{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Monte Carlo法以及MCMC\n", "## 简单的Monte Carlo\n", "令$\\left(x_1,x_2\\right)\\in\\left[-1,1\\right]\\times\\left[-1,1\\right]$,以及:$$h\\left(x_1,x_2\\right)=\\frac{1}{2}\\exp\\left\\{ -90\\left(x_1-0.5\\right)^{2}-45\\left(x_2+0.1\\right)^{2}\\right\\} $$\n", "为了计算:$$I=\\int h\\left(x\\right)dx$$\n", "我们可以先在$\\left[-1,1\\right]\\times\\left[-1,1\\right]$的均匀分布中进行抽样,其密度函数为$f\\left(x\\right)=\\frac{1}{4}$,从而数值积分为:$$\\hat{I}=\\frac{1}{N}\\sum_{i=1}^{N}\\frac{h\\left(x_{i}\\right)}{f\\left(x_{i}\\right)}=\\frac{4}{N}\\sum_{i=1}^{N}h\\left(x_{i}\\right)$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Intgral= 0.0236223188067\n", "s.e. of Integral= 0.0014760911681\n", "95% C.I.: 0.0207291801172 ~ 0.0265154574962\n", "Ratio of >0.01 samples: 0.0475\n" ] } ], "source": [ "import numpy as np\n", "from numpy import random as nprd\n", "\n", "##设定参数\n", "M=10000\n", "h=lambda x: 0.5*np.exp(-90*(x[0]-0.5)**2-45*(x[1]+0.1)**2)\n", "\n", "##抽样\n", "x=[(nprd.random()*2-1,nprd.random()*2-1) for i in range(M)]\n", "\n", "##计算h(x)\n", "sample=list(map(h,x))\n", "integral=4*np.mean(sample)\n", "se=4*np.std(sample)/np.sqrt(M)\n", "subsample_001=list(filter(lambda x: x>0.01, sample))\n", "print(\"Intgral=\",integral)\n", "print(\"s.e. of Integral=\",se)\n", "print(\"95% C.I.:\",integral-1.96*se,\"~\",integral+1.96*se)\n", "print(\"Ratio of >0.01 samples:\",len(subsample_001)/M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 重要性抽样\n", "### 算法1\n", "首先,我们可以使用一个工具分布,比如$x_1\\sim N\\left(0.5,\\frac{1}{180}\\right)$,$x_2\\sim N\\left(-0.1,\\frac{1}{90}\\right)$进行抽样,假设该联合分布函数为$m\\left(x_1,x_2\\right)$,然后计算$$\\hat{I}=\\frac{1}{N}\\sum_{i=1}^{N}h\\left(x_{i}\\right)\\frac{\\pi\\left(x_{i}\\right)}{m\\left(x_{i}\\right)}$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Intgral= 0.0246826829898\n", "s.e. of Integral= 3.14956233782e-20\n", "95% C.I.: 0.0246826829898 ~ 0.0246826829898\n" ] } ], "source": [ "import numpy as np\n", "from numpy import random as nprd\n", "\n", "##设定参数\n", "M =10000\n", "h1=lambda x: 0.5*np.exp(-90*(x[0]-0.5)**2-45*(x[1]+0.1)**2)\n", "domain=lambda x:(x[0]>=-1)*(x[1]>=-1)*(x[0]<=1)*(x[1]<=1)\n", "pai=lambda x: 1/4*domain(x)\n", "h=lambda x: 4*h1(x)\n", "mu1=0.5\n", "mu2=-0.1\n", "sigma1=np.sqrt(1/180)\n", "sigma2=np.sqrt(1/90)\n", "m=lambda x: 1/(2*np.pi*sigma1*sigma2)* \\\n", " np.exp(-1*(x[0]-mu1)**2/(2*sigma1**2)\\\n", " -(x[1]-mu2)**2/(2*sigma2**2))\n", "\n", "#从m(x)中采样\n", "x=[(nprd.normal(mu1,sigma1),nprd.normal(mu2,sigma2))\\\n", " for i in range(M)]\n", "\n", "## 计算积分\n", "H=list(map(lambda x:h(x)*pai(x)/m(x),x))\n", "integral=np.mean(H)\n", "se=np.std(H)/np.sqrt(M)\n", "print(\"Intgral=\",integral)\n", "print(\"s.e. of Integral=\",se)\n", "print(\"95% C.I.:\",integral-1.96*se,\"~\",integral+1.96*se)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 算法2\n", "在重要性抽样的第二种算法中,为了计算第一部分的积分,我们首先使用拒绝采样法,从$$g\\left(x_1,x_2\\right)\\propto\\exp\\left\\{ -90\\left(x_1-0.5\\right)^{2}-45\\left(x_2+0.1\\right)^{2}\\right\\} \\cdot1\\left\\{ -1\\leq x_1\\leq1\\right\\} \\cdot1\\left\\{ -1\\leq x_2\\leq1\\right\\}$$\n", "中进行抽样,然后使用公式:$$\\check{I}=\\frac{\\sum_{i=1}^{N}\\frac{h\\left(x_{1i},x_{2i}\\right)}{\\left|h\\left(x_{1i},x_{2i}\\right)\\right|}}{\\sum_{i=1}^{N}\\frac{1}{\\left|h\\left(x_{1i},x_{2i}\\right)\\right|}}=\\frac{\\sum_{i=1}^{N}\\frac{h_{1}\\left(x_{1i},x_{2i}\\right)}{\\left|h_{1}\\left(x_{1i},x_{2i}\\right)\\right|}}{\\sum_{i=1}^{N}\\frac{1}{\\left|4h_{1}\\left(x_{1i},x_{2i}\\right)\\right|}}=\\frac{4}{\\frac{1}{N}\\sum_{i=1}^{N}\\frac{1}{\\left|h_{1}\\left(x_{1i},x_{2i}\\right)\\right|}}$$\n", "计算该积分。(详细推导过程见讲义,注意该方法是错的。)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Intgral= 0.254715617302\n" ] } ], "source": [ "import numpy as np\n", "from numpy import random as nprd\n", "\n", "##设定参数\n", "M =10000\n", "h1=lambda x: 0.5*np.exp(-90*(x[0]-0.5)**2-45*(x[1]+0.1)**2)\n", "domain=lambda x:(x[0]>=-1)*(x[1]>=-1)*(x[0]<=1)*(x[1]<=1)\n", "pai=lambda x: 1/4*domain(x)\n", "h=lambda x: 4*h1(x)\n", "l=lambda x:np.exp(-90*(x[0]-0.5)**2-45*(x[1]+0.1)**2)*domain(x)\n", "\n", "##拒绝采样法的参数\n", "mu1=0.5\n", "mu2=-0.1\n", "sigma1=np.sqrt(1/180)\n", "sigma2=np.sqrt(1/90)\n", "m=lambda x: 1/(2*np.pi*sigma1*sigma2)* \\\n", " np.exp(-1*(x[0]-mu1)**2/(2*sigma1**2)\\\n", " -(x[1]-mu2)**2/(2*sigma2**2))\n", "x_star=mu1\n", "y_star=mu2\n", "R=l((x_star,y_star))/m((x_star,y_star))\n", "r=lambda x: l(x)/(R*m(x))\n", "\n", "##拒绝采样,从g(x)∝l(x)中采样\n", "def sampling(N_samples):\n", " X=[]\n", " for i in range(N_samples):\n", " while True:\n", " #从m(x)中采样\n", " x1=nprd.normal(mu1,sigma1)\n", " x2=nprd.normal(mu2,sigma2)\n", " #拒绝\n", " if nprd.uniform()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from numpy import random as nprd\n", "\n", "##设定参数\n", "M =20000\n", "alpha=0.5\n", "beta=0.5\n", "domain=lambda x:(x>0)*(x<1)\n", "pai=lambda x: x**(alpha-1)*(1-x)**(beta-1)*domain(x)\n", "q=lambda y: 1\n", "#从均匀分布中采样\n", "def sample_q():\n", " return (nprd.uniform())\n", "\n", "\n", "##独立的MCMC算法,输入:\n", "## N_samples : 抽样次数\n", "## pai(x) : 目标密度函数\n", "## q(y) : 工具密度函数\n", "## q_sampler : 给定x,从q中抽样的函数\n", "## x0 : 初始值\n", "def MH_independent(N_samples, pai, q, q_sampler, x0):\n", " X=[]\n", " x=x0\n", " for i in range(N_samples):\n", " y=q_sampler()\n", " rho=min(1,pai(y)*q(x)/(pai(x)*q(y)))\n", " if nprd.uniform()<=rho:\n", " X.append(y)\n", " x=y\n", " else:\n", " X.append(x)\n", " return X\n", "\n", "## 计算积分\n", "x=MH_independent(M, pai, q, sample_q, 0.5)\n", "## 取h后面80%的样本\n", "subx=x[int(M*0.2):]\n", "## 诊断图\n", "import matplotlib.pyplot as plt \n", "%matplotlib inline\n", "# 设定图像大小\n", "plt.rcParams['figure.figsize'] = (15.0, 8.0)\n", "index=[i for i in range(len(x))]\n", "plt.plot(index,x,label=r'MCMC Samples x',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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JyiAWsuySLGRFVAZOIkmSJGm3KistZNnECZkkSZKUQXJ9QhZFUX4URdOiKPpbKgM1FwuZJEmSlEFyvZABNwCzUhWkuVnIJEmSpAySy4UsiqIewL8B96c2TvOpJLFkpoVMkiRJygC5XMiAu4D/AmpTmKVZOSGTJEmSMkQcw+bNuVnIoij6LLAijuMpu3ncNVEUTY6iaHJpaWmTBUwVC5kkSZKUITZvTtzm6IWhjwXOjaJoIfA4cHIURY/s+KA4ju+N43h4HMfDu3Tp0sQxm56FTJIkScoQVVv22XNxQhbH8XfiOO4Rx3Fv4BLgH3EcX5HyZClmIZMkSZIyRC4XsmxlIZMkSZIyRBYXsoI9eXAcx+OAcSlJ0syShayIysBJJEmSJO1S5ZZ99iwsZE7InJBJkiRJ6S2LJ2QWMguZJEmSlN4sZNnHQiZJkiRlCAtZ9qkkcQ0DC5kkSZKU5ixk2WczhYCFTJIkSUp7yUKWoxeGzkq15FNNvoVMkiRJSndOyLJTFS0sZJIkSVK6s5BlJwuZJEmSlAEsZNnJQiZJkiRlAAtZdrKQSZIkSWFF0e63yy9O7LMffHiLeh/LdDlfyIqoDB1DkiRJ0i4k99mT1xLOJjldyCpoSUsqQseQJEmStAvJffbktYSzSU4XsnJa0Yry0DEkSZIk7UJyn30TrQMnaXo5Xcg20ZrWbAodQ5IkSdIuJPfZy2kVOEnTy+lC5oRMkiRJSn+tKKeKQmooCB2lyVnILGSSJElSWmtFeVZOxyDHC5mHLEqSJEnprzWbsvL8McjxQuaETJIkSUp/TsiylBMySZIkKf05IctSTsgkSZKk9OeELEslJmTlQBw6iiRJkqSdcEKWpZItO3nlb0mSJEnpxwlZlkq2bM8jkyRJktJXazZZyLJR8ofqeWSSJElS+mpFuYcsZiMnZJIkSVL6c0KWpZyQSZIkSenPCVmWckImSZIkpT8nZFnKCZkkSZKU3iJqaUmlE7JsZCGTJEmS0lvyElVOyLKQhyxKkiRJ6S25r24hy0JOyCRJkqT0ltxX95DFLOSETJIkSUpvTsiymBMySZIkKb05IctiTsgkSZKk9OaELIttppAa8pyQSZIkSWnKCVlWi9hEaydkkiRJUppyQpblymnlhEySJElKU8l9dQtZlnJCJkmSJKWv5L66hyxmKSdkkiRJUvpyQpblymnlhEySJElKU07IstwmWjshkyRJktKUE7Is5yGLkiRJUvpqRTmbKaCawtBRUiLnC5mLekiSJEnpqzWbsnY6BhYyJ2SSJElSGmtFuYUsmzkhkyRJktJXazZl7YIeYCFzQiZJkiSlMSdkWc4JmSRJkpS+nJBlucR1yMqBOHQUSZIkSTtwQpblkm27JRWBk0iSJEnakROyLJds255HJkmSJKUfJ2RZLvnD9TwySZIkKf14HbIslxx/WsgkSZKk9OOELMttpA0AbdgYOIkkSZKkHRVTRhnFoWOkTM4XsvW0A6AtGwInkSRJkrS9mLZsqNtnz0Y5X8g20BawkEmSJEnpphXl5FNbt8+ejSxkW3647VgfOIkkSZKkbSX30S1kWcwJmSRJkpSekvvoFrIs5jlkkiRJUnpK7qN7DlkWS67YYiGTJEmS0osTshwQk0cZbTyHTJIkSUoznkOWIzbQ1gmZJEmSlGackOWI9bSzkEmSJElpxnPIcoQTMkmSJCn9OCHLERYySZIkKf0k99E30iZwktSxkJEoZC7qIUmSJKWXdqxnA8XEWVxbsvcr2wOeQyZJkiSln7ZsyOrzx8BCBnjIoiRJkpSO2rIhq88fAwsZYCGTJEmS0pGFLEdsoC2tqKCAzaGjSJIkSdoicQ6ZhSzrJY9LdUomSZIkpQ/PIcsRydZtIZMkSZLSh4cs5ggLmSRJkpR+LGQ5IvlD9lpkkiRJUvrwHLIc4TlkkiRJUnoppIoiqjyHLBd4yKIkSZKUXpL75k7IcoCFTJIkSUovFrIcYiGTJEmS0ouFLIe4qIckSZKUXpL75p5DlgM204IKipyQSZIkSWnCCVmO2UBbC5kkSZKUJixkOcZCJkmSJKUPC1mOWUd7OrA2dAxJkiRJQHvWAYn99GxmIdtiNZ3oyJrQMSRJkiQBnVhNDXku6hFFUcsoiiZFUfRuFEXvR1F0a3MEa25r6GghkyRJktJER9awlg7EWT5DKmjEYyqBk+M4LouiqBCYEEXRi3EcT0xxtma1mk50YnXoGJIkSZJITMhW0yl0jJTbbSGL4zgGyra8Wbhli1MZKgQnZJIkSVL66Mga1tAxdIyUa9T8L4qi/CiKpgMrgFfiOH67gcdcE0XR5CiKJpeWljZ1zpRbQ0daUklLykNHkSRJknJeJ1ZbyJLiOK6J43gI0AM4MoqiAQ085t44jofHcTy8S5cuTZ0z5ZLjUA9blCRJksLryJqcOGRxj86Qi+N4LTAOODMlaQJKtm8PW5QkSZLCc0K2RRRFXaIo6rDlfivgVGB2qoM1NydkkiRJUnqIqM2ZCVljVlk8APhDFEX5JArck3Ec/y21sZqfEzJJkiQpPbRlA/nU5sSErDGrLL4HDG2GLEE5IZMkSZLSQ3JIkgsTsuy+ytoecEImSZIkpYfkkCQXJmQWsi3W045q8i1kkiRJUmBOyHJSxFo6eMiiJEmSFFiykDkhyzGr6eSETJIkSQosOSRxQpZj1tDRCZkkSZIUmBOyHLWGjk7IJEmSpMA6sZpKWlBOq9BRUs5Cto3VdHJCJkmSJAW29aLQUegoKWch24YTMkmSJCm8TqzOicMVwUK2neSiHhG1oaNIkiRJOWvrhCz7Wci2sYaO5FNLWzaEjiJJkiTlLCdkOSrZwj1sUZIkSQrHCVmOSv7QO7MycBJJkiQpd5WwykKWi1bQFYAulAZOIkmSJOWmVmyiLWV1++bZzkK2jeQPvSsrAieRJEmSclNyOGIhy0EWMkmSJCms5L64hSwHbaQNm2hlIZMkSZICsZDltIgVdLWQSZIkSYFYyHKchUySJEkKx0KW4yxkkiRJUjhdWcFGWrOJNqGjNAsL2Q4sZJIkSVI4XVmRM9MxsJDVs7WQxaGjSJIkSTnHQpbjVtCVIqpox/rQUSRJkqScYyHLcV6LTJIkSQrHQpbjLGSSJElSKLGFLNclf/j78WngJJIkSVJu6cBaCqnmU/YLHaXZWMh24IRMkiRJCiPXrkEGFrJ6VtIZsJBJkiRJzc1CJjbTgtV0tJBJkiRJzcxCJiDxC+A5ZJIkSVLzShayUroETtJ8LGQN+IT9OYDloWNIkiRJOaUby6ghz0KW65bSne4sDR1DkiRJyindWcon7E8NBaGjNBsLWQOW0p1uLAPi0FEkSZKknNGdpSyle+gYzcpC1oCldKeIKjqzMnQUSZIkKWdYyARQ90vgYYuSJElS87GQCdhayBKHLUqSJElKtVZsoiNrLWRyQiZJkiQ1t+QwxEImlnMAtUQWMkmSJKmZJPe9LWSimkJW0NVCJkmSJDUTC5m2s4xuFjJJkiSpmST3vZfRLXCS5mUh2wkvDi1JkiQ1n+4sZQPFbKBd6CjNykK2ExYySZIkqfnk4pL3YCHbqaV0pzOrKKIidBRJkiQp61nItB2vRSZJkiQ1HwuZtrOYngD0ZHHgJJIkSVJ2y6OGbixjCT1CR2l2FrKdWEhvAHqzMGgOSZIkKdt1ZymFVLOAPqGjNDsL2U58TC/AQiZJkiSlWnKfOzkUySUWsp2oooildLOQSZIkSSlmIVODFtLbQiZJkiSlWG8WUktUd5RaLrGQ7cIC+ljIJEmSpBTrzUKW0Y0qikJHaXYWsl1YSG96sph8qkNHkSRJkrJWbxbm5OGKYCHbpYX0poAaerAkdBRJkiQpa/VhgYVM9bn0vSRJkpRa+VTTk8UWMtVnIZMkSZJSqztLKaDGQqb6FtOTWiILmSRJkpQiubzkPVjIdilxLbLuFjJJkiQpRZL72gvoEzZIIBay3VhAH/oyL3QMSZIkKSv1ZR415LGYnqGjBGEh242POITPMCd0DEmSJCkrfYY5LKQ3m2kROkoQFrLdmMNn2J9PYd260FEkSZKkrHMIH/ERh4SOEYyFbDfqfjnmOCWTJEmSmlQcW8hCB0h3db8cH30UNogkSZKUbT75hLaUWci0c/PoSy2REzJJkiSpqW3Zx57DZwIHCcdCthuVtGQRBzohkyRJkpraln1sJ2TapTl8xkImSZIkNbWPPqKCopxd8h4sZI3yEYckClkch44iSZIkZY+PPtpyilB+6CTBWMga4SMOgfXrobQ0dBRJkiQpe8yZk9OHK4KFrFHqfklmzw4bRJIkScoW1dUwd66FLHSATPA+h2+5837YIJIkSVK2mDsXqqq27mvnKAtZIyyhB7RrZyGTJEmSmsqWfWsLmRohgsMPh5kzQweRJEmSssPMmRBFzOKw0EmCspA1VrKQudKiJEmStO/efx8OOohyWodOEpSFrLEGDIBVq2DFitBJJEmSpMw3c2ZiHzvHWcgaK/nL4mGLkiRJ0r6prExc59dCZiFrtMNdaVGSJElqEh99BDU1W/exc5iFrLH22w9KSpyQSZIkSfsquU/thMxC1mhRlPiFee+90EkkSZKkzDZjBhQUwCG5fVFosJDtmaFDE4WspiZ0EkmSJClzTZ2aOFyxqCh0kuAsZHti2DAoL4cPPwydRJIkScpMcZwoZMOGhU6SFixke2Lo0MTt1Klhc0iSJEmZatkyKC3dum+d4yxke6JfP2jZ0kImSZIk7a3kvrQTMsBCtmcKCmDwYJg2LXQSSZIkKTNNnZpYMG/w4NBJ0oKFbE8NHZooZHEcOokkSZKUeaZOTayuWFwcOklasJDtqWHDYN06mD8/dBJJkiQp80yb5uGK27CQ7anhwxO377wTNockSZKUaT75BBYvhiOOCJ0kbey2kEVR1DOKotejKJoVRdH7URTd0BzB0tbAgdCqFUycGDqJJEmSlFnefjtxe/TRYXOkkYJGPKYa+FYcx1OjKGoLTImi6JU4jj9Icbb0VFAAI0ZYyCRJkqQ9NXEiFBa65P02djshi+N4eRzHU7fc3wDMArqnOlhaGzkycexrZWXoJJIkSVLmmDgRhgxJHHEmYA/PIYuiqDcwFHi7gY9dE0XR5CiKJpeWljZNunQ1ciRUVbn8vSRJktRY1dUwaVJiX1p1Gl3IoigqBp4CvhHH8fodPx7H8b1xHA+P43h4ly5dmjJj+jnqqMSthy1KkiRJjTNzJmzaZCHbQaMKWRRFhSTK2KNxHD+d2kgZoFs36NUL3nordBJJkiQpMySHGRay7TRmlcUI+D0wK47jX6Y+UoY49liYMMELREuSJEmNMWEC7Lcf9OkTOklaacyE7FjgC8DJURRN37KdneJc6e+EE2DZMpg3L3QSSZIkKb3FMbzxBowaBVEUOk1a2e2y93EcTwD8ru1o1KjE7RtvwMEHh80iSZIkpbMFC2DJkq370KqzR6ssahv9+kHXrolCJkmSJGnnkvvMFrJ6LGR7K4oShy2OHx86iSRJkpTexo+Hzp2hf//QSdKOhWxfjBoFixYlNkmSJEkNe+ONxDDD88fqsZDtixNPTNz+4x9BY0iSJElpa8GCxJbcd9Z2LGT74vDD4YADYOzY0EkkSZKk9PTKK4nb004LmyNNWcj2RRQlfrFeeQVqa0OnkSRJktLP2LHQsyccemjoJGnJQravTjsNVq2CadNCJ5EkSZLSS00NvPYanH6654/thIVsX516auI2OYqVJEmSlDB5MqxdmyhkapCFbF/tvz8MGgQvvRQ6iSRJkpReXn45MRk75ZTQSdKWhawpnH02TJiQaP+SJEmSEv72NzjqKCgpCZ0kbVnImsI55ySOj3VKJkmSJCUsXw7vvJPYV9ZOWciawlFHJa48/vzzoZNIkiRJ6eGFFxK3FrJdspA1hfz8xGGLL74I1dWh00iSJEnhPf889OoFAwaETpLWLGSNFEW73i58+BxYs4YTCyfU+5gkSZKUUzZtgldfTUzH3CHeJQtZE3mJMymnJRfwVOgokiRJUlgvvZQoZaNHh06S9ixkTWQjxbzIWVzAU0TUho4jSZIkhfOXvyTWWBg1KnSStGcha0J/4UK6sZyjeSt0FEmSJCmMioqvxfPDAAAgAElEQVTE+WOjR0NBQeg0ac9C1oT+xmeppAUX8efQUSRJkqQwXn4ZysrgwgtDJ8kIFrImtIF2vMSZXMSfyaMmdBxJkiSp+T3xBHTqBCedFDpJRrCQNbFHuZzuLONExoWOIkmSJDWvDRvg2Wfh85+HwsLQaTKChayJPc85rKctV/BI6CiSJElS83rmGSgvhyuuCJ0kY1jImlgFrfgLF3IBT9GS8tBxJEmSpJRLXn937FWPMJ8+RMcevdvr+HrN3gQLWQo8whW0YwOjeSZ0FEmSJKlZdGcJp/Aaj3I5YNNqLAtZCozjROZxEF/ld6GjSJIkSc3iizxEPrU8xBdDR8koFrIUiMnjd3yVUYznMD4IHUeSJElKqYhavswDvMbJzKdv6DgZxUKWIg/yJaoo5BruDR1FkiRJSqmTeJ2DWMD9XB06SsaxkKXISrrwFBdwFX+ATZtCx5EkSZJS5mv8H6vpyDOMDh0l41jIUmgM19KRtfDkk6GjSJIkSamxcCGjeYZ7uYZKWoZOk3EsZCk0nhOYRT8YMyZ0FEmSJCk17rmHmIh7+HroJBnJQpZSEWO4Ft5+m6HRtEZfi8HrMkiSJCkjlJXBfffxFy5kCT1Dp8lIFrIUe5gr2UAxN3JH6CiSJElS0/rDH2DdOu7iG6GTZCwLWYqtpSO/46tcwuP0YX7oOJIkSVKD9vRIrryolo+u+zUTOYq3GRk6fsaykDWDX/KfVFPAt7gzdBRJkiSpSZzJSxzCHKdj+8hC1gyW042HuZIv8wBd+TR0HEmSJGkfxXyX/2ExPXiKC0KHyWgWsmbyC26iiEpu4Neho0iSJEn75FRe5Tj+xU/5DtUUho6T0SxkzWQOh/AUF/B17qEd60LHkSRJkvZSzK38gI/pye/5SugwGc9C1ox+yndoz3q+wV2ho0iSJEl75XTGcgxv8T98lyqKQsfJeBayZjSNYfyFC7iRO+jCitBxJEmSpD2UmI4tohcP8OXQYbKChayZ/Tc/oRXl3MKPQ0eRJEmS9siZvMRI3uYn/DebaRE6TlawkDWzjziU3/MVrmUMBzEvdBxJkiSpUfKp5md8mwX05iG+GDpO1rCQBXArP6CaAm7je6GjSJIkSY1yNfcziBn8Fz93OtaELGQBLKcbv+KbXMZjHMHk0HEkSZKkXWrPWm7je4zneP7ChaHjZBULWSA/57/4lK7cw9eJqA0dR5IkSdqp73EbJazack3dKHScrGIhC2Q97fkWd3IUk7ia+0PHkSRJkhr0GT7ieu7mAb7MdIaGjpN1LGQBPcrljGMUt3MznSkNHUeSJEnaQcxv+H+U04r/5iehw2QlC1lQEf/Bb2nLBn7Gt0OHkSRJkrZzJQ9zBmP5Dj9lBfuFjpOVLGSBzaI/d/ItvsyDHM/40HEkSZIkALryKb/im0zgWP6Pr4WOk7UsZGngNr7HPA7iIb5IMRtCx5EkSZL4Df+PNmzkau4ntjakjN/ZNLCJNlzFH+jNQu7gxtBxJEmSlOPO41ku5s/cyg/4kH6h42Q1C1ma+BfHcQc38lXu5UxeDB1HkiRJOWp/lnMf/840hvALbgodJ+tZyNLI9/kRMxjA7/kKnVgVOo4kSZJyTEQtf+QLtGEjl/EnqikMHSnrWcjSSCUt+QJ/pDMreZAvEVFLFLHXmyRJkrQnbuIXnMpr3MCvmc1hoePkBAtZmnmXIXyLOzmX57mRO0LHkSRJUo4YwSR+zC38mQu5n6tDx8kZFrI09L9cx5NcxP/wXZfClyRJUuqVlvJnLmIZ3biGewEPt2ouFrK0FHE19zOPvjzOJezHJ6EDSZIkKVtt3gwXX8x+fMoFPMVaOoZOlFMsZGlqA+24kL/QgbU8zecooiJ0JEmSJGWjm26CceO4hnuZwvDQaXKOhSyNzWQgV/AIx/AWD/BlIA4dSZIkSdnkoYfg17+GG27gj1wZOk1OspCluWf4HDfzUy7jMb7HbaHjSJIkKVu8+ir8+7/DySfDL34ROk3OKggdQLv3M77NoXzIj/gB8zmIR7kidCRJkiRlsunT4XOfg3794KmnoNDrjYViIcsIEV/ld/TiYx7ii6yjPX/jnNChJEmSlGYacy3aXiziLc6mhvYcPfNFlnbskPpg2ikPWcwQm2nB+TzLVIbxJBdzAm+EjiRJkqQMsx+fMJbTac0mzuJFltIjdKScZyHLIGW05Wz+zgL68DzncASTQ0eSJElShuhMKa9xCt1Zyr/xAu8zIHQkYSHLOKvozOmMZRUlvMqpjGBS6EiSJElKcx1ZzaucykHM57P8jTc5NnQkbWEhy0BL6cGJjGMVJbzCaRzFxNCRJEmSlKa6sILXOIV+zOY8nuMNTgwdSduwkGWojzmQExnHCroyltM5jn+GjiRJkqQ0050ljOcEDuVDzuM5XuH00JG0AwtZBltCT05kHMvoxiucxnk8GzqSJEmS0kRf5jKB4+jGMs7gZV7mzNCR1AALWYZbRneOYwLTGcJTXMC/c2/oSJIkSQrsSN7mXxxLMWWcxOtM4PjQkbQTFrIssIrOnMJrvMSZ3MtXuY1biKgNHUuSJEkBnM8zjONEyijmWP7FVI4IHUm7YCHLEptow/k8y/18hVv4CU9yMWzcGDqWJEmSmksc85/cyVNcwLsM5mje4iMODZ1Ku2EhyyLVFPLv3Mc3+SWf42k4/nhYvDh0LEmSJKVaWRlceil3ciNP8zlO4nVK6Ro6lRrBQpZ1Iu7im3yWv8HcuTB0KLz0UuhQkiRJSpU5c2DkSPjzn7mZn3IRf6aCVqFTqZEsZFnqRc6Gd96Bbt3g7LPhllugujp0LEmSJDWl55+H4cPhk0/gpZf4GTcDUehU2gMWsmx26KEwcSJ8+cvwk5/AaafB8uWhU0mSJGknoqhxW8uogjujb8G55zJl/cEcuGoK0emnhY6vvWAhy3atW8P998NDD8Hbb8OQIYn/SZEkSVJGGsAMJnEk3+KX/JavcRwT+JgDQ8fSXrKQ5YqrrkocwnjAAXDuufClL8G6daFTSZIkqZEiarmBu3iHEezHp5zNC3yd33q+WIazkOWSww+HSZMS55P98Y8wcCC89lroVJIkSdqNg5jHWE7nLr7JWE5nIDMSawYo41nIck2LFnDbbfDmm9CmDZx6Knz1q7B6dehkkiRJ2kEBm/kvfsZMBjCCd7iG33Eez7mkfRaxkOWqI4+EqVPhxhvh97+Hfv3g4YchjkMnkyRJEjCcd3iHEfyMm3mRs+jPB9zHNbiKYnaxkOWyVq3gF79IFLODD06cZ3bSSfDBB6GTSZIk5azOlPJ/XMtERtKFUkbzNBfwNMvoHjqaUsBCJhg0CCZMgPvug/feg8GD4frrYeXK0MkkSZIyTmOXrt9xaxFV8Q1+xRw+w9Xczz18nf58wLOMDv0lKYUsZErIy4Orr4YPP0zc3nNPYmp2xx1QWRk6nSRJUhaLOZsXeI9B/Ir/ZCIjGcR73MDdrKd96HBKMQuZttelC/zf/8GMGXDssXDTTYnzy/70J6ipCZ1OkiQpqxzHPxnPCbzAZ8mjln/jb5zFi8yif+hoaiYWMjWsf3944QV45RVo3x4uvzxxaOOf/wy1taHTSZIkZbQhTOMFzuafnEBf5vE1fssAZvJ3/g0X7cgtuy1kURQ9EEXRiiiKZjZHIDWdvT1+ObkBiWXxp06FJ55IrMB48cUwdCg8+6zFTJIkaQ8dyds8w/lMYxhH8TY38XMOZi5j+BqbaRE6ngJozITsIeDMFOdQOsvLSxSxGTPgkUegvBxGj05cWPqhh6CqKnRCSZKkNBZzCq/yKqfwNiM5gfH8kB9wEPO5g5sop3XogApot4UsjuPxgFcNFuTnJw5d/OCDRDErLIQvfQkOOiix+Mf69aETSpIkpY2IWs7jWd7mKF7lNA5jFt/iDg5kEbfyQxfsENCE55BFUXRNFEWToyiaXFpa2lRPq3RUUJAoZtOmwUsvwaGHJhb/6NkTvv1t+Pjj0AklSZKCac9avsGv+IhDeJbRlLCKa/gdfVjAL/kWZbQNHVFppMkKWRzH98ZxPDyO4+FdunRpqqdVOosiOOMMeO01eOcdOPPMxKSsTx847zx4+WXPM5MkSbnj/ffha19jKd35Ff/JJ+zP53mcQ/mQ+7iGKopCJ1QacpVFNY3hwxMLf8yfDzffDBMnJgraIYfAnXfCqlWhE0qSJDW9ykp48kk4+WQYMAAefJAn+DzDmMLxTOBJPk8NBaFTKo1ZyLRTe7U6Y+8Dif7nJ7RYsZhLeIzx87rBjTdS0bk7j0WXcmb0EvlRze5Xd5QkSUpn06fD9ddDt27w+c/DvHnw05/CkiV8hQeYxrDQCZUhGrPs/WPAW8ChURQtiaLoK6mPpUy3mRY8wSWMYjwDeY/7uZrTGctLnMXH9OKn3Ew/ZoWOKUmS1HirVsE998CwYYnLAP3ud3D66TB27NajhDp3Dp1SGSaK47jJn3T48OHx5MmTm/x595XTl7BaUMln+RtX8QfO5u8UUMMkRvAnLuPPXMQyugOJy51JkiSlhQ0b4Lnn4LHHEsWrujpRxr78ZbjsMujUqd6nuM/ZvNJ13zGKoilxHA/f7eMsZAqhK59yOY9yJQ8zhHepJWICx/EEn+ee5RfA/vuHjihJknJVeTm8+CI8/jg8/zxUVCRWk77kkkQJGzJkl5/uPmfzspA1wEKmPXEIH3IxT/J5nmAA7ycuRD1qFHzuc3DOOXDggaEjSpKkbLdmDbzwAjz7bOKyPhs3soIuPMnFPMalvMXRxC6/kJYsZA2wkGlv9ed93v/+k4nVimbPTrxz8ODEMvrnnps4ZnsXP8h9/Rmn6x9oSZKUAosXJw5HfPZZGDcOamrggAPgvPM4fcxo/sHJrpCYAdJ1/81C1gALWWao+5X86KPEYQLPPQf/+lfimmbduyeK2Wc/m5iitWmz3edayCRJUtKO+wX5VDOSiZzBy5zN3zmCqQDMoh/Pcj7Pcj7vMMJJWIZJ1/03C1kDLGSZocFfyZUr4e9/T5Szl1+GjRuhRQs47rjE6kZnnAGDBhHl79tfoOn6B1qSJO25KIKefMwZvMwZvMypvEoH1lFNPhMZyfOcw3Ocx4f0Cx1V+yBd998sZA2wkGWG3f5KVlTAP/+ZWOlo7Fh4773E+7t25ZEVpzGW03mdk1hCz6Z/bUmSlN5Wr4bx42HcON7/9SsczgcALKYHL3EmL3Emr3EK6+gQOKiaSrruv1nIGmAhywx7/Cu5fDm88gqMHcuKR8fSlVIA5tOH8ZzAG4ziDUaxgD7Arn8J0vUPtCRJuWp3+2/tWcsJjOdExnESrzOYd8kjppyW/JPj60rYLA5jd/sBykzpuv9mIWuAhSwz7MuvZF5UyyDe21LB3uAExtOZVUDif8a2LWgfcQg7/sWcrn+gJUnKVdvvv8X0ZDHH8CbH8CbH8i+GMo08Yioo4k2OYRwn8jonMYkjqaIoVGw1o3Tdf7OQNcBClhn25Vdyx59xRC2HMauuoI3iDfbnUwBWUsLbHMVERjKRkUziSNbF7fchuSRJ2tG+7H8VUsUQptcVsGN4kx4sBWAjrZnEkbzBKF7nJN7mKCpp2USplUksZA2wkGlfNGUha+DZ+QxzOIHxW2rYRPrzAXnE1BKRd1g/GDkysR11FBx+OBS43K0kSXursftfEbUczFyGM5kjmMII3mEE79CKCgAW0WubWnYM7zGIagpTmFyZwkLWAAuZ9kVqC1l97VjHCN5hJBP58WffhokTE6s6ArRsmbgO2tChiWugDRsGAwZAUdMeArEvv5vp+peQJEmws3/jYvoyr658DWcyw5hKe9YDUE5L3mVwXfl6i6NZRvdmza3Mka77QhayBljIMkNzF7J6rx3HMH9+ophNnbp1W5/4R4KCgsTkLFnQBg9OlLSOHYPkTte/hCRJAmgTbWQAMxnEe3XbYN6lA+sAqKQF7zKYyQxnCkcwmeF8QH+nX2q0dN0XspA1wEKWGYIXsobU1sKCBTBt2vYlrbS07iFL6M5MBjCTAcxgIDMZwCwOo5zW+xZqbzNLkrSNlP/nX/Lfyvfe226rnTuPPBJPsIFiZjCQ9xhUV77e53A202Lvwynnpeu+UGMLmSfHSI2Rlwd9+ya2Cy9MvC+OYelSmDEDZs7kH/81gwHM5Dr+l5ZUAlBLxFwOritqH3Jo3VZG24BfkCQphJT9x2FzqqyEuXNh1qzENnt24vbDD2HTpsRjoggOPhgGD+aHc79QNxtbSG9i8sLml9KMEzKlnbSckO3Ba+dTTV/mbalgMxlIoqh9hjnkU1v3+GUcsF1BS24L6U0t+c2aeW+lxY6BJGWQdPh3qpGvRFdWcDBz+QxzOIxZHMYs+jGbg5hPATV1j1zIgcymH7PpxwwGMoOBvM/hbKLN3oeV9kC67o94yGIDLGQKqQWV9GVeAxXsQ0pYXfe4Slowl4P5kEOZR1/mc1DdtogD6x3WYSGTpMyRToUsopZuLKMv8ziYufW2tpTVPbaKQj7iEGZxGLPpV3f7IYdavBRcuu6PeMiilGaqKGIW/ZlF/3ofK2FlvZLWj9mczd/rDn8EqCGPJfTYrqhdEm0tbKsoYceLXUuSclQcw5o1sGgRLFrEDSzkQBbRhwUczFz6Mq9uSXlIlK4F9GEuBzOeE5jLwcyjL3M5mPkcRI27jVJKOCGT0lhELfvzCQcxn77M22ZWltgO4JPtHr+R1nxMLz6mF4vpWXc/uS2hR5NeNDPU/0i5KqWkTNWkE7I4hhUrYOHCutJV735Z2Xafv5HWLKQ3c/jMdoVrLgezmJ6WLmWkdP233QmZlAVi8lhON5bTjX9xXL2Pt2YjfVhQV9CS1asnixnEe/UKG8CndN2upC2mJ8s5gGV0YxndWM4BbKS4Ob48SdJOtKCSbiyjO0u327hkKSxbllhUaunSxAIb2+rQAXr3TixCdfLJcOCBibcPPJDOww/0SAopDVnIpAy2iTa8zwDeZ0CDH29BJT1Yst2crCeL6cXHHMYszuBlitlY7/PW03a7graz+3jegCTtkSIq2I9P67b9+YTuLK1Xvrqwst7nbqIVTOkO3bvDyJGJ21696goXBx4I7drt9LVXpfDrkrT3LGRSFquiiPn0ZT59d/KImA6s5QCWcwDLt1StxJZ8+2je4gCWb3eeQZ327aBr14a3Ll22f7ukBPK3rh7pIcSS9lWow5e3f92YNmykKyu2K1o72ypYX+/5aolYQVeW0p2P6cVbHM0yuu0wG+vOWjoQz/EvTynbWMiknBaxlo6spWODi41slShu2xa1bizjgPXL6bK+lK5zV9CVeXTlLbpQut3y/km1RKykMyvoygq68jhdWEUJqyhhNZ0avL+WDnt0CQAp03l+ZGBxDBs3wsqVsGpV4nbb+1tuX2EVnVlJZ1ZSwqqG/8MKWEWnuio2lWE7rWnLOYBqChsV0f/MkrKPhUxSI2wtbh9w+G4eWUsnVm+pXTvfhjCdElbRkTUNFjhIlLi1dNhpcVtDR9bSgbV0YB3tt7vdQNsGLz4acmfGHWalq+wqgjGt2URH1mz522HtdveTb/PltbB2bWIVwtWrt5avqqqGnzaKoFMnKCmhFZ35mF5MZRirKGElneuVrFK61LtMiSQ1xEImqUnF5LGKzqyi826mbgkRtbRn3ZaatYpOrN7udtv7XVlBP2ZTwiraN3DYz7ZqiVhPu3pFraHbdbSnjGI20LbuNnl/E63xBPgwsqskZK8mWzUwjhMLVKxfDxs2bN128fYTO5Ss5P1Cqnf5mhsohlc6JBbA6NAB+vSB4cOhc+fEVlJS/7Zjx7rDro/zrwRJTchCJimomLy66ds8Dm705xWwmfasq9sBS97f8Xbb+z1ZzEBmbKlg63Y6mdtWLVG9ktbQ7bb3N9F6u62cVoliN781tGoFrVsntsLGHaKkzJLth5TlUUMrymnDxu1+07d9e2f3iymjHeu3/IlJbBy4TeGq3nWRqtO6NbRty6Atf8pXUcI8+rKWDttNzhu6v472icMDl5DYJCkwC5mkjFRNYd0kbu/EFFNWV9iKKaOYMtqyYae3297vztIdHlN/tcp6dlxbJT9/azlrvUNZ2/F+y5ZQVLT1tjHb7h5bUJD97SHrxBSyuW5rQVXdLbMqoKIiMWWq2LP791FBSyooopKWW+63orzBcrXtxeobq4IiNtGajbRhPe3q6tgn7M/Ak9pB27b1t3YNvL9dOygurptUHeavr6QsYCGTlKMiymhLGW1ZQs8meLZa2rCRtmyo25FNbjt9u2YTrTdsotWGhj6+htYsrZtEHNBhy050ZSXU7n6y12iFhYmtoKD+/Ybe19jH5udDXt7W2223Hd+3k8fcQB6122w15BPvcPhoRNzg29dGu/74rt7+37tqEt/jmprElrzf0PsauD+GGvKpIY9a8re5X0D1dmVq20K1s23HjxdQs/Of5e6PEN5efn6itLdsyVkUbalhLamkiMotBWo1nep+MzfSZq/v73Jxnj/sYW5JyjIWMklqAjF5dQUvJdZuvZtP9ZZd5vpbcsqx7fb0nyq3lrnkVlEBmzcnturqnd7/y+ObtysSW+9vavD9ydtkGSnpUJsoLNuWmm23XZzsdVdqvpO7943dfHzbEpmfX+/+eVvKYw35dUWyljyqKahXuSopooziXVSyQqposcuPb6awrkhtW6p2db+SImpqCmAjNGa4K0lKHQuZJGWYGgrYRAGbGnlh7uiyFAfahXjN7h4Q1y9pW4pbh/Zb52PJKVMetfWmZE39dkNlKvm+mAhqIxpx+qEkSY1iIZMkhRNFW6dMO1gXII4kSc3NQiZJShnXDJEkadfqXzVVkiRJktQsLGSSJEmSFIiFTJIkSZICsZBJkiRJUiAWMkmSJEkKxEImSZIkSYFYyCRJkiQpEAuZJEmSJAViIZMkSZKkQCxkkiRJkhSIhUySJEmSArGQSZIkSVIgFjJJkiRJCsRCJkmSJEmBWMgkSZIkKRALmSRJkiQFYiGTJEmSpEAsZJIkSZIUiIVMkiRJkgKxkEmSJElSIBYySZIkSQrEQiZJkiRJgVjIJEmSJCkQC5kkSZIkBWIhkyRJkqRALGSSJEmSFIiFTJIkSZICsZBJ0v9v735C7DrrMI5/HxOrC6uCs5E2moIpGIvQEmrFhUpFki6STZEGilaCWVWxilCxoOhKRQQh/qkYqoLW2oUOomShFUVMaaBQTCEwRGmHCq1aA1Jsjf5c3FsZJuPMmzbnvDl3vh8YuOfeA/NbPHPvfea85xxJkqROLGSSJEmS1ImFTJIkSZI6sZBJkiRJUicWMkmSJEnqxEImSZIkSZ1YyCRJkiSpEwuZJEmSJHViIZMkSZKkTixkkiRJktSJhUySJEmSOrGQSZIkSVInFjJJkiRJ6sRCJkmSJEmdWMgkSZIkqRMLmSRJkiR1YiGTJEmSpE4sZJIkSZLUiYVMkiRJkjqxkEmSJElSJxYySZIkSerEQiZJkiRJnVjIJEmSJKkTC5kkSZIkdWIhkyRJkqROmgpZkv1JziRZSXL30ENJkiRJ0nawZSFLsgM4BhwA9gKHk+wdejBJkiRJWnQtR8huBFaq6mxVvQDcDxwadixJkiRJWnw7G/a5CnhyzfYq8I71OyU5Chydb/4jyZmXP94ltwT8pfcQWljmS0MyXxqS+dKQzJcGlVy2GXtzy04thSwbPFcXPFF1L3Bvyy/tJcmpqtrXew4tJvOlIZkvDcl8aUjmS0ObesZaliyuArvWbF8NPDXMOJIkSZK0fbQUskeAPUmuSXIFcBuwPOxYkiRJkrT4tlyyWFXnk9wJnAB2AMer6vTgkw3jsl5SqckzXxqS+dKQzJeGZL40tElnLFUXnA4mSZIkSRpB042hJUmSJEmXnoVMkiRJkjpZuEKWZH+SM0lWkty9weuvSvKj+esPJ9k9/pSaqoZ8fSLJ40keS/LLJE33n5BetFXG1ux3a5JKMtnL/Gp8LflK8oH5+9jpJD8Ye0ZNV8Nn5JuSPJTk0fnn5C095tQ0JTme5Okkf/g/ryfJ1+b5eyzJDWPP+FItVCFLsgM4BhwA9gKHk+xdt9sR4NmqegvwVeCL406pqWrM16PAvqp6O/Ag8KVxp9SUNWaMJFcCHwMeHndCTVlLvpLsAT4NvKuq3gZ8fPRBNUmN71/3AA9U1fXMrtr99XGn1MTdB+zf5PUDwJ75z1HgGyPMdEksVCEDbgRWqupsVb0A3A8cWrfPIeC788cPAjcn2ejm19J6W+arqh6qqufmmyeZ3bdPatXyHgbwBWZl/59jDqfJa8nXR4BjVfUsQFU9PfKMmq6WfBXw2vnj1+F9bXURquo3wN822eUQ8L2aOQm8Pskbx5nu5Vm0QnYV8OSa7dX5cxvuU1XngXPAG0aZTlPXkq+1jgC/GHQiLZotM5bkemBXVf1szMG0EFrew64Frk3yuyQnk2z232hprZZ8fQ64Pckq8HPgo+OMpm3iYr+nXTa2vA/ZxGx0pGv9df1b9pE20pydJLcD+4B3DzqRFs2mGUvyCmZLre8YayAtlJb3sJ3Mlvu8h9kR/t8mua6q/j7wbJq+lnwdBu6rqq8keSfw/Xm+/jP8eNoGJvsdf9GOkK0Cu9ZsX82Fh8P/t0+SncwOmW92+FN6UUu+SPI+4DPAwap6fqTZtBi2ytiVwHXAr5P8CbgJWPbCHmrU+hn506r6V1X9ETjDrKBJW2nJ1xHgAYCq+j3wamBplOm0HTR9T7scLVohewTYk+SaJFcwO2F0ed0+y8CH5o9vBX5V3h1bbbbM13w52beYlTHPvdDF2jRjVXWuqpaqandV7WZ2nuLBqjrVZ1xNTMtn5E+A9wIkWWK2hPHsqFNqqlry9QRwM0CStzIrZM+MOqUW2TLwwfnVFm8CzlXVn3sP1WKhlixW1fkkdwIngB3A8ao6neTzwKmqWga+w+wQ+QqzI2O39ZtYU1sXC5wAAACiSURBVNKYry8DrwF+PL9WzBNVdbDb0JqUxoxJL0ljvk4A70/yOPBv4FNV9dd+U2sqGvP1SeDbSe5itpTsDv8prlZJfshsOfXS/DzEzwKvBKiqbzI7L/EWYAV4Dvhwn0kvXvw7kCRJkqQ+Fm3JoiRJkiRNhoVMkiRJkjqxkEmSJElSJxYySZIkSerEQiZJkiRJnVjIJEmSJKkTC5kkSZIkdfJfd2OjjojZEucAAAAASUVORK5CYII=\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 设定图像大小\n", "plt.rcParams['figure.figsize'] = (15.0, 8.0)\n", "from scipy import special as scsp\n", "index_den=np.linspace(0.005,0.995,500)\n", "density=[1.0/scsp.beta(alpha,beta)*x**(alpha-1)*(1-x)**(beta-1) for x in index_den]\n", "plt.hist(subx,label=r'Histogram of x',color='blue', bins=50,normed=1)\n", "plt.plot(index_den,density,label=r'Beta Denstiy',color='red')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "plt.acorr(subx,label=r'Auto corr of h2',color='blue', maxlags=2000)\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 使用独立的Metropolis-Hastings算法计算积分\n", "为了计算以上积分,我们将密度函数改写为:$$\\int\\int\\frac{\\pi}{90\\sqrt{2}}\\cdot1\\left\\{ -1\\leq x_1\\leq1\\right\\} \\cdot1\\left\\{ -1\\leq x_2\\leq1\\right\\} \\cdot f\\left(x_1,x_2\\right)dx_1dx_2\\overset{\\Delta}{=}\\frac{\\pi}{90\\sqrt{2}}\\int\\int h\\left(x_1,x_2\\right)\\cdot\\pi\\left(x,y\\right)dx_1dx_2$$\n", "接下来使用独立的Metropolis-Hastings算法,选取工具密度$$p\\left(y|x\\right)=\\frac{1}{4}1\\left\\{ -1\\leq y_1\\leq1\\right\\} \\cdot1\\left\\{ -1\\leq y_2\\leq1\\right\\} $$进行抽样,得到$\\left\\{ x_{t},t=1,2,...