{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Nejjednodušší evoluční PDR (?) -- konvekce\n", "==\n", "\n", "Transport veličiny $u$ podél toku o rychlosti $v$ je popsán rovnicí\n", "$$\\frac{\\partial u}{\\partial t} + c\\frac{\\partial u}{\\partial x} = 0$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T09:55:46.147828Z", "start_time": "2023-04-24T09:55:45.566780Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:29.898736Z", "iopub.status.busy": "2024-06-14T19:41:29.898568Z", "iopub.status.idle": "2024-06-14T19:41:30.195053Z", "shell.execute_reply": "2024-06-14T19:41:30.194751Z", "shell.execute_reply.started": "2024-06-14T19:41:29.898697Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "from pylab import *\n", "from numpy import *" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T09:55:46.151409Z", "start_time": "2023-04-24T09:55:46.149350Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.195714Z", "iopub.status.busy": "2024-06-14T19:41:30.195605Z", "iopub.status.idle": "2024-06-14T19:41:30.197433Z", "shell.execute_reply": "2024-06-14T19:41:30.197247Z", "shell.execute_reply.started": "2024-06-14T19:41:30.195707Z" } }, "outputs": [], "source": [ "#dimensions of the computational domain:\n", "maxx = 10.\n", "maxt = 20.\n", "\n", "#flow velocity\n", "v = 0.5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We discretize the simulation domain:\n", "$$t_n = t_0 + n\\Delta t$$\n", "$$x_i = x_0 + i\\Delta x$$\n", "and seek for the numerical approximation $U^n_i$ to the actual solution $U(t_n, x_i)$ on the grid points" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T09:55:47.582827Z", "start_time": "2023-04-24T09:55:47.575842Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.197788Z", "iopub.status.busy": "2024-06-14T19:41:30.197710Z", "iopub.status.idle": "2024-06-14T19:41:30.199823Z", "shell.execute_reply": "2024-06-14T19:41:30.199546Z", "shell.execute_reply.started": "2024-06-14T19:41:30.197782Z" } }, "outputs": [], "source": [ "#discretization parameters\n", "nx = 100 # number of unknown grid points in spatial direction\n", "CFL = 1.0 # Courant constant v*dt/dx\n", "\n", "def wave_init(maxx, maxt, v, nx, CFL):\n", " #choose time step according to CFL condition\n", " dx = maxx/(nx+1)\n", " dt = CFL*dx/v\n", " nt = int(maxt/dt)+1\n", " \n", " #define array for storing the solution\n", " U = zeros((nt, nx+2))\n", " \n", " x = arange(nx+2)*dx\n", " t = arange(nt)*dt\n", " return U, dx, dt, x, t" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To obtain an explicit scheme for propagating the solution in time, we may replace the derivatives with forward differences in time and central differences in space (FTCS)\n", "$$\\frac{U^{n+1}_i-U^n_i}{\\Delta t} + c\\frac{U^n_{i+1}-U^n_{i-1}}{2\\Delta x}=0.$$\n", "This leads to a simple explicit formula for $U^{n+1}_i$\n", "$$U^{n+1}_i = U^n_i - \\frac{c\\Delta t}{2\\Delta x}(U^n_{i+1}-U^n_{i-1})$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T09:55:48.498810Z", "start_time": "2023-04-24T09:55:48.493003Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.200234Z", "iopub.status.busy": "2024-06-14T19:41:30.200154Z", "iopub.status.idle": "2024-06-14T19:41:30.201845Z", "shell.execute_reply": "2024-06-14T19:41:30.201677Z", "shell.execute_reply.started": "2024-06-14T19:41:30.200227Z" } }, "outputs": [], "source": [ "def convection_solve(U, dx, dt, nx, nt):\n", " xint = arange(1, nx+1)\n", " for it in range(0,nt-1):\n", " U[it+1,xint] = U[it,xint] - 0.5*v*dt/dx*(U[it,xint+1] - U[it, xint-1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's try to propagate a square initial condition" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T09:55:49.043386Z", "start_time": "2023-04-24T09:55:48.929267Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.202484Z", "iopub.status.busy": "2024-06-14T19:41:30.202376Z", "iopub.status.idle": "2024-06-14T19:41:30.252250Z", "shell.execute_reply": "2024-06-14T19:41:30.251937Z", "shell.execute_reply.started": "2024-06-14T19:41:30.202477Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.0, 1.1)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL=1)\n", "U[0,:] = 0.\n", "U[0, (xmaxx*0.2)] = 1.\n", "#U[0,:] = sin(x*5)\n", "plot(U[0,:])\n", "ylim(0,1.1)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T09:55:49.691799Z", "start_time": "2023-04-24T09:55:49.588730Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.252657Z", "iopub.status.busy": "2024-06-14T19:41:30.252572Z", "iopub.status.idle": "2024-06-14T19:41:30.300884Z", "shell.execute_reply": "2024-06-14T19:41:30.300626Z", "shell.execute_reply.started": "2024-06-14T19:41:30.252651Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "convection_solve(U, dx, dt, nx, len(t))\n", "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ":-( Does it help if we choose smaller time step?" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T09:55:51.193383Z", "start_time": "2023-04-24T09:55:51.010609Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.301386Z", "iopub.status.busy": "2024-06-14T19:41:30.301274Z", "iopub.status.idle": "2024-06-14T19:41:30.393282Z", "shell.execute_reply": "2024-06-14T19:41:30.393084Z", "shell.execute_reply.started": "2024-06-14T19:41:30.301379Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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pwljVn2xXHfdW2JzbUF5gpjKlpS0YMC27U1c1tO8k1Jd5z2KMljBreMr6nB1ZnJOZMjz/0Hyd5opzA1IfCt3Ii3I4redzHIq+6KsVd6q+88XdmErKD5FKT0VRzL/WPwRjZ8o0oCnOSIQm58PBORWDMJYo4IKV3YraAZNt8zwsBzlx1vrhiYv5a6u+rqvRfafzCd2O4j0l9iX2rk3IXYkfo1M+dZIAXjiEv/WuvcivKJWdqu+YSGsm4pGmzfrgetW5Tt+EKbi3xAq6vHv8IRQnEwKCGTdhIi2wERVSxw7XKfkWG416cI69VMGBWPvVxXO9Zn5dB16KTZt9sXMZGdWRcRcch+/opypYZAt9sedv1ghbngCJZBSXXvdsneJ09TrcNueGifigkTbrX1p8JaJ3O4Jsp05qCUxbFl6MTT1AQ0BwPoiOsakE848/GJg8dva0Tb6ZZdq5UXQg440IbpNZfE1YpK/Uh2/4vg1EH8IANN2Xvr0IwF8u1+1y33XceWRU99mJtKcX36s67hs3YduLWiNi4FrEihLwWd0Tx0U4u78Txvo+1aK6tqvXWMnJLGJ6IPaenaeSUfsKm62f0EWfHxwvPuW5+YcszWyfNnvyt7iZqFFGgP5rFs6ZqLO4jWSqBn/7eBUuREc36d6N4CrUOssRcF+ojlr+HtDt1ahFtpHzE9X9t9qmHKBhwnriw+12wIXh4b+RPN/BXHJr2uiHWEndwbtwTrT9ZOB4YwRf0nwFqWjK6tQvnST8V9Jh/9KH33lw6mccqGnD+12XFafwOtHWeDtqLZl74c5TonAMs7t6GCkdS7QTM3Tkff/GiSFNvpFtvx97C9UpAI3WvvjIR2BMK3h48ztuLeo7G/6CGlBa0YBiwQszFo3JkKDTIaUYwWOWI2Rfpw+ji7lyK5ByNxfP0SzZT7ITJQcffDj4rmiSreDGRccdRKeSzWPevWctlj7NNAHNUSyKc3CAhnO/Yc95eTuaazHbweE9/+Nz1hA0c6jN9cj6H2S7S4JTMmTOVG60D3E/teg+22NERI762mdhjIncvd3slcvsd/krE5PvqrJ99hWKM8/XpQvXrkFS6WwCaI6ar9sQNf/ZmgJnJQu5k1lJvM731H1fF7lIvNsEarrzt11SvFrzqYHitIuy29/81C6zkRaicxbFdeiIAM6F9qwOhDhrUBNmpNkKcs5v0/mKXlLI4N3cAWPueizrZElgx3J7RfKJsmlAIyIBPwKa7iSW6NW8aF/5lP2uUqJ9JWkUKdhrybmUkUpxQhy1/r2Wv8OCYcmvVhTP90m/S6cu+uH2E40RvB/545kWBJ7riLUXwFhUkEW/7Wu63WvdU/bRksOj+OLe/yr2YgkRDvNIAndJjZtw11WstFz4NzqHNPYwaT6lTIscrHbDkWZ0TUREV3I6kabVr6lag3PNHcXozqdrn1SdL7dhi+0x7Z+aGC2P/83mfX3jpH/Hm21a38YW+j/H2btmtfE2HW+nyY3g5eru08iRWBqdaSaApsnqpC6NMtCKfJbL9r0LxhjYd7sRPrAZuOedb55+25QDNEIAjceNQKVrHJ19aDv2/DA/qW3CNvci7PTMJsOCW3ABZ1b+LSvjfKJd22H/rmtsGbvAjGYgoFn2Yx2xt/z7urDvT46yr2gSEYmsNxbAKnQCLX6Snx7HlBNLXSaSeFy2881PJz17iH0/LRGR//z3D1v+ZtEe1jX6rYg4Zgd04GX/1w8OPlLZLiSIF+pwvq0gukfr08X1yPnqYTrBvAPhs2grut4K28DEoRTWc4RuGVybroCxe7oPI0dauVK1dTE4oncQ1xcv6VP47P6ZMFYvWLKeqMaKo5SBn6uVwrDP7cLvZJytwpgyhbVQR3aeCJt6gMaLS72LMDw7eyMw1rphAqt/0jrU/oNa3eKfX1PczmnWwxfCWJugsJf2OrL77PPAV1dj93Fm2oqmMwK6e5ndYgUr+RPQGbX5noYxzwC+JgUSocmM6HQk4u81QcJbk5LURHye+dEvVOdqe+ITMDZrgomrGtv4eR1JdbKv170B+UPDZyAHL+DAOfOt9jPIGe2BsbaX0RW/w/L8t3s3dhGRc/9u1d5qE6bngzb3ZF1q6vd9yIvavAHLmdsMQPPBGXgdN8Ux4hgnODb7sq4yKdaK6e58U3EAr3S1LuKdT+h0eb576P1FXUcxNuUAjdOD0ZgcWZ2c+ye3hPNgsXlfwFD25LY0O3isfzE+4xIHgiMfVvBLgUibeIZ0eidd5+oA2NvJZn1IBwaGP3pwENPnfB1D6CwVOHihPWGZlVSzDs6D83VaS1tfaIGxmQagcUUiqnMxa75Sp6fyVtj+bxQfYWtR9ucyjVU0sXLsp3dgeim8zf6ZfjaM3JifFrB1RXsGwUv1Op03HpuDtIk5dcjZ0ljtsxhRYXfW1Ll5o+M0EhoTZVMO0Lg8GI0ZT6LIkaY6RYRJ7B8cBGCt5cZ0AoJvN9PodgwvQGcxkkeQ4yeAJkFEkr3DujlzyzG32h4z7xYUHZvxf2AX/fy1P7c9Zntm8udkdg9ypZhFPmR/3HWvIM9hhmAUMj9fF6Kvf9p+Eev8BOPW6fg4Wv0ebW8h01rvvhjGZhMJf2Zf/Oh9quNY40zPI/YtI5LnIF8m6tT5bN9mvB9le+wZcR4HqXIiJPeXkxjtKX0RBfPYN86bjZIAR5TbNyFlvKDCS0iHYOYg6uOu0snVSLOzKQdonC58mdMpvA2RAd1L371Ct+t6sw2Z5SJvN7BFzaG73z981eyxJdJg5J7DjbiL7ssiGdw7hnMhUYPX4SJtTFh7iBP99jvJ1p8ggZs5suwpusaIbyd7z4+/AmN1bxGY+2Hr3cYIWeS36bgJc2p0ZdAl6+2J5PEji0sn/DPW9RlG3rcHJrN/r0tFsCjTRWHd3P3WS+fCmCZl2LOs+CWvdD++t95YcT3zCgTQ7CK7JC0H75goRoHqvfYFKr8ZLl5bzUHAS7b5zW+H8z9tygEatofOD2OEpnSfTgbxX860V+Kc/0vcbbOctfMwbF7HFqedWfsdbOA/UYNBaw63TnflW72sT4xxLiWwete2M8lxuOvY/jO2gKMjK73PvpHcu1twF71uDFVlfUMIJfJunDN+ssakFuKuS2PZHt3i9+NbWD803Dm1PoqicbMNtVzWkO+tsLof6MBL7+cnnwCsaUNQsxrnh6sUQc67a3Ge3j2GaQYND+3uFSzShdHFA1E//ubndGR7sFXrVYdt+xaTu9dFmWbeVFx66cTT1xf1ORGR8o3odx15omWlOJenH5feVwaxlUdAKUT5yXLk6exiYjeG/eKV42BMyyXLV0dgrPtIe8L5+rQO8BZjUw7QMPMOIvfB00vyfmS3/cVyewfa/G2dg/7rn3UO5F/OvoiMvmr5S1teyiz+lyYyiuHc1UvsOSMP33u76juzJyJ4YbbrnF+qjtMQXj8YRifw0U2fwHONEUDjQUDjzKCT7TtURxQu1hZ6dBUrsz9mT7D+5PM6R3ZhxzFk9M1PXa77uo4AvPSl98NYtdiXQWuNpQXyc1tg7B1B3PxcvAO7pYvY9+da4tUBlS/djUBW2y/pfaUYwTTtkv1MQFC3YD36vv8kozopAccz61XHmfbzRp30waYMhlsdmzBqWliIgoRytBn1wDUiSPrTdvZFYIwVhTuOQMnfBhd+Ryxv/gb0FSUvFC/YmGjACM3oofb8wF/3I4iaKJtygCaXw1SBn1WEjuGEHjsaO46+FZZ/+VX7gw7AtFLxbzczQ9ysp0hvB0YpIlkMvbCGpgVSdql5wTOFYpVpJtY0C5iIyL7lOvByIEJvE2l1X8U9M2OpjH3AvkTdbJ8hwrunx07D0tdmNy4AO1/BXk6tBNC4Z5u+Rylo90N79eMDsXU3YFqqTCn22KLoL/ZW2Xc6zoaxfIIQySO4YYm14WbHtHA7PoWRNt3mp2eF7r7lqSy+1eqeiuHnyHGuMEYSRxsQPhw3z74L+sp21j5kYmzqAZosAhqvkoQ9NHtyu/ZOtr1/F/JKROzVUf+vWOYQc5HB8La3V/dK5D0Yjcl70IG0Ntun/k5/9XwY88ge1XUczHbY99/8sm1muc24qDPrfId9suD6vhPJKC5O8XqcC05B31ParuOEDRxdXHNKjfqxSPFtUcp+9/ZXqma2tgOB5iziK9NluCbEsX0bmL8LN0kuon3GbKRVx+8cydsDpPw65ea4HudfCmV55JQK+/MluzFSNFFM1CkHaPJJ/MmBAbJfC+FuKnVk8b0wDgbb+/M2GCubQoCm8zj78GqoHcfyPqKI6UVAkynBRewLMx6z/c7CDWyxQkDjrmee8uAlAGs7qM/7LyvH7K2q5rr3NMZHsqZ27n8eo06shcb4XOTg7c/hzqnmBZ1P6T9j8ngHIiKtn988qed/K+xAIoTejbpU7lgDAprsLHvCtnMLcmM8Y4xviHbkESj+yWxXxtqaYGu6+A15vC0CY+MNuG5+NGS/noR2ERDYPDFSsFMO0DjieDMZUz1Vh6TSixbaE9a0LQ3eCiv77dtrN+VuQJIcc0hzn/4YjLWQ43xHkfprwyI7ceHIlBGl4AC+zOkI7jPODpLSJ8O8f1lte4yIiNyhKwu/ZmCO7nwHic34N3sAE/v45OvXaHgptc/q9pKLZyKx94lxJJzLc7rf8KPld9kec+bWd5JRXcPD22coS76LNNb2QWuf2cfI3/ZAsOMduhTOTTGMxpRv1S2w8Ubc2Myss1/UmVyGU1kwdW0TE6rD6M5ao8Bh3SD+Tp+0q75zeBZChVBDTPVZ08ra0XfGmyemc/eUAzSuOCm3TWDIeGgBIvTLK+wVJef/O5bKsZz1jh/pJOW/3ccqn9Dar57cjsWHrv4gjNUKhhdRGAuvo/WPOp2KgV/qNA0abtFVZV0x10qUfj6FT8bbjoSq0eMQWLn8CHzSlZNbwv+XOX9VHff0BawUE9Muu++yJy++mCquLHWibeX3riejGHE7+VXkPrjFXo9Da+VP4bkKIVxMTqnCiMd9fUwmXyd+9q6gfYSm704ETFEloNFasW0TNl9FyLNiH70UEXn+DzifWRm/qcBdd6Su0ODHm06CsZm7EXAwiFNowucyN2ytUEwVdO8QUx9n1qzkHpkAZu8WbK7cpgQ0YzMQuB1do7u/ppXsZZu8idGvmXKAxk38gqOAD2u8ujjEmN2h65678b0/JqO4o3jkOmSEM9LdV8/X9e8xbez9OmDV8K9EYZl88sXP3WCM4G9q+xJWF7EizOeX/JGMomkEtURE3lNiXTx+NITktMJQDMbSZQ0w5vbir8+W6RSAEwWdJECxpuWMbDv+N7bHfPrHX4Cx2rcgJVTm1FVjDN+Nu9AoATTuViTtajYBrKTatQjnUZsPo24/60a5+yYCaIq9tpqHdSJsB2JfeOJDlr/nKNsLXHyiDrywtFzds7q0XN9hVkTw0RpdH7wC0RFyDuFizQBNbRSJ9GXGIvNoQkniJVziYsUNRUS6Y9YsQ7BTh5gcLsxiFKLos9pKdNISprkGGWl1GtAUZR5yL/MefNDjcyZXnp71cGGmJd19qqw43ZkjvqLrl5TbqHMOmt9VyL01zRVMxc6792CFRmQY89OJahiSgB/nR2lYN2dOXG9tChkhndEPFqu9XgdeBv/C0lxvPr8n+gvd9W6+VEey/d0oYT4aFluMlXFN7hiM5TfrFrau0xWsUmLZvfbl3iIivf9SvH7Pgu9Yhd60gOmrFVjyzOzEZ/4FxmY9t1712ZNPtfqyj0QY2MJnUPcc+RWk8SJWmokcXd0OYy4D+tzafSy5DgSymRBu6wqLWWRLp7qc3W+NplVv0fnd/Ark8syow8j10SU6v3X7qLUpa6GXpeQwelSMTTlA4ybRrkwIUxaLW3XS6D8aajnAK3pr7Uf1uh3W283cLYSvYDjtwU3Y/ZiBi2QdOrxKH4KXORHdjiV/r6lnhN/JdkkHs7241FTU5TbrHkw3tikd9ETa78/6CRlFP/BvL1gVaU0xQhGRoXm4IcqQ/EHFqzpextjx9hGJbiJZr7XTLyw+wqYBTclzmTaNDjA1/kaXPmZ2U4NJztYByMBK0iy3EoHs+GzkAa0oRb2vh4esgGDNDvRFbQTQ5KKYmorN06lQs1YvwX3WORh6Ff0TA6S9h5NUbhSf+2JvjHwar/eXe6yALjCmEwssxqYcoHGlEQWz0rujKnQ3/aaN1jAyI6O+FcaEoaaSDR1tv8stJf26GJDwlWOe0u9G51Pv0+m4VD9uv8vt/he2KOiiaQeztX3eHrw4fZPfGHaZT7dwBjfZX0uyAedCdw6LCkJ7dJVKZ862rzi6rOMsMmovdS8i8h81k+ujOk4v/rPev775G6x8Cp+LsxS5QolqXC5bPBi56EtZF3V3l70ujYhIMIzVUePVus/+rR9V233GdCjsJ2p+xBhfptWPYKjapeNT7dtvBYJtSvXjYmzqARpCXxgnfXk+GGaVSYj4K++1z3FqogUTbefc9yUY0zaIO5hN2yKh+3R7Il7VeqIFUYs7nbYqwnNw4m672YfObSCPu+3sTvsX+j+/oFNE1rQ0EBFxHsqaGR4c4Nu07EO6fjAb0pPfz6jh79YcNeN6zZ6JC8VzYyiR4NqARQUsCaCJmr5yP7YNqJ9gbtOJm7BfkqYq5omzfkBGD14RPWapeiIkRypxmtz4BLf1W+dvmXL9XlyD8+iFGbr79uJGTIfN2G/1gdpGxM2L0J/O9WFPKaarxKxksw6UTYRNOUDjyKNLYiJYWhXL0rvsQcLATboHqumNJCIiR7EqFuviNO9GXXiR2Xf756mOG7jIPhff+nfdgosVN3guEZHRG7AtQ4AAmn896i/kfFZzr8NUT2YpLkRHkz4pW0Yx5xt0Ilq+upfJfNvnsk8N6J6WpqWBiMjRt6+3PWbWIweH5MDK+X9WHfeRH30ZxhhhmTUI1Rp0HibNUU+oQn7II934DgVGcWVjMvYaoNl8O56LzRjXYvYu64Bs4UZCHlMAGm0VzmTbs0ncdERcuijZ8CzkAibq8L31CdFU6bJGaCr36qqcTo2iyu4rVHsKrWItLuX+XmvEWKv08pkZT8NYtYuBIdzMM1J3+XbrfTsQorOdTTlAU3AieMk36XZ6N8aKazSordZZ+x5GAEPHteimjbbn0lZbMXvqc1j55CANy166yr6XzuyP6hZcTcWNiEjgPhQxY8ZI0lsy1mgJ27HE2jDFcEgQq0cYoBknypz3voLE4zbSF2uy7d8q7dMYbZ/QgZftPymeIzGRpiUsb/0ae68ehRFNxMexDGUUlgbx/f7VbgSyLNSulbE3TduFecv/w0iD1vwPKPWRirR20kZCa86l9hHH3w2gdlE8y4oWMFU8TKaMpxLB0BhpWxLssIIcfw/+TgYuzirBCN49UVbqj1b9LBJtHQkrz08LaD5QiqnL7RkdofjO4SUwVrrDen8dk9gEd8oBmjz5xTXREdVn796Hk0vbDVVjmlSEiMgPaovjUiTerVuIHE8fHJL1E21/GGaduq0Wr0PAW+tCh5clpM/BHJYeBra/eeHWN8t2nX+z6rhfDhdXrTPR9q7jdUDtO/tQw8asRhmdic+4zIkLna9b51q1MvY7s8WRgD+wYnLTzAeiXv2xLR+FMa0/7T0qYnvM6h5M9acy+FzqCaDJ1mO0NRzAsb4cRmj8BrZwjmMBgbMGo1/VLiTUVvp0Jeu5TSjVwIVJjWOaUeaAPb+0Mr30YqwFxhy9VkHTQkVEda5ibMoBmmwAF6wTanQvUd9z+PI2TyLBaaJt5BM64PZ/1X6zwQroWknUKTEHnVbURch6WSSVbhnD+VG3yl5zZvhjk6+C+1bYfWcw6Xld9eBEmraSb9NKTDeaOjGDC9Cx5wR9SmQ7Y9ugHXG4rpz5/a9Y04FR0ckoXF1NKngm0LZ8lfEDdZb+LUY5GaBhoCn+DnuAN/oyViXlArrnsnx2O4ztG8No16Y0goZwuwFgshjdSByqi/ZXeA+g3Q7RVzNt6FhM4TPrI5u1AZKGemk3/q7ZPdYNeH4eA1ETY1MO0KRJhPe4EDoHJn7W8IT94uQ4sric+Jth65fZy6e/HU1bJlq62j53u6xV1xRyKIEM/0Giohp53D46MOMzOj2HYiXg3yrL7tGBl+77zPQBPrvJFiMUEWn+K6YGzCUhPw/v9/YULsxlO7DK0Oz2LiJyVdMD5Epw8cg9XHzrAI3NeuRCGNOkRu879wYyquNIhH+j09jqPgeFBi9bdJ/t56rXIJAYnqWTQ/hU7VMw9u1tSJJ+cQyvzb/biEgEMEo7sEAXuc1r5YOZBewr9Kh4NbFdaYwoeQgX0LvL/jvHaycvaj31AE0Exw71It/izlFMoroUi9OOL7w1t9QULzqYTRvmXPLiB2CsRpALsv99OkG72mftK1Y+WIMherY7GR7HFzc5hGMRxXX9ftbfFUeJbP828ga8RKl1+y3LyKfx/n5yr8nzeGsieC8feaftMYf/4lIYayIE4AMp+S6s3mB7zFHN7TD2/AhWmLj3oE9JH4rHzfPoFFLr/2AFvYwAPP4eneo3s7k/QgCmSYYt9urAy/cHW1XHMRs/BYHmRWF7DlHZ08hJSVTq+pwxUv6XEsi/WT+IKuLeDmuRQvZofG9H5+g4Kb0p3IEzsjOzXNRIYZHOPU2H6toXbElgJCpdwLWubLd9VGi8ioG06eaURVm2FG9chRPTB38fxLJIjc7DtcvvUV3HcRveDWNBQSKv1kF/+1nr7kFLPM0rJ1L6DN0iecwr51v+LiVv0eavohNg5vtTRHXcJw7R8QQcr1qvxUVyzEf5n4WxpxN4vak47jK8fcWLgmlMq9Gx8tQbyCjm5zf9wkpwLSctNTTkyzfDZv6Xrqqn/yNsy6kjkmtscQhbH9y/H5VVS2O44I60sJYGOsv22vd86sTOCmrLr8O+bBNpP1uLF8eqHZl9cE5xlXbZPiTKOrOYVtRachzf+V4HAo76lLWIIFmBfiFYq+NE9SYQ8N4/zFK56MfTESsA84cxZfaOOt1z7xhHIq+TfGew2746M6PTCizKphygKUSwhM7nwNuw6lWM0Gj6lrynRMfcL7sQQ+hsKnTcyXY26KDn3mjdYWnxbtsf/x+MMb2aa372c/JpvG+lZ9g38Nz1bh2pNHKbLiT9r5VbVMflx633aPwULJOvJcS8daRLsiOGTqp04nogHpC1unUeo/zX9vf3I3f9TXWuyW5iqa3qOeQzOs7Iv3QeSUbxnXQst4KVpYE74Jif7sXmhnMSuDkZQNxDrdho6w/e+duiPvfPWO8XimuC23xH8crXmgo9reVdB9DVuQ83l2MJ+yV0tBl/+/FN9n5SRGTfAAKJjn4cm8kkLpqsAMzXgxuzr1Q8Qb4VIyjbh3BOjmQwYhXcjZv+vNd6HamojsdUjE05QBOpwBz4QB6rFCLrdbttp7e4fCBrcsds41HoQJkVu8Oa+w0sAWfB0KN8b6+p8kTS3nH1Hqb7TWsGkTjnjeFLH96tW9RjHzdJwAcHx4rZh0OD9geJyDc+8RkYc74Fysa3NGGEjdmjf8Vd7gySwuo9wgoOI4QgXrIbfQXT2qhbpOu39p2174KxWbLe9nPnlej4VGq9K2LHfKy4aIn34YOjxUqGcCi1wqfBfehTkkQ92LTRmbi9PC1iL70hIpLrRF6eN6YDZWMGPzfYjz9eK443SD6bSOG8b25HkruzzipWmg3jCuMaPwCu0P+wt9cqNQFWF0KewPo09u2oeRFDggxX9n3SLAU+SF7c01iJMr6kWvXIt5t9aeMFMFYt1kiOd0lMda6dXSjMRqQaJNCOg5TrcJ49V+We+MEhTqY155M68LL9Vt28nGxrud+eACwiEltkdb6xHAKV0B78pOnERUQ+04KCZczCT9hLyrujxZOE77sDNXK0KsM/qZ9cbRp3HWtSqJsfd5MqJNMSRGMxMZcJCKKF2xGY5AL2C3F5K/qFo/wM3GJktWQvgpeSHl2EI9VijTiO9uoaIjNz9SN4Gc8QTTfSRiLXZJ2r7hByHguEk1iMTTlAU+FD8tvGBO7AnVsxf8AiFwPLJjfUXqx1H/1/T/9ERMTdyngI6PDir9p3ST6uURf2LQygI/AwHDgYU53vS/PtScBfeRYBGeVFrVhCPn3wRnx2nMZaOlgXhRUvvweOCImuvFlroAD8BhZptGqUdGYx3B/oQx+QrcbF9dRgO/kGoj2yzh5sDb+DcUEeI2NoTX/FqJuOoqqzA0k/xk5oKfqzd/WYaUSill6OW4xElW4ZDHZidC42257UvbgS06VRp24BD/QjeCnp1FX81VZb5+5wRAfcmLnHELwUXLr7lqy0+k8vKUWfqBrGKQdoKr24Ev2tBwnAzpiu5PT6E+wrNK7oQbXYiWJ1v5EtP1MX0jxY7IO730FGsTfS1s/p2sw3Pm7vVK+oZsACIyNm11oREf8gLgGMhMiMqRibNu8/MYrDFp3sd3QpIU2Xa2dQ12zuQEwT4o58BTkH7LePfmjy9XvOaLLyN14YxUolfxf6lMGlCHwYPytDlGY11VZ97y2+j1Vug45z5p6Nv1Vzfy9YeQmMzRFdZKf7nbqKxVtHcHFe97J1s9NGAE20KQZj8RodZ8m1mUg6HIukebchmveRKgSaHsLbXJPG3x4m5f/urhiMsUjwOxusrRR+Xa37naxztw+/Uhw5XeprtMn6Pgd86JunAU2RFnDhzdyxGxfJOUoBME3e+qnrUSclTCpKtJVE79t1CjnOWgXx62ZdeJuZVuht1oMXwVib4bh6H9D1kun/JuaxnQTQfP/s28n50Dx/w9SfyWtgPWfWpzFkWrofd0neEd2ettgqIab8yezvCx5UHafpcp26X9fzKFWY3KhkbqNONG7G53T36Dv9rGIRzVyIRERODlkXo69uxuhRzQj6gFibfYRQRORbvaxixd7+fNRNZHRiy0e2/ktxO/q224ufH9888iHVcb9sPxbGIpvticcn1WOk74Fy3UKfi8VgLE8C4flG6307OYC+gr1Dvx/CdcJFMgX5hK4f1UciVh/46wrm19F+04Hl/94R9IGOvA7QxA0ucrlj8jbzUw7QMPN1KQnARXYs1gpI7fuYriHhpr/ZK5oy+9FQi+r83o/o2szPvwYjDeYvWHfE71Xncj6h42BoiY/UFpgVY7jIPxlHAOYfwOfiSukATWxh8b103mx7bCETeUObf9/nYKxtAkujtXbnTF2K5bb16KBZyXBqAaaem93WsP1gP4KGmhxGaNINukjDw3sRbDGtJdPaPDrw8qUuBph0fuaUFcWpDGtbp7hIT59PlekibJ17kUPU2GX/Ti4rweqze71MmFNnOUJLSUXt00ldOQQlL/Xj/PMM6oQ+mZkNln0BHdDcux/vbQ0JoeSVhWsszTdZNuUAzUiWiJ9t05Gs9p0emeCrsdr2E29VHdf07zoCn2k/ffBMGJtJyIBPKVQ4RUSy7cW/bG+FdR1bZnvM7/fiAhDpxAUr78dXx0EqW3qOntzU4lthbZ/TgZc3IyWksYZ7dRuW7uW4OoWNDJlvD1nBiCLr4tZ9qu/MPq9r1Id9eXT38dHfY3m6lgD880bdRqxY630vi5w9ofps+cv4/pXstRfOPKsE01BfP4BVMF2BIGqs0X6+PZvAiPTu3ZjqmSMT52MjJbo0ZXALznFXCv2YI69bN8N11vR5mvS/miibcoCmK4E75vJXdd1QS060j4IczNZ2K17/m4edJ8+0KYX4UZiPNq13C6ZdygeIU6nDXYyzAXvOnLLMnsukFVl0hd5elU8/+t6NZBSd/ft3nWyM6LhIWgvcqwNg6SUY/Rs0wuqlJBOdrcLn8gEinc+s/hndIrPvfS2q40xr/Ml6GJtIiH38xvNgTNtgMn5a8d22q1/CTYZryDrGfFvAgYu1kwQuHk7oiiq8Nfj84nX20bOHB7FFTsku3XLsKiXnn8V6MllBr9+ti9BEX8U7l3djeslNpi6rvpsXta476zp1wqrF2JQDNPtGENBUbMbFg9nPFzDhKuvu7OxtZ5BjdKJgB2Is/29adouuZ9DBYtqKptseZyqkmE76f4fYLzLlmwibP45AqODF+51oxZf52vrfkW+xkm/Td+DOjAGabVcy/ZBnYOTUzWfBmPMtaAq5zKeLjAx+w+qMnQTQJM7T9es6EDtzNqZ61qesbTpK9+OiMNaMEZp3liAIXpPG+6FNz5SdqUsDm2aKSb6RjXy4uGja+N0I4rWA5vqlf1Adx6zwAkmHzWqx/KntBO4ex3f+r0OHks9iGvHQOmwdsGY/irKa9nx7C4xVk7JwZo5a9D29y3SRPo2VvozrVewo0uJhGKNThQa8tvkh6z1/Id4Cx0yMCs0UBDSxMdJAkLz0rOJjidc+N7r9aVyEZ7wJgGboHawi4eC0m2K6bqt7z2cOCS26XkdO+3jYjJZgyWVoL+E+5PDFzfkwbBqvxdep3GlfOVS5sh3G2O7y/HfoIg0Df8LdWhUBNIOfLk71daLN+ZT9or7vbJ2z358rftd/bBmSjF8Zt95LzygCmthsBCpRJ86tn47oIonMrmi1V2w+ELJ29wnFFW7XPIa+TRv1PSOg4xntzeqeacFnjapk6yOqz7mJBMOOMUYURvCyJIzv1epS+xYXhS5MTwf6dPcjW4kRwTFF0+yMkvTCmsrmj0OfzVJO6Sj6u2qPUbGZnE45TZhliHw1s+TxC8mofU659WfKnjOfZZ2TcUH5e0L38HvPKq7wzXkY+514HUetfy+MhQUjPtt/Zu6k8Vx3fBuVUEtIROXjH3+EXBta5Z9QJZm5Z3ORGcljzDSwgXAf/BimTofx1RmZVZysulbW/7oa3W6+6qc6jsRN3/yxMYIL84JVH4GxJtFpuEyk7TiTtcvAfd1JzyJhmcnCuxZik8JTgvh+/9iQEwiN4Hs2OlPXoPHObcjPalbey7OD9pGWI1Z/HMbqZRM5Eu3OU39GRu2Xh+xOXTRGq8bL7LK9mJI1qzpFRLKV1vd7cL7uuQQGcGHe1Y/R1mYCaC4II7n81hBrEmq18lfRV/j2o1QDWzvYfMvOtZ8fo8nihfUyJXi9QbLHGGvEVF2tO2b52zWKa1rBMzHtEKYcoPH36QBC99HFNRrULk4f/BfdYv0vt6OkfDMh9V2/vLjw7Y6v6H5n9ELcJbGXbde59n2aSu7WNZO8vEInfJcbHoYxjYbGd/sQVGa7MLTPzpWI4jzKthWvDfJWmCYl1PRe3YKrVaYu1rQS7TV/0G1Yuk/EHTiLpu0zqmnmC27n/S26LuXOdToOVOE4pltlfy9Dd9uT3t/ItK1N/lKkouve9xXPm1i7BvvZzSaAZqzRumCPKHuBsoaKvTHd72R907xe+xhVdD2JOg3YNz8WERlpwXdhRYs9sBwbxd+kjX6lyNRyFBCExOuJsrHTugnwjOAx6Qnq7zQFAY3uuIrlur4rWvKYadrFesa/Y5qBPXpzB/fZfSwnjih++wm3qa6DLfQHs3WdZi/A98dXcOFoE+xVk63GtzlJItJHzNB1pzx3++nGyNvr3jI763pdCfU3epUdGou04J90abnYMl14P7jHCvpypbjLXd6A2iZDeXzXqtcoy2ZP00UWTAvdoatKcjcycKEDn59f+THL39py/fJTi0+7a1PKo03WhT5br4taB/bjou6MR1SfZUbWeTyGKFUXGNmXWLwV59GZUfuNR34Y16p7R5GczCxNKDoFJz6XRB2GbeJ5QymY4P908Z08LDblAI2PCAQxe0+TLrz/vR3W9Akjcx6IFQh/Q2Mrt6KeCtPeeLvZGGkkymx4nj3nwr9TF4JNVaAjSJMdy7KILvy+YYM1/N5GAE32lIOj55HWvlyu++333XsMjDUZEUd3VXHdpv8ZmzsDF9hEARdAv6HtmAlhVOuQUmw0uzGN0Z7gDhSKZHt5zyKMOE6k9Z7O0j86q3q+OPrmxTN0VV/Pp/COhHfrgEmy0urbQ2FdxNQxiCusI188yTZbbFmyQwfcItUIwBb7WLNj6xx0j+GzWz/KyDck9VWK/rRALjcfxuc3mrcCdFYdNVE25QCNvx9vuLsZCU9fLv+L6nxjf7ZGAiYa0BRr0ceKz5cezHb8OuQJVBlNJ0VETj96ve25ap/X7dLHGvA1SVfjLumdpaxEG8mhzQ/bg+o9n9ABWY1as4hI/sTDyKfffIDUdJU9v2fzv7EqEWxTcSAk2EuanoCxF1IYki/ttD6HsXqcC0cE8J2/cxB5FNkdOt9w06F32B7zy2EdYZ5Z4P3FR0sitxWnTaPt2v7ve86GMe8GrBhjQNA5wxoVqw7hwr8lg6X52U4SIXU0w5C7DVNf7B1Kj1o3QAykMXOEMELjJmOnNiF5faHHvvjAN4AIZF0PRutqCKBxViKoLDjxXYhWIxjfnbJKYXjHJia9xGzKARrvCDrB8cWmaJXe6m63ElLfjJ4zTGHTtKqHMKU10ZozDrc9B+Oje04gozEY2XuVjiTtul8nKX9Tg30o3PcEln6yuE6cTI+yKnSM8zz2jepERHx/tu9r89jxTMMFORjzryUN+Mgny/7dXugNU2Eib0U67PnzfkBG0bEvfe6TMMYIyyzic3YQ59Zl3Qj6fANWR96/GBeOJjfOhUd3zYWxGYLzjb3LxynoG9c8eg6Mmb253si0wpnF2tgHGClW5++2rsPoUeuADkQtqrcHag+NEemDAr71eT9JnczV5UVcA1a/+KcYa2lDvrMG50I2hBvT95czRW976oMZbRQRGehGn4IiEiK1UQQqBTe+V7MjpP/emPWMnjG2Sk5M4faUAzROgpb7FxbflI/19zAt8CkWDkS7ZD/T2sAUy/6P2ytsZntwoXMtQifLHM18UtnCqjF2/Za1grB2hO65Apl5DsF03s0fZVUWaJW/wY7TWqEws6Q3T5rBMUvWIwieU67bcT6RLK7yifWZYpbd1a467p7WlbbHZC5hpFIENMX2p9JaNWniyCx6pw5A9r+TdabGiM9j+/C42nHrs080KXfbm3W/YeRk9k4+Yfu51nt0c/dArFhNra7Ti986Veoy/eI2NGdERI6psALGJ/uxkm1lL/Od6J+dIXznh1t03KZgl/Wdf7ITIzsRUiE63ozvfLIcF/rDvTreZrtB+A32I5AY6ddBgDkRXE92OBHQzA/h/Hhgr5WnU5ZkHnsa0BRnjJndpFsSbx8tLrf/6zkshIyTd+XjSFKdRUrF40cUl4TsPl63wyi/R7dQbDjuFjJq3Z1ohcM0u1IRPQhhdssQysCbxsS4/OUIKusCusqWu/rZblUndvZmm7Yh5tbPTmwTxGIt9AiWJLO9X2yuDlTGevGdrHVY3zVfFN+94TyR4dftYWRwfnGOXNv7zDUfF3Ut+NzyUguMzVIAmuPmFS/gWbZL59vSTRipbfNZCzn+ksFoTM8IPuMGAmhKSjDFkqrQARq/UQY+MITvS4R8Ll6N3BvG1dPai0krlcIzgkDTE9fxfRr9MRjbQTg/oDkjIrFha8AgPIndYKYcoMmT8sTWBTrvc+ULmN/VEG21u+05N7TDGNvr/Gj5XarzmVZ6ni53HrpTF7r2OYorbZ9oy56qI9Deutaa1moTjPYkFiOfak4VCk3NCJD4LbG/vYw6P3PE2gXXtVjXkfxgsV1n/1J1XOvdF8MYU3B2KnecpuVGdSWnjUfq+ioFd+N8zpZY38AFNegr1qeQWBndqAOt5St01ZTF2o6PFU+wbv0Dlqhr2A+3KQnA98TRL7rWYKd1tv4NLsAdUJvHWsI6EMeN2XinDozPjqJa9boanR8P77SCssFFOiA0SsrMc34d34QJSj4wYE33ewdwTnrGdFzLRQF8hx4n+4QmD/GL3dZn5ShMXnRxygGaTBk6z880Pav6bNVK+4fv9BWn0yCi17B5VxAjBhp9iMnOnb9VtvdUpZbO0/YL58ACPNeRZZh2qfFgTnkgj1yKijX217brfTpekLalwYGU5U6kzf6iDhjv/HdTcO5Felyx9rWZf4WxPFkmQx24eKSi1jmzlCjDPjaEaQzXq+0wxqJH1835IxnFqM37dp1ijOj0Jz7yridUxzErrLYvBT6QCNA1W7FZbjSBgMbhwijCSCs+q4jTOjYyhIDG36uLSBwRQSLyhqiOiO1+1fpZ/zE6hWjnHAQluZRuiX4+iUS/NfutQHvmcAyOcSV01VxtXgTeDoK1Ik4ETWYKLu8qLg2vsakHaEpxQp8aZDs4fBmiq+2bO8bPZD1AdFoNB2K/6TbLYSe2wd9bYd/uYyrGaBULdb81+rJ9N954I442+FDwyufAHPuraZwzkR32u5HSw3TRnn1PYySgmQCavR/UleUeSJXQRNq7TrEHMFp+GbNTAxjnXJPGMf8gQo7xKqu/qPfiXPjzPkxthGOYdmFA8xi/bvFf87JV3LFNCWj+rRL7U02k9R9VvIDI0E5cTNnZXHWoKZWrwvcqZ7zRjmFc3jykzYErEoGxOX6sSAv4de9LbtA6R9zKDPOCGgQNu4Z0m51NCYwsJ4aMTW4C3xeHMv1TwTp4EvM78b0y3WfBM1Gdm9CmHKAZr8abyfquMMtuRQEt07oumHyyHrM1L1oJja1vEaDRlJP2XaKraPrDfdh0kqkk/2TBneR8GBlhYlamlc3BBaveg2OjOQwj/2UYwazveSwpN5fN3x/yK3IlGBqfdRMukiwlecWn7yajaEv+6wuWv9m9fTPs+joUMzTtmd9jBVIdu94VS8incW79fggBkq8feRN9h1p9Q5Ubd9G9u3HRwRa4IsNHKRruvIHN+PMkEg9E5JhXzoexUrEX/xw6VQcqmVWu0+3UU3MR0MxsQEDXl7O+8/4+9PUelqVswvMf48doecBb3AZAC2g+UYeZgp/nWJUo2hM9SGj3dVnvR4EAGmYMeFc4SWNV0suJWWif9b6lQ9O9nCbMxu0FZEVE5OfDxUl1/2kFq9bBxW/ZuvfBWIUgKVOrH1K9urja/s/sY+ACUyft39OBkFuuOdfyd5iQmj/+OUwBMJv1a+QrsAVc29VZY+9qQqKpn0Rj9uSQm/DofqxYiY5hCN00Jp/OLNur25V/NKQDs83ftgcwe/5d99wn2xp/gWCUpXD2nqarWPxrO6YBmsZxM5Kot+5yk3mca6W7lP3WlhUfavf+1T6KFX9v8eXSiQewWFcDaP79iPtV5+/OYWgk+hJWCrJnOtSGqf4TK9A3bElbN1MB8rq40ugnx1uQeVurrLQzK4mYaRd+1q/rjz70xfQ6OqpgLGy4ASbSWiAIINOC5wo6MV3vyOLvShKCvN/oUTW6nMXhJgawTzlAk6rVlRT+YL2ZsxaZJettP7fYqyOAeX6rCyXufK9usS5/zrqjSCh767x0G0YVqsjO9/mPM20QXDzCv7HXjPhiebvtMSIi2XbMY2tNk6JgZNzzIrfDWHsGX8COJD6/oV3KEDrwDg5eAvCWC3Xl9K2PoibMRCpTawnAdcfoCP7JHbiIFVzIiwrWWRfijgw+98hOnQhi42HY3JBZsaX+3e8urkGtiEjtb1AjR/OrPlCq6z/01X3vxPNvtAf7IiIjs3DhbPVjGfHaeIvl70Af/oJ0GUZtRpp1y2A8hYv6r4fsG1HmvcUDWZ9Lt1752/HafENGCs6Jvz1LqJfxBhzMEa0eJwE0owVywn3WVFr6tAnqc0BsygEaT0T30nu26HZ67prqoq4j8jd8mZkDOXyJTl3UXPwHz9NFmOr+jBwM9gqxxn1vhbF8N7OV23EHPsvQvxmZh+daQLq+vpzE396bwooHf68uNxxbYg9mteqiB4s1/lHnSg5EdE1jFzTap69ERAI9uMjk/bh5qCmzLth7EhiZC/RgKN8ZxDlzbj2CBmY/2ncqGbWvhvrwouLJ1LkxQi5hdpS5AdI9u+f2tMAY64LOLEdUuUMuvOfbR62RBU8cF2HWVDapXF+TpG/f6kHGV7OCagYatJbJ66J/AcR34k4YvsyN72iO1EmkIujHUgX0RyxCw1LxplZbRlcsVpRNOUAzq1oXjm98TKeHsP8Dpky7vYCZCBLH3sjunvWo6jjTkit0Diq7BwHNwWx972Wibk/CSPgJ+0hZz5G4qAUcGN7encQQ7M4YLmxlu3Wh5e5j7Y/7yLOfhrFWIkg4/p7JBQha8z9gr34sIlL7OXuA/rUeRqzX2WfDughNWTsudqlKfPYLwtaVYt0gbhRCHehTcgtQTO2L5TrF2y2P42ebFYDmqipMlzL71QjTgtXZnnfp+Iam+dboPueegTyjFsKXYbal17q5bB7BFGKmBEFrskG3ecgN4uq/NYWcwTYD0KQjeC737Fk4SN7bWFoX8Y/sJCRpnxWYOIJ4rizJrBVIUqA/j6DSmcV3qDvL2GNWS1Xg51jFVDE25QDN4oiuNForCBd655svDc/y0aZ9YdHjb8KVTJz9cIiIMBAbPV0H1Gr+jM0STbfVvFS3+G0bwwWgbwC3GbN360Dwacvsycm19+n0ITIX6iqkZv0VAVLbBJdHa0yjWPznPyBvp4GkQV2HsHJYXBSY3knJfnxWA4tx0W3yWzceD3diRdPcwVdhbOAAGkA2P2zPm2D957RA9ruPnQtj2q7Zi08qTjSv5iVdZHx8AZIcl1fiPO3L4jNNdVmfnzONvoJ1jS6r1aUz/X0YLSn020dQklUYex9boNMH6hzF1CiTHPBvQ8A7vsgAWyGc35kyRBJZwn3uIPfbkcHr6FUoATqrMbpW6DmAMNb/sCkHaNr8CEBuHSkubSQi8sDC3xkjGGoutoLgjeyyDtQjEbE63ksiOjExZixczkzDU9n3TR2p9L/+gDLrZhdmEZEfLNVV8Gg0fb4y82+qc+2MYUza0Y+Aw92JHIkc6Xd1Tb0pu4/3u+SPOg2X55cwHRO0+d/C+WACvJ4vHhwE4OafIUBg6dg9Z+s0NH61/1gYcw8iaBivQ4fvM8pVvXtJjD6Hjn1o0QFsOZ+zv+cdF2DzRK213F88AfPXLX82RnAh+t0oplS9L2HBAyUAz8X3ZXEQo8jPjmBVj5nyLRC9k1QUv3VBhW5TECQUKE1kIViPwGp4ln0kQ0SkfxCBxHOkWIlF2nNLrdo0uRBJB4VIKimNKaftadzUOTN4L3sooLG+a02VmJ3Y21N8s9X/aVMO0FS4cXL9sZc1D9NNcg23ZOBFXQWB48jFMMYWlBd2t8BYq9insO4a0y0A/R9aQkYxXP7Eg1iBZYKQw87CxYlZ4991tY1MVLBYOyOgK7EfHkVH4BkhRL9RnFuuVtypvxV8JA3Am3G+jq+ljaYVa5r+aCIi6UW6ObOtE9+/OVn8DhYKzxSsO3A/aeHl8CO49TbpIon3ETVbjSUOK679iYiI7wmMENLuOmRjU+q030n/oRv9aW5UF8keJ9mwKPHZXQkEBF5Ddb/gxuiJI4zhhxo/yvUnChhRCgyQKiGnPeG3qTwGY7ujOkBTGEaA92pKx4/M+azXlgvicu/yI6DJEVjQyUJbeZw1wzRFZgU0M0IE0Mg0oCnKSpw4UZ/fhDnrOQTQuOexJnf2u6lZd+MDZLuTXefr2FIlL+KkcZXalxl+4xmMFDH5/6Wf0e3Km75jX/Z7+wzktzBzPLNedRwzbYm98zBTqA9/5/o0AqZ8HzpxorUn+QTp83MYmzNW05R+vhl2f5suYnXHjzCaFiXRtPQZbKMwcRGfry99WHWcZytxskRPxl2Lz68zaXXkpftI/r8WOVYfmKMjJ39rI6Z/6sWeC3PT8t+qzs8sn9JtCgbfx7hM9jygTetaYKyVNTkNkOcyEyNnJQ7ceGzvx5RNqVHVkw4TkjeJDtT7sLrtmSQCzdI9eG3ZkL36+MlVWADy0zpU9mUW6EZQ9iLrkUCkNtIha6TFM04kB0L4HozkEMhujSPSdOQwPDWYwmdqxnuWh3Hj9LQwbuQ/b1MO0DAdifKXdbdh77nouDSWe0Wn1nnKyboy1+q16HgzsHCiSFPDX3S/8+bGt0ZgrVi7bvXpMNYmuKDsO9l+V/TX0UNgzDuIIVizJFJExOHBuTWw2L7y6cJtH4Ixt+zF8ysjeJNt0Zt18yPxhZjquGsGmHy+vX2qTNcHKbIdn1Uugk67uRLDL9uMyplgN4KBRAvuXj9XgRsFpj7ufFq3UzeNqR8zO3Mrlkuz7tLM+k8prgy8co2uTLmw0CyoEFlYj8AnXkDQMN6L97Ji1Ao2k1H0d/PKsRzIT1RwH4ohmHPsxvvmmo1cJnO2nRvCd/S2KEvXo5Xuw7m7JYYUiYAgZzAVsf7tiaMvqiDaN6PDCEraRzCNGCKNnkdTuPkzZ/gxARSo/T6MFGcTDmiy2axceeWV8rvf/U66u7ulrq5OPvGJT8i//uu/ivP/r4MvFApy1VVXyc033yxDQ0OyfPly+elPfyoLF/73DjqVSsnll18ud955pyQSCTn55JPlpptuksZGRobTWwfRFKl+SdeEreoUe0fwMCnt09pNDTpinmcdToiuT7DFzmrBe3S8jIPFEuexlx6dQ9VjunvuOtY+Lfe3biSasmiMd5Ts1COYP/YviNl+Z9eTOKebCKDZ8SFdemL5uvfCWESK74BcrGn5PbfffbLlb8adcreyXSnOBRbtCu1Cp52oRac9N4Rp4Kf2WKO3s2K4mehbguBIqz7e8KgueosNWHVAdt/DmPKsVwKarx1hHwFj/cuiL2LVF4NfsfkYVT6hHKvl2tO4kfT14NLlzFi/ZbwKgdXCUiTCjOfRfzzTjVVIFYPIA3LmMDpsrh1tHvyd1SQywqysHUFlRwwj+YyCnjSCWL4YApqGAL4b7Xm8333D+BtCRHA0mcHnYgIarVZbMTbhgObaa6+Vn//853LbbbfJwoUL5aWXXpJPfvKTEg6H5Ytf/KKIiFx33XXywx/+UG699VaZM2eOfPe735VTTz1Vtm7dKqHQaw/r0ksvlQcffFDuuusuiUajctlll8lZZ50la9asERdpVqa1LlJD59xOCFXks19oMcmcaP+5G6MFbLd9IMZExsaaJqju7U0w1hmWWe/huuccXaNTHD1/pv0isL8Pd9thQldwZfB+F8L40i8h3ZlNi27SCbMtPUJHJE+uZJFEBDSuhQeHwF/jY/ZcmIFjdBLfD45h/y/3AG5YEvMRhEQ8+KBTMSs/xpHFYxJK9XHWO0sbve09rLiNkra6iNlFYXve1W3DWPWV29GuOn+8FgFHoxff5c0JTM94kPYiYpyOlUvXkTYmpiCfiMhAH4IGph6V96CPcs8yz4fvVdCta6Pg6SGVWgkdNSEbsvqVnBevNejCdF4hg88lTdJVBQfC1GwOP6stMpkIm3BA89xzz8m5554r73rXu0REpKWlRe6880556aXXQrCFQkFuuOEG+eY3vynnn/8ap+O2226TmpoaueOOO+Tiiy+W4eFhueWWW+T222+XU055TbH3t7/9rTQ1Ncmjjz4qp5+OoEFrG2L4cuQGdaXc55XYl1P2/g132/UE0LhJwzU28dekdcTV8ALCVpxAY5ULzAY/bVbK4G869q9fhrE5gjuzo0/dqPpOreKoplGfs50QgOMkvUQATaIJHc1Hqu3TM6V/RcE1RtLUahLV3qBLCe36tj3B8++Jyeu78g/T8Kf6T9PxPn6982gYq4thxCDegJyAgBPfNeiH4yYpxLk6AvC3eo8ko7qKI010mJnr7zouj2M5plo1APfmTVhBNiOrExCMt+KCWO9GwPGHGKqe+0nKN+e1PptUNW4Uat3Il2mPY9Tet0cnm5ANEV2bavuqWa9Lt4kp7GzHwfGlqs96q63gO7cdN1wMxDvZO8/G3AiWc3kCaOqK1z36Z23CAc2xxx4rP//5z2Xbtm0yZ84cefnll+WZZ56RG264QUREdu/eLd3d3XLaaae9/hmfzycnnHCCrFq1Si6++GJZs2aNZDIZyzH19fWyaNEiWbVq1QEBmu29uHudIQhoWIMuzQve/ADmaFm4tfM9TFgJ7Ru73k1GsQT3nGZr5YIWgAx8Rleqe82t74cxpg1y6r8gd8e0eT/DBYC59V83P217rom2UqIz6E6S6BehCTAJ9ZNJJdWmjHVxZmTiN8O2HIttHkz7wq8/A2ONrCkkKMiKTGTE59vLzHJhbmMbybzPozBboh4XlARJPZgKrNkIAt5TZuqiLH9cj1WBjJTP7I55dxgjuDjdPVYcH0dEZM+Zut5Fpnle0n3OXY9VLLUzcBPmIu2fdxACcOUwvpOpMutLGahGP8P6su0cREBTolS9SFTiOz/WYM+bS+Z0S2+ebGgdaR1HaWaltbBlP+kZFyARGtc4uX7iAvM+9hvwvcrUR97oEifcJhzQfPWrX5Xh4WGZN2+euFwuyeVy8r3vfU8++MEPiohId/drpK+aGitqq6mpkT179rx+jNfrlfLycjjmH583LZVKSSr134hxZITFJEXSZkv1N7Cxw4vj6mg6couIDC/Wkfq27UJHMIcAmiNLrOmIX3ayLq0ItgaP1kWAmu8jaqjkuKur7Xdn+XW6Um5mO7O63bDzcAyFmwss41v4Bwm0IuS3vAedCpNQdwLHX+Se4cPJtRnm0LVRmGxr+SOCATZz95yl44wM5ZWthw3TNtwsYYEMHwIVVznuLmMZBCu+Eeuzz4TxXMeW6fhJwe3F8+s0zRJv2HUyjGn1rgoLla0PDAvv0kWYck24kWyNYOQ6nsfISGoYfbYrTUrsS6zLWTSEEfWMYKRhJIYpkcZ+XQQlFcb3NFFjn/6PZ4qfC1pV3Rkl1mjXPgcybZzkZKSrBN3A5T342x1kVUhHJq55sJ1NOKD5/e9/L7/97W/ljjvukIULF8r69evl0ksvlfr6evn4xz/++nEOh/UOFQoFGDPtfzvmmmuukauuusr2+vydup+8/yQdCn66SFmUjx6lSwuUryVt24lY27E+K4D73DqMAM0mgOa2E25RXUduMxLi3gq7cOuHYcwn7TC290x7xcrre98BY8EuXOgS1ehks0GcH4kmHUj97avWcmbW02b0Ayw9gerVWm2hYi27RbdY/+cHblMdt+yJS2CMtXQo1qKb8fkVKiMw1lyF0YHdJKrpH7Q66NFG9B/nlrBNFs6ZulU6Z5F+F3v29tGusUeK65gtIvK9JfepjtuSsYKE8IuIINlbMLgAAe+7wliZsyeN0RhPD/GBGYy0pIzHd1gYwXh3NgJj7m4EF8H9ukKRcSKf4pphT00YGMP7oS0oKSh7XR4earf8vaqwRPU5L2blhLRokmwAwaHLhe/fWO2bV0w94d/0la98Rb72ta/JBz7wARERWbx4sezZs0euueYa+fjHPy61ta9xR/5RAfUP6+3tfT1qU1tbK+l0WoaGhixRmt7eXlmxgqVIRL7+9a/Ll7/839yMkZERaWrCviBM7ZHZKSt0eeCL137E8neT2Mvai+j7rlStxZfDuQDLHUud1tC1tnTyuIlRnD5gYyFp5sT7H0cOVAMBNDUn2HMO/rIVCaRzBjGCMNaENylDAE2kPmb7nSIivrX20Yzu03Tg6F//jKnAVqIVouVsFWtnk/JPZjNutefkaBtYMn6PbweCdpCAF5G2MowOPL0XNwENCQPQkLQi6//Frs35hE6WoeOU4nhLjfdj6pzNIkbSfE+Jjqj/9T3WFLi2F9zwbHxf2nwIBB8YRH6In7RyKpAIaarSGrWZEUDQuiOJoC/Yiedy9cRgjN3LZAMCqyPq7TmZ8RgiBPbbTeV1EZGCWxeiWeK3znHC4ZU8QUemQKGISJIEWbIl5P3z4Jckihfi/6dtwgHN+Pj46+XZ/zCXyyX5/19VcObMmVJbWysrV66UpUtfe4DpdFqefPJJufbaa0VE5PDDDxePxyMrV66UCy64QEREurq6ZOPGjXLdddfR7/X5fOLz2RO5Srt0C8XPG3WN5IIr7Rnn7rkIQLSLifMV3CEPn8MIfFarfEFXOjnZtimjW+g6PqRTn236awzGWND7V3PNlhQiItZn5d+ITsWRxO0JAy9M4XtpJTqykTzyY6rX2qf5vrRc1+R0zi0oAMmC5Vu+1mJ7Lk2PsAM196P2nJHud+rSoNftQYE/Zxdq04y8Ezc2NcRrp3pJNUbe+tbkWnR8px/vO4WM6tRyTzmmOKCZ3YkRD2ax84sTzBMReWWd9T2drWiaKSKSn4V+IOLEsY1DCD59MVzAM0FMdzirrIt/uRs3g08NouZR6X70IAWm+l2B0dC6BiQxHxFphzE4Vx8ihOe7W2CsSrbgh/26NN9cA1y4SGFVKo8QwDeM509W4v3OlKBfLPWRVG5V8a02/lmbcEBz9tlny/e+9z1pbm6WhQsXyrp16+SHP/yhfOpTnxKR11JNl156qVx99dXS1tYmbW1tcvXVV0swGJQPfeg1gbFwOCwXXnihXHbZZRKNRqWiokIuv/xyWbx48etVT8WadxifquMAysCrXrQugOzRDR2ma0TGypnz4yRiUEfytoZUd267Tsae2Ya0zmmnzrYPjX/0lU/CEewlTR5hH6YV0fNvWtz2QJOJVglJaeZIFCtLgizNZEe4IY0g27/LCjYZ0PwcdYr43HObdKnAj5z4jO0x577yCRh7K/Rrzlygi15u34NRp7Y08ssYt8njRNjnHkE/kPdYj6uviqmubeNejCTOVgKaz1U/Rkat4PvGWPG9nAYWKXMWxEK77LldrHFmQ2VMdf7eYXxvownSQDGAvyFUagU0LuKNO0YiMFY6QFb6DHkrGxFstUYwIjjDa982x0tapwwTLg8TYHB4ce6yqFuZ0zpnSBEfBTSeOGvxgM8968ffECDl6PmQjo80ETbhgObGG2+Ub33rW3LJJZdIb2+v1NfXy8UXXyz/9m//9voxV1xxhSQSCbnkkkteF9Z75JFHXtegERG5/vrrxe12ywUXXPC6sN6tt956QBo0IrwpXfZoJkqnCw/n19o73+4TdQj1G/veRUYxYjDahhPkBUOhsZAj5Cxlbv6clZ+HsTmkM3PuX+yJmmU323NZRERuPtK+4mairXwj3tt8EAFIhvAx0xF0sjNJbPxPpOQ0u6vdOkAIwIxMfCCmSXGW/DiiOlfX5ZPbxPIn9VjCz6zsZcI5IPeScZuYYrifTOd02OoiT67RAbzSdbpcrrsFiZqLvfb38vrnToMxbff0pccWz4erWW2/8RhfiAv/Uaxjdg59Q7oHo6ZuAmjGavE5z45YNxTjhGDc24OVYNEu9AMFss6Mt0Zg7L3lT8FYi8f0AyRNiThIUuW6UvFgKUZBnFUEtRvmJfITiRy+Q2zTn/fi+5Ihm7pKP86PjvLiCgGKsQkHNKFQSG644YbXy7SZORwOufLKK+XKK698w2P8fr/ceOONcuONN07o9TkSCFN7T9VFUFifH429e5lOC+Lpl+fCWBvRZ6luwUjAgzEz/4qApuNkHRhsu00n+vT04nttj/E9qFucTvSTSiKlRkf6TF3PoAfHjV3MFgzRZ47CniIZEuzJR/AehV344j66F59prVijTJlTsZyXEYCLJaBrzfM33YL47o+iE2c2f9VHYKxZyTHTWOXL6NjdxLFH6jG91JXEhY0pQo9XWRfOU0IIDPeSarnql3RRzp5TdX3ITKtbWfzG7uctD5JR3OGzKJDjRevcZWyOwXm4+B1e0g5jW5MIfPx95HcVEJCmyPrdHLT6xa40aWC5HxfwQi8iWUcZ7mKGZ+FyeUIQSdfJggm28HMl3YRrUqVbjqOlCBryUfuNo3cU14RkDp+VaxQdTTbA0rE4VO3Dd6EuzCuOJ8OmXC8nZiNLdGqan9rwcRijOU7D/qOGLep467U9pY6uwYX4sX3WXk7V5LqOOVqXrjmQRpETaR9txyokIV3FO07XOffvGn1tIgncbSdqyE4khG+uN4TAOFPA5ze+w14bpGuFrrrhU89/AsZmEeBDm/5NoGkJ7dW/0V1H4t1miwsEoww0+F4lCt/NmIaaH8U01J5R5EN44/icB2ZYF6dFXgStN8NmQsT9PN4jBs8Hjy1OybfsTxhBZud3HIHR53KnLpr2000o/aARzRudjQtnkwfTMA8MLIExH8nWsPLgdCV+R7XXOkdWD7XAMawoJD+MC66jBVOGozMQvrUSbRdz47syQSI0nQh4vS06BeCGEowo9YTtIzQeEnlhejiOcZyT2VKSNiqg320gu4LBkuI6yhdjUw/QePAnz52hy23HX8GyTjPH6W7Dzt0eh86BlLXjhHP6MHQ9K4Dk0/t6rE6VEcs/XaPbWR8s9txmJFOzsHrzQp3Sc/8O60vP+CFMV6Lgx+cS8CGgiZEutYFue75CZrZuNx9YowMIsfOXkNE3v4+X/wFddK5nmT0g/R3R7sn2YNw+fUQLjNX6ccHa2IvRgTISmEyXW2FC2Inv46oBfOfzaZ1PObpNx3Uz9XuY4Bqz/qW6RZJZfqe99g3jH/pqEPT5SYkNA5VMlTvnI+qzIVx0fUaTya4x0lttiBCASXo+W47POV+pu+ejeetnXxrH6jnXMN4jZ1r3rCq9GKHpDNq/Q65x0qogT1LbpCReSvAe5TOk2aULr62CXO9k2ZQDNKzL7mXN96s+O+Nh+4Wn83SdzHOGhFGDG3D7UJiL1T9tPtyVl+y0Fy86WEq0tVyemsd00xNVVEWYkmr1antwMU6qm12ks3EpATS7kggjw7vsCXEfXKRTi226qx3GGKHY9wkdwPtw+4nGiH3zzsmwk0+156v9agPydlh0KkbSAnVEWGOkH3eNLGgfbLDu+hm36ZWtmJqZoyQA/7j5L2QUr+0TO03FcN35YycUr0JdvcY+5es4BFOqRzRg5CxJopedvREYqx0lPA9SYVNZQdTGjVRPbx8+0dZOAkoI72qsAaOmrY06+eCdaasfeLQH75GvD0NRzoxu7WjyI+VgTcCec+eKkVQVU8wjhOggaWg3nsLvZJG4Hq+ORzkRNuUATbIaV/VTyYLFzPG0vQDY+HE6NHrNAIaCs/tQOyV+NJacMvnucLvV+bgbMGTKQIO2RcLwx7BHDjvf3Kc/Zvm7hRyz5z06bkz5/ci3YPBAo6IqIlLxrBUwUl2JGvwGnx+P9BM2/6ZhREOluzFV4ohELH9/pZJ1NcZoTHa/TkTpiYU6gL7tFmtn8QrS0mDwwsklAIvousxro1OjLbggehz4TD39uAHIBvCzC6utZcmsEjG8SSljfzympqLK9M/WJ627/BlKQPPFw1jFFNr2DAKE8Gp70byhRZhSPTuMLUs6MiQl0kMUgDPoG1JEO3JWWQzG+g32PhPM8/YgX6ZQhpGRsUZc6N9ZpRMpfDlu9dm792OtUltM17DYVYq+rdGLn2VRLDCSWssXkIjszOMzaCqPwdjWUXx+DW78jq3OSSb//Q+beoCmfHKb7Z00U1cF8bfO+TDGVD3jpEQ7WUBnHOizLrCZWTq0f+NO5KmESSqm90QdUTj0mH2+9OxDdKKFubGJ1UXJtu+x/O0KozN2lpHeJk58wZlkeNco7kTqBkkp/gwr2DTLK0V4BG+irfo+a1NPqvB6os4ZXdbNiM0TV64Z3q07F0sLsOiAh0ytDCkFbi21VqzsIgzxsr26axuaXzy3KbqpOC2PT4eZP8JF7DdDKGaoEc2L1+E9m+FF0LA1hSk+VrrMjFUZlhMuU1/aeqA3Rs4/hp9zhPALklF8v+f4dSBy77h1k+gcVCoAkyCLoxKBYMiJ0RJCZ5GxvNEzLk7SXA5ybaREu6kkBmM7PBiRrnDifWO+crJsygEa9gIy++UwU661t+/XP05GEcn2voKTgQGa0VnoyNrTiPh9+63IuPNUpmCAlvwbHscAzd9O/hH5NDqC6C/sWzr8qF5XTcOscBxT08Rd7j1x+3x0vg1TBSyUnUiT3TzJPQ/14HfWDuIud+gE+z5hn+k4iYxObLVAdsBeL+Olk35KRjFt+7e7TWIvb17qWoThd03Ep2wNSccSobOZDUTuPkWqXYi8O4sEHBK0LuqPjqK6dOgVXUPaweU6DgazsgetmwAGb/InIKgMKPl7d2zASsHZCumKsdn4S5tJx+y7+nB+MAJwjigAZ6L4HRUejIS/OGB9n4PduJAWiK5Xfja+j65GPO5wHwN46AO39ll9aqBLt+bkSNV2th4nJRMkZGBon8ENYppmfif6rLQH/d2SUowKPeNFblCli1RDGTaZAp5TDtCMN+h2OteuxY7erOeMe561uqhUGUKu0BWKiK8JH/4rY2RBHLZGAoYX6Xr8NNyv68XS5imuG6/WtCXJe0/X7XK/9fK5MGa2pRieh7+pIYTKp9v6EfQlSHM5Xzc6gkIW7+bgAnsH9/QqXDhZS4Ni+/5ordxp76BERJp/gR2nWdxi9/vsqzFuH0UZBRYtcCxHxewl5MXaNoKbB0Y+HSNadQ3G4vzjToxohnbqGtK+e4muZxX7/WwxMm3fO4onyZWuUermGC00mloQQLId+aZ+TMf6SMfsTCmR4o+ic2BpxH0DVp9Xz1Th8/id4w04xxfUtcNYsxsRhxkFEREZ77H6lapeXYQiS1zbeC0R5nSS30W+YidL8xkWdCPITvvQLy4PInn9F+7jYIxxzFKG5tPOjM6nFGNTDtD46nUcl8hTuoVz3xn2kRDW1bl8EwIVp8GtEBFZUIML7Pp+BDTlOeuWc+FcXY8VMw3zVtm/vPJBGDP1WkREDj1RJwrmfcY+QhMj/WUW+4jwYg7Td6NJdDRMLMtZiim4wLyY7bU1PKFLY+x9vy419Z1+THFOpOUGdYTiFWfYpxv/YyNuJhplI4zF5uK9nUcqAB/ZMw/GSkgGNVeFzt1pxEK6d5IUgCCgYWq53635E34pSf987+UzYWyG2N+3+mN0pFVmNS/pxM+Si6y/69hqjLbGiLR2rBffx4ZxXIVHG3FBrA6j/xzP44Yi02v12f5ewl8L4LWNNmG+5pwKjJb7HLhheSaJ5/N3W88XGNC9o1myZ0xU6igSRPhadqURyJsWcmO12CARFz3cSzrWu3TBgUFDVr09o9N9K8amHKCpi5BYM7HoyzrgM7LQnlty/ygSgF1dJN5agw+6OYiaM+s7UIyr3GN1SCuiOgLbZBtz7CyCkNoYUZ3vSw1/Y98CI9GN9uH9FCEAe8nuJ5dFJ5vP4ViAVGgIyc8vqravQipdq4ucfXyJrhz71y8cA2Om+rNrPva5mWgC8LfqGAHauthldujKV+O1pEEoETeMj+CiQ9rQSLCM7LYLVkce6NYtMMk5GJFgTSyZOTYXFw39cKOuTJ5FQz3bMaXH5ttok3VRnx/Az3XnCDctRvROcrggZsnmvdyHnJFYBjec3pj1nXQSgTgJ4udYa4y5fl2l4Ksp9MVmOtM9RloVEK2oHBEXZf2SMiS/5CDYopc1nDOshACafMC+YlZEz40ZyVrfv8Hc5EX7pxygWVJh34VZRESe1znyjx1p39TtV9uxQqh2P0YfUmdh+qDFjzugQhe+DIWo1Ym8twzz3/fFdURhTY8mEZF3bDoHxjxijfjs/riu50zTo7qc01E+3ZTVNEGsbUFQmc3jgpVNke/MkT4mg+hVMvURGDu70qoHxCJ4rOKN2b9VYqqH2Zxf2QO8bRfrKt6+P4i6K1rT9NiqeUG384u34pLrJJ7dOYC7y5wXn9/MCiyH3ZKyErgj23XX1nOEjgjKrOEJe7E9dw3uvj9VpvNZ39l9Fow5e3QR3Vib9b7N8+LC/+eRJTDm7yMIkgylKnCRrPRjNLtzHEETREgJCTbXhBH1VCNuSg/1YmQ8UcBn+sxgG4wFe4yK03GiL0b4X9lSnFvpMPqjWB5RnzON921f0vwO5OAxSYP1IR2gYZ26mfWmrO98gHXJnCCbcoBmcRDDss+niq8o0aimpl6JqM7FpLVLnOjcmFhbss6Kehnn5SMbMZTNxOX2nq9cUH6LpeERA9AcfZauosn5hK531oGYKVJ4bC3mhTvGCfcoiU7FkcRdkjuO82h0BoLP4wJWgt01PSfjd0pxCrJvaM/ZL3bXvovp+aD98n7sI9RCCMDu2UgaVBGAX8DFlb2hDS1YTTNI4va+QdItnWwSZ4eQD/LScIv12raQ0ldybdnDdMRH1o3d9bh9q5T+Mxio1HVob1+LUdNZogM0ztnW31Xhwnm6Pobn95OMJGtumIviYlfqQjDeMRSBsUi38SQIf228Dt/HugacR80EeG/KIEDa0I3FI/W91t/gSON15CsjMOYI4W/PxtHP9GUx8uJK4yzsT5opWQJoPPhgMqW6KGSORKmZdY9b7yVLc02UTTlAw4R/frD/DHIkIbuRjqYai76qAwhMWjtOGqwF+vG4kWZ7VD3yEu5OGKD50XF32p5LRCRym3106pamZ1XnYpY7CdVh2YJ4haGS/JqRcPZyK49keek9cMzqfiR9UvAyRhpKEg2N0SZ02nUuq6N5aNMiOKZNcFFjVSwTmRJ6TwlGipjN/jWWrzLAsfuDRKWQmCkNz/R23K0oMHlMNQLS7Un8Ti8pDkuSYFStD3erj3VY03ANO7Hag6UPPjJPV8n3pf2nkFF7MNR7bPGbsOo1ulSBazFyj5Y1Wn9/huzSt/Whnykn6dh0Kb5DwQgCvBwJ5cQH0BfX9RrAh1TrjDXgYn1ClY5HuD6JQC3ViTwuz6Ax4RwEUFfjnPGXYJQ66ceo0L40Tl4WoYmlrN8RJAKCzR6MSqbKdEAlk9UBn4G49R7VBnV+phibcoCGidIxTsosAmgyyxmx0rqopwpkh7EXJypraZCP4k5kKEteGFKhMdJiH/4r261zZGcH37zuqP+b9R+q4xzcvw05SkzQb7jVes/NChYRkeEEPhdnBu8t2TRSS1USXQajEsDXrvudPct0lSis8mIiLbtDJ9fvOkzHV/tV9/HGCG460k0YOWv1oyDfY4P4jrrI7ciW6gT4Rges7x/TRjIrHUVE3h1mgna4CD+1C9t7zJL15LNWW9CmTJ0TC+1AfiDzDIlmjAQsKLVWao0Scm4yRgTzUvgN2Sp8r8oCuHtPsAaKI7h0uccMMOTH94oB2bYAppeY7Uxhyt47RDY241bnwNTp0yEEAwEfrh0JF943U0BQRMSZxeOSWes9CpXgdVSRVgU5Ejljpo3QJJLWOZLOTx7smHKAJk/KyvzrdJGXjlPtF57v9pFGddtJ9UETpmvqamMwtjOOux3vGEYC4k32YCX6Ai4UEyd9prdrBhj5FK1wYkx1XOnjuuZng0aVb4Sk84aH8FzeJAE0BPPl/GTH0oA7TlOHoXqNbrddebpuETtq9afwMgRTo4yHMZF292G/JKN4f198wTofWHn6wEJcJOf5kL/xs0ETHIm4M6Q/UAUuHhmiTuZvt498Di1FVulCj86nlD5XXNT3upkYXWSAiVW3FV7SdTwfmIfLw5FGd+ktaSKY14P3zEH6JaUj+J0zgggYexOY/gn0kP5ORn+kXJQI5jXgu7YsgIUXIvgbXhycQa6DfDRufedzdQgMWfVSmQ+R9yABNPtIWpxFh9MZ6/NzRJB3NMONzzij7CWZSergQ3rEADS1kyduO+UATXcWH2r1Wt12+5Dj7VWA73r1CBib1Yf6E5mlLTA2J4IlyVuHcNHxk8kbrLe+RGtI87rcZjy/i5DTmJnN8d7I3I1mtAsjJTc/h1185whWaPxw8R9U31n7EKYBGESoX2hNlcSJ4rJziIwRDhtLA7Pc86waXHSfT1p3eqUvtMMx7PrvmX8XGcVFrOxuXZVQ+0VmdAA5GHeN6eYHs3kenWesXWUPxofn4pwPEUn1WB8uYpVkw1lSjkCzE0iUImV77K9tYJFup8qs7gmMEtJNxoollj8XenSpxts3oqAd64HFbGwOzsIWjzXq9ufYEjjGj5QUKbjwIaQq8JlGvPhcNg2QirE+8lyMporJGkzrRBow/zjLg75ybxbn1vZe3FxW9RA6gdE6IF2GyyyLFNWR62DWNY7vt5/o62SNCEo+imsfq7xjyszMCikdMHGNvnkwY8oBms1JjIz4XtgKY8yp3NLyIBm1vjSBtTr9muFZGKptJMy5p/oxJN1MnMPcKmuK7L4Y41ugDb4L8+QiT8DIsS9cBGNMG6T9E7iLMa3ucd0CcHJAFz/K7tXpb3yoycpr2EUUl1kImTQKpiAnWY6fPawMxWkeGjrU8jfrGs1MK3IXulNXyn3Sefbk028+fAGMzSaduxHIimj5PeGnrSksBuaqZmN0MU7SHe5eVtGE56sOYR5/xxjKJoT2WJGrw03ajizSafDcF0eAl3tFV6W2/4TiIjnaHljuKEaZGmdi2t1vlOquG0ReiS9GFlfSVqIQwQXcTQRVhgbxvjX1Ed9gcETG6nB5O7QK+VlRJ57/eaIvk+nCZ+DvJyDEaB2QIpVKLDrldZHfRKopB0bxehsK9sA7U6mbC0zgj5kzofPjnlHrb5jMVghTDtDsHkenlRvVScqznjtwTLuOAJwgenxBQswojKADZRLZdQHrzmltDJtaiuDLPDRfly91vqDrmOpZZu/cI+uRiPZmpL6OC1ojbH8eRaVZN5EfIusmJR2wUG2VFxfOP++zkoBZqwlGgp1oTZjr68zKJHQHNc/r5sfgibryfGYaQLcwipGuvhzuVFmPJqLzJhES3t8dw21z7YB1Qjiq0X8cVacjlf6+F6MljC/EbHxucW0TIopu7yIi+RkYBVkQwVSMmb3rGcZnUJ7UEYB9JfibmGxCYRR9oGeU7Ch81uNYK4s5JTq+zI4UIZfH8De44uQ6vNbryAZJNVdA1x/OQQBNOkXSoOQ1dRp9ldIhZRNVrw5wONM63+Aygm5u0htvomzKAZqNJHxZQcrZiuUXhNdiBUieEIATTUTAjQgmeQcIug/hhGvxWx3jQxuQKNtGAM28Y3QEz+bb8Ti2k35gqcmbQIfHUl/aBfxbvVgRxKxw7BIYM8P0/zaE38kWROYYmaVIGDnsxlRdr6E2ywBN96nF9RL7Z8zjsH/9Q3fYV7KJiAydoxOi/Ow+1rXdeo+ch2Hbh1PL/wpjGxMI2r0xPDt7fmUeBDSsF1ddb7vl7/R8/M7PVt+HX0D6t72wFsnDbUpA84El9lVTzyZJWu5FjF6y93ZoEW5YPh7ZAmMdWes9SnUhincTQDOGgXGpKMV3I5bGTaOvH32gO4YbhVzY+tnxerwfRxAJf1bI8XwMJQeCpDelawznUaHUeh2pCH6uUIZPgfWHc5CChGwc39sCie543NaxRFSXIsr7dIDDPa4DNGbbLbZxnyibcoCmvwvziExObOB0nc6D2Xclu6sdjmFVEOV1CKIGyBbfF8OrSJXjRCo1Sjn8u3TCXj+k5EJMoma7dJ1mmX6DxrQL+O9WrYCxNsFql64V9iH6TV0IbsMJdMapChIuJ74hXY6OwOxjIiJStsM+VDt8LHIJmJ26mYikEU0RliqZSLt12a/JKLqXlc9jVMxMYQ0ciosrawz4+25sqEh7NLXglTEBPv9+0otr3PocBucjUFni1VWfVa/WLQDuagzfXl39qO3nvrsH50JeKdA4NJe1AcHPPha3pqj9fWQuF3QE4Ao/6Zg9jr7Hj5kvcSZxURxvtHpybwOC7LlEd6WLBLE29qJviPSQAzMITDLV1t+QxiVH3AEEUeNZUs1FChIKbnQ+ORJVCXis3zGq3JgVlBEaM/LyRma+kxGP8oNF2JQDNO4h3U8emqdzPnd1mU4VoyDpWrLzCyFA6CdqX27y7NmO01RtDOpoGdLqntymk4mCTkQpNl+3K4hs1O0yWBdg09IDuBukfd+YzyaXUShBh2f2MRERKTEFwIgdN1vXuqJ9nU4kLXU60+qxV1PWmlbBObzVHsyNEe2eCsIb6xiJwJib0RBK8H4nSSmwV0GFGT+AwFlkK4b/2NKRPMSeh8ZsazteXJvoAE2mDgFClKQGdhm5cg/J1rP3hZXJ+934so0kMJ9eOkLuEiHBmlyVujBeXMSJ83RDGr8zHkPfUD2q5PSVWL8jF8T76HWTzU8Or435IyYjkfeS6l23FdAMKl29g1RWMdMGWszjWLuFibIpB2iCnTqgMutoXV5822qr85lFAE1sNu7glpdiqPnlASRWuknEYIQEj/qNUHBoD+4AWKSIpXX2Eil+akSoybQP7TybjGIe++SjdaWkdX/Rqci+41BsLWFaYB8DR3i/mWwCI5p6y/BF3R1HzkXZDuvCxuDNjxofIaPoZGfer9Oc2fMeexB14ibsUO6TdtX5tVb7pL10QGY+7tw9RG5hoBsjOTXEF7vC6HlRRVWklABNR5n1vcrP06XWfjWCmiWF1bo53rWiuLYJ4XW6z5kds0VE2lpwg+UhgnBrBqwpNz8jAAdJ77NyIv9P3rXxIaKVMoBAouDFd9fs7XV0FNNtAdJgcm2yBcY8XXgvvaZgnogIiZYko1aHkQ+hh/J6CJgjRGQixCx5D+nvVIL3PGrwxPZElNwVZdNJpu/EzFzDahgKniCbcoBGszsWEfn+rD+SUaJO+Zz9+UaIAnzUTCyKSM8QRnIq2I6zHF8Gk+zs78LzDx2m63L6gU2fgDHWUXjg00eRT1tLQjc/iehrBgE0P214CsbY9Mzu0Um0f60Wm1gO5K2OoKQTHSqNvJAxRswuJaJgWwcxfVDXYf39jkNQK6TMqSMAO57WleD+8DhW8m21kfuQ6FBFAE38vey56643txErCk07fhbOtR6iY+LrJoR5sqaXlhItoBEEQ9XdCHzytdY0xsmz7K9fROSmHShNEBXdZ0uWk7pnhVUrO2YnDkEe0DurH4exGImC7O+2hofrxvCYRBVp3BoiKrgkIuEawDHPMD6/fCku/uN11mtZVoqk5lQBfefqYeTSMb6Mk/Bl8iVEvM+gBLgJ+dlBCMDjSQKiCKBxkAwna2JZ5TM2ThGlurRuz0+5UszMtgz1JO03UTblAE2wF3cKjF+gFcYKPWNNDbApk2/R5QyzA2SmksnlC+OLtWPYClbKhhHQDCyKqK4jvhIJ0QzQ5M7GaiXTGhWN9kQ4QTVPYxdoTtLanvWy+uWwNSRf0k16L5EWElTYkgAaM2ctIrJ/H5bDVg9YScADZ7PI2cTaeSX2kYXa32AEgQXZu87RxZq/0Yt8GWYmIfz8KHbkfoUIuPnIus+6NYcD+L7s7UBw3zCI92is1Qp8PhhFvhazsbX43ElTZ2pXtLHonNWYOKVjNYonsiVnYAHO8aODSEzfniES+z3Wie9igm6kIJIRgIdSGHH09xMRyzjOt2QNRtgKddbnzBpn9ufxHd3YhxGrYC/xPSnSa6kWf6xJCQj48XN5QgBOx/G5+MmCwqqe02V432p81kgIA5XMGNhixqJH9HxGaVw9UWifKJtygMY9ii+Hs41V2Oj4Bdk+q1dl4Ki6AkNsCVIL7CKNyNhiyiSyTW2CsjxOmmyTbkJXr9Udd0kbi6pYzbe+Ha9DdXaRn8ZaVMflD2MtKbAqZNWwVdPHM0YqzXyEGEpyynkSjmeOwEU4WwUj2jCqpEzcGCu+NFpjuVFdqvG8RbpozH07ENA0CYKmxGwruFjoRRboncPY14sEOSm/zEO0TZxEOp81ERyvtobnjvAxL47otqxdtyi4W/Dhn1fC9IGs1/tQJ1aCBbO6isXxery2BqJX8NAYzjfvsP32nckXmHwOEZGBcaLKTaagI0fKwIm2S3m5VbqiinR17iAiKyMxRMGRYQLlC6Q/XCmJIhunKyHppQQpvS6kSRNcdhnkEWTJXtissCz16xBIQdlFm7VbyJAImOkWo1o2cRE25QCNcxQf6uARur0Ty4ub5jgEd05LKzG6sT+B1HfmLDJsx+knCqn7jZ2CFx3U8W14Hcy0na8vCuMOyLTsAHImsqegmjJLWVy/Ghv3saaN+0/SKdI+s9ua+5s9hnMhU4oOr0DekgIBL9kc6c9COqObzQwDS+wjXSIi179wKoy1MeB99KE4NoEaNj+o1c0P7zO6ire+JVbn3kIq5Z4ZwNQlawEyNoP01iHPyseqc4iNzLJ+limrbkijg65UthkZOB7TfJpy+p51GFWYKTpA42vFDValExfYF4YxV26oQ0iO8DlYtV+QAJrdw/iu1QziZwtk8zBeQ0QsK638xRC5j+uTCCBdXfhMfSRax5pdJsvxnc+WWZ80E8wbyZCCBCJUR4rxqD/KkKhYvSdm+btC26NPCWhcpCFmls1yQ/Sv0TXd+mDCzJHFGz6gi4zLdRtOg7EZ8orl78HFOLPODiJR+M4BVnKK30mKZMTnIiSzPoNZX4EffH/VX/Bkb4F1HqcjL1Y9oTvOc7QOELi3Gegwj9G6NFuDnSRC4yY58DQ6vGAvaU5paBx9arZO66Xm77rS693n6dKlH9xtdhbXaaJorf4xnaz/+CL7iOC2TtxM1JLMVzqMK8B4BudRgKSr8kESNW2173z9s74TYSy3CbWWmPUuK041tWq9krhJ+FnHNhLBPJLefaUP03yBYev1MtE4Rxg3CmYVpohIYZAAiSH0bfkAzvtxsrc8PGQt5MiRhNuLIy0wRjcdI0RfJmjPlxERcZRawRsD1KwPkntcB7KZ8B0T6qt1xyx/V/p1hHamTsyMRc5yTLHYAKSlTp3MQTE25QANY8dHF+pIeL5n7evemPJulRvjqN2DCHzKiF9PkuARE2DyGWtHog4XtZOJ7sP3B+fiFxBz17N6Vdz1X9ZttlzAJaxiuU6ts/IhjCixdNU35iHngllku/VlK/hJuLiUVLqwtYMBmgQuiJFB/P2pmdYUy2fDbGeN11b+Z5TJZwDhlHfoiMIvP2x99k1iKgeLpM46kn1SdX6trP+JcxSL/350ggUCNKUMIwEjpIN6aIBwP6K4a17RhOJypv1tywIYmy26KNaypbqo6fMp68yPvIjvEBXMOyQCYxeW48amk0yk4S70UaFx630bbUR/GgwhoIkTUOkdRD/G0sCZMH6WlZkv8FtL1Afz+Iw39qMfY5sORwrPn4lGYIyJ5vmC1jmYI/6a9UFiZdCsBD7nJyrDpJIv6rT6+7BS/6WgBTRKLF5wK1nGE2BTD9D48eU4plbneKObicy1Ybl6Hf8kO4rXwRbOXICgeyIPburVJCqIsyAh2Hv3YXqiVFADZXiFjujx5+1WJd8Wsvi9u1G3IGZ7iaIWsfeVDtsfJCLBbsPRBAi/hfSPcsSJHDvT2kjiTtKdwPON11qP06QYRERysZjquCtqmAgbhp5qXrSfzz3LdNfGVGqpkVL/48JWQqrZjVxExBsj2hskYOVlgmUEaFbECdCM4G81d/3M3HuVO07y28+p0oHPu4eswDK7SycrMVaP963Vg+9VRzYCY+4Yznunwf9iJOygFxfXeBqfgYfyZQjQDJFUbhjnSJXLGoHoIz0vBodxU9owQtAca/YYtOfLiIgEDc5MhikAk7YBrD8crbokERofmfdBgzvmY6I2xFi7hYG8MrpDjPnKybIpB2jS5TjJPxtl5Fac+N5HcddlTq0jW9HRDOTwXB5SnsgqmnKl+LKNpTD06TXUGEdm6FDxwGqM3TJA0/lO3ctQ8pQ9n+XyCp1o3IHYygTeX/9ua0plZAn+dhcpvZYx4lVY3xVCNHWmCN9pNimRMuznw6zZo84YB4WZ92F7Of3DTtWB/c9v+iCMVQlGNwrHIoA+t/RZy9+PJUiqgwhFpkmpasCPi+lwJ0Ya3Amcz4NzESG9o8Raaj1CFqfKDTowlz8Of/uHQzpAc98m62dnF3QRoPhcXOhmkejiA0Tcyt9L0kTGEFMAriKApnMIOYNlQ2SLT1IWrAx8XjVOCFMI8IUEvkOFbvT/vgESuXDhd6YqCKAJEzkBQzBwnIA5V1LXBJeBdlcQn2lVGQK8kPGstIBGskTEMss2dbo1JkdE/ybLphygGa/BGcJKfJmZ1SkiIg6D4HRW5Xo4Zm28BcZYSwOmoSEkYhAfxwXRb5TGJRt0qpa1q3WT/PKjUNeFWd3frbs/bUXTt/uwaoNZ+l26FMhN+01+iEi+yxqmj5+OC6fHR0LeebIDJ5wA9yh5cQmhMdlqX23wo00nwVgzqRByLWIpw4kjAP+u5QnVcdknWQMRtJ7DMa1jdhH/2xD2IQsQsugIIQAHiFSwZ5CxuvE5x5txMZ3nsQJ0VhgQWYMRDzbve45UtjEmVrLePgrEWia0zUTiPhOXe2GwBcb8BHDkfNZ7nomQ+01IsKlhwpeJ4TPNE0oA48scGkbRPHM2vDTaAscwvoxrBAFNIYDOOFlOQEgpblhcRio0lSJ6O6SlAYvQs87XAaJrUxfEcJffYb2XLsKTYkru7Dr2kwgeSRSIi/i7nG865TRpNl6tu7naBTa/wsooPi7wJBxz6z7sP8TCrazc0UOECDJEr8BcOEO1iNiZAnDwSR0v45IIOhBm2S3W9IHzUOQXsAX39jUo1sYqePadoGPIv7yxBc83btUQSRBH6SJy71mmBUFeetbYMlOCr9jCFvt76XleF2XpOFNXoXdFD2t9MHFdbxsex8oZdvbRJfYaNs/tb4GxSpoiIoCGnI+1NDAXZhERd5N9WP3O/Ujmd27XRRwThxVfrlq93h4Es5YJZ1Y/AWMjZBHb3o1gqGYYAU3K0DtxEnXsDKn2Yy1nvKRjdrYEfVuqBp/9wgC+Q8PGhNswiBVklC+TIF2/q+31ZUSQLyOCBGiWiiaBRGo5MqErS5ALWR+IwZjTCPnniNr2vizRZSMRmp4sRtiYYrFbSNXX5HGAyfdPMWMhUmYP7cOFuEKQvGi2Nahz4QzsGsaXI0AmNOvW7GQy1EmcNKZeTW0ZLjBrU1jqqdUeKdaGF5B6QmIlm3UVTaXzdKJMwb0sTWTsLklFDINLjjzLBZKdHllzsiV4xsPK7dWOy7fpYlvxRTptiXs3Y7pjlqHq7G5jDVl10Z7CyzoV3JmN9k3GxvqJ/D3jNJSQMZISYv3QcgF8Lg3lMdtr292FgnytpHcWsyXNuk3Bg+P4+307rYULbHaMNuHCuSiA19ZHdizZGEZQnEQ0z+SReMmGi/Uk8owRzkgaz5+MkgaNEZzjtS7kzQ0YkdQ+wpepNlGPiAjh7TBgxfgyfqIxkzMATSFNpASUPeNyfpzjYS9Ghcrd9iXZrNKsN4c/im3WRgmyyhOyr4vwxBjwmSybcoAmWadcKFaj42KAZmCJdcIxgud4N75YJUyUiHACPEysjQjwZYzyybYyDIPf3Ye7SxEECO4ZKI3OFra/J+yjJb3LbQ8REZGGxxFYMRL9t+f/WXW+qpdx5+EKG+CqEh0l05JhzoftYhigSVTiszotZE0djZHy8ZInESCwyNkXj3iMjKJVPGK/Tdp7vr3OkojIpgw6zwLZ6TH7VNOztscEOpi4IZ4/FyZpIyIfHybNDRlp/swqrDYby1sXD99mXdqICeZd1vAndiSM3NB+Mh7Vbk8CjpGO2Uu8KGnwRALfb1834X/l8P6anaNDRIV5eJzwVMg+hBGAE5X4/jVX4W+oduEcfDZh1c3JdBFgOEBeUsaXKcf7wSQBIgTQxFPWOUj1ZYhPYe1U8qThbV0QN6s1HgR4Zil+gnAa2jO4zjFAM0wATdZPQCqJArG02WTZlAM0ZdX2uhIiIjUv6Bz07MXWXZfpAEVE/N2EUMWE2UjJsIugaleCCPAZmKnWi5P+YVJe2koATc8ZDNCgXb7pvTBWbRBBFy5tV52r8JKucZ9Gwl9EJPgKdhkuNFj1X6LlOBf6BzHV4yVIglUCMODD8v+HGUrPP4uhVkhuWFe59cXydtVx0Xs24ncYf1efqosgfHbLh2EsSETdnIdh2vaCUhRGXGPs1EtQtkmyQXyHvCEMvaTG0GmzBq/DM9HxHlmCqaMXUtY8cHSTjpsWW478LG1H8j0bkMzaKnttP+dpw3e+2oWL+jMj2GojQAoKGUciFbHeywqyoPcP4DtUStJXBQIkkqTd3DER1jgTz/dy3Oq3Aj2k0jNG9GX8RDCPAF4h5egsRZ1OW5+zli9DxOPFFcJ1qM6HvqHCjb5svGCdq2ME0Owj7S2ERKTHSMUYGaI2nXKaRKsO6VIswS0YGqddnautO+kusqthBGAWhiv40Fnmc/hiEV09CId6yOrq6NLNrNh8HbdibAsmlc0uUOfWrFed60BsSwZBTnY/ror5NqtGToSUzvRlMFfMnA/VpiGWjqDjNdVm/943j3wSr98Z1AnmMdOkFj8/Qxft6dqMvb5aCaAZnosLG4tgrjWqmhhZ1IxAioh4yGKaGcJtLpXOj8CQNBhCZCIij45ZQVlJB841NhVGWoqv7CjdYx+idzci6JlThaiE7Zh3jiJq8JAmk3kPfjYXtP5aJhpXGGeiceT8pPolHcbjZhAVxAzZ6LXHrXwyL9kTOEg/JtZgkim0u1ljJWK5jPV3uUmJNhPjZYJ5PkK2qSBtKvwO/F1J40uSOQRuQ4y4SYylEcnpqDGgNlk25QDN3DAuYu2ELJtVhHhFRD4dsaZi/jRKdj/9RISNkJOd5IXJkv4epAeipKIGs57U+4W36XKZxyzXlerWP2u/qn+qDAXA7h5D0MAsdzL272Gpr6v2nU2OQ9Xb4ZlWx9VGlDN3jJFXggEaknJiO1pHrb0u0eaNGBFrI4AmfjpW/4igyrApwqY1bfSr/kmdolbf4br59kCPld/jHyJ9f+pw0WE9zVIjrLyUpHfrcaFgvX8e6rICGt9GnRBe8lAdAZjpe1Sts58z44cioDm76iEYG8pjamYHIQDXjeAkT5WRVEmZ9b4x0Th3jHBo4nhvM6WEQFqDx831YaUW435s67P+rnLWYDLDhPvQHzHAy5pMst+fM1SAvSzYz/gyRHOMNfVk6SUGaAaNHNZYBt+hHqeO45ghBB9GWGamjeRMhE05QNNiNiMRkV8PYYUNM9dC7NMUdVoX2EcGMMzuI43OhmeRUj6S28jGdQJ8Zv+QzmQEjinfphP9+89GdIxMl6fkCaIzQjpfm3btttNhLCrIGdl3gr1ei4jIC+tnw1gbATSjLdYF1k8WMPeYbmdNRRDJT28i+X9zkSnfqKvc6jxWd22ffxU1YRj/y93caIzoCMClK7GrM0vENBxq3+tLRGTTHms1SlucEE0riPYSYVl5R0jZKHGotTUxGMsQnNa+y5ozbEvhRsfszSUics68V2CM2Q/6j4Yxz1rsfG3e34F56D+OIx2zd2QIH6kLr9eVJHyZJpyXfqNkmAnmeWMwJE5yc+N1OJ+ryPtS68ZU2qsprGBK9FijDXX9OtoA5ctE8AUPE2SSIvosznHrGEtFM32ZQikeyMqxoy5dlmEgb70fo2mdP2V6aFmi8KflxjCgNlk25QBNJWlDcPsO1DaplVdhrHcFSfAatm6PuUiItCTR3bNusS7S1VmIABNjw7tKrC/b9hG8Vv9OjJYUyO6k2qXT5WE8D2w8ieJt46ux1JgVHzes0HE6KtfoFvrUDKszZiFYEs2lap2Mscz6bs2L4D1/KWXdFVWu10VGFi/TNR9MPsHmKQKaznPtu3cz1d7cmI6HdlHz06rjfO2mo2WABhcYHysPJpeWNhXGROTwKIKtjizhfmyzd5G5w1EL6POVPyFH4vnv2boExlpG7YHl6Fy8R7PdOJ9vHsbKNabFwuZzigRSQ0bH5qFRjJSEdPQvSUQJibkC02YlJPqwYRyjmv4e63zwxEihgY/oy1SQqF4ZRvCYvg4jQDtTxu9imx8Csr2l+J2sHDvowOPGC/i7ujMR6zGk/USeoJcCW4eIsSpDZnnSqmGybMoBGhfZWo/uR0eDBc4iI9h8Fq2XxddwArJmYrRkmKQ2GKBxG9Gd3lH8TY0DuCAWFmN0g9n+nG5XEJttH6GJ7NC9CB9oIJ2kiYV36CJP4QrrasdCsC5yqizDd6ySm0UCfLi7fDlhrYBx79H15Xlvje5+VG7Q7Uxji+1TUz8eQA0lZu4qBFEnB1lFE95Mv7GGFQh3Ix8km4IMui8fkUNgNIFGP5LhWcVHSbf9XB1twa2qVq05v0fHi3IYYCVSi/PKRwTzNseRnOwlrzLrt8MAutuQkaDtPghfpuAihQwk29EUYA1N8bN74khmNTkzDhJ1Yv3b2PxwET4js2waz+fM2KdaGa8kSFKoUdKx2E9CPjFSUz5spOXSrIKTcaDI+uIkiJdxfqh5pwHNpFmScUu26kL+VUvtmyqGdpOQNyG/OUgTvTyrnDHRvvCXwWMopMZ78S3NJzCv37dM53i/vOc8MopkvcHD7BfJ8qewYoN96qKwLmXhfh5TII5IBMYOqbKeb+sQklvdBNCYpaoinNSXLcMXt84Tg7G79lujWO4uvB+uED6XD4d0XcU1LQ1ERD674nHbY+56Huvu22Q1jI0ei5GAWhLpe5j0VQrts87dTBm+o14i4JZKkO7mBNDEMWgqrT58l58cRnJ2ZIt19WeueWBR8TobUV1xnzgOsaa7T2zQ6f6s6SWRDKK6nPWTclsi6w/XNUwE8wjBOBskBOBqfOvnB5A7Nkj4MlsHkAdkiuY50oS3U4V+kQnm+YlQGOXLkCaTbvOjjC8TxGcQJRw2xpdhir+jeQTVPQZiTBHwxaxAWmO4nWQulCh7Q7Ey0UmyKQdouowwnIhIxWadbOMlM5+wPaasnWk3kOZqhOyVGMOIgZugfZZ/NZE205VgNrRUt5tf8yKSnVsJoDlqob1qanYfllQzHgKzJ0gJZD5Nnt8RWKK+IGSNGKzajSE30rSWAkhGNC2U4bP3OPBl3tVu5WXMISW5iWNY5dMzMMI0YbT21Qp7gmvN0zqw37NMd9ydvchXC/RYUeTwbFzASoIIaGKkR5ODCPClq/C5RIiOyQudqB3TsNM+7Vm2CPlazP5C0hMV61lEAm1okfW3nh5BJMTSg71dERhrGcMFMV5Ddu+kTNnc5XuGSRUmIaUzfZlgFUaZ6t26yNlwDwL+aJ/hy0hfqHQ56dxNKqvKSD8qFuEQosVlBlBM0VMRkQLRl6kvwftRRfhDzGIE9PWnrRuKLOP7MD9GAA3zY66ADtAwtfvJsikHaHaPE27JZowEsEfAdshmRUlwH6LsnqNwi19KyvHiA0S1kal6ktxlxpisrJkfK/s9diESCZlVr9aFFy+us+7674nrIkDjp7IKnudh5Mqd58CYT9phbGAh/tZGj/X55ftJiS/VhyC/nWzKWQ58lPSBKtlpX+/Ye4SuJvKK3e8ho7jLddexJKo9V6NiJYIe9m5El9orAItwENk2Yn1nEpW4iy4lpX0jpGkoUy8tiSJ4yRBi1NgeBEi5mJVL556N1/+BFtTWYfbzfSfi+TcgsZ7ZkCGat4wo1b1IpMZ9nTiPnGQDkCojzVxJuGvcEC6kpdGkTD5Zjs9lZgX60zInhkj/nkACMNuweYaMXJoXfzsTVMyTjYiX9AQbJBtOJ2syaXyUpaI9xFfU+RG8hMj9SBbwtzPhuwFDQymXJb+dvC8FH+GrkTRXkMndE/MReYXJsikHaLoTuMAWutEZu+sx98wWgMfHrJEA5zA6z3QZATRufMgOIpFNUpwUQWeNyeol6qjOSnR4p1W8AGPMwttw98fC78cYeeDP7juEHIXnGpyrm4p7d2KaqI0AmnH0geIybiZvJolD7H4zEmWAEDj6Mzjfgj324DAxUxc5e3UH0SNhJd+H2xOAmWV7ieIasRPrdMC40IPe3WFEFhi3ggmYuYnAJIteVoZwkxHLIWhiQmympZowP3FSKZM5wEjA5n0IKltFl1Y1y8yjTrz+rUmc9AxwMGN8GZ8HF/XRMevzI9qGnC9D9jUNQd3FdSTwnrPf5Uxa71HBy/gyOrkMBxM+ZREOxWuaIxuiErKhLVfry+AkHyPqdeNZ63EF1sKFmIP4OwZoArQeHc2kQ0ymTTlAs2cAF/WmLKZARo/ULQD37Fli+btmDHdOyRqSkyShAIb2GVej4CEv27h18vqHCIlyJoKBj4YwbcQsvwaVZpm8u8dhBX2Pb0QV3DZS+ZQ/ShdarVytS22k29DTjhpbJVLBz8spyY6F9XIyK0BERLaNoVRweJd9/6XjFmBVErPK53SRnH3vsL9v3x9kvZzQWKTv0uhKciRyaEI7yY7QbZ33yUrC8WAVTSTbxgieM0rxndySwA1LWbs90BxYhLv0wxVSBSIi/o3KtgkNCEwWzkQfZdozQ0jwZxpYVNCOCECGSFVPdtSI0BC+TM6LzzhFnumcElQAjpNqnc0D+A4F+0iTyaR1gc3U6hpMMr5MgTjeTILwhQjH0STVUn2ZoE5fhhWxDObwvRogE38kZfV3BeKzmDH5kCDp6xLy6YoxfGTzPlk25QBNsl/nVPqW6hbO4S1WgFTjJFuHKnzwTHmR7TgZoUxIWZ3DEITzjOFLajbSfCNbSV5cZsPLWBTLauH1ugX38wueUB1X9SxGDNjrcngLNuXbnbISCX0x+27Crx2ITqVAuE0BN+5Ytg4SEbO9RqidRAP/Xy3rWYXPpfpJXBTY/ThuBRKnTbvppRNgrE0wnZI8AbWWql0o8Lc+jfM+TDhmuZB1Xjor0HmOp0nTQhIdSJH6/wZS+rpuCJnCoV32fKTh+brdJuOzVG7UOfbEIoy6vbf6YcvfmQKea0MXzqMaorqcLtURgAkFRdyGcCGraEqHSDPGKnxYM7y4mdqfQcQx2IvhnRl9TNzF+lvTEQRHDLhFSWQ1TaIxQgjAtMmk+ZoS8mwd4ctUuHRyCIwvM5RGQMPeGdMYh8ZLqq2CTqJY7NOJR/qYtP0k2ZQDNN4+3U92LdaFQyNbjIWtFCdWTSVOXrOBmYgImTO0wyszSJ8QcuSIbgMu/7H7TDw/Ia72LbEP0Vev0ZFWPxu234GKiGS3IqfD6UOgdkoUdYT+3GtNf7G0XLye9M4iO5YcKbJnJZBDhLxY0229l6ljkcDM+v5sz6DDy+7QadP8vIm1NbA6vIpndcJb3ct1IPW2gWNgLLCf9Jxpsu44y0in+LE4XhvhVUo6goMhUovP1HLndBAeULX1uNa5pNEUsZuHsBFsySv4WebqB+bj/T2hxBqx28ma23ais3CP4zeMV5F+V6WkiixLeCqGcKEzSwBTGP1CXRT9acSJvuGJOEZ03T1EvG+IaDd5rNfL9GVyhC/DOB7D47jxdTC+DBM5NT7qKUGAUEv4MoyoniF8mT6ilxRLow9ksgamuUkUzkUyACVOnB9hrw7QMP2eybIpB2g8OjkVObxOJ+pWus86WXNhdCrVQXSUm0cxjMqeOxU5IkPgs50kZFqrI3Ht3st4KqTUusk+5OjejRGEnEsX/WI7fGaO2ZgebPNhaXHHyPGWv0Np9EY5Ur7qdOFxeXJ/s0wGfghfsULK6hxGm3Qpiz+OHGZ/0BsY0ygxLbpRJ/CXnqV7Lqv7MCUZGSENJSNWjlmpj1Q0DZBcEssQleqcZ24AAVJhmKQ9Z1nLno+KYuqV2ZO9mP5x77VvMCkiMl6PP6zJ4KU8nSQ6LEOsqzMBPuRWerykOpMsiCzNpzk/U7z1koqHfUkdX8Y1TtJEBmeG82XwO9lGhEVoqL4MmYN5AxBwvgzeSA+pb6N8GcIyTmTxOCgzJ5fvIhGaACHgsyqngIZAJCJuwn+bLJtygMZPpDyY5sena55SnS+4zZoCGT0EgcrcIObwXx5FfQhW1s/4MkLE9jzGxjdTio+2dYaOgFj2sm6BPX4ORkvMMuJsFwKa/AlsYV4LI99qP48ch79h8DDMM7R5cHEa6rLm1JnMRoZoyXgJoHE4cfFgSpzBLuJFHNbPxubrKshu24KaMDMEJfZRrVlE1dbgOV3rg3MW6mT9u7diFCQy3g5j8RrrPYp6CceI9NhiCs7BMgRMQ4TxGtxHdu9EATk+1wq2PlzOSPR4/vZXkQczm2wKTME8ERE/6Zpd5rRu+58eRXXiIJHJYgRd1qfIT9IMw0O4OQsYt4hVyZh95UREWksxVcyqdZg2FOsE7kggSMhWWiN9lC9DKrfyhC+TJhpHbgVfRgQ5M0xfpt6LawIDeH05XJsG0sihYS0oTF0zBwEvjN9SSt6/IInQlLl1ERrGF50sm3KAhnXyLcxGcHEcoZuwporZ3VYnNXoWOrKoFx2lc0R361nDQ2eGRAKMTTMLt55ZoysRrVqv24G/vwqd+22DZpoB73f3ch2XZ/OaFhhjVSGDi/CzHrId8Xda73me5HYLRPCQ7eDYbofJoId68bOusBVYheaic2PmXqtrSdF5nA6Q/moEwTeYA+fal6qeIAei4y3bwSRHccwkzTNVUjcp0Wa9s6pD+K51jOPKFtrHnile29Bc69g8j647ceRVZU+wxajvdEKTvT7Qqr6ZMBbo10UcKQGYCKcVRnFR9xicmSzpgp6rxHdopg9RSXc2AmM9fUjkbVTwZUSQM5Miv7OCEPcZ4TxfLF9GBHamtSQ6pefL4HzrJ3yZJOHLFIwIjZNE+/2E9xfxov9n1ValTIWUGPWfk2RTDtC4k/giJGt1TmplDMmQUjA1NPAQ5qBdcV1FkxBU7SChTxPcs/41i/yYRhvJI8r27sHyn0IpLqZLvBju+l5vi+XvoCDHIz5LRxIL79Cx8gsk9TVK3iFTuoMpOHuDeC5W8UB736TQqURHSBgoYnXaiyt1kbPwbt1OJzdXlzr6bYc14uMRbLzoWoQNWZvd61TnL+ki1+vHVE82bJ0PWbLtJUUWkiOUnxDZXfaMk3YLAzgHXSUYkUjU2qewNqTxHQrtUxKAG/HaDivF52CSgHuGcOGvSxBA4yPaIwH8TaynD6u6NBf1dCnZOBA+DuOHdGQwbVYYRpTqGSWpDQdJqZdYQQhT4zVbN4hwrhCV0GAaVUzk1GibUO7F3844KWkScmQ6VuNZvEe5HFlPDB/lcrPoM6locuO1eR060VBGVp8GNJNoLgJoBhfodrSPbUPn3ipW555uJhUaRGqWcXnYy8GqnFxELdd82RIYuZUlZJd02wiCtGw7OtTCcUthrNaFvXo6t1i/eDYBNEcfotMsqXlWp6J6fCueb0ua9OXpMaogSEVTqISAIxJ5YZoO+Tg+QN8gETFrtjrycyr/DscM5BGURFbrKpo+f8gTZBSt8zlrNc0MAmh6jsFFh9nto3i/Q7tJY8tKjOSYwndjpCsw67HFWlKUkd3l5i6MRLV24v111GCKrKHNXofnVohKipRs0Il10q7ZAVTb3mboTOX2EwJwnAjhVTMFYAQIjC/DOpc7ctZ3KBXGYxrKYzDGUhZbSJ8pfy86PM8w2WT48V1LmqJ5ROmYEVRjcSQAO1PE8ZJ1OefDwdJS6/XWejGFyBpMMr4M07EaTqE/MnXIRBDzuYkeTKkHryPiQYDuJ4CGRW0SBXtezVC+eHVzO5tygIapWI7O0u18/a/al3zPbEQH2JVEz2tyXkQ4CKEEYLJbNcF9qhYnYLUTr/8PHYfDGIuq9C/WlbuXK0LtX65/hIySXccrTLAM7QOVmPr6OwFq/n7rPRk7BL+z2o8vc2wEF48C2RG5hkkH9XF8wWNLrPfyxAAClduGMY+W3dUOY8w+H9GRT+tW2TufwSN0xL/f7MOWBt5OLMsdPQqJwjVl1sWfNValFYAhQvAkL0yuhyxYQxiFTLUh8DmrwZ5L99AurFJr3qNr0jQ2B+9vmwejNmZ6MNhpDzZERFIREkEhuitJEl30swIK43RpwlNpDeG9zZOd2ZYYOjxSPyFOQgDOhfGZmpwZf4muCCJNfjvroUcb0pImw6bGjFZfxtTJEuH6MowvY6aXRARUWX2E+F1KojFhwo1xEuoAi9CMkgiNyVHqIWvwRNmUAzR5D5FGb9GJulW8SkrcKqxv0eGVuMtl+W7Gp8oTtM/keKlzN96FkmrcgWZJfKNzKzoVFlUZnqcDfRWvWn+YeX9EuBDZfXFd2s95KC4ex/uxC/WV27FGPTRqvXHJSkLiJTnlXJoQmUhI2jvMPB4B0DMMEixRff19OwLNiGAkKn88Rs5UBGAR8T9uXXTZE37HYh2o3LkFuWNzh3FRH23AezkvYJ2r7V0Y7SmlFU3oPJM5XJwCXcTZJ0kl1SyMDJ0bMu8lPqvCq7r2Hkx9fPYsBLPMnhyykoADRFiOdSlPRfBcpWRhGx9GgEDazYFoXqYCzzUziJu6AdKyvqsfL662j/V6ISKhYXx3zd8aDuAz1jaYZCK4jADMtANMjRl9PyacW0Np3EwlM4wvg+dzG12uWfVSGeHBlJJwKCMsU0BD7q8JaPrI75wom3qAhvAmZlXomsuVdJAwdbXV+c724wLwwCjutktIOSVrguhgHbhJ7NrkE1SHcHs1nMcJTZ09MV89/nYmHubZb00T5VtIDwJi9/SzypwYjIzNRu4AK0nu6cfjQjnrjcuESI6dlRiScC6rNKMlrW6yyFTZ8zJ69yMQjJDjhubqImc7s6R1Rcqe1HdeVMeXCXQS0EeU2Wjlics6L/NE2JHRmLwB0t8pg6DExySlCAcjQTjSczzW+zuWx3tWopOmkVwTprQOKbcXPBQR2R6zftY7SvgyBNBkCRJksv6syaIrTRTJfYYODUlfhYni4SBZxHKMLzOmK7vPlBKSuMGZYfwQKpin5cuQ1dLlw+8IGykbPylvzhF0xPgyY2Q+m3373shM0TwmcBdw4e6YiehpLU7SZiagieWV4mpF2JQDNBmiknliFGXmWRdjxzaMvoydZBWCmuvF3Hm8H19mEi2XvBffIldC19/JTLXODWPsdgOp14xs10Vejm/GvP7DcWzUZ6ZFBi9coTr/s+uxDLVNMJXUt1QHwNztuNAXjF4pbqJeyrRkhDwDVmnmIVzcbAiddkVzzPI3I9KFX9W9moNH6MinV+x5Nxm1zhF3G0a1zg7qoj3lW0krD9IiIVnPdECsn3WxppOEX8aa4/XFMRJQ0k1eNiKAmZiF53MaqZJ746gwbEYl38iG5uN3nhHGEnjGMejutCLBWcMkOlVBtEiIkBwjubO+ZkxmJGVkzyvLESgzAvArY3jffL0kMhLDzxaIyGSyHD9bCFufH1vAx5L4DJhgHtWXIRH0EsK5qzcQdMkB8GVGCZ+MEYBZOszsocQI8yy9xAjLzBiRfDSP12sex4QBJ8qmHKBJERXLIwKYYvndEHICcqMY9YjNtt7CMjIZWGfYPCmhYz2DnDHy4sKISDpi/eyMAEadnhlD0BDaieFQJwmNn1qOBOA7uvEemYvk0CJdvjS6Rrfr8C/WlTiXEhpJNmR1IrUkMjdGtGQYQdCZJlpARAaeLTKHVVurzV7J4HOPbtLtkk5agorIzF5+EcFKq/Gs+o5lJC60v7Dy9O04jwrVqA8UrMEFcCxjPZ9nlJQCk0r/Ei/eo87eCIxV9BPNkiqM4LW12Kd//tCFkUTvFqweZDAzNgd/1xE+vG8vk7Jc3z7rPHKmcOFPluNi4inFBSuZJoJ5Y4STQyJs5p5oXpnufdw6jHPLT/jWzjj6z3wJ/i4W6fMZ1VUsEsW4QuxdZpbz2/NlRJAz4yGE2gESsdLyZfIE0DCNGb+RYmKEeZZeYmTfHAEvLMrE2jKkjbL4aUAzgcZyyi1ka/3XvSjBXS2o4zI624qCmVgUE4bK+YgDIWV1JCJItQ8cEeuBLOz7ty7knwT2YSQntQiJm0t8GHn6yi7U72kzFsm6BUTti1jVc0ggZcHn989CAb4tGXx+oQ7SpTZqvXGzQuiMWSM81mOLpI/FmUGnwqpMDgtZI32PjuFz8b+KeYx8AKNO36j7G14IaQpZs9oeWPYfrovW/Vfn8TDm6MD5kTocQdSMCvxd/UmrE6QVTURTxEO0UxwDuAC4RkgrBZK6PLfaXqdp4w6MNMzpxWarrB2How3BXLkTF4CnxubBWEDxGjHfFvDjezA+jgAhSIoUWIoFNk4lKN3AyK37B/HiokQ3x5EmpcB1eL1MHLDUUORlC24mSdo5EEDDRBsZX6aG3LgKt73GDGswqebLsB5bZO0wWzqECF+GRWO0KbIMuUmMB2TyloaYlPQE2ZQDNOxe+omg1nAXOjy2f/VXWxH6QB6/gPUMYjoxDGUTcE/D76YCpotQPJlTmTWCnjLegItChEj9u0iPFdOOrMI0HbP8FkxpMTupFCMS61O4yHiHEAmOzLA+mwoP7q7Gk/ib2DNgPCaWd0/jNJIGjxVIPT6AC1iuB1Gwcy6Sy1vdOrG9ss24qJuXG52p221v6qyFsVnD2BIgUYnupdmPzn7jgPV87H7n/IRzRnaN7hEm/8/6GeFxhwbs56p/v66PlbMB71Frla6z/eZRjJD6hq2/v+AifBni20pIqS4jubP0Uo4UUBQMzky5GzcTw2SXnhpBUMJ4QMyyJXi92RJ71dsMEcwrkFQxe28ZoGF8mXIv/n4TJDAwECepmYnky4hgs9yACx+yj0RjWEUTq1LLkTGWSjN1pcaYgNQE2ZQDNOlyfFgZAnlLt+tuzbHN1nTVywnsKxQYxBchXqc7P+NnZcgiWVtmXSiYU8nvJWOEGBqbrQvBlu0iC0rUmmb4UMXDcMzDCVyECzm8R+7ZyNE5yoecjuv3YysFN2leN24IKEYIoEmOkt0rSSlrnWCiBudWhdP6rNbswUhXaxYXv8HDSStpYvtzmBrNv2yfmvp/rbp2H+5XSaUPeX6jzejwakiK5ZkR63MOMhAfxPMniDqqn/H7CQF4DG85Tf88m7RGGyLbdSnU8fm4/Tm/mkXT0F7uQiJ9jSEEmCWtTczoiYhIKSPcjeJnmRQEa4wbjFgjvwzQbIxjt3BvLz4r7xDhy7jxJUqWk8qZMC7EpurtUAJ/gLrBZJCsCQq+jAhyZsYLuEk6EL4Mmc7AlxFBjRnGl2HRGFZSzjIPKbKzHmfyG0aEZjijK2QoxqYcoDFTMyIi+4mGemQnWWCjuKCcGllj+fuuniPhGM8IeuhMiFRyELE2ElWXLKnOqTGarHSQ5nUl+8j5SWg8NRO9WwfZKYR3EX2I2VZnxkq0z972DhijPZqWK6T5RWRNO65Oc1MYCk/V2RNoHaQlBe3BxkS2vGRHW4330tzFuHfqXvCBQ+yPERH5t84zyChGRtwzrPftU2U6AnDFZpIqID2J4o0kDE5CW1DtwproBfBzowmcu+EBEskhHIzcDHTuLP1z/7C1LD6ymYBFGBEZnIPz6MTgVhhrJ9Gj1H4EjJ4x62I61kTEHsPk3rKGqWOEE0bkBTIkitwYsS7gTEF2JxFZ9BN9GdcYvhuFIPqLZDleh7eUELgN8JagfBldUUG+SL6MCHJmelk/Ji1fhqwJDlKJafJlRFBjRsuXYZYmgCbJAA0p1c0aoIxFoibKphygKQ3hQ92QxJRFyS50XOZiLSKyzH+/5e9vdZ0Dx8xIkbwwaYJYYOXBjG1PSqRMee1to1giWrqfkI4rEfi0NqL3WZtEXo2/A3e0g8vsowibNpLu2ATQ9DOJFWIeBgg8OLXDddbrZaFPb4zsiHSVpJIhfW2qojiPOrNWRmPZbt2uv3axjo/0+Hrk5LQJdh8fWoHz2bRnibJ22ZYYjDGV3WAD/vYEcXhuQ5CQcTc8flLVM0aEEWP4sFIV+JznNu7HLyG2ssOqDl63o0P1udE2vI55HlwA7oljNCa4n1UcWZ8Di1p4iZAcI8GyarwC2fYz3lJjScx6frKo7R0kvbMI0HSkiGJxlJBKIzBEK9xM8Mb4MowATPkyJCJYLF+GRcsHUhil5voyJNVPqmEDRDjHVPwNOZm+DAHBJJU0TlJkDLyMmIJoIpIxGhKywouJsikHaEp8+CLsTGJ42DmAyHt0GQKfSqd1Eqb72W6bsBzJC8N6NGl3q24jlNMzhruCclLqWSjH49rKkEuwaRwXP8cI6U5cS5pZGVayR5cXds3Q9SRihMl8Kb6A9WUxy98xEvokXGpeVkaMvMtST5zgnpT1HgWJmJiL9M46rkbHMyrZpXuth2fZ71YfHsGwkKOHKMHWIaCpKUNAM5LBm2S28mAcMRfTBxonqZMkSU1V4XGHlenAYazbmt+tHkbisCuMSuCBGpy7HgdeB3uvfDG8DhNwMC6gSQIVERlP4OJB+jPSRZ31QooaGyemnZIYxbEo48vkic4N4ctkiJZOBYlImFyNfIZo6zC5jAnky4ggZ2Y0h35mPIuTXM2XIWlEjcYMSy8xY5wf1mcqS8bSZDdiRplMgDORNimAZv/+/fLVr35V/vrXv0oikZA5c+bILbfcIocf/pr6aaFQkKuuukpuvvlmGRoakuXLl8tPf/pTWbjwv+XqU6mUXH755XLnnXdKIpGQk08+WW666SZpbERQ8c9YmEjbPz/QAmPuPiRlDs3GKEXQaXUYwQ6ioUHE/DwkZJrtxonPnHsoxPRTrN8b6yOVLoMIrBJNSMhZSmqeb9mN/Woq4niPxtrsX5rq9bqS5PPbdCmQ8C78zlQ1evwjwtbFaM0AziXWkoJFDFiPrQzh5zYEERivG7ameoJ7ceEvtGEU67MVN5MLQUBavUZ3fwtLmba91e7ZsQTGmnpRATixAvlOh0QQgO0Zw4igScMg9ALxEdKjh0gaONP42+N1uKgfF8L0z/YMPvzSHfYuMj8Xn9UxTSgFwezZPrxvwV7SPNJn/a2s5UAZATSjA/gesCbJrCzeVY6LddRoQteZxAtx9ZGeZkMkvUT5MkQwj6TSWJfoEbPHURLPxfgyuYCOL1NLOFZMY8bkzAwStvaB8GW85DmznkylBjGKpZdYqxBWvUQjNESVe5RsWMyUE+O+TZRNOKAZGhqSY445Rk466ST561//KtXV1bJz506JRCKvH3PdddfJD3/4Q7n11ltlzpw58t3vfldOPfVU2bp1q4RCr3mzSy+9VB588EG56667JBqNymWXXSZnnXWWrFmzRlyu4hEek7Z/eS/uklpTGFqOz8aJNGwoh4Y6yAQpwwcYDODLEU9iaJIRwutL0PGaRCs3qUByjON3jsxAQNPkxR14bwc6rqgHq2JmtljTVUxN2LcGFzqW1bmwYhWMPZzABTHQgaCh7yiMFM0yEvkPku7poThTtyWNKMkUzJThZxnx+Mm91nLmWf1IAI6d2AJjzW5c6RkB2PcCLtbs/n50LqahTCts0mlGDLfgDWkhDN1nO7FSyySkJqvJzp04e2+MXAhZAeINeL6FXozQPDHeBmPl2+3zjbG5iGQvKkfQx1SG2/djZKt1CH1UpszqqjMRXR8rBxEppIJ5ERyLhjEiYarI7hrDFLO/j1WfkQaTAdZgkug7kc0fU/Q2OTMOpb5Mnuh/Mb5MtQf9J9OYMTkzE8+Xwe8s8+D9DRvS5doITYbwZVgkLp4lIIdEnsxUoKlLM5E24YDm2muvlaamJvn1r3/9+lhLS8vr/10oFOSGG26Qb37zm3L++eeLiMhtt90mNTU1cscdd8jFF18sw8PDcsstt8jtt98up5xyioiI/Pa3v5WmpiZ59NFH5fTTTy/6+li4Lj9EFn8Cmlh/pE7Dr/gHcLKlw3guH2GlJ0jKibVDKCOKj7G0dcKRBq9UKCtJKC8esvx5+slU8eGEXlBuFSd7MYXpvNwgAiF3IwGVpCT5lkEscXYM43NJRkn3Z6c1spUiFU1kM0jBCw3Rk0Z1bL4lB63gs5BEZzRWr3PGDxLNEiYAycjfZ4ZMJWY8pkRHNZEkrsuUhDgWx+8oNW5b3ksaTBJyqxfXHBoNzVegI69w4f1dN0YqFLvt20PEa/Fc8whg6iLNI50DrDEi/rBMieEISCkYSxWwJos8SoFj5QG8jrzxHX3j+I56SeDPkSHl42X4payyyufTqWFnjZSNg7QnYSl8Jmga9uFzN/3HG5kZzWBRC7qoEwVnpwuvzeu2Ty+JYESGl2MT7hRxbqyiyUzxiYikibM0eUDZtxOgeeCBB+T000+X973vffLkk09KQ0ODXHLJJXLRRReJiMju3bulu7tbTjvttNc/4/P55IQTTpBVq1bJxRdfLGvWrJFMJmM5pr6+XhYtWiSrVq06IEDDpO0DXSTX+j8iSv+woxvaYeyFhHXH6e8mugyz8FxlJAfMFKfTUULKJO3ddwxakYmfSF7kfTgpEw2swZhuYcvXYNTmhDKrovBdvVj1JYKAZuRIXSrxoT1IeK0fI+0mmohIoQEu3KSU1El6bBWIHgdLQzlIX5sUOTCw3zrmIDpIo/N0u6n/2ompwKhghCZ7FN63JV4roBnJ47yqeBUXNQaOWNUQs9wgCTkatzwfICR60t8pQvWd8F1uqCeaPsSRP7sf0z+Nu6xzK0ueFYvcznHjTuR3o0gALtlPFjGy+JskYFMVV4QrAHvihATL0qVhfF/qSbrUFM3rG8AIXh0TzCO/KR3G9y9Vjs+0ipB+mMaMSQJ2sQ0ieW/dBBzWkFbjrKUDi2YMGo04Y2nSGZykXZhgnosAmhKSXmJNJoPGgnJABGBSCTyexbEEidCYkScWbZ0om3BAs2vXLvnZz34mX/7yl+Ub3/iGrF69Wr7whS+Iz+eTj33sY9Ld/doOvqbGWpJbU1Mje/a8Rkbt7u4Wr9cr5eXlcMw/Pm9aKpWSVOq/H+AIUQcV4QzrACkpLNRi6OIdkUdh7MH+Qy1/OwfwexPVERgjUjJUFZhVNHnIFmt4yBrWrB/CY7JhorFSS0iraVIh1YXXMd6IodTFPqsS7Nd2nA/HzCaApm+JDrXHt0VgzOHBBSvUhM/BlOVmoXHGAGZpPxah8ZMqk94UOvygib8iOBsWzNaFRkZfxnnK6sx6jiAkCcN+FlsMY55t5DqacGFuJaBhiHAHGO/FXBOchJBZIARgN2k1kYji+Y+JYmuCwTy+H/FdSO7N9lj1e9ytmDJrnIm/nRGAn4xh65FgDwHQpKGpqcIQ8CHgHR3FhdPPoliEwpCP4GJX5UXf0Je2zmemzOwbIsUHTtKktRzvUS6Mzz5AFvAE8eN5A9CQILjktPoy/hiMMQIw02cxOTOML0PTSwfAl9FqzJjGABkTx2MVockc+Syp1GKtGibLJhzQ5PN5OeKII+Tqq68WEZGlS5fKpk2b5Gc/+5l87GMfe/04h/H0CoUCjJn2vx1zzTXXyFVXXWV7faMmcUxEgv1kR9SIzm2JDx3jlfvPsvzdmiQS8KS7MnvwrDzYGyK7ExZaNhyLd5ToW0TRCbRG8Xo3kVJSP+mH07cEHWjIyPn6t9ovpCIinsWsJTJaeDt5/mEEBIfUoMT+dqOdsn+QpB9JNIZsTqTgwc+GyU5y/xjOI5P0manDYz5Qi4KEzCpf0amtxg+1T53ctetwGKvuxaqe9GEtMLa8HOX/9yQQWnnJYza5hU432aoSLoiL9MBiqa9DCcl9Qwo1jkJEKNK08TZMZZ5U85zt50REXupCvaSqPlKtE0TfkDYiFyFSrpNlVV9kk8Sq8YJluCCapFIRka2j1vvm6yMFDyOEAOzHa0sQvoyLRDlZ1+yBOPGfpOeaaQfElyGp+IE8ptxMzgzjyzACMEsvMWoCi9AXqzGj1ZKJM0CTJeKOTJ3ZAG9MdXiibMIBTV1dnSxYYA1vz58/X+655x4REamtfU0SvLu7W+rq/lviu7e39/WoTW1traTTaRkaGrJEaXp7e2XFCt69+etf/7p8+ctffv3vkZERaWpCB8IY1sE44bNU43EVpNIi3Wss6gRwOcvQq2iJUQE/YdETMpbZ0M+ZxZcjFcbHXUmk6HePkkqUcdYbCQGN2c6odL+u5vmIOp2+R0k3CZtWYCSgrQQX4k0jVqDmIQTgNOnGzsBLnox5ifMZHEdSQHTM6P9Vic9zmb8dxlJkNxVqJ2qrMCIyr9m+8eJwBwIr1u5jvBavo8FH+mKNoPw/U6SF6jDCO3KRflrMUkQ7pZ6Q15mid0mPPThkCt+HBBEwsY7Z8UGcC3XkvcqEyQJISqhNoyq4LEpBAE0kgA+GKcb2GpwZxpdxJsk7SgTzKF+G+Dtm6QzRmDF/K+PLEA0X1oWa8WXY/WDpGZMzo+XLMAIw58sQlWQCXszrZeklLV8mRaIxrPyaATXQ0iEOSvd229uEA5pjjjlGtm615vC3bdsmM2a8VvI8c+ZMqa2tlZUrV8rSpa8pp6XTaXnyySfl2muvFRGRww8/XDwej6xcuVIuuOACERHp6uqSjRs3ynXXXUe/1+fziY+QVE2Lx/GYmnFS7tiEL6CH5M9L2o2HWoJvaTURVxscxeM8BLiy3UNvgnTjNYVxmWxHNU4bJt399G5sKjg7g44m1YQvUXvWGi0p34ycIrbgfrr6SRjbnsHfXrKL5PXnIpdnYQCjaffsWmL5u2KYpNGqCamUkFQZyGHNEkcG8VnVjFnv28AinGuLvQgWfzmMPX4c67fhGOG4XNRg39Yg8qoOZI/MJPOIgIb2IQTGpBgDoyrE2bNyetZrKFeD87TKhR9+qh8rmkK78DjzNRqZhd+5zIfRwI1pTDWaHbNFRFzjOMdHW/DZO8usN45xAd1xAmjIy5YJ4WBdKUYk2O69d8j6uyqJYJ4QvgwDaaxjdiUBVuy3plO4dJk6XnkS6WN8mTpScVosX0YEOTMMfDFzk0gUA1savowI9vNjar8MkI0RxMs4NGkSoaH8mIKZjcFDDlpA86UvfUlWrFghV199tVxwwQWyevVqufnmm+Xmm1/T0HA4HHLppZfK1VdfLW1tbdLW1iZXX321BINB+dCHPiQiIuFwWC688EK57LLLJBqNSkVFhVx++eWyePHi16ueirX8GAlVZnEyjDeS3TbJu4fbDRRciY5sRhk6vO7uCIy5SG67gujmbOnDfXPJkHWWsGoPVg7LpOjzRA+nQHYKVbUxGHtp3EqsdG7F3assnANDx/hRc+bbfcvxs51IeBo+HVMbtS4CfLqtzqea7CQzpYSsR3Z1QgANY/27SBWLI2+db2MturTR7/YhwdqXascDVyyBofNKzIomkVTBCqyim+zTUiIi6ZlMcZSQy4kGSpQUrJh9cwqkOoW0DJJMCR5XW61LXW7pwOjRvH0Igp3VVrSVa8X3kZXT/yaG1Wcl6Aaod09E8XcFDH4Wk/V3j+tUcHNl+KyqfAjmWLlxbsC6ALKqTmYpoi+TJaXnjC/DogP5FJ7PnTMADWlfUEIas7H+YsXyZUSQM8OiFgxpej2kH5Ob8WUQbOn4MsXry2jTS/S3wmOYKPiCNuGAZtmyZXLvvffK17/+dfnOd74jM2fOlBtuuEE+/OEPv37MFVdcIYlEQi655JLXhfUeeeSR1zVoRESuv/56cbvdcsEFF7wurHfrrbcekAaNiIgzTnJ8JDQSIrLtW9KYPy/psDq4RB1GXhYGYjDmIA3iGPnU7MchIhIfQsBRPmKdNZlSMtkqcdKzfKm/h3TyDeHFzavABeBJY+ebiyFHZ+Rd82GM2QN7FsFYzQhq2DBAwPK0/k7jnhdYjy1yIQS8iJuk9MhOzDdIKi181uMCM+wF7kREOl7FRXi2tMNY31ISyyd2y7CV4OrdSlbcBuRTzSatMUzCtYiImwisMV+WN8rdC6QbNBODS0XwZEvL8dq6s8ix8uwhAmC9WBroWGbVKlrSjHOe2dP9GOUM9hCys5c0/cPAlpR5rQvbQAwjAwFSaEbWJnGVoR9gOiY7x9Df+fqtz8Y7TPRlyG9irRqcRCDUTzZOw2OkppyI5kG1HImslpco+zEp+TJ9aRwzOTOUL0PoC+y3h714j1gLAxVfhjTJpHwZpb4MUzZWpZwm0SZFKfiss86Ss8466w3/v8PhkCuvvFKuvPLKNzzG7/fLjTfeKDfeeOOEXpspsy4ikvPhg6ktQ9S+NYUhf/eAdWeTmI+OnZHrmD5E3oeT3EnytgwMuYx+UUzunZV6st4bHrK+smaadX50BC91WnlLjaRH02iTboIPd+JCVOsk6YhqfOlHSOm5SfMouMlcIKqhQpyPg4ylyC6GbKYkG7DOt1kVrEU0Guvxw2ysWcdbetzQ9Ml2IxhwHkb6QpVth7G+LCJBliZiEYOCxzrHHaSBICunz5IITaMfU1+dGcxtMFkDKRCScY11MV1RhlVfGQKMO0g/o3pC1M8Rsmy2hKRKDMJonoA+EmylmyQ/6YPkJhG2ASL0aepbOVOkoon8pgzB2F7Sn4uJA7KNgkpjhunLeIm+DCHUMmPRDLb4Q+TiQPgyJPKi7ZBtcmZYhIalFZmWDOPLsEotCl6UrWMmwqZcLyfWqydDtCsOCSOJ8tnB2fjhwZjlz7FGrJ5gE9BN9CFSlaRygUwk3wBz+NaXgXWorQxh3L4jjo43QKp/EpV4HXWkZCW1x15ZNrFA50BCWwnxj1U0NWBkgYHPki7rS58Nkh1GKToVBwkPM0DD+uYwrZRkpdWJnFWJPJj2LKLK6GZdeD+8SAeQXtrSYvl7TgHLj4fn4vM8orQdxlaN4LtBK5rIAuswAI0rRtwScYrJKA7O9ONvWD2C+jJl7bqOo7FW67UcX4pk8705nM+sY7abCEAmGnClz5ISarAxssiTn0QyIlJfSrhCZNHtjuG7FjZ8gyNNhERJsQBr1RAJ4n1jaduUgi8jIlJwWa+N9byrCeB7VUE4VizCq+HLiOg4M4wvw/VlcMHyMQIwIU2aEZk4AWSsWWyShPUYX4aJXRZyDNBYxxiva6Js6gEaRkok4dBZAXSMD+1AqfxZCetuNdlAugITFMx27qlSnORjZAdAFOVhE8DC1jOIKEXHSATGykbJbm0+ARdkV1C6xz76sqJN1+emfDvZ/ZEmiEeXIz9kzTD23Qr0WR3GaDPeWzfRpMiRiAGz7Dh5zgkCfGqs51sewDTaQ2OYlivZjGGFfBAXxPfPWPu/Xuc/rGyTfU+VWCs+z1YvRnJ+OXgsjHnGCDAmxHQTHLooF4RUmlXiAsDC8Wv6SFPZvbiIOUII3kZnWuf4YqLNsnIcqymD+5hqLy5EiQo8zkdKqM1dP+PLsHReJoTvaFUAgRWL1KYHcMw/aPgGwgFi1ZRpwpcpIYRXFuXMkq7ZrMlkwUgxMb5MHSmCmEi+jAhJuyj5MmUevI5Skmtl18vMrGBi6aUxIo7H0kuML5Mn4IVFaGCZIOB5omzqARqSamTRDMZyz3fg4uHwWidEpAFTVSzP6kRfLF4mzEakxf2DJLzoN/pllJMeIKQja4wQNyNpElUghOJhUndZtsf6orprkMD8gaqnYWxLhvSN2RmDsXhbBMYO9SPx+Fdbj4axJqOfTKqcpKVYmTzZhdEXl6QCGVdv3KDCtHjwt393D3a5LuzGLuhyBILsj4RXwlimQDogv6rIu7faS6qLiHT3Ysl3DfG7rFTXNLIplawf73dFFMEFK0Pt3x+BsepuIhPQgBylUIt1ASx34lx4ghCAS7tIZRwRl0sSAnCQpITGk1Y/QwnArMCkTMfL6EkSntEAzmeTM1Nw6/gyjjJcmFlfPdZKQQgBmO3yc0bK/q3gy4ggoGFqvwGiFB8iPCYG0D0kFMdKss2N9DgJj7KUGQOVjC9DBfNoysm+bHuibMoBGtbHJBPRfdbXTxaxoNXBNZXF4JiBFAE05DoCPnRkIwlciCJxogIcsE6uAkmdUCOha1bznSOKxaZqqIiIv9+6iuVrkVh4uA8jDQ+OYRmtYwD5EPFj8XxRFwICpvnhSFudGbl8qiXDSuALRG/IRXhRzPNmy63PxkO21jt78HfOzCF/I96Mv7PWhfPtaRKZ9O+3gu9CABfraBUp5yVKooVh0g8tT1SXiQaKCQ4ZCGSpqqogPvfRPP4GL+lDVojjYpedhenitqi9YvO2YYwa+ogkQMFDuAlkDpYSLsWYITfhJfeIKQC7A0SojpBthpJ43xiXzmVUBhYI/5AUR4mHpH9YnzOq2cL4MsyMasS3hC9DjKWnfWRzeSB8GWZmmTlrw5ImYwfGl1FwaKYBzeQai2awqg0mEpevsiaHl0RegWNWduIOjj3UEFGa3deJuaMqkhKKG2Jn/jJSik5Cid5BMnlJVY8viru6baPoyD3d1gUwdjhGaNiC+4dOVKl1DSKPaRSV52kriECHfTolRTgYQbKbYnlh5mLZrpktxGW11pVinITtnTvIqkBsYKEuHfZfPcfDWGHbbsvfjrnINVlRg+nB/VlCsiWKsQXiyM0S7dcGrZ9lgCYdwbGZpab4ksiuJJE0IIVJhSQhyM/ERf3sCiu/aYj0u2rfj+CzbQA3J1mixcJ8D+NXmOlMpj8HAoUiUlaKC7iLOJ+eEURWAby94kxYH066Cv0k48uEg3jfGG+HlaM7KV8Gv8PkzDC+DI28TzRfxvhdJqFbRM+XMbubi+j4MiKYYmLtC2h6SVu9RFNOMIR7umlAM3FGw7Jh9KAdKdQ2KekiarmN1om/iAi63TG0DM9FXkg2yZ2DOFGdGZz4pkhVpASPGWRVC4S4mSnBm8QIxe0DCLZmjVhBSKwNw/jMdu5AEm8biUjkZ6JD6svh4l/aQcBnwPpC5yt0qqSOLAutEjVbsvljWilzo1Z+1k4SIizbqXvrc/OIQAuxZ7YTscS0lWszPgev4+iyHTD2CuGMMF4XbRlBGk+akvWM3JomCsBMP2TtEF5baB8henvRkY+04LNaEbT+/i1kUfPuw4XCNUaii/WYlpMIzsECq4oxIqlsk86qo6IkipUgoZxEDH9XxQALTVq/g/NlCLfOhwCSVdOkE6xhLKkIJZuuUoMzU2OWZIlI0DHJfBnBCiYf6cdURqJHtB+TQ+ejeAsD6/UmyAvJ+jGp9WXYPNVUOU1zaCbO2L30BhGodLGcMulRMjTfCmgYYz5LxPzIuyxu4qXMlgYib5A2MzYUfpKfHoiTyguyCGcDhK9ACHz7YqQNYs56cYlaXTWJr4vwT/zoQBoqYzC2n5TlBogzzgWt3+ErRWfBmPskxU4nEossZIiERmPQutjtSpOoQi9+qZOkhObWks6qxNz77HtqjdXhb29yI1K5P74UxlgbiZyPzF2i3+MwtaGYVk0Q7wcLx+8fRdBQOYjP2VGK70KqCq+t1pBcWJlEgjGodIuI5Eh36RCRHCCpGNZJ2pm2XwSY7ANrZBgnRFAH6ZXlJi1hzNYubPOTL8HfxDRW4qTBZIFtHgi2LxAV4ICRh2MAgQlAxvK40WMk6aSik7QIdr9hvaj8hMzpo+kl8l4pWxiYIIelnNhcyyr6Mb02iENvZok2sykHaAjRW0KksmX7EKZTosP4gow1WUO1jIHuGSQlb2R9yRNPzna+TAU4HbW+ND6Whx8lxFDSsTgVJkRFApB83SSt47Pe4OpZzNujRbaTtEs1hvJXVO2GsdWjGH0IdJFeOk3WRayK8Z1GcaFjO0QGjGlkgYTfWwwRlKdiqJwcaMdrk1kYfbig7nE8jlj5FntPMzobF/RqEqJ/tQ+5JmWjeP4R0nzQ6cHvcBraUAzse8t13IehLtyI1PXgS5SvxuhiaAaGKyuc1vnMOmaXdDPtIh0BOERKl1m/ObPyi6xNlADMhDn3xRH0MSkIzxheW97QmEmRggpvCEGUl7QF6Se/UxQNJkVEhKgAVwWtm8lKN6acnCRdw+gFg2n0AwmSXmLRNJfBw2Pqx6x9AScAE+0iVtpOeG1mymmcAFmmwqxPLxEwRzk002Xbk2aM01DixQnX0YUOL5rBxTnRZOi/kIlF+vZJGv2uJEgHbtYROlNKBNwq7Hu9FIaJo1TyFZgFSHCgUGH9YafWvwrH7MxiFKtsJy6c6RkIaI4swQX8P7afCWPRAfyO+BFW8DmTlK929UdgTCXixYcoR8KM4q3txF1/SzcRJDwetV7eWYKVT88SgmfkVaJy57bOh9KZuKDnyK8a7UK+RXkaf2cmRMLx5CaZYpeEjykVIZwfQyQt4CeRPhkjaZd5GF08sm4TjOWMFMvabnxWVT0k0ldCuhOTgGYF8T2xEZIaNnAJ25gx4Uw3AxJjpHKSbJxcpHFmtsz6u1g/JrZBZBZPkUgRkUhgNAGmMVNtcGaibpzzGUG0PJH6MiJYWMCiZAzQUAIw5cugH2caMyaJmfFlWEWTWu1XGbWZTABj2pQDNMwRsKaCjj7iVUnbhWhjzPI3S3+QVK4k6nCijqQwghIawmtLkr4oFWVWhz9OwrmeESbTSioNwmS3TfLHgX5S3l1vXexOLsNF4v7RxTDm7kDdn/5TUUumxYOet7cD73k0iVwms1ya7V6z4/hKEMkICl6Y43VU2GtGpDrQoeZJ08KhOWT+OXFR/90A9sBy7sAyZUer9f4e28AIwIi8/d2ssoO1kSClyyyYYfhxVtpdU4K77Y5xfO60XxJJ/4w043M+LowCh/uMz47uQzBXP4QLZ4qQZbMVeI+owivRMzLvUZrQccqZUB0Jd40SvkztED4YRxavLR22XhvjNtWR/nOML5MiBGAHiwSw9BIpba/xWecI58vgdx4QX4ZqzFifcynRl2HVVlq+DGuSyTRmTK4U48uwZpK0HJvyZcjFacDLdIRm4oyRyRjbnnFXCgGcNC1ha/qgiwAaV5J8J8l3x5N4/kiS5eLxsVX4rC/IwDi+pIy0yqoFzN46IiJx8oJ7SPl4Mmq9tlluRHO/iGGpUmEEFyzWHdxP8jrePt00zhhkRVY2ahJURYTvRIixNIA/iE7KLC329TMkRCpACAhmtqYXU1ORGLYryC+xVjUtCCIa6MhgWIERyfOsjQRJC7AFy3ykOQKE2KLQGUew5YuRe8S0UjD4J7M8GHLsyFqRg2+AaKIQtVzWS81Zgr+BpSxo2sXsU0T8R5BEApjqK5NqYO8ykyYwOTOU20TS3VSYLUMAAuMhk55MJUTiosLoYEobppJcv5Yvw54V68nkMUjBJaTBJO2OfQB8mRQjehvPnpVjM0DDKpW0PvCt5tVMPUBDHEGaIFcWgk1Hcdd1QqTd8veG0QY4xk0AjaMEw4upUVItQcK+ySgeV+Gz7orae3EhCpKsQ85LFhhybUNx3NU1jKHjGpxrvbZGNwKrF9ubYWx2YiOMxWcSh0R2IqWkobcE8Xo9tdaoB3P2rnHiZJUvJONF1Ybwprcbq2npPsIfIi0eIrNJ7pLYwDZcrSOCgGZorvWClwWQn3RLH5Z7s8hcJkgWYTKPChkCCAwHmiXqtiUuXBT2D0ZgrKmb7HLLMAKWnIHHMYHDW4aswoVBzASK5IgadBXej9IQ7ijYwsnmoBkSzJWQPkU+PP9gilRlEakG2mSS6OaYIqSuMiK8yAQ8SRqUdcymqi4EGLPqLcaZMY3pFGn5MowA7CGcMJMzEyLpJVaOreXL8A7Z9i0MkoTSQNsXUM0ZGHqDiqbJq2DS2NQDNCRCM0Zyub4YcVK1OCEW+a2pjT/uwQoQH9G4Y9UN2X1Ee6RAAA2pxvAaTiQ7ir+J9Mik4X12balhXK0dGVK50GQfRXDvRKfCKpqqmpGztC2NhNTQXpLrr8RFrClqPV8sjb/JlWAhbxiiu44sqWhiMvNbR62/oaQTrz9fixyudzRgHyFm4a06pzI82/oj6onjXdeHAD0QIy06Gog8PWk+mBvC52z6QEeI3A+S5Ev34OT1GL3VRETSNZgmamjAuRV04HL63IA1mljaRfKPbOEnEaBoAO/v8DhOGtr6wbi9jlImmEf4MqSykVVluRLkWZUQzkXE+neI6NywyOc4IQAzvgwJSHC+jB83ChFDYJPxvyaaL+MhQpxlBuGJVVux4hEtX4YBGo3GDC3HJlVlBVbpqRHMkzeXL8NsygGaAgE04wmcDKUkBDsyg3TlNlIqA72kyoJsO/xE6jM9RByZh0QMKommgxFlcg+TkDdr+0CUStlLmiUNAwtMMKrRukvqzSEXpGw3iVhFMVW3rAZDL7SiqROd22gbkgwWhqxhN9bjh5WxM0VhRqLJBVl3X3Rmz+1vsfzd2Ecqsmbgl55ehqKNTAG4fCvODwfhf3ln2e9oezsjMNaawPnB9EjchHxUIOXH5mIdIKmZ0QzpK9RL3o1x/OzYITi3jqtux+/I4/Vu328tqW/tI7yrMvQfTLQxQCoFuxI4TwlPGIoZ2D1iNjKMoK+SbNYcGfztmWrS36nc+tkaxpchC2eCEYBZ9SDp2cX4MnV++55MB8SXIYs6Sy+ZfBkRTI+Wklw/jcaw9gUKwTwRrmKcNAi/jAPE2xfgUNF8mTfZphygETIpM6T5mTNLUlMRPJ3fmJjOmFJzhoCBPNFIyxFp8RBJY5iEL9q8jhhLk3gJzGbdwXM+fBkaIzHL3x3kRQv2ofPMRxEIzg3iAv5QzyIYc44gIEhU4CJW4bXe4DECZEn6n84ZtmMpkNC4k7z18WHrjtCZQOc8Xo3Pvc0Tg7E/jmLPJ18XYaFXYgpydqWV/zVKnDiTHJA8UcElwUU2A1mXZJN7VMZagGTwWZE+g5R1zMql2/yoQt1Hdr6FAevY/9feuwdZdlbn3evc7336NtM9oxlJIyGQYYQtRpjPQmVhC4tKRFwu6guOrzghVRADkSIIFytVSJSsAf7AKhOkRBQBFxiLcowdcFE2I8cIiL4YMkIgWbYQRmhG0ox6+nr63G/7+4PQ9l7r1/RSd89MT5/3qZo/es8+5+zr+653rWc9T7Jlr21nrz15cm2nzMWAfIrIfUPFJeUcZCWhPBERyR1MQ+m6kcaMDtrJk4iOo9/1+TFRBr0IEV4V3H21x1EDshZuvgzqy0BAAxozBdU6St5n5MdE6Dn0ZUSYdK05M8yX8doXbIFDcw4xcgEN+WoQSY58aNr7ofyjlpf55+2Np1IEvRw0QHdh5XtgzO4434oPquTDQl04JEWfoloxfF933L5EPzMRL8F9rWk1Voon7JfVL7cBzZU5S1K9+5kb7H4Nm8lp2OSLIQ1SGY06mog4TRNAogjkULjo6dNqhdUHrtCl9icvTtuszReeswFN4Wnb4TU4YvVTbpx+MPb334PAX/EUZVSALFqFMqjZwn5XOqgmVdlTq/b5KM4BkTVnf7V+wN6rl+asCvWjIJpXfFbZMrTsGNCatu9obtyuTkhKQRo09tjd+oozUwGhy2XokkwvgcFkDdSJqWw2DlmKajwjQ3yZBVAkH0JAk6RJMmffhemSvZZ7gC+jLR22wpehbrwUZI+IiK05M2hfADeZupeoHbsFGRrUmFHntSW+DJJ9N8eXCTo0ZxmpBqTigOw1PmNXZ8/1x2N/F6zvIpq1JeHhKq7Y32xN2v1eVrQBzZNn4kKARbuAQfO6QQFWZvCCw5jCx6asH+4/9dNmn8T8stm2coPNqIwnbTo78zSklKAbo33Rxk7SSSijeVeNtF8WjACXu3ZwLzwf/zvKAQHxUrCcBpz4Hhgqtn5gj+MKO7i/Ssn6/9my9dMqPg9GqEXoWAFRN0pxA81DBooETF0yK0v2Ok4swG9WSZrZpvwvStsH+tPztpxZUq7Z1PnTmrbbyHqEpBSIAEzzhO4moszI83Ub8BJfJt2E65a3z6Dmy4iIlBVnhtTNyYEaO7fgJUoC74r4MlUQfNScmW3Xl8HyEmWP4vee+DIE6l6i8lIdghePhQHxZah7yWVfIOefL0MYuYCGItI0EEEp3fqiSdv69FgrvqrLL9kXvDkLD1LXXvpqE1QsX2Q/O56xL3NnOR7JV+AdalueqUR5qJ1DCY4IxZQFmU3Hg62/e8Z6Ob24/QOzrX6pjxCHHU0VO3Dt3bdstun6eXYFyh8k1QM6GPQcES9qrmmPrbAQ/77+hJ2sX3qRbadZgJpk5cmN3X5FRFZeZI/3UrWS/N/zl5p98hA0NGfsfcmAmBqVGXKw+qPWX43Egl2pZmogmDdjA94X7dvYMVtE5P9Au/vY8/F7GhXsuRMBmLglp2s2y0QkdHTNVnYCVMpcWbWTdXXZflcSpCA6MzDRT9jfmFYmk0TWboL8hECLNr1rJZA5IM+uMVjs6PFiK3wZEoAk9fWxjH3uNWeG+DIE9GOCshnxZVpQNuspk0lS+/WK422llBSE9c4m4AZCRlD6ebvffiCiPd2KcxPSTTtYDPLwMlP7ag+ErEBRmGrxKWNeB9o31KJNkzV0H9D30bGZVOq8ffkSCfj+KRsxzQ3AAXge+DdjdjC+uGqF+nS6GcrwqCUjkGomggjxomotO8FWV+P79cCF+RVjluPxAxi0is/7RoveLFhXqPtwatESVC+Gya9XAtFGWL32QCCOkMjGrweRSjM1eHZB/4VEJ6+q2LRpA1bDS4t2ApxajV+3QREmjjEot0EqqgOLGMpYUVddJhs/VwokSJCPPLYSxJcpAO8FytGa2Ez3qg9uzagv4+bLQKYWOCiaM0N8GZL6R74MEYChWULzZURsiYmOldqxqeRE/ktdpyfTUAVqpKNDpTWPfcEPt9lN5xsjF9AQs56yDx1Q4rwE6kn//cQrYn+XoAOkNwZmXzD4UCTb20OkO+hYUR1SNGgNIBtPhNckEAnRMHB6Y9G40gnITpVtRuLy/TYA+U7T6tWUnrWDW+simwX5mbFHzLb/NR8XkqOApmVpJJihoZGAhLFIlXW6Hn9GapfYAOH/KVuX6wcblgdDlhHpGXsShy553mzTXT3Dk/a+pDo2C9KBTF8+C5mcNjz38Dhoc9hV4IKgASSgsc8+qK8oW3uIH/TsSZCBZ2o1npVtXEYSvfY9oEVHt2nvM/jiolJ3tRAfpMgmhUqouRXoNEtBiXYCFhlVyD6oEgvxdijDi2wLSNdNQq2c9GU0X0bEjj3MlyHBPHto6aQ9NuLLUIZGl5i8fBkqL+E2WNigcKEK1LaUoblAMHoBDXRZEOG8Q74rKTu4n34+PsBdPgSiYsUO9oka8CaAMV+esi/4mY6dwLVfFCm30oqLoL11RFiAb3IKROO6SjTuWZB2nxk3266eeNRs+8aitT5InbHp59VX2OtxKGcDpPsX4xwR6nylri/KYqEDMMn6Q9dbshsfGBtW6kUuz9jg+d6TrzHb0iesum3/0D6z7ef2fsNse7I3Hvu7+Ays4JJ2W2cSlFth0E4CAZgyYNoleaVpb8L4gv3NYQ7UUffb47gia4O5B+tXmm0kmqfbmVvT0HVYtRMudZ0IOFqjnhFlRhRnhmxSciD7kAHxSy9fpgh1a82ZIQVxzPDar3fzZSbBk8mjMVODVv8uZMYJJF2Bnkwpu8CiriYNLC85/JhEmC+jy0siwGEj+wKaEryk4B2I0QtonBLOPVArpUg7oQ0foX6VzNqXI9mG9m4IGqbKNoha7NiVtM7KUh2eyK00oCZBK4Q8sPaCWudJFQnmlkAGfcIONBfnLD/pz5VKq4jIJS27H5n+kbR4WykxV0DhlYwRvW8zSYun6xu7B3cmYTUItYin521W4bKa9V9qzdrM1k8ULI/k+6qrKQ/6JMMsDJSgUkslEFo8ULZLl+pWwUSVpPkHBcgEgHcWuRg/2bBZrDz4GWkyRXfMnlMlb3+TTP+SJCRHC2TIXOhAogU+SMBzliSYhvZL4Olj1wRShfZ5Da11IsL2FnSeGVAcHc/4AgRqZ9a2BpTJ8PJlKKDJQ3mJDCU9nBnSnKFzopITlZdcHUznIBtzvgOf0QtoIHimNHhUtTuSD0jhdPzDpBuTA4KgAIGP/F+uKFu5+0fn7Qq8UI8PXPX98IADAThBnShwjXqgKLy/aLMl317aH/s7N2/Pff4VNm2/P2PPs3USFO2GNvOiHc9FWHUzNR8f4LCbpADXCHVo7CbiSGSX7X6DfPw+Z/bbLFwPDm74FOidNOxnly+3z9HLszb98IH5m2J/F5+H4BNkA1JVO9HRCpECYwqGjITBMnB0INPQmbQT1iWzttWfyhPfOWPfocnn7YM/LMaPhQjAB3P2GT9VdxKAYQROgjKuvkYtsElBwbwB8PIq9l51x+1+EwX7bGmNGQqshATzYDFVLthAcE/WZrsooFkd2rF4Scme1yl75OTLUKddFYItFs2LjyFsX2CfcZpfqB2bdHNQY0YFlluyLwgZmp0JWj1Q9qEE9eNToKyXV5UBGixywC8YgK9Sp2qPbSZvX/CvLbzIbKu04k8ctYonKEPTgokIFhg9iC2o2+p/zcWl4q9o2GVjHbqjiH9SOgmRZsEGgtrxXETkDLlEz8evL2WxhAIaODYi2HUg61aF+6yfkZfstWWjH/RtG3vlKSC0Z+wrXL8MtDxS9lo+/Fz8RhxYsoHK8pU2ki2XbSBLSrD4HIGXml5dZpcgyO4ACXTG/uY1EzagWdCqdCKy8qwNqmcX7bPaq8Ynme60PSma/OpN8GWDhAc9gzlo/9fZP5MZFpEcyD5Qm3kH9GVoAUclFp316HVIRwcCGtBomoSAaRoErygz7tGYIb4M+zHZZwv5MiAjjhYG6nipvETbqLzk5sugaN7GJacLpR3bi5ELaFAHA3gTM1Dq+X7TLs8KC/EvpC4LIghC1yG2VdMKIDUPMuKK4Nkv+57UBKyisa4PJTjtKisiMjytBpohqBqDRswC5LyRfzNtA5Wr99iyyz+0bUlB84zIx4q0ZGjQJgxaoMraJOXa+EDzsqrNnvyfxmVm29gP7LElQQF4z6WWQduB5VnnZPyakwpuC1R2x6HEUlu2F5OE9QSyhDqzRVktQstK8MhVJSsq+GTHSgfkn4NOnCa4VR+KX6PsJDDJAd2GjwDcA2fxIqgAN5W2S3YZVJ3r9viHWbtfZ9ze0wIYZ2YhIj2jVkokmId8GRDM21uwY8NUClYAAI/GjJcvQ/oy2o9JRKQM3SMevgwRgCnD1CJejaMdW8RnYbDd9gU7MfAZuYCGbiAYlUoJIvTTTZumSCvtmP4Bn4Nssgutk2UfvyezujF5c5D3PW3U9YUdTaAVQi2QGTXQRsDBKExA9ksRVEVE8ovQMTZhVzGXF22G4zs18GlSWazOhD3RNNTOqWsDU9dtyCxAlkJ7Q+2DGfz/rFxqtuXmwRF50gZ4L560JNgzsKrLLmzM7+lBa34O1GFpYiMkoLW9pyYeWLijpxmVSUhB9v+r24ymDm5FRBJA6O9U479bLpKPGpw7dHgRiNeWgVVXQ2XAqEMvBXwZ4kBR9raU93VqacfmiMYPKOFkgEdIJRzipHj4MiJ28vfyZUhugfgyRQhoPHwZEszrQa2xNYDgBXh5A6e6r8nIXCD2BVtBCGiETQXLafuC/8OczdAcVKqbnXH7UKZAiRLMcqU3CS7G8OLqMpeI7UKKyiRwASULh7eOiEimbK/HIhBrCiq2GIBGzOXTvgAkN2ezZAtX21LBS3I2w/G5Bat6W1LZkl7FnnsR0s9NkqyHAYRUX9FCIy7qbMQIRUQePm2vx8VzdhZu/OR+s+3/nXjQbPtOx7ZSlZ9VKrjA/+pMA6GdMo5NX4t2EhS4+0rCILtKwT4Ez/vsrD6etNu+tWSvZfkUlGfS9oBb6l5dBER4EmtLblIBWIQn2FYj/hvjYJNCBGAaj0gw7yDxZWAy1YFVAgTzBIjfxJfZC3yZYgKMSR18GRHLmaFFRxKuLakua/sCEbYw8GjMeN2x2xDQdIF03XeXnOJ/b6d9wU7F6AU0NDfBoII6EvN2ck724y9gdxz0SYAsSoFVGjIXz4Mddn4RiH4qu5MCYmEffGMog0CcoiI43j7XsMv3woKqH++xL+7hMRvQPHDCaqwcWLXXo35w3Gzbk7ID49Lz9rpVlOFoF/yHKlBGw1WoU3Gaunf7ezdOUzdP2OOP6pYfsnLI3tOfzJ802z4+d73ZVnoufvN7VeB9QNcQdVl4W7RTZMq6qo1VQTUadFIO7bEdb9TO+73Te8y2S8E1e1gG48I98WdmPAsdU0t2oUPPAgnm0XuKAmi1+GRHfBnSDdAZJhGRYdVXYqH24I4uv1JmAExaiWCM+jKb5MuIWM4MXcc0ZL8oG79ZvoyI5ceQ4jkFNH6+jI/Ia7hMu4wvQxi5gIYmGBpU6GXOzsMqVIlU0WAxBG4FrV4nx+xL/3TdkkNzy5BFeHH8ZdDKoiIig0Xg3kAip18iBU/wjqnZSXevOrbaxfYl3Ze1y8vVU8A67tvVcPti6ESBKDV3mlzP48eWgG4dAq5CybwOeFGkOF1V+j0LA8sHKD5D6XK7bfVSeyCzkBr/m9O2lXtmMT5o1y63k8QkGKGSVw9pF5GeCqmQZmrx80r17LNLXJ6XVq2a8mnlrSYiEj1nJ8T0ij2v9j57/sOp+DOShXJbw0kAhjlMMqDFQq3Q6Vp87MmuwjgDZTniy+Sg4YFKLKc79p3sO/hkXr6MNosV4Y4gvyfTxmU+r74MqROTFAShHcXfD8qyo30BkJjdfBkMcjb4+wXgQgl8Ri6gofpuGuq7FC1ngK82VGlqEosaNGByhSs/4fR/2UPaEioDSyth1IcAUF0/BZkLnQYXEUmpbpRuFboxSLthEQYj6OApASlzGbpYMpCS1zo/WqFWhOvu1IZKLzhlu4hwrtVQ54Coov2eREQkD22oe2DVCFmKlQU7KexrxR/o7pg99yo4X8+t2okOpe2h9EBdJtD1bEBcHgqMnwMuFgnOkW1CjzoUlRnjEAKyHixYYN7E9yoL7ylNzJozk+r4+DJgZyQFIB2TNxRx5MzESZwUJ1+GMh7oDeVUy9VS/9SdmAXx0iJEnzRGkRQEWxjE7wN1NJHwIvFl6H1Bh2yPhcEF3I7txcgFNFROKUA2Y7FlJ0kiEupBsFC0q5/WGTBEg5X7dN6uWJ58yuplzMBgrEtdBfJ7glU0ZYqGBcojAzDjoyTaZ2GghBe8aBfbMqjae/DyGepise0uhXkoGZbjJ1uFe7XaAj4ElZycAU0PBMsOlOIT8d+t2nusy0EiIsPpcbPtyoP2wi1AUJY7AQ9+P36fm2D7cAiC7Keft51V8Aqh9sgQsl16oTDIQKvxXjsRHcjabq6/XDxstqECMMwAzb322PaMxQ+OeA4CpVx0bQeiPmUMajWbfaio2I34Ml3gy3SgBL4PeECEegdSSvr+gc8Z68vY1WA+YQOJBvBN5uElIo0ZPfmTvkwOOpoqYF9AYozEl6HssA5gWhiQ2W1dj9qvvAALA+cwvpswegENrBqpbY+ca/esAumuGn8IS6Cu2W1AFA8twyUgIqfPgPcIMOt7E/GXLYsmnD6eQwJSxvSykV6IzlgN9thzooxE6TRcW3AAPlK1vjzfrlmX5PwyOJdfFj+HfTBZLyzbwdPRmflDwCTWBeuf6Vx8cP+rky82++ybs5mo9gF7bDdOHTfbHu9AgGTjQJFM/Hp09pDJoi/jSIiAABx1IPug5ldyus/v8U2Ijy3YFu3SHASHZJtAAV0hfnBLbftMEhncK9pIXL1h3R5bthbfj8jmHciw9cftb47n7GRNgRqK5unJFNrwq/BezUDKlAKEzfJlRCxnhvgyFeAKEV+GyksevoyIJQHXSRwPsl/El6GAxm1hEDn2AVwo5SXCyAU0xMCndGu/Bd1KHehYUSJVeSjNYD0dShGErJUGkQhE0lKqfEJMeOLLRLBqTKYhuKC6Piz0tO5FsWInZiI6Z2tQ9ttrf/Ngxq7Kv1B/udmWakN7sMqm5YEPMQB5+vQWJMP7oIybU0ECabhc1LQ3vgkaPC/K2RbtJ9qgJA1E8mFBkSjHgJ8EKbwktKdT6SFBLuXQDZXqqe6zImQvx2xAQ/LxS8t28huvQUBTAL7CGHDH1CLjGYhQaaEAnbqSgACPWnCp/V9LDlDA1IfrpscFEebL1Hs249EnToqeJGGsIIIxdQhRuYYyNJTNwIlegdux7bNAx5alwRJAGjNttQ0ds8mlHLZReWnTFgYXcKDixegFNJB9oLptcgUk37EtMv53kUo9wBHoWK4v1qzztpEDa/1lFTjUV8G8DjuaIA0Orcutth1UyrZJQbrKWfwi6C/93ortCimvQPr5p+yksz9t634nT1lFwkt79ry6yjOJ6ukCfAgqJaE5JY3/QBLXbunp01AOAmLs6sX2Ob0sa60g/tuzrzbbCs/bVWhnOv6MjE/ZIKreAwIwZSRQbMluos8m1b3qzNjzvGrMvgikBp04ZZ/7dA0IwLM28Imm7ESsM1QrTcjQAFeUFIBTlPkESYfMCpTlGvHjIL4MGUyWnYJ5ta69lgPIpumhkkjNpG4+Dsa+NO4uAelnuQuO3pAx1pyZHCg4l9Pg9YX2BbDYgQCMMjT1vvaUghZt8plylpe2ZGGwyzFyAQ2tKHBQASVOKkpqNwQilVKGpl+xgxuZTlKLti5ziYiMF+NR08ockDdoEoYWS1pt9yANnmlAxkq1115esIPb15+1uf0Xd+1A07zIZxCaOgVkWSD1JdSERask0g/xus+SQGO+bM9ruRefFAunUO3LbGpBh9cYlF2++4zlFL1k2U4oy1fEj+MiTdQQkeUOTOB2/MeWZEK6SYOsCmjAbPRQ0YovfR/UoOlaJtrQNbXHHnB1wj6rWoulWwcFYORO+RYKXSjrFCArqzOO/SJ1NNnPHSjaDCkBXbP70Gmnsm4k50B+TEQA9vJlmhBUE1lWc2a0i7sI82WovOTmy0BLtiYxe9uxMaChJoURsDDYLEYuoCFhLzIVzMGgMkxDa2o1/uC3IDhCMUkQvjvThPZdKMXUL7IvyJ5M/KX0Cp0JOPviy7EKGSvIgjT2x69RCVZECSBJR2lIjV9kywzU4lw4be/LoGDPf0pliyj7QBOud2CgMuJEyabnnm3GyxbFM+BvVLWBxMxFy2ZbLYJzOGkPJNGxwUpTZUKIlP7Uos1+UUaiAy3aFAhimVK9V70p+yyQZsnfLF5qthXnqJ8eOmf22G0HK5Ch0qvruk9TigjASShHk10GlZmTisDdrYBBIfBlqHOyCyUQLZgnsk5XpBo/x+H7p6EdlMr628mXERHJqIyrV1/G245Nir/UgaVbsokvs1n7ApHttTDYbUHP6AU0wHwnrx5ogMHuC1EaNpTtAT8+SUFrI3XYVMCUr1e2L3haDZbU0UQlgCR0WdDqB78POkWoq0cjUwNyMqTQZ6uWL/N833IYaAIgYul4QWWxgOBJTuNYTgFQmaEAg+p8Iz5oFyBo7Y3ZZ+FQ1QrrnYEALwdlSknaa66ziwVIJbZbdsAGbitmaChdDvQNo3KdqfgUWU+t2jJJZcXuF2XsDaQ28LGMndgWVYYqBQKClNGMss4WkxbwZdobzzL9AvwopIo0B0hEpOucYImroTPcRLKtUI0d4OXL4LEB0iqgORd8GerY1JwZohKgO7bHvmC9bYRdFqx4MHIBDbXyRU2fqSB5LWVL8RekA2TiLDx/OfBOaS7bCTbRty9lZxoInuohT5FqLdX1SYoeaue5BrV8E09FZaygDkPWDd0Ju9+RyWfNtm/XrUCcNggVEalfZM/hClX+OrFoiUyQUOIgDS00iFRqZ/CnT8drKodW7D6rl9gsC3V4fat5qdlWfg6ejxKQPmfizyB23KzCQ0OlSyDbJ4BgTdkdTZuYgdIP+fmQGvT0on2v+mP2WlIbOJUjvrccv1cpyOCRWCdlPrVOiohIum4/nKnDIkOJ5nWge640Zo+/ABEklbbpnaflu+bMTOdtNqaasmUuL1+mBuRkD19GRCSnFmdj1I7t5MsQiC/DnlLxsYzsC4ia4LEvEBkNC4PNYvQCGvKhgUGFeC+tafvQFFSb9vIySNbDVc6DcEd7CSYPWD1Ek/bgdPkEhC6NjLsIdwIMIf1MZnh6ZS0ikqzGZ6z5th208kugAbLH3oMrC1ZA5A+f+WmzjVRTW/B9esLq1OzgCWV3LtUBqC2XEC3EfzfVsRdXl+5ERF6St9fjvz13ndlWOgWr8kkbLI9PxycjUi9NrW5MDBXhgIa6oWju6CrOzMUVS/x+vmdncFKDTq3amlb9cuiqm7IvSBretVo9ft0g4YHcqSRkYLUJpwiXttMtKE3l49dSZ9dERPaWfHyZWsdOwkM4NnruC2ohNpPbPF+GAhrUlyEPOlhMFVU2lMpLlD2i7B8F0FReIkNJzZlBvgzwk1z2BSKBL/NjMHIBDbXBZer0IAEBeMzuV1GrAuKukNaLLhGJsKLpIG+/rzphV0V6kILMqgyAAEyKInQOSGyGNlHdVXGqDpozq3YAWbjYXqT9GV9H0+XUfQaminrgStbgxjgVb3FFBJocVD/PzW8cIREhejJp7/vjp6zuyuWLdtBeumrcbLukGr++FHzSu4ElOGjRxjIlQItCXlSwfJ/vN21nXMF2rEtiAB16ENzuHbcTMWUTe4oEDJJVMoB27xQ0H/SaQKyHTsFk335fa1yRk8FpfCpvAxpSnyXrCvIrozbzaiH+fk/DCWQE+IFDOw4sdG2miPgyaDMC11dzZsZgVZdzikpReYlMJhsOT6ZttS94IdsURiHoGbmAhvgh4DeH6NtFrknTo0kfvaNkTgmEyX4BuCBAxNO+SiDSKhG0aOPqB3Q10PMJhEQLasRfrtuLVqGWalA0zdJyfgkGY3DoTYCmiq5tUwsxZh9oAocbSIRz6tDQcwDxh2TCRpDUZdFbIAKwfZDI02cyF9/vyRVr4kh8SeTLEGWL5g4ax5VWTwGi8dNN0i4iuWbo/gG+zEXgt4AqwIrjQpMCNLpgJlg6pC9jd6PJyXBmSvbiEl+mD2kWaoLA7ADIGlQUz4gUdQnMl4EyqENfRsTyZURE8qpNmywNvHwZIgBTyYn4MTqIZL7MJu0LREJ56cdg5AKaAaRWMxBIEAG4X9lYGItcdsmUjlZO0O2ILdqHinal/oNn4ytYCmiSYMJJqU/s9IHMRQ/8JKcVSfD5ZRDcgTdX8zlEeBAsnLbHS1ms6Sm7yl9SHRS0OqY0O2ZoAORhU2vZgKO4HP8+8rs6OGsdyecG9oIXnyEyJ5T0bCLHyNE/VDtk9qFgv2OTZDjRE1+GyjPaZT4PkdDJBfsc7ZsHrgkI5lGplbgfJ8AINq1UvtEqhDoFAckGjT2gpgy/0VHZ4fyYvbikNH6mbQlgXQho6P6lQTdHd8KNA1+mJ8B32oK+DC0yNF9GxGrMlJ18GVoodLwO2fBAa84M8WW2Yl8wCpmWzWLkApoIvGSIH0IuyVHFDrS6PkqDeBcm/jboT0zU7dPbmLHHO5G1EViiplRfqeMSRLC6IGMPyuj4fb0KZCnU25ZZgnQrTPx791oywcmeFSQp2HleulX7GF+qyikiIqfUKp8C2R6Y+SHpE0CrxuaqHQTHV+PXqDVlf+CVE5Yv811QAC49CyT3gh1kO/vAEFStVjsrdoKBKhr6odFgTGXPPrS2T1fjNwIniTmb6csu2ZetOw6+aXvsuZdh9b7QtDdfk+sxWwcBzQAm5swqlLubwGHL2Xe+q2KtybIdtJADBJyUQZf4MvY50nwZEZEZRfqhlmfKZHj5MjT5E1ld82VELGeGuDxevgwtpqgk6dGYcfNlNllKWg+jGPiMXEAjbeCHkKXBFAw+ICPeUgTaDKTZSZOi2wZdF2jXpNVwBtIl6dX4S0OTDhmzddt2hiHhNCqb6VKBiM08ZVfsdeyVoQNpwire/l0DJPyho6mxz37f/sKy2fbo6fj3UWt+G6432WV4EdWAuKqckluX2mfhCojcvr70IrOtdJp8vYAAvNemozTJMbns1FgBHYJEDwZoEpyDhN1MKX5sz4NqbX4ORBDb8D4esuc+NrlsfxSwCv5t2pqNsq0JEMwjCw3QmGSTScjKas7MdMFG42RTQYJ5xNVIwDM+VrAviNaYobLwIkgJbIUvQ4KErDETr995+TJt0HIiAnAdAho6B51l8mdjnOWlEQxUvBi5gIYGXvAww5VkGtKcnXb8gSb5CTLEFCh9keEc+csMIAera/EU0BAROQF1fSovEbFZgGSs062QkUavnr3QLfH3Nat4m26C2uqYvZbU4dBWBM8ykC+HpDUEq1cCiX2lQGckMVDaRdCCS62vJ1bGzbbxGmjH7LGT2N6yLbGsqoc8Da35zCmCgMYnOC39AkycqvtsoWNX81lbQRQZwEKhYn9Vq2iLsL/OABY7ekFPgT1JQQzJhBMCaLpulB0eKo2ZMmjm9EiaH3SxiL9BXVmkMUNlHI3t5sukyJMJbA00Z8avLwM2EnCjiWNF1AGt+It8mVBKOisYuYCGOi8wkICBsQgZjuZSfFWHDyVFOaQ4SjogQA5d7YFfjZqv2pbfKQUYeDVHQIQJwLDokiSUsFbb8YELuJfShlX6RTlbIvrS/EvNtgNt6GKZAb0MOImkJhSTlgxMuDSBE0i6nEQEI6WM25m115F4JHOnxs22qVVbqmu83AYEP1G2IoUnm/HvA4FXDGSxRbvuc5wejG2s//L4og1kC/NwX0AwrwXP/ZUl4lPZjAGpYWsOwwCyrQkSrIROQbIKoWtE3ZQ5JYdAfBkaF9pdXxYE+TI5mwXSnBkyCF0Z2EyXV1+GomAKXsYydmDRwZaXL4N+TA59GRGRLnUwqQAGDSaDfcFZQQhohEl4RABO0OJdDVxIQIcJIL0M5GEYe8Ym7Ep9Doh+WhCOykHk7Ev8IQKMUUiCbTXiL32hC2U0KOeRgmfnFBBaxK4aoz3gAwUpqqxqi0eCJ5BG6L4T+sBNKEGZoa80Rcp77E4k2JV/1j4giT7wrmylznAfRET+5nRcpBC5ZHQLqEUbOuMoGEpB91lKjeQL85Z0dskCENpL0HWyx16Piaw9sceXLEs6DUGZnv+GsDiBxCd+F+nLDEHLiUTzxsvxCRwNJskx22EwKSKSz4HdRM5GuJqXQsHAAnQLrDr5Mim4mKS2TRlYfWy0qGHvJXtsdQheSIKBNWbUNlJc3kb7ApEQ+PwIIxfQUF2fSJ8kkkZtdabFmSY/yIxgezeUiShdTpL9+ryI50ArIrQxodZa+L4sDD7dTnxwwJQ6GHNS+3gWXIejjN1WGbMTVg1qhjoDge3HMGFhCy6AxMlIv0eX3KbKdiW8OICyi01iSZSGVm7QKCkCW73eiF+jKlAOcIFPlSmyQ4DP5sHM0JRKIFOSbtmD6xeB3AoBUw4mf5pg0fZCX15oH6QVODUHpCC41wrAIiJ9mzySCjH1FYjPQXonVCIjI8cq9JTrrEdjCGRfzGT4phoSzKMMDSkgezgzxDNqo6WBL3jpwzZTTvK2Xge+zJYxcgENlYAHOchclIBAC/Vo3QWBXBMA6U90wVrhYMGukr793H6zbUzxCRKgU0HtmiW6HhBYUaqdkFCqy5QFSU/ZH13s26xT3vKEpVux53BoAsopDVvX0m3alH1IQuo9gswLApRxyZenW43f55dW7PF/t2HLLqXnIetWtoFbctY+XDSQDxZV8EmiccAlo/gOdYrgs6Rmq9vpc/MQGLbtOdUP2qCkOglRH2C5ZqMGihnMIgO0hiKSgoDyHQrmTUJAAyaT00o0T7uAi3CQxgRgEMwjk0kwBE2pGhxlEvX9FGEuDxKAsR3bBsFkYUBlWnMclKFBcTy7rQ0dTcQD0kFk4MucO4xeQAPPPAnm0Uqy3bYPtM6GEmkQlS5h8KT2bkqXd5btIBKpukgWOrJI6h/bzEGILIKMFWVVtFgddYXoNl0RkRPQXlRYgO4zmAAuLtpJ7KvPXWa/T3EYWnshkIUyWhfIooQUSf3DRK9PdV/ecjy+cuoKs61whny97AU+OH3abKO22ezixueFgSyl0CmgqdrPTgCpSrfTFyCQJQJwE6xILh6z15IsHfqrYLoJAZ2Js4lPBfYQJAlA4wCRmFNVmMAVz4gk91sgBUGrfjLGJad1IqZrzgxlEt1+TM5sTBk8mYicrIMt4ssQYRn1ZRzt2CLrKP6qa77d9gUhGFofIxfQYCspEF7Lul9TRBpL0Nap4gZKF1PbHmTBkdBI6fL0Mmm7xP/OQwq5W7eDD60aB9BlQTLofVqZqvmKgsVLy5bP8Q81qzmTBRfqxSvtI7sHFAlXFu1NLav2fDIbpY6KBLVdAsgQlEau7oRyLIbB+fScJVK8eNlGn6svt+f5ijHr/nmyaTNWunOISnBUahSQyScMS6DmCg7IT67EA5rxRciCgJoyEd/3Fe2ztQAZA/KoovKoJzNJnWxpMLeNUiBhAIuHKpRQCyr7QJ1glIEl5HL2HlCX4Rg8l5ozswTCTZQpQkVymJm9fBlSKNacGebL2ECWAl4MaCDLhBozpuRkd9msfUHAj8foBTQ4aNltGRBJEyDY6e+jScEboZNbM7dob2yvkIXjTzq9dWgSS5KJJbzMOutLZGKt6Cki8g+LNqCZAM4BTQAZCPoS5NOkMCyAng/u6LtuyMGAJEhU2djdN7EMBOAetB+TpQEILz5Zs15Ier7Ccim6aPvau6mtnyaxtiKSk3ruoGAvZG8M/Hwg5fgUiDlhcwBJg2jODGZbITDuwTmQ+jgsgMo5ew5JNdDQhEvvI/H3aLFDQQN1CWnODGU3iC9DkgY0pnj5Mh6HbPJjonZs4stgOza2X2+8LdgXnDuMXkBDC84yDNrkyg3ePzqgMQOgiAho3xD6VRhAYPVAmhw6E0It2mg0SATgog2GUrQftKbqcYaEAXX6XESkNm8zDVNQZujsBSE5GJDIAHKouANDICfTIinhzEig1D/ws4rj8cCEykFk8UBo7gNZf/B0eG7ZZnwqqgTXnoTnAzJzyaa93hQMZYvg+g0TRXJRBTSr0PE2Afy1afscUUbzTB26AoHDhiRx/T5DiYG6w5IUjJdBAbhqr+8eh2geOmZDQJOAoIG84OiZ0SUcEcuZofb3DrVjA0jok/gyVbjAxJfRJSbqwCIVam7Htg8DE4AdAnmBQ3POMHIBDWpjlEHpE1oKSXhMBwQ0KCZhQqSVe6ZiX+bFjh0waABtKJ4wrSaIqEgEYIGAhpAgzoh6Ub0dTel5miTtgFeatoP9GSAf5SzP1giWZcpgAEldIc6SE2VoerAC31uJ34hnWzbYIIuHYRFW5bPUpmbRWQD1YHX6lC1IAGeEyqXEHSsBD42k+HPz8eub7IEcwBSIBU7YSZhE0lZr9tyRDA+ZWh3QJUABmPgylAkm0n+iau8f8eZa6gI3ne1nqay9WZpgLMKeTKwxE39Iak4/Jlog5uD9rmZtsEXlJQq2Bur8We3XV15qQ0AzdCr+mlMN7djnDKMX0JDBMnQ0UQskrupS+m9nizZc+XLJDm5nmrC6hM6ZvprTO/BCos4ITGLU6UMvcxIGd3N9obxCWafcAvALSnZgPDixbLadAH5IbgW4K0qwrFiw17u2Yi8ITeAEIsaSCvBUIX4jflCzaawiGC92J+11m92zYLatwE3NQMCYUDoE9CwQKMAjrkkp6/NLykPwqdG2FTO5vGxTlVr9WITtJ7CjC4J7HdAlYVFD7xWNM2TmWqnaQYXKZnOd+Ie9gnnEl5kCfZlKEtzHIUqdV4TDVSAAe/2Y8mm7AqhA6Ys0qlJUutRBHxCAG86AhoIyJAB7MjShHfucYfQCGsqMwEvfBcIrrcD1qo41OjbmvIiIFMAIaqVpB2hIKMlQ8RWIwFYmkbsJWNVBW2evBSl/B2ckW7A71SGg4WDLHht1Y3x/xfJv0i3oipmJf18BeEbRFjI0BFr1a4n2xbqNJPaDxUN7yt6DWVDuW4a0EGUR9KRL2kXYjQHZB1OaEZEMeIo02zZqGFelL9TWgWCAVvMrXZuNSVIm0X4ddyjq74LFSbLnIwBTwDieJ74MPLuqLEKEfNKPorIO82XgXjk6grx8GbKNKUJAQ8EL8WWSkKHpqsGHArIOiOMRX0ar/Yqsw5cJ6r47CiMX0FBmhFQy63U7E0FFyA60xL2h1SCQZclB9lRt3B4HvTDK66XTsi8zdINihxcNPl0UIoOVutqtCGWHOcg6ZVdhxQWcjn1528Xyv586ZLZd1IYBbzw+4o/DYE9aMk5LGFacBqn/tJroO2egrNiwE13jpTYYuLxsO5r+bsVq2GSX7bHpzl8dFIuswxEAkBAllRk6y8AJq8V/t18CUTNwzB4H+fvvrtjWJ+SOmS3rBXTxz1InWwoMJsmPqQd8GTKZJKwozgzyZUDoEvVliC8DUerywD6XK734wNUifRkA6svAeFeGYMvDlxER6UQ6QwN8GXJyh6CMbEzcJpPqMQrt2OcOoxfQQFqZPJpWGptPU9sftZvIpI86kxIrwJuAxZnWneku2IAMVXvLdmMG3iwysaTz0gENlR3mV23ZYQraXFcut4MF6U8Mz9hJMgFqVl0QLNPA1TzJlAOww61sB2Ntcpc9Q1LVIMK21+62N2MDvL9cvtJsK0DAaDyDyPaByopkAQKfHUCEl16iUmj8GrX22Ge+OGkn4TREmmdqUKKlkhDZNpHnmuK/pSH+oMxtpwpZ2XG74yT4JVHXTaMbH2hock2Dt9okBDSTKWcQBQHNcice0GyFL0PNAZvly4hYjRlvOzaRmCmg2bSFQQhUzhlGLqAhobcsvGypOryopDGmVnXYok3HAQENkWUzNVB4hSBKt2IOIGjAUi5wXIZUA4dWXboeg2L8DaeyQxuEARPknDxtP0vpYe5ogkyZYsFS10ISNEW8AxLel5IN6JZVWSRvaTAyzEGb8iy1r9prtLpg730FSnCNWdVeSiq40MmGZVuYTPUkLCKSW9q4ZEOZuf3jli9DE39rFTKr1H1GfCFqUVeBPPHoqH5Fmc9CxU7WVP6hkmGjo68lWIUAAXgP6MtUUj6+zCJ032nODI0V5MdE2eet8GXQ0VutVuvwQhI3koIyChgpWxlasncWRi6goZUZgVLL+OxqErA3GofVIClRkqIwZZnSqj2Tjh8neSIAk2YEZKfwelDbuv6uBgwgRNaGLiTqUoAMugzA9C+n+Dx4vaEs5wU9W3mYZHTLLXaf5SFwq9qHgbp6kqDBkxiStovaB1r9STqfiO9pyC4ScdVjhkp8mUlQGKYVuMCzReaRMK/hM6g7FOn5oAAP/ZiAL5OBg9MZPBEOvjWyGXsPKGDKkmkjBDR0fXV5ht72FGnfgKCily9DoAyN1pjpOvVlKChjh2w4kJB92VEYuYBmkAXxOnigkUSJZoaqCwJKFjTgUXq/ATwVSnGT+m5OrWJ4krQvaQG0QrRjtohIGvgyGBwqLgUNIJh1Av5CFZzGn2uNm235ZeBqjNnfmCzHv49KXzDGYlaP4O300b87vWwntc6EvW4Xg0/RHCgN6jZoEUHL8J7SX3IHNEQABo4EdYxNQ/fZIKf0Q6btPnvyNmo9Be3uaVAARhFLKhVDJkAvDFIdOH4Inrtg+7C3ZF9KIreSdcBAkYCJLzOWt8HLNAwEFDScGdoochEyRbqdmQjAXr4MmV96/JhEmLCs+TGkL0Pt2MiXgTlhOy0MAl/m7GDkAhoi/tFKnVaSsHCSSHUEJejlgMwI+amstuxLCmOUNGfttrR6Aen4SROlRBYPi3ZHIsaiorA6L0rxUkZFO1CLiOyrWH7IydVxs02TSkVEVg7ZezqrVvnPnrLt3uDpiQRuwhACGiy5LcUzNOmG3Wf5Rfa6/WTFEoCfbtiW75yNe9hwVPGnUjA54X2H84R4SaJVew5E/u6r9vzhlE/+/uH6QbONAnkqCdE4QBOWnnMpU0kWGgOwLqcOPcqwsWie0uqB8uAU6MtMpu0FIW4TmcN6NGaoIwv1ZYDAXUzajBXxZXT3kgjbGujs7dbase2mYGGw8zFyAQ2ly+khp5V6H2T3E/pdoJZWWDRSazR5sUDzCGYM9CoDFkRoG0D8IQEiKL2kKCKoSl9tOCcQA8WgYSwDMvbztkV7L7Sjw/hsSdcOKwsRLkUQIigjDmE2TamySHIA6sdQdqGunseW9pltGSBYUxZBVLnR6wpMATq1r2qjUhEWzeuMx69Hoeyb6GqwAIA5UmCxjedApE89DqDSOLTmp8DpsgSWH8QDoiyCzoTQ+EGWIrmEr0MIO4LIXkHL+lNAA+WlAtTqKBtDfJke3ECyMNCGnaTFRdl4eu4DX+bCxFkPaI4ePSq/8zu/IzfffLPcfffdIiISRZHccccdct9998nS0pK86lWvko997GPyspe9bO1znU5H3vWud8kf/dEfSavVkhtuuEHuueceOXDgwNYOCAayNrjUjoF4XWsGHl6VpqdV3iDn6yTqQGdVEsiygxJ8VgUOeUiNk7NvGmZwJMYCqCskowbadssOlCCOKi0QTqMuiDYo3ibAYLMzubGPEBkUYuBGDssEaHvuQfYvuxS/vjQmtmegBRfSbqcXbZQ6A1mQxiwEF4rIO+xBVxKl1OG+06IgU/NptrSVFtJs1WbmcMIFBWB6tohqQ3wy8qjSiSG6V0QAHhuDjAQIN53p2A+ja7ZCATKr0yCYV4IIj/gyC117HM2eveaaX5eF8lLJaTBJwRaBsjHagkFEpKluNGnO9CEb4xfMs5tC6Whn4awGNN/85jflvvvuk5e//OWx7R/+8IflIx/5iHzqU5+SF7/4xXLnnXfKL/zCL8gTTzwhlcoPl6a33HKLfPGLX5T7779fpqam5J3vfKe8/vWvl+PHj0sq5fMKIdDKrNuEQAISF30wj9TAFT7wdghEliUMwZpAnwNUOlATBTMIRIimVS4EahoDZ/t7dxzKVxBdZBZg9UpZpgk7qOqVL1lZYHnC+ZYkgZRpu1OsF9cwBxd32mdp0D9jJ3XSRelWgCemBCXbLVDZpRgeJrEOTMIlG5eIJIHMqapm++GDyz0IZFeA/Ey2DJCZFNKlI40Zh4Fnb8w+pweAL0Nt5rUelHVA20Xzm4hgzHwZcKwf2OCFri+VizWyJNyXhXZs6G6gDA2RfSkAazkySpihQXdsXwfnZktJIeg5dzhrAU29Xpdf+7Vfk49//ONy5513rm2Pokjuvvtuue222+QNb3iDiIj8wR/8gczMzMhnP/tZectb3iIrKyvyiU98Qj796U/La1/7WhER+cxnPiMHDx6UBx54QF73utdt+rio1i+ggouu3ODO7HJiplIEqWk2qP3Yfl0KWmSHNaVTQXP1GGiiwKBFJotERMY2X3U9qOxAGIAxp04hi4jkoMW5n7e/MTZusxla6xWW/QAAYH9JREFUQwPoBeyOTWkKQAYCmiZlqBSHqFuxP7p3yvoBLPXANgBa1mkpieVGVR4kzRlSn01CuaMPiwJv95nOpk1n7Y357qoV4cmsbOwlJrIOqdtBABaxGSUi1pOp7N6CPQd655eBL0OTrr7mE9D1NUEdBAASzNNSAiLraMyov8kduwKlL9KPQn0ZLIeBYjEQfnVAs632BSLBwuACwFkLaN72trfJTTfdJK997WtjAc1TTz0lp0+flhtvvHFtWy6Xk+uvv14eeughectb3iLHjx+XXq8X22f//v1y+PBheeihhzCg6XQ60un844tUq9HyUHAgo1QzPruUafGIrkHJggYtUALHgIYmFFHnQBkVsiEgUSls0YbOFs2XEbE1dpKKR04RcA7IIiFDFgkF+xvVAjh6t+OTB1k3QMzg5tBQdqffhtZlVQ7sloAQDQqyi3BwoKsnEWRBtD4QAlu07W7w9SJtINZTRxC4j0slfiPIMXu5bSdcqGLge4uWBiRNAM+DXthgdxQQ3UrAGSECcBt4KsTfSCuyfRn4ZVReIr5MHco1bSjPkPy/5sxknXyZLKTO2I8JOEVA1mvBjdAdlVReCvYFuxtnJaC5//775eGHH5ZvfvOb5v9Onz4tIiIzM3F59pmZGXn66afX9slmszIxMWH2+dHnNY4ePSp33HHHxgdHjrTAGUGTSZh0o3p8QEItC0jRD7qgMwKiXbS6JEJgsh7/YfrcGEzyy+AjlKXACoI5Og59Xtn2xvYIIiLlsj220w3LjM3WfBYJF0HHx7Nn4s/TGGSiOrbxCQNSAhEkZRU8sNREX99vj/9gybYqPVmzsv45aFmnAG8Irud6IGdXeN+5p+r2wU8BD609Cdk01Z5PnTMLNRvM5dwKwJS2sZtI80kfCgW8pTEQzAP+F5WX2DXbbtLCmdNZG/BS1xCVa5ag3bEOkhGUUdLeUNSOvSW+DBxvHVjX1JKtNXKQALxJ+wKRYGFwIWDbA5qTJ0/KzTffLF/+8pclnwf6//9FQtV+oigy2zR+3D7ve9/75NZbb137u1arycGDtq2TGO00kFFqnEwse0uq1AMTgHbsFWEFVhLtou4fugLaLJeEvSagB/zMnNXyIGoMefWkaWxQAQ3qusBjMQHB1tyKDWj2NqFF+3J7LanjY7ASv1fcim63eQMaXFnDRK9F7jpT9vupo+mZpXGzbZoCvAngy5Tt92mxNuSfQHszpe3JLyk5AH0d+7jJgbF4mokE3TqgLg0SSlgapZIhBW/wyBibEeo+u6hsy0s0ga/27cmjaza8V1peYU/W1vNIMO8MlJcWuzYqI74JQWvMUKZoS3wZRzu2CHdgaY4c8mVImmArLdoBOwrbHtAcP35c5ubm5MiRI2vbBoOBfPWrX5X//J//szzxxBMi8sMszL59/9hyOjc3t5a1mZ2dlW63K0tLS7EszdzcnFx77bX4u7lcTnK5jRXQyDmZOCM06RJHoq8GRmxlJsNKyAqh1xIcBwU0elFEK0lyt01ABgGzTKQoTClpJSzI5Gq7rQDH1lmyJ08WCZ2pjTuaRETSKxuTroknFZHgHIAckKHxxJRA+tOQjodaJppYgglnp2pvYCEPqsvKgJUUdSkYGADXpkh8JAcBWERkthCfnOdhwqV7R88W0C1wkUFZWQq+h2ph0xuzF2mP02CSeCr0zFBJeVx5MpG+DIn0EV8GicgOvoyI5cxshS/Tg8GSutkazoBGnwPaF8C20I69e7DtAc0NN9wgjz76aGzbv/7X/1quvPJKec973iOXXXaZzM7OyrFjx+Tqq68WEZFutysPPvigfOhDHxIRkSNHjkgmk5Fjx47JG9/4RhEROXXqlDz22GPy4Q9/eGsHSA+003SS5N31ogjT2wByqqYVAAqAwQpZD+6gicWBlZPjQkJelJEwK1/K9oMwGx2b1msREYz6ojJ0fYFCse56xs4t7FO2mwjkgIzBcib+hRmweCC+RWoVDhg0bMCCR0pQ9tRt2klsaYLsovM8ibtCZqi6RPG9uu3hTzd97wsrANtN9P6xiKDaUALRuKzNfhG5lbqGMKsHC6eyEm8i2wDUl3EGAwN6lyHC1ZyZLfFl4AUkfRlqvyYFcq3FtRX7glA2ujCx7QFNpVKRw4cPx7aVSiWZmppa237LLbfIXXfdJVdccYVcccUVctddd0mxWJRf/dVfFRGRarUqb37zm+Wd73ynTE1NyeTkpLzrXe+Sq666aq3rabNIQKoZ1T8htZyFwV0PjIMSTfwwATi9olCVFfRC9DnQSpI7q4BvAZMCZafadbBI0AESEWXhGvXhGmWXgX+TsdsK43ZCodWwJtDSeZKWjDfVHEHmgsqZPUUCnq7a1fYZ0AXJk6VBym6jFvhxmJwi4HFpoB1CA8QSwfyyB1ye5KS9IHpSfL5uXz7qSKMOLLyncAokwIcZUvUY5YB4ReVB6tAjs046thz4f02pVJ9XX2YJ0qGoL0PvH7Rka84M8WUo2CLQ8aK+DESpHWht1xnjrdgXeBECn52F86IU/O53v1tarZb89m//9pqw3pe//OU1DRoRkd/7vd+TdDotb3zjG9eE9T71qU9tSYNGhAMaeqCpLIKmjapSEkEmYwABCCn5YsswEFpwIlLnQC7atDIj9+AutPjmYYXfguPQAR76WJWgvRkG2cyK2YQy81MVm/Kfa9iAQHdIdcbt9yfAkiKCDh5CAvYjXpT+3UtLlg/xTMMeHFka9KFraAhtxATtO4alNYqhsL3Z7teZsPtNjNt7pTMLy8v25avAc0odgGTHgWVmCDQ9rtlTZctELsAEvtAdN9uaFNAAyI5kj2plJ07KAshjE18GlYjhONiTKR5IEV+GvKKIL4PlJeBP0bhFdjUDXTYL9gUjh3MS0HzlK1+J/Z1IJOT222+X22+/fd3P5PN5+ehHPyof/ehHt/VYsNQDIC4FckbUbglob44goMEUPY135F4NE6fO3mbAlGgVNC+wJAIZFEo/JzqwAtIlOCg7pICPU29DizZQE7pj9h4cAA7Ddxb2m21TquumAe3SxF+InMp6KejoolV/V3FDx7N2knzijO1oGgcTSxLMy8LsTxNAQr8L1J4Oj18aAprEEAQrITA+AMGb5nQMl+2LQM8pKfRSyZAWMdSyT89qrxq/5nuBLJSCm1wDoboe8GWoYaCSs0HCpENjZsXJl+lCdoNKvqQxoz2ZtsaXAX0ZyMZQqY41ZnSGhp7TwJfZzRg5Lyeqk9NATpkR0jXQAz654AqsiNwdNrBqNhOR2ExIPmdH7BZ0VJCiMPGAyFUXeQjq9FEYkMpXoDSbJ5n8KfubeZidBiD0ZjRF4Hon4XoTv4DgDpZVwEi6K626Pbgp8KxqTdtnku49+pWpn6UJnSYFCi4wuwFcHlKRXVWrciTsAhl8COVHlFsAnhh2dFHLt1rYUDs2mT16fJBERFKg5USt0NSSbX7T6cdEzzNJDrDGTPzZykM3F/FlGsB5oZJTF24C8mXQk0mdV2jHHjmMXECDnREkvJWnjiYoKegMDbX4UiaDWqOdiqZJEALUC5sKpK3nFi03Aag2IkUgmkIwRxkJc1xQAsgBubpZs6tLKmN0J2DghagstQSPtvoocXmyKDVrNxEw60aT5LjyUIIJMbFAxov2vmhjRxGRCZDFn1u2997wv4A/RHytlLP805+wxzsB2ajHl+L28dkVmogg0CRVCCqRwftCgTzQliSjODOToP9CBpPomA3vUA7e06mc/Q1d2mG+jI0gG9vIlxERKauH3NuO3XG3Y9vjpRIZKv6q391O+4KACwMjF9BgZgRKPVQW6RNnRHNgiThMZo8o0e7skKKARo2fBRiMhnXosiBF4SKs8ClNDQGH/j7s0oJJJ1H38VT6476OJiIUD3X5rgxCiaRTQWJcAK/mTqESn5x0hkJEJLdAF8lu6kCAl4cW+B7Ye2hHDnoWSEWbrTGAcD4O7s+wophbjUcSYEkkEZCfMaMJcCQ3RIQd2quqfEck2AVIRSEBGFDMgskkWD/kE/H9lgf2Nxe6dlHg8WMSEclBeYmyadogFfkykPJuYHlpc+3YIutozOj3NNgXjBxGLqBBN2Uqi0AquAtGgxqUukXSP71XxJeBHTHLpA4tTZyXNqRpIY6gjqZWA3gNjuOgc8LUO6k1U7kNske0qiPKge6QSgIBmFZ+WHcHYLAM80lZZVBq0GOPPlOgZIh8J3gGiUhudiNbEJIIgPMEyogUCxBUk5haM37/xpyEeROgiuAkhlYe1FFI6tqKz0Jmj0RkRV0X+M0CyHIT0VaXcUiATrtNi6xTJgekYbzT5SURW2Ly8mWoHZvKS8T12qyFQSgRjR5GLqDB1kwYyNLU8QGlIyRSKrhLEcRdAUIjnUOvvPHbS6q1NOFqmXURkfoClIRINE8tHCMw5tR6ESJWI0aEfX8qY7beMd8CjyMICHTnWi4PPCPgrlDgRuD7YreNF+LnQBYPebA06BUhuIAsCLXAY5ZQg8o1RHSmgMapoEsiaZoEnAbLBOpuI281CrZoQUGLmD7YQ+x1iOZ5herI+6wKWRCPySSVl2o9CmjgOGCxQ1m9yiZbsjHYwo4mKi/Zz9I5uCwMAl9m5DByAQ1hCNwB7OqhDIfahJozZK0ApQhq+fa2mWvyIolRUYs2NEZgd0MSRO6QB6QmmQR0nVDprggBDZFKx4v2JMgioQq6KK298WtJeh9NSDV4S06EPgSaWrH5+yv2RGfqPkuDCnQ0tYA3wRkws8l+DoJxym70qvZ4yXH6TBva6ZUKcLIPzwwsOqDSiAEYBTn0feRGvzcX78oiwUOvY3YOyNqTYEhV0T4mYjkzFNCskh8TZDKoHXssa290FQYM4sxooB8T6ctAQEMWDLp7SUR8FgaBQzNyGL2AhgJ78quhVS50sehMC7186OoMLa00+VOLNirXKq8l6miiwKptRVmxbIYTIl1LXQaA7xp2wLARFn5dWPVXwDvmxIptcZ6ADil9zcsw01HQip1xAAoQBqBirEtCg0USKISSJ1gaTBfspLPQsJOdS8nXKUCHCsCgfUOy+E+tTJltWXAM10ACMPHVQNyQAm8K5MsV+4KMqUmdeB8NCCTo5ShAQLMHvDEoaNAtzssQeJPYHHHCiC9DnkzUkq05M8SXwXZsCF68fBlS4HZZGIR27JHDyAU0yAkjWX/4LGVL9IINXzRqjSauHvFASbiWyJtKP4VWOtiqCtkpaonElTrxeOFaGlB7M006MIkhN4gsEgCDwsbLMzIt9Kaf8XrA9dUloTQQohNDMEKFAK+QAQ+sLhC44RmM1LxDXCHknxDnDJzok6TP0rKTna5s0PON7wuAjpdAjQBTYJCqScxEAO7AJEwPDWU+vToumlRL5Rpqb6bFyWb5MnRs7QiOA14E6gSjLLKXL+PJvoTy0uhh9AIa8ikCciiZxlGmRU+S5HODK0TH5CrCWSEk8ion8FbbDjRFIq2Cai8R87BsRl0mOkNDq37KgsB+ZN9AyCwT2Rn4SIptSvohdGzeNDVNulmwhK6rklB2Gb4L7nF3HLgPQPDpAoEbuNTmGlFpjYJgcrQmbhO1ozdr9sOTqupC9hZkAYLPFhlMwi3tV+y19IjmrUBmBIXqIHukCcYiPr6MiMjKIP67RCRH3g4cRxE6IDfLl6HgBe0LoMbXhUUX8evcAnm+4SJgF2P0Ahri9ZJdAfA8QETWBBcJSHkj54U8g2ATt5mTCFb8w61VytFbpGCma4HIHSq1QsbAXCSYJCloQKNIsG/QwYCISBYsEogjkVcmkG3IZHg5IwRSeiaRu6VWvN6Rg+Mf5OCCTPi6hqS+sQaPCDy7ELBjoAncpr1AgqJ29OQycLs68R/pgBo0EYApAPPqTEVjdkcq/+iglwIJJLkDT4X5MjaQoC6hJXXRV4EATHwZr77MZvky3nZsem9JX4auJbZfe1qyQ+Zl5DByAQ1K8UOk0gfNFi7/qFUuZVSIfAnCfdjRBIP2sEgkZvX2QhmGMjvU6dNu2cEHYgs2zlTHQT5IXmfmNOjh1Np2QgHZDuyKqaiSwuKKJahCg5db74SuRx4mlAVFAp4CAnC3AsdftZMO+nORMzVB3askiOgR+pA5m8xD91kbus8gm5ZQKsBUahwCvyzl5DuRL1u+bB9Cj2jeCgQ0FEgUoQQ3qc3EZB2TSegSWu7FT6Lt1JfJgojlZvkyIjbYonZsrx+Tmy9DGZoQrAQARi6gQWl00t+gwZ1WuWq3FMisezgvIiICZFkCDe4aWKoiET2YcFs1mlFgE+iA6GvpbTunNvYsdCE1QAuoCJYAtMqvqHOlLBxNiJ5uIBHf9RARGSiRuxQdPxCAybSQTD1J6h91j7SVk1OvhbKLZD9xsj1utlF7vvl+knuid4jI2pQNhbm/UrCTOmUkVlR9jYi3BOLLaIKxCPOM2uTUrUg/1JpP2E6+jIhIT00ZbdSccdoXePky22hhEAKh3Y3RC2hgcGMxvE2ucqHkRJN1Gng7PTDlI1D6Xa8SSXeEMg0FSI1jyYLGFMoy6eMgvycqo5EwGwQ0S4t21V+BUn+varflNN+EWtG3ENBEVEYEJFfiD2GqCx1N4/ZzB/I2GvjB0qTZBnQIfAY1kLwOj2SyYie/NEzMS6s2NVIiwUB1fftOSwN8R2ETtc7vhQPJQUCz2p+I/U2ZERLMI4PJCXBbpaABTSZVZuh88GVEbEt2HW5WHTI0FAhieYnasb3t1yFYGXmMXkBDZFEyXnRmWsznyMWXrBVg5TRwZlUSIFanfaaoDZpS+SnoGko3fIrCSQpo1CBFGSuvAB2ly6MalQKhZAO6KBopOE/mmjhHSjA0JYJ1RnkVURakM7mxfo2ISBOEAEt07x1lM8rQ0DNTLtsJsQ8PanfF/ijpAw2y2lOK0ix2E2aU4DkdgMXF3jxEVoAlZSdAgQS9y5M5m40ZT9mAlPgyiw6NGTKYJH2ZrfBlqCVbl8O89gX0HqAfk0cwTyS0ZAcgRi+gcUrxbzagwewDBRIwCNKKM4LyUgI+q8XqgBoj3TFfMIeqvcRxgSxTt6ZE0pxB2qBgz4kIr5kacYNgAgT9fN0milwTGjudb0kSJhQiWGvdlWHW/uhwwt5AtDQgrpeTGGs6RUhFGzJn09DejPYNy0CsB/5UO54EYf8vZwcWBW4ZSOERAbhHJpMqkKCxopC33z8BfBzKgjBfxl50XVqk93a7+TLYpaZWZ6T8TP5RyJeBexpRY0QoLwU4MXIBDYlxUeoT7IxYC0NrH1CLNmVo4Ksw5e8g3oqIDFWbObt5w7lTMEdS8XDuJOWuuUfeEg4FmuTaS+3jyL8BQrFOe7u1dcgGA0BO6z1o/8+p39UZChGRDBw/mXBSaZHWrhj0OSpk9MyUYNVPXSzpFmXnIDOp2rTpWDGgoXeNyqoQ3RfgISfuR0tlG9yBRNp+P5WXVoc2ECRSrYczsxW+DKGLejLx69GClQ7yZeD4WV8mmEcGbB6jF9BAxmMIBGAqHdFqVa9yvZozxOulFHqPujtoxiKfKQXieBAngIKGjhV4RZE7nWXCzjAUoLOTQhvUjsmjqVcEAnDRnsRqKz55ZOA8qRWdNGEIGQh8eg3qQorvRx1N42WbJtPZAhGRzCqscuHYKOgzwSZ1zIJOEZW+Tq/aC0ft9ARDGaHyJlga8HfZs58qQbYEotnndKpIRJrKNZv4dmUdoYrIVGbVbCMCMAU05A2lBee2my/jNZnUGjNkX4Dt2OSOjfoydrfAlwnwYvQCGhgIIlhFY2aByj+bXOXSigV/E3gZhIQKaLDEnIOgAUoiJQrmYKKghweF6RQoY5UALaB22x4bqNOjLsoEkDIX5uOTLkjEcBbOyaGhyS4BBGu9aG6CDcYM6LrMN+2JUnmQAkZ6djWBnYKeJDwMVPpaBcG8cQg+h+AYbhYK5LLuLV2C+/gMCOaRa7bHToACiXF41qopn9Cg1pcR4cBVBzTngi/DhpLxY3O3Y2+nvkxAwDoYvYCG3g2nASRyaNQLyNYKEEQ5tRXI3wnrzColjwKCpLdDrctYrgJ7CCJTO7LZOLlC0EBt1UhcBZ0RKgNoXyw8TwponCUnLxdLP1ukk0JZkAbYBsAc5rYJ0OdPgVAagmDiNg2akOmDdnSvy7wGWjfQ+1iwO1YzThVjiLR1OZq4b2UgBlFZxxs0dMESQL9rVF4i1WhvNoauB/F7dFmOyL5e+wIcx+ymYGEQ4MboBTQQqejsxjq7sYZNd+NAgjIjZK0AiRxJApmHxKd0yR79diALQp0oCPBNIO6RHj/pOGgCo24radrBnrJYRHamLEJqVQU0RCuBm+DWoSEuVoMyC6rkhJYGIHgIHU2UZYImGe6W06LO8CiMgV4LivmtQPdPx15L0tcZ6FIoBftOTlvOKZhHjtDkmq2DtyLoNtH3s8GkfZ4Xu/ZmUclGZ/8oYK9ADbUIwn2ofQPXowkPhFZ/bsOz0IcgBz3ugn1BwDZjBAMaC6+eBZMVVamHuAqQGdEkXhHO7lAQMmiT8aRqfSX9EHInJhdtmPzIfLAHQoAFNY4DHYAzVpTtadIsbDcNKj4/Ks03IW4MZaK8Sz+6p2TVo+eORNWuovtkNLgCnkGUsfLJGZmgnQTzill7bCttW5rJrsD969vrRjw08zw4xRhJX2ZPyWZjKkAK04J5Iuu4ZiswX8beZOoaWh1YcSTiy1DJRmvdEF9mHDJRXn2ZDmRjuCU7/nCRCa6XL+MuL4XMS4ATIxjQUFePs0XboVaKPAQosfTrPq0XSnGTX5RZbUN3FJ1SCoIGatEm1d5m3U4KeoKlbAyVnGgFR23VKFIIbbk0OaUVlQJLMxTQOFeNEdwXalPWJObymJ1wKQuSqflSRZRlQuiubWidN2KEIjJfA8sIy4HFd4jKa/p5SDlFLanVfw/wZUgwr6YE80REWiD+pjMj1SzwZYDIRCUc0pchvgzx69IqI0N8GWrH9vgxifg9mfRzScEXvcvuEnsoLwVsAaMX0NBLBKtcnP0pkaOz5WSiB+UUnVFZ7/uT9FkgSGpQ0EDnTgJ8lGUiEiIacTq+i9qbqVyDIoXOYIsmJ32ulC0QCCDRrhlA98XjVl0GSwMyH6TuMwoasKOJJgB9uCDYSKW7TsveBGgq42NDWwP1GzQhUlUYMkrjWZulIGBrNLnMq/ePuE1evkwLTl5rI4mIRHCvNGdmu/ky5MlELdn6eL18Ga99QUDAVjByAQ2tHtChl64MzQo6bU+aMxS7wOSHkzWViRwlMtR1gdUUVBRwoi/CRJ+CcpXGEEpmdB0jaJ0nnRiSxS/n7Y6LNbsarqrdOtY1AJ3Xhx1f33YSuFhEZu2prqYqGDs+t2LLE1DZwICR7j16HKnTSuVJXA2CC1Br1q3oIqyvQ91yGl4F4DR0YE2DYB5N4Mtd+5ATJ0y7pbNgHvCMYCDwdFGtB+0NRURnL1+mCdkYOt4mBH1dVWJiPybIIAf7goBzgJELaEigiwZQ9JOh79MBDUyI1CRDCrpkbkgTCtkJ6MmJMjQDp94O+QhRS3IKSkJ64qG2c+xkoDIa6fKATkwBLLL7q2DaqDgdVP4gsUDqXiKknFopvUr8OGjVX1+1D+A4tayDZQQFNNROr/fLAcOYSJ9pUGsmP6r2BPiaUUlPi1PCOzqAzGcFLBgmoPxDk7W2EoDDEBGRkor4iS+TBcby4sDeGG2jIMJcL/KGyqtnZAwJwJvzYxIRqYOcOZU9NWGZFknBviDgfGHkAhokHHpVgR1A40gqp8BxoPw/tQJDEDJQvAkiIhPHA60aitDeDedAJoiakJogAjCcO/EmkAhaIm4QaOTApGu+y6mtI+TqDKD5hDJ9g7F4pIaWBpAF8Yo9oiowZWjUvclD6W61bSd+bd0gws8RHhsFuGoCxHZ64IRNFX2Cec92LF+m0YUOOvuzUs7Gv48MJglLTr4Mlbk0X0bEcma8fBm2LwC+DAjkoSeTIr677Qs2z7UPfJkAN0YuoKHVH7ZoIwdl4xUFBhJORUyaiChDg5oc+k5SVYq6DwCUKaKBlybwgcqgEH8oglkeeUG00APC6xB2TIHsvh7bIyixEPCZAXhLl7q0Q6t0ImuTCecwQ9fNF9DoZ5yUn+ugfQO+iwjyMMNOQY/KNfB7SNAuBSdKfBnOjID6rsqMUBYE9WWg1WyzfBkRy5nx8mXo2HpQv2s5j3eoyklu+4KAgHOAENCsA+QhUBCixwty8yaVTJpgILuDejWYUdq4FSfhbE8ncbJuF1q00Z1ZZYpoAoPgBUtwpHgLUvxk30AWCXrMplZ0yqahXgbAa5ZYUlopVP7I1HyBCtlqYDBLz5vKllCmqFu3E13Z0YouwiU9EopMKK0e1Mwp2Yu7JwetVYAV4K5Qd04WNGamcvGTLQFPBTVtevbk6TklaL6MiOXMbEVfRtsXiLCFAfF7DGcm2BcE7CCMXkDjW5TLkDI0pHap3m9S4x00fZeZ5P9JLRezOyoYokmYyMTYZg4u2r2W3bHoCGiSmCnydQORISYFIY0OGCOSY7gaxzOQoenABA4NJQgsu4DI3aQiMS+DrgtYAWE2xojSrQNaNOv7TNnARM3e90wLAqvc5gjAIvZZpQxhoeTTf2kDS3oZnMB1pkFEJAeGklrbBS0TQKqagijMxAHBTvNlRCxnZmt8mY3bsUX4eI3GzDbbF4TyUsBWMHoBDdV8iW5BK0kg4+q0PZJKgYzLOjeQ3XG0RovYYIi6hpiIbL+LxPyGdbsjKu0qHhAFXxRYeV3KM8DzaLfsjrqjSUSkMx7/Owut6G24bt6sHoE4P1oUbW7JMp2rUNahbA96fdGEQmKJKqDpQNYis0rdZ6A4XQECMGT6UDZBazlBpnICBPPIp4gE8+oOwTwRkQqUsCaUMiKVdYhQW4O2e1TWhjKfR2NmK3wZKsE1wC29Cxka3SWKCsBb0JcJCNgKRjCgsdtQ44K8kNAOQe3jzEhgWYB+gIIh+qwOpFpew027jYIy4jlgaUBxHajGToRoAh0b8Qva0FaNZGc17+TpPIFn5DEg/eGOdhNxfnRpZwDZr2QPyj9lmDwgI4jPDLX/q3IgTWDgsYhBCQZbEBh72nep3DsGwQZlS9AbCZV3N+bLiNhMCHFSqIRD9gWUActu0pPJy5ehjBXpy/Sgvost++p9Du3YATsJoxfQIBkX9qNOESo5UWlKfxdM4EiOpNGBXIbheLUa8ZBE3pxZEHooSHOGOC561T9oA5nYJ16Kasd5EhpcBZIxEGhJKt8cG2ThvAENulwD50dPFEko66CUAJSvkIQO15yCT91NQ5muMnCRCOR4TiVUyhwagG/YdM6Wl4gzglovEFxQYEyifBUV0TFfxv5mCzIeBOLLeDyZ6NwbEFXWQX+CCMsUgLksDAIpOGAHIQQ04hfRw4BAjW+UZPHyQwg0waL6rproqbxEwK4h0r6BFm0SEUyrktBgBdpjPeRqsa3oIuz5lGr4bCSiSjyS2qw79nrA8h1wfnT3SGaFJnkIyIhkSyR0CsAoW6JOddAAcjURgFEwz3ds4vAOyxZtycUrmFeD4IIkB0qgzkwmkzmlAryyBb4Mka6JL7NZTyZyx/byZYgkTSa4ngxNaMcOOF8YuYCG21dhP4oH6AVUgzaqZMLEOSR3aWzR9nX/GDEuygrRXI0TIgQNThsCLRWPdgAUVFKARx5YMDmRojBmsVT2iL7LGwgSUM0WOD+6e4TKOmgb4PVoolIB8bPUJhLfS3Uh4CVtHcimUcYRgy31DObgmpXhJlM5hSZrCoKJP0W/kVLnQEEDdQjRs0XXg8pLOogSsWaXXvuCDtwsysZs2sIgBCUBOwgjF9AgkZVatAkOLQ8SmoKxk9vCScWYAgnIjOhP4oKOuEJkkQBlAbJI0BL+IiI5NXF6Mx5YugPtkT6120JHEyk955QVOLWiw4KZM3gAbNEGFePVVvzgoJoiA+hoGkJbGVqOOTM02gQxDYappADcqfoIwHhsFKCrZ3CiZG+o1zGbWuAJWjBPhEnG9jdthqYO5SUymMzDs0AEYDoOrUbchegZFZHhRSD1Z3qveHGmdzK7hCAn4Lxh5AIagrf8Q9AcBtKcQQ0Q6qJyajqgAab6bIZUZYHnQMcxBO0bEvOjttyMWg2jHQAt/IhyADyHPhCAC+T5BCWQYj4+eSys2ogM5hzkGRGG0EJNXI0V1RoODTx4/JK3NwFX0QTI0GiNI6jqILkaJFZQu4gyIzjZqeu2pwClH3TMtmZcLdB6Yb6MDZBIfVeL0JG+TNPJl8mCArCHLyNiOTM96F5y68sQX4a0slCEVGdoAl8mYOcgBDTi15xBqIkicqrxIr+AWoadGSXdnYOqtRQI0XGQcisFVmDVoAdGKgdReQnvAQU+7c0TaM2E0nR2gvluKXc00QxeVyUnKOu0piHTl7Mn2ofrQU8uda4NOvHPpiFTROdO/lHJDJCfqWOMjk3pAXkF84iMS1wQcoonk0kSzWuowIF+08uX0e36IiIV8A8hvowuMVE2htqxKXtEgnnMlzGbzAIr8GUCdhJGLqDBBQXxSOgF9LRaezVLiD3sDIaIW2L0ILDF3DmqONvMSY5eBzQgvioRGX86j43UjpGsDZwODXQtp4/RvQJQmzLbMmgPBvtdZBug26x/+ANO9Wfa1tk4+GQuD3w9Bui+Y8uoQK0MAneosQKpMyr1FKnUA7+RhKhd81LoN5GLBRw5Tzu2iOXLEHrUjg0rhR4EW0SGDxYGAbsBIxfQ4MRMtgHOiUIHNBG1WSOZgLIsTiKvQ3vEoya8HpIg5ockW/Bg0CUhMHDGDBOW4OBwU+QaDddoUN64BELdUQQUXgRQmzJpu2Tq6oDhRKnFPEu+WBQEQwCGmREVWKXbTgXgsq+01qfAGAKfsUI8S6HF7EQ4I7HcsVEfLUQKkBkZAya2JgCLiKwM4hkZMpgk1WGyUdgsX0bEcmaovNSA8pKXL+O2MAik4IAdjJELaFAMzll28ZQeSDSOAxr4rDMYIj8cUz6hGQwyKqT06bVISINFQrcWH1SRAwSlGbwH1NEEnBxsYwcCre7uoFZ0bPd2aA2JsMJyB4jHWcVVwa6hErVZ+4JgJH/DhJVRJGAqfXWqYLcAOjHYKEiZAHgGJ4txEjBlLZ4HBjpxV0y3n7CJZRW8Mci0cUlxZug3WTBv83wZQkcR/bgd26cvQ35lXgsDT+kolJcCzhdCQCPCJQVanThKD5hlcU6I1OKM2QEYMXQwhOeJCsA+TgqRdlPwfUlQKLbf5RSvQPsGuxsIn0q2aHdsdeI7gtyHQOOMm0ND16PbtAdXVL/bz8PEUQJpe+o6oecNA1f7WT2nkxhhrwgBL3hgIQGYdH5Al2c6H8/IUMnFL5hnAwntgySyeZNJUh3ebr4MQR8bBTTEl+kCwX9Iz4zTwiAgYCcjBDQinM2g1SVq0yihKSr10FWmOd2pYoylr/7GAQ1mQWiF7xQfpBS9ye44S3xYrScTS3Iah2CLdEYajfgkAHInnKFxcmgIEZiL6qCMVHa14rIIZwIw5U+7wbXUczqW7iDASxJXyEmip/OiiV6DCK/EXcmB8m4pbYMXsk3QBGARkbaKlskiYLv5MmxhED8Or30BcYooWxcsDAJ2A0YvoPFaDmBwsTHPA3U2yECQRPRggu0RuRU26UCCOomIVEoTHV0OItlSrJVqqeOgchBJ4gMXhMp3Ho8mEZECcBhqzXjkQK3o3D4O25xINem84teyDx5NOehoImsCFG2kgBdKqJq+EaXsBynYSkNHUw+6rehBKuRt5km7ZpN4Xa1nbzJN1jm47+TKTQRg0pjRJpMUuFEXFRpMQuBGiwIqfWkDzCYEeG1oWXfZF6y3LZCCAy4wjF5A41QFxvo/kVmHDjKupytJxC84BwONXuih8q4no7IO3BYJajFMAQKu8MnzydmFRHo4NFGkGuo3KHAjuwVnBxZxE4h4nFDMVWqDHoOJubFiJ3VMHtF9huur71XfSQDOQWmtQ0qz8OxWdb1NLDG2CeUUIuMSKiiYZ/kyQ8iC1CAdpV2oUXXYyZepJCGggcCqGdmXRgc02I5N9gVOBeDNWhiEslTATsLoBTTe1mXaDYmrquTk/BxxH1CAj4IoqnercXFQ8AVCVMKnsgt1JmlhNhGRvJpPehX7XSno0hqSBo+zfXxAejhwrkYJlxaqlE1zjtrETSAV46HKhPShIysFkTEaO2JZAM69BcGncvTujMEFKW3cQiwiTCCF+zyVtxdEi+bNAQGYzB61zYYIG0xSqYeyIMTToayHBvkxbYUvQ6WvuiL8ksUDddSRvgxnaOBAQrAScIFh5AIat0eTLx7ggUB/jvgszhZtbMF1BDRb4e2g1D+Vq6hDSs3NmKGhDAKUf2gbXUtqR6dyhJ5PkJ/kFPgjEPEWA0Z9fSEgI/0aLZ64HuieEpla74f3CjgvCCqDQiaunAG/JPUS6clbRKQH95NaxUugL5MFngoRgKntua9+F/kywNuh4IWCVOLLkCdTS+nfdAf2JaVnHrO5Tvf4gIALDSMX0GCGhjIXToG1BK2aN/s51JyBz4IWi8aQtHWQpwK7lXw6MUMgvNpMERCAaZCl8pLTxDIBejjtDkjgq+QAdUcJZWgoU0QAnkoKAhptr5OCjiyanPAa0aFBoIkGmGo3Kn1loKMJCcBUioHPTuuedbGTOrlXkwIwOWaTUzURgM8Mbeqw3rOZkYE6VwqiSKSP+DJ0HJQp8lgYUDs282XsJha38j3jocQUsJMxcgENlo2c3SNGFVjETHaYjXFmWegwqDOJyLJmYiPzS5Kidxpnkr6HgK+S+S7wN6IJMeXk8lDmiTpnutCOrue/LphrUpkkglQ+gYi3lBnpVuN/54EoS/o1qFNEzuvwfHgcyXsg5lcCLk+7S1ElfBZMtiYytuSkMxK1Lgnm2XOi1mgS5SMQAZiMLXWrfBZUh6tQ5vLyZVaH9lyxJVsFNFReooyppzwtEgKVgN2B0QtovCUn79fpUo9zMU+BBNsTwzZHMISZKCcRGbo/WdmYJli9wSnmh4EVJW3giU1CwEhdN/o3yHQSO8GczwcFHGjLoOYrChrqTTup4TVyBjTo2p5WHWlOc02UyYdntwAOqVSK0eUf4odQJ2IRuCtkYjmAVQa1gVPbs0YGCMAF+E3KxhAoQ9OBh1z7RVHLOgrmeVv9Q0ATsAswcgGNe6InUGJEf9apWUKTDnJXAB5FYdSccZSqRISDEGdWRY/PxMHAUhWJ+UE7NnVbpemaO4wnB9AdlQCOhPf5SHZ8+2lbA9JOWWrbfuk0HQdETGRdQQGNLn1FZXscxPugiTMBgY+HACwiMq9qXSTXT0HrGDhmU2aE2sCRAAxlHM2ZKZGNAtgX5CmwgqiPMjSr0KKuFYrRHdtrXxDasQN2KUYuoMHSibObBr9PTZJINCWODuqpODVnaPLXYzaqCZPvj90kJHxHXUgQWGliqcceQYSvB1rOeG0IQP9F31Pi9+AL4QxoiC+Dtgaqq4lI0kMo5+Gin1rn4TiSA7A1UCrAaeDyEIZwPeg+T+Zs+YfKLlqNlxSAqTV6EspXlBlhfRkbNFDWQ2eotpsvQy3qZICpr8nA6ce0WfuCF7JfQMBOwcgFNGxz4DM8JOgMDWUQsGTh1KvBAYlKD/C7GtRx4+1okqZPCFAHNNRai5kMOnXiAZGGDU2wcLymogCeRMTV8HaFcFnHbkuoVmjS80ELCWepAPkyEMn3VRKIRO+oXEO/mQcX0inoWacshSYBayKuiEgZvn8cAhrKKK2AnwXpuHg0Zspb0JdZHkJgpdNk6xxbR3Fm6JkP9gUBo47RC2gINGFtsr0bZfKdqyScO5z6EJYsS22/TlIpnYOTXKgn8LSTe0NAQUIItqgEAvQNc42QAIwBpLMDhJSHgT+bUSrAlBnwXiMkr5N0DOn3qIwgKd5ScEFAd2lw/8QshSoxUWBRAL5MESI3CsDIqbsDbc8EzZkppHx8GQrcvHwZylDpEpM7eAl8mYARwugFNB4ejAhmcnCy06RgqnQ4J0Rs0XYOXKYUQ1oklFGhDAK2mfvOQSvtYgIIRN4wmKPrQdQBEPgjE2Od3aeW5G7DRiBQ7UBQQKOzICIihXw8VUbibSnKYuGza7dhJg4CK60CTFyeWstmEOj5GANHawpotOKtiO0uIgLwGOjXbEUwrwtBA/2uDqTGoLyEfBkIyiiwWoUMDXGIDGfGaQYa2rEDRgmjF9AQvCJ6HnlwJB07j4M+612pq8mfvJEwo0LO14DNWiSQngpyTWDCxfZx+lFvu/RE/G/KSHRAiwQVi50g9+5xlc2YX7FRDyQCOJvmEDcUEYGmHqMCTB08RD5NQmZrMg/E2IQ9iWf7E2abnsCps4pao8kxexXsC2oU0AzsxUxRoKYCKbJRoAwNCffVIXjR+jIiPo0Zb4YmBCoBo4QQ0Mg6mjDObImBU0QPuylJcwY6kzibEZ8EULiPMjsU0MBKjwIEdKZWQQjaI0BAQwaT3pJQEgIaGsj7yg4iB/we0pLxcmjQrbpIrdDxCbDftpMflcxgnsOsGxp4gmhetrQxCZg0g9JkaZD16b9gtkQFF5QpIsG8JDzQKxDQECeFzisP9uuaM+O1L0CDTSeXpwvvjAlggn1BQIBBCGhEXkCGxhHQUFkAVYdhP285jH5Wf5+3zEVZIWf7J2ZVdKaIMgjYpUXtXHYTdaR5Myg6e0QlBnT49krFUzkMtF0MvEGUr2sbQQFjHkTiNIjPkoGAo5QGPgtckDbIM2tSdC5lv7/gDCQ8HULrQQeaIpYzQ1knAtkXIF/GaWGgA/nQjh0QYBECGllncEBirN1kBO0oQ0NkXBTRo8/Cb1JruPpdl5qwyJYUhSkI0fo3pDlDK0lsWafrQQES6eHQAlZ1NWkVWBF/BxaBArxkwd5APWElQTPH4xEmss7zAc8W2VlMKunkHpRhqEOPLAe0Y7YIT+qsAhz/2+uYzXwZ20lEnBQKZlljJp6h2Rpfxtb9iD/FFgZ6oAnt2AEBGqMX0HhZ/95siSdpgwqvvrQQBSbYaq12o4UkBlHk+QTCbG7+jQ7ooP0Yk1/koUQxDnCKsF2agot8/EZ0QcvDK45HwI4mIB7rjEEKWsyxC4646xTQkPZNyV5fbR1QawMBGH6z4iQAk/5LA12z4ydLgnmoMAxlHQoavHyZMgQ0FXVeXr4M+TGRV1QHnkFyyNaZzmAwGRBgEQIaWWfF4iQFu7K8sBMGNHQYWOrZ+LPIC/JaKzhLOJ5zcNkjiHCmiFrPyYcGNX3stlQmPhnRShh4wmwFAaCAJovE4/jBIT9pk8KOIuscb8HumFYcImp5pkwGTfw00XtLLFo7pgSscdJ1qYPKLpFsSeeHhPrywMT2cGYoU9SC0loXbkyfsmKebqXQjh0QYDCCAY2ztZHKHVCi8Fgd4KQDXSeoOeOcrPV+LjVhEbeiMF42yNAk1GDsNlQEpdmILBI26ZckIpJRAU1r1e5EtBKvJYVuWRcRyYE+y8pqnByagxZz5FhRMI7lO7stW7QTc1p9mBytU9BxNA6CeR4FYBHOluQVJ2f7BfPMJskCD6gCLdlF6v9XaMLL3IAHkLJTdM0jclrXpx/asQMCDEYuoPEaDWLmgoILPfY4a9vItfEK8JGBoiMl7cnsiLCOCQYh1IWksh7Eb6HASmdPRET6DdAKoewR0Z1gUs+pbEmr7fOUwswWYAhlM5qIBy2VoaGuL2j39q7K6bPl4sYTM4no5aDzhzqOPArAP/wNu58ufREfh0BdQ8SXIZBQn0djhvgyVF4iPyadmRNZhy9DpW1NCg6BSkCAwbYHNEePHpXPf/7z8vd///dSKBTk2muvlQ996EPykpe8ZG2fKIrkjjvukPvuu0+WlpbkVa96lXzsYx+Tl73sZWv7dDodede73iV/9Ed/JK1WS2644Qa555575MCBA1s7wC2karG0oU0hnd+/FZNMV0s5qgn7yjrerArp5iSUaB6aToLLdQqCowGZLDpVcIdAMtblE7IXwHvsLDlFno4mEUnUVUADGTyY+9ydT0QALkMaqK8eXiJJF0Dq300ABs4IYUyRgD2O3CLrCeZtni9D55VUq5gO8HbqkI1B+wLotvLwZURgXAkBTUCAwbYHNA8++KC87W1vk1e+8pXS7/fltttukxtvvFEef/xxKZV+KCD24Q9/WD7ykY/Ipz71KXnxi18sd955p/zCL/yCPPHEE1KpVERE5JZbbpEvfvGLcv/998vU1JS8853vlNe//vVy/PhxSaWcMwxhC62NLq6Gd6ChVb+X6EfBUH/jFRy3aNtNTGKG/ajc5jgOKuGksMPLV16iDAqZWOoWZGcnMNtZABLwm8RL0Vkrb6CCQSqdO7ilU0aiTyVUhTxZDjgDDhKII28vzV0hR27qGqIWcLrelCUjvgz9rn4uu8QLgm1t4ApxeWkLFgYBAQExbHtA8xd/8Rexvz/5yU/K3r175fjx4/KzP/uzEkWR3H333XLbbbfJG97wBhER+YM/+AOZmZmRz372s/KWt7xFVlZW5BOf+IR8+tOflte+9rUiIvKZz3xGDh48KA888IC87nWv2/TxeVO1Xh2aSA/QzizLlgT44LNJrSTqbNH2KgprUToRJowajgsFNJA9wU50Z8cRCvzloYSlVG9Tba8Fg+swJAllMyozpBsbnxerAtttyIsq2TRWEQKTM624QjHdz3HoaKKJf643ZrZR+ScDAU1VlbCykNabG9jvpwwQlc0KOXvh9G+K+AjAFFiRwaTLvkDE7ZDtWYiFMlTAqOOsc2hWVlZERGRyclJERJ566ik5ffq03HjjjWv75HI5uf766+Whhx6St7zlLXL8+HHp9Xqxffbv3y+HDx+Whx56CAOaTqcjnc4/pq5rtRofEA0W3qSNp2Lj/H6aOJPoKQVf5/GLcioRkzIuZgKAAEyia1Su0iDNmRR8F1kkENCPCoK3ngouoJrCwZGzI02TjkVEul17cPp3McsCxwF6c1i+y5XthctCXUv7GZHlgJ8AbMs/ZLpZytpjmwCNGQ0iALecfBnN0RFZhy8DWge6g6mJ5SUb0LRQX8ahACzrdPKFYCUgYEOc1YAmiiK59dZb5brrrpPDhw+LiMjp06dFRGRmZia278zMjDz99NNr+2SzWZmYmDD7/OjzGkePHpU77rjDcVC+Y/f6ouhsCbZL0xzvFNHDFlzsTFK/SSt8Cmi8KrtEKCaRO30cFC/Bd5FjdtppkcACf3ZW6HfiFyUPPNkeWAQw98iCSnDdup3Y8o6Ahrvn7PWmbq6JAkRqAF1yIm8rIgD3IGVFJFgq/5B4XVkFF136fsqCkKmnky9TBqfuDLyAmjNTI2sFaBWnzNyQ3jXMxthNoeQUELAxzmpA8/a3v12+853vyNe//nXzfwml2BVFkdmm8eP2ed/73ie33nrr2t+1Wk0OHjy4iaP+cQcA23RixKtpQ7uhRYJXplZdT2dnjlss0CkEqFeXHnsEEe72gIQHZ1DQlRuCpnb8cXcTgL3XErZR67kmNsNc7aZ6kbhhAXrPSYtFl2cK0GJOZZgBnGnTmS3RLdoiInkVSJCuSwOCBuo48vJlihDQEI9Lc2ZIRwfNJCFAR77MJi0MQsYmIMDirAU073jHO+QLX/iCfPWrX411Js3OzorID7Mw+/btW9s+Nze3lrWZnZ2VbrcrS0tLsSzN3NycXHvttfh7uVxOcjlHVwUGHDRZb/xVImInOxi0thJckLYJKgqryR8/RxUtt6IwlJyA86N5HsMiBBvQ0TQEQz6v5xOW0uxHRVrx40UTR9IHcpacMB5t2WukzwsaZ/gEHHYOIiJVUNrVHU0itmRYAssBnT0REamjCi4oAMNsPQYZH83JWepb93FS2aUW8DyUtCrgM4WBmsPC4FzwZUKwEhCwOWx7QBNFkbzjHe+QP/3TP5WvfOUrcujQodj/Hzp0SGZnZ+XYsWNy9dVXi4hIt9uVBx98UD70oQ+JiMiRI0ckk8nIsWPH5I1vfKOIiJw6dUoee+wx+fCHP7zFA4RNm298MqMPr/o3l90QEcyMeAT4kMhKMY7XWgFbtDcmFONkTQGT06CRylVCJSHYlALncg00k3RmybBs1tj4vMBPcR0OFOwHCsDljJ3Al7skbBOHbp8WsdkTEZGFQcVs60LmglSSqYSlOTlsG0AXyYK6ssaALEV8mSE8mDp4q4O1AvNlNtmOLRLKSwEBm8S2BzRve9vb5LOf/az8j//xP6RSqaxxXqrVqhQKBUkkEnLLLbfIXXfdJVdccYVcccUVctddd0mxWJRf/dVfXdv3zW9+s7zzne+UqakpmZyclHe9611y1VVXrXU9bRre6MWtPa/+dpYxvAMZcWgok6O/zyO+J8JZEDSKhIMjRWGNIXlFARKOYEOESyxIqoXgIqu6mrjl2Ve+IgzgemRBI04/WliWo8U8vK25ko8ATGUR3dVEE38Sokqv/suYJgsJa71oUT76fsqCJJ22DGMp+5vElyHFXxPQQGDVhewi6cuQcOZWOH0BAQFxbHtAc++994qIyGte85rY9k9+8pPyW7/1WyIi8u53v1tarZb89m//9pqw3pe//OU1DRoRkd/7vd+TdDotb3zjG9eE9T71qU9tTYNGtsZx2ez3YwnHXdKiKMfT9ru5z4n4pf5Rr0afqzN74iVTI0EXxW4g6NOlHiQs2wnc+3jQJIadWrqz3Uk6pv3ywJehIAT1WdSzVYLSDIF8ioZwlcgviVq+Nb+nBSkr6phivgxwdKiuCiDuTlOdK4njUemLH1740S2lhwMCAv4pzkrJaSMkEgm5/fbb5fbbb193n3w+Lx/96Eflox/96DYe3QvAZgMf5NCQD4FzIKNSDyjoGhBR1itU51UUBlsDMycQ54UyRaA5w55PYLdAysaQLdHBBWVGEpRRct4r/E2IEXTAiFoyAOIPVZ0dTbpFW0Qkpwi61MqMCsBdYDEDxqD0RdwVnRmpOTum9PGLiFQgy+TxY6LjELHdW03I0GzWvkAkZF4CArYTI+fl5A5UNjnQuDNATlVg1KuhIESv+kl8jzRn6DedLdroe6SDEGifToCHEi2iaaJPAi9j2IEdKXhTv0GeRykImLT30nrwnpcmHrusLIT5PUQAHsJDQ4Jz5Vw8uKik7HeRkBx1NFGHEInXkSv3vOLkUFmHurSIL0MGk5ShIb4McncUZ6YDpTW3fQF2NMG2gICATWH0AhovNksedmjViKxTT3fq1eDqT3tKkfieIxASETcR2eVyTd/vJEcSsZm0dLi85Ggph+9Pkn6Nc9JJkRO4Q92Xnw/7OcpOkQIwdTRRSUi3UFOwQZN8D4hdGSgvFZzKiC0VNPXAkZtALeCUAaLzovKSx8KgD8dGfC3myPkyfSFrExCwOYSARl5AGXuz5W4KLrbg6oyTpB5nPbYE6/wmtkFDmcvTheSyRxB/C3UKAo4hfR8FNOpQBmDnQGq5qNUDICsFV9BHvlPwm+k8ZCSgxLLULdrvg4dcl4Ro4qc2ZSpfFZxqvARdYiICMHlAlUF5kdrMtcGkiEh7aM+LzrWhskXkxxTasQMCdgZCQLMe3N1Qjn2w5OTUq6FEDhFoHVopNMm7FYUdlgYi6ygK6+8C7g1+F2jppOh6wHmhY7i6vtTNhS+EU02Z+DIEnfTA+w73oFigjiYbGaMpJERWFAxpoAIwla8goKESFnFyVlRXUw9ItuQBVYbjryR9QRTyZSCgaXXjxzuAjiZ3eSkgIOCsIgQ0Ihw0eAX4XN/vKymgqzM19RBvVfMyYNKBbl4OQJxBA2ql6LZnmJzQ74kWudBCTXEbkZM9juERaLgQvBka4p5SwGgCKbrvQAuqgFdDCh4QcnpGnybFcaEyDBF0CaR9Qx1NHlE+yiahvoyTL4NWDXgcNsjRXU1kX4DPh1OWIWRtAgK2DyMX0GxlAPE6cNsfhW20gsP2bmfqWk+KtI9X6p++nkpkKP62sdAgfhe6XIN9AaXyIS7xtM+TYrFbnh6AysYOqwZy86CMG5ksEojjQiWbnGJJU0DTxe+yx1aC8g+ZWDahJZsCMA3qaCqApYGXL6N5O+sdhy4x0fMR2rEDAnYGRi6gceNsd0PBwIgmi87ARM87HvG99X6Tvt9drtJBAtkjEK8EhGAjIMFSR0mG7BuI6qB+I5Wzkx85InvLbWguCpkW3a1Ewn1ETh6HjqYeRIJEqi2DCnBRkXYp2CAV3DQQgKm7iITvauCarTkzxLsi8nMVXLqJL9MYWk4RZZ40X0YELAwCXyYgYMciBDRbhR64aAHnDISw5LRZvRpnmQQVhalcRYrCpEav51d35w95PkGGBgIObI2GJ1sHF2lwv+w07EmlnRwaaqfv2bkUu5XMb0KwRZwR6syhkg1xXHRJ6HSnar8fLiRlikgBGEtYwFPRARjxZUjFmDqaCNR6vuq0MOgrzkywLwgI2LkIAY2Iv3tpOxWFkUMDOxLNw9Fq7bUS8ArwoS0DcFz0jh57BBHg3ojgTBF1IIPiUSwWkaE61xxMnBF0c1Ewh6AOe9C6SapAirJO2az90TK0QS9SxAQoO1SAKdggFVwKjii4QFE+FM2LP295SLkRX6YEpCXiy9ThvIgv0+3Zz+p7g3ILzkVHyNoEBJxdhIBmq9DUFS/BmIDkYWemRe2G/GKKU6ilnLIqdA6uzirfcRDXBL+Pjs1pCKqNMokLknCWyLxAcUBVTqJVfy5jL1waWN1kCkkgvolGGywNCGQv4NWwIZ6Kzihl4DxJ0yYJESTaF2ySL/PDg1P3xpsxDQgIOOcIAc0LgIsU7BzvmNgL25zZB+P6TVkWCl6cLtoEnfH44cHFfxc7mujryXIAO5qIPUzHBtvUb5D6LKkpewMaui+Dov1wRvGMKENTztnsAwUNpNpLHBcq2ejJnxR6iQfDCsA2yKmDkBCVdTRnhjJAVNKiVvRV0JehdmyyMOh7LAyIXxYyLwEBOwIhoFkHmx6ksL3G+VnKGIAKqUevxiW+J8JZISIAYxCysSAcWhrQcRA5mQIOh9mjyDp+VGobdUyRp5TbpoKIyAX7YR0kUFBZgTZoAnUhYYaDPJRUwLGV4IhAJSzi5GjbBGoB3xJfBspcFFh5LAy8fJkQ5AQEnHuEgOaFYCvlpM1+P+qpOEo95AXkEL0T8YnSiQjzb7qac2A/BpUI9HyKukAA9hhiCnNydJBD/BASx/PeYzSZzNsbmFSBawrax8ewownk+iFAoGCoCCc21x2Lfz8ERwXoLiqDYB5xV7Rgngi7ZuvyGmWAyGCSDCtX+pZTRJmndndjvowIPL+hHTsgYMciBDTbjE1r1az7hbDN0TXlJh2Tzo33s0TU0fM3ejQ5xfycCqwY0ECQoNujySU5uzHVZF1QQJPKQkCjIiTSiMkD56UPAQeVzbKQVSEBvpbizFCAl4VsDwnmtSGgIU4OeUrpjFJxC/oyHj8mET5XJpk5MjQBAQE7AiGg2Socbdteo0skFJNeDXUEGbtt2IU8gyi2oHIVdiHZTUlHizN9F2mPCCkAO7VeEljCiv85wAyQ/Rh5ShHoOKhbSZ9rFgjA1NHkbtF2dDSJWG6Jt907DzdhsV8y2ygzQtAaM5QB2na+zGYtDEJAExCwYxECmhcCT6LFK77nJQ87O3g8Ay9+zpkFwXIKwPg0efktMJmiezUlhSigoRKW6mDCFm3StPGp/6PZZTkHmRZVdsmlfV09y1DCIZQgoBnAjWj24xM9BZVU/knCA0J8mRZwcqgzSZfXKKAhkI3CStdeIy9fBi0MHF1NIWsTELAzEAKanQ5vMORpJ8Uuqs0L8CEZUn0fVtswoIHvcgraUbcVqe9qEnDCw5mQdcptdByQeaLyjzZ3zIKsP3UXdSFDQ0EItWj3HKUYKn1RYEVogcoicpTgvujyWj5hj5/4Mm2Isr3t2JSNCdmXgIALGyGg2Wa4VYG30N6NisKewISCEmqDBmC5Cn5Ti9ChVxQFNEAWpWwJatiAK7cm3orYYIs6mrYS0ER5+2EKVlpKwK0EZR3yQaLJmjqaWOQOAhplvEjfVQYyMXFXSHmXCMAFIClp0Tw2mPSpDlOZC/VlgoVBQMCuQwhozgWQHAOb3O3d8Fk9BxDnESZ5SCAwKAviKFch/4QCK1A29jhmi4hEzu4tURkfUx4TWYd75Pt66mjKgQidNqMkngqBApo8BEw5kDZe6FmOi+5qqkJnlfZ7EmEFYFLeJQIwBW86oGGRPltKooCm0bXHMdgsX0bEku1DgBMQsGMRApotwgxw3kBlKyOjQ6/Go1Uj4tecQf4NBSFqUsBWcdK+gUwRkpMhQCITS+zeUueaIs0ZgLfdPVuwmYU0lHF0aYeCBnS+BtPJ8ZwNQjIQ0DQgstQlIY/fk4jIfK9itqEoH0SHZXDlrjg4M6QvUwNOUQeyMUN4xpEvE1qyAwIuaISAZifBbZEAm9S8iUkhr84NZYAcJRwCEoABbndweGJJmC5yOIbjihyDOdgPkAZyL03qehtlcSigoS4kau8m6BZtAn0XtXtT+Yo0bOh5o9/QQRPxZcgJXJfMRNbhyzhbtEP2JSDgwkYIaM4FvBwa5woRd9MBDU3yDhKvyAvQiaHsju4e34oCMABbvqGjibpY0qrEhC3gZGrpzNCUcr6T0MTYAmRBKGjAEg5kPIYQEFBJSGeKyACSQK3RfcgeEX+oAirDmgRMwRzZKDTQvgCiT+xespsCKTgg4MJGCGi2G1tx7vYGPg4TS5yEnZozyHshXyXyadIBjZN741UnpvMiAvAQNGZ0ZQc4sMyXoZIWoJT1BTTaToA6ic50y77fdJJ2PYRiavem76LWaN25JSJSgZZ1Cpo0Z2ZlYNV+l8FVvNHdgr6MM3gJWZuAgAsHIaA5X/Dq1Xi/Ts+5qFXjJcE6syqU4VBPVAIUe4UcrZ0EYG9w4eLkUEmLtODIOBNAhFeCDiSIBEsquyQuRy3aVJ7pQHmmkIl/lrqjqDW63t+cYJ6ISDXd3PBzxJepQxdV26svQ+XH4JodELDrEAKanYQtCPDpz3JZyrdSRVIwzenExdVzjFP7BsX84OnkUtrGBGARDpo8v4ldWQDqOELDR1XqIc0ZsjkggjEFQ3VgTvfhpmpbAyIT16G8RORk4ssUoRxGKsMaFJDRdaS2cG87dkBAwO5DCGjOE7wcGu9+ek5EIbztbtGmYMiUhOC7qFTlVCdOOPVwUmSboM4f3bEh+UB+TAQivFL3Tx5IwBpUIiJfJQpoGpDNYFuDeIkJgyOoP6JjNgRbFShhUdeULmvV+rakRXyZ3ja2Y4uE8lJAwIWOENCcA3DbtvfDzv30b8BkTbor6ClF5SqnZovluBAB2NkuTQRgmDgjmNjoN0xLOQQvAxDpS2d8AU0WMhxkHqkDGtqnCxkaaqtGjyMIaEhRuOIgAZPWCxGAC6Qv4yAAi1jODOvL2Jvlti8I7dgBASOBENDsIHj1alwrSWqzphYep4t2EiYPgsnQwOrYQyYW8ROAI/g+Uhk2ZTnK0EBAk4V2bAIJ2nFAo9qU4Sb04V6RXg1BezSJiKQh8NGaMNwdZYMLIgATX2YsZX2gCJozU4PfbHeJL+NTAA6Zl4CA0UAIaHYS3O3djq9ytHaLrKM5Q5+llS/tp7I7EU0wTu0bKn1R6UQrAK/3G6YDy6k6nIK2cAJxYQhpVTrqw4FQIKQ/J8KaLZTdoZJQztEuTaUv1JcB/hBZGBA0Z8bPl4EvC+WlgICRRQhozhe21N7t+DBldrCTyDeyU0eTR1HYS851dzRh+zj4QDmOdwAlLcnZg6PJmkAidBSY6EwOcVIIZbQhsJ8l0i7xdnTGh8i4qAAMz1YZ+DLFpK8NXHNmUF9mm9uxAwICdh9CQLPT4c3QeGIcEtFzisbRZ12qvS3oiIE4ZVCA44DMCKm+koUB2iao440goEkCAZgE4ghJZJ9a6ICGnKrxcxCUUIszqfZO5mz5R5OAiYzbhWBL6+iIiIxnbDs2ZWjIk2lZWRg0iS+Drf7Ekwp8mYCAUUUIaC5EeEpTTk8pVIV3CvBRQKB/19thQhkasluInNkYz28MoaSVAc0ZIt5uBRlV/qkBP4myIGm4CR3oQqKsUBaCIR2AUbZH+z2JMAGY9HDI9qENyoVac4ftCwLZNyAg4McjBDQ7HG4Ojd6PYg2q4FDJiXgvzrZqDexochKAMetEgnkU0OBvxP+OcqDrkrFflnVbklt4AhMS0SPNGcp4PD+wRpEE6mjSJGDqjqLgiLqtPAaTIqxrU1O2DJ0eDEteDk3gywQEjCxCQLOD4B54vXo1ZifYRC3aDtNJkXUUhdUk47U0oGwPuj5AgETcU7oeug08ARydLLRoU4cQgbqEKKBJqYvUhcwIac5QxqMJQYino0nE8lnI74mg9WtERMoQ0Hj4MiIi9W78dwdufZmQoQkICPhHhIBmp8NZOrIZGp9uDOnVUNcQgQIaPfFQ9oS7i4hYsznBvPV+Q7dkk2AeEYApW+IFBTR6m5fES0CPJsgoFcDWwNNdRN9VzVg+DunLtI1stOXLiFiNmYGXLxMyLwEBAf8EIaDZLVCju3uwdxhdrguHXxTydjxkYhFWRKauKfoNCmhUAJYFnykivHoDmoG7dU0dl7NFm9y2qUXba5FQG8aDCyITU7s38WWIZ9SBUhp1UhnOjNNzLJSXAgIC/ilCQLPTsVlXbufATuWfJHVDOVq0RUQS7fiOzL2h3mvI9gBfxqkth/wezZnJAV+GOomo1IO/SYGJo1xFPktko0ABB2V3xnPgaE0+TZ14cNGD7ypnbXmpmvYJ5q1AeanWtWUtbWHgti8ICAgI+CcIAc1ugafkRMERKQo7he+oCympMyjoaA2/SUtrJwHYw5cRsZyZfMYGDUQA9grmeTk0OvAhVWBSHSZOCnUhkaIwaeSsKoIu+z3Z7yK+DAn8efgyIiL9bvy8Qjt2QEDAZhACmt0CT4aGYhzaBmUdJADTZzUJmKoHkKHBWAsCGqjEuC0M0rl4kECWBkjG3UJ6gAIabXVAmR0q65BeDZWhSiByR+UwDwnY68fk5cs00cJAKx76Sk6hvBQQEPBPEQKaXYLNlpwIXk4KflZNRmhpAKUqyg6gvgy1noMuHWrMKM5MBoOXjUm864GCC+9nNVLwuQaRjwCY3SFFYXVTKUtWgGwP8XGaoIfj4suIWM5MCFQCAgI2gRDQXIBwzZHEs/H5S3LJCVu0Nw5C0NLA2dGEjtlOknGUB+8ixZnJUUfTNpM1KKAh7yYN7bMkItICzRki41J2hxSFW714toT4Q2OgX4MO3wOrL7Pcsdt6oDET9TXvKpSXAgICXjhCQLNb4ODQYCe3s3uEMjQRzP06GIKFO/J2pGN/wK0vA+UlsjDIq4CGy0vwXc6UwYCyTPBZvZ83K7QVAb6lXtFs0yTjMSATEwGY+DLL8P0NB19GxGb1KGgN5aWAgICNEAKaXQqXVo2In5tAHU0g2a+/D8m5zo4mLDmRYCzyZSigiU/0FAxshS9D8JCCUXwPjoNatEmvBlu0QaFXE4pJfK8I+jVETvbyZXQ2RkRsGTEELwEBAZtACGh2C1ykYJ/WC4KyKg6xM7ebN5S5PAaTP9xmfyMHhF8dJGyFL0PgLicbmOj9vFkh6obiriz7m5Td0aBW8Rxke6h8RXyZLlkYeDVmAgICAl4gQkAzQsDWa69eDQQmyc7GpBx08ybuDXk+Ufzl5ctkbeZCqwBvN1+GQMFKzxHQeEX0xsFFm9Ds24BDi+ZVoKNJ2zSIiNTdfBmoU5IwYuDMBAQEbANCQDNKoHnDOZkkKBii9m61H1ka0ASW6viOgzg5SSovAeFXc2Yok+Hly2wFOkPjDawoQ0MEYOpoQlsDdT0m0k3XcRAfZxUCmiFYGHhasgNfJiAgYDMIAc2ow1uFIosE6obSMjTUou1VgnW6cqfAUDILAY3OhGylvLSdQK0aSKdRa3vWKcBHKsDap4navbVmjohIA6LKDrRjR+SQvTMueUBAwC5ECGh2Kdx0GZpgqJIEnzWqwAIlIVIibjs7mlAwD7p6oLxELcjnosSkQRkfXU7ispQ9eSpDFUmADzguZJtQVV1NFVAA7oCHxFLXZmjaSAAO5aWAgIBzhxDQjBKcJSdv4EM2BIOCrh/YfVBfBrI9QNVAvgwFNNSSrQ0fz0V5iaDbtinQIvVgOl5y0T7TLbu+T6sAEwF4vme1b4gv0+/aoYQtDMymUGIKCAjYFoSAZsSBmRyvAB99lkjA+nNOAjA0ziBfprDNnkznGt4MDYFatBv9jS0NRCwJmAjAS30fX2YAbffIlwkICAg4SwgBzSjBW3LC/ZxdSHpeI2Nt7fe0Dig4SoNgntfCYKfAtm37MjRkTcB6Nfa1putRTlnPJw0KjtqhHTsgIGAHIgQ0AQYRCd85SwUmCAFiqFcwbwCCeciXcVoYnK8S00bwZmi8QoDU0ZQFTpEOaOg3/XwZuM8Q5OzgODMgIOACRwhoAizIRdtJ5tRt2tTaTQRg4J5KVLCZl2LWckZILXe7FX/PNShDQwENgQIaamPXJODVoS0lLXasAnAfbCroPu/Q+DEgIGCXIgQ0Iw63RYKTPGzatFvk3WM/RwRg5MtkbTTEmYsLZzbFTiggMjF52O5HHU2TIMCnScDPd8bMPqwvQ+1ndlNAQEDAuUQIaERCHlzB3d7t0KshSwM0v9wCX+ZCKi95QS3aXr0a7dEkwrYGmgTs5cuQjlAoLwUEBJxvhIAmwAIzNHYTZmgU/yZJCsCwaZAH0mrOTsK7sbxEIOduykQR74UCmvEMuGYr4tJ8t2T2aXds+SqUlwICAnYiQkATYOHl0Djau0lzhtrChwU7WZdyli9zIbVjbwXekpO3vXssbQMa/dnFjiUA99owRIR27ICAgB2IENC8EOzCidMNKhPBXKrl+ZEATPoyBZt5KWQgoKEW7RFJD1AmqgMt2tTeXYWAZkVpzCy1bEATAV8GBfNG4xYEBATsYISAJmDzgPZuXYciAjAFNMSX4WzM7isveUGZqD5EldpFW4RVgBf78RKTly8TgpeAgICdiBDQbDd26WjvVhRWcykFNH1tjyAilYIVeSum7SS8G8tLXlAmqucsTeUTYGugLBKaLRtpJpwiiAEBAQHnGyGgCdg0KKDRAmsUfxBfpkx8mREuL3nRBw4NCQ2SovCZdjyg6QNfJpSXAgICLhSEgOZ8YTfMCkgednwubwOVPGZjRre85AV2Qzmv24rSmCG1393wmAYEBIwGnDaE5w/33HOPHDp0SPL5vBw5ckS+9rWvne9DOrdIRPbfTkEC/g0SsX9RUsy/dLFn/pUzXfMvmYjMv4A4hlHS/MumBuZfN0qbf0utQuxfops0/wICAgIuFOzoDM3nPvc5ueWWW+See+6RV7/61fJf/+t/lX/2z/6ZPP7443LxxRef78PbWdghk70uUZClQblk+TKoL3OWy0vnIkA6H0EYlerqIMVcb8S3kb7MDnmsAgICAjbEjg5oPvKRj8ib3/xm+bf/9t+KiMjdd98tf/mXfyn33nuvHD169Dwf3QUI7+y0hVlMVzuoo2mq2DDbsuhY6cOFnrnZ7uOna6k7mkRE+o14tJkKFb6AgIALGDs2oOl2u3L8+HF573vfG9t+4403ykMPPWT273Q60un848p/ZWVFRESG7bbZN+DcoQ+k0kJv1WzrNiwpOBCANweyTVjq2PJRtBy/5kNSAA4ICAg4x/jRvB1FL2wO2LEBzfz8vAwGA5mZmYltn5mZkdOnT5v9jx49KnfccYfZfvL9d561YwzYHJ463wcQ8H/xx+f7AAICAgLWxerqqlSrVff+Ozag+RESifiqMYois01E5H3ve5/ceuuta38vLy/LJZdcIidOnHhBFyRg+1Cr1eTgwYNy8uRJGRuzTs4B5wbhPpx/hHtw/hHuwfmH9x5EUSSrq6uyf//+F/T9OzagmZ6ellQqZbIxc3NzJmsjIpLL5SSXs27B1Wo1PLznGWNjY+Ee7ACE+3D+Ee7B+Ue4B+cfnnuwmUTEju3LzGazcuTIETl27Fhs+7Fjx+Taa689T0cVEBAQEBAQsBOxYzM0IiK33nqr/MZv/IZcc8018jM/8zNy3333yYkTJ+Stb33r+T60gICAgICAgB2EHR3Q/PIv/7IsLCzIBz7wATl16pQcPnxYvvSlL8kll1yy4WdzuZy8//3vxzJUwLlBuAc7A+E+nH+Ee3D+Ee7B+cfZvgeJ6IX2RQUEBAQEBAQE7DDsWA5NQEBAQEBAQIAXIaAJCAgICAgIuOARApqAgICAgICACx4hoAkICAgICAi44LFrA5p77rlHDh06JPl8Xo4cOSJf+9rXzvch7VocPXpUXvnKV0qlUpG9e/fKL/3SL8kTTzwR2yeKIrn99ttl//79UigU5DWveY387d/+7Xk64t2Po0ePSiKRkFtuuWVtW7gHZx/PPvus/Pqv/7pMTU1JsViUn/qpn5Ljx4+v/X+4B2cX/X5f/tN/+k9y6NAhKRQKctlll8kHPvABGQ7/0Xk13IPtx1e/+lX5F//iX8j+/fslkUjIn/3Zn8X+33PNO52OvOMd75Dp6WkplUryi7/4i/LMM8+8sAOJdiHuv//+KJPJRB//+Mejxx9/PLr55pujUqkUPf300+f70HYlXve610Wf/OQno8ceeyx65JFHoptuuim6+OKLo3q9vrbPBz/4wahSqUR/8id/Ej366KPRL//yL0f79u2LarXaeTzy3YlvfOMb0aWXXhq9/OUvj26++ea17eEenF0sLi5Gl1xySfRbv/Vb0d/8zd9ETz31VPTAAw9E3/ve99b2Cffg7OLOO++Mpqamoj//8z+PnnrqqeiP//iPo3K5HN19991r+4R7sP340pe+FN12223Rn/zJn0QiEv3pn/5p7P891/ytb31rdNFFF0XHjh2LHn744ejnfu7nop/8yZ+M+v2++zh2ZUDz0z/909Fb3/rW2LYrr7wyeu9733uejmi0MDc3F4lI9OCDD0ZRFEXD4TCanZ2NPvjBD67t0263o2q1Gv2X//Jfztdh7kqsrq5GV1xxRXTs2LHo+uuvXwtowj04+3jPe94TXXfddev+f7gHZx833XRT9G/+zb+JbXvDG94Q/fqv/3oUReEenAvogMZzzZeXl6NMJhPdf//9a/s8++yzUTKZjP7iL/7C/du7ruTU7Xbl+PHjcuONN8a233jjjfLQQw+dp6MaLaysrIiIyOTkpIiIPPXUU3L69OnYPcnlcnL99deHe7LNeNvb3iY33XSTvPa1r41tD/fg7OMLX/iCXHPNNfIv/+W/lL1798rVV18tH//4x9f+P9yDs4/rrrtO/uqv/kq++93viojIt7/9bfn6178u//yf/3MRCffgfMBzzY8fPy69Xi+2z/79++Xw4cMv6L7saKXgzWB+fl4Gg4ExsJyZmTFGlwHbjyiK5NZbb5XrrrtODh8+LCKydt3pnjz99NPn/Bh3K+6//355+OGH5Zvf/Kb5v3APzj6+//3vy7333iu33nqr/M7v/I584xvfkH//7/+95HI5+c3f/M1wD84B3vOe98jKyopceeWVkkqlZDAYyO/+7u/Kr/zKr4hIeA/OBzzX/PTp05LNZmViYsLs80Lm7V0X0PwIiUQi9ncURWZbwPbj7W9/u3znO9+Rr3/96+b/wj05ezh58qTcfPPN8uUvf1ny+fy6+4V7cPYwHA7lmmuukbvuuktERK6++mr527/9W7n33nvlN3/zN9f2C/fg7OFzn/ucfOYzn5HPfvaz8rKXvUweeeQRueWWW2T//v3ypje9aW2/cA/OPTZzzV/ofdl1Jafp6WlJpVImqpubmzMRYsD24h3veId84QtfkL/+67+WAwcOrG2fnZ0VEQn35Czi+PHjMjc3J0eOHJF0Oi3pdFoefPBB+f3f/31Jp9Nr1zncg7OHffv2yUtf+tLYtp/4iZ+QEydOiEh4D84F/uN//I/y3ve+V/7Vv/pXctVVV8lv/MZvyH/4D/9Bjh49KiLhHpwPeK757OysdLtdWVpaWncfD3ZdQJPNZuXIkSNy7Nix2PZjx47Jtddee56OancjiiJ5+9vfLp///Oflf/7P/ymHDh2K/f+hQ4dkdnY2dk+63a48+OCD4Z5sE2644QZ59NFH5ZFHHln7d80118iv/dqvySOPPCKXXXZZuAdnGa9+9auNXMF3v/vdNTPd8B6cfTSbTUkm49NaKpVaa9sO9+Dcw3PNjxw5IplMJrbPqVOn5LHHHnth92XTVOYdjB+1bX/iE5+IHn/88eiWW26JSqVS9IMf/OB8H9quxL/7d/8uqlar0Ve+8pXo1KlTa/+azebaPh/84AejarUaff7zn48effTR6Fd+5VdCq+RZxj/tcoqicA/ONr7xjW9E6XQ6+t3f/d3oySefjP7wD/8wKhaL0Wc+85m1fcI9OLt405veFF100UVrbduf//zno+np6ejd73732j7hHmw/VldXo29961vRt771rUhEoo985CPRt771rTWpFM81f+tb3xodOHAgeuCBB6KHH344+vmf//nQtv0jfOxjH4suueSSKJvNRq94xSvWWogDth8igv8++clPru0zHA6j97///dHs7GyUy+Win/3Zn40effTR83fQIwAd0IR7cPbxxS9+MTp8+HCUy+WiK6+8Mrrvvvti/x/uwdlFrVaLbr755ujiiy+O8vl8dNlll0W33XZb1Ol01vYJ92D78dd//dc4B7zpTW+Kosh3zVutVvT2t789mpycjAqFQvT6178+OnHixAs6jkQURdGW8kkBAQEBAQEBAecZu45DExAQEBAQEDB6CAFNQEBAQEBAwAWPENAEBAQEBAQEXPAIAU1AQEBAQEDABY8Q0AQEBAQEBARc8AgBTUBAQEBAQMAFjxDQBAQEBAQEBFzwCAFNQEBAQEBAwAWPENAEBAQEBAQEXPAIAU1AQEBAQEDABY8Q0AQEBAQEBARc8AgBTUBAQEBAQMAFj/8fUgxoZp2zqUQAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL=.1)\n", "U[0,:] = 0.\n", "U[0, (xmaxx*0.2)] = 1.\n", "convection_solve(U, dx, dt, nx, len(t))\n", "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Not really, this solver fails to reproduce the expected solution. See Von Neumann stability analysis or matrix method...\n", "\n", "The Lax(-Friedrichs) method stabilizes the solution by replacing $U^n_i$ with centered approximation $\\frac{1}{2}(U^n_{i-1}+U^n_{i+1})$:\n", "$$U^{n+1}_i = \\frac{1}{2}(U^n_{i-1}+U^n_{i+1}) - \\frac{c\\Delta t}{2\\Delta x}(U^n_{i+1}-U^n_{i-1})$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T09:55:52.411608Z", "start_time": "2023-04-24T09:55:52.405226Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.393691Z", "iopub.status.busy": "2024-06-14T19:41:30.393603Z", "iopub.status.idle": "2024-06-14T19:41:30.395649Z", "shell.execute_reply": "2024-06-14T19:41:30.395468Z", "shell.execute_reply.started": "2024-06-14T19:41:30.393684Z" } }, "outputs": [], "source": [ "def convection_solve_Lax(U, dx, dt, nx, nt):\n", " xint = arange(1, nx+1)\n", " for it in range(0,nt-1):\n", " U[it+1,xint] = 0.5*(U[it,xint+1]+U[it,xint-1]) - 0.5*v*dt/dx*(U[it,xint+1] - U[it, xint-1])" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T09:56:07.444623Z", "start_time": "2023-04-24T09:56:07.315180Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.396048Z", "iopub.status.busy": "2024-06-14T19:41:30.395957Z", "iopub.status.idle": "2024-06-14T19:41:30.443034Z", "shell.execute_reply": "2024-06-14T19:41:30.442773Z", "shell.execute_reply.started": "2024-06-14T19:41:30.396041Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL=1)\n", "U[0,:] = 0.\n", "U[0, (xmaxx*0.2)] = 1.\n", "convection_solve_Lax(U, dx, dt, nx, len(t))\n", "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Courant-Friedrichs-Lewy (CFL) condition\n", "$$\\frac{v\\Delta t}{\\Delta x}\\leq 1$$\n", "determines the stability. Look at the sensitivity to violating this condition:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T09:57:16.591360Z", "start_time": "2023-04-24T09:57:16.452544Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.443401Z", "iopub.status.busy": "2024-06-14T19:41:30.443317Z", "iopub.status.idle": "2024-06-14T19:41:30.490259Z", "shell.execute_reply": "2024-06-14T19:41:30.490005Z", "shell.execute_reply.started": "2024-06-14T19:41:30.443394Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL=1.05)\n", "U[0,:] = 0.\n", "U[0, (xmaxx*0.2)] = 1.\n", "convection_solve_Lax(U, dx, dt, nx, len(t))\n", "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What if we need better time resolution?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T09:58:57.486522Z", "start_time": "2023-04-24T09:58:57.384857Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.490666Z", "iopub.status.busy": "2024-06-14T19:41:30.490587Z", "iopub.status.idle": "2024-06-14T19:41:30.578102Z", "shell.execute_reply": "2024-06-14T19:41:30.577874Z", "shell.execute_reply.started": "2024-06-14T19:41:30.490660Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL=.1)\n", "U[0,:] = 0.\n", "U[0, (xmaxx*0.2)] = 1.\n", "convection_solve_Lax(U, dx, dt, nx, len(t))\n", "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The stabilization also causes \"damping\" of the solution at smaller time steps." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T10:19:38.180809Z", "start_time": "2023-04-24T10:19:38.175842Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.578510Z", "iopub.status.busy": "2024-06-14T19:41:30.578422Z", "iopub.status.idle": "2024-06-14T19:41:30.580513Z", "shell.execute_reply": "2024-06-14T19:41:30.580304Z", "shell.execute_reply.started": "2024-06-14T19:41:30.578503Z" } }, "outputs": [], "source": [ "def convection_solve_upwind(U, dx, dt, nx, nt):\n", " xint = arange(1, nx+1)\n", " for it in range(0,nt-1):\n", " U[it+1,xint] = U[it,xint] - v*dt/dx*(U[it,xint] - U[it, xint-1])" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T10:19:39.635762Z", "start_time": "2023-04-24T10:19:39.468343Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.580881Z", "iopub.status.busy": "2024-06-14T19:41:30.580796Z", "iopub.status.idle": "2024-06-14T19:41:30.663930Z", "shell.execute_reply": "2024-06-14T19:41:30.663655Z", "shell.execute_reply.started": "2024-06-14T19:41:30.580874Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL=.1)\n", "U[0,:] = 0.\n", "U[0, (xmaxx*0.2)] = 1.\n", "convection_solve_upwind(U, dx, dt, nx, len(t))\n", "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T10:33:46.984727Z", "start_time": "2023-04-24T10:33:46.806045Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.664937Z", "iopub.status.busy": "2024-06-14T19:41:30.664837Z", "iopub.status.idle": "2024-06-14T19:41:30.753075Z", "shell.execute_reply": "2024-06-14T19:41:30.752807Z", "shell.execute_reply.started": "2024-06-14T19:41:30.664929Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def convection_solve_LeapFrog(U, dx, dt, nx, nt):\n", " xint = arange(1, nx+1)\n", " #start the solution with upwind method\n", " U[1,xint] = U[0,xint] - v*dt/dx*(U[0,xint] - U[0, xint-1])\n", " for it in range(1, nt-1):\n", " U[it+1,xint] = U[it-1,xint] - v*dt/dx*(U[it,xint+1] - U[it, xint-1])\n", "\n", "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL=.1)\n", "U[0,:] = 0.\n", "U[0, (xmaxx*0.2)] = 1.