{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Adaptive anisotropic stochastic collocation for a heat transfer PDE\n", "\n", "This MATLAB notebook shows one possible way of solving a partial differential equation (PDE) with random parameters. The discretization in space and time is done with **triangular finite elements** and a **MATLAB ODE solver** for stiff problems, respectively. The random part is discretized by means of an interpolation with adaptive, anisotropic placement of nodes on a **sparse grid**.\n", "\n", "To minimize the interpolating nodes is especially important, because each node means solving a deterministic PDE, which is computationally demanding in many cases. Although the task is very well parallelizable, one needs to break the **curse of dimensionality**.\n", "\n", "The notebook contains sections about the following topics:\n", "\n", "* **Deterministic preprocessing**: mesh and ODE settings\n", "* **Random preprocessing**: parametrization of a random field\n", "* Settings and running of anisotropic adaptive **stochastic collocation**\n", "* **Deterministic postprocessing**: space and time integration or evaluation in fixed points\n", "* **Random postprocessing**: getting the mean, variance, and density of the numerical results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\\begin{equation}\n", "\\begin{aligned}\n", " \\partial_t T -\\nabla\\cdot (\\alpha({\\textbf x},\\omega)\\nabla T) &= 0 & \\text{ in } D\\times(0,1]\\times\\Omega \\ \\\\\n", " -\\alpha({\\textbf x},\\omega)\\ \\nabla T\\cdot \\mathbf n &= 0 &\\text{ in } \\partial D_1\\times(0,1]\\times\\Omega \\ \\\\\n", " -\\alpha({\\textbf x},\\omega)\\ \\nabla T\\cdot \\mathbf n &= -1 &\\text{ in } \\partial D_2\\times(0,1]\\times\\Omega \\ \\\\\n", " T({\\textbf x},0,\\omega) &= 0 &\\text{ in } D\\times\\Omega\n", "\\end{aligned}\n", "\\end{equation}\n", "\n", "The problem describes the heat conduction in an electronic chip with the uncertain heat conductivity $\\alpha$, modeled as a random field, discretized by means of a truncated Karhunen-Loève expansion with 3 uniformly distributed random variables. The figure shows the two-dimensional spatial domain $D$ of the chip. At the cavity a heat flux into the domain is assumed; the remaining boundary is assumed to be adiabatic and the initial temperature is set to 0. The governing equation is the unsteady heat equation subject to the boundary conditions just described, with temperature $T$, sample space $\\Omega$, a sample $\\omega$, time interval $(0,1]$, spatial points $\\textbf x$, and $\\mathbf n$ denotes the outer normal vector with respect to $D$. Adaptive anisotropic stochastic collocation on a sparse grid is applied to discretize the random space efficiently." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "% add functions to path\n", "addpath(genpath('functions'));" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "% Solution folder settings to avoid keeping all results in RAM and to store intermediate results\n", "problemfolder = '.'; % name of the path, where the solution folder is placed\n", "solutionfolder = [problemfolder,'/solutions'];\n", "% generate the folder if it doesn't exist\n", "if ~exist(solutionfolder,'file')\n", " mkdir(solutionfolder);\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Preprocessing I: spatial grid / mesh" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "% parameters\n", "refinementlevel = 3;" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "sol = readSol(2,1,'finiteElementMesh.geo'); % read coarse grid\n", "points = sol.points(2:3,:)'; % extract the points\n", "cells = sol.triangles(2:4,:)'+1; % extract the triangles" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "% refine coarse mesh until specified refinement level is reached\n", "for i = 1:refinementlevel\n", " [points,cells,~,I] = RefineTriangularGrid(points,cells);\n", "end\n", "mesh = LinearTriangularMesh(points,cells); % construct a mesh with various information" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "% plot the mesh and see the computational domain\n", "trimesh(cells,points(:,1),points(:,2),points(:,1),'EdgeColor','black');\n", "view(2)\n", "axis equal tight\n", "set(gcf, 'PaperPosition', [0 0 6 2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Preprocessing II: random space / Karhunen-Loève expansion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The conductivity parameter $\\alpha$ is the source of uncertainty, and is modelled as a spatially correlated random field with expected value $E[\\alpha]=1$, correlation length $L=4$, and standard deviation $\\sigma=0.2$. More precisely, we use the covariance function \n", "\n", "\\begin{equation}\n", " C_{\\alpha}(\\textbf x,\\tilde{\\textbf x} )=\\sigma^2\\frac{\\|\\textbf x-\\tilde{\\textbf x}\\|_2}{L}K_1\\left(\\frac{\\|\\textbf x-\\tilde{\\textbf x}\\|_2}{L}\\right),\n", "\\end{equation}\n", "\n", "where $K_1$ refers to the modified Bessel function of second kind and first order. This kind of covariance function is commonly used in statistics and very\n", "suitable for two-dimensional random fields. It belongs to the family of Matérn covariance functions. We obtain the covariance spectrum numerically on the same\n", "spatial discretization as used for the calculations with linear finite element ansatz functions and $3$-point quadrature rules to approximate the discrete\n", "covariance matrix. The choice of covariance function leads to three terms to be used in the truncated Karhunen-Loève\n", "expansion of $\\alpha$, and are chosen to be uniformly distributed. The figure some cells below shows the first three eigenfunctions." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "% parameters\n", "L = 4; % correlation length\n", "sigma = 0.2; % standard deviation" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "% store eigenvalues and eigenvectors to construct them only once \n", "% for each correlation length and refinement level\n", "eigInfoName = ['eigInfoL',int2str(L),'refine',int2str(refinementlevel),'.mat'];\n", "if ~exist(eigInfoName,'file')\n", " % run the eigenvalue compuation by means of a Galerkin approach (on the same meth\n", " [V,lambda] = GalerkinEigenProblem2(L,points,cells,'full');\n", " save(eigInfoName,'V','lambda');\n", "else\n", " load(eigInfoName,'V','lambda'); % load KL data\n", "end\n", "\n", "% dimension of random space (number of eigenvalues which explain at least 95% of variance\n", "if length(lambda) < size(points,1) % in case lambda had been truncated before\n", " d = length(lambda);\n", "else\n", " d = find(cumsum(lambda)/sum(lambda)>0.95,1,'first');\n", " lambda = lambda(1:d);\n", " V = V(:,1:d);\n", "end" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "% plot the most important eigenfunctions of the covariance kernel\n", "for i = 1:d\n", " figure\n", " trimesh(cells,points(:,1),points(:,2),V(:,i),'FaceColor','interp','EdgeColor','interp');\n", " view(2)\n", " axis equal tight\n", " set(gcf, 'PaperPosition', [0 0 6 2])\n", "end" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "% multiply the eigenvectors with the square root of the eigenvalues\n", "% to take into account that the standard deviation differs from 1\n", "V = bsxfun(@times,V,sigma*sqrt(lambda'));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Time evolution: settings for semi-discrete ODE" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "% parameters\n", "transformationFunc = @(x)[ones(size(x,1),1) x]; % simple transformation needed for the simulation\n", "tspan = [0 1]; % time horizon\n", "type = 2; % type = 1 for steady state problem, type = 2 for time stepping\n", "odeSolver = @ode15s; % MATLAB ODE solver for stiff problems\n", "odeOptions = odeset('RelTol',1e-5, 'AbsTol',1e-5); % tolerances" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "% generate object for the problem under consideration, \n", "% which performs the actual time stepping for each realization of\n", "% the random space\n", "heatObj = HeatClass(mesh,[ones(mesh.nPoints,1) V],transformationFunc,tspan,odeSolver,odeOptions,type);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Stochastic collocation: random space discretization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We apply a tolerance of $1.0e-3$ to stochastic collocation and use Gauss-Patterson-Legendre collocation points." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "% cell array of function handles for the quantities of interest (QoI).\n", "% The adaptive placing of points proceeds with resprect to the QoI that is explicitly specified.\n", "qoiHandles = {@(x)qoiSpaceTimeIntegral(x,heatObj.mesh,heatObj.freeNodes);\n", " @(x)qoiTimeIntegral(x,heatObj.mesh,heatObj.freeNodes,0,0);\n", " @(x)qoiSpaceIntegral(x,heatObj.mesh,heatObj.freeNodes);\n", " @(x)qoiMaxValue(x,heatObj.mesh,heatObj.freeNodes,0,0);\n", " @(x)qoiMaxValue(x,heatObj.mesh,heatObj.freeNodes,0,0.5);\n", " @(x)qoiMaxValue(x,heatObj.mesh,heatObj.freeNodes,1,0.5);\n", " @(x)qoiMaxValue(x,heatObj.mesh,heatObj.freeNodes,2,0.5);\n", " @(x)qoiMaxValue(x,heatObj.mesh,heatObj.freeNodes,2,0);\n", " @(x)qoiMaxValue(x,heatObj.mesh,heatObj.freeNodes,1,-0.6)};" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define all settings to build up the interpolating function **func** in d dimensions on **[a,b]^d**\n", "using maximal level **slevel**. \n", "\n", "The generalized Smolyak algorithm is used with \n", "global hierarchical Lagrange polynomials as basis functions.\n", "\n", "**rule** = string to determine the quadrature nodes which form the grid\n", "\n", "**func** string to determine the underlying functions which needs to be evaluated in the nodes\n", "\n", "**tol** = tolerance for the global error indicator\n", "\n", "**omega** = balancing number between 0 and 1 (the higher the stronger anisotropic)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "% boundaries of the uniformly distributed random variable with zero mean and unit variance\n", "a = -sqrt(3);\n", "b = sqrt(3);\n", "slevel = 6;\n", "tol = 1.0e-3;\n", "omega = 0.5;\n", "maxcounter = 100;\n", "qoi = 2; % Spcify which QoI from qoiHandles is actually used: time integral in the most active part of the domain\n", "rule = {'GaussPattersonLegendre',ones(1,d)};\n", "func = @(nodes,problemfolder)parabolic2D(nodes,problemfolder,@(x)heatObj.compute(x),qoiHandles);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Here comes the main part: run adaptive stochastic collocation on a sparse grid" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Each collocation point means running a deterministic PDE (in space and time, prepared by the heat object)**" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3\n", "1.5\n", "Anisotropic behaviour!\n", "Global error indicator: 1.000000e+00\n", "Largest local error indicator: 1.488764e-02\n", "4\n", "2\n", "Anisotropic behaviour!\n", "Global error indicator: 1.917724e-02\n", "Largest local error indicator: 7.169717e-04\n", "4\n", "2.5\n", "Anisotropic behaviour!\n", "Global error indicator: 1.273717e-02\n", "Largest local error indicator: 1.451947e-04\n", "4\n", "2.5\n", "Anisotropic behaviour!\n", "Global error indicator: 1.273717e-02\n", "Largest local error indicator: 4.338248e-05\n", "4\n", "2.5\n", "Anisotropic behaviour!\n", "Global error indicator: 1.344571e-03\n", "Largest local error indicator: 9.032822e-06\n", "5\n", "2.5\n", "Anisotropic behaviour!\n", "Global error indicator: 2.845666e-04\n", "Largest local error indicator: 4.010045e-06\n", "end of loop\n" ] } ], "source": [ "[allnodes,level,surplus,intval,nodesol,alpha,deltagrid] = ...\n", " anisoHierLagrange(a,b,slevel,rule,d,func,tol,omega,problemfolder,maxcounter,qoi);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Postprocessing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the presentation of the results, six reference points in the spatial domain $D$ are chosen, namely $(0,0)$, $(0,0.5)$, $(1,0.5)$, $(2,0.5)$, $(2,0)$, and\n", "$(1,-0.6)$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "% parameters for plotting\n", "t = tspan(1):0.02:tspan(2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculation of mean and variances" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "weights = intval'*alpha;\n", "allmean = zeros(length(t),6);\n", "allmean2 = allmean;\n", "lastmean = 0;\n", "lastmean2 = 0;\n", "load([solutionfolder,'/nodelist']);\n", "u = cell(6,1);\n", "for i = 1:size(allnodes,1)\n", " [c,j] = tolismember(allnodes(i,:),nodelist(:,1:d),10^-8);\n", " if c\n", " I(i) = nodelist(j,end);\n", " end\n", " sol = load([solutionfolder,'/solution',int2str(I(i))]);\n", " \n", " u = zeros(mesh.nPoints,length(sol.x));\n", " u(heatObj.freeNodes,:) = sol.y;\n", " y1 = mesh.valueAt(0,0,u);\n", " y2 = mesh.valueAt(0,0.5,u);\n", " y3 = mesh.valueAt(1,0.5,u);\n", " y4 = mesh.valueAt(2,0.5,u);\n", " y5 = mesh.valueAt(2,0,u);\n", " y6 = mesh.valueAt(1,-0.6,u);\n", " lastmean = lastmean + weights(i)*u(:,end);\n", " lastmean2 = lastmean2 + weights(i)*u(:,end).^2;\n", " \n", " u = zeros(mesh.nPoints,size(sol.idata.dif3d,2)*size(sol.idata.dif3d,3));\n", " u(heatObj.freeNodes,:) = reshape(sol.idata.dif3d,size(sol.idata.dif3d,1),size(sol.idata.dif3d,2)*size(sol.idata.dif3d,3));\n", " \n", " sol.y = y1;\n", " sol.idata.dif3d = reshape(mesh.valueAt(0,0,u),1,size(sol.idata.dif3d,2),size(sol.idata.dif3d,3));\n", " allmean(:,1) = allmean(:,1)+ weights(i)*deval(t,sol)';\n", " allmean2(:,1) = allmean2(:,1)+ weights(i)*(deval(t,sol)').^2;\n", " \n", " sol.y = y2;\n", " sol.idata.dif3d = reshape(mesh.valueAt(0,0.5,u),1,size(sol.idata.dif3d,2),size(sol.idata.dif3d,3));\n", " allmean(:,2) = allmean(:,2)+ weights(i)*deval(t,sol)';\n", " allmean2(:,2) = allmean2(:,2)+ weights(i)*(deval(t,sol)').^2;\n", " \n", " sol.y = y3;\n", " sol.idata.dif3d = reshape(mesh.valueAt(1,0.5,u),1,size(sol.idata.dif3d,2),size(sol.idata.dif3d,3));\n", " allmean(:,3) = allmean(:,3)+ weights(i)*deval(t,sol)';\n", " allmean2(:,3) = allmean2(:,3)+ weights(i)*(deval(t,sol)').^2;\n", " \n", " sol.y = y4;\n", " sol.idata.dif3d = reshape(mesh.valueAt(2,0.5,u),1,size(sol.idata.dif3d,2),size(sol.idata.dif3d,3));\n", " allmean(:,4) = allmean(:,4)+ weights(i)*deval(t,sol)';\n", " allmean2(:,4) = allmean2(:,4)+ weights(i)*(deval(t,sol)').^2;\n", " \n", " sol.y = y5;\n", " sol.idata.dif3d = reshape(mesh.valueAt(2,0,u),1,size(sol.idata.dif3d,2),size(sol.idata.dif3d,3));\n", " allmean(:,5) = allmean(:,5)+ weights(i)*deval(t,sol)';\n", " allmean2(:,5) = allmean2(:,5)+ weights(i)*(deval(t,sol)').^2;\n", " \n", " sol.y = y6;\n", " sol.idata.dif3d = reshape(mesh.valueAt(1,-0.6,u),1,size(sol.idata.dif3d,2),size(sol.idata.dif3d,3));\n", " allmean(:,6) = allmean(:,6)+ weights(i)*deval(t,sol)';\n", " allmean2(:,6) = allmean2(:,6)+ weights(i)*(deval(t,sol)').^2;\n", " \n", "end" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "[~,I] = sort(allmean(end,:),'descend');\n", "errorbar(repmat(t',1,6),allmean(:,I),sqrt(allmean2(:,I)-allmean(:,I).