diff --git a/BootstrapInteractions.m b/DGSA_computations/BootstrapInteractions.m similarity index 69% rename from BootstrapInteractions.m rename to DGSA_computations/BootstrapInteractions.m index aeee0cb..983418e 100644 --- a/BootstrapInteractions.m +++ b/DGSA_computations/BootstrapInteractions.m @@ -40,7 +40,7 @@ for j = 1:NbClusters idx_c = find(Clustering.T == j); % find points in the cluster - + q_prior = quantile(ParametersValues(idx_c,:),(1:1:99)./100,1);% distribution of parameter p in the entire cluster: F(p|c) % Bin the conditional parameter and store the indices in a vector for l = 1:NbBins if l == 1 @@ -55,12 +55,19 @@ BootInteractions(:,j,l) = NaN(NbParams,1); else for i =1:NbParams - q_prior = quantile(ParametersValues(idx_c,i),(1:1:99)./100);% distribution of parameter p in the entire cluster: F(p|c) boot = zeros(NbDraw,1); + ParametersValuesi = ParametersValues(:,i); + x_redraw = zeros(length(idx_cl),NbDraw); + for iter = 1:NbDraw + x_redraw(:,iter) = ParametersValuesi(idx_c(randsample(Clustering.weights(j),length(idx_cl),0))); % sample points + end + + %x_redraw = reshape(ParametersValuesi(idx_c(randsample(Clustering.weights(j),length(idx_cl)*NbDraw,'true'))),[],NbDraw); % sample points + q = quantile(x_redraw,(1:1:99)./100,1); % bootstrapped distribution for iter = 1:NbDraw % resampling procedure - x_redraw = idx_c(randsample(1:Clustering.weights(j),length(idx_cl))'); % sampling from F(p|c) - q = quantile(ParametersValues(x_redraw,i),(1:1:99)./100); % distribution of parameter p conditioned to pj in bin l: F(p|i(pj,tl),c) - boot(iter) = norm(q_prior-q,1); % L1-norm + %x_redraw = idx_c(randsample(1:Clustering.weights(j),length(idx_cl))'); % sampling from F(p|c) + %q = quantile(ParametersValues(x_redraw,i),(1:1:99)./100); % distribution of parameter p conditioned to pj in bin l: F(p|i(pj,tl),c) + boot(iter) = norm(q_prior(:,i)-q(:,iter),1); % L1-norm end BootInteractions(i,j,l) = quantile(boot,alpha); end @@ -69,4 +76,4 @@ end BootInteractions(CondIdx,:,:) = []; -end \ No newline at end of file +end diff --git a/BootstrapMainFactors.m b/DGSA_computations/BootstrapMainFactors.m similarity index 74% rename from BootstrapMainFactors.m rename to DGSA_computations/BootstrapMainFactors.m index a9c5f2e..7f1e2b3 100644 --- a/BootstrapMainFactors.m +++ b/DGSA_computations/BootstrapMainFactors.m @@ -5,6 +5,9 @@ % Author: Celine Scheidt % Date: August 2012 +% Later added by Jihoon Park (jhpark3@stanford.edu) +% Date: 14 May 2016 + function BootMainFactors = BootstrapMainFactors(ParametersValues,Clustering,NbDraw,alpha) %% Input Parameters @@ -24,18 +27,26 @@ alpha = 0.95; end - BootMainFactors = zeros(nbParametersValues,nbclusters); +%% Modified by Jihoon to evalualte multiple vaules of alpha + + BootMainFactors = zeros(nbParametersValues,nbclusters,length(alpha)); + +%% Resampling for i = 1:nbParametersValues q_prior = quantile(ParametersValues(:,i),(1:1:99)./100); % prior distribution for j = 1:nbclusters boot = zeros(NbDraw,1); for iter = 1:NbDraw - x_redraw = randsample(size(ParametersValues,1),Clustering.weights(j))'; % sample points + x_redraw = randsample(size(ParametersValues,1),Clustering.weights(j),0)'; % sample points q = quantile(ParametersValues(x_redraw,i),(1:1:99)./100); % bootstrapped distribution boot(iter) = norm(q_prior-q,1); % L1-norm end - BootMainFactors(i,j) = quantile(boot,alpha); + if length(alpha)==1 + BootMainFactors(i,j) = quantile(boot,alpha); + else + BootMainFactors(i,j,:) = quantile(boot,alpha); + end end end diff --git a/DGSA_computations/ComputeConditionalEffects.m b/DGSA_computations/ComputeConditionalEffects.m new file mode 100644 index 0000000..b9c647d --- /dev/null +++ b/DGSA_computations/ComputeConditionalEffects.m @@ -0,0 +1,100 @@ + +% +% Distance-based generalized sensitivity analysis (dGSA) +% Evaluation of sensitivity of the conditioanl effects + +% Author: Celine Scheidt +% Date: August 2013 + +% Updated by Jihoon Park (jhpark3@stanford.edu) +% Date: 14 May 2016 +% - Use data structures +% - Separate computations and visualizations +% - Display the conditioning parameter computed + +function DGSA_ConditionalEffects = ... + ComputeConditionalEffects(DGSA,alpha)%(Clustering,ParametersValues,ParametersNames,NbBins,alpha) + + +%% Input Parameters + +% DGSA: (Stucture) Previous results of DGSA. +% +% .Clustering: (Structure) Results of clustering +% .ParametersValues: (matrix, # of models x # of parameters) contains values of each parameter from Monte Carlo sampling. +% .ConditionalEffects.NbBins: (vector, length=# of parameters) specifies each number of bins of parameters to compute conditional effects +% .ParametersNames: (cell, 1 x # of parameters) contains the names of parameters +% +% alpha: (optional) alpha-percentile (by default, alpha = 0.95) for bootstrap percentile + +%% Output Parameters +% +% DGSA_ConditionalEffects: (Structure) Results of DGSA after computing conditional effects. +% .ConditionalEffects.SensitivityByClusterandBins: +% (4D array, (# of parameters) x (# of parameters-1) x (# of clusters) x (maximum value of bins)) +% Element (i,j,c,l) corresponds to conditional effect of i-th parameter conditioned to l-th bin of j-th parameter from class c. +% +% .ConditionalEffects.StandardizedSensitivity: (vector, length=(# of parameters) x (# of parameters -1)) +% Conditional effects averaged over bins and classes +% +% .ConditionalEffects.H0accConditional (logical vector, length=(# of parameters) x (# of parameters -1)) +% Results of bootstrap hypothesis testing. If the value is 1, corresponding conditional effect is sensitive. +% +% .ConditionalEffects.Names_ConditionalEffects: (cell, length=(# of parameters) x (# of parameters -1)) +% contains names of conditional effects + +%% Assign varaibles. +DGSA_ConditionalEffects=DGSA; + +Clustering=DGSA.Clustering; +ParametersValues=DGSA.ParametersValues; +NbBins=DGSA.ConditionalEffects.NbBins; +ParametersNames=DGSA.ParametersNames; + + +%% Computations of conditional effects. + +NbParams = size(ParametersValues,2); +NbClusters = size(Clustering.medoids,2); + +if nargin < 2; alpha = .95; end + +% Evaluate the normalized conditionnal interaction for each parameter, each +% class and each bin +L1Interactions = NaN(NbParams,NbParams-1,NbClusters,max(NbBins)); % array containing all the Interactions +BootInteractions = NaN(NbParams,NbParams-1,NbClusters,max(NbBins)); + +for params = 1:NbParams + fprintf('Computing sensitivity conditional to %s...\n',ParametersNames{params}); + L1InteractionsParams = L1normInteractions(ParametersValues,params,Clustering,NbBins(params)); + L1Interactions(params,:,:,1:NbBins(params)) = L1InteractionsParams(:,:,1:NbBins(params)); + BootInteractionsParams = BootstrapInteractions(ParametersValues,params,Clustering,NbBins(params),2000,alpha); + BootInteractions(params,:,:,1:NbBins(params)) = BootInteractionsParams(:,:,1:NbBins(params)); + NormalizedInteractions = L1Interactions./BootInteractions; +end + + +% Measure of conditional interaction sensitivity per class +SensitivityPerClass = nanmean(NormalizedInteractions,4); + +% Average measure of sensitivity over all classes +SensitivityOverClass = nanmean(SensitivityPerClass,3); + + +% Hypothesis test: Ho = 1 if at least one value > 1 (per cluster and per bin) +SensitivityPerInteraction = reshape(permute(NormalizedInteractions,[2,1,4,3]),[],max(NbBins)*NbClusters); +H0accInter = any(SensitivityPerInteraction >=1,2); + +StandardizedSensitivityInteractions = reshape(SensitivityOverClass',1,[]); +%% Save variables to output data structure + +DGSA_ConditionalEffects.ConditionalEffects.SensitivityByClusterandBins=NormalizedInteractions; +DGSA_ConditionalEffects.ConditionalEffects.StandardizedSensitivity=StandardizedSensitivityInteractions; +DGSA_ConditionalEffects.ConditionalEffects.H0accConditional=H0accInter; +DGSA_ConditionalEffects.ConditionalEffects.Names_ConditionalEffects=CreateNames_ConditionalEffect(ParametersNames); + + +end + + + diff --git a/DGSA_computations/ComputeMainEffects.m b/DGSA_computations/ComputeMainEffects.m new file mode 100644 index 0000000..9b8c69b --- /dev/null +++ b/DGSA_computations/ComputeMainEffects.m @@ -0,0 +1,140 @@ +function DataStructMainEffects=ComputeMainEffects(DataStruct,alpha,ColorType) +% This function computes/display main effects from DGSA. +% Author: Jihoon Park (jhpark3@stanford.edu) and Celine +% Scheidt(scheidtc@stanford.edu) + +% Input: + +% DataSturc : Data structure having inputs required for computing main effects. +% .ParametersValues: (matrix, # of models x # of parameters) contains values of each parameter from Monte Carlo sampling. +% .ParametersNames: (cell, 1 x # of parameters) contains the names of parameters +% .D: (matrix, # of models x # of models or vector, length =# of models x (# of models -1)) +% Distance matrix or vector of distances between the model. +% .Clustering: (structure) results of clustering +% +% +% Inputs for Display:: +% +% .MainEffects.Display.StandardizedSensitivity: (string) specifies the method to visualize standardized main effect. +% 'Pareto': Pareto plot +% 'CI': Add a confidence interval to the Pareto plot +% 'None': (default) do not display +% .MainEffects.Display.ParetoPlotbyCluster: +% +% Optional:: +% +% alpha: (optional) % quantile of bootstrapped idstribution. If only Pareto plot is used to display standardized main effects, It should be scalar. The default value is 0.95 +% If a confidence interval is displayed, it should be a vector of length 3. The value of sensitivity (length of Pareto bar) is based on the first element. +% ColorType: (optional, string) specifies how the Pareto plot is colored when confidence interval is dispalyed. If 'RB', the bar is colord with Red/Blue scheme (default). +% If 'jet', the bar is colored with 'jet' obejct from Matlab. + + + +% Output: + +% DataStructMainEffects.MainEffects: Results of Main effects are added to DataStruc +% .SensitivitybyCluster : (matrix, # of parameters x # of clusters) contains main effects by parameters (rows) and clusters (columns) +% .SensitivityStandardized : (vector, length=# of parameters) Main effects averaged over clusters. +% .H0accMain: (logical, length=# of parameters) Result of bootstrap hypothesis test. If true, a parameter is sensitive. + + +%% Create variables +DataStructMainEffects=DataStruct; +if nargin<2 + alpha=.95; +end + + +%% 1. Check the visualization method. +if ~DataStruct.MainEffects.Display.StandardizedSensitivity + DataStruct.MainEffects.Display.StandardizedSensitivity='None'; % Default is not to visualize sensitivities +end + +switch DataStruct.MainEffects.Display.StandardizedSensitivity + + case 'CI' + if length(alpha)~=3 + error('In order to disply confidence interval, alpha should be a vector of length 3') + end + + [~,idx]=sort(alpha); + + if ~all(idx==[2,1,3]) + error('In order to disply confidence interval, alpha(3)>alpha(1)>alpha(2)') + end + + + + case 'Pareto' + if ~isscalar(alpha) + error('Significane level should be scalar for Parteo plot only') + end + case 'None' + if ~isscalar(alpha) + error('Significane level should be scalar when sensitivities not displayed') + end + otherwise + error('Enter the right type of display method'); + +end + + +%% 2. Create variables + +ParametersValues=DataStruct.ParametersValues; % Values of Parameters +ParametersNames=DataStruct.ParametersNames; +Clustering=DataStruct.Clustering; + + + + +%% 3. Compute Main Effects + +L1MainFactors = L1normMainFactors(Clustering,ParametersValues); % evaluate L1-norm +L1MainFactors=repmat(L1MainFactors,1,1,length(alpha)); + +BootMainFactors = BootstrapMainFactors(ParametersValues,Clustering,2000,alpha); % bootstrap procedure + +SensitivityMainFactors = L1MainFactors./BootMainFactors; % normalization +SensitivitybyCluster=SensitivityMainFactors(:,:,1); +StandardizedSensitivity = mean(SensitivityMainFactors,2); + + +%% 4. Hypothetis test: H0=1(reject, so sensitive) if at least one value > 1 (per cluster) +H0accMain = any(SensitivitybyCluster >=1,2); + + + +%% 5. Save Main effects to Data Structure +SensitivityStandaridzed=StandardizedSensitivity(:,:,1); +SensitivitybyCluster=SensitivityMainFactors(:,:,1); +DataStructMainEffects.MainEffects.SensitivitybyCluster=SensitivitybyCluster; +DataStructMainEffects.MainEffects.SensitivityStandardized=SensitivityStandaridzed; + +DataStructMainEffects.MainEffects.H0accMain=H0accMain; + +%% 6. Display main effects. + +% 6.1 Sensitivity by cluster. +if DataStruct.MainEffects.Display.ParetoPlotbyCluster % display main effects by cluster + ParetoMainFactors(SensitivitybyCluster,ParametersNames); +end + +% 6.2 Display Standardized Sensitivity + +switch DataStruct.MainEffects.Display.StandardizedSensitivity + case 'CI' + if nargin<3 + ColorType='RB'; + end + Pareto_GlobalSensitivity_CI(StandardizedSensitivity, H0accMain, ParametersNames,ColorType); + + case 'Pareto' + + Pareto_GlobalSensitivity(SensitivityStandaridzed,ParametersNames,H0accMain); + + +end + + +end \ No newline at end of file diff --git a/DGSA_computations/ComputeNetConditionalEffects.m b/DGSA_computations/ComputeNetConditionalEffects.m new file mode 100644 index 0000000..fdada35 --- /dev/null +++ b/DGSA_computations/ComputeNetConditionalEffects.m @@ -0,0 +1,75 @@ +function [NetConditionalEffects,Bin_MaxNetConditional]=ComputeNetConditionalEffects... + (ParameterSpecified, DGSA,YTicktxt) +% This functions compute net interactions and visualizae in bar graphs +% Author: Jihoon Park (jhpark3@stanford.edu) +% Date: 16 May 2016 +% +%Input: +% ParameterSpecified: string, a name of parameter that wants to see net conditioanl effects +% DGSA: Datastructure contains results of DGSA. +% YTicktxt: Labels of y-axis of horizontal bar graph. + +%Output: + +% NetConditionalEffects:matrix (NbBins x (# of Parameters-1)): contains net conditional effects of the specified parameter. +% Bin_MaxNetConditional: scalar, the index of bin that has the highest conditional effects. + + + +%% Assgin varaiables + +ParametersNames=DGSA.ParametersNames; +IdxParametersSpecified=find(ismember(ParametersNames,ParameterSpecified)); +NamesConditionalEffects=DGSA.ConditionalEffects.Names_ConditionalEffects; +ParametersNames=DGSA.ParametersNames; +ConditionalEffects_by_bins_clusters=DGSA.ConditionalEffects.SensitivityByClusterandBins; +if isempty(IdxParametersSpecified) + error('Enter Right name of the parameter') +end + + +%% +NbParams=length(ParametersNames); + +SensitivityInteractionOverClass=nanmean(ConditionalEffects_by_bins_clusters, 3); % Average over cluster +NetConditionalEffects_temp=SensitivityInteractionOverClass(IdxParametersSpecified,:,:,:); % Take according to varable specified. + +[~,NumConditionalPerParams,~,NbBins_Parameters]=size(NetConditionalEffects_temp); + +% Transform the form of variable NetConditionalEffects_temp + +NetConditionalEffects=zeros(NbBins_Parameters,NumConditionalPerParams); % Initialize + +for k=1:NbBins_Parameters + NetConditionalEffects(k,:)=NetConditionalEffects_temp(:,:,:,k); +end + +%% Visualization + + +figure; +barh(NetConditionalEffects,'stacked'); +if nargin<3 + if NbBins_Parameters==3 + set(gca,'YTickLabel', {'Low','Med','High'}); + end + if NbBins_Parameters==2 + set(gca,'YTickLabel', {'Low','High'}); + end +else + set(gca,'YTickLabel', YTicktxt); + +end + + + + +xlabel(ParametersNames(IdxParametersSpecified)); +ylabel('Net conditional effects'); + +legend(NamesConditionalEffects((NbParams-1)*(IdxParametersSpecified-1)+1:(NbParams-1)*IdxParametersSpecified),'Location','EastOutside'); + +[~,Bin_MaxNetConditional]=max(sum(NetConditionalEffects,2)); + + +end diff --git a/L1normInteractions.m b/DGSA_computations/L1normInteractions.m similarity index 88% rename from L1normInteractions.m rename to DGSA_computations/L1normInteractions.m index b156636..c476dc3 100644 --- a/L1normInteractions.m +++ b/DGSA_computations/L1normInteractions.m @@ -44,7 +44,8 @@ for j = 1:NbClusters idx_c = find(Clustering.T == j); % find points in the cluster - + q_prior = quantile(ParametersValues(idx_c,:),(1:1:99)./100,1); % distribution of parameters in the entire cluster: F(p|c) + % Bin the conditional parameter and store the indices in a vector for l = 1:NbBins if l == 1 @@ -56,14 +57,13 @@ end % Compute the L1norm - if nargin < 5 % compute distance for all parameters + if nargin < 5 % compute distance for all parameters + q_inter = quantile(ParametersValues(idx_cl,:),(1:1:99)./100,1); % distribution of parameters conditioned to pj in bin l: F(p|i(pj,tl),c) for i =1:NbParams if i == CondIdx continue else - q_prior = quantile(ParametersValues(idx_c,i),(1:1:99)./100); % distribution of parameter p in the entire cluster: F(p|c) - q_inter = quantile(ParametersValues(idx_cl,i),(1:1:99)./100); % distribution of parameter p conditioned to pj in bin l: F(p|i(pj,tl),c) - InteractionSensitivity(i,j,l) = norm(q_prior-q_inter,1); % L1-norm + InteractionSensitivity(i,j,l) = norm(q_prior(:,i)-q_inter(:,i),1); % L1-norm end end else % compute only the given interaction diff --git a/L1normMainFactors.m b/DGSA_computations/L1normMainFactors.m similarity index 100% rename from L1normMainFactors.m rename to DGSA_computations/L1normMainFactors.m diff --git a/DGSA_computations/NetConditionalEffects.m b/DGSA_computations/NetConditionalEffects.m new file mode 100644 index 0000000..b2fbbf3 --- /dev/null +++ b/DGSA_computations/NetConditionalEffects.m @@ -0,0 +1,80 @@ +function [NetConditionalEffects,Bin_MaxNetConditional]=NetConditionalEffects... + (ParameterSpecified, DGSA,ParameterLegend) +% This functions compute net interactions and visualizae in bar graphs +% Author: Jihoon Park (jhpark3@stanford.edu) +% Date: 16 May 2016 +% +%Input: +% +% ParameterSpecified: string, a name of parameter that wants to see net conditioanl effects +% DGSA: Data structure contains results of DGSA. +% .ParameterNames: (cell, length= # of parameters) Names of parameters. +% .ConditioanlEffects.Names_ConditionalEffects: (cell, length=(# of parameters) x (# of parameters-1)) Contains names of conditional effects. +% .ConditionalEffects.SensitivityByClusterandBins: +% (4D array, (# of parameters) x (# of parameters-1) x (# of clusters) x (maximum value of bins)) +% Element (i,j,c,l) corresponds to conditional effect of i-th parameter conditioned to l-th bin of j-th parameter from class c. + +% ParameterLegend: Legend of parameters. If omitted, {'Low','Med', 'High'} or {'Low','High'} are given as default for three and two parameters, respectively + + +%Output: +% NetConditionalEffects: matrix, # of parameters x # of bins of specified parameter, contains values of net conditional effects +% Bin_MaxNetConditiona: scalar, an index of bin that shows highest value of net conditional effects. +% This bin will be chosen to decrease uncertainty of model parameters later. +%% + +%% Assgin varaiables + + +ParametersNames=DGSA.ParametersNames; +IdxParametersSpecified=find(ismember(ParametersNames,ParameterSpecified)); +NamesConditionalEffects=DGSA.ConditionalEffects.Names_ConditionalEffects; + +ConditionalEffects_by_bins_clusters=DGSA.ConditionalEffects.SensitivityByClusterandBins; +if isempty(IdxParametersSpecified) + error('Enter Right name of the parameter') +end + + +%% Compute net conditional effects +NbParams=length(ParametersNames); + +SensitivityInteractionOverClass=nanmean(ConditionalEffects_by_bins_clusters, 3); % Average over cluster +NetConditionalEffects_temp=SensitivityInteractionOverClass(IdxParametersSpecified,:,:,:); % Take according to varable specified. + +[~,NumConditionalPerParams,~,NbBins_Parameters]=size(NetConditionalEffects_temp); + +% Transform the form of variable NetConditionalEffects_temp + +NetConditionalEffects=zeros(NbBins_Parameters,NumConditionalPerParams); % Initialize + +for k=1:NbBins_Parameters + NetConditionalEffects(k,:)=NetConditionalEffects_temp(:,:,:,k); +end + +%% Visualization +figure; +barh(NetConditionalEffects,'stacked'); +if nargin<3 + + + if NbBins_Parameters==3 + set(gca,'YTickLabel', {'Low','Med','High'}); + end + if NbBins_Parameters==2 + set(gca,'YTickLabel', {'Low','High'}); + end +else + set(gca,'YTickLabel', ParameterLegend); +end + + +xlabel(ParametersNames(IdxParametersSpecified)); +ylabel('Net conditional effects'); + +legend(NamesConditionalEffects((NbParams-1)*(IdxParametersSpecified-1)+1:(NbParams-1)*IdxParametersSpecified),'Location','EastOutside'); + +[~,Bin_MaxNetConditional]=max(sum(NetConditionalEffects,2)); + + +end diff --git a/kmedoids.m b/DGSA_computations/kmedoids.m similarity index 100% rename from kmedoids.m rename to DGSA_computations/kmedoids.m diff --git a/InputData/DistanceMatrix.mat b/InputData/DistanceMatrix.mat new file mode 100644 index 0000000..469f8e3 Binary files /dev/null and b/InputData/DistanceMatrix.mat differ diff --git a/InputData/FWPT.mat b/InputData/FWPT.mat new file mode 100644 index 0000000..a583217 Binary files /dev/null and b/InputData/FWPT.mat differ diff --git a/InputData/PriorParameters.dat b/InputData/PriorParameters.dat new file mode 100644 index 0000000..d8c150f --- /dev/null +++ b/InputData/PriorParameters.dat @@ -0,0 +1,1001 @@ +Runs oilvis dtmax kvkh mflt1 mflt2 mflt3 mflt4 oilexp owc sorw swc watexp scen prop size +run1 9.7737400000 365.0000000000 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2.94823002815246000000 -1061.51660156250000000000 0.18728739023208600000 0.14059518277645100000 1.86319839954376000000 \ No newline at end of file diff --git a/InputData/responses_PUR.mat b/InputData/responses_PUR.mat new file mode 100644 index 0000000..6e510e5 Binary files /dev/null and b/InputData/responses_PUR.mat differ diff --git a/KPCASOM/KPCASOM_test.m b/KPCASOM/KPCASOM_test.m new file mode 100644 index 0000000..b88d960 --- /dev/null +++ b/KPCASOM/KPCASOM_test.m @@ -0,0 +1,37 @@ +% Scipt to get spatial rank for spatial models using KPCA and SOM +% there are two test cases: one is on the gradual deformation example +% the other is on an emsemble of 500 realizations of 2D 68*64 permeability grid + +% Author: Guang Yang + +clear all; close all; clc + + +%% example 1 +model1='gaussian_realz1'; +model2='gaussian_realz2'; +%read in the two SGS simulated models +r1=read_model(model1); +r2=read_model(model2); + +%theta vector +theta=0:0.1:1; + +%realization matrix resulting from gradual deformation +r_ensemble=[]; +r_temp=r1*sin(theta*pi)+r2*cos(theta*pi); +r_ensemble=[r_ensemble r_temp]; + +%run the KPCASOM_rank script +%we used Gaussian radial basis function kernel +%For Gaussian RBF, kernel_para is for setting up the sigma value in RBF function +% sigma= kernel_para * mean distance between models +kernel_para=5; +[Y_eig,ndim,rank]=KPCASOM_rank(r_ensemble,'gaussian',kernel_para); + +%% example 2 +%read in the models +temp=load('ModelsExample2.mat'); +r_ensemble_2D=temp.perm_ensemble; +%get the spatial rank for the models +[Y_eig_2,ndim_2,rank_2]=KPCASOM_rank(r_ensemble_2D,'gaussian',kernel_para); \ No newline at end of file diff --git a/KPCASOM/ModelsExample2.mat b/KPCASOM/ModelsExample2.mat new file mode 100644 index 0000000..611b08a Binary files /dev/null and b/KPCASOM/ModelsExample2.mat differ diff --git a/KPCASOM/SOM_process.m b/KPCASOM/SOM_process.m new file mode 100644 index 0000000..987e861 --- /dev/null +++ b/KPCASOM/SOM_process.m @@ -0,0 +1,26 @@ +function [ classes ] = SOM_process( Y, NumNodes ) +%This function runs SOM to get the spatial rank of each realization +% Y is the coordinate values (obtained from kPCA) in the NRealziations dimensions; NumNodes is +% number of nodes in the SOM, here we set it equal to number of +% realizations because we attempt to get a distinctive number for each model +% Author: Guang Yang + +input_vector=Y'; +%put NumNodes nodes in the first dimension +net1 = selforgmap([NumNodes 1]); + +%train the SOM +net1= train(net1,input_vector); + +%plot the SOM +plotsompos(net1,input_vector); + + +%use the som to classify the cluster +y1=net1(input_vector); + +%change the matrix to a vector of classes +classes=vec2ind(y1); + +end + diff --git a/KPCASOM/distanceMatrix.m b/KPCASOM/distanceMatrix.m new file mode 100644 index 0000000..87d86be --- /dev/null +++ b/KPCASOM/distanceMatrix.m @@ -0,0 +1,19 @@ +% X: data matrix, each row is one observation, each column is one feature +% D: pair-wise distance matrix + +% Copyright by Quan Wang, 2011/05/10 +% Please cite: Quan Wang. Kernel Principal Component Analysis and its +% Applications in Face Recognition and Active Shape Models. +% arXiv:1207.3538 [cs.CV], 2012. + +function D=distanceMatrix(X) + +N=size(X,1); + +XX=sum(X.