{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Quantile regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "This example page shows how to use ``statsmodels``' ``QuantReg`` class to replicate parts of the analysis published in \n", "\n", "* Koenker, Roger and Kevin F. Hallock. \"Quantile Regression\". Journal of Economic Perspectives, Volume 15, Number 4, Fall 2001, Pages 143–156\n", "\n", "We are interested in the relationship between income and expenditures on food for a sample of working class Belgian households in 1857 (the Engel data). \n", "\n", "## Setup\n", "\n", "We first need to load some modules and to retrieve the data. Conveniently, the Engel dataset is shipped with ``statsmodels``." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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incomefoodexp
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" ], "text/plain": [ " income foodexp\n", "0 420.157651 255.839425\n", "1 541.411707 310.958667\n", "2 901.157457 485.680014\n", "3 639.080229 402.997356\n", "4 750.875606 495.560775" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import statsmodels.formula.api as smf\n", "import matplotlib.pyplot as plt\n", "\n", "data = sm.datasets.engel.load_pandas().data\n", "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Least Absolute Deviation\n", "\n", "The LAD model is a special case of quantile regression where q=0.5" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " QuantReg Regression Results \n", "==============================================================================\n", "Dep. Variable: foodexp Pseudo R-squared: 0.6206\n", "Model: QuantReg Bandwidth: 64.51\n", "Method: Least Squares Sparsity: 209.3\n", "Date: Fri, 21 Feb 2020 No. Observations: 235\n", "Time: 13:57:36 Df Residuals: 233\n", " Df Model: 1\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 81.4823 14.634 5.568 0.000 52.649 110.315\n", "income 0.5602 0.013 42.516 0.000 0.534 0.586\n", "==============================================================================\n", "\n", "The condition number is large, 2.38e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] } ], "source": [ "mod = smf.quantreg('foodexp ~ income', data)\n", "res = mod.fit(q=.5)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualizing the results\n", "\n", "We estimate the quantile regression model for many quantiles between .05 and .95, and compare best fit line from each of these models to Ordinary Least Squares results. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Prepare data for plotting\n", "\n", "For convenience, we place the quantile regression results in a Pandas DataFrame, and the OLS results in a dictionary." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " q a b lb ub\n", "0 0.05 124.880097 0.343361 0.268632 0.418090\n", "1 0.15 111.693659 0.423708 0.382780 0.464636\n", "2 0.25 95.483539 0.474103 0.439900 0.508306\n", "3 0.35 105.841294 0.488901 0.457759 0.520043\n", "4 0.45 81.083647 0.552428 0.525021 0.579835\n", "5 0.55 89.661370 0.565601 0.540955 0.590247\n", "6 0.65 74.033435 0.604576 0.582169 0.626982\n", "7 0.75 62.396584 0.644014 0.622411 0.665617\n", "8 0.85 52.272216 0.677603 0.657383 0.697823\n", "9 0.95 64.103964 0.709069 0.687831 0.730306\n", "{'a': 147.47538852370585, 'b': 0.4851784236769232, 'lb': 0.45687381301842295, 'ub': 0.5134830343354234}\n" ] } ], "source": [ "quantiles = np.arange(.05, .96, .1)\n", "def fit_model(q):\n", " res = mod.fit(q=q)\n", " return [q, res.params['Intercept'], res.params['income']] + \\\n", " res.conf_int().loc['income'].tolist()\n", " \n", "models = [fit_model(x) for x in quantiles]\n", "models = pd.DataFrame(models, columns=['q', 'a', 'b', 'lb', 'ub'])\n", "\n", "ols = smf.ols('foodexp ~ income', data).fit()\n", "ols_ci = ols.conf_int().loc['income'].tolist()\n", "ols = dict(a = ols.params['Intercept'],\n", " b = ols.params['income'],\n", " lb = ols_ci[0],\n", " ub = ols_ci[1])\n", "\n", "print(models)\n", "print(ols)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### First plot\n", "\n", "This plot compares best fit lines for 10 quantile regression models to the least squares fit. As Koenker and Hallock (2001) point out, we see that:\n", "\n", "1. Food expenditure increases with income\n", "2. The *dispersion* of food expenditure increases with income\n", "3. The least squares estimates fit low income observations quite poorly (i.e. the OLS line passes over most low income