{ "cells": [ { "cell_type": "markdown", "metadata": { "cell_style": "center", "slideshow": { "slide_type": "slide" } }, "source": [ "\n", "\n", "# Class 12: System dynamics models: Damped oscillator and bungee jumping II\n", "\n", "---\n", "\n", "\n", "\n", "This notebook is licensed under a [Creative Commons Attribution-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-sa/4.0/)." ] }, { "cell_type": "markdown", "metadata": { "cell_style": "center", "slideshow": { "slide_type": "slide" } }, "source": [ "## Load packages" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "cell_style": "center", "slideshow": { "cell_style": "split", "slide_type": "-" } }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import numpy as np\n", "import pandas as pd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The physics of springs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Newton's Second Law\n", "\n", "\\begin{equation}\n", "m\\dfrac{dv}{dt}=\\sum{}F\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hooke's Law\n", "\n", "\\begin{equation}\n", "F_{\\text{spring}}=-kx\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Equation of motion\n", "\n", "\\begin{equation}\n", "m\\dfrac{dv}{dt}=k(x-x_{eq})\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## System dynamics diagram" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<img src=\"../../img/undamped_oscillator_diagram.svg\" width=\"600px\">" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Forward Euler method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<img src=\"../../img/forward_euler_method.svg\" width=\"600px\">" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Two stocks instead of one\n", "* The numerical method we've been using, the (forward) Euler method, states that each stock should be updated at the same time within each simulation step\n", "* It's worked so far!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Constants" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# related to time steps\n", "sim_time = 5.0 # s\n", "delta_t = 0.01 # s\n", "sim_steps = int(sim_time / delta_t)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# related to spring weight\n", "mass = 0.2 # kg\n", "spring_constant = 10 # N/m\n", "gravity_acceleration = -9.81 # m/s^2\n", "weight = mass * gravity_acceleration # N" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# related to spring length\n", "unweighted_length = 1.000 # m\n", "weight_displacement = 1.962 / 10 # m\n", "weighted_length = unweighted_length + weight_displacement # m\n", "init_displacement = 0.3 # m" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# initialize stocks\n", "length = weighted_length + init_displacement # m\n", "velocity = 0 # m/s" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation history" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "trace = [[0, length, 0]] # step_index, length, velocity" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Algorithm: Forward Euler method" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "for step_index in range(1, sim_steps + 1):\n", " restoring_spring_force = spring_constant * (length - unweighted_length)\n", " total_force = restoring_spring_force + weight\n", " acceleration = total_force / mass\n", "\n", " length += -velocity * delta_t\n", " velocity += delta_t * acceleration\n", "\n", " trace.append([step_index, length, velocity])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Convert results to data frame" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "simulation_df = pd.DataFrame({\n", " \"time\": [x[0] * delta_t for x in trace],\n", " \"length\": [x[1] for x in trace],\n", " \"velocity\": [x[2] for x in trace],\n", " \"method\": \"forward_euler\",\n", "})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualization" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "figwidth = 5 # inches\n", "figheight = 0.618 * figwidth # golden ratio\n", "figsize = (figwidth, 1.5 * figheight)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 600x556.2 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=2, ncols=1, figsize=figsize, dpi=120, sharex=True)\n", "ax[0].plot(simulation_df[\"time\"], simulation_df[\"length\"], \"-\")\n", "ax[1].plot(simulation_df[\"time\"], simulation_df[\"velocity\"], \"-\")\n", "ax[0].set_xlabel(\"time (s)\")\n", "ax[0].set_ylabel(\"length (m)\")\n", "ax[1].set_xlabel(\"time (s)\")\n", "ax[1].set_ylabel(\"velocity (m/s)\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Mid-point method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<img src=\"../../img/midpoint_euler_method_schematic.png\" width=\"600px\">" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Constants" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "sim_time = 5.0 # s\n", "delta_t = 0.01 # s\n", "sim_steps = int(sim_time / delta_t)\n", "\n", "mass = 0.2 # kg\n", "spring_constant = 10 # N/m\n", "gravity_acceleration = -9.81 # m/s^2\n", "weight = mass * gravity_acceleration\n", "\n", "unweighted_length = 1.000 # m\n", "weight_displacement = 1.962 / 10 # m\n", "weighted_length = unweighted_length + weight_displacement\n", "init_displacement = 0.3 # m\n", "\n", "length = weighted_length + init_displacement # m\n", "velocity = 0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation history" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "trace = [[0, length, 0]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Algorithm" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "for step_index in range(1, sim_steps + 1):\n", " velocity_old = velocity\n", " acceleration = (spring_constant * (length - unweighted_length) + weight) / mass\n", " velocity_half_step = velocity_old + acceleration * (delta_t / 2)\n", " length_half_step = length - velocity_old * (delta_t / 2)\n", " \n", " acceleration_half_step = (spring_constant * (length_half_step - unweighted_length) + weight) / mass\n", " \n", " velocity += acceleration_half_step * delta_t\n", " length += -velocity_half_step * delta_t\n", " trace.append([step_index, length, velocity])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Convert results to data frame" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "simulation_df_midpoint = pd.DataFrame({\n", " \"time\": [x[0] * delta_t for x in trace],\n", " \"length\": [x[1] for x in trace],\n", " \"velocity\": [x[2] for x in trace],\n", " \"method\": \"midpoint_euler\",\n", "})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualization" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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2C/aVZa3qta5bn4kkaSrS8yKKEwKPalktBDev0sCpyEuW58+/IhTviCEUQo1z/YZMeQzbS01C4HA6RlxoH3YBwKqFDQBsLkhBRoIDAISlr2Bi2osznWxU3Y3lq7t5AixszJsnHxLTYWRmPH55Ws5NG7Nhs65ONCfH2rFzLWuefETss4w/QGUFeV9Z1rKri+cSY7PiRsmYPNIyBJ8Iz8twT97OtWlIl2TrSiGE4MaNTP4cuzwiRmBGCM0rhISQMkLIw4SQZTV7IoTEE0LaCCG6TlSKsVlx3XqW9Pxa64iYuSuhvMnxfKnVYLEQ7JcUntdah8X0AYmjrUNy1ev+suyrP3iJ3CDt85nOMYxPi5m7APDG5WG4vUyZWG24mMO9X1dGpnFFMp7MzvnucYxLHRtuXmGRw1z4PjvdPpzrFqNGAWawd0jNqG8oD4/cuFF6nVlfAG9cHg7LawpC0axCSAi5mRDyBoBmAJ8GsNweDF8GUBL2hanA3g1M4AxPzeJiv5jyAACHLzGBkJkYg025yWF5TS5wpj1+nGwfC8tr6p3DUvg8zm7FzpLVhTE5/AYRoJBHDpodvg82C8HeJY72Woz9inDokRbhJQSA1xTnbW8YDEkAIaPYjlwS5xkI/V6H6zxftz5Trp4XYePIoFmFEMA+AC0A3gLg4eU8kRBSA+CfAbwegXVFnX0bgoL9qBDs8PgCOCZZiPs2ZMJiWVk15lz2bciCVXotkbjM2vrwMOa1pRmIsS2vSfJC7FibJs+QFvmajNdb2XmuKU5DQszqwpicjblJyJZmSB8W+wwgqKisz05cdd4xJzs5FhulCUlC8Wbw+1RmoiNsBntCjA2717E0iFcvDoouBRFAswohpfRBSukHKKUHASz5kyeEWAH8DMAfAbwcqfVFk+KMeKyR+jAJjwpQ1zkGl5RDstqkcCUp8XZsL2ZeMKEQAhf7nRh0svnO+8OQP8iJsVlxbSnzGhy+NGT6NIiBSTdaBqcAMC9IuCCEyF7CY20jpk+DmJr1oU7Kh70+jPsMBOXQua5x0w8R8PoDeKOVVbbv3ZAVNoMdCEZxeifcuDwk0iDCjWYVwlXwSbBQ8b+ovZBwwt3uJ66Mmj6hVpk/eH2YwhEcno/YNuQy/Zikw4p93h9GxRsI5hEOT83iQr+5289w7yAQifPM9nna48fpK+ZOgzjeNgKfZHyEK4zJ4a8XoMDrJs9vO9c1DqfUIi3c+6w0mI61iXZK4cZQCiEhZC2ALwH4NKV0yS4eQkg2IaRS+QOgNELLXBE8j9DjC8jNa80KD8tUF6TI857DxTWlwakFtSYXOFxRWZMRjzUZCWF9beWNorbN3Of5NWmfE2Ns2FK4sukkC7F3Qya4g+aIyaMLyjzN3SucTrIQO9emI0ZqcG32qm7lOQu3J7YsJ1HuBlEr+muGnfAkq2iHHwE4DeC/l/m8jwP44nx/qK2tRX9/PwoLC1FSUoKjR4/Kfztw4ADq6+sxOMh0z/LyciQkJKCurg4AkJCQgD179qC2thYuF3Nv19TUwOVyobm5GQCQnZ2N6upqHDx4UH7dvXv3or29Hd3d3QCAkpISbM5Jh4UwC/R/Xj2L/WU3o66uDmNjzOqvqqoCADQ0NAAA0tLSUFNTg6NHj8LjYZWcu3fvxuDgINrb2wFA9WvKzs7G8ePHAQAOhwN79+5d9JpKN1ajUWpoXGSfwtTUVFivacI5BYcF8ASAg/WdSBq9GPFr0uLndKWzCyfaWLh4R1Gy/JhwXVNBQQFyk2PQPzmLp45fxNrZNs2fvUh8TvHx8Xi9lV3L+uQADh96NazX1HaxAUWJBB1Oitcu9WOgJk3zZy9Sn9ML5zoAABuzYuAggZD3Dsc1VWY5UNfnxssN3TiYOhSVa9Li5/RcHQuZr0mxof7k62G/po0ZNrzu8uDIxT50dXUhMTFR82cvWp9TbW0tVgPRQ2ImIeQhAF+klC6YjEAIeR+AXwGoAXBR+vUXADwIwA4gQCmdt0kUISQbwNyYWCmAJxsaGlBZWbmq9YeLu3/4Ouo6x1FdkIKn7r9e7eWowsELA/jIr08BAH794V1hD2UCwH2/OI6jLcNYkxGPw5++MeyvrwfqOsdw9w/fAAB8991b8M5tyy3yX5xP/s8ZPHG2Fylxdpx58Oaw5hrphZYBJ27+7hEAwEN3VuCD14W/McJXnm7CL15rh81CcP6hW1bde0+PDE66sethpgB86uYyfOLAhrC/xw8PteKbz7Mb9LHP3xS2ohU9MePxY/OXXoDXT/Hh60rwhTsrwv4ev63twINPMCXshU/uQ3nu6prlG4nGxkauqFZRShuX+3wjhYy54lcPwCv9PCj9zYureA0ppYOU0kblD4DLkV7wctlVwsIcjb0TcLrNmbh8vJ2FF60WIs/FDTc8bNwxMo3ecXOOsTuuCOPuLglveI2zRwrbTcx4TZtHqExLCGdBiZLdJawy0xegON1hzjxCZZrNnjCHiznK78mJdnOmQZzpGoPXz5xMu6RzF26uUXx+x0yerxlujKQQ3gtg55yfn0l/2wngIXWWFT64YA9QmFawc4WwKj9ZnuASbpQ3jOPt5sxT4dddlB6H/NTIeDpC9tmkeYQnpEKP9AQH1ksTXMINn1gCmHifJbnhsFqwOcx5mpzqghTE2tkt9bhJFUKlIrza8YsLUZqVgCypnZIoLAkvulUICSF2QkgFIcQCAJTSekrpKeUPgF7pb6copVfUXG84qFmTBiJF1cxogbpmfWjomQAQOesTYII9QeqTd8yEics+fwCnJEUlUt5BgBWr5CQzwW7GAh5KKU5K3+Mda9JASGRC5mkJDrlPnlkNHC4vtxalItYenn6ac3HYLKiR2laZUT4Dweten52IjDAX/HEIIbKX8Hj7qOnbVoUT3SqEAN4O4A0AO9ReSLRIibPLTT5PmrDS+HTHGPzSlz+SiordasEOyatiRgu0sXcSU1LbiEiF1wAm2PeYWLB3j82gf5K1NoqkgQMEowvnuibg9pqrbdXEjBfNA2zCU7im7SwE/xxbB6cwPDUb0ffSGh5fQO7zGOnzzNN6xqeDn61g9ehCIaSUPjS3oIRS+hilNJVSemI5z9M7u0ws2Ln1SUhoGCwS8I74XaMzGJw0Vz9CpRdpd4QFuzKP0GxjGZVG3Y6In2e2zx5/8KZtFk53jILXTkZabigVoVMmM9rreybkedyRlhvKcLTZznMk0YVCKAjCv2gefwBnu8w1SJ0rKhtzk5ESb4/oe+1YExRoZsvXPCHNcc5PiUVRenxE30t5gz5tMsF+UgrLx9mtqMwPz3ivhVAqKmYLZ/LzbCGIWCEap6Y4DXYr80GYLY8wNH8wsgrhusxEpMSxe4DZG66HE6EQ6gylJ+GkiQTOrM+Pc11S/mCEkpWVbC5MgU1qg2ImhZBSijOSYhZprxUArMtMQKqk3J8x0T4DQQ9hzZpU2K2RFcWZiTFYl8mai5vpPAPBfa7IT0ZSbGQNyVi7FVsKUwGYT/Hm+xzJQjSORdFlwmyGZCQRCqHOyEqKwbosJthPmkiwN/ZOwuNn4YjtUVBUYu1WVBawakQzCZyOkWmMuFhT1Zri1Ii/n8VCsK2IvY+Z9nnU5UGrNL9Y6Y2OJNukgoezXeOmydd0e/04380iKZH2WnG2SwbrxX4npj2+qLyn2lBK5dBttM4zVwg7RqYx5DRXvmakEAqhDuGVbGc7x0wj2OsUym80FBUA2C7tc0OPefI1lfk4NREOr3GUgt0sifhKL12kE/A5fJ+dbh8uD01F5T3VpqFnQu6LFy1Fhctnf4DifPdEVN5Tba6MTGN8mvXG3RYl+cz3GTCf1ztSCIVQh/AvwqTbh7Zhl8qriQ5npHzJ7KQYFEQ4HMHhN1Cvn8rtbowOVwhj7RZsyotsXhtHqXjWmUSw8322ENYKJRrUrAm+j1kS8ZV51lujpKgoFSLz7HPwOrcVRceQ3FqUCquU1mOWfY40QiHUIWYUODy/bFtxasT6tc1FeQM1iwV6uoPdQDcXRj6vjbOlMBV8ap1ZwsZnO9k+l+UkISFCDdbnsiE7SW7mXtdhjoI0rhBmJcUgPyU2Ku+ZnRSLwjRmtJ7pNMc+8+uMsVmwMS86o+TiHMFiLLNVdEcKoRDqkLKcJMRLjZPNIHD6J9zonWCtX5RhgkiTlxIneyPNoBBOzfrQLI2Qi+Y+J8TYZG/kGRMoKiyUyK5zWxT32WohsjfSLIYkVwi3FkXPkASCn+uZzjFQavy0Hr7PVQUpUTMkgWAUp6Fn0jRpPZFEKIQ6xGohciXbGRMIdjXy2jhyJVuH8QX7+a5x8JTUaOVpcrgCeq57HB5fIKrvHW1aBp1wedjNa1uUwsUc/rm2DE5hYsbY89CHp2bRPcZmkUcrLM/h+zw85ZHXYFTcXj+aepkhGf3zzOSGxx9AU58556GHE6EQ6hQeNr404JSnShgVrvTaLATVBZGZQ7oQfJ9HXMYX7EovqFqK96wvgAsGF+xKr360EvDl91N8rkbvY3pWuc9RVlSUnl+je2MbeyfgkyzJaOVpcpSK/nmDn+doIBRCncItowA1/hehThLsFfnJEZtDuhCbCxUCx+AVg1xBKE6PR2aE5pAuhFIxOtdt7PPMFZWkGBtKsxKj+t41ReYp4OHnmRCgujC6hmRFXjIcNnZ7NXpaj/L6ou2JLUyLQ5rUx/ScweVzNBAKoU5RWmJnDKwQev0B1EsVvtHMa+NU5ifLDarPG1xR4fu8Oco3T4ApoXzyAG9AblTOSBWZW4pSYbFEd7JmSrxd7mNq9PPMFcIN2YkRb0g9F4fNIkczjO4hVBbuRKsDBIcQgi2SEmp0QzIaCIVQp2QmxqBYGitm5DzCloEpOadMDUUl1m5FWQ6rmjOywBmcdGNQau4a7bA8wAQ7/3yNrKg43V60SA2po+1N4WyWPt/6ngnD5sUGAhTnFAUlasDf90LfJGZ9xi144B7CaBfucHgUp23IhUm3sfNiI41QCHUMt4yMHMps6A1eW5UKigoAbCli79vQM2nYRuBa2GeuELYOTcFl0LzY890T4DqYagphYbDggVfvG4224Sk4pTO0NUp98ebCz7PXT9Hc71RlDZFm0OlGzzjLrY52Pixni8JR0GDge2E0EAqhjuGW/qBzFgOTxhTsvCF0rN0iz2KNNvwGOjXrQ9uwMSc8NPQECzmq8tVSCNk+UwrDNgJXepm3qKYQBj/feoN6Y9XMa+OYIf/4rMb2+axBz3O0EAqhjlEmShtV4HDFoCIvGbYo9rdSoryBnjVofhvf56L0OKTERzffirPZBOe5UVK881JikZUU3cIdTmV+itwI3KiJ+DyvLc5uRVlOdAt3OGvS45EUyxqB1xt8nwkJVcyiiTJ38bxB5XO0EAqhjqnMTwZP2TCipe8PULm3lFphTIA1Ao+RKgaNmt/GFUI18gc5uclBJcmo+Zo8NK/meY5zBPNijaqo8PNTXZiimiFpUbTJOm9QjzdXCMtzglNw1MAM+cfRQCiEOiYp1i6HUY0ocC4PTcHtZQUlaoUxAcButcgjkozoURmZmpVzySpV3GdCiJwPVG/A8zwx40XHyDQAdc8zEHoDNVphidvrx8U+lrMX7f6Dc+FRnEsDTsNN0ggEqGxQbFHJO8jh3sneCTcGncZMn4oGQiHUOfyLUN9tvIpBZR6Zmh4VILjPF3onDTdJo6FXkT+okX3uGJnG+LRH1bWEm6aQfU5WcSVAtbTPk26frKQahaa+SblRslp5mpzNBez9ldEOo9AxOi0X7lSp0AFCibKwRISNV45QCHUOD0mMuIxXMcgLHRw2CzaolAfE4ZXGHn/AcBWDIYp3vtqKinHzCBs1UMnN2ax4f6NFF5TnWc0UCGBuAY+x9rleQ/tcVZgip0+JsPHKEQqhzjFyxSAX7Jtyk6I6MH0+lCERo+W3cUUlPyUWGVGeUDKXLSGVmcbaZ36eMxNjkK1SQQlnY14S7Fap4brBGtvzfU6OtaEwLbqNkudSmBaHVHmShjH32WYh2JibpOpakhXpU0ZM64kWQiHUORX5yXLFoJE8KoEAlRWVSpWtTwBYm5EgVwyeM9gNlFv6anutACA9wSHfxI10noFgaL6qIFmVBr5KYmxWbMxl3mBl1a3VAAAgAElEQVTjeQiDhWhq7zMhwcISo3kIuUK4IScp6iNF54Mbk0bMi40WQiHUOfEOGzZkSxWDBhLs7SMuuDwsCVvtBHyAVQwGE/GNs88T0150jbLGslpQCAGlYDfOPrtmfbg8xHpYauE8A8HoQkPPBPwGabju9vpxaYCldKgdxuQYseE6pVTRmUDdNBMO3+exaS+6x2ZUXo0+EQqhAahWKCpGsYy0lAfE4QUPLYNOTHuMIdiVE0q0ss/8PPdPujFokIbrF/om5QklaheUcPgNdNrjR9uQMRquXxpwygUlWogsAEB1QbDhemOvMQpLOkenMelmMlA7ciOYbmLUxvaRRiiEBoAL9omZoLdH73DBabMQlOWqW1DC4YIvQIELfcYoLFEKzkqNKSqAcfKBQvZZIx5CrqgAxtlnLRU6cEIbrhsj3aReQx0gOJvykuT0KaWhK1g6QiE0ANUhFYMGETjSDYo1hVY/PwWA3IsQAJoMInC4YM9OikF2UqzKq2EobzCNBtlnnj+YEmdXvdCBU5aTKDdcN0pBGs8fTIyxYU16vMqrYeSlxCJTKtYySloPvw6rhWBTnjYMyXiHDaVZzHlgFE9stBEKoQHYlJcMm2QaGSFxmVIqW3hasfIBoFgxiko5+1fPcMGppX1OjrVjTQa7mRtFsCsnwahd6MCxWS2okIycBoPsMzcgKvKTYbFoY58JMV7+sVxQkp2oiYISDjfaG3qMkz4VTYRCaABi7VZskEZRGaG1QdfoDJxSfopW8q0AJti5wGns079gd7q9aB92AdBOvhVH3mcDeFTcXj9aBlmOnlbC8hxuCDT1Tuq+sMTjC8gTSrRk4ABBr3f7sAtOt1fl1awOVlCi/kjR+eDrGZ7yYNA5q/Jq9IdQCA0Cr/Rq7J3UvWVUH5LXpi2Bw/O/mvudup9YovS+ae0Gyve5d8KNUZe+J5Y09ztlZUsrFcYcvp4Zr/4LS1oGnfD4pVGXGlO8lQ3f9e717hqdwcQMU2q1JjcqQvZZ/8ZktAmLQkgYaYSQXEKINhKRTAb/YjrdPnSO6nsUFQ8XWy0EFRrJT+HwG43XT+X2FnoldDSgtva50kCCvUFDE0rmovRY6j0Rv1GRxqE1xVs5gUfvFbBaLCjhKAu2jJLWE01WrBASQnYQQr5HCDkDYBbAMIAeAC5CSB8h5ElCyH2EEG1k9hocpSdN74nLXGCuz9JWfgoQKnCadG7pBydnOJCbrC07TrnPeveoaLHQgVOWkwSHlReW6HufudyLs1uxLksbnQk4ucmxyEhwAND/eeb7bCHQnMGeEmdHUTor2tK7IakGy1YICSHlhJAXAZwA8HYADQAeAvBPAP4ewOcBPAIgDcDPAbQRQj4crgUL5qciLxlWKYlaz5aRsuGp1vKtAGBdZgJi7exro3ePCi8kqMzXTqEDJyspBjnJrDJT7x4Vvn4tFTpw7FYLNuax/GP9n+fgPls1ts+EENmbZhSDfUN2EuIc2jLYgaB3WM/3QbVYlkJICHkbgJMAxgDsopSWUErvo5Q+TCn9EaX0vyml36SUfppSug9AOoAHAXyBEPIIIcQW/ksQAFJhSTazivV8A+2dcGNsWpv5KQCrzOQjv/Rs6U97FJMzNKh4A0HBrmdPrMcXQHM/Sy3QWhiTU6nY54BOC0t8/gAu9EmFDvkaPc/S9+zy0JRuG9tTGhwpqrVwMYevq2d8BmM6zz+ONktWCAkh6wH8AsA9lNJ3U0pPLfYcSqmLUvozAFUAEgF8dcUrFSwKF+wNvfotuVe2zdGuwGGCXc+VmU29wckZWlS8gWAeYduwC1M6Hfml5UIHDv/8p2Z9uDLiUnk1K+PykAtuL99nbZ5nbhBQql8jR2mwa/U8KwtLmvr0uc9qsWSFkFLaCmAdpfTF5b4JpXQKwD1g3kJBhOCVxuM6nuXIrU+iwfwUjrIys31Yn5WZWpycMRdlXuwFnQr2kEIHrSoqIYUl+tznBg0XOnCU69JrFEcPcqMqX//7rBbLCuFSSt9kPhJCMgDsApAJ4E2JG5TS30j/1aeJryPmCpwijSWwLwX+BV6XmYCEGG1mGMwteFifnaTialZGvaSopMZrZ3LGXJSVxg09E9i5Nl3F1awMntcWa7fIUxS0RllOEmwWAl+A5e/etSVf7SUtG56X57BZsD5bm/tcmBaHlDg7Jma8ulW8lWkyFRoNzWclxSA7KQaDzlldp/WowarazhBCbgPQBuBpAL8G8Ks5P79czesLlkdFfjKIjmc5UkplRUWrVj4AlOUmypNh9GqBynlAGiwo4RSkxiE13g5Av/mackFJnvYKHTixdivKpMb2ej/Pm/KSYbdqs70uIUQOz+t2n6V1l2QmIFGjBjsQvH/o8T6oJqv95nwNwCUAewGUzPOzbpWvL1gGylmO9TqssBp0zmJ4inWX12oCPgDE2IKTYfSoqCgnZ2hZ8VZOhtHjDdQfoHIOk5b3GQiGjfU48ssfoPL3UKsFJRzeOaFlcApur1/l1SyfRrkzgcb3WVpf+7ALLp3mH6vBahXCMgBfoZS+QSntmO9nNS9OCCkjhDxMCOlawmPTCCE/IoT0EkJmCCGNhJD7CSHaNBcjBLdAG3Uo2PWQB8Sp0vHMzAt9wWIYrSaGc7hh0KrDG2jb0FSw0EHDBg4Q/L5Nun3oGtVX/nH7sAvTHnY2tC43uHz2B6ju8mKHp2bRP+kGoN38QU6looBHb/usJqtVlgYAhP1uSAi5mRDyBoBmAJ8GULjI420AXgbwDgBfkf77EoD/AvC5cK9Py3DLaMTlQd+EW+XVLA9lfy6t5qdwlDdQvRXwNGh4ZN1c+DnwBfQ3GUYZrtJiT00lIfnHOguzKRsQa17xVhY86Cy6oIyGaN6QLAjNPxYsjdUqhD8G8HlCSFo4FqNgH4AWAG8B8PASHn8XgBoA90n9EF+glH4SwDNgzbJNQ7WOK9l4I9E1GfFIibOrvJqro+fRag1Sa5+kWBuKNV54pFRU9Bae55M/HFYLNmi88GhTbjJ4iqPe5AY/FzYLQVmuNgtKOMXp8UiScu8adbfP2q8w5hSkxsn3EL3JDTVZrUL4EzDvXT8hpG2en8sreVFK6YOU0g9QSg9iaR5IL4DfAXhtzu+bwJpjm4aKfP1aRlpveKpkU56igEdn+ZrcA1SZn6zZghJOSUYC4qVpCHo7z3yfy3OT4LBpO3MlzmGVq3P1NkmDn4uynCTE2LQ3OUOJxUJkb7He9pm3UMpLiUW6NIZPq7DJMFJaj1AIl0w4PIQFYIrY4Xl+jqzy9ZcEpfQpSun7KaVzY6Q3AHhlsecTQrIJIZXKHwClkVhrpEmKtWNdZgIAfX0Rhqdm5RC31sM+AJAQY0OJtM968hDO+vxy6FXr4WKA3UB5P0o9WfqBAJWbD2s9vMbhhlhj76Ru8mLZ5Ax9FDpwuHy7NODErE8/ebGNsiGpfbkBBNfZorN9VpPV1o2/DcAXKaWam0BCCPknANuwtJDxxwF8cb4/1NbWor+/H4WFhSgpKcHRo0flvx04cAD19fUYHBwEAJSXlyMhIQF1dXUAgISEBOzZswe1tbVwuVgLx5qaGrhcLjQ3NwMAsrOzUV1djYMHD8qvu3fvXrS3t6O7uxsAUFJSguzsbBw/fhwA4HA4sHfvXtTV1WFsbAwAUFVVBQBoaGhAptWDNjAL9OjRo/B42Pie3bt3Y3BwEO3t7QCgqWu6OB60TbyDl3Hw4JWQawKAtLQ01NTUaOaaKnJT0TbkQl37EA4ePLjsz0mNazrdPgSvn93sk/3sRhrOsxeJa0oOsHU29ozD5w/g1MkTUf0+reSaBlwBebpKGp2S16MVGTHfNTlcbL2jLg8ee/Yg0mOJpmTEfNeUXrQBEzNscoZ9qh91dX5NyYj5rmlDJpvR7fVT/OH5o/i7t92gKRkx3zU99fzLuDLCOkBszElAc3OzpmTEfNeEUSY3fAGKo+cvg4x1Letz0uI1LfY51dbWYjWQ1ViChJAxAO+ilC7qhVvFezwEpnQuObZFCLkFLH/ws5TS7yzh8dkAsub8uhTAkw0NDaisrFzGitXnp0cu4+FnLwIATvzrAWQnx6q8osX5waut+NYL7HCfefBmpGk8JAEAPzl8GV97Tl/7/PsTnfj8n+sBAAcf2K/ZZslK/niqC5957DwA4MV/2Sf3zNMyT53rxf2/PwMAeOJ/X4etRakqr2hxTl4Zxd/8+BgA4Cf3bcetlbkqr2hxnm/oxz8+choA8Ng/XoMdOmhe3jo4hbd85zAA4Gt3V+O9u4pVXtHiHG8bwbt/ypSNn/3dDtxckaPyihZHj/u8WhobG7miWkUpbVzu81cbMn4WwO5VvkZYIYTsBPA4gJ8uRRkEAErpIKW0UfkDYEX5j1pAGXLVS54Kn2FckBqnC2UQ0GfBAz8PCQ4rSjISVF7N0pg7sUQP8PxBq4VgY672FVggNC9WLwUPylGXmzQ66nIuJZn6y4tVph/pJTSv3Gc9pfWoyWpDxlcAfIEQkgNgdJ6/U0rpV1b5HkuGEFIG5hl8CsD90XpfrVEZUmk8iQObtG/NNcgFJfoQNsCbFZUbN2aruJqlwW/0lfkpsGh0csZcNmQnwWG1wOMPoLF3EnfXqL2ixeEJ+BuyExFr13ahAydRyottG3LpJv+YG2IlGh51ORerhTVcP3llTDcKIVeo0hMcyEvRfiQEYPtckZeMUx1juiv8U4vVfoM+L/33Ewv8nYL1BYw4hJA8AC8AOAHgA5TSQDTeV4ukxNlRnB6PztFpXXgIx1weuZefHgodOKnxDhSkxqFnfEYXHkKvP4AL/aygROt98ZQ4bBaU5SaioWdSFzdQSqnCwNHPeQbY969tyKULuQEEPWx6KERTUpmfgpNXxnCh3wmvP6DZcXscbuDooTOBksp8phBe7J+Ezx+ATeP7rDar2h1KqWWRn4iYxoQQOyGkgk8hIYQkA3geTMH9TwC7CSHXK36MnzwwB3liiQ5c5UplqlJnN9BgawPt73PLwBQ8Pn1MzpgLX29T7yQCAW1XwPaMz2B8mhU6aH2U2lz4Pg85ZzE4qe3G9oNONwadrNBBL2FMDpfPHl8ALQNTKq/m6ri9frQOsTVqfWDAXPj9xO0N4PKQS+XVaJ8lK4SEkBxCyN+u9I0kBe6mlT5/Dm8H8AaAHdL/1wDYDNYT8UUAR+f8fDhM76sbuAeob8ItzwfWKg06mjQwF97aoHtsBuPTHpVXc3WU+1xdqLd9ZufZOetD19i0yqu5OnoawTgXpedY60ZO6OQMfe2znibDNPc7g6MudSaflevVg3NEbZbjIZwCm0ry34SQZWVJE0L+BsAhAMsei0ApfWhuhTGl9DFKaSql9IT0/4copeQqPw8t9331jjL0qvXwD19fbnIsspJiVF7N8lDmPGo9bMwVlVi7Re5VqRcqdVTAw/OV9FTowFH2mOOTVrRKkw4LHTilWQmItbPbr9YLeEJGMOpsnzfkJMIhhYlFHuHiLFkhpJS