{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Taylor Approximations\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demmath01.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2021-Oct-01\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from compecon.tools import nodeunif\n", "from matplotlib import cm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Univariate Taylor approximation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the function \n", "$$f(x) = (x+1)\\exp(2x) $$\n", "\n", "the first-order Taylor approximation is\n", "$$\\hat{f}(x) = 1+3x $$\n", "\n", "and the second-order approximation is \n", "$$\\hat{f}(x) = 1+3x + 8x^2 $$\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": "
", "image/png": "iVBORw0KGgoAAAANSUhEUgAAAecAAAE3CAYAAACQM4l7AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAABflklEQVR4nO3dd3hT1RvA8W+S7l1WkT1llY2AijJl7ynIBtl7KA5UQLYKQtl7oyBDxMEPEUEBhYKyN7JbRnfTpm2S3x9pbxu6IW3S9v08T5/mnnuT8+YS8vbce4bKaDQaEUIIIYTNUFs7ACGEEEKYk+QshBBC2BhJzkIIIYSNkeQshBBC2BhJzkIIIYSNkeQshBBC2Bg7aweQwGAwoNfLqC4hhBB5h729JsVym0nOer2RkBCttcMQQgghsk3Bgu4plj9Xcv7444+5ffs2mzZtMivv2rUr586dS3Z8ixYtWLRo0fNUJYQQQuQ5mU7OO3bsYMeOHdStW9es3Gg0cuPGDZo1a0bz5s3N9hUtWvTFohRCCCHykAwnZ71ez7Jly/Dz80tx/71799BqtTRt2pQOHTpYLEAhhBAir8lQctbpdHTr1o0rV67QsWNHjh8/nuyY69evA1C2bFnLRiiEEELkMRkaSqXT6YiIiGDBggXMnTsXO7vkOf3atWtAYnLWaqVzlxBCCPE8MtRydnNz48CBAykm5QTXrl3D1dWV2bNn8+OPP6LVailevDjjx4+nTZs2FgtYCCGEyO0ylJzVajVqddqN7OvXrxMZGUl4eDjz5s0jLCyMjRs3MmHCBGJjY+nYsaMl4hVCCCFyPYuNc+7evTsGg4F33nlHKWvTpg1t27Zl/vz5tGvXDo0m5cHWQgghhEhksek7e/bsaZaYAZycnOjQoQNPnjxROowJIYQQOY3BYCAqKirb6svyubXz5csHSAcxIYQQOVN0dDQdO7amZEkfNm1any11WiQ5BwYG0qZNmxTHQN+6dQuAYsWKWaIqIYQQIlv98MNeTpw4BsAvv/yYLXVaJDn7+PgQHh7Ojh07iIiIUMofPnzIrl27qFevHgULFrREVUIIIUS22rZts/K4Tp26aRxpORbrEPbJJ58wcuRI3n77bbp160ZkZCRbtmzBzs6OTz/91FLVCCGEENnm9u3/OHr0d8A0cql7957ZUq/F7jk3a9aMJUuW4OzszBdffMG6deuoUaMG27Ztk1nDhBBC5EjffLNVedy4cVOKFMmetSJURqPRJhZRjo3Vy5KRSaxZs4J161alecy6dVsoX75CNkVkLjg4CCcnZ5ydnQGYOfMzfvrpB/7445RV4hFCCEszGAzUqVOVe/fuArBmzUbateto0TosumSkyD59+gygVKnSKe7z8Xkpm6MxOX78T6ZN+5h167YoyblDh87Zdi9GCCGyw9GjvyuJ2dvbm+bNW2Vb3ZKcbdwrr9SjVq061g7DzMWL54mICDcr8/Wthq9vNStFJIQQlrdt2yblcdeuPXB0dMy2urN8nLMQQgiR04SEBLN//z5lu2fPPtlav7Scc7iuXdtRuPBL+PmtTLO8a9d21Kv3KtWq1WDTpvU8eHCPQoV86NatJ126dDd77oUL51m3biXnz59DrVZTpYovw4aNpmzZcsq9ZYBu3dpTo0Yt/PxWpnjPOSDgIatWLeWvv47HL4RSki5dutO+fSflmJkzP+PChXNMnTqdJUu+5tKlC7i4uNK06VsMHz4aR0enrDp1QgiRql27dqLT6QCoVq0Gvr5Vs7V+Sc42LjIygpCQkGTlbm5uaa4SlpITJ45x6NBBunbtQb58+dm7dxcLFsyjSJEivPpqAwD+/fcM48aNIH/+AvTq1QdHR0d27NjO6NFDWbNmEx06dCYyMpIjR35jzJgJlC5dJsW6Hjy4z5Ah/YmJiaFLl+7kz5+f33//jXnzZnLv3h1GjBirHBscHMz48aNo0qQZzZu34sSJY+zc+Q0ODg5mxwkhRHbZvj1xbHPPnr2zvX5Jzjbugw8mpVi+aNHyTN+LfvQokHXrtlKuXHkA3nyzER07tuLAgZ+V5OzntxAPD0/WrNmEp6cXAK++2oDevbuxe/cORowYS9my5Thy5DfeeKMRL71UJMW6VqzwIywslFWrNlKhQkUAOnfuzpQpE9m2bTMtW7alTBnTELvw8DDGjZtE165vA9C+fSd69+7GgQM/S3IWQmS7CxfO888/ZwBwdHSkc+eu2R5DrkjOS5cuZv782URGRqR/cDZxdXVj8uQPGDFi9Au9zsiR45RkmlS5ci9n+rVKlChp9lr58xcgX758BAU9BUzDoy5fvkiPHu8oiTnheatXb8THp3CG6tHr9Rw79id169ZXEjOYBvD37TuQY8eO8uefR5TkDNCkyVtmr1G2bHkOH/410+9RCCFe1KZN65THrVq1wds7X7bHkCuS87Jli20qMYPpcvSyZYtfODlXqFDRYr21vby8k5XZ2zug1+sB0z1io9FIsWLFkx338ssVk5WlJjQ0hKgoLSVKlEy2L2FYWEDAwzRjc3BIjEsIIbJLZGQkO3Z8o2z36TPAKnHkit7aw4ePxtXVzdphmHF1dWP48BdLzC/CYDAkK1OpVGk+R683PUetfrGPRVrz2iTEZW9vb1b+onUKIYQlfP/9bsLDwwAoXboMDRq8aZU4ckXLecSI0S/cQs2p1Go1sbGxZmVxcXGEhIRkepq5woVNl60TBt0ntXTpItzdPejTp3+6r+Pl5Y2zszO3b99Otu/OHVNZoUI+mYpNCCGyw8aNa5XHffoMSLdRk1WkuZLD5c+fnzt3bqPTRStlf/55hJgYXaZfq0CBgpQr9zIHD/5idpvgwYP77Ny5neBg071pjUYDpNw6T9hfr95rnDx5gitXLivlRqORLVs2oFKplA5oQghhK86fP4e/v2k4qIODA2+//Y7VYskVLee8rFmzFixYMJ+JE8fQvHkr7t27y/ff76Zw4eeb2nPMmAlMmDCKwYP70q5dR1QqNd999w1ubu68804/ALy8vADT7Dn1679GgwYNk73O8OGjOX36FKNHD6VLl+4UKFCAI0cO4+9/kh493kl1CJYQQlhL0o5gbdq0o0CBAlaLRZJzDtepUzfCwsLYt28PCxfOp2zZ8syaNZ/t2zej1WZ+IZFateqwaNFyZeENR0dHqlevyYgRY8mf3/RBbdq0BYcPH+LHH/dx5ox/ism5aNFirFy5nlWrlrJ37y50umhKlizNlClTadu2wwu/byGEsKTIyEh27vxW2bZWR7AEsiqVEEKIPG/r1k2MGzcSgDJlynL8+Olsud+c2qpUcs9ZCCFEnmcrHcESSHIWQgiRp507d5bTp/0B63cESyDJWQghRJ62fv1q5XGbNu3Inz+/FaMxkeQshBAizwoJCWbnzsQZwQYMGGLFaBJJchZCCJFnbdu2haioKACqVKlKvXr1rRyRiSRnIYQQeZLBYGDdulXK9sCB71q9I1gCSc5CCCHypN9+O8h//90CwNPTi86du1k5okSSnIUQQuRJa9asVB737NkbV1dXK0ZjTpKzEEKIPOfmzRv8+uv/ANOKff37D7JyROYkOQshhMhz1q9foyxv26RJM8qUKWvliMxJchZCCJGnaLVatm3brGwPGmQbw6eSkuQshBAiT/nuu28JDQ0BoGTJUjRp8pZ1A0qBJOccYu7czxk16vn/utNqIwkODrZgRBk3c+ZnNGhQxyp15wZr1qygQYM6PHz4IFvrjY2N5fHjR8r2jz/uo0GDOpw+fSpb4xDCkoxGIytXLlW2Bwx4F7Xa9lKh7UUkkvnhhz3s27fnuZ9/+fIlevXqyq1bNywXlMg2DRs2YerU6Xh5eWdbnQEBD+nbtwcnT/6llFWvXpOpU6dTqlTpbItDCEv77bdfuXLlMgCurm707t3XyhGlTNZztmF6vZ6NG9eydu3K9A9Ow82b13ny5LGFohLZrVy58pQrVz5b63zw4D53794xKytatBhFixbL1jiEsLQVK5Yoj3v16o2Hh6cVo0mdJGcbpdPpGDKkPzduXKNlyzb4+5+0dkhCCJGjXb58id9++xUwDZ8aPHiYlSNKnVzWtlExMTFotZFMmzabjz+ehkajSfG4sLAwZs78jM6d29C48at0796B5cv90Ol0gOl+5axZ0wAYM2YYXbu2S7PegICHzJgxlbZtm9GkyWv069eT77/fbXbMzJmf0atXF3bt2kHLlo1p2bIxJ04cA0wf/vHjR/LWW2/SsWMrduzYnmI9jx4FMmPGJ0o9Awb04sCBnzJcT0r8/U8yceIYWrduSsOG9ejYsRXz5s0kPDzc7DV79OjI+fNnGTSoD02avE6vXl3Ys2dnsrozelxqMaZ3Lp88eUKrVk3o1q090dHRSvmBAz/ToEEdli/3A5Lfc16zZgVvvfUGt27dZNy4ETRr1oCOHVuxZcsGjEYjW7duokuXtjRv3pAJE0Ynu1ed3nn68cd9jBlj+tKaNWua0l8gpXvO0dHRLF/uR9eu7WjUqD5du7Zj2bLFZu8n4XnXrl3ls88+omXLxrz11pt88MGkbL+PLvK2pPeaW7VqS+nSZawYTdqk5WyjXF1d2bZtF3Z2af8TffLJFK5du0K3bj3Jn78A58+fZfPm9YSGhvL++x/RsGETnj59wvff76ZPnwFUqlQl1dd68OA+Q4b0JyYmhi5dupM/f35+//035s2byb17dxgxYqxybGBgAOvWrWLgwCE8efKYypV9uXnzBqNHD8Hd3YP+/QcRGxvL+vWr0Ov1ZvU8efKYIUP6YzQa6dr1bdzd3Tl69HemT5/KkyeP6dWrb5r1pOTvv08wadIYqlatzqBBQ1Gr1fz99wm+/343cXFxfPjhp8qxoaGhTJw4mvr1X6d167b8/vtvfPHFHMLDw+nTZ0Cmj0spxoycywIFCjB69HhmzZrG+vWrGTZsFEFBT1m4cD5ly5Zn0KChqf5bxcbGMnbscN58sxGNGjVh//7vWbZsMf7+pwgIeECPHr0ICQlhy5YNzJo1jcWLV2T4PFWvXpM+fQawadM62rfvRPXqNVONYfz4EZw/f47WrdtRsWJlLl48z5YtGzh79h8WL15h9vmdMmUCpUqVYejQkdy/f48dO7bx5MkjVq3amOr7FMJSnjx5YtZYGDZspBWjSZ8kZxulVqvT7UEYHBzEqVN/M2LEWHr16gNAu3YdMRqNPHhwHzDdr/T1rcb33+/mlVfqUatW6r2mV6zwIywslFWrNlKhQkUAOnfuzpQpE9m2bTMtW7ZVBurrdDomTpxC69aJLfF58z4HVCxbtgYfn8IANG7cjAEDej1TzxJiYmLYuPEbChQoAECXLj2YNu1jVq9eTqtWbfH2zpdqPSn55putFCrkw8KFS7G3twegU6euDB06gMOHD5kl54iIcLp168nYsRMB6NixK2PHDmf9+tV06NAFDw+PTB2XUoxffjk7Q+eydet2HDr0P7Zv30yrVm1ZsWIJUVFapk6drryPlMTFxdG8eStGjRoHQPXqtejTpzvnz5/lm2/24O1t6jwWEPCQ//3vZ2JiYnBwcMjQeSpatBivvFKPTZvW4etbjRYtWqcYw/79ezl37ixjxkyge/deymuVLl2GpUsXsW/fHjp16qocX7FiJWbOnK9sR0dHsWfPd9y9e4fixUuk+e8rxIvasGGNckWxevWa1Kv3qpUjSluuuKy9dKk9pUu7UaiQu838lC7txtKlqX+5WoKrqxvOzi7s3r2Tw4d/VZY9+/DDT/n666XpPNucXq/n2LE/qVu3vpJMwPRHQt++AzEajfz55xGz59Stm/jhNhgM/PXXCV599XUlMYNpDGHduvXNjjt69DDVq9fEzs6OkJAQ5adhw8bExMSY9RB+tp7UzJu3gDVrNpkltNDQEFxdXYmK0iY7vk+f/spjjUZDt25vo9PpOHXq7+c6LmmMmT2Xkyd/iKOjI5Mnj+XIkd8YNGhohjqAvflmI+VxQnKrWrW6kpgBXnqpCEajkaCgICDz5yktf/xxBFdXVzp37m5W3q1bT1xdXTl69LBZ+bNjScuVexmAoKCnmapXiMzS6XSsXZu4+tTQoSNsZvWp1OSKlvOyZQ5ERtrWiY6MVLFsmQMjRsRmWR0ODg5Mnvwh8+Z9zscfv4+DgwM1atSiYcMmtGzZBkdHxwy/VmhoCFFRWkqUKJlsX8LQmYCAh2blSZNAaGgoUVHaFHvzlihRCjii1BMREcHRo4eTfXknCAwMSLWe1Gg0Gh48uM+qVcv577+b3L9/z2yMblIeHp7ky5ffrKxYMVNyCwh4kOnjno0xs+fSx6cw7747nIULv6B06TJml/XTkjS2hMvHz56rhKsvRqMByNx5Ss/Dhw8oUqRoslsv9vb2FClSNNnn5dmhYA4ODgDJbnsIYWm7d+9UPucvvVSE9u07Zf5FYmJQP3mMoUhRC0eXslyRnIcPj2H+fEebStCurkaGD4/J8nqaN29J/fqvcuTIYY4f/4NTp/7m779PsHv3TlauXK98AaYnYY7ZlBgMpi/2Zy+zJu2klvBXaEyMLs3X1utNr9WoUVM6dOicYn1Fnvnwp9YZLqk9e77jiy9mU6JESapXr0nDhk2oXNmX7777JllHM3v75B97g8GUIJLeSsjocc/G+Dzn8t9//wHg7t073LhxnfLlX071NVKqM0F6rYHMnKf0pP0+jcneo623VETuZDAYWLp0kbI9aNCQDH8vJlA9eoRXp9bYXbtKxNTpRI0eZ+Eok8sVyXnEiNgsbaHaKq1Wy7VrVyldugxt23agbdsOxMbGsnTpInbs2Mbff5+gQYM3M/RaXl7eODs7c/v27WT77twxlRUq5JPq8z09PXF1dU02NhbgwYN7SerxwsnJCb0+jldeqWd2XEBAAFevXsbZ2TlDMSfQ6XT4+S2gVq06fPWVn1lLbvXqZcmODwoKQqvV4uLiopTdvXsXSGwZZ+a4Z2X2XP7++2/89ttBevfuz48/7mP27OmsXLk+3c6AmZXZ85SewoWLcOHCWeLi4sxeKzY2locPH1C9eg1LhC3ECzl48BcuX74EmG4F9u07IJ1nPMNgwGP0UOyuXQXA3v8kUZYOMgW54p5zXnXz5g1GjhzMDz/sVcrs7e15+eUKAGg0pn/exEubqbd0NBoN9eq9xsmTJ5TZcxKes2XLBlQqFa++2iDV56tUKt58szF//XWcmzevK+UPHz7g+PE/lW07Ozvq13+dY8f+4Fr8hz2Bn99XfPjhJEJCQjLw7hPpdDqio6MpXryEWZK4du0K//xzGjB1oEr6nnbt+lbZjouLY8eOrbi5uVGnTt1MH/eszJzLsLAwvvpqDmXKlGXw4GGMHDmWq1cvs3Wr5XswZ+Y8JbTKE1r6KXn99TeIjIw0O0cAu3fvQKuN5LXX3rD0WxAi0/z8vlYe9+nTP9Mz7Tkv88Mhfmw0QNSAwRaLLS25ouWcV1Wp4kv16jVZtWopjx4FULZseR49CmTnzm8oWbIUdeqYWqYJH8bdu3fy9OlTmjdvmeLrDR8+mtOnTzF69FC6dOlOgQIFOHLkMP7+J+nR4510xwQOHjyM48f/YPTooXTv3guNRsPOnd/g4uJCTEziJf6EekaNepfOnbvj41OYY8f+4Nixo3To0DnTS7d5eHhQubIv+/d/j6urKyVKlOTmzRvs27cXlcr0h4lWq1V6VwOsX7+agICHlC5dhkOHDnLu3FmmTJmKk5OT2Wtn9LjnPZeLFn1JUFAQM2bMxc7OjhYtWrN///esX7+aN95oZNFxmJk5TwmfGdOlbiMtW7ZN9nrt2nXk559/YPHiBdy4cZ2KFStz+fJFfvxxH5Ur+9KuXUeLxS7E8zh58i9l3gF7e/tMD5+yO+OP68zPlG3tqHHENmxsyRBTrztbahFZQqVSMXv2F6xdu4o//zzK99/vxt3dnUaNmjB48DDlnl+dOnVp0uQt/vzzCP7+J2nYsHGKncWKFi3GypXrWbVqKXv37kKni6ZkydJMmTKVtm07pBuPj09hli5dw9KlX7N160bs7R2UL+hNm9Ylq2f16uXs27cbrTaKIkWKMnr0eLp2ffu5zsWMGXNYvHgB+/d/T0xMLIULF6Z3736UKlWajz56j9OnT9KoUVPl+K++8uOLL2bz448/UKpUaWbOnE/DFP7TZfS4Z2XkXJ44cYyff95Pu3YdqVathvLciROn0L9/T2bPns6yZWue63ykJqPnqWTJUnTt2oMff/yBS5cuUrNm8iF4Dg4OfP31MtauXcWhQ//jwIGfKFiwEH36DKBfv4EWvywvRGYtXrxQedylS/dk/VnSogoPw2PIAFTxV5Nia9ch8oOplg4x9fqNaV3rzEaxsXpCQjI3lEOIzJo58zN++ukH/vgj7ZWVMnqcEMI2Xb16hQYNXlG2jx7922xoY5qMRtyHD8Jpl2lGQIO7B8GH/sBQspTF4yxY0D3FcrnnLIQQItdZsiTxXnOLFq0ynpgBp62blMQMEPHl11mSmNMiyVkIIUSu8uDBfXbu/EbZHjVqfIafq7l0EbcPJyvbUe/0Rdexi0XjywhJzkIIIXKVFSuWEhtrGl5bt2596tWrn84z4kVG4vFuP1Txsy3GVaxExMx5WRVmmuSesxBCiFzjyZMn1Knji1ZryiebNn1DixatMvRct7EjcN62GQCjszPBB35Hn4nL4c9D7jkLIYTI9VauXKok5sqVfVMdOvosx2+3KYkZIHzOl1memNMiyVkIIUSuEBISzOrVK5TtCRMmZ2jaWM21q7i/N0HZju72Nrq338mSGDNKkrMQQohcYdWq5UREhANQvvzLtGnTPv0nabV4DOqDShsJQFy58oTP/QqsPBe8JGchhBA5Xnh4GKtWJc4RP27cpAwtmuM+ZSJ28XNvG52cCFu1AdzcsizOjJLkLIQQIsdbt261Mi9/qVKl6dSpa7rPcdy2GaftW5TtiDlfoq/im1UhZookZyGEEDlaZGQky5YtVrbHjZuU7vSxmosXcH8/yX3mHr2I7tk7y2LMLEnOQgghcrSNG9fx9OlTAIoVK063bmnP0a+KCMdjcF9U0dEAxFWoSPicL61+nzkpSc5CCCFyLK1Wi5/fQmV79OjxyqI/KTIacRs/Grvr10ybLi6ErdkErq5ZHGnmSHK2YX/9dZwRIwbTtOnrvPXWG4wdO4Lz589ZtI6uXdsxatQQi75mTqg7Nxg1aghdu7bL9nqDg4OIikpcbn7mzM9o0CD5qlVCZIe1a1fx+PEjAIoUKUrPdC5NO69ejtPeXcp2+PyF6F+ukKUxPg9JzjbqzBl/Jk0aQ0REOEOGjGDAgHd58OAeo0cP4eLF89YOT9iAfv0GMmbMxGyt8/jxP+nZswshIcFKWYcOnZk6dXq2xiEEQEREOH5+C5Tt8eMnp7nWut3Jv3D99CNlO6rfIHTpXAK3Fllw1UYtWvQlhQr5sHLlBuXD1rJlG955pxsrVy5l4cKlVo5QWNsrr2RwvmALunjxvDKONIGvbzV8fatleyxCrFq1nKCgIABKlCiZZqtZ9fgxHoP7Ja7PXKMmEZ/PyZY4n4e0nG1QWFgY169fo0mTt8z+CsyXLz81atTi/PmzVoxOCCGsLzQ0hKVLE3toT5z4Pg4ODikfrNfjMWwQmocPADB4e5vuMzs6Zkeoz0VazjbI1dWVrVu/w9nZOdm+0NAQs4H1Xbu2o169V6lWrQabNq3nwYN7FCrkQ7duPenSpbvZc3/99QCbNq3nzp3bFC1alPHj38twTP/+e4a1a1dx8aLpnnelSlUYOHAINWrUMovllVfqYTAY+N//fsbT04u1a7fg7e2d4brPnz/L6tXLuXDBdOne17cq7747nMqVfTNUz7OMRiN7937H/v3f899//6HXx1G48Eu0bt2Od97pp0zt17VrO+rUqYuvb1U2bFhHcPBTypd/mXffHUGtWnXM6s7ocanFmN65PHHiGJMmjaFx42bMmJH4l/3cuTPZt283X3yxiPr1X2PUqCEEBDxk5859gOketIuLC+3adWT16hXcvXubIkWKMXLkWKpXr4Gf30J+++1XNBoNDRs2ZsyYCTg6OmX4PM2c+Rk//fQDAN26tadGjVr4+a1Uyv/445QSa0DAQ1atWspffx1Hq9VSvHhJunTpTvv2nZRjZs78jAsXzjF16nSWLPmaS5cu4OLiStOmbzF8+GglNiFSsnz5EkJDQwAoU6Zsmj20XebOxOHoYQCMKhXhS1dhKF4i64N8AdJytkEajYbixUtQoEBBs/Lr169x7ty/+PpWNys/ceIYCxd+QePGTRk9egJOTs4sWDCP48f/UI758cd9fPrphzg5OTFixGhq136F994bp1wSSssff/zO6NFDCQwMoF+/QfTrN4jAwADGjh3OH3/8bnbswYO/cO3aVcaMmUi7dh3x9vbOcN0nT55g1KghREZG8O67w+jXbyCBgQGMGjWEf/89k249KVm1ahlffDGHUqXKMHr0eIYMGYGDgyPLl/vx88/7n6n/L776ah6NGzdh8OBhBAcHM2HCKM6c8X+u41KKMSPnsn7912jVqi2//XaQv/46rpybfft207FjF+rXfy3Vf6srVy4za9Z0GjZszLBhowkNDeGTT6YwadJYAgIeMnToCOrUqcvevbvYsmVjps5Thw6defPNxgCMGTOBfv0GphjDgwf3GTy4L0ePHqFdu06MGDEGDw8P5s2bydKlX5sdGxwczPjxoyhRoiRjx06iatXq7Nz5DWvWrEjxtYUACAp6yooVibf2Jk2akuq4Zoef9uO68AtlWzt+MjFNm2d5jC/quVrOH3/8Mbdv32bTpk1m5Xfv3mXu3Ln8/fffADRq1IgpU6aQL1++F480j9NqtXz++acA9O7dz2zfo0eBrFu3lXLlygPw5puN6NixFQcO/MyrrzZAr9ezbNliKlWqjJ/fSuVD/PLLFZk1a1qa9cbFxfHVV/MoUKAga9ZsxNXVNK1dhw5d6Nu3B19+OZf69V9XXlOn0zFjxhyKFi0GkOG6DQYD8+fPplKlKvj5rVSuDnTp0oMBA3qxcOF81q3bqhz/bD2pxf7dd9/QtGlzPvroM6W8XbuOtGvXnMOHf6VVq7ZKeWBgALNmfcGbbzYCoEWLNvTs2Znly/1YsWJdpo97NsbMnMvRoyfw998nWLBgHitWrGPOnM8pWrQYI0eOS/Pf6+nTJ8ydu4DXX38DADs7O776ai56vZ6vvvJT6jt79h9OnjzBwIFDMnyefH2rUbZsOY4c+Y033mjESy8VSTGGFSv8CAsLZdWqjVSIX9Wnc+fuTJkykW3bNtOyZVvKlCkLmKZcHDduEl27mlo97dt3onfvbhw48DMjRoxN872KvGvp0sVK34cKFSqmOhuY5sY13EcNVbZjGjdFO/mDbInxRWW65bxjxw527NiRrDw4OJh+/frxzz//MHjwYAYMGMChQ4cYMGAAMTExFgk2Nc5LF5O/dBEKFvKwmZ/8pYvgnOR+yIuIjo5mypQJXL9+ld69+1OzZm2z/SVKlFQSM0D+/AXIly8fQUGmQflXr14mODiI1q3bm/112aJFa9zdPdKs++rVyzx6FEiXLt2VZALg7u5O587defz4EZcvX1TKixYtZpYwM1r31atXePDgPm+80Yjw8HBCQkIICQlBp9Px+utvcO3aVR49Cky1npTY2dnx/fcHeP/9j8zKQ0JCcHFxNRsOBFCyZCkl4QJ4e3vTsmVrLl48T3BwUKaPS+lcZPRcenh4MHnyB9y7d5d33+3H48eP+PjjaSne6kjKwcGRevVeVbaLx1+6e+ONhkqZSqWicOGXePLk6XOdp7To9XqOHfuTunXrK4kZQK1W07fvQIxGI3/+ecTsOU2avGW2XbZsebPzKERSgYEBZnNoT578QcpzaEdE4NH/HdThYQDoS5QkbNlqyMB827Ygwy1nUwtoGX5+finuX79+PQEBAezbt4+yZU1/FVevXp0BAwawZ88eunfvnuLzLMF52WLUkRFZ9vrPQx0ZgfOyxUSNGP1CrxMeHs57743j3Ll/adOmPUOGjEh2jJdX8ku69vYO6PV6AB4+fAiQLJlpNBqKFSueZv0P4ztQlChRMtm+UqVKAab7iwm9db29za+SZLTu+/fvAbB06dfJLn0mePQokEKFfFKsJzX29vYcP/4HR4/+zp07t7l37y7h8f9ZDQbDM++ndLLnFytWHKPRSEDAQ6XOjB6X/Fxk7lw2aNCQhg0b8/vvv9GxY1eqVq2e7HnP8vT0NPsjKOFL69lY1Go1RmPi+8/MeUpLaGgIUVHaVN5jaeU9JvXs59fBIfGzK8Sz5s+fo/zB6OtbjbZtOyQ/yGjEffwo7K5cNm06ORG2dhPGfPmzM9QXkqHkrNPp6NatG1euXKFjx44cP3482TH79++nbt26SmIGeO211yhdujT79+/P0uQcNXw0LvNn21SCNri6ETX8xRJzcHAQEyaM4tq1q7Rv34nJkz9McW3S9NYrTdgdE6NLts9oNKb53LT2GwymfUln41GrzS/GZLRug8H0ZTx48DCqVKmaYn0lSpRKtZ6UGI1Gpk+fysGDv1CtWg2qVq1Ghw6dqVGjFmPGDEt2vJ1d8lmFEhKTWq3J9HHPxpjZcxkVFcXVq1cB04Q0UVFR6bacU1uFJ63PSGbPU1rSfo+mc/Ts7E0Z+bcUAuDGjWts2bJB2f74489S/Pw4L/Mzn2hk3gLiqtXIjhAtJsPJOSIiggULFtC6dWuaNGlitj80NJS7d+/SokWLZM+tUqUKhw8ftkiwqYkaMfqFW6i2RquNVBJzjx69GD16QvpPSkWRIqZW6507d8zKTS29B5QqVSbV5xYubLqvePv2f7zxhvm+O3duAyit2RepO+H+pYuLC6+8Us/s2EuXLhAWFoZjJoc9/PvvGQ4e/IX+/QczeHBikomLiyMsLJQiRYqaHf/gwb1kr3H37l00Go3Z/dWMHveszJ7LFSv8CAh4wIgRY1m2bBErVvgxbtzkNN7x88nseUqLl5c3zs7O3L59O9m+jHxehEjLrFkzlKsqb7zRkMaNmyY7xv7333CdPlXZjuo/CN3b72RbjJaSoT9Z3dzcOHDgAK1bt05xf2Cg6V6gj0/y/3QFCxYkIiKC8PDwZPtE6r78ci7Xrl2lW7eeL5SYAV5+uQIvvVSEPXt2Eh0/0TuYehMnLLGWmooVK5E/fwF2795JZJIrE5GREezevYP8+QtQoUKlF667YsXK5M9fgB07vkGr1ZrV88knHzBr1rQMrc2aVGhoKJD8MvS+fXuIjo5Odun00qWLZtOjBgU95cCBH6lVqw4eHh6ZPu5ZmTmXZ8/+w65dO2jfvhO9evWhTZv2fPfdt/z77z+ZOgcZkZnzlPBvkNqlbo1GQ716r3Hy5AmuxF9SBNMfY1u2bEClUvHqqw0s/RZEHnD69Cn27dujbH/88WfJrgip79zGY+gAVPGfz9g6dYmYYbsTjaQlQy1ntVqd5qWnyMhIgBQvuSW0drRaLe7u7s8TY57z33+3+OWXH3Fzc6N8+Zf55Zcfkx3TokXKfyilRKVSMW7cZD78cBJDhw6gTZv2PHnyiO+++xYPD880n2tnZ8f48ZP55JMPGDSoL+3ame7v7Nu3l6dPnzBjxtw0PxsZrTtpPQMH9qZduw44ODiyb99uAgIe8sknM9JdAu5ZVatWw9XVlcWLvyIwMAA3N3dOnz7FoUP/w8HB0eyPADDd65w0aQw9evTC0dGRXbt2YDAYk/WQzuhxz3sudTodc+bMwMvLm2HDTFeEhg8fzdGjh5k9ezobNmy16BjgzJwnLy8vALZt20T9+q/RoEHDZK83fPhoTp8+xejRQ+nSpTsFChTgyJHD+PufpEePdyhdOvUrNUKkxGg08vnnnynb7dt3StYxFq3W1AEsfoim3qcwYes22/REI2mxyCQkGekwIveVMu6ff0zjZSMiIlId6pSZ5Azw+utvMG/eQtasWcGKFX4ULFiIKVOmsmtX8p73z2rUqClffeXH+vWrWbduFXZ2dlSu7MsHH0ylevWaFqs7oZ6NG9eyfv0a1GoVZcqUZc6cr5ShQZmRL19+5s//mmXLFrN+/RocHOwpXrwkn302i4sXz7Nz53aCgp6SL76TSOXKvjRr1oING9YQERFB9eo1GDZstFlP+Mwcl5KMnMu1a1dy585tPvlkhvIHraenF8OHj2HOnBmsXr2CkSMtN8woM+epadMWHD58iB9/3MeZM/4pJueiRYuxcuV6Vq1ayt69u9DpoilZsjRTpkxNufOOEOn47bdf+eMPUy9/jUbDhx9ONT/AaMR9wijs42dPNNrbE7ZmEwafwtkdqsWojOn1CEpBkyZNKFq0qDLO+fLly3To0IGpU6fSu7f53KZz5sxh3bp1nDlzBhcXl1RfMzZWT0iINtX9QmSlrl3bUbjwS/j5rbTIcUIIy9Dr9TRr9iYXLphuJfXrN4j58xeYHeO8dDFunyUOBQz/4mui+w7I1jifV8GCKV9RtkhztkgRU0eXx48fJ9v36NEjPDw80kzMQgghREq++WarkphdXFyYNOl9s/32hw6adwDrMyDHJOa0WCQ5e3h4UKxYMS5cuJBs38WLF/H19U3hWUIIIUTqTLf2EpcjHTFiDD5JLlVrbl7HY+hA8w5gs+Zle5xZwWI3gps3b87x48e5ceOGUnbs2DFu3bqVai9vIYQQIjV+fguUmQELF37JrK+FKiwUjz5vo45f/EJfpCih67bk2A5gz7LIPWeAoKAg2rZti0ajYeDAgeh0OlavXk2JEiXYvn176kt5xZN7zkIIIRLcu3eX116rrQzBXLRoGW8njFfW6/Ho+zaO//sFMM0AFvL9z8QlWSUvp8jSe84A+fLlY/PmzVSsWJFFixaxYcMGmjVrxurVq9NNzEIIIURSM2dOUxJztWo16N69p7LPdc7nSmIGCF/glyMTc1qeq+WcFaTlLIQQAkwTjrRsmTgT5d69P/Hqq68D4LhjOx4jhyj7tKPGEfnJ9GSvkVNkectZCCGEeFFGo5GpUxOXdWzTpr2SmO1O/Y37hMSpmnXNmhP50afZHmN2kOQshBDCZuzc+Q0nT/4FmBZJmTrVNBGT+v49PPv1QqUzLaITV6Ei4SvW5pglIDNLkrMQQgibEB4exrRpiWOW3313OGXKlIXISFPP7MePADDky0fopm8wprMefU4myVkIIYRN+PLLecrQKR+fwqYJRwwGPEYNTZya087ONDVnCuuq5yaSnIUQQljd1atXWLlyqbL92Wef4+bmjuus6Tju/14pj5j7FbHPMdd+TiPJWQghhFUZjUY+/PA94uLiAKhf/zU6d+6G47bNuCz6SjlOO2Q40X36WynK7CVDqYQQQljVDz98z8CBpkWT1Go1Bw8epWZYKJ7dOqCKjQVA91YLwjZuz3UdwFIbSmWRJSOFEEKI5xEZGcknnyQOnRowYDDVXZzx6NJWScxxlX1zdc/slEhyFkIIYTVffjmXe/fuApA/f34+GDICj55dUAcHA6Av5EPolm8xuqXcwsyt5J6zEEIIq7h48QLLl/sp29M++IQSY4Zjd9O0gJLR2ZmwTdsxFC1mrRCtRpKzEEKIbGcwGJg4cYzSCey1+q8x6M+j2P91HACjSkWY30riata2ZphWI8lZCCFEttu0aT3+/icB00xg21+uiNPuncr+yE8/J6ZdB2uFZ3XSW1sIIUS2CgwM5PXX6xAWFgrA9uYt6XHgZ2V/1IDBRMz5ElQqa4WYbWThCyGEEDbh008/UBJzXx8fuh86qOzTNWtOxMx5eSIxp0WSsxBCiGzz668H2LXLdPm6BrA6NBRV/H3nWN9qhK1cD3YykEiSsxBCiGwRHh7GxIljASgBHHJ0wj46GgB9seKEbd0Bbm5WjNB2SHIWQgiRLaZP/5QHD+7jDRzQaPDWmRKzwdOL0G3fYSj8knUDtCGSnIUQQmS5P/88yoYNa3AE9gAV9HoAjA4OhG3chr5CRWuGZ3MkOQshhMhSWq2W8eNHoQa2AG8m2Rfut4LYV1+3UmS2S+66CyGEyFJz5nzOf//dYinQJUl5xGcz0XXsktrT8jRpOQshhMgyJ0/+xcqVS/kYGJ6kXDtsFFEjRlsrLJsnk5AIIYTIEpGRkTRp8jpNb91kVZLy6C7dCV+yEtTSPpRJSIQQQmSr6dOnUu3WTZYnKYtp2Jjwr5dKYk6H3HMWQghhcYcOHeTWutX8BCSswhxbvSZh6zaDg4M1Q8sR5E8XIYQQFhUcHMTakUPYCzjFl8WVKUvo1p15bl3m5yUtZyGEEBa1eNRQNj99gkf8dmwhH8K+3YOxYEGrxpWTSHIWQghhMQfWrmTS/34hIQ3rXF2J3Pk9hhIlrRpXTiO9tYUQQljE/X9O49KyCS8bDABEazRE7fuFuDp1rRyZ7ZLe2kIIIbKM/ulTnDq2VhJzDBC8eoMk5uckyVkIIcSLiYwkqmkDKmpNVz/1wIUPP8GuTXvrxpWDSXIWQgjx/HQ6jJ3aUPrBfaVob9v2FBs3yYpB5XySnIUQQjyf2FicB7xDoX9OK0Vfly7La6s2WDGo3EGSsxBCiMzT63EfOQS3gweUotnOzjTesx+NRpPGE0VGSHIWQgiROQYD7uNH4bTnO6VoPlB02RpeeqmI9eLKRSQ5CyGEyDijEbcpE3HavkUp8gNuDBlBq9ZtrRdXLiOTkAghhMgYoxHXTz7Aef0apWg1sKFWHfZ8Mt16ceVCkpyFEEKkz2jEddpUXFYsVYq2AB94e/O/NRtxkMUsLEqSsxBCiLQZjbh+/hkuSxcpRTuBfsDmpasoWrSY1ULLreSesxBCiNQZjbjMmYHL4gVK0S6gJzB63CSaNm1utdByM0nOQgghUmY04jJvFq4LvlCKvgfeBl59oxHvvfeh1ULL7eSythBCiOSMRlzmzsT1q3lK0X6gG1C4eAlWrlyHnZ2kkKwiZ1YIIYS5+EvZSVvMPwFdALWTE+vXbyF//vxWCy8vkOQshBAikdGI66zpuHz9pVK0H1Ni1gFLvlxE1arVrRVdniHJWQghhInRiOuMT3HxW6gU/YApMccAQ4eOoFu3t60UXN4iyVkIIYQpMX/8Pi6rlitF+9VquhgMxABvvNGQTz/93Hrx5TGSnIUQIq8zGHB7bwLOG9cqRT87OtJJpyMWKFOmLKtXb5AOYNlIhlIJIUReptfjPm6kWWL+xdOLdvGJ2dPTiy1bvsXbO5/1YsyDJDkLIUReFRuL+4jBZotYHCpajDahIcQBGo2GNWs2UrZseevFmEdJchZCiLwoOhqPgb1x2p247OPRChV56/499PHbs2d/wZtvNrJKeHldrkzOjju/wavNWzitWw1Go7XDEUII2xIRgec73XD85Sel6O+69Wl45TKG+O2hQ0fQv/8g68QnUBmNtpG9YmP1hIRoX/yFjEbyVauAJjAAAO3w0UR+9jmoVC/+2kIIkcOpQoLx7NkVe/+TStk/rdtS88cflO127TqyatV61Opc2X6zKQULuqdYnvvOvEpFTNO3lE2XZYtxGz8K4uKsGJQQQlifOjAAr45tzBLzpT4DqP/r/5TtevVeZcmSlZKYrSxXnv2IuV+ha9Ne2XbeugmPd/uDTme9oIQQworU/93Cq21z7C6eV8qujpnIq9/vRhf/3ViuXHk2btyGk5OTtcIU8XJlcsbRkbBV64l++53Eov3f4/lOd1QR4VYMTAghsp/mwnm82jZHc/s/AIwaDTc+nUGDbZsIDQ0BoGDBQmzb9p0MmbIRuTM5A9jZEb5wCdqhI5UihyO/4dm5LarHj60YmBBCZB+7v07g1aEVmkeBABidnLi9wI8m69bw+PEjANzdPdi+fRclS5ayYqQiqdybnAHUaiKnzyJyysdKkf0/Z/Bq1xx1/F+QQgiRWzn8/CNe3dqjDgsFwODuwb3VG2i9bDF37vwHgJOTE1u2fEvVqtWsGKl4Vu5OzgAqFdoJ7xH+xdcY4zs42N28gVebt9CcP2fl4IQQIms4bVqPR/9eqKKjATAUKMjDbTvotOALLl26CJgmGVm9egP1679mzVBFCnJ/co4X3XcAYas3YnR0BEDzKBCvDq2wP/q7lSMTQggLMhpxmT8b94ljUBlMo5b1pUrzYMdeun4+Df8kPbUXL15O8+atrBWpSEOeSc4AMW3bE/rNbgzuHgCow8PwfLszjrt2WDkyIYSwgLg43CaNw3X+bKUotnpNHu78nl6ffMCJE8eU8tmz59O1aw9rRCkywOKTkHTt2pVz55JfLm7RogWLFi1K9XkWm4QkAzTnz+HZqyuagIdKWcQnM4gaOUYmKxFC5EwREXgMHYDj/35RimIaNeHxsjX0Hfkuhw4dVMqnTZvF8OGjrBGleEZqk5BYdP0vo9HIjRs3aNasGc2bNzfbV7RoUUtW9UL0vlUJ+fEgnj27YHflMgBu06eifnCPyBlzQKOxcoRCCJFxqsBAPHt3x/7fM0pZdJfuPJm3gMEjBpsl5o8++lQScw5g0eR87949tFotTZs2pUOHDpZ8aYszFCtOyL5f8OjXC4fjfwLgsnoFmrt3CFu2BtzcrByhEEKkT3P1Cp49u6C5e0cp046dyNPxkxk4uC8HDx5QyidNmsLYsROtEabIJIvec75+/ToAZcuWteTLZhmjlzeh3+4hukNnpczxl5/w6tgadZJL3kIIYYvs/ziCV9u3lMRsVKsJn7+Qx+Mn06dfT7PEPHbsRCZP/sBaoYpMsmhyvnbtGpCYnLXa7LmH/EIcHQlfsRbt6PFKkf3Zf/Bq1RTNhfNpPFEIIazHaesmPLt3RB0SAoDRxZWwzd/wtGsPevfuzu+//6YcO2HCe3z44SeopE9NjmHx5Ozq6srs2bOpWbMmNWvWpFmzZuzfv9+S1VieWk3k1GmEf7kIY/z9Zs39e3i1a4HDwV/SebIQQmQjgwHXGZ/iPm4kqvgFffQ+hQn5/iee1K1Pz55d+OOPI8rh77//EVOmfCyJOYex+GXtyMhIwsPDmTdvHrNmzcLV1ZUJEyawZ88eS1aVJaL79Cd0604Mbqbec+qIcDx698B5uZ+sCy2EsL7ISDwG98Nl8QKlKK5KVUJ++Y2AIsXo3Lmd2XCpjz+exsSJ71sjUvGCLDqUatu2bRgMBt55J3HBiejoaNq2bUtUVBRHjhxBk0pP6OwcSpUezaWLePbubtbBIqpPfyLmfAn29laMTAiRV6nv38Ojb0/sz/2rlOmatyRs+VruhQTTvXtHrl+/puyT4VI5Q7as59yzZ0+zxAymeVs7dOjAkydPlA5jtk5fqTLBPx0itk5dpcx503o8e3RCFfTUipEJIfIiO/+TeDdvZJaYtUOGE7ZhG9cDHtKuXQslMavVahYs8JPEnMNlywxh+fKZliDLER3E4hkLFSJk1w9Ed+mulDn8cQTvFo3RxM9LK4QQWc1xx3bTCJL4FaSMdnaEz19I5OdzOXP2H9q3b8H9+/cAsLe3Z9Wq9bzzTl9rhiwswGLJOTAwkDZt2uDn55ds361btwAoVqyYparLHk5OhC9dReSHnyhFmtv/4d2qKQ7791kxMCFErqfX4zptKh4jh6DS6QAweHsTumMv0f0GcuDAT3Tq1IYnT54A4OLiypYtO2jXrqMVgxaWYrHk7OPjQ3h4ODt27CAiIkIpf/jwIbt27aJevXoULFjQUtVlH5UK7bhJhK7fisHVNDGJShuJ54B3cPliDsRPLC+EEJaiCg7C8+3OuCz5WimLq1CR4J9/I/b1N9iwYS19+/ZUrkZ6e3uzc+deGjVqYq2QhYVZtEPYwYMHGTlyJOXLl6dbt25ERkayZcsWYmNj2bZtW5qTk9hSh7DUaC5dxLPv22iSrAWta9mG8CUrMMYvpiGEEC9Cc/ECnv16mn/PNG9J+LLVGNzcmTNnBgsWfKHsK1GiFNu3f0e5cuWtEK14Ual1CLP4whcHDx5kxYoVXL58GScnJ+rWrcuECRPSnTUsJyRnMP1F6/HuAByOJA7wjytXnrD1W9G/XMGKkQkhcjrHvbtwHzsSlTZSKYuc8B7a9z4kSqdj3LgR7N79nbKvevWabNmyg0KFClkjXGEB2Zacn1dOSc4AxMXhOm0qLiuWKEUGVzfCFy8npm17KwYmhMiRYmNxnf5Jqt8pgYGB9O/fE3//U8r+pk3fYtWqDbjJOgA5miTnLOC4awfu40ehiopSyrSjxpk6kNlZdE0RIUQupQoMxGNIf2UBHoC40mUI27ANfcVKnD9/jj59eig9sgH69x/EzJnzsJd5F3K8bBnnnNfoOncj+Mdf0ZcspZS5+C3Es0s71IEB1gtMCJEj2J04jnezN8wSs65la0IOHEZfsRL79++jbdvmSmJWq9XMmjWPuXO/ksScy0lyfkH6Kr4EHziMrulbSpnD8T/xbtIA+2N/WDEyIYTNMhhwXrwQr06t0cT/IW9Uq4n46FPC1m8lzs2d2bOnM2DAO2jj7z+7u3uwdesOBg8eJvNk5wFyWdtSDAZcFn6By9yZqOJPqVGtJvKDqUSNHg9q+TtICGHqVOo+ehiOB35Wygz58hG2fC2xjZoQGhrC8OGDzZZ7LFmyFJs3f0uFChWtEbLIQnLPOZvY//4bHsMHoY6fGAAgplETwpaswpgTx3kLISzGzv8kHu/2R3PvrlIWW6cuYavWYyhajEuXLtK/fy9u3bqp7G/cuCnLl6/B2zufNUIWQEgInD6tQa+HBg30ODtb7rUlOWcj9cMHeLzbH/u/Tyhl+kI+hC9fQ2yDN60YmRDCKgwGnJcswnX2dGWZRwDt8NFEfvwZ2NuzffsW3n9/AlFJOpiOGTOBDz6YmuqCQcLy4uLg0iU1/v6a+B81168nnv93341h5kydxepLLTlLl+IsYHipCCG79+M6bxYuX38JgOZRIJ5d26MdPxntxPelN7cQeYTq0SM8Rg3B4fAhpczg6UX4omXEtGpDVFQUH0wex9atm5T9Li4uLFq0jPbtO1kj5DwlIEClJGF/fw3//qtBq039nn5wcPbc75eWcxazP3QQj1FDzC5zx75Sj7BlqzGUKGnFyIQQWc3+8CE8Rg5RFq0AiK1dh7DlazGULMX169cYPLgfFy+eV/a//HIF1qzZJPeXs0BUFJw9q+H06cSW8f376fcHsrMz4utr4NVX9UyYoMPT03IxyWVtK1IHPMR9+GAc/jyqlBk8PIn4YiG6jl2sGJkQIkvodLjOnIbLcvOFgLRjJhD5/kcY7ezYtm0zH3442Wy1vi5dujN//kKZWMQCjEa4dUulJOHTpzWcP68mLi79lm/RogZq19ZTq5ae2rUNVKtm2fvMSUlytja9HpfFC0y9ufV6pTi6Ry8iZs2TubmFyCU0ly/hMWwQdklaw4YCBQlbspLYxk0JDQ1h0qRx7N27S9nv6OjIzJnz6NOnvwyTek5hYaZOWwmJ2N9fTVBQ+q1iFxcj1avr45OxKSm/9FL2pUVJzjbC7tTfeAwbjObOf0qZvngJwpesJLb+a9YLTAjxYgwGnNatwm3aVFTR0UqxrulbhH+9DGOhQpw4cZyRI9/l7t07yv7y5V9m+fK1VK1azRpR50hxcXD5stosEV+9mrFOc+XKmVrDtWubEnKlSgardgGS5GxDVOFhuL03AafvvlXKjCoVUaPGEfneh+DoaMXohBCZpb5/D/exI80WxDE6ORHx6QyiBw5BFxPD3LkzWbLka5J+5fbp05/p02fj6upqjbBzjMBAVXwiNiXkM2fS7rSVwMvLGH9p2vRTs6Yeb+9sCDgTJDnbIMfdO3F7bwLq0BClLK6yL2GLl6OXv6KFsH1GI447tuP24Xuow0KV4rjKvoQtX4O+YiXOnTvLqFFDuHTporLf09OLr75aRLt2Ha0QtG2LjoZz59TKJWp/fw1376Z/eVqjMVK5cmKLuE4dPWXKGLH1uwSSnG2U+sF93EcPx+HoYaXMaGeHduL7aMdMAJk/VwibpHr0CPf3J+C4/3ulLOkVsFi1msWLF/Dll3OJjY1VjnnzzcZ8/fUSihYtZo2wbYrRCLdvq5JcntZw7pya2Nj0M2rhwgbq1DF12qpTx9Rpy8UlG4K2MEnOtsxgwHnNClxnfGp2ryq2ek3CFy1DX6myFYMTQpgxGk1XvT6cjDooSCnWlyxF2OIVxNV/lbNn/2Hs2JFcuHBO2e/s7Mwnn8xgwIDBqPPodL7h4XDmjCZJq1jNkyfpnwsnp4ROW4kt4yJFbCJ1vTBJzjmA5sY13EcPx/7U30qZ0d4e7YT30I4eDw4OVoxOCKEKDMT9vfE4/vSDWXlU34FEfPY50XZ2fPHFHJYs+Rp9klEZtWu/gp/fcsqWLZ/dIVuNXg9Xr6rNJvi4ckWN0Zh+q7hsWYNyr7hOHVOnrdx6EVGSc06h1+O8zA/XuZ+j0iVOERdX2ZfwhX7E1ahlxeCEyKOMRhy3b8Ht0w9Rh4QoxfpixQn/ajGxjZpw9OjvvPfeeG7cuK7sd3Z25v33P2bo0BG5fgrOx49VZpN7nDmjISIi/UTs6Zm801a+PDSNuCTnHEZz5TLu40Zg739KKTOq1UQNG0Xk5A9AencKkS3Ut27iPmksDkd/NyuP6jeIyE+n8ygqmk8//ZCdO78x2//aaw346qvFlClTNjvDzRYxMXD+fGIiPnVKw5076V+eVqvNO23VqmWgXDlDnl60T5JzTqTX47xqGa6zZ6BKMhm+vkRJIuZ+SUzT5lYMTohcLjYW5+VLcJ0/y6wviL5EKcK/WkT062+wefMGPv/8M0KTjLhwd/dg6tRp9O07IFfcWzYa4e7dxE5bp06ZZtrS6dJvFRcqlNBpy5SQq1fXI5OfmZPknIOp/7uF+8Qxyf5yj+7YmYgZczH6+FgpMiFyJ7u/TuD+3jjskgx/Snrl6u8L5/nww8mcPfuP2fM6derC9Omz8fEpnM0RW05EBPzzT0IiNrWOHz/OWKetatVMiTihF3XRorY/lMnaJDnndEYjjt9sNd3zCg5Wig0enkRO+Yjo/oNlpSshXpAqOAjXGZ/ivHmDWXlclaqEL/TjfuGXmD79E3bs2G62v2TJUsyd+xVNmjTLznBfmMEA166plQ5b/v4aLl9WYzCkn1FLlTIoHbZq19ZTubJB+qw+B0nOuYTqyRPcPvsIp2+3mZXH+lYjYu6XxL1Sz0qRCZGDGQw4bduM6+efon76VCk2urgQOXEKT/sOYMXalSxatIDIyAhlv5OTE6NHj2fUqHE4Z9XKCBb09Glip61Tp0ydtsLD00/E7u5GatZMTMQ1axooUMAmUkeOJ8k5l7E/+jtuk8dhd/OGWXlUrz5EfvQZxoIFrRSZEDmL3elTuH0wCfszp83KdS3bEDZjNjv+PsHMmdN48OC+2f62bTvw2WefU8JGl36NiYELF9TKfWJ/fw3//ZexTlsVKhiURFy7toHy5fN2p62sJMk5N9LpcFm2GJcF8806jBncPdBOfJ+owUNlbLQQqVA9eoTr7Ok4b9loVq4vVpyImfP4n4sLn3/+Gf/+e8Zsf8WKlZgxYw4NGzbOznDTZDTC/fsqs0R89mzGOm0VLJhweVo6bVmDJOdcTH3nNm5TP0g2MUJc2XJEzphNTLMWVopMCBsUHY3zymW4LPwCdUS4Umx0dEQ7cizHGzZm+hdzOXr0sNnTChQoyJQpH9OrVx/srNy/IzIS/v03IRGbWseBgek3bR0cjFStan6vuFgx6bRlTZKc8wCHXw/gOvUD7K5fMyuPadSEiE8/R1/F10qRCWEDjEYcfvget2lTzZZsBdC1bM2//QYxY8tGfvhhr9k+Jycnhg0bxejR43C3wrrrBgNcv27eaevSpYx12ipRIvHydK1aenx9DbLonY2R5JxXxMTgvGYlLl/MQR0ephQbVSqie/VB+/5HGAq/ZMUAhch+dn//hdu0j7E/+ZdZedzLFbjy7nA+/vMIe/fuNlvOUaPR0KtXHyZOfJ8iRYpmW6xBQab5pxMuT58+rSEsLP1E7OZm6rSVdIKPggVt4utdpEGScx6jevwY1zmf47RlAyqDQSk3urigHTaSqBFjMHp4WjFCIbKe5sY1XD+fZrZyFIDB25ubfQfx4e1b7Ny7i2e/Btu378SUKR9TrlzWzoUdGwsXLya2iP39Ndy8mf7laZXKSMWKBiUJ166t5+WXDeTyGUJzJUnOeZTm0kVcp0/F8df/mZUb8uVDO3YSUQMGg5OTlaITImuoH9zH5ct5OG3diCrJAhRGe3vutuvI5LAwvj34S7LntWjRismTP6BatRpZEteDByplGJO/v5qzZzVER6ffKi5QwKCsyFSrlmn+afeUv9NFDiPJOY+zP3wIt2lTsUuyhB2AvmgxtBPfJ7pHL1k7WuR4qidPcFn0Fc7rVpktHANw9/U3maKPY+uJY8me16xZcyZP/oCaNWtbLBatFs6eNc2ylbBE4sOH6beK7e2N+PomHcqkp0QJ6bSVW0lyFmAw4LhrB65zZibrEKMvWYrIie+j69pDZhoTOY4q6CnOK5bgvHI56iSThADcr1CRSXoD269fTfa8li1bM3bsRGrXfuWF6jca4cYNldnl6YsX1ej1Geu0lXRVJl9fg1zMykMkOYtEMTE4bVqH65fzUD95bLYrrkxZtOMno+vSXZK0sHlKUl61wmxYFMD9IkWZHBvLtsePzMrVajUdOnRi7NhJVK5c5bnqDQlBaQ0ndNoKCUk/Ebu4JO20ZUrKPj428RUsrESSs0guIgLntStxWfK12XzdYGpJa8dMMF3ulolMhI1RPXqEy8qlOK1dlSwp3/PyYqJWy7cxMWblTk5OvP32OwwbNpIyZcpluK64OLh0Sc2pU5r4hKzm+vWM9byqUCGxw1bt2noqVpROW8KcJGeRKlV4GM4rl+G8zA91WKjZPn2RokSNHENUr76yhrSwOvXdO7gs+RqnrZvMlnEEuOXiwvtaLTuBpF9q+fPnZ+DAIQwY8C4FChRIt46AAFV8Ijb1ov73Xw1abfqt4nz5DEpr2DT/tB5PGRAh0iHJWaRLFRqC85qVOK9YkqwlbfD2JmrAu0QNHoYxA19wQliS5vw5XJYtxnH3TlRxcWb7rtjZMTUuLllSrlSpMu++O5wuXbqnuihFVJSp01bCBB+nT2u4fz/9Tlt2dqZOWwm9p2vX1lO6tHTaEpknyVlkmCoiHKf1a3FZuijZPWmjkxPRPd4hashw9OVftlKEIk8wGrE/fAiXpYtw+P23ZLtPAbOAPSQmZbVaTfPmrRgyZDivv/4GqiTZ0miEW7dUZveJz59XExeXfkYtViyxRVyrloFq1fTkgEWoRA4gyVlknlaL0/YtuCxdnKx3N4Cu6VtEDR1JbMPGSJNBWIxWi9POb3BeswK7SxeT7T6MKSknHblfsGAhevfuS58+AyhWrDgAoaGmmbYSk7GaoKD0W8UuLkaqVzcl4YThTIUL28TXpMiFJDmL5xcXh+MPe3FevBD7c/8m3/1yBaIGDEbXvSdGK8w9LHIH9Z3bOK9bjdOWDahDQsz26YHvgC+Bv5OUv/lmY/r06cdbb7Xl5k0npUXs76/m6tWM9bwqV848EVeqZJCBCiLbSHIWL85oxP7PozivXIrDLz+heuajY3RxJbrb20T1HySLbIiMiYvD4eABnDasweHQwWSfqQhgDbAQ+C++7KWXitC+/VDKl+/LnTsv4e+v4cyZjHXa8vIymo0prlVLj5eXRd+REJkiyVlYlPrmDZzXrMBp6+Zkkz4AxNaqTfQ7/dB16oLRTeYZFObUd27jtH0LTls2onn4INn+G8BiYB0QhiMODvWpUKE/rq5NuXevCPfupd8q1miMVKliulec0CouU0Y6bQnbIslZZAlVRDiO327Hed0q7K5cTrbf6OJKdMfO6Hr0Irbeq6BO/56fyKWionD8cR9OWzfjcPRwst0G4ADghw8/0QgDr+Hq2pTo6Iro9ekn4yJFks60Zeq05eJi6TchhGVJchZZy2jE/vifOK1fjeOPP6B6ZgIIAH2JkkR3e5vobm9jKFPWCkGKbGcwYH/sDxx3foPD97vRRCS/yvIIe9ZQh1UM4BYdgELpvqyzs5Fq1fTKYhC1a+spUsQmvsqEyBRJziLbqJ4+xWnHNpy2bEyxNQ0QW6Mmuk7d0HXohCEb18oV2cBoxO7sPzjs+Q7Nt9txemb6TAADKn7hNdYxij10Jpa0Z6ErW9bUKq5VS88rr5g6bck6LSI3kOQssp/RiJ3/SZy+2Ybjnu9Qh4akeFhM/deIadseXZv2GIoWy94YhWUYjdid+xfVzm/RfPct7ikkZIDrlGUdA9hIX+5RPMVjPD1N808n3CeuWVNPvnxZGbwQ1iPJWVhXdDQO//sZp2+3mXrlxsameFhszVroWrcjpkVr9BUqyvhpWxYbi+b4H0Rs3oD7oV/xfmbq1wSPKcA39GAzvfmLekDiv6labaRSJdOlaVMyNlC2rEG6Jog8Q5KzsBmqkGAc9+/Dcfd32P/xOyqDIcXj9CVKoWvegpi3WhL76uvIOno24NEjQr7ZgnbnfkpdPYenPirFw0LxYA8d+ZbuHKA5cZiuQRcqZBpPnDCuuFo1PW5u2fkGhLAtkpyFTVI9eoTjz/tx/GEv9n8cSTZvcgKjkxOxr75OTOOmxDRqKq3qbGKMjubet3t4tPUXil46Q5WoW6hJ+SsjBE/20U5JyEZ7O6pXN1CnjlHptFW0qAxlEiIpSc7C5qlCgnH45SccD/yM/W+/JlsKMClDgYLEvP4GsfE/+nLlJVlbgC4sgtMrfiB8/x8Uv3mBOtEXcCE61ePvUow9dGQvHbhYoAa16jnw+usO1Kmjp3Jlg6w2KkQ6JDmLnCUmBvsTx3A48BMOhw5id/1amocb8ucn9pV6xNapR2zd+sRVq44Mck3fzeOXubDmf6hPnqP8oyvU1l/ECV2qx8eh4Riv8bO6GWeL1CFfo6q0aJmf2rUN5M9vE18lQuQokpxFjqa+cxuH33/D4bdfsf/j92RzLz/LqNGgr1CJ2Bo1iatRi7iq1YirWDlPr0kdeu0//ll/kIjfz1Lw7i0qR92gNPfSfd5VyvO7XV2uFq+BY6s3eKt7RSpWVEunLSEsQJKzyD0MBjQXL+Dw5xHs//wD+xN/ppusAYwqFfpSpdFXqUpchYroy79MXPkK6MuWyz2tbKMRVVAQ0Wf/4eb+Pwk/fhmve/coE3WXl3iaoZe4RmlOOfvyoGwVPDs2pnH/unh4ZGwRCSFE5khyFrmXwYDmxnXs/z6B3cm/sD/1N5prV5MtopAWfdFi6EuWQl+qNIaSpdAXL4GhaDH0LxXB8FIRcHTMwjeQCUYjqohw1AEBqO/dRXX7PyIunEV78SrcuE+hkEd4GjL+/ygKJ86oK3EtXzmiqlWh/IC3qNq8qty+FyKbSHIWeYoqPAy7c2exO3Mau7NnsLtwHs31a6kO20qPIX9+DAUKYihYCEOBAhjzF8Dg6YnR0xujpycGd3dwccHo4orR2RmjkzPY22HU2IFd/I/RCAaD8lsVEwPR0ah00aiio1FFRqAKD0cVYfqtDglGFfQU9dOnqIKeYnhwH7tHgdjpUr8nnJYonDirqsRV11KEli1D/rdqUm9wU9zz5d1L/UJYmyRnIaKjsbt6Gc3FC9hdvYLm+lU0V6+guf0fKr3e2tFZTASuXOVlrlGGW65FiCxVhAKNKvF6n7qULCODioWwJZKchUhNTAyae3dQ//cfmv9uofnvFuoH99E8uI/6wX3UAQ+fu8WdFbQ484Ai3KMY/1GK/yjFbYrzxM0TVYWCVGhUlJatClCligaN3CoWwqZJchbiecXFoXr6FPWTx4k/T5+gCg1FFRaKOiQEVVgYqugoVFotRm0k+vBw4nQ6DDodxpgYjHGxxOr1xOn1xBkMGAEdEI0d0bijw4twChFGccLwJhx3gsjHEwrwlPw8JT8BFOYBRQjDA1dXLRUrRtCggT1vvOFEzZp63GXZbCFynNSSs102xyFEzmNnh9HHB72PD7EGA48fP+bhw/vcv3/f9NvuPg9idNx9/Ih79+4SGBhAyn/zOgP1gPpJfqe/0IednYFKlWJoUE8dP/90JCVKGFGpEnqY555L8kIIE0nOQgAGg4GgoCAePQrk0aNAAgMDCAwMICDgIYGBgTx8+ICAgIcEBDwkLpUpRpMrjykBJ/xUIyP/5YoXNy0EUauWaTEIX1+DTCsuRB5j8eR89+5d5s6dy99//w1Ao0aNmDJlCvlkzTeRzbRaLUFBT3n69AlPnz7h8ePHPH36lCdPHvP48aP4H9PjJ08eZyLppsQbqEtCi1ilqofRmP5n3sXFtDyiKRGb1iz28bGJO01CCCuyaHIODg6mX79+xMTEMHjwYPR6PWvWrOHKlSvs2LEDB5loVzwHnU5HSEgIoaEh8b+DCQ4OJiTE9Ds4OIjg4CCCgkw/psdP0Wqzpg+Dl1cBvL3fxNGxIbGxtQkOfpmgoIJmx6TWk6NCBX18q9jUOq5Y0SCdtoQQyVg0Oa9fv56AgAD27dtH2bJlAahevToDBgxgz549dO/e3ZLVCRtnNBrRarVEREQQERFGREQE4eHhREREEBYWSnh4OOHhYYSFmX7Cw0OVx2FhoYSEhBAWFkpUVMrLElqap6cXhQoVwsencPzvl/DxKYyTU2mCgytw715Rrl/35tw5e27dSn+Wjnz5DNSubWoNJ/x4embDGxFC5HgW7a3drFkzihUrxvr1683KW7ZsiY+PDxs2bEj1udJbO/sZjUbi4uKIitISFRVNdHQUUVFRyu+oKC1abRRabSRRUVFotVq02shnfpseR0Ym/ETEJ+MIIiMjUukYlT3s7e3Jn78A+fLlp0CBghQoYPqdP38BChYsFP9TkIIFC1GgQEGcnZ2JioKzZzWcPq3G31+Dv7+G+/fTn0Tazs6Ir69BWRqxVi09pUvL8ohCiLRleW/t0NBQ7t69S4sWLZLtq1KlCocPH7ZUVTlOQhKMjY0lLi42/nEccXGxxMTEEBcXF//btB0bm/A7hpiYWGJjY9DpdMTGxsb/jiEmxlSW+Dvxsekn2uxxdHTC74QkbPptsKHxu6nRaDR4eXnh6emFt7c3np5eeHl54+3trfz29s5Hvnz58PY2/RQoUAA3N3dUaWRHoxFu3VJx4oQpCZ8+reH8eTVxceln1KJFkyZiA9Wq6XF2tuS7FkLkZRZLzoGBgQD4+Pgk21ewYEHlkqZ7NgzGfPDgPjt3fkt4eBgGgwG9Xo9er8dg0Mc/NmAwGJJsJ+6Pi0vYjjPbp9friYuLU8pNxyUk3Dhlf2xsLHp9HHFxeuLiYpX9eZWTkxNubu64ubnh5uaOu7vpsbu7Bx4eHri7e+Du7q5se3p64uHhiaenl/LY1dU1zSSbUaGhcOaMRmkRnz6tJigo/Vaxi4uRatX08cOYTEm5cGHptCWEyDoWS86RkZEAOKfQfHCMXzRAq9VmeXI2Go307t2D8+fPZmk9uYVarcbZ2QVnZyecnV1wcnKK33bG2dkZJydnXFxccHV1jS8zPXZxccHFxfTbzc0NFxfX+HLX+ETshqurG3Z21hmtFxcHly+rOX06IRmruXo1Yz2vypdP7LBVu7aeSpUMWOltCCHyKIt95WTk8qg6mxaAza56MkOj0WBnZ4e9vQP29nbY2dljb2+PnZ09Dg5JHztgb2+vHOfg4IijoyP29qZ9iT+OODjYx+93wtExocwBJyen+DLTcxO2Tb8dcXJyxtnZVGZvb2/tU2MRgYEqpTXs76/hzBkNWm36rW0vL6PSWatOHdNvL6+sj1cIIdJiseTsGr+IvS6FFXMSylyzYaF7lUrF5s3fsGfPd0RFRaHRaFCp1Gg0GjQa02+1WoNanVCW+NjOzk7Zb9rWoNHYKcclHJPwo1Zr4pOq6ThTuX18ErZDo7GL329nk38w5FTR0XDunFq5T+zvr+Hu3fTPr0ZjpEoV8wk+ypSRTltCCNtjseRcpEgRAB4/fpxs36NHj/Dw8MAlmxa0L1z4JYYNG5UtdYmsZTTC7duqJPeJNZw7pyY2Nv2M+tJLSROxqdNWNn0EhRDihVgsOXt4eFCsWDEuXLiQbN/Fixfx9fW1VFUiFwsPN++05e+v5unT9FvFTk5GqldP7LBVu7aeIkWk05YQImeyaDeX5s2bs3HjRm7cuKFMQnLs2DFu3brFoEGDLFmVyAX0erhyJaHTluky9ZUraozG9FvFZcuaJvdISMSVKxvIJbfPhRDCspOQBAUF0bZtWzQaDQMHDkSn07F69WpKlCjB9u3b05y+UyYhyf0eP1aZTe5x+rSGyMj0E7Gnp9EsEdesqUemahdC5AbZtp7zzZs3mT17NqdOncLJyYmGDRvy3nvvpbvwhSTn3EWng/PnEzttnTql4c6d9C9Pq9VGKlUyxI8pTuy0Jf3phBC5UbYl5+clyTnnMhrh7l2VWSI+d05NTEz6rWIfn4R7xKaEXK2anmzo1C+EEDYhy6fvFHlHRAT8809ihy1/fw2PH2es01bVqqZ7xa+8kthpS4YyCSGEOUnOIk0GA1y9qja7V3z5shqDIf2MWrp0Ys/phE5bsmqoEEKkT5KzMPPkiXmnrTNnNISHp5+I3d3NO23VqmUgf36buGMihBA5jiTnPCwmBi5cMCXiU6dMyfj27Yx12qpYMbFVXKeOgXLlDNJpSwghLESScx5hNML9+6okk3toOHtWjU6Xfqu4YEGDkoRr1dJTo4YeN7dsCFoIIfIoSc65VEQEnD2b0CI2TfQRGJh+09bBwdRpK2EoU61aeooXl05bQgiRnSQ55wIGA1y/rlZ6Tvv7a7h0KWOdtkqUSEzEtWvrqVLFQPwKn0IIIaxEknMOFBREknWKTWOLw8LST8RubkZq1jTvtFWwoHTaEkIIWyPJ2cbFxsLFi2qze8U3b6Z/eVqlStppy3Sv+OWXDWg02RC0EEKIFyLJ2cY8eKBSek+fPq3m3381REen3youUMCgJOE6dUydttxTnnhGCCGEjZPkbEVabUKnLbVymfrhw/Rbxfb2pk5bCR22atfWU7KkdNoSQojcQpJzNjEY4OZNVXyL2JSIL15Uo9dnrNNW4n1iPb6+BpycsiFoIYQQViHJOYuEhKAsAnH6tOknJCT9ROzikjjTVq1apsvUPj7SaUsIIfISSc4WEBcHly4l7bSl5vr19HteqVRGypc3DWWqVcvUOq5QwYCd/KsIIUSeJmngOQQEqJTpLhM6bWm16beK8+UzddpKuERds6YeD49sCFgIIUSOIsk5HVFRpk5bSReDuH8//U5bdnZGfH3N7xWXLi2dtoQQQqRPknMSRiPcumU+//SFC2ri4tLPqEWLJg5jql1bT9WqBpydsyFoIYQQuU6eTs6hoYkzbZk6bakJCkq/VeziYqRGjYRhTKbWceHC0mlLCCGEZeSZ5BwXB5cvq5VE7O+v5urVjE2XVb58Ys/pOnX0VKoknbaEEEJknVybYgIDVUrPaX9/Df/8k7FOW15eRrP7xLVq6fHyyvp4hRBCiAS5MjnPnevAl1+mv7SSnZ2RypXNZ9oqW1Y6bQkhhLCuXJmcN260T7G8cOGkyyMaqFZNj4tLNgcnhBBCpCNXJueJE2NYtcqBggUNyuQetWvrKVJEOm0JIYSwfSqj0WgTGSs2Vk9IiNbaYQghhBDZpmDBlJcPTH/ckBBCCCGylSRnIYQQwsZIchZCCCFsjCRnIYQQwsZIchZCCCFsjCRnIYQQwsZIchZCCCFsjCRnIYQQwsZIchZCCCFsjCRnIYQQwsbYzPSdQgghhDCRlrMQQghhYyQ5CyGEEDZGkrMQQghhYyQ5CyGEEDZGkrMQQghhYyQ5CyGEEDYmTyXnO3fuUK1aNf766y9rhyKE1d29e5dRo0ZRt25d6taty3vvvUdQUJC1wxLCpn388cf06dMny+uxy/IabERYWBgjR45Ep9NZOxQhrC44OJh+/foRExPD4MGD0ev1rFmzhitXrrBjxw4cHBysHaIQNmfHjh3s2LGDunXrZnldeSI537hxg1GjRnHz5k1rhyKETVi/fj0BAQHs27ePsmXLAlC9enUGDBjAnj176N69u5UjFMJ26PV6li1bhp+fX7bVmesva+/evZsOHToQEhJCt27drB2OEDZh//791K1bV0nMAK+99hqlS5dm//79VoxMCNui0+no1KkTixcvpkOHDvj4+GRLvbk+OV+5coU2bdqwb98+atWqZe1whLC60NBQ7t69S5UqVZLtq1KlCufPn7dCVELYJp1OR0REBAsWLGDu3LnY2WXPBedcf1l7woQJcv9MiCQCAwMBUmwBFCxYkIiICMLDw3F3d8/u0ISwOW5ubhw4cCDbknKCHJmcHz9+nOZ+FxcXXF1dASQxC/GMyMhIAJydnZPtc3R0BECr1UpyFgJQq9Wo1dl/kTlHJucGDRqkuX/YsGGMHz8+m6IRImcxGAzpHmONLyMhRKIcmZw///zzNPdXqlQpmyIRIudJuKqU0rDChLKEY4QQ1pEjk7P0uhbi+RUpUgRI+fbQo0eP8PDwwMXFJbvDEkIkIdeuhMhjPDw8KFasGBcuXEi27+LFi/j6+lohKiFEUpKchciDmjdvzvHjx7lx44ZSduzYMW7dukXr1q2tGJkQAnLoZW0hxIt599132bt3L/3792fgwIHodDpWr15NlSpV6NChg7XDEyLPk5azEHlQvnz52Lx5MxUrVmTRokVs2LCBZs2asXr1ahl+KIQNUBmNRqO1gxBCCCFEImk5CyGEEDZGkrMQQghhYyQ5CyGEEDZGkrMQQghhYyQ5CyGEEDZGkrMQQghhYyQ5CyGEEDZGkrMQQghhYyQ5CyGEEDZGkrMQQghhY/4PkXSPNUmqVG0AAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-1, 