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PRML/notes/GaussianProcess.ipynb
{
"cells": [
{
"metadata": {
"ExecuteTime": {
"end_time": "2018-08-09T06:22:45.191483Z",
"start_time": "2018-08-09T06:22:43.786635Z"
},
"trusted": true
},
"cell_type": "code",
"source": "import numpy as np\nimport IPython.display as display\nfrom scipy.stats import multivariate_normal\nimport matplotlib.pyplot as plt",
"execution_count": 1,
"outputs": []
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2018-08-09T06:22:45.213308Z",
"start_time": "2018-08-09T06:22:45.199425Z"
},
"trusted": true
},
"cell_type": "code",
"source": "def sin(x):\n return np.sin(2 * np.pi * x)\n\n\ndef generate_data(func, noise_scale, N):\n x = np.random.uniform(size=N)\n t = func(x) + np.random.normal(scale=noise_scale, size=x.shape)\n return x, t\n\n\ndef display_predict(truefunc,\n X_train,\n t_train,\n X_test,\n t_test_m,\n t_test_s,\n text=None,\n name=None,\n show=True):\n fig = plt.figure(figsize=(8, 6))\n plt.fill_between(\n X_test,\n t_test_m - t_test_s,\n t_test_m + t_test_s,\n color='r',\n alpha=0.15)\n plt.plot(X_test, truefunc(X_test), label='Target Curve', c='blue')\n plt.scatter(\n X_train,\n t_train,\n facecolors='none',\n edgecolors='black',\n label='Observated Points',\n alpha=0.6)\n plt.plot(X_test, t_test_m, c='r', label='Predict Curve')\n if text is not None:\n plt.title(text)\n plt.xlabel('$x$')\n plt.ylabel('$t$')\n plt.ylim((-1.75, 1.75))\n if name is not None:\n plt.savefig('{}.png'.format(name))\n if show:\n plt.legend()\n plt.show()\n\n\ndef display_predict2(truefunc,\n X_train,\n t_train,\n model,\n text=None,\n name=None,\n num=200):\n X_test = np.linspace(0, 1, 200)\n t_m, t_s = model.predict(X_test)\n display_predict(\n truefunc, X_train, t_train, X_test, t_m, t_s, text=text, show=False)\n func = lambda x, w: sum([_w * x**i for i, _w in enumerate(w)])\n plt.legend(loc='lower left')\n plt.xlim((0,1))\n if name is not None:\n plt.savefig('{}.png'.format(name))\n plt.show()",
"execution_count": 2,
"outputs": []
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2018-08-09T06:22:46.179178Z",
"start_time": "2018-08-09T06:22:46.174610Z"
},
"trusted": true
},
"cell_type": "code",
"source": "class KernelBase(object):\n def __init__(self, p):\n self.p = np.array(p)\n \n def update(self, diff):\n self.p += diff\n \n def get_param(self):\n return np.copy(self.p)\n \n def __call__(self, x, y):\n return self.p[0]*x*y\n \n def backward(self, x, y):\n return [x*y]",
"execution_count": 3,
"outputs": []
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2018-08-09T06:30:54.255096Z",
"start_time": "2018-08-09T06:30:54.248075Z"
},
"trusted": true
},
"cell_type": "code",
"source": "class GaussianKernel(KernelBase):\n def __init__(self, p):\n assert len(p) == 2\n super(GaussianKernel, self).__init__(p)\n \n def __call__(self, x, y):\n return self.p[0]*np.exp(-0.5*self.p[1]*(x - y)**2)\n \n def backward(self, x, y):\n dcd0 = np.exp(-0.5*self.p[1]*(x - y)**2)\n dcd1 = -0.5*self.p[0]*dcd0*(x - y)**2\n return [dcd0, dcd1]",
"execution_count": 9,
"outputs": []
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2018-08-09T06:32:08.037188Z",
"start_time": "2018-08-09T06:32:08.031525Z"
},
"trusted": true
},
"cell_type": "code",
"source": "class PolynomialKernel(KernelBase):\n def __init__(self, p):\n assert len(p) == 3\n super(PolynomialKernel, self).__init__(p)\n \n def __call__(self, x, y):\n p = self.p\n return p[0]*(x*y + p[1])**p[2]\n \n def backward(self, x, y):\n p = self.p\n dcd0 = (x*y + p[1])**p[2]\n dcd1 = p[0]*p[2]*(p[1]+x*y)**(p[2]-1)\n dcd2 = p[0]*dcd0*np.log(p[1]+p[0]*x*y)\n return [dcd0, dcd1, dcd2]",
"execution_count": 22,
"outputs": []
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2018-08-09T06:31:55.389826Z",
"start_time": "2018-08-09T06:31:55.385664Z"
},
"trusted": true
},
"cell_type": "code",
"source": "class SigmoidKernel(KernelBase):\n def __init__(self, p):\n assert len(p) == 3\n super(SigmoidKernel, self).__init__(p)\n \n def __call__(self, x, y):\n return self.p[0]*np.tanh(self.p[1]*x*y+self.p[2])\n \n def backward(self, x, y):\n dcd0 = np.tanh(self.p[1]*x*y+self.p[2])\n dcd1 = self.p[0]*x*y/(np.cosh(self.p[1]*x*y+self.p[2]))\n dcd2 = self.p[0]/(np.cosh(self.p[1]*x*y+self.p[2]))\n return [dcd0, dcd1, dcd2]",
"execution_count": 17,
"outputs": []
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2018-08-09T06:31:55.792506Z",
"start_time": "2018-08-09T06:31:55.786631Z"
},
"trusted": true
},
"cell_type": "code",
"source": "class ExponentialSquareKernel(KernelBase):\n def __init__(self, p):\n assert len(p) == 3\n super(ExponentialSquareKernel, self).__init__(p)\n \n def __call__(self, x, y):\n return self.p[0]*np.exp(-0.5*self.p[1]*(x - y)**2)+self.p[2]*x*y\n \n def backward(self, x, y):\n dcd0 = np.exp(-0.5*self.p[1]*(x - y)**2)\n dcd1 = -0.5*self.p[0]*dcd0*(x - y)**2\n dcd3 = x*y\n return [dcd0, dcd1, dcd3]",
"execution_count": 18,
"outputs": []
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2018-08-09T06:31:56.146648Z",
"start_time": "2018-08-09T06:31:56.136673Z"
},
"trusted": true
},
"cell_type": "code",
"source": "class GaussianProcessRegression(object):\n def __init__(self, kernel, beta):\n self.kernel = kernel\n self.beta = beta\n \n def fit_1(self, x, t, lr=1e-1):\n pred_param = kernel.get_param()\n self.X = x\n self.t = t\n self.lr = lr\n self.K = self.kernel(*np.meshgrid(x,x))\n self.cov = self.K + np.identity(x.shape[0])/self.beta\n self.invcov = np.linalg.inv(self.cov)\n dcdw = self.kernel.backward(*np.meshgrid(self.X,self.X))\n term1 = np.array([-0.5*np.trace(self.invcov.dot(d)) for d in dcdw])\n term2 = np.array([0.5*self.t.dot(self.invcov).dot(d).dot(self.invcov).dot(self.t) for d in dcdw])\n updates = term1+term2\n kernel.update(self.lr * updates)\n new_param = kernel.get_param()\n return np.allclose(pred_param, new_param, atol=1e-4, rtol=1e-4)\n \n def fit(self, x, t, param_itr=100, lr=1e-1):\n for i in range(param_itr):\n if self.fit_1(x, t, lr):\n break\n else:\n print('[w] hyperparameter(s) may not converge yet.')\n print('[*] {} iteration(s) has proceeded.'.format(i))\n \n def matdotsq(self, X, A):\n return np.sum(X.dot(A) * X, axis=1)\n \n def predict(self, x):\n k = self.kernel(*np.meshgrid(x, self.X,indexing='ij'))\n mean = k.dot(self.invcov.dot(self.t))\n c = self.kernel(x, x) + 1/self.beta\n var = c - self.matdotsq(k, self.invcov)\n std = np.sqrt(var)\n return mean, std",
"execution_count": 19,
"outputs": []
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2018-08-09T10:15:36.646814Z",
"start_time": "2018-08-09T10:15:35.996540Z"
},
"trusted": true
},
"cell_type": "code",
"source": "beta = 50\nN = 30\n\nX, t = generate_data(sin, 0.3, N)\n\nkernel = GaussianKernel([1.,1.])\nmodel = GaussianProcessRegression(kernel, beta)\nmodel.fit(X, t,10000,1e-3)\ndisplay_predict2(sin,X,t,model,text=r'$N={:2d},\\beta={:.1f},\\theta_0={:.2f},\\theta_1={:.2f}$'.format(N, beta,*model.kernel.p.tolist()))",
"execution_count": 48,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": "[*] 1284 iteration(s) has proceeded.\n"
},
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 576x432 with 1 Axes>",
