5a - Quantitative Yield Curve Models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.interpolate import CubicSpline, interp1d, make_interp_spline, UnivariateSpline\n",
    "from scipy.optimize import newton, fsolve\n",
    "import matplotlib.pyplot as plt\n",
    "import bond_pricing as bp\n",
    "# from sympy import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generalized Bootstrap Method to Determine the Yield Curve - Cubic Spline Interpolation\n",
    "by Richard Deaves & Mahmut Parlar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If an analyst were able to possess a sufficient quantity of reliable friction-free government bond data, a technique known as the bootstrap would straightforwardly derive the spot yield curve. This technique is based on the notion that individual coupon-paying bonds can be viewed as “packages” of pure discount bonds. For example, a three-year bond is comprised of six pure discount bonds, namely the five coupon payments to be paid every six months, and the final payment which is the sum of the final coupon and the return of principal. This suggests that a bond’s value can be viewed as either the present value of future cash flows discounted at the yield to maturity, or as the sum of the values of individual pure discount bonds, each of which is a present value of a cash flow discounted at its own time-specific yield.\n",
    "\n",
    "The classic “textbook” explication of the bootstrap usually begins by assuming the existence of a set of perfectly spaced bonds: for example, a 6-month, a 12-month, an 18-month and so on. If these bonds have frictionless market prices, the bootstrap renders the correct yield curve in a straightforward fashion, as will be illustrated below.\n",
    "\n",
    "The problem with the bootstrap is that it relies heavily on the existence of a suitable body of data. In particular there are two problems: **illiquidity** and **missing data points**. Quotes coming from a thin market may be at divergence from true market prices due to spreads and asynchronous trading. This is why applying the bootstrap to a raw sample of bonds is likely to lead to an unreasonably “choppy” yield curve. One approach is to perform some form of curve fitting to arrive at a reasonably smooth representation of the yield curve. This can be done either before or after utilizing the bootstrap. Nevertheless there is a problem with any smoothing procedure which is unavoidable: the final curve will always be a function of an assumed functional form. For example, the Nelson and Siegel procedure allows for a single hump while the Svensson approach allows for two humps.\n",
    "\n",
    "There is another approach for eliminating inappropriate shapes, namely to make use of **averaged yield data**. For example, one could take all bonds in the neighborhood of the five-year maturity, average their yields and then use the **resultant average as the yield on a hypothetical five-year par bond in the belief that some of the bonds comprising the average will be discount bonds and others will be premium bonds**. This, in fact, will be the approach that we will employ in some examples discussed later.\n",
    "\n",
    "As for the second problem with the bootstrap — the lack of a full set of data — this must be solved by imposing conditions on the intermediate points. Of course, one can never avoid the arbitrariness of the choice of various interpolation procedures. We argue below that a **cubic spline** is an appropriate choice.\n",
    "\n",
    "The procedure described below is a generalized bootstrapping method. Using python to construct and solve for algebraic expressions, it straightforwardly deals with any data set regardless of time spacing. **Different interpolation assumptions can be accommodated**. The **illiquidity issue is dealt with by using highly liquid T-bills at the short end of the maturity and average yields beyond one year**. \n",
    "\n",
    "More specifically, beginning with a series of bond value expressions for a given set of fixed income securities, one cannot — except under ideal conditions — solve for the yields corresponding to all payment dates, since there are more unknowns than equations. Each maturity date is accounted for by a single bond value expression. Generating equations for the points corresponding to the coupon dates, however, requires the use of an interpolation approach that involves the combination of bond value expression along with an interpolation function. By using SciPy's interpolation and optimization subpackages, it becomes possible to generate inputs, perform interpolation (linear and non-linear) and solve for bond price equations (non-linear) to obtain the points on the yield curve.\n",
    "\n",
    "A key advantage of our approach is its simple “one-shot” nature. Unlike the methods used by McCulloch, Vasicek and Fong, and Svensson who make a *priori* assumptions about the form of the yield curve, we let the available data determine the exact form of the yield curve by solving a system of nonlinear equations. It is worth stressing that our simpler — yet, general — method requires the structuring of linear and non-linear interpolation functions and bond pricing equations in a way such that the system of equations can be solved using a root-finding algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The Textbook Bootstrap"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The bootstrap method — as discussed in standard texts — is used to solve sequentially a system of nonlinear equations which has at least one equation whose solution for a single unknown can be obtained in a straightforward manner. In this section we provide a brief review of the bootstrap method by utilizing a numerical example. The data on the maturity, coupons and prices of four bonds are given below.\n",
    "\n",
    "**First Example**\n",
    "\n",
    "| Bond No. | Time to Maturity (Years) | Annual Coupon (Dollars) | Bond Price (Dollars) |\n",
    "| -------- | ------------------------ | ----------------------- | -------------------- |\n",
    "| 1        | 0.50                     | 0                       | 94.90                |\n",
    "| 2        | 1.00                     | 0                       | 90.00                |\n",
    "| 3        | 1.50                     | 8                       | 96.00                |\n",
    "| 4        | 2.00                     | 12                      | 101.60               |\n",
    "\n",
    "* **Note**: We will be using continuously compounding yields in all cases \n",
    "* **Coupons**: Coupons are paid semi-annually\n",
    "\n",
    "$$PV = FV \\times e^{-rt}$$\n",
    "$$r = \\ln\\left(\\frac{FV}{PV}\\right) \\times \\frac{1}{t}$$\n",
    "\n",
    "Denoting the discount rate for a maturity of $t$ years by $r_{t}$, we can use $t = 0.50$ and $t = 1.00$ to solve $94.9 = 100e^{-r_{0.50}\\times 0.5}$ and $90.0 = 100e^{-r_{1.00}\\times 1.0}$ and obtain $r_{0.50} = 0.1047$ and $r_{1.00} = 0.1054$, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "years = np.array([0.5, 1.0, 1.5, 2.0])\n",
    "coupon = np.array([0, 0, 8, 12])\n",
    "price = np.array([94.90, 90.00, 96.00, 101.60])\n",
    "face = np.full(4, 100)\n",
    "freq = 2\n",
    "\n",
    "r1 = np.log(100/price[0]) / 0.5\n",
    "r2 = np.log(100/price[1]) / 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Implied Spot Rates (c.c.) =  [0.10469296 0.10536052 0.10680926 0.10808028]\n"
     ]
    }
   ],
   "source": [
    "# Securities maturing in 0.5y and 1y are zero-coupons\n",
    "cc_ytm = [r1, r2]\n",
    "\n",
    "for i in range(2, len(coupon)):\n",
    "    pv_cf = np.sum(np.full(int(years[i]*freq)-1, coupon[i]/freq) * np.exp(-np.array(cc_ytm) * years[:i]))\n",
    "    cc_ytm.append(np.log((100 + coupon[i]/freq)/(price[i] - pv_cf)) / years[i])\n",
    "\n",
    "cc_ytm = np.array(cc_ytm)\n",
    "print(\"Implied Spot Rates (c.c.) = \",cc_ytm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Discount Factors =  [0.949      0.9        0.85196154 0.80560595]\n",
      "Implied Spot Rates (s.a.) =  [0.11036963 0.11111111 0.112722   0.11413718]\n",
      "Implied Spot Rates (c.c.) =  [0.10469296 0.10536052 0.10680926 0.10808028]\n"
     ]
    }
   ],
   "source": [
    "# Using Discount Factors\n",
    "df = [price[0]/100, price[1]/100]\n",
    "\n",
    "for i in range(2, len(coupon)):\n",
    "    pv_cf = np.sum(np.full(int(years[i]*freq)-1, coupon[i]/freq) * np.array(df))\n",
    "    df.append((price[i] - pv_cf) / (100 + coupon[i]/freq))\n",
    "    \n",
    "df = np.array(df)\n",
    "print(\"Discount Factors = \",df)\n",
    "\n",
    "spots = df**-(1/years) - 1\n",
    "print(\"Implied Spot Rates (s.a.) = \",spots)\n",
    "\n",
    "spots_cc = np.log(1/df) / years\n",
    "print(\"Implied Spot Rates (c.c.) = \",spots_cc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the third bond which matures in 1.5 years there are three payments of USD 4, USD 4 and USD 104 at t = 0.50, 1.00 and 1.50, respectively. Since the discount rates at t = 0.50 and 1.00 are already available from the previous calculations, the rate $r_{1.50}$ for $t = 1.50$ can be computed by solving $96 = 4e^{-0.1047\\times 0.5} + 4e^{-0.1054\\times 1.0} + 4e^{-r_{1.50}\\times 1.5}$ for $r_{1.50}$ which gives $r_{1.50} = 0.1086$. In a similar fashion, it is straightforward to calculate $r_{2.00}= 0.1081$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Second Example**\n",
    "\n",
    "| Bond No. | Time to Maturity (Years) | Annual Coupon (Dollars) | Bond Price (Dollars) |\n",
    "| -------- | ------------------------ | ----------------------- | -------------------- |\n",
    "| 1        | 0.50                     | 0                       | 99.00                |\n",
    "| 2        | 1.00                     | 0                       | 97.80                |\n",
    "| 3        | 1.50                     | 4                       | 102.50               |\n",
    "| 4        | 2.00                     | 5                       | 105.00               |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "years = np.array([0.5, 1.0, 1.5, 2.0])\n",
    "coupon = np.array([0, 0, 4, 5])\n",
    "price = np.array([99, 97.80, 102.50, 105.00])\n",
    "face = np.full(4, 100)\n",
    "freq = 2\n",
    "\n",
    "r1 = np.log(100/price[0]) / 0.5\n",
    "r2 = np.log(100/price[1]) / 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Implied Spot Rates (c.c.) =  [0.02010067 0.02224561 0.02284449 0.02416379]\n"
     ]
    }
   ],
   "source": [
    "# Securities maturing in 0.5y and 1y are zero-coupons\n",
    "cc_ytm = [r1, r2]\n",
    "\n",
    "for i in range(2, len(coupon)):\n",
    "    pv_cf = np.sum(np.full(int(years[i]*freq)-1, coupon[i]/freq) * np.exp(-np.array(cc_ytm) * years[:i]))\n",
    "    cc_ytm.append(np.log((100 + coupon[i]/freq)/(price[i] - pv_cf)) / years[i])\n",
    "\n",
    "cc_ytm = np.array(cc_ytm)\n",
    "print(\"Implied Spot Rates (c.c.) = \",cc_ytm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the bootstrap succeeded because there were four equations and four unknown yields. What if in our example we had a 2.75-year bond (with coupon payments at 0.25, 0.75, 1.25, 1.75, 2.25); or what if the 0.50-year T-bill did not exist? (This methodology can also straightforwardly deal with extrapolation. This would, for example, be necessary if we had a 2.75-year bond, since the first cash flow would come before any of the known yields.) Given that the textbook bootstrap can no longer be applied in such a case, the generalized bootstrap methods covered here can easily deal with such problems. Naturally, the generality of our method implies that simpler problems — easily amenable to the textbook bootstrap method — can also be solved in essentially one step instead of sequentially.\n",
    "\n",
    "In the general model, the necessity to use natural cubic spline interpolation for certain quantities along with bond price equations requires non-linear root solving. The program we will use for this purpose is SciPy's cubic spline interpolation function `scipy.interpolate.CubicSpline` and SciPy's `scipy.optimize.fsolve`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mathematical Representation of the General Method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A particular bond can be characterized by its maturity, annual coupons, the time sequence of coupon payments and its price. Thus, if we have data on $K$ bonds, the $i\\text{th}$ bond $B_{i}$ can be represented using vector notation as:\n",
    "$$B_{i} = [n_{i}, c_{i}, \\mathbf{t}_{i}, p_{i}], \\space i = 1,\\cdots,K.$$\n",
    "\n",
    "Here, $n_{i}$ is the number of coupon payments, $c_{i}$ is the annual coupon (in dollars), the time vector $\\mathbf{t}_{i} = [t_{i,1}, \\cdots , t_{i,n_{i}}]$ is the list of occurrence times of coupon payments (in years) with $t_{i,j}$ being the time of the $j\\text{th}$ coupon payment, and $p_{i}$ is the bond price (in dollars). Note that $t_{i,n_{i}}$ is the maturity of the $i\\text{th}$ bond and if $n_{i} = 1$, then the $i\\text{th}$ bond is zero-coupon implying $c_{i} = 0$. Conversely, if $c_{i} = 0$ for bond $i$, then $n_{i} = 1$ and the bond is zero-coupon. We assume throughout our discussion that the bonds are listed in increasing order of their maturity dates, i.e., $t_{1,n_{1}} < t_{2,n_{2}} < \\cdots < t_{K,n_{K}}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# B[i] = [n[i], c[i], t[i], p[i]], i = 0, 1, ..., K\n",
    "K = 5\n",
    "n = [1, 2, 3, 4, 6]\n",
    "c = [0, 2, 8, 12, 10]\n",
    "t = [[0.25],\n",
    "     [0.50, 1.00],\n",
    "     [0.50, 1.00, 1.50],\n",
    "     [0.50, 1.00, 1.50, 2.00],\n",
    "     [0.25, 0.75, 1.25, 1.75, 2.25, 2.75]]\n",
    "p = [97.5, 90.0, 96.0, 101.6, 99.8]\n",
    "\n",
    "# We assume that bonds are listed in increasing order of their maturity dates\n",
    "B = [[n[i], c[i], t[i], p[i]] for i in range(K)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the available information on the $K$ bonds, we can write $K$ nonlinear equations that relate the price of a bond to other data. Dfining $r_{j}$ as the discount rate (to be determined) for the payment at the end of $t_{j}$ time units (years), we have\n",
    "\n",
    "$$p_{i}=\\sum_{j=1}^{n_{i}-1}\\frac{1}{2}c_{i}e^{(-r_{j} \\dot t_{i,j})} + (100 + \\frac{1}{2}c_{i})\\dot e^{(-r_{n_{i}}\\dot t_{i,n_{i}})},\\space i=1,\\cdots,K.$$\n",
    "\n",
    "In the unlikely case that the number of unknown $r_{j}\\text{s}$ is equal to the number of equations, this system can be solved to obtain the discount rates. This, however, is an exception rather than the rule, and the number of unknowns generally exceeds the number of equations. Thus, we now examine the more general case where additional equations must be introduced (via cubic spline interpolation) in order to solve the nonlinear system of equations.\n",
    "\n",
    "For each bond $i$ , we define a set $\\mathcal{T}_{i}= \\left\\{ t_{i,1},\\cdots, t_{i,n_{i}} \\right\\}$ that is obtained from the bond’s time vector $\\mathbf{t}_{i}= \\left\\{ t_{i,1},\\cdots, t_{i,n_{i}} \\right\\}$. Thus, the union $\\mathcal{T} = \\cup_{i=1}^{K}\\mathcal{T}_{i}=\\left\\{ t_{1}, t_{2},\\cdots, t_{N} \\right\\}$ is the set of all distinct time points at which a coupon and/or face value payment is made for some bond. The cardinality of $\\mathcal{T}$ is $|T| = N$ which corresponds to the total number of distinct times at which coupons and/or face value are paid. The elements of the set $\\mathcal{T}$ are listed in an increasing order as $[t_{1}, t_{2},\\cdots,t_{N}]$. Clearly, any element $t_{i,j}$ of the vector $\\mathbf{t}_{i}$ for bond $i$ defined above can be found in the set $\\mathcal{T}_{i}=\\left\\{ t_{1}, t_{2},\\cdots, t_{N} \\right\\}$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# T - Distinct time points at which a coupon and/or face value payment is made\n",
    "T = np.unique(np.hstack(t))\n",
    "T.sort()\n",
    "# N - Total number of distinct times at which coupons and/or face value are paid & Total number of equations\n",
    "N = len(T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When $K < N$ the system of $K$ nonlinear equations produced by the bond price equation is ‘underdetermined’ since there are fewer equations than there are unknowns. In such a case, additional equations can be introduced by **interpolating some of the intermediate maturities**.\n",
    "\n",
    "We can note that many of the elements in the set $\\mathcal{T}$ correspond to the maturities of the $K$ different bonds, namely, $t_{1,n_{1}}, t_{2,n_{2}}, \\cdots , t_{K,n_{K}}$. We denote the set of maturities of the $K$ bonds by $\\mathcal{K} = t_{1,n_{1}}, t_{2,n_{2}}, \\cdots , t_{K,n_{K}}$ with cardinality $|\\mathcal{K}| = K$.\n",
    "\n",
    "Naturally, for each of these time points we have exactly one nonlinear equation produced by the bond pricing equation. For the remaining $L = N - K$ maturities we can develop $L = N - K$ additional equations using some form of natural spline interpolation as we will see below. This would bring the total number of equations to $K + (N - K) = N$ which matches the total number $N$ of unknowns. (By substituting the system of cubic spline equations into the bond pricing equation, we effectively reduce the problem to the solution of $K$ non-linear equations.)\n",
