{ "cells": [ { "cell_type": "markdown", "metadata": { "ExecuteTime": { "end_time": "2018-12-23T01:30:46.418526Z", "start_time": "2018-12-23T01:30:46.414550Z" } }, "source": [ "# Numerical simulations of SDE" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2019-02-06T03:40:38.424495Z", "start_time": "2019-02-06T03:40:38.402849Z" } }, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2\n", "%matplotlib inline\n", "\n", "figheight=8\n", "rc('legend', frameon=False,fancybox=True,shadow=True,fontsize=14,loc='best')\n", "rc('lines', linewidth=2)\n", "font = {'family':'serif','size':35}\n", "rc('font',**font)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sources:\n", "Pavliotis, stochastic processes and applications, Chapter 5\n", "\n", "Hingham, 2001, An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations, https://epubs.siam.org/doi/pdf/10.1137/S0036144500378302\n", "\n", "Platen, 1999, An introduction to numerical methods for stochastic differential equations, https://pdfs.semanticscholar.org/fbba/5c93f3021b12aceb676e18290375e5eb20c2.pdf\n", "\n", "Holmes-Cerfon, 2017, https://cims.nyu.edu/~holmes/teaching/asa17/handout-Lecture10_2017.pdf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 1) Euler-Maruyuma vs Milstein : Qualitative Assesment\n", "We consider the SDE, whose solutions are asumed to exist and be strongly unique.\n", "$$dx=adt +b dW,\\;\\;\\; x(t_0)=0$$\n", "\n", "For $t=t_0=0...t_N=T$, and prescribe (BM) W, we write write $\\Delta_i = t_{i+1} - t_{i}$ and $\\Delta W_i = W (t_{i+1}) - W(t_{i}) \\overset{law}\\sim \\sqrt{\\Delta_i} N(0,1) $\n", "\n", "##### Euler-Maruyama Scheme:\n", "$$X_{n+1} = X_n + a_n \\Delta_n + b_n \\Delta W_n$$\n", "\n", "##### Milstein:\n", "$$X_{n+1} = X_n + a_n \\Delta_n + b_n \\Delta W_n + b_nb_n^\\prime (\\Delta W_n^2 -\\Delta t_n)/2 $$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2019-02-06T03:40:38.534457Z", "start_time": "2019-02-06T03:40:38.427760Z" } }, "outputs": [], "source": [ "def Euler_Maruyama(sfunc,z0,time=np.linspace(0,1,100),W=None,args=()):\n", " M,NT=len(z0),len(time)\n", " z=np.zeros((NT,M))\n", " if W is None:\n", " W,DW=np.zeros((NT,M)),np.random.randn(NT,M)\n", " for i in range(NT-1): W[i+1]=W[i]+np.sqrt(time[i+1]-time[i])*DW[i]\n", " z[0,:]=z0\n", " for i in range(0,NT-1):\n", " tau = time[i+1]-time[i]\n", " drift,diffusion,dummy=sfunc(z[i,:],time[i],*args)\n", " z[i+1,:] = z[i,:] + drift*tau+ diffusion*(W[i+1,:]-W[i,:])\n", " return z\n", "\n", "def Euler_Milstein(sfunc,z0,time=np.linspace(0,1,100),W=None,args=()):\n", " M,NT=len(z0),len(time)\n", " z=np.zeros((NT,M))\n", " if W is None:\n", " W,DW=np.zeros((NT,M)),np.random.randn(NT,M)\n", " for i in range(NT-1): W[i+1]=W[i]+np.sqrt(time[i+1]-time[i])*DW[i]\n", " z[0,:]=z0\n", " for i in range(0,NT-1):\n", " tau = time[i+1]-time[i]\n", " DW=W[i+1,:]-W[i,:]\n", " drift,diffusion,diffusionprime=sfunc(z[i,:],time[i],*args)\n", " z[i+1,:] = z[i,:] + drift*tau+ diffusion*DW+0.5*diffusion*diffusionprime*(DW**2-tau)\n", " return z " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Example 1: Multiplicative Brownian Motion\n", "$$dX = \\lambda X dt + \\mu X dW$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2019-02-06T03:40:38.789034Z", "start_time": "2019-02-06T03:40:38.536906Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,'512 Steps')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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YYyaMMXPGmAX3MWeMmWj2vOD4wQ8af4711f/u63iJbFqDg4Oy+SyJIKBFENtU17aJIGNM1H0Mu8mc8gTNrDFm1H0vWqXt21oNp52UNO4GDvsqh9x5LMlpIzdmreW/PHg2NCRlMtwgAfwWi8U0PT2tgYEBLS4uVjxmcnJSIyMjun79eum1sbGx0vGjo6NaWVnRjRs3PJ3Pi/LxAaCVJJPS6dNSNuvvmOfOEecAfiC2Abxx7wstyFk4/JK19pK19pKcji8vG2OWDukKc9CYU8aYG8aYG/fu3WvEtE+cO3caf477d97ydbyCLai7p0f5XIbOLoAPiG2OR7DZE6iHe6FeOeSQYkKm/DMD1tr43gOttcvGmGuSrkha1gEVQe6xcUljblXQijFmWVLxv66LkkYlzcsJMPadC6jmn/5T6bd/W/q5n2v2TIDOMTw8rJdfflnxeFwzMzMaHx/f9X4sFtPw8LAGBwc1NTVVen1ubk7Dwzv/LhwZGal6ruXl5dJ41ewdHwBaRTIp9fT4O2YiQSII8AuxDeDJsJwFw5N778+4i3bHjDErkpaMMWPWWk93Ba211yVdl6SLFy9an+d8It292/hzvL++6ut4eVtQd2+vCvkcFUGAD4htjkdbVgRZa2PWWlPj48DEjLV22j1mzEsCp3i8nFUkK+7jqqQBa+2+IAPwqr9f6u6WWFgE+G9yclKxWEzx+O6/omOxmIaGhvYdX+vFPh6P6+rVq56P76RgAo3V6NYlxphRj8dFaaNyMiQS/ieCkklawwF+I7YBDhVThSTQHtNytgiYO54poZLjSARtZhLqDoR9G6/gJoLyhaz+YP6HlPWzjBo4wYhtGqstK4JaRXHfIKASW+faoBdflK5fl77wBX/nAzTM9rb05pvHe85nnpH6+mr+2OXLl3X16lXNzOx0Ex0c3L/F3PLysl566SVdvnx512qTong8rq9+9asaHh5WPB5XLBbT6Oio4vG4FhYWtLa2pvHxcQ0PD2txcVGxWEyDg4P61re+pZmZmX3jLy4u6vLly5qeni6NubCwoNnZ2X3nxsnhtrZ9RdLEQZXNPp1jyRgTl7O6dUFSzFobc98bdh+flTQh6Zqc6md0MCqCcOJHK7ZHAAAgAElEQVQR2xDboK0Vu7l4OG7ejYFGjTET3ONpjnT6eM4TCYZ8Gcdaq7wtKNLTo0I+q/WtmNLptEIhf8YHGoLYhthGbVoRBLSDhw+l6GG7Ux0gEpFOnZI2NvyfE3DSTU1N7eonu7i4qNHR/cUQo6Oj+0qRy129elUXL17U+Pi4JiYmNDw8XAogLl26pKmpKQ0PDysWi2lmZkZTU1OamJjQyMiIrl27tm/84jhLS0ulr2/cuOG5by06h1t1M+62oV2Xk3yRnN72jRSV0yZ3QU77W+uef0nOKtkJSZettQe20EXnyOUkv+9lUBEENAaxDXBkxXb/Lzd1FidULicFAo09R6FQ8HW8fD6vLmMU7u5WNpeRlVUul/P1HMBJRmzTOFQEAQ2yuipduFDfZ594Qrp929moGWh5fX3SWNUFdy0hGo1qfHxc8/Pzmpg4vMNVpbLjosuXL+vSpUulAOLKlSsVj5ufn1c0Gi1tLli+iqXS+GNlv8fBwcF95dDoXG7LtWJbkpicqptLchIzzbYoadrtpw/UJZGQPvQh6Y03mj0TwANiG2IbnCTLcvaZHjXGRGn1f7wyGac9fqEgdTVoqXraLTnK+5QQchJBXQpGIsrkMpJEazi0PmIbYhuRCAIaZnXVqYKsx9mz0v370tNP+zsnAE4wMDMzo+HhYV28eLGuMQYHB7WysqLl5WXNzs5qcnJSc3O7W4svLy+Xjj1slQrgWpSz12ApivS6d48PliU9J+cmyLCkEUlxSd+StOx182TgMMmk1Nvb7FkAnYnYBjiSlbKvL8qJyXBM0mlpcDCnra1gwxbCptNpBUyXcoW8L+PlcjkFSomgdOk1AP4htmkMWsMBDfLuu9Jjj9X32WIiCID/xsfHFYvFdOPGDUXr6d8op8S42F+2vB9sNBrV2tqaJGltba1UKlyuuMoEKGetjTdzBap7/nlr7TVr7WVr7bT7PUkg+CKR8H/fIQAOYhvgSNbKvu6sXcHbQCx2U8uv/ZDm5qRGFdWk02n1BCPKWX8SQcWKoFBZRRCJIMBfxDaNQUUQ0CDZrBQO1/fZoSHpwQN/5wOcVMV+r8WN/0ZHRzU9PV1aVbK4uKhXX31Vkkqlx8vLy3r11VdLq0Li8fiu74eGhrS4uFgqGb58+XLpeWZmRvPz8xodHdXw8LBmZmZK/WXj8fiB4y8uLmp5eXlXwDM7O6uZmZm6Ax8AaBWJBBVBgF+IbYCDGWMW5FT2TFtrr1c7Hs117966NtP39B/+g/S5z/m/R6EkbW+n1R2MaCublLVWxpgjjedUBAUUDIWUytMaDvADsc3xMNbaZs8BFVy8eNHuzUaivczOSu7fMXW5fl2amvJvPgDglTFmyVpbX/01fOO2hltyvx1pRHWOMSYq6TVrbcMbRhPbtI9iDHPUWGbvmFNT0iuvEN8AOH7ENq2jkfHNnrFj1toRD5+ZklRcKj5prZ33ej5im6P7nd/5pl6c/ISe+nBe3/ymdOaM/+d4443v61M//ff1/tZ9ZbJZBQKBI4137949ffiDT+l3/uj39fnn/1fd3Litt956S0/T2x/AMaontqE1HNCiyNECAIBOYa10xAW4AABUU95m12tfn/Il3Ms+zgUebG+nlbUF/bN/llKjuqttbqYVDgQVMAFfKneKFUGhUEiZfLb0GgC0OhJBAAAAABqKJBAAoNHc6qKYnEojrzWtz7rPMfZGPH6JhNNa7fHHNxqWCNraSisSDCrY5U8iyNkjyCgYDCqVozUcgPZBIghoUdwwAQAAzTI6Oqrt7bXqB3pUKBT0cz/3c76NBwA4mdy2toeJa3eVTzXj7vPsoUehIRLbKUlSJvOwYYmg7W0nERTwKRFU2iMoGFTa3SMok6EiCEDrIxEENMDWltTX1+xZAABQG2PMhDFmzhiz4D7mjDETzZ4Xjt/KyooSiXXfxstktjU7O6ucu3IWAIBaGWMWJK0bY9aNMcMHHHZV0ozH8abkJI3i1tprPk0TNUhsJSVJqVTjEkFbW05ruKBPreHy+bwCXV0KhUJKu63hSAQBaAckgoAGePdd6cKFo43BHkEAgONijBl1b64MSnrJWnvJWntJzs2Ul40xS4fccEGHMUZKJhLKZBK+jVkcK5Xa9G1MAEBbGqznQ8aYce1U70QlTVc6zlo77x5/aDLIjWuKVUDP1TMnHF1qa9t5Tj1UPt+Yc2xvpxUJhXxrDZfL5dRluhQMBlWwBUlSOk0iCEDrIxEENMDqqvT4482eBQAAngzLWTk7aa29bq0tbbRsrV221o7JueFSczLIGDNljLlhjLlx7949f2eNhikU8srmcj4ngoorfjd8GxMA0PqMMVH3Mewmc8oTNLPuYpTh4nGHDFVLv9JJSeNudfO+2MWdx5KcNnJj1trlGsaGD9bXpd//fSldTARt3m9YRVBiK+nuEdSlTMaPRFC+1BquKJVijyAArY9EENAAq6tHrwjq6lLDVsQAAFAmJicJFD/kmGk5yaC5WgZ2E0sXrbUXH3nkkaPMEceomLTxMxGUzTpjJpMkggDgpHCTMOvuY0XSgqTRskOKCZmV4nEHJYPcZE2xfduyDqgIco+NuwtZliWtuJXNs+5jyZ3HoqSnSAI1RyIhvfWWlEo4sUbm4e3GJYI2t9UdiSjYFVAyefSETSaTU1eXUSgUKr1GRRCAdkAiCGiAZFLq7T3aGIODUvywW3IAABxR8UZJlSRQsc1KXNIoewZ1vmLSppgQ8kMxqZTLbSjDNkEAcCJYa2PWWlPj48CYxFo77R5TNXYpP15Oq9sV93FV0oC1ttoiGDRQOi3duiVlEm7F8MO7DUsEpTa31d3tJIJSqaOfJJvNK7inIog9ggC0g2D1QwDUypijjzE0JN2/7zwDANACbshZufuypPkmzwUNtJMISshaf+Ka4pjShjY3iW8AAMenuG8QWkcmI62tSeGks1Dkl//vf6unxv6+fvzHP+X7uVLb24p0+1cRlE7nFOgyu1vDJVnlAqD1UREEtKizZ51EEAAALaLYOmW0Sg9/tLli9Y4tbCud9nlM6ySCAADAyZXJSOGwlE7uVB/fXv1BQ86V2k6ou6dbwUDAl718Mpm8Al2BXa3hMmn2CALQ+kgEAS2KRBAAoMWslH19sWmzQMMVW8KZ/EOlUv6OWcjHSQQBAHDCFRNB+UxSn/npn1awq0tB05imRenthHp6uhUK+LdHUMDsrgjKJH1aOQMADURrOKBFDQ1JDx40exZA+1tcXNT09LQ++9nPKhqNamZmRsPDw5qcnFQ8Htfs7KwWFhY0PDzc7KkCrW6t7Gv+h+lQ2axUKDhJG5v2LxGUzToVQfnkAxJBwBER2wBod9/970uK/91fKZNO6uMf/5gi6aAyqcYkU1KJbQ0MdSvU5V9FUDCwe4+gdNKngAk4oYhtjgeJIMBnqZQUiRx9nFBIDdssEThJYrGYXnvtNUWjTierYvAwNTUlSRofH1c8zj6xOHmMMQtyKnumrbXXmz0ftIZkUjLGrd7JbPiXCEptSZJy2/dJBAFHRGwDoN39X7/6i/rGt7+m556eVKTnvELhkHLpxuyzk00m1dPbo5BvreFyCpiuXYmgbIo9goCjILY5HrSGA3z23nvShQv+jGWtP+MAJ9ng4GApmKhkdHRUa2trB74PdCJjzKikcUlRSdMePzZY9jX/03Qop1W/kwjKZzZV1rr/SHKph5Kk9DYVQcBREdsAaHenuk9LkjY30gr39CgUDCmbaVAiKJNUT3/vgYmgWu+7OBVBXbv2CMo2qJoJOCmIbY4HiSDAZ6ur/iWCABzdxMSEp+NGRkZ0/fp1zc/Pa3JyUouLi6XXJGl+fl4DAwNaXl4ufWZxcbH0melpr/fSgZZQvpxq0eNnyiPz5QOPQsO89lrjF4nsTgRt+VYRlE9uaLCnR8mtdRJBwBER2wBod32RfklSMpFSpLdXwXBQ+QYlgvLZpCI9bkVQcv85vv516Tvf8T5exYqgBlUzAScFsc3xoDUc4LPVVeljH2v2LIDjZYw59nNaH++Gjo+Pa3x8XEtLS5qdndXw8LBGR0d3BSMTExOanZ0tfR+LxTQzM6OFhQVJ0tramq5du6YrV674Ni+gUay1MWNMTNIla23M48eedZ9jNXwGPvrzP5dGR6WBgcadI5mUbN5p45ZN+5MIKhSkXHpL56NRbW0+VPboXVmAhiO2IbYB0Dj9oT5JUjCYUqSvT6FQ4yqCcjkn2RQKBpSuUBEUj0u1/JWfzeQUDHSpq6tLRpKVlElTEYTWR2xDbEMiCPDZxoZ0+rQ/YzXh72igLn5e3JslGo1qZGREklN2XM38/Lyi0agWF51iisHBwSqfAI6XMSZqrT2skXJcu6t8qhl3n2cPPQoN8/ChdPPmMSSCcpvqCQaVTW/50hrOGXND54aGtLGxcfQBgWNAbENsA6BxbK4gScp2rTmt4UIhpRuVCMq6VUfBoDKJ/YHN9rYUrOHuaCadVSAQkCQFTUBZm6ciCG2B2IbYhkQQ0MI64O9ooK3UGhQMDg5qfHy8+oHAMTPGLEgaN8bEJY0dUMFzVdKMpEsexpuSkzSKW2uv+TpZeHbmjHTrlvTRjzbuHMmkZNMbGurvVzqd8KUiyEkEbevc+fOKrawcfUAAnhHbAGhFmbSTkNku3FOkv1+hcFDbW40pGc5l0+ru71coHFKmQmCzvS111bBxRjadUSDg3E4NmC5lbV45EkHAsSG2qR97BAE+o4oH6BxDQ0OKx3cKKm7cuFH6emJiYtf3kkqrTACf1LVcyRgzrp3qnaikio2QrbXz7vEzVcYb1k4V0HP1zAn+OH9eun27sedIJqV8elNnz5zxLRGUSEi5zJbOf+AD2kgmWegCNBGxDYBWUEzIrD68r0hvr8LdkQa2hkuX2s9lkvsDm3RaNe1f6CSCnNupAfcGUJbWcEDTENt4RyIIaGGBgJTPN3sWQGdYXl7WtWvXtLy8XNosMBaLld5bXFzUq6++umtTwampKa2srGhxcVHz8/MaHx/X1atXFY/HNTw8rJmZGV27dm3X+0C9jDFR9zHsJnPKEzSzxphR972oMeawlm5rNZx2Uk7l0IKb8Nk7p3FJS3LayI1Za5f3HoPj09Xl7LfTSMVE0NDAgFLppG8VQflcQufOn9eGH73mAEgitgHQvvI5J8DI5vMKRyIKhUPKZxuTCMrm0uo+dUrhUFjZ1P6ETSCgmvYvzKWzCrm95ILGua2aZQNEwBfENo1FazighQ0OSuvr0tmzzZ4J0P5GR0c1OjpacVPA0dFRLS0t7Xs9Go3u2miwfBNCaWezQuCo3CTMYT2zigmZ8s8MVNoDyFq7bIy5JumKpGUdUBHkHhuXNOZWBa0YY5YlFZdMXZQ0Kmle0ktV9htCh0gkpGx6W4ODg/rB2rovewQlElI2u63zFy5ow4/MEgBJxDYA2lcum9bZ06d1f2NDkUhEoUhI+dx2Q861nUno9MCAQuGQsj7EIdl0Rl2lPYKciqBcg6qZgJOG2KaxqAjCiWets/myH7JZZzWJX4aGpPv3/RsPANCarLUxa62p8XFgYsZaO+0eM+YlgVM8Xs6+QSvu46qkAWvtJEmg1mBM4/cPTCalTHJTQ0NDSuayyuV8GjOT0iOPPaZkNqtCgXJnAABOslwupQ8PO8XokUhE4XBYuVxjqmq2s0mdOXNG4UhYmQot3GqNrXKZrELBkCQpoC6FA0ESQQDaAhVBONFyOemLX5QiEelf/aujj3f7tvTYY0cfp+jsWRJBAIDjU9w3CCdXOi1l0glduDCshE83NZyKoKT6BgfVH4koldqUs30VAAA4iXK5tD78kY/or7/9baciqDukfIPaq21nk4pGo05FUIVE0NraLQWDYUnnPI2XzWQUCLoVQV1d6glGlKM1HIA2QEUQTqxUSpqZkf7Fv5DCYX/GXF2VLlzwZyyJRBAAAHDk884eQcYcwz5BiYSGHnnEt0RQMimlshn19PfrdHe3UqkNX8YFAADtKZfL6Id++IclSeFwWKFwWIWCD2XIe1grbWVSOnPmjCKRcMXKndd/9xe19Cf/1vOYuUxGwZCzrj7QFVBPJKycHyXUANBgJIJwIm1sSNeuSV/4gvToo85rfrRaWV2VHn/86OMUDQ5Ka7Vs+Q0AADrSxoZ05ox07px0925jz5VMJjV07pyvFUGpfEY9PT063dOjZJJEEAAAJ1k2n9WHn35aktw9giLKN6A1XCJRUCKX1OnTpxUMh5WtENtkEnFlth94HjOXzSkYdBJB3eEu9US6aQ0HoC2QCMKJc++e9Cu/Il25Ip0+7bz2wQ9Kt24dfewHD5zkjV9CIfnSmx8AALS3eNxJBPkVsxwmmUxq6Px5JTIZWR9WyhQrgnp7e6kIAgAAyuRzetRdlZvNZhUMh1XI+58Iev/9LXUHwwoEAop0h5XL7G8Nl05vKpP0vnF0Lr1TEdQdDqinp7th+xsBgJ9IBOFEuXlT+s//WZqelrq7d14fG5OWl/05hzH7X/vEJz6hN954o67xGr0pNAAAaH3xuBSNHlMiKJ3W6bNnZSTlfbgpk05LyWzWqQhyE0HENwAAnFzZQk6RSESvv/66nnnmGQXDYeUb0Bru/fcf6lSkR5IU7o4om91fuZNObytdwyKVfDZbqggKBgLq6emhNRyAtkAiCCfGd78r/d7vSb/4i5J7zS75wAek998/+jkqJYEKhYKWl5f1W7/1W0c/AQAAOJEePnQSQcexf2Aik1FPb696w2FlMgnfxixWBBUKG0r4MywAAGhDuUJO4XBYH//4x2WMcSqCCv5X1cTjO4mgSE9Y+Qot3FKZpFKpTc9j5rJZhcI7iaDenp6GVDMBgN9IBOFE+OY3pddfl37hFyonaxrpzp07stbqK1/5igqN3t0ZAAB0pGJFkDGNrxZOZpz9fHrDYWWzSX/GLFYE9fTIFh5q0/v9FgAA0GEyeaciqCgYiaiQ97+qpjwRFI5ElM/vTwQlcmklM97jnVw2p1AoJEkKBQLq7e9TLpfV9rY/cwaARiERhI73p38qvf229PnPH36ctY25sfL222/rYx/7mKLRqL7+9a/X/PnjTlwBAAB/+bEOpLhHUKMZs5O08asiqFDIK5vPKxKJ6HR/v2z2AYkgAABOsGJruKJGtYaLr8d12k0EhQ5IBCVzaSVz+/cOOkg+ly3tERQMBNTT26tCIafZWX/mDACNQiIIHe0P/9DZoPiFF6of+/jj0rvv1n+uQqFy0uadd97Rk08+qRdffFFf/vKXax6XHvoAALS33/xN6cGDo42RTu/e37CRDksE1dPSLZNJqicUkjFGpwcGlE/cJxEEAECb+spXjj5Gdk9FUKinR4UGJII2HtzXqb4+5xyRiAq5/S3ckrm0ErmU5zFz2ZxCYaciKBgMqruvT/l8ruGtewHgqEgEoWN96UvOytlPf9rb8WNj0vJy/ee7e1c6d27/62+//baeeOIJfe5zn9P8/LyyWXrHAgBwkrzzjrS11exZeJd09/OplAj69/++9vGyWScRJEmnBwaUIxEEAEDbmp8/+hj7KoJCIeXz+aMPvMfmvds6dSoqSQp1dytfYS+fVC6jRNZ7Iiifyyro7hEUCgTU09+vfCGre/f8mTMANAqJIHQca6VXXpF++IelT37S++cee+xoFUGrq9KFC/tfL1YEDQ8Pa2RkRK+99lpN4wYCUs7/hTEAAOCYvPeefO0bHww2NjY4rCLozTdrHy+TSag3HJYknR4aUiqxTiIIAIBj9td/7c84b7999DgkUykRZP1PBKU3N9Tb3++cIxLZlwjK5YoVQWl5zUPlczmFI84Cl6mf/3n95Cc+oUI+r/v36egCoLWRCELH+drXpNFRp8KnFkfdi2d11Wkvt1exIkiSXnzxRX3pS1+qadyhIWl9/WhzAwAAzRMI+FsR9NhjTnKpEfL5nPKFgkKhkHpCoX2JoL/7u9rHzGaT6ikmgh55RMntOIkgAACO2euv+zPORz4iffe7Rxsjm8/uTgQFg8r7saniHpl0WkG3KrlSRdDGRka5Ql7JbEqplLcsTi630xru+S98QR964gnlbV5ra/7sCwkAjUIiCB3nrbecRNBxu3NHevTR/a8XK4Ik6YUXXtAf/uEfKplMeh53aEj0mgUAoI319/tbEfTBD0q3bvk3Xrli0sYYU7EiKJeT5xWzRbsqgh59VNvbG23VKg8AgE7gRyxirfTRj0pvvCEtLdU/zr7WcMFgQyqCcpmsQpGyRFBhdyJofX1bfeFudZkubWykPY1p8zuJIMmZe66Q1/b2XaXT/v8MAOAXEkHoSPVW93zgA/WvsLVW6ura+5rVO++8U6oIOn/+vMbGxvRHf/RHnsc9e5ZEEAAA7cpaqa/P34qgD35QunnTv/HKZTI7+/n0RiLKpnfuGm1tOW1wHz6sf8zT585pc2uL1ikAABwzPxJB2aw0MODEBK+8Ut8YObevXDAYLL3mJIL8L6fJZjIKu4tRnIqg3T3t1ta21BuKqC8c0YMH3sqV84WsAqHdiaC8LWhp6Zx+4zd+3b/JA4DPSASho2QyUtn1uGZjY9Lysn/zuX//vrq7u3Xq1KnSay+++KK+/OUvex6DRBAAAO1rfd1J3PhZEXTmjLSx4d945bLZskRQb69yyZ2sz5070jPP1N6yNptN7lQEnT2rjUSiyicAAIDf/FiUkk5L3d3OWH/7t/WNkclkFOwK7notFAo1pDVcLpMp7ecTikSUL+xOBK2vb6kvHFFfuFvr694SQTafL7Wbk6RwOKysm2Da2iLGAdC6SAShoywt1b43ULnHH6+/1UqlKqTy/YGKnn/+eS0uLuqhx+W0g4PS2lp9cwIAAM1165aTPGmXVmjlSZvevr59iaAf+ZHaE0GZTGKnIujMGW3U0CIXAAD4w491GKmUFIlI8bj0Yz9W3xjpdFrhPYmgYns1v2WzWYW7nRZ0oVBo3zmKiaDeUMRzIqhQyO2qCBocHNRGxlnxc/p01KeZA4D/SASho7zxhvTjP17/5+ttKXeQ8v2BigYGBvQzP/Mz+r3f+z1PYwSDtffiBwAAreHWLenJJ/3ZPPiLX/yi3n777aMPdIhMxtkjSNqfCLp920lq1bpApbjvkCSdPn1aG6mUb/MFAADe+FGdXKwI+uf/3IkJ6hsjrVBgfyKoMXsEZRTudiuCQqF97ecePnQTQeGIHj70likrFHK7KoLOnTun9ZRTqt3Xe9qnmQOA/0gEoaMUClIgcPznPajPfaWKIKn29nD00QcAoD29/76zB+FRFArOYpUv/eqv6huvv+7PxCrI56Vsdqd6p/fUKeXSm6U45MED6cMfrqM1XGpTve6G0KdOndJmKqVCgeAGAIDj5Ed1ciol9WXj+vCH67/3kk6nFapQEdSIPYJyZRVBlaqONje21RsOKxIMans77WnMfD6ngLvARZKi0agy+awkqZAnvgHQukgEoWMUb5Ic1blzzorXWqytSUND+1+vVBEkSZ/5zGf0+uuv6+7du/VNEgAAtAU/FqlsbUmnTknr6+tafestfyZWQSolGbOzR1BPf7/y2S2l3fsihYIUjUoeu9uW5JIP1dPbK0kKBALqCYeVyfi4aRIAAKjKj4qgmzff1f/5Cx8/0hiZTKZyIqgBewTlc1mFu52kTaXWcNub2+qORNQd8p4IsjavYFkiyBijR087+0JnUxmfZg4A/iMRhI7xne9IP/qjRx9nbMzZa6gWq6vO/kJ7HVQR1NfXp09/+tOam5urc5YAAOCkiMedBMx6MqlVd2fmri5/2s2VSybdRFCxNdzp08pnt1Teya2rq/ZK5VxyQ71uIkiSTnd3K5msMZsEAACOxI9E0