{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Reliable uncertainty estimates for neural network predictions\n", "\n", "I previously wrote about [Bayesian neural networks](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/bayesian-neural-networks/bayesian_neural_networks.ipynb) and explained how uncertainty estimates can be obtained for network predictions. Uncertainty in predictions that comes from uncertainty in network weights is called *epistemic uncertainty* or model uncertainty. A simple regression example demonstrated how epistemic uncertainty increases in regions outside the training data distribution:\n", "\n", "![Epistemic uncertainty](images/epistemic-uncertainty.png)\n", "\n", "A reader later [experimented](https://github.com/krasserm/bayesian-machine-learning/issues/8) with discontinuous ranges of training data and found that uncertainty estimates are lower than expected in training data \"gaps\", as shown in the following figure near the center of the $x$ axis. In these out-of-distribution (OOD) regions the network is over-confident in its predictions. One reason for this over-confidence is that weight priors usually impose only weak constraints over network outputs in OOD regions.\n", "\n", "![Epistemic uncertainty gap](images/epistemic-uncertainty-gap.png)\n", "\n", "If we could instead define a prior in data space directly we could better control uncertainty estimates for OOD data. A prior in data space better captures assumptions about input-output relationships than priors in weight space. Including such a prior through a loss in data space would allow a network to learn distributions over weights that better generalize to OOD regions i.e. enables a network to output more reliable uncertainty estimates.\n", "\n", "This is exactly what the paper [Noise Contrastive Priors for Functional Uncertainty](http://proceedings.mlr.press/v115/hafner20a.html) does. In this article I'll give an introduction to their approach and demonstrate how it fixes over-confidence in OOD regions. I will again use non-linear regression with one-dimensional inputs as an example and plan to cover higher-demensional inputs in a later article. \n", "\n", "Application of noise contrastive priors (NCPs) is not limited to Bayesian neural networks, they can also be applied to deterministic neural networks. Here, I'll use a Bayesian neural network and implement it with Tensorflow 2 and [Tensorflow Probability](https://www.tensorflow.org/probability)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import logging\n", "import numpy as np\n", "import tensorflow as tf\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "from tensorflow.keras.layers import Input, Dense, Lambda, LeakyReLU\n", "from tensorflow.keras.models import Model\n", "from tensorflow.keras.regularizers import L2\n", "from tensorflow_probability import distributions as tfd\n", "from tensorflow_probability import layers as tfpl\n", "from scipy.stats import norm\n", "\n", "from utils import (train,\n", " backprop,\n", " select_bands, \n", " select_subset,\n", " style,\n", " plot_data, \n", " plot_prediction, \n", " plot_uncertainty)\n", "\n", "%matplotlib inline\n", "logging.getLogger('tensorflow').setLevel(logging.ERROR)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Training dataset" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "rng = np.random.RandomState(123)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The training dataset are 40 noisy samples from a sinusoidal function f taken from two distinct regions of the input space (red dots). The gray dots illustrate how the noise level increases with $x$ (heteroskedastic noise). " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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QTj2mUCiUKfhBO9MDcWlpqWBamivmukTJdtTTzhk+5wB8PUPiUCg5xVwyTeQa4uuWyeuYLSUlN7lueqJQLktyLXxyrg5+2biO0ddprl47MXNbegrlEiTTSWIzke3M5lTJxnXkz+H3+3H06FF0d3fjqaeeimgWNhehioJCyTHkLHGfMC0tYH/yE7AffZTQYJttZSZFpq+jy+UScrX27NmDzs5OsCyLgoICvPvuuzl5jRKFmp4olBzEYrEgFAoJnQwzSksLXDt2wM8w0Dz1FDS//jV8DQ0xB1un0yk4cFM277S0gN27N24l2lRMOJkKQ2VZFg6HA+FwGH6/H8eOHcPnP/95eDweNDY24k9/+hOGh4dRVFQkqxxyQRUFhZKDZNNHwe7dCz/DgAmF4FcqoTpwAMNWKwghYBgGZrNZGHidTifsdju0Wi2MRmNqg3KUYpJqYzqb68HLk06FIXUsQgg4jkNPTw8aGhowMjIClmWhUqlw6623wu/3z3iMXIUqCgolx5ipfIbcMFu2QPPUU5NKguPgb25GOBwGIQR9fX3w+XzQ6XQwm80IBoPQarWYmJhAcXFxSnJGKyZ2714wIkWRjuuRTsUrdSyGYWC1WuHz+VBRUQGTyYQzZ86A4zgwDIMVK1aA4zhwHAdCSM4FK8zE3FBnFMplRNZ9FOvXw7JrF8oefhjWl1+GbvVqqFQqEEJACBEqowKT2cZGoxEVFRVCsluyMFu2QMOyYJVKyUq0s70e6XRqxzuWxWKBXq/HmTNnoFQqYbVaYTabYbVawTAMfvOb38But0seI9f9F3RFQaHkIFkv8bB+vTCrtwBC7SK+sB0/YKdFzinFFM9HIXWeRM+bagVZqePPdKyzZ89icHBQUuaqqip0dHSgsrIy4hjia5qrqwuqKCiUHCWX7Ne8LFIDdlrkFCmmmWQAIs0/Yp9JLOWRrEKLZxoSHyv6mB0dHVi5cqWkLLW1tdizZw+2bNkiKF7gs2KBuVxJlioKCoWSFNkeyMSmG6fTKfhMAMSdmSezkpjJJyLVU4LjOPT29uL222+H0+mE3++HTqcTZKmqqoLNZkN/fz8CgYCwX7r6ZcipZKiioFAoSZPNmS9v/vH5fOA4DoFAAMPDwygsLBT8J7ORbybzEu9P8Pl8EecDgG9961twu904ffo0GIZBUVGRsOJRKpW44YYbYLfbI/ZLh/lObuc4VRQUCiUxpnId3KtXw79oUVZt6vzgOjw8jF//+tfYvHkzSktL09bJLtbgzQ/IY2NjCAaD4DgONpsNbrcbHR0d0Gq1gmLgK8gCnynWvXv3wm63Y8WKFUIRQWB2q7RMRMnlnjGMQqFMI+tRMVO5DvZf/hKOv/97MK2tGS+LEY3L5cIbb7yBbdu2Ydu2bejs7ERPT0/alJfUSoKP9vJ6vTCZTDAajTCZTPD7/Th58iScTic0Gg2KiopgsVhQWloKt9uN3t5eOJ1OqNVq9PT0IBAIpO3aZSJKjq4oKJQcRDwrzIWYez7XQRkMggSDCB08CF1zc0bKYkh9d5Zl0d/fD6vVivnz54NlWeh0OrzyyiuoqalJOVQ3HmKTVH5+PjiOg06ng1KphEajQU9PD6666ipYrdYIWcWd7crLy9Hb2wuNRhOx4pBrBZQuqKKgUHKM6IieaFu4XINBvGOLk/Csw8MwX301GJmVVjyTCsMwKCkpwXXXXQeVSgUAKCoqgsFgQHt7OywWiyzXKVbEU15eHrRaLerr6wX5eMT+joqKCjQ1NUGlUqU9NFZOpU0VBYWSQ0QPji6XCyMjI4ItXK7BYMZVSwK5DulGPINXqVQR372zsxN//OMfcd1116GgoAButxsajQbLli1DOByWddCU8itotVp89atfBSFk2vbRs/2HH354Wh/tXA6NBaiioFCyilROgnhwDAaDKCoqQigUioi9T7cMMzlDWZYFk0CuQ7qxWCxwvvsu/J98AtfatbBs2waWZXH69GkYDAb4fD4YjUb4/X6UlZVh69atkvkNwneQaSAeHByERqOJ+blYpgsXLqCvrw/r1q2bFl2Vq8qCKgoKJUvEmsWLZ6D8NjqdTrYBZKZw0KwWKPzoI/R/73sIA1C88grMTz4JZsMG9PT0YN68eYKvQCz3Cy+8gJqaGtTV1Qnyyv0d3n//fdTV1WHZsmWSn4vPz3EcWltbsW7duogqwWmpwisTVFFQKFkg3ixe/P9MlfKIPo/YDi9V2yhjs9733wcJBsEpFCDhMLBvH7BhAwwGA9avX4/8/PxpcqtUKly4cAFVVVURjYTkNPH09fXhyiuvnPZ38fn5nyUlJXA6nWBZVvBRjI6OYnx8fHZVeGUkdyShUC4jYoU0SnWTy9SAIZaBb8ATLScf6pmpbnfMli2TzvPhYViHh4WCgTt37hSURPR3qK+vx/nz54XrKnf4aE9PD7q7u8FxXMTf+XvpdrsxOjoKp9OJsbExaLVa5OfnY3h4WFAgvJKYmJiY5o/JBeiKgkLJElKzePHMMxuzSnEDHoVCAbPZLMjpcDjQ09OD8vLyz+Q7cADs3r3AVVeB2bgx/QJJONGPHTsGhmFQWloKp9MpOPp5c01TUxMOHTokNAkSZz+nG5ZlMTExgeuvvx6hUEhyJdbX1yeYD4PBIOx2O+6++24UFRUJjY7y8/Oh1+tRXFwsS2jvbKGKgnJZkitL+2hH9ujoKLxeLwoKCrLm3OQb8IgjeA4ePIi//vWvGB8fx5o1a9Dc3AzmwAG4duyAs7AQ3K5dsP30p7Bs25Z+gaKc6G1tbVi4cCF8Ph+CwSAIIfD5fMK1UigU+PKXvwyWZSN8A0D8WlCpwDAMdDod5s+fH7FaEZcZIYQgLy8P4+PjUKvVUCqV6O3thcfjQX19fcwCg9HE+1zu54QqCsplRy4ksEnhdDrhdDpBCIFGo8mKc5NhPmvAI3agezwefPnLX4ZarYZarZ4c2P7zP+FTKBBUKkEA+A4cADsVdSQXHMfh4sWL2L59O4LBIFQqlZD4Jj5vS0sLBgcHUVVVJeSiAJhVPkqsffi6Tlui+mjwqxidTge/3y80dvL7/RgfH8fp06dRX1+fUBmPeM9sJp5nqigolxXZ7h6XiFwejwcsy4LjOFgslozLGW0S8/v9uPbaa+F0OuH1enHhwgWcP38e21evhu6pp6AKhcAxDDQOB5gDB2TNsbhw4QL8fj8CgQBKSkqEkGHxtWFZFoFAAOfOnUNlZSVCodC06rLJXst4g7Hb7cbixYsl92MYZpqMLMtCr9dj//7907aPFdYbL/AhE89z9t8QCiWDZKIuTirwJoyCggIYDAaUlJRAoVAgFAplRU7+fIFAAL/4xS/Q1dUFu92OoaEhKBQKtLa2Yqi6GuaXX8biK69EiduN4Ouvw7VjB9DSIotMLMtCqVTiwQcfFGol8c7qaNlramrQ2dkphM5aLBZYLBaUlZUlPeueqUPewMAAiouLJfeNFZxQWFgIv98vrHRibctvH/3MiqPPxJ/JBV1RUC47st49Lg5FRUXQaDQwGAzTmvJkgzNnzqCsrAxKpVKIyjEajaipqUFXVxfqr70W7L59CCoUMXtez4bosh1dXV3QaDSoqamJe10qKytRVFQEtVot1FSSUiqJMFOeSXV1teA4j5bd7/fD4/FgYmICAARHNSFEMOWJt421MpDKrRErQN4fw9eRSrcJKvfeFAolA+SakuAHCqVSCYPBIETxZFvO9vZ2LF68OKI39qJFi3CV0YjQCy8ALS0z9rxOFXGYLk9XVxfy8/MlB0LxTJ9hGDz88MPQ6/VpKzseazVy4403CgO+GIZhoFKpMDExAa1WG1EEEAB0Oh1GR0eFbWda6cbLa+GvlcfjkaWqL11RUC5bMl3mIR7Rs1alcvqrmQ3ZKisrUV9fH5nY1tIC83e+g3yGgWv3blh27Up7HSiWZQVnvkqlElZWTqcTpaWl07Z3uVyCA54fzPv7++FyudDU1DRreYDIMhw8nZ2dOHv2LLZv3y65D7+C4IMSxPuePHkSXq9X2DeRla7U6oZlWQSDQWHFxzvN0wlVFJTLEn75rlKphJc529FQ8XoxZ0M2lmWxevXq6cp0quT48fFxmNRqmPfuBfODH6S9DhQfossnsvHNgoxG4zQ5o5UKMOlkPnXqFOrq6tKiZKXuAZ9hHQ+r1Sp5Xy0WCzo7OyO2TUTGaIXCKw+j0ShbHgZVFJTLDinbsdlszoloKLENmldi2YrUevPNN+Hz+YSwT2GQ5EuOKxS4EAhgQ5pMTWIYhoHNZosI083Ly8MjjzwiWaE1WqkwDIPKykq89957aTE9xboHAwMDsNlsCX0fKd9Cf39/SvJEf59Luh8FIeQ6AL8AoADwLMdxj0d9vhnAnwCcn/rTqxzH/TiTMlIuPaJtx/wL7PP50mbTTgbxCx4KhXD69GkhSQuYnJHGc6bKJVNXVxeWLFkyPQdh7VpYdu3C6j/+EX9mWdnCYaMHP75DXDRSSgUA5s2bB4PBIITGzoZYDu1wOJzQCk9K0QSDQdTX16O/vx8lJSUJHWMms5RcZE1REEIUAJ4EsA2AHcBBQsjrHMd9GrXphxzH3ZRxASmXNPzynF9ZKJVK6PV62Gw2Sf+AXETPMoeHh3Hq1Cm0tbVh+/btwmAZzywlB4QQ9Pf3w2azSecgrF+PsjVr4P3Xf43IfOb7aqfLVxGdRBcrwkhqRk0IwVe+8pW0KIpY5/jc5z6X0L7RigaYDD1ubm6OyCqPRbbNotlcUawB0MFxXCcAEEJeAnArgGhFQaHIAm/W4TNnYzmR5SJ6ltnX14fi4mI88sgjOHz4MHbt2oXy8nLBQStlvpALv9+PNWvWRHRsix7MFAoF7r//frhcrslQ3vZ2uO++G36Ggeapp2DZtWtWyiL6fA6HA2vWrIm5vdRAq1Kp4Ha7UVJSkhYFK95/YmICH330EbZu3ZrQvtGKRqPR4PXXX8e8efNQXV0dc79cSBLNpqIoB9At+t0OYK3EdusJIccB9AL4DsdxrZkQjnJ5wDBM1vIq+Fkm3+p0165d+NznPoeqqiqsWLECBQUF0Ov1EeGOmRgwWJaFVqvFzTffHFcxOZ1OHDlyBBzHodrvx+jvf4+xwkKYBwdnnU8RfV6+JHc85Sh1Pc6fP4+Ojg5s2rQp7Qp2YGAA586dw5YtWxK+D9G5EXV1dYKfLN4+mTY9RpNNRTHdIwVwUb8fAVDNcZyXEHIDgD8CqJM8GCEPAXgIAKqqqtIoJuVyIFMmHSm6u7vR3d0Nt9uNyspKQR6tVov3339f6NoGQPYBgx+gDxw4gMWLF8NgMEgqplAohGAwiFAohOPvvQfj0aMIeb0Yy8+HcWQEulnkU0jNoDmOwx133CHpoxDLLVYEvMnuo48+kkXBDgwMCAX+UlVAVqsVhw4dmnG7bCeJZjObxw6gUvR7BSZXDQIcx41wHOed+v9bAFSEEMlceY7jnuE4bhXHcatyqdAbJffhwysz2WeBP+/Y2BgmJibQ0dGB6upqhMNh4fOKigo4HI6I8EuLxRJRUjvd8vA+m2PHjmFsbEwyCczpdMLhcGBsbAx1dXXwt7XBODQEjuNgHB1F2aJFszI7SSWfhUIhzJ8/P67cYkXAZylzHIehoSGoVKq0l21xuVzTFGmyJHMvs5l8mc0VxUEAdYSQeQB6ANwD4PPiDQghNgBOjuM4QsgaTCo2d8YlpVwSSM3IXC4Xenp6MDw8DIvFktHuYgzDQK/XQ6vVYvHixaitrY3wkRBC0NTUhE8//VQIwZTTR8FHg42Pj2NkZAQmk2laQTun0wm73S50YrPZbChsaID+1CkoVSrowmEon3121o7s6Bn00aNH4Xa7ceONN0rKHe0o5hUHy7K48cYbhYS9dN7XzZs3C4o8VQVkNBpxzTXXpE0muciaouA4LkQIeRTAO5gMj32O47hWQsjDU58/DeBOAF8jhIQA+ADcw0W3kaJQEiCWaaKvrw9utxuBQAA+n0+WrNZ4WCwWqNVqNDQ0SBaWq6urw/vvvy/IK7ePwmq1YnR0FNXV1UJPDB6pDGClUomv/NM/oeCee4D3309btBMQOYN2u90xC+8B0o5i/n4vXboU4XA47deqs7MTtbW1UCgUKR/b5XLhz3/+M1avXp22DHI5yGoexZQ56a2ovz0t+v+/A/j3TMtFubSIHmD5ZvbA5KydbyZTXl4uhM1m0h58+PBhhEIhXHvttdM+q6qqwv333w8gc07NBQsW4Jvf/Oa048fLAO6fPx+2NHe4E9+DgYEBNDQ0xN1eLK94JbR7925oNBrJntazkW3Xrl343ve+l3IZGJZl4fP5EA6H0dPTg8WLF2fVvBQPmplNkZVcqNIqHmDHxsbgcDiEyqwlJSUwGo3QaDQZLeUhrgR6/PhxrF+/PkKBiWXv6OiARqNBZWXltJaeclzf48ePw2QySQaFSDlVu7u7cfr0adx1111pkyH6HsybNy/h0hTR+xYXF+PcuXMR28z2ug0PD0Ov10OlUsU9dzzcbjdGRkagVCoxMjKStDzR36G9vR0AhJDmdJKb6otySRBdXz/dFS2TwWKxoKSkBHq9HoQQOJ1OHDt2DOfOnYtQEjP1HkgH/HVxOp3w+Xzo7+/H+Pg4jh49ira2tmnb9/f349SpU8Lvbrcbvb29aGtrk8UBf/LkyYg+CdHXQKp8hNPpTNv5+XtACBHuwaZNm2AwGGbcNxQKwefzRdy/kpKSiGsUq+9DMrS3t0OhUEQcI5lnh9+2qKgI1dXVMaO5YiH1Hdrb2zE8PJz0d0kEqigossAvq/mXJhtRRWJcLhf6+/vR29uL9vZ2fPrppxgcHMQf/vCHiMJuUhE36UQ8mASDQSgUClx55ZVgGAZqtRperxehUChin8rKSnR3d0fsDwBerzdiME0X4kY8M903l8uFQCCAvr4+Qa7ZwjCMsPIbGxtDf38/Xn755Rn3c7lcOHPmjBBqzN+/4uJiYXWUjokAy7IoKCjA+vXrI46RzLMj3rapqQm33nrrtHPEO7/Ud4jXQGm2UNMTRRb4ZTXHcSgpKUEwGJz2YGfKJCUeXBUKBdra2qBWq7Fw4UI0Nzfjgw8+wNKlS4Xt5YxZ5yOL+LLTBoMB27dvR0dHB7xeL/Lz86eZn6xWK/r7+xEIBKBWqwUzWn5+vtDBLV2yBoNBeL1emEymaRFO0ddE3EPj2muvRbriTFh2slWoXq8HAKGP+Ez7+Hw+BINB6PV6GAwGwU+hVqtx3XXXAZCOkOL3TyZpTq/XIz8/f9q1T+bZEW+7Z88eXHHFFVCr1TOar2L5quRUFHRFQUk74mW10WiExWKJmGnxppNMrS74F4uX7eLFi9i+fTuamppw9913IxQKweFwTNtHDlwul1AO22Kx4K233sKJEyfQ0NCAJUuWTHPYulwutLe3Y8uWLYJZgW+i09DQkFJrz3ioVCp8+9vfBjAZYspHOKlUqpjObZZl0dDQAI7j0rKyEd8vjUaDwcFBmEymGffR6XRQqVRQKBTQ6/WCvC6XCy+++CIOHDgA4LPrByBlE96ePXsQDAZjDuSJwm/b1taGgYGBhFc8Uo2UHnnkkYTMc6lAFQUl7YgHEL6aJ/9gS5XzzgT8+X0+HzZu3Ijy8nJhdv/ggw/KUsM/mmizUygUgt1uR3l5uWAai7Z587NklmXR2dk5bTWWboU2MDCAwcFBYUXIsizKyspiXh/+ul64cAGvvfZa2iYA4oFweHh4mj8gGj4Le/HixWhsbIwIgfb7/VAoFLDb7RHP22xMeAMDAwlVfE2U4uJiuFyupM1XPCMjI3C5XDOuvFKFKgqKLEjNePiEJzl9APFgGAYNDQ1YuHChMOi4XC6MjIzgnXfeiciKBtLvfBd/97GxMVy4cAEOhwNFRUWSylM8S+7q6sKHH34It1vefNPW1la0trYKK0KO4xAMBuM6qxmGgdlsFlZlfDVUMalcSz5hbvXq1WhoaIi4NuLjiR270Ul1/DU3mUwRkUXiVUuyJryxsTGEQiHk5+cn/Z2k4Af4s2fPAkgt+76zsxOHDx9OizxSUB8FJW1El8GO9dJFZ/tmioGBAZw6dQqLFi2Cz+dDKBQSZpunTp1CdXU1Fi1aBEC+EFmLxSKYunw+H1asWBE3P8JiscBkMiEUCqGzs1P26qFutxu1tbVCsUJCCEZHRwXFKu7WJsZqtcLhcKCjowMqlUqoeMsX8+O/G58hnSiEEOzbtw+bNm0SVqfiexO9QpUKMbZYLGhsbBT6U4v/nmzpdpfLhcHBQTQ2NqZl9s6veJqbmwXTnfh6JVoEUU7/BEAVBSVN8C/v2NiY0PxH6iHPVl19lmVx+vRpuFwuWK1WhMNh6HQ6YYAuLS3FoUOHUFxcLHu3O6VSKcxmN2/eLJjmpAY58fb9/f0YHBxERUVF2mSJZmBgAGvWrBEGUY1GIzi0+ZUF74gX3z+9Xo+mpiYht8Dn88HpdAq1o8xmsxAOLO5rPRMjIyNwOByoqKgQBnTxvQE+y8IW58hEH7+iogJ33nmn5DmSSZDz+/0wGAxobm5OS1AGP0kIh8Po6+vDvHnzEnr2ou/DwMBAREBGuqGmJ8qsSTRkMzpkNlP+Cd40cezYMSxbtgzhcBgcx8HhcMBkMsFms6GhoQHd3d0Rg4+c5jGLxYLW1lahFabL5YLD4ZC0w7MsC4PBgJ07dyIvL29awl06ueaaawTbO8MwsFqtqKiogNFoFKK1pO6fQqHA9ddfD51OB4VCAY1GI2xLCEEgEADHcZ91yUtQbr50R7TJSHxveFMN78CO9ey9//77GBkZEf7mcrnw6aeforW1NSG/Cn/ujz/+GO3t7WkLyrBYLCgvL8fu3bsRDodnfPb4aDSPxyN81/Xr18ftaTFbZnwDCCGPEkLihxxQLmsStffyDlJxjLvc8EqM4zh0dHSAYRh4vV5wHIeRkRH09vZiaGgIlZWVuOWWWyIGn3RHFIllAiYzmvPz8yNmyVL2ff766vV6uN1uwU+RjsQxMaFQCCUlJdOSv6xWq+DQjjeIffrpp/D7/WhsbITVasXY2BicTidUKhWqqqpgs9mm79vSAvYnPwFaWiRlkqrxZDabp90bftUVfXyW/aySbGtrq+BHEQcKhMNhyesuhcViQSAQgMViiXvPEkG8j1KpRFFREQYGBiICP6T2Edfb4jPDi4qKhHBiOUjE9GTDZJvSIwCeA/AOLcxHiSaWvbenpwcmkwlarRb+Q4dgOnIE4RUrYG5szIhc/CA7Pj6OO++8E3l5eTAajcjLy4NSqRRmuGVlZdPyAORQZLzpTaVSob+/H1arVZDR6XSC4zhJ04zZbMaBAwfgdDpRXl4u+FfSaR7r7u7Gvn378OCDDwKINMnwP+PlCajVavT39wvPAJ9rwF/Xab6plha4duyI2xFv5cqVEQmI8UyX0bK5XC74fD7B9FVQUACn04n6+vqIQAH+mid6/YaGhlBSUgKGYeLes3hIfQ8+g9xqtcb0U/DPirje1sDAAF544QX87d/+bcLnT5YZrwzHcf8/TDYL+hWALwI4Swj5CSFEujg85bIlelBpb2/Hiy++CK/Xi4G338bwt78Nx6uvwvfd74KZimnPBJaODgw/+SScx4/jyJEjGB8fR01NzbQZ7rlz5xJqIpMq4pWDx+NBeXk5tFotAAgDGe8fkVpVGAwGnDt3DmNjYzFn0KnKBUQ6ROOtVmKdy2KxCNvzAxq/uuTNNOKoLXbvXvgZBkwoBD/DgN27d9oxz549KygKqRyDWOVFxMmAhBCEQiGUlpZiYGAgQt7ocNqZ4L9PUVHRjPcsFrFyJdavXw+tVgu73Q6HwxHTjMavOPiQZbkd2UCCPoqpFYRj6l8IgAnAHwghP5VRNsocxu/3489//jN27NiBkpIS/PXFF3F6YABWhwP60VGE9uzJjCAtLXDedRfeeOUV9O3ahQKPR5jxRpuXKioqYLfbZRNFbF/nOA5bt24Vwk75Ga6U6YT/WVVVhVAoBK1WKyl/KogVAj/gpFrmoqSkBEqlUth+ptwZZssWaFgWrFIJDSvdEe+tt94SWoVG+yfi+QjE2/J+lk2bNuHmm2+etl2yUVhf+cpXhAREqXs2E7FCxPmeI2LlFuu44r+5XC7ZFcWMpidCyN8C+AKAAQDPAvgux3FBQggD4CyAv5dVQkpSyBk6mSgulwvnzp2D0WgUHGxXfv7z+Lc33sBKjQZBgwGO5mZoXC7ZI5/YvXsRADDs9aJeqQQ5fx6GtWuF6CLxtbLZbOjv748ZfZQO+Oimffv2YWJiAqWlpQAm/QDR5rto80N+fj7Wrl0bMbjNdiUhHsBLS0sjTGHJljMvKCjAtm3bIlqD8vtKHm/9elh27ZrsrS3RxyIYDGJsbAyFhYUR149XNL29vXFNb9GmLkIIjh8/jmXLlqUc2srP9letWhUhT7L3QWo/vvbYAw88AKvVmnAocXFxMXQ6XXJfJEkSeRuKAdzOcdwF8R85jmMJITfJIxYlFbIVeiqGr95ZVVWF8vJysCyLs2fPwmu1ovCrX4Xb50PpTTeBWbZM9pwAYHLWGvr3f4fG78emtjYU//jHUEr0NeCv3bZt26Z9Jkd4bHd3N9RqNebNmydkXvMKINq2zl8ni8WC2267Lam4/3hEK4Tly5cLn6UyALIsiw8++AALFiyA2WyO2D/m8davBxOj0ZHb7YbJZJq2D/+7uGZW9DZS78LAwABeeeUV5OfnY8GCBQl/L/H3u3DhArxer/B7sisSqe/BU1RUJNxncR2qmeBzf+QkER/FD6OVhOiz0+kXiZIsvK02G6UxxPDVO1tbW/Hqq68KJhK+5v7yG25Awz//MzSrVmUuM3v9epS9+CIe/MpXYNu1C0qJ5jria2c2mzE2NiZcv3RHFvGEQiEsWrRI6IURz7Yu/vyTTz7B66+/nrBMMz0HvHmosLAQ//Zv/xaRnZ7svXG73bDb7Thz5oyk+SzRXAUeo9EYYSqKzsYW18yKPoaUL8Pv96O4uBh9fX1Jvx/8c9DR0SGU20j3c6FQKFBUVAS3252wfKFQCL/4xS9kf99pwt0cRzxzijfDkhtxuGFfXx90Oh3MZrNQhnp8fBylpaUYGhpKalmdDgLNzajesAGIajIjnhHyM+uuri588MEH2LZtG1QqlTBop3P1w3EcBgcHUV9fj7y8vIhjimWRuk46nQ49PT1YtWrVjDIl20RnfHwcfX19Ka1I+YG4pqZGWAklK0P0tuFwWLJXuNjnIV6N8cQynfFOaKkmQfGuo1jx9Pf3w2QyyZaQuXbtWgwPD4NlWahUqhlrkJ05cwZerxdut1tWKwJNuJvDiB9gPguWn2FlekXBO/bGx8dx9uxZlJWVwel04uLFiygsLITRaIRer8fbb78t5DNkSsa33nprWkOg6BmhuCJrX1+fYAIaHh5Oe94HIQT333+/cOxoxE7q6HNarVZ4PJ4ZV2SxVpjRP/l+E2fOnBF6ZKeyIuUHZ5PJBK/XK9zfRBMspeR999138emnn077DJg5IVLK0W+xWLB9+3asW7cuYltxI6l4341lWdx3332oqamRLSFzxYoVKCgogMfjgd1uj5BJKomwt7dXyOmQ832iK4o5DP8A8313FQoFgsEgHA6HYLLIpK/CbDajoqICer0excXFOH36NCYmJpCXlweTyQSlUomysjKcO3cOFotFshSEHPT19WHr1q3C71KDEr+ysNls8Hq9mJiYAMdxKC4uRigUkkx+SgWWZTE0NITOzk7U1tbGnJGKfxd/XlxcDJvNhtLSUigUCsnjR6+S+MEsuszK6OgoxsfHJ8tzfPopqo4dA1tTA82qVSkNfhaLBYWFhdg4Zd4T9ySx2WxxjyklL19OROqzRHwoUp8VFxdHdIHjnwWPxyNEV0nN4i0WC8bGxnDx4sVpgQepIrW/y+XC66+/jrVr1wplU6QCG/jvx/d6l9uKQBXFHMdiscDhcMDr9WJ4eFgwQWk0GhQWFmY0CophGOTl5eGBBx7A0NCQEOvPl8kIBoOYP38+/vjHP6KiogJqtRomk0lWGS9cuDDNJh0vqkepVOKmm26CzWbD2NiYUJsoVfmiE8D8fj/OnDmD3t5eYWYa79jR5pihoSFcc801GBwcnKZgo7eNjqISl1nJy8sTlMREaysqnnwShtFRqN5+G5aXXwZSVN4qlQonTpxAXV2dUIE2UUUrlpfjOLjdbmE/qYE5lXtit9vx1FNP4Vvf+paQNKdSqTAxMRExMEsd2+l0Yvfu3dDr9RFFD1ORI5ZJrrCwEMPDwygrKxPKeQCIWfjw6quvzsg7ThXFHMfpdKKrqwvt7e1Qq9WYP38+JiYmMDQ0BIVCkXFfhdPphE6nQ1lZGRQKhRDFwVcdLS0txZVXXinIqFQqZZPR6XSiu7sbS5cuRSAQSCgKh2VZrFu3DhzHYWxsbFbnj2VXdzgcqKmpQVlZWdzvHr3y4bOxjx07hqKiImGVBiBmprY4jJZXjvn5+SCEID8/H3q9HkVtbdjjcmEVw0CvViO0Zw+UMSKRpGSM/g779+//LBvf709K0fLbhcNhrF27NiLsc6ZrNdM5+G3UanVEDSl+BTGTf8/pdIJhGLjdbqhUKrAsm9KqONaKFpg0qfFdDvlQZf7vUoUPX3vtNdx4441Qq9WyKgyqKOYwLMvC4XDgo48+QldXF8xmM9RqNVQqFUpKSmAwGDKeV3H8+HGsXLkSFosFZrNZ6B42MjIidG+rqqpCd3e3rDLyL7HJZBJKNcQz7wCTA7vT6cSBAwcQCARwxRVXRISnJhsqGqvKqdfrFWaz8Yhe+fArNK/Xi8HBQVRVVUXMOMWVe2PZ7cUrDP4n2boVn/7sZ1hbUICxJHJcYs2K+QxtvsJqKvdWqVTi6quvTmjbRB3mYj9KdMlxcfn0WDIPDAygsLAQhBCEw+GUAx3irWgBYOHChYJvB/isKRNfnp5/pjweD9rb23HLLbfIHhpPFcUcxul0or+/H6Ojo7j//vtRXFyM8+fPw+l0IhAISA6OcsJxHHp6enDLLbcAANiPPoJ3716oGxvhrakRlszd3d04c+YMmpubZz1rjwX/Mra2tqLA6cSK0VEgKqlL/HLzjlf+Zevu7gbHcQiFQimZnuLZ1W+99VYhiWymASZ65WOxWFBfX49PPvkEDDNZkA6YHFj1ej1sNlvcZEHxCoP/6WlshOmBB1Bjs8HR3JxQjku8WTFfs0h8nmQ5fPgwPB7PjMoinhxSWCwWbN26FQzDRCQG8rLGG3DXrl0Lr9cLpVIprHSSTUoUyxH9/PH/v/baa4XtouURP1O9vb0oKChAT0/PtJybdL/3VFHMUZxOJ9rb2+H3+7Fp0yZUV1djcHAQR44cwfnz53HvvfdmPOlueHgYKpVqsm9vSwvcO3ciUFmJ8b17UfI//geUK1eCZSdbax44cABWqxXDw8Ow2+1JF1VLBIvFgtCZM8h/8kn0ajQRheeiX0A+akuj0cBqteLw4cOw2WwRJa5TOb/US6tWq6HT6ZKaCYspLS0Vcj2iB6xUMsoHBwdRvHIllF/8IjQimZJ1PvMsWbIEwWAwaTnE9Pf3J6RMZ5qdS+3f1NSE3t5eAIgYWOMpHZZloVAoMG/ePHAcJznAJ0u074p/DoaHh9HS0oLt27dPk0f8TLW2tqK4uDgi52Y2/rS4sqb9iBTZ4R/oiYkJvP7660JCkU6nw8qVKxEOh7OScGcymfDII4+AZVk4//IX2K1WFHo8MLrd0J86hba2NtjtdqhUKgwNDSEYDKbUoyAZ3AcPIl+pjCg8Fyt0lC8St3XrVqxZswaFhYWzfumi93e73XjhhRdiypAINpsN3/zmN4XwT77sdqqRWfPmzcN9990HQDqsNBaxtjUYDNPayiYLX3fK5XLBbrfHTWyLJ7NUYpzT6cQLL7wAp9OJsbGxaX6c6LBXviTNz3/+87Q41MVIPQd5eXk4cuRIzN4U/M/Nmzdj06ZNYNnP6lnJNTmkK4o5CD/7dbvdKC0tRWlpqZDNqdFosGTJEgwPD2fckX3u3DmEw2FoOzowODAAbSCA8bw8qMNhMKtWoa+vD4QQcByHjRs3wmazYWRkRLYkQY7jYFyxAtYjRxAWF56TmIWKnb8sy2Lnzp2yKK6BgQFhQE+lnhIwOds+ceIE5s+fD4PBMM0/kexgce7cOZhMJqGERDJOY6lgALJ/P5750Y/w7R/8ADqJQn+JwCds9vT0CKHffDkPKflirSSkVghGoxFutxslJSUghMQNcuCPMTQ0BJVKhZ6enqRWv4mE8EY/B2q1GiUlJejt7UV1dXXMoIuPPvoIV1xxRcQKRy6oopijhMNhdHd3o7a2VijDzMexz58/X1hVZFJZvP/++6hjWSiefx4DhYUoKihA3YoVYG69FX1WK7wXL4LjOBQWFqKpqQkejwehUEiyDEM6IITggR//GOz27cD770cUnhMPCOKlPzBpjjh48CAMBgOWLVuWlph5HrfbDaVSKdjHZ4p8iobvbnbs2DEQQlBfXw9CCLxeL/Lz81OyUX/88cdYt26d4KCNpWxmMpW5XC74Dx3C2He+g8DQEP766KNY/v/9f7BI1M+aiTvvvFNIKOObTH366acghMBmsyX0vEgNwvyMvaCgAENDQygtLY0b5MAfw+FwwGw2Q6FQJHyNEzUtSj1f1dXV6O/vR3V1teR5+vv7cfToUVx55ZVp6d09E1RRzEFOnz4Nu92OiYkJNDQ0CDMKt9stvERdXV3o6uqCwWDIiK+C4zicP38eC8NhuAoLYR4agnZiAubSUjBbt8Jnt0OhUKC/vx9Go1GIhtq2bVvc2PXZcPHiRZw6dQpNTU3QffWr065DtF2a71SmUCgwMjKCkZERLFy4MGaf6FSwWCxCkAEfDZUofCSXVqsVEuZ8Ph+8Xq/Q3jWVldnAwACKioqmZVGLjzOT01jI0zh8GCM6HQrGx+EOheA7cADslPM4GXlOnjyJLVu2CJ3yGIYRviN/nxI5ZqwJAW9aTNTE1tjYCL1eD4fDgfz8/BnPnayTPfqzbdu2TVvtiDly5AgMBgNcGajADFBFMecIhUIYHx+HTqfDsmXLoNFohGU5y7JC1c4333wT9fX1WLRoUUZWFh6PB+FwGFWbNoH74ANoJiZgmJiA8uqrgSlTGcMwKC4uhsViQUFBAVpbW6fZX9PJ+fPn0d3djdLSUqhUqukd1hA56/T5fBgYGEAoFILBYMD58+cl+0QnI2t0wh3frjLZ780fR6OZ7G62cOFC4Xj8MWeKeJIiEAhgbGxMeH5imcJmchoLn69ciYIXX0SjSgVGpYJuqix69LWIR19fn9BgiPfBuN1utLe3IxgMCr2xE0XKUb01SeUlDkVO5Lsk4mSPBcuyIITg1VdfRXNzM/R6fYQyYFkW586dw5IlS6Yl4MkFVRRJEgqFpjmVMolSqUR+fj4+/vhj5OXlYf369RgeHobT6RRmOnwjk9bW1ojS0XIyPj6O1atXo0OrRel3v4v5p05NKgkJUw8wGbfu8/lilqKYLS6XC2fPnhUiQjiOEyqOSsX9h0Ih9Pb2Ii8vD6OjozCbzWhtbYXVao2YiSZzz6MT7iYmJvDcc8/h85//fFKDerQJg2VZhMNhoawE75tIZbBgGAYPNDYCjz8Oy5YtYEUDezQzmeAsFgvY7dvBFBai8C9/wcSKFcDU85dMnD+/whHLaDabUVlZCYVCAY7jklbY4oFbpVLB7Xbj6NGjEaGosXA6nfi3f/s37Ny5U6j2mwipmCzFrXI7OzthtVol/RQ333yzkBQqTsCTi6xGPRFCriOEtBFCOggh35f4nBBCnpj6/AQhpDkbcvIcPXoUTz75JJ599lmcPHky7aWnE6Wurg6BQAD19fVC5qvNZoNerxcydBsbGzE4OCjYeeWUlZ/haLVaEEKgW7ECzD/8w7RGNOIHXafTYeHChbMOo4wlD5/YVlFRAZPJhJKSkmkrAzF8bDyfTW42m/HFL35RCElMtpOcVMJdf38/BgYGEAwGEx7UY0VH8XW9+Huf6iDh/+ADsF//OuxPPw3n7beDefbZuNvHGvR4uRiGAbt2Ldy3347/e+xYREZ5ohFe58+fRzAYjHhm+QCOVM1rwGdmv2AwiJGRERw7dmxan3Sp78UPxEajUahmm+g7lexKgr9OwWAQ9fX1OHfu3LQIrOPHj2N0dBSVlZXC6oq/rnJFO2ZNURBCFACeBHA9gMUAdhJCFkdtdj0m+3XXAXgIwH9kVEgRra2tePfdd3HmzBns2bMH77zzDrq7u7MShgpMNni32WzQ6XQRLxCfvctxHGpra6d1AZOLgwcPore3F4SQhF/k2267TehZkU6YAwegev553LZgAZYvX47KykpYrdaEKo42NTVh0aJFKCwsRFdXl1DdNdmBKTrU0uVyweFwQK/Xw+fzTatUGusaSIVs8n9744034PP5BKWTynU88MILeE+jwYWqKpyePx/OH/0IaGlJ6hjRIaj8CsDj8QBAUv29WZZFfX09GIbB2bNnI77TbFu/8j4ej8eDoaEheL3eaRna0TAMg6GhIRQXFwuypxrWPBPR93rDhg1CqRFefr/fj8OHD6Orq2va9vFaw86WbJqe1gDo4DiuEwAIIS8BuBXAp6JtbgXw26me3fsJIYWEkFKO4/oyKWgoFEJHRwdKSkqg0+kwOjoKu92OU6dOQafTZaTDlJjR0VE0NTVh/vz5kvZfs9kMn8+H1atXw+l0QqFQSEZ3pAu3243BwUEsW7YMDQ0NM9bQ5zl58iT6+vqwePHihGrvJ0RLC5w7dsBeUICO3/0OV//7v4OZirpJtOIoX87h6NGj6OrqSnlgkmrbyWfXih34M5llpOS2WCyYP3++MCNOtYRDZ2kpiNmMYYMBhSMj8KtUk61Jk6j1JOW0tVqtqKmpESJyEjXDhEIhfPLJJ6itrY3ZayJVGOazAoA6nQ4lJSXo7+9HQUFBzH1cLhdCoRDq6+uF65qq7yERoq/TI488IlxDhmFACEFHR4fgY4l+xoDIJMJ0kU3TUzmAbtHv9qm/JbsNAIAQ8hAh5BAh5FC6Nerp06fx8ssvw+fzwWg0wmq1orGxEYQQjIyMCOGpmcJoNOLOO++M+QIxDIOxsTHs3r0bp06dQn5+ftrKZEfD2/bdbjeKioqSHlTPnj0rWXs/VZx/+Qsu2mw4r9ej1eebjLphIyvHJgL/Erpcroj9k51B8iuAsbExlJSUYOPGjSgsLIwI10xkhiolN+8/iWfaiSlvSwtC/+//C9fQEGpvvhn5Y2MwjoxAx+eaJPH9Yq0WGhsbYyfetbSA/clPJn+KZBwaGsLFixdhMBjSkvAYDZ+YZjQacdddd8Vticrfm8WLF6OhoSEiMVO8skmnySd6gA+FQti7d68wIWhtbUV1dTXy8/OFbcTPWHQSYbrI5opCKvg32mCYyDaTf+S4ZwA8AwCrVq2Kb3hMglAohKNHj8JisaC0tBQ1NTXw+Xw4fvw43nzzTRQXF2NoaCij5TJefPFFFBQUYMGCBUKhPTEsy8JgMKCurg7vvfceLly4gGAwKLntbOB7O1+4cAGNjY1C3aFEKS0txeDgYEIlnhOBZVkEV65E3q5dGFIoYFIooJnqZ5AKFotFMKnxg2Gq1UL1ej2OHz+OBQsWRPRmmE10TGNjI/r6+uBwOCQLAsZcZbS0wLVjB/wMgxqFAjW/+AX069fDfPBgRABCosRaLVx11VXC/yNCjDs6hPOP/f730P/sZ9CsWiUo5sbGRsyfP1+I5hLDn2c2zwm/YpyYmEBLSwvWx/i+DMNAoVDg5Zdfxs6dOyUnZnwhSb7nxmzGAan7pdPp0NbWhry8PKxcuRL19fWoqamRLDGi1+uRn5+fkrN/JrK5orADqBT9XgGgN4VtZIVhGLS1taGiokIon11RUYG1a9di3rx5CIfDQlx3JgiFQjh58iRUKhW8Xq/kaoYffGprazEyMoLCwsKY26YKP9vyeDzgOA5NTU1xl/DR+wKTSYN8mYLo3tGpwDAMNKtWwfj44zAuXYraRx9FcPHilG225eXl2LJlCxiGQV9fHy5evAiPx5O0bZq/H21tbVCr1RgaGpLsrpfsIMMPTAzDCAUBxbNcqVUGy7Jg9+6FT6EACQZxZTiMqpMnwaxYAccXvgDXggUpPctS983pdOK///u/hSRB/tqF9uyBn2GAcBgjOh3IkSOCjP39/airq0NVVRWASKcx7ws5ffr0rHuGM8xk0589e/bEfS9CoZCQKS11bL7972zHgVj3i2EY3HXXXfjkk0/wy1/+Emq1Glqtdtq7wj9js3H2xyObK4qDAOoIIfMA9AC4B8Dno7Z5HcCjU/6LtQA8mfZPtLW1CWUyxLVUdDodKioq0Nrairq6uoyFyhJCMDY2BqPRKNStl4Kf5dXX18PlcqG6ujqtsda8vTcQCKC3txcOhwOLFi2a8ToI4X+ffgr/J5/gq2vXgissTCkHQAo+RHPrmjXo7++fZjtPBq1Wi3A4jPHxcXAch7y8PExMTKRUKLCoqAhjY2PIy8sTsnzFcqXy/ITDYfznf/4nvvrVr0Kn00VcP6mVitDhrrERwaIinB8bg8vtxhc3bxYGKafTKTRrmu0qWafT4cSJE2hsbJxskDR17ZRXXw3Nf/wHnCYTAlotBhcuhG1KxubmZuFaiAdO3rw2NDQEp9MJm802Y2Oumfw2arUaFosFvb29gmKKpru7G9XV1ZKf8ZFYKpUKHMfNqiAf/z5JlbMpKirCo48+iv7+fsEUKu7TwZPOCgLRZE1RcBwXIoQ8CuAdAAoAz3Ec10oIeXjq86cBvAXgBgAdAMYBPJhJGUOhEIaGhtDU1IRgMBgxQJjNZlx55ZXo6ekRzBKZUBaffPIJ8vLykJ+fH9eUxLIsXC4Xrr32WhBCUFdXl3ZZeOfz0aNHUV1dPaMzWpg1tbbC9b3vwZOXh3Ovv47Khx5C2Ze+NGt5xINuMBhEUVHRrOtIHTx4ECtWrBDucUVFRUpO9+HhYeh0Omi1WoyPj6el0qdKpUJRURH0er2kDypmh7uKCtj++Z/R/sorsC5cCGbjRmimzIjRRRpnYwY0GAwghMDv98NoNKK4uHjy2lmtMP/Xf8G3dy+KVq9GaNEiQf7x8XGhYU90Lw5+YpKXlyfkGsQL100kM7qqqgoXLlyYpij47YeHh2MqEf4aSyVyJguf4yNODBXDcRz8fj+CwaAwWYyVQCoHWU244zjuLUwqA/Hfnhb9nwPw9UzLxaNUKnHs2DF4vV5cddVVQgw18NmMLRwO48SJE/D5fLJHP/HL4DvvvBMTExMzZmRyHIcTJ05gdHQUpaWl6YkqisLa2Ynwm2+i/v77Z9yWv2a+Tz5BmGWRNz6OwNgYOv76V8y/9lqhxHcqiGePRUVFePbZZ/H9738/5dk6j9lshsPhwIoVKxAKhWYVmnnbbbcJZVbMZnNaXuqSkpKIQoPR55TyheTn54OzWuHt70fV4smIdF6p6HS6WUf0iO9FQUEBXC4XamtrI+4ts3EjdHwe0FQC28TEBJ588kk8/PDD0Gq1kkmaAIQBNd6zkqjvZ9OmTVCr1RHXjO9PPTY2hqVLl0Z8Lt4uXQO0WKnx1y56RSdevXg8HigUCpw9ezblQpDJQjOz48CyLEZHR7Fx40aUl5dPcx5pNBocOHAAeXl5YFlW6A0tF0qlEp2dnSCEoKqqasYGNSUlJYKpIxgMpj/VfyoUlZmYAHfgAFBaOqMj1GKxgN26Fbpf/hLOwkIUKZXomOo4xkc9JassomePbrcbBQUFUCqVSdmMo19+lp0s33zx4kVhEE1lQOATEvnih+lSEgDQ0NAgeSwps4t4Bsqyk31BSktLhX3E4ZazWUmIa2ddd911gklFKsSXH5h7e3vh3LcPBa2tIK2t8Dc1Scoh7kQ3E4l8l7y8PHz66aeora0Vamd5PB4YjUacP38e4XAYy5Yti3h3pIpIzmawFiZQM6zoLBYLTCaTEGrNV2OQIxx2moyyHfkSwOl0oqenB3l5eZLOI74UssvlglqtFvoyywXLsujp6UFJSQnKyspmPJfVasWyZcvg9XqFVP90hg7zPSc2lJRMDsp79ya0H7NhAyy7dmHx5z+PjT/7GYLFxRgYGIDP50N/f39KIajiEM3BwUGhl0GiTs/obfnfi4qKsHbt2pQTvfgX+OzZs3A4HLM2N0Vfm+rqaqEJEo9UuCz/fcQJhNdccw3Ky6dHm886oGDqXuh0OgSDQRw7dizurJ43R5798Y+BM2fQ8b//N8YOH465fTLyRSt+KY4cOYIzZ87A759sbToyMgKn04mzZ89Oe3eiFWF0IcVUsVgsqKiogM1mi5uYKO6ux0c4yVUrTQxVFDFgWRZerxdXX301iouLJZf2VqsV27ZtQzgcFjJu5bxh/MxLoVAk/HDU1dWhZGogBzDrB5qHD0Ud9fmwLxiEKsn4e6xfD+YHP4Dl+uvxyCOPwGQyCTbtVBBHDplMJjQ3Nws2+Zm+c/SKRDzQ5ufnJ10KnEfcdCcYDGLRokWzDp8UKzOWnSwv8c4770QoBD5clh9wAExTHGNjY/jjH/8Y87rMdtDj70VRURHOnDkT83vziiX0yScoUiiwhGFQ4PFAd/JkWidd8SYNZWVl+PDDDzE2NoZQKISCggLYbDa4XC5s3LgxokwGgAhFqNPp4g7sycCv6KInJdFRWfw2DQ0Ns8pUT0o22c8wR2GYybLGFRUVcRXAwoUL0djYiKqqKuj1etlWFLwZDJgM20w0gY4Qgm984xsIhUJpTcbhQ1EnHnkEeatXwzrVYjSV44yNjaGgoABms1lwZKYqEwAUFxdj4cKFCScgRa9IxCUn1Go1fv7znyedI8KykzW2BgcHhdlodIhlsmYxKedsYWEh2tvbIyYC0eGy0d+PYRj09/fjwoULkoNnMiuxWPDX22QyCfb+WJjNZlRs3YolIyOoYhioOC6i6uxsiZfUyLIsampq0Nc3GUxps9kEJWEymVBRUTHt2okH89mWFYmWE/jMNAhMRl0eP34cbW1tEduKfU+ZgPooYsCyLN566y3U1NSgrq4upg1QoVDgqquuwsDAQEJ16lOFYRjk5eXhnnvuSbrMcnt7O3p7e1FfX5/WZByLxQJSV4cFy5alpCR4PvzwQ6HG0mx9KC6XC7/97W+xZcsWlJSUJJyAFG3PFv/OmxfjRb9IyTE0NASGYWAymbBz586IBLJkS27Ecs5WVlYiLy8PbrdbWGmKI4VifT++dEW04kk0WihRCCEoLy9HT08P6uvrJa+T3+8HW1GBF265Bd8pLwdz9dVgNmxI+ZzRxHNsMwwDg8GAnTt3guM49Pf3Q6PRYPny5Vi6dCkAaV9HuiONpPweCoUCXq9XMIdlopx4LKiiiIHL5UJnZycWLFgQ1xzCsixOnjyJ/v5+NDY2oqioSJboImDS8TZv3jyYTKak9rt48SJOnjyJ4uLiiKzgdDA+Po7KysqZN4yBy+XC+Pg49u3bBwCzym7ls217enowPj6OkZERFBQUJGwWiN6GHzj5jOFEFQWfwW2xWODz+ZCfnx9hVkt1MJYasHj5xsbG4Pf7UVZWJvldxH9jWRYej0dwDIvLZicaLZQMt912G/Ly8iL/2NIymXjX3AxPVRXOnTsHdV0dlN/61qzPJ0U8xzZvrnznnXeE3hehUAgrV64UFLmcM/dovwcw6YsIh8PIy8uD0+kU+sxnsgKEGKooJGBZFiMjI1AqlSgtLZ3xQVEqleju7kZTU5OsEQhHjhwBy7K4+uqrE96HHxTsdjuGh4fR2NiYVpluu+22GUs1x5ONH0gvXryIYDCYVPeyaBhmMn+CjzX3+XwwmUwpv1z8LK+4uHj6QIfYzWv4wZbPHejp6cHx48fxuc99LuLzVAZjKWW2Y8eOGY/Fy8qXnODDpYuLiwXfFz8opjtxS6PRoKOj47O8H1EJkdGCAkz88IewDwxArVbD6XTKNtGa6R22WCx44403kJeXhxtuuCFtq6pE5OKfB95Rzd/PsrIy6HQ6qNXqjMgSC6ooJGCYybai8+bNQ35+/ozx2suWLcO+fftQWFg466iWeAwMDMQtYiYFy7LIz8/HwMAA3G43+vv70xbCGw6H0dLSgo0bN6a0Px85xlcZValUs75+hYWFWLt2LbRarZBZncrLJZ7l1dTUCFFm/HGSqfh6/PhxoVS01OezRaFQoLe3F2vWrJH8XNwMx+/3IxAI4Pjx49iyZUvM1U26n+FXXnkF3/3ud6Gaqk7rUyigDAZhGBmB8cwZFC5YICRIyj0Yxjr+mjVrsGrVKkGhylUhVoro50H8f71en1FZpKDObAn4DNzbb78dBoNhRqfjvHnzsHjxYsyfP1/WpaFUQ5eZUCqVqKqqwh133IGSkhKEQqG0OdyHh4dx6NChWTV3t1gsWL16NW666aZZRwUBk+UO7rvvPqFCaKovl9gBzLIsnnzyScHBG885Gn0MYFLBRysK8eeJMFPU1kcffRTzM3EzHI1Gg4mJCbS2tgq+rkR7RaSKuFQGALhXr8ZIUREGiouhYVmUbduGrVu3oqmpSfbBUMpRL762Yh8V76SWM+RdTCy/Rzod5qlCFYUEDMNg7969OHr0aMJRQg899JDsUU+NjY2wWCxJh7guWrQIFRUVSdnrE+Hs2bPC7Gs2MAyDZ599FsPDw7MTqKUFLV/7GtpeeglWq3XWLxf/gpaXl8Nut8Pv908LkUzkejY1NUUktiXLTFFIfJjsxYsXI/4GTI/oslqtMJlMgqOWH7zlHhTnzZuHc+fOTSquRYtAfvhDBO64A+xzz6G7ogJ//etf48qQrpBuqfwSPoQ5+hz8sy13h8iZZM4FqOlJAj60sb6+Xhj8ZxoMOjo64HA4UFNTI1tKfXNzMwKBQEqDvcPhgNFoRFNTU1pk4QcnvknSbM0FFosF/f39kjPvRGRhDhyAa8cOHJyYwMpXX0VDdXXCzXfiwX8nq9WK/v5+LFiwQAiRTOQ78+WnR0dHEQgEkn4uZnJ8syyLQCCAkpIS2O12VFRUCCUoYvkcePPj2NiYYPsGUm9+lAjNzc3gOA4MM9U8qKoKuvp6BI1GnG1vh8FgmGby4WVIl1zRviHgs/LnfFCGuHRGuiPAkkUo4igqIZ+tVQVdUcSgt7dXSExK5OEYHR3FyZMnZzRHpMqhQ4fw/PPPpzzrtlgsQlZuOmAYBsuXL8f8+fPh8XhmfWyLxYKBgYGk9+NnfM6//AXOwkL0aDQIm0wJZ4knSnl5+bRcCnG8OyA9+3M6nXjuuedSfi5mMg3xn990002YP38+gOnJdfx2PM3NzTCbzejq6kJXV1fMpLx0wUe28T/55kEGgwEajQbt7e2or6+XHJgTNfMlSrQZh+M4cByHYDAIhUIx7ZrJbZaLBf+9AcDr9QrFFbO1wqArCgk6OjqQl5cHg8GQ8IpCrVbj4sWLQtG3dD5ULMvCbrcLD20qM3iLxYITJ06kTSbgs0xSvpDcbGZcCxYsgNfrTWqfiEGkuRnBP/wBfo5DgVYLbN6ckhyxzrNx40YhfFEcQRSv5g/LshgcHERRUdGsBpt4qxc+PFar1QrKmp81S1VXdTqdaG9vRzAYhNlsRjAYhMlkkiUsFogsJ/LRRx/B5XLhyiuvFI4fCARQWFiIqqqqmDKkWy7+GAzDwGazwefzQa/XS5bDkLN090wyRhRxzFCpjlhQRREFy7LIy8vDvffeO2MpY/E+oVBISIpJd9vRs2fP4uDBg0L4YHl5edIPTGlpKTancfB0uVx45plncNttt0Gj0cz6Ia6pqUl6n4iwwtWrUfF//g/+bv9+5K1bl/aErbGxMRw8eBDLli0TanxJxb7zCpM3/7S3t2PevHkplwERyxCNuGtcOBzGSy+9hPvuuw8ajUYoxOdyuQTFxdcvevXVV3HHHXcgGAzCYDAISVzpHhSjTSerVq3C+++/jw0bNgh1lcLhMO666y5hH6nS2XIO1tGl2KPNenJEgImJ973iyZbMcdIBNT1FwTAMTp48ie7ubuTl5SUc080wDL7whS+kPXMyFAqhp6dHKKtsMpmSTrgDJmdlNpsNgUBg1jLxuRmhUAglJSWzbgEJTIba/sd//EfSS2uxKSHU1ATfjh2wbNs2K1miaWtrQ09PD/bv3y8oCCB2zR8AEUpEPNtPF9Fd44qKijA8PAy/3w+fzydpwgkGgxgeHobJZEJdXR2WL18+radJugYb8WqPLyeydOlSaDQanD17FhqNBuPj43jppZfgcDjQ29uLtra2iMKFseRKt/lFvMLgyYQTO5FzSMmWynFmC1UUUbAsi66uLqhUqoRCY4HPlrCEEMFhly74WfOSJUtgNpsjZoDJ8qtf/QoHDx5MS5TS+Pg4CgsLodVq06IcFQoFAoEAhoaGUrLjA5Mrr+7u7rQOJKFQCF6vF0VFRZiYmMDo6OiMNX/4exYKhdDU1IT58+en1b7MD/p81ziVSgW1Wo2Kigr09PRIFqtjDhyA6vnn4T15Eo2NjbBarbKWg4i27yuVShBCcPvttwv5SYcPH8bChQuF6zIyMjKjLV7OQZE/p1T1XTnOlY5zpNuHEwtqeoqCYSb7I9fW1iZVQM9isWD//v0YHh6G1WpNW3Ypw0wmfB06dAh33XVXymGWLMuioKAAQ0NDaYngqK6uxi233JJWs4DFYsHp06dTihxjWRYDAwMoLCyMyDKeLUqlEvn5+fB6vaipqRFyAqSINpf4/X78+c9/xs033wytVpu2CQQ/CEd0jQNwxx13QKvVCitO4b5MZUIHGQYNwSAqn3suLXLEg/edRD8b/LX71a9+hYKCAmzfvh0ejwdOpxOBQACDg4MxfXxyRiGJzWQ6nU7wW8jlF0iXT0gu31I0VFFE0dfXJ1T6TNSRDXw2G2lraxNqAqVLWRBChHIiqcKvevr6+tLyQOXn52Px4sVpDanMz8+H3W6HyWSC0WhM+NrzMpw7dw6bN2+e5nSeLQ0NDQiFQli0aFFEr+KZvrvb7QbDMCn5lGYiloLu7u5GIBCIqMLL7t0LP8MAwSDyFQoUHT0KXH99WuURM9N1YVkWX/7yl4Xf+RDroqKiuD4+uQZFcYRRX18fCgoKoFar09bHPRbpmmRlwuFOTU8ieKf0fffdB5ZlE3JkizEajRgcHBQevHQtAwcGBqaVqE6FysrKtCmvXbt24dSpU2lb9rIsi+bmZixZskQwpySqoHkZtm/fjrKyMgwODqYlZFcM3y3v/PnzccM2+c+AST9CSUmJbC+w+LhOpxNdXV148skn0dXVJXQLBABmyxZoWBZ9hOBVrze5viFJMpMpRJzgJv4evKlsphIucmQpi81k/HOXbhNyvHPn0nFiQVcUIhiGEZq3l5WVJTWoMgyDhoYGrF69GiMjI3A4HEmVpY7H6OhoSoloYliWhdFoxPLly2e9bOcr6/IlF9Ixw2MYBoFDh3D8j3/E1s9/HtaVKyNkj3Vs/iXn80tKS0sRDodjtpOcDSMjI/jDH/6Ae+65BzqdbloYqsvlQl9fHwghsNls8Hq9s1oFJgrvs+Cr1LrdbpSWln4WMbN2LSy7duHUc89h+eLFsyoJPxPxZv18TxS+57W4JWwys+J0riSiz8+bnbIZipoMmQrdpYoiijNnzsDtdqOioiLpfc1mM+bNmwetVguFQpGW+vEulwtGoxEcx0WEOiYL/wL/6le/wj333JPyw8XncQwPDyMvL08ynDEVXO+9B8+PfoSPnU5s2b0bmGqElKhpi2/wUlpaKuR1pOtl51/G4uJi2O12OBwO5OXlCaa3YDCIvr4+9Pf3w+12Q6lUwmg0CrkXAGTtJcDfW5PJhOXLl6Orq0vIMuaViGbBApxfvx6bNm2SRQYxUoO+y+US+lHzOQtS3yNTSD1XfIACr8xm875lAjkz6aOhikIEy7JwOp2w2WwpzUaVSiX2798Pk8mEFStWzHpg4AflQ4cOYeHChbO2u1ssFpjN5lmZiBiGASEEDQ0NQtmF2cKyLHz79wMMA5KXh1MGA5i//AWWtWtndF7y12hgYAAFBQXw+XyCkk+HbOKX0Ww2w2g0Ynh4OGIQ9ng88Hq9CAaDwj1Xq9XYt28frrrqKnR0dMDr9SI/P39aOGq64Afn66+/HidPnoTZbEZfX59QurqwsBDz589HdXW1LOePJjqclc+bMBqNMBgMyMvLy9qMXeyTiH6u+Hsqh8M8ncjp2Jci965AFmEYBg6HA+FwOKWWoSzLYsGCBTAYDEJZ6tnKo9VqceTIEajV6lmX4OYHvf37988qvLCyshJf+MIX0jaLYRgGunXroABgVKsx4fcjOGV6mqmEAm/f9nq9KC4uFq5RuhSY+GUEgDvvvBPV1dWCo1OlUmFgYAB+vx+EEFRVVaGhoQEajQZHjx4Fx3FCbxOv1zut/3E6YZjJbnwNDQ1CqGkwGITD4YDb7cZVV10FlUol2/njwd9Hq9WKysrKyWenpQXsT34CtLRkVBaGYWK2yRWHNuey+Sk6/Jj6KDIIy7JYs2YNqqurhRljMjeAYRiUlpbi6NGjSTvCY6FWq1FZWYnly5fP6nj8zLu4uBihUGhWq5O9e/dibGwMa9euTZuysGzbBvOTT8L07rvAmjXQTPUFiGW7jrYvX3vttSgqKpq1L0eMlL29sbERIyMjKCoqEs7tdDoRDoehUqlQUVEBpVKJU6dOoaKiAkNDQwgEAhgfH5c9ioaH74W9ceNGBAIBGAwGvPXWWygoKMC8efNkPz+POEOdb8Ij3EdR8yLNU0/BkmLP9VTl0uv1CbfJzVUyWV5k7l0dGXG5XCguLsbExETKWnrJkiWoq6tLum9ELNra2qBSqWYdwcPPvJuamoQM2VS+H8uyaG1txfDwMBwOR1oTfJgNG2D81rcwPtXXgz92tJxSSVe1tbVpVRI80VE2TqcT//Vf//WZzFOTA7PZDIvFIigCu92O0tJS+P1+zJs3D9XV1airq0u7fFIsWbJEyH4uLy/HyMgIOI7LmNkJ+Cy6yeFwRKzIhOiwqZBdJhSCn2HSXsQxHvwEQKp+kthMls0ifImSKQVHFcUUfEb2e++9B6PRmHK9pvz8fDQ2NqYtZLS4uBjXXXdd2ipnFhYWYs+ePejv709ZkQ0NDQkO9nQzMjKCPXv2xMzAlbLNjo2N4V//9V/TLguP+GW02WwYGhqKqCRrsViElQcv79VXX401a9YI5gG+SVAm0Ov1WLduHf7rv/4LPp8Pe/fuxec+97mMnV882BJCBDMO33LV5XIJIbusUgkNy8oasisFPwGIfs8zbdKZK1DT0xQMw6C3t1fotTybTMnXXnsNGzduRGVl5aweNLfbjYsXLwrRRbN9aFmWRTgcRmdnJ9auXZuS+cntdguF6AghcLvdaTM/uVwuhEIhXLhwIaJXglhGKXOQ0+nMWHSKQqFARUUFLly4gPr6+snwU5ZFf38/wuEwFAoFCgsL0dHRgcWLF0Or1WbFtLFx40ZotVpoNBpcddVVqK+vz9i5xffIarUKg3Fvb+9nyZBTIbvs3r2TSiJDZicx0X07eKRMOnPVPJUuqKKYgrfh19TUJJWRLQVf92k2gxc/Kzt27BhWrVqVloq0DMNgYmICWq0WdrtdaMKTrExf/epX4XA4UFRUlLaIC/7YarUaBoMBHo8HZrNZclYX/SI7HI609QFPhIaGBjgcDgSDQdhsNpjNZqHOFyEEfX19eP/997F48WIAmQ375FEqlaitrYXf78fChQsjonoyIY/UYKvRaOB0OsFx3GSDoPXr09JcKhVmihqKDu3NVBhqrkIVxRQMwwiRRalEPIlRKpU4c+YMKioqZp33EK/2TbLwJpCqqiqMj48nbcpiGAbd3d3o7OxEXV1dWmvki2ehN998M+rr66FWq+Mm2vHk5+dH9ICQcyBkWRalpaWCA5s3QVmtVvh8Puh0Opw5cwa1tbWyyZAo0YN19IAne0hl1LH5Uh1yJEOmIptUYqDUSiKbXe6iydb5qaKYgmVZrFu3LuL3VJ29arUaHo9HaBWa6o0tKChAKBSCVqtNS/IPw0y2oVy0aBFUKpVwzETlO336NI4fP47BwUFcddVVaY/i4Qcvq9WK0dFRaLXaiM9j3RO+/3MmZn78NXzhhRewc+dOIRxXnHj45ptvRjxL2UQ8AIoHPHEvi0zNkvmAikT7vMiJVNHCWM9PJoruzSQrw0i3ic0Ul6/RLQp+hgFg1g9EdXU1li1bNmtnr9PpxPLlyzEyMpK2CAyLxQK9Xi+YABIlFAphfHxciAhTKpWyhHoyDIOenh689tprEX+P5dwOh8N49tlnEQgEMlJuGZgsE1JXVwePxxMhGx+Z1tzcDLVaLWt/gGQRO2n5pkaZuFbRWCyWiKZK2UD8LPHvuVRpcX47AGmvL5WsrHzyZDbuGZAlRUEIKSKEvEcIOTv1U7ITDyGkixBykhByjBBySG650lFwjGEYlJSU4L333hPiyFOBLy7X2NiYVJG8RLBarTh69KhQsC6Rh44vt+3z+VBXV5eWIoWxsNlsEaG38QrNuVwuDAwMoL+/H2NjYxmJVmFZFlVVVejq6oLP5xOCH/x+PxwOB9RqNbRabdbCK2Odk3++rVZrVntBZ0tJ8eeXUggOhyPi+QEie4hnA15Wj8eD3t5ejI6Oxrxncl/HbJmevg/gLxzHPU4I+f7U79+Lse0WjuMGMiVYOl6a4uJiwXadql2TYRgcPnwYLMti06ZNaan6yi9d+VDNoaEhDA8PC3X3Z1KQDQ0N+NrXvoaRkRH09vYKXffSDd89r62tDQ0NDTHtycBkJE1RUREY5rNOanImtfHK32KxwOVyCfLwsu3evRtWqxX5+flZMVXMZJ4QJylmw94d715m4/zAZwoh+vnJtsmJN3PyASgGg0Hy+c6ESSpbiuJWAJun/v8bAPsQW1HMORiGQUFBAdrb22dVdiMcDmPhwoVpGYzFM6mJiQkolUp0dHQgPz8fdXV1CSm0cDiMtrY2wRnJv2jpVBZ8i8+mpiYMDw/DbrdPRsjEGNh8Ph+qq6vBHj8O1eHDUG7dKluopbiwHV90z+v1oqCgAGVlZbh48SJOnDiBRx55ZNY9slMhWcdrtnwEFotF1iKJiZxffG3ECkEsU7aUqRj+3eL9SdHXLFPO9mxdASvHcX0AMPUzlh2DA/AuIeQwIeSheAckhDxECDlECDmUbdswy7IoKyuDWq0WQm1TIV19KIDpiUSbN29GcXExVCoVwuFwQrMmp9OJ9957D2q1GuPj49BoNAgGg2lb9vJmCa1Wi6qqKuHFEL8A0eeqr69HI8ti9DvfQfCZZ+DasUOW2kHRSWR8ct1LL70kRJDt378fCxcuBCEk7edPhLmSLMaberL5noqvTTyTcy5cQ6vVGle+TNxz2VQ6IWQ3AKng9v8nicNs5DiulxBSAuA9QsgZjuM+kNqQ47hnADwDAKtWrUp/ynASMAyDLVu2zNq3UF5enpb8CR7xDCkYDMLtdgvZqYnI6HK5UFZWBpPJBKVSCYPBkNaHk3/o+azvt99+Gzt37hTOEb3EnpiYwNtvv42rL17EuFaLguFh+BWKySSuNK8qxCYLlUoFhUKB8vJyFBQU4K9//StuvfVWrF69Wpj5ZStZS1z6JBfJtXBTnlyQIR7x5EtXqf+455frwBzHXcNxXJPEvz8BcBJCSgFg6md/jGP0Tv3sB/AagDVyyZtuAoEAPvzww5RLZbhcLqxYsUJoyJMu+IcpEAjg4MGDSYXH9vf3o7a2FmVlZVi0aJEskSD87G7R8DAC770H09mzwuAXPcD09fVhcHAQWLkS+RMT4BQKWctBWCwW2Gw26PV6wbn/4IMPQqlU4vDhw5g/fz7q6+sjrkmsaC05EZfKAET1laJ+Zou5sOqZK0RH3MlFtnwUrwP4AoDHp37+KXoDQogeAMNx3OjU/68F8OOMSpkiLMsiEAjg448/TqmPBMuyOHjwIC5cuIArrrgiLeU7oiktLYXL5RKyiROhuLgYSqVScObK9ZIzBw7Adc89yPP5cGLnTqz/8Y+BgQFoVq+Gf9EiYYCx2+2TCmvbNjCFhUI5CHbtWtlmQEqlMsKmnZ+fjx07dgjXItvJWrHyJcbGxqDX64Wf2YjFF68Is+HDudTI5POVrTv1OIBthJCzALZN/Q5CSBkh5K2pbawA/koIOQ7gEwBvchz331mRNkkYhoHBYEBBQQFGRkZScmh3dXVhdHQ07SsKHp1OB51Oh/7+/oRmmH19fRgfH89IWCNfWbTCaES/2YzTP/85ep9+GnjwQZRdvCgMcHa7HdXV1ZPXdv16MD/4AVwLFsg+gxfbtOOtGLLhM5DKlwAAr9cLjuPg9XoFH0smVxbRg9pcJNsrsWgy+XxlZUXBcZwbwFaJv/cCuGHq/50AlmVYtLRhsVhQU1ODcDic0v6BQABFRUUIh8NwuVyyhKHW1tbi0KFDKCwsnGYyEeN0OtHZ2Ynf/e53+MpXvoLi4mJ57aFbtsDzwgswWa3QTExg3OdDwcgI/AoFsG8fsGEDAODuu++OSBrM6AxryrE+0/myETkjPic/i8/PzwchROjBkGmzT7bDYmdLrtZ7yoR/AqAlPGSDZVmhgmeygxbDMMjLy4PNZoPFYhEii9L5MIRCIZSWlsLj8WBiYkKI3JFK5OFNFxaLBeXl5bIoLTHO2lpM/PCHCJ8+jT+1tuL6zk5Yo/wPfX198H74IeZ3dABT1UczNRjx1ynW+eIVmMsE4vOLlUb0z0wzV6uy5qoDnvbMvgRgGAYcx+HcuXOoqalJ6sFyuVy47rrrhBh9OQY9pVKJkZER7N69G7fcckvMHsb8YDjR2ooFnZ0o7eoCSkvTKosYXjGpFy2CoqgIZQYDfBs3omR0FGpRjsTB3/0O5P/8H+h0uogOaXLP4KNfTql6QT6fDxqNRnaFmoh8wGeKSsqPkmnE587VWXo0ubgayrTyyv43vkThB7xDhw4llUvBsiw6Ozvxpz/9Cf39/VAoFLK9RLW1teA4DrW1tXHDcC0dHWCefBKFx4+j7StfkbXHsThEtry8HHV1dfjI4cDpm2+Ga8ECAJOrif1/+hMKi4slO6TJuZKIV2+HZVk4nU50dXXhzJkzcDqdssiRqny5xFyTNR3lfdJJpv1fVFHIBMNMtsgcHh4WzBSJMjAwgO7ubigUirQmtIlh2cnOcMFgEMeOHYPdbp8WTskT2rMHpUYjahgGXq0WoT170i6PFEVFRWhsbIRWq4XD4UBfXx9CoRDO/vnPyLtwAWGzGQMmE1ThcEY6pEm9nNHO7HA4jFAolBWH8VxJuAPmjqxSBQSzifh5yqTyoqYnGSktLUVhYSH6+vqgUqkSuqG8UqmqqkJhYeGsSoDMBMdxWLRoESYmJqBQKGKWnw4YjXi9pwc3l5bCMDEB5dVXyyIPEJkBHQwGodPpcNVVVwlLa7fbDUNPD1ZVV8MyOIgwIfDffjtcCxYgE3M9cUKbVCRPWVkZCCEghMh672aSLxcGtZnIdVlzzTcRz6woN1RRyAjLsqiurkZfXx8mJiYSzocIh8NYuXKl0HtbDhiGgc1mw/bt2+Hz+cBxnHT56ZYWnPxf/wuFgQDKnU6UPvaYrG0ro+3B/Avx/PPPY9myZWhpaUGJ2QwzIdCPjcFjNkN5000ZfZHFLTSjbdcWiyVjkSixyNWBV4pcljWXfBPZVlpUUcgIy7KorKxEMBhMKnLp2muvRTgclv1BsFgsGBwcxIcffoidO3dOK5Phdrvh27MHrTodSkMhhJVKsAMDstsro8M73W431q1bh9bWVvj9flQ1NSH0N3+D8c5OKJYsgbusDLYMvcjRL2xZWRmAyAEvlwc/SnJkW+nzZFtpUUUhI3xBu7179+Kmm27C0NDQjOYnjuNw4MAB1NTUQKvVym5/NBqNQl8FvV4fYVrp7e2Fcs0ajL38Mor0eoxxXEZ8AcBneQo+nw/BYBAmkwm33HILVCoV7HY7tGVl8C1eDJvNhnA4nNaaWDPJlSuzzGTIttlkLpLtqCz+PZQKdc409MmRmTVrJstT1dTUzOjc5HsdvPfee4LPQG5n6ODgIAgh+Mtf/iI4ZPkHUaPRILRoETY/9hhW3XMP9D/7Gdi1a2WVRwzDTLbO5Ivw6draYP31r1E1NASTySQkj2XaF5CIEzGXoniyUW9qrpPtqCyXy4VPP/0Ura2tEfctW8qerihkxmg0CjkL8TKa+dnL8ePHodfr4Xa7YbPZZH0w+Bl7eXk5xsbG4PP5EAgE4PF4hJkUy7LoYBis/uIXszKDFmz++/fD/eCDsCsU0D31FMpefhnsmjVJR5Sli3jnzPZMVEy2bdtzlWyuHMUraUJI0rXi5IAqCpkZGBjA0qVLASCmeYR/mQHg7NmzQpltuc0p/Ix95cqVCIfD6OnpgdPpRCAQwLx58+D3+9HW1gaj0ZjVIm4Mw4Ddtw+9RUXgGAaKcBgDu3djfKooX0NDQ1bkkiLXBmZ+wPP5fFmJwprLZLMLIL+SzsaKWQqqKGSEHzQ2btyIwcHBiG5tYsQv84IFC5Cfn5+xB4N/GX77299Cr9dj/vz5QkMinU6HM2fO4K677srKgxqR8bxqFYZ27wYTDKJgbAwTDQ1QT63UstktLZq56sOgSJOt+5cL0XNicuPtukThB42zZ8/i8OHDuOOOO2YsHufz+aDVamOW1Eg3/Dn5/g5WqxVVVVUoLy/H+Pi40Kc304jNN2azGcHFi2H5xjfgO3ECpevXY3gq7FilUiUUJJBJcik/QJyXkgsrHEri5NJ9yh1JLlEsFgtMJhMuXrwIt9sdd5bZ1dWF3/3udxm1bTPMZFP52tpadHd3w2q1ori4GA6HA36/H1/60pcy3tpTKpFNo9HAuHo1Kh9+GNZrr0VdXR1qamowb948QdHlErnyks+VDGhKbkNXFDLDsizy8/Oh1WpBCInrp+jq6kJpaSkCgUDGmtwwDAOz2Yy1a9dicHAQOp0OPp8P4+PjeO211/DII49AoVDIKkc0UuYbqVm6Xq+H0+kU7Li5tKrIBfjrlUsrHIo0uX5/qKKQGYZhoNVqUVtbi4mJiZgPA8MwOH/+PMLhMLq7u2Uf+KIjc3Q6HW688UYolUp0d3fj1Vdfhc1mQ3t7OxYtWiSbHLGQGtzEFVr53tUFBQXUrCJB9P2l1yV3yaUouVjQpycDWCwWXH/99SgpKYHT6ZQ0k7Asi4qKCixcuBB6vV5Wc4pUZI7FYoFSqYTL5UJLSwtqamrQ3NyMnp4e9Pb2yiLHTEgNbmLZ+ZpU1KwSSbZzACiJM1fuFV1RZACn04mjR4/i4MGDWLlyJSoqKqYlbLW3t0OtViMYDE4ml8kYEidl2nE6nejp6YFWq8Xtt98Oj8cjKIienh4QQlAqYx+KRJGqBUVXEpHQyKu5w1y5V1RRyAw/Y1Cr1Whra8OiRYsQDofh8/mEsM5QKIS2tjacOnUK27ZtQ0NDA9RqtaxyRXc+CwaD0Gq1mJiYQHFxMUpKSuD3+9HX1weXyyX0y85GM554sgO54zjOJagCnTvMhXuVu5JdIvDJM1arFQsWLBBKevt8PjgcDrhcLgwNDaGrqwuEEASDQXg8nozJxv/kmwVVVFTAbDbD5/OhpKQEeXl5UKvVWemvEI9cfqlyhbl2jXLl2coGuX6v6IoiA/DJM+vXr8f58+fBsiwCgQAMBoPgi/D5fGhsbIyoCZXp+kV8rakzZ87A4/GgoKAAer0eY2NjUCqVOZEhmovk+mxwLjAXHLqXM1RRZJCFCxfCYrGAEAKO4xAIBODz+TAwMACWZVFSUgKO47Jqq+RrzOj1euj1ehgMBiiVSrAsm7EKrbHIxQGZDnCzJ9fKnlCmQxVFhuBfgmPHjsFoNGLJkiUYHh7G0NAQGIbB9u3bYbFYYLPZslaOIrrGjN/vRzgcBsdxshconIlcHJDpAJce5opD93KG3pEMwZub8vLy0NbWBo1GA47joFAo8PLLL8Nut8Pn82W9ZpHFYsHChQtRXFyM8fFxEEJgNBqzuprI1RBCmvWcPjLZ/5mSPHRFkUEIIbBarfjwww9x4cIFmEwmOJ1OFBcXY+XKlQCyb15xuVzw+XzweDwRUVC5UAE1F2ec8SJWsn0v5xr0WuUuVFFkCL6Ugs/nwzXXXIPTp0+jvr4eH3/8MW699VYAgEqlyurLIi4gRwiBwWBAcXFxzoXE5toALCVLLprKKJRUoYoig/ADLh+KOjo6ipUrVwplKILBIFwuV9YGFvHM3Wq1wmw259yAPBcG4FAoRH0XlEsKqigyjMVigcPhAMMwQknxixcvYnx8HLW1tVkfWHI5+WcuOI95RTY2Nga9Xp9zpjIKJRWoosgCXq8XLMuioKAADMMgPz8foVAIwWAwY30o4pHt88cil30VQKQi0+v1WY1go1DSCX2Ks0BBQYFQzptlWYTDYZSWlqKysjLnBr9cI5dXPNGKjCoJyqVCVt42QsgOQkgrIYQlhKyKs911hJA2QkgHIeT7mZRRLhiGgc1mQ1FREQoKCjB//nxUV1ejrq4uJwe/XCSXrxMN86RcimTrjTsF4HYAH8TagBCiAPAkgOsBLAawkxCyODPiyYvFYkFVVRVsNhtYloVer8/pwY+SHPReUi41srI25jjuNICZWmyuAdDBcVzn1LYvAbgVwKeyC5gBaOcxCoUyV8jlEaocQLfod/vU3yQhhDxECDlECDnkcrlkFy5dUCVBoVByHdlWFISQ3QBsEh/9PxzH/SmRQ0j8jYu1McdxzwB4BgBWrVoVczsKhUKhJIdsioLjuGtmeQg7gErR7xUAstOTk0KhUC5jctnucRBAHSFkHiFEDeAeAK9nWSYKhUK57MhWeOxthBA7gPUA3iSEvDP19zJCyFsAwHFcCMCjAN4BcBrAyxzHtWZDXgqFQrmcyVbU02sAXpP4ey+AG0S/vwXgrQyKRqFQKJQoctn0RKFQKJQcgHDcpRcgRAhxAbiQ4u7FAAbSKE66oHIlB5UrOahcyXEpylXNcZxkSYFLUlHMBkLIIY7jYpYVyRZUruSgciUHlSs5Lje5qOmJQqFQKHGhioJCoVAocaGKYjrPZFuAGFC5koPKlRxUruS4rOSiPgoKhUKhxIWuKCgUCoUSF6ooKBQKhRKXy1JRzLbDHiGkiBDyHiHk7NRPU5rkmvG4hJAGQsgx0b8RQsg3pz57jBDSI/rshmknkUmuqe26CCEnp859KNn95ZCLEFJJCNlLCDk9dc//h+iztF2vmboxkkmemPr8BCGkOdF9Z0MCct07Jc8JQsjHhJBlos8k72cGZdtMCPGI7s8PE91XZrm+K5LpFCEkTAgpmvpMlmtGCHmOENJPCDkV43N5ny+O4y67fwAWAWgAsA/AqhjbKACcA1ALQA3gOIDFU5/9FMD3p/7/fQD/O01yJXXcKRkdmEyUAYDHAHxHhuuVkFwAugAUz/Z7pVMuAKUAmqf+bwDQLrqPable8Z4V0TY3AHgbk+Xz1wE4kOi+Msu1AYBp6v/X83LFu58ZlG0zgD+nsq+cckVtfzOAPXJfMwCbADQDOBXjc1mfr8tyRcFx3GmO49pm2EzosMdxXAAA32EPUz9/M/X/3wD4XJpES/a4WwGc4zgu1Sz0RJnt983a9eI4ro/juCNT/x/FZIHJmA2wUiTesyKW9bfcJPsBFBJCShPcVza5OI77mOO4oalf92OynH8mmM33zuo1i2IngBfTdO6YcBz3AYDBOJvI+nxdlooiQeJ12LNyHNcHTA5EAErSdM5kj3sPpj+kj04tPZ9Ll4knCbk4AO8SQg4TQh5KYX+55AIAEEJqAKwAcED053Rcr0S6McbaJqlOjjLIJebLmJyV8sS6n5mUbT0h5Dgh5G1CSGOS+8opFwgheQCuA/CK6M9yXrN4yPp8ZaV6bCYgGe6wlyjx5EryOGoAtwD4B9Gf/wPAP2FSzn8C8C8AvpRBuTZyHNdLCCkB8B4h5MzUTChl0ni98jH5Qn+T47iRqT+nfL2iDy/xt+hnJdY2sjxnM5xz+oaEbMGkorhC9Oe0388kZTuCSbOqd8p/9EcAdQnuK6dcPDcD+IjjOPFMX85rFg9Zn69LVlFw8nbYcxJCSjmO65ta3vWnQy5CSDLHvR7AEY7jnKJjC/8nhPwngD9nUi5uskw8OI7rJ4S8hsll7wfI8vUihKgwqSR+z3Hcq6Jjp3y9okikG2OsbdQJ7JsqCXWJJIQsBfAsgOs5jnPzf49zPzMim0ihg+O4twghTxFCihPZV065RExb0ct8zeIh6/NFTU+xiddh73UAX5j6/xcAJLJCSYRkjjvNNjo1WPLcBkAyQkIOuQghekKIgf8/gGtF58/a9SKEEAC/AnCa47h/jfosXdcrkW6MrwN4YCo6ZR0Az5S5TM5OjjMemxBSBeBVAPdzHNcu+nu8+5kp2WxT9w+EkDWYHK/ciewrp1xT8hgBXAXRM5eBaxYPeZ+vdHvn58I/TA4KdgB+AE4A70z9vQzAW6LtbsBklMw5TJqs+L+bAfwFwNmpn0VpkkvyuBJy5WHyhTFG7f87ACcBnJh6GEozJRcmoyqOT/1rzZXrhUlTCjd1TY5N/bsh3ddL6lkB8DCAh6f+TwA8OfX5SYii7WI9Z2m6RjPJ9SyAIdG1OTTT/cygbI9Onfs4Jh3tG3Lhmk39/kUAL0XtJ9s1w+SksA9AEJNj15cz+XzREh4UCoVCiQs1PVEoFAolLlRRUCgUCiUuVFFQKBQKJS5UUVAoFAolLlRRUCgUCiUuVFFQKBQKJS5UUVAoFAolLlRRUCgyQwhZPVV4UDuVvdtKCGnKtlwUSqLQhDsKJQMQQv4XAC0AHQA7x3H/nGWRKJSEoYqCQskAU3V2DgKYwGQpinCWRaJQEoaaniiUzFAEIB+TXfa0WZaFQkkKuqKgUDIAIeR1THYXm4fJ4oOPZlkkCiVhLtl+FBRKrkAIeQBAiOO4FwghCgAfE0Ku5jhuT7Zlo1ASga4oKBQKhRIX6qOgUCgUSlyooqBQKBRKXKiioFAoFEpcqKKgUCgUSlyooqBQKBRKXKiioFAoFEpcqKKgUCgUSlz+/7bC+keAQc+fAAAAAElFTkSuQmCC\n", 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