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@doraneko94
Created June 3, 2023 04:55
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Simulator of Kalman filter.
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "3f490924",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from matplotlib import pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "72951905",
"metadata": {},
"outputs": [],
"source": [
"# Definition of Ultrasound Car.\n",
"class UsCar:\n",
" \n",
" def __init__(self, t=1000, dt=0.01, v_sigma=0.1, w_sigma=4, p0=0.05):\n",
" \n",
" self.x = 0\n",
" self.v = 0\n",
" self.dt = dt\n",
" self.p0 = p0\n",
" self.v_sigma = v_sigma\n",
" self.w_sigma = w_sigma\n",
" \n",
" self.step = 0\n",
" self.x_save = np.zeros(t) # saved position\n",
" self.s_save = np.zeros(t) # saved position calculated from the output of the sensor\n",
" \n",
" def update(self, a):\n",
" \n",
" self.x += self.v * self.dt + np.random.normal(0, self.v_sigma)\n",
" self.v += a * self.dt + np.random.normal(0, self.v_sigma)\n",
" \n",
" self.x_save[self.step] = self.x\n",
" if np.random.random() < self.p0:\n",
" sensor_val = 0\n",
" else:\n",
" sensor_val = np.random.normal(100-self.x, self.w_sigma)\n",
" self.s_save[self.step] = 100 - sensor_val\n",
" \n",
" self.step += 1"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "50777eba",
"metadata": {},
"outputs": [],
"source": [
"def run(u, t, dt, v_sigma, w_sigma, p0):\n",
" uc = UsCar(t=t, dt=dt, v_sigma=v_sigma, w_sigma=w_sigma, p0=p0)\n",
" for ti in range(t):\n",
" uc.update(u[ti])\n",
" plt.plot(uc.x_save, zorder=1, label=\"actual\")\n",
" plt.plot(uc.s_save, alpha=0.5, zorder=0, label=\"sensor\")\n",
" plt.ylabel(\"position (m)\")\n",
" plt.xlabel(\"time (step)\")\n",
" plt.legend()\n",
" plt.show()\n",
" return uc"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "dc672752",
"metadata": {},
"outputs": [],
"source": [
"def kalman_filter(uc, u, t, dt, v_sigma, w_sigma):\n",
" x_pre = np.zeros((t, 2)) # prior estimate\n",
" x_post = np.zeros((t+1, 2)) # posterior estimate\n",
" P_pre = np.zeros((t, 2, 2)) # prior error-covariance matrix\n",
" P_post = np.zeros((t+1, 2, 2)) # posterior error-covariance matrix\n",
" \n",
" # Initialization\n",
" x_pre[0, :] = [0, 0]\n",
" P_post[0, [0, 1], [0, 1]] = [1, 1]\n",
" \n",
" g = np.zeros(2) # Kalman gain\n",
" A = np.array([[1, dt], [0, 1]])\n",
" b_u = np.array([0, dt])\n",
" b = np.array([1, 1])\n",
" c = np.array([1, 0])\n",
" \n",
" for ti in range(t):\n",
" x_pre[ti] = np.dot(A, x_post[ti]) + b_u * u[ti]\n",
" P_pre[ti] = np.dot(np.dot(A, P_post[ti]), A.T) + v_sigma**2 * np.dot(b, b)\n",
" g[:] = np.dot(P_pre[ti], c) / (np.dot(c, np.dot(P_pre[ti], c)) + w_sigma**2)\n",
" x_post[ti+1] = x_pre[ti] + g * (uc.s_save[ti] - np.dot(c, x_pre[ti]))\n",
" P_post[ti+1] = np.dot((np.eye(2) - np.dot(g, c)), P_pre[ti])\n",
" \n",
" plt.plot(uc.x_save, label=\"actual\")\n",
" plt.plot(x_post[1:, 0], label=\"estimated\")\n",
" plt.ylabel(\"position (m)\")\n",
" plt.xlabel(\"time (step)\")\n",
" plt.legend()\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "5c956926",
"metadata": {},
"outputs": [],
"source": [
"# Control inputs\n",
"t = 1000\n",
"u = np.array([np.cos(np.pi * ti / 50) * 500 for ti in range(t)])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "cd4eb214",
"metadata": {},
"outputs": [],
"source": [
"# Parameter settings\n",
"dt = 0.01\n",
"v_sigma = 0.1\n",
"w_sigma = 4\n",
"p0 = 0.05"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "9b52d943",
"metadata": {},
"outputs": [
{
"data": {
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lJWzvrWZToztymSy10DQPlr8XgM1NbiSC7b3VyQ9UBCpbKBSd8dQYJPPWKLX3URlRKbOqwxR4lvmVI1oWtITRSrMkXKeoup3dBsCA38D735zL3781hVtfX8CRS4Nw+In8lR3FiUEL3T4zm1pGYOYmbWHQrwnS5nkAtNcPYTXE2RXCKi01UqhQyqkBqGSUerEkdO6Cnf8Np18dvS6t2EUptomegzDUD8CDp5s57bHwd4vOYxCS//2ae3Se5FzL1Qk19JuaBsExU1tY1xazTZVBsq5hkG3RI4VEcycKjBIKOVPMhnyceB+VVe+2DFHXJzFBv/btupC/Y4Z0NXHX3O038NCZZm5pdfLhmT18YnYX23pr2NVnz1/ZUWzrrWaq1ccM2zA0zoarPgONc0Ztt6nRzVtum6bOgohHlLIpFJp89AQneG8ymcqoXLyP8lUP5eYbSzAAI0OJ15VUmOU35tZvLjlw+U18YnYXAPdO76Gpys83356U9TGT1krCjt4aNjS6EejqILMt4babGzXPpLBdIV6VpqKkFppUNzxNQ7OigpmAz8DRp+C1/8xOAJQivHmW/PRcI7Ptw6yq9wCaS+hHZ3bxSk8tZzxVGR4t9bU66bHQO2JiQ8PgmNd1Wd0QtaZAxK4QnjtRZiMFIUSDEGKpEGKOEKLCBUkc+ZydWg7hohWU1Siw2Pf88qEU5Rbr+czj9U9QpwtDZva77HxQjz8U4s62fgCejc5vkIdzCqmk1jg8YwbdMxlgfcNgRCiUk01BCFEvhPiyEKID2A58F/gFcEYI8UshxPXZFiqEcAghfiWEOCqEOCKE2CSEaBRCPCeEOK5/N2R7/IqiYI1GLt5HhWzIEniTjDvGQd1D+v1S0HsSjv0udlmeDL4Ar+kN7tVxk8im20ZYUjvEs1fq0zpOuuXu7bdTb/Izt3p47DrOuY5NjW5OeSxc9JqjbAqZVSkXUvX6fwWcA66WUi6UUl4lpVwrpZwO/BNwlxDiY1mW+w3gGSnlImAlcAT4IvCClHI+8IL+vzCoyWvjgBLbLtKpw0QcuYUNs1n0UPP5Xp3fnb9jxfFadw3NVSMsrBk9Qe3mVhd7+u30+0ITyHK/x/tddlbUD6V9eUJ2hTd6qstrpCClvFlK+UMpZX+CdbullJ+RUj6YaYFCiHrgGuBB/Vg+vYy7gIf1zR4G7s702Hkl7Re+1N5HiolNke95SDucaKRQ9obmBMS1xEEJr/fWclWTO2EjvblRm0C2s1839MpgTuc9FBAcc1tZqdsuWP2HY+whWVTrpd7kZ1d/ddQkuuKRrk1hhRDiTiHEPaFPDmXOBrqA7wkh9goh/kcIUQ1MklJe1Le5BMS7AYTqcr8QYpcQYldXV1cO1aAMe3rZ1KcY51AC76Nk5Nv7KCUFGlGW+hqmRD/nEvRQc2fs63p0wEqPz8RVTW6oicpfMO8mANodHiyGYMT7561n4MAvsi73sMtGQApW1A/BpCVQPzX1oZrmYRBaPfb026NmeZeRoVkI8RDwEPBu4F36544cyjQBq4FvSylXAYPEqYqklJIkV0FK+YCuxlrb0tKSQzVKQTk3BnHk0nDlo9ErWsNZ5h5oxRYg4eC/RchCpuMcMfI/p5v5uyNTIv75BeJ13Z5wVdMA+IcjK/RZxRaDZGW9h93RIax7T2ZeUGAEht3sd2mupyvrPLHlJaOmFa7/EqvrPRxzW3G5+jMvO0fSuQMbpZRL8lhmJ9Appdyh//8VmlC4LIRok1JeFEK0AVfyWKZCoUiL0EghkaE5/wLq9GAVH3hzDpeGNTfQxy86eHrTcabYRuKKzrLsuP1e76lhXrWXyVY/BKIa6SinyrUODw+cbmEoILAZszRwH/gF9J/lgHM6kywjTLL6oefttKu92uFBIth/JcDVUpbd5LVtQoi8CQUp5SXgnBBiob7oRuAw8CRwn77sPqAwQUiA9NQCad6ESgiIV1bqjjjvo3HpNFBO1zOOsE2hOOqj/zrVSq/PxK/Wn+CpTccYDhr4myNjqFiSMcZzGpSwu7+aDY2D2oLonrvBHP65xjGIXwoOOHOY3dx/FoADTjsrQvaEDGh3eBBI9vTZiq7KS0co/ABNMLwlhDgghOgQQhzIsdxPAj/Wj9MO/B80j6abhRDHgZv0/wWmzF7Osmx8i71vPo+RTjElVpONXUgRyogiJGTPvD7aLXQsMrwe/iA8f6WO2yY7WdvgYWmdlz+bc5kXuuq0JPYxRtbcr8Mxt5UBv5E1jsHR9a2yw6oPwawtrHZojfiu/txCXrj9Bk56LKyo02eIL7g17X1rN36YhQ7Jm/3VEBwB59mc6pIJ6aiPHgT+AOgA8qJolFLuA9YmWHVjPo6vUCiyJDRS6D6ufS+4JbIuz0Jwd381fSMmbml1hZfdO62Xb749iR+da+Jr27+T5/KiJpElwjEdXOdpqAowt9rLnv5qNJ+YsUh8Xd4etACwIOT6Wjcl/crWTmLLzBp+eAC8h5/G2ntMX1EeYS66pJRPSilPSSnPhD4Fr9lEJOeXqlQjiTL0Pkr2f6IwcAl6TxX3/Ib6wRfXYEqpzXJOJ5x1hqq8567UUSWCXLso4mjoqApwZ1s/T1x04BrJNHhCgmsVVafd/Xaaq0aYYfNp4atXvj/pkdY4POzut2uX32BMul0qTrg1oTCvRldTiRTHmboGGmbGLFo/1YJPGjh0sjOysAgBJdIpYa8Q4idCiN/Pk0uqIill1MCVurEdFyE/8mP8TMiu78H+n2V3/GzZ/u3Ry048D4efhAt78lpUUMKTlxxc0+ymZu5mqJ8WXveBqb14AkZe7MpDuImo/fY77bSHJpHNuS5hlNJQT3yNY5D+ERMnPZaxhV2Sup0YtGIWQWbadKGQSrgsuAXaPxizaNUUK6DNiA5jKKx3FqQnFGzAMHAL+XFJLT3p9GjKotEZpxTz2uVsaK7Q+3zkN1q2sxDxeQRCdO7Svn1u8nmtTnqsXBk2c0urE+xNMfdxlcNDS9UIz12pS3GEzBjwGzg5aGF5XQLVUYKGNqRi2t1nz7p3fnTAytzqYUyh3TNs0Ftrqphq9bE3F4N3FoxZSynlR4pRkZIwrvzpi1xWUkpdh1KXX2wKdL6XOrTvYBAMhrHdJfP57A12a141wKqGYTBVEa0rNwi4qdXFkxcdDAcFFkPSaUtp1/Ggy4ZEn0Q2L8p0edVnEjb6c6qHcZi1WcXvE0lCiY9RlQ6XjWubByILM1VDGYysilJjCQF4nbD/5zDrqrEnwmVJqoB4fy2EaEyx/gYhxPgeMUwEKs4lNcR4Pu8yup4juieOyTLGhnms87mdbOvV4g/Nq9aNsHEjvptbXQwGjGzryU++4g6nJoRW1Htg+vrICrMt4bkbpq9jVb2HfU59pHDqFRjsSXL00dfmyrCJbp+Z5XVRAiVT1Y8wsr5hkIveKs4N6eG8nee0yXTnd2V2rAxIVcsO4NdCCC+wB80MbwXmo7mRPo/mSqoA8jL3oawa3zTrUrB5AhXoknruTW1C1ayrCldGCKMJAn7wDWoJ5I1j5BDIMQZQzKECI2zrrWZjiw/RHjL2xj5HmxvdmEWQ7X01XNfiHn2QDDnosjHF6qOpKk2ffwHt9R5e6q5lYGiY2tOvw+XDsPETaZcHsDQnoWBgox4cb1tvNTPsPm2mdDbHyoBUAfGekFJuAT4BHAKMgAv4EbBeSvnnUsocgw+VMyogXuIqlNj7p6jlFfncTjwPpxLkJy4IsTGOpNHCp/ZPZ/7vlnH7G/N55Lwj9lJ37iLnCZ0HH4XO3bzd4+XScBWb12+Ehll6dWKFgtUoWVzrZX9In57WfU8Rg2jAxpLa0VFRR9G2EprmwfSNtOuzijv6rWMePwavk4MuGwLtHMJkapswGJhfPcwky0is0R3GFuI5kI5N4ThwvGA1KAnjcRZsMibgBKp0KKtR1ThGBsHTy6NvDfHkpQZuanFxdqiKzx2cQY0pyK2T9DkEUkLf6dzK6noLut7ijcuzANgyrylq5eh3cmW9h0cvNBCQWo80W7wBwclBC7dNco69sdkKK96rla/38vc67WxuGkzeO49/Fvf/nIMDNcyuHqbGpLvyLro981G1MCAE3DbJyU86GxnwG6gNHa+AM/krPIuaaliSUupGtxzCNI9ZhwK5pMaENSjwdXCdx/36f/OVVwZYVT/IA6tO8/SmY0y3DfPfp7MMODlGg/X6ZTPTqiUzGqO8ahLs017vYTBg1Pz9jzypqbtSkeS6HnNbCSJie+1p4KgKMNs+rNkVIH1D8bCLQy4by2qjVEc1CYM+p0ZXFd3Z1o8vaOA3Fx2RdefeTC/AXhZUuFDIA3ltvMaDzSE3L5CilF/S4+WBgK94ZbnO8+uLDtx+I3+96CIGoaWE/MC0Xnb1V9M5FIkJlLYeO0WMroCEbd0WtrRJRLQgaFs5apd2h9ao7nPatYl1r/xrVnGAjgxo6p/FtZl7EbXXe9gXnsSW7Pxjz7fHZ+KCt4pl0faEbLQTulBYVe9hQY2Xn52P8/sZ7M78mGmghEIyCtGwlUWjngWp6l2ygHTj9FqmQzGFgs/Dk5cczKn2sjoqcNsdkzVVy28v10e2zSUwm/4MHR2w4hoxsKkt7rlpWQjXfylm0Wz7MHUmf6SnDppLZoYcGbBhNwaYac/8urbXe+jymbngNYPzfOKN4pYfcGpCKEYoZPOeNM8P7/qBaT3sd9rDAg4oWHjzdPIptOi5mh8QQjwU+hSkNsViXEbWTELB3SYrsNEPX9NCjdzi9vMPR2INQcTDJKcy0qPbPcyO3mreOckZ81rMtPtYUefh8QtRqdKzSdEZ3ldrwEKRR9tbkzQ9Ina+wuo2C29G5zZIaayNulZ+nxZQL+jn8ICVhTVeDFk8yqGMaR26NxHDA6M3evvFiGAI+DnQa0YgWV6f+cgkBqMZpq0D4Pfa+jEJyeMXHJH1udyPFKQzUngCqEdzQX0q6qMA0mu88vVil6KhLLNYQ/kuv9TnA7DvJ9Dxq8h/X+4umGOjnffvzlcRRCQ0wr57Sh+HBmwcdum902xHCsEAvP0CAAdcNurNAWbWJWl61n4U6trCf9e1mTgxaKUnlDM53d5