    "\n",
    "We denote the set of those points for which interpolation is necessary by $\\mathcal{L} = \\left\\{t_{j} : t_{j} \\in \\mathcal{T} \\space \\text{and} \\space t_{j} \\notin \\mathcal{K}\\right\\}$. Solving the resulting $N$ equations in\n",
    "$N$ unknowns would produce the points $r_{j}$ on the yield curve for each maturity $t_{j}$ ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set of maturities of the K bonds\n",
    "# For each of these time points (k) we have exactly one nonlinear equation\n",
    "k =  [t[i][-1] for i in range(K)]\n",
    "k.sort()\n",
    "\n",
    "# For the remaining L = N - K maturities we can develop L = N - K additional equations using some form of natural spline interpolation\n",
    "L = N - K\n",
    "# This would bring the total number of equations to K + (N - K) = N which matches the total number N of unknowns.\n",
    "# We denote the set of those points for which interpolation is necessary by l = {t[i][j] : t[i][j] ∈ T and t[i][j] ∉ k}.\n",
    "l = list(set(T) - set(k))\n",
    "l.sort()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example 1**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solved values:\n",
      "[10.13 11.53 12.5  12.59 11.63 10.61 10.44 10.73 10.9  10.82]\n"
     ]
    }
   ],
   "source": [
    "# Inputs\n",
    "K = 5\n",
    "n = [1, 2, 3, 4, 6]\n",
    "c = [0, 2, 8, 12, 10]\n",
    "t = [[0.25],\n",
    "     [0.50, 1.00],\n",
    "     [0.50, 1.00, 1.50],\n",
    "     [0.50, 1.00, 1.50, 2.00],\n",
    "     [0.25, 0.75, 1.25, 1.75, 2.25, 2.75]]\n",
    "p = [97.5, 90.0, 96.0, 101.6, 99.8]\n",
    "\n",
    "B = [[n[i], c[i], t[i], p[i]] for i in range(K)]\n",
    "\n",
    "# Computing Continuous Rates of Available Zero-Coupon Bonds - Used as Guess Input\n",
    "r1 = np.log(100/p[0]) / t[0][0]\n",
    "# Used to Collect all Rates\n",
    "r = [r1]\n",
    "\n",
    "# Ordered Set of all Unique Time Points from t Input\n",
    "T = list(set().union(*t))\n",
    "T.sort()\n",
    "N = len(T)\n",
    "\n",
    "# Set of Maturities of the K Bonds\n",
    "k =  [t[i][-1] for i in range(K)] # Used as x-axis input in natural cubic spline to determine the shape of the curve\n",
    "k.sort()\n",
    "\n",
    "# Set of Unique Time Points ∈ T and ∉ K - Interpolation Points\n",
    "l = list(set(T) - set(k)) # Cubic Spline output = CS(l[i])\n",
    "l.sort()\n",
    "\n",
    "# Define the System of Equation\n",
    "def equations(unknowns):\n",
    "    r1, r2, r3, r4, r5 = unknowns\n",
    "    \n",
    "    # Calculate the natural cubic spline interpolation coefficients\n",
    "    cs = CubicSpline(k, [r1, r2, r3, r4, r5], bc_type='natural')\n",
    "    \n",
    "    # Solve for interpolated r values corresponding to l\n",
    "    r6 = cs(l[0])\n",
    "    r7 = cs(l[1])\n",
    "    r8 = cs(l[2])\n",
    "    r9 = cs(l[3])\n",
    "    r10 = cs(l[4])\n",
    "\n",
    "    # Define the bond pricing equations such that price - calculated price (given r) = 0\n",
    "    eq1 = 97.5 - 100 * np.exp(-r1 * 0.25)\n",
    "    eq2 = 90.0 - (1 * np.exp(-r6 * 0.50) + 101 * np.exp(-r2 * 1))\n",
    "    eq3 = 96.0 - (4 * np.exp(-r6 * 0.50) + 4 * np.exp(-r2 * 1) + 104 * np.exp(-r3 * 1.5))\n",
    "    eq4 = 101.6 - (6 * np.exp(-r6 * 0.50) + 6 * np.exp(-r2 * 1) + 6 * np.exp(-r3 * 1.5) + 106 * np.exp(-r4 * 2))\n",
    "    eq5 = 99.8 - (5 * np.exp(-r1 * 0.25) + 5 * np.exp(-r7 * 0.75) + 5 * np.exp(-r8 * 1.25) + \n",
    "                   5 * np.exp(-r9 * 1.75) + 5 * np.exp(-r10 * 2.25) + 105 * np.exp(-r5 * 2.75))\n",
    "    \n",
    "    return [eq1, eq2, eq3, eq4, eq5]\n",
    "\n",
    "# Step 3: Solve the system of equations\n",
    "r_guess = np.zeros(5)  # r1, r2, r3, r4, r5\n",
    "solution = fsolve(equations, r_guess)\n",
    "r1, r2, r3, r4, r5 = solution\n",
    "\n",
    "# Calculate r6, r7, r8, r9, r10 using the cubic spline\n",
    "cs = CubicSpline(k, [r1, r2, r3, r4, r5], bc_type='natural')\n",
    "r6, r7, r8, r9, r10 = cs(l)\n",
    "\n",
    "# Step 4: Output the results\n",
    "print(\"Solved values:\")\n",
    "res = np.array([r1, r6, r7, r2, r8, r3, r9, r4, r10, r5]) * 100\n",
    "print(res.round(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_k = [r1, r2, r3, r4, r5]\n",
    "r_l = [r6, r7, r8, r9, r10]\n",
    "\n",
    "t_linspace = np.linspace(0.25, 2.75)\n",
    "r_interp = CubicSpline(k, r_k, bc_type=\"natural\")(t_linspace)\n",
    "\n",
    "plt.plot(k, r_k, 'o', label='Spot Rate Curve')\n",
    "plt.plot(l, r_l, 'o', label='Computed Spot Rates')\n",
    "plt.plot(t_linspace, r_interp, label=\"Interpolated Curve\")\n",
    "plt.xlabel('Maturity (Years)')\n",
    "plt.ylabel('Spot Rate (%)')\n",
    "plt.title('Interpolated Yield Curve using Cubic Spline')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example 1 - Optimized**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = [1, 2, 3, 4, 6]\n",
    "c = [0, 2, 8, 12, 10]\n",
    "t = [[0.25],\n",
    "     [0.50, 1.00],\n",
    "     [0.50, 1.00, 1.50],\n",
    "     [0.50, 1.00, 1.50, 2.00],\n",
    "     [0.25, 0.75, 1.25, 1.75, 2.25, 2.75]]\n",
    "p = [97.5, 90.0, 96.0, 101.6, 99.8]\n",
    "per = 2\n",
    "\n",
    "r = {t[i][0]: np.log(100/p[i]) / t[i][0] for i in range(4)}\n",
    "\n",
    "K = 5\n",
    "T = np.unique(np.hstack(t)) # list(set().union(*t))\n",
    "T.sort()\n",
    "N = len(T)\n",
    "k =  [t[i][-1] for i in range(K)]\n",
    "k.sort()\n",
    "l = list(set(T) - set(k))\n",
    "l.sort()\n",
    "\n",
    "def f(r_k):\n",
    "    cs = CubicSpline(k, r_k, bc_type='natural')  \n",
    "    r_l = cs(l)\n",
    "    r.update({timings: rates for timings, rates in zip(k, r_k)})\n",
    "    r.update({timings: rates for timings, rates in zip(l, r_l)})\n",
    "\n",
    "    res = []\n",
    "    for (price, coupon, timings) in zip(p, c, t):\n",
    "        app_r = [r[i] for i in timings]\n",
    "        app_r, timings = np.array(app_r), np.array(timings)\n",
    "        cf = np.full(len(timings), coupon/per)\n",
    "        cf[-1] += 100\n",
    "        pv_cf = np.sum(cf * np.exp(-app_r * timings))\n",
    "        res.append(price - pv_cf)\n",
    "    \n",
    "    return res\n",
    "\n",
    "r_guess = np.append(list(dict.values(r)), np.zeros(K-len(r)))\n",
    "spots = fsolve(f, r_guess)\n",
    "\n",
    "spot_mat = np.linspace(0.25, 2.75, 100)\n",
    "spot_interp = CubicSpline(k, spots, bc_type=\"natural\")(spot_mat)\n",
    "\n",
    "full_spots = [r[i] for i in T]\n",
    "forwards = np.array([ ((full_spots[i] * T[i]) - (full_spots[i-1] * T[i-1])) / (T[i] - T[i-1]) for i in range(1, N)])\n",
    "\n",
    "fwd_mat = np.linspace(0.25, 2.75, 100)\n",
    "fwd_interp = CubicSpline(T[1:], forwards, bc_type=\"natural\")(fwd_mat)\n",
    "\n",
    "plt.plot(k, spots, 'o', label='Spot Rates')\n",
    "plt.plot(spot_mat, spot_interp, label=\"Interpolated Spot Curve\")\n",
    "plt.plot(fwd_mat, fwd_interp, \"--\", label=\"Forward Curve\")\n",
    "plt.xlabel('Maturity (Years)')\n",
    "plt.ylabel('Spot Rate (%)')\n",
    "plt.title('Interpolated Yield Curve using Cubic Spline')\n",
    "plt.xlim((0,max(k)))\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example 2**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.10469296 0.10536052 0.10680926 0.10808028]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = [0, 0, 8, 12]\n",
    "t = [[0.5],\n",
    "     [1.0],\n",
    "     [0.5, 1.0, 1.5],\n",
    "     [0.5, 1.0, 1.5, 2.0]]\n",
    "p = [94.90, 90.00, 96.00, 101.60]\n",
    "per = 2\n",
    "\n",
    "r = {t[i][0]: np.log(100/p[i]) / t[i][0] for i in range(4)}\n",
    "\n",
    "K = 4\n",
    "T = np.unique(np.hstack(t)) # list(set().union(*t))\n",
    "T.sort()\n",
    "N = len(T)\n",
    "k =  [t[i][-1] for i in range(K)]\n",
    "k.sort()\n",
    "L = N - K \n",
    "l = list(set(T) - set(k))\n",
    "l.sort()\n",
    "\n",
    "\n",
    "def f(r_k):\n",
    "    cs = CubicSpline(k, r_k, bc_type='natural')  \n",
    "    r_l = cs(l)\n",
    "    r.update({timings: rates for timings, rates in zip(k, r_k)})\n",
    "    r.update({timings: rates for timings, rates in zip(l, r_l)})\n",
    "\n",
    "    res = []\n",
    "    for (price, coupon, timings) in zip(p, c, t):\n",
    "        app_r = [r[i] for i in timings]\n",
    "        app_r, timings = np.array(app_r), np.array(timings)\n",
    "        cf = np.full(len(timings), coupon/per)\n",
    "        cf[-1] += 100\n",
    "        pv_cf = np.sum(cf * np.exp(-app_r * timings))\n",
    "        res.append(price - pv_cf)\n",
    "    \n",
    "    return res\n",
    "\n",
    "r_guess = np.append(list(dict.values(r)), np.zeros(K-len(r)))\n",
    "spots = fsolve(f, r_guess)\n",
    "print(spots)\n",
    "\n",
    "spot_mat = np.linspace(0.25, 2.75, 100)\n",
    "spot_interp = CubicSpline(k, spots, bc_type=\"natural\")(spot_mat)\n",
    "\n",
    "full_spots = [r[i] for i in T]\n",
    "forwards = np.array([ ((full_spots[i] * T[i]) - (full_spots[i-1] * T[i-1])) / (T[i] - T[i-1]) for i in range(1, len(T))])\n",
    "\n",
    "fwd_mat = np.linspace(0.25, 2.75, 100)\n",
    "fwd_interp = CubicSpline(T[1:], forwards, bc_type=\"natural\")(fwd_mat)\n",
    "\n",
    "plt.plot(k, spots, 'o', label='Spot Rates')\n",
    "plt.plot(spot_mat, spot_interp, label=\"Interpolated Spot Curve\")\n",
    "plt.plot(fwd_mat, fwd_interp, \"--\", label=\"Forward Curve\")\n",
    "plt.xlabel('Maturity (Years)')\n",
    "plt.ylabel('Spot Rate (%)')\n",
    "plt.title('Interpolated Yield Curve using Cubic Spline')\n",
    "plt.xlim((0,max(k)))\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example 3**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.13447071 0.12967957 0.12651868 0.12036136 0.11672696 0.1103297\n",
      " 0.10240416 0.10357446]\n",
      "{0.08: np.float64(0.1344707081620012), 0.25: np.float64(0.12967956502444486), 0.5: np.float64(0.12651867927838173), 1.0: np.float64(0.12036135667118394), np.float64(2.0): np.float64(0.11672695573098511), np.float64(4.0): np.float64(0.11032970044562437), np.float64(7.5): np.float64(0.10240415639089699), np.float64(18.0): np.float64(0.1035744619182917), np.float64(1.5): np.float64(0.11734309495459438), np.float64(2.5): np.float64(0.11578030322928108), np.float64(3.0): np.float64(0.11419766459665945), np.float64(3.5): np.float64(0.11228035770986047), np.float64(4.5): np.float64(0.10859264381689251), np.float64(5.0): np.float64(0.10709867138141073), np.float64(5.5): np.float64(0.10582289983312601), np.float64(6.0): np.float64(0.10474044586598531), np.float64(6.5): np.float64(0.10382642617393559), np.float64(7.0): np.float64(0.10305595745092383), np.float64(8.0): np.float64(0.10184954258518444), np.float64(8.5): np.float64(0.10138424721464512), np.float64(9.0): np.float64(0.10100380435752036), np.float64(9.5): np.float64(0.1007037480920515), np.float64(10.0): np.float64(0.1004796124964799), np.float64(10.5): np.float64(0.10032693164904687), np.float64(11.0): np.float64(0.10024123962799378), np.float64(11.5): np.float64(0.10021807051156194), np.float64(12.0): np.float64(0.10025295837799268), np.float64(12.5): np.float64(0.10034143730552739), np.float64(13.0): np.float64(0.10047904137240735), np.float64(13.5): np.float64(0.10066130465687394), np.float64(14.0): np.float64(0.10088376123716847), np.float64(14.5): np.float64(0.10114194519153229), np.float64(15.0): np.float64(0.10143139059820676), np.float64(15.5): np.float64(0.10174763153543319), np.float64(16.0): np.float64(0.10208620208145291), np.float64(16.5): np.float64(0.10244263631450728), np.float64(17.0): np.float64(0.10281246831283768), np.float64(17.5): np.float64(0.10319123215468534)}\n",
      "[0.12742491 0.12335779 0.11420403 0.11130657 0.11487854 0.11199369\n",
      " 0.10628447 0.10077652 0.0966751  0.09469619 0.09365292 0.09306518\n",
      " 0.09283345 0.09285819 0.09303986 0.09327894 0.09353034 0.09393952\n",
      " 0.09453628 0.09530274 0.09622104 0.09727331 0.09844171 0.09970835\n",
      " 0.10105538 0.10246493 0.10391914 0.10540015 0.10689009 0.1083711\n",
      " 0.10982531 0.11123486 0.11258189 0.11384853 0.11501692 0.1160692\n",
      " 0.1169875 ]\n"
     ]
    }
   ],
   "source": [
    "n = [1, 1, 1, 1, 4, 8, 15, 36]\n",
    "c = [0, 0, 0, 0, 12.05, 11.45, 10.74, 10.64]\n",
    "t = [[0.08],\n",
    "     [0.25],\n",
    "     [0.50],\n",
    "     [1.00],\n",
    "     [i for i in np.arange(0.5, 2.5, 0.5)],\n",
    "     [i for i in np.arange(0.5, 4.5, 0.5)],\n",
    "     [i for i in np.arange(0.5, 8, 0.5)],\n",
    "     [i for i in np.arange(0.5, 18.5, 0.5)]]\n",
    "p = [98.93, 96.81, 93.87, 88.66, 100, 100, 100, 100]\n",
    "per = 2 # Coupon frequency\n",
    "\n",
    "r = {t[i][0]: np.log(100/p[i]) / t[i][0] for i in range(4)}\n",
    "\n",
    "# K - Number of Bonds & Number of nonlinear equations formed using bond price function\n",
    "K = 8\n",
    "# T - Distinct time points at which a coupon and/or face value payment is made\n",
    "T = np.unique(np.hstack(t)) # list(set().union(*t))\n",
    "T.sort()\n",
    "# N - Total number of distinct times at which coupons and/or face value are paid & Total number of equations\n",
    "N = len(T)\n",
    "# k - Set of Maturities of the K bonds, len(k) == K\n",
    "k =  [t[i][-1] for i in range(K)]\n",
    "k.sort()\n",
    "# L - Number of linear equations formed using natural cubic spline interpolation\n",
    "L = N - K # K non-linear equations, L linear equations (cubic spline), and N number of equations\n",
    "# l - Set of time points where interpolation is necessary\n",
    "l = list(set(T) - set(k))\n",
    "l.sort()\n",
    "\n",
    "# Step 1: Define x and y values\n",
    "x_k = np.array(k)\n",
    "x_l = np.array(l)\n",
    "\n",
    "# Step 2: Define the equations for solving\n",
    "def f(r_k):\n",
    "    # Calculate the spline interpolated values\n",
    "    cs = CubicSpline(x_k, r_k, bc_type='natural')  \n",
    "    r_l = cs(x_l)\n",
    "    # Assigned interest rates to each element of t: (x_k to r_k) + (x_l to r_l)\n",
    "    r.update({timings: rates for timings, rates in zip(x_k, r_k)})\n",
    "    r.update({timings: rates for timings, rates in zip(x_l, r_l)})\n",
    "    \n",
    "    # Non-linear equation - Results of given price minus spot rate computed price should equal 0\n",
    "    res = []\n",
    "    import operator\n",
    "    for (price, coupon, timings) in zip(p, c, t):\n",
    "        get = operator.itemgetter(*timings)\n",
    "        app_r = get(r)\n",
    "        app_r, timings = np.array(app_r), np.array(timings)\n",
    "        cf = np.full(len(timings), coupon/per)\n",
    "        cf[-1] += 100\n",
    "        pv_cf = np.sum(cf * np.exp(-app_r * timings))\n",
    "        res.append(price - pv_cf)\n",
    "    return res\n",
    "\n",
    "# Step 3: Solve the system of equations\n",
    "y_guess = np.append(list(dict.values(r)), np.zeros(K-len(r)))\n",
    "solution = fsolve(f, y_guess)\n",
    "\n",
    "print(solution)\n",
    "print(r)\n",
    "\n",
    "# Forward Rate Calculation - Using Approximation Formula f_t1t2 = [(r_t0t2 * t2) - (r_t01 * t1)] / (t2 - t1)\n",
    "spots = [r[i] for i in T]\n",
    "forwards = np.array([ ((spots[i] * T[i]) - (spots[i-1] * T[i-1])) / (T[i] - T[i-1]) for i in range(1, len(T))])\n",
    "print(forwards)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = [1, 1, 1, 1, 4, 8, 15, 36]\n",
    "c = [0, 0, 0, 0, 12.05, 11.45, 10.74, 10.64]\n",
    "t = [[0.08],\n",
    "     [0.25],\n",
    "     [0.50],\n",
    "     [1.00],\n",
    "     [i for i in np.arange(0.5, 2.5, 0.5)],\n",
    "     [i for i in np.arange(0.5, 4.5, 0.5)],\n",
    "     [i for i in np.arange(0.5, 8, 0.5)],\n",
    "     [i for i in np.arange(0.5, 18.5, 0.5)]]\n",
    "p = [98.93, 96.81, 93.87, 88.66, 100, 100, 100, 100]\n",
    "per = 2\n",
    "\n",
    "r = {t[i][0]: np.log(100/p[i]) / t[i][0] for i in range(4)}\n",
    "\n",
    "K = 8\n",
    "T = np.unique(np.hstack(t)) # list(set().union(*t))\n",
    "T.sort()\n",
    "N = len(T)\n",
    "k =  [t[i][-1] for i in range(K)]\n",
    "k.sort()\n",
    "L = N - K \n",
    "l = list(set(T) - set(k))\n",
    "l.sort()\n",
    "\n",
    "\n",
    "def f(r_k):\n",
    "    cs = CubicSpline(k, r_k, bc_type='natural')  \n",
    "    r_l = cs(l)\n",
    "    r.update({timings: rates for timings, rates in zip(k, r_k)})\n",
    "    r.update({timings: rates for timings, rates in zip(l, r_l)})\n",
    "\n",
    "    res = []\n",
    "    for (price, coupon, timings) in zip(p, c, t):\n",
    "        app_r = [r[i] for i in timings]\n",
    "        app_r, timings = np.array(app_r), np.array(timings)\n",
    "        cf = np.full(len(timings), coupon/per)\n",
    "        cf[-1] += 100\n",
    "        pv_cf = np.sum(cf * np.exp(-app_r * timings))\n",
    "        res.append(price - pv_cf)\n",
    "    \n",
    "    return res\n",
    "\n",
    "r_guess = np.append(list(dict.values(r)), np.zeros(K-len(r)))\n",
    "spots = fsolve(f, r_guess)\n",
    "\n",
    "spot_mat = np.linspace(0.08, 18, 100)\n",
