdk-python.readthedocs.io/en/stable/_apidoc/braket.jobs.metrics.html)).\n",
+ "When running on AWS, ``log_metric`` records the metrics in [Amazon CloudWatch](https://aws.amazon.com/cloudwatch/), which is accessible\n",
+ "through the Braket console page or the Braket SDK. When running locally on your laptop,\n",
+ "``log_metric`` prints the iteration numbers.\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from braket.jobs.metrics import log_metric\n",
+ "\n",
+ "\n",
+ "def qubit_rotation(num_steps=10, stepsize=0.5):\n",
+ " opt = qml.GradientDescentOptimizer(stepsize=stepsize)\n",
+ " params = np.array([0.5, 0.75])\n",
+ "\n",
+ " for i in range(num_steps):\n",
+ " # update the circuit parameters\n",
+ " params = opt.step(circuit, params)\n",
+ " expval = circuit(params)\n",
+ "\n",
+ " log_metric(metric_name=\"expval\", iteration_number=i, value=expval)\n",
+ "\n",
+ " return params"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To run the entire algorithm, we call the `qubit_rotation`` function to see that it runs correctly."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Metrics - timestamp=1700084056.91118; expval=0.38894534132396147; iteration_number=0;\n",
+ "Metrics - timestamp=1700084056.9852457; expval=0.12290715413453956; iteration_number=1;\n",
+ "Metrics - timestamp=1700084057.0590365; expval=-0.09181374013482171; iteration_number=2;\n",
+ "Metrics - timestamp=1700084057.128326; expval=-0.2936094099948542; iteration_number=3;\n",
+ "Metrics - timestamp=1700084057.1863492; expval=-0.5344079938678078; iteration_number=4;\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "tensor([0.67679672, 2.32609342], requires_grad=True)"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qubit_rotation(5, stepsize=0.5)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Great! We see the expectation value change with each iteration number and the final parameters were returned as a list. Now, instead of running on our laptop, let’s submit this same function to be run on AWS."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Running as a hybrid job\n",
+ "\n",
+ "You can execute long-running algorithms asynchronously with Amazon Braket Hybrid Jobs, \n",
+ "which fully manages the classical infrastructure so you can focus on the algorithm. For example, you\n",
+ "can train a larger circuit, or increase the number of iterations. Note that each hybrid job has\n",
+ "at least a one minute startup time since it creates a containerized environment on Amazon EC2. So\n",
+ "for very short workloads, such as a single circuit or a batch of circuits, it may suffice for you to\n",
+ "use quantum tasks.\n",
+ "\n",
+ "We now show how you can go from running your local Python function to running it as a hybrid job.\n",
+ "\n",
+ "
\n",
+ " Note: Only Python 3.10 is supported by default. For other versions, you may use hybrid job scripts, or specify a custom container image from Amazon Elastic Container Registry (ECR) (see \n",
+ "containers documentation).\n",
+ "
\n",
+ "\n",
+ "\n",
+ "The first step to creating a hybrid job is to annotate which function you want to run with the\n",
+ "`@hybrid_job` decorator. Then you create the job by invoking the function as you would for normal\n",
+ "Python functions. However, the decorated function returns the hybrid job handle rather than the\n",
+ "result of the function. To retrieve the results after it has been completed, use `job.result()`.\n",
+ "\n",
+ "For algorithms that do not need priority queueing or scheduling for on-demand QPUs, you may specify the device as `local:/` or simply `None`. For example, when using a simulator that runs on the same classical host alongside the rest of your algorithm, such as the PennyLane Lightning CPU/GPU simulators, you may set `device=\"local:pennylane/lightning.qubit\"`. \n",
+ "\n",
+ "\n",
+ "The required device argument in the `@hybrid_job` decorator specifies the QPU that the hybrid job\n",
+ "will have priority access to.\n",
+ "The device string you give is accessible in the hybrid job instance as the environment variable ``\"AMZN_BRAKET_DEVICE_ARN\"``.\n",
+ "In the following code, we annotate the `qubit_rotation` function from above.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from braket.jobs import hybrid_job, save_job_result\n",
+ "\n",
+ "\n",
+ "@hybrid_job(device=\"local:braket/default\")\n",
+ "def qubit_rotation_hybrid_job(num_steps=1, stepsize=0.5):\n",
+ " device = qml.device(\"braket.local.qubit\", wires=1)\n",
+ "\n",
+ " @qml.qnode(device)\n",
+ " def circuit(params):\n",
+ " qml.RX(params[0], wires=0)\n",
+ " qml.RY(params[1], wires=0)\n",
+ " return qml.expval(qml.PauliZ(0))\n",
+ "\n",
+ " opt = qml.GradientDescentOptimizer(stepsize=stepsize)\n",
+ " params = np.array([0.5, 0.75])\n",
+ "\n",
+ " for i in range(num_steps):\n",
+ " # update the circuit parameters\n",
+ " params = opt.step(circuit, params)\n",
+ " expval = circuit(params)\n",
+ "\n",
+ " log_metric(metric_name=\"expval\", iteration_number=i, value=expval)\n",
+ "\n",
+ " return params"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we create a hybrid job by calling the function as usual. This returns an `AwsQuantumJob` object that contains the device ARN, region, and job name."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "AwsQuantumJob('arn':'arn:aws:braket:us-west-2:318845237731:job/qubit-rotation-hybrid-job-1700084057462')\n"
+ ]
+ }
+ ],
+ "source": [
+ "job = qubit_rotation_hybrid_job(num_steps=10, stepsize=0.5)\n",
+ "print(job)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The hybrid job automatically captures the function arguments as [hyperparameters](https://docs.aws.amazon.com/braket/latest/developerguide/braket-jobs-hyperparameters.html).\n",
+ "In this case, we set `num_steps = 10` and `stepsize = 0.5` as the hyperparameters."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can check the status with:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'QUEUED'"
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job.state()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Once the hybrid job starts, it will change the status to `RUNNING`. We can also check the hybrid job status in the Braket console.\n",
+ "\n",
+ "We can monitor the metrics in near-real time in the [Braket console page](https://console.aws.amazon.com/braket/) as shown below. \n",
+ "\n",
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "After the hybrid job completes, we can get the results with `job.result()`. For this example, it should take approximately 2 minutes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'result': tensor([0.03642036, 3.10081929], requires_grad=True)}"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job.result()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Any objects in the return statement are automatically captured by Braket. Note that the objects returned by the function must be a tuple with each element being serializable as text. \n",
+ "\n",
+ "Additionally, we can plot the metrics recording during the algorithm. Below we show the expectation value decreases with each iteration as expected."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "{'timestamp': [1700084189.268808, 1700084189.3246114, 1700084189.3840628, 1700084189.1557567, 1700084189.2123241, 1700084188.8748374, 1700084188.9313, 1700084188.9881024, 1700084189.0439024, 1700084189.099711], 'expval': [-0.9771543186187628, -0.9940804663947356, -0.9985062848699056, -0.7715298984378987, -0.9193547392516985, 0.38894534132396147, 0.12290715413453956, -0.09181374013482171, -0.2936094099948542, -0.5344079938678078], 'iteration_number': [7.0, 8.0, 9.0, 5.0, 6.0, 0.0, 1.0, 2.0, 3.0, 4.0]}\n"
+ ]
+ }
+ ],
+ "source": [
+ "# May need to wait a bit before metrics show up\n",
+ "# If metrics aren't there, try again after 5 seconds\n",
+ "import time\n",
+ "\n",
+ "time.sleep(10)\n",
+ "print(job.metrics())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "import pandas as pd\n",
+ "\n",
+ "df = pd.DataFrame(job.metrics())\n",
+ "df.sort_values(by=[\"iteration_number\"], inplace=True)\n",
+ "\n",
+ "plt.plot(df[\"iteration_number\"], df[\"expval\"], \"-o\", color=\"orange\")\n",
+ "plt.xlabel(\"iteration number\")\n",
+ "plt.ylabel(\"expectation value\")\n",
+ "plt.title(\"Simulator results\")\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Running on a QPU with priority\n",
+ "\n",
+ "The next step is to see how well the qubit rotation works on a real QPU. We\n",
+ "create a hybrid job with the Rigetti device as the priority QPU. We also increase the number of\n",
+ "steps to 10.\n",
+ "\n",
+ "Using hybrid jobs for iterative algorithms is very beneficial because you retain priority access to the\n",
+ "target QPU. So once your quantum tasks are created in the hybrid job, they run ahead of other tasks\n",
+ "waiting in the *quantum task queue*. This means your\n",
+ "algorithm will not be interrupted by other quantum tasks, so it will run more efficiently and\n",
+ "predictably. Quantum tasks submitted as part of a hybrid job have priority, and are aggregated in the *priority task queue*.\n",
+ "\n",
+ "Hybrid jobs have their own *hybrid jobs queue* so that only a single\n",
+ "hybrid job can run on a QPU at a time. Each QPU has its own hybrid jobs queue. Note that this is a different queue from the quantum tasks. For a single quantum circuit, or a batch of circuit, it’s\n",
+ "recommended to create quantum tasks instead of hybrid jobs. For more information on quantum tasks and hybrid jobs queue see the [Amazon Braket documentation](https://docs.aws.amazon.com/braket/latest/developerguide/braket-task-when.html).\n",
+ "\n",
+ "To get QPU priority, you must ensure that the device ARN used within the function matches that\n",
+ "specified in the decorator. For convenience, you can use the helper function ``get_device_arn()`` to\n",
+ "automatically capture the device ARN declared in ``@hybrid_job``.\n",
+ "\n",
+ "
\n",
+ " Note: Only hybrid jobs running on AWS receive priority. Hybrid jobs running locally, or with a mismatched device ARN do not get priority task queueing. \n",
+ "
\n",
+ "\n",
+ "In the previous example, we declared the local simulator outside the decorated function scope.\n",
+ "However, for AWS devices such as QPUs or on-demand simulators, the device must be declared within the function scope. \n",
+ "\n",
+ "
\n",
+ " Note: AWS devices must be declared within the body of the decorated function.\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from braket.devices import Devices\n",
+ "\n",
+ "\n",
+ "device_arn = Devices.Rigetti.Ankaa2\n",
+ "\n",
+ "\n",
+ "@hybrid_job(device=device_arn) # set priority QPU\n",
+ "def qpu_qubit_rotation_hybrid_job(num_steps=10, stepsize=0.5):\n",
+ " # AWS devices must be declared within the decorated function.\n",
+ " device = qml.device(\n",
+ " \"braket.aws.qubit\",\n",
+ " device_arn=device_arn.value, # Make sure the device ARN matches the hybrid job device ARN\n",
+ " wires=2,\n",
+ " shots=1_000,\n",
+ " )\n",
+ "\n",
+ " @qml.qnode(device)\n",
+ " def circuit(params):\n",
+ " qml.RX(params[0], wires=0)\n",
+ " qml.RY(params[1], wires=0)\n",
+ " return qml.expval(qml.PauliZ(0))\n",
+ "\n",
+ " opt = qml.GradientDescentOptimizer(stepsize=stepsize)\n",
+ " params = np.array([0.5, 0.75])\n",
+ "\n",
+ " for i in range(num_steps):\n",
+ " # update the circuit parameters\n",
+ " params = opt.step(circuit, params)\n",
+ " expval = circuit(params)\n",
+ "\n",
+ " log_metric(metric_name=\"expval\", iteration_number=i, value=expval)\n",
+ "\n",
+ " return params"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To get a sense of how long we will wait before the hybrid job runs, we can check the hybrid job\n",
+ "queue depth with `AwsDevice(device_arn).queue_depth().jobs`. We can also check if the device is\n",
+ "currently available with `AwsDevice(device_arn).is_available()`.\n",
+ "\n",
+ "You can check the queue depth on the devices page of the [Amazon Braket Console](https://console.aws.amazon.com/braket/home). Below, we show the devices page for Rigetti Ankaa 2.\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "When there are no other hybrid jobs in the queue ahead of you, and the device is available, the hybrid job will start running.\n",
+ "\n",
+ "
\n",
+ " Note: Running the following cell will only run once the QPU is available. This may take a long time and will result in usage fees charged to your AWS account. Only run the cell if you are comfortable with the potential wait-time and costs. We recommend monitoring the Billing & Cost Management Dashboard on the AWS console.\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "AwsQuantumJob('arn':'arn:aws:braket:us-west-2:318845237731:job/qpu-qubit-rotation-hybrid-job-1700084458165')\n"
+ ]
+ }
+ ],
+ "source": [
+ "qpu_job = qpu_qubit_rotation_hybrid_job(num_steps=10, stepsize=0.5)\n",
+ "print(qpu_job)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next, we wait for the algorithm to complete and download the result. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'result': tensor([0.0205, 3.1065], requires_grad=True)}"
+ ]
+ },
+ "execution_count": 17,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "qpu_job.result()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next, we plot the expectation value per iteration number below. We see that on a real QPU, the data is not as smooth as the simulator, but the minimum still is detected correctly!"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "{'timestamp': [1700084730.969484, 1700084698.0504165, 1700084679.9848497, 1700084664.1287766, 1700084648.2972944, 1700084632.2871127, 1700084616.684862], 'expval': [-0.972, -0.784, -0.548, -0.36, -0.07, 0.11, 0.388], 'iteration_number': [7.0, 5.0, 4.0, 3.0, 2.0, 1.0, 0.0]}\n"
+ ]
+ }
+ ],
+ "source": [
+ "# May need to wait a bit before metrics show up\n",
+ "# If metrics aren't there, try again after 5 seconds\n",
+ "import time\n",
+ "\n",
+ "time.sleep(10)\n",
+ "print(qpu_job.metrics())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "df = pd.DataFrame(qpu_job.metrics())\n",
+ "df.sort_values(by=[\"iteration_number\"], inplace=True)\n",
+ "\n",
+ "plt.plot(df[\"iteration_number\"], df[\"expval\"], \"-o\", color=\"teal\")\n",
+ "plt.xlabel(\"iteration number\")\n",
+ "plt.ylabel(\"expectation value\")\n",
+ "plt.title(\"QPU results\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
\n",
+ " Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. \n",
+ " Estimated charges shown may differ from your actual charges. \n",
+ " Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2)\n",
+ " Estimated cost to run this example is $39 USD.\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Conclusion\n",
+ "\n",
+ "In this tutorial, we showed how to migrate from local Python functions to running algorithms on simulators and QPUs on Amazon Braket.\n",
+ "We adapted the simple example of rotating a qubit using gradient descent, running this on both a\n",
+ "local simulator and a real QPU. \n",
+ "Using Amazon Braket Hybrid Jobs allowed us to run algorithms asynchronously, scale classical compute using AWS, and obtain priority access to the selected QPU for the duration of our algorithm."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "conda_braket",
+ "language": "python",
+ "name": "conda_braket"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.10.13"
+ }
},
- {
- "data": {
- "text/plain": [
- "tensor([0.67679672, 2.32609342], requires_grad=True)"
- ]
- },
- "execution_count": 4,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qubit_rotation(5, stepsize=0.5)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Great! We see the expectation value change with each iteration number and the final parameters were returned as a list. Now, instead of running on our laptop, let’s submit this same function to be run on AWS."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Running as a hybrid job\n",
- "\n",
- "You can execute long-running algorithms asynchronously with Amazon Braket Hybrid Jobs, \n",
- "which fully manages the classical infrastructure so you can focus on the algorithm. For example, you\n",
- "can train a larger circuit, or increase the number of iterations. Note that each hybrid job has\n",
- "at least a one minute startup time since it creates a containerized environment on Amazon EC2. So\n",
- "for very short workloads, such as a single circuit or a batch of circuits, it may suffice for you to\n",
- "use quantum tasks.\n",
- "\n",
- "We now show how you can go from running your local Python function to running it as a hybrid job.\n",
- "\n",
- "
\n",
- " Note: Only Python 3.10 is supported by default. For other versions, you may use hybrid job scripts, or specify a custom container image from Amazon Elastic Container Registry (ECR) (see \n",
- "containers documentation).\n",
- "
\n",
- "\n",
- "\n",
- "The first step to creating a hybrid job is to annotate which function you want to run with the\n",
- "`@hybrid_job` decorator. Then you create the job by invoking the function as you would for normal\n",
- "Python functions. However, the decorated function returns the hybrid job handle rather than the\n",
- "result of the function. To retrieve the results after it has been completed, use `job.result()`.\n",
- "\n",
- "For algorithms that do not need priority queueing or scheduling for on-demand QPUs, you may specify the device as `local:/` or simply `None`. For example, when using a simulator that runs on the same classical host alongside the rest of your algorithm, such as the PennyLane Lightning CPU/GPU simulators, you may set `device=\"local:pennylane/lightning.qubit\"`. \n",
- "\n",
- "\n",
- "The required device argument in the `@hybrid_job` decorator specifies the QPU that the hybrid job\n",
- "will have priority access to.\n",
- "The device string you give is accessible in the hybrid job instance as the environment variable ``\"AMZN_BRAKET_DEVICE_ARN\"``.\n",
- "In the following code, we annotate the `qubit_rotation` function from above.\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {},
- "outputs": [],
- "source": [
- "from braket.jobs import hybrid_job, save_job_result\n",
- "\n",
- "\n",
- "@hybrid_job(device=\"local:braket/default\")\n",
- "def qubit_rotation_hybrid_job(num_steps=1, stepsize=0.5):\n",
- " device = qml.device(\"braket.local.qubit\", wires=1)\n",
- "\n",
- " @qml.qnode(device)\n",
- " def circuit(params):\n",
- " qml.RX(params[0], wires=0)\n",
- " qml.RY(params[1], wires=0)\n",
- " return qml.expval(qml.PauliZ(0))\n",
- "\n",
- " opt = qml.GradientDescentOptimizer(stepsize=stepsize)\n",
- " params = np.array([0.5, 0.75])\n",
- "\n",
- " for i in range(num_steps):\n",
- " # update the circuit parameters\n",
- " params = opt.step(circuit, params)\n",
- " expval = circuit(params)\n",
- "\n",
- " log_metric(metric_name=\"expval\", iteration_number=i, value=expval)\n",
- "\n",
- " return params"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now we create a hybrid job by calling the function as usual. This returns an `AwsQuantumJob` object that contains the device ARN, region, and job name."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "AwsQuantumJob('arn':'arn:aws:braket:us-west-2:318845237731:job/qubit-rotation-hybrid-job-1700084057462')\n"
- ]
- }
- ],
- "source": [
- "job = qubit_rotation_hybrid_job(num_steps=10, stepsize=0.5)\n",
- "print(job)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The hybrid job automatically captures the function arguments as [hyperparameters](https://docs.aws.amazon.com/braket/latest/developerguide/braket-jobs-hyperparameters.html).\n",
- "In this case, we set `num_steps = 10` and `stepsize = 0.5` as the hyperparameters."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We can check the status with:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "'QUEUED'"
- ]
- },
- "execution_count": 7,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job.state()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Once the hybrid job starts, it will change the status to `RUNNING`. We can also check the hybrid job status in the Braket console.\n",
- "\n",
- "We can monitor the metrics in near-real time in the [Braket console page](https://console.aws.amazon.com/braket/) as shown below. \n",
- "\n",
- ""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "After the hybrid job completes, we can get the results with `job.result()`. For this example, it should take approximately 2 minutes."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{'result': tensor([0.03642036, 3.10081929], requires_grad=True)}"
- ]
- },
- "execution_count": 8,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job.result()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Any objects in the return statement are automatically captured by Braket. Note that the objects returned by the function must be a tuple with each element being serializable as text. \n",
- "\n",
- "Additionally, we can plot the metrics recording during the algorithm. Below we show the expectation value decreases with each iteration as expected."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "{'timestamp': [1700084189.268808, 1700084189.3246114, 1700084189.3840628, 1700084189.1557567, 1700084189.2123241, 1700084188.8748374, 1700084188.9313, 1700084188.9881024, 1700084189.0439024, 1700084189.099711], 'expval': [-0.9771543186187628, -0.9940804663947356, -0.9985062848699056, -0.7715298984378987, -0.9193547392516985, 0.38894534132396147, 0.12290715413453956, -0.09181374013482171, -0.2936094099948542, -0.5344079938678078], 'iteration_number': [7.0, 8.0, 9.0, 5.0, 6.0, 0.0, 1.0, 2.0, 3.0, 4.0]}\n"
- ]
- }
- ],
- "source": [
- "# May need to wait a bit before metrics show up\n",
- "# If metrics aren't there, try again after 5 seconds\n",
- "import time\n",
- "\n",
- "time.sleep(10)\n",
- "print(job.metrics())"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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79mG3l9KTXOHtIaiGOTA613FCmM+Ha60jERGRkmIzDCOPv8oCkJaWRkhICKmpqQQHB1/ei52fNQbkWoaq3wYdZ1/ee4iIiEiB/36X0tMnZVR0d2g/C4Kqu273r2z+PPhf2Dez5HOJiIh4KY/6aqxMiO4O1e8wZ4edPmyOCQpvD5uehu2vws8PQkhjCGlgdVIREZEyT0XICnafnFPkm70Ix9dAyiJYdhd0WQ3lKlgST0RExFvoq7HSwu4LbT6HwChI2w6r+oOGb4mIiBQrFaHSJDAS2s0Emy/s+xJ2TrQ6kYiISJmmIlTahLeBa9407294Ao4sszaPiIhIGaYiVBpdOQhq9QIjG5bfo9WmRUREiomKUGlks0GrKRDSCM4kw/Ke4DhndSoREZEyR0WotPItD+2/Bt+K5lT7jSOsTiQiIlLmqAiVZsFXQutp5v0db2qxRRERETdTESrtou+EBk+Z939+EFK3W5tHRESkDFER8gTNXoTI6yHrlLnY4rlTVicSEREpE1SEPIEWWxQRESkWKkKeQostioiIuJ2KkCdxWWzxSTiy3No8IiIiHk5FyNM4F1vMghX3wOlkqxOJiIh4LBUhT/P3xRZPH4YVWmxRRESkqFSEPNHfF1s8shQ2jrQ6kYiIiEdSEfJUwVdC66nm/R1vwL5ZlsYRERHxRCpCniy6OzR40rz/cz9I3WFtHhEREQ+jIuTpmr0EEZ3+WmyxuxZbFBERKQQVIU9n94W2X2ixRRERkSJQESoLtNiiiIhIkagIlRXhbeCaN8z7WmxRRESkQFSEypIrB2uxRRERkUJQESpLbDa49gMttigiIlJAKkJlTbkKWmxRRESkgFSEyiIttigiIlIgKkJllRZbFBERuSQVobJMiy2KiIjkS0WoLMux2OIALbYoIiLyNypCZZ3LYoszYOdbVicSEREpNVSEvIHLYotPwNEV1uYREREpJVSEvMXfF1tcfrcWWxQREUFFyHs4F1tsqMUWRURE/qIi5E202KKIiIgLFSFvE3wVXPexeV+LLYqIiJfzuCL0zjvvEBMTQ0BAAK1atWL16tV57jtlyhTat29PpUqVqFSpEvHx8fnu7zVq3gUNnjDva7FFERHxYh5VhGbMmMHw4cMZPXo069evp1mzZnTp0oUjR47kuv/ixYvp1asXixYtIjExkejoaG688UYOHjxYwslLoWYJENFRiy2KiIhXsxmG56yw16pVK1q2bMmkSZMAcDgcREdHM3jwYEaMGHHJ47Ozs6lUqRKTJk2iT58+BXrPtLQ0QkJCSE1NJTg4+LLylzqnk2HeNebg6Zo9oe3n5qBqERERD1fQv98ec0YoMzOTdevWER8f79xmt9uJj48nMTGxQK+RkZHBuXPnCAsLK66YniWwqhZbFBERr+YxRejYsWNkZ2cTGRnpsj0yMpLk5IKtifOvf/2LqKgolzJ1sbNnz5KWluZyK9PC22qxRRER8VoeU4Qu18svv8wXX3zBN998Q0BAQJ77JSQkEBIS4rxFR0eXYEqLaLFFERHxUh5ThKpUqYKPjw8pKSku21NSUqhatWq+x77++uu8/PLL/PjjjzRt2jTffUeOHElqaqrztn///svOXurlWGzxXnBkWZ1KRESk2HlMEfLz86NFixYsWLDAuc3hcLBgwQJat26d53Gvvvoq48aNY968ecTGxl7yffz9/QkODna5eQWXxRaXwCYttigiImWfxxQhgOHDhzNlyhSmTZvG9u3beeSRR0hPT6dfv34A9OnTh5EjL/wBf+WVVxg1ahT//ve/iYmJITk5meTkZE6d0lTxXP19scXtr8O+r6zNIyIiUsx8rQ5QGD179uTo0aM899xzJCcn07x5c+bNm+ccQL1v3z7s9gvd7r333iMzM5MePXq4vM7o0aMZM2ZMSUb3HOcXW9z+urnYYmhjsyCJiIiUQR61jpAVyvQ6QnlxZMHCePMrspCGcOMq86szERERD1Hm1hGSEmT3hbZfQGA1SN0GqwaA+rKIiJRBKkKSOy22KCIiXkBFSPIW3hauft28r8UWRUSkDFIRkvxdNcS8DpkWWxQRkTJIRUjyZ7NBqw+12KKIiJRJKkJyaeUqQLuvwLeCFlsUEZEyRUVICiakvhZbFBGRMkdFSAquZg9zsUUwF1tM2wmObEhZDHs/N386sq1MKCIiUigetbK0lALNEuCPNeZXZAvjzfWFTh+88HxQDWgxEaK7W5dRRESkgHRGSArn/GKLfqGQccC1BAFkHIRlPWD/15bEExERKQwVISk8/3Cwlcvjyb9WoF43TF+TiYhIqaciJIV3dBmcPZrPDgZk7Df3ExERKcVUhKTwTh92734iIiIWURGSwgus5t79RERELKIiJIUX3t6cHYYtjx1sEBRt7iciIlKKqQhJ4dl9zCnyQO5lyICGI8z9RERESjEVISma6O7QfhYEVXfdfn422bZXIP33ks8lIiJSCFpQUYouujtUv8OcHXb6sDkmqOKVsOB6OLkLFsRB/FIIirI6qYiISK5UhOTy2H0gspPrtrgFML8DnEqChXEQvwQCIiyJJyIikh99NSbuF1QD4haaA6bTdsDCG+DscatTiYiI5KAiJMWjQgx0XgABVeHEL7CoC2SmWp1KRETEhYqQFJ/gK8yvyfyrwPG1sLgrnDtldSoREREnFSEpXiENofN8KBcKx1bC0tsh67TVqURERAAVISkJlZrD9f8D34qQsgiWdYfss1anEhERURGSElLlWug0F3yC4PA8WNETHOesTiUiIl5ORUhKTkQ76Dgb7P5w4DtYeT84sq1OJSIiXkxFSEpW1Tho/zXYy8G+GbCqPxgOq1OJiIiXUhGSkle9K7SdATYf2DMN1jwKhmF1KhER8UIqQmKN6Duh9SeADX6bDOuHqwyJiEiJUxES68T0glYfmfd3ToBfnrU0joiIeB8VIbFW3X4Q+455f+tLsOUFa/OIiIhXURES6135T7j6DfP+L6Ng+xvW5hEREa+hIiSlQ4Ph0HSceX/DE7DrXWvziIiIV1ARktKj8bPQ6Gnz/tpHIenf1uYREZEyT0VISpemL8BVj5n3Vw2AvZ9Zm0dERMo0FSEpXWw2uOYNqPd/gAGJfWD/11anEhGRMkpFSEofmw1avgO1+4KRDSvuhYNzrU4lIiJlkIqQlE42u7nGUM2/Ls66rDsk/2R1KhERKWM8rgi98847xMTEEBAQQKtWrVi9enW++8+cOZP69esTEBBAkyZNmDtXZxY8ht0H2nwCNbqB4ywsuQOOLLM6lYiIlCEeVYRmzJjB8OHDGT16NOvXr6dZs2Z06dKFI0eO5Lr/ypUr6dWrF/3792fDhg1069aNbt26sWXLlhJOLkVmLwdtv4BqN0F2Biy+BY7lX35FREQKymYYnnOBp1atWtGyZUsmTZoEgMPhIDo6msGDBzNixIgc+/fs2ZP09HTmzJnj3HbdddfRvHlzJk+eXKD3TEtLIyQkhNTUVIKDg93zQaTwsk7DklsgZRGUC4W4hRB2tdWpRESklCro32+POSOUmZnJunXriI+Pd26z2+3Ex8eTmJiY6zGJiYku+wN06dIlz/0Bzp49S1pamstNSgHfQOgwG8LbwrkTsOhGOLHV6lQiIuLhPKYIHTt2jOzsbCIjI122R0ZGkpycnOsxycnJhdofICEhgZCQEOctOjr68sOLe5SrAB2/h7BYOHsMFsZD2q9WpxIREQ/mMUWopIwcOZLU1FTnbf/+/VZHkr/zC4Hr/wehTeFMMizsDKf2WJ1KREQ8lMcUoSpVquDj40NKSorL9pSUFKpWrZrrMVWrVi3U/gD+/v4EBwe73KSU8Q+DzvMhuAFkHIAFceZPERGRQvKYIuTn50eLFi1YsGCBc5vD4WDBggW0bt0612Nat27tsj/A/Pnz89xfPEhABHT+CSrUhfQ9Zhk6nfdXniIiIrnxmCIEMHz4cKZMmcK0adPYvn07jzzyCOnp6fTr1w+APn36MHLkSOf+Q4cOZd68ebzxxhvs2LGDMWPGsHbtWgYNGmTVRxB3CoqCuAUQVBNO7jLHDJ05ZnUqERHxIL5WByiMnj17cvToUZ577jmSk5Np3rw58+bNcw6I3rdvH3b7hW7Xpk0bPvvsM5599lmefvpprrjiCr799lsaN25s1UcQdytfy5xK/1N7SN1qziaLWwh+oVYnExERD+BR6whZQesIeYjU7fBTRzh7FCpfB51/hHIVrU4lIiIWKXPrCInkK6SBOWbILwz++BmW3ApZGVanEhGRUk5FSMqOSk3NqfXlguHIUljaDbLPWJ1KRERKMRUhKVsqx0KnH8C3PCTPh2V3Q3am1alERKSUUhGSsie8DXScAz4BcGgOrLwPHFlWpxIRkVJIRUjKpshO0P5bsPvB/q/g5wfAkW1xKBERKW1UhKTsiuoC7b4Emy/snQ5r/g8Mh9WpRESkFClSEfrkk09o27YtUVFR/P777wBMmDCB7777zq3hRC5bjTugzXSw2SHpQ1g3FLRihIiI/KXQRei9995j+PDhdO3alRMnTpCdbX7dEBoayoQJE9ydT+Ty1boHWn1s3t81CTb+S2VIRESAIhSht99+mylTpvDMM8/g4+Pj3B4bG8vmzZvdGk7Eber0gZaTzfvbX4PNY63NIyIipUKhi9CePXu4+uqrc2z39/cnPT3dLaFEisUVD8M14837W8bCtleszSMiIpYrdBGqXbs2GzduzLF93rx5NGjQwB2ZRIpP/WHQ7CXz/sYRsPMt874jG1IWw97PzZ+aYSYi4hUKfdHV4cOH8+ijj3LmzBkMw2D16tV8/vnnJCQk8OGHHxZHRhH3ajQSsk/DlnHm4OnUbXDoe8g4cGGfoBrQYiJEd7cup4iIFLsiXXR1+vTpjBkzhqSkJACioqIYO3Ys/fv3d3tAq+miq2WUYcDGp2D763nsYDN/tJ+lMiQi4oEK+vf7sq4+n5GRwalTp4iIiCjqS5R6KkJlWHYWfBUKWXmNbbOZZ4Zu3wN2nzz2ERGR0qhErj4fFBRUpkuQlHHHludTggAMyNgPR5eVWCQRESlZhR4jVLt2bWw2W57P7969+7ICiZSY04fdu5+IiHicQhehYcOGuTw+d+4cGzZsYN68eTz55JPuyiVS/AKruXc/ERHxOIUuQkOHDs11+zvvvMPatWsvO5BIiQlvb44ByjgI5DFULija3E9ERMokt1109eabb+arr75y18uJFD+7jzlFHnDOErtY9ds0UFpEpAxzWxGaNWsWYWFh7no5kZIR3d2cIh9U3XW7bwXz56/vwq+TSz6XiIiUiEJ/NXb11Ve7