Hvv3dZ/W/075Y/Qvz6bzSq4JxHktG1rQGu4XFbhyE4iaO85Uhtb6umOqDsU0vaWt9Zw+fzuPYIk6dFTbiIo7S2ZBADNQCIIHeNb35Keffbo43zoQ9LNm7V9ZnVVunBh/+sHVQRJtbWH83vvIgAA0D7icen06YLi6bRW3T2CzpypvTKnmmRSknYqgnrPnFE+t+2+Xl88ks9LhfSGevr6Sq+d7u5Wyu2lDwAAjocfew9vbqaUsYW69iwsFKS7d92KoD3l0g2rCMpnFe7pllS5Iii5uaVId7e6uyNKbXnLlBUK+X2JoHOnnb2BcpmcD7MGgMYgEYSOUdy08Kjqucnx/vvS+fO7X7PWHlgRJEk/+7M/qzfffFM3PWSd2CMIAICTKx6XAoGHspJuvf++JKcl7YMH/p4nmZRsblM97n4+vWfOKJtJ7KoIqmvM/KZ6+/tLrzkVQSSCAADwwze/6bSrr8aPBabb205Q8OY3vlHzZ7e2pD/5EymZzCjUVSER1ICKoEI+W2rjVikRlNreVm+vmwja9LaJUqGQVbis0lmSHnX3CsikqAgC0LpIBKEjWNvcZEkuJ+1ZEKJ4PC5jjKLRaMXPhMNhPf/88/rKV75yDDMEAADHza/9C+NxSVpXOBjU6vq6JGlw0NtNn1okk5KyO23cegcGlM0ePRFUyG6rx22ZIkmne3pIBAEA4JObN6WNKpdVv+6XbG867dPe+qu/qvmz6bSUyUjb2xkFA/v3CMo1oiKokFOo++CKoNTWtnr7etTT3e25Iiibzyq8ZxXyuQ98QJKUy2R9mDUANAaJIHSEt9+WnnrKv/EeecQpWT6KYjWQOeQOkNf2cMGgk2wCAADt4+5d6dFHjz7Ow4dSPr+upx99VHc3N5XL5RpWEVRIb6inmAiKRpXOJI+UCEokpEJuWz17KoJoDQcAgD/S6er3CzIZqTtwhAu6q1g18+b/+B81L3bJZKRsVkomswpXag3XgIqg/J6KoPyeRFAmua2evh5193Yr7XETpWwhr4hbPV304s//vD5y7kMkggC0NBJB6Ahf/7r0Uz/l33hjY9LSkvfjKwVAh+0PVPTJT35Sd+7c0fe+971Dj99rUpsAACAASURBVBsa8n/VLwAAaKxbt6QPfvDo4yQSUiKxrnOnT+tsf79u377dsIqgfGZzJxHU369ULqNk0mnnUrbNT01jZjPb6j1zpvTa6e5upZI+b3AEAMAJlU47CZbDpFLSd5YfU+ooqzskJTc29cjpM3rrvfdqrjLKZJxHIpFRKLi/IqgRewQV8jkF3aRNKBRS3u4+RzadUE9fr3r7epROeE0E5RR2k0tFP/HJT+p/eupHlU1n/Jk4ADQAiSB0hI0NZ9Nkvzz5pFNldBTvvPPOgfsDFQUCAX32s5+tWhU0NCTdv3+0+QAAgON186b0oQ85Xx+1JUt87YEGenv1eDSqW7duqa/PSc74KZmU8qnNUvVOT0+PUrmMUinpzh3p3Lnax0wkpFw2oR53E2VJOt3fr0xijT0QAQDwQSpVvSIolbJ6mIsrnT7aHjbJzS199Mmn9L3339dv/x8/omy1DFSZYiJoezu9ryLISdI0oCKokFfITQQ57efy+rM/23k/l0kq0tOj7p5u5TMJT2Nm8/sTQZIUDIWUq+H3AQDHjUQQUIEf/fzffvvtqhVB0k57OHvI3ZCzZ0kEAQDQTN/+du2t2O7fd67hflh77z0NRKN6fGBAq7du+RKr7FWs3ulxS396e3tLiaDbt6Xz5+sbM5NJqrdsz8TT0ajyyftVVy8DAIDqvFQEbW1lZWVrStxUkkluafjxx5TMZPSXt9/URrXNico/W2wNt5lUaM8my05ruMbsEVTeGi5XyOvP/7zs/WxS3X196u7tVc5jIihXyO1rDSc5C31pDQeglZEIQtu7c8ef/vv12tiQyha5lnipCJKkZ599VtZaLR3Si45EEAAAzbO9Lf2n/yR997u1f9avhM36++9rYGhIH/zAB7T6/e/7M+geiYSUTW2r59QpScVEUHZfRVAoVP2GU/mYmWxKPeWt4QYGlE/dl8dW/AAA4BBeEkEbG04l0MOHOcXj9Z8rn06ot69PP+z2vs1mvW9mnEzmtb2dVGoroXBod0VNIBBQvlBQxufOanlbKCWdQqGQcjav99/feT+XSaq7v1+R3l7lsklPY2YLeSqCALQlEkFoe3/5l9JP/7T/43ptx7a6Kj3++P7XvVYEGWNKVUEHGRhgjyAAAJpldlb6N//GueY3y/qdOxp49FE9Pjys1bfeasg5Uikpk95Wr7vCpbe3V8mMs0fQgwdObJTNZhWNSuvr3sZMJqVULq1eN7kkSaeHhpRNrpMIAgDAB15aw21uOnsDvfVWTn/zN/WfK5/ZVndPj37+l35JkpRMek98/Nn/N6//9v98WuntpMKR3YmUrq4uGSPduuVve7hcIa+gux9RKBRSvpDX7ds772ezSUV6exXp6VHeayLogNZwgWCQiiAALY1EENrenTv1tSqpZmxMOqRIp2R1VbpwYf/rXiuCJKc93KuvvqrCAZsjBoNSA/ZNBAAAVfzX/yr91E9Jjz3mVAHXKxRS3atcjZHW79/X4PnzevyZZ3TrBz+ofyKHKBSkZGJnP5+enh4lshklk1aFgmSM1ZNPPqlw+KHnRFAiIaVyWfX09JReO332rDKpuBLeOrAAAIBDeKkIKiaCtrZyVZNGh8llEuru7dXnP/95nesbVDrtbbBsVtp4cF+ZVFyp7WTlipqugN555wiTqyBfKJQSQcX2c9//26+X3s/l0uo+dUrd/f3KZVKexswVKieCQuEgFUEAWhqJIOAAw8OSl/ss777r3Bwqt7m5qVQqpbMeNwb4yEc+oqGhIf3FX/zFgcewoTIAAMdrbU1aWZF+8iePPlZ/v45UAbO+tqaBxx7TB3/sx7Ra3tPEZ8lkspQICoVC6jJG6XRWxkgbGxt67733VCjcrakiKL03EfToo0olH1IRBACADwqF6hVBW1tp9zlbOnZ1VXrvvdrOlcskFOntlSSFugKeK4K++EUpnUiqUMgonUhW3GMnGOjSzZs+J4JsvtQazhijgOnSd7/300omneqfbC7ltIbr61Mu5y0RlC3kK88/FFauhlZ5AHDcSAShrW1sSGWdRnxljLfkSzotdXfvfq1YDWRq2BigWns4AABwvP7qr6TPfKa+z+ZyUiCw831fn/dE0N7KIWultXhcAxcu6PEnn9RqA/vFJlO79/PpDYeVySRkrfSee7fI2jXPLWszGSmRyajXvWkkSafPnVMiuUlFEAAAPvCyd9/WlpPk2N7OlY59+23pnXdqO1c2k1R3X58kp4InlfKWCPre96RUIqm8zSqdTO1rDSdJoUBA8bi/iZTy1nCSM2dJ2tpygrJcLqNIX5+6+/uVzXpNBGUP2CMooFzW502OAMBHJILQ1v76r512La3G6/5A5T73uc9pfn5eGb93RwQAAHU5SvvZ997bXTHc3y9tbXn77K/9mvTmm7tfW9/e1sDZs3rsscd0e2ND+by/PfQlZxFMMp1WT9kqm55QSJmMk7F59913JUm53APPFUGSlMxmdlcEPfKIEultKoIAAPDBWuz/1c2V7x56zPZ22n3eaQ2XzTr7C9Uin02qu79fkhQMBDy3hvv+96VMIqlCwUkERbr3V9T0hcNKpTZrm1C1+dpCqSJIkgLGSQStrztBSCafVXdPjyL9/crl0p7GzBbyBySCwsrn/I/PAMAvJILQ1mIxp4VbowwOOpsjH6ZS0U8t+wMVPfnkk3r66ae1sLDg+TwAAKBx8nlnn7563LwpfehDO9/XUhEUDEpf+5rzdbE6eT2R0MDAgMLhsAb7+nT79m0FAtVbwdTCWimZzaqnrHqnWBFkjPTu6qokKbH9wHNSS/8/e28eHtlZ3/l+Tu27SlJJam1t9+Z967bagxsDjrGdGYIBLzBhhoQEiEkITy7MMM5kBhK4XJLBZDGXG57g4c5lAgQcL5jN2BgvBDAQd3u3u927utVaq0q1L2epc/84VaWqUlWpSi211fD7PI+eUp3znvOeVshzXr/f3/f7o4kjqKeHdLEgQpAgCIIgrAEHfnkXz//s/rZjsllL8cnl6oWgckJax2haYUkIstk6cgSZpjWPWiigl3TUQgGPd7kQNNzTQzK5tvG3jY6gihAUjVqLEK2k43a7cft8aHpnRbl6+ZpGHE4Hhi49ggRB2LiIECSc9aynQLJrFzzzTPfXHT9+vGshCNrHw0mPIEEQBEE4szS+e+32laNXKszMwPDw0vduHEEVgcc0LfEoEFgSggDGe3uZmpqitxcSic7u2QmKYglBvgYhSNOsXaJTR48CsDjb+SaNaZZQDQNPTY5uKBQiUyxINJwgCIIgnAaVdUrJKKAV2rtZKkJQNqtV1zKrcQTp+pIQ5LR3Fg2XSMDQEBRyBQxTRy0UcXs9y8YN9/aSjneZVbcChllqIQRZi7KioeHxePB4vaillatrKo5se23+bxmn24mxlhU6giAIa4wIQcJZS7EITdy4a8q2bVaT6G6ZnJzsOhoO4F3vehff+973yMnOiCAIgiBsOEZGYHa2s7HJJNS02iEQ6NwRBLBzJzz3nHWfYNAgUyzSU77hWDjM1MmT9Pev7FzuBtOEXLFYF+Pmc7lIJHIEAjB9+DC9Hg+xsjOoEzQtj8fhqOubGAqFSBXyZLNS5SIIgiAIq+Vv/9b61I0iutpeCMqVhaDUzHFyJw8CsPDsv7Dw/FNdzanqRTzlCFmHzY6qrix8TE7C+edDPmc5grRiAY9vuRA0MjJCbvbVrp5nJYySURcNV+kRFI+XHUGGjsfjwe12oxkri1rFYhGHrbld3OFyondaMSQIgvAaIEKQcNaydy9MTKzvHDZbeydOLgc1eyVVVusIGhoa4qqrruJ73/vesnMOR+dVyIIgCIIgrD1jY9CpBtIYK+f3d+4IAqsH4s9+ZlXROhwJQh4PNpu1dB8bGmLq8GH6+iAe7+If0AF5TVsmBM3N5RgaglOTk1y2ZQvxubmO76dpebwNlTsulwtFUaQvoiAIgiCcBpX0Et0oohWLTc9VKGStRchTP/k8j3zr/wLg0R9+mScf+3+7mlMzdNxll6/D3lk03AsvWGkr1Wi4YhGPr0k03ObN5GJH13Tfw2iIhnMo1loqHrf+Hqqh4Xa78Xg8qMbKolYup+JqIQQ5Xc516eEoCIKwVogQJJy1vPQSXHLJa/sMp05Zm0KNrNYRBK3j4SKRtd/sEQRBEAShNY3xs90IQY100yMIrGIUsN79irJIb01c2/i2bZw8cGDNHUGVaLhGIWhhoSwEzcxw6c6dxObnO76nqubx1lTiVgi43ahqF8qYIAiCIAh1HD5sFZ4YRhFdqy+uaKwtNQrWOzdfSKMWLXeQrqkUcp2/i03TEk4qca/dRMMV0s9RLObRSiU0tYjH3yQabvt2itnJjt3XnWCYpTpHkLO8uEvOW5sraqnGEdRBNFwmo+K0txCC3C7pESQIwoZGhCDhrKVUsjL0G3n66af5+te/jrZGZSThMCwuNj83NbVcCMrlciSTSYaGhlY1380338zjjz9OoiH0v78fotFV3VIQBEEQhC4plZYLQb29qy/KcLk6d/ZW5r36anj4YTCMeiFo7IILmDp2bM0dQaYJeVVdJgQtLlpC0PTiIpfu3k28i0lVNYevSZZvwO2mWBQhSBAEQRBWg2mCx2O5jTVDxdCXHEGGAY3m3YoQpOp5dN0SjTRVRVPzHc+5uAgG9UJQsdje3VsqgdsNH/zwTl489a9oZomSoeJuEq0ysmMH6ez8qotumqE3OIKc5TVWOm5t8tRGw6kdRMNlMkWctiYbUVg9gvQOXEWCIAivFSIECWclhrFUKdvIJz/5ST796U+zbds2/u7v/o50On1ac+3atdxWXWFqCkZH64+dOHGCzZs3V+NbuiUcDvOmN72JH/zgB3XHIxERggRBEAThTBGNWkUYtTQKQ53y1MMPc+rkya6v27ULfvKTJkLQxRczNT2N1wv5hv2bZ59d3TMCGIZGyTTrKme9bjdOW4pw2GA+nebiiQliyWTH92zpCPJ4RAgSBEEQhFWysGD1NE6nQTM0DG1JCFpcXL4+MMrvXE0rUKoIQZqKoXfen3huDnRzSQhy2B2ohfa9iXQdwHoYGwqaaaDrKq4mQtDw6CjzmQSnuYVTh2E2RMOVRZxMWQiqi4brwBGUy7VxBLlclHSJhhMEYeMiQpBwVtIqFi6ZTPLTn/6Up59+mgceeICf//znbNmyhY9//OPMdZFnX8uOHXDoUPNz2awV9VLLavsD1XLxxRdz5MiRumMiBAmCIAjCmWNmBkZGVn99rWj0qY9+lIfvu29V97jtNshnY/TWLDjGtmxhqoUr5ytf6XqaKpV+PkrNw/t8Pnr9SRYW5ujz+xnatIl4Fxl37RxBhYIIQYIgCILQLQ8/DMePw2WXWUKQqqtVcQesfQO9QdMwVOvdrRoFSmXXiqGraFq+ZQJKI7OzoJn6kiPI6UTNtReCDAOi0cMAFLU8WsnA0Is4Pcuj4UZGRpjPJCm2v2VXGKX6aLig347DZiOXSGIYoJa0pWi4Dtw8mYyKy9EqGk4cQYIgbGxECBLOSvbuhYmJ5ce/+93vcu211xIMBpmYmOCf//mf+cUvfkE8HufCCy/kj/7ojzh8+HBXc9lslu26U06nP1CF8fFxTjZUDvf2to6oEwRBEARhbZmZgeHhtbnX4elp0qus5viTP4HFU1P09fZWj42OjjKTSjVtSPz889amy2pQ1fwy0cbn9xPpSXHq1ClGw2H6+/uJZbMdu6Mq4lIjEg0nCIIgCKvju9+F6Wm44IKyI6hkYNTEmkWjVsR9LYZqOX80vYBRssYahoam5fkf/6OzeRcWQC/VCkEOtEKh7TW6DrFTLwCQ13NoJQPd0HDVOJ0rDA4OEstmyOXWTkzRGxxBLpeDTX19FHIJMplSVSjyeDwdRcMlk0VczXoUAC6Pi1IHriJBEITXChGChLMSVbVyZhu5//77ufXWW+uObd++nS9+8YscOHCASCTC1Vdfzbve9S727t27Ls+2Fo6gZkKQ3W7l6wqCIAiCsP7MzMCmTad/H1VVOZ5Ok4rFVn2PxdlZeiOR6ne3203Y62V+fn7ZWEWx+gV0i66DYSyPcfMFAly4I8X09DQjPT309PSQKRZxOPRlsTPNaOUICooQJAiCIAir4qWXIBaDc8+FVAqKJQOjwRFUs2wAloQgtVSsikaGoaHqRX7+886KX7NZKOgq7vJmjMPhQM2v7AhaPPZLAIqlAoZZsqLhmghBDoeDSCBANLp8fbNaGh1BTrud4cFB1Hya+fkcbocTRVHwer0UDXXFPZdkUsXdxhFkiCNIEIQNjAhBwllHqwVKJpPh8ccf56abbmp6fnBwkE9/+tMcO3aMPXv2cMstt3DdddfxyCOPYK6w6gmFoFkcfrNq2LVyBE016ZDYjTNJEARBEITV06roxGbrznFz7NgxSqZJqgtbb+P7fnF+nt6BgbpjY729y4pGEgkYH7c2hbolkwGXq7kQlEulOHXiBKO9vdhsNnq8XlyuxRWdyoYBup5r3iNIhCBBEARB6Jps1ioQ1XXo6ytHw5X0OkdQLGadq0WvOIJK2pIQpKuohkY4bPU/XolCoUQ8l6O/3ETR6XKhFds7glKpLI/97Bv0+QPWnGYJzVBxNYmGA9gU6mFubnrlh+mAinO6tn+zy+lkeHQUrZhhbi5N0GU9h6tctJJOt3cFJZMqHlcLIcjjpiTVu4IgbGBECBLOOo4eha1blx9/6KGH2LNnD7010SnNCAQCfOQjH+HIkSP8/u//Ph/72Md4//vf3/aaXbvgmWc6e771cgQJgiAIgvDas2mT1Sy5Uw7t3w9AKpFY9ZyL0Si9DfakoWCQhYWF+rkOWdG5qxGC0mlwOJbHuPlCIXKZDKcOHWJ0bAyAfr8fmy2+ohCUSIDLlsHbZLMn4POh5lb/NxEEQRCEX0cqjmXThP/7E3/MzEwctWRQMpYcQboOjTUYurZk460KQSWdoqFzySWWy2jpfPO5M5kFQuV+OmCJKlqhvSPox48/ymCgl7f9m6urx/K6WhVeGhnpDbO4cKLtPTtF13UctvoYt7/7xje46aabKBTTzM2l8LuX1igeh4t4PNf2nqmUitvZXAiyO50SDScIwoZGhCDhrOOpp+Dqq5cfbxYL1w6n08nv/M7v8NBDD/G9732vrSvovPPg4MH6Y6q6fHEFa+MI6uvro1gskllNtosgCIIgCOvG2NjKVbOmueTqOfSv/0p/MEi6Q3Wm2XJkMR6nd3S07lgkFCI6O1t37OBBuPLK1TuC7PbljiBvMEguk2H62DFGt28HoM/vxzRXFoLicXCRwNck/iUQDKJmVtc3SRAEQRB+XZmehh07IJMx+czdX+Tll59a5ghqRp0QVLKUHt3QKRga27bBibL2Eo/DV77S/B7JpNUvsILT5URX2wtBhXyRHl8Qf2BpLZDXi3VxbbWMjIyQnX217tiJVepCuq5jV+q3PS/ZtYuB0VHUYo5oNE2wpljF63QRi60kBBXxOJv3CHI4ndW/rSAIwkZEhCChjm9+85uce+65fO1rX9uwltZ02opqqyWfz/PII4/w9re/vev7jY2NYbPZ2jpwmvXnmZ6Ghj0ZisUi0WiUkZGRrp+jFkVRmrqCOm3MLAiCIAjCGlIsWjkrptmREFQoQGVf4fALL7Dr8stJdVjcUSwuj6SLJxL0NQpBAwNEG9YJ6bQlVK3WEWSzLY9x8/X0kMtmOXXyJCPnnw9YjiDDiBGPt79nLAZ2M423mRAUCqHlOo/LEwRBEATBcgRdeimcOGH10bHZ3GUhaMmJUmyizehaAZfdcrLoZbHCMA3ymsqhe/+4Ou7kSWsd04z0/GFGyrFwYAlBWrPJaudVNWx2Oz5/vRDUyhE0vHkz2YUjdcfuuaftFC3RNA27bfm2pz8UoqAXiMXS9HjrhaDFxfZCUDZdwOtuLmI5nE5K5sbcRxMEQQARgoQGDh48yOWXX84XvvAFdu/ezeOPP/5aP1JHPPLII+zatYuBhvz8TlAUhd27d/P00093dd3UlLXZUsvJkycZHR3Fbm9eIdINY2Njy4Qg6REkCIIgCGeOr37841y6aRPnjo4S2byZr37mM0Qi0JDItoxkEnp6rN8PHT3KrquvJtVqV6WBbBb8/vpji7kcvTUbLwCRTZuITk3hdIJWLgJWFKtYZvVCUB5fYzRcTw+5XI5T8/OMXnwxYDmCtGK0I0cQegpf4z8ICITDaHmJhhMEQRCEbpidzfKp/3QOJ46/DMDUccsdbJSsxcDBg1aiSSOaVsBXjkGrOoJKBvFCks8+8kXyeasp8smTzYUkgOzMK9WYWACX24VWVJsPrsxb1HDY7XgDgeqxQhshqG9oiHyDYzgWaztFS5pFwwGEw2HSao54NEGoRgjyuVzE49mW9yuVoKTmcLVwM9ntdnEECYKwoREhSKhjenqaG2+8kV/84hfccccdfOADH+Ctb30rr7zyymv9aADMzsLQ0PLj999/P7fddtuq7zsxMbGiEBQM1m+sTE0tdwStRX+gCtInSBAEQRBeGyqFFz964gne/aEP8cTTT/PHt9/Oc/v2deTOrROC5ue5cvdu0oVCRwUdLYWghh6IkdFRorOz9PVR58xpXK90SjoNmLnlPYJ6e8nn85xKJBgdHwegv6+P1MJ0y4rhCvE4YGTqNn8qBMJh1PKmkyAIgiAInRGPT/Lq7AmM2BMAHH/VsilXXD6//CW84Q1QMup71eh6Eb/Xa/1uWmO1kkHBsFSf+XIc2+zskqu5kcz8YUa3bKl+d7lc6Fp7IUhXVex2O96axU1eay0EuX0+dK1+gRFdZZKspmnYleVC0MDAAMlihsXZKD2hpTWKz+kikWjtCLrrLiipWVyN1u0yDocDQ6p3BUHYwIgQJNQxMzPDyMgIiqLw7//9v2f//v28+c1v5tprr+WDH/wgsw1Z9Gean/4Urrmm/lixWOT73/8+N99886rv24kjaOdOePbZpe+JxNImT4W16A9UoZkQ5HRavYkEQRAEQVg/Fhehrw9OxmJctWcPW7Zs4YKJCaZWyoQrUxGCisUi08kkl112WVeOoC/f/SF++tOfLj1PMyHonHOIzs/T328JLpV9B4ejdZPndmQygJ7G27D74+vpYSGZpKjr1WfoGxggPj294j1zOVALaXzB4LJzgd5e1EK6+wcVBEEQhF9jEvHjAMRnfwLA7stngCUhKJeDV17Zy4f+eMm1Yhig6kWCZTGmGg1X415JHv8lYLleWgWcJBenGN2xo/rd5XGirxANpxV17HYH3pq1QLtoOE8ggK7Xr5lW6wgqFJo7ggYGBkgU00Sno4R6lvoO+NwuksnWQtCrr0JJy7d8drvdjiHRcIIgbGBECBLqmJ6erutv43a7+ehHP8qrr75KMBjk4osv5lOf+hTZbGu77HoyP7/cEfTYY49x0UUXMTw8vOr77t69m3379rXti3TBBXDgQP2xxqrg9XYERSKrXwQJgiAIgtAZ09MwPAwn43HGyy6Ysc2bmVqpKU6ZihB09OhRNvf20tfXRyqfX/lCLCFoet8P+fbXvgZY1aw5VSXYIKZENm8murhIX5+1Npifh8HBLv6RDeRyYBRSeMvVwhV8fj+HFxYY6elBKS98+oeHic3OduSOKmSzdZs/FQKRCGoxXY21EwRBEARhZTLT+wGI5w5xztAQdqUSDbck6rzy8kvV359/3nrH540iPQHrfVwRgirOIIDE5L7q763e77limnDNYsPldnfgCNIsR1B5LeC2OzEx8bSwHbn9fnStXlxarSMok9Gb9gjy+XzYbTbcthOEwuHqcb/bRSrZeq9rehrymVxLIcjhcEiPIEEQNjQiBAl1NApBFXp7e/nrv/5r9u7dy4EDBzjvvPP48pe/jLGaktM15nRj4cCqCAmHwxw+fLjlGLvdqo5px3o7gvr7RQgSBEEQhPVmZgY2bTKZSiQYK2fhj42NMZXorKdNRQg6fOAA24eGCIVCpItF7PaV3TrZrFUp+/gjjwCQSCTo8XqxNWxkRIaGiGYyVUfQoUPNewJ0imlCIZ3C6/PVHff5fCTzeUZrNkr6RkaILyx0FHWXayUE9fejahly7XsyC4IgCIJQQ2bWEoIOz8+yY8sWFubngSVxB2BxZqb6+5e/bLl+C3qBvvK7vOJaqVyjKAoLc1Y0nGm27k2s6mpd3KvL40JfoaJD13RLCApZzhuv0xKA+vr6mo53+/3oRr24tNo65HTa6k/UjMFgAKfrGMFaIcjnIZNoHVvr80FiIUkgFGp6XnoECYKw0REhSKhiGAbz8/Ns2rSp5ZgtW7bwjW98gwcffJCvfvWrXH755fzoRz86I8+XTFoNkGvRdZ3vfOc73HLLLad9/07i4WppViVzJhxBq62GEQRBEAShM2ZmwOWK4XU68ZdjVEZGRphJJjEMA5utfXFIKmUJQYeefpod27fjLmfJu1zFFTczslkoGDrPTk4Sj8dZXFykr0GcAYhEIkQzmaoj6PBh2LZt1f9kAHKpVF2GP1B1CNUKQf2bNxPr0B2Vz+fxNWbpAsFIhKKWX/XmjiAIgiD8OpKMHgVAL5XYvn07C+VKUa2kc//91pjFcpStaVrx9pkM5PQCveX3cUWsqAhBW4eHieUWq3MoLcSMoqHVOXlcbheG3kGPIIcdb3luZ7mwpdHpXMHt86E13FNRWotT7chkdJwthKCBYJCjJ04QrBGkAn4fmXjrop+REUjFY4Qa4noriCNIEISNjghBQpX5+Xn6+vpwOp0rjt29ezdPPvkkf/mXf8l73vMennjiiXV/vqeegte/vv7Yj3/8Y7Zs2cLmzZtP+/4TExMrCkGBQLmZcgvWwxFk1qx4RAgSBEEQhPUnn4dY7CTjNf+h73a76fX5mJ+fZ2DAimJrha5bff0OPf88O664AoCg243NlrJ68ZRpJiblcpDXVM4bHOTHP/4xi4uL9DYRgvr6+ljMJ0LoYQAAIABJREFU5bDbDTQNisXWzZ07QVEgn8ngq6n0BcsRBDA6MLA09+go8VRqxXuapiUEeZsIQYFgkLxeFEeQIAiCIHRBLDXLeCQCwHkXXMDC4iI2RcEwDR56yBqzWO7tPDkJAwPWuiarFauOoMYeQVvGx8loVoTtvh//PXf9eXOLsWpodRGyTrcbw1jZEeRwOKpOIq3GhdQMt8eD2nBPr9f6N3RLIlHA1UYIOnLqFMHy3xIgEAygZlo7gkZGoKQuEurvb3re4XBIjyBBEDY0v3JCkKIop5cR1vk8YUVR7lAU5dGan88qihJe+eqNyczMTFd9dhRF4W1vexv/9E//xLvf/W6OHj26jk8Hx49Do8Zy3333ceutt67J/TtxBF1xBTz3nLXB07ie0DSNmZmZaoTM6dLT04PNZiNRE0MTDlsNrAVBEARBWF9OHjzIeI34ATDW28vU1BRXXgn/+q8r3+PQ0aPsmJgAIOT1Aqk6B8zf/z11whBUouFU3rpnD48/+KAlBDW4dMDabAh5PNV1wmoqZWsxTUsI8rYQgkZqHM99/f3EO7Ty5PJ5fOHly+NAIEBOK4gjSBAEQRC6IK1mOX/LFpw2G5t37GAhmSTgdqOXDF5+2RqzuLAAwEsvwaWXQqEAWbVAf79V4KI3OIK2bN1KVrWUlp//7H+xP9p8b6fYIAQ53G5KxgqOIM3qEeQpX6cZetvxHo8HrbQ0xjStgtzVrBcSiRz+siu7kYG+PhZSqTohyOf3Y+qplqJTKAQ2ZZFQw/qwgt1uFyFIEIQNza+MEFQWZu4F7l1vMaYsNh0D+k3TvKHyAxwBjimKcvt6zr9etOoPtBLXXXcdn/jEJ3j7299Oup1dZg2oLRoxDINvfetbayYEXXnllTz//PPoeuuFyYUXwv79MDcHjQl6p06dYtOmTR05qjqlMR7Obj/9jR5BEARBEFZm6uWXGRsfrzs2NjDA1MGDjI9DQ3prUw7Pz7PjggsACHk8QLpO+DlwABrbDhWLkC0WuekP/oDHH3uMxYWFpkIQQCQQINrEKrzatUI+l1vWz6caDVfTgKi/v59YBzsyigJ5VV0WNwcVIUgcQYIgCILQDaqhMzo2xpDPR6i3l2gmQ8DjQTOM6n5BJb51etpkZATSaR3N0OnpsbL2ddOofgacTs7dsYOsXqBQgHjiVJu566PhnG43pRr3ztGj8Mor9dfomo7D6aiuJzSzvRDkdrtRa8QiTTOJvfxO0unuFzeJRJaA29X03MDQEAChWiEoGMTrTLVd4/l9KUKDg03PSTScIAgbnbNaCCqLP9crivJZYBGouIGad51bmzlvB+4F/sA0zT+tPWea5t3Am4EvlZ/prGK1QhDAhz70Ifbs2cN73vMeSu1C81dJoQCNhRxPPfUUmzZtYvv27WsyR09PD2NjY7xcKaNpgsNhNXmemoJG48/k5OSa9Qeq0KxPkAhBgiAIgrD+nDx4kPEdO+qOjY2PM9W4w9GCQqHAbCpVXRsEPR4Mo94RlE4vF4JKpRIFXef1N9zAdDzOK889R2+LLPqKEFQqge00V/WK0lwIcjqdOBWF0Ysvrh4LhULkVRWbTaNYbH/fnKpWXUW1BAIBcurKPZMEQRAEQVhCNTRGzz2XTT091T47QbcbzTA47zxrbTFfLtDVNA1FgcXFNH6XG2d5U6W2R1DI42HL+eeTVfMkEibxbOsIEtVQl0XD6WUh6LHHrKLZ73yn/hqj7Ajyer3YFAW1TeEtWEJQrSMomVTZO3UfsVj32XCpRAa/p7kj6Pc/9jHectFFXHDhhdVjvmAQQ02Ty8H09PJrvnTn64nlF1pGw9ntdox12A8TBEFYK85KIUhRlNsURTGxxJ8vlQ/fcAbm3Vqe7z7TNO9rNsY0zWeAO4E7FEXZtd7PtJacjhCkKApf+MIXWFxc5M///M/X+Mng6adh9+76Y2sZC1dh9+7d7N27d8VxU1MwOlp/7Pjx42vWH6hCMyFIEARBEIT1xTTh5OQk4xddVHd8bPt2pg4dAmB8HE6caH390aNH2dzXh8PhACxHkKEl6hxB4fByIUjT8ngcDhwOB2/asYNvffe79LbYcKgIQc0KVLrFNMtCUCi07JzP4WC0RhRTFIVevx+PJ96yd2GpVBaXtPoYmQputxvDLJFItI+UEQRBEARhCdXQOP+yyzjvoosIld/ZAY8H3TDYuRMUc4Gj5Wi4fN6q1kgk0gQ9Hhwuyx1jVBxBJZ3eoSFGx8ZAgbm5AgVDxetoLp40i4bL5zQSCXj4YSs5xdVgwDE0HXvZEVTp1xNssi6o4Ha76+LjkskCALFY95UjmVicgH95MQrAxVddxfdffrluD8cXCqGpGXI5uOee+vGmCQdP7OOl6WlCTXofgvQIEgRh43NWCkHAj4Be0zQV0zS3lZ058TMwb8Xl81crjKucv3cdn2XNOR0hCMDlcnH//ffz9a9/nXsa35qnycsvQ00hKqVSiQceeIDbblvbllCd9Any+62mizUOYuDMOYIEQRAEQVg/Ks7bqViMsS1b6s6NXXghU+X38rXXwpNPtr7Pof372VGOHQEIBYPo2WjVAVMoWDGzjUJQoZCt5tn/xutfz8uHDtFXc59aIj09RKenicehwby0KnK5HN4mmxvfePe7l61x+nw+nM7WQlAyaQldOVVtKgQpikLA5WZxUSxBgiAIgtApaknjLW99K1//4Q+rjqDr3vIW9JLBxAQ8+6338R/f+U5Cbj/5vIrDAfF4hqDbU3UE1fYIuvc73+Gaa64h5PZy6pS1rdbvbS50LIuG83jo79fZtw8OHwZVtfZLatF1HafTaQlB5eKYQBOncAUrGm4pbi6RsJxA8Xj364Xs4iKBYGDlgWV8PT1oRUsIauzNrKomBV2loGlVAa4R6REkCMJG56wUgkzTTJimmVh55NpR7jt0G5Aou35aUn62Z4CtZ5MraHp6muHh4dO6x8DAAA8++CAf/vCH2bdv3xo9mbUpUxt58vTTTxMMBrmwxsa7FkxMTKwoBF1+OTz7bH2/IjhzjqDGeQVBEARBWDtSKejpgZOLi4w39gjasoVTsRhgNQxu1xrx0NNPs6MmvjYYCqGmF6qOoCNH4MorlwtBqprFXy6nve73fg+A3sbGhGUiAwNET55kaAgalyDdRskqCuSLRXzh5a02/91dd2FryJ7r9/tRlBjlouNlxGLQ12c5gppFwwEEPG4WFzNNzwmCIAiCsBzV0KtizPDwMF/43Of42Cc/iYHBjh2QyBznxltvxWmzUyioeDywsJAm6F1yBNUKQdu2bcNms9Hj8fLqq8cBMFssIhodQU63G6Okkc9bwkkmAx6PVexSwSj3COrt7eXictVKsCGGthaPx9MQDVcRgrpfLxQySQKh5n0Wm+ELh1GLuaZC0OKiioH1d2klBEmPIEEQNjpnpRD0GnF7+XPl3LD6cR9ch2dZF2ZmZk7LEVTh8ssv5x/+4R+4+eabmZ2dPe37Gcby3Pv1iIUDuOKKK9i/fz+F2pVLAxddZG1uNCI9ggRBEATh7GdmBoaGSpxKJBhryFsbGxtjqka5URQrAq0ZR158ke2XX179HgqHySUWqj11Dh60iktyufrrVDWHr7xRc/HEBAMuF72NebRlIsPDRE+d4j/9J3A6l44HAnTde8c0Ia+qeBtLeQGa9Cjq8/splVo7guLxshDUwhEEEHC7yedFCBIEQRCETql15TgcDj78sY/h8XgwTIPE3AGimQyRgQFcdgf5fBGPB2LRFCGPG4fbjQ0FvWRgmiaGWcJZXkCEvF4mJ639G7W0vI+PYRgYpRKumuw3h9tNqaSTy8HICJw6ZRXTJJM11+kGDqeDUCjEUy+8wNuvv54PfOADLf99bre7bv6KELQaB7GWTxFoIzo10js0RDy92FQIikaX5m/rCJIeQYIgbGBECOqcSg+iox2OP1L+fNc6PMu6cLrRcLXceuutvP/97+eWW26huFIX4RV44QW47LKl76Zpcv/996+LEOTz+TjvvPN4/vnnW45xOuF971t+XHoECYIgCMLZz+QkBAILBD2eZQLG6OgopxKJaqXszp3w3HPN77MwP8+mmry2UG8vmZpdhbk5aJb4ViwuRcPZbDY+/fa3c+U11zSdIzI2RnRujsY9jp4ey9nULe1Em0b6AwHy2YW6zZ5a4nHo7S1R0PW2QlCxKEKQIAiCIHSCrlsCSaX/YAWn00nBKPL6101YQlAkgsvuoFBQcbshn4oT9Plwut34HFZ8ma7r2BUbSjlyJOzzcmpqhoDLU9ejp0I+X8Bld1THAzhdLkqmQT5v9VCOx5cLQbpuOYIqPPjoo/yX//7fW/4brR5BS9Fw6bRVpJtIdL9e0AspfF0IQVdedRXPnDhOOl1a5tiu7VEUCDSPm7N6BBldP6cgCMKZQoSgzpkofx5pO2qJimAULsfKbWh0XScajTLUIoN+NXziE59gZGSEP/zDP2xpLV6JV1+F++6zolMqPPfcc9hsNi6vqbJdS3bv3s3eve2NX42tiQzDYGpqalmEzOkyPj7O1NRU3d/P5YLT1NYEQRAEQWjB5CTAFGNNXDA+nw+fy0WsbA3evRtaJcomMhl6ahoKBvv7STWUlzaLe611BAF88J//mXNaFJpEzjmHaJNstlCoOyGoVLLc13lN61gI6uvrY3H6VMvz8TjY7UlCHs+yWLkKQY9HhCBBEARB6JBisYjT5lh2vOLqWchmmU4miUQiOB2WEPTY//dRCok5gsEgDrcbt92OXbFRKBSw2+zVe/T2BIlOnyDk9tf16KmwuJjH7XDVHXM6neglg0LBEoIikWaOIK1OCFoJt9uNVtKreyCplOUIymfb5PG2QC2k8TfpfdiKwcFBBoNBjhx5hcaQmEqPooDDgd1ub3K1RMMJgrDxESGoA8pCTkXM6dQRVDtu69o+0dozNzdHJBJZVllyOthsNv73//7fPPvss9x1110dX2ea8MQT8Hd/Z+Xnf/rTlvhRoRILp6xTs5zdu3ev2CeokZmZGfr6+uoaJ64FPp8Pv9/PQs0mTyTSPJpOEARBEITTp1SC6SMHGa8RcWoZC4eZmpoCwOGwImxrKRatdUsilyNcIyaFIhFSNTsjrZYxtT2CViKyeTPRxuwSuheCMhkrTq4bIah/aIj4zEzbe+bzUSItqmbBcgQVCt1v7AiCIAjCryOFQgGX3bnseK0woRkG4XAYl91OIjHFXQ/cRXThAMFQCIfLhctux26zk8vlcChL14XDPaRiU/R4fKil5UJQMlnAba/fL3I4HGjlKDSfD265pXU0XKdU9qQq7qdMxhKCjFy843tUUIsZ/E16H7bjdeefz7GXHqdR66kIQaGya7sZEg0nCMJGR4Sgzug7zes3vBA0PT3N8PDwmt/X7/fz7W9/mzvvvJNHHnmk7VhVhXvugc9/HsJh+OhH4S1vqe8PtJ6xcBUmJia6FoImJyfXPBauQmM8XH+/CEGCIAiCsBoMA/TlaSfLOPnSS4y36Ps31t/P1JElg7jHA/n80vlk0toESeTzhGs2H0KDg6Rq1JlWZmktn8TfYWFJZGCAaJNmQKsVgtKFQsu4k0b6hoaIzc21HROLRelv1nOoTMDtppAXIUgQBEEQOsESgpaLKrVFspFAAEVRcDkczB77PgD5bAx/IIDT5cLlcGBXbLzwQg5njdrR09tLJj1N0OPBKJUoNQgai4t5PM0cQYZRLW55/eubCEFGd44gAJfNyd13WzEo6ZS1ztGy3W+CqMUsvi6FoOGxMXILJ2hcviQSWc7pjXDN7t0trxVHkCAIGx0Rgjqj9s2RaDmqntpxpyskrTszMzNr1h+okXPOOYd7772X3/3d3+XgwYPLzi8uwt13Wz/XXAMf+YiVud+MV155hVwux+42L9/T5dJLL+X48eOk051vTBw/fpxzWmwYnS6VeLgKkQgtGzMLgiAIgtAcw4A774SvfKX1GNO0fqYOHWJs+/amY8bGx5l65ZXq90sugf37l86nUmUhKJerF4L6+0nnctUxrSLr9VwCn8/X0b8pEokQzdRHq+Xz+a6FoHTaep50odCyAXIjfaOjxJvE0tUSja7gCPL70XLLHU2CIAjCrz6Koty28qg1mSesKModiqI8WvPz2bMhwr+RTKa5I6iWSNnZ67I7mD3xMACF/CLeQACHw4HT4cBhs/OZz2Sx1ziCguEwuVwUr8uJ02Zf1us5Gi3gcdXP7XQ60XQd04S5H/wVpmEQCpQahCADp7v9MzfitDv41res+fMpa19Gz3W6FbeEqubwN4n6bYcvECCXWWTm+OfqjieTObYPDHLPE0+0vNZut6OLECQIwgZGhKDOOF0hZ8MvMKanp9dNCAK45ppr+MxnPsPb3vY2EuWue0eOWO6fb38b/sN/gA9/2MqVbUfFDbResXBgLWYuvfRSnnnmmY6vOZOOIBGCBEEQBKE7DAM+9zl43/us6LZWvfYWFmBoCE6eOMH4RRc1HTO2dStTNYUtO3bAoUNL55NJCIVMEvk8PTW59MFgkFTZOnT4MJx3XvNn0HOL+Dt05YTDYTKFQjU+BWDP617H8eMvdC0Eud3WH8XdJvKklv5zziEWbx3TYpoQW1hoLwQFg+jZ7qNeBEEQhLOXsjBzL3DveosxZbHpGNBvmuYNlR+s3s/HFEW5fT3nX2tSqQJuxwpCUPm963bYOZWYBCBfSODx+3E4HLjKQtCOHTkcNT2CAuEwuWIMn8eDy+6k0NAkJxbL420QgsbHxzkcjZI68jx/8eB/40t33ME//7ePodUky5W6jIaznt3B615XFoKS1oJGW4UQVNCL+DoscKngC4WILh7npRc/WXc8vZgk4Gsfn1txBK22R7YgCMJ6s3YNYX61OSNCTnkRcjvA5s2bz8SUVVYrBO3fDz/6EbjdzSNObDYrMsXjgaGhD3DBBS/w5jf/Nu9617e48EIvH/4wy7JX23HffffxxS9+sevn7JZKn6A3velNHY0/fvw4O1vZmE6TRiEoHIZE92sgQRAEQfi15PhLr/D//MHf81u/+wbC7n/LO98Z5t574T3vWT52/3648EI4GYsxvrV5su/oBRfwL9/8ZvV7b2/9ezmZhL6+LG6HA1dNr59QKESqvKly8CD823/b/Hm1fBJ/bwu7UAM2m42wz0c8HmdwcJBcLscLL75ILDaDql7W0T3AioZzu1MEu+h12Dc8THwF93R0aopIi15LAIFQiKlZcQQJgiD8qlMWfCaAG4A7ak710XnqSrdz3g58CXinaZr31Z4zTfNuRVH2AvsURdlmmuafrsczrDUrCUEDvb1E+vsBcDkc1V4/BTWJNxDA6XTicjqxKyp9fXkCvhohqLeXnJrE69uGy+4kmy1Sa6aJx/P4G4Sg0dFR/uOtt/IvD/8lJvBP3/8+QUXhbef/bXWMYeg43d1tPfo9DrxeSwgqZq21hlZItrukKQW9iL9NRG3TuXt6yOSjGKX6LOFsPE4w0N6xrSgKDpsdTdPq1oCCIAgbBRGCOmM1jqDa8sb+Ti4wTfNu4G6AiYmJM1pCMD09zVVXXdXx+Hwe/tf/gpERy8nTyqBjGEuVt4UCXHDB3/Jf/st7+cpXdvHVr34Vu32i4zkPHTrEwsICe/bs6fia1bJ7924eeuihjsdPTk5y8803r8uzjI+P8+KLL1a/22yt+woIgiAIglDP3378b/nO0Ud56M6HOPZ//C6fee97cVz6P9F1cDSshA8fhj174GQ8zvj4eNP7jW3fzlSbSDRLCEoQ9tZXjYZCIdJlISiZtAo7mqEXUvg6dASBVfkbjUYZHBzkxRdfpGSaJNo4dZphOYLShLoQgvojEWKZDIpirUsa14KKYglB/UNDLe8RCIdRj0l1iyAIwq8qZUfOveWvR4H7sMSgR9d53q1YItB9jSJQBdM0n1EU5U7gDkVR7jFNs/NIkNeIdLqAu3HxUsPv/t7vcdPb3gaAuyxEhDweCnoabzBIX18fQ+edx/QvnicUqu8RFOjro1DK4/N5cdkdpFL1jqB4PI+vScTbeeedx94nfwjAvmPHcDscvLVUohJAVCoZOJzdRcN5nE503ZpfL6RQFAW10H1PwdUIQb6eHjKFRTSzXghSs4v4Ayvfy2lzUCwWRQgSBGFDItFw68eG7wtUSzeOoEcfhS99yaqkvfnm1iIQWG4fn8+qlh0ehh07HDz44Nf5i7/4C97ylrfwqU99Cq3WN9yG+++/n1tuuQWbbf3/ZzsxMcHTTz/d8fj17hFU6wgCEYIEQRAEoVNOTU7yh7f/Ca8cO8aPf/pT/ud3v8s73mFF0zaiaWC3l5hJpRhtkVc7NjbG1GJrF0syCaVSgnBDn59gMFh1BDVSea/rOujFFP4uYkwqQhDAc+VY28TsbFdrhXQaTDPdnSOor494LtfWqRybnSXSZn0ZCIdR891X+AqCIAhnDT8Cek3TVEzTrDhvzkQm6GfLn3+1wrjK+XvbjtogpNMFPG0cQVfs2sWbrr0WAK/XEiIGAiFLCAqFuOiii3j48cdx2Ow4ky/VCUH+PmsLyx/w4XI4lwlB6Xgan3d5fKyvp4dM3loI5FSVVKHA3Nyr1fOlkoHT1Z0Q5HY60TTLEWQUs/QHgxRXIwQZWsd9Fyv4wmGyWgK9IeJNzyfxt2rwWIPT5kBV1a6fVRAE4UwgQlBnnO5CJbYmT7GOzMzMMDw83HbM9DR89rNWBetHPmI1Ql4tv/3bv82zzz7LU089xZ49ezhw4MCK19x3333ceuutq5+0C84//3wWFhaIxVb+P51pmpw4ceKMCkGCIAiCIHTG7MIc5+3cAViFHulikVzqJU6ebF5YMTc3R9jrbdkrZ2xsjKlEomX+e7EIudxyR1AwGCRdKCy7LhCAbNb6PZeDkp7B38ou1IRIIEC07FB69sknCbhcLM7Odnw9WPNrWopgh/2BrOcOoOo6oVCxZe/C6MICkTZxx4G+Por5LpoZCYIgCGcVpmkmTNM8o9bPcgzdbUBiJZdP+dmeAbYqirLrTDzf6ZBJF/C0cdds27at+rvPZwlBgz0hCkYOb02RiYnJn37ujqpTGay4VoBA0I/H4SCdrm+oaBTSeJsUjPjCYdI1sW2XjI4SXzha/V4q6di7dAS5HQ50vYhpgl7MEOntRVWzXd0DVhkN19tLzsgA1BUtax0KQQ6bnWKrZpSCIAivMSIEdcbpLlw2fOZFO0eQYcA//qPlBPrP/xl2716bOUdHR3n44Yd53/vexzXXXMPnP/95SqVS07HHjx9ncnKSN77xjWsz+QrY7XZ27drF3r17Vxw7NzdHIBDoeoHRKaOjo8zMzGAYxrrcXxAEQRB+lVnIJTjnHMvdY7PZePtv/iYPfuEL3Hij1eewkZMnTzJeG4rfQCgUwqYopFJLAkZPT70rJhGPL3MEORwOPE4nxWKuToCqddRks6BrGXxdVNtEwmGi09MAPLtvH2+84goS8/MdXw+WIJbNpgl52zdBrkVRFCKBAA5HlMakvMpyLhqLETn33Jb3CPb3oxa7r/AVBEEQhDbcXv5c+T/m68d9cB2eZU3JprK43c0jx9LpNFdffXX1u7ss2mzq66VECU9N7GysYC08JmuiZAPl816/D7fDSTJZ7wgyCkm8TdYJvlCIjGoJJ06bjR2jo+jppYKUUsnA3ibOrhluh4Pjrz6CpoGmZon091NQc13dA6BoaHi6cDsD+AIBTKyFWq2zRy2k8HewPnPZxREkCMLGRYSg7um8RPMsQdO0apPhRvbtg7/5G3jzm+G9712epX+6KIrCH/3RH/Hzn/+cb37zm9xwww2cOHFi2bgHHniAd7zjHTjW+gHasHv37o7i4SYnJzm3zSbH6eJ2uwmHw8zNza3bHIIgCILwq0osn6wrdnnH+97Hgz/8IRddBLWG5GTSEnSmDh5kbGCg7T3HenuZmpqqft+xAw4dWjqfmJsj3CTeLejxsLiYIhJZOtYoBKlaFn8bIaqRyOAg0ZMn0XWdl06e5E1vfCOJDhzNtZgmpFOprqLhAAaDQUql+WWOoHTa+ltG02n62zjOA5EIhVVU+AqCIAhCG24ofx5tO2qJI+XPd63Ds6wp2URzVw4sCTkVXC4XDputuh7x1hSoqEZ9/5va672BAF6Xg4WFeiFIy0QJNnEs+3w+MpolBI2GQoTDYdTU0t5FydCxd9kv5+dHj3LPg3/BK6+kUcwcAwMD5MsOoW7QDb2lw7sVtVFytYKOVkh3JAQ5yj2CBEEQNiIiBHVGbTRcp71/at+QZyIDd9XMzs4yODiIvSYfNpmEu+6CWAzuuANaxOSvGTt27OAnP/kJ119/PRMTE3z1q1+ti045k7FwFXbv3t2RI2g9+wNVkHg4QRAEQegeTdNIqdm6Ypdrf+M3ODg/z/SpU/j9kLH2Lti/Hy68EE6+/DLjbeLMoCwEHT9e/b5jBxw8uHQ+OTdHuImYE/J4gBTnnbd0rFEI0rQcvm6i4UZGiJ46xcGDBxnp6WHz9u0sdikEAaSiUUINm0grMRgMomnLhaBYDPr6IJbNEqlVvRoI9PauqsJXEARBENowUf480nbUEhXBKFyOlduwJKNp/P7OijZcbjchl6sqADW6eex2O3/yJ39S/V4rBPncTuLxejGjmJoj3OSd7vP5KJSK9PsC/Jsbb6Snrw81s2QVLplG19Fwb37d6wB4/vkcTnuOoaEhcnqBFq0WW6KVuheCapNe6hxBxUxHhTrSI0gQhI2MCEEd0JAr2+nCYGvN751Worwm1MbCmabVPPlrX4Pbb4cbbzxzz+FwOPizP/szfvjDH3LnnXdy2223sbCwwKlTpzhw4ADXXXfdmXsYrD4CG8ERBCIECYIg/DqjKMptZ2iesKIodyiK8mjNz2c3+qZIO2ZnZ+l1B+uKXZxOJ295/ev5zj/8A299K3zve9bxV1+F88+Hw88/z5bLLmt737HRUU6++GKgI3IzAAAgAElEQVT1eyhkuWAqJObmCPf3L7su5PFw7rkpduxYOtYoBBX0Iv4mbqJWRMbGiM7N8ewzz7BzfJzwyAiJZHLlCxtIR6MEu5gXLCEoHpujJkIfgHgcentLxLNZ+vpa11AFgkHyehFJvxUEQRDWgvKapbJu6XQfpnbc1pajNgDpxQz+YIdCkMfTVgi66Td/k89//vPV71UhKBjE53ERW6h37OYzUXo3bVo2T8VBc8XYZr55zz309PdTzCxViJRKpa6FoEd+9jPGQhGOHs1ilPIMDQ+T1/OkumgraBgGJdPsOlWm1hFULNYIQWquYyFIHEGCIGxURAjqnEry+7a2o5ao/lfvSg0KX2tmZmYYLsd2HD8Oug5//MfQEG1/xrjiiit4+umn2bZtG5dffjl33HEHN910E64u7cSny5YtWygWi0yXc/db8Vo4gtxuuq6GEQRBEM4uysLMvcC96y3GlMWmY0C/aZo3VH6wqmmPKYpye/s7bEymp6fp9y3/073j/e/nwQceYHCQan+bfB68Xth34AC7rr227X0vueYanvvxj1ueT0SjhJvEywU9HsbH09TuxSwXgtSu+g5GzjmHaDTKsz/5CVdcdBG9g4Mkst3HraXj8aaRL+0YjESYbxLpG4+Dw5Eg6PHgbLP5EwgEyOtFcmIKEgRBENaGThNcWrGhhaBiNovf31k/P7fHQ8jrxVPe2GnslXNFQ/PnytrDGwrh87rJJep7+OWzcXqbxL1WhBN/+bNnYIBCbrF6vlTq3hEE4HW5mJzMYugFhkZHyWqFroSgYrGI0+5AUZSu5q0VgrLZJSGoqObwd7BOckqPIEEQNjAiBHVOpZ1wpwuLimC0oUUgqHcEHT0Kl1/+Gj8Q1iLlzjvv5J577mHv3r285z3vOePPoChKR66g18IRFIlYsSuCIAjCrxZl8ed6RVE+CywCFTfQ6W5stJvzduBe4A9M0/zT2nOmad4NvBn4UvmZziqmDh+hz7/cmfObb3kLTx09SjKZZHgYKjUfuq7zwvQ0O3fubHvfPTfeyFMvv9zyfCIep2doaNnxkM9HquEF7vVSFUKyWShoat0mxEpExsaIJhI898tfsvPGGwmHwyyuQllJxWKE2rh3mjE4MtJSCCqVovSvIGhVhKBV6FaCIAiC0IzanfpEy1H11I5bt/XWWqCp2aqwsxIuj4eQz4enIvDUVKFMTk7y3z/+8brxlbWHJxjE4/VQUjN157OFFOEma5vKdb5yZF3P0BD53NKftGQa2FfR69nvcrGwkKOoFRgcHiarFqpxvp1QLBZx2bqft3YNlsstCToFvYg/GFzxeqfNLo4gQRA2LCIEdc495c9dHY6vjLun7agNQK0QNDkJK8Tin1He8IY38Oqrr3LDDTesPHgd2L1794pC0GvhCOrvFyFIEAThVwlFUW5TFMXEEn++VD687i8/RVG2lue7zzTN+5qNKTub7wTuUBSl03XQhuDIs68yMLi80WEwGOSNl1zC9//xH/mt34Lvf986fmD/fkZ7euhZoRnwzp07OTg/TzpdXy1baW+YWFwk3KRqNhQMklpYqDtWW6iazUJOK3bnCBoYYCGT4dnDh9l5/fWEw2ES+TyKQldNldPJJMEuhaCB8XEWmjinUykoFGJEVug5FAgEyGviCBIEQRDWjNMVcla0fCiKcruiKHsVRdm70PBOX28MNde5EOT1EvL78TYRgjZv3rwsMs1ms+F3OPAGg7g9HoxCveqSUXP0NlknLAlBS46gbGFpfVQyzVUJQQG3m2w2S6pQIFJ2WadSnceiqKqK0752QlC+Q8e2Q3oECYKwgREhqEwHkSsVR9DWDuNZri9/Nt1U2UjUCkGaBmc4gW1Ds5IQZJomk5OTZ1wIikRY1phZEARBOKv5EdBrmqZimua2sjMnfgbmrbh8/mqFcZXz967js6w5x145zNi25ikvN/3O7/CDb34Tr9eKZvN6Ye+jj3LlBReseF+3280V4+P8609/Wj1WW6SRyGSaRsOFwmHSbV7guRzkNa07ISgSYTIex2W3s2l42HIEZbN4PGZXMbKpZJJgkybQ7RjcsoX52dmm52Kx6IpCkNfrRSvpJJN6V/MKgiAIQgvWva+haZp3m6Y5YZrmxECTd/16ouYTHcWTQdkRFArhqfT+8a4cKRco9xTyBQLo+XpDVVrNEW4y95IQZK1desJhslq+er5klup6NXaKz+Mim0nx0vQ0F110EUG3l0Si82y4YrGIYxWOIKfTibNcpbPMEdTB+sxpd1LI5VccJwiC8FogQhCgKMqjwKKiKIvlythlmKaZwKqGBXjXCverxLjcbZpmpw0KXzNqhSChnomJCfbu3YvZoqQ2FovhdDpXrBw+XUQIEgRB+NXGNM1Eea1xxigXttwGJFbqZ1h+tmewCmLOGlfQqRMnOfeS85qeu+Gtb+VHL72EaZq84Q2waxfse+wxrlyhP1CFPddcw1MPPFD9vmMHHDpkOXwSuRzhJg2Fgz09ddFw3/mbv2HyyJHq91IJsmqxq2i4UCiEXVHYOT4OWCKV027H7c51laWfTqcJDQ52fgEwuHUr8y0sytH5+RWFIEVR8DndxOOSDScIgiCsCatxBNUW3izPk91AZNMLRMrv+5XoHR1laPv27oQgrxev10vv4CDF1FzdubSao7fJ2sbtdqNQIwT19CwTghrdR50Q9PvILD5PwO1mYGCAoMfD4mIKw4C//uuVr89mi7hW4QgC8JWft14I6iy61+l0kU+L1VkQhI3Jr5IQtCoLsKIo17Pk3gkDf9pm+F9h5ceulJH/Z+Vx7e61YZienma4HF/STYTIrwMjIyN4PB6OHTvW9PyZ6A9UeY6FhQU0TQOgp2epsbQgCIIgrJLby597OxxfGffBdXiWdWE2HuWCK5o7grZu3YrP5eKlF17gda+DSy+FfQcOMHHddR3de89NN/HUz39e/b59Oxw4AA4HJPL5plWzob6+OiHo//zc5/jxD35Q/V4qlchrWldCkKIoRPx+rti2rXos7POhKInuhKBstntH0MgI8y0miZ48SX//yvtpfrebaLSL0H9BEARBWFs2dF+gWjLZOP1jYx2N/Z3bb+dzX/4y3lAIBXB1EP0SGRujt7eXvuFh8un5+rlbCEGKouBzOPCWBaeenh4y6uk7gvwBP4XMv3BFOX0l5PGQSKTI5eDb3wbDWH5NebsEgHR69UKQ3+3GrtjqhSCjM0eQy+kimxQhSBCEjclZKwSVmymHFUXZWhZzasWZLymKsqt8LrxClFvHsSvlatgry/M3jUZRFOVLwFbgzWe6sne1zMzMiCOoDe3i4c5EfyAAh8PB4OAg0+UcfttZ+/+5giAIwgai0oOoU/dyxbrS1hm9kVjIJTjnnNZrnBuuuYZH//EfAdB1neenpti5c2dH995zzTX84uhRSqUSAIEATE9DKFR2BDUTgiIR0skkAJqm8dLCAvFTp6rndb2A2+HA1uWLPuJ0srPGydTr82Gai10JQalCgVCXDufBwUHm02lcLpPavsi6DrHpaSKbNq14j6DbQzwuQpAgCIKwJpxurO6G7sSbKmaJdOjetdlsOJ1OPMEgHrsdpbYpYQse+9nPuPjii+kfGyObiaGXk1s1TUM1NAItnL6NQlCtI0gvrU4ICgb9xJPPcMnllwOWEJRMJslm4aqrYP/++vGxGNxbs0uXyZyGI8jtJuTxkc8vLW467RHkdLnJpcXpLAjCxuSs3E4ux7ctln+OAI8CtTEl1wP7yucWsWLfmopBNQ2QwYo8aeviKUe9bQHCiqLsUxTljrLodJuiKPuACeDKlSJWNgrFYpFkMsnAwADJpOU0EeppJwSdKUcQLI+HE/eWIAiCcJpMlD+PtB21REUwWqnIZsMQzSUZHR1tef6Gd7+bRx95BID9r7zCWDhMKBTq6N6Dg4NEAgH2v/JK9VgyCaGQSSKXaxobG4xESJWFoFcPHKBYKhGbmameLxaz+FfRrPGTt97Kje99b/V72OulVEpQnqotlfVEulAgGAx2NW9lQyQQyFYja2dnYWAAojMzRNr87SsEPG4WF9MrjhMEQRCEDjjdYtwNXcybLGY6ctvW4vH78XYYzVZ5r/dt2kTJnuKxx6zjsVgSv9PbslDF63TiK6+fQqEQOW2pSeGqewQFg6SKCUa2Ws7ukM9HejFONmu5sOfqk+soFKjrjZjNqrhWEUkH8F8/9jHOHxgln7FuqKoGmqF3FK/ncrspZKRHkCAIG5OzUggyTfNouZlyNz8tX+imaf5pecyVnbh4yjn+NwBvxlooXI9lJ35n+R4bvi9QhdnZWYaGhrDZbBw7Blubp6f8WrMRHEGwXAgSBEEQhNVSFnIqYk6n65bacRt+xZDL5VANtWmMSYXrbriBnx05QrFYZN+PfsTEhRd2Nceeyy7jqe98p2ZOcLly5R497mXjQ4ODpMo2neeeeAKA+PxS9EqxmMXf5LqVuPXuu+npW0q2Cft86Hpn0XC5HPj9kC4WuxaCAAaDQRyOBRYWrO8/+AH8u38H0YUFIps3r3h90OMmkRBHkCAIgrDmnBVFK52iaZBUs0S6jHH1er14nc6urunr6yOrZ6m0MZyfTxJwtxZBfC4X3rIQ5HQ6KZkmRjm7bdXRcOU1yeCWLQCEe0LkFufJZmHLFpivT65rIgQVca9SCHr/f/2vhP1BCjkr4i0Wy+FxuDpyVblcbvJZiYYTBGFjclYKQRuFsiB0t2mad5Y/zxoBqML09HQ1Fu7oURGCmjExMcEzzzxTXcjU8lo6ggRBEAThNDjdPPwNv2KYmZmh3xtu+x/tvb29XDg8zFNPPsnexx7jyje9qas59vzWb/Gzhx+uft+8GRQlQbhFj59QOEy6vEvx3JNPcun55xOLxaquHFXN4VuFI6iR3kAANTvfkRCUTkMwCKl8vmM3VC2DwSCl0nzVEZTNWjF50ViM/g7WSEGPm1xOhCBBEARhTaiNhut0rVMrGJ1utNy6MTurk9cKTaNn2+HxePB0ubbo6+sjns1S0W+SyTweR2sxyed2V4UgRVFw2uzV/sardgSV7zdY7onU0xuuCkHDwyxb4xSLzYSg7gSwWlwuF8Ws5eyJxXJ4nZ39Dd0eD4WsOIIEQdiYiBD0a8709DTDw8OAVVHRZXHJrwV9fX38/+zde3ycd3nn/c8tjeY8o9HJOlh2fMzBIcSxnaMTaGInFLKU0nUCD6VboDShlC19oE8C3QJlty0lQHe7IWUTStvdpy1NE5aybQohB5KUHEjikINjJ3Z8lkZnaUZzPuneP2Yky7YszYxGc4803/frpZc9o3vmd8mE+Jf53tf1W7VqFW+++eZZ31NHkIiILFOzP0UodgzK7Otq/mDl/r4+2t0Lz7y98aabeOR//k/2HjjA9uuvL2mNa3bv5plZ+4Nrr4WmphCBc4wO8fl8TE4HQfv3s+sXf5HxSH4smmlCOl3eaLgzBVpaiI0Nkijic4hIBJzODNmpKZxOZ8lrrfL7yWaHGRnJj4Xr7Mw/PxaNFnVGkNfhIJUo4TAjERGRczhjRH+xicnsm1tq9ubet94ap9npLvkcQb/fj7/EcXKtra2Mx091tUxOJucNVdxOJ+5ZI3FtDTbS6TQAOdMsryOo8H6rCmci+QPNpKNjxGL5TuYzndURFE1gt5W+7jSHw0Eymv8zCIViuJqK69i2O50k4wqCRKQ2KQiqcwMDAzMdQQBFdLrWpXONh1NHkIiILFOLDXJqftxK/6FDtHoXPlD5xg9+kB/+27/xan8/l23btuD1s23ZsoWhyUlGCnPRrrkGTHOejiC/n8lkEtM0+XlfHzfs2sVYLIbXm++kSafjZY2GO1NLezvh4aGFLwSiUWhoiOBzOosaeXKmVT4fkfAgk5OnxsIBjEajRY2v8Xq9ZOI1ewO2iIgsP9M3rmws8vqZPVEtn/X81lujtM6VgCxgy5YtPPz00yW9pqWlhXAiwdTUFACRSHLejqANV19Nz6xzAZsaG0kk8kFQ2R1Bhc6n6SDI5fGQTcXOGQSd2RGUiMRx2MvfU9kddlKFO2pCoRjuIjuCnC4nqXhy4QtFRCygIKjOzR4NpxDo3OYKgkKhELlcbt6zByppzZo19PX1VWUtERFZ8aoS5BiGcZthGC8ahvHidFhSLYdfPkh7V++C1119zTUcGh5mTUtLyaPRGhsbuWrTJp6ZPk0ZCE1MnLMjyO/3M5lI0NfXh72xkS1btjAeixEIQCgE6VS0IqPhAu3tTJw5PP8cIhEwjEn8ZXQDQf4DmpETx4FTY+GmpqaYiMdpbV04b/T6fGRiCoJERKRiHi38WuxNL9OBUc2GQAAnTozR7is9CDIMg46OjpJe09jYiM/pJJEIA4UgqOnc5+38z7/9W6688sqZx7YGG7HY4oIgT0sLBtBW6GZyuFzkMgnGx+MED+496/ozO4KS0TgOR/l7KofDQXp2EFRkqORwOUklFQSJSG1SEFTnZgdBcm5zBUHT3UDl3D1bjjM7gpxOihr5IiIiModyOoJmf1pf1IyRwhmKO0zT3FHqhxCLdezNI6zeuPBRRna7nXdu2cL2Cy4oa51t27fz2pNPzjwODQ4SOEeg5PP5iKRSvPzss2xdt462tjbGZgVBmUQYzzlCpFIEuroIjY0VdW0kAqaZ7wgqR8fq1QyfOMHgIExPgguFQvicTmxFHNLs9fvJxCbKWltERGQO9xd+LbbNd/q6++e9ymKjwT66W6rXkN3qdhOL5m8qiU7GSjpnyN7YuOggyO330+50zrzW4XaTyST48Q/vZccv7Jg5X3FaKgWztx2JSKyskbfTHC7HTGfP5GTxo3udHjd//9gDfPu/fK3stUVEloqCoDo3HQTlclDiqNm6sm3bNl577bWZObeQD4KqdT4QQGdnJ6FQiFQqBeTPcyryMx4REZFKqPlzgWbrP9nH+kuKC3d+5z//Zz5yxx1lrbN5xw4Ovf76zOPw0BDN5+gW9ng8JNJp9j78MFt37MDv9xNPp/F4MoRCkEtM4DnHWLlStHR3EwoVd/RTNAq53CS+MkfSrVq7lpGBAV59ddZYuNFR2r3eol7vbW4mnSj2mCoREal3hmEslIZMdwRtKOJagN2FXx8sv6qlFx8+SFcVb+LdeuGFDL7yg/za4SjOEvYJTY024vFFnhHk9bJq1rlDTq+XbCaJtyl/w0wo1H/a9clk/mbZmcexGE5n+aPhnE4HmWT+ztvJcKTo0b1Oj5NENs1zT9V0g5mI1Cl99F/npoOgYBBmjXSVM3i9XtavX8++fftmnjt27FjVzgcCaGhooKenZ2Y8XFubgiARESnbYmdx1fzfQIOhcbZsXV/Ute9673u58eaby1pn86WXcqj/1IcRoaEhAucYidbQ0IDX4eDfnnmGrTfcQENDAy1uNzCe7wiKhXCXMf//TIHubibC4dOeGx2d+9pIBHK5CP4yO5FWbdzI8NAQX/jCqZn9o6OjtBf5c3hbWsgkwgtfKCIidc8wjEeACcMwJgzDmLPt1zTNEHBX4eGtC7zfnsJv7zNN80jlKq28+NhRuteurdp6N956K2+9/E/5tcMRXK7iu2tsDaefEVRMh/CZtm7dyh987VRXjcPtJpdJkSvsGY6//I+njYJLpWB2VpOMxXGWUPOZHG4n6cICsfEJ3EXuk1ze/P5nYlxjb0Wk9igIqnMDAwN0d3dz5AisL+6zkrp15ni4ancEwenj4drbz/2hjoiIyAIW24JR8y0cI7EQ69Yt/Z2zmzZt4tCs83hCo6ME5hmD53e5ePbwYbbu2AFAq8dDLjdOOFwYDefzLbqmQGsroVnzY198ET71KYjHz742l4N4bLLs0XCr1q9neGKCrVtPPVdKR5CvrY10crKstUVEZFkqq8PYMIzdnOreCQB3znP5V8jvVb66wNt+vnDdfO9VEybH++jasPDI20q5/qabeHXoIACJSBSXu/gbRuyzO4KmcmV1BAUCAT74a78289jh8ZDJJmfGyU5FXuOtt05dn0qd3hGUjsdxusrvCHJ7XKRT+SAoHi7+Rh2nN//nNFlkZ7aISDUpCKpjyWSSSCRCW1sbx45BFZtblqUzg6BqdwSBgiAREVkS1Rs4XyWmaTKaCNHd3b3ka3V1dZHMZGZGsYXGxgh0dp7zep/TiWEYbNq0CYA2j4dEYpxoFLLJSdwVCIJaWlqYiMcxDNi7F/bvhy9/GZ59du7rJ0dH8RcZ3JxpVWcnw5HIac+NDQ/TVuxouNZWksnIwheKiMiyZBhGoPC1oRDmzA5n7jUMY1vhe4EFRrkV3WJR6AraXlj/gXPUdS+wAdhVuL6mTUaG6N68uWrrtbe3E8vkbypJRqO4SwiCmhobZ4KgqTJHw53J4fWSzabJJMK0+XxkkkEOHDj1/UTCxGbLzTxOJRI4PeWfu+jyOMkUxvInI7Gif363Px8YTSaiZa8tIrJUFATVseluoIaGBpJJqMDZxCtarXUENTdDWJNURESkPLM/TCn2ztzZH87U9LyLcDhMo9GIrwKhykIMw2BTRweHDh0CIBQKEZgngPI7HFza2zvzoUir18v40CCJBExlJvH4/YuuKRAIEIrHGR+HffvgP/wHOP98ePPNueqHyOgovjLXbW9vZyQSYWpqaua50ZMnaZ+nK2o2b3s7qVSsrLVFRKS2Fca3TRS+DgOPANtmXbIb2Fv43gT5sW9zhkGmab7EqZFvL7FAF09h1Nt6IGAYxl7DMO4ohE57DMPYC+wAthfet+aNJcJVPSPI4XCQncoxNASxyRjuEkIVu81GMpkB8qPhKhIEud35ICgZZsN55xGaGD5tVP6rP/s7/vlb/27mcTadLKmL6Ux2p5NcthAExWO4PEV2Them4EXTc7Rhi4hYTEFQHZs+H0iKc+mll3Lo0CHihbkqx44dszQIMoyqLi0iIivIGR96FNsRNHseSU3P0Q8Gg7S7q9fotHn1ag69/DIAoUiEwKpV57zW73Sy9ZJLZh63tbUx3tdHLAZTmSieWQcjl8vv9xNJJvnkJ6f49V/PP3eufUMqBZGxMXxlrutwOPA4HDMdUQCj/f20d3UV9XpvIEAik1j4QhERWXZM0zximqZR4tc5u3NM07yzcM32Yrp4TNMMmaZ5I7CL/Ai43eRvgLml8B41vZ+ZbTw5SVeRf7dWgsPhIJ3L8MQTMDwQw+11F/1ae+OpM4JyFQqCnC4X6akM6WSE9evWMRKJnLa3SYQHiEdGZh6nU0lc3kUEQS4X2Wx+NFw6Hi86VApH8qPrYtrbiEgNUhBUxxQElcbhcLBlyxZefvllotEo8XicVfN80LMUZgdBAKZZ1eVFRGRlmf4AZWOR1890DtX63bP9J0/S7lp8oFKszVu2cKjQNRyKxwm0tJzz2sCqVVx2/fUzj1vb2xnr7ycWg0wmijuw+ACrsbERn9NJLnd667DbDbFZzTfDw9DRAZPj4/hbyzqyAYBVPh/Ds85JGh0cpL3IPabX6yVRuONWRERkKRQCoftM07yr8OuyCYAApqamCCUjdM4zerbSbDYbU6ZJNDrFZCiO21fcGTlQ6AhK5P9ur1hHkMNBOpcllYywfsOGs8bS5lIx0rPCl2wmgdNdfHh1JrvLRS6bD7NSiXjRQZjfnx+NG00rCBKR2qMgqI5Nj4YDBQrF2rFjBy+88ALHjx9n7dq1GFVuyzkzCBIREVmERwu/FpsATAdGNR0CAfS/eZCAv3p3zW7esYND+/cDEEokCMwT5vy3736XX7v99pnHrZ2djA8OFoKgGJ55QqRSBFyu07p0AHbuhGeeOfX4X/8Vbr4ZIuEwvkUGQSMjp+7CHRsZoW3t2qJeqyBIRERkfvF4nKYGG01NTVVb0zAMmhptxGIpYtE4Tk8JQVBTE8lYPgipZBCUmcqSSkXZcMEFZwdB6RiZWfuJXCaJY5FBULbwfvlQqbiOoI997GP8r//Vp9FwIlKTFATVsemOoFgsf4eoLGz6nKDjx4+zbt26qq/f29urIEhERCrl/sKv2+a96pTp6+6f96oacOLAEdpXVa/refOll3Kovx9YOAjq6enB6Tw1Z75t9WrGhoeJxSCdSeCpQEcQQIvHc1YQtGkTFI4yAiASAZ+vEAS1t5e91lkdQePjtBe5T1IQJCIiMr9YLIbDZq/6uvYGG1NTKcxcorQgyN5EMpYPQqZMs3JBUC5LMpOkd906oskk2ULHDkAuFSc963E2m8JRQs1ncvn9ZDP5/UkuXfzP39DQwIc/3IMJJJPJstcXEVkKCoLq2HQQdOwYbNiw4OXCqSDIivOBIH8gcyKRIBbTocoiIjK/cx22PMt0R9CGIq6F/Fx9gAfLr6o6+o8NsGrN6qqtt3nzZg4ND2OaJqF4nOYSzttp7e1lfGwMw4BkNoXb661ITQGXi4mJidOem93I3N8P09PbJicn8S9i3G1HczPDweDM49FIpPgzgrxeEhkFQSIiIucSjcZx2RxVX7ep0UYmk8JuT+AsYX9it9tJxxPEYpU7IyjfEZQhkU3h8/lo93qJxUZnvp/NxEnPurEkm01hX8Qdz+7mZpKFUXPZTLKkUMkwDLz2szuzRUSspiCojk0HQUeOKAgq1pYtW+jv7+eVV16xpCPIMAx1BYmIyIIMw3gEmDAMY8IwjDn/li8csnxX4eGtC7zfnsJvl8Vc/eHBIbo3FDearBI6OjrITU3R19dHY0PDaR0/C2nr7GQsEiEQyAdBnkXcvTpbwO0mdEYQBODxQDQKP/oRvPvd+ecisdjiOoK6uhg+dmzm8Wg0SnuR7+d2u0nlMiSTubLXFxERWcnGxmK4mqrfEdTUYKP/ub8jljleUhDksDtIxeKMjFR2NFwql53ZK3X6/UxODs58P5tOkMplZh7nchnsruLGuc3F7fGQyuU7jLLZ0sfMeZvcCoJEpOYoCKpj00HQwAAUedNm3bPZbGzdupV/+qd/sqQjCPHv2rMAACAASURBVHROkIhIHSnr0BbDMHZzqnsnANw5z+VfAULAVxd4288XrpvvvWrG2Pg4ay9YU7X1DMNg86pVvPDCCwRK/NChtbWV8XicQAAS2QzuCs3rbWluJjQ0dNbz114LTz8NicSp0cCTySQ+v7/stVb19jJc2JscPnyY7NQULUWeddTQ0ICryc7oqGbpi4iIzGV8PIbbgiDI3tjEj576Cw6E3sLp8xX9uiZ7E6lEguHhygVBTqeTdDZDaiqF1+tlQ1cX4/2vMTWV/342kyA1deqmklwuQ1MJN+acyePxkCx0GGUyyZJ+fgBPk5NwOFz2+iIiS0FBUB0bGBigu7ubqSlo0D8JRduxYwfDw8OWdATB6UGQywVxfW4iIrIiGIYRKHxtKIQ5s8OZew3D2Fb4XmCBUW7jxa5Z6AraXlj/gXPUdS+wAdhVuL7mjccjnLe+/FFn5djc28sLTz1FoMQgp62tjbFolLY2SGQq2BHU0sLEwMBZz2/YAI8/DrPvZ4kkk/gXEwStW8dwYa3Pf/7z/H/XX4/NZiv69e4mByMjkYUvFBERqUPj4zHc9uqPhrM32ogmowAlnRHkcDoYHkjywgtmRc8ISs/qCNp84YXE+14gmi8v3xE0lQXANCGby9LkKP/PzO12k8xOdwSVft6QvbGJVEqjb0Wktujj/zoVj8dJJBK0tpZ1s3Fdu/zyywFqoiOovR3GxiwpQ0REKqgwvm2i8HUYeATYNuuS3cDewvcmyI99mzMMMk3zJU6NfHuJBbp4CqPe1gMBwzD2GoZxRyF02mMYxl5gB7C98L7LQigZpbOz/FFn5di8ZQsvPPNM2R1Bt90G8XS6ckFQe/ucHUGGAbkc3HTTqeciqfy8/XKt2riRkdFRnn32WZ59/HH+3z/5k5Je77Y7GBuLlr2+iIjIShaaiOJ2WNARZLMRTefPJ3aWsL9xOB0cP5Lgb/4mR4NhYMw+pLBMDoeD7FSWRDbfEbRp+3bGB/cRDsPBg/nxbampLNksfPvbkDVzNNnL/zObHQRlsqmSRuNBfqxeOp0ue30RkaWwpEGQYRhfmed7W5dybZnfdDeQYRhU4O/kunL55Zdjt9vp7u62ZP3ZQVBbm4IgEZFqWqq9jWmaR0zTNEr8Omd3jmmadxau2V5MF49pmiHTNG8EdpEfAbeb/Gi6WwrvUfPnAs0WTsWKPqOmUjZffjkvvv46zSUGQT6fj1QmQyaTIpZOV2403KpVhEZH5/ze178Os2+SnUwkFtcRtHYtQ6EQn/3MZ/ijd70L96WXlvR6j92pIEhExEL67Ka2hUcm8Lgqsz8ohcNmI5rJjyAp5fxDp8tJMpHi3e/O0Vih8TMOh4OMmSWWLnQEbd1KcKKPcBjuvhtS6SSpXJZUCgYHITeVK6k7+Uwej4dk4YygTC6Lo8Qxc7aGRtLqCBKRGrPUHUHb5vmeYRjGt7SpsMb0+UCmaXUly8/mzZv52c9+RoNF8/TO7Ag6x2c8IiKyNFb03qYQCN1nmuZdhV+XVQAEkMlkSGSTBALzTc+rvM1vfzvheJxAiYGKYRi0ejyMjY0Rr2AQFOjqYmJ84SmB2WyWVDa7qHU7Ojp4Y3CQRH8/H/6zPyv59V6Hg4kJBUEiIhZa0fub5W5ydKJiHcOlsNts5Mz8ITylBEEOl4MGknzuc5ULgmw2G1PmFA2Ggc1mY9OmTZwIjRAOQyoF0WiKnDlFJJJlbAyyUzmamprKXs/tdpMqdASlpzI4Shwz12RrIhlPlr2+iMhSqNgn2YZhjBuGMWYYxv2GYXx2oU2CaZo/N03zt4AbtaGovukgaGgIurqsrmZ5MQyDrVut+0dWQZCISHVob7M8jY+P47N7qn7DxubNm4H82TylavN6CQaDOGy2iszRBwj09BAKLXykUzQaxetwLGpsS1tbG02NjXx9zx4aOztLfr2CIBGR6tH+ZvmJToTw+UsbTVYJjlkdNaUEIU63E783RTqdpqlC+5rpfcr0WYwdHR1MJKKEQiYXXwyZwvlAo6MJxscXHwS5XC5SuQxTU1Okc9mSgjCAJpud+KQOdBaR2lJ+n+TZbgVuB24EbgFMAMMwHgZ+DDxmmubLZ77INM2vFdqQz/qeLJ3pIOjIEVi/3upqpBTTQZBpmvj9BuGw1RWJiKxY2tssQ6OjozQ7qn/XbFtbGy0OB4G2tpJf2+p2c/LkSdyLmGV/ppbOTiaiC4crk5OT+EscZ3emxsZGDn3sY5z3x39c1ut9LifhiclF1SAiIkXT/maZiYfC+JrLP8uvXI6mU/uSRCJR/OtcTlpbRhgeHmbVIs4gnEtboTPK4XDQ1NjI0FAcp9ODw52BEAwOJohGfWTNqUUFQQ0NDdgbbYTDSdK5MjqC7HYSEQVBIlJbKnarpGmaj5qmeYtpmq1AC/ABIAxsBL4G7DUMI2cYxsOGYfyeYRg3zHp5dWd3yMwZQQqClp/m5mYAwuGwzncSEVlC2tssT/kgqPp3zQJs7uggUMbZRK0+HycOH8ZTwSAoEAgQii/8AUQkEsFX4ocbcznvvvugzEDJ5/MSHVOLs4hINWh/s/zEIpP4W8o/y69cjsK+5O677+ayyy4r+nV2p5PenhSD/f10LeIMwrm0zgqWml0uRkbyd8Y22jMA9PUlSaXyZwQtJggCcNrsfOxjMTJTZXQENdlJRIsPz0REqmFJZmaYphk2TfNB4EXTNDdxanPxl+Q3F3cBjxQ2FznyhxFLFU13BMViUOEbNGSJGYZx2ng4ERFZetrbLB8jff34Xc2WrL3loovoWLu25Ne1tbVx8q238FQgkJlWUhBU4ocbleZv9hGbWPg8IxERqSztb5aHZCyCr8WCjiBnfl/ykY98pKRQxe5ykU6lGDh4kO5VqypaU+uszuuA2008nh+Dm8rmR8MFgwmamiBnLj4IctkcuFxxkulsWR1ByZiCIBGpLWeNhjMMw2+aZkVnM5imGQYeLHxhGEYzsIP8gYQh0zS/Xcn1ZGHTQdDhw1ZXIuVYs2YNfX19XHLJJVaXIiJS87S3qS/9h47THCi9K6cS/vv3vlfyBwUArR0dnDx2rLKj4VpamCgiCJqcnMRvdRDU4md8cMLSGkRElhvtb+pHOhnBG6h+M9b0nsZVYsev3eUiHYsx8MYbdK1eXdGaWmcFS80uF+FwmPXrIZnJYG+0EQwm8HoXf0YQgMeR7wj61++VPhrO7nCQjCsIEpHaMtcZQROGYbRUaEPx1bmeLGwuHit8iQUUBC1v6ggSESmJ9jZ1pP+tPto7uyxZ21dmm3VbVxfPvvZaRUfDud1uMrkcqVRq3g8vIpOT1ncEBQKkjyoIEhEpkfY3dSKdiuJpaan6ug6nE3tDI42NjSW9rsnp5DtPPUXrz37GZ3/ndypaU0t398zvAy4XI8PjtLXlg6AWt5vh4SSBQGWCoIDXTiAQh8bSR8PZ7Q6SseSi1hcRqbS5RsMZwIZKvLlpmtos1KjpIMg0ra5EyqEgSESkJNrb1JGhvgFWra3s3adLrbWnh5ODgxXtCDIMgxaPh3A4PO91kbEx/F5rzlSa5g0ESCcqelO7iEg90P6mTqQzcTyt1Z/K53Q7cTbMdf/4/OxuNwDjqRRdGzdWtKbWWUFQs9+PmRiitTU/Gi7gdjE+nsDjqUwQ5LbbicViJDNldAQ5naQSCoJEpLac64yg7VWtQqoqGo2SyWRwOpup4Ch6qSIFQSIiJdPepk6MjoywelPp5/RYqW3NGoLj43gKH5xUSsDl4p577uE73/kODzzwANnC/PzZJoeH8VX4IOdSedvaSCcVBImIlEH7mzqQyiTxWPB3tcvtwtVYRhBUGCVnGAbdZZydeC53f+Mb3P6JT8w8DgQCeG2D+Y6gbJaAy0U4NMrhn32+ImcEue12opEI6VyujCDIoSBIRGrOuf6NfifwnWoWItUzMDBAT08PJ04YrFtndTVSDgVBIiIl096mToyHJlh3Ya/VZZSktaODKdOseBD0+7fcwt6nnuJkOs2P9++ntbWVXbt2nXZNZHwcnwXnDszmbW0llYxYWoOIyDKl/U0dSGRTeCzo3vU3O/G7S+9WjhbOKPzCF77ApZdeWrF6PvWZz5z2uLm1FbdvhNee+ivCiQQtXi9vjb3G8cH/UZGOIJvNxr9773sBaGg41330c3M4ncQnQ4taX0Sk0s71b7KNhmH8RaUXMwyj2TCMFyr9vlKa6bFwR47Ahoo0kku1zQ6C3G4o4ixoEZF6p71NnZhIRunu6bC6jJK0tbUB4PZ4Kvq+H/nmN7n7Jz/hr55+mg9ddx1PP/LIWddMjo/jt+Dcgdm8bW0k0zFLaxARWaa0v6kD0XSCFivOCHK7yxpbmyl0IH/5y1+mp6en0mXNCLS3k4qO8JnPfhrTNAn4fKTiQ2RzabJTOWy20ruZZnvo1VfLfq3D7SSVSi1qfRGRSjtXEGQAnzAM408qvN4GYFuF31NKNB0EnTwJvcvrhlkpWLNmDX19fZimSXs7jI5aXZGISM3T3qZOhFNR2tvbrS6jJK2Fuf8en2/J1rj2fe/j6R//+KznI6EQvkIQZRVvczOJjD4sEREpg/Y3dSCajhOwoHvX4XLhdjpLft1HP/pRhoeHl6Ci0zWvWkVofJxgLH8zidfnYyozQGYqU5GOoH+45x6uLrOjye5ykk5qbyMiteVcQdBu0zQbgFbDML5VwfV2VPC9pEzTQVAuB42NVlcj5fB4PDidTsbGxmhrg7ExqysSEal52tvUiWUdBC3h/P9r3vc+njtwgFwud9rzkXDY+iDI6yWZ1YclIiJl0P6mDkQzCZqbm6u+rsPjwVNGENTY2EhHx9J3Zwe6uggODTFlmgD4m5vBHCA1lSVnTi06CPrAJz/JHV/6UlmvdbpdZNLa24hIbZkrCLrRNM3HAUzT/ARw1DCMhxeziGEY6wqbknsX8z5SGQMDA3R3d1tdhizS9Hg4dQSJiCxIe5s6kUwmyUxl8S1hZ81S8Hg82BsacC9h3e3t7XQ3N7Nv377Tnp+MRPCvWrVk6xbD6/USz+pAZRGREml/Uwey2SzpXAavBWcEOdxu3C5X1dctVufatbx24sTMY19LC+nMABnTpNFowDCMRa/xS+97H08/8UTJr3N6XKQ1Gk5EasxZQZBpmo+d8fgu4NuGYbxgGEZJ/3VqGMavFObKHgZuW1SlUjHTHUGyvCkIEhEpjvY29WNsbIxmh7ci/+FfTYZh0Op04lniu313bt7MT8/4MCMSi+GzuIPK6/VqNJyISIm0v6kPoVAYT5PLkr2Nt70d3+rVVV+3WGvWruXo6CgbOzr42Ic+hL+1lUgy/+FIY0Nlxt80NDRwzTvfWfLrnF4XmUy6IjWIiFTKuUbDncY0zQeBzwMvGYZx3nzXFu4g+YphGGPAA+TnyhqFL6kBwWCQ7u4eltlnJHKG6SDI54PJSaurERFZXrS3WZlGR0dpdlT/jtlKaPN4cC/x/P+dN9zA0w89dNpzkWQS3xKOpCuG1+slodFwIiKLpv3NytPfH8LnsKYr5/233sp//eu/tmTtYqxZswaAjR0dfOfv/g5fezvJXH4/YTOsPQfB5XMrCBKRmlNUEARgmuajwAeAxwzDuP7M7xfuIHmY/B0kdwAtnNpEhIC7gCOVKFoWJxgM4vH0YPE4eFmk6SBIgZ6ISHm0t1l5RkdGlm0Q1Orz4WlpWdI1dt56K0/v3Xvac6F43PJReh6Ph2Q2zdTUlKV1iIisBNrfrCz9/SH8Trclazudzqqc9VMut9tNm9tNe+GsxdmjbhutDoK8btIKgkSkxhQdBAGYpvkScBP5duP3G4bhP+MOkt2cfgfJo+Tn1raapvk54HMVrF3KFAwGSSR6WL/e6kpkMaaDIBERKZ/2NivLwLF+mj1L21WzVG669VYuvOSSJV3j/C1biKfT9PX1AfDII48wNTXFxo0bl3TdhTQ2NuJobCIej1tah4jISqH9zcoxMBAiUMPn9FhtbXMzHYUAyFcIhABsFRoNVy6310kmm7W0BhGRM9lKfYFpmkcMw/gq8OCsp2f3JISA+4B7TdM8esbLHwEeQywTiUQAGBrysXWrxcXIovT29ioIEhGpAO1tVo4Tbxynta1271ydzx985StLvoZhGOzcsIGnf/pTfuXf/3s+fdtt/NmnP43dbl/ytRfianIQjUYtOQxbRGQl0v5mZXhz3yhtAY/VZdSsNZ2dtBfOwPbPOmvR6iDI5bKTyeUsrUFE5ExnBUGGYdxvmuYH5njeT37W7G1AgNM3ECb5TcK9pml+71yLmaYZJn9Xilgkfz5QN6GQwRJPH5Elpo4gEZHiaG9TPwaO9tPR3WV1GTVt5xVX8NOHHmJwcJDepiZ+6Q/+wOqSAHDZ8kGQiIgUR/ub+jDaN0BH+/Lsdq6GG9//fjYWOqr9s848tDoIcjjsZKbUESQitWWujqBbDMP4E9M0XwEwDOMG4HZgT+H7Z95B8iLQYpqmNgnLQDAYpKenR+fKrAC9vb0Eg8HCPP2SpjyKiNQb7W3qxEhwgAsv32Z1GTVt5wc+wH0f/jChH/yApx58EKNGNoUum4NIREGQiEgJtL+pA+nJIVbNGnkmp/vUF7848/vZZx5aHQTZ7XayU+oIEpHacq5Pj//SMIzfMwzjEPmW4D2cPj/2JeCWwvzY6bmzLxiGYe1Js7Kg6SBIlj+n00lzczNDQ0NWlyIishxob1MHxkZHWHPBeVaXUdO2X3cdJ8fG+PCOHVx0U+18Fui2OxkfVxAkIlIi7W9WuInga/Sef77VZSwLszuCGhusvVnWbldHkIjUnnOdEbSt8AWn30VyH/DVM+fHmqZ5n2EY48BLhmHsNk3zeOVLlUqYDoJM0+pKpBJOjYfrxjRRp5eIyLlpb1MHJqIhejfqhpf5OBwO/urDH+bmP/ojq0s5jcfuUBAkIlI67W9WsGzW5OdHn+NPP7j05wiuBNMdQU5bE02N6ggSETnTuYIgOP0OkntN0/z2fG9kmuaDhmEcAR41DGPPdHuy1Jb8GUG92Ob7X16WjekgyOO5gngcPDpDUkRkPtrbrHDhVIyOVR1Wl1HzPvTXf211CWfxOJyMD4esLkNEZDnS/maFeu21w2TNLG9729usLmVZsNvtOBobafV4aVJHkIjIWc71b0YDeBDYbprmjoU2EtNM03wJeBfwPcMwrq9QjVJBAwMD2O3drF1rdSVSCdNBUHs7jI5aXY2ISE3T3qYOhFNR2tvbrS5DyuDxegkNj1ldhojIcqP9zQq2f/9RNrR218x5fsuBz+mkzeunyVAQJCJypnP9m/E20zRvNU3z56W+oWmaR4AdwNcMw/iNRVUnFRcMBsnletiwwepKpBKmg6C2NgVBIiIL0N5mhTNNU0HQMub1+QkPazMjIlIi7W9WsJGBMfxut9VlLCufv/NOLujtweu2PgjSaDgRqTXn+jfjo4t5U9M0Q6Zp7gA+YBjGn8z+nmEYH1/Me8viBINBUqkedQStENNBUEcHjIxYXY2ISE3T3maFi8fjGIBbH5gsSz6/n8i4RsOJiJRI+5sVbKxviObmZqvLWFY+84Uv0BLw43RYex6CgiARqUVzBUFHTNM8Vok3N03zJqDVMIz7DcPwGYbx74F7K/HeUjrTNAkGg7jd3djtVlcjlbBmzRr6+vpYuxaOHbO6GhGRmqW9TR0YHR2l2eG1ugwpk681QDSkIEhEpATa36xwoaERAi0KgkrldLlosvhg7HwQpNFwIlJbzgqCTNPcVMkFTNP8BHAMCAH/WMn3ltKEw2FsNhtOp8/qUqRCpjuCGhpgasrqakREapP2NvVBQdDy1twWIDYZtroMEZFlQ/ublS88OkpLR6vVZSw7tRAEOZ1OUrmMpTWIiJypKkMzTdO8E/hL8gcZikUGBgbo7u62ugypoJ6eHoaGhshmswqDRESqSHub2jM0NKIgaBkLdLQSi05aXYaISF3T/qa2RCbGae9qs7qMZcfhctHU1GRpDXa7HdM0SafTltYhIjJb1U5PM03zdkC3+VkoGAzS09ODoS3ditHU1ERHRwcDAwNcfDHs3291RSIi9UN7m9py4o0TtDa3WF2GlCnQ1UY8HrW6DBGRuqf9Te1IxkMEOjusLmPZcbrdlgdBhmHgbnISjWpvIyK1o2pBUMFXqryezBIMBuno6MHvt7oSqaTp8XA7dsDzz1tdjYhI3dHepkYcf/0oHV1dVpchZQp0tJJMxqwuQ0RE8rS/qQGJRJjmzk6ry1h2nB6P5UEQgMvmIBKJWF2GiMiMagdBe6u8nswSDAZxuXpYv97qSqSSpoMglwuSSaurERGpO9rb1IgTBw+z/qKKHpcgVeT1+0lkU1aXISIiedrf1IBEKoq/vd3qMpYdp9dbM0GQOoJEpJZU+/S0F9GsWcsEg0EaGtaxYYPVlUglTQdBgMb+iYhUn/Y2NWKg/wS/+JH3WF2GlMnr9SoIEhGpHdrf1IBoJoG/udnqMpadK3fvpqOnx+oyNBpORGpOVYMg0zTDVL8LSQoGBgbw+6+hQyNmV5Q1a9Zw7NgxAHp6oK8PenutrUlEpF5ob1M7RqKjrDt/o9VlSJm8Xi/xjFqbRURqgfY3tSGeSdKsIKhkO666ih1XXWV1GRoNJyI1R3+x15FgMEhzc7e6RlaY2R1B11wDzzxjcUEiIiIWGIlP0Ks7IZYtn8+njiAREZFZYpkkfh3yvGw5m1xEJyasLkNEZIaCoDoSDAYJBKxvj5XKmh0EdXTA2JjFBYmIiFTZ1NQU44lJempgDIiUx+v1ksgoCBIREZkWSycUBC1jTqeXqD6gEZEaoiCoTpimSTAYxO/vtroUqbDZQRCAaVpYjIiIiAWGh4fxNLlwOBxWlyJl8ng8JHMpTG1kREREyGQypHJpfD6f1aVImZwuP6GhUavLEBGZoSCoTkxMTOB0OnG5PFaXIhXW2dnJxMQEqVT+LlqfDzSGVkRE6snJk310uANWlyGLYLPZsDXYSCQSVpciIiJiufHxcbx2N42NjVaXImXyeP1MjGg0nIjUDgVBdWJgYICOjh5Wr7a6Eqm0xsZGuru76e/vB+Dqq+G55ywuSkREpIoOvn6ETn+b1WXIIrlsDqLRqNVliIiIWO7kyVFanF6ry5BF8AYChMfCVpchIjJDQVCdmB4Lt2GD1ZXIUpg9Hm7jRjh0yOKCREREqujN5/ezenWv1WXIIikIEhERyTtyZJRWj4Kg5czXGiA8riBIRGqHgqA6EQwGcTh6WLfO6kpkKcwOggzD4mJERESq7NiBQ6y7YKPVZcgiKQgSERHJO3F4gHaf3+