*X,2); +XX1=repmat(XX,1,N); +XX2=repmat(XX',N,1); + +D=XX1+XX2-2*(X*X'); +D(D<0)=0; +D=sqrt(D); \ No newline at end of file diff --git a/KPCASOM/gaussian_realz1 b/KPCASOM/gaussian_realz1 new file mode 100644 index 0000000..c06763e --- /dev/null +++ b/KPCASOM/gaussian_realz1 @@ -0,0 +1,40003 @@ +gaussian (200x200x1) +1 +realz__real0 +-1.4295181036 +-1.19235134125 +-0.694361627102 +-0.686537206173 +-1.24573421478 +-0.934699892998 +-1.66518378258 +-1.61213779449 +-0.887484133244 +-0.573317110538 +-0.195173501968 +-0.426091611385 +0.118392691016 +0.171109035611 +0.860024094582 +0.0781109556556 +-0.345875859261 +-0.403893321753 +-0.0656999796629 +-0.232051581144 +0.3817461133 +-0.302731961012 +-1.03417515755 +-1.71480691433 +-1.5346493721 +-1.889939785 +-1.81845283508 +-1.38292324543 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+-0.492046356201 +-1.19677960873 +-0.96806704998 +-0.973016083241 +-1.07936799526 +-1.46839916706 +-1.4270825386 +-2.398853302 +-2.31473660469 +-2.02783870697 +-1.50013411045 +-2.07476854324 +-1.54030656815 diff --git a/KPCASOM/kPCA.m b/KPCASOM/kPCA.m new file mode 100644 index 0000000..21df2ae --- /dev/null +++ b/KPCASOM/kPCA.m @@ -0,0 +1,47 @@ +% X: data matrix, each row is one observation, each column is one feature +% d: reduced dimension +% type: type of kernel, can be 'simple', 'poly', or 'gaussian' +% para: parameter for computing the 'poly' and 'gaussian' kernel, +% for 'simple' it will be ignored +% Y: dimensionanlity-reduced data +% eigVector: eigen-vector, will later be used for pre-image +% reconstruction + +% Copyright by Quan Wang, 2011/05/10 +% Please cite: Quan Wang. Kernel Principal Component Analysis and its +% Applications in Face Recognition and Active Shape Models. +% arXiv:1207.3538 [cs.CV], 2012. + +function [Y, eigVector, eigValue]=kPCA(X,d,type,para) + +%% check input +if ( strcmp(type,'simple') || strcmp(type,'poly') || ... + strcmp(type,'gaussian') ) == 0 + Y=[]; + eigVector=[]; + fprintf(['\nError: Kernel type ' type ' is not supported. \n']); + return; +end + +N=size(X,1); + +%% kernel PCA +K0=kernel(X,type,para); +oneN=ones(N,N)/N; +K=K0-oneN*K0-K0*oneN+oneN*K0*oneN; + +%% eigenvalue analysis +[V,D]=eig(K/N); +eigValue=diag(D); +[~,IX]=sort(eigValue,'descend'); +eigVector=V(:,IX); +eigValue=eigValue(IX); + +%% normailization +norm_eigVector=sqrt(sum(eigVector.^2)); +eigVector=eigVector./repmat(norm_eigVector,size(eigVector,1),1); + +%% dimensionality reduction +eigVector=eigVector(:,1:d); +Y=K0*eigVector; + diff --git a/KPCASOM/kPCA_NewData.m b/KPCASOM/kPCA_NewData.m new file mode 100644 index 0000000..a58f37c --- /dev/null +++ b/KPCASOM/kPCA_NewData.m @@ -0,0 +1,19 @@ +% Y: new data martix +% X: training data matrix, each row is one observation, each column is one feature +% d: reduced dimension +% type: type of kernel, can be 'simple', 'poly', or 'gaussian' +% para: parameter for computing the 'poly' and 'gaussian' kernel, +% for 'simple' it will be ignored +% Z: dimensionanlity-reduced data +% eigVector: eigen-vector, will later be used for pre-image +% reconstruction + +% Copyright by Quan Wang, 2011/05/10 +% Please cite: Quan Wang. Kernel Principal Component Analysis and its +% Applications in Face Recognition and Active Shape Models. +% arXiv:1207.3538 [cs.CV], 2012. + +function Z=kPCA_NewData(Y,X,eigVector,type,para) + +K=kernel_NewData(Y,X,type,para); +Z=K*eigVector; diff --git a/KPCASOM/kernel.m b/KPCASOM/kernel.m new file mode 100644 index 0000000..1d04ae7 --- /dev/null +++ b/KPCASOM/kernel.m @@ -0,0 +1,32 @@ +% X: data matrix, each row is one observation, each column is one feature +% type: type of kernel, can be 'simple', 'poly', or 'gaussian' +% para: parameter for computing the 'poly' kernel, for 'simple' +% and 'gaussian' it will be ignored +% K: kernel matrix + +% Copyright by Quan Wang, 2011/05/10 +% Please cite: Quan Wang. Kernel Principal Component Analysis and its +% Applications in Face Recognition and Active Shape Models. +% arXiv:1207.3538 [cs.CV], 2012. + +function K=kernel(X,type,para) + +N=size(X,1); + +if strcmp(type,'simple') + K=X*X'; +end + +if strcmp(type,'poly') + %constant is set to be one here + K=X*X'+1; + %kernel for approximation + K=K.^para; +end + +if strcmp(type,'gaussian') + %the L-2 norm + K=distanceMatrix(X).^2; + %kernel to approximate the dot products + K=exp(-K./(2*para.^2)); +end diff --git a/KPCASOM/kernel_NewData.m b/KPCASOM/kernel_NewData.m new file mode 100644 index 0000000..c6429d2 --- /dev/null +++ b/KPCASOM/kernel_NewData.m @@ -0,0 +1,31 @@ +% Y: new data matrix +% X: training data matrix, each row is one observation, each column is one feature +% type: type of kernel, can be 'simple', 'poly', or 'gaussian' +% para: parameter for computing the 'poly' kernel, for 'simple' +% and 'gaussian' it will be ignored +% K: kernel matrix + +% Copyright by Quan Wang, 2011/05/10 +% Please cite: Quan Wang. Kernel Principal Component Analysis and its +% Applications in Face Recognition and Active Shape Models. +% arXiv:1207.3538 [cs.CV], 2012. + +function K=kernel_NewData(Y,X,type,para) + +N=size(X,1); + +if strcmp(type,'simple') + K=Y*X'; +end + +if strcmp(type,'poly') + K=Y*X'+1; + K=K.^para; +end + +if strcmp(type,'gaussian') + K=distanceMatrix([X;Y]); + K=K(N+1:end,1:N); + K=K.^2; + K=exp(-K./(2*para.^2)); +end diff --git a/KPCASOM/kpca_process.m b/KPCASOM/kpca_process.m new file mode 100644 index 0000000..379e53c --- /dev/null +++ b/KPCASOM/kpca_process.m @@ -0,0 +1,27 @@ +function [ Y, eigVector,eigValue ] = kpca_process( r_summary, type, kernel_para) +%this function does the kernel pca based on the choice of the kernel function and kernel parameters +%function is modified based on scipts of Quan Wang, 2011/05/10 +% two types of kernel functions are implemented: gaussian and ploynomial +% +if strcmp(type,'gaussian') + %% Gaussian kernel PCA + % d is the number of the models + d=size(r_summary,1); + DIST=distanceMatrix(r_summary); + DIST(DIST==0)=inf; + DIST=min(DIST); + %the sigma squared para (c=5) + para=kernel_para*mean(DIST); + disp('Performing Gaussian kernel PCA...'); + %running KPCA for different realizations + [Y, eigVector,eigValue]=kPCA(r_summary,d,'gaussian',para); +elseif strcmp(type,'poly') + %%polynomial kernel PCA + d_poly=size(r_summary,1); + para_poly=kernel_para; + disp('Performing Polynomial kernel PCA...'); + %running KPCA for different realizations + [Y, eigVector,eigValue]=kPCA(r_summary,d_poly,'poly',para_poly); +end +end + diff --git a/KPCASOM/kpcasom_test.ipynb b/KPCASOM/kpcasom_test.ipynb new file mode 100644 index 0000000..3a83a79 --- /dev/null +++ b/KPCASOM/kpcasom_test.ipynb @@ -0,0 +1,186 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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MIyLyer1///vfJ0+e/P3336s1NpE4DSQistvt/kzq168fiyK1B6URca/XYXrk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\nPLwxli/sD9bB7z649faMCKd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LgoOD6WjUuXPnlStXGrZIAADAw2QDEj29mKWlZURExP79+4Wv5wYAAPpnyk12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\nRK5CYII=\n", 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xq8IIMGQHAJZFsIDEtGzZUtjwo5Wzs/OxY8d27ty5f//+kpIS1U1NmzYNCQnR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\n+Adr1dq1a7XOf2hra7tx40bW061tkLOOcPioiYH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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Performing Gaussian kernel PCA...\n" + ] + } + ], + "source": [ + "%test scipt to make realizations and run KPCA and SOM\n", + "% the test case is on the gradual deformation example\n", + "\n", + "\n", + "clear all; close all; clc\n", + "\n", + "model1='gaussian_realz1';\n", + "model2='gaussian_realz2';\n", + "r1=read_model(model1);\n", + "r2=read_model(model2);\n", + "\n", + "%theta vector\n", + "theta=0:0.1:1;\n", + "\n", + "%realization matrix\n", + "r_ensemble=[];\n", + "r_temp=r1*sin(theta*pi)+r2*cos(theta*pi);\n", + "r_ensemble=[r_ensemble r_temp];\n", + "\n", + "%run the KPCASOM_rank script\n", + "kernel_para=5;\n", + "[Y_eig,ndim,rank]=KPCASOM_rank(r_ensemble,'gaussian',kernel_para);" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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D8A/ewqTanZO7f1T6qiiROlAAPIHtDdhXpILJk/vTrhjSp2nVhWLhZpJQrLANKQbAFCQK\nBzDY55lWzwvyYg1B1IBKiSolVXWw7tY1KXpxeBCAKiVRKq/1Zm7+kZQBKJVc8XfZJBJVnEN6syY5\nzwwX35NfqhOvyU0HisvVObk7RwZLZByAC6WCoEN0D7JH5DkMDqYDALcKtGIaKlKRYzzchOVBNnlS\nTsM5PhyTwk1Yn0/nAKzF5Q1/PGKKrfh9r/xiKosy6r8rngbw5HgDQCMtvZ1umzxZRR7AUlKbVLtb\nB9w7MxjeLLKA9F2gSZGfKg1eOI7Wz/OVXqo9yHbO0XGDJzrYWXn8Eik9ExwSj/F2VApTNUplVUqM\nqU0nNigAazCcLOSvG8H6Pe16ktulozEGQEqkQb8+AABIgbLjjWPm+igxxWP8f3iPAThqbq7F5ePa\nxhwGnwsPipX+ulvnTCE0xigPPQ5jRfMIV7i9pqcJRZXQGEyBlEipZ0iJZG6pYaDoRV8fEDkmXjkK\nTNGLxo1855C5DeBaUMvJHgChTajwYJ3kbHWzKjvvJqueujmmhAA2ifV0eLgqOyaJtqPSiXDhS6kc\nMWVMGxhSfEqeMqVoTu7WiQfAJvHPSI0xHu5Phz1J+0/q4brmAjgRzoWpait+lMqy4jPP0EYKAM8t\nmVavqg4ATKpdL6ceUZtzZOBCGee+SJ4cVptn/ektv8JSuVpdTUzvjo+ItxSrSelq+yFR8P8vUeF/\nL37lVnG+kZYuB/VJtfsVZt+aSAFohqW+VyY0RkIDk4usqTpSohyuvPaQW3fkN+b4APqJ5emqrcaN\npHyyd2/V2H3ManycHVmUWwCWktop6ojqy3v0y/v46PPp3FpcXnH2JrFBaAzAUHy3rhAaE4AzxQvy\nRbOrSRGAtj+m0liTonZU4ExpOXWR74oUX6VxrbDd9scMxRd/aTMsATgxWijK7s9ZFyzEQl9wn7np\ncNUig19Ir/aItilZAE6lewC0mH1itCAOL8quSEI+HR8BMKN0RQayBk9Eozk23JN6JRr2iDbPhytS\n/q/4IQA2IqEhClM1YgpLZQA1uyliLYBGWnpKWq8gOJz0bkimztiKlBeRW0zF7sxIeBPJAtLt8nVv\nXqSYjqM1xsOLtAzgdakg9GMbxG7wAjgq1NmKymu9GTEXO1RqmCQ6v/WgEC8BSBQ+3OtbO4Y5pCQm\n3PTBaJoL1HZR25VhMAAkJvzq3tEYu+Hv2YmJl2cAntMmZN0JmPpMYolU22NWo59Yg34dRgyZpf9Y\nCQDoiSynjqNaPTbsF6bbw9G9shXHAAXgTkZk7LquDUQG46jeEmk3MbkTc9LPSdGc3AVwBLuibLvA\ne+U09MmNvcy9LlkGT7Yka4q7f06/1pDyHVU/pewBUCeuA+U5Z8FPFSETsqWoTj3xDgAeTW5oiPXU\n/l/JUoPmDc5mteEpdY9Yda31ZsxyK2IKcwvU1emVfT09AbBeT6REOmcFptVTpQSAJkXvsi+5XP05\n64Jl3axRXVL7/psxMN4ydKIiGC3mdoqyW5adj4dHhdymRp2npPWfMRsdore4+aiydTKeFBVKEY2q\nxm4bSH2LqEES2Kh3DBq7tERonMRG0ezWtd6GP+7ExoV4RuTTqsauIcUtZnup+nfO/WGqCkknS2Uq\nJX/DVAA6jSrU6WmDEY392KBS4rml/HUjNHmiQF6xVD2Ok8ookPVpJxcjNIt9IFFQ29u4JZbTpEhk\nmIXUDUCFOq96U0XZBXBIb1qIXSizGB4m3TEaGjzZE3sADJII24D7+XKPaJuyVcs5AFbjMoDtqHTe\nmxIFTpNEkNFIy+9UVj3I8+nwumT5RA5A96budckykYhHo5GUhcYPlIl//c0pH2iNuaY+rKqDy6ze\nlu0javOSUnK4UhOTOR7PYggVNuJT0VTvTRoed4YsIN0u/7f+pVIaguGGZAIYAzaJNcVdkUr+BpsQ\nqoetqKzTSOQrtqLyldaC2VXNth4EMuRUvFWupUaBkiSSLKf51yW3b1hFf9CxEjnVg4TqMTdYuGMa\nFwiZYkEgS4BV9HmiS7rZVcbdApdjtI307zGb26WqybVWicQkODgAgHWL6rEcyMOcDMA5ziMzCouB\neAZMq/egvSqqXA2l9JS0vkMMACLzFjBV5FW+7s2vu3Ue6abVO2RuV2VHpNEr1AGDLUVvJ9vLKM/S\noYlkirsm2ewQ/WA6MHjyk9aGwRNRZjuYDpBil2gGZz6hn1dm1klO/DqkqEmOkBKZUmSq3WN7N876\n02vDqZlKox0V/DFlTBuMElMk4kTu5WG7IQTfJ+NJL1WfT2wAF0YzY9pAYavKmzAu3josmNt79r5o\nk5vakItR/WpQO2putpj9cXZUjI0adcCxKLfeqawupeOuudlO7PPNxfyWFhTSJCjKMaIcDQOFyClC\nlSbSIFLT1rQ/08MoLyVSOiDrY4wWugDWO3PUGiSxIZZlSWCbVs+PDVHbnzQ6Hdgtpy6WWcwtaCNF\nTOa0Xcr2etF103WUUsVLAbfAAegeiQzWcuoAIl0WSyhDikX4bEeFiCkrQBIbjmJMGp0XevedVubE\nGktEFyGXEMUth6uL0g6AB9juFFyQGxUEe+XlANRX5F2idYgOQCwiZ6WhB3kV+YvSWCMpC8ncll+Z\nt6/fusK92JrJb667dbVdZPWOSmO/GovY/Li5IrKgQpLX5GadeN9gE+3EFuWu7ag0ob61gxGQBaTb\nZz8b9ojWk7Rv0jEADV4Qw84kUUu2Lwd1y4hecufu0Vs16gg1pzgwUXgy45tbappQAMO2uq/ZBrB+\nb9V1lCCQ80Xf7RvF+ognEhNPckzkvR72Am3d2uOEJh8ZKdcia8cAgMs5rehrBhvu9ZN7elFsMCkR\ny38qJazajwAqJfNGZ1Ltvle+KvQXAEwkIv2yKO08wHZ9csNIk4oUfIHPilPtJ9bacAqVpUN6Uzwh\nTqqKJZTH1SvD6aY22q+3AHwDExaJPjX6EXHgk7lLbqqC4mA6KPEwAD2QDko8FMupI6kLoEHzHaIL\nyZNFoifJ5ufTucvehBfkwajW17VdORxLqIKd5oI37gMQU2P4ltlVBxM9Q/HPe1MlxV1GPWDqL1tn\nxdroHZVrDldekp3hnRwQbzmmMDos7XyDTVwO6gDaUUGVEpGpM0nUSy0Aq3G5Kju1N142qXarsvPo\n3le8ugrgsjehSknUmdA9kihSWAzSXIBRfjjlWNulROFRLh5aTNadJLBBGTFcNihrvhSOuQCIGnhu\nCZSZayWmYK1uAKjZzVFigsY5Y3eUN0lseBMBrysAUHfuKzVmlG47sauyU5McG3GTW2f9abEYerJ4\nusktm0RnwmkAkL0RTD82ZvKbx4wNAD9lXrrVCSQ0GlEqb/kVP1VKiluhzuficjexJ9WuyCt6RC4j\n7Era3tQz+M0llAe5RrwKD4yUVUggqkRCZX5LOyf+XgB0aImJqXWlGhRSXgzaGNtnNb/uzYvoZZLo\n6968OH9Rn/ul3NkmN9+rXZnmziuoPntnR8UdJgtIt4uIRhekMoAWN49g15ZjyK1PDX9kWyrdo7fE\nsO4wu0ad/636D0vpeJ24S2bNlqIXevc5cllKpFSP6WH2OgXxjHzT1+wQwKBj6XqSmNzLR9wcgNHC\nuplcNzU7dGduZqG46cuKb89v74aFdKLnSQkAGYiYwpnCAColSWxMWs1jxoaIN11J2yD2jqj0E7hQ\nANiIf1660uH6Z6X9AJ5zF1pOnXgG1yKRDNGAl7AoK/7DhdfFLK8dFarqQKTm+av7rjgHqB6HY0lk\npIXKthMbfLfyueYUs4LngFtZtaLsipTLVlQ+pDeFyOrWM+/HxpeUIwCmjR0YOwFT21ZBmkpYbLDY\noANb6+sAWH8PjJQWulO160KvJSS5h9H9V8mNIJYDcv26ZO1NXACRtPPCnR8WbyEmuPv+aKWiBD9v\nXtkgdsUMTvCpeam/xKoA/q194SG0L5GSw5WfiDd/mV/uqVqfaA0pvxeeQZJP03lTil71pvbVX+9X\nLJ7KCPKcKTB9AIHJUznllBVzO1Eqc1dnVoBIhczCYgRGD5YawM2Md/+gNQpzptCF+mNVY7ftj4ms\n3cH8hkmiI2qzTrx9fCQW3KDtBd4T5/YIufG/6MsB6Dfp2Ffi2ZtrI3+MM4V4BmRGrUE7KpxIFupa\nr0UdL1VFUceJDSHHyF83grh6XeFXahEMd5/VfKn14EuUzeQ3J9Xu59KDojgqmuIBtLhpI34F1cOk\nK87nVl+HWHtNGp3JwuviIm/ly1t+hRUQT8RRbJBRHmqwNpyymrY6cz1g6mGjCUC0JB7Rdqe4uzdx\nhWwKwDG+kwWkjJtcl0wx8e8RbUuybBI7XNmvt46ozeNoeZB/xm4sowzgK/GsSHeIDoOnSq+2c/as\n0hVtpGGqRro8lCtcjQDI9SQB9I6kKlKSWGmp7x50bMUvyu6wNwPKCI2L2qiu9SrUuUdvXQ1qbX8M\nwMH8Ri+2JnJrs0p3NS7f6rGF0Lax4RyG1yVrb+qKVlYheXo+2V+Vnaek9Snu/qS1cSVXeDo4YpLo\nsjURBnkwCkYTZp/afXuqx4Vi0+/W1rSStVzSEqnblblKShUWFgPq6oPOBDd9eayjvrGU8WMj7BV1\nj3RjjMbYRrlVVQdrcfl8PDVKzKo6iFJZdCCJhdEGAMAfVpBQH8htqcMDA2//DgDRzCiakR2uLvDe\nAnrH2I7BGQAdSY/gEG8/ZPU6g8kbxBJPbMa/GJnzl5S6B3mMhz+RbC7LpV/kl/1UtmjsUmWB98SI\nmk2H5+j4slTqQPeI7EJ5Rao2uWUjsqXoydyll9y5ouy2o4KpDwFU1YGfKm06xplCh1ZkyQAe2f8N\nUYs658wC8IK8sFEAcEhvnvem9lnNLb8ypg0A7IYFKiVJYDM1uNybM/XhtaD2ZO7SCorzpO9w5Uf5\njV2iWYj/xrtfTIPm5G4d3nvlqxU52CD2f5aOieaKV70pAJoU7YaFK52JKzLbV2mMEtOPDbVd1LYN\nSWYsoUkiYZ8LgDNlbTh1qPJ6L7b8VOkwG8A1r3YunQUgtD+PWY150j+M7jrJNbkpUvdrKNe1nkki\nU7qZAt2KyqJxioQqLXRzsqdKCbSR6Pv2yjcFCy5XP6gumbg5mH1CGzRfTsOepAlNPLB0BwfFnSYL\nSLfL3yn7m9ysU+/BtFPioYlkgff2pt6Py5tbsCZT97PSftFw107sa0Gt75W/3J7lWrSGGZEZP+9b\nMNyqsSvmTdVKw0+Vx6xGve420lJ7xhYTTCc2VBr3R+Mjdyo/IPApDMZG1etyekNOh5MhEgpASqQr\nozw3/TYdW+oV01K/auw2w1Itd+kbbKIl9TpUN5Gsk5zQ1D5JNj1Zvj/tXlDLAETnB4CD6eA9+mWH\nK9eCmu8ZuV0a7piaHfJEIrKcGtM5nw46pURPNDukNwhCsJHK+zXIqaknSZIDwABp3mVWAKZU9jZK\nirvhjx81t7ejkk6jgKlhqgq/JVVKcrK3GxbGjF1Rbd6KynptR0jm2uVCUUpEDbwXW8JGRUxIPciT\nqfvf5D2TqQtAB9uTugDgWQXigkPn7E0aGm8RrtK8TWzRVQPgsbh5QzIfYdcNuvde1tORVJTeM/ze\ni7TcIXqFBzvE+FjvX93qURUyAbGeFkUgoWgQ9ZiWaTupalcjJ1W3ovLpwYGT7kMwXIzykBkNlN61\ne3tAGshETlme+UOqBUonmAUQBrRcd9x6ou8YXp55jMLqCY1c3XSb3Pov/N4accDxc9aFfXzkQd4h\nxjj3D6SD2XR4DDsP6+3rxPyaPGHb0YvDg1Eq24oflVtekF8bTpFIlQIFgDfv5nYp9VMKYFfWB5JT\nUQDcuPZA0DfkvV5r3Jd1Z9LoiFF9SG+Ka+Vw5QxqdXgARA7QJNG1oAbgPfklh6vCvqgou8hBK0St\nwURLSAd9a5DQdrkl3idiyqTROZ9OCUskAFXZWaTtcckXdjCi4vsWJgtIt0uTm09g20jZrZn43tS7\nIJXF0P+stP84WiA4Q2pv17ZNdXk1nz8VTZ0fzPNIF9kGu9jUpEhowavqYFLtCieheaVfkxxHUrei\nct8rF81ulMq1wvbIMof5PPEMWugmsUGHlla9UZW9MFWFq15VHQgfnW2j1PbHwlTdr7dsEi1HdYeq\n/xAtiAdmTurNYiie0tO0upSOP0JuXJEKotWjwQstZq/F5UGYg8xGNYaZXuRbuZZKYpKOlP51g6tE\ns0MWKG6JFipu6Gh53Xfm3SBQ7I4EYLDPA2WmPvRjQzQVRUw5t3MfgHaoAuCmInQnSgAAIABJREFU\nP2pOAQiBQamPUb6TVOQYmwrkGOGYu6LsZW7ByHdEBHqy2AAgUvOTqYsUW5IlLvuWZI3xsJSGNySr\nz7UG8mUpLPHwupStkL4nKjx8gO3ey3oAdCQADqW7TWKXeChs61YwM8ldk9AKD+bT4RgJ/6j01c+F\nBz2uFt94E6HUFzrvSaNTlp0Ws1uALUUdZr/qlQZhTlhyqMWmExuJFhFGmRUMdSoFSqrfnCfxcQaA\nMEqtgQ6M3EKupTIFyA3lN5qNAPydc/9uWJi3r19m9cfNFdE/1EhLi7TtEfmz0v4j0q5Yxi2x6mln\nTshTJ9TedlRyYqNodgedCa5FgBIWA6IGQ02nrp7KKWRm5DtpbHCmDGWD79tluoPYSAJ73S1wNTL1\noaj0XGktqCMlLAbF3M4gzPFIF1kNKiXMLfzVaFzoiYgawLfUkRLHpLh/A4ATG2q+M23sAKhQRwi7\nK9TpMLtCnXPO7LSxczmovxjdbCUGsNabmcVn7uiwuLPcoYCUpulXv/pVAI8//rii3K4Yqt/vX7x4\nMUkSWZaPHj1q2/Z39Uu/x8P/CR9kl2bTYY9oB4wNHqtxop6Spu5PuwAC0CniGjzpStoT2AbHK6g2\nufWIuvlXpeduSBaAUhrqSPpEK/JwVcrrYEdZ66vKNACDJT6RQTeuWIXGG1KCrahsqIO+lPRRnjQ6\nfcWqlxrNsFRS3MNq45b96I+nm7YWryjFun1BOLydCadNEnWYrdNoTuoJn64rUqHFzRq8h1kbFAfY\noCtpognfJcrFpN4MS4+WXkMJthRdDuq+obToBAnV3JaUr0ayHQ4nQ8DXRwqLCcZc4pH8ljasJ4P9\nLvEMUCYrvoi7Y9qgpLgAzFx0YTSTwAYARlM95pS9b++Lq3HZy6u92BKtIWJCncRGrbzxS7mzDlcc\nKEtJTVhbApin/ZW0+CQ2Szzck3g3JFM08I/x8BlppkY8T5K/jKk2Ln4v9/d75y0wyGfToY6kQFxF\njuJEDbh6Q7KEfdyLZI9N4hNkapHsHEwHYirmcOUd2jWxKJnibomH1yWzA33VzAtXAhPJK6g20tKc\n1FvU25YeC+WYSCEAkHWHuQVQRnVnstIR9R5D8cXC65DeFFYgTkHFXoh6zygx21GhauwCuEdvvcu+\ndBwtADfrScAibQtDBADiJB0ol4N6lMrCEBnAkhRNqL3L3oSUSPrQCEwOygzF95iSlvoA1HbRT2rc\n9AFwLZJ1R6UxS+WC2RX10YCpQnQAww1VBYwO+nXhNWzqQ1FJjfKx361xLQJl8C2uRuFYRPVhUXbX\n3frB/MaV4fQK22srfhOlvlc29SEMHNc2Gkn5JwoXhTojYsoIZiglgzBXzO18L/f37ucOBaRPfOIT\nf/ZnfwbgzJkzxWLxO77+i1/84ic+8YnXXnvtv//hsWPHfuM3fuOxxx77QR/+z/I1ee9FXu4QfToe\nn2NDHexe1tUQD2Bco3lwABD5d4Mnv5Re0ZHUuZNTnFJcGjdbkW+zuWtzfTtVkn1qou2UuRI/OlB6\nRKtzJ4TyGi0/zNrTkgMJkPCKXBVr/8uyK0QBDhRba5yKpr40OCJMJAGcMBeezF0SXQ6PqJuNtCQM\nTz2mvl+/KHyISzwE0EhLJ+I5Uzs/zZ2upAEQeepHWRMaLO3Kfxw9LHJoOo3W3TpRA6o7Q9PIv15I\nHM28rAFANQAQ5eJwLKJDCzIDowDAaALjVpfi5d6csPEe0wYjGgMQ5kniSr5Xu9LghWfCxaOFlQuj\nmS2/otLYVvyS4j4THDqsNhelnQbK71eXhT/Fx+MjNeqIs+1J2p7UuyGZk6m7JVk14gmr6atBzYyb\n/7I7+/3ih32Qr8P+a+UAAOF8ChljPNwl2jrJjXPfgTLLh5Bg8uSKVKjwYJz7C+h1uG4iOcK6PaKt\nSPn5dDjHh/eTrnjPANSm8c9LVzrQV3keBDXJsZToHdq1k+YkRL+nreKNJUI3sR8tvXbOmRUtrv3E\nEkVH0TotajZekBd9suJD3+EqCDpEF2b2QsAJ4AG2W5ECcHSIXgOOmyc9U/5ccs+i3GpyS5Ryc7Kn\n1jejVE67NeIZ8qZNC5xZgaw7rN6BW9B2rSgXc8pYKvupDCBKZZ1GQpsjzudgfqMZ3lz5IVDAqB8b\n0/mNgKlrvRkiLgSjXDhK0DhiSjsq7LOaK85eQ/FFN/p2VCqa3aLsHlabdeLVFc9CvGjtAGhoGwCE\nULDvlUv/glv7w8OdCEjLy8t/8Rd/cZsvZoz94R/+4Re+8IX/8b/Onj37K7/yK7/wC7/wkY985Ad0\n+LehwQsNFESa2CeyztlJeQ+AEg9XpLxwzjeR/FiycZ7WAKxK+Ruw7o0VAJvehE9oacUq7rkqxbJ/\nY0ZVHMSqhhjQAASQf1RqvML2idVMgxc+0z8mnkMnNtaGU/lNm8RksM8jjBr5Do90ALLuFGV3Oaov\nAzNKt07bb6fbS+l4jTp/IP2jn8oP8F1x8k8k1/81XwXFjdS6IJXFZHY/uymT9om8S7Rfyp1dYlWL\nRItya0MZ94eVhDLq6sMDAwDC1MfaMQKTczXSdi05JnJH44kEYNApAYj324NyBABqxNyCR9l0ZQeA\nIcVXWguifrYal1+K5kTfosfV+3NrphSJT6IZpWuRyCZRi5sflC9uEPsL6SwAL1VbsL9AZ1vc7iR2\nhTpIIdIaNeqI7HzLqe9JFf1fcF+/T7wFBnkrtZZYVeyD0EBhjgyWURZqBQdKK7UhocVsi0R1uNNw\nPMgbxAZgpOwMrd6cMRBN/CuC1jrJLbHqM/HNeYaYIQH4G/f+Lb/CBmUARrkFoCmV+l5ZVnyhZTCk\nGLLX9seOFlYAiHqMSFvJii9W4e/RLwOwEHegiyzij6ebAWSRYCzx8MF4R5yP+KFH5PfLl0wkIFjM\n7Syl42f96ZvL9OpqmKp9s0wilTAqDH9JQkUDH/GM/LqZmByAW1duKnFiQ8hzSopblF1NilpOneVd\nMRW7MpwGQBhFbkh8i6vRTf06II7qJ5YQeQMQ7pHC81tcHACTalcMcuGzDA0XSeRpvfC7va8/VPzA\nA9La2tqv/uqvRtHtOjH/90/a7OzsE088MTc3d+HChRdeeGF3dxfApz71KcMwfv/3f/8Hcfi3QXS/\n2lL8Cqon4rkZpeswdVFugWAWwzGE+9kwIFREo4DQEg/3pF6PaCUeTio7o9gewFht3idEYmGsVApb\nltKf2a0OYOlIXkznVmh+neSeD/ebUiSU1gDGtMFEbm3bLrWcupAtPWivzhXP1on3fLi/m9gAAqa2\niX0yVYXDwll/GgZsEoFgjgyEIdgDbLfEw1Ia3o+uwROfyE+r8wfTwS7RPp/OgWORtgGsxuVlXlel\nJLIGY9qgrY6BKWDUyHe8IO+VIxguAYypzSiViZTEqRwxhcSG1bRpDLOreuWI0LhQ7AKYUbob/vgI\n4GokS4koL+VkbxDmxMw3iQ1TH4o577pbFxm/e/RWQyoBuBzURbX8WmK9s/DiEuCl6snevTzSa4Xt\nDX/8R/NXhLBwJr9pyu6b5dTw1hjkKkmFVY+XW+sm9meigihd3Crgt1L77XRbvNjjcgWBsCss8fBY\nugPgJaUO4DStivywmKWNS/6q1mty6yvxLIDTgwMARNucUW7dqqAAOJfKXpAX5iazSnde6jdt85nh\nYl3ridEiFtPz9vWAqc2wdJJOdph9XNuwEYOgQ/Un+PUiD48lO6IGdo6O62ABqGjTdqHs46OPJ0dq\n1HFTtZ3Y/cQ6WlgR8WC/3roQGwmjhNFI2HHlbqpbUcLMTPeF3n0slYUYXZWSQ4WVy94EgPfol0/G\nkx1m7yr+pNHpJ1Zd6zWlkhMbDMAor/qSHKuBd09YSVM5zTflwT4PVu9brkijPGQWFpvCbn+Z1gOm\nCnelGaW7lNRm5WGdeLa6aZP4b7+rm/rDBuGc/+De/fz587/5m78pHhLBt89mfPGLX/zQhz4kvv7g\nBz/4oQ99SJKE0xo8z/vwhz984sQJ8e2nP/3po0ePfn8P///iAx/4wMsvv3zhL6e+Js1sSdYyyjXi\niRYHscWLqEYKXc195ibe2GTvTDj9R9qpDvQD6aAraZdI6WQ8+aiy9Xy4X7S5ldNQ7LwC4BVUa8T7\nD70fO2Rui43LTjtzT+Yuifam087cIMw9WnpNWFW2E9uUItGyKvySx7lfQSDeZJo7wlUvYKqw6mrw\nwsWoPqt0301ubk6zQexp7nw6PQhA7Dch/PnDVBWpcN0jdEhZoCQTflgMtL4eGSlkxikTbv9W0xbb\nuAEgNOZM+c36V4Q/So3eNFkRRqjiNwqn8LY/Jrb+45FOXd0akPANm1fITEwk/619QfQzft2bF+4v\nE2rvHdo1AA5XxA5sADyuPqk1GmnJSdUOswdffFl//suf/OQn7/AW5m+BQf7yyy9/4AMfOPzue8d+\n6qHP9I8JGSRzC0goZAaAq5HIkok9FcWkYVFuCa/FdyqrAETbZiO9OZMQgppF2h7n/i17UACnBwfY\noCwcs7S+HhZvOkJFqRy296R6LFp//FS5FQsB6DR6UmsAOBVNiadD2Hyc6y4Uze595uY7ldVvsIlb\n2zZ2oIt8bwf6Kb5nUdr5BpsAcNqZE/bkADDKm0MKwCtHhWJT1LTEXkoiXsK3OGWy7tyfWxP7Ck6o\nvSNq0+HqWX+6LDsXRjMARIfGrVZWoVoSpo5tf8zcLske4QoHEJpc84hb4GJPy2p5I0xVoSn1Y+Ng\nfkMkCW7dl3mpbyE+eLPH3BSNVs/+2tNve9vbPvnJT97Onf2h4wcYkP76r//6ox/96D+ZNn6bZzVN\n06eeemp7exvAu971rj//8z//Jy9gjL3//e//5je/CeDYsWNPP/309/Hwb4MISM9/7L6XlPrXMCF6\nqpPY0HYtfSA5lZTlXSIE0+bNixkWA1l3ktio2U0A7e60SFiJ3b3qWu/WxpoP242npPUD6cAnMoBz\nUsVC/ADb3ZKsz6dzwkekw+wZpbsWl8V4FYb5sxgKJWiH6F+JZz8oX5xjwx7RfCKLbIkH+SLG6sRb\n4D2Ds3NSZZz7x1lbnKFP5FIafkmZAiCeZNHQfrk3B0aF0MgcUtkjTseyKy5PpNDR9KIfFNIoF1fL\nGwCErYu4FOGY+2D50rWgJtzDRJ59EOYK2kgI5wDYUlSTHPFbbq32RL5OhCuxfmr7Y1KvmMop1yKi\nBgColDxVetVJ1Rp1VuPyO7Rrz4f7RXek8BDyuCo99zX/Sy/d4YD01hjkIiA9/tP7/6ef3v8X0bHL\n3oRYvIJRa8cQVorIDUUjkRCniANvGd+JlJrY6lQ0mSaBTRiF4YoB8EF16QxqAByutpj9qLJlIf7P\n7jEAa8ObM4xbDqrTxk6FOmLuJdp6HCjH0ZpM3delgolE6M4BiPesE08oF2zEYhexMR6KfkGxxZFw\ngROR7MtbjwJQR0qiwBoQAHykOPOumISJP5abvqkPD5nbF0YzonwFICd7R81N4eWj00g8kgBWnL0i\nxzipdsXmMuIiiGasiCliZy9Div1UEeJYAP3EutmKq0biWRA6DgDHjI3lqC6aMZrc+kV+2Sfyi2TP\nUlKzpejKb/zHt3BA+oGk7FZWVj7ykY+cPXtWfKvrehAE3/GokydPiicNwIc//OH/8QWU0j/5kz95\n73vfC+Ds2bMrKyvz8/Pfr8O/I/9eOVYnnthlSzyrmkd4IllNia1VALiBHA0ls5yoeizHxMurBPA3\n50OTSwoQFJ3tUl/hkZEO5Hqh2ATwC/l/tEl8gA0A7BLtBJ9CikVp53WpAOBnpMbHk0XvjR2OTRLV\nJEek4A6kgz2ptyyXDie9Zbn0B9I/dqF9IHz34+bKcbRMnvyp96iwbBAGDfey7n427EkagD2p9xot\ndSXtglT+BpuoSY6Yxn48PDqjdI/XN4Ql0urK/V45yntaet9gCLF8GUSRSq2BQePWYIKEaqEpA7k0\nkNNyjF1rZfOh4V4fAFEDHumEUU6ZIyXnw3nOlJn8ptiWaUwbHCo1NvzxB+3V98pXL2IMKgCITTxP\nxpNtfyzV41xLZYohe+awniSm/1z7IeDmvukXrJkkNs7T+aqxe4/euhbUBv160V3+zkKC7x9vvUH+\nMts74rOmFD1or25F5fW0Dhp7eVVKJAD6dsnLM90j8FR33BeCbPGZKzJpOdk7P7j5uzhTbu0Rfo/e\nmpO7n0/nxG70y1G9F1tzcreV2uKTt2h2AYg9t0RP6xHs7hBDrOx/PN18XSqsIu9B/tP0R2rEsUl0\nhO+eQe05Z+GouSlG7wJ65TTsStrhpNeTtBUpL+QYK2lRrNRnlO5qXL4W1I7Wl46oTZESaJfG1HYx\nqrlIaCqn3sSQRzoJ1XdVXxHqvocLr18NamIbwEhXvuyPCes5k0RtUc4EDpfPCQNAYSOyxsuGFD9m\nNQDYZiQ22hDSPuHb3UrtdmL7qVI03BvNSmRQP1KRUE+L/P5UomBdn0NC/1OlBECTItdULUSt5GZP\nfSZq+O744z/+489+9rO3vn3ggQd+8Rd/8Xd/93e/44Ff+tKXxBfHjh2bmpr6Z1+zsLBwzz33XL16\nFcCzzz77O7/zO9+vw78jF6P6c1FJlFUfLF/yuNorWG1/TIxgKZF0j+iA2O5B9kgupiQmicnlmIRj\nDhiFZ2geSRQplRl/dd9SZepcfiG/aX90r3+rU0FtF78IRNU+fAuAiFtF2T05vLdq7HYTu6F2bSk6\nRSJXUufQu6SU9vERJJTT8JetsyZPhPj1D8yT8+mwl2pCYtcnGoCjrDWAoSN5qvRytzO7KuUrNLhE\nSk1uLqVVUV+tE++IvDtF3Y/eEwHYLpeG3WnhKGHqw0hRWCpDZG9M3z3oTxqdW1ZdkWGIpZVwiBHT\nZNqsUEDblddnVGK4fLfSLskAfrZ4tpXap/geoUoQWxy5iroVlQvaaH9h5TwWASBPzSGluzYApoDG\n4COFrZbuW36WqPYrD/5YMDlMAzmXi9XdO2fO/5Yc5EXqi+2pWoMJ0+qJXRyvaTXha6DU/aoUjcom\ngJrsie0e/FSJmCL8Q2eU7ulUHYQ5ALLi892K0im39nnt7vRLlBE1eC76VovPZxJTNAlMGp37zE1b\nipxUfdWbgoatqNzSb4rX24ntKKqbqsKwY1FuidY0AMfResLeLqehzlgAKlLfc2xY4mEP2kPJziG0\nn6XzC6T3iuqKPcvfoV1bUboieCzStmVFq2qva9l+qty0DkplIS4VTt7CTMS0emIwqzT2UzlM1VFi\nipZ2Yb0qDBUBrMbllmQ/qTVORVPLUb1CHVeK6rQtohEAhytiK1sAwilVn78gHIZaTp3QOKoGVEr2\nGR0/VTrX56ym3He055MHrKIPg4mM323ezR9Svv8BSbRiAFBV9dd//dd/7dd+7dy5c7dz4OnTp8UX\n3z7x/cADD4iH7eWXX/4+Hv4d6Sb2blh4uPC6yCQs0vafDt/JI93aMeiQuvXk5mdlOU4UThNKkIps\nnqkPEeQJo95ETxRO1JHiVFIAYHQ005OlRKSbDcXHhC+0pKE22q+3HlE3hUGRY66IXMei3FpKahaN\nFmn7+XD/rNJ9lDd9Iu9JPdGdI6ososNuTu7WJW8fH82nwwB0AKNGBqrhwDMrSk+LY5/IniT/anzJ\nJ/T/0WYBVHjQIfrf8vluYj9urgB4bKrxkjt36/kkauAPK1AjIUZYi6cIjWuF7d2wkGg0zQWiRNT3\nynRoyWOdKEdhuGFRF8k3a0CGlh5q6q0KeYvaAE47BwBcDg5QV9c9smROcSsQNQYxSbc7khwjDWTP\n0czZ8NKen9CLvlLvDnNDsSOUvj7A8nd1S//lvCUHuYrEItFv5k4vWeMuVxdpu8lN0fczpg1upmcD\nmzDqGy5niscU6Jg0OqLMcz6eAmAovueWuKunejycBHX1tNSfsZoA2koh0pUfL73aTmwAphQtyi0x\nvAEspTWxh3JZduakXpNbdeJChsjQWog9yId590Q6JbIUi3LLgXJE2q0gEB11AMSe6/vZUEdymVQB\ndKA7UH6Sbxg8OYm6TSIbcSMtXUzq3cQWu8S2E/vCaCaJb5ogMKA1mCBqQCIVgN+t+TLjlCUAUQNR\nalLN5MRo4Zn4QQBCZCEkSDnZ81S1m9jtqAADgLMg9QzOniXf2un1VW9KaMTp0BI7O0dUFo7mtuIP\nwtx6Zw4A5HQ0GeV2Gb3n+ig2hFllVI3Hbv+O/hDyg1LZvfvd7/693/u9vXv33ubr4zi+lYtYXFz8\nNq986KGHPvOZzwBYWvqWp9P3ePjtMKl2HzdXGklZWAs/H+4/mN8ImNrPWX2vbDXt0ORi7c9Nn04M\nc7JH3jBlOJS/shaXr7QWoEZpqc+kJKf4+/WWqPl/1Pjq32L+f7a+LPLdt1zovVR1oNTgjcM/xfe4\nXP1t+s17k+6qtOlDfpZPV2UHgLAssuWokZRr3BEpEVFzFme+jPLnMfeUtO4T+dEk6fnlEg9fo+U9\nxD3KWqU0vEbzQlghNqgWm/6B0Rurh7Rd+eWmrekMgCanAFxHoTIvTA0BOy9sjRS0J7DPavra4B69\n5aUq9BYAsxJ5qfqOyjULMYCD6WCTWJXxwIMsdnEWsisApwcHxrTBblgwrV7o7lH2b3idCerqiXJz\ni08ATiVNS30e6Vpfd4zUKK8TKeGjcTCFeIZRHlr0Tgti32KD3CaxyPHaJLJJJO7aUXNTDMWRbvrD\nipnviHJ9SXEDpvYTa8uvTBod4YctBCawV68GtQm1J3YtETsrVnjgmfJx1vYhP6POiCzWUlKrUafF\n7Dn55qYnYveTw+jaUvw37v3C3U7oToXVr6hNalLkqeoRtTnFXeG67UE+g5pB2X42PCuPC8lriYd7\nUxcUojHc4YrD1WdGi05siKw7gP92bVrqKlo5tjwiehhCR/O6sllO5Df2iwGAauBN9AzFzxm7AMSK\nSljtXWktGPkOAJGftKXoEXVz1hwC8Ij8aXYQgMNUUSsVUlKhDVGrQ79bYwDesA76ltFDqNJC11Z8\np2Cw2ACQBDbe2NT8Lcz3PyC9733ve9/73rd///7v6qhXX3311tffvts8n8+LL6Io8n3fMIzv/fDb\noUYdsTDfjkqidH9rUBIaH7z3lVuyt9W4fNNiQOoDaHITwBrKMFxT8VUp6f+/7L1rlFvXeab57nP2\n2ecKoIBCFVCsC6uI4k00RYm0LFHSspcjWVLijqV0u50epT0ZR+41k0w6Kyt2Lj+SjFcms9rp5Eec\nTGeWVzpxJ+5o+RZHju1IsiRr7CXaohSSIimKtypWsS4kgEIBBeBccK57fnzFssYXWbZkNaWV/QsS\ncECQ2Ad77+973+ftj0ALLCWaUdueFMeV8mF59c+TmyqqexdbbqldgOL0MC8LJOdb7E1aRu8Enwwz\nsdEf4YabZryg97sbVSkiOriQVfZg6WzZcAGQGo0+VTNxft+/h3hFlOI6IgMAV2EPoK4o9lFUIDGj\ntV+eShmZWVJNSmY31aC0Nd/Vw4FaLPudluVddeyhoL+3RYUdWhrfp8wD8MHLGJChiuhEpLAImLrG\nTKKPH4knarztZiXy3tMPHAH/V0T3t6wjfp4Ttos0C6tR8WZrmZQXGAcAKoPUczb9IwMI+MXvY8z5\nyYy35CTXkFky8ZhGGd4AXCnoNONLMSq6G0MJ6XHCTJzrVEneRt0gm0UutBP+JPGrmsHwuOi4mRjl\nbiNzGnAAHFCb/yG5d1prH2DNGdkDUNF8APMs2srfWjHKzwJ/M3BIE7QIMN8EAJ6S5I+gc93ihqnE\n30hmv5QcIPsO+WpPo+pLUYZ7cVAxlXiPUQcDMlA9sKp3SGhjakHaLZFk1M+nFmXEFKRocN/Vk0QB\n4Lc5gKFtQVaK/fHO7vzSnLu58yDpTdXpUJV7vNoh98Uhc4maoN9OJutaG8BCVCL9LSnLw0xQC8pw\norLq3qMtWEMJgAXkTyaVF/1Jkv8QLWUrIYmkEwAsFh0Wy/9C+/7Rxo9h8QHQ6Xwne+rGG298hVda\nlrX1+PTp0ySpeo2Xv5rxi/LcBaVwK2vOO/mnMQ6Apsuzbm13fonEoI3UaWaOpURnouogFTBxQFmr\nse7Dg/2DVGy36wCIO9ndqB4Jc6qSCDU+wScpRWlW2fAln5LunXH9GB9ZZraD+EF+9rKW224dOYOS\nw+LPejd202oycFTPiP1i3meJJfxSRHs3anHRW5FEhz78YbE8yl3a6uJaHN/9xjkSyD6S7GylzlIw\nErQr4KnoazxmA+s78stEk9H+pqkFh52FF/3J2WtMl8Psqs82p9CUdMkmCQAS32RjDmJXamCYR4H6\nvTOyR6WVf8WOXJH2Om+QSgrAflEHcCsaNCWJyTSn5Ef4xSez7YfFMoGRjgVT1CoD8K7k6vN8BBL/\nmNVqSueyknuVX+VrH2/JSV7NfAvJwawFIGDql7MZSvLdSOxumNtu13UlItxGVe9U9c4gFStRaesw\n9FR/Lx36fSluLsyd88eJGtdOHJotR+IJEuYciSdIKe5BIwdPibt7hl8gAdseo/7Y1dtSr6AOtC2p\np9TU3qQLgNndYb0bZqIZFabMtduMOoCK4u7Hus840Uae6RwAgFS9LKoFvU/0kI3+yIZfYpFAoqbB\nUL6ryETATL2C5D5LCjIc9qLRDVMLckqyBdxTlWSYe0GmzbnbyMd6aVDxB/lI0/qJRSaqpWCEpHSP\nRvtJTTch2qQkPCyufluOOSya0dpnoipBv8ihcShZG8R8D5oAFlE6xpvIn15iDqGV3muddVhcVX1X\nageM5lw29Gh3P4DVqGjh1cqD34zjeoGrvlyh9Mobup07d249DoLgdbn81YxNAI+a98Fp9p9OqvTU\nUjBCSESLRe/RL31psIcgV4929z8KkNevxN0T3VlyNlj25i/LFjNxJSr5XDgi2ovOEnNeUovrTJ+U\n3iQ8Uya+wgEQIPWQufSuqbn5pOQoEW1INeDma9U/Q43oiLNd9gG8E1edRG5LAAAgAElEQVRNmYxl\n/pj0dOqsMiwmQwaSohIeT0dWFHsBebLTdridG11YDwtqPt5trQIghsKlQWVG70xrbTcT92gL9xQW\nPGgUaj6W+gOmBoyPZd6CkidtxQWl0IKxD+2jslJl/sl0tKZ0HBbfmy0Tsmhf0hmT3ljmX1LzZ5QS\nWbIALDHnv4YHtrpf78bqbNbbkfbuZcuPK5Mz4kwZg7N204PmMe1IPPFwtm/VLRI3r6K7bXm9g5Cv\n80muQfrgFkt8cADU/KfVSEbG5aC2qfZW025rXEkU0uUDaKZTUkRDVntTLz5wmBgU9P56WCCfzblB\nNci0m61lAK4UB3iDkA0utDu0FVuLT2YjDotsLfKlcDNxcORFOnOsBGVZioui24wKB63VGa19LJgC\nQH4gikSykGwjB3oWTjlPlrLwBXvYkomF5CgqrhSksmuoKfNNESgAEg3sbZeL3NtI7CzMdfOaZfR4\nqgGIUi3H/a0U1/mk9AC/WMYADkyZmjIxnPRUvrTGzLq0TkdVAD9dOE1tLT8TpN87N6geMpfq0rJZ\nPMs25rKhA8raL2rnIFFMwg7Tj6jVs1pxr+x0Mr2YhfuGX5zRXjxbv6mkhLeheUVYAHzJSaD0RLgD\n16i1e4z6+Vf5db45x/WyIMVxvPVYVdVXeKVhfB9AzGu8/NWMJ766+G9/JiQ6qinTr2kT+0V9Pind\n5swDeHz9JgC780u0Gu00Gs92d6UZN7WAawE5Fe4dfgHAk523Bb