"image/png": 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VLoAQ1V96ejo+Pj5YLOem4Pj6+pKWllaifR47doxdu3bh4+ND27Zt8fDwKIumCiGEKER1TqIU1VR4eDhJSUkcPHjw7GNaa/78809at27t1L601nz22WdMmTKF6Oho/vrrL8aNG8eBAwfKuNVCCCHsSQ+ETXJyMiNGjKB///7079+/sptTo7m6ujJo0CDeeecdevfuTUhICOvXrycpKYm7777bqX1t3bqVnTt3MmHCBLy8TE7tli1bePfdd3n11VfP6+UQQghRNiSAsPH19WX+/PmV3YxqKSYmhi1btuDi4kKnTp0ICQkp9jkdO3akbt26/PHHH+zYsYN27drRvXt33N3dnTr2unXr6NOnz9ngAaBdu3YsX76cAwcOEBUV5fTrEUIIUTwJIESprFixgtWrV9O1a1eysrJ47bXXGDhwIBdffHGxzw0LC+O2224r1fFzcnJwdT3/z9jd3Z3sbFlvTQghyosEEKLEDh06xJ9//sn48ePx9fUF4Morr2TSpEm0adMGf3//cm9D+/bt+e233+jUqdPZQOLAgQOcPHlSeh+EEKIcSQAhSmzTpk306NHjbPAAEBoaSuvWrdm6dSuXXJK/EGjZ69q1K5s3b+a1116jS5cuxMfH888//zB06NACeyaEEEKUDfmEFaViynKcy2q1Vlg1SYvFwgMPPMCOHTvYtWsXAQEBjBs3jqCgoAo5vhBCXKgkRV2UWKdOnVizZs0561jExsayY8cO2rZtW2HtUErRqlUrBg4cSL9+/SR4EEKICiA9EKLEIiMjufLKK3nllVfo1KkTWVlZbN68mUGDBuHn51fZzRNCCFGOJIAQpdK3b186dOjA1q1bcXFx4YYbbiAgIKCymyWEEKKcSQAhSi00NJQ+ffpUdjOEEEJUIMmBsMmtRLlixYrKbooQQghR5UkPhI1UohRCCCEcJz0QQgghhHCaBBBCCCGEcJoEEEIIIYRwmgQQQgghhHCaBBBCCCGEcJoEEEIIIYRwmkzjFNWb1QrZ2eaWk2PuW62Qu8iXUmCxmJuLC7i6mptFYmchhCgNCSBscgtJ9e/fn/79+1d2c0RBMjMhPR1SUyEpCVJSICPDBAm5ClgdlPwrg2oNnp7g7Q3+/uDlZe67u5dv+4UQogaRAMJGCklVQTk5JkiIj4czZ/KCBaXMxd7d3QQBJZGdbQKRuDhzX2vw8ICgIAgIAB8f02MhhBCiQBJAiKolJ8f0Lpw8aYIGMEMOth4DrTV7Dh7kYEwMwQEBtGveHFfXEvwZ5w5leHnlPZaVZY579Ki5HxQEtWuDn58EE0IIkY8EEKJqSEmBU6fg+HHTG+DubnoC7IYfsrKymPPxx5yOj6fVRRexfe9evvzhB54YOpTaQUGlb4Obm7mBaUNKSl4QExpqggkfn/OHRIQQ4gIkAYSoPFYrJCRATIy5WLu6mpyEQhIcf1izBlcXF1585BEstm1+XLOGxcuX8+Q995Rt25QywyPe3qadcXEmuPHygogIE9xIr4QQ4gImqeii4uXkmN6GLVvgv//MBTow0AwVFDE7Yv22bVxz6aVngweAy7p25VBMDMkpKeXXXosFfH3NkIaLC+zdC5s3m4AiO7v8jiuEEFWY9ECIiqO1CRwOHzYzKnx9zZCAg6xa45IvwLBYLCilsBY0+6I85CZvZmfDwYMQHW16JEJCTA+KEEJcIKQHQpQ/rc1QxZkzsG9f3mwHJ6dNdmjRgh/XrEHbBQt/btxIvdq18ff1LetWF83V1fSaeHvDoUOmN+XUKdObIoQQFwD5yiTKV2qqucAmJJihgMDAEu+qb69ezFi0iMnvvkvrpk2JOX6cvYcO8cTQoWXY4IKlpqXx67p17Ny3Dx8vLy7u2JE2zZrlBRJZWSY4iomBRo1MLocQQtRg0gNhk1tIasWKFZXdlJohJweOHIGtW03xp6CgUld/9PTwYPTw4Vx9ySVkZWfTvHFjXn7sMcLq1CmjRhcsPSODNxcu5NjJk/S79FLaNmvGZ//3f3y/enXeRm5uJpCwWGD7dpPbkZFRru0SQojKJD0QNlJIqgwlJppv45mZZrZCGZaNtlgsdGjZkg4tW5bZPouzev16wkJDGXbLLWcfaxEVxSuzZtGrc2e87WtJeHiYW1KSGdZo0MBMAZWpn0KIGkZ6IETZyU0s3L793G/k1dx/Bw/SuXXrcx4LrFWLiLp1ORgTU/CT/PzM7cAB2LkT0tIqoKVCCFFxpAdClI2kJDO9MSvLDFdUxDfupCSTX3H4sMmxSEnJu2VlmeqVuetceHubnoCICIiMNBd3B/n5+HAqt+S1jdaaMwkJRSdvuriYc5GSYoZyGjaU3gghRI1RLQMIpVQI8DjQQGt9dxHb+QOTgINAY2Cq1npvhTTyQmG1wrFj5kLu5LRMpxw7Bhs2wMaNpofj0KG8KpH2cgtAubmZ3Iv09IL3V6uWSXZs2xbat4d27SA8vMCL+6WdOzN7yRJaREURUbcuVquVb3/7DT8fH8Idyb/w8TFBzIEDZl2Phg3NMIcQQlRj1S6AUEo1BwYDA4HDxWz+DrBUa71cKRUGLFdKddG6oooG1HCZmSbXITGx7Icr0tLgjz/gxx9h3TqIjTWPe3tDq1bQpw/Ur28uxpGR5pu+j4/pcbBvh9VqkhlTU00QEh1tkjuPHIE9e+Czz+CDD8y2tWvDxRfDFVfAJZecDYYaRkRw89VXM33RImr5+pKUkkJocDAP3nEHytHehNzeiORk0xvRtKkJYoQQopqqdgGE1noX8IIyn9ydC9tOKVUbuAm4z/a8WKVUOnAx8EdFtLVGS0w0Mw1KOTXzHKmp8PPPsGoV/P67CSICAqB7d7j3XujYEZo3d65gk8ViggovLwgONsGHvawsE0hs3mx6OH79Fb76yvRg9OgBV18N/frRrV07rFYrK3/7DYDIevVK9hp9fU3gtWOHGU4JD68ReSJCiAtPtQsg7BRXQ/gS4IDWOsvusZ3AtUgAUXJamxLOBw6YPAIni0EVaN8++OQTWLbM5DXUrg033gh9+0KXLsUGDKlpaeTk5OBXkmJSbm7QsqW53XmnSQTduBF++sncxo2D114jukMHdoSFcdvgwQT4+7Nu61YmL1jA2BEjnD+uu7vpjYiNJXb/frYlJeHu40OnTp3wl/oRQohqojoHEMVpBJzK99hpIKwS2lIz5OSY3IPjx0s/ZGG1mgv04sXw11/mQt63L9x+O3TqVOhCVdnZcCbBhfQMxbFTyXzx/W8cijmFi2sOEXW8ufP63rSIql3yuMbVFbp2NbcxY2DLFrKWLKHOypUMz842ww9Dh9JgwAAyMjP57Z9/uP7yy50+jAa+Wr+eNX//TecWLUgPCmL58uXcdddddOzYsYSNF0KIilOTAwgfICvfY5lAcCW0pfrLzDRd/SkpZiigpKxW+OEHeOcdMwQSHg5PPQUDB5r1JGyb7D/kxsbtHmza6cn+aDeij7kSfdSVoyddycmxzztoe87uJy8wP328rTSOyKJxpLlF1c+kffMMOrbKwMvTwRQYpaB9e/b7+/N9w4Y8FhQEH38Mzz0H77zD5ddfz1cBAVCCAGLvoUOs//dfXnrqKXxcXCAlhSu6d2fa++/TokULvOxrSwghRBWkqms+oVLqJaC71vqaQn4/Guintb7C7rFJQJTW+rb82wcEBGilFL6+vvj5+TFw4EAGDhxYXs2vXrKzzewBMD0FDsrKyiLHasXTwwOsViw//USTTz7Ba98+0iMjOTZ0KPGXX062duHfXf6s/SeQjVsC2LXHl+QUE9u6ulqpVyeduqEZ1AnNoG5oBsGBmeRYk0lMOU3TRvVwc7WSmWUhNdWF/dEJWHO8yc4OJOaoJzGxXsQc9SQ9w/RouLpYaRKVQpuWibRvk0DPLnHU8i96NCwtPZ0tu3bRrV07FOC3bh11PvwQ33//Jd3fn9N33smpm25COzGzYt/hw7i7ueXlUlitkJnJ9pgYQiMjqV27tsP7snf69GmCSxPgiWLJOa4Ycp7LX4cOHTZorQvNJSxOTe6BiAaC8j0WBBwoaOOwsDB27NhR7o2qdhITYdcuU7/A09Ohp8QnJrJo2TIOxsTg7uZGw/h4hm7fjvfOnWbWxJtvkt6rP7/8XIuVk334aa038YkuWCyaji0zuGtAMh1bpdOxZQatm2QUOBzx69//cuTYMYbcUP+cx1f9sZ34xERuu/ZaIBUwaRsxx13Z8K8Hf2/15O8tXny7qh6ffRWOxaK5uGMa11+WwvWXp9AiKrPAMg3/rF7Nro0bufnqq/G48Ub2dujAqunTuffECcLnziV8xQp4+mno18+hOg+7Nm7E19+f9vbJmFrz548/0qxWLdpffnmJVvfcvHkz7du3d/p5wnFyjiuGnOeqrzoHEMV9Sq8BopRSFq117hKJzYDJ5dusGuTUKTNs4USypNaadxYvpn2LFjzcrx8ub78NX3xBsocHux97ip1Rj7P420C+ed6HjEwLEXWzGHh1Mn0vSeHKHqkEBTi2mmXD8HB+WLOGnJwcXGz5Elprtu/dS88OHc7ZVimIqJtNRN1sbuiTAph0jvX/erLyVx9W/OLDs1Nq8+yU2rRpmsG9AxMY3D+J0OCcs/u475ZbWLx8Oc+++SaeHh5YLBZuvf9+vFq2hLVr4fXX4cknYdEikzuRrw35dWrViveXLTunFPaR48fZe/Ikw2rXNkFb06Zlk6QqhBDloDoPYUwBumite9s9NhlYo7X+ynZ/GbBQa/2NUqou8K3tOTn599eyZUstPRB2jh41My0CApz6Jrzn4EGWrFjB+KAg1PTpkJpK/A13M+LYUL7d1J2UVHdCg7MZdF0Sg/sn0rlNRokKM2qtmbNkCVatubZ3b9xcXfnl7785HBvLmBEjcHXy2/uRY658/ZMPH3zlz7qtXri6aq7rncJ9tyRw3WUpZ/NFk1NSSE1PJyQwEIt9EmlOjpn++dZbcPIk3HwzPPusOX+FtP/LVatYt3UrnVu3Ji0jg007djC4f386t2lj6kUoZaatOpEPId/ayp+c44oh57n8KaVKNYRR7QIIW/2HUZhKlKHAXGCa1vqQUmob8LXWepxt22BMj8NBIAJTifK/gvYrAYSN1nmFlkow02LrDz8QMmUKYQcPEtfyYl7wm87sdZ2wWDTdOh/kheHu9OmZWpLe+fNkZ2fzw59/8s+2bWTn5NCueXP6XXrpuYtblcD2Pe68/6U/Hy735/gpV5o1ymTUsDjuuiERT49i/r+kpMDcubBwoTl/48bBNdcUOqxx5Ngxtu3ejbu7O51atSLAfhpnWppJXm3RwtSPcIB86JY/OccVQ85z+bvgAojyIgEEJng4dMhUbAwMdG7NBq3hk0/Qb7xBaqbmzdDpvHx0BMEBVh64Ix5vz/foeHFD+rVtW/y+qoisLFj6vR9vLgxk0w5PQoOzeXRIPI8MiSfAv5ihlp074fnnTdntK66AF1+EunWdb0RGhgkkmjVzqHKlfOiWPznHFUPOc/krbQAhJfCEYbWaIYvcGg/OBA/HjqGHDYOXXmKdS09a5OxmZupAXnxkG79/9DvNGi0kO+cwodUso9rNDQZdn8SGLw/z4/vRdGyZwQszQoi6qhFTFgaSll7EOWrRwpTJHjMG1qyB66+Hb791vhEeHqZ8986dBa/9IYQQlUQCCGGCh337zNi9s8HDH3+Qdf1NpP21hQeZw21+3/LCBHeWvv0D3p4f8uWqr/H39eXpYcNwKc+SzVqbPITMTHPLyDC33Ps5OWabElAKruyRxv8tiGHDl4fo0jqd0ZNr07RvQxZ+7k92YbNAXV1NCe4VKyAqyiRZjh1rhjkcflmanzds4Pn33uOh4cN5Y/x4du7cWaLXIYQQZak6z8IQZSE3eIiLc25Ni5wckifPxvv9WeyiFSMDP+aOR2sz49ZDeLhroBOXd+907nMSEkrf3uxsExhkZZmAIDfY0drMWHB1NVUsc4MVq9U8JyvL3HLlBhPu7uZbvoNJGR1bZfDdwhh++cuLsdNCGD6uLlPfC2TW+BNc3j2t4CfVr28qbs6ebfIjNm6EKVOgTZtij/fd77+zaedORtxxB+EhIWzbsIGFM2fywJNP0qRJE4faLIQQ5UECCJvk5GRGjBhB//4X/taoAAAgAElEQVT96d+/f2U3p2JYrbB3rykSVchsgYJkHT3J0aHPUv/QnyxS97D3ngl8+0gafr5lECDkl51tluTOvfi7u5tppf7+pi6Fm5u5ORIA5PZSZGfn9VIkJpr1N5KSzDaurmbWQzH7u7x7Gms/jearH30Z9XoIVwyNZHD/RKY8e5K6tc+b5GPa+Pjj0LOnqRdxxx1mlsZddxXa45Odnc0Pa9bw3AMPEBJkSpp06NaN1PR0Vi1dSpOxY4t/zUIIUU4kgLDx9fVl/vz5ld2MipPb8+Bk8LB92W5qP/8AITnxvNV0Dte93ZehjVLLtm1ZWWZlTqvVXMhDQkwbvbxKVxdBKbM/V9e8oli5FR9zj5mQYHINkpLM9t7ehR5TKbjpqmSu6ZXCpHlBvPFuICt+8eHVJ04z8s74gpfz6NIFli83uRETJ8K2bfDKKwVO1UxKScHN1fVs8ACAiwsXtWrF/y1caPJV6tQp+fkQQohSkByIC5HVCvv3mwulg8FDeoZi8cg1NBpzOxnanXXPfc0Ty6+gaaP8y42UkNam9sGZM6Z3IDzcdPF37AgNGpgZCOVZVMnNzRyjfn1o3x7atjXHzckxbUpIMP8ugJen5pXHT/PvN4fo3j6dx14NpdfgSP47UEjZ71q1YNYs0yOxYgUMGgTR0edt5ufjQ1Z2NqfyJU/uPXKEepGR5j08frzUL10IIUpCAogLjdZw8KCpMulgzsPajR7M7b2EIT/dS2xwG2p99ymXDW1QogJQ58nKMvkXCQmmPa1bmwt4WJj59l8mBykBLy/z7b5dOxNM1KtnApy4ODP0UYAmDbP4bkEMH005yq797rS/sQEzPwzAWtCMT4sFRo6EefMgJgZuuQX+/POcTVxdXbmqZ0/mf/YZh2JiyM7OZvPOnXz1449c3auXCf727ZMgQghRKWQI40KiNRw+DCdOQFD+ZULOl5UFr073oemCZ3mCjzja/SYumv+ySTosrcxMc0F2dzfrYwQFObVQV4Xy9ja3evVMoBMTY3olPD3N43aUgjv7J3FZ11SGj6vLY6+GsuwHX96bdIwG4QVM1+jdG5YuhUcegfvvh/HjTX6EzTWXXoqHuzvzP/uM03FxNIyI4N6BA2nSsKHZIDDQ9ERYLHnDMUIIUQEkgLiQxMRAbKxDwcPBI64Mf9KH57YO4gp+IePhJ6n36AOl7xHIzDTTGD08oEmTElW7rDQuLubcBQaa4KeIQCKsTg4r58ewcKk/T74WStsBDfjfa8cZ2Df5/P02aGCWCX/qKVNwKjoaRo0CiwWlFFf06MEVPXoU3qaAAJMMW13OoxCiRpBPnAvFsWPmwhQUVGAQcCY+np/WruXHNWv431LoM8CLN/+9lsssq+HNN/F47MHSBQ85OXnTLy+6yAwLBAdXz4ueUmYmSPPmZsjF09MEEunp5202/NZEti4/SPPGmdzyWBiPTqhNRmYB59HX10zzHDQIFiyAJ544b3+FcnExeRX//Vfo8IoQQpQ16YG4EJw+bapMFlIkavX69Sz74QdaN2nNkm+uZO9ad351vYT6brFYZs423ewlpbWZ0WC1motu27YUPD2hmvL1NYFEYqLJLTlzxrxOu+GYRpHZrP4omjFTa/PW+4Gs3eTFp9OPElU/XwKqq6vpgahfHyZPNrkNc+Y41GOEq6uZ2hoTY9piv6aGEEKUg2r49U84JSHBfDOtVavAb/txCQl8uWoV9978CAuWjuTYWlc2e/Ug1HKE+BnTSxc8pKebC2pwsEmM9PKqWcGDPX9/M2ukSRPzuuPjz6l86e4O08aeZNmsGPZFu9Hxpvos/8nn/P0oBcOGwYwZpnz14MFmZVRH5NbE2LnTqWqXQghREhJA2OQWklqxYkVlN6XspKTA7t3mG3EhhZE27diBr3cfrr6vHXrnTjZ49yLAN4ffH3+cv0s6vGC1mtkKWpsu/kaNyncKZlWhlAmW2rUzMzji4sxCWHZu7JPCpmWHaNIgixsfDmPinKCCK2z37WtW9DxxAu680/QgOcJiyVs7I62QyphCCFEGJICwyS0kVWOqUKanm4tIMcWXVvzahEnzB9HFZSOrXa/Ao5YXfPwxiWFhJTtuWprp9YiMNN/I/fxK+AKqMVdXkxjZpo0JKuLisJ/L2TAim9VLohl0XRLjpodw+xP1SEktIC+iSxf44APzXg4ebN5PR+SW5t61S3IihBDlRgKImigry/Q8uLoWOuUyOxsenVCb6e/35JqgpSxLuQpXfx/48EPia9Vi3bZttG/RwvFjam0ulEqZXoewsOqZIFmWfHzMuYiMNEMadj0CXp6axVOOMXn0SZZ+78sld0ZyKKaAXqJWreCjj0wQOGQIrF/v2LG9vc17sns3ha/2JYQQJXeBf8LXQDk5ZkpfTs55UwtzJacobnw4jHcWBzJtwC8sS72PBGsOK+69l8+2bePVOXO4qmdP6oWGnn2O1pr/Dhzg8//7P5b98ANHjh3L22Fmpsl1qFvXXPB8Chjbv1BZLCaYatvW3M8d2sHEWqOHx7FyXgwHjrjR9db6/LO1gICvcWNYssTUeRg+HP7+27Fj+/qa92bvXgquZiWEECUnAURNorUZK09KMhePAsQed+HSIZH83+8+fPbAjzz52024BQRg/eAD3Bs1ws/Hh6eHDaNvr152u9V8snIlH379NT7e3iilmLFoET+tXWvqIaSlQYsWptu+piZJlpa3t+mNqFcvr1y3Tb/eqfz16WG8PTWX3R3JN78UEICFhZkVPcPD4YEHHA8i/P3NkNKBAyVezlwIIQoiAURNEhMDJ08Wur7F1l3udLutPnsOuvPLi79x62e3md6CDz4gpHVr+vbqRb/evambr6Lh3kOH2L5nD88/9BDX9u7NjX368NwDD/DNd98Rn5Fhvl07sSDXBcvFxUzRbNHCBF3JeUWlmkdlsfbTw7RonMkNI8OY90mt858fEgKLFpkgYsQIWLvWseMGBppkzJiYMnohQgghAUTNcepUXqGoAvz+jxe9BkeiNfw9Yw2XzhlkLmjvvQcREUXueuvu3fTo0AHP3HyKnBwCc3Jo06ED/2ZllU1p6wtJQIAJujw8zpnuWbd2Dr9+GE2/S1N48MU6jJ0acv7IQ0iISayMjIQHH3Q8iAgKyitjLoQQZUACiJogKcmMc9eqVWChqBU/+9D3vnDCQrP5e84mWk68yyxdvXChWYeiGK4uLmTkdrlnZpou8agoMvz8cJPgoWQ8PExPRJ06ZkjDlujo66P5alYsD9wez+vzgxj+fJ3zcyCDg00QUb++48MZSpmeiH37TKEpIYQoJQkgqrv0dDNdz9e3wFoPH3zlx02PhNGmaSZ/zPmX8OeGmgqH8+ebCooO6NKmDWs3beJ0bKzpem/VigMpKfz333+0zU0OFM6zWEzeSNOmJgi0Tbl0dYU5L5/gxUdO896XtbjjqXrnl78OCjLDGbk9EVu2FH88FxczrXbXLhNACiFEKUgAYVMtC0llZ5sqk66uBdZ6mP5+AEOfrcdlXVP5ae4egseOMN9AZ82CDh0cPkxYnTpc160bry5YwIL165n94Ye8/fbbDBs2DC8vr7J8RRem4GCTYJmVdTYvQil46dHTvDX2BF9878eAh8LOrxURFGSGoEJCzOyMXbuKP5a7u+n92L37nEROIYRwltKSmQ1Ay5Yt9Y4dOyq7GY7TGvbsMcMJtc5PuJswK4jxb4dw89VJLJkcg8czj8MPP8D06XDNNc4dKz4efH1JrFOHf3fvxsXFhbZt2zodPGzevJn27ds7d+wLSWamCQjT0s55T/+31J/7X6hD93bprJwfQ4B/vsSII0dMoanMTHZOn06Lbt2KP1ZSkpkZ0rSpzJxxkvwdVww5z+VPKbVBa925pM+XHojqKncp6XzBg9YwfkYw498O4e4bE/j0raN4TJsEq1bBmDHOBQ+5xaECAqBZM/yDg+nZsyfdunWTngcnZGVlYXWkDoO7u8mLCAgw760tuB92SyKfvnWUf/715IqhEZyOy/ffNiLC9EQoRdSoUSagKI6fn8mFOHRIpncKIUpEAojq6MwZk1EfGHjOw1rDc9NCmDA7mPtuSeC9ScdxXfy+SbgbOhTuucfxY2htjlO7tll+W76lOi06OpqpU6fyxBNP8MQTT/Dhhx+SXtwS3S4u5nzn1ouwBR63XJPM17Ni2LHXnT73FhBENG4M//sflrQ0uPdeswJrcQIDTT6MfVEwIYRwkAQQ1U1Kihm6CAg4Z8aF1jB6cgivzw/iwTvimT/hOJZV38Hrr5uFmcaMcfwYucFDeLhZCOtCL0ldAnFxccyYMYPu3bszY8YMJk6ciNaaefPmFf9kpUxyZaNGpgfINg2jX+9Uvp4dy8597lx5TwSnzpz7vuhmzdjz2mvoEyfg/vvPqTNRqMBAswx5fHwJXqUQ4kImV4bqJCvLjJF7eZ0z40JreGpSbab+L4hHhsQx+6UTWLZsgtGjzTLakyc7HgRYrebba2SkuRUwLVQU748//qBz585cfPHFuLq64ufnx5AhQzh27BhHHBliAFMavGlTk+eSlQVA316pLJ8Ty+4D7lx5T+TZIGLPwYNMmjePX7Kzmd+jB9adO8l5+OHiEyUtFlOtMjf3QgghHCQBRHVhtcL+/eanp+fZh7WGMVNCmL4okCeGxvH2uJOo2Bh4+GFzAZo9+5ztiz1GXJypDRERIcFDKZw4cYKG+WpsWCwWGjRowAlnijkFB5u8iOTks8HA1ZeYIOK/g25cMTSSnfsSmPfpp1zTqxc9O3ZkyLRprL35Zlz++gvGji1+HQw3NzMz47//zgYqQghRHAkgqouYGHNxz7c89svvBDN5QRAj74xn2tiTqNQUGDnS1BSYO7fQypTnyQ0eGjQw6y6IUomIiGD37t3nPJadnc2+ffsIDw93bmcBAdCypandYKsVcdXFqayYG8ueQ25cN6IBHVr0oGOrVgD4eHvT/ZVX+K5zZ/jmG9MDVRwvLxM87N8vSZVCCIdIAFEdnDljylTnS5qcNC+Ql98xCZMzXziB0lZ45hnzTfKttyAqyrH95862kOChzFx88cXs3LmTlStXEh8fz5EjR5g7dy7NmjWjTp06zu/Qz8+sdJqebm5An56pfDkzlsOxwUxecBPJKXk9Ri4uLvx39dWcvv56M0Nj0aLij+Hvb3IhHB1iEUJc0CSAqOrS0kzSZL4y1dPfD+C5abUZ3D+Rea8cNykOM2bAjz/Cs8/CpZc6tv/chMmICAkeypCvry9PP/00x48f55VXXmH27Nk0bNiQe5yZCZOfj48JIjIzz+Yr9OudyrP3/8S/ewIZ8FA46Rnmv3R6RgYHY2OxPP889Oljkml/+aX4YwQEmGD1zJmSt1MIcUGQQlI29evX19dccw39+/enf//+ld0cIzsbtm83/7aru7Dgc3/uH1eXW/om8fG0oyafcsUKePppuPVWmDDBsfwF+9kWFZAwKYVhykhqKuzYYXIXvLxISk7mzqc3svLX++jR5RQLXtrKyl9XUa92bQYPGGC2HzLELOm9ZInJqShKbkXMNm1MsSlxDvk7rhhynsufFJIqI76+vsyfP7/qBA9am+l1GRnnBA/LfvDlgfF1uKZXCh9NsQUPO3bA889Dly4wfrzjgUB8vFnMSWZbVC/e3qYnIisL0tLw8/Xl/UltGHrT96xZV5tbHguiTbOWDLr++rzt58wxQxQPPGBqPxTFzc0k3kpSpRCiCBJAVFUnTsDJk6ZL2ebXv70Y9FRdurVLZ+nbsWb5i7g4eOQRkx8xY0aBa2IUKD7ePKdhQwkeqiMvL5NYmZUF6ekEBwby3qTGPDVyHzv2duDrH29AKbv/3nXqwLx5poT1gw+aeiLF7T872/RaSC+lEKIAEkBURUlJ5oPbLnjYtMODAQ+FEVU/i2/mxuDjrSEnxwxbnDgBM2eaKX+OSEw0SXlRUVIkqjrz9jZBREbG2dkZd912hGeGn2HOxwG8OjvfDJzmzc1aKLt2mb+bnJyi9+/vb4a4jh4tpxcghKjOquXVQyk1Xin1glJqqlLquiK2+1wppe1up5VSbhXZVqflLqjk43O2fPTeQ25cMzycwFpWvl8YQ1CAbV7/jBnwxx/w4ovg6LLaycmml0LKU9cMuUFEWtrZOhGvP32KoTclMP7tEOZ/mm+htd69zXDXzz/Dm28Wv/+AALNeRkJCOTReCFGduRa/SdWilBoGBGitn1Kmj3aNUmqr1jq6gM1jgEZ291O11lV3UFdr0/MAprAPcPSEC1cPC8dqhVULjxBR15Q1ZtUq0yV9220mcdIRueswNGtmxrlFzeDjY4KIHTvAakUpeHfCcU6eceGhl0IJDc7mxj52QxZDhpj8mvfeM1N3Bw0qfN8Wi+mt+u8/k1TpaFEyIUSNVx17IJ4AvgDQWluBH4GhhWybobU+aHdzogRgJYiNNbkJtmJR8YkWrhkewYkzrnw7P4ZmjW2xz759Zqpm27bwwguO7Tsz0wQQzZufDU5EDeLra97brCzIysLNDT6bfpQubdK548l6/P5PvtVTx46Fyy4zM3b++qvofbu7m96qvXuLH/YQQlwwqlUAoZQKBNoAO+0e3glcWzktKkOJiWaFTdvy3OkZigEPhbFzvzvL3omlS1szxk1aGjzxhAkCZs50LGkyJ8fkVTRrJtPyajJ/f/P3k5QEOTn4eGtWzouhUUQWAx4KY9tuu78VFxeYOpXsyEisjz2Gji6oA8+Or69JvCxuOyHEBaNaBRCY4Qir1tq+ys1p4LwKSEopdyBKKfWcLVditVKqxPNdy1VGhuki9vMDiwWrFe4ZU4fV67354I1jXHVxat62r7xiCku9+aZZ66I4Wptejaios8GJqME8PEx+S1wcWK0EB5q8GV9vK9cMj+BQjBm1jD1+nNcWL2Zqp06kp6Vx/I47OLRnT9H7DggwCZWOLBUuhKjxqlUhKaVUL+BHrbWH3WNXAF9rrf3ybVsLeFZr/Zzt/h3AZOAirfV5SxQGBARopRS+vr74+fkxcOBABg4cWK6vBzAX+IQEM2XOlpcw891G/O+j+jz+wH7uGZT3jS/wu+9o8PrrHBsyhGPDhzu2/4wM0+vg61serXfK6dOnCXZ0pogokbPnODXV9ETYchb27vdm2GPtqR2Syf/e3sDuA5upHxZGnZAQ/Neto/HYsexr1474yZNxLSo/xmo1f6uBgeesCHshkb/jiiHnufx16NChVIWkqlsA0QX4W2ttsXusL/Ch1jq0mOdagDTgCq31n/l/37JlS71jx46ybnLxjhwxN9uiV7lVJkfcHs/cl0/klWjYswduucXkPbz3nmMf3rnTNZs0qRLTNaWyXPk75xwfPmzyamx/W7/85cXV90XQqeUJbr92Fk/eOyTvie++C1OmsP/WW2n86qtFHyR32e9WrS7IIEL+jiuGnOfyd6FVoowGlFIqwO6xIOBAcU+0JVyeAQKL27bCJCaaMWVbvYdVf3jz4It16HtJCrPG2wUPKSnw+OMm237qVMc+tNPSTI9G48ZVIngQlSAyEkJCzHAGcHn3NN6dcJy/t9Zh5a+3nlsfavhwYrp0odHSpfDbb0Xv18vL9GwdPlx+bRdCVHnV6sqitT4G7Aea2T3cDDjvE08p1Uwp1cHuvhsQDOwt73Y6JLfegy3vYdtud255rB4tozL5bMbRc2OEV14xyyxPnQqhRXa0GFlZ5gO+aVOZrnkhUwoaNTLJlYmJANxzcyIj7zzAT3+1YfK7eTkxVq1Z3LUr6Y0awahRedOJCxMQYEpin6jaE5uEEOWnWgUQNm8Dt4LpigD6AnOUUm5KqflKqYtt290HfKyUyr0U3wT8rrXeVeEtzi+33oNS4O5O7HEXrnsgHD8fzcr5Mfj7WvO2XbECvvoKHnoIevQoft9Wq7lYNGlyzhoa4gLl4mL+Ftzdz5avfntcJp1a/cuYqXWYviiZXfv2Mefjj3H398dj/nzTwzVypCk6VpSAAPN3XFxZbCFEjVQdA4iZQLZSaiLwFvCa1voA4A5cB7SybfcCsAyYp5R6HrgaGFLA/ire0aOmW9nPj+QURf+HwjmT4MI382KIrJedt110NLz0EnToAA8/7Ni+4+Ohfn2T5CYEmICgWTMTXGZk4OKi+G2xKy0vOsHoyW2YuXgPTRo04JHBg7FERpoKp4cOwejR5jmFcXExSZp795rESiHEBaXaZUDZchnGFPB4ChBudz8DGFuBTXNMUpL5cA4MJCcH7hxVj807PVg+J5YOLTPytsvONh/gAFOmOJb3kJRkAoew82a1igudh4cpNLV9O1gs+Hi78euHSXS/LYCl349k9H2HcXOzBQHdusGYMTBxIixYACNGFL5fLy8TtB48aKYKy8JsQlwwqmMPRPWVlWVmU/j6gsXC82+FsOIXX6Y/d5LrLsvXDTx7NmzaBC+/DBERxe87Pd0kSzZuLB/iomA+PmY4IzERrFZqB+Wwcl4MmVmK6x4IJyHJ7uPgrrvguuvgrbdg7dqi9xsQYFaOPXWqfNsvhKhSJICoKLl5D1YreHiw+Gs/3ng3iAduj+eRIfHnbrt+PcyZAzfeCNdfX/y+c3LMvH9JmhTFCQw0iZVxcaA1zaOy+HJmLP8ddOfOUXXzKlUrZcpcN2oETz0Fx44Vvd9atUyib2pq0dsJIWoMCSBskpOTGTFiBCtWrCifA5w4YSr4+fvz9xZPho+rQ++uqcx84cS5HQaJiWboIjzc8XUu4uNNz4OPT7k0XdQwdetCvXrm7wYzvXPmuBN8+5svz00LydvOx8eUS09PN+XTM8+rv5bH1dXkQ+zZI/kQQlwgJICw8fX1Zf78+fTv37/sd56aanofAgI4csyVGx8OIyw0m6UzYs/tMNDaLM194gRMm+ZY9ciEBKhd29yEcFT9+mZ6Z1ISAA8OSmDknfFMXhDE4q/tirpGRZlciE2bYPLkovcp9SGEuKBIAFHecnLMtzIvL1IzXblxZBjJKRZWzI0lJChfhvtXX8G338Jjj5mKk8VJTzdDFg0bSt6DcI7FYtbMcHU9W1ly+nMnuKxrKsPH1WHdVrtlu6+9FoYOhQ8/hJUri95vrVqmPoSslyFEjScBRHk7fBgyMtCeXgx7rg4bd3jw8bSjtGqSrzv40CFTMKprV3BknYvcvIcmTS7IcsKiDLi5mbyZjAzIzMTNDT6fEUtYaDY3jgwj