\\right\\} $,最终计算积分为:$$\\hat{I}=\\frac{\\pi}{90\\sqrt{2}}\\frac{1}{M}\\sum_{t=1}^{M}h\\left(x_{1t},x_{2t}\\right)$$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Intgral1= 0.0246826829898\n", "Intgral2= -0.000539202684445\n" ] }, { "data": { "image/png": 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\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from numpy import random as nprd\n", "\n", "##设定参数\n", "M =10000\n", "pai_cons=90*np.sqrt(2)/(2*np.pi)\n", "pai=lambda x: pai_cons* \\\n", " np.exp(-90*(x[0]-0.5)**2-45*(x[1]+0.1)**2)\n", "domain=lambda x:(x[0]>=-1)*(x[1]>=-1)*(x[0]<=1)*(x[1]<=1)\n", "q=lambda y: 1/(2*np.pi)*np.exp(-1*y[0]**2/2-y[1]**2/2)\n", "h=lambda x: domain(x)\n", "h2=lambda x: np.sin(10*x[0])**2+np.log(abs(1+x[1]*10))\n", "#从均匀分布中采样\n", "def sample_q():\n", " return (nprd.normal(),nprd.normal())\n", "\n", "\n", "##独立的MCMC算法,输入:\n", "## N_samples : 抽样次数\n", "## pai(x) : 目标密度函数\n", "## q(y) : 工具密度函数\n", "## q_sampler : 给定x,从q中抽样的函数\n", "## x0 : 初始值\n", "def MH_independent(N_samples, pai, q, q_sampler, x0):\n", " X=[]\n", " x=x0\n", " for i in range(N_samples):\n", " y=q_sampler()\n", " rho=min(1,pai(y)*q(x)/(pai(x)*q(y)))\n", " if nprd.uniform()<=rho:\n", " X.append(y)\n", " x=y\n", " else:\n", " X.append(x)\n", " return X\n", "\n", "## 计算积分\n", "x=MH_independent(M, pai, q, sample_q, (0,0))\n", "## 第一个积分\n", "H=list(map(h,x))\n", "## 取h后面80%的样本\n", "subH=H[int(M*0.2):]\n", "integral=np.pi/(90*np.sqrt(2))*np.mean(subH)\n", "print(\"Intgral1=\",integral)\n", "## 第二个积分\n", "H2=list(map(h2,x))\n", "subH2=H2[int(M*0.2):]\n", "integral2=np.pi/(90*np.sqrt(2))*np.mean(subH2)\n", "print(\"Intgral2=\",integral2)\n", "\n", "## 诊断图\n", "import matplotlib.pyplot as plt \n", "%matplotlib inline\n", "# 设定图像大小\n", "plt.rcParams['figure.figsize'] = (15.0, 8.0)\n", "index=[i for i in range(len(H))]\n", "x_x=[x[i][0] for i in range(len(H))]\n", "x_y=[x[i][1] for i in range(len(H))]\n", "plt.plot(index,x_x,label=r'MCMC Samples x',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "plt.plot(index,x_y,label=r'MCMC Samples y',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "直方图:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.rcParams['figure.figsize'] = (15.0, 8.0)\n", "plt.hist(x_x,label=r'Histogram of x',color='blue', bins=50)\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "plt.hist(x_y,label=r'Histogram of y',color='blue', bins=50)\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "诊断图:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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xBjuOM8txnFkbN270YHneC1Ts9uyJ7jqiaelSm4LZr5909tmRPz8blQMAAACFvAh2Tgn3Hfjr9nhJTVzX7SDpS0mjS3sx13Wfd123s+u6nevWrevB8rwXqNjl5ER3HdHiutL//Z9tQP7vf0dnDd27Sxs2sFE5AAAAIHkT7NZIKlqBayhpbdEHuK67yXXdQH3rBUnHenDeqKnMFbt166ztctIk6cEHpQYNorOOU0+143vvRef8AAAAQCzxItjNlNTScZymjuNUlTRA0odFH+A4TtFf/8+VtNCD80ZNoGJX2YLdkiXS8cdLu3bZRuGDB0dvLa1aSSecID39dGHQBgAAACqrsIOd67p7Jd0gaYIssL3tuu4Cx3HudRzn3H0Pu8lxnAWO48yVdJOkK8I9bzRVxordDz9YkNqxQ5oxQ5o50zYLj6YhQ6QVK6Tx46O7DgAAACDaPNnHznXdT1zXbeW6bnPXde/fd98/Xdf9cN/HQ13Xbeu67tGu657iuu4iL84bLYlyjd2ECVLHjtKyZWU/7vvvpdNOkzIybN+6rl3t+rpo69tXOuoo6dFHo70SAAAAILo8CXaVTbxV7L75Rnr77eL3TZ4snXWWNHeubVdQmmnTpNNPlw49VPr6a9tmIFYkJ0s33SRNncpm5QAAAKjcCHYhiKdr7AoKpMsuk/r3l2691T7//nvp3HOltm2lqlWlWbNKfu7ChdIZZ0j160tTplh1LNZcdZVUo4Y0alS0VwIAAABED8EuBPFUsZsyxbYE6N7dwk+fPlLv3lK9etLnn1vVrqRgt2mTDSbZu9eqew0bRn7tFVGrloW7t96S/ve/aK8GAAAAiA6CXQji6Rq7l1+28DNxogW7Tz+VUlOlL76QjjhC6txZWrxY2rat8DnLlkmHHSY9+aR03nnSkSVtNx9DbrrJ/ps89VS0VwIAAABEB8EuBPFSsdu6VRo3Tho4UEpPtymS06bZVMtmzewxXbrYhuM//FD4vG++Kfz48ssju+ZQNG1qg1See07auTPaqwEAAAAij2AXgni5xu6tt6Tdu6Urryy8r1s3qXHjws87d7bjzJmF982YUfjxGWf4u0av3H679Pvv0gsvRHslAAAAQOQR7EIQLxW7V1+VsrIKw1tJDjtMatKkeLCbPl06+WSr+CUn+71Kb3TvLvXsKY0cKeXmRns1AAAAQGQR7EJQ9Bo7143uWkqzerXtOTdokOQ4ZT+2c+fCASrbt0vZ2RaSatb0f51e+vvfbYDKa69FeyUAAABAZBHsQhCo2LmuTY2MRW+9Zcf+/ct/bJcuNjnzt9+scldQYC2b8aZXL6lTJ+mhhwr/GwEAAACVAcEuBIGKnRS77Zhvvikdd5zUvHn5jw20as6ebW2YktS1q39r84vjSEOHSkuXSv/9b7RXAwAAAEQOwS4ERdsvYzHYLV4s/fijNGBAxR5/7LF2nDnTgl2bNlLt2v6tz0/nny+1aiU9+GDstskCAAAAXiPYhcB1papV7eNY3Mtu7FirXl18ccUeX6uWhaHvv7eJmN27+7s+PyUlSX/7mwXbCRPsvt27pa++IugBAAAgcRHsQlBQIFWrZh/v2hXdtRzIdS3Y9egR3Mbixx0nff65tGlTfAc7yQbGNGokDR8urV9vg2BOOUWaNCnaKwMAAAD8QbALgetK1avbx7G2IfaiRXbr1y+453XrVthWGu/BrmpVq9p9+60F3OxsKS2N6+4AAACQuAh2IYjlYPfBB3Y877zgnheYglmzpl1jF++uusoqlkuWSKNGSb1728+m6OAbAAAAIFHEyfbTsaWgQKpRwz6OxWDXubPUsGFwz+vQwapaXbtKVRIg7qemSi+9JH3zjTR4sJSRIb33nk3+7NIl2qsDAAAAvEWwC0HRil0sXWP36682/GT48OCfm5IiPfOM1KKF9+uKljPPtJsknXOODVZ57z2CHQAAABJPAtRmIi9WWzHHj7djsG2YAVdcIZ14omfLiSmHHmpDVN5/P9orAQAAALxHsAtBrLZivv++bUjetm20VxKbzj9fWrjQ9vkDAAAAEgnBLgSuW7jdQawEu+3bpYkTrVrnONFeTWwKVDKp2gEAACDREOxCEIutmBMnSrm5Up8+0V5J7GrUyAbLEOwAAACQaAh2ISgosKmLycmxE+wmTLCwefzx0V5JbOvb1wbMrF0b7ZUAAAAA3iHYhcB1rd2xWrXYCHaua8Hu1FNtc26U7vzz7fjhh9FdBwAAAOAlgl0IXNf2eouVYLdsmbRyZeFof5SuTRupZUvb9gAAAABIFAS7EBQUxFbFbsIEOxLsyuc40gUXSJMmSb//Hu3VAAAAAN4g2IUo1oJd8+Z2Q/n69ZP27mWICgAAABIHwS5IrmvHKlVsL7vt26O7ntxcafJkqnXB6NRJatZMevvtaK8EAAAA8AbBLkgFBXZ0HOmQQ6StW6O7nmnTrGpIsKs4x5Euvti2iNi0KdqrAQAAAMJHsAtSoGIXCHZbtkR3PZMnW/Xw5JOju454QzsmAAAAEgnBLkhFWzFjIdhNmSIdc4xUs2Z01xFvjjnGrkmkHRMAAACJgGAXpJJaMQP3RVpOjm22TbUueI5jVTvaMQEAAJAICHZBOrAV03WjN0Dlu++kPXuknj2jc/54d/HFUn4+e9oBAAAg/hHsgnRgsJOi14751Ve2jpNOis75413HjlKLFrRjAgAAIP4R7IIUaLsMXGMnRS/YTZli4SSwDgQn0I45aZL0228Ve47rSsuW+bsuAAAAIFgEuyCVVLGLxpYHe/ZI06fThhmuQDvmZZdJK1Yc/PX8fOn33ws/v/VWqWVL6eyzpYULK3aO77+XrrnGXgsAAADwA8EuSLHSivn99zY8hWAXno4dpUcekb7+WsrKki6/XLroIqlbN6lRIyk1VapTR7rjDun116XHHrPnTZtmjy3P5s3ShRdKL74oLV/u7/cCAACAyotgF6QDtzuQohPsvv3WjieeGPlzJ5pbb5UWL7ZA99FH0k8/STVqSKefLv3tb3b/yJHSpZfaBNLcXOmf/5RmzpQWLSr9dV1XuvZaac0a+7ykiiAAAADgheRoLyDeFN3uoFo1+3jnzsivY8YMawk87LDInzsRHXmkVeRKkpMjLV1q/53HjZNSUqQ//lH6y1+kV1+VHnig+ON37bKBLM89Z/+dbr5Z+ve/CXYAAADwDxW7IBVtxUzeF4sjfe2U69r1dd27R/a8lVVamm0tMXeutWVKUv360plnSq+9Vhj2s7OlG2+UjjhC+tOfrA3z3/+2Vs+0NIIdAAAA/EPFLkhFWzEDwW7v3siuYeVKacMGgl0kpaYefN9ll0kDBkh//atdczdtmlS1qrVuDh4s9ehhbwBIUtOmBDsAAAD4h2AXpKKtmNEKdjNm2LFbt8ieF8Wde64dR460/fAeecTCXkntsc2aEewAAADgH4JdkEpqxYx0sJs+3a7va9cusudFcenp0qhRNkBl1Cj7vDTNmtnkTdctrOIBAAAAXiHYBSkWWjFnzJC6dCk8P6JnyJCKPa5ZM2n7dtsTL3CdHgAAAOAVhqcEqWgrZpV9P71IBrvdu6U5c7i+Lt40a2ZH2jEBAADgB4JdkIq2YgbaMSMZ7GbPtvNxfV18IdgBAADATwS7IBVtxZSkpKTIBruZM+143HGROyfC17SpHQl2AAAA8APBLkhFWzGlyFfsfvjB9kmrXz9y50T4qlWTDj+cYAcAAAB/EOyCVLQVU4pOsOvUKXLng3fYyw4AAAB+IdgF6cBWzEgGu507bbT+scdG5nzwVrNmtrk8AAAA4DWCXZCi2Yo5d66dn4pdfGrWTFq9WsrLi/ZKAAAAkGgIdkGKZivmDz/YkWAXn5o1k/LzpV9+ifZKAAAAkGgIdkGKZivmDz9IdetKRx4ZmfPBW2x5AAAAAL8Q7IIUzVbMH36w6+sC50Z8IdgBAADALwS7IJXUipmf7/95c3KkBQtow4xnRxwhVa1KsAMAAID3CHZBilYrZna2neeYY/w/F/yRlCQddRTBDgAAAN4j2AUpWq2Y8+bZ8eij/T8X/MOWBwAAAPADwS5I0ZqKmZ0tpacXXqeF+NSsGRU7AAAAeI9gF6RotWLOny9lZVk7H+JXs2bS779LW7ZEeyUAAABIJAS7IEWrFTM7W2rf3v/zwF+BiivtmAAAAPASwS5IB7ZiJiX5H+x++01at05q187f88B/bHkAAAAAPxDsghSNVszsbDtSsYt/TZvakWAHAAAALxHsghSNVsxAsKNiF/9q1ZIOPZRWTAAAAHiLYBekaEzFnD/fwkCDBv6eB5HBZEwAAAB4jWAXpGi1YrZrVxgmEd8IdgAAAPAawS5IkW7FdN3CYIfE0KyZtGqVlJ8f7ZUAAAAgURDsghTpVsxffpG2bSPYJZJmzaS8PGnNmmivBAAAAImCYBekSLdiLlpkxzZt/DsHIqt5czsuXx7ddQAAACBxEOyCFOlWzMWL7di6tX/nQGS1aGHHZcuiuw4AAAAkDoJdkCLdirl4sVSjhlS/vn/nQGQ1bCilphLsAAAA4B2CXZAi3Yq5eLFV65iImTiqVLHr7GjFBAAAgFcIdkGKRismbZiJp0ULKnYAAADwDsEuSJFsxdy506ZiEuwST/PmFuwCf54AAACAcBDsglRSK6Zf+5EtXWpHgl3iadFC2rVLWrcu2isBAABAIiDYBenAVsykJP8qdoGJmJmZ/rw+oofJmAAAAPASwS5IkWzFXLzYztOypT+vj+gJBDsGqAAAAMALBLsgRXIq5uLFUuPGUnq6P6+P6DnqKPuzQ8UOAAAAXiDYBamkqZiuW3i/l5iImbiSky3cEewAAADgBYJdkEpqxZS8r9q5rrRkidSqlbevi9jBlgcAAADwCsEuSCW1YkreB7t166Tt26nYJbJAsGPLAwAAAITLk2DnOM5ZjuMsdhxnmeM4fyvh66mO47y17+vfOY7TxIvzRkNJrZiS98FuyRI7UrFLXC1aSFu3Sr//Hu2VAAAAIN6FHewcx0mS9JSk3pKyJA10HCfrgIddJWmz67otJI2S9FC4542WSLViEuwSH1seAAAAwCteVOyOk7TMdd0VruvmShor6bwDHnOepNH7Ph4n6TTHCUSj+FFQIG3bZh/73Yq5ZImUmio1auTt6yJ2NG9uR4IdAAAAwuVFsDtS0i9FPl+z774SH+O67l5JWyXV8eDcEfXzz9KAAfZxSood/Qx2LVrYBuhITE2bWuWXYAcAAIBwJXvwGiVV3g4cB1GRx9gDHWewpMGS1Lhx4/BW5rFDD5VGjpRq1ZI6dLD7/Ax2bdp4+5qILWlpVpEl2AEAgFi1ebO0cqW0apUdN26U+veXjjkm2ivDgbwIdmskFW0YbChpbSmPWeM4TrKkWpJKHBnhuu7zkp6XpM6dO8fUvMBataTbbit+nx/BLj9fWr5cOu/AhlYkHLY8AAAA0bRzpwW2ouGt6MdbtxZ/fJUq0kMPSQMHSvfeWzgzANHnRbCbKaml4zhNJf1P0gBJfzzgMR9KulzSdEkXSZrkuokx5N2PYPfzz1JeHoNTKoMWLaT33ov2KgAAQKJbv1766ivpxx+Lh7eNG4s/Lj1datLELhk54QQ7Bj4PXEby8MPSY49J77wjXXON9I9/SA0aRP57QnFhBzvXdfc6jnODpAmSkiT9x3XdBY7j3Ctpluu6H0p6SdJrjuMsk1XqBoR73lgRCHZ5ed69JhMxK4/mze0v1K1brSIMAADghU2bpClTpMmT7bZggd2fkiI1bmwhrW/fg4NbvXqF099Lc//90g03SMOHS88/L40eLQ0ZIt1xh3TIIb5/ayiFFxU7ua77iaRPDrjvn0U+zpHUz4tzxZrAEBWCHUIRaF9Yvlzq1Cm6awEAAPGpoECaNUv64AMpO9u6v+bNs226MjKkE0+ULrlEOvVU+30j2YME0KCB9NRT0q23WsXugQekZ56R/v536frrrfKHyPIk2FVmfgW7mjWlunW9e03EpqJ72RHsAACoXPbulWbPtjd4d+2Sdu8u+5iXZx0+hx1mt0MPlX76yQLd2rU2Tb1NG+mII6R77pFOOUU67jipalX/vofmzaU33pD+8hdp6FCr2j32mDRsmHTFFd6ESFQMP+owBf5to9o6AAAgAElEQVRH8TrYtW5dfhkc8Y+97AAAqDxc10LcF1/YbdKkg4eTBKSlWbUtPb3wmJIiLV4s/fZb4fMyMqSzzrK2ynPOsbAXDR07Sp9+atfxDR1q196NHGltmxdcwO+1kUCwC1OgYpeb691rLlliJXMkvmrVrJVh+fJorwQAAPhh924LPJ99ZmFu1Sq7v3Fj6aKLpF69LBRlZBQGuLQ0mz5Zlrw86fffrYKXlub7t1FhJ58sTZsmffihtWVedJHUpYtdj9erV2wFvN27pdWr7b/JqlVSnz5W7YxXBLswed2KGfgDxvV1lUfz5lTsAABIJHl5FuLefFN6/31pxw67zObUU61VsVcvuxwjnJCTkiIdfrh3a/aS49i2XX/4g/Taa9Ldd0tnnimddJJ0331Sz56RWcfu3Xa9YSC4BW6B+9atK/74I44g2FVqgVZMryp2y5dbmb5lS29eD7GvRQvp88+jvQoAABCOggJp6lQLc+PG2VTK2rWlAQNsz7cePSrf9WZJSXad3cCB0ksvWdXu5JOl00+3gNetm3fn2rrVqqKffiotWmTBbf364o9JSZGOOspu55xj00CL3uJ9y4ZK9sfLe15X7JiIWfm0aCG98optEFqtWrRXAwAAKsp1pblzrSo1dqwNMMnIsGrVwIFWpfJzcEm8SE2V/vxn6U9/kp59VnrwQal7dwtX994b+gC5lSul8eOt7XPKFBtGU6eOdMwx1lZ5YHCrX9/CZqIi2IXJ6+EpgWBHxa7yKLrlQYcO0V0LAAAo37p10pgxtn/b/Pn2Rn/v3hbm+vThjdrSpKdLt9xig1WefFIaMUI69ljp/PNtimf79mU/v6BA+v57C3Ljx9vWDpJNAr3tNvvZd+uW2OGtLAS7MHk9PGXJEns3oWZNb14PsS8Q4pctI9gBABCrdu+2QDF6tDRhgoWMrl2lp5+W+veP3jTKeFS9uvS3v0nXXWdbIzz6qF2L2L+/bZPQunXhY3futOsVP/xQ+vhjacMGC249etjz+vQpfJO8siPYhcmPVkzaMCuXQLALVGsBAEBscF3p22+lV1+V3n7bruNq1MhCyaWXSpmZ0V5hfKtVywar3HijbY3w73/bz/nSS23/vY8/liZOlPbsscf27i2de65t71C7drRXH3sIdmHyenjKkiXWl43Ko0YNq9IS7AAAiA0rV9p1c6++apdKVKsmXXihdPnlNvyjvK0IEJxDD5UeeEAaMkR66CGrgo4eLTVrZlW9c8+1rcACBRWUjGAXJi8rdiNGSBs3cn1dZdSqFcEOAIBo2rxZ+u9/Lcx9/bWN7D/lFOmf/7QNtqtXj/YKE1+9etIjj0h//au0ZYv9ThxL+97FOoJdmLwcnjJhgh179Qr/tRBfWrWy3nEAAOCPdeukyZOlr76y67Rc124FBRbqZsyQ8vPt3+T775cuucQ2EUfk1atnNwSHYBcmL4enJCfbRbjHHBP+ayG+tGpl/8hs2SIdcki0VwMAQPz7/XcbgT9pkt1++snur1XLApvjWEul40hpaVYlOu88qUsXqkSITwS7MHnZirl5MxOVKqvAwJylS+0fFAAAEJzt26VvvikMcj/+aBW5jAzppJPs+rhTT7U30CvrOHwkNoJdmLys2G3ZIjVvHv7rIP4Egt2SJQQ7AADKsnmztHChVeACx59+klavtq9XrWqbXw8bZkHuuOPYJByVA8EuTI5jLZReVexow6ucmjWzdhAGqAAAYJW2DRuKB7fAx+vWFT4uPd22HDjpJNukumtX6fjjrUoHVDYEOw9UrRp+sHNdq9ixJ0fllJoqHXUUwQ4AULm4rrRmTckB7vffCx9Xo4aUlWX7mLVpYx9nZdm/nWw9ABiCnQdSUsJvxdy5U9q7l4pdZcaWBwCAaCookKZOld54Q/rf/2yzaK8uEcnPl1atOrh9ctEiuzYuoE4dC2z9+hUPcEccwUAToDwEOw94UbHbssWOVOwqr1atpGnT7N1L/vECAERCfr792/Pf/0rvvGOBLiND2rNH6tnTtgcIZn/dvDxp2bKDA9zixVJOTuHjGjSwwHb55YXhLStLqlvX++8RqCwIdh7womK3ebMdqdhVXq1a2buW69dL9etHezUAgGAsXizdd5+0aZOFk6I3Sfr5Z7utWmWth9u3S7t325t5DRvatWGnnCKdfLLUpIm/a83Ntb3c3n1Xev99u5YtNVU64wxp5EipTx9p+XLptNMs3E2caNWzonJy7Hs+MMAtXWodSAFNmthzTz/dglubNnbj9x3AewQ7D6SkhF+xCwQ7KnaVV9HJmAQ7AIgPS5dKTz4pPfOM7YXWurUFnY0bpV27Ch9XpYp05JEWdLp1k2rWtMqY60orV0qffCK9+qo9tkkTC3iDB9t0Ry/s3i1NmGCVufHjrVOoWjXpnHOkCy6Qzj7brmML6NDBwt9pp9lavvzStg8YN84C3MqV1roZ+N6aN7fg1rdvYYDLzLRzAIgMgp0HqlYNv2JHKyaKBrsePaK7FgBA6fbulT76yMLc55/bdOzLLpMeeEA6/PDCx+3aZQEvP9+qcmWN3C8osMD01VfW/vjBB9Irr0gDBkhXXWUBL9iQtG2b9PHHFuY++cTWU7u2bcJ94YVWRUtPL/35bdvaBt+nnmpBT5JatJA6dZIuuaTwGriWLS3UAogugp0HvKzY0ZpQeTVqZP/oM0AFAGLTr79KL74oPf+8tVM2bCjde6909dV2zdiBMjJsamNFVKkitWtntxtukHbskEaMsNbIsWMtPHbpYtWznj2tMui6FggLCuwN5vXrperVpexsa7P88ku7v359u5btggvsuYE9eCuidWvp66+lp5+2/eD69WMKJRCrCHYeYHgKvJCUZO+EEuwAIHbk5lpAGj3aKl9799q1aE88If3hDxa4/FC9uoXGO+6Qvv3WKnlTpkgPPyw9+GD5z2/SxALiBRdYtS+cMNa8ufTII6E/H0BkEOw84OXwlFq1wl8P4lerVnYxOgAgevLypEmTpLfflt57z/6Nrl1buvlm6dprg5sSGa4aNaSzzrKbZJW86dOtYlilSuEtKcnaQHftsq0BOnZkwjJQ2RDsPOBFK+aWLXYhdVKSN2tCfGrVyq6DyM/nzwKA2JPIfzft3WsVsbfessrcpk0Wqvr2lfr3l3r1KvsauUipXt3WAgAHIth5wIvhKZs3c30dLNjl5kqrV0tNm0Z7NQBg0xTffdeuLZs6VWrfXjrpJKtanXmmXYMVi/LybEz/2LHSnDk2wv+KK4pvuL18uU16nDjRvseNGy04nXuudPHF9v0xFARAvCDYeSAlpfimm6EItHmgcis6GZNgByCa5syxMPf669LWrRaIbrxRWrBAevllaedOe9yJJ9rwkIsuKntqY0GBhcScHDtu2yatW2cDSTZtkk44waYtBts+uHmztGiRbSVQv75djzZ2rAW1TZvsEod27Wxi5fDhNnW4d2/rjpg61V4jPd2C38UX29j/siZFAkCsIth5wKvhKVTsUDTYnXlmdNcCoPLZtk16800LdLNm2abVF15owa1nz8IBHPn5Vu16/33ppZesEvZ//yfVqWOhKDm5MMAFjhXpbGndWho0SPrjH4tX1g7kutY2+eKLFuAOfHO1WjWrug0YYH+XpqZK//uf7RP3n/9IQ4fa37cPPWRtja1asd8agPjnuK4b7TWUqnPnzu6sWbOivYxynX++/QM3b17or9G+vU1EfO8979aF+OO69u7y5ZfbxDUACFV+vvTOOxZkJLte7MBb9ep2TE+XPvvMhoXs2mX/Jl1zjYWsQw8t+zyuK33zjYW8rVstxOXlWQtjenrh8cCPq1e3LQLq17c1fPKJNGaMBTbJNvEeNMiub6tb1+7bu9eugXvoIWn+fPv7ctAgm1K5fr30yy+239o559hWA6WtN7BVAcNFAMQDx3Fmu67bubzHUbHzwIHDU267zd75u/feir8GFTtI9ktGq1ZseQAgdHv3Sm+8Ya2Hixfbm4aHHSatXStt315427u3+POqV7dNp6++WurcueKhx3HsmruTTgpv3ddcY7fVq61qOGaMtX4OGWLBrXt3awFdudI2xX75ZQt9wbZNOo7tGwoAiYZg54EDh6c8+qgdgwl2XGOHgFatbJQ1AASjoMAqbnfdZV0kRx8tjRtnXSUH7mHmutKePYUhb8cOqVkzC3fR1rix9Ne/2m3+fAt4b7whffqpVfEee8z2j2OTbAAojmDngXC3O8jLs4vQqdhBsmA3dqxdM8I0NgAV8eWXFoR++MFaEd9/364xK63q5jj290taWmGbYyxq317617+s+vi//9E+CQBl4f0uD4Q7PGXLFjtSsYNkwc517R13ACjLDz9Ym2KvXjYB8rXXbHz/eeclVgCqUsXaJxPpewIArxHsPJCSYi0todq82Y4EO0iFkzGXLo3uOgDEruXLpYEDpWOPtXA3apRdT3fJJbQoAkBlRSumB1JTw9ugPFCxq1XLm/UgvrVsacdFi6K7DgCxxXWlmTOlF16QRo+2NxXvuku6/Xb+/QAAEOw8kZoaXsVu2zY7co0dJPsFrUEDe/cdSHQ7d9qeZ6mp0V5J9OXn2xCTHTsKB5oEPl661KZAZmfbGP+rr5b+8Q/7uwIAAIlg54m0NBsbnZ8vJSUF//ytW+1Ys6a360L8ysykYofEVlAgPfmkDfyoVq1wg+sWLaK9ssjYtEm67z5p4ULp11/t9ttvZT+nSxfpueds023+vQAAHIhg54HAO8179oQ2xTBQseMfagRkZto+Tq7LsAAkntWrLchNniz17m0VqH//28bYDx4sDRsm1asX7VX6Z/JkuxZu40apY0fbZuCEE6TDD7d/BwIbhwc2D69e3faha9Ik2isHAMQygp0Higa7UC5aDwQ7rpFAQGamXXu5YYP9sgckAte1qY033mgVuxdekK66yt68+PVXG2n/zDPS669Lf/+7dPPNwW8+Hcvy821/0/vusyFJH30kHXNMtFcFAEgUzM7yQNFgl5MT/PMDrZg1ani3JsS3zEw70o6JRLFtm1WpLr/cNs6eN8+uEwtUpBs0kJ54QlqwQDrlFGnoUPv/4I03LATGu3XrbFuCe++VLr1Umj2bUAcA8BbBzgPhBrtt2+xd6ZQUb9eF+EWwQyKZNUvq1EkaO9aqVZMnS02blvzY1q2lDz6QJk2S6tSRBg2SunWTpk6N7Jq9NHmyhbhp06T//McmWlarFu1VAQASDa2YHghcVxfqZMxt22jDRHENG9p1RwQ7xLOCAttfbehQqX59acoU6cQTK/bcU06xQBhoy+zRQzr/fOmhhwq3BImU/Hxp/nzbc3T7dvs7e9u2wo8rcl/r1tLnn0vt20d27QCAyoNg54FAxS4nx64hCda2bQxOQXFVqtgvggQ7xKsNG6zt8rPPLJC9+KJ06KHBvUaVKtJll0kXXSQ9+qj0r39JH34oXXmljfpv1MiftUv2d/mcORYs33zTrgEsSVJS4cCTmjXtVru2dNRRhfc1aCD9+c82BAUAAL8Q7DxQtBUzlGC3dSvBDgfLzJSmT4/2KoDgTZxo19Nt3iw9/bRtYxDOdNeMDNuI++qrbcDKs89Kr74qXXedVQO9nKDpujbA5amnpJ9+shb5s8+2cNmwYfEAV6OGtdEzuRYAEAsIdh4oGuxCucifih1Kkplp1yTt3p1YkwER/3JybFT/hg2Fx8Bt1Spp3Dj78zthgtShg3fnrV9fevxx6dZbbQjJ44/bZM1bbpFuukmqWze819+2zbZbeOstqWtXC3j9+tm1fgAAxDqCnQe8CHaMtMeBMjOterB0qbe/HAPBmj/ftihYs8aCXGCLlgOlplr17LrrpBEj/BsQ0qSJDSH5y1+ku++Whg+XHnxQOv10aeBAa/0M5s0y15XGjJHuuENav96u47vjDipxAID4QrDzQNHhKfn5wT+fVkyUpOhkTIIdomHmTNuCYOxY+zvq9NPtTah69Uq+Va8e2TCUmWnVtbvvLrwW7oorpGuvlc45x0LeOeeUXfGeM0e64Qbp22+l446za/i6dInYtwAAgGcIdh4oWrHbuzf459OKiZK0bGm/JDNABZG2aJF0553Sf/9rYe3aa21YiZfXsnkpK8uuvbv/fmnGDAt4b79t669RQ+rb10Le6acXbiuzfr10zz3Sc89Zq+VLL1korMImQACAOEWw80DRqZjJQf5EXZftDlCy9HRrOSPYIVLmzrVwNG6c/fkbPtxaMOPljSfHkbp3t9ujj0pffWUh7913pddekw47zIagJCVZK+eePdL111vAq1072qsHACA8BDsPhFOx27nTwl28/OKEyMrMJNjBf999Z4Fu/HircA0dKg0ZEv4wkmhKTrYK3emn22TOzz6zkDd6tP1dPWiQTdps1SraKwUAwBsEOw8UDXZF23hct/zrTbZutSPBDiVp3do2dS4ooEVswwbp66+trS7YyjgO5rrSl1/a0JHJk22PuXvvtevNEq16lZoqnXee3XbvlnbsiO/QCgBASSr5r4reKDo8JSen8P6KTMgMTJejFRMlycyUdu2yaYSV2apVUtu2Nnr+ww+jvZr4lp9vrZZdukhnnCEtXiyNHGk/43/8I/FC3YHS0wl1AIDERLDzQNGK3Z49hfdXZEJmINhRsUNJik7GrKyWL5d69rRKi2QVTAQvN9euK8vKsoC8dav0/PPSihXSbbdZCyYAAIhfBDsPFA12RSt2FQl2tGKiLJU92C1caKFu505p6lTptNOsHTNRrFsn/elP0lNPSdu3e/Oarmt/D23eLK1dKy1bJj32mNS8uXTVVVJGhm0RsGiRdM01hX9/AQCA+MaVKh5ITrbrn4qGOqlig1So2KEs9epJhxxS+YJdXp61B95zj/2/MWmS7eXXo4c0bJi0ZYv9XOLZ0qVSr17SL79Ir7xiA0suu8ymNGZmSr/9Zu2Rq1ZJP/9sx19/tdbc3btLv+XkWLg7UI8e0gsvSGeeycbbAAAkIoKdR1JTi7dhSsG1YnKNHUriOJVvMuasWVZZmjfPRtM//rjUoIF9rUcPCy3ffmsbT8ern36yaY15eTaRsqBAevJJC15PPWXXgQVaTwMOOUQ64gipWjX7eu3a9nl6+sG3jIzin2dmsuk2AACJjmDnkbQ0C3ZF3wnnGjt4ITNTmjAh2quIjGeesamM9etL771nEzCL6trVNpj++uv4DXbz5lmoS0qy6wWzsuz+V1+VHnlEevllq8w1bWr7GB51lN3ivUIJAAD8RbDzSKBiV3QkfUVaMQPX2DG4AKXJzLRWva1bE7uyO2mSbYbdu7c0ZkzJ32t6unTccfF7nd3s2TaJMiPDvt+WLYt/vW5d6S9/ic7aAABAfGN4ikcCwS6UqZjVqrEvF0oXGKCyeHF01+GnVaukiy+2ffvefLPsAHvSSdauuWtXeOfcsMGGl0TK9Ok2/KVmTQumB4Y6AACAcBDsPBIIdrm5hfdVNNjRhomyJPpkzF27pPPPtwr3+++XX73u0cMeO2NG6Ofcs8faOhs0kL75JvTXqaivv7ZKXd269nHTpv6fEwAAVC4EO4+kpto0uqLBrqKtmAQ7lKVZM6voLlwY7ZV4z3Wlq6+W5s61Sl1FqljHH28tz+G0Y44aZVVCySZTjh8f+muV59NPpbPOkho1sjU3auTfuQAAQOVFsPNIYHhKKK2YBDuUJSXFAk8iVuweecQC3fDhdm1dRdSqJXXsGHqwmzDBznfeedaO2a6dVQxfeSW01yvNkiXSBRdIZ59t//2++qpwuicAAIDXCHYeCacVM5EHYsAbWVk2Ij+RTJgg/fWvUr9+todbMHr0sGvWiv7/Vp69e6W77rIA2bSp9MQT1ho5aZJ0yim2UfjDDwe3jpL89pt0001S27bSF19I991na61XL/zXBgAAKA3BziOhtmJu28ZETJQvK0tatuzgvRLj1bJl0oABFn5efjn4DbN79LD/32bNqtjjt2yxlsv775euvNL2jgu0RNaoIX38sdS/v02kvP1221cuWDk5FgxbtLC96K66yjYhv+sum4IJAADgJ2YxeiQjQ/r99+D3sduxg2CH8mVlWdhYskRq3z7aqwnPjh22P12VKjYspVq14F/jxBPt+PXXds1dWfLyrCr47bfS6NHSZZcd/JiqVaU33rAK3iOPWIvmSy9ZG2xFLFli39PChdZ6OWKEhVYAAIBIoWLnkfR0affu4Fsxd+yQqlf3b11IDIFNrBcsiO46wlVQIF1+uQWgt96ywTChqFvXfiYVuc5uyBDpyy+l554rOdQFVKkiPf64tU6+9pq1bG7ZUv7rf/aZ7a23caMNSvn4Y0IdAACIPIKdR9LTbWx7bm7hnnQVacXcvp1gh/K1bm3BI96vs3vgAem//5VGjpROPz281+rRw7YqKOsNlCeflJ5+WrrjDruGrjyOY62To0dbaDzhhMLpmQdyXavMnX221KSJNHOmTb8EAACIBoKdRzIyrGK3Z4+FPKn8il1urt1oxUR5UlPt2q14Dnbjx0v//Kd0ySVWRQtXjx72xsjcuSV//fPPpZtvls49V3rwweBe+7LL7Plr19p+d99/X/zru3ZJgwYVDn/59lsLdwAAANFCsPNI0VbMwKCE8oLdzp12pGKHiojnyZiLFlmg69RJev754IellOSkk+xYUjvmypWFw1nGjJGSkoJ//ZNPtmmW1apJPXvakJdVq+y1TzpJGjvWKpBjx4Z2nSAAAICXCHYeyciwd/H37CkMduW1Yu7YYUeCHSoiK8umLAYz4j8WbN1qg0VSU6X33iusaIerYUPbtuDAYLdrl+0f57p2vnD+/8rMtAmaxxxj0zSbNrXrApctswrk0KHehFQAAIBwMRXTI+npNhhixw7pyCPtvvIqdtu325FWTFREVpa9WbBsWeEwlVhXUGCVuuXLbb+4wBYDXunRQ/roIwtxjmPH666z9syPPpKaNw//HHXr2ubiU6dKK1ZIv/5qWyO0bh3+awMAAHiFYOeRQBVi61a7FkoqP9hRsUMwik7GjJdgd889FrCeeqqwddJLPXrYoJOFC+1n8swz0quvSsOG2VATr1StKp12mt0AAABiEcHOI0U3IKYVE35o3dqqUvFynd3770v33mstjNdd5885evSw45QptjXBzTdL55wj/eMf/pwPAAAgVnGNnUeKXjdU0eEpgVZMgh0qIiPDru+Kh2C3cKF06aVSly5WrfPrOrTmzaUjjpDeflu66CKpcWPbg64Kf7MBAIBKhl9/PFI02FV0u4NAxY5r7FBR8TAZMzAsJSPD9qxLS/PvXI5je8199ZVV7N57T6pd27/zAQAAxCqCnUdoxUQkZGVJixeX/2crWgLDUlaskN55xyZX+u2MM+z49NNShw7+nw8AACAWcY2dR0JpxSTYIVhZWVJenk2ZjMWpjIFhKU88UXj9m9+uuEI6/vj4GSgDAADgByp2HilasatoK2bgGjs2N0ZFBcJLLLVj7t0r3XmndNRRNizliiuk66+P3PmTkwl1AAAABDuPlFSxq0grZkaGlJTk37qQWDIz7bhgQXTXEbBjh3TuudIDD0hHH23tkM8+y6bdAAAAkRZWK6bjOIdKektSE0mrJF3suu7mEh6XL2n+vk9Xu657bjjnjUWhtmLSholgVK9ulbFYqNj9+qv0hz/YZuDPPScNHhztFQEAAFRe4Vbs/iZpouu6LSVN3Pd5SXa7rttx3y3hQp0UeismwQ7Bats2+sFuwQKpWzcb5PLhh4Q6AACAaAs32J0nafS+j0dL6hvm68WtUCt2bHWAYGVlSYsWlf/nyy+TJ9sWA7m50tdfS2efHZ11AAAAoFC4we5w13V/laR9x3qlPC7NcZxZjuPMcBynzPDnOM7gfY+dtXHjxjCXFzmhXmNHxQ7BysqS9uyRVq6M/LlffVU680zbFHzGDKlTp8ivAQAAAAcrN9g5jvOl4zjZJdzOC+I8jV3X7Szpj5IecxyneWkPdF33edd1O7uu27lu3bpBnCK6im7CHMwG5QQ7BCsakzFd1yZeXn65dOKJ0rRpdq0fAAAAYkO5w1Nc1z29tK85jrPecZwGruv+6jhOA0kbSnmNtfuOKxzH+UrSMZKWh7bk2FSlSESuaCvm9u1S48b+rQmJqU0bOy5YYBMp/Zaba9fQjR4tXXaZ9MILUtWq/p8XAAAAFRduK+aHki7f9/Hlkj448AGO49R2HCd138eHSTpBUgzM9PMPrZjwU82aUsOGkanYbdki9e5toW7YMOmVVwh1AAAAsSjcYPcvSb0cx1kqqde+z+U4TmfHcV7c95g2kmY5jjNX0mRJ/3JdN6GDHa2Y8FtWVvh72e3YIV1zjTR1aslf//lnG5Ly9dcW6O6+m/3pAAAAYlVY+9i5rrtJ0mkl3D9L0tX7Pp4mqX0454k3FWnFdF22O0Do2ra1jcDz80Pf4P6556QXX7SBKC+/LP3xj4VfmzVL6tNH2r1bmjBBOvVUb9YNAAAAf4RbsUMJAhW7sloxc3Pt62x3gFC0a2ehK9TJmHv2SI8+ahW57t2lQYOk4cPtDYfx46WePa3l8ttvCXUAAADxIKyKHUpWkVbMHTvsSMUOoWjXzo7Z2VKLFsE//9VXpbVr7dq5k06ylsx//MOqc9OmScccI330kVS/vrfrBgAAgD+o2PkgNdXa4wh28Etgy4Ps7OCfm58vjRghde4snXaa/XkdPdquofv2W9vSYMoUQh0AAEA8oWLng6pVLdiV1Yq5fbsdacVEKKpXl5o2DS3YvfuutGyZNG5c4TAUx7Gpl3fcIVWr5ulSAQAAEAFU7HwQCHZU7OCndu2CD3auKz34oNS6tXT++Qd/nVAHAAAQnwh2PkhNlZKTCXbwV7t20uLFNoinoiZMkObMkf76V6kK//cDAAAkDH6180FycvmtmAQ7hKtdO/sztmRJyV+fOtX2n5s1S9q50+578EHb3HzQoKGbId0AABH5SURBVIgtEwAAABHANXYeevFFadQou16JVkz4rehkzMDHAY8/Lg0ZYq2Xkv2ZbNLEtkcYNcrahQEAAJA4CHYeuuoqu0nlt2Lu2mXHwGbmQLBat7Y3EBYsKH7/ww9Lf/mLXUM3fLi1a86fbwGwbVvb2gAAAACJhWDnk/JaMQOtcQyrQKhSU6VWrYoPUHnkEQt1/ftLr79ubzBkZZU8KAUAAACJg2vsfFJeKyYVO3ih6GTMUaOk22+X+vUrDHUAAACoHAh2PimvFXPnTnsM1zohHO3aScuX21CUW2+VLrpIGjOGUAcAAFDZEOx8Ul4r5q5dVOsQvnbtbEDK3/8uXXCB9MYbUkpKtFcFAACASCPY+aS8VsydO7m+DuHr2NGO558vjR1LqAMAAKisaNjySUWmYlKxQ7iaNZPmzZPatKH9EgAAoDLjV0GfVGQqJsEOXmjfPtorAAAAQLTRiumTikzFpBUTAAAAgBcIdj6pyFRMKnYAAAAAvECw80lFpmJSsQMAAADgBYKdTyoyFZOKHQAAAAAvEOx8wjV2AAAAACKFYOeT5GSmYgIAAACIDIKdT6jYAQAAAIgUgp1PyhqesnevlJtLxQ4AAACANwh2Pilru4Ndu+xIxQ4AAACAFwh2PklJKb1iFwh2VOwAAAAAeIFg55Oyhqfs3GlHKnYAAAAAvECw80lZwY6KHQAAAAAvEex8QsUOAAAAQKQQ7HxCxQ4AAABApBDsfELFDgAAAECkEOx8QsUOAAAAQKQQ7HxCxQ4AAABApBDsfELFDgAAAECkEOx8kpws5eWV/DUqdgAAAAC8RLDzSUUqdmlpkVsPAAAAgMRFsPNJSooFO9c9+Gs7d1obZhV++gAAAAA8QLTwSXKyHQsKDv7arl1cXwcAAADAOwQ7nwSCXUntmDt3cn0dAAAAAO8Q7HxSVrCjYgcAAADASwQ7n1CxAwAAABApBDufULEDAAAAECkEO58Q7AAAAABECsHOJ2UFu927pfT0yK4HAAAAQOIi2PkkEOzy8g7+GsEOAAAAgJcIdj6hYgcAAAAgUgh2PklJsSPBDgAAAIDfCHY+oWIHAAAAIFIIdj4pLdi5rpSTI6WlRX5NAAAAABITwc4npQW7nBw7UrEDAAAA4BWCnU9KC3a7d9uRYAcAAADAKwQ7nxDsAAAAAEQKwc4nBDsAAAAAkUKw8wnBDgAAAECkEOx8QrADAAAAECkEO58Egl1eXvH7mYoJAAAAwGsEO59QsQMAAAAQKQQ7n6Sk2JFgBwAAAMBvBDufULEDAAAAECkEO58Q7AAAAABECsHOJwQ7AAAAAJFCsPMJwQ4AAABApBDsfEKwAwAAABApBDuflBXskpIKvw4AAAAA4SLY+aSsYEe1DgAAAICXCHY+CQS7vLzi9xPsAAAAAHiNYOcTKnYAAAAAIoVg55OUFDsS7AAAAAD4jWDnkypVJMc5ONjl5BDsAAAAAHiLYOej5GQqdgAAAAD8R7DzEcEOAAAAQCQQ7HxEsAMAAAAQCQQ7HxHsAAAAAEQCwc5HBDsAAAAAkUCw8xHBDgAAAEAkEOx8RLADAAAAEAkEOx8lJ0t5ecXvI9gBAAAA8BrBzkcHVuzy8y3opaVFb00AAAAAEg/BzkcpKcWD3e7ddqRiBwAAAMBLYQU7x3H6OY6zwHGcAsdxOpfxuLMcx1nsOM4yx3H+Fs4548mBFTuCHQAAAAA/hFuxy5Z0gaSvS3uA4zhJkp6S1FtSlqSBjuNkhXneuECwAwAAABAJyeE82XXdhZLkOE5ZDztO0jLXdVfse+xYSedJ+imcc8eDA4NdTo4dCXYAAAAAvBSJa+yOlPRLkc/X7Lsv4ZUW7BieAgAAAMBL5VbsHMf5UlL9Er50p+u6H1TgHCWV89wyzjdY0mBJaty4cQVePnYdGOz27LEjwQ4AAACAl8oNdq7rnh7mOdZIalTk84aS1pZxvuclPS9JnTt3LjUAxoPkZCk3t/DzQMUuNTU66wEAAACQmCLRijlTUkvHcZo6jlNV0gBJH0bgvFFHxQ4AAABAJIS73cH5juOskdRd0seO40zYd/8RjuN8Ikmu6+6VdIOkCZIWSnrbdd0F4S07PiQn24bkAVTsAAAAAPgh3KmY70l6r4T710o6u8jnn0j6JJxzxSMqdgAAAAAiIRKtmJVWSkrJUzGp2AEAAADwEsHOR1TsAAAAAEQCwc5Hpe1jR8UOAAAAgJcIdj6iYgcAAAAgEgh2PqJiBwAAACASCHY+Kq1iR7ADAAAA4CWCnY9KqthVrSo5TvTWBAAAACDxEOx8dOAG5Xv2cH0dAAAAAO8R7HyUklI82OXk0IaJ/2/v/mMsO8s6gH+f7s4qVLEoFqUlUmOjogkBN7XYxCiQgmisGkhqjDSmSRODiqaJgv5Bov6hSSNKoo0NoGAIlVQaiEWwIgkx0WJL0bYWwqYgrK12SUslCt3+ePzjnqHXzWw77dz33jnTzyfZ3HPee3bumd0n78z3Pu85FwAAVk+wG+jUYKdjBwAAjCDYDbS1tbjGrnuxr2MHAACMINgNtLW1eNy+gYqOHQAAMIJgN9B2sNtejqljBwAAjCDYDXRqsNOxAwAARhDsBtKxAwAA1kGwG0jHDgAAWAfBbiAdOwAAYB0Eu4F07AAAgHUQ7AbSsQMAANZBsBtIxw4AAFgHwW4gHTsAAGAdBLuBdOwAAIB1EOwGWg523Ytgp2MHAACsmmA30HKwO3lysa1jBwAArJpgN9BysPvqVxfbOnYAAMCqCXYDLQe7Bx9cbOvYAQAAqybYDaRjBwAArINgN9B2sDt5UscOAAAYR7AbSMcOAABYB8FuINfYAQAA6yDYDaRjBwAArINgN5COHQAAsA6C3UBHjiwedewAAICRBLuBdOwAAIB1EOwGco0dAACwDoLdQDp2AADAOgh2Ax06lFTp2AEAAGMJdoNtbenYAQAAYwl2g20HOx07AABgFMFuMMEOAAAYTbAbbHkp5uHDyRn+xQEAgBUTMwbbDnYnT+rWAQAAYwh2gwl2AADAaILdYMvB7siRTZ8NAABwEAl2gy1fYyfYAQAAIwh2g+nYAQAAowl2g7nGDgAAGO3wpk/goNsOdmecoWMHAACMIdgNth3sqgQ7AABgDMFusK2txY1TEksxAQCAMVxjN5ibpwAAAKMJdoP5uAMAAGA0SzEHc40dAAAwmmA32HawS1xjBwAAjCHYDbYd7B59VMcOAAAYQ7AbbDvYPfKIYAcAAIwh2A22HewefthSTAAAYAzBbrDtYPfQQzp2AADAGD7uYDAfdwAAAIwm2A3mA8oBAIDRLMUcbGsr+cpXFtuusQMAAEbQsRtsa+uxbR07AABgBMFuMMEOAAAYTbAbbDnYWYoJAACMINgNpmMHAACMJtgNJtgBAACjCXaDCXYAAMBogt1grrEDAABGE+wG07EDAABGE+wGWw5zgh0AADCCYDfYcpizFBMAABhBsBvMUkwAAGA0wW4wSzEBAIDRBLvBBDsAAGA0wW4w19gBAACjCXaDucYOAAAYTbAbzFJMAABgNMFuMEsxAQCA0QS7wXTsAACA0QS7wVxjBwAAjLanYFdVr62qO6rq0ao6+jjHfa6qbquqT1bVzXt5zblZDnOHD2/uPAAAgINrr1Hj9iQ/k+RPd3Hsj3b3F/f4erOzHOyqNnceAADAwbWnYNfddyZJSSynZfklAAAw2rquseskf1tVt1TVFY93YFVdUVU3V9XNJ06cWNPpjbN8jR0AAMAIT9ixq6q/S/JtOzz1W939/l2+zkXdfXdVnZ3kxqr6VHd/bKcDu/uaJNckydGjR3uXX3/fEuwAAIDRnjDYdfcr9voi3X339HhvVV2f5IIkOwa7g+bQoU2fAQAAcNANX4pZVWdW1Tdubye5OIubrgAAALACe/24g5+uquNJXprkhqr68DT+vKr64HTYc5P8Q1X9S5KPJ7mhuz+0l9cFAADgMXu9K+b1Sa7fYfzuJK+etu9K8qK9vA4AAACnt667YgIAADCIYAcAADBzgh0AAMDMCXYAAAAzt6ebp7A7V12VnH32ps8CAAA4qAS7Nbjyyk2fAQAAcJBZigkAADBzgh0AAMDMCXYAAAAzJ9gBAADMnGAHAAAwc4IdAADAzAl2AAAAMyfYAQAAzJxgBwAAMHOCHQAAwMwJdgAAADMn2AEAAMycYAcAADBzgh0AAMDMCXYAAAAzJ9gBAADMnGAHAAAwc4IdAADAzFV3b/ocTquqTiT5902fxw6ek+SLmz4JDiz1xUjqi5HUFyOpL0bbrzX2Hd39rU900L4OdvtVVd3c3Uc3fR4cTOqLkdQXI6kvRlJfjDb3GrMUEwAAYOYEOwAAgJkT7J6aazZ9Ahxo6ouR1BcjqS9GUl+MNusac40dAADAzOnYAQAAzJxgBwAAMHOC3ZNQVa+qqk9X1bGqeuOmz4d5qKrnV9VHq+rOqrqjqt4wjX9zVd1YVZ+ZHp89jVdVvXWqs3+tqpcsfa3LpuM/U1WXbep7Yv+pqkNVdWtV/fW0f15V3TTVyl9W1ZFp/Oum/WPT8y9Y+hpvmsY/XVWv3Mx3wn5TVWdV1XVV9alpHnup+YtVqqpfm34+3l5V76mqrzeH8VRV1Tuq6t6qun1pbGVzVlX9QFXdNv2dt1ZVrfc7PD3Bbpeq6lCSP07yY0lemORnq+qFmz0rZuLhJFd29/cmuTDJ66faeWOSj3T3+Uk+Mu0nixo7f/pzRZKrk8WklOTNSX4wyQVJ3rw9MUGSNyS5c2n/95O8Zaqv+5NcPo1fnuT+7v6uJG+ZjstUk5cm+b4kr0ryJ9O8B3+U5EPd/T1JXpRFnZm/WImqOifJryQ52t3fn+RQFnOROYyn6s+zqIFlq5yzrp6O3f57p77Wxgh2u3dBkmPdfVd3n0xybZJLNnxOzEB339Pdn5i2v5zFL0XnZFE/75wOe2eSn5q2L0nyrl74pyRnVdW3J3llkhu7+77uvj/JjdlHkwmbU1XnJvnxJG+b9ivJy5JcNx1yan1t1911SV4+HX9Jkmu7+8Hu/mySY1nMezyNVdWzkvxwkrcnSXef7O4vxfzFah1O8oyqOpzkmUnuiTmMp6i7P5bkvlOGVzJnTc89q7v/sRd3oHzX0tfaOMFu985J8oWl/ePTGOzatGTkxUluSvLc7r4nWYS/JGdPh52u1tQgp/OHSX49yaPT/rck+VJ3PzztL9fK1+poev6B6Xj1xU6+M8mJJH82LfV9W1WdGfMXK9Ld/5HkqiSfzyLQPZDklpjDWK1VzVnnTNunju8Lgt3u7bR+1mdFsGtV9Q1J/irJr3b3fz/eoTuM9eOM8zRWVT+R5N7uvmV5eIdD+wmeU1/s5HCSlyS5urtfnOR/8tgSpp2oL56UaXnbJUnOS/K8JGdmsTzuVOYwRniy9bSv60yw273jSZ6/tH9ukrs3dC7MTFVtZRHq3t3d75uG/2tq6Wd6vHcaP12tqUF2clGSn6yqz2WxRPxlWXTwzpqWNSX/v1a+VkfT89+UxZIV9cVOjic53t03TfvXZRH0zF+syiuSfLa7T3T3Q0nel+SHYg5jtVY1Zx2ftk8d3xcEu9375yTnT3dpOpLFBbof2PA5MQPT2v+3J7mzu/9g6akPJNm+y9JlSd6/NP666U5NFyZ5YFo28OEkF1fVs6d3OC+exnga6+43dfe53f2CLOalv+/un0vy0SSvmQ47tb626+410/E9jV863XHuvCwuCP/4mr4N9qnu/s8kX6iq756GXp7k32L+YnU+n+TCqnrm9PNyu8bMYazSSuas6bkvV9WFU72+bulrbdzhJz6EZLGOu6p+KYv/6ENJ3tHdd2z4tJiHi5L8fJLbquqT09hvJvm9JO+tqsuz+MH22um5DyZ5dRYXfv9vkl9Iku6+r6p+J4s3GZLkt7v71IuDYdtvJLm2qn43ya2Zbn4xPf5FVR3L4l3uS5Oku++oqvdm8QvVw0le392PrP+02Yd+Ocm7pzc178piTjoj5i9WoLtvqqrrknwii7nn1iTXJLkh5jCegqp6T5IfSfKcqjqexd0tV/k71y9mcefNZyT5m+nPvlCLNzkAAACYK0sxAQAAZk6wAwAAmDnBDgAAYOYEOwAAgJkT7AAAAGZOsAMAAJg5wQ4AAGDm/g9oOGn51tvqigAAAABJRU5ErkJggg==\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "average_H2=[np.mean(H2[:i]) for i in range(len(H)) if i!