{ "cells": [ { "cell_type": "markdown", "id": "d8b05cac", "metadata": {}, "source": [ "# Fit polynomials 1\n", "> Stay fit with polynomials plus a tour through named matrices." ] }, { "cell_type": "code", "execution_count": 2, "id": "d2bee436", "metadata": {}, "outputs": [], "source": [ "#hide\n", "import numpy as np\n", "import matplotlib.pyplot as plot\n", "from numpy.random import default_rng\n", "from sklearn.datasets import load_diabetes\n", "import math" ] }, { "cell_type": "markdown", "id": "7e504339", "metadata": {}, "source": [ "## Introduction" ] }, { "cell_type": "markdown", "id": "bc7a02c7", "metadata": {}, "source": [ "Fitting with polynomials is the natural step-up from linear regression: fitting with a line. This article is on interpolating series and functions with polynomials, both exact and approximately. \n", "\n", "What started as a small idea to generate a moving image of a polynomial chasing random points has evolved in a tour through nice mathematics. There is both code and mathematics so pick whatever suits you. I hope you enjoy it!\n", "\n", "We start with defining the problem and some notation. No worries, we also add graphs to make the problem explicit." ] }, { "cell_type": "markdown", "id": "3dc262ab", "metadata": {}, "source": [ "### Example inputs" ] }, { "cell_type": "markdown", "id": "97ebdd62", "metadata": {}, "source": [ "We can either be given some points $p_1,...,p_n$ or be given a function $f()$ that we want to approximate. I use these interchangably, because a function is convenient as ground truth and to approximate a function we will be sampling from that function.\n", "\n", "To make it concrete lets use some functions and sample 5 points $x_1,...,x_5$ from $[-1, +1]$. Additionally, we use the diabetes dataset from SciKit." ] }, { "cell_type": "code", "execution_count": 3, "id": "4bc75940", "metadata": {}, "outputs": [], "source": [ "# I pick an odd number since linspace then also includes 0 (the middle value)\n", "d = np.linspace(-1, 1, 101)\n", "x = np.linspace(-1, 1, 5)" ] }, { "cell_type": "code", "execution_count": 4, "id": "f3137258", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#collapse\n", "fig, axs = plot.subplots(2, 2)\n", "fig.set_size_inches(18.5, 10.5)\n", "\n", "f = lambda x: x**2\n", "axs[0, 0].plot(x, f(x), 'o')\n", "axs[0, 0].plot(d, f(d), '-')\n", "axs[0, 0].set_title('Quadratic')\n", "\n", "g = lambda x: 1/(1+(5*x)**2)\n", "axs[1, 0].plot(x, g(x), 'o')\n", "axs[1, 0].plot(d, g(d), '-')\n", "axs[1, 0].set_title('Runge function')\n", "\n", "h = lambda x: x**14-x**3\n", "axs[0, 1].plot(x, h(x), 'o')\n", "axs[0, 1].plot(d, h(d), '-')\n", "axs[0, 1].set_title('Recliner')\n", "\n", "DX, y = load_diabetes(return_X_y=True)\n", "dx = DX[:,2] \n", "# Map to [-1,1]\n", "dx = (dx - min(dx)) / (max(dx) - min(dx)) * 2 -1\n", "y = (y - min(y)) / (max(y) - min(y))\n", "\n", "axs[1, 1].plot(dx, y, 'o')\n", "axs[1, 1].set_title('Diabetes dataset')\n", "\n", "for ax in axs.flat:\n", " ax.label_outer()" ] }, { "cell_type": "markdown", "id": "a0081867", "metadata": {}, "source": [ "# Interpolation vs fit" ] }, { "cell_type": "markdown", "id": "5f90fd78", "metadata": {}, "source": [ "The goal is to recover the ground truth, given the samples. As can be seen in the examples this is possible for the first few examples, but for the diabetes example there are multiple values for the same $x$. Let's make it concrete what we're trying to do." ] }, { "cell_type": "markdown", "id": "ef37f839", "metadata": {}, "source": [ "We are given points $x_1,...,x_n$ and values $y_1,...,y_n$ and we want to select a polynomial function $p(x)$ of degree $k$:\n", "\n", "$$ p_k(x) = c_0 x^0 + c_1 x^1 + ... + c_k x^k $$\n", "\n", "For _interpolation_ we want that $p(x_i)=y_i$ for $i=1,...n$." ] }, { "cell_type": "markdown", "id": "0789b9f4", "metadata": {}, "source": [ "For _approximation_ we want to find a polynomial that approximates the value. For this we take the $L_2$ or squared difference distance:\n", "\n", "$$ \\min_{p_k(x)} \\sum_i ( y_i - p_k(x_i) )^2 = \\min_{p_k(x)} || y_i - p_k(x_i) ||_2 $$" ] }, { "cell_type": "markdown", "id": "94fd6657", "metadata": {}, "source": [ "# Interpolation of a polynomial with monomials" ] }, { "cell_type": "markdown", "id": "8071f79a", "metadata": {}, "source": [ "For $n$ points there exists a unique polynomial of degree $n-1$ that passes through these points. To find this polynomial we can solve a linear system of $n$ equations with $n$ variables. \n", "\n", "## Example for n=2\n", "As an example take the points $(-0.5,0.25), (0, 0), (0.5, 0.25)$ and we want to find a quadratic polynomial $p(x) = c_0 + c_1 \\cdot x + c_2 \\cdot x^2$.\n", "\n", "The linear equations will be\n", "$$p(-0.5) = 0.25 = c_0 + c_1 \\cdot -0.5 + c_2 \\cdot (-0.5)^2 $$\n", "$$p(0) = 0 = c_0 + c_1 \\cdot 0. + c_2 \\cdot 0^2 $$\n", "$$p(0.5) = 0.25 = c_0 + c_1 \\cdot 0.5 + c_2 \\cdot (0.5)^2 $$\n", "\n", "\n", "For this example we can solve by hand by noting that $c_0=0$ (second equation), which leaves\n", "$$ 0.25 = -c_1/2 + c_2/4 $$\n", "$$ 0.25 = c_1/2 + c_2/4 $$\n", "\n", "and thus $c_1=0$ and $c_2=1$.\n", "\n", "This is a good thing since I picked the points from the function $f(x) = x^2$ :)." ] }, { "cell_type": "markdown", "id": "5c56f76e", "metadata": {}, "source": [ "## Matrix notation" ] }, { "cell_type": "markdown", "id": "cb10b218", "metadata": {}, "source": [ "It is convenient to write the equations above in matrix form and make the _coefficients_ $c$ explicit. In the optimization we keep degree $k$ fixed, but have to pick the best $c$." ] }, { "cell_type": "markdown", "id": "2f3bb846", "metadata": {}, "source": [ "We can do this in matrix form and state $A_k(x)c=y$, where $A_k(x)$ is the matrix for the values $x$ and the powers up to $k$ (the _monomials_):\n", "\n", "For $k=2$ it would be \n", "\n", "$$A_2(x) = \n", "\\begin{bmatrix}\n", "1 & -.5 & .25 \\\\\n", "1 & 0 & 0 \\\\\n", "1 & .5 & .25 \\\\\n", "\\end{bmatrix}\n", "$$\n" ] }, { "cell_type": "markdown", "id": "a42ee8d4", "metadata": {}, "source": [ "For approximation we would write\n", "\n", "$$ min_c ||y - A_k(x)c||_2 $$" ] }, { "cell_type": "markdown", "id": "e22da3a9", "metadata": {}, "source": [ "The matrix of the _monomials_ is called the Vandermonde matrix. Using the functionality in NumPy gives the same matrix as above (but for two extra points):" ] }, { "cell_type": "code", "execution_count": 22, "id": "1fe608fb", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "array([[ 1. , -1. , 1. ],\n", " [ 1. , -0.5 , 0.25],\n", " [ 1. , 0. , 0. ],\n", " [ 1. , 0.5 , 0.25],\n", " [ 1. , 1. , 1. ]])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.vander(x, 3, increasing=True)" ] }, { "cell_type": "markdown", "id": "3172506b", "metadata": {}, "source": [ "## General" ] }, { "cell_type": "markdown", "id": "9faede5b", "metadata": {}, "source": [ "Equiped with matrix notation we solve $Ac=y$ for $c$. For example by taking the inverse $A^{-1}y=c$. " ] }, { "cell_type": "code", "execution_count": 23, "id": "05f710fb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0., 0., 1.])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = np.array([[1, -1/2, 1/4], [1, 0, 0], [1, 1/2, 1/4]])\n", "y = np.array([0.25, 0., 0.25])\n", "c = np.linalg.inv(A) @ y\n", "c" ] }, { "cell_type": "markdown", "id": "770fcf14", "metadata": {}, "source": [ "We can do the same programmatically for the Runge function and degree $4$" ] }, { "cell_type": "code", "execution_count": 24, "id": "ae53a4ec", "metadata": {}, "outputs": [], "source": [ "#collapse\n", "def interpolate(f, x):\n", " M = np.vander(x, increasing=True)\n", " c = np.linalg.inv(M) @ f(x)\n", " return c" ] }, { "cell_type": "code", "execution_count": 25, "id": "e95ed352", "metadata": {}, "outputs": [ { "data": { "image/png": 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dXU5HkUBTvi54cyB1C8YYutfsztwdc9mfvd/pZCIiIsWGSo8jqFChIQMiajI+awc7dyx2Oo6IiJRQ6Qd282nyEjqbKBrUO9vpOBJoyv91Bxffuh5n1TyLXG8uMxI1U1VEROQvKj2O4upOjwDw0a+6/lpERArmm5kPkOoyDG51i9NRJBCVr+t7zlvXo1mFZsRFxDF1s+7iIiIi8heVHkdRtWob+oRU4puDG0lOXu90HBERKWGys9L4aOcs2tpQWjS9zOk4EogiykFYLCStA8BlXHSr0Y3ft/9Oek66s9lERESKCZUe/+Ha9veTZeDTX+51OoqIiJQw380YwW63YXCTa5yOIoHKGN9sj71//3Kme83uZHmymLFVl7iIiIiASo//VLvWmXQPKstnqatITd3idBwRESkhcnLSeX/rVJp5g2jf+kan40ggq1APktYe+rJVpVbEhccxaeMkB0OJiIgUHyo9juH6dvdw0GX4bLpme4iIyPGZ8OujbHPD9Y0GYlz6USuFqFITSNsBB/cCvktceiT04Ndtv5KWneZwOBEREefpTOwYGtQ7my4mmk/3LeVA2g6n44iISDHnyc3mvU0/0sDrovOptzsdRwJdpaa+511/HHqpd63e5HhzmJ443aFQIiIixYdKj+NwQ5vb2e8yfPnLfU5HERGRYm7K70+yyQ3X171Qszyk8FVu5nveufzQS80qNKNaVDUmbpzoUCgREZHiQ2djx6Fp4wvpSAQfJ80nPT3J6TgiIlJMeT25vPPnt9T2GLp1uMfpOFIaRFaA6Cqw8++ZHsYYeib0ZM72OaRkpjiXTUREpBhQ6XGcbmh5C8kuw5hf7nc6ioiIFFPT5zzPepeX62r3w+UOcjqOlBaVm8Gu5f94qVdCL3JtLlO3THUolIiISPGg0uM4tWw+kLY2lFE7fycrM9XpOCIiUsxYr5e3135BDQ/06qiCXIpQpaawZzXkZh16qWG5hiSUSdBdXEREpNRT6XECbmh+PXvchm9/ecDpKCIiUsz8Ov81Vrk8DK7Ri6DgMKfjSGlSuRl4c2HPmkMv/XWJy/xd80nK0KW5IiJSeqn0OAGnthhMCxvM+9unk52l28CJiIiP9Xp5e+WHVPFYzun0sNNxpLQ5tJjpH/94uXet3nitlymbpjgQSkREpHhQ6XECjMvFjU2uZafbMG7Gg07HERGRYmLWwpEsc+VyXfXuBIdGOh1HSptytSEo/F/retSJrUO9svWYvGmyQ8FEREScp9LjBLVvfSPNvcG8t3UqOVkHnY4jIiIOs14vI5d/QBWPpX/nx52OI6WRyw2Vmvxrpgf4FjRdtHsROw/udCCYiIiI81R6nCDfbI9r2OE2jJuhtT1EREq72QvfZJkrh8HVztIsD3FO5aa+0sPaf7zcK6EXABM3TnQilYiIiONUehRAxzY308wbpNkeIiKlnPV6eXPF+1TyWPp30SwPcVDlZpCZAvu3/ePlGmVq0LxCc3748wdncomIiDhMpUcBGJeLIY2vZrsbxs8c4XQcERFxyJzF77DE5DC4aldCQqOdjiOlWaUjL2YKcE6dc1i7by1rktf86z0REZFAp9KjgDq1vYWm3iDeTZxCTk6603FERKSIWa+Xt/54lziPZUDXJ52OI6VdpcaAgZ3L//VWr4ReBJkgzfYQEZFSyS+lhzGmlzFmjTFmvTHmniO8X8MYM90Ys9gYs8wY08cfx3WScbm4sfGVbHPD9zM020NEpLSZu/hdFplsBlftolke4rzQaChXC3Yu+9dbZcPKcnr105nw5wQ8Xo8D4URERJxz0qWHMcYNvAH0BhoDlxpjGh+22