oyZBH8ba1MhqobBD3x8E/4szu/UtU1RWT5UBBUJ4LBID5fDy6X1ZXIUpgdBAE0NUEmY2FBIiIiVTTQd5zzt19kdRmySK4mBUEiIiIAA28do2NVh9VlyCK0dLVXfV/zw+/+Cz/8/j9XdU0RWT4UBNWJYDBIc3OP1WXIElm7di1HjhyZeXzppfDKKxYWJCIiUkWjk8Osu2iz1WXIIrltDqKRiNVliIiIWG70ZB/dvV1WlyGL0NbdRiRW3SBo4PgJ4nHdVCMic1MQVCcUBK1s11xzDU899dTM48sug5//3MKCREREqmg4HqK3V2cELXcOu5vI+LjVZYiIiFhufChI9/rVVpchi7D2vC5GY5NVXXNoIEg8lajqmiKyfCgIqhMDAwM0N3dbXYYskUsvvZSxsTH6+vqA/Gi4bNbiokRERKrANE1G4hOsXq0PS5Y7p8NHdGzM6jJEREQslUpBLDpMx9q1Vpcii7BhQzejseqeETQaGiM+la7qmiKyfCgIqhP9/UG6utQRtFI1NDRwww038Nhjj808Z5r5LxERkZVsbGwMp82Ox+OxuhRZJIfTR2RUQZCIiNS3p5+OcWTsDdZv2WJ1KbIIPT1dTKQi5HK5qq05kYyQzKaqtp6ILC8KguqAaZoMDAywdas6glayXbt28eijj8483rgRZh0bJCIisiL19fXR4W6xugypALfXz8RIyOoyRERELPW3f/4nXHb+ZnZee63VpcgiNDU14bO7efdll3Hy5MmqrDmeDBPPJKuylogsPwqC6sDY2BgOh4eLLnJZXYosoV27dvHYY49hFtqArr4ann3W4qJERESW2MH9x+j0KghaCTz+ZsLjCoJERKQ+3XXnH/JvP3mS/jef4+YP3oJhGFaXJIvU5mzmkdde480DB5Z8rUwmQzgVI6GOIBE5BwVBdSAYDOL399CthqAVbePGjdjtdt544w0A/H6YrO65hCIiIlV34Pn99PTofKCVwNPSQmSiurP0RUREasWdd32ZX9h1PQPjxzl/+3ary5EKaCt0rQ9WYVzL0NAQAYePRDY1c4OwiMhsCoLqwMDAAM3NPTTof+0VzTCMs8bDiYiIrHTH9h9k3eYNVpchFeBrbSUyGbG6DBEREUtc2LaOKdPk4PgJzr/gAqvLkQpoDuTP6j75xrElX+vQwYOs8a+iqcFGIpFY8vVEZPlRNFAH8h1BageqB9Pj4aa1tcGYzlwWEZEVLHj8GJu3XWh1GVIBvvY2IhEFQSIiUp+mzCmuumgLNsOgs7PT6nKkAq7e82UuXfdeTr51YsnXeuXJZ1nTuRGXzan9lIjMSUFQHQgGgwQKdyHIyrZr1y6efPJJstksADt3wjPPWFyUiIjIEhoLD7L+Yt01uxIEOlqIxeNWlyEiImKJZDbF7/yn3+fGy7frfKAV4tYPXMm7bt7NQH9wydd66annuWDbDlxNDqLR6JKvJyLLj4KgOtDfH6S5WUFQPejs7KS3t5e9e/cC0NsLJ09aXJSIiMgSGomH6F2zxuoypAJa23xEUkmryxAREbFEIptm53XX8X3dzblibNkCl127nuHRpRvV8sKzz/Jfv/AF3jx0kCt/8RrcNoc6gkRkTgqC6sDRo0HWrVMQVC/OHA8nIiKyUpmmyUgiRG9vr9WldbN8QgAAIABJREFUSAW0tfmIpVJWlyEiImKJZDaFx+OxugypsPXrOxmNTZ723HUXv5M//k9fK+l9pqam5nz+G3fdxWf+6I84OjHEFVddjMvmVEeQiMxJQVAdOHFigLe9TUFQvdi9e/dpQZDTCUndXCsiIitQOBzGwMDv91tdilRAW5uXeEZBkIiI1KdkNq0gaAXq6upkInl6EPTT/U9x319+s+j3GBsbo7Gxcc7vtXiaAQgnI6xduyY/Gk4dQSIyBwVBdWBoKMhll3VbXYZUyTve8Q6ef/55EokEADt2wIsvWlyUiIjIEujr66PDHbC6DKmQ9nYv8bSCIBERqT/ZbJacmcPhcFhdilRYT08P4VSU1Bldz2MTI0W/x8+efhpg5jzo2Xx2HwAd7hYaGxtxO9xMDI8vomIRWakUBK1wU1NThEKDbN6sIKhe+P1+LrnkEp4ubBQuvhj27bO4KBERkSVw6M3jdHpbrC5DKqS9vZXJdIxMJmN1KSIiIlUVi8VwNjowDMPqUqTCmpqaWOVp5fDhw6eea7ARyySKfo+f3P9PACTnGPeSS+b3Td3edgD8za0MHulfTMkiskIpCFrhRkdHcTr9uqukzsweD9fYCKZpcUEiIiJL4OWn9tHbo/G3K4XH46HT08ob+/dbXYqIiEhVRaNRXE363GalWt3czZuvvDrzuM1V2ljjp3/6HMDM5JfZopP584A62s4DYFV3NycPHi+3VBFZwRQErXDBYJBAQB+Q1Jtdu3addk4QwDnOFRQREVm29j3zM7Zes83qMqSC1ndv4ecPP2x1GSIiIlWV7wiyW12GLJF1G7ew95FnZx47bfnQb2JioqjXj0zmz/yZqyMoHokBsGbzFgC6N6xl8KQ6gkTkbAqCVriBgQGamxUE1ZurrrqKAwcOzGwqtmyBAwcsLkpERKTCjp08wI4b32F1GVJBnZvfwUtPPHHac+Pj49y2c2dF13nttdd4zw03VPQ9RUREyhWLxXDZ1BG0Um297nL2vXiqIyiZTQMwNjY27+uSySQ/f/FF4tkkBsacHUHxWIytG9/HL3/8EwCct2U9I0ODFax+8b74e7/H9/7hH6wuQ6TuKQha4Y4fD9LSovOB6o3D4WDnzp08Ufgg5fLL4YUXrK1JRESk0o6Fg1yydavVZUgF9Wy6jpcOHTrtucfvv5+/efZZpirY3nzwjTf40U9+suAHMCIiItUQi8Vw2tQRtFJtu+4STgwHZx6ncmkCDh+xWGze1z3zzDN8/Jf2EMskaXH65u4Iise55YPvYdeNmwFYd8FaxiKhyv4Ai/RfvvEN7r37bgAGBwcX/LlFZGkoCFrhDhwIsm6dOoLq0ezxcG43xOMWFyQiIlJBIyMjpHMZVq9ebXUpUkG9vZfxcl/faaHPE9//PhnTZGRkpGLrDB4+jAk8ojF0IiJSA6LR2My4MFl51q8/j8HoOAAnT+Y7ggJO74KBSDKRYCwUIZ5JEnD65uwISiYTrNkYwF7IETs7VxFKRir+M5Qrnc53P60pHFvxW+//IN/+xp9bWZJI3VoxQZBhGAHDMO4wDOORWV9fNQwjsETrFTWQvlDXnqWooRh9B95gS4tVq4uVdu3axaOPPlqx9zt2DAYGwDQr9pYiIiJle/GFV9nYshrDMKwuRSrI7W6lzePhrVldQU/s24e9oYn+/srNux86epQuv5+H//7vK/aeIiIi5ZoYCeOyO60uQ5bImjVrGE2EiEQifPw9H8kHQQ4vsdj8d+zGIzHGUzGmzCm8Ta45g6BEKklzm2/m8apVq5iooSDo1VfzI/GSkRQA+/e/yStPv2xlSSJ1a0UEQYWg5SjQZprmjdNfwGHgqGEYt1V4vQCw1zCMiULYtNswjA3T3zMMY5thGHsMw3gAmAAur+T6pbjnf32DT2zdAD/4gVUliEW2bt3KyMjIzIcmPT0QDC7wonN45RV4+GH42c/gvvvgf/yP07++/314+WUIhyv4AywBhVgiIivHU99/kgs3X2B1GVJhXV3wtvXn81LhZpbh4WFOToTY4L2QvjNGxp3L8ePHee/VV897zeDJk/zqnj38+Kc/xdQGQURELBYaGsftdltdhiwRp9OJz+7mJz95ksf3/f80NTTicbgJj0/O+7rIeITIVApPkwuHzT7naLhkNoPff+qfnba2NiLpGLlcruI/RzkOFw6sDocmME2TE7Fxjhw6bHFVIvVp2QdBhZDnAeA3TdO8c/b3TNO8D9gF3GsYxleXYPkAcAfwCHDYMAyTfPCzt1DTHuD2M+uqpq6uLlp/4zdg9Wr48z+HTMaqUqTKGhoauOGGG2bGw11zDTz9dOnvMzoKP/kJ3H47/PIv53/9xCdOfd1+e/69k0l46KFT4dCf/ilUcJT/osVi8NnPWl2FiIhUymvPPceVu66xugypsCuvhNbe63ipsH958nvf4+LVb6O7+zz6Cx8kLOStt97iX557bt7zf4YGB9m5ezfOpib27dtXkdpFRETKNT44gcfjtboMWUJdnjYe/fFTZJnCYbPjcrqYGJqY9zXRUBQAd5MDe6OdRDR61jXJbBqP51QQZLPZ8Ns9DA4OVvYHKFM8HMbb5GEyMsnAwADJXJoXT+6nI6BjLESqbVkHQYUunHuBB03TfHCua0zTfAm4C7ij2HFuFfIosL0QRllvxw741V+Fu+6CoSGrq5EqmT0ebtUqKHW0fjabD3V++7fPfY1hQGcnXHUVfOhDpwKiK6+EN99cRPEV9o//mP8zEBGRleHowFtsv2Gn1WVIhfX0gK/nnby0fz8AT/zv/03vRb9E++qNRXcEjZw8CcBTjzxyzmsGJyZ4+Y11vOvSS3lYnfMiImKxgz/fz/oLN1pdhiyh7rYunvpRfm/itDlwebyER0PzvuZUEOTC7nARnTh7DEsql8blcp323Nt6NvPQA7VxDmJ4dJJWbyuTiTiHDh1ifXMP8WyS0fCA1aWJ1J1lHQQB010+X1nguunvP1DBtV8CWoBbgDuB+8gHTrcAGwvj6V6q4HqL194On/scPPhgfsaXrAymmW/bmaNFeNeuXTz22GMzI09KPUbhnnvyHT9NTaWXtWMHvPBC6a9bCplMviOoRedliYisCFNTUxwLD3DJ299udSmyBNas3c5LJ09imiZPvP46G9/2bgJrLuDE0RNFvX746FFsDQ08+cC5t/6D4Ul++MMubvp/PsSP5rlORESkGt46uI+r3nOd1WXIErp4x1ZeP/IaAM5GOx6Pl8kFgqD4ZCEIsjlw2J1Ex88++yeVzZw1VvC9H/plfvCX361Q5YsTGZ+kPdBOLJXk8Gv72NihwFPEKjarCyhX4ZyePUBoocDFNM2QYRgvAdsMw9hWqYDGNM0QMGcnUs1qbMy3dzz0EPzd3+VbOHTIcm0yzfyhO8Hgqa85DgbEMKCtDQ4ehF/7NejtnfnWpk2bsNlsvPnmm1x44YV4PBCJgM939tuc6Xvfg3e8Azo6yivf54M5upYt8f3vw6/8Cjz+eL4mrzruRUSWtRMnTuBpctKihH9FamnpxNXUxPPPP08wFGLLlq0EA2M89G+jRb1+5ORJbrz6ap54/vk5v2+aJkORSX7tpk7aL9jDz978JLFYDI/HU8kfQ0REpGjHJvp427atVpchS2jXLTfx3//+WwA4Gux4fF4ic3T4zBaPxIF8R5DT5SYamiMIyqXPCoJu3PNevvXNb1Wo8sWJhKN0tHQQHD7B4VfepLPnPP7PH32OPR96n9WlidSdZRsEAbcVfn2xyOtfBLYBtxe+6tvNN8Mbb8DXvw6f+hSc0UYqFjlyBB59FNJpsNuhuTk/I2X9+vxBPPMdHjk1lZ/jduWVsH07AIZhzIyHu/DCC7nqqnwz2O7d85fx4ovQ0ACXXVbBn80iU1P5DK2nB9atg2PH4G1vs7oqERFZjBeefYkNrautLkOWyCWXwIU9m/ivX/wil6y5hGuvbeT113u5LzT/XbPThoNBLr74F/np3j9mfHyc1tbW074fDoexNdj41V918/jjsG3NGp584gnec/PNS/HjlOzJhx7iwN69fOKLX7S6FBGRiivc1HsbcOOsp18CvlK42bbS6xV1M3Chrt3nOnZgKcXjcUaTYTZt2lTtpaWKdlxxBQCtbj+uxka8zX5i4bODndnisXwQ5HJ6cLrdROe4fq7RcG1tbUQzZ0+NsUI0HKG9vZPYvgTHDx5j9abLeM+ed5H5YA7TNDF0c7pI1Szn0XDTm4YjRV5/uPDrrUtQy/J04YX5w1z+23+Do0etrmZ5SCTyrTL33APf+Q78/Of5g3QW49ChfIDzzW/CgQPw67+eD+duuw0+8AG47jrYuHH+EAjyyc0nP5n/3/Khh2aenh4PB7B5c365+QwNwTPPwPvfv7gfC/KdN1Z3Bf3wh/Dud+d/v369/lEXEVkJnv7Bk2y5+BKry5Alsm0btHRfzYOPPEL3Bb/EunWwdetqBiYnZsbdzmd4eJjHnt3M1Rs38m+PP37W94eGhmh1+untzd8wctO11/Hw/fcvwU9Snh/dfz+/9aUv8We///tWlyIiUlGGYewBjgJthXH6N5qmeSP5z2uOGoZx2/zvUPJ6AWCvYRgThmF81TCM3YWzpjEMI2AYxjbDMPYYhvEAMAFcXsn1ixUMBtl+/lZstuV8r7YspKenhzXtHVy6+WJcDie+lmaikcl5X5MsBEFerx+n201sMkbf8eOn7YeS2bM7grxeL4lMqvI/RBnikRirOjuJZ5L09/ez4dILaWxspLGhgXQ6bXV5InVlOQdBOwq/Hp73qlOmA6NAYTMgkJ/f9bnPwRNP5DtR5Gy5XP7P5u678+P0rroqP17vwx+GVAr+6q/gW9+Cv/iLfOpQzN2qb7yRf83dd8Phw/Cxj+XDn5tvBodjcfXu2QOBQD6oMk127drFE088QS6XwzDyE+fOJZ2Gb387nydVwuWX57uLrHTwIFxwQf733d357iAREVneXt/7Ilf+4jusLkOWiMMB7ZtuIGeabLj4PRgGrF7tB2Bycv4PTACGQpN4mnu4/Oob5jwnaHBwkIDDh88HV1wB5117Gw/96EdFhUzVMNTfz5c++1nuue8+7v7DP7S6HBGRiiiEPA8Av2ma5p2zv2ea5n3ALuBewzC+OtfrFykA3AE8Ahw2DMMkH/zsLdS0B7j9zLqqZdOmTTyzf+5xprKyvPbWId6x82q8Hhf+tmbiC9w5m4jngyCfvxm318vw8DCXnH8+P/6XfwEgk8kA0HTGwc4ej4dENlkTe5tYNEagrZWmBhvHxwa58NJ1ADgam0jMdfyBiCyZZXm7QSHImQ5ziu0Imn3dBvKtxwL5M2Y++lF48km47z74+Mfz3SX1zDTz3T7PPJP/87n++rPnqTkc+VDoqqtOvebYMfjXf82f7QP5lpgrr8y34rz+Ojz1VP7W0wsvzP85n/GXdcXs3AmdnfC1r9H1u7/L6tWr2bt3L1dccQWNjfkmprluNvrmN/MhUKVuRLrggvw/Vr/wC5V5v1L99Kdw7bWnHjc0zB+EiYjI8nBk5DiXv/NKq8uQJbRu/RX0dnaybt3bgfy42w53gP7+fpqbm+d97VA4wqd/t4OJsVt54uEPnf39/n5aXfn/lLjiCnj++StJZ7McOHCALVu2VP6HKdHQ8DDvv/ZaPvLbv80vbN9OV28vt3z841aXJSJStkIXzr3Ag+cavWaa5kuGYdwF3GEYxv2VOtu5CI8Cd1ZxPaljzc3NbHj7+Rw/9gbNHS0kErF5r08lErR5W2ntWY3b7eIv/vc9NDU08vh37+dd730viUQCR6P9rNfZ7XYajAZSqRROp3OpfpyiJOJxfK3NeOwujocHWLeuJ19jYxPJZG2MrxOpF8v10/7WhS+Z14aKVLHSvPOd+RlaX/867N1rdTWnTE1Vb62jR0+NaUsk8p0/v/3bUMyHAoaRnz32oQ/Bb/1W/uuXfxlOnsx3/4yM5Me9fepT+VBpqUKgaZs2wW/+Jtx1F7t27pwZD7d1K7z66tmX/8M/wI03Quti/981i9XBywsv5LuSZtP4WRGR5S2TydAXHeaiiy6yuhRZQuvXr+Yvvt3P5Zc3zjzX7m6l79ixBV87Goty5ZWrCLRewaHhYUJndGsPvvUWPn8nkN8XNDQYvHfbdn5QI+PhhiYn6ezpYd369XzxS1/iX/72b60uSURksaa7fL6ywHXT3z+7nbN8LwEtwC3AncB9wF2FxxsL4+kUAknVfPCjH+XPv/tdAqtaSCTi816bSib57O/+J/7wnrtw+70AbN70qzz65LNA/nwpp+3sIAjA3eQgavWsfiCRSOBvb6bN6WfKNOnq6gLA0WhXECRSZcs1CJo92q3YwwRnX1fBj7rzc24Nw3jAMIxHCl8PFGbfLj9r1sAdd8DEBHzjGzAwYF0tY2OnQplvfhPuvXdpDnjp74e/+Zv8mLZ9+/Jj2v7jf8x31Sw2NfD5YNeufJvN9ddXrtWmWC0tcOed7M5keOyf/xmAyy47O+d77rl889IlS3TcghVh0KuvLt3PIyJSDYXZ9XfM2l88UphvvyQjbg3D2FZCXZbtcw4ePEinu+WsQ3FlZbnySvjOdxp5+9tPPdfS3EP//v3zvi6dThNLJ7ngggAOh50r128465ygoWPH8LasmXm8cydccN3H+T/f/W5Ff4ZyDYYj/PCHnQwNwfnbtnHwxAmrSxIRKVth37IHCC0UuJimGSIf3Gwodl9SDNM0Q6ZpPmia5l2mad5umuadhcfFTpgRqRi73Y7f78ff4iO5wDk+qVSS1Wtb6Ohw4An4APjcH/wGrw+dBCASieCyzX28gMvmrIkgKJlKEOho5sb3fBEAR+E4BHujTaPhRKpsuQZBiw1yKvIBSuFgwUcK9fzmrIMOvwJ83jCMvdMHES47u3fDpz+dPxvn/7J33/FRVfn/x183vfeekEINvSUUQQEBF6WpYK+71rUgrl/rFnd/i+uuuvaKuq67urv2BbGCgmtFQlcEQklCIL0XQtr8/rgTSGCSTJKZCeX9fDzmkZl7zzn3Mw9Lbu7nnPN54QVzdYyr7NoFjz8OK1bAlVfCokXmKpqf/xy2bTOTQi++aK606Y66Oli5Ep55xnytWwcLFpjJn7lzwcv2bIoTlqcnUx57jO82bODgypV4eYF1G1nArJmzfj3MmeOcyycnQ3a2c8buyGefmTk4W7Q9nIgc71RMuX0Z32TQLzKpty4vLpKUBEFBbefQBEWkkLtjR4f9ioqKCPYOIDjYjYkTYdDgaXzxdttdiPJzc/ELP3KLPnIkNAWdx/bcXPLz8x36PbrKYrFQWFXJz34WzerV8Nnng9iRX9irMYmI9FDLPYu91WNb2t3ghFhEjhv+/v6sy9vGmSOntdvmUP0hAqwJIN9APwDOPTedZouF2tpaMxHk2V4iyJuqqirmT7qK+vp6x38BO9TV1VHbUE9wiB/X/t+1/O53RxJTXloRJOJyJ2SNIByUyOmhvpjLmy+wzlo5zDrLZaxhGLsxH6qMtWemifWhzvUAiYmJTgi5izw84IoroLzcTLwkJMB55zlvb61vvzWXpvTrZyZl3N3bnvfygtmzzfd1dfDJJ7BsGfj5waxZEBdne1yLBXbsMAvGHDoEPj5w+ulmsusU2ScsKDiY4aNH801GBtPLyjCMC7FYoL4e/vY3uPde51173Dgz75ac7LxrHC0ry7yerX+84eHmYrOICNfFIyLSFdb7gRcw7zHaPMG2WCxLDcPIwLy/6OeEosYtxZTvssZiq80N1qLOveKsOWeRdlpab11eXMQw4Nln2x4LjBlEbtYnHfYrKioi1CcQw4ARI8A78UL+99+r2rTJzy8gZWL/Ntfy9/di5uChvP/f/3LdjTc67Ht0VVlZGd4eXgwd6sOECVBWFskjf2qmpKSE8PDwXotLRKQHZlp/2rv6Zrf154UoGSQnMX9/fwBWb1nTbpuGpnp8A8x2pdWlAAQG+hLsHUBJSQlVVVX4ediuAeTr4c2+fftY/s0/2Lfvd/Tr18+xX8AOU0eNYkdJNv7+vowaBaNG+R8+pxVBIq53oiaCurMiqLTVe0f8FbUHG0mgo9yNubftW8DYzga0PlRZCpCWlnb8rFkICTFX5ezcCQ8/DFOnmk/3HaGpyVz5s2cPTJgAt99uXz8fH5g/33xfUwMff2xuY+fvbyaLvL3h88/NYxYLpKaaSS1v2zMlTgUzZszgs6oqpg8cyBlLn2bv7pt45z03mzk3RwoPh9LSzts50rJl5iIyW1JSzH/dlAgSkeORiil3LjY2ltjY2N4MQVwkIKDt57j+A9i4/B8d9iksKCDEx5w5axiQkDiWH/PyaGxsxMO6vCivtJwz+vZp02/2bNjz1YUsf/XVXk0EFRQUEOodRKD5FQgNNYgPiCIzM1OJIBE5UbXM3tjdYasjWhJGIYZhhHTyzEXkhOXjYyZw+of2abdNfVPj4Xajx44m3N9M5gR5+1NSUkJleQV+nu0ngr5f+z0AOTn7DyeCaq1lifz8HPI1OpSVtZ+DjYfws3ExL3dPrQgScbETdWu47nBYXSDr/rJjO7shsT7AKQfGnLA1g1obONCsH1RTA488Arm53R+rthZefdXc5m3oUDMBNHFi98by9ze3drvlFli4EFavhvffN5NVN90EN99s7hF2CieBAKZPn86qVatg1CgSbj2ftec+yPypFQQH93ZkjlVYCGFh7Se3+vZ1TqkpEREHUTFlkXakDu5DbmnHzwOLsrMJ8j+SMOnXL4CYwGAyMzMPH8urrGTgwOg2/eLjIXTItXyxaRM1NTWODbwLCgoKCLUmslrEhSSwc9OmXopIRKT7rFvPtuzoYu+KoNbtTsyt9kXsMHjwYD7/fA3V9bXttqlvbjicCJoz5yyuu3UXYE0EFRdTml+Mn0+Azb5+3r58ufJLALZvOpKH/fMDu1j+7i5HfY0OVdWbiR5btT293b04WNv+dxcRxztRVwT1dH1BiUOisE8GMAO4F7A5s/eEM20anHEG/Oc/UFlp1vExDDNB1NGrvt5s19Bgbjt3wQXmchFHCgyEiy5y7JgniYkTJ/LTTz9RXl5OyOA40v9zB/0/egr8Z8OQIU69tre3uSufK3Jxb78Nv/hF++dDQ83dDkVEjjddLaZsGMYGzMkmYxyVoLFOcjk57lfkpDN8eDwHKso6bFOYlYV/4JEkz/Tp0Ccwkc3ff8/gwYNpbm6muKaKYcOij+nbt18oY+KT+PSTTzjv/PMdHr89CrKzCfEPbXMsMm4YmevWQS+uVBIR6aaeTsjtizlRReSkYxgG48alUVpXicVisbklc+sVQW5ucM015vEg32CK9u+n5EAx/oGBx/QD8PMLYO2mDNwNN/ZsMmssNjU18cc/DWBMyhguvny9c76YVUNDA7WWRmssNlYEeXhxsLr3Jt+InIpO1ERQTx/juvIx8AbMRNCYk2pZs7s7XHYZVFTAm2+aiR1//7avuLi2n728ejvqU5q3tzennXYaa9as4dxzz6X/MB8Ydif8+9+wezfMneu0a48eDZs2wfjxTrsEAFVV4Olp7hwoInIC6k4x5TGY++drD3056Q0dGkl1fR11dXWHH4ocrTAnB//Q+MOfAwIgOiGNzatXc/FVV1FWVoavhzdJScfOTpkzB1Y+fxbLX3219xJBu3cTGNR268Pg5HR2/PBir8QjItJDres72/sspHU7h+3sAmDdqeUijsRVDrzR3na8Is7m7++Pu+FGZWUlwTa2a6lvasC71Yza/tYSh8EhEezfuY/y4moCg2xv8+IfEEj5wUomjEjjx/V72LwZamrWAhDmaTt55EjlrWbg2lwR5OVLVWml0+MQkSNOhq3hQjpv0qta74N78lU2Dg6Gn//crL9z/vnws5/B5Mnmk/9BgyAhwVyCoSTQceHw9nCtXXIJREfDU09BY2O7fbOysrBYule6avhw2LKlW1275M034cILbZ9rbGzkyy+/dH4QIiLd15NiyiInPW9vN8J9gzhw4EC7bQoO5BMQldzmWETqmWzeYE4oN7deC7J5a+rrC2FjrmTdOntzsY6Xn5WFf2hCm2ODx4xk+779vRSRiEiP9DSR45DnPYZhjDEMY6U1nuus293OxNxq917DMNZb6zSKuFyYTxAFBQU2z9U3Ndic/BIeFU3e3v2UF5cRGNpOIijITPYsuPA8PvrxLX5948UUFZorq6urnV/IuazsyCpuW4kgL28fqsuqnB6HiBxxoiaCWv8fy94bi9Y3EK4sXd/6WrqxkF41ffp0Pvvss2NPjBtnZlD+8hcoLm5zKi8vj4ULF5KamsrZZ5/N3m4U2PH07DDH5BD19VBXR7s1j55++mmmT59OXV0d3cxniYg4W4+KKTshHpHjTqRfKPv37Wv3/IH8YmL7Jbc5ljxwHJtzcgDIz88nzCeo3f4/O2cImYWFNDr7xqUd+fsP4BfR9k+GqVMHsKu4qNsTckREetHxcH/SF7MG4wUWi2Vp611aLBbLBovFMhYzTruSQYZhXG8YRoZhGBlFRUXOi1pOGWG+weTl5ds8114iKLJPHBkb15GzL4vg8FAbPaGi3tx2bUS6+SfGnt3rKT5QSnRAGBWHnJ+AKSsrw8263Z2t7+Dj50d1uRJBIq50QiaCjtoH394bi9a/0O2daXsMwzBWGoZRZhjG9Z23Fjm+jBo1isLCQvbvtzGrNDoa7r4b/vUvWL+e5uZmli5dyogRIxg0aBBFRUVMnTqV9PR0Hn744Y4fkFRWmjWk2pnV4gzvvAMLFtg+l5uby5IlS4iKimLr1q24uUFTk8tCExHplIopi9gnNDCa3J9+avd8YUUl/QbEtDk2bVoSlQcPUVxcTH5ODiF+7f/5MHWqH2E+QWRlZTkq5C7Jyy8kKqVfm2PDhwfj4+5FXl5er8QkItID3VkR1HoyrSOKCu/BTAJ1tDXd3Zj3YW91Npg1mZS6iPHaAAAgAElEQVRmsVjSIiMjHRCenOoigkLZvS3L5rmG5kabSZTQuAi+2L6e5es+JTTK9n8mJbXmipwpU6Zw71134WUYlOQVEx8eQ8WhaofF356y0lJi/SPwMjxwczv28bOPjy+1lc6PQ0SOOCETQVYtv8T7ddjqiMM3IN0tqGwYxhjMej8hmDcKXbourl2JJHIMd3d3pk2bxueff267gYcHLFrEju++Y9qwYbz88st89tlnPPDAAwQGBnLPPfewdu1aPv30U9LT01m3bt2RvocOwbJl8PTT8N//wtSpsGKFWYOouZnoaMi3Pcmlx5qbzZxTTIzt84sXL+bmm29m1qxZZGRkkJAAtnJhIiK9yBHFlEVOesHhyezfsaPd80XVVQwc2PbB3PDhBn1D4tmyeTMFu3cTFBzXbn/DgMTAGLZ3kGxypryySvoPbFsjyMMDEgKj2NnB9xYROYk4rC6QxWIpt1gsYzur1WytEVSOWdt5oaOuL2KP8IhIcnfk2DzX3oqghVcsJCnaLMIcHhdhs+8r//kXq1dtxNvbm6t+8QuKasspLyylT1Q85XXOT8AU5ebRNyKJWROvsHneN8Cf2qoap8chIkecyImglkIn9t4ktCSMupUEsmp987Cq3VZttZ5y2JNriziEzTpBVvX19TzwwANMuv9+zp87l28uuIARqalt2vTr149PP/2UO+64g7lz53Lb+edT9cgj8OqrZm2oW26BK680szLXXAMTJsBDDzE5bBtr1zrnO61YYRZ4tuXDDz9k8+bN3HvvvaSlpZGRkUFKCnRjhzsREWc67oopG4bxlnUl9Errez0YkV4XGDWA3N3t755YerCa1NSoNse8vaFP1GA2f/EF+VlZBIT26fAa8RF92b5+vUPi7aqCqkoGD44+5nhsWDKZG/SnhIiccHo6GbbEIVHYp6VA3L0uvKYIUbEx5GfnHnO8ubmZhuZGvL29jzk3YEAfXn3jIQAiE2wnggYMSGTq9FEAxMfHU3ywnIriMmJjYqlvbuDQoUMO/BbHyttzgPDQKJZ9/Teb5339/amtViJIxJVO5ETQG9afY+xs39LujQ5bdcBisezBXFbcz2Kx3GBnt3Trzz3W/iK9asaMGXz22WfH7DO/du1axo4dy9dff8369eu57S9/wf3aa+GRR9oun7FYMDZs4PLycn741a+otFgY+uSTLI+JgcTEYy+YkgJ3301U+U5C//2sWcjHgSwW2LUL+vc/9lxtbS233HILzzzzDD4+PqSlpbFu3TqSk6GXdnwREWmPiimL2CE4IZWcXNvLeg8ePEhDUyOhocfWAIrqfzqbv/6avH37CYju+F/h8KSx/LQuo8M2zmCxWCiprWLYsGMTQeHxw9mZ4fqYRER6yN7JLc7q3xUt2fYxqr0orhSbkkDxgSPbv54z9hzq6uooLy/Hz8MHd3d3m/0GDhwAQHBoO4WSWwkICMDTzZ0DB/YREhFKsHcAxUfVh3a0gn35hEbaTlKBuSLoYE2tU2MQkbZO5ERQy5KGvnb+kp5h/fl2R43sGKucrj1sabnuC13oI+I0/fv3x83NjZ07dwJQVVXFokWLmD9/Pvfddx8ffPABSUlJZuOQELjnHnPJzbvvwnPPwTPPQH093HwzEXfdxSvvvcff//537rjjDhYuXMiBAweOvahhwLnnkpl+qTnGmjUO+z5ffGHuQmfLAw88wLhx4zjrrLMAGD58OLt27cJiqeXgQYeFICLiCMfDAweHFlMGFVQWxxswKJF9xWU2zxUVFRHiHYBhLUzcWuzgKWzeuZP9eYXEp9qYPdLKwNMm8cM212/DVl5ejqebByEhvsecixw0nu3btrs8JhERBzoe7nU60nq5aVqvRSGnnMTByZSUFAJw6NAhPtrwEd9+k0FpaSlB3v7t9ouJicHHzZPAwEC7rhPhG0LWgb2ERoW5JBFUkl9EeMyxk1ta+AUFUlurRJCIK52wiSDrw4mHrB8v7Khtq61Mlna0Ksc6A7bMMIyyDh5wPIj5kKRThmFcj3mzU26xWB7qrL2IKxiGcXh7uA8++IBhw4ZRWVnJjz/+yCWXXHLswxM3N7jhBhg+HK691tz6beJEM7ljdeaZZ7JlyxZSU1MZOXIkzz33HM3NzcdcuzEghKZFt5t7tDzyCDjgoeDGjTDGxrrAn376iaVLl/Loo48ePubt7c3QoUPZtGlTj68rIuJgJ10xZVBBZXG8kSOT2V1cdMzKZrAmgnxsPww5c/pwfsovYF9pKQMGtV8jCGDaWSPYmZ/XYRtnKCgoIMz32NVMAOmnDWP7AScVWxQRcZ7W9yr23uu0Thi5ss5y62tp9bO4TExiHBU15u13S3Jmxd8+oLCwpMNEkGEYXHreZSQnJ9t3naAQsgr3ERYTRohPAHl5zk0ElRUXE5UY2+75wPAQaqurqKnR9nAirnLCJoKsHsRcodNZYuZea7u722tgGMYMjqzeCWmvrbWIIIZhdHhNayKpZRXQ9E7iE3GpGTNm8Jvf/IZFixbx8ssv8/e//53w8E6eIQ4YAJ6e7Z729fVlyZIlrFmzhtdee41JkyZx9OzvYcPgxx8xE0m33QbLlsEbb5j7u3XDxo0watSxxy0WC7/85S/53e9+R1xc24c9LXWCREROAiqmLKec0aPj8PXwYdvWrcecK8zLazcRNH68H9F+oWQW5zFsWEwn14iisanZ6TNlj1ZQUECoj+1E0LRp/cgpK6apqcmlMYmI9ITFYmld3MzeFUGtkzDd3l7fWuOwzDpBV+S4FREZScUhMxnS8gxl49dryM4qItQ3oMO+L7/9ChER7W+/1lpcVDTldeWExEQQ7OfPgRzn3ueUV5QR1z++3fNh8bFUVVcyJDmZwsJCp8YiIqYTOhFkfVgxFsAwDJszUw3DeAHzRmJ6Jw83ujLT5AJghvXG4piZItak0nrMByVjj7r5Eel1c+fO5f7772fr1q3MmDGj8w5dMHToUL788ksSExN5/fXX25wbMwYO11729DRXGKWnw0MPwY6ub8GyerXtbeH++c9/Ul1dzU033XTMuZY6QSIixxkVUxaxQ0gIDE6eyOrXXjvmXFFWFoEBtleeBQRASqi59e3AgR2vTnN3N0gMimH7dtduxVaQnU2IX6jNc/HxvoR6B5Gdne3SmEREHKDlOUw/O9sfnujS3WcphmGMwZzo2+4k346ui2tXIskpLiIigopD1QAU5BcS5RfK1oLt5O7MJTTEcTsqJvYz74MCQ0MJCgqhMNu5q58ra2uI7dP+PVdsfDjltdXklpRQUFDg1FhExHRCJ4IArFu9pQAh1gLGd1kLHS80DGM95t6unSZjrOdbtm/bQAc3Cy2zZq3tdluv+4L1tR5YiVnDKEVJIDkeBQUFsXjxYvz8/JwyvpubG5dddhnLly9vc9zXF+rqjmrcty/cdZe5VOipp8z6QTa2lTtaTg4kJ7fZoQ6A0tJS7r77bp5//nmbRRXT09PJyMjAx8dGLCIivUfFlEXsYBiQOGYhq1etOuZcQVYWAUHt70Ufm5RGqIcP3t7tr3Bu0Scknu1btvQo1q4q2L2bwOD2VyslBEWT2Y2JMyIivazlf9j2rmRuSRj15FlK6/uiY39h2Nb6nkbPccRlWhJBFouFnJ25DI8fhJeHG6s+/oLwSPtW+9ij37ABAAQEBBASHkbJfucmX6rqawgLsz3BBSAmJoSC6jKaLRZKS5V7FXGFEz4RBIcTMzMxt2Arx5z5EYa5z/3YjuoCHTXO3RaLxbBna5TW7TG3qNttfT0IhFosls722Bc5qc2YMYOMjAz7fqEbBpx/Ptx6K4SFwbPPwjPPwE8/tdtlxQqYO/fY4/feey8LFiwgLc12fc8hQ4awb98+IiIq0aRaETlOHe/JFRVTll7Vf+AM1uzceUw9wtzduYTH9mm3X0TqDEK9O95ipUVk/HC2r13bozi7Km9vNgGh7ccfHdGXnd9/78KIREQc4g3rTxuVXW1qafdGh606YH0GtAfoZ7FYbrCzW7r15x57nyGJOIKfnx9uGPz4Yxn7tmcRERnFrEkT+DpjBdFx7U9w6ao+Q1IBMxEUHhVBaUHPazZ3pLK+ltDQ9hNBoaEhFB0sA6BEK4JEXMKjtwNwJGviZWkvXPdtV19T5Hjn5+fHtGnT+Oijj7jssssOHw8OhvJyc2sXm0aMMF9NTfD557BqFfj7w5w5EBUFQEODWVbo6JJF3377LStWrGDbtm3txuXh4cGIESOort7I3r1TGDSop99URMQhVExZxE79+8cR5hfAlg0bGNVq4kdebj4DJk9ut9/s82ZTUfR6u+dbSxh5GhvXPNrjWLti395covvPavd8eJ9R7Ni40YURiYg4RMuKnL6GYYTYMWG2Ze/yDp+z2DFWOV2bXNNy3Rc6bCXiBFeeN59bzz2PAYP6Ep0Qx+R5k/nbxx8SmxLXeWc7xSUmAhAYGEhEXBTZuzc7bGxbqjtJBIWEhNBsrRddkpPj1FhExHRSrAgSkePTvHnzWLZsWZtj48eDXZNZ3d1h5kxzldCFF5oFgZ56Ct5+m4/fO8js2W2bNzY2cuONN/LII48QHBzc4dBpaWnk5Kxj374ufiERESdRMWUR+82YAYNSJh9TJ6iguITkwYnt9hs/3pvQPmfZdY3TZqbz077cHsXZVXn5RSQObj+3mjJmPD/9tMuFEYmI9Jw1WdOyDf+FHbU1DGOh9e3SjlblGIaxEiiz3r+09z/OB4G/2BOj9R4oBCi3WCwPddZexNHu+vOD7MjfRlFePnH9+jD97LMxgOiU9lcKd1V8fDxgrgiKToqhsrzMYWMfraGhgfqmBgIDA9ttExgYiIG5139x7gGnxSIiRygRJCJOM2fOHD799FMOHTp0+FjfvrB7dwedbAkIgIsuMpNCp52G77uvkfz+U/D11+bSIODJJ58kKiqKiy++uNPh0tLS2LAhg6amLsYhIuJcKqYsYoewMIgZupDPP/+8zfGi6ioGDmp/C5XQUPjlL+27xrRpfcmvKqfOhQUF8ysrSB3S/szf005PZWd+vsviERFxoAcx73M6S8zca23X7j2JYRgzOLJ6p937l5adWwzD6PCa1kRSyyqg6Z3EJ+IUoaGhVNXXUlpaRNLgZMLCwpiYmkpccrLDrhEdHY2ft7e5IqhPLDW1FQ4b+2hlZWUEePliHF3UuRU3Nzf8Pb0ByMvJc1osInKEEkEi4jTR0dEMGTKENWvWHD5mGOaru3YfjOPgZdeZSSFPT3jiCfY99xx/+tOfePbZZzu80WiRnp5ORkZG94MQEXEOFVMWsdPA1DP5ctcuGhsbDx8rO1hFnz6RHfZLTbVv/IAAT2L9w8nMzOxJmF1SXF1Famr7iazJk5MprK5oM8FGROREYF0VNBbAMIy3bLUxDOMFzNXO0zvZ8q0rk1AuAGZYVz8fs3LImlRaj3k/NLa7E2tEeio4OJjaxjrKasuJ6WNOClm5fj1Tp01z2DU8PDzYk52Nr68vIWFhVB+qcdjYRysrKyPA06/TdoEe3rgb7hTmO7dekYiYlAgSEaeaP3/+MdvDweGFPF320Udw9tnWD+PGweLFLH7/fW4ZN44Bq1dDSUmnYwwcOJDCwkJqa523FFpEpBtUTFnETmeeGUV0QCgbWu03W1ZXRZS1nqAjJAbFsL2DuoOOZLFYKKurJK6DotD+/p5E+4exZ4/+sxORE4/1niEFCDEMY71hGHcZhjHGMIyFhmGsB9KwIxljPd+yfdsGOlg9ZLFYyi0Wy1hru93W675gfa0HVmJOhElREkh6k7u7O74e3uyvKiIiIgIw6y7bM9G1K6KjzfuMkJAQqhsOOnTs1srKygj09u+0XYC7D+EBcZSWaJMBEVdQIkhEnGrevHksX74cS6vMT//+sKsbW9zX15ulgzw8jhxbsWIFWzIzuefdd+Gyy+CDD+CJJ+Cnn9odx93dndGjR5OdrVVBInJcaVNM2Y72dhdT7mQcFVOWE86YMdA38YzDdYJqasxZrf7+nT90sFdM1EC2r13rsPE6UllZibubO35+Hc+ejQ+KYaeLklMiIo5mTczMxNyCrRzzniIMuMBisYy1d4KJxWK522KxGNY+Ha0eatMec4u63dbXg0CoxWK5wJ4xRJwtyMuf0rpKIiM7Xt3sCCEhIVTX1zpt/PKyMgLtWBHk4+FPQmxfSqqqnBaLiBzh0XkTEZHuS01Nxc/Pjw0bNjB27FgA0tNhxQoYMKBrYy1fDnPnHvlcW1vLrbfeytKlS/Hx8TEPXnklNDfDp5/CJ5/AkCEwc+Yx+9GlpaWxf38G5eUzCenK408RESexWCzlhmE8BNyFWUx5aXttu1hMeYZhGC1bnthq21JMeWZnMaqYshwv3Nygz6iF/PutG2nOy+NAeTkhPoEOnTkbPWAcW9ctd9h4HcnPzyfMJ6jTdtHRA8n8/ntYsMAFUYmIOIc18dLufY4Tr9vh5BmR3hTo5UdeDYSHhzv9WmYiyHkrgspLKvD19u20nZ9PEIkDBpLx1U6nxSIiR2hFkIg4lWEYzJ8/n+XLjzxICQ6Gysquj7V/PyQkHPm8ZMkSJkyYwMyZRz27dHODWbNg8WKIi4Mnn4TXXoODR2500tPTKSjIYO/erschIuJEKqYsYqdJp/+MCeddSsWgQXiPncm5l7/q0PFnXnIRn61fz6ZNmxw6ri0FBQWE2pEICk0cw45Nm50ej4iIiLhWoLcfQV7+eHg4f85+QEAADc2NHDzo2GTQrl2QnQ3lheX4+na+IijtrLs595LLqXBivSIROUIrgkTE6ebNm8ett97KH/7wh26PsX07DBrU+vN2XnzxRbZs2dJxx2HDzFdREbz+OjQ0AJDW1MSd29eyd4+F0aMdu++uiEh3WVcFjQXWG4bxlsViueDoNk4spvyZdQXRDUevHLImld7CTD5N1z76cjyYMyeA4uIncHeHxEQ491zHjn/6GQlcO/1mrliwgIxt2/D29nbsBVopyM4mxD+s03Z9R6fxyd9fcVocIiIi0juC/AMJruo8eeIIbm5uRPmFkpOTw6DWD1p6aNkb6wgI9KCiqBzfTra7BZh41sVMnVZHZX0NFovF4TWRRKQtJYJExOlOO+009u/fT3Z2NklJSQD4+kJtLdhxbwDAypVw001HPj/88MPcdtttxMbG2jdAZCRce+3hj/3y86m+5x48Xn8YiqwzcPv3N/etCw62b0wRESewWCx7DMNIAd6yFjJ+A7N+UF/MlUDQ/jZvrcfZ0GqruU6LKQNjrauCdhuGsQFoKaSWBozBrEV0nfbRl+NFeLhZK+j009vWD3SU0FCIm/FnknZ+xO/uuYe/PPaY4y9ilbVxK8Hh8Z22mzQ5lacfLnRaHCIiItI7QkLCCC0rctn14oMi2Lplt0MTQZ//+/d4+wYweHQK/gEBnba/9FIwDB88DHeqq6sJDAx0WCwiciwlgkTE6dzd3Zk9ezbLly/n1ltvBSAtDdavNx/edObgQfDyAnd383NhYSHvvvsuO3d2fx9ZIyaGsRMm8GncMObdeA5YLOY65g8+OLJvnYcHJCVBv37mVGMXLNEWEYHDiZmZhmGEYNYLmoG5GucCewspW8e5mw4SQO21t9Yg6ms9vBJYpQSQHI+mTXPu+IsWGRwqW85fHxnB3AULmDx5slOu89/3/svMy//UabsJE+KpOFhLdXU1AXY8YBEREZETQ2hEOCElna8OdpSkPols+XILCy84x2FjFhTvIdAvmKrycPztSOq0LAAK8vanpKREiSARJ9NTTRFxifnz5/Pss88eTgQNHgwvvWRfImj5cpg//8jnF154gYULFxIZGdmjmNLT0/nhhwzgHPMOZMAA89WioQH27YPdu2H1amhsbDtAZCT07WsminTDIiJOoGLKIr3LMODO+5PJ/nYR99/yf3y26TuHXyMnO5sfDuxnxa/mdtrWz8+N+MAoMjMzGT16tMNjERERkd4RmxRLdWVXdnbumYHDB7Fr01aHjrm/uojI5gZqKqoIiQi1u1+QdwClpaUkJyc7NB4RaUuJIBFxiZkzZ3LVVVdRXl5OSEgI7u7mIhx75OdDTIz5/tChQzz77LOsXLmyxzGlpaXxwQcdFJb29DQTPX37HnvOYoHiYjNJ9P77UFVlHrNYwN8fxo41s11ubj2OU0RERHqPYcAv/3oJsye97JTx//WXv5Ce+jNCQ+2rQRQfHEvmDz8oESQiInISufG3i6muqnLZ9YZMHMXXq5532HiHDh2isLYUsFBTVU3ioGS7+wZ5+VFSXOywWETENiWCRMQlAgICOOOMM/j444+5+OKL7e73ww8wbNiRz2+++SbDhw9nWOuD3ZSWlkZOzq1YLEeWJNvNMMwVQZGRMGFC23PV1ea+dy++eCQ5FB8P48dDdHSP4xYRERHXSkzsQ0FNicMLGVssFv7+9ntcedubdveJjEll59q1cMUVDotDREREeldCQoJLrxffry8lNY5bgbRr117CfUMoPlhBdXUVQeH2114O9A2mJC/PYbGIiG1KBImIy8ybN49ly5YdTgQlJEBurvmzPZ9/DrfcYr63WCw89thjLFmyxCHxJCYmYrE0sHHjfsaM6bxAs90CAmDKFPPVIjcXvvoKCq0Fnt3dYehQcys6f3/w8+tGNkpERERcISgoCE83T0pKSoiIiHDYuJszMqisbWDRbZPs7hOalM7Ore84LAYRERE59YSGhlLTcNBh423dvIe+oTHsKG7kQEkeIZEhdvf18w+nNDfXYbGIiG1KBImIy8ydO5e7776b+vp6vLy8GD8evvgCFi603b6mBnx9j+yu9uWXX1JTU8OsWbMcEo9hGAwfnsbKlRmOTQTZkpDQNuPV2Ag//mgmh2pq4OBB+/bKs1ggPBzS0iA5WckjERERF4kJCCMnJ8ehiaDXHnyQ9NEXEhBg/1ay/UaO4b3vHndYDCIiInLqCQkJoaq+1mHj7flxL1EREZQdrCan7ADBXUgEBYREUZCz32GxiIhtSgSJiMvExsYycOBA/ve//zFjxgwiI6GoqP32//0vnHfekc+PP/44t912G24OrLszaVI6336bAcx32Jh28fCAkSPNV1cVF0NGBnz8sfnZMMwiSmlp5hZ0Sg6JiIg4XJRfGNl79zJmzBiHjNfU1MTrqz7jvge+61K/0yYN5KE/FjokBhERETk1hYSEUO3ARND+nXuJjY+jvKKcnaX7CAgOsrtveGws+ft2OiwWEbFNiSARcan58+ezbNkyZsyY0Wnb4mJomXS7Z88e/ve///GPf/zDofFMmpTGihXPOXRMp4uIgKNXRR04YNYlev/9I8cSEyE9HaKiXBufiIjISSg8NJ7sH7fBggUOGe/z998n2CuUa64Z3KV+aWmRNDY1U1JSQnh4uENiERERkVNLQEAA9U0NNDY24uHR88fDhfv2MWJ8IqVFRZAFfn5+dvcNj49h+zddmxgjIl2nRJCIuNS8efOYPXs2Tz75JIZh4OkJ9fXg5dW23YYNMHr0kc9PP/0011xzDQEBAQ6NJy0tjezsdQ4v/uxycXHmq4XFAvv2werVUFAA0dEwd65Zi0hERES6LC55IDs3/eSQsSwWC3+8807GnXlXl381+/sbJARGkZmZqUSQiIiIdIubmxv+nr5UVFQ45H6irPgAfQZOoWh/AazrWiIoKimW7z6o6HEMItIxx+2vJCJih6FDh+Lh4cHmzZsBc2e0LVuObffVV3D66eb7yspKXn31VW6++WaHxxMXF4eHhxfZ2dkOH7tXGYa5Iuiii2DRIpgyBf71L3jiCfjyS/vqEYmIiMhhySOHk5W5xyFjLX/1VYqr65h/0Q3d6h8XmsDOTZscEouIiIicmgK8fCkvL+92/5KSUn558RMAVNaUEtM3hcQBSQD4+/vbPU5cn3Aqamu6HYeI2EeJIBFxKcMwmDdvHsuXLwfMRJA1J3RYVRUEBBwpdfPKK68wY8YMEhMTnRJTUlI6GRkZThn7uBETA9deayaFAgLg6afhuecgK6u3IxMRETkhDB03mJzC/B6P09jYyN13382UOc8yf757t8YIjx1C5rp1PY5FRERETl0Bnn6UlZV1u//Kj7/kvXfvB6CsrpLomBjiBvYFurYiKC4uhMq6g92OQ0Tso0SQiLhcS50gMLeEa2hoe/699+C888z3TU1NPPnkkyxevNhp8aSkpLF27UmeCGphGOaee7feCtdcA1u3wpNPmquFqqp6O7q2mprM5WJvvAGffgqbNpm1kI7+F0ZERMQFRo1OJq+y+w9LWrz0wAPERMQwacocurslf1D8CLIzd/U4FhERETl1BXj5UlbW/RVBP3y9heKGSpYtO0TZoUqioqKItk7g7UoiKDo6hKp6JYJEnE01gkTE5SZPnkxWVha5ubkkJCS0OWexQFkZhIaan1esWEFERAQTJkxwWjzp6Wl88MEjThv/uOXlZdYNAiguhrffhpoa8PQ0VxD17QspKeYKIlcoKIC1a2H/fvOzmxsMGwYzZ0JFBRQWwvr1UFRkOxlkGOYrNBTCwsxXy/vWS8xERES6IT4+hqr6Wurq6vDx8enWGFVVVfzhr3/lihtWc+GF3f+91GfwUD79/olu9xcREREJ9AukcH9ht/vv+WEbTVi48YpEahoPEhkZeXiFUVe2hgsODqZGiSARp1MiSERczsPDg3POOYfly5dz0003ER5u5iEiIuD772H8+CNtH3/8cRYvXozhxIf4M2ak8eCD62lubsbN7RRdKBkRAT//ufm+uRny82HvXvjvf6G6+kg7wwAPD7P+UN++5k9Pz65fr77eXOGzeTM0NprHoqLMf/jz5h3bPizMTEp1prkZSkvNV1kZ/PST+b71d7DVZ/hwOO00JYtERKRdbm5uRPiGsG/fPgYMGNCtMf756KNMHDKSwUPG4uXV/VjS01NY+mhp9wcQERGRU15QUAgFe/O63T9vn1k7sRiulxgAACAASURBVLi6hILiQry8vIiOjsYwDLy9ve0eJzg4mJqGg1gsFqc++xE51SkRJCK9Yv78+bz00kvcdNNNTJhgLgSZPRu++84sYwOwadMmMjMzWbhwoVNjGTUqEh+fEHbv3t3tBzsnFTc3iIszX5MmHXu+vh727YM9e2DNmiOJnKMZhrnEq+V9i6YmczXSqFFw9dXdSyR1FHtEhPnqiowMc4u8oCA4/3wIDnZcTCIictKI9g8jJyen2/cLX378McHJV3LRRT2LY8yYeIqqK2loaMDTkb9HRURE5JQREhZGYW736x8WVhUxMDaJYMODsLAwACIiIvjPP/7RpYSOp6cnnm4eVFdXExgY2O14RKRjSgSJSK/42c9+xi9+8QsqKytJSAjigw+gvBxCQo7kDB5//HFuueUWpz/g8PaGxMQ0MjIylAiyh5cX9Otnvk4WaWnmq6LCLFJVUWEmwdLSejsyERE5jkQGRZOzfTtMn96t/t/s2Mk1Z59JF7bNtyk62pMwnyByc3NJsWfFrIiIiMhRQiMjKc3v/tZw+TUl/HrRHQS2Wv1jGAYXXn55l8cK8PKloqJCiSARJzpF90ASkd4WGBjIpEmT+OSTTw4vHHnvPTjvPPN8fn4+y5Yt47rrrnNJPElJZiJITnHBweYqpUWLzJVPTz4J//xnx1vLOUNzs2uvJyIidgmJ7Ev2Dz90q29eXh4VtYe45JKBPY7DMCAmIJzsrKwejyUiIiKnpvC4KMqLSwDI3r2bokL7k0LNzc1UHKpm0X33cd3dd/c4lgAvP8rLy3s8joi0TyuCRKTXzJs3j2XLlnHBBRdgGFBZae7MBfD8889z0UUXER4e7pJYkpLSWLfu/7nkWnICMAyzZtBpp0FJCbzxBtTUwNSpMGKEc65ZWAgffWT+h+DpabtekaenuWVfQgLEx7ddQiciIk4XnjSUPds/6Vbf71avZlBEf/r3d8z/tyOC48jauhWmTXPIeCIiInJqiU6K4+uPygD4zc9vImlAP5a8/KxdfSsqKvD18MbDwzGPlv09zRVBIuI8SgSJSK+ZO3cuv/nNb2hoaGDCBE/c3c3jdXV1PP/886xevdplsfTpM5aXX95IU1MT7i2BiACEh8M115jL1r74Ap54Anx8IDUVxoyBnixdP3AAPvnETDJFRppL4lqyobbU15t99u+HH38091ME8PODK67ofhwiImKXlFHDWbH0b93q++3y5ST2P8Nh+fuQqIFmIkhERESkG2KTo6msrgRgb9YBKqrqefiee7jzz3/usN/27bBxYxkBXj3c67aVAC8/yoqLHTaeiBxLiSAR6TUJCQmkpKTw1VdfMa3VbNb//Oc/jB49msGDB7sslqioUKKjY9ixYwdDhgxx2XXlBGIY5oqgqVOhqQl27IBly6Cqyjzv6QlDh8KoUeDr2/44OTnw6adQV2eu7rnwQvD3ty8GLy9ITjZfIiLiciNGpvBMaUm3+n6TkUH6bPtm2dojKH442ZnvOGw8ERERObWER4ZRdagWgIKqCn4szOL9TWv45W9+Q0BAQLv9lv7lCdZ+/wFBXnb+HWuHqOhB/PjFF8yZP99hY4pIW0oEiUivmj9/PsuWLTucCLJYLDz22GM89NBDLo0jORkGDjTrBCkRJJ1yd4chQ8xXi4YG2LYN3nwTDh40j3l5mVvJBQXBmjXmip7ERLjsso6TRSIiclwaO7YP+ZVlNDc34+Zmf7nV+vp6NubksuS8CQ6LJTR+MOs35jlsPBERETm1hISEUF1vJoJK6yooP2TWxv3xhx8YP6H9e5bt33/E1l3fMDCsj8NiiR0xh+++eMph44nIsez/60VExAnmzZvH8uXLsVgsAKxZs4aGhgbOOussl8aRkgIxMWmsW7fOpdeVk4inJ4wcCVddBTfeaL4uvdTcUi472zx+yy0wb56SQCIiJ6jISD98PX0oKioCYH9ODl9/9FGn/TZv2kSMfziTJ3ew/WcXDR6Swt7i7q1OEhEREQkNDaW64SANDQ1UWJNABgbrP/+qw34HivdQVV9DaKDj7muGjJ7GN5m7Dj8bEhHHUyJIRHrViBEjaG5u5ocffgDg8ccf57bbbsNw1Ab6doqLg7Awc0WQiMP4+EB6OsycCd7evR2NiIg4QIx/GNnZ2TQ3N3PpWWdxy3XXddrn2/ffZ0D8KBxUTxmA0aP7kFdZQWNjo+MGFRERkVNGy4qggoICQnwCCXH3ZcTAsXz3ydcd9supzDf7h4Y5LJZ58xKpq2+kWHWCRJxGiSAR6VWGYRxeFbRr1y6++eYbruiFovdubtCnzxi2bNlCQ0ODy68vIiIiJ4bIgAhydu3iuf/3/6hvamJ3SQmlpaUd9vl21Srihs12aBwpKV6Eegdw4MABh44rIiIipwZfX18ONTXQp08f6psamD37Tm6/dzE/7vyp3T4lJaXUNtQBEBEd6bBYkpMNQr2DKCwsdNiYItKWEkEi0uta6gQ99dRTXHfddfj5+fVKHN7egSQlJbFt27Zeub6IiIgc/8LCklnz4Yfc//DDvLJ8ORP79+eLTz7psM/X2zM5Y9Z0h8YRGgrR/uFk7d3r0HFFRETk1NB6J5YR/Sby2rI/MPOsaewu289NF1xPeXk5ALm5+cwbezUA336znQHh8fi7eRIZH+3AWCDUJ4iC/HyHjSkibSkRJCK97owzziAzM5NXX32Vm266qVdjSUtTnSARERFpX1BMKs+8/jp3L1pE7v7BhETPYvUbb7TbPj8/n4raOhYsGOjQOAwDIoLjyd6yxaHjioiIyKll2ti5fLVtFQCxsbFYLBaee/vFw1v4P7DoQT7Y8A8qKyv59tN1pCYlE+UbRGxKrEPjCPYLpSA726FjisgRSgSJSK/z9PTk7LPP5pxzziEhIaFXYxk7VnWCREREpH0xg05nyuAh3PzbJWzdCsljLuDz778/pt2hQ4f438qV3H/ttaRG9icw0PH1D0OiBpC1davDxxUREZFTx88X3XD4vWEYpATHAbBz004APv7sLYJ8/Pno/a/Y/v13jJwwiv7JMcSk9HFoHIHBsRR2caXz3r17+ekncys7i8Xi0HhETjZKBInIceHJJ5/kueee69UYwsNh4MB0JYJERESkXWdMn8Vrn/7A66+7c+WV0K//GHLLy9vsaf/uyy8TERTEHddfT3B0NLN+8W+nxBKcMJyszEynjC0iIiInv+3bLVxxZds6hnMWXs6A6L789P1Wmpqa2F9dxCXnzGX5S++Sf+Anhp5+Gi9+8AFnz53r0FiCIxLYv6drK4LuvPxyRg0fzumjRjFr/Hglg0Q6oESQiBwXIiIiCA4O7tUY+vaFgICRbNu2jUOHDvVqLCIiInJ8io+HtWsN/PzMSSRnnOHBqLhBrPnwQwCampq49777eG/ZMr7btZcxM1/mjCmDnRJLUMxgsrWXvoiIiHTToEHHHlvy7O+48tKryNqeSX5+PoFeflxy6/V8lfEBWWX7SR02jKSkJHx8fBwaS1RyMvuzD3Spz4YdO3jvnXcYHhVFUV4e77/zjkNjEjmZKBEkImKVkgJ5eX4MGDCALdpvX0RERGyIj4dXX4WLLzY/DxoEcf3nsPrNNwF486WXiAgOptntZzz+OEycCNOnOyeWqKhksopLutTno0ce4c3bbqOxttY5QYmIiMgJb8jE4Rw4sI/s7Byi/cOYPGUK7p6NxEUFMXCgY+setogf1I/8giK725eXl1NYXc3P5szh2U8/ZfKYMezVlrki7VIiSETEKjQUSkshLU11gkRERMS2yEh4+mlwdzc/GwYkjV7A6g0baG5uZsnvf8/8qx7Fy8vgjjsgKcl5sQwblkhueRnNzc12td+9fj1X/uEPPPHNNwxMTOSpSy/lkBJCIiIicpS+A1IoqCnhp407iQ2JxDAM3v7kQ1Z8+w3uLTdBDpY6pA+7CvPsvq/ZtHEjQ2Pi+eILd378EarrYijOzXVKbCInAyWCRESsDGsN5/R01QkSERER29zcIDGx7bGhQ0dQVFXN03/5C/6+vrj7zGbqVOfH0q+fD0HefuTl5XXatqmpiasWLOC+3/2Or9et4/X33+fV9et55c9/dn6gIiIickLp378/+6uL2PzVevokpQAwJj2d6Ohop11z+vQxBHgH8a9O6kf/+be/5bnHH+exX/+agf3OISwMvv4a8Iknb5+2zBVpjxJBIiJH0YogERER6Yozz3RjRNwQ/u+3v+XSGx5m3DjDJddNSIAY/3Cy9uzptO0jv/gFnpGR3HbHHQBMnDiRSy65hO0bNzo7TBERETnBBAQEkBIcx4pVyxkw0kYhISfw8TGYeNZ9vPvKKx22+8tjj3HT7bezdccOxp37CKNGwfXXQ+LgJAoKil0Sq8iJSIkgEZGjDB8+nMzMTGq1VYqIiIjYIS4O+gw5j+FxcTR5nM/pp7vmusHBEBaUQFYntQ23rF7NI+++y9/ffhs3tyN/Ag4YPZpd2dnODlNEREROQBPSJrGvZB/n/eJCl10zZfB0vt6RicViabfN5AEDALjj5pvx8PA+fDy+bzzFZeVOj1HkRKVEkIhIK25u4OHhzZAhQ9i0aVNvhyMiIiIniHEz7+K5t39gyBDXrAYCc1vbsL6nsezFFzt8YPLAXXfx29//nqSkJDZsgOefh2XLwHAbQGZBocviFRERkRPHnQ/fy9+eepEhw4a57JqLFiViaTLYu3dvu20aGxr49e23c96N9xEYeOR4UnIEJTU1LohS5MSkRJCISCvx8XDggLaHExERka5JTHTnzTeDmDXLtdedNud3ZDc3c/9559k839jYyMpt21h4ySUcPAhr1sANN8C4cbB7d1+yS0tobGx0bdAiIiJy3Bs8fChX3PwLl14zMNCgX1gSW9av54Ff/YqhiYk0NDS0aVNafZBJM8/nnXd8WLjwyPG+fSMoO1jt0nhFTiRKBImItJKSAnv2QHp6uhJBIiIiYrepU+Gcc8xVOq7k5eXH+6tW8fr33/Py7bcfc37dV1+REBpKXFwcL70E115rxhgbC3Pn+hDmG0ROTo5rgxYRERFpR3BwHHmZmezeupVt+/bx3//8p8350qpDfPhhEMHB4ONz5Hh8fDgVh2o6XCUtcipTIkhEpJXkZMjK0oogERER6ZqgIDjzzN65dlRUFB+tWcOvX3mFNa+/3ubcJy+/zKxZs/j+e0hNNeNs0acPxATEsGvrVhdHLCIiImJbWFQSOdt3UVRYzMRRaaz617/anK8+dBAIYsGCtv18fX3xcHOnoqLCdcGKnECUCBIRacXPDw4ehCFDhpCdnU1WVlZvhyQiIiLSLk9PqK+HgQMH8tgzz/D73/++zfmPv/qKMxdewv/+BzNntu3r5QWR0YPYtXat6wIWERER6UDcgAHk7N5HTmEFHoHXs3LdOgBefOABsrOyqG04xO9/H4i//7F905PHMXfSJBdHLHJiUCJIRMQGT09P/vjHP5Kens4LL7xAc3Nzb4ckIiIicoz4eGjZ2W3hhReSWVzMFmtip6SkhG35+eTnT+bqq233D0kYRebmza4JVkRERKQTKcMHsD8vn4KqCu68czr5FVVUVlZy75/+xNXnnENNw0ECAwNt9p1z/dts15a3IjYpESQi0o5f/epXrF69mpdffpnp06eze/fu3g5JREREpI0pU+Ddd2HXLnMiy4033sjT99wDwKo33mDKsGHU1HgTEWG7f1jCSHbt2+fCiEVERETaN3hoAnmV5ZQerOTMM2OI8gvn66+/Btz4NjMTd8MNLy8vm339/UMpq63VZF4RG5QIEhHpwLBhw/jmm2+YPXs248eP59FHH6Wpqam3wxIREREBzCLJd94JX30Fn30G1y9ezFtr11JaUsLH//43U8+9mICA9vtHRfUns7DQdQGLiIiIdCA1NZY9ZXl4uXvg7+9HTEAEy955h8SARKJ8w/Dz9G237/Dhnni7eVFZWenCiEVODEoEiYgcxdsb6uqOfPbw8OD//u//+Pbbb1m2bBmTJk3ixx9/7L0ARURERFoxDLj6arNWUGZmNLOnTuXl3/yGT7ZuxSvoXGbNar9vQkI/skpKNNFFREREjgvR0VE0NjdR02A+mAkPT2LZu++SmDiCaP9w/Dy82+17+ukQ5O1PaWmpq8IVOWEoESQicpSkJMjOPvb4gAEDWL16NVdffTVTpkzhj3/8Iw0NDa4PUERERMSGs8+G77+HW++/nwf+/nf8vLwwjH5ER7ffp39/H8L9AsnRfvoiIiJyHHB3d+eaS55l5qhzAQiLH0x+WRn9J11FZFgSAe4eHfYP8lIiSMQWJYJERI6SkgJ799o+5+bmxo033siGDRv45ptvSEtLY/369a4NUERERKQd48YBjGdgQgIzp56Jd/uTZgHzvichNI5dGze6IjwRERGRTo2c+EtmX/0eACmjRhLl7cf5F84kLC4V3w62hgMI9PajpLjYFWGKnFCUCBIROUqfPtBZzeTExEQ+/PBD7rjjDs4++2zuvfde6lrvJyciIiLSCyZPhq+/hn+uWMH4cx5l5syO2yckQHDYIHatXeuaAEVEREQ6cfPNcPnl5vvzL5rHkHGfMH68O/3GpuHpHd5h30DfYErz8lwQpciJRYkgEZGjeHiAPdvkG4bBlVdeyZYtW8jMzGTkyJHs2LHD+QGKiIiIdGDECKirG0R1dRzJyR239fCA4ITRZG7Z4pLYRERERDrj5gbh1nzP4MGBTJg0GXd3uOTqi5h93Ucd9vUPiKA0N9cFUYqcWJQIEhHpoZiYGN5++21uuOEGrrrqKhVbFhERkV41fTp88omZ5LFHRPwwdu3f79ygRERERLrB2xv+9Cfzfd++HkyZEtFhe5+AKIoPHHBBZN1XV1eHxWLp7TDkFKNEkIiIgyxevBgvLy+effbZXrl+Q0MDO3fuZPny5Tz88MNce+21nHvuufzwww+9Eo+IiIj0DsOAsWPNhJA9IiL6k1lU5NygRERERLrJMMyfXl4wbVrHbYMiY8nLOb4TQZdOmcKj993X22HIKcbOOWIiItIZNzc3li5dyuTJkzn33HPp06ePU65TUlLCjh072LFjB9u3bz/8fu/evcTHxzNo0CBSU1NJT0+nrq6OadOm8dhjj3F5ywa7IiIictKzNwkEEBnZj6ySEpqamnB3d3deUCIiIiJONnr6Qv7066d5vK4OHx+f3g7nGHV1dXy6aRMbdu1i8ZIluvcSl1EiSETEhqAgqKiA4OCu9UtNTWXRokXcfPPNLFu2DKNl2ooDrFq1issuu4y6ujpSU1MZNGgQgwYN4oorrmDQoEH079/f5k3OtGnTWLhwIV999RWPP/74cXkjJCIiIr0nJMSXCP8A9uXkkJyS0tvhiIiIiHRbWvpoUuP78o8nnuD6u+/ulRie/sMfWHjDDcTExBxzbs2qVfQLSaS6sYqtW7cyatSoXohQTkXaGk5ExIaUFNi7t3t977nnHnbv3s3bb7/tsHiys7O5/PLLee211ygvL2ft2rX84x//4Ne//jULFixg2LBh7SZ4RowYQUZGBsXFxUyePJmsrCyHxSUiIiInvuRk6BObzK7ly3s7FBEREZEeCQuD8298lIceeYSKigpqa2tdev26ujru/OMfefWvfwWgubmZ3bt3Hz7/4pIljEi/isTg/mz66issFguD+/ShSNv0ipMpESQiYkPfvt1PBHl5ebF06VJuu+02ysrKehxLXV0dCxYs4K677mLmzJndWmUUFBTEW2+9xeWXX8748eP54IMPehyXiIiInBySkyFp5ByefOklmvPyejscERERkW5LTgbcp5E+fDjR4eFcP2eOQ8ZtaGiwefymSy8lNSHh8OdvvvwSL09PXnj5Zd586SVmpaUxfPBg/njLLTy3ZAn/2/oDk+cuJrbfaWxcvZrc3Fy25+by1eefOyROkfYoESQiYkNUFBQUdL//pEmTOPfcc7nrrrt6FIfFYuHmm2+mf//+3H777T0ayzAMFi9ezLvvvsuNN97Ir3/9axobG3s0ZlccOnSIl156iSVLllBTU+Oy64qIiEjH4uPhjDN+Q3lICPdfcgm086DDFUry81n20EPcd/bZ/P/27js8iqpv4/g9JBg6ofcWinQlAQEVLBSlSG8iIIqAPoLKq4I8YkFUmg0pUhQRfVAMvUkkiogoLYiIoCBBegkl9AAJ8/4xGwyQhE2ydfb7ua69NtmdnXOCZ3Zv9zfnzNsdO2rWf/+rdfPnKykpyWt9AgAA/iMkRCpWTHpjSpSWR0drydq1On36dJb2mZCQoDKFC+vgwYM6duyYvpo5U1euXNH58+f10Zdf6q8DByRJ27dt02sDBqhRzZ564tF+GvDcczp/9qwWLvle8xct0osjRujZIb+oa9c8qn1fE62P2aKtv/0mSVqzYEGW/3YgPRSCACAVrri0z8iRI7V8+XKtWrUq0/uYNm2a1q1bp48//thl1xu66667FBMTo3Xr1ql58+Y6kpWKlxPOnz+vDz/8UJUqVdKcOXO0bds21ahRQ4sXL3ZruwAAwDlBQVK2bLdozty5+jw2VpF9+7pkvytmzND8MWO0f9cumaapw3v2aPrzz+uRevX0wRNPKP74cUnWGbZfvPqq6pYtqwoVKuijBQsUcscdOlWhghb+9pv6PPecqhQrpg+eeEKnXTDbGgAA2FunTtLXX2dXuXL3KqJMmFZ++22W9he1aJGOnD6tmHXr9EC9eurft6+ily3T3r17ValIEeUJCdGq77/X3XXrql379gpvMV4lbxulJVE/qtuAFdr6R21t3rdfBXLmVakytRQaKnV9+C79efiQFn7xhYrmDNOqNetc9NcDqaMQBABukj9/fo0fP179+vVTQkJChl+/fv16DRs2TPPmzVOePHlc2reiRYsqKipKd911lyIiIrR69WqX7l+STp8+rVGjRiksLEwrV67U/PnztXz5cs2aNUvTp0/XCy+8oPbt22vv3r0ubxsAAGRc0aJFNX/hQv1nwQJtW7gwy/t76sUXNT4yUuF16qhI3ryqXr26orZvV+MnntD6o0dVoUwZPVK3rioVK6bpy5ZpxJQpOnHmjJb//LNeGz5co995R7OXLtXWPXv0vyVLtPbwYZUrVUoPVK+u19q21XeffSbTNF3wlwMAADvJlk3q21davVrKEVJJuzdvztL+Fk6dqsJ58+m9t95SQkKCxr75piYNH649u3crf1AhFc9ZTJ3btdPYN99Ui16j1LBhiAoXlpatCFeRYuU0aFA+Fc0VqrJ5y+qxx6x9VqiQR03q9tKU2bPVrNnj2nrogC5cuOCCvx5IHYUgAEhDgQLSRx9JmzdLmf2OoV27dqpRo4beeuutDL3u6NGj6tSpk6ZNm6YqVapkrvGbCAoK0ogRIzRt2jR16tRJ77zzjku+TDl+/Lhee+01VaxYUb///ruio6M1f/581a1b9+o2999/v7Zs2aLw8HCFh4fr3XffTXO9XQAA4Dl16tTRM4MGaaLjAseZdfLkSR05c0Yr1q7VkVOntGXHDh2Jj9fsZcvUv39/zVq0SNtjY1W/Z0/NiYrS9xs3qkWLFgoODk51fw0aNNBXS5Zox549enrUKF2uUkWPPvusor7+Okv9BAAA9lS0qNSrl5S/eFXt3vZnlvb19549yl+gs36IiVGvPq9r76n/aPW2bfpx+XIVDi2t0gVKKbthqHClZ/TLL1Lz5lLr1tKrr0pdulj7KJ+/pEqWjbhmv62fmKDnB/2o/3vtGZXPV0Ib1l07K+jo0aNa9OWXunz5shbOm5el72xeHzBE0UujdOhgnA4fOpbp/cB/UQgCgDR07WqdQXL2rDRpkjRxorR0qZTREzQmTJigyZMna+vWrU5tn5iYqG7duqlnz55q27ZtJnqeMS1atND69ev19ddfq0OHDlq+fLn++usvXbx4MUP7OXz4sF588UVVqVJFBw4c0C+//KL//e9/qlmzZqrbh4SE6JVXXtHatWsVFRWliIgI/fzzz674kwAAQBb06NVLkb/+qsuXLmV6HxvXrFF4uXIKCgqSYRgqWbKksmfPfs02xYsX1zPPPqt69eo5vd8iRYqoTZs2envsWI1+/32NHDbshm08eQ1EAADg28rVqqVdO3dnaR//HDup2+v1Utd7myu4QF91755bzcJb6u0PP1T+opVVtmoTdWvdW1euBKtPH2vZXcmamZS8yn+95m+pUafnrtlvjx7Z1KJVI91+e15VKVdPa66bkT38ySfVtWdPtapfXx07dVL/Ll20ctmyDPU9Li5Ofdu104RpH6lj+/ZqUucuPdOx3w3bnTx5MlOr2cB/UAgCgHQEB0t33y09/bR1q1ZNmjVLmjBB+uwz6eDBm++jZMmSGjFihPr27evUhY6HDh2q7Nmz64033nDBX+CccuXKafXq1apdu7bee+89tWrVSvny5VOZMmXUuHFj9e7dW2+88Ya++OILrVmzRocOHbp6JsrevXs1YMAAVa9eXRcvXtTmzZv18ccfq1KlSk61XalSJUVFRenll19W586d1a9fP504ccKdfy4AALhOaKiUvFprhQoVVKlCBUVPmpTp/W1YvFj1GjRwUe9S17VnT+2Lj9fP0dFXH/t761YVzpNHLapX1zfTpunKlSuZ3n/ckSOaNWKEHm3QQA3KldOGFStc0W0AAOBBNcMra/fRuEzPprly5YoOnz6lN9+8QxUaROnuu7OpenWpUuMxkqT8ZcurUYcRKlFnnNq1S3s/rbq1VftONa55LDhYatLEKhhVvrOdVq1YefW5hIQEzVy6TPfUbqPQXIXVsfVi7dyyQ48+0kPnz593uv/LFyxW9Ir1mvH5InVp3lHbj+7U9p2/SZJM09SiyEidP39e/Vq1Uf826fwB8HsUggAgA8LCpD59pAEDpA4dpHXrrJlCkyZJGzemvYRcv379FBQUpMmTJ6e7/8jISM2ZM0ezZs1SUPIpJB4SEhKinmiYOwAAIABJREFU4cOH69tvv9Xff/+tc+fO6aefftLw4cPVuHFjXbp0Sd98841eeOEF3X777cqdO7eqVq2qOnXqKHfu3Nq+fbs+/PBDlSlTJsNtG4ahrl27atu2bQoJCVH16tU1c+ZM1v0HAMBDOneW5s6V/nSsnNK9b1/NmjUr0/vbsH696j3wgIt6l7rg4GC9OHSoRj7/vCTp0qVLerhlS7388svq+sILenn0aNUoUUJHDh3K8L5jd+5UlfLlNXvFCtXv0UNPvvqqWrZvry9GjpQknYqP15jHH1fzqlV17OhRl/5dAADAderVK6dtR/epTpkyOnPmTIZff/ToUeXOnlO33ppDSUlS/frW461aV1CbO59Wm64dVbGiVLJk+vt58EEpva9Luj/eRL/8vVNnz56VJP31118qnLOg2vefp7u7fKspM1up72u/KX9QQa3+4Qen+79q3gq1btVJrbvcq7FfjNdXn3ymv+MP6MyZM3qsZUu17dJFcz//XN/G/KoFq37Url27nN43/IvBl2y+qW7duubGjRu93Q0ATrpyRVq1Sjp0SOrePfVttm3bpsaNG2vz5s0qXbp0qs/fc889ioqKUnh4uJt7nHVnz57VP//8o1KlSqlAgQIu3ffGjRvVv39/5c2bVx999JGqVavm0v0jfYZhxJimWffmWwLOI9sAvs80pU8+kW67TSpb9ohurVBBB48cUa68eTO8r9IFCmjVxo2qWLFipvqxebN0+LB07px08aI1K7tWLem61eWUkJCgCsWK6dvvv9f/xozR1v37tfinn2QYhkzT1OAnn9T+LVv05S+/ZKgPfe6/X6Vq1dIb48ZdfWzr1q1q26SJqhcurJ//+UcP3nef8hUsqN/XrFH0H38oR44cGf5b4RlkG7gD2QbwD6ZpKlu2bGpet64iatTQ2zNmZOj1GzduVPfmHbTjxN4bnuvSRZo+Xcqd2/o9eRm4zCqdp4gOnz+uhbNn69SZM5ryxhSt+ufa6wa1r9dVEQ1Katj493XlyhXt2rVLlStXTnOfESWq6pWJ76pdh1b/tpO3qJ54pq/mfzxLhcv21P7903XpfJJqVWqk6rXza9Sn07L2h8DtMpNtmBEEAC6QLZt0331SrlzSpk2pb1O9enUNGDBATz/99A0zXU6fPq0OHTpo7NixflEEkqQ8efKoZs2aLi8CSVLdunW1fv16dezYUY0bN9aqVatc3gYAALiWYUhPPCH9+qt0+XIxNahTR4vHjs3wfg4dOqQLly8rLCwsQ69bt85afnfSJOuajDVrWvmqTRvp8mVpxgxp8mRp6lTrNmGCFBKSQ88NHKje7drp86gofbpggQzHtzCGYWj4++9rQ2ysln3+udP9iN25UwvXr9eg11+/5vGaNWtqw/btuu/RRxXzxx/635IlmjhjhkqGhalPs2bMZAYAwAcZhqFJk0z1GPi+lqVYTtZZ+3bvVpHchVJ9bsYMKU8eK0NltQgkSe3ajNTDncbqhYED9fuq1Spe9vYbtolo1kxrvl8jSRry+OOqUbWqDqUx+3nvnj3669ge3Xn3tddjrFi4nObNnqNK5Rtq4ud9tS8uTh06vq7nRv9X02dHatbkyRrcq1eGlqCD76MQBAAu1K6dNTPo5MnUnx86dKh27NihuXPnXn3MNE317t1b9913n3r37u2ZjvqBoKAgDRw4UF999ZU6deqkNWvWeLtLAAAEhEcflZYskbr3769ZCxZk+PUbV65U3YoVrxZkUoqPl778Ulq61LrWomlKK1ZI770nJSX9e13GO++0lk8pVEjKm9dahqVvX+nJJ6V+/azbAw9ICxdKTw0erMPnzmnGV1+pSJEi17SXK1cuTZ45U08984zTy8G81b+/nu7T5+rJLgcPSgsWSImJUsGCBfV/gwerfPnykqTTp7Pps0WLtCsuTq/27k0xCAAAH/T331LcsfrafeyEhvbsqfj4eKdfu2tjjAoVrpDqc7lyuaqHlm7/eUIvDhukAyfPaNl3P6j2vY1u2Oahro20Ydd2vfvWW/oicqEiyjbRw/c31T+xsTds27FxCz3eeaCKFi16zeOVq9bQ77t2qNodt6lq1TKaNees3vmkv+5vervCCldR3wHPKnLed1ocOfeGfcJ/sTScj2KKMeC/Ll6U3n1Xeukla6bQ9X766Sd17dpVf/zxh0JDQzVq1CgtWLBAq1atUkhIiOc77AeioqLUs2dPLVq0SA3cfOFpsHwK3INsA/iX8eOlnj1Pq1yJYtq9c6cKprKsbVpefeQRXQkN1UO9JmrzZuuxK1esQkpoqNSypXT2rLX82/79UqNGUu3amevnuHHSU09JQUFJCgoKkmlKH39snZUbEWHtNyhI6t2mjXImJanXoEHau3mzLpw9q56vvHLDNRl37dih+uHh2rlvn37+uYBiY6USJaQ6daR586wC1V13WbOXVq+29l23rlSlyhE1veMONbj1Vk1YvJhM52PINnAHsg3gXxITpZ4tXtC5s2tkJCVp4fr1Tr2ua4NGKlq9i8ZPH+jmHv7r7nJ19cfh7fpt536VLXvtKiymaarjPa/r1IGlavrIKHXvU09d7+2k22oU1JQls69u99vmzWra8F4dOnNMwcHB1+xj0jtT9fSL/bVgwbdq27bZNc/9GrNfq6K26fihjYpe9pXeGD9KTVu0SPUEH3hPZrINhSAfRaAA/NvevdK331rLq6TmySeflGma6ty5s3r16qX169enet0g/GvZsmXq3bu3li1bprp1+f94d+LLErgD2QbwL7/9Jp04IX0yuatKHT2q0StXOv3aFjVq6Mm33tK+/e00YIAbOynp6FFp2TIpeVL1lClS8+ZSqVLWcr1RUdYsouDg42rRsKGMK1dUtkwZ/RUbq+6tW+uliROv2d/j992nMrVrq8Pj43TggFW0Smn1aqsIdMcdUuPG1mPz5lkFrnr1zujRhx7SkX37NHf1ahW/2VWj4TFkG7gD2QbwP+PGSaVLn1LvR4opLj7eqev7VS5UUu9MX6q2bet4oIeWYc8s0OEDp/Tx3EdTff7iRSsDlSlj/f7zz5vU7cEW2nv6yNVtujVupfyFwjRl/vgbXr9hw0bdcUc9xcbGqkKF1Gc7HTp0WM1r3afTF0/owWYt9N7nE5U7+WJI8DoKQTZCoAD834oVUkjIv18SpHTq1CnVqFFDCQkJmjt3ru655x7Pd9APLVy4UP369dPy5ctVp47nQlig4csSuAPZBvA/48ZJ3bvHKbxWLU3p21ctR4y46WtM01SRvHn1w9od2rKlpLp3d38/p0yRunWTvv9eKlnSWkYuWVKSNGqUNVM75eSfffv2qW716lo4f74aNG0qSfrs7bc1dMwYbY39R9OmhWrIEOf7sGiRtf8WLa7ojRde0Beff64/9u9nZpCPINvAHcg2gP/ZuVM6c0bq+UAFTfhymu5zZIC0XLhwQQXy5tepc2cVEnKLh3opxcVZxR5nzxc2TVPFcxdS9NofVKt2bcXHx6tM0ZLauXe3ihcvdsP2Z86cUclCpXTy/IkbZgvd2JdjurNqhM5eOq+Dp48yM8hHZCbbcI0gAHCTZs2krVul1K7Zlz9/fs2cOVMffPABRaAMaNu2rSZNmqQWLVro999/93Z3AACwtdBQKXv2IpoVGanHP/xQ+5y4Xt8/u3crJDhYv/5a8obZNO7Ss6f03/9KwcHXFoEkqzjTp480deq1j5cpU0aTP/5Y3bt21alTp/Tuc8/p1Xff1fdr1+qbb0IzXMBq08a6ntF772XTM8PeU5WyZfXJyJFZ+8MAAIBLVa4shYdL1aq30tjBg/VQeLja1K+f5jX+1vzwg8JCS3u0CCRJRYo4XwSSJMMw1KxhB73y1HP6c9s2zZoyQ+Gla6VaBJKkvHnzau+RuJsWgay+FNaOY//IvHJF27dvd75T8DkUggDAjfr3l6ZPt9aivd7999+vHj16uK3tS5dSL0L5u44dO2rcuHFq3ry5tm3b5u3uAABgW23bSgsXSo0aNdKgoUPVtXt3XT56NN3XbFi+XHWrVtWpU1YhyRNy5ZJee0166KHUny9eXKpRw1pCbv166ZNPpEmTpDaduurBZs1Ut0IFfRwZqZ82b1ZoaFVduvTvUisZ0aCBNHCgNHu21PqxiRr5wQe6ePFi1v44AADgcg/2fEfZb8mpe1q10Z4Dh/TVlCk3bPN027bq16OHbqvTwQs9zLjXJr+qrVt3qfXdTfXJh5PV6//Sv6ZRgQLOz1o2DEN3Vq+vLyd8kdVuwosoBAGAGwUFSf36SZMnu2f/V65Y1yOKjrYujDxlitXW5MnS559Lv/wiTZggffSR9Mcf7umDMy5fllaulCZOtL54+eor6fjxzO+va9euGjt2rJo1a6Y///zTdR0FAABXhYZKp05ZP784eLBKhocrvE4dLR00SOalS6m+ZmNUlGo2uFcFCqT6tNsULZr+840bSzlzStmyST16SB06SOPHS+9++qk69uih1b/9pmLFymjaNGuGUWaFhEhPPSUZQQ1UM6ySPn7rrczvDAAAuEXHjjlUs8kaGaGvq8EDX+jFIS9p199/X33+2LFj+nz5Cl1IMPT44P5e7KnzKlcuq53x/yg4W25duHxF3ft0dOn+uw7sreULF7p0n/AsrhHko1hrFrCXX36R4uOlFi0yv48zZ6QFC6Rz56TkJVkNw5ouXKWKVL68tSRKahITpR9/lLZts74AadRIqlnz3/24Q1ycdZ2k+HirX40aSVWrWm0eP249d/y4VSxr0EC67baM92fGjBkaNmyYVq5cqcqVK7vnDwlArKMPdyDbAP5p61bp11+t4ohpmlq0aJFeevFFFbtyRW/36aM7hwyxwoVpasXrr+vRcePUZ+Bi/d//NfJ4MSijfv9d2rJFeuQR64LLU6dKTz8tl/Q7Pl4aO2adPpv0gP4+fNipi1HDfcg2cAeyDeDfkpKs7yMOHJBe7v9fLVk5Ttt271bRokX1Uu/eWr/2sB4f9o169PCva+KcPXteOXKEKDg46OYbZ8CZM2dUrGARxcUfV+7cuV26b2RcZrLNzRcCBABkWcOG0owZUmysFBaWsdeePSt9+aVkmlLXrlL+/BlvPzhYuv9+65aUJK1ebc3OyZZNuvtuqVatrBeFTFP67Tdp7VqrjSJFrMJXal+mFCpkXdRZsopU69ZZs5ZM0ypsNWki5clz8zZ79+6ty5cvq0mTJvrhhx8UltF/XAAAkK6aNaXTp6U5c6ROnQy1bdtWrVq10owZM9T99ddVZcYMDe7WTV9/842i9u/Xp7Nna+dO3y8CSVb+OXzYykSJidJLL6V9Uk1GhYZKZcrWV+2KlfXJW2/p6REjXLNjAADgEkGOOkmpUlLvF97Wkf1/qknt2jqXmKgzFy5rxtd/qVUr/yoCSVKePLncst+8efOqaqHy+nbJMhUtXFhnTp7Sg53auaUtuAczgnwUZ5YA9mOa0qhR0qBBkjMnhZ4/bxWALl+WHn44cwWgm0lKkn76yToj1jCsglXx4lZfk/uc8ufr703TOlN43z7rsdtus2b3BGXhxJP9+6XvvrNmPoWESM2aSWXLpv+aSZMmacyYMVq1apXKlSuX+cYhibNm4R5kG8C/ff+9lU1at/73sUuXLmnmzJl6d9QoNbrnHr3z/vtKSsqnpUut5df8xd9/S5UquX6/p05JY0Zv0NRx9+qTDz9Umz59XN8InEK2gTuQbQB7mTfvuBbOjVKFyhGqWLG8evZ0/ho6gWL4c29pzbdLteNgrLJny66dJ/Z5u0sBKzPZhkKQjyJQAPZ0+rQ0bZr0/PNpb3PhgnUNnYQEqwDkqQstJyVZF1A+dsz63TCuXYIurZ9vvVVyV+0lIUGaP9/6uVu39Gctffjhhxo3bpxWrVql0qVLu6dDAYIvS+AOZBvA/33/vXXNwcqVpaZNb5w9Y5rSu+9Kjz1mzf6Fdf3GCuV+VP+eHdU8PFzvzZvHcipeQLaBO5BtAHsxTeniRedO3A1UcXFxKlGsuBpUqq+/9/+p3DlC9PzQIapQPkwtOrfxdvcCSkAvDWcYRqikfpKapXh4k6SRpmnG261dAP4pXz5rhou1vMq1zyUkWAWgc+esAlDBgp7tW1CQNSPIl+TIYf1b/PWXNHq0dfHltGZGPfPMM7p8+bIaN26s9u3bq1SpUipduvTV+xIlSuiWW27x7B8AAICNJC8zu2OHdWJLYqI1E7huXes6QtHRUocOFIFS6t5dGj++sTb+uUvPP9ZDERUqaP6KFap2223e7hoAAEjBMCgC3UyRIkW0afMO1aoVpp9Wb9UHr76tpwcP0h2la+jBTg/pl9WrVbpcOZVlpRafZIsZQYZhdJI0TdJU0zSHpHi8n6TRkoaYpjnVn9rlzBLA3iIjpWrVrHX3L16UZs+2lg/p1s26tg5ulJAgTZ5sFavq1097u6ioKG3ZskUHDhzQ/v37r94fOXJEBQsWvKY4lHx/xx136NZbb5WR1Qsl2QRnzcIdyDaA/ZimNZt43Tor1zRrdvPXBKLDh6VZs6wldPf+OVFDhgzRJxMn6qFHH/V21wIG2QbuQLYBEOguXbqkdWs364EmjdXzofaauXCuWoQ30rwN33m7azeVkJCgbNmyueyE4RVz5+rQvn3q+eyzHvluKSCXhnMUXaZI6mya5pxUng+XFCNpTMpija+3S6AA7O+dd6yiz6lTUteuUrFi3u6Rf/jmG+ngQWvZmWzZnH9dUlKSjhw5ckOBaO/evVq9erVuueUWtWzZUi1bttS9996rnDlzuqS/x48f1759+1S4cGEVKVJEISGuWWf4woULOnLkiA4fPqzDhw/r3nvvVaiL1hHkyxLfYLfZzmQbAIEuJsaaNVW75hr17dFaPVu21NOjRql0mTLe7ppXmKapp7p10y0hIfpgxgxly0iwyyCyje+wU74h2wCApUWdh3TyxFF9GDlZzRs10p6jBzRrwgQ1atlSNevU8Xb3UtWx4V3ac+igvvtts/Jn4aLcFy5c0KNNm+qHzVuUP2c+3VqmqFq3b68nX33Vhb29UcAVggzDCJO0S9Ic0zQ7p7PdaEmDJUWYprnJH9olUAD2l5BgFYEoAGXcvn3S559Lffq45t/PNE1t3bpVy5Yt09KlS7V582Y1atToamGoQoUKTu0nLi5OMTEx2rRpk2JiYhQTE6OTJ0+qbNmyOnHihOLi4pQzZ04VLVpURYoUSfM+f/78OnHixNUiT2q3CxcuqHjx4ldv7733nipWrJj1fwzxZYkvYLYzANjT5cvSxx9LBQocUvSs/pr33XeqXaqUevTure7PPadcuXJ5u4tpunDhgkzTdFkfx77yij6fNkO5c+bQrbWr65N58xQUFOSSfV+PbOMb7JZvyDYAcKMaxarq7MU4JSZmV7UyZRS9fcM1z48ZNEi177xTOfPnlxITFd6okX7duFGlypZV8eLFXX4txaSkJE14/XW1fewxlQ8LkyTN/fRTPfmfQSpXuJq6dGuswWNH3/C648eO6eD+/ap1++3p7n/amDF6d8wUhTcYqKeGPKF3hr2hlWsn6Ej8cZedYJyaQCwERUrqpJsUWhxnfpyUFGuaZpa/JfNEuwQKAEhfYqJ1fYKqVaX77nPtvk+ePKkVK1Zo2bJl+uabb1SwYEG1bNlSrVq10t13361bbrlFhw8fvqbgs2nTJp0+fVrh4eGKiIi4eqtYseLVM1xN09SpU6d09OhRxcXFpXkfHx+vQoUKXVPouf4WGhrqtunGfFniXcx2BgD7+/lna0m9okUvKunSEkV+NFrrtm9X/44d9Z+331aJkiWv2T4xMVE7d+7UxYsXdfnyZRmGoYIFC6pQoULKly+f2zLBxg0bNG/aNP24cqU2792rkOBgPdqhg54ZMULly5e/ZlvTNDXhrbd0Ii5OQ0aPVo50LrSwdN489enVW88O3aKg7EW0dFp9lShfQp8vW6bs2bO7/O8g23ifHfMN2QYAbrR7d5xe7Pu2Jn81TBVKltHmbVtUsVIlSdL6NWvU/P7muph0SYVzhSoh8aKyBxs6ce68cmbPrmqlSiv8tlq6tUZNDRwx3CX9eb57D82Yt1j5cgarcP58uqtBfc1e8q1eG7VExUoE6cmezfTKi4P0UK9eKlexohITEzWwfXst+GGVLieaGvL0k3rxnbGSpG+XLFGjJk2uFnguXryoKsVKacjwL/WfZ/+dcBpRspbuax6hNydPVo4cOZSQkKD5n32m0IIF1aJzmnNKMiSgCkEpiizxpmkWcGL7GEnhyuKsIE+1S6AAAOesWiVt3Sr16ye54XsDXblyRZs2bdLSpUu1bNky/fnnn8qTJ48uXLhwtdiTXPwJCwuzxXWG+LLEe5jtDACBJS5O+uEH6zpCp0/v0O61/1Vk9FLVKllSbdu0UaV69bR42jQt2rBBBXLlUs7styibEaSkJFOnEs4r/sI55cqeXU893E1PjhihYlmcKp2YmKj9+/cretEiTX7vPcWdOqv6VVqoZHg3Vbv9Xp0+FafVswZr9V9L1aJhAw2fMlmVK1fWxYsX1b9jR61b95uK5S+pI+f2aXrk12p499037P+n1avVqdVD6t9/gd56v6lMU5o8OUELJt6jX/ds0wMNG+rBRx7Rg61bq1ChQln6e5KRbbzLrvmGbAMA6Rv4yOuKXvGJNu7+U6/17asvFy9Vz0fHKbR0hFq1ulWHD5/Shg0HdTJ2jfbF7paCgrVv90btOLhec5cuUPyhQ3ro4YdlmqbTS8gmJSUpavFiRX32mfKEhmrirK+14qfteq7nSwoODtKVhEN678uvVK9eYUnSU72na+P3Hyko6LSmL52v/737vpYsW69uz8xUg/r51L5FTUXOj9ShAwfU98mnVLVEad12a0X1HDBAS7+eo9Wrdyhm/7Wznr6Y+Yfe++8jOnF2jy5euSJJKpmnrHo89bQGvfKkS/5tA60QNFjWFN5o0zRvellSwzCmyFoPdqppmv19vV0CBQA4Ly7Omh3Uvbt03cmpLnf06FGdP39e5cqVs0XRJzV8WeI9zHYGgMB19qy0eLF05EiCdu2M1pEtH+vI4Z0qW6OrKof3VtGiZZU/v1SggJQrl7XM3KVL0sYNf+jHyJe1fue3uqtimArmy6s8efOqat266jdsmFNLuU0ZM0YjR4/WodOnVThXXlUqWEG1739ZrTq3U7Nm2ZRyxTbTlH788YzGDx2i7zZ9ps4PNtcff/6lKxfy690vo1WyZG6N+L+pWhL1gqqWLqHCBQqoQKFCOnDggNb8+ZcK5whVq5avaPys/1zTh9mzpb937tbRzZ/q7+2L1POFZ9Xtscdc8m9LtvEuu+Ybsg0ApM80TTWp2VLnLu/V7v0H1bvPNI0Z3+mmr6tX/k6dOr1Pl5ISdfryGV1OTNS8OV+rSevWNy0IfTRylEa+OVa31eqgy+ePq/Xjz2jAc/dKkhw1mRuuN52YmKR65e7U3uPbZBjZ9P26Hapd2zq55uVnp2viRwNVJFdB9X32Ha1cskSxe7co9vhWhRWsqLk/rFHNmkVu6Mfhwxc1sP9nqlP/LuXOHaynn75VwcE3/zdzVqAVglZIaionCywpCjhOzeTxdrsECgDIGNOUZsywvhipVs2aHXTLLdZ9yp+T7920BL0t8GWJdzDbGQCQLCnJmvF88KB0zz1WvkmPaUrR0cc1b+5qXbpwUolnj2vHpvnaHfeH3hj2kh5/4QUFp/Htw/jhwzX6nXHq+Z9olS1fS+XLZ1e9elLhwjfv5y+/HNfoAc/qlhz59cny8cqbN3k5XGnWrJPatH6DLp3cr4T4/cqer4zqN2utNm2KqEA6nzZHj1rL5t13n5Qnz8374AyyjffYOd+QbQDg5s6fT1Cd0jV1zz3tNHX+O0695vRpKThYOnfusjZsOK4dW37Vm8O76cyl8+pwdyPt33tAzw77rzr1efTqay5duqQXe/TUpwsWaeaX36tdx4YZ6uelS9I//5zSnj0n1axZ+WueO3bMVOHC1onAyaWUWbP+VLt2VZQ7t3MzlVwt0ApBJyWFyrqo3xgntu8kKdLxawHTNON9uV0CBQBkzj//SIcOWWfJJp8pm9p98pkgpmndUk7uyZ3bmllUvrxUokTGikbnz1szlI4ete7j4qSEBOs5w7CKUMHB1i355+vvs2WTzpyxws/p0//2NTWmaX051KtXBv+h0sGXJd7BbGcAgKtN//gXfTDsCe07tUe1S5ZWxO01ddu99+i2Ro1UrVo1TXjjTb37wSRN+mKD2rUP83Z33YZs4z12zjdkGwBwzsWLScqePZuyZcv8qipHj55XbOxhjXz2TZULD9esT19S9VKlVK5EcT3+8kua8OZY7d5zVmNmRKpp03Iu7L1vyky2ceGEJM9xnNkR6vg11smXpdwuTFKGzyzxVrsAAOclF3Cy4uxZac8e6bffpG++SbsQk1w8Sj6nwjCknDmlIkWsW61a1tm0jusI6soVKTHx39vly6n/nJQklS0r5csn5c3L7KUAkvwlhbMZY5fjvoukTH9R4sV2AQBu9vgTDfVYnz+0du0Brfj2V23/6Qf9Om62/hk2UgfPHVPBkPxa+uMmhUfY/wsTeA35BgACXEhI1r/UKFo0l4oWDdPCddMlSUGXLitX0Qo6sPNPdWzfVRWLVdPqv1Ypd+6cWW7LrvyyECSpYBZfn9mCjLfaBQB4UJ48Uo0a1s2VsmWzlqa75RbX7he2kXw2z650t/pX8hcboYZhhGZ2trMX2wUAeIBhSA0bllLDhqUktb76eIJjynKOHDm81DMECPINAMDl3v9kUIrfXvJaP/yJdxaxy7rQFD87++GccrvMFnS81S4AALAxF8069pt2AQDelyNHDopAcCvyDQAAvsNfC0FZLaiE3nwTn2oXAADYmytmHftTuwAAwP7INwAA+Ah/LQR5q6Di1nYNw+hnGMZGwzA2xsXFubMpAAAWeH1VAAARGElEQVTgW5jtDAAA7IZ8AwCAj/DXQlBmPpRPpPi5kC+2a5rmVNM065qmWbdIkSKZaAoAAPgpZjsDAAC7Id8AAOAj/LUQlBneOqODM0kAAMDNMNsZAADYje3yDdkGAOCv/LUQdOLmm6TruJ+1CwAA7I3ZzgAAwG5sl2/INgAAf+WvhSBn13h19eu91S4AAMD1mO0MAADshnwDAIAb+GshKCXbTTUGAAABh9nOAADAbsg3AAD4CH8tBKX8UHf2rI2UhZvMhgJvtQsAAOyN2c4AAMBuyDcAAPgIvywEmaa5KcWvzs7MCUvxc6w/tQsAAAIKs50BAIDdkG8AAPAivywEOSSfoVHRye2vzuC5rqDjL+0CAAD7YrYzAACwG/INAAA+wp8LQdGOe2c/1JMLN1ktxnirXQAAYFPMdgYAAHZ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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def MultiplicativeBM(z,t,lam=1,mu=2):\n", " drift,diffusion,diffusionprime=lam*z,mu*z,mu\n", " return drift,diffusion,diffusionprime\n", "\n", "NT=2**11 #Timesteps\n", "M=10 #MC sampling\n", "lam=1\n", "mu=2\n", "\n", "time=np.linspace(0,1,NT)\n", "W,DW=np.zeros((NT,M)),np.random.randn(NT,M)\n", "for i in range(NT-1): W[i+1]=W[i]+np.sqrt(time[i+1]-time[i])*DW[i]\n", "z0=np.random.rand(M)\n", "\n", "\n", "rc('font',**font)\n", "fig,ax=subplots(1,3,figsize=(3*figheight,figheight),num='Samples')\n", "\n", "every=2**6\n", "z= Euler_Maruyama(MultiplicativeBM,z0,time=time[::every],W=W[::every,:],args=(lam,mu))\n", "z2= Euler_Milstein(MultiplicativeBM,z0,time=time[::every],W=W,args=(lam,mu))\n", "a=ax[0]\n", "i=1\n", "t=time[::every]\n", "a.plot(t, z[:,i],'b',lw=0.4,label='Maruyama')\n", "a.plot(t, z2[:,i],'r',lw=0.4,label='Milstein')\n", "ztrue=z0[i]*np.exp((lam-0.5*mu**2)*t+W[::every,i]*mu)\n", "a.plot(t, ztrue,'k',lw=1,label='True')\n", "a.legend()\n", "a.set_xlabel('$t$')\n", "a.set_ylabel('$X_t$')\n", "a.set_title('%d Steps' %(NT//every,))\n", "\n", "every=2**4\n", "z= Euler_Maruyama(MultiplicativeBM,z0,time=time[::every],W=W[::every,:],args=(lam,mu))\n", "z2= Euler_Milstein(MultiplicativeBM,z0,time=time[::every],W=W[::every],args=(lam,mu))\n", "a=ax[1]\n", "i=1\n", "t=time[::every]\n", "a.plot(t, z[:,i],'b',lw=0.4,label='Maruyama')\n", "a.plot(t, z2[:,i],'r',lw=0.4,label='Milstein')\n", "ztrue=z0[i]*np.exp((lam-0.5*mu**2)*t+W[::every,i]*mu)\n", "a.plot(t, ztrue,'k',lw=1,label='True')\n", "a.legend()\n", "a.set_xlabel('$t$')\n", "a.set_ylabel('$X_t$')\n", "a.set_title('%d Steps' %(NT//every,))\n", "\n", "every=2**2\n", "z= Euler_Maruyama(MultiplicativeBM,z0,time=time[::every],W=W[::every,:],args=(lam,mu))\n", "z2= Euler_Milstein(MultiplicativeBM,z0,time=time[::every],W=W[::every],args=(lam,mu))\n", "a=ax[2]\n", "i=1\n", "t=time[::every]\n", "a.plot(t, z[:,i],'b',lw=0.4,label='Maruyama')\n", "a.plot(t, z2[:,i],'r',lw=0.4,label='Milstein')\n", "ztrue=z0[i]*np.exp((lam-0.5*mu**2)*t+W[::every,i]*mu)\n", "a.plot(t, ztrue,'k',lw=1,label='True')\n", "a.legend()\n", "a.set_xlabel('$t$')\n", "a.set_ylabel('$X_t$')\n", "a.set_title('%d Steps' %(NT//every,))" ] }, { "cell_type": "markdown", "metadata": { "ExecuteTime": { "end_time": "2018-12-23T02:45:43.273284Z", "start_time": "2018-12-23T02:45:43.255669Z" } }, "source": [ "##### Example 2: Langevin Dynamics in a Double well\n", "$$dX = -V^\\prime(X) dt + \\mu X dW$$\n", "$$V=-a_2 x^2/2+a_3 x^ 3/3+x^4/4$$\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2019-02-06T03:40:38.824920Z", "start_time": "2019-02-06T03:40:38.790957Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,'$a_2=2.00 , a_3=0.00 $')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def V(x,a2=1,a3=1):\n", " return -a2*0.5*x**2+a3*(1/3)*x**3+0.25*x**4\n", "\n", "def Vprime(x,a2=1,a3=1):\n", " return -a2*x+a3*x**2+x**3\n", "\n", "def WwellDiff(z,t,a2=1,a3=2,mu=0):\n", " drift,diffusion,diffusionprime=-Vprime(z,a2,a3),mu,0\n", " return drift,diffusion,diffusionprime \n", "\n", "rc('font',**font)\n", "fig,ax=subplots(1,1,figsize=(1*figheight,figheight),num='New')\n", "a=ax\n", "a2=2\n", "a3=0\n", "x=np.linspace(-2,2,1000)\n", "a.plot(x,V(x,a2,a3))\n", "a.set_xlabel('$x$')\n", "a.set_ylabel('$V$')\n", "a.set_title('$a_2=%0.2f , a_3=%0.2f $' %(a2,a3))\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2019-02-06T03:40:40.820267Z", "start_time": "2019-02-06T03:40:38.827118Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,'65536 Steps')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def Doublewell(z,t,a2=1,a3=2):\n", " drift,diffusion,diffusionprime=lam*z,mu*z,mu\n", " return drift,diffusion,diffusionprime\n", "\n", "NT=2**16 #Timesteps\n", "M=15 #MC sampling\n", "a2=1\n", "a3=0\n", "mu=1\n", "\n", "time=np.linspace(0,50,NT)\n", "W,DW=np.zeros((NT,M)),np.random.randn(NT,M)\n", "for i in range(NT-1): W[i+1]=W[i]+np.sqrt(time[i+1]-time[i])*DW[i]\n", "z0=np.random.randn(M)\n", "\n", "rc('font',**font)\n", "fig,ax=subplots(1,3,figsize=(3*figheight,figheight),num='Well Samples')\n", "\n", "every=2**7\n", "z= Euler_Maruyama(WwellDiff,z0,time=time[::every],W=W[::every,:],args=(a2,a3,mu))\n", "z2= Euler_Milstein(WwellDiff,z0,time=time[::every],W=W,args=(a2,a3,mu))\n", "a=ax[0]\n", "i=1\n", "t=time[::every]\n", "a.plot(t, z[:,1],'b',lw=0.4,label='Maruyama')\n", "a.plot(t, z2[:,i],'r',lw=0.4,label='Milstein')\n", "#ztrue=z0[i]*np.exp((lam-0.5*mu**2)*t+W[::every,i]*mu)\n", "#a.plot(t, ztrue,'k',lw=1,label='True')\n", "a.legend()\n", "a.set_xlabel('$t$')\n", "a.set_ylabel('$X_t$')\n", "a.set_title('%d Steps' %(NT//every,))\n", "\n", "every=2**2\n", "z= Euler_Maruyama(WwellDiff,z0,time=time[::every],W=W[::every,:],args=(a2,a3,mu))\n", "z2= Euler_Milstein(WwellDiff,z0,time=time[::every],W=W,args=(a2,a3,mu))\n", "a=ax[1]\n", "i=1\n", "t=time[::every]\n", "a.plot(t, z[:,1],'b',lw=0.4,label='Maruyama')\n", "a.plot(t, z2[:,i],'r',lw=0.4,label='Milstein')\n", "#ztrue=z0[i]*np.exp((lam-0.5*mu**2)*t+W[::every,i]*mu)\n", "#a.plot(t, ztrue,'k',lw=1,label='True')\n", "a.legend()\n", "a.set_xlabel('$t$')\n", "a.set_ylabel('$X_t$')\n", "a.set_title('%d Steps' %(NT//every,))\n", "\n", "every=2**0\n", "z= Euler_Maruyama(WwellDiff,z0,time=time[::every],W=W[::every,:],args=(a2,a3,mu))\n", "z2= Euler_Milstein(WwellDiff,z0,time=time[::every],W=W,args=(a2,a3,mu))\n", "a=ax[2]\n", "i=1\n", "t=time[::every]\n", "a.plot(t, z[:,1],'b',lw=0.4,label='Maruyama')\n", "a.plot(t, z2[:,i],'r',lw=0.4,label='Milstein')\n", "#ztrue=z0[i]*np.exp((lam-0.5*mu**2)*t+W[::every,i]*mu)\n", "#a.plot(t, ztrue,'k',lw=1,label='True')\n", "a.legend()\n", "a.set_xlabel('$t$')\n", "a.set_ylabel('$X_t$')\n", "a.set_title('%d Steps' %(NT//every,))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2) Euler-Maruyuma vs Milstein : Assesment of strong convergence" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2019-02-06T03:40:47.629782Z", "start_time": "2019-02-06T03:40:40.823327Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "NT=2**12 #Timesteps\n", "M=10000 #MC sampling\n", "\n", "time=np.linspace(0,1,NT)\n", "ttime=time.copy()\n", "ttime.shape=NT,1\n", "ttime=ttime@np.ones((1,M))\n", "\n", "## PRESCRIBE BM\n", "W,DW=np.zeros((NT,M)),np.random.randn(NT,M)\n", "for i in range(NT-1): W[i+1]=W[i]+np.sqrt(time[i+1]-time[i])*DW[i]\n", "\n", "## PRESCRIBE SDE : MODEL AND INITIAL CONDITION\n", "lam=1\n", "mu=2\n", "z0=np.random.rand(M)*0+1\n", "\n", "## STORE ERROR AND DT\n", "err_tab,dt_tab=np.zeros((8,2)),np.zeros(8)\n", "\n", "## COMPUTE APPROXIMATE SOLUTIONS\n", "for i in range(8):\n", " every = 2**i\n", " z= Euler_Maruyama(MultiplicativeBM,z0,time=time[::every],W=W[::every,:],args=(lam,mu))\n", " z2= Euler_Milstein(MultiplicativeBM,z0,time=time[::every],W=W[::every,:],args=(lam,mu))\n", "\n", " ztrue=z0*np.exp((lam-0.5*mu**2)*ttime[::every,:]+W[::every,:]*mu)\n", " err_tab[i,0]=np.sqrt(((ztrue[-1,:]-z[-1,:])**2).mean())\n", " err_tab[i,1]=np.sqrt(((ztrue[-1,:]-z2[-1,:])**2).mean())\n", "\n", " dt_tab[i]=every/NT\n", "\n", "#PLOT ERROR VS DT\n", "fig,ax=subplots(1,1,figsize=(1*figheight,figheight),num='Strong Convergence')\n", "rc('font',**font)\n", "\n", "a=ax\n", "a.plot(dt_tab,err_tab[:,0],'bo',label='Euler-Maruyama')\n", "a.plot(dt_tab,err_tab[:,1],'ro',label='Milstein')\n", "\n", "a.plot(dt_tab,err_tab[0,0]*(dt_tab/dt_tab[0])**0.5,'b--',label='$\\propto t^{1/2}$')\n", "a.plot(dt_tab,err_tab[0,1]*(dt_tab/dt_tab[0])**1,'r--',label='$\\propto t^{1}$')\n", "\n", "\n", "a.set_xscale('log')\n", "a.set_yscale('log')\n", "a.set_xlabel('$dt$')\n", "a.set_ylabel('$<|X_{true}(1) -\\\\tilde X(1)|^2>^{1/2}$')\n", "a.legend()\n", "a.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2) Euler-Maruyuma vs Milstein : Assesment of weak convergence" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2019-02-06T03:40:47.792126Z", "start_time": "2019-02-06T03:40:47.631517Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "NT=2**9 #Timesteps\n", "M=100 #MC sampling\n", "\n", "time=np.linspace(0,1,NT)\n", "ttime=time.copy()\n", "ttime.shape=NT,1\n", "ttime=ttime@np.ones((1,M))\n", "\n", "## PRESCRIBE BM\n", "W,DW=np.zeros((NT,M)),np.random.randn(NT,M)\n", "for i in range(NT-1): W[i+1]=W[i]+np.sqrt(time[i+1]-time[i])*DW[i]\n", "\n", "## PRESCRIBE SDE : MODEL AND INITIAL CONDITION\n", "lam=1\n", "mu=2\n", "z0=np.random.rand(M)*0+1\n", "\n", "p =1\n", "## STORE ERROR AND DT\n", "err_tab,dt_tab=np.zeros((12,2)),np.zeros(12)\n", "\n", "## COMPUTE APPROXIMATE SOLUTIONS\n", "for i in range(0,9):\n", " every = 2**i\n", " z= Euler_Maruyama(MultiplicativeBM,z0,time=time[::every],W=None,args=(lam,mu))\n", " z2= Euler_Milstein(MultiplicativeBM,z0,time=time[::every],W=None,args=(lam,mu))\n", "\n", " t0=time[::every][-1]\n", "\n", " ztrue=np.exp((lam-0.5*mu**2)*p + 0.5*p**2*mu**2)\n", " err_tab[i,0]= np.abs(ztrue-np.mean(z[-1,:]**p))\n", " err_tab[i,1]= np.abs(ztrue-np.mean(z2[-1,:]**p))\n", "\n", " dt_tab[i]=every/NT\n", "\n", "#PLOT ERROR VS DT\n", "figheight=10\n", "fig,ax=subplots(1,1,figsize=(1*figheight,figheight),num='Weak Convergence M=100')\n", "\n", "a=ax\n", "a.plot(dt_tab,err_tab[:,0],'ro',label='Euler-Maruyama')\n", "a.plot(dt_tab,err_tab[:,1],'bo',label='Milstein')\n", "\n", "a.plot(dt_tab,err_tab[0,0]*(dt_tab/dt_tab[0])**1,'k--',label='$\\propto t^{1}$')\n", "#a.plot(dt_tab,err_tab[-1,1]*(dt_tab/dt_tab[-1])**1,'b--',label='$\\propto t^{1}$')\n", "\n", "\n", "a.set_xscale('log')\n", "a.set_yscale('log')\n", "a.set_xlabel('$dt$')\n", "a.set_ylabel('$|(1) -<\\\\tilde X(1)>|$')\n", "ax.set_title('Average over %d realizations ' %(M,))\n", "a.legend()\n", "a.grid()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2019-02-06T03:40:50.696892Z", "start_time": "2019-02-06T03:40:47.793355Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "NT=2**9 #Timesteps\n", "M=100000 #MC sampling\n", "\n", "time=np.linspace(0,1,NT)\n", "ttime=time.copy()\n", "ttime.shape=NT,1\n", "ttime=ttime@np.ones((1,M))\n", "\n", "## PRESCRIBE BM\n", "W,DW=np.zeros((NT,M)),np.random.randn(NT,M)\n", "for i in range(NT-1): W[i+1]=W[i]+np.sqrt(time[i+1]-time[i])*DW[i]\n", "\n", "## PRESCRIBE SDE : MODEL AND INITIAL CONDITION\n", "lam=1\n", "mu=2\n", "z0=np.random.rand(M)*0+1\n", "\n", "p =1\n", "## STORE ERROR AND DT\n", "err_tab,dt_tab=np.zeros((12,2)),np.zeros(12)\n", "\n", "## COMPUTE APPROXIMATE SOLUTIONS\n", "for i in range(0,8):\n", " every = 2**i\n", " z= Euler_Maruyama(MultiplicativeBM,z0,time=time[::every],W=None,args=(lam,mu))\n", " z2= Euler_Milstein(MultiplicativeBM,z0,time=time[::every],W=None,args=(lam,mu))\n", "\n", " t0=time[::every][-1]\n", "\n", " ztrue=np.exp((lam-0.5*mu**2)*p + 0.5*p**2*mu**2)\n", " err_tab[i,0]= np.abs(ztrue-np.mean(z[-1,:]**p))\n", " err_tab[i,1]= np.abs(ztrue-np.mean(z2[-1,:]**p))\n", "\n", " dt_tab[i]=every/NT\n", "\n", "#PLOT ERROR VS DT\n", "figheight=10\n", "fig,ax=subplots(1,1,figsize=(1*figheight,figheight),num='Weak Convergence M=10000')\n", "\n", "a=ax\n", "a.plot(dt_tab,err_tab[:,0],'ro',label='Euler-Maruyama')\n", "a.plot(dt_tab,err_tab[:,1],'bo',label='Milstein')\n", "\n", "a.plot(dt_tab,err_tab[0,0]*(dt_tab/dt_tab[0])**1,'k--',label='$\\propto t^{1}$')\n", "#a.plot(dt_tab,err_tab[-1,1]*(dt_tab/dt_tab[-1])**1,'b--',label='$\\propto t^{1}$')\n", "\n", "\n", "a.set_xscale('log')\n", "a.set_yscale('log')\n", "a.set_xlabel('$dt$')\n", "a.set_ylabel('$|(1) -<\\\\tilde X(1)>|$')\n", "ax.set_title('Average over %d realizations ' %(M,))\n", "a.legend()\n", "a.grid()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2019-02-06T03:40:50.715162Z", "start_time": "2019-02-06T03:40:50.699408Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "
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