{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Approximating using the CompEcon toolbox\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demapp00.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2021-Oct-01\n", "
" ] }, { "cell_type": "markdown", "source": [], "metadata": { "collapsed": false, "pycharm": { "name": "#%% md\n" } } }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initial tasks" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from compecon import BasisChebyshev,nodeunif\n", "from matplotlib import cm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "## Univariate approximation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Approximating the function $f(x) = e^{-2x}$. Its derivative is $f'(x) = -2e^{-2x}$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "f1 = lambda x: np.exp(-2 * x)\n", "d1 = lambda x: -2 * np.exp(-2 * x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fit approximant\n", "\n", "The CompEcon toolbox defines the ```BasisChebyshev``` class for Chebyshev interpolation. Its positional arguments are `n` (number of nodes), `a` (lower bound) and `b` (upper bound). The optional keyword argument `f` indicates a function (the lambda `f1` in our example) to be approximated." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "n, a, b = 10, -1, 1\n", "f1fit = BasisChebyshev(n, a, b, f=f1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, `f1fit` is an instance of the `BasisChebyshev` class. Once a function is specified (as with the keyword argument `f` above), it can be evaluated at a given vector `x` by *calling* `f1fit` as any other function\n", "```\n", "f1fit(x) # returns a vector containing the interpolation of each element of x\n", "f1fit() # without arguments, it evaluates the function at the basis nodes\n", "```\n", "\n", "When a function is specified with the option `f`, the `BasisChebyshev` object computes the interpolation coefficients $c = \\Phi(x)^{-1}f(x)$, where $x$ represent the nodes of bhe basis. Alternatively, if the values `fx` of the function at the nodes are available (instead of the function itself, as is usually the case), then the basis is created by:\n", "```\n", "BasisChebyshev(n, a, b, y=fx)\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Graph approximation error for function and derivative" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To evaluate the precission of the interpolation, we compare the the fitted function `f1fit` to the true values `f1` over a grid of 1001 points. We do the same for the derivative function.\n", "\n", "In the figures, the red dots represent the 10 interpolation nodes (where residuals equal zero, by construction). These are returned by the `.nodes` attribute of the basis." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": "[]" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": "
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fdz1ussznSfVLYLPZcMkll2Dx4sWYNWtWSJU78vLyMHPmzG7/E0+WweByufDII49ApVIJj40dO7bLdmwi6OjoEB7bvHkzAPgtAzhnzhx8+eWXOPfcc0Maz5YtW4TX9JfNfN555/kcW4y/cefn5wMALBZLwONmZGTg6aef9pmwOI5DZWUlVqxYgYaGBgDo4ukC4Pc9Mn/jL7/8EvH24hsaAKiqqkJVVRUGDhyI4cOHd9l+5MiRGDhwIKqrq1FZWSk8PmnSJMyZMwf19fW47bbbAAB/+9vfgk56ysvLQ58+fXwey8nJAQCMGDGiy/aZmZkAIFiSRo8ejeeffx6zZ88WtnE4HNi/fz8+++wzaDQav+c3GNj1cPbZZ3d5zmg04owzzvDZjjFmzJgu27NrRnytdwf7vMQTrvh1hg8fjsbGxi43fZ0/UzEFBQVdloYj+V4EOhYRHJHM2WI6L00Hun4AXjQA6OLx9HeN+MNoNOLss89Ga2urj8Vk5cqVcLvdPj7aiy66CK+++irKysqExzo6OrB9+3b88MMPAHgbXziw44gtJi6XC99++61ggwH469ftdmPChAl+r/NTTjkFQNfz0Rmaz3uG5vOuJNN8nlTVS2w2m2CgP//884UvaGe2bduGF154Adu3bxcSGIqKiiQpGciSIocMGdIlu9nfl1aj0QDwLflTX18PnU4nXNRSwJICevfu7ff5oqIi6HQ61NfXd3mOTQpi2I9WdyULO7Nx40Z8/PHH2LdvH44dOyZMMOymhOtU8igjI8Pvj19xcbHP+wl3e6Br3XX23rs7RwDQp08fHDlyBA0NDejbt6/w+D333INvvvkGjY2NuOCCC7pEgQLh7/yy85Kdnd3tc2IcDge++uorrFy5EuXl5aiqqvKbnBMq9fX10Gq13Yoh9uPCfmwZ/t6Tv2u9O2pqagCgWz8ro7a21sfn5++4gZ6L5HuhhFJh8U44czbArzDeddddghhobW0F4P1M2PXz5z//GX/+85+7PX5dXR1sNpvwXQl0/XTmwgsvxGeffYaVK1cKkcwVK1ZApVJ1SV5rbW3Fhx9+iPXr1+Pw4cPC9eTvuxwK/fr1w/jx47Ft2zYcP34cffr0wc8//4ympiZcccUVgvBg52PZsmV+o8SMYP25NJ93D83nXUmm+TypRHd6ejpWrVolCEJ/rF+/HrfccguGDx+OO++8E+Xl5fj444+xZ88ebN68GRMnToxoDGyZr6SkpMtzwU6wUny5uiPQGNxud1QaMjz88MP46KOPoNVqMWrUKMyaNQslJSWYMGEC/u///k+I9ohhX+jOsC945+dD3R7oei7Ytj2dIwBd7qL37NkjJKCsX78e9fX1PsuZgQh0vQZDe3s7rrvuOuzatQtpaWkYM2aMkNx04okn4vzzz+9xRaI7OI4L63xEKiZcLpdf8dKZzhNloGXBQM+F872I9D0Swc3ZdXV1uO6664Q5226349NPP8U111yDt956CyNGjBCCHSxaxa7LU045RYgyMjo6OrB69WoUFxdj2bJleO2110ISEIyTTjpJWI5ftGgRGhoasH37dkyaNEkQhwCwb98+zJ07Fy0tLSgoKMCYMWMwbNgwlJWVITU1Fb///e+DPqY/Zs6ciW3btmHlypW44YYbulhLAO/5GD58eMCIXucIrT9oPg8MzeddSab5PKlEt1qtDvhBuN1uPPLIIxg9ejTef/99aDQa4Y5dr9fjiSeeEKIA/u6EGOyC7yyOa2trhTasBoMh7PdRUFCA48ePo6mpqcvdflNTE7799luMHDnSxxvVEywTV7yMJqa6uhoul0vIgpaKTZs24aOPPsLAgQOxZMkSn2gCgG698m1tbbBarTAajT6PMy9br169ItreHz2dI/Fz4vNktVqF7PZzzjkH33zzDRYtWoTFixf3eEwpeOutt7Br1y7MmDEDzzzzjM+EYrfbw56gAf6cVFZWora21m90hJ2PYJbkQz3u8ePH8ec//1ny1+58HCD23wuCp6c5G+Cj3OI5GwCuvfZaXHzxxXjiiSdw6623wu12Y8CAAVCpVKivrxdWFc855xxhyTw1NVXwYa9evRpOpxM33XQT+vbti7Vr12Lp0qWorKz0O4/4Q6PR4LzzzsO7776Ln3/+GQcPHgTHcV2ExRNPPIGWlhb88Y9/xE033eTz475+/fqQzpc/zjvvPPz1r3/FqlWrcP311+O7775DUVGRkF8EeG2MEyZMwMMPPxz2sWg+jz40n0d2HEDe+TypPN09sXv3blRUVGDGjBlobW1FU1MTTCYTAH7ZZ8+ePcIyyCmnnNLtf6w+d+fSOv/973+DtlsEgpX9W7duXZfn1qxZg4cffhjffvstgODvziZMmACAr/3pzz/IIvSRRvo7s2PHDgB8NKbzBN3U1IQ9e/YA6GpTcbvdfktYrVmzBgCfgBLJ9v7o3bs3evfujaNHj/qtP8qun/79+/tMWM8//zyOHDmCWbNm4Z///CdKSkqwatUqIeIUbdg5njdvXpc7+A0bNgh/h3Ntsutm1apVXZ6z2WxCVEvq6+aEE04AAPzvf//ze9xLL70U1113HRobGyM6jlzfCyJ4Ojo6fObspqYmWK1WnHHGGdizZw9efvllAMDRo0eFOZp5nB966CHhsX/9618AeEtGaWkp8vPzUVpaihkzZuDWW28FwIuaTz75JOixsfJ+a9euxapVq6DT6XDOOef4bLNz505oNBrceOONXeZrJroj+d3Izc3F1KlTsXPnTqxYsQItLS244IILfG5m2HW+YcMGv37gDz74ALNmzRJK0XUHzefRh+bz8FHCfE6iWwTLyP373/+Ok046CSeddBJuv/12AF4vG8u6fuKJJ7r9b968eQCA5cuX+wjvzz//XJJxzpkzBwDw3HPP+WQR19TU4MUXXxQiLIA3os5uHrqjX79+mDZtGurr6/Hwww/7XJDbtm3D4sWLodFohIxkqWDLrD/++KPPMZuamnDXXXcJjRT8fUGefvpp4SYI4KMs7777LrKzs4UatZFs749rr70WAJ99Lva11dXVCY2H2OcD8D+o77zzDrKzs3H//fdDq9Xi0UcfhUqlwuOPP+635qnUsHPMfpAYu3fvxiOPPCL8W1wLnl03nZshdObaa6+FWq3GCy+8IPwYAPzn9eCDD6KhoQFnnHFGQN9kOFx77bVQqVT4xz/+IdQwBviEuccffxy7du2SJGIh1/eCCA3xnM3+YwJx3759GDp0KB599FFhjn7ooYeQlpYGlUqFSy+9FE888YRQoeTXX3/F/v37cezYMYwaNarLsTZu3Bj0uMaMGYOBAwfim2++wY4dO3Dqqad28e0WFxfD5XJ1ERxfffWVUEWhc58Gg8EAm80WdILlzJkz4Xa7hbwkdjPAGDBgAE477TQcOnQITz75pM/r7tq1C88//zz27t0rNObpDprPaT4Ph2Saz5PKXtIT7M7wzjvvFMrl7N27V+jsdf/992Pw4MEA4JM53BmXy4VNmzZh9+7dOO+88zBp0iRUV1fjyJEjGDp0KA4ePBjROFm3p1dffRUXXnihkPG7efNmdHR0YOHChUIWdN++faHRaLBlyxbceOONwr7+ePzxx3Hdddfhs88+w08//YRx48ahublZyOS97777/GYpR8L06dPRt29fbNu2DWeffTZGjx4Ns9mMLVu2wOFwYPDgwTh06JBfO4/dbsd5552Hk046Ce3t7di0aRM0Gg2efPLJLj7NcLb3x7x587BlyxasXr0aZ511lnDuN27ciI6ODpx77rnCTZfdbsef//xnuFwu3HPPPcKy2YQJE3DZZZfhk08+wRNPPIF//vOfYZ694Lj66qvx2Wef4c0338RPP/2EAQMGoKamBjt37kRaWhqKiopQW1uLhoYG9OvXDwAwcOBArFu3Dn/+858xevRo3HvvvX5XTcaMGYN77rkHf//73zFnzhxMmDABOTk52LZtG+rq6jBs2DA8/vjjkr+ncePG4e6778azzz6Lq666CmVlZSgsLMRvv/2G6upqFBQU4Omnn5bkWHJ8L4jQKC0tFb7DTqcTra2tOHLkCBwOB/r3749XX31VuLYZQ4YMwfz58/Hpp59ix44dGDx4MCoqKrB3715otVo888wzXZKxNBpNUNUYxFx44YV48cUXAXQVuwAwd+5cLFq0CPPnz8ekSZOQlZWF/fv348iRIxg4cCAqKiq6JK4NGDAA+/fvx1VXXYUhQ4bgH//4R8AxzJgxA6mpqaipqcHgwYN9Su0xnnjiCVx77bX48MMP8d1336GsrAzt7e3YsmULXC4Xbrzxxh4TBmk+p/k8HJJpPqdItwiWJJKamoqpU6di6tSpQqRDo9HA5XIF7eV78803cfXVV0On0+GHH34Q7oBvueUWSca6cOFCLF68GKNHj8bmzZuxceNGYfIVi+q8vDw89thj6N27N37++We/HdIYhYWFWLp0KW6++WakpKRgzZo1KC8vx5lnnon3339fmHykJC0tDe+9954Qmfjhhx9QWVmJU045Be+9954Qbfj++++77PvGG29gxowZ2LRpE/bu3Ytp06bhww8/7DYDOtTt/aHRaLB48WI8+uijGDx4MH7++Wds3rwZI0aMwNNPP43nn39eWLZ96aWXcODAAUycOFGot8u45557kJOTg+XLl+O7774L+vjhMGLECLz77ruYOnUqamtrsW7dOrS3t2P27NlYtmyZIATEkZP58+fjtNNOQ3NzM9avXx+w3voNN9yAN998EyeddBL27t2LH374AVlZWbjrrrvw8ccfB51gFCo333wzlixZgqlTp+LIkSP43//+B6PRiLlz5+Kzzz7rIrLCRY7vBREa+/btw88//4yff/4Z27dvR0NDA4YOHYorr7wSn3zyid9r4aSTTsKnn36Kiy++GCaTCWvXrkVbWxuGDBmC3Nxcv+XLXC5XUMmEYtj3KzU11W/1lWuuuQZPPfUURowYgV9//RWbNm1CWloaFixYgM8++wyjRo1CdXW1jwXi8ccfx/Dhw7F//378+OOPQnWW7hAfu7tktaKiInzyySe4+eabkZaWhvXr16O8vBwTJkzAiy++iHvvvbfH90rzOc3n4ZIs87mKCyUdO8GYPn06+vTpg/feew8AX4aHtQL+4osvkJaWBoBfkrnoootgt9uxdu3asLKPX3zxRSxevBgbNmyIaqJAMjB9+nQcP3486HMZ6vYEQSiTWMzZH3/8MR566CE88MADPj/ATz75JN599128//77PkmIRGTQfE4kE2QvEaHT6fDQQw/hrrvuwqWXXorLL78cBoMBS5cuRVVVFZ555pmwy/0cPXoUKSkpNEkQBEFIRDTm7EsuuQRLly7FP/7xDxw5cgQlJSXYsGEDVq1ahSuvvJIEN0EQYUOiuxPnnHMO3nzzTbzyyit4+eWXoVarMWzYMLzyyitCaalwaGlpEVoREwRBENIg9Zyt0+nw+uuv45///Ce+/fZbwZ7ywAMPYO7cuVF4BwRBJAtJbS8h4hNajiQIgkgMaD4nkgkS3QRBEARBEAQRZah6CUEQBEEQBEFEmaTwdLvdbrhcFNAnCCL+0Ok0cg8h5tCcTRBEvBJozk4K0e1ycWhpCa2hAUEQhBIoKMiQewgxh+ZsgiDilUBzNtlLCIIgCIIgCCLKkOgmCIIgCIIgiChDopsgCIIgCIIgogyJboIgCIIgCIKIMiS6CYIgCIIgCCLKkOgmCIIgCIIgiChDopsgCIIgCIIgogyJboIgCIIgCIKIMiS6CYIgCIIgCCLKkOgmCIIgCIIgiChDopsgCIIgCIIgogyJ7hB5e+Mx/HHZLuyrM8s9FIIgCAJAY7sdf/lqDz7dUSX3UAiCILpFK/cA4onfqtvw0o9HAPCT/NvXjJd3QARBEAS+3VePVfvqsfZgAy4a3QtatUruIREEQXSBIt0hsOFIs/D3rhoTWjocMo6GIAiCAACHyw0AsLs42J1umUdDEAThHxLdIXCwvt3n33vrTDKNhCAIgmDoNd6fMruLRDdBEMqERHcI1JhsPv+ubLHKNBKCIAiCodN47SROEt0EQSgUEt0hUNPmK7IrWiwyjYQgCIJg6Hwi3ZyMIyEIgugeEt1BYnO60dTJw32cIt0EQRCyQ/YSgiDiARLdQVLXyVoCAFVtJLoJgiDkxtdeQpFugiCUCYnuIGnqsAt/F2UYAPBlAwmCIAh50VGkmyCIOIBEd5C0WZ3C34PzUgEAzR0OON0UVSEIgpATsb3EQaKbIAiFQqI7SFqtXj/3II/o5gC0dMRntLui2YIfDjZQrXGCIOIercheQpFugiCUCnWkDBJ/kW4AaGi3Iz/dIMeQwua/O6rw99UH4eaANL0Gz19ahrF9suQeFkEQRFj4Rrpp9ZEgCGVCke4gafWIbhWAgble0d3YHl+R4n11ZvzDI7gBoN3uwn1f7oHZ5gy8I0EQhEIhewlBEPEAie4gabPw4jrTqEVeml54vDHO7CVv/nwMLg7QqFU4d0QhAD4h9KNtx2UeGUEQRHj42kso0k0QhDIh0R0kzF6SadQiO0XX5fF4oKrViu8PNAAAzh1RiEXnlaKkIA0A8N8d1dTJjSCIuIQi3QRBxAMkuoOEiesMow5peg1YYKXNGj/2ktX768FiQHNO6AOVSoUrxvcGANSb7dhwpFm+wREEQYSJuE43iW6CIJQKie4gabd7RLdBA5VKhQwjH+2Op0j3Gk+Uu39OihDhPqu0EHrPD9YPBxtlGxtBEES46LXUBp4gCOVDojtIOhwuAECKTgOAt5kAQKslPkR3S4cDv1WbAADThuZDpeKFdqpeg8kDcgAA/ytvhIvqjhMEEWfo1GQvIQhC+ZDoDpIOOy+6U/W86M7yiO54sZdsP94q/D1lQLbPc6cNyQMANFsc2F9vjuWwCIIgIsbXXkKBA4IglEnciO6mpiY8+OCDmDp1Kk444QRcd9112L59e8yOL4huIdIdX/aSbR7RrVGrMLp3ps9zk0UifGtFKwiCIOIJagNPEEQ8EBei22w245prrsGKFSswZ84c3HnnnaitrcX111+P/fv3x2QMFkenSHeKx14SN5HuNgDAiKJ0wSLD6J1pRHEG3+BnS0VLrIdGEAQRERq1SkhupypMBEEolbgQ3a+//joOHz6MV199FX/4wx9w/fXX44MPPgAAvPHGG1E/vtPlFpJzUuIw0t1hd2FfLe/nHuen86RKpcIJ/fjHtx9vA8fR8ixBEPEFi3ZTIiVBEEpF8aKb4zh89tlnmDZtGiZNmiQ8XlBQgD/96U+YOHFi1MfAkigBb6SbJVK2212Kj6zsrzOD/Q6N6WQtYYzuxT9usjlR2WKN1dAIgiAkgVUwoURKgiCUilbuAfREZWUlamtrceONNwLgRXhHRwfS0tJwzTXXxGQMzM8NeD3dLJESANpsTuSm6rvspxT217cLf5cWpvvdZkRxhvD3nloT+uWkRH1cBEEQUqFV8/4SSqQkCEKpKD7SffToUQBAXl4enn76aUycOBEnnHACzjrrLKxZsyYmY/Af6fZ2pVR62cADnook6QYNemUa/G4zLD9N+NHaVWOK2djiHbLiEIQy0Av2Eop0EwShTBQvutva+ATA559/Hj/88AP+8pe/4Omnn4bRaMTtt9+On376Kepj8Il0e0R3hijSbbYpXXTzke5h+WlCfe7O6LVqDPM0zNlTS2UDe2JfnRk3/Wc7pvxzHS5Zsgmr9tbJPSSCUByxrDpF9hKCIJSO4u0ldrsdAC++v/nmG2Rl8Ql/06dPx1lnnYVnn30WU6dOjeoYxKKbJVKm670VQMx25Ypul5vDwQZedA8t8G8tYYwoysCeWjP21prgcnPQqP0L9GTnYEM7bvloB9o910VlixV/Wb4XVocbF40ulnl0BKEMWNWpuro6zJs3D5mZmfjggw9w/fXXY+nSpSgpKZH0eGyljhIpCYJQKoqPdKempgIAzj77bEFwA0BmZiamT5+OXbt2ob29vbvdJcHi8EZOmOhO03vvV9ptri77KIWKZgtsTn78LJLdHaVFvCi3ONyobqNkSn84XG7c/8VuQXBfOKpISKr923cHcKSxQ87hEYRiiHXVKWYvoUg3QRBKRfGiu6ioCACQm5vb5bnc3FwhsTKa2JxeUW3wLGGmG7yR7nYFR7oPN3nPzdD8wKJ7SF6q8Hd5Q3RvZOKVj7dV4WizBQBw80kD8Mi5pXh21iioADjdHJ5dWy7vAAlCAchRdUpHopsgCIWjeNE9bNgw6PV6HDx4sMtzlZWVMBgMfgW5lIgTc5jo9ol025Ub6T7mEYgA0L+HiiSD87yivLyBIradcbrc+GBLJQD+XM6b0g8AMK5vFi4d2wsA8PORZuymRFQiyWFVp5j1j+M4YUXymmuuwRVXXCH5MVkreLKXEAShVBQvulNTUzF9+nSsXbsWBw4cEB6vqKjAmjVrcOaZZ0Kj0QR4hchh9gzAK7pTxZ5uBSdSVnhEd3aKDlkpuoDbZhi1KEznSx8eaqRId2dW729AvZnPMbh+Uj+f1tPzJvcTPPD/9ghzgkhW5Kg6xewlSu+bQBBE8qJ40Q0A9957LzIyMjB37ly88soreOONN3DNNdfAaDTi7rvvjvrx/YlujVqFFB3/t7Ij3XzEul92cHW3h3gsKBTp7sonO6oA8Dcw54wo9HmuONOIM4flAwDWHmxU9I0YQUQbOapOUaSbIAilExeiu2/fvvj4448xadIkLFmyBK+88gpGjBiB//znP+jXr1/Uj+8rur0R7nSDpyulghMpj3m6S/bPDU50M4vJkaYOihiJqDXZsP04LyQuHFUk3HyJuWAUn39gc7qx5kBDTMdHEEpCXHXqww8/xKWXXoqLL74YH3zwATIzM/Hss89KfkxWMpDqdBMEoVQUXzKQ0a9fP7zwwguyHFssuvUabxm9NL0G9VBuIqXZ5kRjO//jNyDIDpND8vlkSqebQ0WLFYNEyZXJjFhEzygt8LvN5AE5yE3VoanDgRV76nBRGZUPJJKTnqpOffbZZ2hvb0daWuDk7lBgJQMpWEAQhFKJi0i33Ng9otugVfs0l2HJlGaFRrorW7xJlMHaSwbkekW2OAkz2Vm9rx4A0DvTgJFF/uuda9UqnOUR5NsqWshiQiQtclSd8nakJHsJQRDKhER3ELBIt17je7rSPMmUSo10h1K5RNhOJM4rWkh0A0Cb1YFfq3lrybRh+d129QSAUwbzIsPF8ZVMCCIZkaPqFHWkJAhC6ZDoDgKbyxvpFsM83WaFJlKKRXe/IEV3VooWGZ73xZIwk53NFa1we4JnJw3MCbjtCX2zhQTbHw83RXtoCUG92UbNmBIMOapOMXuJgyLdBEEolLjxdMuJzelfdAuRboXaCFikuiBdL3TS7AmVSoX+OSnYVWMSyg0mO5uO8hFrvUaFcX2yAm6r16oxuX8OfihvxIbDTeA4LmBkPJmxO9148tv9+Hp3HQB+leDJC0b4lOMk4pd7770XmzZtwty5czF37lzodDq8++67Uas65bWXUKSbIAhlQpHuIBDsJZ1FN6teotBId3UrHz3snWkMaT8WFSdPN88vx1oAAGP6ZMEYxM3LFE80vKnDgaNNdA67Y/G6w4LgBoAfDzXh0ZX7ZBwRISWxrjqlI3sJQRAKhyLdQcASKY2d7SWeiFyH3QU3x0GtsIhmjckGACjONIS0H/N115ntsDpcQQnNRKW6zSrcfEzunx3UPuP7eqPhW4+3YiBVgOnCrhoT/rP1OABgWEEa0g1abKtsxfcHGrDhSBNOGhjdLrNEbIhl1Smdx17i5vjqS8xuQhAEoRQo0h0ENicfye6SSOmJdHPghbeScLo51HlEd68QI93ipMtkT6bcVtkq/B2s6B6cl4oso7bL/oSXtzceA8D7cJ+eORJPzRwh2LXe/YU6ehKhI56fqWwgQRBKhER3ENicfGJOd55uQHkWkwazDSyfqFeIkW5x0mWy+7p/reKrlhi0apQW+i8V2Bm1yuv93lrRAo6jxC4x1W1WrD3YCAC4YGQR+uWkIDdVL9Q133ysBeUN7XIOkYhDdKL5mXzdBEEoERLdQcAi3YFFt7KSKavbbMLfxRFEuo8muej+rdoEABhZlA6tJvivC7OY1JntqKLKHD6s3OP1cc8e39v79zjv39966qITRLDoRHYSqtVNEIQSIdEdBN1VL2ElAwHlNcgRl2AL1V6SbtAiO0UHAKhqTV7BaHW4cKDeDAAo65UZ0r7jRL7uHZ728QTPN3t50T0kPxUlBd6OhP1yUjDC03ho9f76uFsheGvjMcx5Zwu+2lUj91CSErKXEAShdEh0B4G9mzrd4ki30roP1vhEukOzlwBeS0oyi+7dtSbBolPWOzTRXVKQBp2Gj7ztqTVLPbS4pbrNivIGvv77jJKCLuUUzyzhO3oeabKgsiV+rr0D9Wa8/OMRHGxox1PfHUSrxSH3kJIOnZYi3QRBKBsS3UHgjXT7VvFgbeABwOJQZqQ7O0UXdI1uMX2yjD6vk4z8VmUS/h7dKyOkfXUaNUoK+Kjt7hpTD1snDxtEXTpPHty1QsnUQd7mQ5uOxU9Hz7UHGoW/bU43NnnKTBKxQxzpJk83QRBKhER3EHRXpztF7/230qqXsEh3qEmUDGZJqW6zwR1ny/xS8ZtHLBdlGFCQHvp5ZFaJfXVmON3JeQ47s8HTpTM3Vec3MXVIfhpyU3lr06ajLbEcWkTsrvW9sTpYT6sbsUarJnsJQRDKhkR3EHTn6U4VRZCVGukuyghTdHsi3U43h3qzXbJxxRP763jhxMRzqIws5qPjNqcbhxupGofTzQmNhk4cmOO3rr1apcIkT2nGLXFS+YXjuC6rGYepKVLM0ZO9hCAIhUOiuwdcbk6IUho6Va8Q2zaUFOnmOE5ojBNqEiWjd5Z3v+ok9HWbbU4c97xvZhMJlRHFXkvKnhqKfJY3tAulNSf2y+52u7GecoutVicq4sDX3WxxoKnD18N9pLFDptEkL2J7CXWlJAhCiZDo7gGxN7BzpNugVYNVqVJSpLvV6hSi8+FGusWt45Ox5N3Bem9kepiowkYoDMpNFbqYdrYfJCM7q7xVXMYESEwV++d/q1Z+5RdxLXtWbrOy1RIXUfpEQtyBkkQ3QRBKhER3D9gc3YtulUolRLs7HMqZ5BtEdpCCdH1YryH2gidjBZP9ItFdEmRTnM5o1CrBt7yvjiLdrNFQllHrUwu+M0Pz04TvGquTrmSOi74frD67w8WhzaqsikaJjt6nOQ7d8BAEoTxIdPeATRQx6ZxICQCpnrKBFgXZS+rbveUCw0kABACjTiMktCVjBZP9nkS4dIMm7GRUABjqiZKXN7QnbUIqg0W6R/fO7FIqUIxWoxZ89PEQ6a5s8Ua6xRH8hvbkzIWQCx3ZSwiCUDgkuntAPHnr/XQk9Ea6FSS6JYh0A15fd5Wo5neycMAT6R5WkB5QIPbE0HxedFsc7qRcMWA0ttuFiHAgawmDNSPaX98Ou1PZAop9P/LT9EKpTYBEd6zx7Uip7GuGIIjkhER3DzhEy5Ss2YkYVsFESZ5usb0kPy180c2SMJNNLDrdHMobeNFdEqafmyH2g4t94smGOGI9OojunsM9thyXm8NhhSclNph50V2YYUCe6PvWSKI7pohXIh1kLyEIQoGQ6O4BcaRb5y/S7bGXKKl6Sb1HBGQatTCG0RiHwUR3rcmWVHWmjzV3CImo4VYuYQzJF4nuhuQV3Xs9XTlVAEYU93xOh4puVg40KNsPz1aWCtL0Pje5DUlaalMuxPOz0ldHCIJITkh094DDHX+RbiYCIolyA0DvLN7L7HJzQjQvGfCpXFIYWaQ73aAVPOHlSSy6WWJq32yjTyfX7hiQkyJ83w4ofIWA2Ujy0/VI02ug94y7hVrBxxQDdaQkCELhkOjuAXFnM506gKdbSZFujwiIxM8N+Nb4rk4iXzezM6jAl/2LFBbtVrp4jCYHPImpw4JcOdBq1MK5V/J5szpcQpWSwnQDVCoVMox8AnKbjaqXxBKf6iUU6SYIQoGQ6O4BsTdQ6y/S7WkFr6RIN4tKh1u5hFEoqvFdZ0oe0X2kiRfdvTINEdlzGCyZsqLFAquCrpNYYbI6hZu2khBWDpgf/kB9u2JrXouTJfM9N7mZBj6STyUDY4teQ4mUBEEoGxLdPWDvydOtsOolLjcnJHBFGukuFonu2iQS3Yc9ontgXuRRbsArHt2cV9AnE6z8IhB8pBsAhnq2bbE40NihTKuGv5r4mUZedJusyhxzoqJSqQThbXMq8yaNIIjkhkR3D/RYvURUp1sJ0bhmiwNsyPlpkUW60/QawbNelySebqebwzFPh8GBElhLAEqmFNtDQqkGM0h003NUoTcr9aJId4Hn+5ZhpEi3XDCLCUW6CYJQInEpuvfu3YuysjIsXrw46sdyuoPzdLs4ZXRBqzeLG+NEFulWqVRCG/lkiXQfb7EIN1pS+LkBvjU4u1870mQJvHECwvzcmUatcD0FwwBR10qlim4fe0mab6SbRHfsMWj5+Zg83QRBKJG4E91OpxMPPPAAHI7YLN326OkWeX6V0JVSqsY4jMIM/jWSRXSL7R+DJLKX6DRq9MnmBaRSxWM0YZHuoflpITUa6pVpFOwCR5uVebPS0sF/39QqIDOFF9uZnkRKEyVSxhyDYC+Rfy4mCILoTNyJ7tdeew0HDhyI2fF863R3FQysTjegDF93gznyFvBiWGSyLklqDosbsUhlLxG/VrJ5ujmOw1FPdH9wiDcxGrUKfYWbFYWKbgsvrLOMOqg9NxQskbLd7kqq+vZKgNlLyNNNEIQSiSvRvW/fPrzyyiu47bbbYnZMcZ1uf23g0xQmulmkWwUgL1UX8esVeoR7U7vd5wYkUWGiODdVh6yUyM8fY2AuLx4rWqw+ZSgTnXqzXfhehHMTM8Czz9FmZd6ssFrc2aLvWrrRW4fcTNHumMLmaPJ0EwShROJGdDNbydSpU3HRRRfF7rhB1ukGFGIv8XhMc1J10Pq5SQgVFunm4GtdSVQOeyKqUllLGEw8utwcKlutkr62kjncFNnKAfN1V7VaFenTbWaiW3SDliaaE5RUvz8ZMLBESgVeKwRBEHEjul9//XUcPXoUixYtiulxQ/F0KyHS3SBRN0pGYRKVDeStEJ5ygRJaSzq/XjL5usXvNZwSjAM8KwRuDqhsVZ7FpMWP6E7Vk+iWC8FeQpFugiAUSFyI7gMHDuCll17Cfffdh+Li4pge29FTnW69siLdTZ7ErlyJRHdREjXIaexwoN3zGfYXVc6QAnEljmSqYMLea4pOjcIwEnsH5HiF+jEFnrdWQXR7LSVi0d1uJ3tJLBHsJRTpJghCgShedLtcLjzwwAOYMGECrrjiipgfX+zp1qqVH+lu8jQRkcLPDfiK7kSPdFeKKmRILbqzUnTI9XwmyZRMeVi0chBK5RIGi3QDyqtg4uY4QXTniCPdCpsTkgkD1ekmCELBKF50L1myBHv37sUf//hHNDU1oampCW1tbQAAi8WCpqYmuN3Rm2BZpFuj4qspdMYn0i3zDyzHcd5Id6o0ke50g1ZIFk30BjkVLV5R1y9bWtENiJICk0h0R2rXyTTqkOVJTKxsUZboNlmdQiOqLLKXKAIW6bZRpJsgCAWi7XkTeVm3bh0cDgdmz57d5bklS5ZgyZIlWL16Nfr27RuV4zNPd3dJiakKSppqt7uE8eZIFOkGeF/34caOhI90M9GtVgG9s4ySv/7A3BRsq2zFkSYLOI4LK/IbT5htTiH5NhKPfO8sI1qtZlQpLAGV+bkB8nQrBT0lUhIEoWAUL7rvu+8+IbLNaGhowL333otZs2bh4osvRkFBQdSOzyLd/mp0A4BR5xXjcke6G0Xd8fIk8nQDQFF6kojuZl7UFWca/fr3I4X5k002J5otDslWI5RKpEmUjD5ZKdhTa8ZxBYtu8U1uGolu2SB7CUEQSkbxorusrKzLY5WVlQCAfv36YerUqVE9Pmtu4a9cIACoVSqk6NSwONzosMs70TM/NwDBPywFydIKntkX+mVLH+UGIDR64Y9lTXjRLU4YHZgbvl2HrTrUmGxwujm/uRVy0H2k2zutkqc7tpC9hCAIJaN4T7fc9BTpBry1uuWOdDd3eCPdORIKOtYKvqnDkbANcjiOE+wl0fBzA0C/HK+YV5o/ORoc87xHFYC+WeGf0z6emyCXm1NUBZ3uRLdeoxLyP9op0h1TvB0pE3OeIggiviHR3QPMIx3IbsA8nHJHtRpFkW6pqpcAncoGJmgyZbPFWy6wn8SVSxh9slLAbt0qFFaJIxoc94juogyDIIbCoY/IX39cQbW6m0XfN3H1EpVKJVhMyF7Cs3fvXpSVlWHx4sVRPY7BM0873RxcbmoFTxCEslC8vcQfffv2xb59+2JyLK/o7jnSLfcPbJPI050tYaQ7P90ruhvMdvSJIGqpVMQiuG+UIt0GrRqFGQbUmmw+lVISlcoW3oPdN0K7jlh0KymZstXK1+A2aNUwihKqAX5OaLM6Zb8RVwKsm7DD4eh54wgR39w5XG5o1JoAWxMEQcQWinT3gNPN7CXdnyql2EuYpzvLqJXU91ogSspsaE/MVvBMIAJA/yiJbsDrFxcfL1FhFppIb2KKMwxgl7OSkilNNl50Zxi6xi6MzObgIJvDa6+9hgMHDsTkWAaR6CaLCUEQSoNEdw8IJQMDiNgUTwUTq+yiW9pulIwCUSdBVgIu0RD7j6NRLpDBBGiie7pNVqcQCY5UdGs1ahR7LE5KinS3e0R3uqFrNJWJP6szuSPd+/btwyuvvILbbrstJscTR7qpgglBEEqDRHcPeBMpe450y72ULHU3SkZWik5IDEvYSLfHXlKcGZn/uCdYkmar1Sl0M0xEKlvFdp3Ib2LYjVDcRLo9c0IyR1uZrWTq1Km46KKLYnJMg4Yi3QRBKBcS3T0QWvUSuUsG8oJYysolAF8WMd8TPW9I0ETKaFcuYfQVJWlWKkhASo3YPhNJ5RIGE91KinSbbPxNdrof0S1EupPYXvL666/j6NGjWLRoUcyOSZFugiCUDInuHnD0UKcb8Ipuue0lrJqClDW6Gcxikqj2Em/SX3RFt7gGeGUCVzAR22f6SBDpLs7gX6Opw6GYboNmwV4SwNOdpPaSAwcO4KWXXsJ9992H4uLimB1XL4p0K+U6IQiCYJDo7gFvG3hlVy+xOlxCyTspu1EyWKS7PgHtJSarU7AK9IminxvwFfWJXMHkuOcmJjtF51eUhkpRpvLKVpqDsJdYk1D4uVwuPPDAA5gwYQKuuOKKmB7boPXO02QvIQhCaZDo7oHgPN0sacoNNydPbdimbmoGS0WBp2xgQwJGuqvavJaFaCZRAvwNGruBSeRkSubplsLPDfjWiq9pU4boNgWIdBuSuEnLkiVLsHfvXvzxj39EU1MTmpqa0NbWBgCwWCxoamqC2x2d86Kn6iUEQSiYuKzTHUu8beC7j3Sz5jgAP9Gn6GJfG7ZJ1I1S6uolgDfSbbI5YXW4utQljmeqRT7hXlEW3QBvMWlot6MigcsGMruOVCsHxSLRXauArpQ2p1tYBfNXvcSoVUZFIzlYt24dHA4HZs+e3eW5JUuWYMmSJVi9ejX69u0r+bHFiZTk6SYIQmmQ6O4BIdIdoKKFWIB22F0yie7odKNk5Kf71uqOtvc5lvhEukU2hmjRNzsF2463JWxXSpvTLbRrl+o68Yl0m+S/WWFRboCql3TmvvvuEyLbjIaGBtx7772YNWsWLr74YhQUFETl2D6JlEl47gmCUDYkuntA6EgZRJ1uQL4GOS0i0Z0dxURKgLeYJJTo9kS6U3RqZEfBmtMZlljYbHGgw+7yWSlJBKparWAmK6mqwRh1GmSn6NBicSgi0m22Bhbd3jrdbnAcB5VKumZVSqesrKzLY5WVlQCAfv36YerUqVE7tjiR0kaRboIgFAZ5unsgGE93qiiyLZvotog93dLbSwrSvJHGREumrPZ4hHtlGmMijsS+cXGUPVEQe9Wl8nQD3mi3EjzdZrtXdAeqXgIkZ7RbLgwU6SYIQsGQ6O4B5ukO1JHS6CO65ZnomejWa1Q+kXepyE8Td6WUX/RICYt0RzuJktE703ucagXVnZYKcS1tKavBMF+3EiLdYnuJ346UOt88DyI2+CZSypPUThAE0R1kL+kBIZEyiJKBgHyR7maP6M5O0UUlWpuVooVWrYLTzaExgSLdHMeh2hNtFovhaCIWokpq9iIVbOVAp1FJmtRbpCTRLbaXGANHuq1ON7JiMirl0rdvX+zbty/qx9FTIiVBEAqGIt094PRM3JpA1UvEolumWt0s0p0VJU+ySqVKyAY5rVanUN88VpHu3DQ99J6buES0l7BEx+IMA9QS3gAWe5Jc2+0uoUa2XJhF3/N0vb9ESrKXyAHZSwiCUDIkugPAcRw8eZQ92EtEiZQydaBr9YjuaNToZuR7fN2J5OmubottuUAAUKtU6JWpvLbmUiH2yEuJkmp1m3uIdBu03hvxZCwbKBdatQpspk7WbqAEQSgXEt0BcLm9nsCAkW69ciLd0ay+wSLdDQnk6RZ7qmNRLlA4VlYCi27Pe4qm6JbbYsI83Rq1ysdKwqBESnlQqVRCECQZu4ESBKFsSHQHwCkS3Vp1oI6USkik5EVANEW30Ao+gewlx8WiO0aRbvGxEs1eYnW4hPyCYolvYpRUq5vZW9L1Gr85FAYfTzdFXGOJUZu8NdIJglA2JLoD4Awy0m2UOZHS6XILkbeoim5PpLvd7pItYVRqmBUiTa/xW285WrCkTbPNhTaro4et4wex7UPqSHd+ugEsn1luewn7vvmzlgC+cwKJv9girpFOEAShJEh0B8A30t296NaqVUJinBxitEXkL41WIiXQtUFOIiAuFxjLBibiqHp1awLZdUQRaKkj3Vq1CnlstUXmvAKWfOsviRLoVL1EptWvZIXZS2wJEhggCCJxINEdgGA93YDXYiKHvUTcGCc7JXrRWt8GOYkhFKtiXC6QIU7aPJ5AFpPqKNt1CtI9ybxye7o9N7rp3US6yV4iH8xeQpFugiCUBonuAAQb6Qa8ortDhuhKq7gbZRRawDPyEizSzXGcIBJj6ecGgD4ikZ9IyZTMrqNReQWylAhlK2WOdAv2km4sSWQvkQ+ylxAEoVRIdAcgnEi3HOXBfCPd0U+kBICGBCgb2GxxCD/MsSoXyMhK0Qr13ROpKyUrwViQbujxRjUcmJCX+6ZPnEjpD6peIh9kLyEIQqmQ6A5AKJFuNtHL4umOkejONGqF89DYHv/Jf3KVCwT40maJWMGkRqjRHZ3zySLdJptT1vrXZht/7O4SKXUaatIiF2QvIQhCqZDoDoArBNHNanXLUadbLLqzjNET3WqVCrke+0pjR/xHuuUqF8hgwvR4Aka6o7VyIF5tkat0pdPNCTay9G7sJTqNd75wuDi/2xDRgdlLaIWBIAilQaI7AE63d9IO1tMtRyJlcwcvutP0Guj9NOqQElY9ojEB7CXiBitSl7cLBib0q1ut4Lj4F2YOl1sQwsVROp+FIp94nUxNmtpFLei7E91qlUqYM2wuEn+xRGiOQ/YSgiAUBonuAPh6ugOfKrakKUciZSy6UTISUXSn6TXdiqdowkS31ekWGsrEM7UmG9g3pldGdOwl+QpI5jWJRHeGwb+nGwD0HouJg0R3TCF7CUEQSiVuRPe6detw9dVXY+zYsRg/fjzmzZuH7du3R/WYoXi6U/XyRVdaY9CNkpGIorswClU2gqF3glUwiWZjHIb4s5KrgonZR3R3f7PGLCbk6Y4tZC8hCEKpxIXo3rRpE2666SaYTCYsXLgQt99+O44dO4Zrr70WO3fujNpxQ/F0K6FOdyxFd4vF4XN+4hEmuouiFJXtCbGPPBFEd3Vb9BrjMNINGkFU1ctkL2FJlPx4uhfdzOpFnu7YIlQvcbrhTgDbFkEQiUNciO6//vWv6NWrFz7++GPMmzcPN954Iz7++GOkpqbiueeei9pxg20DD8hbp9sruqNvkchL5UW3m0PcWyLqPPaEwgx9D1tGh8QW3dGJdKtUKm+tbgXYSwKJblbBxE72kpjC7CUARbsJglAWihfdra2t2Lt3L84991ykpKQIj+fn52PSpEnYtm1b1I7tdIUe6Xa5uZh7OJnojmYLeEZ+mvcY8WwxcbjcaPKMX65Id7pBK9gTamTusCgFrDFOXprepyOj1AhdKWWKdJuCtJfoPfYS8nTHFvG1Z5Nh5ZEgCKI7Yp89FiLp6elYuXKlj+BmNDc3Q6PpPpEpUpxc8JFutqQJ8LW6xXV6o4nV4RIShmJpLwHiW3TXm+1C0p9cnm6At2GY6p0+lVTilRpWLjDKNc8L0uSNdJt9It3dzz/eSDdZHGKJeC62Ol0Aoj8vEgRBBIPiI90ajQYDBw5EUVGRz+N79+7F1q1bMX78+Kgd2yfSrekhkVLU9rkjhrW6xTW6c0h0B02dSOQWxbgxjhgWZa9OgAY5LNJdnBHd8otCV8p2uyylFsWiO00fKNJN9hI5ENtLqIIJQRBKQvGi2x/t7e247777AAA333xz1I7jEke6VcHZSwDAGsMlzVh1o2TkpiaG6BZHluWMdLMqH+LKH/EIx3FC3exo23WYp9vmdKPN6uxha+kxeRIp0/SagCtg3kRKEn6xhOwlBEEolbgT3RaLBfPnz8fevXtx8803Y/LkyVE7llP0Y9lTpNsojnTHMJky1qI7Va8RovqNHfGbSClurCKXpxsAij3Hbre7fCKo8UaLxSFU6Yj2ykGBqFa3HGUD2efUU213vVAykOwlsaSrvYQgCEIZxJXobmtrw+9//3ts3LgRl112GRYuXBjV44US6WZ1ugHe0x0rWixeoRYL0Q0AeZ5kykSIdMvVGIchLq0XzxYT8cpBUXp0q8EUiGt1y5BMyUR3oCRKgKqXyAXZSwiCUCpxI7obGxsxd+5cbN26FVdeeSWefPJJqHoQwpESiqc7WewlQGI0yJG7MQ5DHGWPZ4tJrcl7LcTKXgLIk0xpEkR34CRu8nTLg0Ec6SZ7CUEQCkLx1UsAwGw244YbbsCePXswb948PPDAAzE5rm9znMD3Jyky20tUADKMsfk4E0F0sxrdclpLAN/OjfFcNtDHIx/lc5qfJhbdckS6PZ7uHiPdVDJQDnzrdJO9hCAI5RAXke5FixZhz549mDt3bswENxBecxwg1vYSXnRnGrU9jlEqWIOcxo74Fd1CpFumxjiMvDS98LnFc6SbeeQ1apVPsm00MOo0Qqm+pvbY5xWYgrSXCJFusjjEFF9PN517giCUg+Ij3eXl5fj888+RkZGBESNG4PPPP++yzaxZs6Jy7NDawIs83TEsGciqN8SiMQ4j37O8b7a5YHW4fJJI4wFxYxy57SUatQpF6XpUtdmEOtfxCCvBWCC6iYgmeal6mG0WWW78gvV0Uxt4eRBXLyF7CUEQSkLxonvTpk0AAJPJ1G2UO1qi2xmS6JYn0t1m9Ua6Y0WeKJLZ1OFA76z4Et3ixjhy20sAvmV6VZstIewl0baWMPLS9DjabIm5xYnjOFH1ksDXPSVSygPZSwiCUCqKF91z5szBnDlzZDl2KJFug1YNFQAOgCWGS5pCpNsYu0h35wY5vbOi2wxFaupi6D8OBlbBJK4j3TGq0c2QK6+gw+ECmxaCLRlInu7Y4hPpJnsJQRAKIi483XIRiqdbpVIhVc9HWGJpL2n1iO6YRrrTvAI/HpMpfcrbKUF0Z3g7LDrjUKBxHCfcyMTKrpMviO7YerpZEiUQSslATpbOmcmKRq0SkljJXkIQhJIg0R0Ap9s7YQfjU2Xe5ljaS1otMthLxJHuOEymVEpjHEaxp4KJm/NWVYknWiwO2GPUGIfBrsEOhwsdMbzJNYkaGPUc6fZOr+IbeCL6MIsJ2UsIglASJLoDwOwlahWgDqImOEumjJXodrrcaPcIjljaS3JSdGBnI54j3ak6DdL08vvRxQ1yakzxZzGpE9fojnJjHIZcqy1mUdv5niPd3jnDRjaHmMIqmFCkmyAIJUGiOwAsOtWTn5uRIkS6YzPRi6NusYx0azVqoRFPrJf3pYCJ7qIMQ9QbLAVDcYaoVncclg2skcEj3zmvIFaY7aJIdw/fObG3mHzdsYXNxdQGniAIJUGiOwBMdAdbAi0lxvaSVlHULZYlAwGv6GmIw0g3s3DIXaOb4RPpjkPRLYddR1xBJ5YWJx97SQ+rJDqRvcROZQNjitFzwxNL6xFBEERPkOgOgEuIdAd3mmJtL2mzyhPpBrzL+/FsL1GCnxvgb9ayPJ9fPNpL2PmMRWMchlyRbpNVlEjZw3dO7OmmSHdsEZLaydZDEISCINEdAMVHui1ea0dWzEV3fLaCV1JjHDEsmTIuI90xbowDANkpOrBDxfIabBfbS/TBe7qTsVb3unXrcPXVV2Ps2LEYP3485s2bh+3bt8fk2MJcTJFugiAUBInuAITt6Y7RRO8b6Y6xvUTUCj6eyqE1tCurMQ6DlQ2MS9Ftjm1jHIC/Ec5JjX3ZQJPnO2fQqoWOk93hE+l2xs93RAo2bdqEm266CSaTCQsXLsTtt9+OY8eO4dprr8XOnTujfnw2F3fEsJIUQRBETyi+OY6cuEIU3cKSZowSKVutokh3ijyRboeLg8nmjLnoD5faNmU1xmEIDXJMVnAcp4gEz2CpjXGNbkZeqg6N7XZZPN09lQsEAJ1W7OlOrkj3X//6V/Tq1Qsff/wxUlJSAAAXX3wxzj//fDz33HN46623onr8FM9cbCXRTRCEgqBIdwBCtZew2rCx9nSrEJwIkBJfT238VDARJ/0pS3Tz9hKLw+2zgqF0xI1xYr1yIIfFiTXH6SmJEvB2pASSS3S3trZi7969OPfccwXBDQD5+fmYNGkStm3bFvUxpFAiJUEQCoQi3QEINdLNEimtTjfcHBdUbe9IEDfGifaxOtO5TvKgvNSYHj9cxN0oi5UkujN8K5jEuhpNuIgb48S6Gow8opu/IeopiRJI3kTK9PR0rFy50kdwM5qbm6HRRL82vnfVkUQ3QRDKgSLdAQg10p0qin7FoilDmwwt4BlyVY+IFKU1xmH0itMGOeLGOLG+iRFEd4cD7hjlFYRiLxHfrCdTR0qNRoOBAweiqKjI5/G9e/di69atGD9+fNTHwDzddheXVOeeIAhlQ6I7AKFGulkbeCA2CTxe0R37qKhcdZIjRWmNcRhFmfHZIKdWRrsOE90uN4c2S2wsOSzS3VPlEoBvIsVwJHmd7vb2dtx3330AgJtvvjnqx0vRiQMgFO0mCEIZkOgOgNPNR6uDjnTHeKJniZSxTqIE+Og6uxmJp0i30hrjMHJTdUKJOXGHR6UjtuvE3NOd6r3ZbIjRjZ9JsJf0vEqSrJHuzlgsFsyfPx979+7FzTffjMmTJ0f9mCmiVSzydRMEoRRIdAfA6QqvOQ4QGy+hnJFulUoVl10p62SqtNETapVKEK01bfFkL/E0xlEhZo1xGPnpsbc4CZ7uYKqXiCLd7AY+2Whra8Pvf/97bNy4EZdddhkWLlwYk+OKAyDk6yYIQimQ6A6Ai2OiO7jtfewlMYiuCJFuGTzdgHd5vylOqpc4XG5BnCmpRjeDVTCpjid7iUd056cbYtYYh+FjcYqB6LY53ULSaKie7mS0lzQ2NmLu3LnYunUrrrzySjz55JMxs3TFOgBCEAQRDCGL7ubm5miMQ5GwSLdGE9xp8rWXRDey5XRzQvkyORIpAe/yfrx4usWNcZRULpDBEhFr48hewkowynETE+tkXhblBoKs061Rhr1EjjnbbDbjhhtuwJ49ezBv3jwsWrQopjkUKTHOryEIggiGkEX3JZdcgpdeeikaY1EcQqQ7yB+LlBguaZpl7EbJiLdW8OLGOIqMdHvG1NBuh90ZH3YEOe06aXoNDJ5lqFjUijeJRHcw9hIfT7eMJQPlmLMXLVqEPXv2YO7cuXjggQdiemzAt5JUrJqVEQRB9ETIIdKmpiYUFBREYyyKwxVqcxzRkma0oytydqNkMNHd3OGA080FXeVFLpTaGIdRLCobWGe2oW921zrHSoLjOCExVY6bGJZXUNVqjclqS7tPpDuYREqxp1u+SHes5+zy8nJ8/vnnyMjIwIgRI/D555932WbWrFlRHYPY6mehREqCIBRCyGpt5syZ+OijjzB16lT07ds3GmNSDEx0B6slfet0R3eib1NQpJsD0NJhR77CkhM741NpQ4FjLc7wlg2sNSlfdLdanLB5IvJyVYPJS+VFdyySeUONdIvtJXJ6umM9Z2/atAkAYDKZuo1yR1t0p5K9hCAIBRKy6Far1Th06BDOOecc9O/fH3l5eVB3qu6hUqnwzjvvSDZIuWD2kmAj3b4+wuguafpEumVOpAT45f14Ed2pOk1QkcpYUySKdMeDr1vOcoEM1hk1Np5ur3gLvTmOfBaHWM/Zc+bMwZw5cyR5rXCJdflWgiCIYAhZra1fvx45OTkAAJvNhqqqKskHpRTY72Q4zXGi7elWRKS7U53kUllGETziGt1KaozD6NwKXumIG+PIJ7pjl1dgCjGRUqOQ6iXJNGczfKx+ZC8hCEIhhCy616xZE41xKBIW6VYHKdC0ahX0GhXsLi7q0ZVWH9EtT6RbjjrJkSDuRqlEjDoNsoxatFqdcdEKvk4U6Zar7jkT3W1WJxwut09tbKkxh2gvUalU0KpVcLrlbUWeTHM2w6BVQ60C3ByVDCQIQjmErdZcLhd+++03HD9+HHq9Hr169cKoUaOkHJvshJpICfAWE7vLGfXoSpuFt5eoEJwAiAaxrpMcKUptjCOmONOIVqs5PiLdosY4YqtRLBGvtjR1OKJ6Q8VEt0blWwc6EDoNL7odMlYvYSTDnM1QqVRI0WnQbndR9RKCIBRDWGrt+++/x2OPPYba2lpwnmiwSqVCYWEhHnnkEUyfPl3SQcqFkEgZouhutTphiXLJN2YvyTBqY96UhGHUaZCm53/YlC66ld4Yh1GcYcC+OnNctIJn1WDkaIzD6FyrO5qfrcnj6U43aIO2J/EVTNzCXCIXyTJni2GimxIpCYJQCiGL7s2bN+MPf/gD8vLysHDhQgwZMgQcx+HQoUP497//jTvuuAPvvvsuTjjhhGiMN6a4Q6zTDXiTKaNdpoolUsplLWHkpenRbrfEpE5yJCi9MQ6DlQ2sbbOB4zhFes8ZtQpYOYhlgxzm6Q7Gz81gFUzk9HQn05wtJlWvAdqpZCBBEMohZMW2ePFi9OnTB5988gkyMjJ8nrv66qtx2WWX4ZVXXsHrr78u2SDlwilEuoPfJ8VTNjDaPkLm6ZYriZKRl6bHsWaL4rtS+viPFSy6WaS2w+GCyeaU/fMNRJ0CPPK5IotTU5SvQWYvCcXOxZKw5axekkxzthijp3ESeboJglAKIWcd7dy5E7Nnz+4yeQNAeno6Lr/8cuzYsUOSwYmpqKjAggULMHnyZEyePBl/+tOf0NTUJPlxwHHQbvkFGTfMBRobAQBp77+NjBuvh3brZoDrJmLl2S+9fB8AwLluHfIHFPW8X5hj6/j5FwBAwc//k/YYIY6leNc2AEDLzl3Sv99IEZ+v6+cJDw9+ZpFyxiiG49CnoVL4p3XiRMWe0/Qb5qKuoQ0AMOA/b8p2DRbu2yn80/Lgw1H9zlnXrQcA5Gz5Oej5QN/UAADQ/OdD2T5LueZsuUnzBEDaKdJNEIRCkDzVX6VSweGQ1mrQ3NyM66+/Htu3b8eNN96I3/3ud1izZg1+97vfwW6XMLrlcCDj1huQddlMGJZ/AaeKPz1aux2Grz5H1qUXIuPWG4DO70+0X3rNcQBAh84IlcUSeL8IxtZqSAUAZLe3SneMMMZSdPA3AEBDWo6071fCMRqWf4EaY6bw1ICvlipjjGI84x366J+Eh6ozChR7TjvWfA+blo8y926ulu0aLLriImRYzQCAhrTsqH7nTHq+WVFmR1vQ84HOzN+YODRaZX2WIqIxZyuBNM+KBJUMJAhCKYQsuseOHYtPPvkEHR0dXZ4zm81YunQpRo8eLcngGG+//TZqamrwzjvv4Oabb8b8+fPxwgsvYO/evVi2bJk0B+E4ZCy4BfqVy6Hu6IDK7YbbI7o1nBsqtxvqjg7oVy5HxoJbvJGqTvul2i0AAIuO7y7Y7X4Rjq3FyEetsq0maY4R5lgKzM0AAJMhDRatIbZjCXKMKrcbVRl8G+w0WwcyLSb5x9jNePvWVwgPV2XyY1biOa1JyxWe6mVqlPcabG8BwItuIHrfOZPnRjfT1h70fKBz8YLPqdZIN7YQkWPOVgIs0m22O3vYkiAIIjaELLoXLFiAY8eO4cILL8Sbb76JNWvWYM2aNXjjjTdw0UUXobKyErfddpukg1y+fDkmT56MIUOGCI9NnToVgwYNwvLlyyU5hnbrZui/+Rpqi0V4zOkxc2vc3kiJ2mKB/puvod22xe9+qQ6+vnK73reFd+f9IhmbS6VGmzENAJBlNUlyjHDHUtDeLDxX7xE9sRpLd/j7LGsy8gAAxeZGsNREOccoRjzeAnMzdC4+6njcI7oZSjqn1RnesRWbGmI6xs5jyfdcg/VpOT7bSfmdA4A2QzoAIMPW3u0xOu/HPkuHxtebH8vPUo45WwmwhNd2G0W6CYJQBiGL7okTJ2Lx4sVwuVz4+9//jttvvx233347nnnmGTgcDjz33HM48cQTJRtga2srKioq/NaTHTVqFH777TdJjpPyyotQWX0bkrg80SlNpyQoldWKlFde9Ltfqp3/u0PXNblMvF8kY2szpIHzROGzLWZJjhHuWHxEd7qv6In2WLrD32fJRGIvkUAE5BujGPF41eBQbOJzCaoz87tsq5RzWu25iQGA3m2xPafdXYOdRXckY+l8DJdKDbMo0t3dMTrvp/XcsDvUGnQmVp9lrOdspeD1dFOkmyCSlR3HW/HvLZXYdLRZKJcqJyFXL2lubsaZZ56JadOmYdeuXais5BO/+vTpg1GjRkGrlbaEXW1tLQCgqKioy3MFBQUwm80wmUx+k4QY9fW13Wbmn376DIwaNQaGb1dC1UlcuwR7iW+kROV2Q7PiK7z88j/xwIqvfPZjkW6LzggOgKrTfuqvv8TLL/9TeOzyy69BYSH/3tau/Ra7d//aZYydj9GS4n2vOZa2LmPTffO18O9du3bihx++8/veAeC22+4W/l669H3U19f53W7kyNGYNu2sLueJ2UuArqJH5XZDu3K5z/sVU1BQiNmzrxX+3d12gPdzCuY9Pezns2QisVdngeh2w/DtSpTX1eKTTz7o9jWD+ZzCfU+dz2nvtnpUZBcL9pLO42XXnj/Y5wQAdRK+p/mdxliTwd8QaNwunxsvNkbDtyvxs8TXHntPWZ2+D53tJZ3H0vk7x95ToM+p83fOLFq5yrR2Et2iY3S+9vQuXvA5NF3nxWCvvUceeaTb54Ih1nO2UmCRbruLg93phl4bvW6lBEEoC5ebwz/WHMR/d1QLj10wqggPn1MSdJfxaBDybHvJJZdg9uzZuP322zFmzBiMGTMmGuMSaG/nf+BSUlK6PGcweMqrdXQEFN1B0SkyygFwdxPpBgCtJ/FI1ykBiYlup0YLu0YLg8s3yqJ1hh516XyMFmO68He21dx5c6htUWys0uk8FbZ3L7oBQCNlomuwdBqjQ60RovCdI90AAJGFQBY6jbdPWz0A+BXdgPfaiymdVw48Yys0N0HD+SmHF8Vz2vn7wEQ/yytIcfpe/1J859pE37mMTpFun2N0Ok9aN/+4U93NVBuDay/Wc7ZSYJFugI9267XydE0lCCL2vLL+iI/gBoDlu2oxvDAdV53QR6ZRhSG6m5qaUFDgXwxEA3cQ9W3VPRTSLigo8omq+cVo9PkBZFFuwLtE7ENKCv+aTz/tsx+zlwB8tNvg6mT/YPv5Ydq0s4SIng+djiGOdIs93eKxMUaNGiNEiHtCHPnrlk7nKbejFSrODU6l9iu6EeD9dibY7Xp8T53OV216rmDH8Su6U1JQWBjENeKh28/JD0G9Zqdz2ruNj/jWpOfBqVJD21nUBnlOJX1P9/zRZ4zCyoG/8+kZo+TXHvj3hJQUn7GwSDfAR7v7tdb67BPoO8fo8nyna6jVkCb83dle4nOMTvvpPDfddj+RbgAhX3vhEOs5Wymk6b3nvN3uQk6qjIMhCCJm/FrVhnc28UUJBuWl4i9nDcPDK/ahqtWKNzYcxcyyIp/5IZaEvN42c+ZMfPTRR8ISZbRJS+N/7Gx+orfsMbZNJNjOOhecSLw7RR5MdSfRw6nVsJ11rt/9WKQbANp1Kd3uF8nYWOUSAMi2+IrucI8R7li0nBt5Ha0Auka6oz2W7ug8RmaFAHyT/gD5xiim83iZBcat1qA2Pc9nW6WdU3+iO9bXYH43ybyRjKXzMUwi0d050h1oPtC5fauXSDG2UIn1nK0U0g3ec84aG8mB083haFMHjjR2wOmSr0kSQSQDbo63lQCAXqPCPy4aibF9snDn6YMB8I0FV+z2b2WMBSFLfbVajUOHDuGcc85B//79kZeX1yXSrFKp8M4770gywN69ewMA6uvruzxXV1eHzMxMpKZGHsKwzF8A/XffQOUpq+VWB4h0G4ywzF/gd78Ukei26A3d7hfJ2MSR7i72kjCPEe5YACC/vQUNaTldI91RHkt3dB6j2KbR2dMt1xjFdB5vb5P3Wq/KLEAf0b+VcE45AFVMdHc+n0DMr8GCQBYnib5zrFoQ0NXTHWg+6K56SSRjC5VYz9lKoXOkO9ZYHC68seEoPttZA5NH9KfpNTirtAA3njRA1k6uBJGorD3QgD21vC66dlI/DMjl9eG0oXkoTNejzmzHyj11uHxcb1nGF3Kke/369cjJyUFRURFsNhuqqqpQWVnp819FRUXPLxQkmZmZ6Nu3L3bt2tXlud27d6OsrEyS4zhPmAj7OefD7bFmOFXeKInYs+pOSYHt3PPhHD/B735pIntJh6dWt7/9IhmbONKdJRLdkRwj3LEA/qtHxGIswY6xRlRpQxyZlXOMYjqPl3m6Ad8bBqWc0xZjBmye6jydVw7kuAbF9hKprsHOx2gTRbqzRJHunuYDbTeR7lh+lrGes5VCmk+kO7aiu7LFgmve3YJ3f6kUBDfAi/9lv9bgyrc3Y83+roEkgiDCh+M4vPMLv6KXadTi+kn9hOfUKhXOGV4IANhR1YaaNqvf14g2IUe6P/nkE+Tm5va8oYScffbZePfdd1FeXi7U6v7pp59w+PBh3HDDDdIcRKWC6cXX+MYW33wNl+jUaNwufsnYYIT93PNhevE1gGW/dtovxeVNHGzXpXS/XwRjY5HuTKsZGs4tzTHCHIvKahUqmNSnZ8d2LEGOkQnXVLsFmbZ2ZYwxwHiLzY3CU8czC5QxXtEYq7Z4b4DZTYyc12Cu1VvBpyFNomuw0zFMnRIpg50PdG7f6iVyfJZyzNlKIN0n0h07e0lNmxW3fLQDdWb+t2B0rwxcVFYMtUqFNQcasP5wE9rtLtz35R48MMOBS8fKE3EjiERja2UrdtfwltvZ43ojVe8b7DiztADvbeZF+aajLbhodHHMxxiy6L700ktxxRVXxLSZwk033YTPP/8c8+bNw+9//3vYbDa88cYbGDVqFGbNmiXdgXQ6mF5dAu22Leh4zVtiUK3VwjbzYlhu+4P/yJRoP92bHwoPd2RkBt4vzLE1LdsJgPdzc6mpsJ11rjTHCGMsKS8vRkEHH22vT8uFdebFsMZyLEGM8fjnvEjsZWoA5DhfwdDpnGZazWgzpqMqt5d015BEYzz47SbgVz6fopepURHXYI6lDc0pmajPKojOd+7jH4WH0zQIej5Qf7YNAC+6ZTlPkGfOVgJyRLodLjce+GqPILjnTuqL208dJJQou2h0MX442IBHVuxDu92Fv313EDqNGjPLYv/jTxCJxsfbqgAABq0aV47vejM7vDAdGQYtTDYnfqmIE9Hd1NSE/PyuTTuiSW5uLt5//3387W9/wwsvvACj0YgZM2bgT3/6E/R6ictAqVRwnjARbc+OBl7bCACwPvE3mHqKRnj2c/cfAbzDd5mrefUdmDzLGVKOreGwATjSjLThw9BwpEa61w9jLKY33kHqlkpg7SE4NFocf+F1ZKX48a/KgWeMVXs0QI0JeeNHo+GvMp2vYBCd06J3t6Ctvh1HLp4D0yXSWKgkQaVCdVE/4FdPosq6dWiQy5sqOl85b29Gc2MHjl8yB6ZZXRtpRXqMxtYcYOtxpOk1aDlcFfR+aMoCdlTDXtRLtu+qHHO2EkiTIdL99sYK/FbNR9ouG9sLC04dBFWn1YzTh+bjpdkG/OGTX2GyOfHXbw+gf04KxvbJiskYCSIRabM6sO4Qv0o8oyQfOaldtaFGrcKEfllYe7ARm4+1gOO4Lt/PaKP46iWMwYMH4/XXX8e2bduwYcMGPPXUU1FdMnW6vZ2LQimknqLzRlesjuhkqrdZ+R+QLKMyxG2e6OJu7JChLncP1Jr4qGw8JS6xsda0RbHmepjUec6nWgXkpSmj9nGuZxyN7dGpYc58uazhSrBo1fzc4XDJ1wktWauXGLRq6DT8+Y9FImVliwVvbzoGABhWkIa7pw3p9gd9VHEGnr14FLRqFZxuDvd9uQfNCpw7CSJe+G5fvTDPnj+yazNFxgn9sgEADe121Jhi//uq+OolciHS3NCogxfdqSLRbXFEZ6Jvs/LCIitFGZ3kxMKrsd2OwXmRl3CUCqfLjcZ2/sesMI5Ed7FnrLUyTAo9wcaUn6YXRKXc5KXyN6DRuuljJecyjaF959jc4Qyi30C0SJY52x9pei1aLI6YlAx8/odDsHt+9O+fMazHDpjj+2bh3jOH4m/fHkBjux1PrjqAf8waGfPIG0EkAl97ygAWpusxwSOs/TGyyJufs6fWjF6Zxm63jQYhqzaWCQ9AyIRPRFwi1R2K6DbqvBNtR9RENxMACol0+4huGbolBqC+3Q72ScaV6PZMBCabE2abM+QIazSp9fhVlbRykCdEuu1RWTJk37lQPwedhp8P5Ix0J8uc7Y80vQYtFkfUI93768xYe5Bf2r5gZCHG9M4Mar9LRhdj09FmrN7fgB/KG/HFbzWYNbpXNIdKEAlHZYsFO6r4hPpzRxQF1GwlhelQq/jA6t5aE6YPi631LuRf8jVr1kRjHIrDR3SH8ANu0KqhAt9G3hoF0e3mOJHoVoYQy0vzin8WVVYKdaJIsZJEYk8Ui8Zaa7IpSnSzc6qkmxhmcbI53ehwuCTvNsbsJRlh2kucbk4W/yCQPHO2P9j3pj3Kke63NvIlFzUq4MaTBgS9n0qlwgMzhuHXqjbUme144X+HceqQPOT68aMmOk0ddmytaMVv1SbUmmww2RzQadTISdFhUF4qxvbJwqjijJCCYATQYnHgl2MtKG9oR43JBrebQ6ZRiwG5qZjULxsDclPifnVF3Ozm/JGB8+hSdBoMyE3F4cYOoZ53LOnxF2TBggWYN28eJk6cKDzGcRz27duHAQMGICXFt+viF198