DJY2DIPk5GSOHj3Ku+++69ZwIiUiujtUv8OcHXb6sDkmqEo72PgE7JwIax4BRyZcNcTqpCIi4maFLkLdunVzeWy32wkPD6dTp07Ur1/fXblESpbdByI7uW67ZjzY/WH7q+YK1I5MaPCEJfFERKR4XNaCit5ACyp6OcOAX56DrS+Yj5u+AI2fsTaTiIhcUkH/fhfojFBaWlqB31hlQcoUmw2ajQO7H2x+Dn551jwz1GSM+ZyIiHi0AhWh0NDQfBdRBHOskM1mIztbV+2WMqjJKPDxM69Yv+V5cJyDZi+qDImIeLgCFaFFixYVdw6R0q/hv8wzQ+uHw7YEcJyFq19XGRIR8WAFKkIdO3Ys7hwinqH+Y2YZWjsIdrxpfk3W4i2VIRERD1XoWWPnZWRksG/fPjIzM122N23a9LJDiZRqVz5qlqHVD8OuSWYZavke2Ny2LJeIiJSQQheho0eP0q9fP3744Ydcn9cYIfEK9R4yy9DP/eC3D8wydO2HWoVaRMTDFPo/YYcNG8aJEydYtWoVgYGBzJs3j2nTpnHFFVcwe/bs4sgoUjrV6QttPgWbD+yeCj/3BUeW1alERKQQCn1GaOHChXz33XfExsZit9upVasWN9xwA8HBwSQkJHDLLbcUR06R0inmPrCXgxX3wd7p5myyNp+a20REpNQr9Bmh9PR0IiIiAKhUqRJHjx4FoEmTJqxfv9696UQ8Qc27od1Ms/zs+xKW94TszEsfJyIilit0EbrqqqvYuXMnAM2aNeP999/n4MGDTJ48mWrVqrk9oIhHiO4G7b8xL8lx4BtY1h2yz1idSkRELqHQRWjo0KEcPnwYgNGjR/PDDz9Qs2ZN3nrrLV566SW3BxTxGNVvgY6zwScADn0PS7tB1mmrU4mISD4u+1pjGRkZ7Nixg5o1a1KlShV35So1dK0xKbTkhbDkNsjOgMjOZjnyLW91KhERr1LQv9+FPiO0fPlyl8dBQUFcc801ZbIEiRRJ1c5w/TzwrQApC2HRzXDupNWpREQkF4UuQp07d6Z27do8/fTTbNu2rTgyiXi+iPZw/Y9QLhiOLoNFXSAz1epUIiJykUIXoUOHDvH444+zZMkSGjduTPPmzXnttdc4cOBAceRzOn78OL179yY4OJjQ0FD69+/PqVOn8t1/8ODBXHXVVQQGBlKzZk2GDBlCaqr+GEkJCW8NnRdAuVA4lggLb4DMP61OJSIif1PoIlSlShUGDRrEihUrSEpK4u6772batGnExMTQuXPn4sgIQO/evdm6dSvz589nzpw5LF26lIEDB+a5/6FDhzh06BCvv/46W7ZsYerUqcybN4/+/fsXW0aRHCrHQvwi8K8Mx9fAgjg4c8zqVCIi8pfLHiydnZ3NDz/8wKhRo/jll1+K5RIb27dvp2HDhqxZs4bY2FgA5s2bR9euXTlw4ABRUVEFep2ZM2fyj3/8g/T0dHx9C7aWpAZLi1uc2AIL4+DMEQhtAp1/goAIq1OJiJRZxTZY+rwVK1bwz3/+k2rVqnHffffRuHFjvv/++6K+XL4SExMJDQ11liCA+Ph47HY7q1atKvDrnP9lFLQEibhNaGOIWwyB1eDEZvipE5w+bHEoEREpdCMYOXIkX3zxBYcOHeKGG25g4sSJ3HHHHQQFBRVHPgCSk5Odq1mf5+vrS1hYGMnJyQV6jWPHjjFu3Lh8v04DOHv2LGfPnnU+TktLK3xgkdyENIC4JbCwM6Rth586QtxCCKphdTIREa9V6DNCS5cu5cknn+TgwYPMmTOHXr16FbkEjRgxApvNlu9tx44dRXrtv0tLS+OWW26hYcOGjBkzJt99ExISCAkJcd6io6Mv+/1FnIKvgPglUL4WnPzVLEPpv1udSkTEa132GKHLcfToUf74449896lTpw6ffvopjz/+OH/+eWHGTVZWFgEBAcycOZM777wzz+NPnjxJly5dCAoKYs6cOQQEBOT7frmdEYqOjtYYIXGv9N9hQWc4tdssRXELoUIdq1OJiJQZBR0jZOlgmfDwcMLDwy+5X+vWrTlx4gTr1q2jRYsWACxcuBCHw0GrVq3yPC4tLY0uXbrg7+/P7NmzL1mCAPz9/fH39y/4hxApivK1zDNDC+Lg5C7zzFDnheYZIxERKTFFHixdkho0aMBNN93EQw89xOrVq1mxYgWDBg3i3nvvdc4YO3jwIPXr12f16tWAWYJuvPFG0tPT+eijj0hLSyM5OZnk5ORimdkmUmhBNSB+MQQ3gIwDsKAjpG63OpWIiFfxiCIEMH36dOrXr09cXBxdu3alXbt2fPDBB87nz507x86dO8nIyABg/fr1rFq1is2bN1OvXj2qVavmvO3fv9+qjyHiKrCaWYZCm5izyBZ0Mqfai4hIibB0jJAn0DpCUiLO/mGuPP3nBnPxxc4/QaXmVqcSEfFYxT5GKDMzkyNHjuBwOFy216xZs6gvKeK9/CtD3AJY2OWvFag7m9cqqxx76WNFRKTICv3V2K+//kr79u0JDAykVq1a1K5dm9q1axMTE0Pt2rWLI6OId/CrBJ3nQ5XW5jXJFsbBsZ+tTiUiUqYV+ozQAw88gK+vL3PmzKFatWrYbLbiyCXinfxC4Pr/weJbzKvWL7wBOv0AEe2sTiYiUiYVeoxQ+fLlWbduHfXr1y+uTKWKxgiJJbLSYcntkLIQfIKg0/cQ2cnqVCIiHqPYrjXWsGFDjh3T1bNFipVveeg4B6reCNkZsLgrHJ5vdSoRkTKn0EXolVde4amnnmLx4sX88ccfpKWludxExE18A6HjdxB1C2SfhiW3wcG5VqcSESlTCv3VmN1udqeLxwYZhoHNZitzixXqqzGxXHYmrLgXDnwD9nLQbibUuMPqVCIipVqxTZ9ftGjRZQUTkULy8YN2M2DlP2Dfl7CsB7T9HGr2sDqZiIjHK3QR6tixY3HkEJH82MtBm+nmz73TzTNEjv9AzH1WJxMR8WhFWlDxxIkTfPTRR2zfbl4XqVGjRjz44IOEhIS4NZyI/I3dF66bZpah3VMh8X5wnIM6fa1OJiLisQo9WHrt2rXUrVuX8ePHc/z4cY4fP86bb75J3bp1Wb9+fXFkFJHz7D7Q6iOoNxAMB/zcD3770OpUIiIeq9CDpdu3b0+9evWYMmUKvr7mCaWsrCwGDBjA7t27Wbp0abEEtYoGS0upZBiwbgjsmmQ+jn0HrvwnOLLNhRhPHzYv6Bre3ixPIiJepqB/vwtdhAIDA9mwYUOOBRW3bdtGbGys8+rvZYWKkJRahgEbnoAdb5qPa/eDlPmQceDCPkE1oMVEiO5uTUYREYsU24KKwcHB7Nu3L8f2/fv3U7FixcK+nIgUlc0GV78ODUeaj/d87FqCADIOmrPM9n9d8vlERDxAoYtQz5496d+/PzNmzGD//v3s37+fL774ggEDBtCrV6/iyCgiebHZoMnz4JvXf+38dcJ33TDzazMREXFR6Fljr7/+OjabjT59+pCVlQVAuXLleOSRR3j55ZfdHlBELuHYcsjKb1V3AzL2m2OHdL0yEREXhS5Cfn5+TJw4kYSEBJKSkgCoW7cuQUFBbg8nIgVw+rB79xMR8SJFWkcIICgoiCZNmrgzi4gURWA19+4nIuJFClSEunfvztSpUwkODqZ79/xnn3z9tQZlipSo8Pbm7LCMgzjHBLmwmc+Hty/pZCIipV6BilBISIjzIqvBwcE5LrgqIhay+5hT5Jf1AGzkLEMGNBmr9YRERHJR6HWEvI3WERKPsf9rWDfUdQq9zQeMbKjSGuIWgk+AdflEREpQsa0j1LlzZ06cOJHrG3bu3LmwLyci7hLdHW7fC3GLoM1n5s+uv4BfJTiWCIkPmJflEBERp0IPll68eDGZmZk5tp85c4Zly5a5JZSIFJHdJ+cU+fZfw6IbYd8MqFgXmr1oSTQRkdKowEXol19+cd7ftm0bycnJzsfZ2dnMmzeP6tWruzediFy+yE5w7Yfwc1/Y+hJUqAt1H7Q6lYhIqVDgItS8eXNsNhs2my3Xr8ACAwN5++233RpORNykTh849RtsGQerH4bytaBqnNWpREQsV+AitGfPHgzDoE6dOqxevZrw8HDnc35+fkRERODjo1kpIqVWk7FwMgl+/wyW3QU3roSQhlanEhGxVIGLUK1atQBwODTYUsQj2Wxw3UeQsQ+OLofFt8CNP0NgpNXJREQsU+SVpbdt28a+fftyDJy+/fbbLzuUiBQTnwBo/w382Nr8qmzp7ebsMl9dIkdEvFOhi9Du3bu588472bx5MzabjfPLEJ1fZDE7W1e4FinVAqpAp7nw43Xwx2pI7APtvgRboVfTEBHxeIX+X76hQ4dSu3Ztjhw5QlBQEFu3bmXp0qXExsayePHiYogoIm4XfAV0+BbsfrD/K9g40upEIiKWKHQRSkxM5Pnnn6dKlSrY7Xbsdjvt2rUjISGBIUOGFEdGESkOEe2h1b/N+9tfhd8+sDaPiIgFCl2EsrOzqVixIgBVqlTh0KFDgDmYeufOne5NJyLFq3ZvczYZwJp/wuEfrc0jIlLCCl2EGjduzKZNmwBo1aoVr776KitWrOD555+nTp06bg8oIsWs8SiIud+8JtmyHnBii9WJRERKTKGL0LPPPuucQv/888+zZ88e2rdvz9y5c5k4caLbA4pIMbPZoNUUiOgIWSfNafWnD1udSkSkRLjl6vPHjx+nUqVKzpljZYmuPi9e4+xxc1r9yV0QFgvxi8G3vNWpRESKpNiuPv/ggw9y8uRJl21hYWFkZGTw4IO6fpGIx/IPM6fV+1eB42thZW9waDkMESnbCl2Epk2bxunTp3NsP336NP/5z3/cEkpELFKx7l/T6v3hwHew8SmrE4mIFKsCF6G0tDRSU1MxDIOTJ0+SlpbmvP3555/MnTuXiIiI4swqIiUhvC1cN9W8v+NN2PWupXFERIpTgYtQaGgoYWFh2Gw2rrzySipVquS8ValShQcffJBHH3202IIeP36c3r17ExwcTGhoKP379+fUqVMFOtYwDG6++WZsNhvffvttsWUUKTNi7oVmL5r31w2Gg3OtzSMiUkwKfImNRYsWYRgGnTt35quvviIsLMz5nJ+fH7Vq1SIqKqpYQgL07t2bw4cPM3/+fM6dO0e/fv0YOHAgn3322SWPnTBhQpkcyC1SrBqOhJO/wu6psKIn3LAcKjWzOpWIiFsVetbY77//Ts2aNUu0WGzfvp2GDRuyZs0aYmNjAZg3bx5du3blwIED+RawjRs3cuutt7J27VqqVavGN998Q7du3Qr83po1Jl4tOxMW3wQpiyCoBty4CoKK7z94RETcpdhmjS1cuJBZs2bl2D5z5kymTZtW2JcrkMTEREJDQ50lCCA+Ph673c6qVavyPC4jI4P77ruPd955h6pVqxbovc6ePesy/iktLe2y84t4LB8/aP8VBNeHjAOw5FY4V7CvpEVEPEGhi1BCQgJVqlTJsT0iIoKXXnrJLaEulpycnGMgtq+vL2FhYSQnJ+d53GOPPUabNm244447CvxeCQkJhISEOG/R0dFFzi1SJvhVgk7fg384/LkBVt6nafUiUmYUugjt27eP2rVr59heq1Yt9u3bV6jXGjFiBDabLd/bjh07ChsRgNmzZ7Nw4UImTJhQqONGjhxJamqq87Z///4ivb9ImVKhDnScDT4BcPC/sOFxqxOJiLhFgQdLnxcREcEvv/xCTEyMy/ZNmzZRuXLlQr3W448/zgMPPJDvPnXq1KFq1aocOXLEZXtWVhbHjx/P8yuvhQsXkpSURGhoqMv2u+66i/bt27N48eJcj/P398ff37+gH0HEe1S5Dlr/B5bfAzsnQoW6cNVgq1OJiFyWQhehXr16MWTIECpWrEiHDh0AWLJkCUOHDuXee+8t1GuFh4cTHh5+yf1at27NiRMnWLduHS1atADMouNwOGjVqlWux4wYMYIBAwa4bGvSpAnjx4/ntttuK1ROEflLzbuh+cuwcQSsHwYVakP1W61OJSJSZIWeNZaZmcn999/PzJkz8fU1e5TD4aBPnz5MnjwZPz+/Ygl68803k5KSwuTJk53T52NjY53T5w8ePEhcXBz/+c9/uPbaa3N9DZvNplljIpfLMGD1QEj60LwWWfwyCLva6lQiIi4K+ve70GeE/Pz8mDFjBuPGjWPTpk0EBgbSpEkTatWqdVmBL2X69OkMGjSIuLg47HY7d911F2+99Zbz+XPnzrFz504yMjKKNYeI17PZoOW7kL4Xkn8yZ5J1WWVOrxcR8TBFvvp8ZmYme/bsoW7dus4zQ2WRzgiJ5CEzFea3gdRtENoMblgG5SpanUpEBCjGdYQyMjLo378/QUFBNGrUyDlTbPDgwbz88stFTywinsUvBDp+DwGRcGITrLgXHFlWpxIRKZRCF6GRI0eyadMmFi9eTEBAgHN7fHw8M2bMcGs4ESnlKsRAh9ngEwiH5sK6oeYYIhERD1HoIvTtt98yadIk2rVr53KZjUaNGpGUlOTWcCLiAapcC22mAzb49V1zar2IiIcodBE6evRojlWeAdLT03VhUxFvFX0nXP2aeX/9cDjwnbV5REQKqNBFKDY2lu+//975+Hz5+fDDD2ndurX7komIZ6k/HOr9H2DAivvgj7VWJxIRuaRCT/d66aWXuPnmm9m2bRtZWVlMnDiRbdu2sXLlSpYsWVIcGUXEE9hsEPu2Oa3+8DxYcps5rb58TauTiYjkqdBnhNq1a8fGjRvJysqiSZMm/Pjjj0RERJCYmOhc9VlEvJTdF9rNgNAmcCYZFt8C59KsTiUikqciryPkLbSOkEgRpO+D/7Uyy1DVG6HTHLCXszqViHiRYltZGiA7O5tvvvmG7du3A9CwYUPuuOOOMr2woogUQvmaZvmZ3wGSf4S1g6Hle+bXZyIipUihzwht3bqV22+/neTkZK666ioAdu3aRXh4OP/9739p3LhxsQS1is4IiVyGA9/B0jsBw5xV1uAJqxOJiJcotpWlBwwYQKNGjThw4ADr169n/fr17N+/n6ZNmzJw4MDLCi0iZUyNO+CaN837G56EfV9Zm0dE5CKFPiMUGBjI2rVradSokcv2LVu20LJlS06fPu3WgFbTGSGRy2QY5ldjv74DPgEQtxiqtLI6lYiUccV2RujKK68kJSUlx/YjR45Qr169wr6ciJR1Nhu0mABRXSH7DCy9HU7ttTqViAhQhCKUkJDAkCFDmDVrFgcOHODAgQPMmjWLYcOG8corr5CWlua8iYgA5rT6tl+YV6k/cwSW3AKZJ6xOJSJS+K/G7PYL3en8qtLnX+Lvj202G9nZ2e7KaRl9NSbiRhkHzGn1pw9BZBxc/4Om1YtIsSi26fOLFi26rGAi4sWCakDHOfBTe0hZAGsegWunaFq9iFim0EWoY8eOxZFDRLxF2NXm12RL74Ckj6DiFdDwX1anEhEvVegxQmPGjMHhcOTYnpqaSq9evdwSSkTKuOq3wjUTzfsbR8C+mdbmERGvVegi9NFHH9GuXTt2797t3LZ48WKaNGlCUlKSW8OJSBl21SC4aqh5f+X9cDTR2jwi4pUKXYR++eUXatSoQfPmzZkyZQpPPvkkN954I/fffz8rV64sjowiUlZd/QZUvw0cZ82vyk7tvvQxIiJuVOSLrj799NO8/PLL+Pr68sMPPxAXF+fubKWCZo2JFLNzp+CnjvDnegiuDzeuBL9KVqcSEQ9XbAsqArz99ttMnDiRXr16UadOHYYMGcKmTZuKHFZEvFi5CtDxv+aMsrQdsOwuOHcaUhbD3s/Nnw7PX4pDREqnQs8au+mmm1i7di3Tpk2jR48enD59muHDh3PdddcxduxYnnrqqeLIKSJlWVAUdPwe5reFlEXwdRXIzvjb8zWgxUSI7m5dRhEpkwp9Rig7O5tffvmFHj16AOa1x9577z1mzZrF+PHj3R5QRLxEpaYXBk//vQQBZByEZT1g/9cln0tEyrQijxHKzbFjx6hSpYq7Xq5U0BghkRLiyIbZMebq07mymWeGbt8Ddp+STCYiHqhYxwgtW7aMf/zjH7Ru3ZqDBw8C8Mknn7Bjx46ipRURObosnxIEYEDGfnM/ERE3KXQR+uqrr+jSpQuBgYFs2LCBs2fPAuaCii+99JLbA4qIlzh92L37iYgUQKGL0AsvvMDkyZOZMmUK5cpduFhi27ZtWb9+vVvDiYgXCazm3v1ERAqg0EVo586ddOjQIcf2kJAQTpw44Y5MIuKNwtubY4DI5wKsgTXM/URE3KTQRahq1ar89ttvObYvX76cOnXquCWUiHghu485RR7IswwFVi2xOCLiHQpdhB566CGGDh3KqlWrsNlsHDp0iOnTp/PEE0/wyCOPFEdGEfEW0d2h/SwIqu663T8CbL5wfC2sHwbum+wqIl6u0AsqjhgxAofDQVxcHBkZGXTo0AF/f3+eeOIJBg8eXBwZRcSbRHeH6neYs8NOHzbHBIW3hwNfw/J7YNckKF8bGgy3OqmIlAFFXkcoMzOT3377jVOnTtGwYUMqVKjg7mylgtYREilFtr8OG54EbNBuJtS8y+pEIlJKFfTvd6HPCJ3n5+dHw4YNi3q4iEjh1X8cTu2BX9+FxH9AYBSEt7Y6lYh4sCItqCgiYgmbzRxQXf02yD4DS2+DtF+tTiUiHkxFSEQ8i90X2n4OYbFw9g9Y3BXOHLM6lYh4KBUhEfE8vuWh43+hfC049RssvR2yTludSkQ8kMcUoePHj9O7d2+Cg4MJDQ2lf//+nDp16pLHJSYm0rlzZ8qXL09wcDAdOnTg9Gn9D6aIxwusCp1+gHKhcCwREu8Hw2F1KhHxMB5ThHr37s3WrVuZP38+c+bMYenSpQwcODDfYxITE7npppu48cYbWb16NWvWrGHQoEHY7R7zsUUkPyENoMO3YPeD/V/9NaNMRKTgijx9viRt376dhg0bsmbNGmJjYwGYN28eXbt25cCBA0RFReV63HXXXccNN9zAuHHjivzemj4v4gH2fgYre5v3W7wNVw2yNo+IWK6gf7894tRIYmIioaGhzhIEEB8fj91uZ9WqVbkec+TIEVatWkVERARt2rQhMjKSjh07snz58nzf6+zZs6SlpbncRKSUi7kPmr1k3l8/FA58Z20eEfEYHlGEkpOTiYiIcNnm6+tLWFgYycnJuR6ze/duAMaMGcNDDz3EvHnzuOaaa4iLi+PXX/OebpuQkEBISIjzFh0d7b4PIiLFp+EIqPuQOU5oRS84ttrqRCLiASwtQiNGjMBms+V727FjR5Fe2+EwB00+/PDD9OvXj6uvvprx48dz1VVX8e9//zvP40aOHElqaqrztn///iK9v4iUMJsNWr4L1W6C7NPmGkOn9lidSkRKuSKvLO0Ojz/+OA888EC++9SpU4eqVaty5MgRl+1ZWVkcP36cqlVzvxp1tWrVAHKsft2gQQP27duX5/v5+/vj7+9fgPQiUurYfaHdl/BTB/hzIyy+GW5YCf5hVicTkVLK0iIUHh5OeHj4Jfdr3bo1J06cYN26dbRo0QKAhQsX4nA4aNWqVa7HxMTEEBUVxc6dO12279q1i5tvvvnyw4tI6VSuInT8Hn68DtJ2wtJu0PlH8AmwOpmIlEIeMUaoQYMG3HTTTTz00EOsXr2aFStWMGjQIO69917njLGDBw9Sv359Vq82xwXYbDaefPJJ3nrrLWbNmsVvv/3GqFGj2LFjB/3797fy44hIcQuKgk5zoVyweRX7n/tpjSERyZWlZ4QKY/r06QwaNIi4uDjsdjt33XUXb731lvP5c+fOsXPnTjIyMpzbhg0bxpkzZ3jsscc4fvw4zZo1Y/78+dStW9eKjyAiJSm0MbT/GhbdBL9/AeVjoHmC1alEpJTxiHWErKR1hEQ83O5p8PMD5v2Wk+GKhy2NIyIlo0ytIyQiUmR1+kKTseb9tf+Eg3OtzSMipYqKkIiUfY1HQZ0H/lpj6B44vt7qRCJSSqgIiUjZZ7PBtR9A1XjISofFt0D671anEpFSQEVIRLyDvRy0mwWhTeBMMizuCpknrE4lIhZTERIR7+EXYk6rD4yC1G2wrDtkZ1qdSkQspCIkIt4lqAZ0+h58K0DKIlg1ADR5VsRrqQiJiPep1Nz8mszmA3s/gc2jrU4kIhZRERIR7xTVBa5937y/ZRwk5X0xZhEpu1SERMR71e0PjZ4x768eCId/tDaPiJQ4FSER8W5Nx0HMP8DIhmU94M9NVicSkRKkIiQi3s1mg1YfQUQnyDpprjGUccDqVCJSQlSERER8/KDD1xDcAE4fNMvQuTSrU4lICVAREhEB8KsE1/8AAVXhxC/m12SOc1anEpFipiIkInJe+VrQaQ74BEHyfFj9f1pjSKSMUxESEfm7sBbQbgbY7LD737DlBasTiUgxUhESEblY9Vsh9h3z/ubnYM8n1uYRkWKjIiQikpsr/g8aPGXeX9Ufkhdam0dEioWKkIhIXponQM2e5qDpZd3hxFarE4mIm6kIiYjkxWaH1lMhvB2cS4XFXeH0YatTiYgbqQiJiOTHJwA6fAsVr4SMfX+tMXTK6lQi4iYqQiIil+Jf2VxjyD8c/twAK3qCI8vqVCLiBipCIiIFUaEOdJwDPoFwaC6sHaQ1hkTKABUhEZGCqnIttP0csMFv78P2V61OJCKXSUVIRKQwatwBLSaa9zeOgL2fW5tHRC6LipCISGFdNRiuesy8//MDcGSppXFEpOhUhEREiuKa1yG6OzgyYWk3SN1hdSIRKQIVIRGRorDZofWnUPk6yPwTFt8Mp1OsTiUihaQiJCJSVL6B0HE2VKgL6XthyW2QlW51KhEpBBUhEZHLERAOnX4w1xo6vgZW3AeObKtTiUgBqQiJiFyu4Cugw2yw+8PB2bB+mNYYEvEQKkIiIu4Q3gbafArYYNck2DHePDOUsticYp+yWGeKREohm2HoP1vyk5aWRkhICKmpqQQHB1sdR0RKu+1vwIYnzPt+lSHzjwvPBdUw1yCK7m5NNhEvUtC/3zojJCLiTvWHQ7Wbzft/L0EAGQdhWQ/Y/3XJ5xKRXKkIiYi4k+GAE5vzetL8sW6YviYTKSVUhERE3OnoMjh9IJ8dDMjYb+4nIpZTERIRcafTh927n4gUKxUhERF3Cqzm3v1EpFipCImIuFN4e3N2GLZ8drJB+r6SSiQi+fCYInT8+HF69+5NcHAwoaGh9O/fn1OnTuV7THJyMvfffz9Vq1alfPnyXHPNNXz11VcllFhEvJLdx5wiD+QsQ+cfG/BzX1jRGzJTSzCciFzMY4pQ79692bp1K/Pnz2fOnDksXbqUgQMH5ntMnz592LlzJ7Nnz2bz5s10796de+65hw0bNpRQahHxStHdof0sCKruuj2oBrT9Epo8DzYf+P0z+KEZHF1hTU4R8YwFFbdv307Dhg1Zs2YNsbGxAMybN4+uXbty4MABoqKicj2uQoUKvPfee9x///3ObZUrV+aVV15hwIABBXpvLagoIkXmyP5rFtlhc0xQeHvzjBHAsZ/N65Kl7zGvZN/oWWg8Cuy+1mYWKSPK1IKKiYmJhIaGOksQQHx8PHa7nVWrVuV5XJs2bZgxYwbHjx/H4XDwxRdfcObMGTp16pTnMWfPniUtLc3lJiJSJHYfiOwEMb3Mn+dLEECV66DrRoi531x7aMvz8FMHOLXborAi3skjilBycjIREREu23x9fQkLCyM5OTnP47788kvOnTtH5cqV8ff35+GHH+abb76hXr16eR6TkJBASEiI8xYdHe22zyEi4qJcMLT5D7T5DMqFwLFEmNsc9nxqdTIRr2FpERoxYgQ2my3f244dO4r8+qNGjeLEiRP89NNPrF27luHDh3PPPfeweXNeq77CyJEjSU1Ndd72799f5PcXESmQmF7QdROEt4Osk5B4vwZSi5QQS8cIHT16lD/++CPfferUqcOnn37K448/zp9//uncnpWVRUBAADNnzuTOO+/McVxSUhL16tVjy5YtNGrUyLk9Pj6eevXqMXny5AJl1BghESkxjizYmgBbxoKRDeVjzCvah7e1OpmIxyno329LR+WFh4cTHh5+yf1at27NiRMnWLduHS1atABg4cKFOBwOWrVqlesxGRkZANjtrie9fHx8cDgcl5lcRKQY2H2hySioGg8re5sDqX/qAI1GQeNnNZBapBh4xBihBg0acNNNN/HQQw+xevVqVqxYwaBBg7j33nudM8YOHjxI/fr1Wb16NQD169enXr16PPzww6xevZqkpCTeeOMN5s+fT7du3Sz8NCIilxDe+qKB1GP/Gki9x+pkImWORxQhgOnTp1O/fn3i4uLo2rUr7dq144MPPnA+f+7cOXbu3Ok8E1SuXDnmzp1LeHg4t912G02bNuU///kP06ZNo2vXrlZ9DBGRgnEZSB3810DqZhpILeJmHrGOkJU0RkhELHdqLyT+48LCi7Xug5bvgl+IpbFESrMytY6QiIhXqxADcYsvWpG6uVakFnEDFSEREU9wfiB1/DIoXxvS95rjhn4ZY842E5EiURESEfEkuQ6k7qiB1CJFpCIkIuJpcgykXml+VbZnutXJRDyOipCIiKeK6QU3bzIXXDyXZg6o1orUIoWiIiQi4smcA6nHXjSQeqW1uUQ8hIqQiIins/tCk+cuGkjdXgOpRQpARUhEpKzQQGqRQlMREhEpSzSQWqRQVIRERMqi3AZSr/yHBlKLXERFSESkrLp4IPXe6RpILXIRFSERkbJMA6lF8qUiJCLiDZwDqf9x0UDqvVYnE7GUipCIiLcoFwxtPoE20/82kLqZBlKLV1MREhHxNjH3aSC1yF9UhEREvJFzIPUYsNk1kFq8loqQiIi3svtCk9F/DaSO+WsgdQfYPFYDqcVrqAiJiHi78DZw88a/BlJnw+YxrgOpHdmQshj2fm7+dGRbFlXE3XytDiAiIqWAX4g5kDrqZljzyIWB1HUehP2zIOPAhX2DakCLiRDd3bq8Im6iM0IiInJBzH3m2aEqbcyB1DsnuJYggIyDsKwH7P/aioQibqUiJCIirirUhs4LzSn2uTLMH+uG6Wsy8XgqQiIiktMfieYZoTwZkLEfji4rsUgixUFFSEREcjp9uGD7/fwAbBxpDqLOzizORCLFQoOlRUQkp8BqBdsv/XfY9rJ5860AkZ0h6iao1gUq1CnejCJuoCIkIiI5hbc3Z4dlHMQ5JsiFzSxLzV6G5B/N25kjcHC2eQOoeIVZiKrdBJGdwLd8CX4AkYKxGYaR2/+Fy1/S0tIICQkhNTWV4OC8Bg6KiJRB+782Z4cBrmXIZv5oP+vCFHrDAX9uhMP/g8PzzBWqjb8tymj3M8vV+bNFIY3BZiuBDyHeqqB/v1WELkFFSES82v6vYd3Qi9YRioYWE/JfR+hcGiQvvFCM0ve6Ph8YdeFsUdV48A8rjvTixVSE3ERFSES8niPbnB12+rD5dVh4e7D7FPx4w4CTu8xSdGgeHFkM2acvPG+zQ9i1ZjGKugnCWhbu9UVyoSLkJipCIiJuln0Gjiy7cLYodavr836VoOoNf50x6gJB1a3JKR5NRchNVIRERIpZxoG/StH/4PB8OHfC9fmQxhfGFoW3Bx9/S2KKZ1ERchMVIRGREuTIgj/WmGeKDv8P/liNy0BtnyBzBlq1v4pRxSs06FpypSLkJipCIiIWOvsHJP90oRhdvNBj+doXxhZFdoZyFfN+rcsd6yQeRUXITVSERERKCcOAE5v/NkV/GTjOXXje5gvhbS+cLarUzByIDXnMfqsBLSbmP/tNPJaKkJuoCImIlFLnTpkz0M7PRjv1m+vzAZFQ9Ubwrww7J5JzYchc1kOSMkNFyE1UhEREPMTJpAuDrlMWQFZ6AQ6ymWeGbt+jr8nKGBUhN1EREhHxQNmZcGwF/DYFfv/80vsHREH5mhAQDv7hF3663K9i3rf6UiEa61QgBf37rWuNiYhI2ePjB5HXw+nkghWhM4fMW4FeOzDvspTbtnLB7pvZVpbGOpWSQucxRejFF1/k+++/Z+PGjfj5+XHixIlLHmMYBqNHj2bKlCmcOHGCtm3b8t5773HFFVcUf2AREbFeYLWC7XfNW1C+Bpw9CmeOwtljf7t/9MJ9x1lzVeyMfeatIOzlLpxRKkiB8g+7MMj775zXfrvoi5yMg+Z2TxrrVIoKnccUoczMTO6++25at27NRx99VKBjXn31Vd566y2mTZtG7dq1GTVqFF26dGHbtm0EBAQUc2IREbFceHvzD2zGQXIOlgbnGKEr/3npsxGGAVmnXAvSxUXp4m1Z6ebMttOHzFtB2OzgV9n1Kzm/yn+d2crtMxjm51g7GKq0AZ8A8yK39nLmTLrSts5SKSt0HjdGaOrUqQwbNuySZ4QMwyAqKorHH3+cJ554AoDU1FQiIyOZOnUq9957b4HeT2OEREQ8nPMPL7j+8S2BWWNZp/M+u5Rbgbp4VW13sJczi5GtnPmVoa3chW15/XTZN5/9cvuZ3zE2H/Pf4uyRPMK6b/C6148R2rNnD8nJycTHxzu3hYSE0KpVKxITE/MsQmfPnuXs2bPOx2lpacWeVUREilF0d7Ps5PpVzITiPfvgGwi+0VA+umD7O86Zxenis0spi+HA10XL4Dh3Yb2lc/nvaj0DMvabY4ciO5XIO5bZIpScnAxAZGSky/bIyEjnc7lJSEhg7NixxZpNRERKWHR3qH5HqRicmy97OTPbxWObQpsUrAh1XgDh7cCRCcY5c/accc587Pj7z9y2/e1nrsfk8Rr5vs9FP8/+kc/ZoL+5eAXxYmRpERoxYgSvvPJKvvts376d+vXrl1AiGDlyJMOHD3c+TktLIzq6gE1eRERKL7tPiZ1lcLuCjnWK6Gh+Th+/kk5YMCmLYcH1l96voIPc3cDSIvT444/zwAMP5LtPnTp1ivTaVatWBSAlJYVq1S78QlNSUmjevHmex/n7++Pvrysbi4hIKWL3MWdULeuBObYpl7FOLSaUvjNcFytooQtvX2KRLC1C4eHhhIeHF8tr165dm6pVq7JgwQJn8UlLS2PVqlU88sgjxfKeIiIixcbKsU7uUgoLnceMEdq3bx/Hjx9n3759ZGdns3HjRgDq1atHhQoVAKhfvz4JCQnceeed2Gw2hg0bxgsvvMAVV1zhnD4fFRVFt27drPsgIiIiReUpY53yU8oKnccUoeeee45p06Y5H1999dUALFq0iE6dOgGwc+dOUlNTnfs89dRTpKenM3DgQE6cOEG7du2YN2+e1hASERHP5cljnc4rRYXO49YRKmlaR0hERMTzFPTvdy5reIuIiIh4BxUhERER8VoqQiIiIuK1VIRERETEa6kIiYiIiNdSERIRERGvpSIkIiIiXktFSERERLyWipCIiIh4LY+5xIZVzi+8nZaWZnESERERKajzf7cvdQENFaFLOHnyJADR0dEWJxEREZHCOnnyJCEhIXk+r2uNXYLD4eDQoUNUrFgRm83mttdNS0sjOjqa/fv36xpmpYT+TUoX/XuULvr3KF3073FphmFw8uRJoqKisNvzHgmkM0KXYLfbqVGjRrG9fnBwsP6PuJTRv0npon+P0kX/HqWL/j3yl9+ZoPM0WFpERES8loqQiIiIeC0VIYv4+/szevRo/P39rY4if9G/Semif4/SRf8epYv+PdxHg6VFRETEa+mMkIiIiHgtFSERERHxWipCIiIi4rVUhERERMRrqQhZ5J133iEmJoaAgABatWrF6tWrrY7klRISEmjZsiUVK1YkIiKCbt26sXPnTqtjyV9efvllbDYbw4YNszqKVzt48CD/+Mc/qFy5MoGBgTRp0oS1a9daHcsrZWdnM2rUKGrXrk1gYCB169Zl3Lhxl7yeluRNRcgCM2bMYPjw4YwePZr169fTrFkzunTpwpEjR6yO5nWWLFnCo48+ys8//8z8+fM5d+4cN954I+np6VZH83pr1qzh/fffp2nTplZH8Wp//vknbdu2pVy5cvzwww9s27aNN954g0qVKlkdzSu98sorvPfee0yaNInt27fzyiuv8Oqrr/L2229bHc1jafq8BVq1akXLli2ZNGkSYF7PLDo6msGDBzNixAiL03m3o0ePEhERwZIlS+jQoYPVcbzWqVOnuOaaa3j33Xd54YUXaN68ORMmTLA6llcaMWIEK1asYNmyZVZHEeDWW28lMjKSjz76yLntrrvuIjAwkE8//dTCZJ5LZ4RKWGZmJuvWrSM+Pt65zW63Ex8fT2JiooXJBCA1NRWAsLAwi5N4t0cffZRbbrnF5f9PxBqzZ88mNjaWu+++m4iICK6++mqmTJlidSyv1aZNGxYsWMCuXbsA2LRpE8uXL+fmm2+2OJnn0kVXS9ixY8fIzs4mMjLSZXtkZCQ7duywKJWAeWZu2LBhtG3blsaNG1sdx2t98cUXrF+/njVr1lgdRYDdu3fz3nvvMXz4cJ5++mnWrFnDkCFD8PPzo2/fvlbH8zojRowgLS2N+vXr4+PjQ3Z2Ni+++CK9e/e2OprHUhES+cujjz7Kli1bWL58udVRvNb+/fsZOnQo8+fPJyAgwOo4gvkfCLGxsbz00ksAXH311WzZsoXJkyerCFngyy+/ZPr06Xz22Wc0atSIjRs3MmzYMKKiovTvUUQqQiWsSpUq+Pj4kJKS4rI9JSWFqlWrWpRKBg0axJw5c1i6dCk1atSwOo7XWrduHUeOHOGaa65xbsvOzmbp0qVMmjSJs2fP4uPjY2FC71OtWjUaNmzosq1BgwZ89dVXFiXybk8++SQjRozg3nvvBaBJkyb8/vvvJCQkqAgVkcYIlTA/Pz9atGjBggULnNscDgcLFiygdevWFibzToZhMGjQIL755hsWLlxI7dq1rY7k1eLi4ti8eTMbN2503mJjY+nduzcbN25UCbJA27ZtcywpsWvXLmrVqmVRIu+WkZGB3e76p9vHxweHw2FRIs+nM0IWGD58OH379iU2NpZrr72WCRMmkJ6eTr9+/ayO5nUeffRRPvvsM7777jsqVqxIcnIyACEhIQQGBlqczvtUrFgxx/is8uXLU7lyZY3bsshjjz1GmzZteOmll7jnnntYvXo1H3zwAR988IHV0bzSbbfdxosvvkjNmjVp1KgRGzZs4M033+TBBx+0OprH0vR5i0yaNInXXnuN5ORkmjdvzltvvUWrVq2sjuV1bDZbrts//vhjHnjggZINI7nq1KmTps9bbM6cOYwcOZJff/2V2rVrM3z4cB566CGrY3mlkydPMmrUKL755huOHDlCVFQUvXr14rnnnsPPz8/qeB5JRUhERES8lsYIiYiIiNdSERIRERGvpSIkIiIiXktFSERERLyWipCIiIh4LRUhERER8VoqQiIiIuK1VIREJFedOnVi2LBhVsfIwWaz8e2331odo9iMGTOG5s2bWx1DxGuoCIlIrr7++mvGjRvnfBwTE1OiqzvnVQgOHz7MzTffXGI5RKRs07XGRCRXYWFhxfK6mZmZl3UpgKpVq7oxjfc4d+4c5cqVszqGSKmjM0Iikqu/fzXWqVMnfv/9dx577DFsNpvLNdqWL19O+/btCQwMJDo6miFDhpCenu58PiYmhnHjxtGnTx+Cg4MZOHAgAP/617+48sorCQoKok6dOowaNYpz584BMHXqVMaOHcumTZuc7zd16lQg51djmzdvpnPnzgQGBlK5cmUGDhzIqVOnnM8/8MADdOvWjddff51q1apRuXJlHn30Ued75eb82ahPPvmEmJgYQkJCuPfeezl58qTL57r4DFnz5s0ZM2aM87HNZuP999/n1ltvJSgoiAYNGpCYmMhvv/1Gp06dKF++PG3atCEpKSlHhvfff5/o6GiCgoK45557SE1NdXn+ww8/pEGDBgQEBFC/fn3effdd53N79+7FZrMxY8YMOnbsSEBAANOnT8/z84p4MxUhEbmkr7/+mho1avD8889z+PBhDh8+DEBSUhI33XQTd911F7/88gszZsxg+fLlDBo0yOX4119/nWbNmrFhwwZGjRoFmFeanzp1Ktu2bWPixIlMmTKF8ePHA9CzZ08ef/xxGjVq5Hy/nj175siVnp5Oly5dqFSpEmvWrGHmzJn89NNPOd5/0aJFJCUlsWjRIqZNm8bUqVOdxSovSUlJfPvtt8yZM4c5c+awZMkSXn755UL/7s6XwI0bN1K/fn3uu+8+Hn74YUaOHMnatWsxDCNH3t9++40vv/yS//73v8ybN48NGzbwz3/+0/n89OnTee6553jxxRfZvn07L730EqNGjWLatGkurzNixAiGDh3K9u3b6dKlS6Gzi3gFQ0QkFx07djSGDh3qfFyrVi1j/PjxLvv079/fGDhwoMu2ZcuWGXa73Th9+rTzuG7dul3y/V577TWjRYsWzsejR482mjVrlmM/wPjmm28MwzCMDz74wKhUqZJx6tQp5/Pff/+9YbfbjeTkZMMwDKNv375GrVq1jKysLOc+d999t9GzZ888s4wePdoICgoy0tLSnNuefPJJo1WrVs7Huf0+mjVrZowePdol67PPPut8nJiYaADGRx995Nz2+eefGwEBAS7v7ePjYxw4cMC57YcffjDsdrtx+PBhwzAMo27dusZnn33m8t7jxo0zWrdubRiGYezZs8cAjAkTJuT5GUXEpDFCIlJkmzZt4pdffnH52sUwDBwOB3v27KFBgwYAxMbG5jh2xowZvPXWWyQlJXHq1CmysrIIDg4u1Ptv376dZs2aUb58eee2tm3b4nA42LlzJ5GRkQA0atQIHx8f5z7VqlVj8+bN+b52TEwMFStWdDnmyJEjhcoH0LRpU+f983maNGnisu3MmTOkpaU5P3/NmjWpXr26c5/WrVs7P1PFihVJSkqif//+PPTQQ859srKyCAkJcXnv3H7vIuJKRUhEiuzUqVM8/PDDDBkyJMdzNWvWdN7/e1EBSExMpHfv3owdO5YuXboQEhLCF198wRtvvFEsOS8eJGyz2XA4HJd1jN1uxzAMl31yG3f099c5P7Yqt22XynPe+fFPU6ZMoVWrVi7P/b3sQc7fu4jkpCIkIgXi5+dHdna2y7ZrrrmGbdu2Ua9evUK91sqVK6lVqxbPPPOMc9vvv/9+yfe7WIMGDZg6dSrp6enOP/orVqzAbrdz1VVXFSpTYYWHhzvHSgGkpaWxZ88et7z2vn37OHToEFFRUQD8/PPPzs8UGRlJVFQUu3fvpnfv3m55PxFvpsHSIlIgMTExLF26lIMHD3Ls2DHAnPm1cuVKBg0axMaNG/n111/57rvvcgz+vdgVV1zBvn37+OKLL0hKSuKtt97im2++yfF+e/bsYePGjRw7doyzZ8/meJ3evXsTEBBA37592bJlC4sWLWLw4MHcf//9zq+hikvnzp355JNPWLZsGZs3b6Zv3745zsgU1fnPtGnTJpYtW8aQIUO45557nEsHjB07loSEBN566y127drF5s2b+fjjj3nzzTfd8v4i3kRFSEQK5Pnnn2fv3r3UrVuX8PBwwBz/smTJEnbt2kX79u25+uqree6555xnMvJy++2389hjjzFo0CCaN2/OypUrnbPJzrvrrru46aabuP766wkPD+fzzz/P8TpBQUH873//4/jx47Rs2ZIePXoQFxfHpEmT3PfB8zBy5Eg6duzIrbfeyi233EK3bt2oW7euW167Xr16dO/ena5du3LjjTfStGlTl+nxAwYM4MMPP+Tjjz+mSZMmdOzYkalTp1K7dm23vL+IN7EZF3/JLSIiIuIldEZIREREvJaKkIiIiHgtFSERERHxWipCIiIi4rVUhERERMRrqQiJiIiI11IREhEREa+lIiQiIiJeS0VIREREvJaKkIiIiHgtFSERERHxWipCIiIi4rX+H0HDQ1UntDG8AAAAAElFTkSuQmCC",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "import matplotlib.pyplot as plt\n",
- "import pandas as pd\n",
- "\n",
- "df = pd.DataFrame(job.metrics())\n",
- "df.sort_values(by=[\"iteration_number\"], inplace=True)\n",
- "\n",
- "plt.plot(df[\"iteration_number\"], df[\"expval\"], \"-o\", color=\"orange\")\n",
- "plt.xlabel(\"iteration number\")\n",
- "plt.ylabel(\"expectation value\")\n",
- "plt.title(\"Simulator results\")\n",
- "\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Running on a QPU with priority\n",
- "\n",
- "The next step is to see how well the qubit rotation works on a real QPU. We\n",
- "create a hybrid job with the Rigetti device as the priority QPU. We also increase the number of\n",
- "steps to 10.\n",
- "\n",
- "Using hybrid jobs for iterative algorithms is very beneficial because you retain priority access to the\n",
- "target QPU. So once your quantum tasks are created in the hybrid job, they run ahead of other tasks\n",
- "waiting in the *quantum task queue*. This means your\n",
- "algorithm will not be interrupted by other quantum tasks, so it will run more efficiently and\n",
- "predictably. Quantum tasks submitted as part of a hybrid job have priority, and are aggregated in the *priority task queue*.\n",
- "\n",
- "Hybrid jobs have their own *hybrid jobs queue* so that only a single\n",
- "hybrid job can run on a QPU at a time. Each QPU has its own hybrid jobs queue. Note that this is a different queue from the quantum tasks. For a single quantum circuit, or a batch of circuit, it’s\n",
- "recommended to create quantum tasks instead of hybrid jobs. For more information on quantum tasks and hybrid jobs queue see the [Amazon Braket documentation](https://docs.aws.amazon.com/braket/latest/developerguide/braket-task-when.html).\n",
- "\n",
- "To get QPU priority, you must ensure that the device ARN used within the function matches that\n",
- "specified in the decorator. For convenience, you can use the helper function ``get_device_arn()`` to\n",
- "automatically capture the device ARN declared in ``@hybrid_job``.\n",
- "\n",
- "
\n",
- " Note: Only hybrid jobs running on AWS receive priority. Hybrid jobs running locally, or with a mismatched device ARN do not get priority task queueing. \n",
- "
\n",
- "\n",
- "In the previous example, we declared the local simulator outside the decorated function scope.\n",
- "However, for AWS devices such as QPUs or on-demand simulators, the device must be declared within the function scope. \n",
- "\n",
- "
\n",
- " Note: AWS devices must be declared within the body of the decorated function.\n",
- "
"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {},
- "outputs": [],
- "source": [
- "from braket.devices import Devices\n",
- "\n",
- "\n",
- "device_arn = Devices.Rigetti.AspenM3\n",
- "\n",
- "\n",
- "@hybrid_job(device=device_arn) # set priority QPU\n",
- "def qpu_qubit_rotation_hybrid_job(num_steps=10, stepsize=0.5):\n",
- " # AWS devices must be declared within the decorated function.\n",
- " device = qml.device(\n",
- " \"braket.aws.qubit\",\n",
- " device_arn=device_arn.value, # Make sure the device ARN matches the hybrid job device ARN\n",
- " wires=2,\n",
- " shots=1_000,\n",
- " )\n",
- "\n",
- " @qml.qnode(device)\n",
- " def circuit(params):\n",
- " qml.RX(params[0], wires=0)\n",
- " qml.RY(params[1], wires=0)\n",
- " return qml.expval(qml.PauliZ(0))\n",
- "\n",
- " opt = qml.GradientDescentOptimizer(stepsize=stepsize)\n",
- " params = np.array([0.5, 0.75])\n",
- "\n",
- " for i in range(num_steps):\n",
- " # update the circuit parameters\n",
- " params = opt.step(circuit, params)\n",
- " expval = circuit(params)\n",
- "\n",
- " log_metric(metric_name=\"expval\", iteration_number=i, value=expval)\n",
- "\n",
- " return params"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "To get a sense of how long we will wait before the hybrid job runs, we can check the hybrid job\n",
- "queue depth with `AwsDevice(device_arn).queue_depth().jobs`. We can also check if the device is\n",
- "currently available with `AwsDevice(device_arn).is_available()`.\n",
- "\n",
- "You can check the queue depth on the devices page of the [Amazon Braket Console](https://console.aws.amazon.com/braket/home). Below, we show the devices page for Rigetti Aspen-M-3.\n",
- "\n",
- "\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "When there are no other hybrid jobs in the queue ahead of you, and the device is available, the hybrid job will start running.\n",
- "\n",
- "
\n",
- " Note: Running the following cell will only run once the QPU is available. This may take a long time and will result in usage fees charged to your AWS account. Only run the cell if you are comfortable with the potential wait-time and costs. We recommend monitoring the Billing & Cost Management Dashboard on the AWS console.\n",
- "
"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "AwsQuantumJob('arn':'arn:aws:braket:us-west-2:318845237731:job/qpu-qubit-rotation-hybrid-job-1700084458165')\n"
- ]
- }
- ],
- "source": [
- "qpu_job = qpu_qubit_rotation_hybrid_job(num_steps=10, stepsize=0.5)\n",
- "print(qpu_job)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Next, we wait for the algorithm to complete and download the result. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{'result': tensor([0.0205, 3.1065], requires_grad=True)}"
- ]
- },
- "execution_count": 17,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "qpu_job.result()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Next, we plot the expectation value per iteration number below. We see that on a real QPU, the data is not as smooth as the simulator, but the minimum still is detected correctly!"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "{'timestamp': [1700084730.969484, 1700084698.0504165, 1700084679.9848497, 1700084664.1287766, 1700084648.2972944, 1700084632.2871127, 1700084616.684862], 'expval': [-0.972, -0.784, -0.548, -0.36, -0.07, 0.11, 0.388], 'iteration_number': [7.0, 5.0, 4.0, 3.0, 2.0, 1.0, 0.0]}\n"
- ]
- }
- ],
- "source": [
- "# May need to wait a bit before metrics show up\n",
- "# If metrics aren't there, try again after 5 seconds\n",
- "import time\n",
- "\n",
- "time.sleep(10)\n",
- "print(qpu_job.metrics())"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 19,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "df = pd.DataFrame(qpu_job.metrics())\n",
- "df.sort_values(by=[\"iteration_number\"], inplace=True)\n",
- "\n",
- "plt.plot(df[\"iteration_number\"], df[\"expval\"], \"-o\", color=\"teal\")\n",
- "plt.xlabel(\"iteration number\")\n",
- "plt.ylabel(\"expectation value\")\n",
- "plt.title(\"QPU results\")\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "
\n",
- " Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. \n",
- " Estimated charges shown may differ from your actual charges. \n",
- " Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2)\n",
- " Estimated cost to run this example is $39 USD.\n",
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Conclusion\n",
- "\n",
- "In this tutorial, we showed how to migrate from local Python functions to running algorithms on simulators and QPUs on Amazon Braket.\n",
- "We adapted the simple example of rotating a qubit using gradient descent, running this on both a\n",
- "local simulator and a real QPU. \n",
- "Using Amazon Braket Hybrid Jobs allowed us to run algorithms asynchronously, scale classical compute using AWS, and obtain priority access to the selected QPU for the duration of our algorithm."
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "conda_braket",
- "language": "python",
- "name": "conda_braket"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.10.13"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 4
-}
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
\ No newline at end of file
diff --git a/examples/hybrid_jobs/7_Running_notebooks_as_hybrid_jobs/result/ankaa-2/0_Getting_started_papermill.ipynb b/examples/hybrid_jobs/7_Running_notebooks_as_hybrid_jobs/result/ankaa-2/0_Getting_started_papermill.ipynb
index 8a9179a98..2c8b48ac6 100644
--- a/examples/hybrid_jobs/7_Running_notebooks_as_hybrid_jobs/result/ankaa-2/0_Getting_started_papermill.ipynb
+++ b/examples/hybrid_jobs/7_Running_notebooks_as_hybrid_jobs/result/ankaa-2/0_Getting_started_papermill.ipynb
@@ -1,522 +1,522 @@
{
- "cells": [
- {
- "attachments": {},
- "cell_type": "markdown",
- "id": "21a58fee",
- "metadata": {
- "papermill": {
- "duration": 0.003786,
- "end_time": "2023-02-21T16:43:45.362940",
- "exception": false,
- "start_time": "2023-02-21T16:43:45.359154",
- "status": "completed"
+ "cells": [
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "id": "21a58fee",
+ "metadata": {
+ "papermill": {
+ "duration": 0.003786,
+ "end_time": "2023-02-21T16:43:45.362940",
+ "exception": false,
+ "start_time": "2023-02-21T16:43:45.359154",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "source": [
+ "# Example notebook \n",
+ "\n",
+ "This notebook is a copy from `examples/getting_started/0_Getting_started/0_Getting_started.ipynb` with a small modifications for use with [Papermill](https://github.com/nteract/papermill) and Amazon Braket Hybrid Jobs. \n",
+ "\n",
+ "## Papermill parameters\n",
+ "\n",
+ "Papermill is a tool for parameterizing, executing, and analyzing Jupyter Notebooks. \n",
+ "To parameterize a notebook, we need tag a cell that contains all the parameters. \n",
+ "We can only tag one cell, and for simplicity we place it at the top of the notebook. \n",
+ "Full instructions are available here https://papermill.readthedocs.io/en/latest/usage-parameterize.html#designate-parameters-for-a-cell. \n",
+ "\n",
+ "Below, we tag the parameter `shots=1000`. \n",
+ "We can then run the notebook as usual cell-by-cell to see the results. \n",
+ "\n",
+ "We additionally add two Braket specific parameters called `device_arn` and `results_dir`. \n",
+ "These will be overridden when running a Hybrid Job. \n",
+ "\n",
+ "**In the following cell, we added a tag called `parameters` for Papermill to recognize. If you don't see the tag, follow the instructions above.**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "2436f1be",
+ "metadata": {
+ "execution": {
+ "iopub.execute_input": "2023-02-21T16:43:45.371205Z",
+ "iopub.status.busy": "2023-02-21T16:43:45.370808Z",
+ "iopub.status.idle": "2023-02-21T16:43:45.379588Z",
+ "shell.execute_reply": "2023-02-21T16:43:45.378335Z"
+ },
+ "papermill": {
+ "duration": 0.015001,
+ "end_time": "2023-02-21T16:43:45.381543",
+ "exception": false,
+ "start_time": "2023-02-21T16:43:45.366542",
+ "status": "completed"
+ },
+ "tags": [
+ "parameters"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Papermill parameters\n",
+ "shots = 1000\n",
+ "\n",
+ "# Braket specific parameters\n",
+ "device_arn = \"arn:aws:braket:::device/quantum-simulator/amazon/sv1\"\n",
+ "results_dir = \".\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "a0fb6bd8",
+ "metadata": {
+ "execution": {
+ "iopub.execute_input": "2023-02-21T16:43:45.389513Z",
+ "iopub.status.busy": "2023-02-21T16:43:45.388977Z",
+ "iopub.status.idle": "2023-02-21T16:43:45.393453Z",
+ "shell.execute_reply": "2023-02-21T16:43:45.392426Z"
+ },
+ "papermill": {
+ "duration": 0.010707,
+ "end_time": "2023-02-21T16:43:45.395539",
+ "exception": false,
+ "start_time": "2023-02-21T16:43:45.384832",
+ "status": "completed"
+ },
+ "tags": [
+ "injected-parameters"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Parameters\n",
+ "shots = 1000\n",
+ "device_arn = \"arn:aws:braket:us-west-1::device/qpu/rigetti/Ankaa 2\"\n",
+ "results_dir = \"/opt/braket/model\""
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "id": "c8f24ceb",
+ "metadata": {
+ "papermill": {
+ "duration": 0.003094,
+ "end_time": "2023-02-21T16:43:45.402021",
+ "exception": false,
+ "start_time": "2023-02-21T16:43:45.398927",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "source": [
+ "# Getting started with Amazon Braket\n",
+ "\n",
+ "In this tutorial we prepare a maximally entangled Bell state between two qubits. \n",
+ "We then run our circuit on a local simulator and obtain the results."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "472c72f6",
+ "metadata": {
+ "execution": {
+ "iopub.execute_input": "2023-02-21T16:43:45.409445Z",
+ "iopub.status.busy": "2023-02-21T16:43:45.408896Z",
+ "iopub.status.idle": "2023-02-21T16:43:47.305956Z",
+ "shell.execute_reply": "2023-02-21T16:43:47.304998Z"
+ },
+ "papermill": {
+ "duration": 1.90327,
+ "end_time": "2023-02-21T16:43:47.308212",
+ "exception": false,
+ "start_time": "2023-02-21T16:43:45.404942",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "outputs": [],
+ "source": [
+ "import time\n",
+ "\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "%matplotlib inline\n",
+ "\n",
+ "from braket.aws import AwsDevice\n",
+ "from braket.circuits import Circuit\n",
+ "from braket.devices import LocalSimulator\n",
+ "from braket.jobs.metrics import log_metric\n",
+ "from braket.tracking import Tracker # cost tracker\n",
+ "\n",
+ "cost_tracker = Tracker().start()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a7a2db04",
+ "metadata": {
+ "papermill": {
+ "duration": 0.002877,
+ "end_time": "2023-02-21T16:43:47.314835",
+ "exception": false,
+ "start_time": "2023-02-21T16:43:47.311958",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "source": [
+ "## Build a circuit\n",
+ "\n",
+ "Let's build a Bell state with two qubits. By calling `Circuit()` we create an empty circuit, and we can just add gates to the circuit. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "0928121e",
+ "metadata": {
+ "execution": {
+ "iopub.execute_input": "2023-02-21T16:43:47.322937Z",
+ "iopub.status.busy": "2023-02-21T16:43:47.322367Z",
+ "iopub.status.idle": "2023-02-21T16:43:47.329784Z",
+ "shell.execute_reply": "2023-02-21T16:43:47.328703Z"
+ },
+ "papermill": {
+ "duration": 0.014274,
+ "end_time": "2023-02-21T16:43:47.332315",
+ "exception": false,
+ "start_time": "2023-02-21T16:43:47.318041",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "T : |0|1|\n",
+ " \n",
+ "q0 : -H-C-\n",
+ " | \n",
+ "q1 : ---X-\n",
+ "\n",
+ "T : |0|1|\n"
+ ]
+ }
+ ],
+ "source": [
+ "# build a Bell state with two qubits.\n",
+ "bell = Circuit().h(0).cnot(control=0, target=1)\n",
+ "print(bell)"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "id": "253f5e35",
+ "metadata": {
+ "papermill": {
+ "duration": 0.003065,
+ "end_time": "2023-02-21T16:43:47.338674",
+ "exception": false,
+ "start_time": "2023-02-21T16:43:47.335609",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "source": [
+ "## Submit the circuit to the local simulator and obtain the results\n",
+ "\n",
+ "Next, we choose either a local simulator or an Amazon Braket device. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "b7c90b2f",
+ "metadata": {
+ "execution": {
+ "iopub.execute_input": "2023-02-21T16:43:47.346544Z",
+ "iopub.status.busy": "2023-02-21T16:43:47.345827Z",
+ "iopub.status.idle": "2023-02-21T16:43:47.822456Z",
+ "shell.execute_reply": "2023-02-21T16:43:47.821578Z"
+ },
+ "papermill": {
+ "duration": 0.482774,
+ "end_time": "2023-02-21T16:43:47.824541",
+ "exception": false,
+ "start_time": "2023-02-21T16:43:47.341767",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "outputs": [],
+ "source": [
+ "# set up device\n",
+ "if \"local\" in device_arn:\n",
+ " device = LocalSimulator()\n",
+ "else:\n",
+ " device = AwsDevice(device_arn)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "2366ca95",
+ "metadata": {
+ "execution": {
+ "iopub.execute_input": "2023-02-21T16:43:47.833244Z",
+ "iopub.status.busy": "2023-02-21T16:43:47.832639Z",
+ "iopub.status.idle": "2023-02-21T16:44:18.319776Z",
+ "shell.execute_reply": "2023-02-21T16:44:18.318577Z"
+ },
+ "papermill": {
+ "duration": 30.49638,
+ "end_time": "2023-02-21T16:44:18.324694",
+ "exception": false,
+ "start_time": "2023-02-21T16:43:47.828314",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "{'00': 494, '01': 22, '10': 50, '11': 434}\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Run the circuit and get results\n",
+ "result = device.run(bell, shots=shots).result()\n",
+ "\n",
+ "# get measurement shots\n",
+ "counts = result.measurement_counts\n",
+ "counts = {k: counts[k] for k in sorted(counts)} # sort results\n",
+ "print(counts)"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "id": "c41e8691",
+ "metadata": {
+ "papermill": {
+ "duration": 0.003065,
+ "end_time": "2023-02-21T16:44:18.331341",
+ "exception": false,
+ "start_time": "2023-02-21T16:44:18.328276",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "source": [
+ "Hybrid Jobs enables logging of metrics during the job. \n",
+ "In the example below, we track the total cost of running the circuit on simulators or QPUs by using the cost tracker.\n",
+ "\n",
+ "We also track the number of counts in the \"00\" state. It is best practice to log all metrics per iteration at a common timestamp to avoid duplication."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "0e6ee106",
+ "metadata": {
+ "execution": {
+ "iopub.execute_input": "2023-02-21T16:44:18.339367Z",
+ "iopub.status.busy": "2023-02-21T16:44:18.338979Z",
+ "iopub.status.idle": "2023-02-21T16:44:18.365109Z",
+ "shell.execute_reply": "2023-02-21T16:44:18.364151Z"
+ },
+ "papermill": {
+ "duration": 0.032881,
+ "end_time": "2023-02-21T16:44:18.367429",
+ "exception": false,
+ "start_time": "2023-02-21T16:44:18.334548",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Metrics - timestamp=1676997858.3620458; cost=0.65;\n",
+ "Metrics - timestamp=1676997858.3620458; counts_00=494;\n"
+ ]
+ }
+ ],
+ "source": [
+ "total_cost = float(cost_tracker.simulator_tasks_cost() + cost_tracker.qpu_tasks_cost())\n",
+ "\n",
+ "timestamp = time.time()\n",
+ "\n",
+ "log_metric(metric_name=\"cost\", value=float(total_cost), timestamp=timestamp)\n",
+ "\n",
+ "log_metric(metric_name=\"counts_00\", value=counts[\"00\"], timestamp=timestamp)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3f4a07f0",
+ "metadata": {
+ "papermill": {
+ "duration": 0.003183,
+ "end_time": "2023-02-21T16:44:18.374145",
+ "exception": false,
+ "start_time": "2023-02-21T16:44:18.370962",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "source": [
+ "**The following cell saves the results to a file**\n",
+ "\n",
+ "The use of `results_dir` is that any results are saved to the correct directory when called from a Braket Job. Below, we save the measurement counts to a .pkl file. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "31102e41",
+ "metadata": {
+ "execution": {
+ "iopub.execute_input": "2023-02-21T16:44:18.382365Z",
+ "iopub.status.busy": "2023-02-21T16:44:18.381771Z",
+ "iopub.status.idle": "2023-02-21T16:44:18.386881Z",
+ "shell.execute_reply": "2023-02-21T16:44:18.385954Z"
+ },
+ "papermill": {
+ "duration": 0.011421,
+ "end_time": "2023-02-21T16:44:18.388857",
+ "exception": false,
+ "start_time": "2023-02-21T16:44:18.377436",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "outputs": [],
+ "source": [
+ "import pickle\n",
+ "\n",
+ "# save measurement counts to a file\n",
+ "with open(f\"{results_dir}/results.pkl\", \"wb\") as f:\n",
+ " pickle.dump(counts, f)\n",
+ "\n",
+ "\n",
+ "# re-load the results with\n",
+ "# with open(f\"{results_dir}/results.pkl\", 'rb') as f:\n",
+ "# counts = pickle.load(f)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1347bd65",
+ "metadata": {
+ "papermill": {
+ "duration": 0.003234,
+ "end_time": "2023-02-21T16:44:18.395896",
+ "exception": false,
+ "start_time": "2023-02-21T16:44:18.392662",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "source": [
+ "**The following cell saves the figure to a file**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "5da96893",
+ "metadata": {
+ "execution": {
+ "iopub.execute_input": "2023-02-21T16:44:18.404309Z",
+ "iopub.status.busy": "2023-02-21T16:44:18.403735Z",
+ "iopub.status.idle": "2023-02-21T16:44:18.607364Z",
+ "shell.execute_reply": "2023-02-21T16:44:18.606471Z"
+ },
+ "papermill": {
+ "duration": 0.210402,
+ "end_time": "2023-02-21T16:44:18.609650",
+ "exception": false,
+ "start_time": "2023-02-21T16:44:18.399248",
+ "status": "completed"
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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EiRP16aefyufz6ZprrgksnzNnjuLi4kI2HAAAQFd16szOpEmTdPr06aDQkaSEhATdeeedIRkMAAAgFDoVO3v37lVzc/MFyxsbG/WHP/yhy0MBAACEyld6G+vdd98N/Pn999+X1+sN3G9tbdWrr76qr33ta6GbDgAAoIu+Uuxcf/31stlsstlsmjRp0gXre/furfXr14dsOAAAgK76SrFz4sQJ+f1+ff3rX9fBgweVmJgYWBcTE6OkpCRFRkaGfEgAAIDO+kqxM3jwYElSW1tbtwwDAAAQap366LkkHT9+XHv27FFtbe0F8bN8+fIuDwYAABAKnYqdZ599VnPnztWAAQPkcrlks9kC62w2G7EDAADCRqdiZ9WqVXr44Ye1ePHiUM8DAAAQUp36np3PP/9cP/zhD0M9CwAAQMh1KnZ++MMfateuXaGeBQAAIOQ69TbWN7/5TS1btkz79+/X6NGjFR0dHbT+H/7hH0IyHAAAQFd1KnaeeeYZ9e3bV6WlpSotLQ1aZ7PZiB0AABA2OhU7J06cCPUcAAAA3aJT1+wAAABcKTp1Zufee+/90vXPP/98p4YBAAAItU7Fzueffx50v6WlRe+9957q6uou+gtCAQAArNKp2Nm+ffsFy9ra2jR37lx94xvf6PJQAAAAoRKya3YiIiKUn5+vtWvXhuopAQAAuiykFyh/9NFHOn/+fCifEgAAoEs69TZWfn5+0H2/36/q6mq9/PLLys3NDclgAAAAodCp2HnnnXeC7kdERCgxMVGPPfbYZT+pBQAA0JM6FTt79uwJ9RwAAADdolOx0+7kyZMqLy+XJA0fPlyJiYkhGQoAACBUOnWBckNDg+69914NHDhQN910k2666SYlJydr1qxZOnv2bKhnBAAA6LROxU5+fr5KS0u1Y8cO1dXVqa6uTr/97W9VWlqqn//856GeEQAAoNM69TbWf/zHf+jf//3fNXHixMCy733ve+rdu7d+9KMfacOGDaGaDwAAoEs6dWbn7NmzcjqdFyxPSkribSwAABBWOhU7brdbK1asUGNjY2DZuXPn9MADD8jtdodsOAAAgK7q1NtY69at06233qpBgwZp7NixkqQ//vGPio2N1a5du0I6IAAAQFd0KnZGjx6t48ePa8uWLTp27Jgk6a677tL06dPVu3fvkA4IAADQFZ2KncLCQjmdTs2ePTto+fPPP6+TJ09q8eLFIRkOAACgqzp1zc7TTz+tESNGXLD8uuuuU3FxcZeHAgAACJVOxY7X69XAgQMvWJ6YmKjq6uouDwUAABAqnYqdlJQUvfnmmxcsf/PNN5WcnNzloQAAAEKlU9fszJ49WwsWLFBLS4smTZokSSopKdEvfvELvkEZAACElU7FzqJFi3Tq1Cn97Gc/U3NzsySpV69eWrx4sQoKCkI6IAAAQFd0KnZsNpseeeQRLVu2TB988IF69+6tYcOGKTY2NtTzAQAAdEmnYqdd37599a1vfStUswAAAIRcpy5QBgAAuFIQOwAAwGjEDgAAMBqxAwAAjEbsAAAAoxE7AADAaMQOAAAwGrEDAACMRuwAAACjETsAAMBoxA4AADAasQMAAIxG7AAAAKNZGjuFhYX61re+pX79+ikpKUm33367ysvLg7ZpbGxUXl6e+vfvr759+yonJ0c1NTVB21RUVCg7O1t9+vRRUlKSFi1apPPnz/fkrgAAgDBlaeyUlpYqLy9P+/fv1+7du9XS0qLJkyeroaEhsM3ChQu1Y8cObdu2TaWlpaqqqtK0adMC61tbW5Wdna3m5mbt27dPmzdv1qZNm7R8+XIrdgkAAIQZm9/v91s9RLuTJ08qKSlJpaWluummm1RfX6/ExERt3bpVd9xxhyTp2LFjGjlypDwejzIyMvTKK6/otttuU1VVlZxOpySpuLhYixcv1smTJxUTE3PB6zQ1NampqSlw3+fzKSUlRfX19bLb7SHdpyFLXg7p86HjPl6dbfUIAMIIP4+t010/j30+nxwOx2X//Q6ra3bq6+slSQkJCZKksrIytbS0KDMzM7DNiBEjlJqaKo/HI0nyeDwaPXp0IHQkKSsrSz6fT0ePHr3o6xQWFsrhcARuKSkp3bVLAADAYmETO21tbVqwYIG+/e1va9SoUZIkr9ermJgYxcfHB23rdDrl9XoD23wxdNrXt6+7mIKCAtXX1wdulZWVod4dAAAQJqKsHqBdXl6e3nvvPf33f/93t79WbGysYmNju/11AACA9cLizM68efO0c+dO7dmzR4MGDQosd7lcam5uVl1dXdD2NTU1crlcgW3+8tNZ7ffbtwEAAFcvS2PH7/dr3rx52r59u15//XUNHTo0aH16erqio6NVUlISWFZeXq6Kigq53W5Jktvt1pEjR1RbWxvYZvfu3bLb7UpLS+uZHQEAAGHL0rex8vLytHXrVv32t79Vv379AtfYOBwO9e7dWw6HQ7NmzVJ+fr4SEhJkt9s1f/58ud1uZWRkSJImT56stLQ03X333VqzZo28Xq+WLl2qvLw83qoCAADWxs6GDRskSRMnTgxavnHjRt1zzz2SpLVr1yoiIkI5OTlqampSVlaWnnrqqcC2kZGR2rlzp+bOnSu32624uDjl5ubqwQcf7KndAAAAYczS2OnIV/z06tVLRUVFKioquuQ2gwcP1u9+97tQjgYAAAwRFhcoAwAAdBdiBwAAGI3YAQAARiN2AACA0YgdAABgNGIHAAAYjdgBAABGI3YAAIDRiB0AAGA0YgcAABiN2AEAAEYjdgAAgNGIHQAAYDRiBwAAGI3YAQAARiN2AACA0YgdAABgNGIHAAAYjdgBAABGI3YAAIDRiB0AAGA0YgcAABiN2AEAAEYjdgAAgNGIHQAAYDRiBwAAGI3YAQAARiN2AACA0YgdAABgNGIHAAAYjdgBAABGI3YAAIDRiB0AAGA0YgcAABiN2AEAAEYjdgAAgNGIHQAAYDRiBwAAGI3YAQAARiN2AACA0YgdAABgNGIHAAAYjdgBAABGI3YAAIDRiB0AAGA0YgcAABiN2AEAAEYjdgAAgNGIHQAAYDRiBwAAGI3YAQAARiN2AACA0YgdAABgNGIHAAAYjdgBAABGI3YAAIDRiB0AAGA0YgcAABiN2AEAAEYjdgAAgNEsjZ033nhDU6dOVXJysmw2m1566aWg9X6/X8uXL9fAgQPVu3dvZWZm6vjx40HbfPbZZ5o+fbrsdrvi4+M1a9YsnTlzpid3AwAAhDFLY6ehoUFjx45VUVHRRdevWbNGTz75pIqLi3XgwAHFxcUpKytLjY2NgW2mT5+uo0ePavfu3dq5c6feeOMNzZkzp6d2AQAAhLkoK198ypQpmjJlykXX+f1+rVu3TkuXLtX3v/99SdK//Mu/yOl06qWXXtKPf/xjffDBB3r11Vd16NAhjRs3TpK0fv16fe9739Ojjz6q5OTkiz53U1OTmpqaAvd9Pl+I9wwAAISLsL1m58SJE/J6vcrMzAwsczgcmjBhgjwejyTJ4/EoPj4+EDqSlJmZqYiICB04cOCSz11YWCiHwxG4paSkdN+OAAAAS4Vt7Hi9XkmS0+kMWu50OgPrvF6vkpKSgtZHRUUpISEhsM3FFBQUqL6+PnCrrKwM8fQAACBcWPo2llViY2MVGxtr9RgAAKAHhO2ZHZfLJUmqqakJWl5TUxNY53K5VFtbG7T+/Pnz+uyzzwLbAACAq1vYxs7QoUPlcrlUUlISWObz+XTgwAG53W5JktvtVl1dncrKygLbvP7662pra9OECRN6fGYAABB+LH0b68yZM/rwww8D90+cOKHDhw8rISFBqampWrBggVatWqVhw4Zp6NChWrZsmZKTk3X77bdLkkaOHKlbb71Vs2fPVnFxsVpaWjRv3jz9+Mc/vuQnsQAAwNXF0th566239N3vfjdwPz8/X5KUm5urTZs26Re/+IUaGho0Z84c1dXV6cYbb9Srr76qXr16BR6zZcsWzZs3TzfffLMiIiKUk5OjJ598ssf3BQAAhCeb3+/3Wz2E1Xw+nxwOh+rr62W320P63EOWvBzS50PHfbw62+oRAIQRfh5bp7t+Hnf03++wvWYHAAAgFIgdAABgNGIHAAAYjdgBAABGI3YAAIDRiB0AAGA0YgcAABiN2AEAAEYjdgAAgNGIHQAAYDRiBwAAGI3YAQAARiN2AACA0YgdAABgNGIHAAAYjdgBAABGI3YAAIDRiB0AAGA0YgcAABiN2AEAAEYjdgAAgNGIHQAAYDRiBwAAGI3YAQAARiN2AACA0YgdAABgNGIHAAAYjdgBAABGi7J6AAAIN0OWvGz1CFelj1dnWz0CDMWZHQAAYDRiBwAAGI3YAQAARiN2AACA0YgdAABgNGIHAAAYjdgBAABGI3YAAIDRiB0AAGA0YgcAABiN2AEAAEYjdgAAgNGIHQAAYDRiBwAAGI3YAQAARiN2AACA0YgdAABgNGIHAAAYjdgBAABGi7J6AOBKNWTJy1aPcNX6eHW21SMAuIJwZgcAABiN2AEAAEYjdgAAgNGIHQAAYDRiBwAAGI3YAQAARiN2AACA0YgdAABgNGIHAAAYjdgBAABGI3YAAIDRjImdoqIiDRkyRL169dKECRN08OBBq0cCAABhwIjYefHFF5Wfn68VK1bo7bff1tixY5WVlaXa2lqrRwMAABYzInYef/xxzZ49WzNnzlRaWpqKi4vVp08fPf/881aPBgAALBZl9QBd1dzcrLKyMhUUFASWRUREKDMzUx6P56KPaWpqUlNTU+B+fX29JMnn84V8vramsyF/TnRMdxzPL+LYWodjayaOq7m669i2P6/f7//S7a742Pn000/V2toqp9MZtNzpdOrYsWMXfUxhYaEeeOCBC5anpKR0y4ywhmOd1ROgu3BszcRxNVd3H9vTp0/L4XBccv0VHzudUVBQoPz8/MD9trY2ffbZZ+rfv79sNpuFk4UXn8+nlJQUVVZWym63Wz0OQoTjai6Orbk4thfn9/t1+vRpJScnf+l2V3zsDBgwQJGRkaqpqQlaXlNTI5fLddHHxMbGKjY2NmhZfHx8t814pbPb7fzHZSCOq7k4tubi2F7oy87otLviL1COiYlRenq6SkpKAsva2tpUUlIit9tt4WQAACAcXPFndiQpPz9fubm5GjdunMaPH69169apoaFBM2fOtHo0AABgsciVK1eutHqIrho1apTi4+P18MMP69FHH5UkbdmyRcOHD7d4sitfZGSkJk6cqKgoI7oY/x/H1VwcW3NxbDvP5r/c57UAAACuYFf8NTsAAABfhtgBAABGI3YAAIDRiB0AAGA0YgeSpKKiIg0ZMkS9evXShAkTdPDgwcC6xsZG5eXlqX///urbt69ycnIu+BJHhKcvO67PPPOMJk6cKLvdLpvNprq6OgsnxVfxxhtvaOrUqUpOTpbNZtNLL70UtN7v92v58uUaOHCgevfurczMTB0/ftyiadFRlzuu//mf/6nJkycHvu3/8OHDFk165SF2oBdffFH5+flasWKF3n77bY0dO1ZZWVmqra2VJC1cuFA7duzQtm3bVFpaqqqqKk2bNs3iqXE5lzuuZ8+e1a233qp//Md/tHhSfFUNDQ0aO3asioqKLrp+zZo1evLJJ1VcXKwDBw4oLi5OWVlZamxs7OFJ8VVc7rg2NDToxhtv1COPPNLDkxnAj6ve+PHj/Xl5eYH7ra2t/uTkZH9hYaG/rq7OHx0d7d+2bVtg/QcffOCX5Pd4PFaMiw76suP6RXv27PFL8n/++ec9PSJCQJJ/+/btgfttbW1+l8vl/9WvfhVYVldX54+NjfW/8MILVoyITvjL4/pFJ06c8Evyv/POOz081ZWLMztXuebmZpWVlSkzMzOwLCIiQpmZmfJ4PCorK1NLS0vQ+hEjRig1NVUej8eKkdEBlzuuMNeJEyfk9XqDjr3D4dCECRM49rhqETtXuU8//VStra1yOp1By51Op7xer7xer2JiYi74Rant6xGeLndcYa7248uxB/4PsQMAAIxG7FzlBgwYoMjIyAs+XVVTUyOXyyWXy6Xm5uYLPqnTvh7h6XLHFeZqP74ce+D/EDtXuZiYGKWnp6ukpCSwrK2tTSUlJXK73UpPT1d0dEtesooAAAb0SURBVHTQ+vLyclVUVMjtdlsxMjrgcscV5ho6dKhcLlfQsff5fDpw4ADHHlctfnUqlJ+fr9zcXI0bN07jx4/XunXr1NDQoJkzZ8rhcGjWrFnKz89XQkKC7Ha75s+fL7fbrYyMDKtHx5f4suMqKXBN1ocffihJOnLkiPr166fU1FQlJCRYOTou48yZM4HjJv35ouTDhw8rISFBqampWrBggVatWqVhw4Zp6NChWrZsmZKTk3X77bdbODUu53LH9bPPPlNFRYWqqqok/fl/PCUFzsLjS1j9cTCEh/Xr1/tTU1P9MTEx/vHjx/v3798fWHfu3Dn/z372M/8111zj79Onj/8HP/iBv7q62sJp0VFfdlxXrFjhl3TBbePGjdYNjA5p/7qAv7zl5ub6/f4/f/x82bJlfqfT6Y+NjfXffPPN/vLycmuHxmVd7rhu3LjxoutXrFhh6dxXApvf7/f3bF4BAAD0HK7ZAQAARiN2AACA0YgdAABgNGIHAAAYjdgBAABGI3YAAIDRiB0AAGA0YgcAABiN2AHQ7SZOnKgFCxZccv2QIUO0bt26Hpnl448/ls1m0+HDh3vk9QBYj9gBYLlDhw5pzpw5gfs2m00vvfRShx+/adMmxcfHd2jblJQUVVdXa9SoUV95TgBXJn4RKADLJSYm9sjrNDc3KyYmhl+aCFxlOLMDoEecP39e8+bNk8Ph0IABA7Rs2TK1/2q+L76NNWTIEEnSD37wA9lstsD9P/7xj/rud7+rfv36yW63Kz09XW+99Zb27t2rmTNnqr6+XjabTTabTStXrgw810MPPaQZM2bIbrdrzpw5F7yNtXfvXtlsNpWUlGjcuHHq06ePbrjhhsBvlG63atUqJSUlqV+/fvrJT36iJUuW6Prrrw+s37t3r8aPH6+4uDjFx8fr29/+tj755JNu/BsF0FHEDoAesXnzZkVFRengwYN64okn9Pjjj+uf//mfL9ju0KFDkqSNGzequro6cH/69OkaNGiQDh06pLKyMi1ZskTR0dG64YYbtG7dOtntdlVXV6u6ulr3339/4PkeffRRjR07Vu+8846WLVt2yfl++ctf6rHHHtNbb72lqKgo3XvvvYF1W7Zs0cMPP6xHHnlEZWVlSk1N1YYNGwLrz58/r9tvv13f+c539O6778rj8WjOnDmy2Wxd/nsD0HW8jQWgR6SkpGjt2rWy2WwaPny4jhw5orVr12r27NlB27W/pRUfHx/0dlNFRYUWLVqkESNGSJKGDRsWWOdwOGSz2S769tSkSZP085//PHD/448/vuh8Dz/8sL7zne9IkpYsWaLs7Gw1NjaqV69eWr9+vWbNmqWZM2dKkpYvX65du3bpzJkzkiSfz6f6+nrddttt+sY3viFJGjly5Ff6+wHQfTizA6BHZGRkBJ3pcLvdOn78uFpbWzv0+Pz8fP3kJz9RZmamVq9erY8++qhDjxs3blyHthszZkzgzwMHDpQk1dbWSpLKy8s1fvz4oO2/eD8hIUH33HOPsrKyNHXqVD3xxBOqrq7u0OsC6H7EDoArwsqVK3X06FFlZ2fr9ddfV1pamrZv337Zx8XFxXXo+aOjowN/bo+ytra2Ds+3ceNGeTwe3XDDDXrxxRd17bXXav/+/R1+PIDuQ+wA6BEHDhwIur9//34NGzZMkZGRF2wbHR190TM+1157rRYuXKhdu3Zp2rRp2rhxoyQpJiamw2eIOmP48OGBa4fa/eV9Sfqrv/orFRQUaN++fRo1apS2bt3abTMB6DhiB0CPqKioUH5+vsrLy/XCCy9o/fr1uu+++y667ZAhQ1RSUiKv16vPP/9c586d07x587R371598sknevPNN3Xo0KHAdTFDhgzRmTNnVFJSok8//VRnz54N6ezz58/Xc889p82bN+v48eNatWqV3n333cAZoBMnTqigoEAej0effPKJdu3apePHj3PdDhAmuEAZQI+YMWOGzp07p/HjxysyMlL33Xdf0BcJftFjjz2m/Px8Pfvss/ra176m//mf/9GpU6c0Y8YM1dTUaMCAAZo2bZoeeOABSdINN9ygn/70p7rzzjt16tQprVixIvDx81CYPn26/vd//1f333+/Ghsb9aMf/Uj33HOPDh48KEnq06ePjh07ps2bN+vUqVMaOHCg8vLy9Pd///chmwFA59n87V90AQDosFtuuUUul0v/+q//avUoAC6DMzsAcBlnz55VcXGxsrKyFBkZqRdeeEGvvfaadu/ebfVoADqAMzsAcBnnzp3T1KlT9c4776ixsVHDhw/X0qVLNW3aNKtHA9ABxA4AADAan8YCAABGI3YAAIDRiB0AAGA0YgcAABiN2AEAAEYjdgAAgNGIHQAAYDRiBwAAGO3/AeKJjps72M6GAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.bar(counts.keys(), counts.values())\n",
+ "plt.xlabel(\"bitstrings\")\n",
+ "plt.ylabel(\"counts\")\n",
+ "\n",
+ "# Save figure to a local directory or Amazon S3 location\n",
+ "plt.savefig(f\"{results_dir}/histogram.png\")"
+ ]
+ }
+ ],
+ "metadata": {
+ "celltoolbar": "Tags",
+ "kernelspec": {
+ "display_name": "conda_braket",
+ "language": "python",
+ "name": "conda_braket"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.10"
+ },
+ "papermill": {
+ "default_parameters": {},
+ "duration": 35.15558,
+ "end_time": "2023-02-21T16:44:19.133234",
+ "environment_variables": {},
+ "exception": null,
+ "input_path": "/opt/braket/input/data/input/0_Getting_started_papermill.ipynb",
+ "output_path": "/opt/braket/model/0_Getting_started_papermill.ipynb",
+ "parameters": {
+ "device_arn": "arn:aws:braket:us-west-1::device/qpu/rigetti/Ankaa 2",
+ "results_dir": "/opt/braket/model",
+ "shots": 1000
+ },
+ "start_time": "2023-02-21T16:43:43.977654",
+ "version": "2.4.0"
+ },
+ "vscode": {
+ "interpreter": {
+ "hash": "5904cb9a2089448a2e1aeb5d493d227c9de33e591d7c07e4016fb81e71061a5d"
+ }
+ }
},
- "tags": []
- },
- "source": [
- "# Example notebook \n",
- "\n",
- "This notebook is a copy from `examples/getting_started/0_Getting_started/0_Getting_started.ipynb` with a small modifications for use with [Papermill](https://github.com/nteract/papermill) and Amazon Braket Hybrid Jobs. \n",
- "\n",
- "## Papermill parameters\n",
- "\n",
- "Papermill is a tool for parameterizing, executing, and analyzing Jupyter Notebooks. \n",
- "To parameterize a notebook, we need tag a cell that contains all the parameters. \n",
- "We can only tag one cell, and for simplicity we place it at the top of the notebook. \n",
- "Full instructions are available here https://papermill.readthedocs.io/en/latest/usage-parameterize.html#designate-parameters-for-a-cell. \n",
- "\n",
- "Below, we tag the parameter `shots=1000`. \n",
- "We can then run the notebook as usual cell-by-cell to see the results. \n",
- "\n",
- "We additionally add two Braket specific parameters called `device_arn` and `results_dir`. \n",
- "These will be overridden when running a Hybrid Job. \n",
- "\n",
- "**In the following cell, we added a tag called `parameters` for Papermill to recognize. If you don't see the tag, follow the instructions above.**"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "id": "2436f1be",
- "metadata": {
- "execution": {
- "iopub.execute_input": "2023-02-21T16:43:45.371205Z",
- "iopub.status.busy": "2023-02-21T16:43:45.370808Z",
- "iopub.status.idle": "2023-02-21T16:43:45.379588Z",
- "shell.execute_reply": "2023-02-21T16:43:45.378335Z"
- },
- "papermill": {
- "duration": 0.015001,
- "end_time": "2023-02-21T16:43:45.381543",
- "exception": false,
- "start_time": "2023-02-21T16:43:45.366542",
- "status": "completed"
- },
- "tags": [
- "parameters"
- ]
- },
- "outputs": [],
- "source": [
- "# Papermill parameters\n",
- "shots = 1000\n",
- "\n",
- "# Braket specific parameters\n",
- "device_arn = \"arn:aws:braket:::device/quantum-simulator/amazon/sv1\"\n",
- "results_dir = \".\""
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "id": "a0fb6bd8",
- "metadata": {
- "execution": {
- "iopub.execute_input": "2023-02-21T16:43:45.389513Z",
- "iopub.status.busy": "2023-02-21T16:43:45.388977Z",
- "iopub.status.idle": "2023-02-21T16:43:45.393453Z",
- "shell.execute_reply": "2023-02-21T16:43:45.392426Z"
- },
- "papermill": {
- "duration": 0.010707,
- "end_time": "2023-02-21T16:43:45.395539",
- "exception": false,
- "start_time": "2023-02-21T16:43:45.384832",
- "status": "completed"
- },
- "tags": [
- "injected-parameters"
- ]
- },
- "outputs": [],
- "source": [
- "# Parameters\n",
- "shots = 1000\n",
- "device_arn = \"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\"\n",
- "results_dir = \"/opt/braket/model\""
- ]
- },
- {
- "attachments": {},
- "cell_type": "markdown",
- "id": "c8f24ceb",
- "metadata": {
- "papermill": {
- "duration": 0.003094,
- "end_time": "2023-02-21T16:43:45.402021",
- "exception": false,
- "start_time": "2023-02-21T16:43:45.398927",
- "status": "completed"
- },
- "tags": []
- },
- "source": [
- "# Getting started with Amazon Braket\n",
- "\n",
- "In this tutorial we prepare a maximally entangled Bell state between two qubits. \n",
- "We then run our circuit on a local simulator and obtain the results."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "id": "472c72f6",
- "metadata": {
- "execution": {
- "iopub.execute_input": "2023-02-21T16:43:45.409445Z",
- "iopub.status.busy": "2023-02-21T16:43:45.408896Z",
- "iopub.status.idle": "2023-02-21T16:43:47.305956Z",
- "shell.execute_reply": "2023-02-21T16:43:47.304998Z"
- },
- "papermill": {
- "duration": 1.90327,
- "end_time": "2023-02-21T16:43:47.308212",
- "exception": false,
- "start_time": "2023-02-21T16:43:45.404942",
- "status": "completed"
- },
- "tags": []
- },
- "outputs": [],
- "source": [
- "import time\n",
- "\n",
- "import matplotlib.pyplot as plt\n",
- "\n",
- "%matplotlib inline\n",
- "\n",
- "from braket.aws import AwsDevice\n",
- "from braket.circuits import Circuit\n",
- "from braket.devices import LocalSimulator\n",
- "from braket.jobs.metrics import log_metric\n",
- "from braket.tracking import Tracker # cost tracker\n",
- "\n",
- "cost_tracker = Tracker().start()"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "a7a2db04",
- "metadata": {
- "papermill": {
- "duration": 0.002877,
- "end_time": "2023-02-21T16:43:47.314835",
- "exception": false,
- "start_time": "2023-02-21T16:43:47.311958",
- "status": "completed"
- },
- "tags": []
- },
- "source": [
- "## Build a circuit\n",
- "\n",
- "Let's build a Bell state with two qubits. By calling `Circuit()` we create an empty circuit, and we can just add gates to the circuit. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "id": "0928121e",
- "metadata": {
- "execution": {
- "iopub.execute_input": "2023-02-21T16:43:47.322937Z",
- "iopub.status.busy": "2023-02-21T16:43:47.322367Z",
- "iopub.status.idle": "2023-02-21T16:43:47.329784Z",
- "shell.execute_reply": "2023-02-21T16:43:47.328703Z"
- },
- "papermill": {
- "duration": 0.014274,
- "end_time": "2023-02-21T16:43:47.332315",
- "exception": false,
- "start_time": "2023-02-21T16:43:47.318041",
- "status": "completed"
- },
- "tags": []
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : |0|1|\n",
- " \n",
- "q0 : -H-C-\n",
- " | \n",
- "q1 : ---X-\n",
- "\n",
- "T : |0|1|\n"
- ]
- }
- ],
- "source": [
- "# build a Bell state with two qubits.\n",
- "bell = Circuit().h(0).cnot(control=0, target=1)\n",
- "print(bell)"
- ]
- },
- {
- "attachments": {},
- "cell_type": "markdown",
- "id": "253f5e35",
- "metadata": {
- "papermill": {
- "duration": 0.003065,
- "end_time": "2023-02-21T16:43:47.338674",
- "exception": false,
- "start_time": "2023-02-21T16:43:47.335609",
- "status": "completed"
- },
- "tags": []
- },
- "source": [
- "## Submit the circuit to the local simulator and obtain the results\n",
- "\n",
- "Next, we choose either a local simulator or an Amazon Braket device. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "id": "b7c90b2f",
- "metadata": {
- "execution": {
- "iopub.execute_input": "2023-02-21T16:43:47.346544Z",
- "iopub.status.busy": "2023-02-21T16:43:47.345827Z",
- "iopub.status.idle": "2023-02-21T16:43:47.822456Z",
- "shell.execute_reply": "2023-02-21T16:43:47.821578Z"
- },
- "papermill": {
- "duration": 0.482774,
- "end_time": "2023-02-21T16:43:47.824541",
- "exception": false,
- "start_time": "2023-02-21T16:43:47.341767",
- "status": "completed"
- },
- "tags": []
- },
- "outputs": [],
- "source": [
- "# set up device\n",
- "if \"local\" in device_arn:\n",
- " device = LocalSimulator()\n",
- "else:\n",
- " device = AwsDevice(device_arn)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "id": "2366ca95",
- "metadata": {
- "execution": {
- "iopub.execute_input": "2023-02-21T16:43:47.833244Z",
- "iopub.status.busy": "2023-02-21T16:43:47.832639Z",
- "iopub.status.idle": "2023-02-21T16:44:18.319776Z",
- "shell.execute_reply": "2023-02-21T16:44:18.318577Z"
- },
- "papermill": {
- "duration": 30.49638,
- "end_time": "2023-02-21T16:44:18.324694",
- "exception": false,
- "start_time": "2023-02-21T16:43:47.828314",
- "status": "completed"
- },
- "tags": []
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "{'00': 494, '01': 22, '10': 50, '11': 434}\n"
- ]
- }
- ],
- "source": [
- "# Run the circuit and get results\n",
- "result = device.run(bell, shots=shots).result()\n",
- "\n",
- "# get measurement shots\n",
- "counts = result.measurement_counts\n",
- "counts = {k: counts[k] for k in sorted(counts)} # sort results\n",
- "print(counts)"
- ]
- },
- {
- "attachments": {},
- "cell_type": "markdown",
- "id": "c41e8691",
- "metadata": {
- "papermill": {
- "duration": 0.003065,
- "end_time": "2023-02-21T16:44:18.331341",
- "exception": false,
- "start_time": "2023-02-21T16:44:18.328276",
- "status": "completed"
- },
- "tags": []
- },
- "source": [
- "Hybrid Jobs enables logging of metrics during the job. \n",
- "In the example below, we track the total cost of running the circuit on simulators or QPUs by using the cost tracker.\n",
- "\n",
- "We also track the number of counts in the \"00\" state. It is best practice to log all metrics per iteration at a common timestamp to avoid duplication."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "id": "0e6ee106",
- "metadata": {
- "execution": {
- "iopub.execute_input": "2023-02-21T16:44:18.339367Z",
- "iopub.status.busy": "2023-02-21T16:44:18.338979Z",
- "iopub.status.idle": "2023-02-21T16:44:18.365109Z",
- "shell.execute_reply": "2023-02-21T16:44:18.364151Z"
- },
- "papermill": {
- "duration": 0.032881,
- "end_time": "2023-02-21T16:44:18.367429",
- "exception": false,
- "start_time": "2023-02-21T16:44:18.334548",
- "status": "completed"
- },
- "tags": []
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Metrics - timestamp=1676997858.3620458; cost=0.65;\n",
- "Metrics - timestamp=1676997858.3620458; counts_00=494;\n"
- ]
- }
- ],
- "source": [
- "total_cost = float(cost_tracker.simulator_tasks_cost() + cost_tracker.qpu_tasks_cost())\n",
- "\n",
- "timestamp = time.time()\n",
- "\n",
- "log_metric(metric_name=\"cost\", value=float(total_cost), timestamp=timestamp)\n",
- "\n",
- "log_metric(metric_name=\"counts_00\", value=counts[\"00\"], timestamp=timestamp)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "3f4a07f0",
- "metadata": {
- "papermill": {
- "duration": 0.003183,
- "end_time": "2023-02-21T16:44:18.374145",
- "exception": false,
- "start_time": "2023-02-21T16:44:18.370962",
- "status": "completed"
- },
- "tags": []
- },
- "source": [
- "**The following cell saves the results to a file**\n",
- "\n",
- "The use of `results_dir` is that any results are saved to the correct directory when called from a Braket Job. Below, we save the measurement counts to a .pkl file. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "id": "31102e41",
- "metadata": {
- "execution": {
- "iopub.execute_input": "2023-02-21T16:44:18.382365Z",
- "iopub.status.busy": "2023-02-21T16:44:18.381771Z",
- "iopub.status.idle": "2023-02-21T16:44:18.386881Z",
- "shell.execute_reply": "2023-02-21T16:44:18.385954Z"
- },
- "papermill": {
- "duration": 0.011421,
- "end_time": "2023-02-21T16:44:18.388857",
- "exception": false,
- "start_time": "2023-02-21T16:44:18.377436",
- "status": "completed"
- },
- "tags": []
- },
- "outputs": [],
- "source": [
- "import pickle\n",
- "\n",
- "# save measurement counts to a file\n",
- "with open(f\"{results_dir}/results.pkl\", \"wb\") as f:\n",
- " pickle.dump(counts, f)\n",
- "\n",
- "\n",
- "# re-load the results with\n",
- "# with open(f\"{results_dir}/results.pkl\", 'rb') as f:\n",
- "# counts = pickle.load(f)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "1347bd65",
- "metadata": {
- "papermill": {
- "duration": 0.003234,
- "end_time": "2023-02-21T16:44:18.395896",
- "exception": false,
- "start_time": "2023-02-21T16:44:18.392662",
- "status": "completed"
- },
- "tags": []
- },
- "source": [
- "**The following cell saves the figure to a file**"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "id": "5da96893",
- "metadata": {
- "execution": {
- "iopub.execute_input": "2023-02-21T16:44:18.404309Z",
- "iopub.status.busy": "2023-02-21T16:44:18.403735Z",
- "iopub.status.idle": "2023-02-21T16:44:18.607364Z",
- "shell.execute_reply": "2023-02-21T16:44:18.606471Z"
- },
- "papermill": {
- "duration": 0.210402,
- "end_time": "2023-02-21T16:44:18.609650",
- "exception": false,
- "start_time": "2023-02-21T16:44:18.399248",
- "status": "completed"
- },
- "tags": []
- },
- "outputs": [
- {
- "data": {
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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "plt.bar(counts.keys(), counts.values())\n",
- "plt.xlabel(\"bitstrings\")\n",
- "plt.ylabel(\"counts\")\n",
- "\n",
- "# Save figure to a local directory or Amazon S3 location\n",
- "plt.savefig(f\"{results_dir}/histogram.png\")"
- ]
- }
- ],
- "metadata": {
- "celltoolbar": "Tags",
- "kernelspec": {
- "display_name": "conda_braket",
- "language": "python",
- "name": "conda_braket"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.7.10"
- },
- "papermill": {
- "default_parameters": {},
- "duration": 35.15558,
- "end_time": "2023-02-21T16:44:19.133234",
- "environment_variables": {},
- "exception": null,
- "input_path": "/opt/braket/input/data/input/0_Getting_started_papermill.ipynb",
- "output_path": "/opt/braket/model/0_Getting_started_papermill.ipynb",
- "parameters": {
- "device_arn": "arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3",
- "results_dir": "/opt/braket/model",
- "shots": 1000
- },
- "start_time": "2023-02-21T16:43:43.977654",
- "version": "2.4.0"
- },
- "vscode": {
- "interpreter": {
- "hash": "5904cb9a2089448a2e1aeb5d493d227c9de33e591d7c07e4016fb81e71061a5d"
- }
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
diff --git a/examples/hybrid_jobs/8_Creating_Hybrid_Job_Scripts/Creating_your_first_Hybrid_Job.ipynb b/examples/hybrid_jobs/8_Creating_Hybrid_Job_Scripts/Creating_your_first_Hybrid_Job.ipynb
index efa68bb88..c9e0ec7af 100644
--- a/examples/hybrid_jobs/8_Creating_Hybrid_Job_Scripts/Creating_your_first_Hybrid_Job.ipynb
+++ b/examples/hybrid_jobs/8_Creating_Hybrid_Job_Scripts/Creating_your_first_Hybrid_Job.ipynb
@@ -1,606 +1,606 @@
{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Getting started with Amazon Braket Hybrid Jobs\n",
- "\n",
- "This tutorial shows how to run your first Amazon Braket Hybrid Job. To get started, we consider small circuits with only one qubit and one gate.\n",
- "\n",
- "\n",
- "## Learning outcomes\n",
- "* Get setup to run your first hybrid job\n",
- "* Write an algorithm script to run on Braket Hybrid Jobs\n",
- "* Understand how to run scripts or functions\n",
- "* Create a hybrid job on Braket simulators or QPUs\n",
- "* Monitoring the hybrid job state\n",
- "* Save results from a hybrid job\n",
- "* Using a specific AWS session\n",
- "* Running hybrid jobs with priority on QPUs\n",
- "* Use local hybrid jobs to quickly test and debug scripts\n",
- "* Create a Braket Hybrid Job using the Braket console"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Getting setup to run Braket Hybrid Jobs\n",
- "\n",
- "When you use Amazon Braket Hybrid Jobs for the first time, you need to create an IAM role with the right [permissions](https://docs.aws.amazon.com/braket/latest/developerguide/braket-manage-access.html#about-amazonbraketjobsexecution). This role allows your hybrid job to perform actions on your behalf while it is executing your algorithm, for instance, access S3 to return the results of your hybrid job. To create the role or check if you already have one please visit the Permissions tab from the left menu of the Braket Console.\n",
- "\n",
- "## Writing an algorithm script\n",
- "\n",
- "To create a Braket Hybrid Job, you first need a Python script to run. In this example, it's contained in `algorithm_script.py`. The script is printed in the code cell below for convenience. \n",
- "\n",
- "As shown, each of the circuits has only one $X$ rotation gate with a random angle. The circuit is repeated five times with different random rotations. Note that the algorithm script does not specify the backend Amazon Braket device ARN explicitly. Instead, it is provided through environment variables such as `os.environ[\"AMZN_BRAKET_DEVICE_ARN\"]` that are passed to the algorithm script when creating the hybrid job. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "pycharm": {
- "name": "#%% md\n"
- }
- },
- "source": [
- "#### This block is a copy of the algorithm script.\n",
- "\n",
- "```python\n",
- "\n",
- "import os\n",
- "import numpy as np\n",
- "\n",
- "from braket.aws import AwsDevice\n",
- "from braket.circuits import Circuit\n",
- "from braket.jobs import save_job_result\n",
- "from braket.tracking import Tracker\n",
- "\n",
- "t = Tracker().start()\n",
- "\n",
- "print(\"Test hybrid job started!\")\n",
- "\n",
- "# Use the device declared in the creation script\n",
- "device = AwsDevice(os.environ[\"AMZN_BRAKET_DEVICE_ARN\"])\n",
- "\n",
- "counts_list = []\n",
- "angle_list = []\n",
- "for _ in range(5):\n",
- " angle = np.pi * np.random.randn()\n",
- " random_circuit = Circuit().rx(0, angle)\n",
- "\n",
- " task = device.run(random_circuit, shots=100)\n",
- " counts = task.result().measurement_counts\n",
- "\n",
- " angle_list.append(angle)\n",
- " counts_list.append(counts)\n",
- " print(counts)\n",
- "\n",
- "# Save the variables of interest so that we can access later\n",
- "save_job_result({\"counts\": counts_list, \"angle\": angle_list, \"estimated cost\": t.qpu_tasks_cost() + t.simulator_tasks_cost()})\n",
- "\n",
- "print(\"Test hybrid job completed!\")\n",
- "```"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Creating your first hybrid job\n",
- "\n",
- "Once the script is finalized, you can create a Braket Hybrid Job with `AwsQuantumJob`. When the hybrid job is created, Amazon Braket starts the hybrid job instance (based on EC2) and spins up a Docker container to run your algorithm script. Other configurations can be specified via keyword arguments. See the [developer guide](https://docs.aws.amazon.com/braket/latest/developerguide/what-is-braket.html) and other example notebooks to learn more about how to customize your jobs\n",
- "\n",
- "This example uses the following inputs for `AwsQuantumJob`:\n",
- "- device: The ARN of the Braket simulator or QPU to use in the hybrid job. It will be passed as an environment variable to the algorithm script. \n",
- "- source_module: The path to a file or a Python module that contains your algorithm script. It will be uploaded to the container for running the Braket Hybrid Job.\n",
- "- wait_until_complete (optional): If True, the function call will wait until the Braket Hybrid Job is completed and will additionally print logs to the local console. Otherwise, it will run asynchronously. The default is False."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [],
- "source": [
- "from braket.aws import AwsDevice, AwsQuantumJob\n",
- "from braket.devices import Devices"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "pycharm": {
- "name": "#%%\n"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Initializing Braket Job: arn:aws:braket:::job/\n",
- "...............................................\n",
- "\u001B[34m2021-11-10 20:55:24,467 sagemaker-training-toolkit INFO Invoking user script\u001B[0m\n",
- "\u001B[34mTraining Env:\u001B[0m\n",
- "\u001B[34m{\n",
- " \"additional_framework_parameters\": {},\n",
- " \"channel_input_dirs\": {},\n",
- " \"current_host\": \"algo-1\",\n",
- " \"framework_module\": null,\n",
- " \"hosts\": [\n",
- " \"algo-1\"\n",
- " ],\n",
- " \"hyperparameters\": {},\n",
- " \"input_config_dir\": \"/opt/ml/input/config\",\n",
- " \"input_data_config\": {},\n",
- " \"input_dir\": \"/opt/ml/input\",\n",
- " \"is_master\": true,\n",
- " \"job_name\": \"BraketJob--\",\n",
- " \"log_level\": 20,\n",
- " \"master_hostname\": \"algo-1\",\n",
- " \"model_dir\": \"/opt/ml/model\",\n",
- " \"module_dir\": \"/opt/ml/code\",\n",
- " \"module_name\": \"braket_container\",\n",
- " \"network_interface_name\": \"eth0\",\n",
- " \"num_cpus\": 2,\n",
- " \"num_gpus\": 0,\n",
- " \"output_data_dir\": \"/opt/ml/output/data\",\n",
- " \"output_dir\": \"/opt/ml/output\",\n",
- " \"output_intermediate_dir\": \"/opt/ml/output/intermediate\",\n",
- " \"resource_config\": {\n",
- " \"current_host\": \"algo-1\",\n",
- " \"hosts\": [\n",
- " \"algo-1\"\n",
- " ],\n",
- " \"network_interface_name\": \"eth0\"\n",
- " },\n",
- " \"user_entry_point\": \"braket_container.py\"\u001B[0m\n",
- "...............................................\n",
- "...............................................\n",
- "\u001B[34mRunning Code As Subprocess\u001B[0m\n",
- "\u001B[34mTest job started!!!!!\u001B[0m\n",
- "\u001B[34mCounter({'0': 88, '1': 12})\u001B[0m\n",
- "\u001B[34mCounter({'1': 58, '0': 42})\u001B[0m\n",
- "\u001B[34mCounter({'1': 54, '0': 46})\u001B[0m\n",
- "\u001B[34mCounter({'0': 100})\u001B[0m\n",
- "\u001B[34mCounter({'0': 100})\u001B[0m\n",
- "\u001B[34mTest job completed!!!!!\u001B[0m\n",
- "\u001B[34mCode Run Finished\u001B[0m\n",
- "\u001B[34m2021-11-10 20:55:58,953 sagemaker-training-toolkit INFO Reporting training SUCCESS\u001B[0m\n"
- ]
- }
- ],
- "source": [
- "# This cell should take about 5 mins\n",
- "job = AwsQuantumJob.create(\n",
- " device=Devices.Amazon.SV1,\n",
- " source_module=\"algorithm_script.py\",\n",
- " wait_until_complete=True,\n",
- ")"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this example, the algorithm is defined by a single file, so the `source_module` is `algorithm_script.py`. Depending on your application, there are other options for setting the source module. For example, if you wish to only execute a part of `algorithm_script.py` at the start of a Braket Hybrid Job, you can package that part to be a `starting_function()`. Then assign the function as the entry point by adding the `entry_point` input argument."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [],