=0]\n", "plt.plot(index[1:],average_H2,label=r'MCMC Samples Mean',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "plt.acorr(subH2,label=r'Auto corr of h2',color='blue', maxlags=2000)\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 使用随机游走的Metropolis-Hastings算法从Beta分布中采样\n", "为了从Beta分布:$$f\\left(x|\\alpha,\\beta\\right)=\\frac{1}{B\\left(\\alpha,\\beta\\right)}x^{\\alpha-1}\\left(1-x\\right)^{\\beta-1}$$中抽样,在这里使用随机游走的Metropolis-Hastings算法,每一步令$y_t=x_t+\\epsilon_t$,其中$\\epsilon_t\\sim N\\left(0,0.05^2\\right)$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from numpy import random as nprd\n", "\n", "##设定参数\n", "M =20000\n", "alpha=0.5\n", "beta=0.5\n", "domain=lambda x:(x>0)*(x<1)\n", "pai=lambda x: (x**(alpha-1)*(1-x)**(beta-1) if domain(x)==1 else 0)\n", "\n", "#随机游走\n", "def sample_q(x):\n", " return x+0.05*nprd.normal()\n", "\n", "\n", "##独立的MCMC算法,输入:\n", "## N_samples : 抽样次数\n", "## pai(x) : 目标密度函数\n", "## q_sampler(x): 给定x,从q中抽样的函数\n", "## x0 : 初始值\n", "def MH_RW(N_samples, pai, q_sampler, x0):\n", " X=[]\n", " x=x0\n", " for i in range(N_samples):\n", " y=q_sampler(x)\n", " rho=min(1,pai(y)/pai(x))\n", " if nprd.uniform()<=rho:\n", " X.append(y)\n", " x=y\n", " else:\n", " X.append(x)\n", " return X\n", "\n", "## 计算积分\n", "x=MH_RW(M, pai, sample_q, 0.5)\n", "## 取后面80%的样本\n", "subx=x[int(M*0.2):]\n", "\n", "## 诊断图\n", "import matplotlib.pyplot as plt \n", "%matplotlib inline\n", "# 设定图像大小\n", "plt.rcParams['figure.figsize'] = (15.0, 8.0)\n", "index=[i for i in range(len(x))]\n", "plt.plot(index,x,label=r'MCMC Samples x',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import special as scsp\n", "index_den=np.linspace(0.005,0.995,500)\n", "density=[1.0/scsp.beta(alpha,beta)*x**(alpha-1)*(1-x)**(beta-1) for x in index_den]\n", "plt.hist(subx,label=r'Histogram of x',color='blue', bins=50,normed=1)\n", "plt.plot(index_den,density,label=r'Beta Denstiy',color='red')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "plt.acorr(subx,label=r'Auto corr of h2',color='blue', maxlags=2000)\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 使用随机游走的Metropolis-Hastings算法计算积分\n", "在这里,我们令$\\epsilon_{1,t}\\sim N\\left(0,0.3^{2}\\right)$,$\\epsilon_{2,t}\\sim N\\left(0,0.3^{2}\\right)$以及:$$y_{1t}=x_{1t}+\\epsilon_{1,t}$$ $$y_{2t}=x_{2t}+\\epsilon_{2,t}$$\n", "对马尔可夫链进行更新。" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Intgral1= 0.0246826829898\n", "Intgral2= 0.000607347351824\n" ] }, { "data": { "image/png": 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9tWxJCF/QYJ8giOYIKW3NhM8/Tz5nzixXDkbRL90pU5LPyZPNy5g2zY0s9QgtLCdCgfV1y5eXKwdBEARBuISUNoIgjKEZbyI0WJukiYT6hfqd2ibEZ/PMM8uWgCDkkNJWo+y5J/Dtb6unD+0lF5o8BEEUD/UDBEGEALlTE7WAUsh/Ijxmzsx3deTNYoU2OCpaHpp9J4jmAT3r9U9o7zOCIIgiIEtbHVILL7SyZKSBnFtogBwGy5cn+wsR1CYJgiCKYOFC4P33y5aieUFKG1EKKkrbxInJJpeffFJMfYQ5NEAul223BX72s7KlCANS2uof6s8J3yxZAtx9d9lShM1uuwGdOpUtRfOClLaAOfhg4I9/1M8XsnukTsj/664DXnoJePll9/UTbgilXTV31q4Fnn++bCkSym4TpLQ1X8pue0T9cNppwOmnA+PHly1JuCxdWrYEzQ9S2gLmlVeAq68uWwo/qLxc16/3LwdBhEJjI/C//5UtRbH4HGST0la/8NrNK68A7dtXtnchwidkJfvTT5PP1avV86xdC+y+ux95CAIgpY0oiSI669deA265xX89BOGCm28GvvOdZCN4HUIe+JQBXY/myWOPJWtsRo0qWxKintDpTz76CHjvPX+yEAQpbc2E5jiQOfBA4Kyzkv+b4/kXAbmiuWP69OTzgw/08lHbrobaZP0javPpYwsX+peFqE9c9h/URxOuIKWtmRDaQEalE3PV0T31VHjnX2/QdbXHtI3SgIDPggVlS0CUTWNj2RIQPGrpfeGif6U+mnAFKW3NhNA6jSLl6dmz8n8tvSwId8Qx8P3vA08+WbYk+dSL0la2PKz+e+4pVw5frF0LPPpo+de5TJrzuRPhktd3U3slXEFKWx0yb17yyesoyu48dKJHkoJFuKKxEXjxReAXvyhbknzqRWnTwYfstXw9VOjXDzj2WODZZ4ur8+67gTffLK6+PETvD96xem8LhH9cjEOoHfKZMoWujS6ktNUhLVsmn1tsUa4cIuhBrQ9q7T7WgrzNSWkj9Pnww+Rz8eLi6jz9dGDffYurz4SQt7oh+NTC/fHlHrlmDTBnjn3ZtcrYsUC3bsCNN5YtSW1BSltgzJmTuL/Y0KJF8rnZZpXfQlvTVeSaNtdlERVM2hVt5cDHtI3Sup1q6FkPg7PPBn73Oz9l0z0mfOM7EMnJJwO77gq89Za7emqJ2bOTz4kTy5Wj1iClLSBWrUoe4vPPtysnFMVMhM5L1+X51MK1qWfeegto1cq+jdczZGkj6oGbbwbuvLNcGWr92Zg/P9l/rl6R9XUh3D8XYxVeGWPGJJ9LlmiLVFeEcI9rCVLaPDJiBNC9O7BokVp6tonj/fe7l4X3YDz8cDIbWiQ6a9pcQh1DGLBw9v/+tzjdunXAddclny4JuR2Yymaab8MGYNiwsK+JCfV2Pnk0l/PkoRryX4UVK8IdOB9/PHDwwWVL4Q/ZvaqXNi6KL1D2Obp+x6pCE+hmkNLmiTgGfvpTYNIkYO5cvbxFNeYTT0xmQ4vEpIMqu1MrCqa01yKu2+zNNwMXXujO370W2lDRgUiuvRY46ijg8cfN8ruQhwKREK4wXdP21a8CW2+d/P/aa8n+nrNmuZXNlBdeKFuCcgnhWdbpj3UsbSGc2+jRQJs2SbsvixCuQy1BSpsnbrml8r/qQ9+cGm9zOldV3n+/bAn00b2PqumXL6/+bA4UrbQxq+enn5rlJ8qlOc9Uq7Z5lXSff175f+DAZAD78stmctUD8+cDnToBt99etiRhjBNcTEK5tAyb8pvfJBOhaZ55JvG4+O9/i5EhTXPuv2wgpc0T6cWlLl8wOoQY+tjEPdJlyN2QO4pQ7pEJute1FtYylIXutbQNRFJv17rezofQw+b+h+KyViZz5yYTiH/7m786VPu4mTP9ySDDdyASlWMuuffeZMlBGvbu2IQ0gZqBblVAuFIsaiH0cVnykNJWLrrn6Op+1cK1LXpNW1nrS31Tb+eTR3M5Tx6+JkJDfj8UzYYNZUsATJ9etgT+ApGE8PwypY3afe1ASluK9euByy+vbE5dNK6UthA6AxkUiKQptRC6fdas6rV3tgoDUaFo90i6B0S9U/RECFE/uOwfecHoXFl133rL3J2X1V2mpY2eNT1IaUsxdixwySVAv35uy20ujfK444AddlBLW/Q+bbVA6Of7+efAHnsk+8tkca0A+HQVDp2iQ/4Xca3XrCluUqKW7rUNLp652bOTdS21Bu8e16vluGiKvH71dq/ynkmeUuXq3L/+deC73zXLW6aljSYNzSClLcWaNclnQ4NdOWvXVjYO1MHVQ1yWe+SQIcDHH4vTlPViXbGi2PpMCP0Fxixszz1X+c1XIBJGLXXsjY12ikm9WtqWLwfatgV69Wp6jKJHlssvfgEccUTZUviD2kJtU2/3r337yv8hrJ8MYa1/vd1j35DS5oHf/Q548UX9fK4foBADkTBU5HHZkSxYkHy2bu2uTNeEdo+yiBRulXu1cGFl4F5LypgqBx8MtGjBPxbHwEUXAf/5T35+0+c/9EAkS5YkMorOndDHxX1LB8xSYelSYJttgHHj7Ou2QScKrY7rWKjWujLkCe0a1CshKG1luEfW4xigCEhp42D7EKUtESb1+mjMRT4go0fL0xTdUW2+efLZrl2x9epQhvXxuOOSEM8qsI7dVM5Ro8zyuaCIayva6+bzz5N90Y48Mj9NWYFI6o16H2yWed8uuSRZn/Otb5UnA6A+cXTMMYnr2MKF/mWqF4p4fmqp73FxPUIPRELRI2sHulUpfEWqCyFSYpEyHHaYm3JcyhyCG4CMotvJffclLq2XX66WnjcL7Uvmsp6ZVq2Aiy8uvt7Vq4GHH07+L3pNm28o6JBbfJyfqrXWxO2/TKZNSz7TwZNEhPx+ELF+PbBsWdlSFMfnnyeeC6r31QSTtiDLE1pkb4oeWXuQ0pbC1cMTSsQq3uA6lIez6H3afJTlmlqIHgmYu0eaUPT9Wr/e7/5Eedx3n3ne0JSU0OSpV1w+G6rh3UPpo0LY9yokjj0W2HLLsqVwT969vOqqxHPh1luLlcclIbRTih5Ze5DSxqGskPu0T5t9Wp9l6PL888CcOerpQ7tHWUJd76FC6DKnB8O1Hj2y7LonT3ZfZoi4vHa1prTxKGoz5DKQyfPEE8XVZcrIke7KWrs2+Vy/3ryMKAL239+NPCa4DkTCrMo6qLpHTp2aWDddEvIEesiQ0sbB9SDI10agJpT9MtIZ+Nf6S/hHPwL22Uc9va2MCxb4PU9bpS2dr7l12LJrlr4eRQUiMbkHo0cDf/+7Xp6in71aDGGvg49nR1VpK/v9wfAlR3Prl4pEN+hNEYwfL09TK2varr9eP4+Ke+SaNUDXrsn6UB+E0qfUCqS0pfC1pk03n64cq1fLfbtDezBU5HEpM+uciroOrL6VK9Xz2Mj27rvAV76ivj7NhCItuEXsHRYqIVvaDjsM+Mtf7OojwqPWlDbCPyHca5kMRUxS+irTtaVt3Tr9PCpjTtY3mEREF0ETJGaQ0uYB24dQtzHvsw/QubOaHKE8KEy2Hj2A7bYTK50uZC56T5QZM/Tz2Mj22WfJ54gR5mWo4mKtZCjtMBRkL82+fYE33+Qft40eGcLgTMavfgX86U9lS1EOCxcm28h88EHyvcxAJKG0FVrT5o8ir1+9Rb6VyeXT4mZSjsqaNnZMdWKH8AspbRyKdo/csCFRWkzrfe89YO7cyvdQO7Q07FwnTkxCzi9dWkx9tvd2663V0jGlLb2ZpgwX60WKWCtIgyK/sOd30aLk/yuuAK65BujTh58+tIGPj/bx+OPAP/7hvtxa4IkngDvvBG66yV8dtKatmtD6uNDkKZtaUCyLLle1vCFDKlFgdaJHktIWBqS0BcDPfw60aVN+9MoiyJvdL0pm23qWLFFLxxZId+liV1+IFNm+ynZZdlW+zpq2Vq2Sz4aG5HPAgOrvorLffBM480y9wXWZ1ybkvioUmNsTCwRQ5pq2UJQ232vaqF0SLgmpDzzuuOQvXbdK9Ehfzz49a3qQ0sbB9KU4ZkySl7mqqfL008mn67D8eQ9DHFf2hBLRvj1wzjluZJHJ5BtWr+uOJ475EazYby1b6pVlI4cupmunXNxDEzeSkHHZrtq0qf5k5F2TdN2//30SBpu50okIwSJfxp54RFNqTWkTUWt9R2gUcf1U+548WULou1R5+eVkewLA7965rLz16xPPjJkz89OyACzseT7ppCTgiKhc19TSPQwJUtocwpSvLHGcuP9NnVqMHLKH4ckngRNPlJfz2Wf+XHKKtrT5WtN2yy2JZeSTT6p/L1ppKxLemrbmQmMjP7iMy8GsbPZz2TLg29+uPJvpezBvnnl9ZXDbbeXVTVR4/321dKEobSGv1y6b5cvduLK57hdq7f642lz7pz/lj/1cj0niOHk+W7VK1kCfcYZaHsaCBW7k0KW5jSFsIaWNg0ojmj8f+PrX1ffhOuWUJGxqkWbyvMH1okV+6xVRlvuJr+iRDz2UfKbXFAJmSlutUItKmys5jz4a2HzzptZ028EsbwY2OwBg32fPBsaOBc49tzp99v9QCFEmIoG54v7zn/zjDQ3AL35R+W57L9esAW6/vXjlT3UAHqpioXrd164F2rUDzjrLrzzNCds2n7e/mY/x3uuvV75nxyQ8VJ5DsrSFBSltKXQa0SOPJPuO3HijWvphw+RpinKPNE3nknqxtGXLZ+QpbevWJW60vGiZLmTzeR3L8MsPrWNnm9guXFj9uw9LW/bc2e9sY1n2nS0qT1PmdStbSTvggHLrryUOPzz5zGsvF18M/Pvfle+27fzSS4E//AEYPNiuHN99Udlt2BTm4vbgg/ZlFREow3YtsM/75MrSlnfcx5hEZ4shoNolslbbfHODlDZDVHeSB/SVJ98DrrzBYJGo1OlDrqJcPpjS1qJF9e9DhgCHHsp3O62VTrMIOV3WsWgR8Oyz7soDmsonG8zqBCKR9QMsMAVrWx99pF7Pc89VJpBs+pmy2mreuos0HTr4l6NekA0cddu5DDbZsXy5XTk8QpvgKZOi10cXTRH32uQ6mCiZZV7vWbPKq5swg5Q2Q3hKm21HUlYI2DLWKWTrFMnqcp+2oiIg5Vna2KAlPdDOK8Omfl958vLpllWku9I55wC//KV9OWlcD2Z1zpNZ2phrG6Ndu8r/effjxz8Gjjqq+rd02rlzgY8/lstQVnTKt94qtr56R9dtPOQ1bUTY8Pq49G+ivVqz1MP99z3eU3mnbLONfrmuqYd7WSSktBmiY2lLY9NAP/ssmSmXmcB568bKcG3jwZSYa65RlyF7bPHixFKVXZsnwpd7pMzSRmvayufDD92XmR28+nCPzIMpbZtu2jSfTjvn9RMdOwI77CDPW9SePWvWAGefrVdvLbRJF5ThBhjKtfXtjh3KeTLy5Bk+HBg9Wp4uVJi8Tz+dRMvNC+ZWBj7cI3m4DERSZn5dyDJuBilthvA2JVR1MclD5hZ13nnJTPnNN+uVl8XGPfKSS4CddlJPn2WLLZLPL39ZnjbvOtx/f2I9GThQvV52jm+8UXEvc0n2GrK1T1lrSCjKM1B9fT/7LNnfiykEPFzKl31usou1Qxt8xHH1gCIrX1qZePPNZB8cUxcwmeLF2i9rW6aWT5uXZlEWl4cfru7vVOqdPt2fPPVGrVraRNj0HbU0kFy5EujVCzjssMpvtbqeb9y45HPCBDVZXN+not7LRYT8d50ntHdxc4eUNkNYQ9a1tKmUmdchrViRfOZFI8orz1U6ALj88vxNfnVQURzz5GLXQWdQzMoaMgQ48ED1fKYwpbRtW/5xX4MD0w62b99kf68hQ/zVm5fmnnsSZV60r0zZ3H038LOfVb6L3CP/+tfkOrK9cHjpRcQxMGNGYlHmkecema5Htz5dRBavdHnPPAPstpt++Xn1qCgNW29tXl8toduHLF4MDB1afU1117SZtJXHHmvq+ubDKlBLCpcLeM9grQ+wBwwoW4IKqu3phReS94NOHsCP94+N5Vwlbzo6pU29rvI2R0hp46DSiFiH6dI90rWSFaJ7pEldeaHPTcuYODHZ66oIXA6eL7002ajTth4ebDDM2yhchIuk+wHyAAAgAElEQVS2M3x48hmyhSS7WbVIaWOTCjrXJjsD27lzfhREVlc2yI1IPlmduqhaXB54wKz8vPUtZYaornX69Uu2rBg7tvKbrqXt6KOTz/32U6/3mGPcRDMk1And4laEgr1qFXDBBfz14yqonv8PfgCcfrq/8ssqj8eoUWZ1L1gADBpUG5b60CGlLYWsI2GDMUAvEImrIA2q5bD8vAeEV3YZSpuLGVzTQTGQdLQucPnykZ3PgAGJO4wPmAJgulbJpo2L1pGEOnsuWtNmO6nAroNMgRY9Q7aTBe++K87jc03boEHJ+pZZs5peS5WXfr0NDFy9V+67L/lctappGaplMQ+CXXfVq/uTT6q/+wzaFbrCYoIPrxmVMj76iL+liGtMl5ak18R1717dZ44cCVx/PfC3v5nX75pPPkmWIaTrDGVNm025cZy4uOYtrzj/fOD444HJk93K1hwhpS2FrHHus0/TtEUO2lXTyY6bDIRGjAC++U15uloh7brmAlUl1Hawkecyl4dKiHRATWkL3SLrE9n95T1DRb1EecqaraVNtq/koEHy8lXlyPLII8nn2283PaaiLLpWKB95BPjvf92WWQZpZY0hs7SF9hz6xsck0dSp+ZuXu4a31t6GDh3s3JuL4uSTgUmTqt+PTIH47DOzMvOu4bJl+h4paW69tfq77jP2n/8Ae+7ZNMCWybOajhTMe6+MGqVW7vTpwLe+lVg2844D1Upd0ROyY8YA7dtX7ztZi5DSpoHKDvM2FGEuz/tt8GDg/ffzy3ruuaaLhPPo1k1PJtHvrvC1J1VolqC0rJMmAa1bV9wPRWlNLW3NbVDHUFHaROmzuAxopJtWh549k8+su6hL2Fq9Rx8Nw9J2wgnAIYe4LdMFLrdC8ZXeF7qbCJfZTx9/fGJpYNu9uCKUJQ822Mopuq8ijyMdsjJuuSVw4ol2ZQLmbfLGG5P137I14Crli8p49FHghz8Ebr9dXs78+clnniUthLY6aVKiwI8ZU0x9viClLUURwSFUGq8r98i89NnyFy0CevdOBicy2VTgBUgwKSePokLxuiB9vsOGJS9vlbQ29TDYouFnnuHnSStoTGkzfcGZyv7++3pbN6gyZgxwxRXuy2W4cO9VLVv3uGoak/zbb69XTva5W7MmfxKBwfqPhx8G/vjH6mPN0T0yDxdtTmZp+/RT+zp4mMq+dGnyyVtDFGq4/ilTks9aaZehXT8RKhOqpv2laMxgGrBLtW6X6U3LZUaKtHts3jVhz6XO2LXoMZnKWvBagJQ2S3hrc3xj4kYpUghZCPFXX7WTS0emote02WDS6fPy3HWXeT26CruMAQOqFUimwM2ZI89runaKR6dOlcAILjv2Qw9Noji6QmRZ+/hjYN68yndXa9pEadLfeel9bX5tqzD++9/ydZnpvQ2z1gmV8ypqD7mysH3PpPMzi2nePUu3a1E6nTpdoLLJug0u3i0jRlQHE7KdlHvlFWDJEnm6UBG1AV3vApX25KrNheDhoFp3WfXLlmG4tLTNmQPccIN+PtPggaFR4+KHha/Z7SzZF6ltebx0aV9nnbJ00+bVJyI0l0QTdM/B5l7yfrv00urvX/1q8pm3RYFMBt17LguIE/LgA6iW78ADE39+URrTsnm/i46brGnzea2zZatsVyLakJ4sbfak7wmbpMlrA6J7YUOofbjLZ+K55/JDpOvS0AAcfDBw6qnidEVa/GuF0M/D1Xsi+73IZ0x1LaWLe9GnT7JncTa4kQymtJGljZDi2j3yuefU6s0LtpG3ToSVv2gRsMMO/LptySvnoIPU06oerzVc+33rdNps9klnsK9bRz3dr/S5ZNe6+oyM57IMX+s8RagoVCL3ahUrWr0rbT6eo7wymReGz7pN4LXd0BRBm2AVWdgavryQ61lcu9qHik/3yGw5rilyg3BX+U2X7oiOP/+8nuzTpiWf2X7+mWeAn/4UeOopfj6WnheQqZYgpc2Q++93X6ZMaWOIZqujqNJos9GFZPUyfO5h5lv58IFJh16WuyevDF4UviyuXnCqlH1PbXG9DsFVUAkdS1s6n8pvJpgEErG1tNW7e6RLZK5CWaWNUMdU4Z0yBXjtNX5e24BHLliyBLjtNru6XLr4ytK4VGaKnDCREdJyHJmlTbT04fPPgTfesJdryJDEJTlvvSGT8aab9OsKCVLaDGGRFtNufa5m2F2ZmFXlUTFtF7nuRTXtmDHhDCp0ffJ105rMZLH7md5M1xe+LDtFKnc698rnJs+699pU6TIZ1Ngqqyr5N9ss/5hL98jPPqvNWVcfz0TRlrYiXXLzeO+9JNgNY9Ikt9fW1NK2//6Jy3Ua3mSMz8kWEX36AGeckayxM0W1X5D9LtqaxIdiWJbS1tiYLGkocp8zl+8F2fH0HsgyZIphXl31MplHShsHncY6cKDb8lTKce3+k23sZb0MsqQfzvfeq7wE2e+vvebH4pmloSH/mOmLwdeaNp+4lKHINW1Fv2h9BSJRIe8Z/vjjpkEMmG8/z43al3uVSt/1ta/p5R85MsnDJtBU+8dddxVHzK0n2D5JWWQDHRYVzgWTJ8uDMakimqQSMXMm8OSTyf/f+EZ16Pbu3cXl62KqtK1e3fQ31Xe/y7FB3jVg+57x5HRdVx5vvpl8TpzopmzVCVOXSzZ03hOzZyfBw04+2awuFWwmXm0sbYDbyfe886gXt3lS2lIUMavvYt2SSbr0/9nzLPLhN5m9mTcP2H134LLLmqaZMcNeJhmyxd+88l27R/pW2kJbh6USxdI1Ote/TEuBySBkhx2AXXap/m333ZPPL31JXTZbVF6cIpc9Xv5rrgHefbeimKjU8cknwPLl8k3ETQhhgiVLly6V/3Um5bKKPks3dizw4x/rDdzL3NSWyd2rF/DznyeDxOXL/daZVdp8ub8XUUeXLsBhh7mry+R9s2QJsOOOieLSurU47Q9/CPTtm/xfyxOADNanzZ7tdkmGLjKFyHQc4WL9p2wCqlkpbVEU/SSKohlRFM2KouhPOWmOiaLo7SiKpkVR9IhbMZsHqu6RrhufiavXunXqCpMtbB+vJ55IPtPXRxS0wBWyNYSqlBH4wXc9vgKRsMHgV7+aWFRVog66qNdFmWyhtI4M6euou3Gr6iA8u1Y11EAkorJ5Li7ZUM4qdfhyM+rbN3HvVF1PXAY6SlueAj1vXhIQa9YstTqjSDxxqItpfra+16WVKA8f1gPVNW2u+7zp04HRo5P/XUbY1FFC2dYqDzwgv/+jRlXapq2lTTXdY4+plZHl008Td1MVK/SGDWKXUZceEiNHmufVTWeitOlOpDYb98goiloAuBXA4QC6AOgdRVGXTJo9APwZwMFxHO8N4FwPsnrH18DYlQVNVz7V9NkXgcpLvW9foHPnpDO/4YbKfj+yek1eKqIOWjUktS93L5fl2FjadGXMDsZMB0Gm10bmHplepHzggcCf/1w5Nm1aYllxjc65iAZPbEuOMvoTdqx7dz+Kg+052U448V682VlenZfzdtvZyZPl1luTwbrqtiwumToV+O53gcGD1fPo9schWhGzqLy/8pQ2XYVk1SrgyiuBxYubHnMZPVL1PoVuVXJFEVGLdde0mb6TRo1KArv06ZOfRlVpTxNFwL33At26mck1Zkx13dn/09i2SzbBsXKl/DqaxnxoTpa2/QHMiuN4dhzHawEMBvDzTJrTAdwax/FiAIjjeL5bMesHFrpXhA9Lm2v3SDbr9tpryZ4ZZ5+tX0aWjh3VOq40RVjabB52E3dQ23IYonZkslcJTwa2D5GvFzxzYXr++cpv++wjXvdUBCrn63LQpkJWpn/9S5yetY9ly4oLyOHjxZn1UFAZZKget5XJZ5msD2b873/Ayy/LZ+xdTZjZYHt92L6SaXQULpnSpspjjwH9+gE33tj0GPMMYbiYOFS1tNWCV4dunaZyharIsnuk0yc2Nurd29/8JolG6hvbNW3sXXnGGcm7XcVKnWdpy7tHzcbSBmBHAOk524YvfkuzJ4A9oygaG0XRa1EU/YRXUBRFv42iaEIURRMWLFhgJrFHiljTtvXWwNCh/GOqHYJs93mGamcgMzOfey5w++3Vv7FrxWRRdZMRMXeu/kL1UCxtKqZ6XvuaPVuvHl058shT2nRk+PDD2hj0+rAiqKS96CL18lz1PSYD8v/8B/hJpsd29bxky/ERdTM7UFW5lr7abREbljPuuaf6Oxv4yCZkdNwjdV2QfNOzZ/Kpss5YRHZvRVOYy3F2OONrVj9drug++rxPIWzXorMeUeVaiMZUqpNApu6JOuMLn9YimzZjorSlYX0XCyxn4y6ZrSuKgF//unkpbbzbkL0FLQHsAeB7AHoDuDuKoq2aZIrju+I47hHHcY/27dvrylqzZBvRiBFq6XSPZ0kvsrcJ58+bRWTudbwHwbXF6PHHk0/eoExVabNBJLPtC2yvvexlMCF73UzOI73OzLXCqTJjrLpmpAirB490xD6fSqgL95+XX9ar27TO0Cxt9QR7Hkz6xFq5Tm3bJp9t2ujlY+e3xRbJp+85Yx3FWLc8VQXDN0XUdffd/PrYlksqqMjJ25s2pJD/DFH/yVNWXKDSn5rsHyiKHun6Oj/4YBJ8qh5QUdoaAOyU+t4BQNZjvwHA8DiO18VxPAfADCRKXE3iuzNau1Zcb5H78MiO5cGUNlMXMJ0633orP0+oljYZ7B6n24LNPVK17DHY4EW3HtU0tqg8C66DCbh6eZrganPt0BwYTDbXFiEaDMs2ilYtzwVlKEGqSpuNQuFrYKgK29ZBt79j7LyzWj2hKbFpef7EDQXXNB3jnXeAm282q4uHi3uuWsZLL/mTIY3q/dZRmmSYWOVlltY0vIBYInyNkR5/PGmDonQ6kVZN92nLblhfq6i85sYD2COKok5RFG0K4DgAT2bS/BvAoQAQRdG2SNwlZ6PGKCqilUulTbQGjFc2r3yVQCRZRIv+fb3w3n47CfdbC5Y2124qrq9phw7V3124lC1dmpSrEkWrqFlMV+X6dhPTuf6u6i7Dzalo90hVt79QeeSRZM2UCkUoba4wbXvsfWPaRvK+M8pwU9YtT+TayXu+TjwxWXOusp7eJ6I+32f7czkRWYSlbcKExF39Bz+obP5epnwq5YvcI3/1q2JkkbWlIre28YlUaYvjeD2AMwE8C2A6gEfjOJ4WRdFlURQd+UWyZwEsjKLobQCjAVwUx/FCX0L7oqhBo2koYJ58umvAeA+Vyew3Wzehey621/iBB6q/23jZXnhh042zp08H+vevltNmoJl27zAtQ3Rs0SLg2Wf5IfFFAxDRsaVLgd//Pv8ln+eG1tAAfPQRfz89FUSDySKUPJ3yRBuu+2TdusrA1Xb9lI3LtCrZcny6R+Z9LwNXMpxwQmXLExlFuEe6mo03LYe5RxY1OI3jplaAlSuTMO2mZdqi8tym62IbUNsqurbYlmea31ZpU223rhT+555L3umvvAIMGqReX5n9nu0+bVlUrrNsQm7lymo32qIDg/lCyaEkjuNn4jjeM47j3eI4vvKL3y6J4/jJL/6P4zg+P47jLnEcd43jWCPocHiwPWXyLGJ5qD40MkubT1zNsrIHh/cgFNl5qEaP5Ml03XXASSdV/3baaYnSMT8V/7So8zFR2i66KJmV++c/m6YztRBecQVwxx3Jn44s7Pe8gbnI2qtahwmisr7/feArX9Ev0zYQgglRBGy6aWJtdlWeLrYDIB9Km43Lki+LaZnukTLKkM3VYE7l+tq847Jy9u0L7Lpr9W8/+lESvVLknl2EwuPLYlqkVaeIQb5pnyWaKMw7ZnJN8iad9pAsMHLdxjZsAA45BPjHP/Tz2owhefltriP7PPJIoFOnyvFmpbQ1N+IYuPzyZJNU3gJVW/J8a03cI11g8sCYrmkrwh1Ch6z8vCiYLjpi2zx5x1gULd3Np7NtLP2dDYJ13GbTLyxX67OK4MUXK+vAbF/8IooYTBWl6OrUZbKmzdeA3DZP6LA1LLJz47V39n+PHsm+Y4zspFjZ102ktPnYu+vaa5vudzh2bPJZZEAQ1Qkvn32YSv26+XTGAy6v6dSp1d91I227XNeX957NU2pMIzTKWL0a+O9/m66ZVJkI9tEvLF8O3HSTedkvvFD9nZS2OiT9MNx3X/K5UMPJU/Vhat1aLZ3ucZW8jY1N3d5mzNAvzzYQiQ0uLQQqCmsRLhGyekzahul1kuWTzXbn5fdl2SmiDN+UcW2KmBzKyliEe2QI2Mr00kvAM8/o5dlqK7W6Tzut6W8sz8SJ1WvodttNTwbfFGXJ1C2/yG0minBrViGk507nmsycCXTtKk6jWpYPZEqSLxnS5aYnblTatol7pOyenXNO8sfG4rJ8sgkA02VJoUFKWwnkNTqmAPkMrjF9etOXNovOqAM7B966J5VOZcYM4NFH9estg6JnAXUwtVyKLG3Zsm1/V6k/mz+vrLw9DvMYNUo9bZmDkNA2w/Wl0KmsBdI9H9EzUKvukd/7HnDEEXp5bLwYTCe1fFi3RPCu7/Tpye/Mg0WlHehOOPEowqrFK8+30iYrQ/UaxTFw6aVqdbm6XtdeW4lUmK2DsXRpvhwyRJY203PIa5sm0XBtSMvxyCP83/POUVVpk/Uz6fzMYPKb3yQh+2VlydoSWdrqHJedbnYxaUMDf8aZzQSortNyRXaNXd6577gj8NvfJv9vtlnyOVszRmi6bN6Mr4ocKtHhVMuyVchMZ5Z0O32dQdVZZ8kDoIhmq2ytPun8kycD226rpmzxXg7Z8zv6aD25Jk4Ma0bYJdn7JHLXUsmfJnvN1q5NXnq21/LOO+3yu5p5rsc2oTsALsvtCbCfFEjLdeyxyefIkcnn5Ze7r/edd4Dhw83yMlx4ygD6gUhc1G/Cp58CAwa4K09F/quvBg48UJxP99rwnhOX7pF58snGOa7vsY0XhM9JCiAJymIrC1na6hwdt0gZvAiPvM0hZUqb7MH46U+1xNqIzn5XXbokn1tumXzywqiqPsBsPVbomKzD8d2JiY7fcgtw+unm0SNNZeAxfXryLD3+eHmD6xBcX1zNXrti+HBgzhz19JttBnz722ppix4chmRpc1GuTLH1sc2IbAZdls5VfTJ4A90pU9TrM633xz8GevWqjuRZr5Y21bJkx3nbAfHKcLG3ZFqWrPePqdImirTNO8YC2OmiorTJ5OKVIyP73ORN4thObJtgUqcsj8sxfZkUsMtV7TFmjF56E+sEr4GlQzabPAQjRujnAdSVtigyCyxQi6h2WmWvaXPtXqIqT/Z4HNvLwLvmLjczDRmbgYvJdejVS7/MceOAvfYyr1MV3bKz6cvYf84l114rPl5kXxDaM+bK/VRXIfngg+RTN6K0Km++mYR6v+iiym8XXMBPK7oGrkOvi+rnsWgR8Je/JN5EPXvKy5g1Sz16r6niWpSlzbRNipQ2n89ft25iOXi/yyZ3TD2PZOfMu/ejRwOrVgF7712dJrQ+yzWktElQXWBsorhlKcs9MhvNMq/RqyptLP977yUP1T77yMvOq0/G9OlqZblyTfFRvkoZJgM1HUtbeiDAfOlNB88uo0e++6487eTJwODBySDHZt++ImfOs/zxj/7KVt3nSwWf12HRoso+XDqIrEEqAxEflDmJUguWNlNUJnNEqAZZktUvQ1cx2Hff5DOttF1/PT+vb/dIm3v82msVS/HTT1cf48n98cfmdcnKZtgqbbx0RUzW5rlHhugd4GOftryymJfaaacl7/v09kwsbz1D7pEOuPnmZLPpbOMR4cPSplsfQ2eWP7s4VuQCsfvuTaM06aByDfr3Ny9ftU6XgyDTPK5nllUCkZiiUpbq4Ii3ADlbRv/+yd4yzz4rLssHffu6KWfVKnmaTz4xK/s73zHLVySLFgHbbNN0PUoW0fNZ1HMqwsYSNH58kl93nTBD9zoUqdy6throlvWvf7nxClEdPOvIl95W6C9/kZcn6jvLXnJQ5sRXXj0qSpuobaiuodc5v2efFa9pM4lG6sPTRbVcZokGEvdUlf4kz9LGvvPSLl5cXV567NpcLG2ktKUwHbiee27ymW64JtiuaTMlG63S1tImQuUcTj0VeOABuzJU86hsBB1CJ6BqaTOR1cVLybelUZSerWFgEwimirzJOTzxhL+yXZGNpuaC229PNqbnRY81gb2MJ082bwcmhPBsM+69N/mU9akhrWkryxVV9xz796/sY6eSX1WJddF+0nts/v3v8npF11xl8kcVlWv06qvV11UVNvn70ENm8uhcd1tLG69e23b/k5/kB45KK226HjQ22IyFxo2rHN98c+B3v3MrG6u3yA3tQ4WUthRF3nReXczVb9NNw2yAUdTUdU7kHmnKffcBffrYlaGKSlQi1Vk4W2wGW2y21mT7hryBmO7ARudl6MOy19iYDFouu0xNBh14ZSxc6G+Niw6y8/MRdGblysR6wRuwFW3xMnEJ892/ltF/+1DafCgpJqxaVe3VYSKHSvQ4HfdI3Uksl1ZLE3QtsGkLYF79Bx2kbslP51Ndx5YHC4RmguqYRbRuzUUwECaHrVKZTuNjAktlYr5Fi+ST3ddsxHQTWUzXDYY4dnYJKW0BwTqi9u3dNzxReTrWsjxLm2t5ReHLyxoUZrnqKuCFF5L/P/ssP4+L2TKZ/O+9J06nM0NuOsi3nYUUXTNRmaZr8ET1q7DttsCHH9rVacusWcmeh0XhaxDv4vk85BBg662rLRdFY+MeqbP/lej3IjwRXLBhQ7KPF2/frDT33pusdTzkkMpvonPs3Jn/ezrPHXeI6yxL2c+DZ2kTDe6LkJPVkXZZ81lvumzVtezZfLzveb/xjrk8v7x7xRQWV+srdeVR/Z+X13QMkM1nooAW2fbLhJS2FLyG9sorwI03quW3bSyyxZxFNUaRdSQrG29Nm+4MZIiodFR//nPlfxdRDlWvW2MjsGKFPI9pIBJbePvRDR4MnH22OJ/uy3H8+MRFj1m7VNw7TAk1IuH++6v3Tz7wobTp9h/p+75kSbWFQNdaXCauJh1c9Dd5aUxl5D0/w4Yl+3hdeKE4L5uQeuWVyr21fceMHi1PY1q2TjqTesvui3xb+lTyZa2Aov7DVGkTWXpUNr5m1qc8ZEpb0biYOJMpbcuWJfsoLlyYv22CqYzNRWmj6JESTjgh+ZRtBK2LqOPwEerVxd4uafdIRhEhhrMUbSK3rc+10vbznwNPPQWMHetuEKXiimAygEunSUcxdDGDf9ZZyXqtjh3V5RFRi519dmF20YRkaSuqvrLLL3JNm6wsG+sgm2xhE1B5pCcG//c/NblUZbApQ7fPd9XGTd/lZSmctnW0a2e21jWvLpV7s3ateILI17KI229PFBtWPntGir4nuhOoLI3svf7II8lfFAH77Scur+jJgVqBLG2KFLEfmU8FyJX1K2uR8RGIRAZb9Coi6zJm8sJatw6YONF+Rtq10sZmiT/6SK1cHUw7S113hkmTkhk3UXkymEsqm0hobPQ3eZC3vkOVen2RuDovm/5VtC2Ey+s+eDDw+9+LN2ktwj3y4Yf5v/tQ2lyG/M/mFV2rdIAb3XXTNjKazvQXOWnpYgLWBbp1mV6jFSvkwZRUg2nlHc+2sTxLrE67M5nQ+MMfkrXCUZR4Dbz4otyVV0U2FU4+WV6ubHJHZmkbOTL5XLxY756ppKvXd2wWUtoUKXKmQ2WDQdOyVY6JXkzZF62ue6QLhg1r+ltjY3W9tlHt4jhxf+zRw37dkqrrhchP33QmPC+dSUhhVVQ740susaubtb10IBLTsmTpVF+cRaI6KHAZiER31lq17ZtMcrhAp67TT0/aAbP2lMH69fnHdJU2ncGYD/KUtgkTkgh0Tz6ZfHeltOlMSKlcj/T/zz9f7UnAyz9vHr9M3b64Vt0jy8LE0rZ6tVkgkl697OVbvjwp/9NPk+833OB+PMiD7X9mgmpsA/aMmCjWqtS78kZKmyIm1hbdtGW4GuqQdo9ksvq0QOpczx/+EDj++Py8qmWlr/3Eier1u5gBUhmQZX8Tla0a9dLF+rY8WWyfCRHZ61XGwLNM4li+bqIIGXR5+23zcnTrc9kmdAKclNHmQrG0XXMN8Oab1b+J1q9kyxw/PvkcMSL5LHJi0NTSNmMGcMYZ4rwHH5xYTkzQVdps+uIiBswu26gs3SuvVFvOdK8NT1HPuweTJqnJmIYXgdg0UJir5yJdTroPkPUTsusjK0c29lC5T/X6vmeQ0qZIkZa2TTYJd7Y5a9Uo0nVFxIsvJu5LtvX4yKda5t/+Zl9GGp2tClQUNZkirNphq5RvammzmfCoxc5+p53KrV92zXj3Y/PNxeWEfh98yaeyfYSvQQsvz6pVwPz5+mX17Qt84xvydKqTQ7x+bPZs4IIL+GH8XSjqLCqwThlpt/28dGPGqMuQV69K9Mjmhuy8dZW2PKvs+efryyZjwgT+73n3uejJSZVy2UScqdJmO3ZIl1HvzwAFIgmItKWtyA5ZtVPgWdp4s6CusHmAbddi6LjS8MrXmZ0zxcbSloUnm85GrXlysNlyH/CUtlA77DLkkgV4cIErN5ey7luZA50s99zjpk5X58SzHLm8n6qz6rx+jLnI89zRXJz/c88lbmqisk28OUwsMTr4eteI6ioKVxZAm7EVa3dt28rT2tyD7FKUMhV0nXpsxxx5dar0bcxCX++QpS1FkQt8RQ9h0e6RqueW7khMLW2q2F6DkF4oJrLcfTcwapS8DFWlLZsub91ZWlm98ko1WUU88oh6WtmLlYX+ZmQnDGxnIENV+EzhDTpVUb2WJtfMdNNUk/p8zEqL8rrcOkO37uzAZv169X7pjTea7o3JIpOeeqq6fHmTeLyJSNU+XjQx+OijTX+zuedpmXSseICaGxnPyqwCz9Kmmt6mLh4uxidlvJ8/+ihp46qWNhE8S7LuOW2xRf4x0TVOjwts6nSbLVAAACAASURBVBeR9y5WnaSz3WNO9xmePr3iFVBv7/EspLQpUkRDyLO0mbioZNGRX2VQMmdO8ukzeqTPF49rXCttp5+erNMTlSFbY6NyH3WPMYYPBxoa+PX5mnT45JPq764DkdQati9GF7iqQ2dgQPBJK2233AK0aiUO9pPl1VebltetG7DVVk3ryPuuo+DllZFF9I655Rb1ej74QG8igyeXSDHz2YZVlTbX76Ess2dXlHld609Rk9E8GdavBzp0AH79a/l9zSuDh82afpECn54gLxsfY7bsUgbe2EG07j4LiyStI0OtQkqbIioNwXSRsayOv/9dXQaX9WaJIqBTp+R/FoLXp3ukCSw4halFwPQaizp9F/eNV8ZvfuNmU28TGXr1An772+pjLpU2Fdmz9dm6R9Z7Z6+DzfNiMlPvK6CR6YyubZ4yLW0ff5zsYQgAd90lL/Pww5NPnmVJd/D4r3+JZcuWzTuWrc/VxOAxxwBz59qVY6uoqWzKLKPMkP8HHZTsD2qCrWw2CiEbFwwbpt9nZT08eOWayCQ7H5OQ+K5QtbRlz9HVGCDvOcu7DmVeq6IhpU0RnwNgRjoCT/q4bch5E1l4RBHw9a9X/xZKIBLGrru6qceXqwFDt1PLk0c14qQPl5c8S5+vQCSyDvvCC9Xa4/TpwDPPmMloShkvkiL2e3zvPWCzzcR7pZmU6xtf9fEUkSVLipncYnXylC8R2XXK2fLSiobL66a6pk332vmw/qqUrdLfuugbXT3Xhx6abFytQ9qiYUMR46k06Takqoyz63zBBcnnhReay8fD1ipZVJ+pI6dqBHTXz4dK2fUCKW2KlOlqJBqY+6jX5CENBabgmlraTPGtqOaVIbr+vGOTJgH331/tF79mTbWF0mQvI5fXd+nSpnthqbpz8hTJbFj8n/wEOOKIpunqvbPXQbUNPPRQEvXwwQft6lNtS7r3SMfStnZtxfVLlFZHhg0bgK23Bk47TT2PCJVro3stmVKWN7nkwrLDK0NUb5oi3zGyGXvRtVW5Fo88Auy5p5lsDObtIpKPN2bIph8zRh5sJYvKur08ylynfsMNyee6debr8K+7zq1MOtGdVRg1qnqvQFfojAdNr4fqs+RT2asVSGlTpIgBXV6HyGaJynC5SSNya3I9gLd9CF2/6DfdtPL/W281PW7rNiMjXUZaMdFV2k44ATjllOrfBg6szCLqyOpaMWb5s2vlZOWnByi8NGyQw/jgA33ZapEZM5I9ilxurm2aLo1NIBKf/OIXwJe/7KbvYOfDgnvcf799mSNHqtWpIn86jczS5sv1SLYWVXY8j5AtbQAwc2b1d12rSnqNoQ62/V7r1nqTIKGiammzxXf0SB5nnmleZ5q8tpyVw9Q9UjY5bDMhMHq0XRCu0CGlrSREHUf2mAtLm6tOyNd6A9fYdsLZTuVXv6r8f+218vps6ubB25AY0FfaVq0CDjxQXFdeZ6p6TU1fVjxlWKXM9CDIZsBdCwMOHUaNSjb0NWHpUrV0JtYnUTlFwauPuczK2pCupc0VskE3717kPTdbbQWsXl2dZuXKpulcBkTIDv5sQv6r1mODqaXtpZf0AqSYyqJL9+52+V1ZVWzz2uJSabOZnJWld7lkoaxxVx6yiZo8Zs9Wyydah1jrkNKWoswFvkC+pc230mbjHpmN4CfLXxSuZdBxm/EhS3Z2lqGqtKUHdCp7zKiQfWGx7+PGATffrF8es2a6HAyU3RbTwVp84MstJO/lqHJ9Ta65a8u0alkq8u+yi3m9NkrbZpvllyuqU+VaLl9emY1mlrajj+aXJ+r7bO6V6vYIRQa7ctHPf+97wIABLqVSfz5ce3WkcRFExQadcYluObzfRGWOGAE88YR6nTxs3SPLUMRULW2LFgGzZonLNelXfvADeVmA3/1hy4aUthS+O0NZeXkPR8jukTwL0Jw59oqmr+hDuvl48pi+zG3OKa98XUubzC3BFWefre+i4CKEvY0S4eP5GjjQX9mq5eoGpgD0FXud8ytynzbGhAmJW3CeMqqDyuDRhdLWubM8zdixlXPStUyxdHmDcdZXuOgvsmVk3b9EZLf6kOHT0pa2Rs6ZA1xxhft6bfApQ3ZtcK3Cu0YmIf+PO04/j2r67PPBs4L7JG8syiKZM/I8r9avB/bYQ1y+SFHWvZZZOYoONFYkpLQpUrSlLY3vmUYdpS37cGyzDT/tRRfZ1aWb1mVeXn7ZLKNISeTNgLtCN+R/HIvPRUepy7O0MUzbrc11Mt1vh8eKFUCfPsnaMIKPjwGyD0vb7bcn68rYDKyrCbp+/fLD3APu++6sbN/+NvCd71Qf01WAZUF+fK9pE83eP/ZYskZFB1cy8u7dX/5S+f+OO4AFC9zXy8P3+2TtWnkal5Y2W2u867rff1+/nHXr7Kx/qkobUHnGy0DnHG0n35h7p6p7fnOElDZFipgpT3fG6d+LXtMmcqlRfUgff1y9Ph/onO9TT/F/z9vc0cWMmquQ/yKljTeYlCllOoNZl2t/ZPk2bFArz+Watl13Tfa50tmguGh8WU3jOAlVL+t7XPWLviME5