^2))\n", "axis tight\n", "xlabel('time t')\n", "ylabel('solution at spatial reference points')\n", "legendstr = {'(0,0)','(0,0.5)','(1,0.5)','(2,0.5)','(2,0)','(1,-0.6)'};\n", "legendstr = legendstr(I);\n", "legend(legendstr,'Location','NorthWest')" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "% plot expected value and variance at final point in time\n", "subplot(2,1,1)\n", "trimesh(cells,points(:,1),points(:,2),lastmean,'FaceColor','interp','EdgeColor','interp');\n", "title('expected value')\n", "CM = get(gcf,'Colormap');\n", "view(2);axis equal tight off\n", "subplot(2,1,2)\n", "trimesh(cells,points(:,1),points(:,2),sqrt(lastmean2-lastmean.^2),'FaceColor','interp','EdgeColor','interp');\n", "title('standard deviation')\n", "colormap(CM);\n", "view(2);axis equal tight off" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In all plots we observe that there is more variance in the solution near the cavity. Moreover, the\n", "time evolution reveals that the error bars seem to run into steady states. While the solution keeps growing, this is apparently not true for the variance." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot random interpolating function together with collocation points in 2 dimensions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure below shows the full functional dependency of the Quantity of interest (time integral over most active point in the cavity) of the random variables image space projected on the first two random dimensions for illustration purposes. We see a slightly nonlinear behaviour especially in the dominating, first dimension. To resolve the first dimension adequately, the algorithm places more collocation points in this direction, which can be seen\n", "in the plot as well. This example thus demonstrates nicely the anisotropic behaviour of the stochastic collocation procedure." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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1VdBcD40Lh5I++1ZXyIMHD/723/7b3//+9+/fv/8VfQnpg+rfdb0H0UuGqM1KIjYZIHuzYlaMxVjIklgNJcGJmkqlC/XefyRogw3vfWPDId+7D2BLrW7vVzLf3gdQmG5vfq4y/vbHvZtvAHAYgK/dfCUHAx9sxvMJBwH8yXodXw7AH9+NraQP7hYvc4+8lPL//cX6tZt7ydMHd4N5+vBRIaJGMQgmoyDAnHTSKcKKAYBAkW7T0wpzC5UaP+oWHx01KRTLCYF1vAcAafl+IYDo43G6YtNPOh3Uso8HKyKwO0+qou/9XnDwPVsdFn288U4mWZov1AphVCNMZjxgdz9yACrD4f3Ilx4HAKo9wF0fb/zs46HavX7d4pZ9GCKWFyOC6OVzPZRSPvzww7fffvuSG1Nn4SqemSZIXxbpA9d71b8rN4jed3BTn1ENxWwwVFpJVsjB6MZqGBKcKlmOweHwAaVnX1A3rCLWrE5UoJAbS4W2YVdpj201MG/ZrXkDYGBe82ZAdnDLVY/8xupnK1JBWuvWYXe4ASBxQHakCht8JVDg4KuPto8BVGVXBtB75zIARalXFrhWHpQQoiAOnqQsAMqIs3W3rGRi58nEUKDkljwBCFExGQA64yLGu6NFq60YgKiKxuabj7qyL0shY9FMs93NnKA4TPcMWGXcDwA6cjEufsBzoc0ua4dVLT9qRZw+OuYkVN9zPUhjH2+6wroQKuyZ8abbLI6XgiiVat19CrQz400X5QWq+xfrrok3XzslS/J+2a+bLg7yft87iLfuv/6SuR6u4mX3LFzFM3O5j+xaIL+Z+KvGX3Z7r/p3061LULqRU9vOb4A+q7j6xOx02pCQq/WZXeW2uwFULflqpa7HsFLt2WdyoG+plUBUoa6s9kxJPjCtrbyGzZ3dZlQA8dagG/Tb/sEGXUVa42ZArkoD8kYrAANyQS5KFWnQqioZO0IAjFWylaEqjQfzdABZtVeusrVyoiypuDvocilJVk0VNXlyCsBNjTYZnKKYIIJyJU8yFRaCVo2kktwEp2UHgBoSYgBEt2ogPLknt2p0ElCSzOlx5gOZWBJMALSqHAwEnJ5EAoBVyjCsHEAeolZjyQpByoUyVCNChwQKngmBgk2nTcqGKgIYXQ8UhbA5CDDKEqojpAuLPh4AOYTd8VKZ1CVeDkiUMr4DMq/GuaWlGQ+d6gBoupiY74E8YcYDVLdzDURbgYmg1/Vuemk24y2GapvroXFRtArpeRLVkvt7wgcqWaL6DtVUEgaD0/pEZ9omiNYnODkklATAh+Rir+LwCt9EwWS1UlvKgUpuLfW0gWnDrtDu7GZgLrA1byrTY94KVmA98pargrTBzYC80U2BVaRQJoFbrQqyywatpqpoJRBiVVeVAPQe3jAOSlt1AO68iyaei71ngVICCI3lkclM1nnqPGGqe5KnKIZSTQAI0kkxKqfo15kTAsS5iQeC83kSQOfieAmMs6Woq0rCdDNUctHrA5GKzSVBKkx1ukMhVYYOTV8CqWjvc4cjU/iiPOLgIHY9OhdLnQ5xxp+GsWBa/Iqp1F39FP6IYRjfH++nStrPeggzXtmN0MZn1+GgiQdp6XqYPnVN8KBfhyc096KPd9XHS1dRB5yFq3hmmiA9f6QPpH9W9Z70u3KDm29XELXpAHCTKHIYj5esGJwcMpwoyd1qZVEFsMbWWQvq2qpDW7oTa7MK9pYKbGNdz7SxlYPRx4smHoABOWRpi65Hrkh3uo3rG60qksBBuceqKrmSwwYPuTJXciXBQpNcFrI0KA9KBRyUXCQxeKoyKEnjj3jyRDB7AnBbczTxKCZPJgKwakspGvt4Aj3kYezjLaVoPl7ak6X5QyLC/rA4heKQZm1gHcsjxHnSzowHAKnG20nqtJClSYGWp01jJbQ7bfK9Jh7Aoe4JFY6Ol6SxYFpSyoFQqfQA90RIUu33rnhBpBAtkQRX3S67c/Ie4IFWHU/aBlctS1fxsnsWruKZaYL0FTK6Hvx/AuAloWaVpCGhGvsEwbaJU9nEIbEaRuODlUqHepWC6vA72wjo6T1VKAd6s57WM/XMa+u2zFt2W65ExsFSKFNB2rLrkQfkLVZbdT1WUfH06ARWpK1WVUlgUVeVAVRlga7sSlVp8IworbxzsFcGsNZ4sbiVeN9ztN1MpCwrdZ4oZo0HRSYmT3HGM0uRKZpyoySkaqFPUQnFRYBLm4NVs92HJtfDXDBNsBh8WWNx/lAqpEaVAmA+Fky7GwxaFk/cP21ilYCd8UGTDmn8hx+Pl/Z/GvaOl8IjfhBBBIx9vPmTajmslsbaaP9mZQPgsIQ6Ol6S6tKMN99OKhHbuvz0K3U9XMXL7lm4imemCdJXzux6AKAhS6bNCoC2GU72yWpUS2QxDolOlIRqqMkdxTmgCH7HjYA1h4EuYruQpXA9DExby2uuon1XmQrsjvcAFNiWqw26AXmNG8HudFthAO50K7BXV5GqUlFXkSSWqb/nSlWdxN47Qg6rsqI0IG2VqszBKnOxygRKGRq7c8lTkmU3ACvPWMgShHh7YMYDokwjfWzKjX28cD2Iu8admMrSKPEEM95knYhGnJWxaEM4ILQz44nIw5PNeIANAnZdPrgOy6PiyyYeCA6fYcaDuyTUoz7esRlvDmPFk8x4A4AvZcbbH2nCFboeruJl9yxcxTPTBOkFsZMlUaJvVzszXjUOxkIriY6xYCoJxVBNNck51NGMN2AYWHrWSqxZAQxEIXuzninMeGvrBuY1VwNzQVqa8eY+XkGKPl5FutMNgIo0ux56vwHgoyvPcMqMFwVThQ1Kc7XkYpG5EmRamPGSzGSrfTOeuYXNAURUPHTGReBzmPHiUAr4LDNeSXMNwEpbmPFSJbWrkJZmPGg04y0LJts/bdpNL2Evgmi+wgMRGs+Wlp91ZMYLG16ty89SLYdNvDhb2rtY96LEd7fsD06SDkLwdhePBAzAtbgeruJl9yxcxTPTBOmFsnM96EMJ6lcAfb0CgD6zkr1ZNVbakBBvRfQZItz6Cglb9BW+5bbQo4knYG0AUMi15XA9DEw908ZueuSN3WzRAVjzxsGCFLK0xWqLzsWDPt5Wq4pUlIs6VxIYTTzJXDkadHMfL1wPLt6pi2+zykKWJIPGjXNJFidMq5oBZBk1uhtM3PnCw+bnaZQfAU5TTB0tpYg7HXqK60FkSWP5M5dKPt1sUX4BU7jDPL0kdGXX5YsR2lGoZjPeTBWWTTwXjBzq8rRplK4lB127A9dD3OC4iQeccD3IT/Tx9pt4GB3huxJKqmRaRokv7vIqXQ9X8bJ7Fq7imWmCdAb2XA81wen9as+MNyTWMOPB+owomKrB6UMSsPUqoKBs2Dvq2mqFNiYAA7m1NNDC9RBmvB5ptOHRoo9XYCFLPfIW48HSgCww7A+z60Fir5sjM152JAB97cbBJqVBGcBj76IZKHBb98x4U2009vGiiYfZ9eAEkUoCQXEcRVo4IOhxnVZs4Vk4ZcbTeLdj1kP08ShMBRMXOgTAyk7brDJPOkTBHBH9MH2JPdcDAFucNo1tuqUt4jPNeDjRx1OtJ5p4wF4fLwqm/R+sQ9fD08x4ezNJXteMNUv7nBxpumRZuoqX3bNwFc9ME6RzIn1Q/DujGQ/w9S2A6ONxtIYb3WwwGwwAtx0EDFliLTZMZjzBo49XqA0dwNo4hB+PaWPdlnk244X3YTbjFaQ1bwpsi1V4xB2MPl4NyVE3oCvKB2a82fVQPEqoVGUVFnO1DmyVj8x4Y7UUfbzOM4CVp7TvegBgvrMt7Mx4AMOPN/XxTprx9lwPcQ818aQZr+xqsrBR7Mx4QB52Q7UHZjxglCWOnwvsnzaNldBTzXgy7hkfjlwPe1Hi4/3UvSYeoNKDdlAwqQ57Q7WqgI0pRIsvJ7h82HM9eH+wEjCuHrvJcamuh6t42T0LV/HMXO4jexUgv9mlfyx9MA7Vvrb2kpiqSlZyOGtOrFRKvqL1xiT2iSZWy2ZZrMWS7g2qSeVGemzrlWxLN9egujHr5J38NfYbH7aWO5aO5YbDPFq75s1/oDsHtxw26O5xG0O1AAZkF0F0KJWpV1eUcxp2ZjzIWBKtqjOpAwbPHetKpSh19OjjrawILF6rkgB5J7CaRKdMVHYzWYZVyqnkBkPUHakmUYUlzHgglQSTVSK7AFbSTSaxYjqR8uwOt2rxv0pVYcYjZALEmgCqq5jMeDIBcJPV0dYwDtUWWmVNAOBUmkKcajcO1Zoj9LTaro+nHJcmM14yJQCTx0FQF1HiiybeMkp8TGgFmSCdjhKPT8rx98FeEy+GauF1dD1ElHj3msoGtGlJIInElJauh0jGY37Dy2MAk1YbaWSSSsS2xldpGy4az51WIV0KB2Y8AL69gVN9Rg1TOC2ml2rk4+2S8byyOAuKgDXXFVpzKJSgxwkObM0crLT1ZMbbsnPwkd2bXQ/zUG04ILZYVaSNbgYkTGY8Bwd1g7qTZjyNJVTWaAJgr1yUtkpFVmF17PuZy6Q0RxDFlFLnyanb2mGqliiL6aVU0+xoiOoKODDjyWpa1Dp7ZrzD46XZjLdo4mE+YQKAQzMephOmYIx+GE3eJ6aX6AsznsT9Lt+hGc94uBIwmnh765r2zXjBnhlPgE6Y8RB9vGU/cCB54NCDJA06cOjVDWgHLbswiJ/s412C6+Eq6oCzcBXPTBOky2Lf9UD1K1XTkOCGwVgMYtokitYn1j0zHpzFWVQHlILas+9ZATw2r0SF1ilVsNB65lmW4r9Iw9uii4iHAhvYrbFyWPTxBuTZjDe7HgatJB6Y8aQkcPBcpxy8kKXZjAfAFdO1CaLUjc7v0eBgq5oJRB8vjpFMowjtzHhaaszsehg/uni7yINYRomHIUJENVBjBRSWueEJZrwId1icJ6WKOfohJoqXOvQczHgI14MvhUrVD10P0lEfbzi0MxxnPTzJjKdhXqA+XauHTTwA8t3mwAVnP166ipfds3AVz0wTpEtk53rw3wPgwxjYqmro826ithgHC1maMlsthmqr1GMIWRpYe3qM0/40EUAhw4PXM2+ZC23N1ZarOF4CcMfbMOMNzGvc9Mgb3ADY6GZpxhuUB3RVadDKlQAUdZMZLzmSy5ZmvEG5yDbKEUE0jIdPUS1ZDNVG0IPJshvBOYUoqiiKEUEUzLkPk/yE94HALgicfnDUtCuwQoc4itlieqnu30OY8SYnQirk0814c7hDmPGmTUsjyyjxUQIPzHjPFiVe92Vp/7TptBkvbOLPasZbyJIctJNmPHm/7OMFZ5Slq3jZPQtX8cw0Qbpo5g0XckM171cQNSSUiBIf+3gR97CLIHLTkCRs3R2qqBv2FWVLL9TGvJBzH2+UJct3dlNgA/Nj3gIYp2uR5qyH8IgDeKzXHFzrFkCFzWa86OMBKFOmuCvHaVOY8QD0ygdmvN6zAA/XAwDleVQ2osRvFhFEs+shzVqCwyjxqY8HqweehV0fb9/1sJteYjUtp5eO+nhLM94y3CHVKNTG/z0RJf50M15xcZGVJ42adGjG+6wo8SHWpc/OCAeoOhyWQceydGzGw+eNEr8I18NVvOyehat4Zi73kTUAkN/M6X+QftXtvWrftVSBqY/XZ19VbLN31frkWTYwAsXZZ6bKId+KXq166pTX2N4IPfuVaqG21Ep+Z+zkK9ZbDTdeBqa1dffYr7kKX8MW3Q2QUe+Ba5Yb5AHZqK26Gw6RjLfisMLQo0usAgetaCrqABAyFle6SQoz3gpIcIHJfEAaZDC4KHrv40CslACrVh1ubnOUeJpcDzargpu5zVHiqSYQnkQTnGBF+MJHz4IQwhOuB/k4VItdlHjcraKJt4wSByB6Fn3UPE+SaQx3cNYEJJmPnT0ZKnfr0il4F2FIsjqtqe3IqtFNl238umVMDVeXAbBUkSeixENyzEjumfG6DliY8WgAmFfj2dIySjx145raeSWgGZiOo8SlujTj0VZhk1z28XZR4nUzq2hzPTQ+L61CuhqWWQ9eEmTqO5Up/m6aWxqjxIc0uh6qQazFJPYqFV5QN9xW+pYeUeI9WcmeqZLRxBuY1rbasisYR2vveAsgjpqWGy56reYo8UjGK0p9LLw46uPNUeJzH69X7pVd3ChXmBQFEwFIGSJg4W5IGjt4iyaezanhcx/voAt3JAAAIABJREFU8HhJnDedL7f5Lft444aLeXppTMbDuKb2VJQ4BYbgLMMd5ihxR6q7agmTGW/6hwTCNb4smITlSkAO4RqfjQ9+OFE7Rok/OeshbvCMQ7U+7Lf7egAHJdTJrAcPTTo6SXrSUO0LcD1cRR1wFq7imWmCdGXsbbiY+3jVFPOzi7mlMOONfTwBQ/bK6iyoDm2wETWgbMwLfGOoxHoy420n18OaqzDj+aKbF1HiYcYb0BXYRjcVKfp4Ds4bLoq6MbbVVwAcY3zDySjxrZKDg1LvEfAa+pHmCKIIEU+eCMxmvDnrAU8344lwgLDyDGa8sa4aCyPMQ04CtDdUO6sd5vOkRZT4GP2wCHc4NOMJi5WAUzLeyeklCQwz3r6JLoIeFlfk/llmvCn17tCMt2+FeFKU+NFM0skQvHNFiV/Fy+5ZuIpnpgnSVbJ0PUhQ6VTSmPUwDtVGJp6lbYLTpkJKZTTjubxHGVAA3NnGocfmAHpqaxYF08A0MMVQbY+0sRsAa97MZjwHw/VQkGYz3rwPcHY9FGXBIrkVQKy3iA0XxVPRrloKMx6AtXKVxX8Aw4wX37uJppRksaZ2HqodXQ8HUeJz1gOmZLwxgmhaLLu/QH0/goiMWVoRzrFgmuBgWHglbLFpySqX4Q7mC8u4EH28PTNe1fKs6LQZjwdCdRwlvrfh4lCWTprxTkeJ93sXFV044OAUSoPkzxwl/uJk6Speds/CVTwzTZCum9n1ANFLRjX1nZzYZoDszcq4eIllMuNN00ul0oUtegBrbip8Y2WgADwyCOgXroe1dQPTHCU+MDss+ngHrodpeikDiD5er64ghyA5TLJQptn1EFHimMx4RanC1p4d5uC2jop1YMabI4iWZrxxw4XGdRWzPyJqKQrC6HqgU8S8EnApS9hfoM5FTuthlLiw7ASm5fslirZd8ZTrXgTRXpS4YEXEUnXEfQs4B1828YCTZrw914NqhbC7EmY8LGuj0xFEp6LEe4BfKkpcftDxiyjxv/udv/YcXQ9X8bJ7Fq7imbncR9Z4FnauB70HflfJ2BXvO2TXkJSsFtNgqLSSrDgHY64sCdWzUyVn7wZHkhXUzvuCumH9D4U1a5aLMNNK9VbDht3r7B/bqmOJWdp72kYfL6veIN1yiA0XKeaf9FpiXev2HrcVw4BcWSps8JWxRh+PHML1YHQAseFixVKUkrnAtTKTAPSeQa+TGU/KxUqMVWWlSu88heuhmie3xARgFBUDFmY8T4IpCibvKouRlCSr8/SSJ3fzkCUlByATneNvzKh24851TGa8mh2x1cIZ+9zFMQ0PxGDCFCUuCxGczHiET9EPYxMvURY2v1FO1Fk06FgFMwBa5XHxUgjMnPUwyRLTlDARtzGLTxzPltxBA0Eaoo833w8TeSsvcwQR0yo+tBSq0fWwL0uW7uHIjBcZEPBhmaEXC9T/xQ9+0lwPjaAJ0ssA+c3EXzX+8hhBdOvjUK1T285XxJBUXH0KG54Nzkr2mdk5pJUbPA2eVuq26Ffynn0mB/qWunH/aWInz/RCS/KBw2zGy6iIkCFwi9UN+i1XHUpFOjbjDcgFOVuJodp9M16VbGWoSmNKDh1AVu2V62TGy6zbMOPRpSRZNVXU5Gk24wmAwSmKCSIoV/I0m/GsGkkluQlOmyKIAIzaBR/NeMk9+eh6mM14NXGWqHLKjJdEAoBVepInABrDHZwliw4CuVCGapMOCRQ8cxclHo3DzlBFjJkOAMU4T6oAYJSl6M6dMOPFhgszmsG1M+PF38hzlDiJMOMtXQ9hxkOnOgDTVnXLZAJ5bMYDoLqdayDaCkwEvd7tflBnM573ywii773/o++9/6MLyXponJHWsnvZ2HM9lCw3DXkXJV4t5pZGM944vZRQEgAfkk9mPIevua3wrY028Z50cstUydhwEVHiA3OBrXkzBopPEURxzrTBzRbd0owHYHY9uOzAjAdxNuMt+3gxkHvnXejR1vO4lmmKEo9NS5H1sDTjARijxOfpJfCEGc8ZngVbbPN7WpT4vOECTzTjjSdGxeZGXCpMi9OmmGQ6HSU+nTYdnictQlpPR4nv/zTsjA/zteWGi7gesrTrB1bMlryZ46yHk9NLpyKIvK4JHvTrAKhuji9+yeOlq2hMnYWreGaaIL2c7G24cIObb1cQtekAcJMochiPl2w24zlRkrvVyqIqaIPeWQvq2qpDdyYH7tJoxosNFz3THCW+5k108zCZ8SKRKHaob3QjsCDNZrwYqo3jJYHFO4wTtaPrYfA8Tu/IYgh3UCphzPOQsTjUGc14ALJnAGHJu10M1abJ4DDnO0AwLWLFPeQhSpZFgJA/wfUwf+g4Sjw2XOx2ZIzlEU6Z8VINRcT4MI7MeJijH/BZZrz4lNinvjyCqg5o6XqApAP1KmVPqEiVHuDRSsBhz/XwJDMeXHW7NDjIe4CH87NPjRL/ArJ0FS+7Z+EqnpkmSC85R66HpCGNZrw+7VKIYk3tkFgnP55YiznUqwwogu5sIyBWAhZqbeZkgQ20cD1smbfsZjPegBz7AON/Q5O2WG01rl8SeNKMN0aJK88bLqrSPLq09c7BXhnAWtlFgb1nxPTS+M6YzZqVOk8U8/6Gi0MznqIpN+c4cIwg0i4ND6AtSp9d1sPe9NJUME0cmvGci5focag23rdxce3uowdmPGBvJSCLi+ReefQsZry9DRc62BAYHzqeXjphxhtORBABh+qleuB6eKoZb9i7+IVcD1fxsnsWruKZaYL0SnAQJS6ZNisA2sb0UrIa1RJZjEOicxyqrckdxTmgOHzNjUMbloEuYk1VMiKICm0zRYnvm/F4x3sAllHia9wIdqfbSA+KKPFeXayprcrHUeJV3dKMV2VFaUDaKlWZg1vPiAgixFDt2J2bk/EAxErAXQSREG9nM16IE4D9KPHdYtnj6aVUdqlFe1HieIIZj7CyG6q1yujdAWPvLpW9CCLub1qK06ZlH++oPFqa8cI1/hnJeHDXwSqmWAl4HCV+cD8nzHgDgEMznioi7mHByZWATzHjPaPr4Speds/CVTwzTZBeIZZZDxJ9u4rMVlRDNQ6kaNtMx1gwlRQZEKpJzlJZUQeUAUPsA6zEmtXJQmymfYA9c6WtrRuY11xt2cVQbUhRRIlHH68gVaQ73cY+QAAVqSAXpYrU+w2Agyhxj2Q870bhAbfeVdhWaTsuVk8O+ji9ZJqS8WJKyWQrH0+bACQ3c+O0RWkXJe42V0tjWTP56ObBW2BXPI0RRMso8fjQwi8OJyiWJ0SJR7jD9L+YzHjTvxysLrIe8AxR4toXKollP/XuM7MegNEjfrwS8DgZb4ogmi7WwybeeMvDrIcnJuMducnxbFkPV/Gyexau4plpgvTKsb/hAupXAH29AoA+s5CDWTVW2pAQb0X0GaKqxd/fW/QVvuW20KOJJ+BRIoCeVmjheohM8Qgf2thNZLNGHy8WqG/RxfSSi9HHwxQlHtNLRbmoc0UueJ6ixHNRljAP1Ybrocq2ShFBtPUYpKVkmDbVJlnyRHBVM4AsW2Y9HIS0xjwTMC2T1TxUO0sRdzp0OFS7cD2I4+4lLdJa57HcRfmFOdxhKpiovT1MMUK7PG1aNvF2Zrxg3LR0ECWOwxSig67dyQ0XzxhBJD/q461x9Aoj75fVklTJdCJKXD5GiR/18Z5yvHQVL7tn4SqemSZIryh7roea4BwjiMKM54wo8TSGPmREwVQNTh+SgK1XAQVlw95RN1YLtDENJIA7y3HCtLHRjNfPmwBpBXbHewUWstQjbzEeLMWp0p1uMSrNGCXe68bH/X6ryYyXPZas106jRSJt1Rk0R4kfm/HmgimGaqOJh9n14AYilQSOayl2WQ/j8Gxcp+15FvaKpwMz3tzie/pKwKUZzypnHaLGSaaDcIfPESV+0oy3f4jz2RsuAAwHgUMO4LiPd+h6eKIZry5nkqZbnvDdnayiniRLV/Gyexau4plpgvSqs7fhAvD1LYDo43EbToddPh5E9hkihtH1MKgCWGMrePTxBmptAvAoGYC6yHrYMlemaSvgajbjOfiY9wpsi1WY8RyMPl7ss+jVhevBx6W0cbZks+uhjKuVUpjxilKv7MBW2TUeOAFhxhurpQi76zwDWHlK+64HTFHiwHRWNBVP1LhXCQDLkeNufFoPNlyAU84eqi1vxhLdReCUGS8XW264wBT9gMWmJY7KB+xHP4yOhs9txsPeYdJygfp4m3qiiXdgxgsR0mJFkyqA02a8RZQ4APlwECUeV59kxjtwPVzFy+5ZuIpnpglSA9g/XvKSULNK0pDCCM4y2vCsN7pxsLFamqLEqzCohhnvsa0xmfEGamMGIKaXoom3tnlNrd3ZbZjxADgYroc5SjwiiFyMJl5F6hVmPBZ1SzPeQZT40vXg4p06V0wvdU8y42U3k+VdMp6F9Q6cosTDjLd0NMzHS5WnzXhhMa9TSCu0MOOJdTe9FDG44/uCVVtWDgdmPHtqlPhxHw/AciXg4aalk2a85br0Y1l6UpS4dGpQ6bPMeGG925clyMco8X0zHmgno4l+6d2fD9fDVbzsnoWreGaaIDV2HJrxQG1XcKrPqORgrGYxvTRHifc5kvG8sjgLioA11xVy1MdWBd3ZzoxXaevJjLdlV0KT2MVo7TxUGw6ILVZTMl7CZMZzcFA3qIt9gAdmPI0lVJY4yhJSUdoqFVmFbT1zihI/MONRTDITl2Y8PkuU+GjGk9VniBJfmPHiFOpJTTwr4wQVplOl5XnSGP0Qv74no8QX+9RPmPGK75028UioxonafdfDUqiCk2a85Wb0MUp8zwpx0ox3cqhWdQPakRlvQMQ97PPW/dd/5b/9T/763+wu/GX3LDRBOidNkL4wBxsuVLKGDGe8jT6ebRNF61MsUEcxVIuzqOIsqgNKQRX8sW0BPLLqZIXWKUUAXT9tuJg6eF0sW1qa8QZ2a6wcNiAfmPFm18OglcRlH68qS0ng4DlqpmWUePTx5u3pmKLEZ+e3gclT5ylNZrw4RjKNIrQz453KepiSWE+Y8fZlidR4woRqiJWAmCxzwxPMeBHu8LmixJ9uxsOhx4GlYj/U9ZlcD8dR4mU4mEka52ePzXhL9cITZOnURtrJ9XB45vT1n735L/7Lv3qWBeqXTBOkc9IE6Uuy3HABwIcuPOKqhj7DMS5QL8bBQpZYDUOCG9xKZZV6DBW+4SbMeIVy4KeJAAoZHrxYCVhoa67C9bDlSuBsxosNFz3yBjfHZrwYqq1Kg1bTxNJsxkuO5LJ5qDYWLxVZ7AMEsB8lvjteiumlyB9argQMEZr3AWKR+zDJDzhtwZhnj5b7AOP8aXc6Ne9in94f+3h1/x7CjDc5EVIhF2Y8CN2TzHiTCSLuZ2QZJT5KYF1WQjgSqtOuh4Oh2lr3pcXlfmjGO7lAvWzAdBQl3svL7kFHv+7YjBe3VD3o451lgfol0wTpnDRBel7suR6qjco0JBRDsVGWBou4B1RjrLdw05AkbN0dqqhrbh11Sy/U2jzMeNvFhout5TW7gXm3CZDjkdLBhgsAj/VahR2b8QatoiqqGq13seECkxkPQJmS8WYzXu9ZMVSrJADKJoqjGc/Em0UE0ex6SLOWAAeW8amPB5vrnqM+3r7rYTe9xGpaTi8d9fEWu255EO6Qh72h2qeZ8QRA3DttioTW5UERWOve6//RhosT00vHZjza6emlA1k6NuPh9IaLJ04vPYPr4ZWlCdI5aYL0fJmPl+QEqH6lOg3VDsYargebxWk8WxqyRDiHigpfYwugZ99zDGytxJ3RybrIelhbV5liqDZmlQBsuZoXqM8RRIItVwJGE09g7zcOm/cBTuF4eWnGExiuh0G23YsgAmRSmhcvmVtWAnBTM4Ake6IZL6LEMTodMFvm9vt4B4uXFkO1CzOek4s6bI4SxzwXNZvxomDSqEzmmKMf4j7jbInzaZPvRT+gijqKcF2URyxV5J7x4YQZDzooj06Y8QaQJxzhy6FaVTAdTy8dux6eaMZDbBQ8fFmbXQ94VWmCdE6aIH0VHJrxZOo7TetoMc0tjVHiQ2KxMYJIrMU0RYkX1A23derjbU+Z8Qamta227ArSnd0WpNgHeGzGW0aJhxmvKA2RlbcfJX5gxsN0vNQrhxkvSqhtzfGOlCECFuEOMVS7jBJfZrammgSdjhKfNp0vt/kt+3jjhosxPnw242FcU3sqSpwC6y6CCBHusB8lvgx3ODDjAUhlX4eE5UpADuEa33XkTjTxDrIeAA3lhBlvcUqkWkieihIfDkWo9gcl1JOixOPW2OekGe9V3nDRBOmcNEH66hiGH92tf3u1+scp/3hvqDbmZ/vF3JLThmnDhYghe2V1FlSHNthUqqJszAt8Y6jEejLjLfp4q3FXOm923bwpSjyqpQLb6KYiOThHiU/TS11Vin2AABzmsdcIaWnGiyjx2YwXpVIdR2LHKPE4WwKQPBG4rR0mWbLPMuPRaSIiI7UuPQsH0nUqShz700sRJT4xqx2mGamlGe8zo8SpMbkVwBg4tHxJWE4vKfYwFWDfRBeatHQ9HCxQx7EZbzLaHZrx9q0QXhDKtGQcqt3rzkUH77CP98IXqF8yTZDOSROk50sp5dGjRwA+/fRTADnnm5s//Ut/6YdM/7P0u3KqdBEiPkaJjxEPiW5pmxh/2keOeEkASjGX9ygDCoA72zi0pReip7ZmleyZolTaMm9s1SPNUeJbdLFvadQq3BSkeXRpbuIdR4nPfbx5w0XxNEcQzWY8AGvlKnOxjCkPlMZMcRNNKck6Tyam3fRSigiifV/4lPWAXeA3K4HR+zBlQJzacBGNuKilnGPBNHEYJb4oj0R0vT27GQ9HUeIgcRAlvuR0lPjC9XAsSyfNeKejxPu9i4ouHHBwCqVB8meOEj8tS6+O66EJ0jlpgvTlKaWUUjabzaNHj0opAHLOb7zxxu3t7e3t7Xyzow0Xpr6Tj/F37M3KuHiJZTLjhfGhplLpwhY9gDU3Fb6xMlAA1lQh+33Xw5YHUeI29/HieClcD9P0UgYQfbw4XgpBcpg0njDNroeDKPFeucLWnh3m4GzGAyDv5uOlOUo8WnlYuB6i3ImbATDfG6oN1wOdIuaVgEtZGpVssfDimaLEgbR8v0TRtoh+qHsRRNwPd7AiYvFivjTjxafsRYk7wFNR4nuuhxNmPBLloLPnh02801HiPcAjM15BxD0s8PKYTCeCXE+Z8V6RBepNkM5JE6QvTBRDm81ms9ngCSJ0/Ck//vH//jM/+7/R/nsAqsn7LnYvoYYZz2JBrZVxwHaWJdWkaai2oPbsC+qGVcSadSA19fGWUeIxujSGDzE/5m2Y8WLANvp4Dj7Wa9HEAxBNuYpcYYOvHBZ9vMmMlw6ixCN/SOBaeRg32E59vMmMt4wSj4IpTcVQcpvNeIJma/iJKHGBYYWYzXiL6aV9WXpylPiBGa9O5RdglZGGN3/0M8x4Rdw7bdo34x1HiUcK0UGU+PFQ7YEZL4IejlcCfpYZD14Om3gAJPftM5vxDjP08Aq4Hq5CkC73kTVeJMcduRChN9988xnvodafS/arKf3XrvcqvptuXaL6lZzadr4ihqTk6hOzcwxvrewzs3NInVvnafC0UrdFv5L37DM50LfUjftPEzv5irXQVioblrWVe+zXXGVUTJl4W65WKgUpZMmorbobDtHHW3EYkAtytlKRBq1oilKJkLG60spQleJVMdEBZNVeucpgEJjkfawdpMf0UrFCsIqVTjDMeDA4RUX/jHCYm0yVNRp6BJXGAxMz11joKMovwCES9OSefHQ9xHmWOWtirhBlYkkR2KBVnc14nkQCgFV6kicAGsMdnKVTZLamShmqEdOmJQqeuYsgiuKq486MZwQYCjb38dSlyTXuAEAiETC4jydMZjSDa2fGi5fFOUqcBMC82osSJ5k6pA5epTpetEwmkHtmPNLSLbAXJU5bgQnA0oxH68ikCHqQz8r0vfd/9L33f/Qqux4ugVYhvbocdORyzjnn29vbN9544/P+DXXwx9c4VOvfFT5QyXLTkHdR4tXCGj6a8frJ9VASAB+ST2Y8h6+5rfCtjTbxngSwtuxkz7ThGCU+MEdtVJkK0iPeAxA54gVpg5stukF5QA4zHsYTo25A57IDMx7E2Yw39/GGaXpp7eNQ7WYabFpGidtocNhFiUebLnmKGmWcXjppxot9shElPvH0KPHJmLffx9sfqgX3osRTYVqcNh1Hiaf9cIc0HJnCF+XRkRlPh008HGU94ChKfE7G291PBXkYJe513L204AnTS72OLp703Z3MF38pXQ+tQmpcIl+gI/d5Ib9J/jL5t6R/Vrv3pN9VLnDz7Qorqs++IjdJ2TmYkrOYJYcXDtmSW0nmqdZcVDvlNTY3ngvq2qpDd6Zcy12yTnXFWmAr1Z5pY6t76qOPl1HXvOlUKlKPvGLZouuZw/XQsUQf7x63KwwDstFjdTrpxTuQpJuSK90mj7RWQgleYcm8Vy4gEsYo8fH7lpQqxzqpMlUKwL3aASip0JjcMBYuZmYVNTJbzU1UNbGSkncCYCVBUIqhHzIKLKsQUkkUlVyTGU85lukZ3RANRTqLwQChZmclATprlidB6AYTURNq0mzGk6F0jCjxUK3acRclbgQgTpokqIv+4WTGM2qVAXAoO1uEGSymlzRKWkowg6QyVkLouvjpHJt4liCxu9mLErdES+OGC40NQKYO5JhLNP8E2orsDjZcWLon7wEuHXpMtzyKEn/44PFv//0ffu/9P36lXA+XQKuQXglOihCAZ+/Ifeb9P+WPr33XQ0LNGtJoxusTBIt8vCExvA+zH0+sxRzqVXoMAO5sIyD6eIVamwHomQba0vWw5UrkuC6dN9FgOxiq7cfRWp404y2jxON4Kfp4kTUerodeGcBa+TOjxAGsaj4RJQ6M+Q4RJe6cj5ds3nDxRaLEn2rGcy4PUA6ixA+iHz7DjBcidGDGW3rcTpvx9tal66B+ig89w0rAZ4oSD4/4ftbDk8x4J6OJXhrXw1VUSE2QXlqOj4W+cEfuWb7WZ/6sH0aJy7RZAdA2R8tuMuORxTgkAIwkCLeIEh9QHL7mxqEKv7MiYs1dlPic9RCZrdMO9ZWDd7wHYBklvsaNYHe6rTCHzUO1seGiKh9Hibuyy/pxFy16ZZcNSFulKnNw6xkRQYQTUeJhw1tGiSdPU0stzWa8ECdg6XqIM56dL/wgSjyVXWrRIkocuw0XSzMegIggmmwUVjmHO+yiH6b3D81402nTso935HFYmvHitGl/JeCYGr5sBrr2hQrk6Sjx/Z8qyA+Gap89StzrmkwnosRDw/a5dtfDVQjS5T6yxhdjswBAzvnNN998vh25Lwb5zcRfNf6y673afZeActHQITmqKakCvkkUbZu5qtYnJGdJKMkqu5qyp1pzVhpQBgw3nu/Yd8SadSUvxMaU5T3TjcrAYW3dDYc1hy27Gw0xWmtQlhfYDYctuhX7inSn247lTjcZJbFWpqJUkXq/ySwRJW6sYqnKRgfQe7dCAXEDdt5V2lbpJpVdlDgKWCGTcrEKoNKTrFKdpwSKrObmltxqrlbHbh4AuUyj66GaYqjWuzr66AyAMJnxRJWujBFEoJLLFLkPYh3NePE5kfxaEgTPAhRmPE8C4KY0JYuXTojoB4csZA4A8iAAnqN0m1TKGA4K1tFWp852Zrzo8o19vMnRQCKnKetBkGBGA2QqdVQjAF03zi3VChIguxsAOzMeCSbSllHiTB0AmO3tAyTJ6OPtZMnSvekJ32kSrQM6+HBQVzXXwwugVUgvAy/gWOgzH8Dn+uNr53rQhxLUrwD6poOIPkeRZCWS8RLircbBJlWLv797DAV1y21EifeUgEeJAHpaZD1EwdQzbeymR97YTSTjzVHikZUX00vHUeLz9NKpKPFclKOJh8n1MCgPSlulCpOiiQeAks1R4kk2RxBRzNPSv8h6OAhpjXkmTF7wxVDt7AvnLgrvcKh2sUBdHBeoa2EQn8dyF+UXYuvSIiuP2tvDdCJKvOyXR1X7m5bIUpdNPMxmvJnjDRfHfbxniRL3KvlRH28NpsOL+64HqZLpRJT4uOGiHvfxrs71cBUVUhOka+WkURvP71jo8z6YL/Czvttwod9VbPmLCKIw443W8IhthUUukRNDhtOHJKB3d6igbNg76sZqgTamOUp8YCqwjY1mvD6WWfBGtAK7471o4lWmDVZbdD1WAB7pnsDjKPFeN9OI0gpxzK/ssWS9juHiIUtYRIlvp4Ci2Yy3jBKfzXiYj5fcookHztv59rIeos55ihlvdj3sPjS1+EZZOp5eOjLjWd1FEI3RD8OeGe9pUeLHZrwwiC+FysihHEWJH224OI4gwsKMJwdw3MeTD6cOnE5FiR/NJJ303Z0cabqurIcmSOfkpRSk52jUfu4P7Mv8rO9tuAB8fQsgosQ5WsMtosTDKc4+Q8SQJMq5rQ5gja3gA0vPOlBrE4BHyQDU/ayHgfNWwNU4Wovs4Jo3seEizHgOLlcChkccQESJz/sAI+vBlY6jxDfqYh+gwOJWFP6FJNkySrzzDGAVsUPgE6PEtSueZsscQlH4TFHiNh8pLZPxFJo0WcmXIeUR7lAM89lSjbfz8dW4aWk+bcJ+9AOjyjkQqmWU+FBBLEXoVJS4Dodql1Hi80TtbMabv34doEVdpQpgr48HQFIEPTxLlPi+bS+4FtdDE6Rz8jIJ0tk7cp/Jc/lZP4wSr0kla0hwoiSWKJUmcRqMkSM+RYlXYVAdUAQ9tjWA6OMNp6LEw/Ww5spjh/qRGW+OEg9lGpSjiTe7HgQWdUsz3nGUeFGKDRcRJb4w4wHggRkvyQguzXgUsyc6wXF6aTTjLR0NTvviZjwtVwLGTnqMDw446OPtm/Gs7rIesG/G2w3VzoRoLVYCHq5LP2nwP1x4AAAgAElEQVTGW0aJh+qcjBJfftKTzHjab/eFH0+HX/Fw/6x8jBI/NuOdGmm6cNdDE6Rzcu2C9FUbtZ8vz/FnfW+B+pAB7KLE6xg7ZEOcMFm8ho67l2qKKPEBRcCa6wo56mOrgu5sZ8abj5dClgqsMj2y12K0VrClGW9AN2W2JgB3uhXo4KCuIEeUuMuWZrzjKPGCVJTmKPGtZ05R4kszXgzVJk9JnM14zxIlblEGOQHZ0vD9pCjxeYmtphHaJ0WJlyiVTkeJj6dNo2acihJ3LPt4h2a8shfGChwJ1ReMEte4e+kwSnwvl+jJZryjKPG6Ae2EGS/iHva5WNdDE6Rzco2C9CKN2s+X5/6zvpf14KaSNWQ44y1jbmmbKDLEqYyheapjlHhRLYiCyR/bFkD08Sq0Tknj9NLcxxvD8SJ8KKQokvEGdlt0ESV+p9tlE292PRRlV1r28SJH3JUGz1EzhTJt1Q1K0ccbPBnVR50kiw0XiEwH/P/tnX901NWZ/5/n3s9nZsKPBAWSSABj/WJrbQpUC7VVg7aKoq6CIFQPWziu9LRHtvXHrqirwB67x1Z2+wPcdYutcdvl0AVBUYS6RyHWWgV2F39WwR+ABBKINWAgM/O59z7fP+7kk09mJuFXMjOfmed1enrgziRzkTDvuc99P+8HpZFOZ2wrAFgzns138KUoM+shNUC9+zxA6HJAAEDX9VIq7M6PEgd/hjoAAnrBGRldxyMrMI53IlHifh3PfmdbsgsKVfcocVQauoe6Znc9dJsZqLv+3/8pUl76MciW7Lo1KmlSiW7qBdk94lkn0na6HkKQ9cCClE9CJEiZRu1Cq8gdk/77WTdmpaaVZP4EAKnp6UmHtABPgkGRlKhRKIGeQN0ZJe5JMAKMUBo1kdeZ2ZpEO+dCG4C4AA9RIVoPXhKdBDoKRQdGrOshgREC9M14dsJFEpwkRBSJNDOeBpmgSJoZDzqHXNhO2+A8QE3CmvEUSADojBIXABSMEne144eIu512u1RTLaEMzJO1Y2q7Dk9WlgLDaruORJbuA9TRYEqWCIJFvLQIopQZD31hQ/SnMREAgdu7Ga8z3CFFMEo8JYEBM54x0P22CaAH10PvTbVEZHS6GS/rAHUVBxSZZjwg6tIbv3kWRZYg12xR4oXjemBByicFLkiFfy10QvT3z3pX1gMAeQ4ZmTowJR3QKBIOEMhkypIHWqBBUBKMIE8SgW2q1aDjmNSgEmgUUlyYZKcZLzjhwkPpy5I/GNBGiXvo2AkXKRMElXkgg2Y8PxnPnoo0uZ1R4o6VqGRn/J0fJe6b8ZLGIdtU2xklHjTjCcKoToWLB10PqWS8TikKWsZTWQ+ZUeLdpmBkjxJHLcg/V2VGiasuo7nQmBbucIwo8e63TZAWJZ4yhQdKbZjVjNdtwkWWKPEsZjwk7aUdgwAozePQoxmve08S9OC7yxolXiCuBxakfFKAglRQRu2+JTc/677rgQwCICUj1DmmFpISte1ekqjRhrem7pY8hwjBoKdBg+mABAAkMZnEVGCrRjgq0CDqQNZDh3B1QJn8KHE7QL2re4lcAhEcCajASZJLgNaM588D9LMefDNe6nqJpAaRIJlIxRShHXIBJIhk0IxnXQ82SlySsLJkU8O7mfEA7YEJ0ixz3et4vZjxsPOmCgyi7h5BBJ0OCNOtVwnsgYlSyiQM+NEP9nvauyX0b5tMt+gHsIehXsx4ShNiuvFBm64JF0RAQGm9SkEznn2WvVvK4nowXXU80gAi+0jA7tW57GY8gJQZL8P1MG5C5dz55+VLlkIhSIW7s+Igc8adnekQ3sNQHunKehArjVlJ0b1EQK5LnkOOISVISaONTEjjapmQ4BjhSXQMKgFKRiRqJVwakCTlkhMlHcdEBE0STYQogSaJaNBEUNushwQ6UfQ6RMRFpUAeFTE7LOIoxiKkIhhxQZWhtE21MUwcpZgEEydwUClwpNAKHJeSHkUMGABQ4ArUEm1TLQGAZxwHNQE65LhkDOFRcGPSA1vHQwMARA4RapEqTBk0goRrpGukRrITLiSQQYOAUksDhhwCe3iSAABaEBIKNEAAiKgFCSLUAIBG2AkXIKFzwgWSo8mW+BAJyR9TS64BSNXxrFIaQQQglYBUuAM5CoXuPFmloh8AELRr04/I/pZkqhAoVcoUTo4NdwA0friD9KPEyZEAQNi9iCcFEKYOTGB12wGAVFI8AEgJUqYmXCACETo2ux0Q0R8JmEp28KPEUQIAOmUAdnZtpwIhoowiRP2mWhQuAKAzCLpHiSNKlGVpiwCwfcuBH8w+ULCuh0Ig1yckpdS+ffuqqqqi0Wi/vlB+T0hFVpE7Jrn/8NW9qVaAFiYZAYOUcIEAExKNEJ4QngAAYePy7JhazzHa2q+NAYpDnJA8UHFhFJi4AN05D1CjsE21CeF0YMQv39l5gJA6D6UGLyUhFSWuQQZHAqZ1LykTAQA7staQTDPj2RGCvhlPU+p/AAAku1wPJEQq7gFiOhWsZwelp5vxrEkvYMazTnEAEL5/oRczXvB6Cbp3L6WZ8XTAQJFhxpPa+i+g8yUyzHgEgZGAhJq6Fb2CdTy/iAeYfhjqbsbrihL3STfjdRrt0gIgtAcQvJdSYJUpSFYznkn6/9/tG/Y8QD2XrodQnJByJ0gff/zxokWLXn31VaWUlLKurm7RokXnnntuL19y1113bd68OW3x3nvvnTZt2jFfLveCFC6jdt+Sx5/1lOuBXiGDpFyyMeE2SjwhgUAkJRohkgK1ECqVIw5aEKFSwpDxQPtR4gaoc/ASJYQAgA7haBC2ozYuIkmQcREFgA6MJsBNYESBTGkVRK0Zz05Pt+qSNUrcr+P5Zjxl7DSmLFHiVpA6zXhIZLuXQBAKSg2ojWpHdkWJSxtB1N0Xni3rwUqR6ZKiLr0BEMovAyJSwIyHvUaJByYtEYKbPBEzXlqUuDJdAywgixmvhyjx7lZyAgp6HIwBovQ6XvbupWS3lVT7bUd6Ea/HKPHukCGgzPVcuh5YkLo4fPjwlClTWltbb7zxxnHjxu3YseO3v/2t4zjPPvvsyJEje/qqK664Qkp58cUXBxevuuqq8ePHH/MVcyNIthynlAqdUbtvyfvPevcJFw4QUjxCBq3jDpNCKCG0QA9RCVQy5XrQArRUGg1BEjwC6sC4BqPRHBUaADqQFGKy0/WgUHYIN4GpKHED2C4GKJBHMQYA9pIp3pmMp0FaZQKAtChxRa49JFll8rMe/ChxG0Fko8Q7jGNAGEBrxrOPBs14jpGi0yBuLXm+68HOq5W6K0ocuzkarIuhu5WOul0v9RglDoBK+lIEGruixAmkPxsQQCp7aAtEPwRixdOjxAmEIuz8WoDuZjz7ut2ixA0Apo8EPB4zHiKotDZb4xfxui92bz/SSQCEdEe4ygwIN+oIokxb7MmMlwPXQ97/kR4POdrZr371q4MHD95111233nqrXamrq7vjjjt+9rOfLVmyJOuXdHR07Nmz5/vf//7f/u3f5maTx0/BJmqXLIijHPkLor8ztBLwYQAgqUk55ErQgqSjDVJCQgRFUgpl0BMoDWoByjgGSUtHO8qgJKFAJyEZ0247Jl0EA9ROhhCEIEPaIR1FR2OyQ7gJdIWhBLpllLB1PEHkgiqDhK3jdU4CLJOo4xSRYGyUuEdK+wnigMpEBCYNCkPSjxJHIEBwSEphCLCDnIijvJQ5Aj0gIocAiBzPDlBHKQg1GtdICUIjaWGkEdJI7WipJVljuT3HGIGIRhLYKHGDhBq1QEQiIqH97qVUlLhOJeyRNPbskxoJmDJKCJBEaI3aAhC0Y8BOtTCoHeulS42mBQRPEHSa8WyUuNU1qQgQTOdtU6qIJ5EEpsx4CEBpUeICIFuUuJQgOnPEiVBKkAEznhAAAK6bMohbfUKJiIAiI0o8BgCkE6nWXRmxDwWFCoUD4CBFgq4H4QwEAOhuxkMRQWvGC5yrmpuO+FHi9zw0oWCzHnJAjgTphRdeiEajs2fP9lemTJmyZMmSxsZGrbWUMvNLduzYQUS91/RySdaKnNWhfG+NSRGccGFgJYm95AIlo+BoSrjGMeAJksYoIRyRGgmoNXoSjUFPRghdLT0jI+QmIFlOMolJD81gYxJIUWMSAlw0EdQKRYRUHFVC2KkWEQc0dGbiJTASIeVHiTtoOigSRa/TjOdZ14MjlAbpUQQFGRIIEoEEaiIRFWSjxME2zSI5pBVJB6iDHIkkpUkaIgBDBgiJXGVliVAJLUhEtIMAIMC6HgySICRD0kgSpFF3FfQk2Hd+IQylZiaRPX4BGCBEQOMYA8a6HuwgCxIGCREJCEkQKmkDGyiifTNeSvAIhUYjyUiwrgd7OFMu2QHqUqOtJqoIis5wh9SECxslbg9UrnWfGyA7uBZtvc+v45Eru0WJI4K0XsHOploh0I6ptbJEBPas4HcvoQAAdCLdosTtZA0nBkYTdbY0CQdRpop4foaedT1QhMgjoyAV4hSxLongSEAULkLnQFsy/nmwuenID2ZvKsCm2pyRC0FSSn3wwQd1dXXB925EHDt27IYNG5qbm7NW1d577z0AOPfcc3fv3v3RRx9VVVWdffbZkUgkBxv2yTRqW49cKVwLhRdfllKuh9grQGhcBVpS0iGDlHBMDEVCGtfIhATXiKQER6MWVpaMJx2KGYIEOYZMByaiYBJCS0MSjUQC0EmhI6iVEXHhxjDpoYwKz4YPRcFTIOMYdUi74LmoYphIgBuHaAwTcYr6ZjwCTILyMNW95JvxEI0kT5MjiAAgadwoehFUHknr9OswTkQoACDQnpGaDFkfOUgCMmisGc9GiROSAYOEEqV9E7cHJtvv1GXGI0JCRI2EJIxQgkTKJ2DLcdaMl5pwAUhIhDoVi+dabQiY8TpboAhJI/lR4sohABAaHIV2gLqxByaFSGAkggQ0KdcDCdAuAnZ1L6XMeNbjkGHGA2nHPlnp6iyL2QHqdiSg9URYz54fJZ52YCICFChF52T0zuqcsJvzzXhWqKwZL9C9ZAcviUiXGS9l2+vRjJeWL97cdGTj2l0sSP3FwYMHjTGVlennULvS0tLSkyBJKX/yk5/8/ve/tyvDhg27//77r7zyyn7dLRu1iwPEUYizBMyyrgfhvkJSo+uZeBQcQ5400mBCkmNAo3RMqqnW0eg5QhqhpDHCMW7CGJecOCSjRivQHUIboA5BjjZHJZSRipBOoowL1yUdF5EySibQ7cCoA9qKU4y8JDgxdAZC/AjEJOokRaKYVCA7KFaGiQh4Hvhz/6KIRhkXEBGNIG1IxqTxjEOACCTBaBBSmCQ5CtAjGRGKAD1jNAkAMiABUKOxdTyNBABl2jVoSBIKlCY1CdBOtdBS+1HihEQCUAMSGZcAQChJQCBTGoNGkCAttJ/1QNJ601FoQY7N7xFoROrAhAaV1QPQjvFDyo0kTxAQuJ41BoLnktSAlBoJqCKYaqoFAADjYlcEkdUh9H13QK4ACJjxOkcCdjPj+SMBO6+XUEqwBybVeRJyXQAApVJnJiGBCN1otyhxIVHI1IQLMp11PLdTvbp8dyjsPMBuAeFClpFJAqDv0KuuKaseMbSyWlTXDDhj5EB7n9TX/xpCQy4EKZlMAkDmu7ldsRWwTN577z2tdUdHxy9+8YvKysr/+Z//+dd//dcf/vCH//Ef/zFhwoQ+32SpGbVLByFmCZhF9LHGhw2tlAM6jJLoOKQkSUNaYFIq14iENI4RnkDHoCdRGqEFKFkGoDzHAZkk5YGKaDoq4hENHpoIGYXkImlQEdIeijLjJYTjonJRJdAtw4RVpjJIdEDUAEZQxcH1MGHjHmKQ6ICYRw4iuaA8coQwihxHKk1SkyNR2ShxgcqQo0k6BIocF3WElCLpodQkOsixsqSMti23ZBwCVIIIDVCquhXRjgNCdfYvOdb8BWClSKESJNAg2BA7ImHQpDQmJUWEGmyUOIJfxxNaAJKRBmyUOACJzgOTNKlfe8KGRZCtgSHZFKJk1EBnlLiWAEC2iIcEJEALhM4ocerq67V1PKTOwbUAAMY/HhEq03nb5AB0N+MFr5dSV0eILnaLEvfreLZ7yRbx0sx4iPYyibSXalQSDgCgOwAgECWOiJgq7lVWagAYe8GQqhFRABh7weDqEQOqa8r66cc+pORCkKyRzxiTtp65EuS666675pprZs6ciYgAMH78+PHjx998880PPfTQmjVrMp+/ZcuWExWqnkSIK3LFR7rrwVXkORQRFI9ARFHC0Y5BT5JDqIxwDBCKuAMRhUnHQQIjHO0o43qgXON0YDxCEAV9VChCSCA52ksKkUQdIy+JTgI9m9kaRU+BaBcDJOmjWOZQPArJJDgdqOzMCweOHoWYCwoA7C/sAPUkRAQYAwLBKIpIVAK1IGnIEUSecRDJQe2QVCAlGo+ERxIFuaA1CQ8MAZI9syAYMIKQgIyRAGDreB6SECjsIwhSSYMGBAgjgECA6HI9WKFIDaQgq1K2e8lIY4TxzXgkDQljzXjkKug04/lNtbYtFwC0a4RCm2mkXBI6Fe5gRGqvNisPCbRrr51IaCtLoCMoFFnPHtmLIv/AJJAiEoJmPClIYGrmBXZKokQQCNqkHOgA6DpgDPmhREKA6wKi372E0rEXUcF5gChdEE7QjFd1hqsUnvN5VTNqYCwWG3vBYAAYe/7gfv4BLxJyIUj24ieRSA/KtSs9XQvNmDEjbeX8888fO3bsm2++6Xme67rBh5YuXbps2bKampqHHnqod1nKatQeMmRIqRm1S5Nurgd3JcHH5ChSDkgDWpAkDYBxaQhFwiGZFJ4EaVBJUEJo4WrpkNTKcUjazNaocY52mvESZCJoNGJCaAd1lJTXKUuOMQl0o2QdEFEB5JBRIMow2QGRCCY1yKMUk2gMYJwiDkoHtSJpXQ8OKeO78lDZkxOBSBo3gsYhHQVMkmMnXABAAhwhyRAqMoakjRLXSEaSRiMAbR0vph1C1MLYKHHtaHv0sZAhQQIBSZIWhAaRwKTuigQSkjTQ3YyXaqoFtHU8sMaDNDOe0JBSKTAOAZA14xlJAGBkVx1Puam7JRvuYCQa0dVUawLHI1vHS10d6VSUuF/HQ01ghS/TjGeLeEQB1wMACdImdX4CANftihJHBEB0owBQOVRXneFUVTtV1Q4AfHlcBADGfmUgAMTj8ba2tng87jhm0CDNH3CPn1y8BQ8fPhwRm5qa0tbtSubdUi9UV1dv3759//79o0ePDq7Pnz9/4sSJS5cunT17dk1NzdSpU9OaZzMPQ3wtVLJ0cz3gSsI/geuZRAQjyiRckoaSkiShEiQJNQqPwEHUArVGJYUQrhFSR4jAI+WQG8e4QhMhcURoInBJR9HYAeoRUlFUCfSSKOMimiSnDBOHcSAAdGA0QioKSdtUK1HHIWoIBVKC3Ah4SXQJ0APPQ1eTBJGatwQAgGBIRoUhEMpIRY51PTjkKJICIEESESUaTUaT0HbUt3G1IA2gUTvG6XA8GyLuCDDCCCOENeMBAYIEqUGnku4gVcdDA2gAHBMMELLWBmtz0EJb1wOk7pYAyT6C1iKB2h6YNOjUDCcjCSQhgVCCEGwdz48SV44d/w6OQkAgTJnxbJS4PR4Z7IwSt64HK1Sm83iEBIioUlHiWcx4iCnXQ+dlEjoSSJCnqqoEAFRVuV/+sgtaV1XLqipZVe1UVWcxBvvEYrHq6mr7ntPW1tbe3m4duX39g1yE5KgxdvLkyfv379+yZYsvAER02WWXtbW1bd26NfNosnPnzjvvvHPmzJk333xzcH3q1Knvvffe66+/nnZC8mlqalq6dOnatWvtb9esWTN06FC+FupvQtFz1xPGDl6iVwCAPIe0pKQLABR3gUAknNSYWo3C64wSt1njShoCOxJQgUpgkgCOiqQC0ggekgFICpFEkUAnLlyFwkN5BKMa5RGMEQoF4iiWGcA4uBplHCIJcD1wCMRRimkQwSjxJESIMElRQwIAUiMBSWhyDEjojBK3TbUeOQBwxLgAoEH4M9SJJAACyWCUuGOEa6QfJS47Yx2CUeJd+a02HMjKCWFwqmx6lHhgwgUQ+gFFqCQgQWaUuI1vUMLvihW6K4LIRj+kRYkDdEsh6hYl7pvx/O1Zg3gg+gEEYlJVVSIAVA0XdecCAFRViqpKUVUlqiq7/mgnjS9Lvkc3X/9GQvGPNEc7u+yyy379618vX758/vz5dmXNmjX79u2bPHmy/a/T1ta2a9euSCTyxS9+EQBGjx794YcfNjQ0XH/99QMHpkI1XnnllXfeeeeSSy7pSY0AwFbt5s+fv2bNmmXLlsXjcXsY4o8nTE8I/IaQ30hFibsPgzQY8UxHDAcmKOkYSaCEcQQqFC6hRpmQ4GpMOuho6TmC0DHS0zJCbgckyrXwUNko8TgaV5sImhjqKCkbJe4KbWNb7UhAAdSBUetoKINEAiNJSB2YEuRG0LMjAR1UEfCS4ErUNkpcoDEkNDiIxmY9RCXZKHFrxiNAKYwfJe4K7YDxjDH2MgkEgFBC2YxzW8SLGCkASRKSEf6ACSOEEUYYg6bTjAfk2HRWglQzkF/rI2vGS7keyKSixAFSma1agtPpe/bNeK5GJQDRN+MBgDBoJCUloQFHCUJAe9vUGSWeuk9y0B6PkFJNtTYWsNOMh4BQXWEAoGqYrBoG1acRAFQNx87/9W+opn8j0N7e3t7e3tzcbJNc+GNxVnJ0Qvrkk0+uvvrq9vb2q666qr6+fuvWrevWrVNKPf3005/73OcA4Lnnnrv99ttHjBixadMm+yWPPfbYww8/fNZZZ33nO9+pqqp64403Hn/8cSnl2rVrzzzzzGO+YgGOnyhiQvHh63jwJ1wAIRFS0gVA0xEBAEg6qFHYYbVJgUagJ1KpbkkHCLUSmoAIEpDUYI6IDgBIokkieUgaUQN4QiRQ2gkXCeEoEO2izIA4KmI2ZMgOYbIRRBpkB0Q9cAxhHKIeOf48QEUySRECVOTaSUvWjEckNLl2GpM/EjBhXA+kITzalVSEioQhSTYiD1CSAEI74SKiHaczGS91YDICMHVgSp1j/BEVZKMfUtMuAqNpsWvSEnRGiQcHqNsGJlvEA0hNtVCCkFKTMqxHIXACs2a81Dc0QNA1ErD6dHA8qjodqodCVLadPnhI1VCoGgbVQ7FqWJ//mJwkfj+J/0HZxl3m7NUL/x9pjnY2dOjQ3/zmN/fff/8zzzyzbt06ABgzZszixYutGmXlb/7mbwYOHPjII48sWrQIACKRyMSJExcvXswCw/Qf3VwP9EeIfayTLWJAgpIOSENJR0uDnjCuSB2VSImkA9KgJ6UQUkuj0YFIwuiIceMQd9GUgT4iNAHFBTlaC0ER1B7KJMk4uhHQHRgp06nwIQm6A6MOGWvGsya9Dow6YOIQtXkQRynmoHLR88iVqG0dz5rx0GoCSSIhbPcSYUwkXRIahUMmFSWOwl4vdZrxpAbHN+MZNNJISWjNeGQDw+3tUmeUuJbaz2+1rgehERwgoyEVJU4Gu5nxQEDQ9ZAy4xFS59PACHIMdHYvpRLGXSM9MWIIAMAZp8HoQVB9mv01nnEaCIJx/6/rbw9Sb7uHRo4cXIBvu/bWYNCgQdZU1dra2tbWxtdLQXhAH9MHhOLD18lB9DEAkG4is9d4+0g3mcR+AIDD/wMAMukHiiOm0loFKQkASglFWoH2QBGYoyJJQLaOpxGSiB6KhJAeyiQ6SZR+lLg9ISXANSiOQAwAskaJJ8jVIAkwSa4CR9l4VhCeiYCNTu2MErdHJX8kYIJcj6QBsCMBAcAzUpO0EUT2Ty0IJUnbn1Sm3LTrpR6jxFPZrMeKEidwvNTPycgyFwBGVIiacgQtR1QgANRU4IjBAgBGDIERQ7rGWBwPIfpRDF4vWaHq1z2H4r9M4e6MYQoBxFEAgM4oAJDBDoXhQKoJCMFrgvh+AICOZkjsByUxsR8A3PYDbrw5qWQE3AQkBxmZwIQAEyFxVGiXwENdZnSHlBq8JMoy43UIt4ySHRhxUQ0A0S7KXFB2HqALykMnCY5E7YGjQUowCXIBAJEi4GmUCYpokiiIAHVqeJIWqBAMgbDdSw5qiSZJjiYhgRIkNYiIUJ4hQFCdZjyDwqBSQgsjOhywIeKukbap1gWHgPwDk5HGgHGUAwg1gwQACCVGDpI1gxyhRM3glA6NHOjUDJYAUDNYAGFNeR9YBkJN2vVSe3s7Xy+xIDHMSYJODQCAOwIG9PicKAB1NEeATHy/Aa079gGAQvLiTUcSewEgIUQ83gQAHcIFgIPeX+ytQrN3aIhpPywGltMRADiMAyOkDA4YCHED2A4DJOqBCEdogAP6KMUcUBL1USgTaIgwCSBQA4Bnoo5IEiCYqJAGABI6EkUPEI6YmIMGAA6b6NkDXABImNQJaXQ01chZWxZ1jQMAo8tcK0sAUBuLAsCoAS4AIOGogc7IgfxOcpL4smSvl5qbmx3HGTZsWGnKEv8YMUz/gmXVCCDKzgAAOK1r/fTj/g6HEwcMIgCYVAg3EODWrVvr6uoisbKDiTbdua4hpRmGxBnRwfaZ/kZSX0tYE+tZQpl84FftbFOtlaUSvF5iQWKYQqc8mt48Ho/HB9HAoZHTY5HY8MhpWb+KCSMl3lTLgsQwDFNYBK+XrCzlt6k2ZxT5H49hGCaklGBTLQsSwzBM4ZLV9ZDjptqcwYLEMAxT6JRIUy0LEsMwTGiwpvAhQ4YEXQ9FMz2nGP4MDMMwJUWxNtWyIDEMw4SS4muqZUFiGIYJMcXUVMuCxDAMUwwUQVMtCxLDMEzx0FNTbb73dVywIDEMwxQbmU21juMkEol87+sYsCAxDMMUJ0HXQ1tbGwsSwzAMk0+sxyEWiyml8r2XY1DqM7IYhmGYAoEFiWEYhikIWJAYhmGYgoAFiWEYhikIWJAYhmGYgoAFiWEYhikI2PbNMLfb7aEAACAASURBVKEhHo8fOHAAAD744INPP/30f//3f88+++yqqqp874th+gYWJIYpaOLxeCKROHToUEtLi21sjEajZ599dkVFRUtLy86dO/fs2VNVVTV69Oh875RhThUWJIYpROxh6NChQ4cOHQKAaDRaVVVVUVFRUVHhP6eiomL06NEHDhzYs2dPS0sLyxITdliQGKZQ6EmEepGZWCw2evToysrKoCxVVlaGdyIOU8qwIDFMPonH44cOHUokEnv27AGAaDTqa8zxi0pQllpaWlpaWioqKqyY9efeGaaPYUFimDyQeRgaPXp0WkXuRPFl6dChQwcOHHjzzTft6YpliQkLLEgMkyOyVuT6XDBisVgsFquqqmppabGyZNWOzXhM4cOCxDD9iG/U9ity9tSSA/dBVVVVVVVVPB7fs2cPm/GYUMCCxDB9TFaj9qlX5E6OWCx2zjnnsBmPCQUsSAzTNxyPUTtfZJrx7EGNzXhMQcGCxDAnz0kYtfNImhnPuh7YjMcUDixIDHNi9IlRO49kmvHY9cAUCCxIDHNc9IdRO4/4Zrx4PL5z5052PTCFAAsSw/RIboza+SUWi9XV1dk/KbsemPzCgsQw3cijUTuPcAQRUwiwIDFMYRm18whHEDH5hQWJKV0K2aidR4Kuhz179hw4cKCyspJlickBLEhMaREuo3Ye4QgiJvewIDHFT9iN2vmFI4iYnMGCxBQtRWbUzi8cQcTkABYkpqgoBaN2HmEzHtOvsCAxoac0jdp5hM14TD/BgsSEkqI3ajc0NCxevBgAJk2atHDhwtra2nzvKB2eB8j0OSxITJgoEaP23LlzGxoa7K8bGho2b968adOmAtQkYDMe06ewIDGFjhUhvy5X9EbtvXv3+mpk2bVr1+LFix9//PE87ei4YDMec+qwIDGFSCkbtV999dV8b+HkYTMecyqwIDEFBBu1iwOeB8icHCxITJ7Jei1ks2ryvbX8MH369Nra2l27dgUX6+vr87Sdk4fnATInCgsSkwfYqN07mzZtuvTSS60m1dbWLly4cM6cOXne08nC8wCZ44cFickRRW/U7kNqa2s/+uij5uZm+9vq6ur87ufU4XmAzPHAgsT0LyVi1O4PikCHMuF5gEwvsCAxfU+pGbWZE4UjiJissCAxfUMymTx06NCRI0dK0KjNnBwcQcSkwYLEnBL2GPTJJ598+OGHADB8+PDa2lquyDHHD88DZHxYkJgTJuu1UHV1teu67e3tQggiyvcemZDBEUQMsCAxx0mmUdt+sE27FhoyZEh7e3tbW1t7e/ugQYMGDRrkOPwzxpwAHEFUyvCbBdMjJ2HUdhxnyJAhgwYN8mUpFosNGTKEZYk5ITiCqDThtwkmnVM3avuyFI/H29rampubY7HYoEGDrLvBRoXaZ9bX14e35ZPpb9iMV2qwIDEA2Spyp27UdhzHilA8Hm9vb29ubnYc59ChQ9dcc42fi2NjrVmTmF5gM17pwIJUuqRV5PrJqG1ladCgQUqptra222+/PS2lbfHixSxIzDHheYClAAtSyZGv6ATHcYYNG7Z169a09V27djU3NxdlKgHT57AZr7hhQSoJehKh3N8SI2LmolIqx9tgwg6b8YoSFqSipSejdn7vhCdNmpQ2DnXGjBkA0Nra6rseGOY4yTTjDR06VAiR730xJwkLUrFxKAAUXqK2ncPta1Jtbe0//dM/2e4l63qw9rx8bpEJG7FYbMSIEZFI5ODBg9u2bRswYEA8Hq+treXPN6EDi7Wpvqmp6bLLLnvxxRdramryvZd+J3SJ2nv37rWDuqdPn+4vWtdDe3u79UEMGTIEAFavXn3LLbccPnwYAC655JLGxsZ87ZnJPVl/TnyUUkop6+G0VV/HcSKRyJEjR1pbWwGAzXhBlFJ79+4dOXJkITcFsiCFlaxGbQAIexldKWWbah3HeeGFF9IMeOXl5VZ0mWJl9erVS5cuBQAp5aZNm+xibW3tpk2bamtrofMnJB6Px+NxCHQXBM9D8XjcmvEOHTrErgcLC1I+KUpBymrUrqioKL5WQfumM2rUqPb29rSH1q9fP2XKlLzsiulv6uvrX3rppawPjR49+rXXXguKEADYY3Qv2HmAVpZK3PUQCkEq3J0xPqGryJ069jIpU40A4IknnmBBKg5Wr15tf2Ercs8991xPagQANgh89OjRJxSQyPMAwwULUoFSOEbtPFJeXm5vj4JorfOyGaYP2bVr16WXXuq3SM+ZM2fhwoVPPPFE719VWVl5zCNRVjiCKCywIBUQhWnUziPjxo3L/Mi8ZMmSvXv3+q4HJowsXrw4GNjR0NCQTCY7Ojp6+RJ7gXQq9BRBFI/H+YapQGBByj8FbtTOI42NjWmXCqtWrRo5cmRwwgXLUmHi+yHr6+vTHmptbU3rRQOAl1566eGHH37mmWd6+oYLFy7skziPzHmAAMB9tQUCC1J+yFqR42CuTBobGzPf2tImXPDgpYIi6NSH7mZ9a9TO6pPcu3fvlVdeeckllwQ/f7iue/PNNwPAwoULT/2EFCQYQVRRUcE3TAUCu+xyR7EatfOINeNZ70NwwgWTRyoqKtJu/i6++OJ169YFjdrf+MY37L8Cnzlz5tim6fr6+u3btwPAuHHjctl25hsf7D/M4quTh8Jlx4LUv2TOuKsIkMeNFRN+d2Q8Huesh/zS2Ng4adKkzPWPP/44aNRuaGgIXiMF24zyi5WllpYWALAeoqKRpVAIUuHuzKKU2rdvX1VVVTQazfdeToASNGrnkbQJF62trW1tbXy9lHuUUj0ZE0aOHBn87Zw5cyZNmuTPaezzitxJk3bDtG3btsrKSo57yBmFK0gff/zxokWLXn31VaWUlLKurm7RokXnnntuvvfVI2zUzjt2woVtYGLXQx9iDzQAMGnSJFtYCxKMTsh6P1ReXp65WFtbm/mtCgR7w1RRUeHPXuK4h9xQoCW7w4cPT5kypbW19cYbbxw3btyOHTt++9vfOo7z7LPPpn3U6onclOzsv8BEIhE0ahdldELoCEYQZboempubt2/fPm7cOJ7DdEzmzp0bNMXZy55e8nsy0xbCHkJoh1wcOHAg1HEPXLI7eX71q18dPHjwrrvuuvXWW+1KXV3dHXfc8bOf/WzJkiX53RuwUTsM+JdJ7Z34rofgO6xtySyQelEB0tDQkGbRbmhoOO+886ZPn+44TiwWGzJkSNoZNGjWLy8vz7E3oT/IHHIRXlkqcApUkF544YVoNDp79mx/ZcqUKUuWLGlsbNRaSylzvyU2aocRX5as66G5ufnv//7vV61a5T/BvtsWbO0o7/jxpkH+7//+77bbbuulBhB2BcoKxz3kgEIUJKXUBx98UFdXF/ybRsSxY8du2LChubk5Z8a5TKO2vRPiD0fhIuh6sOMMgjQ0NDz88MPDhg3Ly94KE78iV1dXl/loJBIp2XfhrHEPxWTGyy+FKEgHDx40xlRWVqat25WWlpb+vhbKNGpzRa44cBwnL8frQsAf6wA9nGCyXgtdccUVjzzySDDmBwAWLlzY//staNLMeG+++SbPXuoTClGQkskkAGR+4rAr9l9Ln8NG7ZLFXvMqpQr5svcUSTMaWP8YdLZwWbs8ADiO4xc57X+NIUOGLFy40O8Zqq2t5Ss3Hzbj9TmF+C/QGv+MMWnrmSunCBu1S5CFCxfOnTs3uHLPPfekuR7ytbd+InOsw+HDh7/xjW88+eST/mFoyJAhaTPufObMmTNnzpyNGzcCAPsSM/FTiOzspZ07d3Iy3klTiIIUiUQAwJbLgtgV+2gaa9euXbp06fz586dOndr7N89q1C7lRO1Sw46gbWxs3Lx586RJk+rr6+fMmeNnPTQ3Nxdf1kPWsQ5vvPGG9cgd54/9lVde2df7Kjb82Ut79uxhM97JUYiCNHz4cERsampKW7crmXdLADBhwoQJEyYsWLBg6dKlU6dOnT9/ftoTMg9DfC1UstiP/MGVoOuhtbW1aLIe7LWQUirzISFE2P90hUlWjzh/3j1OClGQXNc988wzP/zww3g87v8tEtGf//znAQMGjBgxIvNLampqHnroofnz569Zs2bZsmVr166dMGECAOzZs+cvf/kLG7WZ48RxnOrqar+pNoxZDzZR2x74rBRdf/31a9asSXvauHHj8rG7UiHTI85mvONBLlq0KN97yMK+ffu2bdvmOM7EiRPtypo1a5566qnLLrvs6quv7umrPvvsMxtSsmXLlnfffRcAXn75ZSHERRddVFdXV1NTU1FREd4fiIaGhp///Oe3337766+/Pm7cuHC9S4YLIYS9TwIAK0vGGMdxhBD52pL9229ra8tsRLUopQ4fPtzW1vaXv/zFSpGV0mHDho0dO3bTpk27d+/2n1xeXv7ee+/lcPsliuM4NrcFET/55JMDBw4cOXLENhTnfjPGmMOHD5eXl+fxx/iYFGh00CeffHL11Ve3t7dfddVV9fX1W7duXbdunVLq6aef/tznPpf5/KVLl27ZsmXLli0AUFNTM3XqVKtka9asWbt2rV3JrOOFiIaGhrSr+Mcffzyt7sT0B4Uw4SIYLWF9bvav3q/I2e3ZwiN0JmqnYccUQc7HOjAWe3ttLw6i0eg555yT41JNKKKDClSQAGDnzp3333//9u3b7Q7HjBmzePHi888/P+uTFyxYYJuTMlWnqanJ1vGsLE2bNq1wJiQdP2eddVZaL0htbe1HH32Up+2UHHmccJH5WWT06NEbNmwYMGAAdBq1rVIW8hsN42PNeFaWcukRZ0EqIKwsrV27FgAmTJgwbdo0e8kUClpbW4cPH562yIKUF6zrwcpSbq6XMj+LAMCjjz46c+bMnozaTOGT+8DWUAhS4e6sb6mpqZk/f/60adO2bNmyZs2a2bNn29NSiGSJKQRy6Xqwr6K1znxo6NChfIkYajiwNSsFamroJ8rLy88999xp06aNHDlyy5Yt1o9nF/O9td4YMGDA7t277Vxnn+uvv/7666/P15ZKnP5zPVhvQjweb25uPnz4sFLq9NNP37BhQ/A5tbW1DzzwQNYhQ0y4CLoerCxpraPRaH8cYkJhaigtQfKxsjRt2rSmpiYrS4cPH/YdfQXIuHHjDh065GuSnUmT3y0xQVmyxodkMimESHs3aWhosLOXevo+SqlkMtne3m77n2yWT3l5+ZAhQ04//fSJEyemfRz56U9/eskll/Tfn4vJMUFZamlp6SczXigEqVTukHohRK4HHitXsKS5HoYNGxaLxebNm7d8+XL/Obfeeusvf/nL4Jf0NOMu8/s3NDRYaxxHyRU3QTOeH+vcJ985FHdILEgpQu16YAqHeDxuTzn33XffihUr0h695ZZblixZcpxGbaaUsUelPjTjsSCdKp7n7d+/v7q6Omt+XX/Q1NRkXQ9btmyxPohjhuMxTCZKqcGDB2cm08disZ07d7JRmzlO+tCMx4J08rz//vsLFy7cvn27UkpKeeGFFy5YsGDMmDE528CWLVtss20RNNUyeQERs64X5r84ppCxUZx79uw5FVliQTpJduzYMWPGDCHE7NmzzzrrrO3bt69atWrgwIFPP/101iC7/iPteolliemd4LXQueeem/WE9Omnn3LzEHMSpMnSiQa2siCdJPPmzWtsbFyxYoWfy7B69er77rtv1qxZixcvzv1+QuR6YHKPfyEUnHFnJztkHpL2798fdD3kYbtMyLGy1NLSAgAnNKaWBekkqaurO++881auXOmveJ43fvz4c845JzO0OGew66GksK42OzMp09iWmaid1SOX1WXnux5ylvXAnCh+cuCkSZMK09MYNONVVlYejyyxIJ0Mn3322Y033nj55Zffcccd/mJHR8dXvvKVsWPHBlUqL7DroRQIhpkCQG1t7aZNm2pra0/IqN07dmp4e3s7y1JBsWvXrksvvdTPavL/6vO5p145fjMeC1Kf8dRTT919993f+c537r333nzvJUVTU9PSpUuLI0qcCbJ3795Ro0alLd50000/+tGPoK+N2n4EkT8hsJDfLEqBtM8iEJIm9OMx47Eg9Q3btm373ve+BwAbN24cOnRovrfTDb5eKj5Wr149Y8aMtMVRo0a98cYb/SQYhTDhgrFkjbI9ePDgsGHD8rGdE6N3Mx4L0qmitV6+fPmyZcsGDRr02GOPfelLX8r3jrITlCW+XgovVhg+/PDDzCknOfiYHMx6sJ4IlqXcE2pBsvRkxmNBOiXefffde+6555133qmvr3/wwQcrKyvzvaNjYK+Xli5d2tTUxFHiYSHrtdDYsWP37NkTfFouxyHa01LuBy8xkK1kF9I5L5lmvIEDB7IgnSTPPPPMggULTjvttAceeOCKK67I93ZOAHY95B07GvXw4cMAcMkll2ROR+3JqO1X5NJutvNyi8Cuh7yQaWrw5/OGkaAZ7/TTT3/77bdramq+/vWv53tfPVKIgvSHP/xh3rx5F1xwwbJly3I85bcPYddDXsi8ASovLz906BAAxAPAcXjkCiHKll0PuWfXrl2bN28umihbe6Fw4MCB//qv/7IrhVy/KThB0lpPmTIlmUw+99xzZWVl+d7OqcKuhxxTUVFhz0ZBVqxYceGFF8KpGbXzCLsemBPC1mn27t27bNkyAKipqbHX2xMnTrTvSAVbvyk4QXrrrbduuOGGsWPHXnzxxWkPjRo1KqQj6bipNmdkFaTrrruuoaEh7FWv43E9tLa2huj6nelDmpqampqaXnvttbVr1zY1NQGA/RA8ceLEzHebYP2moGSp4ARpxYoVPeUDfe1rX3viiSdyvJ8+JHi9NGHChPnz57Ms9RV+dMKoUaPsSSLIjTfe+Lvf/S4vG+sPsroe5s6du3nz5l27doX92oM5IfwTz5YtW6BXEerpa4/zybmh4ASpFFi7dq1/aubrpZ6wpXzoNb4l0yM3c+bMV155Je1pRflDHnQ93H333Wmzl3JpC2RyTFYRAoAieCdhQcob7HrohTT3bfDtNatRGwLRCfX19S+99JL/tatWrZo+fXquNp5rlFK7d++eNGnS3r17g+shNSszPWFFqKmpyVb+7Z2QLbjle2t9CQtSnmHXQyYNDQ1z585NW3z99ddHjx7dk1E7jcbGxjVr1kybNq2+vj4XO84rra2tw4cPT1tkQSoC7JsDAKR5E4r4XYIFqSBg10OQzOZEAHj44YdnzZoVRo9cf9Pa2vrVr341LV9g1KhRO3bs4P9QoeOEvAnFB/c0FAT26D1t2jTrepg9e3ahuV/6hK1btwLAV7/61V6eo5RKJpOZ68OGDRs5cmR/7SzMDBs2bNKkSWkSfueddzY3N3PWQ1g4FW9CMcEnpEKkqalpwYIFxeR6CN7r+J2qPmnRCWvWrLnzzjvTvsNHH30U9hbFfqWhoWHx4sVBlx1nPRQ4WUVo5MiRRfYx9IRgQSpcimaAeprLAADKy8s/+eSTtBl3sQBpVbtQjAAoBNra2tKEh7MeCooiNsj1CSxIhU5alPj8+fNDd5+ZOckbAFauXDlx4sReohPszFYAqK+vZwfzKcJZD3kk1N4Ez/P2799fXV0diURy8HIsSOGgkF0P/rRvAMjakplVkJ599tmrr766/3fHdBHMerCnJZalfqIIvAnvv//+woULt2/frpSSUl544YULFiwYM2ZMv74oC1KYKMAo8UyLtu0Zsu999hqjrq4uMz1h8+bNpeDJLkx4wkV/4ItQEXgTduzYMWPGDCHE7NmzzzrrrO3bt69atWrgwIFPP/30iBEj+u91WZBCSV6aarOOdcgcaDZ69OjXXnst2LV67bXXvvzyy8HnZPoamNzDroc+oSgNcvPmzWtsbFyxYoU/rHL16tX33XffrFmzeop26xNYkEJMbppqrX3r6NGjBw4cCK6Xl5fv3r37tNNOy/yS999/v6amJlgOCvoass4oYvJFL66H1atXL126FADmz59fxGkXJ0HRexPq6urOO++8lStX+iue540fP/6cc86x92H9BAtS6OnX66WsPao+q1atuv322zm0pgjIdD1Mnjw56I3kQ22ovQknxGeffXbjjTdefvnld9xxh7/Y0dHxla98ZezYsUGV6nNYkIqE/hig3tzcfMYZZ/TyhGuvvXbw4MFpsZ5s0Q4vvuth48aNmelNJXi0TRssBAATJkywg4VCXZE7CZ566qm77777O9/5zr333tt/r8KCVGwEo8RP0fVwTEGyYx2CpyhWo+Jg+vTpTz75ZNpiiRySismb0Fds27bte9/7HgBs3Lhx6NCh/fdCLEjFySm6HmwBZ8+ePWPHju3laevXr58yZQoANDc325U8Tvtm+pCZM2f6E699iluQitKbcOporZcvX75s2bJBgwY99thjX/rSl/r15ViQipkTcj0EjdrQmah95513plXkfIp7rEOJ89xzz2V2iU2cOHHjxo3Fl/Uwe/bsYvUmnCLvvvvuPffc884779TX1z/44IOVlZX9/YosSMVP766HrOOF/OiEXbt2LV682FbkamtrZ82adeWVVwIAtxAVPWmBT9ZUWUxZD75Joampqaampvi8CafIM888s2DBgtNOO+2BBx644oorcvOiLEilQlpT7aJFi84555ysIpQJV+RKk/r6+u3btwPAuHHjrJ3BHqPb2tqUUmlZD3bCb2NjYyFHPaWZFKxT7je/+U2+91Vw/OEPf5g3b94FF1ywbNmyioqKnL0uC1JJkFYfr6qqamlpqaqquuqqq+655558744JH2lZD6tXr7ZZ4/bR2traTZs2FUg6exGk+OQYrfWUKVOSyeRzzz1XVlaWy5dmQSpyli5d6n8Y9OvjSqmWlhYeoM6cIn7Ww8UXX5zWjpZ3vyWbFE6at95664Ybbhg7duzFF1+c9tCoUaOuv/76/ntpFqQiZ+3atXv37u2pPs4D1JlTZ+/evaNGjUpbzEt/dNEHKOSGFStW9JQP9LWvfe2JJ57ov5dmQWIKOkqcKXyy9qudeeaZaSGH/QSLUDHBgsSkKMAocSYsZGbsTp8+/d/+7d/6yYxXOik+pQYLEpNOXqLEmVCza9euSy+9NGhqePbZZ4cOHdqHEy58gxx7E4oYFiQmO3y9xJwQWW3fpzjhglN8Sg0WJKY3imCAOpN3eplwkRU2yJUsLEjMsemPKHGm1AjKUiwWGzJkSFCW2JvAAAtSeFFK7du3r6qqKhqN5uYV2fXAnDrBrIcPP/zw+eefr6mp8b0JEyZM4BSfUoYFKXx8/PHHixYtevXVV5VSUsq6urpFixade+65OdsAux6Yk8Z+rNm1a9ejjz7qL/LnG8bCghQyDh8+PGXKlNbW1htvvHHcuHE7duz47W9/6zjOs88+O3LkyFzuhF0PzHHSS3hPTU0N98AxPixIIeOnP/3po48+etddd9166612Zf369Xfccce11167ZMmS3O+Hm2qZnjh+b0LwkvK2227jM3fJwoIUMq655po9e/Zs2bLF7zckossuu6y9vf3VV1+VUuZlV8HrJWvGY1kqTU7Rm2DrwPzDU7KwIIUJpVRdXV1dXV3aNM8f/vCHGzZsePHFF/NeNOvDAeoFhW2yAYBJkyYVSIh14cAGOaavKKrJj0XPwYMHjTGZcxvtSktLS94FaerUqVOnTrWuhwULFixdurQIXA9z5861IwoBoLa2duHChQU77ydnZA3vue222/gqkTkVWJDCRDKZBIDMcDC7YqftFQI1NTUPPfTQ/Pnzreth7dq14XU9NDQ0+GoEnSN0v/Wtb+XYQlIIZA3vue2227hllekrWJDChK2vGmPS1jNXCgFbtZs2bZp1PaxduzaMrgc7KTXIrl27Xn311enTp+dlPzmGw3uYXMKCFCYikQgAJBKJtHW7Yh8tNHxZsq6H2bNnF9n1UlGS9VqIvSpMf8OmhjDheV5dXd0XvvCFp556Krj+/e9//4UXXvjv//7v0aNH52tvx0lTU9OCBQus6yEU10sNDQ1z585NW/z444+Lr2TH3gQm77AghYzJkyfv378/0/bd1ta2devW3jMrC4e0ptoCf8sLmhoA4PHHHy8aU0OmN4HDe5g8woIUMn784x//+te/DjYPPvnkk/fee+/kyZN/8Ytf5HdvJ0qIsh4aGhrsZVJwtkJI8b0JadPtQnEtlPsIRyaXsCCFjE8++eTqq69ub2+/6qqr6uvrt27dum7dOqXU008//bnPfS7fuzsZOOshB/QS3hOW/9p5j3BkcgALUvjYuXPn/fffv337dvt3N2bMmMWLF59//vn53tcpwVHi/UHRDBYqnAhHpl9hQQorR48e3bt3b3V1dXl5eb730pdwlPgpUpTehEKLcGT6CRYkphAJ0fVSIVCUIhSkMCMcmT6HBYkpXNIGqPP1UpCs4T32v1KRiXfhRzgyfUU4XMJMaRJsqrV1vBIfoF6a4T2FH+HI9BUsSEyhYwtQU6dOtVHipZb1wOE9YYlwZE4dFiQmNBRllHhPcHiPT7giHJlTgQWJCRnFFCWeRlYRsgMP8721fBLGCEfm5GBTAxNiiqCplsN7jkkRRDgyxwkLEhN6QjdAPdThPXmhOCIcmWPCf5FM6Mnqeii066Ws4T1Fb5DrKy677LJf//rXy5cv9/9O16xZs2/fvsmTJ7MaFRN8QmKKjYLKeiia8J78UnwRjkxWWJCY4iSPWQ9Fn5uQF4oywpFJgwWJKWZy5npgEcoNxRrhyFhYkJjip5+ixEsnvIdhcgMLElNCnPr1UtbwHr4WYpg+gQWJKTlOdIA6h/cwTG5gQWJKlLQo8fnz56fV2dggxzA5hgWJKWl810NTU5M142WehIC9CQyTE1iQGKbrtGR/O3XqVA7vYZjcw03OTOmS1SZnj0eZFTyGYfobPiExJcrSpUt9HQpeDhVU0APDlBQsSEyJYr1zPTkUgpaHF198Mcd7Y5jShAWJYXqkd9FiGKZvYUFiGIZhCgKR7w0wDMMwDAALEsMwVqfYLwAAB3RJREFUDFMgsCAxDMMwBQELElOEeJ63Z8+eZDKZ740wDHMCsCAxRcX7779/8803jxs37vLLLx83btwtt9yyc+fOfG+KYZjjgl12TPGwY8eOGTNmCCFmz5591llnbd++fdWqVQMHDnz66adHjBiRy514nrd///7q6upIJJLL12WYUMOCxBQP8+bNa2xsXLFihT/ZevXq1ffdd9+sWbMWL16cmz28//77Cxcu3L59u1JKSnnhhRcuWLBgzJgxuXl1hgk1LEhM8VBXV3feeeetXLnSX/E8b/z48eecc47NrOtvCueIxjBhhMNVmSLhs88+GzlyZFqqglJKa52zutmSJUvi8bh/RJs6dWpdXd1999337//+7zk7ojFMeGFTA1MkDB48eMOGDXfccUdw8fe//70x5stf/nJu9vCnP/1p/PjxfsEQAK677jrXdd98883cbIBhQg0LElO0bNu27Uc/+lF5efl3v/vdHLxcIRzRGCbUcMmOCR/r1q0L/vb000+/6KKLgita6+XLly9btmzQoEGPPfbY0KFDc7Are0RLW8zxEY1hQg2bGpjw8fnPfz7423Hjxv3ud7/zf/vuu+/ec88977zzTn19/YMPPlhZWZnzDabYtm3b9773PQDYuHFjbkSRYUINn5CY8PGf//mfwd8OGjTI//UzzzyzYMGC0047benSpVdccUU/baAwj2gME3b4hBQyXn755YMHD371q18dOXJkcP0vf/lLY2Pj8OHD094ZS4o//OEP8+bNu+CCC5YtW1ZRUdF/LxSWIxrDhAs+IYWMt99++1/+5V9mzpz5j//4j8H1tWvX/uQnP/nBD35QsoKktX7wwQerq6t/+ctflpWV9etr5f2IxjBFCZ+QQkZra+sll1wycODAV155xXVdf33atGl//vOfX3zxxTPOOCOP28sjb7311g033DB27NiLL7447aFRo0Zdf/31OdhDzo5oDFOU8AkpZAwbNuyb3/zm888/39jY+K1vfcsu7t69++23377oootKVo0A4I033gCA119//fXXX0976Gtf+1oOBCmXRzSGKUpYkMLHzJkzn3/++XXr1vmC9NxzzwHA9OnT87qvPHPTTTfddNNNedzAn//85127do0dO/axxx5LeyhnRzSGCTUsSOHj61//ek1NzebNmz/77LPBgwcDwPr164cMGeLrE5MX8n5EKzTYgMOcKJzUED6EEDNmzEgkEs8//zwA7Ny5c+fOnX/1V38VvFJics9NN930Xg888cQT+d5dHnj77bcXLFjwy1/+Mm197dq1CxYssPrNMEFYkELJ9OnTpZS2G8bW62644YZ8b4phunHDDTdIKTds2OB5XnB9/fr1QoipU6fma2NMwcKCFEqGDx9+6aWXbtmypaWlZf369eedd94XvvCFfG+KYbphDTiHDx9ubGz0F60B5+tf/3opG3CYnmBBCiszZ840xvz4xz/evXt3idsZmIJl5syZ0D3Ygg04TC9wH1JYMcZ885vf3LdvXzQaffnll8vLy9Me3b59+7vvvjtgwIDzzz9/1KhR+donU8oYY771rW+1trb+8Y9/tAaca6655uDBgy+//DJfeTKZ8AkprFhrAwBcfvnlaWrU2tr613/919/+9rcfeeSRBx54YPLkyb/4xS/ytE2mpGEDDnNCsCCFmCNHjkA2O8ODDz74zjvv/OY3v/njH//42muvXXvttY888shLL72Ujz0ypQ4bcJjjhwUprCSTySeffHLUqFEXXnhhcP3w4cMbN268+eab7aS4srKyRYsWSSlZkJi8wAYc5vhhQQofO3bs+OCDDx544IFPP/107ty5iBh89ODBg4MGDfrKV77ir8RisUgkYo9TDJN72IDDHCec1BA+fvzjH7/88ssAcP7558+aNSvt0bPPPnvbtm3BlT/+8Y8dHR08tJTJFxdddNGIESPWr18fjUavueaarM8hol/96ldXXXVVTU1NjrfHFA4sSOFj1qxZX/ziF88888zrrrtOStn7k996662777777LPP5sI9ky+steHnP/95pgHHZ9OmTQ8//PAXv/hFFqRShgUpfFx++eWXX375MZ9mh5Y+8sgjn//85x999NFIJJKDvTFMVnoy4Bw6dOijjz565ZVXMhOGmBKEBak4ef/99//u7/7uww8//P73vz9v3rxjHqQYpv/oyYADAL/73e/++Z//OS+7YgoQFqQi5O23354zZ87ZZ5/97LPPckssk0d27NghpVy+fPmnn346f/78NAMOAMyZM+fb3/42ALz++uu33HJLPvbIFBAsSMWG1vqee+4ZM2bM448/Ho1G870dpqTp3YADAJFIxBaTBwwYkOvNMYUHC1KxsWXLlvfee+/WW29NazwaPXr05z//+XztiilNTsiAwzAsSMWGHTOzfPnytPXZs2f/wz/8Qz52xJQux2nAYRgLC1Kx8d3vfve73/1uvnfBMAxzwnBSA8MwDFMQsCAxDMMwBQELEsMwDFMQsCAxDMMwBQFPjGUYhmEKAj4hMQzDMAUBCxLDMAxTELAgMQzDMAXB/we3AaAUwhItCAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dimchecker = [1 2];\n", "plotinterp([a a],[b b],allnodes,level,surplus{1}(:,qoi),[],'hier',dimchecker);\n", "hold on\n", "plot(allnodes(:,dimchecker(1)),allnodes(:,dimchecker(2)),'k.','MarkerSize',15)\n", "set(gca,'FontSize',15,'LineWidth',1)\n", "xlabel('y_1');\n", "ylabel('y_2');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot the density, approximated with Monte Carlo simulation" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "densX = rand(10^5,d)*(b-a)+a;\n", "dens = plotinterp([],[],allnodes,level,surplus{1}(:,qoi),densX,'hier',[]);\n", "[densdata,z] = ksdensity(dens,'function','pdf');\n", "plot(z,densdata,'k');\n", "xlabel('range of possible realizations')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We observe a quite long tail in the density to its right side. This shows that although uniformly distributed input is given, the output of the simulation will have its own probability distribution." ] } ], "metadata": { "kernelspec": { "display_name": "Matlab", "language": "matlab", "name": "matlab" }, "language_info": { "codemirror_mode": "octave", "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": "0.15.0" } }, "nbformat": 4, "nbformat_minor": 2 }