gfvvvx+7d++WfrQxxMWFF+lWqVRI1WvQbnfBEgVPt8nqFCK3ShHdGQYtdBoVHC5OcaJbbM8oSleOSOyJ4kzvWGtMNgzJV4Zlh+M44ZwWKuh8dl5tkVp0mwXR3bWzZCCYpxjgb+S1muj/uCXrnO2PNE/JMHMUI92VLRas9tTcPnt4Ifpmp/Swhy9ZKTr86cyhuOfz3WizOvH8D4fw2HnDozFUxcFxHNYfbsLH26qw6WgzeloQyknR4YJRRbh8XC/0yQrtPCcTHMfhp8PN+GjbcWw82uxjl+3MkPxUzDmhD84fWSSszMUTHMfh6z21APjqJMH8Vg4vTMfhxg4cqG/vcVup6fEMf/fdd6iurvZ5rKWlBZdccgm2b9/udx+Ok28pVSrEkW51iHfWRo+vOxr2EhblBpSTSKlSqYRIo9ISKWvjNNItHmutTEX8/dFmdcLm5G8mlXQ+o73aIkS6Q/zOaUXeaWegXz4JSdY52x+C6I5ipPvTHdVCIGTu5H4Bt+2O04fm4/QhfBOvr3fXYfOxFmkGp2C2Vrbg+g+2YeFnu7DhiFdwa9Uq9M9JQVmvDJQUpCFbVA2r2eLA+5srcemSX/D4N/tQb1Zezovc/Fbdhhs+3I67PvsNG454BbcKvN+5d6YBRlG+QXlDB55YdQBz3tmCjUeb/b+ogtlZ1YbKFv438vxR3SdQihmUx3epbGy3w2SNXQ1/IAx7CSNRJ2mGmwvPXgIAqTo1GhEdewlLogSUk0gJAPnpetSYbIqLdLN6uSk6NdJDjFLKSX66ARoV4OIgS4Z1d9SJfuSUZC8RL8c3SXzj53JzQp3nSCLdDhcHOe+TE33O9keGMbr2ErvTjS938VG28X0yMTSCFal7pg/BxqPNsDrd+Pvqg/j39RMUk6gsJWabEy/87xA+2+ktoZmm1+DcEYU4q7QAZb0yYeiUhFpnsuGnw01YsacOWytb4eaAL36rxaq99bj91EG4YnzvkKqMJSI2pxsvrTuMD7ceFx5L1Wlw/shCTC/Jx5jeWcJ5dXMcjjZZsPZgAz7ZXoU6sx1Hmy1Y8MmvmHNCH/zhtEFxE/VmCZQaFXDO8IIetuYZ5GkNDwCHmzqCzsGQAuWoNoXhm0gZ2r5CpDsKS5qtorsypSRSAl5PrdISKcVWiHjyrWnVKuSnG1BrsimqbKB45aAwXTm+084VdKREXOM53JKBgLwVTJIVNke2RimatfZgA1os/JwXaWfJ4kwjbjppABavO4zDTR1YtrMal49LrG6V5Q3t+NMXu3Gs2QKAz4G6dmJfXD2hT8Dfs8IMAy4e0wsXj+mFA/VmvPLjEaw71ASr041nvy/nGw6dWyokoCcbR5s6cN+Xu1He0AGAv9mfc0JfzJvcT7jxFKNWqTAoLxWD8vrjuol98dG2Kvzrp6PocLjw4dbj2FNrwrMXj1KUxvCH3enGt/t4a9dJg3KDzoUYKBLdRxpjK7rj41ZGBlxhlgwEvLW6LU7pf2TbfES3cu6ZxNUjlERdHNboZrBkSkVFuhVq18lO0YF9TRs7pL3xM4mipOEmUgKxs5cQXtgc2W53wemSfj5evpuPcmcZtThDgioIV57QB72zeOH42k9HY1LqMFas3l+PeR9sEwT3pP7Z+M/1E3DryQNDEnfDCtLxz0vK8NLlo9Hbk/uyuaIVc9/fhi0VLdEYuqLZeLQZv/v3dkFwl/XKwH+un4g/nDbIr+DujFajxjUT++Lf15+AEZ5yetuPt+Hmj3Yo3r7z46FGYX4+b0TwjQj7ZhsFXXekqSMqY+sOEt3d4AqzOQ7grdUddXuJokQ3P2k2WxxR+XELl1oFVtoIFpZMqSRPNysXqFbxdbqVgkatEryfUt/4ma3e73GoN7piT7eLRHfMEc+RJokFbEuHAxuPtgAAZpQWdLFEhINBq8aCUwfxr29xCFVR4p2l26vwwJd7YHW6oQJwy9QBePHy0SEnnYqZPCAH/75+AmZ5Wnk3Wxy4/ZNf8fG24z3smTh8/ms17vzvr8K1PW9yP7x+5Vj0zwn9vPbJSsHrV43DjBL+5rG8oQO3fLRDcYE0Mcs91pI0vQaneXIigkGrUaO/59oj0a0QxJ7uUH11rFZ3tO0loUbdool4eb9J4khjuIgb4ygpKhssRRl8xKvWbFeMYGOR7rw0PbQK8/xFa7Wlzea9nkO1l2go0i0r4giq1BaTNQfqhe/l2UF6SYNhRkk+Rvfil7s/3FqJ460WyV5bDpb8fBR/X30QHPiA1HOXluHGkwZI4sFO02vx4NklePicEug1KrjcHP6xphzP/3Ao4XMY/r2lEk+sOgAXx9+sPXnBcNx+6qCI5mWDVo0nLhiBS8fwteIrWqz4w39/jXmyYTC0dDiw/nATAGBGSYFg6w2WPtn872tVjINaQX06LS0tqKqqEv6rqeETIJqamnwer6qqQnNz/GW/+iPcNvAAkKqPZqSbv/jT9BpFiR4ltoJviNPGOAwW6Xa5lVOKsVbBdh12DUp902eyeb/Hod7oyiW6k3HO9od4ZaJNYuGwyuMlLUzXY1yfLMleV6VSYeG0wQD45NuX1h2R7LVjzVsbj+HV9UcB8BawV64Yg5MH5Up+nJllxfjXlWOF1bf3N1fisW/2J+SNLsdxePPnY3hu7SEA/Jz08uwxOHt48PaKQGjUKtw/YyhmlfErCAfq23HP57vgUNAKNgCs2lcn3PSePyr0997HY+OqarXG9AYtqF+Qv/71r/jrX//a5fF77rlH8gEpBXeYdboBr6e7Iwp1upm9REl+biC6iWzhEq81uhniBjk1JpsibhzqFFijm8EsTtLbS0SrSyHbS3zrdMeKZJyz/ZHlI7qluxmrN9uwtaIVAG8tkbpyxujemTi7tACr9tXj2331mHNCH4yOYbKXFHy09The/vEIAN6K9srsMRiYlxp4pwgY1SsTS+aMwx/++yuONVuwfFctTFYn/nbhCOglsP4ohbc2VuCV9UcA8HXLX7x8NEoK0wPvFCIqlQr3nzUMrVYH1h5sxNbKVjz7fTnunzFM0uNEAqta0jvTENZNL8udsDjcaLY4YtaQqsdfkEsuuSQW41Acvh0pQ9vXqPUkUkYx0q20rGLFi24FCNZQETfIqVVAMiXHcULJQCXcAHSGXYNNHdK2go8kkVKOSLeS5uyKigo8/fTT2LRpEwBg2rRpuP/++5GbK3200x/iuupSRrr/V94orKKdVSqdtUTM7acOwvcHG+Bwcfi/Hw7hjavGxk0Fpq921eCZ78sB8BHul2aPjqrgZvTOMuL1q8birk9/w55aM/5X3oj7v9yNp2aOTAjh/Z+txwXBXZCux8uXR+9GRqtW4fHzh+Pmj3ZgT60Z/91RjWEFabgswio9UnCkqQO7akwAgHNHFoV108si3QAf7VaM6P7b3/4Wi3EoDvFKSqiR7lQ9/+W2Od1wuTlJ29a2WpTVAp6RmypuTqIMT7dPebsM5ST9BUtxhndSqFFAMqXJ5hS6rCqpXCCDTZoOFweTzSnZjWmbR3SrVV7rWLBoZIh0K2XObm5uxvXXXw+73Y4bb7wRLpcLS5Yswb59+7B06VLo9RJdQxwH7dbNSHl5MQzffQNYrYDRCNtZ5yL3pgXCZl083QH2s9z2BzjHTwC6+TFfV857SfPS9BhZnBHW2Ho6Ru8sI64a3wfvba7Ezqo2fH+gAdNLIhD4EYwlFLZUtOCJVQcAAOkGDV68bDQG5wVZv1yCMeam6vHKFWNw539/w46qNqw71BQ94R2jcwoAX/5Wg2c9NzI5KbrgBXcEYzTqNPjHrFGY+/5WNHU48I815RhemI5RvcJcdZHofK3wVA0CgPM7Vy0J8hi9O4nusuKMmHyW8X/rFyXEbeBDvYtKERn6rU5po91siVRJlUsA/svJms8oJdItboyjpKTTYEk3aISOekqIdNeZvJ+rElcOOreClwpmL0k3aEOeC+SylyiBt99+GzU1NXjnnXdw8803Y/78+XjhhRewd+9eLFu2TJqDOBzIuPUGZF02E4blX0BlsUDFcVBZLDB89Tn6XnWRsKlJbC/pYb+sSy9Exq03AI6u15HF4cIvx3gf/CmDc7u/JiI4BuN3U/oLc/3idYfD99VKMJZgqGi24L4vdsPl5qDTqPB/l5ShtChI64OEY0zTa/H8ZWUY67HkMOEtqS85RucU4MstPrFqPwD+d2HxZUGuHEgwxqIMA/4xaxQ0aj5R9c/L94ZXylKi8+XmOKFqSVmvDAwQ1dwO5Rhi0X28qSNmnyWJ7m7wbY4TXht4AEJkUCqUai8BoLhW8PHaGIehUqkEcauEBjm1ZmXbdaLVCp7ZS0KtXAIkd/WS5cuXY/LkyRgyZIjw2NSpUzFo0CAsX7488gNwHDIW3AL9yuVQd3RA1an5kMrthq69HZlWMwCgzbNKGMx+6o4O6FcuR8aCW4BOSVabjjbD7mnkcOrgbsqURXgMRoZRi5tOGgAAqGyxYun2qp7PS5TG0hMmqxN3L/tNWFF48OwSjA3WaxuFMTLhPcZHeO+RRnjH6JwCwE+Hm/Dg8r1wc4BRqw7+RkbCMY7pnSmUsqxqteLJVQdCSz6UcCybj7UIv+0Xitu+h3iMNJ1GcAw0r1gVk88SINHdLe4IRHeqWHRLWDaQ4zjFJlICymuQE8+NcRjM162EBjm+dh3lndNotYJnojuc1ZJkjXS3traioqICo0aN6vLcqFGj8Ntvv0V8DO3WzdB/8zXUlsAl9bItvPfTVF0b0n5qiwX6b76GdtsWn8eZtcSgVWPKgOyIxtbdMcRcOraXUHd5yc/HQk4IlXIs3eF0c/jzV3twpIk/xrzJ/XD+yKIe9or+GNP0Wjx/aZlQgvF/5Y3481d7Iu4lEYtzCgDbKlvxpy92w+lZOXhm1qigb2SkHuPVE/pg6qAcAMB3++ux7Nea4N6ExGP5ahf/PdZrVD75FOEco8Bjk2xoMkX9sxReJ6K9ExixvUQTsr3Ee1qlTKbscLiETpkkuntGyUl/wcJ83UrwdLObGBWAAgU1xmGI7SUNUka6PZG7UCuXAMkrumtr+R/GoqKuwqugoABmsxkmkymiY6S88iJU1p6/F9lW/jjm8iMh7QcAKqsVKa+8KPzbzXFYd6gRADCxX3a3tYEjOUZndBo1/uCJMrZZnVjy87GgXjcaY+mO/1tbjp+P8pabaUPzMP+UgSHtH80xphu0eOGyMpT14r33aw824sGv90a08hSLc7q31oSFn/0Gm9MNjQr46wUjMGVgjmxjVKtUePTcUqEs47Pfl+NIY3CNZaQai9nmxJoDDQCA04fm+6z4h3OMgjRPA7qU7IjHFizKU24KIRJ7SYpebC+RTnSLs++zlGgvEUS3/ImUTpcbDR5Pd1yLbk+ku9XqhMXh8skXiDVKbowD8DeiWrUKTjcn6TUYSaQ7We0l7e3tAICUlK6d8QwG/pru6OhARkaAJMQeMHy7sstSsD+ymL3EZAlpP4BfWtas+Aovv/xPAECDOxVNtpEAAHflNqxdW41p084CANTV1eKTTz4AADyw4quQjqH++kvhGAUFhZg9+1rh+Zdf/ic4DihSl6LWnYH/bKmA/bcVyFDbcfrpMzBq1BgAwK5dO/HDD991ef1Qx6Jd6bX+iN+TPy6//Bqsq3bho2287SVX1YG+lVvx6ivf+Gzn7z1FMkZ2vm677W7h8aVL30d9fZ3ffUaOHI3Fl52B2z/5FbtrTFi9vwGHypfhNN1hdP55v/zya1BYyN8srl37LXbv/rXL64U6Xt03Xwv/7u5zYtx229040tSBO/77G9o9K+VTtYew+9vN2P2t73vyd+2FO0b1119i6dL3A35OADDBlYFvUAKb040Hv96LN+eMw4F9vwV8Tw+H+J0zfLsS5X7e035nPmzOgQCAU/p4f9fXrv0Ws8J4v42jLgKQj5r04KopsbFFEi5Q3i+nQvBtAx/avinaKIlui1d0KzLS7alg0uFwRaUbZyiIG+PEs71EPPZamX3dgkdeoedTrVIJVXSktJeYBdEd+g2PNklFtzuIHz+1OsKfnyCjWkx0txjSQtqPoRUlT1W5vFUb+qhbu91HF2LCldYZODFNpQIm6fiW8G6osdnZN+jXDnUsGnvw350d1e34x+qDAIB0LYcz9QegU4Vu3ZD6fPkj3aDF4svKMCSXn78Ou/KwzjEI4XwtQx2v2hb83F3TZsWCT35Fs4U/xhTdUQzVNoV0PCB657S3xoQyLW8t2VdnxqueEoYBCfE7h26sHgdcfA5FKuwY38s3kTSc95uq4q/1hrRsOFVBzkc92FB6PG5EeycwkbSBT4lSImWryMuXmaK8j863FbwdqfquUa5YEe+NcRhFPg1yrDGpddsdzK6j5JuYvDQ96sx2RSZSuiJMwIkn0tJ4gWvzIzbYY2ybsDEag/oBZJ7ulpTMkPYTSEkRIqoLPtkJHG1Bnywj7rtxgc9mhYVF3sjr00+HdAyV6BidET/uWL4H3+ytxxFXLk65eDpGiRrmjBo1Roh6+xDiWCBanfB5T5042tSB33+4HS6O99e+MHscRvc+PahDdHlNCc6XOELbHZlGHV676gTctnQn9te345ArDyNKR+Chc0r9rmhPm3aWEE2OZLzic9rt5wTemnnzRzuE369bpg7AjSed1uPL+/2cwjinnc9hd5+9w+XGDR9ux55aM97bXIkTLx/d7bbhjAUpKV3e04F6M956dysA4PJJQ9CruFh4btq0s/hzHOL7PW/aadjx3UG41RrUp+egl6kxqLFFAkW6u8Ep0spqBdpLFFm9REENcuK9MQ5D3CBHzgomHMeJqsEoz8/NkDqvwOlyCzfO4awu+dhLFNZGOZr07s030Kivr+/yXF1dHTIzM5GaGtkNpO2sc8EFES3PtfAR6VZjOpxuLuj9AIBTq2E761wAgN3pxvbjbQCASf2zJRlb52P0xO2nDoLe063tH6sPBrV6Eo2xtFkduHvZLuE36aFzSiPqmBmt8+WPrBQdXpo9BsMK+Ju+5bvr8Ndv9/sE2noiGuNtsTiEbpoAn7h4w4n9gx5TLMbI0GnUWHT+cBg9dc8fXbkPLZbuI81SjIVV7lEBuGxsL0mOkZ8mWklO76YSURBjCwUS3d3gVmAipThrXWl1ugES3dGgMN0AdvXJWcHEbHMJ4lPJ59NrL5HG0x1JN0oA0Ip+BJIp0p2ZmYm+ffti165dXZ7bvXs3ysrKIj6GZf4CcEZjj9sVtLcAADiVCi0d9qD3AwAYjLDM5yPav1a3weaJxvQkusM9Rk/0yjTi2om8tWRvnTmoEoJSj8XpcuOBL/cI4vD3U/rh3M4NSkIkWuerO7JTdHjp8tEY7Fk5/OK3Wvzt2wNBC2+px9vcYcdtS3fiQD2fC3FRWRHuOn1wRKVuo31OB+am4u4z+HKg9WY7nly1v9sygpGOpc3qwApPbe5TBuf61NiO5Bjipnk1QYhuKa49Et3dEFEiZdTsJZEJgGjjWz1C3mRKJrpTRU174hGdRo18T2RZTtEtrtFdqGC7DrsGmzvsklQLMdm8N83h2Uu8fztdySO6AeDss8/Ghg0bUF5eLjz2008/4fDhwzj//PMjfn3nCRNhP+d8uHtY7s11eCssNHY4gt7PnZIC27nn853oAGw61iI815PoDvcYwfC7Kf3RN5sXF6/+eKTHxllSjoXjOPxjTblwLs4Ylo9bTh4Y9NhjMcZgyUnV4+XZYzDI01xl2a81ePyb/UGtSEk53qYOO+aLBPc5wwvwwFklEfeWiMU5vXh0MaYN5cXq2oON3ZYRjHQsX+2qhdVzw3vFeP9t6MM5RoHot6wmtzjAXtJdeyS6u8En0h2J6JYwoZAt5Rm06m5LVclJTopOSDqVu0FOrahGdzw2xhFT7Iksy9mVUlyyUGx5URqsQZOL882BCJdII93iVbJkKhkIADfddBOysrIwb948vPXWW3j11Vdxxx13YNSoUZg1a1bkB1CpYHrxNdjPvQDu1NQuS8ucWg0uJRXZo0cKjzV12IPez37uBTC9+JrQ+vmXoy0AgGEFachJ7cFiFeYxgsGo0+C+M4cC4JPWn1lzMGZj+XDrcXy6sxoAMLwwHY+dVxpyl9ZojzEU8tL0ePmKMRjgqYP+1a5a/PHzXT0XApBovDVtVtz68U6UN/A3huePLMRj5w0POY8smmMMfAgV/nJ2iVDv+p/fl+NIk58yghGMxelyC9Vx+uekYPKAbsomhnGM3FQdPG4tHB8zKSbXHonubnD6VC8J7SRr1CrBdxcNe4kSrSUA/76zU/jlfaXYS5RshQiWIk+t7loZa3WL/eTFmUEu4clArjiZV4LVFnHr8HA83eLSislkLwGA3NxcvP/++xg+fDheeOEFvPPOO5gxYwbeeOMN6PUS5QXodDC9ugStn34F24WzwKWmglOpwKWmwjbzYrQsWw7jo48ImwvXRBD7mV57E9Dx85nZ5sTumuD83KGMTXyMUDhxYC7OGc43Bll7sBEr9tRGfSz/K2/E/609BIDP6/jnJaOkLWEaxfMViPw0Pf511ViM8HR5/OlwM279eEfPv2ERjndfnRm//3A7DntqXV84qggPd5PQGTYxOKfZKTo8em4pVACsTjce/nqv/66fYY7lm731qGrlf/uuOqFPYD0W4jHUKpWwOlp1yoyYXHvKVG+dMJvN+L//+z+sWrUKTU1NKCwsxMyZM3H77bdLN3l3IpJIN8BHu+0uZ1QSKZWYRMnIS9OjqcNBoltCWGS51mSDm+OkiSyFCLO2aNQqoTmCEuncCn5oQWQVMiK1l2h9IjbJJboBYPDgwXj99dejexCVCs4TJsL0xjt+6+fmilYrfEpJ9rCfmG2VrUJjsqBFd4jHCJWF04Zg09EWNFscePq7gxjbO8uv11WKseyqMeHB5XvAgW9F/s+Ly3yW5iUjiucrELmperx6xVjc9+Vu/HykGXtqzZj7/lb8beZIoY28X8Ic7//KG/HQ8r3o8OiDK8f3xt1nDInO3B6Dczp5QA6undgX722uxJ5aM15dfxR/OG1QxGNxuTm8tZFvBpWfpsdFZYEtIOEcg1W8arY4YnLtKT7SzXEcFixYgH//+9+YPn06/vKXv2DSpEl47bXXsHDhwqgd18fTHcb3gEUApBTdrYLoVu69khK6UtqdbiGRLiFEt+c92F0cmiVKEAwVZi8pStdLG4mRmDzRsr8UFqeI7SVJWjJQSaTpNcLKY7hNk37xeJg1ahXG9w2uDXe0yUvT46FzSgAA7XYXHo6wy2J3HGpsx53//RUWhxsqAE9cMBylnqhwIpGq1+C5i0dh5ii+MU6dmS/f9+HW4yFVNgmE0+XGCz8cwh+X7UKHwwUVgIXTBuOe6UNlCaZIyfxTBmJ4IX9dvPdLBTaLciDC5bt99TjqSdi9blJfGLTSS1a2Oh+r31bFi+7Vq1djw4YN+Mtf/oJHH30Uc+bMwdNPP41bbrkF3333HbZs2RKV4zLRrVYhLE+wV3RLl0jJ7CUkugNTZ06MyiUMn7KBMvm6mb2kSMHWEkD6CjomcfJyWPaS5PV0KwWVSoVcz81YuE2TmOgeVZyBNL1y5t9Th+Thck/5tB1VbXjxf4clff2qViv+8MmvQsDnvhlDcfrQfEmPoSS0GjUeOqcEfzpzKLRqFVxuDv/8vhy3frxTqNYSLsxO8t7mSgD8zeDTF43E1ROCb3SkZHQaNR4/fzgMWjU4AI+s2BuwjGBP2JxuvPQjfz3npOhwyZiuZQKlgFW8ItHtYdOmTQCAiy++2Ofx8847DwCwbdu2qByXLSWGG9Vjtbo7omAvUWILeEaBSHRLFR0IlUQpF8gozvAKXbl83UzsFyv8fKbpNUI0RIpW8OxGV69RCTVpQ0GcSJlMHSmVBvP6hyO6mzrsONjAV5YIyVoSI+48fTCG5vM2qg+2VOLzX6sled2KZgtu+WgH6sz8ObvtlIG4bKz/yhGJhEqlwuxxvfH6VWPRyxPw2FbZijnvbMZza8vRHOI1VGey4envDuD697diTy3fHXVYQRrevfYEnDEssW5gBuZ5ywjWecoIhqsD/r2lEtWeYM8tJw+QNn9ARHaKp+KVxdFtyUMpUbzovu2227Bs2bIu3cuam5sBAFptdKIO3kh3mKLbU6vbGhVPt3IiLZ1hWcwuTrpayaGSaKK7SOZIt9PNod6zetBLwZVLAP4HM88TuZDCXtJq8eZRhLPipUnSNvBKI5L67ZtDKBUoB0adBs9ePEpYJn/qu4NYfyj0tuFiDja046aPdgjzzXUT+2Le5H4RjzWeKOuViQ+vn4ArxvE3GnYXh39vOY6Zr2/Coyv3YfOxFv8Jg+BtJL8ca8ajK/bikiWb8MmOarg4fj6YN7kf3pwzDv1z5OvYHE0u6VRG8KV1oa++HGnswJKfeS/3kPxUzBodnSg34J0bbE63pM6E7lCuevOQnZ2N7OzsLo9/+OGHAIDx48dH5bjs7izc0j1S20usDpfQmEHJojtflFzTYLbJknTnI7oVLhKDIcuohVGrhtXplqUrZb3ZBqYXlW4vAfioZlWbDU0S2EtY2cGslPC+cxq1CioAHMheIifM6x+O5YjVpDZo1RjdK/yui9Gkd5YR/7hoJG77ZCccLg73frELf79oJE4ZHETDj078r7wRD3+9F+2esnk3ntgfN08dEPelV8MhTa/FvWcOxbkjCvHiusPYWtkKm9ON5btqsXxXLYxaNUoL09ErywiDRg2r04WaNhv21ZmFutKMEwfm4I7TBmFYQeL54cWoVCo8eHYJDjdux9FmC979pRKF6QZceUKfoPZ3utx4dOU+2Jx8DgGz+kSL7FSvc6Cpw45UfXRvhmRTb/7aA4tJTU3tEt1mLFu2DN988w2mTJmCsWPHRmN4EkS6pU2k9GkBn6Jce4m4RXid2Y7hRbEfAxPdmUZt1JakYolKpUJxpgFHmiyyRLp9ygXGwcqBILCkiHRLUDFIo1bB6eYo0i0juZ6qNi0WB1xuLiTbIPNzj++TBX0UErmkYlzfLDw1cyTu+2I3HC4Of1y2C3eePhhzTugTlGC2O914fcNRvL2pQnjsjtMG4bpJyRXh9sfo3pl49Yox2FzRgk+2V+OH8ka43BysTjd2VLVhR1Wb3/10GhVOG5KHOSf0wdg+ykjAjQVZKTo8f1kZfv/v7WjqcOCZ78vh4rge/eus+dKuGr5+yNUT+uKEvtlRHWuuSHS3WBzom52govuUU04J+Pytt97qtzrJ6tWr8eCDD6KgoABPPfVUtIYniO6wPd0ee0k0RLdS63QD8IlsN5jlSfpLpHKBjKIMj+iWwdNdY/Ies1ccRLq9ybzSeboj+c5pPaKbIt3yweYlN8d3K80PstxdZYtFqBE8eUB2tIYnGacNycPTF43En7/aA5vTjefWHsKmoy24Z/qQbsUEx3H48VATFv/vMA57Gpuk6jR47LxSTEswz3EkqFQqTOqfg0n9c9DcYccvx1qwuaIFRxo7UGOywenmoFWrUJRhwKC8VIzvm4WpA3ORpeAgWTTpk5WC5y8tw21Lf4XJ5sRzaw+h1mTDH04d5NO/gMFxHF768YjQfGlEUTrmnzIw6uPMSRFHuqNviZVNvT3xxBMBnx8xYkSXx7766ivcf//9SEtLw+uvv47evaOX1MHKe4W7qsEirD12tgqS1gibdMSK/DS9sJzOEnBiTSKKbpZMKUdXSnGkOx7OKYtctFoccLrcfif4YJEieZnduJPolg/xdVtrsgUtun9RuJ/bH6cNycPrV43FvZ/vRq3JhvWHm/Dzm02YNiwfpw/Nw5C8NOi1ajS227Gzqg2r9tYLiaIAUFqYjkXnl2JwXmQ17hOZnFQ9zh5eiLOHF8o9FEUzvCgDr14xBgs++RXNFgf+veU4tla04s7TB2NCvyxhBaaq1Ypnvy/H/8obAfAr5s/MGhWVEoGdEXeXbUlk0T179uyQtv/Pf/6Dxx57DFlZWXj77bcxfPjwKI2Mx+2xY4Uf6eZFt9XhAsdxEfvhfOwlCq5eotWokZOqQ1OHAw0kuiWDlQ1s6nDA6nDBGEPbDBPdWUYtUvXKt+uwSDcHPiM93CYeHMeh1RJ5mU7mRyR7iXz4VAAy2TAqyLwsJrqzjFqUFMaPF3dEUQbev+4EvPDDIXy5qxYuDli9vwGr9zd0u0+6QYPrJ/XDtRP7RnSjShBiSgrT8ebV43D/l3uwr86MvXVmzF+6E72zjBicl4pWiwO7a0xCxbjeWUa8dPloFMbo9zunk6c72ig3ZCpi2bJleOSRR1BYWIi3334bQ4YMifoxvZHu8MQyEycuDnC4OOi1kYpu7x2Yku0lAFCYbkBThwP17bGPylocLuEGJZFEt7jTXFWbNaZRKGYvUXL7dzGda3WHK7ptTjfsnl+CSJaIKdItP+K5INi8CDfHCZVLJvTLjrvmJdkpOjx8bimuHN8HH2ypxP/KG4XkSDEDc1Nw/sgiXD62d1i16AmiJ/pmp2DJnHF4e+MxvLe5EjanG1WtVsG6xTirtAD3nTk0ppacFJ1GKFTQHEFd8WBR/DesvLwcDz30EHJzc/Hee+9h4MCBMTkuq14STjdKAD6RyA6HK+IEnHiJdANAfroeqAPqZYh018aZFSJY+ohFd2tsRTerlRoPSZSAb2JMYwTLheLGDlJEukl0y0dWihYGrRo2pztoi9bB+nbhRzge/NzdUVqUjkXnD4fD5cb++nZUtVrhdLuRYdBiWEE6CtP1SVmZhIgtBq0at5w8EJeN642Ve+qwpaIFtSYbUnQajCrOwPkjCzG8KEOWseWk6lDdZotJgxzFi+7FixfDbrfj1FNPxY4dO7Bjxw6f50tLS6NiNRGql4RrLxGJbKvDBUR458aqKGjVKiFJU6mwWt2yiO4Eq9HN6Cy6YwXHccKNTHGclF+UqiulVMnLGsFeEv0asIR/VCo+we1YsyVo0b1J5Oee3D8nSiOLHTqNGqOKMzCqWB5hQxAAn/d17cS+uHaicjpx5qTqedFNkW7gl19+AQB8/vnn+Pzzz7s8v2DBgqiIbtaYKFJ7CSBNV0pxC3ilRyXYcn6LxQG70x3TMluJKrrz0vRCpO54DEW3yeYUrt94tZeEizh5OZLlTvJ0K4OQRfdRvgFbr0wD+mbHx7VPEETosKCKONASLRQvutevXy/Lcd0RVi8R20ukaJATDy3gGQXisoHtdh8/crQR/6AWhunlVSIqlQq9PLW6Yxnpro6zGt0A79FL1WnQ4XBFVALK19IVeaSb7CXywq7fYL4/dqcb2ypbAfBRbqUHOgiCCJ9MQXRHP9KtbJ+CjLgijHSLLSBStIJvjYMW8IwCkTirj3Gtbia6c1N1im5kEQ7s5iWWkW6fxjhxYi8BgDxPM5SIIt0WcfJy5ImUFOmWl36etttNHQ6YbYEjWr9WtwkdBePZz00QRM+wPLlYRLoTS5VIiDvC5jip4kRKCWp1t0lQuixWiCPdsfZ1J2K5QEafLF40VLVawXGxEXC1osY48WIvAYDcCNp+M1olinRr1fw0S5Fueeknag5T2WIJuC2zlgDxU5+bIIjwYFV7TFan4HKIFiS6u4Gd+HAXFX3tJVJ4uuMn0i22ddRHIHrCIZFFN4t0t9tdPoIwmjB7iU6j8qkKonSYrzuSuqutFv4cG7TqiOqiU6RbGbBINwAca+5BdHuSKEsK0nyaZxAEkXgwTzcH9LgKFikkuruB/T6GHenWR0t0K1/4ZKVoofPUWqyPYQdFjuOSQnQDsatgwtrOF2UY4qpOsRSt4KVoAQ8AGhV5upWAONJdESDS3Wblm3UAwOQB8V+1hCCIwGQYvHN8tC0mJLq7IdLmOCla6RIpHS63UEEiHiLdKpVKsJjEMtJttrmE85SIortPZuxFN/OP944jawngrdVtsjlhc4b3/ZPqRlfruQF1xcgSRPgnVa9BvmdeChTp3nC4WQi6nEiimyASHvEcT6JbJrgIRbdRlEgZaaQ7nhrjMPI9FpNYJlImarlARh9R2bJYJVMycR/LCjRSIC4b2BymxYSVDMxKiTDSzewlLhLdcjMwLxUAUN7Q0e026w41AgDS9Bqc0C8rJuMiCEI+xKuZ0a5gQqK7G7zVS8Lb36BVC/tKKbqV3gKeIUeDnEQX3ekGrbDSEYtIt9nmFLzj8Sy6w02mZJ7uiCPdaop0K4WSAr6T66HGdjhcXVdAnC43fjrMJ1GeNDAHOg39RBJEopNhJHuJ7Lgj7EipUqmQ4km+itReIr7zyoww6hYrCkSR7lhV2qhui89KG6HAbB6xEN3iY/SJN9EtSvpsCNPXzbqT5UTYTZbawCuH0sJ0AIDDxeFwY9do9/bjbTB5EqlOHZIX07ERBCEPWSS65YdVL9FEkDsmiO4ISwa2xqG9hHm6LQ432iUomRgMrNKGRq0SvJuJBos4V7WR6A5EvqiCTkN76BYnl5sT6nTnRFi1hSVSUvUS+SnxiG4A2Fdn7vL89wcaAPArnFMH5sZsXARByEeGSFeZqHqJPLDfx0g6kbEGOZHbS8RNOuIk0p0h6koZI4sJi3QXZxjCrjqjdJj4rWq1Rj1yKhb28WgvYZdAXRgVdFqtDrCzG3GkW0OiWykMzE2FwdM0a5enQgnD6XLj2331APja3NlxVCKTIIjwMWjVwrzAbIXRgkR3N3gj3eGLN6NgL5EykTJORHeaN9JYF6NkSlberlccdU4MFSZ+nW4u6kmqLNKdolMjO0LhGWu0apXg664L46avWdQ+XqpIN9lL5EerVmFM70wAwC+eWtyMjcdaBEvRuSMKYz00giBkJFat4El0d4NL8HSH/xqpEolutsytVvHJdPEAS6QEYpdMWeWxl/RKUD830KlWd5QtJsdFlUsiWfGRC9akKZxIt6Sim5rjKIrJng6Tx5otPnkgX/5WA4CPek0bmi/H0AiCkAkmusleIhOcUL0kAnuJp0FOpJ7mVlG94HhpUFKYEdtIt83pFqpUJI3ojnIyJRPdrP18vMFu/MK5/sSdLCPtSEiJlMpC3PBmXTlfHrC6zSr4uWeU5MdNcIMgCGlg+XLR7vZMorsbIm2OAwDpEonuFk+kOztOKpcAfBIpu3OsjUFXSvExemUlsL0k0wh2RVa2RE90cxyH6jit0c1gZSPDWWlh3znA22gnXCjSrSyGF6ULFrQvfqsFx3F4bf0RIY9nzoS+Mo6OIAg5yDSQvURW3ILoDv810jwfYsSRbgtrRx1fvlomemIhuqtFUd9EjnTrtWoUewRDRYCuepHS1OGA1dPJMV5FNytb2W53wRzikmGTx16iQuTfO29znMhKhxLSoFapMHNUMQC+gsl9X+7B8t11AIDTh+QJZQUJgkge0j1BQrMtutXWSHR3g9vz+xhJFYw0FumO0CPU4smmjbdkNia6a9piILrbkkN0A0C/bN7uUdESPdEttq7EWwt4RmFG+HkFLNKdlaKLuBIOs5dQoFs5XHVCH6ESFLOVGLVq3DVtsJzDIghCJrzOBLKXyAKLdKsQgb3EE+m2Ot0RRbmkakcda2Ia6faIbrUKKExPzBrdjH45vOg+1myJWuMhcZt5cfv5eKJQVKs71GRKFumOtFwg4L1xd1NHSsWQYdTi6YtGIt3A/9CmGzR4+qKR6Jsdn/kLBEFEhuBMsLmiOlfHl4qLIULJwAhuS1ikG+CXuLNSQn8xjuNEnu74inQXe0S3yeZEu92JNH30LjfWGKcw3QBtgrdu7u8R3e12F5otDuRGmOjnj4SIdItEd22IyZQtnkTKSCuXANQcR6lM6JeNL2+agvKGdgzJT6PkSYJIYlikmwNfcS5aeiWx1UkEuCSoXiKexM1hLllYHG44PIOJO0+3qF52tKPd1UlQo5vRTxSNi5av+3gr/7o5KTqkim4e4wnfspVhRrolEN1qql6iWNINWoztk0WCmyCSnDSxXouir5tEdzewZXt1BH7OdHGkO8wPUVxFIf4i3d4IafRFN//6xXEalQ0Fseg+FiXRzcQ8s7LEI0adRvDt1plC83SzJilkLyEIgkh8fPRaFH3dJLq7QWiOE8FrpEkQ6W4Vt4CPU083ANRGMZnS6XILkcxecVppIxT6ZBuFqjrRSqY85ilHGM+iG/DWiw+lVrfT5Ra6wEph3dGqvImUySK8zWYznnjiCZx22mkoKyvD9OnT8dxzz8Fuj02jLIIgiFCIVaQ7vlRcDGErwRTpDp/CdD1U4D1SNVGMdNeabcLn1Ssj8e0lOo0axZlGVLVao2Ivabc7