QPAV9balsAlwMiTPW5x0KntbTTxunlny2TN9hARKUWs18ubf7zjm+XR5Qmn44j4VGr6r9vW/qVv7b7sztjN3J1ziziUiIiIs/wx0+NUYL219k9rbTbwBdDvsG0sUCbvzzHAdj8c13HG5eKmxlexzQ3jf3nQ6TgiIlJE5ix+59Asj9CwGKfjiPhUbg7Jf0JW2r/e6hzfmejgaH7YoEtcRESkdPFH6VENSMz39da81/J7GBhojNkKTABu8cNxi4VObW+jmTeItxMn604uIiKlgPV6eWPZO1TyWM7v+pTTcUT+Vrmp73nXyn+9FeoOpUdCD6ZumUq6ZqeKiEgpUlQLmV4KfGitrQ70AT4xxvzr2MaY640xC4wxC/bs2VNE0U6Ocbm4uem17HAbvv3lPqfjiIhIIft9wRssdeVwffVuWstDjsix85nKf93B5d/regD0rdOXjNwMft7yc9FlEhERcZg/So9tQHy+r6vnvZbftcBXANba2UAYUOHwgay171hr21hr21SsWNEP0YpGh9Y30cIG8862n8nKTHU6joiIFBLr9fL6ivep6oHzOmstDzkyx85nylSDsNijruvRMq4lVSOr6i4uIiJSqvij9JgP1DPG1DLGhOBbqHT8YdtsAc4CMMY0wld6lIypHMfBuFzc3OwGdrkNYzTbQ0QkYM2Y9xIrXB5uqNGT4NBIp+OI/JMxvtkeR7htLYDLuDi79tnM2TGHPekBcxomIiLyn0669LDW5gJDgcnAKnx3aVlhjHnUGHNu3mb/A64zxiwFPgeuttbakz12cdKu5XW0tqG8t30GmRn7nI4jIiJ+Zr1e3lj1MdU90Lfzo07HETmyys1g1wo4yq1p+9bpi9d6mbBxQhEHExERcYZf1vSw1k6w1ta31tax1j6R99oIa+34vD+vtNZ2tNaeYq1tYa2d4o/jFifG5eLmFjexx234evo9TscRERE/mzb7WVa7vNyY0Jfg4Ain44gcWeVmkJsBSWuP+HatmFo0q9CMcevHEWC/fxIRETmiolrItFRo22IQ7QjjvV2/k56e5HQcERHxE68nlzfWfk6CB/p0GuF0HJGjq36q7zlx7lE36V+3P+tT1rM86ciXwYiIiAQSlR5+NrTVMJJdhs9/Hu50FBER8ZPJvz3OOpeXIbXPIyg4zOk4IkdXvg5ElIfEeUfdpHet3oS5w/h2/bdFGExERMQZKj38rEWzy+lkIvkgaT5p+w+/iY2IiJQ0uTmZjNwwhrpeF701y0OKO2Mgvh1smXPUTaJDoumR0IOJGyeSkZtRhOFERESKnkqPQnBLu3vZ7zJ8/POdTkcREZGT9P2MB9nkhqENLsPlDnI6jsixxbeD5A1w4Oh3aOlftz8Hcg7w0+afijCYiIhI0VPpUQgaNehHd1csH6f8wb7kDU7HERGRAsrOSuPNLRNp6g3izNN02aKUEDVO8z1vPfolLm0qtaFGdA2+XadLXEREJLCp9CgkQ09/mEwDH0zTbA8RkZLqm+n3sMNtuKXpYIxLPzKlhKjSAtwh/3mJizGG8+qdx4JdC9iyf0vRZRMRESliOoMrJLVrncU5IXF8nraO3bu0OrqISEmTkZ7Mu9tn0NqG0r71jU7HETl+wWG+4uM/7uACcG6dc3EZlxY0FRGRgKbSoxAN6fQEHgPv/HKX01FEROQEff7znSS5Dbe2vFWzPKTkqdEOti+GnMyjbhIXEUenap0Yv348ud7cIgwnIiJSdHQWV4ji49szIKw6YzK2sHXr0aeYiohI8XIgbQcfJM3jdCJpdcqVTscROXHxp4EnG3Ys/c/Nzqt7HrszdjNr+6wiCiYiIlK0VHoUsuu7Povbwpsz73M6ioiIHKcPp95OqstwS7t7nI4iUjDxp/qeE//7ly5nxJ9BubByjF03tghCiYiIFD2VHoWsUqXmXBZdj++zd7Nu/SSn44iIyDEkJa3m45Tl9HSXpXHD/k7HESmYqDgoVxu2/Pe6HsGuYPrV6ceMxBnsST/6LW5FRERKKpUeReDabi8RZeHVWY86HUVERI7h3Wl3km1g6OmPOR1F5OTEn+ZbzNTa/9zs/Prnk2tzGbNuTBEFExERKToqPYpATGwC15RvxS82jcXLPnU6joiIHMXWrXP4Kn0T54VVIyGhs9NxRE5OjXaQngTJf/7nZjXL1KR9lfZ8s/YbLWgqIiIBR6VHEbm824tU8FheXvQS1ut1Oo6IiBzByBn34bYwpOtzTkcROXnx7XzPW469mPrFDS5mV/ouZm6dWcihREREipZKjyISEVGBIdXOZJHJ5tf5rzkdR0REDrNm3Y/8kLOby8s0oFKl5k7HETl5FRpAWMwxFzMF6BzfmbiIOL5a81URBBMRESk6Kj2K0IAznybeA6+s/ACvR9NHRUSKk9dmP06UhUHdXnI6ioh/uFy+2R6J8465aZAriAvqXcDv238ncX9iEYQTEREpGio9ilBwcARD6wxgrcvLjzMfdjqOiIjkWbzsU2bYAwyq0IaYmBpOxxHxn/h2sGc1pCcfc9MB9QbgNm6+Xvt1EQQTEREpGio9iliv0x+kodfFGxu/Izsrzek4IiKlnvV6eXHRi1T0WC4/60Wn44j411/remydf8xNK0VWomt8V75d/y1ZnqxCDiYiIlI0VHoUMZc7iNubXs82N3zx8/+cjiMiUupNm/0sS0wON8X3IDyinNNxRPyrehtwh8KfM45r84saXERKVgpTNk0p5GAiIiJFQ6WHAzq0vZn2hPPOrlnsT9V1syIiTsnJSeflNaOp7TH07/Kk03FE/C84HBI6wvqpx7V5uyrtqFmmphY0FRGRgKHSwyG3n3Y/qS7D+1OHOR1FRKTU+nbavWxyw7BGVxIUHOZ0HJHCUbcbJK2BlC3H3NRlXFxY/0KW7FnC6uTVRRBORESkcKn0cEijBv04O6gCo/evYeeOxU7HEREpddIP7Gbktp9pZUPo0u4Op+OIFJ663X3P638+rs371+1PeFA4n678tBBDiYiIFA2VHg66pcszeA28MX2401FEREqdj6bezl634Y42wzEu/TiUAFahHsTUOO5LXGJCYzi3zrlM2DiBpIykQg4nIiJSuHSW56Bq1U7l0sg6fJe9k7XrJzodR0Sk1EhKWs2ofUvp7orhlKaXOB1HpHAZA3XP8i1mmpt9XLtc3uhycrw5un2tiIiUeCo9HHZ991eIsvDS7484HUVEpNR46+c7yDFwa6cnnI4iUjTqdoPsNNg677g2rxVTi07VOvHl6i/J9hxfUSIiIlIcqfRwWExsAtdVbMdvHGT2wrecjiMiEvD+3Pgz32Rs4fzwGiQkdHY6jkjRqHUGuIKO+xIXgIGNB7I3cy+TNk0qxGAiIiKFS6VHMXBZtxep6oHnl72J5zinnYqISMG8+OsDhFu4qfurTkcRKTphZaBGe1h3/KVH+yrtqRNTh09Xfoq1thDDiYiIFB6VHsVAaFgMw+qcz1qXl/G/3O90HBGRgDV30TvMsAcYXKEt5crVdTqOSNGqexbs+gP27ziuzY0xDGw8kFXJq1i4a2EhhxMRESkcKj2KiV6dRtDcG8RrWyaSnq6V0kVE/M3ryeX5pW9Q1QMDu7/sdByRole3m+95w7Tj3uWc2ucQGxrLp6t0+1oRESmZVHoUE8blYnibO9njNnw05Van44iIBJzvZzzAapeX2+oMIDQsxuk4IkWvUlOIqnxC63qEBYVxYf0LmbZlGolpiYUYTkREpHCo9ChGWjS7nO6uWEbtW8buXcudjiMiEjAy0pN5ddMPNPMG0bvTQ07HEXGGMb7ZHhumgddz3Ltd3OBi3MbN6FWjCzGciIhI4VDpUczc3uVpcgy8Pm2Y01FERALGRz/dym63YXjr/2Fc+tEnpVjdsyAzBbYd/xodlSIr0ad2H8auG0tKZkqhRRMRESkMOvMrZuLjO3JZZB3GZe1k9ZrxTscRESnx9uxewQfJS+juiqFl84FOxxFxVu0uYFyw7qcT2m1Q00Fk5Gbw+erPCyeXiIhIIVHpUQxd3+M1Yiw8O/tRrNfrdBwRkRLtlam3kWvg9i7POB1FxHkR5SC+Haz+8YR2qxNbhy7VuzB69WjSc9ILKZyIiIj/qfQohmJianBzla7MN1lMm/2s03FEREqsFavH8l3OLgZG1yc+vqPTcUSKhyYDYPcK2L3qhHa7ttm1pGal8u36bwspmIiIiP+p9CimLjjrOep6DM+vGU12VprTcUREShzr9fLMnCco57Vc3+MNp+OIFB+N+/kucVk+9oR2axHXglZxrfhoxUfkeHMKKZyIiIh/qfQopoKCwxjefAhb3fDplNucjiMiUuJM/u1xFptsbq3ek6joKk7HESk+oitBQidYPgasPaFdr212LTsO7mDSxkmFFE5ERMS/VHoUYx3a3ERnE8U7SfNISlrtdBwRkRIjM2MfL67/igZeF/27PuV0HJHip+n5kLwBdiw5od06VetE3di6fLD8A7xW646JiEjx55fSwxjTyxizxhiz3hhzz1G2ucgYs9IYs8IY85k/jlsa3HnG02QZeP2nW52OIiJSYnz8063scBvubnEr7qAQp+OIFD+N+oIr2Dfb4wQYYxjUdBDrU9bz69ZfCymciIiI/5x06WGMcQNvAL2BxsClxpjGh21TD7gX6GitbQIMO9njlhYJCZ25NLIOY7O2s2rNd07HEREp9nbvWs57exfTzRVD25bXOh1HpHiKKAd1z4Ll38IJ3imuV61eVImswrt/vIs9wctjREREipo/ZnqcCqy31v5prc0GvgD6HbbNdcAb1tp9ANba3X44bqkxpMfrxFp4WrewFRE5ppem3kKugTu6POd0FJHiren5sH8rbJ13QrsFu4K5tum1LN2zlNk7ZhdSOBEREf/wR+lRDUjM9/XWvNfyqw/UN8b8boyZY4zp5YfjlhplYuK5tXoPFplsJv76iNNxRESKrcXLPuWH3CSuLtOY+Pj2TscRKd4a9IagsBO+xAXgvHrnUSmiEm8tfUuzPUREpFgrqoVMg4B6QBfgUuBdY0zs4RsZY643xiwwxizYs2dPEUUrGc7r+jSNvG5e2DCG9AOaKCMicjhPbjZPLXyeSh7L4F4jnY4jpViJOZ8JjYb6PWHFt+DJPaFdQ9whDG42mMW7FzNnx5xCCigiInLy/FF6bAPi831dPe+1/LYC4621OdbajcBafCXIP1hr37HWtrHWtqlYsaIfogUOd1AI97UZzm634d3JNzkdR0Sk2Bk77W5WuTzcWfdCIiIqOB1HSrESdT7T9Hw4uAc2nfiipAPqDSAuIo43l76p2R4iIlJs+aP0mA/UM8bUMsaEAJcA4w/bZhy+WR4YYyrgu9zlTz8cu1Rp0exy+gZV5KO01WzZ8pvTcUREio3U1C28uu0nWttQep7+oNNxREqOej0gJKpAl7jkn+0xd+fcQggnIiJy8k669LDW5gJDgcnAKuAra+0KY8yjxphz8zabDOw1xqwEpgPDrbV7T/bYpdHt3V8j2MKzvwx3OoqISLHxxqQb2W/g3g4PY1xFdeWmSAAIDoeGZ8PK8ZCdfsK7H5rtsUSzPUREpHjyy5mhtXaCtba+tbaOtfaJvNdGWGvH5/3ZWmvvsNY2ttY2s9Z+4Y/jlkYV45owpGI7ZtgDzJz7itNxREQct3b9RL7M2MyF4TVoUP8cp+OIlDytroKsVFj+zQnvGuoOZXCzwSzavUizPUREpFjSr8NKoIHdXyXBA8+seI/srDSn44iIOMZ6vTz524NEW7ilpxYvFSmQmh2gYiOY9y4UYLbGgHoDiAvXbA8RESmeVHqUQMGhkdzbbAhb3PChFjUVkVLshxkjWGiyGFa9BzGxCU7HESmZjIFTB8POZbB1wQnvHuoOZXBz32yP37f/XggBRURECk6lRwnVoe3NdHfF8u7exWzbNs/pOCIiRS5t/zZe2DiOZt4gBpz5rNNxREq25hdDSDTMf69Au19Q7wKqRVXj5YUv47VeP4cTEREpOJUeJdhd3V7FAM/8fLvTUUREitzISUNIdsH9pz2Ayx3kdByRki00Gk65BFaMhYNJJ7x7sDuYoS2HsmbfGiZtnFQIAUVERApGpUcJVrlKS4ZUOJXpdj8z577kdBwRkSKzZu0PfJa+kYvC4mnS6Hyn44gEhraDwZMNiz8p0O59avWhftn6vLb4NXI8OX4OJyIiUjAqPUq4K3q8Ri2P4akVH5CVmep0HBGRQuf15PLErIeIsXBLrzedjiMSOOIaQkInmP8BeD0nvLvLuLit1W1sPbCVMevGFEJAERGRE6fSo4QLDo3k/hZD2eqGDyZpUVMRCXzfz3iAxSab2+N7a/FSEX9rOxhSt8C6KQXavVO1TrSu1Jq3lr5Fek66n8OJiIicOJUeAaBdq+vp7S7HeylL2bLlN6fjiIgUmtSUTby4+QdO8QbTr+tTTscRCTwNz4boKgVe0NQYw7BWw9ibuZdPV33q53AiIiInTqVHgLiz+xuEWHhi+h1Yr1ZNF5HA9NLE60k18GDHR7V4qUhhcAdD66th/VRIWlegIVrEtaBrfFdGLR/Fvsx9/s0nIiJyglR6BIi4Sk25pUpnZpHB5N8eczqOiIjfLfljNGOydzAwsi4N6p/jdByRwNVmEASFw68vFHiI21rdRnpuOiOXjPRjMBERkROn0iOAXNztJZp43Tyz/mv2pyY6HUdExG9yctJ5ZMGzVPZYbur9jtNxRAJbVBy0vRaWfQl7NxRoiDqxdbiw/oV8vfZr1u9b7+eAIiIix0+lRwBxB4XwYPsRJLvg1Uk3OB1HRMRvPpk0lPUuL/c2vJKIqDin44gEvg63gjsEZj5f4CFubnEzEcERPLfgOay1fgwnIiJy/FR6BJgmDQdwaUQtvsrYwh8rvnY6jojISdu2bR5vJs2ji4nmzA53OR1HpHSIrgRtTm62R9mwstx4yo3M2j6LX7f96ueAIiIix0elRwAa2vsdKnrh0XmPk5uT6XQcEZECs14vT/18Gwa4r9trTscRKV063uZb2PQk1va4pOElJJRJ4Ln5z5HjzfFjOBERkeOj0iMARUVX4Z76l7Ha5WX0lFucjiMiUmA//f4kM+wBbqp4GlWqtnY6jkjpEl3Jt6jp0i8g+c8CDRHsCmZ42+Fs2r+JL1Z/4eeAIiIix6bSI0B163APXUw0b+yezdatc5yOIyJywlJTt/DUui9o5HUzsOfrTscRKZ3+mu0xs+CzPTpV60SHqh14c+mbuoWtiIgUOZUeAcq4XNzf/Q0M8NjPt2K9XqcjiYickJcmDCbZBQ+1H0FQcJjTcURKp+jK0PpqWPo5JG8s0BDGGO5qexfpOem8tliXqYmISNFS6RHAKldpyW1VOjOLDH6YMcLpOCIix23Bkg8Zk72DKyLr0qThAKfjiJRuHYf5Znv8/GiBh6gTW4fLGl3GN2u/YdmeZf7LJiIicgwqPQLcxd1eork3mOc2jWNfcsFWXxcRKUpZmak8suhFqnngprPfczqOiJSp4is+VoyFTb8VeJibW9xMxYiKPDbnMXK9uf7LJyIi8h9UegQ4d1AID3d6kjQDz028zuk4IiLH9O7EG9jktoxoNoSIiApOxxERgNOHQUwNmHAXeApWWEQGR3J327tZnbyaz1d/7t98IiIiR6HSoxSoV7cXg2Ka8H3uHmbNf8PpOCIiR7V+wxTeT11O36CKdGh7s9NxROQvweHQ83HYvQIWjirwMN1rduf0aqfz+uLX2XVwlx8DioiIHJlKj1Li+t7vkOAxPPLHW6Qf2O10HBGRf/HkZjNi5t1EWxje+12n44jI4RqdC7U6w7TH4eDeAg1hjOG+dvfhsR6enf+snwOKiIj8m0qPUiI0LIZH29zFDpfl5R+vcTqOiMi/fDr5Zv5w5XJfnQspW66O03FE5HDGQO9nISsNpj1W4GHio+O5rtl1TNk8hd+2FXyNEBERkeOh0qMUadl8IJdH1OLzzC0sXPqR03FERA7ZvPlXXts9m66mDD1Pf9DpOCJyNHENod0NsPBD2L6kwMNc0/QaEsok8Picx0nPSfdbPBERkcOp9ChlbjlnFNU88NDC58nM2Od0HBERvJ5cRkwfRgjwQM+3MS79aBIp1rrcA5EV4IfbC7yoaYg7hIc7PMz2A9t5edHL/s0nIiKSj84sS5mIiAo80uIWNrth5I+DnI4jIsKXPw1jkcnmrhpnE1epqdNxRORYwmJ8l7lsXwS/vVTgYVpXas1ljS7j89Wfs2DnAj8GFBER+ZtKj1KoXavruSC0Kh8dWMcfK752Oo6IlGLbts3jpR2/0JEI+nV9yuk4InK8mg6AphfAjKdP6jKXW1veSvWo6oyYNYKM3Az/5RMREcmj0qOUuqPPB1T0woNzHyMrM9XpOCJSClmvl4enDsUAI7q/octaREqaPs9BZEX49gbIySzQEBHBETza8VES0xJ5ddGrfg4oIiKi0qPUii5TjYeb3sAGt9VlLiLiiK9+GsYcMvhftW5UrdrG6TgicqIiysG5r8Oe1Sd1N5e2ldtycYOLGb1qNIt3L/ZjQBEREZUepdrpp97C+SFV+DBtDUuXf+F0HBEpRRITZ/PC9ml0IJwLu73odBwRKah63aDNIJj9Bmz6vcDD3NH6DqpEVmHE77rMRURE/EulRyl35zkfUckLD8x7goz0ZKfjiEgp4PXk8uDPt+AGHumhu7WIlHjdH4OyNeHbIVDAc4m/LnPZvH8zz89/3s8BRUSkNNOZZikXFV2Fx1rcyiY3vPrj1U7HEZFS4LMpQ1losrirRh8qV2npdBwROVmhUTDgPUjbAWOvA6+nQMO0q9KOq5tczVdrv2Lalml+DikiIqWVSg+hXavruSQsntEH/2TBkg+djiMiAWzTphm8svM3Opso+nd92uk4IuIv8W2h9zOwfir8UvA7Md3S8hYalWvEQ7MeYk/6Hj8GFBGR0kqlhwBw+9kfUs1reGDRCxw8sNPpOCISgHJzMnlg+u2EAA/1ek+XtYgEmjaDoOVAmPkcrP6xQEMEu4N5+oynyczN5P7f7sdrvX4OKSIipY3OOAWAiKg4nmg9nO0uy3PfX+l0HBEJQKMmXs9SVw731z6finFNnI4jIv5mDPR5Aaq2hLE3QNK6Ag1TO6Y2d516F7N3zOaTlZ/4OaSIiJQ2Kj3kkFanXMk10Q0Yk72DX+a84HQcEQkgK1ePY2TyInq7y9Gn8yNOxxGRwhIcBhd9AkEh8MXlkLm/QMNcUO8CusZ35ZVFr7By70o/hxQRkdJEpYf8w83nfEgDr4uHVo1ib9Jap+OISADIzNjHvbNGUM4L95/zkdNxRKSwxcbDBaNg73r4ciDkZp/wEMYYHunwCOXCyvG/X/5HalZqIQQVEZHSQKWH/ENIaDRPdXqGAwYemXAN1qtraUXk5Lz8/ZX86bY81vwmYmITnI4jIkWhdmfo9zpsnAHjboQCnE+UDSvLC11eYGf6Th747QGt7yEiIgWi0kP+pV7dXtwW14Hpdj/jpt3tdBwRKcFmLRjJ6IxNXB6eQIc2NzkdR0SKUovLoNvDsPwb+OnBAg1xSsVTuLPNnfyy9Rc+WP6Bf/OJiEip4JfSwxjTyxizxhiz3hhzz39sd74xxhpj2vjjuFJ4BvYcyak2lKcTJ5KYONvpOCJSAqWmbOLBZSOp5TEM6/ux03FExAkdh0G7ITD7dZj1WoGGuKzhZfRO6M1ri19j7o65