2yandJm0Tbq2G9S1U+Ms/+l8Ft\nlJs3OrpQ1LxNvJssODL+AOYCqLfyxhmUbs+tNqRFPLczUZWiHMiQOCzD80qBYsU7in6JbcJUOky/\nIW0TJ9tAOpv1JuAFjK/zxuXcSl1ajhM/FdYuDSrd1jh4OlpaIqsvmU8fyXaTCeOk1q4pHShwoVWZ\nfxdWASwxx1f4u5KrpLv9vfjYJTW/Xen74E9m29/XvIdrwf2l40/zcQA11gUwI3s++JfljMMiNxOW\nEvmpqKgu5UvNKfk5JT+ReZPSO5SsAagpvaf5toa0/EyMcpd+oQw1uviVF69+5diP982+YeM6n+Qr\nF9a3f+X/vfPeacIcQIOridWoOGqu9zVLKAnRP3PcX9c21T3f7O0GEMQmC2xXM28rXABwJLsBgBub\njhaQ65M2XjaLarwDgA76pG2jNCCyJX0rG5/W2gAe4Bd9nc/LgmOdBTCDXtkaPI3xKvMbwnGUiKTe\ndDiuKC6dJFwqNirWfrm+gLzDYjcTDossJRpV3H2VuifFlnOoG+a6rfF8ncsdfaSqUJIpc43cgQAo\nf7bGug6PAbRgWEi2Sb/D9AusMCm9MgYutAfFGQCnMdwAarz9mLuX6P6Vwiqtgt+4FvI0q29Q0vTW\nsK9J7wwkZ9bf1lH0MXiH0ys5zW3FRR3x57WdACrM/23tuXWmP6zstecvdr/67I/xzb6JxvWyIP14\n4+W36E/68lN7bs5zjaymWxX2Gm8fDac6sW1qAYCtjMgX/UnaJ1Ik85DVbgbDj7lVrgVpxqWaDuvd\nzQPNIM+1oNme+mIwbGpB0K4g1zO1AKmqFtqDUzsXCtl5821PXHPd/veu0t2xGY5eceovj6K4GFeK\nmrcYlywWfU6bdWR0KxrLzN7SSriZeJCf/Qdt5t3JFUOmVxSbzEmUJGQhOShbAOrCntbai3pnKRhp\ndMebwTCVFoWS7DAaE6IN0uMq4kF+9igqJ9NRqJjLhshE9d/4bkrSfESbprddY+bt6urd1ctbQQAn\n/MmtztPdyuUPYO44K89J8R/VF6DihrS9k9cvJtWX1JIpkxfU4SnpBky9qtgDqFPS9ZhGNdKn+nvJ\ntOhGRVab5fNzr2U+XJ/jDZvkJy762u5dnpil44UPfphdnc1tzGVDz3i1MBMsEkFURr4F4EV/klyc\nQkmgBULv7zAaRzo3ACDQYqKmG7FZ1TujorvHqD/ZeVuJuwsoAViNinfa82eiqsU6RNd9UZskcTmA\nJDYfwy1DVpuiWCjmDoClRKezKi0VrtTm5FCVee9T5i0kvuREUH0k3D3KXZcJh0XvzK66TAOwJUyl\n1WifqN86vPSYuxfmOkbRC4bhmxsY6YY5VUmoEFdRXFeKR6Ld+0V9Afmv+ntL3D3nj09RunFUoHbs\nU2kNADEVXSnGRYec7wCOr72NhULq0aKaci2gcM6K6j7j1W62lu9WLlNR+ua0ASCEZmRJUYZdmDm4\nAOrMGZbhsAwDpn5K3tCMHV+KMotXoL+WyXD9jzf3gvTqIf+v/XJ159RpRI3MORpP4dosbGROWXXJ\nH0cMxF1Z94JSeDLbfkKJGt1xbrgAumGOopcJQAITphI3o4JQEq4FN+YWCXh8vjflLBrRIMe2+fkY\nsp/vzXpIVCVRusv5oWo/saRbzgqXcoklvermOwMgFH9R86a1NokAyQN4VO/sE3XarFHY3RmUTsaV\nBrdm0PMZ//P0pgNK495s+bxSeHiwn+4lwitsltHtTkAkFTXuhrk298Bdwi5UVPfhZO9KVDpkLrlS\nc1jUyByKyqUyOgmo7tEWRmRgIXlKTjYSp6K6FcWlmImTSeUObcWSyXGlvF32t7P+p7IbDqjNgKlX\nM3uO533w02x4Pi61UufD+gnKG6Qa4GPuXlqMCbrsvPew8tggeCsuSG/YJB/7V4emf3aHJQOf8SfT\n7cTFmGUbDotIPNkue++y5k5HVSoLd2I76JV9EbFIBIl6XB8Zyq1t+CVKavjpwmmaEhXd3Y/128ur\n87JAkutT/elHk/0AwuYYobXJJJDaA5aqEBFT4359kg+3ANABi0p/W2QdF9phdnWNmZAgI52bCU9u\n5pUQ/J7yMurSamSOo0QOizqx3U+sOXdbMnAsu+N7RRYK5HrSClgkZGSkYuAPnLlUs67xex5z9xY1\nz1A3VQnne1NkELycVBatgNAS5wGZahRjRu9JoRUAoKZqz3aqbTJOkGfr3KC6qJZu1ZdqrEuk44Cp\npSz872oVwMFsZAfrAdiWeUSauFu5bInkDErYNXzPb+z/4/9t9bXMh+t8XC8L0stvmyzLtvBc3zuS\n5PvksL3Gy1/NeOyJ+11XGEYSHlinAK5Rc72fWHus1dWoSO4/qGnFqZtKTN51Wo3SjKtKcr43pSoJ\ngGG922xPAbDaItCk1DB3aSTVkGhSAO6sZ+ZbEthmfif4xGLR/l31o+HUJkK42vf6I1wLwkzcXJij\nPnBFcUl49j4xf0uy1uH6XD5vIVlizi/yc0fU6na9PyzDdegVzf8v/dvGRWdGa1dU12Hxx5LbrSya\nc7dtIrwA+oHIjNhPN43haXMIufhyUGs3RL8SSRGdUGOCIW0dU8hBRWGXrdSpqO6L/mQl5xJt7xm3\nth4WyGmBwB4tLa2HhRWzFGQa9YEGqXiXNUdN9SuK9ZScJGRZRXVrvL2AfF3aT/X2bvglpCoLRW5d\nbVYiKaJ0faylYXjtvP3jfbVv1LjOJ/lZf/xbV9+LVN1TvmCxqJ04F7PKF4Phgt4f4t7yyh4AX/D3\nJprcMm5LNWW+iVxPvZaOSPN/I7Ef7e4nZi5JnJPYZL5plhoEbSur7h3aijukOSy2EXvQtlf7BFY4\nE1WXgpHRiXozKtC8omlD778QlyhE1QcfkQGlhr8bq2eVIoA70voRtQoAEl9wb3y/c2o/1quqT3/E\n+51TJ5PKcXdmuLDabM6oicJjJMkQYUEQqDBNryDVDeP4wCGsPv2hW1zj7XY9MLWtsgRN+IZbBUD1\nTBYKZ9HISir3WeLqqiH6E9HmjBUDXEtmub903JXCY9o8Ct/GWBWeq2hV+K7UziuFf2JTNdZ9JNxt\nKVErdgBstaifkjXgsR/jy32zjOtlQXp51TsMw1fo2Z47d+57r3qNl7+aod12wc54lGqITRYJKUC1\nLKJdbQGpAFCk0D5Rd1hEG3kqPpAjvZk4KKGoeeVt7nF3Jk21nu2onjE5cQ4AdYDcTPxH9QVK/APg\ng/vg+/X1J4fbJCsfdeYJbXdAbX5J7gFAFK8bs/Yn2b6jvPIzcokUAR2mD5hKv/LrTJ/IPF/h5JZ4\nqr93wy/RynqnPU9uEgCt1AFglSKKVCcnoO6zKAfR13rbNlOciT43525ztIAqk0FURqI2ASJyLuVH\nfK/49/2Rrd2o1KNut4RcD6ZHRuDFzjTUtAFQptlj7t6j2hQd1KiGQwuY0hmyu4zFTCaKnU+9kUBJ\nlFRDriFYrCeuLniqhNe7if06n+Q294VT7ydWPSySn6GfWNvt+mWv6sYmG26lXsHLR0yNby7MWcWI\nwhG27EGkiqYezEZiH3QWakNt0hSMcveEP3lf9ayDuMJ8wlntlZ074zqADtOpazWshiMscPTofuPc\nE+GOEncJ+UOibbqhaqJzMql80j0cZfygs/D7ylFKsq+x3hXFLsrw38cXFpT8C+rwbzrP+IwvyPy3\nw0lLiR7kZy+z3B3ayh3FlblsqDHVoDbkCX9yPSz0Jk3mm8RbUWNEppBWMCq6ZHuqOHXqCq8EZVoa\nw0wIJSFFEm2PwNN0fSznM28isrusNxGKfpYA4CmFKiGwYXrT+WUAT/X3Ang04yTPo+RyAM2okON+\nw60iVe+sHCdNbD0sDrgIMg0aBqm43mf5axvXy4L0chjlpUuX9u3b94Ne6Xne1uP9+/e/Lpe/mkFm\nOhYJBlAWQ+5sGWaq7F6q6h3C/VosOtWfDjNxV+5sI3XOpE4/sYSSHCydPd7e+0x/hHK+fa/YTNXz\n1yDKLBSGz8hptFWe/iYb28faWxDJdyVXizK8UW1fYVaJnwsY38Y9SCDBv1cv7NKXpBYDSKzgXd2z\nPb90ThkGcIyPbMu8K4r95+lNJM99QD//8GD/tNZ+1q1t+CW6PQw1esarNdxq07h2PwDUvh7i3gZK\nAGYPPA/gXH6cxWaaccJE0jIT99R8DASqV00yniHXI62tqcSHCqfPRNV6WBwtLgaZth4W0rCkdIbY\ncGvWubIUjKiewWOk1Rb1vQ+ZSwCmtXZFceeTEm1F0c9nRpz6IrGycMgHYK+Z3kjgFwf5iyUAqhGH\nw4m++BPk1r8u4/qf5OthIYnNQI3Rzzcsk0Wi3dgmLBmNboya66EWANjoj5At7ACffyqsWSzqZHaJ\nu3cXX3zWra1GxaLmVfXOxUHlIir0k024B9KkUVVtIS65YrmlGZToClIuYLCAvIN4Lhsa5S71h7Zl\n/hzPTzj/fDBZA6AjrjNnYHEDyVXFNmUyADeQEJv4imLPs/xZVtwrO89j9Av9G+m8DuDPwlsIqn1H\n8aVW6tTD4m3O/LlBdafRMJV4BeU0Fx8uvvSiPwlAjc1Z5wppZat651yn1uiO56+YALqVSLW7AEiU\nBOC+sWdP+JN32vNV5tWlfSyYao4WpFeMRj2yBkamarXFwJJGu3i5tKmzpeMj9Z6FGl/2qiTBDdIy\nt7upyo8s3SYCJRwaAIjXpvx82uQpTG/61X+db8JxvSxIL79tms3mK9xsvd7mQUQIseW3eI2Xv5pB\nOeKuZlJoHotEb1eX+ab17K6zruA8Cwfq8ERP3TDlUPBEMpPmUwChJdMYJ3JVZnoSQKoGvTJLVNLL\nIlVlqjLAq7rEHmWRWFSLQUE74DSo6UKkopZmTEn3vfHCDakGQEect9o9v5S32heCqVPBjsFAHZJh\nsfsdWkGH6aZMOkzflnn/D77+kl3alnmfkbMf1k8sIO9ayy29A2DO3SbUeMpcGy+dJZVBU3QsJXqm\ncVDkkjATXAsmzNZqVDSVmPSBjhZQflpkaKngYSFJuyURyM0eQGC7SvK2wjKAM1F1WmtbLNov6kfD\nqaLmTRdfPDeorgRl+nP10auU+0k2RtJBdWLbVOISd29z5mtK5ynNs1hkbYscJXp8/SbRHEo0mb9i\nppqZWHJgSSADkFqvNo7of9S4zie5l1gAaMNklRphcyzNe6Gl8ZiJ06MBL4euzrf56pITjJlPFGqP\n84yyvdOMkx7htsKFVuqQVq0Du59YRXPNYpGlRCtR6T36pbq05pPSi/7kbc58Xdp12AtRidYwi0Wj\n3K0pHcI0bJf9icwzkI5lnimTK4p9XB0Zy3w6S+1BcxElQgTpiHOaO1Nuyfq2rrRfUkslhGOZDw7X\nOQvgaDg1qrg1vhnuMKts1LlVM0570FwhKqrrcwETG4ndSh06l1NuJH3yVurcWT7pKNFjuI0brgoQ\nopsyogC4maDVyGHxLNvwDPHz9qkjzsRKVCKktyj1ZAll7jeD4e12nWJwKV55qzfmZmLFLlFl5e8b\nd7BIKIkSmRmVpkNLXvvFeE0Nxet/XC8LkqZpo6OjzWYTwOLi4iu88vTp0/Tg5Tfka7z81QwiyTta\nECxPqoDlM6+gZTzD6MAZHShtzR6LZaAaQ8Em/bppqMUBjwFAGWjMTtLAhumZWhD0yqpnZEZMTxHv\nbiOxh6w2LOwwGqPcfSqs3aovHdAWyKPzvBwFw99oe09j+GfkEoDleO8DWKwHU6ZMNxQ9YPyKYgdM\nfR6jT4W1MnPv4Csn01HqLX3BvZGaRo3EcblWZf4d2orLtafC2v2l41XmVZg/LwvE+aYO0J7yhaVg\nhNwPQaZRfXJ7eT7ItGZ7Ksq3hJLcmFu8NKi4sakW2qFlUtltiHtk/q3xNkEzSR0LHRQkA4AEwVs3\nPEFomokzo7XLqnurvtTInLuVy2vMPJmOUl3o5KW3AyhUl7ujQD8f5VJloGVGTAZ+KSJkP7Cncp2M\n632Sx1rqFXwR2WumesXUYubC3qR55uJwzTKGggTAnn4YgzYfLFWT2NzisK1EJUON7nPOno6qO40G\nxaYAqChujbe39AU7jMYBtelKzWHxAX3N0zVSuAA4mVROotJKnbv0+X9EraZ0blGapSwEsKLYbUU3\nZRow9SVZWmb2pPTWmb4/bc9jZmndmeeFW9HYsjrU0t425neYvl9fJ3lnTe02pPWlwZ6y6jaUTRM3\nWYgMNRoCKBqmqHnk6t1pNADsE3VKP5ouLtIr61pAanVKh6H0L6J8zctCTenUpVVRXWLYEx5iiHsb\niV3Q+yXuUse3kTkUxXKrvvSl3gHiR/he8erlm7Ddh+llSV5JFDbc6uc4AhtqyrXA+Rd00Bs2brnl\nlq9+9asAjh079qEPfegHvWwLoPJdtYjXePkPHaOiS3WqtNpKBo7um8mLBceJMDoAYL3j7FbWlu8V\nh3Jr3VLVzLfILaIC78yff1arkb99YtsCAPJeNKQ1nxVJO0RmI4Ia1PTOO+XV86xA+IMKfAALyO/H\nOmlyJuFdVax5Nf9n0aHD6nKF+f9H872beL3EPr+x9xn1IAsFACVRrBVxPlHPjAfq+NUj8Q0kRhik\n4rJXretFXYlIoddKHeoJDXGPUC6X2xVqCOVXdADrg22MZ06iALY0khM7c6PmeqTyHPf7apzj/n3O\nWVeKX7KP3ZSuB5KvK/oEvGIaBozfmy1fVWwYZzpMvyO5WmDeOYxeVSwoCARfZ3qLGfOy4PD2N/xZ\nQ43+MKyRl4USd8rb5gGYSqwrUV/brO8DoJ88m0VLuZXWj/SN/o8Y1/MkH7I6BdpwjA+Pmuvu3Kzh\nM9nXokoUmZmcbKpGL0q1LONhZEBNC7k1mjl0JBrl7u3q6rws3IrGraIBoKUZt6XNAdQ2dAAtGPuV\n9UnpLQvbksmwDA/Fax2mX1WstqLP8N4aM09i1M3EXfp8XdpuJqDg4+FhAARKGKSixF1ijqxEpS3M\nPIkmAHze6JHQAMCd9jyRJkixfdBZaKXOPlHHtVwuAG5WOu7OCCXZDOXr52PSDQEu8MzIuGV3psw1\n6mZRGuc92gIMzMvCv8kukVm+I/WA8QCqL/lu2QVgysRACgVjwltQ8kUezqt5U6brTLeQmDL9nJxd\njEvn0iqAz28cAmBqQZRq3HDjGzo81RwtgN6n+Q8A10LFKqr7qiC+b9pxHS1IP/VTP0U329NPP+26\n7veldS0vL584cYIe33vvva/j5T90HDKXnurvDWITgL5hpBryQ0GWqMkVi2/zm82ZQnkVwKjoXo7N\nbpgjWzudMBZ7k48NbqGQlQPKGvlYP+kfJtMS1Sv2i3pDWu/GKsF4LCSHkrWiGgKYU/LDMjRl8oIK\nH9yXvKUYFpJvqmMOiw+L5fms+AX/RlVJOrHdDIZlqkFElBnoFaTdZWElisxMBAo/NZkz0w1rqDHs\nWUZvu10vcZfwWW4mPqyfePjaqYXskFPlNQAWi2Ym2wCIFXQyG5lVNurScqXwpHAzUePt+aTkZ4L2\nfQ1pvaBid9a1kBxOr4TQdMQGi6qpa44tJvZAiXniBLvdpT1LUxqPTicT57VJACQLXuxNVpw63Y07\njAaA9+iXXLGpyHok3O1r3iD9DiJskIpD5lKRBdf/gnQ9T/J9oj6nRitB+ebCnC9Fo+qySCCfOosG\nL8VhIfAHeRLRNbUCADc2u1kOgKnElhK5mZhXCu/G6rbML2ZhR9EtJXlWHS3LgYWEvKXDMtyWeUUW\nnlJKFktIzhAwbsq0zAa70u52pX9G2US3rUQlcjsFmTbrXKmHxQ2/hPwyHcqTgcMNlzK30m6J8RSJ\n6gOkC2Wp+siVWq66PMQ9X4o91uo92sJJdcRh0YPGaQAns5FG6qxEJYqIfE/h0ogM1kbNurQo9ZFM\nC3doKwDoMHcyHa2orgftYNYqs8GKYgeSAzivFH46Xjaw2c0CsJPX40QA6Eq7ml7pwhyS4TE+4oNf\nZjkX2kJUIg36Hmu1GRXoM1B3zWER3VbNxLmETWYm/S1GFXdW2fiXBekNGvfee+8f/uEfdjqdJEn+\n9E//9Hd/93e/9zV//Md/TA9mZmbe/va3v46X/9BBR3tqQmI8kIA7buYvltREYT7L+zwIJs8NjVh2\nhyIyT/Wng9hcSTUAQ1Z7h9G4XV1tSKssB8eCKaojV/XOXfo8xXYR6viptEY92MNieUk4u7MugInM\nA9BW9Cnpbsv8scw7xkdaMCrM/1Y6fkBt3q6u1pzOt8WkLwXloRE+9f+u3rpNjZaCkahdydd5Ysnk\nxmUAKrDnmsXvsle9o/jS7erqlOL64B/j3woYP66V67pFOnIKCLgFzSXmPBzuG+WuzaK9srMXnRYz\nLJa0VMOSybv5aikLD6ZrL6G0I+1VWPccRjuK/lVtZlvmD6DOZL2rqv3OlhtcdSgIA8BAikZc+IY2\nNiVdSgqwWVRx6v3ESjMeZZwMhif4AfJjZTxTC20SJi0OplmqrttdocZf9N5RDZcMnP6RvtM3flzP\nk/xMVJWpmDBbROmezi8banSutcudBngqY5NT7xCYMteo5fOsWwszYSoxKe72YzPH/Xk+cgYlAA7i\n27LmnJIHcBSV+bQEoKK4s2xjDabPOUW7mjIBcFotAXBYvF32HSVuCCfINPq9BjDgIjI4ufccLdiR\nW7SU6FnscrSgq+ZUJUm7JeabhfLq26xlqgOTRobWFQ/aBzAHCUgsM9thkcPbfiYqqnssmjrJR+9W\nLpNle5PKCtyjLVgyWWOmC20+Ld6urloyeSBaDJh6jI/U0h4pKahCOKeMDMtwR9q7pOaRYIPpHaaP\nZX5H0a8oVgsG0Yaq8GfQI/TqKrAaFYWSPNvdlQycS7k1ABR/jpeJJjb8ElEwmonzpWug1bfquI4W\nJE3THnrooT/5kz8B8OlPf3p8fPy7ihJ/9Ed/9Pjjj9PjX//1X399L/+h48iVW3INofa1TstikVQs\nFMpelii9DRNAfihAIWJi4A/yMHrtxLkxt7jVrT3nj7cT52vKzEpUqptLE6Jd4u5qVLRY9FV/L4A9\nRv2X7GMNabm87UpxJqo6LG5Ia54VCLHTkBadD86qxSPZREW6AKrw7lYuWzJ5ONnrKJuIFDcTxFd2\nM1Hibjtxpsy1u3Y8Oz9dBED5yhRn2Ug3E49qrDsvC2CYl4WHs9IB3tgn22CwEZ/MRhqJc4A3nsco\nyWc32cMC9A4V1XUQnY6q+0X9F3DxCB8zZfKSWnwJxXdni2qxeaW1s4CADknI8DXsmmG9nbzOtEjG\nQrM6Rq/47+I5AAtKflLxlpntWYLyOg+ozfqQdTScGqSCYg4WO9MA/EGe+aYeKImGNClFhTaAQar/\nmFSoN3Bcz5N8kGl1r4rAXmvvVdoa41k4nNgxSzRpdPmgoCWa3Ry9plFWNynUVb1zq75E5+P/Gt68\nT9TBQJF6rhQOoj/Ibm3Fzl36/K1o3HoNp3syHX2fMu+DH2WVquLfkdZfUIcb0ppB72Q6SqruUdEt\nat646JAPoRkVyF3gpyrUdNSZ/2ZvdxKbLqAqybDe3Tl1YQu3P621K7oLwJXiw/x0Lel9Rp39lLwB\nAPHLD4vlk0llRms7LDpkLjVS57QyfG5QNZXYUKPFuFRWXU/ZAMNcNuSwyGbRvCxUmX+MjxRl6IMf\nVUeJFLw/bY9l/gBq8dri+pJaCpgKYCzzTZmYMn1XenXAVACn1dJRVA4oawso7TQaK1GJYtGRA67R\nIwnnCKBsuStR6WDpbDtxDvDGt6PJf5F9v6HjoYce+trXvnbq1CkAH//4x7/+9a+///3vHxoaqtfr\nn/3sZ8+c2cxfe+9733vfffe97pf/0NGvRDlAm11TBpqxaHaWbJHPnB09AGhrfNUEwGPmVXE5Ni8D\nAMJMvM1aHhXdZlQ4ZC45RgRgJfqOG5RQVwC+lY7XlA5RU8uqS2EwvhSfD0Zy3KdYGpKrDnFvBaWN\nxKZ+qRubZGKYEO1v9nb/26FjW0kzniK2Iv6IzTWluM+LUdqEHuWVv127U+kMpXmPSjFBpu00GvNZ\nsc7sY/7URmJvpnlCqzL/QXHGQgKOFjP+2jtEpqVG6jSAGa3dyJwPuO+nfg/VAAOVY2N2XdMBzGa9\nsczbYLqB1JQpgChwGrJQ6YmutAfgAVPJl77GTPqpWlPMk+loM3EsFpWF+zHrG6ZMj9tlUmoBONK5\n4ebCHK36ANZY9t1f2HU5rttJPohNBDYJlNNqx647PGbcZ3ANaSndPpEAACAASURBVMTJvJ0kCt8N\nFVjWynaXhZaMzKzLq6iAClAAyqpLjDsqVlOfb5CKb0eTJ5UKNW9I//2PvNZMHIIC/7fs0LjoEMck\nzASAHPc3EnujM81CYfVUvxSZ+RblQA473Zut5Yri/nThdHXIq0vbYdE3/NktkCOBWV1FkO3vQ913\n3FyY26/WK4pbZX5d2cyRcZSImkykbXOl+Hn71HbZbzGjIa2TSeXlOUx0n37eH6eg2y1VDmgVkQIJ\nZrS2o0bzSanG27eiMSxDOh6ZMn2ej1D36Ck5uRCXvpHMbiQ2gbg24wEHzp7yhRm1fUBb22INfysd\n/3n71Fw2RLKgin7e07XP/cgz7s00rq8FSVGUT37ykx/60IfI2ffcc899b+TlnXfe+Z/+03/6SVz+\nykP0tbTa6k9z8qhjdECZM4Mlxx5zJaDwNNEQ5SIWCTpBmPkWhWA2o8Iea9VhEaVC/Lx96pPdw4M0\nvtVamk9KFdX1pKCCXit1Wik6sb0eFi5nVaUzxGM0zexcNSZJRRCbG/0RlqpSRIRhZmJwub4LwPqi\nwRL1H4rb+sOp1CMWCrPUeFZJqPNcVl1wPBzupxMbUZkPjrw4U25TQ2g/1teYuVd2/iw6RH/lbpi7\nqFTe75xyodmIfcYfiXce4A1XarQ8kBKByM11gFpivhTI4GciEOoScwgYc1nNQcV22d+ftl9Siw+z\n2SnulrLwGBu5IW0PwK8qFiGXKorrQnOhzcelGm/XROcL7o0Afj2bpPcn0vNj7l5ajcJMnO8N/+vy\nc1fNq1d/jO/1DR/X7SRnoRB9LdEkgPyyg0DttuxC2QPgbZiGkbiuMLoKgO52v18cILAJ8k27oiQ2\n7yyfBLAYl3Lc31qKABCEfj+vu1KQVTzK+PFBnkUi1xAAQks2hj1+TUIm18tdnoGnUFNpBT4XUk39\nQT7sjdldFmDkW5j1CnILN074/FHRJfXau6y5b/izvhodd0dGRfdfl5/zpGhkDunfbkXjspKby4bc\nTBADyWIRhQTWpeVCc6V2Kxr3KsuBygGc1wonsxESHPlSTOc3RTQAqswDUJf2o+5+AOcwvqW1mUfp\nSOeG3fmlu/R5MMygd5nl6rDOhFXKZJKRcS7jdNYvlFe7GT/XqZ1D7VGjR6kW+0S9mTifHVRL3PW4\n+GZv9zvz5+9WLv+oX+uba1xfCxKAUqn0uc997pOf/OTf/u3f9vv9lz81PDz80EMPPfTQQz+5y19h\n8JhFXkGqab4hEKjhcKIbMeOZXRwgUN39zVFz3QJIvUb7qXbi+JnYY9RJn/OYu5dK8IQn2EhHyAZ7\nMasUNa+ZOJYSdWKbON9qob3drsOul7h7qj+92JkuXLa8eo5SLJ2ylw1slou9gnQuWwBkooBnSFQA\nzqLhuwXOs3S70h3dQGDfPHGEKhUEQRBKMiq6e4ovnhtULSWiIrsPvl32z7LiA/r5eVmAgGOdpf7W\nu7H6mXT3s24NQEt3AJxmVYqgnk+LACqKeyyYIplsRXWpMfs0xhupY7OIjmgz6AH4v9gtFcWtwv+y\nnPEgbldWv8nGbkHzLCsezFpU5zkaTZVVlzKqAVA030JcAkAKqyrzx0XHUqL/PfdsQ1oUd70kXwmA\nfV2N63OSixAdMyNaAQCZKJxn7brDIikFM4xEuanTA8h7BMAZqkcZ32E0VqPikOkFunZxUCGgTpiJ\neijIHL2R2HqmAfhSeEBXomZ7SqqpvmGoGrLiRrKztZlY4ZvWSkEmSpao3AmzgfAnImBT2c8SVQSK\naAgJsFycarBWRJao/p5UiiiITVMLStx1paATGKEU79Ln57MiAFKZu9BcKR5O9wKo8fYBbQEaAFgy\n2ZV1X2DDf+0dotJFQ3NIUFeWgynpeopGIoiy6m6xIn0pnoltAGR+pyV50SsyMajrfWKgLAUjfxcW\nSVtb4u6M1p7W2kvBiIwMlqphcwx5Ty20ART0fpRxf5D3B/klIMf9M6jSck51RWIDfluO/Rjf7Jto\nMCl/gv72RqNx4cKFJEkURZmcnPyREjazLHvyySdPnToVhqGu64cPHz58+PAr8Lte38tfPj74wQ8+\n99xz/p98nJAeLFUpwo5CVO0xtz+cSitAqlp2J+iVAUg1tddMNUZ/OFUSxe6yVMPA2tzTWXYnIJWB\nq7uuUG7qiEAxJ5cpjtNU4sXO9HRxkdAPlhJdHFTCTBBBZ5O7BfSH09yKCF0dgOdq+X7Sy/FS1ZWJ\nohhJbyKUYtN7C4B4l0JJqnqHfuvr0t6KX9vwS1wL0m6JGsIUjwTgdFQd5e6/U8774PvTtiHTL2g7\nKFGNihVUbwkyjcp9zWDYWi36pQgATI9y0CuF1Zut5dvV1Z+OlwdMpcr7U3KSjIQUCEt1xblsqJE6\njhItxiWi0WwSbFOHPjDFHm4kNp359on6M16NBMeLcan7leeMJx7/9Kc//epDF1+X8RaY5M8999wH\nP/jB+J676+/6NwCISJJbNAEkF42hwF8eyhWnvHA44TFLNMlj5udTSnH9DkgUAMDUmKSbFNctUy2/\n7ISWTDQAoPlPd1BkZtIKmBoX9D6B4IJemaQrm3+74oZoDhldRWoytKS+ztOBhtEB9xmAQSGLzGwr\nSRaAmW8R5QSAo0Q1pUOhySe6s6qSTJitZlQIYvPe4RdqSmc+K9aUjgttPiltYZEpn4UClCl+s6Z0\nTiYVKnJEqZZ6BWfOBqAYidS+88tJNYlKYfVOe95hEfFnaa7SatSMCgCmzLV6WCTZArlrCf9vaoE/\nyBN7LEo1SrOF6QFQleTG3CLFzpK/mP3G773jHe/49Kc//aN+y2+K8RM5IbVarU996lOPPPJIq/X/\nE+Latv2+973voYcempycfOV3+MpXvvJXf/VXL7300tb/+cu//MtDhw79yq/8yp133vlDP8BrvPz7\njoZbZZGQaqra3aFSN8xEdzyHwO4nKnhq152BJbXL42E5IxxWaEmA5etcarI/3ZGRQXCqzQgv0d0o\n22Fs2mocpZpZDqKMd2L7PufsfFKaqLTv0Fa2yz4ljLU0p6w2VnhpQ+/rSrTRrwFwFg3wLEkUw0js\nfRspUGyIXs0l7xHNdQqWteu8PyF8K/ABNzbhXPnCoHKnPb9f1BvccTPR0jsWi1b17s3W8vuUeQJW\n7sd6Te960PbFnTHpvaSW5tW8jfgBfvHhbN9W0DKAfmI1Y9PUglFzvT8dFJSEQEq0uP6Sfexb6fjJ\nbOSRbPdqVBwXndWoeJ9zdj4rkhP2ML+6gPzJdJT+nRfjUj0sdjeqZr5VV4oXlagZDD/fvD3R4LQU\nqUmvIDfsQTNVz6m7uOFuytyBYnz6jRQ1vCUnOQBHCyI1FlaCmzDEvcVdk0EkVNXvAfaaqbQ1nWcw\n09y66hUUHoP3nEST4bDHteDu4ouUIwxgQeRPirajRIvFEsWyrIcFFSAsyKC8eWIgz+mp2PS9IkTE\nEjO1B/qGAYCvFgeWHBSyREPGs6GD59fDAhF9CJa/21wjdLe9ZoaTa75XbAIl7tItRhHDJ/zJ7XZ9\nsTdZyrnNqGBqQU3pAKDKMCUezaD3QLx4jI9cUAprzByRQSNzSFO3gHxFdWtW+7Fsb6gI14Y7C3J0\nMDEgyn7DrZJl1VTiL7UPphnfbtep+PE2a9nPxD6zXrW8k0mllTqkYm/Gw8pAS9U0gcnUOEo1rgX8\n4rbQknrM1J6a5lOvGiFV01Q9hWkAw3qXOIFv7fH6n5C+/vWv/9Zv/dZ3VRJePoQQf/AHf/BzP/dz\n3/fZNE1/+7d/+8tf/vIPuvwXfuEXfv/3f/8HPfsaL/++g05Ii//nXwJAP79V00DTUI3YqyaZEVtt\nofY2S0bhcBLlYtHXEg2ZEZv5llASXYloSTPzLfLo0ZZn6zhCajoi17WYQZk0Z1CistXWs5dZblP8\nljoASOawGRixUZUiUnu23WX9SqQMNB4j0ZDaA6gpAKKVjIvOycW3Uzj0yK6ztIkDsMkviUrvsuZI\n6UfHFCLL1Vi3LAeUh0ZuIZtFz3g1Os9xw01ik2j81NbaBFLYXTqZAejXJ3mMcGhg2Z2wOZYVN1Ql\nIb640hlK7QFRUhCoMFMAacdQjTjNp2gaCk99VzeMROFpNNA4z7gTApCJIhMFgD8RDX/z8/Y/f+6N\nOSG9xSY5nZD4fe/s3f0zpCmg8hGLBADV7m4i6gl5RT/Hakw/x/R60tdEGafQLNqvHFCbxAohGSfN\nYRJSk4mtyryTSYUQogStv11dBUB6NnL/EOmOqm0AyKBD548Sdy8NKpQ/QnUzWgC2igob/ZHp4uIW\npBXAAbVZl5aD2GHxXtl5GuP7sU4GqWVm78q6AePEIF5RbLJPrTHziXAHsRuoILnJVH2ZZIPCBskz\nd6I7e3Nh7j36pZPpKPkOG9Kio9iL/iRVQdbDglDjLW5kxakTaziITWpR081rdJVBIQOweRY0PVML\nKr/za/9yQnq14+mnn/7lX/7lrf+85ZZbDhw4MDMzs7y8fPz4ceq+RlH0O7/zOwC+7+368jttZmbm\n3e9+d61WO3Xq1JNPPrm+vg7g7/7u70zT/M3f/M3v+wFe4+WvMHJny50lW7FgdtKZ+tyl6qxXVAvF\nAY+h101vwwRgOWF/d28otzakRE1zmOZWlGpCSfqJVXHq46JzaVB50Z/UlagDe1x0tkxwVd0fkcFR\nVBzE9cw+oKw9HO471Z+miUutKfokVLOie6OoeXflznqOWIxLO6qNS4NK1ze9giL6WpSLE2g8hj3v\n9KcDZaB1fRO5XsOtHpz+Z1wTI234pe5GFcA5EVlGL0q1v+lNWkbvoLNwQG+cTCpuJmwmvpbMAHCU\niBRupMQlGvee8oVObI/nFskV304cKlBIESUDJ1FTH0CqMp4ZLW50rfWVqu3EwhCKkchEoUIQ/K0K\npzR8Fk6upV7BagulrWVAp2UBMIwEAN/mA3CXHMsJs0QdDLjlhE5LecPIQW/VSb7erYZzs2oMBCoH\n7IGmGnF/IlLr5ZZWlrStUdMhq/2/Fr5NgadbYJEK8+f1Qo11qaXnSQGAlKLgaMA5N6g2jDopRbfq\nvc/E9npYSL0CbdoeX7njcQCmRycMWttooQLwrFsjlyiuxYBt6H0iLNDWBwC9+UpUKmretLa8eC0P\nzGIRLWPNxKEy9V25s1BQQ3dB5h0WU4xkWdkMiT+iVgnP6kJzM/Ee/RJISnqtpAyAlNkAjvRu2G7X\nTSW+NKgAkKm2GhX/c/ceevZL5JoyGu3EIYkTiUJp3Df6PIAT/iRt4KSaskQFT9O8l0WC+PrhsKev\n25EJVUmE8mOm57xZxut5Qur1evfcc0+n0wFQLpc/8YlPfJcv78SJE7/6q79KJQ4hxOOPP75t27aX\nv+ArX/nKRz7yEXr84Q9/+CMf+chWQdz3/Y9+9KNPPfUU/ednPvOZm2+++bs+wGu8/AcNOiFd/Kkn\nWCRzYZqOySRRAGQ3tZWBRgU6ryANn3GfuddKdv3h1OqpA0vyGLrPZF8DEFUiAFEupqOM4bOBJSmj\nbFjvUgf4Nme+orif3zi0x1o9549T44eOU6QXoE+1xcKiDVqjO14prFLeJUEkF+ISbRUb3XGqgQDQ\nfcZi1psIKevlnfnzxOMihCs1bGtKhyy3dMn7lPkWM/6gda+jBd2NquhroiGyRFV4qhjJd3ZwgFpo\nT5gtWpO2NIFbSTlUGc+v6L1qAp5KNYWaMt8UgaL7jNoMWXGDDlij5nozGKbEKRLNh80xHoNKQ44W\n9OuTGc+22hiW0XOefNR+8tGf9AnpLTnJ6YTkvf0Dg13/E+MZ9Wx4zMLJNQCpVwAA01OVhHKQt3oe\n9PtIFdo5d1sSmxT8s3X2paxhkjnQ+YmCWSnbIohN0RyKcjFNBiIAbVFHyYq0ZZA419pF70xFv05s\nU2zgKHcfu3ob1M2yueEzP58CkFZAqj9Sx1A+yxozAWyXfToSUTDupPR2pL1v8LEF5AE8FdbON/ZS\nC3YzyelaqhOV4/YY9ZrSoS4sAAqgob8d9YeG9S4AIiyQBX6rtTyUW3ubtQyAQH/NxKF73I1NocZB\nr2y1hTcSsFQtDNU328bFDZlqhAYPYnP69/7DW/iE9HouSH/xF3/xiU98AoCqqn//93+/d+/e733N\nxYsX77///jRNAXzwgx98udU8y7K77757dXUVwH333Udv9fKRpumDDz74wgsvADh06NDDDz/88mdf\n4+WvMGhBanz8zyi8JOiVqd8oI0PfMBINdp3DTCmtRyYKid/sLgPAYiY1Ga5Z+ohPvg16T7PUILv7\nFsaR2kuUj067zn1o++C7si6Ax5VJijsqZuFVxVpRbDI0ADjnjwOgW50yVwp63403w3LUejnRYHeZ\n7Gu+qztlTyYK1cS8gqSQm92Vs1RGcLRgwy8dLJ29NKiQMpVYXud7UzIyVM/AuU2ZHy3J9pgLILSk\nObkMYOsXBMBOo/EAv7jGzM96N1JBoxvmRs110iA81rxF7dlUNqT2OBX3yKNOa/MmkJ+aYfRLF4pC\neXUr7kxVktsKF7YSm4pf/8ehb37xJ70gvSUnOS1Ig/fc273rvVSY8gd5ikClFwSxScKwTZStmtLu\nBwAtNm5sqvWyOblMRxYZGZXCKgCqbgWZRpBDAB/A3HGlfCSeILOOD05tG8qhuAWbKNULSuHbcmxW\n2aBXkvGW/DrkZ6CZ1gyGtz6YCBRctnUnBECsfT+fqoV26hUKQ/WtomKO+3fa86TzJkXDPrTPoESq\nmfO9KWpJkhpourhImp0Sdw+L5bq0AZBsgcLUAVSZTx1QwthTrlhFdSl4ZdObEQpSc2wvzwOgSrjN\nomPB1EpQ3lq8iYdEtyGLhGp3k3iTWdxtjVO9dOZj/8tbeEF6PUt2jz76KD342Z/92e97owLYuXPn\n/fff/8UvfhHAE0888fJ79ciRI3SnAfjoRz/6vdeqqvqxj33sgQceAHDs2LG5ubnZ2dnX6/IfOkZF\nlyyfcBYcJXrWrUVa4Kt5y+j1iyZlmdhrJvezrK/xNS3lmVockBZIKXiIofss0ZSMZwCCduU8KgDA\n08D0msHwHcWXqOJxKxpguMxyLRhT0l1RbB/cYbEP/iVl2lW0o+GUxaJLg8oQ95pRgTZfaV+zYsZ9\nNihoG8MaAH3dFg3hu3qSKF2A8yxJlPalHACrlAwGPF1gtmPrPLuyeLA/HYgXhzInzAPz/B1Sk5aG\nRJPpxthFbSzXZSxmvZ1t851XKceFlpbVqEgU8PvzJ2kH6jP+y9HpOnOuKjYyXFEsIlAAeCqsASBF\n3HR+ec9ofTEuLZVGEJuUmB54BTPfIjjmRmIjsM18izYBs84VOiMCuKhE/cQKemWrIY5Mc/TzvNAW\naqz5b4SH4S08yQehHfTKyLemzLWyswCAqAFbzcXNjUVrXB1oLa9md5lXkAHP1ELb0QJ9+zyFUBT0\nPvR+MxgGQD/uTI0/nxzaY63OaO2AqQez1vtxyUiSDaYPybAq3RAamaPJkfaCOuxB8zIxIgNHib7h\nz24kdnejSnpxHjNlcfvyRGT4TFlywoGqcgmAO5HqhKQ7FUkMINdT094IgG4y3s3l0M9bPbVlyUdQ\ny4z4SKKCp8+IiKSzALaX5//nkWeISU8izy3N54zWnkHvXrlMxPEPq2fnFTIi4mk5TrUKQ40mzJah\nRhcHFV8Ii0VUTj83qAaZdrO1fG5QvexVt9uboRUuRDMq0CIk1DiITcvu0O/MqhKthwUSJWmXct2J\nkNYza+0HpjK+Ncbrdg/HcXzhwgV6fNddd73CK2+//Xa6V+v1+suTmLdu9UOHDv0ghdLevXt37tx5\n8eJFAP/0T//0a7/2a1tPvcbLf+jYY9R/AycIujWW+s/kz/vgBKimF8wnpWeNXb5XUAYZzumcZ6mG\nwflCmrBi2Wc8A8CtJIFCRbz+cIpcT+kMYTCU5r2VqPTXUemQuXQyrQA4wBsjCEyZbpO+KZOA8VNK\niRD99AOxw2j4UkyZaw8Wv04RnCfTUTcTx90Znmp3F1/8prHb2u4HYUEDhvUumYSoxAGAbiHi7VM1\n3JmImolzojuLfl4ECvVRrbZINOkVZK66dIe1/CA/exQVEjjsT9tjun/VtObV/J1xvcK6wnRlLFoo\nDsABdJjeggHgZFK5OKjQKZCEeSXu2iwqq+4SRkbN9UZ3nImBaneDdiUNlGh0Q6badHm+GRUmzNZ7\nrbO01JXl4CgqF1ERShKYXm9bisiwSg3fK8ZHK6Lz/E86wvytPclncys/tf0f7kjrAeOmTKir/zxG\nAVRU39NW6tI6HVUx0fClqIfFDXukUlgNM9GvT27kPRJwRxknZUGbe3RWplVqVHQtJXJY9GU5c5hd\nXea2hWQi8zpMH1w7hw2YSqrr3VnXlMmIEiwgX1M6B+zmXtl5Oj9+NJyq54oAuuM5GRlytJOOFLVU\nVQZaag+k3bnRWSB6kCeFzTYNdmQtmNHa1REPwFf9vXS0okKCUGMAQkkofGsGvV2y+4vGOYpiKqYh\nFCzw/EzSG7EaqeV7rQmDRQCCjBOjj5CP+0S9kToH9EZd2o4ePebu7ScWLFD5uhkMP+ZWkarccFeC\nctotLZUaVA/4/9h79yi5j+re91u/92u6p3t6pnue0mhG1svyyFIk2ZaPwRgwwQfMwzc25hDwAW4W\nJhfddU5QsnJyTyBZHOKElcU9ZLHIMg5hgR3Ma9kxBAy2dU38kGwkeTQeSyPN+6Hpnunpnu7+vfr3\nqvtHycNEtsXYGj35ff6q7qmqrureNbt+u3btzZSQwnua5rEogjaVUqJVjyRZrtR0zW8BtVLgQ21e\nZS7vVzCrppCKxeIHPvCBWq2Wz+eTyeRZaorib3JMhWG4tFYPHDjACmc3fG/bto0ttjMuqJ9j89/K\nDfzMAbQUqJYldhc101G9yJ3WRj2kYkEcQfqahvHjfLujqnSXRZVqfa6V7C7IlhLZBICdCNFQ5bmA\n5/0AWMOkMDk86maZn9st8kiW2AVy+szzIW/L9dJUlrMBsIcMdmEiAxccALRF9ilOO4ZUf9jSw5WP\nu7mNSr5LnZ90mucCg4UQvlEfuYVMAVi6WjHup+9WBraFCx8WR6dlvSOyWiMbQBnyUSm9tTmfa7F1\n+BnqdkQWOnBzNF6gSRabK+eb/wdOVqDOchrLlrYxWmikdQAvkdZdOFnzDRn+Wrq4NsS3xU0aggx1\nPyCcfF43n7F6llKfFUODxcG7KTE07qcXFDPw1bCW4AIuENFwLANg/Co0aqUJK/dTgIX+Y/YZfV49\nfQmGDxOnVEDVywqfsZRC/TU/2ipzZQu5TuomFb9NNuaI1U2qbwtmXcIXeWUMiefC9ndyEyZEdrBf\n8oycXGaKx6YScmDGPZnzGgXL4DyD89gV5neLY1aD2EydR4L1J91sUTTuVgZsCCxs3bfJxl5ucTsp\nsn3eNKcDmCANNoQMcW0idNPqAJpAsR/tJpU04jG/gEbBclQxJVplwa4F2va2sWJosDRaACwqsdsL\n15NZG8LdwrHeqOpSvkRkGwK0Y3mq9zYcWkNrAFh019bIciMBEVK0zuJ2A1AQZMQyET3Z9itQH69f\nnXLrCglH+cTmsLQurLrgARzksgb8Pm5+hHjs0tJGJf8e49jTdq9NJXYvih2JAXCqGSp50BzbSsmL\nSr3JCiNhkQvWCaZNJXagyzLb8lzAgqlLc426f/p8Omx2ruzoqqumkFpbW++7776V1BwaGmIFSZKW\n1q3v+0u2iL6+vrM037lz5w9+8AMA/f39S2+eY/OV0B81/6yytUWq3KYd+0XQze4J9ZDKc2G7wfl4\nVVuMSVMmxEerfY2ChY6KE4lqyp/zkrabYOGTWaJJnXgG8Zj/dIthMmvyD81rPttwgIUt2ETLhuw3\nU6czsvYEsxmxXPRTh/nmEic/RruZX9OLXMtP7U0sKsQ4TSu890T56g612KXOs2D1AAqh8ef2u/9b\n8le7aeEgBzNKrxVLz4XtFi/+52ACEUqcDMAhwhCX1GiwGwVQbA1LI3zica5zJEqdEJLs7ApAHWKZ\nyACYEmpsPSlWEkfq2bfJx9o0u1rsOMJnXfBsc91JLZUGLGimQbx2qcyStmnwhqpdTAjubd5/lzw0\nqRgsL9QRu7NQaVe3z9QCrZELvEhoURcmij3jkkds9XTSTIBdhARQy3pU8tDmCIqpz1fe1A/6Friy\nhXzA6Xx68j/TV13pvimXM7xZrBtlX0+J1kPEsKm0Rcr3CCUW7Oq4m3ubNjzg5a4zRpjj2VJuqj5u\nXqPBPK8WqPa818nixQGYdJr7peZebnEkSpmcOOjlDNkb4pI3B6eYRE1zuknF/qgFQA9XNoj/tNXL\n3LvZsWhoJSkfCorJrLhb9DwAtjDZLNgTxt+GOYX37lYGMtQdRHqQO319wqQSO3nNSRYL8/pg6TqJ\n938/OdDLLW6i5S1BWQHPbImzRBsLE91+9VmhtS2yNodlh/BjXGKK6AuCbEM4HVwVC/NE7Y+ax/x0\nt1iyBUknnkmljUp+LjCmvXSHVPqj5PMA+sOWOW2Gba1UpSo1BI2vpiIb99PDZtuQddo9ldhq2HA6\n7S/fPmv7Ks8FDaLTKFi4ornQoYOiKFryWN22bdvS+0spxQC8bpaXJRKJ06Zbz/Mcx1FV9dybr4T/\nO+rvS82znd2t3BRCsEeEbdyCEoWtkeVCGOUTINAQ5JLP6/C7qKnSMEXrpzTNhnAQ2RyxATzrd9wg\nzvzC7+4TCtlXQz3eqR9tps4AbcrA3RPmFYQqCQ9zGQ3Bv4pri2Rjl2iezgbLmxYn5Yneyy0qvMeS\ni7NB9hqnhgqbEPDJzMxQtUsVHebA85UX/kutKWRBSljKO1OSHg033q4c30TLTMldT2dZCs6dwTyA\nLUH5Rppvy5wEwPkigGKlw4Wg0rBMZJfwr/C6Opd6iW+yeHHYT9gVASI0BGydG/CznP37/tT2cB7A\nLNFd/tgpTv8+32tRiZnRATxZ73menL7AyBzqtje/zM6ZutdhYQAAIABJREFUyr7OzInr2woADpvd\nAFqkSke2xCwwY376SKWXALzoGKLj+uolEu37MhXydcqck/jNJV/mP71DnbRECQC78TqGhEF8EBtA\nVjNzxIaU34oFW5nZEFWmiJ6BC+BF2pIlNjPxtbyaUk8jni1aY376Ga/nDuPoSJT6nPyiDcGGMMCn\n2QU7ACPh6XyVJkRQbFTyR+xOsBu7kYBE0SllwzA5DPQap5hvgheK8yc2fVfbSJqKLFMfi3rw9/Wb\nrjNGmMcpO3NlHgoARoRUljNHgvR/zzylw9doMECbhmnjY/zp3R4zg6+htYN8ywCadvOF7/G9APJU\nt6LTX0gvtwjgDv90pr5ZXmsN7FleK1P5Jb4JAHgUJC1PdWY2tKk0bLZJr17hYkZsACwn4S3ySD59\n2mOexZJg3/lD3ham0ZcuflzBXGiF9L3vfW9qaoqVb7/99qX3mR8t45prrjlLD5qmLZUHBgaYS9U5\nNl8JN038dzRUr00OP+hmgdOJxv86OrA9nJ8lOgs4zxK5HuYyLBVsBu4kZ7CbgDp8M5J0UilQ7VPC\nwCQMFinLhtAJC8AClZtofXc01x1V2dFumch7wnyK1kf4hEaDYyRlUtENpecnboiESE0XmINpSrRY\naAPOFSMhoppDVD8a6mpweABOUyD7pNppCqLToRaZEy1LUp6vp/KyphPfggiKMSRAYBOhzMkAUlG9\nTOTywtVlTl4XVstEBsEon9gRzM9y2o+4dexCkh1IGuf9MpKYxwFzTGe3GjPUHRRSPyTrAGyPigAW\niNxH5gtU69HKOzH3GO3+WWUrgK2Nh1gQ/sOlTdOi0yRX6pF0e6IfwFYsjCFxE51NJQ6WiTzEJUdo\n8mm792ht7ZLrXSB7JtBwyaQwv0yFfGx4PZHXCUaditTR6BG1nU+WbtOO7SRjLLPcGE3cRGcd8PvR\nzmKVbo+KU0QH0EXNX5FW5oTWx82DQqPBe+nkzdJMEcrucO4Urx8WM83UycDdwpWVIJjl9FRQB8BM\nZDsxP8tpDhG6OPMx2v3j4q5bm1466Kc1wsJEjTxZ2+SFoiE6GzsOlwJjIn/VyYXMSeAZ3QUQ5MyN\nqZHd8uTSvSgL4rN+B7uWe4s0NSilR6KUGUks4vhIkB73uzTiPepuZEaLLGcaxBsJ0hYnmZw4EqRZ\nnO/FQDd99Qev3u++WpvqEwrsG2NGv0EhpdKQ3asFhzKRS5zMMpktELkL5iRnPOTlWLJaGJh0mhfq\nyTASWOCJLVKeJe38OD3OjOeDQmqSGCYnGvCfiNYAYA9b5UivBVp2Jb/lZcsFVUijo6MslQuAnp6e\nD33oQ0t/cl13qXz2Dd369euXyo7jrErzFdFQpaHILg1U6g1Hiu3Xdhz+G3E7gDE/XfJO37a7nsyy\nA5gM3N6oupWWdvITvi8dR4slihnqbqCVBSJ3UfMYSWkIrolKLC/DjmjeIfwikce4BHNhmCfqLeGM\nQsMtQXmW065B6VFubVowO9Y9x2K7FULjsNnNvHFIwDfkptiNB6mmW0mKZMACU3otVU10WJivPqGw\nE3M2hGho2t2w9h/s3T+PRBYLvACjn+Wq4ZtzxOrmqmNIdKPaSS32SDTApzUEvxA7dgbzOd42BJ+l\naGJ7SZZks4+bZzZMg/gTLMcLoMOfIvo1UWmByB/0x5g9xIWg8uGfGYcHhRTL4KcIodvyXGtkPy20\nAtAQ9EbVA3zLSJj6qbvpv+qHNBqwO/y3acegoT/Ivmx3VsIcqUv8YkY/OfQmfs3zxuUr5IIUoMUN\nABbwW3I4T0h+Pbo5KdcAsHs2zysFdlOtABjEX4DcSa09wSyAd2L6X8W1g0iz3A0QMEYS/UH23eLY\nQb4lA5fd/lFpwJwXVBo8LbReE5VcnFafJU5mms+Ad2/z/iyxWWAFAIXIaBQsFhdu1M0u1ppJQ7VB\nruHVW1BuKLEMgZ2wUlHdBX942L6NDosb2sdoYgRJA/47uYl5Xv1lfZ0ueiyduUWlA2ZPTi4zI9vg\nq2pjKxZyoq2LPju7ZdeY2IXfd3ITLMLpx+lxBSGAVFRP0XqKr7vgFRoqJNwRzLM95buD+WfE3HXh\nXJf8vErDdWHVFfhyQt4clkf5xClOA2BDGKRpi0pfCG54lzy6htbYwyKz5/fxc78MjANmT2Uxh4BP\nvTi8wl/zMuXCKaT5+fl77rnHsiwAPM9/+ctfXh4F0vf9pTLPny1ss6K8jmHmHJuvhLZv/W1mY1OW\nswqRDqAaahOHtFnOTwlWI+9cTRyTijVEL6JuEWE0SFdDxQoyumADW5sEUyKRFc3qnNfBVZPUC8BZ\nZHoQ3P8HNFLPh1OGnIKjotYSuQEhCh2VEf2A032QNK074APCv0SDDBkYC1I/CHQ/sOEvav5Mg8UR\nOYocIYqIIgWKQanstapFJ5ISvM0GXw01n3IFzhsUKicRATj5k5e1q8ptV81miZWh9VmiFiLDo1yW\ns2YhzQIVVOagTpAQQImqPgVQmqg3AZC4FFBWOa9ZsAx4OvEBbI0Opqg3ymlJvFJBFFFPRajQsBF2\nEYaL6CACGd5P04sk5LiQ43wBIT8SqDI3NBppJhEDcA4RBpGWMOVBmPRSXpTkidMiHqr7yW9xfjXQ\nIlqGL4K4EAL4dbk0mxWiQIbgEHF28K39sqvIZS3kvHW47cnnxd4unfNm/YQXiX4gg4tEzg8pn+Zd\nkUQu541QbgRworl+ynuRKHFU4doEEogkAkzA7OArdTp8kjg68SOqP0Z5nfzG3yQLxyNchtZ9EKD4\nMuBAEBEJiBLUBzDF6T64CSruDxsAOJG06BtAmTfn3QB1lRI+TAGKbHXLRZ/yIgklBB2whmj6YfYR\nnNlIvWd/Mgxgy/vqHuVb4EwQiWVuyNDjNSANKSKWCrQF/T7l/j3QQ8pHtFAIBIT8U7zEiU5arDYL\nU1li6TTwEKaBLZH1EpdowCsAfkYDERRAjlouhCQ3Di48CfgJCwDR6tyifoyPBGtkIeIhemFdmQAW\noQH4Ft8IlCRaLECdCZJmSFvE0Vkv9S1A571FJyS+JPgBMP9rjgj1MTmYyAoRDThx7uIL+XnlAimk\n+fn5j370o/n86ZODv/zLvzz7qewKWb5Ez3dzafRkdfRkddk7zE7vAA7w2kw8ItD4anmplQMUX1Pz\nzTDGmp/Fv1l99YOWfy4bTwAsz6Zin5ixT8ycMfKlJq+bW2j55wZvUOf1WD4Q9g86ArxlIzWXVRhb\nGrD4amP2/zWx0o+7OFzuQi6NngyA4OSks+zLP4Olpy1WYUnvBcBSTJuTAP6jnC8vv4V8Po3Lyssf\nDJeL3/Jul3/c4GOvLA3pDJY3f90FxST8NUI+94YDPQ2TcBVgt+CXvjMm8Gwt5Jc3UIDqsjEsn+/v\nGhdCIU1MTHziE584dep0ivi9e/feeeedq9Lzcufa89f8Sr0UHbOKXNZCvmvXriW3wJiYi8h5Pwc+\nfPjwRz7ykeUL9d57731tteXLJorOlos6CF4nvOA5No+JORdiIY+JWRXOr0J69NFHP/7xj7MIxAC+\n9KUvve5CxX+0etfrZ7vhyDI3n9HqHJvHxLxlYiGPiVktzqNC+spXvrJv3z7P8wAoivKNb3zjjjvu\neKPKjY2/MZyOjo6epVt2YszYunXrqjSPiXlrxEIeE7OKnBeFFIbh3r1777//fvYyk8k89NBDN998\n81maLF82c3NnOzasVk+fkEuStHTf4hybx8S8WWIhj4lZdVZfIdXr9U996lM///nP2cvNmzc/8sgj\nW7ZsOXsrURRbWl5NYj0+fpaaAwMDrLC8z3NsHhPzpoiFPCbmfLDKCimKonvvvfe5555jL2+66aYH\nH3ywubl5JW137tzJCocOHTpLtaUAKmfYIs6xeUzMComFPCbmPLHKCukLX/jCM888w8q33Xbb/fff\nv3KLwTve8Q5W2L9/v2mar1tnamrqyJEjrHzrrbeuYvOYmBUSC3lMzHliNRXS/v37H36Y3ZXG29/+\n9r//+79/U81vvfXWVCoFIAiCr371q69b5+/+7u9Yobu7+4zU0efYPCZmJcRCHhNz/uC/8IUvrEpH\nURR98pOfrNVqAARB2Lt379zc3NRvo62tbSm2Cs/zlFJmCTl69KhhGGckfbnvvvt++MMfsvIXv/jF\nM1JhnmPzmJjfSizkMTHnFUIpXZWOHn300X379r3ZVkeOHFlu7oii6M477zx69Ch7uWvXrjvuuKOx\nsTGfzz/88MODg6fjON12222vuzM9x+YxMWcnFvKYmPPKqimkz33uc48//vibbXXGWgVQKpXuueee\n5Tf7zuDGG2/8+te/Lsvy6/71HJvHxJyFWMhjYs4rq3aGdPaLESsnnU5///vf/+xnP9vQ0HDGn5qa\nmvbt2/fAAw+cZaWdY/OYmLMQC3lMzHll1Z6QVp0oig4cOLCwsOB5niRJ7e3t27ZtWx7M/7w2j4m5\nAMRCHhOznEtXIcXExMTE/E4Rb6ZiYmJiYi4JYoUUExMTE3NJECukmJiYmJhLglghxcTExMRcEsQK\nKSYmJibmkkC42AOIeYtEUfTUU08BeNvb3rY8ufXZWVxcHBgYCIJAEIRrr73WMIw3+7nn3sNrKRQK\nJ06cCIKA47jOzs5169Zd4CGdj0nFnDtXkpAjlvMVECuky5UHHnjgK1/5CoCDBw8uzyX6RvzkJz95\n4IEHXnnlleVv7tix4957773xxhtX8onn3sMZFIvFb33rW4888kixWFz+vq7r73//+z/5yU92dnae\n7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PBya8VS2dcBNApWpd5g+ioVgYCvrKsRW+UCLhIiKnsSF/x+cmDMT894qQUluSd5wuA8\nAGYkWVSa9tKLgT4ZNZ8UsjfqIwD6uPn+qHk4aswRK0vs68K5MpE7qPUsn9Ph56n2Et80QpNbsQDg\nJjr7K9I6EBilwGBb4xbBBHAXN6TS8F7j6ONcp0H8X9bXPet3ZHjzU8LA96INj5p9MufdqI88gTV9\nZE6Hr9EgQ12VhttpMUXrY0H6uN2+UZtZlGs5ubyuo9Atlp6xelKiBeDWjmd14g16OQDHyz18kvqm\niWMXRzauDKR0qSU9OVfqCiNBEh0AG7UZjfNu1EcGvVwhNOxIejaSiqEBYK1YAnDI6XIi0RAdAI2C\ntUXKG8QzDA/AmJ9+xuu5UR9hda7VpvJEt6h0Fzd0TJ9rpg6APn1uOGo85HQFrlFbyBxtUgPXGLdS\nc3q5QbDnvKQgOmHOUUXH9NXANXhLAaAoQbq7Eoqw055SE201QkN1T+qVk272psRQljOf5no3Knmd\neLvlyR5SGaBNA16uRTALMMxIMgXRgL+G1vTTytIfiHK3CFNNtD5EkgWqPU9ac7BsCD8TOwtUyxJb\no8GvhNYn3Z6vOc3sO5kLjBbB7BZLAPq4+QLVrm+aGolSWc40qQSCPw5enuU0AD/i1hnEZ9+wC35z\nVGqNbAXB9eGpcdI4y2kagixn5ojdo5VNiD1yxYK4RqhpCIqakml2j5GUScX+IMs6mbnggnEhiRXS\nSvm88YzdIAD4oD+WCutlIv8716rSYJC0mlTKcuZIkJ4LckdrawEYolP29YV6skMtGpwHmGw7dhc3\nZEOwIbxXmjzMZUxZNIg/rDYCeLK2aVxOsyU9EqT3iNObaLmfeI/UN7QI5vFyz3H0fDy3H8DBetdu\nebIbVVPKjwTpeiQt2mlTVFFL0IDTpqUo7Qv5hkCjADCno4Wv1Nt/XGznk6UmuXJ7+jD7CIPz+oQC\ngDnBcCKxUbAADHq5fD31JDb9r8QvikQpUO2R+oaH6NZb5BEQgCIPzaRSBm4B2kPeluulqSfoGlBs\nlfIfFkaf5XPN1NEQsGkWiTJGEibELOxusWQQD8AkMe4hr/wP/cVTnP6OYPI413SQtmTgsj9pCAAM\nccl38aN3S4Maggm5waTig9XfY/8cc8QyIR6sdwHI8KbBeZmM+ax9HYJYmM+JnfJ0wji21XhGQ9BE\n6wtELhJlQ1QZ4pKWKPVwZRPiz81Nc06TKjrDZluTXGmXyhrnZXkzR6w81dk+5v3cCIBeoeoK/DTR\nb9Gmmmj9V6TVhMgEYHtUHOKSGepuj4omETcqeScgQ3ySAAAgAElEQVQpzoVdUj4TNvgt6claoBUq\n7dnkTA2a46teJIRWUtArAaDp5WpKZQOmnuK1WKglABw2uyUumAuMORj/VT+k0cAmggWRbZu2SguP\nBOsNzusRSoXIOOinn0TPFil/PZmdh7pVyj8UbNojTuvwu1EFAYAxJEwqjgRpO5KWdkJ/lnqqP2o+\n5HQxhcf2l13U3EArQ1wyy9sWxGEqFSLjRaFZQ5CO6n8SvKTS0CH8LKc7RPhXcW1vVG2NrBRFK7Va\nQ6s1sreSUpnIDhEcwttU+GAwBsCFMMtpJU7eRMsAtgglAA8Fmy6KbFwwCKX0Yo/hUudjH/vYCy+8\nIP+//48bShuVfB8/B4Dt7NKCOepmTV+9pmGcrcxnrJ56JAHwIsHxVTg6AKgWDUXC+2v0/A51so+b\nZz1bEAHoOL2B2hYuTHP6BGlYQ2tbw5JDhKNcupNaDuEBtEV2mchDXLI/amYLG0AhMsb99C3yyA/N\na8zhXjvtbcgey/DmYbPbtlK8pZCmYhgJ1yaHAYy62dsT/Tdj5hhJMbtfM3Wep61jfhrA4fmrwYdZ\nI79eKewRp5/1OwC8bHcyRTXnJSUukDlvvVLoEUo5YjPFw/RHEQoAZhUBsIbWBpF+3uscdbPXGSPH\n3dxGJX8DP3NdODfMJXYG86N8YoHIvVH1Jm4EmvUL81qHCCoNFIRHuXQGrkrDKaI/T1sLobFHnGaP\nhgbxdqNQJEqGujuD+TInA3DBlzj5RbRM/PSlwcde+c53vhM7NbxZXnjhhY997GPq799ov+vWtGBe\nL00xlV/2dZXzASwGuhcJLVKlQyodNrsdXwVAQ5F4EuVDTS9v1GZaBJP9j76LG7rRzx8Smpnc2hDY\nBqUjshxyetPAfutUVGf/c4tQ5om6iZZtCAAOIss0gU0lAGVfb5fKLYI5FxgzXuo9xrEeUslQdxDp\nby1e16XOa8TbKuV7SMWCuD0q3k5eIaLnOcZxtLiEV2gIYJRPHOYyw1GjQTyTSn+A4cNcpj9s+VV1\nQ4tUcSIRgMr5O9RJJmZs2BqCSWJsCxde4pvYyAtUY4WRKHXczQGYsHI8F1yXPJHlzV5u8Q5/1CV8\nI60vErmR1lO0niQW3zTHVRqn/WYADuEXiXyK01kZQBFKBm46qrOv4pqoVCbyurCqIMhRUyFegSbZ\nFFzwe+/999ipIQaTTrNTzUyouZ97CgBNL9tuYsKTKB8C6F/4PQCCD69lURVPH2aqomN7Cgl5Gors\nnQkrN2HlHik3hrqr6eUudX63PLkVC09Ea27gZxSEE6TBpOIg0h3EYmuAuUt8M9haDA03lADcph0D\nkKf6IadrMdCv1qZ+am8CYPQOi5E06TQPh21NcqUrM39L+8gWlJpo/Vt0sxlJf5F46pFgfYEzerjy\nINL9frZHKFlU0jhv2ktvb36ZPd4dNrsPhFd1qMW0YP5R8vk1tNZE61+TtgHoEwpbUALQFNUXiNxE\n64e5TJ5qA15uxkupnL8Y6DLnpURr2GzrUIu3J/pzxO7T5wAUqHaUS78tmAWwOSzlqJnQSkeddaNW\nYl1UneW0aU4fRDpL7BdpS3+YfdnuBJCTy7ro68TvRvWqqJKidQAKDQeFlEpDAAtE1hBsQalIgwsm\nDFckOuelpdK0l/7H2n8KIwGOzrmi4CMQYRS5cFGdF6KyUa9nIrVllnkQNCYshfcmneYZL1UKDCcS\n1yuF/x3s+BsqZUKzRygZ8G+isylaLxM5RevdUZVt/BWE68LqIaE5Rettkd0Ge5hL/G9vx4yXqkfS\n1drUu8UxZk/7ZX2dJnnvkkdNKt4lDR2TU83UYXprJ+buavjuxmgBQMVXDwnNm8NSitZf5NY0BvVF\nIpeJrCAE0EjrADbR8hpSG0TahPRvpKsHFZ14f5Z6yoK4htb+NeoBUAgN8OYE16DDz1B3S1DegvLP\nxE4Av/C7s7zJrMQa8dhOFMCe1CvsGTFLbAvii0IzgI7IKnHylqCcEfNFP+UW1ysIsqTiUsmB0RrZ\n7Dv/ibAmTzWTSgbxDM7vRlVDUCZyW2QpCAA8z7c5RGDzSkV19uYVTKyQVgp/eE1Dg19tC/V5FQB/\nSiVZD8D25pdtKq1tLfVw5SyxmdH5F343O5ixASp5hPdV0WmRKmyn2dC20C6Vt0p5A35/kB1BGoDG\nBUe5NHtwAXCCS3ZRcz/a+2mzQbyTbnahngx8tVErMfWj8F5aMNOC+bLduU4pHLfbvVBkD2on3WxK\ntMq+/vXqzXD0WzueBdAjlJ6I1twtHJsgDY+6G9nJ0zOV7eBDQXSa5MrR2lq6kCkio9gkbD99FJSn\nmk58AO8Wx7qoeYykNBqkozo7THqSduaoVYiMbrFkU+l4uQeAplTnnCaeC6adzNOAE4nspcT7242x\n5/lWi0r/DUdmoaOeHRYSAL7Pbwcw5qWP2+2Or6qi0yDYABoFK8ObADQaXBVVuqMqgPVC3g+kciSz\nhy2V06Y5/UnaOYv5iyAWVxBTs2vLQzd4LYvUU/R5la/yYSJ0NRomLL+l2ipV8Opm6CY6q9LgJb7p\nF353MTQaBPtGfcQgXo7YOnz2DGEQn9maHMKrlJ8iukoC9sSwlZsu+ikAO4J5AK/wKQAaghbB1DjP\njiQAzAxgwO8WSxaV+sOWLGceI6k7/NFWarkQHMKnaP0w3/yU0LU5LI1xCYfwh4TmtsgGUCbyCS45\nT9Rf1texrVJaMNnSmJvrhhDyeiXw1bWJqTEh3S2W8kRjB8A6kQCYVOyPWgpceb/QblKp4Bt9QsHg\nvDE/na+n1ikFjfOuM0YOmD0ADM475HQpvDdstkm8D4DZEm7UR4qCMhtpjiA4hJ8kxghNGvBHotRc\nYHRzJYtKPbS8FQtX0YoDYUcwn4QDoA4xI5ZPBjn2uwxxSdY8Q10tVkgxjNrmMl/VScjb7WUANBQb\ntVKjYJUCYzHQNeId8TpTorVbnnzS3aoRb9rJsIaE91vUBZXzNyr5426uQypNe2mbSj9Y3NEg2MwK\nb0fSE9Ea5rnEzkWYIX43Cr20OkwSPQ2VXyjdANiRcr6eQqAv1ppJyCcb86Nu1gvFwDWOYm1oJQEU\n+JDUJS7gFJv80n072+dGiv9zaWfWyBcq7STkoVrgQ76qBzpf8FXiSVR35UVFsAkcXUl4R+xOZn6U\nOa8WaABuSgwNk0YQGNQzqcSOc97JTWTg9iqLu3OThchgx2l2JL1LHmW7v96GQ3vC/ONc5xaUnqSd\nAD5QvUvigkbBYk5Wk06z7SYE0Ql8NTFl1LXGoogwYZmiOl5eezKZTYlWhjfZPtQgVz2LjpN2NiVa\n+XqKja1LnedC9aIIxhWDn7IBoJYgQmg1OyQhaVU+UnwAtpuYA1qkSn+QzfLmt+jmPv60Y8IWKW/I\nngEfgEnFTSh3wSxCmYf6GO3u4+avC+cAsDPCWU5XaTAbrmkk9bUoNasmFf0Oe77mG5VQbePtMi87\nAj9JDAAFquWpxv7X3yKPjESpkSjdz7XcwM+M0ORIkDZ4b9xPrxVLWcE0qTRYz2nEaxHMLGcOeDn2\nBBO4hryozDX445JHeJ96CmSP1CVDdExgaTFOOs1eKEq836XOrxVLI1Q67ubG+fRasTQXGHdLgxm4\n4NAnzz376plZf5D9i8RTAJ6I1nRIJTuS/qjp35myAXDcbv9RYc+PAGYDf9nuZDZPJxJrgeaF4pGo\nd42eNyVphEs9FBjXS1NDUjJDXWaxnyBbTUEciVLjfloLPJtK+XqKHQ0AT1wkAbkQxApppWSN/IKY\nhJVsOJYhQhRodLGZr0gNGxKTciSWAoN5f23FQk6x81S7u2lwnqjN1GHGcZWG30dvh1TqEwrMleB5\n4mmc97LdmZPLAI7YnQA+0XDIpKJB/IM0W4iMI3bneqUw7aaZxAMo+3o9ktjBzLrmQotgjvtpAJpS\n0JLegcpVvF4JXAMA1ZyMkZ9zmqinRCHPuSICXi8Zc4luwhxJeYVIbiRE+rxqNTucK0YKvAafby/u\nMcYAsOV9xO5k//GPF686InTWIyknl/P1VKNg3akf3UnnJolhU2ENrW2nRYfjAbyXn5wS9Ef89dNe\nOi2YffL8t8nGJ6ubFmvNa1PjE1YOji415gEMzVwNIeRcEborKb481QzAUyM+WboxeaJPKPQHWYPz\n3slNjCExEqXywCG7q0MqpURri5RfUt5NtP4z/tTTF0k2rhgCEYm8QAMpdEXBqFORJhvz65QCgKO1\ntWz3YBDvejLLjGZfJs8qYbh01HEcLWVObo2stSiNI+1CKFOZGaB6wuopTncgqDRQaKjSsAJ9zG1t\ndOr/LrRu5UoAXPBtkVUmchr1FK07RHDBv1edZO4V3Vw1w7n70d4fNeeI1SOURoK0Rrwjduec09Si\nLgAYrrcFvko8iRkbeSBUI8EnQkmy2y0aioJiBq7BJ0vrlEKLYc4Fxtu04aft3gbBvjYxdcTudENp\nHOm1YoltH01eepc8qtFgkhjdtDoPtUcomVTKEjvLm48E6wGw81oiucfFdgCOryblWpc6vzYx9ET5\naqaNAHSp824o3aiPjPnpw6VNWSPvRGKPUOohlQKnmRDvCk4pNNxKSqc4/V+jnhv4mSxvM+Wa4c1P\nJY5k4NoQ/u7iiccFIFZIK+U+44n9RrvR5D+Z7dGId9xuv9EYA7BHnDZlcSfm2OHnZr+chFOBOson\n2NprpdYs0QH0ifMFYpkQTSoVQqMUGC1KPieXJ51mAE41QyXvn7GDWdvWK4VpL61yfjE0btOO5an+\njNuTEq12qXy0tva4m3Mi8Ui+j0pe1sjXI4n5UKiiI3FBo1pUeI+5+e1JvcI0mcZ57D/7AJp6SOUX\nfjd7vztTsqh0xO6s6RpbMwCKobFbnjSp1MstmooE4GW7U1DMubluAItyM/gQGv65toN9OddqUzfw\nMxOkIU+1mzFzmMvo8N8tjlni9HDUWKCaRaWrtam+xK/7g+wOdfLJ2ib2b66j6wAAg/OYizyuqgDg\nAt2LhGdP7XwWoHxIJPcJ7upe4xT72tnpRYdUMoj3R9xBF3x3UHUhbI6KsUI6F7LSYkPH8fTa06at\nWqBtN8b6hEKW2F3U7GncD2CET+wI5lO0Pkv0tXSxAjUJpyFZgK37gXSNOgrghNN1HC0AFASAzFQL\n88d5LmzvE+YAsC0agAGSLhJlhE8cI6n+sKWHLxvE1+E/F7b38XP9Ycucb2yV8qAoRMZcYJQCo0Mq\nDYY5N5ScSCxU2hsb5pk2SonWeqXwbnGMXZZ4LmyfCwx2HQrA87SVTbOPm7dw+hLSDfKMRoOCYvRw\n5ZEotV4pGJxnRpJOvByx+vS5Zuo8H7XmiVYIjf9BXywT+SW+SUNwTVjahoVpQQewJzWdb9RMKllU\n0onXyy02UycDd5IY2SYzR+yeRIk5XOjwLYi98uIHWofYYPqj5ke8DRrnFUPj6bDXicR2qVyqG2nB\n/JvqOwB4oXh7+nAvt5ihbjqq99DqhRaLC0uskFZKT1gFD5WGt4pTJU6GdOid/vQrfPpJtO/EXE9Y\nbSOnjddZVPSmaaXYXSbyGJcoQz7FacyCPODlmAdBWjDfpg0b8E1e2pLMF0JjepmNPqvYBapleZOp\nin80/xM7gAFgR5IhOswpaE1mhFkAHF/l2TV1NwGluhjo6wTT5aQOtbhHnGbjf9TdaEfeI9z6LG+C\noE8oPO91Xi9N/dTeNGHlPpR54cnapgxvHna62RXaIW8T54qkqRhaSV6v8PkMFdGQF0JXdNdyoe5W\nFnOUDxsb5nNy2Yykh/yt7IlqP9feg0oXNVUa/oq0fpweBwUwdUJI2kRgDz23J/p7SKWLmgAmiWFB\n7OHKz3udLYLZx8+xC1tPhCIzP7KpDZtthuiwWyDF0DjpZqHgH/ktvdzij7h1JpVqnAcMXAzRuELY\nIBQT2nAPqWwLF6YNnT0D7Q7nAIzwiUZadyG0RTZzG0vCEpPlfLVnljSVzbbHuc4tQmkiaNgeFYfE\n5HNhew9XBnB7NM7cGVK0fnNwagNXQQTmmcLcIzsiq4nUv4/ePjJ/Az+zpCp04jVTJ8uZEMAswKNu\n1osEABNWjm28AGh6+WptyuA89nEmxH+ydtymHctQ9/3cyDfRVwiNR7AewKeEARvCk7SzP2q2qGRG\nEoCBKKdxXo9QGolSZiQZnHfczSm8l+VN9mjORnIzZl7kWn5C1qyhNSbYLvjNYXlzWAbwC7HjvwQn\nAKRo/RU+rQZBa2QfEpo30MoGVNpCq5HWX+HTSw51zKt+iuid1NJIUOCMw2b3dmPssNNtu4kCcppS\nHS+vPW1UryUexXZDdJbs28CVHMYsVkgrZYBPN9F6itZd8CoNh7jkE2JHOqr/lfAEFf1aJdsgmjXf\nOM417SdrlXIneDzKrX2y3pPhzaJvDFW72Fl9PZIqi7lxyTsqrm2SK+uVwiGnC0BaMGe81JLDArOJ\njVc7NaUaWklSkgbs9mou0Kp8cEqLjLq1qApCZJkiL1BFCSTFJ0IEgAYpJ+sdachtyB7bIuUfdTcy\nO/hueTJH7O1R0SH8i7QlS+xPSf07g/md2lybYh/gWnqTi83UeXdq7LmwnRkKTh9opTwAB8Qe01dJ\nsYVXfL1CagoPQJ9XK/V2x+kcallMyjUAh+1NWSP/HuNYAVp/mH23ODbN6U20viOYfzd3ggje1/w9\nWdF+LmwvwChw5TzVC4HxTLFPU6oSF4y8vOt5gIo0FCEDALiSSASj3hQAqIkY9DvrTZamVL1QXKgn\nJd63rVQ2OTPnNDXahcZYIZ0DPrgeUrk5OOUQoYnWB0l6C0qnOF2lwY1+vlObmbLbW0PLhfAK15mK\n6qlKcpGT2cMNKAaRHglTw6QREeYCY5ymy77+pNhzizySh86crXPEGolSS8ojR2yTE02IhcB4jkq/\nqm5gC2TRThNbfSTgIsVPTMtuMmLBGpy0p5WkhE2oSBc7TWKr13YcNjhvLjB+ZW9gvhVv04aZxduk\n0lYp/146ye48TRJjQ1S5hUwx7/M2YgEoC/I0pxeJ8sfRywBmoX1b9QzibcWCLQoaDR4J1puQHuO7\nmYeFDeGhYBNTVO8XR9j31htVmUffeu7ETdp0oDk03+aQHLu6sMDLB5HNEXs4ahz0crvlSWaKL5g5\nwvvMdb5hXD2qtoUa1X0CQLAbEiK1khRuY6T4fD5TE+GwY2AhWnuRxOPCECuklbIzmG+lFoAkscaR\nfkcwWYcow5+y2wHMctoIum1RYHcJHQgpWr81mrpVnHqc6xzhvC2Z/JO1TbVAaxBsZpcfdbP16HSU\nBJnzbCoVzFzWyF+rTR13c7cn+g/Wu+QF3WmQKB+6GhVE2rDA1zUqG/W6KcvztNFxrBZRUQLXFfhZ\nQjpDXvGJEEkFKRAxNnzNbGVbtaM+BEC1RuXsOqXwLNdhcF6WM7PAINLs9z/KpQGYVBymjWNe+nPS\noSKUnGw/63cUQ2PakxTe+4vEUzYRCk1af5Bltr5RN+slhBbBrkcSHwmmr4aRQHi/UGn/tpljl67+\nqnKVITrsMLZkG+w64WA9xwJYjCDFbryvTUxNOxmnmkFHnXPFSIgkhxN8YuVMbW3VKWW1Km8nQj5Z\nqvuqvKA7qmqMK0SIaMAlGnxnZIPmitFw8iw/X8xvZXtYvNvjADDv5HWkmqJ1Fm7gFT5VduQyLx/g\nWzLU7YisMicPcqmesJqO6pu4skpDlQbTXOkgsgC6xVIvtwgFeaqNRCmdeGx/MwgA0CXPolIfP8ec\nrdk1NTOSNmozx+12Nhgqe/qCWh9ujBRfck+PMGETMxOFOVNe0AFQzRk8+XtH1IhqjqZUF+pJS5PG\n/PQP7HaJC3Jyea1YGuKTGeoC2BYuKAgdwjtE2BPMNmuFqp0GcARZjTvtunar/PKteHnezrKnuifE\njg8IJzNw2WPNk1HnMBqLoXHYbG6RKnOCwSKSmJHUI5QAPI5Ow/HhwBREg/gmRIP4e8J8E5l0wOuc\n36ss/mPl+kbBKpg5eUH3GnwCcK7IbRtbrDUnTqm0JkZpv5oLpP+fvTcPjus67wV/595z99srGugG\nsZAgwE0UBUk0o4V6chTall8cx3pxMnHJfySZKJVtniuJnZepVMqTTOUfJ6lXSWamZjLPWSaJVUkc\nZ+xEsizbtF4U0SKjkBQJUgRFgACxEN2NRq9338788UF4niwybckypXrfXxfAPWig7zn9nfN9v8WX\nzDW13zU4zxIgSaQwYQDedeml3ls2Ib4b8RYlpCzLvva1rwF497vfrSjKLY7qdrtzc3NJknDO77nn\nHtu2v6UXfYPD/1m8xIf/XZLsN1b8Xc19m5213p4n1ZnGa+sNAAQAuJnqyoojFFuKCavayGyLRY3U\n/unCiwAWsuIL7vTFwR4i+nhCdfyKA6Ph1Ipme5CYp51pJzb+fO2gVedwNJNnEk/ldy1qUtRwakjl\nsAimtsz10pYilNxmavWkjPuvERXVgRLl4kKxTguSXnqat8+Ek+tRqaS4gLMcT0JbWUzKT0eHCImu\nSkmU8YfzVx/Trj4nxgizFKQq/TRKlU+09gN4qHquldor/vB2/TDIR4pyV24ZwHpUIt0gQgTt1RtH\n1Pqi2j7d228rvifUMnee3br7QH7FZFEns4hfaa6XzpcjGK6h+J4aIZUzLgOIjIzHMvMM5XqOJ1Ka\nT3NrqptUZCBRACArx9xjjGfE65ZLgTYSYuWNPOE3Gm/3Sf5VaSKvjN6XNjtCKyF8Rpm4kA03UpuA\nnSaLTEReolKNi2B1z8ljjcxuRvb1oFrTOiaLppQ2MXWe8Y/Qr81xr+kPFbSBExtJbHDFX5GHVSl5\ntvUwSVtJiXSD7y9U1vfqDSrEQe/7seEW9KzaDeWU6w6pE3W9sty3tC0rLAbbNPPqCgliDRLzPaVL\nz/cPHDTXAWhSBOC0M30a01HG6ZvtxC5z5zHt6vPKKGI4ikJ1Y0Okf89HN5nxJ/EBB8ojyvpLGCEK\nB6EKZ6XNicyl5pOtRSe0RaJp05tQZxaAuaj2mHbVhULc2yo8B8pXwr1fEAc7sUWI0JrWoZ4xk2PN\nY5Ehg6c8RnZ10uro4ZivDsA9luuraaCAp2nCbDsJAs55li+GWSIvfu/hyl9920/4bRBvUUL6wz/8\nw9/5nd8BcObMmWKx+E3vf+qpp/7wD//wlVde+cZvHj169Od+7uceeuih7/TwfzXOoPokDlUjZ3Zl\n04ViqfGTwRGTRZ5QTRa1E1uXo8NqvSo5C1mxkW5/Lpz3DgEgGsQf9B643160WLRPb/ywffFp75Ap\nRe3IHtJ6W2HB1Pt0yJjMr9SBaGRDqiVRmAtTBYCZ8e5gGADXndQtYJD3ypGRbyE2jAu7AHjjkd2S\nqLgRAZoUdWKLVsJ92spiUgYwpnaeUC8MifB5PupAqcpO1dgm9B3Ies+zUZvFJB5BtYW5qNaMCj9S\nPEtFBgDU61al5IXWbNFsE6QVwKnOHfCtQd4EMKL27jRXW6n92e5Rzy0BGGxVBphIrYCl8lVMFrRB\n+k/TaaCYPON2mIvV0FRSFGUFAHSPcY8JRbgFofpSYgo5pgNiontMjtHf5Wtd3R32mRocyK+s+MN+\nu5rbkmM7+vae7JsVb/dJHgv5yejw/57cN662PaF6gUpw/J0bWKSOlFfCTF3jZepibqNp2lWhRb1u\nDcDVthpObFIpVXb1TI89Nara9dbNad1jSc3ZEcrbXXsVQJk753szBW2wV29cHOyhtaDKsUgVbWSD\n9klhczT2mFeOWCJnPEMssVQm+vkzvSN0GCop7nlv4l57aZq3H9OuLopCI7NpYzTCHSdT/6P8MhT4\nTDay9H7R/Iy07z40hrLweTb6qFi9L2v6jJ+WRyDMFWbbiBdFYZr1SCXEFMkfizvm3RoVM0jvkUhX\nAE6G0/WwFGX8fx3sIR6S55a47qQZN9dLXj4F0ATkQnveKyOVWSojkVMFqi+FQ35YTDXPABDlYgB6\nT0oDReIpy8WFcs+tOZR6b7SmjXwrBfCOTkhvhXTQ5cuXP/KRj0RRhFtYq2ma/sqv/Mrf/d3f/Vs3\nfPSjH/3kJz/5HRr+rwZJB5V+/1eOqHVHqM/0juS4R7ycEbW35ld2AGBekCfW0Va4XT766NBpUvdZ\n8Yf92KBDjGz1ANDcJXkhIadcd4a0HvF+aBtFNfFGahMIjXZYh9X6ycGhE7krAC5HtSBVdTm62jgk\nBUqmxzDcgjbodWuy1UszXtAG1Ad+OH+VZPSGRAiAVEkA1IRDgMAFKe+BE0J9Ou0DeI7v2mGwNxP7\nelDtDoZNq0P/NYAydwB4Ql1wdpHY826r3k2sXpjb0V2m9yEJbBaqAIgX5Q77WlfnMUsUoTbUrBzT\nd7aPPjwDT5HI2+8+T2G4AAraoMjdcbV9XFnb4dWTviohA9mzz+HZr323pIPe1pOcpIPw6PeVPnAM\nwPWg2muNARBaBDllngFASqSs1FWbRc1j/V0+JRvCQG7/Ft/KNVQWM6dl4eDAXFMlPQEQFDJtiwMQ\niRRVo7TWSmLjYGmRyrazvDGF/iYzTqTrX5D2EJ12hdkXsuEPsiXCxThQAPzpyqNSoGSlLnyrUKz3\nWmPC9AEglSGn36jL5UKhX0JM0hb0JeTrwqI6IdF1PxAv9WD4TDZEepYPE7K8IUwHyn1oAPDASc6n\nJMKn+G4iY5AmFtGDKrJDtWtPqKSx5GfKVlhIAtvaNMKJzSQ2tC0rUcBjREYmTJ/JMQZ5oUWUk6RE\n2v6RFjE1EKli6n1a9TNSd7cYnEGVGm8ACOvYgv5//MxT/1066NuP5eXln/qpn6KFeivxjSttamrq\nkUcemZ6evnjx4le/+tWtrS0An/nMZwzD+OVf/uXvxPDXiXlv7PK1d2keS03RKAbWpuHWnOUgD2C+\ntZ/0DpDKj468dNqZviu3/IC6CuAYmgZLtzQNGv42m3Yy9cXrD6YGxyCf+hIAGBl4mr9phKYe9EYA\nBIXsqjFm9uWuIp4ZM4n1TUwgAibMFF60EPRYskwAACAASURBVC+KAqkt3HBrSGQeA7ESweqmyp7K\n4lFjhZQfiWw7KzevoLRbDI4nGwH4uLI5l4wDmJeGzsgjE8IlzR4L8d+JqZrsLmalj4irLegnxcSD\n8vqiVPCE6sRGjnuGFK/5lSQ21hRfleOD5vr9hVcJLLtNG7IjQs3aLHZsxYEyF9VIV6bpDym1gZnx\ntDsamMJuSdATtJV8DDFQEkfj0wOtJ6eKLMfoXM0LlWl6ioMKG2pFGdfl6FTnjmtGdZCYB831B9TV\nKvNOaKvjmbsmWV9XVk59qw/1TYp3xiTvxvbS5p35m0ZoClEMaA9h6n1Suck8I7dcYjFLTKF1dQCh\nlTI1GDG29umNc86Uqg16Rg5ALpHEmhoFCgIlCLjeTYQed28aaj6Do2ExV6i4V8cPwXCbUWFNLb/b\nXGik9gIrzrJNAIZITSQfZEvPYWwurrUTG8ANt2a2VTlGP69wq+fExj3j546o9TmSe/fG7rWXbCmy\nWURqqh44fXwPidCT+JTog+EwW72B3AqzJ4Xzf6pH7k+bpSz8f9UpUyQAXCjkunKGVReTMhlSuFCr\nsvOIWN+VeTclc1fmjcNdk9ozyvkAsi9zAFtMG1LDLab9bTZtWYuXoxoq6MTWQI79kVhtFkGpHZCl\nxNySQ1MPiwEDUi0yr+Y1noVDUjQS7Mmv0rnTFepXwr0kRjwrbf6HeOkVubw36W9IJqRv6ZG+/eI7\ne0I6f/78z//8z9MioXj9zeNTTz318Y9/nK6feOKJj3/845K0/QQ8z/vEJz5x8uRJ+vIv/uIv7rnn\nnjd3+L8VdEJa/k9/KV0qhIGs6SnhCHQ96XU1TU85z/guj0RWkMpcd+7KLc97YyNq70eti45QAFSZ\n92RwZIcQThoNpPeTxEbVrg8S03NL+ZsGfNmtJVaPARhUo0KxHmXc71dkqzek9SgzbZMwnNp2BQCQ\nrd640WpGBRLd2QoLqVsg4UtSnzSl6H3K0iPJTdLR8pn8ilwmgayOpJ2UxyzEF7LhpbjcTuwbbo3U\nYDHI7669Oq62AVwLqgAGiekF+YOlbYjRCW2xyrxFUagxb0fUDkDTHzqQXwlStRkVolShIxSdcigz\nSZ2i1WMsZlnAJT3JAu45mjXquAWR6bGRb9EbRUWbbeU07h7U68tx+bBa/x+wUBLhaOYSJ+YlPvzn\nT21uPHX2rT8hvQMmOZ2QvMMfae3+8eqK25i0OM+SRNL1xHFUzjPTDgd3dOhwnwQ2bedJqYQIpLQB\nImmPrlc29f52PUCO4VtCjQAwz0Cuvy3JqkZy38r0WKiRqfcnjU0qL1P1m/6qbmIVuUuKJ2nGZSmh\nQz/9tBfmAMhSQu2lmtYhLY8TbLXF9Enh7Mo8EuolTi7BrFeZ9dVsN2G+KeUAqDH3YbGxxTQqEjhC\neTGaMKWI6nU79iuGSNqS9unkyCVvQpOiMFNJd/gD5hWSIFmKy1NKu5Ha28lMqABIgHXNrwxpPUOK\nb9T3I9cHICIdckp40SGtB4CY9Z3YusdcbSb2A+rqYbRNJLsy74603WFal2lP8d1/9dOffQefkL6D\nCenP//zPP/WpT/2zbePrrNUsy97znvesr68DeP/73/97v/d7/+yGNE0ff/zxl19+GcDRo0effPLJ\nN3H46wQlpM5v/WeqY5h9OVEEj5lXjpDIyPUL2oAaPJDTotkG0OvWKJFQN3U9Kv2wfXExK512pnvd\nmlAjq257+RS5/j2FhRHuvEe6QarbxFLyM4WKdaduHlMHitpQBwf6JAW0U5dzYsNW/CjjlIEoUR1W\n65ejGqUfL1NpbXcTC0BN6+yIN4+rbepLEyKDFMo1KdoKC2mvnFtTGc8SR8NIwD3WryUAdtde7SZW\nr1sz8q0ddeQxteMJlcqGJJrgZOpaVKaPJyJ2zMrNHTeXtahMKZNkWOmN2lHwJMHZEbV3ozWda6j9\nCQcAV/wdgT6qZ5Le63jmjmZeR9ICyCUR/q40m33xH17+u/m3OCG9MyY5JaTuv/tw53sf47pDRo5U\ni9tt1QGMq+33KUufDw8QoqHGvJ1PbeIAEWvHYpHNoj/dfEiWEsIvACBnP7oHwFpUJsGeMndGuHPa\nmd7pQhVzmyT2QyiGnY3IzkUvzJFuPTVuAVwPtl2CKEPQouh65XvLVzyhUh+UlIFy3NunN7xMpbmE\n1xpgtDUc4c4PSouECD8nVXaLQYvpLhRHKFRRBLBbDABQyQ4A/bMAGplNDgD114TAz4STJGpFzWNi\nUFERG4AhxR8wr5wMp2lbuWMhRm/ROWcKwKSx+bg+B6Aigh+Jrz2tTB1NNkkj/H/+2efewQnpO1Ky\nW1hY+OQnP3n27Fn6Utf1IAhefwiAU6dO0UoD8IlPfOJf3iDL8q//+q8/9thjAM6ePbuwsDAzM/Nm\nDf+m8aH8hTm9QVKPJJRgA4PE9PuVbLkkF0RqBUyOe93aSHnl5yafAkBQHADv1a4vZEUC4xn5lueW\nqFcpS8m8N+YZm59Geb4zzSJ1d2WRjiN/0/oeQ/Flq5daGBRtrjuqtX2umlLaS3EZOtqJTSeGiuy0\nUvtj2ks3WO4ytjUZp5Q2QZ601yb9HrP9E+wVIswvJmVCnPfC3G6rThnCVnyn0DZGeqB/LTZIZ9PL\np8v9CQBmvpXj3lFj5QRbncn6ABakfIvp1EMmYbH/ZJ7ywDcl417WOidVtp0jpKgqObO8ARM2i2nj\n2RDmol0ijQayt6B9rl6NUIUUlrqDYShoJ/Z5t2aul7jHnEr2BwC5YDzGr00IF8Cz0sRZb9LzpyzM\n3/oDfYPxzpvko3ajWnl158jbyGwiDAFwoHw5ngLwPmUJwIGsVxLhz0iXu0wbTb0NYf6iuIgU1+X8\nAstj+AWyrgCwFRa+0L5XleNnY4OMi4Tpd02ryF2CMNA+CeVGlCqaFGlaFCo+AfYAkP0ESLwR+KHK\nP9osmotq1E+tyM5PF148FY+vReXt/0FBkbu1UseUIi9V/96bAeBnynapOSrrcrQelAC8375iI34x\nmqA1YrHoMson2QQAZDjEOgey3vFkQ0OcU5yXkt03JYsaTsdY80NYJuFtEpvYkEw/5YZI5uTyTNa/\nKZkfVq77Kt9iGgATyRWt9JVwL+Ge6mFpKyzUDetxfc4UyRLyNovrwrQREzhiR9/y6+kYAItFppKU\ns/BZPuExvije4dyGNz8h/eqv/urnPve5nS/vvvvuH/uxH/vFX/zFbzrwmWeeoYujR49OTEz8q/cc\nOnRo3759165dA/DFL37xYx/72Js1/JuGI9TrQfVc+xBSmYWq0KI9peWSsdnh3vsnr1AjtMX0u9Mt\nn/HnMUr2kY9gHUA5DYclfw5Dd5qra1EZak+Xo/nWfju3eae5ShUAFqkAbtT3N8uNEbVHAIF77aVL\n3kQkxwfN9etBlTTCHaGOcIco5QSXWMHwiNr7Le/4Qb3+IX0ewG4x8MAnhLuqbVS0YDrtn5FH5jD0\nqeh7yLfGkiNbj+aDGsni6XL009ZFABbiL8dTl7wJVUpUbQBtUCy5AG64tZ1qyTO9I19I7wWgyvHD\n+avNxJ73xuigZrLopDIxI3WPp/V7083HzJdFrGbFbro18iImDJEsyvkV2KQg/rDYeJhtbGnaDZaD\nBQDDwp/DkJepD6iri0pptvAi5bNuYu29Y4HgUqRlDuC3nYeozrmntKzL0bC21br1x/nG4h05yQ/w\n1g0WPe0d8jOFTszLSvmEtghgmvU+gZcNlvqxPD00nykJb1XiTO1lloa4kPmkIbQ3xWjmgsNR1Vl9\n88ngyJjaea92/UI6shyXA0td8yuqHBMlAOZCI7MB3KetnAknD6v1F9xp+iymw9blqDbfmaaiFpW1\n6YYH1NUjap1OaVQPpxP5rNz8g94Dzajgx8ZVYMTYov+CdI2bif2YdhUAdHw+PHAmnKzIjilFS3F5\nj9Imxi4A4mn8hTjwoLz+vDJKdrEVOSBAkM9kDzyAHDD5oGj2YAG4677th3Jn32ChIi/uXUZ5ScoP\nAVelwv1p83DWOc7rvsJ9JpeVkGTIXSgNmA+LjS1ox7M6AGiY0vpUYyyKcAOWIRIfvJSGl3mJ/Aa/\nX6w8f4uP8+0Zb35CIioGAFVVf/Znf/ZnfuZnzp07dysDT58+TRevX/i+++67abH94z/+/yQ03uDw\nbxon2OpsYfNCbvjk4BBy2/0Mi0VLrDwX1eZQ2yleATis1mkUKXQBqMJZTMqXvAnCdstSwtQgyvgL\njXtNq9MLcyPlFTr9uEIlPeMj2Npkhm1H9KUnVE+oJKftCtXPlGZUmDQ2/31hDgDRy+cw5AjFgbIb\nA49xCOzPeqfk2hVeshDX4H2Yf50MxR2hnIxqHzCvOFCmzSsA6KOf/uw7zdVrQZX8yqirJEsJcTvC\nTPWCPCGvWF9+0RsLClmiwC91d1v1dmIfUeuOUF6VCmuSNROWAZzsj5El80sYqQvLzbbRFo+rlwEs\nIf9iOEGqEF6mjnDHEyrJGn0l3AuApP5JYcySo2m7vQNDP2iuX0yVG24tf63cbF8tvFWqKu/ISW6J\n5DHt6qJaOBNOVuQGOaU+mq3STwNw0mXY6FgADJFMiX6HaQGsl/jwTNYPUALQlrQbLDfDuouicJ+2\nAoAeYkV2jutrw6ZP7nMQWGXWfVLjMso2ix/X51worrn9WmTpvcTKhDoDx1humbYjthTVhUXAsyn0\nJ4RbVbxFUbgc1ZxM1aSoyN0mACDM1O5guFpYL3OHzu50vFhMylRjoMIdyRkDcDK1KjuUqGwpWhSF\nL/Rnd1arKsfkTzjLG57EKwg6mfZItgwAp+8GoBrOplfdYFZJhGBoS9oVVrIQ35RMIp7PYQhATfaG\nhU8IuhrzVmHtz3o+41tMI+OoALIu0i7TyL2wJMKOpE2n/efksS85h76idoDnbv2Zvu3iO4Wy++AH\nP/hLv/RLu3btusX74zjeqUXMzs6+zp3Hjh377Gc/C+DChQtv1vBbiTOo1uCdYKu1vLtTVl7Iiu/V\nrg8Ln7SoLTUiXXrqBllMvZDZAKalzsNiw+frVwprZBhjs/gv3bvK3JkqzFFZj2gNd6dbbUm7gtKZ\ncPJL8SGyXfh8coA4fdeDKlVCSMO7mNucb+2fl6eLZrs7GKZz273Dl0wpeoSvY9uKJrk3a+1N+xuS\n6TP+rDSxmJUelNfr2K5315h3IR2h1Xg5qq34w55bYqks1OihyoXLUY1Ej5LYcFaHE0UkCvI95haE\nuaZ6jpYkEm9l1qjTt3RYWO7sWe5PULpS/e1mu+axVEE4sQmAAB3EXlpCnmomZFRBdZ55b4w6Ctdz\nVdrenndrAGQpGTdaAKj30HBqVt0+V3OoaYc7B2LlreYhvcMmeZepAB7Bek33LMSTwvHA20zblXl7\n0z4AXSRk7Lso5z3wm5JFVSkAF6Xy/qynI51O+9Po35Ssq1JhURTOhJOUlijmMGRKCW1NqITgCHWW\nbX45nprm7eW4TJZaSGUALFTlQrvhjkFOG+kYAMKyztg3bW0FArsx2GLapHAaMD+kz+8Wg8t242nv\nEGlvq9qgmNsEYEoRMpB3EQnVvzAYrhbWyQnwkOgQDfa4svaVcO9htU6+l7T9SmKDybHYqvh63Myj\nzJ0/7t7vt6sjI0sNpyb3LQAZz3JbcqrAy6fg6YHqlSBVu54VZZzUaY+h+RzGaszbLQYnswlIuJCO\nzMrNr4R7qSf3CNZvsNwZVGuSB+A46qSR8Tlp7997M2t+5f7Cq7NokIYLu/Un+jaMNz8hffjDH/7w\nhz+8d+/eb2nUpUuXdq5fn22ez28z9aIo8n3fMIw3PvxW4gi2KiIwRPqoWF2TLDLwPiHWT2Lsyegw\nqVDTfmq3VS9zx5aiHXrpg9r6VVb4ejq2HJc7sfV++0oV3o9aFy+kI43UnlHWdosBuYCT8R2AE9oi\nNHym/66AqwTROd+bAVDQBr3WGHJ9lsq9bs1qq+TPVC2sG1K83J8gdN/vZ0epZv3f/oEUQapSVrNy\n0eWotuDsuto4JNSIqO+0RP3YIAkTllNPRcfIfD3sFPM9Bl8uXMyqa/8k1Fxz5EBvvwzAtiMAYqDk\nb6Jz4w6tkAHQPMZi1ts7oPJmlEsBGHJMFoVhpr5PWbqQDf+1c1eYqRcHe9KMY5DPbcmDPZ3dVr1b\nSYhxtRSXPaH+xsjT1F5+2jvUTSyCXZl6356pe+3JnjeGXF/qFAuheouP8o3HO3KSjwqfZAtOZOul\nLNwx/wbwZWWcUGRerAIIQnWHhUbniVm5OcHc0dTrSBpx2u5Ot0wpmdZ7hMA8ntZPybUj2KKTgY2Y\nxLzPexOXldp8Z/oFbDOKuOInMJhnCNO3Fb+X8QP5lcpriDg61vy9N3PUWDkZTZNzKznmXZCiZmKX\nudO0OlTi7rXG8nU+h32Jo3kzrlFuBKla0zpRxpv+EIBz2dRKaamK7Z7ZlNKmVyEIn6H4SGV4Bo+R\nQEkHo5cxGhYDlus3emP5mwYZQXvlNFVkAGZfBuR5dZor/rjR0uXofcrSk8GRRaU0H9TW/AqBbw+a\n649pVxvC9IT6XuX6sPCvsNIh0fmB9AaADtM+J23PqxrzDup1AJe8iZZmk2n1nlt5lm/bePMT0rdB\n8QHQ6XR2ru+6667XudM0zZ3rubk5glS9weG3Evuz3ppkXZFKAOrCpIPFs1t3F7TBoD6R6XEYKFaP\nDYbSG4M8aq9eD6pdr3zVu1NokVmNAFzyJu63F83XFEe2S3mycyoePwWsReU1vzJutPxMKSkuqf7c\naa6ec6ZUOd4KC4QT7XrlYmWdXtFesACoSrE7pABgkSoHigfcaFeXtYgA3wCoFLYelRpOran30/XR\nv7x8BIBlx6YdisTKynEUqs7CjBxDKojBUKqa29hLtVkMi0GmxwMdMFwYpd5DRwHIfQn5QAektuLs\nCaREsuo8vqbLAJtIBU+RiwvXc0Ehi4yMsMJRqtyo7xemzxX/f2l+oKANalqnIm8L/k8Pt4/s3QJg\nIiG4RCkNN7g5lfWfFROLKHy2e/Th/FVSQqK/7ZI3IeRUDhRruTSoRkL6jlO8d+IdOck3mHGFlcBQ\nF+a03CNa9G95x3U52iO1v9Q8Zup9zy0RC/UGcLz0yrwztrR+Vzjknrfrp/QGeQVBwGZRRQqo7THN\nehey4bpkNlJ7OS4vOLtIjmFI691jrt5jrjqZSujwQrFOrADDaL27ttDI7K927jQUf8UfDlQVQJk7\nTX+IwJafu/kw1537C6+eyF0h5VZXqOtR6f32lfNr9y5cnAgdTUqkbiLli77EU/DUb1eXtRJTA1J5\nEKmiaoM/co/Shz6Bg6ioXtAGvTDn9ysskaVEAsBjqA3VczRz0+7nuKanKPrSQAKQ91gWcG88SvMu\nk2NrvQTYN/Jl1Zc+WdxvWp16WPpQ/kLNuugI5Qn1gge+CeNhsTGl9e9K2wtS/nhaH828l/jwZZRf\njCaOqHXy2mhw57w30bo5nfGshzEA9Me8g+N2EVf9RoTS62/o9u3bt3Pt+/6bMvxWgrYtR8TWp8N7\nyCWvOxhmajCoT2Q8QyJnPAtNSUokq8faW4fcgrA8JsdwC/qpm8dkq3dXbtnJ1HZinxTTAHYaToQQ\nvcdc1eUoSNUwU4M0nk9r237n3AszNce9fYVXCRFeUtxohHtuKapGAMIhlyu+rfiRziermyaLzEr0\nBJ+7wkp1Yd6HxpG0/Wn1kClFhHM1JlbJpjrVnUHGZSlJAjt3NZ8lMvRY7yjcDoNCBkAKlLAYEOmE\neUZuuURvhdRW0nLsDvvvHz1NWNVZ3qjvs+yHI8LakbulrfihV2ZyrMpxmsra6rAcYwAj0eSDlVf3\nKO35oGYr0bTUeRSrvuAADJGURDiV9cuVJSlW9g13ADyBf+Ku/onk5a7QFqX8S3zkMNo3WM62o6be\nWC+UwppqZFwxnFt/mt+VuM0n+fWkrGVFV6jNxD4jJknJkGyrTjvTRbNNqh9y3yJ9gZeaDyYK0mIA\nYCsskKTQQb3+oLxOjnamSMDgQnmAbXw6vIcO6ETHAdBwas/6QyRTAjnlVm87G0nxml85I0ed2Bo3\nWt3EcmKDpn07sY+XXiFrvtn8P02h/+nwHgCzytLnowPz3ljYHP1rb0ZVRDiU8HwalSMmp0Ol5W5i\nSfWJTI+1rg7ovpGXC21IiRMbTmzQSwC4tlWxW5KZSL6j5ezQrSVZqTtbWLgeVDUpMqbiWbVNRhgA\nemGOYNxNf0ikCld85haQGGjqAOx2SsvT71c8NUIeAIjtZCL5geTGaOZ9H1ZCKHvTfgG+zqI9cfd9\nMB5WNs6xSk32hqUbAKbtzuLMKl5rcb3gTt/i03ybxu2SkOI43rmWZfl17tR1/U0ffiux69UrPznl\nVVnv3fLGhmJ+Ttr7JenQmNq50HkXcn2SVKHOCnLxoBqZbZXk5tIgDyAJ7Hl521wOiaVJEUHmFpNy\nR7IMKZ6WOtNax4FCgGwyfZk0Nqkkct6bON3b//HK107F4wDuK67USt6p6riXqYQ4Iu0GEnKdkbp/\nl03ZiM6Ek2cwSfSjnQ+XEe6clyZKeXfB2QXfSuSUhergQF/r6rwnBXv8rNSVOkWrznWeoWX2x+Vi\nsQ4TvVxORDpLZXlik0zDjqf1V1GoKt79aXM0czckq8O0L2qTi7KzbeYkReSY6RuuO5wCgJwCmO9M\n181S1ysDaHK7qnlkqjYpHGTQmaW1xo3RZbVry54plBie1WXaVNb/Hv2aEd0N4Eja/gHcuKlYW6p2\nBlUb8X9dueh9e4/2rYrbfJLHCysz0ujxtF6Sw0U5//vRUQBkakzbC79f4VYvDdUEklFukIIUAHKD\nNKS4GRUAVE2HoDeNzP5BaREMm8zYo7ShoCo5BBYdL7RbqV2RnenhdiOznUxtpfbVxqFCsb5PbxBR\n6SFr0WZRI7PJJ4kkf/4iO+AItSo7DpRPh/csOLtW5PhUfIeh+F6QZ6WuVwIdgLx+RR0oiaJsdA8m\nCsiLHSQZZ7gAhrRe0x+SpcSJDVL/Wtd6gxETgAwY3PsP9pUa84aFv6ldtxCbItmf9Z7lEyPcaSa2\naa6SdFDTH6IaXVOOvSAfHm0PaT0irUNOqR92Jpz8kD7/PBslrqvP+HU5vzeFjqQAv87smnDmpSGf\n8VVm/XB8HUDA5OK2cRS/LufPKRUAK6tn3zIo6XclbpeE9O3FNy7R7/Tw8Or6xvTYdZbvMA3AEWzB\nvvL33gwbaiHjiYJwl8/UwB9Kxo3Wg3od4yDOac72iLIXpYoX5EnKoefWUAZ1nkhxlVz+5uSyI6tV\nw3m3uXAmnPyY9lKL6QDeY9940RpdyIoAWqltS1EDNgBTiu5DAwLjmft4unCWD68yCwIXxEiDFjxv\nL8plL1NJ4b+V2s3Efr99ZTEpd7ReqPgAemmNpXKUi6MRV5YS9Mq52qofT0S5GIlsttVBMMGGWobi\nq9qA6vWuUE/F4w5XTobTAIh+ueIM++3q8cnTVdkhleitsEC9Xwmw6hxAOJQkCnSPpe1SnmfL+7EM\nzOtjUarMG7Uyd46o9e9nK0hR2ji0q3LNm1qX8j6Au0+rYBCxekfaXpLyz/Fd2JZ7Mald/MVX19/I\nZLht4y2b5Mm1lXuz6VelgonERPIx9exL6khdWJ7eaHO7GRWEGqlyfHD8nCfUE9oigdwMkbwqFTZ1\nwxHKi3wCAKFJNSkqKe5JNXIz9UF5/QelRRPJ4aTzUfsagAUpfwybl3mpnIVTWb8kwkDi18dPEq2t\nIcz3KUumSDaZAQkHsp7P5MNJB8AvSec70HwmrzDbUesnhhYXsxLpY+E1BROqB45UFpfVCQApSZm4\nOvGvhRohVWxtQEKLqhxHqULMWfKcJXlvek8WRWFBFBuJDeBaUG36QxjkjXJjh6gLAL4Fq3fDrUmd\nItNj45WSUx6WTaF7DEBgisxwr/Ynf6s/uYPWIyL5cXXteFoH8D7pVaZER821dmuKGE4bkhVAJoPa\nu9MtAPdmrZII+wtrX3ojs+G2j7d3Qrp1kf83Pnzrg+/pZNd1pKQgMochR6gH9XozKkCOvbzCPAOp\nnAK+1vvSxv0AtK4ejXRlKUndAgxXbRZNj4mB4hwJDlSvPKGdnxDuHWn7FVb2mdyCfoWXHKEQgHsJ\neZNFv+F8L1koDRJzRO3RDpQWAxmf57j3sXD/kNZ7yFqcUbvEsAPwEekqJLyEEZvFjqw+wDeWkL+Q\nVbchrUl5mrehw8tUT6haOSJpyIZTSwGj3IgyHr6mZhaYIit1ZYCKh+3EbgPbMCQdndiilJPxLF/n\nCnC+f1ymz0BftngmFCEGCgDk4t5qnnczzrMgkQDoekL1n/TGiKHHq+MVjM/PoQYVNo+PoWl0h/2e\nfDTZ3JCse0TDqqwhVvb023uyto6UGu9TWZ+2CF//gZlTTy28kflwe8ZbNsl3/8DsOalC2/MNyXxZ\nHnKE4gp1hDvtxM5xDzo8t3S+XzHyrc+EpSJ3m1HhXnsJGQC0UrsTW4PEDJujmR7/0MRzM1L33qx1\nPN0oZO5z0h4daUfS6KkdSzZ3XvcVuUyyPfuz3kzWh4QDoneVFb6a7a5KDoC/woyNCBwe+A2Wo8MK\ngBNs9TLK01Knqjq0KSE3JtgAMBfVxisXqrJz1p/0MyXMqVHGDSnBa8TqS95EkbvdxCJtLRAeD3CF\n+mRwhBR7dTm6T1v5Qm8/qVdoXV3vSWJrl28KHjPJFAB4DN4elmOkHR0wMgBN2eQpGWZacZp6pUQR\nkZFZdR4UsuWhvKn3TTM6FY8Pcx/Ay+yBR4Kbup/qLBkVbkXp7AMGsa2zaCrr7+P1a0mNjHr3vr/w\npaffyHS43eN2SUjfuGyyLNuR5/qXkSTJmz78VqLGvFNybSErPsA2KghqzDuVlE/39qe9cr7O5ZYF\nwK64QSFrYhJqxDwjUUCt+4Csj/IqzfIhYI/SnsPQp6N7ACAFOazMss1h+B7jd6XtCeY+rGz46vbG\nEICO5FlzYgn5k+H0grMrCWzT6hhSG0pJBAAAIABJREFUbCt+0x/6G3+ItL1/pHh2mvWeaH2Y/JZG\nuFOVHFLomubtLzmHKPdULed9ylJDmHVhQQWAy1GtVFpc8YfT9VEeM00Rek8SimAxQ6ucBdzntcF4\n1OMp6Y/VtM6pzh0EtdA95g5H+l1LYaa6XlnbsrQtnuZTqa1ISATAcnF7qcAiUe26AOxgcHXvLm6H\ndktKTAGesVxs9diytWdNd5DDCHcgoSp5pkj+L37YZvEXpD3o3Wez+BDvlLPwZXnIlJJ3JxtLUn4q\n628wa0R8Cx3B70rc5pP8e7LNn4rSDtP2iO5o6upIXVk5E09e7U+SOBZLZcipkFMATmyQHM4Lrdmf\nr325LqzjypqjKQ4UuxgvZqVZaZO29n+r7AHwI/G183KVshGpKW5IJm01dJEeTTYBUPHKEAkpzTcT\nez6pjattW4rO+pOf8e/Ha1xs4kc3nNqe/CpBEhqwv5LsJXv7HVOYx/g1EwkMkHeRA8VGfCGprkXl\na68ZojuxsZLxHPcaTo1FqpDTYm6zpnUoFQH4knPIVnxN622FhdGp5XG1fcmbkDMeNEfpDCTHcAtC\n95hcCsRAyRLZcVQycc4S2dvjAxByylI5MeXIyLjie0H+YqrYit/S7IrsPM6vPMV3E7zWFAnheh5g\nqw1RKCEEMD00D8BtjddGr3wbT/ZtFLdLQvrGqncYhq/Ts52f/2/yMDuj3uDwW4m/dO8iCTgCNZQU\nN