\n", "convection_solve_LeapFrog(U, dx, dt, nx, len(t))\n", "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T10:35:05.966977Z", "start_time": "2023-04-24T10:35:05.787222Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.753491Z", "iopub.status.busy": "2024-06-14T19:41:30.753406Z", "iopub.status.idle": "2024-06-14T19:41:30.842391Z", "shell.execute_reply": "2024-06-14T19:41:30.842114Z", "shell.execute_reply.started": "2024-06-14T19:41:30.753485Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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XQfA0rHXHjMNGMdJ1g3bZtazJXm2/DTI6Jx0xJSWtehgs0e4TNYcUWj19TJk7zFjfzYJFL2oS7DhCU5c6v6yND9EmbQn0ZyKkal4EqcEwmWDR6lTlApDjKIX09duMsdpFUXhMfX2NCddGR0khudaEpc84DcOuGi3wnSzcT0Y5scsJ2olyJ2TaH1KOFZSzgMsJxJwUNZVe8zUoQDScpkgiJ8alUgrdHHwXweLTzY0egwTosyfkN5by5lAQBEmq0qKvMH4O23baMbS2YjR60h+eJzy7ZDmzpQ9K36GSNoAdR2i2BLIaNJoSaSIiAV+yrzdLSt0OHdPoJqQ5typ7qc0iWzMBbiQso5YuFiuqVdAJ/qCZLcxZqKHxBAy2EYzLSS76a1x1ps4bkQ2qvN7NwvsHQt4BkCGsEp0Oa1/OrFB3BYUdiYCRJmUIUUKI1C0H78tgN4wNi2lC/1BYlTQow1RXZPsHYIRejzmU0I0N90XLIUiInYrVjW6nMGy7EZpxsG6XrE2/rhO76s9dTq5/jVLSIK/jdpGzWGgtRelqRK5+WLTrxpHta9011rphBMDjjjF5t7qARdufIVs9Q7l/al6OHi3SU5RygB5AXOFXWASFNq/Oglcu/i6FtlKXkuWKJKpVXoxkgWXOs2loatCjk11LGnSINu0s+islZGOgzyv9/ssJl8320iJhPzSl97nGUoTtRBNrwbMftw0uloXjlavL4uzSxn01Br1mb7DeA1l80LgRbdQQ5rSBVdLsAzA2elGTZoPp+fyYEIFFeW5s9eqVeShhQInekk2zkHMGRbYgsCYrZ7fmSE6aV4mqftO562dSuo5S4TTmmbKkr2JhupkJUhuhqUVpaIR9QHqM0EDYcdhMrab2lA3J29apgnuEFNfpiueFdVCwr5oaSgSVu8j1z4bKnt2Z6W41wlD5khqNxJAsCLZyN5jz19KkdBExOJ9yAoz+ObM3dzkNyL0Ez6R1sU/BMShqKr2n5EabyvlXDCiBJxIEV4U61dVkJRkiYggEDxO8SssnvgtChoARTVSPyUoYaO5Izn9KfP9NG8KOIzS61oRd5ZaOA3MfwDZ7Y42+Qq7S7YNqKqtqxl5B+jTS/mr6qliJKBeLzAbKk18hCbbPvCVbcrwqGaPVD9XoZejGFH5YawgpW29HO+TU/NJCA/1TKYVujljI6IEHEBc+A9nNZygbL32OQBu0BsOYoVINyfWdkwJgtvTBvkSQ4Jrj2BKQqLvPxKoRkelQ0EKzwUn0CCnRKm1D2HGEZsNhzc+aRMG2Cj2BQp/jKPX3jum/ZmzFx6yBOVdL5mhbTYRXljQO2mh3ntxXbOMMwHDI3p8t4VLYJkbDKuOl1EqVWqNsREyNRbq0RlzVM0O7muFugqW59Lxqsm3rHErpoqDQjWvQCE0lSkNwi4s9Rjg9Qc/WBxTmQZbQdJWBvl00rZZbJAgbLiju8RtlM94SlCZl7M7J3zURTToKQpibaybEvueOpL/exeuWWInQdiwRIHVMlI232zu5hMEUJNFbw4KNUqcCkVUzu/JxDKfAlJMeAzRAVGMLa8bhPYBtUB8vDdNGVyDspy0v9hlPU2hQ96i7gr7sJ4W+7en5i28bVvwWaIQmYsM/lvYDjZM13ViRMRaZ8mQd3d+Pwz1MpqyB1nP0Lbzd6FWR1WoY1BAaDKeHTcJlY1d53h1GZBaOkZ5rRTRXjUUTz9+8C9ZiqtvR9U3cBzQOOTmRO4VcU4NTk8W4HeR6mf8muaryTeSeyEKegyf/GSjVkH5nZ5fy/kHX678VcLOwSnkyDls0dGpRaleknjFtZzONWxKFcwwVZU0G1w0mr0qJiBvsPEKz0ZlV0Xcu95Ura/a1Jh+avrNaYrlmMUnKSWe78JSaGlil7ZDw1uRYKXXBVbkxYGd6BkVSSIx+QXdboVZoHPpMLFulTTAWGndth5SHRlYajz35jejSPFNwzDWyWpD1gbaBNYYEooNBru7NSN80kDQoo0B5YiwoginVO9H1HpD1iHLa0AyNVvt8U0pWUOyL1jToX7oHcdGchm2b6LbmcuoZfQqAe54klY+zxjSuxyEaWWLVd6mGjdYU1XSXjq3CgtAncdX5WvoUAEfk5K3PIq1ngLMpqK7CqMCvBrkKKMdMKofQ7kFJbissbMrtXqU5k9vS4/b83bVWe3XImlw9MmNxNjKlOyoYTzRCszmQq0sdodFnxls7SaL/dXJ/NeekJ6zSD03PKC7fYMcvPyDltYAq7jvBWhzTlaS9dzUCYLureH7r3EtnOqJv0xettikyR1634TKUMDg52Yc8fyw/wNoiFKckPQtYd+jbMAelGvJcPXmTbhZDfaAhWU3zTRTRZGoXzZyC/bBEghsa3tJSfSedOkiW0NIHIerTaeFkKK2QDUG0ITRCE9GvXkZ+tLB/mgAwhHXyOFCcVTNR0ApAhHxXZdfcLivmisnUEAktqMWSBnIJbr6Cxnoyrv+Kdyhd5ddUEEfY583kx+jZk0soDsWna0STDqXiJ48hVZIWloDV88DVA+ULaGxUqTtzc0XEGsyw6TUi1/zgPHBp2Weczp1qPgndIOlPiOBNgehnahZeEMrLk9b/ooSH1r1LzazbfRNNnzuP0Gz0BwkFfXkz9I3ihALNpAAzb1SuH7KhtFldFJokpDiNsiTjh1cnXUs35G0QPc9iJpuyLUrHBUJhm7ESSjclCwnLLY5Z9lYUONKOsM1+jK1eJj0vqyWz1phCS6K2CpHVBnUZcP9gkpx+YHQbjQPzv0DBSvo2DGcghw1YMyizcVa3ip6jWRA6y/wvtPAgMfV0StTgmSEisQbkiCxsXLmcrnnZd4veDSJbREinIPlgBrOAs1bgBDuP0Gw0aqwPNpSDPqCFxbx6X3KWfoxrGva5ApCWhqrq4On9s51pi0SFBiVr5HbkgnnShVVc5Rq2lZJbi02w0JQHJDhfhI4+AxTX/6oQXOuouqyROyYOo09dXs0zU/WdSbqypU5qFlPixphx6LEmaIQmosq1YV5whBTE+ZTvk/si6I+KKWkQYFWR54R99a2RKLXQ2O5tf4WTgs4AbDVWhnzWlFugey9dl1n/ljBpX2D5rhlKNUtjjmm0Y3zmQFQotJaiesiSCq6NzAILYyUvxvBBkBqXABdubRpKKcxBJBWGDCcAl9MQwtOttQvz2iSLS3rmU3F1RMQQcvDgs0Aup5icp0Pnl7HvAWot4Rol5++SEcoxJGiEJqLOSpEmmtKTk+tep3zvsX6PXkWXTrp6mQTNajRK2wRGBIthrj2fk3LB9VmjacwxMJ+R6Z8OWZG/x5Tk6D+JntyWNhFlR8YeE68RTEQgCp49OTlsG3PaPCBdPYC5Y6644yDJ40Lf2LUpcmm5hwvdd7TgTN7dabkYxGOCy2kAmiJccKbEygqAUd8DJ0rfKFEZXVloCj/gjdCcAYo/ZnbiLzXHR5QPzuoQLGkwk2SNW26jTf41K3e7UjfnUGOhKXXpVVkarPVI6BVqXHwWsh5JNl6pkfPjkNv67L8i27Z4ZPwxKXdKxTOYW6ntjq5Zn98e/TzXLPSM5RPvFREVe1Axjmah2cYw7oMeiz1GVGo6xH5YhoBWUzSO1HQtSZo9J/vBK54ATT2fM4Es6ZAd0/qs7YfMTJw2oq5PAXBEdg5eACzIUfDYNlxDI1fDSohsge8jbDPCzTFIXU7k5hksAjGEitkkOh6KpKFjx5a6bGhihrDigUwKqd3uaWV08C/hMwljY8tL2f3jMHbY1md9uIiI5dEOTVSnTg2RoBGaOBOtRuFX0K5YsEaOFfolTWpy1UjSoNwiMoKgZtXYe9HGPiFEtTqEn9rpKtSTJ0lfP0r2LyPjTP/WX6/JbanVrU+x6LhDmrHVuALputHESXlX0ogjee6Dk/lUk0ZMRfBENnc/uMOAqK2lrhg6peX8gsw8AFl74f0j1xEXaJzscqJv5xACQGhxSZFgFJKdkU16RTG/DGwDlxPXWxIPb7PQ9Ii+TdfmwltXAfloLZEoBZrZacaCTWLiwQ9ljRBtg8UxNRlYtbk83SZTiNtx9JqsTZvJYBNFp5iaUrrismtWY6FRIfY16DOXjiSamMdEXqR0Ahzscg/99J7cQkPCWCboIACGgpKZhYa+bVSGAGZwLERpCY2x0GAYNJAGsraCJcd4AXx6CCeHMALgiIiZRFNlvgFWX5Vi5xGaGpRqH6RZGYVQWkgohAhasQz9E8zHuGcNRq9J+bQfe7LQLSKKr2WvFoQzQbqvjWiqKQqpymVAV84rwKghyxucEmCjUZV8UJVYkXoLgs3fA1BRb31r8PostV5T3NZGvqYGGklesHxBj8+RSjbaLDSbACOSs5NTYbHHiAo2LqGLk5nMqtYlYg0BNSJpVSlS9k8otZYUXtuIM1l1ib50hJAcW6G7saqslxU5lpL7vi00hS9qTY2mjrRSUOV6GiJsphNDi3XDDE7mvo25Y+BygpOYgarZU2ugv0nLJkhX9CwkAhyABYiuB7ln8oGBpUsmwsP7DFFZM8t04MlEAqtj0/s94z4OaN3fROw8QmOjMexKIX0uK0x4VSnws0blL0yVsDLdqC1Mbhy91miyAmAb2WJdTuklsiJYDMstn/0zc7bMAIyQ5BOzS6dfIXi+OYpDjUwvMvD9KyUw1oBX41pM+5LRKVjLCVcPk11OlDsFr+1CfnEHu93kN4QaR4Pz4WYl7qTUQnF6Ix0B8tyAZqSTVcTzSwnusV0U4gVDk0EFwxkYWyLg7iATsdar0eBowQIENw3jV/NcEwX3jFLBoa0gKz/2NeZ9BZyIpLmEiFVq9bX5a6w1t4JsKWsawM7pxSHOFc9MuUsylClY51CiU7BRIQmhs5F3iJ7fl141M1XWv6lv9+f4/om0k9gXLDQUkZa9z6iRc5Y5yi+DBAzGgaUU0n3lN3b2ZD7etV1gBaH8OvNwDPOdkYnDMOIUrsfsKTrE5MUl1vWiBYV1kYm5o5sWL0KhoacRmi0C5+Ogh8E16xX04FsrQsqsJQHRmqLtAquXEZayqig7NKsXzsJWqGLytcQZuLBUMkbZV99WkO1CaATq3N3UTuwq88tYSwNe7kKNWZXL2sKQ5Z4t0ngOG+zaJpDrkurqlWhoWpSThJ48CtPH+48KNENzvLSMpOY/uwKtSm0PE9tgelITL1SsWZWXwgqASz8qEfkz03cWXDuBm4gjW9LAWhxR4zJxGB7WOlWhYTPH7J2Lm0mSInOs5VPel2F6DKrIDZls6aCDxbwd5rAhDQqVUkjaUcQNliGYpygqcjmRC46+gck46HsNLie6bjRech2lWZJPb0vN5XA9ILKKiArOV+CCo/FmWZ3Nd7KQeO44QtM7hIaG9TLuobElDYpXHjqfhTQ5GvQdbVV63IpJpyqjafod6D0WmA5aeH31AkCSPlwlimHUCJYlAVMr5Bqi0qd+r+Z9pEkH+AHnR0ra0CQMuV7Q1QMVs/13MZ+60jIBWB2bNB5w7trlRAQsOS5pgEgUPENpO8i9BC4yEk4P5pPrQc+8zIdmHy4VUGK6ai6nfuETdAn3QY0p22oCCmEnCqrvUaqbqLJIoKajR0JQIQBGmLBWq0mpiIJDApZ+fDADsPMLoN6CjF30xVGKV9pv8m5n0l+v7ogNttroaC6CzdRNWYbT+kBU44esCjDRDRbzbWvnuZvQ7YO8NkntKbqfAyI0lPgOopw6k7wuIj9/ukaQrTmL0oqIAG0ToQPry2D36DEoC/P0LIi11yizXr6J6kxx7qmkK/MeNAtNOXqsTakb9T1ZF59DjahUNKspadD7JCbGoRtWaDqUpahGAIwDmTwMhHVfVZCt9Bp5cbXc1ic2Q9ZVyHy0q9HqWfB7ZAbijtl3UdnsHOTHp4poFi5yOeeYmyfs3JF1T9mPK/LL1OjmNgqN0EScgdhS9GUFk7SKKf2ARJT7/wFotkfxn3AzVEy42KxCb6HS0NA4al7S0ntqk47VlIxIu7fRYrQK2+giqlKL5Yu+9ufirEqMaJHqripyAeG9wusxmQVT9twZcjmBBY9ypwzT0gpjMJjOp67ZE5MTGpF7ie47uZJmwEKzNhAuJ2hDz8c0nDtZj2ZP5vviOexKtDz2FtPcZL+LgqQqGYWUWqRohCaiWMw5dpvp30anyBo5eTr9vIku7GhzE4hSDeiqkhFNNUUni/eV16hYLyPHURwCPnYgk1eEKvvq6Y35Fip8R3wXXU7J3zbtuV5dSpFjjYDddGZhvg3WimrFz3SJMCAh2Q0zzdJ+4BJZyJsNyOVE12NPzpDWxHSGLnE6dxD7Dhdgoqc8PMkxqOgkzzn5x7KjYq4wYHpOB3sml4KYn8tf3JWgAk9EDqVFKT2sWfw0l1PP6FWnUm6O1+4IdQBpgrVuLhN6XjPh4kHltj51tlXuJdpWphmxAVi2v/wArqsq68ZGl8ug+aomIi3dbSvcXHTcGldjRQ2sjFihm6Tcxe5TX0OzQgF335mpUzkLJTLUkUTWCoJWdaHvxPkF7h96HtzYNhON0EScgbsDViPpva9YDWLWaCIXAzDppt8Z6Io1GHBONZEipi8ahs2S3KcAmMZhrWm4s9xmyhD0rS8Q11ffq74FwKnxwc5pmzCpl5KVvpM2ZrDVx3VxWPsRTP6m8gjgmtFCchkKPBzkD9f8faMWDhTHU5I+IX6OYIvEGsoJRv8eUMFGctVB9FIW8hwR0yv5NjrGcGFy9fG1ZSg/QSUe6FpaHWj6d3M59Qftdin8kKlokjFAEy8dwzDjmuW8tXiU6nYk6auZsBCmPymYtP2zGyc9JvRVYbHSqzpBDusS5sG2Uhet7J+gM06bsW2BXiYCzpXuu31OrWsNvkdpO9RbyJByWsANd+cfSyRlEDm0lrTDsgQ0Xvru0vWgulWQTyariwVlH4ZLxKLyg3aUbmcWiBW46rrzEjZEdaxgbCQzIlg3c7bYNs9pIdHfcYRGY4P1MjXi1j4LvHK4plz9Yc6BxMxptTxbUPahxmSqM9KWPjM9l4ww996uwnRJA5ooDAFDkzocwKaarYnqUSSnRi9TdgO1WFvo3CK8Nc2UPqB8LVpwDhaaaRAZU12ltJQClSUgUXBan+r0QGAThYFTSabkmlCo+MxSvm0WtrGAO9/UEcmZSwVP+X6kl8H7Bxoo/GZTxLf4zmT7tDw0G49SMSeb0Cevfsaix4imGk2KygTbs6VIh3wXglfzdtJxu5pGfQuiEYUfjb4tNKrERc8C4LMOhcS49xD4NI19acmEiLrkgNvknppqNbyAq/iG03tlMnrLjwpaXnQCvq3FziM0dlYozf9SI7y1lpHCPAS+rhJss0XohA7DkoYavUyx3qRGW2E/2uluNdmaCbJOmHI5SQ2Gfo4ISrBcruviSRd2NhNs3+4lQHF5CJtlV7pGaVuWQgmfq7x/TEBH3woopTCk+wf7ru1JLCO78h3peeYoJEmMYbyD1HpEEVMy2sq+t2sPysU20+BOyg5J930GTFa2ArdYDBuSXbpI3YGERjbDCUtYG3SKduofttEz2acLyxaKtImxhK/f12jaYAGw1ctYa4xdcRa84BFnYJ2qOIesiQnDDA7P1yJjIy6vIUc9Xg88ZN+WM/HtsW5b68rVRQqTiRhdWuSGwVU/+UDA5XTKVeWePZGMDYInpqke0zy9zO6mDkgUnWwj12s61oiIaam1pFIKA9DkpOUV0EAD2+ZBnDyEEHsaL3HqdFNzOW0XiIe8ytyPuV5cXZTSB6AqRJv6MxYatDDBSqFioigWn0rWoK83Err0736X/aVVrlnQbu87DQQ2FeZQ0iHl1rxvnzdjtq9B6Tgq3Bh4r0pderI+UAcWGiy8CyUBujnQ0JCVYneioQGhLEbwUC4Zupb0rQRx8iDR/NC3giLBhtIaQ2UZpvbloU/TybeYinV2QPpIU0QaK05smW+zQTF9YOcRGjv5lX5AtV6mv9Xr6YbpAcp1Koji3DcVffVt3jf3inazz0epFaHmmZQWieKkgoXkaNwxVQoeu2CWAuCzDoLkVOUCqvneTc7V1q9gPsIvPDYYRi9DDafIDFLxfUbSILrriDCRkLxvLdYmYucRGoJ8AZX2Q/usqS84Zk2otWiD71VVYqx0P/fCFIf4VqAqF0kVSTW+HtVVXfbn7F5BE63vof6l3z1tZrVIPYeUb8XHuFwvk2+qIZ90ffHdTV1ONqszgd4DcDnNQEkAun9ZlBAUKqK+yG2EWhuwKA3BekTHSDF3f76NLCPkliML2+AU5JNJry/lw1nKx0+lFQb4LOTtzDtvvpOl+slGaCL0hMVpxMVuOuR0cv9jkdUcgBfBThR2pS4mdfzgWYGq1fJIKGsa7phv6tOCUpUHqU9LHF1bq8GwOZTMBFhjvey57laK3km2fI4yMa69V3IxpcPAjYWN9FQgjLXWB5zoSRScbMpS/wfrT4YkHqbnlKpmk+trNrkAxB9X84s0ALdcB+c+2JOz2dnzoPp4IlfooHI3Ca4HCzA2cHOR2wznOpvYpgc0QhPh7WmFpjj8CNKNRw3D5P7pGPjdtR9PGdFk8oxoArLBOWdO75usLq22wo5Njlc9bjqiiY5JHxqhbarIAFwl2k2NnBWkoarMCHa4scJ0HXyQERq5G+plyp+t7NuA1kC3SLIWabJ40DOYtutmwXoCuV4oyy7nq3EPTToOulezJ2DH3XCe8P0nEfNgCS5IkgV4CgTRc/c7C01NoU+lkcs6F20AjdDEGSxyxc0qNiFDX+OOWfzBr/JZw6Ye6/JsdEmD0wcp3K93Lc/kDqueyUIneO81x2R+HdUXNev7kdku5MW4geUDUuVaK9Xp1CxO+tQG1eh2TP8RrlBwjdsW3YOyP+E96N2i2ZOVs3SOa4TmTFCYtEu7UyCiqTTXC8Lm8uhTAGYn3E1AnxlpNQGr+UCb/WpEmaUiaZuzxJ57OlfbFb7NuyJrk20JNLmY8PeZ9A/Xg15JCsvN0tjLJG9kzWV3NDxbVIIB3DNpwM4QyhJ0oKsZggtnCO4ZyjnTodYmsYxgxFS+bXUvRHjBeU7tyU0j0xAdlo52OAWupF1O50btKAfREFyLmYXNPPON0EhoV0GhnqVvsWGPFhodKWJDdcXEo11mOmdJBQMrtA5UuUCEHqnOxZJvK7Xu2DwYlN68KgLLFKKzCSYtzjpCM9mNoRPmSb2MEV1jqnuRkC8iMFknPYNUFBJDoZN2QyiZMHNycmHfCHbPdKAZIR2JcTlNL+fbUN8D92CQljSIiA40OVMnRrfRWOfud64kIi9UJBPlCun5N0KzsegzMZZfHdPHwg7ENSvdrypSJO3LErKe9TIq4Zy9VzXj7dHN1XuFaJEUUgvJaRg9ugqQGNdYEuXgehUB96m70tY01644ZL8iQaEuMyLR50JPd6X8J7ANySe1A3JI+xJpykiwXBT07ZbL2oiHt9CKv/MITc2kXur/t5FENgFRod6EQ7SpoTwmvWzpSq9QTHx6bGUui3FwYlw4ZM8WGnNMRM+C1/R5610ArMdb9jz3LgDeYHgB8OSJRxeYrBEAi+8RPh9gba0hDZSFmkoppB4VSpiHvPg8KF8wDw8NVc0Ga8kw2RcF3DCQtX1QuXs233l2d25CWVvOb8QwK+mQnxMVzkTnBEU5QUFMcjmlhS1VpuBmoZHw1SPzTcb/b/31NuS0TxeI/njCQ16qQ0ByBNtqtDwEUc/Iapv0QGQNJUWMa6w9PVridJp8u8K3Voq0idTL2P5Lk/5VocY1al56qZfBXaXLKRuGvN42CzVG2smK79PJvh2UTKC8K3Tq05T7Blw2sxAllLls5HM6WISMyFDlGovdQ+mDdGzkcqKIJnIBU+0pImWY0ydp1/LQ9AjtXqpICFc6EK0PMWZq+6GxtaJsavv06yD9+oiaCabU5dS3BkpM6r1njbb9Ca2UtabVEI7sVZBkjt/Hc1AAHM5aYhcdnECxzB2Bx7SibgI9HzKvzTAR2lLRSbbQ5CxqkOaSiYiO8tAAUEeS9kVC530kXsk3zS7k412F92+wmFwPHBZYWebzVmR5SQnk6X0p909yLU3OKpnXKtutaK9zDRUJ7dSKBWBdWtp9kE3WFSJbbCibFa76sa++NTRZo3zThruXarDRmiJqUhOCa5/nLHRGTq50yLNNL2MHMvkS1fVfqJvTz4d1HyMJlg9+ny+gHVthok+0EFakrkBrl9DQcGcV74uQXLTilFuAUkFj/8UeYVupP7rCjVGaLEu7dXoWCDrLCLWpcQu47pT3oEL0ic8HmYzTiBXMg+HGoSE+gn2XYNiCsj+MPhc78jzxWSABqU2qmFpkdIg99C+PydFWoKFJyzJQ5W5wuwxmwF3zAIR3Q6K++fvETYV7NVjI91tdcIK11eV8vDMn6BxG96XoJUwgSEUs5XegmxEVzpsoeGNhEw7hB8P4qKVexkp5DLRrjWyw1hUjdBN6kpT3QIfYG9S4J2zSOKshKuy/ytqVkk8izzUaDDpkaTV2Epf3bGHrEzV5ioyMC9dDNffKXt/0edNuLvl8UDOqoQTP6lRykchFNKQXBkofrNFAYBxrkDssfY+w9hKVL9ibx0Gn5QsiIqYpFP8k5ZhJxwHuJSqtsNuJuuk+D0GIvZZ88KYgZ07W9VpZToadR2isudzua9rQRwuIRDFhop1tHSRr4tX9JX5bKyaWdWNqNFBphzXh43YliTDNalwsdEiRJG1Ifv2KNPbF2hWp59gUi1KfQJMHXCRDDqV2xeRBijiDhY3RNsjvDBIrmqxpaEYoPEWCXbDQUIHGE0RU8pHMH5tMEoh80ca16ZxdkJWJrse8ECdri5g2Jeab1uClTC00NemjJmHnERpAnxWLa/rvFRXu0irdRIq+i05WENKsMHpFjo4qmDIEFSS7lGzV3Peq7NLpvrqvrXixaBxyG6HQTanJOBaxrLCWqGNCs4qisvpammtku7Kk3Sy66L3SC1XYJguTFhfBtd/YwvtitEKleqJGaCK07borTYFv9SHSBVL8zbbj6LFEQpULwJ6n/Taki6KayW+jrRRVBKHM2qUtHiYb6Jh92eKTaB9s5N3Zppeh+1IaHWb1MmgZce0yvUzk11yHv1uLI7k9beqAFOSqoueIoqF2gWUEnt3V8/ILsHbeaH9Y9uH8XLyysJibUFYeAJ8QEJrhA3loUmopIp0UusN2w82SqTyoVENa0Xt+FwwkHUM3uQ2hEZoIbwMz7hM08bqPFr/MFdaMHseBMGG/PWswcN/SyV9baMp0DrY7uxrUETylIbgyVFJHHOlQ/7R/auT66h3i/a6qNG7bpUTCrvAx+kWOQ1gW8D0QAvSxkKeFYebJudKcOEV5UqDG0ewJmsDzbXNQNXsqYWADqjs1lROV5VP5OKZBG0PXd+7+fBxGbE8aGmKQuC8l1htMniM7M38VznG9E5q1tbW44YYb4jd/8zfjyJEjcckll8RP/dRPxS/+4i/G9N8XBuu6Lm688cZ45zvfGffee2884QlPiF/91V+NxzzmMev9LC8vx6tf/er4rd/6rVhaWoqnPe1p8fa3vz0e+tCH1g3QTkRkjTHXGFdhYr/wE0CvxQ1R+Od0E6xrSO2ccMyeMwBbHZCaBOzzYasdlz4z1hUIKM4tVKFPYguQJEjpI6MF+dQZbOvTC2VJpXXFaDH15P69Xoasz3BMIrjp+60JiGuH91QWQ410X9KE0XipsOMiEZp8V3oXVh48+gJSzpy58/NiTlTSYHU6t7x0oKsZAPFJx8uEBsjWoltED+G6YTHNJNvx+buhkFU6hoBCUQK9E5pbbrklfu3Xfi3e8573xGMe85j4kz/5k/jpn/7p2LdvX7zyla+MiIhbb7013vKWt8Ttt98ej3rUo+KNb3xjPOMZz4gvfelLsXfv3oiIuO666+IjH/lIfOADH4gLL7wwXvWqV8Wzn/3sOHz4cMxAmF0ValZdCUrzfZzeueyYGjUfdnte6btGk7CN8LIovb528tvoe9r382EtPllOEUdkqyp8E3p92bYxqp6jpKFddFS4RpW+Aq2B1h9WMY4+IfMe2RQa+TcQJnk6T7qlVsAt3knpBfWwaS+S858TVXCnbaXcBL0Tmj/8wz+Mf/2v/3U861nPioiIRzziEfFbv/Vb8Sd/8icRcdo6c9ttt8Ub3vCGeO5znxsREe95z3ti//798f73vz+uvfbaOHbsWLzrXe+K9773vfH0pz89IiLe9773xaWXXhof//jH45nPfGa/g7YveOEKv8oyQrtKi0TWBN0O0pIhrQjZt8wq0aQGw6JYX9H3HLnRx7Th47Rr+rzZ0Hz7rZGEMYu+oEeGVtvbWS9DzaRlS03q0vKJ7h96bzHCbfI4rEZH14eTMNeyw9w3zjo8s5S3o+rSM2BsGCQVvTtwzax0ueVlatVFW6XVvCPY5TRYTPqX6RA4SV++69QAcvVAxfAusXatDCYbJAaiDaF3QvOkJz0pfu3Xfi2+/OUvx6Me9aj40z/90/jkJz8Zt912W0RE3HXXXXHkyJG4+uqr1/dZWFiIJz/5yXHnnXfGtddeG4cPH47V1dWRNgcPHowrrrgi7rzzzipCY7UPGGonPtC+VJQ0UxOMEq9wlT5uHPyRgoc3LaaGfRWSowi9CsXzUjlQ5KRTurLGY7quvMvJrYa79O2n3eQEYBO96dQB2Y5yWw1Ef1VRIRXPkVpM0Tta82ypYxbezxhj1ZMkx4jL8ZkUQueIMen/SfAKE/jwwYngF8a6sCcXBa8u5dPxoMtFLt0caFzgYqauI/oukHvJ6rOGkL+HcszM7xllghfshgJSCda6yW4pQu+E5rWvfW0cO3YsHv3oR8fMzEwMBoN405veFD/2Yz8WERFHjhyJiIj9+/eP7Ld///64++6719vMz8/Hgx/84KzNt/ZPsby8HMvL/3ARjh8/zgPUiTvktvQDLc2t9ELi0CosPlmTGl1Gj5aLqhBfieKaTFIvs228HTUWwfTDVZH4p0qwXEpoJGryGRXDPh+SHKr3W7p/NCkT6yZbwgVh78EG36uqzNToYknbwH7oXiLLtbRmC7B7rOJDJlfvMzOjA56dFidg2gB6JzS//du/He973/vi/e9/fzzmMY+Jz33uc3HdddfFwYMH44UvfOF6u6nEidh1XbYtxbdrc/PNN8eNN95YfwLfQmEIdV0ESH8TSk3qfO1sxTD2dAP0VZOTos8Vbc2kQ82sdCA9f3vbpeVsK3Io1RT1VAVNbQmQjczaFVHFZIsFwBHFZFx/j7AI6WSdDrucpIWwIg+UivSEcVBiPQK5lzqYe/D6gkA3xTK4l2aO5dNxWr4ggt1cM6fgIGk6BBhrmsX3dEPoC597ECKDmHp5btTKdHIVzF/puFbL3rPeCc3P//zPx+te97r40R/90YiIeOxjHxt333133HzzzfHCF74wDhw4EBGxHgH1LRw9enTdanPgwIFYWVmJe++9d8RKc/To0bjqqqvwuK9//evj+uuvX//7+PHjcemll+YNezbvlycFg230bFE4vjmGrhUlxYUys3Fmpq6I+rKVgvVqW+SPr7K8FPK0KgtChWsxu/d0UDsJ11T4Todhyf4moNiSU+paixiz6p/sUrbuQUsO6ZnJ7p9NtyBd7HhM+X5k7TA6yl2jIcyMg13uHKb3jbKhDq7R7Hz+EVyDdmsQUj6cBzcXcITV81KXU95mCC4nAr4He/PJaQbO68IHjca2H9hDMeajWN0uUU4nT55cD8/+FmZmZmL499l1Lrvssjhw4EAcOnQoHve4x0VExMrKStxxxx1xyy23RETElVdeGXNzc3Ho0KG45pprIiLinnvuiS984Qtx66234nEXFhZiYWGhaMxaQCoWMVXCW8JWfMetG8OsysmCUENKSt0p1M5GY/R9DwyptvNE1Qo8+VtGn9XcKzVeY/mrhbz1Zj9sZs/dWi7SdjLXiw2ntzmI0vfZHhPXV9bdUSg3JPJMxRjpxlMSuqzIYjCRH5xKptXl/IauzeRT79w38m1keZmBuZ4XiZMtwbReZtE4bFuC+lHQ34lTo2zrm/O7oFUyrlNlL3zvhOaHfuiH4k1velM87GEPi8c85jHx2c9+Nt7ylrfEz/zMz0TEaVfTddddFzfddFNcfvnlcfnll8dNN90Uu3fvjuc///kREbFv37540YteFK961aviwgsvjAsuuCBe/epXx2Mf+9j1qKdS6AKQwtwaES6lfM/+f4UKN4ad1NVK2rLFKl+u3CbM5VXkpXSys+lWpb6neJK0eoia50gQmr4zAG+JXqbCUqusXTZ5IqCmBpZxl/KOMI7trGOS98Xmzckg6/uVJuukbXrus4tXCkcH7cvc7OiJnVUamre97W3x7//9v4+XvOQlcfTo0Th48GBce+218R/+w39Yb/Oa17wmlpaW4iUvecl6Yr2Pfexj6zloIiLe+ta3xuzsbFxzzTXrifVuv/32/nPQxDixFGwrFY/V1EYqfOv9ahAeSp04bfIxqkSDEr6it/gYV3xACIo02SSO1r1kV8PJcaeGLkNoTUZroyOxmaq1vmejJ05AVVZuo22i90oKgLPotgi8cObZtaLjKgub1aYZ2RztB88uZcFFlxMVrEyielYgKzBh7TwIgwaLEroWYdPantGHhPajSCVyI1J5CEoOuLCQ23wetu++kb8vWJgc5bQyLHM5TXUd5k4863H8+PHYt29fPPyWN8b04j8E5FPqa3rBqQw67Tud5ATQ5jp4QNAfC+ZKRPJS4nlSeCKdJzz4lPuAXvD0wZ9+IP9iY18LpBvIN5GmiDJx0nmlX7NpMmvWiEptmYeVsmcGDwnXkp6j1b1wYkmIJV0P2obhq/N5/9P0HJ3M+0snGfLrU1ZSjurJNtVNsJlPGdrAOEh8ys8udEfPbjKOaTD3z5x07zzV6sEQXBhGmop/etk9f/TM2NxCdnFmLLD0/BHRJJfT6j64bkRI0zpNx6GKNpzT4t/CgoKsNqRnhHGs7Zm8X6qzGdcO6zudlzdMyVxExMX7RjUze+cnh2SvPbAcH/9Xvx7Hjh2L888/f2L7b2Hn1XKy7iWCXBFmsBaaPksClO4XdWbOfAUn96txKdjrKxK4VVWkJZgEYLJ/X0JDiErpwDb6zLoH7fNsMhYTtslSrE4vIx/CLD2E241LRli9zGTCyBFv7vnbigzA9l2jGkdE+uhaLuwaJTQU0UTXdnWPY9m6hEGy4KTku9ZCE7tzhrf7/Fzgc/6unKw8fO+9I3/vmiEh0yhKLTQ7j9AA6twHozujn7UiA3BN7pi8M9nO5q5Qk6Q8pnWxUDMtUt0C30OfsNej1MWJJLh8IioWqfZ9m7aLVoOg38lkN62XcZZPPmahBmor9DKEiu+pTfrHJQzEQoGsekQ4rMJC3FOdVoK2AXGbgesxA9qX2Q3PpfCPjrVpR9rG0ATBhChqUzYNRG4jiC+GJlbWxCt0RjYnhV1esl6mjDBuyntmdFE1JS+oe3uNknujQ/OlALi0KKu20NTAXsz0tKyV1k6cMt9VllPEhtOjXgY2SSuTyv9SoZfRQRA43uQa2TpI1D1M4FjUE8aRZvyduR+qaINLa/6+fBtXw4Z2EIGVRmXRua/R9aZClIv5TT21nA9ufi4/sW+cGvV9TYubvHqqWWgUfEZTaFa6Ouk7G68xSWurhdtmc4NMrU1PahJDSj9uRX6WWFk3gBgHosJKofqyAnEUfbpJMv1AI6esSWgnTf7Z+yHdsdrF0qd1oOYAFc9uunrnSvfUP7xrNFlb8iLcpUzcYGwbreC2bj+4HkgkSG8IzaYTvRfphyAnXayeB9rCxbwdPR+kccm+A3Q/d+csh0jawnk5wXjQnqVs23fsPpFte/h53xz5e0UIBFcGjdA46BWn3Kb6pxeX+u/xZa5YWdeE6uYhybIviyoNVLJzxXmq/vtG3/qe7F4RAXEmCaolo6/vZlhkSiGEplXJNO07abJL14S7yxB7k5Vhy94Xc6/sMPCZdA90WsLARqT1XhImbWffZeh/diYnPnOwTYVkbyB2HqEhiNXruG3pg1+VMK9m8heHtaG1dl+Tl0dbWSS0id4WVewT+p5OHojWU2GxPXev1L2vmJysFcFYaKwFyFeH7RHaFSjH1qMYtzRhHh3zdIdpI/n8aXMajk4hG29F/xzwAOQFvjPd6qj5ZeF+F01JFbOtp2B6LT+G0d8MpF5y7by8sxPLeXrixdlc8Pu3p/aO/H1ybXIY++pSs9A41OhIAMqdZE3oPZJb7ebqu9IzpZ5M+6pJJWSFbfRNNf7znheNxbkxqqoku4OY62EJuk0KptyNNa7XjRafWr7Up+Us7L0qP+ZG5wzqG8pSJu8Lhc5TKoipWXopiayMHoQikOh9XN2TN1s93y1OBnuI+Uz4OwKjl6Zn8r4edF7uXnrwrjyfzMWLucvpQXOj+54YTK7l1FxOEtrKWeizryIS0oyM/ZWagqUuw68kR7dp37kEWplwAujR+mBRs/or7UsmSUOLVfoM1tjoLRkvFHVXuQ9qkIpxawTAmhxOdjlxODZ0RnoZqy8ThGBTNIMEYRGskuiQtYssmitwskkOIiowSd+eWcg310GCP9Y7TWaWWKYBKMAAnplTe/N2x6byEgaLMzlBSjUz962QMGgUa0uTc9UQdhyh0dBm5GTDFhXRy6B1O7QvbJOZk5VosNQHPG4ctKs515px6GNK85FoYkNJETQBiHtl3T9VGWPTdlvrhh+BKlOBO8pt1MwspuSzoK1/paLrGk2bhNYtCY2cjTTDIpk0OOHK1QJuCR3YkkVTuv0oRHsWrDYUok0RTMNkHOnfBNOGsPMIDVop8k0UVkdQqy5rpu5Rb1KTK8RPbPnGNBoDBe32I6tFlLRt8gcaJSQ1mqW+RX0pLHkp1aDYCdGu8NGKINxEkgVrrYaFeWksfzTnGeGTD6bkk6LPekyYN3YcaRJEe0xClYVGtMEFETzj5F4iy5ZNDph+Z8ilRZl9oSvKTkz3bwhZe7NnawFEvLtzzQuVL3jI3mPZNrLGfMdiLgRKycksJdxJsNpcTg74AMqqy33qZXRWVtnMuTFkZ9YKQqbx7MNrJ8kKgacs9JY3Em0i/Ie3T0IjJ3AUfVoXnJgkcQU3cOnji+sU1Ux0FYQXUajLQNhnF2a2jIxbwkQo1ZeFJDD2G2ghFicRTnemn0kSOxMRhNI0af6XmVx+giSHqmhTqQZ6PgZ0Ysn1oFw1RKKGIDA+dl7uJjoBF5wsNCuJO+y+ZeFyOtlcTsWwLwdOzuIFL/VPn95W5ghGk6m2CskZpbBysoUOSUYTuuyvFDXC1TNvcvqQ9mNcGt1RMyHSXC1zoJj+EX3rZcwhtStQ9id0aHQMFoP3p9E53ZB2FuOg3axx0d77HnOCdSD2naopppkuFLCWH40j37Z2HowN7t9gb05NsjxTVL5gT04cqHzBpefdl22bhhf1ooVcFHzf6qjWxmQObhaaGlQI/Uo/qr1LbdSq33VlzKgRbkVUkzW0V81BkN7pzIf07fovvqc1E7gkeMYlxOHe0j1BKCzBsFUC4OJ7Kl0biFLXs0xex4s1974QtkQzWOqylwJ0Ji+WucLYZBZnA061IfdNhjEjyxdQzpl50GAMJZtN2w3Fh9e0ITRCE/4BVCtkWnFV6GWqMuia/QD4nNKLK8rY16Sx90nB7M5i5tyEojPpIfh+krBLftkxRFs8SNbrRyngUS+Tb9MWNjOQzYBK9W8tms4aY0SkNXoZI+anY+JxtYsv31RT5kC9pyRQlW5Vm3NmFqrdTyeylGkwNpC2kNx+M1Dtniqc4zyR3PsBnCYEVqEg9+j83mzbGjwgqXspIuKby7tH/l4SeWjWlsqoSSM0EX6FbJO6pbDJ62om8HRfy3qkm4tN4/mu2fNsCRnBJoizhNQsKCz5lB9ZRehqiKb4kNn+fEmDyX2d3lZIwOx17DHC63Q7153oXkcFmrxNETmRqEleRwEPNmfQhqPmXiW7YkCCrUQPL5Z9r7LoQXI5USoWGAaVNBjOwftxPlhQkvHuehBUx96db7vkvOPZtoftvjfbtgRCoL2zeX+phWY3JN9L0VxOFUBBHC1sRBIpbY7v+VuRfeBM+vQxzeyqi3VG6d+OHOkkaTUJCbdAc1EcpWYJgnQplJLgqSGIEsV9P71NajpEWv8tg3it9D2294WQ3gYUg5PA2Jl97XmV1t3SoOtR6GLBsdVYtuBakrUkm08qiOw0iY7hmGvT+VSeRlWfmpuc0C6Chb207dQgP+Z5s3lumr9ZOm/kbxOS3Sw0EjqlvBboioNaF9FGT7iFrqqIM3FXbbDoUwqA+0Sfq3mLqsSINRYf0ZcVAPcaRdZnX+MO0aeFhvovrV4d5fqvqhD7wqSY3pVUZvEYty0bL+aXAdJOQ6PyAqVygppvvV3o0bkmDSkD8DTkkrH5ZQikfSnNKVOCHUdotKsATZOT+6sSi/Z43/s+Jq/0YFP6RMn+NYFEi4G0+PRItrTupdTlZt0YqG0S/Qc847jCt33BRnS7GO0D9F9jSaxwGWbuA63BcM1K8/cYzUREaKuQjppKu6t5Xwg1C4XkIEOwYunoJatDw3GM/kmur8GiJAi7oIr2NHwD905241x8YZ4jZu9C7iJ6+Hm5e+mCuQeybd+EWg0kHl4ZjL40poDl6rC5nIqBJnS6MjQhphN9qbk/ok74WCgKxmrK1uwrVwoKFatcmwMlE+PaaI+tkBLgZELPH3zcCi1xVdZLW9JAhimrgRB6Xg3mbgy50CGIXEARgbmFVHSRJKRs3YBjGhJZQRY9+ZRWrPSd12U24LqtumuZCoBxXBU6N5PnJiJi7dTkqfzYyTz/yyosEMkac+/c7mzb8ZU89nwekub97clRl9P87ORVUnM5SVR9F43Jv2LyqyoJkHVWcUwM1XWC4sLgAzK88L6lKdo3AbbMg0ljb2GrUKsq5XYyQfeEfeDEthr3lT1mYbsa4X5VwVFzfWtcWqVukb7JviRIKseMfY5wASe/gUqbRm3chdOlY8iVlrTD8gUwDpMnZhzI5dQlhzDuK+viSrHjCI2OOCLRHcAURMP+e9auFEO6REg4zUmqSmcF+dUqFQhiI7lto2H1C7SrnDiNxYoswbYOTVXhxQnjGt8Q+q+5fz1qeUxm5jM6hnEPWguQtLA5PZy0clrYfUXUGwYk0AGk8N1YY04fN/mbCnI7fW50CxDlNJNf87nzchfNdHI9HvHgb2ZtqHzBQyGiiYjP34HVhtqlGprz5yZnAW4uJwv7gpcSDu1ecv2XosZqgeJF+g4QeUmPoZOwSR2CTNGu3AB9+/UL76ldcWHDmhxKpi9055Xpy8ZuM7Ara9td4T2tIlsY3Qe7ivfKCoy9Rse1y5pUuJdqCCmudZJzYL0MWBDgGs2Qy0l+F1OLBJfbobFB/+j6ApfTMkQ5JRaZbyzlmpcFIDRkZUl1MBERJ1YdKzt2ajTyaWVx8sdo7ZT5YOXYcYRGv+CyRo6dUMwx/b792cZ1XSUrJEwnYqr7Y5X7Ni38RkdjbDRsRJO1oBQS6KrEi9LlpB5dLdyU23DfMoGnPk8ZEYPWLuHSmyLtlM4vM7n/iHC5dPomlaV6mYj83th7tUomFGhnrcOphQZmWesBIAtNB3lodp+XWz3mZkdXf4/c93dZGypf8JBd92XbHljL9TJpSYNxmE8yD1+0mAuMU6xGs9CUw06whebVrdBzVBXRK3xx6RhVOmddAdgJGpU1rYbklN7nCoJXU1Mq29R3SQNZ9FUlhZTvY+9QL3jFNuhfEbqaCbdvjVIp+n7XTGg76mWge5lh2WhcfAoGaIb9g+4FQ7JH29VoYwYUjl340BCJSoGuQYGdR2jQhA7t6KUH81+5Cb3ctlpcTkD7/1270kKDNfOQyk5ssUUWGpEYF2HLEJRqcrTw21ZQp+fIENLNcC+Vvn7akij7p/siVu+YRsEmtKsRdSfH8CHxchtBZolOi0zSpNiBxZjyy5BepjgVRmn+sghM5kd3eXk1n8rnutEXMC1BEMGlCk4N8gzA31zOrTFUwqCDD8HS6mg7I/glF5rBziM0AGv2JVdM+uGybLz3xWWhlsf64lFUWlN4UgA/2gS7Aip0D1o9Uuk9rarMbLVN1J9wHyB5qSg5oAjuVgnme3TVeb2M6zB9J7UYXB8TthmNS0VyPIR0y3FNJtE/6YyINEgChmNLri9+O62kYd4Jdx60ZynfNQmPfsSeXBRM5Qso58zu2fOybUR8qGDlyYT4XLIrL62QYqWJgsthIzQgxD57obeNOZcgvypalyFeSta8SAFwzSoXGyb9bzBRGQuVUwT2qxAnG4KurV/SIlZcksKKKCtEpWoc4e69zo0kLSNYNTuNppSTsC7GWCrqrnhObb4ka0Gfyr7jkrzAd90mlDTBB/h9stY0agfzFYl2U3xjJRcFH1/Jc9PcP5dv+/oD52fbBhAdRhaaQXIOKrHeSiM05dDaku3CTMqgK3fTNlvUrTATrNcclPfX64q+cDWv+9oMgmf6kwLgmgzZxSH2FlU+vWQbajDKBcA6R0k6eVh9WQ1B32iXbKkwO8JZZSv0Mr0K5O09JpC1Dt4/Klcwl4hxdfkCkjlUrOpSHVDLQ9Mn5CpJpykX/W9GOE3xISRJo/Tdqjqz1dDIvBp2lYvos+ZTDbdNb5a0SPiQdWmJS/sjWcac1csUCoAj3MPbd74Td4h8vBXFUdEaI92DqbvU14CCY9os1OaaV7iSELJkCeeYSdqQNkbqZWrIYeZyovdRWs6m5/OXfha2XbQ7dxOlWXsfsngftMlNUedDxWwCkQ4iQ2m7SyHPTYrlTib9SbDzCA2BHi70i4u+SgW747DRKd/tcO1H0KT8pVWHDXO1Cdw22kJTAeXGkATB678mb9Ph3njf6csO++KKFraJQ24FcByW0GjtymTShN+iKr2Mna0nP7y9irBjjNussC7bNOV1qfi0lebv0YRJLgrI5ZSSi79dyXUwR5ZyV9J9M7l4+Ov378u2kVWIxjubWIpmUbsxitXl5nJS0DlLZBSBmWC3TVZgOqZc9dtIotLIQJsUDC1FpDnAYprJNh0ePLmrsfsSSoWmmAG4/Byy5xknRGvtKbcY9FofSJvy5TYxDtSJoZtEWhroGMnzrF1aNr8MoCLKN+/LEhppuSC3S9bG5pepKMBqsmbbwp/0LMwv5INbnM+tFxcs5qLgNEz7O+ZPZG3W4MO+ZzbPabMGbG73rLOi7J0btfg8dLFZaPqDJReFNYO2JOdMRP6hrSFR8mOs+uvbX1+TdG2bIHtG7GRNzaSFBssaJMcdWnKEA5HtNrqvihfQCYCJ9VHDsv4jwrm1JMlm4l2ofYPj1omw5fNWmselZ71M8XeRcg0RF6dt0D/lnKEcM9OCkVIuGYpUYlcSlGWAfWeTVXPLQ9MnKkSlVcnqNhqCSNjMnD61faEVBFCzSsL+RA4ULZ6tssaUCU319aip9Jz2JSvM6yrldAxjId0EvYz2MwjNCFtLKrQrpXlt7DEJMq2/Qo2XXOqMMOFcYsWq0ctYcqhcTvZbIXRBEREz8DCsEQlJrC/fXM2jnI6c3Jtto/pO95zIXVPH5vNoKEJaIoFIT4qVU83lpGAFpDYs0k6w2wI2LwiZVullo49sug360tYv6R6s8dkXQ658e131EyqKWGZjwxBip3fCFX7pinYTYud9pE/i6tFJJ2GjXBTg+yEIKbljvYXN3dONjhQsLWNyeudkN/kN1+UhpLs7e2fIJU7fUzCjLi7kDGwXuJzOn8tdTilx2Ati3wct5Nt2z+RkghLwHdh1f35MuKmpGPni+cl5aE51Nm5+FDuO0Fj4GjnpW1TRF6DX73jNKpomIsi6mbkxSvUccQbzWqkAuEfNSxXsql+SqFKCp3VBFW4XI0jdLgLgCBhL3+8Q7iy21bhmqFmfi4IKFw4SaK35mUw+i3MjxRm8H+aa43nm20h4SxYarnKd/k3uJdgmHxoMrYZNc8mNmBEPiGlD2HmERn6gdRFLo4foGcqLYQrLjYEPJXXNDFjwCttE0rGIcBaDGgHwRsOWIajIMpz2VxpCHDFmlWuqsUcot07v7l6tpUv+ts9HYcK8CBeJoywDY8ahq2FvMJj00TY3caalaVAvU2VhcxbM0oKm07Ogg4ETTYs9RkSsihIG90UevfR3p/JtJ2fzDMB/dzJ3V1mkBOn42uSilitLTRSsoLPU6hwoyX41kQE2aqNwhsVVmPzwYn+FSfR0RIwN0daVjXv8alv3krlEG13SYAyy6yuzxfYuBN1oC01Nh+lNlURT1xeTRRCN/ksn7iPLRel97lkvg+khqD+RY6ZvvYx26aULBWhD5GUGtu2Zz90/pHGhyKQUC5BzZs9c3v/5c3lfZMm57Ly8lALh/9t9dOTv3dOTx7o0bC6nYqCvlUKG581bv11UwgDLjXoO1c0gBYjan77RK86+JR2i5EDNOKjmmKlDgwRSJjwkFGcsrqpe6oimT+44+ZAsordi3LLri9a0GpdWjY7LQFoX0eVk3cwitF1bgmV+GbbQjG5DvQwMjqKXsB24oVaAbZ1cGxXjrkznJ3V8ORf2Uoj2fUu5VeVvZnNBsYmGImKVYrlZaCSspoNQ4aPuFT2unHTitB597FVhkiLp2DioebLUJ34GxyzWZWiBp2wnakpZwbJegRNKCUzPphyjI9G5JAtdWuO2pdDWGDynLXA5aTIA+yIxmUw+a0qFaA2U+V5gHp18tzQBXQSTFwzRFjeQcs4QASEQqaSxERmaS8bbSh9sMKwgzqw4+zaXb7RAUutUZCipy4Lr9qtxOXHDycfcFEFqOklK96Y1x+sssml/6J7oWQBMzQzB24yFg/gOMHGDbTZhnnaXpscst9AgidpgAbAlYCZhXkRkepmI/Fr2r5eBdoKoEXmZmcsHR9qY88AlROUKKPuuyci7G/p/0Hwe+UTk5bI9f5dtG8AL8uhd94y2EaGZS4PmcioGZpUFqAl2M2bJPruzH0aIaEJff/pEyRWi/uBVFOUrLx7ZsyUgXV3K8dcUF9V5UVJY96B1uxgL2xYRGnZRJAeWlga8V9K1bVIpeL2MI0wb7V7CZ0GKxktrMuGCSyaitLXrjNWGwrHJArEwl0/i1lJBLqdUFEzWmJNJjpgIJi8PQLu/OZW7nCgfTupiWhrkouMUyyeby8kB/cfQzJohxepSawkk+pxf9dhsXh5jodHXOz/AtJwU7IfLtOlZ0uHcGBUlDTAVP/UnCA3XlIJN9hrhBN4fW6kqSSFE7kheKrJXly6mtMDd6mX6hNXLOH21vm7K0kfjwISSsE2+k6mViaxOC5BLZg4sKoszeTuyvJDLyZChRShfQBYaEiI/YnduoVkFc9d37vrrkb/vH0xOyNcsNBYykZVeZWy0jkSiVB+iEw1q4Wr37f78+4OWj8NmkVUT22ZYAkpXwzUWGjqkIeiT9Y1n1H9VBu7SgUhYwWg2tpr8MhWVurPj1pQAsdt6fBdqNFZGL3O6Xdk4dAi8fSfTyFcgQjNU0kDqZTDnDJYwmPq2f58JaGxpfplxx5i2+UJ6wI4jNFr5bnMkpCuFvjUYG7167TlUN6t8oFegrn9fEmAzxDBlcJEzti95fdG8n5BPFABLsl/6gETkz5t85GuSU2rXpTmm1DaRdVG7G42GhrqqqV2kDpBvspoU1MvQ2IReJsJ9Gzjbr9XLWN3S6DYKxyaCYIs9kk6FBL+nBqMnS2RjZUDRUblLiFxJf7uSu5yWhvm+qcvpyEpeRiEbV3M5SViLgay7onKx9I3S1ZS2OtHHouw89cez76KT28RCo5Ig1rhJ8BysaTzZQGZ8KeCmEhfsDoN2GwxdgFsk02RiCJtkfhkdRpwel+5BYYHJKlhya/PLwDnYmkylGTTQ5WTfIdqWnCtl+12cI1cSWEHAvUSEhiw0qRuKXFDz4Ep60DyUUYD+H77rG9m2k4OFbNv/t/g3I3/vnpmch+ZUczk56Jp0Mg9BeXRAzx8fow+hkvUyogl1RuYUdOikI1a4ysX+3HEz2ArA9r6oAp7QpMIViIc0uYWsBUFYe8YNpDTLdd/Zmu1CJLsPFa5ATL8hF1PpOOwxrQaqT1j9IeaXIfeS1O9lEWnwDQcDAr/fRCqFXoa2zYPYl4gKRS8RyBpjLDREaDo4qVRMPA7fWM0tNA+s5YQmLdVw19JFE/teeaAVp3SwX8ZSTccWGGx6h52vSsPYpUVC629qLBwbDXMO0l+vo1OkJa7rJjZBVOXD2ZI6EgA7NkEkELYcBw2jNK9NqT7J9k/dS4JnV35MymDbhutl7DbYlPRXo5cx+WUiyvUxnLjPxbuThsaALEwlbQg7j9DIFS2mLqdnK+2v5mNf0y6FneQxxIYuCGwrDGPHFSjNJTJFO96rQqtK/5YAccye3W3WuqhqKBHss2XeF+y/woQgx1GcnbmmHAcd00ZTFkakaYt06T2VImksMLnRehnMsQXfHh29BAchQpDkmLF6GRuiTe4f0rik/SGJgm37oHI3jW3/3LFs2yL4Ah86P1oi4RSayUaxvNY0NAraYmC1JcJc3jvMx4fMizXiRQCakVMLPZWQsD5rSsFqct+M62+DrWnFVa6liwW+PbpmFd77rDqxEwD3XmMr1alshhGnlBzSZI3aGEdo8N4LnY4WNfetWRLfGQ5vhmeyT70Mji1vwnoZaId6mfyg01CuIJ38US8DN5DcUEhe0OWUP0jpNiIltG0ZPtBptt+IiGODvLDlN1bPy7YNkof8Lx74jqxNitWTzeXkYF0ntlp1JkSzX0rYVvMhT47rV1zOGqOJoEpEM7lJxJmsop3FRx225h6UppTXVj1JNKV4MX2ea2pK8UB67q/wmN5VN1m7YsW4aI2X75AhuEiYaqwxEop8ardc+Tmo2mRV5QvKrTZpTSYiKqWp/SPYvVTqckJiBdsw902hwp8IWUkbQiM0EWMUfLBNCOx6d1n0KeCjF9JGXtiX3hTW0yHacgK3z74wl2uxpfzIKiKo85jAIUsFwBH5vaJJwlYYriESGw05cZrJ2YaA22cXK6gbTQcNpLRYbES5hqYiYR5etxXpqhOEhjwbOuxefu8oC3AqAia3DiXMI70MWUsw5wxFOSXjncfEfbnv7vy5PLEe5ZK5YOaBfBxz+QOxb+bkyN8HFo9nbVKsNJeTA3o2ZJprMof2OY6avBrZNktACisMjxuHmpvRbC8/ZHJFq1BjTbPtsMzDZGuaJlHSupgKgCPgmvdN9u37sl1yBhW615C8aNc2bBNVz3XkT98QBU31/cQ0AWV6mYh8YWNdr6XRSxERs5BjZi4hMKyXyfczyfEiIlYGrsiksdqQpQgFuWCKun+YZ/w9CrlpTs6Mlk34yxMXThzXaotyqoBl44XuA1080UJ0py1F9DEmAXChFUFHQVjhptU7CVRZ02RIMsKQTzwmbCLyYrVSJsGfXYHbgoeboY9JD2lTBwgxtSWaeG2tNc0Q3Bq9TMXCKRsIXDNyb6JehrZZvYyIBNMlDWyUIbxX02R9SQiMzfZLILEvgchLahmi4pdkKToP8sSkodcREbunc9Lx4LmT2baF5KZesJC3SbGy1ghNOSpSlyuT9JmP6NvDdGjDJOVEZHN2FZM+DHPNN2Gmzy2YJPsMka3KZGszmuIEmM7WsFtFevqaopulqHJzmYnNXMcx7Wx+FvM8aAtez8gtwXIgUNxWk+DCa2mjlxDSapPqZSIi5mbSKCdXe4ktNPmJ9qmXIUsRkRcbPp4KgCMiVhMXiCFp1I9BIzQxLkS73BWT91W435kcIjMFUyNpVahZWSfH0CZem8LfRtiYc+iTpEX4yJnS/D3Ulw05NW4R6RLRz4yciHqFFGZry2E6iVmXCB1ThhGrpE+o57O+S7erce9ipCN11bNehg6SaWakCxEF8xQRREUmZ/Obn1lGZF6XVYpeggtM24jkkEUmBQmAiUxQTyegyOTfre7Jts0kN/DrD+ybOK61ByZnEybsOEJji6RZsSyGIIv9atBrnSJNJGR/ZpIE2NWazkLaZ6mG0uilcR2aoUlTHz0LOgNr6h6UNXhshW+ESRpX83iXuv1Cki3ML1NBxu17lTzPNaWzNAzZkuktUC+DWYHd0FD3mGrTZPi4rTM1A9YYSpqXamZsNBCREgrHxgKQRMCSl4HcS2mdpQguTUCWotSVdHrfyWLevXOTycrqXHM5OVhhnk0uZ8hFhcVDf5CyBDDQpjDj5rj+zIe8JqIJeUQpsYro1dVTEyKrCKnVD9VEjCXD0CZ6WRqDB7LB5kp5X9AqK+4LEm+tl5HHFJZUbS2usMYgxPPWwTVCvQzMWaV6mYiILrXQ0EJH9jVNFbKB0OyCiTd17ZAVxCbHs2JfIjSppYiIFbnDiLyswocXLTQreW6atL+jD+S5alIMTjYLjYM0L5aKRjZl5VT6QaIPpZ045TUyBeKq/P99WqesarXmkDWTRzoMaV3EiKbCc9jOAuC654g6hG0pkbDHlETWeonyrM4bLxwzomArAN5ovczpbaU3iyw0ZI1xmXb7zM9i9TKG0BCxovIFOH4gNOSaIjKUEjUic1k/hR+PHUdobJ0UGxap8sjJDKG9Wm3suwwfH6svUNdDClR11eHSCSCc/mZL9DLW3QYRMfgs4IQirGm6BIO00GywALgm0aAON07DpSE1Pz0LnA1bjgMT9ZkPjbSwFeplxu6bNqHnmUoa9KmXgXaol6Hd4L6X6mUinGaG9DLWakMgwW+6jdxLRGho2xBMW0RoMNtx8uwuwnVMsQb5cQx2HKGxH1nrGk7vae/ZVu1H0HRlJ04rvC0sEMfECrahn7xsHAjJ3KqsbuIQVf2T/590HsYtUhHurd06hYSmimiW6mUiMjetjz4D8jknCQfqTcQxawiktGakVhDsvuf8MkYvEwGEX8oLrF6GIppsjpkUvetlYFtavZvcS0hA4OWg+kvkhjq2sivbtpJ8CO47mbdJMVhqUU4KKKKkd5k0B8YES/WHCFUfGrGf1QAVWp3G7Zt9yOky0moN+hpgjo4K30ahZasqRNvoMiyhkYQDcwshcU02SHG8fkAKLX1V5MWc55hxGJ2YrXfFFgRnrSyNsPTkRe5rcr1YvUxpPaYx2zK9TET2/BJRQfcS5pfJt6X5ZSJ86YAUfetlKKIpJTBkoaFwbBvKTVmMiTSlhGZhbjKTHYg2hB1HaDTQhC7IRc+ax9IquDhUa8mwnKyUDPWscyi1cPSemt9OFFka+/xE7QRjI5rUit72tVU1n0r3k5YtQ5D8O0TWDerfumKMr0dus1DvstTLVLiXlF6G9pXXg8jLLBAEQxoickKwBoy6Jr+MiWiKyInVDLy4RFRobJhfBs6LdEApoRkI97dpQ9iQrBBf//rX4yd+4ifiwgsvjN27d8f3fu/3xuHDh9f/v+u6uOGGG+LgwYOxa9eueMpTnhJf/OIXR/pYXl6Ol7/85XHRRRfFnj174jnPeU587Wtfqx/cFPyGU9lvqovs103nv6z7Yf4jdNNd9qtCJ35D+OHYJp/n6YZT+S+9tgC6RtRVr+MYRwKTH913vJZ4YuKYNF7bF/y6Lv/R9eXnOXkG4TLSMzM1yH98/3p8xnFw5dctpuEHx5haG/3Rs9DNwI+GO91lP7ovU4Op7Jcd154n/vKD4ruGL0NyuelZW53Kf/RdpGsJ4xjO5T9q1810Iz8696npTv0WZgfZb3ZqmP3mp9eyX4rV4Uz2W+um1Y9A45idHmS/hem1kd/0VJf9CIOYyn5Lw/n8N5jLfsdXF7LfA6vzI7+TSwsTf0tL8zi2SejdQnPvvffGE5/4xHjqU58a//2///e4+OKL4//9v/8XD3rQg9bb3HrrrfGWt7wlbr/99njUox4Vb3zjG+MZz3hGfOlLX4q9e0/XgrjuuuviIx/5SHzgAx+ICy+8MF71qlfFs5/97Dh8+HDMzJRV4owYw+yJ7INpGQvJZY2g+75XSTg5j26sicbQVhC6lOk7KK8trsysi0WfV9qQDuoO6a0xoi86pqxDY68vh8BPPlnUPpj7XgP5wmjLXEXxT6NdQQsC6WUImNcGxpEa9ezzB7AiaXVPN0MvQ88pfItzayW0kdYYimgiMSuVMEgtHJujl5lsPbIRTWShIZDLiZCeF+mTMpg2gN4JzS233BKXXnppvPvd717f9ohHPGL9313XxW233RZveMMb4rnPfW5ERLznPe+J/fv3x/vf//649tpr49ixY/Gud70r3vve98bTn/70iIh43/veF5deeml8/OMfj2c+85n9DrpHE3rVx54+KqVkCN0ObqIr9yWFu0Y2IkZH3RSOY4tcTtlx7eXGFXK/pKzXvmqI/EaPA1XMIj0/PqfC/TEO1hWT9V9xTOxPHiPZhMnxpGjcjgO/AybpH717sI2S46XlCyLGlA4QN8sWnbQgQkPi3pRskXuJwOULIBybMhtDu8FwMsFLUVzeoWivb4MPf/jD8cxnPjN+5Ed+JO644454yEMeEi95yUviZ3/2ZyMi4q677oojR47E1Vdfvb7PwsJCPPnJT44777wzrr322jh8+HCsrq6OtDl48GBcccUVceedd9YRGnrItYhSrJBpgrEJy+RKnWBWkjZ8XCecw4Gk+7lri2Sfzt3kvomIoUpeV0HSaiZwMTQdMitX+KYqN+uuJDFGzYhjasW59qy1xN5mTJo3eWefMI+O6SwcWVcViySE1c2lImkSBctSEFgVnrbJdAVpZPEUWTdg5U8FJneRAFjoZSJyzYzNL2MKTEawNYaI1cLU5Ky9None0iB3Aa3AR/vkat5uaXVUwb16ajLtGIo2hN4JzV/+5V/GO97xjrj++uvjF37hF+JTn/pUvOIVr4iFhYV4wQteEEeOHImIiP3794/st3///rj77rsjIuLIkSMxPz8fD37wg7M239o/xfLyciwv/0N2wePHj+sx16we+syWqyHGqysMlxIm2R9+nC1xI41SaT2tiPwrKN1y2rxfOjPX9CVX+KqsgVxtI2qeI3Ff+hcAExGcTA5tdXNN5uT7oUiZdTkhWS5bdNXkl6FnkqLDUKuI7tLk2yNLGizMOmsM6WMIg+Rm2XpMBMwvA4Rm10yesTi15Fj3EhEasjKdGjj6kCb6pCzMGazcIEHvhGY4HMbjH//4uOmmmyIi4nGPe1x88YtfjHe84x3xghe8YL3dVGL767ou25bi27W5+eab48YbbywbtNV0iJwfrFNxN6c0oonGURVJRCi0HtkJ0Ye5lltVMot0z9E6emhCyqNLGkiNy1AUCcV7JaP9qnRipRYaqwuisdF5iYkYQ8BrCoTKiCBTFLLqvliLcVpTqkIvo6/lnEuglZIVKnNAehlyL1F+GdLLEFKLzGboZdANJT6+GKkE2x5YIwsNWHJW8w/5yuoozRisTP64DVfLrAC9E5pLLrkkvuu7vmtk23d+53fGBz/4wYiIOHDgQESctsJccskl622OHj26brU5cOBArKysxL333jtipTl69GhcddVVeNzXv/71cf3116//ffz48bj00kvVmPW8acWypi8L+zFOJ2srmOzRTVK1n17huwErt1nPehkNEz9uXRa96mWkAHij9TJ9Q75DiuBKSyKi9JgR+TlUfVPKiY9xOXmxNmzDiuRwDGWxIgGwLWng3DoYfp3cnM3QyxB5MZqZvvUyQ/g+Z+dvno/Cb3PvhOaJT3xifOlLXxrZ9uUvfzke/vCHR0TEZZddFgcOHIhDhw7F4x73uIiIWFlZiTvuuCNuueWWiIi48sorY25uLg4dOhTXXHNNRETcc8898YUvfCFuvfVWPO7CwkIsLCxMHiBdKNQclK26TDbhiArdQIwxjWdCU9A5oDm+/JjGXYUExOoc8GLKfWksgvR595LbVkp4mZDRCt/dZ3evYCMdkzQNlpCWeuX6JlZE3kSFdq31wp3L9DIRcH3tc0qQ1h3jgqOEeX3rZXTIZjJciqahnDOolyEBsHTZpJP/ZuhljDWGQOOg6CVyOS1rl5NYwKUo/FD0Tmh+7ud+Lq666qq46aab4pprrolPfepT8c53vjPe+c53RsRpV9N1110XN910U1x++eVx+eWXx0033RS7d++O5z//+RERsW/fvnjRi14Ur3rVq+LCCy+MCy64IF796lfHYx/72PWop2JI37kO9TTuA/s1rrGWmJWeHJt+lgrrFOGEa0Lix/VnNQGZ3V4yEHndbHel/ccAonBkpWdyYWUEz06uuuJ5zawrUEjcInz5huwYUkND7yiW+DHHpG3WjV1RMw4tgolmxibRIyLIehn4HlmXnsgUTKHXJuR5HFaFPmYr9DKnt432Z/Uy5HI6uQalDwaQRG81v9GDtdHjdmuTr4dpQ+id0Hzf931ffOhDH4rXv/718cu//Mtx2WWXxW233RY//uM/vt7mNa95TSwtLcVLXvKSuPfee+MJT3hCfOxjH1vPQRMR8da3vjVmZ2fjmmuuiaWlpXja054Wt99+e1UOmogx3wEroqT+kkkAP6h0b+B9sZELykKDO8pJuKJEQrYv7UfkRV6jqkgw843qWS+jIpqsAE5eD4y6QWHN5MlJi2yNiy+iWPDL1sUyIWtEjCngCbsmzyXmotJ6GXdME7pcxQvtYk3UlNJ6mYr8Moa80DbrXlqEQoimfEHEOAvN5DDlrdDL2Gy/S4OcvJB7aQUIDb7e6XdGPLvKpUj7dV2qQT43cPz48di3b188/JY3xvTi4vp2+hDMnARf4CL4S+eBQR8fvak0WQ/25PtRdAASGqozAoW7pqkKcNY/nNMCfBhgpT69DGZT2DfF7Ml8vwHsN9gLL+Rqfp4zp2Ac8+QCybtL96VJhxKisV/fHZNXsImPfSFv1IEQcnopH8jMkrsvw10wkOT8Zx6gPCxw/6Aveu6xYr1w61hgOC8ltINNM/AO4bVMJuK18+E5XYRruwz9w3cGn2eK/knuqSXBLLJ1C5vpU/l4Z0+Mbps7AQeFyzGAeoSre+E7cF5+fafmYVKfhfcj2bZ7V27JuGD3yWzbJXvyiNi9s8vZNsIDEM58fGVx5G+KBiJSQkLkCxceyLZdMJdv2ze7BMcYvR4nB7kk477V3dm2o8t7821Le7Jt9y7l+56EDL9riQh4YMK2l07F1172S3Hs2LE4//zzJ7b/Flotp3EQSaWoGfrY7TccV9GumYK2AMn+rGA5gTWDF1fRDmmJ03qZfjm/0UNY/RD2X6jJQctcaQZZ3rUcNTyoIhw9I03kcqLvAr23lsyVJuqTGjmdZ4oMqemc27deRoZa07mm4cBkodk1t7F6mdPtJouCdbZfeFCxyKQYr9XLUPTSCpAyEgAP1uB6JK5y8x6ULnx2HKHRUTK42haTTM+Tn668mx6WLAg1bhKrvzF5eWSiLKrai5BuBnXvdcIy2c6gogJ8aUmDCJjEatxXSCCda7TUfeJdtLARyRscYyb927o3y922paLuutB5mHTJ6pty8Rq9DFxLzi+Tg1wSKUnAYpIw4AVwORHhWJbh10YzY0kUkReb8TfFMpQoJw0QWZTSbL8REatAXtDfk4mCx4/xjNoAdhyh0RVe6YURqzoyF2vQNxbJy+SPcV1EE20sE0lzpVzZfdW9mvwx1mZ7y6uEBS9CapPJXWOJpry+mYVmssxmbP/FKfwjNvQDFzHu3PNtihyKXFSn+5d6GYDS79nrYfUyJJKGbSa3XJ1exllopkALM5ckyKOcM+TW4XBscAXCh4usGem+RI4oomlxJh/bHJ2nNC+m+pg04V9ExCmplzm1BhYaiqSl7256Cib4QAYopGiEJqJ8JorIPywV4at2aKW1i+w4ysN18mZazFkx6SDELd0M9xJBnYO87zqKBYWxSZMKElzjIlPQ7yjsK0X0NguwO2a+Sdd5KyVvhe9oxBgCJspq2DQVVoeGYlD6HNEiJpn8rRWEthFs+HXevxMAU+K+aV1oMEcqAuZcMvk2il4i91Iq9h23TWUCz/YRbQA7jtBUJSIzEyx9oGo+7BhmDs3SZ1CHMpe74BDpA03kBcNcBbOP0Bl0XYE/N4waFJMmG4VjShpE4IpHrbYrShr06l6SEx0SWVlbCCOYsvpA0BfcK5kl3xMaY4GtuEZKL0PtpAV2CEJkyuSL1hjUy1AE0+i+Xi+TH5MmeqpdZEjOVuhlaBxL4PcjCxPllyGX0wDSSNAD16WRcc3ltLGo8sUnLxH6hUUE0umd4Zj6w5iMo0YvYy1A4iA44dJuVBOGJkStYZjcRpM02tcKKwmiKKRMg8F1hNB1KdibjNwi9GpJtBMzNZOlILSANiU5OPETGbcLBbrmhSsg/c6X6WUi8mcc9TIQdcgLG4j+RJcTtMt7i4UkxwyRBtLLEEhbUqqXsXlu+tTLROSamVUgL1YvswbkBa0x5jtjTqnwtHceobFmX4BygfS5LI3oV4dQ07/cN4v6klEW8M3iQ0pvGCZLzO6VO2bvUC6nfi1nJoqFyWe5AHjboCIQwFjTrEaHd3bN1HfG3gKsKg7bCiMWbfoJnW1buJci8hwzpFMhvQwBI5okycmLQpIrKd9Gehk7XlPCAItkkuWFtDHW5WQ8w+ZbUfg92XmEhqDNsnADKe9F2r0UOLGQ0C5NJ/w99piunZ04M3dpYdXUM0KpdaCwwvAZwbicsKQBDMOmrJdyE6d3gm1SM4Iwk1iPtYZOb8vb+bT7yZ8oeqw4prVg9gh7DuQ2y95vFADDNri2NNETeSGrTSoAjshrHJHIlt01ThtDkz/BEJpdMDZyOVkLDSXIS7eRAJisNhy9BHOfFe6mp382lT44K1Fa5oD2rfkY2ZVeqfbDCjd7JEPaRWTzDkhXDwswC91yFVBaB7s6pr5oQqTnyCRerMiC26eWWuuOaLiypAHpZZRIlSZ+0poArF5GPZf2Gsms37omU0potF7GbaNzoPpLlGMmjWDaCr1MRG4Zsi4nil6yehmT8Rez/UL0EuplsBQBfAcEWTaLdL2QT9AITYzTQ7gLmn0YrftD5h7RZRlKLTQ1Lq1Cgmfrv+CK1t4rc93sO1NDfIzLwuYssS6hwtIVm6K76pFEcrFOty+SC1NPTJY0QNToZUoZo9T82MR66TOIehlaxEiXE5EXstBgjpmESFBVakKfepmInEj1rZch9xIlyEuJGtVjGsCzS3qZKqvsJhjpv4VGaMbB3gTzjKOYmI4phbGl/nNNXsqfwOxdk+dpM44StNtMTODWMtIrEdTPmrzvotwC7tuzdbEqQ3bhMXW6JKv9SPojrZc+Zp/Xo4J8Wr0McuU0h5KMskOxr3QvEcmZE4SGXDiEPvUytI0sRRyiLfU9cPMxJDsL2ya9jBP72m2bkPXi26IRmohy6wNss4Uj8b7bVVKpLsPqgqpccOnf0AiL3oE51+pv7GSajk2Hv0hYi0RyzWsmRJthmTO6Ji44WTVaV+W2bpGsjeqedUEwNl3dXRXwJDM7DQ6O2adexl4jq/mhYrl43ZK/6ZxIV2ifBWhHehmyZpBmJsVG62VoG1ljiGzNyVh/0r0M4MKlmhkUDlOpAiQv1moj5h3zvSskRjuP0FSIC00m0SnyNVqrcp+ZRKn/GquCRJYqniZcMttLC42dxHBspeGwNTBDs+OnlAD2epS64DY6A3BUuL4qXHWYI5PmsGSOnJJaE7Zc0Djsx0G0kZZP0suUVv3m3D0wydOzaxPOgVmMMv6mlpCt0MtE5MTK6mUIZD0awINkKmSfWnUup7T2UkRoKQViEyMgdx6hsbAuECHw7JvQFLuXNoPQiA+0J1bStIUTSqFbTqLqHU2eEbwe9KzVRBwZixUm5KMK3NAXYYP1MlXPkdHLRGTWxJpacBtOqK1epkKrl2lmsB6Te0DIlUTh2IuzYOGAdmQJSVGjl8ESBkJ4vBV6mYhcM0Ph2GuQFRjzy1iLf0VB4T6w4wiNrkRMLzit6pJ9S9XZ4wcC7TaY8Hpfv9yWwk4K8r5oXWy6re+VQ6nvSD5rbEGRAk8aRin51AJgEMGWXvKKjydeS50BOSU07pg6JYB1dxtgEU44ZMV1y0iOzi/j2qXZfk9vyweMOWbEidXoZQiG5GD0Us96GbIypdFKFL3EpQpgU8X6cDN1NTuO0FiBZ3GWWmuNkWI9W3k37c9PRPJJtXN16oKj7mkhZT/2dqVgJrEKYlWDPNEUNLKTMOmReqzK7UPiJ3bVO7S1BDQdeE/hXNN50+plKINu1XMk9sUsybTNZh83OWbmIIsvWl6cy2mGShpIvUxKLjZDL2MsRbRfjV7GVshOidrm6GU2z71E2HmEpgLmo63zqciIJvowItKHq4YVS0KjrAgyFT2mgCf9jS4JMHlsva8c5HVzGVilBUHmhEGtg7FYVZC+Kktf2sSuJGWov66anbpsrF5GHhNR6FLGEhowb1otPOeYSR5eWY+JwBO9q5CNkUPJRSHrRt96mXkS/KYJ/mSiIp9fZj7bRqRseXX0XJG8SB2aff/0QnqDsPMITc/6kKzwVo0PsU8LSqH344xgPtpy1WgyLp9u6MahCMFmvGj4gqfMCtpY8br9gJh09DaCh9CjhQbPqcJSRBFNWCBPVJc2ocwR0ppbA7R8SvejLHLKOWaS/nU9Jme1mYeIplK9zBqcVN96Gdq2O7Ee1ZQvQL0MtMMcM0k7KiaJ4di2HtomEhWLnUdoJHwa+Mk+dpPfYuw4bHI5153b0dajMhNxaemGcc1MPa0z6M8dVF4PQuGHAAmZNftif6JRTURTn6hY+eF1s2RLhjhnsM9fn3oZS/r61MtETtTYlQTjqIhooky7Ri9D7pq+9TJcp2l0bFYATBYlstCQhobIUBrBhBYamxNsO9dq+0dohCbCf1To5c187PDQUCRARYh2VTG8HmGsIOgikmZ7Xqk7YlW8Qu5b6UauxfReFZLniDPQQwjxpq1UXZxfpgI61wt90ciySryHNDTJcW1Om43+/uO9qrCw2ZpMU4nLyZIXuhymHlOE08tE5LlYNkMvs2tmZeK+hnxFRJwaUuj15OilCBb8ppoZ1MZYHYwlOeIz0GfeyBQ7j9DYD6+NMjE+dnrpLQGxK/XC+aRKzGlWnNpC486zWB8ypr+NhqpyTW8hukSofyDQhVlw2QpCQqaNncDZX++Ezjg2InM0+WNZg7R/GFpFFJWGuFd95peJAL0MHHgKUyfD2Kg6Nop9c4aOlhx4mVOxrNXLEOiYpJeZo3MQmplVOTbML0OiYKjJNEwIzFDrZfJtNVm5NxM7j9BYyJDTNCurTj5rtSCFfKBmgrHeJTyGcMHZ8/RuBneMdHKyeogNhwyzm7LRByKjNUI/bK5ZMeyHssf3JYKtGSYB96akVhALBV2PyVb9JgtNmhndXm9oRyHaVKPJ1mRKRbUo9pU3hnQvnHMGthWunNC9RGHmVMIAtmXnr60sZZaX7YBGaMaguFCfvPHWlI+5b1Dol+ys80PQ6GQ7YVWxIcQ6RJugQ5w3mK0UrmJqikJySQPY1+i/rPvKEkj7ETTvkCRuJC7HSVeW38j6twJgez30Akjcq4r+SQBM5zUzmxKacm3MooxesjWZUguNJQMELn7ZX5FJUx07gl1OS+ByIn1MWiGb6zHlY8O3oGlotif6vi+UiTODNG/wRAEfaEpNbY5Z1U5+tFOzpp2IyPqla+S4mVO5+WrsqIVhz9btZ1MCsAuLCJ64V+jb2GC9jIxogtQb/HzQKYD53aQG2Qq9TARo9eC5kqlNAqQarJeZFzdCamiwHpMoGxDh9DIR+eTfZz2mCCYvmDSvkNBQ2HapXiYi8gfT6mV6rqLdEuttNqzZ1IRAVvRlV3rFAuC+P7zCTaQtCAQZ0aQjgkRffmXtBLTK5E/jty4Fez3wOUrdg87vtxWJBm3UoS6wKeuJpfcKyWdNEVXZLr1GSF5w8QDNSC9jyEvkie9sdWxyw2B+GVjFGL1MRK6Z2Qy9jHGHkV6GQsofoPwyFMpNehlyr2ULFvlNAWxHvQyhEZoxMPqQiDzawEeASFcMwTxcVl8gn9TSsdUUtOYaR7TcLuuv95V1qfajwj1RFbJuiIR1L9XAVB/XxM1dJLQCmfwsW3A9IiKv+i30PuO6Yr0MWIIFMUaeSRFCkK+GooZm5PeIrBnppN63XobIltHL0DiwrhKFmaNehlxHsC05BpYvOIv1MoRGaMZBRt1kYZ1WpkHdy7thqkvrNCl9r7aFW6QmRBtX4DKKJTtZacmoecFV8jfjuosx973GBVd4r3pHRqykpchaNKlAow1nTi00eEzLJNwxVbkQfF9gG3xTvF5m8vKdLTSQCA+il4g0kGWEgEUmk5u/XfQylCPGRy+RXgZITrHLKd/U97O7mWiEJvykbszUbPK2B4Bt9iE0q/6+IVa5fbqIIpj0lYbFe6uTcy/p1DSmKKTUkWDIOn3HbfbPrFG+SUekUXdS2Jwdk4iVXTzQtbR6pOR97tWKOq5DvEaTLTQErZcBMTW6jtKwbWmNsXoZgtHLRESsQOXoFDV6mRl4kEgvk1qPONtvf/llItj6YqI6z2ZrDGHnEZqaiV58jKvCpUXRyQgWyw7TD1LPlgbtJkonTukSsRM4W1VopjfC6RoBMG2TbkSjI6+oXVRTxDLr31okbERa4eoPr6O0RE3LkgDKPVOjl5EfB1OTCUlghV6G8smYmkxYHRtOYKP1MhFOM0PkhYhVqV4mIrfIDOHGcESTzC9D3xnMMVNmodlqK0sNdhyhqVqVl6ZBtzqSChKyFVF1ZtK1aQ7Il2vD2HFshdaH4r7OANl5WfcBwZbGMB+zjRb71sAWnZSuS18TLB1Hvw+DzoYtVtv6fZF6Gcz4Kyw0ZI3ZaL1MhNPMkOYFNTSFehkaxyoQlRWqjk25ZKxeBjU0o3/3PUVsR+Kz4wiNhfJjA9A0bj8+sI1Wl6p0gFVW1lhyBLtHlwjAp2iX/WFEUKEVq+J6qAKedB17DlmnxaW6V5sgnM5LQVi9DEy4qD1Su/ocMwY175CpkG2+ARExXHDXchr0MrjmEoRmK/QyEU4zs9F6mYjcQoPVsaVeBhPmYdoOobnrWS+zHbHzCE2FgM/lMZH74deiZ/3NBqN41S/PEycTrKfl2GHm0kPNEmyrgbkvGKJN4893tW7K0iKLrHeSepxS95I8T6s5U7migtMJmLBtFGtX6K5sFuPskIX1mCLGFZmkbaN/E0GwehlyL220XoaI1S4cW5leJiLXzBAhs3qZNayQnW3iwqrZjvmm7WhlqcHOIzQALfA0bhFLSmSiOk+GYJs5Zg0KJyc90dW45UpPtULnoBumMiObsh4JnttXCW/7zgBM3ZW6AisqZvuK045A9wqZjLH0/mFhXBsdJgS0lIXZWkEsyBpTqpehbZQcz+plCGnSPB2OTfNLoXspwln1zjXsPEKjJ0Rnuk77s9yl9+ywaY2VCu2NVcMrN5ENISadKUUi0gd6VdY42gIrluFHllDrpG7S7ZL1X5NxuUfTtT5P4h/WRWsEwOOOm8IK2uU2kzTPFiDtFpw1hiZ6QhqSzdYYl5SOLB7L4J4hvYnRy5A1xmYiJpJDwPpLyYfrJJwTWWNWVqnAJBEa+b1L9z2Lw7Etdh6hsZAfKZOnQ09OcmKjiT57vyu8VxqCNOiQalqdiDwYEYERPIQ+w6WrXIFpf8ZcHGegH8Kq0c6FVYwanVHaBEgEPkd03WzCPJoThIaohqgQUC8jnkH6Bli9DOWXMe4l2mb1MtZC06dehoTIZHkhvYzFKtVaSmLlOXqJXE5giSK9DFpgzy0tTCkaoQl+GLQbIHM5uWNaVwwtFDrKLZF9eK3pxYHzhxgXHHRmrUekV7CnZdxVfb/wUuidZVO2IcRym831kob6awtNDXkx5F7rrvIHpEYvY+6ftk5R9/SdsZbP1EJToZexEU1ouUgIwRy4l6xehqOXKCLIZXdMCYwVItt6TKiXgY9xSnJYLwMkDc6T3Es+Qd7on2eLlaUGjdBE1GkwjI9dzjq+FpAx5ZSbY6oEnsJCAwsnPigVsawRtm2BywmRXhRJyJDg2dUaoZR89p5eOune6lakNUYXSDWRVHATqgheYUi51ctMQ5I7IipsjQHrTnLdyAqCIc9wY9BdI0O0DawrqTR66fQ2ICZp1W/Uy5DYV7pL0YK3XT5uW4tGaCK8CY92LU0NTx8VK17s8a7pj7EdW/pRlUnv8H0kFwCuaOlrDP2lkxgKSCssW1IMU1oU0upITHqBCHiOZNQQd+aa4a7pIeQ7Ra41X8AT2hkLVc0qV+plTFyB18vAMXFFQe2I0Izua/UyBCIqpXqZiNwisxV6mYiIU0nSPCIvy1V6GWuhEQsnwNlsydl5hKbQxHu6ITQzbgypZzE1miJCWoVgmyXxNWzf7IorZjcMnUFXiTn7XdVoWU36vafx05vZc1Vuk5eHQ8Bhm+h+LAQJZrewdNHSIwOp/tlCJSYFaTXEfDjSypTOm1ovM5cflKwxNiJoPiEwNXoZKglQqpc5fdzRsZBeZvf0iuqLQAQs1ctE5C6yU6tUjwnIS4UmbCeEZBvsQEIjP4xWVGsmTjvRFRbMs/ACXdmOdjUiaVPVOILDS1ecyd+UHNACz97F1JM71CHU9MGDDyNGBxtLyBbojNC1RufpSgHhs6Vz+qTfBkuCrV6m0CpL5zQ9T+TFERWsySQy/m4XvUxETq5IL8PErT+9TETEqcTKRG6pAeaXIQsNPEfZltiRAmDCjiM0VQW6jGiwoi9vLrczeCGqrlHhm1WhmyCotPg1H4GauHhzDqTxQD2SND8jQUr1IZObVMOItQlojZHWuppEfWkTe41q9DLUnaj6TWJfG45tiU8mvN0ivYwpV9C3XgZLGAChWU1IGWb7xVwyha6kcdsEzjUrzo4jNNr6YP3uKWrcGJgtF9rRCtboJlCI7FaSCDHpWi2SshbEGbjlhOVMi2ctSl1O0nrC5Tjc/VNVueXHsyahNed/EfeqRi9D/csQ+ExnVXGN0BOjCVjyN+llSBRcmAE4wuWY2Sq9DLrDUkJDYdsVehnaluplInKitrJK1bFt9FLhgihiR1ptdhyhsSssdNua7L7ospCrJBm+i9aMjEmoQ3qBmd01uW7WpK4tNIXupYiARFPykDU6YeHS0xlqa1wWxoVFffVdCkKMw7pmtIuW0hzIPFDFoa/yWtocOZlmBgjZLOhlrHvJ6GUictKwVXoZykacamYWwCdp3UtEXqhCNrnIUsHvkCw0aza/TL6NcK5ZWkqx4wiNZrwyz0MKTUqseFiKF4sf6AqRY3mEF2yjZGq4yi2MaIrIE/BV6GWqdNMJsUILAkY0gSUALBfaCpKmsYcPb+/VMgx5o6FCfhn7TNYQRmVxlckYa6IY0/OaqiAvBKOXicg1M1ullyGX067p0bFZdxuBCBhHNOXtUncV6WXwW09Rl+dY8ciNxs4jNHbFCS+DmsQqJskq0pB+eK3OpsYaIyJnbH4EnTlZCor5IElf0txfA/NN1ce0OVZK3aV9kxdL+jJLkXQv0TFlSQBysaAAM9NdSRetFAUTTI4ZEsyzK6ncvYREIrkRVi9DLqc+9TI0lhq9DNZfQl1N3i5Nmsfh2PKDqjU00C7BTrDi7DhCY1Pb60nGPCQ1FpVCV0xxCPGZQBE8qQuiD68WfUoBrdHf9P3WmxW+LRYodSScwn8ywd2MqC/1XsnSDVZ/YvUy6nmTj4fVy1jymWpmZiBh3ixsw7FJl1NpjhnUy0iXE8HoZSJyzYzVy5A1hitkF9ZksgVI7fvXMBaN0ITTgkSEqviL8wY1lIxDi2UnW+19FlU8AGwrzYdDQkW6tpTGXk5iSitVIW5FaEIwulGTzxr9Fz1H6b4VUUMIfIcmPzP0nGK5HZonyEVboc8yz4y1nBXrZSIyUjZbVY+pTC8T4TQzazKiqU+9TESumbF6mQE8qEtUJJNcTmtA1JIXeogFU8tJ+06wtJRixxGaqqKChf13muUArK+/8CHvO2Kl1/0q3IPqwD0HORFKs74W6znG9YfMR1hoamBE9BHKFagtiaTFsgJra94X++nxot4J2iXnZbP9EtiF4xLkkWYmBblhtHuJrEc0Xqy/NHls6F6qIGBkoUndSRTRhCVc8k0M+Z7uROKz4wgNWiFLI4lCPjRSFKytQsp1Apsw8gIagoneu+Amj00XQbQCYGN9CB8V0ytMaLEWALtDmqrREXB9a9xLWmMF21LXlywwaRPmkfUP6+EIC5V+h+RkQkUyMeNvkjQvrakUwdYYzCVD7iogNJyYbrSd1ctoAbDMPLyLEvoZdxg8gMsg7CUNzRIUmSR9TCYCrrDG9F437RzHziM0UnirQ3XNA4eTCXQlC86ZD68uG0ComMQU6DzJU4A1jmgcsLO5RqjlgW12RVRqQaHdME0+rPRsRmEcyIS/x/VV83zQvUpM8tY1Su5YjgqEdwhr5MCuwhCidXnSGsM5ZhIxLgp2nSjY5JeJYL1Megya0PvWy2A24sKaTGQ9Yr0MVcgWepkAwa98Ppp7qR47jtDQw9X3xFYKVe03IqYoDFAdQDZDi5Vrlw0XLSrSBWBJn000uF0+DhmhceY6fT0Ki3pWieOthYZ2TSaAabLQUP81ehlZGypv47Ypy1xEDOcn62UiImZnR28+WWMI5K4h/QnpZRZQuDSKTdHLwAU2OWZsfpkH1haybXQOy0IvExFZ+DVGz1VY9QiN+JzGziM0BPsRJCiXk1uuWWLF1ZnFMKoimsqFlVkT4XYY21fhJBkBwmk5CVeluyeIa+mj8Sqc8aX3ylpeSp8Zu5utx6TDYcW2mtQHaIGFhuASSjP++pIG+Tarl2FR7WiHfetlyOVE4yBSloL0MkNYmRF5IRdZGo4dwWQl26aftX5Jzk7EjiM0nBY+38Z1c/ofz+gBZLvCiV5XYe4xFwtPuDDprMrkUzX6m7QvSWT16qdiYsuOSZERAHp2VVLBqCS4CaxVzyQHtNFA6I6tSEjoCE3eRPM2ci+hXia/AKmbyCbMs/llSC9DSK0efetliLyQXoYsTynIzXWSShVg9BLpZYAgobU8fZ5b9NJmYccRGoTVy6i+yp9KHY0B3x6VXI5eLEk4TBK9v984eRzUpKLoJCc2E/vW3HcrEDdWhIpEchjVI6166hg2YsrCumwSIKGRWbQ7We+qVC+j88vAOzpcBOvDLIRLixwzNMn3qZeJiFhNHq7N0MuUFpkk6xGRF62XWYOaTDQMVf8LtjVUoxGa8Kt+nHSFoB1BHzzSgsgETFkNJfnBRmFlj8J6q8GoKjppI5rS70yfwu8xUJYLoW8Z15fOU4QTceLrl++Bd0PBNjgv1MwkqMkvw3Wg5KpZhLZbyyfpZciilOplIpxFhtxLfeplInICsyl6GRFtFZFbj2w9JjoHyi9D7iWy0KQBDjoYwwYfNDI0Fo3QxDgisfnj8DlncAk+eT9CDXkxE31NDhDdXxnpM7lZqmEmemu1QHJkJ/XC85I3xtYrK03uqEO0cecetQkVwnqrl6GQ7BTG5RLRr14mImKQJo3rWS+DuW8KSxgQoSGLErnIsFyBFd2ZW9PCsTcEO47QWNcJCQlVfryakFZa2EhXQZYzTpKGDY/wsgJg+oDYsWFEE/RXKv6uWRGZzLjSWsBWCujPRt2k3VVEKumK8lSAL+Xi8t2Ygmy5eK+sy0m4BnRNKauXWQByIYsxppgDi0efepmI3GXTd34ZtMbIFzB1dXlrjHM5DXSF7Mkup2Zl2RjsOEKjE7Ot2K97+sWTu1ltAr1EBnZFXhPhZWCjhqwQFMXacpWUnmuf2qkxUGmKbF0XK4ylCVwkFey7MKe1PGWEhrQmc7Rjvon0MijmFy44GhuiRi8jazKZMG1yS/Wpl4nILRx19ZhobFTmwBGwU8NRYkIh5VYvs0auJFp0YYXstFHWpGGDsOMIjU0Lb7PKGsuIhvAk2X0xZ4nU7aBHSw4ja1iY9C6i34imCGlt6FkvY8oa2AzAaKEhoBVECMJrrIso9JbRRelu9FXSlkQic5IwmpW083hqvczcHFhoCmdA0suQZaRULxORWzisy6lGL0NA61FCYNBCA+RlGcW+jryoEiUVLs9myTkz7DhC02eOjirIcZSWKapKorfRsKp/OzapN8m+gZsRfSD8lLZgqs3/UhyJ0/PXszRXDxLZCgFwnynlbfJBr5cps8agJqVCL0NI9TIRUHgR2myFXub0ttGxrEBJg1XUy0A4Nlq4e9TQNGwIdhyhsRMFJ6+bHCaqo37tBxpWtMqNofUyNCH2aKWQK3fsi5KkaQGtWG73nMxP5+8RKzibNM4Kok1V7r6Lktp7lRXrpOdUZj/W+XasrsGElFfpZfJ2RAhS4mDzy1AYNIHCmWmb0cxshV4mIrfIeL0MEDdy9RemHGhWls3DjiM0eqUHLpth/i7Ajmc2nNEDkO0a2hUKTXnlS+OY2P23OXBKGqCJ7d8mZis8V3L11FQft9Wl02cLJ3kaP0zqeEhb3NHUlLIwpvcY48pNCQ2RF3rmZUp5nRKglAPT3If5Zcoy3kbkJGcr9DIRTjOzFXqZiNzlxHqZfPxrQNJUBuDg4JHSSMlGfOqx4whNVXipse7YFb714WNBQmO3h022kKE9h8I3UJdukJNYcVHF7fIBsSSq5tkl9OluLBXURv5cck0z2A/6RwFwn1EmKAAGognkpdS9REAriMy8SyDXkd2WjQPOk4iVKSZ5+piT9TIRedVs0suQqwrJS02F7JI2Db2g77iGDDfffHNMTU3Fddddt76t67q44YYb4uDBg7Fr1654ylOeEl/84hdH9lteXo6Xv/zlcdFFF8WePXviOc95Tnzta1+rH9AU/Lop+EX262byn+pfjyP/TQ3zH+071Y3+CN1s/st2rF0mlF7b6fyH57k2lf/gFLrZLvtlQx1OZT8am72ndKp4iZLxY19z8KP+16byHzTEfae7kZ8dP54T3IOpAfzEvYoZ+MGNoftHz0fNORgMF7rsl17bmO5ifm4t+01PddkPxzbVjfzmZgbZb3Y6/y1Mr2U/wvJwNvutddPZb9hNjfxo/PPTg+xHY5uDH2G1m8l/w+nsd2owN/JbHc5kv+XV2ew3HE5lv4AfPh/0ze7xc9pwZthQC82nP/3peOc73xnf/d3fPbL91ltvjbe85S1x++23x6Me9ah44xvfGM94xjPiS1/6UuzduzciIq677rr4yEc+Eh/4wAfiwgsvjFe96lXx7Gc/Ow4fPhwzMzI9KsGucu2qX8Cn63crACRSSTsWL5a/XcXiYWlB0CHD8hSUJa7mY7PBFhRdAwtWoRjhtsEZoTn3Dax80cKR/E3kky6urMekra3G8CkT/M0u5sSBEuaR64isA6l1x+pljB7n9DZXoDGF1cvsLqzHFMFWlaXBfLZtJdH8nFqlekxw7qiXkdaYwm9IIzobgw0jNCdOnIgf//Efj9/4jd+IN77xjevbu66L2267Ld7whjfEc5/73IiIeM973hP79++P97///XHttdfGsWPH4l3vele8973vjac//ekREfG+970vLr300vj4xz8ez3zmM4vHhR9xG/aLItWpiW0sbIXl0vwpOgwaXSDODZBBJyKTY5MrbtOfdyu6sTGJEq4Y+naSjgRQdT0KCY0tD4ELbrLkJ+HoU+hqhL4Kw8IjonhyolITnF8m74xCl5FwwHHTdlYvQyDycgpCnEv1MlxMkvRDTi+zDFqeVTiHVDNDUVoDm18Gv8X0oha6oRo2BBvmcnrpS18az3rWs9YJybdw1113xZEjR+Lqq69e37awsBBPfvKT484774yIiMOHD8fq6upIm4MHD8YVV1yx3ibF8vJyHD9+fORnYU2J6BYpPkAF0G5vXAzwq/EzGEiXk3XrkAsOT4F+Y+7ryK9n4K1PTNnW3UYnStcDHw84Rq+33VzbMfc5O3f5nNpz7xXgSpqaHWa/men8l7qNbMXsiNPWjH/8m50aZr9p+BFWu+nsl7qSxv1SzE4P89/UIPvNwY8w7KazH7mc1ob0mx75DeCH7iV8VuV3q2FbYUMsNB/4wAfiM5/5THz605/O/u/IkSMREbF///6R7fv374+77757vc38/Hw8+MEPztp8a/8UN998c9x4442TB2dNzXalXjoT0IK5IkFclm2VyJYV2RJEgjjaZr/ZeBlt2QcZvZVF/6BbjseXtZOXTbmXZN4VfD5qctiIqt8IenZtckBMmjfZF0ir6GnpciLY0Pb0Wg4X3L1amKeCiuUzYFrWwIZBE8jiQSHOJscMFbqk87TRXFR/icZxElxOaXXtlVWKXnLuJRvC31xH2wu9E5qvfvWr8cpXvjI+9rGPxeLi4th2U4m8v+u6bFuKb9fm9a9/fVx//fXrfx8/fjwuvfRSNWadd8VId+xEJ03ednJSbgya5OVEhDAvsyWLtjAn3Styz4jZyfLTKusFuZxSHoE5Z/JtdK9wUqdhGBecfCYtGWDCCGQlKWuAjzzoHGiR3+eaIyJyfY/Wy1BEE5y70MtE5JqZrdDLROSamc3QyzwwWMi20XiXV5OyDJQwD0kwLRQqXJcJGunZPPROaA4fPhxHjx6NK6+8cn3bYDCIT3ziE/Erv/Ir8aUvfSkiTlthLrnkkvU2R48eXbfaHDhwIFZWVuLee+8dsdIcPXo0rrrqKjzuwsJCLCzkD76CXuVOnnStjoJgNR1G8GpzeZCoFGEnhULSgCRNFhXEVT8dwnykajRQaHWbvB/eKxIAr7rieLqoZymIpJH1iJ5dyOU0lZ0W7Ejkxaail1ZZJLPJ2EgvMw8h2qSXsSBikmpmSC8zA/thcjzYVlqTifQysxX5ZVAvA+PFHDPJzUK9DNxkVY8poge/bMNGo3dC87SnPS0+//nPj2z76Z/+6Xj0ox8dr33ta+ORj3xkHDhwIA4dOhSPe9zjIiJiZWUl7rjjjrjlllsiIuLKK6+Mubm5OHToUFxzzTUREXHPPffEF77whbj11lvrBmhXlzJni2Hf+uWoWV2mhKYiakiTOfMRRP+Y7Kpi1Y+oSRhYCnF97b2ylpEhWUHMc2S5nLwvbCUURJtM+6JK90YgtWxRPSayqNS4l8iakVpGdPkCuAlEcmxNptRSRORlRr5oZCkilxO5w7AadrJgwfIFwmJ6ul2+qVlatj96JzR79+6NK664YmTbnj174sILL1zfft1118VNN90Ul19+eVx++eVx0003xe7du+P5z39+RETs27cvXvSiF8WrXvWquPDCC+OCCy6IV7/61fHYxz42Exn3Ar1aE080tZHaByZW7i1K98VkX30vMMzHoZAHYV/j9pVWsUxn1Lt7SW5L76ksaWCLeiIZJ5dTISGw0XgUEcTRVpN9cNZaVwW6vGmRSajHtAh6mTMR/KZI9TIRuWuH9DIU1WMKTEb4mkypZqamwCSSF7TGTNbLRESsJC4n0l3pd6iRl7MSW5Ip+DWveU0sLS3FS17ykrj33nvjCU94QnzsYx9bz0ETEfHWt741Zmdn45prromlpaV42tOeFrfffntdDpo4A1+/DJvN9pWWhiqxrGg4rKhUrUOGCz8ENXWssD9Z50cJp62liHbFY8L1Tc+fyCcZMqTeyT+7k69v6T2OCCZqpmI4lG7gPDewrdCKGsGuuvQZQb2MzNpLRIKIj8kxY/UyNPFTBl2CyTGzAOHjtsAkjW0JShqQXubUGpRlSL+BoLvq8Fvcn17mdH+uXUP/2BRC8/u///sjf09NTcUNN9wQN9xww9h9FhcX421ve1u87W1v63cw9uNW6rJBwa6z0GD3lr+lbxG5HWRaeO3C6fPFRQEwNLP5VIT4ryZnEEJ+GLv0rbPjR3IkhyGGZl2jNhqPtE2YyynbEawFsj5VjVbI1GRCvczsxuplInJ9TI1ehoiVHVuqmSGXE7nDyL20DIKqtHxBxLiaTOBySgkMflOshabpZc5G7LhaThaa0KjOKvYtXXHKwo72mP2mlaX+oVmFvgdJpCCfOqszodBywWH40kpRSF4i5HnVWGjI8oSWw2TA0i0gNPrjQYcQ4yW9DG2zMHqZ09smk6aN1svQOKxehrAKpAT1MuQiw2R4k8vHN73MuY2dR2gqPsb6BUnbyAWcXlkboal0Y2hBdA3hMG3saopcFpKEZNsqOJp2xVCorrGWkE4FtlEF+GJ3qRSqa70M5kKCbcl5kTUG8w/VWGMwAgtOLNHMkF7GhiQTjF4mwulSbHXsUr1MRK6ZsXoZqo5NGhrUy4DLKdXLRIAFeoPLF0Q04rPdsOMIDU7Css6NenjlshGboaZDvjHpvuROWZFmJ9rX5m9Ix2stKjJ0clhREiCPLqrQClG7Hss8oIvFar3omhshb81K1RIESpq3NvoCWjJXI+ourclEVgvSwZBVgUgD9WeS1ZF1A4WyhfllTo8NiFXiDrN6GSJRS1BugVxky0IvExExTMK0sXyBjHxqouCzEzuO0BBqLCMGShg6BvoDnbTDiCY74VoytwUvfWkYO6JQcH0mwF2TuchmJcX+MeeMNJ0pc5rbhgnzyEoI3aVk1lo0q0CWMyCHM4lmpm/3Em0zWXVJk8JJ9GrcS5NdTlYvYyOaSLCchmNHjIlgylYsjajsNOw8QiNnayQchRMbVj+W2WH9QdK/na5E50CxmTOzHaUVxFZmRpeF1Juk2hVRbPSMIK1/2b3CHCswDnxmpIXGfNypK5vskb4khfmBehcA2+doYbI+hqJ6yPIyoGtJAuDZvD/M7ZLsuwwnVVpgMmKcAHgl2zauBtM/BlmnKGEeuciWQABMGX8zAXBE9vxai6m2wDYytO2x8wgNQEfOmJWj1dlUkBd2m01+26qqSxe+zFqHLCszs7aJ+oPVauoCsVa4nkXd2UQPEzhJE5CT2PB8EeFWk0rACGrH7ZwRGGsEkZZVzGyf5peJwBwzuxZGo3qIlPRtBelTL0MWD46syjP+Uo4ZQ2jIGsN6mZy8rJFeZi3fhhWyU0ufLWnQiMo5g51HaGpoNqXNTjdJ90FpaO1YmH3pI1CRr6YYNkuyySobEVOkDTLWkppTEsE6p48piKaM6kFNii0aSsc17WSmZ6vl6UiLlU1EYlxjhoYgd5isyTSXZsYFUoKkgaKXRH6ZiHEWn6lv+3dEnV7GWmiMZoYI3gNrUI8JXE6UX8aQl9MbJ/zdcM5j5xEagrUimJWjFVZaQmOF+hmxkjvWaFL69ELVWLHsh0u4QHrXCpmIJktobAV1zJLco15GVjennaegvk626K94X7SbkkoYQI6ZGs1MilK9TEROEvoPx3YkJ9XM1JQvICJI4di2hEGuocmbNLfRuY0dR2iqzPammdRgoIm+Rr+R9IcZMSnslxbgpEkpdHMh5IcGL4ccLx7WNKuJBba620Jfv9VdYQX1HuseYYSQFACTXmhmZbKFxtZQ7VMvExExD5qZrH8ikD3qZSJyAmNdToSN1sssDfLQ6xVImHcKXU5UIdtZYLP3qIK8NOJzdmLHERptGUHNwWTze02YaxXScdiaJVKTshWFHXUJBppzDHHt+TyRvAgdCZZ40G4d2EZWEGN9sZYRIlEmYV5ETJHg11xzSxZl9JLRy0SUF5m0VhDSqRBSUa21eGyNXiYfB+llKL8MaWisyynTzLQopx2HRmgixhSUpDzooj/r/6cVLdVVckFZ+cYaN4zNCbOxgU8MGdGkkrrJ8/RaDdkuITB2/GgRE0U4I0LXPcrbgAiWCIJ9jgqrZtu6W9aKZfQyETkxsXWQLJGgsGfSx6QkYbvoZYjQWL3MshX70jVHwe+YQTbsGOw4QqOjbgon3U2x0Bgrk2UbaJ2q2NdEztiaR1bwasXOxppWoxXC9MSwafjt/47gzLuWMPVpLuc8OlIATInNYNFfXDRUXm+rl5mFrL3GQoMFJpFIOHLB+WSmJ7Yh9KmXoXGsVellnIZGa2EKo/Yazh3sOEKDk4KYdCLk6t1EQo05prbumG+ZdWPA5KRrU1rrUbaj64sFr3BMsnBASYDcitWvcLqYLKMg2rlO8Hr3aHnCPDoVAuDpFXHQQg1oRJ1ehnLMpLBEYh7IEbl1bJHJNMfMVuhlInLNzEnM9tuzXgaL+xaK3AGN+Jw72HmEpveY0ASY0A26t4JamtTFy6wjq6iZDdE2Y7OkwRJNqvNDk7UII+41FB36H9ssJZt0GQ0hi4iACaDXDzRqeSD9P+llIJze5MOpsgrReyX1MmTNMASmz/wyEZyELrV6bIVehsZG5Ivzy0ByPNjGLqd8HDWW34ZzFzuO0NjCiKXp123hPoR2V4mGNuyXYDUpgNLJ1FqxqviosYwQaiw0Rs9iJ2bZf3HpADmOKVFgMoLJi5nTbW01qzPSehkYMLlPUvStlyHri9HMcKkCIHOFepmIiEGy8qB6TES2sB6TtLxw/aV8U7O0NOw4QqP1ENLSksFaRqg0gd3X+I8xHhv2o0PqjMI0jlKlsGxXUyIhjS4qFcpGjNFvWBdZaioqH4cutlf4tbcFU7G2jo20S5vpewDbYN6fJpIDLqFS2MKOVi9DRSaLLUVYMZvG5moypZoZci9R9NIASA6LffNNfWbvbqTn3MaOIzS8ipZujNJj2no7BOtyEh88W59KlQ0YexDXLIOtfC1DtINcThnpgyY1Fc9pV3q2kvkELQ3yelcl5RPeQbwv1BdotlAvQ2NL5j9T0HPs2Oad2HfXbG5BIRgisdF6mQinmWG9THkoOuWYSTUznO03Hz+5l4bwzBAxxhIGLSS7AbDjCI1mKmQJsKLMbD8xrnHjsMTHuFOk+Fnnq6FDmIgVOqR1p+CEKK0lqd6EBNwkxq2wGBhx+QBLGpDIlkz05WNTbWwuICAvlATXiJPpfmKULnlhKvQyhJTQ9K2XoZwtRKJSN47XyzgLDQG1PMlFx/wyVEyS9DIVtZaapaWBsPMIDaEmQ69BzxFNvGJJlZWuL1tMs1e9XSlJi9BEU5GLGgJJkOPNIKtol+ZwGYfsnkoyh942zDlTOA7rgqMIPRAskwWFyhAYEJFg95K7MTbsWY1DhmNbvQzlmMlFwUBedDi2+/Y091KDxc4jNPSBlitJRUxQz1HBEHQMdWFf8gOC31hj3ZFkzmheIsaIrmXeLXUpqwhNGeEgESwKbynCi8Lz6RjCUqZrRUnhpiY0pmgojYO0MQtgkQBCQ5YWcp9kw4AHcF7qZTBhHhzTCIDpmESsdk/nAmCrl+EK2aNlDXD8qy5hntZYNWLSILHzCA2gKhmeIjTl/U9JN0Y3LSY26ktOiOhysh8kMQ5sJt1hvkRCoc6oAmZSx8y71JcNWbfP22QPXEyR1Qbu+/SyI3Mmky+2oVu3FXoZEtnCNtLLkCuGSNRW6GWIvGAEU3JzTq2CXoYsNJBegOvNNb1MQzkaoYkzmNSF2caKSrWroDhlsWyno7Jgk0pZX6Y7GtvOjg3dP6KvCjABA4F1OneQZoRkNVJfoDPoptDESlTMDr4eIMvICSmdJlb4hkm9oh4TEZp0X7LszNfklwFCY3LMWL3M4rQjc2RpIXfYidVRCw26nGwxSbkgqvpeNOwo7DxCU2HSFLUpq8Kbq8oyFFpGtF4Gw8ylD7wUtop2oVtER5/VfFBpW3pc6wqUImlbpTzb2d68Cr2Mej9oHLIgps0vYzP+ZoSmIildqV5Gj0MKnQmol4EK2SmBGdTUXmoEpKFn7EBCUxHmarq3Ya41glSasdLj2r5olURuBtTQlJMyA3RZ2EgcUcQSE7jZ6CKC1NCkC3VMXgfjn6ZK1QSbO8aIceU5SSPFmGv+7f+OCLRizUHCvPnZfBtZVbC2EJxrui8nzHN6GdpWWmSS9DILUy6Z3yrljiG9zGA+b5dYclZW874os6+qjh2ho5waGgg7j9AAcMIq1VJoUlK+L06Syb7YFfqsoZnNCkwLUzVJwm7SImEz6KIbMQ0EsxmcLeQCOcsxQ9cIxm8JntWg5ESCiGG+aQZCtEv1MhGRvWtIWudcPSbSy9iEdoRUM1OjlynNLxORE6savQwdU2f8TQgM6mUgRLuJfRs2AzuO0Niik2Q1NdCiUpkDhRNwiP511lroHp4KlGUY64Nx040bG52CTItP1vesv4qEhzZRsCm0iMJv6dbh4pHyGRRWPdTLSLJFzxElaMzun9TL7F7MI3jIFUOgSZ1Dskf7s3oZsniU6mUicstQjV7mFBQKI31PqpeJyC00rJdxUXBNL9PQN3YcodGwlhZjkaDdKl5InjhNvDSgOL55zL4b/KXx9agmu8OqNEsEyUfVOdhbYCOCCKYduZfIMifdtiZjMSYVtHoZWWDSCIAj8nw1M/LGEHmpqZCdEjU696rcNzBesr6kCfIwHNsm62xWm4aeseMIjRVuFmtB7IRrV/N9ZoKtEdlKC01p5JAuOmkzFqsiiFKMKx8GvB50LRP3CUU0kVuHywbYJa3cljahEG1nCBhjPYJ2qcsJ2swvgDZG5pexhIb2TS0jpF3B/DJwEqV6GTou6WUIqJcBonJibQHa5eNdXRvdxtWxpV6mVcdu6Bk7jtDorMByosi+WzQzS1GpdjkZPw5GIBWeU4TOOaNcbjUfMjp1rPQMH1qTwM0+H5qAwcbU5VSTAVgSFVWniUgrCZElkWULzWTR/BTpZaCkwZ45SBoHJ2ES5kU4IkF6GRT7Uoi2NC8SsUo1M6TlIbBeJnclkevrlKiQTWJffIekq7+hoQY7j9BUeFMQqRuDwksrQlp1hI1pZj8gtiAmHSKdnHoOk0eLhMxSm+k3KLqopl6SrQ2VHJd0KhjRRNcDIrxs2H3WROp2aC6l5x71MiaCSeaX0XoZ+TITkUhrMk3Dw3BymFs30OUk3Vwmx4wNFa/Ry6yBuHeQWGh0duy+XewNDYAdR2h0sraqDhPUvJClCfjsMWUStuJEgDV1sqybxIoLe9SuIDB/iuhQalK05UXe00ycTO4lES02bhxsnZpMwMgaQ/WYaJuFrYVEVbNTYDFJWXTSFrtMNTN914rCxHrgIstc4BUu2qaXaegbO47QYCiwNJfjyjQTBVNOERsHDdtKXQ81ligkNNZVl/xdM1kbAWmMcYvQpCsy0vYdZWG8HUQaaL4CT0EdGc8OIPUyeG2hHVpjqN1oh7PzoI0hvQwlzIMLQhM41mSayXU6KXEYwkkRaehTLxPhNDNWL5PWY4pgATBZaFJ9DOeXgcE1vUzDJmDHERpeuVfE4Ja6eqwniVwgxn0g9a4qg2wEE0GRwI3InM9O7MZmCWN2DLogKGhU3fvijukm61YU7quxEI+RJVZcmiDfhjWqKIIpaTcNbVAvAzeGtCAEJBLCMkJ6GcrhUuPmohwzRjNDZO6BQe4OI7K1BDWZKJ9MlgVYJipt4dgNm4EdR2h0/pfSqGf5IatZsKh9e/4w6AiePsdhr5GedFO3nPsYa6DwFrYlxy2uSj3umJZApwYrqsdkkieGJ3OYJSCZ1Odmwb2EFa0posl90ogMKdJA7iUZou3dXHCu4sHEqCSqhk3jBSJP29J3rW+9TENDDXYeoSFI1wbv26O1pEctiNW84EREQj+wIqisvRUh8Tbqi3Kd4THS73jPoeh2Uk+PYUsa2KriGsPJxAqT+ZEAeH5y9FIE55NJK3rvmgcBsKxTVGMZoaR5qQh4eZi7a5jk5CdvwsIjOMfMnEjodxLGRuTlpBQAU4Vslcyp1W1q2CLsPEKDuTwq+kuFlbLiMqayJdh6Sel5qUbhV/iF101nt62xxpDVzWTQXZEp2ivILUbYJwQGywbIjMg1xTTTazktc99A4AyPl8gLWSkSzcwcCYDBejIEZmVDo4m8kGUk1cyQXuYUFHEkbLRehixFXi9DAmB4r5KFjc6YDWjupYa+sfMIDaHmzcpyeVT4kmxhttJonZqoIetySt0YWi9TTrZUiHbkFh8sj0Cmd5uTqFAXZcsGoIVG11vIN6WamRqr3hByx+DzAdcy1cycN7+ct4HB0QROKNXLROSaGapAvRV6GSqtcAJU42ShWYKCkkOZTyZ73MoLfDc09I6dR2hs6GtpfxUJ0TSvEixhM1Y/bAQSJumawWHCQGhmrEd962UsoUknCjv+wvpiY5G6nCoEwOheolsPJCcN0yaygQUmYXBELii8mywjhLQ/DMfeAr2M1fKQAHgIFppM7BvhFljNvdSwjbDzCA3ApsA37uKqDK9yAY4R1OK4pEnhRHIVmg4jGhS5SMZBWxGE3gQrchMkkUAXC91TkbWeLEza3CVdhulciuUi6PEgvQy9Q0IvExGxe340gsnml7GWESIXWK0aXqLVbtS/1meByQivl0nda6yXyT/nXi8D7iW01Lbw64bti51HaCpcGwoV5h5M128tAeZDU0GirEXCkISqygfyGimxsyRbPBD5HGH23ZQFw36ysKOpWXV6Z7AiCC2P1csEEkiwUsxRjpnRA9PET7Ah2tQfFZnEHDMJgbFlFEjzU6qXichdTKyXyW+WKTAZwXoZXOwIlzKh6WUaNgM7jtBw9Au8bTQxG85QM0naZjQ0Y7moKZxJoOtmInZ6FLKO7Q8m2PQa4QebhL22+ri0nKULcLqfqEnRFhqYnKi7dH6l7jGiyellKKKJcsykmhl0L9kCk9JdZV1OaY4ZneemR71MRMQguRFWL3MK9DJEaLR+L3M5QZuGhi3CjiM0XhhbZkbQKxHpFtC6jFJtco1nA4O3hIXGur6kOFkVXozINSPWnVcBU3iSw73lASzXohW4clPCRhmlZvQyEbk1gzQkFF1E2hUrALZFJtNj0DEJmOemUC8TkVtoyL1Eehmy0JA1xodfN5dTw/bFjiM0MqpTT+pZO5u4zx5TZOPFhjL7sQ0ZVkn0IneBMNmAbbYsDwponSYny/dSE8JfGNFEILcOR5D1aI0JcFeRpWgBri1aXvKDEqFZFDlmrIWGwHoZqspdVmRyK/QyEbmlaAWirZZAL0PWGMovk9VoijPQAzY0bBPsOEJjo5zQ0mLCd62VRWbYtMnl0v76XkiVinZtan7UxpAlR0cElYWU10Qv2ZDytB0SMnKZ2bo5ANI25fcq34/Cx6fQHZZvmpl1odG7Z3PCkcJqVxaxHpO7SESaTI4Z0stQnptd05PPM4JDstNtrJeByCeTHC+82NdcyqaXadgq7DhCw9ltK95AE4JbMSESVDIra4kiCw20s5aLdNLtMFpH9lUTbQUwGXmttYd3zjehSDrVJkPUEIU8W52DdS+l28hShBFN8ABOk9UG2u3BHDOj7axehtw1lK9mgawg8IIsgS7FWIZsFNWMNHmkepmIiAfWRq1HrJfJbyCGY0v3rtbVNDRsE+w4QlOFUjGrzi4nj0nIVv12Pxv6BJuEDsi6+Gr0Q/YUVI6gGsuW1Pxku2m3YsU4hEvPRi+RK4nGi3oZUTUbc73Y5HUVehk6rsk8TALgPvUyETmBWUW9DFg5acGCt69pYxrOfuw8QiMFwJqDFPqZdT6V0oimihU+HpOOITKJWusJWoqctZzJlghDJS9GVUi5EABHAHGwFbNlZmOroUkBBgrWy8jopYW53DJiikwOZbFH6svml6GaTCbHzFboZWhslF+GBMBYj0kUnYxo7qWGsw87jtDoEFwChsWYSpGuK9ZvkI5kMjFh7U3FOGR/2TZrPam4LTYxYjr/kT4EyYXUruC1JEKTHLcDTQrdYx0JRgJgQRhRtwMh2mShmQZrDBdjnJw4hyJ4CNS/DcdeBSJhdDqYXwYubo1eZhnO/0RSk4nEyWurLvxMV8huZKXhLMOOIzRVJQeou9J9tRmkcN+KXC96aEYjXUqExsFGTYlVKI6t5vkwtW8irw01RZYoImT2ullLXEZo8jZTFL1EGhoKUy4sOVDlXpIPEha2FIsTOk/S6JBehsa2SlYhcjklLiZ2LznLSwvHbjhX0QhNRN1KxFgkalxVdrzie6TTlkuzjQlJxgyyq/nEoXPfWLGzyVhM4dLYUB5Thp5n3g6K5sJK4NK9JLU8qQh4uABJ6aR7ibbtnsutFERCUnJhBcBEjmgbC4Dzm2+IFCfMo7Bw0O3AOzSAsT0AFbJT4rO8QgJgIDk11kVAczE1bGfsPEJjw6AlMpJgNbZixTz+mJPb2OR1urQCsgth4bAaICsWwoqHcK5G3yPFrdZ0ZpP+ZceVeicTAh4RuhxCSmjI5USh1+RysnoZyoybVrC2uV44koisIE7sS9vS4/atl0mjlyLY5baUEBgiXx1lABYpHhoazhXsPEJDk4dN6kbIwqWtXwe2VehNVHVpstBYF44lZWkUO63ma9Lx2gR/EKKdjc0KlitcTliTKQuFhgOQhcmGaMtnK31mpubzF8G6l8hycR5YaAhGM0P9Y9i2KDAZEXFKWmhSUta3Xoa0PCdA8JtaaAakl0E9lQ0VdM0aGrYzdhyh0Un0dIeT+/dlDqzfhfaFbSlq6kwRMCty2n/5OOqKWNLG5G9TwPIMBqJvX6qh6Vu4aceREDqqvYQCYCppUCHQTYmELmlQ2P+4bYSUSJGFqUYvQwJgKmEwTIgrhWP7ekxNL9NwbmLHERrr62FiItwYdEz5AdGpaXDCmsysakor2BIJJjMwWOPPwPUF21AMCWQrHS9Ze6RlxG4bUmLB9Lg6HFvqIWiyo/xqi6MNZ2RyPNpm9TKElMBYvUxNwrzSIpN7ZiAxoNTLkIXmJLickPgkRSabXqahIcfOIzQAXbPETGI1FqDSnDMh9Tfl8pC6KKQUREBo4rcgzgCL93QxzKUVpLXEAu7LVGIZ6agsAelgLHkBoFcnGcfsfH5QcjnNzUKqf4hoImsGJbQji0TWP1pGNlYvE5FrZuryy7gK2UuY8Tex0IBexiS6bGg4l9EIzTgURkMVJ8KLOiFvus26LChU10bT4Pcz/T5LsgGBHdo9aPOzZNYS6t+mhZdAC03S4RToIWz0kg7FJ86QWGhoQp8h9xIMbvcsJbTL912C+gqp+wcz71JCPjBtDeGBLtXLRORWJquXOQXnifllQC+zBmQlyzFjLZXWZd3QcA5g5xEaOUkW1++xifAkNtzsa1Psl5ZIsB9Um/4f1a3QjJBqV5B8VogohV4G25EUROsh3DiGlDQvSYZH1hjaRiSHijFSXaXS0OhZGRNPIttS91JETqSsXobOk8ZGJQyGMN7MQmPF4BLNvdRwLmDnERq5ssGJyEx2NuTZakbIYoCRSclkLaMbakTMphq2tXjYqtwE+zHOEsnhs0A7lvUfERFkGRHXiKxY1mKFkboLoIVJQrJnIdsvEZpFsMaY/DIRXF7AaGhIL0MgK4gVAGMxzUQzU6OXObG6mLcTepmInMDorNGNqDTsIOw8QkOQEUc67DmFibgZg+J8NZbQ2Cy7EtncIT+ynFFYrkIl6csqf6P7CvqXoHPAsgbpBE5VwIVhZ+w4SKwNFpq5udGTJfJCJIcyAC+IkgYRY7QryclSrhciG0QaiDCRTqW0JpPVy5wYUH6ZMr3M6YOkOQfyJq06dsNORyM0Z4LCj0OvLq0Ids+IY+paUTqjMGxLu7OCWjonSS709U0JB2qFKBRd3ngSANO+yTWxCfN09XHKfQNanrQaNrngyCKBBSbJ7QIDdi6nfgXAmHkY+mMNzeSHcCAtUURoSC8zpAR5GaFpodcNDSkaoQk/+RcnkaX9hCti7DZDJEotO9GviFkn9qIcKBRCbesUkZUidctRCQZZ9ZuAifpouOlxpR7C8mk69+lFqDc0XSYKRgEwXLglCEkmcpHleoG+ahLmEWwW48Xp0XMlvcwxqNxNrq8HpAB4CM99mndGi8YBzQ3VcK5i5xGamkR1lEiulNBUmG2UxUBbaGjfCs2PAFoQMKOw7dD1lxWBpLwd1j0oA0rQApYcdzrnBxqol1kEQkAuJwi/TjE/mxMhsqAQGbIWmjTk2+plKMNwjQDY5JghvQwVkzxB+WVAALy2lm9Dwa9xOTWi0rDDIdeeHjfffHN83/d9X+zduzcuvvji+OEf/uH40pe+NNKm67q44YYb4uDBg7Fr1654ylOeEl/84hdH2iwvL8fLX/7yuOiii2LPnj3xnOc8J772ta9Vj2+qy39BP8IQflPJD/qiY3ZT+Y/a4XjpvIZToz/ab7rLf9TXIP9hh9OR/bJmg6ns101H9puCXwynst/UMLIfoZvNf+ngptemsh/2BeOl+9fNddkPr+/K1OhPPh8IuAfDmfw3v7Ca/aajm/ibmRpmv8WZ1ew37Kay38pgNvsR5qfXRn7TU8PsN4zp7Lc6nMl+a9109iPQOcxND+G3NvIbdtPZ7+RgLvutDGay39LqXPYbDqeyHz33+XfFPiANDTsHvROaO+64I1760pfGH/3RH8WhQ4dibW0trr766njggQfW29x6663xlre8JX7lV34lPv3pT8eBAwfiGc94Rtx///3rba677rr40Ic+FB/4wAfik5/8ZJw4cSKe/exnx2BQU3ipDkgSUkKjO4OfJVZmXwB+A8cRuuSnv59ZQ+iPxo99yetBEOQNiZsdL/3wmHnDjOQRSYP+kUQB2YrZLvvNzgyz39RUTPzNzwyy39zUMPsRLLmYnRqO/IhYDLqp7Ef9E7GanuqyX3rM079B9puJbuQ36Kaz38pwFn4z2W8wmM5+Q/h1w6nslxF7u9CR7RoazgX07nL63d/93ZG/3/3ud8fFF18chw8fjn/+z/95dF0Xt912W7zhDW+I5z73uRER8Z73vCf2798f73//++Paa6+NY8eOxbve9a5473vfG09/+tMjIuJ973tfXHrppfHxj388nvnMZ5YP0L7Q6IqBTUJoisOAZtbFYhPw5Y3kQOg8RfHLiFAiYMqJQl9aLJFA47Dun2Qj6j2taw0z/EE70jqk51XxTGK4+y4Q1UK0Uuomoignq5cht4sV46YuLNLLLINOxSbMW4QILIrKSvUyhJOklwHLk9fLkP8VDtyISEPDRGy4hubYsWMREXHBBRdERMRdd90VR44ciauvvnq9zcLCQjz5yU+OO++8M6699to4fPhwrK6ujrQ5ePBgXHHFFXHnnXcioVleXo7l5X/wgR8/fpwHVGOaFR8VnSa/pqYUHndyQyRCVpCqx5FugEa2KCRFHFGCOOoOJvo07wyFSyO/k1FONnfRzEqyzT0KCJhfYxq0MYughUkJDBaYhAeaLDK2XhKVSNgF4dIpSGRbo5fZBeTF5Jixepk1qZfBSDuTY6YRnIaGDBtKaLqui+uvvz6e9KQnxRVXXBEREUeOHImIiP3794+03b9/f9x9993rbebn5+PBD35w1uZb+6e4+eab48YbbxSDOtOz+AeoKCdLBuRq3gt5kz/7jmiiyZqMFEl/WEOIFqXQF9ZjstYYCqFONTIU0QQEAQHHpLDnWIZIqvS85D22YuoFEdFEIPKye9al+qeQZALWZEoeJCowSVl27TEpvwwJm02OmRNQo4NqUS1Bcry0YnZEcA6lworvzZ3UsNOxoYTmZS97WfzZn/1ZfPKTn8z+byr5+nddl21L8e3avP71r4/rr79+/e/jx4/HpZdeCp2IgZ8BshpKG02Yxg5E7GddTgQ9jskMj5PoQV8VCQmZMCYuJ+NCHNOXNvSZSCo7p1HiPhm9RO6kLjkIkR5yL1GkDyWXI1B/RC5SYIZh69KCY1IkFYVkLycWGbIUcX4ZiF6iumwy/LqRlYaGydgwQvPyl788PvzhD8cnPvGJeOhDH7q+/cCBAxFx2gpzySWXrG8/evToutXmwIEDsbKyEvfee++Ilebo0aNx1VVX4fEWFhZiYSE3/RYD/diTTSPF2YTHHNNqV9JvtrXQWIsSnroxjVtLEU38knDwNYedU70C3WNpBbGguTrV0EAdQ7aI0bWEEG3Sy9CknmbaJa0JuZeISIwT/JpxzCUmKyINVQUmRX6ZcUiLTFKo+EnQywy0XoZcrWpoDQ0NCXonNF3Xxctf/vL40Ic+FL//+78fl1122cj/X3bZZXHgwIE4dOhQPO5xj4uIiJWVlbjjjjvilltuiYiIK6+8Mubm5uLQoUNxzTXXRETEPffcE1/4whfi1ltvrRxg3e4ZhCi4hlzoqt/FREIes1iITBYaaFeRndgSjjQsmzgPVse2LiHiIMuTiZoWOpOYejaf/fbMOzdRapEhrQlZMqyehawlxXoZS5jgHM6bya+HrcmUamZOrNr8Mo68sF7GCfUbGhpG0TuheelLXxrvf//747/+1/8ae/fuXde87Nu3L3bt2hVTU1Nx3XXXxU033RSXX355XH755XHTTTfF7t274/nPf/562xe96EXxqle9Ki688MK44IIL4tWvfnU89rGPXY96KoZNGlcInWlWmpWHhTWOOl1FGzYVWoUIWsszJgdM1p/NKEzHSMib1jZZrkVWJmHFQm0MZjrOt83vygkCuY7I5ZQ+WlYvYwtAkgBYuZfg5EmnQiArU6leJiLXzJB76RTpZcBCQy6nUvdSc0E1NOTondC84x3viIiIpzzlKSPb3/3ud8dP/dRPRUTEa17zmlhaWoqXvOQlce+998YTnvCE+NjHPhZ79+5db//Wt741Zmdn45prromlpaV42tOeFrfffnvMzNj44UqUhtLW6GBM/+E+ZiZseVxfXsQsIqsq3G0Ibe0icpFugN2khgZBExYlvU2DnOicZIg2uZdmpNI7JTnkDiLYeknUH+lUUhEwVaD2FhogL2CGNHqZiJy8EbGicGxVYDKiWV4aGnrEhricJmFqaipuuOGGuOGGG8a2WVxcjLe97W3xtre9rcfRbcLKBglNeRw0GpQKLSN47jYhjs2NkXYnXVXFBSbxoDy21JKD/ZPLyU5EcNkwl05KaOCYKACeB/0JCIDJMkITcdrOWE8iXIHJCBYAU/6XQdJfjV5mHi74bnA5EVK9TESumUG9DLjbOiA5/P7JbQ0NDROx82o5EaxOxXQl58OafDVTZkKxAwFoNxHMf9lELK8tuo2kBQXPSkQXoRi3VCsUEdNU7JKuUcItOBw73zYFGpo9C6APkaw9taCQXoZ0JbYAJIVLU9K8k8NRXYq1xtB51uhlyJWWambQQrMKVmN6v3XOgRzNxdTQMBk7j9DUfBi24qsiXUfZpkJX1ZjuteYnm4tqIrxoUteWJ7HNupfsbacQXNiWESkaBxErcC/NgTWGJnCCqXJN+V9suPS4kgiT+qtJmEdWJnLBraKwGfQxSRZgdC9hOHZ/epmGhgaHnUdoAFZvUtoZhxpXHNLkZ5GaF9aMyNBogBEUq0yoMSaqh0D9oWUr6R/GOiUTCCqNTjiROJaCgHHMQcK8OekmIqQCWnIRLUMG4D4FwBG5CNgmzCMRM+llaFsash4RcXxtMduWWmSWV3LrFJIX+Yw391JDQ39ohGYzgASBTA20r+pOuYm8mwu21ehvRF/6nARRiQjlXhvOu9nEkrmspMHY4yYb6DxBVzMLehmqtUQuG2vNyPqyCe3gppILi7IAP5BEEqHAWJZlsHqZk0DUiEgtrU4eG+llWGPV3EsNDRuJRmjGoFjHW5NLpsZCk97JmhBtIlFSR6KIFelKMO+KOuQYLc/kY2DyOoIkYHociUUG61OB5UzrZciDVZgThhLJEUgvMwPHXAUin5ImKwDeM7ucbbN6GbLQUI6Z1EIzQL2Mi2hqRKWhYWPRCE1Er3lodP+WMFlrRp9kS+8LkTgijN2On0sk2HBYoY+x9ansatsGYKVzotTQzFIGYLBcpLqPiHElAUZJAuVhqQmXJgHwape7bNJjWAsNhmNLvQxnIwZdTWJ9GZJepmljGhq2BRqhORMYwmGTsJG2gqwl1oiQZSymY5KYWE7qVvOT9mczoRK5oF2l8BaR9kfh0rSylon7KESb5CDDhdEBkzVmdiHvjEKerQCYEs6lJMcKgJlcyBw2cEFSKwiRL7IAkUvL6mUegArZlPF3OUma1/QyDQ3bFzuO0OiVU58fH2uh0S6QycIaLeKVZQN0BuRkGyWWw8gfmUiOzssSmmxRTmJtqI6N0Utywsr0MhE5eYPznIZte+acPoRgaigtwWAp4siWSCAsQch3aqHZDL0MhZ4/sJK3ywgMkZcWjt3QsC2w4whNFTY4Xw22KyQmVZoX+YFGApY00+OgSB/alawl1tWTEhgic3YFToe0GqX5yRaaxfncIkGRRENpEsScMMmAiWzUFIAky4jJMkzkpX+9TE5eMEPxyug2tNBYwtvQ0LChaIQmYuM1NARhZTndTvaXEgmpeakJ0easvQn6/rBbsSVmGU6akAZIZjG2QKKWkk+4jpQBmCb6miR0pX1xrpcyAXAEEBppAepbL0MVsjMCY11JjdA0NGw6GqE5A6h8NRWzn+U46hgV1au1bkfsa11VOjuxdC+V1mSaXnUWIKspGiySO2l05xmomE3WmHnQwaxAZA66l4CEpESCRMEE6t8KgI1gmfQ+c1IUTNaY+1fz/DJkjUn1MhE5odHVsQHNatPQsLFohKZn2EglGzU0RatGka9Ga176DtFOCQ2lOqEvu9QP6arc6EpL2lA+FZkcD48JbxNZaGbnJrucdoNehlwsNmsv1ThKCQzlYeFwb6ddMXoZOgaNddd0TX6Z/MaQXoYimCJ9/2SB14aGhs1HIzRjoDUufX7MBEEY2y4FTcK6UjVssun500mBtDcVehkdbUXFHUVI+cyy1OgAkETtyhlSSmDIvURWCgIRmsVZF/2zlEz+JAAmSxFFNFHCPHIvGZEx6WVo/LYe03GwYlEJA8oxk0bV6Yi6hoaGTUcjNGeCLdDalOacwdqUNW4dmcU4m/zt+GURThybiLaKiIhsTnTlC2xJCi4oCe6Z5Fxn0b1UXtKAXEIECtNOQVYh0tCkFbMjnAA4Ih8vESarlyGX06k1yi9D5EW4k5pepqFh26IRmlqYPDSFwt6IcFmB5TEwKsnqQ2xGYXOu0vVl08ejJkeEfHegl8Fzl2/JYAH0MmCNmkk1NORygjpFBIpywiR3cGNMhl7qi6wlZBk5uUYx6zlSaxTl27F6mWOru/J2YClapYy/WJ9rssWR0NxQDQ2bj0Zo+kaPod0R42ocCWJixTy44pQh2gShv9HEilxOZHkSkUR/v/foXzDWaagGgNn/aTEP7RYWoCRA4mLZNZe3ISsLalzgwpmSBqf7m/z6U7g3IXVfRbB7CfU9CYGp0suA6Pgk6GUwokk8b42oNDRsXzRCcybo0+VU0VdxdfDS/aIiAZ8taWD6Ggdy9Rg+V1O+QNRoiuByBWm4OEUgUeXrIUQNEax42IRp2wzAmGUYLhyXYEhdTuV6GSJ9pJeh8Hz1PDRC09CwbdEITc+weouqDjF3jOiK3DA2UR2Bjpnsq8OnKf+LjS5Cd9hk8c4UGB8wizH1DxiCADh1L0Xkk3pqsYkYI7y1Vahlkru0P9LtmIrcEV4AbIpM1uSXObach2gToRmu5dtKq7Y3q01Dw/ZAIzSbAZ1ghvaFTSa6SPaPSfRkGQJ0EyXjwIgm6ovM/VQIkBbWdAxAOk/aGjx47igAhoy/EHE0SK75eRSibV1OcJ+txiWtoURjpYR2RI7I/WMjsNJj6Pwyay6/zCrkl+GkQS0ku6HhbEYjNH3DJgCuseTQMUwiPRsWjhmFYZPICWMFtZpcWL0MRkiNbpteke42eQ6zuybrZf7+yCN/kdWCktwhQRBFJyNY45L3lY+fyMWJAYRBS70M1mQSmpmaekzDQr3M6YYTh9bQ0LBN0AhNJXpdwRGPsGn906RxNlGwrqIt+zMuJxyHLbfgtnXoPkiPSQOBvqQgehZCtInQ5Kn+K0K0rUtI6GVsuLd1L9kEf6QhSmEsTBEs9qWEefi8NfLS0HBWoxGazYAlJRbGCmST6FXknKFJISND9jxlgT8bok3XPC1rUFWWAY5JCfJMyQGyjJCg1uRwGQciISkMsYhgATC5w0jfY5LmkXuJCM39K7mlaHUN8ssAybHRfSmaC6qhYfuiEZrthBrXVGqhkblqOAzaHXKKktmmaTuQbED0C/RF585ZhkFTtAqiz0xDA/0TeZl3pGHPggs3TokDCYCpbACBNC5EfIz+ZhfFrANOruVEgkDuMBpvSmhODnO3EeWXWYYQbcwvgyUNml6moeFcQyM0fcMSkKoEfJRVN+nK5KqJ4CgO0n1IfUF2XIxocuNga4m8SHAKZr6GuTRCCpvnQfBKbpcsUzBZcUAzgpqUwoimiDyqyfZVmgE4IuK8mdxCk8LWYzq5kpM+yvarK6g3QtPQcFajEZpzBcmE0qG/pqirsfsql5B0VWFfMrqIYAtsZseU7qUpCrWWGXqzsO2KopO0L7lnDOGYgf7JClKaMC+iXC9D5QvYvSTD/1vG34aGcw6N0GwRdHI8Oy+LEgxWeGs1KWhVSa0ZOgIJugevC7qcqD9R2JJkJZTTZmbeaUso/PoUEII0qolDtPP9bM6ZJbhwZFVJ952liKaOrCUufHwPVOWmpH+pFQj1MlBgcgDEqoP8Mq1CdkPDzkAjNJuAqsrdMubbuJy01UKGaOPQRE4YE+4dEdHNSb0MJUlDt1byNzz9g0WwglByPNhG4ddEaIiYpOAQbQgLxxBtp78xJRIeAL0MWWisXmYR/H6pZob0MitUYHIl30YuJ7bQwLaGhoazGo3QbBUktyjOV2MtNNS/jZAyx5UTDAqAbfg49DcjcsyQ+JmsU3NzpH7OQYTjOFgW0naUcwbdOjKBIEU0kZ4ltcjY8gg2YzFFNBFSzQzllyG9DIZjy3xGhGa1aWg4u9EIzbkKKzquyCiMJCS1DJGRxeZ/qdHLiGMQeSGrENVjIpDbhWBCra3IdiBJCGcUHu1vCEzWhHtHsHWKkvIRUhcTWbVQL0MEHfPL9F2PpKGhYTuiEZrtBJuvxsyb5HKSeVfYrUPtYFs678CchiUNaBxzLtpKu8OSY2ANqEWoZwSEhiwSJucMtSPNCGEXaFIwRBsSzlGdpoXETbQKVqGTa7llhMjRbpFfJsLlmKH8MqSXCdTL5Jt0kdOGhoazGo3QbBU2I7w7BfEDWXhR1zhKJrspmdSM88vAJnJhEWkS5A01OnBOCxCOTSDBq8mWSwJg7J+ikGREE2XonU4eiKVBXhuJEvwRmcP8MrBtGQTL967sGfmb9TJkock2afLS3EsNDeceGqE5R2Cs6ug2slFDdt+kGZaFshmAycqEAmBZByp1OcH4p2X5AgJFKxHSUGtyG9mik0uQOAdJCIwtPQZlAK4RAFNIORWPTKOmyMLE4djNvdTQ0PAPaIRmm8PmhMkg99NVtCms2mhcZGQVW3uov3yTTHCbJc0jQjO/4HKnmEilcUiJD1lokNDAMY+T2wWQupcINA6TkC/CJcyL4MKWqWbm1DIlzIPzbNl+Gxoa/hEaoTkbUZivprTQ5dhhCDJUVdIAMC3yy0S4mk9TCyBkhXpMNIHXICUmGJUkCRNFBJHri8oapGTl5NrkitwREbtBy0Okz9ZkOr486uqiApOtOnZDQ8MkNEKzjWAJh8pXY0sVUBZca1Uh40DqBiBXFel2TF8RvCqXhGa4MHqu5F5anMsnfuOuGQfTjhLVUdQQwZIhSsCXkgtyL6FeBl1O+XVbBfKS6mUiIlaSCCbSy+CzIBNFNqtNQ8POQCM0Ox01omNRLwqLX2JJg8n1qSLGJMxzMqDMCkQJ8yiiiWsoSV0NCYUTExiXOZBVtGWINpY1SAmN7IsExqSXOQnMlUKyU82MLV/QiEpDQ8M/RiM0ZyOMqNaKI8kCRGHVGKINA0mqXOO8XCEANgnzIrjIZEpoFkgvA+4l63KiBHnGQmOzApN4mAS0u2fJypSfw9pwMfnbCYDPnz2VbSMcX8ujpojQLC2n4iZnmSM0ktPQsHPRCM12R2nQRo9WlrHtqFC3mPuHWNIANq2WJcyLGONKSzQzsyI3S4QPxyaYdmQZIYsKuZcooonIEOGBJEMvESsiRxRtNYBxGL1MRJ7xt+llGhoaStAIzbmCdA6wAmAACnltOYR0cqrJAAzkhQiT0ctE5JqZXVDSgFxJlrwQuaB9KSNvChLxUlg1gUgZJ+Cb/PqTe2k3RDRpvQxYlAaJZgZzDUm9TENDw85FIzTnCErTb/iq37ZEQroBGlmrUGF+mQiOmppNCA1ZaFgAvLGpZq2GZigT8JF7CcsaJASJyBeRoxq9DJcwSMbWyEtDQ0MBGqE5C6G4hay9hCisoh2RlyHAY0JftAKftnoZKC5N411cGLV6UKix1cvU1G0iLYzpv6aKNh0zJRxkndor9TImv0wE55jJiKsUfje9TENDwz9GIzTnCszcb3XCsho2VtJOJhnSy6AAeAUEtTSxSWvM9CIIfpMcM4tQ0qBGL2OISgRbZFKQToW0NkSYSH9zAnLMpCLg8+by/DKUAZj0MkS2jp3ale8LFppINTMt229DQ0MBGqE5R6Fy1Yxph6UJyEIjaulQzpkpkIJQZBUVxKS5jvUykFwuyTFTlV9GKlJRQyNcPbSNkuhhzhkgQyTQTQkN5b7ZO5NbaCiay+tlSPA0elOb5aWhoaEEjdCcq5BaEx0pgmUIhMaF9DLUvcwzghmAgbzMzEEW4GTCZiIBJKcinIb6Sy0ctn8uOpmf5wwwTYqQyvsCixWMnwpMkntpeRU+L1h/acLf0UhOQ0PDZDRCc66g1OVkzftATIzGBV1ONGFRX2QUIr3MXD7p7lrI3SdpkUkiA9ZCQyDLBbdLCI08JuWJOX9OalzWco1Lety90BcJgE9AVe6Ta/mNWV7OPy8dVktvLqaGhoZ6NEKzk1BhoVFlDqiddS/JSW2IehmIVoKMv2mSuBryYlHqciKghkbWUCIylAqgSS9DOCn1MkOoyZSKxiOa9aWhoaEfNEKz06FdThSZRO2Sv8nlRBFNWgCcb2P3EtUzmhx+XeNeKoXOcwPWtDkK7xYh2hG5hqhGALxM4dhEUkVIdiM4DQ0NJWiE5hwF6k+khUZXTYDVdjpvYsZeyACMAmDSjy7mE/gcFJncBRE7KXEg60bfIIKUJuBjK467Cbug8vUqWGOwREISxk4CYEqY983lXACM+WVWQbfTMv42NDRsEBqh2UnQSfRkd2DwGCQRR1NUHmEVXBHYV76N9TJ53hXKJ2MrWG800vBuJj1Oj0OWqPtWwf0D9/m82dGMvxQqfmwt74v1Mvk2stBMN71MQ0PDBqERmh0OG0mE+xI/EPuSNcYm85vZle9M5IWKKqYRO1vhXiKQhYasLISFKSiRMDxP7ZtadyiiaWmQ56+5bwkIExQSJQtei2BqaGjYKDRCs5NgF8d2hkEyNLoRI5polU5yC9TLgMsJCM1mCH5LYaKhbMQUnecKhGhjWYNEM0PHXIKwsuU1iF6SZSoaGhoaNgqN0Ox0SA0NFgykfdMwbSxpAOMgQgN6mXmIXtoNepmapHmbDdLykBiXRM0zcJ4nISsw7Xt+UtaAjvl3Wi9DbsTmXmpoaNg8NELTkIOMA5YLJCJgFACDXoasMRk5iog9u/JKz5gtl3LMnEUmA0qEZ8dPFprds7lrajGp6H1iTeaXOZVv4wrZ+di2KadsaGg4B9AIzQ6HnmDsajvRvUwtw8odtDfD3KgQM7ud2Jf0MmcTLFExYecREafAJXT+XE4EFxJCc+9abo355snd2TbSy2T1mBoaGho2GY3QNGSoCu9OGBLmqgFQRmGrlzmb3EsWaWh3BJ/TAHQvHZZImEz6qIAl6WWQ3Db3UkNDwxajEZqGHDajMLmmkn2nl91EN9iVk5KFuXwS3iPyy5we2tlNaKhyN0ZDQVZgIkMPmluaeMy/Xd6bbcN6TFBg0hY5bWhoaNgoNELToEAaCbbQJH9S8j2qkwgWmvMWndh3MxLkbQfQuVN+GdpGCfjSIpOkl1lZguJZpsBkQ0NDwyajEZqItpRMYV1OREySdtO5DAbz3EzvAb3MbG6hOdv1MhYUQs2Vr/NXmCw5+2ZzC82phNB844FcQ9NBPaaml2loaNiOaISmoRwYt500oYgmEADPzudWlgVMjnfuuZcsTKHLCL4elAX43uEogTm1Ctl+gbxQea62JmhoaNhqNEJzJtjBX22bUThNsIYlDXZT7aV8wj0P9TJSZXwOgojKKtwEEk4TofmbU6OaGdLLTIFeZofwx4aGhrMMjdD0jR1EeojQpFobtNCAXuZBu3OXCOaX2cGEhrAGfj+6bnNQb+LE2mixrJUHSC+Tb9pBj3hDQ8NZhEZotgrnwqxAUoqE0JBwuFugDMD5hNvIy2RQNBRdtwGEpB1fSap/gl6mZfttaGg4WyDLEG4d3v72t8dll10Wi4uLceWVV8Yf/MEfbPWQNhdTXf7bzlibGv1NRfZbOH85+y3OrmW/2elB9tsumJ7qst92weLMWvYbdtPZ7+j9e0d+2b1bmzrtXkp/DQ0NDdsQ29pC89u//dtx3XXXxdvf/vZ44hOfGL/+678e//Jf/sv48z//83jYwx621cPbXjATat+TLtV8Sks5gRdjYT63xlAm240W+24GCdnoY3A0VH7MY4O8Qvbyyujrj1mdG4FpaGg4S7CtCc1b3vKWeNGLXhT/5t/8m4iIuO222+J//I//Ee94xzvi5ptv3uLRncOomMVSbwfVaLp47/3Zthrry3ayjpTAjt+2o6zAJweQBfj4qMuJopcaGhoazhZsW0KzsrIShw8fjte97nUj26+++uq48847s/bLy8uxvPwPq/xjx45FRMTw1KmsbcPmIY16iojYtZoTmrUHNt9Cs5PwTbC+dPeNRpFRiHa7Aw0NDZuNb83bXXdmX6BtS2i+8Y1vxGAwiP37949s379/fxw5ciRrf/PNN8eNN96Ybf/qL71xw8bYUIa/2uoBNPw9/n9bPYCGhoaGsbj//vtj3759uv22JTTfwtRUEjXTddm2iIjXv/71cf3116//fd9998XDH/7w+MpXvnJGF6ShPxw/fjwuvfTS+OpXvxrnn3/+Vg9nx6Ldh61Huwdbj3YPth72HnRdF/fff38cPHjwjPrftoTmoosuipmZmcwac/To0cxqExGxsLAQCwsL2fZ9+/a1h3eLcf7557d7sA3Q7sPWo92DrUe7B1sPcw9KDBHbNmx7fn4+rrzyyjh06NDI9kOHDsVVV121RaNqaGhoaGho2I7YthaaiIjrr78+fvInfzIe//jHxw/8wA/EO9/5zvjKV74SL37xi7d6aA0NDQ0NDQ3bCNua0Dzvec+Lv/u7v4tf/uVfjnvuuSeuuOKK+OhHPxoPf/jDJ+67sLAQv/RLv4RuqIbNQbsH2wPtPmw92j3YerR7sPXY6Hsw1Z1pXFRDQ0NDQ0NDwzbDttXQNDQ0NDQ0NDRYNELT0NDQ0NDQcNajEZqGhoaGhoaGsx6N0DQ0NDQ0NDSc9ThnCc3b3/72uOyyy2JxcTGuvPLK+IM/+IOtHtI5i5tvvjm+7/u+L/bu3RsXX3xx/PAP/3B86UtfGmnTdV3ccMMNcfDgwdi1a1c85SlPiS9+8YtbNOJzHzfffHNMTU3Fddddt76t3YONx9e//vX4iZ/4ibjwwgtj9+7d8b3f+71x+PDh9f9v92Bjsba2Fr/4i78Yl112WezatSse+chHxi//8i/HcPgPVXPbPegfn/jEJ+KHfuiH4uDBgzE1NRX/5b/8l5H/N9d8eXk5Xv7yl8dFF10Ue/bsiec85znxta997cwG0p2D+MAHPtDNzc11v/Ebv9H9+Z//effKV76y27NnT3f33Xdv9dDOSTzzmc/s3v3ud3df+MIXus997nPds571rO5hD3tYd+LEifU2b37zm7u9e/d2H/zgB7vPf/7z3fOe97zukksu6Y4fP76FIz838alPfap7xCMe0X33d39398pXvnJ9e7sHG4tvfvOb3cMf/vDup37qp7o//uM/7u66667u4x//ePcXf/EX623aPdhYvPGNb+wuvPDC7r/9t//W3XXXXd1//s//uTvvvPO62267bb1Nuwf946Mf/Wj3hje8ofvgBz/YRUT3oQ99aOT/zTV/8Ytf3D3kIQ/pDh061H3mM5/pnvrUp3bf8z3f062trelxnJOE5vu///u7F7/4xSPbHv3oR3eve93rtmhEOwtHjx7tIqK74447uq7ruuFw2B04cKB785vfvN7m1KlT3b59+7pf+7Vf26phnpO4//77u8svv7w7dOhQ9+QnP3md0LR7sPF47Wtf2z3pSU8a+//tHmw8nvWsZ3U/8zM/M7Ltuc99bvcTP/ETXde1e7AZSAmNueb33XdfNzc3133gAx9Yb/P1r3+9m56e7n73d39XH/ucczmtrKzE4cOH4+qrrx7ZfvXVV8edd965RaPaWTh27FhERFxwwQUREXHXXXfFkSNHRu7JwsJCPPnJT273pGe89KUvjWc961nx9Kc/fWR7uwcbjw9/+MPx+Mc/Pn7kR34kLr744njc4x4Xv/Ebv7H+/+0ebDye9KQnxf/8n/8zvvzlL0dExJ/+6Z/GJz/5yfhX/+pfRUS7B1sBc80PHz4cq6urI20OHjwYV1xxxRndl22dKbgE3/jGN2IwGGQFLPfv358VumzoH13XxfXXXx9PetKT4oorroiIWL/udE/uvvvuTR/juYoPfOAD8ZnPfCY+/elPZ//X7sHG4y//8i/jHe94R1x//fXxC7/wC/GpT30qXvGKV8TCwkK84AUvaPdgE/Da1742jh07Fo9+9KNjZmYmBoNBvOlNb4of+7Efi4j2HmwFzDU/cuRIzM/Px4Mf/OCszZnM2+ccofkWpqamRv7uui7b1tA/Xvayl8Wf/dmfxSc/+cns/9o92Th89atfjVe+8pXxsY99LBYXF8e2a/dg4zAcDuPxj3983HTTTRER8bjHPS6++MUvxjve8Y54wQtesN6u3YONw2//9m/H+973vnj/+98fj3nMY+Jzn/tcXHfddXHw4MF44QtfuN6u3YPNR8k1P9P7cs65nC666KKYmZnJWN3Ro0czhtjQL17+8pfHhz/84fi93/u9eOhDH7q+/cCBAxER7Z5sIA4fPhxHjx6NK6+8MmZnZ2N2djbuuOOO+E//6T/F7Ozs+nVu92DjcMkll8R3fdd3jWz7zu/8zvjKV74SEe092Az8/M//fLzuda+LH/3RH43HPvax8ZM/+ZPxcz/3c3HzzTdHRLsHWwFzzQ8cOBArKytx7733jm1jcM4Rmvn5+bjyyivj0KFDI9sPHToUV1111RaN6txG13Xxspe9LH7nd34n/tf/+l9x2WWXjfz/ZZddFgcOHBi5JysrK3HHHXe0e9ITnva0p8XnP//5+NznPrf+e/zjHx8//uM/Hp/73OfikY98ZLsHG4wnPvGJWbqCL3/5y+vFdNt7sPE4efJkTE+PTmszMzPrYdvtHmw+zDW/8sorY25ubqTNPffcE1/4whfO7L4US5m3Mb4Vtv2ud72r+/M///Puuuuu6/bs2dP91V/91VYP7ZzEv/t3/67bt29f9/u///vdPffcs/47efLkeps3v/nN3b59+7rf+Z3f6T7/+c93P/ZjP9ZCJTcY/zjKqevaPdhofOpTn+pmZ2e7N73pTd3//b//t/vN3/zNbvfu3d373ve+9TbtHmwsXvjCF3YPechD1sO2f+d3fqe76KKLute85jXrbdo96B/3339/99nPfrb77Gc/20VE95a3vKX77Gc/u54qxVzzF7/4xd1DH/rQ7uMf/3j3mc98pvsX/+JftLDtb+FXf/VXu4c//OHd/Px890//6T9dDyFu6B8Rgb93v/vd622Gw2H3S7/0S92BAwe6hYWF7p//83/eff7zn9+6Qe8ApISm3YONx0c+8pHuiiuu6BYWFrpHP/rR3Tvf+c6R/2/3YGNx/Pjx7pWvfGX3sIc9rFtcXOwe+chHdm94wxu65eXl9TbtHvSP3/u938M54IUvfGHXde6aLy0tdS972cu6Cy64oNu1a1f37Gc/u/vKV75yRuOY6rquq7InNTQ0NDQ0NDRsMc45DU1DQ0NDQ0PDzkMjNA0NDQ0NDQ1nPRqhaWhoaGhoaDjr0QhNQ0NDQ0NDw1mPRmgaGhoaGhoazno0QtPQ0NDQ0NBw1qMRmoaGhoaGhoazHo3QNDQ0NDQ0NJz1aISmoaGhoaGh4axHIzQNDQ0NDQ0NZz0aoWloaGhoaGg469EITUNDQ0NDQ8NZj/8/UU8nAdjhD5UAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def convection_solve_LeapFrog(U, dx, dt, nx, nt):\n", " xint = arange(1, nx+1)\n", " #start the solution with upwind method\n", " U[1,xint] = U[0,xint] - v*dt/dx*(U[0,xint] - U[0, xint-1])\n", " for it in range(1, nt-1):\n", " U[it+1,xint] = U[it-1,xint] - v*dt/dx*(U[it,xint+1] - U[it, xint-1])\n", " \n", " #extrapolate values on the outflow boundary\n", " U[it+1,-1] = U[it+1, -2]\n", "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL=.1)\n", "U[0,:] = 0.\n", "U[0, (xmaxx*0.2)] = 1.\n", "convection_solve_LeapFrog(U, dx, dt, nx, len(t))\n", "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T10:41:15.933757Z", "start_time": "2023-04-24T10:41:15.830911Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.842793Z", "iopub.status.busy": "2024-06-14T19:41:30.842702Z", "iopub.status.idle": "2024-06-14T19:41:30.928088Z", "shell.execute_reply": "2024-06-14T19:41:30.927826Z", "shell.execute_reply.started": "2024-06-14T19:41:30.842785Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def convection_solve_LeapFrog(U, dx, dt, nx, nt):\n", " xint = arange(1, nx+1)\n", " n_equilib = 50\n", " #start and smooth the solution with upwind method\n", " for it in range(0, min((n_equilib, nt-1))):\n", " U[it+1,xint] = U[it,xint] - v*dt/dx*(U[it,xint] - U[it, xint-1])\n", " #U[it+1,xint] = 0.5*(U[it,xint+1]+U[it,xint-1]) - 0.5*v*dt/dx*(U[it,xint+1] - U[it, xint-1])\n", " for it in range(min((n_equilib, nt-1)), nt-1):\n", " U[it+1,xint] = U[it-1,xint] - v*dt/dx*(U[it,xint+1] - U[it, xint-1])\n", " \n", " #extrapolate values on the outflow boundary\n", " U[it+1,-1] = U[it+1, -2]*2 - U[it+1, -3]\n", " U[it+1,-1] = U[it+1, -2]\n", "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL=.1)\n", "U[0,:] = 0.\n", "U[0, (xmaxx*0.2)] = 1.\n", "convection_solve_LeapFrog(U, dx, dt, nx, len(t))\n", "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T10:45:51.417161Z", "start_time": "2023-04-24T10:45:51.410549Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.928492Z", "iopub.status.busy": "2024-06-14T19:41:30.928410Z", "iopub.status.idle": "2024-06-14T19:41:30.930671Z", "shell.execute_reply": "2024-06-14T19:41:30.930495Z", "shell.execute_reply.started": "2024-06-14T19:41:30.928486Z" } }, "outputs": [], "source": [ "def convection_solve_LaxWendroff(U, dx, dt, nx, nt):\n", " xint = arange(1, nx+1)\n", " for it in range(0,nt-1):\n", " # less efficient but more readable:\n", " Uplus = 0.5*(U[it,xint+1] + U[it, xint]) - 0.5*v*dt/dx*(U[it,xint+1] - U[it, xint])\n", " Uminus = 0.5*(U[it,xint] + U[it, xint-1]) - 0.5*v*dt/dx*(U[it,xint] - U[it, xint-1])\n", " U[it+1,xint] = U[it,xint] - v*dt/dx*(Uplus - Uminus)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T10:45:52.866552Z", "start_time": "2023-04-24T10:45:52.641635Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:30.931043Z", "iopub.status.busy": "2024-06-14T19:41:30.930949Z", "iopub.status.idle": "2024-06-14T19:41:31.026969Z", "shell.execute_reply": "2024-06-14T19:41:31.026703Z", "shell.execute_reply.started": "2024-06-14T19:41:30.931036Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL=.1)\n", "U[0,:] = 0.\n", "U[0, (xmaxx*0.2)] = 1.\n", "convection_solve_LaxWendroff(U, dx, dt, nx, len(t))\n", "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T10:46:15.606638Z", "start_time": "2023-04-24T10:46:15.599350Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:31.027342Z", "iopub.status.busy": "2024-06-14T19:41:31.027252Z", "iopub.status.idle": "2024-06-14T19:41:31.029704Z", "shell.execute_reply": "2024-06-14T19:41:31.029520Z", "shell.execute_reply.started": "2024-06-14T19:41:31.027335Z" } }, "outputs": [], "source": [ "def convection_solve_LaxWendroff(U, dx, dt, nx, nt):\n", " xint = arange(1, nx+1)\n", " for it in range(0,nt-1):\n", " # less efficient but more readable:\n", " Uplus = 0.5*(U[it,xint+1] + U[it, xint]) - 0.5*v*dt/dx*(U[it,xint+1] - U[it, xint])\n", " Uminus = 0.5*(U[it,xint] + U[it, xint-1]) - 0.5*v*dt/dx*(U[it,xint] - U[it, xint-1])\n", " U[it+1,xint] = U[it,xint] - v*dt/dx*(Uplus - Uminus)\n", " \n", " #extrapolate values on the outflow boundary\n", " U[it+1,-1] = U[it+1, -2]*2 - U[it+1,-3]" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T10:46:23.326431Z", "start_time": "2023-04-24T10:46:23.140148Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:31.030156Z", "iopub.status.busy": "2024-06-14T19:41:31.030038Z", "iopub.status.idle": "2024-06-14T19:41:31.124393Z", "shell.execute_reply": "2024-06-14T19:41:31.124160Z", "shell.execute_reply.started": "2024-06-14T19:41:31.030148Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL=.1)\n", "U[0,:] = 0.\n", "U[0, (xmaxx*0.2)] = 1.\n", "convection_solve_LaxWendroff(U, dx, dt, nx, len(t))\n", "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T10:46:38.467203Z", "start_time": "2023-04-24T10:46:38.194460Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:31.124812Z", "iopub.status.busy": "2024-06-14T19:41:31.124729Z", "iopub.status.idle": "2024-06-14T19:41:31.219917Z", "shell.execute_reply": "2024-06-14T19:41:31.219656Z", "shell.execute_reply.started": "2024-06-14T19:41:31.124805Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def convection_solve_LaxWendroff(U, dx, dt, nx, nt):\n", " xint = arange(1, nx+1)\n", " n_equilib = 50\n", " for it in range(0, min((n_equilib, nt-1))):\n", " U[it+1,xint] = U[it,xint] - v*dt/dx*(U[it,xint] - U[it, xint-1])\n", " for it in range(min((n_equilib, nt-1)), nt-1):\n", " # less efficient but more readable:\n", " Uplus = 0.5*(U[it,xint+1] + U[it, xint]) - 0.5*v*dt/dx*(U[it,xint+1] - U[it, xint])\n", " Uminus = 0.5*(U[it,xint] + U[it, xint-1]) - 0.5*v*dt/dx*(U[it,xint] - U[it, xint-1])\n", " U[it+1,xint] = U[it,xint] - v*dt/dx*(Uplus - Uminus)\n", " \n", " #extrapolate values on the outflow boundary\n", " U[it+1,-1] = U[it+1, -2]*2 - U[it+1,-3]\n", "\n", "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL=.1)\n", "U[0,:] = 0.\n", "U[0, (xmaxx*0.2)] = 1.\n", "convection_solve_LaxWendroff(U, dx, dt, nx, len(t))\n", "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Can we break the CFL condition with some naive implementation of implicit scheme?" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T10:47:52.179002Z", "start_time": "2023-04-24T10:47:52.138487Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:31.220390Z", "iopub.status.busy": "2024-06-14T19:41:31.220277Z", "iopub.status.idle": "2024-06-14T19:41:31.244332Z", "shell.execute_reply": "2024-06-14T19:41:31.244036Z", "shell.execute_reply.started": "2024-06-14T19:41:31.220383Z" } }, "outputs": [], "source": [ "from scipy.sparse import dia_matrix, eye\n", "from scipy.sparse.linalg import factorized\n", "def d1matrix(nelem):\n", " elements = ones((3,nelem))\n", " elements[1,:] *= 0\n", " elements[0,:] *= -1\n", " return dia_matrix((elements, [-1,0,1]), shape=(nelem,nelem)).tocsc()\n", "\n", "def convection_solve_CN(U, dx, dt, nx, nt):\n", " alpha = -v*dt/(dx*4.)\n", " M1 = eye(nx)-d1matrix(nx)*alpha\n", " M2 = eye(nx)+d1matrix(nx)*alpha\n", " LU = factorized(M1.tocsc())\n", " for it in range(0,nt-1):\n", " U[it+1,1:-1] = LU(M2.dot(U[it,1:-1]))\n", " \n", " #extrapolate values on the outflow boundary\n", " U[it+1,-1] = U[it+1, -2]\n", "\n", " " ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T10:47:55.897391Z", "start_time": "2023-04-24T10:47:55.892325Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:31.244773Z", "iopub.status.busy": "2024-06-14T19:41:31.244688Z", "iopub.status.idle": "2024-06-14T19:41:31.246205Z", "shell.execute_reply": "2024-06-14T19:41:31.246031Z", "shell.execute_reply.started": "2024-06-14T19:41:31.244767Z" } }, "outputs": [], "source": [ "from scipy import sparse" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "ExecuteTime": { "end_time": "2023-04-24T10:47:56.602140Z", "start_time": "2023-04-24T10:47:56.503688Z" }, "execution": { "iopub.execute_input": "2024-06-14T19:41:31.246537Z", "iopub.status.busy": "2024-06-14T19:41:31.246460Z", "iopub.status.idle": "2024-06-14T19:41:31.295124Z", "shell.execute_reply": "2024-06-14T19:41:31.294793Z", "shell.execute_reply.started": "2024-06-14T19:41:31.246530Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL=2)\n", "U[0,:] = 0.\n", "U[0, (xmaxx*0.2)] = 1.\n", "convection_solve_CN(U, dx, dt, nx, len(t))\n", "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It sort of works, but not very well..." ] } ], "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 4 }