9rhL3rajR0PHjjBunJm2WRilTBCxb19eyWshRI0kAUR5OnPG1HyoVYuJc4L49Ft/Xh91iusvzzfjIjsbnnnGfKC/+aaZX1+c+HiT4CZ5D6I0vLxMjYikJLBaCQmysnxOLEkpFm58OJy0dFvPlpsbTJ9utn/00aKLTLm6mu337SMvK1MIUdNIAFFe0tPNN7VatVj2ox8vzAjhrhsSGT087vxtFy6EzZtN/oMjS3QnJUFwsGNlrYUoTq1aZhjMtmZG66aZLH7zKP9s8+T+cXXy1syoU8dM6zx4EMaPh6IW4vPxMT1kMTHl3XohRCWRAKI8WK1mSpurKzsO+XD3M3Xp2jaN+ROOn5+qsGuXyXS/5hoz1lyc3Ex4yXsQZaluXRMg2GZm3NAnhVefOMVHK/yZ/K5dVdNu3czCbitXwmefFb3PWrVMAJGQUI4NF0JUFgkgysPRo5CYSIL256aHw/D2svLFzKN4euT7xpaZCc8+az5oX3yx+IBAa9P7kLu2gRBlRSlo0AC8vc8OTzz34BluvzaRsdNC+H61d962I0bAJZeY2Rm7ilhaRimzWNx//5k8CyFEjSIBRFlLSoLoaKz+Adw1ui77j7jx+YyjRNQtYG78rFnmA3jCBAgKKn7f8fGmKqW/f9m3W4jchbesVsjMRClYOPE4bZpmMmhUPQ5E25J1LRYzpdPf39SHKGoxLXd3s9/9+4se8hBCVDsSQJSl3FLVPj68OteUqZ425iSXdikgG33LFpg/H26+Ga64ovh9p6WZBDZZ50KUJw8PMzMjKQlycvDx1nz5Tixaw02PhJGaZuslCw42y8sfOmQWfCsqOPD1NcMYR49WyEsQQlQMCSBsSl2JUmvzYWq18s2aIF56J5i7b0w4p0x1ZmYmq9ev5+PPPyf50UexhobC888Xv++cHBNAXHSRYzM0hCgNf39T2dSWDxFVP4slU46ydbcHI16wS6rs1s2sErt8OXzxRdH7DAgw/z+KWyJcCFFtSABhU+pKlKdPw8mT7DkTzJDRdenQMoO5L+eVqU5JTWXS/Pls2bWLXr//ju/x48xr1479cQXMysgvIcEkTXp7F7upEGUiNNRUN7UlQPbrncorj53moxX+zPwwIG+7hx6C7t3NMNyePYXvz2IxPRFS6lqIGkMCiLKQlgb79pHkGsiND4fh6gJfzozFyzOvW/e71auJiozkkYsuImLVKrjrLrqOGMGSFSvQRXX/JiebJMs6dSrghQhho5SpM+LhcXaBrOcePMOAK5J56vXa/P6Pl9nOxcUsN+/ra2ZnFLKYltaaxKwsMtPSzDRQIUS1JwFEaVmtsG8f2s2dYS+Es2u/O59Oj6VB+Lnfsrbu3s1lrVrBc8+Z3oRRo+jYqhVxiYkk2NYjOE92trk1aiRTNkXFc3Ex+RCZmZCVhcUCH0w+RlRkFrc+Xo+Y47akytq1TRCxf7/pichny65dvPj227w0cyaj587lo8WLyYyNreAXI4QoaxJAlFZsLKSkMHlJBEu/9+ONp09xZY/zkybd3dzwnTXLJJK98QZ4eZGdnU12djZuhZWizh268PQs+PdClDdPTzMzIzERtKaWn5Vls2JJTbMw8NF6ZGTaAtsePcxwxpdfmjVdbA5ER7P466+58/rrmTpmDK8+8QSpSrF49mwpdS1ENScBRGkkJkJ0NKv+DeO5t0K4/dpERg0rOKehn4cHAd9+S85dd0H79mit+W71apo0bIhPQbkNyclmaqessikqW2CgmccgBj4AACAASURBVD5sy9dpeVEm779+jL+3ePH4q3Z/n488YtZyeeklU8Ya+OXvv+l36aU0j4pCKYWfry93DxzItgMHSNi82fTgCSGqJQkgSiorC/bu5UBCEIOeDqPVRZksnFhApUmA1FQ6LFlCQnAw44H/LV3Kq7Nns3nnToYMGHD+9rlDF1JtUlQV4eEmF8c23DawbzLP3n+GeZ8GsPBzW12S3HwILy9THyItjVNxcUTWq3fOrjzc3QkJDSXu+HEpdS1ENSbLOJaE1nDwIOlpmlueboDVCstmxeLjXUgy5PTpqOhoai1ezMP163P46FEu7tiRpo0aoQoKEBISTLexh0f5vg4hHGWxQFQUbNtmciLc3Zn45Ck2bPdg5MuhtGmWSde26SbZd/Jks6LspEk06N6d7Xv30qRhw7O7ik9M5FRcHHUbN4YjR0xgIsXRhKh2JIAoidOn4dQpHnu7BRu3e7JibgxR9bMK3nbTJvjgA7jzTujShTAgrKgZFblDF8HB5dJ0Z50+fZqff/6ZQ4cOERwczOWXX05Du4uBuIC4u5ukyn//hcBAXFwsfDLtKJ0GNmDgo/XYuOwwtYNyoFcvE0AsWEC/du2YsG0bHm5udGrdmlNxcXzx/fdc2aMHnp6eJjDZswfatJHy7EJUMzKEYeNwISnblM1Fv9Tn3c8CGPvA6fOX586VkWFmXdSrB6NGFd+InBwzdNGgQZUYujhx4gSvv/46FouF66+/nsjISN555x22bt1a2U0TlcXPzwyt2YpMBQda+XJmLCfPuDD46bp5q3c//ji0aYP/66/zzHXXcfTkSaYvWsTXP/3ElT16cN1ll5ntcoOGgwel1LUQ1Yz0QNjkFpIqkm3K5taD/jw0oR6XdzPFdQo1e7aZ2rZwoZknX5yEBFMBsIrMuli5ciWXX34519pWCW3evDnh4eF8/PHHtGnTpuDhF1EpUlNT2b59O/Hx8aSmpuJdnkXH6tY1uRCJieDvT8dWGcx84SQjXqjDK7OCefmx0yYwmDYNbriB2pMmMWzRIihstpGfn+nVCwiQJeqFqEakB8IZsbEkHE/nljFRBPhZ+Xja0UI/E9m+Hd5916x1ccklxe87JcWMA1ehWRd79uyhc+fO5zzWvHlzkpOTSSqsdoWocBs2bOD555/nn3/+4eTJk2f/XW5yi0y5uJxdZXP4rQkMvSmBCbOD+O53W/BSv76ZkbF+PcydW/Q+AwLgwIFCC1EJIaoeCSAclZSEPhzNsDeasT/ajU+nH6VOSE7B22ZlmaGLoCAYM6b4fVut5oO4ihWM8vPz4/Tpc3tYUlJSyMnJMePXotIlJCTw0UcfMWrUKEaOHEnLli0ZPXo0H3/8MXGOlEkvKTc3k+ibkgI5OSgFs188QZummQweXY9DMbbI+oYbYMAAs/Ls+vWF78/FxfS87dlD3jiIEKIqkwDCEbZVNt9a1pAvfzDFonp1LqIIzrvvmmW6X3rJZJgXJyHBfFvz8iqzJpeFSy+9lC+++IIE23oImZmZfPLJJ3Tp0gV3SXirEjZu3Ei7du2IiIg4+1hYWBgdO3Zkw4YN5XtwX18T9NryIby9NEvfjiU7G259PCyvyNSLL5o6Ek8/fXZtjQJ5eUF6upmZIYSo8iSAKI5tlc0/NnrzzFt1uemqJJ66t4hvdvv2mdyHa6+FPn2K3396uvnmVbdu2bW5jPTs2ZN27drx0ksv8dprrzHG1pty6623VnLLRK7MzEw8Cpju6+HhQVZWITODylJoqJkxlJgIQJOGWbw36Tj/bPPkqUm24ThfX7P098mT8MILRSdLBgSY2hDx8YVvI4SoEiSAKM7p05zYHcftz19Eowjz4VjoKIPVCuPHm1Uzx40rft9amy7gxo3NdLYqRilF//79mThxIoMGDWL8+PEMHz68wAuWqBxt27Zlw4YNpKTkzQRKSUlh/fr1tGnTpvwbUEA+xM1XJzNq2BlmLwlgyQq/3Iaa4lLffw+ff170/vz9Ye9eU29CCFFlVb2rVlWSnk7Onv0MmtCSMwkWlr4dSy2/IkrvfvGFGed95hnH6jgkJpopnn5+ZdfmcuDt7U2jRo0ICAgofmNRoerVq8cll1zCxIkT+fbbb4mOjmbixIl069btnGGNcpUvHwJg0lOnuKRTKve/UIcde23DXffdBz17wsSJJkAojLu7CSQOHJCpnUJUYRJAFMY2ZXP8gvr8/LfP/7N33uFRVVsffk96bwTSSAwgJAbEgKAfgoKIIFKkKlwLIEVRmoCFIoJgoyPlIiiKiijCBRT0Iio2QK4KoSX0DiEhBdLbzPn+WElIQspMMiEk2e/zzANzcmbPnslk9u+svdZv8e/psdwVWsoV0ZUr4sB3zz3Qt2/Z42dlSdThZn3JK2osjz32GEOHDiU1NZXs7GyGDh1Knz59bu4k8vIhcnMcbG3hqwXRuDob6Tvaj+QUTT7vuY3kGD8+P2JRLK6ukJAAsbE36QUoFApzUQIilxuMpC5dYus2G95e5cuw/tcY3Cep9AHeeUdMpmbMMK2SIjlZvnBLrANVKEynUaNG9O/fn4YNG9KoUaOqmUS9elJ5lFvi6+9j4Mv50Rw7Y8fw130kmFCvnoiIo0dhzpzSx8sr7UwtwahNoVBUKUpA5JJnJNWjRw9ITubMX1d4+s3bCb8jg/enlnEV9OuvsHUrPP+85DOURZ5dtaenZSavUNwK5OVDQH7+Qod703nrpTi++s6NJZ/nboG1bw/PPAOffQY//1zyeNbWkk904oQq7VQobkGUgChKdjYZh07Qb2oIRiNsWByNo0Mp+7BpaRJ1aNgQRowoe3yjUcpCbxG7aoXCotjaSr+MlJT8Vt2vDEukx4MpTHivLn9G5PqHvPwy3HEHTJoEMTElj+fgIFsd586Ve0pnz57l448/Zvbs2axZs4ZYtS2iUFgEJSCKcvYs4+YE8E+kE5++d5mGgWWUwi1eLGVnM2ea1gwoKQkCA28Zu2qFwuK4uoqvSW4+hJUVrH7vMvV9suk/1o8rCdbytzJvnoiDV14pPcLg7g6XL0tOhJlERUWxePFiAgMD6d27N25ubsyePZsLymtCoagwSkAUJD6ezz7V+WBjPV4dnkDPh8rYe42MhNWroX9/KGL5XCy5bZAprRunQlET8POTcsyUFAA83Y1sWBxduOlWo0YwZQr8+af0iymJgqWdpSVeFkHXdTZs2MAzzzxDp06daNy4MT169KBbt25s2bKlgi9Qoaj+WFVQA1RLAaFp2jRN017XNG2epmndSjnPX9O0DzRNm6Bp2nJN00ptNHFw2yWem9OI9vekMWtcXOmTMBjEFMfTU8KxppCXOGltbdr5CkV1RdNkW89gyM+HaBGWyZJpsWzf6czMZbllzv36wSOPwKJFUFqXV1tbSTg+dSp/a6QssrKyuHz58g1+GHfffTfHjh0r18tSKGoMSUk4QIUshaudgNA07VnAQ9f1mcDLwOuapgWWcPpaYKmu6/OAj3JvxWLMNtJvcmPcXY18WVqTrDw+/xwOHZKeF6bYVScnizeEKecqFDUBe3u4/XbZtsv1cxjaL4nBfa7x5lIvtv3uJEJj5kypzhg/Pj9iUSwuLjLW5csmPb2trS22trZcLeJqeeXKFdzV36GiNmM0wunTtTICMQ7YAKDruhH4ERhU9CRN01oC/rquH8g99y8gvCSxcemyPScv2PPVgmh865aR8X3pEixcCPffL5bVZWEwQE6OJE4qFLUJT08ICMi3ptY0WDotlmaNs3hyoh/nLtnI9sTcuZJLNGNG6eO5u8PZs6ULjVysrKxo27YtX3zxBRkZGQAkJSWxbt062rdvX+GXplBUW+LixHaggpglIDRN61/g//U0TetQ4RmY9/yewJ1AVIHDUUBxq3j7IucBHAW6Fjd2coot74yP44HWZbypug5vvin/vvGG6Z4PQUFyRaZQ1Dbq1xfzqNxW3XlNt7Ky4fFxfrLDcffd8OKL8M03sHlzyWNZWUkk4vhxEeVl0KtXL9zc3Jg0aRKzZs3ijTfe4I477lACQlF7ycqCM2eIyaq4jUCZLkaapvUAHgT+CzTOO67reqymaY01Teuv63op5vYWpQFg1HW9YDp2POBfwrlFExlKOhcX5xwmDjWh/fEPP8COHZI5HljSzkkB8hIn69Ur+1yFoiZibS1W1wcPyt+CjQ1NGmSz6u0Y+o/15+XZdVk09Yr4qOzaJV1sW7QQ0V0c9vbShO7MGdkiKQUbGxuefvppevXqRUJCAnXr1sXJycniL1GhqDZcuECWwZrHxpTw92UGptgg7gJCkHyDtpqmPYRsG/yY+7OnKzwL03EGil52ZAHFNZ5wBorWYJZ0LlbW5/C69x5cnJ1xdXGhb48e9O3Ro/A5qancMWMG2bffzrHOnSE6uuwZZ2aKo97Bg2WfW8OJj48nIiKiqqdRo7ml32OjEc6fzy9hvv0ueLK/kfc/q49/g2i6dLyC7SuvEDJ0KJljxnB88eLSnVoTEiQUa0ZJdGKiCRcJZXBLv8c1CPU+VwLZ2ZCQwOyVTdmz3xGXCg5XpoDQdT0emAvM1TRtFvA78AiwGggEfgE+reA8TCUDsC1yzBYobt8hA3A08VwCfLyJLKu06+23ISEB2+XLCTcl+pCSIuVsTZqUfW4tICIigvDw8KqeRo3mln6PdV3a3V+9KnkPwMdvpHH6RDqz5oby2P85EhruB2+9hc3YsYSvWwcTJpQ8Xk6ObA+GhMgWyU3iln6PaxDqfbYwRiMcOsTXB0JYu6E+4wYl8OHqig1pbhLlHl3Xt+m6/pKu62HAbcBjFZuCWZwHNE3TCraF9AJOl3CuV5FjJZ1bNlFRYr37xBPSmrgs8hwnSwrDKhS1DU2TRGIrq3w/B1tb+GphNA72RvqN9Sc1TZOyzv79YeVK2L275PFsbGQ74+RJZXWtUJRFXBzHjhgZOiOQ/wtP570JVyo8pFkCQtf1b4vcT8ithLgp6Lp+GTiFbKnkEQL8WszpO4ucV9q5pWM0Sna4h4eUmplCUpJknyvHSYXiOnmtvwtYXdf3zWHt/MtEnrDj+Tdym25NniyeKS+/fIMDZVp6Ov/97TcWf/YZq7dt49Tx41LBoVAoiicri7Qj5+j3eih2trBuYbRJxsllUR3LON8H+oOEIoAuwL81TbPVNG2Fpmltc8/7A0jTNK1Z7rktgCO6rkea/YwbNsC+fZI4aUr9eHa2JI75+pr9VApFjcfVVSIRuVbXAJ3uS2PG6Hg+/8aNFV+5SxOt+fNlu2Py5HwfidS0NN5dsYJLsbE80Lo1AT4+fPDdd/y5bVuh8RQKRQEuXGDU3GAOHbdnzdxoAv3KrmAyheooIBYDOZqmvQUsAN7Wdf004qjVDWgKoOu6DvQDXtY0bQrwPMX4RZRJQoLUqLdqBb16mfaY5GQIDlatuhWKkvD1LWR1DTBlZAKP3J/KmFl1+eeQvTTbmjhRqp6++AKAn//8k0ZBQTzbrx93hYbS6b77GP3006zfuZOcqCizrK4VilpBcjKrPjLy8bfeTB2ZQJf70yw2dLVb4XK3TF4r5ngqEFDk2GnKIxoKMn++CAJTPR/S06VO3ato+oVCocjHykqsrvfvl4idrS1WVvD5nGha9L6NfmP8+ec/Z/EaNAh27oR334VWrTh6+jTdO3QoNFR9X1/c3Ny4GBfHbadOQWio6nSrUAAYjez7LpoX593OQ21SeWNUvEWHr44RiJvHvn3w9dcwaJBplRS6LmY5wcHqC0yhKIs8q+tr1/K3KOp4Gvl6UTQXY20Y9JovRl0T8eDmBhMm4GptzdXk5ELDGAwGklNTcfb2lrFMKa9WKGoBV4/F0m9CEN6eBtbOv2zxNkxKQJRETo4Y2vj4iEOeKSQni2GUS0WraxWKWoKXl2xnJCXlH7r3rgzmv3aFLTtcmP2hp/SQee89OH6cvhERbP3lFxJz8x2MRiNbduzA38cHby8vSXQ+e1b+FhWKWowxLYNBI+w5F2PPuoXR1PWyfKVStdvCqCxSUlMZ8frr9HjwQXp07Ch7rkeOSJdAUwSBwSC3+vUrf7IKRU0iKEgW/IyM/KqlF5+8ys69DkxZ4M29zTN4sF07ePZZvFetos+LL/Lm0qUE+PgQl5iIm4sLjQIDeXfFChzs7GjTtCn32NmhNW8uVR8KRS1kzrRkvvm9LoumxNKmRUalPIcSELm4ODuzYuZMuRMbK82y2rWDLl1MGyApSaytVb8LhcI8bGxkK+PgQVnwra3RNFjxZgwRUfYMGO/Hvo1n8X/pJdizhxZr1hD61VecNRiwt7fn002bSM/MpG/nzqSkpbH1l1+4cPEifV1dpWRUbScqahk7vklm8gJvnng0idFPXy37AeVEbWEUx3vvSWLXtGmmfflkZcmXoOp3oVCUD2fnG0o7XV101r8fTUqaFQPG+5FjZQfz5kFmJo6vv05ocDBnLlygnpcXg/v0oXFwMC3Cwnhp8GD+iIzk6pkzcjGgUNQiLp3LYcAQB5rclsmHs2IqVT8rAVGU3bthyxYYMcL09tspKapsU6GoKL6+0v67QP5C08ZZrJwZw+9/OzF5vreYS02dCv/7H6xcycnz52kRFlZoGGcnJ26/7TZOJyfD6dOQmnqzX4lCUSVkZ8MT/XJITbdiw5LLuDjrlfp8SkAUJCtLHCeDgmD4cNMek5EhV0+qbFOhqBiaJkLcaJS/xVz+1SOZkQOvMucjLzb96Ax9+0LXrvD++zSIiyMmrnDTXV3XiY2Px93DQwypTGz9rVBUd14bn8Uffznw4awYwm7PKvsBFUQJiIKsWiVXLFOnmm5BnZqqyjYVCkuRV9qZnJxf2gmwYPIVWjXLYPBrvpw8bwdvvgm+vrT/6iv+2r2b42fOAJCTk8N3v/6Kna0tDerXl7/j7Gxp/a1X7tWYQlGVbPjayPwldowaEMeA7illP8ACqJh7LlbZ2bBsmSRNtm9v2oNSUqTEzNW1cienUNQmPD2li21srJRlAvZ2Ol8vukTLPrfRb4wfu77MwXHOHGyeeooJ584xe/16bGxsSM/MJMDHhxf+9S+0PFHv7i5tv93cVJ6SokZy7BgMeRbubZrCvCkJZT/AQigBkYvtlSvSv2LSJNMeoOsSZjWlrbdCoTCPwEBJqExPz2/VHVw/h89mX6b7cwGMmVWPlbPuhhdfxHPxYt7q2pXLbdvi6OCAZ3H9atzd4dQp2W50dr7JL0ahqDxSU6FvHyP2Nga+XnzZIk2yTEVtYeRinZoKo0bJlY8pJCXJublfbgqFwoJYW0sJZnp6oVbd3TqkMvn5eD782p1P/uMGI0dCq1ZYzZyJf0ZG8eIhbzyVD6GoYeg6jBypczhS44u3zxIYcNOaYwNKQOSTY2PDyFOn+Pbnn8s+2WCQ35ypYkOhUJiPk5NUXRTpsjljdDwP3pvGyOn1iDjmBHPmSAXU+PGFki9vQOVDKGoYK1bAZ59pzBh2gYcfurniAZSAyMfg68u/33pLXCjLIs806mbGihSK2ki9ejeUdtrYwNr50dTxMNBnlB8JTvVh1iw4dEicY0vD3R2uXFH+EIpqz19/wZgxOl3bXGXK2JuTNFkUJSByMZi6FZHbOVAlYykUNwFNkyhEXs5RLj7eBjYsjuZijA3/muCHoVMXePxx+PBD2LWr9DE9PKTaKqVqvnQViooSGwt9++r4eefw2ayzWNmWo0vWqVMVnocSEOaSnCwGU5Zua6ZQKIrHzk7yIYqUdt57VwZLpl1h2x/OTHu/jiRAN2wIr7wCCaVkoltbSyLlsWNyQaBQVCNycuCJJySQtvGtSOrUL0ceXkqK5A9VECUgzCEzU5ImPT2reiYKRe3C3R0CAuBqYV//4Y9fY1j/a7y9vA4bd9aDBQvknEmTSs9zsLeXn586pfIhFNWKV16BX36BFa+eosU95WgWp+swZQpcuFDhuSgBYQ55plFW6m1TKG46AQEi4NPSCh1eMi2We5qnM+hVH47Y3gmvvirfsB9/XPp4rq6QmAjR0ZU3Z4XCgnzxhWjkMU8n8nTPa+Vrn/DFF/Df/8LYsRWej1oJTSUtTYxo3NyqeiYKRe0kr7QzM7NQaae9nTTdcrDX6fViAEm9noGHH5bGWxERpY/p4QFnz95Q6aFQ3GpERMCwYfBAm2zmDj8KLi7mD3LwILzzjpglDhtW4TkpAWEqGRnSI0NZVisUVYejY7GlnYF+OaxbGM2Jc7YMes0P46y3wccHXnrphm2PQlhZSSTi2DERJiaQnZ3N77//zm+//cbV0sZWKCxEfDz07g1enjrrXj+IbZ1yXMgmJcG4ceDtLR2nLRBJVwLCFPIsq8uj+BQKhWWpW1ea1yUlFTrc4d505rxyhU0/uvDul8GwcKFkmpWVD2FnJ9GN48cLRTaKY8+ePfz9998cO3aMkydPMmPGDH799VcLvCiFongMBhg4EC5d0vnP/DP4+GD+1oWuy9/B5cuyB2KhPD4lIMpC1yVTu379qp6JQqGA66WdVlY3GEeNG3SVgd2TmLqwDtuu/R9MnAg//wyrV5c+pouL5DidO1fiKUlJSXz55ZfcddddDB06lCFDhjBlyhS++eYbYpWvhKKSmDIFtm+HZe8mcc9tMeW7kF29Gn78Uf4eWrSw2NyUgMglJTWVEa+/fqMTZXKyeD4oy2qF4tbB1vZ6aafxugOfpsHKmTHc2SSLgRP8ONVxGDz0kLhV7t9f+pgeHnKFVoIY2LdvH82bN8fJySn/mLe3N/fccw///POPRV6WQlGQr7+W3YbnhuYw9L4jUo1kLhER8vl/6CEYPNii81MCIhcXZ2dWzJxZ2InSaJT4kb9/1U1MoVAUj6vr9aZbBXB20vnPkkvoOvQZ7U/qtHev50OUliypaSIiTp0q1mTKYDBgU0zo2MbGBkMZWx8KhbkcOgRDhkCbNjqLXjgqpcfm+g8lJkreg6+vJE9aOIdPCYjSSEqS0jF7+6qeiUKhKA5/fwnpFlnwGwVl88XcaA4ctWfIOyHo8xdATEzZ+RAFTaaKbI/cdddd7Nu3j8wCyZYpKSn873//Izw83KIvS1G7uXpVkiZdXWH9+9HYZ6dIbxhzMBrFNCIuTvKByhO9KAPVzrskDAZRaz4+VT0ThUJRElZW0KgRHDhw3WY+l67t05j9chwvz67LnU0e5PWJE+Hdd+HTT2HQoJLHtLcX8XDyJISE5Ger16lTh0cffZR9+/Zx4cIFrK2t2b17N23btqW+ypFSWIi8pMkzZ2DH1jT8c85JZMxcli6F336D6dPhzjstPU1ARSBKJilJEidty+H0pVAobh4ODnD77bI9USS6MOHZRJ5+LIlp73uzMWAUPPig7AcfOFD6mK6ukl9RJKmyU6dONG/eHDs7OzRN48UXX6Rnz56WfkWKWswrr4jP07LFBtp5H5GImLkll7/+KgKiVy8YMKByJoqKQBRPdraUyaiGWQpF9cDLC/z8pGyzwNWapsGKmTEcPW3L06/6sWfFfJoe7Sb7wps2lW4M5+4uLpVOToW+C5ycnLjvvvsq89UoaimrVsH8+TB6NAzvdBoSDeZXXZw/Dy+/LNGz6dMr1btIRSCKIyVFTKNUwyyFovoQFCTbD+nphQ472OtsXHIJdxcj3V5tSuL0hablQxRMqizQTlyhqAx27oTnn4dOnWD+5DgRw+bmLWRkwJgxkv+weHGlVw8qAVGUrCwxlqlTp6pnolAozCHP6joj4wZDKH8fA5uWXiQmzppeK7uRM26i1MV/9FHZY7q4wNGjJjtVKhTmcvasJE0GB8O61enYnD1ZvqTHN9+EyEjZpgsKsvg8i6IERFHyog+qYZZCUf1wchKTqWIspls3z+Sjt2L47S8nRp17Bb1LF+mXsWdP6WPa2cn3wdGj0ktZobAgKSnw2GNy7frNRgOe8Sckkmau2+TXX8OGDdKm+8EHK2eyRVCrZC4pqamMmDyZb//3P9lPVSgU1ZO6dcXvv4jVNcC/eiTz2ogEPljnycrwpXDbbeIPERNT+pguLhLZOH26kiatqI0YjfDMM9Lj6quvINTlgjRuNLdk8+BBmDED2rWTBIqbhBIQubg4O7Ni4kR6PPOMapilUFRnNE1iwVZWxW47zBoXR/cHU3hhbkP+GPKh5EyMHXuD78MNeHhIV6PU1MqZt6LW8cYbsHGjBMK6tE6AS5fML9lMSJDPb926MHfuTc3dUwIiD12Xq4xKMNtQKBQ3GVtbaNJE4sMFrK5Bvl+/mBtNs8aZPPpee869+B7s2wezZ5c9rqenjBkfX0kTV9QW1qyBWbPg2Wdh7HMZcOKEVAWZcwGbkyMRtCtXYNEiizXJMhUlIAqi2nUrFDUHFxeJRBSTD+HqorPlg0u4Ouu0+/w5UvsPhs8+g61bSx9T0yQn4vhxVZmhKDe//SbCoUMH+PcSA9qJ4yJ6zfUdeu89+PNPmDkTmjevlLmWRrUTEJqmtdM0bammaa9pmvaOpmklxms0TeumaZpe5Na32JOtrMQ8RqFQ1Bx8fa9HDYpQ3zeHb5dfJOGaNQ9Fvo8hvCVMnSpXgqVhZSXi5MgRyYtQKMzg6FHxd2rYEP7zH7C7fE7yHpydzRto48brrqq9elXOZMugWgkITdO8gA+A8bquvwskAGNLeUgA0B5okHsLBjYWe6a1tYo+KBQ1jbzW37pebI5Dy6aZrJ0XzV9RLoxwXYvu6AijRhUrOAphZydXi0ePivGcQmECV67Ao49KgcXWreBpiJMOsObmPRw4ANOmQZs2Yl1ZRVQrAQEMBnbpup6XGbURGFnK+XWBCF3Xz+Tezuq6bizlfIVCUdOwsyu29XcePTqmsmDSFVb93oTl96wS++pXXy323EI4Ocke9IkTN/hOKBRFSU+Hnj0lT/Lbb6GhT6r0W3F3N+/iNTYWXnxR3FEXLDC/3NOCVDcB0R6IKnD/JBCkaVqTEs5303X9xlouhUJRu3Bzk5LNnxY0BgAAIABJREFUYvIhAMY8c5VRTyXywvc92dnpDTGZWras7HFdXaVc9PTp0l0tFdWemJgYvvjiC+bMmcPq1au5cOGCyY/NK9fcswc+/xzubZktHV8dHc0TAFlZUqaZnCy9Lm5y0mRRqpuAaADE5d3RdV0HEgH/Es530DTtJU3Tpmqa9pOmaVUX61EoFFWLn5984ZaQ/Lhg0hUebZ9C++1TuNimn1gBb99e9rientIy2YwFRVG9OH/+PHPmzMHV1ZXHHnsMPz8/Fi5cyJEjR0x6/KRJsH69GET27W0Ue3SjURrBmYqui9dDRIR0lQ0NLeersRyaXoWqWdO0DsDUMk7br+v6hNzzTwJTdV1fW2CMc8BLuq5vKGb8GcBiXdfjNE1zRSIWz+i6/t+i53p4eOiapuHi4oKrqyt9+/alb9/i8y0V5SM+Pp46yiK8UlHvcRkYjVI3b21drNtsapo1Q8fcRcx5K4773otn7CmOL11KRsOG+efEp6VRpzijn4wMiXRUcv+B2sKt9Fk+fPgwXl5e+Pn55R+Lj4/n/PnzhIeHl/rYDRvqMGtWIP37xzFp0gW01BRJmrS3N2sO3hs3Un/RIi4/9RSXhw0r1+soyv0dOkQl63pYeR9fpQLCXDRNOwy8p+v6pwWORQNDdV3/zoTHrwTQdX140Z+FhYXpkZGRlpyuoggRERFl/rEpKoZ6j00gORkOHZLIQTEi4vIVa+4bEIhzcjT7rFpj4+Igl4+5iW4R0dGEF1hI8jEYZIskJES52VqAW+mz/NJLL/Hmm2/iWqBSz2g0MmrUKBYtWoRtCeWXmzZB377QpQt88w3YXI2TrYs6dczLe9i1C4YNgwcekK01S7Ra0HVcQ0MrJCCq2xbGeaDoX6YnYKq/bFzu+QqForbi6lpqPoRvXQPbPrpIjHUAj1tvQL98Wcx6yuqDYW0tCXFHjxZro62ovri6uhIXF1foWGJiIvb29tiUkMPw228wYAC0bi1tKmzSkyXh1sPDPPFw8qR02GzUSJwmb6E+TbfOTExjJxCSd0fTtGDgKnC06ImapjlqmvZYkcO+QBlF3gqFosZTRj5E4+BsvltxkR/S2jK9zmK5Apw7t+xxbWxEoERFKcvrGkT79u1Zt24dybmfl/T0dNauXcv999+PVowY2L8fevQQr4etW8HZOkOEpYuLeUmTCQnw3HOy3bF8uTzeEug6JCaSDRXqDld19R/lYxWwXdM0R13X04HewMK80kxN054GgnVdnwk0AjZqmtZe1/XfNU1zAToCD1XV5BUKxS2Cpsm3+8GD0i+jmP3oVndmsnHJJbo9N4LmPvvp+/G/JXHt3ntLH9vOTr6gIyOhWTOVE1ED6NixI1evXmXatGnUrVuXK1eu0LJlS3r27HnDuSdPypaFmxts2wZ13HMg8phEqOzsTH/SrCwp14yNFZfUgADLvBhdF2Hi50cmlNEApnSqlYDQdf2ipmnjgCWapp0BXIFJBU75P+BOYKau64c0TesJjNM0Lc9MaoSu6yoCoVAorvfLOHhQrgqLaUL0cNs0Vr97mQETFrHX8zDNXn8dpwULJIJRGvb2krAZFQVhYeZl2ytuOTRNo2/fvnTt2pXY2Fjq1KlTKB8ij8uXoXNn8RbbsQMCA4xw/KSIVHP6LOk6TJkCe/eK18Ndd1nmheSJB39/ad1QQaqVgADQdf0H4IcSfvZikftbgC03Y14KhaIa4uIikYjTp0tMfBzYPZmYOGsefGcDUc6taTB1qkQi6tcvfWxHR9nGOHJERIQ5V5+KWxInJyeCg4OL/dm1a/DII9IZ/qef4I5QHc6clVwbc/0ali2TrMtx48S60hLkiYf69eVmAefl6pYDoVAoFJalXj3w9i4xqRJg3OCrDBtuxf2p35OVapB9aVMSJZ2dJRJx5IiyvK7BZGSIy2RkpPS3uPdeIDq6fDbV330H778v/S2ef94yE6wE8QBKQCgUitqOpknXTnt7qc8vgXcmxPHA4750z9qE4dQZyYw3RRS4uEgFhxIRNZKsLHj8cfj9d1i9WrYwiI2Fs2cl8mDOYh0RITbqrVpJh01LLPRGo7SfDwqCwECL9nxSAkKhUChsbCQfIiurxEVe0+Df02Nx6hTGUONK2L1bnAFN8dJxcZGxjx0ruxxUUW3IyYEnn5TeFkuWwMCBQGKiZFJ6eJhXcnn6tEQcfH3FBdUSW15Go8wnONhySZgFUAIil5SUFEaMGMG3335b1VNRKBRVgaMj3H67bGaXIAqsrWHGa0dIergvs5giBf4ffmja+K6u0lHp6FElImoABgMMHiweY/PnwwsvIGXBx45JCUYxSbklcuUKDB0qKnXlSssYkeW5rgYHS9JkJaAERC4uLi6sWLGCHj16VPVUFApFVeHlJWHexMQST7GxgbXzL7Or3at8yRPiD7Ftm2nju7kpEVEDMBolDWbNGnjrLfEZIzVVqm6cnaXCx1RSUmD4cPnMffCBLPgVxWAQ8dCoUdkVQxVACQiFQqEoSEBAqSZTAPZ2OhuWXubj1svYRRtyxr/MyS1biI6NLXv8PBGhciKqJbou6S8ffQSvvw6TJyO5M5GREsUy1+th1Cg4fhwWLYLmzSs+wTxL9UaNwMen4uOVghIQCoVCURArKynttLKS9PoScHTQ2fBBHK80WMa5HH+8J73Jp4sXs2j1atLS00t/Djc38QaIilIiohphNEo37aVLYeJESYEhPV1+j3Z25jXIMhrhtdckl+att6TPRUXJyZFIxk0QD6AEhEKhUNxInslUenqpWw1/H9pDlx7reKPZ12Rn2TDyp/9R38aGtVtMsJ9xdRXxEBkpYkJxS2M0wsiRIh5efhlmzwYtM0PEg7W1eY6jui4tubduFSXSq1fFJ5iTI/k7TZpIafJNQAkIhUKhKA5n5zKTKnfu3cvjXR/gg8/dmN50PTbxMbT/8D8cPXSIDFNEgaurhJwjI0uNdiiqFoNB0hRWrJAti/feyxUPkZESqSquvXtprFolNZ9PPy1dNitKQfHg7V3x8UxECQiFQqEoiTp1xHinhKTKtIwM3FxccHLUmb0mgLfu+ByPS1EM+H4/WaY203Jxkez7w4dL9aFQVA0GAwwZImv+G2/ArFmgZaSXXzxs2iThi65dRY1U1JchO1tMzUJC5PN6E1ECQqFQKEojL6myGOfJOxo25M/9+wFwctSZ+uWdvBc8n5bXorg45F2Je5uCk5Nsmxw6VGrypuLmkpUlPg+ffSa+TtOng5aeVn7xsG0bTJoEbdqIiKhoa+6sLPm8hIZapvTTTJSAUCgUitLIS6q0tZWciAJ069CB/x04wKebNrH38GF+3PUTce0P8VHwFO44spk/+89FN5pgNAXScMvJSSIRCQmV8EIU5pCaKi25v/oK5syBqVNzDx4+LJ8Fc8XDr7/ChAnSGGvZsoobRWVlyXzuuMN8u2wLoQRELspISqFQlEheUmVmZqGogqe7O5Ofew5vT0/+jIggPSODV4cPYvDWp9nWZDT/d+gjtvdbbnIgAjs7qdA4ckR6KSiqhIQE6NQJfvxRyjUnTkQiUIcOidAzt7vqnj1SvtG4sSRSmCs+ipKVJdtdYWHmdfm0MNWuG2dlkWckpVAoagd6bmKkZuoetKOj7DP/+aeIiNzws6uLC4+2b3/D6Z03v8juXsl0PryQdb1d6fX1U6ZddNrYSDj6zBkRLEFBFQ91K0zm4kXo0kWsGdavh969EUVx9KgkvZobOdi/XyyqAwNFjbi5VWyCmZkSCQsLk/yZKkQJCIVCUatITU1l/fr1/P333xiNRpo3b06/fv2oY0oCmru7LACJibLIlyI+NCuN/9v4Kgf7pPL4kZks6eHK0+t74+5qQjjCykrGj4mRBaNRIxEWikolKkq6Z8fFwfffQ8eOSCTo9GnZJjD3d3DwoFRZeHtLFmZF8xQyMuTz0LSpVAlVMUrWKhSKWoOu6yxatAh7e3vefvtt5s2bR2BgIPPmzSPTVC8GR0dpeHTtWpmnatZW3LlhOueadmXUmVeY2+0nzkebuAhp2nVHzMOHb8i/UFiWX36B++6TnYEdO6BjB6N01DxzRhb+8oiHZ5+VqMUnn1Tc2Ck9XbYubhHxAEpAKBSKWkRUVBS6rvPEE0/g6uqKg4MDjz76KPXr1+fvv/82faDbbpOFwZSKCRsbgr6cTXyz9syIGcm8njvYf8SMMLibm/hQHDwoFsUKi/Ppp9KG289P0hVahefIHkZ0tIgHc7eQCoqHzz6reCfMtDSpJ23atOL5ExZECQiFQlFruHz5Mg0bNrwh76FRo0ZcvnzZ9IGsrMRkysbGNO8GOzvqrHmf1LvuY37ScP7d/2e2/mLGVaSTk9yiomST3pQW4ooy0XUpzRw0CO6/H3btgmCfdIn4JCeXuU1VLAcPinGEm5tlxENKikw0LMw8t8ubgBIQCoWi1uDv78+JEyfyEyjzOHbsGH7mdi3Mq8zIzpbQclk4OOD66TKyWrVlWdYwNjy3jfdWeJquBezsZEvj/HlpGW3KcypKJC1NPB5mzJC23N9/Dx56oggAXS9fsuOBAyIe3N0lrFFR8ZCcLDbZYWHmV37cBJSAUCgUtYaQkBDs7Oz4/PPPSUhIICkpiU2bNhEbG0urVq3MH9DRUUx8UlJMa8/t4IDDR0vR27TlQ4ZxdN63PDnRl7R0E69y85IrU1JkoSvG3EpRNqdPS77Dl1/C22/Dqg+N2MVekPJZZ+fybRPs2SOhDA8Py4kHW1vxeTCnSddNRAkIhUJRa9A0jdGjR2NjY8OsWbN4/fXXSUxMZMKECdiV19jH1VXq+69dM8150sEB6w+WobVry0cMw3XLWu5/MtD05Mq857S3l1D7hQumO14q+PFHaNVK8iO3boVJ4zPRjh2V99HTUxZtc9mxQ6ot/P1hzZqKi4erVyXicMcdFTecqkSUgMhFGUkpFLUDJycnBg4cyPz581m0aBFDhgzBo6JOfnXqSGJlYqJp+Qn29mjLlqF1aM8HPM+jxxbSsncQ//3NjCvfvC2NixfFWllVaZSKrsPcueLx4OcHf/0FXf8vUbYd0tPLlywJ8N13MGqUbGd99lnFqy0SE2ULJCSkfGLmJqIERC55RlI9evSo6qkoFIrqiJ+f3EpovHUD9vawZAl068bM7Em8wyS6Dg9g0jxvk3ZDAFnwPD1l++TAAfGNUAmWNxAXBz17ShvuPn3gzz9yuN3mjGxZODqW35Bp3ToYPx5atJDumhX1ecjzF8lL0L3FufVnqFAoFNUBTRPXyOxsWQhMiWrY2kqjBRcXhn01l9sbxfPQipX88Y8Da+dfpr6viUrCyUkEyenTslo2aHBLlftVJb/8IsmScXHw/vsw6pkktFMn5fdUnioLEJG2dCksXgwPPCADV6RCQtflM1OvHgQHVxvn0eoxS4VCoagO5DXeMtUjAiTLfsYMGDGCDic/5lR4HyIjNcIfu40N28y4Mra2lgUxO1sSLC9cEO+AWkpODkybJm6SLi7w5+/ZjO5+Gi0ytxmWh0f5xEN2NkyZIuKhTx9pjFUR8WA0ilW2v78Iv2oiHkAJCIVCobAs1tYSgra1lWoJU9A06dQ4cSK3RXzD+UYdaO4TQ78x/jw5wZeEq2Z8VTs5yR76xYvSh8HUvIwaRFQUtGsnLbifeUbnnx/iaWG1X8IQXl7lT0xMSZG+Fhs2SN7D229XLE/BYJDfz223SfSqPIKmClECQqFQKCyNra0kwWmaaUZTeQwfDnPn4nR0Hz9l3c+iZ/5h3X9dadY9mO9+NcN4Ki83ws5O9vmjoqT1cw0nJwfefVdSEo4fhy9WZfDJxMO4RB+XKIG7e/kX6ZgYeOYZ2L0bZs2S7poVWfBzcqTaolEjiT5UQ5SAUCgUisrA3l48InJypAmSqfToAR9/jJYQz5itXTj41jd4eRjoNiKAwa/5cCXB2vSx7OykQiQrS5IsT5yosdUahw5BmzYwaRJ072ogcsspBt4RIVf5Xl4VixQcOAD9+kmOyb//Df37V2yyWVni4RESInkP1RQlIBQKhaKycHSUWv6MDPOcI1u3hrVrwdGR0DcGsO/5FUx+Pp4137oR8kgwy9e6m5fe4OQki2hSkiyGp0/XGCGRlCTVFS1awNmzOuuWxLD+1b/wsb8qr7mi9s+bN0sWpq2tOE8V07rdLDIyJCoVFlbxqo0qRgkIhUKhqEycnWWxSEszT0Q0aiRlgqGh2E4Yw1tM5cDGU4SHZjJyug//93gQfx80w6FQ0ySb0MNDkvb275c4v6l5GrcYRqMYPoaEwLx5OoN6J3F49T/0v/e8bN+UtzQzD4NBKmReeQXCw2H9enmyipCWJkmYTZuWzyr7FkMJCIVCoahsXFyuW15nZ5v+uDp1xJyof39Yvpw75jzLT4sjWTM3mgsxNtzTP4inX/bl9HkzKvI1TapE8lqFHzokt8TEalO18eef0K6dzqBBEFQ3nT0fHuLD105Qt6GrLMwVTUZMTITnnoMPP4SBA2HVqopHC1JSZF63UDvuiqIERC7KiVKhUFQqbm4iIpKSzBMRdnaStDdjBuzejda/H/8K3cuR78/wyrBE1m9zIaRrA8bMqktMnBn5EXkRCS8vuZw/dgz27oVz5yTh8has3Ni3T/Ib2rSBk0dzWDXlJLtXH6N1O3t5LZaoYti7F3r1EpUyfbrcKuoIee2a5MTcok2xyosSELkoJ0qFQlHpeHiIiEhONq35Vi7no6P5zMGBrwYMICMhAb1/f9y3r+fdCVc4sf0MQ/pcY9kXHjR6uAGT5nkTHWuGkABZ1PLC/leuSEQiIkK8JKpaTOg6h/5Kp1/3DFq2hJ07dd564QIn/nuSIc8YsHK2UItrXYePPoKnnxYXyC+/lOhDRcdMSJDqj9DQW96a2lyUgFAoFIqbiaen9E0wMRJx6NgxFn36KfXq1KHZE0/ww4QJnPLwkHKDiRMJcL7KB2/GcnjLGbq1T+W9lZ4Ed2zA0Mk+RJ4w0+/A2vr69oa9PURHiynV339LBUdCgiRfVragyMxEz8xi2+rLdG2XxJ33OPLDDlumPR/L6Z/PMHlsGq7uFly+EhNh5EiYPRsefBA2boRmzSo2Zp5BlJ+f+IJYmynqqgHKylqhUChuNl5ekpB39Kgs2CVcmeq6zvpt23i2b1/Cbr8dgKaNG7OlXj2SNm6kxXffSVXF/PmE3HknXy2M5u1ztsz/2JOP/+PGqg3uPNo+heGPX6Nb+1TzLoBtbOTKGWQxTE6G+Hi5n5dH4eoq+/l2dnK+ra3pToq6LlGY7GxJLk1Ph5QUUi6nsGarB++tDeP0ORd8vbN5c0wcL/zrKnU8K6Hr6C+/wNSp4skwebJ4PVR0KyQ7WwRicLAIiBpKtRMQmqZZAX2BSUBnXdfjyjj/BSDPpeOUruurKnmKCoVCUTaenmWKiOTUVJJSUrijUaNCx+8JD2fh/v20GDwYJk6UUPuLL8KwYTQKgqVvxDJjdBzLvvDg31960PtFF+p65fBUz2QG975G81AzqkFARIGz8/XkP12XRT8mRkRA3oKr63JunqCwtr4uKIxGueWJhgKPy87R2P4/dz7fVpfNvzYiLd2KO5ok89nsaB7vmlw5Ha1TUuCdd6S6okkTWLlSSm4rSmamVFuEhsrvuAZT7QQEMAUIAVpQxvw1TesIdNJ1vU/u/W80TTuo6/pflT9NhUKhKANPT1m0jhy5fiVfAHs7OwwGA2np6TgXaI4Vf/UqLk5O0KoVbNoEb7wBCxfCDz/IohgaireXkWmjEpj8fALb/nDm4/+4sWSNBws+8STs9ky6d0il+4OptAlPN7/xo6bJFod9MWWkui7VHEajCIW87Q5Nk5u1NdjZkZJuzY49Tnz/mzPrt7lwJcEGT3cDzzyWxNOPJeHoe5oW/pV09b5nj2wBRUfDiBHiKmkJlZKSIq+3WbMaU2lRGtVOQOi6PlPTtNuBJ004fRzwVYH73wDPAUpAKBSKWwN39+siQtcLLcr2dna0bNqUdd9/z1M9e2Jra0tySgobt2/n/lat5CQPD1i0CLZtk0qNvn2lBPH558HODhsb6NYhlW4dUolLsGLtVjc2/+TM/E88mf2hF57uBrq0S+W+Fhn8313p3BWaWbG1VNOKbUWdnKKx/4g9O/c6su0PZ/7Y60h2toaTo5Fu7VN5qmcSj9yfmv/cEdEVmENJxMdLnsOmTdJ/Ys0aaNnSMmNfvSqGXY0bFy+saiCafguW6pSFpmnBwGnAT9f1y6Wcdw14UNf1vbn32wJf67p+g/F4WFiYHhkZWTkTVgAQERFBeHh4VU+jRqPe48qn0t7jlBSIjJSKiAKlfplZWXy8YQMnzp2jnpcXl2Jj6XDvvTz20ENoRffqExOlwdM330ji3tSp4u9cDNeSrdi+04lvdzjzw05nLl+RRd/ezkjLppk0a5xJo8BsGubebvPPxt3VWGoeRVYWXIyx4fxlW85H23Au2oaDx+zZe9iBY2ds0XWZb/OQTLq0S6XL/am0uzsDe7sb16GI6GjCLZU/YDTC11/DvHmyvfDss5I0WVGXyryxr14Vz46GDatVsqSmaf/out6qvI+vdhEIU9E0zQtwAwrmSMQDPpqmWeu6Xj0cUxQKRe3AxUVC31FRsgWQGwK3t7Pj+YEDiU9MJOHaNfzr1Su0nVEIT09xT+zWTVpRDh4MnTuLm2JgYKFT3V2N9HskhX6PpKDrcD7ahj37HdhzwIE9+x3Y9KNsKxTF3s6Im4sRV2cjug4ZmVZkZGlkZGqkZ9yYQBnkn03LsEye7JFEy6aZtGqWgY/3Tfz63b9fRFVEBNxzj/g6FMkpKTd5yZJBQdIQq5p106woVRqB0DStAzC1jNP267o+ocjjgikjAqFpWiBwDvDXdT0691hD4CTgret6fMHzfX19da8CTmN9+/alb9++5rwcRRnEx8dTp06dqp5GjUa9x5VPpb/HBoNc0ep6hXwDtMxM6q1bR701a9AMBmIHDCB24ECMJYmPYkhJteZitAMXLjkSE2tPapo1aenWpKTakJZmjWalY29nxM7OiL2djqODAZ96mfjWy8Snbga+9TJxdCxf5UR8Whp1zJhrUezPncPvww/x+O03sj09uTRyJIkPP2y5RT4nR35X7u7VdsuiRYsWFYpA1NgtDE3T6gKxwG26rp/LPRYCHAGcdV0v1GNXbWFUPiq8Xvmo97jyuSnvcXa2OEOmpkqOQ0W4fFmiElu2yFjDhklzqAoszjeDcm9hxMbC0qWyZWFvD0OHwpAhlk1qTEqSPI8mTW7597E0KrqFUZONpOKAdKCggbkXEFtUPCgUCsUtha3t9TLAhISKGTf5+sre/7p1skUydy489JD0d6ghHTkBOHsWpk2T17Z+vZS2bt8Oo0ZZTjzkmUO5uUlPi2osHixBdc2BKDMGpeu6rmnabqTkMyL3cAjwqzlPZDQauXDhAqmpqebPUlEITdOIioqq6mlUGra2ttSrVw+3GtBlT3ELYG0tiZAODmIp7eFRsQS9u+4Sq+a9e2HxYnjvPVixAp54QhZbX1/Lzf1mcvCgeDj88IMIr969JcoSFGTZ58nKEjOt224Tc6halu9QHNVVQOTJyUIptJqmPQI8quv6mNxD7wNPc72U8zFgjjlPFBcXh6ZphISEYGWqw5qiWNLS0nCqoYpd13XS09O5ePEigBIRCsugaZL8aG8Pp05JomVF/QpatoSPPxZ76o8/FhGxciU8/LD0gbj77lt/cUxOhq1bJdJw8KAYcQ0fLi6Sdeta7GkuX7lCXGIiAS4ueLq41Jg23Jai2gkITdMeBsbm3v1A07Sluq5vzr3fHHhU07QJuq5n67q+WdO0xpqmzQOygK26ru8y5/muXr1KcHCwEg+KUtE0DScnJwICArh06ZISEArLUq+elBweOSL5EZYIybdqJbcLF+CLL2Qx/u9/5cr90Uehe3fxNLhVyM4W0bNpk8wzI0NyECZPFu8LFxeLPVVGZiYffv015y5eJMDdnbMJCbR68EEGtGxZo/f9zaXaCQhd17cD20v42WxgdpFjcyvyfAaDAdsa1kFNUXk4OjqSbU6rZoXCVFxd4c474fhxqdKoaHJlHvXrS5nn6NHw/feSbLliBSxfLgt0ly7Qtq08t9mWlRUkJQV++w1++kn+TUoSofDYY9Cvn8ypEqIl677/Hlc7O9559lmsGzQgw8ODJcuW8fPPP9OpUyeLP191pdoJiKrgBrMWhaIE1GdFUak4OEBYmCQMxsRUPC+iII6O0KeP3OLi5Cp/yxZYskRyJlxcxEehTRtJxmzSxKJX/YC8pn37YN8+Gu/ZIx1As7MlmbRTJ0mQbNvWMgZQJZCdnc3f//zDO2PGYN28Obi64gD07t2bzz//XAmIAigBobhpVMeSYYXilsPaWhwPXVzg9GlZTAs4V1oEb2946im5JSZK74hdu2D3bvj55+vnBQVJtUjDhrLNUq+e5CB4e0veRl6HThub66ZLycnyb2KiCKGzZ+HMGfn3yhUZ194ePSREyi/bt4cWLW6Ow2N2NtmxsWBvj2Pr1oXyTdzd3UlLUwV8BVECIpeUlBRGjBhBjx496NGjR1VPp0w++eQT5s2bx5NPPsnx48dZtWoVM2fOJCcnh5UrV7Jx40buueeeKpvf8uXLiYqKokGDBpw9e5ZPPvmEYcOGMWeOWTmsCoWiJOrVk1yIEydkS8PdvXKSHz094ZFH5AbSgCoqSvIxjhyRbqI//SSmSuXB21sqG+6/X7qTtmwJoaGciI+3nJW1KSQng9GIY/Pm+IaGEnHoEC0L9MnYvXs3d1iiW2cNQgmIXFxcXFixYkVVT8NkkpKS2LFjB97e3pw4cYKtW7cydaqYenbt2pVLly5V2dzGjh2LwWBgyZIl+ceGDx9e6L5CobAAzs5SGXDunIT/XV0t01WyNPz85Nax4/Vjef4IsbFyu3LlesvuvJuNjVSshzvQAAAgAElEQVQw5N3c3aXCxNLbIOaSFxmpUweCg9Hs7Ojfvz/Lly/n/PnzBAUFERkZyYEDB3j55Zerdq63GEpAVFNGjBiBQ27Y0sbGBpsCyU333ntvpYbafv/9dyIjI3nuuedu+Nlff/3FqlWrOHfuXKHjYWFhvPDCC5U2J4Wi1mJjI1sInp5w8iRkZoqQuJlYWUkkwdtbcjSqA7ouwkHTJPLh6ZkfwWncuDGvvvoqv/76K3/++SeBgYFMmTJFVVcVQQmIaopDGXueBoOBsWPH0qZNG9asWcPatWtxdHRk/PjxXLhwgcDAQPbu3ctvv/3G7NmzcXNzIzIyku3btzNt2jQGDhxIUlISkyZNonXr1hw4cIA333yT5ORkZsyYgbu7O/Hx8UyYMAH7Aj7wmzdvplWrVnh6et4wp4YNG5KZmcn48ePRdZ1ly5axc+dOhg0bxrZt2wgICLhhfqNHj2bgwIFs2LCB9u3bM3jwYFq1asXUqVP5448/2LhxIw0bNsTKyoqRI0da/H1WKKoNnp7QvLnkE8TH35xoRHUlI0Nswn18JApSTKVdvXr16N+/fxVMrvqgBIQZjBsnDd0qk/BwWLiw4uPs2LGDsLAwBgwYwJYtWzhw4AD33XcfgwcPplOnTuzbt4+6dety+PBh1q1bx99//42u6wQHBzNw4EAAXnnlFdq0acOgQYNYtWoVixcvZtKkSbRr147g4GAGDx58w/PGxMTgV8q+pb29Pb169WLNmjUAtG3bFi8vL4xGI9bW1jfMz9HRkTVr1mBvb4+HhwchISFMnTqVpKQkhgwZwt69e3F1daVjx450796dwCIdBxWKWoWdnVRHJCRIgmV6umwXqOogISdHch0cHKSS5GZHamoYSkDUUHr27AlI4k9UVBRZWVkAeHp6EhoaSlCuzaurqyuJiYnk5OSQlpZGkyZN8sfYtGkT/v7+LFy4kNjYWDxMqDv38fFh167SvbqK+moUvF90fgADBgzg888/Jzw8HN9cu91du3ZhbW3NRx99BEBgYCBxcXFKQCgUAF5esjhevCjNtBwdK7X08ZYnb7sCIDhYKkWUOWCFUQLCDCwRGbhZREVF8eabbzJ+/HjuvPPOQj8ruGAHBQUxe/ZsJk6cSNOmTVm9enX+zzIzMxk9enSx2xEl0bt3b+bMmcO5c+cKiQCAEydOEBISAhQu6Sxa3llUYHTv3p1Ro0YRGhrKkCFD8ucWEhLCuHHjTJ6bQlGrsLWVxdLbW7Y1EhIsY4Vd3UhJkT4Wfn7g71+hFumKwigJVgPIzs7GaDQWOrZs2TJat25N69atycjIyP+5wWC4YcF+4403mDNnDsOHD8ff3z//eJcuXVi/fn3+/bx2587OzsTHxxc7l7vvvpsXXniBfv36ceHChfzjJ06cYMOGDdjb2+Ps7JyfZJmcnMzx48fz51Tc/FxcXHjggQfYvXs3AQEBgGx97Nu3j9jYWAASEhKIiYkx8R1TKGoReT0cGjeWhTQxUUL5txi6rpOalnbDd1m5SUm53jnzrrukVFSJB4uiIhDVnLi4ON5//31iYmKYPXs2Y8aMwcHBgYcffpjp06eTnZ2Nk5MTH3/8MXfffTcbN27k7NmzHDhwgObNmwMQEhJCgwYNcHR0pG7durzxxht06dKFxYsX8/zzzxMREYGLiwtDhw4FZHtk0KBBZGdnM2LECLy8vArNacGCBSxbtow+ffrg7u6Ol5cXYWFhTJgwAYCWLVvi7u7O448/TrNmzWjQoAGbN29m3Lhxxc4PoG/fvhgK1Jl7e3uzcuVKBg8eTEhICL6+vqrESqEoCU2TMkUPD3GZPH+ea9eusfvECRJTU2lQvz6tmjUrVM11M/ntr7/47tdfycjMxNbGhofbtqVeo0bmD6TrkhyZlSXbOAEBlmvlrbgBTbkDCmFhYXreFXZBoqKiarR5yIkTJ3jllVdYv349VlZWHD16lMGDB7N7926LP1dN7sZZkKr8zERERBAeHl4lz11bqAnv8aljx1i2YAHhfn74eXlx4Nw50rKzGT9kCI6WdrUsgz8jIvju118Z/vjjBPr5cfnKFT5av57wNm3oZur7bDRKcqTBIPkNvr5KOJiApmn/6LreqryPV1sYueQ5UX777bdVPZWbyuHDh/H398/vNhoQEEBwcHDVTkqhUFQauq7z2dq1/Gv4cJ6aMoWHBgxg3IAB+Ds788NPP930+WzfuZN/de9OYG71lm/dugzq3ZsLly+XbX+fmSlbMklJIhrCw6FRIyUebhJqCyOX6uZEaSm6devGL7/8wpIlS6hXrx7Hjx9n9uzZZT9QoVBUSxISEkhJSaFFixayteHtjVanDu2trVnz0Uc8lpgox52db0rOwJXERG7LzW3KI8DHh+zsbAwGw43bKjk5sk1hMMgcb79dXC2raPulNqPe8VqOjY0NCxYsqOppKBSKm4StrS05OTmFF2dNI9PODlt/f7mKT0gQa+yUFBETTk6VVr0R5OdH5IkT3N2sWf6xY6dP4+jgcH1+2dmQliZbFTY2UlHh5SXzUlQZSkAoFApFLcLNzY2goCB++uknunTpAkgl1/fffy8N+OztZYH29RUjqqtXpbdFYqIMYGsrRkwWuuLv1qEDq9avJ8dgIKRBA05fuMBXW7bQ6ZFHrj+ng4OUYHp4iGhQxli3BEpAKBQKRS3jmWeeYdGiRezduxd/f38iIyMJCQmhQ4cO10/Kizw4OcninZkpUYCrV+HaNYlO5OUo5LXszruZgq6DwcAdAQEM69aN73//nfWbN+Pj5cW/OnfG6OMjrppOTiJqFLccSkAoFApFLaNOnTpMnz6dqKgoEhMT6dSpU77HSonY28stz1guO1tERWamiIn0dOkxkZxcOEKQJzLyjum6/F/XJbLg4EBI69aEdOgg2yS50Y2IiIjrz6W4JVECQqFQKGohVlZWNG3atPwD2NrKzcVFPCby0HXJVTAYrv8fRDTk3ayt5aao1igBoVAoFArLoQRCrUH5QCjy+f7772nevHm+zXRlogzMFAqFonqjBEQu1c1Iavfu3bRv3x4/Pz/ef/995s+fT58+fdixY0e5x+zatSt2dnb5XvSTJ09m5syZFZ7r8uXLGTt2LEuWLOGll17C09OTKVOmVHhchUKhUFQdagsjl+pmJNWmTRuefPJJfvrpJ8aMGQPA/fffT+fOnYmLi8O6nOFDFxeX/P8PGzYMrYLlUmPHjsVgMLBkyZJ8K+vhw4ezfPnyCo2rUCgUiqpFCYhqjJ2dXaHW16GhoVy9epXk5GQ8PDwqPH7Dhg3LPOf3338nMjKS55577oaf/fXXX6xateqGLZGwsDDGjh1b4fkpFAqFoupQAqIGsXTpUjp37syhQ4eYOHEiTz31FPPnz2f58uV07tyZ6dOn4+3tzblz5xg6dCghISFkZGQwceJEmjRpwrVr1/JbcF+8eJGJEycSHh7Oq6++CsCSJUvIyMhg37593H333QwcOJAZM2bg7u5OfHw8EyZMwL5AvfbmzZtp1aoVnsWUYjVq1IjMzEzGjx+PrussW7aMnTt3MmzYMLZt20ZAQADjx4/nwoULBAYGsnfvXkaPHs3AgQPZsGED7du3Z/DgwbRq1YqpU6fyxx9/sHHjRho2bIiVlRUjR468OW+6QqFQ1FKUgDCHceMgIqJynyM8HBYuNPn0I0eOsHTpUpKSkqhTpw4bN27EyckJHx8fzp49y+HDh3F0dOTLL7/k7NmzTJ8+nVOnTjFy5Ei2bdvGO++8Q6NGjRgzZgy6rrNq1SpAmmrdd999xMfHA/DHH3+wa9cuvvjiC9LS0ti+fTt+fn60a9eO4OBgBg8efMPcYmJi8MttkFMc9vb29OrVizVr1gDQtm1bvLy8MBqNWFtbM3jwYDp16sS+ffuoW7cujo6OrFmzBnt7ezw8PAgJCWHq1KkkJSUxZMgQ9u7di6urKx07dqR79+4EBgaa8cYrFAqFwhyUgKjmhIaG8uKLL95w3NPTk86dO+Po6AjApk2bsLOzY+HCheTk5FC3bl1AKi8++OADADRN47bbbssfw9XVNV9AfPvtt9x7770AODk58dhjj5U5Nx8fH3bt2lXqObZFmvUUvO/p6UloaChBQUH5xwYMGMDnn39OeHg4vr6+AOzatQtra2s++ugjAAIDA4mLi1MCQqFQKCoRJSDMwYzIwK1AwcU4MzOTJ554gt69exc6JysrK7/qojQyMzPJzMw06/l79+7NnDlzOHfuXCERAHD8+PH8YwVLOouWdxYVGN27d2fUqFGEhoYyZMiQ/LmFhIQwbtw4s+anUCgUivKjyjirMdnZ2SUu/gaDodBi3KVLF9avX59/PzIyEoAHH3yQ7du3A2A0Gjl16lT+4wo+vnPnzmzYsCH/+fbv3w+As7NzfpSiKHfffTcvvPAC/fr1y8+tADhx4gRfffUV9vb2ODs75ydZJicnc/z48fznLfoaQKpEHnjgAXbv3p1vvdu2bVv27dtHbGwsIO2KY2JiSn7jFAqFQlFhVASimnL8+HE2b97M/v372bBhA3379s3/2enTp9m/fz/btm2jbdu22NnZMXz4cI4dO8ZTTz2Fv78/HTt2JCwsjBkzZvDCCy8wadIkfH19CQoKYvPmzQwdOpRt27aRmJhIdHQ0jz76KBEREfTp04egoCC6du3KXXfdRc+ePRk0aBDZ2dmMGDECLy+vQvNcsGABy5Yto0+fPri4uFC3bl3CwsLyfSBatmyJu7s7jz/+OM2aNaNBgwZs3ryZcePGsXHjRs6ePcuBAwdo3rx5/ph9+/bFYDDk3/f29mblypUMHjyYkJAQfH19efnllyv5N6BQKBS1G005AgpBQUH6I488Qo8ePejRo0f+8aioKO64444qnFnNIc8HoqZTlZ+ZiIgIwsPDq+S5awvqPb45qPe58tE07R9d11uV9/EqApFLdTOSUigUCoWiKlE5EAqFQqFQKMxGCQiFQqFQKBRmU+0EhKZpVpqm9dc0ba+mad5lnNtM07T/b+/ug6uq7zyOv3+EBAkQgkrAtDwEVh5EVqy0ysOAIIFYRRQkjkPRXVyoqxU0FrDDKq5FYLSlNEuJsCyd1ifQBQFxnEjslg4GdVkBKQmQEiyKghojTwl5/O4f9+YSIA/3QO693uTzmskk99zf+Z3v/c7JOd97Hn7Hzvt5PFyxioiINFfReA3EPKAvcD2Nx58MTAFqj2b0eYjiEhERaTGiroAws1865/4BX2HQmM7AHjP7JLRRiYiItCxRdwrDrzLIdknAl6EMREREpCWKuiMQHnUGJjvn2gEjgHxgjplVNTybiIiINCSiRyCcczc753Ia+fn1JSziGJBtZouBO4BxwPQmCT5KvPXWWwwaNIjCwsJIh+LZyZMnmTFjBjNnzox0KCIicp6IHoEwsz8Dfw5h/7+t9Xelc+5VYBLwwvltv/nmG6655prA60mTJjFp0iScc5SUlIQqxCaxe/duXnzxRbp160Z5eTmHDx9m4sSJjBo1ilGjRvHFF19w+vTpiH+OyspKTzHExMQwbtw43njjjQvme+edd5g3bx5VVVX89Kc/5fTp0+zYsYMnnnjinGGv6zJt2jRuueUWpkwJ5jIa78rLy9kV6se+16OoqChiy24plOPwUJ6/+5r7KYzzfQ10quuNyy+/PPCAqdry8/O/08Mvb9++nYyMDLZs2UL79u0BKC0tZdKkSZSWlnL33XfTtm1b2rZtG/HPcTFDWV9xxRW0bt36gvnuvPNOPvzwQ6qqqnjssccAeP3115k+fTp79uxpsM958+bRpUuXkOUjLi5OQ1k3Y8pxeCjP333RehGla7SBb7yIu5xztYukrsDfQhfWWUVFRWzYsIHVq1fz7rvvcubMmZAsZ8aMGTz11FOB4gGgbdu2LFu2jIceeojS0tKQLNer6upqMjIyOHHiRJP1GRcXd87jvvv168enn37a6HwDBw4kKSmp0XYnT57kwQcfvKQYRUSaq2gtINr5f7etPdE5l+acy/S/7AisAe71v9camAgsD3VwBQUFLFy4kIqKCvr168fBgwd59tlnm3TnCXDw4EHy8/NJTU294L1evXrRqVMncnN9Q2C88cYbzJw5kzFjxgQOCxYWFjJ79mwyMzO54447AvNmZWWxePFinnzyycD8q1atonfv3rz66qskJSWxdetWUlJSyMjIwMx4+umnmTBhAiUlJWzYsIGFCxfyxBNPsGrVKgBycnJYu3YtmZmZrFu3DvA9UvyRRx5h1apVLFiwILD8nJwcZs6cSVZWVmD+xlRVVfHCCy9wzz33BKatWLGCpUuXsmTJEl566SUA9u3bx2233cbLL78MwJIlSxg+fDhZWVn85Cc/ITU1NVB0ZWVlkZ2dzYIFC9ixYwfFxcXMmjWLlStXMmzYsKDiEhFptswsqn6AVGAzYMA7wIRa783Bd4Qh1v96KLAeeArIAqbW12///v2tLnl5eXVOr091dbU988wz9tFHH50zfc2aNbZ27VpPfTVm27ZtlpycXO/7Q4YMsZdfftl69Ohh2dnZZmaWm5trNZ91yZIltnz58sD0mt+jRo0yM7OSkhIbOHCgmZlVVVVZp06dbPPmzVZSUmJmZr/5zW9s7ty5gb8///xzMzO755577MSJE1ZQUGCpqamBeLp37x74u7Ky0q699lo7dOiQmZlNnTrVcnNzraioyPr06WNnzpwxM7PVq1fb/fffX+fnmz9/vqWmptqyZcvsmWeesVdeecUqKioCn2Pq1KmBtqNHj7a//vWvZmaWkZFhv//9783M7MSJE9amTRs7ePCgmZndd999tn79ejMzO3TokI0cOTLQx/r1623OnDnn5KsuXteZprRz586ILbulUI7DQ3kOPWCHXcL+OOqugTCzLcCWet57Dniu1utcfEcdwub48eMUFxdfcO5u+PDhrFixgvT09CZbVteuXfn222+prq6mVasLDyYdOXKErl27AgQuEB0yZAhffPEFX3/9NWlpaYwePZrc3NzAEYCNGzcSHx/P0qVLAejZsyeVlZW0bt2ahIQExo4dGzhtkJ6eztChQ1m4cCFHjx7lqquuAmDNmjUcP36cdevWUV5eXmfsBQUFHDt2jA0bNgAQHx/P8ePHef/99+nXrx9t2rQBICUlha1bt9abgx/96Ec8/PDDF0zfuHEjN9xwQ+D1ddddR3Z2NgMGDKBDhw6B6R06dCApKYlevXoFlnf8+PE6lzVs2DB+/vOfk5eXx6JFi+qNSUSkJYi6AuK7Li4ujqqqKsrLywM7QYDTp0+f87op9O7dm169erFt2zZGjBhxznt5eXmUlZUxdOjQC+Zr1apV4EK/ffv28fzzzzNs2DAKCwspKyvjlltu4dFHHwUI/K5R+5qD5ORkunXrxpIlS7juuusC0+fNm0diYiK33347b7/9dp2xl5WVcdVVV13Q/4YNG6iurvaWiHr6ry0mJuac2Gurq/iqS1JSEnv37iUrK4uRI0eyd+/eQIEmItLSROs1EN9Z8fHx9O/fn82bN9ecVqGsrIxNmzbVuTO/VCtXrmTevHkUFxcHplVWVjJ79mx+97vfcdlllwFw+PBhAPbu3cvVV19NQkIC2dnZdOzYkQULFpCQkEBJSQnjxo1j/fr1gdjz8/MDf1dVVQX+rjF58mQWL17MhAkTAN/Fo8uWLWP27NnExMScUwy0a9eOoqIiAPr378+pU6cCd76UlpZy6NAhbrrpJnbt2sWpU6cA35GK85dZo6Kiot5iIy0tjY8++ijweufOnYwdOxbgnP7O/0zV1dWBPmvHC75rM2JjY3nssce48cYbOXbsWJ3LFhFpCXQEIgSmTJnC8uXLmT9/PsnJyRQUFDBo0CBGjhzZ5MsaMmQImZmZ/OIXvyA5OZn4+HgOHz7M7NmzufnmmwEYP348W7ZsYffu3ezYsYM//OEPABQXFzNnzhx69erFlClTSExMJC0tjd27dzN58mR69uzJ4MGD6d+/P++99x5fffUVmzZtChQLAHfddRd79uwJ3BKZmJjIDTfcwIMPPkhKSgonT55ky5YtpKamMnXqVKZPn87kyZO59957ee2113j88cfp27cvHTt2ZO7cucTHx5OZmcm0adO4/vrrKSsr48CBAxQWFgZOM4CvIMjJyaGkpITRo0czZsyYc/Iybtw49u7dy/LlyykuLuaBBx6gb9++HD16lG3btnHw4EEmTpxITk4ORUVFbN++nT59+vDBBx+wf/9+0tPT6dy5M3379mXWrFmkp6cTGxvLz372MwYPHsyAAQMaHW9CRKQ5c/V9u2tpunfvbmlpaYwfP57x48cHpufn51/UPf1mxieffEJRURE9evSgc+fOTRluVLqYcSCi0cWuM01B986HnnIcHspz6Dnn/s/MBl/s/DoC4de+fXtWrlzZZP0550hJSSElJaXJ+hQREfmu0DUQIiIi4pkKCBEREfFMBYSIiIh4pgIiCLrQVIKldUVEWgoVEI2IiYmhoqIi0mFIlCgtLa13wCoRkeZEBUQjEhMTOXbsWJOMjijNl5lRUlLCkSNHgnrSp4hItNNtnI248sor+eyzz9i/f3+kQ4l65eXlxMXFRTqMkImNjaVLly4kJCREOhQRkZBTAeF36tQpZsyYccFAUq1ataJ79+4RjKz52LVrV8QGWBIRkaalAsKvqQeSEhERac50DYTft99+G+kQmr1169ZFOoRmTzkOPeU4PJTnsLjyUmZWAeFX+2mWTenNN9+Mqn5D2XeoNgjK8VnRluNQ9h1tOYboy0Uo14toW5ej8X8EuKSHNKmACDGtrKGnHIdeNOYi2nIM0ZcL5Tj0/Ya670uhp3H6OedOAqG41aIjcDyK+g1l31cCX4egX+X4rGjLcSj7jrYcQ/TlIpTrRbSty9H4P9LXzDpc7MwqIERERMQzncIQERERz1RAiIiIiGcqIERERMQzFRAiIiLiWYsaidI59xRgQCLwJzN7q552ycB84ABwNfCkmX0VtkCjmIccDwAeBv4O9AHWmtk7YQs0igWbY7l4XnPsnHPAPwNpwDQzOxX6KKOfh+3FtcA04FOgJ/A/ZrYhXHFGM+fclcAsoIeZ3ddAuwRgEfAJ0Av4tZn9raG+W0wB4ZybBiSaWYZzrhWQ65z72Mw+raP5q8AjZvaxc+6HwH8Bd4Qz3mgUbI6dc1cAOcAwMyt0ziUBB5xzA8zsSARCjxoe1+Pa8y0CXjOznWEJNIp5zbFzriPwr8AfzWx1OGONZh62F5cBfwSGm1mJcy4G2OGcyzOzAxEIPWo45/oBU4BJwOFGmi8D/tvMNvm/RG9yzv3QGrhVsyWdwngUWAdgZtX4dmD3n9/IOfcDINnMPva3/V9gkHOuWxhjjVZB5RgYDsQCh/xtvwROADeFJ8yoFmyOA5xz4/F9A+kY8uiah6Bz7JxrB/wHsNTMPg9bhM1DsHm+FogxsxJ/2yqgAPjHMMUZtcxsn5k9CaxvqJ1zrjNwF/C2f77PgTPAsIbmaxEFhHOuEzAQyK81OR/4cR3NR57XDnwDTN0amuiaB485fgvoXlPZ+r9hJBO6QViaBY85rpknEegHfBna6JqHi8jxYuBVMzsT6tiaE495/jvQzzmX4Zxr5ZzrCgwB3g99pM1GZSPvDwcOmVlFrWkNblughRQQQApQbWbf1JpWhG+nVVfb80c/q6+tnBV0js2ssubbhN+/4DsasTW0IUY9L+txjZlAVkijal6CzrF/JzgR+J5zbpFz7k/OublhijPaedlefAU8ACzA92XuFWCSmX0WjkBbiIva77WUayDacWEFVg5cUU/biiDbyllechzgnOsNzAXGn1f9yoU85dg5NwLYZWanfNf4SRC85Hgs0B7INbNVzrl44KBzbqcuCG6U1+3Fu8Bf8B21GALcCHwYsuhanova77WUIxBn8J1zry0WKL3EtnKW57w55+KA1UC6me0KYWzNRdA59uf2NjPbFI7AmhEv63F3YJ+Z5QH4j6ptBu4OaYTNg5d1uQuQC/wK3zflZ4Glzjld2N50Lmq/11IKiE/x3WmVWGva5fgv4quj7eXnTauvrZzlJcc1fgksMLPtIY2s+fCS40eAFWGJqnnxkuNSfLcg1vYVOloZDC95fghfoZZjZuVmtgDfnXENXjwsnlzUfq9FFBBmdhQoBPrWmtyXus+5v3deu4baip/HHOOcSwXyzGxLrWm3hTTIKOcxxz2Bmc65pc65pfg2BrOcc7NDHmgU85jjj4Ee7tzzQ12ABu+dF895bg98c9603UBZaKJrlho7h5kL9PbfTluj0f1eiygg/DKByRAY9GUckOWci3XOrXTO1dyusg0o8Q9cgnPuemodppQGBZVj51x74HZgrXPuMudcgv+e8GsiFXgUCSrHZvaImT1a84PvNtlMM3s+YpFHj2Bz/Bd839zG+tvGA6OA/4xI1NEn2G3y68AI51ztx06PA14La7TRrR3QtvYE59xzzrk7AczsML7baH/sf68rkABkN9Rpi3mct7+yWghU4Uvmu2b2pv8+7gPAv5vZSn/bFOBp//TuwFNmdiwigUeRYHPsv1J9cR1dXGtme8MXcfTxsh7728cD/4RvY/0SsMjM9oc98CjicVvxfXzrcgHwPWCdmTW40RUfj3m+FUjHd2vh94E9ZqZCrRH+wuxxfOPAJAEvAEvM7O/OuT3ARjP7N3/bK4Dn8I1E+X18I1E2OFBXiykgREREpOm0pFMYIiIi0kRUQIiIiIhnKiBERETEMxUQIiIi4pkKCBEREfFMBYSIiIh4pgJCREREPFMBISIiIp6pgBARERHPVECIiIiIZyogRERExDMVECIiIuKZCggRERHxTAWEiIiIeNY60gGISMvjnOsDjAC6AiXAGaA/8KGZvRjJ2EQkOCogRCSsnHOtgFvN7LfOuSTgENAdmAF8E9HgRCRozswiHYOItCDOuRgg3sxOOjO75lUAAACuSURBVOfuBGaY2Y8jHZeIeKMjECISVmZWBZz0v7wVyAZwzsUBrczsTKRiE5Hg6SJKEQkr59wPnHO/ds61AcYDH/jfuh+IjVxkIuKFTmGISFg558YA0/AVDl8Cg4E8IM/MtkcyNhEJngoIERER8UynMERERMQzFRAiIiLimQoIERER8UwFhIiIiHimAkJEREQ8UwEhIiIinqmAEBEREc9UQIiIiIhnKiBERETEs/8Hs268a70Q+8kAAAAASUVORK5CYII=\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2018-08-09T06:36:04.663408Z",
"start_time": "2018-08-09T06:36:03.553369Z"
},
"trusted": true
},
"cell_type": "code",
"source": "beta = 50\nN = 30\n\nX, t = generate_data(sin, 0.3, N)\n\nkernel = PolynomialKernel([1.,1.,1e-2])\nmodel = GaussianProcessRegression(kernel, beta)\nmodel.fit(X, t,10000,1e-3)\ndisplay_predict2(sin,X,t,model,text=r'$N={:2d},\\beta={:.1f},\\theta_0={:.2f},\\theta_1={:.2f},\\theta_2={:.2f}$'.format(N, beta,*model.kernel.p.tolist()))",
"execution_count": 45,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": "[*] 2000 iteration(s) has proceeded.\n"
},
{
"name": "stderr",
"output_type": "stream",
"text": "C:\\Users\\tmy19\\Miniconda3\\envs\\tensorflow\\lib\\site-packages\\ipykernel\\__main__.py:38: RuntimeWarning: invalid value encountered in sqrt\n"
},
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 576x432 with 1 Axes>",
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2018-08-08T05:04:45.960729Z",
"start_time": "2018-08-08T05:04:38.789883Z"
},
"scrolled": false,
"trusted": true
},
"cell_type": "code",
"source": "j = 0\nfor beta in np.logspace(-1,2, 100):\n i=30\n j += 1\n kernel = GaussianKernel([0.9,1.])\n display.clear_output(True)\n model = GaussianProcessRegression(kernel, beta)\n model.fit(X[:i], t[:i],10000,1e-3)\n display_predict2(sin,X[:i],t[:i],model,text=r'$N={:2d},\\beta={:.2f},\\theta_0={:.2f},\\theta_1={:.2f}$'.format(i,beta,*model.kernel.p.tolist()),name='./imgs/1-11/{:04d}'.format(j))",
"execution_count": null,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "",
"execution_count": null,
"outputs": []
}
],
"metadata": {
"varInspector": {
"window_display": false,
"cols": {
"lenName": 16,
"lenType": 16,
"lenVar": 40
},
"kernels_config": {
"python": {
"library": "var_list.py",
"delete_cmd_prefix": "del ",
"delete_cmd_postfix": "",
"varRefreshCmd": "print(var_dic_list())"
},
"r": {
"library": "var_list.r",
"delete_cmd_prefix": "rm(",
"delete_cmd_postfix": ") ",
"varRefreshCmd": "cat(var_dic_list()) "
}
},
"types_to_exclude": [
"module",
"function",
"builtin_function_or_method",
"instance",
"_Feature"
]
},
"kernelspec": {
"name": "conda-env-tensorflow-py",
"display_name": "Python [conda env:tensorflow]",
"language": "python"
},
"language_info": {
"nbconvert_exporter": "python",
"version": "3.5.5",
"file_extension": ".py",
"mimetype": "text/x-python",
"codemirror_mode": {
"version": 3,
"name": "ipython"
},
"pygments_lexer": "ipython3",
"name": "python"
},
"gist": {
"id": "",
"data": {
"description": "PRML/notes/GaussianProcess.ipynb",
"public": true
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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