0hVW/G1kSWMYFRxg1Rd8ytiq4JEhgph+ulrvkSGFBPcs5NZ+/TGWlRuJnYTNlUYfjx31kJss5j0\niV0oNyUTwNFkMwAviZD+gOtyHkCVeSe0xYrstGz7an9yLVVsxd9t1f1MafTGmBr86eZDpGPfTawy\nd2bl5rDwJzLXEMlo5j1hXOkwjUrVFRFMwpnO+oty3hDpOb3rCMXW579i7qX1TKpfhHCVkAhFSImk\n92VvzB1Re/WwVNAGmrG1FRYO3HGFKL3NxG5zdxkTxkTbkKIwU7OXpzxHg6PJXOQrvnNAwJcdFApw\nE1MEpgBQefASdbkOap16WDrfmxGpcrC0SBSoHymenRL9YfibzNgtBivMviKXfiC5AeDv+SiAogh1\nJDsY5ds2bvNJ/rI09KQ6fSDrPSNNmCL5arYbKSqyYxYWppR2Lf9PDpQz4SSABWfXjH1zxR8eMbZK\nikuMImKS0dZqWuo0hLkmBZdRJkOHeWnIEEnAZGqfBJB9xvV0+5gLQEfytDJliJS4TRbiEe68V7v+\nJ4OjW2Fh3GjZit8Lc75b+FKQp8YM5NTPFCK9OplKQgx3S1tUdRwS4R1JOwD/QbH8ilymV7wqFR7j\n1zYVoy5M6k5dMIYbqX3OmTpYWtwRoNujtAE4Qp2RuqQqOcsbHzEWiiL8Bz5q5udWmL1Y3FbxIeW6\nXremDpSkEGU8Y1onBKJQJfOUHecUezxajssAOrFFBUOTRbYU/Ybzvfv0xn+UXz6abOpIKkoHtvu8\nc9cdaRvAILbDVsm69x81K0iUBHhDJ+bbPG6XhPSNYpTXr18/fPjwv3Wn67o710eOHHlTht9K+Jly\nurf/nBz7sSF1io28K/ct3WPRnpuqlCw4BWJ0P7bvywCI67qYlEl6oCo501ZvURTeq13/Srj33ebC\nYlI+rqxZWgzgQjb8ANswkQAgcTYqTbzEt20rATztHToo1+e9GhGJqED/c8PPPSw2rkoFAH/kHr13\n+BKpRQAgCYb70DgWb5ZEOK5swnLjfmlZlDtMW2XWEvKfT/ad7u0HcH/h1UvexJ3mKkm2kPLeUlyu\nyk5LsRtyOtjTIa1lWUo8vYBBfjlV9uRX6QT2fGKe27zznJyael+Vkr164wO1Ly9mJdI5Hrv/tClF\ns7zxYjSxHpWo9e25JRaq4Gl+TQPQwrTVY6EpVtf3SzyVxiMA1/p3gWdRIfl/6o8glauFdaIJk5Ty\nB90Het1afk0LCtkvj3RHjC0l+aqC+q0/0Lc+bv9JvigKXxdjSNFMbAD0vMbV9lJcfiGapve/ldof\nr3zNEYqjrZBNA8la15j3X/izcyiDbWso3JG2j2GT8g2A0cyjzRCAl+WhC9lwAzaJHM6ltYuDPUSa\n3goLSWyQIvhXFf89pUtNteMJtVffL7SIag/kmLW79uqPWhcBnEjXSwj3RF0Ay6xIv98DX+WWx/iX\n46nj8tqpeNyWolk0J+GYIrFYPC33GsKsMdfmUcuwAZzIXXGFuhyXiUX7ofyFYeEfYp0VxW4I83el\n2VlpkwzRTZE8gvXnMAbgsFqvyE41d4WExslUyUZcF9aOmdl8Z3oZE6Q2S4ZJsiK6xWA+4/PAw/mr\ny3H5i3zyf2N3k0Kj78mexKmj9vV0zMnUJ+bGAbSgA0/d+gN928XtkpC+cdk0m83XWWz9fp8uVFXd\n4Vu8weG3EsHFfWkt8Uz/3vKVdaM0SMywbyWK4Mu70raiJTIAWY+/lH80MEXGs0JlvRfmZCkZ0nrv\nt698PR1rJrajtD2h0jImq2NHqDaLlpCfQv85jDWEbSGiFX7emyB7Vn91gsfsRn4/gBsAUXn26Y0L\nSRUcU6I/IdzPqp8nLYa9aT9gsp/xUhYe4WvIu4npDzb2zA92g0EXaUmEd2VtSDjGm7NDjWNoeuCX\n843FrORkapU7x9P6D2fXryv5q1LBVdQgr5JGER31dPumyaIR7hD2CcCDpfULheFGap/q3KFqg3Zi\nfyZ4lyZFTX9oxNh6r3bdEcqj2WpV8xqq+bR36F57yTPXydZsrNYxpehU547UK0VGFs24AFRfiozM\nKDf82ABAZm5+plReU/WnbaZs9Xp7DaTyQ6VXTvf2F1L9Nt863uaT/KXe/rB7dETtHdTr2wK+wJpf\nIcg1gB0P4gvpiMWis/7kUWPFZtEJtjqeuQA6TBsS4WHWNpFsMe0sHy5nYVvSWtDvS5sbkkmn2ItS\nmVR8iOVKhG7mGT7A+rIZYzCUqr4UDkVpr7xslwFUZOe+vV8k4+PjyhoA0vs5ka53mEZAgM8q+8iO\nb3/Wo2qhz3gpCw/Ivb1x/xDvEBLdAz+Stkczb0My6cRzg+Voo0MnoVm9CR2OUB4WG0eTzQ7TDqOj\nI3mWT0Bgu00FkBUTAIJ4HEZ7JusfEe0z8ojHOIAp9Jd4/kJSDVL152tfJgDtJW8Cit+Vy6RdSRLg\n572JfXpjMSm3UvvJ7PBj2lVTJPRLKiKwWPSgsm5k6fNs9MVo4r8npLciFEUZGRlpNpsAlpeXX+fO\nubk5uvjGBfkGh99K9MdDdaBEMC7036V7LFUEv2GpeuzsCZBP6TNU9aUoF8tWT8QGgB+q/GONbesM\n3Sc1xrm7xqwPaktXWAmAI5RjaHqM02Iezbz7WJMEgwH8Z9zzkLX4TO9IkbuYWK1pHXLYJET4kNa7\n5E3UtM4FoKp4fyVmLqe135L+q89k2pA+VDorxUqrN97p10q9sMO0g9nWMiuWRAgBAIZIiiIsS6GO\n9LQ8ckw0HUkB7Lmo5ihqjbs2i4m6C4AcmMgN3RFqI7WrktMQZpV5F7Jhumeaty9RwyxVi9x9t7kA\nG4tJeVj4FotflQqmSKbQ/x+tsxUR/H54jLhcFwd7bMUfMbbuuetlAORe0U2sNDb+fWHu5OBQdzB8\nbeuu1ApkV+/G09FId1s0Wou47pASxKmbxw5Ur2haq/8tPdG3PG7zSa5onpASP1Pmg1qZO0RcSzNu\nSLHJoj1mm6gwdEpoMf2EuXos2SSRG5/xDtN2Ze696WYA7jN5Q7L2pn2fyY9kbYVHc2IcwKhwkeEu\ntO8Tzaf4btu+QgZaXPFR8G3F10aiMFPRrSWKJPctq8fmtf2m1elw61I2cSJ35QG2YYpkSISGSB5I\nby6zYkfWAibrYptPfTjr6Ehekct70/6ocM/Jw3vTfkfSWtApC5IhxRPa+QoCQ6Q3WG63GNR5u5HZ\nJPPTEvomM46hCeAFpVbOwjXJGhKhx3hDmNOsR9jOx9XLL4pRAMTUvoxyS9ZdKMfTOp0Cv8gmKccA\n+Ez/XXeaqwA+mv+nurBO4pBmR5TmyQP6VOcOAAVt0PXK63aJQEy6HJ3QFmek7oVs+Mvp1CxvPKZd\n/eNbf6Jvw7hdEhKAY8eOPf300wDOnj37Ez/xE//WbTsCKv+sFvEGh3/TGCmvhEXVAKKMe/2KkNNC\nTyICKXiqeXKiSJrHIkMGwBW/65W/EN87pPV+PHf2kOgcTjoBk6eSPoD3iLUCcxui4DOZukQ6kiUp\nT/P4olQ2kfxcdlEX6QPFjU1mWIj/yD2qyxFV2DDINwd5sy/PDw8Xc5unwjuoSP3r7MEjav0leaTK\nvLle2QNfUvJk2PqAslplHoDPhwemlDbZuVqIaWk5mQoJ35+trEoWVHiMmyJ5d7wxzH0TCXQ4mTqt\ntReTMklPtlKbltlhtT4jdRey4ozUtRD/Wv5rFQQvYYRKFh/KliHhIratAQhM3BJ6i+mP63MVLTiD\nbWtO0soEcCGrjqttXY4C7p71J53YgJxmPGOhmlpBpgaG4udGtog7mboFyOnu2qtUOQwk/zZPSLi9\nJ/mo2pnJXSF/uaW43ErtIneL3C1zxxPqfFBb7uwxrc4LrxkIATgpbyu7+4yXRHgw2wJQUTqD2N6v\nrUS+vYxyQxQQ4yBrBkJ9Ud7VlrQVZgOwEP9PyaXryoqvyp7N/zabPu9NlBR3wSmoA4UANamCamG9\n2Z70gUKx/kzvSK3oVpnngd+XNak6tytzb0qWnqaU//6Bjw6JsCTC63L+MitNp/3rcv6qVKiI4Ai2\nKgg+zK+XRLiIvCHSo8lmSQ4vSuXvFyvn5Mq9Wctn8v6stx89AC/LQwBakm4i8Zl8IOtVWHAkaRdF\n+CyfoGwE4HF+hQprthwDeFUqzGFomvVq8GweL0pRk9ll7szyBgCyY6fyuJOpXqZSOYQMD6OMV+26\nIcXg3rja9jL1QlI91blDpMpDlQsXkuqOqeA7NW6jhPR93/d9tNiee+45x3H+VbWu1dXV8+fP0/Wj\njz76Jg7/prFPb0zz9hFsfTXb3TTX16NSeKdalKKtsJAE9szsS0QhlGPjrtzy9aAKxY8y/pC1uJAV\nh5n/J/zAo9nqnFwez9xSuqnwqBD7HRQDJvuQN5h5U7J2Ze6OcM5o5gbg7842rst5QyT/t/5Mh2mr\nQ9ZXs92nlWknNjxesDaNXjgmF9oEwPUzxRPqHqX9195dO+ZjhhTrcuRAqWfDNeZ6Qn3BnXYWZsKJ\nTVWOJ43NelgqctfV1a9jbFZqDgvfhXJBDH8e+6rCAVCVHMA+E04Gqfqj1sUvBAdNFp3vzRS0wWG1\nvlsMHKYAqIhgPHNLIjSkFEBJhKflkQvZ8CzbXBQFwjgBuA8ND3xRFCoInkivfJofWkzKNt8uXRIO\nkN5SpgYFbaBpPdggBBQGeU/TI10Z0nqqHHtyWi2sAzClqCo5Kdwb39IT/W7E7TzJq5J7gq3OSP3T\n0sgD6sbO9zeZMSx8j3FYZz8fHsBr/l5k2VAX5im5tlsMdmVuD0aHaZ2sakjJsdhReLQP9VZc0hDP\nYySQZJ/xFWZfyIapyfqMgoYwp9A3kXxEujqba34l3Puh8rnPxcfTmp+6BbOtNptTyPUNxSd5Q5KB\nB/B5sY+4Sh7jrxXoZEOkx5LNy7z0qfjfXQ+qJ3JXLic1k0UkUjcjdV/MRj8oLelZSvf/F/UQgchX\nmeUI5Xk2WhfWrLz59XSMOqCE8ZuVmxbiCraVMrpMqyD4MTFPGevJ+NC1oLpPb/yJd5QgrFRpJ973\nnvxqMyp4Qf66WSUPJ1uKyMCJ9ACf7x+YNDbJYDBKlYY7BqCY2yTiMAASpwA5AUqbt6Qq/7aN2ygh\nPfroo7/5m7/Z6XSSJPnd3/3dX/u1X/uX9/z2b/82XUxNTb3rXe96E4d/06jKzlxUs9V4Wuo4kvrz\nudNPBkc6sfWe0iWLRa5Qq5JzvLBG7qh79Qb1SF5wpw0pts0IAIF/dKQBOFMiPYkOohlk6tPK1BVW\n+kJwcI/SnkYHEurCggxXqD8oLR5LNgMm/4U8UxeWjchikSZFPbcGwCtHQo2SwO4qfpQqjaAGu06I\ncPLcbDg1rviqHF+7cVdqBVx3hrRemKnK3pVh7o6r7cf5FVNLVphNOePerLXFtLowidZKiIyz/mSZ\nO4Qh/IPkASc2Pjp02ixFBMa9LNdIgPwec/U90o1NZhAX6jBrN4R5gq1C4IDorTILwBLyVCE5IHrn\npMplufzZ7lEA08X2B9lSC/oS8g9Ziy9geiy3vB6Vwkzd9pZN5ZHyCpU46mGppLhhpsLaBsSvRWUv\nU9OsAtzuPKTbeZKrLD0pJlryZkUEJhLC1ldEQP68AHSk9/NmAHlNWMPMX0KeeEIX0hFLjp/iuwHU\nhfnh7PqocJkSxYU+9wz0SnVm/wk/AOBCUvVidUppLyblWd64kA3XmPuiGJ2VNhdF4UwwuUdpn/Un\nyQFdHSiBKcBTAF6QD9Te37S+p6AN2om95lfSjF8zqoPEjFJlxr654OyyFf9+e7EqOTZi8kyaZr0P\naku7Mq8D7ZxUsRDXmPsSRiCBJOPOBJNEHv+ScyjM1F63Jlu9k4p/p7l6UK+fdqbJ1/jZ8G4Ajw69\nPC11Pp3OjnDndH96r94gqdnDan3abtuIbXPbxinM1PvtRcdcBXC6tz91C1Zbjfb0AdA5adZqAiA7\nWk+7aopkScvTjs1GbLMYwKl4fAcSRfs5sqG59Qf6dozbKCEpivKTP/mTv/M7vwPgz/7sz8bGxv5Z\nUeJTn/rUs88+S9e/8Au/8OYO/6bRSO0R7pANeU3rfD47UJEdk0WnnWknNkim3lB8qvySlThZJtPu\n7BGsU0/14v/H3rtGx1Gd+d7/Xfeqru5Wt+62ZFuWjG2Mb/g1xuBAiJMhiUMggTNk8GISFmTNCcnE\n7zpJnHnPh4TMrKwMM1msZOYs3swiJHOGgQEmkxcHhkuAeMHBYENsYwuDL7pZsuyW1OpWt7qruq77\n/fDIHcU2wsaykTX1+2BXd9feXSU9W0/tvZ/n/wjpPFPfdVK2KAGwmQhgYzC4VM1Xiye1C/kS5A5h\nrDZ0Kkw8LsSWIWcK3g6vJRuYw3YtfJGrLgtEEuoujDXBFxkwbLUpthDoYexoQ6HJjxVF0TPHG12e\nKDPR6zCPA1invgegnRXqeKUjLKZCx5Kk3/ptpuBCQHeYeil/BQBF9K40e0uhQnMvJ1QU0bvCGLBC\npZ0VTMm7jp/YExveVllCwVelUOkUatfxoS5e0x2kybJIZqIjLKa4c1wwWnl5D6s7gHQGsSHPBHBd\n4tBKcTjDje2YS2G4AFJyuUEqkTJ/iSu9XtowBugh0YQHFd1himTU1ysDVLDnbbH2TbF44Fx/qRed\nmWzkMe4vEMao6kQWGgSsCkYp68BmUpeQoP18+osZg9cIKxPWdwhjy4XROl6xIAGoh31MiOUE9YQT\nO5412oOixoIUd74UdNlMWisNPx4ubmLlsqDs8xvbpVwjs9pQ7OUJE14lUPZ6raSdqsu2VSsz0Yv3\npRxDdmoqR7PtAMYCeSyoB6COabaVshtdLgYZOVWVyDPhtaE4MZvh0HlQgQggww2KicgGE7LZe8Qr\nJK1Ulzz8itVBi5AHpTKFaazD0C40/o/kq+QAXrE6aDYDYLmSecXqcEOJQhABvFZuH3WSHebxdWr/\nUGiuU/u7xdJeq5VWKQAo47K8sB9A3ov9yltBYv9D3OgOUxBgwiszGRzLMQqgDpU5gVWBWC/ZFpOu\nDobzXJ0TlpeEowXor8lNs7tAH+P8gmsk//73v9+8eTMd79q1a3L06imEYXj77bfv37+fXl511VW3\n3XZbTU1NJpN54oknDhyY+IOzadOmBx54YNqbvx933nnnm2++mf+7B0hOkRKJlmiZV4uLAdi5Rgpf\nLrY40MuwY/EhxTG45LFyU4lWhDXR7bfrFcGnsn4k80XVxujPMe3NtEu5V6wOTXQN5lIVCRIQIhHi\nhdpQzjdJGcX3dEm2g0I6PiqO1wYAuGFT3A4XA6ZUSLH/SKVx3DcAuIHsV0wAYlkDUDenmx4tqcLQ\nVmNH9Yl44qHVbW2Tc0OBeaTSuNoY6PPSlBL0mWQnTZ7yXmyukt+bWckVVyzGgkSZ6gUAIF2v642u\nfx9bowj+2Hi9EcvTNQShVM3JoEdFKs70WGV5nVjaU2prUAq0OSRUZLXhhO3pJAJNyzUdwtjGYPC4\nYFAkVVtYJIWVFHe6xcSepw89/Z8DjzzyyNkruE8jl7SRv/nmm3feeeeymy6fv2lVI7Nu8I9X6x5R\nAM62yhIS11ltDMSY+/L40oITT6rjC7Uhyj+jeAfaf+oQxkjV9yiLl7hMJbo73abqE8Zue94SLXOw\n0tSi5Gixi6YCFGtunFzRAjDmxyYScvUyMCFSR1YBvUxZUBSBSduKfsUkCw81b35dtx3KG2LdFIVR\nDR36lbwww/8Qefh8aSmpNpC+KmmQUxhnnVgiDX5aQOaBDKDGyFGu0ibjvTfcVgB7Rq7AyepNQTmp\njMuuHiJeFAXf93TKhQBQcOJCvgZAKIViMkfSD7SSMWalJdleEe8D0CCV7sV+DQGlZ6wIc6uDoQJ0\nDX6eqSnufOwvD1511VWPPPLIWf5yLy1mlkMCkMvl7rrrrsmZfaewYcOGBx98UFXVC9H8jFQd0nim\nNVZg5SQnWbZ8f4wrDEBi3JcWVcpjuiSFACoVKdladAzuxj1Ka4cYMFdpSPcDWG0MACBJbAA1UpnK\nHQ0V5hqxvBvIiujZnq4M17gNY7BjYqwQhBMTWbOzQdB83+C+zJ2aCgvEav80VYIYNJoZACS6hXiR\nCjlXA9ApFJuGMU4O+Jr4CKlyLU70k+OkC7NDmS74YKXJDmWS+TKZSxkYFG5X3ZvtqTQ2qXlKpyVV\ncqoiSPpDRlEUPcAWxxfYeiILYJ4+Qt/VpOa7SnPIuQKALZab/FDzlHF5oq7SfIsplWtT7wKgQkq9\nXpqyIOt4ZXmQo2Di/+/ZwX97NjPzHRJmnpGTQ1r0ueWrb1ryRHkFABJbI1VfSh2jAGWSiav+22Ee\nrxpSydMpkYhEUSl8juYQNMMGQDKmpDBkVRI1Rm7MStOf+FEn+QfL10Nu2IZWpPDOtFQ6aM21yikj\nlq8Kwb1jtQIg30A7PRQcaHGF8lupCCTdAvm8nG9Whb1r1UI1lr2qm7UgMUChBN9UdtNe1wG3iS6A\nNCCoKAx5XMoRBnCoOK9BHx0qzI2N6BWD42AcQHhFwSiKvsyd2jKzdMSLADCeEHwhlEIAf3Sgecq4\n7NSWa4xck5q/Q+us45UDSDcyiyastdy5PMjpPGhkhRXfGJjFDmkGLdkR6XT6ySef/Kd/+qd/+Zd/\nGR8fn/xRbW3t3Xfffffdd1+45lNgD7TGLBbIiBUY9wWrpAoGJClo7C/3NySSiUBLlHyZA5Bk+A0n\ngkC+Nnn4Hau14MR5IHPFpdzsV/2JpzOqIdai5Ibd5LBdyxwFMfiezkfrFA9aQZC8VMXggZ+GFAgV\nGUCpowwgWZORgRrBHfcNytLVLCZZzI2LxoheQkfF4IoHN+6Jgj9s1y5O9F9tdvd56WVK5oBcXiDn\nSFebyoJZCYn2df7OuvZgvn1BYmCT8V4js+p4hQKfrhEH2438G26rFSq9YfpTas97SN0a9Fwe5G0m\n7hbqLUECcFSNd4U1lPROtQq5q5GipVYQ/JJarkhORUz5AhArdZR7B5udmgpi+UPFeaLgc9Udr1WM\nrhgAHNQFQDGdIO35Rpg4rpeT2g57rVCRd2hrVzftO2jNfeyklgT5SAAnBBczOzG2ysw08l4/9dsT\nm6iUCfzYIWceD2SqVCRUZAEYl23f04fLST2RTcnl1cYAzfWfH17LRE8UfDeQIaHXSzdIpQaptF4Z\noOSBYd/cP74AgO/ptOOoCH7czDihQgV/dcFr0bPDbjKpjl+99O1SqKyUhpYhdwBpSo9rUAq2ZJHv\nAWCFCoX/AaCJlwlvZWyYkpMaNasafq1z/5jZbUEy4D8mLLVDGTKuMAZWSkONzDK4/5S4qF3KNTGr\n3rQBUPZPlmuLw8IXgt4xSbVlaafYMMQNUz4Wg7cvrKc7yjgpWpGDHcvmaxCriEXRyAljRcFI+1pG\n4jK35o7B1bhhMzumJ7KWqoWSmDimcl8oj+mKFALQauxSnezUVMRibAwoefrf2vVLjMFBN0WL4abg\nAlgpD5/8RQ18iF/upcKFnSENDQ0dPnzY931BEFpbW8+pwmYYhi+99NL+/fsdx1FVdf369evXr59C\nv2t6m0+GZkj8gb/pK7YCEIsxrU/3fcH3haWdR95bvkjTfMl0SnUhFTNmHisvHiYVYZrs06SEqiNv\nMt5bhhwAKsbVU2kseTrN9KmAxcQkrMACGRWDh5onVGRKxKHroTpgpLdPNdOYoyBepKpFRlG00q4y\nLgOQPGalXTFWAEAxdbTwRTKUj45eTTEOV5vdVNaI/rhTQB2N9upEhEQt94X1k5dlOt2mBqm0Uhzu\nCmsOuE0H8+0IxMRxnXkTdZbDiuQ2uq4eGkURgJUIEhmJyncaRbFi8CBWUcc01WLFOTZTKokjad/g\nAMSiCD0Yb3SFikzu1je4kJPdRpemhosb31sg52iRJ+eb1xtdR55558Qzuy/+DGkWGDnNkJo/t2b1\n5xa/4bbSyvBQqYlZOlWEC2IVqqQgaSVSCp4fy7QoOZIuXaP3kzz2PF5KhxN7Ttf6J/JMrUD6Z2lx\nCfIrVgeFn1nlFABJKwGYWOCKe1xxKeiZZsz0zETXRkVsB1jMYlI3T7azAkkhdPvpI5VGJ1RItYT2\nb2j/vw1Fi0nzeOlvnfWkKmSFyj3KPiqdDoA0kEhQlRK3q6oK7UK+O0zFmNvEymsx3M9M8m05QaUC\nY3QjpN/vezoAZumUhpjISAB8g4senBFDmjNRDoXE7gDECqzYWprQPQJYIBoHE/5cG4A6KgEYX2Ab\nOQVAud6mQogN+uhcJQ+A/NNqlq9OAAAgAElEQVQ6tf/V//6/oxnSuZHNZn/5y18+9dRT2ewfFe+I\nxWKf//zn77777tbW1ql7eOaZZx5++OF33323+s5DDz20Zs2ae++9d8OGDR94AefZ/IwMu0lDK8Yl\na1istaRQsQXNY73zmoP6EctRFFvQ+vRSSXE0XzUdo6feMXgQ96RYgYrALlMyTYy2TD2D+++xFDja\n5BwV++Ji4Mbh1LqxjDne6AIYT5XJwXAx0CwFlo5Jls1dzQYMrQjAiOWX1A/SQtkxuU6us5OAm5AA\nyIIvZFoDP33tvJ17Sm04mcT3z+U1FFo9XEgDeDHTut2D3jqww4kDmB/LaKK7XhkoQX49mEu3/yXh\nUD8z17MTrWLZZmI6cFLceVzxAGS4QQXRmejB0otzbADMUeLHFCaFOBpL1Ni+wa20C18sNvliclgE\nFrf0TWyJacnxUIKrwY4VWxyhIhvHFEhhIAN6OfQTFUMI027imMrjnjoqSZ5eMfjB7GVdWokWXobd\nJAykmX3i9F/bBWP2GbkCvwR5uZLpFtJWqDiGcnVD985S+0JtqEEq0cLXjvzlXAwkwadC8qbmXm90\nrcOQxaURplMOqQWpDpV3xYl9oEZmZcJ6ALREZiEFgHZQoLhuHFxxAdA+il2sK8X0vBobVszlSqbE\nlTpWSXOnFeXL/dy7YvpVNJvMM+E1yRYl5fR66UE3tc1ZuTnx+xLkRmb18kSJy0+5i7tKcw6Vl3LF\nRSB+XemgXB9aNlyn9rezgsH9N8JmAAfcpmVKBoDJPFqUW8rz7UFxGc8fkFJvi7WvB3Op3C1t37bo\n2RqpPCbHAIQD8/i4LPlicUkRAPQyD+QlK/ZV1+QBFIutzNLHGwPmKvBFxIvc1YSKLF992PF0v2K6\nDRVdtsVAtnSJBr6YnJg7kgb5XCX/KbXnc/7RKKjh3Pjd7363devWU1YSJqMoyl//9V9/4QtfOOOn\nQRB897vfffrpp9+v+ebNm7/3ve+936fn2fyM0Axp8YNf32u1zlXyJDzaIJUo2ruq+kUfkQABgBqp\nTOEJhuCSYBeAdlYAUIYcg0cSVTQfpzUKWp0AcKTSmJLLtLiRksv9dr1VSWyo20epCVXduVKo3CId\n6UUCwDLkPu/15Zmq8+BdMUV6LRaTHqssX6ZkqmW/aQ40FE68pIrgFMC2HKOkXlrLnQEWq0OFFq9T\n3OkSEgA6wmJzWG7iJQCUcXJCMJpD6xWp+efOanreJP96tdl9sNJ0vdFFlZgH3RTFUNSqhdvM/VT5\nqYY7J4RYl5DoCIvbhAW09U3ZSDRF22S8B2Cf35gNzIyTol0uWkQS8jVUtDQ+KhZbSyT5LD23/cDT\n716cGdIsM/JqUMOyzy27MswCGGUqRQFQwAiAdOhQ9iuALiFBRkLNDfgH8Af3Q1HjACxIL/PWJlYu\nQR4KzZXicInLb7ithuDuLFxG+0/H7DraVaLdTUzaZL1H3WvAbwnLJIjVzMsqPI25suS6czLqSBrA\niNW4R6ynEACK5JwTWmRUFPxC8gp0bdWZUzp0DgvJOlSy0Fp5mYpfUEgbADLyAnQAJC/UKyRygrod\nc9tZ4bdeW7uUo9kYxcVVUx0yPEa7m/N4qT0oNocW6ZenuENF9ijery0sjjG1hjtVOYleIUHDgQqp\nDLDYCJtQzqV1CJKW6ETtZ3n/X31tezRDOlu2b9/+ta99rfpy7dq1K1eubGtrGxgY2LNnz5tvvgnA\ndd2/+qu/AnDG4Tp5pLW1td1www3t7e379+9/6aWXRkdHATz66KO6rn/nO9854wWcZ/MpOFhpohqv\nnW5Tzjf3jy9o0bNHy03c1SiKrC3WXebKX6lv9DNzcVgg0WLKIrIh7Ue6lZdtiBakMpOpoMuRSuOG\nWDeAviD9RqhQ5g0tTNOB7ekTWpOW/taha8S5J7qCOVcnD1uh0iiW7hLffRbzaFT8Jmx/jC095qav\nN7oAkAICOJYpGZO5ZcEd9k3Kru90mygyCoDJ3PXSEdJQGWCxGLyjLE5/XCwmfcYbyAuqzv21/sgC\nPjahPAQ4kFuNwTmGhdErSIP8Zu3gfD7+m7C9LZ5bz05cFhYOG0ef8hfdIb13VI3HVM/gPnk4C1J7\nULSZVMOd5rCcCp28oN4YDhwWkmAowcvwGFWKAofNxDap2CqWF4rFVxLNT/mLyDmVan1R9OYrhXRL\nabmSoZBFg09VRHUama1GTilHnw26CjyWZ+r/kZqzTKNSrVloliB1hEXSzP6Yf0LnwS3G2yNWY52c\nP+bVf4ydqEA6IRgaggpEDcFxwaBAcFoKriqWUvFZAIeGltJkot+udwMZwHBuHlfcPrm8QM4tkHMW\nk8BBj1YDUuwN3tzrpRvE0ufRvbZ/hNIhdNEH0ByWU3BIH0hnAQCd+zoPDOaD4yv+oQoTKWyavIKG\ngFTvKIbNgazCi8ulI2HTAuQqXClAT8KOJ4fmyN7x7CIAWWif5f2jUO+ROnUe6PARTkg5XBtkjgmx\nlrDcHFop5sBFnqkr9B6nPhfKfltZkwsJL1lsUHwAxaNLAVQg9QqJhUFxuXTM85W1Yt7zlZYlb8i5\nuGTpR4rt5MBS3Mkz9R7xPZtJC73il2Z8mt35M50zpGKx+Cd/8if5fB5AXV3dT3/601Py8vbu3fuN\nb3yDljgURXnhhRfmzJkz+YRnnnnmW9/6Fh3fc8893/rWt6oL4pZlffvb33755Zfp5eOPP7569epT\nLuA8m78fNEMa+OH/63t6jZErOPFrU+/SZOWYm05LJUodz/AYgD/oAcO3MDGGNQQAHsBqio59rrCc\nQq4p+plymwCUPJ3W+iSPiR6Yx8YycUkKYzU2AIqk8H2hpmm82OLAFyEFYqxAu8G2p4uCD8CU7cJY\n0xdbtx9wmyiCCMDRzGUk/kYBexR7TaLjK6Wh6/iJARZr5WVS/aLHNBJpbQ6tHjFB5ckBvCzOJU1Y\nE94y5F7mrSuFEYP7vZhI6yOB855KoxtKpMfqhApFEiqit8QYXK5kPsv7qSBhJ2oBvGJ1VPPh67kN\noBO1VLfpeqPr+dLSuUqe5lgUN5+WSrTWN1fJ00JlX7GVid7c//OE/NuXLvQMaVYaOc2Q/ttn5yz4\n/IqOsKhz/7gQoww5nQcARpn6Mf8EBdlfGYyo8PpYzQI+BkBjboUrsbpjgicfKbb3ConDQtJiEi32\ntgv5m8M+AI8Kiyjye2fhMj5aF2oeFwNSfKcAM1rLEnwhVmDMY8UmH1QrMpBXxPtI7DXnmyQTRQsJ\nK6Uh2vtpl3LtrPBYZTnVse1ELZWpJOFgitkx4Os8sJlonXwK/5g/scRbgbSAj8Xl0rhnHhRqaUZI\nUxyS6SPx1t1SPU25qvqN69kJACNMp1LOAJpYeRlya/2RZl4+wWLNvLxData5T5O8E4LRFhYpWE6W\n3LeC+RRYT81N5tIOGXVlMo8eBWgO9zJv7fXSn1J7nvyLf5/FM6TpdEgPPvjgT3/6UwCiKP7Hf/zH\n0qVLTz/nyJEjN998cxAEAO68887JqeZhGH7yk58cHBwE8OlPf5q6mkwQBHfcccfbb78NYM2aNY89\n9tjkT8+z+RSQQxr623+gymDtUo4qrpa4AmC3PU8TJ4oejfmxzYnfm8zrCms2sgEAvwnbd5baaflu\nmZLZlrtSET0KQqMcoGo9pDLkem4/5S+inIyDlaaqxvYibYh2gKj43mOV5aT3k5ZKbXJuPTvxUjif\nzrfKKUkrdZjHlykZUsU+mG9nls5VFwBzFEoVQiDWxEeuMAaulY/t8FrapdwuZx6FtAKg0mptYbEC\nSYM/xtS2sKjCOyjUAtB4QOVEy5BLXC5BLnGFxPFozY2WB7OBObnmZqfbdNCa6wbyJ1PvNAqlJmbt\n8FoaxVL1B0Jb03XiRNlA+slneGxb7koAiuhR1C8pstBjAQDuaiwQxVjBlO3Uy8/ghd9daIc0K428\numT32U3zarkzJyxrPMgLKq160UIuLZ3RUt764LjG3INoSHHHZuK7YpqWywC0B8Wfi0ubmEXGsFIY\nKUOmdWB6CnkpnE9fSkX2cHJvqbpADYDCVcgJrVcGqJjFs2we5TBR9tJqY4CiFXBywZzmygDIwPYF\nDSvF4fl8/ADS1YdFAFR1bF0wrPGAfGrCyLm2WeGKAxlAvTHEPWVC8UiobQuLvUICADlpCm2gB6/q\nD7BNzlGoZzWhcDlGLwsLVGC6U0yTFySNuzJkqubVLSay0OpQ+VtnfZ1YWikN0QI13T7t29HS/bhv\nLDEG71AOdKI2Cmo4W5577jk6uOmmm844UAEsWrTo5ptv/vWvfw3gxRdfnDxWd+zYQSMNwLe//e3T\n24qieN99991yyy0Adu/e3dXV1dHRMV3NP5C4ZD0/vNbQipahGILb6TYtVzIArje6mphVUuXuMNUu\n5ClI6Zhd9x/etTVGbnPi9yVjYKU0RMvotAlPetgA1uj9vV6aZMHoae4vxbcvRw4hxlRVU4IVes+I\n1ahyLzb/mGgZNGw+Iw68kmh+gzfTn/7H3GUWnwiKO+rp+r45A37rAFCpSJIUqoAkhWJKBMA85hsm\nRUa4Mem17MpjifSYH3tt/Eojlu8qzQFQqxZ6lfRjXAFAKYc01G/AYHUomnCvwSAA2g9oFEuNzLo6\nGE6FTo+YeFVq7g5TQCkL02DuoJt6tHQ1gA7zOPm8Elf2hSbtZpE3AuCESiXwsjB/izYAK6Whfxr9\nGM3neCD7nk7romNWWizGXK04UZ+prAWxCh+tCwusUKy7CLIqs9jIB4LE10duXZzoB7BR7TaZV8/t\nFWFuv5BuCcu08zEH5baw+DtpHm0gtfLynLBsM3Fh4NA0ultMrMNQbeiMMhUMWWgxeAeQbmPFXiQa\nmfUl4RAVgLAFCQaawzIV55ZVF8Axr16DjwAVJv2WtdTKXQOI0Y7UrWFPTlBNw91WXFlw4i/k5nHF\npXDzWrXQU2mkzX+aNnVxpRQq9YLdERY7UNwpNgCgzS2qld4ppg34b6F+FxqbfOtKMTsnLHeLifag\n+LjXYcA3ZF/nwSEh2cnTFKah80DnwXyMz8f4kGCS4gP96PZ6HYsT/Qfz7Uz01tW/1s4KI9DJjS1D\nbhcaTXiURQsFTczaJTYAMOD3IvEGbzaYe8xNH3PTmugCoOiJFfG+T5vvDYVm3ovFJaun0vj3boqS\nq2Yx0+aQPM87fPgwHW/cuHGKM6+55hoaq5lMZnIl5upQX7NmzftFKC1dunTRokVHjhwB8Oyzz37z\nm9+sfnSezT+Q28z9JfO9JmZ9zj96XIiNSupvwnYKTt0X1lOy+r6w8Rb10G+FtuuNrnZW2BfWv+y0\nVwJlpTS0HKM3CINfMg9ZkCjljZS2aV8nw2Pb2dwmZhnwe4VEijtUuOgVZ6ku+DXcacq2AEgYOdgm\ngHXB8AqWy4sqgD1qHdXTO1puEvI1TApFKQQQS1X4uGyVVEkKy0muNpxQBJ9iKObIZQB1Zi9FWzwv\nLF2kDZmCO+ybhuDSo9/N2sEnyit0wRt0U1RQfD4fjzHvs2L/nLCcD1SbSVfKWQAp7jR75UVS5lhQ\nvzAopgQnz04ckpNPhYsbpJLFlblKnoIddpbarza791qto04yKCfFWEERPZwUPx72TYsre0pttqdn\nEyZtlQ26KQCjTtINZFO2Xdn2EwAQFNKCL4SpMQaEgTiuId1nnf1v88Mxu41cYeGf1782ETzNvK6w\nZkfQMiIfi8F7W6y1mbRHqKvndp6pOvevD05o8CuQ8oJKBcgXINeeOujHKqx/niy5ADxfOYiGHjFh\nMB8UUwBJ5wEmkgKQCp13xTR1SzVeF7LicmnkiN+k8+BPvGMnBGMOyp1iepSpjwWrsp7Zb9fbns4D\nGYrLXEUZj/kysqgLEuU9oXRd4tDLTvs6td+E1yGPWZAo/oI0WHehsYlZS3leQ1DLHQCf9I8Zsk9S\nPQDmhJbNpJNeVnpUWNSOwsu8dSMbsCCBgaLGSTi/TiwZhks3YnEFwKcb3iqFyitWxy7RrU74/jNY\nukTLDAGfUntIo9bgPi1W04+aeqBEcgA8kEl/kp53+7x0Si5T8DrV/ojKT5wV2Wz2lltuGR8fz2Qy\nyeRUj6qy/Ic6akEQVMfqzp076WDqhe9Vq1bRYKPd4yrn2fwDoRKoS7RMTPLm8dLH/BMtQvlt1ALY\nyAZ2scZ2wQNQhjwhQgxpIxv4C/lAl5qgvDxazl7K82sxDI72oNgtJrKCRlOcZUpmX2h2sZoylJjg\nNrEyTTuOC7E8V18QWgFc5hSOSbGWsEybUhSNsy9oKIVKT6UxqY4XUigmZCZ6ynANAGdO0Yjl65WC\nJroTVZlDhRYbhwLTChVTcIdCc0Osu0MYK3G5USmVuAIRK4WRq4PhpUaerlznQSp0Lg9y74rp44LR\nLSYsSC1h+cpg5F0xTY/GL2DtiKIDuDbI2Eys45VPqT37ggaqXWYo/tO8baPa3cgsGDgoeH0Vk6ZH\nbigdc9PD7oTN0J+bQ8V5/bJte7ou23HJom1wSjFmlm4BUjLnV0y4GslVGCeFVi8os9vIXS6Q2luf\nN2+ZktnIBiAhC43KMD7L5nV76VukI8eEGO2+pLijorQsdUwo1GS9lGKUitmWQlbPM7XZK1cgJWEv\nwNgJbrSiTHWNy5CfREcHG9suzi1xZaM0AIB2SmgWNSDFenjClkSdB7T18iprpqwjmkDEJcsN5IBK\nByEtzs3WSNbkRT+DuUOhaQr5F52Fk6NeN8bf6xDG9gUNJUEuCXITs+bz8Zfkliy0ftEsQ+4Ka25i\nvTRIDwlJkhsGQHVg5/HSP7hrKOxIFVzSviOJozE/RjumnxSOtrLyqKEeZfGY5hncf4M377bnDftm\nzjdfsq+4OnmYiq2QK2oX8hkeK/OJp675sQwAkoqg51QTHjlX0v0z4ZVndf1yTKNDam5uvv/++8/m\nzEOHDtGBoijVcet5XnUtYuXKlVM0X7t27b//+78D2LdvX/XN82x+Nrwwuoq72lHnshcAMZmrVQuL\ntKF3Sq0k7F0JlGE3+ZlkpwmX1CfruW1BegCrEeIacbCT167DUD23KVfjANLbxbmUnUdb9C87S1XB\nrUqqUIhdUh3fnPi9KXhXhtlDQvI+/5pBN0UiKxP69oHIHEWxBcljEwINDWOLE/1Gsoue2vJerKoL\nWQqVPaW2Y0qa9nUoBh3A68FcKvBMOjGa6Pay9PcLm7irQQxI2WWRNnSH/F5HWJwTWgCOC8ZhIXlM\niBnwaacBwBPlFZro7pMbEE58HYBupPaFjQAoAISC4Nfo/Wv0fgC9Xtriys3awS69hpKZKLBbl+3r\nEodizKVdhDfc1j25pcxVIAYNDb0pudxVmlMTH6Ekyj4vvU7tf10u+uf0Gz13ZreRH3PqRrMrJdkO\nysmDSvtrZgYnoz1JsKcSKC8J8wEcleP0sL84LBwqLl/MC7YsznHSEHF5kGvm/gkW+5W8kPZvSpCf\nLy2l7AWqUE4SQRhPPOULoeZRYA5dAyXPAqAtQ3oisSoJsnOcLJfcoI8OlZo21O0jxSAAVMqWHhmH\nffNVa/GVZq8Bt+5kAaHnCsvn6SMAdjrtVJmFxpqhFSf6D8TepnSbnBvyzWvlY+2s8IvymurYodFU\nlZGkd0gLnH4+BnNfCuf3eWnaQzLhNTKrg401GeUS5F183op437Xysa6wpgR52Df3uq0bYt03sd4s\n0z5vdgOgmMausIaU/puYVeIy9XOtfCzDjUZmRWrf00wYhtWI1VWrVlXfr5YUA3DGKi9VEokEHbiu\na9u2ruvn3/xsMDsb3EZXHZUK2ZiixW3Teau23Y17e5Q0Ez0eyAjE/yhfVxMfKXn6J1Pv0GMRLQrT\nLutRxPcFDZY42M2TFKl8s3awK6zJ+SYA+qO/p9RmaEU3lNxAnh/LfMPY1YnaN5zWJ/wVx+y6Fj2r\nC97m2p2U09eZqH3F6ujLL3DjFSeQxWLMlyHka7oE/+rk4eVSpolZL7KFFE3ge3qjmbHKqb5Kgone\nQfeyxuQgydxhPEECE2FFsqWw3OSTMESswMZrA3vPEnt+eUdD7WvulRsa91A24nqcGGH6i87CqgZr\nSp6QTM3wGJVmb5RKTcy6MsymBKdLSEDCUTYhL3SNPLg4LOwR6jrUsa6wZltlCYBKoJiyfXXqnU8K\nRztRSynxX4nvvjLMNqpWLmGO+bGNJyvI1SVLpPFK+U+dbpMdDs6Qp8dL1MjF44nEgAk76dT6ylDM\nlpJMCgHIQE6eM14bQAr6xAUQg51Gjkr7/MJNU9AjqTY0sTKVlzzK4vuChh1hC2XL6YJHES60KgXR\nA8ANOxQ9KvazrbiyKpk/IWuS7KRImRedhYOSNeoka5OFapUvJ1S+2/yfGW7cgMHtRqnbT5PEzjAz\nyT/FJetIpZFU+MjfJI8ax/1Wp9ZXhhSW9rIGlzwkCwL3k3FfCHoVp54dkK7vrrGLTf5rqmvE8nHJ\nOmjNpd4oZKlWLeh6ljZW2+TczdpBANXCyu1CfpiZtCqe4TEKXp2P8SzThuRcjLmk1p/3YquNgeVK\nZh2GSBNyIxsw4BvcN+DT2rjFJAvSUuSz0Hp5gsbUrJ8e4eI7pMcff3xgYEKL6eabb66+T3G0xIoV\nK6bowTD+oNTb2dlJIVXn2fxsCHqVypgu5oNEmx2mvQDwZXDFXZLqnrgFL0aPPP3MpAKvLUqOQvLo\nYYdO2xfWdwhjpuA1ilYdr1yJ7EZj4CiL7/Ba7pDeu6XmiMUkKgxBmRw3YPAGZdBSpFrdqa7R4aQ6\nTIuSa2nMTWzApJR+u75BKaSl0s7CZa+dTClXBP8zyc4DbtM6tf+zsRcoQcqAT7IoALrqatCGl8eX\n1krlYTfJAlnN1PkyAhmJjFS8YowrriHbruDvOL6WgnSfOylZtFcKxFghKCdHY4V+0dsZXLYi3vcp\ntacErw3FEehPoqMM5Us4ZEG6Msx+LjyqIXiL1w+w2FKep0V5kgWjqeELo6ued6+GGNAPdl/QUC/Y\n83jpH7TfHhaSAAzJN+D3y+YqYfRKYYTCao8JsVeU/nNbhL1gXKJGzoQQtpjvj6VQRtxjHuMyLyd5\nKIVcdZlS0WV7iTFIu4yDbqqqLwWA5OC6wpoSkynRDQDpxdUJlaysURS4po+Q56ClY3r83xfW/4/k\nq3W8UsudUaZmmUaJEwAM7i9VdluKZJlSHSrp0NkhNmW4sRyj4ABDP8wb+GCTbE0UDpehSz5lQZF6\n/ZBhUP3ifY2NtMLWV7MAgLqvVjWdsWwslg+ceqatKYWJQB0VKwY3iqKVFgEM27Wk8B03LcpbIAHZ\nBqVgcaXMleqgpjJI12iDn1J7AFwZZiljjxKJlge5xUJhgMVeEuZnA3zafK/TbdpZad8G/EXyjR1+\nepfU2MQsAEt5ngp5UB6ezn1LkP4fb0+dnH8rmE9h6LNbqeGiOqSenh4q5QKgvb39i1/8YvWjSqVS\nPZ76gW7RokXVY9u2p6X5WRL4rMa2zD3jJS1euEw1pCBMs4PBZRADAI1m5rnC8iFzYrqwTu2n6qib\nhSMpz3lLqv+5u9IQ3FdLi2npgGqBL5BzpUBZKQ01iqXfhO2fFI5WpfJ1HugIrvVP7JCadQSjTKVy\n5tWN0OUYXScNUVTrLeqhMuQXmZvzzTY5t7w2U5X2IhHJ/1vap/lBhYk682mcpOEAeFus/VN0pbhj\nJtxdzrwlxuDezEq/tswsXSwqXA+44kq0bAKIFdmXAeC6xCEkJhblTMGlIrZXmr1HKo0NUqnE5UZm\n3eL24WQdTwR4Sl7Qwss2k44LE8X6Rph+c9AHYH3iBLnh6qoFaeVRev8I9F6eMEWPintSWkk3Tw4J\nxv9mS14eX6oK7lCpqW742TgOn9Mv9EJw6Ro5EziTwtS8MpPCcFweX1ABYBRFKx0A4IFsBfL+QL46\neTjnm5TfRuo+dygHDPjgeNFbCGD/+IJBNQXgoNBkhzKFldJSQcZJZZCiYiIASEaLQsPrUCFvRBdj\nQaKovMVhIc0dm0kAmkNrqZCPMc/ChKoCBSNci4yGIBU6pHegc3+Zn88L6me8gYn8We7/dxzo1RIv\nCK3dWubV4mJrJdxAlJp88ZhiAK7MFVsIZPgy1FGRdCf+vP41AFSRi5SRSV0iLZUo7pQu9SvhoROC\nAflgyneOC7EBFnuVNZuCR/INVOL2xnCgjlVWisPtQt5kHpQMJad3hTW0j9vpNy1XMjv8FvLTYKBh\nO8L0f1SWL+X5rKiNSPoT5RUMM+S564Jw8RzSyMjIXXfdVS6XAYii+KMf/WiyCqTnedVjUZwq5V7T\ntNPfPM/mZ4PUuqveZ4U67o4JAEI1EB2mHGfKcbgal2typVAMXb1YkwkcR1HzGXH8cWhpZr+GeI8/\nH8AGecc7Yd3HcMSG1O+kL9N7il6zJuWO++k3mZ8WTgB4jXltKD7OGwFQlZenmNgVpNZKJwCvIzzu\nQFwCDDMNwCiCQYidXOt3tGcrHarkVlwmSrk3ZFbw0km5DKh1slv00wnJflFEuzDWGpbjsB494r75\nzOFlN10uLWqdw7I2d/uQSLHuuG8BuFl827blXj/t1kgZq0E/IkO11ZIZyoFsiwCCdOHgsL1KG1zI\nyioPCkz9Ig4kudOaLReZnOCegrA2tLu4nWc6AIWHMTjrtKNc8gPVaXbUJtFvLTTXaPmxSgpAHcsu\nFEcGg3RBSOhMWA4AcJHq8eYcDOL18nghlNxAG/NNLxTDUISjG3kJALel0PU8JUgfe0nNvG85hovG\nJW3krLjflVoR6EJFFH0YuUIYiqGja4WTt6CXua/8XlA1ZaRGKimiv5d5C6XMbgQ2xMEgsUrapcEv\nuSdyrln2DFEtJqVKCLi+NuLFwlBMqQMK8xXJfsOLK0wc85sdXxGEoF4pLFZtAGlWWox8hXsCsBSh\nGbpJXipDlYCjYtwOKyXBMSEMsNjjTO0Ka+xQnisWB4NEWrBtSB3CWCO36nllhGmPP/B6/LLmZZ9b\nBiDHY2mmAtDZ8eMe75bc990AACAASURBVMAbKvMplCBvJngosXEwRw2BxHHB1Xgym5NGfdE8qsEX\nIc3j6jy8nWZOkju9SKSZ08itQ8BcbgHYBWQZhpnewIMEH/UwVs9OqDzUmZDgXjveGWCx55mY51iM\nHgHiEDPS3HERozymEtcA1APvhvqIJzqyBcDh0nFnDoCyZzRquTG/2QvFVH9n2X9rqromlz4XySGN\njIxs3rw5k5moDvD9739/6l3Zs2TyEL3QzWt/fd/kl/H3OW0ciAPjAMmcTVaKf27SMQO2AwD2nWxV\nVeg8ZRt64LS2p8OApj9+p2HS9bCT13PK9OHA0+8C756+6129EgY0v/+X7jvtUs8aembvP3mBVc4Q\nKcdOXg8DUh/y6y4Sl7qRa0ffa/rFe+fQM+D9sQ1sn/j/tfjJAULfrU4ySADjAFVqmvwLrRrnzrO/\nAgAnzYP+PaUww/jhEzsfOLPibvUams74MYA/3M608YG3xiaNvvikf6s/qNntjXBxHNLRo0e/8pWv\nHD9+nF5u2bLl9ttvn5aeJwfXXrjmf/mXf3k+3xJxMflIqvPhEjfyWZz5H3FpccEd0p49e77xjW+Q\n5iOALVu23HvvvaefNnnYTE4kPB3fP0Nw73k2n5qP6m9cxKVCZOQREdPChylYd/Zs27bty1/+cnWg\n/vCHPzzjQMUfr3o7jjNFn5MrN1dbnWfziIgPTWTkERHTxQV0SD/+8Y+3bt3qui4ATdN+9rOf3Xbb\nbe93ck3NH1ZHe3p6puiWdoyJ5cuXT0vziIgPR2TkERHTyAVxSEEQbNmy5aGHHqKXdXV1jz322A03\n3DBFk8nDZnh4eIozi8UiHSiKUs23OM/mERHnSmTkERHTzvQ7JMdx7rnnnueff55eXn755U899dSy\nZcumbiXLckPDRCROX1/fFGd2dnbSweQ+z7N5RMQ5ERl5RMSFYJodUhiG99577+uvv04vr7vuukcf\nfbS+vv5s2q5du5YOdu/ePcVpVQGVU9YizrN5RMRZEhl5RMQFYpod0n333ffaa6/R8aZNmx566KGz\nXzH4xCc+QQfbt28vlUpnPGdgYGDv3r10fOONN05j84iIsyQy8oiIC8R0OqTt27c/8cQTdPzxj3/8\ngQceOKfmN954YyqVAuD7/k9+8pMznvP3f//3dNDW1nZK6ejzbB4RcTZERh4RceEQ77vvvmnpKAzD\nu+++e3x8HIAkSVu2bBkeHh74IObMmVNNpxBFkXNOKyH79+83TfOUoi/333//r371Kzr+wQ9+cEop\nzPNsHhHxgURGHhFxQWGc82npaNu2bVu3bj3XVnv37p283BGG4e23375//356edVVV9122201NTWZ\nTOaJJ544cOAAvb9p06YzPpmeZ/OIiKmJjDwi4oIybQ7pm9/85gsvvHCurU4ZqwByudxdd901ObPv\nFDZs2PDggw+qqnrGT8+zeUTEFERGHhFxQZm2PaSpEyPOnnQ6/eSTT37961+Px0/VL62trd26devD\nDz88xUg7z+YREVMQGXlExAVl2mZI004Yhjt37hwdHXVdV1GUuXPnrlq1agr9rultHhFxEYiMPCJi\nMjPXIUVERERE/JciepiKiIiIiJgRRA4pIiIiImJGEDmkiIiIiIgZQeSQIiIiIiJmBJFDioiIiIiY\nEVzwEuYRF4gwDH/3u98BuP766ycXt56asbGxzs5O3/clSVq9erVpmuf6veffw+kMDQ0dPnzY931B\nEFpbWxcuXHiRL+lC3FTE+TObjByRnZ8FkUO6VHn44Yd//OMfA9i1a9fkWqLvxzPPPPPwww+/++67\nk99cs2bNvffeu2HDhrP5xvPv4RSy2ewvf/nLp556KpvNTn4/Fot9/vOfv/vuu1tbWy/0JU37TUVM\nI7PAyBHZ+bkQ5SFdkhw4cOBLX/oSVc7+wLEaBMF3v/vdp59++v1O2Lx58/e+970L2sPp/O53v9u6\ndSsJlZ4RRVH++q//+gtf+MIFuqQLcVMR08gsMHJEdn6OTJvad8RFo6+v7ytf+Uq1HM5Xv/pVTdOm\nOH/r1q1Vc2xra/viF79422231dfXZzIZ27YBdHZ2ViqVa6+99sL1cArbt2//2te+Rn9rAKxdu/az\nn/3srbfeetlllwmCMDg4CCAIgpdeeqmlpWXp0qWXxE1FTCOzwMgR2fmHgEdcUuzZs2f9+vWXTSKf\nz09x/tNPP1098+/+7u+CIKh+VC6Xv/a1r1U/3bNnzwXq4RQKhcK6deuoyTXXXPPWW2+dfo/XXHMN\nnXDFFVcMDg7O/JuKmEZmgZHzyM4/FFGU3aXEv/7rv/75n//56OjoWZ4fhmG1BsGnP/3p73znO5OF\nzgzD+Md//MdVq1bRy2pht+nt4Yx3kc/nAYii+POf//z0InKrV6/+53/+Z1EUAbiu+4tf/GLm31TE\ndDE7jByRnX8oIod0adDV1XXHHXf8zd/8DU3/p16+qLJjxw5aFgDw7W9/+/QTRPEPa7a7d+/u6uqa\n9h5O57nnnqODm2666YzLFAAWLVp088030/GLL744vZd0IW4q4vyZTUaOyM4/FJFDugT4n//zf27a\ntGn37t30ctWqVT/60Y/OpmF1SKxZs+b9InmWLl26aNEiOn722WenvYdT8Dzv8OHDdLxx48Ypzrzm\nmmvoIJPJhGE4jZc07TcVcf7MJiNHZOcflsghXQJQKgYARVG2bNnyb//2bw0NDWfTcOfOnXRwSqHr\nU6hO2998881p7+EUstnsLbfcsnHjxmXLliWTySnOnJx3EgTBNF7StN9UxPkzm4wckZ1/WCKHdMlw\n0003vfDCC/fee+9ZFrzxPK86YV+5cuUUZ65du5YO9u3bN709nE5zc/P999//4IMP/vrXv163bt0U\nZx46dIgOFEWpDtqZeVMR08XsMHJEdv5hiRJjLwFuvfXWW2+99Vzzut95553q8dQp2YlEgg5c17Vt\nW9f16erhQxOGYTVWtfoENy2X9BHeVMQU/Bc0ckR2fhrRDOkS4Dvf+c65DlQAFOFDrFixYoozDcOo\nHnd2dk5jDx+axx9/fGBggI6ru77Tckkf4U1FTMF/QSNHZOenETmkWUulUqkeT/3UU93VBEC5ctPV\nw4ejp6eHBGMAtLe3f/GLX5zGS/qobiriQnBJ20Nk56cTOaRZi+d51WPKdXg/3i++9vx7+BCMjIzc\ndddd5XKZvvRHP/rR5O2ES/SmIi4Ql649RHZ+RiKHFPFHTLbji9/DyMjI5s2bM5kMvfz+978/9X7s\nRbik6eohYubwkdtDZOfvR+SQIv6Isxf5n/Yejh49+qd/+qdHjx6ll1u2bLn99tvP82LO85KmsYeI\nmcNHaw+RnU9B5JBmLZNta3LC3en4vn+Bejh79uzZ82d/9mfHjx+nl1u2bLn33nsvxCVdzJuKuNBc\ncvYQ2fnURA5p1jJ5adhxnCnOPHjw4BlbnX8PZ8m2bdu+/OUvV+XLfvjDH55xlE7LJV20m4q4CFxa\n9hDZ+QcSOaRZy+T6MT09PVOcSTurxPLly6exh7Phxz/+8datW6vyZT/72c9uu+229zv5UrmpiIvD\nJWQPkZ2fDZFDmrVMtq3h4eEpziwWi3SgKMrkpITz72FqgiDYsmXLQw89RC/r6uoee+yxG264YYom\nM/+mIi4ml4Q9RHZ+9kQOadYiy3JVDayvr2+KM6vZcMuWLZveHqbAcZx77rnn+eefp5eXX375U089\n9YHNZ/hNRVxkZr49RHZ+TkQOaTZTVamqiiifkarKyOkT9vPv4YyEYXjvvfe+/vrr9PK666579NFH\