{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Foundations of Computational Economics #13\n", "\n", "by Fedor Iskhakov, ANU\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "## Two very important algorithms for solving equations\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "\n", "[https://youtu.be/gUdYS5PmvWo](https://youtu.be/gUdYS5PmvWo)\n", "\n", "Description: Bisections and Newton-Raphson methods. Solving equations of one variable. Accuracy of solution. Rates of convergence." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Classic algorithm for equation solving\n", "\n", "1. Bisection method \n", "1. Newton-Raphson method \n", "\n", "\n", "Solve equations of the form $ f(x) = 0 $\n", "\n", "Focus on the scalar case today." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Bisection method for solving equations\n", "\n", "Solve equation $ f(x)=0 $, conditional on $ x \\in [a,b] \\subset \\mathbb{R} $ such that $ f(a)f(b)<0 $\n", "\n", "Algorithm: similar to binary search, but in **continuous space**." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "def bisection(f,a=0,b=1,tol=1e-6,maxiter=100,callback=None):\n", " '''Bisection method for solving equation f(x)=0\n", " on the interval [a,b], with given tolerance and number of iterations.\n", " Callback function is invoked at each iteration if given.\n", " '''\n", " pass" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solution is x=-1.000, f(x)=0.000000834465\n" ] } ], "source": [ "f = lambda x: -4*x**3+5*x+1\n", "a,b = -3,-.5 # upper and lower limits\n", "x = bisection(f,a,b)\n", "print('Solution is x=%1.3f, f(x)=%1.12f' % (x,f(x)))" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Converged in 22 steps\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# make nice plot\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "plt.rcParams['figure.figsize'] = [12, 8]\n", "xd = np.linspace(a,b,1000) # x grid\n", "plt.plot(xd,f(xd),c='red') # plot the function\n", "plt.plot([a,b],[0,0],c='black') # plot zero line\n", "ylim=[f(a),min(f(b),0)]\n", "plt.plot([a,a],ylim,c='grey') # plot lower bound\n", "plt.plot([b,b],ylim,c='grey') # plot upper bound\n", "def plot_step(x,**kwargs):\n", " plot_step.counter += 1\n", " plt.plot([x,x],ylim,c='grey')\n", "plot_step.counter = 0 # new public attribute\n", "bisection(f,a,b,callback=plot_step)\n", "print('Converged in %d steps'%plot_step.counter)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "def bisection(f,a=0,b=1,tol=1e-6,maxiter=100,callback=None):\n", " '''Bisection method for solving equation f(x)=0\n", " on the interval [a,b], with given tolerance and number of iterations.\n", " Callback function is invoked at each iteration if given.\n", " '''\n", " if f(a)*f(b)>0:\n", " raise ValueError('Function has the same sign at the bounds')\n", " for i in range(maxiter):\n", " err = abs(b-a)\n", " if err0 else (a,x)\n", " if callback != None: callback(err=err,x=x,iter=i)\n", " else:\n", " raise RuntimeError('Failed to converge in %d iterations'%maxiter)\n", " return x" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Newton-Raphson (Newton) method\n", "\n", "General form $ f(x)=0 $\n", "\n", "- Equation solving \n", "- Finding maximum/minimum based on FOC, then $ f(x)=Q'(x) $ \n", "\n", "\n", "Algorithm:\n", "1. Start with some good guess $ x_0 $ not too far from the solution\n", "2. Newton step: $ x_{i+1} = x_i - \\frac{f(x_i)}{f'(x_i)} $\n", "3. Iterate until convergence in some metric" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Derivation for Newton method using Taylor series expansion\n", "\n", "$$\n", "f(x) = \\sum_{k=0}^{\\infty} \\frac{f^{(k)}(x_0)}{k!} (x-x_0)^k\n", "$$\n", "\n", "Take first two terms, assume $ f(x) $ is solution, and let\n", "$ x_0=x_i $ and $ x=x_{i+1} $\n", "\n", "$$\n", "0 = f(x) = f(x_i) + f'(x_i) (x_{i+1}-x_i) \\quad \\Rightarrow \\quad x_{i+1} = x_i - \\frac{f(x_i)}{f'(x_i)}\n", "$$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "def newton(fun,grad,x0,tol=1e-6,maxiter=100,callback=None):\n", " '''Newton method for solving equation f(x)=0\n", " with given tolerance and number of iterations.\n", " Callback function is invoked at each iteration if given.\n", " '''\n", " pass" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solution is x=-1.000, f(x)=0.000000490965\n" ] } ], "source": [ "f = lambda x: -4*x**3+5*x+1\n", "g = lambda x: -12*x**2+5\n", "x = newton(f,g,x0=-2.5,maxiter=7)\n", "print('Solution is x=%1.3f, f(x)=%1.12f' % (x,f(x)))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "hide-output": false, "scrolled": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", 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kSVKeZSkuyNLS4OGHYY89oE0bWLcu6USSJEl5kqW4oCtXLi7GCxbAFVcknUaSJClPshSnglNPhYsuiod7PP980mkkSZLyHEtxqrj99viYtg4d4Jtvkk4jSZKUp1iKU0WxYjBxIqxdC+3bw5YtSSeSJEnKMyzFqaRGDbjvPpg+Pf4qSZIkwFKcerp2hTPPhKuugnnzkk4jSZKUJ1iKU00I8OCDULZsfEzb2rVJJ5IkSUqcpTgV7bUXTJgAy5bFp1JIkiSlOEtxqjrxRLjyShg9Gh5/POk0kiRJibIUp7Ibb4T69aFLF/j886TTSJIkJcZSnMqKFImPadu8Od5fvHFj0okkSZISYSlOdRUrxlso3nkHrrsu6TSSJEmJsBQLWreGbt3gjjvgpZeSTiNJkpTrLMWK3Xcf1KoFF1wAX3+ddBpJkqRcZSlWrHhxmDQpPrf4/PPjfcaSJEkpwlKs/6peHYYNg9deg4EDk04jSZKUayzF+l/t28dbKG68Ed54I+k0kiRJucJSrP8VAgwfDpUqwXnnwerVSSeSJEnKcZZi/V+77RbvL/7hh3jleMuWpBNJkiTlKEuxtq527fhEihdfhHvvTTqNJElSjrIU6+917w4tW8JVV8G77yadRpIkKcdYivX3Qoin3VWoAOeeCz/9lHQiSZKkHGEp1raVKhXvL/76a+jQAaIo6USSJEnZzlKsf1a/Ptx9NzzzTPxVkiSpgLEUa/v06QOtWsX7i2fOTDqNJElStrIUa/v8Z39xenq8v3jVqqQTSZIkZRtLsbbfHnvA44/HD9yddx5s3px0IkmSpGxhKdaOOeQQGDECXn0VBgxIOo0kSVK2sBRrx3XoABdeCLfcEg/3kCRJyucsxdo5Q4fGq8bnnw9ffJF0GkmSpCyxFGvnFC8e7y/euBFat4Y//kg6kSRJ0k6zFGvnVa4MY8fC7NnQv3/SaSRJknaapVhZ07IlXHQRDBoEU6YknUaSJGmnWIqVdXfcAQ0aQKdOsHRp0mkkSZJ2mKVYWVe0KEyeDMWKwVlnwW+/JZ1IkiRph1iKlT323x8eewwWLYpXjKMo6USSJEnbzVKs7HPSSXDrrfGq8X33JZ1GkiRpu1mKlb3694+3UPTvD6+/nnQaSZKk7WIpVvYKIT6mrXJlOOccWLky6USSJEn/yFKs7LfHHvDUU/D773D22bBhQ9KJJEmStilLpTiEUCqE8HgIYXEIYVEI4cgQwp4hhOkhhGWZX0tnV1jlI9WqwcMPx4M9Lroo6TSSJEnblNWV4kHAtCiKqgGHAouAK4EZURRVBmZk/qxU1LJlvLd45Mi4IEuSJOVRO12KQwh7AMcBYwCiKPojiqKfgebAuMzLxgEtshpS+djAgdCwIXTvDvPmJZ1GkiRpq7KyUpwOrAbGhhA+CCGMDiGUAMpFUfQNQObXstmQU/lV4cLx+cVly8anUvzwQ9KJJEmS/o+slOLCwGHAiCiK6gBr2YGtEiGEriGEOSGEOatXr85CDOV5ZcrAE0/AN99AmzaweXPSiSRJkv5HVkrxSmBlFEWzM39+nLgkrwohlAfI/Prd1t4cRdGoKIrqRlFUt0yZMlmIoXyhXj0YNgymT4drr006jSRJ0v/Y6VIcRdG3wJchhKqZL50EfAI8A7TPfK09MDVLCVVwdO4MXbvC7bfDpElJp5EkSfr/Cmfx/X2Af4cQigIZQEfioj05hNAJ+AJolcV7qCAZMgQWLoSOHaFKFahTJ+lEkiRJWSvFURR9CNTdyq9OysrnqgArWjTeX1y3LrRoAXPmxHuOJUmSEuREO+W+cuXiiXfffRdPvNu4MelEkiQpxVmKlYy6dWH0aJg5Ey6+OOk0kiQpxWV1T7G089q2hQ8/hLvvhtq14wfxJEmSEuBKsZJ1++3QuDH07Alvv510GkmSlKIsxUpWoULxxLsDDogn3q1cmXQiSZKUgizFSl7p0vD007B2LZx5Jqxbl3QiSZKUYizFyhtq1oRHHomPaOvWDaIo6USSJCmFWIqVdzRvDjfeCBMmwL33Jp1GkiSlEEux8pZrr4WWLaF/f3j++aTTSJKkFGEpVt6SlgbjxsVHtLVpAwsWJJ1IkiSlAEux8p4SJWDqVNhtNzj9dFi9OulEkiSpgLMUK2+qUCEuxt9+Gx/VtmFD0okkSVIBZilW3lWvXryVYtYsT6SQJEk5yjHPyttat4ZFi2DAAKhRI34AT5IkKZtZipX3XX99XIyvvBKqVo2PbpMkScpGKb19Yku0JekI2h4hwNixULcutG0LH32UdCJJklTApGwp/vSnT6kypApjPxjLpi2bko6jf1K8eDwKulSp+ESKb79NOpEkSSpAUrYU//rHr+xZfE8ufOZCDhlxCE8uepLIB7nytn33hWeegR9+gDPPhPXrk04kSZIKiJQtxYeUO4TZnWfzROsniIhoObklDcY04NVPX006mrblsMPiMdDvvgudOnkihSRJyhYpW4oBQgicVf0sPu7xMQ+d8RDf/PoNJ40/iZMnnMycr+ckHU9/56yz4NZbYeJEuOGGpNNIkqQCIKVL8X8UTitMxzodWdpnKfc2vpcPv/2Qeg/Wo9WUViz+fnHS8bQ1V14ZrxTffDM8/HDSaSRJUj5nKf6TXQrvwsVHXsyKviu44fgbmLZ8GjWH16TzM535cs2XScfTn4UAI0ZAo0bQpQu86rYXSZK08yzFW7FHsT0YcMIAMvpm0Ld+XybMn0DlIZW59KVL+f7375OOp/8oUgQefzw+u/iss+CTT5JOJEmS8ilL8TaUKVGG+065j6W9l9KmVhvun30/6YPSufmNm/ntj9+SjieAkiXh+edhl13gtNNg1aqkE0mSpHzIUrwdDih1AGObj+XjHh/TKL0R179+PemD0hk8ezAbNm1IOp4OOACefTYuxGecAb//nnQiSZKUz1iKd0CNMjV48pwnebfTuxxc9mD6TetH1aFVGf/ReDZv2Zx0vNRWrx48+ii8/z5ccAFscVqhJEnafpbinXBEhSOY0W4GL5//Mnvvujftn27PoSMPZeriqQ4ASVLz5nDvvfDkk9C/f9JpJElSPmIp3kkhBE6ueDLvd3mfKa2msHHLRlpMasFRDx3F65+9nnS81NWvH/TuDffcE59OIUmStB0sxVkUQuDsGmezsOdCRp8+mpW/rOTEcSfS5JEmzP16btLxUk8IcP/90KxZXI5feCHpRJIkKR+wFGeTwmmF6XRYJ5b2XsrdJ9/NnK/nUPfBupzz+Dks/WFp0vFSS6FC8f7iQw+F1q1hjtMJJUnStlmKs1nxIsW59KhLyeibwXXHXcfzS5+nxrAadH22Kyt/WZl0vNSx227xUW177x0f1ZaRkXQiSZKUh1mKc0jJXUpy04k3saLvCnrV68XDHz5M5SGV6T+9Pz/8/kPS8VJD+fIwbRps2gSnnAKrVyedSJIk5VGW4hxWbrdyDDp1EEv7LKV1zdbc/fbdpA9OZ+DMgQ4AyQ3VqsVnGH/5ZbzPeO3apBNJkqQ8yFKcSw4sdSDjWoxjfo/5nHjgiVz72rVUGlyJoe8N5Y/NfyQdr2A76qh4j/GcOXDuufHKsSRJ0p9YinPZwWUP5ulzn+btC9+m2t7V6PNiH6oNrcYj8x9xAEhOatEChg2D556DHj3A86QlSdKfWIoTcuT+R/Ja+9eY1nYapXYpxQVPXUDtB2rz7JJnHQCSU7p3h2uvhdGj4aabkk4jSZLyEEtxgkIINKnUhDld5/BYy8fYsGkDZzx2BseMPYaZn89MOl7BdNNN0KEDDBgQl2NJkiQsxXlCWkjjnIPPYWHPhTzQ7AE++/kzjn/4eJr+uykffvth0vEKlhBg1Kj4NIru3ePtFJIkKeVZivOQIoWK0PXwrizvs5w7G93Juyvfpc4DdWjzRBuW/7g86XgFR5EiMGUK1K4dD/eYPTvpRJIkKWGW4jyoeJHiXH705WT0y+CaY6/hmSXPUH1YdXo814Ovf/066XgFw3+Ge5QvHx/VtmRJ0okkSVKCLMV5WKldSnFLw1tY0XcF3Q7vxpgPxlBpcCWufOVKflr3U9Lx8r9y5eCllyAtDU4+GVY6cVCSpFRlKc4H9tltH4Y2Hcri3otpWaMld751JwcNOojb3ryNtX84jCJLKlWKp96tWQONG8MPThuUJCkVWYrzkfTS6Uw4cwIfdf+I4w44jqtfvZpKQyox/P3hDgDJijp14JlnICMDmjaF35w0KElSqrEU50O1ytXimTbPMKvjLCrvWZleL/Si+rDqTPx4IluiLUnHy5+OPx4mT4a5c+Gss2DDhqQTSZKkXGQpzseO/tfRvNHhDV447wV2L7o7bZ9sS50H6vD80ucdALIzzjgDxoyB6dPhggtgsxMGJUlKFZbifC6EwKmVT2Vet3lMPGsia/9YS7NHm3Hcw8cx64tZScfLf9q3h3vuiY9s69XLcdCSJKUIS3EBkRbSaFOrDYt6LWLEaSNY/uNyjh17LM0mNmP+qvlJx8tfLrkErrwSHngArr8+6TSSJCkXWIoLmCKFitC9bndW9F3B7SfdzltfvkXtkbU5/8nzyfgpI+l4+cett0LnznDLLXD//UmnkSRJOcxSXEDtWmRXrjjmCjL6ZnDF0Vfw5KInqTq0Kr2e78U3v36TdLy8LwQYOTJ+6O7ii2HChKQTSZKkHGQpLuBKFy/NbY1uY0XfFXQ5rAuj5o2i0pBKXD3jan5e/3PS8fK2QoVg4kQ46STo2DE+tk2SJBVIluIUUX738gw/bTiLei2iRbUW3DbrNtIHpXPnW3fy+8bfk46XdxUrBk89BXXrQqtW8MorSSeSJEk5wFKcYirtWYl/n/VvPuz2IUftfxRXvHIFlQZX4oE5D7Bx88ak4+VNu+8OL74I1apB8+Ywy1M9JEkqaCzFKerQfQ7lufOeY2aHmaSXTqf7892pMbwGjy14zAEgW1O6NLz8Muy/P5x2WjzkQ5IkFRiW4hR37AHH8mbHN3muzXMUL1ycNk+04fBRh/PishcdAPJX5crF2yf23BMaN4YFC5JOJEmSsomlWIQQOK3KaXzY/UMeOfMR1qxfQ9OJTTlh3Am8/eXbScfLWypUgBkzYJdd4OSTYdmypBNJkqRsYCnW/5cW0mh7SFsW917MsKbDWPL9Eo5+6GjOePQMPl71cdLx8o709HjFeNMmaNQIvvgi6USSJCmLLMX6P4oWKkrPej1Z0XcFAxsOZObnMzl05KG0e6odn/70adLx8obq1eM9xmvWxEe2fePZz5Ik5WeWYv2tEkVLcPWxV5PRL4PLj7qcKZ9MoerQqvR5oQ+rfluVdLzk1akTn0rxzTfxVooffkg6kSRJ2kmWYv2jPYvvyR0n38HyPsu5sM6FjJgzgoqDK3Ltq9eyZv2apOMl68gj4dlnYcUKaNIkXjmWJEn5jqVY222/PfZjZLORLOq1iGZVmjHwzYGkD07n7rfvZt3GdUnHS86JJ8ITT8D8+XDKKfDLL0knkiRJO8hSrB1Wea/KPHb2Y8zrOo/6+9Xn8umXU3lIZR6c+yCbtmxKOl4ymjaFSZNgzpz4+99+SzqRJEnaAZZi7bQ65evwYtsXeb396/yr5L/o+lxXag6vyZSFU1JzAMiZZ8Kjj8K778YDPtauTTqRJEnaTpZiZdnxBx7PWxe+xdRzp1IkrQitH29NvQfr8fKKl1NvAMjZZ8O//x2Pgj79dPj996QTSZKk7WApVrYIIXBG1TP4qPtHjG8xnh/X/UiTR5pw0viTmL1ydtLxctc558CECfDGG9C8OaxL4f3WkiTlE5ZiZatCaYW44NALWNxrMUNOHcLC1QtpMKYBZ046k4XfLUw6Xu457zwYOzaefnfmmbB+fdKJJEnSNliKlSOKFS5G7/q9WdF3BTefeDOvfvoqh4w8hA5Pd+Dznz9POl7uaNcOxoyJh3y0bAkbNiSdSJIk/Q1LsXLUbkV349rjriWjbwaXNLiExxY8RpWhVej3Yj++W/td0vFyXseOMGoUvPACtGoFf/yRdCJJkrQVlmLlir123Yu7Gt/F8r7LaX9oe4a9P4z0Qenc8NoN/LKhgJ/r27kzjBwZD/lo3Ro2bkw6kSRJ+gtLsXJVhT0qMOr0USzsuZCmlZty08ybSP4vMboAACAASURBVB+Uzr3v3Mv6TQV43223bjB0KEydGhdjV4wlScpTLMVKRNW9qzK51WTmdJnD4fsezqUvX0rlIZUZM29MwR0A0qsXDBkCTz8dH93mHmNJkvIMS7ESdfi+h/PS+S8xo90M9t19Xzo/25mDhx/ME588UTDPOO7d+79bKTyVQpKkPCPLpTiEUCiE8EEI4bnMnw8KIcwOISwLIUwKIRTNekwVdA0Pasi7nd7lqXOeIi2kcfaUs6k/uj6vZLySdLTs160bjB4N06bBGWc44EOSpDwgO1aK+wGL/vTzHcB9URRVBn4COmXDPZQCQgi0qNaCj3t8zNjmY/lu7XecPOFkGo1vxPtfvZ90vOzVqVN8jvErr0CzZo6EliQpYVkqxSGECsBpwOjMnwPQEHg885JxQIus3EOpp1BaITrU7sDS3ku5v8n9fLTqI+qPrk/LyS1ZtHrRP39AftG+/X8n3zVtCr/+mnQiSZJSVlZXiu8H+gNbMn/eC/g5iqL/PCm1Ethva28MIXQNIcwJIcxZvXp1FmOoICpWuBj9GvQjo28GN55wI9NXTOfgEQdz4dQL+WLNF0nHyx5t28LEifDWW3DKKfBLAT+eTpKkPGqnS3EIoRnwXRRFc//88lYu3erTUlEUjYqiqG4URXXLlCmzszGUAnYvtjvXH389K/quoN8R/fj3x/+m8pDKXPLSJaxeWwD+B9U558CkSfDee9C4Mfz8c9KJJElKOVlZKT4aOCOE8BnwGPG2ifuBUiGEwpnXVAC+zlJCKVOZEmW4t8m9LOuzjPNrnc+g2YOoOLgiN75+I79uyOdbD1q2hClTYN48OPlk+OmnpBNJkpRSdroUR1F0VRRFFaIoOhA4F3g1iqK2wGvA2ZmXtQemZjml9Cf/KvkvxjQfw4IeC2hcsTED3hhA+uB0Br07iA2b8vHZvy1awJNPwvz5cOKJ8F0KjMGWJCmPyIlziq8ALgkhLCfeYzwmB+4hUb1MdR5v/TjvdX6P2vvU5qKXLqLK0Co8/OHDbN6yOel4O6dZs/gM46VL4bjjYOXKpBNJkpQSsqUUR1H0ehRFzTK/z4iiqH4URZWiKGoVRVE+XrpTflBvv3pMv2A60y+YTtkSZek4tSO1RtTiqUVP5c8BII0bw0svwTffwLHHwooVSSeSJKnAc6KdCoxG6Y14r/N7PNH6CSIizpp8Fg3GNODVT19NOtqOO/ZYePXV+Ji2Y4+FhQuTTiRJUoFmKVaBEkLgrOpn8XGPjxlzxhi++fUbThp/Eo0nNGbO13OSjrdjDj88PsM4iuD442Hu3H9+jyRJ2imWYhVIhdMKc2GdC1naZyn3Nr6Xed/Mo96D9Wg1pRVLvl+SdLztV7MmvPkm7LYbNGwIs2YlnUiSpALJUqwCbZfCu3DxkReT0S+DG46/gWnLp1FzeE26PNOFlb/kk4fYKlWKy3D58vF+45dfTjqRJEkFjqVYKWGPYnsw4IQBrOi7gt71ezN+/ngqDa7EZS9fxg+//5B0vH9WoQLMnAlVqsDpp8NTTyWdSJKkAsVSrJRStkRZ7j/lfpb2XkqbWm247937SB+czs1v3Mxvf/yWdLxtK1sWXnsNDjsMWrWCCROSTiRJUoFhKVZKOqDUAYxtPpb53efT8KCGXP/69VQcXJEhs4fk7QEgpUvD9Onxg3ft2sH99yedSJKkAsFSrJRWs2xNnjrnKd7p9A41ytSg77S+VB1alfEfjc+7A0B22w2efx7OOgsuvhiuvjo+oUKSJO00S7EENKjQgFfbvcpL57/EXrvuRfun23PoyEOZunhq3hwAsssuMHkydOsGt90GXbrApk1Jp5IkKd+yFEuZQgg0rtiY97u8z+SzJ7Nxy0ZaTGrBUQ8dxRufvZF0vP+rUCEYMQKuuw7GjIn3Ga9fn3QqSZLyJUux9BdpIY1WNVuxsOdCHjz9Qb5c8yUnjDuBUx45hXnfzEs63v8KAW66CQYPhqefhlNOgTVrkk4lSVK+YymW/kbhtMJ0Pqwzy/os4+6T7+b9r9/n8FGHc+7j57Lsh2VJx/tfffrAxInw1lvxQ3jffpt0IkmS8hVLsfQPihcpzqVHXUpG3wyuPfZanlv6HNWHVafbs9346pevko73X23awHPPwbJlcPTRsGJF0okkSco3LMXSdiq5S0lubngzK/quoGe9noz9cCyVhlSi//T+/Ljux6TjxZo0gVdfhZ9/jovxhx8mnUiSpHzBUiztoHK7lWPwqYNZ0nsJrWu25u637yZ9UDoDZw5k7R9rk44HRxwRj4UuWhSOOw5mzEg6kSRJeZ6lWNpJB5U+iHEtxjG/x3yOP/B4rn3tWioOrsiw94bxx+Y/kg1XvTq8/TYccED88J3T7yRJ2iZLsZRFB5c9mKnnTuXtC9+m6t5V6f1ib6oNrcYj8x9JdgBIhQrxivGxx8bT72691SEfkiT9DUuxlE2O3P9IXm//Oi+2fZFSu5TigqcuoM4DdXhu6XPJDQApWRKmTYO2beGaa6BHD4d8SJK0FZZiKRuFEDil0inM6TqHx1o+xrpN6zj90dM5ZuwxvPn5m8mEKlo03j5x1VXwwANw5pmwNg/sfZYkKQ+xFEs5IC2kcc7B5/BJz094oNkDfPbzZxz38HGcNvE0Pvw2gRMhQoi3T4wYAS+8ACeeCKtW5X4OSZLyKEuxlIOKFCpC18O7sqzPMu5odAfvfPkOdR6ow3lPnMfyH5fnfqDu3ePJdwsWwFFHwdKluZ9BkqQ8yFIs5YJdi+xK/6P7k9Evg6uPuZqpS6ZSfVh1ejzXg69//Tp3w5x+Orz+Ovz6a1yM3347d+8vSVIeZCmWclGpXUox8KSBrOi7gm6Hd2P0B6OpNLgSV71yFT+t+yn3gtSvD++8A6VLw0knweTJuXdvSZLyIEuxlIB9dtuHoU2HsqT3ElrWaMkdb91B+uB0bp91O79v/D13QlSsGBfjunXhnHPglls8sk2SlLIsxVKC0kunM+HMCXzY/UOO+dcxXDXjKioNrsSI90ewcfPGnA+w997wyitw/vlw3XXQvj1s2JDz95UkKY+xFEt5wCHlDuHZNs8yq+MsKu5ZkZ4v9KT6sOpM/HgiW6ItOXvzYsVg/Hi46ab46LaTT4bvv8/Ze0qSlMdYiqU85Oh/Hc3MDjN5/rznKVG0BG2fbMthDxzGC8teyNkBICHEK8WPPQbvvQcNGsDixTl3P0mS8hhLsZTHhBBoWrkpH3T7gIlnTeTXP37ltImncdzDxzHri1k5e/NzzvnvyRRHHgkzZuTs/SRJyiMsxVIelRbSaFOrDYt6LWJ40+Es/3E5x449ltMfPZ35q+bn3I0bNIDZs2G//eCUU2D06Jy7lyRJeYSlWMrjihYqSo96PVjeZzm3nXQbs76YRe2RtTn/yfPJ+CkjZ2564IHw1lvxcW1dusDll8PmzTlzL0mS8gBLsZRPlChagiuPuZKMvhlccfQVPLnoSaoOrUqv53vx7W/fZv8NS5aE556DXr3g7ruheXNYsyb77yNJUh5gKZbymdLFS3Nbo9tY3nc5net0ZtS8UVQcXJFrZlzDz+t/zt6bFS4MQ4fC8OHw0kvx1oply7L3HpIk5QGWYimf2nf3fRnRbASLei2iedXm3DrrVtIHpXPnW3dm/wCQHj1g+nRYvTqehvfyy9n7+ZIkJcxSLOVzlfasxMSWE/mg2wccuf+RXPHKFVQeUplRc0dl7wCQE06A99+H/feHU0+Fe+91Ap4kqcCwFEsFRO19avP8ec/zRoc3OLDUgXR7rhs1htdg0oJJ2TcA5KCD4O234/3Fl14KHTvC+vXZ89mSJCXIUiwVMMcdcByzOs7i2TbPUrxwcc594lzqjqrLtOXTsmcAyG67weOPw4ABMG5cvIL8zTdZ/1xJkhJkKZYKoBACzao044NuH/DImY/w8/qfOfXfp3LiuBN558t3sn6DtDS44Ya4HH/8MdStG2+tkCQpn7IUSwVYobRCtD2kLYt7L2boqUNZ/P1ijnroKJo/1pwF3y3I+g1atoy3UxQpAsceG68cS5KUD1mKpRRQtFBRetXvxYq+KxjYcCCvf/Y6h4w4hHZPtePTnz7N2ocfemi8SnzkkdChA/TsCX/8kS25JUnKLZZiKYWUKFqCq4+9mk/7fcrlR13OlE+mUHVoVfq+2JdVv63a+Q8uUyY+su2yy2DEiHif8VdfZVtuSZJymqVYSkF7Ft+TO06+g+V9ltOxdkeGvz+cioMrct2r17Fm/U5OrStcGO66CyZPhvnz4bDDYObM7A0uSVIOsRRLKWy/PfbjgdMf4JNen9CsSjNuefMW0genc/fbd7Nu47qd+9BWrWD2bChVCho2hPvv9zxjSVKeZymWRJW9qvDY2Y8xt+tc6u1bj8unX07lIZUZPW80m7Zs2vEPrFkT3nsPmjWDiy+G886DtWuzP7gkSdnEUizp/zus/GFMO38ar7V/jf1L7k+XZ7tQc3hNpiycsuMDQEqWhCefhIEDYdIkaNAAli3LmeCSJGWRpVjS/3HCgSfw9oVv8/Q5T1MkrQitH29N/Qfr8/KKl3dsAEhaGlx9NUybBl9/DfXqwdSpORdckqSdZCmWtFUhBJpXa85H3T9iXItxfP/79zR5pAknjT+J2Stn79iHNW4Mc+dCpUrQokU8InrjxpwJLknSTrAUS9qmQmmFaHdoO5b0XsLgUwaz4LsFNBjTgDMnncknqz/Z/g868ECYNSs+x/jee+H44+HLL3MstyRJO8JSLGm7FCtcjD5H9GFF3xXcdMJNzMiYQa0Rteg4tSOf//z59n3ILrvAsGHw2GOwYAHUqQMvvpizwSVJ2g6WYkk7ZPdiu3Pd8deR0S+DixtczKMfP0qVoVW4aNpFfLf2u+37kHPOgTlzYL/9oGlTuOoq2LQTp1xIkpRNLMWSdsreu+7N3Y3vZlmfZbQ7pB1D3htCxcEVGfD6AH7Z8Ms/f0CVKvDuu9ClC9x+O5x0UvwwniRJCbAUS8qS/Uvuz4NnPMgnPT/h1EqncuMbN5I+KJ373rmP9ZvWb/vNxYvDqFEwYUK8cly7djwuWpKkXGYplpQtqu5dlcmtJvN+l/c5rPxhXPLyJVQZUoWHPnjonweAnH9+XIrLloUmTeC669xOIUnKVZZiSdmq7r51efmCl5nRbgbldy9Pp2c6UWtELZ745Iltn3FcvXo8HrpDB7jllvh0is8+y63YkqQUZymWlCMaHtSQdzu9y5OtnyQQOHvK2Rwx+ghmZMz4+zeVKAEPPQQTJ8anU9SuDVOm5F5oSVLKshRLyjEhBM6sfiYf9/iYsc3HsmrtKhpNaESj8Y14/6v3//6NbdrABx9AtWrQunX8MN7atbkXXJKUcizFknJcobRCdKjdgaW9l3J/k/v5aNVH1B9dn7Mnn83i7xdv/U3p6fDmm/FxbWPGQN268NFHuRtckpQyLMWSck2xwsXo16AfGX0zGHD8AF5a8RI1h9ek09ROfLHmi//7hiJF4NZb4ZVXYM0aqF8fBg+Gbe1NliRpJ1iKJeW63Yvtzg0n3EBG3wz6HdGPRz5+hCpDqnDJS5fw/e/f/983NGwI8+dD48bQrx+cfjqsXp37wSVJBZalWFJiypQow71N7mVZn2WcV+s8Bs0eRPqgdG564yZ+3fDr/168997wzDMwZEi8clyrFrzwQjLBJUkFjqVYUuL+VfJfPNT8IRb0WMDJFU/mhtdvoOLgigx6dxAbNm3474UhQO/e8N578ZnGp50GPXr4EJ4kKcssxZLyjOplqvNE6yeY3Xk2tcrV4qKXLqLK0Co8/OHDbN6y+b8XHnJIXIwvuwweeADq1InPOJYkaSdZiiXlOfX3q8+MdjOYfsF0ypYoS8epHTlk5CE8vfjp/w4A2WUXuOsuePVV2LABjj4abrgBNm5MNrwkKV+yFEvKsxqlN+K9zu/xeKvH2bxlM2dOOpMjxxzJa5++9t+LTjghfgjvvPPgppvicrxkSWKZJUn5k6VYUp4WQqBljZYs6LmAMWeM4atfv6Lh+IY0eaQJc7+eG19UsiSMHw+TJ8OKFfF2iuHDPbpNkrTdLMWS8oXCaYW5sM6FLOuzjHsa38Pcr+dS98G6tJ7SmiXfZ64Mt2oFH38Mxx0HvXrBqafCypXJBpck5QuWYkn5yi6Fd+GSIy8ho18G1x93PS8se4Gaw2vS5ZkurPxlJey7L7z4IgwbFk/Eq1kTHnrIVWNJ0jZZiiXlS3sU24MbT7yRjH4Z9K7fm/Hzx1NpcCUue/kyflj3I/TsGe81rl0bOnWCpk1dNZYk/S1LsaR8rWyJstx/yv0s6b2Ecw8+l/vevY/0wencMvMWftu/HLz2WjwaeuZMV40lSX/LUiypQDiw1IE83OJh5nefT8ODGnLda9dRcXBFhrw/jA09urpqLEnaJkuxpAKlZtmaPHXOU7zT6R1qlKlB32l9qTasGhN+e5vNM17576rxwQfD2LGuGkuSgCyU4hDC/iGE10IIi0IIC0MI/TJf3zOEMD2EsCzza+nsiytJ26dBhQa82u5VXjr/JfYsviftnm7HoaPq8EzjA4g++ggOPRQuvDBeNf7886TjSpISlpWV4k3ApVEUVQcaAL1CCDWAK4EZURRVBmZk/ixJuS6EQOOKjXm/y/tMOnsSf2z+g+aPNefoN9rxxsMD4lXj/5xQMXgwbN78j58pSSqYdroUR1H0TRRF8zK//xVYBOwHNAfGZV42DmiR1ZCSlBVpIY3WNVuzsOdCRjUbxedrPueE8Q05dc8X+GDmpPhc43794ml4H3+cdFxJUgKyZU9xCOFAoA4wGygXRdE3EBdnoOzfvKdrCGFOCGHO6tWrsyOGJG1TkUJF6HJ4F5b3Wc5dJ9/F7JWzOezZZpx74R4sG3tPPA3vsMPg2mth/fqk40qSclGWS3EIYTfgCeCiKIp+2d73RVE0KoqiulEU1S1TpkxWY0jSditepDiXHXUZGf0yuObYa3h26bNU/6I/3UecxtcXtICBA+M9xzNnJh1VkpRLslSKQwhFiAvxv6MoejLz5VUhhPKZvy8PfJe1iJKUM0rtUopbGt5CRt8MetbryUOLJlKx4nNcMao1P4b1cPzx0K0b/Pxz0lElSTksK6dPBGAMsCiKonv/9KtngPaZ37cHpu58PEnKeeV2K8fgUwezpPcSWtVoxV1fTyG9wxpuveoY1o57EGrUgEmTPL5NkgqwrKwUHw1cADQMIXyY+a8pcDtwcghhGXBy5s+SlOcdVPogxp85no+6f8TxBx7PNcVmUXHAngw7sjB/tD0XmjSBpUuTjilJygFZOX1iVhRFIYqiQ6Ioqp3574Uoin6IouikKIoqZ379MTsDS1JOq1WuFlPPncpbF75F1X1q0vuQL6l2w178e80sttQ6GK6/HtatSzqmJCkbOdFOkv7GUfsfxevtX+fFti9Ssuz+nN90HbUvLcFzk24mOrgmvPhi0hElSdnEUixJ2xBC4JRKpzC361webfko68rvzennwbGnfsub3ZvC2WfDl18mHVOSlEWWYknaDmkhjXMPPpdPen7CyNNGknFQKY67EE7b9Sk+Oq4K3H03bNyYdExJ0k6yFEvSDihSqAjd6nZjed/l3NHoDt6uvhu1O6yn7TuXs+KoavDyy0lHlCTtBEuxJO2EXYvsSv+j+5Nx0WdcdcxVPHVoUao1zaDn4CZ807JJPB1PkpRvWIolKQtKFy/NrSfdyoqLP6Nr3W48WC+NitVf5qqeVfjp6ovht9+SjihJ2g6WYknKBuV3L8+w00eyuM9Szqp+FnccuYX0LfdzR+t9+X3CQw7+kKQ8zlIsSdmo4p4VeaTtE3zQ/UOO3v8orjziVyp91ImRbSqxcc7spONJkv6GpViScsCh+xzKc73e4s32b1Bxr8r0qJ5B9QkNeLT3CWz5amXS8SRJf2EplqQcdMyBxzHzyiU833wyJUqW4bwyb3DYwH/x4oC2RL/+mnQ8SVImS7Ek5bAQAk1rt+KDG7/l38fcx6+ld6VpmMjxl+/NW8OvhM2bk44oSSnPUixJuSQtpHHeSRex6KYfGV79MpaVjjhm9R2c3qs0858amXQ8SUpplmJJymVFCxWlR+u7WD7gR24t24Y391pL7Y96cEHvfcl498Wk40lSSrIUS1JCShTbjat6TCTj8pX0L3Yij5f+hmovNKX3ZTX4dsncpONJUkqxFEtSwvYsVZ7br3qVFZ0/ptOmWowssYiK4+tyzdVH8PNXTsaTpNxgKZakPGLfAw5mxK3zWXT2a5zxx0HcWuw90odU4sXPJ/LHpnVJx5OkAs1SLEl5TOVaJ/DoXRnMa/Q4DTaWYzLTueKLyxh117ls/N2x0ZKUEyzFkpRH1Tm6JS/c8y1X7taHvaOSdPt9EjWvLc2kEb3Ysmlj0vEkqUCxFEtSHld1r8O4On0gz1S9kWKhMOd+N5y6l+3BSw9dTeQZx5KULSzFkpQPhBA4/dzr+fCOX5iwb29+KrKZU768jYZ9S/Lu+Fthy5akI0pSvmYplqR8pFDhIpzfZQhLBq5hSNkOfLLHeo789Bpa9CjNwon3W44laSdZiiUpHypatDi9e4xlxfU/cMterXht79+otfRi2nfZm88mj4IoSjqiJOUrlmJJysd2K16Sa3pPJuOKr7msVFMm7/szVRZ0o1/7cnz3xHjLsSRtJ0uxJBUAe+1Rjjsvep7lF39Kx5InMOyg1aTPa8/155VnzWPjwAfyJGmbLMWSVIDst+cBPHDpa3zScyGnlarHzdVWkf5BB+5pWZ51D42CjR7lJklbYymWpAKoSrkaTLr8PeZ2eo96ZQ/lsjqrqbKgG6Ob7sOmIYNgnRPyJOnPLMWSVIAdVqEe0y79kNfavUqFfavR5ZgfOXjpRTzecB+i226DX35JOqIk5QmWYklKASccdCJvX/oJT5/zNIUOOJBWp/xCvc+uZvox5YmuvQZWrUo6oiQlylIsSSkihEDzas2Zf8lyHm7+MN9XLE/jlr/T6Mtbea/B/tC1KyxenHRMSUqEpViSUkyhtEK0r92eJZd8yqBTBvFx9T05osNGzvptDJ8cVx1OPx1ef93j3CSlFEuxJKWoYoWL0feIvqy4+DNuOuEmXjl4V2r1CnQsMZ3PW5wI9erBo496YoWklGAplqQUt3ux3bnu+OvIuOhTLmpwMY8eDFUuLszFlTNY3fk8qFQJ7r3Xh/IkFWiWYkkSAHvvujf3NLmHZX2WcUGd9gyuvob0K4sz4MTAL1dfChUqQL9+sGxZ0lElKdtZiiVJ/2P/kvsz+ozRLOy5kFOqncaNB31OxRtKcX+7KqwfNRyqVIFTT4UXXoAtW5KOK0nZwlIsSdqqantXY0qrKbzX+T1qV/h/7d13eFRl3sbx75MEEqRrKApSAlmkdwIivUXcFVwpoiIsgoALAV5WBalSfFFhJaCrC1KElRfBVUBZKVJdJVQjoUaSpURAQFDp9Xn/OMkmlECAZM5M5v5c17nmnJkzk99cjyfenDylFgMKbeZ3YwozY2RbLm2Nhcceg3LlYOJE+PVXt8sVEbkrCsUiInJTtYvVZnnn5XzV+SuK5itGNxZQeXB+Pp0yAFu4EAwYAMWKwYsvwo4dbpcrInJHFIpFRCRDmoU1Y3339Xza4VOMCeDJg28T0fUSK5a8B+3bw/TpULEiNG0KH38MFy64XbKISIYpFIuISIYZY3ii/BNs7b2V6Y9P5/CpwzSP6U2Lpkls3LQIXn8d/vMfeOopZ2DeK6/Anj1uly0icksKxSIictuCAoL4U/U/Ed83nrdbvU3s4Vjq/LMV7cpsZtf6xfDll/DIIzBhAoSHQ/PmMH++7h6LiNdSKBYRkTsWEhRC/7r9SYhKYGSjkSxNWErF9yvT/cInHJgRDfv3w+jRzjRuHTrAgw/CoEGQkOB26SIiV1EoFhGRu5YvOB8jGo8gMSqRqDpRzN46m/DJ4QyMm8Cx/+kFiYnOFG716sH48c6CIE2bwuzZcPq02+WLiCgUi4hI5imUuxBvR75NfJ94nq78NBPXTyQsOoxR/x7LyaaPwIIFsG8fjBrlPD73HNx/P3TvDv/+N1jr9lcQET+lUCwiIpmuZIGSTG8znbjecTQPa86I1SMoM6kMk9ZP4nyRUBg2zBmAt2YNtGsHc+dCgwbOwiBjx8KBA25/BRHxMwrFIiKSZSoUqsCnHT8l5vkYKhWuRL8l/Sj3Tjk+jP2Qy/YKNGzoTOV2+DDMmOHMdzx0KJQsCS1bwpw5cOaM219DRPyAQrGIiGS5iOIRrHhuBcueXUboPaF0XdiVKu9XYcGuBVhrIU8e6NoVVq927iAPGwbx8fDMM1C4MHTu7MxocfGi219FRLIphWIREfEIYwwtyrRgY4+NzG8/n0tXLvHEx09Qb1o9Vu9dnXpimTLw2mvO4LxVq+Dpp+GLL6B1a+dOcp8+8O236n8sIplKoVhERDzKGEO7Cu3Y/uJ2PvjDB/x48keafNiEVv9oxeaDm1NPDAiAxo1hyhSne8WCBc7xtGlQvz6EhcGQIVpaWkQyhUKxiIi4IiggiOdrPE98n3jGtxjP5oObqTW1Fh0/6Uj8z/FXnxwcDG3awLx58NNPMHOmMyhv3DhnaemqVWHMGNi925XvIiK+T6FYRERclStHLgY+PJCEqASGNRzG4vjFVHi3Ai98/gJJvyVd/4Z8+aBLF1i6FA4ehOhop0/ysGHw0ENQubIz5ZvuIIvIbVAoFhERr5A/JD+jmowisV8if679Z2bGzqTspLK8tOwlfj7z843fVKQIREXBN98407hFR0OBAjBypHMHuWJFGDECtm1TH2QRuSmFYhER8SqFcxcm+tFo4vvG81Slp5iwbgJhk8IYs3YMpy6cSv+NxYs7AfnrryEpCSZPhkKFnGWmK1eGChWcPsgbNsCVK577QiLiExSKRUTEK5UqUIqZbWeytfdWmpRqwrBVO4CkMQAAE0RJREFUwygzqQzvbHiHC5cv3PzNDzzgzFKxerXTxeJvf3NWznvjDYiIcAJ0z57O0tPnznnk+4iId1MoFhERr1apcCUWPLWAdc+vo3xoefp+2Zdy75Rj9vezuXzl8q0/oGhR6N0bVq50BunNnu3MXjFnDjz2GISGwpNPwqxZ8HM63TREJNtTKBYREZ9Qt3hdVnVZxZJnllAwpCDPLXiOan+vxqLdi5wFQDLivvvg2Wdh/nw4dsxZEKRzZ4iJcQbvFS4MjRrBhAmwc6f6IYv4EYViERHxGcYYWpVtxaYXNvFxu485f+k8bea2of70+qzdt/b2Piw4GCIj4b33nEF6GzfCq6/CiRPwl784fZBLl4ZevWDhQjh5Mmu+lIh4BYViERHxOQEmgA4VO7D9xe1M+f0U9v26j0YzG9H6o9bEHo69gw8MgFq1nEF5W7fC3r3w/vtQvTp89BG0bevcZW7aFN56S7NZiGRDCsUiIuKzcgTmoEfNHuzpu4c3m79JTFIM1f9enU7/7MSe43vu/INLlnQG4n32mdPPeOVK6N8fjh6Fl192ZrMoUQJ69HAWFDl2LPO+lIi4QqFYRER8Xq4cuXip/ksk9ktkSIMhLNq9iPLvlqfXF704ePLg3X14zpzQpAm8+SbExTldLaZOhTp1nEDcsaMz9Vv16k63iy+/hFM3mTpORLySyfDghCxUq1Ytu2nTJrfLEBHxSjNnzgSga9eurtbhSw6fOsyYtWOYsnkKQQFBREVE8Ur9VyiYq2Dm/qBLl5y+yCtWONu338KFCxAUBHXrQrNmzhYR4YRrEXGdMWaztbbWdc8rFIuIeDeF4juXeCKREatH8NHWj8gXnI9X6r9CVEQUuXPmzpofeOaMs7peSkjevNnpe5w7NzzyCDRoAA0bQu3aEBKSNTWIyE0pFIuI+CiF4rsX91McQ1YO4fP4zymapyjDGg6je43u5AzM4ru3J044C4isWAFr1jgD9MCZ+aJOndSQ/PDDkDdv1tYiIoBCsYiIz1IozjzfHviWQV8N4uv9XxNWMIxRjUfRqXInAoyHhtj8/LNzJ/nrr2HtWudO8uXLzuwX1as7IblBA6hXz1mBT0QynUKxiIiPUijOXNZaluxZwqsrXyX2cCxVilTh9aav0zq8NcYYzxZz6pSzcEhKSI6JSV12ukQJp19yyla9urpciGSC9EJxkBvFiIiIuMUYw6Phj9KqbCvmbZ/H0JVD+f3//Z76D9ZnXPNxPFLiEc8VkycPNG/ubADnz8OWLbB+vROQY2KcGS4AcuRwgnHaoFyqFHg6yItkU7pTLCLi5XSnOGtdvHyRad9NY9SaURw6dYjHwh9jbNOxVC1a1e3SHIcOXR2SN250BvSBMxVczZrOVqOG81iihIKyyE2o+4SIiI9SKPaMMxfPMHn9ZMZ9M45fz/1Kp8qdGNV4FGXuLeN2aVe7dMkZsBcT44TlLVtg+3anbzI4K+/VqJEakmvUgLAwBWWRZArFIiI+SqHYs06cPcFb377FxJiJXLxykR41ejCs4TDuz+vFA9/OnnUWFtm82QnJmzc7wfniRef1/PmdrhdVqjir8VWpAhUrOlPFifgZhWIRER+lUOyOQycPMXrtaKZumUqOgBz0r9ufl+u/TIGQAm6XljHnzzvBOCUof/edc5zS9cIY5w5ySlBO2cqWhcBAd2sXyUIKxSIiPkqh2F0JxxMYvno4c+LmUCCkAIPqD6JvRF/uyXGP26XdvitXIDHRuaucsm3dCnv2OK8B5MoF5cs720MPpW7h4c78yiI+TqFYRMRHKRR7h+8Pf8+QlUNY/MNi7s9zPyMajaBb9W7kCMzhdml37+xZ2LEjNSRv3w67dsH+/annBAQ4d5bTBuWU7d571WdZfIZHp2QzxkQC0UAg8IG1dlxW/BwRERFPqVq0Kl88/QVf7/uawSsG02txL8avG8/oJqPpULGD5xYAyQq5cqXOYpHW6dMQH+8E5J07ncddu2D5cqd7Ror8+aFMmdStbNnU/WLFnEAt4uUy/U6xMSYQiAdaAEnARqCTtXZHeu/RnWIRkfTpTrH3sdbyrx/+xeAVg4k7Eke1otV4venrRJaN9PwCIG64fBn27XMC8u7dkJDgdMFISIC9e50ZMlIEB0Pp0qlBuVQpKFnSmTquRAkIDdVdZvEoj3WfMMbUA0Zaa1slHw8GsNb+b3rvcSsU9+/fn9jYWI//XBGR21GtWjUA/b7yQhbLkSJH2Ft6L+dynSP/L/kpnVCa/L/ld7s091jr3EU+ezZ1O3cudT+l73KKgAAnOIeE3PgxOFh3mrOhatWqMXHiRFd+tie7TxQDDqQ5TgIiblDQC8ALACVKlMiCMkRERLKWwVDkpyIUOlKIQ/cfYl+pfcTWjOW+Y/dRKrEUeU7ncbtEzzPGCbQhIVCw4PWvX7zohOZz565/PHUqdRq5tAIDnXCcM6ezpbevWTPkLmRFKL7R30Cuux1trZ0CTAHnTnEW1HFLbv0LRUTkdqR0n9DvLO93+sJpJq2fxBvfvMGW0C08U+UZXmv8GmEFw9wuzXecPw9JSc4gv/37nRX9Dh68/jFtn+YUefNC4cLOSn8pW2jo1cdpn8udW1035L+yIhQnAQ+mOS4OHMyCnyMiIuJVcufMzeAGg+lZqydvfvMm0euj+Xjbx/Ss2ZOhDYdSJE8Rt0v0fsHBqYP00mMt/PLLjcPy0aPOtn+/Mz/z0aNw4cKNPyckxJk5o0ABZytYMHX/Zs/lzQt58jgDFBWqs42s6FMchDPQrhnwI85Au6ettdvTe48G2omIpE8D7XzXj7/9yOi1o/lgywcEBwUzoO4AXnr4JfKH+HGfY0+zFk6eTA3LR4/CsWOp+ydOOAH7l1+u3v/ll+v7P1/LGOduc548N99y5766r/S1++m9liOH0yUkKCj1Me1+YKDT3zorgrm1zoDKS5eu3i5evP65lO38+VtvKd1lLl+GUaMyv+4M8Og8xcaY1sBEnCnZpltrx97sfIViEZH0LVmyBIDIyEiXK5E79cPPPzB89XDmbpvLvbnuZVD9QfSp04dcOXK5XZqkJyVMpw3JKaH51KnU7fTpq4+v3VJeT+9udWa4NjCnDcnX5ry0xzd6LSXgXr6cdfWC0wf83DlX7rRr8Q4RERGXfXfoO15d+SpL9iyhWN5ijGg0gj9V/xNBAVmybIB4kytXnGCcdmBhypb2OO1+2oB67f61j2n3r3Vt8Ex7fO1rOXKkBuxbbWnPTRkMee2WdhaRtJuLM4ooFIuIiHiJNXvXMHjFYNYlrSP83nDGNB1DuwrtfHsBEBEfkV4o1tUnIiLiYY1KNeKbbt+w8KmFBAcF0/GTjtSeWpule5biDTerRPyRQrGIiIgLjDE8Xu5xYnvGMqvtLI6fPU7kR5E0ndWUmKQYt8sT8TsKxSIiIi4KDAikc9XO7PrzLiY/OpkdR3dQb1o92s5ty/Yj6U7cJCKZTKFYRETECwQHBdOnTh8SohIY3WQ0q/auovJ7lem6oCt7f9nrdnki2Z5CsYiIiBfJkzMPQxsOJTEqkYH1BjJ321x+N/l39PuyH0dOH3G7PJFsS6FYRETEC913z3281fIt9kTtoWu1rry78V3CosMYsWoEv53/ze3yRLIdhWIREREvVjxfcab8YQrbX9xO6/DWjFo7irDoMP667q+cu3TO7fJEsg2FYhERER9QLrQc89rPY1OPTdR8oCYDlw0kfHI407ZM49KVGyzYICK3RaFYRETEh9R8oCZLn13KyudWUixvMbp/3p1Kf6vEJzs+0RzHIndBoVhERMQHNSndhHXPr+Ozjp8RGBBI+/ntqfNBHb5K/Mrt0kR8kkKxiIiIjzLG0PahtmzttZWZbWZy5PQRWsxuQbNZzdjw4wa3yxPxKQrFIiIiPi4wIJAu1boQ3yee6Mho4n6KI+KDCJ6c9yQ7j+50uzwRn6BQLCIikk0EBwUTFRFFQlQCrzV+jeUJy6n0XiW6LezG/l/3u12eiFdTKBYREclm8gbnZXij4ST2S6R/RH/mxM0hfHI4A5YM4Ojpo26XJ+KVFIpFRESyqdB7QpnQagLxfeN5tvKzTNowibBJYby2+jVOnj/pdnkiXkWhWEREJJsrkb8E09pMY1vvbbQq04qRa0YSNimMiTETtQCISDKFYhERET9RvlB5PunwCRu6b6Ba0WoMWDqAcu+UY8Z3M7QAiPg9hWIRERE/U7tYbZZ3Xs7yzsspnLsw3RZ1o8p7Vfhs52daAET8lkKxiIiIn2oe1pwN3Tfwzw7/xGL547w/UndaXVb+Z6XbpYl4nEKxiIiIHzPG8MfyfySudxzTHp/GoZOHaDarGS1nt2TTwU1ulyfiMQrFIiIiQlBAEN2qdyO+bzx/bflXvjv8HbWn1qb9/PbsOrbL7fJEspxCsYiIiPxXSFAIA+oNICEqgRGNRrBkzxIq/q0i3Rd158CvB9wuTyTLKBSLiIjIdfIF52Nk45EkRiUSVSeK2VtnEz45nIFLB3LszDG3yxPJdArFIiIikq5CuQvxduTbxPeJp1PlTkxcP5Gw6DBGrxnNqQun3C5PJNMoFIuIiMgtlSxQkhltZhDXO47mYc0Zvno4YdFhTFo/ifOXzrtdnshdUygWERGRDKtQqAKfdvyUmOdjqFS4Ev2W9KPcO+WY9f0sLl+57HZ5IndMoVhERERuW0TxCFY8t4Jlzy4j9J5QuizoQtX3q7Jw10ItACI+SaFYRERE7ogxhhZlWrCxx0bmt5/PxSsXaftxWx6e/jCr9652uzyR26JQLCIiInfFGEO7Cu3Y/uJ2pv5hKgd+PUCTD5sQ+Y9Ithza4nZ5IhmiUCwiIiKZIiggiO41uvND3x8Y32I8Gw9upOaUmnT8pCPxP8e7XZ7ITSkUi4iISKbKlSMXAx8eSGJUIkMbDGVx/GIqvFuBnp/35MfffnS7PJEbUigWERGRLJE/JD+jm44mISqBF2u/yIzYGZSdXJaXl7/M8bPH3S5P5CoKxSIiIpKliuQpwqRHJ7G7z246VOzA+G/HExYdxti1Y7UAiHgN4w3TphhjjgL7XPrxoYDWq8ze1Mb+Qe3sH9TO2Z/a2D+42c4lrbWFrn3SK0Kxm4wxm6y1tdyuQ7KO2tg/qJ39g9o5+1Mb+wdvbGd1nxARERERv6dQLCIiIiJ+T6EYprhdgGQ5tbF/UDv7B7Vz9qc29g9e185+36dYRERERER3ikVERETE7/ldKDbGjDbGbDXGxBpjlhljHkjnvC7GmB+Sty6erlPunDHmLWPMruR2/swYUyCd8/YaY+KS/1vY5Ok65e7cRjtHGmN2G2P2GGMGebpOuTvGmPbGmO3GmCvGmHRHqut69l230ca6ln2YMeZeY8zy5Fy13BhTMJ3zLidfx7HGmEUerdHfuk8YY/JZa39L3o8CKlhre11zzr3AJqAWYIHNQE1r7QlP1yu3zxjTElhprb1kjHkDwFr7yg3O2wvUstZqPkwflJF2NsYEAvFACyAJ2Ah0stbu8HS9cmeMMeWBK8Dfgb9Ya28YeHU9+66MtLGuZd9njHkTOG6tHZf8j5qC6fy/+ZS1No/nK/TDO8UpgThZbpzQe61WwHJr7fHkILwciPREfXL3rLXLrLWXkg9jgOJu1iNZI4PtXAfYY61NtNZeAOYCbTxVo9w9a+1Oa+1ut+uQrJPBNta17PvaAB8m738ItHWxlhvyu1AMYIwZa4w5ADwDDL/BKcWAA2mOk5KfE9/TDfgyndcssMwYs9kY84IHa5LMl14761r2H7qeszddy76viLX2EEDyY+F0zgsxxmwyxsQYYzwanIM8+cM8xRjzFVD0Bi8NsdYutNYOAYYYYwYDfYAR137EDd7rX/1MvNyt2jj5nCHAJeCjdD6mvrX2oDGmMLDcGLPLWrs2ayqWO5EJ7axr2QdkpJ0zQNezF8uENta17ANu1s638TElkq/lMGClMSbOWpuQORXeXLYMxdba5hk8dQ6wmOtDcRLQOM1xcWD1XRcmmeZWbZw8OPL3QDObTsd5a+3B5McjxpjPcP48p/+JepFMaOck4ME0x8WBg5lXoWSG2/idfbPP0PXsxTKhjXUt+4CbtbMx5idjzP3W2kPGmPuBI+l8Rsq1nGiMWQ1UBzwSiv2u+4QxJjzN4ePArhucthRoaYwpmDw6smXyc+IDjDGRwCvA49baM+mck9sYkzdlH6eNt3muSrlbGWlnnME44caY0saYnMBTgEdHM0vW0/XsF3Qt+75FQMpsXl2A6/5CkJy7gpP3Q4H6gMcGU/pdKAbGGWO2GWO24vzi7AdgjKlljPkAwFp7HBiNcxFuBEYlPye+4R0gL86fUGONMe8DGGMeMMb8K/mcIsC/jTHfAxuAxdbaJe6UK3folu2cPBCvD84/ancC86y1290qWG6fMeYJY0wSUA9YbIxZmvy8rudsIiNtrGs5WxgHtDDG/IAzi8g4uDp/AeWBTcnX8ipgnCdnGPG7KdlERERERK7lj3eKRURERESuolAsIiIiIn5PoVhERERE/J5CsYiIiIj4PYViEREREfF7CsUiIiIi4vcUikVERETE7ykUi4iIiIjf+38iGwCSEPa9eQAAAABJRU5ErkJggg==\n", 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\n", 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3xW0Q++8PFRVpJ5IkSWpRlt9807Mn3H03fPghnHpq2mkkSZJalOU3H+20E5x5Ztz7+/DDaaeRJElqMZbffHXRRTBsWJz+8OmnaaeRJElqEZbffFVUBPffH8eeHXggLFyYdiJJkqRmZ/nNZ+utB7fcAq+/Duedl3YaSZKkZmf5zXf77Qe/+AVceik891zaaSRJkpqV5VdwzTVQWgqHHgpffZV2GkmSpGZj+RW0awcPPgizZsUCXFmZdiJJkqRmYflVtNFG8Kc/wbPPwiWXpJ1GkiSpWVh+tcRRR8Ehh8D558MLL6SdRpIkqclZfrVECHDjjTBoUBx/NmVK2okkSZKalOVXdXXoEO/6Nns2HHSQ+38lSVJOsfxqWRtuCNdfH7c+XHhh2mkkSZKajOVX9TviCDj88Hgb5GefTTuNJElSk7D8avmuvx422AAOPhgmT047jSRJ0mqz/Gr52reP+3/nzo0H4BYtSjuRJEnSarH8asUGD4abboKXXoLzzks7jSRJ0mqx/GrlDj00zgC+5BIYNSrtNJIkSavM8quG+dOf4l3gDjkEJk5MO40kSdIqsfyqYdq2jft/58+H/faDBQvSTiRJktRoll81XEkJ3HorvPYajByZdhpJkqRGs/yqcfbbD045JW6DuP/+tNNIkiQ1iuVXjXfZZbD11vCLX8AHH6SdRpIkqcEsv2q8oiJ46CHo2BF++lOYPTvtRJIkSQ1i+dWqWWutWIDHj4+3Qk6StBNJkiStlOVXq26bbeAPf4BHH4Urr0w7jSRJ0kpZfrV6TjsN9tkHzjoL/vWvtNNIkiStUIPKbwihSwjhryGEshDC2BDCViGEriGEZ0MI46o+rtHcYZWBQoDbboMBA2D//WHy5LQTSZIkLVdDV36vAUYlSVIKbAKMBc4Cnk+SZCDwfNXXykcdO8atD99+G0ehLVyYdiJJkqR6rbT8hhA6AdsAtwIkSbIgSZJZwJ7AnVWX3Qns1VwhlQUGD443wHjlFTjjjLTTSJIk1ashK7/rA1OB20MI/w0h/CWE0B7omSTJlwBVH9es7xeHEI4JIYwJIYyZOnVqkwVXBtp/fzj5ZLj6anjwwbTTSJIkLaMh5bcVsBlwY5IkmwJzacQWhyRJbk6SZGiSJEN79OixijGVNS6/HEaMgCOPhPfeSzuNJElSHQ0pvxOBiUmSvFH19V+JZfirEMJaAFUfv26eiMoqRUXw179Cly6w114wY0baiSRJkmqstPwmSTIF+CKEUFL11A7Ah8CTwOFVzx0OPNEsCZV9evWKB+AmTYIDD4TKyrQTSZIkAQ2f9nAicG8I4T1gCHAJcCmwUwhhHLBT1ddSNGwY3HADjB4Nv/lN2mkkSZKAuJ93pZIkeQcYWs9LOzRtHOWUo46Ct96Cyy6DzTaLB+IkSZJS5B3e1LyuvnrJAbh33007jSRJynOWXzWv4uIlB+D23humT087kSRJymOWXzW/pQ/ALVqUdiJJkpSnLL9qGdUH4J591gNwkiQpNQ068CY1ieoDcJdfHg/AHXBA2okkSVKeceVXLevqq2HrrT0AJ0mSUmH5VcsqLoaHH4auXWHPPWHq1LQTSZKkPGL5Vcvr1Qseewy++gp+9jNYsCDtRJIkKU9YfpWOLbaA226Dl1+GX/0KkiTtRJIkKQ944E3pOfBAeP99uOQS2GgjOOmktBNJkqQc58qv0nXRRXHv76mnwujRaaeRJEk5zvKrdBUUwN13w/e+B/vvDx99lHYiSZKUwyy/Sl/HjvDkk9CqFfz4xzBzZtqJJElSjrL8KjP06wePPAKffBJvfuEtkCVJUjOw/CpzbLNNvAXy6NHw61+nnUaSJOUgpz0os/ziF3ECxNVXw4YbxlsiS5IkNRFXfpV5rrgCdtoJjjsO/v3vtNNIkqQcYvlV5mnVCh58ENZbD/beGyZMSDuRJEnKEZZfZaY11oC//Q0qK+FHP4JZs9JOJEmScoDlV5lr0CB47DEYPx722QcWLkw7kSRJynKWX2W2bbeFW26B55+H44+HJEk7kSRJymJOe1DmO/xwGDcOLr44rgY7Bk2SJK0iy6+yw4UXxgJ85pnQvz/89KdpJ5IkSVnIbQ/KDgUFcMcdMGwYHHIIjBmTdiJJkpSFLL/KHm3bwuOPQ8+e8OMfw+efp51IkiRlGcuvskvPnvDUU1BRAXvsAbNnp51IkiRlEcuvss/3vgcPPwwffggHHACLFqWdSJIkZQnLr7LTzjvD9dfD3/8Op57qCDRJktQgTntQ9jr22DgB4sor462QTzst7USSJCnDWX6V3S67DD77DE4/HdZZB/bdN+1EkiQpg1l+ld0KCuDuu+HLL+HQQ6FXL/jBD9JOJUmSMpR7fpX92rSBJ56Afv1gzz1h7Ni0E0mSpAxl+VVu6NYtHn4rKoLddoMpU9JOJEmSMpDlV7ljvfXg6adh6lT40Y/g22/TTiRJkjKM5Ve5ZejQOAP43Xdhv/2cASxJkuqw/Cr37L473Hhj3AZx3HHOAJYkSTWc9qDcdPTRcQTaxRdD375wzjlpJ5IkSRnA8qvcddFF8MUXcO65sQAffnjaiSRJUsosv8pdIcAtt8DkyfCLX8QZwLvsknYqSZKUIvf8KrcVF8Mjj8CGG8LPfgZvvpl2IkmSlCLLr3Jfp07x8FvPnvEwXFlZ2okkSVJKLL/KD716wejRUFgYtz5MnJh2IkmSlALLr/JH//4wahTMnAm77gozZqSdSJIktTDLr/LLppvC44/DuHHwk59ARUXaiSRJUguy/Cr/bL893HsvvPoq7L+/d4GTJCmPWH6Vn/bZB66/Hp56Co45xrvASZKUJ5zzq/x13HHw1VdwwQWw5ppw6aVpJ5IkSc3M8qv8dt55sQD/4Q9xFNqpp6adSJIkNSPLr/JbCHDddTB1Kpx2GnTvDocemnYqSZLUTCy/UmEh3HNPHIF2xBHQoQPsvXfaqSRJUjPwwJsE0KYNPPEEDB0KBxwAzz2XdiJJktQMLL9StQ4d4JlnoKQE9twTXnst7USSJKmJWX6l2rp2jbdBXntt2H13ePfdtBNJkqQmZPmVltarV9z20KED7LwzfPRR2okkSVITsfxK9Vl33ViAkwR23BE+/zztRJIkqQlYfqXlKSmJWyBmz44F+Kuv0k4kSZJWk+VXWpEhQ+Dpp2HSJNhllzgOTZIkZS3Lr7QyI0bAY4/B2LHwox/Bt9+mnUiSJK0iy6/UEDvvDPffD2+8EcegzZuXdiJJkrQKLL9SQ/30p3DXXfDCC/EOcN99l3YiSZLUSJZfqTEOPhj+8hf4xz9g331hwYK0E0mSpEaw/EqNdeSRcOON8NRTcOCBsHBh2okkSVIDWX6lVfHLX8I118Cjj8Jhh0FlZdqJJElSA7RKO4CUtU46CebPhzPOgOJiuP12KPC/JyVJymSWX2l1/PrX8eDbuefGAvznP1uAJUnKYJZfaXWdc05cAb744liAr7sOQkg7lSRJqoflV2oKF10UC/AVV0Dr1nDllRZgSZIykOVXagohwGWXxdFnV10FRUVw6aUWYEmSMozlV2oqIcDVV8fRZ5ddBkkCf/iDBViSpAxi+ZWaUghw/fXx4+WXxwJ82WUWYEmSMkSDy28IoRAYA0xKkmSPEMJ6wANAV+Bt4NAkSbzdlRRCPPRWUBD3AC9eHD9agCVJSl1jZjKdDIyt9fUfgKuSJBkIzASOaspgUlYLAa69Fk48Ef74RzjttLgKLEmSUtWg8htC6AP8CPhL1dcB2B74a9UldwJ7NUdAKWuFEO8Cd/LJcS/wqadagCVJSllDtz1cDZwBdKz6uhswK0mSRVVfTwR6N3E2KfuFEKc/VB+GS5L40S0QkiSlYqXlN4SwB/B1kiRvhRC2q366nkvrXdIKIRwDHAPQt2/fVYwpZbEQ4taHgoL4cfHiuCXCAixJUotryMrvCOAnIYTdgTZAJ+JKcJcQQquq1d8+wOT6fnGSJDcDNwMMHTrU/+er/BTCkkNvV14ZC7B3gpMkqcWttPwmSXI2cDZA1crvyCRJDg4hPAzsQ5z4cDjwRDPmlLJf9fizgoL4cfHiOBatoDHnTiVJ0upYnTm/ZwIPhBB+B/wXuLVpIkk5LIR444vCwngHuHnz4NZb49eSJKnZNar8JknyIvBi1ecTgC2bPpKU40KASy6Bdu3g3HPhu+/g7rvjLZElSVKz8g5vUhpCgHPOgbZt4de/jivADz4IbdqknUySpJzmZkMpTSNHxn2/Tz4JP/kJVFSknUiSpJxm+ZXSdvzxcNtt8PzzsNtuMGdO2okkScpZll8pExxxBNx7L7zyCuy4I8ycmXYiSZJykuVXyhQHHACPPALvvAPbbw9Tp6adSJKknGP5lTLJnnvG/b9lZbDttvDll2knkiQpp1h+pUyzyy4wahR8/jn84AfwySdpJ5IkKWdYfqVMtO228NxzMGMGjBgB77+fdiJJknKC5VfKVMOHw0svxc+32QZefz3dPJIk5QDLr5TJNtwwToDo1g122AFGj047kSRJWc3yK2W69daDf/8bBg6EPfaAhx9OO5EkSVnL8itlg5494cUXYdgw2H9/uPnmtBNJkpSVLL9StujSBf7xD9h9dzj2WPj97yFJ0k4lSVJWsfxK2aRdO3jsMTjoIPjNb+DXv7YAS5LUCK3SDiCpkYqK4O67oWtXuPLKOA7t5puhlX+cJUlaGf9tKWWjggK49to4BeKCC+Drr+HBB6F9+7STSZKU0dz2IGWrEOD88+Gmm+Dvf4ftt4epU9NOJUlSRrP8Stnu2GPh0Ufhvffi3eAmTEg7kSRJGcvyK+WCPfeEf/4Tpk+HrbaCt95KO5EkSRnJ8ivliq22gldfhbZtYdtt41g0SZJUh+VXyiUlJfDaazBgQLwb3F13pZ1IkqSMYvmVcs1aa8FLL8XV38MPh0svdRawJElVLL9SLurUCZ55Jt4M4+yz4cQTobIy7VSSJKXOOb9SrioujjfD6N0bLr8cPv8c7rsPOnRIO5kkSalx5VfKZQUFcNllcP318PTTcSvE5Mlpp5IkKTWWXykfHH88/O1v8NFHMGxYnAksSVIesvxK+WL33eHll+PhtxEjYNSotBNJktTiLL9SPhkyBN54Y8kotJtuSjuRJEktyvIr5ZveveMK8K67wnHHwciRsHhx2qkkSWoRll8pH3XoAI8/DiecAFdeCfvsAxUVaaeSJKnZWX6lfNWqFfzpT3DNNbEIb7cdfPll2qkkSWpWll8p3510Uiy/H3wAW24Jb7+ddiJJkpqN5VcS/OQn8MorEAJsvTU8/HDaiSRJahaWX0nRkCHwn//AppvCfvvB+ed7EE6SlHMsv5KW6NkT/vlPOPxwuOAC2H9/mDs37VSSJDUZy6+kulq3httvhyuugEcegR/8AL74Iu1UkiQ1CcuvpGWFAKefDk89BR9/DFtsAa+/nnYqSZJWm+VX0vLtvnssve3bw7bbwt13p51IkqTVYvmVtGKDB8Obb8L3vw+HHRbvCLdoUdqpJElaJZZfSSvXrRuMHg3HHx/vCLfrrjBtWtqpJElqNMuvpIYpKoLrr4fbboN//xuGDoX//jftVJIkNYrlV1LjHHEEvPwyVFbGrRD33JN2IkmSGszyK6nxttgC3noLhg2DQw+FU06BhQvTTiVJ0kpZfiWtmjXXhGefhZNPhmuugZ12gq+/TjuVJEkrZPmVtOqKiuDqq+MItDfegM03j7dIliQpQ1l+Ja2+Qw6BV16BwsJ4R7jbbks7kSRJ9bL8Smoam20GY8bE8nvUUXDkkVBRkXYqSZLqsPxKajrdu8OoUXDOOXDHHbDVVjBuXNqpJEmqYfmV1LQKC+HCC+GZZ2DixLgP+JFH0k4lSRJg+ZXUXHbdNd4EY/Bg2GcfOO00x6FJklJn+ZXUfPr2hZdegpNOgquugu22i6vBkiSlxPIrqXkVF8c5wA8+CO+9B5tuGucDS5KUAsuvpJax335xGkTPnrDLLnD++fEWyZIktSDLr6SWU1ISb4Zx2GFwwQWwww4waVLaqSRJecTyK6lltW8fx6DdeWdcCd5kE3j66bRTSZLyhOVXUjoOOwzefhvWWQf22CNOg5g/P+1UkqQcZ/mVlJ5Bg+C11+DEE+M0iBEj4Ov465IAACAASURBVOOP004lScphll9J6WrTBq69Fh5/HCZMiNMg7rsv7VSSpBxl+ZWUGfbcE959F4YMgYMPhqOOgrlz004lScoxll9JmWOddeCFF+Ccc+D22+Otkd96K+1UkqQcYvmVlFlatYILL4Tnn4dvv4Xhw+HSS50JLElqEpZfSZnphz+Md4T76U/h7LNh++3hs8/STiVJynKWX0mZq2tXeOCBOBP4v/+FjTeGe+9NO5UkKYtZfiVlthDiTOB334WNNoJDDoGDDoJZs9JOJknKQpZfSdlhvfXgxRfhd7+Dhx+Oq8Avvph2KklSlrH8SsoerVrBb38Lr74a5wNvvz2ccYZ3hpMkNZjlV1L22WKLuAf46KPh8ssdiSZJajDLr6Ts1L49/PnP8MwzMHMmDBsG550HCxaknUySlMEsv5Ky2267wfvvx0NwF14YS/D//pd2KklShrL8Ssp+a6wBd90Fjz0GkyfHbRC//z0sWpR2MklShrH8Ssode+0FH3wQP/7mNzBiBJSVpZ1KkpRBVlp+QwjrhBBeCCGMDSF8EEI4uer5riGEZ0MI46o+rtH8cSVpJbp3h4ceijfH+PhjGDIErrzS2yNLkoCGrfwuAk5PkmQDYDjwqxDCYOAs4PkkSQYCz1d9LUmZYf/94yrwLrvAyJFxFfiDD9JOJUlK2UrLb5IkXyZJ8nbV53OAsUBvYE/gzqrL7gT2aq6QkrRKevWCxx+H++6D8eNh003hggucCCFJeaxRe35DCP2ATYE3gJ5JknwJsSADazZ1OElabSHAgQfChx/CvvvC+efHA3Fvvpl2MklSChpcfkMIHYBHgFOSJJndiF93TAhhTAhhzNSpU1cloyStvh494N574W9/i3OBt9oKTjsN5s5NO5kkqQU1qPyGEIqIxffeJEkerXr6qxDCWlWvrwV8Xd+vTZLk5iRJhiZJMrRHjx5NkVmSVt0ee8RV4GOOgauugo02guefTzuVJKmFNGTaQwBuBcYmSfLHWi89CRxe9fnhwBNNH0+SmkGnTnDjjfDii9CqFey4Ixx1FMyYkXYySVIza8jK7wjgUGD7EMI7VY/dgUuBnUII44Cdqr7OONMqpvHVt1+RJEnaUSRlmm23hXffhTPPhDvvhNJSuPtu8J8XkpSzWq3sgiRJ/g2E5by8Q9PGaXo3v3Uzv/3nb+nSpgsl3Uoo7V5a59F/jf4UFRalHVNSWtq2hUsvhQMOgF/+Eg47DG6/Pa4Ml5SknU6S1MRWWn6z3R6D9qBDcQfKppVRNq2M0eNHc+e7d9a83qqgFeuvsX4sw92WlOKS7iV0bds1xeSSWtSQIfDqq3DzzXDWWbDxxvHj2WdDmzZpp5MkNZGcL78b99yYjXtuXOe52fNnUz6tvKYQl02PH/8+7u8sXLyw5roe7Xoss1Jc0q2Efl36UVhQ2NLfiqTmVlAQV3/32gtOPx0uvDDOCL7hBthpp7TTSZKaQM6X3/p0at2JLXpvwRa9t6jz/KLFi/h01qdLSnHV47Gyx5hWMa3mutaFrRnYbWCd1eKS7iWUdCuhY+uOLf3tSGpqvXrFsWhHHAHHHw877xxnBf/xj/E1SVLWysvyuzytCloxoOsABnQdwB6D9qjz2rSKaXVWi8unl/PulHd5dOyjLE4W11zXu2PvOqvE1Z/36dSHODhDUtbYcUd47724J/j3v4dnnoHf/S6uDrfyH5+SlI38p3cDdW/Xne59uzOi74g6z89fNJ/xM8fXKcVl08q4+727mT1/yb1A2he1p6R7yTKleGDXgbQtatvS346khmrTJt4V7qCD4Fe/ghNPjPuCr7sOttkm7XSSpEay/K6m1q1aM7jHYAb3GFzn+SRJmPLtlDqFuGxaGa98/gr3/e++musCgX5d+sVi3K3u/uI126/parGUKQYNgtGj4dFH453htt02boW4/HLo3TvtdJKkBrL8NpMQAmt1XIu1Oq7FD9f7YZ3XKhZWMG76uGUO3P3r038xb9G8musczyZlmBDgZz+D3XaLWyEuuwyefBLOOQdOOQVat047oSRpJUJL3vxh6NChyZgxY1rs/bLN4mQxE2dPXObAXfn0cibPmVxzXWEopH/X/o5nk9I2YQKcemoswAMHwrXXwq67pp1KWm133HEHAD//+c9TzSGtqhDCW0mSDK3vNVd+M0hBKKBv57707dyXnfvvXOe1+sazlU8rZ9THo1hQuaDmOsezSS1o/fXhiSdg1Cg46aS4IvyTn8SpEP37p51OklQPy2+WaOh4tvJp5ZRNX/l4ttqH7xzPJq2mXXeF//0Prr4aLroIBg+OZfi3v4UuXdJOJ0mqxW0POaz2eLbah+4mzJxAZVJZc53j2aQmNHky/N//wR13QLducMEFcMwxjkZTVnHbg7Kd2x7y1MrGs9Vso6g6cLe88WxLH7pzPJu0AmuvDbfdFkeinXZaHI923XVw5ZVxW4QkKVWW3zy0ovFsX839apkDd69+8Sr3v39/zXWBwLpd1l3mwJ3j2aRaNt0U/vnPeBhu5EjYfXfYZRe44grYcMO000lS3rL8qkYIgV4detGrQy+267ddndcaOp6tc+vOyxy4czyb8lYIsOeeccX3hhviFohNNoGjj4YLL4Q110w7oSTlHff8arXUN56ten/xysazVR+6czyb8sb06bH03nBDvHPcyJFxa0RHD50qs7jnV9luRXt+Lb9qNkuPZ6suxeNmjFvheLbqPcaOZ1PO+uijOAnir3+Nq7/nnhtXg4uL004mAZZfZT8PvCkVDRnPVvvQ3YrGs9U+dOd4NmW9QYPg4YfhjTfgzDPhhBPgqqvg4oth332hoCDthJKUsyy/anGtCloxoOsABnQdwB6D9qjzWvV4ttqj2d6d8i6PjX2s3vFsS0+icDybssqwYfDCC/EmGWeeCQccEG+Z/Ic/wI47pp1OknKS5VcZZXnj2RZULmD8jPHLHLi753/3LDOebVC3QcscuHM8mzJWCPFA3M47w333wTnnwE47xcfvfw+bb552QknKKZZfZYXiwmI26LEBG/TYoM7zyxvP9trE13jg/QdIiHvalzeeraR7CT3b93S1WOkrLIRDD4X99oMbb4Tf/Q6GDoW9945TIjbaKO2EkpQTLL/Kao0Zz1a9leKlz16iYmFFzXX1jWcr6VZC/679KS70AJJaWOvWcMopcMQR8XbJf/wjPPZYLMXnnw8bbLDS30KStHxOe1DeWXo8W/m08pptFI5nU8aZOTPeHe6aa6CiAg46CM47DwYMSDuZcpjTHpTtHHUmNVD1eLbaB+5WNp6t9qE7x7Op2UybFg/DXXcdLFgAhx0W9wevt17ayZSDLL/KdpZfaTVVj2erPbe4erW49ni24sJiBnUbtMwUCsezqclMmRKnQdx4I1RWwlFHwW9+A337pp1MOcTyq2xn+ZWa0fSK6cusFJdNK2PCzAnLjGcr6V5S58BdafdSenfqTUFwrqsaadIkuOQSuOWW+PXhh8NZZ0H//unmUk6w/CrbWX6lFCxvPFvZtLI649naFbVbZqXY8WxqsM8/j9sh/vIXWLgw7gk++2wYPDjtZMpill9lO8uvlEHqG89WvXL82azPHM+mVfPll3EyxI03xoNxP/tZvIXykCFpJ1MWsvwq23l7YymDNMd4tuqVY8ez5bG11oLLL493irvmGrj2WvjrX2GPPWIJHj487YSSlBFc+ZWyQO3xbDWH7hownq16NJvj2fLQrFlw/fVw1VUwfXq8XfKZZ8IOO8S7ykkr4Mqvsp0rv1KWKwgF9O3cl76d+7Jz/53rvDZ7/mw+mv7RMgfuRn08qt7xbEvvL3Y8W47q0iWu+J58Mvz5z3DFFfGWyZtuCiNHxptmtPJfAZLyjyu/Uo6qXFzJp7M+rVuKp8eV46kVU2uuczxbnpg/H+65J5bgsjJYd1049dQ4Kq1Dh7TTKcO48qts54E3SXXUN56tfHo542eMrzOebe2Oa9d74K5Ppz6OZ8tWixfD00/H/cEvvwxrrAHHHQcnngi9eqWdThnC8qtsZ/mV1CBLj2erXZC/mf9NzXWOZ8sRr78eS/Bjj0FRUbxr3OmnQ2lp2smUMsuvsp17fiU1SHFhMRv02IANemxQ5/mlx7OVTyunbHoZr018jQfef2CF49mqD905ni0DDR8OjzwC48bFMWl33BHnBe+2G5x0Euy8MxS4wi8pt1h+Ja1UQ8ez1V4pXtF4ttqrxo5nywADB8b5wBdcADfdFD/fbTcoKYkl+LDD3BcsKWe47UFSs6gez1Yzmq0B49mW3krheLaULFgADz0U5wWPGQOdO8eDcSecAOutl3Y6tQC3PSjbuedXUkZZ3ni2cTPGLTOeraR7SZ0Dd45na0FJEvcFV98wo7ISfvKTOD5tu+2cF5zDLL/KdpZfSVmhvvFs1Vsplh7PNrDrwGUO3DmerRlNmgQ33BBnBk+fDhtuCL/8JRxySFwZVk6x/CrbWX4lZb2lx7NVf+54thY2bx7cf38swm+9Be3awUEHxSK8+eZpp1MTsfwq21l+JeWs2uPZlp5dvLLxbCXdShjUbZDj2VbVmDHxgNz990NFBWyxRSzB++8P7dunnU6rwfKrbGf5lZR3ao9nqzl0V3Xg7rNZny13PFv1aDbHszXCrFnx7nE33QQffBC3QRx2GBx7LHzve2mn0yqw/CrbWX4lqZZ5C+cxbsa4ZQ7clU8vdzzb6kgSeOWVWIIffjhOjfj+9+HII2G//aCj+7GzheVX2c7yK0kNsDhZzKTZk+qW4ulx5XjSnEk111WPZ6vvLneOZ6sybVq8acatt0JZWdwbvN9+sQhvvbWTIjKc5VfZzvIrSatp6fFs1fuLP5r+UZ3xbN3bdV/mwF1ej2dLEnjjDbjtNnjgAZgzBwYMiCX4sMOgd++0E6oell9lO8uvJDWTpcez1T5053i2pcydG2+nfNtt8K9/xVsn77JLLMI//jG0bp12QlWx/CrbWX4lKQW1x7OVTyuvOXDneDbg44/jtog77ogzhLt0gX33jXODt946FmOlxvKrbGf5laQMUj2ebenRbCsbz1b9eU6NZ6ushOeeg3vvhUcfjavDffvG2cGHHOK0iJRYfpXtLL+SlAWqx7PVjGZrwHi2pQ/dZfV4trlz4Ykn4ti00aNjMR4yBA4+GA480P3BLcjyq2xn+ZWkLNfY8Wwl3UvqbKPIuvFsX38NDz4Yi/Cbb8bpED/8YbyBxt57Q48eaSfMaZZfZTvLryTlqPrGs1Vvp1h6PNv6a6xf74G7bu26pfgdNMC4cXFbxH33xc8LC2H77ePotL33hm4Znj8LWX6V7Sy/kpSH5syfU++Bu6wdz5Yk8N578NBD8fHxx7EI77BDLMJ77WURbiKWX2U7y68kqUbt8WxLH7pb2Xi2km4llHQvoVPrTil+B8Qi/O67S4rw+PHQqlUswvvuG0enrblmuhmzmOVX2c7yK0lqkBnzZtR74G5l49lKuseDd6mMZ0sS+O9/4y2VH3oIJkyIe4RHjIA994wrwgMGtGymLGf5Vbaz/EqSVsuCygVMmDlhmQN3KxrPVnsSRYuNZ6veGvH44/Hxzjvx+e99L5bgvfaCzTf39sorYflVtrP8SpKaRZIkfD3367qFeHrcY/zprE/TH8/26adxfNoTT8BLL8Xxab17xxXhPfeEbbf1znL1sPwq21l+JUktrr7xbNV7jJcez1a9baJZx7NNnw5PPx1XhEeNgnnzoH172HFH2H132G03WGedpnu/LGb5VbZbUflt1dJhJEn5oW1RWzbuuTEb99y4zvNLj2erLsTPT3ieu969q+a6Jh/P1q0bHHZYfFRUwPPPw9//Ds88E1eGATbcMBbh3XeH738fiopW5y+BpAzkyq8kKWOszni2ku4l9OvSj1YFjVzXSRIoK4sl+Jln4vaIRYugUyfYeee4IrzLLnl1hzlXfpXt3PYgScpq1ePZlh7NtrLxbDWH7xoznm327LgqXF2GJ0+Oz2+wQdwiseOOca9w587N8J1mBsuvsp3lV5KUs1ZlPFvNHuOVjWdLEvjf/+DZZ+G55+KqcEVFvLnGllsuKcPDh0NxFt0+eiUsv8p2ll9JUt6pbzxb+fRyxk4dW+94tpLuJXW2UQzsNpB2Re3q/qbz58Prr8ci/Nxz8OabsHgxtGsXV4N32CF+HDIk3nQjS1l+le088CZJyjvFhcU1Rba2+sazlU8v542Jb/Dg+w8uM55t6dFspZuX0nObbQgXXQSzZsG//hWL8LPPxgN0AB06xJtsbLstbLMNbLFFTq0MS9nM8itJyishBHp26EnPDj3Ztt+2dV6rPZ6t9oG7l99+uc54tk6tOy0pw91KKT1+e0rPPZ7+37Wl+NU3YiF+6SX4zW/iL2jbNm6NqC7Dw4fH5yS1OMuvJElVVjaebekDd8sdz/aDUkr33p3S1kdT+nkFJW99Srd//QcuuCDuIy4qgs02g622WvJwxrDUIiy/kiStREEoYJ3O67BO53XYcf0d67w2Z/4cPpr+0TIH7v4x/h9LxrN1ge4Hdqf0uGGULuhE6eQFlHz4NaUP3EC/a6+m1WLiKLXaZXizzbz7nNQMLL+SJK2Gjq07svnam7P52pvXeb5ycSWfffPZMqPZnpj1X/5SPBWGAEOguKCIgaE7pbMKKJ3wLCV3/pXSK6FkdhGdNtwchg2DzTeHoUNh0KA4aULSKrP8SpLUDAoL4haI9ddYn90H7l7ntfrGs70/rZzHO02mcpPqqxay9ndvU/rVm5Q8uJjS66H02zaUrrURfTYaQcHmQ2MhHjgQCpYzqk3SMiy/kiS1sK5tu7LVOlux1Tpb1Xl+6fFs5dPLKZs6lvu+/pBvFs4BvgP+Q7sF/2HQy1D6GJTOKaa0c39K+w1l4Ebb0W7IFlBS4nQJaTksv5IkZYiGjmcrnzqWss/e4o1pZTy4aBpJGAuMJYy/m75vQ+n0QGnSLZbidTal9Hvb0nPodoRevdL5xqQMYvmVJCnDNWQ8W/lXH1BW/iplX7xNWafxvJxMo6LwDfjuDXjrJjq9AqXftKKUHrEU99mE0pKt6b/ZDhR37ZHSdya1PO/wJklSDqoZzzbhTco++BdlX/yXsm/GU8Y0JrVdWHNd4WJYf3YhpZVrUNp2HUrXHMz4pCtrdejHCceeCiGk+F1Iq6bZbm8cQtgVuAYoBP6SJMmlK7re8itJUvrmzJ3JR++/SNnYlymb+C5ls8dTXvk1H7Wbx/xa/0+4e0WgdH4HSlv1oqRzf0rX3ojSgd+n30Y/oNUa3dL7BqSVaJbyG0IoBD4CdgImAv8BDkyS5MPl/RrLryRJmauychGflb/Bn566gynzJ9Hx208pXzCZsuI5fN1ucc11xYtg4DeFlC7sTEnx2pR2HUjpOptSUjKCTqWbQNeurhgrVSsqv6uz53dL4OMkSSZUvckDwJ7AcsuvJEnKXIWFrVh/8Ag2eXMcmwA///nPa16bMe0Lyt//F2XjX6d8ygeULfyE95OpPN7mfSp5H754DL6AtR+FkpkFlC7sTGmrXnF/ca8N6bPuRhT0Ww/WXRd69XI8m1KzOuW3N/BFra8nAsNWL07TO+WUU3jnnXfSjiFJUtYYMmQIANttt90KrupHL/qxZljMd60rqCj6horWc6hoW8GYjt/xcs9ZLGozExgL85+i4H1o9y9oOw3aTYd2s4po920b2s5rS2FhmziarXXr+Cgujg9Xj7PekCFDuPrqq9OOUcfqlN/6/o5cZg9FCOEY4BiAvn37rsbbSZKkTFOQFNDuuw60+64DzFnyfELCwqKFVLSroKLtXCpaz2Feu7nM6fcdUzdcBGEhsBCYQ+tZ0G5arceUWJKL57citK5VjKs/FhXFR3Fx/NjK4VVquNX5u2UisE6tr/sAk5e+KEmSm4GbIe75XY33WyWZ9l8bkiRlujvuuANovn+Hzls4j49nfFzrts9jKZvyAeUzxzGpcl7NdZ0WB0orWlE6A0onz6b007mUTIcBM6C4stZvWFQE3bvDmmtCjx5LPlY/1lhjyaNLl/ixc2dvFZ2nVqf8/gcYGEJYD5gEHAAc1CSpJElSzmpb1JaNem7ERj03qvN8kiRMmjOpVimOj39OL+euvjNgeLyuMBSyfutelBasSemiLpTMbUvpjAJKpyyi25ez4JNP4OuvYc6cet69SgjQqdOypbi6GHfsCB06LP9j7c9dec4qq/zTSpJkUQjhBOAfxFFntyVJ8kGTJZMkSXklhECfTn3o06kPO66/Y53X5syfw0fTP1pSiqeXUT6tnNHTX2V+0XzoCfSE7lt1j3fJ6/ZDSjqvT2nRWpSGHvSb35ZWs7+FmTOX/ygrix9nzYJ58+oPWZ82baBdu/ix9qNt22Wfq/1a69axODf2saor1kkCixdDZSUsWrTk0dCvFy6E+fMb9xg2DO67b9XyNpPV+k+VJEmeAZ5poiySJCkD9MrA2yB3bN2RzdfenM3X3rzO85WLK/nsm8+W3Pp5Wjll08t48qMn+Xru1zXXFRcWM7DrQEq6l1Dap7TmNtIl3Uvo1LrTsm9YWQlz58K338bHnDnL/3zOnFiWv/uu7qP6uVmzln2u+rF48bLvnYkKC2Pxrj6UWP1o06bu11261P16o41W/nu3MO/wJkmSctKMeTMon1ZO+fTyOtsoPp7xMZXJkk3Da3VYq6YM13706dSHgtDMI9mSZNmV1oY8VnUSRkHBsqvIK/u6sDDrJm802x3eGsvyK0mS0ragcgETZk6Iq8RVWyiqi/Gs72bVXNe2Vdu4Uty9lNJuS0rxwG4DaVfULsXvQCtj+ZUkSVqJJEmYWjF1mQN3ZdPK+HTWpyS1Jrqu23ndOqvEJd1iSe7VoRchy1ZJc1Fz3eFNkiQpZ4QQWLP9mqzZfk22WXebOq8tM56t6sDdX97+C3MXzq25rlPrTktKcbfSmpXjAV0HUFxY3NLfkurhyq8kSdIqqm88W/Ue44mzJ9ZcVxgKWX+N9eusElc/urXrluJ3kJtc+ZUkSWoGDR3PVvvQ3ejxo5lfOb/muu7tutdbivt16UerAqtaU3PlV5IkqQXVHs+29KG7pcezDeg6YJkDd8sdz6YaHniTJEnKAssbzzZ+5ngWLV5Uc12q49mygOVXkiQpiy2sXMiEmRPqHLhr6Hi2ku4lDOo2KK/Gs1l+JUmSctDyxrOVTy/nk5mf5O14Ng+8SZIk5aDGjGer3kqxovFstQ/d5ep4Nld+JUmS8sjS49nKp5XXbKOobzxbSfeSOgfusmE8myu/kiRJAho2nm3pA3fPjn92mfFsS49my5bxbK78SpIkaYUqF1fy+Tef191bXM94tqKCIgZ2G1hz4G7L3luyZ+meLZ7XA2+SJElqFjPnzVxmpbh8ejkfz/iYHdffkb8f/PcWz+S2B0mSJDWLNdquwfA+wxneZ3id5xdWLuSb+d+klGr5nIIsSZKkJldUWET3dt3TjrEMy68kSZLyhuVXkiRJecPyK0mSpLxh+ZUkSVLesPxKkiQpb1h+JUmSlDcsv5IkScobll9JkiTlDcuvJEmS8oblV5IkSXnD8itJkqS8YfmVJElS3rD8SpIkKW9YfiVJkpQ3LL+SJEnKG5ZfSZIk5Q3LryRJkvKG5VeSJEl5IyRJ0nJvFsJU4LMWe8MlugPTUnhftSx/zvnBn3Pu82ecH/w554e0fs7rJknSo74XWrT8piWEMCZJkqFp51Dz8uecH/w55z5/xvnBn3N+yMSfs9seJEmSlDcsv5IkScob+VJ+b047gFqEP+f84M859/kzzg/+nPNDxv2c82LPryRJkgT5s/IrSZIk5Wb5DSFcFEJ4L4TwTghhdAhh7eVcd3gIYVzV4/CWzqnVE0K4PIRQVvWzfiyE0GU5130aQvhf1d8PY1o6p1ZPI37Ou4YQykMIH4cQzmrpnFp1IYR9QwgfhBAWhxCWeyrcP8vZrRE/Z/8sZ7EQQtcQwrNV3erZEMIay7musurP8jshhCdbNGMubnsIIXRKkmR21ecnAYOTJPnlUtd0BcYAQ4EEeAvYPEmSmS2dV6smhLAz8M8kSRaFEP4AkCTJmfVc9ykwNEkS50lmoYb8nEMIhcBHwE7AROA/wIFJknzY0nnVeCGEDYDFwJ+BkUmS1Fts/bOc3Rryc/bPcvYLIVwGzEiS5NKq/3hZYzn/bv42SZIOLZ8wR1d+q4tvlfbEcru0XYBnkySZUVV4nwV2bYl8ahpJkoxOkmRR1ZevA33SzKP/b+f+WaOIojCMPy+ICpJCkMRoFBRSWAoiSBpBDRaSaCdYCBZWAUuRgIIi5ANYWNikUMRGFKJGRYNYiEbwTyQRNU1CgiksLUQ4FjuB1ewmGzOZ7My8v2ZnZu/ePXA4u2dn587qaDDP+4GvETEZEb+A20BvVjHaykTEeER8Xus4bHU1mGfXcv71AoPJ9iBwfA1jqamQzS+ApKuSpoBTwMUaQ7YDU1X708kxy6czwMM6zwXwWNJbSWczjMnSVy/PrudycC0Xn2s5/9oiYhYgeWytM26jpFFJryRl2iCvy/LN0iTpKbC1xlP9EXEvIvqBfkkXgD7g0r9T1Hht8a4Bybml8pyM6Qd+AzfrTNMVETOSWoEnkiYi4sXqRGz/I4U8u56bXCM5boBrucmlkGfXcg4sludlTLMzqefdwDNJHyPiWzoRLi63zW9EHG5w6C1giIXN7zRwsGq/AxhZcWCWqqXynCxUPAYcijoXsEfETPI4J+kulb/V/IXZRFLI8zSwo2q/A5hJL0JbqWV8Zi82h2u5yaWQZ9dyDiyWZ0nfJbVHxKykdmCuzhzz9TwpaQTYC2TS/BbysgdJnVW7PcBEjWHDQLekzclKxO7kmOWEpKPAeaAnIn7WGbNJUsv8NpU8j2UXpa1UI3mmsiimU9IuSeuBk0Cmq4dtdbmWS8O1nH/3gfk7aJ0GFpzxT3qvDcn2FqALMTQVXgAAANxJREFUyGxRYyGbX2BA0pikD1Q+IM8BSNon6QZARPwArlAptDfA5eSY5cc1oIXK35/vJF0HkLRN0oNkTBvwUtJ74DUwFBGP1iZc+09L5jlZENdH5QfsOHAnIj6tVcC2PJJOSJoGDgBDkoaT467lAmkkz67lQhgAjkj6QuWuHQPwdw8G7AFGk3p+DgxkeUePQt7qzMzMzMyslqKe+TUzMzMzW8DNr5mZmZmVhptfMzMzMysNN79mZmZmVhpufs3MzMysNNz8mpmZmVlpuPk1MzMzs9Jw82tmZmZmpfEHJ5kCSk8nrs4AAAAASUVORK5CYII=\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Converged in 7 steps\n" ] } ], "source": [ "# make nice seriest of plots\n", "a,b = -3,-.5 # upper and lower limits\n", "xd = np.linspace(a,b,1000) # x grid\n", "def plot_step(x0,x1,iter,**kwargs):\n", " plot_step.counter += 1\n", " if iter<10:\n", " plt.plot(xd,f(xd),c='red') # plot the function\n", " plt.plot([a,b],[0,0],c='black') # plot zero line\n", " ylim = [min(f(b),0),f(a)]\n", " plt.plot([x0,x0],ylim,c='grey') # plot x0\n", " l = lambda z: g(x0)*(z - x1)\n", " plt.plot(xd,l(xd),c='green') # plot the function\n", " plt.ylim(bottom=10*f(b))\n", " plt.title('Iteration %d'%(iter+1))\n", " plt.show()\n", "plot_step.counter = 0 # new public attribute\n", "newton(f,g,x0=-2.5,callback=plot_step)\n", "print('Converged in %d steps'%plot_step.counter)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "def newton(fun,grad,x0,tol=1e-6,maxiter=100,callback=None):\n", " '''Newton method for solving equation f(x)=0\n", " with given tolerance and number of iterations.\n", " Callback function is invoked at each iteration if given.\n", " '''\n", " for i in range(maxiter):\n", " x1 = x0 - fun(x0)/grad(x0)\n", " err = abs(x1-x0)\n", " if callback != None: callback(err=err,x0=x0,x1=x1,iter=i)\n", " if err