- "source": [
- "source_module = \"algorithm_script.py\"\n",
- "entry_point = \"algorithm_script:starting_function\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "If your algorithm script requires other dependencies, you can put them all in one folder, say the `algorithm_folder`. The input arguments would then be"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {},
- "outputs": [],
- "source": [
- "source_module = \"algorithm_folder\"\n",
- "entry_point = \"algorithm_folder.algorithm_script:starting_function\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Checking hybrid job state and loading results\n",
- "\n",
- "The status of a Braket Job can be checked by calling `job.state()`. The state will be one of \"QUEUED\", \"RUNNING\", \"FAILED\", \"COMPLETED\", \"CANCELLING\", or \"CANCELLED\". "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "'COMPLETED'"
- ]
- },
- "execution_count": 6,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "job.state()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Once completed, the result can be retrieved using `job.result()`. Logs and metadata are also accessible via `job.logs()` and `job.metadata()`. If you lose the reference to the hybrid job object, you can always reinstantiate it using your hybrid job ARN as `job=AwsQuantumJob(\"your-job-arn\")`. The ARN of a hybrid job can be found in the Amazon Braket Console. By default the ARN of a hybrid job will be \"`arn:aws:braket:::job/`\". "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "counts: [{'1': 12, '0': 88}, {'0': 42, '1': 58}, {'0': 46, '1': 54}, {'0': 100}, {'0': 100}]\n",
- "angles: [-0.6634809825751307, 1.8729107298836103, -1.8816578492668359, -0.04308463076559567, 0.03224990551866221]\n"
- ]
- }
- ],
- "source": [
- "results = job.result() # will return once job.state() = \"COMPLETED\", should be 6 minutes\n",
- "print(\"counts: \", results[\"counts\"])\n",
- "print(\"angles: \", results[\"angles\"])"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {},
- "outputs": [],
- "source": [
- "# print(job.logs()) # uncomment to print logs"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "You can also download the result to a local directory."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {},
- "outputs": [],
- "source": [
- "job.download_result() # download hybrid job result to local directory"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Task Summary\n",
- "{'arn:aws:braket:::device/quantum-simulator/amazon/sv1': {'shots': 500, 'tasks': {'COMPLETED': 5}, 'execution_duration': 0.081, 'billed_execution_duration': 15.0}}\n",
- "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
- "Estimated cost to run tasks in this job: 0.01875 USD\n"
- ]
- }
- ],
- "source": [
- "print(\"Quantum Task Summary\")\n",
- "print(job.result()['task summary'])\n",
- "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n",
- "print(f\"Estimated cost to run quantum tasks in this hybrid job: {job.result()['estimated cost']} USD\")"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Increase performance by running hybrid jobs on QPUs\n",
- "\n",
- "With Braket Hybrid Jobs, you can run hybrid algorithms on all QPUs available through Amazon Braket. When you select a QPU as your device, your hybrid job will have priority access for the duration of your hybrid job. Quantum tasks created as part of your hybrid job will be executed ahead of other tasks in the device queue. This reduces the risk of certain tasks being delayed or drifting calibrations on the device. To secure priority on a device your job needs to wait for the device to complete running or already queued jobs. Before submitting the job on a device, you can check the queue depth for the hybrid jobs. To check the number of hybrid jobs queued on the device call `device.queue_depth().jobs`."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "'2'"
- ]
- },
- "execution_count": 7,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# Select the device on which you will be submitting your hybrid job.\n",
- "device = AwsDevice(Devices.Rigetti.AspenM3)\n",
- "device.queue_depth().jobs"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "You can seamlessly swap the SV1 simulator for a QPU by changing the device argument in `AwsQuantumJob.create()`. For instance, the code below will create a hybrid job with priority access on the Rigetti Aspen-M-3 device:\n",
- "\n",
- "
\n",
- " Note: The following cell uses the Rigetti Aspen-M-3 device; before you uncomment and run it, make sure the device is currently available. You can find QPU availability windows on the Devices page in the Amazon Braket Console\n",
- "
"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {},
- "outputs": [],
- "source": [
- "# qpu_job = AwsQuantumJob.create(\n",
- "# device=Devices.Rigetti.AspenM3,\n",
- "# source_module=\"algorithm_script.py\",\n",
- "# wait_until_complete=False,\n",
- "# )"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "You can check the position of your hybrid job in the queue by calling job.queue_position().queue_position. The queue position is only returned when the job is in \"QUEUED\" state, else None is returned. You can also check why the queue position value is not returned by calling calling `job.queue_position().message`. Here, `job` is the variable to which you assign your job creation. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "'3'"
- ]
- },
- "execution_count": 8,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "# qpu_job.queue_position().queue_position"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "When you create the hybrid job, Amazon Braket will wait for the QPU to become available before initializing the hybrid job. Note that the Braket Hybrid Job will automatically select the AWS region where the device is available. As mentioned earlier, the specified device is provided to the hybrid job in the environment variable `AMZN_BRAKET_DEVICE_ARN`; the script `algorithm_script.py` uses this variable to choose the Braket device to use.\n",
- "\n",
- "In variational algorithms, there are usually optimization processes that update parameters of a fixed parametrized circuit. When executing such algorithms on a supported QPU with Hybrid Jobs, parametric compilation can improve the performance of the hybrid jobs. All you need to do is to submit the parametrized circuit using free parameters in the algorithm script. Braket will compile the circuit once and manage the compiled circuit of the Hybrid Job. There is no recompilation for subsequent parameter updates to the same circuit, resulting in faster runtimes. An example of algorithm script that uses a parametrized circuit is in `algorithm_script_parametrized_circuit.py`. Use this algorithm script in the place of `algorithm_script.py` and submit a hybrid job to a supported Braket QPU to use parametric compilation. See the Amazon Braket developer guide to learn more about [the usage of free parameters](https://docs.aws.amazon.com/braket/latest/developerguide/braket-constructing-circuit.html#braket-gates) and [parametric compilation with Hybrid Jobs](https://docs.aws.amazon.com/braket/latest/developerguide/braket-jobs.html)."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## AWS Sessions\n",
- "\n",
- "You can customize the default location where Braket Hybrid Jobs saves and loads results in Amazon S3 by providing the AWS session information. The name of the S3 bucket needs to start with \"amazon-braket-\", and it must be in the same region as the hybrid job being created."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "metadata": {},
- "outputs": [],
- "source": [
- "from braket.aws import AwsSession\n",
- "\n",
- "# Set Amazon S3 bucket\n",
- "aws_session = AwsSession(default_bucket=\"amazon-braket-bucket-name\")"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "To create a Braket Hybrid Job with this S3 bucket, pass `aws_session` as an argument to ` AwsQuantumJob.create()`:\n",
- "\n",
- "```python\n",
- "job = AwsQuantumJob.create(\n",
- " device=Devices.Amazon.SV1,\n",
- " source_module=\"algorithm_script.py\",\n",
- " aws_session=aws_session # using specific S3 bucket\n",
- ")\n",
- "```"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Debugging with local Braket Hybrid Jobs\n",
- "\n",
- "For faster testing and debugging of your code, you can run a hybrid job locally in your own environment. This feature requires Docker to be installed in your local environment. Amazon Braket notebooks have Docker pre-installed, so you can test local hybrid jobs in hosted notebooks instantly. To install Docker in your local environment, follow these [instructions](https://docs.docker.com/get-docker/). When a local hybrid job is created for the first time, it will take longer because it needs to build the container. The subsequent runs will be faster. Note that local hybrid jobs will not be visible in the Amazon Braket Console.\n",
- "\n",
- "To run a hybrid job in local mode, make sure the Docker daemon is running, and then simply create a `LocalQuantumJob` instead of an `AwsQuantumJob`. Local hybrid jobs always run synchronously and display the logs."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {
- "tags": []
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Using the short-lived AWS credentials found in session. They might expire while running.\n",
- "Boto3 Version: 1.18.33\n",
- "Beginning Setup\n",
- "Completed 50.5 KiB/50.5 KiB (72.5 KiB/s) with 1 file(s) remaining\n",
- "...............................................\n",
- "...............................................\n",
- "Running Code As Subprocess\n",
- "Test job started!!!!!\n",
- "Counter({'0': 79, '1': 21})\n",
- "Counter({'0': 84, '1': 16})\n",
- "Counter({'0': 91, '1': 9})\n",
- "Counter({'0': 85, '1': 15})\n",
- "Counter({'1': 94, '0': 6})\n",
- "Test job completed!!!!!\n",
- "Code Run Finished\n"
- ]
- }
- ],
- "source": [
- "from braket.jobs.local.local_job import LocalQuantumJob\n",
- "\n",
- "# This cell should take about 2 min\n",
- "job = LocalQuantumJob.create(\n",
- " device=Devices.Amazon.SV1,\n",
- " source_module=\"algorithm_script.py\",\n",
- ")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Task Summary\n",
- "{'arn:aws:braket:::device/quantum-simulator/amazon/sv1': {'shots': 500, 'tasks': {'COMPLETED': 5}, 'execution_duration': 0.046, 'billed_execution_duration': 15.0}}\n",
- "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
- "Estimated cost to run tasks in this job: 0.01875 USD\n"
- ]
- }
- ],
- "source": [
- "print(\"Quantum Task Summary\")\n",
- "print(job.result()['task summary'])\n",
- "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n",
- "print(f\"Estimated cost to run quantum tasks in this hybrid job: {job.result()['estimated cost']} USD\")"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Creating a Braket Hybrid Job from the Braket console\n",
- "\n",
- "Besides creating a Braket Hybrid Job programmatically using `AwsQuantumJob.create`, there is also an option to create a hybrid job in the Braket console. Follow [this link](https://us-west-2.console.aws.amazon.com/braket/home#/job/create) to the \\\"Create hybrid job\\\" page. First, we need to give our new hybrid job the algorithm script. The script can be uploaded directly from your computer in the console or selected from files that are uploaded to S3. Here you also have the option to provide input data and parameters to your algorithm. After the algorithm is specified, you have the option to skip directly to the review and create page.\n",
- "\n",
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Next, you can choose a name for your hybrid job or use the default name. You also have the option to change the default execution role and the default S3 location for uploads.\n",
- "\n",
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Third, select a container environment for your job. The default \"PennyLane\" container is enough for the example in this notebook. For information about using other pre-built or custom containers, see the [Pennylane](../2_Using_PennyLane_with_Braket_Hybrid_Jobs/Using_PennyLane_with_Braket_Hybrid_Jobs.ipynb) and the [BYOC](../3_Bring_your_own_container/bring_your_own_container.ipynb) example notebooks. \n",
- "\n",
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "You may also select a Braket on-demand simulator or QPU for your job and configure the execution settings. You also have the option to customize the default locations for checkpoints and output data. We dive deeper into these advanced use cases in other [example notebooks](../2_Using_PennyLane_with_Braket_Hybrid_Jobs/Using_PennyLane_with_Braket_Hybrid_Jobs.ipynb).\n",
- "\n",
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "After finishing all the settings, you can review your selections before submitting your hybrid job. You can now create the hybrid job by clicking the \\\"Create hybrid job\\\" button or return to any earlier step to make edits. We can now view the progress in the Braket console.\n",
- "\n",
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Summary\n",
- "\n",
- "In this tutorial, we have created our first Braket Job with a simple batch of five circuits using the Amazon Braket SDK and, as an alternative, from the Braket console. We learned how to change the Amazon S3 folder and the AWS region for a job, and how to save results, and how to retrieve queue depth for a device, and queue position for the hybrid job. We learned how to seamlessly change the device to run on simulators or QPUs. We used local mode to quickly test code. Finally, we created the same job using the Braket console."
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "conda_braket",
- "language": "python",
- "name": "conda_braket"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.10.9"
- },
- "vscode": {
- "interpreter": {
- "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2"
- }
- }
- },
- "nbformat": 4,
- "nbformat_minor": 4
-}
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Getting started with Amazon Braket Hybrid Jobs\n",
+ "\n",
+ "This tutorial shows how to run your first Amazon Braket Hybrid Job. To get started, we consider small circuits with only one qubit and one gate.\n",
+ "\n",
+ "\n",
+ "## Learning outcomes\n",
+ "* Get setup to run your first hybrid job\n",
+ "* Write an algorithm script to run on Braket Hybrid Jobs\n",
+ "* Understand how to run scripts or functions\n",
+ "* Create a hybrid job on Braket simulators or QPUs\n",
+ "* Monitoring the hybrid job state\n",
+ "* Save results from a hybrid job\n",
+ "* Using a specific AWS session\n",
+ "* Running hybrid jobs with priority on QPUs\n",
+ "* Use local hybrid jobs to quickly test and debug scripts\n",
+ "* Create a Braket Hybrid Job using the Braket console"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Getting setup to run Braket Hybrid Jobs\n",
+ "\n",
+ "When you use Amazon Braket Hybrid Jobs for the first time, you need to create an IAM role with the right [permissions](https://docs.aws.amazon.com/braket/latest/developerguide/braket-manage-access.html#about-amazonbraketjobsexecution). This role allows your hybrid job to perform actions on your behalf while it is executing your algorithm, for instance, access S3 to return the results of your hybrid job. To create the role or check if you already have one please visit the Permissions tab from the left menu of the Braket Console.\n",
+ "\n",
+ "## Writing an algorithm script\n",
+ "\n",
+ "To create a Braket Hybrid Job, you first need a Python script to run. In this example, it's contained in `algorithm_script.py`. The script is printed in the code cell below for convenience. \n",
+ "\n",
+ "As shown, each of the circuits has only one $X$ rotation gate with a random angle. The circuit is repeated five times with different random rotations. Note that the algorithm script does not specify the backend Amazon Braket device ARN explicitly. Instead, it is provided through environment variables such as `os.environ[\"AMZN_BRAKET_DEVICE_ARN\"]` that are passed to the algorithm script when creating the hybrid job. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "pycharm": {
+ "name": "#%% md\n"
+ }
+ },
+ "source": [
+ "#### This block is a copy of the algorithm script.\n",
+ "\n",
+ "```python\n",
+ "\n",
+ "import os\n",
+ "import numpy as np\n",
+ "\n",
+ "from braket.aws import AwsDevice\n",
+ "from braket.circuits import Circuit\n",
+ "from braket.jobs import save_job_result\n",
+ "from braket.tracking import Tracker\n",
+ "\n",
+ "t = Tracker().start()\n",
+ "\n",
+ "print(\"Test hybrid job started!\")\n",
+ "\n",
+ "# Use the device declared in the creation script\n",
+ "device = AwsDevice(os.environ[\"AMZN_BRAKET_DEVICE_ARN\"])\n",
+ "\n",
+ "counts_list = []\n",
+ "angle_list = []\n",
+ "for _ in range(5):\n",
+ " angle = np.pi * np.random.randn()\n",
+ " random_circuit = Circuit().rx(0, angle)\n",
+ "\n",
+ " task = device.run(random_circuit, shots=100)\n",
+ " counts = task.result().measurement_counts\n",
+ "\n",
+ " angle_list.append(angle)\n",
+ " counts_list.append(counts)\n",
+ " print(counts)\n",
+ "\n",
+ "# Save the variables of interest so that we can access later\n",
+ "save_job_result({\"counts\": counts_list, \"angle\": angle_list, \"estimated cost\": t.qpu_tasks_cost() + t.simulator_tasks_cost()})\n",
+ "\n",
+ "print(\"Test hybrid job completed!\")\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Creating your first hybrid job\n",
+ "\n",
+ "Once the script is finalized, you can create a Braket Hybrid Job with `AwsQuantumJob`. When the hybrid job is created, Amazon Braket starts the hybrid job instance (based on EC2) and spins up a Docker container to run your algorithm script. Other configurations can be specified via keyword arguments. See the [developer guide](https://docs.aws.amazon.com/braket/latest/developerguide/what-is-braket.html) and other example notebooks to learn more about how to customize your jobs\n",
+ "\n",
+ "This example uses the following inputs for `AwsQuantumJob`:\n",
+ "- device: The ARN of the Braket simulator or QPU to use in the hybrid job. It will be passed as an environment variable to the algorithm script. \n",
+ "- source_module: The path to a file or a Python module that contains your algorithm script. It will be uploaded to the container for running the Braket Hybrid Job.\n",
+ "- wait_until_complete (optional): If True, the function call will wait until the Braket Hybrid Job is completed and will additionally print logs to the local console. Otherwise, it will run asynchronously. The default is False."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from braket.aws import AwsDevice, AwsQuantumJob\n",
+ "from braket.devices import Devices"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "pycharm": {
+ "name": "#%%\n"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Initializing Braket Job: arn:aws:braket:::job/\n",
+ "...............................................\n",
+ "\u001B[34m2021-11-10 20:55:24,467 sagemaker-training-toolkit INFO Invoking user script\u001B[0m\n",
+ "\u001B[34mTraining Env:\u001B[0m\n",
+ "\u001B[34m{\n",
+ " \"additional_framework_parameters\": {},\n",
+ " \"channel_input_dirs\": {},\n",
+ " \"current_host\": \"algo-1\",\n",
+ " \"framework_module\": null,\n",
+ " \"hosts\": [\n",
+ " \"algo-1\"\n",
+ " ],\n",
+ " \"hyperparameters\": {},\n",
+ " \"input_config_dir\": \"/opt/ml/input/config\",\n",
+ " \"input_data_config\": {},\n",
+ " \"input_dir\": \"/opt/ml/input\",\n",
+ " \"is_master\": true,\n",
+ " \"job_name\": \"BraketJob--\",\n",
+ " \"log_level\": 20,\n",
+ " \"master_hostname\": \"algo-1\",\n",
+ " \"model_dir\": \"/opt/ml/model\",\n",
+ " \"module_dir\": \"/opt/ml/code\",\n",
+ " \"module_name\": \"braket_container\",\n",
+ " \"network_interface_name\": \"eth0\",\n",
+ " \"num_cpus\": 2,\n",
+ " \"num_gpus\": 0,\n",
+ " \"output_data_dir\": \"/opt/ml/output/data\",\n",
+ " \"output_dir\": \"/opt/ml/output\",\n",
+ " \"output_intermediate_dir\": \"/opt/ml/output/intermediate\",\n",
+ " \"resource_config\": {\n",
+ " \"current_host\": \"algo-1\",\n",
+ " \"hosts\": [\n",
+ " \"algo-1\"\n",
+ " ],\n",
+ " \"network_interface_name\": \"eth0\"\n",
+ " },\n",
+ " \"user_entry_point\": \"braket_container.py\"\u001B[0m\n",
+ "...............................................\n",
+ "...............................................\n",
+ "\u001B[34mRunning Code As Subprocess\u001B[0m\n",
+ "\u001B[34mTest job started!!!!!\u001B[0m\n",
+ "\u001B[34mCounter({'0': 88, '1': 12})\u001B[0m\n",
+ "\u001B[34mCounter({'1': 58, '0': 42})\u001B[0m\n",
+ "\u001B[34mCounter({'1': 54, '0': 46})\u001B[0m\n",
+ "\u001B[34mCounter({'0': 100})\u001B[0m\n",
+ "\u001B[34mCounter({'0': 100})\u001B[0m\n",
+ "\u001B[34mTest job completed!!!!!\u001B[0m\n",
+ "\u001B[34mCode Run Finished\u001B[0m\n",
+ "\u001B[34m2021-11-10 20:55:58,953 sagemaker-training-toolkit INFO Reporting training SUCCESS\u001B[0m\n"
+ ]
+ }
+ ],
+ "source": [
+ "# This cell should take about 5 mins\n",
+ "job = AwsQuantumJob.create(\n",
+ " device=Devices.Amazon.SV1,\n",
+ " source_module=\"algorithm_script.py\",\n",
+ " wait_until_complete=True,\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this example, the algorithm is defined by a single file, so the `source_module` is `algorithm_script.py`. Depending on your application, there are other options for setting the source module. For example, if you wish to only execute a part of `algorithm_script.py` at the start of a Braket Hybrid Job, you can package that part to be a `starting_function()`. Then assign the function as the entry point by adding the `entry_point` input argument."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "source_module = \"algorithm_script.py\"\n",
+ "entry_point = \"algorithm_script:starting_function\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If your algorithm script requires other dependencies, you can put them all in one folder, say the `algorithm_folder`. The input arguments would then be"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "source_module = \"algorithm_folder\"\n",
+ "entry_point = \"algorithm_folder.algorithm_script:starting_function\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Checking hybrid job state and loading results\n",
+ "\n",
+ "The status of a Braket Job can be checked by calling `job.state()`. The state will be one of \"QUEUED\", \"RUNNING\", \"FAILED\", \"COMPLETED\", \"CANCELLING\", or \"CANCELLED\". "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'COMPLETED'"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job.state()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Once completed, the result can be retrieved using `job.result()`. Logs and metadata are also accessible via `job.logs()` and `job.metadata()`. If you lose the reference to the hybrid job object, you can always reinstantiate it using your hybrid job ARN as `job=AwsQuantumJob(\"your-job-arn\")`. The ARN of a hybrid job can be found in the Amazon Braket Console. By default the ARN of a hybrid job will be \"`arn:aws:braket:::job/`\". "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "counts: [{'1': 12, '0': 88}, {'0': 42, '1': 58}, {'0': 46, '1': 54}, {'0': 100}, {'0': 100}]\n",
+ "angles: [-0.6634809825751307, 1.8729107298836103, -1.8816578492668359, -0.04308463076559567, 0.03224990551866221]\n"
+ ]
+ }
+ ],
+ "source": [
+ "results = job.result() # will return once job.state() = \"COMPLETED\", should be 6 minutes\n",
+ "print(\"counts: \", results[\"counts\"])\n",
+ "print(\"angles: \", results[\"angles\"])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# print(job.logs()) # uncomment to print logs"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You can also download the result to a local directory."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "job.download_result() # download hybrid job result to local directory"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Task Summary\n",
+ "{'arn:aws:braket:::device/quantum-simulator/amazon/sv1': {'shots': 500, 'tasks': {'COMPLETED': 5}, 'execution_duration': 0.081, 'billed_execution_duration': 15.0}}\n",
+ "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
+ "Estimated cost to run tasks in this job: 0.01875 USD\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Quantum Task Summary\")\n",
+ "print(job.result()['task summary'])\n",
+ "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n",
+ "print(f\"Estimated cost to run quantum tasks in this hybrid job: {job.result()['estimated cost']} USD\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Increase performance by running hybrid jobs on QPUs\n",
+ "\n",
+ "With Braket Hybrid Jobs, you can run hybrid algorithms on all QPUs available through Amazon Braket. When you select a QPU as your device, your hybrid job will have priority access for the duration of your hybrid job. Quantum tasks created as part of your hybrid job will be executed ahead of other tasks in the device queue. This reduces the risk of certain tasks being delayed or drifting calibrations on the device. To secure priority on a device your job needs to wait for the device to complete running or already queued jobs. Before submitting the job on a device, you can check the queue depth for the hybrid jobs. To check the number of hybrid jobs queued on the device call `device.queue_depth().jobs`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'2'"
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Select the device on which you will be submitting your hybrid job.\n",
+ "device = AwsDevice(Devices.Rigetti.Ankaa2)\n",
+ "device.queue_depth().jobs"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You can seamlessly swap the SV1 simulator for a QPU by changing the device argument in `AwsQuantumJob.create()`. For instance, the code below will create a hybrid job with priority access on the Rigetti Ankaa 2 device:\n",
+ "\n",
+ "
\n",
+ " Note: The following cell uses the Rigetti Ankaa 2 device; before you uncomment and run it, make sure the device is currently available. You can find QPU availability windows on the Devices page in the Amazon Braket Console\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# qpu_job = AwsQuantumJob.create(\n",
+ "# device=Devices.Rigetti.Ankaa2,\n",
+ "# source_module=\"algorithm_script.py\",\n",
+ "# wait_until_complete=False,\n",
+ "# )"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You can check the position of your hybrid job in the queue by calling job.queue_position().queue_position. The queue position is only returned when the job is in \"QUEUED\" state, else None is returned. You can also check why the queue position value is not returned by calling calling `job.queue_position().message`. Here, `job` is the variable to which you assign your job creation. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'3'"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# qpu_job.queue_position().queue_position"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "When you create the hybrid job, Amazon Braket will wait for the QPU to become available before initializing the hybrid job. Note that the Braket Hybrid Job will automatically select the AWS region where the device is available. As mentioned earlier, the specified device is provided to the hybrid job in the environment variable `AMZN_BRAKET_DEVICE_ARN`; the script `algorithm_script.py` uses this variable to choose the Braket device to use.\n",
+ "\n",
+ "In variational algorithms, there are usually optimization processes that update parameters of a fixed parametrized circuit. When executing such algorithms on a supported QPU with Hybrid Jobs, parametric compilation can improve the performance of the hybrid jobs. All you need to do is to submit the parametrized circuit using free parameters in the algorithm script. Braket will compile the circuit once and manage the compiled circuit of the Hybrid Job. There is no recompilation for subsequent parameter updates to the same circuit, resulting in faster runtimes. An example of algorithm script that uses a parametrized circuit is in `algorithm_script_parametrized_circuit.py`. Use this algorithm script in the place of `algorithm_script.py` and submit a hybrid job to a supported Braket QPU to use parametric compilation. See the Amazon Braket developer guide to learn more about [the usage of free parameters](https://docs.aws.amazon.com/braket/latest/developerguide/braket-constructing-circuit.html#braket-gates) and [parametric compilation with Hybrid Jobs](https://docs.aws.amazon.com/braket/latest/developerguide/braket-jobs.html)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## AWS Sessions\n",
+ "\n",
+ "You can customize the default location where Braket Hybrid Jobs saves and loads results in Amazon S3 by providing the AWS session information. The name of the S3 bucket needs to start with \"amazon-braket-\", and it must be in the same region as the hybrid job being created."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from braket.aws import AwsSession\n",
+ "\n",
+ "# Set Amazon S3 bucket\n",
+ "aws_session = AwsSession(default_bucket=\"amazon-braket-bucket-name\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To create a Braket Hybrid Job with this S3 bucket, pass `aws_session` as an argument to ` AwsQuantumJob.create()`:\n",
+ "\n",
+ "```python\n",
+ "job = AwsQuantumJob.create(\n",
+ " device=Devices.Amazon.SV1,\n",
+ " source_module=\"algorithm_script.py\",\n",
+ " aws_session=aws_session # using specific S3 bucket\n",
+ ")\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Debugging with local Braket Hybrid Jobs\n",
+ "\n",
+ "For faster testing and debugging of your code, you can run a hybrid job locally in your own environment. This feature requires Docker to be installed in your local environment. Amazon Braket notebooks have Docker pre-installed, so you can test local hybrid jobs in hosted notebooks instantly. To install Docker in your local environment, follow these [instructions](https://docs.docker.com/get-docker/). When a local hybrid job is created for the first time, it will take longer because it needs to build the container. The subsequent runs will be faster. Note that local hybrid jobs will not be visible in the Amazon Braket Console.\n",
+ "\n",
+ "To run a hybrid job in local mode, make sure the Docker daemon is running, and then simply create a `LocalQuantumJob` instead of an `AwsQuantumJob`. Local hybrid jobs always run synchronously and display the logs."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Using the short-lived AWS credentials found in session. They might expire while running.\n",
+ "Boto3 Version: 1.18.33\n",
+ "Beginning Setup\n",
+ "Completed 50.5 KiB/50.5 KiB (72.5 KiB/s) with 1 file(s) remaining\n",
+ "...............................................\n",
+ "...............................................\n",
+ "Running Code As Subprocess\n",
+ "Test job started!!!!!\n",
+ "Counter({'0': 79, '1': 21})\n",
+ "Counter({'0': 84, '1': 16})\n",
+ "Counter({'0': 91, '1': 9})\n",
+ "Counter({'0': 85, '1': 15})\n",
+ "Counter({'1': 94, '0': 6})\n",
+ "Test job completed!!!!!\n",
+ "Code Run Finished\n"
+ ]
+ }
+ ],
+ "source": [
+ "from braket.jobs.local.local_job import LocalQuantumJob\n",
+ "\n",
+ "# This cell should take about 2 min\n",
+ "job = LocalQuantumJob.create(\n",
+ " device=Devices.Amazon.SV1,\n",
+ " source_module=\"algorithm_script.py\",\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Task Summary\n",
+ "{'arn:aws:braket:::device/quantum-simulator/amazon/sv1': {'shots': 500, 'tasks': {'COMPLETED': 5}, 'execution_duration': 0.046, 'billed_execution_duration': 15.0}}\n",
+ "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
+ "Estimated cost to run tasks in this job: 0.01875 USD\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Quantum Task Summary\")\n",
+ "print(job.result()['task summary'])\n",
+ "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n",
+ "print(f\"Estimated cost to run quantum tasks in this hybrid job: {job.result()['estimated cost']} USD\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Creating a Braket Hybrid Job from the Braket console\n",
+ "\n",
+ "Besides creating a Braket Hybrid Job programmatically using `AwsQuantumJob.create`, there is also an option to create a hybrid job in the Braket console. Follow [this link](https://us-west-2.console.aws.amazon.com/braket/home#/job/create) to the \\\"Create hybrid job\\\" page. First, we need to give our new hybrid job the algorithm script. The script can be uploaded directly from your computer in the console or selected from files that are uploaded to S3. Here you also have the option to provide input data and parameters to your algorithm. After the algorithm is specified, you have the option to skip directly to the review and create page.\n",
+ "\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next, you can choose a name for your hybrid job or use the default name. You also have the option to change the default execution role and the default S3 location for uploads.\n",
+ "\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Third, select a container environment for your job. The default \"PennyLane\" container is enough for the example in this notebook. For information about using other pre-built or custom containers, see the [Pennylane](../2_Using_PennyLane_with_Braket_Hybrid_Jobs/Using_PennyLane_with_Braket_Hybrid_Jobs.ipynb) and the [BYOC](../3_Bring_your_own_container/bring_your_own_container.ipynb) example notebooks. \n",
+ "\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You may also select a Braket on-demand simulator or QPU for your job and configure the execution settings. You also have the option to customize the default locations for checkpoints and output data. We dive deeper into these advanced use cases in other [example notebooks](../2_Using_PennyLane_with_Braket_Hybrid_Jobs/Using_PennyLane_with_Braket_Hybrid_Jobs.ipynb).\n",
+ "\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "After finishing all the settings, you can review your selections before submitting your hybrid job. You can now create the hybrid job by clicking the \\\"Create hybrid job\\\" button or return to any earlier step to make edits. We can now view the progress in the Braket console.\n",
+ "\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Summary\n",
+ "\n",
+ "In this tutorial, we have created our first Braket Job with a simple batch of five circuits using the Amazon Braket SDK and, as an alternative, from the Braket console. We learned how to change the Amazon S3 folder and the AWS region for a job, and how to save results, and how to retrieve queue depth for a device, and queue position for the hybrid job. We learned how to seamlessly change the device to run on simulators or QPUs. We used local mode to quickly test code. Finally, we created the same job using the Braket console."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "conda_braket",
+ "language": "python",
+ "name": "conda_braket"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.10.9"
+ },
+ "vscode": {
+ "interpreter": {
+ "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2"
+ }
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
\ No newline at end of file
diff --git a/examples/hybrid_quantum_algorithms/QAOA/QAOA_braket.ipynb b/examples/hybrid_quantum_algorithms/QAOA/QAOA_braket.ipynb
index 498b9c9c7..d220741ed 100644
--- a/examples/hybrid_quantum_algorithms/QAOA/QAOA_braket.ipynb
+++ b/examples/hybrid_quantum_algorithms/QAOA/QAOA_braket.ipynb
@@ -1,1121 +1,1121 @@
{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [],
- "source": [
- "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
- "from braket.tracking import Tracker\n",
- "t = Tracker().start()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM (QAOA)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this tutorial we show how to (approximately) solve binary combinatorial optimization problems, using the __Quantum Approximate Optimization Algorithm (QAOA)__, as introduced in Ref.[1]. \n",
- "The QAOA algorithm belongs to the class of __hybrid quantum algorithms__ (leveraging both classical as well as quantum compute), that are widely believed to be the working horse for the current __NISQ (noisy intermediate-scale quantum) era__.\n",
- "In this NISQ era QAOA is also an emerging approach for benchmarking quantum devices and is a prime candidate for demonstrating a practical quantum speed-up on near-term NISQ device [1,4]. \n",
- "To validate our approach we benchmark our results with exact results as obtained from classical QUBO solvers. \n",
- "\n",
- "We provide a step-by-step walkthrough explaining the QAOA quantum algorithm and show how to build the corresponding parametrized quantum circuit ansatz using the ```Braket``` SDK, with simple modular building blocks (that can be re-used for other purposes). \n",
- "We use open-source off-the-shelf ```scipy``` optimizers for classical numerical optimization. \n",
- "While we demonstrate our proof-of-concept approach using classical simulators for circuit execution, our code could in principle be run on actual quantum hardware by simply changing the definition of the ```device``` object (provided that the gate set used in the ansatz is supported by the device, as is the case here for IonQ; for Rigetti we need to apply one more extra trick as shown below). "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## BACKGROUND: HYBRID QUANTUM ALGORITHMS"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Quantum computers hold the promise to outperform even the most-powerful classical computers on a range of computational problems in (for example) optimization, chemistry, material science and cryptography.\n",
- "The canonical set of quantum algorithms (such as Shor's or Grover's quantum algorithms), however, comes with hardware requirements (such as a large number of quantum gates) that are currently not available with state-of-the-art technology. \n",
- "Specifically, these algorithms are typically believed to be feasible only with fault-tolerance as provided by quantum error correction. \n",
- "In the current __noisy intermediate-scale (NISQ) era__, near-term quantum computers do not have a large enough number of physical qubits for the implementation of error correction protocols, making this canonical set of quantum algorithms unsuitable for near-term devices. Against this background, the near-term focus has widely shifted to the class of __hybrid quantum algorithms__ that do not require quantum error correction. \n",
- "In these hybrid quantum algorithms, the noisy __near-term quantum computers are used as co-processors__ only, within a larger classical optimization loop, as sketched in the schematic figure below. \n",
- "Here, the undesired effects of noise are suppressed by deliberately limiting the quantum circuits on the quantum processing unit (QPU) to short bursts of the calculation, and the need for long coherence times (as required for the standard set of quantum algorithms) is traded for a classical overhead due to (possibly many) measurement repetitions and (essentially error-free) classical processing. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "__Variational Quantum Algorithms__: Specifically, variational quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) [1] belong to this emerging class of hybrid quantum algorithms. \n",
- "These are widely believed to be promising candidates for the demonstration of a __quantum advantage__, already with near-term (NISQ) devices in areas such as quantum chemistry [2], condensed matter simulations [3], and discrete optimization tasks [4].\n",
- "\n",
- "__Variational Quantum Computing vs. Deep Learning__: The working principle of variational quantum computing is very much reminiscent of training deep neural networks: \n",
- "when you train a neural network, you have an objective function that you want to minimize, typically characterized by the error on your training set. \n",
- "To minimize that error, typically you start out with an initial guess for the weights in your network. \n",
- "The coprocessor, in that case a GPU, takes these weights which define the exact operation to execute and the output of the neural network is computed. \n",
- "This output is then used to calculate the value of your objective function, which in turn is used by the CPU to make an educated guess to update the weights and the cycle continues. \n",
- "Variational quantum algorithms, a specific form of hybrid algorithms, work in the very same way, using parametrized quantum circuits rather than parametrized neural networks and replacing the GPU with a QPU. \n",
- "Here, you start with an initial guess for the parameters that define your circuit, have the QPU execute that circuit, perform measurements to calculate an objective function, pass this value (together with the current values of the parameters) back to the CPU and have this *classical* CPU update the parameters based on that information. \n",
- "\n",
- "Of course, coordinating that workflow for quantum computers is much more challenging than in the previous case. Quantum computers are located in specialized laboratory facilities, are typically single threaded, and have special latency requirements. \n",
- "This is exactly the undifferentiated heavy-lifting that Amazon Braket handles for us, such that we can focus on our scientific problem. \n",
- "For the sake of this introductory tutorial, we simply use a classical circuit simulator (that mimic the behavior of a quantum machine) as the device to execute our quantum circuits.\n",
- "Within Amazon Braket, the workflow, however, is exactly the same. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## BACKGROUND: QUADRATIC BINARY OPTIMIZATION PROBLEMS"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "__Combinatorial optimization__: \n",
- "Combinatorial optimization problems are ubiquitous across many areas of science and application areas. \n",
- "Applications can be found (for example) in logistics, scheduling, planning, and portfolio optimization.\n",
- "In a nutshell combinatorial optimization problems are problems involving a large number of yes/no decisions with each set of decisions yielding a corresponding objective function value, like a cost or profit value. \n",
- "Because of the combinatorial explosion of the solution space with the number of variables, finding good solutions is a daunting task and extremely difficult. \n",
- "\n",
- "__QUBO problems__: The QUBO ([Quadratic Unconstrained Binary Optimization](https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization)) model unifies a rich variety of NP-hard combinatorial optimization problems: \n",
- "Famous examples include Quadratic Assignment Problems, Capital Budgeting Problems, Task Allocation Problems and Maximum-Cut Problems. \n",
- "For more details we refer to the excellent review and tutorial on QUBO problems presented in Ref.[5].\n",
- "\n",
- "__Maximum Cut__: Among the class of QUBO problems, Maximum Cut (MaxCut) is paradigm combinatorial optimization problem. \n",
- "Given a graph $G=(V,E)$ with vertex set $V$ and edge set $E$, we seek partition of $V$ into two subsets with maximum cut. \n",