households)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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C66+/TlBQkN9jZmdnY7Va6dKlC+np6Z4kR18UFhayY8cOHnnkEYKCgnjgAe0/k7p3agQFBTF+/HgsFovmKxdaawlJj68A/yGlTAb+A/ig+nhtmSSynuN3EELMrc6LOPxD7EipKIryfXP06FHeffddT98GLYIFKSU7d+7km2++0WSLo9lsJi8vj6KiIr/Hqo3dbmfRokWeFtqtWrUiNja2Sa6lpZawwjALWFD9/SpgSfX3eUDNB09JuB5X5AGjbju+q7aBpZSLgEXg2lap1YQVRVEU36Snp2MymYiLi/N7h0FVVRU6nQ69Xs8TTzyBwWDweUyLxcKVK1fo1KkTKSkpzJ8/X/NP/O4tnYGBgQwaNIh27dppOn5NTqeTffv2aTpmS1hhyAdGVn8/Bsis/n4d8Fz1bonBQKmU8hqwBZgghIiqTnacUH1MURRFaYEKCgpYv349TqeT4OBghg8fTkCAf7cfm83GkiVLPJ/SIyIi/Fqt+Prrr/n88889vRq0DhaMRiNLliwhP9+Vpjdw4MAmL8J09uxZTcdr7m2VnwH7gC5CiDwhxIvAHOCvQogTwB9x7YgA2AhcArKAxcA8ACmlEfgdcKj667fVxxRFUZQWKC8vj/Pnz1NaWqrZmHq9nr59+9K7d2+fx5BSYrVaARg1ahQzZswgPDxcqyneIiQkBCklVVVVTTI+uB517N27F5vNRkBAAM8995ym46tKj4qiKIrmpJSUlJQQFeXa9V5VVeV3sySHw8G2bdvIyMggLi7O7/m5t3ROnz69Sao1lpSUcPjwYcaOHYsQwu8qkw25cuUKH374IY899hg9evQAVKVHRVEUpYXbunXrLe2eteisWFlZydmzZ7l48aLfYwkh6NChA/fdd5/fY9UlKyuLQ4cOUVhY6Lmm1qxWq6eGQ0pKCq+88oonWNCaWmFQFEVRNFdUVMTFixcZMGCA3zfKgoICYmNjEUJQWVnpc50CKSV79+4lPj6ejh07+jWnuphMJkpKSkhMTERKSUVFhSadNuuyfv16Tp48yeuvv15ra221wqAoiqK0OBcvXmT37t2Adu2ec3NzWbhwIcePHwf8K2pkt9s5efIk58+f92tO9Vm9ejX//Oc/PY2pmiJYqKys9KzcjBw5khkzZtQaLGitJWyrVBRFUX4Azp8/T05ODkOHDtVsl0FSUhLjx4+ne/fuPo+Rm5tLQkICer2eF154QZPHIzVZrVZ0Oh06nY6JEycC+L0LpC52u52FCxeSlJTE448/TkRERJOuYNSkVhgURVEUn9ntdsrLywGYOHEiL774ot/BQkFBAcuXL8dsNiOEYMiQIT73mLhx4wZLly7lwIEDgGuFQstcgqqqKt5//3127doFQFxcnN8JmbVx7+YIDAxk9OjRDBs2TPNrNEQFDIqiKIrPVqxYwaefforT6USn02nSPMrhcFBSUkJZWZnPYzidTgBiY2N59NFH6d9fk8f4dwgODqZHjx5N2oI6NzeXN954gytXrgDQu3fvBos+Wa1W9u/fr+k8VMCgKIqi+Gzw4MGMHDnS7yV4u91OVlYWAAkJCbz66qs+V0LMzs7mrbfeori4GIBevXppEsi4FRYWsmzZMkpKSgAYM2ZMkzSncm9KiIuLIy0tjbCwMK9fe+HCBbZs0bamoQoYFEVRlEY5duwYJ0+eBCAtLY2uXbv6PeY333zDp59+6rnJ63Q6n8eKiory1H9oCoGBgZSXl2taiOp2R44c4eOPP8bpdGIwGJg2bRpt2rSp9zUmk8mzCtG9e3deeuklTeekAgZFURTFa1JKTp48yZkzZzRp9OR+dHD//ffzzDPP+HyjLyoq4ttvvwWgdevWPPfcc5oGDSUlJZ7eDK1bt+bVV19t0pbXer0evV7vyV3wxtq1a1m9ejUOhwMhhOa9KtQuCUVRFKVBZrOZwMBADAYDTz31lF+Nntz27t1LVlYWM2fOxGAw0KlTJ5/HOnnyJIcOHaJ3795Nsmvg+PHj7Nu3j+7duxMZGan5LgiHw8E333xD27Zt6d69Oz179qRnz54N/o6LioqIjIxEr9d7dmj4szpTH7XCoCiKotTLbrfzwQcfsH79esCV6KfFDdO9JdDhcPj0eqvV6nmEMWLECF555RVNgwWz2eyp0jh8+HBeeeUVIiMjNRu/JiEEmZmZnkcKQogGg4Xy8nLef/99vvnmGwDatm1L27Ztm2R+oCo9KoqiKF44cuQIcXFxJCUl+TXOtWvXMJvNmlRa/OijjzCZTLz88suaf+KXUrJ48WKklMydO7fJyjrv27fPs23UarV6lZxpMpk8CZBHjhyhc+fOdQZKWlZ6VI8kFEVRlDtIKdm9ezedOnUiMTGRfv36aTLmpk2bsFgsvPzyyz7dhN0fcoUQjBgxAimlpsGC1WpFr9cjhGDixIkEBwc3WcOo69evs3v3btq2bUt6erpXwcLRo0fZvHkzL7/8MtHR0Zr8vXhLBQyKoijKHSwWCydOnMBms5GYmOjXWHa7HXDtLnjssccIDAz06SZss9n44osv6NChAwMGDCA1NdWved2uvLycDz/8kCFDhjBgwIAmSWqsqqoiLy+PtLQ0UlJSeO2114iOjm7wdXa7ncDAQNLS0ujfv3+jtlhqReUwKIqiKB5lZWVIKQkODmbOnDmMGzfOr/HsdjtLly711ARo1aqVzze7wMBA7Ha7JwDRWnh4OKmpqcTGxjbJ+ODq4rlq1SoqKysBGgwWpJSsXr2aL774AoDIyEgmTJhAUFBQk82xLmqFQVEURQFcWwcXLlzI0KFDGT58uCYNjQIDA+nSpYvPW/yklBw+fJgePXoQEhLC008/rekjgps3b7Jt2zYeffRRQkJCmDJlimZju1VUVCCEICwsjNGjR9O/f/8Gm2hJKT2Jj/Hx8UgpPcfuFrXCoCiKogCuT/+DBw+mR48efo0jpWTPnj3cvHkTcHVU7NKli09jFRUVsXnzZo4dOwag+Q3Tbrdz/fp1ioqKNB235viLFi1i8+bNgGtnSEJCQr2vKS0t5cMPP/TsmBg6dCj333//XQ0WQAUMiqIo9zS73c7mzZspLy9HCMHIkSP9LnhkMpk4cOAAp0+f9nkMdx+JmJgY5syZw5AhQ/yaU02lpaWedtnx8fHMnz/f790ft6uqqgJcKyzjx49n5MiRXr82JCQEu93ueWzRUqiAQVEU5R5WUlLCsWPHPH0c/FFcXIyUkvDwcF5++WVGjRrl0zjnzp3jzTffJDc3F4B27dpp+un622+/ZfPmzZ4bcmCgtk/nc3Jy+Nvf/kZOTg4APXv2JCYmpt7XXL58mTVr1iClxGAwMGfOHJ9XZZqKChgURVHuQe6W1DExMcyfP5+MjAy/xsvPz+edd97hxIkTgGvp3deb/H333cfgwYM1bRNtNps9qxbjxo3jpZdeajCPoLHcWz7j4+NJT0+nVatWXr+2tLSUvLw8zxzv9uOH2qjCTYqiKPeYnJwcPv74Y5588kk6d+6syZjuug0DBw70KVkyMzOT48eP89hjj2lehMnpdPLuu+/SunVrZsyYoenYbgcOHODcuXM899xzXs1fSsnp06cJDAykW7duSClxOByar3ZoWbhJrTAoiqLcYxITExkwYADJycl+jVNcXMznn39OVVUVQghGjRrl884Kk8lEUVERZrPZrznV5C45HRAQwLhx4/zeIlqf0NBQwsPDsdlsXp0vpWT//v2eXAohhObBgtbUCoOiKMo9wGw2s3v3bsaPH6/ZjSk3N5eVK1fy9NNP+5Q0WFxcTGlpKR06dABcN3itGicVFxfzySefMH78eE3ab9/Obrezc+dO4uPj6dGjh1dbHp1OJ0eOHKF3794YDAYqKioIDQ3VfEWlJrXCoCiKojTK1atXOXr0KFevXvVrHKfT6UlGTE5OZsGCBT7vMPjyyy/56quvPC2uteyyGBkZSWxsrOZ5Cm4BAQHk5ORw7do1wLucg/z8fDZu3MiZM2cAV6GopgwWtKZWGBRFUX7AKioqCA8Pv+N7X+3Zs4ddu3Yxb968BjP/a2Oz2TzL70ajkYCAAFq3bu3XnNxu3rzJN998w8MPP9wky/tVVVXs3buX4cOHYzAYPOWa62O1WsnLy+O+++4DXEFDfHx8syU1qhUGRVEUpUHHjh3j73//u6eAkj/BgvvD5cCBA3n00Ud9DhaWLFnCtm3bAFdZZK2CBXBtEb148aKnJbXWbty4wd69e7l06RLg3XbMrVu3smLFCk9uRkJCQovcAeENtcKgKIryA1VeXs6+ffsYM2aMX5+4jx49ynfffcfTTz/t9xL6rl27SEpKIi0tza9x3EpLSykoKPDs9vC2RbS3TCYTeXl5npoIJSUlDQY5NUtBl5eXU1xcTEpKimZzagy1wqAoiqLUymg0snPnTqSUREREMGHCBL+X54UQSCm93gFQk8ViYd26dZ5P/aNGjdIsWADYsmUL69at88xNy2ABYPv27axdu9ZTubGhYMFms7Fw4UJPs62IiIi7FixorVkDBiHEUiHEDSHE6duO/1gIcV4IcUYI8ecax/9bCJFV/bOJNY4/UH0sSwjxi+Z8D4qiKC3ZuXPnOHToEKWlpX6NYzQaPZUKMzIymD59uk8dEi0WCxcuXPAkSmrBbDZ7buAPPvggs2fPRq/XazZ+aWkpFRUVAIwdO5bZs2cTHBxc72tMJhMAer2eCRMmMGLECM3m01I06yMJIcQIoAJYLqXsUX1sNPBLYLKU0iKEiJVS3hBCpAOfAQOBBGA74K4wcgEYD+QBh4BnpJRn67u2eiShKMoPlZQSs9lMWFgYUkoqKiqIiIjwa7xly5ZhMpmYN29eox9DSCnJysoiLS0NIQQWi0Wzdsw2m4133nmH9u3b8+ijj2oy5u3jv/nmm9x3331MmzbNq9dcvHiRFStWMHPmzBa3mqDlI4lmrRIhpdwjhOhw2+FXgD9JKS3V59yoPj4VWFF9PFsIkYUreADIklJeAhBCrKg+t96AQVEU5Ydq+/btnDlzxlPu2Ndgwel0IqVEp9MxdepUAgICfMpZOH36NGvWrOHZZ58lLS1Nk2DB6XQSEBCAXq9nxIgRDXZ8bCyz2UxoaCh6vZ4HH3zQq/HddSOSk5Pp27cv0dHRms7JL1VV8Pbbmg7ZEnIYOgPDhRAHhBC7hRADqo8nAjXXsPKqj9V1XFEU5Z7UvXt3+vbt2+CyeX0cDgeffPKJXzsY7Ha7Zz6PPfYYHTt29Hk+NRUWFvLee++Rl5cHQN++fWnXrp0mYwNkZ2ff0iyqe/fuDXbs3LFjB8uWLcPpdGIwGHjwwQf93rKqCSlhxQro1g1+9jNNh24JAUMgEAUMBn4GfC5ce05q23ci6zl+ByHEXCHEYSHEYfe2IkVRlB+C3Nxc3I9ZExISGDFihF/b9XQ6HfHx8T43fDp06BDvv/8+FouFgIAAevToodn2wfDwcMLCwjwFnrTiHi8xMZE+ffo0uEIgpfRsL42NjSUpKUnzOfnl229h8GB45hlo3Rq2b9d0+JYQMOQBa6TLQcAJxFQfr1noPAnIr+f4HaSUi6SU/aWU/du2bdskk1cURbkbDh06xP79+z2f6n0hpeTw4cMYjUYAxo8f73PXyri4OBITtVvsvXnzJps2bUJKSXBwMM8//7ym+QF79+7lo48+8qwQTJ48ud5HOVVVVaxcuZLTp105+z179mTixIkto/9DZiZMmwbDh8PVq7BsGRw5AmPHanqZFvBO+QIYA+wSQnQGDEAhsA74VAjxf3ElPXYCDuJaYegkhEgFrgJPA9PvxsQVRVGak8PhwGazERwczEMPPeR3d0Oz2czXX39NUVEREye6NqKVmK1kF5ooq7QRGaInNSaM1qG1b1W8ePEiJSUl9OvXj5SUFE1v6Lm5uZw6dYqBAwfSpk0bzcZ1i4yMJDo6Grvd7tVWTIPBgMViwWq1aj4XnxUWwu9+B+++C8HB8Pvfw3/8B/jYAKwhzb1L4jNgFK4VhALg18DHwFKgD2AFfiql/Lr6/F8CswE78LqUclP18UnAG4AOWCql/END11a7JBRF+T6TUvLZZ59htVq9bqFcl5oloouKioiOjkYIQYnZyrErxYQaAgnR66i0OTBb7WSkRNUaNHz++ecUFwU6IFoAACAASURBVBczZ84cTXoilJaWUlpaSkpKClJKKisrfe5+eTu73c7WrVtJTk6mZ8+eXr3mxo0b7N69m6lTp2IwGLxqMNUs3AmNv/89lJfDnDnwv/8LteR1fJ93STxTx49qbVBeHQjcEQxIKTcCGzWcmqIoSosmhKBnz544HA6/bs4FBQUsXbqUSZMm0bt371s+vWcXmgg1BBJqcN0a3P+bXWgiI8UVMJSUlKDX6wkLC+Phhx9Gp9Np1kDpiy++oLS0lNdee42AgADNggVwNYu6fv16o5pRVVZWkpOTQ1FRUbP2f6iTlLByJfz3f8PlyzBpEvz5z9C9+x2n5ubmsn//fk0v3xIeSSiKoih1OHv2LHq9nk6dOnn9ybg+bdu2JSMjw9NSuqayShtRt60khOh1FJtdy/A2m40PPviAlJQUnnjiCb92ZbhVVlai1+sJDAxk8uTJPm/lrI3ZbOabb75h9OjRGAwGZs2a1WBHzEuXLlFSUkLfvn1p3749CxYs0LQolM++/RZ++lM4cAB694Zt22DcuDpPr6ys9Lsz6e1aQtKjoiiKchspJU6nk2+//ZaDBw/iz+PjiooKvvzyS88OhgceeIBWrVrdcV5kiJ5Km+OWY5U2BxHBrs+W7hoFYzVKpqusrOS9995j586dAMTExGhay6CwsJBDhw55tkt60z778OHDHDx40LP74a4HC1lZ8NhjroTG3FxYutSV0HhbsOBwONi0aRMHDx4EoFOnTrz22muaTkWtMCiKorQwFouFwMBAdDod06dPJzg42K/l8KKiIs6ePUuvXr1ITU2t87zUmDCOXSkG8OQwGEtKuHxwO60njOe+++4jPT3d53m4uXMBQkJCGDBggKa9JcrLy8nLy6Nbt26kpKSwYMGCenc/SCk5deoUqampREREMGXKFPR6vWarHD4rKvp3QqPB4Pr+P//zjoRG9+8yICAAo9HoCXDcLcS1pFYYFEVRWhD3sv/mzZsBVw0CX/7DL6WkoKAAgPbt2/P666/XGywAtA41kJEShSEwgGKzFUNgAP07tiMkOEizegMFBQUsWrTIs5Vz+PDhxMfHazI2uAoqrVu3DovFAtBg1cuysjLWrVvHoUOHAAgJCbm7WyUtFvjrXyEtDd56C154wbXK8Ktf3REs5OTksHjxYiorKxFC8MwzzzCunscU/lIBg6IoSgui1+vp0aOH35/k9+/fz6JFi3AXrfM22a91qIHu7cIQBd/RKzGStq3CmDVrlmarAMHBwZ7eF1oxGo2eZlHjxo1jzpw59ZajdjgcZGVlAdCqVStmz57N6NGjNZuPT6SEzz93VWj86U9h6FA4eRIWLrxj94P78ZT7d+l+7029KqICBkVRlLtMSsmBAwc8LaBHjBjR4GpAQ/r06cOECROIiYlp9Guzs7PZtWsXly9fBvB7d0BhYSG7d+8GXDfol156iaSkJL/GdLNarSxZssRT0jo8PLzBPIj9+/fzj3/8gxs3XK2LEhIS7u4OiL17XQHCU09BRIQroXHDhjt2P0gpWbt2LVu3bgVcxbLmzp1LcxUmVAGDoijKXVZZWcmePXs4cuSIX+OcPXuWf/7zn0gpCQkJYdCgQV7fCKWUnscEXbp0Yd68eZr1gjhz5gwHDhygvLwc8D8AATxjGQwGpkyZ0mAipsVioaSkBIABAwbw9NNPExsb6/c8/JKVBY8/DsOGwZUr8OGHcPRorQmNgCfvo+bulOYMdJq1cNPdpAo3KYrS0lRWVnoeFZSUlNCqVSu/bgCHDh3i5MmTTJ8+vVH1BgB27tzJgQMHmDdvHpGRkT7Pwa2srIzKykri4uJwOBxUVlZq1pwpKyuLFStWMGPGjFq3h95OSsnixYvR6XTMnj377tdTKCpyFV165x1XQuN//ZcroTEs7I5TL1++zJo1a5g1a5ZPFS+/t4WbFEVR7hUNlVguLi5m6dKljBw5kv79+ze6M6RbeXk5ZWVlJCYm0r9/f/r27evV9sHbZWRkEBwc7HNr7JqklHz66acEBAQwZ84cdDqdJsGCu510SkoKAwYMaHCFwGw2ExISghCCUaNGeb6/ayyWf1doLCuDF1+E3/621hwFu92OXq8nJiaGdu3atYgmV2qFQVEURWPelFh2Op1s2rTJqxtffT766CNKSkp47bXXGh0o/Otf/6K4uJjJkyd7dX5DQVBVVRVBQUEIIcjLyyM0NFSzugq7d+8mKyuLF154wavkvhs3brB06VImT56sScErv0gJq1bBL34B2dnw4IOuCo09etR6+ueff47T6eTpp5/2+ZJGoxG73U5cXJxaYVAURWmp6iqxfPFGGRU5Zxg0aBDBwcFe36hv526zHBAQwKRJk5BS+rSqYDabMZlMnk/u9akZBEWFGqi0OTh2pdgTBJWVlbFkyRKGDh3K4MGDNUtqdGvTpg0VFRUNlsZ2v5eYmBh69+5NQkKCpvNotL17Xbse9u+HXr1gyxaYMOGO02o+nurQoQNOp9Pn3hVOp5Ply5dr3rRLrTAoiqJobPf5G0SFGm75j72UkitXr3Js2xomT55M3759fRrb6XSyevVqoqKifNpzn52dTVhYGLGxsTidToQQXt2Ujl0pxmp3eoIfALPVjiEwgIyUKKSUbNmyhd69e2tSV8Fms7Fx40ZSU1Pp1auXV685fPgw+/fvZ+7cuV51oGxSWVmuFYXVqyE+Hv7wB3juOaglMMvNzeXjjz/mmWee8Xl3jNVq5eTJk/Tr1w8hBDk5ObRp04aIiAjNVhjULglFURSN3V5i2Wa1UGlzkJiQwKuvvupzsAB4mjL50pjJbrezdu1aTynmgIAArz/BllXaCNHferOzlBWxe/0/MZlMCCF44IEHNCvCpNPpMBqNlJWVNXiu+4Nv27ZtSUhI8OwquCuMRleL6fR02LwZfvMbyMx0FWCqESxIKT07PeLj4+nVq1et5bq9de7cOTZs2EBubi7gKtalVZKpm1phUBRF0VjN5XtT0XX2bVtH+rAHGN2/e61tor1x5swZEhMTad26daOXqk0mE6GhoQghKCgoICoqqtGfwGtbYSgouM7x3Zt49pmnNAkUKioq2L17N+PHj8dgMOB0Out9/OB0Olm/fj3R0dEMGzbM7+v7xWJx7Xr43e9cCY2zZ7sSGuv4vXz++ecYjUbmzp3rU8ElKSXfffcdOp2Ozp0743Q6uX79+h2PYLTcJaFWGBRFUTRWs8SyDGlFu5T7GNi1vc/Bgtls5quvvuLbb78FGrf33mg08s4773hqPMTFxfm0XJ8aE4bZaufGzZtcOncSs9WOLqw1s+e+rNmqgtFo5Pjx4+Tl5QENVy4MCAjAarVitVo1ub5PalZo/MlPYNAgOH4cFi++I1gwGo2e3Q59+vRh6NChfu3a2LNnD+4PwgEBAU2er+H1CoMQIhH4CTACiAYellKeFkK8DuyTUh5oumn6T60wKIrSXCwWCwcOHGDYsGF+leu1WCyeEscFBQXExMQ0OrlRSsnWrVvp37+/30lwJWYrX361nqvZmYx7fBadE6J9DoI8Y5aUcPXqVbpXVzU0m831Pm4pLS1l27ZtTJw4kYiICJ8TAzXxr3+5goT9+6FnT/jLX2pNaAS4du0aS5Ys4aGHHiIjI8OnyxUVFbF3714mTZpEYGAgZWVlhIeH1/tvrNlXGIQQ3YFTwEwgH2gPuP+VtAcWaDEZRVGUH4LMzEx27drleZ7si8LCQt566y1OnToFuFYGvA0WjEYjK1eu9DQlmjhxol/BQllZGSUlJbQONfD0I5P58avzGJjWzu9gAVwFozZs2OBZJWgoN8Nut3Pp0iWuXbsGNG+lQ4+LF+GJJ+D++yEnBz74AI4duyNYsNvtngZg7dq1Y/To0XTq1Mnny5aVlXH27FmuX78OQGRkZLN21fRqhUEIsRmIACYCVYAV6C+lPCqEeAL4f6WU9zXpTP2kVhgURWlqNVcEioqK/LpJOxwO1q9fz5AhQxpdpyE/P59PP/2Up556iuTkZJ/n4J7H22+/TXR0NDNnzvRrLLebN296ikSZTCbsdnu9CX/Xrl0jOzuboUOHAq4dFO42zs3KaHQVXXr7bdDr4ec/d60w1JFcuHr1ai5fvsz8+fN9mq+Ukp07dxISEsKQIUMAV62LmqWhG3I3chiGAX+SUlYAt0cYBUC7O1+iKIpy7zhx4gRvvfWWp1+BL8GCxWJh69atWK1WdDodU6dO9TpYsNlsXLhwAXA1U1qwYIFfwYL7E79Op2PSpElMmjTJ57FqslgsfPDBB+zYsQOAsLCwBncHnDp1in379lFVVQXQ/MGCxQJ/+5ur5fQbb7i2R2Zmwq9/fUewcPXqVc/vbujQoUydOrXR83V/kBdCcPPmTYqKijw/a0ywoDVvA4b6alLGAJUazEVRFOV7KykpiU6dOvm03dHt2rVrHDx4kJycnEa/dvfu3axcuZLS0lLAv5tqUVERb7/9NmfPngWgU6dOfuc/uOcVFBTEo48+yvjx4+s9Pysry9NNctSoUcybN6/5b5buCo3p6a5eDwMGuBIalyyBWhIMjUYjS5YsYf/+/YBru2Rj24JfuXKFhQsXelpWP/HEEzz00EP+vxcNeBswHAReqONnTwJ7tZmOoijK90dZWRkHDx4EXCsKU6dO9WkHQnFxMeCq8Dd//nyvn3NLKT2fZocPH86MGTP82svv1rp1azp06OBzf4vbXbhwgb///e+edtldunQhrJZGS25Wq5W1a9d6doUYDIZGN9Py2759rhyFJ5+E0FBXTYUtW1zVGmuwWCxcvHgRgOjoaB577DEGDRrU6Mu5a0eEhYUREBCAyWQCGt4p0py8ncnvgClCiK24Eh8lME4I8RHwKPCHJpqfoihKi3Xo0CF27NjhVXGhuhw+fJh33nnH82m6MZ0iv/rqKz777DOcTidBQUE+VwkEV97DihUrsNls6HQ6pk2b5vc2PbvdDkBqaipDhgyhXbu6n15LKcnMzERKicFgYObMmTz88MN+Xd8nly65goShQ119H5Ysca0qTJxY6+nbtm3zJJgC9OjRw5PH4g0pJStWrGDjxo2AK/CcM2cOcXFx/r8XjXnVS0JKuVsI8QjwBrC0+vCfgMvAIy19S6WiKIqWrFYrBoOBUaNG0adPH7/aQaenp2MymXxa8m/fvj1RUVE+X7umqqoqrl+/TklJCW3btvV7vB07dpCdnc3s2bPR6/UNlrE+d+4cq1atYvr06XTq1Kne4KJJFBe7EhrfesuV0PjrX7t6QNyWoyClJCsri9jYWFq1asXw4cPp27dvo1dA3MmLQgji4uJuef1db79dh0ZXehRCpAGxQJGU8nyTzKoJqF0SiqJoYceOHVy4cIEXX3zR534F2dnZnDp1iilTpjTq5iCl5MCBA0RHR9O5c2efrl1TUVERBQUFpKenA64VgcBAbXoSnjlzhqtXrzJmzJg6x3Q4HJSUlNCmTRucTifnzp0jPT29eW+YViu8+66rKmNJiauE8+9+V2uOAriqUb755pv079+fiXWsOjTkwoUL/POf/+TFF19s8pUELXdJNPgvQwhhAPYDv5BSbpVSZgFZWlxcURTl+yY1NRWHw+HXjfX69evk5uZiNpvrfZZ/O4fDwYkTJ2jXrp0mAcOOHTvIy8ujc+fOBAYG+vWerFYrX331FWlpafTu3Zvu3bt7ijFB7a2xt234kvz8fF599VUCAwNvOb/JSelqDPWLX7jqKowf7yq8VEujq4qKCi5cuEDfvn0JDw9n5syZJCYmNupydrudyspKIiIiSE5OplevXs2fl+Enb+swFAOPSSm/bvopNQ21wqAoiq8KCgooLCz064ZWVVVFaWkpcXFxSCmx2+1e72TIy8ujXbt2BAYGUllZ6VnK9kV5eTk6nY7Q0FAqKiqQUhIREeHTWDU5nU4+/vhjunTpwuDBg2/5Wc3eGoHSjlUKquySdjoTAU4bXbp08fv6jbJ/v6t+wr/+Bd27uwKFBx6o8/SdO3eyd+9e5s+f79PjJyklixYtIjQ0VLNaFt66G3UYtgG117tUFEX5gdu5cyc7duzwJPH5YvXq1Xz22Wc4HA6EEF4HC0ajkaVLl7J3r2szWkhIiM/BgtVqZdGiRWzZsgWA8PBwv4KF0tJS1q1bh9VqJSAggOeee+6OYAEgu9BEqCEQncPK9jWfkPfdCUINgVQFRTVvsJCdDU89BUOGuJIbFy92JTTeFixIKTlx4gT5+fmAq57CvHnzGhUsSCnJzc31lK4eNmzY3W+Q5Sdv15/eAj4RQgQCXwDXuK2Ak5TyksZzUxRFuWtqrgI8/PDDPj+GcN8wxo0bh8Vi8bq8s7tTY3R0NI888ohfN1aHw4FOp8NgMDB+/PhGL6fXpbS0lDNnztCrVy86dOhQZyBTYqqiTXgIwhBKSqduxCYkE6LXUWxupqZRxcXwhz+4Ehp1Ovif/4Gf/azOCo02m41t27bRtWtXEhISCAoKatTOB/h3Euezzz5LWlpa8z5uaSLePpKoWbip1hdIKRv8f4EQYinwEHBDStnjtp/9FPj/gLZSykLh+pf3JjAJMAPPSymPVp87C/hV9Ut/L6X8qKFrq0cSiqJ4S0rJqlWrkFLy5JNP+vSJ3ul0smnTJsLCwhg1alSjXpubm8uaNWt49tlniYmJafS1ayooKOCzzz5j2rRppKSk+DUWuHpc5Ofn06v6WX9DpYrPnz/Pl19tYNADjxPd+t81IsxWO4bAADJStNnlUSurFd57z5XQWFwMzz/vSmisJWAqKiri+PHjjBkzBiEERqORqKioRv3dFxcXYzabSUxM9OSb9O7du9ENw7TUrEmP1eoq2tRYy4C3geU1DwohkoHxwJUahx8EOlV/DQLeAwYJIaKBXwP9cQUvR4QQ66SUxRrNUVGUe5wQgvbt2/s9ht1ux263N7qjYqtWrTQrmtS6dWvatm2rWTnlPXv2kJ2dTbdu3dDr9XUGC+73HBMTQ1xcLGaLlWCrnRC9jkqbA7PVTpd2TRQsSAlr1sB//ZcroXHcOFeeQu/edb4kJyeHgwcP0rt3b2JiYoiOjm7kJSUrV64kICCAOXPmoNPp6Nu3r7/vpEVp9LZKvy8oRAdgfc0VBiHEP3EVh/oSV1OrQiHEQmCXlPKz6nPOA6PcX1LKl6qP33JeXdQKg6IoDbl48SJBQUEkJSX5PMalS5eIiYkhMjKyUYFCSUkJp06dYtiwYX5vK8zPz+fQoUNMmTJFk0qB169fJywszNMsSkpJeB3L+QC7du3CbDbf0n+itl0SWnS7vMOBA66Exr17/53QOHEi3PY7dTqdHDhwgKioKLp27YrT6cRsNtf7vm5ntVo5duwY/fv3R6fTkZ+fT0REhCZJpFq5G0mPTUYI8TBwVUp54rYfJQI1e8PmVR+r67iiKIrPHA4HmzZtYteuXT6PUVVVxeeff87OnTuBxhXgOXXqFHv37vX0XPDHzZs3uXjxoiZjVVVV8eGHH/L1165NcmFhYQ3eVK1WK1arlZofSFuHGshIiWJkl1gyUqK0Dxays+Hpp2HwYMjKgkWL/p3QWMffw4kTJ8jMzARcJZgbEyyAa1Vi8+bNntLQCQkJLSpY0Jq3OQxLGzhFSilf9OqCNVYYhBChwE5ggpSyVAhxmX+vMGwA/o+U8tvq1+0Afg6MAYKklL+vPv7/AGYp5V9rudZcYC5ASkpKP18auiiK8sNmt9vR6XSe59bh4eGNLshUs+BRbm4ucXFxXo1ht9spLy8nKioKp9NJeXm5z70gioqKKCsrIzU11dNjorGJejUZjUbPsnxWVhaJiYl11g2orKxk27ZtDBo0yLNttNmKLxUXwx//CH//uyuh8Wc/qzOh8fr16+zdu5epU6cSGBjY6FbRUkouXLiA1WqlZ8+eSCkpKCho/qqUjXA3VhjGAKNv+3oMeB54pPrPvugIpAInqoOFJOCoEKIdrpWDmr1Zk4D8eo7fQUq5SErZX0rZX4tSp4qi/LBYLBY+/PBDz6pCdHR0o4OF4uJi3n33XU9nx+TkZK/HWLVqFZ988gkOh4OAgAC/Gkd99dVXbNiwAafTiRDCr2Dhu+++4+233/Y0i0pLS6u3yJC7XHJeXh7QTKWNrVZ4801Xy+m//hWefdbVcvo3v6lz94PZbCY7O5vCwkKg