n6+vrz6btjL2piI+EmWwPkZ2fK5FDms184hOfoIPt27dXq0GfwsDAwN69e+n4xhtvnPYezsh99933\n2muv0fGmTZseeuihs18rmLE3FfGRMJPtIbLzcyVySLOZG2+8MZVKAfB9/yc/+ckZz6lWimxrazu9\nqOX593A627dvf+KJJ+j44x//eLWo5VkyM28q4qNixtpDZOcfgj9UDIy4hDh+/Pivf/1rOv7qV7/6\nfsGaoihyzmnFYP/+/aZpnlIZ5f777//Vr35Fxz/4wQ86OjqmvYdTCMPw7rvvHh8fByBJ0pYtW4aH\nhwc+iDlz5lSFVWbgTUVcCC5dI0dk5x8Wxjn/qK8h4pz5/e9/v3nzZjretWvX5BDPUwjD8Pbbb9+/\nfz+9vOqqq2677baamppMJvPEE08cOHCA3t+0adP7PcGdfw+T2bZt29atW8/uLv/A3r17J691zLSb\nirgQXLpGjsjOPyyRQ7okOfuxCiCXy911112T099OYcOGDQ8++KCqqheuhyrf/OY3X3jhhQ887RRO\nGajTcknTeFMRF4JL18gR2fmHJdpDmv2k0+knn3zy61//ejweP+Wj2trarVu3Pvzww1Ob4/n3UGXq\nlIizZ0bdVMRHzkyzh8jOPxzRDOm/EGEY7ty5c3R01HVdRVHmzp27atWqs6wVPV09TDuz8qYiPjSz\n1R5m632dQuSQIiIiIiJmBDPLPUZERERE/JclckgRERERETOCyCFFRERERMwIIocUERERETEjiBxS\nRERERMSMIHJIEREREREzgsghRURERETMCCKHFBERERExI4gcUkRERETEjCBySBERERERM4LIIUVE\nREREzAgihxQRERERMSOIHFJERERExIwgckgRERERETOCyCFFRERERMwIIocUERERETEjiBxSRERE\nRMSMIHJIEREREREzAumjvoBLgDfffPOjvoSIs+Wqq676qC/hkiQy8kuL2WrnjHP+UV/DTOfOO++M\nhuulwiOPPDJbx+qF480337zzzjs/6quIOFuuuuqqRx555KO+igtCNEM6W8Y+fgsAQfQBiCzwXF1W\nbAABF0UWeI4hKA6dqYsVmYUS80uBXglUAMzWuF4BIAsenR8TnYRoDXvJgAsx0dEFV2a+FSo+lzwu\nAChXEgDAGRhHIKo2A+DoXPSYEEJwGA+ZlwglD57KIXtySRE8OIkAjMuWFAoIRQDgqiuIfuiqYFxT\nyyILZBaGXX1Cd8/Ytf8NAMRAVmyRhZrg6YJbDDS6qYAL9OYyJVPHK3NCS0J4QohJPJDBJYQm9wCM\nMM1nogcGoMAUD0KO6+VQBlAMDIn5BT8GwHMM2RZ9GZIHXwYXuOixwHDhyQBYyABIsXHPNmWHeXpA\nP8mYXqCLqQRqjVzyuOCGsshCkQVuKHuhLJY0IQTdbPKNJy+KIcxanLbL7PmX16hFjwsyC8fsGkg+\nfIl5Ehe4WmIAfBVCCM90AUAINdEJuNCs5K1QASCzMO/HqLcGuaCwcCEbG4KuIARQgqLAL3O1HCp5\nP1YJVPgSOEMokAEoDrgjBL4oCJwJoedKiuFChC8hUAMAYFxW7GYlXwyMMc8UWAhAFyt2oIWBxByF\nSwFCQTOKKalsP/daZf7lXuMVgVkRWKiLFbqwhFgBkPXinq/KkiOyMCWVG8TxRthzedmGmBGMJHcB\nyOASD3QENkSbSQAKTAGQ56oLqdepqzgxAJB8gYWhqzJfVEos9EUAguKHMjyVs5BxgUMImS9y2a8z\nsj6Xir6Rlov040pJ5ZjglkPF48JcqaAgHApjjUIZQJ7rY4FWCvSKE0MgQgj1voPqwIGLZhIXn8gh\nnS1jGzfpsq0IfpOaB1AJlDE/NmalmejxQDa0YlyydMGzQ3nQrtVl26okJNn2PV2SbUX03ECuVQtO\nqLih9JlkZ5krK8XhrrCmQxjL8IZuP72zcBkA39MNrWhVEo1mZtRJ+p4OgLmKMi6rFhuvDeKjYv5Q\ngieYqgWSFFYvT2nw8llDlHjgMzHNJSl0i0KiwZVMZ6zF4YqLQKyJj9RIZVV0Dba2p9JIN5JxUi3a\n0N5Cx421b8eYC6DXS1tcqRNL2cAE8HxpToue1UTXYO4t6iGD+yNMr+d2HSoWpCYAwFEWj8Hr5slu\nP33cTduhPOokTdkGMGalxWIMgNpwYp4+skDOxZhLX3GH1lnHx2u5YzNR54HNxMfDhlKomILb56Xr\nxJIVKobgvmO1LtSGcr55hZYBsNdqzeTmcTFggWjkFCvtwhe5YWuZt9XewxfZKmYTC5bFmzfVrxQw\nxA2TefuChlKo7Cm1BYPNTm0ZgSiWtSBRRiAmjxq+wa1EgHgRdsyo6wZgh/JcJb9SKr1aXOwGctI8\nLjJ3gdqzDB6AxyrLDxXnARAFH0AQSjRGEIgAEsd12KJTkQUpYFKY74/9X+9sL9ctfi8+B0Dr2Phg\nTTxRY1slVZLCshRWKlKspeTKqBi85CFoytaqhXHfmKePGMxtk3MAhjatJUPKOClJcDNOskXPtig5\nU3BjzD3gNgEwmGtxJS2W3rZaa6TysJtcYgwCaJNzTaxcgpzjisncJmYlgBKXY0AJssAVAG8XliuC\nD6DgxHkgM0tXbCFXW240MwA6tCGy3pXSkMm8pbzQz8zXg7mfF6zfhO07S+1dTlyXbTeQbdneGH+v\n10vfoAyYrPFFZ+EGZeANt3VvoYN+Vr6nIxAXpPrSUmlxX2HnA5FDigCS6njJ061KopCdy1UXYkBD\nlB75LcB26wBAL5OdMVdRM6Y6rPlzbbthTBT8cd9QBL9BKRxwmzJO6qDUNObHdkvlYTdpVRI1Rg4A\nZFsV3IZE4ZhdB4BZOjdsZVxWhpTAFxXDDmSk5pWZFFaSoTKkMCksj+mxGtspqaoWOBUxWeOUSopZ\nVw5NCQCXOReDJanujJNqUvOVQKkEyjI90ybnTOYCgNoP4FMNPQC6wpoyVz6l9uzwWrKBWQkUTXR9\nT++rLIAYALBSygI51y7kwfC/yuuuN7q6/fSRSuOokwTgV0zmKIgXk+q4KdtjVlqSbUm2/QSYqzQo\nhTqx1C7kS5DvUfYZ8Nv9YqeYHmXqx/wTY0wF8CXxUFbQLgsLkJHiTl5Sc4L6uOmWQsVQcgBWisPX\nxAcR31mG3BXWNM0rlyB3++lGsXRiWfxE70dhGbOFfjeVc5te89qdUBmz0gAQiInjOpOh9cQryVDy\nmO/FfBnFFgeAUJFjfSkA+WOXAyjMt+bW518tLp6njwDot+sBDLopXfA00T2YvQwAUyp+xRTLGk+U\n7ZPfyxwlkCF5oah5hWwsUWMrifDwJ64VpMCo+Irmjc+RMAarpBqmUxzTEzV2rLlSTvIgVhHLmquH\nIjBs165OdllcMQS310v3VBprpHKLklun9g/JuRhzEcN6dqIXiTfc1kE3NVfJ53wzH8YAHCrOMwZT\nuaIoAXtbGgH01A2qgjts1ybV8SY1f6g4j7saUyo8kJmrCBWZvtqKVUDeFGAeA+DUYrUx0CiUSlxZ\nKY+UId/m9RyQUu+xVD2372LvDiDWLuRhdjcmSiWurBRG6nilljt71LodXgv5sEZm3aIeWl6fMeHt\n8xsBNIolk7kmvOsWBTsvrlVcZCKHdA4EodRoZmBi2K5t0EfHfUOJ+2NW2tCKtqfD1yEFPJAVddwq\np2pqMm5CclvlFj0LwA5lJ1RUwdVEt04sLTBzpVBZo/ebzO1W0o3JEoChwGyXciWuAFij9wPYhit9\nT9cKwtiYHv7/7L1pkFzXeSV47n337S/XyqzMQi1AoQobQQAkYZqkSJOmScmyHRLlkLeQOsL2WA5v\nbcfY8jLhidBMxPxpTbsnxvK4Izwhjd0xlltjWTGUtVImrJZEiaQogCyAIACiCoXaM6tyz7e/++6d\nHxeAPW4PTVkSOGLw+5WVlS/X771vO+d8IahvFMuRBCSnzNdGvlEsR+Ku3kjLzQEXhUy3gxDQKR8J\nhshVpQPTo5rmx8yoaX5IjB732rl3irUbJPyr+EQ/c6eNPoyWegMA/kP/Rwwte7h45Wn/zscrL69b\ndQCTxhBAK6k4JPWpscB6p+31Tw5OTxrDRBiGlhVY2AVyg8lcH4RVkhpOsVNg4U95533ot06tv/FP\nPuSurNECAGjoEAvAWVZ/AZMNEtZkfFgMp0RogavvfBMugAXW+7f85QP5wBJpW5Ys8D4xbZmfZfVz\ntLagD9vS6d485C3711nAna32Mc0d5kEJWm4OLDMkiSPTQlbIjNQWXKe5GwN4qHGuofmfaj/IJ0cG\n5WUWVJkfSuPc3p0k15ZzHcCitx3nxozRW2C9tvBQe/WA3vOFASAURigNAP3MbftNaabayPMHdjqi\n1MFoYDMmfN8QIQAEhu56mXdwFFbTMNaPPfgtAOqpQmGENeM+c92XRpMEAFZE5XpWdUjaNPsOSRua\n/3wytx7VJ43hTziXnhb7F2gfwJg754bTzPJVEW/rUTgNWbeY5dtaFsZF9YkqerAe1dejusx1aPmt\naCSszBxYLCMxLACjWb/htSp6oOqt5/wFk6aJMC6aTQAt02kLzxdGQ/P36EBFnQeMDQCPkq19edgn\n5hVaaklngfUexdZpvtdM/QR6iQRtWQLwJX0mBANQQ/wGuMXttbcC0uu1QVgtO72KHvQzV0WjKLML\ndpdoWRgXAZRrWwBSwQZhVQusAeqqqtjVSkedrR73HnJXADxGNgB0iPVjYqMvzVhq/0m7mShpSRdm\nh1oAAuh1GaF6LpDG5WJ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Xu5dIZVmUmyRY8hpX48a00Qfw4uSizHUACuhhuJlBebkZANiM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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%visualize some models \n", + "hFig =figure();\n", + "%set(hFig, 'Position', [0 0 4000 4000])\n", + "index=1:2:length(theta);\n", + "for i=1:length(index)\n", + " subplot(3,2,i)\n", + " imagesc(reshape(r_ensemble(:,index(i)), 200, 200))\n", + " %title(['\\theta=' num2str(theta(index(i)))])\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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qBBs2FBbd/glARZNZpvj32sKx/lX4djE7mEwmrVbrx3UQJApAQRoWQujePnPu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\nbvC3V3WiS91ap2mto/Rm8UurtiTEdmnVFtJtQJl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YtWsXlZDL5fZ2UujRowe99P3OnTsdvcW5c+eoRGxsrEQicaqYCCHkQRiQRKGg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\nk/H5/MOHD7u6uqq5Q4TQ5s2bmdmI7Gf//v3kJYwyACMMEhLQNnw+38n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rGOiG5hEANFSiPUPq3Lnztm3bXF1dxbogaIuLw1gGAGiwhAakVq1aLV++fOzY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\nCwu1T2QtKradOVishISE0aNHHz58uLo1Pl68eLF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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Performing Gaussian kernel PCA...\n" + ] + } + ], + "source": [ + "%% second case on an emsemble of 500 realizations of 2D permeability field (68*64)\n", + "temp=load('ModelsExample2.mat');\n", + "r_ensemble_2D=temp.perm_ensemble;\n", + "[Y_eig_2,ndim_2,rank_2]=KPCASOM_rank(r_ensemble_2D,'gaussian',kernel_para);\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Matlab", + "language": "matlab", + "name": "matlab" + }, + "language_info": { + "file_extension": ".m", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "matlab", + "version": "0.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/KPCASOM/ploteigvalue.m b/KPCASOM/ploteigvalue.m new file mode 100644 index 0000000..fa52636 --- /dev/null +++ b/KPCASOM/ploteigvalue.m @@ -0,0 +1,18 @@ +function [ndim]=ploteigvalue( eigValue,threshold ) +%This function plots the contribution of each eigenvector +% Detailed explanation goes here +set(0, 'DefaultAxesFontSize', 18); + +ncomponent=length(eigValue); +percentage=cumsum(eigValue); +percentage=percentage/sum(eigValue); +%find the dimension threshold +idx=find(percentage>threshold); +ndim=min(idx); + +figure; +plot(1:ncomponent,percentage,'b-','LineWidth',2); +xlabel('# of eigenvalue'); +ylabel('accumulative contribution'); +end + diff --git a/KPCASOM/read_model.m b/KPCASOM/read_model.m new file mode 100644 index 0000000..25f55ee --- /dev/null +++ b/KPCASOM/read_model.m @@ -0,0 +1,13 @@ +function [ realization ] = read_model( filename ) +%this function reads in the spatial model +% Detailed explanation goes here + +fileID=fopen(filename,'r'); + +C=textscan(fileID,'%f', 'HeaderLines',3); +realization=C{1}; + + + +end + diff --git a/Manual_DGSA.pdf b/Manual_DGSA.pdf new file mode 100644 index 0000000..c9ed48b Binary files /dev/null and b/Manual_DGSA.pdf differ diff --git a/Sobol_DGSA_comparision/DGSA_over_time.m b/Sobol_DGSA_comparision/DGSA_over_time.m new file mode 100644 index 0000000..148063a --- /dev/null +++ b/Sobol_DGSA_comparision/DGSA_over_time.m @@ -0,0 +1,62 @@ +function Sensitivity_with_time=DGSA_over_time(DGSA,responses,tgrid) +% The function computes main effects at each time step. +% Author: Jihoon Park (jhpark3@stanford.edu) +% Date: 16 May 2016 + +% Input: + +% DGSA: Results of DGSA. +% +% .ParametersValues: : (matrix, # of models x # of parameters) contains values of each parameter from Monte Carlo sampling. +% .ParametersNames: (cell, length= # of parameters) Names of parameters + +% responses: (matrix, # of models x # of timesteps), time varying response +% tgrid: (vector, length=# of timesteps): Grid for time. + +% Output +% +% Sensitivity_with_time: (matrix, # of models x # of timesteps), Main effects over time. + +%% Assign variables +ParametersValues=DGSA.ParametersValues; +ParametersNames=DGSA.ParametersNames; +NbParams=size(ParametersValues,2); +DGSA.MainEffects.Display.ParetoPlotbyCluster=0; +DGSA.MainEffects.Display.StandardizedSensitivity='None'; +Sensitivity_with_time=zeros(NbParams,size(responses,2)); + +%% Run DGSA at each step + + +for i=1:size(responses,2) + + responses_i=responses(:,i); % Each response is univariate. + + fprintf('Running DGSA at time=%3.2f...\n',tgrid(i+1)); + DGSA.D=pdist(responses_i); + DGSA.Clustering=kmedoids(DGSA.D,DGSA.Nbcluster,10); + + DGSA=ComputeMainEffects(DGSA); + + + Sensitivity_with_time(:,i)=DGSA.MainEffects.SensitivityStandardized; + + +end + +%% Plot the main effects over time + +LineSeries={'b','r','k','m','--b','--r','--k','--m',':b',':r',':k',':m'}; +figure +for k=1:NbParams + plot(tgrid, [0,Sensitivity_with_time(k,:)],LineSeries{k},'LineWidth',3); hold on + +end +legend(ParametersNames,'Location','EastOutside'); +xlim([0 tgrid(end)]);ylim([0 6]);xlabel('Time(Day)','Fontsize',12,'Fontweight','bold'); +ylabel('Sensitivitty','Fontsize',12,'Fontweight','bold'); +set(gca,'Fontsize',12,'Fontweight','bold'); +hold off + + +end \ No newline at end of file diff --git a/Sobol_DGSA_comparision/SobolSensitivity.m b/Sobol_DGSA_comparision/SobolSensitivity.m new file mode 100644 index 0000000..cf0926a --- /dev/null +++ b/Sobol_DGSA_comparision/SobolSensitivity.m @@ -0,0 +1,81 @@ +function [S,S_t]=SobolSensitivity(tgrid,responses,N_unit_simul,ParametersNames) +% The function computes Sobol's first order & total effects and display over time +% Author: Jihoon Park(jhpark3@stanford.edu) +% Date: 16 May 2016 +% Reference: +% Wainwright, H.M., Finsterle, S., Jung, Y., Zhou, Q., Birkholzer, J.T., 2014. Making sense of global sensitivity analyses. Computers & Geosciences 65, 84-94. + +% Input +% +% tgrid: (vector, length=# of timesteps) grid for time +% responses: (matrix, # of models for Sobol's method x timesteps) Responses of each model +% N_unit_simul: (scalar, # of initial Monte Carlo samples to apply Sobol's method. +% ParametersNamses: (cell, length=# of uncertain parameters) contains names of parameters + +% Output +% +% Si: (matrix, # of uncertain parameters x # of timesteps) : containing first order effect +% Sti: (matrix, # of uncertain parameters x # of timesteps) : containing total effect + +%% Retrieve n and k to apply Sobol's method +% In Sobol's method n(k+2) simulations are required where n=sample size and k is the number of parameters +NbTotalSimul=size(responses,1); % This is n. +NbParam=length(ParametersNames); % This is k. + +%% Extract dynamic data + +responses=[zeros(NbTotalSimul,1),responses]; +C=responses'; +C_reshaped=reshape(C, length(tgrid), N_unit_simul, NbParam+2); +%% Compute Sobol's indicies + +A=C_reshaped(:,:,1); +S=zeros(NbParam,length(tgrid)); +S_t=zeros(NbParam,length(tgrid)); + +for k=1:length(tgrid) + sigma_y_i=var(A(k,:)); % sigma_y_i + mu_y_i=mean(A(k,:)); + for i=1:NbParam + C_i=C_reshaped(k,:,i+2); + A_i=C_reshaped(k,:,1); + B_i=C_reshaped(k,:,2); + S(i,k)=((A_i-mu_y_i)*(C_i-mu_y_i)')/sigma_y_i/(2*(N_unit_simul-1)); + S_t(i,k)=1-((C_i-mu_y_i)*(B_i-mu_y_i)')/sigma_y_i/(2*(N_unit_simul-1)); + + end + +end +%% Plotting - First order effect +S(:,1)=zeros(length(S(i,1)),1); +LineSeries={'b','r','k','m','--b','--r','--k','--m',':b',':r',':k',':m'}; + +figure +for k=1:NbParam + plot(tgrid, S(k,:),LineSeries{k},'LineWidth',3); hold on + +end + +legend(ParametersNames,'Location','EastOutside'); +xlim([0 tgrid(end)]);ylim([0 1.01]);xlabel('Time (day)','Fontsize',14,'Fontweight','bold'); +ylabel('First order effect','Fontsize',14,'Fontweight','bold'); +set(gca,'Fontsize',12,'Fontweight','bold'); +hold off + + +S_t(:,1)=zeros(length(S(i,1)),1); % just make it 0 + +%% Plotting - Total effect +figure +for k=1:NbParam + plot(tgrid, S_t(k,:),LineSeries{k},'LineWidth',3); hold on + +end + +legend(ParametersNames,'Location','EastOutside'); +xlim([0 tgrid(end)]);ylim([0 1.01]);xlabel('Time (day)','Fontsize',12,'Fontweight','bold'); +ylabel('Total effect','Fontsize',14,'Fontweight','bold'); +set(gca,'Fontsize',12,'Fontweight','bold'); +hold off + +end \ No newline at end of file diff --git a/VariablesSaved/DGSA_Completed.mat b/VariablesSaved/DGSA_Completed.mat new file mode 100644 index 0000000..42591ca Binary files /dev/null and b/VariablesSaved/DGSA_Completed.mat differ diff --git a/VariablesSaved/DGSA_Spatial_Completed.mat b/VariablesSaved/DGSA_Spatial_Completed.mat new file mode 100644 index 0000000..e1eaf9f Binary files /dev/null and b/VariablesSaved/DGSA_Spatial_Completed.mat differ diff --git a/VariablesSaved/DGSAandSobol_comparision.mat b/VariablesSaved/DGSAandSobol_comparision.mat new file mode 100644 index 0000000..baa41f2 Binary files /dev/null and b/VariablesSaved/DGSAandSobol_comparision.mat differ diff --git a/Visualizations/Bubbleplot/BubblePlot.m b/Visualizations/Bubbleplot/BubblePlot.m new file mode 100644 index 0000000..7d740cd --- /dev/null +++ b/Visualizations/Bubbleplot/BubblePlot.m @@ -0,0 +1,52 @@ +function Xd=BubblePlot(GlobalSensitivityInteractions, ParametersNames, ScaleFactor,... + StandardizedSensitivity, IsSensitive,Fontsizes) +% The function displays bubble plot to display condtional effects. +% Author: Jihoon Park (jhpark3@stanford.edu) +% Date: March, 2015 +% +% Input: +% +% GlobalSensitivityInteractions: (vector, length=(# of parameters) x (# of parameters -1)) Conditional effects averaged over bins and classes. +% ParametersNames: (cell, length= # of parameters) Names of parameters +% ScaleFactor: (scalar) scale of the size of bubble. The size of bubble is proportional to main effects. Higher values give smaller bubble. +% StandardizedSensitivity:(vector, length=# of parameters) Main effects averaged over clusters. +% IsSensitive: (logical, length=# of parameters) Result of bootstrap hypothesis test. If true, a parameter is sensitive. +% Fontsizes: (Scalar) Fontsize at bubble plot +% +% Ouput +% XdL (matrix, # of Parameters x 2) Coordinates of bubbles. + +N=length(ParametersNames); +D=GetDistMatrixfromInterSens(GlobalSensitivityInteractions,N); % In the bubble plot, the distance between parameters are defined as the inverse of the average of conditional effects. + +% Multi-Dimensional Scaling (MDS) using distance D. +rng(123433); +Xd_ = cmdscale(D); +dims = 2; +Xd = Xd_(:,1:dims); + +figure +hold on +for k=1:size(Xd,1) + + +if IsSensitive(k)==1 + colorv='r'; +else + colorv='b'; +end + +filledCircle(Xd(k,:),StandardizedSensitivity(k)/ScaleFactor,100,colorv);axis('equal'); +alpha(.5); + + text(Xd(k,1),Xd(k,2),ParametersNames{k},'HorizontalAlignment','center','Fontsize',Fontsizes); + +end +hold off +grid off + +set(gca,'XTickLabel',{''}) +set(gca,'YTickLabel',{''}) +set(gcf,'color','w');box on; set(gca,'LineWidth',3); + +end \ No newline at end of file diff --git a/Visualizations/Bubbleplot/GetDistMatrixfromInterSens.m b/Visualizations/Bubbleplot/GetDistMatrixfromInterSens.m new file mode 100644 index 0000000..19e6aea --- /dev/null +++ b/Visualizations/Bubbleplot/GetDistMatrixfromInterSens.m @@ -0,0 +1,35 @@ +function D=GetDistMatrixfromInterSens(A,NbPara) +%% +% The function computes symmetric distance matrix from conditional effects. +% Author: Jihoon Park (jhpark3@stanford.edu) +% Date: March, 2015 +% +% Input: + +% A: : (vector, length=(# of parameters) x (# of parameters -1)) Conditional effects averaged over bins and classes. +% NbPara: (scalar) # of parameters +% +% Output: +% D: (matrix, # of parameters x # of parameters) Distance matrix used in bubble plot. +%% +NbInterPer=NbPara-1; % Each parameter has one less conditional effects +A_reshaped=reshape(A,NbInterPer,[]); +A_augmented=zeros(NbPara); + +for k=1:NbPara + + A_augmented(:,k)=InsertNumVec(A_reshaped(:,k),k,-999); + +end + +D=zeros(NbPara); +for i=1:NbPara-1 + + for j=i+1:NbPara + + D(i,j)=1/((A_augmented(i,j)+A_augmented(j,i))*.5); + + end +end + +D=D+D'; \ No newline at end of file diff --git a/Visualizations/Bubbleplot/InsertNumVec.m b/Visualizations/Bubbleplot/InsertNumVec.m new file mode 100644 index 0000000..cbca018 --- /dev/null +++ b/Visualizations/Bubbleplot/InsertNumVec.m @@ -0,0 +1,26 @@ +function y=InsertNumVec(a1,i,Num) +% The function is used to construct matrix used for bubble plot +n=size(a1,1); +y=Num*ones(n+1,1); + + +for k=1:n + + if k==i + break; + else + y(k)=a1(k); + end + +end + +for j=k+1:n+1 + + y(j)=a1(j-1); + +end + +if i==n+1 + y(end)=Num; +end + diff --git a/Visualizations/Bubbleplot/filledCircle.m b/Visualizations/Bubbleplot/filledCircle.m new file mode 100644 index 0000000..8889d68 --- /dev/null +++ b/Visualizations/Bubbleplot/filledCircle.m @@ -0,0 +1,55 @@ +function h = filledCircle(center,r,N,color) +%--------------------------------------------------------------------------------------------- +% FILLEDCIRCLE Filled circle drawing +% +% filledCircle(CENTER,R,N,COLOR) draws a circle filled with COLOR that +% has CENTER as its center and R as its radius, by using N points on the +% periphery. +% +% Usage Examples, +% +% filledCircle([1,3],3,1000,'b'); +% filledCircle([2,4],2,1000,'r'); +% +% Sadik Hava +% May, 2010 +% +% Inspired by: circle.m [Author: Zhenhai Wang] +%--------------------------------------------------------------------------------------------- + +THETA=linspace(0,2*pi,N); +RHO=ones(1,N)*r; +[X,Y] = pol2cart(THETA,RHO); +X=X+center(1); +Y=Y+center(2); +h=fill(X,Y,color); +set(h,'edgecolor','white'); % Delete the boundary. Added on 30 Mar 2015 +axis square; + + +% COPYRIGHT STUFF... :D (Since I am modifying Zhenhai's code.) +% +% Copyright (c) 2002, Zhenhai Wang +% All rights reserved. +% +% Redistribution and use in source and binary forms, with or without +% modification, are permitted provided that the following conditions are +% met: +% +% * Redistributions of source code must retain the above copyright +% notice, this list of conditions and the following disclaimer. +% * Redistributions in binary form must reproduce the above copyright +% notice, this list of conditions and the following disclaimer in +% the documentation and/or other materials provided with the distribution +% +% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE +% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +% POSSIBILITY OF SUCH DAMAGE. \ No newline at end of file diff --git a/cdf_Interactions.m b/Visualizations/CDFs/cdf_ConditionalEffects.m similarity index 65% rename from cdf_Interactions.m rename to Visualizations/CDFs/cdf_ConditionalEffects.m index 7acb7a0..a86ebde 100644 --- a/cdf_Interactions.m +++ b/Visualizations/CDFs/cdf_ConditionalEffects.m @@ -5,16 +5,36 @@ % Author: Celine Scheidt % Date: August 2012 +% Updated by Jihoon Park (jhpark3@stanford.edu) +% Date: 16 May 2016 +% - users can specify the name of conditioned/conditioning parameters -function cdf_Interactions(ParamsValues,ConditionalParams,Clustering,NbBins,WhichCluster,LabelName) +function cdf_ConditionalEffects(ConditionedParameter,ConditioningParameter,DGSA,WhichCluster) %% Input Parameters -% - ParametersValues: vector (NbModels x 1) of the parameter values (e.g. x in x|y) -% - ConditionalParams: vector (NbModels x 1) of the values of the conditional parameter values (e.g. y in x|y) -% - Clustering: Clustering results -% - NbBins: Number of bins for the conditional parameter +% - ConditionedParameter: string of conditioned parameter (e.g. x in x|y) +% - ConditioningParameter: string of conditioning parameter (e.g. y in x|y) % - WhichCluster: index of the cluster (class) for which cdfs should be plotted -% - LabelNames: label for the interaction ('x|y') + +%% Check the names of variables +idxConditionedParameter=find(strcmp(DGSA.ParametersNames,ConditionedParameter)); +if isempty(idxConditionedParameter) + error('Enter correct name of conditioned parameters') +end +idxConditioningParameter=find(strcmp(DGSA.ParametersNames,ConditioningParameter)); + +if isempty(idxConditioningParameter) + + error('Enter correct name of conditioning parameters') +end + +ParamsValues=DGSA.ParametersValues(:,idxConditionedParameter); +ConditionalParams=DGSA.ParametersValues(:,idxConditioningParameter); + +Clustering=DGSA.Clustering; +NbBins=DGSA.ConditionalEffects.NbBins(idxConditioningParameter); +LabelName=[ConditionedParameter,'|',ConditioningParameter]; +%% Plotting type_line = {'--','-.',':','--','-.',':'}; C = definecolor(WhichCluster,length(Clustering.medoids),NbBins); @@ -46,7 +66,7 @@ function cdf_Interactions(ParamsValues,ConditionalParams,Clustering,NbBins,Which end end xlabel(LabelName,'fontsize',14,'fontweight','b');ylabel('cdf','fontsize',14,'fontweight','b'); box on; - +title(['Class conditiona CDF from Cluster ',num2str(WhichCluster)]); end diff --git a/cdf_MainFactor.m b/Visualizations/CDFs/cdf_MainFactor.m similarity index 56% rename from cdf_MainFactor.m rename to Visualizations/CDFs/cdf_MainFactor.m index 443e9de..7c1ed6b 100644 --- a/cdf_MainFactor.m +++ b/Visualizations/CDFs/cdf_MainFactor.m @@ -1,22 +1,45 @@ -% +% This function plots the cdf of a specified parameter for each class +% % This function plots the cdf of each parameter for each class % Author: Celine Scheidt % Date: August 2012 +% Modified by Jihoon Park (jhpark3@stanford.edu) on 14 May 2016. The user +% can specify the name of variables of parameters. If not specified, cdfs +% of all parameters will be displayed. -function cdf_MainFactor(ParametersValues,Clustering,ParametersNames) +function cdf_MainFactor(ParametersValues,Clustering,ParametersNames, WhichParameter) %% Input Parameters % - ParametersValues: matrix (NbModels x NbParams) of the parameter values % - ParametersNames: list containing the names of the parameters % - Clustering: Clustering results +% - WhichParameter(optional): Parameters specified. If omitted, CDFs of +% all parameters will be displayed. +if nargin<4 + WhichParameter=ParametersNames; +end + +ParametersIndex=zeros(1,length(WhichParameter)); +for k=1:length(WhichParameter) + ParametersIndex_value=find(strcmp(ParametersNames,WhichParameter(k))); + if isempty(ParametersIndex_value) + error('Enter correct name of parameters') + else + ParametersIndex(k)=ParametersIndex_value; + end +end -nbparams = size(ParametersValues,2); + + +%nbparams = size(ParametersValues,2); nbclusters = length(Clustering.medoids); C = definecolor(nbclusters); -for i = 1:nbparams + +for k = 1:length(ParametersIndex) + i=ParametersIndex(k); [f_prior,x_prior] = ecdf(ParametersValues(:,i)); % prior cdf figure; axes('FontSize',12,'FontWeight','b');hold on;box on; diff --git a/Visualizations/DGSA/DisplayConditionalEffects.m b/Visualizations/DGSA/DisplayConditionalEffects.m new file mode 100644 index 0000000..0debaac --- /dev/null +++ b/Visualizations/DGSA/DisplayConditionalEffects.m @@ -0,0 +1,107 @@ +function DisplayConditionalEffects(DGSA,Type) +%% +% The function displays conditioanl effects according to the type specified by a user. +% Author: Jihoon Park(jhpark3@stanford.edu) +% Date: 15 May 2016 + +% Input +% +% DGSA: Data sturcture containing results of DGSA +% .ParametersNames:(cell, length= # of parameters) Names of parameters +% .ConditionalEffects.SensitivityByClusterandBins: +% (4D array, (# of parameters) x (# of parameters-1) x (# of clusters) x (maximum value of bins)): +% Element (i,j,c,l) corresponds to conditional effect of i-th parameter conditioned to +% l-th bin of j-th parameter from class c . +% .ConditionalEffects.Names_ConditionalEffects: (cell, length=(# of parameters) x (# of parameters-1)) +% Names of conditional effects. +% .ConditionalEffects.NbBins: (vector, length=# of parameters) +% Specifies each number of bins of parameters to compute conditional effects +% .ConditionalEffects.H0accConditional: (logical vector, length=(# of parameters) x (# of parameters -1)) +% If it is true, corresponding conditional effect is sensitive. + +% Type(string): Visualization method for standardized conditional effects +% 'Pareto (default)' : Pareto plots. If there are a lot of parameters, it is not recommended since there are +% N(N-1) items to display which is not practical. + +% 'Hplot': Use h-plot +% 'Bubble': Use bubble plot + + +%% 1. Assign variables +% Assign sensitivities to varaibles +% +% 1.1 Names of parameters +ParametersNames=DGSA.ParametersNames; + +% 1.2 Clustering information +NbClusters=length(DGSA.Clustering.medoids); % # of clusters + +% 1.3 Conditional effects +NormalizedInteractions=DGSA.ConditionalEffects.SensitivityByClusterandBins; % Conditional effects by clusters and bins +StandardizedSensitivityInteractions=DGSA.ConditionalEffects.StandardizedSensitivity; % Conditional effects standardized +ConditionalEffectNames=DGSA.ConditionalEffects.Names_ConditionalEffects; % Names of conditional