/s0nIiIB76RLD2OMG3gD6A00Bi41xjQ+wnbRwG2AflqVAC53EE/0fBc3cM/Um8jJSXc6koiUINbr5eHvB5Lsgqc6PExYeFmnI4mIE4yBnk9Bk/NgygOweHQBhjA83OFhEsokcNfMu9h1cFchBBURkUDlj5kepwLrrbV/WmuzgS+AfkfY7jHgGSDTD8eUIlC5SktG1LmIZa5c3vrhGqfjiEgJMvbn4Uz1pnJrhXY0aTjA6TgiRcoYc70xZoExZsGePXucjuM8lwvOextqd4XvbobFn57wEBHBEbzU5SUycjO4/ZfbyczV6aSIiBwff5Qe1YDEfF9vzXvtEGNMKyDeWvvjfw2kk4Tip9cZIzgvpBLvpq5g/hJdSysix7Zx0y88s3Uy7Qjjqt5vOx1HpMhZa9+x1rax1rapWLGi03GKh6BQuPRzqNMVvhsKi078krfasbV5qtNT/JH0ByN+H4G1thCCiohIoCn0hUyNMS7gReB/x9pWJwnF0z19P6OG13DvohdJTd3idBwRKcays9K4e/owQoEne43C5Q5yOpKIFBfB4XDJ51D3LBh/CywYdcJDnFXjLG5rdRsTN03k7WUqVUVE5Nj8UXpsA+LzfV0977W/RANNgV+MMZuA04DxWsy05IiIiuOZ9g+z1wWPjL9ct7EVkaN67fsrWeXy8EiDK4mr1NTpOCJS3ASHwcWjoV4P+GEYzHv3hIe4tum19K3dlzeWvMHkTZP9n1FERAKKP0qP+UA9Y0wtY0wIcAkw/q83rbWp1toK1toEa20CMAc411q7wA/HliLSpNH53FL+VH7ypjD25+FOxxGRYmjWgpF8eHA9F4dW58wOdzkdR0SKq+AwuPhTaNAHJtwJ0x6HE7hU5a+FTVtUbMEDvz3AiqQVhRhWRERKupMuPay1ucBQYDKwCvjKWrvCGPOoMebckx1fio+r+7xDO8J4eutk1m+Y4nQcESlGkvas4t4/RlLHY/jfuSd+dwYRKWWCQuGiT6DVlTDzOd8Cp56c4949xB3Cy11fpmxYWYZOG8rWtK2FGFZEREoyv6zpYa2dYK2tb62tY619Iu+1Edba8UfYtotmeZRMLncQT/f5mAhg+Iw7yUhPdjqSiBQDntxs7plwJenA852fJzyinNORRKQkcAdB31ehy72wZDR8fglkHTju3cuHl2fkWSPJ9mQzZOoQ9mbsLcSwIiJSUhX6QqYSWCpUbMRTzW5ig8vLM99d4nQcESkG3p9wLXPJ5N74XtSt08PpOCJSkhgDXe6Bc1+DDdPhwz6Quu3Y++WpW7Yub5z1BrsO7uLmn2/mYM7BQgwrIiIlkUoPOWEd2tzE4DKNGJO9gx9/GeF0HBFx0MKlH/FG8mL6BJXnvDOfdTqOiJRUra6ES7+AvRvgnS6wZc5x79oirgXPd36e1cmrGTZ9GDkncJmMiIgEPpUeUiA39f2EljaERzeOZfPmX52OIyIO2Je8gbsWPkd1r2FEvy8wLv1IEZGTUL8HDP4ZQqPhw3NgwQfHvWvn+M483OFh5uyYw/2/3Y/H6ynEoCIiUpLoDFUKJCg4jGd7vkcwcOe0oWRlpjodSUSKkNeTy/0/XM4+Fzzf8XEioyo7HUlEAkFcQ7huGtTuDD/cDt8Pg9ys49q1f93+3N76diZumshDsx7Ca72Fm1VEREoElR5SYJWrtOSJRoNY7fLy1LcXOh1HRIrQ+z8O4ld7kLsqd6VRg35OxxGRQBIeC5d9BR2HwcJR8H4P32Uvx2FQ00HceMqNfLfhOx6Z/YiKDxERUekhJ6fzaXcwOKoBY7J38N20e5yOIyJFYO6id3g9eRF9gspzcY9XnI4jIoHI5Ybuj8DFo2HfJni7M/zxzXHteuMpN3J98+sZu24sj815TMWHiEgpp9JDTtrN535KWxvK45t/YO36iU7HEZFCtGvXMu5a+ioJXhcP9ftK63iISOFqdA4M+Q0qNYYx18J3QyE7/T93McYwtMVQrmt2Hd+s/YYn5jyBtbaIAouISHGjs1U5aUHBYTx79idEWbhj5l0cSNvhdCQRKQQ5OencNfEaMoCXur5ERFSc05FEpDSIjYerJ0Cn/8HiT+HtTpA4/z93McZwS8tbGNR0EF+t/YqHZz9Mrje3iAKLiEhxotJD/KJCxUY81+pOtrosI8ZdhPVqKqlIoHll3GUsMtk8XPt8atc6y+k4IlKauIPgrBFw1XjIzYYPesBPD/3nIqfGGIa1GsYNzW9g7LqxDJ8xnGxPdhGGFhGR4kClh/hNmxZXc1uFdvzkTeHjiTc4HUdE/GjSzEf5KH0DF4fF06fzI07HEZHSqtYZcOPv0HIg/P4yvNMFti856ubGGIa2HMrdbe9m6pap3PTzTRzMOVhUaUVEpBhQ6SF+dXWfd+nuiuHFPbOZs/Btp+OIiB+sWz+JERu+4hRvMHf3/9rpOCJS2oWVgXNfg8u+hvRkePdMmHw/ZB+9zBjYeCBPnP4EC3YuYPDkwezL3FeEgUVExEkqPcSvjMvFY+d9Qy2vi+HLXmP79gVORxKRk7A/NZFhM4cTaeHFPh8THBrpdCQREZ/6PeDmOb5ZH7NfhzfawdrJR9383Drn8lKXl1i7by1XTLyCTambii6riIg4RqWH+F1kVGVePvM1coFhkweTmaHfpoiURF5PLvd8dyHbXZYXWt9FXKWmTkcSEfmn8LJw7qtwzSQIiYTPLoIvr4CUxCNu3rVGV97r+R77s/Zz+YTLmbdjXhEHFhGRoqbSQwpFQkJnnmx4NatcHh779gItbCpSAr05/gp+tQe5q3IXWp1ypdNxRESOrmZ7uOFXOPMBWDcFXm8Lvzx9xNvbtoxryeizR1MxvCI3/ORb5FRERAKXSg8pNF3b38mQMk0Zn7Obzybf7HQcETkB02Y9y1v7l3NucByX9HjV6TgiIscWFAJnDIehC6BBL/jlKV/5sXwMWPuPTeOj4/mkzyecWuVUHpr1EM/Pf163tBURCVAqPaRQ3XjuJ3Qx0Ty361dmL3zL6TgichzWrp/IPWs+pqk3iAfP+wbj0o8KESlBYuPhwg/h6gm+y1++GQTvd4dNv/9js+iQaN446w0ubXgpH638iOumXEdSRpIzmUVEpNDoTFYKlcsdxNMDxlLL6+LOZa+zZctvTkcSkf+wL3kDt868iygLL/f5iLDwsk5HEhEpmISOcMMM6PsqpG6FD/vAZxfDrpWHNglyBXFfu/t48vQnWZ60nAu/v5AFO7UIu4hIIFHpIYUuMqoyr3Z/GwPcMvUm0vZvczqSiBxBTk46d4y/mD0uyyvtHqJSpeZORxIROTkuN7S+Cm5ZBGc9BJtnw5sdYOwNsHfDoc361unL6LNHExkcyeApgxm1fBReq/XIREQCgUoPKRLx8e15scUwtri83DPuAjy52U5HEpHDPDPmfBaYLB6u2Z9mTS50Oo6IiP+ERECnO+C2JdBhKKz8Dl5vA98OOVR+1C9bny/O/oIza5zJiwtf5IafbmDnwZ3O5hYRkZOm0kOKzKktB3NPlTOZaQ/w8riLnY4jIvl8MekWvszayjVR9ejb9XGn44iIFI6IctDjcRi2DE67CVaM8y12OvYG2L2KqJAoXuj8AiPaj2DpnqUMGD+ASRsnOZ1aREROgkoPKVIX93yVi8Pi+fDger756Q6n44gI8Nu813hq53Q6myhu6/eF03FERApfVBz0fCKv/LgRVo2HkafBZ5dgEudyYf0L+brv19QqU4vhM4dz98y7Sc1KdTq1iIgUgEoPKXL3DBhLRyJ4fNsU3dFFxGFr10/kzhVvU9+6eXbAd7iDQpyOJCJSdP4qP25fAV3ug8S58EFPeL8nNRMX81GP97m5xc1M3jSZc8edy4Q/J2APu/2tiIgUbyo9pMgFBYfx/IBx1LJu/rfsdTZs+MnpSCKlUtKeVdw8cziRFl7r/RERUXFORxIRcUZEOehyt6/86P0cpO2Ar68i6PU2DEnL5Itub1M1sip3/3o3N069kcS0RKcTi4jIcVLpIY6Iiq7CGz3fJ8TCzTPuYG/SWqcjiZQqGenJ3PLDZaQaeK3D41Su3MLpSCIizguJgHbXw62L4eLRUDYBpj5Eww/68WluWe6pfzmLdy9mwHcDeGfZO2TmZjqdWEREjkGlhzimatU2vH7aQ+w1llu/v4SM9GSnI4mUCp7cbO4bcy4rTA7PNLyaxg37Ox1JRKR4cbmh0Tlw9Q8w5HdofiHuFd9y+eSn+C7NzekR1Xlt8WucO+5cJm6cqEteRESKMZUe4qimjS/kqXqX84fJ5p4xfXUrW5FCZr1enh07gKneVIbHdaRr+zudjiQiUrxVbgrnvgb/WwNnv0Bl6+KlZdN4f3cKMRmp3DXzLgZOGMiS3UucTioiIkdgimsz3aZNG7tgwQKnY0gRGT3xJp7e/SsXh8Vz/4U/YFzq40QKw6gfruXFvfO4MqI2wy/8zuk4UoSMMQuttW2czlHa6HwmAFkL2xbBkk/xLB/D+KBcXi1fjiSXoVOFFjSJuYbPfoPtKRlUjQ1neM8G9G9ZzenUIiIlXkHPZVR6SLHxwjfn8eHB9ZyWksDUHUN0oiDiJ+MWb+O5yWuobj9kZdXFnOEpw2tXzcDlDnI6mhQhlR7O0PlMgMvJhDUTSF/8KZ/tXcCHZaJIdbuJPxBL2p5eJGa2IDzYzVMDmul8RkTkJBX0XEa/Tpdio1atlzklLZw5sZs4NfYLtqVkcO/YPxi3eJvT0URKrHGLt3Hv2D8ol/s9a6sson6Gi5kb72T8sl1ORxMRKfmCw6DpACKuGMvgwQvpvaMn/fcGkxq+l5RaX9Cx5t2cE/42306c4JshIiIiRU6lhxQbL/y0gXnb7qJBupu1lRfTImoSGTkenpu8xuloIiXWc5PXUN09lz3VplAlB9Zu+R9pOSH650pExN+iKvJeWjc+2f0Yuetvp+meWmwOcTGp2nr2V3yeb99sTtaP/4P1U30zREREpEhobrMUG9tTMrCEsybxDmomPMe2atNptCWa1SkdnY4mUmK50xeSVfMrIrywd/MQ0rzlAd8/byIi4l9VY8PZlpLBLm9VdiXdAEm5xMbMJqnCTEZEpvHCrkmcu+EbLsjwULtGJ6jbDWp3gXK1wRin44uIBCTN9JBio2psOABp3vLs3DyUsh5Ijf+O1uVWOZxMpGTatWsZITU+xGvAs+UKduXWOvTeX/+8iYiI/wzv2YDwYHe+V4LISu/CHa2/4t0e79IuoTufx5alX+WyXHVwOeNmPEja663hleYw/hZYPgbSdPmhiIg/aaaHFBvDezbg3rF/kJHjIclTnZAtgwmp+S7JFT5k27YzqFbtVKcjipQYqSmbGPLjQNLcUHHbBSzPanbovfBgN8N7NnAwnYhIYPprsdLnJq85wt1bqnNaldPYm7GX8RvG883ab3gwGB6Li+MME0mfDT/SafEnhFkL5etCzQ5QsyPEnwpla2kmiIhIAenuLVKs/HWXib9OFG5svZORW5+krDV8dO7XVKjQ0OmIIsVeenoS133Zg1Ummzeb38oOc/ZRTsClNNHdW5yh8xk5Gmsty5KWMXHjRCZtnMTezL1EuMPoGFaFLpnZdNq2irIZKb6NIytC9ba+R7XWUOUUCI91Mr6ISJHTLWslYC1Z/hnXz3+S6rj5oP84YsvWOvZOIqVUZsY+hn7Vg/k2gxfqXk630+91OpIUEyo9nKHzGTkeud5c5u+cz5TNU5iROIM9GXtwGRctYuvTIbgcpx04QJOdqwjau+HvncrVhiotfAVIpaZQuSlEVdKMEBEJWCo9JKDNXvgWQ/94nbo2iPfO/5HoMvottcjhcrIOctuXZ/Gb9wBP1OxH365POB1JihGVHs7Q+YycKK/1smrvKqYnTmfG1hmsTl4NQFRwFG0qnkKbkAqckp1D471bCdmxDFK3/L1zRHmIawwVG0LFBr5HhQYQFacyRERKPJUeEvBmzn2J21a9T1NCePuCSURExTkdSaTYyM3JZPgX3ZjqTWVElW5c2OMlpyNJMaPSwxk6n5GTlZyZzLyd85i7Yy5zd8wlMS0RgGBXME3KN6FZ2fo0ckXQIDOT2inbCdq9Cvashey0vwcJLQPlakG5Or4ZIuVqQWwNiK0JZaqBW8v8iUjxp9JDSoWffnuS4es/oxVhjLz4J8LCyzodScRxntxs7vuyBxNy93J3XEcG9n7L6UhSDKn0cIbOZ8TfkjKSWLp7KUv2LGHJ7iWsSl5FlicLgBBXCHXL1qVOTG1qh1WklnVTOzOd6mlJBCdvhOQNkLIFrPfvAY3bV3yUqQoxec9lqvkulYmu7HuOqgShUQ594sJz+FpyWvNK5OQU9j9TjpYexphewCuAG3jPWvv0Ye/fAQwGcoE9wCBr7eb/GlMnCXI0P/zyIPdt+pb2JoJXL/6J0LAYpyOJOMbryeWhL3sxLmcXt5VrzeC+HzodSYoplR7O0PmMFLZcby6bUjexKnkVq5NXs3bfWv5M/ZPd6bsPbWMwVIqsRPWo6lSLrEKVoAjivIZKOdnEZR6g4oFkYg/sxr1/O6Rug7wS5R+CwiGygu8Smr+ew8v+/QiLhdBoCCvjm1kSVgZConyPoNBid3nNuMXbDt018C/hwW6eGtBMxYdIARTFP1OOlR7GGDewFugObAXmA5daa1fm26YrMNdam26MuRHoYq29+L/G1UmC/Jdvf76LhxIn0N5E8MpFkzXjQ0olT242D33Vh+9ydnFjmabcdN7nTkeSYkylhzN0PiNOOZB9gI2pG9m4fyNb07ayNW0r2w5sY2vaVvZk7MHyz/8GMBhiQ2MpG1aWssHRlHEFE42LMhbK5OYQkZtNeE4mEVnpRGSlEZZ1gJCsA4RmHSDEWoKxBFsIspYgLEEWXIDB4sKNKyQSgiN8BUhwBASHQ3AYXlcwNigMb1Aw1h2C1x2M1xWExxWM1+3GY9x4jYtclwuvMXiMCw8Gr8uQC3gxeLC+hwGPtXgBDxavtXiN7045Xnyv27xPPn7Jdg7m5P7r7y0yOIh+LaphMLiNwRgXbgxu4ybIuAgyboKMm2BX0D8eoa4QQoNCCXOFEeoOJTgoFFxucAX9/XAH5z1CfF8HhYI71PccFOp7rZiVQyLHq+PT09iWkkGc2UnNcpNYs/d89hNNtdhwfr/nTL8co6DnMv64gO9UYL219s+8IF8A/YBDpYe1dnq+7ecAA/1wXCnFzjvrWfgZHkqcwK1f9eRVFR9SynhysxnxVS/G5+zhpphm3Nj/M6cjiUgeY8z1wPUANWrUcDiNlFZRIVE0q9iMZhWb/eu9HG8OezP2sit9F7vTd7MnfQ/7svaRnJHse85MZlv2ftKy00jLTuNAzoF/DhCS94iOAk70shcvcCDvAVggJ+9RlMof/a25iYtPevggawn3WsKtlwivJdxaIr1eorxeIq0lyusl2uulzF/PHi8xFmJNCLHuEGLd4YQGR0BIZN4jyvccGv33TJrQMr4ZNodm3MT+PevG5TrpzyByIranZOAK34yp+hFrgg8Sm7Ga/elt2Z6S4XQ0v5Qe1YDEfF9vBdr9x/bXAhP9cFwp5c4761lc01w8uOUHbvmqJ69eOInwiHJOxxIpdJ7cbB78shff5+7h5thTGNLvU6cjiUg+1tp3gHfAN9PD4Tgi/xLsCqZyZGUqR1Y+ru09Xg8ZuRlk5GaQnptOek46WZ6sQ49sTzZZniw81kOuN5dcby45Xl+L4bXeQ48jcRkXBoMxBpdx+R64cLlcuI0bl/E9u3HhwhKEwQW+Z2NwYQjChdu4cOd97Sb/WODOO4bLGIwFY1zcNHoRew9mH5bGUj4ylDcua+GbGWI9eK0Xj/Xg8Xrx2Nx8n8/3GbM92eR4s8nyZJOVm0mWJ4tMTxaZnkwycjNJz80gw5NFuieTg7kZ7PRkciA3kwOeTA54ssjlyH8vAOFkUo5sytsUyqVbyqXlUj4nm7isDCrmZlPB4yEu10MFj4fg/Dsad95lSBUhsvzf67L8tU5LdOW/13EJDj+u7wGR/5LjyaFc/M9kRU4lONfFUzsOMCjdNyGjaqzz32NFulSzMWYg0AbofJT39ZsROSH9znwapuErPr7uyasXTiQiooLTsUQKTW5OJg9+1ZsfcpMYGtuCG/p94nQkEREJcG6Xm6iQKKJCAmcx02t7VD/i+gN39WhGjfiiWdPDWktGbgb7s/eTmpXK/uz9pGSl+B6ZKYdm3SRnJLMjM5nlmXtJzkzGGxXyj3EMhgrB0cQFRVLJFUZVE0Rlj5eqOblUzUyj6rbNxO7fjck9wm/cI8pDTPW/7+bz13O52lA2AYJC/r2PSD5r963lgd8eIDtqFXZ/W95LmslGb13AEB7sZnjPBk5H9EvpsQ2Iz/d19bzX/sEY0w24H+hsrT3C6kj6zYgUTL8zn8Y13c0Dm79jyFc9eWPAeKLLaAEqCTzZWWnc/VVvpnpTubVsS64792OnI4mIiJRIfy2s6OTdW4wxRARHEBEccUKzbpIzk9mTsYekjCR2p+8+dJnSroO72HxwJ7MPbiXjr4IjCIiBiPI1qRZZhWph5ajujqKGCSY+10N8ZjpV0/YSvGctrJsK+YsR44KYeChfByo0gIr1854b+maQSKmWnpPOW0vf4pOVn1AmtAyvdH2FnK1laDhlDF96e1GtGN0RyR8LmQbhW8j0LHxlx3zgMmvtinzbtAS+AXpZa9cdz7ha+EtO1ORfH+OeDV9Szwbxdr8xlC1Xx+lIIn6TkZ7M7V/35nfSdVtaKRAtZOoMnc+ISFGz1rI/ez87Du5g+4HtbDuwzfdI28bWA74FbTPylRtu46Z6dHVqRtekZnhFEtwR1Mq11MpIo3zKNkzyn5C0DnIO/n2QyIpQqSlUauJ7rtzUV4a4g4+QSALNtC3TeHre0+w4uIMB9QYwrNUwyoaVhWVfw9jBcMNMqHKK34/r2EKm1tpcY8xQYDK+W9Z+YK1dYYx5FFhgrR0PPIdvlaOvjW9F4i3W2nNP9tgi+fXs9CDhIVHcvup9rhl3Hu+e8zkV45o4HUvkpB1I28HQMX1ZRCaPVO/FgG7POx1JREREiiljDDGhMcSExtCwXMN/vW+tJSkjiS1pW0hMS2Tz/s2HHvN2ziPTk3lo2+jgaGpVr0WtJqdTO7Q8dayb2hnpVNuXiGvXCpj37t+3OA4K8xUgVVtA1ZZQvS2Ur6dFVQPIhpQNvLjwRWZunUnd2Lp83PtjWsa1/HuDzb/7Ftit1NS5kEdw0jM9Cot+MyIFNW/xewxd8jIVrOGdHu9SvfppTkcSKbCUfRu5adwAVpocnqx1Pn06P+J0JCmhNNPDGTqfEZGSxGu97E7f7bvdcb7Hn6l/sidjz6Htwtxh1I6tTd2Y2tQNKUvd7FzqpSVRaddqzI5lkJ2Wt2EMVGsD8adCjfa+IiQkwqFPJwW18+BORi4ZyXcbviMiKILrm1/PwMYDCXYdNrPn9VOhbE24/OtCyeHkLWtFipVTWw7m3eAobpr/OFdMGcxbpz9Ng/rnOB1L5ITt2L6QGyZdwzaXl5caXE3X9nc6HUlEREQCmMu4Dt3Zp33V9v94LzUrlY2pG9mQsoENqRtYv289s3fMZXy+MiQ6LJp6Lc+kXlgl6nss9fcnUW/nGiJ/eRqw4Ar2zQJJ6AgJp0ONDipBirHkzGQ+WvERo1eNxmu9XN7ocq5rdp3vUpbDHdgDSWugxaVFH/QYVHpIQDql