p2HiWU2ffzKK4GTTuKnWbnSTQASGfPmVculei1lSpuKUufTQhrHlXMrA951nD+/8r8rhdzEFW78+MpefKJ0KgwdmrjiTp0qLiOrtOk+Oz49PGzHN9noribX0dU7XbWsOG7qBuhjnOpjoj07Dsnmu+oq9TqBpm0ztKjmLiGlLUWRa9pYeeecU/ktr6HlbRjtWhYZvIXweTLn7S1nY9XTQWT5yqKy/qpI90gWIEAFUb3sJZxOJ7O0mfLee/pKXRbRDHL79nplyH5Tgc2iu9qbSIXf/Ka4ukTEcRKq/sQTm/4u+q5Cke6RMnld96lp69FddwF//KNaPhfnb2ppE/UHLi1t2QlKFVeooi0y6XPl9V+ikPcm76t16xLXXRnZa3f++cCjj4rTqfLvfyefkyaJ09m6R/q0ROrAkyMdHTovjUm5pumjSK28oUPVyrSRzZeljbdmN6+cu+4Slxf6VlQuIaWtZKZMqfyf96C8/rpfGXQeaJcRpGQMH26e1/ahFb2QeecscsvTvUbLlsnlYZhsPCtT2kzcIydMsFfadOrLw8Y9Mi9tkZbu7t2B116zr88WJu+QIWrp8n4zUUZ8zOxm0+soCqaKnk6IddvJhuXLK1YpXUubaE0b4GdNW/q3vPNUHbhm8Wn9TZftwhX7+uv5e0bKWLhQP08e7B0iU8pcWsrKvK+8clq1avqbbTAQW/dIlXRFrHXTOUedd77s+viIAVAPtCxbgFqhCCuX7kypaT02afOUNtcy2w6UdQZaKpYn19EjXVl1TaxZpkqb6Jq2bi1PrwovX170TFneODaTIz3r7Htz+ywHHFBsfTxczhoXkV9WbtEvcV2LNk8+lf0gGd/4RiXMdXqdlUqdZa1pY0rCs8/yj8dx8TPm6XPlTYjZTMZlefdd4E9/UkurWq+JTFmlLa+MsqNHukLl/Z39vmpVMXIwVBWWrJXWh2Lry9Im+t7YCAwbplaWjRy1SJ08hv5x3Qh4gwmR64WtDEUonWXKYVNPGUqbq+tmUo4sEImJTCrWR5NyGe3amefNIxvKPZ03vadR0UpbCKi2N9n1FllYdMrJw/Y5Mnk2ecc/+qjpb0UOck32JRJZ2tKTHT6WDUQR0PKLKePshI+tkujT0iZ7R+vQ0KCe1tTaq4KqpS17XPfZcR0R2rRslWsXx9Vl5k2EiN6BMplceAPptCEf2ChtorQ6S0Rs5KhFSGlTpIhGEEpDMzGHFxFGXgdbS1u2006n0Z2p07mvo0frvQx1XaGy58VD9V6mI47xOmGZbHmDNd65tmihdh11XoSq7muhKm0+nzlVt1sTBUeWTpSnT59kDyBddCc91q7V2x4gu2eTC0ubSTrVtZ/psnhyMrfYKJL3faawsvK2pBg4ELjsMvNybZG5R9rW63KCzFQGQF1pUwlEIsKllVJUtqu0eRPqafI2s7aVw3XfXtSEvytLmw6NjcB++zX9rV4hpU2RIixVzD9ZNgthW48Npj7ML72UrLkI0dKmssDataVt2TLgoYea/n7YYdXrHGW4do/0MShTPe6i7nff1ZdDls5knzMdGXTWPhWFjdKWXRxvWk4ee+4JnHdecq9V21jeJ4+FC4Hf/x7YbTdg8WI1WZlin5548KG0yVCxhjBEE24ffsi3tD35pJlcIuuqqK3p7vVoS5HukT6syzZKG7N85pXRnN0j89ro3/5W+d9X9EhRuqxcrvoRkcL6xBMVZdV0PJiV89xzqyNh6pwHr48mpY3wpkSly02HhzZx2ykDVZm+971k3YUPeHvM6FwrlZlk20WxcQy88Ublt9tvB/7v//jpeYuLbS1t6XJMX76ywYKupU3H+vH228Cdd4rLA4CePau/9+tnH5pbR4k2Ie2mqfuM+7K2mQS4YfTpI05r6x65cCFwww3yiGJAxc1Gp/xddgGeey75f8UKfppPPgGOPrryndfW089Zx47AmjXAp5+qy2GCToQ/FlY7z9MAaLqmbfLk6nTz5wN//Svwyivy+rIKTxEToTbILG1FKm0+3/2mljZdfLpH6jBunFo6WSRRoHqtm0tLq2oQlKwXiI928vzz1d9/+cvKdkIu92kz3VpH1yJe65DSlqLIkP+MomYEXL0gbHyH03vcuORb32r6m05kL9GghWFjaVu9GnjgAfU9h9JlXXSReOPPMt0jVevUPZ73uyySYR6q631qraP3OfBlAznZ8y6rX7UtmawVamyUpx08uPq7ivwqa4v796+2KPLKTfcr22wDHHss8NWvVqdbty6ZkLjggvxzkMmbJjvwFl1/Nkkoix4pYvhw4Ior5PIX+WzVitKmg0+F14XSlt66KI9nnwW6dQNOPRUYOVJdPtdcf708jaqlzeW+oGnyIqeGsnZrxoyk73IpT3a5hSq1YuBwBUWPDJRQG53tfhg+zmvaNLt68l5GOptriwaDI0YAc+aoy5POe+21yYCvKEubjcuOrqXNhduhCqE9S/vvnwz4d9656bFQ1oayexfHQOfO+elMFXPTdLp52GBLpqzxrPU6dWddCbPPWRzztzA55RTg4Yf16hah4x7JkEWP/NnPEos1D9ZOTEKPp2W74orkefj1r/XL8YXvQCQ+LG0q6f77X2DzzSvfXQQiGTgQuPFGcf1MUXv/fWCrreRyppFt/+Daiped3Mx7l9ns22fiHrnJJmaeI67HaTfemCzxcGlpMykHkD+n9QZZ2lLI3L981KUzS2Ajg2re7Ga6rsr1Ce9lo2MR8B09UuW4KK2oAzLpjH0pBrpKW5a33/ZjPTL1s/fF+PH8iQZdbDegF5G+ZjNm5KfLu2bHH5+/SL/I6JEq/cDYsU03ehVFZVN9/lXcrgcNyq9Hte40Jhsgyyxt221nLg8je8+zg/C//hU46ST+HpW62DzHsoG6S0ubjzYvK/OMM4BDDqkO3GAa8l/FXZ3H+ecn63h32kk9T9njDBNLmyulTafMPAYONMsnYuhQf9EjdWhuljZS2hTx1Qh8KGg2PPywnxlAn9g+tCpKX/qFtWxZsj5FtT4VN65s+jQffaQ206dC1gLw5S83Pa66T1v2mK7rXJann07WxrC1Nq5w0UbbtnUrQ2jPfRbb6JGDBiVKuComg2GVdKLJMfa7SIFWHVzw3LF9r5XlYaK0ySxtIlxMJL78csVlbcOGxBJkQz0qbbZ9K+O225r+NmZM8tlS4neVVdpGjTKTgZUTSl8HyK9vXn9ocw4m1iDT7TB0l6aYTsbYTJCqWDZ58NKaRBiuFUhpS1HGmrYQ+fvfxcdt9tHxcR1VlDaXlrYXXkgi2KURraGLY71OKCvrbbcBd9zBT6vbSTY2Vp/vpps2TetqIGnyUnrvvabh04uQ46OPgNNPd1uviND7E9VBCk8pOuYYfloRvixteenT+UyivvGuw5o1YvdI3v8uI84BZsEiZJY2H2tc09ewVauKsnnDDfyouml8KpJpdN0jfT7TqsqijQzZLViypPeutMGkjcrcI333p3nvEF/15rVx02AwvjwyfLlH6sArSzV+QC1CSpsirh9O0Qxw3uyui1lNFR5/XD1tqL7DrgeB2c7pww/V69O1tPHS5rlrheIeyWuzJm3DR3tSufavvQY884z7uvMIXWlzMWMax3zXSpl7pG9L27hxwJVXiuXR5cEHk0FvOjqkitKmw/77y9O4do/0pSAtXlyZ/U+7+arsyyaTaeFCM5my8J6BdDTREC1tLsYIvDL23jv5y0O0x2YWk73N8srlBSFzQRxXb2/hIxCJrH7e/6Z9la/tGnxNXOiUM3WqmzprBVLaFPE1yCpq8OainpNPTj5Nzdiu5FAp01ZJyg5Y0p3efvvx89x2W5InvXUDK8uX1cFHIJK8MOcqZYu+m5ThAp3B/Q47uK9fVF+o2ChtrH0NH66+ds+XpY3XJo86qvKiN9k4nVfn9OlN05RhaXPlHqlqZRMN9NNkI+BefHH1+0TnOvgM1nPNNZX/eQP1JUsq/xeptJnmW7DArA4eNm60afKCA8mQudTZkC173rzqQFl5/aHIKmwj28qVbs/XdT+Tlyb7W17/Kjs3nbZx+OHqaesBUtpSlBG5rWizuw333df0txDlBPRC/qdZujT53GOPyl5NQLJInpG3RQBbw8MCaqRlCUlpy4uKCSQvqrw1ZTL3lFq2tDFUIom6kCFUCzXDZk0bu1bpfQl9YPpMZV1n3nrLT90+lDYZLte0qShuqveAt5YqXX8oShvb1w+ofkZtg13x8PFOyKbL2wtUt44oKndz7aLHZul2AKj1h6r7v6lw++3831XWyfLw5V0jW9PWqlV+XsIMUtpSFOkzLauLN+MfSkN3Gf3NBT4sbVn23Rf40Y+S/2X7uvFe5r4UMd2XuczSxpRWXXjnaNImylLaWJqiBiahPMt56K5pS8P6h7x76co9UiWtirwff6xen0qdLI1r98jXXwf69hWncekeCRSzfkymtGWPFfWMpttv2Rv4itrPLbcATz3Fzzd6tF1daYravzMvj0yp9ImK0vbCC+7q23bbyv8uJnmKUnpV7+2wYcWOt+sJUtoUKdI9cu1as704dOsxxaYDKMs90mUHwRsY3Xln9d5W2fJ9WdpE7SRvcCwa9JisN8ijlixtMqtCkZM2ZZGeKFK9D+++m3zyBha+rYmia3jmmdVpRGnTm2Tr1CEijoGtt+aXk74uun3p3XeLj7tS2kaMaGpt8IWu0lbUADTdt9pODPKwyZ/O27Il0KYNv0xX/cxnn5WrtMnK8n0vbCM9uspbVCASV+6RebRv3/Q3mwB3zQlS2hTxNWjjlcsGQrWETnhv1/CuoU70IN17y+s4586trGvJKmlluUfmKW2iDlxnE/Bsudkwu6EobTplmrxojzhCP0+IL6W0xUl10ii7ZQRQuYauJ5546FoFXFx31UmYdDS+stwjVeTkyfDSS8n2GzKFykW/JrsGvpS2Fi2AE07IPy7rN4pU2lQtta4UwSyffKJmkdUZ7Jft3iciK1vR7uwqSpvv69e1q34eV0GAQnw/hgIpbSlCCfmfV1coDbmMtX+6fPZZ9XcXLzp23nkvL7bo1tbSdvPN6ml124TM0jZzpnld2UXZpm4wrvHtHikLlc2ToX//ZJ1PKM90lvQi/DQqfRO7hr7dI1XcpVzMxJvkPf74/Ikjn/fctXukDFfukWW4vtlaV0JxjwTcXiPf7pGMX/xCL70Pa6dqXUVMQKVxvbm2bnCxOAa2206eJsvcuerlZ6mFcWUIkNKmSJHukWUNXFUJ3T0yjuUbhdog29eIN0uns0j59dfV0+oGjJBZ2kyZM6fpuopasrTJ3CNdM3UqcMYZyQx2iKRD1+vCno8yLW15G/iaTHKo1pklHTI8/dwVaWlTQbRxvKp8Ktdk5EizOrL9rct9JEVlhWppE5GddNO5VrI6XLtHXnNNEvDLhnHjgHPPtbfw1Ip7pGmZixe7k0E3DQ9S2swhpS2FL7cDUXm8csuOoFcP+HJHBPSVtjgGli/Xq0MVE/dI3Zn1efOAs88Gnn8+P82kSU1/MwlqUnbbN3lx2LxssiGRs7LuuqufemXohvznRSTNC/dcxNoY001fXdTNS1OWe6QK7doBEycCPXvyj+t4oBx4YH7avP2UygxEIqpXNulQpNKWzZeXN7vHqst27+q6M5natFF3wROd8003uZHr1FMr/2fbRRmWNt75mt4Dk3ag0jfZtOEsEydW/g89unKZkNJWMjozuaEoXqFb2nTT+FDa0mU2NroN8JHGxO0hLb/KvXz66cRl8y9/8SsbUH77KDOsNY+ddso/pnutdJ7bPPdIFVlk7pGy/DoBMGTXwNbSNn58043tTd1+ddb9mGKitAFA9+7i9YmqbLqpWf0iygpEomtpi2O958blxCK7Ji7ezTbukbbvYhP22cdNOdtsU/k/JPfItCzpZR8611F3LzPfY03ZkpFQxroh4tGJrL6odfdIl4Rmxua9PH1Y2mRr2l59NV8e3bDirrFxj2SDlzVr9PINGKCXPl2XS3xb2myQrV8sIuQ6D901bWlsA5GotjORLK7cI489Vi99Xl1r1oTrHskwkcX2+qrU61Nps1nHnj2+eLEfpTVbV/b9VlTUPR1raJF1m3DIIYkrKZsUk7XjUAKRpBk0SL081h/27AlsvjkweLA4/fr1au8el+6RhBqBzSuHS627R95zj/syQ0ZnMKF6b02tMSGZ+k3cI03bvsnmymWH/PdlacuT4ZVXqr+HsslwnmtjHulJCZN92kxRtQq47L9VJ4XSaebOrSixPpW2vM1sRcgG4zqKjanSpqKAp9MXQUjukaqWNhuZZHnL9EIQPXMm7aF168RCp+p1YjIB5WNNWxrRViV59O2rNrGgssUDKV7lQEqbIulF5S4pyj0ybxG4CaFZ2rLoWtp0kc1mZ+s3leWYY8zyMXgvGt3ZseXLgeHD7eTQoWylrezQ0lmKUHBUEblqpiOHmljaTJ4XE1esIgcaZbi5t2wJHHmkWV6btjZ1arJhrgmy6KtlWdrK3GfQNF9ZljYdXMtoug5Zp12ZtAWb81S1nqoq0iYTRUUHItE53pwhpU2Rv/7VT7m8xlnmnmcqhK60AX4sbTL3yGx5bHNd0w4oLzCACdddlyzY1rW0tWvnVuGXUYv7tNkga6chzXbqvuxN3SN9uDa7trS5yu+6vUURsMsubssTkT6XadPMrg1vLZ1IhqKeUZlrbJmWNh8TAjZr2nTuSd6m8yJk1lhbZGUXvXdu3vW84ILq77rWT5nlXEUGhs3kuCxfSN5JoUFKW4oQZmGJ4tG9F6oDmW9+M+lUQ+iALr0UOOccM/dIRhFt1kcdIbhHyuoNmW23rfyvIq/JPm1pdBQx2QDTl6XNxMrH+92H0uY6r2/3SNn2LDZK22676ZWtQ5FWLZkluoggNyp9o0r9Z51lL0sam4i/qmsDP/hAvw7de/HWW3xZ0mQDivi0tJlEf1ZFdm323NNf3bUOKW0l42NW2TehW9p0Z4B8KG1pJcD0vvm6ziHfP92ohYyuXfN99UNwjzSdGQ/hXulaqWVr2mTluOrn0rPzzcnS5jJPEZbeVq38rWnr0qUSIIpHmUqbq3dUUX2Ei3r23786SqMLXLlHiuBFtL37bv16RaQ3s1a1LOoqbSrnvOWWyec778jT2rhHis7vW98yK7c5QEpbyYSiiOkQwkBShs+1LKrukezFYGpp83WdQwtrn+a119yX6cI90tdzaqu0ld1/8DbhtnWPVEVmaeNduxC8KUJdd8TLq9P+TF3YfFraTNKrYutBYaqI6UyimCiGJu6RuksMdPOJ0rqYqJDJobMNiUqZW20llsn1mjYdTNfE6lD2e6uWUbrlURT9JIqiGVEUzYqi6E+c4ydHUbQgiqLJX/yd5l7UcvnGN9yWxxptCK5z9YgPS5vumjaWNrQOKuQwvbyXmS217B4Z2gSJzuxvntImU6Z8WMVcl+li7RDg/v62b+/++VYtz/S6tGypZ+0ranNt3+gobdnnI5s3FPfIMijCPZKntPmcIFF1VfbhHpm3XYqoTF18ll3vSG95FEUtANwK4HAAXQD0jqKoCyfpkDiO9/3iz7HhuFz23BPo2NFP2eQe6R7edVKdnTzppOTzK1/JT6+jtNWTpa2I9ufjWrlwjyxrtj6kZ013AfuCBWb1qLazDz+UD3x9WtxllLGmzWSWvEz3yCiS90dZdzrVQadqelNCaEtF1qFyHbNlZNcm+XBHNS1T1ZoFAA0NZnXooKK0ZfERiISntJ1/vl49tvDuR15AtLRbaXNA5ZbvD2BWHMez4zheC2AwgJ/7FSss4rj4/ZtCJqSBZB6mynDLlsAOOwDf+U5+ehWlzcWaNl+EOmMK2FmeXbg2hvach+4eyYNdw88/N8sv23CcMWJE/rH04GTkSLfbVhS5lkkXE/czm/WcMguQDJlrJACMG6dXpsng1wSf7UDX0uZKJlEZWZkOOUQ/j417ZB6u1nGKlLgJE/jpTScLVSxtPta0AcDKleK0PCvkddc1TbduXbKfmwkmlrZsEBYGz0W/nlG55TsC+DD1veGL37L8Moqit6IoGhpFEXdHnyiKfhtF0YQoiiYsMJ2G9UiRvsM+3HaIBN5LTWcdAADce29+etlLYuBA4PXXK2lDs7TpbpzMKEJZD9XSZlq3ar2uyg4h6pZMZpdrzVRe/iefbF+Pbr2iND4tba6RDUxtlWG256XoeqZDxDOZRNiugVMljoHNN7fL7woX7pGyvNkxkGyrhqIous/WKWfJEvV8KmvabN0jowjYkTd6NyjTBnKPNEfl9vCaZfaS/gdAxziOuwEYBeABXkFxHN8Vx3GPOI57tG/fXk/SkqkHFwtXhD7QAOwGgbKBiur5f/CB+eJ8nXp06dXLLF8RbXXoUPdl+t6nowubRgAAIABJREFUzea6uF7T6uMepV/4KuWH0j8weU1ng/NQvcZ56dL33PW1slFYTGRJW1N9WdqymEwK+CCO5RuDmyKztOWlLdKKm2XhQnmevDJ695bXb3pu3/1u09+ySq5J2SqWtsWL9cpTLZuhqmBdcknlf5k7oeqaNhts1wU3Z1RueQOAtOWsA4B56QRxHC+M43jNF18HAtjPjXhhEIp7ZCiNPJRBmQhbS5toJky1LWzYkPw99ZRa+qJo08YsXyjtj4foJadjFcm7t75msG3WXNlMCPhEt38YPRr417/M6hK5ZTE5ihrUquJ7YO3yfHXupclAzORdIut/i1zT5tPKLkrrwz1SpsCIznXFimQ/x9Gjzeo++mizfID8HvzjH8CNNzbNI1IoVa+jrG7TLWxcu0dOnapXN+BfabM53pxRueXjAewRRVGnKIo2BXAcgCfTCaIo2j719UgA092JGAZFuUeGvN6oVtB94LOzmLJZLp171LIlMHOmnjwMX4MN5pIko172SnGhtIksYjbrznRdkmSEMKGiawk57DBg2DA/stgOrPPKtHWPnD8f+Otf+dYJG2zOVTUIjyhIky6mFg6b467wqbRly12xQpyPN9BubHQ7+FXpi7LrD00sv4cd1vQ30TOn0h5E1kkbZNckT2nTacMu3CNV602XSUpbmEhveRzH6wGcCeBZJMrYo3EcT4ui6LIoilisqrOjKJoWRdGbAM4GcLIvgcuiKPfIvHpWr+Yvhi2DEAaGMrLXdfx49bSAG6UtjsXBEspCVWmrpe0oRPer7H3abAIH6D5rZbpHMVxNPKlMGsgsbdmBtYvrs3498NBD5vnjGHjySeCKK+xlUanLJg3vnn/pS/nl+FqbKJMpTbr9qbqZmVCk0nbBBep5GS1aqO2VyFxUZWVmn0cXCnfa9fof/+CnAYC+ffXWh6ni2z1SR2nLW9MmwqSv1Xl+yoKUtnyUPMrjOH4GwDOZ3y5J/f9nAH92K1rxiAZWPmZrAfUB5dixbuu3oRaVtjVr+OmyaV1b2mz2HSvb0lZrHaeKwtWqFf9FytK0a+derjgG/pzTO2aff113tKIJbU3brbfK5XAtz+TJdvnj2N/G467dI3mI+o8i2mQog04f44I8OncG3nmnUq9IJl1Uz6FTJ6B7d+CNN9TrN+nPeHnefht47DF+PpN7UAvukSpkn8XWrcUbgauUS+6RYROATl0bFLWmLe+hWrvWT/31iItFri4CkeimdZlXhKnSVqsdaVoxynuO2LnlLYi3tbTlBVixtbSFeE+KdF+TWbx8tGHVgZhoEtDXfRMFsFDNIzvm0hotGqjryCQ6Xg+Wtv33r/zfvz+wbBk/vck9SLvDvfMOcNZZ8rQ8GQG/+07mTbyaKm22yMpYv77pfVLNm7emzdY9UgVWZtol1zVxDFx8sfg4wYeUNkWKco80WVNTNHnXYuDAfNeZkOEpzq6UthBcDbKklTaZe0et4Or5zFNoXSzwVzmmM1Nd5NodnfpCaPN57pEuUG0LZShtJujKIgrWE4KlLX3ch+WcEcd2bd3mWi1dWvnf1rKazn/ffYBoNyZZXaaeAypurKbXSzTxkOceqVqXyKq1di3wgx+olZOWKfu/SBYf7pEff6xfpi5xDEyaJD5O8Ang9Ro+Pl/8qoO0n/3Mbf025MnYtm0Yu9PrDh6y7pGAO/fIerK0mVKUcuFi1jsvBLnNpInoOk6XhGwKQWljvP++2r5cruRSKUfFWuHaXdC2jNAsbXl5834T9X+uz+tXv2r6m2r7atcu2RQ4VEubzubzqvXYKm0yt13ZFg2y+lu1qv7evz+w887VG3Xr4sM9UpXtt5enSfP1r6vVpaPs6uRTKbcIAwGb8DjnHP911RuktCnCa+wiNwJVaEbBD6ZKG5DfsbHfdQKRhLj+rx7dI22vc1lKm4y889pmm0TWIu+R6jWQPR8unwmVtRHp+i67zH+dsnRlKm277GJfpsttMWSBIHjur6oD0wsuAHxuB6vbvx96aOX/ESOA3/8+P62PwXgeafdIWTknnSQ+LmsD11xT/b17d2Du3OoN1HXPpax3bBQBm22ml6dfv0peWdkqv4fg1WBKY6Mfz5Z6p4ZveXG0bKnn26+DqntkSISoiGTxaWlrrmvaTCmqvaxcaV+G6rVJIzu/7ObOf/oT8Otf69eT5vvft8vvE937bbLBMiOvjaq4W7muUye/z0EJ77y32w7o0wc48MD8fDwvCV5ZU6bkl+H6vHjvw1pd09axY+X/Dz7Qq6soS5ttgAjZBGj37upyqWJikTdxj3Q5BtRpw6Jrrvu+UpG3iPd1HCdWXRulLeR3oE9qQEUojryGcsUVZi8Plbpsoi2VheosUFnYDopkAz7VyG+2ljZS2oqrg52ridKmO5AZMADo0UOtbN01hyE8g7oy2Lh+q1x714qEraXtd7/T89K46CLgy19WS5tnaVOZjOrbl78JsSo+rrWue6Ysr0t0+/d0Wl8uaDZKWxzby1XG2vuy3CNdt6+8NW0ifKxpK+Id0tgotrTlbe+QZtQouwm/WoWUNgWOPrq4WdsQBl1lcumlietXkeha2nbaSb3sEO+njnunC0K8BnkU8RKIIvVrK5sgCdGFVXdQsGqVWTmA3NIWotL27rt69V19NfDNb6qlFblHytrdFlsARxyhJ1teXbp50tER05hYN7JrGUOxtKXRVW5knh95/YFu2bbRH8sYz5goIaaKnm05qm0yffzTT/Pry77LVe5/CEobmyDIG4v07+9fhlqFlDZF8h7Y006zK9dmnyYXuOq8GLYDpEMPBXr10svDc7mwXdMmOkcda4zK9f3xj83zmmCqtIWgEKTRjQzXtWv+MRtLm+w+7byzXvo0eRMYUZSEwP7kE/WyiqJNG730zz5rXpdKIJKylDYeW24J3HSTO1lk2D7Dun2Qbvkypc2mjnqytPk8l/SaNpkXia37pAp55yqaoHFVh6gunmXOl3VOdWIv+y4XRbPk1Z9dY8hL4wPW/k3et2lqaULYFaS0KZLnHjlwoP4gBaht98jQ4M0u+1jTxn7TscbYWAt8US8h/3XdSV59Nf+YLBBJWWy6Kf/3Nm2ADz8MaysQhs62H9locmny2t+YMfI06eOu27HqNS9ykJlOJ1oPw2T/3vf4aWxd/otwj5TVEcqatueey5fD135mtpY2nU3feeewww75ZavSsSP/93Hj+L+7WKaSLcf3u09mtfPpHpnmwgvt8pvC2pmt0tYcIaVNkZDcI19+WR4qXBWXPtF5v598spvy8+B1sDaWNpkMRSltoVnaap3NN88/xvYmCs09Mo/LL3cTvdYHOu43ffvql/Pd76rJwK5zdnApitqngu29k12fr35VP49qOiZ7Xh9go/D46C9sFNyyLW2ia+lLuW1o0M+rY2lLn8NWWzU9nufqrEO7dsCiRU1/X7jQvmyGiUupKzdL07p4v+uO30IzCri2tJ13nl15tQApbYr4emBVlbZOnSr/f+c7QOfO9nWbonveDzzgr2weujO+Y8ZU9sxRcXlRHdirus8UrbTpyF8r2F6riROTzyJm/kxdqtJsvz1w0EFu5CkT2/tm4h7ps06VdLKBlsj6qEtWht12Sz6zLrsM2/ccb7AtwqSPybM+Z1Hte7/xDX0ZWF4dpS1NeiJBZY8yE3c+VXQsbbJ6xo/PL9sXrta0pX+7/np5HpF7JHvOdGTSOc7wEYikyAjmrpW2738/cUGvZ0hpSyHqkMqOHnnVVeZ1iQjNHczkmrpQLsaOVU/rek1bkcrRHnuoD3pCX9PmckBQpHukT5dU2/w2kRwZrgYkKpi4R9oOShYvNs+rsg7G5l2TTbd6deJWxq7B3/8OLF0KnHiiWn6dezVqlJmlRwSv/qwLXpasi7vsHM4+W18uhqmlLa20pV1VVfK6RsfSlib7XD35pBt5dNeKmbxjda1sefXoeh2ptsk8b4wiLG1FWuPSYymR14UOoVkTXUNKmyK9e/spV6S0pTdu9NUQzz9fP0/btu7qz85y6nbYeah2xt26JZ8bNgCzZiV/sg5XZ2Cv0qkWaWk75hj1tCGul8rDlfWkKEubrbXG5DlRCYDBe3H6Dl5hU45K9EjXwZ5efFEtnelznd4AW1dWXvqpUyvHoihxP9MdbKrw8cfmeV1y6KHJO0oUeIhh875xFYhEdyCdtcTaulvrWNpEsvbsaS5DmiL6GxP3SFEZLkiXpVruD37grn7dul2QHh+1b6+fv94VNB6ktCly0EFN3fxsGsznnwMrVogHxrvv7qYuESazG8OGAYMGAdddZ1//b39b/d1mDQNDxz0y3XFfdFEyK81bU8LSAO7XtBWpHLVuXVxdvtFpK7LzZvfWJKiQLraDLBPOOENtDZyLfqbIF6mKe6Tq764xVdrSx9mgxkbmtWvVZdBxActiE/LfJUOGJO9Xtn2BzbU76CBgwoSmbn+A3Zo2XaUtzZw5wEMPNZXFBbbukVlcW8xc5tMtx+W5qBxXqe+EE9RlUq27SFSDoukQ0vn5gJQ2DVy6LBx+eBJlbdmy6t9XruSX78vPeKutgK231svTtStw3HFN19WV5dpoE4gkLfOqVcC++yZuPiJcr2lTkc0V/9/emYfbUVRr/62cJGQAAglJCEkgISaQBEggIcwSkkiYw2AEEUFFUBFBEQQEQREuIg7gFQQUEbwgYhjkMjkg1wEnuKLIKHyggiCEGS4KROr7o0976vTuocbu6n3e3/OcZ+/Tu7pqdXV1da1aq1aZKG2+3COb6kTV/fSq1lWmg6g6lLYyTPqYEPWq5jltGrD//mHL8GUhLSrDNMiQT4rKrurLXZS2vHR5SpsJus99myzzugweDMybB8yf3/lbUf+ebkVSds+qlLayfmDiRGDOnOK8y/LNQ3WPfPPNxIVeh1i20rBRkKqsbLqukLbukVWsuab+tgMmxKbQMOS/OVTaDPDdQM4+u9Nadc45+eXF2Dh9KJJ5L3qba7W1IKmdt5TJoL0orzStSUhzFxevEOiuZwPiW8NWRl499/T0rd2pimpWp6VNLc8W02fEprxbb00s6jFTZWlrUmkrwmSQaTMoy57zxhvlZZSF/Dcpvy6lzXSQXpbeNZiIy7k66YrS6Jyj+37OWgB9ThDX8ay10T2ySgFUl8aY5lNFVRTOdMlIHdDSZg6VNgdcG8exx3auKStaL1ZnRB9dfFgeddebFG0yDORbhEw74nSWUecaenrK/fff/e6+7y7ukSE6HxPXztiVNp36SRXs114rT5deq8/IfTY0XedZK48Pd2WgeBASytJWlvdAdI+sI6x5LO6RPvHZVorcI33IkVePumMG1dImZXNjDd26/uUv7c6rOic298gQ6OQ7YYJbGVtuqZ929dX7vtd1H9tOhKpAc5hu2ll13Abd/XN80qQvua7SZhqW2WaQ4muWce+9k8/nn3eztIW457ruCLvskizoV4l5gJVXV2++mazjWroU2G238vPViHM6IbhjILR7ZKh+wcXVL0vM7pF5mM7O+3B/uvde4Jln9O5tGyxtdfLCC8W/+VrT5hq2vUgG3b4+K1coRbUK3feLibdIET7cI20sba59n4+Jcttxri467fnmm4Ebb0yW2bjQ7QpaHlTaDCh6YHwOZtUGnzfj2hR5UQdDKG1F+arrk0aM6AyTrN4DF0ubj3r++9+TzxdeaMY9cu7c4t90rm/MmKRTzboKqnKGWOtkSlXdvv46MHMmcMstwKRJ5WlVpe3ii/3Il8eRR/Yvr4o63CCrym4qeqROuTbukXX1pUVuh3WvabviCr10JuXk0Valreya88Lxp7gobWnbOP10YNy4ShFrsbRdf33yp3teU5N4popLVVvXndgxser4sLTFPElahk4fsvnmyUSq7wjprnEE2gCVNgN8zHJUUaS0NdkQp0xJInJlyevcTTua7PoxnU7wE58AbrutPIS5TfTIKtcQ3XugLvxvwtK21VbFv7ks/FXlrIpEWLdSl1dX//yn/vll63psyi4inXzw8UJuk6XNl+uLD+rqSx94wK589Xd1ssqGM88E9tpLP72LNcFGabN5DtRgXXn4fE+XWXWq+u0qS9ugQcBJJ+lbdcr+z5PF1NJ2wQXJ+semLG26abPvaJt37MiR5eW7WtpslDmbvjfEu8r1/ofy0NA9h0ob+TchZiez5HUmvsvwhatMM2d2msd11hQVvRRTjjoKuOQSPRmykbN81HOR4l2E7xm1sjJ1ZlF9WJD32gu46Sb783WoupaqdWwq2Q15TWjDjKiNZS/U4M1nGTr7tJXJUhdqn2VS/rnn9j9fpxw17Xrr5Vty8qw+eeXklbvWWvll12Vpe/DBesoBygNCFM3q60zCmXp12LRZm0AktmXZlGPL7Nnu+X7qU/nH999ff+xgW7bOebpjzdATd6HOj3E82xaotDngu+H19PRX2kxcalzw1fGY5nPSSZ3bDQwbVj17knUZyr4k//u/zeRI8eUeqau0nXFG8ln0krcdBJVdg692pDOLm157qLY7b17571URI1VclDYTQrgv+iQW674uOoFIsu7CTSptOuWrv0+dqndOUd6mSqIOv/gFcNppncfbMHmRR1n92FjaivJV18r+538Cq1ZVy6ay5ZbFk7o+LG0podwjfbwHRozI31zclGzwlZQrrwTe8x53C47rBH8dfdRJJ4UpOwZLWzrZ0vSyohB04SXZY9oJ+7BIqKyxRj3WPFPqlGnixOo0Ves8bN10fCltugO09CVe1H6qNjot4rDDin8zsbQVscUWyZ9uPnPmAO97X3V6U4YNA44+un9ZKiYBRVw2u+1W61ydL98sa63lZqVW++bp0/vvKdm00mayps2nJVLH2qkzETd7NrDddp3H63KPDB1IQaVKadN1d3v99WSj7pSXXzaTQwjgt78FXnmlM+8idJU2G3fD0JiMOWysVnmTGab5uEyIVF1HKOVOVVKL2nablLaifNJrpNI2wKmjM2siEEnVdRW9JH3LJGXfxqRZyixtefnoog7udBexVuWv1ouO1ctVaTvkkL7vv/1tsilyESauC0VynXhidQQvtZxhw8IG98hj/nzghz/UT+/L0nbZZX3fP/3p4nLqRneDZR8Kg48ByX336ZVVVp9PPw1ceGGn23MTL/K0fJ2Bnu7AdJNNgF137UynMxhVj5W5Rxb1QXl5pvksX55/Thspe25M1rSVuf27bqJc9Jute6TP5+O55+zOq2vM8dBD+cdDj/Vs+gCd83zKkOW224A//clPvj4VtDzq8pxpAiptBhR1pD4bYIyWtiJCyVQ1yKgKgGKjtAHVljbd69V1j6xSjnSVtv/4j0RJMZVNlSEEdbz4ip7BfffV26B0v/2ST1+dvLpHn8tG3T//OfCzn5WnMZH1pZf00uUpVyGjR7r2dzqyPfqoXd4+cVWGV67sPDZ8eOeeSjaWiLK0hx6qf25qaSsLEGXLJz5R/vstt9jnXVY/G2xQ/JtppLpsWpfQ9dm8fLpH+nz2jj1WLy/dfF3bt3rOc88lwap0LcR59WS7RZPr76bpTCjKc+HCxGvB5nydvd9s72PeMSptJJcQDSLGkP+6A6u6HpAY3CPLrlVXafNlaVM7KZ20PtL4KisUumWnrqQu7pFFlN2Tot/S49tvD+ywgx85qmQposlZXV10gj6sWuXHguiCun6pqvytt+5Mk+79qOJyHbp9+qxZ+uWkz5CJXLrt8qyzytcqjx2rX6Yrl1+efD72WLklrqweDjgA+MtfqtPp5AX4Cflvel4Zq60GfPaz/S2MoSZzbJ+D3XdPPtO9+Kr6CJOyffQxOs+GTTmhvT106snnfcyDShsBUK/loKjsOXPClOvrPFsrl0narHUlW6ate6SJ0lZWhjrDWYelzUR5rkv5L2vLvstRP1N020CaTu3kQ8qdLa8KnfaTl78tZc+ZTR5l+Zbl7XO2P5umiRd5qtD84x/l5d9zT35kO9uJM9UalGetM82v7Hh6jU1MMLpsZVJG3nWqLvxlkSzL6nLddZM/k3JNfgfCW9rKuO8+4OST3TcO1/lNp67y+oD11ku+p/ehatsXH0qna/7ZNC7eHLpl1H2+a1m0tA1Qli3rPFaHZanM3P6HP4QPo25CqJdzVYeWZ2lTO1wTS5uqOPnamFF3Vt9Eabv99r7vV13VmY+u3D4CkfgYxMdCntLmixBKVWiEAHbeOfk+YkTy2cTm2rptWsftM/tcu8inrh81IXUzfPXV8mdw9uz8wbauzGXpNtywOp1L3dhY2mxwcQXMw7e8ISwkIS1tIcc1NvelrP7yrslW3tQ1PuVvfyvPc489Ostt+t2WKp66hLLe+Tjfl3VSVdoYiKTLURt03ubApp3b4sVm5Zd1AoMGAZttZv6QhqSpGZUQgUgAfUubbf5f+EL/36rcI9WZ2J4ePf95n5HVXBSMui1tusezpAPNEMpUDG4oNnnecEOy3sN2FtfHjHTe7HgZ++0HHHigngwudbRkid15m2+efNpODJm08yIFddgwu3JNrZ6h+piyfAcP1s/HBFvLTtVxtS/34brsU2nzGfLfdM/SlNVXzz/uy0IlRPI8qEpl1fUsXKhftu+JzzLKLLZ1yVCVr463g89+kZa2AYiPm33kkfkbm5aVabOwNd3vq26aeiCqXiq2YaR9hfxXUesou8dOkaVt7twkCmTRANFlZtSHpU0Xm3wOP9yuDJ1BTB4u7pFjxuSXbVJuFte696EoDhnSuX+iCUUv5NtvT/b40h1k6dbFKacAK1Z0Toqk+LS02fYPtoNXU3SfA9fJjlBKsS1lFh3f8vjeFsY1fdFvuh4nIawRqUw27V6I4vtpO9jXeQ5st3yyQec6dKKK2lB1nSZb5eTRtKLkq6+PFSptBpg+tEIkmzV+8IP2ZaSUdayjR+vnb1Km6XkhB/smlrY63CNt0hXVV7YTHTIk2Ug1e26RgmLy0m3KOqpL0cDbV/5ZXJS2c87pf64PQq2/8hmoxpZtt83f38tVjilTOo/tuSew227J9+y1uwxSbc8t6geWLAF23LH6vKI+0aQPLpKhbC2PEHpRWHVlcKEs31DukXm/7bBD+T0rOtdkMFl1X3XqOOvOp1uWT2yel7qiRwLFFk/XcUAblIUiGU0MDSb5upz3rnfpn0Oljfyboo5zs82Kz9lpJ+BrX9Mvw7UTqRPXGTqTaypT2vICkXzwg8D//E91vqqLoknIf5tBcJGy5TroHzJEv6PSibJWVK86+ZukqaJoz768cmwnEEwDg9iUkVeej/Qh+oS6+xkf5eXlsdlmwEEHJd91LW3Dh1e7GvmwtKnff/Qje08Jn9aasjSm12wil68JD1ulzab81Vfv24Nx/PjidEIAv/xl/l5gphaoqjR516Hr3mzbptUyv/71/DQm90WnHkIGNqmKIJz3jjFV2mzGPNtvb3e+La5l2LbnsvNCba3QRqi0GVDUAG68EbjgAvf8n3nGztIWumHGNptUNvsM9A3SdtwR+MhH9PJ88cXwa9p0LW2mbhrqeo6ic2fOTCKdbbtted55+aeUbdptk19VWpPzsvdN9x5l17S5zNrq4KIktgUfs582baasP9DJ+5ln+u+zl0cI90jb+sjzDNAdSOr26TZ9f+j3gs9AJKNG2Z2X3s+yTbMBYJttgLe8JfmuY+n0ie2aNputStI1m2Uy2CieWXxb2kzK91W2bl5tXZcVQl5bbyIGIhlA6M60AIl74qJFfsptk6XNZydmkq+Oe2T6m66r5Ac+ALz2mrtbRPa3oUOBffYBttgicXnMS2f6sspT2qrk7ukBZsxwuz/p4KMudGbRqgbsZay3HjBpUvI9Dd1dNuj1iY+Bmomczz1nn6eP6JE2ViFfM746lrb119dzA3R1j9xww7Dtq45Z8jryMM3XVmkbP95O3rQ822utakdVyrOOoqVbJ3WtafOZb9UxXUzGWyZl+7QAtU0JCWFpM6ln24nfttCCJlAfLoMTX6Fom7BqVeX9jnfonScEcPzxfmQqK8skmEaV0qbm+89/+g/UIQRwzTXA//5vEmDERsaUovbpO3JakTJp6uqSpi9zISoqO/vd5Dzdc//2t76B+ksvJSHufbrz1K2YlZW5YEGY8mLIw4el7S9/0bv3dVnadNPYPiNFfYbNc1SVRx2U3buy57Cq7yy6lqqJw6q8TPsOmwGtyzrWTTetTus7emSIwX5VPuq5Ve6RPsqdPDn5fNvb9M9Jyxk1Kn8pjq93hC9sJ/7KrkO33504UT/PtkKlzQDTRmXTYIo6uZDukWXnX3RR8ZqLPJkOP9yf1VGlytJW9JIzUdqefDJ/Q+t11un/v69Oz+RlK0Sf0pdd6+WiaJq0HdPZ5QULgNNPBz73Of0yVExenDozz1Vl3HNPuNDhumy9tX5ak3s3dKj/PH0QcpLKxNKmi49AJL5my/PWfOoO7ovWYad781XhY4BlSghLm+t5NspU1W866XX6u7K19lWyXHstcOaZncfVctTvm2ySn3cMljbdurZxj3zySbMy58wBnngC+OhH9WQC+urwmGPy30+24xHbfrAqCE+Id0jVe2LaNODuuxOPJlrayL8p6zhdolcV5RmDe+Raa+kvAq2a8a46P3tc9ZMvU9qk7ByUmlqxUtS9jE4/HXjPe4D77++UwacVRTevW24BfvObZJ1EET42CC86P23jurNmw4YBJ52UH93PN7bXnJ7X0wNMneqWl45MZWvaXnwR2GorP2XryBIKH7PhPi1trrKoxLSm7fTT7S1jvi1taoCj0G1NfXb+8z+TicKyCMpVCqaNcuVqaTN1j6wirz/R9XDIUwCnTQOWLdMr89OfLnYt9jUuSrGdHC+a1DXZLy/v2ch6z+jINGGCXh8ZYk1bGiXbhSYsplV5DhmSbx2m0jaAMG1UISxtOsebJPQDUaXUqb+n4dezaaqUtmy9brRR3/eTTgIuuaTP0jZrVvJ22owtAAAgAElEQVS51lrleepiqliOHZtYr3y5iJiSDvTyrJG+MJklE6J4wB5SSXA5J2WXXTqPZffx80mZrOuvr5fOR1kmaX216exEhovXgqvSpjupouMeN3Nm/rkhrZdF1DG7nZfvkUcCF15oX2YIS5vtoNUkvc75ul4Dvp7XvHS+9yf03bbU/EzdI4F6xmW+okxncZ3o1Pld1y3fVp6897/J5Egb6cJLqo8QjcPG0tbUbEJRuaF9pvNmOQ87DDjvvL7/da1YJi/DE08E/vu/gYULmx3chlYwqixtq1aZl2/Ds8/qp/XhtlZ2TOWUU5JQ3i7tfN68pM26yGJyT8vqR40KWueA21f6KiXF5953PtpZapVK17e43OOq/kudWbfpr20UQCGK10TFRp3ukS59uE2b1VXaTNp0nnuk6WS2C74mLPMG+7EGIlm8OJmgWbhQ/5yQ6F7bnnsCJ58ctsyqe0JLW5eTPrRXX53/e1kn3GZLm+2gIfTaBdPZk7z0PiLfpYwcmWxY6ltBz8oYS+dcFIhEx9IWahYvy2OPJZ+33GJXnin77gt85jPlLqopeW2vKZdnF8XA5zMUMo8ypcTXi9yHe+Q66wCvvgr8v/9XnN7WctzU5F62fo85JlxZPqlyjyw7D8g/V+d5+cc/yn/P5rv66uW/55Vpa2nTdcu75prqvOuwtPlSkEyVNiHCTham8uy4I3DffXobuteBD28E3xOUTXgXNAWVthwmTMg/XtYAfPluq4vLY58x8GVpmzfPrCyd9QS2SptNJ5xdhJ2WffDB5eel6VS3jOOPB047rTht9vvdd/dPV+R+5cNyUYd7pCn33ON2ft3PVdnAwHQA6OOeuuQZEpOAMG2ztAHJxsfpHl868hQ907bn6mLTbnTlqiK7xUiIttmUpS1dJ13FkiWJZT9rlS8rJ0X3GXKJmLt0KfD2txen9z2x6ztKt5qfSdCyMnl0ZArRd/um6L7qKm2m/UBZ2jTWwKmn5p9TND6K5X3mEyptBejOtKT46pwmTAD+9KckHHns7pHZxd+2Lh+//jXw+uvFv2e/+1TabGe0VWzXIuXJuN12+hHcgD43pCI3Dxe5stThHpmWPWZMcRo1qpkvWWw6+hg3Py2692X9k2/rn8mkQd7xnXbqHxBIt7y2WNqy+FS8yhT/utqpr3K+/e384z7d720DgqSWryVL7MrVXcc8Zkxi2R83rlwuF0vbhz+cf1xnEum44/rWeuex5ZaJd4IvbCcki9pM0XtT95mMycKjY/kE9J6f554Drrgi/7eqa8ubBPj736vzKNsnc8kS4Kc/BU44oVomKm2kkCqlzbbBTJ+ebPzrI6+QjB8PrFzZedz0pTp4cN+sM1A9CMuLHplNbzvIsRmUmQww88p23cMkm4evQU02nz32SKJ0FoV3VnFpr089BTzyiF7erkqbq1XSZ9m+XUZs8gmltJlgOxAuIkZLmy/y2lAdA8mytlvXtfqgp8cu38mTgd/+FvjCFzp/06l/G6tOGXl9vvpOLeJ97wNmz+5/zMe2I+nxUaOAiy8uT5vFl3dBGVUKqW5fHLI/MJ1sWXdd/Tyr8l177eL2Y2Np22mn4vTve18S9G3p0uI0PT3AW9/aOdbSHSt2E114SeEoa6y+Q9tmsQ1prIPLwDC7h5lPigYCqSXKh6WtrExdipQ2XSuf6UvKRIHTPUcn7b77JmsxQoWlTxk3Ln8PqhS1ow5haRszprj8EAPfsWOBSy/1l29ZWXfdZZ/HSy+ZleWK6cRLkSKRtbSpEWLroi5Lm+88bM+JQfnXweW9veWW5V4WZfK7upjr1I2OpS17rz7zmb5IzHnX5mOS0wXbSbaiNM8/3/fdVJF2mSBx9UZwSRc65H+e63DZORdf3Ll9ie4egwsXJsaDHXbILytGY4crVNoMKJtd9Glpy3LrrcXr7LqZokXM2Zn4vM5WV2nTsXZUUWbWz/LFL3aW5XPPN1tuuUVvbaHuS9pWHtPzQljahg5N9kzTsSgW5VFE3kznxhtXr390Jb1vM2boyaTyrW8l0ctGjAC++c3qspq0Xuowbx6wYgVw9NGdv4WS0zRst+1Aral6rnoXxkqRrMuX2+ep44pnun+oDToKaba9qOdMmtSZ3sZqbdomy9LbjLPy9iZLz9lvv/7pTImprfusZ5fz1DaUps3WU9U74pOf1JPliisS18u8yOE6sraRiJpc89hED0rRfXh//GNzucqsbFnefLOZaG8qvmZy1A2z02OLFvUpSWkErqef7p8G0B8k+Zg5zL4cy+pTjapmorSZzKLZ1P+YMX37dflUJn0zcmT/5+GNN+ot31ZByztW5dphIou6uXFVWtN0++2XRC/r6QHe+97qPEwsvbpybbBB8W86g7bsi3y//YBPfEKvbJOybM6rctUqSqNzTMcdykfI/zoGSiHytd1cW4eyc326Rwph713hahX14cGRxbfnSRlrr51frm45toFIXIK/mKYrcne1fb9XyZMXc6Ap5SkmpdoXXXhJ7tgMMIYP79ybJi99NnRvGaazsgcc0OzMgu+Znrx1birpQC7PDcTW0maD60DOh5KtHrN5gccyI1Umx/vfn7jorbFG37EQljZd6lBqVfm+/vX8NNts02fBlbL/Ztl5+cSEEMCNN1ane/jh/v/nRdMrUiR0LB+h0XGPzBvI+XhuYwyY44LPScmiwbPLs60zfnC1tOkqZMccA7zrXcVpnnrKLF/dSU6btmZrtXMpq+ie6E7a217/uHHA2WcDU6cWn+Pr/bLWWn7ySTFR2oosbVX5+ppI6JY+T4VKmwPZxlEWvefee4Hf/969HB/pQpStku1ssgMuXVRLW548WWta3sNq2vE9+KBZ+my5JqQWw/nzq/PKu7Yi64rrDFqTimwZgwZ1dv7p2pDs1gemhJht1h0A6Za95ZbF+dvMfpbJZIoqm2keu+2W72Jcls9FF/Wte7CxtOmS3Y8vhKVt1izgQx8CvvMdu/Oz6dTIq64DmKJzigIC6LSzq68Gbr/dnywuVFk8Qg36fK9pK+rzv/jF8pD8m2ySBD4ryjeLS1Af07x183C5R+r7xKelrcoDRAjg2GM7g8AUpXWhaEI3RF8G5Ndp0YSaSb42UGkb4GRDsZsMgGbNAubM6QvcsfPO1eWlg5KyoAwquoP1bNm+G7ZrtLY0fZWlLe0cfK5py9t6oArb+pswIQlr/dWvmuU9eDBw7rnADTfkn+M6Y5/WWejgOj444YRE9uyeTrqE7NTr2lxbJ8/QEz9VbpN1yBXC0jZ3bnWaPNSBMFA+0zxsGHD++XbrqPKuWV2rV7RvoytTpuQf33776nP33RfYdlu38q+8Mn9NoilF0SNdrBw6A9Uqpa1qG5ls3+ziHjlkCDBxov45KrYbKdtiu6atiCKFJo/shuhllrYqd/UQ6PaxoQORqBM3aVnZegrptkhL2wAl72ZvsYV7vtOmJWHyiwbcKhddlOxNoZrQ8zBtmD/4gVn6pshb06ZStm5NV2nLDspsOjSTNYdZDjpIL8hM9vqPOgpYsKAznZSJC+6KFcA++1Tnqw4wfvWr5Hs6oDjjDOCII6rz8InpzO1xxyUv0+HDw5eXJfTLryq9yWCzTmt9XbOoum5/Pvdp0zn33e8GfvIT4NBD7cvUnZkumtQ55JC+/4vqSWdNn+5A0KeVXkeW/ffvi3LoQlNrXqrcI9/2tvLfbYKM+Eprep7P4Dt1W9rOPbfvWN5ERVHZPgLHmbo1F6Xz6cKqc17ehuXqOd/7Xv5etCYKtK58VNoGONmO0rbDX2cdvT1Uhg9P9qbQpekG6rv8vDrKeyDzOgYdWe66q1MpseksJk0C7r+/83idgTyy17vffnr7tqjnP/lk8v1Tn0o+1167f1SmLFl3vTJ5fJKtV5PonSEQAjj55ESRNj1P/XSVoQzXkPMm2LT7PBnUoD2m5+rIYztIrGLhwqRP+MY3+o6l9Z+dra+TOhQqXTfcWAihtOkoulm32yxVculY2qrkyfsthKXNZHKlCt/tSs3vb3/rPK6+W8omjsvytZHFJq8mLW3qpKka8j/P0lbmruubbgxEorGTx8DB1JVu333N0ocmhJJQ18xpHmqAEZMOU01fVidz5wKPP97/mO2AM7sZui981b/JC2G77dzydMFkgBG6PJP0n/2svQzqXkGh0FUQYxpsp+1w1Ci99GXukXVa2vJI+5XnnvNbro7FK8T1ug4wXfD5npszB7jjjuLfQ7WVz3ym/Nwq5bfq3VhVfhG++sNQ1va//90u36IlG+oYomqSOC9sfUz9ZREhFd081LabN6Fum68u3W5po9KWg46Z+YgjOs3lTTUQ13J9Pyyua9rSB71on7YUH4FIsvnWsX+ODaHaVl7d+ZidaltnWZe8antMLaF/+INdXkUvp7xrSdfF+gw1bpJHqFlknTxMLG2+28EDDyRBctI1Q7brRE3lUssJET0ym1faZ9S1VsUHab3kKW2hJ0CrokhXbVlj4h6plrtsWWIF/u53gWeecbf2+7zfOjLsuaf5ebZWyOzv2WsdOdLd0laHMuNqTa3KL0uey2mdFi/V66lt4xAdutB4GA5fs1DdSvqA+nrh6XYOOoFILrmkf6h43TJ0yM64NXnffey90haXglAKhm56m7pWzzn2WPuyTTnooOTTNWpdzPiwtF1xRXmepnJstFESYCSdxdfdokJ3oFV0/GMfS4KC7LprdVof+7S1zS1Slyassjpk1wSV3UPVKjdhQhL4Km9bECDMGMenAmyyZZIOJkpXNu3224d9V/ra2iIrYzbfgw9OXLpdy8mWp1ra6g5YEzLPpmnJ8Kx+qmZhm/C/brocW2zlqxpomQQi0e1cY9xQGrBza9MZqIaytNmi01amTUvSqQPSEOVWuby6WjBcX2R5v1XNzOftaahbni51WLBc8i5L/9e/+i0rJa13XaXZNfz57NnAz3/ef11rnZa2Ng3ATJ6jENgozVUDcfVc1SqX5+JX9n/Vdj0+3xWLFyefy5aZlefL0lYVhTcvAuJuu+VPBtdtgSxLV3X80kuB227zJ09VIJI6yUbx7QaotJFSTB62rKJ0/vl2+56VDYbLXCB1fyvKT01vQtbS5kJTnZuNpdDFZc0EdWEzkARAWbWqf4Q8W8rkPOecsEFOQg6iixg+vH9UQyDMNgQ+8DXTXBT2vg7XpJTU0mZ7TUVy2GxRYlN+Fd1qafOJTd3otpc8y1laXt76N9334bRp5eXq5KM7uTV3bpK2LPiar21oUlmKlKtUEStTeIFEaXvppc4tLOro24v2Ssyio+D7kCdbnhBmk+Yh+o6LLwYeecR/vk1Cpc0SnX1R2vICCyXnqFHAjBl+ynW1tIVU2urA9R6lkSF1iN3SBlTL6OM+zpwJfOUr9uf73qdNp3/RyVPdzN3mfJ+4TBDoPtuua2x9nKsTLdi0XCk7AymZ5OGzHqqUAZ/47qN9y5wqHbqufD7K33xz4J578vPNUzxMvQTWXjv/eN3vCt/lFVnaLrgAOOkkYOlSvbJ9yfW1r/VFIa5q57proU0tcCpTp3YGzZk0qfycpgORqLzxhv12QLGiFYhECLELgHMB9AD4hpTycwXp3g7gewC2lFLe6U3KmvD9MqiapfJF08rh0qXJ3m++5TB1j9x00yQ4zKpVwLx5/X/zrbRlZQvlYuNrYFW16a1v98gmrEgm52ywgV66sroIEeDBhrr3iwtdhi8Lm5pfnZa2vHNclbYidBTSqnbqc01bG90j8/a7dCnzrLOAj3wEHfurhujH1DSzZ+f/rlraspYqHUX+1VfdBv4+sXGPzCOvztTnYKedkr9//lOvnCq3U10++MHOY0V5ZSfEda2eJv1rnpXqpJOA8eMTZehjH+v8PbUADh3aTCASlVWrwvW9TVGptAkhegCcB+BtAB4HcIcQ4nop5X2ZdGsAOArAb0IIWic67m46DX/KFC/iBMfVza1ozxjbjkvXPTIbiGTBAuDRR91kidXSpkuR/OpG5XnpfSttTVN2DXfe2TlzrOtaYkIoRV63rLryOfhg4B3vsNuI3aeFRlcpaYOlTdcqZhLtNuRESghlzTSvQYPKg1IVkXdvXJ7TNdcElizRT19Wlo9NhtX3c1Vd5P1eZqnwuU9bEddcA/ziF8CXvpTvHqkzVsvWY5rPQQcl23B8/OP55+q+F2N+Z/pWrMeOBU48MfmeKm1qGR/5SOKuu2QJ8Mtf6stQZPW05ZxzgMmTgaeecs8rJnSa2gIAD0spH5FSvg7gSgB5S0U/C+DzAP6Z8xsJSBpOusztqQlsB2R55226afL5nvd0pnMJCuPDPVJHyXfF5mVr4opno7TVNZtu047K0s6bB2y4oV6eLjOood24XJ8v09+KuPTS/usrXNuFqVWs6tl2sbT5Io3252MdpoqPgFg+2kOIkP+myvbNNwOnnuqvfJ0ym8rLpDyXQCS6ZfhOqzJ9et81+GpfaT6DBwM77JB8r3qWTJQ23Wv1ae3XnXgM0Q7Vuhs3DjjssMTS3KSl7eij6y+zDnTcIycCeEz5/3EAW6kJhBCbA5gspbxBCGEYyLqd6Kxpq4vFi4EXX+zbi6lpXAerebO2kyZ15lu1l436m2+lrW0WORP3ltjcI994I/l88UV/eaa4uEfq5hEa182jVatjqJeri7LrOmhxsbTZDGrzgkKstlqyMfDo0fplq8ydm5z7+uvAK6/0Hc9alny7RxZRNYEQ8pkoknfnnZM/U0Kuk4ohL9U90nVfsSy+88tjk0368vPlHpl3fhNKW8r553ce8+Um7mNi2pbx45PPzTYDLr+8PK3LO2wgodNd5VXfv2+7EGIQgC8DKDAwKxkJcbgQ4k4hxJ0rV67Ul7JBihbgxjZod1HYQj0gVS9wnRnysrQ+lLai9Cb4tLSZ1pVuXkUvnCbdI02tH9k9tEzztsF3XfjsN3xZjw47rO+7rf+/izXHlaYsbZMndx771a+StTB5jB9vX7+bbQY8+yyw1159x0zXp7j2IWXHY95cu6qO6hogVtVl1XYctuU1bWnzubbbV/TIvLyrKGvbW2xhl+dppyV7OR54YHEa1/aZlXvu3ORz1iy3fHVYvDhxbf3oR8OXVUS3KYA6XezjANTX0yQATyj/rwFgEwD/I4T4M4CtAVwvhOhw1pNSXiSlnC+lnD927Fh7qQORpySE6CTahM2stC9LW5UcTVrasuflhVW2aTtjxpSXU0WR/CHcI8so2ry1qEzf+HJPKVu4X8fEjc3so6kCpV5j3Yu2fSpTPl2SqtJOmpS/TnTrreu1MumsaQuhUBcpbXVYmXzXbyyDuqJ1x1WYKIO+92k0eVe41HOZpa3qPeviPaP7XjzoIL0yssyZAzzwQBJpuwjXfi37zjroIODee5PtCkIzaBCw3XZ6bbvud2tb0Xnk7gAwXQgxVQgxFMABAK5Pf5RSviilXEdKOUVKOQXArwHs1cbokSlNWB3aTJWiYNpZ6y42zgYiKZNNdwCQmvNNEKL/YHfJkiQois3sUlEkM9eBV5VrlE2bT8+57rr+5/7rX31rEG1k8oGvGWPf7pFlexCZ4sudRH1+Q1naTM7L9ieulhJX91GTsnyTLe9vf+v/v0n0yKLjZdfUpKWtSm5dbPpGHwFAdI/nrfvx2c5UL5x3v7tcplgtbWXlrbOOnzxd+pn11tNPq0so90gh/FvZYpn4yCNm2Wyo7GKllKsAHAngBwDuB3CVlPJeIcRpQoi9ys9uP1VuZaQYW8tbet6//tV5zDT/qoWw2Xw//3k9GctYd13gN79J9s4xJdRMtcnAxVQG1WguRLOBTEzzrkrncxD6wgvArrvan68ziBXCrW+yne1XMbGe6e5llYfuIMvW+hwj2fvjEj3SZA+lKrKWthB1a5vnlCnAW95il2+dbUTta9I2++qr9vmlsqtuvBttZJ8fAOy7b/99ukzWtPmoy7w86vKGKnsXuHrIlOHT0haKprc3GkhoDUmklDdJKWdIKadJKc/oPXaKlPL6nLQL22xly1I1O6aTNnZ8y+3LPVIdkIRyj1QHjaNG2W3EGIPyUYWJ8tHkmrbY8tbZp0339zIXGB2KBuhC+HH5A+wHQLb1/c532p2XV3ZZX503KbHaaslnmVW4zBLRRH+vtikpzZS2IgumD0tbmfuaLSbv3jJWWw146CGzcuq0tJX9/vzz/uUAiu99lYzjxwOPKWHpdJ6B0aOTfUL/67+q01aRd19M1gK+//3AX/9qV3ZdrqC+iUmWMkLJmUY21lmy0Qbo/FdA1UBgoLhNugwGq+qw6Hg6cNRV2sqoGpgMHVod1cg3Z5wB3HWXXtq69plzcQm2LTOGoAU+LG11KZ9FkQKbmNUtY/p0/XxdLG1VeVdZ2kaMAO65B7j11uoy9tyz/8C/KU+LqjVtJvfPZf+sIvfINkzEmORbx4A3r4zUTb9MIXGRzVZpy6KznKCnB/j5z4GlS83y1iVbR9lwCWrAntGjOwMI6d7/qneBOuHr0z3SNa+2KG0qLjL/138BF13U9/8aawB//CPw61+7yxUDA0T1sKfoQf3AB+qVwxc//KH/PE3XoFSR1nmVe6S6N1QRLrPJupie/8lP9kVw8lVGlTuKyfmm7o2uiuLpp9udr5O3a/p585JogKk1xpdFy4YyS5tJmSFcl9TzZ8xwy6ssb5t0ZWvaZs/uHOTl5bnBBomLXV2WNl0rk0v0yKK+cerUajmKlLY2Km++LW0m5ahlqf1u+m4rs6Tm5ZfuB1hWHgD8/vfJ55/+VJ22DBvPFF322CN5PqvwtQ+ZS8h/APi//0uivPqmDe6RPlDldNmm5V3v6h8RGUi2jZgwwV62mKDSppD30BY9qPPmhZVFhy23BLbZRi/txhsDt98OvO1t4eTJDuJtLQG6Stu4cYnL2XHH6ctW9ptt59bUbKzKtGnJp7roPOtKpZt/3e6RvjccVvN2Tbf++sBPfgKccIK7TDao963MquKiTEyblsxC3nCDuXwh0d2Quup6u3H98dChyYDZxD0yS5HSdu215nnVoaylhN60vqn81H53q96dcE2jgz71lJkcf/5zcV5Nc/31wN13J9/TkPp5SpyrtVB38rHqveh7QicdY+oGh9Ipc84ce3lcy3ahG/twWzzvDNId2D58dXd4v/qVftpBg4Btt83/zZfcLrMjKrpr2oRINqxN16aUydS0C4wtui4SX/0qsPfexcFPTNZfuShtqqJdRUyz8TYD/7pfJDqWtrz/i3jf+4AvfSmZ+NhwQzfZbCzBVb+vtlqykbQ6m69+r+pv1MGYrz696b4iveabb06eU5c+tyhIkzqw05m9nz8/jKtuWZltyNe0nPQ+LFuWv0RAJ7/VV08mO2wDmPiqCx/5CNGXz/LlwKpVemtuTd/1urIOGgQccUT+Rti2eZZx1VXAHXfo981Vz6pu6P2maLpvbQu0tBWQNqCY16719PiJnBRaofFhaSti2LDy/GN0jwxRxogR/TfezZ5TpGB87GPJ5xprAIcfnszq6S7sjukFb5uni3K3xhrJ58SJ+Wl9R9TStbRVka7pmDHDPTiKLmldmTJyZF9/cP75wO9+15nGt4Kuc05eHj73PdIN0x/C0qaDes4dd9TrHlmnpc1HWzE978039bazcZ0oyUsT88BZd6yz8cb9/9f1OKkKLidEMjmqg496nDoVeMc73POKeQxLzOHtrIANXh/TF0DR77qWNh1MBiYxvrB8yVT08j/2WODllxNX0wsuSMLS67b50aPdZNJ9CV95pXneddzLvfYCLr0U+PjHw5cF6Fvaqli6NHH5PPZYd5l0ZTj3XPcyPvShzgGZDq+95t91ScrOGfDUhcsnWVmz/ZmOAlPnPm1ttrSpVog617RlrZRS1qe0pbgo/7Fx+unJ2n3d59HEPVII4Lnnkj+dPIFk39Y6KLrfS5cmgZSOOKIeOWwpm2SOcWzWFFRJKsgbwG65ZX5a241p206oQCQ+lDZ1MKH70jTFR4dy0EHAokWdx31FkCq7J2kEPyH6L2Sv4nOfSwLy2K7v1FXaQu7Do1uv++wDvP3twFln9R0bNgw4+GBgrbXCyJbFdH1LGTvtVN/+RgCweHG4vIueX/X/t74VePRRYMUKMxehsjy//W0zOU0ouo9VljYb90jbvuXAA/sCW4XYXLsuygbtdVjasm6qb77Z10ZHjjQvxyY4TRrGP2RgkboYMqR47X5enaXrwGfOLM83vT9rr5386eQ/eTJwyinl+fqiqD3MmZOsDzzwwHrkCAHXtPXBNW0VZB+EV14pVs7WWy+8PHVjs/7DdTCQnvfEE3ZyqBx7bOLfv+mmcW+ye9ll5b+7Dh5CdHqzZiXWOVtCKg2+N/geMQL43vfs5fFBkdKWzgCn8AXXn0WLgE9/Ovk+ZYq/fLNRJ+vsR0wsbUW4uo6rW6Wkmwtnre/rrde/H3chtKXNJHCTSzlFbLcdcNttwMknJ2uTzzxTL0iTrjVUJ83b3159jg51PQtXX91/3zi17HSctmpV+f2cMgX40Y+ArbcuL8t2n7YYxhdtgHWmRwvnxcKhPthFa9pGjox7MacNoV+GpqSzi6oLgm1eS5YAP/tZ+caKvta0nXuuvRJTZglUy4id5cv108awT5ttel/sthtwzDHFv5etafNlhfVBEzJURan1IZNJnnUoy9kyXKIYp+3JRz1dckmyF9KZZ/bPsw0TCEOGJMqRzn59IVl7beCZZ5KI0EIkEWvLwpT7dI9MaZulbd99i39Lx2mvv16dz5Il1XtG6ryv0n3r6vRiSGnyPWC6hRGxh0pbDmrjb6O7hw4hXbpc/ZHzFKw2rJU46ij/+/eFco+8+279Db5DobsOpg33Po/dd69Oc+ONwBe/qJdfkdIGtH+W0kXmJttP3WT7g7PPTial1lmn//E8sr8tX56ct/32+ucUMXx4shdS1gslRN2HCETyrW8lLrQupK7ltpYv0zIRQGYAACAASURBVOvy6R6Z0sbxTtF4Q1XabNuhaVTlr3wleSZ32MGuPF/svXe95fnYLoZr2vRo4SNaL23sxHS4//4k6lcVOtev63a47rqJK0PaoVQtkC/LywYXNxKbfH3iW2nbdNMws2Nlcr70EvDii3ppdfMsIobndu5cvwNMX5trhyCGl2qI59vE0lZHHWSVttVXTwaIOmVn2+JOOwErV4bbuwnQ2xxZF9f6tdn03aTMdOuZuqyLPiYrYnhuQ3HhhcABByTKuI97ovNO2WijZEmG7ibnPkjX7xVZSXXLP+us6nV9RRSt8SP+iWBoEzfd0qnlKVDz5xenv+UW4DOf8TNjpJY9aVI9i7vzMNlgOjZ8K22+2Wyz5LNMzjXW6L/5d0hCKoR1ogbw8B3wp1sINRkDAP/4R/Kp42LlE9MBeai24Lou2SSwUWhuvjl5r+lgU5+pZeeNN8zPBfy5dMfkNt0k06YB3/lO/+UspnWiWo5t1vfXwVe/Ctx+ezKmc+ETnwDuu8+PTL7hu64PBiIpoGhNWzeS7WBGjEjCxC5dapeP7kvDxY3DJ0VrYkzPD0nsStsJJ5hHpwq57qXJNW0rViSbvvtgl12SmdQf/ahz30L1OWva2tatA8SXX04+U3fyuixtJl4IQLL9wDPPlEcwbvs9cpV/ww3NN5E3KTNVDl57zawMW9INtF95Jf/3Ju93N5ZtMxaUMnxdrLkmsO22/d8PVHK6FyptFdgqbdOm+ZWjTkw7GdOojLqD9aI1O7YU5ZEu9t5xR/cyYqLMR9w3NrO7uu2gbWva9tvPb35TpiSfVQvlgeR6YnphP/mkveVBl5CBSFI22MBfXiYUWdSyx2+4AfjFL/LdlFLrts2WNG1X9GyxeYa+/vUkqFDdUaSzE0SxTIZ2C+mkmUlwkSYC8XTTvQzZl7cdKm0KeQ+Y7Yz5ihVustSJ7wfCdJZYJ5+QD+1WWyWRKm1d92hpC8P06cBDD9mdazrZEvNL4ZxzkrD1223X/3gMblDpmqUiGVxddlyIoX58U3RNY8cmewnmccwxScCROoMThJxki5WlS4F7721aij4G6po239d02WXAPfeYTXrEVK8xyaJLG8crdTEAnP/MURv5JpvY5cEQqO5uh3l5hWLtte1m0kJTx+basRNyDWSabtgw8zLqYsSIZEF9liL3yPe+tx65gDARSHXbalXIf5+yhCzDBJv+YOJE4MQT7SIGN3m9TUaQa/o+m+Az0A7pZN11ky0BbKmrjuv0rKmbbrseF6i0VWDjUjJQ8e3uFsrS9stfAg8/7JZHXVZAX2WkIcFD49M9so56XXPNJIjKueeGL8s3RQP43XarT4a0f4xpDUuISGZ1X19ReWl4/nHj6pMlNnwM4BYuDF9GXbgEpQnVrge6MhjT9cckC3GH7pEFpIs6m9gksW5CWXGqXiZNvVxmzQJGjfKXX0hcLG3pOautlsy0h8RmkKMbIS+kpW3IEOAPfzDPPyaylrY24iOQSk9P4kq6YEHyvw8rtYmlrY57cNZZwKGHmgfUsCWmduVLliee0HeFj+n6TWmz7CbojCuaVMKbsLSptGkCooiB0pZ1oKWtgG5T2soafTZoiukD8s9/Jp+pi9nKleX52CzSjfmhjd3SduaZfcFWQuEyQA5haYu5vfhCZz/Dm24Cnn66HnlcUPcKc9lk+OijgW228SOTKouLNcMngwcnk06xE9Il3rXuJ0wARo4sT9Omge5A6Ot80bQCVRdtar95tF3+kFBpU1AbSrqR7UAI+X/RRf3/N13Hl7pjpcrfk08mn+PH28mT3oe6XRBjxub6P/ShJEDB8uX+5SnCRM40KqKPvHye2xZUhWLWrOTvox/tn2bSpKQNxM4ll+hFxzTB54s/ljVtdRPT9TYhSx1lurbTGN0jm6Ts+utWBmJQPuq6xxdeCFx6afHvH/94EhTJhhjqMRYGgEpijhDdp7SVNfqJE5P9oADg2GOBG280y/v444Fnn03yUdlii+QzlkAk226bfPpYp+jDnUuHNdawL2PGjMTKMmmSX5nysOlUL7gAOO64YvnqcI/sFt7yliRy3RFHNC2JPh/8YN/36dOBo45KvpveO103Wxu6MQJlW2hyrasJW2zhf8LBhcmTk88mo0fGdo/qpq7xQUwcfjhw8MHFv3/hC8AXv6iX10CpMxu4pq2AbnOP1GXRImD0aLNzBg3SOyc7AKp79uR730tCyI8YUW+5LnzjG8kMlk3ktzqxGdzOng18/vPV6Uw78NGjgZ13NjunjRTVeRsGDD6e/Sb2QIolIEns5YeUO7ZZ9x/+sG+jaxt819XPfgbcfvvADaJW1j4Gontk07L4oBuuwRdU2groNqUtpuhuTVlOVl8d2Hxz93yyhKzb5cvrdW+MCdt6ffZZv3LETlPP9pgxYfJ1WdOWl89AGajFiE8X5zrr16QNjhkT7lnQIVsvkyYB++9vd243EJNSL2V31nFb2WijZLP0NkOlrYBuU9piwDR6ZLfNFhEzeM/LaXpwcued5b+3+f4NGQK88ELi8gO0+1pcSK/bdqP7EG20CQtrSHyvaRuobLllst3Hxhs3LQnviSuhnvEHHgiTb510yYot/3TbmrYmiWVNWyhilq0uQlg1BmrwB12aXm9VFkjmttuARx6xy9f3mjYbhg5N3Khj21y7Kf70p/rLbHJz7SYmROp0RZ09O/nU3fogZhYtAubNS7b7+MEPuuOaXGl6Qs8XqYvvpps2K0dMUCVRGKjRI1Vimhmlpa09pGHW3/lOf3nynpfTtNJWxsKF1dFBi4jBPTK77nagrWVLcZUjxHXUWTfdqigef3zymXoS7btv4jrmikvgLFvmzEms/mmgsTzqVmJiWlfcdPku7Ldfcu/qCKbWFugemYMQdI8MSVUgEp39p2IiZtnqYsYM/Rfjj39s9lzp1u+ppwLjxunn2y0M1PYXYiAmRJLvVVd1Hlc/SXhC7dMWGzG0qauuAt54wz2fGK4lJppqq+p9GNzCUT7bUTEtvJ31QKXNH7YLymlp604WL9ZLZ3rPP/1pY1Fajc6AoI3PTZPukT09wKpVicsVYGZpa2NdhyINO7/zzsB11/nJs1vrt0klNC27p8fPWKdb75EpTVva0vu64YadWzG1gW6bmPHJAHP+02fRosRd4JBDmpakezANRKIS88sgZtnaDK0b5RQpFC++WL8sPvH9wjZpP1V7g9XVFts+aJk/H3jtNeBDH2paEjvasKZt2bLk00bWgbo/W+zy+SJtEx/4QLNyuDJQ7pcJtLQVsNFG3RFpJiWmkP9N5UHaBe+5Htl6eumlZuRwxXcgBpeBt413QNvXb/lm6FD7c0eMADbZpP+xJuoi5vp/y1vc8wilnMZcb3XQ1F60dXPYYcmaQlIfVNpIbZh2YG1xj4xZNl/4DDCiCy1t5ZisCW0DvuWOOVBLFW2U2Sd33w0MH57/Wx3tu4lnqK3PrUqsysqhhwLXXgsccUQ95TXtHlkXF13UtAQDD7pHKsTW0bjQ5AaCqdtGStGsNfdpawdSAldc0Vz5vPflZOsnjXzb7aThoEO2D5OQ/0uXhpNjoJHeW5WmLW2XXw786ldhy7DBp0XZlViVtnXXTSJMtnF9FyEqtLTl0A2DRF9hs2249try8l1CcMdIzLK1hf33B9Zfv/8x1ms5Rc9YW5U20/t9xhnAl7+cRC4NJYuutS62QWrbcXGtDMWBB4bJ17bt+FCQmlw/2s00bWlrs5cBKYdKW5fS5CBCCL3OokrGtdcGnniiL8+Y4CDNL1de2XkstnseG2m0t9Gj+x8PrbR9//vAyy/7z9f0mVq2rNOqHwq66tbHyScD48c3LUX92EZNjSkQCekPxwnEN3SP7FLSzmK77fTSL1mSfNaxiaHuC0NdaB3zSyZm2doM67WcxYuT6GCnntr/uKq0hajDvfYC3vUu//nGQFGE22w9hh6MDeS2/9nP5l9/t250bYuP+gh1nW2ov5Co92a99YCRI4FttmlOnm7ihBOSTbcHKrS0dTnz5gG3316d7uijgd13T6JmhkK3I2/b5tokDLRulDN8OHDBBZ3HB4p7ZBUuLkJF63AHSlu87DLgpz/1m+dddwHPPeeeT50KQRsUxSYUpNNOy9+0OdY1bU2y7rrAK680LUX3cOaZTUvQLFTaFLqpozG9lp6ecAqbj5DcMQ+WYpatzbBe7VCfKx+D5LbTxnbU9Lvo3e9O/nwyd67b+W1QoOqkSQXpU5/KP06lLaHpPqft9d92+UNC98gcmn7gfGAS9awudGe+Y5C1CnYq9dGG9hATqqVt1arm5DBl222TzwUL/ORn84xWnVN3W2Tbb5Y6678b1rSxvRKfsD11QktblxPDzJeppY3ukQSIa8KhTYwZ0/e9Ta6Su+0GrFwJrLNO05JU95tsk6RpYm6DA31SM4ZxlyoH6R5oaYuAs89uWoKwDBuWfO66a/LZbSH/SRh4z+1ocr8w3cBHRYRQ2FzaEQORxEOddfLlLyeW3zYEj4gx5H/TykrT8Pn1w0BvR3lQaYuAY4/1n2dM7pHDhwN//jNwySX2ecTWCbIzIbEiBLDTTsn3OtvpX/8K/PCH9ZVXhc9Nh2PoR0lCHW16s82SAF4jRoQvK6XJvVV9QaWtP03VA+u/e6F7ZJcTS8e+wQadx0zWj8RyHaQ+OFC2p4nB0+TJ9ZVVFxz8xAP7gXxiaqO8RwlN10O3bK7ddvlDQEubQkydnysxX4vNgDK2hzfm+u02Yrv3bWBQb8/OdmpG1Ro2tkUSim4IREIICQuVthxcOrSrropjjVrakQ+K8A5X1e/22ydyf/zj+ufUjRrggQPjMMR2z9tEWndtCkTiGx/7tPHZjgf2B/3x0Ua5uXYYQrbVO+4Arr66PM0OOySf8+aFk4M0A90jPbN8edMS9KeNL7qxY4F//av/sdiu47XXmpag+4ntnrcJKh19+GxHbJMkFmK0tLHfCc/8+clfGXvvDRx+ODBuXD0ykfqI0A5DfJDuzxSjpc2G2AZLeWv0iF9iu+dtgnVnx9SpyWcsg07ex05iuTe+2Hjj5LNqIJ7FVEFaY43OY4weGYYY6oEKW3dCS1uXklqC0nD7MdLmNW3dogzHTGz3vI0M9MGTKT//OfDb33auCeSatubp1rrfcUfggQeAGTPClfHqq/XU34IFwLXXJhGjBzLd2lZD8973AuPHNy1F3FBpU3j++aYl8MfMmcDvfte371FMnUg3BCKh0lYfsd37NsBAJHbXPnEisM8+ncezbbDOUPAkYbXVks8FC5qVIwQbbRQ2/yIlynff+u1vA/feG2a/xTYykPtfG775zeTz8sublSNmqLQpPPpo8jlqVLNy+ODCCxOf5pdealqSTrphc20qbeGJ7Z63CQYi8RP2OjvomjABWLgwzN6aKmz7nUyZAlx3HbD55k1LEgcxBiIZObI7lWpT+PySUHDoqZDOnk6Y0KwcPhg5EnjrW/v+b/uMT2ydYGzydCOsY3tiWFPRTaT1OWwYcNttwO67J//vuWdzMg00hACWLQPWX79pSeLA5RkfMyb5TNfTke6i7f1+2+UPCS1tXU7MA1+6R5IyqHjYw7rzQ1X9fec7wLPP1iNLt7F8OfDUU01L0V5cnvHFi4HvfhfYbTe/MpGE9N688EKzcrSd2MZ9MUClTaGbBzgxNX66RxIdYrvnbYJKmx/3yCpGjkz+iDlXXdW0BO3GpV0PGgS84x3+ZCH9SddfNuWezndn90KlLQc2+HqgpY3oMJAVD1vOOy9Zm7vLLk1LQmxYuBC4+WZgyJCmJSGxw/4xPtZaq2kJugO27U6otCmwgdRDbAqYDd1wDbFDa1EnP/0p8OKL1ekmT04iuRE36rDW5XHJJcCddzIKHylmIPeP110X99rGpid1294mOL4qhkpbDmww8RHbPVE75dGjm5OjmxnIg5Ii1OBCRA8ffUfd/c/48X3BTgjJI7Z3Yp0sW9a0BOX09DQtQbvhO78YOnmRxtB5MC+9FFi0KL4XlKq0xf4CaStU2ogLPtoN2x6JHbbR+GjK0ta0hc83sY37YqDLbrEb3dj5xdjoTWQ6+GDg1lvjuw61c+y2jjIWqLQRH7j0HdOnJ58MNkJig/1jvDQ1Jpg5s5lySX3QPTKH2BSEbqXNLxsqauHhc0ia5tRTE5fUHXdsWhJC+pO6Si9e3KwcpBOOD0gotJqWEGIXIcSDQoiHhRAn5Pz+QSHEH4UQvxdC/EIIMcu/qOFpsxJRRUwD4DQiWkwymcJOuT66+bkk4fDRbkaNAvbeGxjM6U3igauvBv74Rz95bb898OqrwJIlfvIj/mhqTVubx1REj8qhpxCiB8B5AHYFMAvAO3OUsiuklJtKKecC+DyAL3mXtEbY8MPykY8km3rusUfTkthz8MFNS9D90P2HuJDulTR2bLNyEJKy777AJpv4y2/4cH95EX9wUpeEQmf+cAGAh6WUjwCAEOJKAMsA3JcmkFK+pKQfCYDDLEPe/35gm22alqIeZs4EbryxaSnc2GijpiXofqi0EReWLgWOOw44+uimJSGEDCSotJFQ6ChtEwE8pvz/OICtsomEEB8GcAyAoQAW5WUkhDgcwOEAsH6Em2w0OTj8+tfD5DtqVPK5+eZh8ickFFTaiAvDhgGf/3zTUnQXqfWSEFJM095afGd2LzrzAXnNr6NJSCnPk1JOA3A8gJPzMpJSXiSlnC+lnD82Yp+Vph84n2y7beJDf/75TUtCiBnZ5/DQQ5uRgxACXHMNcO+9TUtBCCEDFx1L2+MAJiv/TwLwREn6KwF8zUUo4g8h/PrQE1I3UgKvv84NSwlpkn32aVoCQogObTc80FJYjI6l7Q4A04UQU4UQQwEcAOB6NYEQYrry7+4AHvInYn2woRASD6p75JAhXCdACCGEDBTarnyGoNLSJqVcJYQ4EsAPAPQA+KaU8l4hxGkA7pRSXg/gSCHEEgBvAHgewCEhhSaEdD9c00YIIYSY0S3vzG65Dp9o7T4jpbwJwE2ZY6co37siPhcbCCHxQKWNEEII0aNbLFPdch0hoMNRBjYWQuKAzyIhhBAysOBEbTFU2gghUcMOnBBCSNuYMaPe8rrtXcmJ20603CMHCt3W4AlpM3SPJIQQ0kYefBAYN65pKUi3QaUtAzV7QuKgW5S2H/8YGDGiaSkIIYTURd1WNoDj14EAlTZCSJR0i9K2eHHTEhBCCCGk7VBpU2j74JCQboLWKULazx138FkmhOiz337AddcBZ57ZtCTxQaUtA83LhMTBCScA//gHsGhR05IQQmyZP79pCQgZWLTdADFiBHD11U1LESdU2hTa3tAJ6SZmzwZWrGhaCkIIIYSQ5mHI/wy0tBFCCCGEkDbCcWz3QksbIYQQQhrl4Yc52CSEkDKotCnQPZIQQgipn2nTmpaAkO6AY9nuhe6RGTjTRwghhBBC2gTHr90PlTZCCCGEEEIIiRi6RyrQpExM+P73gZ6epqUghBDigxNPBDbfvGkpCCEkHyptGWheJrrstVfTEhBCCPHFf/xH0xIQYs855wCHHw7MmNG0JCQUVNoUaGkjhBBCCCFtY6edgIcealoKEhKuactASxshhBBCCCEkJqi0EUIIIYQQQkjEUGlToHskIYQQQgghJDaotGWgeyQhhBBCCCEkJqi0EUIIIYQQQkjEUGlToHskIYQQQgghJDaotGWgeyQhhBBCCCEkJqi0KdDSRgghhBBCCIkNKm0ZaGkjhBBCCCGExASVNkIIIYQQQgiJGCptCnSPJIQQQgghhMQGlbYMdI8khBBCCCGExASVNkIIIYQQQgiJGCptCnSPJIQQQgghhMQGlbYMdI8khBBCCCGExASVNgVa2gghhBBCCCGxQaUtAy1thBBCCCGEkJig0kYIIYQQQgghEUOlTYHukYQQQgghhJDYoNKWge6RhBBCCCGEkJig0kYIIYQQQgghEUOlTYHukYQQQgghhJDYoNKWge6RhBBCCCGEkJig0qZASxshhBBCCCEkNqi0ZaCljRBCCCGEEBITVNoIIYQQQgghJGKotCnQPZIQQgghhBASG1TaMtA9khBCCCGEEBITVNoIIYQQQgghJGKotCnQPZIQQgghhBASG1TaMtA9khBCCCGEEBITVNoUaGkjhBBCCCGExAaVtgy0tBFCCCGEEEJigkobIYQQQgghhEQMlTYFukcSQgghhBBCYoNKWwa6RxJCCCGEEEJigkqbAi1thBBCCCGEkNig0paBljZCCCGEEEJITFBpI4QQQgghhJCIodKmQPdIQgghhBBCSGxQactA90hCCCGEEEJITFBpI4QQQgghhJCI0VLahBC7CCEeFEI8LIQ4Ief3Y4QQ9wkh7hZC3CqE2MC/qOGheyQhhBBCCCEkNiqVNiFED4DzAOwKYBaAdwohZmWS3QVgvpRyMwArAHzet6B1QfdIQgghhBBCSEzoWNoWAHhYSvmIlPJ1AFcCWKYmkFLeJqV8tfffXwOY5FfMeqCljRBCCCGEEBIbOkrbRACPKf8/3nusiEMB3Jz3gxDicCHEnUKIO1euXKkvZY3Q0kYIIYQQQgiJCR2lLU+NybVJCSEOAjAfwNl5v0spL5JSzpdSzh87dqy+lIQQQgghhBAyQBmskeZxAJOV/ycBeCKbSAixBMBJAHaUUr7mR7x6oXskIYQQQgghJDZ0LG13AJguhJgqhBgK4AAA16sJhBCbA7gQwF5Syqf9i1kfdI8khBBCCCGExESl0ialXAXgSAA/AHA/gKuklPcKIU4TQuzVm+xsAKsD+J4Q4vdCiOsLsiOEEEIIIYQQYoCOeySklDcBuClz7BTl+xLPcjUC3SMJIYQQQgghsaG1ufZAgu6RhBBCCCGEkJig0qZASxshhBBCCCEkNqi0ZaCljRBCCCGEEBITVNoIIYQQQgghJGKotCnQPZIQQgghhBASG1TaMtA9khBCCCGEEBITVNoIIYQQQgghJGKotCnQPZIQQgghhBASG1TaMtA9khBCCCGEEBITVNoUaGkjhBBCCCGExAaVtgy0tBFCCCGEEEJigkobIYQQQgghhEQMlTYFukcSQgghhBBCYoNKWwa6RxJCCCGEEEJigkobIYQQQgghhEQMlTYFukcSQgghhBBCYoNKWwa6RxJCCCGEEEJiYnDTAsTEtGnASy81LQUhhBBCCCGE9EGlTeGUU5qWgBBCCCGEEEL6Q/dIQgghhBBCCIkYKm2EEEIIIYQQEjFU2gghhBBCCCEkYqi0EUIIIYQQQkjEUGkjhBBCCCGEkIih0kYIIYQQQgghEUOljRBCCCGEEEIihkobIYQQQgghhEQMlTZCCCGEEEIIiRgqbYQQQgghhBASMVTaCCGEEEIIISRiqLQRQgghhBBCSMRQaSOEEEIIIYSQiKHSRgghhBBCCCERQ6WNEEIIIYQQQiKGShshhBBCCCGERAyVNkIIIYQQQgiJGCpthBBCCCGEEBIxQkrZTMFCrATwl0YKL2cdAM80LQTpWti+SGjYxkhI2L5ISNi+SEhibV8bSCnHViVqTGmLFSHEnVLK+U3LQboTti8SGrYxEhK2LxISti8Skra3L7pHEkIIIYQQQkjEUGkjhBBCCCGEkIih0tbJRU0LQLoati8SGrYxEhK2LxISti8Skla3L65pI4QQQgghhJCIoaWNEEIIIYQQQiKGShshhBBCCCGERAyVNgUhxC5CiAeFEA8LIU5oWh7SDoQQk4UQtwkh7hdC3CuEOLr3+GghxI+EEA/1fq7de1wIIb7S287uFkJsoeR1SG/6h4QQhzR1TSQuhBA9Qoi7hBA39P4/VQjxm9528l0hxNDe46v1/v9w7+9TlDxO7D3+oBBiaTNXQmJECLGWEGKFEOKB3n5sG/ZfxBdCiI/1vhvvEUJ8RwgxjH0YcUEI8U0hxNNCiHuUY976LCHEPCHEH3vP+YoQQtR7hflQaetFCNED4DwAuwKYBeCdQohZzUpFWsIqAB+XUs4EsDWAD/e2nRMA3CqlnA7g1t7/gaSNTe/9OxzA14CkwwFwKoCtACwAcGra6ZABz9EA7lf+PwvAl3vb1vMADu09fiiA56WUbwHw5d506G2PBwCYDWAXAOf39nmEAMC5AG6RUm4MYA6Stsb+izgjhJgI4CgA86WUmwDoQdIXsQ8jLnwLSTtQ8dlnfa03bXpetqxGoNLWxwIAD0spH5FSvg7gSgDLGpaJtAAp5ZNSyt/1fn8ZyYBnIpL2c2lvsksB7N37fRmAy2TCrwGsJYSYAGApgB9JKZ+TUj4P4EeIpKMgzSGEmARgdwDf6P1fAFgEYEVvkmzbStvcCgCLe9MvA3CllPI1KeWjAB5G0ueRAY4QYk0AbwVwMQBIKV+XUr4A9l/EH4MBDBdCDAYwAsCTYB9GHJBS/gzAc5nDXvqs3t/WlFL+SibRGi9T8moUKm19TATwmPL/473HCNGm15VjcwC/ATBeSvkkkCh2AMb1Jitqa2yDJI9zAHwCwJu9/48B8IKUclXv/2o7+Xcb6v39xd70bFukiA0BrARwSa8L7jeEECPB/ot4QEr5NwBfAPBXJMraiwD+F+zDiH989VkTe79njzcOlbY+8vxVuR8C0UYIsTqAqwF8VEr5UlnSnGOy5DgZoAgh9gDwtJTyf9XDOUllxW9sW6SIwQC2APA1KeXmAP4PfW5FebCNEW163c2WAZgKYD0AI5G4q2VhH0ZCYdqmom1rVNr6eBzAZOX/SQCeaEgW0jKEEEOQKGyXSymv6T38VK+ZHb2fT/ceL2prbIMky3YA9hJC/BmJy/YiJJa3tXpdjYD+7eTfbaj391FIXEjYtkgRjwN4XEr5m97/VyBR4th/ER8sAfColHKllPINANcA2Bbsw4h/fPVZj/d+zx5vHCptfdwBYHpvRKOhSBa8Xt+wTKQF9PrbXwzgfinll5SfrgeQRiM6BMD3leMH90Y08bVI2wAAAaNJREFU2hrAi72m/B8A2FkIsXbv7OTOvcfIAEVKeaKUcpKUcgqSPuknUsp3AbgNwNt7k2XbVtrm3t6bXvYeP6A3MttUJAurf1vTZZCIkVL+HcBjQoiNeg8tBnAf2H8RP/wVwNZCiBG978q0fbEPI77x0mf1/vayEGLr3jZ7sJJXowyuTjIwkFKuEkIcieQm9gD4ppTy3obFIu1gOwDvBvBHIcTve499EsDnAFwlhDgUyYtree9vNwHYDclC6lcBvBcApJTPCSE+i2QCAQBOk1JmF9oSAgDHA7hSCHE6gLvQG0Si9/PbQoiHkcxOHwAAUsp7hRBXIRksrQLwYSnlv+oXm0TKRwBc3jth+QiSPmkQ2H8RR6SUvxFCrADwOyR9z10ALgJwI9iHEUuEEN8BsBDAOkKIx5FEgfQ55voQkgiVwwHc3PvXOCKZwCCEEEIIIYQQEiN0jySEEEIIIYSQiKHSRgghhBBCCCERQ6WNEEIIIYQQQiKGShshhBBCCCGERAyVNkIIIYQQQgiJGCpthBBCCCGEEBIxVNoIIYQQQgghJGL+P6sWVNKBkGJfAAAAAElFTkSuQmCC\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from numpy import random as nprd\n", "\n", "##设定参数\n", "M =10000\n", "pai=lambda x: np.exp(-90*(x[0]-0.5)**2-45*(x[1]+0.1)**2)\n", "domain=lambda x:(x[0]>=-1)*(x[1]>=-1)*(x[0]<=1)*(x[1]<=1)\n", "h=lambda x: domain(x)\n", "h2=lambda x: np.sin(10*x[0])**2+np.log(abs(1+x[1]*10))\n", "\n", "#随机游走\n", "def sample_q(x):\n", " return (x[0]+0.2*nprd.normal(),x[1]+0.2*nprd.normal())\n", "\n", "\n", "##独立的MCMC算法,输入:\n", "## N_samples : 抽样次数\n", "## pai(x) : 目标密度函数\n", "## q_sampler(x): 给定x,从q中抽样的函数\n", "## x0 : 初始值\n", "def MH_RW(N_samples, pai, q_sampler, x0):\n", " X=[]\n", " x=x0\n", " for i in range(N_samples):\n", " y=q_sampler(x)\n", " rho=min(1,pai(y)/pai(x))\n", " if nprd.uniform()<=rho:\n", " X.append(y)\n", " x=y\n", " else:\n", " X.append(x)\n", " return X\n", "\n", "## 计算积分\n", "x=MH_RW(M, pai, sample_q, (0,0))\n", "## 第一个积分\n", "H=list(map(h,x))\n", "## 取h后面80%的样本\n", "subH=H[int(M*0.2):]\n", "integral=np.pi/(90*np.sqrt(2))*np.mean(subH)\n", "print(\"Intgral1=\",integral)\n", "## 第二个积分\n", "H2=list(map(h2,x))\n", "subH2=H2[int(M*0.2):]\n", "integral2=np.pi/(90*np.sqrt(2))*np.mean(subH2)\n", "print(\"Intgral2=\",integral2)\n", "\n", "## 诊断图\n", "import matplotlib.pyplot as plt \n", "%matplotlib inline\n", "# 设定图像大小\n", "plt.rcParams['figure.figsize'] = (15.0, 8.0)\n", "index=[i for i in range(len(H))]\n", "x_x=[x[i][0] for i in range(len(H))]\n", "x_y=[x[i][1] for i in range(len(H))]\n", "plt.plot(index,x_x,label=r'MCMC Samples x',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "plt.plot(index,x_y,label=r'MCMC Samples y',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "直方图" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(x_x,label=r'Histogram of x',color='blue', bins=50)\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "plt.hist(x_y,label=r'Histogram of y',color='blue', bins=50)\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "诊断图" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "average_H2=[np.mean(H2[:i]) for i in range(len(H)) if i!=0]\n", "plt.plot(index[1:],average_H2,label=r'MCMC Samples Mean',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "plt.acorr(subH2,label=r'Auto corr of h2',color='blue', maxlags=2000)\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Logit回归的MCMC算法\n", "假设$d_{i}$为一个0/1变量,且给定自变量$w_{1i},w_{2i}$,$d_{i}=1$的概率为:$$P\\left(d_{i}=1|w_{1i},w_{2i},\\beta\\right)=\\frac{\\exp\\left\\{ \\beta_{0}+\\beta_{1}w_{1i}+\\beta_{2}w_{2i}\\right\\} }{1+\\exp\\left\\{ \\beta_{0}+\\beta_{1}w_{1i}+\\beta_{2}w_{2i}\\right\\} }=F\\left(\\beta_{0}+\\beta_{1}w_{1i}+\\beta_{2}w_{2i}\\right)$$\n", "因而:$$P\\left(d_{i}||w_{1i},w_{2i},\\beta\\right)=\\left[F\\left(\\beta_{0}+\\beta_{1}w_{1i}+\\beta_{2}w_{2i}\\right)\\right]^{d_{i}}\\left[1-F\\left(\\beta_{0}+\\beta_{1}w_{1i}+\\beta_{2}w_{2i}\\right)\\right]^{1-d_{i}}$$现在给定一个先验分布,比如:$\\beta_{j}\\sim N\\left(0,1\\right),j=0,1,2$,那么$\\beta$的后验分布为:$$\\pi\\left(\\beta|d,w_{1},w_{2}\\right)\t\\propto\\prod_{i=1}^{N}P\\left(d_{i}|w_{1i},w_{2i},\\beta\\right)\\cdot\\pi_{0}\\left(\\beta_{0}\\right)\\pi_{1}\\left(\\beta_{1}\\right)\\pi_{2}\\left(\\beta_{2}\\right) $$\n", "接下来我们使用MCMC算法对以上后验分布进行采样。" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean beta0= 1.45208593007\n", "Mean beta1= 0.993046102073\n", "Mean beta2= -1.09819702089\n" ] }, { "data": { "image/png": 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\n", 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CBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnFk16AACAPaFqdse3Np45AGbDChwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnvA8cwByazftOec8pAOCnCTiAeWq2bzoMAOx9XEIJAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQiUWTHgAAoAdVu39sa+ObA1jYrMABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0YtGkBwCY76omPQEAwDQrcAAAAJ0QcAAAAJ0QcAAAAJ0YOeCq6ilVdVNV/fNwf3lVXV9Vd1TVpVX11GH704b7m4bHl83N6AAAAAvLrqzAvTXJrVvd/8sk57fWViT5XpI3DNvfkOR7rbVfTHL+sB8AAACzNFLAVdXSJK9M8uHhfiV5WZLLhl0uTnLacHvtcD/D4ycN+wMAADALo67AvS/JHyd5bLi/JMn9rbVHhvtTSQ4bbh+W5O4kGR5/YNgfAACAWdhpwFXVryf5dmvthq03z7BrG+GxrT/uWVW1oao2bN68eaRhAQAAFrJRVuBOSHJqVd2V5B8yfenk+5I8o6oefyPwpUnuGW5PJTk8SYbHn57kuz/9QVtr61pra1praw499NBZfRIAAAALwU4DrrX2rtba0tbasiSvTfL51trpSa5N8lvDbmck+eRwe/1wP8Pjn2+tbbcCBwAAwK6ZzfvAvTPJ26pqU6af43bhsP3CJEuG7W9Lcu7sRgQAACBJFu18l59orX0hyReG23cmeeEM+2xJ8poxzAYAAMBWZrMCBwAAwB4k4AAAADoh4AAAADoh4AAAADoh4AAAADoh4AAAADoh4AAAADoh4AAAADoh4AAAADqxaNIDAADs7ap2/9jWxjcH0D8rcAAAAJ0QcAAAAJ0QcAAAAJ0QcAAAAJ3wIibAgjCbFxAAAJgvrMABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0QsABAAB0YtGkBwAYRdWkJwAAmDwrcAAAAJ0QcAAAAJ1wCSUAwDw2m0vIWxvfHMD8YAUOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgE4smPQAAAHOjavePbW18cwDjYwUOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgE97IG9hjZvOGsgAAWIEDAADohoADAADohIADAADohIADAADohIADAADohIADAADohIADAADoxE4DrqoOr6prq+rWqvp6Vb112P7MqvpcVd0x/H7wsL2q6oKq2lRV/1ZVq+f6kwAAAFgIRlmBeyTJH7XWjkxyfJKzq+qXkpyb5JrW2ook1wz3k+SUJCuGX2cl+cDYpwYAAFiAdhpwrbV7W2s3Dre/n+TWJIclWZvk4mG3i5OcNtxem+Rv27QvJ3lGVT1r7JMDAAAsMLv0HLiqWpbkmCTXJ/m51tq9yXTkJfnZYbfDkty91WFTw7af/lhnVdWGqtqwefPmXZ8cAABggRk54KrqwCSXJ/mD1tp/PdmuM2xr221obV1rbU1rbc2hhx466hgAAAAL1kgBV1X7ZjrePtZa+8Sw+VuPXxo5/P7tYftUksO3OnxpknvGMy4AAMDCNcqrUFaSC5Pc2lo7b6uH1ic5Y7h9RpJPbrX9d4ZXozw+yQOPX2oJAADA7ls0wj4nJPntJDdX1cZh2/9I8hdJ/rGq3pDkm0leMzz2mSSvSLIpyUNJfnesEwMAACxQOw241tp1mfl5bUly0gz7tyRnz3IuYJ6qHX01AABgzu3Sq1ACAAAwOQIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgEwIOAACgE4smPQAAAPNP1eyOb208cwDbsgIHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQCQEHAADQiUWTHgDY86omPQEAALvDChwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnBBwAAEAnFk16AAAA9j5Vu39sa+ObA/Y2VuAAAAA6IeAAAAA6IeAAAAA6IeAAAAA64UVMAACYV7wACuyYFTgAAIBOCDgAAIBOCDgAAIBOCDgAAIBOCDgAAIBOeBVK6NRsXqELAIA+CTgAAPYa3oKAvZ1LKAEAADphBQ4mxCWQAADsKitwAAAAnRBwAAAAnRBwAAAAnRBwAAAAnRBwAAAAnRBwAAAAnRBwAAAAnRBwAAAAnRBwAAAAnRBwAAAAnRBwAAAAnRBwAAAAnRBwAAAAnVg06QEAAGA+qJrd8a2NZw54MgKOvcJsv+DuLl+oAQDYk1xCCQAA0AkrcDALk1r5AwBgYbICBwAA0AkBBwAA0AkBBwAA0AnPgWNe8FwyAADYOQEHAABjMJsfSHtrIkblEkoAAIBOCDgAAIBOuISSsfE8NgAAmFsCDgAAJszz5xiVgAMAgAVKOPbHc+AAAAA6YQWObXgeGwAAzF8Cbi8kwgAAYO/kEkoAAIBOzEnAVdXLq+r2qtpUVefOxZ+xt6va/V8AAMDeaeyXUFbVU5L8TZKTk0wl+UpVrW+t3TLuP2uuiSEAAOY737MuLHOxAvfCJJtaa3e21n6U5B+SrJ2DPwcAAFiAFvLVanPxIiaHJbl7q/tTSV700ztV1VlJzhruPlhVt2/18CFJvjMHszG/OM8Lg/O8cDjXC4PzvDA4zwvDrM5zrzE0j+d+zig7zUXAzfRXst3b/LXW1iVZN+MHqNrQWlsz7sGYX5znhcF5Xjic64XBeV4YnOeFwXnu01xcQjmV5PCt7i9Ncs8c/DkAAAALylwE3FeSrKiq5VX11CSvTbJ+Dv4cAACABWXsl1C21h6pqrckuSrJU5J8pLX29V38MDNeWslex3leGJznhcO5Xhic54XBeV4YnOcOVWvbPT0NAACAeWhO3sgbAACA8RNwAAAAnZgXAVdVr6mqr1fVY1W1w5cyrao/HPb7WlX9fVUt3pNzMju7cJ6fUVWXVdVtVXVrVf3ynpyT2Rn1PA/7PqWqbqqqf95T8zEeo5znqjq8qq4d/h1/vareuqfnZPZ24Wv3y6vq9qraVFXn7skZmb2qemZVfa6q7hh+P3gH+/3v4b+HW6vqgqp5/I5abGcXzvN/r6rPDuf5lqpatmcn5cnMi4BL8rUkr07yf3e0Q1UdluScJGtaaysz/QIpr90z4zEmOz3Pg79KcmVr7YgkRyW5da4HY6xGPc9J8tY4v70a5Tw/kuSPWmtHJjk+ydlV9Ut7YjjGapT/Rz8lyd8kOSXJLyV5nXPdnXOTXNNaW5HkmuH+NqrqxUlOSPKCJCuTHJfkpXtySGZtp+d58LdJ3jN8/X5hkm/vofkYwbwIuNbara2120fYdVGS/apqUZL94/3lujLKea6qn0lyYpILh2N+1Fq7f0/Mx3iM+u+5qpYmeWWSD8/9VIzbKOe5tXZva+3G4fb3Mx3rh+2J+RifEf9NvzDJptbana21HyX5hyRr5346xmhtkouH2xcnOW2GfVqSxUmemuRpSfZN8q09Mh3jstPzPPzwZVFr7XNJ0lp7sLX20J4bkZ2ZFwE3itbafyR5b5JvJrk3yQOttc9OdirmwM8n2ZzkouHSug9X1QGTHoo58b4kf5zksUkPwtwbLr85Jsn1k52EOXJYkru3uj8Vsd6bn2ut3ZtM//Alyc/+9A6ttS8luTbT34fdm+Sq1pqrKPqy0/Oc5LlJ7q+qTwzfi71nWGVnnhj7+8DtSFVdneS/zfDQ/2ytfXKE4w/O9E8Nlie5P8nHq+r1rbW/G++kzMZsz3Om/5tcneT3W2vXV9VfZXp5/3+NcUxmaQz/nn89ybdbazdU1a+Oez7GYwz/nh//OAcmuTzJH7TW/mtc8zE+YzjXMz0PyvsUzTNPdp5HPP4XkxyZZOmw6XNVdWJrbZRL5tlDZnueM/292Esy/UO3bya5NMmZGa6OYvL2WMC11n5tlh/i15L8e2ttc5JU1SeSvDiJgJtHxnCep5JMtdYe/yn9Zdnx9dlMyBjO8wlJTq2qV2T6cpyfqaq/a629fvbTMS5jOM+pqn0zHW8fa619YvZTMRfG9LX78K3uL42nOcw7T3aeq+pbVfWs1tq9VfWszPycp1cl+XJr7cHhmP+T6ee3Crh5ZAzneSrJTa21O4djrsj0eRZw80Q3l1Bm+icAx1fV/sMrHp0UL36w12mt/WeSu6vqecOmk5LcMsGRmAOttXe11pa21pZl+sWIPi/e9j7D1+oLk9zaWjtv0vMwp76SZEVVLa+qp2b63/X6Cc/Erlmf5Izh9hlJZlp5/WaSl1bVouGHMy+N78V6M8p5/kqSg6vq0OH+y+J7sXllXgRcVb2qqqaS/HKST1fVVcP2Z1fVZ5JkWJG5LMmNSW7O9OzrJjQyu2GU8zz4/SQfq6p/S3J0knfv+WnZXbtwnunYiOf5hCS/neRlVbVx+PWKCY3Mbhrx/9GPJHlLkqsy/Q39P7bWvj6pmdktf5Hk5Kq6I8nJw/1U1ZqqevzFpi5L8o1Mfx/21SRfba19ahLDstt2ep5ba48meXuSa6rq5kxfIv2hCc3LDKo1l6gDAAD0YF6swAEAALBzAg4AAKATAg4AAKATAg4AAKATAg4AAKATAg4AAKATAg4AAKAT/x9B0jPyppxL2AAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from numpy import random as nprd\n", "\n", "##设定参数\n", "M =20000\n", "#真值\n", "beta_0=1\n", "beta_1=1\n", "beta_2=-1\n", "#样本量\n", "N=200\n", "#Logistic函数\n", "Logistic=lambda x: 1.0/(1+np.exp(-1*x))\n", "\n", "##产生数据\n", "def gen_logit(N):\n", " Data=[]\n", " for n in range(N):\n", " x1=nprd.normal()*1.414+1\n", " x2=nprd.chisquare(2)\n", " d_star=beta_0+beta_1*x1+beta_2*x2\n", " p_star=Logistic(d_star)\n", " d=(1 if nprd.uniform()" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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0KVoSIk9UGq8uXYDWrZ2JIgU1tgRBEOXH17qcLHQEoYaxQheG4bwwDBes+n8IgKZBEGyEyCK3RezUVgC+SUmnfxiGHcMw7LjxxhubilVaWMU1YUKxchD5otJgjR7tTg6CIAhCH93gJmnXNXaXS4IgsjFW6IIg2CwIoqooCII9VqU5E8D7ANoEQbB1EARrADgBwGDT/AiCKB7VxnblysiVmBppgiDqGd06Lu06l/VmGerkV18tWgKC8B+ZZQseA/AOgB2CIJgWBMEZQRCcEwTBOatOOQbAZ0EQfAzgXgAnhBErAFwA4BUAXwJ4MgzDz93cRv1QhsqVsE+9v/c77ohciZ95pmhJCIIg/EHGotcYFbq4XE88UZwcBFEWVs86IQzDEzOO9wHQR3BsCIAheqIRBOErqp2AyZOj7XffWReFIAiC0KSMLpdhWNy6fQThK7aiXBKW8HW0jHBLvb93dn/UCBMEQdRCLpfVpMnlqxJKEEVCCh1BeICvjaoIVXlJoSMIojHgoi4nhU7+GEE0Vkih8wyqqAjfWbECmDVL7RpS6AiCaAzotuEU5bIaUugIQg1S6DyDKqrGSZne++9+BwwYoHYNKXQEQTQGKMqlGz6PhdQri8wEkSek0BGEB5SpgerXT/0aUugIgmgMqFq8iq4TfW17knJ9+634GEEQpNB5B1VUfrFiBS3ybgNS6Pxlzhzg0EOrO0wEQehRtjl0ZXG5XG21yv++ykwQRUIKHUGk8Mc/AtttB0yZ4jafxqLIk0LnH488AgwdCtx2W9GSEET5KZuy4Wvbk5SrSRPxMYIgSKHzDqqo/GLEiGj7/fdu86n3904WOn9hHaWydUQJwgeWLwf69Im8OYDyWeh8bXvSLHS+ykwUT6tW0UB8Y4QUOs+gisovSAGxAyl0/sLeSVZQht13B556Kh+ZCMIXvv8e2HJLYMwY/vE+faJAUX36RL/LptCVZSCnbArd3LnA448XLUXjYtEiYPp04NZbi5akGEihy5mGBuDFF8tRIRH5Uc/l4ZFHgBkzov/rXaFraABWrixaCjWYhS6tDC5bBowaBfTokY9MKkyaBPzyl8D48UVLAsyfDyxYULQUhE2eeQaYOhW4557Kvr//HXjnnej/OXOi7dy50VZXQaIol9WU3UL3298CJ54IfPFF0ZI0Hq67rmgJioUUupz5+9+Bww8HHn2Uf7wMFRVByDJ9OnD66cBLL0W/612h22YbYIMNipZCDfZOyjJSn+Sxx6LO9T/+UbQkwLrrAuuvX7QUhGvOPjsaROBRtiiXTN6i5UiS7AvF5StDXTV1arSlAZ78YIMqjZXVixagsfH119F22rRi5ZBl1CigeXNghx2KlqRYXCva9arIl81aZYrr4DkukLHQ+QwbuV++vFg5mBW6sZV5ohrV76jo767o/EWkKXS+yhyH5iYTeUMWupzJGgXzraLafXegbdva/S+9BFx6af7y5E1eo5a+vXdX2HqejeV56fCf/wBXXCF/voqFjvfcZ80qVpliCh0LSlEUQ4YUmz/hFtmOednm0PlalyblWmst8TEfYfUSKXREXpBCVxBlqJDS+PWvgTvvLFqK/Cj7+/IFWwodNZJi9t8f+Mtf5M9nI8kTJ1bvX7Ei2x0rDIGWLaP5IkWx+io/k6IVuvgcH1OWLbOXVj0QhsDnnxfz3TOXuf795c5XtdAW7eroq8tlknqy0C1ZErmIl+E+ysxnnwE331y0FPlBCp0mU6aI58GlkRVRjj7wxkljee+NRaGbN688rnfsnQwfXr2/adOKkpJVXw0c6EY2GepNoRswAFhzTT+CvPD4+uv8v7+RI4H27YuZJ/nAA+nHk9/GkiV6+VBQlGqKeh62SPN8uOaaaBDsxRfzlakIipyGsMce0bMuum3IC1LoNOnSBTjtNPuuRmWoqAj71Ot7TypwjcXlcr31gHPPLVoKOUw656rvwUXDyhSp6dPtp60jhylPPx1tP//cTnoqTJyY/o4mTgS22gq44Yb8ZAKAsWOj7dtv55svAEyYIHceq9s6d1ZLX6ZOJIWu+rfvA3pAuoXuhx+i7SefFPOd58WwYUDr1sV5cy1dGm19tz7bghQ6Tb79Ntr6WhkSdmgsFUHZKEOD7kPURRlkonKmuVzKMm0asPbaURh4mzBF6vnn7aarK4ct8m5bpk0Dtt02ff4lU5qT1ty88Lk+Zu+riWKvqug+BKtLfatT0xS6op+ZDGlz6NZYI9pec01kedbh66+BceP0rs2LESOibV7xFspQLlxCCp0mbBRz/ny168oWFIWIoCiXdrBlofGt81FmNtss2nbqpH6tSrn9/PNoxDTLhU2V1T2J1WxboUsyZw7Qr5+7uoJZDV5/PfvcIixlZYGCotih7C6XaRa6pk3N099qK2D77c3TcUne0w4ae7+AFDpDPvlEzw+6DBWSLh9/HD2XeiBrziOhxjXX1O4bMAB44w21dMpQcftsTYjDynbRrl+6uFakZGnZ0m36vXpFbrzvvus2nzSK+u58LHdJkm3FdtupXVcUZXi2QPksdGlz6JiFriwsWxZZ2WbPLlqSdJIKZBnKiU1IoTPk+uujhcJffVXu/MZgodt1V2CXXbLPW7YM2G234tx3fKKxTNrlzXPq2RPYbz+1dBYutCKOU8r2LafJa8Pl0tXzyLLQLV0KzJzpJu84a69tJx3Rs2br3C1erJ/2uHHA/ffzj8m8n6KVj6Lz5yEaELFZ3l3WJb4OjtWzhc6XQShZnnwymgf3hz8ULUk6IotgGcqLDUihM4SF+mbuKrLIRrk85BDgqqvU5SoDU6cCo0dHI8++klcHwsY7nj8fGDOmdv+KFcWtE+bq+ZUlgmQZkGnsbEbltV0msjpHhx4KbLSR3TxdInqmSQvQypXAoEFqHfKTTwbOOy99WQQflaa5c4uWQExSoWO/bS4wTi6X1b/LUP+nzaHz9ZmLYPKqRnDN+z4by8C4CFLoDPnZz6KtbMFVdeF7+WXgz39Wl6sMlKlScy3ryy+bp3HwwUC7drX7mzb118WDRaFSxddR5TKjU8Z9+IazFDqZOWE2cP0skopW375Ajx7Aww/Lp/H++9E27fvx4Z0mufzyaOujsilSPHx8jnHefTdyofNVzjSFbtCgfGXRIc1C5+szF8HqWN8VJlF/omzPWxdS6AyxPceqsRS8siDqQIwYAfzqV36NFP73v0VLoM6sWXrXkUJnH51n6oPLpY+dfBNk7+f776u3Kmnz3nUZnmOR332Wa6+phS7t+dv+dlauBPbeGzjrLH/r0rR7Zu7HPlNPCl0Z6gagOE8kXyCFzpCyfZiEHsn3fOyx0bxJXYUkK/16oTG7XJblnZrI6cM9+iBDkiAAfv97N2knw+OrdMjLHuTJR+UjzZJkko5LWF5PP12eslC2oCjs++S1VWWQP45uvZH395rmSt4YIIXOEJujcDrpEW7Jel9Fjlz5UFb22svs+jJ0fhoLOnPpfHgPTAbd9ZxccffddtNLdqpMFDofFaOyIHLr0rXQFRFdtgyLdKe54/tQ72ShEj3Yd8pSb4gsdGUoLzYghc4Q2xOgG0vBi7NoUdESZONjR9YHimqs6PlnI/uM8rbQ2S4zugs6f/ml365byWebfG62FTr6puQQtQWmLpcqedpMj5f2e+8BW28NzJtnN18VkoFwylY+60mhO+GEaOv7OyALHWGE7mic7x9Gnnz3XdESiMkK1x4EUaTOIvChDGU1Vq582n24d9/JI8qeD+9Bt+O0447AttvalycvVBS6xx4DjjpKrv3xuQPqo0dEHgqdS3hyXnMNMHlypNgVxVprVf+Oy6mz9q9P2Cwbec4bs9mmuCAZzbgs36AtSKHLGXK5LCfJ98IW2LzjjmgtvVdesZu+L2mZMnRo+vEhQ/KRowiKjgimaqEra5RLk5HwBQv4+xsagFtvVQuXn1eUy+T9yih0J50EPPtsZQTbd9cpnxGVsx9+iJafYXOmZMuDTD3RGF0u0+553Lj85HCBzfcpU34mTgS++EIvfZOyknf7cPTRfshRFBlxmwhZfB+58JEyPIOsTuKtt0bbceOiqJc2aGiQcx8TPb9vvgE239yOLLoyMLLcaadMcZMvkU+d5MN7cCHDyy8Df/xj5JY5YID99NMQ1TmiOXQ69+9rJ95nRNZN9vvOO6Nt27Zq6Y4caSaXKT58wzzqZZoD73vO+16YJ4JpHe/7O8iKRFvvkIUuZ8hCZ5eBA6NnOmdOsXLYfG+yna00ha4sUFAUd/g6h842LuaqMCuLrSi2aSxfrjeXj+dyOX683DIGNtahGzZM7rx6QdaSzSwmebg861KGTrqvcvmG6+cUryt8fyc+Tw3IA1LoDGksBcVX/vrXaDtxott8XL/neGjjMoTkl+Wyy9KPxxuLhQvdylIERQ40+OY14Cp9lu6oUcDjj9tJk4305uE2e9ppwKabyn/3SQtdPBpgmzbAZpvJp6FKXGnu1k0vjXoj+SxVXS518rCJr9baPC10S5cCG2wAPPWUvTTzUtB9Vuiof5wvpNBZwlbBLdsHULS8roPM5DUJPx6dydRCl+c7Mc0rfq8775xfvnmxwQbF5e3CQpdUOlxGufz3v4Hp07PPi8tw1lnq8vDIU6F74olom/Xdi4JuzJypnmdaXhQUJZ0sRYM9W587v2W00LmU87vvosG3Sy6xn7YPZdaEeF0xeHBxcsjga1nOC1LoLGGr8i5bgSxa3rwqy6z7NH0O8Y6j6Yhp0e9EhbisKlZWH+/RN5lsdijHj7eThywrVwLHHQd06ZJ9rgsZVlutIocseQVFYayzTrRt0UI9LV+tMq4YO7aiOJuSfM9Tp1b/1lXoVPK0iW/1FiNPuVz0I+rRQldWfC3jtiGFLmfqbdmCou+jXix0cVRdr8pM2e/hu++A5s2BDz8sWpJabFroRO6wKu9P511PmmQvXZU1inyup1XmDH75JfD734vTaCwcdVRlLS3bbLhh9W9dhW7+fODtt+3IlEUZo1y6LLOff+4+jziNRaHLu55pbPVaElLoDFEtQPUWFKVoefPqeLm20G25ZeV/04AFZXW5zDNfW7z6KrB4MXDPPcXKtM02QMeO1ftseg347FEQlyGtflWxAPvgJpV8tllrYvI47DDg7rtr9/vaiZdlwgSgb1/583VDtgPABRdE2x49oq2rtqB7d2CfffiDGEUGRVm+vJgFxvOqW557Djj00HzyeuutyLXTh3pTljLVFWV6ri4ghc4Q3QJUtoLX0AD87nfRiG8ck/sowyhVXh071mkA0oODPPNM5X8fypDpwrNlV+hU1gJzyaRJtVZCVQudjtLmOtCJ6rm25GHv9Y033L9bXcVbZjBLdKzo8qoLu+cuXaI6c/Fi93mywbZNNom2We+LBanRLYs85alIl8vu3YH11nOXv4i8LHTMOmc7j+R3+v33QNeuwAEH2Msjno8rymShE+GLHK4hhc4SsgWmrBa68eOBPn2AI46o3l+0vL5Y6ExZc83K/+eeKz4vviSBz1YTWco+IFKUa94TT9TO3Uniq4XO9iCJTddSRlzGvNxps+RLPjeTsse7xpdvSobZs2v3jR8ftU8//ug27yxFgy1G7/PzVHG5fOklt7LIksfzdJnHzTdH248+Ksdgto30yeUyX0ihM8R2h873ApnsVBQtry9z6GzmP2aMWT5FvxMVyiQrj3j5y3P+xQknAL/8ZfZ5qumqpuObhc6FRX35cnU50li2DNh+e+DFF/nH2T2IlrxIjvynySd6HrpRLlmwmDijRhW39mX8md93H/DCC3ZDz+uguw4dI++FqH2tg5NyZQ1gucjTBPaNTZ4cbcu6HFG8rlBduPtvf7MrSxb1MMhtAil0hrCCctZZwCuvqF+ny5QpwDHH5ONykkbRH0peFpKlS9PnYZjmr2NlMMnzyiuBAQP0r7dF8h6WL4+CA6heVxRsLbA0eWx/oyyvadPkzpNNL+24zw2lCwtdmpXclB9/BMaNAw4/vHo/k2/UqGh7xhnVx0UWun/8Axg4UE0G3Xm6yQAgALD77sDWW6vlbwpP6WHKZtqAmCnTptUq2iIF2MRSmKfVxYdvmEdSruOOK0YOXT79NNry1mLt399ePvvuq9b3VCVeV7Rp4y4fl/iT/v/SAAAgAElEQVRaxm1DCp1FZDrIWSPIs2bx9ycbkYsuAp5+2u2HLEPRH4rMiPxrr8lFy0tL/8ILgZ12Eq+LZfM5mFoZZGS57TagZ0+zfGyQ7Fgefzyw7rrZ1xVd7hjxOXQimZo3l1tPzTa2LHQrVthR6Iq25jWJtXZZ18QHb2xb/Zo1q/6dlGXRovTrkxY6IGoLVOApdDL3KXpuKhFETUiTcf31o23z5nbzjN/zFlsAO+4oPm6L5PtxaXX0dT5lEXW8zTzZXEq2dcXHH0fBj1zha/ng4fPAYx6QQlcQogJ25ZX8/VddVf2budk0bWpPpjR8/VBkLHQHHhhFATSBrcPFm7sRl8M1MiOrRb8TFZKNxbPPRltZN7eikbHQARW3GwDYdVezBcdtW6TYeaLzlyzJv6y5SDeuSBX5jWQ9yyw3Sd71qvVPmeqIOOw+mdXbtbstL++0oFW28km65910k1mkziSuLHQrV5Z7+okLl0sXaSdx6c5ZJoVORFnrO1VIoTNEtaBkNTqikc74wtNApcM7fLha/qY09jl0osotL5fLeP5FP3sbiO4hK0y2L/cuY6GLnwdEI6qi+VEyuHAx1Dk/L2y5rJrMabr99kgRd0FWkA3G0KG1cvH+l6EeOml5UcR3weugL1hgL32VoCgqdO4M9OplJy1f6yNZkvInl5UpCzJ9jrlzgZEj85EnjXoY5DaBFLqCEBUw2cqVKXS8NYbyxJd5Anl9sIMG5ZOPiMYSFCVrxNGXe5S10BVB1hw7hkmZ0rlvVeXj+uvTj2fJwBv0UZE7CIA//CFSxE3kyMLketEzFe3nWZnqpW6xbXHKcicV5bfGGnp58ix0Nlm5Mgqfz0h7XqrP8r33gL//XU8u07x9yzPZl2vVKp98TQnD6B2ygbT4ffDcmVeujNydu3SxO+igAyl0RK7YWragHgqoasQkHnm52TBuuy1yQSuKMkxmVyFt3lYZkF2HzmY5jT+zsWOr1yaMoxrYQ6cxzMPlUiZIDiPtOfvy7WTlPWOG3PUmFro0hcGHRdVlUXW5/OwztfT33BPo3Tv9HNmBE1neftttGzNrFvDJJ5XfvrYjvsolS/Ibk62bimboUODss6NBLCDbQhefI5jXXFpVfHq+LiGFzhDduT6mIwl5F1CbIx+DBkWWPV4I7DLgYvRUtmNSL6PoDF0XVl/uUXbZAled5LZtgaOP5h+T7bzmZaEzcXmUTVdW+VS10OWBat1votDpvgtfvjuG6jtVdXU2WYNQt3P7xhvuA2nE0V3CwjX1ZqHLK19TWFAm5pGgMs2j6PsgCx1hhO05dL4rdKYV/NdfAz16REsulIG81wQS5cnL25fKSxSVT0aOelLo8kJnvqVpukWWNVudSl8UOtm8mzblh8lnyMilsw6dz8jM4c7bEtIkpRc1erR6euuuy5czD2u4T+jI9cYb0XqEeRMEwA03VO9LfmNlsdCts060ZcaKrHrTF8+HtPyLlisvSKEzJCvEtCqihrZINz9AvLaP6ofCRi2nTq299owzgLXWUpcNyLeDwsurjPMBbfHll/z9Mu9EtwL25RnF59DlJZNthY6ll/Yu8m4o4+myCLMyuOg05aXQ8fZvsUUUEfWHHyr7eEqCDQtdGa3/qvK4mKeYptB9/bV6Pgcf7L6NkU3XJM+FC7Pnnaahk/dBBwHnn59vnozrrqv+zaLqMk8kW3VTGIrd7G3Anh+T25aFTudbsEWW3GPGROuCfvRRPvK4ghQ6Q9Iq8zREBUzUCYs36GnXu8JWGPk0i8bDD+srrvvuqy9TGrxK2IXyyHse//d/wCWXiM8TlYHNNrMnlwwmVoA8FIVly6K5jy7cmFTn0A0bZl8GEaquwTrPXOcaVeXjf//j7x8zJhoEyqqbTIOiyCKb5uDB6unF1xu9/vronlVcLpPLtujWYUk3wqItfXkqdCLS+gA6gwFNm7pt35Npu2rP1l47igyrG6VW5xno9FPi70iU5/z50Xl/+1t0ztSp2decemq0vfba9PPixx59NIqom8bLL4vd7G0wYUK1TFnlQ7Ze3WorM7lk0O1PzJoFvPhibT+7bJBCZ4jKYrWAmsvlCy/InVcmZOcc+YxOAzhjRvVE9CTxjhJ7RiNGAHfdVX2eTOWZFV3N9jpKojIto1DozkdUKTv33Ret73jnnXp5pSFroWPP6PHHzfJbsQJ48025c1UtdDrn2PqGR4+OQl/zEN3HpZdGg0Cyo6oqCt0ee1T+j5fvxx6TyysN1fsEauWdM0dNoZNxVZR5lw88UP1b5LmRF6r3UQaFDshXUZapt2Q44IDK//H2THcgbcQIvetMED2Lb7+Ntn/7G9C3L7DllhVLefKab76JBqZZ0DcZryOWxmmnVYKRiDCJLK4CT6Eri+dMElm5yhQQigcpdIbEK/OXXuKfM3ZsbYGS6SAdcUTl/1mz9OSzhWgO3bhxaunEFToXHWzbyM6hy6ow2rUDdtlFfDy5cLwIG25Rl18ul5csTZpECutrr1Xv53VKfve76t+iEVWbDQdzi85a204H2XXoGKoN3iOPAP/5T+X3jTcC3brJXWvLeqHqcvnUU+mDUTx22w341a+yZYnDRlNl71NFodt+e/7+k06SyysNnXmjyWNBoKbQyVhl2DlpCnJyioGuh4ot4vdVVGfMhUtunh3jE05Il0WW11+v/B9X6HSV02ef1btOhQcflOtbsXsIgmieHlDp+ySf0eabAyefXPltu13I27W/TGvfiuSbNCk9WrLv9yULKXSGxBs0nuXj3XejSHT33hv9zgqiIKr83n+/+rcvBfCmm9TOjzd+ffua5x9Pb+ZM8/RkEL2jsWNr991wA/DWW2oKeVoDaKNyNfG/5+U5dmy0rtGBB1bv593HlCnVv6dPl89HFzYXwEV0UlULXVKpePXV9OtOPx3Yf//K7y++kJdN9n5NnjXv2mOPrR6MYrBO3osvRs8jqRy89x4/DxdBUVRwPYdO5LYbP4/3LckodKL2hvcsdDreeSt0aZbGZBvJw8UcujR463bJYFr/dekC/PvfZmmYEB+oM7U27rOP2fWzZkVtcJJPPwXOOgu4447KvvhzZ1bwF1+s7G/SRO5bevppd0paXn2/d9+Ntll9Dteu7CqI8t9rL+CXv8y+ru4tdEEQPBwEwYwgCLhBsIMg6BEEwSer/v4bBMEusWOTgyD4NAiC0UEQfGBTcF/IKgDMH5nNA7EV5dIXkp3G5O+bb47cFFwRf16qawzJIDuH7v77I8X97ber9193XfUirjJ89RXwxBP8Y+uvr5aWrbmPDF75PP74ijL73XeV/bznlJw/JHIftGmhY5OxbT8LwMxC9/jjkVWqXz/1/GRoaKhVoGVlSzsWj1Cr8h7+9Kfq399/L38tD5kOfByVjodLy4+OQseT17aFTibMfjIdG2uJqpDWmZax6NgevMhCV+E1DYoyciRw3HH8YyrlOXnuxImRS2EW8XVETQfSLr3U7PqDDora4OQz5QW0mz27Mo+f9SduvbXaQpfs/GeVu7Ja6BhlstClIdM/rHuFDsA/AByccnwSgH3DMNwZwI0A+ieO7x+G4a5hGHbUE9FvbPsU67gP5YEov2RlnVwQ+pprgAsvdCNTUfCsbRMnRts+fezMfxCNrsbX7pNxgxMphq742c8q/4uiX8pg87tiYaxFwTVMUI1yGT+HKZqTJ8vnp9rg/PGP8ufKulw+/TT/vKyIv8kGNU2BECkzYRi5c8YDLWQpNr4FRREpdKL9MmmLnqWKhU5n3bQWLdSvMUFmLmAaeb/3uHVdBZdTLEyUh223jVwKVTBtD02twKNGRVuZbwAABgyo/h1X4uKysLJ4zjn8dB5+uDofFZdqn6gHC52r63wj81MJw/BNAMLqJQzD/4ZhOHvVz3cBtLIkW6PEZiADFyQb1LRRZdcceWStRcw2vA7ijjuKz3/8ceDuu83ztTWqZ9sq9eST8ueedVb6cdtLfmThomzGO8wyC/T6ONop0+HIuhaIwj6rIFs2WfhvILLoHnFE5IrKk0G201SkhS4JSz85OKbicqlqude10JkqVLbJU6ETlQMXz2CvvfLJJw9MLXSmCl180C2OzIAob59sOqLgR7J5+oJPClsWpvI1BgudCmcAGBr7HQJ4NQiCD4MgODvtwiAIzg6C4IMgCD74oUSxQ1VHqxiigue7QpckKa9KJWaKbPhvGyTDfqehsm6WCFvv1/bC6CeemH0OG13+9NP08+Khn5PYtnwDbubQyUZt/egj4LnnsjvmQDSyq+IqGcfk+xPJ/9Zbcp2feFAElfyyOlDxpTtYhLd4tNB//KPyf9JDQJRmUQwdKh8AKU7clZmh0vmw5XLpGz68U9symKbn2zMxrXdNO9nJwbSnn47aKJ3nxPMGyFJ46snlMgsfyp4OZZU7iTWFLgiC/REpdFfEdncOw3B3AIcAOD8IAuFsojAM+4dh2DEMw44bb7yxLbGcs8EG6ceZFYJ9/Lbm0Pnqcvn73+ul4wpT1xX2vuJWgjyQ6UCrjDDmiawyYrLQatH3yJCdQ9erF9C9e3bjuGxZtLYab4Q+np+IZPoynSEmt6jjlYxeyruW8c472fkxZDtq8YW0s+ZspVl9fbDQXX117T6mhKa5XPLeazzQg42FxdOU4bTr8qRfP+Dzz/WvN5Gfd61KkCKTfPK8Po5ri8XrrwPrrZcegdhUBmaha2iIBhGPOSaa952FC8u/TBpZ2F52KAsVl0tdVqywEwNBVZaGhigiKQvIRRY6AEEQ7AzgQQBHhmH4U6zBMAy/WbWdAeBZAHvwUygvWQ3/dddF22TFb9oZz6NhffDByv8s5GvyHpOdwLTQsEAl1LiLEPI8Dk6b/amArec9cqTcebbWIeLJnZcLmYiVK4HevaMJ6CJcKHQu7ttkDh0j7pDAjvMsMjKEIbDRRnrXigY/4vM2efnFSYsklkT2fQwaVPnfJAiHrkJnE5sj8fffry8Hr37RqXOKUPCGDav8H1f2ZbAt7yGH2E0P8GugzkaeaWn07h31Bdg8Nx469TavX9bQUJl7KzNvmaVhOghvw0L34IPAxRdH/yeX/nFNHuvQ9e4NdOiQPu/+lluql/CxwfffAwMHVtb+a/QKXRAEWwJ4BsApYRh+FdvfIgiCddj/ALoBcBCHsFiyGkHWMZszJ9pmLVtQ9AgoY9q06jlQvXpFWxb8gyHrTvHf/wIffFDpAKu4MJogu+iwiKz3xZDtaHbpIneeSSNgwwXEhKxKcfDgaD21uCtdEl++gyzinQWZNRl598Umz4uO8/JLS791a/nz43mKLDS8UN3Ja2XziJP2bSX3zZsXzblLUy5FsHziLoUuypdpx03lWJo1T2Z/EfWCLeL3pDpgx7vHhgbgzDOz2wretV9/XZ8ul6YdW1kZ2Bz4224Tn6Mzhy7eL+PVM8l1HNNIulkmFb08LHRnnQXcc092Oj/+CAwfrieDCFdBUQYMAD78MPqfeXakDWRefbU4yNAnn0RrmcYNBWWpz2yS2Q0NguAxAPsB2CgIgmkArgPQFADCMOwHoDeAlgDuC6ISvmJVRMtNATy7at/qAAaFYfiyg3soFNlCUzaXS1HAAhbSVySHSK7OnaOti0iDaeT1Ua+5ppzLkiwiuXXXNdLhwgujqJWqc36yyjjrWJsERfGlsmadjbffBoYMyT7fdITT5QiiaHBGxUIn4vnn1eWJs956wFFHAeeeq5/GnntW5FV5D8lzZ80CNtxQT4ZPPpE/VyXKpSqsk/bjj8AaawDrritnofNhBNtEBt5znDoVeOih6N3E26ei2mJT7wyb8thQVmRIm3cuq9DF393KlZV6K+5yKQMrX3EPkvi9P/dc9XmydYnuYI4K3bpF1s6lS6Pv2gauAnn17Gkvzauuiqz1m22mdp3swFhZyFTowjBMDYMQhuGZAM7k7J8IYJfaK+qL+GK4JpPUGXkGRWloiCq+pk1rj8nei6xCp5J+GBa/mDBDttKOP0OXbiotW6rlIxOEQwRbP9C2QqdiNdI9njcNDer35cpKpLI+mYwcaR2qW24RH/vmm2g+5d5784O1qI68P/NM/u5GPL7+Wl+hszWCLztX8quv+PtZem3aAK1aRQGMdCyMtlzDVbCt0DGS6yImpw/kVef4ULfltdSHTNoy73vp0mjAhpeeaJ3HNB5/nB8ALGtdWlcWOlnY/FKb74r33IYPjxTeY4+t3q+br6krpSiKdNyiqpJOWbEd5bLRoTvXRYSo8HXqZDcfIHKjtDWKI4sNf3Ig/4hsWY3B2mvnmx/gr8ulDcogow5Z79WGy6Vt0hSvgQPFx3bcMX1OnYrLJcPWQtYmFjreO1y0yNy9W2UEXzUwAlvzkMHuYc6cSjACHeXsppvUrzHF1Tfgy2i9C/dmVWQHMmVkMJWHV/9su23176RHUTxP9q288gpf0eORVOZkv03d9lb2GU2fLneeDOPHy3kV8RTWgw6qLFwfl/3DD9OjV7vCtLzWC6TQ5YRs4yAKFrLVVtW/ZQpuly7R6KuIeNATXdIsdDwZ331XPU0eslYjWxa6rM7OtGlm+SQxbdR1z7eBztyEJC4sdC46aLIdBN75LpRtnU6pTJ6vvKIuS9YSCjrvQ0ehM126Q8YL4bTT7FsPVZ6PjSiXMs+kXbvq3/36qeVrA9sWOlF6SUVCFLChHl0ubS93YwJPlqy5tLxn+OqrlXvImkPXtm22LMyCa8tbSgYbkSCBSOlq0wa44orsc+PBsrLutXt3YMstgSeeMJNPF1WPMV8GcWxBCl1OJOfQiQravvvy9+tU8iNH2h3R4ZG2sPgjj9Sef9FF6mnymDChdp/Nj3H8+Cg9Fn0r77VY4mnMnMnfr5rPN9+YySSLrwqdC1QVujwsdC4apTvuqN3num7h4cIVmzevV3W+S9ZyDVOnmlmW0upZHXjRiGXqOJUopkWR9pzTLJtZz/Sll/TkUcVV3RaGZgOCKteqzpVPS1vGNVumIx+frpDFz39e+V/ktnfqqbV52bLQia6xVf/NmBFtR4zIPldnOkl8KlIe2HIRJoWOUCKrwOy8M3+/7QY9i6Sca60VbZPr7qXJkXTzkUXm3j74QC9tWV54Idoyy1vec0XizyC+Zo5q4xCXOy00tE1szKFjDBsGXHqpmTx5odPxUD2uig0LnSiNNOu/DDouly4a6fgi5bx8ZDpbafKOHw/ssEO6DKqYlpPf/rb698SJ5q5hMqHgs3jtNeDyy9PPMel0LV1qNz0g+7l9+23l/2uv1VfsTV0ud9wRaNFCLh1TF7a4x4ptl8tWrbLTjLd7XVetfrzmmnIDcCtXVh97881qy14SGSViyRLg1lvF8soqdFltjIt+oY7CqvtN2fZQaWyQQlcQooInUhxUTcm2OfnkaMv8pkVyyMplYp0B7M9dzJIhb4Uunl/csqY6AhVf4ywZobRo0tYiZPfWrRtw553i4yr44HJpWo6KmENn+txsfquDB9tJJ/6cVIOzqDzjhgbgnHMq61/JpMsCDcTdyrPqI9N3tO22wAMPRP//7Ge1x4cMSV8jCgC23tpMBgA48kjgr39NP8fkXlXmjJsqUAwWXAqQm3PoqlM7ZoxcOQQqzzhuyTVxUzaBydK0aRSavkuX7H5H/DeLfHjjjRVPgzSXy7Q6Okuhe+wx/vGsNdRsW+hs9MN4TJ5cWYLLBbrlhix0EaTQWUSmMLBz+vYFnnqq9ngRCt1rr2Wfw3zWVdaB0pVRZrFYnbVpTIiPsmZhu1MtqqRkRnJ79678n1dlJZtPWqhqF5asLLc4U2QCF5nel6pCJ/MuktH9bJMc8TYhbZRbhXg9y6tLVC10aZ1D1XtnAZbWX19NBlPY/GbeGqGHHRZZeFwPJMoEezEpS7xr//SnaKv7jG0/E9eDhyrPL8+gN/37Ay++WLs/vuwAU8RUFLr4/T70kJwsyWck6w7NG/T49ttsJciWQqdqWdWxyp95ZvrxuByqFD1/lBS6RgpTbDp2rOyLF6Y5cyJ3MQavoCRDvibTiGNa0D//HJg0iX/swANr98lWaC46GjJzFVwrdMn7t7nGnAyyir0Kvil0aZx3XvpxX1wr4nLIrBFoY75FVvqqz/+CC8zyzCIrkAnvnseOtZd/VqhxVSVZ1VIhqqvi83Sy8smSwea3nUwrzZIuoqEBOOOMaDkE25hYqXnXPvxwtE26Y9qqY1TTceVyqQJ7TvFnomuhk72uVy/g8MPFsjQ0RN+SLU8IHQsdjywvDWb5lk2D95thOgdbh2Saca8fET64XPrSR8gTUugMEX3MO+0UuYupIvpgTefQtW/PH3mVRcdyqPtBqfj4+4xJhSKzts3NNwO7KKz06ItCJ+P6+dZbwBdf2JEnL3RGO1WP61ro/ve/yMKyYEH69Tp5umCPPdym//rrlf95dZvMiPzMmZWFwtM6YDZcOvOcQ5183zfcoJ7GhAmRonTUUXZkipOUb9Qo+TL6/fe1Ie4ZOt+GiPPP17/Wh44oe57xgUyXLpdp7499P/HBKl0LnUyeqgNtqm73MnmK8rvmGr30ROjIq+KJliRLrrwtdC4HxoqAFDoFVqyIQv2vXFnZJyqAuhEFZRWnIoN0yOx3jcyH94c/uJcjDdGzWboUeP75dKtf3N9epCT37VvpUMrky2ARropC1KFKkubm6kOnBzBrQHjvwdV9XXFF5A70/vvq17oKGsH2F/EuP/648n+W9V3U2erYMXtARUWhS+vUJet723Po0tL68EO+TEWRlO/55+WvveCCaIkJHkuWVH8fJhaxvn3Tj7N9vGV8bFopdI4D0Xy75LkuFbq0NiHpHi3jcpnVP0qbQ8fzckirq2x8E7IKnWz0SJculzLeW8uWZS9bw0O3X2saxCeZTlkhhU6Bu+4Czjqr2g9btgCxRl3XXSRZ0NPmH7lAVq74eS4X/5b58G6/3V3+Moie2YMPAr/5DfD00+rp1IPLpQ05fOhYJpGRKf69tGjhXgZfGqgi5eBFNoyH39cdkY9HdRTd30sviecdZz2T+NIsRVroVPISWd+bNQP2319fpjRULaC8ueuMuGXY5TN+5ploWaG99649Zupub0NuXv/iq6/M0xWRFqyFRdgG5F0ubXnHqKZny0LX0BDtmzFDLUJuUrFZsSJaBDyJzHIFItlk7nHdddWXgwGqjSUqxN1yZfOqR0ihU+DHH6Pt7Nn8ApRGmkI3aBAwdGh6ekUvW6DjcnnbbfLpp6Wpen3RZMk/cWK0lV2MvGiF7vTTs0OJ28hHhZUr9St/m5hY6LIipvFwHfLcBWFYWQZEhkWL3MnCiCvTWQrdnnuKj6XtA6KowCLrQ5biFF+0O6v+d2mhU6l/WOc7ed7SpelR/lRIypdUmE0HlFi9IvvNJBdbl+GYY8TLPBT9rcaJlzuVAVrVNiutHxWfgyvrcpk1R1a1jMj283RdDXn3c/XVwKabqinSyXQmTQKGD6/e99JL/PZ8ypTqiKy6eQJRNFmVAHppaeV5vc/9ShlIoTNEdnJ92rEePYBDD61NL05y5NNVpf/jj8C//lW737Z7lKlCp1NZ5I3oPliHVce9QMdFgqFbWT3ySHYocRv5qNCtG7Dhhu7zkUUmIApg7g5VxmULGhqAf/9bfDwu86RJbiyXPJl0kXWPYjD3Nd30eftcuty7VA5dpKlqUeRZbFWOJ2nWLP246iDL6aerna97nsy18XKmUuZs1kPx9yvrcpk1cJa2P+37M62fRfDk//vf9dLipRdHNJB80EHAhRdW77v4Yr3BoyDgB8PKen4yZYw3v5qn6Mc9HBoLpNAZIltxscKl2yF7663q367cGY87DjjllNrRQ9lGKa/RxbyXLdBB9CzYyLushaloCx3juefyyYfxz3+mH9eJvmcb1XdjaqGTST/t+Y8ZA3z0kVqaW21lJtPs2fz9vHsdN84sL1my3puMyyUjK5iG7JInaXkm6wpfXWvzIHmvybbAVhtkS4HKo038y18qcx1t5hdPi9dede7Mt+qY1ItpiJYt0E1P9tq09OLLi7gOiqKbXhyRjLx6+p571Os7IPommzbNPi+JyGodJ20eeFxWtuYgj+nTo+VKkvOny16PlqBb7A+qH3oc2VG/vIOdJGGjN0k3ISaXyfyKNLp0UTs/7cO7+mq+/7YKNhoEW6N5rhpHVbp3d5OuiEcfrf595JH55u+CLB//rHeXNZCR1dE/7zzgF79ITyPJxhvLn7vllrX7ZNaVZOTVoJoMkqh2vkQDNyqDUnkOnJm4XLogq0wnn6OtNjRvxTCLtPu64grg6KPN5UkrZ7xy/N//1lp1kteZulzyLHSMBQsiS9BGG4nTE7lcpi1bIHK5NOkDpsF77jquojKoWiyTJPtWvPsXKXRZz+rBB+VkSMKz0PFc95kyes01wPXXA2+/zU+nrJBCp0H8pas2HlkFpmiFLssSF4bVyp6tjsbIkWpppD3HW26pnfdim6y1tQD/OgS+BEXRvZ/Bg/Wuc0nenV3fG5wrrqjdd8op/HNffTXayrhH2cZkhF91PrNIoWvdWj6drHo2rzl0stj8FrIieqZZ6N55B+jZUy0/1Yh5Igu0bbLkmTJF7jyVPOJl1+Wc5eQzFPWD3ngjsuJ8/XW0VuW4cXy5TPoQJkqbawudqtXYhbIZRxTJMgj0LHQ2ly3gvYu77oq206dHW5kllMoEKXSGxAvgwQebp2f6AX78cVSQX3vNLH9Ro37//dUVqK68ph0QnrUoz86uTMXjwt9e9Xmfc051fllujDbwSelgFTfDldK1aJFc2vHoYq6CosTPcRFRNC1NFasTb2Q/L1fq+D1tv3368axjWe8suYA4Y5115NIHajutec6hc+3mvXRpugdL8l7jyygA6QrdRRcBAwZky2CC6pw7hqqCJPvOs95XMkhG2rXx31nLe4iu0yk/f/5z5f9kGWLBddq2Tbey6cKzjqWlZ2NAytbAuIkiqxPQZY/AP1UAACAASURBVN48sYVOp32Lu6+qwBuE4eXPyjCrM1wu/1IEpNBpwhsB2Wkn83RNG2rWYVSJKheHrY0lW6HlHX3z008j2dZYw10eBxwAXHpp+jk2XB/zcLncbLPK//PnA6eeWn3uwIH8NDp3lpONh0+VYtu2btPv1q3yv435XzYUujjvvht1aJP799032vLcIdmgkChNl++3CAvdeuupXXvggeK0eIhclZNWfptWQZvE3ZJM3VOTjBgRBRXZZBPxOcl779On+nd8zbdknjJzcpKoWjey2mxROr/9rbxMNnnsMfGxpKy6QVFMWLasep1IHWSULBVlUNUypnq9rMulLKKBeRHDh4vXpz3uuOx8kjRpwj92xBHpcmT1u7KQfU+k0BE/sWBBZXSN9/GnLSpu6nIZhumFlo1A6EaBnD8/2qaNesb/X7Ag8qPnHUtDZQSc8ckn0RwgQM/9TnZB69dfV0/bJbbc+ngjrCefzD83/k59QBQEKGvph+QEbpduQ6rvRmcEU3UO3Wef8V3O3nwz2u62W+2xJ56o/v3kk9W/TSPUpl1TBpdL3rmu3RKLXIdOJ1/Z93j44dE2LcBRVpvIloFhmJYnVYUuL+XaljxDhsjnGX/2aXVnmoUp/v/ddwO//316nmuuWf1bJ3q46cLiqumZksxz8WKxgpWGjLsw7755a9WZIGqnXn6Zv799+2ibFTFWBLun5CL0SdhzYcfyHBjLA1LoFGAvf+bM2n1xNt/cPA8RTZpURtd5sE67zBwvFURyLVwYWXOSrm0u8tpll8pcOx3XLJtREbMU0nnzgBtusJefTL42zrfBSy+lH092wGQQLUq8xRbRvApZVCM8quDCvVE1DxvvOzkYlFTwbCt0smnbxHSQ5E9/Mrued52Kha6oZQv+8he5NGSfycKF2eeoDi7ZUOgWLeIH+OFR9Lx3m6SVyfhA59tvy9cD7P+nnoqUubvvlpdD1wXbxELHs46lKfk26twzzqjMKQaABx7QS6eI/gEvDVuup7Lnsb6d7ECdSPElC10jJM0dSeVaHjKNQ3IJA8bPfw5cdVX0v6lClxY5jBc2Nu7zngc6H978+cB339lb4DaNP/zB3jMxcbksQqG74IL048OGqaeZ1qkzdc9R5T//4Q9g5NEYPPWU2/Sfey77PtKOn3++ep4+WuhefDH9+PXXV/5/8km7cst0Gl12RNLSis8BNU1LFlVXZtm1YUWEYRRwQ3Zu3GefZacHVA8E65CHxTCtnN1+e+X/666Tv45x7LHq8qRZ0thxHiZ1iqrSJvO8x45NP/7WW8CvflX5bepJIlJATV05ZVFVxE0VUdkAW8mBguRzJoWuERIvNLZH50zSi693ZBpcIGn6jt/z1VfXnj9nTu15aaSdJ7Nuk86Hd8YZwN578609f/97lKaNiGXvvQeMGqV2zQEHiI+ZKGjx8995R+1aXfKuFFWeiQ3L9f77AzvvbJ4Oj/i98Fxkf/xR/nqZ/Um6d+ePDsetFS7fr82gKNOnV1z6kqR9U6rfGHMDFyHr2pWWbzIse1Eul2Ug/mx0ypPqs82q61l6X3+tLkscUVAS0/Kbdq2oP8KmZoiui3sp6chjWgYbGoDbbosGVnnPLcu6mDw+aVLlWBo33sjfnxaIJk8eeqj6t85zTs5L5z0TG5ZV0+t1FLqyQwqdBiYKXR4uUzL5ZJFWsceXGEieb0Ohk4lKpnN/I0dWJsmLJtqbNrpANGKrsg7e2LH6UUl5iDqryeABrlCd55UnOgrdihW18y9nzao9T7VM3nRT7b74s9EJ6GJjBJY3d2PvvSv/lyUoSseOYkub7TLoeg5dy5bp1+ZloSsCEwtLHpGEZdMzHayIu/m6Qlahy0K0VIkqJha6K6+MrIqyijCjoQH44ovqfWefnS2rTWwqNnGmTDHzMAOAE080k4GH6lIhugOXZKEjfoL3sn2y0NlEddRPVaHjuW2qoLPGSTywhijIRp6w8pTVcbdlocuLIEgPcW27jKvcY/Pm6unvvHMUVfWDD9SvlYX3/UyYoJ+ObVyWI1cul999J5enTQuHCb7MoYuj+yyKHLSxUZ5cyG9atkX1j8vyKypnKktbmMijqwSbfh8q0VFdlBVbCh1bmzCOa/dwHZjbsqlCF3/vjz4qvp6iXBJcVAt0li+1rYZaVDCnT5cLDqKr0Nmid2+gRw/xcdNlC1RH7Yqk6DlxqgRBemVapHVEJ+8vv4y2nTqln5dHUBTX18vgstFzuRxJHNvPyaYlyKc5dKZzNovoIPlmoXONS5dL2TKqqtANGFAdBESEroVOZ542w4dBdVtlUCVCsSzJQEaqcw6TxPtirtu/pIVu0CCz/HyDFDoFeIVF9eO/4w7xsZYt3btctmoFHHZY9vVJORYvljvflvw33hh9bE89BVx+uZ0047jsENlGVaErWgEMAmDJEvFxX0bvZVCZU2lj3SBTyq7QzZ1rnkZDAzBmjPz5NjrEOhYKlXyLWraAzR0qkhYt1M5XUehElhgXVgyb80NdIetyqTKlgEfPntVBQERy6D6ztAFFIHq/Om57psqLLLYUG54nkmnZlgkWpNIv/vRTdRlsuVwm57/63A+UoQRVjN+odJ6zRgNmzcpndIg3By5J8l5eeUUubduV27HHAn/9q900gXKNwsbXNSyLy2WesHtsaIhGJG1+QypLXfhgoXNFXi6XaVZ5WW68EWjXTny8oQE4+mg5eWRJczFOm+eTXCdRRHKuh0tXIZvvOgzl1/8Uze3Zemu1PLPWooqjmrYJrurFIix0WdfZkifLQieq67t21c/ThzrYlqszr17SXRJBlAdP1mbN5KO6xhXEvOfQJSGFrpETr1CyCpNMZ8W1yyXDtgvl44+rnV80PlTasqy3XuX/sih0KtYGU1h6998PHH888OCD4nOZXMuXA1OnmuVr2jDGsWXhDsPadeTKxPffm6chGrBizyUrQp/OOolp0dJ++EF8LHm/y5fzw/TnaaGLY6ODkxWZNQuTOk/X5dK2UgtkT7ewnZ/utXFvHNm6uigX5l124e+Pf4+qsrVpIz5Wln4Dk5NnRIhHux492s6yDknWWw848EDx8Xgkcx2PIlcKXdmp09vKD9vubXlVGFlLA/hecbnytXZ931ttpX6NqnLug8slD9FEZFPYPbL170Sho+Pnnn9+FIrfxMXvnHP0r01iU6FzMcpo2knOE9GahWuvHW2z5Le9TqVo8ewwrB0QvP76aNmTJFkKnSsLnWl5zLKwqMqjer4PZZXJc/HFbtO3RXyNTRsKnUsLnYhklEoVNtsM2Gsv+fN9dLl0ma6NNOLfgs36hix0hDLxQqNioZPBhcslz1fd1fIJeSkQonxklx0oSmFNrielCk/utDJTxH0WXVlOm5Z9zksvRVtZlzcZfHC5tG1dYMSDY9hO32Z6nToBixbxj7HvJCtCX551WDKvxx4Tn5v22yY+DOaZdPJsWOhM4a1TmVf9ZyJ/0muh6LKg+8yy+lGzZ+t5keT1Dv/yF/VrnnqqYpl0OWAtUxdl5RN/vjp96MmTo3eRXFs3672z9EVeLEnvjbJBCp0CvLWn4gXItLOeTE+FZIjueMUjE00qie8KnYi4BexnPxOfV5Sc8fdiq7NRFgudaK0ZU/cHlXt0+Tx8Dopi8759HsVMW85EpNDZQNdCkezMiM7NWrYgCPiumj6Qt4UuTlYwL1fcfXflfya/7XJ39dXAppvaVfbbt7evBJta6GSCcCTJ6kelDfolLefJY75y7LGV/122AzJ91Kx8Bg+WP5d3DuvTJhdKl7XQidoJlTnzPkIKnQIPPxxtRSMKa65pnofuB5cV1UkVXcWyyAqPrWXC2HBD8bkuXZZcIlLobLhGXXihWRrxtHgwxS0pa7NmZvn5otDZQCSfyrqNvDR4c7x0G6+yfCtJZC10OnVfWlTXtM6hbGc8y+XymWeA7bdPl1EWGwNCNqxkxx8f/Zl8s61a6eVtCm/5DdOBqy23rP59yy3AjBnAPvuYpZvEB4Uu7hqX9m3J5KmTv0od4HubEse2QheGtVYyGeLRN5Pv6ssvgVNPjeb3XXEFX+ZkdEpeWmnHRX31tLnQZYAUOg3ihcZk8i0PXUXK9sRW3ysptjZYnOTHmPZMfLDQqbByZTTaLHK5HD+ef53Kff7tb3qyJVGdQ5fnuj/MJde3eQ/sWlEae+xhJgPvGceD7ahgW6HL61tcvDiSPWuBeB15RG6egLxCp2KhS56X/P6//RZ45BGxTGm4tOYOGSIfdObJJ6M/E5fLogIExZU3Zg0yVeguuYS/PznYw3teaVFYk/g0YKMrSzwQj6q1KgzttKdFkpdLdufOwHHHmeWfVBBPOgn45z+B3XaLXE9nzqxNj9VtKgvcxyGFjviJeKGxOQcnmbYJRbm5+FTh+dQwmdKzJ9C8Of/5LlwoDv1bxPtQnUNnqtDdeqv8uz7jjFqZVDo7abiYn6BzvUjpt4XP35XM8+vXL/0a299MWsdRNi9VK+JhhwGnny6Xdhq671pUBx12GLDDDpH8uveuguySCbbyY8QVyQ02iLamCp3u9UuWpLsiJ8kKmMYjWa/GMXW51OHzzyv/x4O8yBCG6dM1eOc3JuJKT3xJpThXXimfXrKuSL7zrKjZorTSjosUOvatlhVS6DQYMYK/v0wWuizKqNDZcL3ztXIeODDaiuRLW+sqb7Lm0CXDuJsqGyqRKpN5vfpq1NkxXSgXcGuhA4AOHfRl8Fmhc2kR0snP9jcjG7QoTcH717/E1/HQ6ZSLZDJNI8mKFZHCs846bmUAzJdM0CWufLEymcdc4TlzauecqQ4633mn2vmA/WWL2DObPdu8vvn4Y3N5GMmItToW5DwQ1SW33mqetkxborIkUJZCJ3stIB8UhecSDQB77imft4+QQqfBhAnu0taNWMgb1TDBx0oqi6TMKi6XeVkd4g2CrTzTOoIy79GWhYoRBMBrr9XuZx2a5LyWPF0ueQodALz5Zu2506YBrVvLp+3aQpecIyq63rWFrkULe2kVQZb7YpEWOtG5yfXqXCql8WttzKV+5hn+OaLlHNLSUj1fZ167jffPU+jyaJM32AA45JDqfTpWSpvoPE92zQ47mOcvCoyjYzlPRtE+/nhg/fXFefOineaBy/6bq2WHGB99VP07Twtd2denK7n4+SFToHxwuWKoNh4LFwJTptiXo0h8nEMXXx/HlyiX11yjLkcWzz1Xu8+Vy6UKycAYbBsv+wzeZG9mKeVhUqb22gvYbjv967NksPWMzzqr/HVD8lkkFyLPU6FL/pbNO69vRudZDBtW/fu88/KXgZFn3RKH1zGcNCmfvMeMqf591VX55CtC5/0xtz4VV9GiSFPajj46PzmSuKqnTb+pOXOqfz/9dOV/2UGeeFqjR1d+yyp0orm1pNARPyGatKyCLQudaj5HHVVtjSCXS/eIXHfT4E3aNbXQJUfEZLjkkmjSMg/R6FcRc69WX736d7LcDxoUbXkuGLxnd/LJduRKMnp0ZPkXTcZXgSe3rcneeYf8d0Eyv6Q7Y1qAEx141mqRLHnMK1NJW6fz1qePuXwmLpfDhkXldOZMPfltW+gYOuH34+jI1dCgFiHXF5jXSLL+zgOVgRUAGD5cfKwoBcFnC92NN1b/vv/+yv9nnll7fpqF7umnq/shsgod77w11iCFrtGQV6fD1iLRWR0vkeuZTl42rssbJidbW7AIZeOFF9SvcWEpTp7/ySfZ12y7LbDvvvxjognlRTzjZHRIl+GobZT9ww4zuz6PgQqfv3Ebc+hsuyCnySE7hy6JS8uTrEL385+LrzctI3FrVtLilAWLKjlqVHFlNW4BsOlar0oQqHdS87JQp5Gm0GVFqfWJoqKsAv5a6FxGkjSRzedgX7KQQidJXg1D0kdbVobGtmyBDGnm+zCMJjS3bAm8915+MpnCq7BMLXTJc3bZRV2uOKL1sFgZVXWr0GXSJOCrr6r3sefnYt6UD9+Mjc50GvXQ6GU9nzzdGZOyyOad1xzgNHk22YS/30YZjLtpXnSRXhphKL9EQvI6U3hz6EzRnYtWpFKhC+v082Rfe207eeQx+FWkhc52O8D6BUW4MdueQ8c7rx7aNlLoJHHVSUqmm1ZZ2ZQh66Msau6BTdLc18IQeP316H/RIpU+cv31tftsK3SyiK4TzQUTLSzugsmTgW22qY1yZ8MtV5YnnjC7XgfXc+jS8vAhPZm0fKr7ktaw776Tuy4rsIupTNdeG631mfYsZOYo63aSyt7+6K7xmMby5UDv3sC8efbTdonJHDqeQlem0PJFKdMu2thnn422pt+m7sCEjfMeeQS47Tb1/MsCKXQF89//Vv9OqwBUGldVl8vGRhhWL3TNGpDZs4uTSUR8EnFyQjGQbm1ypdClXSM6lqdCJ5oX6NLdw4XVT5WvvuLfI6/c6OD7KKYNl8uiAo4sWSJ/bZaMyaVBZPKPX3vTTcABB+jPQTMt+0Uu8GtD/rXWqszLtfXN/POf0fwjlTW+dPL3oW+Q5nK5ySb8gU1b2LRuFTkny3b7s8YakcEh7/JhsoxBkkWLou+HLHSNHFeds0svlc8n7ZhqYIswBHbcUS8vHr166V1nE9HaIjzCsPIBNzRU1qq5/HL7crnG1EIX54031PJV2R9/3nGaN5fPU5a+ffn7RY3RsmXmefqg0J18Mj8Iwvz5dvMRhQIvGt0BjLjVIy9lIvndqnQoTK2MO+2U/f0uX65noVuwwA+FLk2GBQvcvuf4s7HVUWSLZavMIYsPXMqSHGQ2ZckS9YAwTKFLDnCz9nnzzc3lyqN+LspCZxqAR0QQ5K/QffEFcOCBcuf6MO2hSEihk8RVQUl2jNI+lrRjyUhtWTQ0RIEtAL6bp+pHy9amKvKDUllzKK7QxWV2VRHmiYmFLhmBSjf/jh1r9/Oe9557ms/Z48HcaZOIynXfvlFUvDiqZfmcc8yud8mmm9pLKwxr5yaappcnvDIQd5Ercg6dLDZkFH0jsvWH6Njkyebv1Mb9pcmwzjrREhwuUVXkZAckk/VUGvPnqw/2zpihdn4WXbsCG22kdg1bSiRpocvDilIPc+i2395+vRoE0SCIzrzUOKpyHXts7dIyImTLLlnoCCckRwnTRr5VPoSswhmGwLhx4nRVPzofOq+qlSfPBTDvCvjRR83TsDmHTiXCX1qevEiXvOcdBPlWpGmWuKSbmmmZ9uGbsA17V2UO7+yLyyWgX0ZMrUthKHbLTM7rEyGaezx9uh9z6ETPli28/cgj4uts1km26zeVZ3PHHXbz1mXBAr3rRAqdyzbjrrvsLB8DlLueTBIEkcti3msD2hyMrHfqqLi5xVXnLNkw/+9/4nNtdjR+/LESDtqGQucDqgEvmDUu/lzzHqU57TTzNEx9/lUtejLp8TqLPAtd3gpdnvgwF8UFtju8NglDYP/9s89JowwWOpX5dmn5Z+1PexZdumRfX5TCmsaGG2afY7P9+/Zbu9+Limxlr4OSLotMQbLxPEXP8T//MU+bUWQ96aIPt9125YyamoQsdI0c2Y9DtaFVqXBVJkNnFc7DD08/rmOhe+edYiNGqip0/ftH/8c7D2WsrGwGRVF9hqL9G29cu5+n0PlEGEZLKpx7LvDNN/rpnHJKFHbd1/s0wcUIue3nlDWCnFXnFjWHTuU52FgrT/QO49a1tGe11lr8/StXAhMmmMnm0kKX9ZxtlMf4sx02zDy9OPVYr4hItsdl63TXU1AUNvhaD54rPsjgAlLoJJEtAJMnq6Wr0nm47z61tNOIR3O0ZaG74QZ9eWyg0gkYPLjyf/wdlK3BAOy6XKqQNjGdNy+OFxRFZ+FbG4jK/HPPAf36Abffrv9cfv/7aE5evTYaNi10LiwIWc/91Vf5+4MAmDo1X6uGSiCnOKYKXVqdMXZs5X9d5faEE/SuY7ieQ1dmZJe2qAdECl1Z2umyyCkDU+hs1o8qcQ9cUw/vihS6gnHVeWBBSmSolzl0KjLEF6uNv4N68nkH3L7Hyy5TS4M92yJDkgPpyi+zsM+bp1+mWSfEp/WSTC0mDNbo2Vrct6HBbt1hmtawYcCsWXZkySIMq62JX3whf60NC53Ms9Jdh07lHB62XL95yMwvt4ntjqKLNe58ZfXVqxew99kzgEc9WehspZv0SrjwQrP0TGWoJ+qs++oO2QKgWuG4Kli/+52ZDDpyufxIXFqa4tfx1r3xnTTXLZcul6JnJbLg8BS6IubQ3XQTf5R78eJKB9akIWYK3WGH6afhI8zqGob2vhPbdYaNzsY//2lHFpm84qjMpzUdFFmxQk6BTPsOXH63bBkZoLLmmK2olPXameNRdqvD6qtHniCsTiULnTz33GM3PVsWuvj3t9pqxVjpaA5dI0e2EVi0SC1d3Y9jyy2jravROt8sdC4VupUrgb33jv4/9FC9NIqkCJfLzp3V02MVZtICkvcoZu/e/P2dOlVCgptU7kzZqTdr7047FRuxLw/y7OybBEVZuNAs73HjgFtuyT5v993Fx2TKwvTp8jKJYN4m110Xbdmap1mInu3LL6dfN28ecPXVcnmkofr9y5YFG/OcywJzSWb9nbJ1uotsA666ym56tubQxVl99ez0XMRluPZa+2n6gFRxC4Lg4SAIZgRB8JngeBAEwb1BEIwPguCTIAh2jx3rGQTBuFV/PW0J7isHHaR2vg2rko35FDL7dNKxRY8e2efodg7DEOjQIfq/jCFy04KiPPmk+vUy5++6a/R/u3by6bHG2Oc5i0zZDAJgzhy9NMoYWEcFm9/5//7nV6czb1l082PKjUuyOm8y3+7cuXblAeQ7ySLZs1xqd9wReOWV7PTT5hDH5wYXWcdNm1Zc3iY0axZtmTte0jLnW7shoixyymLDQvfuu9W/fan/6+FdyY4f/APAwSnHDwHQZtXf2QDuB4AgCDYEcB2APQHsAeC6IAg8mlkij2yhU1n0EzBTQth2+HC9NJJpZe3LSsPlh/n443Iy6BB3EfSlclEh7dnPm5d9fbwM2rDMZs2hS8JTCouCyd6kib5bWxnddmWYN8/+d9K1q9n1PIt6Wb7h5Hfr20BAVp1eVAdIts2Mf78772xfjqz75627qcJll/G9CVTSGzBAL++i2WqryBVvt92q99u0eOVRT9SDksCwVffHF7oPQ/+8NMqM1OcRhuGbANLGtY4EMCCMeBfA+kEQ/AzArwAMC8NwVhiGswEMQ7pi6C2+TTBl182bl75Ysq4MvrlcymAj2Ma//22eRt7YnKRsA1F6vCAqQQBstJHd/E1gsps0xL51zG3x4ovR1odvnZEMne/bt5CVVzw/mfqLze876SQ3MiUxDYpiAzbflRclN4277qr87+KblFXodJ/TWmsBJ5+sd23ZEc3DtmmhS5s2YIt6c7sPgmiuuU18aU/qQfm2Vdw2BzA19nvaqn2i/TUEQXB2EAQfBEHwwQ+8VYkLxleFDgBGj7YjS5ykWVyG+fPty6GCbrSk664D3nwz+v+rr+zJkye6gU2A6sXsXUaXO/LI2n2+VaKssxgEwJgxemnUq0IHuHlfJmXOt6AqrvNr1gxo3jyfMubLt/n999GW57KdRnwtSRf3ktVZN7XQAXy5fekAuyRLobOBjUixWfjyDdmAzaEbP95uuo2hPOeFLYWOV2zDlP21O8OwfxiGHcMw7Lgxb1XiOkXXuhb/CEznU/A+qPjopmwaOkqgL3z5ZdES6GPT3dWVy2X//uVo3FhncdiwaD06HerV5ZLh2r1aBd78UZ8UxKy8dL63ICh+6Q8gv+85aZWRtdA1aVKZ53bmmfblSiMevVfXpawM9aUrGhr4CnPZ5tDVk4XORURqn1wuy1Km0rBV3KYB2CL2uxWAb1L2lw5XDb3qnDuGzY/AZhjyslPGj/rTT6t/d+4MTJpUjCyM5HNs1879iKsNWEd53Dj9NMhClx9lttCRQicHmwemqiCttloUHfGgg4ADD7Qvl6zLpe67SutA+zKg4oqkha5sihyjbPIWQb2X5TyxpdANBnDqqmiXewGYG4bhtwBeAdAtCIINVgVD6bZqX+nwrdDZlMelm13ZKGMF3L177fMfNEgvLVdlIQzLMVrZt695GvU+OGJSRh54wG56Za93dOTXjTTHQr/boHv3/OtKHYXORvm49Va585LrCLL6Tte1rzErdA0N7ufQ5UEZ2jxZTCx0F1/M3x+GwIQJ+jLZpCxlKg3ZZQseA/AOgB2CIJgWBMEZQRCcEwTBOatOGQJgIoDxAP4O4DwACMNwFoAbAby/6u+GVfsIQ0wr9F/+0m56WWv7EOUgK6R3EpWAOmWw0NmgMVjodOsLFy47ab9N03OJiXuojtWHhYKXJW3Zgp49i1PoZO+dtXGmcoq+52S6jzxS/Zt15mUVUNmyMGsWMHCg3LllRTQAWDYFqd7aN937SQs2N3SoXpq2qYd3JTWWHIbhiRnHQwDnC449DOBhddH8wrcRMVN54h13G/c2caJ5GoQ+yXeoWzmpuhryys7QofzobPVQYcpQzwod4FeQh8am0DFXtLzmnXzyifhYUQqd7Np2u+4KfPxx9bUu5BFhqnykWUROPdUsbd8pm4VONPhRNgU0iwUL9K6bPp2/37d+ddmps+LmDt8Knu6HxSh6jhVhF5/K54QJ8vL41jDboJ4VOt/el23FxneFDtCfQ6fz7u69V/0a1wwZona+aZnVfUem9YAv39qmm+afZ9nm0K25Jn+/r/LqQgP3fkMKnSQ+dZgBYMkSs+uXLq3+7cMkex8osgI+6ii76X3wgd30ePj2XfjAGmsULYFbbEe5XLTITBaZfbKwEPkAsMkm+unIomuhMx3Qs0FRFjpZXEdjzbK+3HxztF1vPf08fFAIilLo6iHKZVnklMHFt0T9B7uQQkcQnrDnnvrX8lwur7jCTB6dfBnJQABbbtl45tDFqbcGy8X72nZb/Wttu1zedFPl/z/8hmC+qQAAIABJREFUwSytLHRlnTMHGDFC/Tqb727DDe2lJYuu/EXVMSeumqgist5k4SJMfFlIulyWTZFj1JPL5brrFi0BkUUdFTe31FvHTIfkpG/Cb/LoAIm+ix9+qPw/Ywaw1VbyadZTIwgAe+9dtAR2sT2HzgRZl8vdd6/dlxXR1HXnUXcOnS6q95N2fpcu/neu48837zl0cZdBlXd2ww1y6edJEXJkLSzuy7PJoixyyuAievPy5fbTbMzUWdfJHaTQ1V9Hu57glU/dxmTjjc3yVUmvMYxCv/NO0RLYwzTKZR7rxsl+C1kRXfOo7/JU6FQR5cVG6vNuE1XriU8+Ad5/390cOtl0VeZ5Xnttdfo+1I26MmywgX6eZYtyKXpGvsrrCzTVxy5U3DxjjTXUw0ursPba+teaNC5krneLrSiXvLRsnSsi6XJ35ZXmacY55BC76RH+kOwsq3S+RZHX0q5R4cYb04+7nuOVRPV+li2zk44tVPPt39+NHDLEZZ05szg58qZ9+8r/F1ygn07S5ZIF4yibhU53DcJ6YsCAoiVoPJBCJ4nPDW9eaZtc27RpMfMuCHVcLS7OKz+vvQacckrl9+TJlWACtqDBBDuw97dwYW1H5U9/yl0cAGbRVFXDzvfqlX7+hhtWu6U3bw60bcs/t3Xr/F0uVZk9m7+fPZe8rQ++zaHLSlcniEvyeh8UFxUZFi+2k2fS5ZJZcnx4Hipst13REtihdeuiJXCP6hq8PkIKnSR5NaQiVwNbmFSI5D7gns6d9aKK2Syfrix0MqGdXTTYVG7twaLjnnNO9f7rrstfFiB9nTRTkuWmX7/08/fZpzqiYdq3sfvuegpdUQNycdhz2W03O+nJoiv/iBFu6pW0Tq6N+jhPhe6229LlkGXOHHNZAHE/iFnkfVPsTN1yfcekPMu6HJt4jxER1NWRJE+FztdKIC83vsbMyJHAXXfZSSuPZ66SR/Pm2eeQQucvQVBR6IYPL1YWRnJ+pspIsm0Li4oVUHcu4jHHqJ3vAia76yigonxVMbUaid6R63olz35A06Z20rG1LqRoYfHx46Otr32kJK7l/POfga23dpuHKbLz5O65x60cjQHq6liiTx97aflaWZkqdL7eV5yy+rzrzKH785/l0rIhT5GQQmcP02/Ydh0Qn2+8xRbAs8/Kh/S3bd3jWVTSvgMdC50Paxyy78lF1DsVslxgXcNbOJw9E1vlPK82My0f3ajHLvoL8+bpp1mPXHEFMGmS/XQ326z6t0l7LtunKkP/0HeoqyNJVoFu0aJ23wMP6OVTj3PoysI33xQtgR46Fa7ofdpwudRtAFxZ6KZNs59uYyMIzDtUokAbulxyidx5vHI1cqT6NVnnJ68ZM0Z8bt5BUT7/3E46vgRFKXKg5vPPgY02qt0fdyt3FV3TBbYUOlsWOpHLJVMOytIXcSnn/fe7S7tVq+rfJmVR1kJXlnfqM6TQSZJVoJOF8dBDge7d9fJx2VDNnat/rYlcPllsGgtpzzxtVC/vKJeuadIE2HzzoqWoDx5/3Ox6GxbwL76o/C/jxgvIdxbYYtAievRIz0Mmn7XW0nO57N1b/lyXFKVIJZ+tSgfQdmdxvfXS23edetHm0jOq2MonrtCZzrviyeSrB00Rc+iS85htwrM+6yLbDyaFzhxS6CyRbOTOOEM/LV8LNrmu5UPHjurXyK7Hxdh0UzsWOtswmW6/3V6arsttp05u0/cFG/WSjbLVrh1/f5p8ooiNaefx0hs4UHztd9/JPaOHHoq2qhY6l8vZqFBGC52JZVikaB1xBH+/LfK04LpwuTRB5KlEFrp8EAUwU+WDD2rdNwl3UBddElULnW6EKtcWuiRbbCF/LgVF4XPQQXbTa9PGTjppzzztXepa6C6+WP46EUyuyy4zT4vh+nvyYV5THtjonNhyyVLlq6/kzotbcg88UC2PDh2qf2d9f2Gopmi46Bweeqj6Nb4M7KnIwYL5iLA1H9BkDlmRnf+0Z6nrcmlyPw0N6S6XZcHVO827P5XHFIr339fLI4vnn3eTro94UjX7T1pHpH9/vXWOeOQdPERl9KSso002efNNYIMNqvfZGs0ygRcUJb4vGTnT1ruMzx296iqxPEXiugPKIq8R2fhULnjEO4yq6xcGgZzCGh/sy1I0XKNTD/jicqkiR1a523ZbM1l+9rP04zIkZcx7jqWIIubQiVwujz5aXaYiyUPOX/7SfR55lEPZuXYqHHQQ35Jer5BCJ0lagT7rLHsKHWAvhLAMP/wgf27yfmTmJf3859HWh4bJBl261FrkeJPjdbA5RzFrvkmTJnZcLl9+WZyHDmVctmD5crfp+4LvFjob8r37rn56sufH58/Nn28/fdf44nKpMs8nq9yZzhl64onq3zbauxUr/HC5VIEpXKaIBrZ79rSTviwtW8qdV2T/5vzz7adp636KnOcKAD/+aD9NnyGFTpKsAp7sNOq6XAL5hoOePFn+3OT9yFj3mjbNf+5Hp07Ab39rP10W5txV5Z1ndFNbLpdbb10ZgLBhqSyjQueLC1oZ8H1gZ+xY/WtVygGzoI8bp3aND/ii0MUXcc9Ctf3OujYpy6ab8vebYDsibBq25tCdemrl/6OO0pcna+qJL99CFnnImYcFyqeo1SqUzUXXFOqKSKI6h84E2Qn8eaPTcW3SJH/XkT//uXbBYRsk58gw3nnHTvq2o4imzedIG3BQfVcsnbhl2aeOe9ELALdv7zb/vPAlKEpe6FjoZO6PfXthCKyzjp5sRWL7e+raVe489j6Y1URl0C7LQmd6Tyx93fJ9yinA8OHV+1TbzW220csbcKM8tW2rdx0QKbMmgyu+kIdCk0ceOhHbgYpshxwif64p8XTK1N7YgBQ6SXQUOt0CmozitskmeunYRud+VMNzH3+8eh68PPMcGbLV8PzmN3bSAWo7l64sdPHzeWn26aOWVj1a6Gy+1yJpDC6XJuklvzmZoEQq35rp/SXXltJN0/b3pOqqygaOVltNft1Q2wpdUuZk+qJ7YlMQkgwYAOy/f+3+vMqHrW9HNOhpm6ItP7LUi0J3991m1x92WPY5pvfBrMON2WOmEd+6Gnm6XCav22svvXRsw7vHLObMqUz8lzl/yy3V5UriWqFbssR+mjvuGLkv6qJioWvZMnqXEyfKpyWTd7x8MOuDqn+/i/cmuk9buJD5oovsp+kDPo2Y2prvw9CZQ2faYT/gAPnrbbUjtsu7bAdMRwlmZF1jOoeOF9CEx4cfZqfVq1clDR8UOpV04wprWZSuNGSfv+i8PEL2yzznTz81y0N3GhCTLS9FP55nY4QUOkmyRvhUXNqySDZwa6+tl44tWFj25P3IWNNmzYq2CxbYlSmNIKh+hraWAWC88ILd9ADzSkhlwOGUU6JtfIFmG3n76urg4n3F+f779OM679bHpRBE97HWWvJp+FQusub26ljoZOc9MWueyvPgDSSde6789SI5VLE9Av7ll2rnp3kEZF0jwnQOHXOdzZJpww3TjwOVQc0wjLxzZJcW8sFCZ5O0aRM68mYpVw88oJ5mFmuv7b7Ok3kWJm7/Q4fqX8tk69oVuOOO9HNN65VJk6JtfN6cT+1NHpBCJ0meLpfJgm1zkWUdWCclfj9HHqk+GVdmgqotlyzbE8pNKjUZXLgJiCx0bG6DrTl0vA7WgAHAokVq6aTJZMIll9hPM06W8mXiqlw08WUpRPzqV/Lp1bPLZZMmch32+GDfzJny6V97be0+lZFvW8/Hdl2lGq5cR6FzHeVS1rNERua4JbJ5c+Drr+2lnSem8vzf/9mRg/Hkk+nHVeqxJEVGOnbtYnjwwfrXxstA1sCEaXl56y2z6+sBUugk0XG51MUkmpdLpkyp/K9TibAOflrFyZvnoUoQADNmVP82xaRSk8G0UlZZtuDss/nniNKSzTt5Dy7WldHBtYU763mlWfBEYbF96ZzJLJRs01KiCsv7yCPVr+3Wzb4sKpbVMAT+8hfzPPO+3nbZlF2mh+dyKbtWoOs5dAwbwdNMXEtl2WMP4PTTa/NMk8c2WYMfsjLJRtHu0kU/P58pi9xFWMvIQkdwydNCpxLAIk/ibpM6LqXMata6Nf/4CSdoiVVDEFQrYK6f33bbmaeRp4WO/S96LqoRQtncHBvP2ZeyrkJWZ/HNN8XHRKG9fXkO8TIksriqyLrHHmby6PDaa7WBpoCK67EIHZfLOKI2Y9my2gAquhQRAMB22VRxxw+CyvcWBHIWZCDbgpZmoTv0ULk8ZFB5dqblL4333gNOO03u2iCoXTjdhjyiADGy1zPiA8150Lo18PjjdtLq1En9mv9v787j5ijq/IF/KglJuCGHyJmLEBKOAHmICIRLIAe3sBDAJXL8IrKcCoLgCj9gXUQElWVRWFhAbthVI4ZTOcSVQERQjg3EIBIiGAFBbjH1+6OnftPTT1V3VXd1d/XM5/16Pa95pqe7uqanr2/XlSyJim8nH/ciyTR9pePabMmHoiXvTcOAzlLWxVdX5O6rymUo4gdHGXn0eRLxMSaaLR8dufguoUtOc9m2aaWkX/lK/2l33gk89ljvBnRZ0n5bU5U5H9vh9NOLp2HzkMUlr75LxWyCopVW8vvALS7e6c+f/mSX5je/6S+gq+N4iQ/W66OjlbznPpfvnnWOnjLF/NnWW9uvOytPZf5eZaa9/fb+0yyyreK9m9qW8BbNjzJkCDB5sp91Pvpo8TSK/u5qDMUyuLSrL2P/tenMJdT77Ty66KuUK2tnHDeu832RTlGSy1U50HiaVVZp/19WQOeriDy+zbbc0k+aZUpuz7zVHk3TXG5oTeu+8ELgvPP6T19zTaCvLzuPdfHV+YtJkQ4XTEMa+Li4+XhaazNkSihBeNpNdllVC+P7/a232h2377wTbns2m30m/sDHx/f4y1/s5iurKuK8ecAnPuE3zTqUVaKneql2VXTfSNu34+0Ky2ySYtrXqjjnHXUU8N572esueg6o6iEDA7ryddFXKZeuuHjs2Ha1BZ87RXLHrrPHO1PVxSIHn5TAf/xH/+k+S+jiB3LRMVSqUPYFwkdAV0V99DK2Q7w9ZRmKVCXx0S7NxPac9NRT5s9c2vzUwWbdUpYX0MVLMF3XEUIJnRCdY0Vus41+vniHEvHrUdVtVJJVLn0YNsx/MOQjEHDdtmUFdI895pauL7b583Xv5bL9qggCVqywu27X0Y42jzras9kEdKE8kPSBAZ0l3c54yinAf/5n9L/uIGtalcsddug/bffd2//HL+QDBhQP6pJ8VkNSB/Iee2TX1dct7yKEG7NkHj78EHjkkfT0TesssyfCLGWeXA8+uJx0i5TQmcS3Q97zwc4728232WZ2+Wiysm4m4h0y2LahU9eGUNrQ2YwVufbaftdZRJ5eLtMUuVYn/fznwKmntocx0K0ri+oN2ldVQhNfD2ht0q9q+bXWArbaqth6swhRzTFw3XXltqOsQt0ldDbHUDd1nMKAzlKdwxbUKZ6XeAcOL7+cP03TtpwwIX+acUK0b0Bcgzm1fBE/+pH7Mr4b7555Zud73Xd66SX9sitW6EuFm3riU9/929+ud/15l8m7b4wbB3z/+/mWdRHKTURaPo47rlh6v/hFvvXr2gwWfRiWtc4iy+uqeKUtE39olOTrfB5fr5TAW2/5T9e12p5pu2+1VTTMUJHfRXUe5hrQ+eqpsypltDc8/vj07vHTesN1ub5VVUJny7Ujs7iqqlxmjVdaV5VLm+G0miKg0CFs6mC/7rr+0wC/AV2VJ9p4qYVuvfETV/wmP63nPhN1QJtOnKec4i9o2HZb4KabOqsTlSW53fLcyPguobNJ3zSgb7eV0PlOM9nhzh575F+/qTq1j4Aua92+1H1jaMNlvDadsWPzLacb7sRnWzCbG8tNNzWP0ZT87fKMHWliO6SAi7wdPWXZc0/g3HP9pWfr8MOBxYs7p6kO1lwDuiLbw+e2vOMO4Cc/KbcNXVbpt8l//Zfb+dS0nmQavnrotll/2r1mnnNK2vYaM8Y9PVPaBxyQPx8+1t8LGNBZUgdKvJvkeM9YPqtcVrkTxk+auvXGO0Ipmi/1tMQ0PpltF9RZVD5nz843BlkdVS7L6OVS2Xlnt+/097/XV0qclc+ZM8tL21a8mt2yZcAXv5g/LVOnI0UDuvvv759OGtM6bPbtJlw0fd/o6CSPmcGDgeeeM6dd1XnjoouAHXe0S8/0MMdHFeCynHUWcNBB+ZdX1+p4N/4mqhqzCrZOPNG9Rka8TfdGG/XvUO3996PXstvOl3Xc7rWX3VAPLiV0hx4KjBjRfm+zn8apzn4GDjTfE+QtoXvrLeDqq9Pnv/zyqDdoV7qgvsqALut7uRgwIPod8+SD7ATSf2L4dPX241356nbGvBfskC6YafXsXQ9AFdDphnhQXLfZEUdEJ9Qf/jB/vpLqWL7M33zlld3yZGqMXSbbG9x//mfgrrvqrf4ZfyCx7rrpnYoA9VS5VDeepot/cvvV2ZubL2l5LXqjY7MdkvPMmQN88pP6+YTwUxJuky9VSmgzr2k7ZT340xk3rtwONVQ+zj+/831eNr/HD38IPPlku41cnmrc8Y5n0qrCu1YFMz08MHHZXkXPYXnEl7/xxs7P0n6rrPX66BUynoapvWTcsceaP3v6aXM7Ztu8qqrSvgM63/dCtuvaYANg6dJi6+5FAYUOYVMnENMBpttx8w43oNLaaCPgnnvypeG6LgBYf/30eYt2re/75nDoUODaa4FzzvG7HtflQ7jpTfstXEuLu63K5S9/6Tft5NhbRduCzJmTvkye84haXrdulyf/IezbPhR9AKC2Q1pblfi2mjYt6j1RR51Hqyqhc3kg4LNUqGh1rSx1tENcay37zobyrk/9BmltwXRshhe4/HLg97+3y0fd8jygEQLYddd863M5Hn22eZ80ST999Gj7NFS7UlW6G4q8+5iPsX17EQM6S1k9a+kCurwHvbpI77BDdvscnzbYAJg/v3Na2lPqvDck8XSOPjp/ms8/n2/9WWyfipmqOfi6UD7xhP28WQGdy1NJUwldUztFyTuOkkm86g9QPKDLaicRUhs63UMf23Uk2wpVydeT6+HD3dLQlZoIASxaBLzyiltauirpvh9e2fQQ6Hp+DF3V+YzfqJ90UrXrXn99YNSo6H/bEuhtt7WrQumqSEma6Xg+7rioGmyR9Sb993/3n2ZzDFx8sdt6klRJ7u23d07PW6K2aJG+xDy5zK9/3e5UregYvnlL6CgfBnSWXAO6IqrcsZMn9bReIYvmy+eTaaA9wG3RqqBJWcurJ6eXXmqXXlZjYJPJk81P+ZPSStV++tPwq1zqji/fPX/6+k7JbV00Xd1T1TIDOpf8+gzife5Tv/0tsGRJeeknxWtNmLhUS3z44fTPp0/vP+1730tfZ5Yiv6Vr9dMqhJIPV/GB2U1taMuS5/5lt92AI4/0n5ci3dibll1ttfwPI03z6K7fuuPunXeAL3wBWGed6P2++2av00ayE668Vcs32QTo6+s/XfdQZ/r0KK34cCW20votYEBXLgZ0lrICulBvfJKSVYayLtRllNCVrWg3tLZPDuOdY9QtLaCbNUv/nUzjsj3/vH4bVvF7xxuB66oaxvPw2mtuaZd1XGXdVGd9rgsSqi6hKzKYvO/teuCB2fNsvnlnlb6sfPoqobvpJvP8urbBut/WJghLlgIDnW22laqql+cJ6Mo+X/ja75Yt85OOLz6+V7zjlaLrKet3LFKzwbVTFNd5FFPtCV0aq6wCfPObdp27PfdcVGKWxpSO63Y57bT09fg+f8dreeVNO9R7y9AxoLOUFdAlb4CLHCSmqnw+jB9vt27Te+Wss8rJn48bL1MvmnnTq0LRdaYFdDffrE8//uQvuV/4rqZoK96GJ28b1Kq5lJI8/TTw4IOd05K/zY47pgd006b1T9cU3Ory5rKvrbuu/bx/+pOftg9lHH++OkVJKzHXnXc237z/tC99yT0vgL5Nle/OlEzj7U2c6J5WWudXIfnrX6PX0G4ii+THpmTF9jh74438+Siy/rxt6PKsKy3NMowfH5WYpclTHVfXREfXMVOZ4tcn2/vJlVZiCZ0PDOgsZQV0WR1JfPe7/aftvru+iqPvqolFlFWVtEiJQBbdjZXL8AW+TyxVnKjStptpION4oHDHHX7y8bWv5VtOlczFb1CzSqZct2sIF4xJk4CdduqclrwpT/5eycB2vfWAz32u/X6NNcw3cEW/s81YYmodI0eWW2p9zz3m/cv01Fwp+pDHxsiRUYc5e+0F/Pu/m+fLeqhmUrT6rE2auoBu1VU7j0XbIPKUU/Lny4av47nM80LRNkhlsv3ekyfXs/6849BlzZ/n905ugyruzVR7ZZcmJVtv3X9a1vFaRVX1rHUdeWR912fdWKFNxYDOkmsvl0nJnvEA89PeMkvosg6wMtvXlHXAVl1Cp763KfAue/wgnaxunLMCupEjgdNPL56PPHXugaghdvKhR1YJXV0XANf9/uWX0z9PnlOSv5cusM1TVS5tms13sul1T7UfKcMeewBf/rL7chMnRu1bdP75n83LZVUz3GGH/vMPGRI9HFHdkOsCYpvf7s037ZarYoibd97JV+UyrT22D00I6OLXovg9wOc+V05HI4pNSVXd7SLVOk0P7vJUuSzreIh3UCZENBSQSZ1VjT/+8f7T6gzobBXdZkXaoq61VrF1h4QBnaWsErokm0DJlFaZJXRp+XK90QsloEvSnex1VZ9MbAO6tOoDVVFP5PIEdMkTva7djqu8v/Fmm3WWOgHZbehclbX/ZQUxWaVWumMyPi0r4NOlkTU9D1M39PFOHpI9spWVlyTTfrFkSbRfm0rot9hCP/3RR7PPjckHELp5/umf+k+zuelU40plpZ+1TeO9kvpoBtCNyvxuy5e3/7/kkvb/3/0u8JOfpOen7HOd6/eeObPzvWnsNFd5HpIXaUP35z/rp7ts71VWsZ83rzzndN8diRXlUmBgU4PL5NVX3ebvVgzoLJXVy2XajXYVxfrHHNOZl2R+0oIT1/zF5zdtz7La0JkunjppY03ZrL9IqaerQw6JXvMEdPGAKbQ2BkDUJiuNEMB3vmOfXlm/w4QJ6Z9nlRgnq+BJmR7QDRtm/3TddzW95D6w4YbAuee237s8Kf385/XTXfJnW21r9931n5v26dGjs9edvHnKOsbS5kuybfuYFhzefnt7DEafqigVtOG6H195pZ90XMQD8xCC4iJ5mD8f+OpX2+9dmjGk5cW1+mTeZbLYXt+y5lPnhbJqCrkGdFmdtMTvHfK0lU1jey+UvOblkewNVKWbtt5uE8ipOXyuO0ayRzJdNTxTWqqajmtgYSO5zrFj2//rTlSrr+5/3VK2B8JMXhR8BA26Hhptu/8HgGuuSf88uS+UNQ6dLu0kta6iJXSmeVxlpZEcdzBNfN80pb/XXvbp+eK6j2Zd2OfMAe6/v/1+4MD0gO3CCzunpT0ttg3orrwyX7WVww7rf27beGO7ZX10epPVNkbt42k3EqbpWUGzzc3Khx9mL+eSr6QBA8w31gceqK8mu+mmbnlJzveP/2i3TF5nn+3WGY+t+MPLqmRdS3yKP4Qoo4QO6KyiXLS9bNZ5sawSOl2pOaA/5vLcj6jzX1lNL1wf4GWV2qmB5suQ9+G2ab7Pfta8jMu4vXGq+uxhh+VbPiQM6Cy5lNBdfXX/i2z8IhpfRldUPGNGNObQRRfly6uLrAMurX57kSqXKqBL1l9Oq5tuky5gPtlfcIFdelmDB+v2hYceMuenzKeGttVz8pzoXfNiw6Wqii7P8XYortu1rqd0WR0mCQHsskv7/eqrd+Y1Wf0u+cT15pvT07ZxzDHZ1VayBkBXQuqdNG9pUtZvZrsuXU+PPgM6ITq7CbcRryKr8vKDHwDHH5++HiV+4+PzgZ/y+c/rn7an5QkA3n1XP98XvlA8T3l9+tPuy+Q5T/3973bDfZjWY7vOQYPagWPRB86//nX652nH7rbb6qfbfI/ddsueJ03WOm66KSodtynlz7OetPUPGNC/KmwoJepZbKpcpn33TTeNOmJyLWVU19cyzmVVa8hPXT81EGy8TnxcnpMjYK6SM3du9fW0daU0ppt+KfPf4Kdtn+OOy5dmnOkEFr+R8W3atHYbNNvfPx7km/KctY3VcjZBg2lZ0+ehiB8HTclzXJ7gIC2gS34ebyeVNl8evsZvK0vWuvLmxVcJnY7NDZZLCd20aW5tSHTr339/4NJL7dOIL1dU8uZcCLttlNzepoeBeR4SlsF1X3Q59gYMcO/J0TY/yXxkdRDnS1r+VNf4yerqNt/JdD72VeVyrbXcg2sd9V1czjO6e7g6A7q8VS5N21jX6UvcxRdHg6K7UPtQUwLfNF3wFarxzW9Grz7bJJiquZV5Q5R2gLk+bXe9UY2XJpm+o201hauu6p8uEFUH+tSn3PKVVLRaQJ4LpWuVsORyeQK6rGA+j6w07rrLPU0V5H/iE/0/c7npqSsAzNOWIp5XXW+BRfbR+LSTT86XJ9dpadN90VW1zrpIm/afFSvcH9IVPW/Y5MuUlsu5OO2hiGmYCtvvlmfMq2SnQrYBnW8hDBPki2kcUdM+7XLt97Wd1JAOUro1SQHa+4zParS2gf8zz/hbZx5p20XXyZPLsXTUUe75SeMS0KW9V84+232dWdQ4lH/5i9tyIWJAZ0mVVOnaRCS5XNjV0/f4k4c6n3An36eNo6NOFFlVFHVpF70omE48111nrtvvsl1feMH8WdYYejbrWbCg833eG5jkDZ1pjCtd+q6lXT5O9s8/777MllsCb78NPPJI53QhgFGj7NOpK6DTDfaaJZ7XeEcEus+zntimsblApinyQMrH7xE/FvNUbzQdyzZd7uctodPNl7wxzXoSrahj2KZnXfVddWNVKabOY2y/20EHmT8zlSTr2iCXWcLUC3yE9ZPIAAAgAElEQVSMuzh3rn76OedEr8cea5+Wrp2naic5YoS+LXTa77vWWtEDnNNOs1t/1j4waFBUgydZ7a7OfSfPgzFdu3Pbe4u5c4EvftFuXlu2x+izz9rlM14VW52j+/ryrVNR9/ZpNV2aggGdJRXYjBun/7zozckrrxRb3pZLPt95x9wluxDRUAC33w78x3/4yVvZXJ5629R/V/vESSdFryqoSm7jZMnS738PTJ3aOd+kSfp1PPhgdl7j6zaNq5VV5dI0T1wZHRXY0vXUJYT+KfI225SbF9eLvOqJ07YKtRDAz37Wfq9rT+SrhM7lfKCrZq1bXt3wJdneZJq6Fc+jyIMSHyV0NscdAHzlK9HrGmtEVR8vv9w+n4D9QzUA2Gor82dFq4qltcs1BcnJGynfAV3T+H7QYUpbt54118xO+6ijovR33RVYujR93n32iV51HW+MGgWcfz7w+OPZedVJdh5VhKo5su++7Wkrr9zZNr5qvmo6JM838+dHfTQkDR/u/5iyfej1y1+6r1tdZ4oOfK+CeFa57CGqIXjaE0jFtGOecordfGVeqJJdrKcdcGk3oOqCceCB7Ztt3cV8xx31y/v8jmWdhEwDQqvvPmJE9H+yHUkyP7NmRfOpG3Ndb4KmkpK0my8gvDZ0Zey7rmnqOiDKk44vqjqRSyB4xx3pnyfHhDLJ6v4+a5vk+TzecU3c66+np6WonhltBinPKvXPyv+sWfkfANjcrNjmSf1OAwdGnZPY3FinSV5rsvKkmHp6s71W5SktTj7Msq1yWWXnO8lSgDzKPv+49jqpOw/MmgXceSewbJl7Gjq33AIsWgSsvbb+87POigJ922E68spKSz2oV/N9/OPAG29kX3/L5Ov+MHmczJxpLn0tm+meCuh8mORShTy5PVyuA/HqvgzoelCRk0yybdcJJ7T/j5+Myzrx33UX8O1vd07zsS6VRjygO+WUqHexU09tTyt6k1KU63c1PVF2GUPv7bfbNyzqBlV34jBd8LIkS+hcLgJ1dDCi60bdJG+wEdqJuYxtG2/4XaTKZRbXjhbS2C6vfr9//Ve39HXHX9a+sOaawK9+pf/MRwmd63y+9hXb8e+K5rmMIVtsS+iqHET5/vuBF18slkbZ59gzz3Rbl+kBxIwZUW0MH/v8yisDm2xin068dN/nedy1F+ivf92up9U6uOxHZ54ZVlD69tvmeU3NRVzp2lKnybp3apLAbn3CJ0TUTfh99/Wfrvs/btYs4D//s/0+fnObp0dL1/GApk/v/xTP5QmraT71f3zaxRe3O5JR4sFdEclGyb7bUmSlpwLzZDVAlX78QhSf56GHoiEt1IXCxwnkD3+IXm+9NT1Nm/ZFafmxHU8pnoau+2AfFxebqjh5litbHe0xipbAZSkzeLbZXqNHR6+mzjiK5C/rnO6zGqbvfVPXOUIRtvtRWpCl69TIlFaVx6pNRy6rrQZstFH5eYlzPV/ErzU2y7o+sMhKo8h8unuIKveB5Ppttt9VVwH33ltenkyBhst2Oe+8eq97WXmPD7Hgmk/TbxQP6A4+2Ly86gBKd9/WVFZfQQgxQwixSAixWAhxhubzS4QQT7T+nhNC/CX22d9jn83zmfkqxXeeQw5J70kxrZQkPjBifL74hdB2x54zB5gyxW5ek+QFWI0P50J3MtbxMdDmBhu4jzPi21VXRdVIkiWOWZ2ijBoFHHmk37w8+2z0qur6m9Zt6r1Oyfrt5sxxy5dPppJQU57LDuhcb7SGDo3aW37/+9WsLy4reHDZJrp86Drj8HWTZ2Py5OhY/NKX8lW59Mn2hkA3n7p5s62WmmbOHOAzn7Gb11epq8014KKLOttLbbcdcPjhwNFH90+zqpurIUPaDwXqbCMcl7YNiw694/t4KPP4qiMQcQnojjrK3ImQD6Z2sS7bpej5vajk+pPHtalnUZu8mOaJt9VOq1q6887Ra1XDcFQh8ysIIQYCuAzATACTABwqhOio9S6lPEVKuZWUcisAlwL479jH76nPpJT7ouF81WtOyhPQCQGceGKx9Q4b1vnephdPwP7JiqlaR166RthVX6SGDNFXI6mjBMa2YxNdpyI2yxXhs7qfS/qhnZgHDACefNKu/W0eRarwJbeVTe+OacunKesGbZNNOsfhuvji9me+9gWbUjXbdkBp50QfpUBTplR/TrQJ6AYP7uxhc/hw4Prr+/eAWGUJXXw9rm3QynL22dE4a7ox/mzz6FpClzetIr9TVnXuImmn9X6ctq66a3HY8B3QFR3myUW8bdx++7V71dx888686va5+fP1aaadh9O+vxra49Ofjl7Luj5XyeZyNxXAYinlEinlhwBuBrBfyvyHArjJR+ZCknWCjN8wuwRkqoMMlwbeVQw4nuWQQ9r/q+/7/vvpy5i2y/XXRw2x8yqzLcWll0Y34zZchi1wmS+NbUCX1a25r5sonxfE3/0u3zrqrHJ5xBHF00jms0hbDtcSum98o/O9qVqx6b0PvkqNfKSVd72Kbamh67nDNR8mpl6bbdM855zoSfcBB0TvfZ2L6wjoQjF2bFTjQtfmvOxjI76/qto6abV2fG2/Kqohu6w/5KEubEuSdcPdpCnjQWhalcsf/rA9PMuwYdm/t6kjsORy//Iv2fMA7b4NNt88+r3ThuhqCpufcH0AL8XeL21N60cIMQrAGACxTrcxVAixUAjxiBBC88zp/y87tzXfwuXLl1tkqx6mnS5vVQjVENSl8wHVU2VyvmuuiUrOTD1L+pSWxxEj9NNNJ8nDD48aYuflu/Fy/Lsdf7z9gX7bbcAuu+jH3CmLbUBn00lCiDc3QHaVywsv7Py87M4SpIxKGnTjMJVRBWfXXfMvm3WjlNx/Ro7sfJ/11NKlmmPZ+5cuKKqyhM6WrhZEFQGdalsSb2NiO46XyZgxwAMPROOC+VJmlctkO77ktkp2ge5zsGEfTQ5s2exHWcGdutlOexhY5sPLIsdCctms8UqTJXS685ppaKGqJcfKM7EdgsTnuScpmaZq+pG8Zvtcd7LWmSl9m7E7m8bmtKnb1KbnF7MB3C6ljI84tJGUsg/AYQC+JYTQPhOUUl4hpeyTUvaNTN5VBMDliY3LSS7PjYKpaHqNNaIBq/M21BVC/z2vvDK95CFtrLSs7+LjSVgo7QJmzIh6Q7O9GSnju5tO9lWV0FVJ5fe00zqrqpm2v8/v9/jj+rHCqnjKWXTZ+BN3lyqZoe8fquOfkErodNM++KD/2Gu6DhDiPZn68N570Ws8oMxqW6v4qJ5nm2ZdVS6B/m2Fs6qqu6iy18S8VS51y5VV5VKXTnxdPs+lt99ut/60gG6nnfzlp0yuv4lLQOfalj6Z5o9/HL0mgy4ps6tcFqH7blUOe1IVm0NmKYB4Z+MbADCNUjIbieqWUsplrdclAB4AsHX/xZojzwnMdxVJU33vFSuiC5DvtgDHHANce6358xdesEunrIt06DeaJrb5/tGPzJ/ZNjK2Ceh8cE0nz/hOrqVOVSqzkbxJcnssWWL+DOgsoUluK9cLaZGOSHwft2pA8ngFjypL6HTz6KrNbb65eeDweBrz5kVjYfmiqmrluVmyDfyTaesGlNalqXrrVdPrOoaT+fd50xfydUqXN9sxTstaf9mlNrp1pa0z5N/Pte1zXmm9XS9YALz6ql06uu0d/99mn3M5j+nOJ/FmQ93C5rT5GIDxQogxQojBiIK2fr1VCiEmAFgbwC9j09YWQgxp/T8CwA4Ankku223iO+YTT7i3BXIpoYsr+lQj2duYrXfeyZ7nE59oBxtZT4VfeAF45ZV8efHBx4n7sMM6x9QpIm2A5WReTTdCrr0R+nwynSbryWkaU/7rbENnWx2mTGPGtP93KYGzcfPNne9DbGuiAjug2gcVunm22SZqK5KcL1lao3tKPnhwvqqMpgd6Ku0VK6JxL10epmRVFzSVbGRVdVM23LCd7zJL6OqsZl5mddok03FpuoHeZ5+ok4p4VTjVvt/U26JLfrLyqNt/6vxt8oxpWRab7fDkk8BTT+VL31eVy+HD2/uMknWPa9pPXapD5j03J6tXd4PMXVRK+RGA4wHcDeBZALdKKZ8WQpwrhIj3WnkogJul7PiJJgJYKIR4EsD9AC6QUjYyoMtblWTy5HZddJ1vfQuYOrXz4pr3Cfdf/2qfR52xY/Mtl/Y0Jf4kZv/9o04XvvGN9O84enR6EGNaR0huuCHqraxstgFd1pPm5E2UuuGcNKnc4Dp5AfAh74OSMtdt4wtf8JcPRZefO++MxoicOtWthG7DDaMOMPIOAJu3KlCR9ZR5E2YbHOy3X3Zb1yra0MUDutdfBx57LD0dU2l/Wtq+htio6pyeNtCxb6H1vhvfxqusEj14iAfgJ54YjZt7zDF2afjKi4+0XZe1qXLp4/c7+2x9m3zV42JeI0Z09jwO2B+Lqpv/or9l0d8wuT9mKaMZVNNZ7aJSyvlSyk2klOOklP/SmvZVKeW82DznSCnPSCz3P1LKLaSUk1uvV/nNfvV87hhCRF1ML1jQefG0LaFLzuej29Wy2rSpajSnnhp1GuLzyb7vg7Wqg9/2AqHys+222Wm4lNDp1qGoUq5Ro8oNrn1ftE1V2Yr68pfbY3uV1aZk++3zpZE2v25/mD49Ch4XLHBbz0UX9Z+Wp8rlAw9EbU3LUkZAl/cpsO28Ps+HprRM1SJN/vhH+3Xm2e/T8lFXhwVlljiXdV3ZZRf7dbkEzYMGRePmph1DRb5TvCO5Kkvo8gYePvJzzjn6XrOr7DAnSRUEvPtusXRcqqWbBk1XXnyx2HrzzNMNAntmFK6QngbE01f5OuKIMKp7mVT5pLwppk6NXr/ylfxp2AZ0umpYaSUMVT1N9h3Q6XpLveyy4uuaPLk9Xo1rnmypUtQibWCTVfRcb1622ML8mXroFD8X5rkB3nln/U1oGao4N6gHHpdckm/5k05yK6GzrcaY5FqKpmv/l1VdXkrglluAZyzq4bg+iCDguef6T9tuu/7TfI5DV0Yat94KnHlmejp1XNd7cZ9UD29dHtzq2PxeqllPVhs5l4CO2rp0Fy2P7xK6IutwycvixW5pbryxfdqmNNKm2eR94sT8edDZd1+7QTSrupCotk62bVlsSkNMF52sGzHT71OktGjKlP6fJ79DGRfJuXM73xd92r/zzsCsWXbzFtl39t47usn5znfyNdi+/37gt78tlp/11vNbSuE6wK8Ppqf8l1zSOei4C11e1XpUoOsydE08PdeA7oQT7NejW2fe3/enPzW304l3oHHwwenn7uuui16TbV1VNW8pw+kUxaduDAjydhrzD//QeV4OpcqlUqSzp7KsumpUVT6Laz5Vlcuiw/3Y/IZqHWqdfX3Rw1Jd7Y8sIbbfrlsXnmLKUdawBXnkWc52AFn1PV2e1hx8sPmzvIEBADz8cP9OGNLWkWX11YH77vOXXlFnnBG1W9h33/T5VKP0bbbp/5ltCV2WMr7z976XPU+ei4iqnmLqYnvCBP1Nfd7v+MAD9qXfRbbjwIHRoKjDhwOnn+6+/C679A8qyn4AlXXjo6tNUDZTAH/yycApp+RLs8xq3a5tx7K2Y1aHGHl/h912i9pRpqVtQ43TmczHww9HVdJWXbX+m+cyVPmdqiqhiwd0edvgx/NS1rAFtutPO0aKPOT2YYcdymlnrZop7LVXsXRcAjpVQrfqqlHHgbrmJEXW26sY0DmqYudR4wVl5UGI4hdpH9RNZNoJPc/JedgwfSlPku/fpKoLyaBBUYcJWfkfNw549NGo5CbJdmBxIGrcbuoBMb4v+WLTqUKebb1gAfB//6/902HXgG7TTdM/r2JcpmSgm9a+IW2dZZ+vss47edZfNM9VnQtd1pO8WTKVCJT5eyXbr5ShyLbfbLN2R1JVtp+Kcyll9b3uKowY0f7fR37i56kiQzzUXeXSJqCbPTt6rbqkteztsN120ffdZBN/aaoHoMnt+Oab0WuVnRH1ki4cWq8cVZbQqQFybZZTPRvp6tFXJXkSrPrk7DvtrDFr6mB6guVSQnfllf7yY1LG75w89rbcUt9TWNImm0RtTnRtgdJ87GPA//5v/+k2D098ff9kOi49DqalU0TRErqqbtDKCOiK5v2WWzp7bktul6xOAnzkxbVTlDxp+woWH3gg33IrrZR9/Uxz0EFR1U+b9rKuqqhibFrXWWdFJfhbbeU3P/GArkh6un3T1/ayCcBsArqiNT2qVvVDfpvtoh6YfPhhuXnpVQzoHJV5wVVcArq+vmicu3jJCxA9iYuPx2RLDT47bZr7snlOgmU84S+qCW0dxo2LfnfbNnQ2dE9Ym3Lx0nn4YeBrX4tKQYHi38VXW4Mq5f3OV15pVz056/iN74+hlJzNmdNZUlHWeuKSAXnyd1FtDc86q1ie0pRZQueyn5V5Til67h40CDjgAD95SariXHrxxcCPf9x/3zz/fHN+irQx9v0Ay1dAF182T0CnU+YDkW5g8yBftZMt8tBFSfsdli/v/Pz++6OxkLtdA25dw1DlU19142i73Nix/actWwZccIF7njbeGFi0SH8BKKJJJXRNCGKeegp4661iAV1y2UmTiufL1pAh5Q9ePnJk1BGG6w2L6ff/6KPoNa1qUVkldHnnzZufY47p337VtoTOVlbe4mm7tB3JytM117g3wk/L67Jldus1pSdEeyiXww93y5dOWW3o0uRJO08+7ror/fOQH8ZVkbdTTgF+9jO3Zeo4Z5mWLaOETp23Fd3vYKoCnTZPVVSNIdt+EOpis33UtTj5m+Qxe3ZUc+lLX+r/2YgR0fVfUT2Kd7uAT39hqqKEzjb9rHF84tUrXGyyiVspRJFtkrVs2dt76dL+00K+KVCGDo3qqSe/e5FtEe8J84038qVhu/7bbvNbj77IfvLTnwILF7bfjx6tn++dd6LXtEC0jot+2