effects +NbBins=DGSA.ConditionalEffects.NbBins; % # of bins of each parameter +H0accConditional=DGSA.ConditionalEffects.H0accConditional; % Result of hypothesis testing of conditional effects + +% 1.4 Main effects + +MainEffectsStandardized=DGSA.MainEffects.SensitivityStandardized; % Main effects standardized +H0accMain=DGSA.MainEffects.H0accMain; % Result of hypothesis testing of Main effcts + +%% 2. Sensitivity by cluster & bins + +if DGSA.ConditionalEffects.Display.SensitivityByClusterAndBins + % If this is true, display Pareto plots to show conditional effects by bins and clusters + ParetoInteractions(NormalizedInteractions,ConditionalEffectNames,NbClusters,NbBins); +end + +%% 3. Diplay Standardized Conditional Effects + +if nargin<2 + Type='Pareto'; % Default is Pareto plot +end + +switch Type + case 'Pareto' + + Pareto_GlobalSensitivity(StandardizedSensitivityInteractions,ConditionalEffectNames,H0accConditional); + + case 'Hplot' + + % Create a dialog box to receive additional information. + + prompt = {'Enter Scale of the bubble:','Enter Font size: '}; + dlg_title = 'Input(Hplot)'; + num_lines = 1; + defaultans = {'30','12'}; + options.Resize='on'; + answer = inputdlg(prompt,dlg_title,num_lines,defaultans,options); + + ScaleFactorHplot=str2num(answer{1}); Fontsizes=str2num(answer{2}); + + + DisplayHplot(StandardizedSensitivityInteractions,MainEffectsStandardized... + ,ParametersNames, ScaleFactorHplot, Fontsizes); + + + case 'Bubble' + + prompt = {'Enter Scale of the bubble:','Enter Font size: '}; + dlg_title = 'Input(BubblePlot)'; + num_lines = 1; + defaultans = {'5','14'}; + options.Resize='on'; + answer = inputdlg(prompt,dlg_title,num_lines,defaultans,options); + + ScaleFactorBubblePlot=str2num(answer{1}); Fontsizes=str2num(answer{2}); + + BubblePlot(StandardizedSensitivityInteractions, ParametersNames, ScaleFactorBubblePlot, MainEffectsStandardized, H0accMain,Fontsizes); + + + otherwise + error('Enter correct names of visualization methods') + +end + +end + diff --git a/Visualizations/DGSA/DisplayNetConditionalEffects_all.m b/Visualizations/DGSA/DisplayNetConditionalEffects_all.m new file mode 100644 index 0000000..ca69acf --- /dev/null +++ b/Visualizations/DGSA/DisplayNetConditionalEffects_all.m @@ -0,0 +1,68 @@ +function DisplayNetConditionalEffects_all(DGSA) +% The function displays net conditional effcts of all parameters +% Author: Jihoon Park (jhpark3@stanford.edu) +% Date 16 May 2016 +% Input: +% +% DGSA: Results of DGSA +% .ConditionalEffects.SensitivityByClusterandBins: +% (4D array, (# of parameters) x (# of parameters-1) x (# of clusters) x (maximum value of bins)): +% Element (i,j,c,l) corresponds to conditional effect of i-th parameter conditioned to +% l-th bin of j-th parameter from class c . +% .MainEffects.SensitivityStandardized: (vector, length=# of parameters) Main effects averaged over clusters. +% .ParametersNames: (cell, length= # of parameters) Names of parameters + +%% Assign parameters + +SensitivityInteractions=DGSA.ConditionalEffects.SensitivityByClusterandBins; +GlobalSens=DGSA.MainEffects.SensitivityStandardized; +ParamsNames=DGSA.ParametersNames; + +%% Compute net conditional effects + +[NbParms, ~, NbClusters, NbMaxBins]=size(SensitivityInteractions); +SensitivityInteractionOverClass=nanmean(SensitivityInteractions, 3); % Average over cluster + +SensitivityInteractionSumInter=sum(SensitivityInteractionOverClass,2); +MatrixSum=zeros(NbParms, NbMaxBins); + + +for k=1:NbMaxBins + MatrixSum(:,k)=SensitivityInteractionSumInter(:,:,:,k); +end + + + +[NbParams NbClusters] = size(MatrixSum); + + +[~, SortedSA] = sort(GlobalSens,'ascend'); +MatrixSum = MatrixSum(SortedSA,:); +ParamsNames = ParamsNames(SortedSA); + +figure; +axes('FontSize',12,'fontweight','b'); hold on; +h0 = barh(1:NbParams,MatrixSum,0.8,'group','LineWidth',1.5); + +P=findobj(h0,'type','patch'); +C = definecolor(NbClusters); +for n=1:length(P) + set(P(n),'facecolor',C(n,:),'LineWidth',1.5); +end + + +set(gca,'YTick',1:NbParams) +set(gca,'YTickLabel',ParamsNames) +box on + +legend('Low','Med','High','Location','NorthEastOutside'); +end + + +% This function defines the bar colors +function C = definecolor(NbClusters) + Cs = colormap(jet(124)); + Ds = floor(linspace(1,size(Cs,1),NbClusters)); + C = Cs(Ds,:); + +end \ No newline at end of file diff --git a/ParetoInteractions.m b/Visualizations/DGSA/ParetoInteractions.m similarity index 88% rename from ParetoInteractions.m rename to Visualizations/DGSA/ParetoInteractions.m index c641742..18124a1 100644 --- a/ParetoInteractions.m +++ b/Visualizations/DGSA/ParetoInteractions.m @@ -3,7 +3,7 @@ % for each cluster and for each bin. % Author: Celine Scheidt -% Date: August 2012 +% Date: August 2012 (updated April 2016) function ParetoInteractions(NormalizedSensDependencies,ParamsNames,NbClusters,NbBins) @@ -27,7 +27,8 @@ function ParetoInteractions(NormalizedSensDependencies,ParamsNames,NbClusters,Nb SensitivityPerClass = nanmean(NormalizedSensDependencies,4); SensitivityPerClass = reshape(permute(SensitivityPerClass,[2,1,3]),[],NbClusters); - + vMatlab= version('-release'); + NbInter = size(SensitivityPerClass,1); [DivFromRef,BarWidth,TextSize] = SetDefaultValuesForPlot(NbClusters,NbInter); @@ -56,11 +57,20 @@ function ParetoInteractions(NormalizedSensDependencies,ParamsNames,NbClusters,Nb for j = 1:NbInter C = definecolor(NbClusters,NbBinsAll(j)); for i = 1:NbClusters - h1 = barh([DivFromRef(i)+j,DivFromRef(i)+j + 1],vertcat(SortedInteractions(i + (j-1)*NbClusters,:)./NbBinsPerInter(i + (j-1)*NbClusters,:),nan(1,size(Interactions,2))),BarWidth,'stack'); - P=findobj(h1,'type','patch'); - for n=1:NbBinsAll(j) - set(P(n),'facecolor',C(n+(i-1)*NbBinsAll(j),:),'LineWidth',1.5); - end + h1 = barh([DivFromRef(i)+j,DivFromRef(i)+j + 1],vertcat(SortedInteractions(i + (j-1)*NbClusters,:)./NbBinsPerInter(i + (j-1)*NbClusters,:),nan(1,size(Interactions,2))),BarWidth,'stack'); + if str2double(vMatlab(1:end-1)) < 2014 + P=findobj(h1,'type','patch'); + for n=1:NbBinsAll(j) + set(P(n),'facecolor',C(n+(i-1)*NbBinsAll(j),:),'LineWidth',1.5); + end + else + for n=1:NbBinsAll(j) + set(h1(n),'facecolor',C(n+(i-1)*NbBinsAll(j),:),'LineWidth',1.5); + end + + + end + end end set(gca,'YTick',1:NbInter) diff --git a/ParetoMainFactors.m b/Visualizations/DGSA/ParetoMainFactors.m similarity index 100% rename from ParetoMainFactors.m rename to Visualizations/DGSA/ParetoMainFactors.m diff --git a/Pareto_GlobalSensitivity.m b/Visualizations/DGSA/Pareto_GlobalSensitivity.m similarity index 98% rename from Pareto_GlobalSensitivity.m rename to Visualizations/DGSA/Pareto_GlobalSensitivity.m index b0c7e9e..97e01fc 100644 --- a/Pareto_GlobalSensitivity.m +++ b/Visualizations/DGSA/Pareto_GlobalSensitivity.m @@ -31,8 +31,8 @@ function Pareto_GlobalSensitivity(SensitivityValues,ParamsNames,IsSensitive) if nargin == 3 % bar are colored - C1 = [0.8,0,0]; - C2 = [0,0,0.8]; + C1 = [0,0,0.8]; + C2 = [0.8,0,0]; h1 = []; h2 = []; figure axes('FontSize',TextSize,'fontweight','b'); hold on; diff --git a/Visualizations/DGSA/Pareto_GlobalSensitivity_CI.m b/Visualizations/DGSA/Pareto_GlobalSensitivity_CI.m new file mode 100644 index 0000000..4a2b4bb --- /dev/null +++ b/Visualizations/DGSA/Pareto_GlobalSensitivity_CI.m @@ -0,0 +1,112 @@ +function Pareto_GlobalSensitivity_CI(StandardizedSensitivity, H0accMain, ParametersNames,ColorType) +% The function dispalys standardized main effects with confidence +% intervals. +% Author: Jihoon Park (jhpark3@stanford.edu) +% Date: 14 May 2016 + +% Input: +% +% StandardizedSensitivity: (array, # of Parameters x 1 x 3) : Main effects standardized by averaging over clusters +% H0accMain (logical, length=# of Parameters): If 1, H0 is rejected (sensitive), otherwise accepted (insensitive) +% ParametersNames (cell, length=# of parameters) Names of Parameters +% ColorType: (string) Specifies how a Pareto plot is colored. +% If 'RB', red/blue scheme is used (default) +% If 'jet', a bar is colored by 'jet' from matlab + + +StandardizedSensitivity0=StandardizedSensitivity(:,:,1); % This is the sensitivity corresponding the first value of alpha. This will be taken as the sensitivities. + +%%% StandardizedSensitivity1 and StandardizedSensitivity2 corresponds to +%%% the second and third values of alpha. This is used to compute the +%%% confidence intervals. + +StandardizedSensitivity1=StandardizedSensitivity(:,:,2); +StandardizedSensitivity2=StandardizedSensitivity(:,:,3); + +[~, SortedSA] = sort(StandardizedSensitivity0,'ascend'); + +% Sort the variables according to the rank of sensitivity + +StandardizedSensitivity0=StandardizedSensitivity0(SortedSA); +StandardizedSensitivity1=StandardizedSensitivity1(SortedSA); +StandardizedSensitivity2=StandardizedSensitivity2(SortedSA); +H0accMain=H0accMain(SortedSA); +ParametersNames=ParametersNames(SortedSA); +IsSensitive=H0accMain; + +NbParams = length(StandardizedSensitivity0); + +if NbParams > 10 + TextSize = 10; +else + TextSize = 12; +end + + + +%% Define Color + +switch ColorType + + case 'jet' + + C=jet; + nC=size(C,1); + C=flipud(C); + + case 'RB' + + C2=jet(64);C=C2*0; % Initialize + + C(:,1)=linspace(0,1,size(C,1))'; % Blue + C(:,3)=linspace(1,0,size(C,1))'; % Red + + nC=size(C,1); + + + otherwise + error('Enter correct types of colors') + +end +%% Visualization + + figure + axes('FontSize',TextSize,'fontweight','b'); hold on; + for i = 1:NbParams + delta_n=StandardizedSensitivity1(i)-StandardizedSensitivity2(i); % define delta_n + if StandardizedSensitivity0(i)<1-delta_n/2 + ColorVector=C(1,:); % Blue + elseif StandardizedSensitivity0(i)>1+delta_n/2 + ColorVector=C(end,:); % Red + else + higher=1+delta_n/2; + lower=1-delta_n/2; + ratio_pvalue=(StandardizedSensitivity0(i)-lower)/(higher-lower); + ColorVector=C(floor(nC*ratio_pvalue)+1,:); + + end + + colormap(C); + if IsSensitive(i) == 1 + h1 = barh(i,StandardizedSensitivity0(i),'FaceColor',ColorVector,'BarWidth',0.8,'LineStyle','-','LineWidth',2); + + else + h2 = barh(i,StandardizedSensitivity0(i),'FaceColor',ColorVector,'BarWidth',0.8,'LineStyle','-.','LineWidth',2); + + end + herrorbar(1,i,delta_n/2); % Add confidence intervals + + end + set(gca,'YTick',1:NbParams) + set(gca,'YTickLabel',ParametersNames) + plot([1 1], [0 NbParams+1],'m','LineWidth',3); + box on; ylim([0 NbParams+1]); + h3=colorbar; caxis([0 .1]); + + axis_object=get(gca); + xlim([0,axis_object.XLim(2)]); + +end + + + diff --git a/Visualizations/DGSA/herrorbar.m b/Visualizations/DGSA/herrorbar.m new file mode 100644 index 0000000..d118073 --- /dev/null +++ b/Visualizations/DGSA/herrorbar.m @@ -0,0 +1,152 @@ +function hh = herrorbar(x, y, l, u, symbol) +%HERRORBAR Horizontal Error bar plot. +% HERRORBAR(X,Y,L,R) plots the graph of vector X vs. vector Y with +% horizontal error bars specified by the vectors L and R. L and R contain the +% left and right error ranges for each point in X. Each error bar +% is L(i) + R(i) long and is drawn a distance of L(i) to the right and R(i) +% to the right the points in (X,Y). The vectors X,Y,L and R must all be +% the same length. If X,Y,L and R are matrices then each column +% produces a separate line. +% +% HERRORBAR(X,Y,E) or HERRORBAR(Y,E) plots X with error bars [X-E X+E]. +% HERRORBAR(...,'LineSpec') uses the color and linestyle specified by +% the string 'LineSpec'. See PLOT for possibilities. +% +% H = HERRORBAR(...) returns a vector of line handles. +% +% Example: +% x = 1:10; +% y = sin(x); +% e = std(y)*ones(size(x)); +% herrorbar(x,y,e) +% draws symmetric horizontal error bars of unit standard deviation. +% +% This code is based on ERRORBAR provided in MATLAB. +% +% See also ERRORBAR + +% Jos van der Geest +% email: jos@jasen.nl +% +% File history: +% August 2006 (Jos): I have taken back ownership. I like to thank Greg Aloe from +% The MathWorks who originally introduced this piece of code to the +% Matlab File Exchange. +% September 2003 (Greg Aloe): This code was originally provided by Jos +% from the newsgroup comp.soft-sys.matlab: +% http://newsreader.mathworks.com/WebX?50@118.fdnxaJz9btF^1@.eea3ff9 +% After unsuccessfully attempting to contact the orignal author, I +% decided to take ownership so that others could benefit from finding it +% on the MATLAB Central File Exchange. + +if min(size(x))==1, + npt = length(x); + x = x(:); + y = y(:); + if nargin > 2, + if ~isstr(l), + l = l(:); + end + if nargin > 3 + if ~isstr(u) + u = u(:); + end + end + end +else + [npt,n] = size(x); +end + +if nargin == 3 + if ~isstr(l) + u = l; + symbol = '-'; + else + symbol = l; + l = y; + u = y; + y = x; + [m,n] = size(y); + x(:) = (1:npt)'*ones(1,n);; + end +end + +if nargin == 4 + if isstr(u), + symbol = u; + u = l; + else + symbol = '-'; + end +end + +if nargin == 2 + l = y; + u = y; + y = x; + [m,n] = size(y); + x(:) = (1:npt)'*ones(1,n);; + symbol = '-'; +end + +u = abs(u); +l = abs(l); + +if isstr(x) | isstr(y) | isstr(u) | isstr(l) + error('Arguments must be numeric.') +end + +if ~isequal(size(x),size(y)) | ~isequal(size(x),size(l)) | ~isequal(size(x),size(u)), + error('The sizes of X, Y, L and U must be the same.'); +end + +tee = (max(y(:))-min(y(:)))/100; % make tee .02 x-distance for error bars +% changed from errorbar.m +xl = x - l; +xr = x + u; +ytop = y + tee; +ybot = y - tee; +n = size(y,2); +% end change + +% Plot graph and bars +hold_state = ishold; +cax = newplot; +next = lower(get(cax,'NextPlot')); + +% build up nan-separated vector for bars +% changed from errorbar.m +xb = zeros(npt*9,n); +xb(1:9:end,:) = xl; +xb(2:9:end,:) = xl; +xb(3:9:end,:) = NaN; +xb(4:9:end,:) = xl; +xb(5:9:end,:) = xr; +xb(6:9:end,:) = NaN; +xb(7:9:end,:) = xr; +xb(8:9:end,:) = xr; +xb(9:9:end,:) = NaN; + +yb = zeros(npt*9,n); +yb(1:9:end,:) = ytop; +yb(2:9:end,:) = ybot; +yb(3:9:end,:) = NaN; +yb(4:9:end,:) = y; +yb(5:9:end,:) = y; +yb(6:9:end,:) = NaN; +yb(7:9:end,:) = ytop; +yb(8:9:end,:) = ybot; +yb(9:9:end,:) = NaN; +% end change + + +[ls,col,mark,msg] = colstyle(symbol); if ~isempty(msg), error(msg); end +symbol = [ls mark col]; % Use marker only on data part +esymbol = ['-' col]; % Make sure bars are solid + +h = plot(xb,yb,esymbol,'LineWidth',2,'Color','k'); hold on +h = [h;plot(x,y,symbol)]; + +if ~hold_state, hold off; end + +if nargout>0, hh = h; end \ No newline at end of file diff --git a/Visualizations/Hplot/DisplayHplot.m b/Visualizations/Hplot/DisplayHplot.m new file mode 100644 index 0000000..f58e81e --- /dev/null +++ b/Visualizations/Hplot/DisplayHplot.m @@ -0,0 +1,80 @@ +function H=DisplayHplot(GlobalSensitivityInteractions,StandardizedSensitivity,ParametersNames, ScaleFactor, Fontsizes) +%% +% The function displays h-plot from conditional effects +% Author: Jihoon Park (jhpark3@stanford.edu) +% Reference: +% Epifanio I., 2014. Mapping the asymmetrical citation relationships between journals by h-plots. Journal of the Association for Information Science and Technology, 65 (6), 1293-1298. +% Park et al., 2016. DGSA: a matlab toolbox for distance-based generalized sensitivity analysis for geoscientific computer experiments +% +% +% Input: + +% GlobalSensitivityInteractions:(4D array, (# of parameters) x (# of parameters-1) x (# of clusters) x (maximum value of bins)): +% Element (i,j,c,l) corresponds to conditional effect of i-th parameter conditioned to +% l-th bin of j-th parameter from class c . +% +% StandardizedSensitivity: (vector, length=# of parameters) Main effects averaged over clusters. +% ParametersNames: (cell, length= # of parameters) Names of parameters +% ScaleFactor: (scalar) Value to scale the size of bubble on h-plot. Higher value decreases the size of bubbles. +% Fontsizes: (scalar) Fontsize of names of parameters in h plot + +% Output: + +% H: Coordinates of each parameter at h-plot + +NbParams=length(ParametersNames); +dims=2; % Dimension of h-plot. + +X=GetAsymmetricDistanceHplot(GlobalSensitivityInteractions,NbParams); +S=cov(X); % Get the covariance matrix. + +[q, lambda_vec]=eig(S); lambda_extract=diag(lambda_vec); % Eigenvalue decomposition +q1=q(:,end); q2=q(:,end-dims+1); lambda1=sqrt(lambda_extract(end)); lambda2=sqrt(lambda_extract(end-1)); +H=[lambda1*q1, lambda2*q2]; % Retrieve the coordinates + +n=size(H,1); +figure; hold on +ColorVector=zeros(size(H,1),1); +ColorVector(1:n/2)=1; + +StandardizedSensitivity=[StandardizedSensitivity;StandardizedSensitivity]; +ParametersNames=[ParametersNames,ParametersNames]; +for k=1:size(H,1) + + if ColorVector(k)==1 + colorv='g'; + else + colorv='m'; + end + + filledCircle(H(k,:),StandardizedSensitivity(k)/ScaleFactor,100,colorv);axis('equal'); % Place bubbles on h-plot + alpha(0.5); + + text(H(k,1),H(k,2),ParametersNames{k},'HorizontalAlignment','center','Fontsize',Fontsizes, 'Fontweight','Bold'); + +end +hold off +grid off + +set(gca,'XTickLabel',{''}) +set(gca,'YTickLabel',{''}) +set(gcf,'Color','w'); +set(gca,'LineWidth',2); +box on; set(gca,'LineWidth',3); + + +lambda_extract=flipud(lambda_extract); +lambdasq_seq_sum=cumsum(lambda_extract.^2); +lamdasq_sum=lambda_extract'*lambda_extract; +lambdasq_seq_sum=lambdasq_seq_sum/lamdasq_sum; +lambdasq_seq_sum=[0;lambdasq_seq_sum]; +indexi=0:length(lambdasq_seq_sum)-1;figure; +plot(indexi,lambdasq_seq_sum,'LineWidth',3); + +%set(gca,'XTick',[0:length(lambdasq_seq_sum)]); +set(gca,'Fontsize',12); +set(gca,'Fontsize',12); +xlabel('Dim','Fontsize',14); +ylabel('Goodness of fit','Fontsize',14); + +end diff --git a/Visualizations/Hplot/GetAsymmetricDistanceHplot.m b/Visualizations/Hplot/GetAsymmetricDistanceHplot.m new file mode 100644 index 0000000..f813aae --- /dev/null +++ b/Visualizations/Hplot/GetAsymmetricDistanceHplot.m @@ -0,0 +1,28 @@ +function X=GetAsymmetricDistanceHplot(A,NbPara) +%The function computes the asymmetric distance matrix to use for h-plot. +% +% Author : Jihoon Park +% Date: March, 2015 +% This scripts returns X=[D'|D] where D is asymmetric distance amtrix + +%% Input +% A: (vector, length=(# of parameters) x (# of parameters -1)) Conditional effects averaged over bins and classes. +% NbPara : (scalar) # of Parameters. + +%% Take the inverse first. +A=1./A; + +%% Construct asymmetric distance matrix +NbInterPer=NbPara-1; + +A_reshaped=reshape(A,NbInterPer,[]); +A_augmented=zeros(NbPara); + +for k=1:NbPara + + A_augmented(:,k)=InsertNumVec(A_reshaped(:,k),k,0); + +end + +D=A_augmented; +X=[D, D']; diff --git a/Visualizations/Hplot/filledCircle.m b/Visualizations/Hplot/filledCircle.m new file mode 100644 index 0000000..8889d68 --- /dev/null +++ b/Visualizations/Hplot/filledCircle.m @@ -0,0 +1,55 @@ +function h = filledCircle(center,r,N,color) +%--------------------------------------------------------------------------------------------- +% FILLEDCIRCLE Filled circle drawing +% +% filledCircle(CENTER,R,N,COLOR) draws a circle filled with COLOR that +% has CENTER as its center and R as its radius, by using N points on the +% periphery. +% +% Usage Examples, +% +% filledCircle([1,3],3,1000,'b'); +% filledCircle([2,4],2,1000,'r'); +% +% Sadik Hava +% May, 2010 +% +% Inspired by: circle.m [Author: Zhenhai Wang] +%--------------------------------------------------------------------------------------------- + +THETA=linspace(0,2*pi,N); +RHO=ones(1,N)*r; +[X,Y] = pol2cart(THETA,RHO); +X=X+center(1); +Y=Y+center(2); +h=fill(X,Y,color); +set(h,'edgecolor','white'); % Delete the boundary. Added on 30 Mar 2015 +axis square; + + +% COPYRIGHT STUFF... :D (Since I am modifying Zhenhai's code.) +% +% Copyright (c) 2002, Zhenhai Wang +% All rights reserved. +% +% Redistribution and use in source and binary forms, with or without +% modification, are permitted provided that the following conditions are +% met: +% +% * Redistributions of source code must retain the above copyright +% notice, this list of conditions and the following disclaimer. +% * Redistributions in binary form must reproduce the above copyright +% notice, this list of conditions and the following disclaimer in +% the documentation and/or other materials provided with the distribution +% +% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE +% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +% POSSIBILITY OF SUCH DAMAGE. \ No newline at end of file diff --git a/Visualizations/Responses/CompareResponses.m b/Visualizations/Responses/CompareResponses.m new file mode 100644 index 0000000..2ce6b0f --- /dev/null +++ b/Visualizations/Responses/CompareResponses.m @@ -0,0 +1,67 @@ +function CompareResponses(Prior,AfterPUR,DataStruct) +% The function compares two responses - 1) Prior responses, +% 2) Responses from parameters whose uncertainies are reduced by DGSA +% They are compared by plotting all priors and quantiles + +% Author: Jihoon Park (jhpark3@stanford.edu) +% Date: 17 May 2016 + +% Input: +% Prior: (cell, # of wells x # of models), each cell has matrix of time(1st column) and response(2nd column) +% Responses are from prior distributions of parameters. +% AfterPUR: (cell, # of wells x # of models), each cell has matrix of time(1st column) and response(2nd column) +% Responses are from distributions of parameters that are reduced by DGSA and net conditional effects + +% DataStruc: Inputs needed for display/ +% tgrid: (vector, length=# of timesteps) Time steps of response +% .idxResponse: (scalar) column index of the response within the cell. In the given example, the response is at 2nd column +% so it is 2. +% .QuantileLevel: (vector, length=# of specified quantiles) Quantiles of responses +% .xlab: (string) legend of x-axis +% .ylab: (string) legend of y-axis. +% + +%% Assign varaibles +tgrid=DataStruct.tgrid; % Time steps +idx=DataStruct.idxResponse; % The column that contains response +QuantileLevel=DataStruct.QuantileLevel; % Quantiles to plot +xlabtxt=DataStruct.xlab; % xlegend +ylabtxt=DataStruct.ylab; % ylegend + +%% +ResponsesPrior=GetdynamicResponses(Prior,tgrid,idx); +ResponsesPUR=GetdynamicResponses(AfterPUR, tgrid, idx); + +NbProdWell=size(Prior,1); +figure; +for k=1:NbProdWell + subplot(1,NbProdWell,k); + Quantiles_k=QuantileComputation(ResponsesPrior(:,:,k),QuantileLevel); + Quantiles_k_PUR=QuantileComputation(ResponsesPUR(:,:,k),QuantileLevel); + + ResponsesPrior_k=ResponsesPrior(:,:,k); + + hold on + for k2=1:size(ResponsesPrior_k,1) + plot([0,tgrid], [0,ResponsesPrior_k(k2,:)],'Color',[.7,.7,.7]); + + end + + add0=[0;0;0]; + h1=plot([0,tgrid], [add0,Quantiles_k],'-.k','LineWidth',4); + + h2=plot([0,tgrid], [add0,Quantiles_k_PUR],'-r','LineWidth',3); + + xlim([0 tgrid(end)]);ylim([0 7E7]); + + xlabel(xlabtxt);ylabel(ylabtxt); + title(['Prod ',num2str(k+1)]) + + legend([h1(1),h2(1)],'Initial Models','Reduced', ... + 'location','NorthWest'); + hold off + +end + + +end \ No newline at end of file diff --git a/Visualizations/Responses/DisplayMDSplot.m b/Visualizations/Responses/DisplayMDSplot.m new file mode 100644 index 0000000..4ca5105 --- /dev/null +++ b/Visualizations/Responses/DisplayMDSplot.m @@ -0,0 +1,32 @@ +function C=DisplayMDSplot(d, Clustering) +% The function displays MDS plot from distance matrix and clustering results +% Author: Jihoon Park (jhpark3@stanford.edu) +% Date: 16 May 2016 + +% Input: +% d: (matrix, # of models x # of models or vector, length =# of models x (# of models -1) ): +% Distance matrix or vector of distances between the model. +% Clustering: (Structure) Clustering results from DGSA +% .T: (vector, length=# of models) Class which each model belongs to. + +% Output: +% C: (Vector, length=3) Color code of each cluster. This value can be used to color the curve of responses later. + +% Multi-Dimensional Scaling (MDS) using distance d +[Xd_, e_] = cmdscale(d); + +% Reduction of the dimension of the MDS space, here 2D +dims = 2; +Xd = Xd_(:,1:dims); +Clustering.label=Clustering.T; + +C=plotcmdmap(Xd, Clustering); +set(gca, 'XTickLabelMode', 'manual', 'XTickLabel', []); +set(gca, 'XTickLabelMode', 'manual', 'YTickLabel', []); + +xlabTxt=['Varaince explained:',num2str(round(e_(1)/sum(e_)*100)),'%']; +ylabTxt=['Varaince explained:',num2str(round(sum(e_(2))/sum(e_)*100)),'%']; + +xlabel(xlabTxt,'Fontsize',14); ylabel(ylabTxt,'Fontsize',14); + +end \ No newline at end of file diff --git a/Visualizations/Responses/dynamicbycluster.m b/Visualizations/Responses/dynamicbycluster.m new file mode 100644 index 0000000..bf26b8e --- /dev/null +++ b/Visualizations/Responses/dynamicbycluster.m @@ -0,0 +1,60 @@ +function dynamicbycluster(Clustering,responses,C,Labels) +% The function displays responses by clusters. +% The color corresponds to the result of MDS plot from 'DisplayMDSplot.m' +% Author: Jihoon Park (jhpark3@stanford.edu) +% +% Input: +% Clustering: Clustering results. See kmedoid.m for details +% response: (cell, # of wells x # of models) contains all reservoir responses. +% Each cell has the matrix of (# of timesteps x 2), where 2nd column has actual response. +% Labels: Labels neede for plotting +% Labels.xlimits: vector of min/max time +% Labels.ylimits: vector of min/max responses +% Labels.xlabtxt: string of lables of x axis +% Labels.ylabtxt: string of lables of y axis + + +%% Assign varariables + + +NbProd=size(responses,1); % # of proudcing wells. +legendtext=cell(1,length(Clustering.medoids)); + +figure;hold on; +for j=1:NbProd + responses_Prod_h=responses(j,:); + subplot(1,NbProd,j) + title(['Prod ',num2str(NbProd)]); + %legend_str={}; + for k=1:length(Clustering.medoids) + % legend_str{k}=['Cluster',num2str(k)]; + idx=find(Clustering.T==k); + data_h=responses_Prod_h(:,idx); + legendtext{k}=sprintf('Cluster %i',k); + + + for i=1:length(data_h) + + data_h2=data_h{i}; + + time_h=data_h2(:,1); + dynamic_h=data_h2(:,2); + h_h=plot(time_h,dynamic_h,'Color',C(k,:)); + + hold