xxy9h+3eQAT9HBmwZ2xNCLKr1YhSSwyGhMNituabG55AO3bPjz7LfZWde9XDEKAxk3bmavg6EoKEqwDXNAzx5KcorrFQjBcAupfyClPIXUspHQp+C1KbYlEODEE251SdMpvUazxPLilwGRKVc1Dn8ZHQlClr0b8/bmGUf1hpNmwOWv1cLzga8c3I/AK/01GobpysU4kfiXW/BeS120j6nnRV1Q4hkRtuaVpixKfx3Q5umxw+PFjp+mV4d9HwG590BBvzGrOwJoLnGzq0e5tCALhT2/wwOP5E0rLjsOcX+RDkUsg1kZ62H1fcB8M5J/Vz0VvFKj5Y9rlB5FtKp6W+EELcXpPSKoZAqmHIVJDlSDt5Hedsufrcx9vMNZnfcDHGOGHijx8ZtIdWRwaSlpdQb7GZLgDn24XDI6cTZ2BIw6vy0/6Ek9ivqB1OrcKOiiS5vNVJlCEaEgqc3vXJ1o/ARp+bPn9YchXhmasJpae2Qlt8hDc75aujxmWiPVx1ZajIvP4R+rd4xycWcai+fOTCDU4NVBbM9pSMUPo0mGLxCiAH94xpzr3FPjhN1cjlmXsrKkaRllVoITWzvo8teE+/bOYfb3piv6Y8zSOGYKXv6qwlIwdVNup48PCEqck1WOwbZ01+tPQ5Z67C1Ri2cxL5uKHXPOWoUYbHXsareE2tXSAez1oiHDLMLpzWl2joxc64DYEndEJeGq+geHsMl1TfI9vOa8NnQGKUCvP5LaYQRSYF+rapNQR5adRoB3Ll9Ps8eK0wzPKZQkFLWSikNUkqr/rtWSpm/8IUlYQIZmguOKGO1VqEp7nkHJHzywAz29dsZDhj4TMcM9u7fW7DydvXbMQpJe0jVEeq9R93vNQ4PPT4TZzxV6Y8U4tGPG05iX+9JTygIA9RNY33DIIcGbLj9GahgjFojfGTAyky7j5pV79HUY/NvSb1fAlbVhzKxjSGYzrzB9t5qGs1+5lcPa6q4eTdlXN5oIu3VrGof31tzitWOQUy2wjTDaV1lIcSdQoh/0z8TKAhesV76AqojCt5gl2OdoKD3LlT/sRLL5Pk8v3emmZ19NXxtaSdPbDpOjTHAA9lOIEuDbb01LKsbwm7Sz8M3Ok3lmgZt2e5+ewY67PjrojVqB5x2Wi0jTLb6UxtJQ/MBLDVQ3cS6VasISMGeMdNjRpWrC6IjAzYWt1q1kcPGP4Zpa9I8hwgr6oewGYNs7x1DBWQ0s6O3hvUNg1rxzfM0Q3GuxAnQlfVDPLzmNDeuXZr7sROQjkvqP6GpkA7rn08LIb6Wei9FbiQbyZRB3J9SjxqKWb4/O4+VsRl9Dv4gfPdUC1c3DXDPlH5qTUE+Oqub3152aPrjPDPoF+zrt3NNU5SLZciDZmbE0Kt50QTY3V+dnWGz+zgcegzQk9g36O62qWYni1hPo9ULZmAUMjMVkhC4/QbOeKpY3JRb8Lgqg2StY5DtvSnKl5JzbgPnvVXhIHZ5o8gu9OmMFG4HbpZSPiSlfAh4B/DOwlarDEi78akE1cpEOMckL1aq+3ypIy55fOF4ubuWLp+ZD07rCbcB907rwYDkl/EzWWG0x1ImDA9woE9zRV3t8ERyB4caakstOGYA2lyBVfUerZeejfrotBbgzzmiJbFf2awvT2ekoG9TY7WwtHaInRkJBQOH9BwKyyflIFRX3QvAxkY3R922iGtsPCeeY8eBwwBsaBzUotDmizIUCgCOqN/1yTZSjEGpe9kTiWKF0kgpFPJXh592NjHZ4uPG1kjPfZLVz/UtAzxyoYFgfFG7vgfuK9kV1neGfboqpj2k32+eD0vvTrj5Gscgb7mtuIbTHClE3xv990GXVt6KplBcqRTHMujNUkhwGIysdnjocNkIpLrkMc+ECE84WzY5h8xlNZMB2Kir0Xb2JplIN+xmR181DrOfhTVe2Pzp7MscRfkJha+h5Wn+vhDiYWA38I+FrVaBKfqM5jTLy6qhK1DjGK5LfN2LNFmvFN5PUmp69eiyUyVbz6WcEL5BvAHBaz013DrJRZUh9vxun9TP5WEzh0KTp6JJNLs2HSw1HHDZmGkbpqEqoDW+y98DrYujKxn+taZBCyG9ryv7ax9qoFe06E1OKlVU3EgBYaC93oMnYOTYYILrANqEsuic1kITCpMtPlodubiDavVdUe/R7Ap9UceK8pKSUrPRrGsYxLDyfXo2uTyRyChfinwKIaSUPwU2Ao8CjwCbpJQ/L1iNiknR0nHmqSEr1UhjQoxw0hAyZ16H178ZyUsM2U86SpcrR9nWW4M3aOD6GaMF0DXNmn76pe7a0ftm27mRkgNOe1QYhtT3d2W9BwOS3Vey70x1OG1Ms/losKUxMznOpoDJwsp2zUC8v9+mCZT4LGhHnoz9r48UltUNgSm9OQaJ66Ldf7MB1joG2RZtbI5qmI8PWugcqtLSb9a0Zl9eulz9uYIdOlU6zkX692qgDejUP1P0ZQpFCSmAoLp8OPxz0G/goMuKeyTF9vlAwAtdtdiMQTa2jJ6M1GLxs6LOk1goZEnPoI/z3ipWhJLYJ2qgQ8JwzrXULriahXU+9nSlKxTkqN8dLhvL6zxRo4B0RgqR48xasg6HRbCv3wa7HoKdD8ROZDOaYw7h9hs4NWjR0mGak4wu0iFK8F7V5OaY28o5j3nUuueuaO6hN7W4Ct+RgIiKrRCHTrHus/r3vyf4/FvBalQ2jJPecbFdUtMpLy91KoH3k25I7fcZeee2+dyxbQGb/u9BfvvmUfB5Rm+fh7oEgvDs5Xqub3ZhdbQl3Oa65gH29tvpT2bkzIRLB+nYpoVoCI8UEp3HonfCtLUwfSPM3MyaRi/7eo2pdfpJcI4YOTtkiY0amuraGUaPJoQQrJxk1iKmhkJGR6vP4jKRHeo3IxGsqM91pBBp+G+f1A/AU5cd2oKoZ+K5K3WsqPNo7rZ5FwrFbYtSpeO8X/95m5Ty+ugPmkeSAsjshuV6cwsxyzqP5Y539LDMf3FwOmc9VXxxwUWm1lXxt78+ivOlbxWkyMM9frp8Zm5pdcG8mxNuc23LAEEEr/bE68azUOec3Bo2+kYa6QT311oP828O90jXNAwxMGLguDvDBlbKcL7iFekKBWHQyl94W8zilZOrOOa2MhiexBYd1iJ2pNDRp402luU6Uohiun2ElXUeHr/giKn+OY+Zfc7qSFDBQo8U9JDahSKd2r+R5rIKJ1XDOZ5nUJdp3fMl+OKOs723mue76vjc/Et8YnYX/3TrJLp8Zn54thnO7shPmVHsu6Tpp9bObkrqxthe76HO5OfVnhxVSH2nYdjNoQErs+1RUTzTuJara7WQCrvHnEA2mrAXUN0Q1E/TAu4tuDX5DkLApj8ZlXhnVZudYJRXEQAjXm3EEKc+2tstmGL10WLx5zWf8b0zejjqtvFUVJ6JJy85AHhXW79e/zwLBUsdTF4W+b/s3fk9fhypbAqThRBrAJsQYpUQYrX+uQ7IwcernCi3Gc3lduwEBAutZNcpUeylH51rotHs52MzNRVFe9evubbZxcNnmxg+Fx9yIve67L3ko9kSYGp1cuFrFLCxcZA3xppROxb7fgrAIZeNJbVDERfU0DyFFMyo9tNcNaJNYhuLuHsXNjKHPJ0W3ALWzEM0rJyiNTvhpDsyCG/+N7zxf0e55+7p1txYgbx6G757Sh+Laob42lttDAUE3oDgx+eaWOcYZJpNfzfyLRSEgMXvgnV/pAnLAntPpqr9rWi2g2nAfxCxJ3wW+HJBa1UOpNsTLYsgdUUs6+jT6eyce/mdb8b+L1A+2mi8AcGLXbW8Y5ITqzFyDh+b2U2Xz8xT3XnyKom6tvvO9tNeN4gY0fXjV30m4S5XNbnpHKrSYhCFyKRx0Mt0jRg4O2RhSd2Qljd47Udgfopee7gowSqHJzy/IRPCRmYYO3RIChprrMyyD7MrNIlNShgePXv4wpCZi14zax35jzZrFPB3iy9w3lvF3x2ZylePTuGCt4rPzY+aTFgo9VFNi6ZWKzCpbAoP6/aDD8fZFO6UUj6aa8FCCKMQYq8Q4jf6/9lCiB1CiBNCiJ8LIfI/t7/cKZBKJGdGosI9ZJEOMWPOvBGOhx9mVD7afJ1j5DgvddfiCRh55+TYc7y6yc0s+zCPvJ3fHlqvz8hJj4U1jkEYuKwtNNtg+vrYDRfcwpYmrfF7fZRdIU10o+0RPS/Aklqv1njVTk5v9q0QtNd7OOmxaAbvkTHyE3hd8Oq/4+zv4+yQ7gUE0Dgnu/oDGExsatQmifmDxGaoiyKk4lrj8MCUVdmXl4SNTR7eO7WXn59v5KedTXxgag8bG6ME0DjP7JhKffQh/ecsIcRn4z95KPvTwJGo//8MfF1KOQ/oAz6WhzISU4ibVjSvnCIzMhSOXVM0Tr6cfF3W13Dse/5CVx11Jj8bGmJ7n0LAnZP72XbFzGVXlIDMMR1nKMBbKOhcmHk3wlV/HvlvrmaOfZg2qy97oaB7Vh3WQ0kvHSt89ShEOFroPqcNXvtPbfGhx+Hlf4nbVmphOPy+sJF5ed0QXPN5qM4ihHUIYxWbG90M+I0ccCUPu7G7vxqbMciimW2w8B3Zl5cMKfnHJef571WneW7LW3xtaZLczeOUVE9FSHlYA9Qm+GSNEGIaWvyk/9H/C+AGIJST8GHg7lzKyLBGOeybTsOQLyGUoKyC52guMy7ug95TeT9sUMJLXbVc0+zGZCBudi/cNaWfIIJnO/LQABx7BtACxBmQWoO5KM6hz2zVQj3rv4WALY1uXu+tGR3yIh30GcSHB2w0V43QUuWPmZE7JkKwvH4IgYzo9AGuHEk8O1kffcQYmXNVq9gcXN3kxigkz1+pSyoUtvdW017vwWwsUI/dbKXKILm51cX8muHxPjAYRSr10Xf1768m+uRY7n8CfwmEFIxNQL+UMnSXO4GpiXYUQtwvhNglhNjV1dWVWy1SJmjPZ6NYpg1soSjkiGjgcmw4g7RJUiddBXF4wEaXz8z1zXrikrgGc459mEnWAHuOnsyi7Dj6zwFwUM5kfo0Xm1FCXYLHPdTY6t4zVzW56R8xcXggCxdLvQHVjMxerSHLcKRQawoyv2Y4ViiEjx+Mve+67aDDaWN6KJxGrhOuzDYcVQHWNwzyfFddQjvT+SEzR902rmseyJ9uf8X7YjsJrYUJWV0upBM6+1+EEHVCCLMQ4gUhRFeUailj9HwMV6SUu8fcOAFSygeklGullGtbWgoXa7405F9PPmHJl+A5/DgAO/u0hi6ku4/v/QoBqxqG2Xs5uneaWx06Lo9oahwY5VIJRLyC9MlXm/W6vdqdhQpJBvAFBcfdupEZMms09e7wqnoP+5127fK7ozpl0WHGT78OTs0mpBmZs8uPnJDNn+TmVifH3FbOdLw2avWLXZpX040trvypiZvmwpT2yH8hsvKeGi+k81TcIqV0AXcAp4F5wOdzKHMLcKcQ4jTwMzS10TcAhxAiZPGaBpSvos43mCAefBEa4oQNYQHKdV1IHZtmIqEbePc77Uy2+LQZqTBaNWEwsapxmDOuYPLwyRlw2WuiyxOINJjGBOkaF92heQdVaZrcVouf+dXeSAjpTARjMMBxt4URadDcUSHjkQJocyb6Rkyc9lTBm/8TWR2fe+LsDvp8xlgjcz6w1HBzizaaC4WWiOb5rlpmVY8wt3qY/KltEzCB3490nopQQ/1O4JdSypzcT6SUX5JSTpNSzgI+ALwopbwX2Aq8R9/sPuCJXMpJTY4Py+vfBI8ekKuYOZqLgbMTdj+seQBlTZbn6Twf6+mE5kny3h1z+fqJSbHb5jlp+X6nnZXRydbj9eRGE6uqtXuejVtmPCFd+/L2DTD76nBO4RhMVbp3UFXYFXG1w8PeUE89k4Yp6A+rncJJ7LMYKazTjeKjspAFfMTf9726mmmVI0GIkByYftUHWFQzxFOXYt0zB/0GtvXUcGObLwv1WAY0zom896s+FJlkN2kprP6DwpRZRNK5ar8RQhwF1gAvCCFagEKkpPoC8FkhxAk0G8ODBSgjjlBs90I31uPIEhWKJ5NtrP5sCQZhzw/gQMRe8IOzTbx7xzze7K/mG29P0hLZh3h7a2bHj7/Hfl/4XPt9Rk57LFru4Hpdtx8/Ugj4WV43hFHIcGOHN/vE6QddNgSwePFSmHVV6o1DM3yv/xKrHB76R0yc9GSYCD4Y4JDLhs0YZHa1rovPYqQwt3qYyRYfr40SCqPdQ3frOaBX1udXKFA/jfdM7WOvs5qDrogwfaGrFp80cON0fUE+VTyh58cxXVMnhQSypTbiEGCp1WZsj3PSCZ39RWAzsFZKOQIMAnflo3Ap5UtSyjv03yellOullPOklO+VUhZ+tlLqyuXzYIUrM9E+OdW9RAIs9JK5LgKau+bfHZnCTS0udlx7mLWOQb58eGp+gsIB7PuRNhOWSEL59mYJS+7WQh/P2BjZtnk+1LVhM0oW1XgjhtaOX2Rd/EGXnbkNJqotmcXFb9cb2ANOW4bqIz+HB6wsqhki7JSTic5d31YIze7yRk+cF1QCT6A9/dUsqR3SDOl55r1T+6g1BfjPqBHkTzubmFYj2dikC6HqAtgcw4JUPyeDKbJsgqiU0jE0m4EPAT8XQvwKbf5AT+q9KolijTaIqKyKQpFVXVGhlKWEvzw4jTbrCF9fcZZJVj//sOQ8noCR751tTnGQDAhNFkNzDRVIlq27VutdrvsY2HV/epNFS0CjewCtcgyyr9+uRQtNlWd4DDpcNpa3Zp4oZV61F5sxyH6nnUzuUTDo58iALTI/YcP/yrDk2BDSffFeUEF/THV8QcE+p12bQFYA6s0B/tesLp7vqufB083sd9rY1lvDB69ahMGvqwHzKRTqp0PLgsjs73BWOFMk1Hc26UrLkHTGj99GUx39P/2zWl+mKDYdvxp7m3yRSsiNNSs1qxFPpJd1wGXjxKCVz8y7HA7atqjWy02tA3z/TBMD/vzqijtcNmZXD1Nniw4hoZcR6k3r57Sq3oM7YOTtwQzVN1FcGTZxedjM0pbMhYLJAMtqhzjgymykcK7Px4DfqNkTTFVgT5D3ORVRo4qQh9bL0V5QHb+CkcgkvL39doYChrDHVCH46MwuNjcO8PdvTeGu7fOpEkHeu2Y6TF2rbWDL8BxTYTRpgehCk+9CbqkVKhTWSSnvk1K+qH8+AqwrdMUKSj5nm2TSAI7HGc3FIsqw+9vL9ZiEDHuZhPjTGxbg9Jt4Os7AmB7Jr/0hl41ltUOxHkDhZyT0rQsFvee7N1tj88hQOLXm8pbsVGHL6jwcGbARyCCO0OErWu9Zc4HN5vmP7NNq8bOyzsPvrsTdh6gkRa/31GBAsjE0Ozw6ymeesJskP7qtig/P6KbB7OfB1adpqbXA9HVw3RfzmxIznvm3wJZPa8Ii5E6cJOzGeCMdoRAQQswN/RFCzAHSzOBd5uR18lo+QmenOEbSmEOFdVOVEn5yrpF735zNjt40ImRmXVAgXN4zl+vZ1OjGURX7mLVPrWWSZSTHENKx16bPZ+S8t4qldd64EMv6PYsbKcy2+6g3+RNP4EqHw0+GPY+WNGU34lla52UoYODU4TdHp6VMwqHLXoxCaknlsyGuI3Vzq4v9Tjvdw4kF22u9Nays91BnDmphOxa/K7tyx8Cw5F383eIL7L7+MFc3R41KCj3N2GCAKv0ZCOVyqKCRwueBrUKIl4QQLwMvAoVLEFruZBXjKA+N9MFHcj9GFvyks5EvH57G6721fHzvTN4ayF5tkhJdfXTUbeW0xxJJWBKFIMiWpoHRRs4cODQQFYYhZgJZqIDYxkUIWFE/xIFshYK3nw6XjTn2YWrNWTRcU1aFJ7wduuCO8dZKxeErXuZWD8dEf82M2Lpu0tVCicJ5u0YM7HfauaqAqiPWfQzWfzx8zwyldPALBRSslJGClPIFYD7wKeCTwEIpZYb+gBOIYnsYDHZryV1GRQktEFE9rAG/gX8/Ppk1jkFeuOotjCYz79k5j4O9Yz02WTQ8uirkt5fqMSC5pTVKKIRcC2WQq5rc9GYb6iEBoYBtS2uHYkcKIcEuYtVHoAV3e8ttxRvIoiWSUlNX1Xmye5bm3sC8ai9VhqAm0NJ0iz10xaedI2hhGzKlYVbM3/Z6D5MtPh670DBq019fchCQQptVDBTEo62mFarz5HSQK/UzoGmelqluApCO95EV+FPg74CvAH+sLxvH5PCQjnqRC2wn6PgVvP1i4qBjUFA7xYtX6ugdMfGX8y8xt3qYR39f88H+5/0F0NW6tXj0v71cz/qGQZotUec79waYcy00Lwz3PjMO9ZDkOh102Zhq9WmqqmihYKnVdNMrPjBq/xX1HvxScMRtz+z6B/z0OF1c8FbpqTCzuHcGE2YDLKzxcijkoz9Gh6HbPczlwUAkpEYaSXVGMe/GmL9GAXdP6eeVnlqcI7HNyC/PN7CgxhuZDFhwVU6e3JSzxWiCFe8tHyGVI+moj34ALAW+Bfxf/fcPC1mpsiDZy57p8tiNMi8zmwc+T4Li2St1tFSNaLNYV/8hsxvM/NmcK7x6ycTuvjwn3zv8JGc9VRwftPKOeNWRyQozN4PBEA71sD0U6mHYneH5xjZQWq9db7yiA7YJAfNu0hKbANH3LpRr+EC/NTOVgd9LhzNKXZXNSEFvYJfVDXFowKad+s7/Hp1/Iop9Z/sBcgs3YTBC66KYRTe3uAhIwbNRqSn39