1, 100)\n", "y = (x + 1) * np.exp(2 * x)\n", "y1 = 1 + 3 * x\n", "y2 = 1 + 3 * x + 8 * x ** 2\n", "\n", "plt.figure(figsize=[8, 5])\n", "plt.plot(x, y, 'k', linewidth=3, label='Function')\n", "plt.plot(x, y1, 'b', linewidth=3, label='1st order approximation')\n", "plt.plot(x, y2, 'r', linewidth=3, label='2nd order approximation')\n", "plt.legend()\n", "plt.xticks([-1, 0, 1])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bivariate Taylor approximation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the function \n", "$$g(x) = x_1^2\\exp(-x_2) $$\n", "\n", "the first-order Taylor approximation around $(1,0)$ is\n", "$$\\hat{g}(x) = 2x_1 -x_2 - 1$$\n", "\n", "and the second-order approximation is \n", "$$\\hat{g}(x) = x_1^2 - 2x_1 x_2 +0.5x_2^2 + x_2$$\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": "
", "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3oAAAEqCAYAAABDQiKmAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAEAAElEQVR4nOydd7wU1f33P+fMzLZbQBCxYCXeqwFpKohdRLFrjLH3kmgSk2hswRZLYkvsLb8k9uSxoGKMGk3sBkVEFMUIiChgQTq3bZmZ8/xx5kzb2d3Zvvfe8369lL1Tz87OnDmf822EMcYgkUgkEolEIpFIJJI+A613AyQSiUQikUgkEolEUlmk0JNIJBKJRCKRSCSSPoYUehKJRCKRSCQSiUTSx5BCTyKRSCQSiUQikUj6GFLoSSQSiUQikUgkEkkfQwo9Sa9HJo6VFIu8ZyS9BXmvSiSSvojs22pDnxd63d3duO+++3D88cdjl112wciRI7H77rvj7LPPxr/+9a+SbrRLLrkE7e3t+Ne//lVyu0466SS0t7fjo48+KvkYxdLe3o6xY8eG2tY0Tdx2223Ya6+97Gv26aefVrmFxbF8+XL88pe/xLx58+xly5YtQ3t7Ow455JA6tkwimDlzJtrb20P997///Q8AcMcdd6C9vR1//etfq9KmZ555BpdddllVjl0Oq1evRnt7OyZNmlTvpvRbiukjq82iRYtwyimnYM2aNfYy8Tz95Cc/qWPLGo+lS5fi2muvxYEHHogxY8Zg7NixmDJlCq688kosXLiw3s2rGR999BHa29tx0kkn1bspWRxyyCFob2/HsmXL6t2Ufkk9xpy5WLduHX7729/iP//5j2d5I/W/fQm13g2oJnPmzMG5556LFStWIB6PY8yYMWhtbcWyZcvw+uuv49VXX8XEiRNxyy23YIMNNqh3cxuKJ598EnfffTdisRj23HNPMMaw2Wab1btZHi688ELMnDkTZ555Zr2bIinA4MGDseuuu+bdZsCAAVVvx6xZs3DRRRdh7733rvq5JJJy+PGPfywHxSF4+eWXcd555yGVSuF73/sedtllFwDA4sWL8eijj2LatGm48sorcfTRR9e5pRKJBACuv/56PPXUU/azKqkufVboffzxxzjllFOQTqdx1lln4ZxzzkFTU5O9/vPPP8fVV1+Nt99+G8cddxyeeuopJBKJUMc+//zzcdZZZ2Ho0KElt++GG25AT08Phg0bVvIxqomY9TnvvPNw6qmn1rcxOQiyxg4dOhTPP/88IpFIHVokycXw4cPxhz/8IdS2J5xwAg466CAMHjy44u0wTbPix5T0HZ5//nlQ2hiOLkH926hRo/D888973mX9mbVr1+KCCy4ApRT3339/1mTSiy++iPPPPx9XXnklxo4di2233bZOLZVI6ksjjTlzedI1Uv/bl+iTV1TXdZx//vlIpVK49NJLccEFF2S9GLfZZhv8+c9/xsSJE7F48eLQg1AA2GijjTB8+HA0NzeX3MZNN90Uw4cPRzQaLfkY1SSdTgMANt544zq3pDg0TcPw4cOx+eab17spkhIZNGgQhg8fjoEDB9a7KZJ+xvDhw7H11lvXuxk5icfjGD58eK/rl6vFyy+/jO7ubhx11FGBHgNTpkzBySefDNM0MW3atDq0UCJpDBp9zAk0fv/bW+mTQu+FF17Al19+ie9///t5fdU1TcNVV10FRVHw+OOPe2IhJk2ahEmTJuGDDz7AQQcdhB122AFTpkzBd999lzNGb9WqVbjmmmswadIkjBo1CocddhieeeYZPPPMM2hvb8dTTz1lbxvkLy1861etWoVLL70Uu+22G3bYYQccdthheOyxxwK/w+zZs/GrX/3KjqUbN24cjjzySDzwwAMwDKPoaydiQJ5++mkAwC9/+Uu0t7fjjjvusNuYy4c6yAe/lO+0evVq/OEPf8CUKVMwevRo7Lvvvpg6dSq+/vprAE4c3rvvvgsAOOqoo+zz5ovRe+edd/DjH/8Y48ePxw477IADDjgAt912Gzo7Oz3bPfXUU/bvNWPGDJx44okYO3YsdtppJ5x99tkNF6vY1wiK0RPPy+LFi3HUUUdh5MiRmDRpEj755BMAwHvvvYef/OQn2HPPPbHDDjtg0qRJuOyyy7B06VL7GJdccglOPvlkAMBrr72G9vZ2XHLJJaHb9dJLL+Gkk07CuHHjMGrUKBx++OG477777EkRf/tfe+01nHfeeRg1ahQmTpyIJ554wt7m1VdfxQknnIBx48Zh4sSJuOqqq7LuQzeffvopfvGLX2DixIkYOXIkpkyZgttuuw3d3d2e7cTze8cdd+DOO+/EzjvvjHHjxuHyyy8v+P2K6Uva29tx9NFHY/ny5fjFL36BnXbaCePHj8cZZ5yB999/P+vYpWx/0kkn4ZVXXrH70x/84Af2tU6n0/jLX/6Cww47DKNGjcKOO+6Ik046Cf/+9789x3nhhRfQ3t6OnXfeGatWrfKsmzZtGtrb23HggQcilUrZ53X3b+7rOWfOHJxyyikYO3YsJkyYgPPPPx+rVq0CYwwPP/wwDjjgAIwePRoHH3wwHn/88azvxBjDM888g9NOOw0TJkzAiBEjMGHCBJx22ml47bXXss751VdfAQAmTpyI9vZ2z7qgGL1i78+ZM2fi+eefxw9/+EOMHj0aEyZMwK9//WvPMxMGcd4dd9wRY8aMwVFHHYUnn3wya9Y+33MR5r5duXIlrr32WkyaNAkjR47ErrvuigceeCCwTe7759lnnwWlFC+++GLWtQj7XAkWLFiAiy66CHvuuaf9W995552B21f7fTN9+nQceeSRGDNmDPbcc0/ccsstWd8vLJ988gl++ctf2tdh3333xe9+97usZybM77RgwQL84he/wK677oqxY8fi7LPPxueff57z3KtWrfL8rrvvvjt+85vf2Pe/m0L9Qi6WLVuGq6++GlOmTMGYMWMwatQoTJkyBddffz3Wrl3r2Va8azo6OnDTTTdh9913x9ixY3HkkUdi+vTpWccudftc7zIg3LO8bNkyjB07Fu3t7fjvf//rOceiRYuwww47YNSoUVi0aJHnvEFjzuXLl+PCCy/EhAkTMHbsWJx44omYO3cuAOCtt97CscceizFjxmDSpEm4/vrrkUwms75X2PdH0Phy5syZ9rqg8WUp9+e8efNw1llnYaeddsLYsWNx8skn22PGsFTqvVup9xkQ7v7x0yddN19++WUAwKGHHlpw2y233BLjxo3DrFmz8NJLL+GYY46x13V2duLss8/G4MGDsdtuu2HVqlXYaKONAo+zfPlynHjiiViyZAm22mor7L333pg/fz4uuugijBo1KnTb165di2OOOQZr1qzBuHHjkEwmMWvWLFxxxRVIp9Me4frUU09h6tSpUFUVY8eOxejRo/HVV1/h448/xrx587Bs2bKik05suOGGOPTQQ/HBBx9g6dKl2GmnnbDJJpvYA41SKOY7LVu2DCeffDK++uorDBs2DHvttRe++OILPPnkk3jttdcwbdo0JBIJHHrooZgxYwZWrVqFPffcEwMGDEAikcj5gn7ggQdw/fXXg1KKHXfcERtssAHef/993H333XjppZfw8MMPY9CgQZ59/v3vf+PVV1/Flltuid122w2ffvopXn31Vbz77rt44YUXynLdlZTG2WefjUwmg7322gsLFy7E9773PcyZMwenn346dF23B5sLFizAE088gZdffhnTp0/H0KFDMXbsWCxfvhwzZszA0KFDMX78+NCB37///e/x4IMPIhKJYOedd0Y8HsesWbNwww034OWXX8Zf//pXxGIxzz7XXXcdVq5ciT322AMLFizAdtttBwB4+OGHce2110LTNEyYMAGKouDJJ5+0X3Z+/vOf/+BXv/oVMpkMRowYgZ122gnz5s3D3Xffjddeew0PPfQQWlpaPPv885//xJIlS7Dbbrth/fr1BWdJS+lLOjo6cMIJJ2DVqlXYZZddsG7dOrz11luYOXMmbr31VkyePLms7ZcuXYpf/epXaGtrwzbbbINYLIZIJIKenh6cdtppmDNnDgYOHIg99tgD3d3dmDVrFt59912cfvrpuPjiiwEABx54IF544QW8+OKLuOGGG3DjjTcC4P319ddfD1VVccMNNxSc5X7vvffwpz/9CZttthl23XVXfPDBB3juuefw9ddf4/vf/z4ef/xxjB07FptuuinefvttXH755SCE4Ec/+pF9jKlTp+Kpp55Ca2srxo4dC03TsGDBAsyYMQMzZszAHXfcgf3339/ug4W1asqUKQVd0Uu5Px988EG8/PLLaG9vx5577ok5c+bgn//8J2bNmoV///vfoWb+b7rpJvzlL39BLBbDqFGj0NzcjFmzZmHq1KmYPXs2fv/732ftE/RciH471337+eef46STTsLKlSux5ZZbYtKkSfj666/tQeujjz6KkSNH4uCDD4amaQC89892221n3z+CYp+r119/Hb/4xS+QTCYxcuRIjB49GnPnzsUdd9yBt99+G/fff799/Gq/b66//nrcf//9SCQS2GWXXZBMJvHnP/85cGBYiBdeeAEXXnghMpkMRo8ejY033hiffPIJHnroIbz44ot48MEHs/qPXL/T+++/jzPOOAPd3d32sWbNmoXjjjsOiqJknfvLL7+0hcYWW2yBvffeG19//TWeeuopvPLKK3jggQew/fbbe/bJ1S/k4tNPP8VJJ52E9evXY8SIEdhzzz2xZs0afPDBB7j//vsxc+ZMTJs2Lat9F1xwAd544w37eXr77bdx8cUXY/78+Xb/Us72Qe8yIPyzPGzYMJx//vm49tprcfXVV+PZZ59FJBKBYRj4zW9+g3Q6jd/85jcYPnx4zmsDAGvWrMHRRx+NdDqNnXbaCYsXL8asWbNw2mmn4fzzz8c111yD7bbbDrvttpt9n69cudLjBVfM+yNofLnhhhvmbF8p9+cHH3yA//u//8PgwYMxYcIELFmyBDNnzsT777+Pxx57DCNGjMh7TYDKv3cr8T5zk+v+CYT1QSZNmsTa2trYzJkzQ21/yy23sLa2NnbFFVfYy/bZZx/W1tbGTjnlFGYYBmOM2f9efPHFrK2tjb3wwgv29ueddx5ra2tjV111FdN13d7+uuuuY21tbaytrY09+eST9vYnnngia2trY3PnzrWXie1+9KMfsRUrVtjLp0+fztra2tjkyZPtZd3d3WzHHXdkY8aMYfPnz/d8n5dffpm1tbWx0aNHs3Q67Tn+mDFjQl2ToO9Y6BgHH3wwa2trY0uXLi3pOzHG2BlnnMHa2trYtddea19Hxhi7/fbbWVtbGzv33HPtZUHXcOnSpaytrY0dfPDB9rK5c+ey9vZ2ttNOO7E5c+bYy5PJJDv//PNZW1sb++lPf2ovf/LJJ+1233HHHfbvnslk7Pbdeeedea+fhPPOO++wtrY2duKJJ4beR/zWf/nLX+xl4rc+6KCDWHd3N2PMeR5PPvlk1tbWxmbMmGFvb5om+81vfsPa2trYrbfemtWeH//4x6Hb8+KLL7K2tja29957s88//9xevn79ertdv/vd77LaP3LkSLZo0SJPW5cuXcpGjhzJxo0bx+bNm2fvs2jRIrbbbruxtrY2ts8++9jLv/vuOzZu3Di2ww47sDfeeMNenslk2OWXX87a2trYpZdemvX92tra2FNPPWUvF+cPotS+RLTV/by/8MILrL29nU2cOJF1dHSUvf0ll1yS9R2uueYa1tbWxk4//XTPPgsXLmS77747a2trY//+97/t5StWrGDjx4/3vBPOOuss1tbWxm677TbP9/X3b+7rec011zDTNO1jjhkzxv6dP/jgA3ufxx57zO7zBLNnz2ZtbW3skEMO8bTZMAx2ww03sLa2Nnbqqad62iLeQatWrcpqj/v+LfX+bG9vZ9OmTbOXd3Z2ssMPP5y1tbWxp59+mhXitddeY21tbWz//fdnX3zxhb189erV7KijjmJtbW3smWeeyTpv0HOR7741TZMddthhrK2tjd18882ee1ncP2LfHXfckf385z/Pe/8wVvxz1dHRwXbddVe23Xbbseeee85enkwm2emnn87a2trYww8/zBir/vvm/fffZ21tbWyvvfbyPEuzZ8+278mw/e23337LdthhBzZixAj28ssv28t1XWfXX389a2trY0cccYR93+f7nXRdZwcddBBra2tjjz/+uOfaifvQPz4Q98mdd97p+X2efvpp1tbWxqZMmeIZBxT6XYM47bTTstrLGGNLlixhEyZMYG1tbey9996zl4u2jhgxgr355pv28s8++4xNnDiRtbW1eX7XUrcPepcV+yybpsmOP/54+95hjLE///nP9j0gfjf3eYPGnMccc4zdL2UyGXbMMcfY6x544AHPd/r+97/Ptt9+e9bZ2ckYK+39EXZ8Wc79efnll7NUKmXvc+mll7K2tjb2m9/8hhWi0u/dSr7P8t0/ueiTrpurV68GgKwZs1wMGTIEAPDdd99lrTvuuOPs4NBcQaKrVq3CCy+8gM022wxTp061Z4YopbjwwguxzTbbFNX+iy66yDPDcdhhh6G1tRVLliyx3UtXrlyJvfbaCz/5yU/Q1tbm2X/SpEnYeOON0dPT43FHrSdhvtPXX3+NN998E8OGDcMll1zimWE755xz0N7eju7u7qITajzyyCNgjOEXv/gFxowZYy+PRqP43e9+hyFDhuA///kPlixZ4tlviy22wM9//nP7d1dVFcceeywANESK4t7Eu+++m7e0wvr160Md54c//CHi8TgA53lcsWIFAHis7YQQnHvuubjiiiuw7777ltX2hx56CABw+eWXe2boWlpacPPNNyMSieCxxx7Lsibvtttu9rMv2jp9+nSk02mcccYZ+P73v29vu8022+D888/POve0adPQ2dmJM844A3vssYe9XFVVXHrppdhwww0xffp0rFu3zrNfc3MzDj/8cPvvfAHu5fQlV155pSe4/4ADDsAhhxyCVatWZaXOLmX7E044wfMdkskkHn/8cUSjUdx0002eOOnvfe97uOKKKwAA999/v718ww03xG9+8xsAwDXXXIOnnnoKr7/+OkaMGIGf/vSnOa+Lm3g8jgsuuACEEPuYO++8MwDgyCOPxOjRo+1t999/fwDcWiHo6urCfvvth/PPP9/TZkqp3acI1/RiKfX+3GWXXfDDH/7Q/rupqQlHHHEEgHD9m3Cb/O1vf4stt9zSXr7BBhvg6quvBsCthn6CngtB0H07c+ZMfPrppxgxYgR+9atfefY54IADbC8cSik6Ojrw0ksv2etff/113HLLLejq6vLsV+xz9Z///AcrV67EoYceioMOOsjePhqN4qKLLsIWW2xh90PVft8It+DzzjvP8yyNGzcOp59+etb1zsdjjz2GVCqFE0880VPWRVEUXHTRRdh+++3xySef4J133vHsF/Q7zZ49G5999hkmTpzosWQ3Nzfj97//vf3sCGbPno25c+dip512ws9+9jPP73PEEUdg3333xeLFi/Hmm29mtdvfL+SCMYZhw4bh4IMPxg9+8APPus0339z+7b/55pusfU855RTsvvvu9t/Dhw/HeeedBwCBrtnFbh/0Liv2WSaE4He/+x1isRj+/Oc/Y8aMGbj99tvR1NSE66+/Puua58LdL6mqantXDB8+3A53EH9vs802MAzDdq2t5li01PszkUhg6tSpHkuvuGfC9G3Veu9W4n0mCLp/ctEnhZ4QAsKFoxDiYWABmYDCZOmaOXMmTNPEnnvuCVX1esMqioL99tsvVDtEW/yunoQQOwNhT08PAN5J/fGPf8TZZ59tb2eaJhYvXozp06fbMSeZTCb0uatF2O80a9YsAMDuu++e5Uahqir+8Y9/4C9/+UvRWZnee+89AM4AzE0sFsM+++zj2U4Q5HIrxGouF1FJMIMHD8ahhx6a87+wz2rQ87jTTjsB4J3oLbfcgjlz5sA0TWyyySY44YQTMHLkyJLbres6PvjgA7vMiJ8hQ4Zg5513RjKZzHqBBLVV3GPuAYEgSJCKZ2LChAlZ66LRKHbeeWdkMhl88MEHnnXf+973Qj8npfYlzc3NnpegQLyQRdtL3R5A1sDho48+QiqVwk477RQ4kbfPPvsgFovhww8/9LT3iCOOwN57740FCxbgsssuQyQSwY033pjVX+di2223zXJ9FCV5/K5lokyIO55mjz32wJ133mn3NQCQSqUwb948O9a7lL66nPvTLU7d2wOF+zfDMPD+++9DVVX7+XOz/fbbY/Dgwfjkk0/Q1dXlWZfvnRp037r776CBqxhYjR492o7DEqxatQr33nsvDj30UI+QLva5EtsHlWVpb2/Hv//9b3tQX+33jdgv6FkqdlIrX1sJITjggAMC25rvdwrq2zbffPOsZznfb+A+TlBclf9YuSCE4Oqrr8bNN9/sWb58+XK88sor+OKLLwAEP3sHHnhg1jLx2wX1VcVu738OSn2Wt9pqK5x77rlIJpM488wzkUqlMHXq1KLKYfnvPdG3bbfddlnPnOjfxHuhmmPRUu/P9vb2rP66mLFbtd67lXqfAeG0iaBPxuhttNFGtqXIPdOYC2EBDIq5ClPb69tvvwUAbLLJJoHrN91004LHEOTyNxcDErc1izGGl19+Gc888wwWLFiAr776yr4Z8onXWhP2O4kZ0VzXsVRWrFgBVVVzxtSJDnHlypWe5a2trVnbCgHaCNe1N1FMeYV8BD2PF154Ib788ku88847uPfee3Hvvfdi4MCB2Geffewg8ny89957ePTRR7OW77///hg3bhwymQw23XTTnKKgmPtH3OO5+hp/Jl/Rt5xyyil5v8Py5csLnjsfpfQlw4YNC3ypiYyQfg+JYrcP6jfE9cvVp6qqio033hhffPEF1q5dawsXALjqqqswefJkZDIZnHHGGfljGnwEXU9xXfzZYXPNovf09GDatGl49dVX8fnnn2P58uUwTTP0rHsQa9euLfn+9MeXAOH7t7Vr19oJGQpNpKxYscKT9TrfvZnvmcn1m4vvJ2LBjznmGLS3tyMSieD000/Hww8/jK+++goXX3wxHn74YQDFP1eiDWGynVb7fbNixQpomhY4MPQP7levXh0YJzl8+HCcc8459vfKJQrEcrFdvrbm69vEsebPn2//LX6Du+66C3fddVfgPkB231YoJi+IefPm4e9//zvmzZuHL7/80mMRA4Lv9y222CJr2YYbbghN0wK9v4rd3v8uK+dZPu200+y+WyRECkskEskSRbn6Nvc6N9Uai1by/ixm7FaN926l32fF1B3uk0Jv++23x5IlSzB37tyCgzwAdnahoIQjYV7Cuq4DyF2jq5gbPOxL3zAMnH322XjjjTcQjUaxww47YNddd8V2222HnXfeGeeeey4+++yz0OetBLmyfIb9TuL6lTPwCYIxlveY4rz+h7DS7ZCUT9Bv0tLSggcffBBz587FSy+9hDfffBPz58/H008/jaeffhpTp07N22EvWbIEzz77bNbyLbfc0k7WUsr9U0o9IP8LXjxT+++/f97kGP7JkWLOXWpfEpRcAXCuh399sdsHfQfRl5bye8ycOdMefLz44ov42c9+ljXAyUVYy18uli9fjuOPPx7Lli3DwIEDMWrUKBx00EEYMWIEtt1221CJw4Io53qU07+J+7KpqcnjUhVEMc9FMb+5aZqYP3++7QLpP4+qqjjvvPNwwAEH4KijjsK7776LlStXYsMNNyz6uRLbh7lm1X7f5NvO/wx1d3cH9m3jx4/HOeecU3BsUs2+TRx73Lhxea1P/omEYs9977334pZbbgEhBNtttx0OOOAAbLvtthg7diymT58eOMkH5O6vGGOB64rd3v87lvMsL1u2zH4O5s2bhwULFoS2epbbt1VzLFrq/Vnu2K0a791Kv8+K+Y59UugdfPDBePHFF/H00097/IuDEFn4NE2zzcDFImawgvy8AWd2oJL84x//wBtvvIGxY8finnvusU3tgrAxT8VCCMkp6Do6Oso6tjCt57per7zyClKpFPbYY4+iahhutNFGWLZsGZYvXx442yjKQYSN6ZQ0JqNGjcKoUaNwwQUXYMWKFfj73/+Ou+++G7feeiuOP/74nO6hRx55JI488sjAdZlMBpqm4dtvv4Wu64EvxWLun6FDh+Kzzz7D119/nXUvJpNJrF+/3mP92GijjfDFF1/gxz/+MXbYYYeCxy+FUvuSoFlqwOkH/S/BYrcPQsRhuku4uMlkMvj222+haZpndnXVqlX4/e9/D03TsMcee+CVV17BLbfcYsfuVZtbb70Vy5Ytw/HHH49LL73Ucx8J97FSGDhwYEXvz2LPyxiriKU+H7l+c0IIjjnmGFu8i1AAP9tvvz222247fPzxx1i3bh023HDDop8rMZOe6930+OOPY+jQodhrr72q/r4Rbf/uu++ysoD7LRvDhg3zWNGCjrV48WIsW7Ysb1tzXVs3Yv9csab+tolrOnnyZJxxxhkFj18KS5cuxW233YbBgwfjvvvuszMfCx555JGc+y5fvjwrv8Ly5cuh6zq22mqrsrf3U+qzzBjDpZdeimQyiQMOOAD/+te/MHXqVDz22GM5xWclqeZYtJL3Z7HnrfZ7V5wHKP59Vix9MkZv0qRJdpDmfffdl3M7wzBw+eWXI5PJ4Ac/+EHJHe/OO+8MQgjeeust27rn5vXXXy/puPn48MMPAQDHHnts1oO1cOFCe1BVaRfDRCKBVCqVVQvoq6++yurIi0VYT2bMmJFlHWWM4dprr8WFF15Y9HF33HFHAPAE6QtSqZT9+wTFmkgam56eHvzoRz/CYYcd5lk+ZMgQ/PKXv8TGG2+M7u5u+2VT7EyfpmkYPXo0kskk3njjjaz1K1euxOzZs5FIJEKlbN5ll10AIDDxyFtvvZV1348bNw4AAs8NAKeffjqOO+44LFiwoOC5c1FqX7JixYrAGl+vvPIKAJ50o5ztgxgxYgRisRjee+892+XezWuvvYZ0Oo0dd9zR81tfddVVWLt2Lc466yzceOONGDJkCB566KGsGItqIa7xWWedlTWAEzWwik0yBVT+/gxLJBLBDjvsgO7u7qz4GID/1gcddBB+/OMfl1zbTSD673//+9+ee1DEfovrlqv/TqfT+Oabb5BIJOzkJcU+V+Ld9NZbb2Vtu3TpUlx++eW45557PO2t1vtGxA0F9SHFjjXc19YPY8xeLhIP5UP0baK8lZtVq1bh448/Djx3ULIVALjllltw5JFHBlokw/LRRx/BNE3stddeWSIvnU7b927QsxfUrnx9VbHb+yn1Wf7b3/6GWbNmYaeddsKtt96KPfbYAx999FHesW8lKeX9EfY9XMn7sxhq8d4FSn+fFUufFHqapuGGG25AIpHAjTfeiJtvvtlO+CH4+uuvcc455+D111/HFltsUVThZD+bbrop9t13X3z11Vf4wx/+4Ok07rrrLvzvf/8DUFlXQBEr8Nprr3keoKVLl3qy94lA2Eoh3AFErAPAB9tXXXVV2cfeeuutMXHiRHzxxRe47bbbPN/rrrvuwldffYV99tnHtuYJk3q+QtMAcOKJJ4JSittvv93ulADe0V922WVYuXIl9tlnn6JiKSWNQTweh6qqmD9/Pv72t7951s2aNQvfffcdNttsM3vGT9wzxVifRZ3Ha665xmN96ezsxAUXXIBMJoMjjzwylBvgEUccgebmZjz00EN4++237eVff/01rrvuuqztjz76aESjUfzf//2f56XDGMOdd96J//73v1i+fHnBWkn5KKcvueKKKzwzts899xxeeOEFbLXVVoEJBYrd3k8ikcAPf/hDpNNpXHjhhZ5n//PPP8e1114LADj++OPt5S+++CJefPFFbLXVVjj77LPR0tKCiy++GKZpYurUqWULkTCIa/zqq696ls+YMQO33HILgOzrG7Z/q+T9WQzivJdddhkWL15sL+/p6cHUqVOxaNEiDBgwoOh4Kj+77LIL2traMG/ePNx6662e9+v48ePtz5lMJuu3XLt2LS666CKsWrUKxx13nH1Ni32uDjroIAwcOBDTp0/3FLdPJpO45pprAHBPIqD675vjjz8eqqritttu80ycfPrpp7bYDMvRRx+NWCyGRx55xBYlABc+f/zjH/G///0P7e3t9sA3H6NHj8aoUaPw4Ycf4t5777WXp1IpXHrppVnJJCZOnIhtt90Wb7/9Nu6++27P7/rmm2/ivvvuw//+97+yLCriuXvvvfc8z1FXVxcuvvhi20Ib1LfdfffdnoH8ggULcNttt0HTNDsbajnbB1Hss7xs2TL88Y9/hKZpuPrqq0EIwZVXXoloNIo77rgjb6H6SlHK+0P0CYXew5W8P4uhFu9doLT3WSn0SddNgMfbPfroo/jpT3+KP/3pT3j44YcxduxYtLS04Ntvv8VHH30EwzAwYcIE3HzzzR53qVK47LLLMHfuXNx///149dVXsd1222HRokVYuHAhNt98cyxdurRsX2g3RxxxBO677z688MIL9s2+evVqvP/++6CUYosttsCSJUuwYsWKopIOFEIUdrz11lvx6quvYsiQIZg9ezZUVcXEiRM9g9dSuPbaa3HCCSfg3nvvxYsvvoi2tjZ8/vnnWLhwIYYOHYrf/va39rZbbbUV3nzzTUydOhU77LADLrzwwkAxLdz5brzxRhx33HF2Ads5c+bgu+++w7bbbmu/rCW9j8suuwzHH388rr76ajz66KPYeuutsXr1asyePdteLxg2bBgURcHs2bNx5plnYqeddvJkCwvigAMOwIknnohHHnkEhx56KMaPH28XsV27di122mknXHDBBaHautFGG+Gaa67BhRdeiNNPPx0777wzmpqa8M4772DYsGFIJBKe7TfbbDNce+21uOSSS3DWWWfh+9//PoYNG4YFCxbgiy++QCKRwK233lqWi06pfYmmaVi2bBn2228/TJgwAd999x3mzJmDlpYW3HDDDVkD/GK3z8UFF1yAjz/+GG+99Rb23Xdf7Lzzzujp6bFj8E477TQ78+LatWvtVP9iAATwor1PPvkk3n77bdxxxx349a9/XfL1C8PJJ5+M//73v3ZhY+EaNH/+fAwZMgSEEKxfvx7pdNq+DltuuSU+//xz/OQnP8G2226L66+/PvDYlbw/i+Gggw7CzJkz8eijj+Kwww7DqFGjMGDAAMyZMwerV6/G8OHDMXXq1LLPQwjBzTffjFNOOQX33nsvXnjhBWy//fb45ptv8OGHH0JVVTDGcM899+Dhhx+2s4kmk0nsueeeSKVS2Hfffe2smEDxz5W4R88991z85Cc/wdixY7Hhhhviww8/xHfffYfdd9/dTp1e7ffNdttthwsuuADXX389jjrqKNuS9s477+D73/8+1q5dG/pYm2yyCX7/+9/joosuwjnnnIPRo0djk002wSeffIIlS5Zg4403xi233BIqLo4Qguuvvx4nn3wybrnlFjz//PPYaqut8MEHH6CjowPbbrstFi5c6Nn+j3/8I0499VTcdtttmDZtGrbffnusXLnStrRfccUVodweczF69GiMGTMGH3zwAfbbbz+MGzcO6XQas2fPRldXF4YPH45FixZlJTcBePKMI488EhMnTgQAvP3229B1HZdffnlgyaxitw+i2Gf58ssvR3d3N8455xxbdGy++eY4++yzcdttt2Hq1Kn4+9//XlJMZVhKeX+I3/SPf/wj3nzzTZx22mm21dxNJe/PYqjFe1dQzPusVPqkRU/Q3t6Of/7zn5g6dSq23357zJ07F6+88gpWrVqFfffdF/feey8eeOABT323Utlkk00wbdo0HHnkkejs7MTLL79sz7qJlMfFxJUVYuONN8bf/vY37Lvvvujq6sIbb7yBFStW4MADD8S0adNw2mmnAcieQS6XKVOm4K677sKYMWMwf/58vPfee9htt90wbdq0UBnJCjFs2DA8+eSTOOmkk5BKpfDKK69gzZo1+OEPf4gnnnjC44t9zjnnYM8998SaNWvw3//+N+/s1RlnnIH77rsPEydOxKefforXX38dAwYMwK9+9Ss8/vjjnmxGkt7FiBEj8Mgjj2C//fbDqlWr8PLLL2PRokXYd9998dhjj3mSRQwePBhXXXUVNt10U7zzzjuYMWNGqHNcfvnluOWWWzBq1CjMmTMH//3vf7HZZpvhsssuw4MPPmjXswnDQQcdhAcffBC77rorPvnkE7z33nuYNGkS7r///sAXx2GHHYZHH30U+++/P7799lu8+uqrME0TRx55JKZPnx6Ylr0YSu1LNE3D//t//w9jx47Fm2++iSVLluDQQw/FE088EZgEq9jtc5FIJPDwww/j17/+NTbaaCO88cYb+PjjjzFhwgTce++9Hu+Ma6+9FitXrsRhhx2GXXfd1XOcK6+8EpFIBPfdd1+WW1ml2XvvvXHvvfdi7NixWLRokX3fnXrqqfjHP/6B3XbbDbque2aPL7nkEowbNw5fffUVZs6ciaVLl+Y8fiXvz2K46qqrcPPNN2P06NH49NNP8fbbb2PDDTfEz372Mzz22GNZrlylsu222+Lpp5/G8ccfj0wmg5dffhnffPMNDj/8cDz11FN47rnncOqpp2LYsGGYN28eAD7rv+uuu+K2227D3XffnRWjW+xztffee+Pxxx/HlClTsHjxYrz22muIx+M499xzcc8993gGm9V+35x22mm45557MGrUKMyePRvz5s3DUUcdhdtvv73oYx188MH2dViyZAleeeUVUEpx5pln4umnny7KajF8+HA8/vjjOPLII7F69WrbY+rBBx8MzErZ3t6O6dOn2yL59ddfx9dff4299toLDz30kKfuWCkoioJ7770XJ5xwAhKJBN544w0sWrQIY8eOxd1334077rgDQPA46YYbbsCxxx6Ljz/+GO+//z523HFH3HfffTnbVOz2uQj7LD/xxBOYMWMGttxyS5xzzjmeY5x55pnYeuutMWfOHI/3VTUo5f1x7LHH4pBDDkE6ncabb76Z1wWykvdnMVT7vSso5n1WKoTJPPFlk0ql8Pnnn2OzzTYLDJg855xz8Morr+D555+v2k0pkUgktaK9vR2JRAJz5sypyvYSiURSD0466SS8++67mDZtWii30WK3l0hqTZ+26NWKTCaDo446CgceeCBWrVrlWffWW2/h9ddfx1ZbbRXafC+RSCQSiUQikUgk5dBnY/RqSXNzM44++mj8/e9/x+TJkzFu3Dg0NTXhq6++wscff4ympiZcd911si6bRCKRSCQSiUQiqQlS6FWIK664AmPGjMG0adPw6aefYv369RgyZAiOOuoonHXWWWUFFEskEolEIpFIJBJJMcgYPYlEIpFIJBKJRCLpY8gYPYlEIpFIJBKJRCLpY+R13VyxInxRYYlE0jsYMqSl3k2oCLJ/kkj6Hn2hf5J9k0TS9+itfZO06EkkEolEIpFIJBJJH0MKPYlEIpFIJBKJRCLpY0ihJ5FIJBKJRCKRSCR9DCn0JBKJRCKRSCQSiaSPIYWeRCKRSCQSiUQikfQxpNCTSCQSiUQikUgkkj6GFHoSiUQikUgkEolE0seQQk8ikUgkEolEIpFI+hhS6EkkEolEIpFIJBJJH0MKPYlEIpFIJBKJRCLpY0ihJ5FIJBKJRCKRSCR9DCn0JBKJRCKRSCQSiaSPIYWeRCKRSCQSiUQikfQxpNCTSCQSiUQikUgkkj6GFHoSiUQikUgkEolE0seQQk8ikUgkEolEIpFI+hhS6EkkEolEIpFIJBJJH0OtdwMkYTBhGDoIoSCEAiAghNS7URKJpJ9DCGCaGTAGq2+ism+SSCQNggHDMOTYSdKvkUKvwVFVgDHAMEwwZoIxsYbKzksikdQNSgFFATIZWBNRAEDA+yMqhZ9EIqkLhPC+SY6dJBIp9BoW0VFZf4EQYndUjDEAJgDTmkknoFSFYTDZeUkkkqqjWm8O0f/wfkf0TQyMOcJP0zTouimFn0QiqTqU8v84+cdOlPI+yTQhx06SPosUeg2IogD5+hp/R0QpRSIRw/r1HXLWSiKRVA3vBFTQetHP8H8ZY2hpacLq1WvBmGGv432TAtk3SSSSSlHs2EnTNCgKRXd3j2vspFgCUHgnyP5J0ruRQq+BIASIxVQwxqDrRuEdnD1dblPZs1YcKfwkEknpUAo0N0fR3Z0KvY/oZ8SsurD4AYYUfhKJpCIQAiQSGtJp3epjwu8nBB0g+icDpukefym25Y/vI/snSe9CCr0GQbgbUErg76e4axQJ3YH5OyIp/CQSSam4rXhKPnNeDnj/QwCwHH2TFH4SiaQ0xNhJUSgoJTCM8EIP8FoAg/snr/AjRLHd0IP2kUgaDSn0GgC3uwEXYsV2HPk7tnDCT7orSCQSL954l8oTTvjJSSmJROLF70YePA+ev68oNHce1D8xZoAQKfwkvQcp9OpIoXiXIo9WxHkLz1pJdwWJpH9TKN6lGkhvBIlEUojcE1DV7QvcfY3wsPIKP5lxWNJ4SKFXJ0Rq8uwZpWz3pjCU059IdwWJRCKo7ARUeUjhJ5FI3OSbgPIvJ0TEBxfnzhmGXN4IPOOwk5RKCj9JvZFCrw64U5M3ItJdQSLpn1TLVZOQyvR3UvhJJP2TYiegVFVBPB6FaZoAgEwmg1Qqg0zGm7ClUv1DUMZhf6kZKfwk9UAKvRoSpqPidam8y+LxKJqbY0ilMkin+X/+faqJdFeQSPo+1XLVrGb/JIWfRNL3CTMB5RZv8XgUlFJ0dHQjnU6B1/NUEYloaG5OAADS6QwYM6vW5lzCTyaektQaKfRqRHEz5cTah6CpKY50OoOOjm6oqoJoNGJ3VKlUGul0BoZRvc4qq2XSXUEi6VOICajqCTIn62a1kcJPIulbFDMBRQhBc3McmYyOnp6Ua2KaeSbJCSGIRDTE41FomgpNU+31mYxele8hMw5L6oUUelWmlHgXQgBNUxGLRdDdnYRhmGCMIZXirgd8G3dHpYFSaovCanVUwW2V7goSSW/FPQFV6mPZyI+zFH4SSe+k2AkoSikiEQ1dXT0FJ7/5eCoNxhgiEQ3d3T32eKq1tRmmaSKd5uMtXZfCT9K7kUKvipQa76JpKhTFREdHd85tREeVSqVBKUFrawsMw0Q8HkNrqwrDMOwZquKKr5dHfuEnLX4SSSNQr4y/9UYKP4mk8XEnqwvz+CUSUagqRU9PqiQPJ9NkSCbTSCbT1vm5aEwkYtC02oynwpeaIVL4SYpCCr0qUUq8C6UU8XgEhmGiqysZej/RGSaTKSSTKev8vKNqaopDVXlHJWL8DKP+wk/OWkkk9aHatfGCaNRHWtYYlUgai2KS1XFPJp6/wDQr5xpummbe8ZSuO8KvWuOp3H0TZI1RSVFIoVdhSp0pj0RURKMRJJNpa1BRHoZhoqcnhZ4e0VEpiEQ0tLQkoCgKdF13dVT1j/GTwk8iqT71qI3XqNmFg5ClZiSS+lDs2EmMmUR4SzQaKfm8hQgaT0WjtR1PSW8ESalIoVdBSp0pTyRiAGAnXKlGDSvDMNDTY6Cnh1sKVVUIv2YoCkUmIzqqdEVnxgoh3RUkkurTSLXxehOy1IxEUn2KnYByj5kcWNGTWHy8UfzzahgGursNdHcXGk9l7PIOlUYKP0lYpNCrEKXMlCsKRSIRs7JnugN+q/8w6roBXXc6KpF6eMCAFlBK7U6KpyCut/Bz3BUSiRi6u9Oy85JIQlIPV00vpQ2mGpF8pWZisag1USbjjyWSMBQ7AZV7zFRfco+nmms2nson/CilUFUVqVRGjp36IVLolUmpqcmjUc3OEFVLC1ouMhkdmYyOrq4eALyjikYjaGqK2+vTad651kv4EUIQjUat+EU5ayWRFKIerpr9BX8/E41GkE7rME1ZY1QiKUSxE1CNNmbKR7jxVO2EH6UKNE2zks3IsVN/Qwq9MiglNTkh3O3ANFlgVs3cz3y+OlSs4g+o6KgAUe5Bs4KRnWKjQcXba0H2rLp0V5BI3FS/Nl5x9IdHkLuXO/2TLDUjkQRTXG28/GMmAe/rGvN5co+nACAS0ezkLoAznspkMlXps/19EyDHTv0JKfRKoNR4F+F2kEym89S6K/4pr/ZgjjF4RJ2o4RdUvL2aNfwIyf6u0k9dIvFSbGpySeVw90+yxqhE4qVUV838Y6bcUFr4earHI5c9nlI94ylew6+075wLOXbqv0ihVySlxrtEoxo0TQ3ldtDoz5K7hh/gLd7uLjZaeeGXz6oJuy3+tsrOS9JfKCY1ea1opLZUl/z9kyw1I+nPlOKqGXbMxMn2bOKTXSSne2Qj9E18PMWLswPOeCoWq/Z4yossNdN3kUKvCEqJdyGEWG4HJjo7e6rTsDrjF36i2Gili7eX0qdI4SfpD8ismvUnyOMg//ay1Iykf6AWMdIkhKCpKQbDqMWYqfESRWWPpwgikYhrPCWEXzr0eCqf2M23j79d/lIzjvCTGYcbGSn0QlDqIEpVFcTjUfT0pEI/kI3sZx6WahYbLXcGTgo/SV+jlglXggYL8vmoDFL4SfoaxY6dShkzCfqqq7ppMs94ilKKaNQZT4mJ9FSqesXbAVljtDcjhV4BSnXVjMUiUFUFnZ09NclS2cjPU9hio6lUoZozhV03iyWs8KNUgXRXkDQSjWDF47G6GhhjeQYcjTdrXg14v1C5/il8jVE5KSVpPIodO1VmzNT373/T9I+nKCIRHt+nqoo1kZ72FG+vRrcga4z2HqTQy0OprppNTTHoulGi20HxRT97G7mKjba25i/eXqxrVCnkEn5eASr91CX1pZ618cRz2NQUA2MM69Z1IJPR7QGHfwKHPyP1aWutqWb/JL0RJL2BYiegyh8zec9di30aCT6RnkRPj794e5PdD5smq1rhdkG+GqPWFjLxVJ2QQi+AUlOTl+N2EKZNfZWwxdur3VEFId0VJI1GvWvjUaogkYhmFS0OHnBErFTiqm3tq2btqP6EFH6SRqPYCahqjpnC0Be7If94SlUVNDXFEY1GEYtFkclkXGOqWhZvFxmHnaRUUvjVBin0fJSamrzWrpp9mVzFRqPRCCilaGlpqkvxdkC6K0jqRyO4avLkUlF0dSVdEy/B9zcfcPRAUagdX+IuGlzPWpzVoN6PuRR+knpS7ARUPB6FotAKjpnkuCsIJyeCjp6epGsiPQZKCdLpWhZvl6Vm6oEUei5KSU0u3A4ymfLdDpxzyxvcjRB+qVQasRi3JDRu8Xa/u4JX+MnOS1IK7gmoepFIxEAIQUdHd0kDAnfRYH/tKMZYTVKIV5fGeral8JPUgmInoCjlmcgzGd2OM6sEpfWN/SN+2J3fwD+R7i/enslwz4tMpnoT6fmFn7T4VRop9FD6TLmmqYjFIujuTlU025G8n/OTq3h7S0sCplm/AWPwwAqy85KURb1r41FK0dQUQyqVBiGlxcoGPRvu2lE8hbjmSyGeLrski8RBCj9JpSnWVdMZMyXtRCGVRN6uweTrs73jKUDTuPBzF2+v9kS6rDFaXfq90FNVgmhUs2uWhCUej4JSgs7O7j7p592IBNWCCa45k128PZXKQNfrJfyku4KkeAgBmpoiSCaL65sqibC6CVdNTSvllVG4g+QpxNP2d3VKsohMco57UTUGiJWhd70IpPCTlEMkQu3kaWGozZip+Puzv9zSYa45Y40xkS5LzVSWfiv0hBWPEEBVKVIhPQgoJWhqiiOdzqCnpxozHL1rsNBo+AeMonh7IhGDplWueHspSOEnCYuYKVcUJXCCoxYkElEA3FWzHEppur8ki5NJzp2ZN41USiZ2qRRS+EnCIMZOlBLrWcy/veMRUK0xk6QwBPxZLo5GmUiXwq88+qXQ87sbhL0hqu12APTNLFCVopTnNnzx9nTNLQVh3BXcok92Xn2fbDdyVpKrZDmIySyRIdPTGjuGuLYdVa7MvAMH8rhBEcObyWRkH1ohwgg/RdFc94Tsn/o6xY6dhEdANcdMglKe+/7SV1TqHdIoE+lhhB/PjUAgx079UOj5M0OFnQ1OJKJ2IgJJvSjfspG7eHtTkcXbK09Q5xWNqlBVxQ6clrNWfZegeJdaC6taTGZVAndCgVxxJVz49dbELo1HUP80cGATVq1a61oqaozKjMN9iaA8BoVexYlEDABqOGbqJ6qtgSg0kW4Yhj1hWMk8Fn6C+qampih0XXeFZfVfb4R+I/Ty1cbL94O73Q5qldUxuD3956asJcHF2yO+4u3pqtacyQUhXNSJwX4+dwVnZl3SG8mXmrxW7yMRQ5N/YMYC21Nrq6ObXHElbvci3n+nq+yu3b/6aP6eEv/lrjGqKAoYKyJjh6ShyJ1wJbgvUBSKRCKWVWezFpTWV/b957ZWoiZoIp273Cc8E+nVjrUmhIBS/9gp2w2dUmfSvC/TL4ReqbXx/IkI6kk/mnzISS2ugaj91d3t1PBzas5QTwaqWsQGueOzcrkraBpBPK6hq0vGP/Q2Cmf8rf49Vm7ccZjnspb9V3ZcCUU02hju2n2ZXDVGN9igBWvX9vSrGfS+Qr4JqKBSUNEot6x3dfXUfGI0N/k8IhqljdWnHrHMhmGgp8dAT497It0fay2Kt1e2L+aTj/nGTiaiUQ2EqEil+nZm5z4v9EpNTV57t4Ny6Q8v0donpQhTc0YUI61G2wghOTtAd4yfTEjR+wiTmpxPTlXv2S7WVbO0OJj61qoyzfzu2s5gI13m4LR/PYPugVTwemJvJ+ldhCs55Vj0COFjJtNkdRszlVqDWN6ftSNXrPWAAc2glNo1/CoxkZ4viZnTN9F+MXbqs0Kv1Np49XQ7kOSnETrkXDVnqlW8PYxLHKVS6PU28s2Ue6ne71p6uvMGeBDLwO+u7Qw2WkApQTqt19Rq31sJkw1WXr/eR9jaeE5CHj5mSiYbOyZ24H8fBkzT/nJrdzup34Q7NKo13T+RLvriRMJJslVqXxymf+IT6X3/JuiTQq/YIp6CxnQ7kLhppI65GjVnZm++G3Zc+l/777CdVSNdF0lu8sUKB1Gsu3m4NhA0NcWQyehVc9XsTRSy2teiYHBvpJiyH4060JR4CT8BJbaniMejDTJmCo4ZBICBM/4GEAoo1LsMAA4+pwZtqz+9YdIlbF8cJrtymP6JUgJdb/zrUi59SuiVasUDgKam+rodSMJQ+7TuxVBuzZnZm++WtUwKvb6DewKquHFv5QbJqqogHo82fFbNepJ78qapZnWjegP1qu8oqTzFTkCJySKAewQ0Mq1vPcw/UAKYjP/rgr1wLwYCWLvL8TVvmyQ/2X0xz5vhzq6caxJOjp0c+ozQK9WKpygUikIb3u2gMH3/bq1nZr9SyFVzpqkpZqceFp3UB2P2DDxG2Fmp+s+mSnJRzgQUY7lnqYslHo9AURR0dvaUMUAvbb/eatAJSuwS9Azzwu11bmyNCTeQ6l19dn+k2GR1YrKopyeFeDxa/QaWQTSqeTvfoH7Y+tID330Ma8cfU5uG1Zi+8Bzyvpj3tUDuSTjhQRXmO/eXyao+IfSKdTcQRKOaVeTR7OUir//Qm5/J3DVnEkgt5wPJ3VfO9mQDDD8r1YsvTB+m1AkoL+WpJDH7rusGOjt7Cu+Qh+DbLH/7+tKtGfwMc1dtVVUxYECznUyg3pmaq02Y2fD+EgPTWyk2WV0sFoGqljtZVB38yViammIwX/iTd6N8A0VKMfC9JwBCsHbHo6rSxvrR2N5QpZDbgyqG1lbVih2N5y2r44ydeulMZEh6tdArdaacEGJliDLR2dmDlpZE5RsnqQIEvBZK30DUnJk1Yld7GSHwFG9XVaVgfIsUeo1JqRNQbsqN0XPPvleqhlzx7em7L1L+DCeRTCaxwQYD0NXVg2g0YmeRq3U5llpSKOsm30b2TY1IsWOnSk4WVRNCnNrH+vP3ZndWQbNuAR3awNnTAKDPCL7e6lFRDH4PqsGDB4Ix01O8XfTF4l1YCdfNo446Ch999FHW8ilTpuD2228v7+AVotcKvVJnyqsx8JHUhr7gfuDnsyn725+jQ3mae3fx9oEDW9DS0mSlHg4u3t5f/Mx7C+W4amZTukiq3ux7Pxg1FA0XNKIOZ39I7CK9DXonxY6detOYyRakz98bWtR511v7WPsO/GA6AGDtmCMq18g60R8fQ29ZHe590dSUgKoquP3227HJJhtju+1GY9iwzUtKGMUYw6JFizB58mTsv//+nnWbbbZZRb5DJeiVQq/UmfJcAx8RB9MfHwRJ/Vh61CH25+jQSNZ6XTdgmgxr1qwHEFy8ff78BQA2hqaVbpW+7LLL8OWXX+Lhhx/2tm/pUtxwww149913AQB77703LrnkEgwaNKjkc/V1KuOq6cAYd0kpht4y+94fqHRW3kZCCr3eRSkTUPF4FIpCG9JV0088HuHlUV74v/Bf1Cfsstdb8XsfPgMAWDv68HKbWSf6nutmsQjvC1G8fZ999sVHH32Au+++HV9//RV+//ubsNlmw4o65rJly9Dd3Y19990Xhx/euPdGrxJ6xWaGcvYLM/CRD0Kjw2dc+sZvtPzUI5HqSHuWjXzv1azt3LNMQamHP/54Lm666Xokk2mMHj0WRx11DIYO3Th0O5544gk88cQTGD9+vGf5mjVrcMoppyCdTuPMM8+EYRj461//ivnz5+OJJ55AJJItTPs7lXDVzKa4+73as++ljvX6uutQmInCQjElQa5FjUxYoSepP8VOQFHKw1t4CZZU9RpWAdzlYth//s+1IuALU+qppZfjgNn7Wg/4wI/+icwuP+p1kzP905CR/wtvuulm2GGH7+PAA38AoLS+6rPPPgMADB8+vPjm1ZBeI/RKTU0eZuAjLXq9h77yG6U7HZEXG6yVdox0BvvvfyCOOeYYfPvtasyd+yFoyLe5YRi45557cOeddwauf+CBB/Dtt9/i2WeftTux0aNH47TTTsP06dNx9NFHl9TmvkipE1BhKCZGrzaJEoo/bl95ZvNT/CSUP6bEnZxJVXmMrsjo2YiJXXiilfztolRa9OpNsRNQmqYiFov0ihIsTrmYFCJvPRIs7gCvsHN/9l+YIIEnsKyE2rtPQgOg7Hk8DMOwki+lG/5a9SfChLO4+6VSJ6QWLlwIwBF63d3dSCQaL+dHwwu9cuJdGjlDlKT/svzUIwEA0ZZIllWvFAghiMcT2GWXXQtvDCCVSuFHP/oR5s+fjyOOOAJvv/121jbPPfccxo8f75mp2nXXXbH11lvjueeek0LPotjU5KVROBlPLV01c33PpqXvAoyBMGvAY/W54u8W5gyESEB/vH74XpVtaA2pxG8vkjMJC4qqKohEnMQumUzGzujZCO+z8Fk3a9MeiZdSXTUp5bXxGuAWy4t7fBd759GC7pfZy0PE8LksgEyss/bT33qM/7nj4XYCNRFHz8utNM4F7EveUGEIkyjK2bb0znvhwoVoamrCddddh+effx7d3d3YfPPNcd555+Hggw8u+biVpqGFXqnxLo4pP9zAhw/SGvtBkB4wfcMNaM3PjoMW15DuTMM0GLSEhkx3Bloil1Wv8D1Z7GVJpVLo7OzELbfcgoMOOgiTJk3yrF+3bh2WLl2KKVOmZO07YsQIvPbaa8WdsI9SbGryUihUR68REiVon72JCDMdkRck6HKN9oVCZgytC17JupnXb7tPtZpdcSp9H4jELt3d/B0mYnRFYhch/DKZ+tTwC5t1U1J7SnHVbGqKI5XKoKensRMFEQIkEnEYBh/fxd99PP9LMJeVTxzMP0vnu3Asl1q2jqu9/yzWbrcf/2w9oxts0HjJlxpId1adWsUGf/bZZ+jq6kJHRwduvPFGrF+/Hg899BDOP/98ZDIZHHHEEVVvQxgaVuiVGu9SmttBb3gC5AsTCD9L04h0/PpkqDENXSs6oCU025qnJTRs+fRzNWtHc3MzXnrpJahq8OO/fPlyAMDQoUOz1g0ZMgSdnZ3o6OhAS0tLVdvZqFQ2q2aoMwYujUYj0LTaeiy4a1Vp8191We+suo+MZYs6xjziL/ugAZ+tQVTrglesv/k5G1f4VX+i0B2jSwigaRqiUQ3NzdxVKJVK1zR2SCZjaUxydOs5iURURKO9w1WT10aLIZlMI5PRucgD8os5N0GDSrHMstoRxhzrnfvYvnO4LXyt8/8DUAXrt93H9YxmF/QWbp69IQa3NxOubypf/B599NEwTRMnnHCCvezggw/GIYccgptuugmHHnoolNoOFgJpOKFXziCqVLcDx6InaWR680+UuuJM6MkMmGki0uQkMkl1pBFtCU5sEjbBQ7FQSvPG8nV1dQEA4vF41rpoNAqA+6L3R6FXnYQruQlyCRUz2qIOaM2Z+y9EmJkt6sS96BZ9boTYIzS/8CMUYM5AiA+osoVfI4m+WvdNjAVn9IzHo2htbYZhmHYplmoNKsMMpigl0HUp9GpBKWOnRCIGAOjo6C7pnLXMb8BFk4aurh6YJkN81jSv+Cr2IbTegcy3n99F00+gCKT8wrcuet12Qc9OvkQRjWp2XbdaxuD2twkX7jJe/Umo4447LmtZLBbD4YcfjjvvvBOfffYZ2tvbyzpHJWgooVeqq6ZwO0inG9/toFr0j2e4d3ZWxnU/Q7orDTXmuGdmunkcTsvGzXn2DP99KzlREealEzbpS1+h9lY8gff3d2a0U8hkajsrHPnfv73iziXsPKLOZ+XLwiUE/YMsz37WIIrAEX7O9hStC60stZQ2RHxfPbumwoNKwxZ+lbLaSIte41Ds2En0I9wKXK4FuPrW7EBBmuudV+BCBPY59jGzrXdZ29vbBLt7tnz+Bm/rNnt6djPN/DG4bjdP+cyUR5hQrDBisFRECaru7tImUCpNwwi92rpqepEPlaSa6D0p24rHTIbuVZ0AYC8bdM9jgfvVK2NdU1MTAB7L50csE9v0BypdG68Y3K6S0aiGSES1Z7RrRfSTl7zizi3sglw3BSEmDDxdvj82Bj7BSCgXffY6ap+nddHrYIRkDa5qR2PFeAcPKrWspBHpdKbkeym80Cvp8JIQlDIB5VjGkmVbkqr9fnLHDrrj3OLvPRlK0OWcTMobtxeis3e5e/rPKfZv/mIGOrfKnSDNH4MbiWieGFxu7UtXxBW7N3tDlULYRFHl3L/Lly/H6aefjgMPPBA///nPPesWL14MABg2rLi6fNWi7kKvnNTkiUQUhJCS3Q687ehnT0IvpDf+RMZ1P4Maj4KZDD2rucDTElEw04SezHisfH7qNZDadNNNAQArVqzIWvfdd9+htbW1IVMIV4Nau2pmw12jmppiME2Gjo7aumpGP3rBK+IKJVsJctcUA6dcFj6x3rAslNYFty87dYs7axO3lY8qgGGAKApaF71uL+vYevcivml5NHp5Hj6oNNDdzYsFi6QRAwbEQAhxCT+9KC8CadGrH8VOQHGXb9GPVM7SUK17X9MUxGLRrEn8+PtP53S79BPoZuknn/XOvT7Agudx82QmGFWduGUATUtmAgC6tpiQt51AIVdsw3bzNIxSPDl64eCpDAhB1V03hw4dio6ODjzxxBM49dRT0dzMvbO++eYbPPXUU5gwYQKGDBlS8vErSV2FXqmpySmlaGqKZc3ylEqjvYj87aGUormZZxFtxNS9taQ3fW162/kgsQgy3SkYqTS0uCPq0l2pvCKPE24gVWnrTmtrK4YNG4Z58+Zlrfvkk08wcuTIip6vEamfq6YXSilUVUFXV7KmBXqjc5/zWu3cVrwgUcdyCD3AE28XWKzYvZ6QrIQs4nyEul04HQFJTGvAZcB5kRCCls/fAKNq3ln1/oo7sQvgtibwCZww1oQwA3xnMNW/BprVptgJKH8Sk0rheBxU9h3klE7w5luIzZmeW4y5J5XykSupStB27qychSyIVLX+VazjOts3LX0XXZuPL9w2cSyfKzavsRlBS0vCZZHniV1q6d3RWwjrulkuV1xxBX72s5/h2GOPxY9+9CN0dXXhb3/7G1RVxZVXXln28StF3YReqanJRYaoSrgduGk0a5HoX4RramdnFwzDzErd634ZN/qscrk0egkMN9q9l0A3GXRRDDnqJFzpXrne/tx6yyM5j8FdN/Ofp1oz5vvvvz8eeughLFq0yK6lN2PGDCxevBhnnHFGxc/XSNTTVdMNd9XUYBhmzURe7MN/5hd2fqtcYJbNAv1ykIu9f4AmRJ0rEYvb4kcozbLwMZi8eyAUxDCsY5ho/mIGQAg6t5yYv11l0Jv6piCCrAmxGLcmmKZpv2u8iV0KvzSl0KsspUxARaMaNK1aLt/5y78US76aoLEP/lG8y2We7Qta+1yTRoX2Y0FWP88xKJqWvQcA6Bq2U8425YLX2Eyip8dvkW+xLPKZihk++gJhE0WVO3aaPHky7rrrLvzpT3/CH/7wB8RiMYwfPx7nn3++pwZxvam50CtnppwH5FbW7QDwxsE0EvF4BJTyWS0x2POn7hWmfUop4nEeXN3oKZLLoTcIWe3eS+zPasyJzUuu6QAARJqioY5DQtapqobQO+uss/DMM8/g1FNPxemnn45UKoW//OUvGDFiBA4//PCKn69RKDY1ebVwXDW70dJSfTfZ2Af/cMSdaWZl0OSfXcIvSPC5EeJPFBz2k8uqJwZGnl0s0eZKxALT5D22S/Blxe+JbQh3qWr+8m0wQkO5UZVCb+ibwhCU2EXEDqmqCsMwkEqFG1Dy/ok03ERqb6R4V01iuWpWLztvJcdOwuoYVBM09sE/nD/8oiyEJS90nJ5/O9cFz5WN0y/yskSfLQb53/GvP0DPpmPytrcQwaVWImhuToAxZrt56nrtvEAaCUJIwXEw94Yq/1yTJ0/G5MmTyz9QFanpsKbUeJfKZogKgjVcjF5TUxy6btiuNX78L+MNNmgFAFewvTPD03fcPBvrNwoi9uBvwaIRmKm0bcXTe1LQk2mo8ag9GhSWvnyEjYGpBoMGDcIjjzyC6667DrfffjtisRgmT56Miy66CJFIcDmI3kyjuGpWy8UqF7E504PFXS5RF5RsxVX0PAthhfNl0vTE44n93AkOgoSfPehyLHciNg/MABPjK2HdE2LPsuwxUBCYPG6GKiXNrPdHTNNEMplCMskTuyiKgmhUg6JQDB48MK8bWYO9VnstxY6dVFVBPB4NFE2VphK/cb5EU7EP/1nQkpc38UrA9t6/c4s7IFgkshzHYIR6j+cTeYzwl0zsm7lIbjKqcFtD4C+1QilBJBJBU1PMnpghhEBRaJ82Arip59ipEamJ0CMEiMfVkkSacF+qZqa5RqqjpygUiqKgu7v4mJyenpQn2D4ajVQlg1O94D9R44rWpseug3ilMt+9Kix7tuiLRQqKvbDuB+U+F6+88krg8m222QZ//vOfyzp2b0DTKBSF1L2Irb9OVDWJv/dkttXOFny+eLt8MXkCI2x7A64xtfpecQi38BODLmZ4xaLbtdOKzSNW/B8jJghVAy17fF9+qKZl74ERgu7NdgzZ9tz0p6QjhmGgu9tAPB7DqlVroaoqolHuRuZOEy+yCZbL0qVLccMNN+Ddd98FAOy999645JJL7BTmfRmeQEVDMhneJc+Jb+up+j1ZiePnSzQVnftcOPGG3Ba3LIKOJzwPrKLp3u0DLHhZ7pzBbqPuYwmRJ7aNfTMXjCpIDR2Rv71FYposa2Jm0KBWtLQ0Q1FoHzUCeAkznq/E2Km3UHWhJ9wNNE1DJmMUkdGrOhmi8p2v3oj4Q13Xyx50CtM+4M7gFENrq+N6k073PjfPRu2Xmqf/EQwAjUZg9CShxKOAyWCkuCVP70lBF6nOLdEXu/aveY8Zblaq8ZIJ9RaEFU9RCFRVqavQq5Zbup/4rGm5LXZ+a51fCPpfin6xJxKtFPKH8fufictuFx8W7QFgGk5SBHtfk8f5CcHnK7VAKAUzdRBCAcJ4cgSxnPDvSWByjy9CKuJK1T+xvBN0HbruTeyiaSqmTr0IyWQSI0eOwfjxu2Ds2B2LnlBds2YNTjnlFKTTaZx55pkwDAN//etfMX/+fDzxxBN90rtAIMZOkYgWylU2X3xbNSl1ktxJqhfsqRWd+1yOExbvusn3y2+5C/SLdcXgEWZ6RF6wuCPwW/H4Z8W7veu4ke/+h/RG2xduf4kYhgHTZFi7lucGCDICuC2CfYFaZN3sTVRV6HndDVjoZCG1dl9qhB87Ho+CUl4qoqkpVlJilVz7ZGdw4q43YoZHFuqsDMyyiCjRCIyUY61j1sBXjfPYPL0nZX/OB/chL+xnLn+y4vHHu9TLol9osFMp4u8+nlvc5RN1bjEXdC/6bz49AzsDHhD8OeiGJQR2YJ7tg+kWfi6XT1v0Mdcgz7BSOItdXbF7pjPocsfsEZhgRAE1dSS+ngOTKCW7UzXCRGEtydfviHfJ9df/AZEIxeuvz8A77/wX228/AvF4vKjzPPDAA/j222/x7LPP2skNRo8ejdNOOw3Tp0/H0UcfXe5XaThKcSOvpaumm1LHCyLJXK6ketGPXggn3gBnu7APYYCgy5eYhblEWfa5g61/fuuiX+SZ1PUDE4LIik8BAOkh24X5BmURZASIRiNoaWmCaZrWuyhTdw+XcpClX7xUReiJjsrj6cNEHFz+C1vdDFG5qddAT8zCZTI6enpKn1Ep5n4VrjfCzdNfqFM86I3m5tmoD2bz9D8CJgONRABmwkyl7YGyEo1A70lCifJSCqm1naFEHhBOxFHaz0aYFcAf78L7ptq3o1oZhP3EZz7miDu/sAP4cpMFi7qgungA317ce1n9tFHgs2uZ323TirvLFn6WZY8SJz5PWBDdLpyUcisgYyCKYmXiNEEI5YMtEbNn6lzsmVZsH+OpXEqPnelfEy5hPQlaW1uxxx57Y4899i7pPM899xzGjx/vyWC36667Yuutt8Zzzz3X54ReKRl/4/EoFIXWxFUziGL7TvekdhDRj//lzFr7D158La6cq7LEnc8ymCuTZu4Mm8Eiz7RcNt3rRa09UYpBbKOsWgRjcO2yNQYlXopGeZkV7uWi226e1XxHVZp61SBuVCou9Ajhmev8z2OhODgheAyjehmiclEv8ZBrFq602jQihXXx38WfWjsa9bt58tp9velBrxWtz98BRCJOkpV13D2CWolYzFQaSiwCI5mGkcpAjUehRDUYP7+p4LHDZt3sL37mlSAoqYEzCVU7EokogNyDnUoQf/v/cdGTqzyCEHfu5zqohILJwIJKJmTKuO+EwLNzrogBluFdLwQdwI16pms76hoMChdOkbTFiukjlqsVUwBicGsjMwmIqjkJWixhyBQVBASxb+bCVLQS3Kn6z3MYdiBVTt+0bt06LF26FFOmTMlaN2LECLz22mslH7sRcYekuhETUf7LTSnPqskniVO1aWRW2wCETJIWZlI7+vG/3DsEHST44CHVcf6C6EHWtwIizycQ3SKPWdeFWIXU3ev9VkL3OenqL2AO2irU96k0pmmipydl30+qqiAajWDAgGZQSpBO60inufdJI066C6RFz0vFhR5jud0HczaiTm4Hbmo9oy8sl+Fn4WrTQMYYksk0klaiEFVVrHotza5A+7Tl5lmTJtk0mnvUgFf+DES4dY6lkjCTSVvgMZNBX9/pGSALq15YZGdVG2pZXoVSgqameFVrHsX/+0i2uHO7YvqtdQExeMy9j73Q9P1Z/MQPEQMyXzfP3BY7AMQMEH6M8b/FiNi0LH0ewce4uKWKJ36P19VjYBQ8K6dheBK0MMUSfAofuBFmFhU7U4qrfW+mFjPmy5cvBwAMHTo0a92QIUPQ2dmJjo4OtLS0lH6SXoBTh9C5mML1sbs7Wec4+3CTZGHGeNFPXqp4AdO8xdA92xU+b66yCZ6kK0K4ud4nLCspi68cA0hW/B9Z8yVft8GWBdtVTXTdgK73eOJvufcXL/nTm72/+lONz5qWVwjqEGqZISoXta6jJxIv5LNcNoqo4Q96kJunu16Lv5ButWiQiwJg4JsPAloELJWyB8DESgxgJlMwU2lb9BnJJJSY+Fy4rIIgfGclLa1hCfYGqo3rZqmDs7D9YvzNh7zCzu+KmUPYZYk6135ZYi5XvbxCWAM4lslkD+bE4MbSbUAO4SeStMBy7xRxeQYABXwc7P6BmQkoKuDKvmmfy+TfmxAKpkW4yBOJFAgBNQBGVUS++x9MqkLfcNsQX7L/KL1aTEJ1dXUBQGBcXzTKJ9i6u7v7vNADvNdSuD52dnbXfXIhTMbyaDQCTcs/xot+8lJp5w/bcQe4ZjrHCGHBc6/PEonB2T6ZSwgS63ub1OtS4haEIAQM1GP1Y2uXgQwcVvDr1YrC3l+NkeQvzOSDdN2sAv7BVL0yRAVTm4Fe+Nn80u6+WnyH4HotvJCurhtIp/u+m+fAdx/jHxgD0VSwdBokEgFLJu0Bs9t1U2AkuRtn+szfhTqP9DOvHdV23UwkoiCkdFfNfPdC/I0H84s7n5BjQdvCJeoKiTnferEfz3bp3dZeZhgua56vRp59WOZbblqheRSMMCsGj4AQaztK7NIKdrweYY6FT1EAQ+cDMAXwWPZcJRiIngEUhcfsGRlA0QAYYIxybUkI1JULC4i90tzmeyu1EHph3iG0whagRkSMncT4IZ3OlBXPX2nydZ2idEK+MV7kf/8OL9hCNSjHPREUf+dZH2B1868rIPKEcHOLPM+2vnO4z8OQ7cbJCAVb9zXogE2Dv1NoKt83+b2/FIUiEom4ajnr9niwEb2OxNipUYwq1aTGQo9f0UZw1XRTC4ue+M7VcrWox3Pkr9fC3TwjHjdPYdrvKwx89zF+sTWND5Yz/Lsz07TEXgo0EoGZTnORx5wsnMKqFxYp9Ho/7sFZmBTpQeT6feOv358dZ+cTdszvlslMrxgTyVlynNCzbYF4K2Z6+3LGTO4iKQZBZkBfLyx2lDoCEPAELPE2WGKSUcfax3yiD3Di+KgJ6KZtobNn8ykFrBg9Zupc7JkGn3FX4RF7lBkwCXfpJAqFsvpzmEQJdKcSWrO/EKbfKbdvampqAgCkUtnxZ2KZ2KYvkOta8deNCk1TG8BV00uu91PYzOmRT1/Otrb5PVTcmXvdy0ppb6Fi6UEEiLygLJ0ekRewLSPU9jhgVgyfOykLgQmTKPYykaDFJBTm+m+htm4c/ov6qMUYwTBM9PQk0dPj1HKORDRssEFjlnHoDwJPUEOhxzv+eDwCRamvq2YQ1fzRi3VPbaDLUhTCn1sUyhUFoFtaEjDNWrt5Vp6BH0wHrCQOAIBOnniFqBoIADPtHZDQaKSs0Z/0M+/dVC6OxpuMIf7qfeHFXT5hF0LQZbkFl5Bcg+Urki5WmT7BBjhWQNE5uyyGxBJ0zIrRIyJezx/HR4Rlj1vyxHGgZ7jbpgrHsmcJTVvsAaDMhEk1EEL5fDsFjLVLgYGb+75Qf7PoFXYppjS823EQm27KrRgrVqzIWvfdd9+htbUViUSi5OP3FlRVAWO1qSdcCn5vCCebcP7M6ZFPX3YdhAZ/zrcsBHlj7/JZ8Pzb5LESsjzvXmaJuqzz+WP4clnzCAEBg0kUZDq+AwNBpGVI7u/UQIgyDl1dPeBlHFSrjEPfGA/2Jqoi9HKZQ6NRXvizp6ferppeqik4w7guBFG8K1njDfa9bp7ULuHA3Tx125+7N2SNHDjveR7vQy0rXioFaFFb9JmdHdyV03LZpLAsGqk0zLTjvtlz0pWhzxkmwYO06DUmlYyjER4H8f/8yXtDWOIuyBWT+UsouP62RZ3vuQuTgIUvKv0LEb/A4wsdMWi7Z/qsgJTYcS6wJze4oCPM79pJubgzTf4gWss938ly5ySGJQ6pwntQy7JnD+wUDdTkfZirml+W2OPddf95EGvhutna2ophw4Zh3rx5Wes++eQTjBw5suRj9waEVcwwzIZLdiHw/75hXdS1+a/y/a3nzLZsWYXJi2pDMSIwYFxV0MoXZMlzLSNg2S6bLgulnWjFd76spCzEScpiH8+VudO0iq6nOlch2jw47DeueUbpIHgZB8erJXs8WNuwn0YyMtWCmlj0NE1FPB6Frht2vY5Go9IPgyiEXMmi7705s5tpmllunjxtbwsIIchkMlXNRFgOrfP/A6ZoIEbSWRiJACnr73QaRHMyapod3mybNFKcy6ZD+IDiBujLJRCumjGk0+XVxXTDnrkNduXFHOLOE1/nE3nMDIjREwTG6hVOuFLqi5KXvPPdrJaljVACZjIQRhz3TMC22LlFn9va5xF9UMGoCSKEJLWSJyiKU/tP/O18GRDTBBSTP+e6DqaqAKO2GydhJqhpwCQExDRAQWGuXQqdarZLVW/tm0uhVm7l+++/Px566CEsWrTIrqU3Y8YMLF68GGeccUZ5B29ghDdMV1cSmqY0dP/ujx8s5KLuF3n5Ple0kcVulyseD7CFXKGYvKDv4im74LLmEcbsQup+a55/356utYg3DQz3ndB4wiZoPJid3T1jZXcvwYsk5D6NIIJrQdWFnpjZ7urqQbTI9PK9FeGyVXoh5MZNxlIp3Gl7CQE0TbPM+k0wTdO29tXbrN/y+Rt8lp+ZPDtfJu0MprUIkEkDqsodtzJpnphFUy1XzrRt4WMlTXAUvg9602/eCFTzfadpCmKxysbhxl+6xyvsAK+4yyXsAG/9u6x9s8Vc1ssxR99VqkVPCDmPdQ2w3CqpLQJt3SkEoFv4WQlYCKG8GDosK5zlqskM3SmcLuL4FFhJW0wAKo/fM+AUkScUUDXHddMSe4QYYCp/ZzmFGgAoAGMUgALKTGQ6vgOasuP2+jK8Rl7+e5z6f+cSOOuss/DMM8/g1FNPxemnn45UKoW//OUvGDFiBA4//PCyj99oEMKzcpum46rJGG3YASl/9CiamuKh+j1twWvel1Y1O+Qc16ygmyaQOx7PtS7QZVN0Xm5rHnUJNb+g9biP+q14zLbyCWueEH4MBF3d69GUaA3+Ljm+VqOSO7u7E9+XSoUzmsiSU9lUTej5M0RRShq2s6ok8XgElNKy/OmD7tFCl64339eMZbt5RqO8hIOqKrabZ60RIo9pPNaO9nTyjtwa/CGdyhoME2sdc8XrsRQXfMWLvb7/vDQKuYoSh4VPaNGKpTyP/+tu7vpbwGrnj63LVSrBFmfW9p4XoesYWSIuhxtVKWKPGZbY87lt8jb4CqW7krPYVkDKrCycxOOqaVvqfFY+ooDH8Zm649IpRKGmwS7TQBmg83MSWAMsqnDBZxp8gGVkeLweeFsUu/kqGCFY++2XaBq8WdHXpLdSi4LpADBo0CA88sgjuO6663D77bcjFoth8uTJuOiiixAp2VOicWluTmR5ATFWGdFcDaJRDapKsX59d8H7QVvwWvbCXAMbT5kU3+dC++YhlMjzr7IEF/8j2GXTWSjcMn0JWKxz+LdnyLZkejNxElvgMfG36xidXR0woaC1KV+sau8L7/CXcYhENMTjUbS2NsMwTNvN0zCyDQG1SBTV26iK0ItEspMQ1CKzZT1xl4vo6koW3kGSE9M00dOTQk+PMOuriEY1KArFoEEDapK9qWnJTDBFA2MMNJMC0dNgqurECaWS/Ka2CqYjneKZ/NJpW+SJ7JvCqtd1zG8q2kbxYu0PEyjVJqgocRjEc5/JGBWJPY69cKct2Dxxdi6R53bFzGuxcws433FYgBh0/syRpMVPMYN4S5CxrAGrq+wCHDEIg1vwREwfA2zLH0wCXiidZlv7XKLPKbngxPER0Za0laRF7Ge/CXWAKfabigGgpulY9ggfgBuEgjIDYIS7dCoKOlZ/W1TsTG8m/GCq/NHUNttsgz//+c9lH6c3EDRB3IjWCdHvGYYJXQ/wBvChLnzDI2AKxuF5rGs5PockbEKW3PsHxPX5XTaB4IQtORK+CGsegTfDJmDF49Fsd03u6qnYApMxXnePgGFtVxIDm2L5vkXe79jI8Pi+tB32xcs4aGhu9hoCRL6HMImiKjEJ1ZuomkUvu8OqTa26eiCCpitZLkIO3h10XYeu64jFolizZr0re5Nw88w9u1MKia/ngCkqiCidoGoQmQ2JnnYG0FqED5K7uzwzjcQSfyydKiM+D+jNnXNvpFiLnlMyJVX2vRd77g4gSNy5E6jkcMUsZK3LJerE8kIlFPyZN8V+titmGIQlLsOchCw5zinEIKHMEX6ubZl1bjDmsfbZok9RLNdOw3brZEIk2mUWCB8+CXdOPQMQqwA75S6dxHo7clfODH9bMgaqAtABU9HAQKCCD0AMqhYdO9NbCTuYysraKslLrnjrRhoPuMc7hmGiKa/A4CLPT1Gir0QKxvoFXujCLpueRb5EK+793OUU7O3dMXeMgfkEnqitRxiDaR2Xl3lRHIufEH6E8WEJeCzf6s40BjVnjzca6NapCLyMQ7YhQOR7MAwDhJC87/P+5t5ZFaGXSunw1zEV5RX6GmFTCVef/nHT+rM3idmdlpZERYp0RpfP44M8xsBULuRsl01Ygz4zxUVe2rLcuhKxiDvc7Owo63uGFR39qK+qKk6dz3AXtNiSKbmI/uMW+/wAvC6ZbmEHuMolhLDWBYizsCUUQiVjsQRXUQjrnL9sn2WdA4Q1z1pu1eBj1r7c8mc47p+GO27PAKMURFFAYNhWPiZcNi1hxx1LTJ60xSqxANMAqMKfY6HXrUYSYvDP1HpVqhpgZEDBB20AYEKDAid+prtrHRJNA4q9Or0KWeOzdgi38kbASRITbryjfvZmsNuli1yCrBQBGDqRSwGRx8/P8lrzss5nTSIF7ecWae7aee5zeax4ViIW4bqZfV5h0XP+I4RhVWcGg5uzc2H05edQGAK6urhHTSIRQzwexQYbDABjzPb+crtD9zehV4X0Rv2HRCIKVVXR0dFdUZFX+v3XIG+DGiJmd9au7cCqVWvR05OEoijYYINWDBo0AM3NCWha4fkMsuZLRJfPszpcDSZVecfNGJiq8jg91dWBMsbLKwBc9Kka4CqjQCJR27JHIlGsP+jcor5XLdKXV4MrrrgC7e3tWL58eda6zz//HCNHjsS1115bh5Zxcl2usBNRhBA0N/MA8XJEXvQftyD6zM1crFj/sUwGLKPDtP5lhsEFmWHwvzMZmNZyxhiYYfC/Mxn+n/jbMMBMBlM3YKZ1mGkdTOfHEtuYhmH/x0wG5tuW/53h/+mG/Z+R0WHqBphpeo4R5j+xr/s/LkCZ65zO+ZnuaqNh8Ovi2xdWUXYhfu1rpPN9YO3LMjrMdBoskwF0HSyd4tdMz/BrbBr8+dUz/F/D4J+ZCaLr/F9DB8mkeQF1nf9LjQyIaUAx06CmAcoMqGYanV0dWN/VmHXPKkFvFHqN3jflwpmEqi+JRAyqSrPGO7napn72pncBId7/CiCsW8X8F4pSrqUvNi/XNjzTZnbtPL9otctKQJSVcBKxuLd1l1oQfxMwO4SEO2862xMwrOj0e5cUH5LQm+HZ/TNYvXod1q3rgGGYiMdjGDx4IAYObIFh6Pj2228qcq6lS5fi5z//OcaPH4/x48fjoosuwurVq4s+TrX7ppoVTO9LOHE51UoSUkKigxwuH32Lwtclu0inO4jXsLM3ubODkTVfcoFnpVFXMtxSx1220mCKBupy2RTxOiRjCTvG+KBQCEE9A6KpYBndFnvF0hsHUgAwduxYPPbYY/joo48wdOhQz7rrrrsOTU1NOPfc4kRvLQgj2ISrZjku2tGn/5DljsnP7y+XwLJdMQMsdh73yxxWOr8FMGs/9/IQmTf9k1rFuHC6t+KWOdd1FFY9092R8Rg+4a7J3AlZLIsftxTy7YiIBbS35xkLiao4BdZNxv8Wgtk0QRTVqtVnJVvSdS7+GAOoFbNHCF9HuHXRJARU1NG03Dg1g0BXIlBZBjpBiNiZ3kmYGBenD2uMF1Pv7ZuAel5DkVivmPJH6qL/VrlVJZBvgBRUBiGgnELBU7gyZQYJT3+5hKzzuJdboo+Ax/C5E7Lw9S4rIRhMZrl6wsTKToYNm/nwvpwkY70R99jJNJmnjIOiKFix4jvcc89d+Prrr7HddiOw334HYOzYHYs+z5o1a3DKKacgnU7jzDPPhGEY+Otf/4r58+fjiSeeKCpZVLX7Jin0iqQSg70wZD/7jfGyrCfFdlbBQbw8tk+4ea5ZthCEcoGnGjzBiqlwwaYYaXt2zVQ0UDPFY/f0tON/pmpWiQWRidO1DrAFX7H0Vove6NGjAQBz587F5MmT7eWvvfYa3njjDVxxxRUYMKDx3NoKWfTKddWMPnUTP08IcZdL2AUmSfElZcmK1/PtE9h2fxyftV+QgMubnCUkhFL7OMTj42/yc8Iblyfi64jpCLog4ScEnu3myVyiTxxDUQAhMCnhrp6U8usiZt9NZiVqERlAre9sZeUEoTwXDKx+wZdkQbxUCeWDulyxM72ZMG7OjTYR1Rv6pqAJ23q6bopSUcWUjLFFnrt4eBDZX7TEVtaWwLIKOTe2YoSDSjJYMXrCOseEh6vl/slFoddaKRKy2GUXoHgycbpdOb/rMKEzBVsMKv879yby9TuGYWDjjTfF9dffCAB4//25SCZLS574wAMP4Ntvv8Wzzz5r1/gcPXo0TjvtNEyfPh1HH3106GNVu2+qitDrJc+rhzCDt2hUg6apZcflSOoDd/NMoqeHP9jpjhUgRIFqpqGaaRiW4OMCzxpcW6IPzAQyKd45KxqInuJFleGy7AnXTS0KZFIglsvousk/LrqtvVXobbPNNhg4cCDmzp1rL8tkMrjuuuvQ1taGY489to6ty0fwYMqdTbezs7SsmpFpN3D3RJew8wgoIcACEqdkiTs7I6d3f2cbbyyeXzSKbYI/ewdkpl4tsedk2rSLoLsgdjIWl7sUdVnp8gg/OxOny9pniz4rE6ew8vEMnjwTKNENPinDLJFnGFwUir/FCFw1QUwDUDUwQrjYc1n2FGtAplguV4qqWYkS0KfEXhgrgRhwNYqnSe/tm+qT34CXilKKKhkTaMkrJPjs7apoeipYnyqcxS7rsAGWuyCrXuBnK+smg39/kZQluOC6iN0jhIEyAwZU7sJJTDAQ6EwFYwSmtc0Xq4DvJxprnFBNwiaKolTFqFFjSj7Pc889h/Hjx9siDwB23XVXbL311njuueeKEnrV7pukRc9Fvn4mkYgBYCUP9kpoTY3O0zuotKjp7loHDcxOZWxAg6on+Sya5cIJS/SJ+Jwsl03xWYt4b5x02onfK5Ew35fSxpoxF4wePRrvv/++HVvy0EMP4YsvvsADDzwARVEKH6AOBMXBlGu9jzx+Pdy18PKKuzyumPmsdYGiThw/pKDLStQSsI91Av5vEQOyYMsdwNzWAd91d4Se5VbpTtRiH4tb/3IJP7+1T4g+CjglGEScC7Pq8gFWiQbTdiPliZm8RZDFb2UXUTdNmFoUlFAQnfcphJkgCt8urcRhEoqVnbrtTtX7CRPPWoNmFElv7JtqjbdUVPjxjvL5DNsNkQT1D/7EJcEnd21TwZdbmBkHn9gLWz/PL/ayXDHd3gLufV3LmWu927VTZNwMzO5plVcAXJY8RkBh8oydjP9NCMPHS9LYYmD+r99XCONWXm5dynXr1mHp0qWYMmVK1roRI0bgtddeK/qY1eybavrWKbcocTVx/OC9jXP809NIp4t3wSu9LcXTCAHbvYHurnUgYDCICkIYNCNlCT6NB0czBs2K0zOpagdfu102haXPfqFlii2Gnp9a1qmqNKNHj8brr7+Ozz//HAMHDsTdd9+NyZMnY+LEifVuGoBc7lHezr8cV03tsd97LW/uWLuQcXYeq10hYecSdUHWt1wWuZxCLmBb5+/iBR4XawVmWD2umtZ+ogarYToDJX88HhzhBwBUpY7ws2LpQImd2ZNZljpbDOoGiKrwZ8laZ1sDAX5ew3DcOX3XiRoGmKqCMv57m2oEFMQaJFIoRIFGUjAphUkovuug2KhF5kCrF43eN9UbRVGQSBQ3udX94X/gH4bmFXxhqfVgMbB8giX23MLULmDuf4nkzroJxkBg2iLOY+GDCTBqu24KcefHnYGTMiHmTFBrneH6FRhzSjCA8X+XrNWwxcDq1R5uFMKUdSm3jp5ImuKPpwOAIUOGoLOzEx0dHWhpaQl9zGr2TTUWekCQmGoMskWoUycrvH96pSheszXiNa0cldCwa7pSUGCAQAUlBlRmgDAThpU6XbNi9ADYVj0GBWqa18kzFQ3UctkkIgGLG1WzkrKoPJmDqmLt+GNKams494NwLse1ZuzYsQCAjz76CLNmzUI6ncYll1xS51blx118nhcCLt5VU/t/v3Msdz5x5y95YIu2IFdMwCfefLF11jp3HJ1HAAZY6Ozjs8JCUCz37x8m6YrYzjmnOI7p2T+rlp4Lt5jzL/eIQELsbfl6ClM3LEufYwUUQs4RiFz0UStejxjWPkLkWcsB8H/Fcuv5JqJ+pq4DWsSJ22Mmd+FkDExlUHXfLD0BQIFvOqLYJPz7v1fifp4aid7YN9WKUkJTlM9nlHYy63kpvF0FxZ7bIyFwfbD7Zq4yC95tLOFWwAXULeL4+ILatfSoaXhKLLiPDUL5voCdiVNY9NwxevZ5iAnDcuEUyVoYCBaviWDrDSo7Kd1o1CLspaurCwAQj8ez1kWj3Juru7u7KKFXzb6pxn4kjWvR4zgitFJ1skqDoVjXzca9ppWivAdzRacBAoVb8AiPwRMWvajebQk+Lu6oqdvuWsSKybNfSnrKI/KYooEYGe6+6U7KUia9NesmAIwaNQqUUkybNg2zZ8/GGWecgc0337zezSoIpRTNzfGiXTW1v1/jEVdhXDKD4uyyjuFaJ47hF3Gm7nXJ9Mb4Zbtr5nLhzOXm6d/WnUgl3/a5yCf2spO0mJ79nH9d7pmGd3+35c8WezrfnqpW0hWryDqjhksIUoAaoKriWPlM5hV/gHN8K04PAGAavOSCotoxh4zxeBnNMh9H9B4QxQRReIKFr9ZHsVlrbScPJY3fN9WrP29qisE0iwtNURa/Ez7+LohCYq9aFyOf4PO7aQfub2ZZ9fz19AhozuyblBlghLoEn+EpnC62MaFkxekJsQdCuYsmX2r93/RY9VRiQIcCMMC0tiGEYdHqGIYPKi0BSW8g/Nip9P7XDBGnTv3FxAtQzb6ppslYii1KXEvc7ly80zNrGI8nqSbfdAAEFBGS4S4OjLtjqshwl03C3bxUg890EWY6mTdd7prUKrXA4CpAmUk7Yk+QTgGRKNaN/UHJL6twMXqN6QLW3NyM733ve5g1axaGDBmCs88+u95NKoimKdA0BevXd4eeUFAf+i0YY44cMb3xeO7MmIXi7AIzbbrWCzxWvpBWujCCrpB4Mw3xt/tYlRMqfmEHmKBKrtg9Z9t8AlAIP7HO1Pk6qire5C06F3ge105h5dM0LvKsenxU07hrqKZxl07DLfh4KnRKKBjlbv5M4UlboDrX06QKTEqxZG2s17pShXlGGnESqjf2TdWEUoqmphiSybSnoHQhlMXveBeEtdAJyhhkVwz/DZqnnEKWVc8n9vy17/KJPcf9MttF023VE2KPwnCVVyhgWSTMdtsELG8C8HaCAMykIIRhwao42gb3zfFtLSbJm5qaAACpVCprnVgmtglLNfummrtuNporhwMDpQSJRKLoTq/iLQkRN9zfKNUSvHSdCo1mwCtoKdCQsRwdLIFnuTUAsC16hGpQTFdpBWrF4ymWJcLIMThTVMDQAat23gYbtAKAVeIhA10Pf09xH/Lq+plXkx122AELFizA+eefj+bm5no3JyeE8ERLjDHouhFqAKs8eCUAa7oqrLjLJezcx0AOIef+O8BK5z6u+2//8dzkEnLFWOuKdePM564pXDu9+2db/zzxeAoJXCeStLiFn9vd07QtfIq9vYjro4ride3UubgjqgKiG/x5E+6emsZr8hkGf+41bvknpuXmSQiYkoEKPlDkNbEcN06iMixek+h1rlS9NSOwoLf0TW6qkd9AlE7o6kqGslAI6OKZtjughwCxx4VOQKOrbM3LlfEyL/6Blz8uz2qTLfhcYg+ALcK853Zl4BRWNWZAlFxwEj25k7uQrELpdlIWy1FTnDvIqme6snhSMIAYdiZOQhhMk4IS9FmxV0xG4FLZdNNNAQArVqzIWvfdd9+htbUViUSi6ONWq2+qeTKWRoUQgng8hs7OnqI6veohlZ6X4izBi9dEuJsmNWAyCoXqPAEL44MsjRh2x20Qy8JnpqGYOheBVIVipGEqKsAYtHSXc3ARr2dkwBTXI6QAxNC54AOwevU6UMqLticSMWiaCl03kE5z4ZfvPgs3mGrMZyqTyeDdd9/FyJEj8YMf/KDezclCvM8VhSKR4LPZum5YmXVzIwReoLgLkUTFnYzFWe5y1wywsAlxF0bUFVrnWOWCXTlzHc+7zu1OmduNU4gvt2upWO7eJpcA9MfnOcd0ua3ags4ReW4roBBy/DP1xu254vnEtoRSx51TUezPwpJH3ALP4IXXYSVjIQZ334RhABr/lwI8OYuooWUN7qIgYBpPzhJXU1i0Ot6rXKlqMZCqFo3eN+XCKTxfmYsaj0dBKUFHR3dR+9HFM3OvrJSVLsSNQ0Kcy71Nru2zBKD73EGizyX4AIDBsfy5BR8Xdt7tuYsmAaNOjB4sQUdMwy65INY5vR3vK7wJXByxx614rmbD8wcY49vwfYidoIWB4tOVTdhuQ9fYpg9Q3ERUaePs1tZWDBs2DPPmzcta98knn2DkyJFFH7OafZO06IF3eopC0d1d3MxWNSnlMjXgpa0YxXy3z1bH7ZkvkzGoVIfBKCgYVCIEn2pb9hyLnlUXzyq7oAB2x29a66ipO+Iuw030xOCWOpJJ2SJv7Q6H8P1MhmQyjWSSz9qrqoJIRMOAAc2glCKdziCVSiOTyfjeMWGzbjbG/ermvvvuw7Jly/CHP/yhIZ93gCceiEQ0dHX12FbRajQ1l9VLiDz/dn6BJ5YFrQ+0+MEr6Pzrss+XW8i5txXHpArJ4cYZLllLLrJj95xj+104nW3gyr7Jtzfc6zJOQheqk6wkLVzcWRZHy9onlhFqgqrUdu204/YUBdQSe0QsUzVAM8D0DEjEcueMGAAzQTUDzMhwEWgaoEYGimZ5FagmGCUwVdqr4mZ6s0WvN/RNQYixU7nXVCSbymR09PQU5zacV+TlOl/OOJ4c76083y+MuCsW/zG9sXYBrp0BVj4G3zKXO6fnCEL0CVEH8IybQuxZVj+3UOOizMqsaZ2fuLJv2tvxQi+uffhyk1G7xp7JqJWhk9kWWZMRzFvRjBFDOsNftAanVvkN9t9/fzz00ENYtGiRXUtvxowZWLx4Mc4444yij1fNvqkuyVgaBXe9mHRab6C2FX8HljM70VsI82B+urLJsuSZlqAjoIxCIzp3W7A6UhXcckcIsy16IApUM2N3/u7kLMKCJzp6Yui8dlYm5bXqFUDXDei6ge5uPqiLRLjgaG5OgDFmC7+wRT8bZSy1du1avPXWW5g/fz7++te/4rTTTsOYMWPq3axAEokoCEHWbHahztU45aqCxyao/FMo+qmgmOG1vz7B87ffaueN9cvt9ukXh2K5928TZg7vY7+Vzo9psEDBVghCCUw9v4XPfVx/sXVCTdcxHKFHFceF023VY4Zhx/YJ0SeWI0OhaCqYoYCkdRBVAdVUIKODGhEnlk/NgBoGkMkAUQPEcuVW9AxIlCdr0cTgTmW89IJCMX9VAu2Di7Ow1IPeJvR6U9+U+5KVP3ZysoinYBjF1QUtReQFUk2BV8r95jZPE5Lf8ue39tkJ22Bb9YToI8Rx07QTtgAuC59pH9Mv9sTxRf08vg+P1wPxJmQRwo8be7nYU2BAt4b2lJgAozABO05PWPUoCEwCUMbw0fIW7DC0o/jr14AUI/TKeabOOussPPPMMzj11FNx+umnI5VK4S9/+QtGjBiBww8/PNQxatU3VU3oBV3EoKLE9UK4bYkMe7FYBI0ilBrk/dirmPPNAERUAxQMlDCYjEKlOih4B6czBREi4vOY5cdOeUIWS1irZhoG5aUTFJfg8wRaK96smsKiRlOl+bqn0xmk03xmlbt5RtDUFEc0GgGlFMlkGul0sJtnIwm9t956C7/+9a8xePBgnHLKKbjgggvq3aSc9PSkGmhSJwy5f+SBf/yb52/3jH0qlXvG/pvTj+BHzmHp45+9lsBsS2GQOHQKnPutg36RmJ1lMxi/hQ/wWvk8VjyfhQ8AFM2VVMHKvukWfuJYpis7JxGJWWwXT+pk5KSEu3IaCsxMBko0AkM3QDXVtvCZBhd4wpJHDB0kwl2DRayeHQOsKSAqAyEM/1vRhB23NJBKZYoejNeKcImiZN9UScr1hionizj5YpYn3g3wuQeGpQiRF0rcFfs9RMy02w3SfYxcxyNByVb82wpBZi233DT57jTLwkfgxBpbkssWi7AsexQGX2cdi4j6LMTnugnLgucSe26rHrfmKZ6aemIdIQwGoyAE+ODbVpgmwbhN1xV1XRuNMM9JJd7/gwYNwiOPPILrrrsOt99+O2KxGCZPnoyLLroIkUgk1DFq1TcRluepX7GidIWvKNkXU9NUKAq13djqRSSiIhqNeNy2olHNsqjULwmLQFUVqKriuU6MMWQy6Zx9UVNTHLpuIJXqXYH9YeGB41F0dGT7k8/5ZgAIYVAIn/WMqdw9U/ila9SAQg2IqjMKMWwXToXoPFECuLhTTT44Fhk4qekIQWpkuAjM8Fl3qjvXmrhq6q3fdp+yv+/AgS3o7k5CVVVEoxooJUindaRSaVsYDhzYgs7OlCfLVhiGDHFquxx11FH46KOPsraZMmUKbr/99vK+RJUptX+i3CMvi5aWRNExK7UiTNv8k1eV4stjDvJZCr1upADADK8g9Lp4Fod736zMm4FunI47pvsY7mUey51Cspa7rXpivVv0ibg9x+WTL1OiEYgSDVTTuIWPUtBIBERTuYunqoFEIkAsDkRjYBH+n6HFoEebkY40o0drQRda0G3EsTYZxx7tvHh1JpNBKsUngxrFQia8EDo7c9+PfJsIenqKf5+6+6feSjljJzVg+j0Wi8AwDGQyxT3XPNlUHKZpoKen+LEB+WIW/zdAeGWJPU9MXO51Wbi2zSnwKhS3Fxbmi4nznohkbRu4ntDs+nuuJCs8Js8bv8tcdfR40iZiJ3ER25jEKrsA19/2Z8rr54nAFEatTOMKDFCYjMIwFZgADJPvp5sUBiMwTArdIDAYwc6brS352tWbwYMHYtWqtQW2GYA1a3qKnjzprX1Tv0vGkkhEAeQKQm6caf5GsXw2Mm8v2QCEAKrCEKUmCOEzVBmDIuoSeybjM23CfdOdcpgwBSq4cCJgMKgKxdTteD3FtASfJfIAx6pnAgBjPCmLqnnEXrkQQqDrOtLpDLq7ubUwEtEQjUbQ0pLArbfehgEDWrHDDjti+PBtS7pfGGNYtGgRJk+ejP3339+zbrPNNqvI92hEGqAbqjhBk1eVYsvHnvf8HSQ6Pzt0PwCO1c/IuJKm+C2BhndARhRqLyMKhTuprfszVQjge8Tc7ptu91BT8Qu8YAufW9gBgKk7WTupqoDqjmAUrpxKhGfU5C6hvDQD1VSYaR00ovJELsLCFzWsOD2du3OaBkgmDZJJAzGr/p7JE0ORCAMUQI9QvPZpDGM2XgtN479rUxMvzFtKBt9K05sTRfVW+KUsro93J5sqNou4EHj2+d0ZIpFf5GXhX5fjvsgSamG3K3S+EnAsl0HHt/5xuWfyD8JFU1jmDOe97HLtJB7LnbVaWPhE0wlfwhhxajkxK+GUtdykist1kzqxfLDcPAE7No8QBsJ4rB6P9aNgrnVgxBovEYAB7yzdALtsvqbk69fIiH6pP42xaxyjV7+LW8ilqS+UNOjt7c+H/75584tBIASIUGtgyXjHqBEu+EQQskYMW9wZ4IKPEB6jBwDEKjIqYvVUV1kFAmYnYQF4508NHSbVQM1M1ouIVahYuvi+/oGS283z4IMPw7x5H+KRRx7EF18sxvXX34yNN964qHMsW7YM3d3d2HfffUP7lEsaj1Iz6FWSrae/kNOKSAjBooMPAOAVecIyaLgHoS6B6LfsmYEiz/W3JRKpQmAmhegzvJY8X2yekTEDLXyKRmHqTq0+LvT4tkZa94g+UzdArGXU4IM7GtFBFQU0nYapaaCRCKDrIHqGW/f0DKhpgOgpEO5Hyl20ogRE45NTAJDJ6PYgnRCCaFRDU1MMqqpC13XL2peuaZmV8ImiatOe/kFxYS98UlAraeKHfDnbFg5AAWEVZOnzuEPmF29hxF1Z5wdyl3goACM8G6b47D0J5c+t9RlwBJ4on+BeZtf9ZOJ/4JNFIlOn7YZpAITCpIrtzklMnVsBCQNgZRIm1K65R5lhJ1gxAQinBwYKE9QWewoxLTdNZpdhoDBBGOFlGCis8REBJcCMJYOw6xari75uksaj5ha9eogREYSc36WpsZOZEELyzqT2h5cqYwz/XrAhNJVBoQyU8AznKphVI4Z3ZLykAqBSnoyFgH8Wnaoos0BgiTuSgWJ12gZ1xJpqZmBQzROv52mPovKkLCJRC4COrXevyHctlMJ80KBBOOKII7DXXlNKnjz57LPPAMDOGCXpXZSTQa+2MOw0YwZWrw6O/VgweT9nS5f1zzCYXZ7B32tTNcCl0xJtuiXyzIzLddMlAq2jZwlAflzFStQSLPz8ok8sE1Y9ks6AqgoUw4BBKRQjAmpl7WSZDEg0A5pO83IM6TRIogmKVXhdibfwwV+EgUUIFq1u8WTiZCw7g280GsGAAS0ghNgTQWIyqFqEsdZRSpAvtlSSm3LzG+T3WsoP+XJ2lnhyW/M8ljzfdnkFHpBf5BUUgMFiz6lT57vX3GVgAvcsDAn6TCk/NnV/V2HRc0owOKY6R9QBIr7PsOL+AFjCjv9tgBEFDAA1LaEJnqGTEOIY+8DHgSZVQK0MnsyqzykStSjEil22Wk5hWmIRtlunwmUlFML4CU0KhTCYQvSZfEJ9z63X9DnrfB/7OgWpg9CrrZiKRjVomlowCJkx8XKqP6U9VI0tVMvlqTkDEFEBSnnNGMMkttgTYk4B4bNXJhfFBIY1ewV7hlxknnLH8BlMtWezAEBxJWgRCMFnKqpt1QPgm6+rJPl/y0p0vAsXLgTgCL3u7u6Sinz2FapRlLhaVCserxoUup5t//l3znX/22NffoyM9yCZHpflTyUwdWaLP6IRjzDkyw1HzLni9/wCkFDTI/yE0DN1J1YP4O6ftgiMqFA0btUTos9Iq57kLUo0wmP40mmwSAQklQaNRbk7ZzoNmk6C6GnETANKLAUaN2BGKBasas5Z1Jhn8O1BV1cP926wXbubYBimVa8zDcOobO9ECCloJeLbVPS0/Zow4xNKCZqa4nZMZ7GQL2dbH7zFzMsWefli8IoUeEGWOV6yIOC4YTpz5k2C4j0w9a4HeJ1M97+ALeIcMWhZ6QixhJjLfTNI+MF0Ze40rOQqhh13R4gl6mBYSV6s5C7gSVuYlaETFLbYYyLDJiyrIgEMpoDChEoAHQoULvPACE/gwijPYUAZA0xAoQQGA95YvAEOH2fY+QGKdQOuNb0pI3CtqHHWTaCWYiSRiIExFpiWPJvG+uH7shtmMUz/cEOoKrigM/mEGiEAJYz/TQCVAhQMhkmgUWbH6gn3TROAYnWg7hILCgwYUHipBSHymM47TcDlymACBFB8vmPUcOroMUVF92Y71vLS8HOXcaMsXLgQTU1NuO666/D888+ju7sbm2++Oc477zwcfPDBFWxl76DSRYmrRTXj8RqN7d98OXD5xzs5CY9MnYFlGAwhBn3dPdGEtY7kXEYUkiUAAS4AuTUvt/AzdQO69ZmqFGpUtVw5KcwMj+dTdROEprjgi6Rt0UfTadB4HDQTA9F1aHoGSiYJahqgCQMkyvDR8g0Kpj5nDEilMnZYgqJQRCJc9FU6qUuY+p39cTBVTQpdS01TEItF0d2dLEnY2yIvRJHxrH1zibwQFrzAc+QTd0GCLtf+AasCXThZwEQZMx1RFrQejktollun+G7inGI9ZZaFLlj4MWKlaSHEY+Wz3TdFshbCDSbM5FY8YbUjJgMFd+c0oPJJaAJrBKTy8BQo3PvJLrVgWfRgQrGko6aYyFhhLtwySPDkLBUHjuhBPB5Da6tqlSTj8cKNUnsaCNfv9Ee38j7puunMbKVDZ9HsCzF6fY1p7w8GIYDC7H4PpknAKHP+ZnzmWFGYkyoYDJQBRHVcNYXo42LPuSd47J5ifTZBiAIQBRGjxy6zIHC7dYIxgHmter2Nzz77DF1dXejo6MCNN96I9evX46GHHsL555+PTCaDI444ot5NrCkihXkjD1AbIR6vERj53quByz8avTcA2C6fAACdgVmxf8RKxOK2/rn/FsuUqCP0jLTj/ini+cyII/QyPdzCR1UFikZhpA0rWyeBomWgRFQYqbQTz9dDoUQ10FQaaiYDlkqDxVKgiTRIKgmaTiKaSUPRk6DNBkgTw0fLBxVV58owTPT0JNHTw10/3Uld3PU6S7EGhx9MNc4AsLeTr7yCUzqhu7RSciFEXi5rnlNOIFjg5bPgeYVfwDGDBESIbJ6hi7SXmdSFuP/1WP8MrxUQVoyfaYk29zEIsVNAM0vg2Vk8qZW63hKAPImKYWXj5JY8Qgwwyp0wGVX4OtOa6CYUhJjW9oABlU94255MCkB1Kwsnj9ejlHBrHmEwCQOjBIYBKJThnx+1YPK2qwBwt/FIJIIBA5pr6jZeiN5W47NW9LlkLE5R0FJmthpJ6XnbwmusaXlLU/QVofq3dwbDSmwHxXKJh8Ktd8J1E+B/cxHH3Tcj1jpRZiFtqFCpCZU6GTgBQGcKKJyYvQhJg8D7khOdo0AxMzCpyounEwWqzs0G1Mw4yVlqTLl91dFHHw3TNHHCCU7R7YMPPhiHHHIIbrrpJhx66KFQFCXPEXonua9bfWKIw9LcHO8F8Xj1ZYcPX8ta9uGIvezPQvBlepybwBF9jgg0NNP+7BaDwvKX6Qao5mTsNBQCqvEELWpUtf91F5IHAGaaoJoKZppQDANmOgMlFgFNpkB7eqDE4zyGL5WClkmhRU9DbU2DNDG8s3RoyZnw3Eld3PU6S0nqImfN60F23yRidHXdCOm15GPJ+74D0qLET2iRV4y4A/Jb7Yop4RBGBJqmE3cXdE5x0f2WgKz1uvXZN3Ei6vi49xVCTiRxMYkjAAlx1SHVHeFHuN2OUQUKMaxSCwpfZyVlATMAqoESLgYpoTCs3ASUGSCUiz8w1RZ7YCoIZYDJ09MphPLtQKBZYyLDpDBBoFDgpfkbYv/2lbbbeHd3kNu4YU8kVdptvBBhvHWl0OvllFMUtF6JYoLwN12I13Q6jaamBEzTtNJsOw9SX7hvH3xrEBTKJ7IMA9A0PlhQFO62qVBL3BEeo0cI426bxHHd5BNgFCox7c7MZNQqhcBnujSfRU8UT1eg846QUD6rxbzWYMJcRY59hdMr77ZZ/Vmp4447LmtZLBbD4YcfjjvvvBOfffYZ2tvbyzpHbyLfrHk9URQKRaHo7OxpiHi8Uu67el7W0fNez1r2/jZO0iRh/WOumm8ececSgEQjUOKUxwUaDGrMcpFSCDb7f88U1S4xBFL+cikvTq8bMHp6eKH2ri7QZDfUni40pbqhDuwBHWTizS82xR5blZcJzzQZkskUkknuel5sUheZdbO6hEnGUnaMriXygsRaYBkFv8AKY8ELcs8sJO5KEXX5tjOD2+nZ1zSytymkGIRA9H92Qwhg6LZIcwQe8fzIxGfRg9iWeAUgUxQQ00nOwt04uTuncO0k1ICpaLaFj5oGDKpyIWgClFCAgpdtsBKzUBAw6iS0MUyFW/MIAaUMmiqW879f+N+GOHD7lZ5Lls9tnPclacttPPclrQRhxkWU9r++qU8IPUJ4PJ5pmqXNbDlHqlibykX06SIep7OzB6lUj+WmSBGNRtHS0gxFofYDZBiNHSSbi/97eSAUxRJuqtNhMubUxRIxegBBRGOghFvvrLhhmCBQiWkJQZ5tkzLAoASalQ3LXWaBH8mKy3PF7wGwM3ACsOvqmUTh8XuW9c627imVK6kgqPdAatCgQQB4cpb+RCPO8onn3zDMhhB5uTEBsDxiuXH6VgAY9/lbgctnb74bACf5i5FhQI/JhV9cAQWw/XvZcYNhivTmIn3m7zx/tzxzC29DOg2sWwOa7EE82YXNBnVB2yiNl+Zvg/3bVwYdqiS8SV1Iwdn5MFk3nQFXY/3uvRX3cxWN8oL1JcfoLnk/Z1xdrsQrYeLwwljwclruAgVnrnOa2etzWeRyuY5mbR/CTdR/riBLoBv3er8QdMfpWeuJEIBW0XTh1ikEINFhCzsQglcnXQYA2OvNm7gQpAqYlQGcURWmoloZUw2YTAUlXPRRZkCnEescYqKbJ2hhhNixKMQq58AzfBIu+HQCkwLPfrwhDh0Z3Af53cYjEX6/NjUlwBizvQeq8T6TrpvBVDUZSy2glKKpqbSioG4a63fnjRHxOOvXd4ExA4RQKAoPnE0me9DT0wPGYMdexOMRRKMRu6huIwXJ+rn12WaoGoWmEscVnQC6zhCNELsfNE3+2yiU/8fj9Pjsl6Yy13YEJgiY5e5JLVcXamWb4iHFQFQR9fNc8Xt2gVOrcSIJC1jO0grVhH/HMLNSpd+0y5cvx+mnn44DDzwQP//5zz3rFi9eDAAYNmxYycfvjTSaRc8dj9fcHK93czy4J7zFgF5RKBgz7ftSdD+NdE0LsePS/9a7Ceg4/Dz788A3HuAfOtdDSyWxSU8nJm3SDaC4mplh4QMx7i0CBM/Oc3du6bpZS8Qz1dTEE8yVHKObQ+Tly3aZT+QVbcHLI+4CzxO0DnAGBjnaZW+Tb33WNjmshuJdLOo5ieX5XF3dx7VLMgRZ/YTQ8wk/gLsygU+VvHnGXfywOoPRY3iyEL8x6SIocQWRQSqUKEWkSQOhBN+/4yoYSgQKoTAVlU9WU80WewZRYVANOjRnPoYChFnhGlbIDGCFxoivpQK6QTD9ww1xxOjCE05u7wBKqVULNAFVVZDJ6HZSl0qIr3BCrzEndatJr7boaZqKWCyCrq5kBURN47huAtydJpXKoLMzaQ2e+EMCCDcOy92Imchk0kilKJJJbkKPxbxBsqlUeSK4ktw8vQmEAqoVF2OazmdKuR+4YQLRiDNAJJY1T1Nhf28h+DKMIKpapRIsa17GoHbdPBXwWOsMU7E/A1wQAoBKHAHofql4ErC4EFY9ANA33LZSl8f6btWflRo6dCg6OjrwxBNP4NRTT0VzczMA4JtvvsFTTz2FCRMmYMiQISUfv3fSGH2AUx/PQE9PyrO8cV5QPGUbY6Y1KUGs55Vb5rnLNbO2cf7tTaKvEVi756n254HvPgbauRYbfvkeejbaGqmhI6p+/qDZeeHmmS+pi3CPkj93ZaCUQlUVdHcnQyeYyyKEyONxWznGUswrrvwWvCCBl7P0gbVNKHHnF2P5RJuvjd51Ad/NdNri2dbXzqB9spINhRWBAJh1DkKpd3tCMfumaTDSVoiIlVFYiVMYPSa0FgWxjZwxiRKx3Mo1rshEzDAALLz4WjtJlBbXQFWKjS6+BIYagUlV6DQCygxQakCnmlVeXYVBTFBiIgUAJsAoQVQBMqDQrGzEEY27coYVe/YlMk309KTs95qmqYhENGywAZ/ILLeEg4wfDqbXCr1KZ5/jP3z930oiY6h4INwz5AIxoLL+gqIQxONxdHR0AjDQ0+O44USjEVdKXN3ypU7XdMD4u0cjUBTKk6soDBFrpkpMYhkGg6YJf3ViWfaE2HNKKmR0QFUIFJW7bgoroMkAML6fSpjtvknhFEwnoo4e5QMShRi8ZgwxnQxU7uQr0GEQFQrT7Rp6gNets1pJWPjvW333gyuuuAI/+9nPcOyxx+JHP/oRurq68Le//Q2qquLKK68s69iNTpg4mHqQK/amcQSeNV5iQuR5BzOO2HPazJPIGFAUZ5lp9i5LX2Gq//usHX8MAGDA/15EdO03iHauxPrhe1X9vG7Sae4psnr1upxJXbq6uqpy7tdffx0//vGPA9c9++yzaGtrq8p5642Y0Oa1EUsYAPuTruSLx8sVi+cXeFl/54m984m5LHFXyOonzifcCPyWulyWQrFeCLB87p0m8wo303sM5v4ePiEoRFuWAHSJSGY6bWRWexc+OwvMNG1Rx0wGI83rbkZbI1A0R8TxDL4iVphn92Um4+MlKpY71kAn+RNz1f5UsOb2m3miqFgERKGI/vh8GEoEKlVhEBVpGrNKM6iAAhiusBee+9PkhalMIKoB3Qbw5JwN8cOxpbmSiyRRznhVCyjhEC5JFG9nmBi93ponvXRqLvTKLUrszjTV1ZUqvEP4ltV99lFRFCQSUfT0pCwhy10Z86FpKpqbE+js7IZpMhDC3Wq4ljKRTqeQTqcsyxmvtbPBBq0AYLvoVMNX+vL7uCuXqlEoIs6OElBCYBgmtIhifWfCc5+YtqeCnXBFNxi38inOMmHdY0zE6jn7UDAwxot8EvDAYQJnG5GYxf4M5wGIUMtVyZ81y4VBsx+XSlvzAH6PhylIXO7Yf/Lkybjrrrvwpz/9CX/4wx8Qi8Uwfvx4nH/++XYR9f4Et5rXrxNwPBSCY2/K6TcrC4+lTaXyDzoJIXacF8/OprisfU5MX2908fRTy99l3fZTAACti15H05KZ6NpiQu1ODud3ypXU5ZprfotVq1Zh1KhxmDhxd4wePaYi5124cCEIIbjuuuuyBmubbLJJRc7RaIgJ7c7ObjQ3J4o/gEvk+ZOoEGYGlk3IStAS4KJZMPbOPzntSXhiBu/jOn6wgPMd130eIejc7fZb8fxizloWKOQY48vc4s0wbMHGXG1jJgMzDHt70zDAdANmJoOVn35lb2Nk+HlEJl5Fo1AiEV6rM6Ly/zQKNRYB1VREBzTB+PlNKETi0d/D6ElabfC1K6it1nIAMB+6E1RVoCoKlGgEPUedg4wShU41KMxAhmigxETa5GMfAgUmCAyTWuNlgkpV+mGMIZlM25nlnRIO4ZJEAeHzG/T1+rN+CMsjf1esCF+3J+vAxBm4u2lqiqG7O1XSDHXZmaYK0NwcLzOZS+m4k66YpgFVVRGNalAUikzGQCbj3OBHnDbXs+8/HhwdeOM6LlOAyPEmnnlCCGIxHtOnqioyGd02m5fy21x8t85nnRTq/Eu4tVG10pDz7IHcxYtSAs0SgXwZ7H8jGhd3hHALnhj/RSNWgXSFi3LFKo6uUuYsI9xNU6WWSybl2TcVKxFLRNEt8Wcth/jXsfQB3KLH/7X+NjOgTHx2ZecbWPk4NhG83NmZuweNRjWoqoZksvjnYMiQlnKa1zCU0z+J+8uNqipQVSVvCZNqIQZ0XV3JwPWJBI9DrnfcLWMMlAKRSASaptrue8LSI6CUoKWlGclkyo738h/H6ZsAwHRZCkmvE32DBg3A6tXran7exFezwYiCnk3H1OychRLPMMYQi6l49dW38MEH7+Oss36KWCwW+vi5+qeLL74Ys2bNwiuvvFJsk2tOuWMnVXXct8Xz09KSKM6DqUBmTX9GTa/wMjzbBrts+twzQ1jucgpC5hNa7va6BZ8Qbm5R518HOKLO5U5pizm3kPNtywzDI+TcIs7M6IBpwtQNMMOAnswgta7LPrYQcEaGCy5T58dvGtKCyG//D/WitbUZ3d1OxubWF+8GS6bA9AyYbvA+N5Ox20+jERBFAY1F8c2kM5BmUaSZhqQRQcrQkNYVJHUFKZ0inSFIZQi6kyjZqhcGUcIhEokgEtFgGIad1MVdwoEnZWT25FMQzc1x6DpDJlP8OLe3jp3qkoylFLczHhtQRqapENRrcBGLcdfG9eu7ADCYpmmloxUzG9yPOR6PYZ8js5MFHHbKh/ZnYcZ/+q8jfW5UjjugsPalUikkk0luHbNiL8IW1P3FTZ2WqLMEnUqtGix8kEYIsdwKvNY8u50EMEwGVbhsuixzhum87ITHBqVWHw3uGy4SsRArRbBhWq6gFKAMABVxe1b8gPXdDcaviQrrcliJV0CyrXlukVdLpJ95feD3Wm37gPAeCvX3OBDumrrOoIs6kpQiEtHQ3JwApQTptA7DMBCPR9HZ2Z2z/3D3TfzYTmyfO4Nnb7D21bNt3ZvtiFWdGWy8cgFMqsIYtE3d2uKmubkZe+yxN/bYY++KHXPhwoXYZpvG+H7VRFUpmpvLnNDOIfKCrHjZgiykBS/ACpdtDQyIt/OLu1yumH5rnRB1uVwuPa6SAaIuSNAJKxjjAg4mg5nJwLBEnZHWHcuYYdri0G0Vi//+vgI/Rn3xe4Ksn/LTrG0GfvRPYP0asFQSLJPh1kvDwKavPwASiYIoChbufCo0aqCHREEpA5cPFIZJEI2U58JZCMaySzjwzMBO5vl0Om2Ni/JPhobZpq9RN9fNYkgkogAqF4/XSDQ1xWAYplX7LzseDwB0XYeu61mWvHz84IyPATi+2sQSYYIn7mn3DKwMI4Ourgw6OrgoO/3Sb+19KKWglqWOEgqqUleiFEfMmYzxinRC3BHn/KbJrKyZ3JrHjwXoGQZVA6hr0Cc6JsZ44U5VlJSxsmg6/TeBQhmo7drJ7GybJiMgjJddAHiZBYAnkRJOP3bRULiFIC9IargfDbGDCZ6tynLhVFurk/kujIsed12SSq+y1FZMFeOhUO8YYifpiveeM03T476XSMSQSPDJong8Zlv7wkxcBE9KCcufU06lEUVfPWMoX5m/MfZqUzBUXwpz3degAzatW1sElb4cjDF8/vnnGD9+PAAglUpBURSoaq9NM5AT02Ql1QIGEM5VM1ccHuCIuoAYvEBrXJC7Z1hx54//C3C19Ig7t7XOMAIFHT+FaQk54ZbpFXZC0DGxTjccAeey5JlWnxy59G7PJRbeCPxzb8gyXDjmf+0Oh2QtGzj3WaCnC9C58Nv2w78D0RhAFby/Na/BqxDFCo2hMAzgidmD8aMdV1X+K/gwDBPd3Ul0d3tLOMTjUZimaWUIDjZU9MdJ8joIvfAPgpN9TreVfF+BEILm5rhdCiGXyAOyXTUDj+eLWXALPP92lBIce+5n9noR0CuEHKEEVFFskSd+L+oSi9QdBEwJqEJBCeGzYwo8otItBGHAjtkTrp3UevAYA4i9jv+tUF48XVEA3QAiqiP6xHYmE1ZAAlCekIW4Bu1ua6HJKJhlyrPr6BEDOlOgumL5sqx7LqueSRTbjbMahLXoNXD1jIZHWIq9y2qXjKVQPF4Q9Rg/8LhfFsplNB6PQlVVrF27HowxKzW/hpaWJjvGIpPJFBS12dY+b5bhxh9Y1ZYf7bgKz368EUYPi2IT+hWMju+gtWxUt/ZUIzvs0qVL0dPTgyVLluDQQw/FwoULoaoq9ttvP1x++eV27c++AH/mspcXk99ACLhQyVYC3DJzWvCyLISuY/q382fH9Is793bujJW+5bYLpnUOIdqyLHWGYW3CAuPo3FY7QdNFd0BVFSvxB++fxFcMiDzi39mXDC8oy3Aj9U2lNmHtqEPtz81fvg2lez1IOgkYBsYtexJM1TBroyNASIT/fIwCIHhkxiCcuOvqyjQ+JGJCkb9n0lbZNaeEgzssqRpCr9ETRdXFohcGVVUQj0fR3Z2CYTRyoeDiETP53d1J6LpRtsjz4xZZ7mVZYjCHyPOINJ8LpnDNdK/znsP7t3DXpPb+PMtmRHH+5sfi/zKTAZTYmTbdYk2UsaHgwk5VkCXmxIvQYMQyxAlBR+0Mm3w75vnbj2F18xQG/+yy6gHVs+bxtoVNxiKVXiWpldWslIzB9bAY8XOaoYRoc3MCjAHr13fay3hqfp5KmxBiidtozoFVLsIMrOpp7WuEJDmHjlyJl+ZvCH0jiqHRFUh3r0dTorUq56qkW/mqVUGuXk6caiKRQFNTExYuXAgA+PDDD3HWWWdh2LBhmD17Nh566CF89tlneOKJJ4qKA+yNOAXo81zcLcbxbcU+1r908UzPZlmWPDixeIFZNIMseH6BB3i3c7tl+l0yc1ntxLYhYuw8bScUPcdcFHhJNE1FU1McHR1dnnguAHYcPE/8wcNjROhKJpPJ2t5P0KQUwKCqjTUpVW7/1LnlRPtz7Ju50JJc9O20+nkwVcN/EweBEhWGSdGUoLj/jQ1w2p5rymx18RAr2V8qlfGUcBBhSXfffRcopRg9eie0t3/fqglaPo2eKKohLXrRqAZNU0t3X2hg3DP5hmEEukMJwoo8t4ALsuS5xRelxF6XS+S5XTbFdvmsee7f0/PZbot1bpfoMwyeGZSZBESFZztCHCueEHTu7JriX9Hn266aYHZdPDvTpl13T5Ra4IJPNylU7/MI0+XGSYlpiz2xP2Vmzrp6lSS8n3nfejbqTSlu5cVACNDUFC85Y3AtBwkiHi/MoL6lpQnpdCZvALw7aQtQ2YFV/a19hV2jasH+7Svxn4WDYQ6m2Ci6Cqs70xjUHKnoOcKlLw/fNx1++AF515999tk477zzsPnmm+NnP/sZDj30UGy99dYAeNbgLbfcEldeeSWmTZuGE088MdyXaHByXToxdiql3ze3Li8zq8gjEJQsSvRrtUpkV4yXQSwWRTSqYd26zrzXTdcNy9MgaSWK05BIxK1keHro2m4iP4H1V4NY+yp7nuQmo+ypmNg3c6HoSUxM/wdM1fBK8ySsJQoMk+Kvr22AM/aurdgLmmQSJRwA4JBDDsf//vcxpk9/CgsWXIff/e5GbLZZ+Qn1Fi5ciE033RQ/+MEPyj5WNaiq0Atyj0KBOJimppjto97XEJ3lunVdBTuqckSedz2xt3OLvEIIl80si53Pmif+Fdk2xTrAss4p3mX2v9a+jDErkQqBZt2N7lIKAL+PMrrjvqmpfKJPcVv8PMlWACI6U6uTM61yC/Z38SVpEYism95ltS02L5Ox1I9qvXzLzRhcW1EfTuRRStHa2mQVcS7Otb6SA6t6u1E1gHeWzeRtV+GVzwbD2IBgULQDKzoNDGmuzKw1EK7fKUaMXHzxZVnLWlocy9z2228PAGhrawt0f/rhD3+Ia665BjNnzuwzQi83tU/IRAiQSMRhGEbOjMC17Jr4xE44L4OmpjgIIVi3rrPgtm5Mk9mlpwCnqHdTU9yqZcgnpcJ43YhJKXdcn0iGxyfTqp9l2Dl/5UluMgoAQFd/AS3Thb2Ut6AnYvjndxNAiIL/e3kgfrzv2qqcO4hC37W5uQUHHHAAJkzYq6LXvNETRdUpGUv2BRaFwrkvbW0H1rWAC1iedKVQR1WKyPMsd1nsxHbCdZIxM6/Lpj9pSy5rHrf4idg9R8QFJWLh52UgipWIhbgtbo7VL6MzKAqBrvMC6u514pj8WABjBJQwZHQCVWGe7Zx/vcsBIQSFO6cJWBk4uQWPeibmbaueWGYJvmq5RAnCCb36u4tJwlFKPF4QtRjk5Uq64kdVVTQ3x9HR0V22a331BlYAXDVFq1msvZGexS+/NmGYCZgbEAyMdWHpOhWbD6jMOzXMoLEYoXfooUdkLSsmhbmmaWhtbUV3d99L1Oan1q7JPM6Jl3UpNOlSi3aF9zIAWlqakMkY6Okp32Dgtgg5WYZ53LEoe1V83HHvzTIchDloK6QApDtWIKp346CNZyOjRDEtM6KmYq8enk69IVFUXVw3/UWJnXi8ZEHXnd5GpZOu2McNkXyFmQxUdbsfel02s9vqddkUxzCpCcVyYzRNBgoTjBAQtxWPEtuN0x/TJ64DMwEDJhRFuH3yc1BiiT8rEyehfNZY15llxSOIaKKNwf/qJoFCwTNjci1nlVng4XUKgSc+T6Bapj/3MrdVz0nYosNgak2se2FEnOMe1bteCI1Crd4F8XgElNKyMwZXO36wGHeoaDSCWCyK9es7q1LqpnIDK5d3AXNb+yo9sGoM103BaXuuwYNvDYJCY9BNiuZICp+tjuN7g8of9NbL2+DWW2/Fs88+i2eeeQbNzc328rVr12L16tXYbLPNKnvCBqTaruVuNE1BLBZFV1ey7rU7OWG9DHj9zp6e4r0MwuDOMkwIn2jIjjvWQz0jzqSU0394rX2VEfe1FI2RliFgALq610MzUjhy+0+RpjHc/eJm+OmU9VU/f6H+qRoisDckiqp7MpZYLAJVVfpkPJ6TdCUFw9CrIvK8iVPCxeW5t/EnYGEmgwmTu27aZRCo91jWOp7VCoDiZNt0447Jo76Bl8m4eyWlDH7LnXDbpKIcA+EDMtN03DbBnGQsbvdNd5kF3ga+zmAUQsu5x6am6wMhzB6zEcIAxkWfCQow/qhU25oHSNfNvoA3Hi/Y5ak4qpcRtBh3qEQiBkVRsG5d6QWhi6E3DKwa0bp+yu6r8ei7g0FIBHqCoiWaxv9WNGH7IV1lHTe8t0FlL8imm26KZcuWYdq0aTj11FPt5XfddRcA4NBDD82xZ9+hVsminDFZd0Pc1+G9DBQ0Nyfy1u+sbLvgiTtWFCfuGHBikouPO668ta/WY+umRCs+XxPFhpE1oDBw3O4rcMs/BuG8w8rrfwpRTEb/QvSlRFF1sS0Sy4IjfL8bJR6vkg9DtZOu8L+zRZ4/Ts/vsimOE+SyKfZ3l1QQy5x4vOx1AtNkXJzBVWaBuGbXXRk23a6bhsmgWFY8gwEAc0Si6+u4vz4lcIqkg7txGowApjUgFucyAYW6CqcTIQC9GTdFFk73Nm5MZFtAq0UxQq+XeXj0CxyXpxQymcoMOKr1W4d1hwK4O5RhmOjoqO7LOhfhBlZ6QVfSvu5GJTh2/Cr87Z3B0AdpIIRBCejXiiV831TZgeUPfvADPPHEE7jpppvwxRdfoK2tDW+//TZeeuklHHPMMdh5550rer56kzu/QXXvxUbKkVCMl4HoB9av76qbBdIwDPT0GOjpSYIQgkjEHXfsZBkuRG+vKSrYZoMUgAS+Wk8RpWmcNGkdbvnHgKqLvUrRlxJFEZanR16xorxZW0q9g3OAW7liMe7OFMb3u5Y0N8fR1ZUs+yXFk64oVureyidd4X97H/Ds2Dp3VkyvCKSqYlvpRM08d+yeYtXQ84tBnnCFCz1FdZK1iEQsvC4ehaIQ7z6E/+6qSq2ae9xKpyj8MwAoVuyeovDaeoTwGnr8HiJWsXUgosFep1jJVUSMHqWAai3j4g5QCOOfwexkLCo17UGPcNPk2/HPlJhQreUUJi+gzhQMbq5+xk0A2GCDVqxd25H3Phw8eADWrOkpqaMvJgamkSmnf+L3WvbylpZEWW6WlYrHCzquovA+s3LwvinMwL21tRnJZMqOo2s0xMAqEtHsgZVw8ywGkTSBWRNO4nO+gZWmqYjHo1i/vvEGMHe/2IpBG2gYNIBgwxZ+LcZtuq7k40Wj3NrT1ZVbCCQSMQAEqVRpA+5c/dPatWtx88034+WXX8a6deuw+eab45hjjsHJJ5+cldK83pQ7dlKUbKEXiagghFSlpnC5ORLK7Tf9FFPaJR6PQdNUdHR0NoQFMghV5XHHmqbCnYG4WFGaXaydL883KTV48ACsWlX6M18JPlregoGxHijEQMrQsPUG1XmPDB48EKtWrc25njGGwYMHYt26wl42zz47PWuZP1HUyJEjc+6fyWQwZswYTJo0CXfccUfB81WTmlv0VFWBqiro6OhpEN9vh0p0Es6MWDcKdVSl1MgDskWegJnME38XJPKC3D7dIs9dUkH867fmeeLyAhKxCPw19EzDdS0UAmLCFnfuGD2+rzuGz3npOVY8AFaWPcPk+xPGYFpZN6k1MFNVr+WOuq14dvydY/ETVj0AThH1Gr886uFnLuEUU5TYj8iqW8kBj7tdlT1eOHcoRVHQ0pJAV1dPQ03K+WHMm9BFDKzc5RvCDKxKLd/QqI/kT6esxx3Pt4CQCAjR0BI38OYXg7DHVqUVNA6bdbMar/aBAwfi6quvxtVXX135g/cCgvIbVIJGy5FQjJcBr9/JPPU7GxFd16Hr/rjjBCglSKd1ZDK9J8twKewwtAP/nLchtt24GxGqVyxmuFj6a6Komk6DxeNRqKoKXTcbTuRxSg925vWk4shkDHR3J10DqWDKSbziPS8FcbtgBog893H8WTS9sXxeIWdb/XwiLqt2nisDp9MOJ+7O7brpzrop0gubVudkmgwm4wXVDbuz4v/yl5wj+qhrMO7/zdzCzjQJDMb/Y5YIdC8zGYXBCHSTwmTOf1zkcateLd02gcr6mUuCydXXl5LghhDuDQCgQvF4uc5T/u9tWoWIef+b/4WnaRpaWhJYv76roUVeELquo7u7B+vWddhFkZubExgwoAWJRByaFm6Ok4cZWH0sUaw+klqeB46bdyNPvpx7UAdWrc5gbQfDmk5uxn510eCSjhUm/k7W+KwO1bim0aj2/9t787hJyuru+1d7d1V33/fMMAwEZBODiEoMS4hiJGLQKC6JgpooEXkYJW4BiUJiEkkQwSDiEp8kxg0NEEFfDPpoNK6P5n3FiFFDABEV2dSZYe7et1reP666auvq7qruru7q7vP9fJS5e6mu7rvu09fvOuf8DgoFFY1Ge6lEHq8yYD3Qiy8zTQPvO67VGtjaqqPf70NVFWxullEuG9A0NVGs57FJFEWIogRBkNzYJHqxKU/x6czj9uKYHS3sa+uwHAF37CmNf9KMycoo6vTTT0ejEd5syJNR1FwyeoIgwDAK3h8lXxTlDb/ZOd2VEJ6RNTvTFWC8yGOPGd2XF+eyybN//DjjTFrY48I/i4Kf7eP3B0+FC0DHcSAFevuCTpzsOX5Gz3HglWnyoenBxIMghP8tOIInqEXBn6/H7g9k8mLEYLRnJTpE3QpcBzvLs5tFReQXXp6X9IsxjQX5dOc1/bdTGtOVQkGDqo4fNLwMBA1dgPjxDb1eP5WhC+CXUel6AaZpevEmjzvq+/d33EybDGmKMkd2jPGfUy73cZecWfdk6TrLduehHw9IU2Ugolw2cl9lkJSgy7AksWxfpWIAEAKGLuN7vYPD2nnfsSTJ7nGRm2zfib+yhS//aAcOKPdx+0MbU5WSR0niyrqORlGZC724QcF5+gIMkz6jl4XpCiet+UqoLHOIy2bw38G5eXED0tlx/J+5y6YNVm5pOw5EG7BhA2C73JbleOabjuDACjwWFj8mAElgxi0iYDsOJE8scqEZ/ix4Ji8oBMPn6f/bgeAe052bZwPu+Dz+f64DJ1+NiMycJaZ8M68s+do7xySPAf7f/nwsyKcJm2nKofig4byXQ03KuIVVvz9+fAPAqzgMV0j2IIoi/PEN+VlYAcCfv6SHK28S3XJ4GYYu4DN3HIAzj4tzlhsO2wQZV/6ajwzCMpOlGYs/8il9D2tWJBV5iiLDMIqo15u5yEDOGsuy0W530W53IQiC1/8bdhnuJyqfVhRmBlOr1b314LyHtQ/j6Ufvw2fuOAAHbli47YFtOPnQ/VMfk4yihpOp0FNVGcXi7I0JsiLt75/bELMm/NmYrnDGma8Me/y4ks3xrxt+XHTAfbBMk/8cJyC9n0MZPj9rx8cr8C8vR2Alm5I7qsG0AdHt4wMcQBQgOG6WL9S7F16YD2TuXIHIjVvYbY43OJ3BhCocAKKFaEXzIZV8faFQaVR2JN0154ZLWfTjxTGNtXq6QcMl9Pt9tNvdiV5r2YhbWA2Ob4hfWFUqBvp903suxo5vWNzCCgAuOauDq25m17dlSyhq6c8j6WKKmD2zmKOXVT/epN9HPCuefH6nuhJVBkkI9hYD7HcX7Tvu9+PHN/gupA33O00MVCLkw2X4zOP24ubbd2CzDHz9J9vxW0dO1jfMWZTQUxQFH/jAB3DNNdfgi1/8Im6++WY86lGPwqWXXopzzjlnpq81KZm6bjKTjcHDz9qhaVYUixr6fTPRbi4ve2i1Osha5LHbopk2ceA2KTIcPViyGey7G5fNG+W2yYWeKIkQBQGizHeKXDfOiOOm5Llqir7Dpuusye8TJcFz3fQcNt3/cmfEoPOmJPlijzlzOp55i+S5bgKiwG/3yzQl0YEkst+VFBipEHTd5LfbDsv0zVvojXOOEkXWn1CvT+ZcRa6bDDlmm6tQUGGa1tAYIAj+WJjZOmCORhQFFIta6h5AllUa348niqwcKqtBw8sIX1gpihJaWNm2g3LZCJm/jCLs5MmzfYsr8bz6/9FhGAq2b2N/AC8+aV/i55bLhjs2ZHjJ3LZtZdRqXUy6MbEK8SkLx3LeAjNpqaWmMdfHWTiLR2GO5e1Um+Vpqgz4mIJFjXbJG6LIMna+y7DpzRTlZfdJKjImcRmeNdd9czsO3MEu9mc9Nl2FQRBJklAqFVGtDn/fzJlZRbs9WcnvssamTF0mliGLFyRJwOFlD6YZNF2Zn8gLmq8EnxMt24wr2RRjxCHHcRyvby8sBgezebyvzn89ISQU2Wsx4Wa7c+14klAMZPxsG96xgsYqg6I27LwZvJ3fN3C7Ozw9imULsN3/cTMWbsgS/TewmGweDUufD3Gf4agvN1EUUSrp6PX6cxV5/LzSPyeZ6YosS6hUDDSbLRJ5AXiMZ4YuTTiOA8MoYvv2jYCAHk/QNIEbJkRNE7hj3jyo7m+j0zFRrVno9hx88KvbEj83zYxPYrZMc33ouuaOfGpncp2lrThIO78TcEjkBbBt5jJcrzextVVHr8cMXbZt20CxWEC320vk0Bpn6CKKg4YuvCIhC855yiN46BcWOl3gM3ccMPFxeGvP+MesX3DK1/CZHDBqB0OSRJRKRXQ6bCd3nOlKWmfNJO6a7LGDfXm8ZDNYtsnvc2wnVI4Zzeax4w/254XOLWC4EsRxxbxl2XBc10yA9d3xcQpMRLLxCrbNBKVl+cHDdv/Hd5FM0/GOZVnu/2zW7xLcbbJtNm7BsgVXwMH/ryO49/kum2wRP/j7Cvbk8X9zV855s6jyA4IT3wfDekMKaDY7CzMASLq7yhdRSUSepikwDB21WiNRJcO6YtsO+n0ToiiiVmug0+kOOOWlX1j5Tp5sccWqD7JeWP3NKx1sPdJGtdpFt5duIyvZYopKN7Mi7WfLN6Yty3arj7IieVlpUpEnigI2Nsro9foZn/vyw7+Ter0+qtW6+3s3XJfhAmQ5mZlcMpfh2cemVz5tPx7+RR/tjoObvjOpIzBtQg2DhF6AUReAosjQ9YLn9DRLZ00AcGJ2h6P9boP3+yIPgNckH3XZHJyJ5wvA6K50NJvnH5sLNPZ4O/LeRS9rGD5/gP1x2Y7j9eh558Idomw/A8geHzZkEUV+jMj7D76W26snxgg5QXAgugPTuegDMJDVi/7viYdpia2OZ0XSOVUk9LIhrg+mUFChqgoajdbCxsIk/X2HRd5oisUCVFVFtVpfuuqLeSNJIioVA/V6yzNzaTbb2Nqqo9lsT72wGsz2ZbuwuuwVNjqtPurVPno9G9femszqnGLPfJjFRxzemM42U580o8dj07hrSJIkVColNJvtROXR6w6fJ9hstkLjG2q1OkzTQqGgYXOzjFJJh6oqidY08872XXBGFQ//vId2x8F139ye+vlJYhNLbKxf/Jr7wHTAX0zl7/sifldK01QoiuQt9GbprAmkM14ZeV+M2cooE5Zof17csW3bgQgboiSNNGKJK90EggIwXAYqeqLOL+vkOA4ToZZrbuCbtrBGYtsdtA7XgZNl+LgBAn8NZuAiCiyrBxG+yWYMsjh4Z7vdgaapMIwi2EDmPrrdXiKr40lJUlqwruUH88BxwkOJmQV/PmY1jftynmTQMJVDjUeWJZRK+lCnv+D4BkFgzfmDhi5mQhOT9MPaJ6W6vwXTtCGIxcTHGreYoriUD1RVhqbN0whvdEYvjemKbyTSzOm85XxRqRjo9UxvfEwQx0HI0EWSfEMXwAmMbxj/Oc9jWPvrn1PHu/7VQKWi4h/+fQOvekY18XOTZvTW8ZLKNKM37DOfZCjxPIjbldL1AkRRQL3ORd7wcqhZiLzYx4wp2Yw+ZlifXzCbN/x8wu9fDBwvmI3jQi46TJ2/ju2ESzRtd9fHsmxWdunA/dkt63S481P8ZxuNG9FrK9irF+zdC2b4vCHpMVk90xZDQ9OP3tGBafbRbDaxb98WtrbqcBwb5bKOHTs2UakY0DRl5Gc5CVR+sFj4Z8/MSRbTjzcJaQYNb2yUYJpmLsRr3mElu6y0NcliiC+sGo0WtrbqaLe7XnZiY6OEYlGDJCX72k1SRjXNbvrVr1PRbnZRq3bR71v420+Nn2+bNKNH5ZuLo1jUoCiyu2aZzxfFqEsiXZWBhkJBQ63WIJE3Bh7Lu91+rMiLw7IstNus75gJaQe6XsTmZhmGoUNRkq1pwpUIfjVCXLYvLQ/etx+PPNJBr2fjvf8nufkJtb0MZyGlm/Ny80mPvyvl17ZnY7oSx+BoAjFWmA0ThwMmJgFjFU6wvDMum+dEvhiirp3BoeeCKLi7OI5X2sn/578H9t+gMIz71Q8zZOFumsHnOm7vnter5/i9en7vHuvRsx0BtsN6+MYhi7YnBqMLK0Gw0el0sH9/DXv37ken04OiKNixYwPbtlWg64XEC7hRJC0/WMdgNQ/YDqW48H68NCQvhxKxsVFCq9VZCvG6aFSVz6FqTLxgXsTCKk1seMdrFNQeaaLT6qPbGX+t5/N7mwD8NYttO6ndeWf1+lHSVhmIouSOBKDvt1EIAnPebre7E5e2siol39Cl2+1BUWRsbJRRqZRQKGieh8O4c2Eb/uG+Yxaf0vcdX/06FQ//bD+azT5M08ZVNxcSvR/aJB/OQko30zTuzhMmQNlC2jDYkPdx/XjA7DJ53PUSGCzDjMu0efcFxFxUmA28bsxIhbjHBjN10aHpAgRPzA0r3YzeF3fe/HhcrAGA4JqmWBZzzbQFAbDYSAWeCR6np4bFJssWIImON0Q9OkZPcIKf6WAZFeB4c7H6/R76/R7qdbaA1jQN5XIJkiSi12MlnpM4GFKwmh/87z2IpsnufLxm7j/jNOVQqz5oeNb4FuX1mV0HfGHFF2ayLLti0p+L1ev1x/4+o8ZYwblYkwxrbzfbEEQBRrmAv/qIiMteMd31kfe/m1VEkkToOluzLMJUKe47K02VQblsuNUT6zG/cxpEkfULNxptmObsNiJN0/SOJ4oiVFVBqaRDEARvfEOS10s2U3R0wueaPyngje+uYtvOEhQ1eb/zuA25dc3oLahHL787g7yGudnswLKsmZuuAPEib9xA9OhzbdsZGI4ePe6ocQqcoGALGrGEHuOKu9jziZRu+sfyRZJl2YAkQrQF2AI7b9gObJHPzxPg2PDm6g2+BsvSSdJgeabtALB53xrczJ0T+Nl9LPxFffDSkwKlnabNPr/jDx4saeO7VuzziC6sbHQ6bbRa7HmapkLTVJTLBizLchd34xdw/HWoznwxGEYBtu24f/eLPpvRpNkpLxTY9bgug4anpVhkZipJ5lBNw7CFlSgK6PVM9Pv9RBnlaYe1v//PNvG6q+ruvFQBQLKF1bBzoWssO+L8DRRFRqEwz368eIKXFqsyGO5lwKH5nemQJMmbQ52lV0Cw7xhg15imKZ6DK9+USt93nHxY+zvfoOHCa6rY2FHGWz8q4a1/NPr9Jvc3GPmQlWRBpZv5/KQVRYIsM9MVyzJHlkNlKfLC4k0YyNaJYtAN0w6UXfplmZygkItm84LHH+q2aduhP77o84K38ddioxH8XRu/ty/8vkNlmV55JvufZTluHx8Ta473bz8w8DgX/ILh7pv+z0zM8fEKDu/NgwDHEeDA/Z8jePeNY9xcLJbpq2Pv3v2o15teLf2OHRsolXQoyvD9FXLdnD9+P57pljTmcxOKk0bkGUYRsiyTyEuIYRQhivMfzBx0ytvaqqPf7w+Mb0jvlBcc3yCNLKN675vLaDc76HX6uOjaycv+RJFi0yxI6m9QLKpQ1fn24w1HiPTjjT4fWZbdzBTN70yCLDORV6s1MxV5cQRdhlutNkRRQKXCXIaLxQIkKRuX4XddpKO2v4l+z8Sb/m70NZKs7WU941PmGb248qg8ZvR0XYMgiF7pTNb9eMMYZ5Yy6rFsFh/vbQuas4Q/a9u2Q2IvCi/7CRqxsNcTvGwd4Ao7kWXsRFGAGKmpdGwHosTPJ5oldLNxFhNmEgTYogPBEVjZZsjBM/ieubiMnrPrrgl/R9v795ispig4sF2R9/THSbAsY2Y7Vo5jod1uuxbsgKZpKBY1VColmKbllnj2vC/pZLtSVLo5KxRFQqGgodnseH/zOQtNIZKXQ7FBw/0+u/6I8ZRKOmzb9jLzi4SPcABYWZ6qKqhUDABCwClv/GJveLbPX1DxTbT6vhqMjRLUojrxeVNsyhZ/7eTAMIowTWsh/XiD5+Vu8ibcgNI0NWC6QhfMONh4r+n6hWeFZdlot7tot7sQBAGKIqNYjLoM9xNtWEfbY+Jcht/5Bg1/8s4WtDFxidpehrOgOXrxQ4kXQXSgqKqyMohhOxTTiLxx2bxRfXlR58u4x3CCIi94bE8EDhF5A0YqgT4+P8PneI6a3usFZuL5QtMXmLb7HM+B047v0YyKQVHwF922m8Wz+SD1yPB09h4Hj8kJDlG3XWMWyzVpsQOZvOx2rESIItDrsV37vXv3o9lsQZJEbG5WsH37BgyjCEmSaFdqTmiaAk1TB+bj5SU2RbFtG7peGJkRBuBeu2V0Oj2024tfBC4DlYrhGW/lDb6wqlYbrvunhWIxOhdr/HHGzcX6yFUHo9PqoNfu4fy/2hN7DHK1WzQOJElAqaS7bov5MFWyLBuFgoJCQR1r4KHrBaiqQvM7E6JprI83DyIvCu8t5i7DnU4XsiyhUkln6AL48SnOZfiRh/ei3+3jwmtaQ+MLCb3hLKx0Mw9rKVH0B4p2Oj1YlomtrRpM0/8iNYyit7DKUuSlfm5g6Dl/jCesnMCiNVDiOeioGXH5jCnd5K/BnTXjHht8HTYuISwGg7P0wj/D/Rn+cyOCzrYcBL0j+HUT99HZNh/bwN8z69lj2cnBxwO+2LNsAb9+SNM9jywWVsEyKrawsiwTrVYL+/Zt4ZFHqrAsy62D17GxUUKhEF+uRYup2dDtmmg02rkP/DyLV6s10Ol0IMuS54wWLeljX7IlNJtUDpWEoEV5u51/I4gkC6tpxjd86G270HX7cqJlVGRfvngEQUCxmC9HYHZN9lCtMiFSKhWxsVGGrrNe1yDlMstK0/zOZBQKGjRNW5rSe9Nkm2XVah2NRhOOwzLP0bX0OKKbUtdfeyT2PbwPrXobr/7rRxDnMkyxZzgLM2OJZqbmjSxLKBa1WNOV4IBJRZHxnJfdPvHrJB6FEOnLizLs8wrOzeOunVETluCMvejuStDpM4rjKqSgy1uwdJOfl+06ogiCwEYRiGHxF36fgmckY1nstQWb9Y6IEpu/J0XEJ+ALO8tiZUeWA0iib0oSXdsETVsAv9kXIndwESCK7PdtOULIlCX0GQTc8AB23fCBo/y+fj/dwFFeRhUdONrtskUbKx9mO3nbtrHZVtytzzStmexK3X///bjqqqtw2223AQBOO+00XHLJJdi+fft0B14iluFLIVqqaZqW66rX8Qw8ymUDgiDAsixIkkSDhhPiW5QvrxFE+HoQoChsJIQkiZ5TXlpDl9qe/SiUde+7gl9/vJKAbdQO+T5KUHpOJCPa9sIqjUS0253c/H1HTVeCrrKqqqBQ8Ev6ZFmaahzAujEvU6issO2wy7CiMJdhw/ANXfr9fqIspSAIuP5dR+DlF9/vrWODayeePBp1rHWOS4Iz4t3v2VOf+gVYg2X4NllmpieLKjvQNAWKIrt9OdZId6hZZ/H8+4YLveD9wWPEDUfnjwkeL+qeGRV644xY+GtFSzejQi/4HO7YJgqAKIte6aaXgRMFSKIIQYSXMRQEuDPquEBEyK2T3eeWcIpsrAK/ngRB8MxcuBun7TDBJwi+8JNEB6LI+vD4RykJDiSRiUtexvnkI2pDf1fD4AsrVVVSL6yi8EC1sVFBrVaFabIvct4rqWkaNE3FFVe8DY5j49d//TdwwgknQ9f11K8lyyZe+MIXotfr4ZxzzoFlWfjgBz+IQw45BDfddBNUdfIenXkybXxi19/g7dzVbNGkMV0pFgvQNAWWZXvXYrebzA57HeEW5c1mOzeZkVnDF1aKIqdeWJ31xz8EANz0/l8FH+PBYo2DZrM51ClP0xTIsoJOZ3KziJ07kw9JziuzXjsxR2AmqmzbWfg1y9ovko124U6RPDalcW1cVwyjCEBAs7n476Es4JuUrDpKQL/fd8c3jI8bL33DjwEAN7z7KC82sWushP3797vtPIMuw47j4IADNrG1NXl5/rLGprUzY9F1DYCAWq01NlBlIfKSCrzoMaIiL/qYuGxeaC5fROTFwc1VhpUL8sfYXJDFlHkKIpuxZ8GBBBFwBV3sMUUB7CVdQwALgASIEDxRFs3MAfD+kJm6c2+MWbBLov8lYjsCBPdLxYKf1ZuGWe5YsYVnCa1WG7Y9uGPV7XbQbnewe/cFePDB+/CFL3wZ11//MVxxxdXYtm1bqvP+yEc+gp///Oe49dZb8ehHPxoAcPzxx+Pcc8/FLbfcgrPPPjv1Z0HMlrSDhh3HwdaWv7hkdtgqSqWi1yC/rFmrWTMvi/JFEzR08cc3GIkWVv12B0qRDSoWBAG67ruRCoKE4ExRfo2yTSmRFu8zRBQFGAZrL+n3TWiasvAeYvb7tRN9r8XN7wybC8GdO5ts/NA6kCdTqKwIjm8QBEBRwtlfvmEeF0tuePdReNGr7wIAN0kge26kzBdh+PiGdWVtBqYLAtsl6fe5hfroQJWls2YS4sxXRpV3xpZJisKAMORlNwOz8kaWcDqw4DtrinHPd8KD1EV5UKSyYwEQmaunICCURRw4f67HALBaTV7mGX5MEHdkn9ef576qP8ZBCD8WAJ56VPpsXhyTLqx4CVmrxbIL4RJP/gGwhZUkyTjxxJNw1FGPm/gL/7Of/SxOPvlkT+QBwJOf/GQceeSR+OxnP0tCb8EknUE1atBw8FqMlhszp9f13E2XZQmlkr525a1pF1a3fPiJ3negrhcgiiIajVaojB8YnCnKsofrd11lgaKw9pJWq+OJpFFls/Mg3fxOzTVdCfeXRV0b+eaoJInehtQihr7ngUqltHaD4x0n3C7FZ1kXiwUAfutMsD3G7PbwgnO/j1uv+zVP5NneKLD4maKsry8H5iALYEE9evP9wP1dsS56PXNsoJpW5M0im8fh/WwjjxMYqTBM8I07n6gRS2isQqB0M4hjOxAk/4vfsV0xFunRY+8BIZUVNWTxy4AwMGaBC8Lw58L+cC1b8IQdf37oPQqON1QdELwsn+Vm84b15k1L0oUVgJDIixJeWDkolze8L8hJqNVquP/++/HMZz5z4L7jjjsOX/3qVyc67jIyalYV+6KY7/mkKYdKU3o4qq+PfYn2EvWYLjt5sihfJEkXVrd8+IkoFn2RF0dwYaUoKmRZdsvNFmTovUIoiuyaRfnX6mL9DdLN7xQEYWx/Gd94GtbX1+2yqphVh232Guh0emvfw2hZFtptC+12x9sICPcdm7jlw0+EJIkolw3U6/GbdsHYJAhApVJGo5E/V+V5sDAzlmnL5pLCTVfYrpiVG5E36v40JZsAE1zc/p9n5qJD04PDzYP3i8Lg+dq2AxH2wHuJE5jBAa7BklEAcITw69qO4/bg8d1geKWbAOvJY+fk9wnyx1kWs5UelYbni3M+U4/36w17HAA89dGzyeaNYtTCSpIkd47euIW2g3K5hH7fQqdjYtK/n717fwkA2LVr18B9O3fuRKPRQL1eR7m8nLXos8C/pucnBpi4TFsOlb70MLwBMfgluqp9fZqmeHO71jGTOYphCytZluE4DprN8SVkzASmgGqVRN6saLW6MW0vi7l2k1cZwP2eMiea3zlofKbCMAor3de3CqZQWRHdCJBl3h7DNqA6ne7YDVkm8kpotTro91fr2knKAjN62b8ON11pNNqZmq5wZt2XF/d4X0zZAyYsA8eKmafHnuuEbo8KwzgjFv481lfnQIIv4AD3C8gGbDHsvOm9Ju/jACC4Yo0LO9t10GTnAiYI4bpyCux8ojpZ9LJ4rOmWuXEOfHTs+LYAiM5AVm9RWJaFTseGqipoNJpeDwxbbPsDR30clEp8+HUf02yStFpsZ75YLA7cp2ma95j1FnpuhnpOC4o05VB80PAs7LajX6Kr2tcXLCEjRsOvCR7z2+2uK/x8l2HmCuxvTMmy7Ik8x5nDF/uakAd/g7RVBuWyMTPBwioR2mi1Vrevj1dmNBrtldxgmzWmySryVFVGvd6AJMkolXS3PcZ0y379z1EQHFQqZbRaXfR66ynygDmZscSRdbAqFjW3dCBb0xXOKIfNNHABBwQzWvbIjF40Kxc/niHstjn4uvE9eo7twEa4XIRn3Lh5C3eGFCKCjBuzQGQjFSS3vw+I9u05cAQ+yJyNWQAG++kkOLDASjWHCbvguAXLFXZiRNjx3r1n/OrW4AHmQLQnD8DAjpWuF7Bv3z782799Hk95yqkoFotTizwAib+w15t59hAnF3l8M6Band7RL45RfX29Xg/d7vLtpi+7RfkiKBY1yLLszTrjCye/75gtrP71X2/F9u3b8Ru/cTKq1TaJvLkwv7aXNFUGvPe10Whl0l83rK9PFMVUjo15Yl1MoWYJ30zg5j6swon1MyqK4m1U/vCH9+B73/seTjvtNLRavbUWecDCzFiywzddsdDpdMYGqqxF3rQum8HnDMve2Y491G2THYvPQ3JCYi+ubJMTnaEXxHYciDYzXPFHJYSFGwBm4BIr7ABbcOcyWb6wY+9V8F5DcPwePylG/LH3BFi2E5qpN3C+3JTFy+oBZzx2a+h7z5JgmUZcb5Vpmt7Cipc4X3HFFdizZy9+93fPxFlnvWSq19d1tiPa7Q42e/PbDMOY6jWWnXntmicthwLYoGHLsuY2aHgV+vq4RTkNZ04O64+SYz+zYNkvAOzceQD+/d+/iKuv/lscdtgRuOiiN2Nzc3POZ7xezKsaKk2VAd8Qmlfv6yr09a2rKdQ08OwnE8aDn1m/7//eNa2Ara0tXHjhhTBNEy95ycvxtKf99rxPOTeslNALWhGzWu5s+/HGMYn5SpJjRYXlqIyeIAqwbTss9hAWiPxxwcVt3Aw9//WGlGa6pZvRrJ4g+IYsNvySTcAXbsExC7DZTD3v9TxBC899UxR4JnFwUR7M6rkJRS+rt0gPBlYrnrS0xcHm5gbOOutsPPvZL0Cn08WePb+c+hx27ToIALBnz56B+375y1+iUqlMNJtvWYkvj8p2MZWuHEpAuVxCp7O4QcPL2Ne3Dhbls6ZQ0KAo8SIviiRJ+M3f/E0cd9yvwbIc/Oxn961V3FgU89mESje/U1Ek1Gr1uZtXcZatr49ModITFnnjsp8OHvWoQ/CHf/hyvOhFf4harTpRv+gqsTJCb96mK5xZmK9EjzNspELS4zm2A1GSYoSmMJD1sx0bkjuEbpgbKhdpcfc5juOVbsadDy/d5E8VA8fgA1TBDWQiYtKymXkLN2IJum96AtEGAH+mXtyvw3bFIx+Q/uzj9g8+KGN4Q3C73U0k8nRdh+MIaDa7AAQUCgU86lGHTX0e5XIZhx56KO64446B+/7nf/4Hj3/846d+jWUnS7OoNOVQvLQnT/0bSfr6+v3+whZ9wHpalE9LGpEnyyIMQ0et1nbdjwUcfvgR2Z8kkblgSVNlwOd31mr5yZjnva+P9VirZAqVgrQir1wuods10e1aAARUKhuoVDbmcaq5ZSWEnqoqUNX5ma5w0vTlDcyzCw0zT16yOSybN8ptM9ifF3zcqHJPwC3fsBzIihQSibx0M3pu/DiQhJjyUcF33rQFOAiXbHKYaHRCmbdQr54r+qxA1m7w+WFnTv6ReSWcc2YSkScIAhoNJvJmzRlnnIHrrrsO9957rzdL7z/+4z/wk5/8BOedd97MX2/5yKYPZrJyqHyX9ozr62PGHfNZ0JBF+WQUCipUVU60YJckEYZheCKPyI55+hukqTLgf2fdbs+dSZxPRs/rM9Hr9eba10emUOmZROT1euZUzuSriOCMWHXs2TN9078gxJtm8CbUaSkWNYiigHq9PRfTFc6s+vKixxw3IJ2/bnQ8QshBM/I8XrY5bLRCdIZe6HUizpvez/y/khhzHwJi0n0tKVwCyjJ0fv8eu074OSAkAkV+m8iMWHg5KP+omDOn787JfzX8ugvedubj55/Nq1RK7gzH8SKvWCy6c6uyEXkAIEl9nHnmmZAkCa985SvR7XbxT//0TzjssMNw4403QlXVTF531swiPrFBquHbVFWGIAjodmfX55FG5BWLGhRFQb3eXNpdX97Xp6rKXPr6yKJ8MjRNhaapicxq+NyqajVbkbdz5/I7/i7D2onDYkwykcevgSTzO/MMj03BubZZxg1dZ6OUqF84OaLIYnoygx/mTG6a9kxM64axrLFpYa6bsxhKzMuFGo35mK4A6d01k4i8pCMVxvXmcbhLZ1DkDT2/YAYwUoYZzOIFfw726A0r3eSGLIiMWuALV8cdeRDnBMrKgfj5xfRQueWgluNn9IK9foLbdxV05lzU7nNakce+DDrIcjdq+/bt+PjHP463v/3teM973oNCoYBnPOMZeNOb3rQ0Ii9LZj2UOE05lGHoEAQsvUvkuL4+VuI5m4UiWZRPRjqRJ6BcNlCrdSiTt0Kk2YDy53c2c2/ENI64vj5dz6avj0yh0pNHkbfMLKx0c5qhxHkzXeHEjieIjEYYVrI5Csd2IMr+1t4wt03v/sBt3Igl6ooZNWxhzxNCC1xusBI9Pi/dHDaOgYu76P1+r130fN0xDqIAEU7IrAUIumqya4aLO/5fNlAdkKRwyZ0ksdvdFkS84Pj5ZvMqlRK63V4ikVcoFOYi8jhHHXUUPvCBD2T+OnlnmBnLLEhbDlUuG+j3+2i3V6u3LK6vjxkmTN/XRxblk5FG5HFDoFqtA8tazgwzMUgakVcosOtlFvM780aWfX2lkgHbtsgUKgWTiDxWpksibxgLFHqYaChx0HTFNOdnujIJcUYq4R46G8P686KPjz4WSD4/b/Q5+MPTufiOK9uMc92MGqjEnYPtOIDFZugNZuYAiGzguZfBCw5gBwBbGHDptB1AtNlMvWAJJ8ey4c3aA4bP3MsSLvLG9woxkacoMmq1+Yg8YjSzcLZjFQuLGTScd2bV10cW5ZORVuRVKiTyVo00Is8wihAEcS16y2bZ10emUOlJK/IMQ4dlOWi1SOSNYoFmLOktzFWVObwlMV0B5mu8kmRUwjCnzWFlYnEmLMNm6Xk/R8xZhhHt7WPPZVkzEUxU8lEMw1w3+cD0gfEG7hgEyT1+0GkzOmYhmmlkf9rCgHsm/z7iWUF2vq7ZJjuN2KweZ57ZvDQiT9NYP1at1gYFqrww3XiFNIsoLlbWNSMVN6+vVBo/r48syidjkkxevU4ibxFklTibZH5ns7l+ZYfj5vUN6+sjU6jJYFUtJbcEP5nIcxyg1eqB1k6jWXhGLym+6UprbKCadRZvFiIPGF62ycRPvAnLsGNE3Tb5vyH6/XmjzjU6Qy/2scKgeyZ7bnzpZrDUM3iX59IZM2Yh2OMXzM7xDXruwBkdvB6cqTfwGTkOLFsYcOScB8lFHqBpGlRVJZGXM4aNGUn63KQij1ltayRWXJL29ZFF+WRompJC5MFddHVgmvQZ54lJ/Q3SmK748zs7MzWlWmaS9PUJAvu7WZfqjFnBzbSazSR91oPjp4jRzEXoTTuU2DCKsCxmujIuUOVB5I0r2YwybqRC3HGi/XlhwxMbAgZrFQUxXrgFbxNFv3QzuuAd1rM3zpAlOmaBnT8bsxD8qNhcPzY4nX0WfsbPdhyICM/UCxLO6rHbeCLgxSfNJ5vHLaeTiDxV5T0PJPLyxqSlm2lEHndhq1and+dbReL7+li2DwCazRYm6e9eV1RVgaZpiUQeW6yWSeTlFP69nGaTY5Iqg2Tlc+tJfF9fCbIsodPp0ueWAi7yWq2kIq+Y6fipVWShGb1xv6RFm67MSuSNO240owfEZ/+iYxH440Q54NAZk+mLztALHiP6/GDpZtR1M0qckOO325Gsnm8OE/NeXaEYHIjOb7csQEJYELL7WPknrPA8PlHk1xY7t5ecvDX0/GdJuWy4jdtJRJ6CQoFEXl6ZJEuUvhzKJhe2FPT7JhRFhmmaaLc7C53Xt2ywzyq5yKtUymg2SeTlFX/tlOz3s4rzO/MEy+iZnlkNmzW5uHl9y0RQ5I13YWbO5IKQ7fipVWTBPXrDf1GSJEHXl8N0JUjUZRNIn80LPidObEbLLr0h6DHPD7puBp0whzl2jhSc0XELIwxZxKhoi2QSHceBDXhZPf66XCQC4fl37JxZVi8qFm1X7LFyTpbRi8siZwVzSzQTDY9VFMUt1yORlwemHUqcphyKejcmJ2pRPklf3zoSFHnj1vlBkdfvk8jLL8mroSaZ31mr1TPrD1xFZFlGqVT0xLFpInVf3zoyicibpzP5KrGALibGqNJNVZWh65rXlJlHkTe8r220yBvlsuk4g4sTJ2YBOa63zj++6LluRj+/aFaQY9vO0J1xx3FCj+XPjfvd2A4GHsuOgdDxBdE3gYkeht3OXzdyfPfxthPMdLKfLYv9bx7ZPF/kjXfWUhQFul5ArdaG42QbqK666nK89rW7M32NdYcvopIOGt7YKKHV6pDIS0mpZMBxHLdcMwzv66vVGm6vow1dL2JzswzDKEJRFriXuWDSizx2fc5D5FF8Skbc7y1paTmPTUlEXqmkQxTFRNcK4cNnC/LYE6XX66PRaGFrq45OpwtZlrG5WUa5bEDT1KndnZeVtCJvnuOnVjE2LVDoxQerQkGFosio11uus+bwQPWCc7+ficgTRHFk2eawks1xZZtxJZtxz0/ithl3PlwoBrN57NiCZ6zihERW/DG97JoTmbcXdM+MEX38OXFiMO7xXMBFf7/8PK2B47ivG3lZy/JFHxd78yCNyJNlGbpeQLXaylzkfeYzt+DWW2/J9DXWnbSDhstlA/V6c2ZDwteFSqUE0zTRanXGPpb39dXrTWxt1dHr9aGqCjY3yyiVdKiqMrcs/6IJluCNF3mOu+jqotfLPnhSfJqOcf4G4Q2o0b9PvuA2TQvNJs16S4Omqe7GbTIzLdNk8/S2tupotdruKAEDGxsl12xwYcvxuZJW5GlawdUE2Yu8VY1NCzVjiWIYzMGo0Whj3qYrnKRDzJMdK33JJjB6NEJ0dl7w8dH+vGjgCLlzSoHnxZRfsvMaNG/xs2fCYClmxJCFz7sLi8Xw8YPwkkzfmZMfV4AoRo1hBh/PXxMAXvbkrYH3M0vKZQOmmVzkGUYR1Wq2mTzLsnDddR/Chz70j5m9BpFO5BUKGlRVWclBw1kyizLX4Lw+SZKgaevR16cosivyklxzDsrlMlqtXuYij+LTbODzbofdlzQ2iaKISsVwS3WpnDANwbg+CbOc17dM+CKvk1DkaVDV7GcMr3psysV4BUEQUCoVXZe1+ZuucJKIvGECLNqbN6pkEwibkgSfG5fNCz0v0J83/LX8jJ4UmRQe7NEDAAlSaB6e3ytnA25vn/8e4103Af+54cHqfh+ffwxEhBlz34Q42LPJM3RBHBuw4ECKHDM6Xy9LuMhrt9OKvOzOqdvtYvfuV+Dee+/Bs571HHznO9/O7sXWmDSmK2zQsJDIBIPw4dbus7QotywLrdbq9/UF5wsmEXmVStk1O8v2vVN8mh3DqqHSVhkYRnFt53dOA3dMnlVcn3Re37LBy8Pb7WQbC5qmzcWZfB1i0wJzxaz8QJJElEpFt3dlcSIvCaP68uKycuGfw1+kw4akB58X15837FyGlY3yzzKUzQPLDIqCOJCx4zvcQkDkOTF9e3GlmHZMv160XHTkYx3H672Lyxbyx/sz+MLlr5blwLIcnPOUrdjPYhaUSjpM00ok8iRJcuv3sxV5ANDr9dBqNXHZZW/HW95y2YDAJ+JJ+ntJVw7FvtBs20GjMdhXRgyHZRnYPKWsFjeDfX3WSvT1TSryut3sBS7Fp1kyWLqZdn6nrhdRrTZI5KWEb95l6Zi8in19QZGXJK7Pc/zUOsSmBWb0HEiSCF0voNlsw7LshYq8WQ1FH/bYkT1/Y9w2Q3PoIuWZQiQrGJ5ZFzBiscPZtaDrpjcmITJ8nM/riYquaFYvmBEM3hYdsRA3ON2/3R+hIAi+II0ewxu5EJmlxy+b806rIitKJd0tuRjfLyTLIgxDR63Wxjxcqg3DwA03fAqyvJyL1LwRHEqcthyqXDZoYO4ESJKEclmfa5aB7ab3vaHQfF6fYRS93fR+v597g4q0Iq9cLrnv28I8HOwoPs0OxwlvFKepMtB1Vh5I8zvTw8biWIn6hWdF/Lw+NkuUjXPq534Mhi/yuglF3nzHT61DbFrYO9M0FaIoolptJgpUixR5wPC+uUnm5iXpz3Ns2x9cPqJnb9x5Dtv9iSv/5OKbHceO/VyihixiQPT5fXqDoo+/hneb12MXeazjwHGE0Ew9PkSd9eohdAzAz+oNy5LOglJJh20nE3ksS22gWp2PyAPCDqvE9PA+GCbwaNBw1kQtyhfFMvb1TSLyej0TnY6JedmUU3yajGH+BoLAvvcEIdloF8AXKjS/Mz2VSgm9Xj9RT35WLGtfHyvDTybyFjF+ah1i09zMWIIYRgG2bXtZvEWYrnCm6csbWi6ZQpgNe524jJ44qgcwMi5Bkln6OZqVCw9ijx7Dn1EXLd0c936GmbZE++yi4pCfow13MHpEIEZflwlJP6vHns/uyyqbx0Vekp08SWIZnXmKPGL28GuKBg1nT1Co5ElELUNf3yQir9+35iryiNniD0y3E/29cAOMTqdLo11SktfZp8vS18evu6Qib17O5OvGXDN6UdOVcrmIUklHr8dNWMJBK88iL+nj02TzggzLqEVfw8sARgxdgoPSg4/j/466bgK+KOSvz81YoqKMP0Ycki1kXz42BEFgJZah0lPu8hl4P4IQ6Lvz3TuD7ps8qxcUgkEDllc9ozb0s5yGdCJPQLlsoFbrkMhbckyzj1Kp6C3oR+2UFosFKIpEg4YnQNNUFApqQqGyOHhfX6fDd9Nlrwyu3zfdEs/5js5gI1uSi7xSyUC/b6Hd7oNE3vJiWRZkWUWppKPb7Y0sLebl0GwmMY12SQM3hWIOkYsXTaMICjtZlqCqbPSDZdneffOOr5VKCd1uL5HIm+f4qXVkbkKP9+O1Wl2YpgnHsVGtNiCKAlRV9eqOu122sMrLzm6aks3xA8yjPXD2kOMMz9wNe804185xrpsD/X4pm3xtx/EEWpxYBJgYExw/+8Zfb1yfHjsWgECvnyAIA+MWgmJv1hiGDtt2Eok8/qVQq3VgWfm4dolkBMujeDlUu81cVYM7pf2+iW63H1owlUo6HMdBrUblUGmZ1qJ8UeShr4+VCRcTju1gIo+VfpHIW25YqebWVt3t2VLd0mLbXTv5C3pVVdw5b1RlkBY+emIZBXKwr08URWhauK+v1+tnXonARV6SLOi8xk+tM3MReooiQde1WNMV23ZCO6Wa5pfH/PtNp0CSJNTrTTzvj/5rpue0iJLN4EiFuOPE9eclPT8uGqMz9IaVbsbN44t9TxHzlaEZQvd8QiMaAqLPshxIAGwxnAkc1qcXO5PPzejxj4ZfQ6/93TZmveFmGEU4joNWa/wQWTb4lETessOup3A5VHCnVFFkFAoqZJkt6CVJQrfbW2jfxrIya4vyRTLvvj7eC5o0k2cYOizLQatFIm+ZiXoZcGOwdrsTWNCXPPdqURRofucELMIUKiuYr0C4r49XImTV1ze5yJvpaRAB5iL0TNNCvd4aa7riOA46nR46nR4KBQ2FggrbdlAuG/i3G0/2eiKmLemc5VB0/5jjv0BHmYUM688bJcxC/XaRjB4v3QRGu24GnxPNxkUNYWz4Riv+cZyQcAuXXoZF4YA4DGT1eJ9eMKvnCePg85xBUxa+mz6rMgXDKAJAYpFXLpdQr5PIW2aSOGvyBb0ksREApmm5wk9Ct9vPfXlPXuB/X6toCjG+r68/1eIxKPLGi0cm