    "spot_interp = CubicSpline(k, spots, bc_type=\"natural\")(spot_mat)\n",
    "\n",
    "full_spots = [r[i] for i in T]\n",
    "forwards = np.array([ ((full_spots[i] * T[i]) - (full_spots[i-1] * T[i-1])) / (T[i] - T[i-1]) for i in range(1, len(T))])\n",
    "\n",
    "fwd_mat = np.linspace(0.25, 18, 100)\n",
    "fwd_interp = CubicSpline(T[1:], forwards, bc_type=\"natural\")(fwd_mat)\n",
    "\n",
    "plt.plot(k, spots, 'o', label='Spot Rates')\n",
    "plt.plot(spot_mat, spot_interp, label=\"Interpolated Spot Curve\")\n",
    "plt.plot(fwd_mat, fwd_interp, \"--\", label=\"Forward Curve\")\n",
    "plt.xlabel('Maturity (Years)')\n",
    "plt.ylabel('Spot Rate (%)')\n",
    "plt.title('Interpolated Yield Curve using Cubic Spline')\n",
    "plt.xlim((0,max(k)))\n",
    "plt.ylim((0,0.15))\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example 4**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jj9i2bVuR5iVptdoCE8fBGLeln7XCPjuWkol8+ReFnDt3juDg4Nv26Xbs7e2Jjo7mgw8+4ODBg0XqH1hOeEqCt7c3Tk5OLFy4sNDtovTISJK4J/L/iN082uLs7Ez79u3Zu3cv9evXp2nTpgUexfnls3z5crPXW7du5cyZM6YracLDw3FycjKbGAnGX7B//PEHDz/8cKFt5/+RvTm5+fTTTwvULSzexx57DKUUCQkJFmOtV68eYFzrSKvVFhpPaWnVqhUVKlTg8OHDFvvXtGnTQkek7rbPjRs3pkuXLixYsIA//vjDYp1du3YRHx8PYEq69u/fb1Zn9erVtz3WjfKT9B9++IFNmzaxa9cuhg4dalbnscceIyUlBb1eb/E9qVGjxi2PERoaytGjR80ShpSUFLZu3VroPi4uLnTp0oXx48eTm5vLoUOHihWXJW3btiU9Pb3AFYdffvllkfYfM2YMLi4uREZGWkz6lFJmSwCEhoYW+P4cPXq00In8K1euNJuIfObMGbZu3XrLhUg7duyIra0tc+fOLVIMN7L0zxJcP3UeGBhoVn7o0KEC63StWLECNze3Ulu36rHHHuPEiRN4eXlZ/OyV1j9MwkhGksQ94ebmRkhICD/++CMPP/wwnp6eeHt7ExoayuzZs3nwwQdp3bo1zz33HKGhoaSnp3P8+HFWr15d6B9MS3bt2sXw4cN58sknOXv2LOPHjycoKIjIyEgAKlSowIQJE3j99dcZOHAgTz/9NCkpKUyaNAmtVmuav2NJREQEFStWZOTIkURHR2Nvb8/y5cstLm6Yn+y8++67dOnSBVtbW+rXr0+rVq145plnGDJkCLt27aJNmza4uLiQmJjI5s2bqVevHs899xwVK1bklVdeYerUqWbxTJw4sdin24rD1dWVjz76iEGDBnHp0iV69eqFr68vFy9e5K+//uLixYuF/jEqiT4vXbqUzp0706VLF4YOHUqXLl2oWLEiiYmJrF69mpUrV7J7924qV65M165d8fT0ZNiwYUyePBk7OzsWL17M2bNnix330KFDeffdd+nbty9OTk4FrvZ66qmnWL58OV27duWll16iefPm2Nvbc+7cOdavX0/37t3p0aNHoe0PGDCATz/9lP79+zNixAhSUlKYPn067u7uZvVGjBiBk5MTrVq1IiAggKSkJKZNm4aHhwfNmjUrdlw3GzRoEB988AH9+/dn6tSpVKtWjV9//ZW1a9cCBS97v1lYWBhffvklffr0oWHDhrzwwgs0atQIMF6lunDhQpRSpvdiwIAB9O/fn8jISHr27MmZM2eYPn16oWsGXbhwgR49ejBixAhSU1OJjo5Gq9Uybty4QvsUGhrK66+/zpQpU8jKyuLpp5/Gw8ODw4cPk5ycfMtFXTt16kSlSpXo1q0bNWvWxGAwsG/fPt5//31cXV156aWXzOoHBgbyv//9j4kTJxIQEMCyZcuIjY3l3XffxdnZ+Zbv3Z0aPXo03377LW3atGHMmDHUr18fg8FAfHw869at4+WXX6ZFixalcmyBXN0miq6wq9tcXFwK1LV05dFvv/2mGjVqpBwdHRVgdtXLqVOn1NChQ1VQUJCyt7dXPj4+KiIiwnRVmlLXr4D5+uuvC+3bunXr1IABA1SFChVMV7EdO3asQP3PP/9c1a9fXzk4OCgPDw/VvXt3dejQodvGsHXrVhUeHq6cnZ2Vj4+PGj58uNqzZ0+Bq1lycnLU8OHDlY+Pj9JoNAWubFm4cKFq0aKFcnFxUU5OTqpq1apq4MCBateuXaY6BoNBTZs2TQUHBysHBwdVv359tXr16kKvlCpMUd63G/umlFIbN25Ujz76qPL09FT29vYqKChIPfroo2ZtWNq3JPqclZWlPvzwQxUeHq7c3d2VnZ2dCgwMVE888YT65ZdfzOru2LFDRUREKBcXFxUUFKSio6PV559/bvHqtkcfffSWx42IiFBAoVdJ6XQ6NWPGDNWgQQOl1WqVq6urqlmzpnr22WctfsZutmTJElWrVi2l1WpV7dq11apVqwpc3bZkyRLVvn175efnpxwcHFRgYKDq3bu32r9/v6lOYVe3FfXnMD4+Xj3xxBPK1dVVubm5qZ49e6qYmBgFqB9//PG2cSil1IkTJ1RkZKSqVq2acnR0VE5OTqp27doqKiqqwOdh+vTpqkqVKkqr1aqmTZuqP/74o9Cr27744gs1atQo5ePjoxwdHVXr1q3NfiYKi0kppZYuXaqaNWtm+t40atTotlfrrVq1SvXt21c98MADytXVVdnb26vKlSurAQMGqMOHD5vVzf8MffPNN6pOnTrKwcFBhYaGqpkzZ5rVK87VbXXq1CnQp5s/E0oplZGRod544w1Vo0YN0++sevXqqTFjxqikpKRbxijujkYpWWRBlH2LFy9myJAh7Ny5k6ZNm1q7O0KUKW+//TZvvPEG8fHxJbaadXkTGhpK3bp1+fnnn63dFXEPyek2IYT4D/n4448BqFmzJjqdjj/++IMPP/yQ/v37S4IkxE0kSRJCiP8QZ2dnPvjgA06fPk1OTg6VK1fmtdde44033rB214S478jpNiGEEEIIC2QJACGEEEIICyRJEkIIIYSwQJIkIYQQQggLZOK2BQaDgfPnz+Pm5nbLW2AIIYQQ4v6hlCI9PZ3AwMDbLo5aFJIkWXD+/PkSuQeQEEIIIe69s2fPlsiSFpIkWZB/s8pTp07h6elp5d6ULJ1Ox7p16+jYsSP29vbW7k6JK8/xSWxlk8RWNklsZdOlS5cICwu77U2ni0qSJAvyT7G5ubkVuLdSWafT6XB2dsbd3b3c/XBA+Y5PYiubJLaySWIrm3Q6HUCJTZWRidtCCCGEEBZIkiSEEEIIYYEkSUIIIYQQFsicJCGEKCUGg4GcnBzs7OzIzs5Gr9dbu0slSqfTSWxlUFmPzcHBoUQu7y8KSZKEEKIU5ObmcurUKfR6Pf7+/pw9e7bcrbumlJLYyqCyHpuNjQ1hYWE4ODiU+rEkSRJCiBKmlCIxMRFbW1uCgoLIzMzE1dX1nv33e68YDAYyMjIktjKmLMeWv9hzYmIilStXLvUkT5IkIYQoYXl5eWRmZhIYGIizszN5eXlotdoy9wfpdgwGA7m5uRJbGVPWY/Px8eH8+fPk5eWV+hIGZe/dEUKI+1z+PI97cTpAiP+a/J+rezGfSpIkIYQoJWVxvocQ97t7+XMlSZIQQgghhAWSJAkhhBBCWCBJkhBC3Kf0BkXciRR+3JdA3IkU9AZVqse7cOECzz77LJUrV8bR0RF/f386depEXFxciR5n8ODBPP7440Wqp9Fo0Gg02NnZUblyZZ577jkuX75cKscT4mZydZsQQtyH1hxMZNLqwySmZpvKAjy0RHerTee6AaVyzJ49e6LT6ViyZAlVqlTh33//5ffff+fSpUulcryi6Ny5M4sWLSIvL4/Dhw8zdOhQrly5wsqVK63WJ/HfISNJQghxn1lzMJHnlu0xS5AAklKzeW7ZHtYcTCzxY165coXNmzfz7rvv0r59e0JCQmjevDnjxo3j0UcfNdXTaDTMnTuXLl264OLiQoMGDfj666/N2jpw4AAPPfQQTk5OeHl58cwzz5CRkQHAxIkTWbJkCT/++KNplGjDhg2F9it/RKtSpUp07NiRPn36sG7dOtN2vV7PsGHDCAsLw8nJiRo1ajB79mzT9lsdLyEhgT59+lCxYkW8vLzo3r07p0+fNu27efNmWrZsiYuLCxUqVKBVq1acOXPmLt5lUdZIkiSEEPcRvUExafVhLJ1Yyy+btPpwiZ96c3V1xdXVlR9++IGcnJxb1p0wYQI9e/Zk79699O7dm379+vH3338DkJmZSefOnalYsSI7d+7k66+/5rfffuOFF14A4JVXXqF379507tyZxMREEhMTiYiIKFIfT548yZo1a8zWxjEYDFSqVImvvvqKw4cP8+abb/L666/z1Vdf3fJ4mZmZtG/fHldXV/788082b96Mq6srnTt3Jjc3l7y8PPr160ebNm3Yv38/cXFxPPPMM3LF4n+MnG4TQoj7yI5TlwqMIN1IAYmp2ew4dYnwql4ldlw7OzsWL17MiBEjmDdvHo0bN6Zt27Y89dRT1K9f36zuk08+yfDhwzEYDIwfP55Nmzbx0UcfMWfOHJYvX05WVhZLly7FxcUFgI8//phu3brx7rvv4ufnh5OTEzk5Ofj7+9+2Xz///DOurq7o9Xqys43vy8yZM03b7e3tmTRpkul1WFgYW7du5auvvqJ37964urpaPN6yZcuwsbHh888/NyU+ixYtokKFCmzYsIHGjRuTlpbGo48+StWqVQGoVavWHb67oqySkSQhhLiPXEgvPEG6k3rF0bNnT86fP89PP/1Ep06dTMnC4sWLzeqFh4ebvW7ZsqVpJOnvv/+mQYMGpgQJoFWrVhgMBo4cOVLsPrVv3559+/axfft2XnzxRTp16sSLL75oVmfevHk0bdoUHx8fXF1d+eyzz4iPj79lu7t37+b48eO4ubmZRtE8PT3Jzs7mxIkTeHp60rdvX7p06UK3bt2YPXs2iYklf5pT3N+sniTNmTOHsLAwtFotTZo0YdOmTYXWTUxMpG/fvtSoUQMbGxtGjx59y7a//PJLNBqNXNUghCgzfN20JVqvuLRaLR06dODNN99k69atDB48mOjo6Nvulz8ao5Qq9JTUnZyqcnFxoVq1atSvX58PP/yQnJwcs5Gjr776ijFjxjB06FDWrVvHvn37GDJkCLm5ubds12Aw0KRJE/bt22f2OHr0KH379gXgk08+YcuWLURERLBq1SqqV6/Otm3bih2DKLusmiStWrWK0aNHM378ePbu3Uvr1q3p0qVLof8B5OTk4OPjw/jx42nQoMEt2z5z5gyvvPIKrVu3Lo2uCyFEqWge5kmAh5bC0gkNxqvcmod53pP+1K5dm6tXr5qV3ZwobN++nZo1a5rq79u3z2yfLVu2YGNjQ/Xq1QHjbSXu9JYS0dHRzJgxg/PnzwOwadMmIiIiiIyMpFGjRlSrVo0TJ06Y7WPpeI0bN+bYsWP4+vpSrVo1s4eHh4epXqNGjRg3bhxbt26lbt26rFix4o76LcomqyZJM2fOZNiwYQwfPpxatWoxa9YsgoODmTt3rsX6oaGhzJ49m4EDB5p9iG+m1+vp168fkyZNokqVKqXVfSGEKHG2Nhqiu9UGKJAo5b+O7lYbW5uSnUCckpLCQw89xLJly9i/fz+nTp3i66+/Zvr06XTv3t2s7tdff83ChQs5evQo06ZNY8eOHaaJ2f369UOr1TJo0CAOHjzI+vXrefHFFxkwYAB+fn6A8Xf5/v37OXLkCMnJyeh0uiL3s127dtSpU4e3334bgGrVqrFr1y7Wrl3L0aNHmTBhAjt37jTbx9Lx+vXrh7e3N927d2fTpk2cOnWKjRs38tJLL3Hu3DlOnTrFpEmTiIuL48yZM6xbt46jR4/KvKT/GKslSbm5uezevZuOHTualXfs2JGtW7feVduTJ0/Gx8eHYcOG3VU7QghhDZ3rBjC3f2P8PcxPqfl7aJnbv3GprJPk6upKixYt+OCDD2jTpg1169ZlwoQJjBgxgo8//tis7qRJk/jyyy9p2LAhK1eu5IsvvqB2bWNi5+zszNq1a7l06RLNmjWjV69ePPzww2ZtjBgxgho1apjmEW3ZsqVYfY2KiuKzzz7j7NmzjBw5kieeeII+ffrQokULUlJSiIyMNKtv6XjOzs78+eefVK5cmSeeeIJatWoxdOhQsrKycHd3x9nZmWPHjvHkk09SvXp1nnnmGV544QWeffbZO3yHRVlktavbkpOT0ev1pv8s8vn5+ZGUlHTH7W7ZsoUFCxawb9++Iu+Tk5NjdslrWloaADqdrlj/4ZQF+fGUt7jylef4JLayQ6fToZTCYDCglPFS/fzXRdWxth8P1/Rl5+lLXEjPwdfNkWahntjaaIrVTlHZ29vz1ltv8dZbb1ncfuMx/f39WbNmDUop0tPTcXNzM9tep04dfvvtt0Lb8PLyYs2aNYW2n2/hwoUWtz311FM89dRTptcLFixgwYIFZnXeeuut2x7P19eXRYsWWYzXxcWFZcuW4ebmVmAuVWm8//fSnX4m7xf5P1c6nQ5bW1uzbSX9O8TqSwDc/OG71aS/20lPT6d///589tlneHt7F3m/adOmmU0EzLd+/XqcnZ3vqC/3u9jYWGt3oVSV5/gktvufnZ0d/v7+ZGRkmCYQp6en31Fbtb3tqe1tXBfoasadtVHSsrKyTP9Mwp3HVhZIbPef3NxcsrKy+PPPP8nLyzPblpmZWaLHslqS5O3tja2tbYFRowsXLhQYXSqqEydOcPr0abp162Yqy8+S7ezsOHLkiGm9ixuNGzeOqKgo0+u0tDSCg4Np3749Xl4ltw7J/UCn0xEbG0uHDh3MFmQrL8pzfBJb2ZGdnc3Zs2dxdXXF0dHRNNpSXhYidHJywt3d3WwkqbzElk9iu39lZ2fj5OREmzZt0GrNT0mnpKSU6LGsliQ5ODjQpEkTYmNj6dGjh6k8Nja2wCTBoqpZsyYHDhwwK3vjjTdIT09n9uzZBAcHW9zP0dERR0fHAuX29vbl4he2JeU5Nijf8Uls9z+9Xo9Go8HGxsb0Ryj/dVmXf6oGrv8TWl5iu5HEdv/K/7my9PuipH9/WPV0W1RUFAMGDKBp06aEh4czf/584uPjGTlyJGAc4UlISGDp0qWmffLnGmVkZHDx4kX27duHg4MDtWvXRqvVUrduXbNjVKhQAaBAuRBCCCHErVg1SerTpw8pKSlMnjyZxMRE6tatS0xMDCEhIYBx8cib10xq1KiR6fnu3btZsWIFISEhZjclFEIIIYS4W1afuB0ZGVngcs18Ny+FD+ZDvUVhqQ0hhBBCiNspeycjhRBCCCHuAUmShBBCCCEskCRJCCGEEMICSZKEEEKUK6GhocyaNcsqx168eLHpqmpR9kmSJIQQAoDBgwfz+OOPF2ufihUr8sMPP5RKf+6Ve53YrF+/nvbt2+Pp6YmzszMPPPAAgwYNKrB69N3SaDRF/t6sX7+erl274uXlhbOzM7Vr1+bll18mISGhRPtU1kiSJIQQwurKy337bufQoUN06dKFZs2a8eeff3LgwAE++ugj7O3trXYftU8//ZRHHnkEf39/vv32Ww4fPsy8efNITU3l/fffv+N282/JU5ZJkiSEEMKidu3aMWrUKF599VU8PT3x9/dn4sSJpu1VqlQBoGfPnmg0GkJDQ03bVq9eTZMmTdBqtVSpUoVJkyaZjZRoNBrmzZtH9+7dcXFxYerUqWzYsAGNRsMvv/xCgwYN0Gq1tGjRosCdFL799lvq1KmDo6MjoaGht/1DPnPmTOrVq4eLiwvBwcFERkaSkZEBwIYNGxgyZAipqaloNBo0Go0pxtzcXF577TWCgoJwcXGhRYsWbNiwwaztxYsXU7lyZZydnenRo8dtb4sRGxtLQEAA06dPp27dulStWpXOnTvz+eef4+DgYGqzQoUK/PDDD1SvXh2tVkuHDh04e/asWVtz586latWqODg4UKNGDb744gvTtvzvRY8ePQp8b2507tw5Ro0axahRo1i4cCHt2rUjNDSUNm3a8Pnnn/Pmm28CMHHiRBo2bGi276xZs8zazR+JnDZtGoGBgVSvXp1x48bRsmXLAsetX78+0dHRpteLFi2iVq1aaLVaatasyZw5c275Pt4zShSQmpqqAJWcnGztrpS43Nxc9cMPP6jc3Fxrd6VUlOf4JLayIysrSx0+fFhlZWUpvV6vLl+6pPRZaUrlZNz7h8FQ5H4PGjRIde/e3fS6bdu2yt3dXU2cOFEdPXpULVmyRGk0GrVu3TqllFJJSUkKUAsWLFCJiYnqwoULSiml1qxZo9zd3dXixYvViRMn1Lp161RoaKiaOHGiqW1A+fr6qgULFqgTJ06o06dPq/Xr1ytA1apVS61bt07t379fPfbYYyo0NNT02di1a5eysbFRkydPVkeOHFGLFi1STk5OatGiRaa2Q0JC1AcffGB6/cEHH6g//vhDnTx5Uv3++++qRo0a6rnnnlNKKZWTk6NmzZql3N3dVWJiokpMTFTp6elKr9erXr16qYiICPXnn3+q48ePq/fee085Ojqqo0ePKqWU2rZtm9JoNGratGnqyJEjavbs2apChQrKw8Oj0Pd45cqVytHRUW3cuLHQOosWLVL29vaqadOmauvWrWrXrl2qefPmKiIiwlTnu+++U/b29uqTTz5RR44cUe+//76ytbVVf/zxh1JKqQsXLihALVq0yOx7o5QyfiYvX1Z6vV7NnDlTAer8+fOF9kcppaKjo1WDBg3Myj744AMVEhJiej1o0CDl6uqqBgwYoA4ePKgOHDigDhw4oAB1/PhxU72DBw8qQB05ckQppdT8+fNVQECA+vbbb9XJkyfVt99+qzw9PdXixYst9uXGn6+bJScnK0ClpqbeMp6isvpikkIIUe7lZWHzTi3rHPv18+Dgcse73/gf/wMPPMDHH3/M77//TocOHfDx8QGMt3/y9/c37fPWW28xduxYBg0aBBhHnKZMmcKrr75qNnrQt29fhg4danp96tQpAKKjo+nQoQMAS5YsoVKlSnz//ff07t2bmTNn8vDDDzNhwgQAqlevzuHDh3nvvfcYPHiwxRhGjx5teh4WFsaUKVN47rnnmDNnDg4ODnh4eKDRaMxiOHbsGN9++y3x8fFUqlQJgFdeeYU1a9awaNEi3n77bWbPnk2nTp0YO3asqS9bt25lzZo1hb6fTz75JGvXrqVt27b4+/vTsmVLHn74YQYOHIi7u7upnk6n4+OPP6ZFixam96FWrVrs2LGD5s2bM2PGDAYPHmxajDkqKopt27YxY8YM2rdvX+j35mbHjh3D3d2dgICAQusUh4uLi9moGBg/QytWrDB9z5YvX06zZs2oXr06AFOmTOH999/niSeeAIzfo8OHD/Ppp5+aPkPWIqfbhBBCFKp+/fpmrwMCArhw4cIt99m9ezeTJ0/G1dXV9BgxYgSJiYlkZmaa6jVt2tTi/uHh4abnnp6e1KhRg7///huAv//+m1atWpnVb9WqFceOHUOv11tsb/369XTo0IGgoCDc3NwYOHAgKSkpXL16tdAY9uzZg1KKmjVrmsWxceNGTpw4YerLjX29ue+W2NrasmjRIs6dO8f06dMJDAzkrbfeok6dOiQmJprq2dnZmb0/NWvWpEKFCrd9H/K3F5VSynQT5pJQr149swQJoF+/fixfvtx0vJUrV9KvXz8ALl68yNmzZxk2bJjZ+zx16lTT+2xNMpIkhBClzc4Jw9hz1rnjur3z3e1+013VNRrNbScYGwwGJk2aZBoZuJFWqzU9d3Ep+ghX/h9yS3/U1S1uV3XmzBm6du3KyJEjmTJlCp6enmzevJlhw4bdcrK4wWDA1taWnTt3FngPXF1db3vc2wkKCmLAgAEMGDCAqVOnUr16debNm8ekSZNMdSwlLzeWWXofipvwVK9endTUVBITE285mmRjY1MgXkvvn6Xvad++fRk7dix79uwhKyuLs2fP8tRTTwGYPkufffaZadQsn62tbbFiKQ2SJAkhRGnTaIynvKyRJJUye3v7AiM4jRs35siRI1SrVu2O2ty2bRuVK1cG4PLlyxw9epSaNWsCULt2bTZv3mxWf+vWrVSvXt3iH9Vdu3aRl5fH+++/b0pSv/rqK7M6Dg4OBWJo1KgRer2eCxcu0LZtW4v9rF27Ntu2bSvQ9+KqWLEiAQEBZiNbeXl57Nq1i+bNmwNw5MgRrly5YnofatWqxebNmxk4cKBpn61bt1Kr1vXTupa+Nzfr1asXY8eOZfr06XzwwQcFtl+5coUKFSrg4+NDUlKSWSK2b9++IsVXqVIl2rRpw/Lly8nKyuKRRx7Bz88PAD8/P4KCgjh58qRpdOl+IkmSEEKIO1a5cmX++OMPWrdujaOjIxUrVuTNN9/kscceIzg4mCeffBIbGxv279/PgQMHmDp16m3bnDx5Ml5eXvj5+TF+/Hi8vb1N6ze9/PLLNGvWjClTptCnTx/i4uL4+OOPC70aqmrVquTl5fHRRx/RrVs3tmzZwrx588zqhIaGkpGRwe+//06DBg1wdnamevXqPPnkkwwePJj333+fRo0akZyczB9//EG9evXo2rUro0aNIiIigunTp/P444+zbt26W85HAuPl9vv27aNHjx5UrVqV7Oxsli5dyqFDh/joo49M9ezt7XnxxRf58MMPsbe354UXXqBly5ampOn//u//6N27N40bN+bhhx9m9erVfPfdd/z2229mcf3++++0atXK9L25WXBwMB988AEvvPACaWlpDBw4kNDQUM6dO8fSpUtxdXXl/fffp127dly8eJHp06fTq1cv1qxZw6+//mo2j+pW+vXrx8SJE8nNzS2QjE2cOJFRo0bh7u5Oly5dyMnJYdeuXVy+fJmoqKgitV9qSmT6dzkjV7eVXeU5Pomt7Chwddu1K4nud5aubnvppZfM6nTv3l0NGjRIKWW8SmrFihWqWrVqys7OzuxKpzVr1qiIiAjl5OSk3N3dVfPmzdX8+fNN2wH1/fffm7Wdf3Xb6tWrVZ06dZSDg4Nq1qyZ2rdvn1m9b775RtWuXVvZ29urypUrq/fee89s+81Xt82cOVMFBAQoJycn1alTJ7V06VIFqMuXL5vqjBw5Unl5eSlARUdHK71ery5cuKAmTJigQkNDlb29vfL391c9evRQ+/fvN+23YMECValSJeXk5KS6deumZsyYccur2/bs2aP69++vwsLClKOjo/Ly8lJt2rRRP/30k6nOokWLlIeHh/r2229VlSpVlIODg3rooYfU6dOnzdqaM2eOqlKlirK3t1fVq1dXS5cuNdv+008/WfzeWPpMxsbGqk6dOqmKFSsqrVaratasqV555RWzq97mzp2rgoODlYuLixo4cKB66623ClzdduPn50aXL19Wjo6OytnZWaWnpxfYvnz5ctWwYUPl4OCgKlasqNq0aaO+++47i23dy6vbNErdxUnVciotLQ0PDw+Sk5Px8vKydndKlE6nIyYmhq5duxY4z14elOf4JLayIzs7m1OnThEWFoaDgwNpaWm4u7tbZ05SKTIYDCUa24YNG2jfvj2XL1+2+q09Sjq24li8eDGjR4/mypUrpdK+NWMrCTf+fN04xw0gJSUFb29vUlNTizzKdStl790RQgghhLgHJEkSQgghhLBAkiQhhBD3hXbt2qGUsvqpNmsbPHhwqZ1qE8UjSZIQQgghhAWSJAkhhBBCWCBJkhBCCCGEBZIkCSGEEEJYIEmSEEIIIYQFkiQJIYQQQlggSZIQQohyaeLEiTRs2NDa3RBlmCRJQgghAOP6PBqNpsDj+PHj1u5aqfr2229p164dHh4euLq6Ur9+faZMmcLly5et3TVhZZIkCSGEMOncuTOJiYlmj7CwsDtqKzc3t4R7Z5lOp7vjfcePH0+fPn1o1qwZv/76KwcPHuT999/nr7/+YtWqVXfc7r2KXZQuSZKEEEKYODo64u/vb/awtbUFYOPGjTRv3hxHR0cCAgIYN24ceXl5pn3btWvHCy+8QFRUFN7e3nTo0IGXX36Zbt26merMmjULjUbDL7/8YiqrUaMGn376KQA7d+6kQ4cOeHt74+HhQdu2bdmzZ49ZHzUaDfPmzaN79+64uLgwdepUAN555x38/Pxwc3Nj2LBhZGdn3zLWHTt28Pbbb/P+++/z3nvvERERQWhoKB06dOCbb77h6aefBowjbI8//rjZvqNHj6Zdu3a3jP3pp5/mqaeeMttPp9Ph7e3NokWLAFBKMX36dKpUqYKTkxMNGjTgm2++uWW/xb0jSZIQQtwjmbrMQh85+pwi183Oyy5S3ZKUkJBA165dadasGX/99Rdz585l4cKFzJgxw6zekiVLsLOzY8uWLXz66ae0a9eOTZs2YTAYAGOi5e3tzcaNGwFISkri6NGjtG3bFoD09HQGDRrEpk2b2LZtGw888ABdu3YlPT3d7DjR0dF0796dAwcOMHToUL766iuio6N566232LVrFwEBAcyZM+eWMS1fvhxXV1ciIyMtbvfw8CjWe3Rz7P369eOnn34iIyPDVGft2rVcvXqVnj17AvDGG2+waNEi5s6dy6FDhxgzZgz9+/c3vT/Cuuys3QEhhPivaLGiRaHbWge1Zs4j1/+ot/uqHVl5WRbrNvVryqLOi0yvO3/bmcs5BefPHBh0oNh9/Pnnn3F1dTW97tKlC19//TVz5swhODiYjz/+GI1GQ82aNUlISGDs2LFMnToVGxvj/9zVqlVj+vTppv0DAgJIT09n7969NG7cmE2bNvHKK6/w3XffAbB+/Xr8/PyoWbMmAA899JBZfz799FMqVqzIxo0beeyxx0zlffv2ZejQoabXTz/9NEOHDmX48OEATJ06ld9+++2Wo0nHjh2jSpUq2NvbF/t9suTm2KtWrYqLiwvff/89AwYMAGDFihV069YNd3d3rl69ysyZM/njjz8IDw8HoEqVKmzevJlPP/3UlDgK65GRJCGEECbt27dn3759pseHH34IwN9//014eDgajcZUNyIigoyMDM6dO2cqa9q0qVl7Hh4eNGzYkA0bNnDgwAFsbGx49tln+euvv0hPT2fDhg1mycCFCxcYOXIk1atXx8PDAw8PDzIyMoiPjzdr9+bj5PfvRje/vplSyiyeu3Vzn+zt7XnyySdZvnw5AFevXuXHH3+kX79+ABw+fJjs7Gw6dOiAq6ur6bF06VJOnDhRYv0Sd05GkoQQ4h7Z3nd7odtsbWzNXm/ovaHQujYa8/9v1/Rcc1f9upGLiwvVqlUrUG4poVBKAZiVu7i4FNi3Xbt2bNiwAQcHB9q2bUvFihWpU6cOW7ZsYcOGDYwePdpUd/DgwVy8eJFZs2YREhKCo6Mj4eHhBSZCWzpOcVWvXp3Nmzej0+luOZpkY2NjijWfpcnilvrUr18/2rZty4ULF4iNjUWr1dKlSxcA0ynIX375haCgILP9HB0dix2PKHkykiSEEPeIs71zoQ9HW8ci19XaaYtUtyTVrl2brVu3miULcXFxuLm5FfgDf7P8eUl//PGHabJz27Zt+fLLL83mIwFs2rSJUaNG0bVrV+rUqYOjoyPJycm37V+tWrXYtm2bWdnNr2/Wt29fMjIyCp27lJqaCoCPjw+JiYlm2/bt23fbPoFxtC04OJhVq1axfPlynnzySRwcHADje+ro6Eh8fDzVqlUzewQHBxepfVG6JEkSQghxW5GRkZw9e5YXX3yRf/75hx9//JGJEycSGRlpmo9UmDZt2pCens7q1atNSVK7du1YtmwZPj4+1K5d21S3WrVqfPHFF/z9999s376dfv364eTkdNv+vfTSSyxcuJCFCxdy9OhRoqOjOXTo0C33adGiBa+++iovv/wyr776KnFxcZw5c4bff/+d3r17s3LlSsA4T2rXrl0sXbqUY8eOER0dzcGDB2/bJzCOsvXt25d58+YRGxtL//79Tdvc3Nx45ZVXGDNmDEuWLOHEiRPs3buXTz75hCVLlhSpfVG6JEkSQghxW0FBQcTExLBjxw4aNGjAyJEjGTp0KK+88spt9/Xw8KBRo0Z4enqaEqLWrVtjMBgKTE5euHAhly9fplGjRgwYMIBRo0bh6+t722P06dOHN998k9dee40mTZpw5swZnnvuudvu9+6777JixQq2b99Op06dqFOnDlFRUdSvX9+0BECnTp2YMGECr776Ks2aNSM9PZ2BAwfetu18/fr14/DhwwQFBdGqVSuzbVOmTOHNN99k2rRp1KpVi06dOrF69eo7XptKlCyNuvlEqyAtLQ0PDw+Sk5Px8vKydndKlE6nIyYmhq5du5bYFR33k/Icn8RWdmRnZ3Pq1CnCwsJwcHAgLS0Nd3f32464lDUGg0FiK4PKemw3/nxpteannlNSUvD29iY1NRV3d/e7PlbZe3eEEEIIIe4BSZKEEEIIISyQJEkIIYQQwgKrJ0lz5swxnVds0qQJmzZtKrRuYmIiffv2pUaNGtjY2JitrZHvs88+o3Xr1lSsWJGKFSvyyCOPsGPHjlKMQAghhBDlkVWTpFWrVjF69GjGjx/P3r17ad26NV26dCmwsmq+nJwcfHx8GD9+PA0aNLBYZ8OGDTz99NOsX7+euLg4KleuTMeOHUlISCjNUIQQogC5LkaIkncvf66smiTNnDmTYcOGMXz4cGrVqsWsWbMIDg5m7ty5FuuHhoYye/ZsBg4cWOiNB5cvX05kZCQNGzakZs2afPbZZxgMBn7//ffSDEUIIUxsbY2rZ9+8SrQQ4u7l/1zl/5yVJqvdliQ3N5fdu3czduxYs/KOHTuydevWEjtOZmYmOp0OT0/PQuvk5OSQk3P9DtxpaWmA8bJkS0vPl2X58ZS3uPKV5/gktrJDKYVWq+XChQvY2NiQm5tLVlZWid4n7H6glJLYyqCyHJvBYODChQtotVqUUgV+Z5T07xCrJUnJycno9Xr8/PzMyv38/EhKSiqx44wdO5agoCAeeeSRQutMmzaNSZMmFShfv349zs4lu7T//SI2NtbaXShV5Tk+ia1ssLGxwcfHx/RPlxCiZOh0Oi5evMj+/fsLbMvMzCzRY1n9BreWbphYUpnt9OnTWblyJRs2bCiw4NSNxo0bR1RUlOl1WloawcHBtG/fvlwuJhkbG0uHDh3KxaJ9NyvP8UlsZY/BYCArK4stW7YQERGBnZ3Vf+WWqLy8PLZu3SqxlTFlOTaNRoO9vX2hi2CmpKSU6PGs9u54e3tja2tbYNTowoULBUaX7sSMGTN4++23+e2336hfv/4t6zo6Olq847K9vX25+oV9o/IcG5Tv+CS2ssXGxoa8vDxcXV3LXWw6nU5iK4PKc2wlHY/VJm47ODjQpEmTAsPrsbGxRERE3FXb7733HlOmTGHNmjU0bdr0rtoSQgghxH+TVcfZoqKiGDBgAE2bNiU8PJz58+cTHx/PyJEjAeNpsISEBJYuXWraZ9++fQBkZGRw8eJF9u3bh4ODg+mmidOnT2fChAmsWLGC0NBQ00iVq6srrq6u9zZAIYQQQpRZVk2S+vTpQ0pKCpMnTyYxMZG6desSExNDSEgIYFw88uY1kxo1amR6vnv3blasWEFISAinT58GjItT5ubm0qtXL7P9oqOjmThxYqnGI4QQQojyw+oztiIjI4mMjLS4bfHixQXKbreIVH6yJIQQQghxN6x+WxIhhBBCiPuRJElCCCGEEBZIkiSEEEIIYYEkSUIIIYQQFkiSJIQQQghhgSRJQgghhBAWSJIkhBBCCGGBJElCCCGEEBZIkiSEEEIIYYEkSUIIIYQQFkiSJIQQQghhgSRJQgghhBAWSJIkhBBCCGGBJElCCCGEEBZIkiSEEEIIYYEkSUIIIYQQFkiSJIQQQghhgSRJQgghhBAWSJIkhBBCCGGBJElCCCGEEBZIkiSEEEIIYYEkSUIIIYQQFkiSJIQQQghhgSRJQgghhBAWSJIkhBBCCGGBJElCCCGEEBZIkiSEEEIIYYEkSUIIIYQQFkiSJIQQQghhgSRJQgghhBAWSJIkhBBCCGGBJElCCCGEEBZIkiSEEEIIYYEkSUIIIYQQFkiSJIQQQghhgSRJQgghhBAWSJIkhBBCCGGBJElCCCGEEBZYPUmaM2cOYWFhaLVamjRpwqZNmwqtm5iYSN++falRowY2NjaMHj3aYr1vv/2W2rVr4+joSO3atfn+++9LqfdCCCGEKK+smiStWrWK0aNHM378ePbu3Uvr1q3p0qUL8fHxFuvn5OTg4+PD+PHjadCggcU6cXFx9OnThwEDBvDXX38xYMAAevfuzfbt20szFCGEEEKUM1ZNkmbOnMmwYcMYPnw4tWrVYtasWQQHBzN37lyL9UNDQ5k9ezYDBw7Ew8PDYp1Zs2bRoUMHxo0bR82aNRk3bhwPP/wws2bNKsVIhBBCCFHe2FnrwLm5uezevZuxY8ealXfs2JGtW7fecbtxcXGMGTPGrKxTp063TJJycnLIyckxvU5LSwNAp9Oh0+nuuC/3o/x4yltc+cpzfBJb2SSxlU0SW9lU0jFZLUlKTk5Gr9fj5+dnVu7n50dSUtIdt5uUlFTsNqdNm8akSZMKlK9fvx5nZ+c77sv9LDY21tpdKFXlOT6JrWyS2Momia1syczMLNH2rJYk5dNoNGavlVIFykq7zXHjxhEVFWV6nZaWRnBwMO3bt8fLy+uu+nK/0el0xMbG0qFDB+zt7a3dnRJXnuOT2Momia1sktjKppSUlBJtz2pJkre3N7a2tgVGeC5cuFBgJKg4/P39i92mo6Mjjo6OBcrt7e