- "In short, we have to color every node either blue or red and we score a point whenever an edge connects two nodes with different colors. \n",
- "We then would like to find the solution with the highest score. \n",
- "Applications thereof can be found in, for example, (i) clustering for marketing purposes (segment your customer base into different clusters for targeted marketing) or (ii) portfolio optimization in finance (vertex corresponds to asset, with color referring to sell or buy decisions. \n",
- "Again, the problem in this specific graph coloring problem is that there are $2^𝑁$ possible solutions for $N$ nodes (an exponential explosion in possibilities), making it impossible to enumerate all possible candidates for relevant system sizes. \n",
- "\n",
- "__Ising Hamiltonian__: Importantly, there is a fundamental correspondence between QUBO problems and Ising problems in physics. \n",
- "Specifically, we can encode the Maximum Cut problem as a __minimization problem__ of an Ising Hamiltonian, where the (classical) cost function reads \n",
- "\n",
- "$$H_{C}=\\sum_{i>j} J_{i,j} z_{i} z_{j},$$\n",
- "\n",
- "with Ising variables $z_{i}=-1,1$ and the Ising matrix $J$ encoding the weights of the edges. \n",
- "For the sake of this discussion, we ignore potential linear terms and constant offsets (that do not affect the optimal solution $z$ anyway). \n",
- "In short, the cost Hamiltonian $H_{C}$ assigns a number to every bitstring $z=(z_{1},z_{2},\\dots)$, and we would like to find the lowest number possible. \n",
- "This will be the optimal assignment and solution to our problem. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## BACKGROUND: THE QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this tutorial we will try to solve for the optimal _classical_ bitstring $z$ using the Quantum Approximate Optimization Algorithm (QAOA). \n",
- "To this end, we first promote the classical spin variables $z_{i}=-1,1$ to quantum-mechanical variables $\\sigma_{i}^{z}$ (with the Pauli matrix $\\sigma_{i}^{z}$ representing the observable corresponding to spin along the $z$ coordinate axis in three-dimensional Euclidean space $\\mathbb{R}^{3}$). \n",
- "This leads to the following quantum mechanical cost Hamiltonian encoding the optimization problem\n",
- "\n",
- "$$\\hat{H}_{C}=\\sum_{i>j} J_{i,j} \\sigma_{i}^{z} \\sigma_{j}^{z},$$\n",
- "\n",
- "which can be written as a matrix of size $(2^{N}, 2^{N})$ with diagonal elements only corresponding to all possible classical values for the cost function $H_{C}$. \n",
- "The ground state of $\\hat{H}_{C}$ corresponds to the optimal solution of the classical combinatorial problem.\n",
- "\n",
- "__QAOA ansatz__: Finding this ground state is generically hard. \n",
- "To approximate this groundstate, QAOA prepares a parametrized ansatz state (corresponding to a parameterized gate sequence), whose parameters are iteratively updated by a classical optimizer in a closed loop. \n",
- "Specifically, QAOA involves a specific ansatz wavefunction parametrized by a parameter family $(\\vec{\\beta}, \\vec{\\gamma})$, embedded into a larger classical optimization loop to find the optimal values for these parameters. \n",
- "As shown in Ref.[1], good approximate solutions to the problem class considered here can be found by preparing the variational state \n",
- "\n",
- "$$|\\gamma, \\beta \\rangle = U_{x}(\\beta_{p})U_{zz}(\\gamma_{p}) \\cdots U_{x}(\\beta_{1})U_{zz}(\\gamma_{1}) |s\\rangle$$\n",
- "\n",
- "with single qubit rotations induced by $U_{x}(\\beta) = \\exp(-i\\beta \\sum_{i}\\sigma_{i}^{x})$, \n",
- "and interactions described by $U_{zz}(\\gamma) = \\exp(-i\\gamma H_{C})$,\n",
- "starting initially from a product of $\\sigma^{x}$ eigenstates, i.e.,\n",
- "$|s\\rangle =|-,-,\\dots\\rangle$, with $|-\\rangle = (|0\\rangle -|1\\rangle )/\\sqrt{2}$. \n",
- "The family of states $|\\gamma, \\beta \\rangle$ is prepared by alternating single-qubit operations $U_{x}(\\beta_{p})$ with targeted spin-spin interactions generated by the cost Hamiltonian $H_{C}$. \n",
- "The depth $p$ can be interpreted as a hyperparameter. \n",
- "For $p$ layers of QAOA blocks, there are $2p$ classical parameters to optimize over, \n",
- "since each layer $k$ is characterized by just two variational parameters, $\\gamma_{k}$ and $\\beta_{k}$. \n",
- "The preparation step outlined above is followed by a measurement in the computational basis, giving a classical string $z$, with which one can evaluate the objective function $H_{C}$ of the underlying combinatorial problem at hand. \n",
- "Taking several measurements shots one can build the expectation value $E(\\beta, \\gamma) = \\langle H_{C} \\rangle$ that we report as the objective function to the classical minimizer (while other choices could be possible as well). \n",
- "Repeating this procedure will provide an optimized string $z$, with the quality of the result improving as the depth of the quantum circuit $\\sim 2p$ is increased [1]. \n",
- "In fact, in principle (in the absence of noise and other imperfections), QAOA can reach the global optimum of any cost function in the limit $p \\rightarrow \\infty$ [1], approaching the adiabatic protocol. \n",
- "Thus, in theory the computational power of QAOA increases with $p$, but in practice the number of layers that can be executed without errors on NISQ devices is limited due noise and imperfections. \n",
- "\n",
- "__Optimization__: Since we are primarily interested in solving the classical optimization problem, within this routine it is sufficient to keep track of the best classical bitstring. \n",
- "This means that the wavefunction prepared by the quantum circuit $|\\gamma, \\beta \\rangle$ has to have some overlap with the optimal solution $|z^{*} \\rangle$ that we can read out as bitstring $z^{*}$ in the measurement shots. \n",
- "To this end, in principle (i.e., without any training), we could just sample from a completely uniform state that is prepared in a superposition of all computational basis states, as prepared by applying Hadamard gates to all qubits: $|\\mathrm{uniform}\\rangle = 1/\\sqrt{2^{N}}\\sum_{i}|z_{i}\\rangle$. \n",
- "In that case (assuming a single optimal solution) the success probability per shot amounts to $p_{\\mathrm{success}}=1/2^{N}$. \n",
- "We can then amplify our success chances by just taking many measurement shots. \n",
- "For large systems, however, this approach is not scalable as we would need to take an exponentially increasing number of measurements. \n",
- "That is why we train our circuits, update the parameters, with the goal to increase our success chances to find the optimal bitstring. \n",
- "We can quantify our success chances as follows [6]. \n",
- "For a given wavefunction $|\\gamma, \\beta \\rangle$ the probability to find the optimal solution in a single shot is given by \n",
- "\n",
- "$$ p_{\\mathrm{success}}(\\gamma, \\beta) = |\\langle z^{*}|\\gamma, \\beta \\rangle |^{2},$$\n",
- "\n",
- "where $z^{*}$ denotes the optimal bitstring. \n",
- "If we perform $M$ repeated measurements, the overall probability $P$ for observing this solution at least once is given by \n",
- "\n",
- "$$ P = 1 - (1-p_{\\mathrm{success}}(\\gamma, \\beta))^{M}, $$ \n",
- "\n",
- "since the term $(1-p_{\\mathrm{success}}(\\gamma, \\beta))^{M}$ gives the probability of _not_ obtaining $z^{*}$ in repeated $M$ trials. \n",
- "Therefore, to have an overall success chance up to $\\epsilon$ close to 100%, i.e., $P \\geq 1-\\epsilon$, the number of required shots has to be \n",
- "\n",
- "$$ M \\geq \\frac{\\log(\\epsilon)}{\\log(1-p_{\\mathrm{success}}(\\gamma, \\beta))}.$$\n",
- "\n",
- "Let us illustrate this results as follows: \n",
- "If we do not know anything and just resort to a uniform superposition $|\\mathrm{uniform}\\rangle$, for a small system with $N=10$ qubits we can find the optimal solutions with 80% success probability by taking at least $\\sim 1650$ shots. \n",
- "For just $N=20$ qubits, however, this number amounts to $\\sim 1.7 \\times 10^{6}$, making this naive approach unfeasible. \n",
- "Conversely, if we can train the quantum circuit to obtain $p_{\\mathrm{success}}(\\gamma, \\beta) \\sim 0.1$, we only need $\\sim 15$ shots to have $P\\geq 80\\%$. \n",
- "Below we will track and illustrate the best classical optimum as our algorithm proceeds towards a local or (ideally) global optimum. \n",
- "\n",
- "__Objective function__: Finally, some more details on the definition of the cost function are in order. \n",
- "Following the standard approach [1, 4], QAOA tries to minimize the expectation value $\\langle \\hat{H}_{C} \\rangle$, but does _not_ explicitly maximize the success probability [6]. \n",
- "However, a low expectation value for $\\langle \\hat{H}_{C} \\rangle$ does not necessarily translate to a high success probability $p_{\\mathrm{success}}(\\gamma, \\beta)$, as can be understood from the following example:\n",
- "Consider (for example) a variational state that is a linear combination of low energy excited eigenstates of the cost Hamiltonian $\\hat{H}_{C}$ other than the ground state $|z^{*}\\rangle$. \n",
- "By definition, this state will have a relatively low expectation value $\\langle \\hat{H}_{C} \\rangle$ while the success probability is zero (as this low energy state does not have any overlap with the ground state). \n",
- "Similarly, a variational state that is a linear combination of the ground state with very high energy eigenstates could have a high success probability $p_{\\mathrm{success}}(\\gamma, \\beta)$, while (at the same time) reporting a high cost value to the classical optimizer.\n",
- "To address this issue, alternative methods for the optimization of the variational parameters have recently been proposed. \n",
- "While for simplicity we follow the majority of the literature and take $\\langle \\hat{H}_{C} \\rangle$ as cost value that we report to the classical optimizer, here we do mention a potential alternative for future research: \n",
- "One approach is to use the Gibbs objective function, defined as $\\mathrm{cost}=-\\mathrm{log} \\langle \\exp(-\\eta \\hat{H}_{C})\\rangle$, with the hyperparameter $\\eta>0$ [7]. \n",
- "As compared to the simple expectation value $\\langle \\hat{H}_{C} \\rangle$, this definition of the cost value shows stronger rewards for low energy states, thereby increasing the success probability. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## IMPORTS and SETUP"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "For classical benchmarking we will be using the python library ```pyqubo```, as used in our helper script ```utils_classical```. If not already present in your virtual environment, you can install this library simply with ```pip install pyqubo```. Similarly, as ```seaborn``` are not expected to be present in the virtual environment by default, we will install them via ```pip install seaborn```. Note the ```-q``` to suppress install updates from ```pip```."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# If these have already been installed, this cell can be commented out.\n",
- "!pip install pyqubo -q\n",
- "!pip install seaborn -q"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {},
- "outputs": [],
- "source": [
- "# general imports\n",
- "import numpy as np\n",
- "from scipy.optimize import minimize\n",
- "import matplotlib.pyplot as plt\n",
- "import networkx as nx\n",
- "import seaborn as sns\n",
- "import time\n",
- "from datetime import datetime\n",
- "import pickle\n",
- "import random\n",
- "\n",
- "# magic line for producing visualizations in notebook\n",
- "%matplotlib inline"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [],
- "source": [
- "# fix random seed for reproducibility\n",
- "seed = 42\n",
- "np.random.seed(seed)\n",
- "random.seed(a=seed)\n",
- "\n",
- "# switch to trigger writing training results to disk\n",
- "store_results = False\n",
- "# switch to trigger printing results of each optimization cycle\n",
- "verbose = False"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {},
- "outputs": [],
- "source": [
- "# AWS imports: Import Braket SDK modules\n",
- "from braket.circuits import FreeParameter\n",
- "from braket.devices import LocalSimulator"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [],
- "source": [
- "from utils_classical import plot_colored_graph, plot_colored_graph_simple, solve_classical_ising\n",
- "# auto reload external files, so that we can edit the external .py file and immediately see the changes here\n",
- "%load_ext autoreload\n",
- "%autoreload 2"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {},
- "outputs": [],
- "source": [
- "# Set up device: Local Simulator\n",
- "device = LocalSimulator()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {},
- "outputs": [],
- "source": [
- "## example code for other backends\n",
- "# from braket.aws import AwsDevice\n",
- "# from braket.devices import Devices\n",
- "## choose the on-demand simulator to run your circuit\n",
- "# device = AwsDevice(Devices.Amazon.SV1)\n",
- "## choose the Rigetti device to run your circuit\n",
- "# device = AwsDevice(Devices.Rigetti.Ankaa2)\n",
- "## choose the Ionq device to run your circuit\n",
- "# device = AwsDevice(Devices.IonQ.Aria1)\n",
- "## choose the IQM device to run your circuit\n",
- "# device = AwsDevice(Devices.IQM.Garnet)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## PROBLEM SETUP"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We consider a graph coloring problem.\n",
- "Given a graph $G=(V,E)$, made of a set vertices (also called nodes) $V$ and edges $E$, our goal is to color each node red or blue, then score a point for each node that is next to a node of different color. \n",
- "We strive to find the optimal coloring that scores the largest number of points.\n",
- "To this end, we will address the dual problem of finding the minimum energy of the corresponding Ising Hamiltonian. \n",
- "To get started, we first use the open-source ```networkx``` library to visualize the problem graph. \n",
- "Feel free to play with the parameters $n$ (for the number of nodes) and $m$ (for the number of edges) below to consider other graphs of your choice. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# setup Erdos Renyi graph\n",
- "n = 10 # number of nodes/vertices\n",
- "m = 20 # number of edges\n",
- "\n",
- "# define graph object\n",
- "G = nx.gnm_random_graph(n, m, seed=seed)\n",
- "# positions for all nodes\n",
- "pos = nx.spring_layout(G)\n",
- "\n",
- "# choose random weights\n",
- "for (u, v) in G.edges():\n",
- " G.edges[u,v]['weight'] = random.uniform(0, 1)\n",
- "\n",
- "# draw graph\n",
- "nx.draw(G, pos)\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 23,
- "metadata": {},
- "outputs": [],
- "source": [
- "# set Ising matrix \n",
- "Jfull = nx.to_numpy_array(G)\n",
- "\n",
- "# get off-diagonal upper triangular matrix\n",
- "J = np.triu(Jfull, k=1).astype(np.float64)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# plot Ising matrix\n",
- "plt.figure(1, figsize=[7, 5])\n",
- "sns.heatmap(J, annot=True, linewidths=.5, cmap=\"YlGnBu\", annot_kws = {'alpha': 1})\n",
- "plt.title('Ising distance matrix');\n",
- "plt.tight_layout();"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## IMPLEMENTATION OF QAOA WITH BRAKET "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this section we load a set of useful helper functions that we will explain in detail below. \n",
- "Specifically in ```utils_qaoa.py``` we provide simple building blocks for the core modules of our QAOA algorithm, that is (i) a function called ```circuit``` that defines the parametrized ansatz, (ii) a function called ```objective_function``` that takes a list of variational parameters as input, and returns the cost associated with those parameters and finally (iii) a function ```train``` to run the entire QAOA algorithm for given ansatz. \n",
- "This way we can solve the problem in a clean and modular approach.\n",
- "Here, we show in markdown the definition of the parametrized QAOA circuit. \n",
- "For more details, see the corresponding file ```utils_qaoa.py```. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "The autoreload extension is already loaded. To reload it, use:\n",
- " %reload_ext autoreload\n"
- ]
- }
- ],
- "source": [
- "from utils_qaoa import circuit, train \n",
- "# auto reload external files, so that we can edit the external .py file and immediately see the changes here\n",
- "%load_ext autoreload\n",
- "%autoreload 2"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "```python\n",
- "# function to implement evolution with driver Hamiltonian\n",
- "def driver(beta, n_qubits):\n",
- " \"\"\"\n",
- " Returns circuit for driver Hamiltonian U(Hb, beta)\n",
- " \"\"\"\n",
- " # instantiate circuit object\n",
- " circ = Circuit()\n",
- " \n",
- " for qubit in range(n_qubits):\n",
- " gate = Circuit().rx(qubit, 2*beta)\n",
- " circ.add(gate)\n",
- " \n",
- " return circ\n",
- "\n",
- "\n",
- "# helper function for evolution with cost Hamiltonian\n",
- "def cost_circuit(gamma, n_qubits, ising):\n",
- " \"\"\"\n",
- " returns circuit for evolution with cost Hamiltonian\n",
- " \"\"\"\n",
- " # instantiate circuit object\n",
- " circ = Circuit()\n",
- "\n",
- " # get all non-zero entries (edges) from Ising matrix \n",
- " idx = ising.nonzero()\n",
- " edges = list(zip(idx[0], idx[1]))\n",
- " \n",
- " for qubit_pair in edges:\n",
- " # get interaction strength\n",
- " int_strength = ising[qubit_pair[0], qubit_pair[1]]\n",
- " # for Rigetti we decompose ZZ using CNOT gates\n",
- " if 'Aspen' in device.name:\n",
- " gate = ZZgate(qubit_pair[0], qubit_pair[1], gamma*int_strength)\n",
- " circ.add(gate)\n",
- " # classical simulators and IonQ support ZZ gate\n",
- " else:\n",
- " gate = Circuit().zz(qubit_pair[0], qubit_pair[1], angle=2*gamma*int_strength)\n",
- " circ.add(gate)\n",
- "\n",
- " return circ\n",
- "\n",
- "\n",
- "# function to build the QAOA circuit with depth p\n",
- "def circuit(params, n_qubits, ising):\n",
- " \"\"\"\n",
- " function to return full QAOA circuit\n",
- " \"\"\"\n",
- "\n",
- " # initialize qaoa circuit with first Hadamard layer: for minimization start in |->\n",
- " circ = Circuit()\n",
- " X_on_all = Circuit().x(range(0, n_qubits))\n",
- " circ.add(X_on_all)\n",
- " H_on_all = Circuit().h(range(0, n_qubits))\n",
- " circ.add(H_on_all)\n",
- "\n",
- " # setup two parameter families\n",
- " circuit_length = int(len(params) / 2)\n",
- " gammas = params[:circuit_length]\n",
- " betas = params[circuit_length:]\n",
- "\n",
- " # add circuit layers\n",
- " for mm in range(circuit_length):\n",
- " circ.add(cost_circuit(gammas[mm], n_qubits, ising))\n",
- " circ.add(driver(betas[mm], n_qubits))\n",
- "\n",
- " return circ\n",
- "\n",
- "```"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## VISUALIZATION OF THE QAOA ANSATZ"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Let us first visualize our parametrized QAOA ansatz for a small number of qubits and fixed (i.e., not optimized) parameters. \n",
- "For convenience, the parameters are displayed in the circuit (up to a factor of $2$ we have added in our ansatz definition). \n",
- "First we prepare the state $|0,0,\\dots\\rangle \\rightarrow |-,-,\\dots\\rangle$, with the superposition state $|-\\rangle = (|0\\rangle -|1\\rangle )/\\sqrt{2}$. \n",
- "Following the discussion above, we choose to start out with this state as it is the minimal energy state of the simple driver Hamiltonian $H_{B}$. \n",
- "This state preparation is followed by one layer of the QAOA ansatz, consisting of evolution with the cost Hamiltonian by $\\exp(-i\\gamma H_{C})= \\prod_{j,l}\\exp(-i\\gamma J_{j,l}\\sigma_{j}^{z}\\sigma_{l}^{z}) = \\prod_{j,l} ZZ_{j,l}(2\\gamma J_{j,l})$, followed by the single-qubit driving term, $\\exp(-i\\beta H_{B})= \\prod_{j} \\exp(-i\\beta \\sigma_{j}^{x})= \\prod_{j} R_{j}^{(x)}(2\\beta)$.\n",
- "Note that the circuit definition depends on the ```device``` object, as the implementation of the ZZ gate depends on the specific gate set supported by the device. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 26,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Printing test circuit:\n",
- "T : |0|1| 2 | 3 |\n",
- " \n",
- "q0 : -X-H-ZZ(2*gamma)-Rx(2*beta)-\n",
- " | \n",
- "q1 : -X-H-ZZ(2*gamma)-Rx(2*beta)-\n",
- "\n",
- "T : |0|1| 2 | 3 |\n",
- "\n",
- "Unassigned parameters: [beta, gamma].\n"
- ]
- }
- ],
- "source": [
- "# create parameters\n",
- "gammas = [FreeParameter('gamma')]\n",
- "betas = [FreeParameter('beta')]\n",
- "params = gammas + betas\n",
- "\n",
- "# for demonstration purposes use small Ising matrix\n",
- "J_sub = np.array([[0, 1], [0, 0]])\n",
- "N = J_sub.shape[0]\n",
- "\n",
- "# get circuit ansatz\n",
- "my_simple_circuit = circuit(params, device, N, J_sub)\n",
- "\n",
- "# print test ansatz circuit\n",
- "print('Printing test circuit:')\n",
- "print(my_simple_circuit)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We see that our ansatz produces the expected result for shallow QAOA with $p=1$. \n",
- "We run one more sanity check for $p=2$ below. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 27,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Printing test circuit:\n",
- "T : |0|1| 2 | 3 | 4 | 5 |\n",
- " \n",
- "q0 : -X-H-ZZ(2*gamma_1)-Rx(2*beta_1)-ZZ(2*gamma_2)-Rx(2*beta_2)-\n",
- " | | \n",
- "q1 : -X-H-ZZ(2*gamma_1)-Rx(2*beta_1)-ZZ(2*gamma_2)-Rx(2*beta_2)-\n",
- "\n",
- "T : |0|1| 2 | 3 | 4 | 5 |\n",
- "\n",
- "Unassigned parameters: [beta_1, beta_2, gamma_1, gamma_2].\n"
- ]
- }
- ],
- "source": [
- "# set number of qubits and fix parameters\n",
- "gammas = [FreeParameter('gamma_1'), FreeParameter('gamma_2')]\n",
- "betas = [FreeParameter('beta_1'), FreeParameter('beta_2')]\n",
- "params = gammas + betas\n",
- "\n",
- "# for demonstration purposes use small Ising matrix\n",
- "J_sub = np.array([[0, 1], [0, 0]])\n",
- "N = J_sub.shape[0]\n",
- "\n",
- "# get circuit ansatz\n",
- "my_simple_circuit = circuit(params, device, N, J_sub)\n",
- "\n",
- "# print test ansatz circuit\n",
- "print('Printing test circuit:')\n",
- "print(my_simple_circuit)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## QAOA SIMULATION ON LOCAL SCHROEDINGER SIMULATOR"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We are now all set to run some QAOA simulation experiments. \n",
- "First of all, you can play and experiment yourself with the number of qubits $N$. \n",
- "Secondly, you may also experiment with the classical optimizer. \n",
- "Since we are using an off-the-shelf, black-box ```scipy``` minimizer (as described in more detail [here](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html)), you can simply swap between different optimizers by setting the ```OPT_METHOD``` parameter below. \n",
- "Some popular options readily available within this library include *Nelder-Mead*, *BFGS* and *COBYLA*. \n",
- "As a precautionary warning, note that the classical optimization step may get stuck in a local optimum, rather than finding the global minimum for our parametrized QAOA ansatz wavefunction. \n",
- "To address this issue, we may run several optimization loops, starting from different random parameter seeds. \n",
- "While this brute-force approach does not provide any guarantee to find the global optimum, from a pragmatic point of view at least it does increase the odds of finding an acceptable solution, at the expense of potentially having to run many more circuits on the simulator or QPU, respectively.\n",
- "Finally, the optimization loop may require the execution of many individual quantum tasks (i.e., single circuit executions for fixed parameters). \n",
- "For example, when choosing the classical [Powell](https://docs.scipy.org/doc/scipy/reference/optimize.minimize-powell.html#optimize-minimize-powell) optimizer for the graph considered here, we find $\\sim 270$ cycles in the for loop. \n",
- "For the local simulator device chosen here by default this is not an issue, but if you run this algorithm on any QPU you may want to adjust the ```maxfev``` parameter to control the maximum allowed number function evaluations (compare comment in the next code block below)."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 28,
- "metadata": {},
- "outputs": [],
- "source": [
- "##################################################################################\n",
- "# set up hyperparameters\n",
- "##################################################################################\n",
- "\n",
- "# User-defined hypers\n",
- "DEPTH = 3 # circuit depth for QAOA\n",
- "SHOTS = 1000 # number measurements to make on circuit\n",
- "OPT_METHOD = 'COBYLA' # SLSQP, COBYLA, Nelder-Mead, BFGS, Powell, ...\n",
- "\n",
- "# set up the problem\n",
- "n_qubits = J.shape[0]\n",
- "\n",
- "# initialize reference solution (simple guess)\n",
- "bitstring_init = -1 * np.ones([n_qubits])\n",
- "energy_init = np.dot(bitstring_init, np.dot(J, bitstring_init))\n",
- "\n",
- "# set tracker to keep track of results\n",
- "tracker = {\n",
- " 'count': 1, # Elapsed optimization steps\n",
- " 'optimal_energy': energy_init, # Global optimal energy\n",
- " 'opt_energies': [], # Optimal energy at each step\n",
- " 'global_energies': [], # Global optimal energy at each step\n",
- " 'optimal_bitstring': bitstring_init, # Global optimal bitstring\n",
- " 'opt_bitstrings': [], # Optimal bitstring at each step\n",
- " 'costs': [], # Cost (average energy) at each step\n",
- " 'res': None, # Quantum result object\n",
- " 'params': [] # Track parameters\n",
- "}\n",
- "\n",
- "# set options for classical optimization\n",
- "options = {'disp': True, 'maxiter': 50}"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 29,
- "metadata": {
- "scrolled": true
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Circuit depth hyperparameter: 3\n",
- "Problem size: 10\n",
- "Starting the training.\n",
- "====================================================================\n",
- "OPTIMIZATION for circuit depth p=3\n",
- "Param \"verbose\" set to False. Will not print intermediate steps.\n",
- "====================================================================\n",
- "Final average energy (cost):\n",
- " Return from subroutine COBYLA because the MAXFUN limit has been reached.\n",
- " -0.586455292294228\n",
- "Final angles: [5.78684986 4.70523429 6.47840919 0.25681156 1.2539245 2.7942261 ]\n",
- "Training complete.\n",
- "Code execution time [sec]: 6.3666791915893555\n",
- "Optimal energy: -6.486032631497276\n",
- "Optimal classical bitstring: [-1 1 -1 -1 1 -1 1 1 -1 -1]\n",
- "\n",
- " NFVALS = 50 F =-5.864553E-01 MAXCV = 0.000000E+00\n",
- " X = 5.786850E+00 4.705234E+00 6.478409E+00 2.568116E-01 1.253925E+00\n",
- " 2.794226E+00\n"
- ]
- }
- ],
- "source": [
- "##################################################################################\n",
- "# run QAOA optimization on graph \n",
- "##################################################################################\n",
- "\n",
- "print('Circuit depth hyperparameter:', DEPTH)\n",
- "print('Problem size:', n_qubits)\n",
- "\n",
- "# kick off training\n",
- "start = time.time()\n",
- "result_energy, result_angle, tracker = train(\n",
- " device = device, options=options, p=DEPTH, ising=J, n_qubits=n_qubits, n_shots=SHOTS, \n",
- " opt_method=OPT_METHOD, tracker=tracker, verbose=verbose)\n",
- "end = time.time()\n",
- "\n",
- "# print execution time\n",
- "print('Code execution time [sec]:', end - start)\n",
- "\n",
- "# print optimized results\n",
- "print('Optimal energy:', tracker['optimal_energy'])\n",
- "print('Optimal classical bitstring:', tracker['optimal_bitstring'])\n",
- "\n",
- "##################################################################################\n",
- "# Compute output and dump to pickle\n",
- "##################################################################################\n",
- "\n",
- "if store_results:\n",
- " out = {'p': DEPTH, 'N': n_qubits,\n",
- " 'ENERGY_OPTIMAL': tracker['optimal_energy'], 'BITSTRING': tracker['optimal_bitstring'],\n",
- " 'result_energy': result_energy, 'result_angle': result_angle}\n",
- "\n",
- " # store results: dump output to pickle with timestamp in filename\n",
- " time_now = datetime.strftime(datetime.now(), '%Y%m%d%H%M%S')\n",
- " results_file = 'results-'+time_now+'.pkl'\n",
- " print(f'Writing results to file: {results_file}')\n",
- " pickle.dump(out, open(results_file, \"wb\"))\n",
- " \n",
- " # you can load results as follows\n",
- " # out = pickle.load(open(results_file, \"rb\"))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## POSTPROCESSING AND COMPARISON OF OUR QAOA RESULTS WITH CLASSICAL RESULTS"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this section we visualize the results we have found with QAOA. \n",
- "Specifically, we display the results found for the variational parameters $\\beta$ and $\\gamma$ for every layer in our QAOA ansatz. \n",
- "Moreover, we show the solution to our graph coloring problem with every node colored either red or blue (recall that there are just two colors since we solve a _binary_ optimization problem).\n",
- "Finally, we compare these results to results found classically using the open-source ```pyqubo``` package. \n",
- "Ideally, the two results should agree with each other but this is not necessarily the case for several reasons: \n",
- "First of all, for the original small toy problem we have set up there are several degenerate classical solutions with the same optimal quality. \n",
- "The classical and the QAOA approach may find solutions with different coloring configurations but the same quality (that is energy). \n",
- "Secondly, with QAOA we are not guaranteed to find the optimal solutions. \n",
- "Specifically, the deeper the circuit, the harder the classical optimization problem, and we may get stuck in a local rather than global optimum. \n",
- "One brute-force approach is then to just re-run QAOA with different random initial seeds for the parameters $(\\beta, \\gamma)$."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 30,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Optimization on graph with n=10 vertices, m=20 edges, optimized with COBYLA and 1000 shots per call; seed=42.\n"
- ]
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
+ "from braket.tracking import Tracker\n",
+ "t = Tracker().start()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM (QAOA)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this tutorial we show how to (approximately) solve binary combinatorial optimization problems, using the __Quantum Approximate Optimization Algorithm (QAOA)__, as introduced in Ref.[1]. \n",
+ "The QAOA algorithm belongs to the class of __hybrid quantum algorithms__ (leveraging both classical as well as quantum compute), that are widely believed to be the working horse for the current __NISQ (noisy intermediate-scale quantum) era__.\n",
+ "In this NISQ era QAOA is also an emerging approach for benchmarking quantum devices and is a prime candidate for demonstrating a practical quantum speed-up on near-term NISQ device [1,4]. \n",
+ "To validate our approach we benchmark our results with exact results as obtained from classical QUBO solvers. \n",
+ "\n",
+ "We provide a step-by-step walkthrough explaining the QAOA quantum algorithm and show how to build the corresponding parametrized quantum circuit ansatz using the ```Braket``` SDK, with simple modular building blocks (that can be re-used for other purposes). \n",
+ "We use open-source off-the-shelf ```scipy``` optimizers for classical numerical optimization. \n",
+ "While we demonstrate our proof-of-concept approach using classical simulators for circuit execution, our code could in principle be run on actual quantum hardware by simply changing the definition of the ```device``` object (provided that the gate set used in the ansatz is supported by the device, as is the case here for IonQ; for Rigetti we need to apply one more extra trick as shown below). "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## BACKGROUND: HYBRID QUANTUM ALGORITHMS"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Quantum computers hold the promise to outperform even the most-powerful classical computers on a range of computational problems in (for example) optimization, chemistry, material science and cryptography.\n",
+ "The canonical set of quantum algorithms (such as Shor's or Grover's quantum algorithms), however, comes with hardware requirements (such as a large number of quantum gates) that are currently not available with state-of-the-art technology. \n",
+ "Specifically, these algorithms are typically believed to be feasible only with fault-tolerance as provided by quantum error correction. \n",
+ "In the current __noisy intermediate-scale (NISQ) era__, near-term quantum computers do not have a large enough number of physical qubits for the implementation of error correction protocols, making this canonical set of quantum algorithms unsuitable for near-term devices. Against this background, the near-term focus has widely shifted to the class of __hybrid quantum algorithms__ that do not require quantum error correction. \n",
+ "In these hybrid quantum algorithms, the noisy __near-term quantum computers are used as co-processors__ only, within a larger classical optimization loop, as sketched in the schematic figure below. \n",
+ "Here, the undesired effects of noise are suppressed by deliberately limiting the quantum circuits on the quantum processing unit (QPU) to short bursts of the calculation, and the need for long coherence times (as required for the standard set of quantum algorithms) is traded for a classical overhead due to (possibly many) measurement repetitions and (essentially error-free) classical processing. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "__Variational Quantum Algorithms__: Specifically, variational quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) [1] belong to this emerging class of hybrid quantum algorithms. \n",
+ "These are widely believed to be promising candidates for the demonstration of a __quantum advantage__, already with near-term (NISQ) devices in areas such as quantum chemistry [2], condensed matter simulations [3], and discrete optimization tasks [4].\n",
+ "\n",
+ "__Variational Quantum Computing vs. Deep Learning__: The working principle of variational quantum computing is very much reminiscent of training deep neural networks: \n",
+ "when you train a neural network, you have an objective function that you want to minimize, typically characterized by the error on your training set. \n",
+ "To minimize that error, typically you start out with an initial guess for the weights in your network. \n",
+ "The coprocessor, in that case a GPU, takes these weights which define the exact operation to execute and the output of the neural network is computed. \n",
+ "This output is then used to calculate the value of your objective function, which in turn is used by the CPU to make an educated guess to update the weights and the cycle continues. \n",
+ "Variational quantum algorithms, a specific form of hybrid algorithms, work in the very same way, using parametrized quantum circuits rather than parametrized neural networks and replacing the GPU with a QPU. \n",
+ "Here, you start with an initial guess for the parameters that define your circuit, have the QPU execute that circuit, perform measurements to calculate an objective function, pass this value (together with the current values of the parameters) back to the CPU and have this *classical* CPU update the parameters based on that information. \n",
+ "\n",
+ "Of course, coordinating that workflow for quantum computers is much more challenging than in the previous case. Quantum computers are located in specialized laboratory facilities, are typically single threaded, and have special latency requirements. \n",
+ "This is exactly the undifferentiated heavy-lifting that Amazon Braket handles for us, such that we can focus on our scientific problem. \n",
+ "For the sake of this introductory tutorial, we simply use a classical circuit simulator (that mimic the behavior of a quantum machine) as the device to execute our quantum circuits.\n",
+ "Within Amazon Braket, the workflow, however, is exactly the same. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## BACKGROUND: QUADRATIC BINARY OPTIMIZATION PROBLEMS"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "__Combinatorial optimization__: \n",
+ "Combinatorial optimization problems are ubiquitous across many areas of science and application areas. \n",
+ "Applications can be found (for example) in logistics, scheduling, planning, and portfolio optimization.\n",
+ "In a nutshell combinatorial optimization problems are problems involving a large number of yes/no decisions with each set of decisions yielding a corresponding objective function value, like a cost or profit value. \n",
+ "Because of the combinatorial explosion of the solution space with the number of variables, finding good solutions is a daunting task and extremely difficult. \n",
+ "\n",
+ "__QUBO problems__: The QUBO ([Quadratic Unconstrained Binary Optimization](https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization)) model unifies a rich variety of NP-hard combinatorial optimization problems: \n",
+ "Famous examples include Quadratic Assignment Problems, Capital Budgeting Problems, Task Allocation Problems and Maximum-Cut Problems. \n",
+ "For more details we refer to the excellent review and tutorial on QUBO problems presented in Ref.[5].\n",
+ "\n",
+ "__Maximum Cut__: Among the class of QUBO problems, Maximum Cut (MaxCut) is paradigm combinatorial optimization problem. \n",
+ "Given a graph $G=(V,E)$ with vertex set $V$ and edge set $E$, we seek partition of $V$ into two subsets with maximum cut. \n",
+ "In short, we have to color every node either blue or red and we score a point whenever an edge connects two nodes with different colors. \n",
+ "We then would like to find the solution with the highest score. \n",
+ "Applications thereof can be found in, for example, (i) clustering for marketing purposes (segment your customer base into different clusters for targeted marketing) or (ii) portfolio optimization in finance (vertex corresponds to asset, with color referring to sell or buy decisions. \n",
+ "Again, the problem in this specific graph coloring problem is that there are $2^𝑁$ possible solutions for $N$ nodes (an exponential explosion in possibilities), making it impossible to enumerate all possible candidates for relevant system sizes. \n",
+ "\n",
+ "__Ising Hamiltonian__: Importantly, there is a fundamental correspondence between QUBO problems and Ising problems in physics. \n",
+ "Specifically, we can encode the Maximum Cut problem as a __minimization problem__ of an Ising Hamiltonian, where the (classical) cost function reads \n",
+ "\n",
+ "$$H_{C}=\\sum_{i>j} J_{i,j} z_{i} z_{j},$$\n",
+ "\n",
+ "with Ising variables $z_{i}=-1,1$ and the Ising matrix $J$ encoding the weights of the edges. \n",
+ "For the sake of this discussion, we ignore potential linear terms and constant offsets (that do not affect the optimal solution $z$ anyway). \n",
+ "In short, the cost Hamiltonian $H_{C}$ assigns a number to every bitstring $z=(z_{1},z_{2},\\dots)$, and we would like to find the lowest number possible. \n",
+ "This will be the optimal assignment and solution to our problem. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## BACKGROUND: THE QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this tutorial we will try to solve for the optimal _classical_ bitstring $z$ using the Quantum Approximate Optimization Algorithm (QAOA). \n",
+ "To this end, we first promote the classical spin variables $z_{i}=-1,1$ to quantum-mechanical variables $\\sigma_{i}^{z}$ (with the Pauli matrix $\\sigma_{i}^{z}$ representing the observable corresponding to spin along the $z$ coordinate axis in three-dimensional Euclidean space $\\mathbb{R}^{3}$). \n",
+ "This leads to the following quantum mechanical cost Hamiltonian encoding the optimization problem\n",
+ "\n",
+ "$$\\hat{H}_{C}=\\sum_{i>j} J_{i,j} \\sigma_{i}^{z} \\sigma_{j}^{z},$$\n",
+ "\n",
+ "which can be written as a matrix of size $(2^{N}, 2^{N})$ with diagonal elements only corresponding to all possible classical values for the cost function $H_{C}$. \n",
+ "The ground state of $\\hat{H}_{C}$ corresponds to the optimal solution of the classical combinatorial problem.\n",
+ "\n",
+ "__QAOA ansatz__: Finding this ground state is generically hard. \n",
+ "To approximate this groundstate, QAOA prepares a parametrized ansatz state (corresponding to a parameterized gate sequence), whose parameters are iteratively updated by a classical optimizer in a closed loop. \n",
+ "Specifically, QAOA involves a specific ansatz wavefunction parametrized by a parameter family $(\\vec{\\beta}, \\vec{\\gamma})$, embedded into a larger classical optimization loop to find the optimal values for these parameters. \n",
+ "As shown in Ref.[1], good approximate solutions to the problem class considered here can be found by preparing the variational state \n",
+ "\n",
+ "$$|\\gamma, \\beta \\rangle = U_{x}(\\beta_{p})U_{zz}(\\gamma_{p}) \\cdots U_{x}(\\beta_{1})U_{zz}(\\gamma_{1}) |s\\rangle$$\n",
+ "\n",
+ "with single qubit rotations induced by $U_{x}(\\beta) = \\exp(-i\\beta \\sum_{i}\\sigma_{i}^{x})$, \n",
+ "and interactions described by $U_{zz}(\\gamma) = \\exp(-i\\gamma H_{C})$,\n",
+ "starting initially from a product of $\\sigma^{x}$ eigenstates, i.e.,\n",
+ "$|s\\rangle =|-,-,\\dots\\rangle$, with $|-\\rangle = (|0\\rangle -|1\\rangle )/\\sqrt{2}$. \n",
+ "The family of states $|\\gamma, \\beta \\rangle$ is prepared by alternating single-qubit operations $U_{x}(\\beta_{p})$ with targeted spin-spin interactions generated by the cost Hamiltonian $H_{C}$. \n",
+ "The depth $p$ can be interpreted as a hyperparameter. \n",
+ "For $p$ layers of QAOA blocks, there are $2p$ classical parameters to optimize over, \n",
+ "since each layer $k$ is characterized by just two variational parameters, $\\gamma_{k}$ and $\\beta_{k}$. \n",
+ "The preparation step outlined above is followed by a measurement in the computational basis, giving a classical string $z$, with which one can evaluate the objective function $H_{C}$ of the underlying combinatorial problem at hand. \n",
+ "Taking several measurements shots one can build the expectation value $E(\\beta, \\gamma) = \\langle H_{C} \\rangle$ that we report as the objective function to the classical minimizer (while other choices could be possible as well). \n",
+ "Repeating this procedure will provide an optimized string $z$, with the quality of the result improving as the depth of the quantum circuit $\\sim 2p$ is increased [1]. \n",
+ "In fact, in principle (in the absence of noise and other imperfections), QAOA can reach the global optimum of any cost function in the limit $p \\rightarrow \\infty$ [1], approaching the adiabatic protocol. \n",
+ "Thus, in theory the computational power of QAOA increases with $p$, but in practice the number of layers that can be executed without errors on NISQ devices is limited due noise and imperfections. \n",
+ "\n",