hUZD/eM8saww3YAD9e0hJVL6fOcksZd4/3a7Oag18dHgKlw4jsOCBQuwadMmXHHFFSgtLcX27dvx2muv4eDBg3jppZfkHiJBEIQPYr0WaonZUCDR3Q1CImUEnm5JIt0W737x5unWatTIT9ej3myPqr1EXJIwGSLdAC+Gq1qtqIhCg5zKZu9r9o3TyiUMb1fK4COszRI2xgF85xAXl/iT7urVq7FhwwY8/PDDuOaaawAAc+bMQXFxMV599VVs2bIFEyZMkHmUBEEQXsR6LdLeKoEge0k3sMhpJF3Xkz3SDcSmbGBVkjTGEcNsHxVRKBt4TGRZ6Z8g9pIWiwNWR3DfQRblBySqXiJaLUuGZMpNmzYBAC6++GKfx8877zwAwLZt22I9JIIgiIDEKtJNorsbpI50h3vnxLpRqsDXlo03YiG6xZHuoiSwlwBe0d3hcKGxQ9q2tWLLSrx7usXlDoO1OIkb6YjLDoZLsonu2267DcuWLUNaWprP483NzQAArTb+5jGCIBKbdIp0y4uQSBmBp9uoVYPZN8O9c2KR7kyjNuLOeHIgFt3RauRS6SlvV5iuh0GbHJd0/yiWDWTJmbmpuqjWVo8FvbK8olnctTQQDaJId35a5ImUvvaSxBfd2dnZGDFiRJfHP/zwQwDA+PHjYz0kgiCIgKTqNUIrRPJ0d+Kuu+7CihUrsG/fvqgdgxPqdIf/GiqVCmkGLdqszvAj3Z4qCllxaC0BvKLb5nSj1eKUJDGtM8c9vuY+SeLnBnwj0MeaOzC+b5Zkr81EfLxbSwBfu1F1a3Cim0W6MwxaGHWR1yhPlEh3fX19wOdTU1O7RLcZy5YtwzfffIMpU6Zg7Nix0RgeQRBE2KhVKqTqNWi3u6Ia6Y470b1q1SqsWLEi6sdhEalImuMAvE+ozeqMONIdb0mUjGKR3aPGZI2K6K70iKk+cV5pIxR6Zxmh06jgcHE40hSdSHe/BDifBekGaFR8AmN1kGUrWfnJ/HRpOn2qE0R0n3LKKQGfv/XWW7Fw4cIuj69evRoPPvggCgoK8NRTT0VreARBEBGR5hHdFOn20NzcjEcffRQ6nQ4Oh7Q+1s64JRLdvK/bFrGnO95qdDOKxJ7aNhuGF2VI+voWh0tIfIv3ShuhoFWr0D8nBeUNHTjc2CHZ65ptTqEbY7z7uQH+PBVlGFDVZgvZXlIggbUE8NbpBuK7TvcTTzwR8Hl/lpKvvvoK999/P9LS0vD666+jd+/e0RoeQRBERKQbtKgz2ynSzXj88ceRk5ODE088EcuXL4/qsVhAShOhRZhlxEYc6Y5Te4m4LXtVkKInFI6LSub1zYp/kRgKg3JTedHdJJ3orkigyiWM4kwjqtpsqGoNLZGyQKJIt9he4ozjSPfs2bND2v4///kPHnvsMWRlZeHtt9/G8OHDozQygiCIyGE5TFS9BMB3332HFStW4Mknn4ReL82PYSDcnh9HlSSR7giql3g83dlxai/JSdHB6ElurArSUxsKlSKR2CeJIt0AMCgvFQDvVQ62HF5PHBEJ+AE5qZK8ptyw2u01pp6vPzfHCZHufAkqlwC+zXHi2V4SCsuWLcMjjzyC/Px8fPDBByS4CYJQPOkGPkia9NVLWlpa8Oijj+L666/HuHHjon48juPAfhojbR6XpmcfYuh3TlaHCzanG0D82ktUKhV6e0RPNET38dbkjXQPzOVFMQfgqES+bmZVUasSJ9Ld27PaUm+2w+75PnVHi8UhCGOp7CUaH3uJJC+paMrLy/HQQw8hNzcX7733HoYMGSL3kAiCIHqElQ1MSE93KJnwjz/+OFJSUnDXXXfFYGR80hUj4kRK4UMM/c4p3hvjMHpnGXGosSMq9hIW6U7Ta+L2xiRcWKQbAA41taO0KD3i12Siu292CvQJUn6xV6da3YFuJsQ1uqWyl2gTJJEyWBYvXgy73Y5TTz0VO3bswI4dO3yeLy0tpcg3QRCKIy1CO3AwyKZSgs2EX716NZYvX453330XRmNs7APietKR1sZmHqFwIt0+LeDjWHT3EUW6OY6L2LIjRqhckmWU9HXjgf45qVCr+OjpEYmSKQ95XmdwXmJYS4BOZQPbrAFFd4NIdOdJFOkW37gng+j+5ZdfAACff/45Pv/88y7PL1iwgEQ3QRCKw6vXEjCRMphM+NbWVjzyyCO48MILMXToUDQ1NQEA7Hb+h7GpqQkGg6Hb2rDhIv5hjFTGMY+Qw8XB5nSH1LylxSqOdMdvFJfZSywON1osDuSkSufJP+6JdPdNgPJ2oWLQqtEny4iKFqsgliPB7nQLKweDEkl0ixrkHO/B4iT2fUvV3dSnTnccVy8JlvXr18s9BIIgiJBhkW6b0w2Xm4tKQ0LZlFwwmfAbN25EfX09vvzyS3z55Zddnj/ppJNwySWXSF77VRyMkirSDfDRboM2eMHZKrKXxGudbsC3FXdVq1Uy0e10c6jy1F5OpnKBYgblpaGixeqTABkux5otwrWfSKK7OMMIrVoFp5vrsXsnq3CiUatQIFEiZaI0xyEIgkhkUvTeZmgWh8unNbxUKDp8Onz4cLz11ltdHl+yZAl+/PFHvPXWWygsLJT8uOJaupF7ur0fotnmQm4IWiaRPN2M461WjOqVKcnr1plsgohJpsY4YgbmpuJ/5Y2oaLbA4XJDF0GNy0ON7cLfg3OlXT2SE41ahX7ZKTjc1IGjPdycsFrexRkGyaIcmiSzlxAEQcQjqTrv72dSiu6srCxMnTq1y+NffPEFAPh9TgrEojtSm7D4QzNZHQCCF4esSYkK8e3pFotuKSuY+JQLTKIW8GKG5PN3cS6OT4IsKQw/mZIlUaoADMhNrJuYAbm86D7WQ6Sbie5eEl5PyWYvIQiCiEfEke6OKPm6E6M8gcS4RVXFNBGq7iyjV3S3hZgR29zhbYyjjYK3KFakG7TCeZCygkmluFxgktpLxCJ7f705otdiTXZ6ZRlh1Gl62Dq+YMmTla3WgA1q2E1h70xprCUA2UsIgiDigVSdV691SNT7ojMkuv0gjkapIxS7GUZxpDs00d3UwSeM5qTGb5SbEY1a3cyfy7f6Tk7RPTAnBTpPMfkD9e09bB2YRKxcwmCi2+Xmur0GrQ6XsLokrngSKeIphCLdBEEQyiRV75XEFOkW8dRTT2Hfvn1Re32fkoERBpgzRfaS1hBFN4t055Lo9gtLHuyXnRLXKwGRoNWoMSSP91/vrws/0m1zunGsKXFFt7i75rFm/77umjZvm/jeEtpLxNemO3BvHoIgCEImUnW+iZTRIC5Fd7QRN8eJtPZzhqjqSKiR7mZPImVOSvTb3kcbVsGkus0m2RI78+cmmv84VEoKPaK7vt3nhjEUyhvaheu+NAJfuFLpL7pGuvN1i61Pkka6RaI7kLWFIAiCkA/ydMuE2yfSHZnoNmjVQm3utiSOdPf1LO873ZyQrBYJDpdbqNHdPyfxIrOhMKyAF8ltVidqTbYetvaPOEpeUpB4ojsnRSdUEupWdLeKRbeEnm4VJVISBEEoHXGkm0R3DPEpGSjBGWJJhG2iZjc94XC5YfIkXiaCp3uAqAtgRUvgChLBcLzFKkRmKdLtLe+3ry48X/c+j+g2atXoF6BjY7yiUqmEm7Puapof9Yhxg1YtWY1uwDeR0k2RboIgCEWSKo50k70kdoh9l5HW6Qa8yZSmEKqXsCg3kBiRbnHr7WNNkYvuoyJf7oAEFImhMCzfG5k+EGYFk/2eJMxhBWlR6cKlBIZ4vOoHurHhHPEkkvbPSZH0HFCdboIgCOWTQp5ueXBJ2BwH8CZThmIvEYtuKdumy0V+mh4pnsLzPdVKDoajIuE+IJSOQwlIhlErlLjbF0YypcvNCWI9kjrfSoe9t+5sOKxk4iCJryeq000QBKF8dBq1UA2M7CUxxLcjZeSvl+lJpgxFdDdZ7MLfiRDpFi/vSyK6PZHu7BRdXHfrlIrhRRkAgN01ppD3rWyxwOLgl3cSWXSLE0Q735x02F2CEB8ocfUWqtNNEAQRHzBfN4nuGCL+XZRimTkjDE93okW6Aa/FpLuSbaHAIt3Jbi1hjO6dCQCoM9tDTqbcU+sVoIlYuYQxrEDsffcV3WK7ktSRbp863SS6CYIgFAvzdZO9JIaIk50iLRkIAJlheLqbEszTDXhFd3WbDTZnZAWLj1K5QB9G98oQ/v61qi2kfXd6tjdo1SgRCdNEI92gFTqX7u+UcLpXdOMxJF/ac6AlewlBEERcwHzdHY7oNFUg0e0Ht4TNcQCv6LY43HC4gvsgmz3dKHUaFdL0idGSm4luDrylIVxaLA60eGqYD0jycoGM0sJ0YVXm1+rQRDcT6cML06HTJPaUwCL5u2tNPsmUzJaTptdIfiPnay+R9KUJgiAICWGR7g57aCWegyWxf2HDRLwCLEn1EoM3Uh2sr5tFunNSdJJE25WA2AoSia/7UKM3Sim1/zZeMeo0QpT6t+rgfd0Wh0tIohzjsagkMuw91pvtOC6qy81E9/CidEm+82LUVKebIAgiLhAi3XaKdMcMt9TVS4zeVvDBdqX0NsZJDD83AJ/6z5GI7vIGr/92qMRWgHiGCcq9taagV1R215iEeuejk0B0T+ibLfy9paIFAGB1uFDewN/IjSzK8LNXZFAiJUEQRHyQRp7u2CP+YZSiOY5YdLcGmUzZ5LGXJEJjHEamUYccT6WRo900KAkGJpBSdRoUS9g5MN5hotvu4oKOdu8U+b+TQXQPLUhDhqeE56ajLQCAbcdbo3rjoaXmOARBEHGB19NNojtmSG0v8Yl0B5lMmUgt4MUM9PhlD0sguofkp0puBYhnJvTLFv7edLQ5qH12HOdFd+9MA/LTEmdVpTs0ahWmDMgGAPx4qAlWhwsbDvPnSqMCJvXPjsox6SolCIJQPl5PN4numCF1nW4WWQOC83RzHIdmT6JgopQLZAz22EEONXT4nOdg4TgOBz2iezBZS3zIS9MLZfE2HWvpcXuHy42tlfx2E6MgNpXK2cMLAfCRjDUHGrBqXz0AYGyfLKSLvqtSodOoMXtcb/TLNuK0IXmSvz5BEAQhDSzSHS17ifS/MAmA1J7uLGNoiZTtdpdQUi8nwRq/MA92h8OF6jYr+mSFVimizmyH2ebyeS3Cy6T+2ThQ345d1W0w25wBReTOqjahKc6UATmxGqLsTB2UiwyDFiabE4+s2Cc8fsGooqgd894zh0bttQmCIAhpYJFum9MNp5vzsQdKAUW6/eAW5aBpJBDd6SEmUja0e7tR5qcnVqRbXANZnBAZLCzKDZDo9sdkj3h2ccCWitaA24otKNGwVSgVg1aN6yb19XmsV6YBZ5cWyDQigiAIQgmwSDcAWKJgMSHR7Qc3xImUkYturVqFdAP/QbL60oFoMItEd4L5bIfke0v8lTe0B9jSP+X13n3Er0XwnNA3CzpPcfkfDzUG3Ha9x8tcWpiecDamnrh2Yl/MKOFFdm6qDk9cMAJGXWLUwycIgiDCI0XnlcVWJ4numCCOdEu1ssBK/zUHI7pFke6C9MSqzpFp1KHQE70PR3Tv9bTvzk/TJ51QDIYUnUawinx/oAHObkoHVjRbhFbopw3Jjdn4lIJOo8ZfLxyOL2+ajC9umpIUNcoJgiCIwIgj3dYodKUk0e0Hl8SebgDI9nizWafJQNSbbcLfBQlmLwG8FpOD4YjuWr4U3oiidEnHlEiwCG6r1dmtxeS7/fXC32eWJKetQqVSoTjTCIOWpkGCIAgCMGop0h1zxLV0pfB0A97Sf6zTZCBYpNuoVSdMC3gxzIt9pMkSdBMXAGizOlDRwncRHFEsfROTROG0IXlC8sfXe2q7PM9xHL71VOwYlJfq47MnCIIgiGTFIPZ0U6Q7NohPs1RloFmTm2A83fUeT3dBuj5hWsCLGVbIizyXmwsp2r231iz8HY3OgYlChlGL04fypem+3VePxnbf1ZWdVW044PHGnzM8OaPcBEEQBNEZH093FMoGkuj2g9stbSIl4C3912Jx9NgKusFjL8lPMD83Y1Sx1z+7K8jOiQCwRyS6h5O9JCBXje8DAHC4OHyyvcrnufc3VwLgE3xnje4V87ERBEEQhBIxainSHXPEdbqlspewpD83x9skAlHviUwWJFjlEka/bKPQMGh3TfCim/m5C9P1yEvQcyMVY/tkYnghf2PywZZK1Jr4G7ntla1Ye5CvanLOiMKEq45DEARBEOEiTqS0kac7Nvi2gZfmNcXt3ANVMOE4TrCXJFqNboZKpcLIYl4Q7gpBdDOBPpL83D2iUqnwh9MGAeDv1u//cje2Vrbgwa/3AgD0GhVumTpAziESBEEQhKIw+thLKNIdE6TuSAl4q5cAQHOAZEqzzduNMpGjkEw4H27sQLu954ZBtSYbqtr4aG1ZLyrvFgyTB+TgojK+y+Jv1Sbc8tFOIeK94LTB6JVplHN4BEEQBKEoUnzsJRTpjgkuH0+3NK+ZK6opHaiCSX27uFxgYnq6AW8iJAffBMnu2F7pLX03rg+J7mC5f8YwnDEs3+ex6yb2xVXje8s0IoIgCIJQJj6Rbqf0kW5tz5sogxUrVuD111/HwYMHUVBQgAsuuAC33347DAbphWl0PN3BRbrF3SgTsUY3Y1Qvr0VkZ1UbJvTLDrj9tuO86DZo1WQvCQGdRo2nZ47Azqo2HG2yYGSvDKFkI0EQBEEQXvRaql6Cjz/+GHfddReysrLwwAMPYOrUqfjXv/6FBx98MCrHE3u6pSrZl+VjL+m+QY64G2Ui20sK0g3om83bG7ZUtPS4/TZPpLusVwZ0mri4bBWDSqXC2D5ZuGh0MQluQhbuuusulJaWyj0MgiCIgKhVKqFBTjSqlyg+0t3c3IynnnoKp5xyCv71r39Bo+H9NqmpqXj77bdxxx13oF+/fpIe0zfSLc1ratUqZBm1aLU6AyZSMs8tkNj2EgCY2C8blS012H68DXan2+cOU0xDux2HGjsAAOP6ZMVyiARBRMiqVauwYsUKuYdBEAQRFEadBlanOzk7Un777bdob2/HwoULBcENAFdddRVuu+02OJ09J+GFirhJolR1ugEg1xO5FltIOlPjSRbMMmqRmoDdKMVM6p8NALA53fitpq3b7X463CT8fdLAnGgPiyAIiWhubsajjz4KnU7X88YEQRAKgDXISUp7yZYtW5CdnY1Ro0YBAKxWK5xOJwYNGoQ777wTgwYNkvyYXBSqlwBAkSdyXWe2dbtNdRvf5rw4CSpLiH3cG4+2dLsdE91ZRi1VLiGIOOLxxx9HTk4Ozj77bLmHQhAEERSsQU40EikVL7qPHj2K4uJibNu2DZdddhnGjh2LcePG4U9/+hPM5p6rXoSDy0d0S/e6hRl8pLsuQKSbie5emYltLQGAvDQ9Sj0NXNYeaPC7jdPlxs9HmgEAJw7MgUbKD4QgiKjx3XffYcWKFXjyySeh1ydufgpBEImFUYh0J5Dorq+vD/hfe3s7AKCtrQ1NTU244YYbcMIJJ+DFF1/Eddddh6+++grz58/3iUpLhW9zHOlEXqEn0t3UbofD1fXD5DgO1R57SbLUUD6zhC9nd6ixA0c8vm0xG440o93OL/GcPDg3pmMjCCI8Wlpa8Oijj+L666/HuHHj5B4OQRBE0Bg9XSmjUadbtkTKU045JeDzt956KxYuXAi73Y66ujrccccduP322wEAZ511FtLT0/HCCy/ghx9+wLRp0yQdm1ukuqWMrBZm8KKbA58c2FlYt1gcQmOc4iSIdAPAGcPy8fKPRwAAqw/U44Y83y6JK/fUAQCMWjVOH5LfeXeCIGJEfX19wOdTU1ORlvb/7d1rbFR1Gsfx37QD0xlogbKlUEBkRdpaBLfZ7S6s202UJS4lqUW5JIQIKFmi7HpJqG80vpAYyAaIYEKiNCihL6TZaKkNxk13VyqarpC9KLjlYpFSxFZ7oaXtFMrsi+kZpjDQi/Ofc+h8P28oM6XnCSQPvz59zv8ET8d59dVX5fV69dxzz8WgMgCIHuv0khF1TvfmzZtv+352drYkyev1SpKWLVvW7/1HH31UO3fuVE1NTfRDd9j0PJrLDFbolqTGdv9NoduackvxM+m+O9Wne9PG6FTTZR384qLW5N0V+kbnh8s9+sfp4NrJb2dNHPE3lgJONthBSVVVlSorK7Vv3z4lJcVHHwMwcnhH4qT7xhB9K+np6Tp58qRSU/uvFkycOFGSQmso0RS+XhLNSXd62BGA4UcDWqx9bik+drotS+dO0daq07pwya+PT3+vh2anSZIO/KtBPb3Bf4zH5/EERcBOgxmUtLW16ZVXXtGSJUs0a9YsNTcHb4Lu6Qnex9Lc3CyPxxOaiAOA01g73f6RFLoHKycnR9XV1Tp9+rSysrJCr58/f16SlJER/TDWa+j0EutGSinyzZTxOOmWpMX3pWv3kbO61H1Vu6rrtGBmqn7o7FHpsQZJUs7kZM3j0e+ArQYzKKmpqVFTU5MqKipUUVFx0/vz589XUVGRtmzZYqJEAPjRrEn3iFovGayCggK9+eabeuutt7Rt27bQ6/v27ZPL5dLChQujfs2AodNLkj1uJbkT1H31mhojTLovtAUn3b5RiUpJcvw/TdT4Ridq/fwZ2vb3Mzrf2q0//uWLfvvtf/rtzKg9GRSAOVlZWdq7d+9Nr5eUlOiTTz7R3r17NWnSJBsqA4DB8YSeSBmHk+7Zs2dr7dq1KikpUVdXl/Lz8/X555/rgw8+0OrVqzVr1qyoX7Nvo0EuRe8x8Or7WpOSPTrX0hXxrO5zLcHTO+6a4I27kPn4Axn6+PT3Olrfpn83XH9QzoqfZSh32nj7CgMwaOPGjdOCBQtuev3gwYOSFPE9AHAS6/SS7ivXFAgEoprHHB+6JWnTpk2aOnWqSktLVV1drcmTJ6u4uFjr1q0zcj3r9JJoPo3SMrkvdFtT7XDfNHdJCobueONOcOnPhTl67a+nVHWySaMTE7Qyd6o2/Ppuu0sDAABxwts36Q5I6ukNyOOOs9Dtcrm0atUqrVq1KibXs04vSTQwbJ4+wat/nmtVfWtXv++guq/06mLfysmM1PgL3ZI01uPWa0uy5b+aqUSX5E50/LObAADACGJNuqXgiom1bhINpJoIrNNLTKx4TB8fDNQd/l61dF0JvV7f2hX6+K4Jvqhf907icScQuIERZMuWLaqtrbW7DAAYkHfU9fzRHeW9bpJNBNcn3dEP3eGrI/Ut14O2tVoixe+kGwAAwE5J7uuT7mg/Cp7QHUFvaKc7+l97eljo/iYsdJ9q6pAUvHlzRpxPugEAAOwQvk7ij/KxgYTuCKwTA01MuqeOSwrtiodPt2sbgw/5mZHq5cmLAAAANkgKXy+5ynqJcdbDcUzsdI9KTAjtbJ/sm25L0v8agx9nThob9WsCAABgYJ7w9RIm3eZZO90GTgyUJGVPDgbrry62KxAI6PvLPfrhcvAJlYRuAAAAe7BeEmPW6SWJhlL3fenJkqS27qtqaOvWfy9cfxhMVjqhGwAAwA4mQ/cdcU53rFkPxzH1TMicKcmhj49/2x4K3aMSXbp/SoqhqwIAAOB2+ofu6O50E7ojCB0ZaGjSPTttrLyjEtR15ZqO1DXrPw1tkqT7p6T0O5QdAAAAsROewzgyMAZ6+9ZLEgzcSClJo90J+tXdqZKkQ1816sKl4JMoH7r3J0auBwAAgIElsdMdWwHDk25JWpKT3u/3HneCfpeVZux6AAAAuD1upIyx3r6/Y3ORW/rNT1P1i7vGh37/hwUzlOobbfCKAAAAuB13git0el20z+lmpzuC0JGBBifdLpdLO4rm6G+nmjTBO0q/nDHB2LUAAAAwMJfLJY87eN8dp5fEQOhGSkM73RaPO0G/z04f+BMBAAAQE0nuRCOhm/WSCKxzug1nbgAAADiMtdfNEyljIFaTbgAAADiLFbr9V6K7003ojiAWO90AAABwHibdMfTA1HF9v/J0SAAAgHjy877T5eZmRDcHugLWodQj2JUrvWpt7RzSn/n2UrcmJ3vkYsUEgI3S0pLtLiHmhtOzASBaAoGALrb7NSUlach/9nY9m9NLbmE4f9EAAAC4s7lcLiM5kPUSAAAAwDBCNwAAAGAYoRsAAAAwjNANAAAAGEboBgAAAAwjdAMAAACGEboBAAAAwwjdAAAAgGGEbgAAAMAwQjcAAABgGKEbAAAAMIzQDQAAABjmCgQCAbuLAAAAAEYyJt0AAACAYYRuAAAAwDBCNwAAAGAYoRsAAAAwjNANAAAAGEboBgAAAAwjdA/BuXPnNHfuXNXU1NhdChygvr5eGzduVF5envLy8lRcXKzm5ma7y4KDvfTSS1q9erXdZcQV+jYs9GwMVbR7tjtqX2mEu3Tpkp555hn5/X67S4EDtLS06IknnlBPT4+eeuop9fb2qqSkRLW1tSorK9Po0aPtLhEOU1ZWprKyMuXl5dldStygb8NCz8ZQmejZhO5BOHPmjDZu3Kivv/7a7lLgEG+//bYuXryoiooK3XPPPZKkefPmae3atXr//fe1fPlymyuEU/T29mr37t1644037C4lrtC3EY6ejcEy2bNZLxnAe++9p8LCQrW2tmrZsmV2lwOHqKysVF5eXqh5S9KCBQs0c+ZMVVZW2lgZnMTv96uoqEi7du1SYWGh0tPT7S4pLtC3cSN6NgbDdM8mdA+gtrZWBQUFqqioUG5urt3lwAHa2tpUX1+vnJycm97LycnRl19+aUNVcCK/36+Ojg7t2LFDW7duldvNDxdjgb6NcPRsDJbpns3/AAN44YUX2PVCP999950kRfwOOC0tTR0dHWpvb1dycnKsS4PDjB07Vh999BFhO8bo2whHz8Zgme7Zcfk/QVNT023f9/l8GjNmjCTRuHGTy5cvS5K8Xu9N73k8HklSZ2cnDRxKSEhQQgI/UIwG+jaGi56NwTLds+MydD/44IO3fX/Dhg16/vnnY1QN7jTXrl0b8HMIWkB00bcxXPRsOEVchu7Nmzff9v3s7OwYVYI7kTVNi3QMmfWa9TkAooO+jeGiZ8Mp4jJ0czc7foyMjAxJkX/c3djYqJSUFPl8vliXBYxo9G0MFz0bTsHPU4AhSklJ0bRp03T8+PGb3jtx4oTmzJljQ1UAgEjo2XAKQjcwDIsWLdJnn32mM2fOhF779NNPVVdXp8WLF9tYGQDgRvRsOEFcrpcAP9b69etVXl6uNWvWaN26dfL7/dqzZ49ycnJUWFhod3kAgDD0bDgBk25gGFJTU7V//35lZWVp586deuedd7Rw4ULt2bOH48oAwGHo2XACVyAQCNhdBAAAADCSMekGAAAADCN0AwAAAIYRugEAAADDCN0AAACAYYRuAAAAwDBCNwAAAGAYoRsAAAAwjNANAAAAGEboBgAAAAwjdAMAAACGEboBAAAAwwjdwBAdPnxYmZmZevbZZ/u9/vLLLyszM1OHDx+2qTIAwI3o2XAKQjcwRPn5+SoqKtKHH36o6upqSdKRI0d04MABrVy5Uvn5+TZXCACw0LPhFK5AIBCwuwjgTtPW1qaCggL5fD69++67Wrp0qdxut8rLy+Xz+ewuDwAQhp4NJyB0A8NUVVWlp59+WtOnT1dDQ4NKS0uVm5trd1kAgAjo2bAb6yXAMD388MNatGiR6uvrtWLFCpo3ADgYPRt2I3QDw9TZ2akTJ05Ikqqrq9XZ2WlzRQCAW6Fnw26EbmCYtm/froaGBhUXF6uhoUHbt2+3uyQAwC3Qs2E3QjcwDMeOHVNpaamWL1+uJ598Uo899pj279+vo0eP2l0aAOAG9Gw4ATdSAkPk9/tVWFio9vZ2HTp0SCkpKWppadEjjzyi8ePHq7y8XElJSXaXCQAQPRvOwaQbGKJdu3aprq5OL774olJSUiRJEyZM0KZNm3T27Fm9/vrrNlcIALDQs+EUTLoBAAAAw5h0AwAAAIYRugEAAADDCN0AAACAYYRuAAAAwDBCNwAAAGAYoRsAAAAwjNANAAAAGEboBgAAAAwjdAMAAACGEboBAAAAw/4P5Tcc/EZ8OuoAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "axopts = {'xlabel': 'x', 'ylabel': 'Error', 'xticks': [-1, 0, 1]}\n", "x = np.linspace(a, b, 1001)\n", "fig = plt.figure(figsize=[12, 6])\n", "\n", "ax1 = fig.add_subplot(121, title='Function approximation error', **axopts)\n", "ax1.axhline(linestyle='--', color='gray', linewidth=2)\n", "ax1.plot(f1fit.nodes, np.zeros_like(f1fit.nodes), 'ro', markersize=12)\n", "ax1.plot(x, f1fit(x) - f1(x))\n", "\n", "ax2 = fig.add_subplot(122, title='Derivative approximation error', **axopts)\n", "ax2.plot(x, np.zeros_like(x), '--', color='gray', linewidth=2)\n", "ax2.plot(f1fit.nodes, np.zeros_like(f1fit.nodes), 'ro', markersize=12)\n", "ax2.plot(x, f1fit(x, 1) - d1(x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "## Bivariate Interpolation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Approximating the function $f(x_1, x_2) = \\dfrac{\\cos(x_1)}{e^{x_2}}$. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "f2 = lambda x: np.cos(x[0]) / np.exp(x[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Set degree and domain interpolation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ```BasisChebyshev``` class can also interpolate *d*-dimensional functions. If one of the positional arguments is a scalar (like the bounds below), it is assumed that the same value holds in every dimension." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "n, a, b = 7, 0.0, 1.0\n", "f2fit = BasisChebyshev([n, n], a, b, f=f2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By default, multidimensional interpolation is done by taking the tensor product of each dimension. Other options are available with the keyword `method`, as in:\n", "```\n", "BasisChebyshev(n, a, b, method='smolyak', qn=3, qp= 3) # for Smolyak interpolation\n", "BasisChebyshev(n, a, b, method='complete', qp=2) # for complete polynomials\n", "BasisChebyshev(n, a, b, method='tensor') # tensor product (default)\n", "```\n", "\n", "Notice that Smolyak and complete polynomials interpolation require the setting of keywords `qn` and `qp`, to control node and polynomial selection, respectively." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Nice plot of function approximation error" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now evaluate the residuals over a 101 by 101 grid." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": "" }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": "
", "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nplot = [101, 101]\n", "x = nodeunif(nplot, a, b)\n", "x1, x2 = x\n", "error = f2fit(x) - f2(x)\n", "error.shape = nplot\n", "x1.shape = nplot\n", "x2.shape = nplot\n", "\n", "fig = plt.figure(figsize=[15, 6])\n", "ax = fig.gca(projection='3d', title='Chebyshev Approximation Error',\n", " xlabel='$x_1$', ylabel='$x_2$', zlabel='Error')\n", "ax.plot_surface(x1, x2, error, rstride=1, cstride=1, cmap=cm.coolwarm,\n", " linewidth=0, antialiased=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compute partial derivatives" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Partial derivatives can be computed by *calling* a `BasisChebyshev` object, indicating the order of derivatives by a second argument `order`, as in\n", "```\n", "f2fit(x, order)\n", "```\n", "\n", "Notice that unlike the MATLAB version of CompEcon, in this Python version the first index of `x` indicates the dimension, while the last index indicates an \"observation\" (evaluation point). Something similar applies to the `order` parameter: `order[i, j]` indicates the order of differentiation with respect to `i` in evaluation `j`." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x = [0.5, 0.5]\n", "f1 = -0.2908\n", "f2 = -0.5323\n", "f11 = -0.5323\n", "f12 = 0.2908\n", "f22 = 0.5323\n" ] } ], "source": [ "x = np.array([[0.5], [0.5]])\n", "order = [[1, 0, 2, 1, 0],\n", " [0, 1, 0, 1, 2]]\n", "\n", "ff = f2fit(x, order)\n", "\n", "print(('x = [0.5, 0.5]\\n' + \n", " 'f1 = {:7.4f}\\n' + \n", " 'f2 = {:7.4f}\\n' + \n", " 'f11 = {:7.4f}\\n' +\n", " 'f12 = {:7.4f}\\n' +\n", " 'f22 = {:7.4f}').format(*ff))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.3" } }, "nbformat": 4, "nbformat_minor": 4 }