qC0deQnvs60c9Spp+ZLM0uZVQp161GdfNgMhlunMksY1DHzsY9lz1sksJw+Pf3zvD2AViG0/SOktudlVrlMdvCm6/xDrSut6rCap+oaGttuC9xxh30PvXUFnjYP/NTDUB8B3fDhUd8Cput1L2rArWv3ynvg2V4QTeknx6oqKq0qT9Eqly7rd/Xqq8D66/tLrw4+g8/491bbxfe2+Nznolddj51FqPTSbpri3yVeyrbjjp2d72y+uX75nXeOXo85xm4dRejS+eUvgRtv7D89rUS/jDZ0LuPQnXGG+bN11wV2371z2g476OetsprT/vv3n6bbjqp6+o03Ajvt1PlEOEsdbQt32il6zfugL83cucDVV0fd0dfpggvSq3PVUV1OlUr4vu4W5btNmK8qkkqRa9thh0Wv8+YBjzzS+dlKK/VvoqLWr6pGv/9+/zRXXjkqLbvwwvz5ymuvvezHJ62rSqjNOU0dCz6qXFJ/DOgs2Rwk6oIZSuN/dULMqkr385/nb4Su4/PkXOa2ND1NDrmELlkP3GcJXRU3mXvvHe23ukC6iOuuA37xC/vhNnbbrf2/7TYcNy7KuynoKNt22wGHHuq2TNn7ctY5aLfdgK23tl/eFCyXXZUvz/KqpHb6dODBB92e3Bd5yu9SVTXugAOih1i77pp/3SYrrwwceWTxMR+LEqJYb4tleOed4p1A3Hln9KeTd3/3dY63aWubxXeVy3POiZok7LOPvgQnuc3UutQQQroqeoMGRW2zTj45f756HQO6cgV26gufz/Yqrg13k8vZltAln+wkl9txR/t1p6mi978q0g65hC75tLGItEBm002jTldmzvS3vrxsblhWXRXYfvv0eeooFckrhKfmedNy2c5qTEHF9FtXGdCV2a2/Eu9JN2sb7bpr1KjfVlp6NlUiy1Z0n5wyJTo31bHuPHwEuTNmuM1f1Th0QLtkukh6vqtcDhhgP3Zo3E47RU0BTNXqQ37Yq4RQ5XK99aKAOrm9fLaho/4asHuGweUEmeeAuuQSu/ni7aZcepgrU19f1Jj/mmui97o2ND5LkpJ6KaArU/wCOGEC8NprwOc/X19+qtLNv3fZ382l2rduXlWaEq+OVrTzlSYEdOPH2897772dJTx5BxYPTd583nUX8OSTfvPSNPGq5S5VfXVCeHhUtIROtWMtun6g/M66ulV8G953H3Dttf2DalWDJoQHS92IAZ0jmxK6PE+y4zt42oXu6qvzpV+mQYOA66+PgoAk9V2SwaXPmw4GdG1F8r7RRp3pDBvmnl7oN5N33JE9Twi/v0sefNYacF2PzTh0aXkwnR9s1uNj3jKWt+EyftfAgZ2lPMl2h8oee0SvpjagobDZJ9Nu0EeM6DxX9aK3347azl57bf4qgL7a0KWNP6vz6KPmvGRNM1m8GHj6afv5i6yrW0ye7F7ymybZBv+II/rPc8ABwA03FBue5ec/7+zEzNaBB0Y1j7oZAzpLVVZhSHPAAcVL6NZbL3o9+GD39du0/YhvB5cBc3VCDxDq5qOai89003pcDIH6zmnVAkMcWD6vum9UhKj+3NmEgK6ItdfWT58/H3jooeyqx3Xbc0/gkEOASy81z3PssdXlp4mEiM5lRxyRv82gr2PO9Rq/7bZ2eXHJ3zrruA27s/fene+bUJXSVdZ57IknzO0y87D5vYSIOqxJVrV3kezEzNbttwPPPpt/vU3QhbtxucoqoYuzrcaUt5fLNdeMXk86KX15nQULogGbddSFRVfa2KQql71izhz/aV5/vf80fQr9Zj2PqtquFq0KWYTreopU6amiymWcr99o0CBg2jQ/aZVpyJBojENdZxVK3ef0Cy8EfvWrevNQNl/b2LWEzlaZ+8AllwAvv9y+Z+nGgK5qZf5eaqxPSsfd2FKVT5mzbtBU/XnbErqsgWZdTJli7uVvnXWAq64CfvKT9rQXX4xe33qrc15VpcZHffWi233EiOJ5CIXLtkirtpR3mzblxGvTccfeewNLllSTn6QQ2rXY8FXlMushlWuVy0WL9GNM2i6f5oQT6u/Nsdv95jf1rv+00/wPrVKlstv8p6VXZNmqHhANGhTVVLKt8t0k6oFUN30nNUQMpWMvl46qKKHLWubcc6MTkq7qgk36n/1s1Fvi2LHu689y1FGd7999N3pNXhxPOCHq6ci2/v/gweaun4tekLbYwq0XuZD4PmlvvHHUHqHuJ+RlcbnRGTYM/cYr8uWZZ6Iu5MtWdgldVnWvIufC+G/lUmq20kpRJyt5x/3K2ke+853oz9WBB/p9QLDBBv7SCs2DD0ava64JvPlmsbTU2GJAd5bQF+WrDZ3vPHz848XTzVJW6WKd6gpSu2kbNlUXxfDlCqUNnRDRuE4/+EG76qSJ6YD+3Oei72M7ZlcRarsl60wPHgycfnp2XWq1Tct8QtPki/x55/lNTwXkefflppzUbUroyjRxIrDLLubPQ3hqnmXEiOy2TkIAa6wR/W/b1uf11/tPczlG06ry2SiryuXttwOPP+4vvaYca3lccEH0Ont28bROPbV4Gt3Id42iIgGEroSujAfOSd1cQlf1+aGbz0dN0UW7cTVsG34WSctXgBHCAebrCZgQ0Q3k0UfrP/PhlluA//kfP2lVJd6Bx2qrAX/8o590Q9h3qlL2cVi2utrQ3X03MGpUen6EAG66KWqTtOWWdus57rjoNV612+W3+OIX7efV8RFEVKEp+2ceQ4ZErz6+Y3wc1l46r2XxtS3Ug+XNNvObF5sO2Io64wzz+puqrlLHbtqGTcUqlx65Vrk0tcPwdaEO4amTz5PL8uX66b6qjIwcCXzyk8XSqsOMGdHYTKor6zjdUBJpiv5eZZzUfd64NuUm2LWHNx/puLIJhIWIqk6ddlr6vPEn9Lvv3v93cik1y9vrHwD87W/V3EjGNWWfrBJvDsun7g9cxkTUGT8e+NnPgO22y5536tT0z+O/e5Hj2NbXvhb9dZPtt496czT1hkvdiwGdpTKqXJbdsD6Ei6KvgK7MUgj1NDiE7ZVHvC1NfDuNHh0Fei66sU1Bt0trK+bzoY5tT7V5BwdOU3bQ84c/RG0aq7iJTOr2gO766/MP/Fz2tqnj966CzXZbc03gK18BDjqo+Pp23TV7nmefjcYn09F14Natv03ZLrsMOPHE9vBUVeE9Q/14yDjy2SmKie8SujpvGJoQIJx/fjR+Wl9f3TnJZ8MNo9czz+ycPnWqe3uiEG8u774b+Md/rG59IeyrTWhD5yOgsz0/lL1fbrhh+ziqmut3C2H/dHH44e7LVPUdQ6jFUhch/LfBTpM2qLP6vT/6qD2NAV0+Q4bYV2/3qYxjdqutgFmz/KfbrXjIWHIpoev2gW1d+GxDl+cznV/8onMYhW23BR54IFe2gqCqWSZLfPPsRyEG4K+84j/NkL5fmcpoQ5e1j+Qpocuq5vjjH9ulQ92hqm7smxbQnXNO1EN1t3rvvfb/DOiapYxr6vXXF2ub2Wt4yDiyCSxCC8jqvHkNscrl9tsXy0to4uPOFN33jjgC+Ld/6z/8hK3QA6XQjk2TskroLrvMT7q6tJU8Ad2//ivw8MPm0hybIR6eeKJdfbpJmrJPVkntN2X1OLrGGtFDveHDy0m/LGef7b7M8cf7z4dv6mFk/Fioui0rUdMxoLPks4Tu/vuBl14qnidbTa5y6bNX0W7lcyDRUaOqGR/NRRm/b6/sM/Hv+cwz0XAJPtLSvVfyVLkcMQK44or8eQOAyZOLLV+XvOfnbg4Eyz4+zzgjqqI+cmS566nbcccBl15ady6yHXsssHBh1MOsOg+whC5sd90V1Q7aa6/ofa9cU0PGQ8aRj6p/pvGnjj4auOoqDltAblRAN3BgOR1SuPja16IBlH2q68a1zhtm3yV0AwYUC+bS0i46j8t83SjkNnSbbJI9VmiZyjoGQ61N40vTvtdGGwH33AO8+257GgO6sE2f3vnex3lpyZIoSCza82qv4iFjqYo2dN14kakioOvlm0GgXcd84iNwyHYAABjISURBVMT6951Jk+pdf5YyequtyyqrdN4A6fg8p9TZyyXVY9GietZb9n7TK/tl077nKqu0/2dA1wxDhkSdyvnY18aM6XxfRkdVEycC++zjP90Q8JBxlLbTfvBB9Pr22/7TvuUW4Mor86UbgpDa0HWbww8HttgiqnI2f357eh3BXVN+i9DzaZO/J56IOvgpmk5eprTjbV9C3851GjUKePHF+h/ChKzsbdPt+2eT962mdVjT68o4ltZYw3+azzzjP81QMKDzaPXVo9d33imWju4kfPDB0Z+v9KrCNnTlEyKc9kPdMLC4Gow99M5zxo/PrppSRwldfKDzuocjCFnR36abt13ZtVV6/ZrRBGWP00t+dPN5qGkY0Fmy2WlVj1mqG3lX//APUSncjjvmWz5Eqn0XL6DVqPvkWvVgpnml7Y9Tp0Z1+V3H8PMpxHHobIctyLP+Xjw/5A1aemFbVdX8oNu3ZZO/39ChdeeAdO69N7o+JjV5X+sWDOgcpe20qqpR3q6W99ij/hty39iGrlqqlBioZ7ustlr163Rhe3wl6/I3Vd3HHUvozHbYAXjhhc5jliIsoSuml48rKtfuu3e+Z8d34WAtZUs2J0gV0OUtofMthANMVRM94IBi6bANnZ1p0+rOgX9l3Jz43meOOMJver7yV2Y7FB8BnQpm6uxJsS5XXgk8+STwsY/lW76bb9qrOqd3+7Wj278fhYP7Wv1YQufIpoQulIBO9RI1dmx9eZg8ubtvPEIT3z+53atz7bXRX2hCL6H73veAbbYBdt3VT56aZOhQYMst3ZfrpRsnKYGvfz0au9WnXtmGvAY0z403hnMPSc3CgM5SE0voJk0Czj8f+Mxn6s4JUX4+b76adoMzalSx5cu4cX3ttejVpjffrPUPHx4N8EwUF69y+aUvRX9lpE/hufNO4OWX685FfQ49tO4cuCmjyuXvfgf8+c/+0usVDOgcNamEbsAA4Kyz6s5FMbzw5tct265pQZgP6lyyxRbF0iljHxg3Dvj1r4H3369u/Rtv7CcdaoZuOXfVZccdo3PI/vvXnRN3M2bUnQNyUUZAN3ZsvTXLmooBnaUmltB1k168qadIL57YN9ggqo44c2axdMq4MVbt3aoYpH3jjYHFi4Fbby2WTjfqhXMiO0XJZ+utgXff7c22qU0lBLDffnXngpqMnaI4SrsQHHpoNLJ9E5+KUffplhu+b3/bf5pCAJddBmy6aXvasmXA8uX+15WHEMDcudH5pGg6vrn0QFh0/auu6iedbrLyytFrnvZ3TVFWL5e77BK9DhvWuZ5uxGCuWVasAH7wg7pzQU3GgM6SzYVliy2AP/whartGRMWoG1Z1U+9D/Dg+7jjg2Wfb79ddFxgxwt+6QtD0gE7plocTPqy9NvDgg8Btt9Wdk/KUFdB99avAY48BEyf6TZeoV3HYgnAwoHPEnbZa3N69a8EC4M03y0m7V/arMr7n0UdHrzbt2oquv6oBpptmp52ANdYoJ+0bbwR+8pNy0rZV1vE5dCjQ19c7xz9R2dZfP3rlMVU/BnREXSrvAPehGDq0vJvWXlFWQCclsM465a+/7oDui1/svRuVQw8FZs2qOxeRsn/3XvttiXx7+GHg+uvbfUhQfRjQWeITYmqav/2t7hyEp9eO47pvWAcV7Har7oDuooua/2Ckier+3YnIzkYbAYcfXncuCGBA56zuG6RexQu7uw8+qDsH4Rk9Onr9xCdqzUZl6j5fNb2EjuoxdWr0WvaNYt3HBxGRLxy2wBJvKOrBC25+H35Ydw7CM2UK8MwzwIQJdeekGur4aepxxICuN40d6+c332qr9M+HDi2+DiKiELCEzlFTb4yaijdy+XH4DL2JE4EBPXLmW2014MQTgbvvrjsn+TCgozw22ih6veEG/ecTJgB77AGcd151eSIiKhNL6CzxhoKa5oQTsuf5zW+Ajz7yu97581k6GAohyhnHryoq8Ob5l1xkPXhdc03gnnuqyQsRURUY0DliCV21uL3zs9l2W2zhf70zZ/pPk3oTS+goD9WRDa8fRNQreqTiUXG8oSAiqgfPv+TijTeiV+43RNQrGNA54hM/IuolJ58MTJpUz7pZQkd5bLhh3TkgIqoWq1xa4g1Fvbj9iepxySX1rZsBHRERUTaW0DliCV21uL2JehcDOiIiomxWAZ0QYoYQYpEQYrEQ4gzN558VQiwXQjzR+jsm9tkcIcTzrb85PjNP3W+ttaLXo46qNx9EVD0GdJQH9xci6jWZVS6FEAMBXAZgDwBLATwmhJgnpXwmMestUsrjE8sOA3A2gD4AEsCvWsu+4SX3FeIFoh6rrgp88AGw0kp154SIqsZhC4iIiLLZlNBNBbBYSrlESvkhgJsB7GeZ/nQA90opX28FcfcCmJEvq2FgFcDqDR7M7U7Ui1hCR0RElM0moFsfwEux90tb05IOFEL8RghxuxBC9TFlu2zweENBRFQt1VvhqqvWmw9qJj4IJKJeYRPQ6U6JyfDmxwBGSym3BHAfgGsdlo1mFGKuEGKhEGLh8uXLLbJVD14giIiqcfnlwA03ANtuW3dOiIiIwmUT0C0FEB/VZQMAy+IzSClfk1J+0Hp7JYAptsvG0rhCStknpewbOXKkTd4rxRI6IqJqrbYacNhhdeeCiIgobDYB3WMAxgshxgghBgOYDWBefAYhxLqxt/sCeLb1/90A9hRCrC2EWBvAnq1pjcUSOiIionDxASwR9ZrMXi6llB8JIY5HFIgNBHC1lPJpIcS5ABZKKecBOFEIsS+AjwC8DuCzrWVfF0KchygoBIBzpZSvl/A9SscLBBGRnU99Cpgwoe5cEBER9YbMgA4ApJTzAcxPTPtq7P8vA/iyYdmrAVxdII9BYQkdEVG6++6rOwdERES9wyqgI6Lm+P73gfffrzsXRET14gNYIuoVDOgsscolNcVnPlN3DoiIiIioKjadohARERE1Ah/AElGvYUBniRcIIiKi8H30UfQ6iHWQiKhHMKBzwPr4REREYVMB3Uor1ZsPIqKqMKCzxBI6IiKi8P3tb9ErS+iIqFcwoHPAEjoiIqKwfetbwPDhwMiRdeeEiKgaDOgssYSOiIgofAcfDPz5z8DgwXXnhIioGgzoHLCEjoiIiIiIQsIa5pZYQhe2//N/gAkT6s4FEREREVG1GNA5YAlduK64ou4cEBERERFVj1UuiYiIiIiIGooBnSVWuSQiIiIiotAwoHPAKpdERERERBQSBnSWWEJHREREREShYUDngCV0REREREQUEgZ0llhCR0REREREoWFA54AldEREREREFBIGdJZYQkdERERERKFhQOeAJXRERERERBQSBnSWWEJHREREREShYUDngCV0REREREQUEgZ0REREREREDcWAzhKrXBIRERERUWgY0DlglUsiIiIiIgoJAzpLLKEjIiIiIqLQMKBzwBI6IiIiIiIKCQM6SyyhIyIiIiKi0DCgc8ASOiIiIiIiCgkDOkssoSMiIiIiotAwoLN0773A22/XnQsiIiIiIqI2BnSWnnqq7hwQERERERF1YkBHRERERETUUAzoiIiIiIiIGooBHRERERERUUMxoCMiIiIiImooBnREREREREQNNajuDDTFlCnAOuvUnQsiIiIiIqI2ltBZkhIYwK1FREREREQBYYhiacUKBnRERERERBQWhiiWGNAREREREVFoGKJYWrECEKLuXBAREREREbUxoLPENnRERERERBQahiiWWOWSiIiIiIhCwxDFEgM6IiIiIiIKDUMUS2xDR0REREREoWFAZ4lt6IiIiIiIKDQMUSyxyiUREREREYWGIYolBnRERERERBQahiiW2IaOiIiIiIhCw4DOEtvQERERERFRaKxCFCHEDCHEIiHEYiHEGZrPvyCEeEYI8RshxE+FEKNin/1dCPFE62+ez8xXiVUuiYiIiIgoNIOyZhBCDARwGYA9ACwF8JgQYp6U8pnYbL8G0CelfFcI8XkAFwI4pPXZe1LKrTznu3IM6IiIiIiIKDQ2IcpUAIullEuklB8CuBnAfvEZpJT3Synfbb19BMAGfrNZP7ahIyIiIiKi0NgEdOsDeCn2fmlrmsnRAO6MvR8qhFgohHhECLG/aSEhxNzWfAuXL19uka1qsQ0dERERERGFJrPKJQBduZTUzijEZwD0Adg5NnkjKeUyIcRYAD8TQvxWSvm7fglKeQWAKwCgr69Pm36dWOWSiIiIiIhCYxOiLAWwYez9BgCWJWcSQuwO4CwA+0opP1DTpZTLWq9LADwAYOsC+a0NAzoiIiIiIgqNTYjyGIDxQogxQojBAGYD6OitUgixNYDvIQrm/hSbvrYQYkjr/xEAdgAQ70ylMdiGjoiIiIiIQpNZ5VJK+ZEQ4ngAdwMYCOBqKeXTQohzASyUUs4D8A0AqwG4TURRzx+klPsCmAjge0KIFYiCxwsSvWM2hpQM6IiIiIiIKCw2beggpZwPYH5i2ldj/+9uWO5/AGxRJIOhYJVLIiIiIiIKDUMUByyhIyIiIiKikDCgsySD63eTiIiIiIh6HQM6S2xDR0REREREoWFA54ABHRERERERhYQBnSVWuSQiIiIiotAwoLPEKpdERERERBQaBnSWGNAREREREVFoGNA5YEBHREREREQhYUBniW3oiIiIiIgoNAzoLLHKJRERERERhYYBnQMGdEREREREFBIGdJZY5ZKIiIiIiELDgM4Sq1wSEREREVFoGNBZYkBHREREREShYUDngAEdERERERGFhAGdJbahIyIiIiKi0DCgs8Qql0REREREFBoGdA4Y0BERERERUUgY0FlilUsiIiIiIgoNAzoHLKEjIiIiIqKQMKCzoErnGNAREREREVFIGNA5YEBHREREREQhYUBnge3niIiIiIgoRAzoLLDKJRERERERhYgBnQMGdEREREREFBIGdBZY5ZKIiIiIiELEgM4Cq1wSEREREVGIGNBZYEBHREREREQhYkDngAEdERERERGFhAGdBbahIyIiIiKiEDGgs8Aql0REREREFCIGdA4Y0BERERERUUgY0FlglUsiIiIiIgoRAzoLrHJJREREREQhYkBngQEdERERERGFiAGdAwZ0REREREQUEgZ0FtiGjoiIiIiIQsSAzgKrXBIRERERUYgY0DlgQEdERERERCFhQGeBVS6JiIiIiChEDOgssMolERERERGFiAGdBQZ0REREREQUIgZ0DhjQERERERFRSBjQWWAbOiIiIiIiChEDOguscklERERERCFiQOeAAR0REREREYWEAZ0FVrkkIiIiIqIQMaCzwCqXREREREQUIgZ0FhjQERERERFRiBjQOWBAR0REREREIbEK6IQQM4QQi4QQi4UQZ2g+HyKEuKX1+QIhxOjYZ19uTV8khJjuL+vVYRs6IiIiIiIKUWZAJ4QYCOAyADMBTAJwqBBiUmK2owG8IaXcGMAlAL7eWnYSgNkANgMwA8C/t9JrFFa5JCIiIiKiENmU0E0FsFhKuURK+SGAmwHsl5hnPwDXtv6/HcCnhBCiNf1mKeUHUsoXACxupdcor7wSvTKgIyIiIiKikNgEdOsDeCn2fmlrmnYeKeVHAN4EMNxyWQCAEGKuEGKhEGLh8uXL7XJfkZEjgWnTgB12qDsnREREREREbYMs5tGVSyVblZnmsVk2mijlFQCuAIC+vr6gWq2ttx7w0EN154KIiIiIiKiTTQndUgAbxt5vAGCZaR4hxCAAawJ43XJZIiIiIiIiysEmoHsMwHghxBghxGBEnZzMS8wzD8Cc1v8HAfiZlFK2ps9u9YI5BsB4AI/6yToREREREVFvy6xyKaX8SAhxPIC7AQwEcLWU8mkhxLkAFkop5wG4CsD3hRCLEZXMzW4t+7QQ4lYAzwD4CMA/SSn/XtJ3ISIiIiIi6ilCBjjIWl9fn1y4cGHd2SAiIiIiIqqFEOJXUsq+rPmsBhYnIiIiIiKi8DCgIyIiIiIiaigGdERERERERA3FgI6IiIiIiKihGNARERERERE1FAM6IiIiIiKihmJAR0RERERE1FAM6IiIiIiIiBqKAR0REREREVFDMaAjIiIiIiJqKAZ0REREREREDcWAjoiIiIiIqKEY0BERERERETUUAzoiIiIiIqKGElLKuvPQjxBiOYAX686HxggAf647Ez2K274+3Pb14bavD7d9fbjt68NtXx9u+3qFuv1HSSlHZs0UZEAXKiHEQillX9356EXc9vXhtq8Pt319uO3rw21fH277+nDb16vp259VLomIiIiIiBqKAR0REREREVFDMaBzc0XdGehh3Pb14bavD7d9fbjt68NtXx9u+/pw29er0dufbeiIiIiIiIgaiiV0REREREREDcWAjoiIiIiIqKEY0FkQQswQQiwSQiwWQpxRd366gRBiQyHE/UKIZ4UQTwshTmpNP0cI8bIQ4onW36zYMl9u/QaLhBDTY9P5+zgSQvxeCPHb1jZe2Jo2TAhxrxDi+dbr2q3pQgjxndb2/Y0QYptYOnNa8z8vhJhT1/dpCiHEhNi+/YQQ4i0hxMnc78sjhLhaCPEnIcRTsWne9nUhxJTWsbS4tayo9huGy7DtvyGE+N/W9v2BEGKt1vTRQoj3YsfAd2PLaLex6Xck47b3dp4RQowRQixobftbhBCDq/t2YTNs+1ti2/33QognWtO533skzPeW3X/Ol1LyL+UPwEAAvwMwFsBgAE8CmFR3vpr+B2BdANu0/l8dwHMAJgE4B8Cpmvkntbb9EABjWr/JQP4+ubf/7wGMSEy7EMAZrf/PAPD11v+zANwJQADYDsCC1vRhAJa0Xtdu/b923d+tKX+tffcVAKO435e6nXcCsA2Ap2LTvO3rAB4F8MnWMncCmFn3dw7lz7Dt9wQwqPX/12PbfnR8vkQ62m1s+h35Z9z23s4zAG4FMLv1/3cBfL7u7xzKn27bJz7/JoCvtv7nfu9325vuLbv+nM8SumxTASyWUi6RUn4I4GYA+9Wcp8aTUv5RSvl46/+/AngWwPopi+wH4GYp5QdSyhcALEb02/D38Wc/ANe2/r8WwP6x6dfJyCMA1hJCrAtgOoB7pZSvSynfAHAvgBlVZ7rBPgXgd1LKF1Pm4X5fkJTyIQCvJyZ72ddbn60hpfyljK7018XS6nm6bS+lvEdK+VHr7SMANkhLI2Mbm37HnmfY702czjOtEondANzeWp7bPiZt27e23cEAbkpLg/t9Pin3ll1/zmdAl219AC/F3i9FeuBBjoQQowFsDWBBa9LxraLvq2NVCUy/A3+ffCSAe4QQvxJCzG1NW0dK+UcgOikC+FhrOrd9OWaj86LO/b46vvb19Vv/J6eTnaMQPeFWxgghfi2EeFAIMa01LW0bm35HMvNxnhkO4C+xwJz7vb1pAF6VUj4fm8b9vgSJe8uuP+czoMumqxvLsR48EUKsBuC/AJwspXwLwOUAxgHYCsAfEVVNAMy/A3+ffHaQUm4DYCaAfxJC7JQyL7e9Z632JvsCuK01ift9GFy3N3+HnIQQZwH4CMANrUl/BLCRlHJrAF8AcKMQYg1wG/vk6zzD3yS/Q9H5II/7fQk095bGWTXTGrnvM6DLthTAhrH3GwBYVlNeuooQYiVEB9wNUsr/BgAp5atSyr9LKVcAuBJRlQ/A/Dvw98lBSrms9fonAD9AtJ1fbVUnUNU9/tSandvev5kAHpdSvgpwv6+Br319KTqrDPJ3sNDqYGBvAIe3qi2hVd3vtdb/v0LUdmsTpG9j0+9IGh7PM39GVDVtUGI6pWhtr08DuEVN437vn+7eEj1wzmdAl+0xAONbPToNRlRNal7NeWq8Vj3yqwA8K6W8ODZ93dhsBwBQvUTNAzBbCDFECDEGwHhEDVP5+zgSQqwqhFhd/Y+ok4KnEG031ZPTHAA/av0/D8ARrd6gtgPwZqvKwt0A9hRCrN2qurNnaxpl63hKy/2+cl729dZnfxVCbNc6px0RS4s0hBAzAJwOYF8p5bux6SOFEANb/49FtK8vydjGpt+RNHydZ1pB+P0ADmotz21vZ3cA/yul/P9V9rjf+2W6t0QvnPOL9qrSC3+IesF5DtGTk7Pqzk83/AHYEVEx9W8APNH6mwXg+wB+25o+D8C6sWXOav0GixDrVYi/j/O2H4uot7InATytthmidhE/BfB863VYa7oAcFlr+/4WQF8sraMQNaBfDODIur9bE/4ArALgNQBrxqZxvy9ve9+EqFrT3xA9XT3a574OoA/RjfHvAPwbAFH3dw7lz7DtFyNqm6LO+99tzXtg63z0JIDHAeyTtY1NvyP/jNve23mmdR15tPV73gZgSN3fOZQ/3bZvTb8GwLGJebnf+932pnvLrj/nq52DiIiIiIiIGoZVLomIiIiIiBqKAR0REREREVFDMaAjIiIiIiJqKAZ0REREREREDcWAjoiIiIiIqKEY0BERERERETUUAzoiIiIiIqKG+n9lNiRBv5+oQQAAAABJRU5ErkJggg==\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "index=[i for i in range(len(beta_post))]\n", "plt.plot(index,beta0_post,label=r'Post samples of $\\beta_0$',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "plt.plot(index,beta1_post,label=r'Post samples of $\\beta_1$',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "plt.plot(index,beta2_post,label=r'Post samples of $\\beta_2$',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "收敛情况" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "average_beta0=[np.mean(beta0_post[:i]) for i in range(len(beta0_post)) if i!=0]\n", "plt.plot(index[1:],average_beta0,label=r'MCMC Samples Mean of $\\beta_0$',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "average_beta1=[np.mean(beta1_post[:i]) for i in range(len(beta1_post)) if i!=0]\n", "plt.plot(index[1:],average_beta1,label=r'MCMC Samples Mean of $\\beta_1$',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "average_beta2=[np.mean(beta2_post[:i]) for i in range(len(beta2_post)) if i!=0]\n", "plt.plot(index[1:],average_beta2,label=r'MCMC Samples Mean of $\\beta_2$',color='blue')\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "自相关图" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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IIqQNo5n+p4IcwOBxTBsAAhsAtJjQBjDiBLbR4v8NMHgMjwQYQRruo81JSwAGi542gBEyNiawcbBSrBMAbSe0AYyQffuaLgEAMF9CG8CI0JvCkVg/ANpLaAMYARrk9KKUZHy86VIAcCihDWDICWzMx9atTZcAgEM5eyTAEBLUOBbOLgnQLnraAIaM4W30kx8AAJontAEMGcPbAGC4GB4JMCT0iLBQptctQyUBmiG0AQw4YY3FIrwBNMPwSIABJrDRBOsdwOIS2gAGlIYzTbL+ASweoQ1gwIyPazDTDqVYFwEWg2PaAAaExjFt5Vg3gIWlpw1gAAhsDALrKcDC0NMG0GIawQwavW4A/aenDaClBDYGmfUXoH+ENoAW0uBlGFiPAfpDaAMAFsz4eNMlABh8QhtAy+idYJhs3dp0CQAGX0+hrZRyYSllZyllVyll0wzPv76Ucn8p5ZFSyqOllHf3v6gAw09gYxiVkoyNNV0KgME1Z2grpSxJ8pUkFyU5NckHSimnHjLb/5rkjlrrGUmuSHJjvwsKMKymL1AssDHM9u2zngMcrV562s5KsqvW+nSt9ddJbk9yySHz1CS/1bn/20l+3L8iAgwnDVhGlXUfYH56CW2vS7Kn6/FEZ1q3a5P8vVLKRJJ7kvwPM71RKeVjpZRtpZRtzz333FEUF2A4aLCC7QCgV72Etpmq1EMvmfmBJF+vta5K8u4k3yilHPbetdaba63ra63rTzzxxPmXFmCAGQYJh7NdAMytl9A2keSkrsercvjwxz9IckeS1Fr/fZJlSVb2o4AAg0yDFHpnewGYWS+h7YdJTi6lrCmlHJepE41sOWSe/zfJBUlSSlmbqdBm/CMwksbHNTzhWAlwAL+xdK4Zaq0vl1KuTHJvkiVJvlZrfbyU8tkk22qtW5L8oyT/rJTy6UwNndxQaz10CCXA0NPAhP4rJVmyJHn55aZLAtCMOUNbktRa78nUCUa6p13Tdf9HSc7tb9EABovABgtncrLpEgA0p6eLawNwZAIbLDzbGTCqhDaAY6QhCYvH9gaMIqEN4BhoQMLis90Bo0ZoAzhKGo7QHNsfMEqENoCjoMEIzbMdAqNCaAOYJw1FaA/bIzAKejrlPwAah9BW09umK8QCw0poAzgCQQ0GR/f2KsABw8TwSIBZjI83XQLgaPnBBRgmetoAZqDBB4OvFD1uwHDQ0wZwCIENhoftGRgGQhsw8ko5+AYMl0O3cUOfgUEjtAEjTUiD0bN1q+AGDBahDRhZAhuMrq1bk7GxpksB0BuhDRg5Y2MCG5Ds26cuAAaDs0cCI0UDDTiUs0wCbaenDRgZAhswG/UD0GZCGzASNMiAuagngLYyPBIYahphwHxM1xmGSwJtIrQBQ0dQA45Vdz0iwAFNMzwSGCoCG9Bv6hWgaUIbMBRK0bACFs50HbPUGCWgAUIbMJCmG1DCGrCYJicPrnvGx5suETAK/F4EDAzhDGibrVudvARYeEIb0HrCGjAInLwEWChCG9BawhowqPS+Af3kmDagdRynBgwLdRnQD0Ib0CoaOMCw8UMUcKyENqAVNGqAYaeOA46W0AY0TkMGGBXqO+BoCG1AozRggFGj3gPmS2gDGqPhAowq9R8wH0Ib0AgNFmDUqQeBXgltAAANGRtrugTAIBDagEXn12WAKfv2NV0CYBAIbcCCGx//zSn9BTaAg3XXj+pIYCZLmy4AMNw0QADmp5Sk1qZLAbSJnjZgwQhsAEdH/Ql0E9qABaHBAXBs1KPANMMjgb7SyADon+k61XBJGG162oC+EdgAFob6FUab0Ab0xVL99gALSnCD0aWZBRwTjQiAxWO4JIwmPW3AURPYAJqh/oXRIrQBR0WDAaBZ6mEYHUIbMG8aCgDtUIo6GUaB0Ab0TOMAoJ3UzTDcnIgEmJPGAED7OUkJDC89bcARCWwAg0W9DcNHaANmZccPMJjU3zBchDZgRnb4AIOtlGRsrOlSAP0gtAEHTjDSfQNg8O3bd3j9Pj7edKmA+RLaYIQJaACjZ+tWdT8MGmePhBFkZw2As03C4BDaYEQIagDMpHv/IMBBOwltMMQENQDmQ4CDdnJMGwwpgQ2AY2E/Au0htMEQsqMFoB/sT6AdDI+EIWCnCsBCmWkfY+gkLC49bTDAnLIfgCbY98DiEtpgQNlhAtAk+yFYPEIbDCA7SgDawP4IFodj2mBA2DEC0EYuEwALT08bDACBDYBBUEoyPt50KWD4CG3QYmNjAhsAg2XrVvsu6DehDVps376mSwAAR0dwg/4R2qCl7OwAGHSGSkJ/OBEJtIigBsAw6R4q6SQlcPT0tAEAsOD8MAlHT2iDFijFzgyA4WdfB0enp9BWSrmwlLKzlLKrlLJplnn+binlR6WUx0spt/W3mDCchDUARs30vm+pg3SgZ3NuLqWUJUm+kuRdSSaS/LCUsqXW+qOueU5O8o+TnFtr/atSyt9YqALDMFi6NJmcbLoUANCcycmp8OZYN5hbLz1tZyXZVWt9utb66yS3J7nkkHn+uyRfqbX+VZLUWp/tbzFhuAhsAAD0qpfQ9roke7oeT3SmdTslySmllAdLKT8opVw40xuVUj5WStlWStn23HPPHV2JYcAZDgkAv2G/CHPrJbTNtCkd2pG9NMnJScaTfCDJPy+ljB32olpvrrWur7WuP/HEE+dbVhh4dkwAcDj7RziyXkLbRJKTuh6vSvLjGeb5V7XWl2qt/ynJzkyFOKDDDgkAZmc/CbPrJbT9MMnJpZQ1pZTjklyRZMsh89yd5L9JklLKykwNl3y6nwWFQeUMkQDQG/tMmNmcoa3W+nKSK5Pcm+SJJHfUWh8vpXy2lHJxZ7Z7k+wtpfwoyf1JPlNr3btQhYZBYccDAPNn/wkHK7Wh86yuX7++btu2rZHPhoVmZwMA/eGSAAyzUsr2Wuv6uebr6eLaQO8ENgDoH/tVENqgr+xYAKD/7F8ZdUIb9IkdCgAsHPtZRpnQBn1gRwIAC6+UZHy86VLA4hPa4BiMjwtsALCYtm6172X0LG26ADCI7CwAoFnT+2Jnl2QU6GmDeVi6VGADgDZxQW5GgdAGPRobSyYnmy4FADATwY1hJrRBj/bta7oEAACMIse0wRH41Q4ABkf3ftuxbgwToQ1mIKwBwGBzohKGidAGEdIAYFgduo8X4hhEjmljpLnOGgCMFmebZBDpaWNkjY05uQgAjKpS9LoxOIQ2RpJf2AAAwY1BIbQxUoQ1AKCbE5YwCBzTxtBbutT4dQDgyKbbCtoLtJHQxlAbH08mJ5suBQAwSAQ32sbwSIaWChcAOFqOd6NNhDaGjrAGAPSD491oC8MjGSoCGwDQb6VMXSoImiK0MRQcOAwALKR9+7Q1aI7hkQw0lScAsJgMmaQJQhsDR1ADAJrW3R4R4FhohkcyUAQ2AKBtSpm6LiwsFKGNgeCYNQCgzSYntVVYOEIbracCBAAGhXYLC0Foo9VUfADAoNF+od+ENlpLhQcADCrtGPrJIZO0igoOABgWzjBJv+hpozUENgBgWGnncCyENlpBRQYADDuXBuBoCW00anxcYAMARodLA3A0ZH0WzdhYsm9f06UAAGjeTMHNcW/MRmhjUfhFCQDgyEoR3JiZ4ZEsmOmhjwIbAEBvpttO2k90E9pYEOPjydatTZcCAGBwCW5MMzySvlPBAAD0hyGTJHra6DOBDQCgv7SvENroGxUKAMDC0M4abYZHcsxUIgAAC2+6zWW45OjR08YxEdgAABaX9tfoEdo4aioMAIBmaIeNFsMjmTeVBABA8wyXHB162pgXgQ0AoF1KSZbqihlqQhs9E9gAANppclJbbZjJ5MzKhg8AMFi622+GTQ4PoY3DCGsAAIPPMW/Dw/BIDiKwAQAMF+27wSe0cYANGgBgOGnnDTahjYyN2ZABAIZdKdp8g0poG3GlJPv2NV0KAAAWSynJ+HjTpWA+hLYR5pcWAIDRtHWra7sNEqFtRAlsAACjbXJScBsUQtuIMZYZAIBpLso9GGTrEWBDBADgSFyUu930tA05gQ0AgPnQfmwfoW2I2eAAADga2pHtIrQNKRsaAADHQnuyPRzTNkRsWAAA9JNj3dpBaBtwghoAAItBgGuO4ZEDTGADAKAJLiO1uPS0DSAbCAAAbTDdLtXztrD0tA0Qv2gAANBG2qgLS2gbAMIaAABtN91mXWosX98JbS02NiasAQAwWCYntWH7TQ5uKSs6AACDrBTHuvWLnrYWEtgAABgG2rX9IbS1zNhY0yUAAID+EdyOneGRLWBFBgBgmLkw97HpqaetlHJhKWVnKWVXKWXTEea7rJRSSynr+1fE4eWskAAAjBpt4PmbM7SVUpYk+UqSi5KcmuQDpZRTZ5jvhCSfSvJQvws5TKZXUisqAACjTLu4d730tJ2VZFet9ela66+T3J7kkhnm+9+T/FGSF/tYvqFihQQAgMOVkoyPN12K9uoltL0uyZ6uxxOdaQeUUs5IclKt9TtHeqNSysdKKdtKKduee+65eRd2EPkFAQAA5rZ1q7bzbHoJbTMtsgOHD5ZS/lqSG5L8o7neqNZ6c611fa11/Yknnth7KQeMlQ0AAI6N9vRv9BLaJpKc1PV4VZIfdz0+Icm6JN8rpexOck6SLaN6MhIrFgAA9I/2dW+h7YdJTi6lrCmlHJfkiiRbpp+ste6rta6sta6uta5O8oMkF9daty1IiVvKLwEAALAwptvao3rc25yhrdb6cpIrk9yb5Ikkd9RaHy+lfLaUcvFCF3AQCGsAALDwtm5tugTN6Oni2rXWe5Lcc8i0a2aZd/zYizUYhDUAAFhc023wUbpId08X1+ZwAhsAADRnlNrjQttRGKUVBAAA2qqUZGlPYwcHm9A2TwIbAAC0x+Tk8J+gRGjrkbNDAgBAO01fmHtYCW09GOYVAAAAhkUpydhY06XoP6FtDgIbAAAMjn37mi5B/wltRyCwAQDA4Bm2C3ELbbMQ2AAAYHBt3To8Z5YU2mYgsAEAwOCbnByOtr3Q1sUZIgEAYPgMehtfaAMAAGgxoQ0AAKDFhDYAAIAWE9oAAABaTGgDAABoMaENAACgxYQ2AACAFhPaAAAAWkxoAwAAaDGhDQAAoMWENgAAgBYT2gAAAFpMaAMAAGgxoQ0AAKDFhDYAAIAWE9oAAABaTGgDAABoMaENAACgxYQ2AACAFhPaAAAAWkxoAwAAaDGhDQAAoMWENgAAgBYT2gAAAFpMaAMAAGgxoQ0AAKDFhDYAAIAWE9oAAABaTGgDAABoMaENAACgxYQ2AACAFhPaAAAAWkxoAwAAaDGhDQAAoMWENgAAgBYT2gAAAFpMaAMAAGgxoQ0AAKDFhDYAAIAWE9oAAABaTGgDAABoMaENAACgxYQ2AACAFhPaAAAAWkxoAwAAaDGhDQAAoMWENgAAgBYT2gAAAFpMaAMAAGgxoQ0AAKDFhDYAAIAWE9oAAABaTGgDAABoMaENAACgxYQ2AACAFhPaAAAAWkxoAwAAaDGhDQAAoMWENgAAgBYT2gAAAFqsp9BWSrmwlLKzlLKrlLJphuf/YSnlR6WUR0spf1pKeUP/iwoAADB65gxtpZQlSb6S5KIkpyb5QCnl1ENmeyTJ+lrr25LcmeSP+l1QAACAUdRLT9tZSXbVWp+utf46ye1JLumeodZ6f631l52HP0iyqr/FBAAAGE29hLbXJdnT9XiiM202f5Dk38z0RCnlY6WUbaWUbc8991zvpQQAABhRvYS2MsO0OuOMpfy9JOuTXDfT87XWm2ut62ut60888cTeSwkAADCilvYwz0SSk7oer0ry40NnKqX8XpKrk5xfa93fn+IBAACMtl562n6Y5ORSyppSynFJrkiypXuGUsoZSf6vJBfXWp/tfzEBAABG05yhrdb6cpIrk9yb5Ikkd9RaHy+lfLaUcnFntuuS/PUk/7KUsqOUsmWWtwMAAGAeehkemVrrPUnuOWTaNV33f6/P5QIAACA9XlwbAACAZghtAAAALSa0AQAAtJjQBgAA0GJCGwAAQIsJbQAAAC0mtAEAALSY0AYAANBiQhsAAECLCW0AAAAtJrQBAAC0mNAGAADQYkIbAABAiwltAAAALSa0AQAAtJjQBgAA0GJCGwAziP0QAAAKh0lEQVQAQIsJbQAAAC0mtAEAALSY0AYAANBiQhsAAECLCW0AAAAtJrQBAAC0mNAGAADQYkIbAABAiwltAAAALSa0AQAAtJjQBgAA0GJCGwAAQIsJbQAAAC0mtAEAALSY0AYAANBiQhsAAECLCW0AAAAtJrQBAAC0mNAGAADQYkIbAABAiwltAAAALSa0AQAAtJjQBgAA0GJCGwAAQIsJbQAAAC0mtAEAALSY0AYAANBiQhsAAECLCW0AAAAtJrQBAAC0mNAGAADQYkIbAABAiwltAAAALSa0AQAAtJjQBgAA0GJCGwAAQIsJbQAAAC0mtAEAALSY0AYAANBiQhsAAECLCW0AAAAtJrQBAAC0mNAGAADQYkIbAABAiwltAAAALSa0AQAAtJjQBgAA0GJCGwAAQIsJbQAAAC0mtAEAALSY0AYAANBiQhsAAECLCW0AAAAt1lNoK6VcWErZWUrZVUrZNMPzry6l/HHn+YdKKav7XVAAAIBRNGdoK6UsSfKVJBclOTXJB0oppx4y2x8k+ata63+V5IYkf9jvggIAAIyipT3Mc1aSXbXWp5OklHJ7kkuS/KhrnkuSXNu5f2eSL5dSSq21zvamO3cm4+NHU2QAAID5GeTs0Utoe12SPV2PJ5KcPds8tdaXSyn7kqxI8pfdM5VSPpbkY0ny6le/7SiLvHDOP7/pEgAAABysl9BWZph2aA9aL/Ok1npzkpuTZP369fV73+vh0wEAAIZQmSlFzaCXE5FMJDmp6/GqJD+ebZ5SytIkv53k+d6KAAAAwGx6CW0/THJyKWVNKeW4JFck2XLIPFuSfKRz/7Ik9x3peDYAAAB6M+fwyM4xalcmuTfJkiRfq7U+Xkr5bJJttdYtSb6a5BullF2Z6mG7YiELDQAAMCp6OaYttdZ7ktxzyLRruu6/mOTv9LdoAAAA9HRxbQAAAJohtAEAALSY0AYAANBiQhsAAECLCW0AAAAtJrQBAAC0mNAGAADQYkIbAABAiwltAAAALSa0AQAAtJjQBgAA0GJCGwAAQIsJbQAAAC0mtAEAALRYqbU288GlPJfkmUY+/MhWJvnLpgsxoiz75lj2zbHsm2X5N8eyb45l3xzLvjltXfZvqLWeONdMjYW2tiqlbKu1rm+6HKPIsm+OZd8cy75Zln9zLPvmWPbNseybM+jL3vBIAACAFhPaAAAAWkxoO9zNTRdghFn2zbHsm2PZN8vyb45l3xzLvjmWfXMGetk7pg0AAKDF9LQBAAC0mNAGAADQYkMf2kopf6eU8ngp5ZVSyvpDnvvHpZRdpZSdpZS/1TX9ws60XaWUTV3T15RSHiql/Hkp5Y9LKcd1pr+683hX5/nVi/X9BklnGe3o3HaXUnZ0pq8upfyq67mbul7zu6WUP+ss2y+VUkpn+vJSyp90/hd/Ukr5naa+1yAopVxbSvn/upbxu7ue68t2wMxKKdeVUp4spTxaSrmrlDLWmW69b9Bs6zdHr5RyUinl/lLKE5397v/Ymd63+ofZdfarf9ZZxts602asM8qUL3WW76OllDO73ucjnfn/vJTykaa+z6AopfzNrnV7RynlP5dSrrLeL4xSytdKKc+WUh7rmta39Xy2/W8r1FqH+pZkbZK/meR7SdZ3TT81yX9I8uoka5I8lWRJ5/ZUkjcmOa4zz6md19yR5IrO/ZuS/Ped+xuT3NS5f0WSP276e7f9luSfJLmmc391ksdmme//SfJfJylJ/k2SizrT/yjJps79TUn+sOnv1OZbkmuT/E8zTO/bduA267L//SRLO/f/cHpdtd43+j+Zdf12O6bl+tokZ3bun5DkP3bqmL7VP25HXP67k6w8ZNqMdUaSd3fqlpLknCQPdaYvT/J05+/vdO7/TtPfbVBunXX3p0neYL1fsGX8ziRndu8/+7mez7b/bcNt6Hvaaq1P1Fp3zvDUJUlur7Xur7X+pyS7kpzVue2qtT5da/11ktuTXNJJ2v9tkjs7r/8XSd7b9V7/onP/ziQXtCqZt0xn2fzdJJvnmO+1SX6r1vrv69SWdGtmXubd/wvmp5/bATOotf7bWuvLnYc/SLLqSPNb7xfFjOt3w2UaeLXWn9RaH+7c/3mSJ5K87ggvmVf9s7ClH1qz1RmXJLm1TvlBkrFO3fO3kvxJrfX5WutfJfmTJBcudqEH2AVJnqq1PnOEeaz3x6DW+u+SPH/I5L6s53Psfxs39KHtCF6XZE/X44nOtNmmr0jys67G1/T0g96r8/y+zvzM7B1J/qLW+udd09aUUh4ppWwtpbyjM+11mVrO07qX+X9Za/1JMtVQSPI3FrrQQ+DKzvCAr3UNq+vndsDc/kGmfrmbZr1vxmzrN31Spg4TOCPJQ51J/ah/OLKa5N+WUraXUj7WmTZbnWHZL4wrcvAP0tb7xdGv9fxI+9/GDUVoK6X836WUx2a4HekXipl6wupRTD/Se42cHv8XH8jBldpPkry+1npGkn+Y5LZSym/Fcp2XOZb9P03ypiSnZ2p5/5Ppl83wVke7HYysXtb7UsrVSV5O8s3OJOt9cyzjBVRK+etJvpXkqlrrf07/6h+O7Nxa65lJLkryyVLKO48wr2XfZ2Xq+O6Lk/zLziTrffOGqo2ztOkC9EOt9feO4mUTSU7qerwqyY8792ea/peZ6lZd2ull6J5/+r0mSilLk/x2Du+6HQlz/S86y+f9SX636zX7k+zv3N9eSnkqySmZWq7dQ8m6l/lflFJeW2v9Sac7+9n+fYvB1Ot2UEr5Z0m+03nYz+1gZPWw3n8kyd9OckFnyIX1vllHWu85BqWUV2UqsH2z1vrtJKm1/kXX88dS/3AEtdYfd/4+W0q5K1PD7WarM2Zb9hNJxg+Z/r0FLvqwuCjJw9Pru/V+UfVrPT/S/rdxQ9HTdpS2JLmiTJ35cU2SkzN18OEPk5xcps6Qd1ymurq3dBpa9ye5rPP6jyT5V13vNX3mmcuS3DfdMOMwv5fkyVrrge7nUsqJpZQlnftvzNT/4ulOF/fPSynndI6l+nBmXubd/wtm0KnEpr0vyfRZl/q5HTCDUsqFSf6XJBfXWn/ZNd1635wZ1++GyzTwOuvrV5M8UWu9vmt6X+qfxfgOg6qUcnwp5YTp+5k6AdJjmb3O2JLkw2XKOUn2deqee5P8finldzrD+X6/M425HTSKyHq/qPqyns+x/23eYp3xpKlbpjaUiUz9ov0XmfqnTD93dabO1LMzXWeHydTZZv5j57mru6a/MVMb1q5MdX+/ujN9Wefxrs7zb2z6e7f1luTrST5xyLRLkzyeqTMlPZzkPV3Prc9URfdUki8nKZ3pK5L8aZI/7/xd3vR3a/MtyTeS/FmSRzNVib2267m+bAdusy77XZkaO7+jc5s+06z1vtn/y4zrt9sxLdPzMjWU6NGu9f3d/ax/3GZd9m/s1CX/oVOvXN2ZPmOdkalhYF/pLN8/y8Fn1/4HnXprV5K/3/R3G4Rbkv8iyd4kv901zXq/MMt6c6aGm76Uqfb9H/RzPZ9t/9uG23RDAAAAgBYa5eGRAAAArSe0AQAAtJjQBgAA0GJCGwAAQIsJbQAAAC0mtAEAALSY0AYAANBi/z8R+Z8W5pzJ9wAAAABJRU5ErkJggg==\n", 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\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.acorr(sub_beta0,label=r'Auto corr of $\\beta_0$',color='blue', maxlags=10000)\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "plt.acorr(sub_beta1,label=r'Auto corr of $\\beta_1$',color='blue', maxlags=10000)\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图\n", "plt.acorr(sub_beta2,label=r'Auto corr of $\\beta_2$',color='blue', maxlags=10000)\n", "plt.legend(loc='upper left', frameon=True)\n", "plt.show() ## 画图" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 2 }