on + end + h(k)=h_h; + + end + + + + + legend(h,legendtext,'Location','northwest'); + xlim(Labels.xlimits); ylim(Labels.ylimits); + + title(['Prod ',num2str(j+1)]); + xlabel(Labels.xlabtxt); ylabel(Labels.ylabtxt); + hold off + +end diff --git a/Visualizations/Responses/plotcmdmap.m b/Visualizations/Responses/plotcmdmap.m new file mode 100644 index 0000000..1a7a3d3 --- /dev/null +++ b/Visualizations/Responses/plotcmdmap.m @@ -0,0 +1,49 @@ +function C=plotcmdmap(Xd,KKM) + +%% Function which maps the points defined in MDS (Xd) and (optional) colors the +%% points according to the clustering results obtained by kernel_kmedoid.m + +% Author: Celine Scheidt +% Date: April 2009 + + +%% Input Parameters: +% - Xd: location of the points to be plotted (from MDS). Rows of Xd are the coordinates in p-dimensional space +% - KKM: results from the clustering in the format given by the function kkmedoid. This is optional. + % If given, point are colored by clusters; medoids are represented by squares + +if nargin ==2 + + % definition of the color of each cluster + C = jet;hold on; + C = C(floor(linspace(1,size(C,1),max(KKM.label))),:); + + %figure + for i=1:length(KKM.medoids) + plot(Xd(KKM.label==i,1), Xd(KKM.label==i,2), 'o', 'Color',C(i,:), ... % points in clusters + 'MarkerSize', 8, 'LineWidth', 1.3,'MarkerFaceColor',C(i,:), ... + 'MarkerEdgeColor','k'); + + hold on + plot(Xd(KKM.medoids(i),1), Xd(KKM.medoids(i),2), 'bs', ... % medoids + 'MarkerSize', 12, 'LineWidth', 2,'MarkerFaceColor',C(i,:), ... + 'MarkerEdgeColor','k'); + end + +else + + figure + plot(Xd(:,1), Xd(:,2), 'o', 'MarkerSize', 8, 'LineWidth', 1.2, ... + 'MarkerFaceColor',[0.7 0.7 0.7], 'MarkerEdgeColor','k'); + +end + + +hold off +grid off + +set(gca,'LineWidth',3) +%set(gca,'XTickLabel',{''}) +%set(gca,'YTickLabel',{''}) + +end diff --git a/dGSA_Interactions.m b/dGSA_Interactions.m deleted file mode 100644 index e2f25f3..0000000 --- a/dGSA_Interactions.m +++ /dev/null @@ -1,65 +0,0 @@ - -% -% Distance-based generalized sensitivity analysis (dGSA) -% Evaluation of sensitivity of the intercations -% Pareto plots are used to display the resuls - -% Author: Celine Scheidt -% Date: August 2013 - -function [NormalizedInteractions,StandardizedSensitivityInteractions] = dGSA_Interactions(Clustering,ParametersValues,InteractionsNames,NbBins,alpha) - -%% Input Parameters -% - Clustering: Clustering results -% - ParametersValues: matrix (NbModels x NbParams) of the parameter values -% - InteractionsNames: List containing the interaction names to be displayed on the y-axis -% - NbBins: Vector containing the number of bins per parameter -% - alpha: (optional): alpha-percentile (by default, alpha = 0.95) for -% the bootstrap - -%% Output Parameters -% - NormalizedInteractions: 4D array (NbParams x NbParams-1 x NbClusters x max(NbBins)) containing the sensitivity -% values for each interaction, each class and each bin. -% - StandardizedSensitivityInteractions: vector containing the standardized measure of sensitivity -% for each interaction - - -NbParams = size(ParametersValues,2); -NbClusters = size(Clustering.medoids,2); - -if nargin < 5; alpha = .95; end - -% Evaluate the normalized conditionnal interaction for each parameter, each -% class and each bin -L1Interactions = NaN(NbParams,NbParams-1,NbClusters,max(NbBins)); % array containing all the Interactions -BootInteractions = NaN(NbParams,NbParams-1,NbClusters,max(NbBins)); - -for params = 1:NbParams - L1InteractionsParams = L1normInteractions(ParametersValues,params,Clustering,NbBins(params)); - L1Interactions(params,:,:,1:NbBins(params)) = L1InteractionsParams(:,:,1:NbBins(params)); - BootInteractionsParams = BootstrapInteractions(ParametersValues,params,Clustering,NbBins(params),2000,alpha); - BootInteractions(params,:,:,1:NbBins(params)) = BootInteractionsParams(:,:,1:NbBins(params)); - NormalizedInteractions = L1Interactions./BootInteractions; -end - - -% Measure of conditional interaction sensitivity per class -SensitivityPerClass = nanmean(NormalizedInteractions,4); - -% Average measure of sensitivity over all classes -SensitivityOverClass = nanmean(SensitivityPerClass,3); - -% Display the results -ParetoInteractions(NormalizedInteractions,InteractionsNames,NbClusters,NbBins) - -% Hypothesis test: Ho = 1 if at least one value > 1 (per cluster and per bin) -SensitivityPerInteraction = reshape(permute(NormalizedInteractions,[2,1,4,3]),[],max(NbBins)*NbClusters); -H0accInter = any(SensitivityPerInteraction >=1,2); - -StandardizedSensitivityInteractions = reshape(SensitivityOverClass',1,[]); -Pareto_GlobalSensitivity(StandardizedSensitivityInteractions,InteractionsNames,H0accInter) - -end - - - diff --git a/dGSA_MainFactors.m b/dGSA_MainFactors.m deleted file mode 100644 index a1259b6..0000000 --- a/dGSA_MainFactors.m +++ /dev/null @@ -1,40 +0,0 @@ -% -% Distance-based generalized sensitivity analysis (dGSA) -% Evaluation of sensitivity of the main factors only -% Pareto plots are used to display the resuls - -% Author: Celine Scheidt -% Date: August 2012 - -function [SensitivityMainFactors,StandardizedSensitivity] = dGSA_MainFactors(Clustering,ParametersValues,ParametersNames,alpha) - -%% Input Parameters -% - Clustering: Clustering results -% - ParametersValues: matrix (NbModels x NbParams) of the parameter values -% (numerical values should be provided, even for discrete parameters) -% - ParametersNames: list containing the names of the parameters -% - alpha: (optional): alpha-percentile (by default, alpha = 0.95) for -% the bootstrap - -%% Output Parameters -% - SensitivityMainFactors: Matrix containing the normalized L1norm for each parameter (1st dim) and -% each cluster (2nd dim). -% - StandardizedSensitivity: Vector containing the standardized measure of sensitivity for each parameter - -if nargin < 5; alpha = .95; end - -L1MainFactors = L1normMainFactors(Clustering,ParametersValues); % evaluate L1-norm -BootMainFactors = BootstrapMainFactors(ParametersValues,Clustering,2000,alpha); % bootstrap procedure - -SensitivityMainFactors = L1MainFactors./BootMainFactors; % normalization -StandardizedSensitivity = mean(SensitivityMainFactors,2); % standardized measure of sensitivity - -% Display the results -ParetoMainFactors(SensitivityMainFactors,ParametersNames); - -% Hypothesis test: Ho = 1 if at least one value > 1 (per cluster) -H0accMain = any(SensitivityMainFactors >=1,2); -Pareto_GlobalSensitivity(StandardizedSensitivity,ParametersNames,H0accMain); - - -end \ No newline at end of file diff --git a/demo_dGSA_analytic.m b/demo_dGSA_analytic.m deleted file mode 100644 index a2ba5d9..0000000 --- a/demo_dGSA_analytic.m +++ /dev/null @@ -1,41 +0,0 @@ -%% Distance-Based Generalized Sensitivity Analysis -% Author: Celine Scheidt -% Date: August 2012 -% Updated: January 2014 - - -% Definition of the 3 parameters (x,y,z) using Latin Hypercube Sampling -NbSimu = 200; NbParams = 3; rng(12756); - -ParametersValues = lhsdesign(NbSimu,NbParams,'criterion','correlation','iterations',50); - -% Evaluation of the response: r = [z abs(x*(y-1)] -ParametersNames = {'x','y','z'}; -r = [ParametersValues(:,3) abs(ParametersValues(:,1).*(ParametersValues(:,2)-1))]; - - % Compute the distance between the responses -d = pdist(r); - -% Classify the response in a few classes using kmedoid -nbclusters = 3; -Clustering = kmedoids(d,nbclusters,10); - -%% MAIN FACTORS - -% Plot the cdf and apply dGSA -cdf_MainFactor(ParametersValues,Clustering,ParametersNames) -[SensitivityMainFactor,StandardizedSensitivity] = dGSA_MainFactors(Clustering,ParametersValues,ParametersNames); - - -%% INTERACTIONS -InteractionsNames = {'y|x','z|x','x|y','z|y','x|z','y|z'}; - -% Define the number of bins for each parameter -NbBins = [3,3,3]; - -cdf_Interactions(ParametersValues(:,2),ParametersValues(:,1),Clustering,NbBins(1),3,'y|x') - -% Sensitivity -[SensitivityInteractions,GlobalSensitivityInteractions] = dGSA_Interactions(Clustering,ParametersValues,InteractionsNames,NbBins); - - diff --git a/main_DGSA_ParameterUncertaintyReduction.m b/main_DGSA_ParameterUncertaintyReduction.m new file mode 100644 index 0000000..c9c14f0 --- /dev/null +++ b/main_DGSA_ParameterUncertaintyReduction.m @@ -0,0 +1,32 @@ +%% Distance based global sensitivity analysis - Application to reservoir responses +% Compute net conditional effects and reduce uncertainty of model parameters + +% The script uses results from the previous script main_DGSA_Reservoir_Sensitivity.m + +% Author : Jihoon Park (jhpark3@stanford.edu) +% Date : 17 May 2016 + + +clear all; close all; fclose('all'); +addpath(genpath(pwd)) +load('DGSA_Completed'); % Load all variables from the previous script. +%% +load('Responses_PUR'); +Responses_AfterPUR=WWPT_PUR; clear WWPT_PUR; + + +%% Net Conditional effects + +% Net conditional effects for a single parameter +[NetConditionalEffects,Bin_MaxNetConditional]=ComputeNetConditionalEffects... + ('oilexp', DGSA); + +% Net conditional effects for every parameter +DisplayNetConditionalEffects_all(DGSA); + +%% Compare responses: Prior vs. After reduction of parameter uncertainty + +ResponsesCompared.tgrid=365:365:7300; ResponsesCompared.idxResponse=2; +ResponsesCompared.QuantileLevel=[.1,.5,.9]; +ResponsesCompared.xlab='Time(day)';ResponsesCompared.ylab='WWPT (stb)'; +CompareResponses(PriorResponses,Responses_AfterPUR,ResponsesCompared); diff --git a/main_DGSA_Reservoir_Sensitivity.m b/main_DGSA_Reservoir_Sensitivity.m new file mode 100644 index 0000000..78d6c29 --- /dev/null +++ b/main_DGSA_Reservoir_Sensitivity.m @@ -0,0 +1,87 @@ +%% Distance based global sensitivity analysis - Application to reservoir responses +% Part1: Compute main/conditional effects of Prior models + +% Author : Jihoon Park (jhpark3@stanford.edu) +% Date : 17 May 2016 + +clear all; close all; fclose('all'); rng('default'); +%% 0. Add directories for path +addpath(genpath(pwd)) + +%% 1. Specify inputs for DGSA. + +%% 2. Load & process input data +load('PriorResponses'); % load responses +load('DistanceMatrix'); % load distance matrix. Distance matrix can be computed from pdist() function in Matlab. + % For details,refer to main_DGSA_analytic.m and the manual included. +PriorResponses=WWPTbyWell; + +%DGSA=ProcessInputParameters('PriorParameters.dat'); % Process Input parameters +DGSA=ProcessInputParameters('PriorParameters_Spatial.dat'); % This data includes two more parameters - permeability and porosity. +DGSA.D=D; +clear WWPTbyWell;clear D; + +%% 4. Compute & display main effects + +% 4.1 Inputs for clustering and display options. +DGSA.Nbcluster=3; % # of clusters +DGSA.MainEffects.Display.ParetoPlotbyCluster=1; % if true, main effects over cluster will be displayed with Pareto plot. +DGSA.MainEffects.Display.StandardizedSensitivity='CI'; + +% if 'CI', the confidence interval will be overlapped on the Pareto plot +% if 'Pareto', Pareto plots will be displayed only +% if 'None' No plot will be generated for standardd main effects +% (default) + +% 4.2 Compute main effects from DGSA. +SigLevel_CI=[.95,.9,1]; % This is needed only when you want to display confidence intervals + % If you do not need to display confidence intervals,set DGSA.MainEffects.Display.StandardizedSensitivity='Preto' or 'None' + +% 4.3 Perform clustering +DGSA.Clustering=kmedoids(DGSA.D,DGSA.Nbcluster,10); % In this example, K medoid clustering is applied. + +% 4.4 Compute Main Effects +DGSA=ComputeMainEffects(DGSA,SigLevel_CI); % If you use Pareto plot or do not want to display main effects, remove SigLevel_CI, otherwise it shows an error. + +%% Display cdfs + +cdf_MainFactor(DGSA.ParametersValues, DGSA.Clustering, DGSA.ParametersNames,{'owc','oilvis'}); % In this example, CDFs for 'owc' and 'oilvis' will be displayed. +%% 5. Compute & Display conditional effects + +% 5.1 Specify additional variables to estimate conditional effects. + +DGSA.ConditionalEffects.NbBins=3*ones(1,length(DGSA.ParametersNames)); + +% 5.2 Compute conditional effects + +rng('default'); +DGSA=ComputeConditionalEffects(DGSA); + +% 5.3 Display conditional effcts + +% Speicify the method to display standardized conditional effects. +DGSA.ConditionalEffects.Display.SensitivityByClusterAndBins=1; % if true, display pareto plots to visualize sensitivities by bins/clusters. +DGSA.ConditionalEffects.Display.StandardizedSensitivity='Hplot'; % If omitted Pareto plot will be used. However, this is not recommended when there are lots of parameters + +% Visualize conditional effects +DisplayConditionalEffects(DGSA,DGSA.ConditionalEffects.Display.StandardizedSensitivity) + +% 5.4 Display class condtional CDFs +cdf_ConditionalEffects('owc','kvkh',DGSA,1) + +%% 6. Check the response + +% Use MDS plot to check the result of clustering +ClusterColor=DisplayMDSplot(DGSA.D, DGSA.Clustering); + +% Specify texts for plots +PlotLabels.xlabtxt='Time (day)'; PlotLabels.ylabtxt='WWPT (stb)'; +PlotLabels.xlimits=[0, 7300]; PlotLabels.ylimits=[0 7E7]; + +% Visualize dynamic response by clusters +dynamicbycluster(DGSA.Clustering,PriorResponses, ClusterColor,PlotLabels); + + +%% Save all variables for futher application +%save('VariablesSaved/DGSA_Completed.mat'); +%save('VariablesSaved/DGSA_Spatial_Completed.mat'); \ No newline at end of file diff --git a/main_DGSA_analytic.m b/main_DGSA_analytic.m new file mode 100644 index 0000000..e614239 --- /dev/null +++ b/main_DGSA_analytic.m @@ -0,0 +1,79 @@ +% main_DGSA_analytic.m +% +%% Distance-Based generalized Sensitivity Analysis: Analytic example +% +% This script is written to demonstrate how to apply DGSA to obtain main/conditional effects. +% Also, it shows how to decrease uncertainty of model parameters with minimal impact on responses. +% +% References: +% +% Fenwick et al. (2014), Quantifying Asymmetric Parameter Interactions in Sensitivity Analysis: Application to Reservoir Modeling. Mathematical Geosciences +% Park et al. (2016), DGSA: a matlab toolbox for distance-based generalized sensitivity analysis for geoscientific computer experiments + +%This script was originally written by Celine Scheidt in August 2012 +% Lastly updated by Jihoon Park (jhpark3@stanford.edu) in May 2016 +% +% - Scripts are written to involve change of functions +% - Net conditional effects are computed in the script. + +clear all; close all; fclose('all'); +%% 1. Add paths + +addpath(genpath(pwd)) + +%% 2. Monte Carlo sampling & Compute responses + +% Define three parameters +NbSimu=500; NbParams=3; rng(12756); +DGSA.ParametersValues=lhsdesign(NbSimu,NbParams,'criterion','correlation','iterations',50); + +% Responses Y1 and Y2, r=[Y1, Y2]=[X1,X2*(1-X3)] +Y1=DGSA.ParametersValues(:,1); Y2=abs(DGSA.ParametersValues(:,2).*(DGSA.ParametersValues(:,3)-1)); +PriorResponses=[Y1,Y2]; + +% Construct distance vector +DGSA.D=pdist(PriorResponses); + +%% 3. Specify inputs for DGSA + +DGSA.ParametersNames={'X1','X2','X3'}; % Name of each parameter +DGSA.Nbcluster=3; % # of clusters +DGSA.MainEffects.Display.ParetoPlotbyCluster=1; % If true, display main effects by clusters +DGSA.MainEffects.Display.StandardizedSensitivity='Pareto'; + +% Perform clustering. +DGSA.Clustering=kmedoids(DGSA.D,DGSA.Nbcluster,10); + +% Compute & Display main effects +DGSA=ComputeMainEffects(DGSA); + +% Display CDFs. In this example, cdf of X1 is shown. +% If you want every CDFs, simply omit the last variable in the following function. + +cdf_MainFactor(DGSA.ParametersValues, DGSA.Clustering, DGSA.ParametersNames,{'X1'}); +%% 4. Compute & Display conditional effects + +%%% Enter inputs +DGSA.ConditionalEffects.NbBins=3*ones(1,NbParams); % 3 bins for each parameters +DGSA.ConditionalEffects.Display.SensitivityByClusterAndBins=1; % If true, it shows Pareto plots of conditional effects by bins and clusters +DGSA.ConditionalEffects.Display.StandardizedSensitivity='Pareto'; + +% Compute & display conditional effects +DGSA=ComputeConditionalEffects(DGSA); +DisplayConditionalEffects(DGSA,DGSA.ConditionalEffects.Display.StandardizedSensitivity); + +% Display CDF +cdf_ConditionalEffects('X2','X3',DGSA,1) % The example displays CDF of X2|X3, Cluster 1 +%% 5. See the distribution of Y1 and Y2 + +% Compute net conditional effects of X3 +[NetConditionalEffects,Bin_MaxNetConditional]=ComputeNetConditionalEffects... + ('X3', DGSA, {'X3<1/3','1/32/3'}); % See net conditional effects of X3. + +% Decrease uncertainty of X3 to X3<1/3 +idx=DGSA.ParametersValues(:,3)<1/3; +figure; +plot(Y1,Y2,'.','Markersize',20);hold on; +plot(Y1(idx),Y2(idx),'r*','Markersize',20);hold off; +axis('square'); xlabel('Y_1','Fontsize',12);ylabel('Y_2','Fontsize',12); +title('Uncertainty using net conditional effects','Fontsize',14); diff --git a/main_KPCASOM_example.m b/main_KPCASOM_example.m new file mode 100644 index 0000000..9343ae4 --- /dev/null +++ b/main_KPCASOM_example.m @@ -0,0 +1,37 @@ +% Scipt to get spatial rank for spatial models using KPCA and SOM +% there are two test cases: one is on the gradual deformation example +% the other is on an emsemble of 500 realizations of 2D 68*64 permeability grid + +% Author: Guang Yang + +clear all; close all; clc +addpath('KPCASOM'); + +%% example 1 +model1='gaussian_realz1'; +model2='gaussian_realz2'; +%read in the two SGS simulated models +r1=read_model(model1); +r2=read_model(model2); + +%theta vector +theta=0:0.1:1; + +%realization matrix resulting from gradual deformation +r_ensemble=[]; +r_temp=r1*sin(theta*pi)+r2*cos(theta*pi); +r_ensemble=[r_ensemble r_temp]; + +%run the KPCASOM_rank script +%we used Gaussian radial basis function kernel +%For Gaussian RBF, kernel_para is for setting up the sigma value in RBF function +% sigma= kernel_para * mean distance between models +kernel_para=5; +[Y_eig,ndim,rank]=KPCASOM_rank(r_ensemble,'gaussian',kernel_para); + +%% example 2 +%read in the models +temp=load('ModelsExample2.mat'); +r_ensemble_2D=temp.perm_ensemble; +%get the spatial rank for the models +[Y_eig_2,ndim_2,rank_2]=KPCASOM_rank(r_ensemble_2D,'gaussian',kernel_para); \ No newline at end of file diff --git a/main_compareDGSA_Sobol.m b/main_compareDGSA_Sobol.m new file mode 100644 index 0000000..e2e8654 --- /dev/null +++ b/main_compareDGSA_Sobol.m @@ -0,0 +1,26 @@ +% main_compareDGSA_Sobol.m +% Author: Jihoon Park (jhpark3@stanford.edu) +% Date: 16 May 2016 + +% The script is to compare sensitivities from DGSA and Sobol's method. +% For details, consult with the paper written by Park et al. (2016) - +% DGSA: a matlab toolbox for distance-based generalized sensitivity analysis for geoscientific computer experiments +clear all; close all; fclose('all'); +%% Specify the time and number of samples +timegrid=0:365:7300; N_Models=1000; + +%% Load responses from reservoir simulator +% The response matrix consists of (n(k+2) x # of timesteps, n=N_Models, k=# of parameters) + +load('FWPT.mat'); Sobol_responses=FWPT; clear FWPT; +DGSA_responses=Sobol_responses(1:N_Models,:); +DGSA=ProcessInputParameters('SobolParameters.dat'); +%% Run DGSA over time +DGSA.Nbcluster=3; % Specify the number of clusters + +MainEffects_over_time=DGSA_over_time(DGSA,DGSA_responses,timegrid); + +%% Compute & display Sobols' indicies +First_order_Sobol=SobolSensitivity(timegrid,Sobol_responses,N_Models,DGSA.ParametersNames); +%% Save the variables +save('VariablesSaved/DGSAandSobol_comparision.mat'); diff --git a/readme.txt b/readme.txt deleted file mode 100644 index 4219a3a..0000000 --- a/readme.txt +++ /dev/null @@ -1,13 +0,0 @@ -Distance-based Generalized Sensitivity Analysis (dGSA) - -Clustering (kmedoid) should be performed on the responses to classify the models in a few (2-3) classes prior to the sensitivity analysis. -The clustering results should be provided as an input (in the same format as the output of kmedoids.m) - -The Matlab function to apply dGSA on the main factors is dGSA_MainFactors.m. -The Matlab function to apply dGSA on the interations is dGSA_Interactions.m. - -An example of application is given in demo_dGSA_analytic.m - -Reference: Fenwick D, Scheidt C. and Caers J. (2014) Quantifying Asymmetric Parameter Interactions in Sensitivity Analysis: Application to Reservoir Modeling. Mathematical Geosciences 46(4): 493-511 - - \ No newline at end of file diff --git a/utilities/CreateNames_ConditionalEffect.m b/utilities/CreateNames_ConditionalEffect.m new file mode 100644 index 0000000..91b1580 --- /dev/null +++ b/utilities/CreateNames_ConditionalEffect.m @@ -0,0 +1,43 @@ +function ConditionalEffectNames=CreateNames_ConditionalEffect(ParametersNames) +%% +% The function creates string objects of conditional effects +% Author: Jihoon Park (jhpark3@stanford.edu) +% Date: 13 May 2016 + + +% Input: +% ParametersNames: (cell, length=# of Parameters): Names of uncertain parameters +% +% Output: +% ConditionalEffectNames: (cell, length1 X (# of Parameters)*(# of Parameters-1)) : Names of conditional effects. +% +% Example: +% ParameterNames={'X','Y','Z'} will gives output of ConditionalEffectNames={'Y|X','Z|X','X|Y','Z|Y','X|Z','Y|Z'} + +%% +ConditionalEffectNames=cell(1,(length(ParametersNames)^2-length(ParametersNames))); % Initialize. +ncount=0; + +% String object 'A|B' will be saved at each cell. + +for k=1:length(ParametersNames) + + B=ParametersNames{k}; + + for j=1:length(ParametersNames) + + if k==j + + continue + + end + A=ParametersNames{j}; + name_handle=[A,'|',B]; + ncount=ncount+1; + ConditionalEffectNames{ncount}=name_handle; + + end + +end + +end \ No newline at end of file diff --git a/utilities/GetdynamicResponses.m b/utilities/GetdynamicResponses.m new file mode 100644 index 0000000..4142623 --- /dev/null +++ b/utilities/GetdynamicResponses.m @@ -0,0 +1,41 @@ +function Responses=GetdynamicResponses(Responses_cell, tgrid,seq) +% The function converts cell to matrix with linear inerpolation of time steps +% Interpolation is carried out since different time steps can be used +% +% Author: Jihoon Park (jhpark3@stanford.edu) +% +% Input: +% +% Responses_cell : (cell, # of wells x # of models) Each element contains the response from a reservoir simulator. +% tgrid : (vectotr, length= # of timesteps specified), time grid on which interpolation is performed. +% +% Output: +% +% Responses: (matrix, # of wells x # of timesteps), contains response which is interpolated over reference 'tgrid' + +%% +n_prod=size(Responses_cell,1); % # of producers +n_model=size(Responses_cell,2); % sample size +n_tstep=length(tgrid); +%% Initialize the output +Responses=zeros(n_model,n_tstep,n_prod); + + +%% Rearrange the output. + +for j=1:n_prod + data_prod_j=Responses_cell(j,:); + for k=1:n_model + data_en_k=data_prod_j{k}; % Acess to matrix + dynamic_h=data_en_k(:,seq); % + time_h=data_en_k(:,1); + dynamic_h=dynamic_h'; + time_h=time_h'; + dynamic_time_adjusted=interp1(time_h,dynamic_h,tgrid); + Responses(k,:,j)=dynamic_time_adjusted; + end +end + + + +end \ No newline at end of file diff --git a/utilities/ProcessInputParameters.m b/utilities/ProcessInputParameters.m new file mode 100644 index 0000000..82c6423 --- /dev/null +++ b/utilities/ProcessInputParameters.m @@ -0,0 +1,27 @@ +function DataStruct=ProcessInputParameters(FileName,DataStruct) +% The function proceses Monte Carlo results of Parameters to use in DGSA +% +% Author: Jihoon Park (jhpark3@stanford.edu) +% Date: 12 May 2016 + +% Input : +% +% FileName: (string) Name of the file that contains name of parameters and values from Monte Carlo simulations. +% DataStruct: Data structure containing results of DGSA. + + +% Output: +% DataStruct: Data structure containing results of DGSA. +% .ParametersNames: (cell, length=# of parameters) contains the names of parameters +% .ParametersValues: (matrix, # of models x # of parameters) contains values of each parameter from Monte Carlo sampling. +% .N:(scalar) # of models (sample size) + +%% 1. Import data +DataImported=importdata(FileName); + +%% 2. Save data at DataStruct +DataStruct.ParametersNames=DataImported.textdata(1,2:end); % Names of parameters +DataStruct.ParametersValues=DataImported.data; % Values of Parameters +DataStruct.N=size(DataStruct.ParametersValues,1); % Sample size + +end \ No newline at end of file diff --git a/utilities/QuantileComputation.m b/utilities/QuantileComputation.m new file mode 100644 index 0000000..42264a6 --- /dev/null +++ b/utilities/QuantileComputation.m @@ -0,0 +1,35 @@ +% +% This function computes the quantiles of Response as a function of time. +% If clustering is performed, each response is weighted by the number of +% points in the corresponding cluster. + +% Author: Celine Scheidt +% Date: April 2009 + + +function Quantiles = QuantileComputation(Response,p,Clustering) + +%% Input Parameters +% - Response: matrix of the responses as a function of time. The size is +% Number of models (n) x Number of timesteps for response +% - p: scalar or vector of cumulative probability values +% - Clustering: results of the clustering (as given by function kkmedoid). Optional. +% If not given, return the quantiles of Response without ponderation by the clusters weights. + +%% Output Parameters +% - Quantiles: quantiles of the values in response. + + +if nargin == 2 % No clustering: each model as a weight of one + Quantiles=quantile(Response,p); + +else % Each model is weighted by the number of points in the cluster (Clustering.weights) + WeigthedResponse = []; + for i = 1:size(Clustering.medoids,1) + WeigthedResponse=vertcat(WeigthedResponse,repmat(Response(Clustering.medoids(i),:),Clustering.weights(i),1)); + end + + Quantiles=quantile(WeigthedResponse,p); +end + +end \ No newline at end of file