+ "__Optimization__: Since we are primarily interested in solving the classical optimization problem, within this routine it is sufficient to keep track of the best classical bitstring. \n",
+ "This means that the wavefunction prepared by the quantum circuit $|\\gamma, \\beta \\rangle$ has to have some overlap with the optimal solution $|z^{*} \\rangle$ that we can read out as bitstring $z^{*}$ in the measurement shots. \n",
+ "To this end, in principle (i.e., without any training), we could just sample from a completely uniform state that is prepared in a superposition of all computational basis states, as prepared by applying Hadamard gates to all qubits: $|\\mathrm{uniform}\\rangle = 1/\\sqrt{2^{N}}\\sum_{i}|z_{i}\\rangle$. \n",
+ "In that case (assuming a single optimal solution) the success probability per shot amounts to $p_{\\mathrm{success}}=1/2^{N}$. \n",
+ "We can then amplify our success chances by just taking many measurement shots. \n",
+ "For large systems, however, this approach is not scalable as we would need to take an exponentially increasing number of measurements. \n",
+ "That is why we train our circuits, update the parameters, with the goal to increase our success chances to find the optimal bitstring. \n",
+ "We can quantify our success chances as follows [6]. \n",
+ "For a given wavefunction $|\\gamma, \\beta \\rangle$ the probability to find the optimal solution in a single shot is given by \n",
+ "\n",
+ "$$ p_{\\mathrm{success}}(\\gamma, \\beta) = |\\langle z^{*}|\\gamma, \\beta \\rangle |^{2},$$\n",
+ "\n",
+ "where $z^{*}$ denotes the optimal bitstring. \n",
+ "If we perform $M$ repeated measurements, the overall probability $P$ for observing this solution at least once is given by \n",
+ "\n",
+ "$$ P = 1 - (1-p_{\\mathrm{success}}(\\gamma, \\beta))^{M}, $$ \n",
+ "\n",
+ "since the term $(1-p_{\\mathrm{success}}(\\gamma, \\beta))^{M}$ gives the probability of _not_ obtaining $z^{*}$ in repeated $M$ trials. \n",
+ "Therefore, to have an overall success chance up to $\\epsilon$ close to 100%, i.e., $P \\geq 1-\\epsilon$, the number of required shots has to be \n",
+ "\n",
+ "$$ M \\geq \\frac{\\log(\\epsilon)}{\\log(1-p_{\\mathrm{success}}(\\gamma, \\beta))}.$$\n",
+ "\n",
+ "Let us illustrate this results as follows: \n",
+ "If we do not know anything and just resort to a uniform superposition $|\\mathrm{uniform}\\rangle$, for a small system with $N=10$ qubits we can find the optimal solutions with 80% success probability by taking at least $\\sim 1650$ shots. \n",
+ "For just $N=20$ qubits, however, this number amounts to $\\sim 1.7 \\times 10^{6}$, making this naive approach unfeasible. \n",
+ "Conversely, if we can train the quantum circuit to obtain $p_{\\mathrm{success}}(\\gamma, \\beta) \\sim 0.1$, we only need $\\sim 15$ shots to have $P\\geq 80\\%$. \n",
+ "Below we will track and illustrate the best classical optimum as our algorithm proceeds towards a local or (ideally) global optimum. \n",
+ "\n",
+ "__Objective function__: Finally, some more details on the definition of the cost function are in order. \n",
+ "Following the standard approach [1, 4], QAOA tries to minimize the expectation value $\\langle \\hat{H}_{C} \\rangle$, but does _not_ explicitly maximize the success probability [6]. \n",
+ "However, a low expectation value for $\\langle \\hat{H}_{C} \\rangle$ does not necessarily translate to a high success probability $p_{\\mathrm{success}}(\\gamma, \\beta)$, as can be understood from the following example:\n",
+ "Consider (for example) a variational state that is a linear combination of low energy excited eigenstates of the cost Hamiltonian $\\hat{H}_{C}$ other than the ground state $|z^{*}\\rangle$. \n",
+ "By definition, this state will have a relatively low expectation value $\\langle \\hat{H}_{C} \\rangle$ while the success probability is zero (as this low energy state does not have any overlap with the ground state). \n",
+ "Similarly, a variational state that is a linear combination of the ground state with very high energy eigenstates could have a high success probability $p_{\\mathrm{success}}(\\gamma, \\beta)$, while (at the same time) reporting a high cost value to the classical optimizer.\n",
+ "To address this issue, alternative methods for the optimization of the variational parameters have recently been proposed. \n",
+ "While for simplicity we follow the majority of the literature and take $\\langle \\hat{H}_{C} \\rangle$ as cost value that we report to the classical optimizer, here we do mention a potential alternative for future research: \n",
+ "One approach is to use the Gibbs objective function, defined as $\\mathrm{cost}=-\\mathrm{log} \\langle \\exp(-\\eta \\hat{H}_{C})\\rangle$, with the hyperparameter $\\eta>0$ [7]. \n",
+ "As compared to the simple expectation value $\\langle \\hat{H}_{C} \\rangle$, this definition of the cost value shows stronger rewards for low energy states, thereby increasing the success probability. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## IMPORTS and SETUP"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For classical benchmarking we will be using the python library ```pyqubo```, as used in our helper script ```utils_classical```. If not already present in your virtual environment, you can install this library simply with ```pip install pyqubo```. Similarly, as ```seaborn``` are not expected to be present in the virtual environment by default, we will install them via ```pip install seaborn```. Note the ```-q``` to suppress install updates from ```pip```."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# If these have already been installed, this cell can be commented out.\n",
+ "!pip install pyqubo -q\n",
+ "!pip install seaborn -q"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# general imports\n",
+ "import numpy as np\n",
+ "from scipy.optimize import minimize\n",
+ "import matplotlib.pyplot as plt\n",
+ "import networkx as nx\n",
+ "import seaborn as sns\n",
+ "import time\n",
+ "from datetime import datetime\n",
+ "import pickle\n",
+ "import random\n",
+ "\n",
+ "# magic line for producing visualizations in notebook\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# fix random seed for reproducibility\n",
+ "seed = 42\n",
+ "np.random.seed(seed)\n",
+ "random.seed(a=seed)\n",
+ "\n",
+ "# switch to trigger writing training results to disk\n",
+ "store_results = False\n",
+ "# switch to trigger printing results of each optimization cycle\n",
+ "verbose = False"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# AWS imports: Import Braket SDK modules\n",
+ "from braket.circuits import FreeParameter\n",
+ "from braket.devices import LocalSimulator"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from utils_classical import plot_colored_graph, plot_colored_graph_simple, solve_classical_ising\n",
+ "# auto reload external files, so that we can edit the external .py file and immediately see the changes here\n",
+ "%load_ext autoreload\n",
+ "%autoreload 2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Set up device: Local Simulator\n",
+ "device = LocalSimulator()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "## example code for other backends\n",
+ "# from braket.aws import AwsDevice\n",
+ "# from braket.devices import Devices\n",
+ "## choose the on-demand simulator to run your circuit\n",
+ "# device = AwsDevice(Devices.Amazon.SV1)\n",
+ "## choose the Rigetti device to run your circuit\n",
+ "# device = AwsDevice(Devices.Rigetti.Ankaa2)\n",
+ "## choose the Ionq device to run your circuit\n",
+ "# device = AwsDevice(Devices.IonQ.Aria1)\n",
+ "## choose the IQM device to run your circuit\n",
+ "# device = AwsDevice(Devices.IQM.Garnet)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## PROBLEM SETUP"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We consider a graph coloring problem.\n",
+ "Given a graph $G=(V,E)$, made of a set vertices (also called nodes) $V$ and edges $E$, our goal is to color each node red or blue, then score a point for each node that is next to a node of different color. \n",
+ "We strive to find the optimal coloring that scores the largest number of points.\n",
+ "To this end, we will address the dual problem of finding the minimum energy of the corresponding Ising Hamiltonian. \n",
+ "To get started, we first use the open-source ```networkx``` library to visualize the problem graph. \n",
+ "Feel free to play with the parameters $n$ (for the number of nodes) and $m$ (for the number of edges) below to consider other graphs of your choice. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# setup Erdos Renyi graph\n",
+ "n = 10 # number of nodes/vertices\n",
+ "m = 20 # number of edges\n",
+ "\n",
+ "# define graph object\n",
+ "G = nx.gnm_random_graph(n, m, seed=seed)\n",
+ "# positions for all nodes\n",
+ "pos = nx.spring_layout(G)\n",
+ "\n",
+ "# choose random weights\n",
+ "for (u, v) in G.edges():\n",
+ " G.edges[u,v]['weight'] = random.uniform(0, 1)\n",
+ "\n",
+ "# draw graph\n",
+ "nx.draw(G, pos)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# set Ising matrix \n",
+ "Jfull = nx.to_numpy_array(G)\n",
+ "\n",
+ "# get off-diagonal upper triangular matrix\n",
+ "J = np.triu(Jfull, k=1).astype(np.float64)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot Ising matrix\n",
+ "plt.figure(1, figsize=[7, 5])\n",
+ "sns.heatmap(J, annot=True, linewidths=.5, cmap=\"YlGnBu\", annot_kws = {'alpha': 1})\n",
+ "plt.title('Ising distance matrix');\n",
+ "plt.tight_layout();"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## IMPLEMENTATION OF QAOA WITH BRAKET "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this section we load a set of useful helper functions that we will explain in detail below. \n",
+ "Specifically in ```utils_qaoa.py``` we provide simple building blocks for the core modules of our QAOA algorithm, that is (i) a function called ```circuit``` that defines the parametrized ansatz, (ii) a function called ```objective_function``` that takes a list of variational parameters as input, and returns the cost associated with those parameters and finally (iii) a function ```train``` to run the entire QAOA algorithm for given ansatz. \n",
+ "This way we can solve the problem in a clean and modular approach.\n",
+ "Here, we show in markdown the definition of the parametrized QAOA circuit. \n",
+ "For more details, see the corresponding file ```utils_qaoa.py```. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The autoreload extension is already loaded. To reload it, use:\n",
+ " %reload_ext autoreload\n"
+ ]
+ }
+ ],
+ "source": [
+ "from utils_qaoa import circuit, train \n",
+ "# auto reload external files, so that we can edit the external .py file and immediately see the changes here\n",
+ "%load_ext autoreload\n",
+ "%autoreload 2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "```python\n",
+ "# function to implement evolution with driver Hamiltonian\n",
+ "def driver(beta, n_qubits):\n",
+ " \"\"\"\n",
+ " Returns circuit for driver Hamiltonian U(Hb, beta)\n",
+ " \"\"\"\n",
+ " # instantiate circuit object\n",
+ " circ = Circuit()\n",
+ " \n",
+ " for qubit in range(n_qubits):\n",
+ " gate = Circuit().rx(qubit, 2*beta)\n",
+ " circ.add(gate)\n",
+ " \n",
+ " return circ\n",
+ "\n",
+ "\n",
+ "# helper function for evolution with cost Hamiltonian\n",
+ "def cost_circuit(gamma, n_qubits, ising):\n",
+ " \"\"\"\n",
+ " returns circuit for evolution with cost Hamiltonian\n",
+ " \"\"\"\n",
+ " # instantiate circuit object\n",
+ " circ = Circuit()\n",
+ "\n",
+ " # get all non-zero entries (edges) from Ising matrix \n",
+ " idx = ising.nonzero()\n",
+ " edges = list(zip(idx[0], idx[1]))\n",
+ " \n",
+ " for qubit_pair in edges:\n",
+ " # get interaction strength\n",
+ " int_strength = ising[qubit_pair[0], qubit_pair[1]]\n",
+ " # for Rigetti we decompose ZZ using CNOT gates\n",
+ " if 'Ankaa' in device.name:\n",
+ " gate = ZZgate(qubit_pair[0], qubit_pair[1], gamma*int_strength)\n",
+ " circ.add(gate)\n",
+ " # classical simulators and IonQ support ZZ gate\n",
+ " else:\n",
+ " gate = Circuit().zz(qubit_pair[0], qubit_pair[1], angle=2*gamma*int_strength)\n",
+ " circ.add(gate)\n",
+ "\n",
+ " return circ\n",
+ "\n",
+ "\n",
+ "# function to build the QAOA circuit with depth p\n",
+ "def circuit(params, n_qubits, ising):\n",
+ " \"\"\"\n",
+ " function to return full QAOA circuit\n",
+ " \"\"\"\n",
+ "\n",
+ " # initialize qaoa circuit with first Hadamard layer: for minimization start in |->\n",
+ " circ = Circuit()\n",
+ " X_on_all = Circuit().x(range(0, n_qubits))\n",
+ " circ.add(X_on_all)\n",
+ " H_on_all = Circuit().h(range(0, n_qubits))\n",
+ " circ.add(H_on_all)\n",
+ "\n",
+ " # setup two parameter families\n",
+ " circuit_length = int(len(params) / 2)\n",
+ " gammas = params[:circuit_length]\n",
+ " betas = params[circuit_length:]\n",
+ "\n",
+ " # add circuit layers\n",
+ " for mm in range(circuit_length):\n",
+ " circ.add(cost_circuit(gammas[mm], n_qubits, ising))\n",
+ " circ.add(driver(betas[mm], n_qubits))\n",
+ "\n",
+ " return circ\n",
+ "\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## VISUALIZATION OF THE QAOA ANSATZ"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let us first visualize our parametrized QAOA ansatz for a small number of qubits and fixed (i.e., not optimized) parameters. \n",
+ "For convenience, the parameters are displayed in the circuit (up to a factor of $2$ we have added in our ansatz definition). \n",
+ "First we prepare the state $|0,0,\\dots\\rangle \\rightarrow |-,-,\\dots\\rangle$, with the superposition state $|-\\rangle = (|0\\rangle -|1\\rangle )/\\sqrt{2}$. \n",
+ "Following the discussion above, we choose to start out with this state as it is the minimal energy state of the simple driver Hamiltonian $H_{B}$. \n",
+ "This state preparation is followed by one layer of the QAOA ansatz, consisting of evolution with the cost Hamiltonian by $\\exp(-i\\gamma H_{C})= \\prod_{j,l}\\exp(-i\\gamma J_{j,l}\\sigma_{j}^{z}\\sigma_{l}^{z}) = \\prod_{j,l} ZZ_{j,l}(2\\gamma J_{j,l})$, followed by the single-qubit driving term, $\\exp(-i\\beta H_{B})= \\prod_{j} \\exp(-i\\beta \\sigma_{j}^{x})= \\prod_{j} R_{j}^{(x)}(2\\beta)$.\n",
+ "Note that the circuit definition depends on the ```device``` object, as the implementation of the ZZ gate depends on the specific gate set supported by the device. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Printing test circuit:\n",
+ "T : |0|1| 2 | 3 |\n",
+ " \n",
+ "q0 : -X-H-ZZ(2*gamma)-Rx(2*beta)-\n",
+ " | \n",
+ "q1 : -X-H-ZZ(2*gamma)-Rx(2*beta)-\n",
+ "\n",
+ "T : |0|1| 2 | 3 |\n",
+ "\n",
+ "Unassigned parameters: [beta, gamma].\n"
+ ]
+ }
+ ],
+ "source": [
+ "# create parameters\n",
+ "gammas = [FreeParameter('gamma')]\n",
+ "betas = [FreeParameter('beta')]\n",
+ "params = gammas + betas\n",
+ "\n",
+ "# for demonstration purposes use small Ising matrix\n",
+ "J_sub = np.array([[0, 1], [0, 0]])\n",
+ "N = J_sub.shape[0]\n",
+ "\n",
+ "# get circuit ansatz\n",
+ "my_simple_circuit = circuit(params, device, N, J_sub)\n",
+ "\n",
+ "# print test ansatz circuit\n",
+ "print('Printing test circuit:')\n",
+ "print(my_simple_circuit)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We see that our ansatz produces the expected result for shallow QAOA with $p=1$. \n",
+ "We run one more sanity check for $p=2$ below. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Printing test circuit:\n",
+ "T : |0|1| 2 | 3 | 4 | 5 |\n",
+ " \n",
+ "q0 : -X-H-ZZ(2*gamma_1)-Rx(2*beta_1)-ZZ(2*gamma_2)-Rx(2*beta_2)-\n",
+ " | | \n",
+ "q1 : -X-H-ZZ(2*gamma_1)-Rx(2*beta_1)-ZZ(2*gamma_2)-Rx(2*beta_2)-\n",
+ "\n",
+ "T : |0|1| 2 | 3 | 4 | 5 |\n",
+ "\n",
+ "Unassigned parameters: [beta_1, beta_2, gamma_1, gamma_2].\n"
+ ]
+ }
+ ],
+ "source": [
+ "# set number of qubits and fix parameters\n",
+ "gammas = [FreeParameter('gamma_1'), FreeParameter('gamma_2')]\n",
+ "betas = [FreeParameter('beta_1'), FreeParameter('beta_2')]\n",
+ "params = gammas + betas\n",
+ "\n",
+ "# for demonstration purposes use small Ising matrix\n",
+ "J_sub = np.array([[0, 1], [0, 0]])\n",
+ "N = J_sub.shape[0]\n",
+ "\n",
+ "# get circuit ansatz\n",
+ "my_simple_circuit = circuit(params, device, N, J_sub)\n",
+ "\n",
+ "# print test ansatz circuit\n",
+ "print('Printing test circuit:')\n",
+ "print(my_simple_circuit)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## QAOA SIMULATION ON LOCAL SCHROEDINGER SIMULATOR"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We are now all set to run some QAOA simulation experiments. \n",
+ "First of all, you can play and experiment yourself with the number of qubits $N$. \n",
+ "Secondly, you may also experiment with the classical optimizer. \n",
+ "Since we are using an off-the-shelf, black-box ```scipy``` minimizer (as described in more detail [here](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html)), you can simply swap between different optimizers by setting the ```OPT_METHOD``` parameter below. \n",
+ "Some popular options readily available within this library include *Nelder-Mead*, *BFGS* and *COBYLA*. \n",
+ "As a precautionary warning, note that the classical optimization step may get stuck in a local optimum, rather than finding the global minimum for our parametrized QAOA ansatz wavefunction. \n",
+ "To address this issue, we may run several optimization loops, starting from different random parameter seeds. \n",
+ "While this brute-force approach does not provide any guarantee to find the global optimum, from a pragmatic point of view at least it does increase the odds of finding an acceptable solution, at the expense of potentially having to run many more circuits on the simulator or QPU, respectively.\n",
+ "Finally, the optimization loop may require the execution of many individual quantum tasks (i.e., single circuit executions for fixed parameters). \n",
+ "For example, when choosing the classical [Powell](https://docs.scipy.org/doc/scipy/reference/optimize.minimize-powell.html#optimize-minimize-powell) optimizer for the graph considered here, we find $\\sim 270$ cycles in the for loop. \n",
+ "For the local simulator device chosen here by default this is not an issue, but if you run this algorithm on any QPU you may want to adjust the ```maxfev``` parameter to control the maximum allowed number function evaluations (compare comment in the next code block below)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "##################################################################################\n",
+ "# set up hyperparameters\n",
+ "##################################################################################\n",
+ "\n",
+ "# User-defined hypers\n",
+ "DEPTH = 3 # circuit depth for QAOA\n",
+ "SHOTS = 1000 # number measurements to make on circuit\n",
+ "OPT_METHOD = 'COBYLA' # SLSQP, COBYLA, Nelder-Mead, BFGS, Powell, ...\n",
+ "\n",
+ "# set up the problem\n",
+ "n_qubits = J.shape[0]\n",
+ "\n",
+ "# initialize reference solution (simple guess)\n",
+ "bitstring_init = -1 * np.ones([n_qubits])\n",
+ "energy_init = np.dot(bitstring_init, np.dot(J, bitstring_init))\n",
+ "\n",
+ "# set tracker to keep track of results\n",
+ "tracker = {\n",
+ " 'count': 1, # Elapsed optimization steps\n",
+ " 'optimal_energy': energy_init, # Global optimal energy\n",
+ " 'opt_energies': [], # Optimal energy at each step\n",
+ " 'global_energies': [], # Global optimal energy at each step\n",
+ " 'optimal_bitstring': bitstring_init, # Global optimal bitstring\n",
+ " 'opt_bitstrings': [], # Optimal bitstring at each step\n",
+ " 'costs': [], # Cost (average energy) at each step\n",
+ " 'res': None, # Quantum result object\n",
+ " 'params': [] # Track parameters\n",
+ "}\n",
+ "\n",
+ "# set options for classical optimization\n",
+ "options = {'disp': True, 'maxiter': 50}"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Circuit depth hyperparameter: 3\n",
+ "Problem size: 10\n",
+ "Starting the training.\n",
+ "====================================================================\n",
+ "OPTIMIZATION for circuit depth p=3\n",
+ "Param \"verbose\" set to False. Will not print intermediate steps.\n",
+ "====================================================================\n",
+ "Final average energy (cost):\n",
+ " Return from subroutine COBYLA because the MAXFUN limit has been reached.\n",
+ " -0.586455292294228\n",
+ "Final angles: [5.78684986 4.70523429 6.47840919 0.25681156 1.2539245 2.7942261 ]\n",
+ "Training complete.\n",
+ "Code execution time [sec]: 6.3666791915893555\n",
+ "Optimal energy: -6.486032631497276\n",
+ "Optimal classical bitstring: [-1 1 -1 -1 1 -1 1 1 -1 -1]\n",
+ "\n",
+ " NFVALS = 50 F =-5.864553E-01 MAXCV = 0.000000E+00\n",
+ " X = 5.786850E+00 4.705234E+00 6.478409E+00 2.568116E-01 1.253925E+00\n",
+ " 2.794226E+00\n"
+ ]
+ }
+ ],
+ "source": [
+ "##################################################################################\n",
+ "# run QAOA optimization on graph \n",
+ "##################################################################################\n",
+ "\n",
+ "print('Circuit depth hyperparameter:', DEPTH)\n",
+ "print('Problem size:', n_qubits)\n",
+ "\n",
+ "# kick off training\n",
+ "start = time.time()\n",
+ "result_energy, result_angle, tracker = train(\n",
+ " device = device, options=options, p=DEPTH, ising=J, n_qubits=n_qubits, n_shots=SHOTS, \n",
+ " opt_method=OPT_METHOD, tracker=tracker, verbose=verbose)\n",
+ "end = time.time()\n",
+ "\n",
+ "# print execution time\n",
+ "print('Code execution time [sec]:', end - start)\n",
+ "\n",
+ "# print optimized results\n",
+ "print('Optimal energy:', tracker['optimal_energy'])\n",
+ "print('Optimal classical bitstring:', tracker['optimal_bitstring'])\n",
+ "\n",
+ "##################################################################################\n",
+ "# Compute output and dump to pickle\n",
+ "##################################################################################\n",
+ "\n",
+ "if store_results:\n",
+ " out = {'p': DEPTH, 'N': n_qubits,\n",
+ " 'ENERGY_OPTIMAL': tracker['optimal_energy'], 'BITSTRING': tracker['optimal_bitstring'],\n",
+ " 'result_energy': result_energy, 'result_angle': result_angle}\n",
+ "\n",
+ " # store results: dump output to pickle with timestamp in filename\n",
+ " time_now = datetime.strftime(datetime.now(), '%Y%m%d%H%M%S')\n",
+ " results_file = 'results-'+time_now+'.pkl'\n",
+ " print(f'Writing results to file: {results_file}')\n",
+ " pickle.dump(out, open(results_file, \"wb\"))\n",
+ " \n",
+ " # you can load results as follows\n",
+ " # out = pickle.load(open(results_file, \"rb\"))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## POSTPROCESSING AND COMPARISON OF OUR QAOA RESULTS WITH CLASSICAL RESULTS"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this section we visualize the results we have found with QAOA. \n",
+ "Specifically, we display the results found for the variational parameters $\\beta$ and $\\gamma$ for every layer in our QAOA ansatz. \n",
+ "Moreover, we show the solution to our graph coloring problem with every node colored either red or blue (recall that there are just two colors since we solve a _binary_ optimization problem).\n",
+ "Finally, we compare these results to results found classically using the open-source ```pyqubo``` package. \n",
+ "Ideally, the two results should agree with each other but this is not necessarily the case for several reasons: \n",
+ "First of all, for the original small toy problem we have set up there are several degenerate classical solutions with the same optimal quality. \n",
+ "The classical and the QAOA approach may find solutions with different coloring configurations but the same quality (that is energy). \n",
+ "Secondly, with QAOA we are not guaranteed to find the optimal solutions. \n",
+ "Specifically, the deeper the circuit, the harder the classical optimization problem, and we may get stuck in a local rather than global optimum. \n",
+ "One brute-force approach is then to just re-run QAOA with different random initial seeds for the parameters $(\\beta, \\gamma)$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Optimization on graph with n=10 vertices, m=20 edges, optimized with COBYLA and 1000 shots per call; seed=42.\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# visualize the optimization process\n",
+ "cycles = np.arange(1, tracker['count'])\n",
+ "optim_classical = tracker['global_energies']\n",
+ "\n",
+ "# print information\n",
+ "info = 'Optimization on graph with n={} vertices, m={} edges, optimized with {} and {} shots per call; seed={}.'\n",
+ "print(info.format(n, m, OPT_METHOD, SHOTS, seed))\n",
+ "\n",
+ "plt.plot(cycles, optim_classical)\n",
+ "plt.xlabel('optimization cycle')\n",
+ "plt.ylabel('best classical minimum')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Optimal energy found with QAOA: -6.486032631497276\n",
+ "Optimal bit-string found with QAOA: [-1 1 -1 -1 1 -1 1 1 -1 -1]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# print the optimal energy found with QAOA \n",
+ "print('Optimal energy found with QAOA:', tracker['optimal_energy'])\n",
+ "# print the corresponding bitstring\n",
+ "print('Optimal bit-string found with QAOA:', tracker['optimal_bitstring'])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# get results for variational angles\n",
+ "gamma = result_angle[:DEPTH]\n",
+ "beta = result_angle[DEPTH:]\n",
+ "# get array [1, 2, ..., p]\n",
+ "pa = np.arange(1, DEPTH + 1)\n",
+ "\n",
+ "plt.figure(2)\n",
+ "plt.plot(pa, gamma / np.pi, '-o', label='gamma')\n",
+ "plt.plot(pa, beta / np.pi, '-s', label='beta')\n",
+ "plt.xlabel('circuit depth (layer) p')\n",
+ "plt.ylabel('optimal angles [pi]')\n",
+ "plt.xticks(pa)\n",
+ "plt.legend(title='Variational QAOA angles:', loc='upper left')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Minimal energy found with QAOA: -6.486032631497276\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# visualize solution\n",
+ "colorlist = tracker['optimal_bitstring']\n",
+ "colorlist[colorlist == -1] = 0\n",
+ "\n",
+ "# plot_colored_graph(J, N, colorlist, pos)\n",
+ "plot_colored_graph_simple(G, colorlist, pos)\n",
+ "print('Minimal energy found with QAOA:', tracker['optimal_energy'])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Classical solution: {'s0': -1, 's1': 1, 's2': -1, 's3': -1, 's4': 1, 's5': -1, 's6': 1, 's7': 1, 's8': -1, 's9': -1}\n",
+ "Minimal energy found classically: -6.486032631497276\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# validate quantum results with classical algorithm\n",
+ "solution, energy_min, colors_classical = solve_classical_ising(J, n_qubits, pos)\n",
+ "# plot classical solution\n",
+ "plot_colored_graph_simple(G, colors_classical, pos)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that QAOA may arrive at a different solution than our classical benchmark code. \n",
+ "First of all, the classical optimization routine may get stuck in a local rather than global optimum. \n",
+ "To avoid this, more sophisticated optimization strategies may be employed (as proposed for example in Ref.[4]), going beyond the scope of this introductory notebook tutorial. \n",
+ "Secondly, even if QAOA arrives at the same classical energy as our classical approach, the coloring may differ since the solution space may be degenerate for the specific example shown here (this means, two different classical bitstrings have the same energy).\n",
+ "At minimum, you may find an inverted coloring (by swapping red and blue colors), because of the underlying $\\mathbb{Z}_{2}$ symmetry. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## SUMMARY"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this notebook we have gone through an end-to-end demo on QAOA and its implementation on Amazon Braket. \n",
+ "We have built modular core building blocks that may easily adapted to other problems. \n",
+ "The QAOA routine is tailored towards solving combinatorial optimization problems such as _Maximum Cut_ [4] and arguably one of the most prominent examples of the emerging class of hybrid, variational algorithms and still very much a field of active research today. \n",
+ "For example, as we increase the circuit depth of QAOA, the classical optimization step becomes increasingly difficult (because of the curse of dimensionality as well known in classical machine learning) and may easily get stuck in local sub-optimal solutions. \n",
+ "To address this issue some heuristics have already been developed, for example in Ref.[4], but further improvements will arguably be necessary to fully unlock the potential of this approach. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "## REFERENCES"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "[1] E. Farhi, J. Goldstone, and S. Gutmann, \"A Quantum Approximate Optimization Algorithm\", arXiv: 1411.4028 (2014).\n",
+ "\n",
+ "[2] Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. Johnson, M. Kieferova, I. D. Kivlichan, T. Menke, B. Peropadre, N. P. Sawaya, et al., \"Quantum Chemistry in the Age of Quantum Computing\", Chemical reviews 119, 10856 (2019).\n",
+ "\n",
+ "[3] A. Smith, M. Kim, F. Pollmann, and J. Knolle, \"Simulating quantum many-body dynamics on a current digital quantum computer\", npj Quantum Information 5, 1 (2019).\n",
+ "\n",
+ "[4] L. Zhou, S.-T. Wang, S. Choi, H. Pichler, and M. D. Lukin, \"Quantum Approximate Optimization Algorithm: Performance, Mechanism,and Implementation on Near-Term Devices\", arXiv: 1812.01041 (2018). \n",
+ "\n",
+ "[5] F. Glover, G. Kochenberger, \"A Tutorial on Formulating and Using QUBO Models\", arXiv:1811.11538 (2018).\n",
+ "\n",
+ "[6] P. Vikstal, M. Groenkvist, M. Svensson, M. Andersson, G. Johansson, and G. Ferrini, \"Applying the Quantum Approximate Optimization Algorithm to the Tail Assignment Problem\", arXiv:1912.10499 (2019). \n",
+ "\n",
+ "[7] L. Li, M. Fan, M. Coram, P. Riley, and S. Leichenauer, \"Quantum optimization with a novel gibbs objective function and ansatz architecture search\", arXiv:1909.07621 (2019). "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "## APPENDIX"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### APPENDIX: Example for Ising Matrix Syntax"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this appendix we provide a small code example to showcase how we obtain all edges with corresponding weights. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Ising matrix:\n",
+ " [[0 1 0]\n",
+ " [0 0 3]\n",
+ " [0 0 0]]\n",
+ "Edges: [(0, 1), (1, 2)]\n",
+ "Interaction strength: 1\n",
+ "Interaction strength: 3\n",
+ "All interactions: [1 3]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# example Ising matrix with edges between qubit 0 and qubit 1 (weight=1) and qubit 1 and qubit 2 (weight=3)\n",
+ "ising = np.array([[0, 1, 0], [0, 0, 3], [0, 0, 0]])\n",
+ "print('Ising matrix:\\n', ising)\n",
+ "\n",
+ "# get all non-zero entries (edges) from Ising matrix \n",
+ "idx = ising.nonzero()\n",
+ "edges = list(zip(idx[0], idx[1]))\n",
+ "print('Edges:', edges)\n",
+ "\n",
+ "# for every edge print interaction strength\n",
+ "for qubit_pair in edges:\n",
+ " # get interaction strength\n",
+ " int_strength = ising[qubit_pair[0], qubit_pair[1]]\n",
+ " print('Interaction strength:', int_strength)\n",
+ "\n",
+ "# get all non-zero entries from Ising, with proper order\n",
+ "interactions = np.array([ising[q[0], q[1]] for q in edges])\n",
+ "print('All interactions:', interactions)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Task Summary\n",
+ "{}\n",
+ "Estimated cost to run this example with SV1: 0 USD\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Quantum Task Summary\")\n",
+ "print(t.quantum_tasks_statistics())\n",
+ "print(f\"Estimated cost to run this example with SV1: {t.qpu_tasks_cost() + t.simulator_tasks_cost()} USD\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.10.9"
+ },
+ "vscode": {
+ "interpreter": {
+ "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2"
+ }
+ }
},
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# visualize the optimization process\n",
- "cycles = np.arange(1, tracker['count'])\n",
- "optim_classical = tracker['global_energies']\n",
- "\n",
- "# print information\n",
- "info = 'Optimization on graph with n={} vertices, m={} edges, optimized with {} and {} shots per call; seed={}.'\n",
- "print(info.format(n, m, OPT_METHOD, SHOTS, seed))\n",
- "\n",
- "plt.plot(cycles, optim_classical)\n",
- "plt.xlabel('optimization cycle')\n",
- "plt.ylabel('best classical minimum')\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 31,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Optimal energy found with QAOA: -6.486032631497276\n",
- "Optimal bit-string found with QAOA: [-1 1 -1 -1 1 -1 1 1 -1 -1]\n"
- ]
- }
- ],
- "source": [
- "# print the optimal energy found with QAOA \n",
- "print('Optimal energy found with QAOA:', tracker['optimal_energy'])\n",
- "# print the corresponding bitstring\n",
- "print('Optimal bit-string found with QAOA:', tracker['optimal_bitstring'])"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 32,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# get results for variational angles\n",
- "gamma = result_angle[:DEPTH]\n",
- "beta = result_angle[DEPTH:]\n",
- "# get array [1, 2, ..., p]\n",
- "pa = np.arange(1, DEPTH + 1)\n",
- "\n",
- "plt.figure(2)\n",
- "plt.plot(pa, gamma / np.pi, '-o', label='gamma')\n",
- "plt.plot(pa, beta / np.pi, '-s', label='beta')\n",
- "plt.xlabel('circuit depth (layer) p')\n",
- "plt.ylabel('optimal angles [pi]')\n",
- "plt.xticks(pa)\n",
- "plt.legend(title='Variational QAOA angles:', loc='upper left')\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 33,
- "metadata": {
- "scrolled": true
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Minimal energy found with QAOA: -6.486032631497276\n"
- ]
- },
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# visualize solution\n",
- "colorlist = tracker['optimal_bitstring']\n",
- "colorlist[colorlist == -1] = 0\n",
- "\n",
- "# plot_colored_graph(J, N, colorlist, pos)\n",
- "plot_colored_graph_simple(G, colorlist, pos)\n",
- "print('Minimal energy found with QAOA:', tracker['optimal_energy'])"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 34,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Classical solution: {'s0': -1, 's1': 1, 's2': -1, 's3': -1, 's4': 1, 's5': -1, 's6': 1, 's7': 1, 's8': -1, 's9': -1}\n",
- "Minimal energy found classically: -6.486032631497276\n"
- ]
- },
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# validate quantum results with classical algorithm\n",
- "solution, energy_min, colors_classical = solve_classical_ising(J, n_qubits, pos)\n",
- "# plot classical solution\n",
- "plot_colored_graph_simple(G, colors_classical, pos)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Note that QAOA may arrive at a different solution than our classical benchmark code. \n",
- "First of all, the classical optimization routine may get stuck in a local rather than global optimum. \n",
- "To avoid this, more sophisticated optimization strategies may be employed (as proposed for example in Ref.[4]), going beyond the scope of this introductory notebook tutorial. \n",
- "Secondly, even if QAOA arrives at the same classical energy as our classical approach, the coloring may differ since the solution space may be degenerate for the specific example shown here (this means, two different classical bitstrings have the same energy).\n",
- "At minimum, you may find an inverted coloring (by swapping red and blue colors), because of the underlying $\\mathbb{Z}_{2}$ symmetry. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## SUMMARY"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this notebook we have gone through an end-to-end demo on QAOA and its implementation on Amazon Braket. \n",
- "We have built modular core building blocks that may easily adapted to other problems. \n",
- "The QAOA routine is tailored towards solving combinatorial optimization problems such as _Maximum Cut_ [4] and arguably one of the most prominent examples of the emerging class of hybrid, variational algorithms and still very much a field of active research today. \n",
- "For example, as we increase the circuit depth of QAOA, the classical optimization step becomes increasingly difficult (because of the curse of dimensionality as well known in classical machine learning) and may easily get stuck in local sub-optimal solutions. \n",
- "To address this issue some heuristics have already been developed, for example in Ref.[4], but further improvements will arguably be necessary to fully unlock the potential of this approach. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "---\n",
- "## REFERENCES"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "[1] E. Farhi, J. Goldstone, and S. Gutmann, \"A Quantum Approximate Optimization Algorithm\", arXiv: 1411.4028 (2014).\n",
- "\n",
- "[2] Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. Johnson, M. Kieferova, I. D. Kivlichan, T. Menke, B. Peropadre, N. P. Sawaya, et al., \"Quantum Chemistry in the Age of Quantum Computing\", Chemical reviews 119, 10856 (2019).\n",
- "\n",
- "[3] A. Smith, M. Kim, F. Pollmann, and J. Knolle, \"Simulating quantum many-body dynamics on a current digital quantum computer\", npj Quantum Information 5, 1 (2019).\n",
- "\n",
- "[4] L. Zhou, S.-T. Wang, S. Choi, H. Pichler, and M. D. Lukin, \"Quantum Approximate Optimization Algorithm: Performance, Mechanism,and Implementation on Near-Term Devices\", arXiv: 1812.01041 (2018). \n",
- "\n",
- "[5] F. Glover, G. Kochenberger, \"A Tutorial on Formulating and Using QUBO Models\", arXiv:1811.11538 (2018).\n",
- "\n",
- "[6] P. Vikstal, M. Groenkvist, M. Svensson, M. Andersson, G. Johansson, and G. Ferrini, \"Applying the Quantum Approximate Optimization Algorithm to the Tail Assignment Problem\", arXiv:1912.10499 (2019). \n",
- "\n",
- "[7] L. Li, M. Fan, M. Coram, P. Riley, and S. Leichenauer, \"Quantum optimization with a novel gibbs objective function and ansatz architecture search\", arXiv:1909.07621 (2019). "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "---\n",
- "## APPENDIX"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### APPENDIX: Example for Ising Matrix Syntax"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this appendix we provide a small code example to showcase how we obtain all edges with corresponding weights. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 36,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Ising matrix:\n",
- " [[0 1 0]\n",
- " [0 0 3]\n",
- " [0 0 0]]\n",
- "Edges: [(0, 1), (1, 2)]\n",
- "Interaction strength: 1\n",
- "Interaction strength: 3\n",
- "All interactions: [1 3]\n"
- ]
- }
- ],
- "source": [
- "# example Ising matrix with edges between qubit 0 and qubit 1 (weight=1) and qubit 1 and qubit 2 (weight=3)\n",
- "ising = np.array([[0, 1, 0], [0, 0, 3], [0, 0, 0]])\n",
- "print('Ising matrix:\\n', ising)\n",
- "\n",
- "# get all non-zero entries (edges) from Ising matrix \n",
- "idx = ising.nonzero()\n",
- "edges = list(zip(idx[0], idx[1]))\n",
- "print('Edges:', edges)\n",
- "\n",
- "# for every edge print interaction strength\n",
- "for qubit_pair in edges:\n",
- " # get interaction strength\n",
- " int_strength = ising[qubit_pair[0], qubit_pair[1]]\n",
- " print('Interaction strength:', int_strength)\n",
- "\n",
- "# get all non-zero entries from Ising, with proper order\n",
- "interactions = np.array([ising[q[0], q[1]] for q in edges])\n",
- "print('All interactions:', interactions)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Task Summary\n",
- "{}\n",
- "Estimated cost to run this example with SV1: 0 USD\n"
- ]
- }
- ],
- "source": [
- "print(\"Quantum Task Summary\")\n",
- "print(t.quantum_tasks_statistics())\n",
- "print(f\"Estimated cost to run this example with SV1: {t.qpu_tasks_cost() + t.simulator_tasks_cost()} USD\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Python 3 (ipykernel)",
- "language": "python",
- "name": "python3"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.10.9"
- },
- "vscode": {
- "interpreter": {
- "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2"
- }
- }
- },
- "nbformat": 4,
- "nbformat_minor": 4
-}
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
\ No newline at end of file
diff --git a/examples/pennylane/0_Getting_started/0_Getting_started.ipynb b/examples/pennylane/0_Getting_started/0_Getting_started.ipynb
index 3947579ad..871e04f6e 100644
--- a/examples/pennylane/0_Getting_started/0_Getting_started.ipynb
+++ b/examples/pennylane/0_Getting_started/0_Getting_started.ipynb
@@ -1,830 +1,830 @@
{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Combining PennyLane with Amazon Braket"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "
\n",
- "What is PennyLane?PennyLane is a Python library for differentiable programming of quantum computers, allowing you to train a quantum computer the same way as a neural network.\n",
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "PennyLane integrates with Amazon Braket to add additional features for quantum machine learning and optimization. This introductory tutorial walks you through how to train a quantum circuit using Amazon Braket simulators and PennyLane's automatic differentiation capabilities."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Setup"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "PennyLane is already installed on Braket notebook instances. On a local machine, PennyLane can be installed by following [these](https://pennylane.ai/install.html) instructions. It can then be imported with:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:09.404557Z",
- "start_time": "2024-02-19T21:42:03.275541Z"
- }
- },
- "outputs": [],
- "source": [
- "import pennylane as qml\n",
- "from pennylane import numpy as np"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "To use Braket as a backend in PennyLane, we have to create a PennyLane device. Here we will first create a device that uses the local Braket simulator that runs on your local laptop (or on the server that hosts this notebook)."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:10.351825Z",
- "start_time": "2024-02-19T21:42:09.405882Z"
- }
- },
- "outputs": [],
- "source": [
- "wires = 2 # Number of qubits\n",
- "\n",
- "dev = qml.device(\"braket.local.qubit\", wires=wires)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Below we will also show you how to scale out simulations to the AWS cloud."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Defining a circuit"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We will choose a simple two-qubit circuit with two controllable rotations and a CNOT gate."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:10.355051Z",
- "start_time": "2024-02-19T21:42:10.352639Z"
- }
- },
- "outputs": [],
- "source": [
- "@qml.qnode(dev)\n",
- "def circuit(params):\n",
- " qml.RX(params[0], wires=0)\n",
- " qml.RY(params[1], wires=1)\n",
- " qml.CNOT(wires=[0, 1])\n",
- " return qml.expval(qml.PauliZ(1))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The ``qml.qnode(dev)`` decorator binds the circuit to the local Braket device. Now, every time that ``circuit()`` is called, the quantum computation defined in the function above will be executed with Braket."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "
\n",
- "Note PennyLane also supports automatic differentiation with PyTorch and TensorFlow interfaces. The choice of interface can be specified using:\n",
- "@qml.qnode(dev, interface=\"<interface>\").\n",
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Evaluating the circuit and accessing its gradient"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Let's set some values for our controllable parameters:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:10.359085Z",
- "start_time": "2024-02-19T21:42:10.356833Z"
- }
- },
- "outputs": [],
- "source": [
- "params = np.array([0.1, 0.2], requires_grad=True)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The circuit can be evaluated with these parameters using"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:10.393070Z",
- "start_time": "2024-02-19T21:42:10.359915Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Expectation value of circuit: 0.9751703272018161\n"
- ]
- }
- ],
- "source": [
- "print(\"Expectation value of circuit:\", circuit(params))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:10.397595Z",
- "start_time": "2024-02-19T21:42:10.394259Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Drawing of circuit:\n",
- "\n",
- "0: ──RX(0.10)─╭●─┤ \n",
- "1: ──RY(0.20)─╰X─┤ \n"
- ]
- }
- ],
- "source": [
- "print(\"Drawing of circuit:\\n\")\n",
- "print(qml.draw(circuit)(params))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "A crucial element of machine learning and optimization is accessing the gradient of a model with respect to its parameters. This functionality is built into PennyLane:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:10.400540Z",
- "start_time": "2024-02-19T21:42:10.398616Z"
- }
- },
- "outputs": [],
- "source": [
- "dcircuit = qml.grad(circuit)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Here, ``dcircuit`` is a callable function that evaluates the gradient of the circuit, i.e., its partial derivatives with respect to the controllable parameters."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:10.523442Z",
- "start_time": "2024-02-19T21:42:10.401286Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "array([-0.0978434 , -0.19767681])"
- ]
- },
- "execution_count": 8,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "dcircuit(params)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Training the circuit"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Suppose we now want to minimize the output of the circuit by updating its parameters. This can be done using gradient-based optimization.\n",
- "\n",
- "First, an optimizer is fixed:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:10.526039Z",
- "start_time": "2024-02-19T21:42:10.524244Z"
- }
- },
- "outputs": [],
- "source": [
- "opt = qml.GradientDescentOptimizer(stepsize=0.1)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The next step is to run the optimizer for a chosen number of iterations:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:11.062067Z",
- "start_time": "2024-02-19T21:42:10.527962Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Minimized circuit output: 0.37261070647126565\n",
- "Optimized parameters: [0.4839502 1.13630274]\n"
- ]
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Combining PennyLane with Amazon Braket"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
\n",
+ "What is PennyLane?PennyLane is a Python library for differentiable programming of quantum computers, allowing you to train a quantum computer the same way as a neural network.\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "PennyLane integrates with Amazon Braket to add additional features for quantum machine learning and optimization. This introductory tutorial walks you through how to train a quantum circuit using Amazon Braket simulators and PennyLane's automatic differentiation capabilities."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Setup"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "PennyLane is already installed on Braket notebook instances. On a local machine, PennyLane can be installed by following [these](https://pennylane.ai/install.html) instructions. It can then be imported with:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:09.404557Z",
+ "start_time": "2024-02-19T21:42:03.275541Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import pennylane as qml\n",
+ "from pennylane import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To use Braket as a backend in PennyLane, we have to create a PennyLane device. Here we will first create a device that uses the local Braket simulator that runs on your local laptop (or on the server that hosts this notebook)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:10.351825Z",
+ "start_time": "2024-02-19T21:42:09.405882Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "wires = 2 # Number of qubits\n",
+ "\n",
+ "dev = qml.device(\"braket.local.qubit\", wires=wires)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Below we will also show you how to scale out simulations to the AWS cloud."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Defining a circuit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We will choose a simple two-qubit circuit with two controllable rotations and a CNOT gate."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:10.355051Z",
+ "start_time": "2024-02-19T21:42:10.352639Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@qml.qnode(dev)\n",
+ "def circuit(params):\n",
+ " qml.RX(params[0], wires=0)\n",
+ " qml.RY(params[1], wires=1)\n",
+ " qml.CNOT(wires=[0, 1])\n",
+ " return qml.expval(qml.PauliZ(1))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The ``qml.qnode(dev)`` decorator binds the circuit to the local Braket device. Now, every time that ``circuit()`` is called, the quantum computation defined in the function above will be executed with Braket."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
\n",
+ "Note PennyLane also supports automatic differentiation with PyTorch and TensorFlow interfaces. The choice of interface can be specified using:\n",
+ "@qml.qnode(dev, interface=\"<interface>\").\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Evaluating the circuit and accessing its gradient"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's set some values for our controllable parameters:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:10.359085Z",
+ "start_time": "2024-02-19T21:42:10.356833Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "params = np.array([0.1, 0.2], requires_grad=True)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The circuit can be evaluated with these parameters using"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:10.393070Z",
+ "start_time": "2024-02-19T21:42:10.359915Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Expectation value of circuit: 0.9751703272018161\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Expectation value of circuit:\", circuit(params))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:10.397595Z",
+ "start_time": "2024-02-19T21:42:10.394259Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Drawing of circuit:\n",
+ "\n",
+ "0: ──RX(0.10)─╭●─┤ \n",
+ "1: ──RY(0.20)─╰X─┤ \n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Drawing of circuit:\\n\")\n",
+ "print(qml.draw(circuit)(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "A crucial element of machine learning and optimization is accessing the gradient of a model with respect to its parameters. This functionality is built into PennyLane:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:10.400540Z",
+ "start_time": "2024-02-19T21:42:10.398616Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dcircuit = qml.grad(circuit)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here, ``dcircuit`` is a callable function that evaluates the gradient of the circuit, i.e., its partial derivatives with respect to the controllable parameters."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:10.523442Z",
+ "start_time": "2024-02-19T21:42:10.401286Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([-0.0978434 , -0.19767681])"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "dcircuit(params)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Training the circuit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Suppose we now want to minimize the output of the circuit by updating its parameters. This can be done using gradient-based optimization.\n",
+ "\n",
+ "First, an optimizer is fixed:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:10.526039Z",
+ "start_time": "2024-02-19T21:42:10.524244Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "opt = qml.GradientDescentOptimizer(stepsize=0.1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The next step is to run the optimizer for a chosen number of iterations:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:11.062067Z",
+ "start_time": "2024-02-19T21:42:10.527962Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Minimized circuit output: 0.37261070647126565\n",
+ "Optimized parameters: [0.4839502 1.13630274]\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "iterations = 20\n",
+ "\n",
+ "costs = []\n",
+ "\n",
+ "for i in range(iterations):\n",
+ " params, cost = opt.step_and_cost(circuit, params)\n",
+ " costs.append(cost)\n",
+ "\n",
+ "# Visualize results\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "costs.append(circuit(params))\n",
+ "plt.plot(costs, \"-o\")\n",
+ "plt.xlabel(\"Iterations\")\n",
+ "plt.ylabel(\"Cost\")\n",
+ "\n",
+ "print(\"Minimized circuit output:\", circuit(params))\n",
+ "print(\"Optimized parameters:\", params)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
\n",
+ "Note The circuit considered here is very simple and can be optimized easily by hand. However, the need for PennyLane's automatic differentiation capabilities becomes apparent as we make the problem more complicated, e.g., with more gates and different types of output measurement. In later demos, we will also see how Braket can be used to parallelize evaluation of the gradient, providing a turbocharger for quantum circuit training in PennyLane.\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Running circuits on Braket's on-demand simulator, SV1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "So far we have used the local Braket simulator. This is a great choice for quick prototyping, but it is not suitable for large circuits with many qubits and does not provide a connection to quantum hardware.\n",
+ "\n",
+ "Amazon Braket also provides access to on-demand, high-performance simulators and quantum processing units (QPUs) from different [providers](https://aws.amazon.com/braket/hardware-providers/). These devices can be accessed through PennyLane by changing a single line of code, unlocking the potential for machine learning and optimization on quantum hardware and high performance simulators!\n",
+ "\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:11.066378Z",
+ "start_time": "2024-02-19T21:42:11.064297Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
+ "from braket.tracking import Tracker\n",
+ "\n",
+ "braket_tasks_cost = Tracker().start()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Each remote Braket device can be selected through its [ARN](https://docs.aws.amazon.com/general/latest/gr/aws-arns-and-namespaces.html). The supported devices on Braket are listed [here](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html). For now, we will pick the on-demand SV1 simulator.\n",
+ "\n",
+ "
\n",
+ "Caution: Running hybrid algorithms on a QPU can take a long time and incur high usage fees charged to your AWS account.\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": false
+ },
+ "source": [
+ "In PennyLane, all remote Braket devices are then accessed through a single PennyLane device named ``braket.aws.qubit``."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:11.437758Z",
+ "start_time": "2024-02-19T21:42:11.067501Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from braket.devices import Devices\n",
+ "dev = qml.device(\"braket.aws.qubit\", device_arn=Devices.Amazon.SV1, wires=2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "A follow up [tutorial](./1_Parallelized_optimization_of_quantum_circuits.ipynb) shows you how to use the remote device to run multiple circuits in parallel, while the [QAOA tutorial](./2_Graph_optimization_with_QAOA.ipynb) takes a deeper dive into graph optimization, including using SV1 to optimize a 20-node graph."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's execute our circuit on SV1, as well as calculating the gradient:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:18.632136Z",
+ "start_time": "2024-02-19T21:42:11.439272Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Result of circuit run on SV1: 0.37261070647126565\n",
+ "Result of gradient calculation on SV1: [-0.19585986 -0.80291741]\n"
+ ]
+ }
+ ],
+ "source": [
+ "@qml.qnode(dev)\n",
+ "def circuit(params):\n",
+ " qml.RX(params[0], wires=0)\n",
+ " qml.RY(params[1], wires=1)\n",
+ " qml.CNOT(wires=[0, 1])\n",
+ " return qml.expval(qml.PauliZ(1))\n",
+ "\n",
+ "\n",
+ "dcircuit = qml.grad(circuit)\n",
+ "\n",
+ "print(\"Result of circuit run on SV1:\", circuit(params))\n",
+ "print(\"Result of gradient calculation on SV1:\", dcircuit(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
\n",
+ "What's next? Check out the other tutorials in this folder to understand how Braket and PennyLane can be combined to solve a range of problems, from graph optimization to quantum chemistry.\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:19.098494Z",
+ "start_time": "2024-02-19T21:42:18.633487Z"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Quantum Task Summary\n",
+ "{<_Amazon.SV1: 'arn:aws:braket:::device/quantum-simulator/amazon/sv1'>: {'shots': 0, 'tasks': {'COMPLETED': 2}, 'execution_duration': datetime.timedelta(microseconds=299000), 'billed_execution_duration': datetime.timedelta(seconds=6)}}\n",
+ "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
+ "Estimated cost to run this example: 0.008 USD\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Quantum Task Summary\")\n",
+ "print(braket_tasks_cost.quantum_tasks_statistics())\n",
+ "print(\n",
+ " \"Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\"\n",
+ ")\n",
+ "print(\n",
+ " f\"Estimated cost to run this example: {braket_tasks_cost.qpu_tasks_cost() + braket_tasks_cost.simulator_tasks_cost():.3f} USD\"\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Running on a QPU with Amazon Braket Hybrid Jobs\n",
+ "\n",
+ "In this notebook, the classical part of the algorithm was running locally. For longer-running algorithms or those requiring more intensive compute resources, it's recommended to dispatch the algorithm to Amazon Braket Hybrid Jobs, which fully manages the classical infrastructure, allowing you to focus on the algorithm. For example, you can train a larger circuit or increase the number of iterations.\n",
+ "\n",
+ "The second benefit of running the algorithm as a hybrid job is that for iterative algorithms that require repeated calls to a QPU, you retain priority for that QPU. Once your quantum tasks are created in the hybrid job, they run ahead of other tasks waiting in the regular quantum task queue. This is because hybrid jobs have a separate queue from standalone tasks, ensuring that only a single hybrid job can run on a QPU at a time. This means your algorithm will not be interrupted by other quantum tasks, so it will run more efficiently and predictably. However, hybrid jobs have a separate queue from standalone tasks, so only a single hybrid job can run on a QPU at a time. For a single quantum circuit or a batch of circuits, it's recommended to create quantum tasks instead of hybrid jobs. Only iterative algorithms benefit from QPU priority queuing.\n",
+ "\n",
+ "Note that hybrid jobs have at least a one-minute startup time since they create a containerized environment on Amazon EC2. So for very short workloads, there is likely no need to create a hybrid job.\n",
+ "\n",
+ "You can run your local Python code as an Amazon Braket hybrid job by annotating your code with the `@hybrid_job`` decorator, as shown in the following code example. Only Python 3.10 is supported by default. For custom Python versions, you can choose to use a custom container from [Amazon Elastic Container Registry (ECR)](https://aws.amazon.com/ecr/) (see [BYOC](https://docs.aws.amazon.com/braket/latest/developerguide/braket-jobs-byoc.html)).\n",
+ "\n",
+ "\n",
+ "In the following code, we create a hybrid job for 10 iterations targeting Rigetti Ankaa 2. Since we specified Ankaa 2 as the device, this job will run once Ankaa 2 is available and has no jobs running ahead of it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:19.442699Z",
+ "start_time": "2024-02-19T21:42:19.099758Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from braket.jobs import hybrid_job\n",
+ "from braket.jobs.metrics import log_metric\n",
+ "\n",
+ "device_arn = Devices.Amazon.SV1\n",
+ "# device_arn = Devices.Rigetti.Ankaa2\n",
+ "\n",
+ "\n",
+ "@hybrid_job(device=device_arn) # set priority QPU\n",
+ "def qubit_rotation(stepsize=0.1, iterations=5):\n",
+ " task_tracker = Tracker().start() # track Braket quantum tasks costs\n",
+ " dev = qml.device(\"braket.aws.qubit\", device_arn=device_arn.value, wires=2, shots=1_000)\n",
+ "\n",
+ " params = np.array([0.1, 0.2])\n",
+ "\n",
+ " @qml.qnode(dev)\n",
+ " def circuit(params):\n",
+ " qml.RX(params[0], wires=0)\n",
+ " qml.RY(params[1], wires=1)\n",
+ " qml.CNOT(wires=[0, 1])\n",
+ " return qml.expval(qml.PauliZ(1))\n",
+ "\n",
+ " opt = qml.GradientDescentOptimizer(stepsize)\n",
+ "\n",
+ " costs = []\n",
+ " for i in range(iterations):\n",
+ " params, cost = opt.step_and_cost(circuit, params)\n",
+ " costs.append(cost)\n",
+ "\n",
+ " # Record the value of the cost function with each iteration\n",
+ " log_metric(metric_name=\"cost_function\", value=cost, iteration_number=i)\n",
+ "\n",
+ " # Additionally, keep track of cost in USD for Braket tasks\n",
+ " braket_task_cost = float(\n",
+ " task_tracker.qpu_tasks_cost() + task_tracker.simulator_tasks_cost()\n",
+ " )\n",
+ " log_metric(metric_name=\"braket_cost\", value=braket_task_cost, iteration_number=i)\n",
+ "\n",
+ " return {\"params\": params, \"costs\": costs, \"braket_tasks_cost\": braket_task_cost}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "How long will it take the hybrid job to run? \n",
+ "Let's first check if the device is currently available with `AwsDevice(device_arn).is_available()`. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:19.614223Z",
+ "start_time": "2024-02-19T21:42:19.443623Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "True"
+ ]
+ },
+ "execution_count": 16,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from braket.aws import AwsDevice\n",
+ "\n",
+ "AwsDevice(device_arn).is_available"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next, we check the hybrid job queue depth with `AwsDevice(device_arn).queue_depth().jobs`. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:19.958746Z",
+ "start_time": "2024-02-19T21:42:19.615073Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'0'"
+ ]
+ },
+ "execution_count": 17,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "AwsDevice(device_arn).queue_depth().jobs"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If the device is available and there are no hybrid jobs currently running, then it should take about 5 minutes to complete. \n",
+ "\n",
+ "
\n",
+ "Caution: Running the following cell will only run once the QPU is available. This may take a long time and will result in usage fees charged to your AWS account. Only uncomment the cell if you are comfortable with the potential wait-time and costs. We recommend monitoring the Billing & Cost Management Dashboard on the AWS console and being aware that hybrid jobs involving a large number of qubits can be costly.\n",
+ "
\n",
- "Note The circuit considered here is very simple and can be optimized easily by hand. However, the need for PennyLane's automatic differentiation capabilities becomes apparent as we make the problem more complicated, e.g., with more gates and different types of output measurement. In later demos, we will also see how Braket can be used to parallelize evaluation of the gradient, providing a turbocharger for quantum circuit training in PennyLane.\n",
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Running circuits on Braket's on-demand simulator, SV1"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "So far we have used the local Braket simulator. This is a great choice for quick prototyping, but it is not suitable for large circuits with many qubits and does not provide a connection to quantum hardware.\n",
- "\n",
- "Amazon Braket also provides access to on-demand, high-performance simulators and quantum processing units (QPUs) from different [providers](https://aws.amazon.com/braket/hardware-providers/). These devices can be accessed through PennyLane by changing a single line of code, unlocking the potential for machine learning and optimization on quantum hardware and high performance simulators!\n",
- "\n",
- "
"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:11.066378Z",
- "start_time": "2024-02-19T21:42:11.064297Z"
- }
- },
- "outputs": [],
- "source": [
- "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
- "from braket.tracking import Tracker\n",
- "\n",
- "braket_tasks_cost = Tracker().start()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Each remote Braket device can be selected through its [ARN](https://docs.aws.amazon.com/general/latest/gr/aws-arns-and-namespaces.html). The supported devices on Braket are listed [here](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html). For now, we will pick the on-demand SV1 simulator.\n",
- "\n",
- "
\n",
- "Caution: Running hybrid algorithms on a QPU can take a long time and incur high usage fees charged to your AWS account.\n",
- "
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "collapsed": false
- },
- "source": [
- "In PennyLane, all remote Braket devices are then accessed through a single PennyLane device named ``braket.aws.qubit``."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:11.437758Z",
- "start_time": "2024-02-19T21:42:11.067501Z"
- }
- },
- "outputs": [],
- "source": [
- "from braket.devices import Devices\n",
- "dev = qml.device(\"braket.aws.qubit\", device_arn=Devices.Amazon.SV1, wires=2)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "A follow up [tutorial](./1_Parallelized_optimization_of_quantum_circuits.ipynb) shows you how to use the remote device to run multiple circuits in parallel, while the [QAOA tutorial](./2_Graph_optimization_with_QAOA.ipynb) takes a deeper dive into graph optimization, including using SV1 to optimize a 20-node graph."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Let's execute our circuit on SV1, as well as calculating the gradient:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:18.632136Z",
- "start_time": "2024-02-19T21:42:11.439272Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Result of circuit run on SV1: 0.37261070647126565\n",
- "Result of gradient calculation on SV1: [-0.19585986 -0.80291741]\n"
- ]
- }
- ],
- "source": [
- "@qml.qnode(dev)\n",
- "def circuit(params):\n",
- " qml.RX(params[0], wires=0)\n",
- " qml.RY(params[1], wires=1)\n",
- " qml.CNOT(wires=[0, 1])\n",
- " return qml.expval(qml.PauliZ(1))\n",
- "\n",
- "\n",
- "dcircuit = qml.grad(circuit)\n",
- "\n",
- "print(\"Result of circuit run on SV1:\", circuit(params))\n",
- "print(\"Result of gradient calculation on SV1:\", dcircuit(params))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "
\n",
- "What's next? Check out the other tutorials in this folder to understand how Braket and PennyLane can be combined to solve a range of problems, from graph optimization to quantum chemistry.\n",
- "
"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:19.098494Z",
- "start_time": "2024-02-19T21:42:18.633487Z"
- }
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Quantum Task Summary\n",
- "{<_Amazon.SV1: 'arn:aws:braket:::device/quantum-simulator/amazon/sv1'>: {'shots': 0, 'tasks': {'COMPLETED': 2}, 'execution_duration': datetime.timedelta(microseconds=299000), 'billed_execution_duration': datetime.timedelta(seconds=6)}}\n",
- "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
- "Estimated cost to run this example: 0.008 USD\n"
- ]
- }
- ],
- "source": [
- "print(\"Quantum Task Summary\")\n",
- "print(braket_tasks_cost.quantum_tasks_statistics())\n",
- "print(\n",
- " \"Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\"\n",
- ")\n",
- "print(\n",
- " f\"Estimated cost to run this example: {braket_tasks_cost.qpu_tasks_cost() + braket_tasks_cost.simulator_tasks_cost():.3f} USD\"\n",
- ")"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Running on a QPU with Amazon Braket Hybrid Jobs\n",
- "\n",
- "In this notebook, the classical part of the algorithm was running locally. For longer-running algorithms or those requiring more intensive compute resources, it's recommended to dispatch the algorithm to Amazon Braket Hybrid Jobs, which fully manages the classical infrastructure, allowing you to focus on the algorithm. For example, you can train a larger circuit or increase the number of iterations.\n",
- "\n",
- "The second benefit of running the algorithm as a hybrid job is that for iterative algorithms that require repeated calls to a QPU, you retain priority for that QPU. Once your quantum tasks are created in the hybrid job, they run ahead of other tasks waiting in the regular quantum task queue. This is because hybrid jobs have a separate queue from standalone tasks, ensuring that only a single hybrid job can run on a QPU at a time. This means your algorithm will not be interrupted by other quantum tasks, so it will run more efficiently and predictably. However, hybrid jobs have a separate queue from standalone tasks, so only a single hybrid job can run on a QPU at a time. For a single quantum circuit or a batch of circuits, it's recommended to create quantum tasks instead of hybrid jobs. Only iterative algorithms benefit from QPU priority queuing.\n",
- "\n",
- "Note that hybrid jobs have at least a one-minute startup time since they create a containerized environment on Amazon EC2. So for very short workloads, there is likely no need to create a hybrid job.\n",
- "\n",
- "You can run your local Python code as an Amazon Braket hybrid job by annotating your code with the `@hybrid_job`` decorator, as shown in the following code example. Only Python 3.10 is supported by default. For custom Python versions, you can choose to use a custom container from [Amazon Elastic Container Registry (ECR)](https://aws.amazon.com/ecr/) (see [BYOC](https://docs.aws.amazon.com/braket/latest/developerguide/braket-jobs-byoc.html)).\n",
- "\n",
- "\n",
- "In the following code, we create a hybrid job for 10 iterations targeting Rigetti Aspen-M-3. Since we specified Aspen-M-3 as the device, this job will run once Aspen-M-3 is available and has no jobs running ahead of it."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:19.442699Z",
- "start_time": "2024-02-19T21:42:19.099758Z"
- }
- },
- "outputs": [],
- "source": [
- "from braket.jobs import hybrid_job\n",
- "from braket.jobs.metrics import log_metric\n",
- "\n",
- "device_arn = Devices.Amazon.SV1\n",
- "# device_arn = Devices.Rigetti.Ankaa2\n",
- "\n",
- "\n",
- "@hybrid_job(device=device_arn) # set priority QPU\n",
- "def qubit_rotation(stepsize=0.1, iterations=5):\n",
- " task_tracker = Tracker().start() # track Braket quantum tasks costs\n",
- " dev = qml.device(\"braket.aws.qubit\", device_arn=device_arn.value, wires=2, shots=1_000)\n",
- "\n",
- " params = np.array([0.1, 0.2])\n",
- "\n",
- " @qml.qnode(dev)\n",
- " def circuit(params):\n",
- " qml.RX(params[0], wires=0)\n",
- " qml.RY(params[1], wires=1)\n",
- " qml.CNOT(wires=[0, 1])\n",
- " return qml.expval(qml.PauliZ(1))\n",
- "\n",
- " opt = qml.GradientDescentOptimizer(stepsize)\n",
- "\n",
- " costs = []\n",
- " for i in range(iterations):\n",
- " params, cost = opt.step_and_cost(circuit, params)\n",
- " costs.append(cost)\n",
- "\n",
- " # Record the value of the cost function with each iteration\n",
- " log_metric(metric_name=\"cost_function\", value=cost, iteration_number=i)\n",
- "\n",
- " # Additionally, keep track of cost in USD for Braket tasks\n",
- " braket_task_cost = float(\n",
- " task_tracker.qpu_tasks_cost() + task_tracker.simulator_tasks_cost()\n",
- " )\n",
- " log_metric(metric_name=\"braket_cost\", value=braket_task_cost, iteration_number=i)\n",
- "\n",
- " return {\"params\": params, \"costs\": costs, \"braket_tasks_cost\": braket_task_cost}"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "How long will it take the hybrid job to run? \n",
- "Let's first check if the device is currently available with `AwsDevice(device_arn).is_available()`. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:19.614223Z",
- "start_time": "2024-02-19T21:42:19.443623Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "True"
- ]
- },
- "execution_count": 16,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from braket.aws import AwsDevice\n",
- "\n",
- "AwsDevice(device_arn).is_available"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Next, we check the hybrid job queue depth with `AwsDevice(device_arn).queue_depth().jobs`. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:19.958746Z",
- "start_time": "2024-02-19T21:42:19.615073Z"
- }
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "'0'"
- ]
- },
- "execution_count": 17,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "AwsDevice(device_arn).queue_depth().jobs"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "If the device is available and there are no hybrid jobs currently running, then it should take about 5 minutes to complete. \n",
- "\n",
- "
\n",
- "Caution: Running the following cell will only run once the QPU is available. This may take a long time and will result in usage fees charged to your AWS account. Only uncomment the cell if you are comfortable with the potential wait-time and costs. We recommend monitoring the Billing & Cost Management Dashboard on the AWS console and being aware that hybrid jobs involving a large number of qubits can be costly.\n",
- "
![](\"aspenm_qubit_specs.png\"/)
\n",
- "\n",
- "\n",
- "**Two-qubit calibration data (Edge specs)**\n",
- "![](\"aspenm_edge_specs.png\"/)
"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "276d680f-887d-4929-bcaa-e276a6303496",
- "metadata": {},
- "source": [
- "We can programmatically access all the calibration data with the Braket SDK. First we load the AwsDevice using the ARN for Rigetti Aspen-M-3."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "id": "a55ea9d5-05f3-4da5-a305-a391e914d012",
- "metadata": {},
- "outputs": [],
- "source": [
- "aspen_m = AwsDevice(Devices.Rigetti.AspenM3)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "a8a42ae1-51ac-4bf1-bd6a-81ffd982b5f8",
- "metadata": {},
- "source": [
- "The properties dictionary contains keys \"provider\" and \"specs\", with \"1Q\" and \"2Q\" keys for the one- and two-qubit calibration data. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "id": "153b5b63-8205-4a7e-bb18-0305ef428f36",
- "metadata": {},
- "outputs": [],
- "source": [
- "aspen_m_specs = aspen_m.properties.dict()[\"provider\"][\"specs\"]\n",
- "\n",
- "one_qubit_data = aspen_m_specs[\"1Q\"]\n",
- "two_qubit_data = aspen_m_specs[\"2Q\"]"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "661cca17-01fa-40be-bd3e-741bacc74ce4",
- "metadata": {},
- "source": [
- "The keys of the \"1Q\" dictionary is the qubit number. \n",
- "For Aspen-M-3, there are 79 qubits indexed by the first digit representing the octagon (0 to 4, and 10 to 14)\n",
- "and the second representing the qubit in that octagon (0 to 7). We can get all qubit indices with `one_qubit_data.keys()` or with `aspen_m.topology_graph.nodes`.\n",
- "\n",
- "The keys of the \"2Q\" dictionary are the connected qubit pairs separated by a hyphen. \n",
- "For example, if qubit 0 and 1 are connected the key is \"0-1\".\n",
- "\n",
- "\n",
- "#### One-qubit noise \n",
- "\n",
- "Let's look at the one qubit calibration data for qubit 0."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "id": "8d4ecc35-f4dc-49d8-b6ff-adaee560ac4b",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{'T1': 2.4443429874176914e-05,\n",
- " 'T2': 1.627681336532139e-05,\n",
- " 'f1QRB': 0.9985669301541129,\n",
- " 'f1QRB_std_err': 0.0004092835114091019,\n",
- " 'f1Q_simultaneous_RB': 0.9977676229871197,\n",
- " 'f1Q_simultaneous_RB_std_err': 0.00021522363993495725,\n",
- " 'fActiveReset': 0.9905000000000002,\n",
- " 'fRO': 0.9795}"
- ]
- },
- "execution_count": 4,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "one_qubit_data[\"0\"]"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "4b676762-e642-4a98-89e3-86d79367071a",
- "metadata": {},
- "source": [
- "For each qubit, there are various metrics of the quality:\n",
- "\n",
- "- **T1**: Thermal relaxation time is related to the time it takes for the excited state, |1⟩, to decay into the ground state, |0⟩. The probability of remaining in the excited state is $p(|1⟩)\\sim e^{-t/T_1}$\n",
- "\n",
- "- **T2**: The dephasing time, is the decay constant for the scale for a |+⟩ state to decohere into the completely mixed state. $p(|+⟩)\\sim e^{-t/T_2}$ \n",
- "\n",
- "- **Fidelity (RB)**: Single-qubit randomized benchmarking fidelities. RB fidelity quantifies the average gate fidelity where the average is over all Clifford gates. RB describes an *effective* noise model with gate-independent depolarizing noise on each Clifford gate.\n",
- "\n",
- "- **Fidelity (sRB)**: Single-qubit simultaneous randomized benchmarking fidelities. These are extracted by running single-qubit RB on all qubits simultaneously. Note that we expect the sRB fidelity to be lower than standard RB fidelity due to non-local crosstalk type noise on the device. \n",
- "\n",
- "- **Active reset fidelity**: Single-qubit active reset fidelities represents the accuracy to which qubits are reinitalized into the ground state |0⟩.\n",
- "\n",
- "- **Readout fidelity**: Single-qubit readout fidelities describes the probability of a bit flip error before readout in the computational basis. The readout fidelity is related to the probability of correctly measuring the ground state and excited states respectively, e.g. $f_{RO} =\\frac{p(0|0)+p(1|1)}{2}$"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "296708a3-771e-42b4-9ba8-f3db1a02970b",
- "metadata": {},
- "source": [
- "Now that we know how to extract and use the calibration data, we can build a simple noise model. For every qubit we will add:\n",
- "- amplitude dampening noise with probability $p= 1-e^{-t/T_1}$ for every gate\n",
- "- phase dampening noise with probability $p= 0.5(1-e^{-t/T_2})$ for every gate\n",
- "- depolarizing noise with probability $p=1-f_{sRB}$ (from simultaneous RB fidelity) for every gate\n",
- "- readout bit flip noise with probability $p=1-f_{RO}$ to measurements \n",
- "\n",
- "Technically, the sRB fidelity already includes effects from $T_1$/$T_2$, however to be explicit we add these as separate terms. In a sense, this model might overestimate the noise on the QPU. \n",
- "\n",
- "For the dampening noises, we first need the gate times to model $T_1$ and $T_2$ errors.\n",
- "From the Braket Aspen-M-3 device page: \"These gates offer fast (40ns and 180ns) 1Q and 2Q gate times.\""
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "id": "cd27adfb-f7d6-4583-b854-794e38152c90",
- "metadata": {},
- "outputs": [],
- "source": [
- "# median 1q and 2q gate times\n",
- "gate_time_1_qubit = 40e-9\n",
- "gate_time_2_qubit = 240e-09"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "5769f2f4-de1c-4b47-9e4e-fd8d39b9e975",
- "metadata": {},
- "source": [
- "To create the noise model, we iterate over all qubits keys in `one_qubit_data`"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "id": "508070bc-b1d2-4737-a2fc-d7711e419996",
- "metadata": {},
- "outputs": [],
- "source": [
- "noise_model = NoiseModel()\n",
- "\n",
- "# Single-qubit noise\n",
- "for q, data in one_qubit_data.items(): # iterate over qubits\n",
- "\n",
- " # T1 dampening\n",
- " t1 = data[\"T1\"]\n",
- " damping_prob = 1 - np.exp(-(gate_time_1_qubit / t1))\n",
- " noise_model.add_noise(AmplitudeDamping(damping_prob), GateCriteria(qubits=int(q)))\n",
- "\n",
- " # T2 phase flip\n",
- " t2 = data[\"T2\"]\n",
- " dephasing_prob = 0.5 * (1 - np.exp(-(gate_time_1_qubit / t2)))\n",
- " noise_model.add_noise(PhaseDamping(dephasing_prob), GateCriteria(qubits=int(q)))\n",
- "\n",
- " # 1q RB depolarizing rate from simultaneous RB\n",
- " depolar_rate = 1 - data[\"f1Q_simultaneous_RB\"]\n",
- " noise_model.add_noise(Depolarizing(depolar_rate), GateCriteria(qubits=int(q)))\n",
- "\n",
- " # 1q RB readout\n",
- " readout_value = 1 - data[\"fRO\"]\n",
- " noise_model.add_noise(BitFlip(readout_value), ObservableCriteria(qubits=int(q)))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "id": "9d20d24c-17e2-4bba-b317-fb2d156bedb0",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Number of terms in noise model is: 320\n",
- "Number of parameters in noise model is: 320\n"
- ]
- }
- ],
- "source": [
- "num_params = sum(len(item.noise.parameters) for item in noise_model.instructions)\n",
- "print(f\"Number of terms in noise model is: {len(noise_model.instructions)}\")\n",
- "print(f\"Number of parameters in noise model is: {num_params}\")"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "790c62f7-776a-4e4c-9405-7b7a14eee5b0",
- "metadata": {},
- "source": [
- "#### Two-qubit noise \n",
- "Next we consider adding two-qubit noise to the model. \n",
- "\n",
- "Let's first look at the data provided in the Aspen-M-3 device calibration data. On the first connect, \"0-1\", the properties are:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "id": "626cbe56-3649-48eb-a2a1-f669eb790b47",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{'fCPHASE': 0.8991973184700036,\n",
- " 'fCPHASE_std_err': 0.019391126441846068,\n",
- " 'fCZ': 0.9406104552003762,\n",
- " 'fCZ_std_err': 0.011069113247524152,\n",
- " 'fXY': 0.8365560014004874,\n",
- " 'fXY_std_err': 0.014585224789608713}"
- ]
- },
- "execution_count": 8,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "two_qubit_data[\"0-1\"]"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "4bcd3be4-a6e4-4cf3-841e-1a451e01803a",
- "metadata": {},
- "source": [
- "Here, we see the fidelity per gate (CPhase, CZ, or XY) and the associated standard error. \n",
- "\n",
- "Next we loop over the entries in the `two_qubit_data` dictionary and add two-qubit depolarizing noise to the model. Notice that Aspen-M-3 has symmetric connections (\"0-1\" and \"1-0\") so we need to add noise in both directions."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "id": "80f57550-6549-46b6-9a6d-ff7f0f03e90d",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Two-qubit noise\n",
- "for pair, data in two_qubit_data.items(): # iterate over qubit connections\n",
- "\n",
- " # parse strings \"0-1\" to integers [0, 1]\n",
- " q0, q1 = (int(s) for s in pair.split(\"-\"))\n",
- "\n",
- " if \"fCPHASE\" in data:\n",
- " phase_rate = 1 - data[\"fCPHASE\"]\n",
- " noise_model.add_noise(\n",
- " TwoQubitDepolarizing(phase_rate),\n",
- " GateCriteria(\n",
- " Gate.CPhaseShift, [(q0, q1), (q1, q0)]\n",
- " ), # symmetric connections\n",
- " )\n",
- "\n",
- " if \"fXY\" in data:\n",
- " xy_rate = 1 - data[\"fXY\"]\n",
- " noise_model.add_noise(\n",
- " TwoQubitDepolarizing(xy_rate), GateCriteria(Gate.XY, [(q0, q1), (q1, q0)])\n",
- " )\n",
- "\n",
- " if \"fCZ\" in data:\n",
- " cz_rate = 1 - data[\"fCZ\"]\n",
- " noise_model.add_noise(\n",
- " TwoQubitDepolarizing(cz_rate), GateCriteria(Gate.CZ, [(q0, q1), (q1, q0)])\n",
- " )"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "id": "82376d08-84bc-4249-9c8d-d7aacdb73113",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Number of terms in noise model is: 612\n",
- "Number of parameters in noise model is: 612\n"
- ]
- }
- ],
- "source": [
- "num_params = sum(len(item.noise.parameters) for item in noise_model.instructions)\n",
- "print(f\"Number of terms in noise model is: {len(noise_model.instructions)}\")\n",
- "print(f\"Number of parameters in noise model is: {num_params}\")"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "5913a8a2-a9de-4e32-a35d-c48191891b1f",
- "metadata": {},
- "source": [
- "### Compare circuits run on device vs simulator with a noise model\n",
- "\n",
- "Let's just look at the first 5 qubits. Note that to ensure the noise model applied T1 and T2 noise during the time between gate, we manually add identity gates to each moment."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "id": "6fabbd05-b480-43c6-b43a-d396d81bd687",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : | 0 | 1 |2|\n",
- " \n",
- "q0 : -Rx(0.50)-Rx(3.14)-C-\n",
- " | \n",
- "q1 : -Rz(0.50)-Rx(3.14)-Z-\n",
- " \n",
- "q2 : -Rz(0.50)-Rx(3.14)---\n",
- "\n",
- "T : | 0 | 1 |2|\n"
- ]
- }
- ],
- "source": [
- "np.random.seed(42)\n",
- "\n",
- "circ = Circuit().rx(0, 0.5).rz(1, 0.5).rz(2, 0.5).rx(0, np.pi).rx(1, np.pi).rx(2, np.pi).cz(0, 1)\n",
- "print(circ)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "id": "e2af07ed-33de-4709-9e7c-5e3c3caaa751",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "T : | 0 | 1 | 2 |\n",
- " \n",
- "q0 : -Rx(0.50)-AD(0.0016)--PD(0.0012)-DEPO(0.0022)-Rx(3.14)-AD(0.0016)--PD(0.0012)-DEPO(0.0022)-C-DEPO(0.059)-\n",
- " | | \n",
- "q1 : -Rz(0.50)-AD(0.00086)-PD(0.0015)-DEPO(0.025)--Rx(3.14)-AD(0.00086)-PD(0.0015)-DEPO(0.025)--Z-DEPO(0.059)-\n",
- " \n",
- "q2 : -Rz(0.50)-AD(0.0018)--PD(0.0011)-DEPO(0.0041)-Rx(3.14)-AD(0.0018)--PD(0.0011)-DEPO(0.0041)---------------\n",
- "\n",
- "T : | 0 | 1 | 2 |\n"
- ]
- }
- ],
- "source": [
- "noisy_circ = noise_model.apply(circ)\n",
- "\n",
- "print(noisy_circ)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "id": "9304dcf1-a1e8-4e41-a6b5-769841f4eefe",
- "metadata": {},
- "outputs": [],
- "source": [
- "simulator = LocalSimulator() # noise free simulator\n",
- "task = simulator.run(circ, shots=100_000)\n",
- "free_probs = task.result().measurement_probabilities"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "id": "0e1d9cfe-03d6-406b-b4ab-89166a907681",
- "metadata": {},
- "outputs": [],
- "source": [
- "noisy_simulator = LocalSimulator(\"braket_dm\")\n",
- "noisy_task = noisy_simulator.run(noisy_circ, shots=100_000)\n",
- "noisy_probs = noisy_task.result().measurement_probabilities"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "b3f370bd-a8b3-4d5b-a724-da549fc4c81f",
- "metadata": {},
- "source": [
- "![](\"Ankaam_qubit_specs.png\"/)
\n",
+ "\n",
+ "\n",
+ "**Two-qubit calibration data (Edge specs)**\n",
+ "![](\"Ankaam_edge_specs.png\"/)
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "276d680f-887d-4929-bcaa-e276a6303496",
+ "metadata": {},
+ "source": [
+ "We can programmatically access all the calibration data with the Braket SDK. First we load the AwsDevice using the ARN for Rigetti Ankaa 2."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "a55ea9d5-05f3-4da5-a305-a391e914d012",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rigetti = AwsDevice(Devices.Rigetti.Ankaa2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a8a42ae1-51ac-4bf1-bd6a-81ffd982b5f8",