6AOwHsBZAGyHk3wghmxd6PCGkgBDyEUJILVgD6w9SSp9e7YIFSyPEMtK4wOHr01NBCadKR6MC+foq8pJ1l0ujp9Fq/Aa6TkeFDpyUODvWZDC7XeueK34OClLjkBqvj84EHJvVIhsLWjfYuQGW4LBirU46E3DsVgs25jH/ldbPsxZY1l2BUjpCKb0JwAMA3g/gDCFklBDSSAg5TAg5RAg5RQgZAtAJ4LsATgEop5Q+G/bVCxYkLYEVPADaFjiTbi+ujLAQoF464CvJTopFtuTV1PI++/wBNPXxyRn62+c4h1XumahlDyGlNFjooMN9BoLGpOYNSZ1NgpmLnBfbNymHZLUIPwcV+cm66UygpFJH+cdqsyI3AaX0N5TSTQD2APgqgJMAnABmAbQB+AWAewDkUkr/iVI6HKb1CpYBDxtr2VXeqFibniqMlShHfmmVtmEX3F6poET3+zyh2dFqg85ZDE+xXFK95Vtx+D73TrgxotH844lpLzpH9WtIAkF5xwoetFlYEtKZQOf7PDXrw5URUVhyNVZbZXySUvodSukHKaVvo5TeSim9l1L6OUrpXyil2s7+Njjccu4Zn8GYS5sFD8pEX70rKu3DLjjdXpVXMz8hhQ46Few8f2l4yiNXl2oNPReUcKpCCku0aeQ09in3WZ8ewpACHo16Yy8PBTsT6C1/kKOH86wV9JVIJFgWeqhk44IwMzEGOcn6KijhKFuLaNVLyMPZDpsFG3K0P65uPpQeCq3eQJXeeL216OBU6WCfQwtK9Kl4l+Ukab7gQRnB0fM+26RQt9bTINRGKIQGpkoHlcb1ioISPTU8VaJs4aLVGygX7JtykzTfBHchKkImw2jzBsoNrzUZ8UiJs6u8mpWhzD/W6nlWGpLZOutMwAkpeNDqPkvn2WHVryEZa7digzT/XKv3Qa2gzzuDYElkJsbIY4YaNXgDdc360DbMcjr0GsYEWLucDGn+shY9hIEAlUPzemv8rURZAatVwS5XzOv4PAPab7jOv2d6m5wxF+51a+yd0GTBA9/nch0bkgBQzc9zj3bzj7WAfj9hwZLgAkeLN9Cmvknw76Ze860AgBAiK1pa3Of2ERdcHj8A/RbucKrkQint7fPI1Cx6J9h0Dz2NBpwPrtB2jWqv4fqMxy8XYeg1f5DDv48uj19zBQ+BAMUFnVdyc7jcmHT75DGpgjcjFEKDwwVO5+g0Jqa1VfAQmoCvb4HDLdDLQ1OY9vhUXk0oRigo4fDz3D/pxpDGCkuUCet63+cqRRqE1rzeF/onwZ1pes1r4yjlntaMyc7RaThnmSyr0Pk+6yH/WAssWyEkhLyyjJ+DkVi0YOmETtLQ1heB54GlxtvlnCW9whUASoELfdq6gXIBaLcSlOXqMw+Io+WCB+V69FqRydHyPjcayMApz1UUPGhM8Q4ZDajz81yRF2xsrzXFW0usxENoAUCW+CM8kCpTreFKY36jqS5I0XUeEDCngKdba/vMBHtZThJibFaVV7M6tOxR4ec5PyUWGYn6LHTgZCUFq/61ts9cUUmKtaEoXd+GZIzNijJe8KA1uSHdLywE2Jirb4UwzmHF+mxmDIvWMwuz7LlKlNIbIrAOQYTIluYDDzlnUa+hwhK3149WKQ9I72EfAChMi0NKnB0TM15NCZxAQDE5wwD7nBrvQFF6HLpGZzSnqJyXbuibC1NVXkl4qC5IwcDkoOY8V1xR0XtBCae6IAVNfZNokBqua+Wa+OdempWIOIe+DUmAyb9LA1No7NHWPmsJ4cEzAdUaTMRv7A2Oa9J7/iDACkuqFJVsWuHKiEvOA9pcpH+FENDmeR6ZmkXPOEtWV7Yh0jPcUNNSw3WPL4BL/VJBiQEMHCAo/5xuH7pGtVHwQClVzJg3xj7zwr8Rlwf9k26VV6NNhEJoAnj+h5YEe333uPzvLQbxqHDB2TI4BbfXr/JqGEov2uYCY+1z34QbwxoZrRayzwZRCJWKgFa8hC2DTnj80uQMAxiSQGgrKK14vXsn3BiRplvpPR+Wo8yD1Fp4XisIhdAEaFGw8/BaWrwdhWn6zgPicI+FP0BxUZr/qTbnuoKNZctzk1ReTXgIyYvVyA1UeYPRe2sfjtb32Sgewoq8ZFiliget5Hmf71IY7EXGMCRDGttr5D6oNYRCaAKqNCjYz/OCksJUw+RyVGvQ0q/vYYJ9U14SHDZjfN21WAHLz3NxejxS4x0qryY85CTHIDNRWw3Xz0kKYYLDinVZ+q6Y58TarVgvXYvWzrOFGMdDmBRrx7rMBABihN1CGOMOIbgqeSnBSRpaEDhTsz65sexmg3hTAKYMJMWwOi0tCBx/gMoVxkbJawPYaDXuVdaM4t0drJg3CoQQzTW2Py+lmlQVpMheNSOgbLiuhUkafJ/LcpIQ71h27alm4eF5rXhitYZQCE2AcpKGFlzlTOixfxsl3woALBYihyW0IHBaB6cwI+UyGiV/kMO9hFqYaTzodMtJ6kZSvIGggquFhuturx/NUiqGUcKYHF5YMjbtlafdqEUgQOWUHiMZOEAwj3BgchaDTlFYMhehEJoE5SQN16y6gv18t/HyUzhcgDb3OzHrU7ewRLnPRqkw5nDFq2d8BqMudUerNYQU7hhrn7miooWG6019k/BJnQmMZEgC2upj2jE6DaebdyYwlnzWYvqUlhAKoUngiooWBDu3PrOTYpCTHKvqWsINFzheP5W9GWrBw3yxdouco2QUqjSUr3lecQOvNJhCqOwRqraiElLoYJDOBJyKvGTwVGq1J0qFGJIGO89KuXG2SyiEcxEKoUkIEewauYEapYGvEqXH86ziBqYGfJ8r81Ngsxrrqx5SwNOt7j5zRakkMwEpcXZV1xJuCtPikBrPrkntdBMjdibgJMTY5IIHteUz70xgtxJszDNGZwJOSpwd67LYPp9TWT5rEWPdJQQLEiLYVcy7Gp/2oHN0GoDxwj4AsDYjXt7ns53qCRyPL4AmyRNstDwgAEhPcMhjy9RUvCmlwYp5A+4zIUSRr6myoiIp/psN1JlASbVGCkuCnQmSdT/qcj62Skb7ue5xTRTwaAmhEJoErQh2ZXjNiAohIUQOZ6mpqFwacMLjYw18txgsf5CzrSgNANtntQT7wOQshpysObYRzzMQbACtZsN1p9uLtmEXAGCLQfeZhzOHpzwYdKrTcN3nDwQ7ExjQwAGCCuH4tBcdI9Mqr0ZbCIXQRAQnaTgx41FHsIdOdDBeyBgICpy2YRcmptWZDKPc52qDVRhz+D4PT3nQPabOyC9lvpVRb6D8utRsuF4f0pnAmOdZC4UlrUPBzgRGy9PkbNVQWo/WEAqhieAVgwEKXOhXJ2zM8zYK0+KQnmCMBr5z2VocFDjnVMpvO69s4CvlJhkN5T6fUUmwc8WbEOMVlHC00Ag8JLJgUI936CQNsc+RYmNustykXyiEoQiF0EQoPRhqNU7mN1CjhtcAYGuh+haosoGvxUANfJVU5ifDIRXLqJWvyT/f0qxEJMYYp4GvEmXDdfUUQrbPeSmxyE4yVmcCTnKsHWsz4gGov89G7EzAcdgs8vQVoRCGIhRCE1GcHo+kWCbY1ahkG3S60Sc1XTVq2AdgkzTWSIJdDYEz4/HLoT2j9XlUEmOzYpMk2M90jUX9/QMBKiuiNcXG3WeLhch5hOdUCmXyylcjG5KAcmKJOhEc7iGsMmBnAiU8bNzUO6l6v1gtYdxPXPAmlIUl9SoInDMKL47RBTsXOGoUPJzvHodfauBrZEUFALZJ+9zYOykX0USL1qEpOKUm79uK06L63tGGX19z/ySmotzYfmRqFj3jLEfUyIYkEIzi9E+6MTgZ3Ukasz4/LvYxQ9JoE3fmwuWzxx+Qr1kgFELTwRWxSwPOqE8sqetkXhyrhRg2YZnDBc6oy4Ou0egWPNQpFG/jKyqSYPcFot5w/Uxn0CtZY/R9ls5zgIYW0kQDZR6uWeQGEJSX0aKhZxIePzOqjC43RGHJ/AiF0GTUrGFfdH+ARr3g4UwHe7+NuUlIMGi+FUcpcKIdzuSKSkFqnOEmwcwlZJ+jfAPlHu/EGBvWZxsz34rD5QYQ6umPBnWS3CDEuIUOnM2FqbBJOb+nO9SRGwCwfY2xFcLi9Hik8X6xQiGUEQqhyVB6MuqiKHA8voCsgBrdmwKwikG54CGKAodSKnsItxk8XAwwwc6r1aMt2LlitKUoBVaDFu5wMhNjUJzO8mKjKTeAoGJUnpOE5FhjTYKZS5zDKlcb10VZ8eb7nJMcg/wUYxuShBA5v1pMLAkiFEKTkZWkEOxRFDgX+iYxK+V41awxvqKiLHiIpqLSPTaD4SnW1NboYR+ACXZlvma0mHR7cWmQ5R7xBtlGh+ejnoliXqzPH5A/1xqDe6043GCu75mIWsEDMySZQrh9TZohJ8HMhacfqNkvVmsIhdCE8HBAXedY1AR7nYnyrThqFDyE7rPxFW8gGDa+MjKNUZcnKu95vivYKNkMnlggqJCNujy4EqUJDxf7nXKj5O1mkRuKvNjGKM2P7hmfwcAkMyTNIp+VfUzPqjwPXSsIhdCEcME+Ph0cBxVpuDcyM9EheyiNDh8Zp5wrHGl4GNNhtYQ0ujUyyjzCaIV/lPlWWw3c2keJ0hMarXxNZR6d0fPaOMrrjFZ43kyFaBxlv9ho52tqFaEQmhCl5yhaXwQu2LYVmyMcAQA71qTL/z7ZPhqV9+QewqoCYw6mn48tKlRmnpTO89qMeGQkxkTlPdVmY14SYu3slhGtfebyKUPR29PoFKTGITuJnaloFfBw+eywWuSJVkYnLcGBDVIxWLTks9YRCqEJKc9JQoKDKQvRsEAHJ91yHzGzhCMANp4vT0rOPnEl8gLHNeuTQ0xm2ueUODs25iYBAE5EQbD7A1T+3uxcm77Io42D3WqR+wCeuhJdhbDGJHltAMuL5d/fqBnsJjQkAWBnCfv+nukai3ofUy0iFEITYrNa5PyJaAic44qbtFnCPgAT7FxhOHVlFIFAZPM16zrH5IbUu0rMo6gAQcXsTNd4xBPxL/QFmzObbZ93SfvcPOCMeCJ+/0TQkDST3ACC19s/6Ub3WGTzNac9PjSZ0JAEgufZ7Q2gUaX50VpC0wohIaSMEPIwIaRrCY8lhJB/I4S0E0I8hJArhJAvEEI0fY1qsV0KZ7YMTkU8Ef94+wgAIMZmkfPqzAK3QMemvbg8NBXR91J6x0ynqEjX6/EF5PFbkeK42GdQCpyMsNf7VIc5DUkgKDcA4HhbZPe5rmMcPsmQ3Gmy87xjbfBcRfo86wFNKkuEkJsJIW8AaAbwaQCFS3jaZwF8BcD/AHg7gD8AeAjAv0dombpmz7rgF/+EpLBFCi7QthWnmiocAQQtUCDyYWOuqGzMTUJqvCOi76U1lIpZpMPGPN8oJznGNAVSnO1r0uSei8cjLDdq24KGJB/pZhaq8pPltB6+D5GCvz4hwNz7/AkAACAASURBVG6TKYSFafFyz8WTUUqD0DKaVAgB7APQAuAtAB5e7MGEJZd8EsAjlNLPU0qfo5R+FsCvANwvvIRvpqY4TW6cXBtBC3RkahYtg8wztrskI2Lvo1U2ZCciJY41041k4rLb65f7tZnNawUAOcmxWCsVHURSIaSUyp6EnWvTTZPXxkmIsaFKUs4irXhzuVRTnIZYu7kMSZvVgh2SMXk8wvvMFfvyHPMZkkDQKxqNtB6to0lFiVL6IKX0A5TSgwCW8gmVAMgB8MKc378EIBPAujAvUffE2q1yu4xIWqDKm8budeZTVCyWYB5hJC3Qc13jclK0GRVvIJhHeLpjDD5/ZBLELw+5MCKlWJjNm8LZI113Q28wlzLcDDrdaJUMyWtKzXmeubzsHJ1G73hk5qHPeIKG5J515txnrniPTXvRNhzZtB6to0mFcAXkSv8dnPN7/v/ZV3syISSbEFKp/AFQGu5Fag0eNr7Y74xYHiFXNh1Wi+kSljm7Sth194zPRCxBXKl47ywx6z6z8zw168OFPmdE3iN0n82pEPJ99gdoxIrSlHlzZlVUlNcdqfD8mc4xeP30Te9nJpRpPccinK+pdWxqLyBMcD/33LI3/5y/L8THAXxxvj/U1taiv78fhYWFKCkpwdGjR+W/HThwAPX19RgcZHpneXk5EhISUFdXBwBISEjAnj17UFtbC5eLNYCuqamBy+VCc3MzACA7OxvV1dU4ePCg/Lp79+5Fe3s7uru7AQAlJSXIzs7G8ePH2cU4HNi7dy/q6uowNia1C6iqAgA0NDQAANLS0lBTU4OjR4/C45E8Grt3Y3BwEO3t7QCAAnvwi/DzJw9he4417Nd0sJ51v99cmIyOttaIX5MWP6cUz5D8nOfPtOPOysywX9ORi+yrnBtPUH/idc2fvUh8Tv7poFfwty/W4tY1trBf01PHLwAA4m1AfgJBW1ubps9eJD6nHdfuAwEL3fzhldMoja8K+zU91sREeazNgtHWOhxsI5o+e5H4nIaa6xFjBWb9TEHOnGoP+zXVTgaNR3dXA8YKYjR99iLxOQUoRUaCAyMuD554own5rtawX9Ohc5fhCQD7KoqwvnRdxK6ptrYWq4FEa3TZSiGEPATgi5TSBZN1CCE3AHgVwI2U0kPz/P4GSunhqzw/G0DWnF+XAniyoaEBlZWVK12+ppnx+LHlSy/C4w/gg9euxUN3hfc6x1webPvKSwCA+29ajwduKQ/r6+sFf4Ci5isvYWLGizu35OP7790W1tef9fmx9UsvYcbrx3t3FeFrd28O6+vrBUoprvv6K+idcOOG8iz86kO7wvr6gQDFrodfxvCUB7dV5uLH920P6+vriTv+8yia+iZRU5yKP3/8urC//k3fPoS2IReuW5+B3310T9hfXy/c94vjONoyjLUZ8Tj06RvD/vr3/uQYTrSPYmNuEp7/5L6wv75e+MTvz+Cv53qREmdH3YM3y4VT4eJ/P1qHZ873oTg9Hoc/fUPEco8bGxu5olpFKW1c7vONEjLm8c64Ob/nnsHZqz2ZUjpIKW1U/gC4HO5Fao04RzCP8Njl8IckjilyE82a1wYAVgvBtVIe1Outw2FPXD51ZUye93rd+sywvraeIIRg7wZm19W2jYS9H+GF/kkMTzFRs7fMvPsMQD7P57onMDET3n6EA5NutA0xT8geE8sNIBjGvTIS/jxCt9ePs9IkFLPmw3Kul+TmxIwXDT3hbVvlD1C81jIMAKguTNF0IZpRFEIek8ud8/sc6b99UVyLrtgjCfbmAScGJ91hfe3DzexjibVbQvo9mZHrNzCBM+ryhH2u8ZFLbJ8tJCjYzApX1NzeAE6HuYjnqCTUAWDv+rkBBXOxr4xdvz9A8Ubr8CKPXh5K49SsBSUcpYF3tGXoKo9cPsfaRuCRiq+uKTW33LhuQ/D6XwvzeT7fPS4bTfvLtC03jKIQXgZTCu+c8/tbAfQC6Iz6inSC8oAeuhQ+gUMpxWHp9a5Zl2G6thFzUSoQ4RY4fJ83F6aasm2EkutKM8EN8CMt4d1nfkNekxGPYpPM1V2IXSXpiLGx28eRMCsqh5pZLlVijE0elWdWqgtSkBbP2lYdag7vPnOD3WYhuG69uRXvgtQ4rMtMAADZmxcuDivuq/s2CIUw7BBC7ISQCt5fkFIaAPBdAO8khHyPEHI7IeRhAO8D8D2q9URJFdlalIpUWeDMLdJeOZcGptAveRy1bhVFg+KMeLmJcTgFzuCkGxf7WUXtPrHPSEtwYLPUJ+9IGA2cGY8fJ9uZx3HvBnN7UwDWtoqHM49cGka4RKw/EDQk927IhMOmy1tU2LBaiPy9fq1lGN4wtlPi+7xjbRqSYu1he129wr2xpzvGMOMJX7oJl0PlOUnIlZpgaxW9ftveDuANADsUv/s6gH8D8A4AT4Ipg/8G4P9GfXU6wmoJ5l0dbRkOW/+2w5eCyuX+8qt2/TENPGx84soo3N7wCBxlGHO/yfPaOPw8N/VNYsh51fThJXPiyqgcXturcSs/WnBFpWd8BpelnL/Vcq57HGPSjOQbysU+A0GD2jnrk3sGrpaOERfah13S6wv5DATls8cfCNtUqYlpr/yZ7dfBeda8QkgpfWhuhTGl9DFKaSql9ITid5RS+jCldC2l1CH992vCO7g4N0oH1en2oa4zPALnyCWmqBSnx8sTJMzOXskC9fgCIQU3q4GH65Jibdhi8vAaR+kpfT1M4Xlu5VstxPR5bRylAXI4TN7YQxeDhuQNwpAEEGqAHA5T2FgZfhaKN2PPugy5uvjVi+GJlr3WOgxeQ6j1cDGgA4VQEHmUN9BwhI2nPT65ge/+sixNV1VFk+s3ZMrjAl9sHFj16/kDVPYQXleaCZtVfJ0BNjM7MYb1IHz5wur3mVIqv862olQki/AaAKA0K1GeAxs2hVB6nYq8ZOQkazu8Fi2ykmLkWc6HLoVHUeGfV05yDDbmJoXlNfVOSpxdHtbwYmN/WNIguCEZZ7fqorBS3EEEyEyMweZCJnBeDYMFerRlWA6vifzBIEmxdlwrJW+/1NQP/yrbz5xoH5UnzNy0UXhTOHarRfZ6vHpxcNXh+Yv9TnSMsAkzt1XNbWRgXgghcjpI7eURTLpX135myDmL892s5ceNG4XcUMLlaEPP5Kq7Qbi9frmSWxjsodxSwb7fvRNuNPaurhuEP0BxUPI07lmXrovCSqEQCgAEwzMX+ibRMbK6fKBnzrMuP/EOq5yXIWDcWskEzvCUB3Wdq2uL8lwD22ebheCWypxFHm0ubq/KAwC4PP5VF/E819Av/5t/fgLG7ZKC7PEH8HLT6ryxr1wMPv9GES4O4cCm4H4oz+NKONQ8KPctFYZkKDdXBOXoC42r2+cT7aMYnmI5zHoxJIVCKAAAvG1znvzvp8+vvG2j2+uXw2sHNuXowiqKJm/ZlCO3RXlhFYI9EKDyjeGa0gzTt5uZyw3lWXJblNXeQPnnVJmfjKJ0kQ+rhJ09FkJ/tn517V6fOseen5nokBvmCxhbi1JRkMrmLjyzCvkMAE9Jz09wWEWe5hzyU+Pk8Pxq03r498FqIbLnUesIhVAAACjLSUJ5Dssleepc74pf51DzIKalkv23Vuct8mjzkZUUgx1rWC7JC00rz1M53TkmV9DeIfb5TSTE2OQw28sXBlbcrqNtaArNA6ytz+06sfKjid1qwa3Sze7IpWE4Vxg2HnS68cZl5sl9a3WeyIedAyEEb5WM9pMdo+ifWFnYeNrjwysXWBjzLRXCYJ+PWyQvYfOAE1eGVxYt8ysM9mtLM5CWoA+DXXzrBDJ3bmEC52K/Ey3STXC5PB1ifYo8oPngYceu0ZkV56lw69NCggJMEMrt1WyfJ2a8qF1hVfcLCi+BXsI+0eYOSVHx+AM4eGFlRQ/Pnu+TqzHv2pofrqUZCh7FoXTl3tiDF4Lh4rdtFvs8H7co0kJWGl1Qhov15BgRCqFARikgnlpBWGLG45dvCCJcvDBKxeKJMz3Lfr4/QPG8JKh2l2QgIzEmbGszEjdtzIHdyuLzK/F6U0rx5Fn2+ZRmJWB9tqjGnI9rSzOQEsfCxs+sUFH5q/T5FKTGoaZY+9WYalBdkIKidClsvMJ9fvo82+ekWBv2ib6l81KWk4j12YkAgL+c6V5RFCckXKyjvGOhEApk1mYmyNXGT53rXfYX4cWmftn6fOtm/VhF0aYwLV4eJv/E2d5lNwN/vXUYfVLISOzzwqTE2eUcqWfO92Ha41vW8xt7J+UpMO/cVhD29RkFu9WCW6WipkPNgxiZWl4z8K7Rabn/6Z1b8kXV6wIQQvDWama0n+4YQ9fo9LKeP+n2yl0kbqnIRYxNGOzzQQiRv++XBqaWHcWZ9fllhf3a0gyk6yRcDAiFUDCHu7YwgdM+7JJ7CS6V359gI6PT4u0iXLwI79peCAAYnppddqufP5zqAgDE2Cy4c4sI+1yNe3cUAWDVxstNxv+TtM+EAHfXFIZ9bUbinu1sn71+ir8s0+v957rg4+8S5/mqvGNbcH/+cLJrWc994kwPPD5mfIqw/NV5x7YCufhvufv8ctOg3A7sXTqTG0IhFITwzm0FcvPkR453Lvl5l4emUNvGFMh7thcK63MR3lqdJzdP/s2xK0t+3uCkGy9K7RDuqM6TQ3WC+bmhPAuZUkj9kdqOJXu9p2Z9eFxSVK5fn4l8qcJTMD8716ZhXWYCAODR450ILLHHptcfwKMnOgCwKu5NeSIsfzU25iZjWzGrwP7Dqa4lF0tRSvGoJM8L0+LkqUmC+SlIjZMni/zlTA+mZpceXeCOkZQ4u+7yjoVCKAghIzEGd0jJ+M839KF3fGZJz/vFa+3yv9+zqzgiazMSCTE23CN5CY+2DKN1cGpJz/ttbQe8fnazff8esc+LYbda8L7dbJ/OdU8seTTj46e75ZvAB65ZG6nlGQZCiLzPbcOuJU/UeLFxAAOTLMT8d9esEeHiJfBeSb4OOWeX7PU+1jYipz+8d1cxLBaxz4tx3541AJhx+Oe67iU950LfJF6TxmW+c1uB7vLohUIoeBMfvK4EAAv//Pxo+yKPZoLpsdPsC3NgYzZKsxIjuj6jcN81a+R///BQ66KPn5r14ZFa5k3ZWpSK7WvSI7Y2I/H+3cVyccmPD19e9PEeXwA/O9oGAChKj8ONonnvkrh3Z5Hs9f7J4bZFH08pxQ9eZec+Nd6Ou7aIPM2lcNeWfGQmsry0Hx++vCSv948OsXMfa7fgPTuLIro+o3Djxmy5iOcnh9uW5I3lcsNCgA9L91E9IRRCwZvYWpSKa0vZiLVHT3Qs2vPqB6+2yrkp/7BvXcTXZxRKsxJlb+yTZ3vRvkjPq1++1o6xadbnTezz0slOjpWTxF9qGkC9NB5tIR6v60b3GPOMf2xfqTzwXnB1kmPtsrJxvH100QkxL18YRFMfS9j/yHUliHPoy5uiFrF2Kz4kKRsX+51yx4GFON0xKs88f/eOItGVYIlYLQQf21cKAOgZn8Ff6q6eG9s6OCV3jbitKhfFGfprYi8UQsG8fOLABgCA2xvAt15oXvBxbUNT+N1x5rW6bn0GdpUIr9Vy+Kcb2T77AxT/8UzTgo8bnHTjp0eY9bkpLxm36aiVgRa4/6YNsEmK3VeeaVrQqzLp9uLbL14CAOSnxOJvdugrKVxt/vGGUsRLit3Xn7+wYAW9xxfAw89eAMBaoPzdtWujtURDcN81a5AmTYj5xvMXZYN8LpRS/MczbJ8dNgv+YX9p1NZoBO7ZXojc5FgAwLdebL5qLuE3nr+IAGVFaP98oCxaSwwrQiEUzMuedRnyXMfH67px+NKbK2H9AYrPPHZezmn73G2bRA7QMqnIT5ZzCV++MDhvThClFA8+2QCnJIw+e1u5yAFaJkXp8Xi/lBN0on10wcrBbzx3UW4o+39uLRfFUcskMzEGH93LvNcNPZP479fnTzn5f6+2yh7xfz6wQRRHLZPkWDvuv4kZk1dGpvFfB1vmfdxvazvkvNmPXF8ij78TLI1YuxWfvrUcAEuN+sZzF+d93LP1fXhJmuV997ZClOfqszhKKISCBfnC2yqQIFn7D/zxbEhIk1KKh5+9gFMdYwCAD167FtVSD0PB8vjsbRvlG+LnHj+P5v7QKTE/OdImT8x46+Y8MX90hTxwSxlyklm47It/bcS5rtACk8dOd+N3UiXmrpJ00XtwhXz8hlKUSBXH33y+Gccuh06JefXiIP7fK0yBKctJxAeEd3BF3HfNGlTmJwNgOcgHL4TO3j3dMSZ7BwtS4/DxG4R3cCW8c1uBPG70t7UdchN1TuvgFD73+HkArOXa527fGPU1hguhEAoWpCg9Hl96exUAYHjKg3t/cgxPnu1BffcEHvjTObmyeEN2Ij5zW7maS9U1WUkx+NY9mwEAzlkf3vPTY/jLmW5cGnDiy0814euSVVqQGocv31Wp5lJ1TVKsHd+9dyssBJj1BfD+nx/Hn051oWPEhf862IJPP3YOABPq3333VuHtXiGxdiu+fe8WOKwW+AIUH/7VSfz+RCd6xmfw6zeu4GOPnEaAsj6a339vDexibvGKsFst+M69WxFjsyBAgY//rg6/OXYFg5Nu/LmuGx/85QnM+gKwEODb925BUqzwwq4Ei4Xgu+/eiiSpYOpTfziLnx9tw5jLg4MXBvCen9Zi0s2iN199RzWykvSbo0lWMpbFDBBCKgE0NDQ0oLLS3Dfh77x0acGQRG5yLB77X9egME1/CbRa46dHLuPhZ+cPSaTG2/HoR/egQvIICFbOI7Ud+PcnGub9W7zDil98YCeukYqqBCvniTM9+NQfz2K+loQ2C8EP/rZGnustWDkvNw3gY4+chn+B3o/feFc13r1TtKhaLa+3DuNDvzq5YL7mAzeX4X4p914tGhsbUVVVBQBVlP5/9t47PI7rPPT+nV30ThCNAEES7AWg2EkVqliSJdmyrTgu147s2HGc5Nq5LvnudXpiO/lif3byJHGKU9xy3Ytsy7ZqTKuQkkhKYgPAClYABAmi97K75/tj5swOlg1lZ3fK+T0PHzbsztmzZ955+yubZ/p6bZppbson71vBF359vWUhKXauKONnv3+7VgaTxO/cuYy/f/ctVrK4YkNtCT/5yO1aGUwSj+5YzL/+xqarLPlVlYV898M7tDKYJB7ZWMNXP7D1qn2uKcnlGx/cppXBJHHf2kq++aFtVvGDoiQvk397dJNWBpPE7cvL+PZvb2dR6dTnXV5WmM+9vSHtymAy0B7C66A9hFczMhHh5ZZuhicirFlQxMpKbybOup3h8Qh7z3TTPTzB8ooCNtaW6PClA6jz3DEwxvLyArYumUeGDl8mnfFIlOdPXKGjb5RF8/O4bVmZ5xr2egG1z609I1QV5/CG1RXkZWXc/IWaGTE2GWXPqS5Odg5SVpDNA2urKM5zRzh+rh5CrRBeB60QajQajUaj8Qo6ZKzRaDQajUajmRNaIdRoNBqNRqMJOFoh1Gg0Go1Gowk4WiHUaDQajUajCTi6BOn6ZAG0tLSkex0ajUaj0Wg0N8Smr2TN5vW6yvg6CCHeCjye7nVoNBqNRqPRzIC3SSl/NtMXaYXwOgghioG7gFZgwqHLLMNQOt8GnHboGpqZo78X96G/E3eivxf3ob8T95Gq7yQLqAVekFL2z/TFOmR8HczNnLGGPRNszYZPz6ZnkMYZ9PfiPvR34k709+I+9HfiPlL8nRyc7Qt1UYlGo9FoNBpNwNEKoUaj0Wg0Gk3A0QqhRqPRaDQaTcDRCmF6uQJ8xvxd4x709+I+fPOdCCGWT/Pn6oQQbs/z9s334iP0d+I+PPGd6CpjjUajSRFCiI8Cn5BSrpjGz/4FcDfwkJRy3Om1aTSaYKMVQo1Go0kBQog3AI8B90gpD03j5zOA54CTUsoPOb0+jUYTbHTIWKPRaGaJEOJuIYQUQtx9k5/LBP4V+LvpKIMAUsoI8HvAB4QQd8x5sRqNRnMDtEKo0Wg0zvPrQA3w9zN5kdmz7GngT5xYlEaj0Si0QqjRaDSzQAhxDiOkC/Cc+ffr8T5gl5RyOOE93iuEOCyEGBZCnBNC/H9CiNyE1/4QeKMQoiJZa9doNJpEtEKo0Wg0s+MdwMfMP3/M/PtVCGNMwR3A8wn//jDwbeBXwCPAPwEfB/454S32AGHg9iStW6PRaK7C7S0NNBqNxpVIKV8TQhSYf22UUr52nR9dAhQBHQn//iDQK6X8pPn3/xZCRDGURztnMOaprwd+MueFazQazTXQHkKNRqNxljLz966Ef38emCeE+LoQ4h4hRI6U8h+klFM8jVLKGNBvex+NRqNJOloh1Gg0GmfJNH+f0uNLSvkj4C3AQuApoFcI8X0hxOJrvMc4kO3oKjUaTaDRCqFGo9E4S7/5e0Hif0gpfyGlvB+YB7wT2AT8UgiRKJvnA32OrlKj0QQarRBqNBrN7ImZv4dv8DPnzZ+b4vkTQvxYCPEVACnlqJTyFxgFJcsxFET1cwVALnA2ievWaDSaKeiiEo1Go5k9F8zfP2TmAD6R+ANSyiEhRDOwIeG/ngf+QQjRBfwSqMKoMn5dStlt+7nt5u/7k7pyjUajsaEVQo1Go5klUspzQogvYkwUuQW4SiE0+TGG0iikOS9USvklIcQk8PvAJ4Fe4FngjxJeex9wDjiQ/E+g0Wg0BnqWsUaj0TiMEKIWOAW8XUr55AxeF8ZoO/MvUsovOLU+jUaj0TmEGo1G4zBSylbg74DPCyFmEpn5KBAF/tGRhWk0Go2J9hBqNBpNChBCZAK7gONSyt+Zxs/fDTwG3C+l1OFijUbjKNpDqNFoNClASjkJPAx0TvMli4CHtTKo0WhSgfYQajQajUaj0QQc7SHUaDQajUajCThaIdRoNBqNRqMJOFoh1Gg0Go1Gowk4WiHUaDQajUajCThaIdRoNBqNRqMJOFoh1Gg0Go1Gowk4WiHUaDQajUajCTgzGaEUKIQQxcBdQCswkeblaDQajUaj0dyILKAWeEFK2T/TF2uF8PrcBTye7kVoNBqNRqPRzIC3AT+b6Yu0Qnh9WgF++tOfsnz58nSvRaPRaDQajea6tLS08Mgjj4Cpv8wUrRBenwmA5cuXs27dunSvRaPRaDQajWY6zCrNTReVaDQajUaj0QQcrRBqNBqNRqPRBBytEGo0GtcjpURKme5l+B4pJbGY3menmYzGiOp9dpzxSJSxyWi6l+EZfJdDKIQIAf8P8GFgMdCBUS38l1LKvnSuLRU823yJr+w5S3N7PyV5WbypoYr/efdySvOz0r00X/HciU6+/NxpGtv7KcjJ4A2rKvjE/StYUJyb7qX5it2nrvDPv2rhUGsfmeEQd60s538/sIq6svx0L81X7D3TzZd2nWLf2R5CAu5YXsYf3L+KhoXF6V6arzh4oZe/ffYEe8/0EJOSrUtK+fi9K7h9eVm6l+Yrmtr7+fxTx9l7pptITLJmQREfv3c5D9YvSPfSXI3wm9UthPgS8LvAF4A9wFrgs8DLUsoHZvA+64CmpqYmTxSVxGKSv/hZE9/ae+Gq/6spyeVrH9jKqqrCNKzMX0gp+fzTx/n3F85c9X9FORl8/YPb2Lx4XhpW5i+klHxpVwt//8uTV/1fdkaIf3t0M/esrkjDyvzHf754hr956hiJj4KMkOBzb2/gnVtq07Mwn/GdfRf4s582kugYFAL+6MHV/O5dy9KzMJ/x+KF2/uAHh6/pgf2dO5fyxw+tRgiRhpU5T3NzM/X19QD1Usrmmb7eVyFjIUQ58FHgi1LKP5dSPiOl/HvgM8AbhRCL07tC5/jrJ45ZymBRTgbv3lLLFlMxae8b5dGv7qOjfzSdS/QFX9rVYimDhdkZvGdbLXetLAdgYCzC+7+6j5bOwXQu0Rd84+VzljKYnxXmPdsW8aaGKgDGIzF+95uv8+q5nnQu0Rf84NVW/t8nDWUwJzPEe7cv4h2bF5IREkRikj987AjPNl9K9zI9zxNHOviTnxjKYFY4xHu2LeI3b11MXlYYKeFzTx3nB6/OqlOIxsaLJ6/wye8fIhqTZIYF79m2iN+9aykleZkA/MeLZ/jyC6fTvEr34reQcTHwXeCxhH8/av5eCpxP6YpSwNNNl/jaS2cBWFaez3c+vIPKohyklPzLcy387bMnuTI4zke/fYAf/t5thEP+tI6cZs+pLv5hl6GkLCrN49u/vZ3a0jwAvv/qBf7wsUaGJ6L83rcO8Iv/dQc5meF0LtezHG7t469+YdyylUXZfPu3d7C8ogCA/z56mY98+3UmojE+9t2DPPXxnZTk6XSI2dDSOcifPd4EQEleJt/98A7WLCgC4N1ba3n/V/czOhnlf//wMM8uLKGqOCedy/UsrT0j/NFjRwAoyM7gmx/axsZFhrH+nu2LeM9/7KV3ZJI/e7yJTYtLWF6hIzmzoXNwjE98/xAxCbmZYb7+wa3sWDofgEe3L+Y9/7mXtt5RvvjMCbYuKWXrktI0r9h9+MpDKKVskVI+KqU8mPBf9wCXgRm7UN3O4Ngkf/ZTQ6gX5WTwjQ9uo7LIENxCCH7/DSt47/ZFABy40Me39vpOH04JY5NR/vSnjUgJeVlhvvqbWyxlEODdWxfxsTcYDcxbOof48vPaCp0Nk9EYf/jYEcuT8pX3b7WUQYD711byFw+vBaCjf4wvPHMiXUv1NFJKPvWjI0xEYggB//7oZksZBNi6pJS/f/ctgOH5/nNTcdTMnL94vInB8QgA//DuDZYyCLC6qoh/e3QzQsBEJManfnREF0/Nks89eZyeYaP93t+8vd5SBgFqS/P4z/dvITsjhJTwxz9uZDyii00S8ZVCeC2EEJuBjwGflVJes1mjEKJCCLHO/gvwRELHP/+qha6hcQA+/dZ1U5QUxZ+9eQ21pUaxw989e4L+0cmUrtEPfHXPWc53jwDwv9+4ihWVV1vxH7t3BeuqjYfqlL06agAAIABJREFUl58/TXufDtHPlB+81srxS0bI/aP3LL9mUcOjOxazc4WRhP/d/Rc4enEgpWv0A080dnDgglFj96Hb69hue3gqHqxfwK9trAEMz+wrp7tTukY/8MLJKzx34goA79qykPvWVl71M9uXzudDt9cBhtH+ZKMO0c+UAxd6+cnBdgAeWFfJr21ceNXPrFlQxMfvWwEYRvt3912dbx90/BYynoIQohajwvhp4Ms3+NGPAH95rf/Yu3cvly5dYuHChdTV1bF7927r/+69914aGxvp7OwEYNWqVeTn53PgwAEA8vPz2bFjB3v37mV4eBiATZs2MTw8zIkThmejoqKChoYGdu3aZb3vzp07OXv2LG1tbQDU1dVRUVHBvn37AMjKymLnzp386uVX+doe49rrF+RzW3WG9T7z5s1j06ZN7N69m4mJCd5WG+Wfewxr/0/+7y7evjzTlZ/pwIED9Pb2AqjkWJqamq75mQC2b99OZ2cnZ88aIXMnPtNoRPLllwwluqZAsHD0NLt2nbnmZ/rjNy7l0W8cYiIa48+/s5uvfeSNrvxMbvyebr/zbv7u6WMAzM+Bt6zIpre396rPtG/fPt5YNsjLLRCV8PlfHOE3l4278jO58Xs60tjIZ18yPkNpfhbb8rqs9078TO9cWcXTTSFGJ2P82Q/28cdbs7jvvvtc95nc+D1JKfnHY9kA5IRhR94Vzpw5c83PdHf5CN/LhKFJ+PyTzWwsFxw72uy6z+TW7+nPv78XgMwQ/PnDa6/7mZbFJAsKMugYivD3zxylYvg02WHhys80m+9p7969zAXfVRkrhBClGFXGQ8A9UsrhG/xsBVCe8M/LgMfdXGX8uaeOWQUO3/udHVNc5IlIKXnkX1/mcGsfBdkZvPLHb6AwJzNVS/U0//JcC180Q5P//r7NPLCu6oY//1vfeJVfHe8kMyx48VP36FY00+Q7+y7wJz9pBOCL71h/0+rWT/3oMD94zRDgz3ziTl1FP02eONLBR79jPGz+4uG1/NYddTf8+S88fZx/NVMgvv87O67pTdRcze5TV3jfV/cDRvTgD+5fecOf/8ruM/z1E4ZB9OXf2MRDDbpFynQ41NrHI//yEgC/eetiPvO2+hv+/E8OtvHJ7x8G4LNvW8f7b13i9BJThq4yvgZCiDzgCUACD91IGQSQUnZKKZvtvwBXJ4GNTET4juny3rak9IbKIBj5hP/rHiPHbWg8Yj1INTdmMhrjm68YeZerqwp54zVCPol87N4V5mulztmcJrGY5Ct7DOOmpiTXClXeiP9593JUfdTX9px1cnm+4j9eNETbvLxM/se2m7eU+eDtdWRnhMzXXt1uSXNt/nO3cSbzssJ88LYlN/35925fRHGuYaT/u97nafN1s6AyIyT4vbtvnun11ltqrBSqr790Tjdit+E7hVAIkQH8EKgC7pdS+jLx5acHLzI4ZiQqf2jnjS18xRtWV1gNfb/x8ll9I0yDp5sucWlgDIDfur1uWv2rNtSWsGlRCWB4vXSn/Juzp6WLM1cMu+2Dty8hI3xz0VRXls99awwF/fHD7fSP6NzYm9HY1s/htn4A3rdjMXlZN88aKi/M5tc3GzlZvzrRSVvviKNr9APnu4d58aSRO/iOzQuZN43BAHlZGbxvh9EZ7VBrH03t/Y6u0Q90Do7xZGMHAA81LJhWNCYcEnzgNuOZebZrmBdOXXF0jV7Cdwoh8BXgfuDTwFIhxB22Xw3pXVryUJ6n6uIc7p1mg95QSPCbtxoCp7VnlFfO+FJXTirfe9Xwws7Ly+StG6qn/boPmEnivSOTPKP7uN2U75s92HIyQzNqhPw+8zyPTcZ47ID2et+M7+w3znNIGC1Ppsuj2419lhK+t1/3y7sZap/BKIKaLu/dvsjyen93vy56uBmPvd7OZNRwbKhn23R415aF5JptwXT/xzh+VAh/E8gEvgHsTvj1T+lbVvI41jHA0Q6jsvLdWxdNy5uieGRjDVlm+Od7+ka4IW29I7xsVlY+srFmRn0FH1hXaTVD/dHrWlG5ET3DEzx71FCa31S/wAqbTYfbl5WxyKysf/zwRUfW5xfGJqP83NyjN6yumFFu69rqIjbUGl7vnxxs161RbkA0JvnJAaPideuSeay8RkeC61Fdkms1un/80EUdXbgBUkp+9LrxDFtRUTCjCVGFOZm8yczR/OWxy3SbnTqCju8UQimluMGvu9O9vmTwmE3BePumm+da2SnJy+JBsyji2eZLDJv9sTRX85MD7dY4r3duntn4ruyMMG+7xfAo7mnp0lNibsBTTR2WlT/TMWmhkOAttxiC/XBrH+e7b5guHGieP3GFIfN+//VNV7fluBkqr7O9b9RqWaO5mpdauugcNBSM2ezzu8x7YGg8wvMndDjzehxu6+e0mWbyjs0LZzyO7t1bjX2ejEor7Bx0fKcQ+p1YTPLzI4aVv2Np6TX7Dt6Mt5qKyngkpgXODXiyyfBara4qZG110U1++mrebj4MpIRnmnTY+Ho8ZfZdqyjMZnvdzKcHvG1D3Cj6ufYSXpcnzIdeXlZ4VnOgH2qossKZep+vz08PGd7BrIzQrCqF71ldQV6WEY14Qisq1+UJ8zkohBHBmSlbFs9jgTl95yktnwGtEHqOw219XB4wrM+H108/p83OHSvKKMg2ksmfbNIC51qc7x7mmBmWf6h+du0f1i8spqbECMtpgXNteoYnrFzWh+qrCM1irOLKykJWmy1nHj90UYczr8HoRJRdxy4DcN+aylmNVawozLG6GTzZ2EFUF6VdxWQ0xq5jRj+5e1aVzyj9QZGTGeYNpsK+69hlHTa+BlJKnmk2zvOWxfOs6VwzIRQSVguxvWe6ddgYrRB6DnUTCMG0WqBci5zMMPeuMQTOr451MjqhBU4iT9sUuAfrb9x38HoIERc4r57rsSbKaOI823zJUizm0nftLabX+1TnkDXpRBPn+ROdjJj3+ZvXz36flRHaOTjOq+d6krI2P/Hq2R5rEtTN+pXeiDeb98LIRFRHca7BsY5BLvQY1e5z2WeVRxiTxjSeoKMVQg9hWEWGorKxtoSKWVhFCuX1Gp2M8sLJzqSsz08oj97SsnxWVhbc5Kevj1ImYxJ+qQXOVaiwfFlB9pyGzas0CEDnA12DXxwx9qQgO8MqWpgND9ZXETa9uL84osPGiTxr3uPhkLC8fLPh7lUVVhWsPs9XY+/cMBeFcPPieZQVGNNkntRRHK0QeolTnUOc7TKSaOdyEwDcvarcylPRszOn0tE/yqFWI2n+wfqqGScr27ELHB02nkrfyAQvt3QBRrg4PItwsaK2NI/6GiPP87kT2sCxMzYZ5VfHjT25f+3swsWK0vwsbl9uzJH+76OXdXjehpTS8jJtryulJO/mvQevR25WPIrzSx02vgqlEK6rLppVHr0iHBI8sM6ItL3c0hX4XqZaIfQQ9sKEuSqE9jyVXx3vZDIam9P7+Qn7Ps82f1ARDgneqATO6S4rnKQxql4jKlw8y7C8nXtWGee5qX2ATrOZuMZIVxg1FYr7Z5lmYkf1Pb08MK7D8zaaLw7Q3md0E5htOo8dJXtGJqI6PG/jXNewde4enONzEOJh40hM8qsTwY7iaIXQQ6hwxKrKQpaYE0fmgrJAh8YjHNRtJCyeM3N2qotzLK/TXFBCazIqecn0iGmwJjkUZGewdRbVxYncvSoeonv+pM67UqgctHBIWN69uXD3qnjIWee3xXnWlhJyfxIUlTuWl1lV3S/ofbb45bH4Pj+QBENyW10phWaR5Ysngy2ftULoEbqHxmk0RxkpRW6u3LE8Lthf1A9QwAiv7TtrVL3etap8TuFixba6UmsW7G49Jgkw2ie9eMoQvrctm0/mDJqrX48NtSVWM/DnddjY4gXz3t60qGRWVa+JLJ6fz5L5RphO73MctRfrqous7gJzoTgvk42LjGbLL2q5YbHblBs1JbmsqJh9frciMxzi1mXzzfe+EuiRrloh9AgvnY6Pmdu5YvZJ4XbKC7NZu8DwgGmBY/D6+V7GJo3webL2OSczzHazXceLJ7t03hVw7NKAVXV95xyKHOyEQ8IqmNh9skunQWBM22npHAKYUzFJIsob+/r5XgbHdBpE38iEZbAn6zwD3GnKoJOXh7jYp5vbj0fiBvsdy8uSYrBD/DvrGprg2KWBpLynF9EKoUfYYypsuZlhNi0uSdr7qhuhsb2fnuGJpL2vV1GKcUgYnqtkcecKI1TX3jfKue6RpL2vV7GHZpKpqKg8wsHxCK+f703a+3qVF2yef3tIfa7cZYaNIzHJSy16JvrLp7utqUY7kxCWV9xlC8/r6MJUg/2OFcnb5ztX2KNlwQ0ba4XQA0gp2WO6ybcvLSU7Y/ZVgoncubLMvIYWOGB4lgDWLyyZU5VgInZvo95nrFZHdWX5c6oSTOTOleUop4HOb4vnnpUVZFnRgGSwo26+NRNdt60yxlMCZGeE2DSDmbo3o6GmmHlmGsQLOq3Heg4KQVLyYRWL5udZaRBBls9aIfQAZ7qGudhvVE3ekcSbAGDL4lKr/UyQLSOAK4PjHDWnk9yZROsTYGVlARWFRvuZoO/zsM17l+x9Ls3Por66GDCmDwSZyWiMl81UkztXlM9qCsz1yM0KW1NLgn6eAatYbFtd6Zza+iQSDgnuMI3JPae6iAQ8DULlD9ZXF1OanzyDHeJG+2vnehmZiCT1vb2CVgg9gLKKIHl5bYqsjBC3Lo0n1AY5v21PS9wy3JnEMCYYU0tUiGPvme5A57ftO9vNZNQ4Z8nMt1LsWGpULDe29zM0HkzBDtBk+/zJDK8pbjdTKtr7RmnrDW4aRGvPCOfNNJBkeq0UymgaGIvQfDG4+W29wxM0XTTyNJ04z0oWTURjgTUmtULoAZRVVF6YPaepGddD3Vydg+OBzm9TuVAF2RlsqE1enqZC5akMjUc43BrcNj/7zhg91cIhYRXbJBPluYrGZKD7t+07G//sTuyz/T3VdxpE9thaSSU7ggPx8wxYBRVB5KXTXY7kaSp2LC21muMH9TxrhdDlRGPSkaoqO9tsPeD2BdQyAthvPkC3LJmXlDYoidy6zC7YgylwAPaan72+uogCs/9XMtlaV2r1b9t7OrjnWXk5Fs7LTUoblETqq4vIN9NNgupRgbhCOC8vM6l5mora0jzr+wuqogLxz56V5DxNRWFOJvXVxve3N6DyWSuELuf4pQEGx4ywz/YkNO+9FquriijKMR7M+wN6I3T0j1rD0rc5tM+VRTksNhOXg7rPw+MRmsz2HE7tc1FOJvU1wc4jjERjvHbOyNPc4YB3ECAjHLIaigfVwJFSWvfyjqXzk5qnaUfJ/v3neogGtE+e8vZvrC1Jap6mHSWTmtr7GQ5guolWCF3OqzZB69QDNBwSbF0SbMFuV9CcUrwBtpn7/Pr53kAmiL9+vtd6oG2vc0ZRAay82Mb2fgYC2CfvaMeAlT/o5HlW3+GFnhFrbFuQON89wpVBo5+mkqFOsN3Mix0ci3CsI3h5hH0jE9a4Oqeeg8Z7x9NNDlwIXtsqrRC6nFdNK7+sIIu6JIyrux5K4AQ1QVxZn9kZIRpqkp8/qFDCbGg8wrGO4M2BVekPQjj7AFVesZiE1wKYR2gPLTrlITTeO9jpJvYcVScVFbvxFESjXXm7wVm5sXVJPBQdxCiOVghdjJSS/abA2bqk1JH8QcU2m8AJ4o2gPvPGRSVWfzUnsAv2/QFUVNQ+r6ospDhv7mPUrseWJfOsBPG9Acy7Uop3dXEOC+clP39QUV9TbOURBjG/TSmE+VlhVlcVOnadxfPzqCwy2lbtD2BhidrnkMCR/EFFSV6W9T0GUfHWCqGLSVU4AowE8byACvae4QlOXjbGe21zMIwJUFuaG1jBPjYZ5XCrkT/opNcKjARxleAftIklsZi0HmY7ls531JDMDIfYbKWbBOs8Q9xztWnxPDIcKERTCCEsY3L/2Z7AzdtV57m+ptiRQjQ7ytN7qLWPscmoo9dyG1ohdDH7UxSOACNBfLNpeQVNsNvDPk7mW4Eh2JXS+eq53kD1fTx4oY8JM2/S6fMMWOe5sa2f8UhwBPupziGrEG1rCvZ5q7nP57pH6DbnUweBK4PjnOkaBuK5wU6i7pnekUlargw5fj23MDIRL0Rz2jEC8X2eiMQ40tbv+PXchFYIXYwqKCnIzmCNA+0MElHK0LnuEboCJNjVPmeEBBsXOZc/qFACp2d4gpbO4Ah2e5L2liXOhX0UKrQ0EY3R1B6cRHy7R3Szg+G1a13jwIXg9Nd8/XzckNySAkXFfs8cCJDX+9CFPiKmRzQlCqHtGkHrY6oVQhejDuPmxfF8KCfZtCgucA4GSLArRWVddRF5Wc6GI2Bq4nKQwpnqIVZbmktFYY7j15uiqARpn83zXJiTwfLy5DeyT+SW2hKr72OQKjP3nzU+a2Y4NYbkiopCK1wapH1+dUpBifMGTkVRDrWlRt7twQDtM2iF0LX0DE9YU0O2pMDKB1gfQME+EYnRZI6D2rgoNftsF+xBUbyllBw0p7NsStE+VxfnUFVkKJ6BUrzNe3fjonmO9cWzk5+dweqq4OVrKg9hfU2xY33x7IRDwpqgFCRP7KFW40wtmZ/H/ILslFxzY60how5e6AtUWo9WCF2KfbTZhhRYn2CEpldWGhVWQbGMjnUMMBEx8tqcGFd3LcIhwS21RuPkg63B2Odz3SP0DE8AqVMIhRCWl/D1C8HI1+wdnuDMFSOvbVOK5AbEvbFH2voCMad7bDLKUbMfYKrOs3Et4ztt6Ryif8T//TWllBwyn4Wpks8Q3+fu4QlrYEEQ0AqhSzloUwjXL0zhjWAK9sOt/YFonHzIrninVOAY+3yqcygQjZPtBkYqwmsKdZ6vDI7T1uv/xsl2AyOlispi4zsdm4wFonHysY4BJqOGgXFLCuXGRlu0KAjG5IWeEXpNxTeV8nljQNOntELoUpSHcGl5PsW5zvVrS0Q9REYno1ZneD+jFMJ5eZnWWLlUoJQiKeFIq/8r2VQYMyczlJICKYU9jzAI4cwD543zLETqIgsAmxfFE/GDkK9pNyQ3ptKQrA1WAc8Ugz2FBs6aBUVkm/1og5I+BVohdCVSSg63pd5NDlO9N3YvpV9RnqsNtSWO9mtLZEOt3QL1v8BRisr6mhIyHezXlsi66iJyMo3rBUIhNM/SyopCinJSZ0jWluZSVpAFwOsBUFSUwT4/P8vRxt+JFOdlsqzcmFgVBLmhvHNZ4RBrFjjX+DuRrIwQDeY8dO0h1KSVc90j9Jlu8lRanwBLy/IpMSdIHPT5A7TXVrhjV9BSQWl+FktMj6TfFe/h8QjHL5mFO4tTe54zwyHWVRuC/Uibv/c5GpOWorIpxfsshLCiC0HyEN6SYkMS4lGcQxf6fN+gWu3z2uoisjOcL9yxo5wjxzoGGJ0IRh9TrRC6kEO23JBUKypCCEsJ9bur/FCbPRyR2gcoxPNUDvq84OFIWz/quZXKvDbF+oWGQnisY9AqIPIjp68MMWw+uDamWG5APJeuvW/U1w2q+0bshmTq5YbKix0cj/i6QfV4JMpRswNEWvbZlFWRmKSx3f9pPaAVQldySLnJM0KsTqGbXKEUlXPdI/SalaF+5JAtFLAhhYU7CmWB9o5Mcr7bv5Vsds9cqj3eALeY3+1ENGZ5Kv1Ik+2hVW+Gu1LJLbZ76IiPH6D2vLZUFpQo7MqRnydpHO8YtCYbpbIQTTG1sMTfzhGFVghdiBI49dVFKc23UiiPCuBry+igvXAnL3X5Vgq7F8fPFYOqz2NFYTYVRc43pE7Efp4P+/gBqu7VrIwQKyqdb0idSINNCfVzodQUhXBh6hXvFRUFVsGDn9Mg0tUBQlFl62PqZwPHjlYIXcZ4JN7fKtXhYoW9zY1fFUIp4/lW6RA2AKuqCskyFf7GNv97rhrS4LUCWDI/n8IcoxH4ER/nazab4/nWVBWmxZAszsu08mL9rKgouVFXlk9JXlbKr58RDrGu2qjU97OH0N4BYlFp6jpA2GkwFf5GH++zHa0QuoyjF+P9rdKR1wZGwYOqnPOrYD/bNUz/qFm4k4a8NjA8OapyrrHdn/s8ODbJ2S6jUfK6NCmEoZCwvISHfXqeYzFJ80XjoZWufYa4MXmkvd+XebHpapSciNrno7bG+n4jnYU7ivXmvXShZ4S+Ef+mTym0Qugy0tXfKhH1APWrBWpvJZDOfVYWaFP7AFEfVgyqpHAwUiDShcpva+kcYng8krZ1OMXZ7mGroCRdnliIy40rg+NcGhhL2zqcorVnNC2NkhNR+zwRiXHysv/6xfaNTFiGZDr3uSEg6VMKrRC6jENp6m+VSEONcRN29I/ROeg/wa72OTsjxKqq1BfuKNab+zw6GeW0DysG7UK0IQ35VgrlUYnJqcUXfmFKQUl1+vcZjGlHfsOe65uOghKF3/O8050/qJiSF+tT54gdrRC6DDe4yWFqsrQfH6AqSbi+pjgt+VYKu5LkR4HTbHoI5+dnWQna6UDNjgZ/7rO6RzPDgpVVqS8oUdTXFBEyxZYf0yCUfE51o+RElpYVkJ9l9OXzY1qP3ZhIp0I4vyCbmhLDMROEPEKtELqIflv7kVvS0AbFzjofW0aT0fi81XSG12BqxWCjDwV7k03xTqeBU1WUQ3lhNuDPPMIms6BkZWVhyhv42snLymBFhaEo+U1uQLygZE0aGiXbCYWE1VrIj/usvJ6L5+elpXDHjvLG+tETm4hWCF1Ec4c9vJa+fCuA4txM6sqMEUl+EzinLg9Zidjp6NdmZ0rFoM8EzshExAqD19ek9zwLISyvt9/Os5SSJrOgJJ3hYkWDbZ/9VFgSjUmrA8T6NMsNiCsqJy4NMjbpr0kazS48z+19o3T5uOE6OKAQCiE2CCE+LoT4qhDicSHE00KI7wkhPieEeEQIkZ76cQ/gljwgRUONPwW7fZ/T7SEEW8XgxQEmo/6pGDzWMWBNKHHDeVb7fKHHXw3XL/SMMDhmFMrUpzFPU6EU7/7RSS70+Kfh+pkrQ4xNGvenm+RGJCatiIcf6Boap6PfyFtPt8EOU6N1fvcSJk0hFEK8RwjRBLwO/C2wE6gC8oD1wG8DPwYuCSH+SQgxP1nX9gsq7JOuBr6JKAu0a8hfFYPqps7JDFmD4tOJeriMR2KcuuyfwhJ1nsEdgt2eiO8nb2zjFEMyvZ5YSCgs8ZE31r7P69Ls8Qb/FpZMnbiT/n22G7N+brgOSVAIhRAlQoj/Bv4DeB54A1AgpVwppdwupbxTSrlWSlkOLAf+D7ABOCmEeHCu1/cTVtjHBQ9PmCrY/RRmU8Jz7YIiMtJYUKKYKtj9k9+m9rk4NzOtFfOKKefZRw2qleIdDgnWLEj/A3T1gkIyw0a+qB/3OSscYmVl+gpKFItK8yjONSYs+amiu3lKq6r0PwvtDdf9JJ+vxZyehkKIXOBFoBOok1L+vpTyBSnlNQPtUsozUsp/l1LuBD4IfEMI8ea5rMEvDI1HrL5LbrDyAdZVF6HqAPxSyRZxUUGJYml5AXlWxaB/BHu8oKQorQUlitL8LGpLzYbrPvKoqHyrFRUF5GSmr9BBkZ0RZnWV/yZpKIPdUHjTb0gKIWwFD/6QzxCv5q0pyWVefnoLShQNquG6j87ztZjrqS4Bviil/A0pZddMXiil/BmGN9Ff2bCz5FjHACpNL52TBuzkZ2ewvNxoYeGXG+FU5xDjLikoUYRDwrKE/RL6GZuMcqpTFZS4Y58h7nGwN8z2MlJK68ysc4E3RaEUlaaL/cR80HA9FpPWmXHTPiuj1k8N1+ORMnc4RiBeRNQ5OM5lH6VPJTInhVBK2SGl/Oa1/k8IkW37c5EQYqMQYoq6L6U8KqV8ei5r8AtT8ybcI3BUmK3RJ6Oo3NIoORG1lmMdA4xHvG8jHb80aE1ecUPYR6Hurfa+UV8UlrT3jdJnTs5ocNEDVO3zyESUs93DaV7N3DnfM8KQqXC5SlGxNVxv9oGR0zs8QVvvKOCeCA74v1+swokq41Izp/Bn5t/rgTPAa8ApIcTKZF/TD6j8lHl5mVQXp7+gRKEeMn0jk9aN6mWabAUlyvvpBpRHZTIqOXnJ+4UlbjVw1trSMfzwAHXrPtuNAD/sc6PLOkAoGnw2QMB+VtwSKQPVR9X4sx/7xSqcSIT4G2Aj8FXz71/AUAh/Degy/1+TQLOtoMQN+VYKvwkc9RnWuKSgRDFlRJIP8oHUeS7MzmBxqXs6TU1VVPxwno0HqBC4oqBEsbKqgAxzZEmzD+SG+gwZIZHWUZeJVBfnMC/PKCxp8sN5vuhOxbsgO8Pqy9vkAwPnejjxRHwY+CMp5Q+EEPnAfcD/MXMGPwfc6cA1PY0938pN+SlgPGTio6i8LXAi0ZjVWNZN4QiAJfPzKcjOAKa2a/EqViV3dRGhkHsMnPLCbCrMiSV+EOxqn5eVF5Bvnh83kJ0RZnmF4YH3g4dQKSorKgtdUbijECI+saTZR3LDPlnILahnhtefgzfCCYWwGDhn/vlOYAzYY/59AEh/4zeXcaxjwMq3cpuikpeVwTIztOr1B+jpK8NWY1k3hdfAGEWlwple91xNRGKcuDQIuG+fIb4mr++zlDJeye2SzgR21D43XfR2/rGxz4bsc/M+n+ocZHTC2/nHze3uKyhRKI/llcFxOn1aWOKEQtgIvE8IUQD8HvBLKaU6pe8Emh24pqexK1quvBGUYPd4YcmUghIXKipqTcc7Bq3Rel7k5OVBJqPuNHAg/lA/2zVsFQp4kcsD43SbhTFuVLzVSMa+kUku9nv3AdrWO0r/qFG448Z9VopKTMKxS9412gfGJjnXbUy2cVukDKY2I/erl9AJhfAzwP8A+oEHgS8CCCGeBH4L+LwD1/Q0yioqzMlgkYvyrRRKCPYMT1gjhbyI8qZkZ4RYUeGeghKFMgYmojFOdQ6meTXBGfUVAAAgAElEQVSzx22TBhJZaz5spMTTI78aXVpQorCvycv5x24/z/Y1eTlf0x7ydqMhaVdS/ZDWcy2SrhBKKZ8BtgGfAu6UUr5i/lcL8GtSyh8n+5peR+WnGI2g3ZNvpbCHSfwg2Fe7rKBE0eCXB6h5nvOywtSVuVfxBm8/QO1nZK0LQ5lrFsQb23s5j1Cd55DLCncUi0rzKMzxfv6xPYXDjQZOcW4mi82JJX4o4LkWjjwVpZSHpZR/J6XcZ/u3j5mFJRobU/KtXOgmh6nl/15VVKIxaSsocZ9QB6gri08s8bJgV2tfu6CIsIsKShQ1JbnWyC8v58Wqe7GuLJ+inMw0r+ZqCrIzqJtvpIx7W/E2zsiy8gLystxTuKMQwh+N7dXaywqyqCxyV0GJwp4+5UeSohAKIV4TQnxECDEvGe8XJOz5Vm60isAQ7Es9XnJ/rnuYETPh2o35KWBMLFlreiC8KtjtowHdep6NykxVwOPN8wxTIwtuJV4o5c19nlK449LzDHGv98nLg55tbG/fZzdGyiDutOnoH6Nr6JoTej1NsjyEjwEfAy4KIb4vhHhAuPUbdRluz09R1Hu85N6+z25+gKp9PtYxQCTqvcKSlivx0YCu3mdTsJ/y6AO0c3CMywPGA8mN+VYKdZ4vDXjzAWov3HH1eTb3ORLzZmP74fEIZ7qMiTZujZTB1Ge0H72ESVEIpZSfk1KuBu4HhoAfAheEEH8thFiRjGv4FbfnWynUjeDVkns1hzQjJFhZ6Z7GsokowT4eidFyxXuC3R7qdtNowESU58qrD1B7Ar6bPVfrPD4Zxu2FOwr72rxotB/tGEA1sHC1Y8RnE3gSSWoOoZRyj5TyQ0AV8BfATuCYEGK3EOIDZqNqjQ2351sp7DeCFwWOUryXVxS4qrFsInZh2OjBmZn2Sm43jQZMZEoFrAcTxKdEFlzsUZlamentfXazh7Bufj75Kv/Y6+fZxYr3vPwsakpyAW+e55vhVFHJiJTy61LKu4DVwIvAZ4FLQoivCyF2OnFdr+GFfCvF1MISb1lGUkrLmnP7Pi8vLyA7w7gtvWiBunU0YCJ18/NtBTzeE+zKKKstzaU4z30FJYrS/CxrNvtRD55nVflaV5ZPoQsLdxShkLCUby8W8KhnSklepqVwuRVltHvRMXIzHJfYUsoWKeWfAosxGlPnA884dT0hxCNCiENCiDEhRJcQ4htCiFKnrjcXTl8Z9kS+FRgl96pHotduhPa+UfpGjMaybt/njHDIam3htX22V3K7OewD5mSYBd4teLAMHBd7BxXKmPSm58qM4LhcbkC8cfKxS4NMeiz/WCne9dXuLShRqJzdtt5R+kYm0rya5JIyE14aPC2lfBdQ48Q1hBC3YxS4nMZQPv8S+DXgR05cb654xU2uUDeC10Z+NV/0Rr6VQu3z0YvxkYZe4GzXkFXJ7QlFxXzIe62Ap2d4gva+UcAb51nt8/nuEQbGJtO8munTNTTOJTNf2s2FOwp1z01EYpy67J282LHJKKc6jfW63WAHb0fLboYjTZWEEGuBu4AyIFHdl1LKv3LiusDHgVbgnVLKmLmWQeC/hBDrpZRHHLrurFAWc1ZGyBoE72bW1RTxRGOHVXJfVuDOXlGJqBCKcGlj2USUd210MsqZK0OscHERjJ0mjxQ6KNbZCnjOdA27utjIjtcMSbtxcPTiADuWzk/jaqaP3ZD0gqJiL+JqutjvCa8mwIlLg5bhu85j57npYj93rChL42qSS9IVQiHE+4CvAdfL3JeAUwrhDuAZpQya/Lf5+zbAVQqhqhRcU1VIpovzrRSJkzTuXlWRxtVMHyXY6+bnU5DtvsayiSQWPHhHITQUlcywuyu5FfUJBQ9eWDNMDb3We+Chb58B2+whhXBqQYn7FZWlZfnkZIYYm4zR1N7Pu7bUpntJ08Jrind5YTZVRTlcGhjzXFrPzXBCC/lTYBewUEoZusYvJ0s8q4DOhH9Tf7+u9iKEqBBCrLP/ApY5tUiAWExaoVcvWEXg3ZJ79QD1isW8oqKQLNNAaGzzzj4r4biqqpCsDPcbOCsqC6x99tR5Nve5ujiH+R7w0lcV5VCanwV4K91EFcFUF8fX72bs+cdeKpRS8jk/K2xNtnE7VmN7D+3zdHDCXbII+ISU8qID730zMoEpSSpSyqiZpHqjO/ojGPmGV7F3714uXbrEwoULqaurY/fu3db/3XvvvTQ2NtLZaeicq1atIj8/nwMHDgCQn5/Pjh072Lt3L8PDRtPNTZs2MTw8zAsHjjFs5ls11BSza9cu63137tzJ2bNnaWtrA6Curo6Kigr27TMmAWZlZbFz504OHDhAb28vAPX19QA0NTUBMG/ePDZt2sTu3buZmDASX7dv305nZydnz54FmNVnKssN0TUa44UjZ1kdOz/lM504cQKAiooKGhoaXPGZ+sel1cA3Z/QKu3btmtH3lK7PVFeaxYkrY+xpPseJleGknj0nPlNMSo609gCwINu4BZN99pz4TAvyJOcHjQdoOu6n2XymV1uM87y4OGz9m5tkxLU+06ryPF4ZnmDfyYvs2tXtKhlxvc90pNW4RkXWBHv37nWdjLjWZ5onjTGoTW19RpFXc5NrZMT1PtMrx4w1r6zI59y5s66TEdf6THnjEQDOdY/w86d/SV6mcIWM2Lt3L3NBSJncpHUhxFHgL6WUP0zqG0/v2hL4jJTy09f4909LKT9znddVAOUJ/7wMeLypqYl169Ylfa2RaIxTnUM0tvdz69L51JoVvG7nd7/5Gs80X2bhvFz2/OEb0r2cm/L8iU4+8PVXAfjmh7axc0Xi1+xO/vjHjXx3/wUKsjM48pdvJOTiHpUA57qGuftvnwfgrx+p59Edi9O7oGnyR48d4XuvtlKYncFhD+xz/8gkt3z2WQD+4P6VfOxeb/T9//xTx/m3F04TDgmaP/OAq3uBAgyMTbL+08Y+f/K+lXz8Pm/s8w9ebeVTjxmZUc9+8k7Xp0FEojHW/eUzjEdifOC2JXz6rcl/1jrBL49e5rf/72sAfPfDO7h1mTvSIJqbm5XyXS+lbJ7p652I6/wt8BkhRL0D730zJoEpTYyEEMozeN25SVLKTills/0XRqWyYyj3/ru21HpGGYR42Litd5TeYfeX3E/NT/FGaB7i+ZpD4xHOdQ+neTU3xysTHRJR6RqD4xFae0fSvJqbYw+5ur21jx211mhMcvzSYJpXc3OOeiyvTbHOY6PV7K3XvJLSA1NlnJfSIG6GEwrh00ABcFgIEb3Gr4gD11RcwcgjtFNp/t7h4HUDQ/1Cb+URqpvVK3lAiikTSzwg2FUeUDgkWF3lbq+EHXtRhhdaSHhW8a721gPUa5XcipWV8fxjL5xnr0zcSaSyKNvqsuEF+TxdnMgh/CpGu5lvABcceP8b8QrwgBAiU0qpcgkfMH+fW3BdA3iv5F4prV4p3FGsqiokIySIxIwpK2/b4EjrzqShKuZXuHw0YCKrq4oICYhJQ1F58/oF6V7SDWkyz3NFYTYVhTlpXs30WVyaR0F2BkPjEU8oKspDWFaQRWWR+wt3FJnhEKsXFHKkrd8TjcCVfM4Kh1hR6f7WawohBPU1RTx/4oonPLHTxQmF8E7gD6WU/+TAe9+Mf8BoRP0zIcSXgWrg88CTUsoTaViP7/BSyf3A2CTnu40woJfCPgDZGWFWVhZytGPA9TONpZTWWfCSNwUgNyvM8ooCTl4ecv15hnhVo9f2WU2G2X+uh6MeUFTinQncPzkjkXXVxRxp6+foxQFiMenqvFi1z6s80nrNTkNNMc+fuMKZrmGGxyPke6Cl2c1w4hsYBmaczJgMpJR7gLcDC4AfAn+NMaXkvelYj1/xSsm9PQ/IS+EIRYNt5Feyi7+SSVvvKP2jhkPeCxMdElFn4+jFAVfv8+DYJGe6jHxSrymE4J3RaqMTUVrMyRle6POYiJLPbs8/jsUkx1QEx4P7rNIgpMQa2el1nFAIfwg85MD7Tgsp5eNSyg1SymwpZZmU8rellO7WXDyGehidc/koqimNZT2UgK9Qgn1wLMKFHvcWPHi10EGh0gm6hyfo6B9L82quz1QDx4P7bButdvqKe0erHb80gJoY6aVCNMWUAQIuzvO+0DPCoNm+xWspPTBV1vklbOyEjzMT+IQQYiXQfY3/l1LKDzlwXU2KmNKgun3ANSX3iagH6Pz8LKqKvJNvpahPmJm52KVNW1WoNeSR0YCJJE7gqS7JvcFPpw97SNs+pswrTH2ADrC6yp1npWnK7HN3rvFGrKyM5x83tffz1luq072ka+K1CSWJ1JTkMi8vk96RSU+km0wHJzyE9wNtwHrgnuv80niY+oQHqFuxTyjxWh4QGMpV2Mz/cbPAUUUCy8oLyMvyXh6Nvd2Fmz0qzR43cJaVF1gTbNxcaaxSYQpzMljkoZZgipzMsDXu0gvyOSRgjUuNgxthFJYYz8JmDxRKTYekK4RSyrqb/Fqa7GtqUou95N6tlWxT8oA8GI4AU7BXGJV3bhXsUkprbV7d54LsDJaWGd5Xt+4zxNe2rsZ7hQ5gVMCuMVsSufkBqhTvtQu8aUgCNNTER9i5NS9W7fOy8gJys7zTmcCOknmnOgcZNSePeZk5KYRCiEVCiD8VQszKLSCEuEsI8e65rEGTelTJPbjXczU1D8h71qei3uWFJZcGxug2G5T7Yp9dep5HJiJW3l2DB8OYirWqgKfDqIB1G5PRGCfMxtleNXAgvvaBsQitPaNpXs3VSCk9WzFvR6VPxSQcu+ReI2e6zNVDeBG4D3hSCDHtWVVCiLAQ4lPAY8C5Oa5BkwZU3tXZrmGGxp3sNT47mjxeYaxQxQN9I5O09bpPsNt7ynmxwlihDJzOwXE6B9xXWHKsI27gePo8u7wC9tTlISbMCmgvGzjrEvrFuo3LA+M+MSTja3d7143pMCeFUEoZAR4E2oHjQoivCCHeIoS46hsWQuQLIW4XQvwVcBb4MHC/lHLfXNagSQ/2kvtjLiy5V73OCrK9mQekaJgyGcZ9AsfuUfPS6KlEEhuuuw17L0ove1TsRoMbowtNF/2xz2sXGA3XwZ1e7ykdIDxs4CwqzaMwxwiQuvE8z5Q55xBKKcellB/EmAhSA/wE6BVCDAshzgshzgkhuoAB4EWMnoBfAtZJKQ/O9fqa9GBXVNzYOFl5rtZWF7m6MevNWGMT7G4UOEqwLy3LpzAnM82rmT3rEiq63YbyeBfnZrJwnjuroKeDmsAD7lRUlJcnJzNk5ZV6EdVwHdwpN+wVxl42JIUQljHpRrkxU5JWEiilfBF4UQhRCdwBNGCMsMsE+oEzwD6tBPqD6uIcq+TebR4Vex6Ql8MRAHlZGSwrL+BU55ArBY767r3YR8xOcW4mi0rzuNAz4kpFJV64491CB0iYwOPCfVaKyuqqIjI8NjkjkfrqYk5eHqLZbLjupnOj5Mai0jyKc71rSIJxT75yppuTlwcZj0TJzvBmgQw4U2V8WUr5mJTy01LK35dS/q6U8lNSyn/TyqB/sJfcu+0Bas8D8nK+lcK+z24qLOkcHOPywDjgzUbJidTbKjPdxNhklFMer5i302Br1eGmwpJoTFoTJ7zYfzARdVZ6XNhw/aiHJ5QkovY5EpOWI8KreNsE0qQVdSO0dA65quTenmvnxQklidTbJmlcclHBQ7NPCkoUap8v9o/RPTSe5tXEOdYxQNRUnHxh4JjpJoPj7prAc657mBFTjnk5r01R79J8zd7hCdr7jAI5Pxg4iQMEvIxWCDWzxl5y76ZZjirsk50RYnl5QZpXM3fs3jc35Wv6JTFcMbWwxD3n2f4wX+/BCSWJuLWwxH6e/aB4Gw35jT+7qQLW6xNKEqmbn0++2UfRTed5NmiFUDNr7ILdTRWwai2rqwo9nwcECQUPLlJUDrfZ8oDyvJ0HBO6dwHPE3Ocij07OSGS1SwtLlKKSERKsrPK+IVmQnUGdarjuIrlhzzn3gyEZCgnrc7jpOTgbvP+01KSN2tJcilTJvUs8V5FozHLb+yEcAe6dpNHY3gf4w2sFUJqfRY05x9hNgl3dW+sXlriqMGC22Eerucmjor7zFZWFni4MsBOvgHXPPqu1VBRmU16YnebVJAeVmnS8Y5BJM3/diyRdIRRC/LMQ4rZkv6/GfUwpLHGJBdpyZYjRSSMP6JaFJWleTfJwWwHP5YF4QYlfFEKIh7DcoqiMTEQ41Wkkqjf4aJ/dNlrNGMHon0IHhRsbrh+xDBw/nWfjs0xEY5y87N3CEic8hO8Bdgshzgoh/kYI0eDANTQuwZrleHmQscn0F5YcsXkq19f6R+C4TbBP2WcfKt6tPaP0j0ymeTVGNaYqxL3Fhw/QgTF3FJac7x6hf9T4vv20z1PSIFzg9e4dnrC+bz/KDXD3nO6b4YRCWAG8EXgSeD9wSAjRJIT4EyFEnQPX06QRt5XcH2kzwpg5mf4oKFG4TbCrfRbCP6F5cF9erF3xbvDpA9QN3tjD5nkGfykqU0bYuUBROeKzAinF0rJ8cjINdcoN53m2ONGHMCql3CWl/KiUciFwO/AE8EGgRQjxUrKvqUkf9gpYdygqZgPf6mJfFJQo7IK9sc0Fgt3c52XlBRRkJ62/fdqxtylyg2BXa5ifn0V1cU6aV5M81iwoImwWlrhhn9V5zgwLVi8oTPNqkodquA4u2edWfyreGeEQaxeYaRAueA7OFkefmEKIDKAEY2LJPCCGMcJO4xOWzM+3FIJ057eNR6LWXGU/CRswBPvi+YZgT7fAkVJaHsL1PvIOAlQU5lBhJrq74QGqPFcNC4t9UVCiyMkMs8IcreaGEJs6z2sWFPmmoEQRbwTuhvNsrKG2NJfS/Kw0rya5KK/3sY4BIh4tLHGiqCRTCPGwEOIbQCdG6Lge+CxQI6V8KNnX1KSPUEhYsyjTHZI4cWmQyaiRcHWLj/IHFW6pGGzrHaXXzK/zU9hHoT5TuhXCwbFJzlwZBvyneENcUWlMc2FJJBqzvms/FaIplNfbDQ3XLUPSh/usFMKxyRinzfvWazjhIbwCPA7sAP4BWCGl3C6l/JKUstOB62nSjFJUTlwaZCKSPsvosE8LHRRK4HT0j9GVRsHu17w2hVIKzneP0DM8kbZ12A0sP+6zqpruH53kfHf6CktOdQ4xNmnILT8aOG5puH6pf4zOQUNu+alwRzFln13gjZ0NTiiEXwO2SSlXSyk/K6U87cA1NC6iYaFhgaa75F7lpxTmZLDYBw18E7HPV02nwDli9h8Mh4SvWnQoNiyKK1+HbTlPqUb1eQR/KiobauP7fCiN+3zEVlByS63/FG+3NFz3a+GOYkVlAVkZ3i4scaKo5A+klK8n+3017sUtlpG9v1Uo5J98K4Vr9rnVuPbKykJyMv2VbwVTH1YH06qoGPtcWZRNZZF/CkoUq6uKrAdoOhXCQ+Z5zs8Ks8xHnQkUbmm47tfOBIrMcIg1VUZBkhs6FMwG/5RhatLG0vICck3FIF0FD/YGvn60PgHm2QR7uvI1YzFpKaN+DPuAUcCztNyYDJNORUV5GRpq/HmeszJCVpeC9CrexrXra4qtyme/4YaG68rAWe6zzgR21JjR5osDxGLpb7g+U7RCqJkzYRcUljT7tIFvIvZE/HRwtnuYwfGIsRYf77MKZx5u7UtLwUP/SDyvzo/hYsXGRfMAOHqxPy2N7ccmo1b/VD+GixUNaW64bnQmiI9g9Ctqn0cmopzp8l5hiVYINUlBWfrpKrk/7NP+VomoPML2vlF601DwYJ9Z7ceKTMVGUznoH53kbBoEuz3fKgiK92RUcrQj9cZk88UBIqYl6WfFO92N7S/02CbB+LADhMKe1uPFsLFWCDVJQQmc8UiMk5eHUn59ZX2WFWSxwEcNfBNJt2BXIdSscIiVlf5p4JvIhtp51p/TETY+eCF+zQ0+VrynFJZcSP0+Tyko8fE+2+VGOs6z3ztAKFZWFZAZNhuut2mFUBNQ7OGWg629Kb/+YVt/Kz818E3ELtiPpEHgHLxgfLfrauIFAX5k9YJCstNY8HDA3OelZfnM81kDXzsL5+VSVmB8vnTkEap7qDQ/i4XzclN+/VRRXphNbanx+dQ9nEpUB4jMsGCNjybBJJKdEWaVWVhi9/J7Bf9KdE1KWV5eQGGOkSh84Hxqb4SuoXEr32qjj/OAAMoKsq3CkoMp9qiMTUZpNvuYbVo07yY/7W0ywyFL+U61QhiLSeuhbW+B40eEEJY39lBaDUl/TYK5FhvNfT54IfV5seoe8uMkmETUPh9p609rX97ZoBVCTVIIhYSVIJ5qC/TA+fj1Ni/2t6IC8c948EJvSgV7Y3u/lW8VhH1W4cxjHQMpLXg40zXMwJhRuON3xRtgo6n0tvaMprThet/IhDUJxs/hYsUmc5+7hye40JO6RuDjkShHzCK4IJxnJRvHI7G05MXOBa0QapKGEjhnuoZTWvBwwPSUhYS/KwUVSuB0D0+kdMKDXfEOgmBPV8HDgQvB3GdIbR6hfZ+DYOBssn3GAyk02psvDliesk1B2GfbPWuXmV5AK4SapGG/EVKZR6huutVVReT7tL+VHfs+v55CgaMeItXFOVT5uHBHkS5FRXnY87LCrKz0X6PkRIxwrfHnVIbn1b0jhP9D82CEa3MyjUd+KtN6ghbBqS3NpawgG4DX05CvORe0QqhJGhsWlViCPVUCZyISs/KAgiBswCh4UI3AU2XpSyl53fxONwZkn+0FD6lUVFRu6C0LS8gI+19EF+ZksqLCUHxTuc+vnTPunVWVhRTlZKbsuukiMxxivdnkPJUeQqV4VxXlUB0AQ1IIYUXLDmoPoSaoFOVksrLCqLBKlcA51jHAuBWO8L+VD4ZgV728UuUhbOuN53cFIYwJUwseUrXPg2OTnDDngQflPMPURuCpmPAwGQ2eIQmw0TxTxy8NMjIRcfx6UkpeM++dzYvn+b5wR6FC4xf7x+joH03zaqaPVgg1SUU9xA639qWkQbX9Qb15Uanj13ML6iF24vIgg2POTx6YmtcWHEVlyxJjn9v7RrnY57xgP9zaj6oT2lgbIEXFNDIGxyOWQuwkRy8OMDZpyCf1HQcBdaaiMZmStlVtvaNcGTQNyQAp3nYjI9VdN+aCVgg1SUUJ9uGJKMcvOS/YlaJSVhDvsxUElJdOytSE2ZTinZURYp2tG7/f2bokbmS8eq7H8evtP9tt/TlID9BU73NQDUm71/m1FOxz0Ap3FA01xWSYc7FTGZ6fK1oh1CSVLbab3mnBLqW08oA2LfJ3Q+pENtrCtmoPnGT/WeO73LCwxNcNqRNpqCm2EvHVHjjJPvMaqyoLKfVxQ+pElpXnM9/8vPtSsM9KIbQ3bA4CFYU51JXlA6nd5+yMEGsXFDl+PbeQkxlmndnHNBWKd7IIjmTXpIS6snwqCo0Kq71num/y03PjQs8IlwbGANhWFxwrH4zJCsvNRHynFZXe4QnL27t9abD2OSsjZIXZnDZwxiNRa1pH0M6zEML6zK+e7XG0v6ZRIGXmtS0KTl6bYru5z6+f72XS4bQeJZtuCZghCbDD3OfG9v6UpPUkg2B9QxrHEUKwfel8wBAGTiaI2xXOHeY1g8QOUzk7cKHX0cbJ+22K0Pa64O3zVlOwn7w85Gh/Tftkg6AphBD/zJ2D447217QbkkHKH1SofR6ZiNLU7lweod2Q3BEwQxLixnNMYhXWuB2tEGqSjrJAe0cmOdU55Nh19p0xFJWinAzWBCgcoVBK8HgkxmEH8wjVPmeERKAqXxXbUpTfZvf0bg+wQgjOer1fOR1sQ3K77TM7GTbedzbY+7xlSSlmGqElQ92OVgg1ScduDdqFQjKRUloewm11pYRDwQr7wFRv3V4HBY76DtcvLCYvy/+NvxPZuKjEOl9OKoTqPNeV5VNR5P9+bYmsriqy5qE7qai8Yu5zcW5moPLaFDUluSycZ+RNOql4K5mUFQ5NyXkOCkU5mVYBntPpU8lCK4SapLOsvMBq6OvUjdDaM8rFfiPsE0TrE4yEeJVH6NQ+949OWmPbtgd0n/OzM6ivNhQHpx6gkWjMymuzeySDRDgkrGrj/eecMySVh3B7XSmhABqSwJR8zahDaT1KJm2oLSE3K+zINdzOdlse4fC4830f54pWCDVJRwhhea/2O5QgHvT8QYXTeYSvneux+uIFMYypUGessb2f/pHkJ4g3XxxgZML4/oKYP6hQn721Z5R2B/o+nr4yTKfZF++2ZQGWG6Z8HhyPcMyBOd09Ac8fVCgjOhqTKR0zOlu0QqhxBJVQ2zU0QYsDeYRKISwMaP6gQineTuURqtBdOCTYElDPFcAdK8oAI0H85dNdSX//PS3x9wxaJbedW23G3Z5TV5L+/q/YDMlbl5Ul/f29gt3osOdUJot9doM9wIr3tiWl1jhXp9KnkolWCDWOYBfsu08l9wEqpbQE+/aA5g8q7MrDKw6EjV88aTyUG2qKKcgOXv6gYuuSUqttxu6W5CuEap+XluezcF5e0t/fK9TXFFOSZ8wVfjHJcgNgr6n8zM/PYmVlQdLf3yssnp9HTYmRR/iiA4q3MtizwqHAjLq8FsV5maypMhwWLzugeCcbrRBqHGF5RQELzEHmL5xMrsA51TlEh5k/eFuArXwwGs2qB9uLSd7nywNjVtjnrpXlSX1vr5GTGbZC5nuSrKgMjUescNKdK4K9z+GQ4Pblxj39UktXUvPbYrF4IdqOpfMD13/QjhCCO817et/ZHkYnkptuooymDYtKyMkMZv6gQkUXDrf20T/q7n6EWiHUOIIQgrtXGQJn75nupOa3PXe80/qzukaQuXtVBWCMsEtmnzy7In+X3mfuMBWVCz0jnO8eTtr77j3dTcRUfO5cGWwDB+BO8wHaNzKZ1D55zRcH6Dbvj1sDHMZU3GWetYlILKnhzAvdI5y5MmxeQ8uNnbZ0k1ccSDdJJloh1FvUvaMAABe0SURBVDiGEgbjkVhS20g8f8JQVBaV5lljmILM3eY+x2Rywz9KISzOzeSWhcHrP5iIsvQhuWkQ6jvLDItAF0gpdtq8pMn0ev/KZkjes7oiae/rVW5bXmal27x4Mnnn+fmTtn1epfd565JSss10EyfSIJKJVgg1jmEXOC+cSI5gHxqP8Np5Q7m8e1V5oMM+ii1LSsk32zoka58j0ZgVGt25oizQeZqKNVVF1rzdZIaNldKzZXFpIPs8JlJdkmu1U0qm4v2r45cBWF1VaOXPBZminEw2LTIMvRdsStxcURGcyqJs1iwoTNr7epWczLBVxPPiySuOjmWcK1oh1DhGUU4mm82E4mQJnJdaupiMGjeUDhcbZGWErLyrF05eScq4wMNt/Va+iw77GIRCwvIS7mnpYjwy9zSIC90jnDPHtN2p99lChdkOXOhNyhzYK4PjHG4zws/aOxhH5ayevjKclDY/Y5NRq3jinlUV2mA3ec+2RXzqwVX826Ob072UG6IVQo2jqNyz01eGae2Z+3xSFS7Oyghx61Kdb6VQeYTdwxM0XZx73tWU/EGtqFjct6YSMDzVyagaVF4riCtBmrhyHIlJnkuC1/v5E3GD9A1aIbSwGyH2PZotr5zpZtycx323DhdbvKlhAR+5ezn1NcWuVpK1QqhxFLsy8ezRyzf4yZsTi0lLaO1YOj+w3e+vhd1bas+Vmi3PNl8CYM2CokCOUbsed68qJytsiE21R3PhySbjPWpKcllXHdx+monctmw+hWabo6ebOub8fs+ZcqM4N5ONtTofVtFQU0x5YTYATzfN/Tw/b8qezLDg9uU6H9ZraIVQ4yjrqouoLTXydZ44cnFO73WwtddqN3PfGm192qkuybUadD/VODfB3tI5ZLWbeXND1ZzX5icKczKtsPGzzZfn1Balc3DMmo38UH2Vqz0HqSY7I8y95j3+3PErc2qLMhGJsdssmrh7VTkZYf3YU4RCggfXGff4y6e759SlIBaTltG/ZXEphTmZSVmjJnXoO0PjKEII3txQDcCBC31cnEOeys8PG56CkICH6hckZX1+4uH1xp6cuDzICVOhmw1PNsY9Mm9q0PucyAPrjLBx9/DEnMZRPdN82RoL+JDe56t40LzHRyejc+pl+vyJTgbNObL3miF/TRx1j0djkmePzt6YfO183GB/03p9nr2IVgg1jvOwTTjYlY2ZEI1JnjBfe+uy+VaYQxPnLeurrT//Yg7e2CeOGPu8ZkERS8uDO83hety3phJVdP3MHMLGT5nnuaooR4cxr8FdK8vJNZsazyVs/Pgh417IywrryMI12FZXSlmBUT3/xByiCz873A4YzcXfVK8jC15EK4Qax1lXXcTi+cY4ridmqRDuP9vDFXMovV3x0cRZND+PW0zF4ueHL86qvUFL5yAnLhvexYe1lX9N5hdks9Wc6/x006VZVXV3D41bvTkfrK8ipNv6XEVuVph7Vhu5sbuOdc6qqntwbJJfHjPCmG9cW6nb+lyDcEjwgAobt3TRNzLzsHEkGuNJU5m8Y3kZ8wu0we5FtEKocRwjbGwoFwcv9NHWO/Nq45+bHq+MkOBBbX1el7eYSty57hGa2gdm/PpfHNHh4umglOX2vlH2zmLKw5NNl6z8Q73P10elhgyOR3ju+MzDxs80X7aqXt+2sSapa/MTSj5HYpJnm2de/PfS6W56zPzDt96iDXavohVCTUp4s83b9OMD7TN67XgkaoXXdq4ooyQvK6lr8xMPr69G1Sb89NDM9jkWkzx2oA2AtQuK9BSYG/Dw+moyw8ZGP/b6zPYZ4IevtQJQXZzD5sXzkro2P3Hfmkqr2ljt2Ux43LwH5udnsXO5butzPbbVlVppOD+YxT7/zAzLZ2WEeOM6nafpVXylEAoh1gkhfiaE6BNCDAghXhZCPJDudWkMBUO11fj+q60zqs58qvESvSNGc9pHtJV/Q6qKc9hRZ7R7eOxA24xmSL90uovWHqPo591bax1Zn1+Yl5/FvauNB9+TjR0zGlp/rGOAI2aT5HdsqdVTYG5AblaYh02P0/Mnr3B5YGzar73YN8pLLUZ18cPrF+jq4huQEQ7xjs0LAaM4pKVz+kVp/aOTPNFoKIT3rq7Q1cUexjd3iBBiKfASsAD4PeC9wCDwpBBiZzrXpjHCxu/dvggwwmzPzaBX3rf2ngcMK1+Hi2+O2ue+kUmrQGQ6qH3OzghpxXsaqH0enYzOyHv1Xy+fA0AIeKf5ENZcH2WcRGPSOqPT4Vt7z6Psznds1gbOzXjXlvgefWvvhWm/7rHX2xibNMLy6p7QeBPfKITAJzA+zwNSyu9JKX8BPAL0AL+V1pVpACO3RIV//mP3mWm95sCFXl4zW3u8c0st2Rm6GfXNeGBdFWVmUvd/7j4zreKSM1eGrB5ib9tQTXGutvJvxh3Ly1hqhtX/65VzRKKxm76me2icHx80wpj3rq6ktjTPySX6gg21JVax1Lf3XZiW13t0Isp39xtKzebF82hYWOzoGv1AXVm+NS3nB6+10j9yc693JBrjv145Z73+9mU6LO9l/KQQtgH/KKXsUf8gpRwFzgKlaVuVxqIwJ5P3mBbk/rM90+rh9q/PnQaMzvcfuG2Jk8vzDVkZIT5w22IAjl8atKY03AhDcTT+/OGdS51cnm8IhQQfuH0JAK09o/zs8M1b/Xx1z1kmzCKHD91R5+TyfMVvmfvcMzxhKXo34tv7zltpJlpuTB91749MRC1F70b84kgH581Z3B+4bYmulvc4vlEIpZRfkP9/e3ceXlV953H8/U1IAgRkEVKVXWBgJOoUqwQBRVzo4jZVp49atNaOS7WiVcepzzh1qXVhcHD3Eav1GTuiFKf6gAUxigI1LoAYEMKWIIzIEhFNwIQk3/njHDLhmiBZ7j0Xzuf1PHlO7jnnnnxPfs+993t/q/ttDfeZWQ8gH3gjmqgk0c9HDahf+uu+2Sv3WXu1aP32+ikjzhvem8O6aAm1/TVhZH86hbWx/zFn1T77bK7dWsGLHwSDSU4dmsfg73ROSYwHg3/6Xp/6zvgPFa6uT/Yas/WrKp5ZWAbAd/t2peBIfU/dXz86+nD6h1NXPfrmWnZW1zR5bkVVDU+8FbRAHNkzV6O4m2HM4B4cFa54NPXtdftcuaS6po4HC1cD0KNTjvodHwQOmITQzA43s6FN/DQ17PRxYDPw1LdcOy8ckFL/Awxs63uQYNDDJSOD2qv3Sj+vn7sqUW2dc+fMj4GgxuuaUwalLMaDQZcOWfXf9j/e9GWTIwfdnd/N/JjaOscMbho/JJVhHvDaZ2Xyy7HBW0VZ+U7+sKC0yXPv/etKdoXNnTefMURL1TVDu8wMJp42GIBtFVU8/MaaJs99uHA12yqCOUuvGzdYg3aawcy4OXwP+KqqhslzS5o899m/lVG6rRKAq04+kvZZ6s5zoDuQZum8B7i0iWN/D6xsuMPM7gTOAsa5e+W3XPuXwG8bO1BUVMRnn31G7969GTBgAPPnz68/duqpp1JcXMyWLUGT3JAhQ8jNzWXx4sUA5ObmUlBQQFFREZWVQQjDhw+nsrKSkpLghZaXl8fRRx9NYWFh/XXHjBlDaWkpGzcGtTYDBgwgLy+Pd999F4Ds7GzGjBnD4sWL2b49aHbNz88HYNmyZQB069aN4cOHM3/+fKqrg295I0aMYMuWLZSWBh9aUd3T0e2cQ3Iy+bKqllumL+brjTnkdc7Z655mldawdENQC3Bab2PVknfYmsb3lI7ldMVJx/PswjV8vquOO14uJr9nFt2yave6pxVfd+XNkmB+txMPz2Tgoe0pKSlJ23tKx3I6Yuc6Ds81NlU6U15fRccv1tG7c8Ze9zR3+SZmfBg0YZ40sBu71i+lcH363lM6llP3rCyO7dOVpRu+4Mm31tJ95wbOHnXMXve0uTaXPywIeg0N7GLklq+goqJL2t5TOpbToNwqhnbPYOXndTxX9Ak/zD+cXeuX7nVP85aUMGl20HTfp0s25x3To/6+0/GeDsZyauyeioqKaA1ryWoG6c7MrgYeAS5292n7cX4e0DNh90Dg5WXLljFs2LAkRBlvryz9lOueXwJAfq9DeO7yEfXzC76y9FMmTluCe9DkM+tXY+iQrW+fLfFmyRYue+Z9AAbldWLaFQX1A04WrtnGZc+8T3VtHT075zD3hpM0x2MLvbuunAunFlHn0Ld7R6ZdUcARXTsAULxxBxdNLeKrqho6Zmcy99cn0ys8Js2z/NMdnPPIQmrqnMMOac+0KwroHw7sWbe1ggunFrH5yyqyMzP4yzWjOCqc6kqaZ315JeOnvM3Xu+vo2jGL6VeOrO9KsuXLr/nJk0WUbqvEDP70ixGcqMEkaWH58uV7EtV8d1/e3OcfdAmhmZ0HvABc6+5PtOI6w4BlSgiTw935zUvFTHv//yfoPf+43pSV76zvnN8xO5MXrxxJfi+NEGyN3838mKfCpsyenXO48IS+lFdUMS2cDzIr03j2shM4URP3tspDhat5YO4qIJgi6acF/dhZXcNzRZ/UNxU/fvFwfqA+ba3y7N/K+O0rwWdd145ZXDqyPx7u3zMf5F3n5jOhoF+EUR74ZizayI3Tg5rBzjnt+PnoAXTIzuTpBaVsCZcR/dW4Qdx4hrqZpAslhA2Y2VhgNnCHu9/TymspIUyy3bV1XP/Ch43OldcxO5MnJ3yP0YOVpLRWXZ1zy4yPmL5o4zeOZbfLYPIFx3KWlptqNXfnrpkreHrhN/sRZhjcfvYwLhnZP/WBHWTcnQfmrmqyH+HEUwdz/WmD1UezDTw+by33zV7Z6LGLRvTl7nPz9X9OI0oIQ2Z2LPA28D5weyOnFLv7jmZcTwlhCrg7z7+3ganz11G6rZLszAzGDc3jNz8cSr9DtXRaW3F3Ziz+Xx6bt4Z1W4OmntGDenDL94eqBrYNuTuzijfxwGurWBd2uP9u367cPH6ImtXa2Oxlm5g0p4S1W4P/86C8TvzL+CGcMUyT17elwhWbmTSnhJWfBauX9OragetPG8z5x/VWMphmlBCGzOx2mhgYEjrF3ec143pKCFNsV3UtmRlGdrsDZvD7AWnHzt3kZGVoVGCSlVdUkZOVWT/9jyRHeTii+NCwb6y0PXdna0UV1TV19OraQYlgmmptQnjQvFO5++00XjMoBwgNHEmNLh21CkkqKEFJDf2fk8/MyOuseWAPdqqKEREREYk5JYQiIiIiMaeEUERERCTmDpo+hEmQDbBmTdNLJImIiIikgwb5SotWGDhoRhm3NTM7G3g56jhEREREmuEcd3+luU9SQtgEM+sCnAxsAKqT9GcGEiSd5wBrk/Q3pPlULulHZZKeVC7pR2WSflJVJtlAH+Ct5sy7vIeajJsQ/jObnWE3R4O5nNa2ZM4gSQ6VS/pRmaQnlUv6UZmknxSXyZKWPlGDSkRERERiTgmhiIiISMwpIRQRERGJOSWE0doK3BFuJX2oXNKPyiQ9qVzSj8ok/RwQZaJRxiIiIiIxpxpCERERkZhTQigiIiISc0oIRURERGJOCaGIiIhIzCkhFBEREYk5JYQRMLNzzexDM/vazLaZ2R/NrHvUcQmY2d+Z2e/NbEPUsQiYWYaZ3Wxmq8ysyszKzOxBM+sadWxxZmbtzOzXZrbCzHaa2Vozu8fMcqOOTQJm9qKZuZmNjTqWODOzV8NySPy5KurYEmkt4xQzs1HADOAvwG1AX+D34XZchKHFmpmdTjBP1EigBr020sUU4ErgfmABcBRwJzAUGB9hXHH3BHARcDvB2qlDgbuAXsAl0YUlAGb2I+CCqOMQIHhN/Bl4MGH/mghi2Sd96KXeRGADcIG71wGY2VfAs2Z2jLt/FGl08XUSsJogST8J+PdowxEz6wlcA9zj7reFu+eYWSYwycz6ufv66CKMJzPrDPyMoFzuD3fPNbNDgVvN7BfuXh1ZgDFnZp2Ax4CFwKiIwxHoDfy3uy+IOpBvo4Qw9QqAOXuSwdDccHsCoIQwAg0SDsxsTJSxSL0uwPMENeoNfRxuuwNKCFOvkuBDbkfC/gqCz5QOgBLC6NwN7A63r0YcS6yZWXuC96kDoguS+hCm3mHAloR9ex7npTgWkbTl7mvc/afuviTh0CnAZmB5BGHFnrvXuftn7r7LzDLNLDfscnET8LS7JyaKkiJmdjxBrfrVwK6Iw5GguRjgWjMrN7PdZlZkZgWRRtUEJYSpl0Xw7a2eu9eGv2anPhyRA4eZHQdcB9ypZsm0sJSgZvA1gr6EV0cbTnyZWTtgKvC8u8/9tvMlJdoDG4Fi4HzgQuAQgq4vaVcBpCbj9KKFpUWaYGZ9gJeB2cDjEYcjgZ8A3YATCfrdTiZI2CX1bgL6AKdHHYgE3H05QZnUM7NFwEqCmtzfRhFXU5QQpt5ugj429cxsT81gVerDEUl/4bRMc4BPgYvcXV+e0kD4gQewwMwygLvN7F53/zTKuOLGzAYSJOQTge1hbWFmeDjTzDIbtERJhNy91MxWAPlRx5JITcapt5WgH2FD3wm3m1Ici0jaM7OOwCyCGvQfuHtlxCHFmpkdZmZXhTW2DX1E8JnSL4Kw4u4mgoqGJwkqHXYDr4fHXgfWRhRXrJnZmHAKoESZpGGLoBLC1HsHGG9mWQ327ZlPrSiCeETSVljTMZ3gS9Tp7l4ecUgCOQRN9hcn7D823Grkd+rdBxyf8LNn4uOrgLMiiivuRgPTGk6kH36RGgIsiyyqJqjJOPWmAP8IvGJmjwNHAPcCr7p7SaSRiaSfpwj6RP0zcKSZHdng2A53L44mrPhy9/Vm9iJwm5kBLCJIBm8F/kvNxann7mVAWcN94XyEACV6nUTmaeB6YJaZTSIYVPpvBFM3PRplYI1RQphi7r7AzH5MsCrGdOArglnMb4w0MJH0dGm4/WMjx94CxqYsEmloAsF71mUEfdc+IZj3bnKUQYmkE3ffbGYnE9TgPkXQrP8OcJm7b400uEaY+maLiIiIxJv6EIqIiIjEnBJCERERkZhTQigiIiISc0oIRURERGJOCaGIiIhIzCkhFBEREYk5JYQiIiIiMaeEUEQkhcxs0H6eNyBcuk9EJOmUEIqIpIiZXQP8dT9PnwC8ZmY5SQxJRATQSiUiIilhZuOAGcAp7v7hfpzfDngTWOXulyc7PhGJN9UQioi0kJmNNTM3s7Hfcl4W8BgweX+SQQB3rwGuAn5mZqNbHayIyD4oIRQRSb7zgF7AfzbnSe6+HJgN3JqMoERE9lBCKCLSAmZWRtCkC/Bm+LgpE4BCd69MuMZFZrbUzCrNrMzM7jOzDgnPnQ6cYWZ5bRW7iEgiJYQiIi1zPnBd+Pt14eNvMDMDRgPzEvafCfwJeAM4F3gYmAg8knCJBUAmMKqN4hYR+QZNaSAi0gLu/oGZdQofFrv7B02c2h84BNiUsP/7wHZ3vyF8PNfMagmSx4bWAdXAMcD/tDpwEZFGqIZQRCS5eoTbbQn75wHdzOwZMzvFzNq7+xR336um0d3rgB0NriMi0uaUEIqIJFdWuN1rji93/zNwFtCbYG7C7Wb2gpn1a+QaVYDmIxSRpFFCKCKSXDvCbafEA+4+091PB7oBFwDDgdfNLPG9+VDgi6RGKSKxpoRQRKTl6sJt5j7OWR+et1fNn5m9ZGZPAbj7LnefSTCgZBBBgrjnvE5AB6C0DeMWEdmLBpWIiLTcJ+H28rAP4KzEE9y9wsyWA/+QcGgeMMXMtgGvA4cRjDJe5O7lDc4bEW7fa9PIRUQaUEIoItJC7l5mZpMIVhQ5FvhGQhh6iSBpNA/XC3X3h8xsN3AtcAOwHXgN+NeE554GlAGL2/4OREQCWstYRCTJzKwPsBr4sbu/2oznZRJMO/Oou9+frPhERNSHUEQkydx9AzAZuNfMmtMycw1QCzyYlMBEREKqIRQRSQEzywIKgZXufsV+nD8WmAGc7u5qLhaRpFINoYhICrj7buBMYMt+PqUvcKaSQRFJBdUQioiIiMScaghFREREYk4JoYiIiEjMKSEUERERiTklhCIiIiIxp4RQREREJOaUEIqIiIjEnBJCERERkZhTQigiIiISc0oIRURERGJOCaGIiIhIzCkhFBEREYm5/wOsXMc7yaDdjQAAAABJRU5ErkJggg==\n", "text/plain": [ "<Figure size 720x480 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=2, ncols=1, dpi=120, sharex = True)\n", "ax[0].plot(simulation_df_midpoint[\"time\"], simulation_df_midpoint[\"length\"], \"-\")\n", "ax[1].plot(simulation_df_midpoint[\"time\"], simulation_df_midpoint[\"velocity\"], \"-\")\n", "ax[0].set_xlabel(\"t (s)\")\n", "ax[0].set_ylabel(\"l (m)\")\n", "ax[1].set_xlabel(\"t (s)\")\n", "ax[1].set_ylabel(\"v (m/s)\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Leapfrog method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<img src=\"../../img/leapfrog_method.gif\" width=\"600px\">\n", "\n", "Source: https://www.physics.drexel.edu/students/courses/Comp_Phys/Integrators/leapfrog/" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Constants" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "sim_time = 5.0 # s\n", "delta_t = 0.01 # s\n", "sim_steps = int(sim_time / delta_t)\n", "\n", "mass = 0.2 # kg\n", "spring_constant = 10 # N/m\n", "gravity_acceleration = -9.81 # m/s^2\n", "weight = mass * gravity_acceleration\n", "\n", "unweighted_length = 1.000 # m\n", "weight_displacement = 1.962 / 10 # m\n", "weighted_length = unweighted_length + weight_displacement\n", "init_displacement = 0.3 # m\n", "\n", "length = weighted_length + init_displacement # m\n", "acceleration = (spring_constant * (length - unweighted_length) + weight) / mass\n", "velocity = 0 - acceleration * delta_t / 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation history" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "trace_length = [[0, length]]\n", "trace_velocity = [[0, velocity]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Algorithm" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "for step_index in range(1, sim_steps + 1):\n", " restoring_spring_force = spring_constant * (length - unweighted_length)\n", " total_force = restoring_spring_force + weight\n", " acceleration = total_force / mass\n", " velocity += delta_t * acceleration\n", " length += -velocity * delta_t\n", " trace_length.append([step_index, length])\n", " trace_velocity.append([step_index, velocity])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Convert results to data frame" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "simulation_df_leapfrog = pd.merge(\n", " pd.DataFrame({\n", " \"time\": [x[0] * delta_t for x in trace_length],\n", " \"length\": [x[1] for x in trace_length],\n", " \"method\": \"leapfrog\",\n", " }),\n", " pd.DataFrame({\n", " \"time\": [(x[0] - 0.5) * delta_t for x in trace_velocity],\n", " \"velocity\": [x[1] for x in trace_velocity],\n", " \"method\": \"leapfrog\",\n", " }),\n", " how=\"outer\",\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualization" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=2, ncols=1, dpi=120, sharex = True)\n", "ax[0].plot(simulation_df_leapfrog[\"time\"], simulation_df_leapfrog[\"length\"], \"-\")\n", "ax[1].plot(simulation_df_leapfrog[\"time\"], simulation_df_leapfrog[\"velocity\"], \"-\")\n", "ax[0].set_xlabel(\"t (s)\")\n", "ax[0].set_ylabel(\"l (m)\")\n", "ax[1].set_xlabel(\"t (s)\")\n", "ax[1].set_ylabel(\"v (m/s)\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compare methods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Join tables" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "simulation_df_new = pd.concat(\n", " [simulation_df[[\"time\", \"length\", \"velocity\", \"method\"]],\n", " simulation_df_midpoint[[\"time\", \"length\", \"velocity\", \"method\"]],\n", " simulation_df_leapfrog[[\"time\", \"length\", \"velocity\", \"method\"]]],\n", " ignore_index=True\n", ")" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=2, ncols=1, dpi=120, sharex=True)\n", "sns.lineplot(x=\"time\", y=\"length\", hue=\"method\", data=simulation_df_new, ax=ax[0], legend=False)\n", "sns.lineplot(x=\"time\", y=\"velocity\", hue=\"method\", data=simulation_df_new, ax=ax[1])\n", "ax[1].legend(loc='center left', bbox_to_anchor=(1, 1.1));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bungee jump model (no drag)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Constants" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We update some of the constants to better match the real-life situation of a person performing a bungee jump." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "sim_time = 60.0 # s\n", "delta_t = 0.01 # s\n", "sim_steps = int(sim_time / delta_t)\n", "\n", "mass = 80 # kg\n", "spring_constant = 6 # N/m\n", "gravity_acceleration = -9.81 # m/s^2\n", "weight = mass * gravity_acceleration\n", "\n", "unweighted_length = 30 # m\n", "weight_displacement = np.abs(mass * gravity_acceleration) / spring_constant # m\n", "weighted_length = unweighted_length + weight_displacement\n", "init_displacement = 0.0 # m\n", "\n", "length = 0 # m\n", "acceleration = (spring_constant * (length - unweighted_length) + weight) / mass\n", "velocity = 0 - acceleration * delta_t / 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation history" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "trace_length = [[0, length]]\n", "trace_velocity = [[0, velocity]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Algorithm" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "for step_index in range(1, sim_steps + 1):\n", " if length > unweighted_length:\n", " restoring_spring_force = spring_constant * (length - unweighted_length)\n", " else:\n", " restoring_spring_force = 0\n", "\n", " total_force = restoring_spring_force + weight\n", " acceleration = total_force / mass\n", " velocity += delta_t * acceleration\n", " length += -velocity * delta_t\n", " trace_length.append([step_index, length])\n", " trace_velocity.append([step_index, velocity])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Convert results to data frame" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "simulation_df_bungee = pd.merge(\n", " pd.DataFrame({\n", " \"time\": [x[0] * delta_t for x in trace_length],\n", " \"length\": [x[1] for x in trace_length],\n", " \"simulation\": \"bungee\",\n", " }),\n", " pd.DataFrame({\n", " \"time\": [(x[0] - 0.5) * delta_t for x in trace_velocity],\n", " \"velocity\": [x[1] for x in trace_velocity],\n", " \"simulation\": \"bungee\",\n", " }),\n", " how=\"outer\",\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualization" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=2, ncols=1, dpi=120, sharex = True)\n", "ax[0].plot(simulation_df_bungee[\"time\"], simulation_df_bungee[\"length\"], \"-\")\n", "ax[1].plot(simulation_df_bungee[\"time\"], simulation_df_bungee[\"velocity\"], \"-\")\n", "ax[0].set_xlabel(\"t (s)\")\n", "ax[0].set_ylabel(\"l (m)\")\n", "ax[1].set_xlabel(\"t (s)\")\n", "ax[1].set_ylabel(\"v (m/s)\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Undamped oscillator model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For comparison, we first run the simulation as an undamped oscillator. We will visualize this alongside the bungee model." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "import undamped_oscillator" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "simulation_df_undamped = undamped_oscillator.simulation(\n", " sim_time=60.0,\n", " delta_t=0.01,\n", " mass=80,\n", " spring_constant=6,\n", " unweighted_length=30,\n", " init_displacement=-160.8,\n", " method=\"leapfrog\",\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compare methods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Join tables" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "simulation_df_undamped[\"simulation\"] = \"undamped spring\"\n", "simulation_df_new = pd.concat(\n", " [simulation_df_bungee[[\"time\", \"length\", \"velocity\", \"simulation\"]],\n", " simulation_df_undamped[[\"time\", \"length\", \"velocity\", \"simulation\"]]],\n", " ignore_index=True\n", ")" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=2, ncols=1, dpi=120, sharex=True)\n", "sns.lineplot(x=\"time\", y=\"length\", hue=\"simulation\", data=simulation_df_new, ax=ax[0], legend=False)\n", "sns.lineplot(x=\"time\", y=\"velocity\", hue=\"simulation\", data=simulation_df_new, ax=ax[1])\n", "ax[1].legend(loc='center left', bbox_to_anchor=(1, 1.1));" ] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }