{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Practical 3 Solutions: Advanced Plotting\n", "\n", "This notebook contains the solutions for the advanced plotting exercises." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup\n", "\n", "First, we import the necessary libraries and enable the interactive widget backend for 3D plots." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Enable the interactive widget backend for Jupyter Lab\n", "%matplotlib widget" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 1: Plotting Algorithm Convergence\n", "\n", "We need to modify the bisection algorithm from Practical 2 to track and return the error at each iteration. Then, we'll plot this error on a semilog y-axis." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "79aa0b2a6f234366b3b1affe5640aaa6", "version_major": 2, "version_minor": 0 }, "image/png": 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Ao0ePEBsbi4CAAHz11VeV/pydnR0+/vhjTJo0CU5OTgCe3ks0duxYfPzxx/J233zzDRo0aICxY8fC3NwcNjY2ePjwIfT09BRuWl+3bh1MTU0xduxYWFtbw9raGnFxcXjnnXfkbWbNmoXff/8dzs7OcHR0hLm5udJeeM/avHkzpkyZgm7dusHFxQWZmZlISkrCF198gSlTprzQeKnKx8dHpXaqjs/zvveKqDomW7ZswahRo+Dh4YG2bdsiPT0d06dPh6enJ44ePVplP2ZmZrhw4QIWLlyIESNGwMTEBA4ODkhLS0NkZCR8fX0REBDw3HE9L3NzcwwfPhzbt2+HkZERRo8erdRG1c+gItbW1jhw4ADGjBkDGxsbNG/eHFlZWdi8eTMOHz6s8HCJsbExzpw5g+nTp8PFxQXOzs4wMTFBbGws3Nzc8Pnnnz/3e6xXrx5OnTqFyZMno02bNmjVqhUEQUBeXh7Wrl1bbf0SaTqJ8N85eCLC9evXkZiYKH8tkUjQoEEDODg4lHvfX1hYGIqLi9GpUyeF41lZWYiKioJMJpMnJuUpLCzEjRs3kJOTg2bNmsHGxqbce+Nyc3MREREBqVSK1q1bK81C5uXl4fr168jKyoKurq78AYuK4gOePowQHR0NPT09tG3bVuF+MgC4dOkSdHV1le4Bu337NuLj4xWWQctz/fp1pKSk4NVXX6203enTp9GgQQOFJcgyqoxPRe/9ReKvakyevUZiYiJatWoFKysr3Lx5EykpKSonuMDTWshRUVHyWsDNmjVTeLL1eeJ6kff66NEj3Lx5U2F5uzxVfQYV9V2muLgY4eHhKC0thbu7O4qKilCvXj0sWLAAS5YsUWqflpaGqKgo6OjowNnZWb55OPB09jsoKAitWrWSz6iXuXDhAkxMTNC2bVulaz5+/BixsbGwsrJC8+bNy70nsLJ+ieoSJoBERFTjjh07hn79+uH333+Hn5+fusMh0jpMAImIqFoFBgbC09NTXjru/v37GDRoEHJychAZGclSa0RqwHsAiYioWhkbG8PHxwdGRkbQ1dVFZGQkXFxccPjwYSZ/RGrCGUAiIqp2JSUliIuLw6NHj9C0aVP5w1FEpB5MAImIiIi0DPcBJCIiItIyTACJiIiItAwfAnkJpaWlePToEUxMTCqsZ0pERESaRRAEZGVloUmTJiqV9ayLmAC+hEePHsHW1lbdYRAREdELiI+PV9pMXFswAXwJZRUh4uPjYWpqqnS+qKgIx48fR58+faCrq1vT4dUqHCvVcaxUx7FSHcdKdRwr1WnqWGVmZsLW1rbcyk7aggngSyhb9jU1Na0wATQyMoKpqalGffE1EcdKdRwr1XGsVMexUh3HSnWaPlbafPuWdi58ExEREWkxJoBEREREWoYJIBEREZGWYQJIREREpGWYABIRERFpGSaARERERFqGCSARERGRltH6BDA2NhaDBw9G+/bt8dlnn0EQBHWHRERERFSttD4BHDFiBLp3744ff/wRv//+O3bu3KnukFBSKiA4NgX7wx8iODYFJaVMSomIiEg8daISyN27d2FoaAhra+tyzxcVFSEhIQENGjSAgYGBws+lpqbiww8/BADMmzcPu3btwpgxY2ok7vIcjXiMxQdv4nFGvvxYYzMDLBzsgn6ujdUWFxEREdUdtXYGMD8/H+vXr4erqytatGiBDz74oNx23377LaysrODu7g4LCwt8+umn8nMJCQmwtbWVv7azs8Pjx4+rPfaKHI14jKlbQxWSPwBIyMjH1K2hOBqhvtiIiIio7qi1CeC9e/dw8+ZN7NixAz179iy3zalTpzBz5kxs3rwZKSkp+PPPP7Fq1Sr8/PPPAABzc3Okp6fL26elpaF+/fo1Eb6SklIBiw/eRHmLvWXHFh+8yeVgIiIiemm1dgm4ZcuWWL9+faVtNm7cCB8fH/j5+QEAvL29MWLECGzYsAETJkyAk5MT0tLScOnSJXTq1Am//PILfHx8KrxeQUEBCgoK5K8zMzMBPF1iLioqUmpfdqy8c/8VEpeqNPP3LAHA44x8BMc8gZeDRZXXq22eZ6y0HcdKdRwr1XGsVMexUp2mjpWmxaMOtTYBVMXly5eV7ufr1q0bdu3ahZKSEujq6mLDhg3o27cvBEFAhw4dMHXq1Aqvt2zZMixevFjp+PHjx2FkZFThz504caLKWK8mSwDIqmx3PCgEKZF1dxZQlbGipzhWquNYqY5jpTqOleo0baxyc3PVHYLa1ekEMDk5GZaWlgrHrKysUFRUhIyMDFhYWMDPzw8pKSnIzMyEubl5pdebP38+Zs+eLX+dmZkJW1tb9OnTB6ampkrti4qKcOLECfj6+kJXV7fSa1vGpWLz7StVvqc+Pl51dgZQ1bHSdhwr1XGsVMexUh3HSnWaOlZlK3jarE4ngFKpVGmat7CwEAAgk8kU2lWV/AGAvr4+9PX1lY7r6upW+sWu6jwAeDs3RGMzAyRk5Jd7HyAAWNbTg7dzQ8ikkipjra1UGSt6imOlOo6V6jhWquNYqU7TxkqTYlGXWvsQiCpsbW2RkJCgcCwhIQEmJiblztipk0wqwcLBLgCAitK7tJxCfH/2Dkr5IAgRERG9hDqdAL766qs4fvy4wrEjR46ge/fukEg0bxatn2tjbPD3QCMzA4XjjUwN0LFZfZQKwIqjUZj462WkZBdUcBUiIiKiytXqJeDY2FgIgoDc3FxkZ2cjJiYGOjo6sLe3BwB88MEH2LJlC6ZNm4YJEybg8OHD+Ouvv3D27Fn1Bl6Jfq6N4evSCJfiUvEkKx8NTQzg6WABqQTYdTkeCw/cwJlbSRiwJghrRreHl6Nl1RclIiIiekatTgAHDhyI4uJiAMCjR4/Qr18/NG7cGEFBQQAABwcH/PXXX1i8eDHGjx8POzs7HDt2DJ07d1Zn2FWSSSXwdlJO7EZ72sHdzhzTt4UiNikHYzZdxPu9W2BaD+c6fV8gERERiatWJ4BRUVFVtnF3d0dgYGANRFMzWjUyxYF3u2HB/gjsC32Ir05EIyQuFV+PckcDE32UlApKs4dMDomIiOhZtToB1FbG+jpY9bo7ujhZYcHvETgXk4wBa4Lwhqcddl2JZx1hIiIiqlSdfgikrnutgw0OvNsVLazrISmrAKv/vM06wkRERFQlJoC1XHNrE+yb2hWGuuVXEWEdYSIiIvovJoB1wPWHGcgrKqnwfFkd4UtxqTUXFBEREWksJoB1wJOs/KobPUc7IiIiqtuYANYBDU0Mqm70HO2IiIiobmMCWAd4OligsZlBhSXkAEAiAXILimssJiIiItJcTADrAFXqCAsCMGnzFSw7EomiktKaC46IiIg0DhPAOqKiOsKNzQywdow7ArrYAwC+O3sHr38XjAdpuWqIkoiIiDQBN4KuQyqqIyyTSjDYrSk6O1pgzm/XEHY/HQPXnMPK19qhT5tG6g6biIiIahgTwDqmojrCwNMEsU0TM7y7Iwx/x6fjrS1XMaGrPeb3bw09HSnLyBEREWkJJoBaxtbCCHve9sYXR6Pww7k4/Hz+Lq7eS8PIDrb49kwMy8gRERFpAd4DqIX0dKT4dJALfhjXEWaGurj2IAML9kewjBwREZGWYAKoxXq7WOPgjG7QlZW/zMsyckRERHUTE0At9zAtD0UlFSd3LCNHRERU9zAB1HIsI0dERKR9mABqOZaRIyIi0j5MALWcKmXkdKQSWBjr1VhMREREVL2YAGo5VcrIFZcKGPbteewLfVBzgREREVG1YQJIlZaRWzG8Lbo4WSK3sASzd/+NOXv+Rm5hsZoiJSIiIjFwI2gCUHkZudc62mLdqRh882c09lx9gPD4dKx/wwMtrE3UHTYRERG9ACaAJFdRGTmZVIJZvZvD08ECs3aG4faTbAxZdw5LhrhiZEcbSCQSlpEjIiKqRZgAksq8nSxxZJYP3t8VjqDbyZi79xqC76Sge4sGWHE0imXkiIiIagneA0jPxaqePn6d4Ik5fVtCJpUgMOwh3tsVzjJyREREtQgTQHpuUqkE03s4Y9tkL1S0yssyckRERJqLCSC9MEEAKsvtWEaOiIhIMzEBpBfGMnJERES1ExNAemEsI0dERFQ7MQGkF6ZKGTkDHSlaNuJ+gURERJqECSC9MFXKyOUXl2LIunMIj0+vsbiIiIiockwA6aVUVkbuo36tYGthiAdpeRi58QJ+CLoDQeATwUREROrGjaDppVVWRm6Mlx0+2nsNf0QkYOnhSFy8k4IvR7rB3EhP3WETERFpLc4AkijKysj5uTeFt5OlvAycmaEuvn3DA//n1wZ6MilORj7BgG+CcPXev1vDlJQKCIlLxdVkCULiUrlvIBERUTXjDCBVO4lEgje97dHerj7e3R6Kuym5eP27i5jTtyXs6hvh/w7f/KeSiAybb19hGTkiIqJqxhlAqjGuTc1wcEY3DHZrgpJSAcv/iMK07aEsI0dERFTDmABSjTIx0MWa0e74bJhrhW1YRo6IiKh6MQGkGieRSOBoVa/SNiwjR0REVH2YAJJasIwcERGR+jABJLVgGTkiIiL1YQJIaqFKGbl6+jro0Kx+jcVERESkLZgAklqoUkYuu6AY434KwZNMLgMTERGJiQkgqU1lZeQmdG0GIz0ZLt5JRf9vgnA2OklNURIREdU93Aia1KqsjFxwzBMcDwpBHx8veDs3hEwqgX9ne0zfFoqohCyM//kSpr3qhPd7t4COjP9uISIiehn8TUpqJ5NK4OVggQ5WArz+qSEMAE4N6uH36V0x1ssOggCsPx2LMZsu4nFGnvxnS0oFBMemYH/4QwTHpnDfQCIiIhVwBpA0moGuDJ8PawtvR0vM33cdl++mYcA3QVj1ujsKikuw+OBNhUoiLCNHRERUNc4AUq0w2K0JDs3oBtempkjLLcKEXy7jna0sI0dERPQimABSrWFvZYy9U7tgnHezCtuwjBwREVHVmABSraKvI0P/KpZ3WUaOiIiockwAqdZhGTkiIqKXwwSQah2WkSMiIno5TACp1lGljFx9I114OljUWExERES1CRNAqnVUKSOXlluExQdvIL+opOYCIyIiqiWYAFKtVFkZOV8XawDA5uB7GLHhAu4m56gjRCIiIo3FjaCp1iorI3cpLhVPsvLR0MQAnv9UEjl96wk+2P03bjzKxKC157BseFsMdmui7pCJiIg0AmcAqVaTSSXwdrKEn3tTeDtZysvI9WjZEEdm+sDT3gLZBcWYsSMMHwde55IwERERmABSHdbIzADbp3hhRk9nSCTA9pD7GLr+PGKTsgGwjjAREWkvLgFTnaYjk+KDPi3h6WCB93eFIyohC4PXnsOoTjY4GpHIOsJERKSVOANIWsGneQMcmekDb0dL5BaW4Ofz91hHmIiItBYTQNIaDU0N8OtET9TTL3/im3WEiYhIWzABJK1y9V4asguKKzzPOsJERKQNtP4ewJKSEhw8eBCPHz9Gz5490bJlS3WHRNWIdYSJiIg4A4gePXrg119/RWhoKDp16oSzZ8+qOySqRqwjTERExBlArFq1Ch07dgQAWFtb488//8Qrr7yi5qioupTVEU7IyEdld/nFJmWjs6MFJJLKKg4TERHVThqdAGZkZGDLli04dOgQXn31VXz00UdKbR48eICvvvoK0dHRsLOzw8yZM9G6dWv5+U2bNiElJUXp5/r16wd3d3d58ldUVISgoCB89dVX1feGSO3K6ghP3RoKCaCQBD77+tPfIxASl4rPh7nCxEC35gMlIiKqRhq7BHz79m20bt0akZGRSExMREREhFKbJ0+ewMvLC7GxsQgICEBeXh68vLwQGRkpb5OVlYX09HSl/woKCuRt8vLyMGrUKEydOlWeEFLdVVEd4UZmBvh2rAfm928FHakEB/9+hMFrzyHiYYaaIiUiIqoeGjsD2LRpU9y+fRvGxsbo169fuW1WrVoFXV1d7N27F7q6uhg5ciSioqKwZMkS7NixAwAwe/bsSvtJTk7G66+/jg8++AADBw4U/X2QZqqsjjAAdLS3wMwdYbibkovh317Ap4Na483OzbgkTEREdYLGJoBGRkZVtjl+/DgGDBgAXd1/l+iGDh2KlStXqtRHSUkJvL290apVK1y/fh3Xr19H+/bt0bdv33LbFxQUKMwcZmZmAni6fFxUVKTUvuxYeedIkbrGqqOdKQBTAEBpSTFK/ykV3K5JPfw+tTM+CozAn1FJ+N/+G7gQk4zP/FxgaqiLklIBV+6l4UlWARqa6KNjs/ry5LG68XulOo6V6jhWquNYqU5Tx0rT4lEHjU0AVXH37l289tprCsdsbGyQmpqKrKwsmJiYVPrzgiBgxIgRAID09HQAT5eDK7Js2TIsXrxY6fjx48crTVhPnDhRaRz0L00bq8HmgKm9BAfuSXH0RiIuxySgi3UpghKkSC/8N+Ez1xMw3L4UbpY1t4G0po2VJuNYqY5jpTqOleo0baxyc3PVHYLa1eoEsLCwEIaGhgrHyhKxwsLCKn9eR0cHy5cvV7m/+fPnKywpZ2ZmwtbWFn369IGpqalS+6KiIpw4cQK+vr4Ks5SkTJPHaiAA/wcZmLX7Gh6k5eHgfZlSm4xCCX6OlmHtaDf0bWNdrfFo8lhpGo6V6jhWquNYqU5Tx6psBU+b1eoEsH79+khNVazYkJKSAplMVm5C9rL09fWhr6+vdFxXV7fSL3ZV5+lfmjpWHRyscODdbuiy7E/kF5cqnRfw9Cniz/64hf7tmtbIcrCmjpUm4lipjmOlOo6V6jRtrDQpFnXR2KeAVeHu7o7Q0FCFY6GhoXBxceGHS6K7lZBVbvJXhmXkiIiotqjVCWBAQABOnjyJy5cvAwBiY2Oxa9cuBAQEqDcwqpNYRo6IiOoKjV4C7tu3L0pKShAeHg5dXV307t0bDRo0kG/xMmLECMyaNQuvvPIKXFxcEBUVhWHDhmHmzJlqjpzqIpaRIyKiukKjE8B58+ahtFRxyc3AQPGX6xdffIH3338ft2/fhp2dHezt7WswQtImqpSRk0qe3gtIRESkyTQ6AezZs6dK7Ro3bozGjRtXczSk7SorI1emVADe+DEEs31bYGp3J0hraG9AIiKi51Gr7wEkqmkVlZFrbGaA1aPcMax9U5SUClh57BbG/3wJydkFFVyJiIhIfTR6BpBIE1VWRs7PvQm8nSzxv/0RCLqdjP7fBOGb0e7o4mSl7rCJiIjkmAASvQCZVAJvJ0ul4xKJBK93tIW7rTmmbwvF7SfZ8P8hBDN7NceMns0hk0pQUipUWIOYiIioJjABJKoGLaxNsP/drli4/wb2XH2A1Sdv41JcKvzcmmD1n7fxOOPfrWIamxlg4WAX9HPlfaxERFQzeA8gUTUx0tPBypFuWPW6G4z0ZLgQm4J5+64rJH8AkJCRj6lbQ3E04rGaIiUiIm3DBJComg33sEHgtK7QqWCZt+xp4sUHb6KktKINZoiIiMTDBJCoBqTmFKK4kuSOZeSIiKgmMQEkqgEsI0dERJqECSBRDWAZOSIi0iRMAIlqQFkZuco2e9GVSdC0vmGNxURERNqLCSBRDSgrIwdUXCu4qETA4LXncOJmYs0FRkREWokJIFENqayM3P/5ucLNxgwZeUWYsvkK/u/QTRQWl6opUiIiqutE3Qg6IyMD27dvx/HjxxEVFYXMzExYWlqiQ4cOGDhwIPz8/KCrqytml0S1SmVl5EZ1ssXyP6Lw0/k4/HguDlfupmLdWA/YWhipO2wiIqpjRJkBzMnJwccff4ymTZti1apVMDc3x9ixY/Hhhx9i2LBhyMrKwvTp09GsWTNs2rQJpaWc2SDtVVZGzs+9KbydLOVl4PR0pPjfYBdsGtcRZoa6+PtBBgasCVLYILqkVEBIXCquJksQEpfKfQOJiOiFiDIDOGfOHGRlZeHMmTPo2LFjuW1KSkpw/PhxrFixArq6uggICBCja6I6x9fFGodndsOMHWEIu5+Od7aGYrx3M3S0r4/Pj0T9U0lEhs23r7CMHBERvRBREsCVK1fC2Ni40jYymQz9+/dH//79kZOTI0a3RHWWTX0j7H7bG18ev4Xv/rqDX4Pv4dfge0rtysrIbfD3YBJIREQqE2UJuKrk72XbE2kjXZkU8/u3xo/jOkJSwaPDLCNHREQvQtSHQMqUlJTg0qVLePDgAUpKShTOeXp6wtHRsTq6JaqTjPR1IFSS2z1bRs7bybLG4iIiotpL9AQwLS0NPj4+uHHjBszNzSGTyRTOr169mgkg0XNgGTkiIhKb6Ang999/DxMTEyQmJqJhw4ZiX55I67CMHBERiU30jaATEhIwevRoJn9EIlGljJyhrgxtm5rVWExERFS7iZ4Aurq64tatW2JflkhrqVJGLq+oBMM3nMftxKyaC4yIiGotURLA+Ph4hIeHIzw8HG3btsUff/yBpUuXIjg4WH687L/U1FQxuiTSKpWVkXuvd3M0MNFHdGI2hqw7jz1X4tUUJRER1Rai3AO4ePFi/PjjjwrHFixYgAULFii13bRpEyZPnixGt0RapayMXHDMExwPCkEfHy94OzeETCrBG17NMHt3OIJuJ2POb9cQfCcF/+fnCmP9annQn4iIajlRfjusXr0ay5cvV6mtiYmJGF0SaSWZVAIvBwukRArw+qeGMAA0MNHHrxM8seGvWHx1/Bb2hT7E3/HpWP+GB1o1MgXwtIxceTWIiYhI+4iSANarVw/16tUDACxZsgRt27bFsGHDlNpVdo6IXo5UKsH0Hs7oZG+BmTvCEJuUA79157FoSBuYG+piyaGb/5SRe4pl5IiItJfoD4Hcv38fKSkp5Z6Li4tDZmam2F0S0TM8HSxwZJYPXm3ZAAXFpZi/7zqmbgtVSP6Af8vIHY14rKZIiYhIXUS7QejOnTt48uQJkpKScOfOHVy8eFHhfGpqKv766y+MGzdOrC6JqAIWxnr4aXwnfHc2FiuOlv9UvoCnTxUvPngTvi6NuBxMRKRFREsAP//8c/mDIAcOHMCyZcsUzuvr62PYsGHo3r27WF0SUSWkUgncbetX2oZl5IiItJNoS8Dr169HVlYWJk+ejA0bNiArK0v+X3Z2NvLz87Fjxw5IpaKvOhNRBVhGjoiIyiPaDKC+vj709fWxadMmsS5JRC+JZeSIiKg8oiSAkZGRePjwoUptXVxc0KRJEzG6JaIqlJWRS8jIh1BBG1MDHXSyr3ypmIiI6hbR9gF8diPo0tJSCILyrxupVIpNmzZh4sSJYnRLRFUoKyM3dWsoJEC5SWBmfjGmbgvFytfawdxIr6ZDJCIiNRDlhrzvvvsOxcXFKC4uxsOHD2Fra4tvvvkGCQkJKCoqQmxsLN5991107doV48ePF6NLIlJRZWXkRnW0hZ5MihM3EzFwzTmE3k9TU5RERFSTRK8TtXXrVowcORIzZ86UH3N0dMTatWvRrVs3hISEoEuXLmJ3S0SVKCsjV14lkDe9m2H69lDcS8nF6xuDMbdfS0zu5ggpt4UhIqqzRH8k9+7du7C0LH87CQsLC8TFxYndJRGpQCaVwNvJEn7uTeHtZCnf98+1qRkOzeiGQe0ao7hUwOdHojB58xWk5hSqOWIiIqouoieAbm5uWLduHSIiIhSO79+/H8ePH4ebm5vYXRLRSzIx0MXaMe3x2TBX6OlIcSrqCQauCcLlu6kAntYRDo5Nwf7whwiOTUFJaUWPlBARUW0g+hJwQEAATp48iXbt2qFVq1awtLREfHw8Hj16hKVLl8LV1VXsLolIBBKJBG94NUN72/p4d3so7iTnYPT3FzGoXWOE3ElFQibrCBMR1RWizwDq6Ohg586duHjxIgICAtC5c2fMnj0b0dHRmDt3rtjdEZHIXJqY4uCMbhjWvilKSgXsD3+kkPwBrCNMRFTbiT4DWMbT0xOenp7VdXkiqkbG+jpY+Vo7nIp6goy8IqXzrCNMRFS7iZIAxsTEICEhAc2bN0dWVhYSEhIqbNu8eXNYW1uL0S0RVaPLd9PKTf7KsI4wEVHtJUoCuHz5cvz444/YtGkTLl68qLAp9H9t2rQJkydPFqNbIqpGrCNMRFR3iZIAbty4EevWrYOuri4CAgKwbt26Ctvq6uqK0SURVTPWESYiqrtEeQhER0cHsbGxSEtLg46ODgwMDCr8TyaTidElEVWzsjrCVd3ddy4mCcUlpTUSExERiUO0p4C//vprNGzYEG5ubnj//fdx4MABZGRkiHV5IqphZXWEASglgc++Xn86FmN/CEFCBpeCiYhqC9ESwBUrVmD37t3o1q0bjh07Bj8/P1haWqJTp06YN28ejh07hpycHLG6I6IaUFEd4UZmBtjo74E1Y9rDWE+GS3GpGLAmCGduPVFTpERE9DxE2wbG0tISr732Gl577TUAQGJiIs6cOYPTp0/j999/xxdffAFdXV1s375d3oaINF9ldYQBoG1TM7y7PRQ3HmUi4OfLeKe7Ez7o0wK6MtG3GSUiIpFU2z6A1tbWGDFiBOzt7WFvb4/t27fj+vXryMzMrK4uiaialNURLo+DlTH2Tu2Cz49EYnPwPWz8KxaX76Zi7Zj2aGJuiJJSocLkkYiI1EPUBLCkpARhYWE4ffo0zpw5g6CgIBgZGeGVV17B22+/je7du6NNmzZidklEGsBAV4Ylfq7o7GiJeb9dw9V7aRiwJghjPe0QGPYQjzNYRo6ISJOIlgB++eWXWLp0KYyNjfHKK69g8ODB+PLLL9G6dWuxuiAiDTegbWO4NjHDjB2h+PtBBr49E6vUpqyM3AZ/DyaBRERqItpNOnFxccjNzUX79u3RoUMHdOzYES1atBDr8kRUS9hZGmHnW94w0it/yyfhn/9dfPAmSkqFctsQEVH1Ei0BXLduHUJDQ9G3b19cuHAB/fr1g4WFBQYNGoQvv/wSV65cQUlJiVjdEZEGC49PR25hxf9/f7aMHBER1TzREkCJRAJXV1fMmDED+/btQ1JSEs6ePYvevXsjKCgIvr6+sLCwwIEDB8Tqkog0FMvIERFptmrbp0EikcDc3Bz169dH/fr1YWJigszMTDx5wn3CiOo6lpEjItJsoj4F/ODBA/nef2fOnMGdO3egr68PLy8vTJo0CT169EDnzp3F7JKINFBZGbmEjHxUdJefBEASZwCJiNRCtATwgw8+wKpVq6Crq4tOnTphzJgx6NGjB7p06QJDQ0OxuiGiWqCsjNzUraGQAOUmgQKAmTvDERKXigWDXGCgyzrhREQ1RbQEsGfPnvD19YWPjw+MjY3FuiwR1VJlZeQWH7yptA/gpwNb48ajTHx7JhbbQu4j9H461o9tD8cG9dQYMRGR9hAtARw4cKBYlyKiOqKyMnID2zVBZ0dLvL8rHJGPMzFo7Tl8PqwthrZvqu6wiYjqvGorBUdEBFReRu6VFg1wZJYPZu0Mw8U7qXhvVziCY1OwaEgbGOrJWEaOiKiaMAH8R0ZGBuLi4uDu7q7uUIi0irWpAbZN7oxv/ryNtaduY9eVeITFp2F0JztsCrrDMnJERNWg2raBqU1KS0sxefJkeHh4qDsUIq0kk0ow27cFtk3yglU9fUQnZmPJIcV7B4F/y8gdjXispkiJiOoGJoAAli9fjokTJ0Iq5XAQqVMXZyscmtENerLy/7/IMnJEROIQZQl4z549CAkJUant66+/Dk9PT5WvHR0djSNHjqBFixYYMGCA0vnS0lKcOHEC0dHRsLOzQ//+/aGnpyc/HxUVhfx85b3GbG1tYWlpifPnzyM/Px/9+/dXOSYiqj5xyTkoLCmt8PyzZeQqureQiIgqJ0oC+PDhQ0RERKjU1tfXV6V2iYmJ8Pf3x71795CXl4fu3bsrJYBFRUUYMmQIIiIi0KdPH6xbtw5LlizBqVOnYGZmBgCYP38+4uLilK7/6aefolevXli4cCFWrFiB8PBwAEB4eDjc3NwgkfBGcyJ1YBk5IqLqJ0oC+N577+G9994T41JygiBg7ty56N27d4Wzc5s2bcKFCxdw48YN2NjYICMjA+3atcOyZcuwfPlyAEBgYGCFfVy4cAHJycmYNGkSAKCkpAQBAQG4dOmSwiwiEdUclpEjIqp+GvsUcKNGjdCoUaNK2+zZswcDBgyAjY0NAMDMzAyjR4/G7t275QlgZbp06SKf+QMAHR0dhdf/VVBQgIKCAvnrzMxMAE9nIouKipTalx0r7xwp4liprq6PVXsbEzQy1UdiZkGFZeRkEgn0pEKVY1DXx0pMHCvVcaxUp6ljpWnxqEO1JYBJSUmIjo5GVlaWwnFXV1d5wvayIiMj0b17d4VjrVq1QlxcHPLz82Fg8HwzBFVtAbNs2TIsXrxY6fjx48dhZGRU4c+dOHHiueLQZhwr1dXlsRrQSIKfMsseBHn2doynKWGJAIz6/iKG2peim7WAqu7YqMtjJTaOleo4VqrTtLHKzc1VdwhqVy0J4HvvvYe1a9eitLQUEokEgvD0L22pVIpNmzZh4sSJovSTlZUFc3NzhWNlr7Ozs587Abxy5Uql5+fPn4/Zs2fLX2dmZsLW1hZ9+vSBqampUvuioiKcOHECvr6+0NXVfa5YtA3HSnXaMFYDAHjcSMTSI1FIyPx31r2xmQHe6+WMYzee4NStJPwWJ0O2kTU+H+oCEwPlsdCGsRILx0p1HCvVaepYla3gaTPRE8ADBw4gMDAQf//9N1avXo3OnTujX79+WL58OUJCQhAQECBaX0ZGRkofYkZGhvyc2PT19aGvr690XFdXt9IvdlXn6V8cK9XV9bEa5G6D/u2allsJ5PVOzfDjuTgs/yMKR28k4ubjLKwb2x7tbMzLvVZdHysxcaxUx7FSnaaNlSbFoi6ib3x3/vx5TJkyBa6urpBIJCguLoaNjQ3WrVsHQRBw9uxZ0fpq2bIlYmNjFY7FxsaiadOm1ZIAElHNKisj5+feFN5OlvIycBKJBJN9HPHb1C6wqW+I+6m5GLHhAn46FydfcSgpFRASl4qryRKExKVy30AiomeIPgOYkpKC5s2bAwAsLS2RkJAgP9e8eXPEx8eL1pefnx9WrFiB1NRUWFhYID8/H7t27cKwYcNE64OINJe7rTkOz/TB3N/+xrEbiVhy6CYu3klB3zaN8OXxW/9UEpFh8+0rLCNHRPSMai190bFjR2zfvh03b97ExYsXcezYMTg6Oqr886tWrcKXX36Ju3fvIjIyEl9++SW+++47+fl3330XDg4OeOWVV/DJJ5/g1VdfRXFxMRYsWFAdb4eINJCZoS42+nfA4iFtoCeT4vjNRHyw52+WkSMiqoToCWDXrl3RokULAMCwYcPg4uKCNm3awNvbG35+fujatavK10pMTERCQgIGDRqEHj16ICEhAUlJSfLzhoaGOHfuHObMmQNBEBAQEIDw8HA0bNhQ7LdFRBpMIpFgfBd77H7bW75M/F8sI0dE9C/Rl4AnTJgg/7NMJsPvv/+OhIQECIKAxo2fb+llxYoVVbbR19fH+PHjnztOIqp78opKKk3uWEaOiOgp0RPAVatWQSKRYMyYMfKNnKva0JmISAwsI0dEpBrRl4AtLS2xatUq2NjYoG/fvtiyZQuys7PF7oaISAnLyBERqUb0BHD8+PG4f/8+Tp48CTs7O8ycORPW1tZ444038Mcff6C4uFjsLomIAACeDhZobGaAygqD6OtI4djAuMZiIiLSRNXyFLBEIsGrr76KTZs2ISEhAVu3bkVeXh4GDhyIX3/9tTq6JCKCTCrBwsEuAFBhElhQXIrBa8/h4p2UmguMiEjDVOs2MAAQHR2NkJAQXLlyBTKZDPXr16/uLolIi/VzbYwN/h5oZKa4zNvYzAD/G+QC54b18CSrAGM3XcSaP2/ziWAi0krVUgv4/v372LFjB7Zu3YqIiAh4enpizpw5GDVqFLdoIaJq18+1MXxdGiE45gmOB4Wgj48XvJ0bQiaVYLSnLf63/wZ+u/oAq05EIyQuBV+Pcud9gUSkVUSfAVy0aBHs7e3x448/YsSIEbh9+zZCQkIwY8YMJn9EVGNkUgm8HCzQwUqA1z81hAHASE8HX450w6rX3WCoK8P5mBQM+OYczscky3+2pFRAcGwK9oc/RHBsCmcJiajOEX0G0MPDA8HBwfDy8hL70kREohnuYYN2NuZ4d3soohKy4P9jCGb0cEbLRiZYejhSoZIIy8gRUV0j+gzgnTt3kJ6eLvZliYhE59ywHn6f3hVjPG0hCMCaUzGYvj2MZeSIqM4TPQG8d+8eoqKixL4sEVG1MNCVYdnwdvj6dbcKnxxmGTkiqmtETwD79OmDffv2obS0VOxLExFVm0ZmhqgstXu2jBwRUW0n+j2ARUVFiImJQdu2beHr6wtzc3OF80OGDIGHh4fY3RIRvRSWkSMibSJ6AhgZGQkHBwcAwJUrV5TOd+zYkQkgEWkclpEjIm0iegI4b948zJs3T+zLEhFVq7IycgkZ+RUuBRvry+Bua16TYRERVYtqrwRCRFQbqFJGLqegBGM2XUR8am7NBUZEVA2qJQGMj4/HlClT0KlTJ/z2228AgDNnzuDIkSPV0R0RkSgqKyP3dndHmBroIDw+HQPXBOHYjQQ1RUlE9PJEXwJOTU1Fp06d4OPjA6lUKt8T0MXFBd26dUOPHj1gaGgodrdERKIoKyN3KS4VT7Ly0dDEAJ7/VBJ5s3MzvLs9DOHx6Xh7y1UEdLHH/AGtoK8jU3fYRETPRfQZwF9//RU9e/bEnj170K5dO/nxhg0bwtbWFmfOnBG7SyIiUcmkEng7WcLPvSm8nSzlZeRs6hth99vemOLz9EG3Xy7cxWsbgnEvJUed4RIRPTfRE8DY2Fh4e3sDACQSxTtpLC0tkZycXN6PERHVCno6Unwy0AU/ju8IcyNdXH+YgUFrzuHwtadVQlhHmIhqA9GXgBs3biyvBPJsApidnY3z589j1qxZYndJRFTjerW2xpGZPpi5IwxX7qVh+vZQ7LpiheiELCRkFsjbsY4wEWki0WcA33jjDezcuRMbN25EZmYmMjIycPLkSfTr1w9WVlby2UEiotquibkhdr7VGdNedQIAnI1OVkj+ANYRJiLNJPoMoL29PX777TdMmjQJcXFx2LlzJwCgc+fO2L9/P6RS7jxDRHWHjkyKD/q0xI5L8UjLLVQ6L+DptjKLD96Er0sj+f2ERETqJHoCmJKSgk6dOiEmJgaRkZFITk5G06ZN4ezsjJSUFGRnZ6NevXpid0tEpDaX4lLLTf7KPFtH2NvJsuYCIyKqgOjTcfPmzcPOnTshlUrRpk0bdO/eHc7OzgrniIjqEtYRJqLapkbXY3NycmBsbFyTXRIRVTvWESai2ka0JeB9+/bh0qVLuHz5Mh49eoSYmBiF86mpqTh48CAWLFggVpdERBpBlTrCALDnSjzcbM1gpCf63TdERM9FtL+F7t69iytXriA5ORlFRUUoLPz3fhiJRAILCwv88MMPcHFxEatLIiKNUFZHeOrWUEgAhSSw7LUEwL6wh/j7QTq+faMDWjYyUUusRESAiAng7NmzMXv2bHz//fdo3rw5evToIdaliYg0Xlkd4cUHb+Jxxr/3+jX6Zx9AcyM9zNoZhtikHAxZdw6Lh7TBqE62ShvmExHVBNHXId566y2xL0lEVCtUVkcYAI7M9MH7u//G2egkfLTvOoLvpOCzYW1RT59LwkRUs6rlb52IiAhs2bIFDx48QElJicK5t99+m7ODRFRnldURLo9lPX38EtAJG8/G4qvj0dgf/gjXH2Rg7dj2aNPEDCWlQoXJIxGRmERPAMPDw+Hp6YmOHTuiZcuWkMlkCud1dXXF7pKIqNaQSiWY9qozPO0tMGNHGO4k52DYtxcw3KMpztxKQsIzy8csI0dE1UX0BHDXrl0YN24cfvjhB7EvTURUZ3S0t8CRmT74cM/f+DPqCXZeildqU1ZGboO/B5NAIhKV6PsASiQSuLq6in1ZIqI6p76xHr57swNMDMr/t3jZ08SLD95ESWllG8wQET0f0RPAnj174vDhwxAE/mVFRFSVy3fTkJVfXOH5Z8vIERGJRfQl4NzcXERGRsLT0xM9e/aEoaGhwvkhQ4bAw8ND7G6JiGollpEjInUQPQGMjIyEvb09AOD8+fNK5zt27MgEkIjoHywjR0TqIHoCOG/ePMybN0/syxIR1UmqlpG79iAdnR0tuHE0EYlC9HsAiYhIdWVl5ICn5eKe9ezrZX9EYfKvV5CWUwgiopcl2gzg6tWrcfTo0Srbvf/+++jbt69Y3RIR1XqVlZH73yAXJOcU4v8O3cSfUU8wYE0Q1o5pj472FmqMmIhqO9ESQCMjI5ibm1fZTk9PT6wuiYjqjKrKyHnYmePd7WGIS87BqO8v4oM+LfDOK06QslIIEb0A0RLAt956i3WAiYheQmVl5No0McPBGd3wSeB17A9/hC+O3kLInVSset0NlvX0WUaOiJ6LKAlgYmIirK2tVWpbWlqK1NRUWFlZidE1EZHWqKevg9Wj3OHtaImFB27gr+gkDFgThDe8mmHHpfsKy8csI0dElRHlIZDPP/8c/fv3x4kTJ1BaWlpum5ycHPz6669o164dTpw4IUa3RERaRyKRYLSnHfa/2xVODYyRmFmAVSeiFZI/4N8yckcjHqspUiLSZKLMAH711VdYv3493nzzTQiCAG9vb9jb26NevXpIS0vDzZs3ERISAkdHR3z++ecYMmSIGN0SEWmtVo1M8fv0rvD87E/kFZUonRfw9CnixQdvwtelEZeDiUiBKDOAOjo6mDVrFu7fv49169bB2toaYWFhOHLkCKKjo9GxY0ccOXIEERERTP6IiEQS8TCz3OSvDMvIEVFFRN0IWk9PDyNHjsTIkSPFvCwREZWDZeSI6EVxI2giolqKZeSI6EUxASQiqqXKyshVdnefRALkV7JMTETaiQkgEVEtVVkZuTKCAEz45TJWHI1CcUn5uzQQkfZhAkhEVIuVlZFrZKa4zNvYzABrRrvDv7MdAGDDmViM/v4iHqXnqSNMItIwoj4EAjytCdy6dWvW+yUiqiGVlZEb4t4UnR0tMX/vdVy5l4YBa4Kw6nU39Gyl2ub9RFQ3iT4DeO/ePURFRYl9WSIiqkRZGTk/96bwdrJU2PdvULsmODSzG9o2NUN6bhEm/nIFnx2+iaJ/loRLSgWExKXiarIEIXGpKCkV1PU2iKiGiJ4A9unTB/v27auwIggREdW8ZpbG+G2qNwK62AMANgXFYeTGYGy9eA/dVpyC/09XsPm2DP4/XUG3FadYQYSojhN9CbioqAgxMTFo27YtfH19YW5urnB+yJAh8PDwELtbIiKqgr6ODIuGtIG3kyXm7Pkb4fHpCI9PV2pXVkZug78HawkT1VGiJ4CRkZFwcHAAAFy5ckXpfMeOHZkAEhGpUd82jdDS2gS+X/+FohLl5V6WkSOq+0RPAOfNm4d58+aJfVkiIhLR44z8cpO/Ms+WkfN2sqy5wIioRnAbGCIiLcQyckTaTfQZQAAoKSnBzz//jL/++guJiYmws7PDiBEj0L9//+rojoiInhPLyBFpN9FnAAsKCtC1a1e8//77yMvLg6OjIx48eIDBgwdj6tSpYndHREQvQJUycjpSCRqY6NdYTERUc0SfAdy8eTMyMjIQFxcHKysr+fGwsDB0794d06ZNQ9u2bcXuloiInkNZGbmpW0MhwdN7/v6ruFSA37pz+Hx4W/i5N63pEImoGok+AxgeHo6JEycqJH8A0L59e/Tu3Rt///232F2+tAsXLuDDDz+Ev78/9u3bp+5wiIhqRGVl5JYNbwtPBwvkFJZg1s5wzN93DflFJWqKlIjEJvoMoLm5Oe7cuaN0XBAE3L17F2ZmZmJ3+VL27t2LyZMnY86cOXB3d4ezs7O6QyIiqjFlZeSCY57geFAI+vh4wdu5IWRSCUZ2sMGaP29j7ekY7LgUj9B76Vj/hgecG9ZTd9hE9JJETwBHjhwJT09PNGjQAKNGjYKVlRXu3buHVatW4dGjR+jRo4fYXb6U//3vf1i7di38/f3VHQoRkVrIpBJ4OVggJVKA1z81hAFARybF7D4t4elgifd2heNWYhYGrz2HpUNdMaKDDYCnZeTKq0FMRJpN9ATQ3d0de/bswaxZs/B///d/8uNeXl44duwY6tVT/V+O4eHh2LhxIw4dOoShQ4di3bp1Sm0uXryIBQsWIDo6GnZ2dvjoo48wcOBA+fm5c+fi0aNHSj83ceJE+Pj44NatW7C2tsZbb70Fe3t7TJs2Tal6CRGRNuvW3ApHZnXDezvDcSE2BR/s+RvBd1Lg09wKy/+IwuOMf7eKaWxmgIWDXVhBhEjDiX4PYHFxMQYNGoSYmBjcvn0b58+fx/3793Hx4kW4ubmpfJ3r168jICAAbm5ucHR0RHp6ulKb6Oho9OrVC+7u7jh69CiGDBmCoUOH4uzZs/I2Pj4+6Nevn9J/tra2kMlk0NPTw5YtW+Dl5YWIiAiMHj1ajGEgIqpTGpoYYMskL8z2bQGpBPjt6gPM2hmukPwB/5aRYy1hIs0m+gzgtGnT4OnpicmTJ8PZ2fmF76lr06YNwsPDAQD79+8vt82qVavg6OiIlStXAgBat26N06dPY9myZXjllVcAAIMHD660n5YtW2Lu3LlwdXVF37590aFDhxeKl4iorpNJJZjZqzk62NXHmz+FoLScR4dZRo6odhA9AbS2tkZiYuJLX0cqrXpy8uzZs+jXr5/Csb59++KTTz6BIAiQSKr+i2fp0qUYOnQo2rdvj6tXr2LKlCkVti0oKEBBQYH8dWZmJgCgqKgIRUVFSu3LjpV3jhRxrFTHsVIdx0p1zzNWglBSbvInP4+nZeSCY57Ay8FCpAg1B79XqtPUsdK0eNRBIghCJf83fn7R0dEYPHgwAgMD4eLiIso1+/XrBysrK2zdulXhuJmZGT7++GOF2sM7d+7EmDFjkJ6ervITx/fu3UNoaCicnJzQrl27CtstWrQIixcvVjq+fft2GBkZqfhuiIhqt6vJEmy+Lauy3bjmJehgJeqvGCJR5ObmYuzYscjIyICpqam6w1EL0WcAd+7cicTERLi6usLOzk7pgYqFCxdi2LBhovQlCAJ0dBTfQtnrkhLV96tq1qwZmjVrVmW7+fPnY/bs2fLXmZmZsLW1RZ8+fcr9AhUVFeHEiRPw9fWFrq6uyvFoI46V6jhWquNYqe55xsoyLhWbb1+p8pp9fLzq7Awgv1eq0dSxKlvB02aiJ4CdO3fGp59+WuF5MffZa9CgAZKTkxWOJSUlQU9Pr1r2G9TX14e+vnJZJF1d3Uq/2FWdp39xrFTHsVIdx0p1qoyVt3NDNDYzQEJGfrkVRADAQFcKV5v6dXrc+b1SnaaNlSbFoi6iJ4BNmzaFi4sLbGxsxL60Ek9PT5w7d07h2NmzZ9GhQwfIZFUvTxAR0fNTpYxcflEp/Nafx/qxHnBtqlkFAIioGraBWbt2Lf744w+xL1uu6dOnIzg4GNu2bYMgCDh58iQCAwPx7rvv1kj/RETaqrIycnP7tkRTc0PcS8nF8G8v4NcLdyHy7eZE9JJEnwF0dHREZGSkKNeysbFBcXEx0tLSIJVKcfLkSTRp0gShoaEAgG7duuGHH37A7NmzMXnyZOjp6WHRokUYO3asKP0TEVHFysrIlVcJ5A2vZpjz2984fjMRCw/cQHBsCla81g5mhlx6I9IEoieA48aNQ9euXdGiRQv069dP6SEQIyMj6OnpqXStq1evKv2r8b9LuwEBARg/fjzS0tJgZmbGpV8iohokk0rg7WSpdNzMSBffvdkBv1y4i8+PROLojQREPMrAurEecLc1r/lAiUiB6Angp59+ijt37mDq1Knlnt+0aRMmT56s0rWsra1VaieRSGBhUfeeNCMiqs0kEgkmdHVAh2b18e72MNxPzcVrGy7go/6tMKmbA0oFsI4wkZqIngAuWLAA77zzToXn7e3txe6SiIg0WDsbcxya2Q0f7b2GI9cTsPRwJA6EP0RiVgESM//dXJ91hIlqjugJoKp76hERkfYwNdDF+rEe2BpyH4sP3MC1h8r7sJXVEd7g78EkkKiaifYU8MWLFxEbGyt/nZSUpLTR4uHDh+X1fYmISLtIJBKM9bSDuVH5D4KU3fG9+OBNlFRWa46IXppoCeAPP/yA06dPy1/Pnz8fu3fvVmgTGBiIK1eq3j2eiIjqpktxqUjOLqzwfFkd4UtxqTUXFJEWEn0fQCIiooo8ycoXtR0RvRgmgEREVGMamhhU3QiAVT3lsptEJB4mgEREVGM8HSzQ2MwAVW328u3pGCRlFVTRiohelKhPAd+4cQNHjx4FADx48EDhddkxIiLSXpXVES57rSeT4nxsCgasCcI3o9zRxdlKPcES1WGiJoCrV6/G6tWr5a+PHTum8BoAXnvtNTG7JCKiWqasjvDigzfxOOPfe/0a/bMPoFODepi+PRTRidl448cQzOjZHLN6Necm0UQiEi0BXLVqFZYuXVplOzMzM7G6JCKiWqqyOsIAsH96Nyw6cAO7rsRjzZ+3cSkuBd+Mbg9rU9XuISSiyomWAJqamsLU1FSsyxERUR1XUR1hADDUk2HFa+3g7WSJjwOv4+KdVAz4Jghfj3LHKy0aoKRUYBk5opcgeiUQIiIisQxt3xTtbMwwfXsYIh9nYtxPl9C3jTX+js9AQua/y8csI0f0fPgUMBERaTTHBvUQOK0L3vCyAwAcu5GokPwB/5aROxrxWB0hEtU6TACJiEjjGejKsMTPlWXkiETCBJCIiGqFS3GpSM8tqvA8y8gRqY4JIBER1QosI0ckHiaARERUK6haRk7VdkTajAkgERHVCqqWkTt64zEKi0trJCai2ooJIBER1QplZeQAKCWBz77+9cI9vLbxAu6n5NZYbES1DRNAIiKqNcrKyDUyU1zmbWRmgI3+HvhhXEeYGeri2oMMDFwThCPXuS0MUXm4ETQREdUqVZWROzLLBzN3hOHqvTRM2xaKNzs3wycDW8NAV6bmyIk0BxNAIiKqdSorI9fU3BA73+qMr45HY+Nfsdhy8R5C76dh3VgPOFgZs4wcEZgAEhFRHaQrk+Kj/q3g5WiBD3b/jRuPMjFoTRBGe9rhyPXHeJzBMnKk3XgPIBER1Vk9WjbEkZk+8LS3QE5hCX48F6eQ/AEsI0faiQkgERHVaY3MDLBlkifq6Zd/DyDLyJE2YgJIRER1Xuj9dGQXlFR4nmXkSNswASQiojqPZeSIFDEBJCKiOo9l5IgUMQEkIqI6T9UycvdSciAIvA+Q6j4mgEREVOdVVkbuWR/tu473d4Ujp6C4ZgIjUhMmgEREpBUqKiPX2MwA3471wJy+LSGTSvB7+CMMXnsONx9lqilSourHjaCJiEhrVFVGztPBAjO2h+FOcg6GfnseCwe7YKynHSQSVgqhuoUzgEREpFXKysj5uTeFt5OlQhm4TvYWODLLBz1aNkBhcSk+CYzAjB1hyMovAgCUlAoIiUvF1WQJQuJSuW8g1VqcASQiInqGhbEefhzfCT+cu4Mvjt7CoWuPcf1hBt7wtMPPF+7+U0lEhs23r7CMHNVanAEkIiL6D6lUgrdeccKut73R1NwQ91Jy8fkfUSwjR3UGE0AiIqIKdGhWHwfe7Qp9nfJ/XbKMHNVWTACJiIgqEZ2YjYLi0grPs4wc1UZMAImIiCrBMnJUFzEBJCIiqgTLyFFdxASQiIioEqqUkZNKABl/o1Itwq8rERFRJVQpI1cqAGM2hWDjX7Eo5cMgVAswASQiIqpCZWXkvn7dDYPdmqCkVMDyP6Iw8dfLSMkuUFOkRKrhRtBEREQqKCsjFxzzBMeDQtDHxwvezg0hk0owtH1TdHGyxKIDN3DmVhIGrAnC2jEe8HSwUHfYROXiDCAREZGKZFIJvBws0MFKgNczNYQlEgnGeNrh9+ld4djAGImZBRj9fTDWnbotXxIuKRUQHJuC/eEPERybwn0DSa04A0hERCSS1o1NcfDdbljwewT2hT3El8ejERKXikHtmmD1yWiFSiIsI0fqxBlAIiIiERnr62DVKHesfK0dDHSlCLqdjHl7r7GMHGkUJoBERETVYGRHW/w+rSt0pOU/O8wycqROTACJiIiqSVpuEYorSe5YRo7UhQkgERFRNWEZOdJUTACJiIiqCcvIkaZiAkhERFRNVCkjpyeTwNbCsMZiIgKYABIREVUbVcrIFZYIGLz2HE5HPam5wEjrMQEkIiKqRpWVkVsypA1cm5oiLbcIE365jGVHIlFUUqqmSEmbcCNoIiKialZWRu5SXCqeZOWjoYkBPP+pJDLK0xbLjkThlwt38d3ZO7h8NxVrx3qgqTmXhan6cAaQiIioBsikEng7WcLPvSm8nSzlZeT0dWRYNKQNNvp7wMRAB6H30zHgmyCcuJmo5oipLmMCSEREpAH6uTbGkZk+cLMxQ0ZeEaZsvoIlB2+isLiUdYRJdFwCJiIi0hC2FkbY804XfHE0Cj+ci8NP5+PwZ1QicgtLkJRVIG/HOsL0sjgDSEREpEH0dKT4dJALfhjXEUZ6MtxLyVVI/gDWEaaXxwSQiIhIA/Vo1RDG+uUv1LGOML0sJoAAEhMTcfXqVaSnp6s7FCIiIgDApbhUpZm/Z7GOML0MrU8Av/rqK7i4uOCdd96Bo6MjDhw4oO6QiIiIWEeYqpXWJ4Dr1q1DUFAQLl++jA0bNmDTpk3qDomIiEjl+sDmRrrVHAnVRRr/FHBYWBgOHz4MFxcXDB8+XOl8cXEx9u/fj+joaNjZ2WHYsGEwMjKSnw8NDUVubq7Szzk7O6NRo0bo3bs3Nm/eDF9fX+zbtw99+vSp1vdDRESkirI6wgkZ+ajsLr/PD0fCpr4RnBrUq7HYqPbT2ATw8ePHGD58OHJzc5GRkYFu3bopJYAFBQXo06cPHj58iIEDB2Lnzp347LPPcO7cOVhYWAB4usR77949pevPmTMHfn5+6NOnD+bPn49Tp04hLy8PH3zwQY28PyIiosqU1RGeujUUEkAhCSx7bWKgg1uJ2Ri89hw+G+aKYe1t1BMs1ToamwDKZDKsWrUK3t7e6NevX7ltNm7ciGvXriEqKgrW1tbIyclB27Zt8dlnn+Grr74CAGzbtq3CPvLy8jB58mTEx8fD1NQUV69eRUBAAK5fv14t74mIiOh5lNURXnzwJh5n/HuvX6N/9gH0sKuPWTvDEXwnBe/v+hsXYlKwxM8VhnoyNUZNtYHGJoANGzZEw4YNK22zd+9eDBw4ENbW1gAAY2NjjB49Gtu2bZMngJXR19eHvr4+Nm3ahPbt22Pfvn3ya5WnoKAABQX/PpGVmZkJACgqKkJRUZFS+7Jj5Z0jRRwr1XGsVMexUh3HSnU1PVa9Wlrh1eY+uHIvDU+yCtDQRB8dm9WXl5L7ebwHvj1zB2vPxGLP1QcIu5+GNaPc0Nxa/UvCmvq90rR41EEiCILGbyDUr18/WFlZYevWrQrHra2tMW3aNCxcuFB+7Oeff8bEiRORm5sLQ8OqC2mHhobi66+/xuPHj9GiRQt8/PHHsLEpfwp90aJFWLx4sdLx7du3K9x3SEREVNNuZ0iw+bYUmUUS6EoFvOZQCq8GAgQAsZkSZBYBprqAk6mAf3JHrZWbm4uxY8ciIyMDpqam6g5HLTR2BlAV2dnZMDMzUzhmbm4OAMjJyVEpAfTw8MCWLVtU6m/+/PmYPXu2/HVmZiZsbW3Rp0+fcr9ARUVFOHHiBHx9faGry6e0KsOxUh3HSnUcK9VxrFSnyWPln12AD36LwPnYFOyIlSG22Bz3UvOQ+Mx+go1M9fHpgFbo26biFS+xaOpYla3gabNanQDWq1cPGRkZCsfKNnM2NjYWvb+yJeP/0tXVrfSLXdV5+hfHSnUcK9VxrFTHsVKdJo5Vo/q62DLJCxv+isWXx27h0r10pTaJmQWYsfNvbPD3qLFawpo2VpoUi7rU6n0AW7Zsidu3byscu337Nuzs7FSa/SMiIqprpFIJ3unuBAtjvXLPs4wcAbU8ARwxYgQOHz6MJ0+eAHi67Ltz506MGDFCzZERERGpz6W4VKTkFFZ4nmXkSKOXgJcsWYLS0lLExMTg0aNHWLRoEUxNTeX34b3zzjvYu3cvunTpgoEDB+LMmTMwMDDAp59+qubIiYiI1Idl5KgqGp0AlvH39y/3uL6+Pk6dOoX9+/fj1q1bmDNnDoYPH84ncomISKupWkauoYnyfe2kHTQ6Afzf//5XZRsdHR0u+RIRET1D1TJym4PvwqWJGcwM+VCEtqnV9wASERGRsrIycsDTsnHPksjbAH9EJGLQ2iD8HZ9ek+GRBmACSEREVAeVlZFrZKa4HNzIzAAb/T2wb2pX2FoYIj41D69tvIAfz8WhFtSGIJFo9BIwERERvbh+ro3h69IIl+JS8SQrHw1NDODpYCEvI3dohg8+2nsNf0Qk4P8O3URwbAq+HNkO5kblbyFDdQdnAImIiOowmVQCbydL+Lk3hbeTpTz5AwAzQ118+4YHlvi1gZ5MipORiRi45hyu3ksDAJSUCgiOTcH+8IcIjk3hvoF1CGcAiYiItJhEIsE4b3t42NXH9O2huJeSi1HfBWOIWxNciE1BQua/W8U0NjPAwsEuNVZBhKoPZwCJiIgIrk3NcGhGNwxq1xjFpQL2hT1USP4AICEjH1O3huJoxGM1RUliYQJIREREAAATA12sHuUOU4Pyt4VhGbm6gwkgERERyV2+m4bM/KIKz7OMXN3ABJCIiIjkWEZOOzABJCIiIjnVy8ip1o40ExNAIiIikisrI/ffCiL/FXwnmfcB1mJMAImIiEhOlTJyALDmzxj4/xCCJ5lcCq6NmAASERGRgqrKyK163Q1GejIE30nBgDVBCLqdpKZI6UVxI2giIiJSUlUZuXY25nh3eyiiErIw7qdLmP6qM97r3Rw6Ms4t1Qb8lIiIiKhclZWRc25YD79P74qxXnYQBGDd6RiM3RSCxxl5AJ6WkQuJS8XVZAlC4lJ5v6CG4QwgERERvRADXRk+H9YWnR0t8fG+67h0NxUDvgnCWC877At9iMcZ+QBk2Hz7CsvIaRjOABIREdFLGeLWBAdndEObJqZIyy3C+tOx/yR//2IZOc3CBJCIiIhemoOVMXa/7Q0jPVm551lGTrMwASQiIiJRXHuQgdzCkgrPs4yc5mACSERERKJgGbnagwkgERERiYJl5GoPJoBEREQkClXKyEkApOUU1FRIVAEmgERERCSKysrIlREATNsehoX7I1BQXPH9glS9mAASERGRaCoqI9fYzADrxrbH290dAQC/Bt/DiA0XcDc5Rx1haj1uBE1ERESiKisjFxzzBMeDQtDHxwvezg0hk0owqF0TdHawxOzd4Yh4mIlBa89h2fC2GOzWRN1haxXOABIREZHoZFIJvBws0MFKgNczNYQBoEerhjgyywed7Osju6AYM3aE4ePA68gverokXFIqIDg2BfvDHyI4NoX7BlYDzgASERFRjWtsZogdUzrj65PR+PZMLLaH3EfovTSM9rTFd3/dUagkwjJy4uMMIBEREamFjkyKOX1b4dcJnrA01kNUQhYWHbjJMnI1gAkgERERqdUrLRrg0Ixu0JOV/+wwy8iJjwkgERERqd3dlFwUllSc3LGMnLiYABIREZHasYxczWICSERERGrHMnI1iwkgERERqV1VZeQkePo0sKeDRU2GVWcxASQiIiK1q6yMXNnrhYNdFPYTpBfHBJCIiIg0QkVl5BqZGWCDvwf3ARQRN4ImIiIijVFWRu5SXCqeZOWjocnTZV/O/ImLCSARERFpFJlUAm8nS3WHUadxCZiIiIhIyzABJCIiItIyTACJiIiItAwTQCIiIiItwwSQiIiISMswASQiIiLSMkwAiYiIiLQME0AiIiIiLcMEkIiIiEjLsBLISxAEAQCQmZlZ7vmioiLk5uYiMzMTurq6NRlarcOxUh3HSnUcK9VxrFTHsVKdpo5V2e/tst/j2ogJ4EvIysoCANja2qo5EiIiInpeWVlZMDMzU3cYaiERtDn9fUmlpaV49OgRTExMIJEoF6nOzMyEra0t4uPjYWpqqoYIaw+Oleo4VqrjWKmOY6U6jpXqNHWsBEFAVlYWmjRpAqlUO++G4wzgS5BKpbCxsamynampqUZ98TUZx0p1HCvVcaxUx7FSHcdKdZo4Vto681dGO9NeIiIiIi3GBJCIiIhIyzABrEb6+vpYuHAh9PX11R2KxuNYqY5jpTqOleo4VqrjWKmOY6W5+BAIERERkZbhDCARERGRlmECSERERKRlmAASERERaRnuA1gNcnJysHv3bty9exfOzs54/fXXeQNsOW7evInNmzcrHf/44481br8odcjKysL27dsRFxeH999/H9bW1kptEhISsGfPHqSmpqJjx44YOHCgGiJVv8LCQuzduxd///03/P394erqqnD++PHjOHXqlMIxExMTfPLJJzUZpka4desW/vzzT2RkZKBdu3YYMGCA0kb2RUVF+O233xAVFQVbW1uMGjUKJiYmaopYfR4+fIg//vgDCQkJaNGiBYYNG6ZQziw+Ph7r169X+rkZM2agadOmNRmq2hUVFeHw4cO4fv06LCws0L9/fzg6Oiq1O3fuHE6fPg1DQ0MMHToUzs7OaoiWAM4Aii4tLQ2dOnXC2rVrkZ+fj+XLl6Nr167IyclRd2gaJzo6Gl9//TXMzc0V/iuvqoq2+eabb9CyZUscPHgQK1asQFJSklKb69evw8XFBUeOHEFmZiYmT54Mf39/NUSrXoGBgXB0dMRvv/2GFStWICoqSqnN2bNnsXv3boXvmTZuAvv+++9j+PDhuHHjBjIzMzFt2jR0794dBQUF8jYFBQXo0aMHFi1ahPz8fGzatAnu7u5ITExUY+Q1b/Xq1ejevTsuXryI/Px8LF26FK6urkhOTpa3efjwIVasWAEjIyOF75ZMJlNj5DXv/v37cHd3x/bt21FcXIzz58+jdevW+OmnnxTaLVq0CAMGDEBSUhKuXr0KV1dXHDt2TE1REwQS1Zw5cwQHBwchOztbEARBSElJEaysrITPP/9czZFpnsDAQMHY2FjdYWik4OBgITMzUwgLCxMACNevX1dq06NHD2HgwIHy16GhoQIA4fjx4zUZqtqFh4cLiYmJQl5engBA2LNnj1KbTz75ROjevXvNB6dhLl68KJSWlspfP378WDA0NBQ2btwoP/bNN98I5ubmwpMnTwRBEIS8vDyhZcuWwrRp02o8XnW6cuWKUFBQIH+dm5srNGvWTPjwww/lx4KDgwUAQlZWljpC1BhPnjwRHj16pHDsgw8+EJo1ayZ/HR0dLUilUmHfvn3yY9OmTRPs7e0VvpNUczgDKLJ9+/bhtddeg7GxMQDAwsICfn5+2Ldvn5oj00zFxcVYuXIlli1bhkOHDqG0tFTdIWmEzp07V7rklpaWhjNnzmDcuHHyY+3bt4ebm5vWfdfc3NzQsGHDKtslJCRg6dKlWLVqFS5cuFADkWkeLy8vhRn2Ro0aoUmTJoiPj5cf27dvH/r3748GDRoAAAwMDDB69Git+1516NABenp68teGhoZo1aqVwliVWbt2LZYuXYq9e/eiqKioJsPUCA0aNEDjxo0VjhUXFyv8HbZ//36YmZlhyJAh8mMTJkzA3bt3ERoaWmOx0r+YAIqouLgYd+7cUbqnwdnZGdHR0WqKSrM1btwYDx8+RGJiIqZMmcLlchXdvn0bgiDwu/YcjI2NkZ2djcjISPTu3RsTJkxQd0hqd/HiRcTGxqJr167yY9HR0eV+rxISEpCVlVXTIWqM+/fv4+zZswpjBTz9Oyw+Ph7p6en48MMP0b59ezx58kRNUarX999/jzlz5sDPzw8XL15UuMc7Ojoa9vb2CsvjZd8z/p2lHkwARZSXlwdBEJQeYDAzM2NSU45OnTohMjISq1evxurVq3Ht2jXcuXMH//d//6fu0DRe2feJ3zXVTJgwAVevXsXy5cuxadMmnDlzBlu2bMFvv/2m7tDUJiEhAaNHj8bw4cPRv39/+fGcnJxyv1dl57RRbm4uXnvtNbRp0wZvv/22/LiTkxOioqLw7bff4ssvv0RERAQKCgowd+5cNUarPvXq1YOpqSn09PRw7949xMXFyc/xe6V5+BSwiIyMjCCVSpGRkaFwPD09HfXq1VNTVJrrv0/JNWjQAIMHD8bZs2fVFFHtUfZ94ndNNU5OTgqvPT094erqirNnz+K1115TU1Tqk5SUhN69e8PJyQlbt25VOFevXr1yv1dl57RNXl4ehgwZgtzcXJw+fVphWbhsmbyMsbExRo0ahe3bt9d0mBph7Nix8j+vXLkS48ePh6+vL0xMTPi90kCcARSRTCZD8+bNcevWLYXjt27dQuvWrdUUVe1SUlKC/Px8dYeh8Vq0aAGpVMrv2kvQ1u9acnIyevXqhYYNG+LgwYMwNDRUON+6detyv1c2NjZa94s6Pz8ffn5+ePToEU6dOqWU8JVHW79X/9WtWzdkZ2fj3r17AJ5+r+Li4hTukSz7nvHvLPVgAiiykSNHYs+ePfJ/2SQmJuLAgQMYOXKkegPTQOfPn4fwTCnq+Ph47N+/H7169VJjVLWDmZkZ+vTpg59++kn+4MyFCxdw48YNrZzRqsq5c+cUXp8+fRo3btzQuu9aSkoKevXqBSsrKxw6dAhGRkZKbUaOHImjR4/iwYMHAIDs7Gzs2LFD6/4OKygogJ+fHx4+fIjTp0+X+6DRxYsXUVxcLH+dmpqK7du3a933KiwsDLm5uQrHDhw4ABMTE/legEOHDpXvkVvm+++/R4sWLdCuXbsajZeekgjP/gaml5aVlYUePXogOzsb3bt3x4kTJ2Bra4tjx47BwMBA3eFplIULF+L333+Hl5cXioqK5H/evXu31m8EHRQUhMOHD+PJkyf4+eefMWnSJFhZWcHPzw/e3t4Ant443b17dzg6OqJ169bYt28fxowZU+7GtHVZVFQUfvnlF5SUlODLL7/E0KFD0bJlS3Tp0kX+xKGfnx9SUlLg5uaGJ0+e4ODBg5g8eTLWrl2rVftO9u7dG3/99RemTp2qkPx16NBBnuAVFRVh8ODBuHnzJvr3749z585BKpXir7/+goWFhbpCr3HvvPMOvvvuO0yYMEEh+bO3t8c777wDAFi3bh02bNgALy8vSKVSHDp0CA4ODggMDESjRo3UFXqN+/333/Hxxx+jffv2sLS0RFhYGG7cuIHvv/9e4R+kX331Ff73v/9hxIgRSEpKwrlz53D48GG88soraoxeezEBrAaFhYU4dOgQ7t27BycnJwwcOFDrNgZVVWxsLP766y+UlpbC1dUVnTt3VndIGuHSpUtKlSsAoE+fPvDw8JC/Tk9Px4EDB+SVQLp161aTYWqE2NhY7NmzR+l4hw4d4OvrK3995coVXL58GfXq1YOnpydatmxZk2FqhE2bNiElJUXpeNu2bRWqyJSWluLo0aPypd/Bgwdr3T9gf/vtN8TExCgdt7W1xRtvvCF//eDBA5w6dQp5eXlo3bq11iYzqampOHnyJBITE2FjY4PevXuXu5XVtWvXcObMGRgaGmLQoEFK28dQzWECSERERKRleA8gERERkZZhAkhERESkZZgAEhEREWkZJoBEREREWoYJIBEREZGWYQJIREREpGWYABIRERFpGSaARFTr3b9/H/7+/sjOzlZ3KNUuOjoa/v7+CjVViYieFxNAIlJZcnIy/P39ERkZCQCIi4uDv7+/Uh3Q6lRen6mpqdi2bRvy8/Orte+y9z9jxgz8dw/95cuX4+eff67W/gHgyZMn2LZtG0pKSqq9LyKqu5gAEpHKsrOzsW3bNiQmJgIAUlJSsG3bNhQWFtZYDOX12axZM2zZsqXc0lNiKnv/69atw86dOxXOnTx5EiEhIdXaPxGRWJgAEtELSU5Oxv/+9z8AwNtvvw1/f3+sX78ewNNasrt378bUqVPx3nvvITAwUOFny5YxHz16hEWLFiEgIACRkZHIyMiAv78//P39MWHCBCxZsgR3796tss+srCwcPXpUYVk0Ly8PGzZswOTJkzF79mxcuHCh3BgSEhKwcuVKvPPOO1i1apVKs4i9e/fGJ598UmHie/XqVUyePFnh2OPHj+Hv74+0tDSF/uPi4vDFF1/grbfekvcfHx+PhQsX4q233sLPP/+sNNsIPJ0JXL58Od566y188803KCgoUDj/op8BEWkHJoBE9EIMDQ3h7e0NAOjVqxf69esHNzc3lJaWYvjw4Vi+fDlatWoFe3t7zJkzB9OnT5f/bNkyZrdu3VBcXIxevXrBwsIC+vr66NevH/r16wcfHx/cv38frq6u8sSkoj7/uwRcUlKCnj17Yv369Wjbti0kEgleffVVbNu2TSmG7t27Izs7G+3atcOmTZvw+uuvV/ne586di6ysLGzYsKHc8/Hx8UozhBkZGdi2bRtycnIU+u/Vqxfy8/Ph6uqKlStXYuDAgejduzd0dXXRunVrzJ07F8uXL1fqo0uXLkhPT4eLiwvWrl2LYcOGyc+9zGdARFpCICJSUVxcnABAOH36tCAIgnD58mUBgJCWliZvs3XrVsHW1lbIyclR+DmpVCrcunVLEARBCAoKEgAImzdvrrLPcePGCZMmTZK/Lq/PsLAwAYCQlJQkCIIg/Pzzz0K9evXkrwVBEJYuXSpYW1sL+fn5CjHs27dP3qbsWEpKSqXvPzg4WFi9erVgZWUlZGRkCIIgCL169RLefvttQRAEITAwUDA2Nlb42cjISAGAEB8fr9BXYGCgvM2GDRsEAMLRo0flx1auXCm0atVKKcavvvpKfuzOnTuCTCYTjh8/LgiC+J8BEdU9OmrJOomozjpy5AikUimmTZsGQRDk/+no6ODatWto0aKFvG2fPn2Ufv7OnTvYvn077t27h7y8PNy8eRPGxsbPFcPZs2fRs2dPWFlZyY+NHj0an376KaKjo9G2bVv58R49esj/XBbbw4cPq5wNmzp1Kr755ht88cUXWLp06XPF96xXX31V/mdHR0cAQPfu3RWOPXr0SOnnhg8fLv+zg4MDPDw8EBQUBF9f35f+DIio7mMCSESiSk1NhY2NDXr37q1wvG/fvvDw8FA4ZmZmpvD6ypUr8PHxwejRo9GpUyeYmpqiuLgYUVFRzxVDcnIyLC0tFY6VvU5KSlI4bmBgIP+zVPr0rhhVnrDV09PD0qVLMWXKFEybNu254quq//8eKy+e+vXrK7y2sLBAcnIygJf7DIhIOzABJKIXJpFIlI7Z2triypUr8Pf3f+7rbd68GX379lXYTuW/D2+U1+d/2dnZISIiQuFYXFwcgKdPDItlzJgx+PLLL7Fo0SKF4/r6+igqKoIgCPJ4U1NTResXAO7du4d27drJX9+9e1c+m/gynwERaQc+BEJEL6xsVi0lJUV+bNy4cQgPD8cvv/yi0DYwMLDKjZplMpnCte7cuaPw4EZFff7XqFGjEBQUhIsXLwIABEHAF198gY4dO8qXWcUgkUiwYsUK/PTTT4iNjZUfb9GiBQoLCxX637Rpk2j9AsCqVavkfz548CBiYmLkD4K8zGdARNqBM4BE9MKaNWuGTp06YfDgwWjfvj26dOmC6dOnY/369Zg+fTo2bNiAxo0bIyIiAu7u7hgwYECl15s2bRq6du0KDw8PNG3aFMHBwWjVqpXCFifl9dm1a1eF6/j4+ODDDz9E79698corr+DBgwdITk7GkSNHVJpBfB6+vr7o0aMHTp48KT/m5OSEKVOmoH///ujRowdiYmJga2srar+PHj1C+/btYW1tjTNnzmDhwoVo2bIlAKBbt24v/BkQkXaQCEI5G0wREZUjJycHgYGB8PX1hbW1NQCgsLAQ586dQ0JCAuzs7NCtWzcAQFpaGoKDg1FUVAQ3NzfY29vLr5OUlIRjx45h7Nix8vveyqSnp+P8+fMoKiqCl5cX0tPTERcXp5C4/LfPNm3a4PDhwxg5ciT09fXl7WJjYxEWFgYTExP4+PjAyMio0hgKCgqwZ88eDBw4UOkeu2fff79+/RQeMImLi8P58+fRokULeHp6yo9fuXIFDx48gIuLCxo1aoQDBw5g+PDhMDIyKrf/hIQEnDx5UmHp9sGDBzh//jxGjRqlEPfo0aMRERGB2NhYuLi4oHXr1krxvuhnQER1HxNAIiIiIi3Df/YRERERaRkmgERERERahgkgERERkZZhAkhERESkZZgAEhEREWkZJoBEREREWoYJIBEREZGWYQJIREREpGWYABIRERFpGSaARERERFqGCSARERGRlvl/G8yQw8k+dPUAAAAASUVORK5CYII=", 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