+ "metadata": {},
+ "source": [
+ "The properties dictionary contains keys \"provider\" and \"specs\", with \"1Q\" and \"2Q\" keys for the one- and two-qubit calibration data. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "153b5b63-8205-4a7e-bb18-0305ef428f36",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rigetti_specs = rigetti.properties.dict()[\"provider\"][\"specs\"]\n",
+ "\n",
+ "one_qubit_data = rigetti_specs[\"1Q\"]\n",
+ "two_qubit_data = rigetti_specs[\"2Q\"]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "661cca17-01fa-40be-bd3e-741bacc74ce4",
+ "metadata": {},
+ "source": [
+ "The keys of the \"1Q\" dictionary is the qubit number. \n",
+ "For Ankaa 2, there are 79 qubits indexed by the first digit representing the octagon (0 to 4, and 10 to 14)\n",
+ "and the second representing the qubit in that octagon (0 to 7). We can get all qubit indices with `one_qubit_data.keys()` or with `rigetti.topology_graph.nodes`.\n",
+ "\n",
+ "The keys of the \"2Q\" dictionary are the connected qubit pairs separated by a hyphen. \n",
+ "For example, if qubit 0 and 1 are connected the key is \"0-1\".\n",
+ "\n",
+ "\n",
+ "#### One-qubit noise \n",
+ "\n",
+ "Let's look at the one qubit calibration data for qubit 0."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "8d4ecc35-f4dc-49d8-b6ff-adaee560ac4b",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'fRO': 0.938,\n",
+ " 'f1QRB': 0.9989513243443735,\n",
+ " 'f1QRB_std_err': 3.143256529775241e-05,\n",
+ " 'f1Q_simultaneous_RB': 0.9980020320287597,\n",
+ " 'f1Q_simultaneous_RB_std_err': 6.0290055170609306e-05,\n",
+ " 'T1': 9.640008015307057e-06,\n",
+ " 'T2': 1.5283124633776463e-05}"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "one_qubit_data[\"0\"]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4b676762-e642-4a98-89e3-86d79367071a",
+ "metadata": {},
+ "source": [
+ "For each qubit, there are various metrics of the quality:\n",
+ "\n",
+ "- **T1**: Thermal relaxation time is related to the time it takes for the excited state, |1⟩, to decay into the ground state, |0⟩. The probability of remaining in the excited state is $p(|1⟩)\\sim e^{-t/T_1}$\n",
+ "\n",
+ "- **T2**: The dephasing time, is the decay constant for the scale for a |+⟩ state to decohere into the completely mixed state. $p(|+⟩)\\sim e^{-t/T_2}$ \n",
+ "\n",
+ "- **Fidelity (RB)**: Single-qubit randomized benchmarking fidelities. RB fidelity quantifies the average gate fidelity where the average is over all Clifford gates. RB describes an *effective* noise model with gate-independent depolarizing noise on each Clifford gate.\n",
+ "\n",
+ "- **Fidelity (sRB)**: Single-qubit simultaneous randomized benchmarking fidelities. These are extracted by running single-qubit RB on all qubits simultaneously. Note that we expect the sRB fidelity to be lower than standard RB fidelity due to non-local crosstalk type noise on the device. \n",
+ "\n",
+ "- **Active reset fidelity**: Single-qubit active reset fidelities represents the accuracy to which qubits are reinitalized into the ground state |0⟩.\n",
+ "\n",
+ "- **Readout fidelity**: Single-qubit readout fidelities describes the probability of a bit flip error before readout in the computational basis. The readout fidelity is related to the probability of correctly measuring the ground state and excited states respectively, e.g. $f_{RO} =\\frac{p(0|0)+p(1|1)}{2}$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "296708a3-771e-42b4-9ba8-f3db1a02970b",
+ "metadata": {},
+ "source": [
+ "Now that we know how to extract and use the calibration data, we can build a simple noise model. For every qubit we will add:\n",
+ "- amplitude dampening noise with probability $p= 1-e^{-t/T_1}$ for every gate\n",
+ "- phase dampening noise with probability $p= 0.5(1-e^{-t/T_2})$ for every gate\n",
+ "- depolarizing noise with probability $p=1-f_{sRB}$ (from simultaneous RB fidelity) for every gate\n",
+ "- readout bit flip noise with probability $p=1-f_{RO}$ to measurements \n",
+ "\n",
+ "Technically, the sRB fidelity already includes effects from $T_1$/$T_2$, however to be explicit we add these as separate terms. In a sense, this model might overestimate the noise on the QPU. \n",
+ "\n",
+ "For the dampening noises, we first need the gate times to model $T_1$ and $T_2$ errors.\n",
+ "From the Braket Ankaa 2 device page: \"These gates offer fast (40ns and 180ns) 1Q and 2Q gate times.\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "cd27adfb-f7d6-4583-b854-794e38152c90",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# median 1q and 2q gate times\n",
+ "gate_time_1_qubit = 40e-9\n",
+ "gate_time_2_qubit = 240e-09"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 37,
+ "id": "cd7f87ac",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "x = rigetti.properties.standardized.twoQubitProperties"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5769f2f4-de1c-4b47-9e4e-fd8d39b9e975",
+ "metadata": {},
+ "source": [
+ "To create the noise model, we iterate over all qubits keys in `one_qubit_data`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 46,
+ "id": "c01c05ff",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "dict"
+ ]
+ },
+ "execution_count": 46,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "type(rigetti.properties.standardized.oneQubitProperties)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 44,
+ "id": "7442cd27",
+ "metadata": {},
+ "outputs": [
+ {
+ "ename": "ValueError",
+ "evalue": "not enough values to unpack (expected 2, got 1)",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+ "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
+ "Cell \u001b[0;32mIn[44], line 4\u001b[0m\n\u001b[1;32m 1\u001b[0m noise_model \u001b[38;5;241m=\u001b[39m NoiseModel()\n\u001b[1;32m 3\u001b[0m \u001b[38;5;66;03m# Readout Noise Model\u001b[39;00m\n\u001b[0;32m----> 4\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m q, data \u001b[38;5;129;01min\u001b[39;00m rigetti\u001b[38;5;241m.\u001b[39mproperties\u001b[38;5;241m.\u001b[39mstandardized\u001b[38;5;241m.\u001b[39moneQubitProperties:\n\u001b[1;32m 5\u001b[0m \u001b[38;5;28mprint\u001b[39m(q)\n\u001b[1;32m 6\u001b[0m \u001b[38;5;66;03m# readout_value = 1 - data.oneQubitFidelity[2] # readout\u001b[39;00m\n\u001b[1;32m 7\u001b[0m \u001b[38;5;66;03m# noise_model.add_noise(\u001b[39;00m\n\u001b[1;32m 8\u001b[0m \u001b[38;5;66;03m# BitFlip(readout_value), ObservableCriteria(Observable.Z, qubits=int(q))\u001b[39;00m\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[38;5;66;03m# Depolarizing(probability=depolarizing_rate), GateCriteria(qubits=q)\u001b[39;00m\n\u001b[1;32m 13\u001b[0m \u001b[38;5;66;03m# )\u001b[39;00m\n",
+ "\u001b[0;31mValueError\u001b[0m: not enough values to unpack (expected 2, got 1)"
+ ]
+ }
+ ],
+ "source": [
+ "noise_model = NoiseModel()\n",
+ "\n",
+ "# Readout Noise Model\n",
+ "for q, data in rigetti.properties.standardized.oneQubitProperties:\n",
+ " print(q)\n",
+ " # readout_value = 1 - data.oneQubitFidelity[2] # readout\n",
+ " # noise_model.add_noise(\n",
+ " # BitFlip(readout_value), ObservableCriteria(Observable.Z, qubits=int(q))\n",
+ " # )\n",
+ " # depolarizing_rate = 1 - data.oneQubitFidelity[1] # SIMULTANEOUS_RANDOMIZED_BENCHMARKING\n",
+ " # noise_model.add_noise(\n",
+ " # Depolarizing(probability=depolarizing_rate), GateCriteria(qubits=q)\n",
+ " # )"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "508070bc-b1d2-4737-a2fc-d7711e419996",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0\n",
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+ ]
+ },
+ {
+ "ename": "KeyError",
+ "evalue": "'T2'",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+ "\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)",
+ "Cell \u001b[0;32mIn[10], line 13\u001b[0m\n\u001b[1;32m 11\u001b[0m \u001b[38;5;66;03m# T2 phase flip\u001b[39;00m\n\u001b[1;32m 12\u001b[0m \u001b[38;5;28mprint\u001b[39m(q)\n\u001b[0;32m---> 13\u001b[0m t2 \u001b[38;5;241m=\u001b[39m \u001b[43mdata\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mT2\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m]\u001b[49m\n\u001b[1;32m 14\u001b[0m dephasing_prob \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0.5\u001b[39m \u001b[38;5;241m*\u001b[39m (\u001b[38;5;241m1\u001b[39m \u001b[38;5;241m-\u001b[39m np\u001b[38;5;241m.\u001b[39mexp(\u001b[38;5;241m-\u001b[39m(gate_time_1_qubit \u001b[38;5;241m/\u001b[39m t2)))\n\u001b[1;32m 15\u001b[0m noise_model\u001b[38;5;241m.\u001b[39madd_noise(PhaseDamping(dephasing_prob), GateCriteria(qubits\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mint\u001b[39m(q)))\n",
+ "\u001b[0;31mKeyError\u001b[0m: 'T2'"
+ ]
+ }
+ ],
+ "source": [
+ "noise_model = NoiseModel()\n",
+ "\n",
+ "# Single-qubit noise\n",
+ "for q, data in one_qubit_data.items(): # iterate over qubits\n",
+ "\n",
+ " # T1 dampening\n",
+ " t1 = data[\"T1\"]\n",
+ " damping_prob = 1 - np.exp(-(gate_time_1_qubit / t1))\n",
+ " noise_model.add_noise(AmplitudeDamping(damping_prob), GateCriteria(qubits=int(q)))\n",
+ "\n",
+ " # T2 phase flip\n",
+ " t2 = data[\"T2\"]\n",
+ " dephasing_prob = 0.5 * (1 - np.exp(-(gate_time_1_qubit / t2)))\n",
+ " noise_model.add_noise(PhaseDamping(dephasing_prob), GateCriteria(qubits=int(q)))\n",
+ "\n",
+ " # 1q RB depolarizing rate from simultaneous RB\n",
+ " depolar_rate = 1 - data[\"f1Q_simultaneous_RB\"]\n",
+ " noise_model.add_noise(Depolarizing(depolar_rate), GateCriteria(qubits=int(q)))\n",
+ "\n",
+ " # 1q RB readout\n",
+ " readout_value = 1 - data[\"fRO\"]\n",
+ " noise_model.add_noise(BitFlip(readout_value), ObservableCriteria(qubits=int(q)))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9d20d24c-17e2-4bba-b317-fb2d156bedb0",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "num_params = sum(len(item.noise.parameters) for item in noise_model.instructions)\n",
+ "print(f\"Number of terms in noise model is: {len(noise_model.instructions)}\")\n",
+ "print(f\"Number of parameters in noise model is: {num_params}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "790c62f7-776a-4e4c-9405-7b7a14eee5b0",
+ "metadata": {},
+ "source": [
+ "#### Two-qubit noise \n",
+ "Next we consider adding two-qubit noise to the model. \n",
+ "\n",
+ "Let's first look at the data provided in the Ankaa 2 device calibration data. On the first connect, \"0-1\", the properties are:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "626cbe56-3649-48eb-a2a1-f669eb790b47",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "two_qubit_data[\"0-1\"]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4bcd3be4-a6e4-4cf3-841e-1a451e01803a",
+ "metadata": {},
+ "source": [
+ "Here, we see the fidelity per gate (ISWAP or CZ) and the associated standard error. \n",
+ "\n",
+ "Next we loop over the entries in the `two_qubit_data` dictionary and add two-qubit depolarizing noise to the model. Notice that Ankaa 2 has symmetric connections (\"0-1\" and \"1-0\") so we need to add noise in both directions."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "80f57550-6549-46b6-9a6d-ff7f0f03e90d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Two-qubit noise\n",
+ "for pair, data in two_qubit_data.items(): # iterate over qubit connections\n",
+ "\n",
+ " # parse strings \"0-1\" to integers [0, 1]\n",
+ " q0, q1 = (int(s) for s in pair.split(\"-\"))\n",
+ "\n",
+ " if \"fCPHASE\" in data:\n",
+ " phase_rate = 1 - data[\"fCPHASE\"]\n",
+ " noise_model.add_noise(\n",
+ " TwoQubitDepolarizing(phase_rate),\n",
+ " GateCriteria(\n",
+ " Gate.CPhaseShift, [(q0, q1), (q1, q0)]\n",
+ " ), # symmetric connections\n",
+ " )\n",
+ "\n",
+ " if \"fXY\" in data:\n",
+ " xy_rate = 1 - data[\"fXY\"]\n",
+ " noise_model.add_noise(\n",
+ " TwoQubitDepolarizing(xy_rate), GateCriteria(Gate.XY, [(q0, q1), (q1, q0)])\n",
+ " )\n",
+ "\n",
+ " if \"fCZ\" in data:\n",
+ " cz_rate = 1 - data[\"fCZ\"]\n",
+ " noise_model.add_noise(\n",
+ " TwoQubitDepolarizing(cz_rate), GateCriteria(Gate.CZ, [(q0, q1), (q1, q0)])\n",
+ " )"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "82376d08-84bc-4249-9c8d-d7aacdb73113",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "num_params = sum(len(item.noise.parameters) for item in noise_model.instructions)\n",
+ "print(f\"Number of terms in noise model is: {len(noise_model.instructions)}\")\n",
+ "print(f\"Number of parameters in noise model is: {num_params}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5913a8a2-a9de-4e32-a35d-c48191891b1f",
+ "metadata": {},
+ "source": [
+ "### Compare circuits run on device vs simulator with a noise model\n",
+ "\n",
+ "Let's just look at the first 5 qubits. Note that to ensure the noise model applied T1 and T2 noise during the time between gate, we manually add identity gates to each moment."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "6fabbd05-b480-43c6-b43a-d396d81bd687",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "np.random.seed(42)\n",
+ "\n",
+ "circ = Circuit().rx(0, 0.5).rz(1, 0.5).rz(2, 0.5).rx(0, np.pi).rx(1, np.pi).rx(2, np.pi).cz(0, 1)\n",
+ "print(circ)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "e2af07ed-33de-4709-9e7c-5e3c3caaa751",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "noisy_circ = noise_model.apply(circ)\n",
+ "\n",
+ "print(noisy_circ)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "id": "9304dcf1-a1e8-4e41-a6b5-769841f4eefe",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "simulator = LocalSimulator() # noise free simulator\n",
+ "task = simulator.run(circ, shots=100_000)\n",
+ "free_probs = task.result().measurement_probabilities"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "id": "0e1d9cfe-03d6-406b-b4ab-89166a907681",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "noisy_simulator = LocalSimulator(\"braket_dm\")\n",
+ "noisy_task = noisy_simulator.run(noisy_circ, shots=100_000)\n",
+ "noisy_probs = noisy_task.result().measurement_probabilities"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b3f370bd-a8b3-4d5b-a724-da549fc4c81f",
+ "metadata": {},
+ "source": [
+ "![](\"console_figures/1-algorithm.png\"/)
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Next, you can choose a name for your hybrid job or use the default name. You also have the option to change the default execution role and the default S3 location for uploads.\n",
- "\n",
- "![](\"console_figures/2-basic.png\"/)
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Third, select a container environment for your job. The default \"PennyLane\" container is enough for the example in this notebook. For information about using other pre-built or custom containers, see the [Pennylane](../2_Using_PennyLane_with_Braket_Hybrid_Jobs/Using_PennyLane_with_Braket_Hybrid_Jobs.ipynb) and the [BYOC](../3_Bring_your_own_container/bring_your_own_container.ipynb) example notebooks. \n",
- "\n",
- "![](\"console_figures/3-environment.png\"/)
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "You may also select a Braket on-demand simulator or QPU for your job and configure the execution settings. You also have the option to customize the default locations for checkpoints and output data. We dive deeper into these advanced use cases in other [example notebooks](../2_Using_PennyLane_with_Braket_Hybrid_Jobs/Using_PennyLane_with_Braket_Hybrid_Jobs.ipynb).\n",
- "\n",
- "![](\"console_figures/4-execution.png\"/)
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "After finishing all the settings, you can review your selections before submitting your hybrid job. You can now create the hybrid job by clicking the \\\"Create hybrid job\\\" button or return to any earlier step to make edits. We can now view the progress in the Braket console.\n",
- "\n",
- "![](\"console_figures/5-review.png\"/)
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Summary\n",
- "\n",
- "In this tutorial, we have created our first Braket Job with a simple batch of five circuits using the Amazon Braket SDK and, as an alternative, from the Braket console. We learned how to change the Amazon S3 folder and the AWS region for a job, and how to save results, and how to retrieve queue depth for a device, and queue position for the hybrid job. We learned how to seamlessly change the device to run on simulators or QPUs. We used local mode to quickly test code. Finally, we created the same job using the Braket console."
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "conda_braket",
- "language": "python",
- "name": "conda_braket"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.10.9"
- },
- "vscode": {
- "interpreter": {
- "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2"
- }
- }
- },
- "nbformat": 4,
- "nbformat_minor": 4
-}
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Getting started with Amazon Braket Hybrid Jobs\n",
+ "\n",
+ "This tutorial shows how to run your first Amazon Braket Hybrid Job. To get started, we consider small circuits with only one qubit and one gate.\n",
+ "\n",
+ "\n",
+ "## Learning outcomes\n",
+ "* Get setup to run your first hybrid job\n",
+ "* Write an algorithm script to run on Braket Hybrid Jobs\n",
+ "* Understand how to run scripts or functions\n",
+ "* Create a hybrid job on Braket simulators or QPUs\n",
+ "* Monitoring the hybrid job state\n",
+ "* Save results from a hybrid job\n",
+ "* Using a specific AWS session\n",
+ "* Running hybrid jobs with priority on QPUs\n",
+ "* Use local hybrid jobs to quickly test and debug scripts\n",
+ "* Create a Braket Hybrid Job using the Braket console"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Getting setup to run Braket Hybrid Jobs\n",
+ "\n",
+ "When you use Amazon Braket Hybrid Jobs for the first time, you need to create an IAM role with the right [permissions](https://docs.aws.amazon.com/braket/latest/developerguide/braket-manage-access.html#about-amazonbraketjobsexecution). This role allows your hybrid job to perform actions on your behalf while it is executing your algorithm, for instance, access S3 to return the results of your hybrid job. To create the role or check if you already have one please visit the Permissions tab from the left menu of the Braket Console.\n",
+ "\n",
+ "## Writing an algorithm script\n",
+ "\n",
+ "To create a Braket Hybrid Job, you first need a Python script to run. In this example, it's contained in `algorithm_script.py`. The script is printed in the code cell below for convenience. \n",
+ "\n",
+ "As shown, each of the circuits has only one $X$ rotation gate with a random angle. The circuit is repeated five times with different random rotations. Note that the algorithm script does not specify the backend Amazon Braket device ARN explicitly. Instead, it is provided through environment variables such as `os.environ[\"AMZN_BRAKET_DEVICE_ARN\"]` that are passed to the algorithm script when creating the hybrid job. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "pycharm": {
+ "name": "#%% md\n"
+ }
+ },
+ "source": [
+ "#### This block is a copy of the algorithm script.\n",
+ "\n",
+ "```python\n",
+ "\n",
+ "import os\n",
+ "import numpy as np\n",
+ "\n",
+ "from braket.aws import AwsDevice\n",
+ "from braket.circuits import Circuit\n",
+ "from braket.jobs import save_job_result\n",
+ "from braket.tracking import Tracker\n",
+ "\n",
+ "t = Tracker().start()\n",
+ "\n",
+ "print(\"Test hybrid job started!\")\n",
+ "\n",
+ "# Use the device declared in the creation script\n",
+ "device = AwsDevice(os.environ[\"AMZN_BRAKET_DEVICE_ARN\"])\n",
+ "\n",
+ "counts_list = []\n",
+ "angle_list = []\n",
+ "for _ in range(5):\n",
+ " angle = np.pi * np.random.randn()\n",
+ " random_circuit = Circuit().rx(0, angle)\n",
+ "\n",
+ " task = device.run(random_circuit, shots=100)\n",
+ " counts = task.result().measurement_counts\n",
+ "\n",
+ " angle_list.append(angle)\n",
+ " counts_list.append(counts)\n",
+ " print(counts)\n",
+ "\n",
+ "# Save the variables of interest so that we can access later\n",
+ "save_job_result({\"counts\": counts_list, \"angle\": angle_list, \"estimated cost\": t.qpu_tasks_cost() + t.simulator_tasks_cost()})\n",
+ "\n",
+ "print(\"Test hybrid job completed!\")\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Creating your first hybrid job\n",
+ "\n",
+ "Once the script is finalized, you can create a Braket Hybrid Job with `AwsQuantumJob`. When the hybrid job is created, Amazon Braket starts the hybrid job instance (based on EC2) and spins up a Docker container to run your algorithm script. Other configurations can be specified via keyword arguments. See the [developer guide](https://docs.aws.amazon.com/braket/latest/developerguide/what-is-braket.html) and other example notebooks to learn more about how to customize your jobs\n",
+ "\n",
+ "This example uses the following inputs for `AwsQuantumJob`:\n",
+ "- device: The ARN of the Braket simulator or QPU to use in the hybrid job. It will be passed as an environment variable to the algorithm script. \n",
+ "- source_module: The path to a file or a Python module that contains your algorithm script. It will be uploaded to the container for running the Braket Hybrid Job.\n",
+ "- wait_until_complete (optional): If True, the function call will wait until the Braket Hybrid Job is completed and will additionally print logs to the local console. Otherwise, it will run asynchronously. The default is False."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from braket.aws import AwsDevice, AwsQuantumJob\n",
+ "from braket.devices import Devices"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "pycharm": {
+ "name": "#%%\n"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Initializing Braket Job: arn:aws:braket:![](\"hybrid_quantum.png\"/)
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "__Variational Quantum Algorithms__: Specifically, variational quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) [1] belong to this emerging class of hybrid quantum algorithms. \n",
- "These are widely believed to be promising candidates for the demonstration of a __quantum advantage__, already with near-term (NISQ) devices in areas such as quantum chemistry [2], condensed matter simulations [3], and discrete optimization tasks [4].\n",
- "\n",
- "__Variational Quantum Computing vs. Deep Learning__: The working principle of variational quantum computing is very much reminiscent of training deep neural networks: \n",
- "when you train a neural network, you have an objective function that you want to minimize, typically characterized by the error on your training set. \n",
- "To minimize that error, typically you start out with an initial guess for the weights in your network. \n",
- "The coprocessor, in that case a GPU, takes these weights which define the exact operation to execute and the output of the neural network is computed. \n",
- "This output is then used to calculate the value of your objective function, which in turn is used by the CPU to make an educated guess to update the weights and the cycle continues. \n",
- "Variational quantum algorithms, a specific form of hybrid algorithms, work in the very same way, using parametrized quantum circuits rather than parametrized neural networks and replacing the GPU with a QPU. \n",
- "Here, you start with an initial guess for the parameters that define your circuit, have the QPU execute that circuit, perform measurements to calculate an objective function, pass this value (together with the current values of the parameters) back to the CPU and have this *classical* CPU update the parameters based on that information. \n",
- "\n",
- "Of course, coordinating that workflow for quantum computers is much more challenging than in the previous case. Quantum computers are located in specialized laboratory facilities, are typically single threaded, and have special latency requirements. \n",
- "This is exactly the undifferentiated heavy-lifting that Amazon Braket handles for us, such that we can focus on our scientific problem. \n",
- "For the sake of this introductory tutorial, we simply use a classical circuit simulator (that mimic the behavior of a quantum machine) as the device to execute our quantum circuits.\n",
- "Within Amazon Braket, the workflow, however, is exactly the same. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## BACKGROUND: QUADRATIC BINARY OPTIMIZATION PROBLEMS"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "__Combinatorial optimization__: \n",
- "Combinatorial optimization problems are ubiquitous across many areas of science and application areas. \n",
- "Applications can be found (for example) in logistics, scheduling, planning, and portfolio optimization.\n",
- "In a nutshell combinatorial optimization problems are problems involving a large number of yes/no decisions with each set of decisions yielding a corresponding objective function value, like a cost or profit value. \n",
- "Because of the combinatorial explosion of the solution space with the number of variables, finding good solutions is a daunting task and extremely difficult. \n",
- "\n",
- "__QUBO problems__: The QUBO ([Quadratic Unconstrained Binary Optimization](https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization)) model unifies a rich variety of NP-hard combinatorial optimization problems: \n",
- "Famous examples include Quadratic Assignment Problems, Capital Budgeting Problems, Task Allocation Problems and Maximum-Cut Problems. \n",
- "For more details we refer to the excellent review and tutorial on QUBO problems presented in Ref.[5].\n",
- "\n",
- "__Maximum Cut__: Among the class of QUBO problems, Maximum Cut (MaxCut) is paradigm combinatorial optimization problem. \n",
- "Given a graph $G=(V,E)$ with vertex set $V$ and edge set $E$, we seek partition of $V$ into two subsets with maximum cut. \n",
- "In short, we have to color every node either blue or red and we score a point whenever an edge connects two nodes with different colors. \n",
- "We then would like to find the solution with the highest score. \n",
- "Applications thereof can be found in, for example, (i) clustering for marketing purposes (segment your customer base into different clusters for targeted marketing) or (ii) portfolio optimization in finance (vertex corresponds to asset, with color referring to sell or buy decisions. \n",
- "Again, the problem in this specific graph coloring problem is that there are $2^𝑁$ possible solutions for $N$ nodes (an exponential explosion in possibilities), making it impossible to enumerate all possible candidates for relevant system sizes. \n",
- "\n",
- "__Ising Hamiltonian__: Importantly, there is a fundamental correspondence between QUBO problems and Ising problems in physics. \n",
- "Specifically, we can encode the Maximum Cut problem as a __minimization problem__ of an Ising Hamiltonian, where the (classical) cost function reads \n",
- "\n",
- "$$H_{C}=\\sum_{i>j} J_{i,j} z_{i} z_{j},$$\n",
- "\n",
- "with Ising variables $z_{i}=-1,1$ and the Ising matrix $J$ encoding the weights of the edges. \n",
- "For the sake of this discussion, we ignore potential linear terms and constant offsets (that do not affect the optimal solution $z$ anyway). \n",
- "In short, the cost Hamiltonian $H_{C}$ assigns a number to every bitstring $z=(z_{1},z_{2},\\dots)$, and we would like to find the lowest number possible. \n",
- "This will be the optimal assignment and solution to our problem. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## BACKGROUND: THE QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this tutorial we will try to solve for the optimal _classical_ bitstring $z$ using the Quantum Approximate Optimization Algorithm (QAOA). \n",
- "To this end, we first promote the classical spin variables $z_{i}=-1,1$ to quantum-mechanical variables $\\sigma_{i}^{z}$ (with the Pauli matrix $\\sigma_{i}^{z}$ representing the observable corresponding to spin along the $z$ coordinate axis in three-dimensional Euclidean space $\\mathbb{R}^{3}$). \n",
- "This leads to the following quantum mechanical cost Hamiltonian encoding the optimization problem\n",
- "\n",
- "$$\\hat{H}_{C}=\\sum_{i>j} J_{i,j} \\sigma_{i}^{z} \\sigma_{j}^{z},$$\n",
- "\n",
- "which can be written as a matrix of size $(2^{N}, 2^{N})$ with diagonal elements only corresponding to all possible classical values for the cost function $H_{C}$. \n",
- "The ground state of $\\hat{H}_{C}$ corresponds to the optimal solution of the classical combinatorial problem.\n",
- "\n",
- "__QAOA ansatz__: Finding this ground state is generically hard. \n",
- "To approximate this groundstate, QAOA prepares a parametrized ansatz state (corresponding to a parameterized gate sequence), whose parameters are iteratively updated by a classical optimizer in a closed loop. \n",
- "Specifically, QAOA involves a specific ansatz wavefunction parametrized by a parameter family $(\\vec{\\beta}, \\vec{\\gamma})$, embedded into a larger classical optimization loop to find the optimal values for these parameters. \n",
- "As shown in Ref.[1], good approximate solutions to the problem class considered here can be found by preparing the variational state \n",
- "\n",
- "$$|\\gamma, \\beta \\rangle = U_{x}(\\beta_{p})U_{zz}(\\gamma_{p}) \\cdots U_{x}(\\beta_{1})U_{zz}(\\gamma_{1}) |s\\rangle$$\n",
- "\n",
- "with single qubit rotations induced by $U_{x}(\\beta) = \\exp(-i\\beta \\sum_{i}\\sigma_{i}^{x})$, \n",
- "and interactions described by $U_{zz}(\\gamma) = \\exp(-i\\gamma H_{C})$,\n",
- "starting initially from a product of $\\sigma^{x}$ eigenstates, i.e.,\n",
- "$|s\\rangle =|-,-,\\dots\\rangle$, with $|-\\rangle = (|0\\rangle -|1\\rangle )/\\sqrt{2}$. \n",
- "The family of states $|\\gamma, \\beta \\rangle$ is prepared by alternating single-qubit operations $U_{x}(\\beta_{p})$ with targeted spin-spin interactions generated by the cost Hamiltonian $H_{C}$. \n",
- "The depth $p$ can be interpreted as a hyperparameter. \n",
- "For $p$ layers of QAOA blocks, there are $2p$ classical parameters to optimize over, \n",
- "since each layer $k$ is characterized by just two variational parameters, $\\gamma_{k}$ and $\\beta_{k}$. \n",
- "The preparation step outlined above is followed by a measurement in the computational basis, giving a classical string $z$, with which one can evaluate the objective function $H_{C}$ of the underlying combinatorial problem at hand. \n",
- "Taking several measurements shots one can build the expectation value $E(\\beta, \\gamma) = \\langle H_{C} \\rangle$ that we report as the objective function to the classical minimizer (while other choices could be possible as well). \n",
- "Repeating this procedure will provide an optimized string $z$, with the quality of the result improving as the depth of the quantum circuit $\\sim 2p$ is increased [1]. \n",
- "In fact, in principle (in the absence of noise and other imperfections), QAOA can reach the global optimum of any cost function in the limit $p \\rightarrow \\infty$ [1], approaching the adiabatic protocol. \n",
- "Thus, in theory the computational power of QAOA increases with $p$, but in practice the number of layers that can be executed without errors on NISQ devices is limited due noise and imperfections. \n",
- "\n",
- "__Optimization__: Since we are primarily interested in solving the classical optimization problem, within this routine it is sufficient to keep track of the best classical bitstring. \n",
- "This means that the wavefunction prepared by the quantum circuit $|\\gamma, \\beta \\rangle$ has to have some overlap with the optimal solution $|z^{*} \\rangle$ that we can read out as bitstring $z^{*}$ in the measurement shots. \n",
- "To this end, in principle (i.e., without any training), we could just sample from a completely uniform state that is prepared in a superposition of all computational basis states, as prepared by applying Hadamard gates to all qubits: $|\\mathrm{uniform}\\rangle = 1/\\sqrt{2^{N}}\\sum_{i}|z_{i}\\rangle$. \n",
- "In that case (assuming a single optimal solution) the success probability per shot amounts to $p_{\\mathrm{success}}=1/2^{N}$. \n",
- "We can then amplify our success chances by just taking many measurement shots. \n",
- "For large systems, however, this approach is not scalable as we would need to take an exponentially increasing number of measurements. \n",
- "That is why we train our circuits, update the parameters, with the goal to increase our success chances to find the optimal bitstring. \n",
- "We can quantify our success chances as follows [6]. \n",
- "For a given wavefunction $|\\gamma, \\beta \\rangle$ the probability to find the optimal solution in a single shot is given by \n",
- "\n",
- "$$ p_{\\mathrm{success}}(\\gamma, \\beta) = |\\langle z^{*}|\\gamma, \\beta \\rangle |^{2},$$\n",
- "\n",
- "where $z^{*}$ denotes the optimal bitstring. \n",
- "If we perform $M$ repeated measurements, the overall probability $P$ for observing this solution at least once is given by \n",
- "\n",
- "$$ P = 1 - (1-p_{\\mathrm{success}}(\\gamma, \\beta))^{M}, $$ \n",
- "\n",
- "since the term $(1-p_{\\mathrm{success}}(\\gamma, \\beta))^{M}$ gives the probability of _not_ obtaining $z^{*}$ in repeated $M$ trials. \n",
- "Therefore, to have an overall success chance up to $\\epsilon$ close to 100%, i.e., $P \\geq 1-\\epsilon$, the number of required shots has to be \n",
- "\n",
- "$$ M \\geq \\frac{\\log(\\epsilon)}{\\log(1-p_{\\mathrm{success}}(\\gamma, \\beta))}.$$\n",
- "\n",
- "Let us illustrate this results as follows: \n",
- "If we do not know anything and just resort to a uniform superposition $|\\mathrm{uniform}\\rangle$, for a small system with $N=10$ qubits we can find the optimal solutions with 80% success probability by taking at least $\\sim 1650$ shots. \n",
- "For just $N=20$ qubits, however, this number amounts to $\\sim 1.7 \\times 10^{6}$, making this naive approach unfeasible. \n",
- "Conversely, if we can train the quantum circuit to obtain $p_{\\mathrm{success}}(\\gamma, \\beta) \\sim 0.1$, we only need $\\sim 15$ shots to have $P\\geq 80\\%$. \n",
- "Below we will track and illustrate the best classical optimum as our algorithm proceeds towards a local or (ideally) global optimum. \n",
- "\n",
- "__Objective function__: Finally, some more details on the definition of the cost function are in order. \n",
- "Following the standard approach [1, 4], QAOA tries to minimize the expectation value $\\langle \\hat{H}_{C} \\rangle$, but does _not_ explicitly maximize the success probability [6]. \n",
- "However, a low expectation value for $\\langle \\hat{H}_{C} \\rangle$ does not necessarily translate to a high success probability $p_{\\mathrm{success}}(\\gamma, \\beta)$, as can be understood from the following example:\n",
- "Consider (for example) a variational state that is a linear combination of low energy excited eigenstates of the cost Hamiltonian $\\hat{H}_{C}$ other than the ground state $|z^{*}\\rangle$. \n",
- "By definition, this state will have a relatively low expectation value $\\langle \\hat{H}_{C} \\rangle$ while the success probability is zero (as this low energy state does not have any overlap with the ground state). \n",
- "Similarly, a variational state that is a linear combination of the ground state with very high energy eigenstates could have a high success probability $p_{\\mathrm{success}}(\\gamma, \\beta)$, while (at the same time) reporting a high cost value to the classical optimizer.\n",
- "To address this issue, alternative methods for the optimization of the variational parameters have recently been proposed. \n",
- "While for simplicity we follow the majority of the literature and take $\\langle \\hat{H}_{C} \\rangle$ as cost value that we report to the classical optimizer, here we do mention a potential alternative for future research: \n",
- "One approach is to use the Gibbs objective function, defined as $\\mathrm{cost}=-\\mathrm{log} \\langle \\exp(-\\eta \\hat{H}_{C})\\rangle$, with the hyperparameter $\\eta>0$ [7]. \n",
- "As compared to the simple expectation value $\\langle \\hat{H}_{C} \\rangle$, this definition of the cost value shows stronger rewards for low energy states, thereby increasing the success probability. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## IMPORTS and SETUP"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "For classical benchmarking we will be using the python library ```pyqubo```, as used in our helper script ```utils_classical```. If not already present in your virtual environment, you can install this library simply with ```pip install pyqubo```. Similarly, as ```seaborn``` are not expected to be present in the virtual environment by default, we will install them via ```pip install seaborn```. Note the ```-q``` to suppress install updates from ```pip```."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# If these have already been installed, this cell can be commented out.\n",
- "!pip install pyqubo -q\n",
- "!pip install seaborn -q"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {},
- "outputs": [],
- "source": [
- "# general imports\n",
- "import numpy as np\n",
- "from scipy.optimize import minimize\n",
- "import matplotlib.pyplot as plt\n",
- "import networkx as nx\n",
- "import seaborn as sns\n",
- "import time\n",
- "from datetime import datetime\n",
- "import pickle\n",
- "import random\n",
- "\n",
- "# magic line for producing visualizations in notebook\n",
- "%matplotlib inline"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [],
- "source": [
- "# fix random seed for reproducibility\n",
- "seed = 42\n",
- "np.random.seed(seed)\n",
- "random.seed(a=seed)\n",
- "\n",
- "# switch to trigger writing training results to disk\n",
- "store_results = False\n",
- "# switch to trigger printing results of each optimization cycle\n",
- "verbose = False"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {},
- "outputs": [],
- "source": [
- "# AWS imports: Import Braket SDK modules\n",
- "from braket.circuits import FreeParameter\n",
- "from braket.devices import LocalSimulator"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [],
- "source": [
- "from utils_classical import plot_colored_graph, plot_colored_graph_simple, solve_classical_ising\n",
- "# auto reload external files, so that we can edit the external .py file and immediately see the changes here\n",
- "%load_ext autoreload\n",
- "%autoreload 2"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {},
- "outputs": [],
- "source": [
- "# Set up device: Local Simulator\n",
- "device = LocalSimulator()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {},
- "outputs": [],
- "source": [
- "## example code for other backends\n",
- "# from braket.aws import AwsDevice\n",
- "# from braket.devices import Devices\n",
- "## choose the on-demand simulator to run your circuit\n",
- "# device = AwsDevice(Devices.Amazon.SV1)\n",
- "## choose the Rigetti device to run your circuit\n",
- "# device = AwsDevice(Devices.Rigetti.Ankaa2)\n",
- "## choose the Ionq device to run your circuit\n",
- "# device = AwsDevice(Devices.IonQ.Aria1)\n",
- "## choose the IQM device to run your circuit\n",
- "# device = AwsDevice(Devices.IQM.Garnet)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## PROBLEM SETUP"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We consider a graph coloring problem.\n",
- "Given a graph $G=(V,E)$, made of a set vertices (also called nodes) $V$ and edges $E$, our goal is to color each node red or blue, then score a point for each node that is next to a node of different color. \n",
- "We strive to find the optimal coloring that scores the largest number of points.\n",
- "To this end, we will address the dual problem of finding the minimum energy of the corresponding Ising Hamiltonian. \n",
- "To get started, we first use the open-source ```networkx``` library to visualize the problem graph. \n",
- "Feel free to play with the parameters $n$ (for the number of nodes) and $m$ (for the number of edges) below to consider other graphs of your choice. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {},
- "outputs": [
- {
- "data": {
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",
- "text/plain": [
- "![](\"pl_braket.png\"/)
"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "PennyLane integrates with Amazon Braket to add additional features for quantum machine learning and optimization. This introductory tutorial walks you through how to train a quantum circuit using Amazon Braket simulators and PennyLane's automatic differentiation capabilities."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Setup"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "PennyLane is already installed on Braket notebook instances. On a local machine, PennyLane can be installed by following [these](https://pennylane.ai/install.html) instructions. It can then be imported with:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:09.404557Z",
- "start_time": "2024-02-19T21:42:03.275541Z"
- }
- },
- "outputs": [],
- "source": [
- "import pennylane as qml\n",
- "from pennylane import numpy as np"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "To use Braket as a backend in PennyLane, we have to create a PennyLane device. Here we will first create a device that uses the local Braket simulator that runs on your local laptop (or on the server that hosts this notebook)."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:10.351825Z",
- "start_time": "2024-02-19T21:42:09.405882Z"
- }
- },
- "outputs": [],
- "source": [
- "wires = 2 # Number of qubits\n",
- "\n",
- "dev = qml.device(\"braket.local.qubit\", wires=wires)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Below we will also show you how to scale out simulations to the AWS cloud."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Defining a circuit"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We will choose a simple two-qubit circuit with two controllable rotations and a CNOT gate."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2024-02-19T21:42:10.355051Z",
- "start_time": "2024-02-19T21:42:10.352639Z"
- }
- },
- "outputs": [],
- "source": [
- "@qml.qnode(dev)\n",
- "def circuit(params):\n",
- " qml.RX(params[0], wires=0)\n",
- " qml.RY(params[1], wires=1)\n",
- " qml.CNOT(wires=[0, 1])\n",
- " return qml.expval(qml.PauliZ(1))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The ``qml.qnode(dev)`` decorator binds the circuit to the local Braket device. Now, every time that ``circuit()`` is called, the quantum computation defined in the function above will be executed with Braket."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "![](\"remote-single-job.png\"/)
"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2024-02-19T21:42:11.066378Z",
+ "start_time": "2024-02-19T21:42:11.064297Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
+ "from braket.tracking import Tracker\n",
+ "\n",
+ "braket_tasks_cost = Tracker().start()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Each remote Braket device can be selected through its [ARN](https://docs.aws.amazon.com/general/latest/gr/aws-arns-and-namespaces.html). The supported devices on Braket are listed [here](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html). For now, we will pick the on-demand SV1 simulator.\n",
+ "\n",
+ "