{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simple Example of a Simulation in astronomix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Imports" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import jax.numpy as jnp\n", "\n", "# constants\n", "from astronomix import SPHERICAL, CARTESIAN\n", "\n", "# astronomix option structures\n", "from astronomix import SimulationConfig\n", "from astronomix import SimulationParams\n", "\n", "# simulation setup\n", "from astronomix import get_helper_data\n", "from astronomix import finalize_config\n", "from astronomix import get_registered_variables\n", "from astronomix import construct_primitive_state\n", "\n", "# time integration, core function\n", "from astronomix import time_integration\n", "\n", "# plotting\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulation Setup" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us set up a very simple simulation, mostly with default parameters.\n", "\n", "First we get the configuration of the simulation, which contains parameters that typically do not change between simulations, changing which requires (just-in-time)-recompilation." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "config = SimulationConfig(\n", " geometry = CARTESIAN,\n", " box_size = 1.0,\n", " num_cells = 101,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we setup the simulation parameters, things we might vary" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "params = SimulationParams(\n", " t_end = 0.2, # the typical value for a shock test\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With this we generate some helper data, like the cell centers etc." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "helper_data = get_helper_data(config)\n", "registered_variables = get_registered_variables(config)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we setup the shock initial conditions, namely\n", "\\begin{equation}\n", "\\left(\\begin{array}{l}\n", "\\rho \\\\\n", "u \\\\\n", "p\n", "\\end{array}\\right)_L=\\left(\\begin{array}{l}\n", "1 \\\\\n", "0 \\\\\n", "1\n", "\\end{array}\\right), \\quad\\left(\\begin{array}{l}\n", "\\rho \\\\\n", "u \\\\\n", "p\n", "\\end{array}\\right)_R=\\left(\\begin{array}{c}\n", "0.125 \\\\\n", "0 \\\\\n", "0.1\n", "\\end{array}\\right)\n", "\\end{equation}\n", "with seperation at $x=0.5$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# setup the shock initial fluid state in terms of rho, u, p\n", "shock_pos = 0.5\n", "r = helper_data.geometric_centers\n", "rho = jnp.where(r < shock_pos, 1.0, 0.125)\n", "u = jnp.zeros_like(r)\n", "p = jnp.where(r < shock_pos, 1.0, 0.1)\n", "\n", "# get initial state\n", "initial_state = construct_primitive_state(\n", " config = config,\n", " registered_variables = registered_variables,\n", " density = rho,\n", " velocity_x = u,\n", " gas_pressure = p,\n", ")" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Automatically setting open boundaries for Cartesian geometry.\n" ] } ], "source": [ "config = finalize_config(config, initial_state.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Running the simulation" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "final_state = time_integration(initial_state, config, params, registered_variables)\n", "rho_final = final_state[registered_variables.density_index]\n", "u_final = final_state[registered_variables.velocity_index]\n", "p_final = final_state[registered_variables.pressure_index]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualization" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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HHXcoKSlJTz/9tMrKyvT73/++1mu89NJL+v73v69bbrlFAwcO1L59+zRnzhxNmzZN/fr1q/P5g8eZn/3sZxoxYsRxya3LL79crVu31osvvqhLL71Ubdu2bfL3CgAQWcOHD9dtt92mKVOmaPny5br44ouVnJysr7/+Wi+++KKeeOIJXXvttfU6R7n11lu1b98+fec731HHjh21ZcsW/e///q/69++vnj17SpIuvvhiderUST/60Y9CF0pmzJihNm3aqLCwsF4xN+VYCTSIwRUlgYgKLqUbvPl8Pjs3N9e+6KKL7CeeeMIuKSk5bp8NGzbYo0ePtnNzc+3k5GS7Q4cO9hVXXGG/9NJLxz3vN5cAfu+992xJ9nvvvWfbtm0vXbrUvu666+xOnTrZKSkpdtu2be0rrrjC/vzzz2vtp28sY2/bztK+HTp0sD0ez3HLAdu2bf/+97+3JdkPPfRQ479BAIAme/LJJ21J9tlnn33c1w4dOmRPmDDBPv30022fz2dnZ2fbQ4cOtR999FG7vLw89Li6jgNLly61R4wYYTdv3txOT0+3L7jgAvvjjz8+7jX27t1rjxs3zu7QoYPt8/nsjh072jfddJO9Z88e27Zte9OmTbYk+9lnnw3tU1lZaf/0pz+127RpY1uWVedy9HfccYctyX7hhRca+Z0BADTUic4zarrpppvsZs2anfDrzzzzjD1w4EA7LS3NzsjIsPv06WP/6le/snfs2GHbdv3OUV566SX74osvttu2bWv7fD67U6dO9m233Wbv3Lmz1mstWbLEHjx4cOgxjz/+eOg91Dx/6dy5s3355ZfXGW99j5VAU1i2fZK58ABi0hNPPKG7775bmzdvPm51SQAAmuruu+/WX/7yFxUVFSk9Pd10OAAAAI1G4guIM7Ztq1+/fmrdurXee+890+EAAFzm2LFjysvL0xVXXKFnn33WdDgAAABNQo8vIE6UlpZqzpw5eu+997RixYpQTxkAAMJh165deuedd/TSSy9p7969uuuuu0yHBAAA0GQkvoA4sXv3bl1//fVq0aKF7rvvPl155ZWmQwIAuMiqVatCKx3/8Y9/DK3yBQAAEM8odQQAAAAAAIAreUwHAAAAAAAAAEQCiS8AAAAAAAC4Ulz0+AoEAtqxY4cyMjJkWZbpcAAg7tm2rUOHDql9+/byeLgGwnEGAMKL40xtHGcAILwacpyJi8TXjh07lJeXZzoMAHCdrVu3qmPHjqbDMI7jDABEBscZB8cZAIiM+hxn4iLxlZGRIcl5Q5mZmYajAYD4V1JSory8vNDf10THcQYAwovjTG0cZwAgvBpynImLxFdwOnBmZiYHCgAII8otHBxnACAyOM44OM4AQGTU5zhDwT0AAAAAAABcicQXAAAAAAAAXInEFwAAAAAAAFwpLnp8AXA3v9+viooK02G4SnJysrxer+kwXIef1fDz+XynXIIaAAAg1vE5MfzC9TmRxBcAY2zbVlFRkQ4cOGA6FFdq0aKFcnNzaSwcBvysRo7H41GXLl3k8/lMhwIAANBgfE6MnHB9TiTxBcCY4AGibdu2Sk9PJ0ETJrZt68iRI9q1a5ckqV27doYjin/8rEZGIBDQjh07tHPnTnXq1InvKwAAiDt8ToyMcH5OJPEFwAi/3x86QLRu3dp0OK6TlpYmSdq1a5fatm1L2WMT8LMaWW3atNGOHTtUWVmp5ORk0+EAAADUG58TIytcnxNpqgHAiGD9e3p6uuFI3Cv4vaXXQNPwsxpZwanrfr/fcCQAAAANw+fEyArX50QSXwCMYipw5PC9DS++n5HB9xUAAMQ7Ps9ERri+ryS+AAAAAAAA4EoNTny9//77GjlypNq3by/LsvTqq6+ecp+FCxfqrLPOUkpKik4//XTNnDmzEaECQGw4//zz9fOf/7xej928ebMsy9Ly5cvD9pyS83fVsixWj8FJ8bMKAMfjfAYAEutzYoOb25eWlqpfv3665ZZb9L3vfe+Uj9+0aZMuv/xy/eQnP9Hzzz+vBQsW6NZbb1W7du00YsSIRgUNACa9/PLL9W6umJeXp507dyo7O1uS88f9ggsu0P79+9WiRYtGPSdQX/ysAsDxOJ8BgMT6nNjgxNell16qSy+9tN6PnzZtmrp06aLHHntMktSzZ099+OGH+sMf/sCBAkBcatWqVb0f6/V6lZubG9bnBOqLn1UAOB7nMwCQWJ8TG5z4aqhFixapoKCg1n0jRoxo0PS3pli39D8qO3wgKq9VLyfszWZVj5YlW5ZkeWRbHtlWkjN6fAp4fbK9KfInpakyOUPyRPy/EA2Q5LV0VqeW8iXRPs/Nzj//fPXv319Tp05Vfn6+fvzjH2v9+vV68cUX1bJlS91///368Y9/LMmZFtylSxctW7ZMLVq00AUXXCBJatmypSTppptu0syZM2s9pyT97W9/0xNPPKG1a9eqWbNm+s53vqOpU6eqbdu2Rt4z4hM/qwnOtqWyEunYQaniqFRxRKo4Jtl+KeCX7IDzOcKbLHmSpeRUKTndufmaObdEa9Zr25K/QgpU1rj5ne9ZiFX9vfLG3lVthJ/p85lDB/dp8xcfROW16u2Efxo8VecynqpzGUu25ZXtSZLtSVbA41MgKU3+5GbyJzWTLD4zx6LcrFSd3ra56TAQYYn0OTHiWZOioiLl5OTUui8nJ0clJSU6evSo0tLSjtunrKxMZWVloX+XlJQ0+vXtub9Sn8o1jd4/1h22U7XfztB2ZWu7na0tgRwtt0/T8sDpKlEz0+ElpOsHd9JDV/cxHUZcsm1bRyuatlRtY6Ulexu9ashjjz2mBx98UPfdd59eeukl3X777Ro+fLi6d+9e63F5eXn617/+pWuuuUZr165VZmZmnX8DJWdp5AcffFDdu3fXrl27NH78eN18882aO3duo2JEeJn6WW3Kz6nEz6prlO6R1s6VVr8u7dsoyXbutwPViZqKo07Cy27Kz6nlJL+S06SkVMnrcxJlwZ9B265KolVKgYDz+rKd+y3L2d9yToLl8UqWt2r0ONtW8OueGo+3qp43UH0L+Gsnomq+z1Biqsbrf/M9SNXPH/KN1wi+znH7n4LXJ2XkSpkdpBadpO6XSt0vl5J8Df92I2aZPp8p3rxafd4d3ej9Y9keO1O77JYqtltok91OXwa6aoXdRRvtdk7yDMa88bNzdWb7LNNhxJ14PZ+R3P05MSanC02ZMkUPPPBAWJ7rUHpHbTp8LCzPFTnOhyxnnlf1tkcBeWTLI7+8tl9J8stnlytZFfKpQpLU3Dqm5tYx5Wm381ReZwjI0hZPZy30naf5vgu1zxObUw7d5ODRCu08eExb9x0xHUrcOlrhV69Jbxl57VW/HaF0X+P+JF522WW64447JEn33HOP/vCHP+i999477iDh9XpD03/btm1bqx7+m2655ZbQdteuXfXHP/5R3/rWt3T48GE1b84VONNM/aw25edU4mc17lUck179ibTqtaokTz15fVUJrHQngeVJqk42BfxSoMKZ5VR5TCo/4swMk+3cyg87t0RXc1ZKze+9v1w6UOjcChdJX86WmrWR+t8gDf2p1Cw7+rEiJoTzfCY5JU2bPPlhea7IOP5cxqNA1fmMLa/tl0d+JatSyXaFUnVMXjm/R9lWibKtEvXSFl2gL0LPuNdqpfd8wzXfd6G2eDtH/y0lsM17S3WsIqBt+4+S+GqEeD2fkdz9OTHiia/c3FwVFxfXuq+4uPikWcEJEyZo/PjxoX+XlJQoLy+vUa8/aPy/GrVfzPNXSMdKpGMHnCu/B7dKB7ZIu9dKWxfLs3+TugQ2q8uxzRpT9rxzBXL4PVK7vqYjd63Xlm/XXbOWK2A38Gox4l7fvtW/V5ZlKTc3V7t27WrScy5ZskS/+c1v9MUXX2j//v0KBJwPiIWFherVq1eTnhuJi5/VOGbb0tz/J618xfl3u/5SzyukvMFVbQ+qZkt5kp1ZVV6flNZSSmvhzNhq6GtVHJHKS6WyQ05CrPKYVFnmzLAKsZzXrplICyWI7Nozt4Llgt+cXWXbtbdlq9ZMMcsreYOv4a16vaqZY56a91fNHPvmrK7g+6k5k8u2a880s7zV/675vMEy0NCMtBr7V5Y536OyQ9KhnVLJdqlohbT8H9LhIumjqdK6edKP3pZSOXGMd6bPZzr3OEua9MWpHxgvbNv5m1J2SDq8SzpU5PwOFa+Udi6XilaodcU+XVv2iq4te8X5O3f5Y1IuFRXR8P1pH+uzzfsVCHBOk2jc/Dkx4omvIUOGHDeNbf78+RoyZMgJ90lJSVFKSkqkQ4tv3mSpWWvn1vo0SYNrf/3wLmndW9LSv0rbFktrXpfWvikNHScNv1fypRsJ282C00oDDbgIj9rSkr1a9VszTWLTkr2N3vebK5dYlhX6o94YpaWlGjFihEaMGKHnn39ebdq0UWFhoUaMGKHy8vJGPy/Cx9TPalN+TiV+VuPaZ3+Wlv3dScJc/6J0RsGp92ksy6ru8dWcXm3HsYI9vlKl9FZSy6rZKL2vkS74tfP5a+4vpN1rpJduka6b7STvELc4nwkzy3IS8slpzt+Y3N61v15ZLn39tvTFP5zfp62fSk8Pd2ZRnn9vw5P5aJDQOQ15r0aJ1/MZyd2fExt8FD58+LDWr18f+vemTZu0fPlytWrVSp06ddKECRO0fft2/fWvf5Uk/eQnP9Gf/vQn/epXv9Itt9yid999V//85z/1xhtvhO9d4HjN20pn3ejcdq2WFk5xSiM+esIZr35G6jT41M+DevNUXQxmxlfjWZbVpOm58cDnc/q++P0nrv1fs2aN9u7dq4cffjh0dfjzzz+PSnyoH35WHfysRsnmD6V59zrbF/02skkvNI032ZmJl9VBmnGptP4d6e1fS5c+Yjoy1MD5TIxL8jm/Rz2vkEp2Sm/+Slo9x5lJufrf0uhXnZ56iAjOaZomET4jSvH3ObHBHQM///xzDRgwQAMGDJAkjR8/XgMGDNCkSZMkSTt37lRhYWHo8V26dNEbb7yh+fPnq1+/fnrsscf05z//maV/o6ltT+kHf5V++A+n+er+zdJfvytteNd0ZK7irbo6wjECJ9O5c2dZlqXXX39du3fv1uHDx/fO6dSpk3w+n/73f/9XGzdu1Jw5c/Tggw8aiBaJjJ/VGHFkn/TPm5wSwz7fl4aMMx0R6qP9AOl7zzjbn06Tlsw0Gg5q43wmjmS2k0b9TfrhC1JGe2nfBmnmFdLBbaYjcy2vJzjji5ManFi8fU5scOLr/PPPl23bx91mzpwpSZo5c6YWLlx43D7Lli1TWVmZNmzYoJtvvjkMoaPBelwm3fGJdPpFUuVR6YVR0hpW3QqX4LRgPwcJnESHDh30wAMP6N5771VOTo7GjTv+JLZNmzaaOXOmXnzxRfXq1UsPP/ywHn30UQPRIpHxsxojPn1aOrJHatNDGvnH2r2mENt6XSl9535ne+HDXBmLIZzPxKEel0u3viO1zHf6Gj830pkNhrDzWCS+cGrx9jnRsu3Y/4kuKSlRVlaWDh48qMzMTNPhxL/KMulfP3KmClte6doZ0plXmY4q7r29skg//tsSDejUQq/ccY7pcGLesWPHtGnTJnXp0kWpqammw3Glk32P+bta28m+H/ysRhbf35MoL5X+cKZ0dL9zrO59jemI0FAVx6Tfd3Ea4d/2vtSun+mIoobjTG18P8LkwFZp5mXOSqqtz5Bune8s5IGwGT1jsd5ft1uPfb+frhnY0XQ4MY/PMZEVrvOZBs/4ggskpUjXzpT6jnJWWHrlJ04fMDRJ9bRgw4EAANxh6d+cpFfLLlLP75qOBo2RnCp1vcDZXmdmeXvAVVrkSTf9W8rsKO39Wpp3n+mIXMdLjy+4EImvROVNkq6aJp12oVP2+M+bnCvLaLTQtGAyXwCApvJXSIv+5GwP/SmrAsaz7pc449o3zcYBuEXLfOn7z0qypC9ekL5+x3REruKhbzFciMRXIvN4pKuflprnSnvWSnN/aTqiuGZxdQQAEC5fvSwd3Co1ayP1v950NGiKMy52xh1LpUPFZmMB3CLvbGnwT5zt138ulR0yGo6b0LcYbkTiK9E1byNd82fJ8kjLn5eWv2A6orhV3QjScCAAgPhm29JHTzjbg38iJaeZjQdNk5HrrPIoSV+/bTYWwE0unCi16OxcJHjnN6ajcQ0PF/PhQiS+IHUZJg2/19l+8x7p8G6z8cSpYI+vOFgvAgAQyzb9R9q1UvI1l771I9PRIBy6XeqM6+aZjQNwE18z6co/Otuf/Vkq/NRsPC5B32K4EYkvOM77hbPSUFmJ9N5/m44mLgVLHf0cJQAATfHlP52xz/dZrcwtuo1wxg3vOSs9AgiPrudL/W9wtt//H6OhuAV9i+FGJL7g8HilSx52tpc+JxV9ZTaeOFRd6shBAmiqJ598Uvn5+UpNTdXgwYO1ePHikz5+6tSp6t69u9LS0pSXl6e7775bx45xcok4VHFMWv1vZ7vvD8zGgvBp10/KaCdVlEpbPjQdDeAu5/3Caduyfr5UtMJ0NHGPvsVwIxJfqNZ5qNTrKskOSG/dx1IeDcQKKEB4zJ49W+PHj9fkyZO1dOlS9evXTyNGjNCuXbvqfPwLL7yge++9V5MnT9bq1av1l7/8RbNnz9Z997HEOeLQ1287s68zO0p53zYdDcLFsqpnfa17y2wsgNu06iqdebWz/eFUo6G4AX2L4UYkvlDbRQ9I3hSnvwjLbjeIt+q3iasjQNM8/vjjGjt2rMaMGaNevXpp2rRpSk9P14wZM+p8/Mcff6xzzjlH119/vfLz83XxxRfruuuuO+UsMSAmrXjRGftc46y+DPfodokzfj3fbByAG53zc2dc+bK0b5PRUOIdfYvhRnyiQm0t86Uhdzrbb98v+SuNhhNPWPo3cdi2rR//+Mdq1aqVLMtSixYt9POf/zysr/Gb3/xG/fv3D+tzxoPy8nItWbJEBQUFofs8Ho8KCgq0aNGiOvcZOnSolixZEkp0bdy4UXPnztVll112wtcpKytTSUlJrZsb8bMaZ44drJ4N1Of7ZmNB+LXr74wHCvl8BYRbu77S6QVO5crH/2s6mrhG3+LEkUifE5NMB4AYNGy80+dr3wZp1atSn2tNRxQXqhtBGg4EETdv3jzNnDlTCxcuVNeuXeXxeJSWlmY6LFfYs2eP/H6/cnJyat2fk5OjNWvW1LnP9ddfrz179ujcc8+VbduqrKzUT37yk5OWOk6ZMkUPPPBAWGOPRfysxpnVr0v+MqlNDymnt+loEG7N20qWV7L9UukuKbO96YgAdzn3bmn9O9Kyv0vn3+v8zqHBKHVMHIn0OZEZXzheSoZ09m3O9kdTaVpVT16LacGJYsOGDWrXrp2GDh2q3NxctW3bVhkZGabDSlgLFy7UQw89pP/7v//T0qVL9fLLL+uNN97Qgw8+eMJ9JkyYoIMHD4ZuW7dujWLE0cPPapwJlTleW33JHe7h8ToN7iWpZIfZWAA36nyO1PFbzgWEz+tuj4BT87JgV8JIpM+JJL5Qt7PHSsnpzsooG941HU1cCE0L5iDhajfffLN++tOfqrCwUJZlKT8/X+eff36tacH5+fl66KGHdMsttygjI0OdOnXSM888U+t57rnnHnXr1k3p6enq2rWrJk6cqIqKiii/m9iTnZ0tr9er4uLiWvcXFxcrNze3zn0mTpyoG2+8Ubfeeqv69Omjq6++Wg899JCmTJmiwAmmYKakpCgzM7PWzW34WY0zh4qd/pqS1JuZ1q6VSeILiBjLks7+sbP9xSwu3jdSsL0kF/PdLdE+J5L4Qt3SW0ln3eRsfzTVaCjxgmnBYWDbUnmpmVs9D+5PPPGEfvvb36pjx47auXOnPvvsszof99hjj2nQoEFatmyZ7rjjDt1+++1au3Zt6OsZGRmaOXOmVq1apSeeeELTp0/XH/7wh7B8G+OZz+fTwIEDtWDBgtB9gUBACxYs0JAhQ+rc58iRI/J8owm41+uVFMEPbaZ+VhvwfvhZjTNrXnd603QYJLXqYjoaREqwvJHEFxAZPS6XkptJ+zdJ2+o+7uHkQn2Lad/SOHFwPiMl3udEenzhxIbcIS1+Rtr0vrR9qdThLNMRxTSujoRBxRHpIUM9T+7bIfmanfJhWVlZysjIkNfrPeEMJEm67LLLdMcdd0hyroT84Q9/0Hvvvafu3btLku6///7QY/Pz8/WLX/xCs2bN0q9+9asmvpH4N378eN10000aNGiQzj77bE2dOlWlpaUaM2aMJGn06NHq0KGDpkyZIkkaOXKkHn/8cQ0YMECDBw/W+vXrNXHiRI0cOTKUAAs7Uz+r9fw5lfhZjTvB2dXdLzEbByIrs4Mzlmw3GwfgVr5mUs+R0peznFlfeWebjijuVC3qSKljY8XB+YyUeJ8TSXzhxFp0cvqMfDlb+ugJ6QfPmY4opnmZ8YUa+vbtG9q2LEu5ubnatWtX6L7Zs2frj3/8ozZs2KDDhw+rsrLSleV2jTFq1Cjt3r1bkyZNUlFRkfr376958+aFGt4XFhbWmuF1//33y7Is3X///dq+fbvatGmjkSNH6r//+79NvYW4ws9qDAj4pU0fONtdv2M2FkQWM76AyOs3ykl8rXxZuuRhKclnOqK4Qt9i1OSWz4kkvnBy59zlJL5Wz5H2b5FadjYdUcyqnhbMQaLRktOdKxWmXjucT5ecXOvflmWF+k0tWrRIN9xwgx544AGNGDFCWVlZmjVrlh577LGwxhDPxo0bp3HjxtX5tYULF9b6d1JSkiZPnqzJkydHIbIqpn5Ww/xzKvGzGhN2LJPKDkqpWVL7/qajQSSR+AIir8twqXmudLhIWj/fKX9EvYXOaUh8NY6Lzmck93xOJPGFk8s5U+p6vrRxobT0r9KFE01HFLOYFhwGllXv6bnx7OOPP1bnzp3161//OnTfli1bDEaEBuNnFeG08T1n7HKes/If3CtY6niIxBcQMR6vU7Wy6E/OBXwSXw1C3+ImSpDPiFJ8fU6kuT1ObaDTV0fL/i75Y2+Fhljh9QSnBRsOBDHvjDPOUGFhoWbNmqUNGzboj3/8o1555RXTYQHH4Wc1SjYsdMau55uMAtGQUWNVRz4wAJHTd5Qzrp0nHT1gNJR4w8V81Fc8fU4k8YVT636Z1KyNM1143TzT0cSs6qsjHCRwcldeeaXuvvtujRs3Tv3799fHH3+siROZTYnYw89qFJSXSls/dba7XmA2FkReMPHlL5eO7DUbC+BmuX2ktr0kf5m06lXT0cQVLuajvuLpc6Jlx0HXupKSEmVlZengwYMx2SgtIbzzG+nDP0inF0j/9S/T0cSkbfuP6NxH3lNKkkdrf3ep6XBi3rFjx7Rp0yZ16dJFqamppsNxpZN9j/m7WtvJvh/8rEZWwn9/v54vPX+tlNVJ+vmXTokE3O1/zpBKd0m3vS+162c6mojhOFMb3w8DPnhcWvCAdNqF0o0vm44mbjz85hpN+88G/ejcLpp4RS/T4cS8hP8cE2HhOp9hxhfq56zRzrh+gdPkHsfxWFwdAQA00MaFznja+SS9EgUN7oHoCPb22vyBVHbYbCxxhFJHuBGJL9RPq65VJRi20+QexwlOC+YgAQCotw1Vje3p75U4gg3uS7abjQNwu+xuUst8p7Q4eJEBp0SpI9yIxBfqb+DNzkiT+zoFL9Sz9C8AoF4OFUu7VjrbXc43GQmiKTTja6fZOAC3syyp2yXONn2K682ibzFciMQX6q/H5VKztk6T+/XvmI4m5tQsdYyD1nkAANM2/ccZc/tKzVqbjQXRk1ljZUcAkdVthDN+/bYUCJiNJU4ESx39Ac5n4B4kvlB/3mSp7w+c7S9nm40lBnlq9GYh7wUAOKXNHzhj1+Fm40B0UeoIRE/ncyVfc+lwsbRzuelo4kL1SvWGAwHCiMQXGiaY+FozVzp20GwsMcZbI/HF1OD6C3D1LWL43oYX38/ISOgZsoWfOmOnIWbjQHTR3B6IniSfdNp3nO11b5mNJU5U9/hK4ONzI/A5MTLC9XOYFJZnQeLI7Su16SHtXiOtmiOddaPpiGKGVSON7LdtfrlOwefzyePxaMeOHWrTpo18Pl+opwCaxrZtlZeXa/fu3fJ4PPL5fKZDimv8rEaObdvavXu3LMtScnKy6XCi68g+ac9aZztvsNlYEF2hGV87nCni/D0BIqvbJdLqOdK6N6ULJpiOJuZZlDo2CJ8TIyecnxM5N0fDWJbUd5S04AGn3JHEVwiljg3j8XjUpUsX7dy5Uzt2cNU7EtLT09WpUyd5PEzubQp+ViPLsix17NhRXq/XdCjRtXWxM7Y+Q2qWbTYWRFdGVY+vilKprERKzTIbD+B2Z1wkyZJ2fuEknIOzLlEnSh0bhs+JkRWuz4kkvtBwfb7vJL42fyAd2Cq1yDMdUUyg1LHhfD6fOnXqpMrKSvn9ftPhuIrX61VSUhJXnMKEn9XISU5OTryklyQVLnLGTsz2Sji+dCm1hXTsgHMSTuILiKzmbaUOA6XtnztN7oMr1aNOweb2lDrWH58TIydcnxNJfKHhWuQ5jSK3fCiteFEaNt50RDGhZn6BKyT1F5y6mnBlTog7/KwirLbS3yuhZXaoSnxtl9r2NB0N4H7dLnESX+tIfJ1K9YwvTmgags+JsY36FzROzdUd+aMoqXapIzXxAIATqiyTti91tvO+bTYWmEGDeyC6Tq9qcL/5Q8lfaTaWGBc8p/FzOgMXIfGFxun1Xcmb4jS5L/rSdDQxwVNjxhdTgwEAJ7RjueQvk9KzpdanmY4GJpD4AqKrXX8pJUsqOygVfWE6mpgWPKdhxhfchMQXGiethdRthLP91ctGQ4kVXk/NHl8GAwEAxLatnzhjp2+zol+iqrmyI4DI83il/HOd7U3vm40lxgXPabiQDzch8YXG6/09Z1z5MuWOUq0m4pQ6AgBOqLCqv1ceje0TFjO+gOjrOtwZN/7HbBwxLnhOEwgYDgQIIxJfaLwzLpaS06UDhdKOpaajiQmsggIAOCnbrj3jC4kps50zkvgCoqfLec5Y+InTaxF1qu7xxfkM3IPEFxrP16y63HHlK2ZjiRHVq6AYDgQAEJv2rpeO7JWSUqV2/UxHA1NCpY7bzcYBJJI2PaRmbaXKo9K2z0xHE7O4kA83IvGFpjkzWO74KuWOkjwelv8FAJxEYdVsr/ZnSUkpZmOBOc1znPHYAWaeANFiWdWzvujzdULV5zOGAwHCiMQXmuaMi6TkZtLBrdL2JaajMS54hYQeXwCAOgUTX53o75XQUjKqtyuOmIsDSDQkvk4pVOrI+QxchMQXmiY5Tep+qbPN6o6hAwUTvgAAdQr298qjv1dC8yZLnmRnu5zEFxA1wQb32z6Tyg6bjSVGBS/kU8ECNyHxhaY782pnXPVqwi//4bUodQQAnEDpHqfHlyTlnW02FpiXnO6MzPgCoqdlvtSikxSorJ6Bi1q4kA83IvGFpju9QPJlOA1aty02HY1RVrDUkSMFAOCbtn7qjNndpfRWZmOBeb6qxFd5qdk4gETTpWrW16b/mI0jRtGzGG5E4gtNl5wq9bjM2V71mtlYDAseKFgFBQBwHPp7oabQjK+jZuMAEk0o8UWfr7rQsxhuROIL4dHzSmdc/e+EnhfrsVgFBQBwAsEZX/T3glQ946uCGV9AVOWf44xFX0rHSszGEoModYQbkfhCeJx+oXPl8uBWaccy09EY46HHFwCgLhXHqo+PnUh8QdUzvmhuD0RXZnupRWfJDjhN7lEL5zNwIxJfCI/kNOmMi5zt1XPMxmIQU4MBAHXauVzyl0vp2VKrrqajQSyg1BEwp/NQZyxcZDaOGMSqjnAjEl8In2C546o5CTs3lqnBAIA6hfp7fbt6JRQkNl8zZ6TUEYi+4MzbLSS+vil4PuPnfAYuQuIL4dNthOT1Sfs2SLtWm47GCK6QAADqFOrvRWN7VElOc0ZKHYHo61Q142v751JlmdlYYoynKkPAYl1wExJfCJ+UDOm07zjbCVruWL38r+FAAACxw7arE1/090IQpY6AOdlnOKXnlcekHctNRxNT6PEFNyLxhfCqubpjAgpNDSbzBQAI2rteOrJX8qZI7fqZjgaxglJHwBzLqr4QQZ+vWqrPZwwHAoQRiS+EV/dLJcsrFX8l7d1gOpqoC5Y6MjUYABAS7O/V4SwpKcVsLIgdlDoCZnUa4owkvmqp7lnM+Qzcg8QXwiu9ldRlmLOdgOWOlDoCAI6ztSrxRX8v1BQqdSTxBRjROZj4+kQKML0piJ7FcCMSXwi/ULnj62bjMIBSRwDAcbZ+5oz090JNoVJHEl+AEbn9pORm0rED0u7EXJirLlzIhxuR+EL49bhckuWsklKyw3Q0UUWpIwCglqP7pT1rne2O3zIbC2ILpY6AWd4kKa/q7/KWj83GEkNCze3JfMFFSHwh/DJypbyzne01b5iNJcqqV0ExHAgAIDZsX+KMLbtIzbLNxoLYkkxze8C4TjXKHSGJUke4E4kvREbPkc6YYH2+WP4XAFDLts+dkdle+CZfsMfXUbNxAImMBvfHodQRbkTiC5HR4wpn3PyRdGSf2ViiyFP1G+Un8QUAkKSti50xOBMaCAo2t6fUETCn4yBnRfqS7dLBbaajiQlcyIcbkfhCZLTqIuX0kWy/tPZN09FEDcv/AgBCAgGn36XknFwBNYVWdaTUETDG10zK7e1sb/3UbCwxIlTqyJQvuAiJL0ROz6pZX6v/bTaOKKpuBmk4EACAeXvXS8cOSklpUk5v09Eg1lDqCMSGvMHOGFyBN8HRsxhuROILkRPs87XhXanssNlYooRmkACAkG1VJ1HtB0jeZLOxIPZQ6gjEhlDiixlfEqWOcCcSX4ictr2cVaz8ZdL6+aajiQoOFACAkG1V/b0oc0RdapY68rkBMCfYg7HoS2ZgqrpnMeczcBMSX4gcy6qxumNilDsyNRgAEMKKjjiZYKmjHZD85WZjARJZVp7UPFcKVEo7lpmOxjjOZ+BGJL4QWT2vdMZ1b0uVZWZjiQKukAAAJEllh6Rdq5xtEl+oS3DGlySV0+AeMMayqmd9Ue5I6xa4EokvRFaHgVJGO6n8kLTxP6ajibjgFRI/l0gAILFtX+rM5MnKkzLbmY4GscibLHmqer9V0OcLMCrU52ux2ThiQPViXZzPwD1IfCGyPB6pR3B1xzlmY4mC4IGCCyQAkOCCje3p74WTYWVHIDbUTHwl+Ad5Sh3hRiS+EHnBPl9r50r+SrOxRJjF1GAAgFSjv9fZZuNAbEtu5oyUOgJmtesreX3SkT3Svo2mozGKxbrgRiS+EHmdz5HSWkpH9kqFi0xHE1FeD1dIACDh2ba0PZj4YsYXTiI044tSx2h78sknlZ+fr9TUVA0ePFiLF5+8xG3q1Knq3r270tLSlJeXp7vvvlvHjh2LUrSIuKQUqf0AZzvByx3pWQw3IvGFyPMmSd0vd7ZdvrojNfEAAB0olEp3O/2bcvuajgaxLDnNGctJfEXT7NmzNX78eE2ePFlLly5Vv379NGLECO3atavOx7/wwgu69957NXnyZK1evVp/+ctfNHv2bN13331RjhwRFWxwvy3BE1+UOsKFGpX44goJGixY7rj631IgYDaWCGIVFACAti9xxtzeUnKq2VgQ24Kljsz4iqrHH39cY8eO1ZgxY9SrVy9NmzZN6enpmjFjRp2P//jjj3XOOefo+uuvV35+vi6++GJdd911pzwHQpwJlqYn+owvLuTDhRqc+OIKCRql6/mSr7l0aIe0Y5npaCKGKyQAgFDiq8NAs3Eg9lHqGHXl5eVasmSJCgoKQvd5PB4VFBRo0aK6W3IMHTpUS5YsCSW6Nm7cqLlz5+qyyy6LSsyIkmCD++KV0rESs7EYxIV8uFGDE19cIUGjJKdKZ1zsbLt4dUeaQQIAtH2pM5L4wqkkVyW+aG4fNXv27JHf71dOTk6t+3NyclRUVFTnPtdff71++9vf6txzz1VycrJOO+00nX/++Se9kF9WVqaSkpJaN8S4jBypRSdJtqsv1J+Kh57FcKEGJb64QoIm6XWlM66e49plgmkGCQAJzl8p7VzubJP4wqkEE18VR83GgZNauHChHnroIf3f//2fli5dqpdffllvvPGGHnzwwRPuM2XKFGVlZYVueXl5UYwYjdbxW86YwH2+ghfyJcod4R5JDXnwya6QrFmzps59rr/+eu3Zs0fnnnuubNtWZWWlfvKTn5zyCklZWVno31whcYnTL5KSUp0lgotXOr1PXMaiJh4AEtvu1U7ZWkqm1PoM09Eg1lHqGHXZ2dnyer0qLi6udX9xcbFyc3Pr3GfixIm68cYbdeutt0qS+vTpo9LSUv34xz/Wr3/9a3k8x88lmDBhgsaPHx/6d0lJCcmveNDxW9JX/5K2fW46EmM81XkvBWxbHlknfjAQJyK+qiNXSBCS0lw67UJn26Xljl56fAFAYgv292o/oHoaMHAilDpGnc/n08CBA7VgwYLQfYFAQAsWLNCQIUPq3OfIkSPHJbe8Xq8kyT7BLP+UlBRlZmbWuiEOhGZ8febaCpVTsWrO+ErMbwFcqEGfyJp6haRPnz66+uqr9dBDD2nKlCkKnGB1vwkTJujgwYOh29atWxsSJmJZsNxxlTsTXzSDBIAER2N7NASljkaMHz9e06dP13PPPafVq1fr9ttvV2lpqcaMGSNJGj16tCZMmBB6/MiRI/XUU09p1qxZ2rRpk+bPn6+JEydq5MiRoQQYXCK3j+T1SUf2Svs3mY7GCK+nZuKLcxq4Q4NKHWteIbnqqqskVV8hGTduXJ37NPYKSUpKSkNCQ7zodonkSXZKQXavk9p0Mx1RWNHcHgAS3DYSX2iAUKkjM76iadSoUdq9e7cmTZqkoqIi9e/fX/PmzQu1cyksLKx1/nL//ffLsizdf//92r59u9q0aaORI0fqv//7v029BURKUorUrp8z42vb51KrrqYjirpvljoCbtCgxJfkXCG56aabNGjQIJ199tmaOnXqcVdIOnTooClTpkhyrpA8/vjjGjBggAYPHqz169dzhSSRpbWQup4vrZ8vrX5NavNL0xGFlUWpIwAkrrLDzoUdicQX6idU6kiPr2gbN27cCS/cL1y4sNa/k5KSNHnyZE2ePDkKkcG4jt+qSnx9JvX9geloos5DqSNcqMGJL66QoMl6XekkvlbNkc5zV+LLy6qOAJC4dn4h2QEps4OU2c50NIgHyTS3B2JOx0HOuO0zs3EYUjvxxTkN3KHBiS+JKyRoou6XS9bPpaIvpX2bpFZdTEcUNh5WdQSAxBXq73WW2TgQP3zNnJHEFxA7gg3ui1Y4/feS08zGE2U1Sx3tultyA3GH5YYQfc1aS/nnONsuW92RUkcASGDbP3dGyhxRX5Q6ArEnK09qniMFKp2ZvAmm5owvPzO+4BIkvmBGz+Dqjq+ZjSPMKHUEgAS2fakzkvhCfQVnkjDjC4gdllU96ysByx0tmtvDhUh8wYyeV0qynLKQA1tNRxM2lDoCQII6VCwd3CrJktr1Nx0N4gWljkBsCia+ti42G4cBlmWFyh1JfMEtSHzBjIwcqfNQZ9tF5Y4eSh0BIDEFyxzb9JBSM83GgvhBqSMQm0Izvj43G4ch1RfzDQcChAmJL5jT67vOuPJVo2GEk8XVEQBITMHG9h0pc0QDUOoIxKb2/SXLKx3aIR3cZjqaqKu+mM85DdyBxBfMCZY7blvsmgOKlxlfAJCYgrMCOgwyGwfiS81SR04wgdjhayblnOlsJ+CsLy7mw21IfMGczHZSp28726vcUe7o8XB1BAASTiAg7VjmbHck8YUGCJY62gGpssxsLABqS+AG996qcxpOaeAWJL5gVrDc0SWrO4aujjDlCwASx551UlmJk8Ro09N0NIgnwcSXRLkjEGsSOPEVLHX0c04DlyDxBbN6XumMWz+RSnaYjSUMKHUEgAQU7O/Vrr/kTTIaCuKMN0ny+pxtEl9AbMk72xl3LJcqy42GEm2UOsJtSHzBrKwOUt5gZ9sF5Y40ggSABBRc0ZHG9mgMVnYEYlOrrlJaS8lfJhWtMB1NVHk9XMyHu5D4gnm9rnLGVa+ajCIsPFwdAcLiySefVH5+vlJTUzV48GAtXrz4pI8/cOCA7rzzTrVr104pKSnq1q2b5s6dG6VokfBobI+mCCa+KkrNxgGgNstK2HLH4MV8m3MauASJL5jXq6rcsTD+yx0tZnwBTTZ79myNHz9ekydP1tKlS9WvXz+NGDFCu3btqvPx5eXluuiii7R582a99NJLWrt2raZPn64OHTpEOXIkpPIjUvFKZ5vG9mgMHzO+gJjVsarcMeESX87o55wGLkHiC+Zldawqd7Tjvsk904KBpnv88cc1duxYjRkzRr169dK0adOUnp6uGTNm1Pn4GTNmaN++fXr11Vd1zjnnKD8/X8OHD1e/fv2iHDkSUtGXku2XmudKmSRb0QihGV9HzcYB4HjBCxoJlvgKXcwPGA4ECBMSX4gNZ17tjCtfMRtHE3lY1RFokvLyci1ZskQFBQWh+zwejwoKCrRo0aI695kzZ46GDBmiO++8Uzk5Oerdu7ceeugh+f3+aIWNRBYqcxxY3Q0YaAhfM2ek1BGIPR3OkmRJB7ZIh+ueee5GXqpY4DIkvhAben1XkiVt/VQ6uM10NI1GqSPQNHv27JHf71dOTk6t+3NyclRUVFTnPhs3btRLL70kv9+vuXPnauLEiXrsscf0u9/97oSvU1ZWppKSklo3oFFobI+mSk5zRkodgdiTmiW16eFsJ9CsL/oWw21IfCE2ZLaXOg1xtle+ajSUpqhe1dFwIEACCQQCatu2rZ555hkNHDhQo0aN0q9//WtNmzbthPtMmTJFWVlZoVteXl4UI4arbFvijDS2R2OFSh1JfAExKS/xGtxbnNPAZUh8IXb0/p4zrnzZbBxN4K36jeLqCNA42dnZ8nq9Ki4urnV/cXGxcnNz69ynXbt26tatm7xeb+i+nj17qqioSOXl5XXuM2HCBB08eDB027p1a/jeBBLH4d3SwUJJltR+gOloEK9CpY4kvoCYFFzZcWviJL48nNPAZUh8IXb0vFKyPNL2JdL+LaajaZTQjC8ujwCN4vP5NHDgQC1YsCB0XyAQ0IIFCzRkyJA69znnnHO0fv16BWp0YF23bp3atWsnn89X5z4pKSnKzMysdQMabHvVbK823aVUfobQSJQ6ArEtmPjasVTyV5qNJUqCPb5sEl9wCRJfiB0ZOVLnc5ztOG1yz7RgoOnGjx+v6dOn67nnntPq1at1++23q7S0VGPGjJEkjR49WhMmTAg9/vbbb9e+fft01113ad26dXrjjTf00EMP6c477zT1FpAogomvDvT3QhMkM+MLiGnZ3aWUTOd3dNdK09FERfBivp9VHeESSaYDAGrp/T1p8wdOueO5PzcdTYN5aQQJNNmoUaO0e/duTZo0SUVFRerfv7/mzZsXanhfWFgoj6f6uk1eXp7eeust3X333erbt686dOigu+66S/fcc4+pt4BEEUp8nWU2DsQ3Hz2+gJjm8UgdB0kb3pW2Lpba9TMdUcRZnNPAZUh8Ibb0vFJ64xfSzi+kvRuk1qeZjqhBPJ7gtGDDgQBxbty4cRo3blydX1u4cOFx9w0ZMkSffPJJhKMCarBtZnwhPCh1BGJf3uDqxNfZY01HE3FeDyvVw10odURsaZYtdR3ubH8Vf03urdC0YA4SAOBq+zZKxw5I3hSp7Zmmo0E8o9QRiH15Zzvj1k/NxhElHouL+XAXEl+IPb2vccavXoq7v7YepgUDQGLYvtQZ2/WVkupeRAGoF0odgdjXYZAkSzqwRTpUZDqaiONiPtyGxBdiT48rJK9P2r1G2rXKdDQN4qW5PQAkBsocES7JVYmv8lKzcQA4sdRMKadqdu/WxWZjiQIu5sNtSHwh9qS1kM642Nle8ZLRUBrKY1EPDwAJgcQXwiWZGV9AXEigckcvfYvhMiS+EJt6f88Zv/pXXP3FZQUUAEgA/gpnERaJxBeaLlTqeNRsHABOLm+wMybAjC9KHeE2JL4Qm7pd4jR7PbCl+qp6HPBQ6ggA7le8UvKXSalZUquupqNBvAs2t6fUEYhtwRlfO5dLFceMhhJplDrCbUh8ITb5mkndL3W2v/qX2VgaoHpaMAcJAHCtmmWOwam+QGMlpzkjpY5AbGvZRWrWRvKXV8/6dSku5sNtSHwhdvW51hm/elkK+M3GUk/B8x+mBQOAiwVXdKTMEeFAqSMQHyyrRrmju/t8BRfs4mI+3ILEF2LXad9xykgOF0lbPjIdTb3Q3B4AEgCN7RFONUsd+fwAxLYEaXAfupjP3yS4BIkvxK6kFKnXd53tFS+ajaWegqWOTPgCAJcqOyTtXuNstz/LbCxwh2Cpo2yp0t19g4C4V7PBvYuTQpQ6wm1IfCG29fmBM656TaosMxtLPYQaQXKUAAB32rFcki1ldpQyckxHAzfwNaveptwRiG3t+kueZKl0l7R/s+loIoa+xXAbEl+IbZ3PkTLaS8cOSl+/bTqaU7IodQQAdwuVOTLbC2Hi8UreFGeblR2B2JacKrXv72y7uNzRYlVHuAyJL8Q2j0fqc42zHQfljkwLBgCX20Fje0RAUlXiy19uNg4ApxYsdyz8xGwcERQ8p/EHDAcChAmJL8S+YLnj2nnOzK8Y5q36jWJaMAC4VGhFR2Z8IYy8yc5I4guIfZ2GOKOrE1/OyIwvuAWJL8S+3D5SdnfJXyatft10NCcVLHVkBRQAcKHDu6SDWyVZTp8XIFy8Pmck8QXEvk7fdsbdq6Uj+8zGEiH0+ILbkPhC7LMsqe/3ne0V/zQbyymESh2ZFgwA7hOc7ZXdTUrNNBsL3CU046vCbBwATq1ZttT6DGd762KzsUSIRakjXIbEF+JD72udcdP70qEis7GcBNOCAcDF6O+FSGHGFxBfgrO+CheZjSNCOKeB25D4Qnxo1UXqeLZkB6Sv/mU6mhPyWsFpwYYDAQCEHys6IlJCiS9mfAFxweV9vjwWpY5wFxJfiB99q5rcfzHLbBwnQY8vAHAp26axPSKHUkcgvgRnfO1YKlUcMxtLBHg8rFQPdyHxhfjR+xrJkywVfSntWm06mjoxLRgAXGr/ZunoPmdmTk5v09HAbSh1BOJLq65Ss7bO7+yOZaajCTtPqMcX5zRwBxJfiB/praQzLna2v5xtNpYTqF4BxXAgAIDwCvb3yuktJaWYjQXuQ+ILiC+WJXUOlju6r88XF/PhNiS+EF+C5Y5fvhiTSydaXB0BAHfaTmN7RJAnyRkpdQTih4v7fNG3GG5D4gvxpdslUkqWVLJN2vKR6WiOw9URAHAp+nshkpjxBcSfYJ+vrZ/E5AX5pghezOecBm5B4gvxJTlVOvMqZ/vL2Gty7+HqCAC4j79S2rnc2WbGFyKBxBcQf3L6SMnNpGMHpd1rTEcTVsGL+SzYBbcg8YX403eUM66aI1UcNRvLN3g9XB0BANfZs1aqOCL5MqTWZ5iOBm7Eqo5A/PEmSXnfcrYLPzYbS5hxMR9uQ+IL8afTECmrk1RWIq1903Q0tVjBqyP0+AIA99i+xBnb95c8fHRCBDDjC4hPnYY64xZ3Nbj3BC/mc04Dl+DTG+KPx1Pd5P6Lf5iN5Rs8oXp4w4EAAMInmPiivxciJZj4CjDjC4grnYOJr49cNT2KUke4DYkvxKd+1znj+gXSoWKzsdQQLHW0OUgAgHuwoiMijVJHID51HOQkrg/tlPZvMh1N2HAxH25D4gvxKft0qeO3JNsvrXjRdDQhrOoIAC5TcVQqXulsk/hCpFDqCMSn5LTqY8MW9/T5Cp7TcDEfbkHiC/ErOOsrhsodg0v/0uMLAFxi55fORZZmbaXMDqajgVuFZnyR+ALiTrDccfNHZuMIIw8LdsFlSHwhfvX+nnOFtPgr58QkBrACCgC4zI4aZY7BFUyAcKPUEYhfNft8uYQndDHfcCBAmJD4QvxKayl1v9TZ/mKW2ViqeC2ujgCAq4Qa21PmiAii1BGIX3mDJcsrHdgiHdxmOpqwoNQRbkPiC/Gt3/XOuOKfMXGV1GIFFABwl1Dia4DZOOBulDoC8SslQ2rXz9l2SZ8vSh3hNiS+EN9Ov1Bq1kYq3e2s8GhY9UHCcCAAgKY7sk/at9HZbn+W2VjgbqEZX+Yv4gFohPxznNEl5Y6s6gi3IfGF+OZNlvr8wNle/rzZWMS0YABwlR3LnLFVVym9ldlY4G6UOgLxrXNV4sslDe6D5zQs2AW3IPGF+DfgBmdc+6ZUusdoKF6ujgCAe2yvamzPbC9EGs3tgfjW6duSLGnv19LhXaajabLqBbs4qYE7kPhC/Ms5U2o/QApUSF/+02goVmgFFA4SABD3aq7oCEQSpY5AfEtrKeX0drZd0OeLUke4DYkvuMOA/3LGZX+XDF6Z8NRY6Z4rJAAQx2y7RmN7Znwhwih1BOJf56HOuPlDs3GEQTDxxYJdcAsSX3CH3tdI3hRp10pp53JjYXhrZL64QgIAcaxkh3S42FmiPrev6Wjgdp4kZyTxBcSv/HOd0RWJL2fkQj7cgsQX3CGtpdRzpLO97O/GwgiWOkos/wsAcS042yunl+RLNxsL3I9SRyD+5Z8ryZJ2r477Pl+hleoDhgMBwoTEF9wjWO644kWp4piREGqWOtLnCwDiWDDxRWN7RAOljkD8S29V3edr8wdmY2mi6h5fnM/AHUh8wT26DJey8qRjB6U1rxsJwVNjxhfHCQCIY6HG9iS+EAWs6gi4Q5dhzrgp3hNfzkiPL7gFiS+4h8cj9b/B2V76VyMh1O7xxYECAOJSICDtWO5ss6IjooEZX4A75Fclvlwy44vTGbgFiS+4S//rJVnSpv9I+zdH/eWtmqWOHCkAID7tXS+VlUhJaVKbnqajQSIg8QW4Q+ehkuVxjiMlO01H02ihHl+cz8AlSHzBXVp2lk67wNk20OS+VqkjzSABID4Fyxzb9ZO8SWZjQWKg1DHqnnzySeXn5ys1NVWDBw/W4sWLT/r4AwcO6M4771S7du2UkpKibt26ae7cuVGKFnEjrUX1SsBxPOsrWMRCy2K4BYkvuM9Zo51x2fOSvzKqL+1hVUcAiH/Bxvb090K0BGd8BUh8RcPs2bM1fvx4TZ48WUuXLlW/fv00YsQI7dpV90p85eXluuiii7R582a99NJLWrt2raZPn64OHTpEOXLEhVCfr/fNxtEEoeb2ZL7gEiS+4D7dL5PSWkmHdkgbFkT1pWuu6kjiCwDi1PaqGV+s6IhoodQxqh5//HGNHTtWY8aMUa9evTRt2jSlp6drxowZdT5+xowZ2rdvn1599VWdc845ys/P1/Dhw9WvX78oR464kH+eM7pixhfnM3AHEl9wn6QUqd91znaUm9xblhXq80WPLwCIQ5XlUtGXzjYzvhAtwZJaSh0jrry8XEuWLFFBQUHoPo/Ho4KCAi1atKjOfebMmaMhQ4bozjvvVE5Ojnr37q2HHnpIfr//hK9TVlamkpKSWjckiM5DJMvr9Bs+sNV0NI1Cjy+4TaMSX9TEI+addaMzrpsnHSqO6kuzCgoAxLFdK51ZN6ktpFZdTUeDRMGMr6jZs2eP/H6/cnJyat2fk5OjoqKiOvfZuHGjXnrpJfn9fs2dO1cTJ07UY489pt/97ncnfJ0pU6YoKysrdMvLywvr+0AMS8mQ2g9wtuN01lfwfMZPz2K4RIMTX9TEIy607Sl1PFsKVEpf/COqL+21uEICAHEr2N+r/YDaS/UCkVQz8cXnh5gTCATUtm1bPfPMMxo4cKBGjRqlX//615o2bdoJ95kwYYIOHjwYum3dGp8zf9BIcd7nK1jqaPP3CC7R4MQXNfGIG8Em90ufi+qHyFCpI80gASD+bF/mjB0Gmo0DiSW4qqPkXLRDxGRnZ8vr9aq4uHZFQHFxsXJzc+vcp127durWrZu8Xm/ovp49e6qoqEjl5XXP0ktJSVFmZmatGxJIl+HOuOn9uExmW1zIh8s0KPEVrZp4ICzOvFryZUj7NkZ1mjGljgAQx3ZUNbanvxeiKTjjS6LcMcJ8Pp8GDhyoBQuqF0AKBAJasGCBhgwZUuc+55xzjtavX69AoLrua926dWrXrp18Pl+d+yDBdfq25E2RSrZLe9ebjqbBqitYDAcChEmDEl/RqomnGSTCIqW51Pf7zvbnz0btZVkFBQDiVNlhafcaZ5sZX4gmEl9RNX78eE2fPl3PPfecVq9erdtvv12lpaUaM2aMJGn06NGaMGFC6PG333679u3bp7vuukvr1q3TG2+8oYceekh33nmnqbeAWJec5iS/JGnjQqOhNIanKkvA+QzcIinSL1CzJt7r9WrgwIHavn27/ud//keTJ0+uc58pU6bogQceiHRoSAQDb5Y+nyGt/rdUukdqlh3xl6xeBSXiLwUACKedX0h2QMpoL2XUXfIERISnxkdyVnaMuFGjRmn37t2aNGmSioqK1L9/f82bNy90cb+wsFAeT/X8gLy8PL311lu6++671bdvX3Xo0EF33XWX7rnnHlNvAfGg63Bp03+cxNfZY01H0yAeSh3hMg1KfDW2Jj45OfmENfF1TQ+eMGGCxo8fH/p3SUkJK6Ggcdr1k9qf5ZSuLH9BOudnEX/J6lVQOFAAQFwJNranzBHRZlnOrC9/OYmvKBk3bpzGjRtX59cWLlx43H1DhgzRJ598EuGo4Cpdz5cW/Fba9IHkr5S8EZ9zEjahHl+s6giXaFCpY7Rq4mkGibAaeLMzLpkZlcZbrIICAHGK/l4wqebKjgDiX7v+UmqWVHZQ2rncdDQNwir1cJsGr+pITTziTu9rJF9zad+GqDS591LqCADxaXtV4qs9iS8YECx3ZMYX4A4er9TlPGd743tmY2kgehbDbRqc+Bo1apQeffRRTZo0Sf3799fy5cuPq4nfuXNn6PHBmvjPPvtMffv21c9+9jPddddduvfee8P3LoCTSWku9Ylek3uW/wWAOFS6VzqwxdluP8BsLEhMzPgC3Kfr+c648T9Gw2goi1Ud4TKNKjSmJh5xZ+DN0pJnnSb3h4qljJxT7tJYwSsk9PgCgDiyY5kztjpNSmthNBQkKBJfgPt0vcAZt34qlR+RfOlm46mn6goWzmfgDg2e8QXEpfb9pY7fkgIV0tLnIvpSweb2HCcAII7Q2B6meZOdkVJHwD1adZWy8pyEduEi09HUW6jUkQv5cAkSX0gcZ//YGT9/NqIfKln+FwDiUKix/UCzcSBxMeMLcB/LkroOd7Y3LjQaSkN4KHWEy5D4QuLo9V0pPVs6tENa80bEXsZT9VvlJ/EFAPHBtmlsD/NIfAHuFCx3jKMG9xbN7eEyJL6QOJJSnF5fkrR4esReprrUkQMFAMSFku1S6S7J8kq5fUxHg0RFqSPgTl2qZnwVrZAO7zIbSz2xSj3chsQXEsugMc6JzZYPpeJVEXkJpgYDQJwJzvZq2ytuGg/DhZjxBbhT8zZSu37O9oZ3zcZST6HzGU5o4BIkvpBYsjpKPS5ztj+LzKwvmkECQJwJ9fcaYDYOJLbgjK8AM74A1zntQmdcv8BsHPVEqSPchsQXEk+wyf0Xs6WjB8L+9MErJPT4AoA4sZ3G9ogBlDoC7nV6VeJrw7tSIGA2lnpgsS64DYkvJJ78YVKbnlJFqbT8+bA/fXWPr7A/NQAg3AIBaccyZ5vG9jCJUkfAvTqeLfmaS0f2SEVfmo7mlII9vjifgVuQ+ELisSxp8G3O9uJnpIA/rE/v8XCFBADixr4NUlmJlJQqte1pOhokstCMLxJfgOsk+aQu5znbG2K/3DHYuoUKFrgFiS8kpr4/kFJbSPs3S1+/HdanDvX44jgBALEvWOaY27c68QCYEJrxRakj4EqnfccZ18d+g3uLUke4DIkvJCZfM+ms0c72p9PC+tSsggIAcSTU2J4yRxhGqSPgbsE+X1s/kcoOmY3lFLyh8xnDgQBhQuILietbt0qWR9q4UNq1JmxP62EVFACIHzS2R6yg1BFwt1ZdpZZdpECltOkD09GcFM3t4TYkvpC4WnaWul/mbC9+OmxPW93jK2xPCQCIBH9FdZNhGtvDNEodAfcLre4Y232+LC7kw2VIfCGxDf6JM34xSzqyLyxPGbxC4ifzBTTak08+qfz8fKWmpmrw4MFavHhxvfabNWuWLMvSVVddFdkA4Q67VkuVx6SULOdKPGASpY6A+51Wlfha/05ML5lYPePLcCBAmJD4QmLLP1fK6SNVHJGWzAzLUwZLHe0YPpgBsWz27NkaP368Jk+erKVLl6pfv34aMWKEdu3addL9Nm/erF/84hcaNmxYlCJF3Nu+xBnb95c8fCSCYZ4kZ2TGF+BeXc5zktz7N0t7N5iO5oS8VSc0nM/ALfiUh8RmWdKQO53txc9IlU2/ympxhQRokscff1xjx47VmDFj1KtXL02bNk3p6emaMWPGCffx+/264YYb9MADD6hrV2buoJ5obI9YQqkj4H4pzaXOQ53tMK8sH07BC/lUsMAtSHwBva+RmudKh3ZKK19p8tN5aQYJNFp5ebmWLFmigoKC0H0ej0cFBQVatGjRCff77W9/q7Zt2+pHP/pRNMKEW2xf5ow0tkcsoNQRSAxnXOyMMZz44kI+3IbEF5Dkk84e62wv+lOT6+2D1TIkvoCG27Nnj/x+v3Jycmrdn5OTo6Kiojr3+fDDD/WXv/xF06dPr/frlJWVqaSkpNYNCab8iLRrlbNNY3vEgtCqjsz4AlwtmPja8pFUdthsLCfAKvVwGxJfgCQNukVKSnNW99rctOWFWf4XiJ5Dhw7pxhtv1PTp05WdnV3v/aZMmaKsrKzQLS8vL4JRIiYVrZBsv9Q8R8psbzoagBlfQKJofbrUMt/5Xd/0vulo6lTd48twIECYkPgCJCm9ldT/emd70ZNNeqpQ4ivQ1KCAxJOdnS2v16vi4uJa9xcXFys3N/e4x2/YsEGbN2/WyJEjlZSUpKSkJP31r3/VnDlzlJSUpA0b6m4cO2HCBB08eDB027p1a0TeD2JYqLH9WdXrtgMmkfgCEoNlxXy5I6vUw21IfAFB377DGdfNc5a4b6RQM0gukQAN5vP5NHDgQC1YsCB0XyAQ0IIFCzRkyJDjHt+jRw+tWLFCy5cvD92uvPJKXXDBBVq+fPkJZ3KlpKQoMzOz1g0Jhsb2iDWUOgKJI5T4mh+T06osSh3hMkmmAwBiRvbpUs+R0up/Swsfln7wXKOeJniFhOV/gcYZP368brrpJg0aNEhnn322pk6dqtLSUo0ZM0aSNHr0aHXo0EFTpkxRamqqevfuXWv/Fi1aSNJx9wO1bCfxhRjDjC8gceSf67RZKdnmXHDP6WU6oloodYTbkPgCajp/grT6dWnVq07/l9w+DX4KVkEBmmbUqFHavXu3Jk2apKKiIvXv31/z5s0LNbwvLCyUx8OEZTTB0QPSvqoyWBrbI1aQ+AISR3Ka1OU86eu3nHLHGEt8hUodyXzBJUh8ATXlnCmdebW08mVn1tcPn2/wU3hZ1RFosnHjxmncuHF1fm3hwoUn3XfmzJnhDwjusmOZM7bMd3o8ArHAW/WxPFBpNg4A0XHGRVWJr/nSuT83HU0tlDrCbbhkDnzT+fdKlkda83r1yVEDVDe350ABADEp2N+L2V6IJcz4AhLLGRc5Y+Ei6eh+s7F8Q3XrFtq3wB1IfAHf1Ka71Of7zvZ7Uxq8u4dSRwCIbfT3Qiwi8QUklpb5Upueku2X1i845cOjyVtjtWPyXnADEl9AXYbfI1leZ/px4acN2pWpwQAQ47Yz4wsxiFUdgcTT/RJnXDvXbBzf4KmR+KLPF9yAxBdQl9anSQNucLbfuq9BlzqCq6Aw4wsAYtChIunQDqekvV0/09EA1ZjxBSSe7pc549fvxFTS26qRJeBiPtyAxBdwIhf8WkpuJm3/XPrqX/XejR5fABDDgrO92vSQUpqbjQWoicQXkHg6DJTSs6Wyg9KWj01HE+Kh1BEuQ+ILOJGM3OoVVt55QKo4Vq/dKHUEgBhGY3vEKkodgcTj8Urdqsod180zG0sNNXt8cU4DNyDxBZzMkHFSRnvpYKH06VP12sVLc3sAiF2hxvYDzMYBfBMzvoDEFOrz9WbMTK+qkfeSn5MauACJL+BkfOnShZOc7fcfkw7vOuUu1as6cpAAgJhi28z4QuwKJb6Y8QUklK4XSN4Uaf8mafda09FIql3qSN4LbkDiCziVvqOcBsjlh6Q3f3XKh3uqfqvo8QUAMWb/ZunofifBkNPbdDRAbZ4kZ2TGF5BYUppLXc5ztte9aTaWKsHFuiTJ5mI+XIDEF3AqHo808gnJ8korXzllo3uLUkcAiE3B2V45vaUkn9lYgG9ixheQuLpf6oxrYyPx5aHUES5D4guoj/YDpGH/z9l+4/9Jh4pP+FAvpY4AEJtC/b0oc0QMCia+bL8U8JuNBUB0BRvcb10sHd5tNhZVX8iXuJgPdyDxBdTXeb+Ucvs4ZTKv//yEzSc9rOoIALFpO/29EMOCqzpKzPoCEk1WB6ldf0m2tHau6WgkVZ/TUOoINyDxBdRXkk+6aprkSXYOSB//sc6HWcz4AoDYE/BLO79wtpnxhVjkrVF+S58vIPH0HOmMq/9tNo4qwT5fzPiCG5D4Ahoit7d04URne/4kacFvj5v5xUECAGLQ7rVSRankay5ldzMdDXA8ZnwBiS2Y+Nr0H+nYQbOxqPpivp+L+XABEl9AQw39mXThJGf7g8ecsscavTgodQSAGBRsbN+uv+TxGg0FqJPH6yykIzHjC0hEbbo7F2b85dLX801HU31Ow9V8uACJL6ChLMtpdD/yCcnySEtmSk8Pl9bOk2xbnmCpIwcJAIgdocb2A8zGAZxMaGVHEl9AQupxhTOunmM2Dil0TsO1fLgBiS+gsQbeLH1/ppSSKRWvkP4xSvrLRRqw6xWdaW2S/JWmIwQABO2gsT3iQCjxRakjkJCC5Y5fvyNVHDUaCivVw02STAcAxLVe35Xyh0kfTZU+fUba9pku0We6JEWqXOaTNuRIyemSL71201o7IAUqq25Vy5bbfkmWlJzm7JPSXErPlpq3kZq1ldJbS+mtpLRWUmqWlJJRfaux5DAA4Bsqy6Sir5xtGtsjlnmrPpoz4wtITO0HSJkdpZJt0ob3pB6XGQsleHpBjy+4AYkvoKnSW0kX/Vb69p3Skme1efm7arl/hbJ0RDq4NfKvb3mcRFhqlpTRXmrZWWrR2Tm56zJcSk6NfAwAEMuKv5ICFc6FgxadTUcDnFjwIlmAGV9AQrIsqecV0qfTpDWvG018eTzBUkcSX4h/JL6AcMnIkc6/Vy9XfE9/XLBOPxuQpPHntHFWESs/4szuCrIsyZPsNLINNrP1eJ2ZYBXHnH3KDkmlu6XDu53x6D7pyF7pyD7na2UlznPaAenofue2f7NU+HH16yQ3k84okPr/l9Tt4qh/SwAgJoT6e53FDFnEtuDKjpQ6AomrR1Xia+1c529BzRVfo6i61NHIywNhReILCDPn4oilvb4OUsc+kXsh25YqjznLHR894CS+SrZLB7ZI+zY606NLtkurXnNu/f9LuvQRp4QSABLJjmXOSH8vxDqa2wPoNMRpcXJkr7T5Q+m0C4yEYVUlvvxkvuACJL6AMIva1REr2A8sTcrIPf7rtu2c7H05W/r0aWn536XCRdI1f6bHDYDEUnPGFxDLSHwB8CZJPS6Xlv5VWvWqscRXVaUjze3hCqzqCIRZsB4+YPrqiGU5J3mXPiLd/LqU2UHat0F69lKpeKXZ2AAgWsoOSbvXONvM+EKso9QRgCSdebUzrv63sZXiPVawx5eRlwfCisQXEGZWLF4dyT9X+smHzgqUlcekl29zVjkDALfb+YUk20n+Z+SYjgY4OWZ8AZCk/POcBVmO7JW2fGgkBG/wYn4sndMAjUTiCwizmG0Emd5KuuYvTs+A4hXSew+ZjggAIi9Y5th+gNk4gPog8QVAcsode17hbK981UgIwYv59PiCG5D4AsKselpwDB4kMnKkkU842x89IW35+OSPB4B4t4P+XogjlDoCCOp1lTMaKnf0xOrFfKARSHwBYRa6OhKLiS9J6jnSWeFRtlPyWHbYdEQAEDmhGV8kvhAHPMHEFzO+gITX5TwpraV0ZI+Rcsdgc/uYvJgPNBCJLyDM4uLqyCVTpKw86WChtOKfpqMBgMgo3Ssd2OJsU+qIeECpI4Agb7LUw1y5Y2jBrlg+pwHqicQXEGZx0QgyNVMa/BNne8lzZmMBgEjZscwZW50mpbUwGgpQL6FSRzOruAGIMQZXdwxezKfHF9yAxBcQZsFpwYFYP0j0u865srxzefXJIQC4Cf29EG+Y8QWgJoPljpQ6wk1IfAFhZllxMONLkpq1lnpe6Wwz6wuAG9HfC/GGxBeAmrzJTn9eSfrqX1F96bho3wLUE4kvIMzi6iAx8GZnXPEiTe4BuIttM+ML8YdVHQF8U+9rnXHVHKkyeknxUKljrF/MB+qBxBcQZt6q36q4mBacf67T+6b8cNSvIgFARJXskA4XS5ZXyu1rOhqgfpjxBeCb8s+VmudKxw5IGxZE7WU9Vec0MV/FAtQDiS8gzKx4agRpWdWzvpbMNBkJAIRXcLZX216SL91sLEB9hWZ8kfgCUMXjrW5yv+Kl6L1s1TlNXFzMB06BxBcQZnFV6ihJ/a+XPMnOSWLRCtPRAEB4BPt7dRhgNg6gIUIzvih1BFBDn+8749q5UnlpVF4ydE4TiMrLARFF4gsIM2+8TQtuli11G+Fsr51nNhYACJftS5yRxvaIJ8z4AlCXDmdJLbtIFUektW9G5SWDqzrS4wtuQOILCDNPvKzqWFPX851x8/tGwwCAsAgEpB3LnW0a2yOekPgCUBfLknpf42xHqS8vpY5wExJfQJhZ8TgtuMt5zlj4qVRxzGwsANBU+zZKZQelpFSnxxcQL4KljoFKs3EAiD19qlZ3/Hq+dHR/xF8u7tq3ACdB4gsIs+C04Lia8ZXdTWqeI/nLpG2fmY4GAJom2Ng+t2/1DBogHrCqI4ATadtTanumFKiQVs2J+MuxqiPchMQXEGbe0LRgw4E0hGVJ+cOc7U2UOwKIc8H+XpQ5It5Q6hhVTz75pPLz85WamqrBgwdr8eLF9dpv1qxZsixLV111VWQDBL6p7w+c8Yt/RPylPPG0Uj1wCiS+gDALljrGXSPIYLnj5g/MxgEATRVc0ZHG9og3rOoYNbNnz9b48eM1efJkLV26VP369dOIESO0a9euk+63efNm/eIXv9CwYcOiFClQQ99RkuWRChdJezdE9KU88XgxHzgBEl9AmMVlqaNUnfja9nnUlkkGgLDzV0hFXzrbHQaajQVoKEodo+bxxx/X2LFjNWbMGPXq1UvTpk1Tenq6ZsyYccJ9/H6/brjhBj3wwAPq2rVrFKMFqmS2k077jrP9xayIvpTHE4cLdgEnQOILCDOvJ04bQbbMl7LynL4BhZ+YjgYAGmfXaqnymJSSJbXixBRxJlTqyIyvSCovL9eSJUtUUFAQus/j8aigoECLFi064X6//e1v1bZtW/3oRz865WuUlZWppKSk1g0Ii/7XO+MX/4joalrBi/mUOsINSHwBYRa3S/9aVvWsL/p8AYhXwcb27ftXd+YF4oWHHl/RsGfPHvn9fuXk5NS6PycnR0VFRXXu8+GHH+ovf/mLpk+fXq/XmDJlirKyskK3vLy8JscNSJK6X+5c3Dm4NaItSih1hJvwiRAIMyuer44EG9zT5wtAvKKxPeIZpY4x6dChQ7rxxhs1ffp0ZWdn12ufCRMm6ODBg6Hb1q1bIxwlEkZyqtTnGmd7+QsRe5m4bd8C1KFRiS9WQAFOLHh1JB7zXupSlfjasUw6dtBsLADQGNuXOSON7RGPKHWMiuzsbHm9XhUXF9e6v7i4WLm5ucc9fsOGDdq8ebNGjhyppKQkJSUl6a9//avmzJmjpKQkbdhwfJPxlJQUZWZm1roBYdP/Bmdc9Zp0LDJltHF9TgN8Q4MTX6yAApxcsMdX3JU6SlJWR6nVaZIdkLacuMcFAMSk8iPSrlXONjO+EI9Y1TEqfD6fBg4cqAULFoTuCwQCWrBggYYMGXLc43v06KEVK1Zo+fLloduVV16pCy64QMuXL6eMEdHXYaCU3U2qPCqtejUiL+GJ15XqgTo0OPHFCijAycV1qaMkdR7qjNvqN5MTAGJG0QrJ9kvNc6TMDqajARqOUseoGT9+vKZPn67nnntOq1ev1u23367S0lKNGTNGkjR69GhNmDBBkpSamqrevXvXurVo0UIZGRnq3bu3fD6fybeCRGRZ1U3ul/09Ii8RbJMZlxfzgW9oUOIrGiugAPGuelpwnB4k2vVzxqKvzMYBAA0V6u81sPoqBBBPKHWMmlGjRunRRx/VpEmT1L9/fy1fvlzz5s0LNbwvLCzUzp07DUcJnES/6yXLK239VNq1JuxPbwXPaeL1Yj5QQ1JDHnyyFVDWrKn7ly24Asry5cvr/TplZWUqKysL/ZvlfxFP4n4FlNw+zli0wmwcANBQwcQX/b0Qr5jxFVXjxo3TuHHj6vzawoULT7rvzJkzwx8Q0BAZOVL3S6U1r0vL/iaN+O+wPr2XHl9wkYiu6tiYFVAklv9FfPNW/VbF7YyvnDOd8dAO6cg+s7EAQEPsWOqM9PdCvCLxBaAhzhrtjF/8Q6osO/ljG4hVHeEmDUp8RWMFFInlfxHfrHhvBJmSIbXMd7aZ9QUgXhzZJ+3b6Gy3H2A2FqCxKHUE0BCnXShltJeO7JXWzg3rU8d9+xaghgYlvqK1AgrL/yKehQ4SAcOBNEVOb2csps8XgDixY5kztuoqpbcyGwvQWKHEFzO+ANSDN0kacIOzveS5sD61x0OpI9yjQT2+JGcFlJtuukmDBg3S2WefralTpx63AkqHDh00ZcqU0AooNbVo0UKSjrsfcAtvqMdXHB8lcvs4/QKY8QUgXmyvKnOkvxfiWbDUMVDhNAtlkQYApzLgRun9R6WN70n7N1dXbjQRpY5wkwYnvkaNGqXdu3dr0qRJKioqUv/+/Y9bAcXjiWjrMCCmWaGDhNk4miTU4J4ZXwDiRKi/10CzcQBNEZzxJTnljkk+c7EAiA8tO0tdz3cSX8v+Ln3n/rA8rYdVHeEiDU58SayAApyMJ957fEnVpY6710iV5XzwBhDbbLt6RUca2yOeeWscb/0cfwHU08CbnMTX0r9Kw++pnURvJItVHeEiTM0Cwiw44TGuSx1bdJJSspxSiz3rTEcDACdXskM6XCxZXim3r+logMarmfgK0OAeQD11v1xqnuMcC9e8HpanjPuV6oEaSHwBYeZ1w9URy5JyznS2aXAPINYFZ3u17SX50s3GAjSFp0YxBis7AqivJJ901k3O9uI/h+UpKXWEm5D4AsIsOC3YH+8Hidyqckca3AOIdaH+XpQ5Is5ZVvWsL1Z2BNAQA292Zj5v+VDatbrJT+dxw8V8oAqJLyDMXLMCSqjBPYkvADGO/l5wExJfABojq4PU4zJn+7O/NPnpLLec0wAi8QWEXfDqSNwfI4IN7ou/csGbAeBagYC0Y7mzzYqOcINgU2pKHQE01LdudcYvZkllh5r0VK5o3wJUIfEFhJnXEzxIxPlRom1PyfJIR/ZKh4pMRwMAddu7XiorkZLSpDY9TUcDNJ0nmPhixheABuoyXGp9hlR+SPpydpOeyuOWcxpAJL6AsAtOC477Hl/Jac6BU6LcEUDsCpY5tu8veZNO+lAgLlDqCKCxLEv61o+c7U+mSQF/k55Kork93IHEFxBmril1lKob3BeT+AIQo0L9vShzhEsESx0rSXwBaIT+N0ipLaS9X0urXm3001DqCDch8QWEmWtKHSUp50xn3LXGbBwAcCI0tofbJKc5Y+Uxs3EAiE+pmdK3b3e233/U6YXZCNWrOrrgnAYJj8QXEGahUkc3HCSyuzvjnrVm4wCAulSWVZdiM+MLbhFMfFUcNRsHgPg1+DbJlyHtWiWtnduop3DNSvWASHwBYVez1NGO9wNFdjdn3PN1o68WAUDEFK2QAhVSemupRWfT0QDhkZzujBVHzMYBIH6ltZTOHutsv/8/jerBYjHjCy5C4gsIs2DiS3JBn69WXSRPkvPhu2S76WgAoLZQmeOg6um2QLwj8QUgHIbc6fw92blcWv9Og3evbt8S5rgAA0h8AWHmrXHyFfdXSLzJUqvTnG3KHQHEGhrbw40odQQQDs2ypUG3ONv/eaTBV+Q9rOoIFyHxBYSZVeO3yhV9vtpUlTvuXmc2DgD4JhJfcCNfM2csLzUbB4D4N/RnzqyvbZ9Ja15v0K6UOsJNSHwBYeaqUkepRp8vEl8AYsjR/dLe9c42KzrCTZjxBSBcMnKckkdJeuc3kr+i3rtWr+oYgbiAKCPxBYSZp0abGVdcIQmt7EjiC0AM2b7UGVt2kdJbmY0FCCd6fAEIp6E/k9KznYtFS5+r927eqkyBK85nkPBIfAFh5qnV48tgIOESKnWkxxei58knn1R+fr5SU1M1ePBgLV68+ISPnT59uoYNG6aWLVuqZcuWKigoOOnj4RLBxFfHQWbjAMKNxBeAcErNlM6/19le+LBUdqheu4VmfLnihAaJjsQXEGY1E19+NxwoWp/hjEf2SEf2mY0FCWH27NkaP368Jk+erKVLl6pfv34aMWKEdu3aVefjFy5cqOuuu07vvfeeFi1apLy8PF188cXavp2VSF2N/l5wK0odAYTbwJulVl2l0t3Sx3+q1y4WpY5wERJfQJjVLHW03TA1OKW5lNnR2abcEVHw+OOPa+zYsRozZox69eqladOmKT09XTNmzKjz8c8//7zuuOMO9e/fXz169NCf//xnBQIBLViwIMqRI2psm8QX3Ivm9gDCzZssXTjZ2f7oCWnfplPvElzV0Q3nM0h4JL6AMPN6XFbqKFHuiKgpLy/XkiVLVFBQELrP4/GooKBAixYtqtdzHDlyRBUVFWrVir5PrnVwm1S6S/IkSbl9TEcDhBczvgBEQq/vSvnDpMqj0r/vOuUqXJ6qcxryXnADEl9AmFluK3WUWNkRUbNnzx75/X7l5OTUuj8nJ0dFRUX1eo577rlH7du3r5U8+6aysjKVlJTUuiGObP/cGXPOrE4SAG5Bjy8AkWBZ0sgnpKQ0adN/pGV/O8XDnXMa15zPIKGR+AIiIDjpyxWljhKJL8SNhx9+WLNmzdIrr7yi1NTUEz5uypQpysrKCt3y8vKiGCWabFtV4qvjt8zGAUQCiS8AkdL6NOk7v3a237pfKtl5wod6KHWEi5D4AiLA47ZmkG26OyOljoiw7Oxseb1eFRcX17q/uLhYubm5J9330Ucf1cMPP6y3335bffv2PeljJ0yYoIMHD4ZuW7dubXLsiKJtnzkjiS+4EaWOACJp8O1S+7OksoPS63dLgUCdD/O67XwGCY3EFxABwZp411whya5KfB0o5IM4Isrn82ngwIG1GtMHG9UPGTLkhPv9/ve/14MPPqh58+Zp0KBBp3ydlJQUZWZm1rohTlSWSzuWO9skvuBGoeb2zPgCEAHeJOm7T0qeZGndm9Jrd0j+yuMeVn0h3yXnM0hoJL6ACAhODXZNTXyzbCm1hSRb2rvedDRwufHjx2v69Ol67rnntHr1at1+++0qLS3VmDFjJEmjR4/WhAkTQo9/5JFHNHHiRM2YMUP5+fkqKipSUVGRDh8+bOotIJKKv5L8ZVJaS2dpdsBtQjO+SHwBiJCcXtLV0yTLK33xD+nFm6TKsloPsSh1hIuQ+AIiIHiFxDXHCcui3BFRM2rUKD366KOaNGmS+vfvr+XLl2vevHmhhveFhYXaubO6J8VTTz2l8vJyXXvttWrXrl3o9uijj5p6C4ikYH+vDoOqP5UDbhLq8cUMawAR1OdaadTfJK9PWvO69PdrpO1LQ192XesWJLQk0wEAbuR149Tg7G7S1k9pcI+oGDdunMaNG1fn1xYuXFjr35s3b458QIgd9PeC29Vsbm/bJHgBRE6Py6Xr/ynNul7a/IE0/QLnwtLAm5VV2lle+d2zWBcSGokvIAJcOTU4OONr12qzcQBIbKHE16l7uQFxKVjqKFuqPFbj3wAQAaddIN26QPpoqvTVy9L2z6Xtn6tA0qqUZO0sypP+2llKb+W0PvE1cxL0yalOqaTlcU5+ApWSv0IK+J3tQKVk+6v+7ZfsgHOTXUdZTPC+qtH2O033g/vbNZ/Drv3441jVzynVeC37G/sHqv9t29WxnVDV81rWN7a/+VZqvt43XztQ4/0EvvG+aiwyYFnV31tPkvO99jV3vvfNc6SW+c6t/QCpBSuT1weJLyACXNfcXpJyq1bJCzaVBoBoK90r7d/kbHcYaDYWIFKCM74kp8E9iS8AkZbTS/reM9LFv5OWPCd9/ZYqd65Uiv+I8is2Shs3mo4QJ9L5XKnfD6Ve35VSWazpREh8ARHgypr49v2d8WChVLrHaXgPANG0vaq/V3Y3Ka2F0VCAiPEmOT13/OVVDe5bm44IQKJo3lYa/ktp+C/19pfb9cg/5umS3MOaMLytdHS/c6s44vQgrDhaexaX5XX+fnmSnBUjPUmSx+vcrKpRVvWMqZqzpWy7euaYLMnjqTHjyes8l+WpcbOcUVL1DC+p1oyt4ASEmjO0asZgeavG4HNZtR9bS83ZY3Vsh3xj35rvNTQ7ruo9hUZv7feuGjPQgjPCKo5K5aVSWYl0aKe0f7O0b6MzIWHLh85twQPS6DlOEhPHIfEFRIArl/9NzZJanyHt/dppfNntYtMRAUg09PdCokhOr0p80eAegBkej0db7FwtTWkp9R9qOhzU5eA26ct/Skufc5Jhf71Sunmu1Kab6chiDqs6AhFQVekov6umfKm6tGjH0pM/DgAigf5eSBShBvelZuMAkLCsqgv5rjufcZOsjtKw8dLY96TcPlLpbif5tXeD6chiDokvIAKCM77cNOFLktThLGfcvsRsHAASTyBQvcw6M77gdsG+Xsz4AmCIK1u3uFV6K+nG16Q2PZ1SyL9+Vzp20HRUMYXEFxABwRlfrip1lKT2wcTXUhdm9QDEtD3rnN4WyenOBzvAzXxVM77Kj5iNA0DC8lZlCmw+88eHZq2lm+ZILTpJB7dKK14yHVFMIfEFRED1qo6GAwm33D5Oc8kje5w/qAAQLdsWO2P7AU7zXMDNQqWOJL4AmBEqdSTxFT+at5XO/rGz/cUss7HEGBJfQAR43FoTn5wq5ZzpbG+nzxeAKCr81Bk7fdtsHEA0hBJflDoCMCNU6hgwHAgaps/3nVUity2m11cNJL6ACAiWOrpyanB7+nwBMKBwkTPmkfhCAqC5PQDDXNu6xe0ycqXTvuNsfznbbCwxhMQXEAGuLXWUqhvc71hmNg4AiePwbmnfBkmWlEdjeyQAmtsDMMzr1sW6EkHfHzrjF7P4D6xC4guIgOpVUFz4h6bDQGfcsVwK+I2GAiBBbP3EGdv2lNJamo0FiAaa2wMwjB5fcazH5ZKvuXRgi1T4ieloYgKJLyACQlOD3TjlK7u7U4JRfkja87XpaAAkguCHtrzBZuMAooXm9gAMo9QxjvnSpV5XOdtf/MNoKLGCxBcQAdUzvgwHEgneJKldP2d7Bw3uAUTB1mBj+yFm4wCiheb2AAzzeih1jGv9RjnjylelimNGQ4kFJL6ACHB1qaNUXe7Iyo4AIq3iqFNaLUmdmPGFBEFzewCGWW4/n3G7zudKmR2lsoPSpv+YjsY4El9ABHiqfrNcWxMfbHC/5WOzcQBwv+1LpUCFlNFOatHZdDRAdPiY8QXArGCpo9+VJSwJwOOROlfNlC9eaTaWGEDiC4gAT2gVFJceKLpeIFleaddKae8G09EAcLPCRc6YN1iq+tsKuF5wVUea2wMwxMOqjvGvTXdn3LPObBwxgMQXEAGhqcEBw4FESnorqetwZ3vlK2ZjAeBu9PdCIqK5PQDDgj2+KHWMY9lVia/da8zGEQNIfAER4E2EVVCCK4WsetVkFADcLBCokfiivxcSCM3tARhmUeoY/9r0cMbd6xJ+6h6JLyACXN/cXpJ6XOGUOxatoNwRQGTsXiMdOyglN5Ny+piOBogemtsDMMzVq9QnilZdJE+Scyw5uM10NEaR+AIiICEOFM1aS13Oc7aZ9QUgEoL9vToOkrxJZmMBoonm9gAMc33P4kTgTZZan+5s71lrNhbDSHwBERBc1dHVM74k6cyrnHHlqyajAOBWmz90xs5DzcYBRFuwuT2JLwCGeBPlfMbtsrs5424SXwDCLHiFxPU18T1GVpU7fint22g6GgBuYtvVia/8YWZjAaItWOpYTqkjADOsRDmfcbtQn6/EbnBP4guIgIRZ/rdZa6lL1Qkps74AhNOedVLpLikp1Sl1BBIJze0BGJYw5zNu1ya4suM6s3EYRuILiAArEVZ1DAqu7rjiRWcFNgAIh03vO2Pe2VJSitlYgGgLJr78ZVLAbzYWAAnJmwiLdSWCUOJrTUJnMUl8ARHg9SRAc/ugXt+VfBnSrlXSl7NNRwPALUJljueZjQMwIdjcXpIqjpiLA0DCqr6QbzYONFHr0yVZ0rEDUulu09EYQ+ILiIDQqo6JcKRIbyWd9/+c7QUP0I8EQNPV7O/Vhf5eSEBJqdXblDsCMMBTdSHfn8CzhFwhOU1qme9sJ3CfLxJfQAR4EqnUUZIG3y616Cwd2il99ITpaADEu12rpSN7nHKv9meZjgaIPsuiwT0Ao4LnM3ainM+4WajcMXFXdiTxBUSAZSVQqaMkJadKF/3W2f7oj9LBbWbjARDfNn/gjHmDpSSf2VgAU2hwD8Agb6Kdz7gZiS8SX0AkJGQzyF7flToNlSqPSm9PTOjmiQCaKJj4oswRiSyU+KLHF4DoC17I95P5in9tejjjHhJfAMLIU/WblVCJL8uSLnlIkiWtfFl68x5WeQTQcIFAjcb2JL6QwHwkvgCYEyx1lCh3jHvZzPgi8QVEgJVIze1raj9AuvwxSZa0+GnptTslf6XpqADEk10rpaP7peRmzt8UIFElpzkjpY4ADAgu1iVR7hj32nRzxsPFzmesBETiC4iAhK6J/9aPpKufliyv9MUL0qzrpOKVpqMCEC+Cs706D5G8yWZjAUyiuT0AgzyemomvRDypcZGUDCmzg7O9e53ZWAwh8QVEQMKt6vhN/UZJo/4meX3S129LTw2V/nqVtPrfTuP7xn5fbFuqOCaV7pEObJX2bpCKV0k7v5R2LJe2L5W2L6lxWyoVrZB2rZH2bZKO7JMC/nC+UwDhtuFdZ6TMEYmO5vYR9+STTyo/P1+pqakaPHiwFi9efMLHTp8+XcOGDVPLli3VsmVLFRQUnPTxQLyrWepIny8XCDW4X2M2DkOSTAcAuJEnEZvbf1OPy6Vb35E+eFxaPUfa+J5zk6SUTKn1ac7Vh+RmzqqQkpPYsgOSv1yqPOYkucoPS2UlUtkh5xZoaumkJaW1lNr2lHLOlHL7Sr2ulFKzmvi8AJqs4pi0qaqx/RkXmY0FMC1U6kiPr0iYPXu2xo8fr2nTpmnw4MGaOnWqRowYobVr16pt27bHPX7hwoW67rrrNHToUKWmpuqRRx7RxRdfrJUrV6pDhw4G3gEQWTVLHRP5lMY1WuY748FtRsMwhcQXEAFWIpc61tSun/SD56T9W6TFz0jrF0h7v3YSWTuWNe25vSlSUoozq8ybLFke56aanTgDUqBC8ldUJdKOSLKlo/ukLR85N0l6+9fSt++QBv9ESmvRtLgANN6WD52VYTPaS217mY4GMMvXzBlJfEXE448/rrFjx2rMmDGSpGnTpumNN97QjBkzdO+99x73+Oeff77Wv//85z/rX//6lxYsWKDRo0dHJWYgmryUOrpLZntnLNlhNg5DSHwBEeBNxFUdT6ZlZ2nEfzu3yjJp73onGVZxxOldUnms6oGWszpkUoqUlOqMvubObCxfc2eGWEpzZ9vjbXgcleXSsQPSoSJp1yqp+Ctp3VvSnnXSwinSov+Trp4m9bgsnO8eQH19/Y4znlHg/C0AEhnN7SOmvLxcS5Ys0YQJE0L3eTweFRQUaNGiRfV6jiNHjqiiokKtWrWKVJiAUTUPw5zTuECwx1cJM74AhIknUVd1rI+kFKfEMOdMA6/tk5q3dW7t+jr3FTwgrXpV+s/vnZr3l8dKP/6PlH169OMDEt36+c54OmWOAM3tI2fPnj3y+/3KycmpdX9OTo7WrKlf/5t77rlH7du3V0FBQZ1fLysrU1lZWejfJSUljQ8YMKDWqo4Bg4EgPEKJr8Sc8UVzeyACKHWMIx6v1Psa6ScfSZ3PdXqKvXiz02sIQPTs2+TMBvUkSV2Hm44GMI/m9jHr4Ycf1qxZs/TKK68oNTW1zsdMmTJFWVlZoVteXl6UowSaplbiixlf8S+Y+Dq4PSGbtpH4AiKAUsc45E2SrvmzlJ4tFa+Q3rrPdERAYllfVeaYN5jFJgCJ5vYRlJ2dLa/Xq+Li4lr3FxcXKzc396T7Pvroo3r44Yf19ttvq2/fvid83IQJE3Tw4MHQbevWrWGJHYgWD6WO7hLs8VVRKh07aDYWA0h8ARHgYcZXfMpsJ33vGUmW9PlfpJWvmo4ISBzBxNfpdZcNAQmH5vYR4/P5NHDgQC1YsCB0XyAQ0IIFCzRkyJAT7vf73/9eDz74oObNm6dBgwad9DVSUlKUmZlZ6wbEE8uyQn2+/CS+4p8v3VnZXkrIckcSX0AE0OMrjp1+oXTu3c72f35vNhYgUVQckza972yfQX8vQBLN7SNs/Pjxmj59up577jmtXr1at99+u0pLS0OrPI4ePbpW8/tHHnlEEydO1IwZM5Sfn6+ioiIVFRXp8OHDpt4CEHHBcxryXi4R6vO13WwcBjQq8fXkk08qPz9fqampGjx4sBYvXnzCx06fPl3Dhg1Ty5Yt1bJlSxUUFJz08YAbBK+OMC04Tg39qWR5pV0rnb5DACKr8GNnVktGOymnt+logNhAc/uIGjVqlB599FFNmjRJ/fv31/LlyzVv3rxQw/vCwkLt3Lkz9PinnnpK5eXluvbaa9WuXbvQ7dFHHzX1FoCI83BO4y4JnPhq8KqOs2fP1vjx4zVt2jQNHjxYU6dO1YgRI7R27Vq1bdv2uMcvXLhQ1113nYYOHarU1FQ98sgjuvjii7Vy5Up16NAhLG8CiDVeSh3jW3orKf8cZwbKmjekoeNMRwS429fBMscLa6+fDiQymttH3Lhx4zRuXN3H+IULF9b69+bNmyMfEBBjnBlfNuc0bhHs80Wp46k9/vjjGjt2rMaMGaNevXpp2rRpSk9P14wZM+p8/PPPP6877rhD/fv3V48ePfTnP/85VEMPuJXHE0x8cZSIWz1GOuOa183GAbidbUur/+1snzHCbCxALKHUEYBhtG9xmZorOyaYBiW+ysvLtWTJEhUUVDee9Xg8Kigo0KJFi+r1HEeOHFFFRYVatWrVsEiBOBIqdeQgEb96XOaMhZ9Ih3eZjQVws+1LpYOFUnIz+nsBNYWa21PqCMAMSh1dJitxSx0blPjas2eP/H5/qPY9KCcnR0VFRfV6jnvuuUft27evlTz7prKyMpWUlNS6AfGEVR1dIKuj1H6AJFta+6bpaAD3WvWKM3a/pHqGCwBmfAEwrrqKxXAgCA9KHaPj4Ycf1qxZs/TKK68oNTX1hI+bMmWKsrKyQre8vLwoRgk0XXWPL44Sca3H5c5IuSMQGbYtrXzV2T7zaqOhADEn1Nz+iNk4ACQsD+c07pLZ0RlLtifcUp0NSnxlZ2fL6/WquLi41v3FxcXKzc096b6PPvqoHn74Yb399tvq27fvSR87YcIEHTx4MHTbunVrQ8IEjGNasEsE+3xtXCiVHTIaCuBK25dIB7dKvubS6SeeCQ4kpFBz+yMJd4ICIDZ4aN/iLpntnLH8sFSWWFV1DUp8+Xw+DRw4sFZj+mCj+iFDhpxwv9///vd68MEHNW/ePA0aNOiUr5OSkqLMzMxaNyCeWFwdcYc23aVWp0n+cunr+aajAdxnZVWZYzfKHIHjBH8nbL/krzAbC4CERPsWl/E1k1JbONsJVu7Y4FLH8ePHa/r06Xruuee0evVq3X777SotLdWYMWMkSaNHj9aECRNCj3/kkUc0ceJEzZgxQ/n5+SoqKlJRUZEOHz4cvncBxBgv9fDuYFlSzyucbcodgfCqVeZ4lclIgNgUbG4v0eAegBGsVO9CWVXljgm2smODE1+jRo3So48+qkmTJql///5avny55s2bF2p4X1hYqJ07d4Ye/9RTT6m8vFzXXnut2rVrF7o9+uij4XsXQIwJTgu2OUjEv26XOuOm9yk1AcJp2+dSyTbKHIET8SZLniRnmwb3AAwIntP4uZrvHqEG94mV+EpqzE7jxo3TuHHj6vzawoULa/178+bNjXkJIK4FSx05SLhAu36S5ZFKd0uHiqpr4wE0zapXnbH7pZQ5AieSnO70YaHBPQADgqWOXPt1kcwOzphgia+oruoIJArq4V3Ely5ld3e2d35hNhbALSrLpS9nO9us5gicWM0G9wAQZazq6EIkvgCEi7fqN4uDhEu06+eMJL6A8Fg9x5lFmdFOOuNi09EAsSs4G5JSRwAGeDincZ9QqSPN7QE0UejqCFO+3CGU+FpuNAzANT77szMOvNnpYwSgbsEG9zS3B2AAM75cKKtqxhfN7QE0lUWpo7u07++MzPgCmq7oK6lwkWR5pbNuMh0NENuY8QXAINq3uFCo1JEZXwCaKLgCCldHXCK3jzOWbJcO7zYbCxDvPv+LM/a8gsUigFNJzXLGw7vMxgEgIYXOach8uUew1LH8kHSsxGwsUUTiC4gAr4cVUFwlJUNqfbqzXcSsL6DRjh2Uvqhqav+tsWZjAeJB217OWLTCbBwAEhIzvlzI10xKbeFsJ1CDexJfQAQESx39HCXcgwb3QNN9MdvpVdSmh5R/rulogNgXPPYUfWk2DgAJiR5fLpWAKzuS+AIigFJHF2rX3xl3LDcZBRC//JXS4qed7W/dKlV9mAZwEsHEV/FKKeA3GwuAhGNxTuNOCdjgnsQXEAFepgW7DzO+gKZZ9ldp73oprZXUd5TpaID40Oo0KbmZVHHE+f0BgCgKtm/hnMZlgn2+Dm41G0cUkfgCIoBpwS7Urq8zHtgiHd1vNhYg3pQdlt6b4mwPv0dKzTQbDxAvPB4pt7ezvZNyRwDRFTqnIfPlLjlVx5Wti83GEUUkvoAIYFqwC6W1lFp0drY5+QAaZtGfpNJdUssu0qBbTEcDxJfcqgsvO5cbDQNA4qF9i0t1Oc8Zt34qVZaZjSVKSHwBEcAKKC5FuSPQcIeKpY/+6GwXTJaSfGbjAeJNcMYxDe4BRJnFOY07ZXeTmudIlcekbZ+bjiYqSHwBERCsh7e5OuIu7fs7I1fdgfpbOMVZybHDIKnXVaajAeJP6KLLlxKfKwBEUXWPL/72uIplVa+uvfkDs7FECYkvIAKCpY5+Lo+4S/DkY8cys3EA8eLrd6QlM53tix9kJUegMdr0lDzJ0rEDCdWIGIB5oVJHzmncJ3+YM24i8QWgkWhu71Ltz3JOPvZtpNwROJUDhdLLt0qypYFjpM5DTUcExKckn9S2h7NNj0kAUUSpo4sF+3xtWyxVHDUbSxSQ+AIigKV/XSq9ldTzCmc7OIsFwPEqy6R/jnZWQG0/QLrkYdMRAfEtlx6TAKLPy8V892rVVcpoL/nLE2J1RxJfQAQEpwXT48uFBo5xxi9flMoOm40FiEW2Lb35K6ckOK2l9P3npORU01EB8Y0G9wAM8FRlC0h8uZBlSV2qyh0ToM8XiS8gAoLTgunx5UL5w5wrJOWHpK/+ZToaILZUlkuv3Vk1I9KSvvdnqWVn01EB8a9mg3sAiBLat7hcAvX5IvEFRICHenj38nikgTc725Q7AtWO7pf+/j1p+fOS5ZGueFw6o8B0VIA75PSWZEmHdkile0xHAyBBhHp8BQwHgsgIruy4fYlUXmo2lggj8QVEgLfqN4tSR5fqf4PT5H7HUvqtRMiTTz6p/Px8paamavDgwVq8+OS9B1588UX16NFDqamp6tOnj+bOnRulSCHblta9JU2/0Jkq72suXf9PadAtpiMD3COludT6NGd753KjoQBIHN7gqo6c07hTy3wpK08KVEiFn5iOJqJIfAERECp15CDhTs2ypZ4jnW1mfYXd7NmzNX78eE2ePFlLly5Vv379NGLECO3atavOx3/88ce67rrr9KMf/UjLli3TVVddpauuukpfffVVlCNPMLbtTI2fcYn0wg+kfRukzA7SLfOkMy4yHR3gPu3PcsZ590n7t5iNBUBCoNTR5SyrutxxyUxncSKXIvEFRICHacHuN6iqyf3Sv0lv3isdrjspg4Z7/PHHNXbsWI0ZM0a9evXStGnTlJ6erhkzZtT5+CeeeEKXXHKJfvnLX6pnz5568MEHddZZZ+lPf/pTlCN3OduWDhU5s7teHy893kt67gpp6ydSUqp0zl3STz6UcvuYjhRwp+H3OMnlPWulv1wk7VhuOiIALmfRvsX9+lzrjKvnSH++UNrztdl4IiTJdACAGwVXdTxUVqEPv6YXhyvZPdUj7xJlb50nffqU/J/P1O78kTrWvKMqUrNV6Wsh25Mk2/LItrzOFRU5Pxh21RgOpw/8jtKaZYTt+UwrLy/XkiVLNGHChNB9Ho9HBQUFWrRoUZ37LFq0SOPHj69134gRI/Tqq69GMtQQe98mle3eEJXXahj7G5tV/7ZtZ9sOyLIDUqBSCvidae7+clnlR6TKo7LKDktH9sg6skfW4WJ59q6Tdexg7VdITldl7x+o8tz/JzujvXNneWU03hyQeDLzZd00TymzfyjPrpWyn71M/tMvkt2yqwIt8yVfhuRNku31OX32ZFUddpp2zEnJ6SarRacwvAEA8SZ4TrOu+BDnNK7VTy3P/7O6LfqVkotWyD/tPO3pdKnKmnVQWbP2qkzOqDqnSZLt8VbtE95zmrSs1jq937lhea4TIfEFREBS1dq/W/cd1X/95VPD0SBybtS5ngH6RdI/1V8blLvhn1GPYHvHT9Sha8+ov26k7NmzR36/Xzk5ObXuz8nJ0Zo1a+rcp6ioqM7HFxUVnfB1ysrKVFZWPZ27pKSk0TFXLJ+t1PenNHr/eOK3LW2xc7QocKbmB87SomNnqmyRT1q0QtIK0+EBCaG57tZTyVM1TF8pafWrEX+98oseku+cOyP+OgBiT3JV4+JnP9qsZz/abDYYRFC62upBTU1+UkO1Sjkbo7ty/ZepA6V+70b0NUh8AREwoFMLFfTM0bb9R0yHggjbo6G61x6iQZVL1KdypVrYB9QycEDN7FJ55ZdHAXltf+jxVo1ZOOG4RpLu84XhWRLPlClT9MADD4TluexmbbQ6kBeW5wqP6p8su9Z29X22JL88suVRQJYq5VWF7VWFknRUKTqqFB2xU7RPmdpjZ2qvnamNdnttsnNVJn7mAJMOK103V9yjYf4VOs3arnyrWHnWbqVZZUpWpZJVKU/Vb3/NY06tWaAN0DWtVVjiBhB/fnh2nrbuP6LySvq3uF+Gfmc/pG9XLFanQKHaBnarTWC30uxj8sqvJFXKki2rqt9bOM9pjjbr2MRnODUSX0AEpCZ79eebBpkOA1E13HQArpCdnS2v16vi4uJa9xcXFys3N7fOfXJzcxv0eEmaMGFCrfLIkpIS5eU1LnnlO/sWdR5wU6P2BYDGuywqr+JL9p76QQBcadgZbTTsjDamw0BUXRD1V+wShdcg8QUAiBk+n08DBw7UggULdNVVV0mSAoGAFixYoHHjxtW5z5AhQ7RgwQL9/Oc/D903f/58DRky5ISvk5KSopSUlLDEbFmW0n0cTgEAAIBYxCd1AEBMGT9+vG666SYNGjRIZ599tqZOnarS0lKNGeOspDl69Gh16NBBU6Y4fbXuuusuDR8+XI899pguv/xyzZo1S59//rmeeeYZk28DAAAAQAwg8QUAiCmjRo3S7t27NWnSJBUVFal///6aN29eqIF9YWGhPFULSEjS0KFD9cILL+j+++/XfffdpzPOOEOvvvqqevfubeotAAAAAIgRlm3bjet0GUUlJSXKysrSwYMHlZmZaTocAIh7/F2tje8HAIQXf1dr4/sBAOHVkL+rnpN+FQAAAAAAAIhTJL4AAAAAAADgSiS+AAAAAAAA4EokvgAAAAAAAOBKJL4AAAAAAADgSiS+AAAAAAAA4EokvgAAAAAAAOBKJL4AAAAAAADgSiS+AAAAAAAA4EokvgAAAAAAAOBKSaYDqA/btiVJJSUlhiMBAHcI/j0N/n1NdBxnACC8OM7UxnEGAMKrIceZuEh8HTp0SJKUl5dnOBIAcJdDhw4pKyvLdBjGcZwBgMjgOOPgOAMAkVGf44xlx8FlmEAgoB07digjI0OWZdV7v5KSEuXl5Wnr1q3KzMyMYISxJVHft8R7573z3uvLtm0dOnRI7du3l8dD1TvHmYbjvSfee0/U9y3x3jnONB3HmYbjvfPeE+m9J+r7lqJznImLGV8ej0cdO3Zs9P6ZmZkJ98MjJe77lnjvvPfE05j3zhX4ahxnGo/3nnjvPVHft8R75zjTeBxnGo/3zntPJIn6vqXIHme4/AIAAAAAAABXIvEFAAAAAAAAV3J14islJUWTJ09WSkqK6VCiKlHft8R7573z3hFdifz9570n3ntP1Pct8d4T9b3HgkT+/vPeee+JJFHftxSd9x4Xze0BAAAAAACAhnL1jC8AAAAAAAAkLhJfAAAAAAAAcCUSXwAAAAAAAHAlEl8AAAAAAABwpbhPfD355JPKz89XamqqBg8erMWLF5/08S+++KJ69Oih1NRU9enTR3Pnzo1SpOHVkPc9ffp0DRs2TC1btlTLli1VUFBwyu9TLGvo/3nQrFmzZFmWrrrqqsgGGEENfe8HDhzQnXfeqXbt2iklJUXdunVLiJ95SZo6daq6d++utLQ05eXl6e6779axY8eiFG14vP/++xo5cqTat28vy7L06quvnnKfhQsX6qyzzlJKSopOP/10zZw5M+Jxul2iHmckjjWJeKzhOJNYxxmJY00s4DjDcSaRjjNS4h5rOM4YPM7YcWzWrFm2z+ezZ8yYYf//9u4mJKo9jOP4cx0dLbAkxLewQCEKKwJFUQspBMGodgrGYFBZaJuESrKYyDIRaSNW9EK1kCRCIVLsxXKh2cZmQNIMGyuCRhCCJCMd/d3FxSHLLp7jnDPO+f8+4OKezsDzZPd84d/kvHnzBocPH0ZMTAzGxsYWvL+3txc2mw319fUYHBzEmTNnEBERgYGBAZMnXxqte5eUlKCpqQkulwtDQ0M4cOAAVq9ejc+fP5s8+dJp3X3O6Ogo1q5dix07dmDfvn3mDBtgWnf/+fMnMjIyUFhYiJ6eHoyOjqK7uxtut9vkyZdO6+7Nzc2IjIxEc3MzRkdH8fjxYyQmJuL48eMmT740HR0dqK6uRmtrK0QEbW1t/3u/x+PBypUrUVlZicHBQTQ2NsJms6Gzs9OcgS1I1c4AbI2KrWFn1OsMwNYEGzvDzqjUGUDd1rAzwe1MSB98ZWZmoqKiwv/fMzMzSEpKwqVLlxa8v6ioCLt37553LSsrC0eOHDF0zkDTuvfvfD4foqOjcffuXaNGNIye3X0+H3JycnDz5k2UlpaGbCS07n716lWkpKRgamrKrBENo3X3iooK7Nq1a961yspK5ObmGjqnkRYTiZMnTyItLW3eteLiYhQUFBg4mbWp2hmArVGxNeyM2p0B2JpgYGfYGUCdzgDqtoad+U+wOhOy/9RxampK+vv7JT8/338tLCxM8vPzpa+vb8HX9PX1zbtfRKSgoOCv9y9Hevb+3eTkpExPT8uaNWuMGtMQenc/f/68xMXFycGDB80Y0xB6dn/48KFkZ2dLRUWFxMfHy+bNm6W2tlZmZmbMGjsg9Oyek5Mj/f39/rcPezwe6ejokMLCQlNmDhYrPOOWE1U7I8LWqNgadoadWSyrPOeWA3aGnZmjQmdE1G0NO6ONEc+58KUOFSzj4+MyMzMj8fHx867Hx8fL27dvF3yN1+td8H6v12vYnIGmZ+/fnTp1SpKSkv74w7Tc6dm9p6dHbt26JW6324QJjaNnd4/HI8+fP5f9+/dLR0eHjIyMSHl5uUxPT4vT6TRj7IDQs3tJSYmMj4/L9u3bBYD4fD45evSonD592oyRg+Zvz7hv377Jjx8/ZMWKFUGaLDSp2hkRtkbF1rAz7MxisTWBw86wM7+yemdE1G0NO6ONEZ0J2Xd8kT51dXXS0tIibW1tEhUVFexxDDUxMSEOh0Nu3LghsbGxwR7HdLOzsxIXFyfXr1+X9PR0KS4ulurqarl27VqwRzNcd3e31NbWypUrV+T169fS2toq7e3tUlNTE+zRiJTA1qiBnWFniIKFnVGHqq1hZwIrZN/xFRsbKzabTcbGxuZdHxsbk4SEhAVfk5CQoOn+5UjP3nMaGhqkrq5Onj17Jlu3bjVyTENo3f39+/fy4cMH2bNnj//a7OysiIiEh4fL8PCwpKamGjt0gOj5vicmJkpERITYbDb/tU2bNonX65WpqSmx2+2GzhwoenY/e/asOBwOOXTokIiIbNmyRb5//y5lZWVSXV0tYWHWPPP/2zNu1apV/Bt4HVTtjAhbo2Jr2Bl2ZrHYmsBhZ9iZX1m9MyLqtoad0caIzoTs75bdbpf09HTp6uryX5udnZWuri7Jzs5e8DXZ2dnz7hcRefr06V/vX4707C0iUl9fLzU1NdLZ2SkZGRlmjBpwWnffuHGjDAwMiNvt9n/t3btXdu7cKW63W5KTk80cf0n0fN9zc3NlZGTEH0YRkXfv3kliYmJIBGKOnt0nJyf/iMFcLP/7mYrWZIVn3HKiamdE2BoVW8POsDOLZZXn3HLAzrAzc1TojIi6rWFntDHkOaf7x+IvAy0tLYiMjMSdO3cwODiIsrIyxMTEwOv1AgAcDgeqqqr89/f29iI8PBwNDQ0YGhqC0+kMyY//1bp3XV0d7HY7Hjx4gC9fvvi/JiYmgrWCblp3/10ofwKK1t0/ffqE6OhoHDt2DMPDw3j06BHi4uJw4cKFYK2gm9bdnU4noqOjce/ePXg8Hjx58gSpqakoKioK1gq6TExMwOVyweVyQURw+fJluFwufPz4EQBQVVUFh8Phv3/uo39PnDiBoaEhNDU18SPml0jVzgBsjYqtYWfU6wzA1gQbO8POqNQZQN3WsDPB7UxIH3wBQGNjI9atWwe73Y7MzEy8evXK/2t5eXkoLS2dd//9+/exYcMG2O12pKWlob293eSJA0PL3uvXr4eI/PHldDrNHzwAtH7PfxXKkQC07/7y5UtkZWUhMjISKSkpuHjxInw+n8lTB4aW3aenp3Hu3DmkpqYiKioKycnJKC8vx9evX80ffAlevHix4P+7c7uWlpYiLy/vj9ds27YNdrsdKSkpuH37tulzW42qnQHYGhVbw86o1RmArVkO2Bl2RqXOAOq2hp0JXmf+ASz+PjkiIiIiIiIiIlJSyP6MLyIiIiIiIiIiov/Dgy8iIiIiIiIiIrIkHnwREREREREREZEl8eCLiIiIiIiIiIgsiQdfRERERERERERkSTz4IiIiIiIiIiIiS+LBFxERERERERERWRIPvoiIiIiIiIiIyJJ48EVERERERERERJbEgy8iIiIiIiIiIrIkHnwREREREREREZEl8eCLiIiIiIiIiIgs6V9K2z6Rxej58gAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(1, 3, figsize=(15, 5))\n", "\n", "axs[0].plot(r, rho, label='initial')\n", "axs[0].plot(r, rho_final, label='final')\n", "axs[0].set_title('Density')\n", "axs[0].legend()\n", "\n", "axs[1].plot(r, u, label='initial')\n", "axs[1].plot(r, u_final, label='final')\n", "axs[1].set_title('Velocity')\n", "axs[1].legend()\n", "\n", "axs[2].plot(r, p, label='initial')\n", "axs[2].plot(r, p_final, label='final')\n", "axs[2].set_title('Pressure')\n", "axs[2].legend()" ] } ], "metadata": { "kernelspec": { "display_name": "jclone", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.18" } }, "nbformat": 4, "nbformat_minor": 2 }