NvZ56zmfVN7ixc91FQglWaFko5QWCal/JiUcqv++TiaYJgAZDHHIJ0XOZ+9d0vEqNrvM/LzzoZRPbNC4A0IXuqu5eZWl6avrdEmCf3B9G4aLZJvngxlIUvw5md5/tt1Q/aWJnfs5LG4mbcbG93s6qtmJIg2d6PraFblDfgNnPJYtAa6ZWHqjaPOqc06QrPdoE16yyQ9acAXtmEsrRvK7jrpLe3SuiH6R0yc9+p2kBQz0Hed6cUsgrnPLF58Z0y00NUOD4tqhvifMy1hG8+/HZ9Ec9UIvz+tN7rSuZU7FnGqLUVupNO67BFChN9QIcQGYFfhqlRqxnpR49YX2s1U94H+n9PNtG9dyhcOTWfli8ui/OTzXb72Ar/eU4MnYOTWUK9db5jtJsm980Z4tbuWXp8xr0P3HX3VNJr9zKsehskrImqOuDI2Ng4yGDCG7QHp2VtGe5odiU44k8F5CAErW82asTnoD4fCHpORITqcdmbahqk3B7O3T9VP01xoITzySJWudNfJLpbWDeVgZNYxGLUwDzpCwP2zuzjmtvK7K3W80VPNG721/PHsLqpNUedW6BHDwndqoUImQNyhciAdobAGeEMIcVqPbLoNWCeE6BBCHCho7cqRYhuaDUY6nDb+4a0pzLIP86m5lxFI/iM+QFze0BqOZ6/UU2sKsCmUZlCLMAbArdP8BBG80FWnCa2hPi2WUI7s7KtmXcOgVlR1U2SWs4htsEOZ0cJB2aqyc5U96MpElRPVoNZOYsVkK28PWhg49DvY+6OYGdJJ8XvpcNlYFtK1Z/ssLbmLJXVe7MZAxPsnkFgoDPkC7D/vZkN8drdsmbIaVt0bnvz2rsn9zK/28ol9s/jgrrlMtvi4d7ruJtuyQN+pwFLBaNKCCk6AuEPlQDpTKguQz67E5KLsTPoi56PHPvoYUpj4P8faaDT7eXLjcerMQQIS/t/JVo7OsbIo3+G0pcQfhOev1HFDi4sqg9RiyUdds6UNQZqrRnijp4b3CgHbvwOOGTmVeWHIzLkhCx+eEeV3HzKux/Ximy2BsF3hj+lKnItgLOqncdAFLVUjtFr8YzfQoeu88v1QP4MV/n1IBB2nLrK5ibR81Ht3PcJ571I+VBs6xyzvkxBUGSQbGgZ5LTRnI4ltY8/ZPkaCMjaHcC4Iod1rfeRoNsA328/xwZ2zmWQZ4SvXNWAd0c/LnGe7k6IopOOSeibVpxiVLCvSmoOQP5XOnm4D23pr+OTcy9pEIODjM7upMQX5l+OTx06gnikyyK7+anpHTNzaqrsUzro6ZhNhEGxoGGRHX3XkcsQYOjM4/5634Y1vsUufIbx+soi49oUaajFatRNjV0jmmZUSyeFoI/OYakB9vdECRhMr27TRyQGXPbauKdgXH0o6x3zTVzcPcMpjoXPInFR9tO3tHowC1uZrpJCAxY4Au68/zDNbjrNp1crIilFuvYrxQOEtluVMwhnNYzzA8S9/RukUMtjY2Qlbv8ZvTgxTZQjynql9evUMOKoCfGL2FV7squPY5YEMKpBWJXn2ch1VhiDXNuvHTtAT39A4yAVvFZ25zk868AvwDbLfacdiCLJoy50wLRS7piFp+TF2BZmGUAhde/3b6w9yfNAacdOsnZxeffUGrrGmium2YS1aKaRVh33O6khO5ug6ZYpeh6t199zXemq1fAZeJ+z6nuaRpfPqiW7aJ5nDMaSYujq7MlPRvCAyeaxQOQwURUPdwXQZuKz1yl0XilPehX0EJfz2jOCapgHtpbY5tLj6G/+Yd0/RhMRzp/Kc2kIG2dpdx1VN7oixMOTyF9XjC+n1d1zOTy9wn9POskaJua41snDxndpEqwRx8WPsChnEAApxtN9AQAptpLD2ozBjc+od5t6gRU4NRd40GFlZP6RHKwX2/RT6UgycpWRvv42Ftd7Ida1pTb59SrRrPq8uqIf9qNGEwrk3YeASXD4EgNMzQkdnP1taoryOFtyaZZlxhATa3OtjAyTGCIXEs8IV5Y0SCumy6yHNoHg4PiFcHkNnRx/DWMXefjuXhqt45/QRuPYLsPGPNRdVYWCy1c/Keg+/OzkCW78GQ/2Jj5Nh+b19/Zz2WFg/hrphfs0wtaYAe8/nHspgJKgZfdub4+pttmoJTRIQbVdIa6QQjW+Qg5eiAsTVtI6dVN4xAzbcHxm1CCPt9R7Oe6u4Mqyb5t5+MenuwYHL7HPaw/kQsNRGMnZlin6+wlTFVaGwH35fxK4xqOVO3naym6CEq20F0PKGwrgLQ6x6T40Uxj0VegfT6LlEN6yhnqju+nhqsCqS8SkrfXYaGE282lODQHLD5KG4iVXa71tanex32bnoNWftqx/D6dfY37EfQPNpd8yI5BWASC+5ZSEGASvqPOx3Jgg3kaFQesttZThoYGVTZj3+jY1u3uyrxu/PIBDZhb2w47scctmoN/mZZh3JTudtMLFKb+D3hCKmmqIm+g/1R67D8AAnX/4JA35jxJ5gb8xe126u1lxDF7+La/TcBtsuGyJC4VIHDFzitRPdVJtFRBAVAq8rEjoaYp0ClE1hXFKhQiFEmoHr9Jft1GAVN7+2gOtfW8Qd2xbwjRNJhv/5GDUYq9jntLOgxkt9oC92nf7ihYLGPXbBkR9X2SuH2e+0IUJ671X3ar3jEPZGbcQyaTkA7Q4PRwds2cUAcndpIxyiDLDNmZ3DWocHT8DIsd50JpDp9yQwAv5hDrm0hDNZt1fCwLL6IayGYMQ1tu+01knw9ML2b8OZ17WR5fHfRc4xHw20waDlBm6cza2TnDSa/fzkZOxEusDR3/LykUtsdDgxG8h/KIjFd2jfgtEdFsd07RMKG2LIwjtMUTIyz/IxERmrDddftn87PpmTHgsfn9XFaU8V//n2JLY0uVnbkOeemKcH6brEPqc94gEUjT5SmFPtY1X9IM9eqedP8iGIvE72O6czv2aYGlOSBjrUAExaSvuVc/il4KDLlvk1uNwR/rnfaafR7GdahuGM2kO5DS6NsCSD/UaCcHTAyodn5pDJLuDDYpCsbRhkW3RI8YAPhvV7durV8OLd/VOpNQWY22wHb/4yzVqNktsn9/Or840MXjhMtf5GP3V8iHNOH3+5Qu9QbPhfkfzb+WDSMk3ATloK7qg5GsKoCSzQPKKqqqFlUeJjKMqSCh8ppElgBOeIga3dtXxgWi9/tfAi31h+luYqP/8VDveQ33kKp8+eoX/ElHjoHzVcv7Z5gANOG339/QmPkzZdbyEDAfY77emFQ1hyZ3i77HILRLrooTJFhr3ZGTYfjVV+9l3JTIV33G3FJw2RqKHZUNsGaKkp33LbNBUe6GkpR1//13tq2NjoxlCnTzrM40z4O9v68QYN/PqSA4DhoODfjk9mYc0Qt0/WZ6Rb6vI7uUsIzZPJZIlVH0XbFEwWmLVlbHuNoqxQdyspUS+t+zKPXGjAEzDy3ilaTBe7SfIHM3rY2l2XU2rGZIQa2vZEOW4NRrjqz0EYuKbZjUTw2uEzmjvimTeyK7DnBJ1eM70jprRj5LRa/Ey1+tg7Siik3+AN+A0cd1s04ZeOkdIcsWEIAascXvZeyUztdDg6/lC2GE0w/xZu0MNDv9gVPYks9vzPDZk5O2RhS6M74ZyLXFnr8NBeP8i/HZ/EUEDwnycmcXbIwl8vvIgx7CpaSL1+1LFLHbFUkTOVKRSSviAJlg9cgoOPsrWrjrnVXtodkYbkA3rQr9+OSg+Zey9wb78duzHAgmSZssyaUXNFnYdaU4DtfTVaXU++nF2BMhh2r2yvH0o75n57vYd96aam7D87KoNch9OGRGiCKB2hsO5jEfUE0N4wzIl+cA6NYVeI6pkfclmxGoLMrs5djTO/epipVh9bu3S32cDIqFHAGz2aXmxLkzuq0czfSMEg4MsLL9LtM7P4+eV8+1Qr75vaG5uJrBiYLMqoPAGoTKEQIuHktbiXddf38PgFO/qqua55AOZcFw7U1mrxs7zOw0vduaSHTMwrPbWsbxiM9PQSYanRErnXDUUmUUHKMMpJCWqqoypDkIU1Q+mpGloW0O7Q3DK7htMwT+39Mex8IGZRjCBKRyhYamOCsq1q1ITBgc7+sffVOTxgY1HtUOprmxYSIeDGFhev99ZoBvddD0FnbLzI13pqabWMaIH+QiOFPAdSXN/g4WY9MdG8ai9/u6hI82mA8DtjcxSxTEWhqGyhkCbbemvwBQ1c3zKg9YYW3hZed2OLi939ds4PZDCrdoz13cNGTnssbG4co6fXfi+gjRaODlgZDuqt3MFHx67LqLKD7HfaWFo7pHmrpOO2O//WsM0jxjU11XkGYt1H9zntzLIPa0luslA9rGj0I5DsffUpGBl7Ip+UmlBY2pIHHwurNkK8vmWAoYAhHPqb3pMx5W3rrWZzo1vrRNe1aclY5l6fe/kAaz8SzvnwQPsZjt7UwTObjyV3FCgENi04HtM3pt5OMS5QQiGGxI3ZS9212I0BLdmMwRRjWHvnZCcSweud+Uva3aHH01lRPwSzr4FFtyfe0OaAprmsrB9iRBo4OpB9QrxgMMhhly0SgiGdIHMGI8vqhjAKGWtsvnxwlJooGfudtogxPYuJT3UWA/Oqh9nXZ9GitY5B55CZAb+RJaOzSGZO83xY/l42NbqxGoJa1Ng43nJb6faZNdURaHMZ1n88f0bf2snQqqU3EULzRjIV+602W+H6L8GkTHzAFOVKhQqFNCevSYmU8GJXHZsbB7EYpNabjerRzq0exmH2s+vkldh9s0E3Ene4tLkCS+uGtIxjqWa+LnsPK8K99eyjUp5ySdwBoxbWedOfpKcbFgZsRsmiGm+sULh0EI4/N+bul70mLg1XsaJN3zc6XEK6CAOrHB729tuRqSKV6kIqkuTGqzXOucbgd8zAatRySj96oYEBf+wr9dwVTVAUNIl9KmFqc2iRXRWKNKlQoZAmQT+HB6yc91aF9bXxIwWDgDUOD7v6sovpH4MeOuCA08ac6mEt3tFYjbPBwFTrCJMtPnbmUIeOHq2c5XVDYbXImOiN0cp6D/ud9nD2LSB2di+MFpRCRDys1l0F1/xF0pAWY9Whvd5D34iJM6dOwNntibe7cgTQDPhVIsiier+mxsm1x653ED48s4fBgDHG6SAo4efnG9nSOECbVTeEp0iGkzWeFEmGHDOzE7aKikUJBUjes/cN8mJXHQLJjbrrIcIY65cNrHUMctJjoced4IXPYtTQ4bKH8wCng9AF04FEISfSLbMHLIYg86szCLCnG01XOTwM+I2xrrmWuJloCa7DAZcNk5AsmeLILicCgAyGQ0fsOXwU3t6acvMdfdWsrM9DFrIQumBcVe9hTrWXX12I6KVe66mhc6gq7KUGFEYozNiUfF1oVrFCkSZFFwpCiOlCiK1CiMNCiENCiE/ryxuFEM8JIY7r3/nQ+mZaO2JUS/1n2N1vZ37NMM2WqIQvcb7ma/TgcXv1BOnJGbshuuw1cXnYHFYJpcuSuiHODllwZZm/uaPXyOLaocz00fooJhS6YW+0a2q8EEgQhmO/086i2iGsVTmEQZBBFtR4aary83LIC+zNBxManQf9BjpcdtY3uvPnOqkfRwh495Q+dvbVcNxtQUr41tuTaKryc8skV2QUVN2U4mBZYot7VRrnwLR12m9z9nYmRWVSipGCH/iclHIJsBH4UyHEEuCLwAtSyvnAC/r/IhPrmhr0+9jbb2d1fVTE0JBNwd4EDTMBTeViFJK9h4/Atv/KqQahpC2ZjBQAltRqjeBRd+aNQDAoOdxvihiZ00VvEOfodpXd/dXQslDr9Y/KOxHrnRWUUp/JPJRzJjyjgBtaXGztqtWS7rivaHGIwtto93V3v52AFGyYOwkW3ZF9mUl436pJ1Jv8/HnHdP7u6BTe7K/mc0sGsNz4RW3ex+Y/K4wqJ/r6OWbA8vdElqmopYoMKfoTI6W8KKXco/8eAI4AU4G7gIf1zR4G7i5YJdJshE71+nD6TZHIlqCpjoTQAsVNWgaAzShZXDvE3pOXtKiROUxMOuiyYUA7XiaEZuceyMLYfOrtI7j9hsyFgo5BaJPYwjObhWHMkcIpJwz4jaysyzJu1Ib/pRmK9Si1N7W4cPlNvBmyq0Q3hgEtf/TrPTWYRZA1V90azjGcT1qqTfzT0k4Ouuw8fLaZlXUe3jsr6ppa8j+fZRQNs7ROS0htFMg9d7aisihpQDwhxCxgFbADmCSlvKivugQkzEwvhLgfuB9gxowc8gKnwd5L2gsVIxSiG5so4bK63sMjFxoISDDmELH0rQErs+w+7KbMBEso5ETGcYiGBzi482VghpZwZsEtme2v017v4eXuWtz+EWqEAbz9movo5UOazjvumhzo0hrzdENqjCLUqOvHvbppAIshyO+u1LO5aVC7T72nYOCiLqi1SWSrHR6qLQV67A0mbpvs4iHjKaSEG1oGEKaEj3HhmKknC2qYCadfg7qpxS1fMe4p2dhSCFEDPAJ8RkoZEwpUSilJ0t2WUj4gpVwrpVzb0tKSWyUSzmiOsPfyCLWmgDYTNeSRE+32WK/PrG2ezyqHh8GAkWNua+w2GRqaj7qtLMwyUFu77pqZEcMDdLhsVBmCzF++HqauyarslfVDSAQHe4XWIHcfh+3f0SKFXtw3SijsvxLEbgwwryZHw6uulrKbJFc1uXm+q0675ELA/p9pYT8u7KXHZ+TQgI2rF7XlVl4ipq2D1sVhT6QbFrVy4zXXaH2GYqtvQh0VxwzY8iltLoVCkQElEQpCCDOaQPixlDI0/fayEKJNX98GXEm2f2GJNOJ7L/tpr/do+WeX3Alzro3tedkc2qSdpnmxxtZkiXfGEBAev+CMp4qFyeIdjcGq+Exg6TAyRIfLxuJaL2ZL9t5LoR7//m4xuiEMBmKFgqeXfedd+sS3rIvUGIkI0JtaXHQOVfGW2zrKyycUf+iq1StyLDAB82+CpXdDW7vmdTX/loj6pgAB8BKy6l5Yc1/ssqo8uEkrKo5SeB8J4EHgiJTyP6JWPQmEnur7gPi8l0XF4wtwtFdGkqJU1WhD80T2CIOJmXYfjWa/plfPRn0kJUcGtOBwS+uyFAqOzENZB32DHHLZWF7niYlAmja6d0tjVYAZtmH2n3cn6B2LGEHp2/YAh50WLd5RrjTMCv+8Uc898dyVulFpU1/rqaXOamL51DTnYGSDvRE2f1LrLBTb0OuYEY7JpVDkQilGCluAPwBuEELs0z+3A/8E3CyEOA7cpP8vECm6pz6tYT2wYytBGWVPMKTofZssehhnj5aaMZsUncEAB11ao7w8ZHzd8umMDrG0dgizCLK7L0oouC4m3wE43e3GHTBqRuZsfNqv+vNwYxROZJ+oIYwaJR0d0PIZZOp2m5Cl92hePWh2lfb6QZ6/EhtuYjgoeKGrli3zmjEaihTFM3QNVChpxTijFN5Hr0kphZRyhZSyXf88LaXskVLeKKWcL6W8SUrZO/bRcq5N7N8olcNBp9ZAhhvoVJOrTNqkrVX1Ht4etOIcjO7pR5URGE4uME6/QofLRnPVCJMsuk2iKjP7gNUoWdsQF7V19/dT7tNxUTu/5XU5uIbq+61Mpr4SImb0tFu3e6xxeNIO0Z0UU5Xm1aPX4eZWF/tddi57I3V48qKDbp+ZD24orGNCQpRLqGKcoZ5YiPRio9z3Dg9YmWQZiUxaS6UbNmpCYbVDm8+w75XHE2935Dew7yeJ153dwUGXjWW55A0GNjW6Oea2jorBE8OwOzwi2ndpGKshyPwabw4NWOwktt298UmHYoXCnv5q2qw+2mz+7EJbJKyCVvebdRVSKAuZlPDg6WYW1Qxx1bzm/JSVDqHzVUJBMc5QT2wMkdb4sMvGkpAX0LybtExbydBHCivqhxBI9vSnMPA5O0cvCwbwBgTHB62aW2i2GM2sqPMgEXREh7wIBrTWMTRKeeNb8Po34MI+9lz0saLek3647EToDd+Keg81FhOvXEmQiS5GKNhZ7fCA1ZFdeYkrAWhJbzY1uvnG25O4Mmzi1Z4ajrpt/NGsbkQxE8CEzlepjxTjDCUUYtBGDMNBwYlBK0tCDfT0dal303XxNaYgC2u8mbuFvvwvHB2wEpAiIhSShctORMjAGBjRZggTZ2x++V/gpX/SvqPwHn6GQ/1mrYGG7Hu1epwj8/LfY9PcJl65bI11tBKEXUfPD5k5761ijWNQC0iXL0J2XQH/uKQTb0Dwvp1z+ZN9M2m1jPCutv78lZUOIQGsRgqKcUZlPrHJeox67+6424JfinDoiDGJ0v2vcnjY57RFIoamOU+hQzcyh4VCqnDZ8az+Q7hOiwrSUBVgjn049Wglqky/FJpuH7JvwBa8Q0s81LKQaxa0cN5j5JQnzmitN5Kv9mj2ji1jJRDKmMg9nVPt40sLL9I/YuTGVhc/WXtSC3teTMLqIzVSUIwvKlMohEgSiiGU2H1JJpPI1t8PaELB5TdxMhQxNE331EMuGw6zn6nWMXINJ0KIGEG3rmGQN/viQlmHCEYbfDXBsSoU2ylb9YrJAlPaQQiuna9NKIwxdl88ABf2asu7aplkGWFBrpPW4okL9/3RmT3su+Ew31hxLvcJctkgowIoKhTjiMoWCmH01jMkFFw27MYAM+0ZxI3Ro1+u1o2te0LqmzSFQofLzvIcjcwh1jYM4vSbODE4tm5/pi0qAmweVB0zmuwsqvfz5EVHZOHAJbhyhAG/ga3dtdza6sx/fvcV74epq5Ov14MXFo0qXSjai2jcVijygBIK0YRHClYW1XrJxqV9TvUwdSZ/xK7w2tdT7zBwieGg4JjbEg5qlyvr9VDeO3prRq/Uz1FK3eDbGNWLzpP++92zR9jnrI7Nr4A2qWw4aOCukH4/n5LBWgcLbtVCOySi/YP5KysdmudpZU5bW9xyFYocqVChkNymICUcGbBlpjoKUTsZg2Mq7fVD6Rubd32PYwNWRqQepfTqz2qfHJhh8zHTNszW7gRROXU1zrmhKrp9ZlYvmBW1Mj+N9F0zRzAgefSCI2b5ExcdTLP5IobtQlBOht2GmfkVfApFESijN6gMkDKS2D1dI3M0az8CS+5mtWOQY24r7lRzBaI4GG1kNlnCLq7ZIvT8Aq/31DAUiGuU3n4R0LKCAayfHiW88tSgtjbUcX3LAD/rbAqX3z1s5LWeWu6c3B/VThagwSwnoaBQjEMq/A2SEPBDQDfuymA4sXtWIwUAo5lVDg9BRNrpMfc67TjMfmbY8hf7/oaWAYaDhnAguHh+d6WOGbZhFrRGeSnlq1dbP41PzL5Cj8/EN9/WQkc/drGBgBTc1daXnzKSobx9FIqcqHChAGz/Ly3uPIAMctBlwygkC7MZKQAYzOFAb+GkM2O4pe7sq2Zdw2DubfLqPwz/XN84SLUxwAtddaM2c/s1YXFzqwsRPSkvX0LBaGFdg4cPTO3hO6da+OvDU/j345O5qmmAhbXRNowCjBSiz6d1cf6Pr1BMcJRQ8EXpt2WQPf12FtcOYcs2sbvBSL05wLxqb9jlM1UmtsteE6c9FjY0DEJNjvkh6qdqobwBi0FydZObrd21o2TSK921+KSBW1pdYM6/+giTNkfhbxZdZH7NMD8610xjlZ//WH5OW+8ocAyikHtqKOFMbZET3SgU45jKFApJeqiBES/7nXbNrTSU8DzT3qwQsOlPWN8wyM7eavxBRgfBC4zAocdgqI9duuBYN38KrPrD0cfLgRtaXVz0VrE/To317JU6Gsx+bVZxVZR6KV9CQQ9fUW0K8tSmY/xi/Ql+t+UYraFAf+HgggUywobumcEEaz4MK4vseaRQjGMqUyiEiOtCv9VnYDBg1Lxjwo1lFg2XtZ4tCybjDhjZ70qQX8HZCVeOwlu/ZVefHZsxyJLJteEedr54R6uTamOAn5+P5CM+6LLx60sN3NXWj8lAXA6FPDXSUfmPzQZY3+ChxhR1DVKFIc8LUedR1xYR8AqFYkxKmqO55MjYHnxowtlqhwda1sPga1kfetPC6fDiSd7oqWFNszN2Zagh9rrY3d/EyjoPZnNT1mUlo84c5PqWAZ66VM9fzL+Ewxzgy4em0mgz8OfvuRH8XbEjoXx67hhMsWlJE1Eod83QcTNMhaoY/4yMjNDZ2YnXm6VNcIJhtVqZNm0aZnOK0P9xVLZQOPxkzN89/Xaaq0aYvu4OLbft6ddgxsasDt1YbWZJ7RCv99TwSX9cZlG9sRr0DHJoYBp/PPtKYVwpJy/nM+5jPHO5nvftnEtzlZ8DLjvfurWO+tZpwLTY7fNZhyo7eF2J12WTmS4TZm6BI7/W8iwoKorOzk5qa2uZNWtWcaPiliFSSnp6eujs7GT27Nlp71fZ6qM49vZX017vQdgbwWDQjLZzrs3uYEKwpcnNnn776LkCeqO4v6+KQCggXSGEwsLbmFczzN8vPo9rxMiOvhpuanFyx4IkE+vy+RK13wuL3hmOoBpbTuhcC/TSTl6m3bs8q+MU5Y/X66WpqaniBQKAEIKmpqaMR00VKhRGPzC9PiOnPBZNdZSPB0oINje68UkDb/bFRSzVhcKuPjsCqSXnKYRQMBihdjK/P72Xndcd4ZnNx/h2+xmEIUlZ+ayDzQFtK6C2LXb5vBu1UZhCUSCUQIiQzbWoUKEwmn3R9oRUqTfTRRjY0OCmSgR5PX4CWVgoVLOgxku9OVi4mbizrtaqI2BRrVdLppOsrELUIeTyWj8N1n0Mpq+PTDDLx3VWKBR5RQkFnb39doxCsuKW+0aFYc4Ogd0kWe3w8EpPnG476Mc5YmRXv521DTnmMkjEuo/Bmvu0383z4NovxOVCTtZ7KEAPK6TCaZwNNa3a75aFmq1mzvX5L0+hGCe89NJLvPHGGzkdo6YmccSCXFBCQWef087CGi/22nwIBMKjgaubBzgyYKMrOpl90M8jFxx4AkY+OK1HW5bPXnNNayQbG2j2Ecvomc2jKMSw25DgvAxGmHu9chVVVDT5EAqFoLK9j3R8QcHefjt3TxvI30FDQqHJzb8eh1d7arhnSj8AXs8APzrbzIo6D0vrdCOQMbcgeGOSKtlL01zoebswQiF0zED+4jopFOnw1V8f4vCFJB5wWbJkSh1fedfSlNvcfffdnDt3Dq/Xy6c//Wnuv/9+nnnmGb785S8TCARobm7mwQcf5Dvf+Q5Go5Ef/ehHfOtb3+LBBx/kjjvu4D3veQ+gjQLcbjdut5u77rqLvr4+RkZG+Id/+AfuuuuuvJ5XNJUpFOIavz39dtwBI9dsvip/ZehCYVndENNsPn56riksFL73/D5Oetp4aPWpyPaF1q/HTBiL899feg+MFCicdcjQ3DSvMMdXKMqMhx56iMbGRoaGhli3bh133XUXH//4x3nllVeYPXs2vb29NDY28olPfIKamhr+4i/+AoAHH3ww4fGsViuPPfYYdXV1dHd3s3HjRu68886CGdQrUyjE8VJ3LSYh2bygbeyN00UPbWEQ8NGZXfzvo1P5zaV6+keMfP3tSdzY4uKGlqiRibHA7pOphI7RBMY01EvZ0DRPyw+RYzhwhSJTxurRF4pvfvObPPbYYwCcO3eOBx54gGuuuSY8V6CxsTHV7qOQUvLlL3+ZV155BYPBwPnz57l8+TKTJ0/Oe91BCQUAXu6uZa1jkBpLHi9HXUTAvH9qH7/obOTP9mspIZfXefjq4vOx29sa8ld2IgoeWiIJQiiBoKgYXnrpJZ5//nm2bduG3W7nuuuuo729naNHj465r8lkIqjnUA8Gg/h8msr1xz/+MV1dXezevRuz2cysWbMKOmO74g3Nl70mjgzYuLY5j/YE0DyYrtGGhdWmII9vPMFXF53nX5ae44mNJ5hmG4lsO+fawhtdo4WCCv+gUBQEp9NJQ0MDdrudo0ePsn37drxeL6+88gqnTmnq4t7eXgBqa2sZGIi0O7NmzWL37t0APPnkk4yMjISP2draitlsZuvWrZw5c6ag51CZQiEqamnIXTTvQgE0lY0e099qlNw3s4f3Tesbnfu5GL14NaFHoSg473jHO/D7/SxevJgvfvGLbNy4kZaWFh544AHuueceVq5cyfvf/34A3vWud/HYY4/R3t7Oq6++ysc//nFefvllVq5cybZt26iu1ia93nvvvezatYvly5fzgx/8gEWLFhX0HCpTfeSPZFV7sauWlqoRFtd6C9RwptErL7pqR40UFIpCYLFY+O1vf5tw3W233Rbzf8GCBRw4cCBm2fbt28O///mf/xmA5uZmtm3blvCYbrc7l+ompDJHCjWageai18xzV+q5s62/cB3pVKqaULIZNbNXoVCUCWUlFIQQ7xBCvCWEOCGE+GLBCjJbYdWH+N9H2zAIyYdndhesqJS98vqp2re9uYDlRzF5eXHKUSgU45ayUR8JIYzAfwE3A53Am0KIJ6WUhwtR3m/OGvntZQd/Of8i06ONvsVk2jqYvCImKU1BUXkGFArFGJTTSGE9cEJKeVJK6QN+BhRk2t7RSy6+9GgHK6fVc/+G1kIUEaGtPfk6YSieQACYfa1m+G5dUrwyFQrFuKKchMJU4FzU/059WQxCiPuFELuEELu6urqyKmjHyV6qq0z8vw+twbTszuiDZ3W8lDTNTb6uUJFRk2GpgaV3qzwDCoUiKWWjPkoXKeUDwAMAa9euzUoPct/mWfze6qnUWUts4C22UFAoFIoxKCehcB6YHvV/mr6sIJRMILQuBnsTtCxSXkcKhaLsKCeh8CYwXwgxG00YfAD4YGmrVABqWmHm5lLXQqFQTDCklEgpMSTLrJgmZSMUpJR+IcSfAc8CRuAhKeWhElcrP8y/GY4/p/2evrG0dVEoKoXjz4P7cn6PWTMJ5t+UdPXg4CDve9/76OzsJBAI8Dd/8zfMmzePz372s7jdbpqbm/n+979PW1sb1113HRs2bGDr1q309/fz4IMPcvXVV3Po0CE+8pGP4PP5CAaDPPLII8yfP5//+I//4KGHHgLgj/7oj/jMZz7D6dOnufXWW9mwYQO7d+/m6aefZubMmTmdYtkIBQAp5dPA06WuR96p0+3ltZO0hDcKhWJC8swzzzBlyhSeeuopQItbdNttt/HEE0/Q0tLCz3/+c/7qr/4q3Lj7/X527tzJ008/zVe/+lWef/55vvOd7/DpT3+ae++9F5/PRyAQYPfu3Xzve99jx44dSCnZsGED1157LQ0NDRw/fpyHH36YjRvz0+EsK6EwYdFzKyjDskJRRFL06AvF8uXL+dznPscXvvAF7rjjDhoaGjh48CA333wzAIFAgLa2SATle+65B4A1a9Zw+vRpADZt2sQ//uM/0tnZyT333MP8+fN57bXX+L3f+71wPKR77rmHV199lTvvvJOZM2fmTSCAEgoak5dFEswXhJCTlApKp1BMZBYsWMCePXt4+umn+eu//mtuuOEGli5dmjR2kcWihZU3Go34/X4APvjBD7Jhwwaeeuopbr/9dr773e+mLDMkKPKF6roCLH4XzLuxcMcPzSBWkUoVignNhQsXsNvtfOhDH+Lzn/88O3bsoKurKywURkZGOHQotan05MmTzJkzh0996lPcddddHDhwgKuvvprHH38cj8fD4OAgjz32GFdffXVBzkGNFIpJobOrKRSKktLR0cHnP/95DAYDZrOZb3/725hMJj71qU/hdDrx+/185jOfYenS5FnhfvGLX/DDH/4Qs9nM5MmT+fKXv0xjYyMf/vCHWb9+PaAZmletWhVWOeUTIcdxHJy1a9fKXbt2lboaYyMlnHoFpq7RZhUrFIqCcOTIERYvXlzqapQVia6JEGK3lHJtou3VSKEYCKFlV1MoFIoyR9kUFAqFQhFGCQWFQjGhGM8q8XyTzbVQQkGhUEwYrFYrPT09SjCgCYSenh6sVmtG+ymbgkKhmDBMmzaNzs5Osg2rP9GwWq1MmzYto32UUFAoFBMGs9nM7NmzS12NcY1SHykUCoUijBIKCoVCoQijhIJCoVAowozrGc1CiC7gTJa7NwPdeazOeECdc2WgzrkyyOWcZ0opWxKtGNdCIReEELuSTfOeqKhzrgzUOVcGhTpnpT5SKBQKRRglFBQKhUIRppKFwgOlrkAJUOdcGahzrgwKcs4Va1NQKBQKxWgqeaSgUCgUijiUUFAoFApFmIoUCkKIdwgh3hJCnBBCfLHU9ckXQojpQoitQojDQohDQohP68sbhRDPCSGO698N+nIhhPimfh0OCCFWl/YMskMIYRRC7BVC/Eb/P1sIsUM/r58LIar05Rb9/wl9/aySVjxLhBAOIcSvhBBHhRBHhBCbKuAe/7n+TB8UQvxUCGGdiPdZCPGQEOKKEOJg1LKM760Q4j59++NCiPsyqUPFCQUhhBH4L+A2YAnw+0KIJaWtVd7wA5+TUi4BNgJ/qp/bF4EXpJTzgRf0/6Bdg/n6537g28Wvcl74NHAk6v8/A1+XUs4D+oCP6cs/BvTpy7+ubzce+QbwjJRyEbAS7dwn7D0WQkwFPgWslVIuA4zAB5iY9/n7wDvilmV0b4UQjcBXgA3AeuArIUGSFlLKivoAm4Bno/5/CfhSqetVoHN9ArgZeAto05e1AW/pv78L/H7U9uHtxssHmKa/KDcAvwEE2ixPU/z9Bp4FNum/Tfp2otTnkOH51gOn4us9we/xVOAc0Kjft98At07U+wzMAg5me2+B3we+G7U8ZruxPhU3UiDygIXo1JdNKPQh8ypgBzBJSnlRX3UJmKT/ngjX4j+BvwSC+v8moF9K6df/R59T+Hz19U59+/HEbKAL+J6uMvsfIUQ1E/geSynPA/8GnAUuot233Uzs+xxNpvc2p3teiUJhwiOEqAEeAT4jpXRFr5Na12FC+CELIe4Arkgpd5e6LkXEBKwGvi2lXAUMElEnABPrHgPoqo+70ATiFKCa0SqWiqAY97YShcJ5YHrU/2n6sgmBEMKMJhB+LKV8VF98WQjRpq9vA67oy8f7tdgC3CmEOA38DE2F9A3AIYQIJZCKPqfw+err64GeYlY4D3QCnVLKHfr/X6EJiYl6jwFuAk5JKbuklCPAo2j3fiLf52gyvbc53fNKFApvAvN1z4UqNIPVkyWuU14QQgjgQeCIlPI/olY9CYQ8EO5DszWElv+h7sWwEXBGDVPLHinll6SU06SUs9Du44tSynuBrcB79M3izzd0Hd6jbz+uetRSykvAOSHEQn3RjcBhJug91jkLbBRC2PVnPHTOE/Y+x5HpvX0WuEUI0aCPsm7Rl6VHqY0qJTLk3A4cA94G/qrU9cnjeV2FNrQ8AOzTP7ej6VNfAI4DzwON+vYCzRPrbaADzbuj5OeR5blfB/xG/z0H2AmcAH4JWPTlVv3/CX39nFLXO8tzbQd26ff5caBhot9j4KvAUeAg8EPAMhHvM/BTNLvJCNqo8GPZ3Fvgo/r5nwA+kkkdVJgLhUKhUISpRPWRQqFQKJKghIJCoVAowiihoFAoFIowSigoFAqFIowSCgqFQqEIo4SComLQo4v+SdT/KUKIXxWorLuFEH+bYn27EOL2HI5fJYR4JWrylkKRF5RQUFQSDiAsFKSUF6SU70m+eU78JfD/UqxvR5tDkhVSSh+a7/r7sz2GQpEIJRQUlcQ/AXOFEPuEEP8qhJgVilsvhPiwEOJxPV79aSHEnwkhPqsHnduuhyNGCDFXCPGMEGK3EOJVIcSi+EKEEAuAYSllt/7/vXoegP16774K+N/A+/W6vF8IUa3H0t+pl3lXVL2eEEK8pMfG/0pUUY8D9xb0iikqDjX0VFQSXwSWSSnbIRxJNpplaJFlrWgzQb8gpVwlhPg68IdoEVkfAD4hpTwuhNiANhq4Ie44W4A9Uf//FrhVSnleCOGQUvp01dJaKeWf6XX5P2jhGD4qhHAAO4UQz+v7r9fr5gHeFEI8JaXchTa7d11OV0ShiEMJBYUiwlYp5QAwIIRwAr/Wl3cAK/Tos5uBX2oheAAt3EI8bWjhrUO8DnxfCPELtGBuibgFLbjfX+j/rcAM/fdzUsoeACHEo2jhTHZJKQNCCJ8Qolavt0KRM0ooKBQRhqN+B6P+B9HeFQNaDP/2MY4zhBaZEwAp5Sf0UcU7gd1CiDUJ9hHAu6WUb8Us1PaLj0UT/d8CeMeoj0KRNsqmoKgkBoDabHeWWm6KU0KI90I4R+7KBJseAeaF/ggh5kopd0gp/xZtBDE9QV2eBT6pRwFFCLEqat3NQsvTawPuRht5IIRoArqlFk5aocgLSigoKgZdBfO6bvT91ywPcy/wMSHEfuAQWvKXeF4BVomIjulfhRAdulH7DWA/WtjnJSFDM/D3gBk4IIQ4pP8PsRMtR8YB4BHdngBwPfBUluehUCRERUlVKAqAEOIbwK+llM+PuXHq43yYKIN03LpHgS9KKY/lUoZCEY0aKSgUheH/APZCHVx3a31cCQRFvlEjBYVCoVCEUSMFhUKhUIRRQkGhUCgUYZRQUCgUCkUYJRQUCoVCEUYJBYVCoVCE+f+zcucnoxof0wAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"uc = run(u, t, dt, v_sigma, w_sigma, p0)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "ad3d830f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"kalman_filter(uc=uc, u=u, t=t, dt=dt, v_sigma=v_sigma, w_sigma=w_sigma)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "b3ae08a4",
"metadata": {},
"outputs": [],
"source": [
"p0 = 0.01"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "325e15fe",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"uc = run(u, t, dt, v_sigma, w_sigma, p0)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "2a829e85",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"kalman_filter(uc=uc, u=u, t=t, dt=dt, v_sigma=v_sigma, w_sigma=w_sigma)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "26d182d7",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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