8hwHaLV6IJG3fHDTsnGmK8EFfamku5U8DioVI3dVUnkmL6ZQWTCPvr40Im+e46fWnbkIPSYOHPcLbvyXjWHoEARga4tZAAsC3JpjthPxhX85Gd2u/4WZRvglFXlps3lpXyvpceKEWfS+uGNxkZekHDNauhk0ZAF8AcjFWfA5ojCY1fOOG8gm8ptt0wZkcWAWXsgu2sbAAPXouAYeg1/37Aaa7nqRl7LwXU0euNIEbL4IbTaTiDzmKNVodGCaFKmWFVkW0O+bib5s+KDhWq3hlb/wngjDYD0RSfsS1pFFWJQvivi+vsLEfX1pRZ6u63AcAc1mFyTylhNFEWDblhtrxrRxCKxHvN/ve/M7WZWUGths6C2FJf8i4GYgeTOFyopZ9/Wly+TNd/zUujOnHj0BxaIGURQDbmWDoi8YqIIDqR0HAzsR/Auz1zPxmY89yUs/z8LAJQuRl8b6n2fS4ufxjTZiiZaPhg1WfDEW7c9zbMeboxc9V/58ZvIyWGo5cF7DSi9DIxOGu28OlnZGZ+ax9/H654QzAuFSFgGKoqBU0iEIAvp9FrhGlSnoenKRJwhAuVwmkbcC8EZw07TczFx89oMbh0TLocKzjljpXvgLs0c7lsiHRfmimLavzxd5zcQiTxAENBok8pYbAYZhQBCC/gWDom/Y/E5WJRXcbPC/E/PiHJsHlsUUKium7eurVAx3EyFJJm/+46fWHcEZcVXv2TProZoONE2CqirurmYf3S4TfdVqDQcfvMv70kuKqipQVcUzSwjukkZF3yxcNoeJvTRum3HHSTooPe61xIDhijeKISajFyzd5MeMjkQI9tjx84k6bwLw5u3xrF50ZEPwONGsHgCIblbPf7xf7ukbvESPE37vf3Jm8tKv8HViodfrhXbTdb0IQUgu8iqVMprNDvr95ftS2LmzvOhTmAmzjU8OZFmEpslQFBmW5Ys+Jti6OPDAnanKDXmGWVUVr2xmEe5niyavFuV5gW8OKIoS29fHe4aSlZM5KBaLEEVxaUXeKsSnWccmlplj14kgCG4s6bnGLFs44ojDUvWU8Sopvhbjw7eXvSdtErgp1Cr0C88avjngXyeDfX0sOWMm2sBb9vFTyxqb5iz0gjhQVRa4vv/9/8Lll1+Oa6+9FpXKJib9cmK7pCoURYZpmq71sL+Y/73z/nvk8ycRefFZt/HZPCFGuEWfFyf0BgWlEHss9rrigNDj/407XlSkhUQnF2sR8eafn+AJyeBrBnv1gmJPlMXw84Tw49nt/mtHs3oXPq+FSZFl2V1Yyd4ulW07aDbHH3PZRR6wvMEqSnbxyYEkMdFnml1ccsklOOWU38SZZ545sSsY3yVVVdVbzMeNlFk1lsmiPA/wvj5VZQt60zShKHIqkccMzDpYRpEHrEZ8ynLtJAj+2ulzn/s/uP766/H+9/9vsN/3ZL9zVVWgaWruh2/PGm4KtYr9wlkQ3DBnhmQiut1kVRps/NRym9Yta2xaoNBjfOMbX8PHPvYRXHnlO3DYYYdAlqVAoJl8qGtwMR/XaBon+iYp2Uwi9IDR8/PGDUoH4jN6QuSYUZHn3ycMCLro8YZn7AbFIn8vouSLteh5DWQGI1k9MdCn5z8nLAy52PN+dp980fMnF3lRDKMIWWYVzOP6+rjIa7W66PWWcDvKZVmDVZSs41Oj0cAb3/g6nHXW2Xje854LVVVg27aX6ZtUo/GRMpqmAMjfSJlZscwW5XlAliWUy4a3oBrd1+egUChAluWlFnnAasSneaydrr/+Y/j+97+Lt73tCmzbtjG2NSYp0Sqp6EiZVcEwdABOoioeYpBKpQSArc9se3Rf36o4ky9rbFq40Pvxj+/FQQcdDF3X3VscKIrkllDxckyemZtU9ElumYI81Czh987775EZvaRib5zIix5rVMnnMKEXvG+Y2BtWuhn877DSzeA5jxJ6vngbFHr8/qBwC94nK+GMHns8vNeOK+HkXPx7swnMul5wS5z8xnW+sxnt6xMEJyDyljdQAcsbrKJkHZ86nQ4eeugBHHXU0e4tjluOyXbT/dlVPffLLX184iNlVFVdKbOEVbIoXwS8xCmYyeN9fcHNS9bXx0Qey/wtt8gDViM+zWPtdNdd/4PHPOaYwKxcP9PHW2P8zNy0VVLxLQ/LyjqZQmUB24AyPS8Nv2KFbV4G+/pWReQByxubFi70RuNAUUQ3MxfswZt8HlCwH8LfhRjcnf/98+/w/p20L8+/Pbv+vPDjuUAaXrrJ7g9k2qL9fQGxF52VJ8mB3r9oqeZASeZg1jDapxd8DUkSBp4XFHr8OcESTgD409+fTWAuFpmZDxd5cfC69N27z8eRRx6FpzzlqXjiE0+AqqozOYdFsazBKspi4xMzCdI0GZomu4ZRffR63alEH9toUCAIwd355RJ9q2xRPg+4yKvXm0N/9/x77MYbb8A3vvENPO1pv40TTzwFBx540JzPdvasQnzKw9qJiz5ZFudSJbUsrLMp1CyIirwo/HvskUf24aKLLsRJJ52EU045FY997OMDmxLLybLGppwLvSDcLEGBqvK5HzwzN6noS2aW8MLddw48d1KRB/jCbFzZ57gevWg2L3ibGD0PafhxowIwJNBixGLwfcVl9eKONUzosXMI9+nx4wdLOAHgTS+an8jzcaDrRXzrW9/GV77yFdx9911417v+DoqizORcFsGyBqso+YlPjluOKXnlmFykxTnkJYGZJbBM3zKZJXCL8np9PSzKZ00SkRdE01Ts2bMHn//8F/DNb/5f/P7vn43f+q3Tsj/RDFmF+JSf2ARw0aeqrEpqNqJvfJVU3iBTqOkplXTP3Xwcosg2B7761f+Lr33tq+h0OnjrW982h7PMjmWNTUsk9II4kGXJdfCUx9qiJ2HQLIE5gsZ9PC/cfWfi3jx27MHMm/+c8f153nGGiL1hGcK4jF7o/sjxYgXaGKEHhHv1hmUHuXDzX9sXhSGRKET7GX2xNwuhVyxqkCQZjUaS5mtWrsm+GFYnM7GswSpKPuPTaIe86fpmVMiy6PbN5M8swbcob668yUwWpBV5qsrHfbSx7OWaQVYhPuUzNgFZtMbw7LKqKrkdKeObQrVXovR0EaQRedzPYNXGTy1rbFpSoReEZfpUVYaqyq5ZQs81S5hU9Aleps+fXzO8b+ZFr74rUW8ekLw/L3j/sNEKo0o3k/boxd2epk+PI8vhEQ9J3DfDLqCDoxaCXHr29DtwxaLmmhUkE3nlcgm9nolOZ/IvwTyyrMEqSv7jky/6VFWBKAruBlJ3KtGnKIpbkjU4UmZRkEX5dHDjmuQiT0GhoK2cyANWIz7lPzYB2bTG5G+kjG8K1crd5tiyMInIW2Zn8mEsa2xaAaEXxLdF90XfdA55g2YJLNM3rvfkrD/+YeLePP/nyYRe9NhMiIVdN4P3DSsJjQo9AANZvXF9esHzGiX2JGmw1DNYwhn87GYh8goFDYpCIg9Y3mAVZdniU9AWfVYOeeNGyswDsiifjrQiT1EUFIsaarX2xJuZeWYV4tOyxabgHFFeJTVta0yaKqmsIFOo6SmVdNi2nci4xhd5XfT7q1MFxVnW2LRiQi8IF32SZ4s+bUlB1CzBH/g+/oJ+8WvvGZnNY7fFZObGisPRc/T4eUfvHzdiYdjg9NC5DenTix4veiwAkOXB1x5mzDKt0JtE5PX7Ftrtyb/k8syyBqsoyxyfshB9izBLIIvy6fBFXrKFKO+BrFZbKynygNWIT8scm4Kij82anUVrTLoqqVlAplDTk17klVbCmXwYyxqbVljoBQk65AVLCqaxReclVL5ZArfiT8JL3/Dj8PESDEuP3j7KjAUYPTA9elx++6jyTX57XFYvmpULHTNyLFESEdR9cVk9zlteOt1CNa3IK5UMmKa9siIPWN5gFWWV4tOgQ153Klv0eZglkEX5dKQVebIswzCKKy3ygNWIT6sUm2bdGjOPkTKqqqBYLKBWa1C/8IQYhg7HcdBqjd/EW6XxU6NY1ti0JkIviC/6VJUNyma7VV3XJW4as4TgkNH0Zgl/cOFPAQxm7SYp3QSGZ/RGici4ckt23/g+PSbgBss3+TkMZgAH308wK/gXfzhdCdokIs+ybLRaqyvygOUNVlFWNT6pqghNU2dmix4/Uma6vhmyKJ+OyUVeO1cmF1mwCvFpVWNTtEpqFq0xsx4pQ6ZQ02MYRTgOEok8blrXbvfQ66125nRZY9MaCr0gs7dFB1jfDFuoTWaWELQof+mFP40VerGln5EB6HF9emkNWdhxeCYubLgSvI/dP+i+yR87zn1z4LiCMJXQKxRU1xwimcgzDB22DbRak5enLAvLGqyirEN8Ctqiz8YhbzqzBLIon5605hDrJPKA1YhP6xCbZt8aM12VFECmULPAMIoAkLAcfzWdyYexrLFpzYVekGxs0ZlZgt83M84sIclu1DlvemCwV29I6Sa7b1AcJh2xwI6TLKsXnNXnGasMOV4wqxd9XQB46znT7ehpmpow2DtuiQLQbK6+yAOWN1hFWbf4NOiQN53o880SFDhOcJMrPu6QRfn0iKKASqWUWORJkoRSSUet1sa6tBmtQnxat9g069YYIH2VlK4XIIpSwtFJRBwk8kazrLGJhN4Q2MBibpYguIugrltSMHnfjKapQ80SptmNesWlD7PzTmHGAsSXbno/xxiy8NtH9emx4w66agaPOWzUAjBfkafrOgABzWYX6yDygOUNVlHWNz5FRZ/lir5pHPLCZgl8QDvvmyGL8ulJK/JkWYRhGGsl8oDViE/rHJuyaI0ZVyVFplDTk1bkrbIz+TCWNTbJiz6BvOI4QLdrodu1PIc8XTcCoi+9Q55pWjBN9kfEzRJ0vRCqR5+05OAjbz849vbz/uKX3r/jyj1txw6JPcd2QqWWtu3EzgPkj/N+dhzAHuyzixJ3LNsBRDeLEHeOSZlE5AmCgEZjfUQesQoI6Pcd1wWPO+QpMIzixLbotu2g0+mi0+l6fTOlEvv7ME3T7XUli/JJSZ/JW0+RRyw7AmwbaLdNtNt9rzWmVCoBmLw1pt83PWHHR8oYhg7TNCFJIvp9k0yhpkDXSeStMpTRSwkXfaqquAGGj1iY3CGvVNIhuf1vszJLGMfuv94HIN7oJW2fHr8/bqYe/zlqyhKXZRQF4LJXTPae04q8YrEIURTXUuQt665UFIpPUWZvi64osjcsVxAEN971SfClQBAEbGyU0Gi0XVOd0UiSiHLZQLW6niJvFeITxaYo2bTGbGyU4ThsM3peI2VWDV0vQBBENJutBI9e/fFTo1jW2ERCbyqmt0WPWpRPa5YwLRe8bWvoiAUgvk+PI0nhfr9hA9TFGCEJAJefN9k5a5oCTdNSiTw24LmDdQtUwPIGqygUn0bBzRImt0XnFuX1egO27cSYJXBHUBJ9w2DmNSU0m0lFHuuDrNU6sKw1cF6JYRXiE8Wm0bANcxmaJgfmiCZvjYkzhYobKdPv99fCwGhSWF+jiEYjmchbh/FTo1jW2JS50HvooQfxvvddi+9+9zsAgCc/+VS89rUXYtu2bVMfO1/Eib7RtujjLMrTmiVkzeuvZk3OceYucVm6aFaP/zcuqzepyFNVBYVCcpFXKBQgy3KmIi/v1/yyBqsoFJ+Skt4WPYkp1CxGyqwyXOQlNa/h5Z1ZirxluN5XIT5RbEoOr5Jifgji2NaYJKZQWYyUWTUmEXlZjp9ahut9WWNTpkKvWt3Ceee9HP1+H2ed9RJYloUbbvgYDjroV/CBD3wUiqJMdfz84kBRJLeEatAhbxKL8rBZQjZDRqfhond3hgq9YSWhwczeJEKPZRw0VKvJRZ6iyKjVshN5y3DNL2uwikLxaRIct2pAch3ymOgLOuRNYgo17UiZVSOPIm9ZrvdViE8UmybF8Tak4lpjJjGFWnSVVB4pFguQpOQiL+vxU8tyvS9rbMrUjOXGG/8Ze/b8Eh/96I044ogjAQCPe9zjceGFr8HnPvcZPO95v5flyy8QAf2+7ZklMIc8DYah44EHHsQll1yCq69+JwqFYuIjjjJLmMWQ0Wm55g2FsY+55B/8wBwsB51G5CXN5GmaBkVRUKu1kWXJwfpe88vHev6uBFiWEzJL0DQZlUoZtm3jve99L3buPADPec5zMZ1Zgm8OM26kzKoxicgrl0uo17Mt11zP6305Wd/flYBu10a32wWvkioWi5BlET/4wQ/wrne9C+9+93tTrXUsy0a73UG73fGqpCoVIxdVUotgEpHHhqdnN35qfa/3+ZCp0PvSl76AX/u1E7xfHACcdNJv4LDDDseXvvSFNfnl+Q55DzzwM/zlX16KN7/5Ehx00IGBRVC6VDjflep2e57o03VmLpJns4QrXyWNf1ACgiJv/KYcE3mqqmYu8gC65pcJ+l35DnmNRgfXXvu3UBQZr33ta0MlVNM45PGRMr4j6GqbJaQXeUC5XEKj0YFpZrvYpOt9eaDfFQAI6PVs9HpdfPe7/4n3ve9avPOd70S5bCRqjYnDtm202120212vSqpUMnJZJZUFxaIGSUo6a5A5kztO9uOn6HrPFnH8QyajVqvhoYcexDHHPHbgvl/91cfirrv+J6uXzi133XUnLr30r3DMMU/A/v0ttNsmFEXB5mYFpZLupqfTfdlz0VevN1Gt1mGaFnS9gM3NMnS9CFmejbjKC9wgIpnIA1RVc904sxd5dM0vD/S7CrO1tYVHPepwvO51F6Ne76JW68BxgFLJwMZGBYWC5mbh08Un07TQbLaxtVVHp9OFLEvY3CyjXDa8mX2rQlqRJwhAuVyei8ij6315oN/VIPfccw+uuupabG7uwv79LfR6FjRNw+ZmBYZRhKJISBubeJVUrdZArcYMp0olHRsbZS/rtUoUixpkWU4l8gQhe5FH13v2ZJbR27uXzW/bufPAgft27DgAzWYTjUbDm6+yDjzjGc8M/CTANG2Ypo1ms+fZorO5epa3m572Dyy4Y86NSnyzhH4i57e8oihpRZ6CQkFFtZq9yAPoml8m6HcVZseOA3D22X/g/ew4QKdjodMxPVt0vvPNevq6qTN9bI4ocxhm5jAqisVCoE9weftmfJHXSSzyKpUyms3sRR5A1/syQb+rQc4++6WBn4a3xvj9wetRJZUUtg6UUa8nE3nFYnFuM4bpes+ezIReq8XqfwuFwd4tTdMAAJ1Om355AJjoc2CafQA9zxZ9Y6OQyCFvGEHRpygyCgUVssyD4XL1zSgKE8FM5I3/IBSFu3HOR+QBdM0vE/S7SooQEH2W55BnGPpEtugc5t7WAcD7ZlRUKiU4juOVUC2L6OMir93uuAvMcY/3RV6/P5/3SNf78kC/qzT4rTH+HNFgqXjPXQNNKvrYWkLXC0s7UqZQ0KAo6UTePMdP0fWePZkJPV7nPKo0JzpHjQC4WUKr1Uer1fNs0YvF8lSib7RZQj/RAmVRMJFXTCXydL2AarWVeGbYLMjymncch/5eZgjFp8lwHN8sgYs+XdcT2aIPg/XN+GYJqro8ZglMtBlotzuJeg/Z40toNrtzE3kAxaZlgmLTpPAN8x6aTcftD2aZOX+dk65Kyo9By1kllVbkFQqFuc8Yzvp6p/iUodDTdQMAXPekMPw2/hhiGFz0mWi1wg55vk2wb4uelHizhAJM0w7sgOWDtCJPluWFiDxgtte8ZVmQJL+/ct0D1ayh+DQ9QdEXdMhjtugmer2uu/OdTvRxd+G8myVw0dZudxOKPAeVShmt1nxFHkCxaZmg2DQLhrfGsA3znrthPnlrjF8lVUS/b+WuSmoSkZf1+Kk4Zn29U3waJDOht2vXQQCAvXv3Dty3d+8elEplFIvJxwsQvkNe0Ba9XGbpbLZb1XV3vtP2zbQB+ENGWZ+gL/oWVUE1icgzjCKq1fbcRR4wu2s+GKg+8YkbsG/fXhxxxJF40pNOxEEHHTTbk15TKD7NGt8hj4k+EYUCs0Wf3CEvvyNl0oo8wEG5XEar1UOvN/+ASrFpeaDYNGviW2OKxelaY/JcJVUoqKlEHhs/NX+RB8z2eqf4FE9mQq9cLuPggw/BD39498B999xzNx772GOzeuk1YFD0qark1TBPaotuWRZaLd8sQVVVVCqLMUuYTuTN4QRjmPSaf+CB+7Fz54HQNA22bXuB6tWvfiU2NzchyzLuueduPPDA/Tj33PMhSRLtUk0JxacsEdDrOQHRJ0HTNJRKulvulF70DTNLYH0z8zdLKJfTibxKpYxOp4debzHClGLT8kCxKUtGt8bwtdM0om/RVVKaxobD12pJRB7mOn4qjmmud4pPycjUP/a0056O//zPb+G++37q3fbtb38LP/vZfXjGM87I8qXXCCb6Oh0L1Wp7ZrbofMhotVpHo9GGKDLDgUqlhEJBzfSPhZVfJhd5kiTBMIqo1RYn8jhpr/kvfekLuPji17sOq4Aosj/Jv/mbv8Dm5iauvPIaXH75O/C0pz0dX/vaV2BZ1loGqiyg+DQPWKav0ehh//4Wut3pbdGDI2W2tuY/UqZSKaHbTS/yut3FlpxSbFoeKDbNA781ZmurhUajC0EQUamUUamUoGmq2zc2+UiZdrsTGimjadmOlNE01R0nlUzkqSp//GJEHmeS653iU3IyHZj+B39wDj7/+c/iDW+4AC95yR+i1+vh+uuvwzHHHIszznh2li+9pkQd8gBNk2AYBkSRlzuld8iLGzJaqfC66tmaJfDMXPJMngjD0FGrtZGH1p2k1zxvEP7e977rClW/Bv3BBx9AvV7H+edf4N32zGc+GzfddAN+8YuHceihh3lBjZgcik/zZpQtOu9xSeeQB8zXLIGJPNYrOB4H5XIJ3W4f3W66XsUsoNi0PFBsmjfZtMbMs0rKF3mNRI+f9/ipUaS53ik+pSdTobdt2zb83d/9I97znmvwwQ/+AzStgKc+9TT88R+/AaqqZvnSBIA4W3RdD4q+SRzywn0zmqbMzCxBliWUSmkyeSIMw8iNyAOSX/M8WG1ubkOn00Gz2US5XAYAHHLIoTjnnPOwc+cu7/GCIMBxHFSrVRx2GAtUDz/8EA4++Ffm+wZXCIpPiyTOFl2ZyhYdyHakjC/yegkezURer2ei00lXppoVFJuWB4pNiySr1piwu7CmKTMbKZNW5C1i/NQo0lzvFJ/Sk6nQA4DDDjsCV1/9nqxfhhiD75DXCYi+4lS26I7joNPpodPpTW2WwESejlqtkSg7KEkiymUD1Wp+RB4nyTXPd5UURUWz2RjoL3r8458AgH3GXDgXCkVs374DAPC+912LBx98AJdfflXIYYpIB8WnPOCbJfgOedPZogOjzRKCgjAJk4i8ft/KjcjjUGxaHig25QG/NabTMd3Nbcnb3ObO52lF3yyrpDRNSS3yFuVMPoqk1zvFp/RkLvSI/DHMFt13yEtvix4dMqqqamKzhPQiT0C5bKBW6+RO5I3j+9//LzSbDRx55KNx0EEHY9euXZAkyTWuYF8AwdICQRDcnx2IooByuYwPfOB/48tf/iI+/OF/XptARawLYdHHHfKmtUWPmiWw+MTchdlibbjoSyvySiUD/b6Fdjt9RnKRUGwiiFEMtsao6ixaYyavklJVBZqmJRZ5ixw/NS0UnyaHhN7aE7VFl6a2RXcchBZGzCGv4Io+fkwm+tKKPPYHW0Kt1oFl5XOI8jAefPABvOY15wMAtm/fgSc84YnQNA2CIOCBB+7HgQfu8gIVD1q8TEFVNei6gTe96UI8/PBD+OAHP46NjU2YpglZpj9jYhUZ5pBXmcoWnY+UabXiRsqEXfcqFcNdbCUXeaxEa7lEHsUmgkgHW+dY6HZn1xqTpkqK9yOnEXmLHD81DRSfpkNwRhQF79lTn+e5ELnCgaJI0DQZiiJFelwmDxKKokDTFMiyBNO0oSgSqtVGor4+7vy5jCKPc9tt/x/q9To+97lbcf/9P8Mjj+xDp9PB8cc/CY9+9NE45ZSn4OijH4OdOw/0nuM4DtrtNl72srPQ7/fx4Q//Mw44YOfAYNCk7NxZnuVbWhgUn9YVxxN9qqoEjA16bo/LZPGJmyWwYzpeaVanMzjIN+6cDEOHbQOtVvoy0zyQh9gErEZ8oti0vnDRp2kKRFFEv99Ht5te9IWPCS82SZIIy7IhioLrZzD++XkYPzUteYhPyxqbSOgRCeAOecrMRJ8kSahUDPT7piv6LLcsK94sgWfyGo0OTHP5IhVfOHL6/T4EQcDHP/4RfPCD/4DHPvZY3HfffWi3W9jc3IYDD9yFc889H6ee+lvec772tS/jmGMeh4MOOmjtF1IAxScC4GU5miZD0xSvhHxa0Vcus34ZvjM82iyBiTzHAZrN5RN5eYpNwGrEJ4pNBMMXfdO0xgThFVKWZcdWSUWRJF41lT8/gyTkKT4ta2xaj7wlMSVhhzxFEaGqzBbdF2jJS5UkSUK5rIcyebIsR1z3fLMEUcRSizwAoUDlOA4kSYIoivj1Xz8Rt9zySZx77m4ce+xx+OIXP48f/vAuPPjg/TjllCeHjvG0pz0dAKZeSBHE6hBniy55tui8byaNLXq5zDageCZvtFmCA13X4TgCms1u4tfIExSbCCIrZtsao6oKikUN1Wrdy8xFR8r0ev1AP3K+xk9NAsWn6SGhlyFXXXU57r//Z3jf+/5x0acyQ3zR12w6kGUpJNDGOeQxt0wdtVozVK5pmqY374qbJdxzz9247rqP4Xd+53fwpCedBFUtzuMNZo4gCF7wUlUV+/btRaFQwLZt23D22S8F4O9ixdWRr2OgImbLqsYmJvostNtmyBZdEIICbbhZQlTkAcPNEi699BIcffTRePrTn4Ht23cNPeYyQbGJWDSrGZuAqOhjrTEaSqXo+Jf4OKIoCorFwkC5ZnSkjKqq+MpXvozbbvsWzjjjDBx77PEQxdVY6lN8moz1mxw4Jz7zmVtw6623LPo0MkaAadpoNvvYv7+FdrsPRZGxsVFBqaRDVRUAfkTiIxGiIi+KaVpotdo4/PAj8b/+13n47/++AxdcsBvXXnv1HN7TfJFlBQBiHUkdx1mbZmFifqxLbOK26NVqG9VqB44DlEoGNjYqKBQKEEUBwfhULhswTXNkTx43S6jV6rjooouxbdt2XHnllTj//D/Cww8/NIf3NT8oNhHzZj1iE8A2zG00Gj3s399Ct2tCVTVsbm7AMIpQFBnB2KQozC1z3Izhft9Es9nCqac+Fc997nPxxS9+Geee+zJ88pP/Mof3NF8oPiWHPokZY1kWrrvuQ/jQh1ZtN2ocvi064Nuib2wwW/S7774bN998Ey688I2JjFcEAahUKpBlFeeddwHOO+8CtFrN7N/GnNnc3IQkSdja2h+6PViuQBCzYJ1jU9gW3YGqyjAMHaIootVq46qr3o6Xv/yc0KDd4TgoFosolUo4/fTfxemnPxvtdhuapmX+TuYJxSZiXqxvbALCrTFdtzVG9aqkvv71r+NHP/oRXvzilyYaqM7GT5VxzDFPwNFHP951KE5iKLVcUHxKDgm9GdLtdrF79ytw77334FnPeg6+851vL/qUFkTYi740nwAACYVJREFUFv3+++/DX/3Vn+Fv//Zq6HpxrC06E3llNJtd9Pv+g3TdmNP5z49SqQzLslCr1RZ9KsQKQ7HJh80RZbbotm3iiisuw2MeczSOPvroBLboDgqFAiRJQr3e8R5TLK5GWXkQik3EPKDYFCTcGvOd73wb//RP/4C///u/h2EUx7bGxI2fEkWR4tOaQ6WbM6TX66HVauKyy96Ot7zlsrWtBw4j4F/+5Qa85S1/gx07Dkaz2YMoiqhUyqhUStA0FWwDhgUlQXBQqZTQanXQ7y9p93AKfv7zh3HUUY/2moUJIgsoNsXzrW99C4cffhRe/OI/wtZWC6Zpo1gsYmOjAl1npgl+CRUTeYoih0TeqkKxiZgHFJvicRzgU5+6CVdccQ0cRx3bGrMK46fSQPEpOTReYYbYtg3btr3a4Be96Lk46KCDV7CpeBYEbdFld/hoH4WCglarh15v9UUep9PpoFAozG2A57JaBEeh+JQcik1pGbRF530ftVobqy7yOPOOTcBqxCeKTcmh2JQWx2uNUVUZtm2j1zNRKKhL7Uw+CbR2SgaVbs4QURQhipQkTUacLbrsOuOtj8gDgEKhAADUPExkBsWmtAzaomuaslYiD6DYRGQPxaa0hFtjJElEoaCg2eyulcgDKD4lhT4dIgf4oo8gCCJfBEXf+og8giDyDhN9zWZv0SdC5BjaRiEIgiAIgiAIglgxSOgRBEEQBEEQBEGsGCT0CIIgCIIgCIIgVgwSemNotVpoNhuLPg2CIIgQFJsIgsgjFJsIIj+Q0BsCnzrxzW9+Hc961m/jU5+6acFnRBAEQbGJIIh8QrGJIPIHCb0hCGyKN0488WRs27YdDz54PwDANJkzZLfbQa1WXdj5EQSxnlBsIggij1BsIoj8QeMVxrC5uQ26ruP73/8eADav484778B1130I3/jG13HOOa/EOee8EpqmDTz35ptvnffpEgSxJlBsIggij1BsIoj8QBm9Edi2DcdxcPzxT8K+fXvx4x//CO9//7vxhjf8Me6990e49NK/xPOf//uxwYrIHw8++ACe/vSn4Pbb/3PRp0IQU0GxabWg2ESsChSbVg+KT8sNZfSG4DgORJHp4AMP3IVqdQuvec1uqKqCF7zghTj77JfigAN2eo/lJQtEPqnX6/izP7vYHXpMEMsLxabVgmITsSpQbFo9KD4tPyT0hiAIAhqNBr7ylX/HJz/5CfR6PZx00m/gggtej8MPP8J7XDBYWZYFQRC8QEfkg5/+9Cf48z//U9x3308XfSoEMTUUm1YHik3EKkGxabWg+LQa0F9WDJZl4Wtf+zLe+MbX4d3vvhqHHXY4du48EEcccRQOP/wI2LbtPVYQBK+5WJIkClY543Of+wzOPfcPUK1W8dznvmDRp0MQU0GxaXWg2ESsEhSbVguKT6sD/XUF6Pf7uP32/8Sf/umf4C1veTNEUcSVV16Dq666BoZh4Gc/u2/gObVaDTfc8HG86lXn4oorLsOPf3zvAs6cGMaPfnQPTj/9DFx33Y14whOOX/TpEMREUGxaPSg2EasAxabVhOLT6kClmwF++ctf4B3vuAK9Xhd/8Rd/gzPOeJZ3X7lcwU9/+mPUalVUKhve7abZx4knngxd13HzzTdiY2MTr3nNG6j+PCe8+tWvhaIoiz4NgpgKik2rB8UmYhWg2LSaUHxaHUjoBTjkkENx442fQrPZgGGUYFkWJEkCABx33BNwyy2fhChKoeds374D27fvQK/XwxFHHIVTTnkygPVqNP7Wt/5ffPSjH8Tdd98JURTxuMc9AeeffwEe//gnZPJ6+/btHXl/sahD13UAoEBFrAQUmyaDYhNBZAvFpsmh+ETMg5FCb+fO8rzOIxdYlgVRFLFzZ3kg4JxwwvG48caP4zvf+SZe9KIXhZ7X7/fxi1/cD1kWcfrpT12rP5DbbrsNF1/8ejzmMY/BRRddBNM0cf311+N1r9uN66+/Hk984hNn/pqnnnriyPtf/epX48ILLxy4vVwuAAA2N/W1u7ZXkXX6HVJsSg/FJmJRrNPvkGLTZFB8IuYFZfQC8F0oAKFg5TgOnvvc5+Lkk0/2brNtG4IgQBAE/PznP8fdd9+NY489FoqiwLbttWkuvuKKK3DwwQfjE5/4BIrFIgDgBS94AZ797GfjXe96Fz784Q/P/DUvv/zykfcfe+yxM39NglgkFJvSQ7GJILKHYtNkUHwi5gUJvQQIggDbtrFr1y7vNlEUvaD105/+FA8//DCe//znL/As50+1WsVdd92Fc8891wtUAHDAAQfgpJNOwje/+c1MXvess87K5LgEsWxQbIqHYhNBLBaKTcOh+ETMExJ6CYnbaeK3/fCHP4QgCDjhhBOGPnYVKZVK+PznPx8KVJz9+/eHdvoIgsgGik2DUGwiiMVDsSkeik/EPCGhNyF33303brvtNhx66KH4yU9+ghNOOAG6rocakVcdSZJwxBFHDNx+11134fbbb8epp546/5MiiDWHYhPFJoLIIxSbGBSfiHlCQm9Ctm3bhjvuuAPveMc70O/3ccIJJ+C+++7D4YcfvuhTWyjNZhNvfvObAQC7d+9e8NkQxPpBsSkeik0EsVgoNg2H4hORFeuTK58xBx54IK688kr84Ac/wCc+8Qns2rULF198Mfbs2bPoU1sY7XYbF1xwAe666y7s3r071IRNEMR8oNg0CMUmglg8FJviofhEZIngOI6z6JNYRhzHgWVZkGVKigJArVbDq171Ktx+++144QtfiLe97W1rNQ+HIPICxaYwFJsIIh9QbBqE4hORNST0ZoBt27Bte22D1759+3DeeefhzjvvxItf/GJcdtllFKgIIgdQbKLYRBB5ZN1jE0DxiZgPJPSIqWg0GnjZy16GO++8E694xStw6aWXLvqUCIIgKDYRBJFbKD4R84J69Iip+Ou//mvceeedOOeccyhQEQSRGyg2EQSRVyg+EfNifXPmxNTce++9+PSnP41yuYxjjz0Wn/70pwces47DUAmCWCwUmwiCyCsUn4h5QqWbxMTccMMNeOtb3zryMXffffd8ToYgCMKFYhNBEHmF4hMxT0joEQRBEARBEARBrBjUo0cQBEEQBEEQBLFikNAjCIIgCIIgCIJYMUjoEQRBEARBEARBrBgk9AiCIAiCIAiCIFYMEnoEQRAEQRAEQRArBgk9giAIgiAIgiCIFYOEHkEQBEEQBEEQxIpBQo8gCIIgCIIgCGLFIKFHEARBEARBEASxYvz/NRFf2EDIvYMAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nplot = [101, 101]\n", "a = [0, -1]\n", "b = [2, 1]\n", "x1, x2 = nodeunif(nplot, a, b)\n", "x1.shape = nplot\n", "x2.shape = nplot\n", "\n", "y = np.exp(x2) * x1 ** 2\n", "y1 = 2 * x1 - x2 - 1\n", "y2 = x1 ** 2 - 2 * x1 * x2 + 0.5 * x2 ** 2 + x2\n", "\n", "def newPlot(title, Y, k):\n", " ax = fig.add_subplot(1, 3, k, projection='3d')\n", " ax.plot_surface(x1, x2, Y, rstride=1, cstride=1, cmap=cm.coolwarm,\n", " linewidth=0, antialiased=False)\n", " ax.set_xlabel('$x_1$')\n", " ax.set_ylabel('$x_2$')\n", " ax.set_zlabel('$y$')\n", " plt.title(title)\n", "\n", "fig = plt.figure(figsize=[15, 6])\n", "newPlot('Original function', y, 1)\n", "newPlot('First-order approximation error', y1-y, 2)\n", "newPlot('Second-order approximation error', y2-y, 3)\n", "plt.show()" ] } ], "metadata": { "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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 1 }