3L3QcoX3mODcp3fBJb2SSxlU0SW9lS0vFYbeK2g4MDTZo0KTDcFxsbS0RExB23Gx4eXqDNdevW3VWbQgghhPjvserptqioKAYMGEDTpk0JDw9n/vz5xMfHM3LkSMB4GiwhIYGlS5ea9tm3bx8AGRkZXLx4kX379uHg4EDt2rUBeOmll2jTpg3vvvsu3bt358cff+S3335j8+bN9zw+IYQQQpRdVk2S+vTpQ0pKCpMnTyYxMZG6desSExNDSEgIYFw88uY1kxo1amR6vnv3blasWEFISAinT58GICIigi+//JI33niDCRMmULVqVVatWkWLFi3uWVxCCCGEKPusPnE7MjKSyMhIi9sWL15coEwpdds2e/XqRa9eve62a0IIIYT4D7P6bUmEEEIIIe5HkiQJIYQQQlggSZIQQgghhAWSJAkhhBBCWCBJkhBCCCGEBZIkCSGEEEJYIEmSEEIIIYQFkiQJIYQQQlhwR4tJnj17ltOnT5OZmYmPjw916tSxeINYIYQQQoiyqshJ0pkzZ5g3bx4rV67k7NmzZitfOzg40Lp1a5555hl69uyJjY0MUAkhhBCibCtSNvPSSy9Rr149jh07xuTJkzl06BCpqank5uaSlJRETEwMDz74IBMmTKB+/frs3LmztPsthBBCCFGqijSS5ODgwIkTJ/Dx8SmwzdfXl4ceeoiHHnqI6OhoYmJiOHPmDM2aNSvxzgohhBBC3CtFSpLee++9IjfYtWvXO+6MEEIIIcT94o4mbudLTk5m+/bt6PV6mjVrRkBAQEn1SwghhBDCqu44Sfr2228ZNmwY1atXR6fTceTIET755BOGDBlSkv0TQgghhLCKIl+GlpGRYfZ60qRJ7Nixgx07drB3716+/vprxo8fX+IdFEIIIYSwhiInSU2aNOHHH380vbazs+PChQum1//++y8ODg4l2zshhBBCCCsp8um2tWvXEhkZyeLFi/nkk0+YPXs2ffr0Qa/Xk5eXh42NDYsXLy7FrgohhBBC3DtFTpJCQ0OJiYlhxYoVtG3blpdeeonjx49z/Phx9Ho9NWvWRKvVlmZfhRBCCCHumWIvjd23b1/TPKR27dphMBho2LChJEhCCCGEKFeKdXXbr7/+yuHDh2nQoAELFixgw4YN9O3bl65duzJ58mScnJxKq59CCCGEEPdUkUeSXn31VQYPHszOnTt59tlnmTJlCu3atWPv3r04OjrSsGFDfv3119LsqxBCCCHEPVPkJGnhwoXExMTw5ZdfsnPnTr744gvAeMuSqVOn8t133/HWW2+VWkeFEEIIIe6lIidJzs7OnDp1CoCzZ88WmINUp04dNm/eXLK9E0IIIYSwkiInSdOmTWPgwIEEBgbStm1bpkyZUpr9EkIIIYSwqiJP3O7Xrx+dO3fm5MmTPPDAA1SoUKEUuyWEEEIIYV3FurrNy8sLLy+v0uqLEEIIIcR9o0in20aOHMnZs2eL1OCqVatYvnz5XXVKCCGEEMLaijSS5OPjQ926dYmIiOB///sfTZs2JTAwEK1Wy+XLlzl8+DCbN2/myy+/JCgoiPnz55d2v4UQQgghSlWRkqQpU6bw4osvsmDBAubNm8fBgwfNtru5ufHII4/w+eef07Fjx1LpqBBCCCHEvVTkOUm+vr6MGzeOcePGceXKFc6cOUNWVhbe3t5UrVoVjUZTmv0UQgghhLinijVxO1+FChXk6jYhhBBClGvFvsGtEEIIIcR/gSRJQgghhBAWSJIkhBBCiDJJKUWmLrPU2r+jOUlCCCGEECUlz5DHVd1V0nLTSM9NJ8+QR32f+qbtSw4t4VTqKa7kXOFKzhVSc1K5nH2Z1NxUvLRe/Pbkb6XSrztKkvLy8tiwYQMnTpygb9++uLm5cf78edzd3XF1dS3pPgohhBDiPmJQBrLystDpdVTQVjCV7/l3D5ezL5OZl0mmLpOreVe5qrtKpi4TJzsnRjUeZar74h8vcjjlMBm5GWTmmY8G+Tr78vuTv5te/3bmN/Zd3GexL1dyrqCUKpWr7IudJJ05c4bOnTsTHx9PTk4OHTp0wM3NjenTp5Odnc28efNKvJNCCCHEf5lSijyVh96gJ8+QR54hD41Gg4ejh6nO8cvHyTHkkGfIQ6fXkWvINT13cXChZUBLU93tOds5f/A8eeSRq88lR59Drj6XbH02vs6+RDWJMtWN/C2Ss+lnycrLIlufTXZeNjn6HADCPML46fGfTHWnbJvC8SvHLcbg6+RrliRdzr7MhcwLZnWc7Jxwc3DDx8nHrPzxao/zYNCDVHCsgIfWgwqOFUwPD0ePUluGqNhJ0ksvvUTTpk3566+/zO7j1qNHD4YPH17sDsyZM4f33nuPxMRE6tSpw6xZs2jdunWh9Tdu3EhUVBSHDh0iMDCQV199lZEjR5rVmTVrFnPnziU+Ph5vb2969erFtGnT0Gq1xe6fEEKIwiml0Ol16NAV+CPu5uCGq4Px7MJV3VXi0+LRK+N2gzKgV3r0So/BYKCye2UquVUCIDUnlW2J2zAog+mhV3qUUhiUgZpeNanjVQeAK9lXWH1ytVldhTI9b+DTgPDAcFO7iw4uQqFMbRkwmJ439mtMp9BOpv5+n/k9O7ftBA1mbSqlaOLXhD41+wCQo8/h5Q0vm/Uhv229QU8z/2a80OgFwDgC8+TqJ00xGZTh+vth0NMioAVvt37b9P5GrIggMy8TvdIXeO+b+zdnQacFpteD1w4mNSfV4vepnnc9Wj56PUnamL2RtP1pFutWq1DNLElKyEjgdNppi3Wz87LNXtf0rImrvSvO9s442zmbvrrYu1BRW9Gs7oSWE9ArPa72rqbPir2NvcXj9Kze02J5aSt2krR582a2bNmCg4ODWXlISAgJCQnFamvVqlWMHj2aOXPm0KpVKz799FO6dOnC4cOHqVy5coH6p06domvXrowYMYJly5axZcsWIiMj8fHxoWdP4xu4fPlyxo4dy8KFC4mIiODo0aMMHjwYgA8++KC44QohxH3LoAxk52Wb/sPP0l37mpfFAxUeMJ0GOZl6km3nt5GjzzF75OpzydXn0rtGb+p61wVgR+IO5vw1B51BZ0x+DDqz5682e5XOYZ0B2JSwiQmpE5iwaoLF/o1vMZ6naj4FwKHkQwxbN6zQWKKaRDGk7hAA4tPieWXjK4XWHdlgpClJSslOYfrO6YXWHVxnsClJytBlsODggkLr6pXelCTl6nPZnbub3Sd3W6xrb2tPH4xJkkEZ2HhuY6HtejldH1DQoOHo5aOF1r2Uc8nsdZ7Ks5gggXEez418nHzQ2mqxs7HDwdYBext706Nqhapmdes51MO3ki9O9k442DoYHzYOaO20Zv0FmBQxCb3So7XT4mTrhKOdI052TjjZOaG1NR98mNZ6WqGx3ayGZ40i17WWYidJBoMBvb7gN+zcuXO4ubkVq62ZM2cybNgw0wjUrFmzWLt2LXPnzmXatIJv9Lx586hcuTKzZs0CoFatWuzatYsZM2aYkqS4uDhatWpF3759AQgNDeXpp59mx44dxeqbEEKUhjxDHhm5GaTnppOuSyfUPRRne2fAmEjEJcaRkZtBhi6DTF0mmXmZxjkdeZm83vx16ngbk4NV/6xi6vaphR7n44c+pm1wWwAOJh9k2o7C/3i1DGhpSpJSc1PZ/a/lxACMIyz5bDW2FuvYaGwKbNPaafF18sXWxhZbja3pa37dCo4VTHVdHVxp4tfEtD3/YauxRaPREOoeer2uvStdw7qa6uT3y0Zjg0ajoZ53PbO6/Wv1N25Dg42NDTZc3+/Guk52TjyifYQaNWpgb2tvOnb+vlUqVDHVtbexZ1LEJLO+5rdro7HBz8XPVFej0fBph09NfbSzsTPFZquxNY285fvp8Z9M9Ww1ttjZ2BkfGjtsbczf4++7f2/x+2FJF6cudG3RFXt7yyM3N2ro27DI7ZY3xU6SOnTowKxZs0w3sdVoNGRkZBAdHU3Xrl2L3E5ubi67d+9m7NixZuUdO3Zk69atFveJi4srcG+4Tp06sWDBAnQ6Hfb29jz44IMsW7aMHTt20Lx5c06ePElMTAyDBg0qZqRCCFG4rLwsrmQbr7S5nHOZ1JxU06Nn9Z54O3kD8OOJH5mXNo8Pv/+QdF06WXlZZu0s7bKURr6NANh3cR+z98wu9Jgp2Smm5w625qP5WlstTnbG//K1tlqz0xbBbsF0DOmI1k6Lg62DcbutPY62jjjaOlK9YnVT3Xre9ZjRdgb2Nvam0QgHWwfsNHbY29oT4BJgqtvUrynj3MfRuWNntA7GY9ra2JqSjhvV96nP771/L1BuSZhHGIs7Ly5SXT8XP95t826R6no4evBa89eKVFdrp6Wdth1d69w+kbCzseOJB54oUrsAEYERRa7r7+Jf5Lqi5BU7Sfrggw9o3749tWvXJjs7m759+3Ls2DG8vb1ZuXJlkdtJTk5Gr9fj5+dnVu7n50dSUpLFfZKSkizWz8vLIzk5mYCAAJ566ikuXrzIgw8+aJzolpfHc889VyAZu1FOTg45OTmm12lpxvO0Op0OnU5X5JjKgvx4yltc+cpzfBJbKffBoONy9mVSslO4lH3J9PVS9iUuZ1/m+QbPm/5gzT8wn3kHCr9IpYlPEzzsjBNq03LS+NfwL5jnRjjZOeFq70pObo4p7ipuVehepTvO9s642rviZOeEi72LcW6HnTPV3aub6j5c6WEinogwJka2jhYTk/y6dSvW5Z1W79w6/mt1vRy8eCjooSLV1Rg0uNi4oNVoscceDKA36NFj+fRQWXI/fCZLy38htpJS7CQpMDCQffv28eWXX7J7924MBgPDhg2jX79+ODk5FbsDN89Iv91lfJbq31i+YcMG3nrrLebMmUOLFi04fvw4L730EgEBAUyYYPm8+bRp05g0aVKB8vXr1+Ps7FyseMqK2NhYa3ehVJXn+CS24tErPekqnXRDOmmGNNLVta+GdB5xegQPG2My81vWb2zI2VBoOwHJAYTahQJwNucsALbY4qxxxlnjjJPGCWcb49e92/aSYGuco2ljsGGwy2CcNE5oNVqcNE44ahxNp6P+3f0vMcSYjtOMZhaPn0UW29l+t29HqZDPZNlUHmPLzCzZhSWLnST9+eefREREMGTIEIYMGWIqz8vL488//6RNmzZFasfb2xtbW9sCo0YXLlwoMFqUz9/f32J9Ozs705V2EyZMYMCAAaZ5TvXq1ePq1as888wzjB8/Hhubgv9tjRs3jqio6zP509LSCA4Opn379mZX8JUHOp2O2NhYOnToUKRz0WVNeY5PYitIKcWl7EskZSaRdDWJxKuJPBr2qOkqmkWHFvHJ/k8wKIPF/Z9v+zyNfRsDkHE0g027N1FRWxEvrReeWk+8tF5U1FakomNFOoZ0JNAlEID2ee0Zq8bibOd820uP5ftWNklsZVNKSsrtKxVDsZOk9u3bk5iYiK+vr1l5amoq7du3tzip2xIHBweaNGlCbGwsPXr0MJXHxsbSvXt3i/uEh4ezevVqs7J169bRtGlT0zc6MzOzQCJka2uLUso06nQzR0dHHB0dC5Tb29uXuw9QvvIcG5Tv+P5LsSmlSM1Jxdne2TQH5/czv/PV0a84n3Ge8xnnyTXkmrVRz7cevm7G308VnCpgUAbsNHb4OPvg4+yDr5Mvvs6++Dj7UMmjkul4vWv15unaT1s8bWWpn3cbW3kisZVN5TG2ko6n2ElSYafDUlJScHFxKVZbUVFRDBgwgKZNmxIeHs78+fOJj483rXs0btw4EhISWLp0KQAjR47k448/JioqihEjRhAXF8eCBQvM5kJ169aNmTNn0qhRI9PptgkTJvC///0PW1vLV2IIIawrNSeVk7qTfH/8e85lnuNs2lnOZZzjXPo5MnQZLOm8hMZ+xhGflOwUtp6/fnGHBg0+zj4EugQS4BJgulIMoEtYFx6q/BCeWs/bJj+Frc8ihPjvKnKS9MQTxpn7Go2GwYMHm4286PV69u/fT0RE0WfsA/Tp04eUlBQmT55MYmIidevWJSYmhpCQEAASExOJj4831Q8LCyMmJoYxY8bwySefEBgYyIcffmi6/B/gjTfeQKPR8MYbb5CQkICPjw/dunXjrbfeKlbfhBAl60r2FU6nneZM2hnOpJ2hW9VuhHmEAbD2zFoWXl0IhazUceOqvC0CWjA5YjJBrkEEugbi5+JXaILj5uCGG8VbmkQIIfIVOUny8DBOblRK4ebmZjZJ28HBgZYtWzJixIhidyAyMpLIyEiL2xYvXlygrG3btuzZs6fQ9uzs7IiOjiY6OrrYfRFC3J0bR5oPJh9k5T8rTYnRzSsBh3qEmpKkUPdQvGy8qOFXgxCPECq7VSbYLZhgt2ACXQPR2l1fsC7EPYQQ95B7F5QQ4j+ryEnSokWLAOPijK+88kqxT60JIco+nV7H+avnSUhP4FzGORIyEoyP9ATOZpxlbPOxPFblMcB408mfTvxktr+fsx+h7qGEuIcQ7BZsKm/u35wx7mPo2r5oi9sJIcS9UOw5STJCI0T5lD9JOvFqoulKsaTMJNoEtaGpf1MAdiTtYORvIwtt42zaWdPzmp41eanxS1R2q0yIewiV3SvjZFf8ZUKEEMJaip0kAXzzzTd89dVXxMfHk5trfmXJrU6FCSGsJyM3g6SrSSRlJlHJtRKhHqGA8VYYYzeN5d/MfwusBg3gbOdsSpICXAPQ2moJdA2kklslglyDCHINopJrJSq5VTIbHfJ28mZ4veLf9FoIIe4XxU6SPvzwQ8aPH8+gQYP48ccfGTJkCCdOnGDnzp08//zzpdFHIcRt5N98NP/KrnPp51hwcIExKbr2yNBlmOq/0PAFnm3wLGC8/cKNd/j21HoS4BJAgEsA/i7+1Pepb9oW5h7Gjn47brs2kBBClAfFTpLmzJnD/Pnzefrpp1myZAmvvvoqVapU4c033+TSpUu3b0AIcUcydZmc0J3g++Pfk5SVREJGgnGtoKvnuZh5kecbPm9KfHL1uXxz9JsCbbg7uOPv4o+bw/UrvoLdglnQcQH+Lv74ufjhaFtwzbB8khwJIe5XeoNi15nLJdpmsZOk+Ph406X+Tk5OpKenAzBgwABatmzJxx9/XKIdFOK/QmfQkZCeYLoa7Gz6WZr6N6VzaGcAkjKTWHR1UaGXySdlXl+NPsA1gOcaPIe/i//1h7O/2RpC+RxsHWge0LxUYhJCiHthzcFEJq0+TMKFkh2sKXaS5O/vT0pKCiEhIYSEhLBt2zYaNGjAqVOnCl3RWghx3Y2XyV/IvMDkuMmcSTvDufRz5Kk8s7o6g86UJAW4BOBt4011v+oEuweb1gkKdAkkwDUAT62naT8nOyciG1peWkMIIcqTNQcTeW7ZHkojAyl2kvTQQw+xevVqGjduzLBhwxgzZgzffPMNu3btMi04KYQAgzJwLv0cRy4f4cilIxy5fIRjl4/xYNCDvNHyDQBc7V3ZeG6jaR8nOyfjlWDXrghr5NvIbNto99FymbwQQgAohT43k9k/xRGkScWZHBw0Vzh7+z2LrNhJ0vz58zEYjDeLHDlyJJ6enmzevJlu3bqZbicixH9ZVl4WI2NH8s+lf8jMK3hH6uNXjpueO9s7M6XVFPxd/Al1D8XX2bdI9w4TQogyJS8XdFchN/+Rce1r5g3Pb9imy7ypnqVHBrYofgW4NpUyDYVHCXa72EmSjY2N2Q1ke/fuTe/evQFISEggKCio5HonxH3qqu4qB5IPsO/CPvZd2Ie7ozvT20wHjCM+5zLOkZmXiYONA9UqVqNGxRrU8KxB9YrVeaDCA2ZtPV7tcStEIIQQhdDrICf9piTl2tecjJsSFwuvc27efhUMulLtcpZy4CpaLhjsgfQSa/eO1km6WVJSEm+99Raff/45WVkF11kRojz489yfxJ2PY/e/uzly+QgGZTBt89R6ms01evvBt/HUehLmEYadTYn8mAkhhGX6PMhNv57A5KRfS3Iybkhqrj+3zU6j2Znj2K5YeG3EJn/btcRIn3v7Y94pG3twdAUHV3BwMT7sncHR7fpzB1dwcC5Yx8HFvMzBle0J2Ty9eD8GjIM3htxMoHeJdbfIv72vXLnC888/z7p167C3t2fs2LG88MILTJw4kRkzZlCnTh0WLlxYYh0Twppy9DkcuXTEbI2gBQcWsOfC9cVSA10CaeDbgIY+DWng28Bs/xYBLe5ZX4UQZZBSxgQlO+16UpNz4/P0a4nPzY8MY70bk6G87GId2gYIBEi9TUVbx2vJitu1xOaGJCU/qTFLXG7+enOi4wJ2Dnf4hlnWtLrCz+M4SanZ1p24/frrr/Pnn38yaNAg1qxZw5gxY1izZg3Z2dn8+uuvtG3bthS6J8S9E58Wz6aETWxJ2MLOpJ3kGnL5s8+feDgaz3B3DutMtQrVaObfjEa+jfBz8bNyj4UQVmEwXEto0q4lOWmQnWr+PD/hMSVBaTc8TzV+vWE0ukTYOhiTEke3a0mM6/VRG0dXU7Kjt3Pi4NHT1GncEjsnj5tGdm7Yx/b+v0DE1kZDdLfaPLdsD6WxiluRk6RffvmFRYsW8cgjjxAZGUm1atWoXr06s2bNKoVuCXFvnLxykp9P/swf8X9wIvWE2TZfJ1/OpZ8zJUlP13zaGl0UQpQ0g8E4SpN1BbKvGJOarGtfrz1sMi/T+PRhbL9afkOSk3o9ASopGhtwdL/2uJbcOLre9NrNPPm5OQlydDc+L+IojUGn4/TlGGrX6wrl4ErZznUDmNu/8bV1kgpeLHM3ipwknT9/ntq1awNQpUoVtFotw4fLfZlE2aKUQq/0pnlCu/7dxWcHPgPATmNHY7/GPBj0IK2CWvFAhQdkhWkh7ldKGefPZF02PrKvXH+edeWmsivXEpwrxuc5abcdxbEFggFutYCzrSNoPUB7Lckx+5pf7nZDmZux3NHt+mt7Z5DfM3etc90AOtT257d9J+g8q+TaLXKSZDAYzNZmsbW1xcXFpeR6IkQpOpN2hl9O/sLPJ39mSN0hPFn9SQDaB7dnW+I2Hq78MK0rtcbdwd3KPRXiPygvBzIvQWYKZF0yPs+6ZExwMi/dkPzc9Ppur5iy015LcioYvzpd+6r1QG/vxj+nz1OjYQvsXDyN5fmJj9bDmPjYa0sielFCbG00NA2pWKJtFjlJUkoxePBgHB2NixFkZ2czcuTIAonSd999V6IdFOJO5ehzWHt6LauOrGL/xf2m8tjTsaYkycfZh5ntZlqri0KUP/q8a4lOClxNNn7NTL6eBJkel66X6a7e+fFs7MHZE5wqGpMdp4rGZMf0uoKFr9cSo1skOQadjuMxMVRvVD5OSYk7U+QkadCgQWav+/fvX+KdEaIkKKX4+K+P+f7491zOMY6V22psCQ8M59Eqj/JQ8ENW7qEQZYhBfy3huXjtkXztcRGbjAs0P3kI2yWfQNa1pCj7yp0dR2NrTGycPcHJ84avFa8lPp43bL+WADl7yukqUaqKnCQtWrSoNPshRInRaDQcTjnM5ZzL+Dn70adGH3o80ANvJ29rd02I+0NejjHhyfgXMi7C1QuQceFa8nPj84vGBKmQi6ttgQCwcCm5xpjAOHvd8PAEZ2/z8vxkyNnTeCrrhoWKhbgfyCp3osw7lHKIBQcW8HqL1/GwM16J9my9Z3mq5lO0DW4rizmK/waljKevMv6FjCRI//fa8wvXvt7wvNijPZrrSY6rrzHBcfFBr63IwVNJ1GneDjt3P+N2F2/jSI+NbWlEKcQ9JX89RJl1KOUQc/fNNd0gNsg1iFENRgHQwKeB3ARWlA/5yU96IqQnmX/N+Pfa62tJUHEmMtvYg4uPMelx9QUXX3D1MZa5+BqTHVdf42snT7At+OfCoNNxOiOG2rVk3o4onyRJEmVO0tUkZu+Zzc8nfwbARmPDo2GP8sQDT1i5Z0IUky4b0s9DWqIx2UlLuP48PdH4PCOpeLeJcPIEVz9w8zN+zX+4+d+QDPkaR3tkLo8QtyRJkihTPv3rUz4/8DnZeuMy/I9VeYyRDUYS4h4CgE5XujdRFKLIdFmQdh7NpTMEp2zGZssRyEiEtPPXkqHz1+b7FJGzN7gFGJMdNz/jc1e/62X5yVAJ3/ZBiP+yYidJf/75JxEREdjZme+al5fH1q1badOmTYl1ToibXcy6SLY+m8a+jXm12avU8a5j7S6J/yKDwXh6K/UcpJ699vXaI+3a12sJkB3QGCC+kLbstOAeCG6B4B5gTHrcA82/SvIjhFUUO0lq3749iYmJ+Pr6mpWnpqbSvn179Hp9iXVOiLPpZ7HR2BDkGgTA8w2fp5l/MzqGdJTVsEXp0euuJ0BXzsKV+GvP468lQglFOwVm74xyDyQ5xwGvKg2wqRBsTHzcg659DZTTXkLcx4qdJCmlLP5xSklJkRW4RYnJM+TxxeEvmLNvDg19GzK/w3w0Gg0VtRXpFNrJ2t0TZZ1Bb0x0Lp+BK2eMyc+V+Guv443zhG5381GNjXH0p0KwMenxqGT+cA8Cp4rGUfaYGLp27YqNTG4WokwpcpL0xBPGSbEajcZs5W0AvV7P/v37iYiIKPkeiv+cQymHmLh1Iv9c+gcwJuZXdVdxdXC1cs9EmZJ5CS6fNj6unLn+/PJp42iQIe/W+9tpjclOhcrgEWxMhjwqX/tayZggWbjiSwhRfhT5J9zDw7j+jFIKNzc3nJycTNscHBxo2bIlI0aMKPkeiv8MnUHHZ/s/Y/7++eiVHncHd/6v2f/RvWp3ObUmCjIYjFd+XTp57XEKLp+6/jW7wAqH5mzsjQlPhRCoGGL8WqHy9a+uvnIaTIj/uGKvuB0aGsorr7wip9ZEifr36r+MXj+agykHAegY0pHXW7yOl5OXlXsmikpvUOw4dYkL6dn4umlpHuaJrc1dJhkGg/HUV8qJa4nQCUg5eT0Zysu69f4uvuAZBhVDrz/ykyK3AFnwUAhxS8UeK46Ojgbg4sWLHDlyBI1GQ/Xq1fHx8Snxzon/Dg9HDzLzMnFzcOONFm/QtUpXa3dJFMOag4lMWn2YxNRsU1mAh5bobrXpXDfg1jsrBVcv4plxBM2+y3Dl1LVk6FpilJdd+L4aW+Ooj2eVa8lQmHlS5CD/zAkh7lyxk6TMzExeeOEFli5disFgnNhoa2vLwIED+eijj3B2di7xTory6Ur2Fdwd3bHR2KC10zKz3Uxc7F3wd/G3dtdEMaw5mMhzy/YUuLtXUmo2zy3bw9z+jY2Jki7bmPSkHIPko5B83Pg85Tj22am0Bjhm4QA2dsaEx7MKeFa99vVaUlShMtjKZGghROkodpI0ZswYNm7cyOrVq2nVqhUAmzdvZtSoUbz88svMnTu3xDspyp+dSTt57c/X6FerH8PqDQOgaoWqVu6VKC69QTFp9WGzBKkC6VTTJFDVJpEHNAm4fTcD9fslNFfiC71iTKEhy8ELbVBdbLwfAK9q1x5VjJOlZYK0EMIKiv2b59tvv+Wbb76hXbt2prKuXbvi5ORE7969JUkSt6Q36Jm/fz7z9s/DoAzEnIphYJ2B2NvIaECZohSkJ3Fk/w46ZvzOA3bneMAmgaqa83hr0szrGoDL1547eoB3NfCubkyCriVEeW7BxMaul8vkhRD3lTs63ebn51eg3NfXl8zMzBLplCifLmZeZOymsexI2gHA49UeZ1zzcZIg3c+UMt45/sJhuPgPXPjb+PXiP5CdSm1gkoVv3znlzQlDICdUIMdVEF3btebBlhGFXzEmt5MRQtyHip0khYeHEx0dzdKlS9FqtQBkZWUxadIkwsPDS7yDonzY/e9uXt7wMinZKTjZOTGh5QS6Ve1m7W6JG+WkG5Ogfw8Zk6L851mXLNfX2JDlFsKfl704rgI5ZqjEcRXISRVIJlqzqt2qtAQ3uVJRCFG2FDtJmj17Np07d6ZSpUo0aNAAjUbDvn370Gq1rF27tjT6KMq4S9mXeO6358jKy6JahWrMbDeTMI8wa3frv8tggCunIekAJB00JkL/HjQuuGiRxjhR2rcW+NS8/tX7ARxsHJj47h8kpWYXmLh9bU/8PYzLAQghRFlT7CSpbt26HDt2jGXLlvHPP/+glOKpp56iX79+ZgtMCpHPU+tJVJMo9lzYw8TwiTjbyxWQ90xejnFUKHE/JO03Jkb/HoLcDMv13QLAtzb41QbfOtcSohpgb/ln2xaI7lab55btQQNmiVL+SbXobrXvfr0kIYSwgju6ZMTJyUlW1xa3dDb9LDl5OVSrWA2APjX60KdGH1k5uzTpsowjQ4n74PxeSPzLOHfI0u03bB2NCZB/XfDLf9QB5+KP+HSuG8Dc/o0LrJPkX9R1koQQ4j51R0nSkSNH+Oijj/j777/RaDTUrFmTF154gZo1a5Z0/0QZtCNxB1Ebo3B3cGfloyvxcPSQ5Kik5eXChUOQsBsS9hqToov/gNIXrOtUEfzrQ0B941f/euD1QIleVt+5bgAdavuX/IrbQghhRTbF3eGbb76hbt267N69mwYNGlC/fn327NlDvXr1+Prrr4vdgTlz5hAWFoZWq6VJkyZs2rTplvU3btxIkyZN0Gq1VKlShXnz5hWoc+XKFZ5//nkCAgLQarXUqlWLmJiYYvdNFN+qf1bxbOyzpOak4uHgQa4+19pdKvuUgksn0Rz8hnrnvsB2UUeYFgTz28EvL8O+ZcaESemNt+F4oCO0eRWeWgGjD8Krp2DQT9BxKtTvbRxBKoV1h2xtNIRX9aJ7wyDCq3pJgiSEKPOK/Zvy1VdfZdy4cUyePNmsPDo6mtdee40nn3yyyG2tWrWK0aNHM2fOHFq1asWnn35Kly5dOHz4MJUrVy5Q/9SpU3Tt2pURI0awbNkytmzZQmRkJD4+PvTs2ROA3NxcOnTogK+vL9988w2VKlXi7NmzuLm5FTdUUQw6g453d7zLqiOrAHi0yqNMDJ+I1k57mz1FAblXIWEPnN0O53YaH5kp2AFVbqynrQBBjSGoCQQ2Mj7cAuSmrEIIUUKKnSQlJSUxcODAAuX9+/fnvffeK1ZbM2fOZNiwYQwfPhyAWbNmsXbtWubOncu0adMK1J83bx6VK1dm1qxZANSqVYtdu3YxY8YMU5K0cOFCLl26xNatW7G/tihdSEhIsfoliudK9hVe3vgyO5J2oEHDqMajGFZ3mJxiK6q0RIiPg/htxsQo6UDB02a2Dhj86nFK50VIxBPYhbQw3qdM3mMhhCg1xU6S2rVrx6ZNm6hWrZpZ+ebNm2ndunWR28nNzWX37t2MHTvWrLxjx45s3brV4j5xcXF07NjRrKxTp04sWLAAnU6Hvb09P/30E+Hh4Tz//PP8+OOP+Pj40LdvX1577TVsbS3f8TsnJ4ecnBzT67Q044rBOp0OXTlb5C4/npKM690d77IjaQfOds68FfEWbSu1JS/PwmThe6A04itRSsHlk2ji47A5uw1N/DY0V04XrOYWiApujgpqhgpqivKri07ZcDA2loAaHVD29mCl97g03Pfft7sgsZVNElvZVNIxFTtJ+t///sdrr73G7t27admyJQDbtm3j66+/ZtKkSfz0009mdQuTnJyMXq8vsHq3n58fSUlJFvdJSkqyWD8vL4/k5GQCAgI4efIkf/zxB/369SMmJoZjx47x/PPPk5eXx5tvvmmx3WnTpjFp0qQC5evXry+3N+yNjY0tsbbqGerxt93fdHXqytX9V4nZb/35XyUZ311RCpecJLwz/sEr4x+8M/7BSXfZvAoaUp0qc8m1OikuD3DJ5QGyHa4tvJgMJP8L/Guqf9/EVgoktrJJYiubymNsJX3nj2InSZGRkYBxwvWcOXMsbgPQaDTo9RautLnJzadklFK3PE1jqf6N5QaDAV9fX+bPn4+trS1NmjTh/PnzvPfee4UmSePGjSMqKsr0Oi0tjeDgYNq3b4+XV/laJVin0xEbG0uHDh1MpyPvxN+X/qaWZy3T6ycp+ly00lRS8d2VtAQ0p/7E5swmNKf+RJNhnvQrWwdUYGNUcDiqcktUUDNctO64AMG3aPa+iK2USGxlk8RWNpXn2FJSUkq0vWInSQaD5bt4F5e3tze2trYFRo0uXLhg8d5wAP7+/hbr29nZmZKZgIAA7O3tzU6t1apVi6SkJHJzc3FwcCjQrqOjI46OjgXK7e3ty90HKN+dxqaUYs5fc5j31zzeDH+TJ6vfH8nRze7p9y47DU5vguO/w8kNcOmE+XZbB6jUDEIfhNAH0VRqhqaQxRmLQj6XZZPEVjZJbGVLScdT8tcBF5GDgwNNmjQhNjaWHj16mMpjY2Pp3r27xX3Cw8NZvXq1Wdm6deto2rSp6Y1p1aoVK1aswGAwYGNjXOHg6NGjBAQEWEyQRNHp9Dre3PomP5/8GYDEjEQr98hKDAbjukQnfocTf8DZHeYTrTU2xivNwtpClbYQ3KLQFauFEELcv4qcJG3fvp1Lly7RpUsXU9nSpUuJjo7m6tWrPP7443z00UcWR2QKExUVxYABA2jatCnh4eHMnz+f+Ph4Ro4cCRhPgyUkJLB06VIARo4cyccff0xUVBQjRowgLi6OBQsWsHLlSlObzz33HB999BEvvfQSL774IseOHePtt99m1KhRRe6XKCg9N50x68ewPWk7dho7JoRP4IkHnrB2t+6dzEvGhOjYOuOIUWay+XbPqlD1IajaHkJagVMFq3RTCCFEySlykjRx4kTatWtnSpIOHDjAsGHDGDx4MLVq1eK9994jMDCQiRMnFvngffr0ISUlhcmTJ5OYmEjdunWJiYkxXbKfmJhIfHy8qX5YWBgxMTGMGTOGTz75hMDAQD788EPT5f8AwcHBrFu3jjFjxlC/fn2CgoJ46aWXeO2114rcL2Eu6WoSkb9HcuzyMZztnJnZbiatglpZu1ulSym48Dcc/RWOrjWuVaRuONXs6G4cJar6sDExqhhqta4KIYQoHUVOkvbt28eUKVNMr7/88ktatGjBZ599BhiTk+jo6GIlSWCc7H3jhO8bLV68uEBZ27Zt2bNnzy3bDA8PZ9u2bcXqh7Dsqu4qA34dQNLVJLydvJnz8BxqedW6/Y5lkV4HpzfDkV+NydGVePPtfnWh2iPwQAfjKTTb8nUuXwghhLkiJ0mXL182m1C9ceNGOnfubHrdrFkzzp49W7K9E1bnYu9Cnxp9WH1iNXMfmUuga6C1u1Sycq8aT5/98zMcXQPZqde32ToaR4uqdzY+PIKs108hhBD3XJGTJD8/P06dOkVwcDC5ubns2bPHbG2h9PT0cjdL/r9Mb9Bja2O8QnBY3WH0rdkXZ/v7e80ovUGx/dQldidr8Dp1ifBqvpbvH5adZjyFdvgHY4KUl3V9m7M31OhifFRpBw4u96r7Qggh7jNFTpI6d+7M2LFjeffdd/nhhx9wdnY2W2F7//79VK1atVQ6Ke6tH47/wNdHvmZ+x/m42Lug0Wju+wRpzcFEJq0+TGJqNmDL0mO7CPDQEt2tNp3rBhhHiI6suZ4Y6a+vsE6FEKjVDWo+ajyNZmN5ZXYhhBD/LUVOkqZOncoTTzxB27ZtcXV1ZcmSJWaX1C9cuLDALUNE2bPk0BJm7JoBwDdHv2FQnUFW7tHtrTmYyHPL9qBuKr+SmsrqFXNoGPo3/v/+aZ4YeT0AdR6HWv8D/3pyDzQhhBAFFDlJ8vHxYdOmTaSmpuLq6lrgPmhff/01rq6uJd5BcW8opfhw74d8fuBzAAbWHsiA2gOs3Kvb0xsUk1YfNiVIduTxoM0ButtupYPNblw12XD+2kbv6lCnB9R+HHxrSWIkhBDiloq9mKSHh4fFck9Pz7vujLAOpRTv7HiHFf+sAOClxi8xrO6wW94e5n6x49QlElOzqKc5xRO2m+hmG4e3Js20/azBh9WGcFo9/iwNmrSSxEgIIUSRWW3FbXF/uDFB0qDhjZZv0LtGb2t3q2hSE/DY9Sm/O3xFVZvrq38nK3dW68P5SR/BXlUN0DDbLowGkiAJIYQoBkmS/uOSs5JZe3otGjRMiphEjwd63H4na9Jlw5FfYO9yOLme2soANpCt7FlnaMp3+gfZbKhH3k0fbV83rZU6LIQQoqySJOk/zsfZh4WdFnIo5RDdqnazdncKl7gf9iyFA1+ZrWWkKofz9vnGfJnRiHQKXoGnAfw9tDQPk9PBQgghikeSpP8gpRSnUk9R3bs6AFUqVKFKhSpW7pUF2Wlw4GtjcpS473q5eyVo+DQ0eBqNV1WaHEzk82V70IDZFW75J9eiu9W2vF6SEEIIcQuSJP0Hrc1ey9Q1U/n44Y9pGdDS2t0xpxQk7IZdi+DQd6DLNJbb2EOtx6DRAOMijzesZdS5bgBz+ze+YZ0kI/8b10kSQgghikmSpP+YL/7+gs05mwFIzEi8Te17KCcd9n8FuxdB0oHr5d41oPFAaPAUuHgXunvnugF0qO1P3PELrNu0nY6tWxS+4rYQQghRBJIk/YesPrGaD/Z+AMCohqPuj0naSQdg5wLjabXcDGOZraNxPaOmQ4wrYBfxqjRbGw0twjxJ+VvRIsxTEiQhhBB3RZKk/4hN5zbx5pY3AWjl2IpBtay4knZeDhz+CXZ+Dme3XS/3egCaDjWOGjnLRGshhBDWJUnSf8BfF//i5Y0vk6fy6BralZaXW1pnocjUc7BrIexeApnJxjIbO+N905oOg9AHZbFHIYQQ9w1Jkv4Dvj7yNVl5WTwY9CDRLaOJXRN77w6uFJzeBDvmwz+/gDIYy90CjafTGg8EN/971x8hhBCiiCRJ+g+YGDGRMI8wnq75NPbY35uD5l6Fv740JkcX/7leHtoamj8DNbqCrXz8hBBC3L/kr1Q5laPPwcHGAY1Gg52NHcPqDQNAp9OV7oEvnTLONdrzBeRcW/TR3sU4z6j5COONZYUQQogyQJKkckhn0DHqj1H4u/jzRss3sLcp5dEjpeDURtj+KRz5FdOSjhXDjKNGjfqB1vKNkYUQQoj7lSRJ5YxSiolbJ7L1/Fac7JwYVHtQ6a2mrcuC/auMydGFw9fLqz4MLUZCtUfAxqZ0ji2EEEKUMkmSypmP9n7ETyd+wlZjy4y2M0onQUpNMJ5S270Isi4by+xdjLcKaf4s+FQv+WMKIYQQ95gkSeXI8r+X89mBzwB4M/xN2lRqU7IHOLcLts2BQz+A0hvLKlS+dkptADhVKNnjCSGEEFYkSVI58f2x73lnxzsARDaI5IkHniiZhvU6+Psn2DYXzu28Xh7SClo+Z7xK7Yb7qAkhhBDlhSRJ5cCFzAu8tf0tAAbWHsjIBiPvvtHMS7BnCez4DNISjGW2DlC3F7QcCQEN7v4YQgghxH1MkqRywNfZlw/afcCW81t4pekrha6mrTcotp+6xO5kDV6nLlm+AWzyMeOo0V8rQZdpLHPxMa6I3XQouPmVcjRCCCHE/UGSpDJMb9Bje+1UV+tKrWldqXWhddccTGTS6sMkpmYDtiw9tosADy3R3WrTuY4/nFxvTI6Orbu+k19daBkJ9XqBnWMpRyOEEELcXyRJKqP+PPcn7+96n48e+ojK7pVvWXfNwUSeW7Ynf/Uik8upaWxY+T6tvDbglnbsWqkGanQxJkdyLzUhhBD/YZIklUEr/1nJOzvewaAMzN8/n6kPTi20rt6gmLT6sFmC5MtlBtjF0tf2d7w06ZAGysEVTaP+xivVvKqWfhBCCCHEfU6SpDJEb9Dz/u73+eLwFwA8Xu1x3mz55i332XHq0rVTbNBAc5whdmt41GY79hrjJfznlDeL8jrRqc//0bxWWOkGIIQQQpQhkiSVEZm6TMZuGsv6s+sBGNVoFMPrDS90kna+i6lpdLPZymC7tTSxOWYq326oyaK8zsQamqDHlvo5DqXafyGEEKKskSSpDLiSfYVnf3uWwymHcbBxYOqDU+kS1uXWO6Unwe7FdN6+gP85XAAgV9my2hDBwrzOHFLmo0a+btrS6r4QQghRJkmSVAa4O7pjp7GjgmMFPnzoQxr5NrJcUSmIj4OdC+DwD2DIwwFIpgLL8x5iWd4jXKSC2S4awN9DS/Mwz1KOQgghhChbJEm6DymliD0Ty4NBD+Js74yNxoYpD07BydaJANeAgjtkXIS/VsCepZBy/Hp5cEtoPoLdqhmzVhwssFv+ibrobrULrpckhBBC/MdJknSfUEpxKvUUmxM2E3smln0X9zGs7jBGNxkNQBWPm25Um5cLJ36HfSvgSAwY8ozlDq5Q9wloNty0KnYnYK6Nww3rJBn556+TVNdC4iWEEEL8x0mSdA/oDDouZl4k6WoSCkUTvyambTEn1/DLsT/Zn7KdK7oLpnJHW0dcHVzNGzLo4fQmOPCN8X5q2anXtwU1gcaDjAmSo1uBPnSuG0CH2v7EHb/Auk3b6di6heUVt4UQQggBSJJUKlJzUvn8wOfs/nc3/179l4tZF1HXViqqVqEa33f/HjAu8jh223soe2NypAx22OVWpWu1doxq2Qt/F3/IToOTG+B4LBxdCxn/Xj+Qqz/U6QGN+oN/3dv2y9ZGQ4swT1L+VrQI85QESQghhLgFSZJKWJ4hjz4/9yEhI8Gs3M7GDj9nP0LcQ4Drq2A7+FUFqpGXUR19ZhWclYFjp0+Tenk+/unb4ey266fSALQVoHZ3461CQlrBtduSCCGEEKJkSZJUQvQGxY5Tl7iQnk24dzf22sYyov4IQt1D8XPxw1PriY3GxlR38k8HCSCZ0ItVqaZJoJ5mA/XtF1JNk4CtRsGN86y9qkG1R6BaBwhrA3ayppEQQghR2qyeJM2ZM4f33nuPxMRE6tSpw6xZs2jduvAbtW7cuJGoqCgOHTpEYGAgr776KiNHjrRY98svv+Tpp5+me/fu/PDDD6XSf71BzzO/jmP/kRAuXgi9VhqMv0ckttXqUadKgPHqs2OxkLAHkg6Qk3SU9TmncdTqLLaZqDzZb6jCA+GPUaXl4+ApK2ELIYQQ95pVk6RVq1YxevRo5syZQ6tWrfj000/p0qULhw8fpnLlgjdtPXXqFF27dmXEiBEsW7aMLVu2EBkZiY+PDz179jSre+bMGV555ZVbJlx3SynFMzFj2ZGyBr2LHzAa0GCHokn6Jgyr3iMr5hxOmefN9nMG0BgXdzyrfDml/DmkwthvCGO/oQoXqQjA7MCGVPEMKrX+CyGEEKJwVk2SZs6cybBhwxg+fDgAs2bNYu3atcydO5dp06YVqD9v3jwqV67MrFmzAKhVqxa7du1ixowZZkmSXq+nX79+TJo0iU2bNnHlypUS77tSivd2zmBHyhqU0pCb/DC+XKGv3e88bfsHfpprx8wEhQaNd3UIagyBjTic68czMZdJVF7oKXxOkayCLYQQQliP1ZKk3Nxcdu/ezdixY83KO3bsyNatWy3uExcXR8eOHc3KOnXqxIIFC9DpdNjb2wMwefJkfHx8GDZsGJs2bbptX3JycsjJyTG9TktLA0Cn06HTXT8lpjcodp25zIX0HHalfs3qs0sBqJjUjrHZf9DJcRd2GgMAF5UHq/Tt2Gyox0v9nqBp9esjY1UMirxNf2JIu37MGxlXwXakUSU3s+OXhPz2Srrd+0V5jk9iK5sktrJJYiubSjomqyVJycnJ6PV6/Pz8zMr9/PxISkqyuE9SUpLF+nl5eSQnJxMQEMCWLVtYsGAB+/btK3Jfpk2bxqRJkwqUr1+/HmdnZwD+StHw3WkbruRqsK+4Ga3/zwC0vejHrKwvsLM1JkfbDTVZlvcIawzN0V17e6tvO8SF4+YrXnf117AwzebaqxsvxTcuFtDFL5O1a34tcgzFFRsbW2pt3w/Kc3wSW9kksZVNElvZkpmZWaLtWX3i9s13sVdK3fLO9pbq55enp6fTv39/PvvsM7y9vYvch3HjxhEVFWV6nZaWRnBwMO5VG5Fj68yZlEwWHT2BAuxcD5kSpMGXsnk5YydoIEbfnA/znuAfVXAuVcfWLWhx073RugKND/3L1Jh/SLphRCnAQ8v4LjXpVMeP0qDT6YiNjaVDhw6mkbfypDzHJ7GVTRJb2SSxlU0pKSkl2p7VkiRvb29sbW0LjBpduHChwGhRPn9/f4v17ezs8PLy4tChQ5w+fZpu3bqZthsMxhEeOzs7jhw5QtWqVQu06+joiKOjY4Hy51YewMbR2aysepYtrpk2NNVdISr1CicMAUTnDWazoV6B/fNvHlvYytaPNaxEl/pBpqUDfN2MN5q9F4s82tvbl7sfjhuV5/gktrJJYiubJLaypaTjsVqS5ODgQJMmTYiNjaVHjx6m8tjYWLp3725xn/DwcFavXm1Wtm7dOpo2bYq9vT01a9bkwIEDZtvfeOMN0tPTmT17NsHBwXfc30qaC/yf3Vd0t91K7r+gU45Mz3uKBfou5FLwm1LUm8fa2mgIr+p1x/0SQgghROmw6um2qKgoBgwYQNOmTQkPD2f+/PnEx8eb1j0aN24cCQkJLF1qnCA9cuRIPv74Y6KiohgxYgRxcXEsWLCAlStXAqDVaqlb1/z2HBUqVAAoUF5UFUnjRbsf6G8bi4NGD8Av+lZM1z1FIteTmwpO9lzJuj5hTG4eK4QQQpRtVk2S+vTpQ0pKCpMnTyYxMZG6desSExNDSIjx1h2JiYnEx8eb6oeFhRETE8OYMWP45JNPCAwM5MMPPyywRlJJGWC7jtccV+OuyQLgT3093s17mkMqtEDdT/o2xsZGc89PmwkhhBCidFh94nZkZCSRkZEWty1evLhAWdu2bdmzZ0+R27fURlF5a9Jw12Rx2BDCtLyn2WSoX6BO/ryjllW9JCkSQgghyhGrJ0n3s8/zunA6two/GSJQ2BTYXtR5R0IIIYQoeyRJuoV0XPjR8GCh22XekRBCCFF+SZJURBpAAWMeeYBQbxeZdySEEEKUc5IkFZGMGgkhhBD/LZIk3cJnAxqRbeMko0ZCCCHEf5AkSbfQNKQiXl6y0KMQQgjxX1Twki0hhBBCCCFJkhBCCCGEJZIkCSGEEEJYIEmSEEIIIYQFkiQJIYQQQlggSZIQQgghhAWSJAkhhBBCWCBJkhBCCCGEBZIkCSGEEEJYIEmSEEIIIYQFkiQJIYQQQlggSZIQQgghhAWSJAkhhBBCWCBJkhBCCCGEBZIkCSGEEEJYIEmSEEIIIYQFkiQJIYQQQlggSZIQQgghhAWSJAkhhBBCWCBJkhBCCCGEBZIkCSGEEEJYIEmSEEIIIYQFkiQJIYQQQlggSZIQQgghhAWSJAkhhBBCWCBJkhBCCCGEBZIkCSGEEEJYIEmSEEIIIYQFkiQJIYQQQlggSZIQQgghhAWSJAkhhBBCWCBJkhBCCCGEBVZPkubMmUNYWBharZYmTZqwadOmW9bfuHEjTZo0QavVUqVKFebNm2e2/bPPPqN169ZUrFiRihUr8sgjj7Bjx47SDEEIIYQQ5ZBVk6RVq1YxevRoxo8fz969e2ndujVdunQhPj7eYv1Tp07RtWtXWrduzd69e3n99dcZNWoU3377ranOhg0bePrpp1m/fj1xcXFUrlyZjh07kpCQcK/CEkIIIUQ5YNUkaebMmQwbNozhw4dTq1YtZs2aRXBwMHPnzrVYf968eVSuXJlZs2ZRq1Ythg8fztChQ5kxY4apzvLly4mMjKRhw4bUrFmTzz77DIPBwO+//36vwhJCCCFEOWBnrQPn5uaye/duxo4da1besWNHtm7danGfuLg4OnbsaFbWqVMnFixYgE6nw97evsA+mZmZ6HQ6PD09C+1LTk4OOTk5ptdpaWkA6HQ6dDpdkWMqC/LjKW9x5SvP8UlsZZPEVjZJbGVTScdktSQpOTkZvV6Pn5+fWbmfnx9JSUkW90lKSrJYPy8vj+TkZAICAgrsM3bsWIKCgnjkkUcK7cu0adOYNGlSgfL169fj7OxclHDKnNjYWGt3oVSV5/gktrJJYiubJLayJTMzs0Tbs1qSlE+j0Zi9VkoVKLtdfUvlANOnT2flypVs2LABrVZbaJvjxo0jKirK9DotLY3g4GDat2+Pl5dXkeIoK3Q6HbGxsXTo0MHiyFtZV57jk9jKJomtbJLYyqaUlJQSbc9qSZK3tze2trYFRo0uXLhQYLQon7+/v8X6dnZ2BZKZGTNm8Pbbb/Pbb79Rv379W/bF0dERR0fHAuX29vbl7gOUrzzHBuU7PomtbJLYyiaJrWwp6XisNnHbwcGBJk2aFBjui42NJSIiwuI+4eHhBeqvW7eOpk2bmr0x7733HlOmTGHNmjU0bdq05DsvhBBCiHLPqle3RUVF8fnnn7Nw4UL+/vtvxowZQ3x8PCNHjgSMp8EGDhxoqj9y5EjOnDlDVFQUf//9NwsXLmTBggW88sorpjrTp0/njTfeYOHChYSGhpKUlERSUhIZGRn3PD4hhBBClF1WnZPUp08fUlJSmDx5MomJidStW5eYmBhCQkIASExMNFszKSwsjJiYGMaMGcMnn3xCYGAgH374IT179jTVmTNnDrm5ufTq1cvsWNHR0UycOPGexCWEEEKIss/qE7cjIyOJjIy0uG3x4sUFytq2bcuePXsKbe/06dMl1DMhhBBC/JdZ/bYkQgghhBD3I0mShBBCCCEskCRJCCGEEMICSZKEEEIIISyQJEkIIYQQwgJJkoQQQgghLJAkSQghhBDCAkmShBBCCCEskCRJCCGEEMICSZKEEEIIISyQJEkIIYQQwgJJkoQQQgghLJAkSQghhBDCAkmShBBCCCEskCRJCCGEEMICSZKEEEIIISyQJEkIIYQQwgJJkoQQQgghLJAkSQghhBDCAkmShBBCCCEskCRJCCGEEMICSZKEEEIIISyQJEkIIYQQwgJJkoQQQgghLJAkSQghhBDCAkmShBBCCCEskCRJCCGEEMICSZKEEEIIISyQJEkIIYQQwgJJkoQQQgghLJAkSQghhBDCAkmShBBCCCEskCRJCCGEEMICSZKEEEIIISyQJEkIIYQQwgJJkoQQQgghLJAkSQghhBDCAkmShBBCCCEssHqSNGfOHMLCwtBqtTRp0oRNmzbdsv7GjRtp0qQJWq2WKlWqMG/evAJ1vv32W2rXro2joyO1a9fm+++/L63uCyGEEKKcsmqStGrVKkaPHs348ePZu3cvrVu3pkuXLsTHx1usf+rUKbp27Urr1q3Zu3cvr7/+OqNGjeLbb7811YmLi6NPnz4MGDCAv/76iwEDBtC7d2+2b99+r8ISQgghRDlg1SRp5syZDBs2jOHDh1OrVi1mzZpFcHAwc+fOtVh/3rx5VK5cmVmzZlGrVi2GDx/O0KFDmTFjhqnOrFmz6NChA+PGjaNmzZqMGzeOhx9+mFmzZt2jqIQQQghRHlgtScrNzWX37t107NjRrLxjx45s3brV4j5xcXEF6nfq1Ildu3ah0+luWaewNoUQQgghLLGz1oGTk5PR6/X4+fmZlfv5+ZGUlGRxn6SkJIv18/LySE5OJiAgoNA6hbUJkJOTQ05Ojul1amoqAJcuXSpWTGWBTqcjMzOTlJQU7O3trd2dElee45PYyiaJrWyS2Mqm/L/bSqkSac9qSVI+jUZj9lopVaDsdvVvLi9um9OmTWPSpEkFyqtXr154x4UQQghxX0pJScHDw+Ou27FakuTt7Y2trW2BEZ4LFy4UGAnK5+/vb7G+nZ0dXl5et6xTWJsA48aNIyoqyvT6ypUrhISEEB8fXyJv8v0kLS2N4OBgzp49i7u7u7W7U+LKc3wSW9kksZVNElvZlJqaSuXKlfH09CyR9qyWJDk4ONCkSRNiY2Pp0aOHqTw2Npbu3btb3Cc8PJzVq1ebla1bt46mTZuahgzDw8OJjY1lzJgxZnUiIiIK7YujoyOOjo4Fyj08PMrdByifu7t7uY0Nynd8ElvZJLGVTRJb2WRjUzJTrq16ui0qKooBAwbQtGlTwsPDmT9/PvHx8YwcORIwjvAkJCSwdOlSAEaOHMnHH39MVFQUI0aMIC4ujgULFrBy5UpTmy+99BJt2rTh3XffpXv37vz444/89ttvbN682SoxCiGEEKJssmqS1KdPH1JSUpg8eTKJiYnUrVuXmJgYQkJCAEhMTDRbMyksLIyYmBjGjBnDJ598QmBgIB9++CE9e/Y01YmIiODLL7/kjTfeYMKECVStWpVVq1bRokWLex6fEEIIIcouq0/cjoyMJDIy0uK2xYsXFyhr27Yte/bsuWWbvXr1olevXnfcJ0dHR6Kjoy2egivrynNsUL7jk9jKJomtbJLYyqaSjk2jSuo6OSGEEEKIcsTq924TQgghhLgfSZIkhBBCCGGBJElCCCGEEBZIkiSEEEIIYYEkSRbMmTOHsLAwtFotTZo0YdOmTdbu0l2bNm0azZo1w83NDV9fXx5//HGOHDli7W6VimnTpqHRaBg9erS1u1IiEhIS6N+/P15eXjg7O9OwYUN2795t7W7dtby8PN544w3CwsJwcnKiSpUqTJ48GYPBYO2u3ZE///yTbt26ERgYiEaj4YcffjDbrpRi4sSJBAYG4uTkRLt27Th06JB1OltMt4pNp9Px2muvUa9ePVxcXAgMDGTgwIGcP3/eeh0uhtt932707LPPotFo+P/27jSoqet/A/gTwqpgkM0QWcQRBcElSG1VFFdQUXFfoAjS2qGAbJaKVXTasbggFikKYoWWqo3tiIKgKIos1lEpiKKkRSxoZbDRChZElpL7f+GYfyNRQKK35Pf9zPAi517OfU6Q45dzb+6NjY19a/l6oitjE4vFmDdvHng8HvT09PDee+/J3Xrnv6qzsTU2NiIwMBBmZmbQ0dGBra0tEhISun0cKpJecOTIEYSEhGDDhg24evUqJk6ciFmzZvWKfzSvkp+fj4CAAFy6dAk5OTn4559/4OLigidPnrAdTamKioqQlJSEkSNHsh1FKerq6jBhwgRoaGjg1KlTKC8vR0xMDPT19dmO1mPbt29HYmIi4uPjIRaLsWPHDkRHR+Prr79mO9prefLkCUaNGoX4+HiF23fs2IFdu3YhPj4eRUVF4PP5mDFjBhoaGt5y0u571diamppQUlKCyMhIlJSUIC0tDRUVFZg3bx4LSbuvs5/bc8ePH8fly5chEAjeUrKe62xst2/fhpOTE2xsbJCXl4dr164hMjIS2trabzlp93U2ttDQUGRnZ+PgwYMQi8UIDQ3FmjVrkJ6e3r0DMUTO2LFjGT8/P7k2GxsbJiIigqVEb4ZEImEAMPn5+WxHUZqGhgbG2tqaycnJYZydnZng4GC2I/XYunXrGCcnJ7ZjvBFubm6Mr6+vXNvChQuZ999/n6VEygOAOXbsmOy1VCpl+Hw+s23bNllbc3Mzw+PxmMTERBYSvr4Xx6bIlStXGADMnTt33k4oJXnZ2O7du8cMHDiQuXHjBmNpacl89dVXbz1bTyka27Jly1Ty941hGMbOzo754osv5NocHByYjRs3dqtvWkn6l9bWVhQXF8PFxUWu3cXFBRcvXmQp1Zvx+PFjAFDaQwD/CwICAuDm5obp06ezHUVpMjIy4OjoiCVLlsDExARCoRD79+9nO5ZSODk54dy5c6ioqAAAXLt2DRcuXMDs2bNZTqZ8VVVVuH//vtzcoqWlBWdnZ5WbW4Bn8wuHw1GJFU+pVAovLy+Eh4fDzs6O7ThKI5VKkZWVhaFDh8LV1RUmJiZ49913X3m6sTdxcnJCRkYGampqwDAMzp8/j4qKCri6unarHyqS/uXhw4dob2/HgAED5NoHDBiA+/fvs5RK+RiGQVhYGJycnGBvb892HKUQiUQoKSnB1q1b2Y6iVL///jsSEhJgbW2N06dPw8/PD0FBQbLnGfZm69atw4oVK2BjYwMNDQ0IhUKEhIRgxYoVbEdTuufzh6rPLQDQ3NyMiIgIeHh4qMTDU7dv3w51dXUEBQWxHUWpJBIJGhsbsW3bNsycORNnzpzBggULsHDhQuTn57Mdr8fi4uIwfPhwmJmZQVNTEzNnzsTevXvh5OTUrX5YfyzJfxGHw5F7zTBMh7beLDAwENevX1eZh/7+8ccfCA4OxpkzZ3rFufTukEqlcHR0RFRUFABAKBTi5s2bSEhIwMqVK1lO1zNHjhzBwYMHcfjwYdjZ2aG0tBQhISEQCATw9vZmO94boepzS1tbG5YvXw6pVIq9e/eyHafHiouLsXv3bpSUlKjUzwmA7AMS7u7uCA0NBQCMHj0aFy9eRGJiIpydndmM12NxcXG4dOkSMjIyYGlpiYKCAvj7+8PU1LRbZxuoSPoXIyMjcLncDn/ZSSSSDn8B9lZr1qxBRkYGCgoKYGZmxnYcpSguLoZEIsGYMWNkbe3t7SgoKEB8fDxaWlrA5XJZTPj6TE1NMXz4cLk2W1tbHD16lKVEyhMeHo6IiAgsX74cADBixAjcuXMHW7duVbkiic/nA3i2omRqaiprV6W5pa2tDUuXLkVVVRVyc3NVYhWpsLAQEokEFhYWsrb29nasXbsWsbGxqK6uZi9cDxkZGUFdXV3h/NLb/4B++vQpPvvsMxw7dgxubm4AgJEjR6K0tBQ7d+7sVpFEp9v+RVNTE2PGjEFOTo5ce05ODsaPH89SKuVgGAaBgYFIS0tDbm4urKys2I6kNNOmTUNZWRlKS0tlX46OjvD09ERpaWmvLZAAYMKECR1u1VBRUQFLS0uWEilPU1MT1NTkpyAul9trbwHwKlZWVuDz+XJzS2trK/Lz83v93AL8f4F069YtnD17FoaGhmxHUgovLy9cv35dbm4RCAQIDw/H6dOn2Y7XI5qamnjnnXdUcn5pa2tDW1ubUuYXWkl6QVhYGLy8vODo6Ihx48YhKSkJd+/ehZ+fH9vReiQgIACHDx9Geno69PT0ZKtlPB4POjo6LKfrGT09vQ7XVvXt2xeGhoa9/pqr0NBQjB8/HlFRUVi6dCmuXLmCpKQkJCUlsR2tx+bOnYsvv/wSFhYWsLOzw9WrV7Fr1y74+vqyHe21NDY2orKyUva6qqoKpaWlMDAwgIWFBUJCQhAVFQVra2tYW1sjKioKffr0gYeHB4upu+ZVYxMIBFi8eDFKSkqQmZmJ9vZ22fxiYGAATU1NtmJ3SWc/txcLPg0NDfD5fAwbNuxtR+22zsYWHh6OZcuWYdKkSZgyZQqys7Nx4sQJ5OXlsRe6izobm7OzM8LDw6GjowNLS0vk5+cjNTUVu3bt6t6BevCpO5W1Z88extLSktHU1GQcHBxU4mPyABR+paSksB3tjVCVWwAwDMOcOHGCsbe3Z7S0tBgbGxsmKSmJ7UhK8ffffzPBwcGMhYUFo62tzQwePJjZsGED09LSwna013L+/HmFv2Pe3t4Mwzy7DcDmzZsZPp/PaGlpMZMmTWLKysrYDd1FrxpbVVXVS+eX8+fPsx29U5393F7Um24B0JWxHThwgBkyZAijra3NjBo1ijl+/Dh7gbuhs7HV1tYyPj4+jEAgYLS1tZlhw4YxMTExjFQq7dZxOAzDMN0rqwghhBBCVB9dk0QIIYQQogAVSYQQQgghClCRRAghhBCiABVJhBBCCCEKUJFECCGEEKIAFUmEEEIIIQpQkUQIIYQQogAVSYSQXqu6uhocDgelpaVvpP8DBw7AxcXljfStDBKJBMbGxqipqWE7CiEqiYokQshL+fj4gMPhKHwsj7+/PzgcDnx8fLrcn7KLGnNzc9TW1soeP5OXlwcOh4P6+voe993S0oJNmzYhMjISAPDBBx9gxIgRaG1tldvv5MmT0NDQwC+//NLjY3aXiYkJvLy8sHnz5rd+bEL+F1CRRAh5JXNzc4hEIjx9+lTW1tzcjB9++EHu6ehvW2trK7hcLvh8PtTVlf8YyqNHj0JXVxcTJ04EAMTGxqKhoUGuIKmvr8dHH32EDRs2wNHRUekZ2traOt1n1apVOHToEOrq6pR+fEL+11GRRAh5JQcHB1hYWCAtLU3WlpaWBnNzcwiFQrl9s7Oz4eTkBH19fRgaGmLOnDm4ffu2bLuVlRUAQCgUgsPhYPLkyQCAyZMnIyQkRK6v+fPny61SDRo0CFu2bIGPjw94PB5Wr14ttzJVXV2NKVOmAAD69+8vW+VKTU2FoaEhWlpa5PpftGgRVq5c+dJxi0QizJs3T/ZaT08P3377LWJiYnD58mUAQEhICExNTbFx40bU1NRg2bJl6N+/PwwNDeHu7o7q6mrZ9xcVFWHGjBkwMjICj8eDs7MzSkpK5I7J4XCQmJgId3d39O3bF1u2bEFdXR08PT1hbGwMHR0dWFtbIyUlRfY9I0aMAJ/Px7Fjx146FkLI66EiiRDSqVWrVsn9x5ycnAxfX98O+z158gRhYWEoKirCuXPnoKamhgULFkAqlQIArly5AgA4e/Ysamtr5QqvroiOjoa9vT2Ki4tlp8GeMzc3x9GjRwEAv/32G2pra7F7924sWbIE7e3tyMjIkO378OFDZGZmYtWqVS89VmFhYYfVocmTJ8Pf3x/e3t746aef8OOPPyI1NRWtra2YMmUKdHV1UVBQgAsXLkBXVxczZ86UnZ5raGiAt7c3CgsLcenSJVhbW2P27NloaGiQO8bmzZvh7u6OsrIy+Pr6IjIyEuXl5Th16hTEYjESEhJgZGQk9z1jx45FYWFht95LQkjnlL9GTQhROV5eXli/fr1s5ebnn3+GSCRCXl6e3H6LFi2Se33gwAGYmJigvLwc9vb2MDY2BgAYGhqCz+d3O8fUqVPxySefyF7/e6WGy+XCwMAAwLNrdfT19WXbPDw8kJKSgiVLlgAADh06BDMzM9lK1ovq6+tRX18PgUDQYdvWrVtx+vRpLF++HDExMbC1tUVycjLU1NTwzTffgMPhAABSUlKgr6+PvLw8uLi4YOrUqXL97Nu3D/3790d+fj7mzJkjl/XfBejdu3chFAplBdugQYM6ZBo4cCCuXr2qcCyEkNdHK0mEkE4ZGRnBzc0N3333HVJSUuDm5tZhNQMAbt++DQ8PDwwePBj9+vWTnV67e/euUnK87nU/q1evxpkzZ2SfAktJSZFdlK7I8+uvtLW1O2zT0dHB2rVr0adPHwQHBwMAiouLUVlZCT09Pejq6kJXVxcGBgZobm6WnW6USCTw8/PD0KFDwePxwOPx0NjY2OG9eXGMH3/8MUQiEUaPHo1PP/0UFy9eVJipqampm+8KIaQztJJECOkSX19fBAYGAgD27NmjcJ+5c+fC3Nwc+/fvh0AggFQqhb29fYdPhL1ITU0NDMPItSm6aLlv376vlV0oFGLUqFFITU2Fq6srysrKcOLEiZfub2hoCA6H89KLodXV1cHlcmVFllQqxZgxY3Do0KEO+z5fPfPx8cGDBw8QGxsLS0tLaGlpYdy4cR3emxfHOGvWLNy5cwdZWVk4e/Yspk2bhoCAAOzcuVO2z6NHj2THIYQoD60kEUK65Pn1Na2trXB1de2w/a+//oJYLMbGjRsxbdo02NradigyNDU1AQDt7e1y7cbGxqitrZW9bm9vx40bN7qd8WX9A8CHH36IlJQUJCcnY/r06TA3N39lP8OHD0d5eXmXjuvg4IBbt27BxMQEQ4YMkfvi8XgAnl3jFBQUhNmzZ8POzg5aWlp4+PBhl/o3NjaGj48PDh48iNjYWCQlJcltv3HjRoeL6AkhPUdFEiGkS7hcLsRiMcRiMbhcboftzz/VlZSUhMrKSuTm5iIsLExuHxMTE+jo6CA7Oxt//vknHj9+DODZtUZZWVnIysrCr7/+Cn9//9e615GlpSU4HA4yMzPx4MEDNDY2yrZ5enqipqYG+/fvV3jR+YtcXV1x4cKFLh3X09MTRkZGcHd3R2FhIaqqqpCfn4/g4GDcu3cPADBkyBB8//33EIvFuHz5Mjw9PaGjo9Np35s2bUJ6ejoqKytx8+ZNZGZmwtbWVra9qakJxcXF/+mbXhLSW1GRRAjpsn79+qFfv34Kt6mpqUEkEqG4uBj29vYIDQ1FdHS03D7q6uqIi4vDvn37IBAI4O7uDuDZqTxvb2+sXLkSzs7OsLKykn2cvzsGDhyIzz//HBERERgwYIDs9ODz7IsWLYKuri7mz5/faV+rV6/GyZMnZYXcq/Tp0wcFBQWwsLDAwoULYWtrC19fXzx9+lT2fiUnJ6Ourg5CoRBeXl4ICgqCiYlJp31rampi/fr1GDlyJCZNmgQulwuRSCTbnp6eDgsLC9n9nAghysNhXrwQgBBCVNSMGTNga2uLuLi4Lu2/dOlSCIVCrF+//g0ne31jx45FSEgIPDw82I5CiMqhlSRCiMp79OgRRCIRcnNzERAQ0OXvi46Ohq6u7htM1jMSiQSLFy/GihUr2I5CiEqilSRCiMobNGgQ6urqEBkZKXefJUIIeRUqkgghhBBCFKDTbYQQQgghClCRRAghhBCiABVJhBBCCCEKUJFECCGEEKIAFUmEEEIIIQpQkUQIIYQQogAVSYQQQgghClCRRAghhBCiABVJhBBCCCEK/B8dwDEhYi0VTgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = [1, 1, 1, 1, 4, 8, 15, 36]\n",
    "c = [0, 0, 0, 0, 4.57, 5.47, 6.33, 7.12]\n",
    "t = [[0.08],\n",
    "     [0.25],\n",
    "     [0.50],\n",
    "     [1.00],\n",
    "     [i for i in np.arange(0.5, 2.5, 0.5)],\n",
    "     [i for i in np.arange(0.5, 4.5, 0.5)],\n",
    "     [i for i in np.arange(0.5, 8, 0.5)],\n",
    "     [i for i in np.arange(0.5, 18.5, 0.5)]]\n",
    "p = [99.7, 99.04, 98.01, 95.94, 100, 100, 100, 100]\n",
    "per = 2\n",
    "\n",
    "r = {t[i][0]: np.log(100/p[i]) / t[i][0] for i in range(4)}\n",
    "\n",
    "K = 8\n",
    "T = np.unique(np.hstack(t)) # list(set().union(*t))\n",
    "T.sort()\n",
    "N = len(T)\n",
    "k =  [t[i][-1] for i in range(K)]\n",
    "k.sort()\n",
    "L = N - K \n",
    "l = list(set(T) - set(k))\n",
    "l.sort()\n",
    "\n",
    "\n",
    "def f(r_k):\n",
    "    cs = CubicSpline(k, r_k, bc_type='natural')  \n",
    "    r_l = cs(l)\n",
    "    r.update({timings: rates for timings, rates in zip(k, r_k)})\n",
    "    r.update({timings: rates for timings, rates in zip(l, r_l)})\n",
    "\n",
    "    res = []\n",
    "    for (price, coupon, timings) in zip(p, c, t):\n",
    "        app_r = [r[i] for i in timings]\n",
    "        app_r, timings = np.array(app_r), np.array(timings)\n",
    "        cf = np.full(len(timings), coupon/per)\n",
    "        cf[-1] += 100\n",
    "        pv_cf = np.sum(cf * np.exp(-app_r * timings))\n",
    "        res.append(price - pv_cf)\n",
    "    \n",
    "    return res\n",
    "\n",
    "r_guess = np.append(list(dict.values(r)), np.zeros(K-len(r)))\n",
    "spots = fsolve(f, r_guess)\n",
    "\n",
    "spot_mat = np.linspace(0.08, 18, 100)\n",
    "spot_interp = CubicSpline(k, spots, bc_type=\"natural\")(spot_mat)\n",
    "\n",
    "full_spots = [r[i] for i in T]\n",
    "forwards = np.array([ ((full_spots[i] * T[i]) - (full_spots[i-1] * T[i-1])) / (T[i] - T[i-1]) for i in range(1, len(T))])\n",
    "\n",
    "fwd_mat = np.linspace(0.25, 18, 100)\n",
    "fwd_interp = CubicSpline(T[1:], forwards, bc_type=\"natural\")(fwd_mat)\n",
    "\n",
    "plt.plot(k, spots, 'o', label='Spot Rates')\n",
    "plt.plot(spot_mat, spot_interp, label=\"Interpolated Spot Curve\")\n",
    "plt.plot(fwd_mat, fwd_interp, \"--\", label=\"Forward Curve\")\n",
    "plt.xlabel('Maturity (Years)')\n",
    "plt.ylabel('Spot Rate (%)')\n",
    "plt.title('Interpolated Yield Curve using Cubic Spline')\n",
    "plt.xlim((0,max(k)))\n",
    "plt.ylim((0,0.15))\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example 5**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = [1, 1, 1, 1, 4, 8, 15, 36]\n",
    "c = [0, 0, 0, 0, 4.99, 5.11, 5.24, 5.5]\n",
    "t = [[0.08],\n",
    "     [0.25],\n",
    "     [0.50],\n",
    "     [1.00],\n",
    "     [i for i in np.arange(0.5, 2.5, 0.5)],\n",
    "     [i for i in np.arange(0.5, 4.5, 0.5)],\n",
    "     [i for i in np.arange(0.5, 8, 0.5)],\n",
    "     [i for i in np.arange(0.5, 18.5, 0.5)]]\n",
    "p = [99.63, 98.87, 97.71, 95.33, 100, 100, 100, 100]\n",
    "per = 2\n",
    "\n",
    "r = {t[i][0]: np.log(100/p[i]) / t[i][0] for i in range(4)}\n",
    "\n",
    "K = 8\n",
    "T = np.unique(np.hstack(t)) # list(set().union(*t))\n",
    "T.sort()\n",
    "N = len(T)\n",
    "k =  [t[i][-1] for i in range(K)]\n",
    "k.sort()\n",
    "L = N - K \n",
    "l = list(set(T) - set(k))\n",
    "l.sort()\n",
    "\n",
    "\n",
    "def f(r_k):\n",
    "    cs = CubicSpline(k, r_k, bc_type='natural')  \n",
    "    r_l = cs(l)\n",
    "    r.update({timings: rates for timings, rates in zip(k, r_k)})\n",
    "    r.update({timings: rates for timings, rates in zip(l, r_l)})\n",
    "\n",
    "    res = []\n",
    "    for (price, coupon, timings) in zip(p, c, t):\n",
    "        app_r = [r[i] for i in timings]\n",
    "        app_r, timings = np.array(app_r), np.array(timings)\n",
    "        cf = np.full(len(timings), coupon/per)\n",
    "        cf[-1] += 100\n",
    "        pv_cf = np.sum(cf * np.exp(-app_r * timings))\n",
    "        res.append(price - pv_cf)\n",
    "    \n",