6SV8FF6OG2bcwdW/38Or6btp22KQ07FEjtu69ZMYMvNOMgy83eJO2rS42ulIIiIiUorFhMbQIq4FLeJa/OP11KxU1u1bx7qUdazft551Kev4ccdvfJlzwLdBJFRv2o4GoeVpkJNL/X07aDBvJNV+ewnjDoH4dlC7C9TpClVa6nKYYmDHgR18uOJDxq4bS5Yniz61+3BLy1uoFvUfi5JumeV7rtmxaEKeAJUeErDq1unBp+EfMWTSNQxZ8iLPHtzNWR3vcTqWyDEtWvoxQxc9Sxgw6vRnaFDvbKcjiYiIiBxRTGgMbSq3oU3lv686sNay4+AO1u5by5rkNazZt4Z1+9YxLW0zNshCtUpEucOo746kQfoOGsx7kYa/PUOdoDKE1esO9XpAnTMhPBaAcYu3OXqnndJidfJqPln5CRP+nADA2bXPZlCzQdSOqX3snTfPguAIqNKicEMWgNb0kICXsm8jN487n+Umm/uqnMnFPV91OpLIUf086xnuXvMJVazhrZ7vU63aqU5HkgChNT2cofMZEZG/peeksz5lPWv2rWFN8ppDpUh6bjoALiAh10ODzEwa5HhoWLYeuRFnMGJZXTbnxBwaJzzYzVMDmqn48IPM3Ewmb5rMV2u+YlnSMsLcYZxf/3yuanwVVaKqHP9Ab50O4eXgqvGFllVreogcRWzZWrx78RTu+qYvj++cTuLX/bljwDe43Pr2l+LDer18MmkIz++eRVOCeb3/15QrV9fpWCIiIiJ+ExEcQfOKzWlesfmh17zWy7a0bazet9o3KyR5NUv2/MHErGRgF6R/TblaHjpkBZGTWYVNGaewN6s+z052qfQoIGstS/csZcLGCfz454/sz95PQpkE7mp7F+fWOZeY0JhjD5JfRgrsXA5d7i2UvCdL/9UnpUJERAVeuWwGz4w5j4/SN7Dtsy48ef54wiPKOR1NhNycTJ4ZO4AvMhPp7o7lCX1vioiISCnhMi7iy8QTXyae7jW7H3o9NSuVtfvWctvHoygbtpq0sD1sj91GdrntRDKRA9Zw/rha1CvfiHqx9ahXth71y9anUkQljDEOfqLiyVrLquRVTN40mUkbJ7H94HZC3aF0ie/CRfUvom3ltgX/e0ucC1io2cGvmf1FpYeUGu6gEO67+EdqTBzCs7t+49ovz+LVvp9TocK/718uUlTSD+xm+Nh+zLQHuDqyLref97VmIYmIiEipFxMa4/sPcW8aS7ZnABBvdtAz7BdqhS/lQGgK6zJWsCB1Cz/y46H9ooKjqBNbh7qxdakbW5fasbWpHVO7VJYhB3MOMmf7HH7d9iu/bv2V3Rm7cRs37au2Z2jLoXSN70pUSNTJH2jz774781QvnlfRak0PKZV+nvUM96z5hLIWXu34JA0bnOt0JCmFtm2bx61TrmOD8XBflbO4qOcrTkeSAKY1PZyh8xkRkZMzbvE27h37Bxk5nkOvhQe7ea17BN1yfoGlX5J6YBvrI2NZF9+K9eXi2ZC7n/Up60nJSjm0T2RwJLXK1KJWTC0SYhKoWaYmCWUSqFGmBuFB4UX/wQpBalYqi3YtYtHuRSzatYiVe1eSa3OJCo6iQ9UOdKreiTOqn0G5MD/PKH6vGxg3XDvZv+MepqDnMio9pNRasXost84aQZqBx+teQo9ODzgdSUqRBUs+5I7Fz5MLPNd0CB3bDnU6kgQ4lR7O0PmMiMjJ+8+7t3i9sPk3WPoFrPgWctKhUlNsq6vYW78bG7P2siFlA3+m/smfKX+yaf8mdqXv+sf4ceFxVI+uTnx0PPHR8VSNqkqVyCpUjapKXEQcQa7iNQvX4/WwM30nG1I2sDp59aFHYloiAMGuYJpVaEarSq3oULUDLeJaEOwKLpww2Qfh6RrQ4Vbo9lDhHCOPSg+RAkjas4rbfricZa4chpRpyo3nfqJLC6TQfTVlGE9tn0p1r4vXznyNhITOTkeSUkClhzN0PiMiUoQy98Pyb2DhR7BjCQSFQ7MLoN0NULnZoc3Sc9LZkraFTamb2Lx/M4lpiSSmJbI1bSu7M3b/Y0i3cVM+vDxx4XHERfge5cPLUy6s3KFHbGgs0SHRRIVEEeYOO6nLaHI8OaTlpJGalUpSRhK703ezJ30Pu9J3sfXAVrbs30JiWiI53pxD+9SIrkGDcg1oXL4xLeNa0rRCU0LdoQXOcEI2TIdP+sPAMVC3W6EeSqWHSAFlZ6Xx6Jjz+C5nF2e6yvBE/2+Iij6B2zOJHKecrIM88+0FfJm1ldOJ5NnzxhBdRquOS9FQ6eEMnc+IiDhk+2JYMAqWfQW5GVCjA5x6HTTqC+6jz3rIzM1kx8Ed7Diwg+0Ht7P9wHZf8ZCxh93pu9mdvpv92fuPun+QCSIqJIpQd6jvERRKqCsUl8uFyfufy7jItbnkeHLI9mST7c0mMzeTAzkHyMjNOOK44UHhVIuqRs0yNakRXYMaZWpQO6Y2Dco1IDI48qT/ugps2uPw6wtwzxYIjS7UQ6n0EDkJ1uvl00k38sLu34n3Gl484znq1e3ldCwJIDt3LOZ/kwaxzJXLNVH1uK3fF7iDQpyOJaWISg9n6HxGRMRhGftg8acw711I2QxlqsNpN0KrKyGsTIGGzPHkkJyZzL6sfSRnJpOSmcKBnAOkZacdes72ZJPpySQrN4ssbxZerxf71/+sxW3chLhDCHGHEOwKJiwojOjgaKJDfI8yoWWoGF6RihEViQuPIzI4snguxDqyPYTFwKBJhX4olR4ifrBgyYcMX/Q8Bw08VGsAZ3d51OlIEgBmL3yLu5e9TjbwWL3L6H76fU5HklJIpYczdD4jIlJMeD2wbgrMfgM2/QqhZaD1VdDuRojRzNsC2bUS3mwPfZ73zaIpZAU9l3EVRhiRkqpNi6v56pwvaWRCuWfztzzxZR+ys9KcjiUllNeTyzvjr+CGP16nvHXxedfXVXiIiIiIOMHlhga94eof4LrpUK87zB4Jr5wC42+BvRucTljyrBgLxgWN+zmd5D+p9BA5TMW4Jrx3+a9cHVmXLzITGfhZJzZtmuF0LClh9uxewQ2fduC1fUvoHVyB0ZdMo1ZCF6djiYiIiEi1VnDBB3DrYt9sj6VfwuttYMxg3+wFOTZrYfkYqHUGRMU5neY/qfQQOYLg4Aj+d8G3vFLvCraTy0XTb2b8NP2GXo7Pb/Ne44IfL2aJN52Hqnbn6UunERFRwelYIiIiIpJf2Zpw9gswbBm0vxlWT/BdrvH11bB7tdPpircdSyH5T2h6vtNJjkmlh8h/OLPDXXzT+1MamzDuT/yee0d35UDaDqdjSTGVk3WQ57/uz42r3qEcbr444yUu6P4ixqV/1YqIiIgUW9GVocfjcPty6HQnrPsJRp7mm/mRtN7pdMXT8jHgCoaG5zid5Jh0Ji5yDJUrt+D9gbO4KaY5E3L2cMHXPViw5EOnY0kxs2bdj1z6WQc+St/AxWHxfH7JL9Sp093pWCIiIiJyvCLKwVkPwm3LoONtsPpHeKMtfHczpG51Ol3x4fXCim+hzpm+v7NiTqWHyHFwB4VwY//RfNjqHlzAoCXP89zX/cjKTHU6mjjMk5vN+99fw6W/380ePLxa/yoeuHgCYeFlnY4mIiIiIgURWR66P+IrP9rdCMu+gldbweT7IT3Z6XTO2zofUhNLxKUtoNJD5IS0bD6Qby76mYvC4vk4/U8u/qwTK1aPdTqWOGTLlt+45tP2vJy8gM7uWL7tN46u7e90OpaIiIiI+ENURej1JNyyCJpdAHPy7vby6wuQk+F0OucsHwNBYb674ZQAKj1ETlBEVBwPXDKRtxrfQBpeLp8zghfHDCAzY5/T0aSI5OZkMuqHazn/5yGst1k8WaMfL14+k3Ll6jodTURERET8LTYe+o+EG2dBzY7w86PwelvfDBCv1+l0RcvrgZXjoF4PCCvjdJrjotJDpIA6th3K2PMn0D+0KqMOrGPA52cwd9E7TseSQrZqzXdc9ulpvLh3Hqe5y/Btn8/o2/VxLVYqIiIiEujiGsFlX8BVP/jWshh7Hbx3Jmye5XSyorP5dziwq8Rc2gIqPUROSkxMDR6+dArvNbsFgMF/vMaIz7uxL3mDw8nE39LTk3hxzAAunX0/u20uL9S+mFcH/kalSs2djiYiIiIiRalWJ7juFzjvbTiwG0b19t3mNmWL08kK3/IxEBLlm+lRQqj0EPGDdq2uZ+ylM7kmqh7js3bS97t+fDX5Njy52U5Hk5NkvV4mzXyUc7/owqgD6+gbUpnvBvxAj04PaHaHiIiISGnlcsEpl8DQBdDlPlgzyXfJy/QnIfug0+kKR8Y+WD4WGp4NIRFOpzluOmMX8ZOw8LLccf5Yvun0IvVNGI/tnMaln5zK0uVfOB1NCujPjT9z3SftGL7xa8oaNx+3vJvHLptKTGyC09FEREREpDgIiYAud8PQ+b4yYMYzvvJj+Riw1ul0/jX7Dcja77udbwmi0kPEz+rW6cH7V87j2YTz2WtzGbjwCe4d3ZUd2xc6HU2O077kDTz11TmcP+M2VnozuK9SZ764Yj4tmw90OpqIiIiIFEex8XDBB3DNRN96H98Mgo/6wq6VTifzj/RkmPMmNO4PlZo4neaEqPQQKQTG5aJ354cZf9FUro1qwE/ZezhnylW8NOZ80vZvczqeHEVWZioffD+IPt/144v0TZwXVp0f+o3j0l6v4w4KcTqeiIiIiBR3NTvA9TPg7Bdg5x/w1ukw8R7ITHU62cmZ9Zrvsp0u9zid5ISp9BApRJFRlRl2/jd83/MjegbH8cGBtfQZ05OPJ1yvW9wWI7k5mXw37R76ftaRl5Ln09odzdhOLzHikkm6Da2IiIiInBiXG9oOhlsWQasrYe5b8FobWPpFybzk5WASzH0bmg7w3cGmhFHpIVIEqlRtzZOXT+PLdo/RwBXOc3tm0+fzTnw26Ways9KcjldqeXKz+eGXB+n/SVseSPyRsiaI95vfxutXzqZOne5OxxMRERGRkiyyPPR9Ga6f7rv85dsbfHd62bnc6WQnZtarkJMOne92OkmBqPQQKUKNG/bnvavm80HzYcS7Qnlq10z6jG7Pl5Nv1cyPIpSbk8mEGQ9x3sdtuHfzOEKNi1fqXcEXVy3i1JaDnY4nIiIiIoGkaku4diqc+xrsWQNvnwET74aMFKeTHduBPTDvXWh2IVRs4HSaAjG2mE6vadOmjV2wYIHTMUQKjfV6mbv4Xd74422WmBzKeS0Dy7fios6PExNTw+l4ASkjPZlvZz7Ix9tnss0NdT2GG+tdRLcO9+ByBzkdT6RQGWMWWmvbOJ2jtNH5jIiI/EN6Mkx7HBZ8AJEVoNsjcMqlvlvgFkeT74c5I+Hm+VDB2cu+C3ouo9JDxGHW62XB0lG8v+wdfiedCK/lgqg6XNr+XqpXP83peAEhac8qvv79MT7ft4x9LsMp3mAGNbiELu3uUNkhpYZKD2fofEZERI5o+xKYcCdsnQ/V20Kf53wzQoqTvRvgzY7QpD+c95bTaVR6iASCNWt/4IP5zzM5JwkvcIYrmksbXU77VkP0H+cnyHq9LF3xOZ8tfYefcveSawxnmCgGnTKEVs2uwBTXNl2kkKj0cIbOZ0RE5Ki8Xlj6OUx9yLdYaMuBcNYIiIpzOhlkHYD3u0PaDrjhV9+aJA5T6SESQHbuXMLXs5/im5QVJLsMNT1wXsU29D31f8RVaup0vGItNWUTE+Y8z9gdv7La5SXKa+kfWYuLT72ThITOTscTcYxKD2fofEZERI4pIwVmPue7y0tQOJxxJ5x2IwSFOpPHWvhmEKwcBwPHQJ0znclxGJUeIgEoOyuNn2Y/x5ebfmSxycZlLR1MFP1q9aHrqbcRGhbjdMRiITcnk1mL3ua7dd8wPXcfOcbQwOviompdOafDfUQUh7ZcxGEqPZyh8xkRETluSethyv2wdhKUreWb9dHkPDCmaHPMeg2mPADdHobTby/aY/8HlR4iAW7z5l/5buFrjE9ZyS63IdJr6RJSkR61etOx1Q2lrgDJzclk3tIPmLJuHNMyt7PPZSjrtZwdWYt+p1xHwwbnOh1RpFhR6eEMnc+IiMgJWz8VJj8Ae1ZBlRa+8qFO16I59p8z4JP+0PAcuOjjoi9c/oNKD5FSwpObzdwl7zF53bf8nLmDVJchwmvpHFyeTtU60fGUqylXztmVlQtL2v5tzFn2Eb8mTmN65k5SXIZwr6VLcHl61u7DGa2HEhwa6XRMkWJJpYczdD4jIiIF4vXAsi9h+pOQmgi1u0DX+yH+1MI7ZtJ6+KAHRFaEwVMhNLrwjlUAKj1ESqGcnHTmLxnFlPXfMT1zO8kug7GWpjaY02Mb0rZWd5o1OI+w8LJORy2QnJx0Vq4Zz/yNk/h973KWkEmuMUR7LacHl6dn3iyXkvr5RIqSSg9n6HxGREROSk4mLHgfZj4PGclQsyN0HAb1uvtvFoa1vgVVf7wTgkLg2p+gQj3/jO1HjpYexphewCuAG3jPWvv0Ye+HAh8DrYG9wMXW2k3/NaZOEkROjNeTy6q13/Hr2m/5NXklf5hsrDEEW0szQmldpg7Nq7ajca2exXYx1H3JG1i5YSJ/bJ/DwpS1LPWmk+Hy/cu8gddFpzL1OL1uX05pfDFBwWEOpxUpWVR6OEPnMyIi4hdZB2DRxzD7Ddi/FSo19S122rjfyc3IyEiBH++A5WMgoROc9zbEVPNbbH9yrPQwxriBtUB3YCswH7jUWrsy3zY3Ac2ttUOMMZcA51lrL/6vcXWSIHJyUlO3sGTVNyzc+isL0jax0uTgyWuDK3gsjYOiaRBVnYTYetSq1JKE+A5Elzn+f8GNW7yN5yavYXtKBlVjwxneswH9Wx7f/unpSWxO/J2NOxexKXktaw9sYWVOKjvcvnzGWupZN20i42ld5TRaNbqAChUanvhfgogcotLDGTqfERERv/LkwB/fwO+v+Nb8CAqHhn2g+cW+u6y4g49vnOx0WDcFpjwI+7dB1/t8i5a63IWb/yQ4WXq0Bx621vbM+/peAGvtU/m2mZy3zWxjTBCwE6ho/+PgOkkQ8a/09CTWrJ/Eym2/s3LfGlZmJrHJ5SU337S4cl5LZYKo5I6kUmgMlSLiiAktS5nwcpSJqEiZyDjCQ2OYs+kAb8/cxsFsNxYXQSaLiGAPgztWpVV8CGnpe9h/cA+pGUmkZu5jT8YedmbtY1fuQXbaHPa4/z6msZZ4r6FxSFkax9ajcdV2NKrTmzIxzt8LXCSQqPQoOsaY64HrAWrUqNF68+bNDicSEZGAYy1sne9b92P5WN+lL2ExULUVVGsFVVtC5eYQFAbW41sjxJMNW2bD6h9hwzTIzYSyCXD++1C9+J8iOFl6XAD0stYOzvv6CqCdtXZovm2W522zNe/rDXnbJB1tXJUeIoUvJyedrdvmsXH7PDbtXc2WA1vZmZ3KLm8mu/CQ5vLPdYIRXktl66KSO4xKwWWIj6pCQtkG1KrShhrV25e6O8+IOEGlhzN0PiMiIoUuN9t3x5e1k2D7Yti9Ery5R9++THVoeLbvUbPD8c8OcVhBz2WCCiNMQR32mxGH04gEvuDgCGoldKFWQpcjvp+ensT+1ERSD2xn/8Fd7E/fQ3ZOBh/NXo8xubiM71+m1gbhtW6sDeL6MxoRHVGBMhFxlImuSkyZ6kRExGFcriL8ZCIiIiIipURQiO8Sl4Z9fF/nZMDO5bBruW+Wh3H7LlsxbqjUBKqcUqxuRVvY/FF6bAPyz0OvnvfakbbZmnd5Swy+BU3/wVr7DvAO+H4z4odsInISIiIqEBFRgcq0/Mfrj8+exrZ9Gf/avlpsOGd1PLOo4omIiIiIyOGCwyG+re8h+ONXr/OBesaYWsaYEOASYPxh24wHrsr78wXAtP9az0NEirfhPRsQHvzPRY7Cg90M79nAoUQiIiIiIiL/dtIzPay1ucaYocBkfLes/cBau8IY8yiwwFo7Hngf+MQYsx5IxleMiEgJ9dddWgp69xYREREREZGi4Jc1Pay1E4AJh702It+fM4EL/XEsESke+resppJDRERERESKNa0sKCIiIiIiIiIBSaWHiIiIiIiIiAQklR4iIiIiIiIiEpBUeoiIiIiIiIhIQFLpISIiIiIiIiIBSaWHiIiIiIiIiAQkY611OsMRGWP2AJsLYegKQFIhjOskfaaSIxA/lz5TyRGIn0uf6fjVtNZWLIRx5T8U0vmMvu9LhkD8TBCYn0ufqeQIxM+lz3T8CnQuU2xLj8JijFlgrW3jdA5/0mcqOQLxc+kzlRyB+Ln0maQ0CsTvEX2mkiMQP5c+U8kRiJ9Ln6nw6fIWEREREREREQlIKj1EREREREREJCCVxtLjHacDFAJ9ppIjED+XPlPJEYifS59JSqNA/B7RZyo5AvFz6TOVHIH4ufSZClmpW9NDREREREREREqH0jjTQ0RERERERERKAZUeIiIiIiIiIhKQVHqIiIiIiIiISEBS6SEiIiIiIiIiAUmlh4iIiIiIiIgEJJUeIiIiIiIiIhKQVHqIiIiIiIiISEBS6SEiIiIiIiIiAUmlh4iIiIiIiIgEJJUeIiIiIiIiIhKQVHqIiIiIiIiISEBS6SEiIiIiIiIiAUmlh4iIiIiIiIgEJJUeIiIiIiIiIhKQVHqIiIiIiIiISEBS6SEiIiIiIiIiAUmlh4iIiIiIiIgEJJUeIiIiIiIiIhKQVHqIiIiIiIiISEBS6SEiIiIiIiIiAUmlh4iIiIiIiIgEJJUeIiIiIiIiIhKQVHqIiIiIiIiISEBS6SEiIiIiIiIiAUmlh4iIiIiIiIgEJJUeIiIiIiIiIhKQVHqIiIiIiIiISEBS6SEiIiIiIiIiAUmlh4iIiIiIiIgEJJUeIiIiIiIiIhKQVHqIiIiIiIiISEBS6SEiBWKM6WiMWWeMOWCM6V+Ex+1kjFlTVMcTEREREZGSy1hrnc4gIvkYYzYBlQAPcACYBAy11h5wMtfhjDE/A+Otta8U8nEsUM9au74wjyMiIiIiIoFHMz1Eiqe+1toooAXQErjX2ThHVBNY4XQIERERERGRo1HpIVKMWWt3ApPxlR8YY7oYY7bm38YYs8kY0y3vzw8bY74yxnxsjEkzxqwwxrTJt20rY8zivPe+NsZ8aYx5PN/75xhjlhhjUowxs4wxzY+UyxizAagNfJ93eUto/hz5snya9+cEY4w1xlxljNlijEkyxtyfb1u3MeY+Y8yGvGwLjTHxxpiZeZsszTvOxYf/HRhjGhljfsnLvMIYc26+9z40xrxhjPkxb9y5xpg6J/7/hIiIiIiIlEQqPUSKMWNMdaA3cCKXdpwLfAHEAuOB1/PGCgG+BT4EygGfA+flO1ZL4APgBqA88DYw3hgTevgBrLV1gC3kzUix1mYdZ7bTgQbAWcAIY0yjvNfvAC4F+gBlgEFAurX2jLz3T8k7zpf5BzPGBAPfA1OAOOAWYLQxpkG+zS4BHgHK4vt7fOI4s4qIiIiISAmn0kOkeBpnjEkDEoHdwEMnsO9v1toJ1loP8AlwSt7rpwFBwKvW2hxr7VhgXr79rgfettbOtdZ6rLUfAVl5+/nLI9baDGvtUmBpvmyDgQestWusz1Jr7d7jGO80IAp42lqbba2dBvyAr0D5y7fW2nnW2lxgNHmzZkREREREJPCp9BApnvpba6OBLkBDoMIJ7Lsz35/TgTBjTBBQFdhm/7l6cWK+P9cE/pd3mUiKMSYFiM/bz18OzxaV9+d4YEMBxqsKJFprvfle2wxUO45jioiIiIhIgFPpIVKMWWtn4Lsc5fm8lw4CEX+9b4xxAxWPc7gdQDVjjMn3Wny+PycCT1hrY/M9Iqy1nx/n+P/IBlQ+zv3+OnZB1trYDsQbY/L/u6wGsK0AY4mIiIiISIBR6SFS/L0MdDfGnAKsxTdz4+y89SweAP615sZRzMZ3G9yhxpggY0w/4NR8778LDDHGtDM+kXnHiT7O8ZcAlxhjgvMWT73gOPcDeA94zBhTL+/YzY0x5fPe24Vv0dQjmYtv9sZdecftAvTFt6aJiIiIiIiUcio9RIo5a+0e4GNghLU2FbgJX0mwDd/siq3/sXv+cbKBAcC1QAowEN/6F1l57y8ArsO38Ok+fIt+Xn0CUR/EN1tjH76FQz87gX1fBL7CtyDpfuB9IDzvvYeBj/IuubnoCJ+pL77FXpOAkcCV1trVJ3BsEREREREJUOafl/eLSGlijJkLvGWtHeV0FhEREREREX/TTA+RUsQY09kYUznv8pargObAJKdziYiIiIiIFIYgpwOISJFqgO8ykkjgT+ACa+0OZyOJiIiIiIgUDl3eIiIiIiIiIiIBSZe3iIiIiIiIiEhAKraXt1SoUMEmJCQ4HUNERCQgLFy4MMlaW9HpHKWBMeZ64HqAyMjI1g0bNnQ4kYiISMlX0HOZYlt6JCQksGDBAqdjiIiIBARjzGanM5QW1tp3gHcA2rRpY3U+IyIicvIKei6jy1tEREREREREJCCp9BARERERERGRgKTSQ0REREREREQCkkoPEREREREREQlIKj1EREREREREJCCp9BARERERERGRgOSX0sMY84ExZrcxZvlR3jfGmFeNMeuNMcuMMa38cVwRERERERERkaMJ8tM4HwKvAx8f5f3eQL28RzvgzbxnESmhxi3exnOT17A9JYOqseEM79mA/i2rOR1LRERERETkEL/M9LDWzgSS/2OTfsDH1mcOEGuMqeKPY4tI0Ru3eBv3jv2DbSkZWGBbSgb3jv2DcYu3OR1NRERERETkEH/N9DiWakBivq+35r22o4iOLyInKTUrldXJq9mdvpvHf51PcEwSDYL+xG08/JlTiwPecjwxcwkV4k6nUblGlA8v73RkEREREREp5Yqq9DguxpjrgesBatSo4XAakdJta9pWpidO54+kP1iRtIItaVv+fjPG97Tb48Vg8bh2EGYMmcCNU0cDUDmyMk3LN6VJhSZ0qd6FumXrFv2HEBERERGRUq2oSo9tQHy+r6vnvfYP1tp3gHcA2rRpY4smmoj8ZefBnUzeNJlJGyexfK9vXeK/yovzEnrReOHnVN+1BuMNY0p2B77ynEkGoVzvnkbv4F8JcaexMzaeladdw4qD21m+dzlTt0zllUWvUDe2Lj0TetIroRcJMQnOflARERERESkViqr0GA8MNcZ8gW8B01RrrS5tESkmlu5Zynt/vMcvib8A0KhcI25vfTs9avagenR1yM2CTwbAznVw9kuM93bk+e/WkWE9ADyfeylvm0t4v80eTv3jIdrO+QyunQzhZUnKSOKnzT8xaeMk3ljyBm8seYPWlVpzXbPr6FC1A8YY5z64iIiIiIgENL+UHsaYz4EuQAVjzFbgISAYwFr7FjAB6AOsB9KBa/xxXBEpOGstc3bM4b0/3mPeznnEhMZwQ/Mb6FunLzXL1Px7Q68Xxt0Em3+D89+HZhdwLuB1h/3r7i2ntqwGTerBJ+fBFwPhirFUCK/ApQ0v5dKGl7Lz4E4mbpzI6FWjGTJ1CI3KNeK65tdxVo2zcBm/rKssIiIiIiJyiLG2eF5F0qZNG7tgwQKnY4gEpDXJa3hy7pMs2r2IuPA4rmpyFRfUv4CI4Ih/bzz1EfjtRTjrIeh0x/EdYNnXMHYwNLsQznsHXP8sNHI8Ofzw5w+8v/x9Nu/fTN3Yutzf7n7aVG7jh08nIkdijFlordU/ZEVM5zMiIiL+UdBzmWK1kKmIFK6DOQcZuWQko1eNpkxIGR487UH61+1PiDvkyDssGOUrPFpfDafffvwHan4hpG6Bnx+F2Bpw1oh/vB3sDua8eudxbp1z+WnzT7y08CWumXwN59Y5lzta36E7v4iIiIiIiF+o9BApJaZsmsIz855hT8YeLqh/Abe1uo2Y0Jij77BtIfz4P6jXA/q8ACe69sbpd0DKFvj1BajaEhr1/dcmbpebXrV60Tm+M+8ue5dRK0YxPXE6w1oN44L6F+iSFxEREREROSn6LwqRAJeek86Dvz/I/2b8j/Lh5fm0z6eMaD/ivwsPa2HSvRBR3reOh7sA/agxvrIkrglMvh9yMo+6aXhQOLe2upUx546hcbnGPDbnMYb+PJR9mftO/LgiIiIiIiJ5VHqIBLC1+9Zy6Y+X8t3677ih+Q18dvZnNK/Y/Ng7rvgWEufCmQ9AWJmCB3AHQc8nIGUzzHv7mJvXjqnNuz3e5b529zFnxxwuGH8B83fOL/jxRURERESkVFPpIRKArLV8s/YbLvvxMvZn7+edHu8wtOVQglzHMWMjJxOmPgSVmkHLgScfpk5XqN8LZj4PB/Ycc3NjDJc2vJTRfUYTHhzO4CmDeXPpm3i8npPPIiIiIiIipYpKD5EAk+vN5fE5j/PI7EdoFdeKr/t+zWlVTjv+AeaM9K3F0fNxcLn9E6rH45CTDr88edy7NCrfiC/P+ZLetXozcslIhv0yjPScdP/kERERERGRUkGlh0gAOZhzkFum3cJXa79iUNNBvNX9LSqEVzj+AQ7shl9fhPq9oXYX/wWrUA/aXAsLP4RdK497t8jgSJ46/SnuPfVeZm6dyaDJg0jKSPJfLhERERERCWgqPUQCxK6Du7hq4lXM3j6bEe1HcHvr20/87ifTn4DcDN/MDH/rcg+EloEpD5zQbsYYLmt0Ga90fYU/U//k8h8vZ0PKBv/nExERERGRgKPSQyQArNu3jssnXE5iWiKvn/U6F9a/8MQH2bUCFn0Mba+DCnX9HzKiHHS+Gzb8DOt+OuHdu8R3YVSvUWR7s7liwhVa4FRERERERI5JpYdICbcmeQ2DJg/Ca7181PsjTq92esEGmvEshERD57v8GzC/toOhbC2Y/qTvtrgnqEn5JozuM5qKERW5ceqNzN4+uxBCioiIiIhIoFDpIVKCrU5ezbVTriXUHcqHvT6kYbmGBRto3yZYNR7aXO2bkVFYgkKgw1DYvgi2FKywqBpVlVG9RlGjTA1umXYLs7bP8nNIEREREREJFCo9REqoVXtXMXjKYMKDwhnV01cCFNicN8G4oN0Q/wU8mlMug/ByMOv1Ag9RLqwc7/d4n5planLLz7fw+7bf/RhQREREREQChUoPkRJo5d6VDJ4ymIigCD7o+QHxZeILPljGPlj0CTS9AMpU9V/IowmJ8F3msmYCJK0v8DBlw8ryfo/3qR1bm1un3cpv237zY0gREREREQkEKj1ESpiNqRu54acbiAqO8hUe0SdReAAsGAU5B32XnRSVU68DdwjMeeOkhokNi+Xd7u9SJ7YOw6YPY9GuRX4KKCIiIiIigUClh0gJsjt9N0N+GoLLuHivx3tUj65+cgPmZsO8d6B2F6jczC8Zj0tUHJxyMSz5DA4mndRQsWGxvN39bapEVmHotKGs31fw2SMiIiIiIhJYVHqIlBBp2WncNPUmUrJSGNlt5Mld0vKX5WMgbQe0v+XkxzpR7YdCbibMf/+khyobVpa3ur9FqDuUIVOHsPPgTj8EFBERERGRkk6lh0gJkO3JZtj0YWxI2cBLXV6iSfkmJz+otTD7dYhrDHXPOvnxTlTFBlCvp2+mSU7mSQ9XLaoab3Z7kwM5B7hx6o2kZqX6IaSIiIiIiJRkKj1Eijmv9XL/b/czb+c8Hu34KB2qdfDPwH9Oh13Lof3NYIx/xjxRHYZCehIs+8IvwzUs15BXur7Cpv2buHXarWR5svwyroiIiIiIlEwqPUSKubeWvsWkTZO4vfXt9K3T138Dzx4JUZWg2YX+G/NEJXSCys19Waz1y5DtqrTjydOfZNHuRTw6+1Gsn8YVEREREZGSR6WHSDE2dfNU3lz6Jv3q9OOaJtf4b+B9m2H9VGh9DQSF+m/cE2UMtBsCSWtg8yy/Ddu7Vm9uPOVGxm8Yz6erPvXbuCIiIiIiUrKo9BApptbuW8t9v91H8wrNebD9gxh/XoKy6CNf4dDqCv+NWVBNzoPQGFg4yq/DDjllCGfVOIvnFzzP7O2z/Tq2iIiIiIiUDCo9RIqhlMwUbp12K1HBUbzU9SVC3X6cjeHJgcWfQr0eEHOSt7z1h5AI3+1rV34HB/f6bViXcfHE6U9QO6Y2d864k8T9iX4bW0RERERESgaVHiLFTK43lztn3Mnu9N283PVl4iLi/HuANRPgwC7fpS3FRetrwJMNSz/z67CRwZG8euarGGO4dfqtHMw56NfxRURERESkeFPpIVLMvLr4VebunMuI9iNoXrG5/w+wYBSUqQ71uvt/7IKq1Bji28HCD/22oOlf4qPjeb7z82xM3chDsx7SwqYiIiIiIqWISg+RYmTm1pmMWj6KC+tfSP+6/f1/gOSNvlvVtroSXG7/j38yWl8De9fDpt/8PvRpVU5jaMuhTN40ma/Xfu338UVEREREpHhS6SFSTOw8uJP7f7uf+mXrc1fbuwrnIIs+AuMuHguYHq5JfwiL9fuCpn8Z1HQQHat25Jl5z7A6eXWhHENERERERIoXv5Qexphexpg1xpj1xph7jvB+DWPMdGPMYmPMMmNMH38cVyRQ5HpzuXvm3WR5sni+8/OEBYUVwkGyfQuY1u8FZar6f/yTFRwOp1wKK8fDwSS/D//XwqYxoTEMnzFc63uIiIiIiJQCJ116GGPcwBtAb6AxcKkxpvFhmz0AfGWtbQlcAow82eOKBJKRS0ayaPciHjztQWrF1Cqcg6z5EQ7ugTbFaAHTw7W5Brw5sGR0oQxfPrw8z5zxDFvStvDYnMe0voeIiIiISIDzx0yPU4H11to/rbXZwBdAv8O2sUCZvD/HANv9cFyRgDBr+yze++M9zqt7Hn3r9C28Ay0YBTE1oM6ZhXeMk1WxAdTo4FvQ1OstlEO0rdyWG0+5kR///JFv139bKMcQEREREZHiwR+lRzUgMd/XW/Ney+9hYKAxZiswAbjlSAMZY643xiww5v/t3Xd4VGX6xvHvm14gIYHQO4QeapSiKAKi2CgqgopUWduquLqru+q6rq66dlcsgCgiKhYQrAiCIiBIJxSB0AktlACBkPr+/jjDz4gggczMSSb357rmysyZM+e5z0wymTx5z3vM4vT0dC9EEynZMo5n8PDch6kfW5+H2j/ku0IHNsPmH0rmBKYnSx4CBzbBVu9PaHrCrUm30r5qe57++Wm2Hd7mszoiIiIiIuIuf01kOgB4x1pbE7gCmGCM+V1ta+1oa22ytTY5ISHBT9FE3GGt5YmFT3Aw+yBPdX6KyJBI3xVb9h6YIGhzk+9qeEvTqyE8FpZO8FmJ4KBgnrjwCUJMCH+f+3fyCvJ8VktERERERNzjjaZHGlCr0O2anmWFDQM+ArDW/gREAJW8UFuk1Ppq81dM3zKdO1rdQdOKTX1XqCAflr8PDbuXzAlMTxYaCUnXwdppkJXhszJVo6vy9w5/Z0X6Ct5Z/Y7P6oiIiIiIiHu80fRYBCQaY+oZY8JwJiqddtI624BuAMaYpjhNDx2/ImXW7qO7eXLhk7RKaMWQFj6eWHTjLDiyE9rc7Ns63tR2IOQdh1Wf+LTMlfWupEedHoxaPkqnsRURERERCUDFbnpYa/OAu4DpwFqcs7SsNsY8boy5xrPaX4BbjTErgA+AwVanTZAyqsAW8Mi8R8gryOM/F/6HkKAQ3xZc+i5EVYJGPX1bx5uqtYYqST49xAXAGMMjHR4hLjyOh358iOz8bJ/WExERERER//LKnB7W2q+stY2stQ2stU96lj1qrZ3mub7GWnuBtbaVtba1tfZbb9QVKY0++OUDFuxawP3J91M7prZvix3dB+u+hlb9ISTMt7W8yRhnZMqu5bA7xaelKkRU4F+d/kVqRir/W/o/n9YSERERERH/8tdEpiICbD+ynZeWvMQFNS7g+kbX+77gig+hILd0HdpyQst+EBzmTMLqY51rdqZfo368u+Zdlu9d7vN6IhLYdDY6ERGRkkNNDxE/sdbyr/n/IjgomMc6PoYxxtcFYdkEqJEMlX04UaqvRMVDk6tg5STI8/1hJ/cl30eV6Cr8c/4/ycnP8Xk9EQlcOhudiIhIyaGmh4iffJb6GQt3L2Rk25FUja7q+4JpSyD9F2dS0NKqzc2QdRB++dLnpaJDo3m0w6NsOrSJMSljfF5PRERERER8T00PET9IP5bOs4ufpW3ltlzf2A+HtYAzgWloFDTv6596vlC/C8TWckas+EHnmp25qv5VjE0Zy/qD6/1SU0REREREfEdNDxE/+M/C/5Cdl82/Ov2LIOOHH7uco7BqMjTrDRExvq/nK0HB0PpG2DgbMrb5peRfz/sr5UPL89j8x8gvyPdLTRERERER8Q01PUR8bObWmczcNpPbW99O3di6/im6+jPIOVK6D205ofVNztfl7/ulXFxEHA+e/yAp+1KYuHaiX2qKiIiIiIhvqOkh4kOHcw7z5MInaRLfhEHNB/mv8LIJULEh1O7ov5q+ElfHOcxl2Xvgp5EXPev15OKaF/Pq8lfZcWSHX2qKiIiIiIj3qekh4kP/W/o/Dhw/wGOdHiM0KNQ/RdPXw7afoM1A8PUZYvyl7UA4tB02fe+XcsYYHu7wMABP/fwU1lq/1BUREREREe9S00PER1bvX81H6z/ihsY30Lxic/8VXjYBTDC0GuC/mr7W5CqIjPPbhKYAVaOrcmfrO5mzYw6zt8/2W10REREREfEeNT1EfCC/IJ8nfnqCuPA47mpzlx8L58KKD6BxTyhfxX91fS0kHFr2h7VfwNH9fit7Y9MbaVihIU///DTHco/5ra6IiIiIiHiHmh4iPvDphk9ZtX8V9593PzFhfjx7yvpv4Gi6c2hLoGk7EApyYeUkv5UMDQrlkQ6PsOvoLkavHO23uiIiIiIi4h1qeoh42f6s/by89GXOq3oeV9a70r/Fl74L5atBw+7+resPVZpDjXbOPvpxjo22VdrSq0Evxq8ez8aMjX6rKyIiIiIixaemh4iXvbjkRY7lHuPh9g9j/DmR6KE0SJ0JrW+E4BD/1fWntrdA+lrYsdivZUe2G0lkaCRPLnxSk5qKiIiIiJQianqIeNHSPUuZunEqg5oPon6F+v4tvvx9sAXQ5mb/1vWnFtdCaDQse9evZStGVuTetveyaPcivtz8pV9ri4iIiIjIuVPTQ8RL8gvyefrnp6kSVYURLUf4t3hBgXNmk7qdId7PzRZ/Ci8PzfvAqsmQnenX0tcmXkuzis14cfGLmtRURERERKSUUNNDxEs+S/2MtQfW8pfkvxAVGuXf4lvmQMZWaDvIv3Xd0PYWyMmE1VP8WjY4KJiHzn+IvVl7GZsy1q+1RURERETk3KjpIeIFR3KO8MqyV2hTuQ2X173c/wGWjIeIWGh6lf9r+1ut86FSY1jytt9Lt67cmivqXcH41ePZcWSH3+uLiIiIiMjZUdNDxAveXPEmB48f5G/n/82/k5cCZO6FtZ9D65sgNNK/td1gDCQPgbQlsGuF38uPbDeS4KBgXljygt9ri4iIiIjI2VHTQ6SYNh/azMS1E+mT2IfmFZv7P8Cy96AgF9oN8X9tt7TqDyERsNj/oz2qRldlaIuhzNg6g593/ez3+iIiIiIiUnRqeogU03OLnyM8JJw/t/mz/4sXFDiHedTtDAmN/F/fLZFxzplcUj6G7CN+Lz+4+WCqRVfjmUXPkFeQ5/f6IiIiIiJSNGp6iBTDjzt+ZM6OOdzW8jYqRVbyf4CNsyBjm3O4R1mTPNSZ0HTlR34vHRESwV+S/8L6g+uZvGGy3+uLiIiIiEjRqOkhco7yCvJ4fvHz1C5fm5ua3uROiMXjIKoSNLnanfpuqtEOqiY5h7hY6/fyPer0oF2Vdry67FWO5Ph/tImIiIiIiJyZmh4i52hK6hQ2HtrIfe3uIzQ41P8BDqXB+q+h7UAICfN/fbcZ44z22JMCOxa7UN7wwHkPcDD7IONWjfN7fREREREROTM1PUTOwdHco4xaNoq2ldvStXZXd0IsfdcZ4dBusDv1S4Kk6yGsnDPixQXNKzbnyvpXMmHNBHYf3e1KBhEREREROT01PUTOwdur3mb/8f38Jfkv/j9FLUB+HiwdDw27Q1xd/9cvKcLLQ8t+sHoyHDvgSoS729yNtZb/LfufK/VFREREROT0vNL0MMZcboxZZ4xJNcY8eJp1+hlj1hhjVhtj3vdGXRE37Dm6h/Grx3N53ctpmdDSnRDrv4Yju5zDO8q65KGQdxxWfOhK+erlqnNTs5v4fOPnrN2/1pUMIiIiIiJyasVuehhjgoFRQE+gGTDAGNPspHUSgYeAC6y1zYF7i1tXxC2jlo8iz+Zxd9u73Qux6C2IqQGJPdzLUFJUTYKa5zmHuBQUuBJheNJwYsNjeX7x81gXJlUVEREREZFT88ZIj/OBVGvtJmttDvAh0OukdW4FRllrDwJYa/d6oa6I3607sI7PUj/jxiY3Uqt8LXdCpK+DTbOh3RAIDnEnQ0lz3nDYvwE2zXKlfExYDLe1uo2FuxfyY9qPrmQQEREREZHf80bTowawvdDtHZ5lhTUCGhlj5hljFhhjLvdCXRG/e3HJi5QLK8eIliPcC7HwDQgOh+Qh7mUoaZr3gXJVYMEbrkXo16gftcvX5sUlL5JfkO9aDhERERER+ZW/JjINARKBLsAAYIwxpsLJKxljRhhjFhtjFqenp/spmkjRLNy1kHk75/Gnln8iNjzWnRDHDsDyD6Dl9RBdyZ0MJVFIuDPaI3UGpK93JUJocCj3truX1IxUPt/0uSsZRERERETkt7zR9EgDCo/zr+lZVtgOYJq1NtdauxlYj9ME+Q1r7WhrbbK1NjkhIcEL0US8w1rLy0tfpkpUFfo36e9ekKXvQl4WtL/dvQwlVbshEBwGP7/pWoTutbvTomILXlv+Gtn52a7lEBERERERhzeaHouARGNMPWNMGNAfmHbSOp/hjPLAGFMJ53CXTV6oLeIXs7bNImVfCne2vpPw4HB3QuTnwc9joG5nqNrCnQwlWbkESOoHy9+HrIOuRDDGcG+7e9l1dBeTfpnkSgYREREREflVsZse1to84C5gOrAW+Mhau9oY87gx5hrPatOB/caYNcBs4AFr7f7i1hbxh7yCPF5Z9gr1YutxdYOr3Qvyy+dweAd0uMO9DCVdh9sg9xgsneBahPbV2tOxWkfGpIwhMyfTtRwiIiIiIuKlOT2stV9ZaxtZaxtYa5/0LHvUWjvNc91aa++z1jaz1iZZaz/0Rl0Rf/h84+dsOrSJu9vcTUiQi2dLWfA6xNWFRpe5l6Gkq5rkjIT5ebQzMsYl97S9h4zsDMavGe9aBhERERER8d9EpiKlUnZ+Nq+teI0WFVvQrXY394KkLYHtC6H9bRAU7F6O0qD9bXBoO6z70rUIzSs1p0edHoxfPZ79WRrUJiIiIiLiFjU9RP7ApF8msfvobu5tdy/GGPeCLHgDwspD65vcy1BaNO4JFeo4I2NcdFebu8jJz2FMyhhXc4iIiIiIlGVqeoicRmZOJmNSxtCpeifaV2vvXpDDO2H1FGhzE0TEuJejtAgKdkZ7bPvJGSHjknqx9ejdsDeT1k1ix5EdruUQERERESnL1PQQOY0JayeQkZ3B3W3udjfI/FfBFmgC07PRdiBExMLcF12NcVur2wgiiDdXuncaXRERERGRskxND5FTOJR9iHdXv0u32t1oXqm5e0GO7oclb0PS9RBXx70cpU14eTj/T7D2c9j7i2sxqkZXpV/jfkzbOI0th7a4lkNEREREpKxS00PkFN5Z/Q5Hc49yR2uXR1csfMM5BeuFI93NURq1vw1Co2DeS67GGJY0jPDgcF5b8ZqrOUREREREyiI1PUROsj9rPxPXTuTyupfTKK6Re0Gyj8DPb0KTq6ByE/dylFbRFaHdEFj5ERzc6lqMSpGVGNBkAN9s/oYNBze4lkNEREREpCxS00PkJONWjSM7P5vbW9/ubpDF4+D4Ieh8n7s5SrOOd4IJgvn/czXGkOZDiAqN4rXlGu0hIiIiIuJPanqIFLL32F4mrZvE1fWvpl5sPfeC5B6Hn0ZB/S5Qo517OUq72BrQegAsmwCZe12LUSGiArc0u4WZ22ayZv8a13KIiIiIiJQ1anqIFDJm5RjyC/K5rdVt7gZZPhEy90Dnv7ibIxBccC/k58ACd0dZDGw2kJiwGEYtH+VqDhERERGRskRNDxGPnZk7+WTDJ/RJ7EPN8jXdC5KfB/NehhrJULezezkCRcUG0Kw3/DwWsjJci1E+rDxDWgxhzo45LN+73LUcIiIiIiJliZoeIh6jV47GYBjRcoS7QVI+goytzlwexribJVB0vg9yjsDCN12NcWOTG4mPiNdoDxERERERP1HTQwRIy0xjaupUrmt0HVWjq7oXJC8Hvn8KqrWCRj3dyxFoqiY5Z8H56VU4dsC1GFGhUQxpPoQFuxawbO8y13KIiIiIiJQVanqI4MzlYYxhWIth7gZZOh4ytkHXRyFIP55e1fUR5zTAc190NUa/xv2Ij4jn9eWvu5pDRERERKQs0F9VUuYVHuVRJbqKe0FyjsIP/4U6F0DDbu7lCFSVm0Cr/vDzaDi8y7UYUaFRDG0xlJ92/aTRHiIiIiIiPqamh5R5JWaUx8I34ehe6Pao5vLwlS4PQkE+zPmvqzGub3Q98RHxvLbc3TPKiIiIiIgEOjU9pEzbcWRHyRjlkZUB816CxMugdgf3cgS6uLrQbjAsfRcObHItxonRHgt2LWDpnqWu5RARERERCXRqekiZNjZlLEEmyP1RHvP/B8cPQdeH3c1RFlx0PwSFwvdPuxrjxGiP11dobg8REREREV9R00PKrBIzyiNzLyx4HZr3hWot3ctRVpSvCu3/BCs/gj2rXYuh0R4igcsYM8IYs9gYszg9Pd3tOCIiImWamh5SZp0Y5TG0xVB3g/zwX8g7Dpf8w90cZckF90B4DHz3uKsxTpzJ5bUVmttDJJBYa0dba5OttckJCQluxxERESnT1PSQMmln5k6mpk7l2kbXujvKY89qWDzOmWeiUkP3cpQ1UfFw0V9g/TewYaZrMSJDIhnaYigLdy1k+d7lruUQEREREQlUanpImTRu1TgwuDvKw1r4+m8QEaO5PNzQ/naIbwDfPAh5Oa7FuL7R9cSFx/HmyjddyyAiIiIiEqjU9JAyZ8/RPUzeMJneDXtTNbqqe0HWTIUtPzqHtUTFu5ejrAoJg8ufhv0b4Gf3Gg5RoVHc0vwW5qbNZfU+9+YYEREREREJRGp6SJnz9uq3sdYyPGm4eyFyjsG3D0OVFtBuiHs5yrpGPZzTBH//DBzZ41qM/o37ExMWo9EeIiIiIiJepqaHlCn7svbxyfpPuKrBVdQoV8O9IPNfgUPboeczEBziXg6By59yJpL97l+uRSgXVo6bm93M7O2zWXdgnWs5REREREQCjVeaHsaYy40x64wxqcaYB/9gvWuNMdYYk+yNuiJna/zq8eQW5HJr0q3uhcjYBnNfdE5RW/dC93KIo2ID6HgHLJ8IOxa7FuOmpjdRLrScRnuIiIiIiHhRsZsexphgYBTQE2gGDDDGNDvFeuWBe4CFxa0pci4OHD/ApHWT6FmvJ7VjarsXZPo/AAM9/u1eBvmtix6AclXgqwegIN+VCDFhMQxoMoCZW2eyMWOjKxlERERERAKNN0Z6nA+kWms3WWtzgA+BXqdY79/AM8BxL9QUOWsT1kzgeN5xRiSNcC/E2i9g7TTndKmxNd3LIb8VXh56PAE7l8LPo12LMbDZQCJCIhi90r0MIiIiIiKBxBtNjxrA9kK3d3iW/T9jTFuglrX2Sy/UEzlrh7IP8cEvH3BpnUupX6G+OyGyDsKX90HVJLjgXncyyOklXQ+JPeC7x+HAZlcixEXE0b9xf77Z8g1bD291JYOIiIiISCDx+USmxpgg4AXgL0VYd4QxZrExZnF6erqvo0kZ8v4v73M09ygjWro4ymP6P+DoPug1CoJD3cshp2YMXPUSBIXAtD+Dta7EuKX5LYQGhfJWyluu1BcRERERCSTeaHqkAbUK3a7pWXZCeaAF8L0xZgvQAZh2qslMrbWjrbXJ1trkhIQEL0QTgWO5x5i4diJdanahcXxjd0KkznQmyrzwXqjWyp0McmaxNeDSx2HLj7DkHVciVIqsxLWJ1/L5xs/ZlbnLlQwiIiIiIoHCG02PRUCiMaaeMSYM6A9MO3GntfaQtbaStbautbYusAC4xlrr3mkSpEz5aN1HHMo+xK0tXTpjy/HDMO0eqNQYLvqrOxmk6NoNhnoXwbePwKEdrkQY0mIIGBi3apwr9UVEREREAkWxmx7W2jzgLmA6sBb4yFq72hjzuDHmmuJuX6Q4jucdZ/ya8bSv1p6WCS3dCTHzMTicBr1ehdAIdzJI0RkDV78CNh++GOnKYS5Vo6tyTYNrmLxhMvuy9vm9voiIiIhIoPDKnB7W2q+stY2stQ2stU96lj1qrZ12inW7aJSH+MuU1Cnsy9rn3hlbUmfC4regwx1Q63x3MsjZi68H3f4JG76FpeNdiTCsxTDybB7vrn7XlfoiIiIiIoHA5xOZirgltyCXt1e9TeuE1pxX9Tz/BziyGyb/CRKaQteH/V9fiuf8EVC/C3z9IOxd6/fytWNqc1ndy5i0bhIZxzP8Xl9EREREJBCo6SEB64uNX7Dr6C5ubXkrxhj/Fi8ogMkjIOcoXP8OhEX5t74UX1AQ9BkN4eXg4yGQc8zvEW5NupVjeceY+MtEv9cWEREREQkEanpIQMovyOetVW/RNL4pnWt09n+AeS/C5h/giv9C5Sb+ry/eUb4K9HkT0tfC9If8Xj4xLpFLal3CxLUTyczJ9Ht9EREREZHSTk0PCUgzts1g6+GtDE8a7v9RHtsWwqwnocW10Gagf2uL9zXsBheOdE5hu2qy38uPaDmCIzlHmLRukt9ri4iIiIiUdmp6SMCx1jJ25Vjqxdaje53u/i2edRA+HQYVasFVLzlnApHS75J/QM3z4PN74MBmv5ZuUakFHat1ZMKaCRzPO+7X2iIiIiIipZ2aHhJwfkz7kXUH1zGsxTCCjB+/xfPz4JOhzgSm170NETH+qy2+FRwK177lNLEm3QzZ/j3U5NaWt7L/+H4+S/3Mr3VFREREREo7NT0k4IxNGUu16GpcUf8K/xb+9mHYOAuuegFqtPVvbfG9uDpw3TjYuwam/MmZrNZPkqsk0zKhJe+sfofcgly/1RURERERKe3U9JCAsmTPEpbtXcbg5oMJDQr1Y+HxsPB16HAntL3Ff3XFvxp2h8v+A798Ad//x29ljTHcmnQraZlpfLP5G7/VFREREREp7dT0kIAyJmUM8RHx9E3s67+iW+bBl3+BBt3g0sf9V1fc0f42Z4LaOc9Cyid+K3tRzYtIjEtkbMpYCqz/RpmIiIiIiJRmanpIwFizfw3z0uYxsNlAIkIi/FP04Bb4aCDE1XUOfQgO8U9dcY8xcOULULsTTL0T0pb4pWyQCWJ4i+FsOrSJ2dtn+6WmiIiIiEhpp6aHBIyxKWMpF1qOGxrf4J+CR/fBxOuhIB9unASRFfxTV9wXEgY3TIDoyvB+f9i/0S9le9TtQc1yNRm7cizWWr/UFBEREREpzdT0kICw6dAmZm6dyYAmAygfVt73BY8fhvf6QsY2GPABVGzg+5pSskRXgps/gYI8eLc3HN7p85IhQSEMTRrKqv2rWLBrgc/riYiIiIiUdmp6SEAYlzKO8OBwbmp6k++L5WbBBwNgz2ro9y7U6eT7mlIyJTSGmz+FrINO4+Pofp+X7NWgF5UjKzM2ZazPa4mIiIiIlHZqekiptytzF19u+pK+iX2pGFnRt8Xyc+HjwbB1HvR5Expd5tt6UvLVaOuM9jm4BSZeB9lHfFouLDiMW5rfws+7f2Zl+kqf1hIRERERKe3U9JBS79017wIwuPlg3xbKz4PPbof138CVz0HSdb6tJ6VHvc7QbzzsWuGMAso55tNy1zW6jpiwGN5KecundURERERESjs1PaRUO3j8IJ9u+JQr6l9BtXLVfFcoLwc+HQYpH0O3R+G84b6rJaVT457Q5w1nFNB71zrzvvhIdGg0Nza9kVnbZ7Exwz+TqIqIiIiIlEZqekipNnHtRI7nHWdYi2G+K5J7HCbdDGs+gx5PQOe/+K6WlG4t+8G1Y2HHzzChNxw74LNSNzW5iciQSMatGuezGiIiIiIipZ2aHlJqHc09yvu/vE/X2l2pX6G+b4pkZ8L718OG6XDlC9Dpz76pI4GjxbXQbwLsToHxV0Nmuk/KVIiowLWJ1/LVpq/Ymen7M8eIiIiIiJRGanpIqfXxuo85knOE4Uk+OtQk66BzWtotc6H3G3CeD0eTSGBpcgXcOAn2b4S3e0LGdp+UGdR8EBh4Z/U7Ptm+iIiIiEhpp6aHlEo5+Tm8u+Zd2ldrT4tKLbxfYP9GGNsd0pbCdeOg9QDv15DA1qArDJwMmXtgbDdIW+L1ElWjq3J1/auZvGEy+7N8f7pcEREREZHSRk0PKZWmbpxKela6b+by2Drf+SP12H64ZSo07+P9GlI21OkEw76FkHB4+0pYM83rJYa0GEJOfg4T1070+rZFREREREo7NT2k1MkryOPtVW/TvGJzOlTr4N2Nr5gE7/aCqIow/Duoe4F3ty9lT+WmMHwWVG0BHw2EuS+CtV7bfL3YenSv050Pf/mQIzlHvLZdEREREZFAoKaHlDozts5g+5HtDE8ajjHGOxvNz4VvH4EpI6BWexg2Ayo28M62RcolwKDPoXlfmPkYTPkT5Bz12uaHJQ3jSO4RPlr3kde2KSIiIiISCNT0kFLFWstbKW9RL7YeXWt39c5GD+90zrIx/xVIHgo3T4aoeO9sW+SE0Ei49i3o8ndY+RGM6Qrp67yy6eYVm9OxWkcmrJlAdn62V7YpIiIiIhII1PSQUmVu2lzWHVzH0BZDCTJe+PbdOAveuBB2rYS+Y+GqFyEkrPjbFTmVoCDo8jdngtOj+2B0F6cB4gXDk4az//h+pqZO9cr2REREREQCgVeaHsaYy40x64wxqcaYB09x/33GmDXGmJXGmO+MMXW8UVfKnrEpY6kaXZUr611ZvA3l5cB3/4YJfSG6Moz4Hlpe75WMImfUoCvc9iNUawWTb4Vpf4bs4s3HcV7V82hZqSXjVo0jryDPS0FFREREREq3Yjc9jDHBwCigJ9AMGGCMaXbSasuAZGttS+AT4L/FrStlz7K9y1i6dymDmw8mNDj03De0ZzWM7Qo/Pgetb4Rbv4OERt4LKlIUMdVh0Bdw4UhYOgFevwC2zD3nzRljGJY0jLTMNKZvme7FoCIiIiIipZc3RnqcD6RaazdZa3OAD4FehVew1s621h7z3FwA1PRCXSljxqaMpUJ4Bfo0PMdTyObnwY/Pw5sXw5Hd0P996P0ahEV7N6hIUQWHQPfHYMjXYILgnavgm79DbtY5ba5LrS40iG3AW6vewnrxDDEiIiIiIqWVN5oeNYDthW7v8Cw7nWHA116oK2XIugPrmLNjDjc1vYmo0Kiz38CulTCuB3z3ODS5Au5YCE2KeYiMiLfU6Qi3z4PzhsOCUfBGZ9j841lvJsgEMTRpKBsObuDHtLN/vIiIiIhIoPHrRKbGmJuBZODZ09w/whiz2BizOD093Z/RpIQbt2ocUSFRDGgy4OweePwQfPVXGH0xHNzqnD3j+vEQXdE3QUXOVVg0XPkcDPwM8nNg/FXw6XBnVNJZ6FmvJ9WjqzM2ZaxvcoqIiIiIlCLeaHqkAbUK3a7pWfYbxpjuwD+Aa6y1pzynorV2tLU22VqbnJCQ4IVoEgi2H9nO9C3T6de4H7HhsUV7kLXOWTH+lww/j3ZORfvnxZB0HRjj28AixdHgErhzIVz0V1gzFV49Dxa84RyeVQShQaEMaj6IZXuXsWTPEh+HFREREREp2bzR9FgEJBpj6hljwoD+wLTCKxhj2gBv4jQ89nqhppQh76x6hyATxMBmA4v2gK3zYWx356wYsTXh1llw5fMQGefboCLeEhoJXf8BdyyAmsnwzd/g9Y7wy1dOQ+8M+iT2IT4iXqM9RERERKTMK3bTw1qbB9wFTAfWAh9Za1cbYx43xlzjWe1ZoBzwsTFmuTFm2mk2J/Ib6cfSmZI6hV4Ne1E5qvIZVl4HHwyAt3vC4Z1wzaswfCbUaOufsCLeVrEB3DwZbpgItgA+HABvXwE7Fv/hwyJDIrm56c3MTZvL2v1r/RRWRERERKTkCfHGRqy1XwFfnbTs0ULXu3ujjpQ9E9ZMIN/mM7T50NOvtH+jc1aWFR9AWDno9ii0vx3CzmHCU5GSxhhoehU0ugyWvgvfPw1ju0GTq+CiB6B661M+7IYmNzBu1TjeWvUWz138nH8zi4iIiIiUEF5peoj4wqHsQ0xaN4nL6l5GrZhav18hfT38+BykfAzBYdD+Nuh8vyYplcAUHArnDYOWN8BPo5zLL19Ao8ud+T9qtvvN6jFhMdzQ2Gl8bGm9hbqxdd3JLSIiIiLiIr+evUXkbHzwywccyzvGsBbDfnvH9kXw0SAYdT6s/Rw63gn3rITLn1LDQwJfeDno8jcYmQJdH4btC2FsV5jQB1K/+82cHzc3u5mw4DDeXv22i4FFRERERNyjpoeUSMdyjzFx7UQurnkxjeMbO2euWD3FmaD0re6wcTZceC/cmwI9noDyVdyOLOJfEbHO4S33pkD3x2DPanivL7zW0TkMJvc4lSIr0adhH6ZtnMbuo2d36lsROXfGmBHGmMXGmMXp6eluxxERESnTjC3CmQDckJycbBcv/uPJ+iTwfLYsjWenryPdzCC86hfcWfMRbgvZCkvHw6HtEFcPOtwBrW90/uMtIo68bFg12TnsZU8KRFWCNjeR1uRyrph1OyGZnTmwvSfVK0TywGWN6d2mhtuJxc+MMUustclu5yhr9HlGRETEO871s4zm9JAS47NlaTw0OYXs3CwqNPyOWlmhDJ/zJzAFUO9i6PmMM39BULDbUUVKnpBwaD0AWvWHLT/Cwjdh/qvUmPcy51dqwM/RcwkN7khaBjw0OQVAjQ8RERERCXhqekiJMfnr6dxrZxJWaREvhEbwp32ZjM2/kllRPflo0E1uxxMpHYyBehc5l8M7Gf3KvxmcMYMF5SMZkfAoVfe1YnJeZ579JlRNDxEREREJeGp6iLsObII1UyHlE97NWUVWcDBXxNYm+nh57sn4N7mEYg67HVKklIqpzlOZV2G4gupHXmNSTBpfZczl5pDv2JJVBWYNgua9oXIzp1kiIiIiIhJg1PQQ/9uXCms+c5odu1c6y2ok80LIrbwbFEF+2FSydlxJHqEAVK8Q6V5WkVKueoVI0jKy2LmvN9H1XuWS6AFcnhFO//D51P3xOZjzX6jYEJr1hmbXQNWWaoCIiIiISMBQ00N8Lz8Ptv0E67+BdV/DgY3O8prnQY8nnT+0KtSm7tLt5C0eSkF2ZfKONAcgMjSYBy5r7GJ4kdLtgcsa89DkFLKO1yQvM5Gg+IV8eeTvXHj1PSQnhjqnfV4zFea+AD8+BzE1odFl0Lgn1O0MoRFu74KIiIiIyDlT00N8I2MbbJzlXDZ9D8cPQXCY80dUh9udP6hia/7mIXGVUjHhu4nOuJksgnSWCREvOPHz8+z0dezedwlRdUdzdecd9G5zjbPCecOcy9F9TlNy/Tew4gNY/BaERjk/sw26QsNuzogQjQIRERERkVJETQ/xjsx054wRW+bC5jmwf4OzPKYGNLna+c9xg0sgvPwpH26tZUzKGGqUq8HnA+8jNCjUj+FFAlvvNjU8zY+uDPp6MYszJpObfyuhwYV+zqIrQduBziX3uPPzvH6607jcMN1ZJ7aWcyaluhdCvc6/a1yKiIiIiJQ0anrI2bMWMrbCtoWwfQFsnQ/pvzj3hZWD2h0heajzn+FKjYr0n+GFuxeSsi+FRzo8ooaHiA8NTxrOHd/dweebPqdvYt9TrxQaAYmXOheAg1t+Hbm17ktY/p6zPK4u1LkAarWH2h2K/PMuIiIiIuIvanrImWVnwq7lkLYEdiyG7T9D5m7nvvAYqHU+tOoPdS+Caq0g+Oy/rcasHENCZAK9GvbybnYR+Y0La1xI0/imvJXyFr0a9CI4KPjMD4qr6zQyk4dCQQHsXeOM6tryo3NIzPKJznqRcU4DpEYy1GjrXCLjfLo/IiIiIiJ/RE0P+a3sI7A7BXathF0rnGZH+i9gC5z7K9RxhrXXau+M6KjcFIryR9MfWL53OT/v/pn7k+8nPDi8+PsgIqdljOHWlrdy3/f38e3Wb+lZr+fZbSAoCKq2cC4dbnNGfu1PhW0LnJFf23925gU5oWJDqNYaqrV0mqJVW0JUvFf3SURERETkdNT0KKsK8p0h63vXwJ7VsGeV8/XAZsA660RXdv5IaXoN1GjnXKIrej3KmJQxxIbHcn2j672+bRH5vW61u1E/tj6jV47msrqXEWSCzn1jxkClROfSdqCz7Pgh2LnMGR2WthS2L4RVn/z6mNhaUKX5r5fKzaFiAwjWoW0iIiIi4l1qegS63ONwYBPsW+9MLpq+Dvb+4tzOz/asZJw/OKq2hFY3Oo2Oai2hfFWfx1u7fy1zdszhrtZ3ERUa5fN6IgJBJojhScP5+9y/M3v7bLrV7ubdAhGxUL+Lcznh2AHP6LEVvzZZU2dCQZ4nVIgzKiShiXM50Uip2BDCor2bT0RERETKDDU9AkHucecUsQc3w/6NTpPjwCY4sBEObuX/R26A8x/WhCbQoIvnj4umziEqYe40HEavHE350PLc2PRGV+qLlFU96/Xk9RWv8+aKN+laqyvG1xOQRsU7Z3BqcMmvy/KynUZs+i+wd61zffdKWDOV37xvxdSEivUhvj7EN/B8rQ9xddQQEREREZE/pKZHaZB7HA6nwaHtkLHdaXAc2u40NA5ugSM7f7t+eIzzB0GNdtCyf4n9j+mGgxuYuW0mf2r5J8qHnfpUtiLiGyFBIdyadCuPzn+UH9N+5KKaF7kQItwz10fL3y4/eYTavlSnibtmGmQd+O260ZWdiVbj6jhN3Qq1oUItZ/6hmBquNXRFREREpGRQ08Nt2ZmQuQcO74Qju5zmxmHP10M7nK9H03/7GBME5as7H+zrd/F84PdcKjaAqIql4rSRY1aOISokipub3ux2FJEy6ar6VzmjPVa+SecanX0/2qOoQiOgSjPncrKsg56RbJudU2cf3OJcti+E1VN+PVzmhMg4iK3pjBaJqf7bS/lqzmF84TGl4j1TRERERM6emh6+kJfjNCoKXzL3QObeX78e2e1cco78/vHhMc6H8diazvwasTWd/1hW8PwXM6ZGqZ/wb/OhzXyz5RsGtxhMhYgKbscRKZNCg0MZ1mIYTyx8goW7F9KhWge3I51ZZNyvEyufrCDfaR5nbHNGxR3e4TSPD6U5y7YvcJomJwuNcpof5apCucpQrsqvX6MToFyCM6IkOsFpyIiIiIhIqVFmmh6fLUvj2enr2JmRRfUKkTxwWWN6t6lx5gfm58HxDGcSvqwDv/16bP+vl6P74Ng+OLofsg+delth5ZwP0tGVnTMWNOwO5av8+t/GmBrO9fByXt33kmhsyljCg8MZ1GyQ21FEyrTeib0ZvXI0b654s3Q0Pf5IULDTJI6tCXVOs07OMc+oup1O4znT04A+ssv5umc1bJz9x+/j0ZUgqtKvX6PinBF2URUhMt6ZvyQy3mnQRMUXuUl9zr+nREREROS0ykTT47NlaTw0eSVVTQpJoceJPxzE3CmzqLe5Aq0q4Zxe8XiG8zUrw/lP4PEM53r24dNvOCj01w+60RWhWutfPwSf+M9gucrOsnJVStR8Gm7afmQ7X276kgFNBlAx0vunwBWRogsPDmdIiyE8s+gZluxZQrsqpxhBEUjCopzDACs2+OP1co87I/OO7oOje50Rekf3Oo3tY/uc5YfTYHeKc/3/z4Z1qprlnAZIRAWI9FwiYp3bEc71xXvymb7oAFUKIDwctmU056HJKQBqfIiIiIgUQ5loejw7fR1ZeVlkNH6Xqw8d4b6DGc4dKz0rhEQU+gAa64y2qNzM88G0wq//tYuK8/znztPoCCun48DPwVspbxFsghnSYojbUUQEuLbRtYxJGcObK95kdI/RbscpGUIjnMlR4043ZKQQayH32K8jALMOOM3zY56vv2mmH3QmZj3RaM89BkAykBwMH1Yox5OV4qmQeiv7chvw7PR1anqIiIiIFEOZaHrszMgCwok6VpkPIiswZ/d9HCaKIzaKRf/uC6GRbkcsM3Zm7mTqxqlcm3gtlaMqux1HRIDIkEgGNx/MC0teYPne5bSu3NrtSKWLMc5IvrBoZ+6ls5GXDccP0fXJaZTjGPsTviIiJ4OM3NrAid9fIiIiInKugtwO4A/VKzhNjb2ZyRwPP8SK4AQ22eqEVaimhoefjU0Zi8EwPGm421FEpJAbGt9AXHgcb6x4w+0oZUtIOJSrTHZsfVZSh0NR6RzObEkuzjwgJ35/iYiIiMi58UrTwxhzuTFmnTEm1Rjz4CnuDzfGTPLcv9AYU9cbdYvqgcsaExkaTP7RxgCERK8nMjSYBy5r7M8YZd6uzF1MSZ1C38S+VI2u6nYcESkkKjSKIS2GMG/nPFakr3A7TpnzwGWNiSq/DROUQ97RRgD6PSUiIiLiBcVuehhjgoFRQE+gGTDAGNPspNWGAQettQ2BF4Fnilv3bPRuU4On+iZRNbIuBbkxlItL5am+STpO2s/GpowF0CgPkRLqxGiP11e87naUMqd3mxpc1Go/2GAKjjagRoVI/Z4SERER8QJvjPQ4H0i11m6y1uYAHwK9TlqnFzDec/0ToJsx/p0BtHebGsx/sBvXN7uUiJiNXNlK80n4067MXUxOncy1iddqlIdICRUVGsXgFoOZl6bRHm7Yk7eCDtXPY/NTfZj3YFc1PERERES8wBtNjxrA9kK3d3iWnXIda20ecAhw5VylF9S4gMzcTFamrzzzyuI1GuUhUjr0b9xfoz1csPvoblIzUrmwxoVuRxEREREJKCVqIlNjzAhjzGJjzOL09HSf1OhQrQPBJpi5aXN9sn35PY3yECk9NNrDHT+m/QigpoeIiIiIl3mj6ZEGFD5HX03PslOuY4wJAWKB/SdvyFo72lqbbK1NTkhI8EK03ysfVp5WCa2YlzbPJ9uX39MoD5HSRaM9/G9e2jyqRVejfmx9t6OIiIiIBBRvND0WAYnGmHrGmDCgPzDtpHWmAYM8168DZllrrRdqn5PONTuz9sBa9mXtcytCmaFRHiKlj0Z7+Fdufi4Ldi3gghoX4OfprkREREQCXrGbHp45Ou4CpgNrgY+stauNMY8bY67xrPYWUNEYkwrcB/zutLb+dGL4sEZ7+N6bK9/EYDTKQ6SU6d+4P/ER8by67FW3owS85enLOZp7VIe2iIiIiPiAV+b0sNZ+Za1tZK1tYK190rPsUWvtNM/149ba6621Da2151trN3mj7rlqHNeYSpGVNK+Hj207vI3PUj+jX+N+GuUhUspEhUYxrMUwFuxawKLdi9yOE9Dmps0lxITQoVoHt6OIiIiIBJwSNZGpvxhjuKD6BczfOZ/8gny34wSs11e8TmhQqEZ5iJRS/Rr3o3JkZV5d9iouHpEY8OalzaNNlTZEh0a7HUVEREQk4JTJpgc4h7gczjlMyr4Ut6MEpI0ZG/ly05cMaDqASpGV3I4jIucgIiSCES1HsHTvUubvnO92nIC099he1h1cp0NbRERERHykzDY9OlbvSJAJYt5OzevhC6OWjyIqNIqhzYe6HUVEiqFvYl+qR1fnf8v+p9EePnBibqkLql/gchIRERGRwFRmmx6x4bG0rNSSOTvmuB0l4Kzdv5YZW2cwsNlAKkRUcDuOiBRDaHAot7W6jdX7VzN7+2y34wScH9N+pHJkZRrFNXI7ioiIiEhAKrNND4CutbuyZv8a0jLT3I4SUEYtH0VMWAwDmw10O4qIeMHVDa6mTkwdXl3+KgW2wO04AeNY7jHmps3lktqX6FS1IiIiIj5Sppse3et0B2Dm1pkuJwkcK9JX8MOOHxjSYggxYTFuxxERLwgJCuGOVnew4eAGpm+Z7nacgDFv5zyy8rLoUaeH21FEREREAlaZbnrUKl+LpvFNmbF1httRAoK1lheXvEh8RDw3NrnR7Tgi4kWX17ucxLhE/rfsf+QW5LodJyDM2DqD+Ih42lZp63YUERERkYBVppseAJfWuZQV6SvYfXS321FKvR/TfmTJniXc1uo2okKj3I4jIl4UZIK4t+29bD+ynU/Xf+p2nFIvOz+bH7b/wCW1LiEkKMTtOCIiIiIBS02POpcC8N2271xOUroV2AJeXvoyNcvV5LrE69yOIyI+0LlGZ9pWbssbK97gWO4xt+OUavPT5nMs75gObRERERHxsTLf9KgbW5fEuES+3fKt21FKtS83fcn6g+u5u+3dhAaHuh1HRHzAGMPIdiPZf3w/E9ZMcDtOqTZj6wxiwmI4r9p5bkcRERERCWhlvukBzmiPZXuXkX4s3e0opVJOfg6vLnuVpvFNuazuZW7HEREfal25NV1rdeXt1W9z4PgBt+OUSjn5OXy//Xu61u5KaJCaxCIiIiK+pKYHcGntS7FYHeJyjj5a9xE7j+7k3nb3EmT0LSUS6O5pew9ZeVmMWTnG7Sil0oJdCziSe+T/D68UEREREd/RX6hAgwoNqBdbT6euPQeZOZmMXjma9tXa06l6J7fjiIgf1K9Qn94NezNp3STSMtPcjlPqzNg6g/Kh5elQrYPbUUREREQCnpoeOMepX1rnUhbtWaTh2mfp7dVvczD7ICPbjnQ7ioj40e2tbifIBPHqslfdjlKq5BbkMmvbLLrU6kJYcJjbcUREREQCnpoeHj3q9KDAFjBr2yy3o5Qau4/u5t3V73J53ctpXqm523FExI+qRlfl5qY388WmL1i9b7XbcUqNRbsWcTjnsA5tEREREfETNT08GsU1onb52szYOsPtKKXGy0tfpsAWMLKdRnmIlEXDk4YTHxHPfxf9F2ut23FKhW+3fktUSBSdauhwQBERERF/UNPDwxhD9zrdWbhroQ5xKYKU9BS+2PQFtzS/herlqrsdR0RcUC6sHHe1uYule5eqYVwEufnOoS0X17yY8OBwt+OIiIiIlAlqehRyVf2ryLf5fLHxC7ejlGjWWp5d/CzxEfEMazHM7Tgi4qI+DfvQsEJDXljyAjn5OW7HKdF+2PEDB7MPclWDq9yOIiIiIlJmqOlRSGJcIkmVkpiSOkVDtf/At1u/ZdneZfy5zZ8pF1bO7Tgi4qKQoBAeOO8B0jLTmLh2ottxSrQpqVOoHFlZZ7oSERER8SM1PU7SJ7EPqRmprN6viflOJTs/mxeXvEhiXCJ9GvZxO46IlACdqnfiopoXMXrlaPZn7Xc7Tom099he5qbNpVfDXoQEhbgdR0RERKTMUNPjJJfXvZyI4Agmb5jsdpQSaeLaiaRlpvFA8gMEBwW7HUdESoi/tPsLWXlZvL7idbejlEjTNk6jwBbQu2Fvt6OIHxhjRhhjFhtjFqenp7sdR0REpExT0+Mk5cPKc2mdS/l689dk5WW5HadEST+WzuiVo7m45sV0rN7R7TgiUoLUr1Cffo378fH6j1l3YJ3bcUoUay1TNkyhXZV21I6p7XYc8QNr7WhrbbK1NjkhIcHtOCIiImWamh6n0CexD5m5mczcOtPtKCXK80ueJyc/h7+e91e3o4hICXRn6zuJDYvlyYVPal6kQpbsWcK2I9vom9jX7SgiIiIiZY6aHqeQXCWZWuVrMSV1ittRSoxFuxfx5aYvGdpiqP5TKSKnFBsey8h2I1m2dxmfb/rc7TglxpTUKUSHRtO9dne3o4iIiIiUOWp6nIIxhj4N+7Bo9yK2H97udhzX5Rbk8p+F/6FGuRoMS9IpakXk9Ho17EXLhJY8v/h5DuccdjuO6zJzMpmxdQY96/UkKjTK7TgiIiIiZY6aHqdxdYOrCTJBGu0BvL/2fVIzUnnw/AeJDIl0O46IlGBBJoh/tP8HGdkZjFo2yu04rvtmyzdk5WXpbFciIiIiLilW08MYE2+MmWGM2eD5GneKdVobY34yxqw2xqw0xtxQnJr+UjW6Kp2qd2LqxqnkF+S7Hcc1e4/t5bXlr3FxzYvpUquL23FEpBRoVrEZ/Rr148N1H/LLgV/cjuOqKalTaBDbgKRKSW5HERERESmTijvS40HgO2ttIvCd5/bJjgG3WGubA5cDLxljKhSzrl/0TezL3mN7mZs21+0ornlu0XPkFeTxt/P/5nYUESlF7mpzFxXCK/DEgicosAVux3HF+oPrWZm+kj6JfTDGuB1HREREpEwqbtOjFzDec3080PvkFay16621GzzXdwJ7gVJx/rYutbpQJaoK49eMP/PKAWh+2ny+3vI1w5OGU6t8LbfjiEgpcmJS0xXpK/h0w6dux3HF+NXjiQyJpFeDXm5HERERESmzitv0qGKt3eW5vhuo8kcrG2POB8KAjae5f4QxZrExZnF6enoxoxVfaFAoA5sNZNHuRazat8rtOH51LPcY//rpX9SLrcfQpKFuxxGRUqhXg16cX/V8Xlj8AnuO7nE7jl/tPrqbrzZ/Rd/EvlSIqOB2HBEREZEy64xND2PMTGPMqlNcfvOvK2utBewfbKcaMAEYYu2pxzpba0dba5OttckJCSVjMMh1ja6jfGh53l71tttR/OrlpS+z6+guHu/0OOHB4W7HEZFSyBjDYx0fI68gjycWPIHza6JsmLh2ItZaBjYb6HYUERERkTLtjE0Pa213a22LU1ymAns8zYwTTY29p9qGMSYG+BL4h7V2gTd3wNeiQ6Pp17gfM7fNZNvhbW7H8Ytle5fxwS8fcGPTG2ldubXbcUSkFKsVU4u72tzF9zu+55st37gdxy+O5Bzh4/Uf06NuD2qUq+F2HBEREZEyrbiHt0wDBnmuDwKmnryCMSYMmAK8a639pJj1XHFT05sINsG8u+Zdt6P4XHZ+No/Oe5Tq5apzd5u73Y4jIgHg5qY3k1QpiacWPsWB4wfcjuNzH6//mKO5RxnSfIjbUURERETKvOI2PZ4GLjXGbAC6e25jjEk2xoz1rNMPuAgYbIxZ7rm0LmZdv0qISuDqBlfzWepn7M/a73Ycn3pjxRtsObyFRzs+SlRolNtxRCQABAcF869O/+JI7hGe/vlpt+P4VE5+Du+teY8O1TrQtGJTt+OIiIiIlHnFanpYa/dba7tZaxM9h8Ec8CxfbK0d7rn+nrU21FrbutBluRey+9Wg5oPIzs/mw3Ufuh3FZ9buX8vbq96md8PedKreye04IhJAEuMSGZE0gq83f83sbbPdjuMzX276kvSsdIa00CgPERERkZKguCM9yoz6sfW5pNYlfPDLBxzLPeZ2HK/LysviwR8fJD4invuT73c7jogEoOFJw2kU14jHfnqMfVn73I7jdQW2gHdWv0OT+CZ0rNbR7TgiIiIigpoeZ2VIiyEcyj7E5A2T3Y7idc8teo5Nhzbx5IVPEhse63YcEQlAocGhPN35aTJzMnlk3iMBdzaXH7b/wKZDmxjcfDDGGLfjiIiIiAhqepyVNpXbkFwlmTEpYziSc8TtOF4za9ssPlr/EUOaD6Fjdf13UkR8JzEukfvPu5+5aXN5/5f33Y7jNXkFeby89GVql69Nj7o93I4jIiIiIh5qepyl+8+7nwPHDzAmZYzbUbxi77G9/HP+P2ka35Q/t/mz23FEpAzo37g/F9e8mBcWv8C6A+vcjuMVn67/lI2HNnJf8n2EBoW6HUdEREREPNT0OEvNKzbnmgbX8N6a99hxZIfbcYqlwBbw97l/Jzs/m2cueobQYH1QFxHfM8bw+AWPExMew9/m/I3jecfdjlQsh3MOM2r5KJKrJNO1Vle344iIiIhIIWp6nIO729xNsAnmxSUvuh2lWMavHs/CXQv523l/o15sPbfjiEgZEh8Rz5MXPMnGQxt5bvFzbscplrErx5KRncED5z2guTxEREREShg1Pc5BlegqDGkxhG+3fsuyvcvcjnNOFuxawMtLX+bSOpfSN7Gv23FEpAzqVKMTg5oNYtK6SUxNnep2nHOy/ch23lv7Htc0uIZmFZu5HUdERERETqKmxzka3HwwlSMr8+yiZymwBW7HOSvbj2zn/h/up15sPf59wb/1n0kRcc297e6lfdX2PP7T46Skp7gd56y9uORFQoJCuLvt3W5HEREREZFTUNPjHEWFRnF327tJ2ZfCV5u/cjtOkR3LPcY9s++hwBbwyiWvEB0a7XYkESnDQoJCePbiZ0mISuDe2feyL2uf25GKbMmeJczYOoMhLYZQOaqy23FERERE5BTU9CiGqxtcTbOKzXhh8QtkHM9wO84ZWWt5ZN4jbMzYyHMXPUetmFpuRxIRIS4ijpcveZkjuUcYOXskOfk5bkc6o+z8bJ5c+CSVoyozuPlgt+OIiIiIyGmo6VEMQSaIxzo+xsHsg/xz/j+x1rod6Q+NTRnLt1u/ZWTbkXSq0cntOCIi/69xfGMev+Bxlqcv5z8L/1Pi309fWvISGw5u4J8d/0lkSKTbcURERETkNNT0KKamFZtyb9t7mbV9Fh+v/9jtOKc1NXUqryx7hSvqXcGg5oPcjiMi8juX172c4UnD+XTDp7y58k2345zWnB1zeG/te9zU9CYuqnmR23FERERE5A+o6eEFA5sNpFP1Tjy76Fk2ZWxyO87vzNw6k0fnP0qHah00camIlGh/bvNnrmlwDaOWj2Li2olux/mdfVn7eGTeIyTGJTKy3Ui344iIiIjIGajp4QVBJognLniCyJBI/jrnryXqePT5afN5YM4DJFVK4uVLXiYsOMztSCIipxVkgvhXp3/RrXY3nv75aT5L/cztSP+vwBbw8LyHOZp7lP92/i/hweFuRxIRERGRM1DTw0sSohL49wX/Zt3Bdby09CW34wCwbO8y7pl9Dw1iG/Ba99eICo1yO5KIyBmFBIXw34v+S8dqHfnn/H8yY+sMtyMB8P7a95mXNo/7k++nYVxDt+OIiIiISBGo6eFFF9e6mAFNBjBhzQQ+Wf+Jq1mW713OnTPvpGp0Vd649A1iwmJczSMicjbCgsN46ZKXSKqUxF/n/JXvtn3nap45O+bw/JLn6VKzCzc0vsHVLCIiIiJSdGp6eNkDyQ/QuUZnHv/pcT7f+LkrGb7Z8g3Dpg8jPjKe0ZeOplJkJVdyiIgUR1RoFK91f41m8c0YOXsk7615z5UcP+38iZGzR9IorhFPdn5S8yKJiIiIlCJqenhZaHAoL3R5gfOrns/D8x5m+pbpfqttrWXcqnE88MMDNK/UnAk9J1CtXDW/1RcR8baYsBjGXjaWrrW78syiZ3j656fJL8j3W/0le5Zw96y7qRNbhze7v6lRcyIiIiKljJoePhAREsErXV+hdUJrHpzzILO2zfJ5zbyCPJ5Y8AQvLnmRy+pexpgeY4iLiPN5XRERX4sMieT5i59nYLOBTFw7kfu+v4+svCyf112ZvpI7Zt5BtXLVGHPpGCpEVPB5TRERERHxLjU9fCQqNIpR3UbRtGJT7v/hfqamTsVa65Namw5tYsg3Q/ho/UcMbTGU/16kswqISGAJDgrmr+f9lQfPf5Dvd3zPgC8GsDJ9pc/qzU2by20zb6NiZEXG9hhLxciKPqslIiIiIr6jpocPlQsrx+vdXyepUhIPz3uY+3+4n0PZh7y2/byCPN5KeYvrp13PpkObeKrzU4xsN5Igo5dVRALTTU1v4vVur5OZm8nArwfy/OLnOZ533Gvbz8rL4skFT3L7zNupElWFsT3GUjmqste2LyIiIiL+pb+OfSw2PJZxl43jnrb3MGvbLPpO7cv8nfOLvd01+9dw81c389LSl+hcszNTe0/lqvpXeSGxiEjJ1qlGJz7r9RnXJl7LO6vf4brPr2PhroXFHk23Zv8abvjiBj5c9yEDmw3kw6s+pHq56l5KLSIiIiJuML465KK4kpOT7eLFi92O4VVr9q/hwR8fZPOhzfSs15PrG11PcpXkIp8JIK8gj9nbZ/P+2vdZvGcx8RHxPNT+IS6rc5nOJiAiZdKCXQt4bP5jpGWm0TS+KTc2vZGe9XoW+RA/ay1rDqxh8vrJTN4wmfjIeJ644Ak6Vu/o4+T+Z4xZYq1NdjtHWROIn2dERETccK6fZdT08LOsvCxeX/46n6z/hCO5R6hdvjZ9EvtwaZ1LqRJVhYiQiP9f11rL7qO72ZCxgVX7VjEldQq7j+6menR1bmhyA9cmXktseKyLeyMi4r6svCw+3/g57699n42HNhIXHkfvhr1pVbkViRUSqVm+5m8O+8vNzyU9K53vt3/P5A2TWXdwHeHB4VxZ/0rua3dfwL6vqunhjkD9PCMiIuJvanqUMll5WczcOpPJGyazeM+v+1k+tDyVoioRFRLF1sNbyczN/P/72ldtz4CmA+hSswvBQcFuxBYRKbGstfy8+2feX/s+3+/4ngJbADhnf6kbU5fcAqfZUXhupWYVm9G3YV961u8Z8KejVdPDHYH+eUZERMRfXGl6GGPigUlAXWAL0M9ae/A068YAa4DPrLV3nWnbZelDwtbDW1m6Zyn7svaRnpXOvqx9ZOZkUjumNo3iGtGwQkMaxjUM+A/kIiLeciz3GBszNrIhYwMbDm5g86HNhAeHkxCVQMXIiiREJtCiUguaxDdxO6rfqOnhjrL0eUZERMSXzvWzTEgx6z4IfGetfdoY86Dn9t9Os+6/gTnFrBeQ6sTUoU5MHbdjiIgEjKjQKJISkkhKSHI7ioiIiIi4qLhnb+kFjPdcHw/0PtVKxph2QBXg22LWExEREREREREpkuI2PapYa3d5ru/GaWz8hjEmCHgeuL+YtUREREREREREiuyMh7cYY2YCVU9x1z8K37DWWmPMqSYIuQP4ylq740ynVTXGjABGANSuXftM0URERERERERETuuMTQ9rbffT3WeM2WOMqWat3WWMqQbsPcVqHYHOxpg7gHJAmDEm01r74ClqjQZGgzPxV1F3QkRERERERETkZMWdyHQaMAh42vN16skrWGtvOnHdGDMYSD5Vw0NERERERERExJuKO6fH08ClxpgNQHfPbYwxycaYscUNJyIiIiIiIiJyroo10sNaux/odorli4Hhp1j+DvBOcWqKiIiIiIiIiBRFcUd6iIiIiIiIiIiUSGp6iIiIiIiIiEhAUtNDRERERERERAKSsbZknhnWGJMObPXBpisB+3ywXTdpn0qPQNwv7VPpEYj7pX0qujrW2gQfbFdOYowZAYzw3GwBrHIxTlkUiO8LpYGed3foeXeHnnd3NLbWlj/bB5XYpoevGGMWW2uT3c7hTdqn0iMQ90v7VHoE4n5pn6Sk0+vpf3rO3aHn3R163t2h590d5/q86/AWEREREREREQlIanqIiIiIiIiISEAqi02P0W4H8AHtU+kRiPulfSo9AnG/tE9S0un19D895+7Q8+4OPe/u0PPujnN63svcnB4iIiIiIiIiUjaUxZEeIiIiIiIiIlIGBGTTwxhzvTFmtTGmwBhz2tldjTGXG2PWGWNSjTEPFlpezxiz0LN8kjEmzD/JT88YE2+MmWGM2eD5GneKdS4xxiwvdDlujOntue8dY8zmQve19vc+nKwo++RZL79Q7mmFlpe41wmK/Fq1Nsb85Pk+XWmMuaHQfSXmtTrdz0ih+8M9z32q57WoW+i+hzzL1xljLvNr8D9QhH26zxizxvO6fGeMqVPovlN+L7qtCPs02BiTXij78EL3DfJ8r24wxgzyb/I/VoT9erHQPq03xmQUuq/EvVbGmHHGmL3GmFOevtQ4XvHs70pjTNtC95XY10mK914p56447+dy7s70vBda71pjjDV/8Flciq4oz7sxpp/ne361MeZ9f2cMREV4n6ltjJltjFnmea+5wo2cgaQ4n5dOy1obcBegKdAY+B5IPs06wcBGoD4QBqwAmnnu+wjo77n+BnB7Cdin/wIPeq4/CDxzhvXjgQNAlOf2O8B1bu/HuewTkHma5SXudSrqfgGNgETP9erALqBCSXqt/uhnpNA6dwBveK73ByZ5rjfzrB8O1PNsJ7iU7NMlhX5ubj+xT3/0vVgK9mkw8OopHhsPbPJ8jfNcj3N7n4q6Xyet/2dgXAl/rS4C2gKrTnP/FcDXgAE6AAtL+uukS/HeK3Xx+fN+2vdzXXz3vHvWKw/MARZwms/iunj3eQcSgWUnfj8Ald3OXdovRXzeR+P5GwTn8+8Wt3OX9su5fl76o0tAjvSw1q611q47w2rnA6nW2k3W2hzgQ6CXMcYAXYFPPOuNB3r7LGzR9cLJAkXLdB3wtbX2mC9DFdPZ7tP/K8GvExRhv6y16621GzzXdwJ7gQR/BSyiU/6MnLRO4X39BOjmeW16AR9aa7OttZuBVM/23HbGfbLWzi70c7MAqOnnjGerKK/T6VwGzLDWHrDWHgRmAJf7KOfZOtv9GgB84Jdk58haOwenGX06vYB3rWMBUMEYU42S/TpJ8d4r5dwF4vt5aVDU9+Z/A88Ax/0ZLoAV5Xm/FRjl+T2BtXavnzMGoqI87xaI8VyPBXb6MV9AKsbnpdMKyKZHEdUAthe6vcOzrCKQYa3NO2m526pYa3d5ru8Gqpxh/f78/g+AJz1DgF40xoR7PeHZK+o+RRhjFhtjFhjP4TqU3NcJzvK1Msacj9M93lhocUl4rU73M3LKdTyvxSGc16Yoj3XD2eYahtNJPuFU34tuK+o+Xev5nvrEGFPrLB/rhiJn8wxZrwfMKrS4JL5WZ3K6fS7Jr5MU771Szl1x38/l3JzxefcMNa9lrf3Sn8ECXFG+3xsBjYwx8zy/+9QcL76iPO+PATcbY3YAX+GMPBXfOuvPRSE+jeNDxpiZQNVT3PUPa+1Uf+fxhj/ap8I3rLXWGHPa0+54Ol1JwPRCix/C+QM8DGcY1t+Ax4ub+Uy8tE91rLVpxpj6wCxjTArOB0bXePm1mgAMstYWeBa78lrJbxljbgaSgYsLLf7d96K1duOpt1CifA58YK3NNsb8Cec/zl1dzuRN/YFPrLX5hZaV1tdKRLzsNO/n4gPGmCDgBZzDKsW/QnAOcemCM6ppjjEmyVqb4WaoMmAA8I619nljTEdggjGmRaHP9VIClNqmh7W2ezE3kQbUKnS7pmfZfpwhMiGe/8acWO5zf7RPxpg9xphq1tpdnj+U/2jIWj9girU2t9C2T4w8yDbGvA3c75XQZ+CNfbLWpnm+bjLGfA+0AT7FpdfJk6XY+2WMiQG+xGnULSi0bVdeq1M43c/IqdbZYYwJwRnWt7+Ij3VDkXIZY7rjNLAuttZmn1h+mu9Ft/+QPuM+WWv3F7o5FmfemROP7XLSY7/3esJzczbfQ/2BOwsvKKGv1Zmcbp9L8uskxXuvlHNXrPdzOWdnet7LAy2A7z1HcFUFphljrrHWLvZbysBTlO/3HThzG+QCm40x63GaIIv8EzEgFeV5H4bnkFNr7U/GmAigEn/8t5oUz1n/nVGWD29ZBCQa5wwgYTgfmqdZZ3aU2ThzYgAMAkrCyJFpOFngzJl+d2z7ieOcPMcQ9wZOORuun51xn4wxcScO7zDGVAIuANaU4NcJirZfYcAUnOPRPjnpvpLyWp3yZ+SkdQrv63XALM9rMw3ob5wzFtTD+aX7s59y/5Ez7pMxpg3wJnBN4eNhT/e96Lfkp1eUfSp8nOM1wFrP9elAD8++xQE9+O0IMTcV5fsPY0wTnMk9fyq0rKS+VmcyDbjFODoAhzxN0JL8Oknx3ivl3J3z+7kUyx8+79baQ9baStbautbaujhzqajhUXxFeZ/5DE+D3PO7rxHOxNdy7oryvG8DugEYY5oCEUC6X1OWPaf7vHR6tgTM0OrtC9AHp9uZDewBpnuWVwe+KrTeFcB6nP/+/aPQ8vo4f6ClAh8D4SVgnyoC3wEbgJlAvGd5MjC20Hp1cTpdQSc9fhaQgvMH9HtAudKwT0AnT+4Vnq/DSvLrdBb7dTOQCywvdGld0l6rU/2M4Bxqc43neoTnuU/1vBb1Cz32H57HrQN6uv26nMU+zfS8b5x4Xaad6XvR7UsR9ukpYLUn+2ygSaHHDvW8fqnAELf35Wz2y3P7MeDpkx5XIl8rnGb0Ls/P/g6c/w7dBtzmud8Aozz7m0KhMx6U5NdJl+K9V+ri0+f9lO/nuvj2eT9p3e/R2Vv88rx7foe8gNPkT8FzhkNdfP68NwPmeT5zLAd6uJ25tF+K83npdBfjeaCIiIiIiIiISEApy4e3iIiIiIiIiEgAU9NDRERERERERAKSmh4iIiIiIiIiEpDU9BARERERERGRgKSmh4iIiIiIiIgEJDU9RERERERERCQgqekhIiIiIiIiIgFJTQ8RERERERERCUj/B4qpk7Ihvzo6AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#collapse\n", "fig, axs = plot.subplots(2, 2)\n", "fig.set_size_inches(18.5, 10.5)\n", "\n", "f = lambda x: x**2\n", "pf = np.polynomial.Polynomial(interpolate(f,x))\n", "axs[0, 0].plot(x, f(x), 'o')\n", "axs[0, 0].plot(d, f(d), '-')\n", "axs[0, 0].plot(d, pf(d), '-')\n", "axs[0, 0].set_title('Quadratic')\n", "\n", "g = lambda x: 1/(1+(5*x)**2)\n", "pg = np.polynomial.Polynomial(interpolate(g,x))\n", "axs[1, 0].plot(x, g(x), 'o')\n", "axs[1, 0].plot(d, g(d), '-')\n", "axs[1, 0].plot(d, pg(d), '-')\n", "axs[1, 0].set_title('Runge function')\n", "\n", "h = lambda x: x**14-x**3\n", "ph = np.polynomial.Polynomial(interpolate(h,x))\n", "axs[0, 1].plot(x, h(x), 'o')\n", "axs[0, 1].plot(d, h(d), '-')\n", "axs[0, 1].plot(d, ph(d), '-')\n", "axs[0, 1].set_title('Recliner')\n", "\n", "\n", "for ax in axs.flat:\n", " ax.label_outer()" ] }, { "cell_type": "markdown", "id": "ee2b9eb7", "metadata": {}, "source": [ "# Approximation " ] }, { "cell_type": "markdown", "id": "13af19e6", "metadata": {}, "source": [ "What if we wanted to approximate with a lower degree polynomial than the number of points? For this we can use the Moore-Penrose inverse, a generalization of the normal matrix inverse $A A^{-1} = I$\n", "\n", "The Moore-Penrose inverse (Denoted as $A^+$) can be defined in terms of solving a linear system of equations $Ac=y$. The solution to $A^+y = \\hat{c}$ is the least squares solution i.e. $||Ac-y||_2 \\geq ||A\\hat{c}-y||_2, \\forall c$.\n", "\n", "With this result we can approximate " ] }, { "cell_type": "code", "execution_count": 26, "id": "81e3c46a", "metadata": {}, "outputs": [], "source": [ "def approximate(y, x, d=3):\n", " A = np.vander(x, N=d, increasing=True)\n", " c_approx = np.linalg.pinv(A) @ y\n", " return c_approx" ] }, { "cell_type": "markdown", "id": "807274f8", "metadata": {}, "source": [ "A good question, that I do not know the answer too, is how the numerical instability (condition number) of the Moore-Penrose inversion relations to the regular inversion. If you know: please tell me." ] }, { "cell_type": "markdown", "id": "8d5c0acc", "metadata": {}, "source": [ "Alternatively we can find the 'best' solution to $Ac=y$ with `np.linalg.lstsq`." ] }, { "cell_type": "code", "execution_count": 28, "id": "d763211b", "metadata": {}, "outputs": [], "source": [ "def approximate(y, x, d=3):\n", " A = np.vander(x, N=d, increasing=True)\n", " c, _, _, _ = np.linalg.lstsq(A, y, rcond=None)\n", " return c" ] }, { "cell_type": "markdown", "id": "638d6189", "metadata": {}, "source": [ "With degree 2:" ] }, { "cell_type": "code", "execution_count": 30, "id": "2fc3e904", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#collapse\n", "degree = 3\n", "fig, axs = plot.subplots(2, 2)\n", "fig.set_size_inches(18.5, 10.5)\n", "\n", "f = lambda x: x**2\n", "pf = np.polynomial.Polynomial(approximate(f(x),x, d=degree))\n", "axs[0, 0].plot(x, f(x), 'o')\n", "axs[0, 0].plot(d, f(d), '-')\n", "axs[0, 0].plot(d, pf(d), '-')\n", "axs[0, 0].set_title('Quadratic')\n", "\n", "g = lambda x: 1/(1+(5*x)**2)\n", "pg = np.polynomial.Polynomial(approximate(g(x),x, d=degree))\n", "axs[1, 0].plot(x, g(x), 'o')\n", "axs[1, 0].plot(d, g(d), '-')\n", "axs[1, 0].plot(d, pg(d), '-')\n", "axs[1, 0].set_title('Runge function')\n", "\n", "h = lambda x: x**14-x**3\n", "ph = np.polynomial.Polynomial(approximate(h(x),x, d=degree))\n", "axs[0, 1].plot(x, h(x), 'o')\n", "axs[0, 1].plot(d, h(d), '-')\n", "axs[0, 1].plot(d, ph(d), '-')\n", "axs[0, 1].set_title('Recliner')\n", "\n", "DX, y = load_diabetes(return_X_y=True)\n", "dx = DX[:,2] \n", "# Map to [-1,1]\n", "dx = (dx - min(dx)) / (max(dx) - min(dx)) * 2 -1\n", "y = (y - min(y)) / (max(y) - min(y))\n", "pd = np.polynomial.Polynomial(approximate(y,dx,d=degree))\n", "\n", "axs[1, 1].plot(dx, y, 'o')\n", "axs[1, 1].plot(d, pd(d), '-')\n", "axs[1, 1].set_title('Diabetes dataset')\n", "\n", "for ax in axs.flat:\n", " ax.label_outer()" ] }, { "cell_type": "markdown", "id": "390f1800", "metadata": {}, "source": [ "With degree 14:" ] }, { "cell_type": "code", "execution_count": 31, "id": "60491203", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#collapse\n", "degree = 15\n", "fig, axs = plot.subplots(2, 2)\n", "fig.set_size_inches(18.5, 10.5)\n", "\n", "f = lambda x: x**2\n", "pf = np.polynomial.Polynomial(approximate(f(x),x, d=degree))\n", "axs[0, 0].plot(x, f(x), 'o')\n", "axs[0, 0].plot(d, f(d), '-')\n", "axs[0, 0].plot(d, pf(d), '-')\n", "axs[0, 0].set_title('Quadratic')\n", "\n", "g = lambda x: 1/(1+(5*x)**2)\n", "pg = np.polynomial.Polynomial(approximate(g(x),x, d=degree))\n", "axs[1, 0].plot(x, g(x), 'o')\n", "axs[1, 0].plot(d, g(d), '-')\n", "axs[1, 0].plot(d, pg(d), '-')\n", "axs[1, 0].set_title('Runge function')\n", "\n", "h = lambda x: x**14-x**3\n", "ph = np.polynomial.Polynomial(approximate(h(x),x, d=degree))\n", "axs[0, 1].plot(x, h(x), 'o')\n", "axs[0, 1].plot(d, h(d), '-')\n", "axs[0, 1].plot(d, ph(d), '-')\n", "axs[0, 1].set_title('Recliner')\n", "\n", "DX, y = load_diabetes(return_X_y=True)\n", "dx = DX[:,2] \n", "# Map to [-1,1]\n", "dx = (dx - min(dx)) / (max(dx) - min(dx)) * 2 -1\n", "y = (y - min(y)) / (max(y) - min(y))\n", "pd = np.polynomial.Polynomial(approximate(y,dx,d=degree))\n", "\n", "axs[1, 1].plot(dx, y, 'o')\n", "axs[1, 1].plot(d, pd(d), '-')\n", "axs[1, 1].set_title('Diabetes dataset')\n", "\n", "for ax in axs.flat:\n", " ax.label_outer()" ] }, { "cell_type": "markdown", "id": "685b5994", "metadata": {}, "source": [ "Note the beautiful overfitting on the diabetest dataset and how bad the Runge function is approximated. This post will be following by some other posts about:\n", "\n", "* Interpolation with Lagrange polynomials and derivatives [in part 2](https://vanderzwaan.dev/2022/05/06/Fit-polynomials-2.html)\n", "* Chebyshev nodes to avoid oscillation [in part 3](https://vanderzwaan.dev/2022/07/13/Fit-polynomials-3-Chebyshev.html)\n", "* Solve $\\geq$ invert [in this article](https://vanderzwaan.dev/2022/02/15/Matrix-inversion.html)\n", "\n", "Hope you enjoyed it thusfar." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }