{ "cells": [ { "cell_type": "markdown", "metadata": { "cell_style": "center", "slideshow": { "slide_type": "slide" } }, "source": [ "\n", "\n", "# Class 11: System dynamics models: Damped oscillator and bungee jumping I\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 numpy as np\n", "import pandas as pd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model of an undamped spring" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Constants" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "sim_time = 3.0 # s\n", "delta_t = 0.00001 # 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", "\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\n", "\n", "length = weighted_length + init_displacement # m\n", "velocity = 0 # m/s" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation history" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "trace = [[0, length, 0]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Algorithm" ] }, { "cell_type": "code", "execution_count": 4, "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": 5, "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", "})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualization" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "figwidth = 5 # inches\n", "figheight = 0.618 * figwidth # golden ratio\n", "figsize = (figwidth, 1.5 * figheight)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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TRPqH3GwyvVW3XjfN7wUWr4aV29LQ2c+R+o6gPa/Tcaw40Vp/VWv9Ea31ZmDCclIpFQP8DPgNsClQ9gWT7JR4Vpca6vqVqgZR10HE2kHnpSWw0tzhBAOlFHeVGQvV4bp2aQAZRK4I6QRRkALcWTYNgP4hD1tONQX1uaOZN0820muFdIIoSAFbkIJsPr1xrDjxgc9hhHM+H2pD/Mld5cYH+FKHqOtg0dozyM6zRlvzd5YXBC2kY2GNOSAF2YKE1prfm4K0oiSTGZlJQX3+G+fn2V1rpddO8HjZDJ2mxMdw84K8oD53QUYiy0qMXmqvVDXIqR2TiBInSqlZwNeBL2qtJ9x3XimVr5Qq874B/umR7SfuEHUddF4/0WiHdN4R5N0UwOIZGfapHRnz4HCmsZtzZkGsd5QHf8wT42LYuNBYHDcdv8zgsDT9DDRDbg9vnjSWi40L80mMC15Ix8LyktY093C6sTvoz+9EAluwIfj8BNgP/GKSj/sU8MhYf9i1axcNDQ0UFRVRWlrKtm3b7L/deuutHD16lMZG44O9YMECUlJSOHDgAAApKSmsWbOGXbt20dNjxLArKiro6enh5MmTAOTn57N48WI2b95sX3fDhg3U1NRw4YJRqbC0tJT8/HzmZCjOdmie21vDl+5awMGDB2lrM3pAlJeXA1BZWQlAVlYWFRUVbNu2jcFBo5DX6tWraWxspKbG6KzrhNe0e/duAOLj49mwYQMHDhxwzGt66cA5AJJjIbGrHsgJ+mtalDHExQ7YXdPC83/YRFq8knEK4Gt68sBIKGVpfox9nWC+pvWzivn90Qa6+of5yf9t4pZF02WcAviajre66TL7J033NLN58+agv6YiWuzHPLPrDB9bUxj243Ts2DF8QYWDC0kp9SjwiNZ6XL+6Uuph4L+BCuCE+euvAV8F4gCP1nrMbYhSKh8Y7cubA7xQWVlJWVmZT/b7i59uPctjvzde2qufv9HvHVKFEQaG3VR84zV6Bt3cu7SQHzy4LCR27K5u4f0/3QXAd+9fwvtWBrZqZbTz3p/sZN/5NmbnpvD6394cEhu6+odY/s1NDLo9PLSqhG+9Z3FI7IgWvv5iFb/ccY4Yl+LAP9xORnLg65uMxV0/2MqJhi7KCtN5+TMbQmKDP6mqqrLEY7nWumqyj4+ksI4lQo4CQ+btq+bfhriKN0Vr3ai1rvK+AWcDbfBk8U6csiqWCoFhd3WrXfPg1uumhcyOFbOyyTInSxnzwNLSPcCBWmNHftui0I15WmIca+cY9XTeONEoOQgBRGvN5uPG92rFzKyQCROAO8zQTtXFTho6+kNmh1OIJHHyPmDlqNvPzL+tBB4NjVn+ozQ3hVk5Rs0FWagCy2bzWGGsS3FTkBPkvIlxKW6abzz/9jPNkoMQQN442YR1EM6q1hoqbjGfv6GznxMNXSG1JZI509hNbauRY3RbCDchMDLmgJ0DE82ErThRSsUppRYppVwAWuujWut93jfgovm3fVrrc6G0119sND/A+8+30dE3FGJrIhOtNZvM3dSq0mzSg1DG+mpYY949MMw+KcIXMCxBmpEUx/KZWSG1xbsI2BuyUAUM70q8ofSWASyZkUFOSjwgm08IY3ECvBvYCawItSHBxFLXbo9m22mpgxAITl7uor7dqCsSypCOxU3z87BOMctCFRgGht1sNeuKbFyQR2xMaKfGkpxkuwjfG7JQBQwrpDM7L4XS3JSQ2uLy8pLuONPMwHB0F+ELC3GitX50dDKs1voZrXWm1nrPZB4X7qwqzSbZrF4o6jowWBMWwG3Xhda9D5CZHE9FibGTf+OkCNJAsKfGGTlG3tyywMtL2iteUn/T2jM4kmPkkDG/2dx89gy62XeuLcTWhJawECfCCAmxMaybmwvAlpNNUi02AGwxBcDsvBRm5oR2N2VhhXbONHZTZ8bIBf9hjXmMS3Hj/NDlGHljjblHw1bxkvqd7WeasXKNg114bTxumuflJY3yzaeIkzDECu209AxKtVg/09U/ZO+mbnLIIgWSgxBotp02mjsuLc4kIym0OUYWK2ZlkWJ6SWXM/c82M4yXHB8T8hwji4zkkXynaB9zESdhyBULVZSra3+zq7qVYdMbdeM854iT66anUZBuVIuVcJ5/udzZz8nLxomYDfNyQ2zNCOIlDRxaa1uQrpmdQ0Js8KvCjsfN5vx+tqmH2pbo9ZKKOAlDCjISWVhgFGDbcaY5xNZEFlaScVyMYvXs4DX6uxZKjSTL7a5ujfpkOX9iLVIAGxwkSGEktNPSM8ixS50htiZyONPYTUOnUUvESYIUrgwxRXM4T8RJmGLtqA7WtdPVL8ly/mK7uVCtmJlNcryzujusNyfRviE3B2vbQ2xN5GAJ0rTEWK4vygixNVeyfu7IwrldNiJ+Y6uDBel1BenkphpHiqN58yniJEyxFiq3R7O7Wmpf+IO61l6qm40eExvmO2s3BXCDWTUURkSU4Bsej7bfy3VzckN+hHg0xdnJzDQLL0bzQuVvLEFamJHInDxnJL1buFyKG+YY88/Osy1289Fow1nfRGHCrC7NJi7GSOuWHZV/8H4fnZRvYpGTmkBZYTogY+4vjl3qpKXHaKbmlFM6o7G8pHtqWukfknCerwwMu9lVbTTau3F+Hko5r9qE5THr6BuiMkoPPYg4CVOS42Pt2hdSjM0/WO9jdko8i6anh9iasbEmrSMX2qVCsB+4Mt/Eed4yGBnzgWEPB85Hd+0Lf7D/XBv9Q0YbCKeFdCzWzZNwnoiTMMaatM429XCpoy/E1oQ3bi/3/vq5ubhczttNwcgu2qPhrbMt17i3cC0sQVqam0JxdnKIrRmbtbNzsDb326J0ofInVr6JUrBubs417h0aZmQm2RVrozWcJ+IkjFnvra4lB8Enjlxop7N/GLjyfXUaK2dlE2/mRUTrpOUvegeH7SqcTvWaAGSlxLN4hpGoK2PuO5YgXVKUSWZyfIitGR9LOO0710bfYPSF80SchDGLZ2SQlmicKJFJyzd2enkhnLxQJcXHsGKWEc6TMfeN/efbGHQb7v11c5075jBi39H6Dtp7B0NsTfjS3jtyJHvdHGd6TSzWzzVCToNuD/vOR9+hBxEnYUxsjMs+wbH9TAtaR2dWtz+wQiSluSlMz0gKsTVXx1qoqpt77AaFwuSxxlwpWFPq9IXKGHMt4Tyf2F3TapesX+twcbJ2do5dyj4a805EnIQ51qTV3D1gV7kUJsfg8MjOZM1sZ09YMKr2hSRDTxnrxMai6elkJDujZP14LJ+ZRUKsMV1L3snUscY8LkaxYqZziiyORUZyHIuLMoHo9JKKOAlz1s4ZWah2yY5qShy50G5n769xUFXY8SifkUG6Gc7bJTVupkTPwDBHLhhHNMNBkCbGxbBylvHZlO/51LG8TkuLM0mKd07J+vFYb+adVF3sjLpwnoiTMGdOXgq5qQmA4bIUJo+3m3xtGCxUMS7FqlJjodpdLeG8qbDvfJvdQykcxhxGhHN1cw+NZul1YeK09gxyosHwLoeDIIURO7U26txEEyJOwhyllD1pGfFUWagmy64aQ5zMzksh32yu53SsSetiRz91rZJ3Mlks975SsLLU+d4ygNVeC+quKFuo/MGemvDahIARzos1E0+ibfM5ZXGilJqmlPqcUuo5pdRZpVSHUqpfKdWglHpLKfVDpdQGfxorjI01abX2DHK6sTvE1oQXA8Nu+zhpuOymAFaXei9U4uafLJa3rKwwnYwkZ+ebWCwpyiAxzpiyLXElTBxrzONjXFTMzAqxNRMjOT6WJWa/p2gb80mLE6VUrlLqcaAO+CcgF9gM/CfwXeBZ4AJwL7BFKXVUKXWr/0wWRrPWK08i2j7AvnK4roOBYSPfJFx2UwCLCtNJS7DyTmTMJ0P3wDBHzZLg4TTmCbExdlXo3TLmk8bKz1pakklinPPzTSyszeexS51RVRV6UuJEKbUCOAJcDzwM5GqtN2itP6m1/pLW+mta609prR/QWs8EFgK/A55VSv2T360XAJiTl2p3sZSFanJ4v1+rwyAZ1uLKvJPocvf6yt5zrXYztXDylsGIx+xsUw+NXZJ3MlFavE4zht+YG99zrWHfuej5rk9YnCilZgIvA49qrddorZ/RWl812K21PqW1/gqwCLhFKfX3vpkrjIVSyp60dldL3slksFy9c/JSyE8Lj3wTC0tM1bf3UdfaG2JrwgdLkLrCKN/Ewvs0WbQlSPqCd75GOHnLAFbMyibGzDuJps3nZDwnF4C1WuufTvZJtNb1wB3Azyf7WGFiWJNWS88gZyTvZEL0D7k5UGvkmzi9INNYeO8Ao2nS8hXrKK5xJDs88k0sri/OJN6sdyIes4lj55vEulhWkhliayZHakIs5Wb7gmhKip2wONFau7XW1aN/r5SKVUpdp5TaoJS6cfTN6/FdWuvL/jJcuBJZqCbPobp2O98k3Fy9YBQPSzXzTqJp0vKFrv6hsMw3sUiMi2FZsbG4yvd84rxlvlcVYZZvYrHG9PBV1nfQ1R8deSc+HSVWSq0EzgKVwJvAG14362chCMzNTyUnxcw7kYVqQnhP7uEoTmJjXKw0++zIQjUx9p1rw0w3CcsxhxG7Tzd209w9EGJrnE9T14DtTQ73Mfdo7NOFkY6vdU5+AAwCHwJuGXXbaP4rBAGllJ2DIIW5Joa1oM/LT7UL2YUbVib/hbY+LrRJ3sm1sI5duxR2A8VwY7XknUwK7yTScBUnK2Zl2X12oqV0gK/iZAnw91rr/9Vabxnr5g8jhYlhffGauwc52yR5J1djyO3hUF07gH3qJRzxnmwlB+HaWLvORYXppIVZvolFRUkW8TFW3kl0LFS+sNcc87gYxdLi8Mo3sUhLjKOs0Mw7iZLvua/ipBOQbnMO4YrCXFHyAZ4qVRc77X46Vs+ScKS8MJ0Us0fI7ijZUU2V/iE3R81+Ok5v+nY1EuNi7EVWvufXxmrqWT4jIyzzTSysQw9H6zvoHhgOsTWBx1dx8j/Ap5VSsf4wRvCNefmpZJrdVfefj4645FTxdvWGq3sfjLyT5aa42hslseipcrS+g0F3+AtSGAntnLzcFXUN4SZDz8AwVRc7gQgYc3Pz6fZoDkTB/O6rOPkGRminVin1+hi3zX6wUZggLpdihVmWeW8UFeuZCtb7Mz0jkRmZSSG2xjdWmmNe09xDU5ckSI7H3ggRpHDlQisbkfE5XNduF9xbESYl68fD+zO7LwrG3Fdx8l2gCOgF1Bg3aSwYZFaYk9aFtj4udUhDuLHQWtu5B8tnZqGUCrFFvrHiioVKROl4WGNenJ3EtDBp8Dgey0oy7QRJ8ZiNj/d7szzMxUlmcjzzp6UC0VEp1lfx8BDwI631XK31xrFu/jBSmDgrvdS1TFpjU9PcQ0uP4QoPd1cvwNLiTLtzqYz52Hg82vYwrAzjfBOLtMQ4rpueDkTHQjVVrHyT2Xkp5ITpiTxvrI3Iwdp2hswQZaTiqziJx+idIziE8hkZdgVJmbTGxtslGu7ufYCk+Bi7gqSM+dicaeq2m6atiABBCiPC+siFDvqH3CG2xnkMuz12bkYkCFIY2Xz2Dbk5ZubSRCq+ipM3gAX+METwDwmxMSwtMjL5ZRc9NtYCnpoQy8KC9BBb4x+sSavyYie9g5GfyT9ZvPNNVkaAIIURYT3o9thVb4URTjR00TNoiLZI2ITAlafMIj2v0B/i5J+UUp9TSn14rJs/jBQmx8pS44t4oqGTzigpdTwZrNyDiplZdkOtcMfaRbs9mkO17SG2xnlYY56RFMecvNQQW+Mfommhmgr7rhCkkeE5KcpKosDMl4r0SrG+HgH+F/Pffx3n7xp4wsfnECaJ4bY+i9Zw4HwbNy/ID7VJjqG5e4Dq5h4g/LP3vfFO9tt7ro0b5uaG0BrnYeUerJiZhStCBGlBRiLF2UnUtfZF/EI1FfaaIZ3c1Hhm5iSH2Br/oJRixawsXjpyiX3njQ704Z7QPx6+ek5Kr3Gb7eP1hSlQUZKF9XmVSetKvN+PSHH1AuSkJjAnLwUYWYgFg4aOfupajZNrkZJvYmHlUuw714rHIy0rLIwTeZYgzY6oBdzyAjV3D3KuJXJbVkxYnCil0pRS67x/p7U+f62UMfVyAAAgAElEQVSb1+MLlFJl/jReGJuMpDgWTEsDxN07GuuobawrfEtZj4c1aR0438ZwhGfyTwZvsRYp+SYWltjq7B/mdKO0rLC40NbH5U6j5k8kbULgytcTyfP7ZDwnicDTSqlHlFKT8rgopVYBO4E1k3mcMHWshepQXTsDw5LJb2ElCZfNyCA5PrIKG1sLVc+gmxMN0lXCwvKWxce47FNNkcLKKFmoJsuVgjSyvGULC9JJTTDmrkg+nTdhkaG1bgJuAt4HVCqlPqCUGleSKqVilVK3KqV+DWwBvqO1/rnPFgsTwlLXA8MeKusj+8jZROkbdFNZb/VWiazdFMhCNR7We7GkKLx7q4zFnLyRlhWRvFBNFmsTkhQXw6LCyDiRZxHjUiwrMby+kRy2n5QHRGt9FqgAfg38CGhUSh1QSr2slPp/Sqn/Vko9o5TaC7QDrwCpQIXW+nF/Gy+Mj/duQSYtg0N17QybcflIc+8DlGQnk5dmFJqK5ElrMnQPDHP8kiHOIy3fBEa3rJAxt7DmvKXFmcTFRF6hcmt+r27uobk7MltWTHrUtNYDWutvANOBh4HtQAqwHFgLlABnga8Cc7XWd2utj/vPZGEiFGYm2T1jZNIy8C7tvjxCijJ5o5SyRdfec0Ymf7RzsLYNK080EgUpjIiu+vY+LrZLy4qO3iFOXTbybyJ3zL367ETo/D5lSWmKlN9qrT+jtb5Za12utV6gtV6ltX5Qa/19rfU5P9oqTBLri7n/vGTyw4hIK81NsT0MkYZV+6Kxa8A+oRLNRFJvlfFYGWUN4a7F/lrvBo+RtwmBK1tWRKpnPPL8XYKN9cVs6x2iujm6M/m924xHYr6JhXc4T/JORibuefmpZCbHh9iawCAtK67EEqQuhZ2bEWkkx8dSZiZ3741QQSriJIK5cqGKzA/wRDnZ0EXXgFHWPdKOFnpz3fQ0kuONpM9or3cy5PZwqM6olhupO2iQlhWjsQTawoJ00hLjQmxN4FhpbrKq6jsismWFiJMIZl5+KumJxpGzvTXRvVB5L9SRvFDFxrioKJEESYDjlzrpNXurRGrugYW0rDAYGHZz+IJxIi/Sx9yax4Y92hbhkYSIkwjG5VL2BzjaY9FW0lh2Sjyzc1NCbE1gsTxDZxq7ae0ZDLE1ocNbnEVarYvRWN9zrWF/FH/XK+s7GBw2ChBG8iYEIj8p1tHiRCk1Xyn1mFKqbgL3zVJK/UQpdVEp1aeUqlJK/fVkC8ZFGtYHuLa1l8ud/SG2JnSMlLLOiqhS1mPhvRBH80JljXl+WgJFWUkhtiaweLes2B+BC9VE2Ruh7SnGIjc1wd5oRWJ+mU8lMpVSscDHgZuBPGD0rK+11rdO4bq3A1/HOJo8fC07TTs2AYXAN4Bq4B3AvwFpwGOTtSFSuLLeSRt/smR6CK0JDfXtfVzsMIRZpO+gwcjkj3Ep3B6jv8jti6aF2qSgo7W2F6qVsyKrt8pYWC0rTjR0RXWukSVIZ2QmMT0jsgUpGAKsurnHblkRG0E1XXx9Jf8K/AewxLyWGnWb6vVvBE4DtzExYXEPRnG4D2mtf6K1fkVr/TngZeATU7QhIlg8I4N48wMbiep6InifYFge4bspgJSEWBZNN6piRuuY17b22sWpIn0HbWG9zkN17XZoI5rweLTtKYz0fBMLq3RAJLas8FWcvA/4R631Iq31xrFuU7mo1vqrWuuPaK03AxMp0DEEPIlREM6bY0Dkb5WvQmJcDIuLjCNn0bqjsuKxCbEuygsjq7fKeFgL1dH6DvqHoq+3UjTlm1hYr7N/yEPVxY4QWxN8qpu7aes1koEjPd/Ewlt4R1oI11dxkoTRNyekaK1f1Fp/UGs9OqniZuD1EJjkKKwP8LGLnXQPRN6Rs2ux16uUtVUPItKxFqoht+bIhehbqCxvWUp8DAsL0kJsTXBYMSqEG21EU76JRWluCjkpRv2eSPOS+jpTvwzc4g9D/I1S6tPAMuDRCdw3XylV5n0D5gTaxmCx0nT9eTQcqo28I2dXo6NviJOXDXdntOyg4cpCc5E2aU0E6zUvK8mKqDj81TDyLBKB6PSSWmOelhjL/PzoEKRKKVuIRVrLikknxCqlPuz140Hgm0qpRODwWPfXWj8xRdumjFLqDuD7wJe01mPaNYpPAY+M9Yddu3bR0NBAUVERpaWlbNu2zf7brbfeytGjR2lsbARgwYIFpKSkcODAAQBSUlJYs2YNu3btoqenB4CKigp6eno4efIkAPn5+SxevJjNmzfb192wYQM1NTVcuHABgNLSUvLz89m9ezcA8fHxbNiwgQMHDtDWZuwWysvLAaisrAQgKyuLiooKtm3bRo9XY6hXD55loNZ4S8L5NQ0OGkdkV69eTWNjIzU1NWO+pqPNbqzva2z7eTZvvhD2r2mi41SSnUxtay9/3H+ahZ7zEfGaJjJOM2Yv4GyT8fdsTzuDg4Nh/5omOk7FiYNc6oCdpxvRWnPw4MGwf00THaftx80co5lZ7NixPSJe00TGKWPI8IZf7hzgNy9vIjfJ5YjXdOzYMXxBTVZpKaUmk2mltdY+9ShXSj0KPKK1nlC6vVJqJUYo5wmt9V9N8DH5GKeNvJkDvFBZWUlZWdkkLHYmt//rFk43drNubg5PfnxNqM0JGv/8ygl+/MZZlIJDX7uDjKTIrRg5mr/5zSGePVBPemIsh752By5XZJ9YsXjt2GU+8cQ+AJ78+GrWzc0NsUXB44m3zvG1F6oAeP0LNzE7LzW0BgWJxs5+Vj1mLKBfvHMBf7VxbogtCh4Ha9u47z92AvCD9y/l3mUzQmyRQVVVlSW0yrXWVZN9/FSOEpdO4TFBQSk1HyPU9CLw1xN9nNa6EWgcdS3/GhdiVszK5nRjNwdr2xlyeyKyjfhYWLH3BdPSokqYgBHGevZAPZ39w5xu7GZBlOReWPkmMS7F0uLI7K0yHitmXpl3Ei3ixLvIZCT3zhqLssIMEuNc9A952Huu1THixFcmvUJprc9bN4yTNBe9f+f1t1Z8rKMyGZRS04FXgD3AR7TW0XeW7ipYX9jeQTfHL3WG2JrgMDg80lslmvJNLLyPU0ZT3on1WhdNTyclIWhTkCNYUJBGmvmao3HM42IU10eZII2PddkiPJISoX3dPtcAK8b52y0YQsHvKKXilFKLrOqvSql04I8YYuiHwGql1HqvW0kg7AgnorEJYOXFDgbsUtbRtZsCmJOXSlay4S2Klm61/UNujtYbp5OiccxjXIpl5kYk0o6WXg3rtS6ekUFinE+ZBGGJNb+fvNxFR29k9Faa0rZCKfU167/Ax8yKrt7EYBRGGyAwvBv4L+AODAFUgVEIDuDVMe7/dSZwaieSKc5OIj8tgcauAfada+Vj6x0bnfMb3gtytNQ98EYpxfKZ2Ww6fjlqBOmRCx0MuY08Ou8QRzSxcmYWW081Ud3cQ3P3ALmpCaE2KaD0DAxTddHwBkejhxRguVcoa39tK7csDP+q0FP1eT5q/quBj47xdw3UAp+Z4vVHLqT1o4wSFlrrZ4BnvH5+k7eXzhe8UEqxclY2Lx+9xL7zbWitIy6vZjSWi7MwI5EZmZFfynosVszKYtPxy0YJ//Y+CiP8ffAOZURLldDRjK53cld5QQitCTyH6tpxewxBujzK8k0sKmYavZW0NsY8EsTJlMI6WmuX1toqV7/e+tnrFqO1LjVFhOAQLDd3U9cAta29IbYmsGit7SS5aPSaWHgv0NHQmdryls3MSSY/PTHE1oSGpcWZxJons6IhnLc3yj2kAOmJcSwsMFpWREreia85J/8PuOwPQ4TAE015J9XNPbT2GDUBojH3wKJ8RoZdFXd/hC9U3r1VonUHDZAUH0PZDKtlRWR/z2FkMZ6Tl0K2WS01GrE2IocutDMwHP4tK3wVJ48AQ0qpknFuo2uHCCFkYUEaKfFGslik76iuyDeJ0twDgITYGJYWGZn8kS5ITzd209lvFKSK1twDi5WmOKus76BvMPwXqvEYdns4WDvSfTqasbxGg8MeKuvDv2WFr+LkHMaJnfFuDUqpFqXUF318HsEPxMa4WFYyUuo4krF2U2kJsVFT32M8LM/RiYZOOvsjI5N/LCTfZARroRr2aPs4fSRyoqGLHlN8RWtIx8K7vkskhHZ8FSefB3qBL2Ekxlq3LwP9wLcwugV/Uyn1Fz4+l+AHrIXqbFMPLd2BOkwVeix39rKZWcRESWXU8bDG3KPhYAT3VrK8ZVnJccyJkuJj47H8ioUqcjciIkhHKMxMshP/I8FL6muForuBr2mtvz/6D2aZ+5u11ncrpdow+tf8p4/PJ/iIt+tz//k27iiLvEz+pq4BapqNXhErozj3wGJ5iffpjVZumh+Z0VZrQl4+MzviT6Jdi7y0BEpzU6hp7mFvBOedWB6CvLQESrKTQ2xN6FkxK4v6Q33sP9+Kx6PDumWFr56TdcB4NfOPADeY/99GBHX5DWeWFmfanoRILdK0/7xk73uTkRzHgmlGaCtSw3mXOvqob+8DojsB2hvLzX/wfJt91DaS0Frbn+cVM7OiXpDCyHzX1jtEdXN3iK3xDV/FSRvwrnH+djdGaAcgHznV4whSEmIpKzSOnEXqQmXtpmKjsLfKeFgL9qE6o7dSpOEdY492976F5SXtGhjmZENXiK3xPxfa+mjsMjsRyyYEGFU6IMxDO76Kk58Cf6WUekYp9QGl1G1KqQeVUk8Dnwb+QykVj5Gb8rSvxgr+wTq9crS+g/6hyMvkt9zYZTMySIqPvlLWY2EtVP1DHruaZiRh5VXEx7ooN4/RRjsrrqhxE3kbEck3eTvz89NIS7R6K0WxONFafx34InAj8CuM0vH/C6wHPq+1/keMUvZbgX/0zVTBX1hf5CG35nCEZfL3DbqpMo/RSb7JCJGeIGlNxEuLMkmIFUEKUJqbQo5Z9yPcF6qxsF5TcnwMi6anh9gaZ+ByKfu7Hu6C1FfPCVrr7wHTMXJK1gIzgWKt9Q/Nv/dprb+gte7x9bkE/7A8gquGHqprZ9iMr4urd4SirCQKzIqpkRbO6+wf4kSD4Q2SfJMRjN5KZhPACBtzGBHZy0oyiY3xeSmLGCwv6fmWXhq7+q9xb+filxHVWru11jVa691a6zqtdeQFtSOI/LREZuYYme2RtlB5ewWiuUroaJRS9sK975zRWylSOFjbjpXvKeLkSqyF6mJHv50wHAm09QxyutFI+IzmIotj4V3vZH8Ye8x8EidKqTSl1LeVUruUUmeVUtWjbmf9ZajgX6wv9P7zbXgiKJPfyjcpzU0hLy2yu7FOFmuhaukZ5FxL5PRW8vYKeB+bFkblnUTQRsT7pGG0V4YdzfXFmcTFGCeXwjmc56vn5CfAF4BWjLySLaNuW328vhAgrLyTrv5hTjVGRia/26M5YDX7E6/J2/BeqCLJY2ZNwAumpZGRHBdia5xFWWEGCWZvpUgacysc7VKwtERO5HmTGBdjJ4WHc96Jr0XY3gH8rZVfIoQPK0Y1AbQ6WoYzJxu66B4wequIe//tLCxIJzUhlu6BYfada+V9K4pDbZLPDLk9HKyzuk/LmI8mPtbF0uJMdte0hv3RUm8sL9CiQuMzLVzJylnZHKxtp+piJz0Dw6SE4Xvkq+dEM34RNsHBzMlLIcvcZUaKu3efFF+7KjEuxTJzlxkpC1XVxU76h4wUN3Hvj431vpy83EVHX/j3VuofcnPkgnEiT/JNxsbyHLvDuLeSr+LkN8D7/GGIEFyMTH7jix0pC5Xl3s9OiWd2bkqIrXEm1kJV3dxDcwT0VpIE6GtjeZS0hgO14f9dP1rfwaBbBOnVWB4BTQB99fVcAL6qlMrGKFc/Gq21/qaPzyEEiJWzsth0/DL17Ubpb6tpVDiitbYXKillPT4rRlWQvKs8vHsrWRNvQXoiRVnh+/kNJBUzs1DKECf7zrWycUF+qE3yCe/cGQnljU1OagKz81KobuoJ27wTX8WJVVjtPeZtNBoQceJQvEMf+861MmPpjBBa4xt1rX1c6jDO9K8qld3UeCwtziTWpRj2aPafbw1rcXJFb5VZIkjHIz3R6K10oqErrE9vWOytMca8ODuJaWbtHuHtrJyZTXVTDwfOtzHs9oRdLRhfK8S6rnGTUo0OpnxGup3JH66uP4tdNS32/1eX5oTQEmeTHB9LmZnJH+4L1ZnGblp6BgFYLYL0qljhj8N17QwOh28ZKrdH23PVqlnyPb8allepZ9DNiTDsreQXKaWUcimlFiql1imlUqzf+ePaQuBIiI3herMxXrgfM9xdbdiflhDLosLwP3kUSKxkucr6DvoGw7e30q6akc/smtmyUF0Na6EaGPZQebEjxNZMnWMXO+kyT+Stni2C9GqsHOUZDzd8FhBKqX8AmoBjGHVNFiilCoAqpdRMX68vBBar3snJy1109odvJv9u03OyYlYWMS5x718Na8yHwziTH2B3tTHmOSnxzM1PDbE1zmZ0CDdc2e3lIV0jHtKrMjMnmdxUoxDl3jBsU+JrhdivAP8A/Ay4D1AAWusG4BzwbR/tEwKMNWlpjV3ALNyob+/jQptRmnu17KCvyfKZ4b9Qaa3ZbXpOVpVmS77JNZiRmURhhtVbKTy/5wC7TA9pYUYixdmSAH01lFK2l3RvTWvYtazw1XPyCeARrfXfAS+N+tt/Arf7eH0hwFSUGJn8EL6hHWsHDZJ7MBHy0hIoNY9a7wnTMa9p7qGpyzgKLWM+MayNyL5zrWHZssLt0ewxPSerZ+eIIJ0AVjivsWuA2tbwalnhqzjJBw6P87dhQIpNOJyMJCOTH2BPTXguVFa+SXL8SNlm4eqsmjXSW2nIHX4JktYOGsRbNlGsHI223iFOXg6/BMkTDZ109pv5JiJIJ4R3LtZbZ1uuck/n4as4OQw8PM7f7geO+nh9IQhYH+BDde1hmSBpxaGXz8wiLsyOy4WKtXOMMe8ddHPkQvjlnVhjnpk8Iq6Fq7M2jBcqGNmEgAjSibJoejoZSUYl8Leqw2vMfZ3JHwEeVkq9jhHi0cDNSqn/Aj4CfMvH6wtBwFqohtw67Ar2XO7stzvsyomNiRPOOyqttb1QrZyVjUsSoCdEaW4K09KNBMlwW6hgRJDmpyUwKyc5xNaEBy6Xsr1Mu6pbwirvxNc6J68C9wJFwH9gJMT+C3AP8HGt9XM+WygEnDWlOXbeSbgtVLsk32RKFGQk2nkn4bZQ1bb20tBpFNyTMZ84Sinbe7K7ugV3GOWdeDzaDjuvkXyTSWFtRC53DlDT3BNiayaOzz5wrfVLWuv5wDxgA7AUmK61/qWv1xaCQ0ZyHIumG7VBwm2hsk5sJMa5WFIkrdMngzVp7TvXxsBw+ITzvN374i2bHJaXtLN/mOOXOkNszcQ51dhFW69R6kDqm0wOa8whvOZ3vwXotdZntdY7tNZHtNbhM9MJwEg8+siFDrrNIkfhgHVSp6Iki/hYyTeZDNakNTDs4VBt+OSdWNWA0xJjuW66FNybDN5iblcYLVRX5JtIfZNJsWBamt2B3juR3OlMejZXSr0+idvmQBgt+B9roXJ7tN27wuk0dw9wtslwU8qENXnWeO1Aw2lH5Z1vIgX3JkdJdrJd7yScQrhWvkluagJz8uQQ6GQw8k6M+fGts+GTdzKVraYLI7dkIjfZyoYJq0pHJvpwWai8J1dx9U6e/LREu7JquCxUda291LebBfck32TSKKVYY25E9tS0MhwGx8g9npEE6NVScG9KWJtPY0PXHWJrJsakuxJrrW8OgB1CiElLjKN8RgaH69rDZqHacaYZgKS4GJaVSL7JVFg7O4czjd0crG2nf8hNYpyze3VaYw6wbm5uCC0JX9bOzuHZA/V0DQxz7FKn43O1Tl7ushs8rpkjHtKpcMXpvOpW5uY7//i9eDYEGyvvpOpiBx19zu+zs+OssVCtLM0mIdbZi6pTsXZUg25PWLQv2G6Kk0yvJG5hclyRIBkGGxFvQbpeBOmUmD8tlZyUeAB2hcGYg4gTwQtr0vJo51eLrW3ppa7VcO+vnyu7qakSTgmSHo+2F9Mb5uRIfZMpUpSVbPelCYcQriVOZmQmSX2TKaKUsr/r4VLvRMSJYLNiZhaxVt6Jw9X1dq/d1A1zZDc1VbJT4llYYLh4nb5QnWgYce9LSMc3rI6+e2taHd2+YHDYY5cLWDdX6pv4gpUA39IzyOlG5+ediDgRbFISYrm+2Ig/O32hskI6WeLe9xnv9gU9Dj5GLu59/2F5SXsc3r7gUF07vWZLDRGkvuEdztt+uvkq93QGIk6EK7jB/AAfv9Rpd311Gh6PZqe5UN0wJ1fc+z5iTfpDbm0f2XQi273c+yXZ4t73BW9xt/WUcxeqHeIh9Rtz8lIpSDeOkW873RRia66NiBPhCm6cn2f/f/sZZ36Ajzd02tUiZTflO2vn5NjhPKcuVIPDHjsPav3cXHHv+0h+eqIdznPyQmWJk4UFaeSlJYTYmvBGKcWN8435cld1q+OrQos4Ea5gaXEmqQnGCXOnLlTi3vcvqQmxLJ+ZBcBWhy5UB2vb6Bsy3fvzZMz9gbUROVTX7sjTeV39QxysM0JOsgnxDxvmGWPeN+Rm/zlnn84TcSJcQVyMyw7tbDvdhMeBzcF2nDFCD0VZSZRI9r5fsBaq6qYeLrT1htiat3Ole19OZ/mDDabI82jsMKmT2FPTajcnXCcn8vyC4XU0/r/V4XknIk6Et2EtVM3dgxxzWHOw/iG37d5fJzFov3HjvJFwnhM9Ztu93Pu5qeLe9wcrZ2WTYPajcuJCZY15rEuxStpT+IWslHiWzMgAYOspZ3pJLUScCG/jJq+8k20Om7T21LTa7v2bFuRd497CRCkrTCfbLNLktByEtp5BDpnu/Q0S0vEbiXExrDZPam091eS42hdbzMVzWclIqFnwHSu0c8zBhx5AxIkwBsXZyXaxI6ep6zdPGvbEuJTEof2Iy6Xs/J3tZ5od1XNl6+kmrOjixgX5oTUmwrjRFHv17X3UNPeE2JoRzrf0UG029bxZxtyveB962OHAcJ6FiBNhTKwP8L7zrY6qffHmyUYAls/MIiMpLsTWRBbWmHf1D3P4QkeIrRlhiylIU+JjWDFLmv35E++FykkbEWsTAiJI/Y23J8pJYz4aR4sTpdR8pdRjSqm6CdxXKaW+opSqUUoNKqXOKaW+ppRy9Gt0KlYOwpBbO6as+fmWHqqbrd2UhHT8jXfIxCmTlsejedO0Zf28XOJj5evsT+ble9e+cM4u2tqETEtP4Lrpzm9SF07ExbjsgmxbTzc7Lpxn4chvulLqdqXUTuAk8EWgaAIP+xLwTeDXwLuBp4FHgX8IkJkRzdo5OcTFGGndWxyyUMluKrBM86p98aZDxvxIfQetZsl6ce/7H6WULUp3nm2hfyj0tS/6h9zsNNtnbFyQLzVtAoAVzmvuHqDqorMOPVg4UpwANwKngduAx651Z2V8ej8H/I/W+sta6z9orb8E/Dfw1+I9mTwpCbGsNF3om483OkJdW7upAq9FVPAvlgA4XNdOY1d/iK0ZGXMQb1mguGWhMeZ9Q25H9NR6q7qFgWEj50kEaWDYuHDkfd10/HIILRkfRy7aWuuvaq0/orXeDExkVSwFpgGvjPr9a0AuMNvPJkYFt103DTCS5U40dIXUlv4ht93v5+YFebKbChC3LxqZtN440XiVewaHN0xv2cKCNKZnJIXYmshkw/w84mOMpeA1ByxUb5qfu1iXkvomAaIoK5nrzJ5kIk4CS4H57+jZ1PpZ5PcUsMQJwKZjof0A76puoX/I2k3JDjpQLC3OIsc8UvzasdCKk5buAbspneygA0dqQqydg7D5+OWQekm11rYgXTkrm7RESXoPFLddZ3ynKus7udTRF2Jr3k6kiJN489/RNZjdo/4+JkqpfKVUmfcNmONvI8ONkpxkFkwzwiehVtevmuIoPsYlR4gDSIxL2W7+7Wea6BsMXQ6CEU40/r9RBGlAsRaqy50DVNaHLgfhdGM3ta1GheKNC2XMA4n35nPz8dB7SUcTLZVtrrUV+BTwyFh/2LVrFw0NDRQVFVFaWsq2bdvsv916660cPXqUxkZjYBcsWEBKSgoHDhwAICUlhTVr1rBr1y56eoxTJhUVFfT09HDy5EkA8vPzWbx4MZs3b7avu2HDBmpqarhw4QIApaWl5Ofns3v3bgDi4+PZsGEDBw4coK3N6I9QXl4OQGVlJQBZWVlUVFSwbds2BgeNhMLVq1fT2NhITU0NwIRe06qidE5e7uLwhQ6eeXkTRTmpQX9NR44e5eWDRrGgG+bmcGjvLp9eUySOkz9f06IM4+h4/5CH/9tRyb0r54TkNT1/2thTpMVBZ/VBdjUG/7Pn5HHy52tK7BwpxvXbnSdozOkOyWt68s1K++eFaUN0d3fLOAXoNSUlJ5OXlkBT1wBPbzvG9J4zfn1Nx44dwxeUExIdr4ZS6lHgEa31uEkGSqkbgB3AO7XWf/D6/R0YeShrtda7rvL4fGC0TJ8DvFBZWUlZWZkPryC8OVjbxn3/sROAx+5bzMOrS4Juw/7zrdz/k7cA+NZ7FvPQquDbEE30Dg6z9BuvMTjs4cGVxXz7/iVBt6F7YJiKbxo2vH9FMd95b/BtiDbe+cNtHLvUyaLp6fz+sxtCYsPdP9pGZX0nC6al8crnbwyJDdHEl589wlN76oiPdXHwq7eT4sdKvFVVVZbQKtdaV0328ZES1rHOPRaM+r3lt7p0tQdrrRu11lXeN+Csv40MR64vyrR7mYQqtPNKlfG8Sl3pihQCQ3J8rF0tdvOJxpA0f9xysolB88TGneUy5sHgtkXG+3zsUicX24Ofg1DX2muHlO4sHz2VC4Hg1oXGmA8OexxV5wYiR5ycxRAo7xr1+zuBi0Bt0C2KEFwuZcejt59ppjvI1WK11rxS1QDA8pIs8tKk6VswuNUc86auAQ7WBb+1+kgrqyoAACAASURBVB/NMU+Jj+EGafAYFG73Ev5/rGwI+vO/6pV0f2eZCNJgsG5uLolxhgx49Vjwx/xqhKU4UUrFKaUWWfVLtNYe4PvAfUqpHyil3qGUegx4GPiBdnrsyuFYu5jBYU/QT+2cvNzF+RYjQe7OMtlNBYs7FhXgMgOpLx6+quPR7wwMu+1jzBsX5pMYFxPU549WymekU5RlHNd++WhwxxywNyFFWUksMo+5CoElKT7GbvS66dhl21vpBMJSnGBUgN0JrPD63beBrwD3Ai9gCJOvAP8SdOsijPVzc8lMNo70vXj4YlCf+w9HR9S8iJPgkZeWwBqzY+3vj17CHcTQzs4zLbaHTsY8eCil+JMl0wHYf74tqKGd5u4B9p1rBeCusgKpYxRE3lFujHlpXqojCi9aOF6caK0fHZ0Mq7V+RmudqbXe4/U7rbV+TGs9S2sdb/77LfGa+E5cjIu7zEVi6+kmOnpHn9gODFprWwyVFaZTYnZKFoLD3UsKAWjsGlk4gsHvzDFPiHVJTZsg8y5zzAFePhI878nvj16yO0/fJfkmQeWOsmns/LtbeOGv1lGU5Zw51vHiRHAG1kI15B7JAQk0lfWddqO/e5fOCMpzCiPcVV5AjBnbeSlIC1XfoNv+fN123TQpwhVkygrTmWVuAl4KYmjn+YP1AMzITKKiJCtozysYCfCFmc6rviziRJgQa2Znk5tq1J148UhwQjsvHDImLKXg7uunB+U5hRGyU+Ltgnd/qLzEsDvw8ejXjl+m1yz8ds/SwmvcW/A3Sil7I3K4rp06syBaIKlt6eVArVEJ+J6lhbhcEtIRRJwIEyQ2xmXHJneebaG5e+Aaj/ANt0fbImh1abb0VQkRdy82xry5e9DubRRIfmcK0vTEWAnphAgr7wRGQmyBxNqEgHhIhRFEnAgTxtrJuj3adsMGit3VLVw2q1a+WyaskHFneQEJscY08dt9FwL6XO29g2w5ZZQseufi6STEyimdULCwIM3u+v3bfXUB7bWjteZ5U5wsLEhjgXQbF0xEnAgTZsXMLGbnpgDw9N7ATlq/2VcHGL103lkuIZ1QkZEUZyco/rGqIaDJ0C8cusiQ2/hM3XO9hHRChVKKB1YUA3CupZe95wJX5+bIhQ7ONhl5ZRLGE7wRcSJMGO9J63RjNwfr2gPyPO29g/zeLAJ1Z3kBGcmSFBlK3meO+eCwhxcOB8ZjprXmqT1GrcTi7CT7GLMQGu5dWkhcjJH7YW0UAoE15i4F71lWFLDnEcIPESfCpLh/+Qz7BMdv9gZm0nr2QL1dDOihlcUBeQ5h4qydnWMX53o6QGN+sK6dEw1dADy4skSSIkNMTmqC3Sri5SOXAlIZuqt/yM5puWXhNAoyEv3+HEL4IuJEmBT5aYlsXGCUNn/x8EW/T1paa36919hNzcpJlh20A3C5FA8sN0Ri1cVOjl7o8PtzPLXbGPNYl+KBFbKDdgKWx6xvyH1F0qq/+N3hi/bJrIdXyyZEuBIRJ8KkeWiVMZH0DLr5rZ9dvntqWjl12WjX/n7ZQTuGB1YU2R6zX+yo8eu1O3qH7Doqt16XT36a7KCdwIZ5uRSa3oxf7jjn1xwzrTVP7jIEaWFGIjfNz/fbtYXIQMSJMGk2Lsi3CzX9YkeNX0ub/2ybsfDFx7pkB+0gCjOTeIeZGPvi4Ytc7vRfmev/2X2eviFjB/2B1TP9dl3BN2JjXHzkhlkAnGnstk9S+YO3zrZw7JLRgfjBVSW28BUECxEnwqRxuRQfXV8KQF1rH6/5qZvl2aZuNh03GgveX1FEbqp0IHYSHzPHfNijeeKtc3655sCwm//eaVxrYUEaG+ZJB2In8eCqEpLjjSPdv9hxzm/XfXxrNQCJcS4+uEYEqfB2RJwIU+K9y4vISDJO0fx0a7VfXL7/tW0kXGAthIJzWFaSRUVJJgBP7q71S77RCwcv0tRl1LP55I2zpeGbw8hIiuOB5YYHc+upJo5d7PT5micbumwvzAPLi8lOiff5mkLkIeJEmBLJ8bF8YHUJAAdq23nTR5dvXWsvz+w38lduXZjP3PxUn20U/M8nb5wNQHvvEL/c7lvuyZDbw4/fPANAQXqiXTZdcBYfXV9qh12+v+mUz9f7t9dPA0Zbio9vkE2IMDYiToQp84kNs0lLiAXge6+e9Ml78oNNp+0CXJ+9bZ5f7BP8zx2LClg0PR2An26r9qko29N76zjfYvRu+cub5xAfK9ORE5mZk8L9FUaV5teOXebIhanXN6qs77C7Hd9zfSEzc1L8YqMQechsIEyZrJR4PmbufCrrO/n90anlnpy63MVzB43S6HeVFbCkKNNvNgr+xeVSfOGO+QB09Q/zH1vOTOk6vYPD/NtmYwddlJXEQ6tK/Gaj4H/++pZ5dlG27/zxxJQ3It995SRgHBn/m9vn+80+IfIQcSL4xMfWl5JlVnD95kvHJp2HoLXmH56vxKONKpHWwic4l1sW5tu5J7/YXsOZxq5JX+OHm0/TaOaafP62+eI1cTjF2ck8uNIQkDvOtExpI/JKVQNbzfDvQ6tKxGsiXBWZEQSfSEuM4+/esRCAhs5+/vXVycWkn9l/gT01rQB8eO0s5k2Txl9ORynF1+8px6VgyK35ynOVeCZxnPxEQyc/N5OflxZnct8yaewYDvzN7fPt5NVvvFRFV//EQ3rdA8M88kIVAJnJcRK6Fa6JiBPBZx5YXsyKmVkA/HJnjb07uhbnmnv4+ovHAMhPSxCvSRixuCiDD5lHQHfXtPKzbdUTelzfoJvPPnWIYY8mxqV47L7FUmgvTMhKibc3Ipc7B/jKc5UTCu9orfnq85U0mLVxvvyOhVImQLgmIk4En3G5FN++fzFJcTFoDZ97+hB1rb1XfUz3wDCfevKAHQb61nsWk5YoDf7Cib+9cwEl2UYxvu++cpK3zrZc9f5aa77y/FFOXjbCQH950xwWFaYH3E7BfzywvIib5ucBRvn5J946f83HPLm7lucOGuXv183NsVshCMLVEHEi+IW5+Wn8033lALT2DPKB/9rNpY6+Me/bMzDMJ5/YZ1eI/Pj6Um41m4wJ4UNaYhw/friC+BgXbo/mE0/s42Bt25j39Xg0//jycZ49YCxSq2Zl8zlx7YcdSin+9X3XMy3d8Hw8+mIVzx8cv+/O7w5f5GsvVAKQl5bAD96/TDxlwoQQcSL4jfdUFNl1MGpbe3nXj3bw+onLV7h+K+s7uP8nO9lp7rJvWZjPl0xXsRB+LC7K4LvvXYJShjfswZ/u4snd569oadDY1c9fPrmfn5t1UWblJPPvH1hGbIxMP+FITmoCj39oBSnxI57S7/7xBH1mEz+A/iE333v1JJ956iAeDUlxMTz+oeXkpUk4R5gYyp/NnCIJpVQZUFlZWUlZWVmozQkbtNZ8/cVjdklygPnTUpk/LY369j4O1o7USLhpfh6Pf2g5iXExIbBU8CdP7anlK88dxdIkMzKTWDEri86+IXacbWFw2AMYwuRXH1tNsRkOEsKXt8628Ikn9tmh2eyUeG6Yk4NLKXacaaalZxCAlPgYfvrhFaybK60JoomqqirKy8sByrXWVZN9vIiTcRBx4htP763lmy8dH/NocaxL8ec3zebzt82X3XMEseNMM1/4zWE78XE0d5ZN4zv3LyEzWcqVRwpnGrv566cOcvzS2GXtFxak8W8PLWO+nMKLOkScBAgRJ77T2jPI/+4+z5ZTTTR2DZCZHM/q0mweXFnM7DwpTx+J9A26+c2+Ol491kBtay+JsTEsLsrgfSuKWTM7J9TmCQHA7dG8ePgivzt8kVOXu9Aa5k1L5Z7rC7nn+kLZgEQpIk4ChIgTQRAEQZgavooTkbSCIAiCIDgKESeCIAiCIDgKESeCIAiCIDgKESeCIAiCIDgKESeCIAiCIDiK2FAb4GDiAc6cORNqOwRBEAQhrPBaO6dU2EiOEo+DUuoe4IVQ2yEIgiAIYcy7tda/m+yDRJyMg1IqA7gJqAMG/XTZORiC593AWT9dMxKQ92V85L0ZG3lfxkfem7GR92V8AvHexAPFwBatdcdkHyxhnXEw38xJq72roZTdjfPsVIrSRCryvoyPvDdjI+/L+Mh7MzbyvoxPAN+bg1N9oCTECoIgCILgKEScCIIgCILgKEScCIIgCILgKEScBJcm4Ovmv8II8r6Mj7w3YzOl90UplaqUKpjgfedNxTAHIJ+ZsZH3ZXwc997IaR1BEKICpVQOsBX4ttb6V9e4bypQDXx8KscgBUHwDfGcCIIQUJRSa5VSLUqp1SG0QQG/BfYB/3Ot+2utu4EPAU8qpa4LsHmCIIxCPCeCIPgNpdTNwBvARq31m+bvYoCFwAmttTtEdn0Y+D4wezI1F5RSvwGytNa3B8w4QRDehnhOBEEIKFprt9a6KlTCxOTvgR9OoRjUPwO3KaVWBcAmQRDGQcSJIAh+QSl1DsNrAvCG+TNKqZuVUtr0qqCU+lPz5weUUvuVUgNKqVql1F8qpWYopZ5WSrUrpVqVUs+MTmBVSq1USm1WSvUopRqUUt9XSiVcxa6VwAJGFVVUSk1XSj1hXqNDKbVFKbXB+z5a673AeeCDPr05giBMChEngiD4i/cCnzH//xnz56vxdQzPxH3/P3vnHR7VdSbu98yo944AdTqIJroxuIBb7NhOcTaO05y+TjabTdtNL7spP6dsNrtJNpu+iZ11nMQ9MbExtoVBNNEkuhAICYR6LyPNnN8f997RSJZAQnPn3jtz3ufRg5hyz3d1Zs75zleBU8CPgD1oLSPeBnwZuAP4D+MNQogytKDWYeDtwL8CDwI/ucI4m4FOKeWhMY8/DWwA/hF4ByCBbUKIBWNetxOtlYVCoQgRqny9QqEIClLK/XqWC8BRKeX+q7zlXVLKAwBCiCo0C8U+KeWn9ef/JoRYDtwb8J6HgXrgjVJKj/5eH/CfQojPSSkvjzPOMuBS4ANCiCxgNfCPUsrH9Md2A39As7KcDHj5ceDtQgi3xa4phSJiUMqJQqGwilbjFyllnd7f4/CY1zQAWQC66+Ym4HuATwhhrF+7ADewCvjLOONkAS1jHmsDjgKfEkIMAtuklOeAreO8v12/flqgzAqFwjyUW0ehUDiFbLQ16zPAUMCP4a7JnOB90WguGz9SSh+aovM4WrBsrRDipBDiQ+O8f1D/d8K4FoVCEVyU5UShUDiFbv3ffwceHef52gne14lufQlEStkKfBr4tBBiDvAQ8FMhxICU8n8DXmq8t+OapFYoFFNGWU4UCkUw8en/uoN9YT0N+DCwXEq5P/AHuKQrG+NxFigMfEAIcbMQ4oQQYoV+7Rop5afQFJA1Y96fDTRJKfuCekMKhWJClHKiUCiCSZ3+7/uFEHeacP3PAjcIIZ4WQrxJCHGHEOJ3wBEhRNoE79kDZAgh8gMe2wskAL8VQrxdCHGLEOJHaHElfxvz/nX66xUKRYhQyolCoQgaelDpd4C70DJrgn39v6EFraYBjwCPocWa3CylnMjtsg3oAW4PuE4PWnrwcbQU5qeA69AyiJ4xXqdnH60D/hTse1EoFBOjytcrFIqwR7eKrJFSTqnSqxDig8A30Mre95ginEKheB3KcqJQKCKBrwLzhBB/N9k36FaTLwJfUIqJQhFalOVEoVBEBHoMzG+AG6WUVVd5bTTwR6BPSnl/KORTKBQjKMuJQqGICKSUzwHvA3Kv9lpAoFWJfY+pQikUinFRlhOFQqFQKBS2QllOFAqFQqFQ2AqlnCgUCoVCobAVSjlRKBQKhUJhK5RyolAoFAqFwlYo5UShUCgUCoWtUMqJQqFQKBQKW6GUE4VCoVAoFLZCKScKhUKhUChshVJOFAqFQqFQ2AqlnCgUCoVCobAVSjlRKBQKhUJhK5RyolAoFAqFwlYo5UShUCgUCoWtiLJaALsihEgFbgAuAB6LxVEoFAqFwknEAPnAK1LKzqm+WSknE3MD8JTVQigUCoVC4WDuAZ6e6puUcjIxFwCefPJJ5s6da7UsCoVCoVA4hjNnznDvvfeCvpdOFaWcTIwHYO7cuSxZssRqWRQKhUKhcCLXFBahAmIVCoVCoVDYCqWcKBQKhUKhsBVKOVEoFAqFQmErlHKiUIQxUkqrRVCEGK9PqnmPMIa9Pry+8JrzsAuIFUK4gE8BHwQKgUtoKcFfkVJ2WClbqJFSsuNkE4/uucDBuna6B4fJS49ny8Ic3nd9MTNT460WUWEChy508OvXatl5ppXW3kGykmLZOCeTBzcWszw/zWrxFCZQ19rH/5TXsP14E5c6B0iIcVNWkM79awt4w9JchBBWi6gIMu29Hv6n/Cx/PXqJ8219uIRg/oxk3rxyNu/aUEhctNtqEaeFCDcNWwjxQ+DDwMPATmAx8HVgl5TytilcZwlQVVVV5chsnbZeD//02CFeOdU87vNx0S6+cOdi3rmuQC1cYcLgsJevP3OMR/bUTfiad64v4Et3LSY2ytkLl0JDSsnPys/y3W2n8Hh9475mfUkGP7x/JTnJcSGWTmEW26ob+czjh+kaGB73+bz0eH78QBnL8qw7jFRXV1NaWgpQKqWsnur7w0o5EUJkA43At6SUXwx4/NPAd4AiKeX5SV7LscrJhbY+Hvj5Hura+gBIjoti66IZZCbGcKS+k73n2vyvfXBjEV++a7FSUBxO7+AwD/56H3trtbmNcbvYsiiH4qxEalt62X68yb95rSvO4FcPriEhJuwMpxGFzyf5/BNH+b99I2UkNs/PZkVeKs09Hp6vukR73xAAM1Pj+L8PracwM9EqcRVB4lev1fK1Z475/78iP41N87LweH28UH2Zsy29AMRGufjpu1Zx44IcS+RUykkAQoi5wFeB70kpDwY8/gbgOaAs8PGrXMuRyklLzyBv/ckuzrVqismdy2byb/eUkp4Y43/NrjMtfOKxQzR1DwLw0I1z+OztCy2RVzF9PMM+3v+bfZSfbgFgZUEa//F3KynITPC/5nxrL//4f4c4dEHzbG6al8Uv37uGaLcKO3Mq//rsMX6xsxaA2Wnx/Oc7VlJWkO5/vmtgiK89fYw/Vdb7X/Pnh65jRoqyoDiVPx6o59OPHwYgKTaKh9+6jDtKR9x2Xp/klztr+fbzJ/D6JLFRLn73gXWsKcoIuazTVU7CamWSUp6RUr5zHAXkJuAyMOU/kJPw+iT/8OhBv2LygeuL+a/7V45STACum5vFUx/bSH6GFnPy45dreO7IpZDLqwgO3/7rCb9icsP8bH7/wfWjFBOAwsxE/u9D69k8PxuA8tMtPPz8iZDLqggOf66s9ysmJdmJPPnRjaMUE4CUuGi+e98yHrpxDgANHf38w6MHGZ7A/aOwN1UNnXz+z0cBzRr+2IfX84alM0dZvd0uwQc3l/DjB8pwuwSDwz4eeqSSpu4Bq8S+ZsJKORkPIcQq4OPA16WU41aqE0LkCCGWBP4Ac0IqaBD48Y4z7D7bCsC9K2bxhTsXTeiumZkaz+/ev46UOM20/9k/HuaC7gZSOIftxy/zy9e0TWrp7FR+8s6yCQPh4qLd/PSdq1gyKwWAn5XX8tKJyyGTVREczjb38MUnqwDITIzht+9fR3Zy7LivFULwmdsWcN+qPAD2nmvjP7afDpmsiuDQMzjMxx6txOP14XYJfv7u1SyZlTrh629bksu/3VsKQHP3IJ987LDjMrjC2ukshMhHy9R5HvjJFV76EPCV8Z6oqKigsbGRvLw8iouLKS8v9z+3ZcsWjh49SlNTEwALFiwgMTGRyspKABITE1m/fj0VFRX09mp+wLKyMnp7ezl58iQAOTk5LF26lO3bt/uvu2nTJmpra6mv18yxxcXF5OTksGfPHgBiYmLYtGkTlZWVtLe3A5CQO4cf6IvOzETB20q8CCEoLy/H49F0snXr1tHU1ERtrbaZ5eXl8Z23lPLhRw7R6/Hy9794hWc+fTtVVVW2uCfdJEhVlbYQp6enU1ZWdtV7svM8BfOe9lQe5pNPamMnxrj45l1z2F3+ylXv6Z3FA3y9CfqH4YtPVPH5sqPERwlb3FM4zlMw70lKyXcOeOjzaBvNu+dLThzYxeBV7unmVMnBrHjOtPTz4x1nyOqrY2lBpi3uKRznKdj39NzFOL9F/N4SN0tyYjl79uwV7+ntN9/MCwfP8lJtLzvPtPCzF49y3+r8kN3TsWMjcTHXQljFnAQihMhAy9bpAW6SUvZe4bU5QPaYh+cATzkh5kRKyf0/q6DibBsuAU9/7HpKZ0+sVY/lM48f5vED2gfth/ev5O7ls8wSVRFE/u3ZY/xcN+1/563LuG91/qTf+/u9dXxONxE/uLGIr7zR3p9xhcaTBxv4xGOHAHjPhkK+dk/ppN9b1dDJPT96Da9PsrIgjT995DpcLhUIb3dONHZx5w934vVJVhem84cPb5j0vHUNDLH1e6/Q1D1IWkI0L33qRjLGuPnNQsWcjIMQIgEtAFYCd1xJMQGQUjZJKasDf4CaUMgaDJ49comKs1qWxrs3FE1JMQH4wp2LyErSPrD/768nGBz2Bl1GRXA509TNr3adA2BNUTpv1c32k+XvVueztlgLkvvt7vOca7niV0RhA/o8w3zjL8cByEqK5VO3LZjS+0tnp/L+64sBOFjXwV+qVJyZ3ZFS8tWnq/H6JG6X4F/vLZ2SQpkSF83X7tYOHh19Q/xoxxmzRA06YaecCCGigMeBXOAWKWWrxSKZyrDXx/dfOAVAVlIM/3TL/ClfIy1h5H0NHf38rmLiOhkKe/DvL57G65O4BHzt7tIpp4K7XIIv37UYgGGf5Hv6Z0hhX/5393ma9Qy7z92xkJS46Clf4+Nb5pGpn5y/u+0kQyo41tbsqmn1Hzzftb6QRTNTpnyN20tzWV8ychBp6OgPqoxmEXbKCfBz4Ba0lOISIcT1AT9LrRUt+Dx16CK1+qn3oRvnkho/9QUL4G2r8ynO0mog/NdLp+kdHL+4j8J6TjR2+bOr7lkxm8Wzpr5ggXaSNlx4zxy+SPXFzqDJqAguPYPD/PQVzZg7f0YS966cfU3XSYqN4mM3zwXgXGsfj++vD5qMiuAipfQfPBNi3P55mypCCH+pCI/Xxw8cchAJR+XkPUA08GugfMzPf1onVvAZ9vr4z5e0INic5Fjesa7gmq8V7XbxqVs160l73xCPBRR2UtiLH7ygzbnbJfj4lnnTutanbp2PWzcT//crZ6ctm8IcfrPrnL+g2ie2jszZtfCOdQXMTtPKCPz01Zqw68kSLrx6uoUD57Ug2fdcV0RW0vgZWZOhrCCdWxfPAOCJgw1c6rS/9STslBMppbjCz41WyxdMnq9u9EdwP3TjnGn3UrijdKbfevKLnbXK5GtDzrX0su1YIwD3rpjtn69rpTAzkTcumwnAc0cuqnRyGzI47OVXr50DYGFuMrcvyZ3W9WKj3HxwkxZ7cr61j23VjdMVUWECPy/XDguJMW4+tKlk2tf76E2a5WVYL9Rmd8JOOYkkjAUrPSGat6+9dquJgdsl+KD+JWjo6OfZIxenfU1FcPn1rnMYCXYfvmH6CxbAhzZrJX18En9hL4V9ePbwJVp6tFiTD99QEpQMm7etySctQXMB//SVGsfVwAh3Tl3u9hdWfNua/NcV0rwWluensU4Pgv/93gt0DQxN+5pmopQTh3KkvsNv8rt/bUHQOlC+uWy233xoKD8Ke9A1MMTj+zV326Z5WcyfkRyU6y6eleKvHPvYPvsvWpGElNJfZC87OZY7lwYnzT8hJop3bygC4HB9p38tUdiDX+lzLgS897qioF3XOND0DA7zB5u77pVy4lAMxcHtErxrQ2HQrhsX7eYBPXblSH0nR+tVkKRdeHx/Pb0eLc37fRuLg3rtBzcWAdA/5OWpgw1Bvbbi2tl3rp3qi12Alq0RExW8Jftd6wuJdmtWmEev0MlaEVraez38uVL7Dm5dNCOozRpvnJ9Die4KfnRvna0tZko5cSBtvR6/y+WO0lxmpsYH9fpvX5uPYTl+dO+kmjgrTEZKySN7tLkoyUrkhvljawZOj83zsslL1z5Hj+yx96IVSTyqz3mM2zWtgPfxyE6O5dbFWvzKs0cv0dE3bncPRYj588EGBoe1eD/j0BAsXC7B/XoIwNnmXn+ash1RyokDeepQA0NebfN45/rgWU0MZqbGc/PCGfpYF5WZ3wZU1nVwtllLGb9/bUHQK3u6AxatE43dHNS7Fyuso7N/iL9WacGqty6ZMa1sjYkwFB7PsI8/VSqLmdVIKf2u26LMBDaUZAZ9jLesyiNG70b++732tZgp5cSBGLUJCjIS/AFOweaB9dqi1efx8vQhFRhrNX88oC1Ybpe45hoXV+O+1XlEuZSZ3y48e+Si/wT9tim0JpgKG0oyKdQ7WP/e5mb+SKCqoYsTjd0A3Lc6f8rFFSdDRmIMdyzVLGbPVzXS1mtPi5lSThxG9cVOjl3SfNBvXZVnyocXNDP/zNQ4QOvnobCOPs8wzxzWiq7dtCBnwg600yUnOY6tizSL2fNVjfR7VBsDKzEOITNT49g4N8uUMVwuwdvXaAeRM009VDV0mTKOYnI8rh9CXEJLTjALY849Xh/P2TQrUyknDuOPeoM+YfKH1+0S3LNCu/7+8+3Utar6F1bxfFUjPXrF3vtWT62HzlQxrDI9g8O8ePyyqWMpJub05W4O6a61t5TlTavo2tW4Z8UsjDPOk4fUQcQqBoa8/oPgpnnZQY8lDGRdcQazjMOnTS3jSjlxEMNeH0/pH6Tr5mSSl55g6nhvCnAfPKUWLcswIvczE2O4eWGOqWPdtDCblLgoQM25lTwRYK2calPHqTIrLd7vHn7m8EVVMdYiXj7ZTNdAaA4hLpfgbv3weeB8uy2LLyrlxEHsPtvq9w++aaW5H16ABbnJ/kZTTxxqUP5oC2jtGWRXjVaM6c5lM4l2m/uVjY1yc6deMfblk8229UeHM1JKH4d44wAAIABJREFUnjuqufFWFqRRNM0qwJPhXn2jauoeZHdNWPdKtS1GBmZijNvvXjWTe1eO1Myx40FEKScOwmj2FuN2ccti8z+8AG/SP8Bnm3s52qBqnoSa56sbMQ6ydy0LTgGuq2G484Z90rb+6HCm+mIX53U36p1LZ4ZkzDuWzvRncDyhYsxCTr/Hy/bjTQBsXTwjaEU1r8TC3BQW5mqFHJ84aL/Dp1JOHMKQ1+fvgbFpXtY1dx+eKncvn+33RxunOUXoMBTSnORYVhemh2TMtUUj/mg156Hn2SMjf/M3hEg5SY2P9rsM/1bdiGdY9dUKJTtONtE/pAWgh0ohhZGDSE1zL8cvdYds3MmglBOHsLum1d+V1DC7h4Lc1DjKCrRNcVtVo+2063CmpWeQirOaif0NS2cGvbbJRLhcgttLtc/Y3to2WvW+LgrzkVL6zfurCtOZlWZeUORY3qCvK92Dw35XoiI0GIeQpNgofyuJUHBXwF7yfJW9DiJKOXEIgS6drSFy6RgYXVDPtfZx8rK9tOtw5vmqQJdO6BRSgNtLtTn3SVTWTgg5Ut9JfbvWzj6UJ2iAmxZk+107qlNx6OgdHGb7Ce07dkuIXDoG+RkJLMtLBTQrqZ0On0o5cQBDXh/bjmmLxeb5WaTEhcalY3BbQIv256vUohUqDIU0N2XEehUqVhWmk5WkdUJVcx46/qK70YQInUvHIDkumuvnafVU/lZ9WWXthIgdJ5sYGNLcaKFWSAHu0K2kNc29/lgnO6CUEwewr7aNDt2lE+oFC6AgM4HFetaO2qhCQ0efh73ntL4Xt5fmhsylY+B2CW7R+668dqZVtTAIES8c007QZQXp5OpxP6HktiWaVba118P+c/btuxJOvKjPeWKMm03zzSm2dyXuWjaTz92xkPLP3hSSzLDJopQTB/CiHsXtdgnT61xMhGHmP9HYTW1LryUyRBIvn2z2n1xDlZk1FmPOPV4fO040WSJDJHG2uYez+ncrFKmk47F10Qx/08/nlWvHdIa9PnacbAZg8/xsYqNC59IxyM9I4MM3zCE/w9y6WVNFKSc2R0rp90euKkwnLSHGEjmMjQq0aH6FuRhxHsmxUawpMqd/0tXYUJJJsl6QTcUgmI+RSgqwdZE1h5DMpFjW6gXZVAC8+Rw4305nv2aV3GKRQmpXlHJic2qae/x+QKsWLIB5OUkU6Q3CXlKnaFMZ8vp45ZR+mlqQTUyUNV/TmCiX31L36qkWlV5qMi/oCmlBRgJzc5Isk+NW3Z13sXPA34ROYQ7GIUQILSBZMYJSTmzOiwGnKSs1ayEENy7QNqr959tVDIKJ7Ktto1svY22lQgr4lZOewWH2n1cxCGbR0efhwPl2ALYsyjGtoedkCHQd7zipDiJmYljLygrSyUwyp6GnU1HKic3ZrmvWRZkJlFgcrGQsWl6fpPyUqoNgFoZC6hJw43xrlZPN87L9MQgv675xRfAZFWNksXm/KCvRv9a8fELNuVnYIcbIzijlxMa09waepmZYepoCWFucQbyeg69cO+YQGGO0ujCD9ERrYowM0hNjWKmnMas5Nw9/jFFcFGuKrYkxCsSwkh6oa6ezT1lJzcAOMUZ2RiknNmbHySZ/Ea4tNvjwxkW72ThXS3V75VQTPlUHIegExhjZYc5hxBd+pqnHlt1LnU5gjNEN87NNb+44GW5aqM251ycpP6OsJ2ZgHEKsjjGyK9Z/CxQTYpjRk+Osy9gYi+HaaenxqEaAJhDoOrGLcmKcokHFIJjBoQsd/hgjq0oFjGVtcQYJMZqVdIdy7QSdnsFhv1X85oXWxhjZFaWc2BSfT7LzjBbXcf3cLFucpgBuDIgoVxtV8Ck/rc357LR45mTb4zS1ZFYKOclasJ6qdxJ8yk+NbP5GhVariY1SVlIz2XO2lSGv9jfdbEHhNSdg2o4nhMgXQqwUQqwXQiwUQtirwovNOXapi7ZeDwCb5tknxWxWWry/zfYOFSAZVAaHveyp1Rr9bZqXZZvTlBCCm3Trya6aVgb07qmK4PCqrpAumplCTnLoq8JOhDHnLT0ejigraVB5VVdIo92CdcWZFktjT4KmnAghXEKItwohnhRCtALngP3Aa0A10CmEOCyE+JIQIi9Y44YrxgkatI3KThhm/iP1HSpYLogcONfu77FhlxO0gRGDMDjsY58qax40Ovo8HKnvAGCzTeccYOdpdRAJJsb6vqowncTYKIulsSdBUU6EEDcAR4HfA6nAj4F3AXcBtwD3A58ADgMfAU4JIb4uhFCzMgHl+mJQlJlgu7LC1+vmXilRrdWDiHGCFgI2zrHXRrWhJMufUrzztJrzYLGrptUf9G4nCynAzNR4f6BmuZrzoHGhrc+fQmy3ObcT01ZOhBAfAZ4DngXypZQ3SSm/JKV8VEr5VynlS1LKP0gpfySlfLeUcjZwD3Ab8KIQIuiOdSHEfCHEN4UQF4J97VDQ5xlm/zktWMqOH97VRenE6lVLjbgYxfQxFNJls1MtTyEeS2pCNEvz0gA158HEmPPYKBeri0LbeXoyGAeRyrp2+jzDFksTHgR+fzbbcH23C9NSToQQc4FPAuullP8spZxUAw4p5QvABuAY8PnpyDBGnluEELuAk8BnAEe6j/bUtuHxauZ9u7l0QEspNrKH1EYVHFp6Bqm+2AXYUyEFuH6u5huvvjgSD6W4dqSUvKoXM1xXkklcdOibvl0NIyh2yCvZW6vcecHAUEgzEmNYMivFYmnsy7SUEynlGSnlfCll1TW81yelfEhKGTTlBNgMnAa2At8M4nVDimE2d7sEG+bYM1jKWLTOt/ap2hdB4LUz9o0xMjDmHEbLq7g2alt6aejoB+wXb2KwriQDt+7PU3M+fYa9Pv/6fv3cLFwuewS92xFTsnWEEJuEEB/Qf3cJIb4ohHhKCPH3ZoxnoLuT3iOl3A44NvfN0KzLCtJIjou2WJrxCdxAlfVk+hgn6MQYt78iq91YVZhOXLS2ZKiNavoExnFsnm9Pa1lKXDTL81IB2Hmm1WJpnM+Rhk669Jo2dj2E2IWgKydCiLuBHcAb9Yc+C3wVyAd+KIT4eLDHDCcaOwc4dbkHgOvn2nPBAlg8M4X0BE1xUsrJ9JBS+hXSDXMyLetCfDVio9ys1dMey0+3IKVj9X9bYMz5jJRY5tm4QqgRd3L8UhfN3YMWS+NsAnuS2dV9axfMWAW/CDwB3Kv//yHg81LKMuBbwIdNGHNaCCFyhBBLAn+AOVbIErjR2y2dNBCXS3CdvmjtOtOiijRNg5rmHpr0Rf/6ufadcxiJO2no6KdOufOumWGvjz1ntRiOjXPtU9NmPALdeSo7b3rsPqv9/ebmJJGbap+aNnbEjFTeRcAXpJRSCLEQmA38Vn/uZeDTJow5XR4CvjLeExUVFTQ2NpKXl0dxcTHl5eX+57Zs2cLRo0dpatKqZi5YsIDExEQqKysBSExMZP369VRUVNDbq6WOlZWV0dvby8mTJwHIyclh6dKlbN++HYAnqrW6IQnRgtZTB9h+RlBcXExOTg579uwBICYmhk2bNlFZWUl7u5bVU1paCkBVlRb+k56eTllZGeXl5Xg8WvDiunXraGpqora2FmDa95Q5pBVmau8bYseh09B+Ydx7Ati0aRO1tbXU19cD2PaeJjtPwbynas9IXJGr5Qw9Pdm2vaeEgZGgzZ8/s5Mb86MiZp6CeU9/2rGf7kHNvL+hJNPW97Qkv5BYNwx64fFXj3LPitkRM0/BvKchr+TAeU2m/Jh+tm/f7vh7utI8HTt2jOkggm2a1dN3vyCl/F8hxD8BH5RSLtafey/wTSnlrKAOOr4cXwW+IqW86pFECJEDjLWxzQGeqqqqYsmSJSZIOD4bv/0SDR393Lwwh1++d03Ixr0WLrT1senhHQD8yx0L+cgNlhibHM9HH6nkuaOXyEyMYf8Xt9r6FO3zSdZ840Vaez3cviSX/37XKqtFciQ/faWGb/31BADln73JdrWMxvLgr/ay42Qzs1LjeO1fbrb1Z9Su7K5p5f6fVQDw4wfKeMPSmRZLZC7V1dWGolUqpaye6vvNcOs8CTwshPguWprwIwBCiDegxZ48a8KY00JK2SSlrA78AWpCLceFtj5/9P76Ens0+rsS+RkJ5GfEA1BxVgXLXQtSSv/fbn1Jpu0XfVdABtme2lblzrtGdutznpceb3vFBEZcOxc7B/xdsxVTY3fAGrmu2P7ru9WYoZx8HihHiy2pAL6nP/49oBn4FxPGDAsCN/j1JfZMIR7Lej1Acl9tG8N6bRbF5Dnd1EOrXjPECQop4FdO2vuGONXUbbE0zmPY62OfXjNkg1O+5wFyGv2fFFPDWN8XzEgmMynWYmnsT9CVEyllt5TyPillspTyjVLKAf2pe4C1UkpVyWcCKvQAueTYKBbPdEZxnnX6otXr8VKlFxFTTJ5AhdSuNW3GEtiozAjqVEyeow2d9Hq05olOOYQsmplCcpwWoqjmfOoMDHk5VKf1UHLKIcRqgtVb5y4hxBWvJaU8JVXu4YQEmvfXFmcQ5bZnOulYAs2Te5RrZ8oYc56VFMucbPumkwYyJzuRLP3kp9x5U6ciYHNf7xCF1O0S/u96xdlWlUY+RSrPt/urfjtFIbWaYO2AvwUahBAP6xk6liOl/OpkgmHtQn17f0C8iXM+vPkZCeSlq7iTa8Hnk/6Nan1Jhu3jTQyEEKzTT397a9vURjVFjO9JQUYCs9PiLZZm8hgWs4udA9S391ssjbMIXBvXOWh9t5JgKSe5aCnCK4EqIUSFEOKDQghn+CZswG4HxpsYGIvW/nPtKu5kCpxu6vH3qHHanK/XT9GtvR7ONPVYLI1zGPL62HduRCF1EoGfUXUQmRrG+r4wN5kMmzX1tCtBUU6klINSykeklLegpeD+FfgccEkI8TshxM3BGCecqajRPrzJcVEsdlgzKGOR7R4c5tglFXcyWXYHFLRynHKiNqpr4mhDJ316vIlTYowMFs9KITlWizupUHEnk6bf4+XQBSPexFlzbiVmBMSel1J+TUpZglbCXgLPCCFqhRBfEUIUBXtMpxMYb7KueKTRllNQG9W1YSzw2cmxzMlOtFiaqTE3J4lM/QRYobrVTprdNc61kLpdgtVFWt8nlbEzeQ6cb2fIq7k+nTbnVmJq1KWU8iUp5bvQ3D7fBm4HaoQQ26/8zsjiQls/Fzu1pCYnfnjzA3znKpJ/cvh80r/AO6G+yVgC4072qADJSWMo70WZCcxMdU68iYGxPtW391PfruqdTAZjzoVwnivPSkKSEqKnF/9USrkBWAocCMW4TsGJ9U3GEhgg6VWFua7KycvdtPdprQqcumAZsUYtPR5qmnstlsb+eIZ97D+nlSh37vdcpZFPlZF4kxTSElS8yWQJeb6qlPKYlPKzoR7Xzhgf3pS4KBY5pL7JWIzFtntwmGOq3slV2RMGCqkqzDU1qi520j/krPomYymdlUJijNZfSc351RkY8nKkXtU3uRaCrpzoHX5/L4S4LITwjvMzHOwxnc5e3We/1oHxJgbri9VGNRX2nddO0FlJsZRkOSvexGBeThLpCdGACpCcDPvPjfyN1jq0fHmU28XqIqPeiZrzq3H4Qoc/3mRtkTPn3CrM6Er8I+AO4FGgwYTrhxUXO0bqm6xx8Ic3PyOeWalxXOwcoOJsKx/YVGK1SLZFSunfqNYUpTsu3sTA5RKsLc5gW/Vlf9yJU+8lFOzTXTqzUuOY5aD6JmNZV5LBK6eaqWvr42JHv6PvxWz264cQgFV6MLFicpihnNwMfFZK+WMTrh12BH54VztYORFC26iePHSRA+fb8fkkLodagcymvr2fy12DgLPnHLS4k23Vl2nqHqSurY/CTGdagcxGSskB/bvu9DkPdEntrW3j3pWzLZTG3hg1bQozE8hJjrNYGmdhRsyJCzhlwnXDEuMEHRvlonS2M+NNDIxFt71viJpmVZhrIvYFmPdXFzr7NBXonjAsA4rXc7al119wb43DT9Cls1KJi9a2jv3nlWtnIny+AIW00NkKqRWYoZxsA2414bphibGgL89PIzbKbbE00yPQLaU2qokx/jbx0W7HFdwby8LcZH+AZGBMhWI0gX8bp1tOYqJcrMhPA/BnHylez6mmbroHtBBLpyukVmCGW+eTwB4hRAlwZJznpZTyX00Y13F0DQxxolHLbHH6CRq0AMmUuCi6BobZf66Nd6wrsFokW3JAP22uLEgj2iENHiciyu2irDCd8tMtoyxCitEYCmlybBTzZyRbLM30WVOUQcXZNk5e7qazb4hUPTBaMULgAc3pCqkVmKGc3A3MAt6s/4xFAko5QetUadSucnIwrIHLJVhdlMFLJ5rYp8y949LR5+HUZc3lFS4L1urCDMpPt1DT3EtrzyCZesdixQiG5aSsMN2xGXmBGJ9dKaGyrp2bFuZYLJH9MOY8PSHacRWg7YAZx7bPAduBQimla5wfZ/sugohhEhUCygqcbzkB/OWtL7T106hXvVWMcCAgADpcTL2B9xF4fwqN5u5BzrVq1VTDZc7LCtIwdCxlMRsfY31fVeicjuN2wgzlZAbwfSnlBROuHVYYwWQLZiSHjVk0MJdfBcu9HsPU6xKwMkwU0hUFaX5rgNqoXs+B8+ETb2KQHBfNwlwtXkrFnbye0SUiwuN7HmrMUE6qAGdH+YUAz7DP36lydRh9eJfmpRITpX2s9qmGcK/DMPUumplCUqwZXtXQkxATRake2KsCoV+P8TeJdguW56VZLE3wMDbdQ/UdDA57LZbGXoRLiQgrMUM5+TbwZSHECiFEwXg/JozpOKovdjIw5APCI97EIDbKzfK8VEBtVGPRSll3AuE15zCyAFc1dNLvURtVIIZCumRWKvEx4ePVNubcM+yjqqHTYmnshTHnMWFQIsIqzFBO/gAsRmvuVzvBT8SzP4wjuY37OdHYRdfAkMXS2Ieqhk48Xk0hDSdrGYycood90m8RVECfZ5gqvddUuJn3Az/D6iAyGuPvsSLP+SUirMIMu/KDJlwz7DB88zNT45gdZuWf1xSl8xPAJ+FgXQc3zM+2WiRbMCq1MMyKMgUq2PvPtbFhjjMb2wWbQxc6/F26w+0QMjM1nrz0eOrb+zVLwQ1zrBbJFnQNDHHSKBERZgppKJm2ciKEiJFSeoz/Syl/M4X3urS3GAm1kYGU0u+TDLcFC2BVweiNSiknGoapNy89ntzU8CplbTQwPNvS629qqBhjIQ2DWkZjWVOUQX17A/tVywo/B+s68IVRiQirmJZbRwgxB2gQQmy5hvcmA08D35iODE4knEpZj0dqQjQL9EJTe1VQLKCXsq7TNqpwXbCMU2Ll+Xa/tSDSMSykJdmJYVn/xZjzDtWywo9xCAmnEhFWMC3lREpZA3wQ+JMQ4qdCiLyrvUcIkSiE+AhwAugEvjIdGZzIgTA27xsYi9ahCx14hn0WS2M9Nc09dPRp8Tfhauo1rIA9g8P+yseRjNcnOVinZ+SFodUEVMuK8TAU0vk54VMiwgqmHRArpXwSuA6YA5wXQlQKIb4vhPiMEOJBIcR7hRAfE0J8RwjxAtAMfBX4ipTyASllxEVMGh/e5NgoFuQ6v5T1eBgN4QaHfVRdVJH8gQt3uFpO1oyKO1Eb1YnGLnoGtd4q4ei+BZibnURqvLYBq95KMOQNzxIRVhCUbB0p5TEp5VZgI7AL2Ap8E/gF8Evgh8C7gD7g74ESKeXPgzG2EzHiTcKllPV4jA2QjHSMv0FqfDRzs5MslsYcijITyEqKAVQxNhitoIWrQupyCb9VSLWsgOqLXWFZIsIKgppKLKWskFJ+TEq5DIgDcoDZQJKUMldKeY+U8jdSyr5gjuskmrsHqW3pBcIz3sRgdlo8s/SgT2XuHVm4VxWmh23QoBDC76bcd66NCItzfx2GgpaVFENRZoLF0piHcRBRLSvGdp8O3/U9FJjWElVK6ZVStkgpL0WyMjKWcCxlPRHG/e2P8I3qctcAF9q0UtbhvmAZ93e5a5D69n6LpbEOKaVfOVkd5r1VAg9Zkd6ywpjz3JTwKxERapzdr92BGFaEKFd4lbIeD2PRau8boqa512JprCMSzPsGowMkI3ejqm/v53LXIBD+CqlqWaEhpfR/11cXpYe1QhoKlHISYgyzX+ns8CplPR4q7kTD2KRj3C6Wzk61WBpzWTwrhfho7XO9P4LrnRyIoN4qgS0rInnOz7X20eovERHecx4Kwk45EULcK4Q4JIQYEEK0CCF+LYSwxSclnEtZj8f8Gckkx2l1/iI57sQwdS/LSyUuOrwV0mi3i5UFmkVQKaQQF+1iyazw762ySo81On5pJEMp0tin4k2CStCVEyHE8mBfcwpjbwT+BNQA96HVUHkT8EerZAoknEtZj4fbJVilR/JHqi+6Z3CYY7pCuipCFiwje+PU5R46+jxXeXV4Ypj3V+anE+0OuzPg6zAOW1rLisg8iBjKeFJsFAtzw18hNRszvjUHhRBVQoh/FkLkm3D9K/GPwAXgPinlM1LKHwH/ANwkhFgWYlleR7iXsh4P4z7Pt/bR1B15kfyHAktZh2nBvbEEKt4HItDM39k3xMnL3UBkWEgB/yEEItdK6ldIC9LCtkREKDFDOfkQcBbNalErhHhZCPF+IUQonO3rgReklIElSV/Q/10bgvGvSLiXsh6PURtVBC5agabeVRGikK4sSMNYmyMxBqEywHKwKgIspABpCTHMn6HV74lEd15rzyBn/SUiImPOzSboyomU8udSyruBTDTXyjngW0CjEOJxIcQ9QgizavrmAk1jHjP+n2PSmJNi2OujUl+oI+UEDbA8L41ot7ZTReKJynBnzctJIj0xxmJpQkNyXDSLZmpm7UjcqAyF1CWgrCC8M/ICMeJODtZ1MOSNrJYV+0cFQEfGIcRszKxz0i+lfAJ4CM3dcgl4C/AEcEkI8WW9K3EwiQZGlcOXUnr1XyfcGYQQOUKIJYE/aOX4g8aJxm56PZookfThjY9xUzrbiOSPrI1qyOsb6a0SYacp4/R4+EInA0Peq7w6vDDM+wtzU0iOi5zeKoYLq3/I64+zihQMJTzKJViRHzkKqZlEmXFRIUQCcBea5eQONKXhb8BngFeB+4GvAzPRytmHgitVAXuICRoQVlRU0NjYSF5eHsXFxZSXl/uf27JlC0ePHqWpSTPOLFiwgMTERCorKwFITExk/fr1VFRU8NzJkf4yeXEetm/fDkBOTg5Lly71/x9g06ZN1NbWUl9fD0BxcTE5OTns2bMHgJiYGDZt2kRlZSXt7dpCWFpaCkBVVRUA6enplJWVUV5ejsejBSWuW7eOpqYmamtrNTmmeU+9vZoZs6ysjN7eXk6ePDnuPeUITV+saujkuW0vEhclHH9Pk5mn+j43fbpCmtB7ie3bmxx/T5Odp9VFufx61zk8Xh+/fvol3nnbBsff02TmaXZ+IZV1eiGuKE1Gp9/TZOfJc/G4/zX7z7fT33DC8fc02XnafkSrabNkVgq7y18Ji3ua7jwdO3aM6SCCXblTCPFHNIUkHjgK/Ab4nZSyaczrPgF8TUoZtFgUIYQH+Hcp5T8HPBYDDAKfk1J+e4L35QDZYx6eAzxVVVXFkiVLpi2blJK6tj4q69q5d8XsiCrQ87fqRj702wMAPPKBdWycm2WxRKHhlztr+fqz2hf01c/cREEYlzAfS2PnAOu/pS1o/3z7Qv7+xqAaIm3LgfNtvOUnuwH44f0ruXv5LIslCh1SStZ/azuXuwa5ozSXn7xzldUihYR+j5dlX9vGkFfy/uuL+dJdi60WyRZUV1cbilaplLJ6qu83w3KyGfgZ8Bsp5cErvK4c+G2Qx25GizsJZIb+76WJ3qQrTmOVp6AKJoSgMDORwszEoF7XCYyO5G+LGOXEcGPlJMeSnxFZpaxzU+PIS4+nvr1fN3lHhnIyuhpw5LhvQe+tVJTBc0cuse9cO1LKiDiEHa7vYMirHfIjbc7NxIyYk+uAz46nmAghkoUQcwCklAeklB8L8ti7gdvGBNzepv9bEeSxFJMkMymWkmxNKYuU1FKtt4oeAF0U3r1VJsKIOzlQ147PFxm9lYw5n50Wz8zUyFJIYaR0QEvPIOdbI6Ol2v5RGXmRFVtmJmYoJyeBiex5NwN7TRjT4Ado7pmnhRB3CyE+AnwX+IuU8qSJ4yqugpGhVHm+neEIiOSva+ujuVvzQ0dKCvFYjMDvjr4happ7LJbGfHw+6W/sGUlB74FEYm8lQyEtykwgOzkySkSEgqC5dYQQXzZ+Bd4vhLhlzEvcwN1o8R+mIKXcKYR4M/A14HGgG6067KfMGlMxOVYXpfPY/gv0erycaOz2Z/CEK5HU7G8iRm9U7cybkWyhNOZztqWH9j4t+DtS53xhbjKJMW56PV4OnG/nvtWhrsMZWrw+6S8RoawmwSWYMSdf1f+VwPvGeV4CdcDHgzjm6weR8ingKTPHUEydsSeqsFdO9BN0QoybRTPDe1OeiLnZSaTERdE1MMz+c228Y12B1SKZyqgK0BFqOYlyuygrTKf8dEtEWE5OXe6mW+8ltLY4MufcLILm1pFSuqSULjTLyfXG/wN+3FLKYimlLfrcKEJLYWYCWXpV3P0RUIzNMPWWFaQTFQG9VcbD5RL++i77IqDGjTHnyXFRzM+JTIUUYLVuQahp7qW1xzRDuS3YP6rZn7KcBBMzVs3fAJdNuK7CwQgh/JHs+861EewUdjvR3uvhTJMWYxGpJ2gD4/4vtPVzuSu8eysZ1rLVhem4Iri3SuBnPtwD4A2FNCMxhpKsyMvENJOgKCeB2TFSygellDXBuK4ivDACQ5u6B6lv77dYGvMIXJBXR7gfOtCdF84Ws6auAX92SqSfoFfkjzS+C3flxLCcrC5Mj8iMPDMJluWkxkgRFkL4hBDeK/wMB2lMhcOIlEh+w4XhdglWRFBvlfFYOjt2D2ZIAAAgAElEQVSVGN2tFc5zHthbJVKDYQ0SY6NYMkvrrRTOc97Q0c/FTs0aGOkWUjMIVkDsDxgpcvZ1rlwqXhGhLJ6VQny0m/4hL/vOtfPmsjyrRTIFw0KweGYKSbGmdIhwDHHRbpbmpXLgfHtY91Yy5jzaLViWF97B3pNhdWEGR+o7Odqg9VaKi3ZbLVLQUfEm5hKUlVNK+f2A378ajGsqwo9ot4uVBWnsqmkN2261A0NejtZrfZTUaUpjdVE6B863c+xiFz2Dw2GpsBmK19LZqWG5EU+V1UXp/PK1Woa8ksMXOlhXkmm1SEHHUEhjo1yUzlIKabAxJY1ACFEihPiS3rPGeOzLQohiM8ZTOAfjhHG6qYf2Xo/F0gSfow2dePQic5Eeb2JgFODzSThYF34xCL2Dw1TrXXgj3aVjsDqg8OD+MI07MVxWK/LTiImKzIw8Mwn6X1QIsRo4hFbPJLBc3luAg0KIZcEeU+Ec1oR5JP++UaZeZTmB0RVywzEo9tCFDrx6eX5l3tfISYmjUG90GY5W0s7+IU5e7gaUQmoWZqh730IrUV8gpbwQ8HgZ8BpaOXlFhLKyIB0jyzIcT1TG5luQkcCMlDiLpbEH6YkxzMtJAgjLuJN9o3qrKIXUwLAc7j8ffr2VKuvaMaohqEOIOZihnKwGvi+lHJUrKqX0Av+F1hhQEaEkxUaxaKYWyR9uJyqfT46kFqoFaxTG3+NgXQdDYdZbybAAzslOJCMxxmJp7INhJe0eGOZUU7fF0gQX43suBJQphdQUzFBOPMBEdq4sTOyto3AGhhn0SL0WyR8unGnuoWtAy5RX8SajMf4efR4vxy91WSxN8Bj2+vy9VZR5fzSBCvq+MHPnGfezYEYyKXHRV3m14lowQzn5K/A1IcSCwAeFEPOBL+vPKyIYY9HyeH0cbei0WJrgEWjeX6MsJ6MY2wQwXDjR2E2vR1OwVbzJaOZkJ5GeoG3c4WQl9Qz7OHyhA1AKqZmYoZx8Bs16Ui2EOCGEeEUIcRyoDnheEcEEWhXCqUiTEW+SlhDNnOwki6WxF/kZ8eTo7eQPhFHciVJIJ0YI4e/UG06B0FUXOxkc1jPy1JybRtCVEyllM7ASLVvnMDAEHAU+CayUUl66wtsVEUBuahz5GfFAeC1a+86p3ioTofVW0psAnmsPm95KRlB3VlIsBRkJFktjPwyFraGjn4sd4dGyYv8ohVRZTszClORsKeWAlPLHUsq/k1JulVK+TUr5n1LKHjPGUziPNf4TVVtYRPI3dg74+wWtUvEm42KcMpu7B6lr67NYmukj5UgA9Joi1VtlPAItC+GSnWe4JWenxTMrLd5iacIXs4qwRQkh3iuEeEQIsU3/971CiPArDam4Jgz/fNfAMGeana+zBqbIKvP++Ix25zl/o6pv7+dylxbfr+JNxqd0dqq/QFk4xJ1IKf3ZWSpt3FzMKMKWilbP5JdoacMpwPX6/yuEECnBHlPhPEZH8jt/0TLcUzFRLpaq3irjsmhmMgkxWmn3cNioVLzJ1YmNcrMiT2t+GQ4u3LMtvbTpla3VnJuLGZaTbwNzgJuklMVSyg1SykLgBiAf+IYJYyocxtzsJFLjjUh+5y9aFWdbAViel0pslOqtMh5RbhdlBdqCHg4KqXEP8dFuf+0exesxDiInGrvoGhiyWJrpsa82sOCespaZiRnKyZuAL0kpXwl8UEpZjpZK/GYTxlQ4DJdL+PtvOH2j6ujz+EtZrysOvwZnwcTYqGqaR06gTmXP2ZGCe9Fu1VtlIoygUa23UofF0kyPPbpykhIXxYLcZIulCW/M+EYlAXUTPFfPxAXaFBGG4aevb+/nUqdzI/n31rb5S1mvK1Ef7ysRmN3g5N5KTV0DnG3pBWBdsZrzK2FYy8DZ7jwpJXt0C+na4gzcKiPPVMxQTg4DD0zw3DuAKhPGVDiQQJ+tk107xmkqyiVUkNxVWJGf5l/UnbxRVQSY99eVKGvZlUhNiGbBDM3K4GQraX17Pxc7BwBYr+bcdMxQTv4VeJsQ4kU9Q+cWIcQ7hRB/Bf4O+LoJYyocyNK8kUh+J5+i99Rqp6mleakkxKiEtCuRGBvFYj0+w8kblXGCjo1ysUwFQF8Vw5136IJzeyvt1ucclPs2FJhRhO154D6gBC1DZxvwv8AS4B1SymeCPabCmcRGuVmuL+x7a525UXUNDHHsotYrRi1Yk8PYqI42dNLvcWZvJcNaVlaQrgKgJ4HhzhsYcm7LCiPGKDk2isWzVAC02ZhVhO0JKWUJsAAtjXixlLJASvkHM8ZTOBcj7uR4Yxedfc6L5N9/rg2fijeZEkaMxpBXUlnnPItZS88gZ5q02jxqzifH2oC4nN01rVd4pX0xLKSri9JVvEkIMDXEXEp5Wkq5S0p5wsxxFM7F8N1KOfLldxLGacol8GcfKa7MuuJMjGKqTtyoAq18ylo2OWalxVOYqZX3rzjrvDlv6Oj3V4BWMUahISgOciHES1N4uZRSbgnGuArns7ownSiXYNgn2X22lVuX5Fot0pQwAiNLZ6eSrFqnT4r0xBgW5qZw/FLXKD++UzDiTWLcLlYWpFksjXPYUJLJ+dY+9p9rxzPs88ebOYE9o+JNlLUsFATr0+ECxCR/nPOJVJhOYmwUy/O1Bd5pp+iewWGqdP+5WrCmxgb99Hn4Qge9g8MWSzM1jHiTFflpxEWreJPJsmGONuf9Q16O1Dur3olhIU2IcVM6WwVAh4KgWE6klDcG4zqKyGRDSSYHzrdzorGbtl4PGYkxVos0KQ6cb8erB5wo8/7UWF+SwS9fq2XYJ9l/vp0b5mdbLdKkaO/1cKJRL7in4k2mRGD67e6aVkf1IzJczqsKVcG9UGHaX1kIkS2EuF0I8YAQIl1/zPQQZyFErBDibUKIvwghvmj2eIrpY5yoYLT51O4YsgoBa5TlZEo4Ne5kT0C8iap1MTVmpMRRkpUIQIWD4ssaOwc416p10VZzHjrMaPwXI4T4OdAA/AUtjbhYCDELqBFClAZ7zIBxfwxcAh4B7iBIliGFuawqTCdGP404KQbB2KgW5ab4+wQpJkdqQjRL9HRMZ825Jmu0W4yqfKqYHOv1g8j+c+0MDjsjjTwwUH+9spaFDLMa/70F+DiwEi3OBCnlRbSaJ//PhDEB4tG6IP8bkGfSGAoTiIt2+wMLnXKK7h0c5vAFzW+uzPvXhhF3UtXQSbdDGsJV6LEHy/LSiI9R8SZTxZjzwWEfhxzSZ8eY87hoF0tnqwDoUGGGcnI/8Hkp5X/z+lL1vwM2mjAmUspOKeUKKeX3pZSXzRhDYR6Ga+d0Uw/N3YMWS3N19ta2MazHm2yck2WxNM7EmHOvTzqifUFrzyDHL2kF966bo8z718KouBOHWMx21bQAsLoww1EZRk7HjL90MhM3/otDuVoU47AhYNFyQh2E185oC5bbJZTl5BpZUzTSPM0JG9WuAKvedUohvSayk2OZm5MEOON7fqGtj/N6vMn189SchxIzlJMK4KNCiECbp15DkweB/ddyUSHETCHEwgl+ppXeIYTIEUIsCfwB5kznmoqpsaIgjdgo58Sd7NSVk+V5qr7JtZIcF+1Py3SCO884QcdFuygrVOb9a8U4iFTWdTAwZO+4E+MQAspCGmrMsGJ8DngFqAaeRFNMHhBCPAzcAGy9xut+C3jPBM8tAqZThfYh4CvjPVFRUUFjYyN5eXkUFxdTXl7uf27Lli0cPXqUpqYmABYsWEBiYiKVlZUAJCYmsn79eioqKujt1dqrl5WV0dvby8mTJwHIyclh6dKlbN++3X/dTZs2UVtbS319PQDFxcXk5OSwZ88eAGJiYti0aROVlZW0t2vm8NJSLc64qkrzpKWnp1NWVkZ5eTkejweAdevW0dTURG1tLYDt7ml1UTqvnWll+9ELbE9psu09dXkkJxo119PCdOG/z0iZp2De00x3N4fR4k46+4eoO3PCtve084wWIzE3BXa+8nJEzVMw7ympT1NIPMM+fvHkdhZmuG17T39+rRqApGjB4lkpETVP072nY8eOMR2ElPLqr5rqRYUoAx4GbmTEOnMY+KyU8oWgDzi+DBL4mpTyq5N4bQ4wttDCHOCpqqoqlixZYoKEirH810un+e7fTgFQ8bkt5KbGWSzR+Dx9+CIf//1BAB770HpVznoavHyyiff+ah8A//OuVbatEFzX2sfm7+wA4HN3LOTDNyjD6rXS2jPIqn97EYCP3TSXT9+2wGKJxsfnk6z5xou09np4w9JcfvzAKqtFchTV1dWGolUqpaye6vvNavxXKaXcCiQA+UCalHJlqBSTqSKlbJJSVgf+ADVWyxVpXDd3xGy6M8Ccajd26bLFR7tZqdJJp8Xa4gx/Gnn5afvO+Ws1Aeb9ucq8Px0yk2JZPFNLIy+38ff8RGM3rb2apULNeegxo87JfwkhrgOQUnqklA1Syq5gj6MIP5bNTiUlTvM0vnqq2WJpJsZQnNYWq+j96ZIQE8XqIk3BKz9t/zlPT4j2b6yKa2fTfG2zP1LfQbuuANiNwHiT65VyEnLMSiUuF0LUCiG+KYRYasIYijAkyu3yn1B2nmnB5wu+y3G61LX2+buTbpyr3DnBYNM8zaN6rrWPOj0zwk74fNJvLbtuThYuPcNIce3coM+5lKOtUnbCUEjz0uMpyEiwWJrIwwzlJAe4Fa067LuBQ0KIKiHE54UQxSaMpwgjNus9Vtp6PVRftJ/BLdDdpEy9wWHz/JG/46s2tJ4cb+yivU8rEqfmPDisKkonXm+aaEcr6eCwl716Bejr52YhhFJIQ03QlRMppVdKuV1K+VEpZR5a0bXn0NKIzwghXgv2mBPIISYTDKuwF5sDGsDZcaPaeUaTKSMxhkW5yrwfDBblppCVpFUDsONGtfO0Mu8Hm9got78UfPnpFsxIzJgOB+s66NfTnK9Tc24JpjrMhRBRQBqQBaQDPsB+x2GFbZidFs+cbK052Cs226iGvD5/0ObGucq8HyxcLuF37eyqaWXI67NYotEYn8P8jHgKMpV5P1gYc36pc4AzTT0WSzOawLVHVQO2BjMCYqOFEHcJIX4NNKG5d0qBrwOzpZR3BHtMRXhhLFqV59vpGRy2WJoRKs+30z2gyXPTgrGZ54rpsEmvvtkzOMyhC/bpudI9MMS+c5p5/+YFORZLE16MtpLaK+5kxwmtNsjyvFSykmItliYyMcNy0gw8BawHfgDMk1Kuk1L+UErZZMJ4ijDjBn3RGvZJW1UOfVk/TQkxemFVTB9DIQV7uXZeO9PKkFdzOdyolJOgMic7kVl6LSM7zXlj5wAnGrsBNedWYoZy8ktgrZRyoZTy61JKVS9EMSXWlYzUvrDTomWcppblpanTVJDJTh6pfWGnU/Qrp7Q5j41yjWpap5g+Qgi/kr+nttU2pexfPjlyhr5poVJOrMKMgNhPSikPBPu6isghsPbFK6eabREsd6mzf+Q0pawmphBY+6K1x/rO1FJKdpzQlOMNczKJj3Ff5R2KqWJYzAaGfP7sGKvZoSsnmYkxLNN7PylCj6ogpbAlN+oxHXVtfdQ0Wx8s98rJEQuOOk2ZgxHTISXsOGm9xexEYzeNXQMA3KTM+6Zw/bwsovTA8u3HL1ssjdbvx8jOumF+tgp6txClnChsydZFM/y/v3DM+lAl4zSVoU5TprGqMJ3UeK3D84vHrN+oXg5USJVyYgqp8dGs01OKXzzeZLmVdP+5Nno9mnvpBhX0bilKOVHYkpLsJEr0lOIXLT5ReYZ9vHZGC8xVpynziHK7uFm3Sr16utnyGARDIS3JTlQpxCayZaF2EGno6Of4pW5LZTHm3CVg8zylnFiJUk4UtuUW3XpSWddOi4UxCLtqWvwpzTeq05SpGBazPo+XirPWZWq19XrYr6cQ3zhfWU3MJNBKauVBRErJi8c15WRlQTrpiTGWyaJQyonCxmxdrC1aUsJLJ6xz7fxNdzFEu4WKNzGZzfOziHZrlikrN6oXj1/GaO1065IZV36xYloUZCawYEYyYG3cyemmHmpbegG4ZbGac6tRyonCtpQVpJOeYG0Mgs8neUEf+7o5WaTERVsiR6SQHBftT9ndbmEMwt+qGwEtxmhNUYYlMkQSWxZpSv/h+k4u60HIoWZbVaP/99uW5Foig2IEpZwobIvbJbhZ90eXn26xJAbh4IV2mrs1l5JasEKDYea/1DlgSfPH3sFhf62VrYtycKsYI9PZGmCp2H7cGivptmOacrJgRjLFWYmWyKAYQSknCltzy2LtRNU/5PX3tQkl26o1q4kQytQbKoxTNMC26sYrvNIcXj7ZjGdY6++jFNLQsCKgsOHzFsx5fXsfVQ2aInybcuPZAqWcKGzN5vnZ/tbqzx25GNKxpZT+zXFVQTrZyaoqbCjIS09gWZ6Wrv3ckUshd+0Yc54Y42aj6kgbElwu4VcKXjvTQnuvJ6TjG4cQgFuVQmoLlHKisDUJMVHcrJ+kXzh2OaSunRON3Zxv7QPUCTrU3LVsJgBnW3o5dil0rp3BYa+/TcGNC3OIi1ZVYUPFXctmAeD1yZBbTwyFdHZaPEtmpYR0bMX4KOVEYXveqG9UvZ6RjSMUPH14xFJze6lSTkLJnfpGBfDskUshG/flk81062njtyuFNKSsLc7wWyefDaGV9FJnv7/z9O2luQihYozsgFJOFLbnxgU5JMVGAaHbqHw+ydOHtAVyVWE6+RmqCFcomZ0WT1lBGqBtVKFy7Tx1qAHQXDqB9TcU5uN2Ce5cqh1Edte0hqy20TOHL2J8vO5ZMevKL1aEDKWcKGxPXLTbH4y6/cRlevWTrZkcqGunoaMfUAuWVRjWkwtt/Ryp7zR9vO6BIX8RrtuW5KpGfxZwp24l9Un4a1VoXDtP6YeQkqxElqrWFLZBKScKR2DEIAwM+UJSnMs4QbtdgjfopzlFaLlz6UwMC3ugi80stlVf9mfp3K0UUktYVZBObkocAM8cMn/OzzR1+9PV714xS7l0bIRSThSOYNO8bNL0gmyP7683dawhr4/ndPfR9XOz/CmOitCSmxrHumKtANqTBxv8ioNZGAppZmIM16ssHUtwuYTfUrn3XJu/YqtZPBWgAN2zYrapYymmhlJOFI4gJsrFvfri8VpNCxfa+kwba/vxJtr7hgDl0rGat63OB6C112NqC4OLHf28dkaro3PXsplEudXSaBX3rc7z//7HAxdMG8frk/y5UlNIl+elqsJrNkN9AxWOwdiopIQ/HjDPevL7vXUAJMdFcUepculYyR2lM0nWg6Ef32/eRvWH/Rf8vXTu0z9nCmuYm5PsD4b+44F6hr3mWMzKTzf748reuirvKq9WhBqlnCgcw+JZKf6AtT8eqMfrC34GR317H6+ebgbg3hWzVVCkxcTHuHmjbr3acbLJlL4rXp/ksX2a4rN0diqlKijScoyDyOWuQdMqQxuHkPhoN/esVC4du6GUE4WjeNsabdFq6OinXFcigskf9l3wpxXev7Yg6NdXTB1jo/JJc6wnr5xq4lKnpvSoObcHdy6b6a8MbSgRwaSpa8CfmfXG5TNVQ08bopQThaO4e/ks/6L1613ngnptz7CPx/TNb3leKotVpUhbsDwvlYW5yQD8tuJ80ANjH6nQNr+EGLfK0rEJyXHRvHG55lJ94fhl6lqDG2P22L4LfsurUkjtiVJOFI4iNT7a7x9++WQzZ5q6g3btZw5f5HKXVvjpgfWFQbuuYnoIIXjf9cWAZub/y9HgFeI709TDdj3Q9t6Vs/3F/hTWY8y5lME9iAwMefnN7vMALJqZwor8tKBdWxE8lHKicBwPbizy//6LneeCck0pJT8rPwtAdnKsytKxGXcvn0VWUgwAv9hZG7SKsb/Yedb/+/v1zVBhDxbmprBxbiagBSx3DwwF5bpPHWrwV5/94KZiVdvEpijlROE4SrKT2Ko3A/xzZT3N3dMvc73zTAsnGjUrzHuvKyI2SgXC2om4aDfv1K1ZRxs62X22ddrXbO4e5E96KunWRTOYk5007Wsqgsv7NmoKY8/gMI/umX7sic8n+Z9XNYU0NyWONy5XhxC7ElbKiRBiiRDiaSFEhxCiSwixSwhxm9VyKYLPBzaVADA47OMnL9dM61pSSn7w4mlAi9x/YJ3yQduRd64vJC5aW7J+8MLpaVtPfvpKjT9+5UObS6YtnyL43LQgh7k5mtL401fPTrt1xV+rGqlp1gq7ve/6IqJVPRvbEjYzI4QoAV4DZgIfAd4BdAN/EUJsslI2RfBZX5LJhhLN5Pu7Pee51Nl/zdfacbKJA+fbAXjPdUWkJcQERUZFcMlKiuU91xUBWvXQ6aSYXuzo538rtLiDtcUZrClKD4aIiiDjcgk+sXUeAG29nmnFngx7fXzvhZMApCdEq0BYmxM2ygnwCbT7uU1K+X9SymeBe4E24H2WSqYwhU/ftgDQsmz+Q7d8TBWvT/KdbacArejaR25QJ2g78+HNc0jUa898Z9tJfNdY6+aH20/7rSb/fPsCFXdgY95QOtOfrfU/r56lvddzTdf5U2U9Z3WryUdvmkuySh+2NeGknNQD/yGlbDMekFL2A7VAhmVSKUxjVWE6Ny/UYk8e23+Bg3XtU77GI3vOc/yS1vjrQ5tKlNXE5mQkxvB+3aV3tKGT3++behzCoQsd/pTxLQtzWFWolgc743IJPnWrdhDp7B/i4W0npnyNjj4PDz+vWU1mpcb545cU9iVslBMp5cNSyi8FPiaEyAJKgZeskUphNl+8cxExbhdSwheeqJpSqevLXQN8R1+w8jPi/XEsCnvzkRtKmJ32/9u79yApqzOP499nBkZgsABl8IahgFLuXlCBuBLBSyEqqJuoqEHW7JrytlpRtLxsWJWslDGJGjWWVoKKukbUZNE1isp6ARQQEeQiIAiCyh0dZJDrPPvHeQeatpu50D39dvfvU9X1Mm+/pznnmTPdT5/3vOdtDsC9ry2s14Tonbuquf1vc3GHstISbju7W7aqKRl0Rrd2/OToCgCem7GSj77YWEuJvd37+kI2RCMut57djWZNNeE97vImOTGzw8ysa5pHuq+7jwJrgD/X8trtosm0ux9A50y3QTKvU0VLrh4QflULVm3iD28urlO5XdXOjeNn8100we7uoT21VH2eaFHWhLuG9gBg09adjHxhTp1P7zzw1mcsiEbKrhrQefdkS4k3M+PuoT0oaxI+sn71/Bw21fHS4kmfruG5GWGk7CdHVzDkGN0vKx/k04pDY4ARaZ7rBuw11mdmdwNDgNPcvbb7bl8D/GeqJ6ZNm8bq1atp3749HTt2ZPLkybufO/3005k7dy5r14ZFnLp06UJ5eTmzZs0CoLy8nH79+jFt2jSqqkIVevfuTVVVFYsWhW/s7dq1o1evXkyaNGn36/bv359ly5bx5Zfh5nYdO3akXbt2TJ8+HYCysjL69+/PrFmz+OabcCqjZ8+eAMybNw+ANm3a0Lt3byZPnsz27eEbQ9++fVm7di3Lli0DKJg2De5Qwostja82O396ZynHHH4gTdft6Q6p2vTUrA1MXRIuR+1/ZBkDu7aLVZsK8feUyTZZVRV9Dilhxppq3l28jhv/8gZDOjXZZ5te/fgLHpkdPtCOqiinu69g0qSVsWlTIf6eMt2mm848mjGvLWTFxi1c8ae3ePjS4ykxS9umdVuqueejMJrarBTOrqhk8eLFsWpTIf6e+vfvz4IFC9gflqnFjOLEzK4GHgYuc/e/1uH4dkBF0u7OwIR58+bRo0ePLNRSMmnpus0MfWgKVdt3cUCTEp644iRO7tw25bFPTF3GXa+EP5xOFeW8ct0plGtl0Lzz3dYdDHloCsujpc1Hn9+T4WnmEkz/fAMjnpjB1h3VtCgr5eXrTtGoSR6qrnZ+8dSHvLMo3Ffrsr4/YvR5PSkp+eGE5lWV33PRYx+wcmO4ku+RS3tzjkZNGs38+fNrEq2e7j6/vuXz5rROXZnZT4GHgGvrkpgAuPtad5+f+AD2b/EMaVSdK1rywLDjKS0xtu2sZsTYGYydsmyvOSibt+1k1IR5uxOTg8rLeHz4iUpM8tSBzZry2PATadU8XHXx6/+Zx92vLNhrLYxd1c7THyxn+F9CYlJaYtx/8XFKTPJUSYlx/0XHcVT0+3t2+gp++fRHP5h39P6S9Zz38NTdick1AzorMckzBTVyYmYDgNeBu9x9zH6+Vg9gnkZO8suE2V9x0/g57IzmIBzRujn9Oh3Mtp27mPzZeiq/D8P6B5eX8eQVfejVvlUuqysZMGflt1w+dsbu3+1B5WWcenQFzZqWMHXJBlZsDCMrTUqM+y48hguOb5/L6koGrNm0lUsen8bn68PpiBZlpQzs2o6Klgcw96vK3esWQbjdxahzu+ty8Ua2vyMnBZOcmNmxwHvAh8CdKQ6Z6+6V9Xg9JSd5aubyjdzw19l89W3qhdlO6NCGB4cdR/s2LRq5ZpItKzZs4brnZvHJl6n/xA9v1Yw/XHwc/aKF+yT/VX6/g1tenMPE+WtSPt+8aSl3nNNNlw3niJKTiJndSZpJrZGB7v5OPV5PyUke27pjF+NnruQfc1exbH0VpWZ0P7wVP+19BIN6HJryHLXkt+pq53/nruLvs75k/teb2FntdGpbztm9DuOSPj/S1VgFaspn63nuwxXMXL6RzVt3ckSb5pzW9RBGnNyBw1o1z3X1ipaSkyxRciIiItIwmhArIiIiBUXJiYiIiMSKkhMRERGJFSUnIiIiEitKTkRERCRWtDRmemUAS5YsyXU9RERE8krCZ2e6G/Puky4lTsPMhgITcl0PERGRPHaeu79c30JKTtIws1bAqcBKYHuGXrYzIeE5D927J5Hikp5ik5rikp5ik5rikl42YlMGHAm8W5/V2WvotE4aUTDrne3tS8K9HZY2ZFGaQqW4pKfYpKa4pKfYpKa4pJfF2Hzc0IKaECsiImZ5CzAAAAp+SURBVCKxouREREREYkXJiYiIiMSKkpPGtQ64K9rKHopLeopNaopLeopNaopLerGLja7WERERkVjRyImIiIjEipITERERiRUlJyIiIhIrSk5EREQkVpScZIiZnW9ms81sq5mtN7MnzeygOpS70sw+NbNtZva1mT1gZs0ao86NZT9is8DMPMXjrMaod2Mxs6PN7B4zW1mHY83M7jCzZWa23cyWm9koMyu4v+X6xCU6vipNf+ma7bo2FjMrMbObzWxx9J6x3MweNLPW+yhT8H2mIXGJyhVDn2liZjdGnzNbzGypmY0xs/J9lMl9n3F3PfbzAfwTsAt4CRgCXAtUAv9XS7lhgAOPA2cDtxHu4zM2123KdWyispXAH4FTkh6tc92uDMXmTOD9qA/sCH+OtZa5FagGxgCDgXujn0fluj05jkub6PjbU/SX5rluUwZj80dgGzAaGAT8CvgOmFjkfaYhcSmWPvNnYAtwS/S39e/At8C4OPeZnAeuEB7AeGA5UJKw7/Ko4x+zj3IzgPeS9o2K3pAPznW7chybltExF+e6DVmMzWjgKeB0whoDXsvxBqxOflMBxhLWJyjJRj3jHpeoTK+ov/TNdf2zGJcKQqL/m6T9I6O2dyjGPtOQuBRRnzkQ2AmMTtp/J+GLcFlc+0zBDOvlWD/gTXevTtj3ZrTtk6qAmZUBxwMTk556k3BDxuMzXckcqXdsIu2jbZ2G9PORu//a3Ue4+yTCm2RtOgKHkLrPtAU6ZbiKOdGAuAAcEW0Ltr8ArYDnCKOQiRZE21SnSouhzzQkLlAcfaaK8F56T9L+zYTPmeYpysSizyg5yYxDgbVJ+2p+bpemTFtC56hvuXzTkNjAnjeOMWa2KTqP/KaZdcl4DfPHodG20PtMQ9T0l2eieQRbzOwlMzssp7XKIHdf4u4/d/fkO70OBNYAqe4mW/B9poFxgeLoM9XuvtrdvzezUjMrN7MzCaNKY929MkWxWPQZJSeZ0ZRwKmY3d98V/bMsTZma/TuS9tdWLt80JDawZ2hxKmGuypVAd+D1QpswXA/F0mcaYgewCnidcI78ZsJpob/lslLZZmYnANcDd7v79hSHFGWfqUNcoPj6zBzCiMkbwMfA1WmOi0WfadIY/0mRa+j9AYrhvgJp2+jubwF7fYMxsyWEZOUS4InsVi0vFUOfScndxwHjEna9Z2bfAM+a2UB3fztHVcsaMzsSmED4cH20gS9TcH2mrnEpwj5zMWES8MmEuY2/JyRw9dUofUYjJ5mxg6Rzd9GcEggzyFOpyeaTz/nVVi7fNCQ2Kbn7+4QreHpmpmp5p1j6TKa8Fm0Lrr9El+JPBL4GLvVoxmIKRdVn6hGXdAq2z7j7fHef4u6/BX4DXGtmh6c4NBZ9RslJZqxjz3m6GodE21VpymwgXJpV33L5piGxwcwGm9mpKZ4qoQC/7dVRzR1DC73P1JuZXRgN5SeqeX8rqP5iZi2AVwntGuzuVfs4vGj6TD3jUhR9xswONbOrotGkRJ8Q2tohRbFY9BklJ5nxATDIzJom7BsUbaelKuDu2wjn/c5NemoQIXNNntyVr+odm8j5wBOJ5cysL+HSuHkZr2V+WEp44xiStH8Q4ZviikavUXz8G/BA0r4zom3B9BczawK8QPjgONPdN9RSpCj6TAPiAsXRZw4gnNq6LGn/sdH2ixRl4tFncn0ddiE8CIv27CIMCQ4FriIscvNqwjElhAmdTRP2XULI0J8BziFMyNoGPJLrNsUgNt0JCwe9EsXmcsIf0lLggFy3KwtxupOk9TwIk4m7s/caMbdFfeYBwiS+ewgjcDfnug05jsvpUT8bC5wV9bMNwJRctyHD8XiS8OVlBD9cOKxXsfaZBsalWPrM84RLim8lLMI2krBA3bjo+Vj2mZwHrlAewHnA7Ci5WE9Yla9VwvP9og/lf04qdyWwMPrD+hr4HSkWxsnnx37Eph8wKXquEvg70CnX7clSjFJ9CP8sanufhH1GWNFyedRnlkdvJJbrNuQyLtH+wYTRuM1RPxsHVOS6DRmOh+/j8U6x9pmGxKWI+kxZ9PteRPjCt5CQqDSNno9ln7GoIiIiIiKxoDknIiIiEitKTkRERCRWlJyIiIhIrCg5ERERkVhRciIiIiKxouREREREYkXJiYiIiMSKkhMRERGJFSUnIlI0zKylmSXf0CzdsUdluz4ikpqSExEpCmZ2MDCdcH+R2o5tCUw1s6FZr5iI/ICSExHJKjP7sZltiO4qnas6GOGutTMJN9rcJ3ffDAwHnjWzblmunogk0b11RCRjzGwA8DYw0N3fifaVAl2Bhe6+K0f1uhy4n3DjyMp6lBsPtHH3WkdbRCRzNHIiIlnl7rvcfX6uEpPI7cCD9UlMIvcBZ5hZnyzUSUTSUHIiIhlhZssJoyYAb0c/Y2YDzMyjURXM7F+iny80s4/MbJuZrTCzq83sCDN73sy+NbONZvZi8gRWMzvJzCaZWZWZrTaz+83sgH3U6ySgC/By0v7DzGxc9BqVZvaumfVPPMbdPwS+AH6+X8ERkXpRciIimfIz4Pro39dHP+/LXYSRiQuAxcAjhAmrK4GLgFHAYODBmgJm1ht4D9gJDANGA1cAj+7j//kJUOnus5P2vwz8GLgBuBRwYKKZdUk6bgpwai1tEZEMapLrCohIYXD3mdFVLgBz3X1mLUWGu/tHAGY2jzBC8aG7j4yef8PMjgXOTyjzW+BLYIi7b4/KVgMPmdlt7r4mxf9zDLAqcYeZtQVOBG5w9+ejfR8A4wmjLIsSDv8UGGZmpTk+NSVSNJSciEiubKj5h7uvCBfUMCfpmK+AtgDRqZuBwO+BajOref96HygFTgD+keL/aQusT9q3EZgL3GRm24CJ7r4cOCNF+W+i12+dWGcRyR6d1hGRfFFBeM+6GdiR8Kg5XXNwmnJNCadsdnP3akKi8wJhsuwyM1tkZr9MUX5btE07r0VEMksjJyKSL76LtvcD/53i+WVpylUSjb4kcvcNwEhgpJl1Bq4BHjOzre4+LuHQmrLfNqjWIlJvGjkRkUyqjralmX7h6DLgOcCx7j4z8QGsipKNVD4HOiTuMLPTzGyhmR0XvfZSd7+JkICclFS+Aljr7lsy2iARSUvJiYhk0opo+69mdk4WXv8W4FQze9nMLjCzwWb2DPCJmbVOU2Y6cJCZHZmwbwbQAnjazIaZ2Zlm9ghhXskbSeX7RseLSCNRciIiGRNNKr0POJdwZU2mX/8NwqTV1sCzwPOEuSanuXu60y4Tgc3AWQmvs5lwefCnhEuYJwAnE64geqXmuOjqo77AS5lui4ikp+XrRaTgRaMiJ7l7vVZ6NbMrgf8iLHu/OSuVE5Ef0MiJiBSDO4GjzOziuhaIRk3+A7hDiYlI49LIiYgUhWgOzFPAAHefV8uxTYEXgS3ufklj1E9E9tDIiYgUBXd/FfgFcGhtxwJGWCV2RFYrJSIpaeREREREYkUjJyIiIhIrSk5EREQkVpSciIiISKwoOREREZFYUXIiIiIisaLkRERERGJFyYmIiIjEipITERERiRUlJyIiIhIrSk5EREQkVpSciIiISKz8P47DPB4bY2gfAAAAAElFTkSuQmCC\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)\");" ] } ], "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 }