8a2ihRAcPHiQQ4cOeYKilhwsaE5K6fMXMAI4C2Q04jUdgNN1/OwyEFP9/WRgEyCAwcDB6uPRQDYQVf2VDUQ3dN1+/fpJRVGUmpxOp9y4caM8d+6cz2PYbDa5cuVKeeXKlUZdV0opc3Jy5IULF3y+dllZmbRarVJKKYuKimRpaanPY0kpPWNZrVa5c+dOabFY6jzXaDTKr7/+2vNe6jtXU06nlKtXS5mWJiVIOW6clMeP13qqw+GQ27dvl/v27fMcc79HbxmNRrlmzRppNpullFKWl5dLh8Ph+/ybSVVVlZRSSuCw9OM+X/PLrxwGKeUe4G+46jQ0SAjxGbAP6CKEyBNC1PcYYyNwCVcZ6sXAvOprGnElSB6q/vpt9TFFURSvnDhxgrKyMoQQPPjgg3Tt2rVRr7fb7ezZswebzUZgYCBPPvkkycnJXr1u7dq17N+/H4CUlBSvW1nfzmw2895773nyJaKjo/1qgrVlyxaWLVuG0+lEr9czatSoeldKMjMz2b9/P0aj6z+/vvbVaJQDB2DECHjsMTAYYONG2Lq1zt0PAQEB3Lx5k6KiIs+xxu4WsVqtnD9/nmvXrgGuYlctqeV0bXbv3s3bb7+NzWbTdFwtuoxcAjK8OVFK+UwDP+9Q43sJvFrHeUv5d9dMRVEUr1VUVLBx40b69u3rc/Og3Nxcdu3aRdu2benWrZvXr9PpdJ6tlr5yF3QKDQ1lxIgRpKWl+TyWrM5hE0KQnJyMXq+/JVHxdvn5+dhsNtq3b0///v3p2rWrX0GK1y5fhv/+b1ixAuLiYOFCmD0baimkdfXqVbZs2cJTTz1FWFgYTzzxRKPrIOzevRu73c7YsWOJi4vjP//zP5snIPJDbm4ubdu2JTg4mNTUVJxOZ71/l77wK0yqrvz4PK68AkVRlBbLfZMODw9n9uzZjB8/vtFjmEwmwNWAat68eV4FC1JKjhw5gslkQgjB448/zvDhwxt9bXDdsN99913PM/jBgwf7XNjJYrGwcuVKTp48CbjabI8ZM6bOm6uUki+//JLt27e7lqcDApo+WCgpgZ//HLp0gS+/hF/9ypWnMHfuHcGC++YYFBREZWWlZ4eIt8FCzZtrWVkZZWVlnmMtPVgoKipi6dKluEsHpKSkMHr0aM3n7dUKgxCitqZTBqAz0AZ4WctJKYqiaKm4uJjly5czbtw4unfv7lNL4RMnTrBhwwZ+9KMfERsb6/WNuqSkhE2bNlFRUcHIkSP9SgiMiIggNDTUrxUKN4PBgM1ma3DZOjs7m5SUFHQ6HY8//jgRERFNn9RotbpWEX7zGzAa663QKKVk06ZNAEyaNImYmBjmzZvXqDnm5+ezdu1ann76adq0acPkyZNb/GOHixcvYjQaGTBgAG3atOHJJ5+kY8eOTXpNb38jAbiSD2t+lQNrgLFSysVNMz1FURT/RUREkJCQ4Ff1xI4dO5KRkUFUlHfVCcvKygCIioriRz/6ESNGjPDputeuXWP79u2A63288MILPmfmG41G1qxZg8ViQQjBjBkz6N+/7h13+fn5LF++nCNHjgB4lrybjJSwdi306AHz50OfPnD0KCxdekew4HS6OhYIIdDpdAQGBt7yiMUb7sArMjKS4OBgqqqqAFp8sACuuh0HDx70/B66devW9CshWmVPtvQvtUtCUe4tTqdTHjx4sNFZ8TXl5+fLzZs3e3YCeCszM1P+9re/lZcuXfL52m579uyRf/3rX2V5ebnfY125ckX+6U9/kjk5OXWe43Q65c2bNz1/Pn36tLTZbH5fu0EHD0o5fLhr50N6upQbN7p2RNQiLy9PvvHGG7KgoMAz58ZavXq1/Oyzz/yacnO6evWqfP/996XRaJRSSmkymaTdbm/wdTT3LgkhxP8IIRLq+Fm8EOJ/NI1iFEVR/JSXl8fGjRs5deqUz2NcvHiRs2fPUlFR0ajXtW/fnkGDBhEfH+/TdYuKijxZ+ffffz+vvPJKo6sQuhUUFHDihKuQbnJyMq+//nq9Tai2b9/OkiVLPO+5e/fuPnXp9NrlyzB9OgwcCOfPux5FnDgBDz54R4VG94pAVFQUUVFROBwOwPsVBbPZ7Pk+ISGBpKQkzRMDteRwODxzdv/9u/NoQkNDm72plbeVHh3AECnlwVp+1g9XjYS7147LC6qXhKLcG2pWXczPzyc+Pr5Rz7NtNhtlZWW0adMGKSVVVVX1Fi1yy87O5uDBgzz++ON+/YdcSsl7772HXq/nRz/6kd/5AmvWrCEnJ4cf//jHdd74HQ4HDocDg8GA0Wjk8uXLZGRkNG2uQkkJ/J//4yq+FBDg6v/w859DHaWV161bR1lZGTNmzPDpcjk5OXzyySc8++yzdOjQwY+JNw8pJQsXLiQmJobHH3/cc6yxfyd3o1tlfTOMAiwazEVRFMUvubm5rFq1iunTp9OuXTsSEmpdGK3XmjVruHbtGq+99hqBgYFeBQvg+vRaWFiIyWTyafeAyWQiNDQUIQSPPvooYWFhPt+wc3NzadWqFZGRkTzwwAMA9QYLixcvJjExkSlTphAdHd3oTo2NYrO5VhH+939dCY2zZrkSGmtp+GWxWDAYDAghPDko7m2l3qhZejshIYGMjAzNuoA2BZvNRmZmJunp6QghGDBgwC29KZqt3HYd6gwYhBCjcJWEdntJCPHQbaeF4KrIeEb7qSmKojROVFQU7dq186ss8vDhwykvL/dqGb60tJSioiLuu+8+unfvTteuXX1aXSgpKWHRokUMHz6cIUOG+PwoA1x9HT7++GM6d0unY7+RNbpDBt7S8MnhEdSplwAAIABJREFUcKDT6dDpdPTs2ZMmL58vpWtr5M9/7toaOWaMq5NkRu1lfK5du8by5cuZNm0anTp1qjc5sy7/+Mc/qKqqYu7cuej1+lu6Z7ZER44cYcuWLbzyyivExsbSr1+/uz2lW9T3/4iRwK+qv5fAC7WcY8VVGnq+xvNSFEXxis1m48SJE/Tr14/w8HCmT5/eqNdLKdm1axd6vZ5hw4Y1alVi/fr13Lhxg/nz53tuvo29thCCVq1a0a9fP5+rPoKrQ2Xbtm0JCQnhoUcfp8AegtXuJCrUQKXNwbErxZ4ukVevXmXVqlU888wzxMXFcf/99/t8Xa8cOgQ//Sns2QPdusGGDbXmKEgpMZvNhIWFERsbS9euXRvdXyMnJ4fk5GQCAgK4//77EULc9U/mdbHZbOzbt4/k5GRSU1Pp27cv8fHxxMbG3u2p1arOdR0p5W+klAFSSveWysHuP9f4CpZS9pVS7mu+KSuKovzbqVOn2LBhg6fxkS+MRiNGo7HBBLgSs5XD2Tf5+kw+x64UM3zMeJ577jmfVhVyc3NZvHixp6DT2LFjfS7CdObMGd59913cHXkdYW2JDAsl1BCIEIJQQyChhkCyC10Jc1FRUT5fq1FyclxNoQYOhO++g/feg5MnYdKkWltOr1u3zlOeWqfTMXXq1EbdPLOzs1m2bBlnzrgWvdPS0pq8NoEv3P/OAgICOHr0KJcuXQJctTHat29/N6dWL69yGKqDBkVRlBbDvaSekZFBXFwcibUU9alPfn4+kZGRhIeH88gjjxAQEFDvJ9ESs5Uj2YWc3Pkl0W1iCRs0iotmSUZK7Ul6DQkKCsLpdGIymQgLC/NpDIvFQlBQEJ07d2bs2LGe30FZpY2o0Fv35BdcOkfelWz6vDCD0NBQn5MHvVJa6mo5/eabrsDgl790PYqoJbejrKyMsLAwdDod6enpJCYmUmK2kmOsrPE4JeyWxyk1lZSUUFxcTGpqKh06dOCRRx5pVLnu5nbgwAFOnz7N7Nmz0el0vPzyy01b20JDdQYCQogUIYS+xvf1fjXflBVFudedOnWKd9991/PpvLHBgsVi4eOPP2br1q2Aq3xwQ8vW2YUmwkOCSOqQRruU1Ds+tXvj2rVrnsZTsbGxvPTSSz4vP69fv56PPvrI0yxq2LBhnryLyBA9lTbHLedXWW3gtGO1Wn26nldsNnj7bej4/7P33vFRlun+//vJlPRKEkpCGiShhBI6oSNNRAUpYtcVEXVX3HbOnrPN/e3Zc3Ytu4i66n5VYEUEFZSiKEgXQVroEkgIKYQkpCczk0y7f388mceUmclMCP15v17zYvLMU+6ZhLmv57o/1+fqAS+/DPffL+sV/ud/nAYLZWVlvP766xw5cgSA5ORkevbpz7HCamU5xWy1k5lfSZXR+bjXr1/Pxo0bleWdAQMGXN0y0HZQXV2tlIAGBgYSHh6u/B5ulmAB3GcYcoGRwAHkttNt1V/e0GWVKioqtw6dOnUiKirKa0c+h8Le19eXuXPneuSYaDab2bJlC1JUD7p360qvgcOU1/x1GipdTGTOyMzMJCsri/T0dHx9fb1eW3eksiVJokePHi4V/4mRgRzOvczZzEw6d40ltEt3IhN7M3lcxhUJQt0MrLmgccIEWdA4aFCrXe12O+Xl5URFRdGpUyfGjBnTTLuRW2ZQgjFA+Te3zEB6nGxnfejQIQYNGoSvry/Tp09v12d5rSgtLeWdd95hxowZpKenk5aWRlpa2vUeVrtwFzD8BMhp8vzGdbdQUVG55TEajZw/f560tDS6devG/PnzvTq+pqaGjz76iAkTJpCSkkJSUpJHxznaGyfqgjBFRSsTGIDJYiPE3327ZEf754iICCZNmsSECRPaNWnX19fzySef0L9/fwYMGOA27R4WoGdA93COfZOL1S6Iio0ntUuEy7T+FdFU0NirF2zcCHfd5VSjAPDFF19w5swZnn/+eXx9fVtZZjtbTmkamJWWlrJlyxYCAwPp37//1a/uaAdlZWVUVlaSnJxMVFQU48eP9/jv7UbGZcAghFjR5PnyazIaFRUVFRfs3r2bw4cPk5CQ0C7XQ39/fwICAjzKSgghyMnJoUePHgQFBfHTn/4Uk00iM79SPpdOg8liw2i2ktrFdW8Jm83GihUriIqK4uGHH74ir39fX198fHzcCjONRiP79u1j/PjxRIYE8NNnnr56/QXy8uC//xtWrYKoKFnQuGCB05bTpaWlSr+GoUOH0qNHD5fjciynNA3M8i/kYDbVQWo0MTExStnhjcrmzZuprKykZ8+eSJLU7u6kNxoeOT3eCqhOjyoqNycOcaPFYqGsrMwrjwK73a6krx3NiTxJXWdlZbF69WrmzZvX7E6+ymgmt8zQphivvr5eWZvOzc0lIiLC6/JAkO9Ud+zYwT333IOvr2+b4z979ixr1qzhkUceuXpuhi0Fjb/4BfznfzrVKADU1tayZMkSMjIyuOOOO9o8fZXRTGZ+JQF6rRKYHd71FcJUwzOLnr4hG0OVlZWxa9cupk+fjr+/P+Xl5fj5+bVbzNqRXBOnR0mS3vfiPEII8WQHjEdFRUVFYffu3eTk5PDoo4+i0+m8NjTKz89n8+bN+Pn50b9//zaDBYetdEpKCrNnz6ZXr17NXg8L0JMe5/6O/fLlyyxbtozp06eTlpZGYmKiV2NuislkIi8vj7KyMmJiYpyOv7KyksuXL5OSkkJKSgrPP/98u4KTNnE4NP7pT1BWBo88An/5C3Tv7mRXCwUFBSQlJREcHMzMmTM9Lm8MC9DTM0zD11u30r3vUKIjI7jvnhlEhQXdcMGCI5i1Wq3k5ORQWlpKfHw8nTp1ut5Duyq40zBMpLluIQwIBaxAOdCp8fhqoPJqDVBFReX2JSIigqqqKq8bBDnKDRMSEliwYIFHVRRHjx5lz549LFiwAH9//3YL0zp16kTv3r3b3YL64sWLlJSUMGjQILp3787ixYvR6VzrJL766iuKi4vp0aMHGo2m44MFIWDDBlnQePYsjB8Pr77qVNDoYPv27Rw8eJAXXniBoKAg+vXr59UlQ/x1VBYXMHroQHrFedZO/Fpit9tZuXIlnTt3ZurUqXTp0oVf/OIXN1x1RkfjzrgpQQiRKIRIBB4B6oD5gL8QoiuyLfQDjduvYkGviorK7UR5ebliZJOWlsY999zj1RfxDz/8wGuvvcbly5cBPC65jIqKavckn5+fzwcffIDZbMbHx4e777673cZI33//Pd9++63SmdFZsHDx4kVMJhMAd955J08++eTV6Vx46JBc8TBzprz8sGEDbN/uNFjIz8+nslK+d8zIyODhhx/2Smuyd+9eNm3aBEBoaCgvvPBCqwzP9UQIQUlJCSAbLnXt2rVZJuFWDxbATcDQgr8D/yeE+FgIYQMQQtiEEGuAvwJLrtYAVVRUbi+++OILNm3apNSte0tMTAzJyckeTVYXLlzgwIEDynFz5871uNlUU+x2O9XV1dTW1ipr8LuySt36BzQlNzeXmpoaQA4AFi5c6HICqq2tZdmyZezZsweAsLCwdjW7ckteHjz8MAwdCqdPwz//CSdOwN13O61+MJlMrFy5km+//RaA4OBgjzQUTTNH9fX1GI1G7HY74DxQup7s3buXd955h6qqKgAmT57crv4WNzOetrc2AfcKIbY4eW0K8LkQIuAqjK/DUEWPKio3LkIIhBD4+PhQXV2N3W4nPNzzVHR5eTknTpxg3LhxXtXjf/bZZxQVFfH00097fYdYXFxMaWkp/fv3B+Sgoabe2kqwZzRblR4OzjAajSxZsoT+/fszY0bL/n7N36PjjvbMmTMkJCR0vOlPdTX89a/wj3/IgcHPfw6/+Y1TQaPJZCIrK4uBAwcCcg+Hbt26eTzRl5aW8vHHHzNz5kxiY2Pb1br5amK32zl16hRdunQhKiqKmpoacnJy6N+//9XJ5lwlOlL06GmGoRiY5+K1+UBJRwxGRUXl9kMIwfr169m0aRNCCEJDQ70KFkDupXDgwAHlLt0dtbW11NbWAjB9+nQWLFjQrnTy7t272bFjh7J04OPj08x0yFkPh6YUFxcDEBAQwEMPPcTUqVNdXuvQoUO8+eabSkq8V69eHRssWCxyFqFnTzlgmDcPsrLkaggX2YvDhw+zYcMGxWciPj7eo2DBYrEA8rJDcHCwklG4kYIFkHUwmzZtUlwoQ0JCSE9Pv6mChY7G0wzDYuAfwGbgE+QAoTNyEDEVeEEI8fpVHOcVo2YYVFRuXLZv345Go2Hs2LEeTxx2u53a2lpCQ0MRQlBXV0dwsPu+DjabjTfeeIOoqCivu1qCbMLk6+tLYGAgRqMRkCd8B7uySgkP0Dd7D0IIKo1mxqX+6Btw/PhxPvvsM5544gni4pw76wshaGhowM/PD5PJxJEjRxgxYkTHTlhCyEZL//EfcoAwbpwsaHTSVlkIQVZWFkFBQcTGxmKxWKioqKBz584eX87R3fOJJ5644QIEkC3Hc3NzueeeewC54iUyMvKGHKunXJOyyqYIIV6TJKkO+CNwZ5OXCoCnhBDelGCqqKioUFBQgJ+fH1FRUUycONHr49evX09BQQHPPPMMOp3ObbDgSHdrNBqmTp3aLkGi2Wzm3XffJTk5mVmzZjULFBw4Mx1yuEEKIaivr8ff35/evXtjMplcCjKFEHz00UfYbDYefvhh/P39O74F9eHDskPjzp2QmioLGmfMcOnQaLPZ2Lx5M/Hx8cTGxqLT6TwKFurq6ggMDESSJOLi4pQA70aZhC0WC1qtnBGqqanh8uXLmM1m9Hr9DekieT3xyrhJkn/DsUBX4BJQKG4S5yc1w6CicuNgtVp5/fXXiY6O5qGHHmrXOQoKCigvL1fW0F1RV1fH6tWrGTt2LCkpKV5fx2KxKKn206dPExMT47J00ZnpkEPDsGvrZkpKSliwYIFLPwFHrwuQ+04ADBw4sGMn1/x8uXvkypUQGSn7Kjz1FDhZTqipqeHw4cOMHz8eSZIoLy8nPDzcYz+ES5cu8f777zNz5kz69u3bce+hgygpKeHf//43s2bNomfPntjtdiRJumGCmY7gmmcYHDQGBwWNDxUVFRWvcHwha7VaHnjgAa88A4QQHDhwACEEI0aMoHv37nR3YhrUEj8/P3Q6nbJW7g1FRUWsWrWKOXPmkJCQQJ8+fdzuLxs7hZNbZqDSaCbYT8vA7mGEBehJTU11W7ZZWVnJqlWrmDJlCsnJyaSnp3s9XrfU1PwoaBRCFjP+5jfg5ndw4cIF9u7dS69evVqVEbrCZrNRWVlJZGQknTt3ZtiwYXTr1q0j38kVYTKZqKmpoXPnzkRGRtKzZ0/FkfFGM4a60fA4YJAkKQSYDsQBLdU2Qgjx544cmIqKyq1FQ0MDq1evpnfv3gwbNqxdngd5eXkIIRg+fLjbu0CLxcK+ffvIyMhAq9Xy6KOPtuuuMTIykvj4eK8sfh1ukEajkTVr1uCTnk74wIFtegqEhIQQHh7e8fX8Fgv8v/8HL74Ily/L5ZJ/+Qs40U4IIcjMzMTPz48+ffrQr18/4uPjvQrsPv30U4qLi/npT3+KRqNh8uTJHfhmrpxVq1ZhNptZtGgRGo2GWbNmXe8h3TR49JcpSdIoYCOy26MzBKAGDCoqKi7R6/UEBgZ6re4vKyvD39+fwMBAZs2apaw3uyM/P58dO3bQuXNnUlNTvQoW8vLyOHToELNmzUKv1zN37lyvxuvA398ff39/twHA2bNn+f7773nwwQfRaDTtEmK6xJmg8ZVXoA3vgMOHDxMWFkafPn2QJMmjYOHChQvExMSg0+nIyMigoaHhhrlbr62t5dChQ4wdOxaNRsOkSZNu6HbYNzKe/kaXABeAoYCfEMKnxcMj2a4kSe9LklQqSdLJJtteliTpjCRJxyVJ+kySpLAmr/2XJEnZkiRlSZI0tcn2aY3bsiVJ+o2H70FFReU6kJWVhclkQpIkZs+erfgWeILZbGb58uVs3rwZkM18XH3RCyEUp8EePXrw3HPPkZqa6vV4a2pqKCoqUkovvaGkpISPPvqIhoYGJEli/vz5bVpMm0wmDIbWZZdXxOHDMHEi3HuvHDisXw87djgNFsrKyvjss8+wWCxIksRDDz3EnDlzPL5UcXExK1asUMoPu3fvrnRpvBEoLi5mz549FBTIK+nx8fHtdvS87XEYprh7INs/T/dk3zbOMxYYBJxssm0KoG18/jfgb43P+wDHAF8gEcgBNI2PHCAJ0Dfu06etaw8ePFioqKhcW6qrq8Wf//xn8fXXX3t1nN1uV56fOXNGVFVVtXnMt99+K/7yl7+IiooKr8d56dIlcfbsWeXaFovF63MIIURBQYF49dVXRVFRkdPX7Xa72Ldvnzhy5EizbR1Gfr4QjzwiBAgRGSnEG28IYTa7PSQvL0/89a9/Ffn5+R5fpqqqSmRlZSk/nzx5st2fWUdjtVrF+vXrxf79+4UQ8udbWVl5nUd1/QAOiSucux0PTxfL8hsn7isNTnZLkpTQYltT98j9gCO0vRdYLYRoAHIlScoGhjW+li2EOA8gSdLqxn1PX+n4VFRUOgaH2j8kJIRHHnnE434OIDsffvLJJ4wePZoePXp4nCXo16+fYvzkDUIINm/ejMlkUu6MvdER5OXlcfnyZYYMGUJsbCzPP/98m8sQAQEBiqixQ+7EWwoa//M/4b/+y6mgUQjB3r178fHxISMjg7i4OH7+85+j17vvwtmULVu2kJeXxwsvvIBWq70hKiBMJhP+/v5oNBoMBoPSa0OSJMLCXK2mq3iDp/8r/gT8RpKkbUKItq3U2s9PgDWNz2OQAwgHhY3boHmVRiEw/CqOSUVFxQuqqqr46KOPmDZtGomJicTHx3t1vFarxWKxKF/47jh48CCXLl3i7rvvJiQkhNGjR3t8ncrKSoKCgtDpdIpeoT2T96FDh7h06ZLiAtgyWLBYLOzdu5fhw4fj7+/P/PnzO65PgtUqCxr/+EdZ0Pjgg7I7o5vPXJIkLl26hEajUfwQ2goWrFYrBw4coH///gQFBTF58mSvA6uryb59+9i9ezeLFy/Gz8+P+fPn3zBLIrcSnv62ZyA7O+ZKkrQPqGjxuhBCPHYlA5Ek6bfIrbM/dGxyspvAue7CqReEJEkLgYWASzc1FRWVjsUh9vPmC1sIwcmTJ+nTpw96vZ4nn3zSo+ONRiMGgwGbzebV5GUwGHjnnXdIT09n6tSpXt+Bnjt3jujoaEJDQ5k+fToajcalA2N5eTl79uwhPDycAQMGeHUn7xIh4Isv4Ne/hjNnYOxY+eehQ53uXlpayubNm5k1axYhISHcd999XjlGVldXs23bNrRaLcOGDbsh7tgvXrxIaGgoQUFBJCYmNgsw1WDh6uDp/7DRyJNyDeAs93RF5k2SJD2GHJTc0bjmAnLmoGmRdSxQ1Pjc1fbmgxLiX8C/QDZuupIxqqiouEYIwalTp+jTpw++vr489thjXn1pFxQUsG7dOiwWC4MGDXJ7bH5+Pjqdjq5duzJmzBivjHZsNhsajYbAwEAmT55Mz549PR6jA4PBwCeffMLAgQOZPn260+6WBoOBCxcu0LdvX7p06cLPfvazjptkMzPhl7+URYwpKfD553DPPU4dGh0ZBJ1OR1VVFVVVVYSEhHgULOTk5FBUVMSYMWPo1KkTzz33HBERER3zHq6Q2tpa3nvvPTIyMpg0aRJdunRRhYzXgo4SQ3j6ABJoLnqchqw/iGqxX1+aix7PIwsetY3PE/lR9Ni3reuqokcVlatHbm6uePHFF0VmZqZXxzUVyuXk5LQpALRarWLJkiXigw8+8HqMeXl54u9//7soLS31+li73S4KCwuVn/Pz892K/L788kvxl7/8RRgMBq+v5ZL8fCEefVQISfJI0PjNN9+IDRs2KD/bbDavLrd582axdOlSYW5DNHmtOH/+vNi7d6/yc1ZWlqivr7+OI7o5oANFj9e0UFaSpI+AfUCqJEmFkiQ9CbwBBANbJUk6KknS2wBCiFPAx8jBxFfAc0IImxDCCvwU+Br4Afi4cV8VFZVrjGhMCCYkJPDQQw8xYMAAj4/Nzs5m6dKlSrfDpKQkl5kCo9GIEAKNRsMDDzzgVdmfg4iICKKiotqVrj527Bjvvvsu+fn5gFw62HIJpKKigqqqKgDGjx/PggULnPab8JqaGvjd7+Rswpo1sq9CdjY891wrO2fH78Px3PGAtl0M6+rqWLt2rdIRc8KECTz77LMdp7doB03fT1ZWFgcPHlS6g6akpODre8VafBVv8DSyAAKB54FPgR1AcuP2+UCvjopgrtZDzTCoqHhHpaFBHMmrEDvPlIgjeRWi0tDQ7PXCwkLx5ptvivLy8vadv7JSrFq1SlRXV7vdr6qqSrz88sviu+++8/oaFy5cEF9++WW7Shftdruoq6sTQghhNpvFwYMHXd6lWywW8fLLL4s1a9Z4fR2XWCxCvPWWENHRQoAQDz4oxIULLncvLi4Wr7/+ulLS6e17NhqN4tVXXxXHjh27omF3FCUlJeLtt98WxcXFQgghTCbTDVO6eTPBtc4wSJLUHTgOvAwkI/spOFrDTQB+1YExjIqKynXG0UTJbLUTHqDHbLWTmV9JldGs7OPv749er8dms3l83traWvbt2wdAWFgYDzzwACEhIW6PCQkJoX///vTo0cPr91FYWMi5c+eUVtTesG7dOlauXInNZkOn0zFkyJBWd+nl5eWAXNkxc+ZM7rzzTmen8g4hYNMm6N8fnnkGevWCAwfgww+dVj84Pn+HANBisQCeCf8OHDjAxx9/DMi/z+eff94rY62Oxm63U1dXB0BwcDA+Pj6KmNHPz++Gqcq4XfF0SeJVoAE5WBhM8wqGXcgBhIqKyi1CbpmBAL2WAL1sw+x4nlNaw+nTsuVJREQETz75pFctgDMzM9mxY4eSundFdXU1H3/8MQaDAUmSmDJlCtHR0R5do6SkhMLCQgBGjhzJokWLPO4FYbfblTR4WloaQ4cOdZnKz87O5o033iA7OxuAnj17um2x7RGZmTBpEtx9N9hssqBx506X1Q9ff/01K1euRAiBn58fjz/+eJsVYU3fo91ux263K0HG9Z6QV6xYwWeffQbIAcxTTz1FQkLCdR2Tyo94GjBMBv4ohMindUXERX70R1BRUbkFqDFZ8Nc1V9L76zRknTzOJ598wsWLFwHP7mKFEIr18ejRo1m0aFGbFQP19fXk5+dTWlrqdj9HJmRXVimZ+ZVUGhpYu3YtX3/9tZxC9fHxuIzRYDDw7rvvcvToUQBSU1OdVmzU19cDkJiYyIQJEzzqmNkmhYXw+OMweDAcOwavvw4nT8rWzi2ubzablQk/KiqKbt26edyJs7Kykrfeeotz584BMHz48I71hfASq9XKiRMnlPczZMgQhg4d2ky7oNI+rsZn6Gk4qQdcGauHApaOGY6KisqNQIi/DpPFRoBe/ooQQmCy2EhNG8CwXnEunRurjGZyywzUmCyE+OtIjAxk746t5ObmsnDhQvR6vcvSPKvVyvnz50lJSaFz584sXrzY7UTmCBYC9Fp87fU0mCWOFlQx5a576RYV7rW4MSAggPDwcKdlkg42b95Mbm4uTz/9NBqNhrFjrzC5WlsLf/sb/P3vYLfLvgr/9V/gIqAqKytjxYoVTJ8+nd69ezNo0CCPLtPQ0ICvr2+rjpjX26/g5MmTrF+/ntDQUOLi4ujXr991Hc+twqZNmwCYMWNGh57X0wzDcWC2i9fuBA53zHBUVFRuBBIjAzGarRjNVi7mnmP7+tXUGIz0iA526V3gSveQ0FO+U2/rLnbv3r2sXr1a0QW0tb9j2UQ0GNj22Uounj1OgF5LrRTgcXVCUVERK1euVJpFzZ07t1UbaofgC+Rlhw5Z47da4Z13oGdPudX0zJmyAdPf/uY0WHCs40dERNCjRw+v7K+3bNnCu+++i91uVzpiJiUlXfl7aAdWq5U9e/Zw5swZQLbzfuyxxzomS3MbU1dXx/Hjx5WffX19r0oFiacZhpeBTxuj0VWN2/pIknQv8CRwT4ePTEVF5boRFqAnPS6c3DID9XYftFoNfbsEERbgOr3fVPdQkHMGq8VC56TemLWdyMhwbZBksVjQ6XSMHDmS2NhYOnXq5NEYq41mIgJ9QRdCSv+hxCam4K/TUNlEmNkWdrud8vJyqqqq6Ny5c6vX6+vrWbVqFf369WPo0KEkJyeTnJzs8flbIQRs3ixnEk6fhjFj5BbUw4a5POSrr77i3LlzPPvss2g0GmbOnNnmZerq6pS+ComJifj6+ir9Pa4HQsgGUhqNhhMnTpCYmEivXr3QaDSqRqGd2O12xbQsMzOT7du3Ex8fT2hoKJMnT74q15Q8XeeQJGkR8Ffk6ghHHqsW+LWQHRVvaIYMGSIOHTp0vYehonJT0NDQQGFhoVKZ4PjCd8eurFLCGwOKfVs3YLNaGTVtFlUmC+NSnQsWN2/eTFFREY8//rhXVsW5ubmsW7+RIZNmEhH249220WxFr/UhPS7c5bE5OTmUl5czrHGSdrg/OkMIwbp160hNTW2zTXWbHD0Kv/oVbNsGycnw0ktONQog6yl8fX3RarWcP3+e4uJihg8f7tFnVFFRwdtvv82kSZOU93g9OXz4MAcOHGDhwoVoNBpleUSl/ZSWlrJq1SruuecekpKSMBqNGI1GIiMjW+0rSdJhIUTrvubtwONwUwjxNrK4cRrwMPJSROzNECyoqKh4x9atW1mzZo1SjujJWrfO3kB1nVzVMHT8NEZNm0m91U6Iv+ulhbi4OBITE71eSw8ODiY4KBCDyYTRbEUIoSyhJEa6r4g4duwYR44cUcoRW07CFy9eZPny5ZhMJiRJYvbs2VcWLDgEjYMGyUHDa6/JgsaZM50GC9XV1SxdupSDBw8CsqFVRkaG22DBZrNRXFwMQHh4OBkZGe2vZyPFAAAgAElEQVSyve4oampqMJvlTE9oaCjR0dE0NDQAqMFCOxBC8MMPP5CTkwPIS1PdunVTlu0CAgKcBgsdjccZhpsdNcOgotI2jkyCyWSitLTU406TFouFpa+/jl9YFEPGT8dfp8FksWE0W0mPC1eWMoQQHD58mICAAPr06ePV2PLy8sjPz2fMmDHKuapNllYiy5bLJo4v25iYGEJDQ6mvr0er1bosISwuLubTTz9l7ty5TpcpPKa2Vs4ivPqqXCK5eDH893871SgIIaioqFCWY3bt2kXfvn09ngTWr19PVlYWixcvvu4TclVVFW+88QYTJ04kIyPjuo7lZseRjRFC8NZbbxEREcH8+fO9OkdHZhi8WZIIA34OjETONFwEvgOWCCHcF