    "    return res\n",
    "\n",
    "r_guess = np.append(list(dict.values(r)), np.zeros(K-len(r)))\n",
    "spots = fsolve(f, r_guess)\n",
    "\n",
    "spot_mat = np.linspace(0.08, 18, 100)\n",
    "spot_interp = CubicSpline(k, spots, bc_type=\"natural\")(spot_mat)\n",
    "\n",
    "full_spots = [r[i] for i in T]\n",
    "forwards = np.array([ ((full_spots[i] * T[i]) - (full_spots[i-1] * T[i-1])) / (T[i] - T[i-1]) for i in range(1, len(T))])\n",
    "\n",
    "fwd_mat = np.linspace(0.25, 18, 100)\n",
    "fwd_interp = CubicSpline(T[1:], forwards, bc_type=\"natural\")(fwd_mat)\n",
    "\n",
    "plt.plot(k, spots, 'o', label='Spot Rates')\n",
    "plt.plot(spot_mat, spot_interp, label=\"Interpolated Spot Curve\")\n",
    "plt.plot(fwd_mat, fwd_interp, \"--\", label=\"Forward Curve\")\n",
    "plt.xlabel('Maturity (Years)')\n",
    "plt.ylabel('Spot Rate (%)')\n",
    "plt.title('Interpolated Yield Curve using Cubic Spline')\n",
    "plt.xlim((0,max(k)))\n",
    "plt.ylim((0,0.15))\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As is necessary for any reasonable yield curve estimation methodology, all forward rate curves exhibit a fair degree of smoothness. This is in contrast to some other methodologies, e.g., McCulloch, where forward rate curves exhibit “knuckles” and undesirable asymptotic properties.\n",
    "\n",
    "In this section we have described a Richard Deaves and Mahmut Parlar's technique for operationalizing the bootstrap methodology for estimating the yield curve given any available data set of bond yields. The problems of illiquidity and missing data points must always be confronted. Illiquidity can be tackled by using some sort of **smoothing technique** (either before or after the bootstrap) or **averaged yield data** (data on four Canadian T-bills and four synthetic par bonds, whose yields were calculated as averages over all bonds in the neighborhood of the relevant maturity.). In the illustration of our methodology using Canadian bond data we employed averaged yields. Missing data points were dealt with by the use of spline interpolation. More specifically, the cubic spline was selected as it provides sufficient flexibility to ensure that the interpolant is continuously differentiable and has continuous second derivatives. We used SciPy's `fsolve()` optimization algorithm to solve the root for a function wherein an interpolation equation is used to solve (reduce) for the missing data points and solve the nonlinear bond pricing equation system in order to obtain the points on the yield curve.\n",
    "\n",
    "The three examples presented here demonstrate the usefulness of the methodology. The yield curves resulting from the estimation appear to have reasonable shapes, and in addition the forward rate curves are clearly well-behaved as well. Finally, another strength of our methodology is its ease of implementation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Polynomial Spline & Exponential Spline Method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nelson & Siegel - Parsimonious Modeling of Yield Curves"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [Interpolation Methods for Curve Construction, Hagan & West 2006](https://www.deriscope.com/docs/Hagan_West_curves_AMF.pdf)\n",
    "- [Methods for Constructing a Yield Curve, Hagan & West](https://downloads.dxfeed.com/specifications/dxLibOptions/HaganWest.pdf)\n",
    "- [A generalized bootstrap method to determine the yield curve, Richard Deaves & Mahmut Parlar 2000](https://www.tandfonline.com/doi/abs/10.1080/13504860010021162)\n",
    "- [Bootstrapping Zero Curves - Rebrained!](https://rebrained.com/?p=23)\n",
    "- [Bootstrapping (Finance) - Wikipedia](https://en.wikipedia.org/wiki/Bootstrapping_%28finance%29)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Interpolation and Polynomial Approximation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Natural Cubic Spline Interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.7999999999999998\n",
      "1.7999999999999998\n",
      "\n",
      "CSI(1.6) = 1.5119999999999998\n",
      "[[ 0.75 -0.75]\n",
      " [ 0.    2.25]\n",
      " [-2.75 -0.5 ]\n",
      " [ 3.    1.  ]]\n",
      "CSI(0) (1 <= x <= 2) = 3.0 + -2.75 (x-1) + 0.0 (x-1)^2  + 0.75 (x-1)^3\n",
      "CSI (1.6) = 1.512\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 650x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3 data points (1, 3), (2, 1), (3, 2)\n",
    "x = np.array([1,2,3])\n",
    "y = np.array([3,1,2])\n",
    "\n",
    "# calculate linear interpolation for 3 points\n",
    "# produces a convex combination of the nearest neighboring points.\n",
    "print(interp1d(x,y)(1.6))\n",
    "print(np.interp(1.6, x, y))\n",
    "print()\n",
    "\n",
    "# calculate 2 (n - 1) natural cubic spline polynomials for 3 points \n",
    "# provides a smooth (i.e., differentiable) fit to the available data points when the degree of the piecewise polynomial approximation is d = 3.\n",
    "# produces a linear combination of all y results. \n",
    "# This result has the important implication that even with cubic spline interpolation, for a given value of the independent\n",
    "# variable x, the point on the interpolated curve is obtained as a linear function of the symbolic data points.\n",
    "cs = CubicSpline(x, y, bc_type='natural')\n",
    "print(\"CSI(1.6) =\", cs(1.6))\n",
    "\n",
    "# Coefficients of the polynomials on each segment\n",
    "print(cs.c)\n",
    "\n",
    "# Polynomial coefficients for 1 <= x <= 2\n",
    "a0 = cs.c[3,0]\n",
    "b0 = cs.c[2,0]\n",
    "c0 = cs.c[1,0]\n",
    "d0 = cs.c[0,0]\n",
    "\n",
    "# Polynomial equation for different 1 <= x <= 2 region\n",
    "print('CSI(0) (1 <= x <= 2) =', a0, '+', b0, '(x-1) +', c0, '(x-1)^2  +', d0, '(x-1)^3')\n",
    "cs16 = a0 + (b0*0.6) + (c0*(0.6**2)) + (d0*(0.6**3))\n",
    "print(\"CSI (1.6) =\", cs16)\n",
    "\n",
    "\n",
    "xs = np.linspace(1,3, 100)\n",
    "fig, ax = plt.subplots(figsize=(6.5, 4))\n",
    "ax.plot(x, y, 'o', label='Data')\n",
    "ax.plot(xs, cs(xs), label=\"Cubic Spline Interp\")\n",
    "ax.plot(1.6, cs(1.6), 'gx', label='CSI (1.6)')\n",
    "ax.legend(loc='upper right', ncol=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CSI(1.6) = 1.5119999999999998\n",
      "[[ 0.75 -0.75]\n",
      " [ 0.    2.25]\n",
      " [-2.75 -0.5 ]\n",
      " [ 3.    1.  ]]\n",
      "CSI(0) (1 <= x <= 2) = 3.0 + -2.75 (x-1) + 0.0 (x-1)^2  + 0.75 (x-1)^3\n",
      "CSI (1.6) = 1.5119999999999998\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 650x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3 data points (1, 3), (2, 1), (3, 2)\n",
    "x = np.array([1,2,3])\n",
    "y = np.array([3,1,2])\n",
    "\n",
    "# calculate 2 (n - 1) natural cubic spline polynomials for 3 points \n",
    "# provides a smooth (i.e., differentiable) fit to the available data points when the degree of the piecewise polynomial approximation is d = 3\n",
    "cs = CubicSpline(x, y, bc_type='natural')\n",
    "print(\"CSI(1.6) =\", cs(1.6))\n",
    "\n",
    "# Coefficients of the polynomials on each segment\n",
    "print(cs.c)\n",
    "# Expected:\n",
    "# [0.75  -0.75]\n",
    "# [-2.25  6.75]\n",
    "# [-0.5  -18.5]\n",
    "# [5        17]\n",
    "\n",
    "# Polynomial coefficients for 1 <= x <= 2\n",
    "a0 = cs.c[3,0]\n",
    "b0 = cs.c[2,0]\n",
    "c0 = cs.c[1,0]\n",
    "d0 = cs.c[0,0]\n",
    "\n",
    "# c[k, i] is a coefficient for (x-x[i])**(3-k) on the segment between x[i] and x[i+1]\n",
    "\n",
    "# Polynomial equation for different 1 <= x <= 2 region\n",
    "print('CSI(0) (1 <= x <= 2) =', a0, '+', b0, '(x-1) +', c0, '(x-1)^2  +', d0, '(x-1)^3')\n",
    "cs16 = (a0 * (1.6 - 1)**(3-3)) + (b0 * (1.6 - 1)**(3-2)) + (c0 * (1.6 - 1)**(3-1)) + (d0 * (1.6 - 1)**(3-0)) \n",
    "print(\"CSI (1.6) =\", cs16)\n",
    "\n",
    "xs = np.linspace(1,3, 100)\n",
    "fig, ax = plt.subplots(figsize=(6.5, 4))\n",
    "ax.plot(x, y, 'o', label='Data')\n",
    "ax.plot(xs, cs(xs), label=\"Cubic Spline Interp\")\n",
    "ax.plot(1.6, cs(1.6), 'gx', label='CSI (1.6)')\n",
    "ax.legend(loc='upper right', ncol=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.512\n",
      "[3.         2.08333333 0.25       1.41666667 2.        ]\n"
     ]
    }
   ],
   "source": [
    "# Using SciPy's `make_interp_spline` function:\n",
    "cs_Bspline = make_interp_spline(x, y, k=3, bc_type='natural')\n",
    "print(cs_Bspline(1.6))\n",
    "print(cs_Bspline.c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.75 -0.75]\n",
      " [ 0.    2.25]\n",
      " [-2.75 -0.5 ]\n",
      " [ 3.    1.  ]]\n",
      "CSI(1.6) = 1.1119999999999999\n",
      "CSI(0) (2 <= x <= 3) = 1.0 + -0.49999999999999994 (x-2) + 2.25 (x-2)^2  + -0.7500000000000002 (x-2)^3\n",
      "CSI (1.6) = 1.1119999999999999\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 650x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array([1,2,3])\n",
    "y = np.array([3,1,2])\n",
    "\n",
    "cs = CubicSpline(x, y, bc_type='natural')\n",
    "print(cs.c)\n",
    "\n",
    "print(\"CSI(1.6) =\", cs(2.4))\n",
    "\n",
    "# Polynomial coefficients for 2 <= x <= 3\n",
    "a0 = cs.c[3,1]\n",
    "b0 = cs.c[2,1]\n",
    "c0 = cs.c[1,1]\n",
    "d0 = cs.c[0,1]\n",
    "\n",
    "# c[k, i] is a coefficient for (x-x[i])**(3-k) on the segment between x[i] and x[i+1]\n",
    "\n",
    "# Polynomial equation for different 2 <= x <= 3 region\n",
    "print('CSI(0) (2 <= x <= 3) =', a0, '+', b0, '(x-2) +', c0, '(x-2)^2  +', d0, '(x-2)^3')\n",
    "cs16 = (a0 * (2.4 - 2)**(3-3)) + (b0 * (2.4 - 2)**(3-2)) + (c0 * (2.4 - 2)**(3-1)) + (d0 * (2.4 - 2)**(3-0)) \n",
    "print(\"CSI (1.6) =\", cs16)\n",
    "\n",
    "xs = np.linspace(1,3, 100)\n",
    "fig, ax = plt.subplots(figsize=(6.5, 4))\n",
    "ax.plot(x, y, 'o', label='Data')\n",
    "ax.plot(xs, cs(xs), label=\"Cubic Spline Interp\")\n",
    "ax.plot(2.4, cs(2.4), 'gx', label='CSI (1.6)')\n",
    "ax.legend(loc='upper right', ncol=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.00368249  0.00604395 -0.00236146]\n",
      " [ 0.         -0.00552373  0.00354219]\n",
      " [ 0.0052105   0.00244864  0.00145787]\n",
      " [ 0.02010067  0.02224561  0.02284449]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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GXJhhwI+fwNTW8Nt68C4Hnd+Dx+dBeedPyRc3p//y3n77bZ588kmeeuopGjVqxLvvvkvNmjWZOnVqnu0/+OADatWqxbvvvkujRo146qmn+Pvf/86ECRPsbWbNmsUzzzxDs2bNaNiwIdOnTycnJyfXju7UqVM8/vjjTJ8+naCgoGvWmp6eTlpamsOjqNwTHsLUHi0IDnT8H1xwoB9Te7QosgFb/v7+PPnkk7z00kusWLGCn3/+mT59+th3qrVq1cLHx4f333+fX3/9lcWLFzNq1CiH16hduzY2m42vvvqKY8eOcerUKYKCgqhYsSLTpk1j3759fPfdd8TGxhZJH0qjm2++mccffzzXFUH16tUjLi6ODRs2sGvXLv7xj39w9OhRhzahoaF8//33HDhwwH46qlWrVpQtW5YhQ4awb98+Zs+ezccff3zNOgrj52iz2fjoo4/Ys2cPbdq0YenSpfz666/89NNPjB49mgceeMDet5o1azJixAj27NnD119/netKQjCPXDz33HN8//33/PjjjzzxxBPceuuteY7nAfNqrrfeeouJEyeyd+9efvzxx6teaXXHHXfw4YcfsmXLFg4cOMDSpUsZMmQId955JwEBAfZ269evZ9y4cezZs4fJkyczb948h3FD1+tf//oXM2fOZMSIEezYsYNdu3Yxd+7cXIOGr1doaChr1qzh8OHDpKSkADBo0CDi4+N59tln2bp1K3v37mXx4sU899xz+XrNyZMns3DhQn755ReeffZZ/vzzT4exgeKmTv4Bcx6Dxf0h4xTUioKn10NEnwIfGS92hhPS09MNT09PY8GCBQ7rBwwYYLRp0ybPbaKjo40BAwY4rFuwYIHh5eVlZGRk5LlNWlqa4efnZyxZssRhfa9evYyBAwcahmEYbdu2NZ5//vmr1jt8+HAD8+Iph0dqamqutmfPnjV27txpnD179qqveS1Z2TnGhn0pxqKE340N+1KMrOyc63q9/Dh58qTRo0cPo2zZskbVqlWNcePGOXx/Zs+ebYSGhhq+vr5GVFSUsXjxYgMwEhIS7K/x2muvGcHBwYbNZjN69+5tGIZhxMXFGY0aNTJ8fX2NJk2aGKtWrTIAY+HChUXeJ1fTu3dv44EHHnBYd+DAAcPX19e49M/s+PHjxgMPPGD4+/sbVapUMV599VWjV69eDtvu3r3buPXWW40yZcoYgJGYmGgYhmEsXLjQqFevnuHn52fcd999xrRp0xxee/jw4UbTpk1z1Xatn2NiYmKu34e87N692+jVq5dRrVo1w8fHx6hdu7bRrVs348cff7S3WbdunXHzzTcbfn5+RnR0tDFv3jyHPnz00UdGYGCgMX/+fKNOnTqGj4+PcddddxkHDhy4aj8++OAD48YbbzS8vb2NkJAQ47nnnrtinWPGjDGioqKMChUqGH5+fkadOnWMAQMGGCkpKfY2tWvXNkaOHGk8+uij9r+bd9991+F1rvY9WrlypQEYf/75p719QkKCQ18NwzCWLVtmtG7d2ihTpowREBBgtGzZ0pg2bdoVa7+873n9Xj3//PNG27Zt7cvx8fFGkyZNcv2ubdq0yWjfvr3h7+9vlCtXzmjSpIkxevRoh+/BO++84/DaF/o5e/Zso1WrVoaPj4/RqFEjY8WKFVesubD2nVLC/bzQMN4INYzhAYbxWiXDWPeuYWRnWV2VYRiGkZqaesXP9ss5FXoOHz5sAMb69esd1o8ePdpo0KBBntvUr1/f4Q/NMAxj/fr1BmAcOXIkz22eeeYZo27dug5/RHPmzDHCw8Pt6/ITes6dO2ekpqbaH4cOHSry0CMiJV9eH/iS/wB8Ke07S7kzJwzjiyfNsDM8wDCm3m4YR3dYXZUDZ0JPga7eunxAm2EYVx3kllf7vNYDjBs3jjlz5rBq1Sr7YL9Dhw7x/PPPs3z5cqcGAPr6+uLr65vv9iIiInLe3m/NU1knk8DmCdGx0OZl8Lr2uLCSyqnQU6lSJTw9PXONQUhOTqZq1ap5bhMcHJxney8vr1wTXU2YMIExY8bw7bffOgxU3rJlC8nJyURERNjXZWdns2bNGiZNmkR6errDJZ0iIiJSQOknzauytnxsLlesBw9+CDXynuLAlTgVenx8fIiIiCAuLo4HH7x4WVpcXJx9MOPloqKiWLJkicO65cuXExkZ6XAp5vjx43n99df55ptvcs0dcffdd+eal+KJJ56gYcOGDBo0SIFHRJxy+W0xxBQaGnrNaTCklDuwDhY9DX+dvyK71dNw97/Ap2DzlpU0Tp/eio2NpWfPnkRGRhIVFcW0adM4ePAg/fqZd0595ZVXOHz4MDNnzgTMm/9NmjSJ2NhY+vbtS3x8PDNmzHC439C4ceMYNmwYs2fPJjQ01H5kyN/fH39/f8qXL59rErVy5cpRsWJFzQwsIiJyvTLPmpMMbpwCGBBYC7pMhrA2VldWqJwOPV27duX48eO89tprJCUlER4eztKlS6lduzZgztFx6Zw9YWFhLF26lBdeeIHJkydTrVo1Jk6c6DA1/pQpU8jIyOCRRx5xeK/hw4czYsSIAnatYPS/HBGR/NM+sxT4fTMs7AfHz88Z1qIXxIwGv4Crb+eCbIYb/campaURGBhIamqqw3wdYI4R2rt3L2XLlqVy5cqafVRE5BoMw+DYsWOcOXOG+vXra6iBq8lKh1VvwPp3zZuE+gfD/e9DgxirK3PK1T7bL6d7b53n6elJjRo1+P3333W+X0Qkn2w2GzVq1FDgcTVJ22Dh05C8w1y++VHo+CaULfzbJZUkCj2X8Pf3p379+le8X5CIiDjy9vZW4HEl2Zmw9i1YMx5ysqBsJfMmoY3vt7qyYqHQcxlPT0/9AYuISOnzxw5z7M7Rn8zlRvfDvW+Df2Vr6ypGCj0iIiKlWXaWOW5n1RuQkwllgqDTBAh/2HXumVVIFHpERERKqz92mvPuJG01l2/sBPe9C+XznlC4tFPoERERKW0uHN1Z/SZkZ4BfIHQcB026ut3RnUsp9IiIiJQmf+yEL5+BIwnmcoN7zKM7ASGWllUSKPSIiIiUBtmZsO5d8+hOTqZ5dOeeN6HpY259dOdSCj0iIiKu7uh2WPTMxSuzdHQnTwo9IiIiriorw5x3Z+0Ec94dvxvOj915VEd38qDQIyIi4ooO/whf9r84q3LD+8x5d9z0yqz8UOgRERFxJZlnYdVY2PC+ec+sshXNoztuOO+OsxR6REREXMVv8bC4PxzfZy6HP2LeM6tcJWvrchEKPSIiIiXduTRYMRJ++Le5XD7EvGfWjR2trcvFKPSIiIiUZHu+ga9egLTD5nLznhDzOpS5wdKyXJFCj4iISEl0OgWWDYbt88zloFDoPBHqtLW0LFem0CMiIlKSGAZs+wy+GQJnT4DNA6KehTuGgE9Zq6tzaQo9IiIiJcWJRPNU1q8rzeWq4XD/RKgeYW1dpYRCj4iIiNWys2DjFFg5BrLOgpcftB0ErZ8DT2+rqys1FHpERESs9PsWWPI8/LHdXA6Nhs7vQcW61tZVCin0iIiIWOFcGnz3OmyaBhjmLSRiXofmPTTJYBFR6BERESlOhgG/fAVLX4aTR8x1TbpCzGjwr2xtbaWcQo+IiEhx+fM3+N/LsGeZuRwUBve9DXXvsrYuN6HQIyIiUtSyMyF+Eqx60xyo7OENtw2ANi+Bdxmrq3MbCj0iIiJF6bcN8PU/IXmnuVz7dvPoTuUbra3LDSn0iIiIFIVTyRD3L9g2x1wuW9Ect9P0MQ1UtohCj4iISGHKyYbN/4EVoyA9FbBBRG+4eziUrWB1dW5NoUdERKSwHPoBlr4ISVvN5ZCmcO87UEMzKpcECj0iIiLX69Qx+HYEbP3UXPYNhLuHQeTfwcPT0tLkIoUeERGRgsrOgh/+bd4+Ij3VXNe8B9w9QnPulEAKPSIiIgXx62pYNvjiVVkhzaDTBKh5i6VlyZUp9IiIiDjjzwOw/FXYtcRcLlMB7v4XtOilU1klnEKPiIhIfqSfgvXvwvqJkJ0ONk+45Sm4Y7CuynIRCj0iIiJXk5NjzrWz4jU4ddRcF9YG7nkTqja2tjZxikKPiIjIlfy2AZa9cvES9KBQaD8KGnXWBIMuSKFHRETkcsf3m5eg71psLvuUh7YvQat+4OVraWlScAo9IiIiF5w5AavHmZeh52SCzQNa9IY7h+oS9FJAoUdERCTzHGyaBmsmXJxvp147aP8aVL3J2tqk0Cj0iIiI+8rJhp8+h5WjIfWQua5qOMSMgrp3WVubFDqFHhERcT+GAXvjzHE7yTvMdeWrwV1DoWk3zbdTSin0iIiIezn4vXn5+W/rzGW/QLg9Flr9A7zLWFubFCmFHhERcQ9Ht8N3r8OeZeayp68ZdG5/QZMLugmFHhERKd1S9sGqMfDzfHPZ5gnNH4e2gyCwhrW1SbFS6BERkdLp+H5YMx5+mgtGjrku/GHz8vOKda2tTSyh0CMiIqXLnwfMsLN1DhjZ5roGHc1BysE3W1qaWEuhR0RESofj+2Hd27DtM8jJMtfVjzFvCFo9wtrapERQ6BEREdd2bA+sfQu2f37xNFbdu8zTWDUira1NShSFHhERcU1J22DdO7BjEWCY6+p3gDYvQc1brKxMSiiFHhERcR2GAb+tN8POvm8vrm94H7R5Eao1t642KfEUekREpOTLyYbd/4P178Hvm8x1Ng/zaqzbBkJwuKXliWvwKMhGU6ZMISwsDD8/PyIiIli7du1V269evZqIiAj8/PyoU6cOH3zwgcPz06dPJzo6mqCgIIKCgmjXrh2bNm1yaDN16lSaNGlCQEAAAQEBREVF8b///a8g5YuIiKvIOAM/zIBJt8Dcx83A4+kLkX+H536Eh/+twCP55nTomTt3LgMHDmTo0KEkJCQQHR1Nx44dOXjwYJ7tExMT6dSpE9HR0SQkJDBkyBAGDBjA/Pnz7W1WrVpFt27dWLlyJfHx8dSqVYuYmBgOHz5sb1OjRg3eeOMNNm/ezObNm7nrrrt44IEH2LFjRwG6LSIiJdrJP2DlGHg3HL6OhRP7z98u4gUYuB3uewcqhFldpbgYm2EYhjMbtGrVihYtWjB16lT7ukaNGtGlSxfGjh2bq/2gQYNYvHgxu3btsq/r168f27ZtIz4+Ps/3yM7OJigoiEmTJtGrV68r1lKhQgXGjx/Pk08+mefz6enppKen25fT0tKoWbMmqampBAQEXLOvIiJSzA7/CN9/AD8vgJxMc90NteDWZ6F5D/D1t7Y+KXHS0tIIDAzM12e7U2N6MjIy2LJlC4MHD3ZYHxMTw4YNG/LcJj4+npiYGId1HTp0YMaMGWRmZuLt7Z1rmzNnzpCZmUmFCnnfCyU7O5t58+Zx+vRpoqKirljv2LFjGTly5LW6JSIiVsrKgF2L4fsPL47XAajREm7tB40eAE8NQZXr59RvUUpKCtnZ2VStWtVhfdWqVTl69Gie2xw9ejTP9llZWaSkpBASEpJrm8GDB1O9enXatWvnsH779u1ERUVx7tw5/P39WbhwIY0bN75iva+88gqxsbH25QtHekREpAT46xBs+Qh+nAmnj5nrPLwh/CHzRqCaUFAKWYGis81mc1g2DCPXumu1z2s9wLhx45gzZw6rVq3Cz8/P4bkbb7yRrVu38tdffzF//nx69+7N6tWrrxh8fH198fX1zVefRESkGGRnwf4VsOVj827nFyYT9A+GiD4Q+QSUD7ayQinFnAo9lSpVwtPTM9dRneTk5FxHcy4IDg7Os72XlxcVK1Z0WD9hwgTGjBnDt99+S5MmTXK9lo+PD/Xq1QMgMjKSH374gffee48PP/zQmW6IiEhxO5EICZ/C1llwMuni+rA2cMtTcGMn8Mw93EGkMDkVenx8fIiIiCAuLo4HH3zQvj4uLo4HHnggz22ioqJYsmSJw7rly5cTGRnpMJ5n/PjxvP7663zzzTdERuZv2nDDMBwGKouISAmSfgp2LYFtsyFxzcX1ZSpA08cg4gmo3MC6+sTtOH16KzY2lp49exIZGUlUVBTTpk3j4MGD9OvXDzDH0Rw+fJiZM2cC5pVakyZNIjY2lr59+xIfH8+MGTOYM2eO/TXHjRvHsGHDmD17NqGhofYjQ/7+/vj7myP1hwwZQseOHalZsyYnT57ks88+Y9WqVSxbtuy6vwkiInJ12TkGmxJPkHzyHFXK+9EyrAKeHnkMa8jJgQNrzJt+7lwMmafPP2GDundCi17mUR0vDT2Q4ud06OnatSvHjx/ntddeIykpifDwcJYuXUrt2rUBSEpKcpizJywsjKVLl/LCCy8wefJkqlWrxsSJE3n44YftbaZMmUJGRgaPPPKIw3sNHz6cESNGAPDHH3/Qs2dPkpKSCAwMpEmTJixbtoz27dsXpN8iIpJPy35OYuSSnSSlnrOvCwn0Y3jnxtwTHmLeGuLwj/DzF7BjoePpqwp1oGk3aNIVgmpbUL3IRU7P0+PKnLmWX0REzMDz9Kc/cvkHhQ2DxrbfmNj0N+r+8Q38eeDik36BcNND0Kw71LgFrnKhi8j1KrJ5ekRExH1k5xiMXLLTHnhs5NDcto+Onpu4x+MHanocg1/OP+ld1jxtFf4w1Ltbp6+kRFLoERGRPG1KPEFq6l908NjOXR4J3OWZQGVbqv35s4YPq3KaUrdtDxq0+Rv4lLOwWpFrU+gREZGLDANS9sC+FdRJ+JoE34342rLsT6cZZfgupzn/y27JmpwmnMWP9yo1o4ECj7gAhR4REXd36hgcWAv7v4P9KyHtdwCqAtjgt5wqrMhpwYqc5mzKaUTmZR8dVcr75X5NkRJIoUdExN2cOQG/bTCDTuIaSN7p+LynL9RuTU6du+i+OpDvT1bEIPdgZBsQHGhevi7iChR6RERKu9Tf4bd4OLjB/PfYrtxtqtwEddpC3buhdmvwKYsH0OeGJL7/9Eds4HAF14UINLxz47zn6xEpgRR6RERKk8xzkLQVfv8BDm2C3zfDySO521Wsb94CIiwaQqOhXKU8X+6e8BCm9miRa56e4Evn6RFxEQo9IiKuKjvLPGpz+Ec48qP5b/JOyMlybGfzhJCm5hGcWrdCragrhpy83BMeQvvGwfmbkVmkBFPoERFxBZlnzUCT9BMkbTMfyTsh61zutuUqQ42WUPMW899qzcGn7HW9vaeHjai6Fa/dUKQEU+gRESlJDAPSjsAfO+CPn83H0e1wfB8YObnb+wZAtWZQrQVUb2H+G1hDsyCL5EGhR0TEKmdOwLFfzCM2ybvgj52QvAPOpebdvmxF8zTVpY8bQsHDo1jLFnFVCj0iIkXt7J+Q/IsZcI7tNsfhJP8Cp47m3d7mCZXqQ9WboGo4BDeB4HDwr6ojOCLXQaFHRKSwnE45H2wuhJvz/57648rbBNaCKo2gSkPzsvGqjaFSA927SqQIKPSIiDjDMOBUsnm05tJgc+wXOHP8ytsF1oTKN0Llhua/VRqb//qWL77aRdycQo+IyJWcOnb+VNT5x7FfzH/P/XXlbW6oBZUbXRJwGkLlBgo3IiWAQo+ISMZpc4xN8g5zMPEfP5vh5kzKFTawQYWw8+GmwcWQU6m+7jQuUoIp9IiI+zAMOJlkznXzx3Y4ev6S8OP7cbzJwgU2CAo1x9xUbnjx30r1wbtMMRcvItdLoUdESifDgL8OwpGEi5P5Hf0JTh/Lu325yubVUhcGE18Yc6MjNyKlhkKPiJQOZ06Y95s6vOXibRnyGlhs8zSvjgq+2bwMvGq4+bV/leKvWUSKlUKPiLienBxzgPHBePOGmoc2wYn9udt5eJlHb6o1N+e6CWlmHsXRqSkRt6TQIyIlX1aGeeTmtw1m0Dn0fd6zFlesDzUioXqEGXSqhoO3X/HXKyIlkkKPiJQ82VnmGJzE1XBgLRzcCJlnHNt4lzNvqFmzFdS4xQw6ZStYU6+IuASFHhEpGf46CPtWwP7vzLBz+ZGcshWhdmuo1RpqR0HVm8FTuzARyT/tMUTEGtmZ5qmqPd+Yj+N7HZ/3C4Tat0NYGwiLNufC0Y01ReQ6KPSISPE5+5cZcHYvNY/opKddfM7mCTVbQt27zEe15uDhaVmpIlL6KPSISNE6lQy/fA27lpinrXKyLj5XrjLU7wANYqDOHebRHRGRIqLQIyKF78wJ2LUYtn8BB9bhMNtxlcbQ8F5o0PH80RydshKR4qHQIyKFI+OMeUTn5y/MAck5mRefq9YcGt1vPirVs65GEXFrCj0iUnCGYc6Zs3UW/LwQMk5efK7qzRD+EIQ/DEG1ratRROQ8hR4Rcd6pZEj41HxcOhPyDbWgyWNm0KnS0Lr6RETyoNAjIvljGOb4nM3/MQclXzh95V0ObuoCzbqbc+hojI6IlFAKPSJydemnYNsc2DQNUvZcXF89EiKfgMZdwNffsvJERPJLoUdE8vbXIdj0IWyZCennZ0f28Ycmj0LEExDSxNr6REScpNAjIo6ObIX178LOxWBkm+sq1IVW/aBZN/Atb2V1IiIFptAj4kaycww2JZ4g+eQ5qpT3o2VYBTw9bBfH66x725wp+YI6d8Ctz0C99hqrIyIuT6FHxE0s+zmJkUt2kpR6zr4uJMCXSbccI+LAv+HwZnOlzRNufgRaD4DgcIuqFREpfAo9Im5g2c9JPP3pj5fMi2zQxuMnYs99QbP15y859/SFFj2h9XMQFGpNoSIiRUihR6SUy84xGLlkpz3wRHnsINZrHrd4mFdinTF8WeDVkW7Pj8MzoKp1hYqIFDGFHpFSblPiCZJSz9HYdoDBXnNo47kdgHOGN59mt+ODrPtJSQ+k7jEvogIsLlZEpAgp9IiUcif/2M9b3lN40GM9HjaDDMOT2dl3MyXrAZIJsrdLPnnuKq8iIuL6FHpESqtzabB2Au3ip+LhmQHAl9mtmZD1Nw4ZuU9jVSnvV9wViogUK4UekdImJwd++gy+HQGn/sAD2GILZ+S5x/jJqJOruQ0IDjQvXxcRKc0UekRKk9+3wP9egsNbzOUKdaHDGI5lNGH7rARscMkVXGbgARjeubE5X4+ISCmm0CNSGpw5Ad8Ohx9nmss+/tDmJbj1afDy5R5gag9brnl6ggP9GN65MfeEh1hTt4hIMVLoEXFlhmHeDHT5q3DmuLmuaXdoNxzKBzs0vSc8hPaNg/OekVlExA0o9Ii4qmO74atY+G2duVylMdz3DtS69YqbeHrYiKpbsZgKFBEpWRR6RFxNVgasewfWjIecTPAqA3cMhqhnwdPb6upEREoshR4RV3IkAb7sD3/8bC7X7wCdxkNQbWvrEhFxAQo9Iq4g8yysegM2vA9GNpStCB3HQfjDYNOYHBGR/FDoESnpDm+Bhf0gxbxXFuEPm4GnXCVr6xIRcTEeBdloypQphIWF4efnR0REBGvXrr1q+9WrVxMREYGfnx916tThgw8+cHh++vTpREdHExQURFBQEO3atWPTpk0ObcaOHcstt9xC+fLlqVKlCl26dGH37t0FKV/ENWRnwsox8O/2ZuDxD4bHZsMj/1HgEREpAKdDz9y5cxk4cCBDhw4lISGB6OhoOnbsyMGDB/Nsn5iYSKdOnYiOjiYhIYEhQ4YwYMAA5s+fb2+zatUqunXrxsqVK4mPj6dWrVrExMRw+PBhe5vVq1fz7LPPsnHjRuLi4sjKyiImJobTp08XoNsiJVzyL/Dvu2H1m+bprPBH4Jl4aHiv1ZWJiLgsm2EYxrWbXdSqVStatGjB1KlT7esaNWpEly5dGDt2bK72gwYNYvHixezatcu+rl+/fmzbto34+Pg83yM7O5ugoCAmTZpEr1698mxz7NgxqlSpwurVq2nTpk2+ak9LSyMwMJDU1FQCAnQ7aSmBDAO+/xDi/gXZ6VAmCO59yzylJSIiuTjz2e7UkZ6MjAy2bNlCTEyMw/qYmBg2bNiQ5zbx8fG52nfo0IHNmzeTmZmZ5zZnzpwhMzOTChWufC+g1NRUgKu2SU9PJy0tzeEhUmKdSoZZf4Nlg8zAUz8GntmowCMiUkicCj0pKSlkZ2dTtarjHZqrVq3K0aNH89zm6NGjebbPysoiJSUlz20GDx5M9erVadeuXZ7PG4ZBbGwst99+O+Hh4Vesd+zYsQQGBtofNWvWvFr3RKyzNw6mtoZ9ceDlB50mQPfPc82qLCIiBVegq7dsl10iaxhGrnXXap/XeoBx48YxZ84cVq1ahZ+fX56v179/f3766SfWrVt31TpfeeUVYmNj7ctpaWkKPlKyZKVD3HD4/vzp4io3wSMzoEoja+sSESmFnAo9lSpVwtPTM9dRneTk5FxHcy4IDg7Os72XlxcVKzpOhz9hwgTGjBnDt99+S5MmTfJ8veeee47FixezZs0aatSocdV6fX198fX1vVa3RKxxIhHm9YGkreZyy39A+9fAO++wLyIi18ep01s+Pj5EREQQFxfnsD4uLo7WrVvnuU1UVFSu9suXLycyMhJv74tT5o8fP55Ro0axbNkyIiMjc72OYRj079+fBQsW8N133xEWFuZM6SIly45F8GEbM/CUCYJuc6HTOAUeEZEi5PTprdjYWHr27ElkZCRRUVFMmzaNgwcP0q9fP8A8pXT48GFmzpwJmFdqTZo0idjYWPr27Ut8fDwzZsxgzpw59tccN24cw4YNY/bs2YSGhtqPDPn7++Pv7w/As88+y+zZs/nyyy8pX768vU1gYCBlypS5vu+CSHHJSjfviL5pmrlcs5U5707g1Y9aiohIITAKYPLkyUbt2rUNHx8fo0WLFsbq1avtz/Xu3dto27atQ/tVq1YZzZs3N3x8fIzQ0FBj6tSpDs/Xrl3bAHI9hg8fbm+T1/OA8dFHH+W77tTUVAMwUlNTC9Jtkevz52+G8WFbwxgeYD6WDzOMrAyrqxIRcWnOfLY7PU+PK9M8PWKZfd/C/Kfg7J/m6awHp0GDmGtvJyIiV+XMZ7vuvSVSlHJyYO0E83YSGFCtOTw6E26oZXVlIiJuR6FHpKic/RMW/AP2fmMuR/SBe97UYGUREYso9IgUheRd8Fl3OPGrOdngvW9B8x5WVyUi4tYUekQK266vYOE/IOMUBNaCrp9AtWZWVyUi4vYUekQKS06OeVf01W+Yy6HR8LePoVwlS8sSERGTQo9IYUg/aY7f2f21udzqaYgZBZ7eV99ORESKjUKPyPX66yDMfgySd4CnL9z3DjR/3OqqRETkMgo9Itfj4Eb47HE4kwL+VeGx2VAj921URETEego9IgW1dTYseR6yMyD4Zuj2mW4nISJSgin0iDgrJwe+ew3WvWMuN+oMD34IPuWsrUtERK5KoUfEGZlnYWE/2LnIXI5+Ee4cCh4elpYlIiLXptAjkl+njsFn3eD3H8DDGx6YBE0fs7oqERHJJ4Uekfw4thtm/Q3++g38boDHZkHo7VZXJSIiTlDoEbmWxLUw93E4lwpBYfD4PKhU3+qqRETESQo9Ilez/QtY9LR5hVbNVvDYHChX0eqqRESkABR6RPJiGLDhfYgbZi43uh8emq47pIuIuDCFHpHL5WTDsldg04fm8q3PQMxoXaElIuLiFHpELpV5DhY8BbuWADboMBqinrW6KhERKQQKPSIXnP0LPusOv60HTx94aBrc9KDVVYmISCFR6BEBSEuCTx82bxrqG2DeQyss2uqqRESkECn0iKTsg08ehNSD5k1De8w376UlIiKlikKPuLfDW8xJB88chwp1oOdCCAq1uioRESkCCj3ivn5dbY7hyTgF1ZpD93ngX9nqqkREpIgo9Ih72vUVfPGEOelgWBtzDI9veaurEhGRIqSJR8T9JMyCz3uagafhfeYRHgUeEZFST6FH3Ev8ZPjyGTByoFkP+Nt/NcuyiIib0OktcQ+GAavegNVvmMtR/SHmdbDZrK1LRESKjUKPlH6GActfhfhJ5vJdr0L0iwo8IiJuRqFHSrecbPjqBfjxv+byPW/Crf2srUlERCyh0COlV3YmLHoats8Dmwd0nggtelpdlYiIWEShR0qnrHT44u/wy1fg4QUPTYfwh6yuSkRELKTQI6VP5lmY2xP2xYGnL3T9BBp0sLoqERGxmEKPlC4Zp2FON0hcDV5loPtnUOcOq6sSEZESQKFHSo/0kzDrUTi4AXz84fF5ULu11VWJiEgJodAjpcPZv2DWI/D7D+AbaN4pveYtVlclIiIliEKPuL6zf8InD8KRBCgTBD0XQbVmVlclIiIljEKPuLYzJ+CTLpC0DcpWhF6LITjc6qpERKQEUugR13X6OHzyABzdDmUrQe8lULWx1VWJiEgJpdAjrul0Cvz3fkjeAeWqmIGnSkOrqxIRkRJMoUdcz6ljMPN+SN4J/sFm4KncwOqqRESkhFPoEddyOuVi4CkfAr2/gkr1rK5KRERcgIfVBYjk2+kU+G/nS47wKPCIiEj+KfSIa7CP4TkfePp8rcAjIiJOUeiRku/08YuDlhV4RESkgBR6pGQ7cwJmPnBJ4NEpLRERKRiFHim5zv5pBp4/tl+8LL1SfaurEhERF6XQIyXTuVT45CE4+tPFiQd1WbqIiFwHhR4pec6lwacPw5EfoUwFTTwoIiKFQqFHSpb0UzDrb+bd0ssEQe/FurWEiIgUCoUeKTkyzsCcx+DQRvALNO+WHnyz1VWJiEgpUaDQM2XKFMLCwvDz8yMiIoK1a9detf3q1auJiIjAz8+POnXq8MEHHzg8P336dKKjowkKCiIoKIh27dqxadMmhzZr1qyhc+fOVKtWDZvNxqJFiwpSupRUmedg7uNwYC34lIceC6FaM6urEhGRUsTp0DN37lwGDhzI0KFDSUhIIDo6mo4dO3Lw4ME82ycmJtKpUyeio6NJSEhgyJAhDBgwgPnz59vbrFq1im7durFy5Uri4+OpVasWMTExHD582N7m9OnTNG3alEmTJhWgm1KiZWXAvD6w/zvwLgc9voAaEVZXJSIipYzNMAzDmQ1atWpFixYtmDp1qn1do0aN6NKlC2PHjs3VftCgQSxevJhdu3bZ1/Xr149t27YRHx+f53tkZ2cTFBTEpEmT6NWrV+6ibTYWLlxIly5dnCmdtLQ0AgMDSU1NJSAgwKltpYhkZ8H8v8POL8HLDx6fB2FtrK5KRERchDOf7U4d6cnIyGDLli3ExMQ4rI+JiWHDhg15bhMfH5+rfYcOHdi8eTOZmZl5bnPmzBkyMzOpUKGCM+Xlkp6eTlpamsNDSpCcHPjyGTPwePrAY7MUeEREpMg4FXpSUlLIzs6matWqDuurVq3K0aNH89zm6NGjebbPysoiJSUlz20GDx5M9erVadeunTPl5TJ27FgCAwPtj5o1a17X60khMgz4+gX4aS54eMHf/gv1ru/nLSIicjUFGshss9kclg3DyLXuWu3zWg8wbtw45syZw4IFC/Dz8ytIeXavvPIKqamp9sehQ4eu6/WkkBgGfDMEtnwMNg94aDo07GR1VSIiUsp5OdO4UqVKeHp65jqqk5ycnOtozgXBwcF5tvfy8qJixYoO6ydMmMCYMWP49ttvadKkiTOl5cnX1xdfX9/rfh0pZCtHw8Yp5tf3T4Lwh6ytR0RE3IJTR3p8fHyIiIggLi7OYX1cXBytW7fOc5uoqKhc7ZcvX05kZCTe3t72dePHj2fUqFEsW7aMyMhIZ8oSV7L2bVgz3vy60wRo/ri19YiIiNtw6kgPQGxsLD179iQyMpKoqCimTZvGwYMH6devH2CeUjp8+DAzZ84EzCu1Jk2aRGxsLH379iU+Pp4ZM2YwZ84c+2uOGzeOYcOGMXv2bEJDQ+1Hhvz9/fH39wfg1KlT7Nu3z75NYmIiW7dupUKFCtSqVavg3wEpPt9PgxUjza/bvwYt+1pbj4iIuBejACZPnmzUrl3b8PHxMVq0aGGsXr3a/lzv3r2Ntm3bOrRftWqV0bx5c8PHx8cIDQ01pk6d6vB87dq1DSDXY/jw4fY2K1euzLNN79698113amqqARipqakF6bZcj4RZhjE8wHx8N9rqakREpJRw5rPd6Xl6XJnm6bHIzi/NyQeNHLj1GegwBq4y8F1ERCS/imyeHhGn7fsWvnjSDDzNeyrwiIiIZRR6pOj8tgE+6wE5mXDTg9D5PQUeERGxjEKPFI0jW2F2V8g6C/Vj4MFp4OFpdVUiIuLGFHqk8B3bA58+BOlpUPt2eHQmePlYXZWIiLg5hR4pXH8dhE+6wJnjUK05dJsD3mWsrkpEREShRwrRqWSY+QCkHYZKN8Lj88FPV8mJiEjJoNAjhePsn/DJQ3DiVwisBT0XQrmK195ORESkmCj0yPXLOG0OWv5jO5SrAr0WQWB1q6sSERFxoNAj1ycrAz7vBYe+B79A8whPxbpWVyUiIpKLQo8UXE42LOpnTkDoVQa6z4PgcKurEhERyZNCjxSMYcDSl+Dn+eDhDV0/hVqtrK5KRETkihR6pGC+ex02zwBs8NCHUL+d1RWJiIhclUKPOC9+CqydYH5971sQ/rC19YiIiOSDQo84Z9tn8M0r5td3vQq3PGltPSIiIvmk0CP5t+cbWPSM+fWtz0D0i9bWIyIi4gSFHsmfgxvh895gZEOTrhAzWndMFxERl6LQI9f2xw6Y/ej5O6Z3gAcmg4d+dURExLXok0uu7s8D5u0lzqVCzVvhbx+Dp7fVVYmIiDhNoUeu7NQx+ORBOHUUqtwE3T8Dn7JWVyUiIlIgCj2St3NpMOth8waiN9SCHvOhTJDVVYmIiBSYQo/klnkOPusOSdugbCXouQgCQqyuSkRE5Loo9IijnGxY0BcOrAUff+jxhW4gKiIipYJCj1xkGPD1P2HXYvD0gcdmQ7XmVlclIiJSKBR65KJVb8CWjzDvpzUN6rS1uiIREZFCo9Ajph/+DavfML++dwLc9KC19YiIiBQyhR6BHYvg6/O3lGg7GG55ytJyREREioJCj7tLXGMOXMaAiCfgjsFWVyQiIlIkFHrcWdJPMKc7ZGdAo/vh3rd0Py0RESm1FHrc1YlE+PRhyDgJodHw0HTw8LS6KhERkSKj0OOOTh2DTx+C08lQ9WZ4bBZ4+1ldlYiISJFS6HE36Sdh1iOX3F7iC/ALtLoqERGRIqfQ406yMmBuT0jaCmUrQo+FUD7Y6qpERESKhUKPu8jJgS+fgV9Xgnc5eHweVKpndVUiIiLFRqHHHRgGLH8Vts8DDy/oOhOqR1hdlYiISLFS6HEHGybCxsnm1w9MgXrtrK1HRETEAgo9pd22zyDuX+bX7UdB067W1iMiImIRhZ7SbO+38OWz5tdR/eG2AdbWIyIiYiGFntLq8Bb4vBfkZMHNfzOP8oiIiLgxhZ7S6Ph+mPU3yDwNde40x/F46EctIiLuTZ+Epc3JP+CTB+HMcQhpCl0/AS8fq6sSERGxnEJPaXIuzZxt+a/fICgMHv8CfMtbXZWIiEiJoNBTWmRlwNwecPQnKFcZei4A/ypWVyUiIlJiKPSUBjk5sOhpSFx9cbblCnWsrkpERKRE8bK6AHFedo7BpsQTJJ88RxV/X1rtnYDHz1+cn235E6jW3OoSRUREShyFHhez7OckRi7ZSVLqOQD6en5FlPds88kuU6He3RZWJyIiUnLp9JYLWfZzEk9/+qM98HTxWMfQ84FndObjLPOItrI8ERGREk2hx0Vk5xiMXLIT4/xytMdPjPf+EIDpWZ34d/a9jFyyk+wc48ovIiIi4sYUelzEpsQT9iM84bZfmer9Lt62bL7Mbs2YrO4YQFLqOTYlnrC2UBERkRJKocdFJJ80A08t2x985DMOf9s51maH82JmP4xLfowX2omIiIgjhR4XUaW8H5VIZab3G1S2pfFzTihPZw4k87Kx6FXK+1lUoYiISMlWoNAzZcoUwsLC8PPzIyIigrVr1161/erVq4mIiMDPz486derwwQcfODw/ffp0oqOjCQoKIigoiHbt2rFp06brft/SpGU1bz4tM55Qjz/4LacKfTIGcYqy9udtQEigHy3DKlhXpIiISAnmdOiZO3cuAwcOZOjQoSQkJBAdHU3Hjh05ePBgnu0TExPp1KkT0dHRJCQkMGTIEAYMGMD8+fPtbVatWkW3bt1YuXIl8fHx1KpVi5iYGA4fPlzg9y1VsjLwnNeLhsavpBgB9MkcRAqB9qdt5/8d3rkxnh62vF9DRETEzdkMw3Dqcp9WrVrRokULpk6dal/XqFEjunTpwtixY3O1HzRoEIsXL2bXrl32df369WPbtm3Ex8fn+R7Z2dkEBQUxadIkevXqVaD3zUtaWhqBgYGkpqYSEBCQr20sl5MDC/8B2z8H73JsiP6Yf673tA9qBvMIz/DOjbknPMTCQkVERIqfM5/tTk1OmJGRwZYtWxg8eLDD+piYGDZs2JDnNvHx8cTExDis69ChAzNmzCAzMxNvb+9c25w5c4bMzEwqVKhQ4PcFSE9PJz093b6clpZ29Q6WRHHDzMDj4QWPzqR1/Xasu/2SGZnLm6e0dIRHRETk6pwKPSkpKWRnZ1O1alWH9VWrVuXo0aN5bnP06NE822dlZZGSkkJISO6jE4MHD6Z69eq0a9euwO8LMHbsWEaOHJmvvpVIG96H+Enm1/dPgvrm98PTw0ZU3YoWFiYiIuJ6CjSQ2WZzPKpgGEaudddqn9d6gHHjxjFnzhwWLFiAn5/jlUjOvu8rr7xCamqq/XHo0KErti1xfvoclr9qft1uJDTrZm09IiIiLs6pIz2VKlXC09Mz19GV5OTkXEdhLggODs6zvZeXFxUrOh6tmDBhAmPGjOHbb7+lSZMm1/W+AL6+vvj6+uarbyXKvhXmXdMBWj0Ntz1vbT0iIiKlgFNHenx8fIiIiCAuLs5hfVxcHK1bt85zm6ioqFztly9fTmRkpMN4nvHjxzNq1CiWLVtGZGTkdb+vyzqSAJ/3gpwsuOkh6DAGrnI0S0RERPLH6busx8bG0rNnTyIjI4mKimLatGkcPHiQfv36AeYppcOHDzNz5kzAvFJr0qRJxMbG0rdvX+Lj45kxYwZz5syxv+a4ceMYNmwYs2fPJjQ01H5Ex9/fH39//3y9b6lw4leY9TfIOAVhbeHBD8BD80eKiIgUBqdDT9euXTl+/DivvfYaSUlJhIeHs3TpUmrXrg1AUlKSw9w5YWFhLF26lBdeeIHJkydTrVo1Jk6cyMMPP2xvM2XKFDIyMnjkkUcc3mv48OGMGDEiX+/r8k4lwycPwuljEHwzdP0UvFzw1JyIiEgJ5fQ8Pa6sxM7Tk34SPr4XkrbBDbXhyTgof+WxSiIiImJy5rNd506slpUBc3uYgadsJei5UIFHRESkCCj0WCknx7xK69dV4F0OHp8HFetaXZWIiEippNBjFcOA5UPh5y/M2Za7fgLVW1hdlYiISKml0GOV9e/Bxinm112mQr27ra1HRESklFPosULCLPh2uPl1hzHQ5FFr6xEREXEDCj3Fbc83sPg58+vWAyDqWWvrERERcRMKPcXp0A/weW8wsqFpN/OeWiIiIlIsFHqKy7HdMPtvkHUW6rWH+9/XbMsiIiLFSJ+6xSH1d3O25bN/QvVIePS/4Ol97e1ERESk0Cj0FLUzJ+CThyDtMFRqYM7F41PO6qpERETcjkJPUco4DbMfhZTdUL4a9FgAZStYXZWIiIhbUugpKtmZMK8P/P4D+N0APRfADTWtrkpERMRtKfQUhZwc87L0vcvBqwx0/xyqNLK6KhEREbem0FPYDAPihsG2OWDzhL99DLVaWV2ViIiI21PoKWzr34P4SebXD0yGG++xth4REREBFHoK14+fXLy9RMzr0KybtfWIiIiInUJPYdn1FSwZYH5920Bo/Zyl5YiIiIgjhZ7CcGA9fPF3MHKgeQ9oN8LqikREROQyCj2FIX4SZKfDjffCfe+BzWZ1RSIiInIZL6sLKBUe+QjWvQ23vwCe+paKiIiURPqELgzefnDnEKurEBERkavQ6S0RERFxCwo9IiIi4hYUekRERMQtKPSIiIiIW1DoEREREbeg0CMiIiJuQaFHRERE3IJCj4iIiLgFhR4RERFxCwo9IiIi4hbc6jYUhmEAkJaWZnElIiIiUhgufKZf+Iy/GrcKPSdPngSgZs2aFlciIiIihenkyZMEBgZetY3NyE80KiVycnI4cuQI5cuXx2azFdrrpqWlUbNmTQ4dOkRAQEChvW5J4w79VB9LB3foI7hHP9XH0qEo+2gYBidPnqRatWp4eFx91I5bHenx8PCgRo0aRfb6AQEBpfYX9lLu0E/1sXRwhz6Ce/RTfSwdiqqP1zrCc4EGMouIiIhbUOgRERERt6DQUwh8fX0ZPnw4vr6+VpdSpNyhn+pj6eAOfQT36Kf6WDqUlD661UBmERERcV860iMiIiJuQaFHRERE3IJCj4iIiLgFhR4RERFxCwo9IiIi4hYUevJpypQphIWF4efnR0REBGvXrs3XduvXr8fLy4tmzZoVbYGFxNl+pqenM3ToUGrXro2vry9169blP//5TzFVWzDO9nHWrFk0bdqUsmXLEhISwhNPPMHx48eLqVrnrVmzhs6dO1OtWjVsNhuLFi265jarV68mIiICPz8/6tSpwwcffFD0hV4HZ/u4YMEC2rdvT+XKlQkICCAqKopvvvmmeIotoIL8HC9wlf1OQfroivucgvTTlfY7Y8eO5ZZbbqF8+fJUqVKFLl26sHv37mtuZ8V+R6EnH+bOncvAgQMZOnQoCQkJREdH07FjRw4ePHjV7VJTU+nVqxd33313MVV6fQrSz0cffZQVK1YwY8YMdu/ezZw5c2jYsGExVu0cZ/u4bt06evXqxZNPPsmOHTuYN28eP/zwA0899VQxV55/p0+fpmnTpkyaNClf7RMTE+nUqRPR0dEkJCQwZMgQBgwYwPz584u40oJzto9r1qyhffv2LF26lC1btnDnnXfSuXNnEhISirjSgnO2jxe40n6nIH10tX0OON9PV9vvrF69mmeffZaNGzcSFxdHVlYWMTExnD59+orbWLbfMeSaWrZsafTr189hXcOGDY3BgwdfdbuuXbsar776qjF8+HCjadOmRVhh4XC2n//73/+MwMBA4/jx48VRXqFwto/jx4836tSp47Bu4sSJRo0aNYqsxsIEGAsXLrxqm5dfftlo2LChw7p//OMfxq233lqElRWe/PQxL40bNzZGjhxZ+AUVAWf66Gr7nQvy00dX3OdcLj/9dPX9TnJysgEYq1evvmIbq/Y7OtJzDRkZGWzZsoWYmBiH9TExMWzYsOGK23300Ufs37+f4cOHF3WJhaIg/Vy8eDGRkZGMGzeO6tWr06BBA1588UXOnj1bHCU7rSB9bN26Nb///jtLly7FMAz++OMPvvjiC+69997iKLlYxMfH5/qedOjQgc2bN5OZmWlRVUUrJyeHkydPUqFCBatLKVSutt9xlqvtcwrK1fc7qampAFf9+7Jqv+NWd1kviJSUFLKzs6latarD+qpVq3L06NE8t9m7dy+DBw9m7dq1eHm5xre4IP389ddfWbduHX5+fixcuJCUlBSeeeYZTpw4USLPsRekj61bt2bWrFl07dqVc+fOkZWVxf3338/7779fHCUXi6NHj+b5PcnKyiIlJYWQkBCLKis6b731FqdPn+bRRx+1upRC44r7HWe52j6noFx5v2MYBrGxsdx+++2Eh4dfsZ1V+x0d6cknm83msGwYRq51ANnZ2XTv3p2RI0fSoEGD4iqv0OS3n2D+b9lmszFr1ixatmxJp06dePvtt/n4449L9P+8nOnjzp07GTBgAP/617/YsmULy5YtIzExkX79+hVHqcUmr+9JXutLgzlz5jBixAjmzp1LlSpVrC6nULj6fie/XHWf4yxX3u/079+fn376iTlz5lyzrRX7ndL534FCVKlSJTw9PXMdCUhOTs6VUgFOnjzJ5s2bSUhIoH///oD5h2oYBl5eXixfvpy77rqrWGp3hrP9BAgJCaF69eoEBgba1zVq1AjDMPj999+pX79+kdbsrIL0cezYsdx222289NJLADRp0oRy5coRHR3N66+/XiqOggQHB+f5PfHy8qJixYoWVVU05s6dy5NPPsm8efNo166d1eUUGlfd7zjL1fY5BeWq+53nnnuOxYsXs2bNGmrUqHHVtlbtd3Sk5xp8fHyIiIggLi7OYX1cXBytW7fO1T4gIIDt27ezdetW+6Nfv37ceOONbN26lVatWhVX6U5xtp8At912G0eOHOHUqVP2dXv27MHDw+Oav/BWKEgfz5w5g4eH45+Jp6cncPF/Ja4uKioq1/dk+fLlREZG4u3tbVFVhW/OnDn06dOH2bNnu8zYiPxy1f2Os1xtn1NQrrbfMQyD/v37s2DBAr777jvCwsKuuY1l+50iHSZdSnz22WeGt7e3MWPGDGPnzp3GwIEDjXLlyhkHDhwwDMMwBg8ebPTs2fOK27vKVRTO9vPkyZNGjRo1jEceecTYsWOHsXr1aqN+/frGU089ZVUXrsnZPn700UeGl5eXMWXKFGP//v3GunXrjMjISKNly5ZWdeGaTp48aSQkJBgJCQkGYLz99ttGQkKC8dtvvxmGkbuPv/76q1G2bFnjhRdeMHbu3GnMmDHD8Pb2Nr744gurunBNzvZx9uzZhpeXlzF58mQjKSnJ/vjrr7+s6sI1OdvHy7nCfsfZPrriPscwnO+nq+13nn76aSMwMNBYtWqVw9/XmTNn7G1Kyn5HoSefJk+ebNSuXdvw8fExWrRo4XApXu/evY22bdtecVtX2Plc4Gw/d+3aZbRr184oU6aMUaNGDSM2NtbhF70kcraPEydONBo3bmyUKVPGCAkJMR5//HHj999/L+aq82/lypUGkOvRu3dvwzDy7uOqVauM5s2bGz4+PkZoaKgxderU4i/cCc72sW3btldtXxIV5Od4KVfY7xSkj664zylIP11pv5NX3wDjo48+srcpKfsd2/mCRUREREo1jekRERERt6DQIyIiIm5BoUdERETcgkKPiIiIuAWFHhEREXELCj0iIiLiFhR6RERExC0o9IiIiIhbUOgRERERt6DQIyIiIm5BoUdERETcwv8D3th6Ix6OFqcAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 650x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array([0.5, 1. , 1.5, 2. ])\n",
    "y = np.array([0.02010067, 0.02224561, 0.02284449, 0.02416379])\n",
    "\n",
    "# Boundary condition type = 'natural' (The second derivative at curve ends are zero.)\n",
    "cs = CubicSpline(x, y, bc_type='natural')\n",
    "\n",
    "print(cs.c)\n",
    "\n",
    "xs = np.linspace(0.4,2, 100)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6.5, 4))\n",
    "ax.plot(x, y, 'o', label='data')\n",
    "ax.plot(xs, cs(xs), label=\"Natural Cubic Spline Interp\")\n",
    "ax.legend(loc='upper left', ncol=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.00302197  0.00302197  0.00302197]\n",
      " [-0.00762508 -0.00309212  0.00144084]\n",
      " [ 0.00734693  0.00198833  0.00116269]\n",
      " [ 0.02010067  0.02224561  0.02284449]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 650x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array([0.5, 1. , 1.5, 2. ])\n",
    "y = np.array([0.02010067, 0.02224561, 0.02284449, 0.02416379])\n",
    "\n",
    "# Boundary condition type = not-a-knot (The first and second segment at a curve end are the same polynomial. \n",
    "# It is a good default when there is no information on boundary conditions.)\n",
    "cs = CubicSpline(x, y)\n",
    "\n",
    "print(cs.c)\n",
    "\n",
    "xs = np.linspace(0.4,2,100)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6.5, 4))\n",
    "ax.plot(x, y, 'o', label='data')\n",
    "ax.plot(xs, cs(xs), label=\"Cubic Spline Interp\")\n",
    "ax.legend(loc='upper left', ncol=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S(1.25) =  15.203125\n",
      "\n",
      "[[ 1.  1. -2.  0.  0.]\n",
      " [-0.  3.  6.  0.  0.]\n",
      " [ 1.  4. 13. 19. 19.]\n",
      " [12. 14. 22. 39. 58.]]\n",
      "\n",
      "S0(0 <= x <= 1) = 12 + 1 (x-0) + 0 (x-0)^2  + 1 (x-0)^3\n",
      "S1(1 < x <= 2) = 14 + 4 (x-1) + 3 (x-1)^2  + 1 (x-1)^3\n",
      "...\n",
      "S5(4 < x <= 5) = 58 + 19 (x-4) + 0 (x-4)^2  + 0 (x-4)^3\n",
      "\n",
      "S(1.25) = 15.203125\n"
     ]
    }
   ],
   "source": [
    "# calculate 5 natural cubic spline polynomials for 6 points\n",
    "# (x,y) = (0,12) (1,14) (2,22) (3,39) (4,58) (5,77)\n",
    "x = np.array([0, 1, 2, 3, 4, 5])\n",
    "y = np.array([12,14,22,39,58,77])\n",
    "\n",
    "# calculate natural cubic spline polynomials\n",
    "cs = CubicSpline(x,y,bc_type='natural')\n",
    "\n",
    "# show values of interpolation function at x=1.25\n",
    "print('S(1.25) = ', cs(1.25))\n",
    "print()\n",
    "\n",
    "## Additional - find polynomial coefficients for different x regions\n",
    "\n",
    "# if you want to print polynomial coefficients in form\n",
    "# S0(0<=x<=1) = a0 + b0(x-x0) + c0(x-x0)^2 + d0(x-x0)^3\n",
    "# S1(1< x<=2) = a1 + b1(x-x1) + c1(x-x1)^2 + d1(x-x1)^3\n",
    "# ...\n",
    "# S4(4< x<=5) = a4 + b4(x-x4) + c5(x-x4)^2 + d5(x-x4)^3\n",
    "# x0 = 0; x1 = 1; x4 = 4; (start of x region interval)\n",
    "\n",
    "# show values of a0, b0, c0, d0, a1, b1, c1, d1 ...\n",
    "print(np.round(cs.c,2))\n",
    "print()\n",
    "\n",
    "# Polynomial coefficients for 0 <= x <= 1\n",
    "a0 = cs.c.item(3,0)\n",
    "b0 = cs.c.item(2,0)\n",
    "c0 = cs.c.item(1,0)\n",
    "d0 = cs.c.item(0,0)\n",
    "\n",
    "# Polynomial coefficients for 1 < x <= 2\n",
    "a1 = cs.c.item(3,1)\n",
    "b1 = cs.c.item(2,1)\n",
    "c1 = cs.c.item(1,1)\n",
    "d1 = cs.c.item(0,1)\n",
    "\n",
    "# ...\n",
    "\n",
    "# Polynomial coefficients for 4 < x <= 5\n",
    "a4 = cs.c.item(3,4)\n",
    "b4 = cs.c.item(2,4)\n",
    "c4 = cs.c.item(1,4)\n",
    "d4 = cs.c.item(0,4)\n",
    "\n",
    "# Print polynomial equations for different x regions\n",
    "print('S0(0 <= x <= 1) =', round(a0), '+', round(b0), '(x-0) +', round(c0), '(x-0)^2  +', round(d0), '(x-0)^3')\n",
    "print('S1(1 < x <= 2) =', round(a1), '+', round(b1), '(x-1) +', round(c1), '(x-1)^2  +', round(d1), '(x-1)^3')\n",
    "print('...')\n",
    "print('S5(4 < x <= 5) =', round(a4), '+', round(b4), '(x-4) +', round(c4), '(x-4)^2  +', round(d4), '(x-4)^3')\n",
    "print()\n",
    "\n",
    "# So we can calculate S(1.25) by using equation S1(1 < x <=2)\n",
    "print('S(1.25) =', a1 + b1*0.25 + c1*(0.25**2) + d1*(0.25**3))\n",
    "\n",
    "# Cubic spline interpolation calculus example\n",
    "    #  https://www.youtube.com/watch?v=gT7F3TWihvk\n",
    "    #  https://www.youtube.com/watch?v=yOUst2672qo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S(0.5) =  12.625\n",
      "\n",
      "[[ 1.  1. -2.  0.  0.]\n",
      " [-0.  3.  6.  0.  0.]\n",
      " [ 1.  4. 13. 19. 19.]\n",
      " [12. 14. 22. 39. 58.]]\n",
      "\n",
      "S0 (0 <= x <= 1) = 12 + 1 (x-0) + 0 (x-0)^2  + 1 (x-0)^3\n",
      "S1 (1 < x <= 2) = 14 + 4 (x-1) + 3 (x-1)^2  + 1 (x-1)^3\n",
      "...\n",
      "S5 (4 < x <= 5) = 58 + 19 (x-4) + 0 (x-4)^2  + 0 (x-4)^3\n",
      "\n",
      "S(0.5) = 12.625\n"
     ]
    }
   ],
   "source": [
    "x = np.array([0, 1, 2, 3, 4, 5])\n",
    "y = np.array([12,14,22,39,58,77])\n",
    "\n",
    "cs = CubicSpline(x,y,bc_type='natural')\n",
    "\n",
    "print('S(0.5) = ', cs(0.5))\n",
    "print()\n",
    "\n",
    "print(np.round(cs.c,2))\n",
    "print()\n",
    "\n",
    "# Polynomial coefficients for 0 <= x <= 1\n",
    "a0 = cs.c.item(3,0)\n",
    "b0 = cs.c.item(2,0)\n",
    "c0 = cs.c.item(1,0)\n",
    "d0 = cs.c.item(0,0)\n",
    "\n",
    "# Polynomial coefficients for 1 < x <= 2\n",
    "a1 = cs.c.item(3,1)\n",
    "b1 = cs.c.item(2,1)\n",
    "c1 = cs.c.item(1,1)\n",
    "d1 = cs.c.item(0,1)\n",
    "\n",
    "# ...\n",
    "\n",
    "# Polynomial coefficients for 4 < x <= 5\n",
    "a4 = cs.c.item(3,4)\n",
    "b4 = cs.c.item(2,4)\n",
    "c4 = cs.c.item(1,4)\n",
    "d4 = cs.c.item(0,4)\n",
    "\n",
    "print('S0 (0 <= x <= 1) =', round(a0), '+', round(b0), '(x-0) +', round(c0), '(x-0)^2  +', round(d0), '(x-0)^3')\n",
    "print('S1 (1 < x <= 2) =', round(a1), '+', round(b1), '(x-1) +', round(c1), '(x-1)^2  +', round(d1), '(x-1)^3')\n",
    "print('...')\n",
    "print('S5 (4 < x <= 5) =', round(a4), '+', round(b4), '(x-4) +', round(c4), '(x-4)^2  +', round(d4), '(x-4)^3')\n",
    "print()\n",
    "\n",
    "print('S(0.5) =', a0 + b0*0.5 + c0*(0.5**2) + d0*(0.5**3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Quartic Spline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The interpolation method that guarantees the smoothest interpolation of the continuous instantaneous forward rates is a quartic spline of that continuous forward curve.\n",
    "\n",
    "A quartic spline is a piecewise polynomial function of degree 4 that is commonly used for smooth interpolation between points. In Python, implementing a quartic spline requires setting up and solving a system of equations for continuity, smoothness, and boundary conditions at each segment.\n",
    "\n",
    "Suppose $t_{1}, t_{2},\\cdots, t_{n}$ and $f_{1}, f_{2},\\cdots, f_{n}, f_{i}:=f(t_{i})$ are known. To complete the requisite spline for $f$, we desire coefficients $(a_{i}, b_{i}, c_{i}, d_{i}, e_{i})$ for $1\\le i\\le n-1$. Given these coefficients, the function value at any term $t$ will be\n",
    "$$f(t) = a_{i} + b_{i}t + c_{i}t^{2} + d_{i}t^{3} + e_{i}t^{4},\\space\\space t_{i} \\le t \\le t_{i+1}^{5}$$\n",
    "\n",
    "Hence\n",
    "\n",
    "$$f'(t)=b_{i}+2c_{i}t+3d_{i}t^{2}+4e_{i}t^{3}$$\n",
    "$$f''(t)=2c_{i}+6d_{i}t+12e_{i}t^{2}$$\n",
    "$$f'''(t)=6d_{i}+24e_{i}t$$\n",
    "\n",
    "Requiring continuity of all of the above functions gives\n",
    "$$f_{i} = a_{i} + b_{i}t_{i} + c_{i}t^{2}_{i} + d_{i}t^{3}_{i} + e_{i}t^{4}_{i},\\space\\space 1 \\le t \\le -1$$\n",
    "$$f_{i+1} = a_{i} + b_{i}t_{i+1} + c_{i}t^{2}_{i+1} + d_{i}t^{3}_{i+1} + e_{i}t^{4}_{i+1},\\space\\space 1 \\le t \\le -1$$\n",
    "$$b_{i}+2c_{i}t_{i+1}+3d_{i}t^{2}_{i+1}+4e_{i}t^{3}_{i+1}=b_{i+1}+2c_{i+1}t_{i+1}+3d_{i+1}t^{2}_{i+1}+4e_{i+1}t^{3}_{i+1}, \\space\\space 1 \\le i \\le n-2$$\n",
    "$$2c_{i}+6d_{i}t_{i+1}+12e_{i}t^{2}_{i+1} = 2c_{i+1}+6d_{i+1}t_{i+1}+12e_{i+1}t^{2}_{i+1}, \\space\\space 1 \\le i \\le n-2$$\n",
    "$$6d_{i}+24e_{i}t_{i+1} = 6d_{i+1}+24e_{i+1}t_{i+1}, \\space\\space 1 \\le i \\le n-2$$\n",
    "\n",
    "Here we have 5n-8 equations in 5n-5 unknowns. Therefore, we need three more conditions. The following three conditions are specified in Adams (2001):\n",
    "$$f'(t_{1})=0$$\n",
    "$$f''(t_{n})=0$$\n",
    "$$f'''(t_{n})=0$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quartic spline coefficients:\n",
      "[[ 4.23166778e-03 -8.00092134e-03  0.00000000e+00  3.39586047e-03\n",
      "   2.00000000e-02]\n",
      " [-2.48966535e-03  7.23308267e-03 -1.03658220e-03 -3.70683513e-03\n",
      "   2.00000000e-02]\n",
      " [ 2.69530899e-04 -2.72557872e-03  5.72467373e-03  5.96058710e-03\n",
      "   2.00000000e-02]\n",
      " [-4.09719413e-04  1.58691566e-03 -1.10730464e-03 -1.00698916e-02\n",
      "   3.00000000e-02]\n",
      " [ 7.53072373e-07 -5.19619937e-05  1.19512586e-03 -9.16263156e-03\n",
      "   2.00000000e-02]]\n"
     ]
    }
   ],
   "source": [
    "def quartic_spline(x, y, left_bc=(0, 0), right_bc=(0, 0)):\n",
    "    n = len(x) - 1  # number of intervals\n",
    "    A = np.zeros((5 * n, 5 * n))  # Matrix for system\n",
    "    b = np.zeros(5 * n)           # Right-hand side vector\n",
    "\n",
    "    # Step 1: Fill in the point constraints for each polynomial\n",
    "    row = 0\n",
    "    for i in range(n):\n",
    "        # First point of the interval\n",
    "        A[row, 5 * i:5 * (i + 1)] = np.array([(x[i] - x[i]) ** 4, (x[i] - x[i]) ** 3,\n",
    "                                              (x[i] - x[i]) ** 2, (x[i] - x[i]) ** 1, 1])\n",
    "        b[row] = y[i]\n",
    "        row += 1\n",
    "\n",
    "        # Second point of the interval\n",
    "        A[row, 5 * i:5 * (i + 1)] = np.array([(x[i + 1] - x[i]) ** 4, (x[i + 1] - x[i]) ** 3,\n",
    "                                              (x[i + 1] - x[i]) ** 2, (x[i + 1] - x[i]) ** 1, 1])\n",
    "        b[row] = y[i + 1]\n",
    "        row += 1\n",
    "\n",
    "    # Step 2: Derivative continuity conditions for first, second, and third derivatives\n",
    "    for i in range(1, n):\n",
    "        delta_x = x[i] - x[i - 1]\n",
    "\n",
    "        # First derivative continuity\n",
    "        A[row, 5 * (i - 1):5 * i] = [4 * delta_x ** 3, 3 * delta_x ** 2, 2 * delta_x, 1, 0]\n",
    "        A[row, 5 * i:5 * (i + 1)] = [-4 * 0 ** 3, -3 * 0 ** 2, -2 * 0, -1, 0]\n",
    "        row += 1\n",
    "\n",
    "        # Second derivative continuity\n",
    "        A[row, 5 * (i - 1):5 * i] = [12 * delta_x ** 2, 6 * delta_x, 2, 0, 0]\n",
    "        A[row, 5 * i:5 * (i + 1)] = [-12 * 0 ** 2, -6 * 0, -2, 0, 0]\n",
    "        row += 1\n",
    "\n",
    "        # Third derivative continuity\n",
    "        A[row, 5 * (i - 1):5 * i] = [24 * delta_x, 6, 0, 0, 0]\n",
    "        A[row, 5 * i:5 * (i + 1)] = [-24 * 0, -6, 0, 0, 0]\n",
    "        row += 1\n",
    "\n",
    "    # Step 3: Boundary conditions for start and end\n",
    "    \n",
    "    # Apply left boundary condition (at x[0]) - second derivative\n",
    "    A[row, :5] = np.array([12 * (left_bc[0]-x[0])**2, 6 * (left_bc[0]-x[0]), 2, 0, 0])\n",
    "    b[row] = 0\n",
    "    row += 1\n",
    "\n",
    "    # Apply right boundary condition (at x[-1]) - second derivative\n",
    "    A[row, -5:] = np.array([12 * (right_bc[0]-x[-2])**2, 6 * (right_bc[0]-x[-2]), 2, 0, 0])\n",
    "    b[row] = 0\n",
    "    row += 1\n",
    "    \n",
    "    # Apply right boundary condition (at x[-1]) - first derivative\n",
    "    A[row, -5:] = np.array([4 * (right_bc[0]-x[-2])**3, 3 * (right_bc[0]-x[-2])**2, 2 * (right_bc[0]-x[-2])**1, 1, 0])\n",
    "    b[row] = 0\n",
    "\n",
    "    # Solve the system\n",
    "    coeffs = np.linalg.solve(A, b)\n",
    "    return coeffs.reshape(n, 5)\n",
    "\n",
    "# Example usage\n",
    "x = np.array([0.1, 1, 2, 6, 7, 30])\n",
    "y = np.array([0.02, 0.02, 0.02, 0.03, 0.02, 0.02])\n",
    "coeffs = quartic_spline(x, y, left_bc=(0.1, 0.02), right_bc=(30, 0.02))\n",
    "print(\"Quartic spline coefficients:\")\n",
    "print(coeffs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.005, 0.04)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  Generate plot using spline values\n",
    "plt.plot(x, y, 'o')\n",
    "plt.grid()\n",
    "\n",
    "u = np.linspace(0.1, 1) - 0.1\n",
    "plt.plot(u + 0.1, np.polyval(coeffs[0], u), 'k')\n",
    "\n",
    "u = np.linspace(1, 2) - 1\n",
    "plt.plot(u + 1, np.polyval(coeffs[1], u), 'r')\n",
    "\n",
    "u = np.linspace(2, 6) - 2\n",
    "plt.plot(u + 2, np.polyval(coeffs[2], u), 'g')\n",
    "\n",
    "u = np.linspace(6, 7) - 6\n",
    "plt.plot(u + 6, np.polyval(coeffs[3], u), 'b')\n",
    "\n",
    "u = np.linspace(7, 30) - 7\n",
    "plt.plot(u + 7, np.polyval(coeffs[4], u), 'k')\n",
    "\n",
    "plt.ylim((-0.005, 0.04))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "class QuarticSpline:\n",
    "    def __init__(self, terms, forward_rates, bc_type='natural'):\n",
    "        self.terms = np.array(terms)\n",
    "        self.forward_rates = np.array(forward_rates)\n",
    "        self.bc_type = bc_type\n",
    "        self.coefficients = self._compute_coefficients()\n",
    "    \n",
    "    def _compute_coefficients(self):\n",
    "        n = len(self.terms)\n",
    "        h = np.diff(self.terms)  # Interval widths\n",
    "        \n",
    "        # Number of coefficients must equal number of equations\n",
    "        num_coeffs = 5 * (n - 1)  # 5 coefficients per interval\n",
    "        \n",
    "        # Initialize the matrix and right-hand side\n",
    "        A = np.zeros((num_coeffs, num_coeffs))\n",
    "        b = np.zeros(num_coeffs)\n",
    "        \n",
    "        eq_idx = 0\n",
    "        \n",
    "        # For each interval\n",
    "        for i in range(n-1):\n",
    "            base = 5 * i\n",
    "            \n",
    "            # 1. Function values at left endpoint\n",
    "            A[eq_idx, base:base+5] = [1, 0, 0, 0, 0]\n",
    "            b[eq_idx] = self.forward_rates[i]\n",
    "            eq_idx += 1\n",
    "            \n",
    "            # 2. Function values at right endpoint\n",
    "            A[eq_idx, base:base+5] = [1, h[i], h[i]**2, h[i]**3, h[i]**4]\n",
    "            b[eq_idx] = self.forward_rates[i+1]\n",
    "            eq_idx += 1\n",
    "            \n",
    "            if i < n-2:  # For all but the last interval\n",
    "                # 3. First derivative continuity\n",
    "                A[eq_idx, base:base+5] = [0, 1, 2*h[i], 3*h[i]**2, 4*h[i]**3]\n",
    "                if base + 5 < num_coeffs:\n",
    "                    A[eq_idx, base+5:base+10] = [0, -1, 0, 0, 0]\n",
    "                b[eq_idx] = 0\n",
    "                eq_idx += 1\n",
    "                \n",
    "                # 4. Second derivative continuity\n",
    "                A[eq_idx, base:base+5] = [0, 0, 2, 6*h[i], 12*h[i]**2]\n",
    "                if base + 5 < num_coeffs:\n",
    "                    A[eq_idx, base+5:base+10] = [0, 0, -2, 0, 0]\n",
    "                b[eq_idx] = 0\n",
    "                eq_idx += 1\n",
    "                \n",
    "                # 5. Third derivative continuity\n",
    "                A[eq_idx, base:base+5] = [0, 0, 0, 6, 24*h[i]]\n",
    "                if base + 5 < num_coeffs:\n",
    "                    A[eq_idx, base+5:base+10] = [0, 0, 0, -6, 0]\n",
    "                b[eq_idx] = 0\n",
    "                eq_idx += 1\n",
    "        \n",
    "        # Add boundary conditions\n",
    "        if self.bc_type == 'natural':\n",
    "            # Second derivative = 0 at start\n",
    "            A[eq_idx, 0:5] = [0, 0, 2, 0, 0]\n",
    "            b[eq_idx] = 0\n",
    "            eq_idx += 1\n",
    "            \n",
    "            # Second derivative = 0 at end\n",
    "            last_base = 5 * (n-2)\n",
    "            A[eq_idx, last_base:last_base+5] = [0, 0, 2, 6*h[-1], 12*h[-1]**2]\n",
    "            b[eq_idx] = 0\n",
    "            eq_idx += 1\n",
    "            \n",
    "            # First derivative = 0 at end\n",
    "            A[eq_idx, last_base:last_base+5] = [0, 1, 2*h[-1], 3*h[-1]**2, 4*h[-1]**3]\n",
    "            b[eq_idx] = 0\n",
    "        \n",
    "        # Add small regularization term to avoid singularity\n",
    "        A = A + np.eye(num_coeffs) * 1e-10\n",
    "        \n",
    "        coefficients = np.linalg.solve(A, b)\n",
    "        return coefficients.reshape(-1, 5)\n",
    "    \n",
    "    def evaluate(self, x):\n",
    "        \"\"\"Evaluate the spline at point x\"\"\"\n",
    "        if x < self.terms[0] or x > self.terms[-1]:\n",
    "            raise ValueError(\"x is outside the interpolation range\")\n",
    "            \n",
    "        # Find the appropriate interval\n",
    "        i = np.searchsorted(self.terms, x, side='right') - 1\n",
    "        i = max(min(i, len(self.coefficients) - 1), 0)\n",
    "        dx = x - self.terms[i]\n",
    "        \n",
    "        # Evaluate the polynomial\n",
    "        coef = self.coefficients[i]\n",
    "        return coef[0] + coef[1]*dx + coef[2]*dx**2 + coef[3]*dx**3 + coef[4]*dx**4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.005, 0.04)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Usage example\n",
    "terms = np.array([0.1, 1, 2, 6, 7, 30])\n",
    "forwards = np.array([0.02, 0.02, 0.02, 0.03, 0.02, 0.02])\n",
    "forward_spline = QuarticSpline(terms, forwards, bc_type='natural')\n",
    "cs = CubicSpline(terms, forwards, bc_type='natural')\n",
    "\n",
    "x_vals = np.linspace(0.1, 30, 1000)\n",
    "y_vals = [forward_spline.evaluate(x) for x in x_vals]\n",
    "\n",
    "plt.plot(terms, forwards, \"go\")\n",
    "plt.grid()\n",
    "plt.plot(x_vals, y_vals)\n",
    "# plt.plot(x_vals, cs(x_vals))\n",
    "plt.ylim((-0.005, 0.04))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 20.0)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "terms = np.array([0.5, 1, 2, 4, 5, 10, 15, 20])\n",
    "zero_rate = np.array([0.0552, 0.0600, 0.0682, 0.0801, 0.0843, 0.0931, 0.0912, 0.0857])\n",
    "cs = CubicSpline(terms, zero_rate, bc_type='natural')\n",
    "qs = QuarticSpline(terms, zero_rate, bc_type='natural')\n",
    "\n",
    "x_vals = np.linspace(0.5, 20, 100)\n",
    "y_vals = [qs.evaluate(x) for x in x_vals]\n",
    "\n",
    "plt.plot(terms, zero_rate, \"go\")\n",
    "plt.grid()\n",
    "plt.plot(x_vals, y_vals)\n",
    "plt.plot(x_vals, cs(x_vals))\n",
    "plt.ylim(0,0.12)\n",
    "plt.xlim(0,20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `fsolve()` to Solve Nonlinear Equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SciPy's optimization package offers an `fsolve()` function which finds the roots of a nonlinear function. As an example, consider the problem where we wish to find the positive solution of the nonlinear system of equations:\n",
    "$$x^{2} + y^{2} = 1$$  \n",
    "$$y = e^{(-x)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = np.float64(0.9165625831005157), y = np.float64(0.39989127429139987)\n"
     ]
    }
   ],
   "source": [
    "def f(z):\n",
    "    x, y = z[0], z[1]\n",
    "    z1 = x**2 + y**2 - 1\n",
    "    z2 = y - np.exp(-x)\n",
    "    return [z1, z2]\n",
    "\n",
    "x, y = fsolve(f, np.zeros(2))\n",
    "print(f'{x = }, {y = }')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Point constraints matrix function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([0.1, 1, 2, 6, 7, 30])\n",
    "y = np.array([0.02, 0.02, 0.02, 0.03, 0.02, 0.02])\n",
    "n = len(x)\n",
    "N = n - 1\n",
    "\n",
    "zx = np.zeros((n-1)*2)\n",
    "zx[1::2] = np.diff(x)\n",
    "\n",
    "van = np.vander(zx, N, increasing=True)\n",
    "\n",
    "A = np.zeros((5*(n-1), 5*(n-1)))\n",
    "for i in range(5):\n",
    "    A[i, i*N:(i+1)*N] = van[i, :]\n",
    "    A[i+1, i*N:(i+1)*N] = van[i+1, :]"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "fin",
   "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": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}