1XfAKgBg4qKe/bt20d+fj7z5s1rl3r+5MmTBIRGUC38XU7gdrud999/n7CwMK/tnR1r+U8//bRXHR/r6upYunQpgwcPZurUqS7HXlVVpbTHvqL1fqsV3nsP/vAHKC2F+fPh//4P3KzVf/3112RmZvL88897LNjMy8sjOjoaf39/SkpKqK6uJjk5+bpUPpSXl1NaWkrv3r0B+W+pV69ehIe7XhpScc+2bds4fvw4ixcvxsfHR2kc5u3fZUcGDB6JHiVJGgB8g1xCuR+5v0Nn4L+BZyVJukMIcaIjBqSionJ98PHxwcfHx+NW0Q0NDWzYsIGhQ4eSkJDgNm1fVFREVFQUOp2Ohx56CD8/P4/GVFJSgkajITIykjvuuIOJEyd6FCwIIcjPzyc+Pp6goCAef/xxt90Mz58/z+XLl8nIyFA+B69pKWgcPRo2bIDhw53uXllZia+vLwEBAQwaNIjo6GiPP5eqqipWrFjB2LFjGT9+PJ07d76ybMgVsn37dvLy8khJSUGj0TBy5MjrNpablaqqKr7//nvGjRuHn58fCQkJ6HQ6bDYbPj4+N0RLcU//VywFypH7R4wVQswVQowFUoAK4PWrNUAVFZWrR01NDUVFcnf4YcOGMWfOHK/c/srKypQySFdUV1fz/vvvs2vXLkB28PPkLthqtfLhhx+yZcsWQC6z9DSzkJmZyfLlyxXHx27dujULAux2O/v27VMaX02bNo0nnnii/VmFo0dh8mS46y4wm2HdOti922WwYDQaeeutt9i9ezcgGzClp6e7vX5NTQ0nT54EZFvt+fPnM2rUqPaN9wqpqKjg008/pbZWtueZPHkyixYt8kq4qiKbcDlKZk0mEwcPHlT+Znv06MHYsWOva/Ovlnj6zTAUeEwIkdd0oxDigiRJfwSWdfjIVFRUripCCNauXUtdXR3PPfecx5NldnY2SUlJ+Pr6Ksp3ZzjS+qGhodx7770elyPW1dURGBiIVqtlzpw5HpdZ2u12DAYDwcHB9O/fH41G49JgymAwsHPnThoaGhg/frxXSxzNKCyE3/8eVqyA8HBZ0LhoETg5n81mo6CggISEBAICApgxYwaJiYkeX2r37t2cOHGCnj174ufnR0pKSvvGfAU4KkokSSI3N5eSkhKCg4NviLvfmw2LxcKSJUtIT09n8uTJdO3alV/+8pdujcOuO550qAIKgHtcvHYvUNBR3bCu1kPtVqmi8iOOToalpaWipKTE4+MKCgrEiy++KA4ePOh2v4sXL4rXXntN6TToKcXFxeJ///d/xdGjR706TgghVq9eLd5++22XHSUbGhqanbeioqJdXSyFEELU1Ajxu98J4e8vhF4vxK9/LURlpdtDtm/fLv70pz+Jyjb2c2CxWMR3330nysrKhBBC1NbWenxsR2O328WqVavE559/3mx8Kt5x9OhRsW3bNuXn/fv3i4KCgqt6TTqwW6WnGYa3gF9LkrRFCFHv2ChJkj9yp8o3OzSKUVFRuSoIIdi8eTN+fn5MnDjR48ZRjmxBbGysUzfEloSEhBAaGuqxAE80VmdERUUxaNAgj6szHOu7kiSRnp6uODY64/Dhw2zZsoWuXbsSHR3dPkGe1Qrvvy8LGktKZEHj//4vuMgUXLp0CV9fXyIiIhg2bBjdunXz2KWxvr6enTt3YrFYGDt2LEFBQd6P9woQQlBcXEzXrl2RJImYmJhmmZjr3ajqZqDpZwjy30NhYSHjx4/Hx8eH4S6WrG5UPKqSkCTpf4BHAT/gS6AEWfQ4HTAB/+bHplRCCPHHqzLaK0CtklBRkb/ANm3ahK+vL5MnT/ZoQs/Pz2fDhg089NBDbifZmpoaMjMzGTt2rFdK/ZycHHbu3MnDDz/sVUlgXV0dH3zwASNGjCA9Pd3lPkajkejoaGw2G5cuXSI2NtbjaygIAV99JQsaT52CUaPkckk3X/hms5l//OMfJCcnc99993l0mdzcXLKzsxWnvqqqquuW7j948CBffvklixYtuq6CypuZI0eOsHHjRuUzdGcSdrW45lUSyNUQDh518vpvmzwXwA0XMKio3M4UFxfj7+9PaGgoM2bM8GpCDwoKQu/nz8nCKuylrv0OTp8+zd69e0lLS/NYdwAoSnCTyeRVwBAYGEh0dLTLltJCCD788EMARWvRrmDh2DHZofGbb+TeD2vXwqxZTk2XzGYzP/zwAwMGDECv13P//fe3qs5w1qDL8VkWFhZy+vRpRo8ejb+//zUNFux2Oz/88ANhYWHExMSQlpamVKioeIbBYODLL79k4MCBJCcn06tXLyRJUgLtm10Uqho3qajc4litVl577TW6devGAw884NEx9fX1nD59mkGDBlFlNHMkr4JAX10rQ6ZgXw3V1dVERETIRkrV1R5Ncvn5+ZSVlSndFh1LEm1RUFDAtm3bmD9/vssSxMrKSsLCwpAkifz8fPz9/T1eemnGxYuyoHH5clnQ+Pvfw7PPOhU0Oti/fz9ff/21y7vyph02/XUaquvqOPn9bkaPGEq/XslYrVbg+qT7LRYLr732GikpKdxzj9oeyFNqa2upra2lW7du2Gw23nnnHUaOHOky63WtuR4ZBhUVlZsMxySs1WqZPXu2V3f9Bw4cYNeuXSQkJJBXJxHoq1NaXTv+zS0zkHNgG4WFhTz33HPodDqP74gPHDhASUkJAwYMUFT3nuDj44PBYKC2ttZpwFBaWsq//vUvpk6dytChQ4mLi/PwHTehrk52aHzlFdmh8Re/gN/+Vg4anHD+/Hm0Wi1xcXEMGTKE2NhYlyl8R4Muf538noP9/TFUXiY7/xL9eiVf80Dh9OnTnDp1ijlz5qDT6XjiiSdUsyUvWb16NXa7XWl5/swzz1z3tuFXC0+Nm54RQrzl4jVf4O9CiOc6dGQqKirtxmw2s27dOtLS0khLS/O4I6DDinbUqFEkJycTERHBics/NpVy4Kf1ocpkYeTIkdTU1HhUK15aWkpAQABBQUHcdddd+Pj4eJSiPXPmDFVVVYwYMYKYmBieeeaZViWg9fX1+Pn5ERUVxbhx4xTHQa+w2WRB4+9/Lwsa779fFjS6aQVts9nYuHEj0dHRxMXFodVq3S571JgsVBeepSAnizF3zkaj1TLpvkeorrd6P952YrFY0Gg0+Pj4UF9fT1VVFSaTiYCAAK+CytuVkydPsnfvXhYsWIBGo+HOO+9s5s55qwYL4Llx0xuSJH0mSVJE042SJKUBh3Gua1BRUblOOLoC1tfXu9zHkR7flVVKZn4lX3y1hffeew+z2YxGo1GU3SH+OkwWuVGT3W7nyLffcCrzACH+OmJiYjyanBsaGli2bBnffPMNIJs3eapXOH36NCdOnMButwO0Chb27dvHm2++qTSLGjNmjHcVBQ5B48CBsHAh9OgB+/bB6tVOgwWDwcCuXbuw2+1oNBoefPBB5s6d6/YSdrsdu11uxGXDB61Wh8UsN2NqsAm3Dbo6koqKCl577TVOnz4NwMCBA1mwYIHHdtS3IzabjVOnTmEwGADw8/MjODhYacwWGxtLRESEu1PcMngaMNwJjACOSZI0HkCSpOeBA0ADMPiqjE5FRcUrLly4oNxBPvroowwZ4nzp0hEsmK12wgP0mK12Gvw6EZfYo1VaPDEyUOkECdBgNlNvNrfZFRJQAhZfX19mzZqlqP/dIYTg2LFjVFdXA3DXXXfxk5/8pFWg4AggEhMT6du3b/sEZceOwdSpcOedYDLBp5/Ct9/CiBEuD8nLy2PXrl2KI19UVJTbpYS6ujreeecdjh07RmJkIKHdkhg4/i50el+PO2xeCfX19YqbZ3h4OCkpKcrSkaMkVaU1jr8vh6vlqVOnAOjZsycPPvigS7HtrYw3zaeikcsnJwHHgAHAa8BvhBCWqzbCDkIVParc6lRVVfH666+TkZHBHXfc4XZfR7BQW1pIg8lEXHJvjGYreq0P6XHN17CFEOw7eBgppDNmyZdgPy1JUUGtqiRaUlhYyMqVK5k3bx5JbtL6LamtreX1119n6NChTgMMu93OJ598QkREhEcBiFOKiuSlh2XL5O6Rf/iDS0GjEIJTp04hSRJ9+/ZFCEFlZWWbd5WOZRIhBOvWraN///4kJye7rZK4Gnz44YdcvnyZ559/vv3W17cRQghWrlxJZGQkd955JyCLdGNjY2/Kz++6iB6FEKWSJL0MjAPSkZci/nwzBAsqKrcyDnFjWFgYc+fO9WhyrjFZCPPXceRkJpaGerr3SMVfp6HSaG61b21tLTu/2cKwYcOYNGmSx+Pq3LkzvXv39ihdK4QgNzeXpKQkgoOD+clPfuJSOOjj40NISEj7jIzq6uDll2VBo9XqVNDYckJP6BTAwYMH0el09O3bF0mS2nxPu3bt4tChQ/zsZz9Dr9cze/Zs5bWwAD3pcVcvQKirq+PAgQOMHj0avV7PhAkTkCTpppzsrhUlJSUUFBQwZMgQJEmia9euzQy22iWevQXx1LhJA/wZ+A/ga+ADYAlQDzwshPj2ag6yI1AzDCq3IjU1Naxbt44pU6bQrVs3j44xmUycuFiN8NGhFVZ8fDRodbpWGYaamhpCQkIA2cchOjq6zUknOzubgwcPMm/ePK+WCBwmQQsWLHDa/6G8vJxNmzZx9913t2+92GaTswm//z0UF8O8eXLL6RbBlWOpRjIbuXDqMMnpozDjQ2onPV06hbp9/waDAa1Wi6+vLwUFBWRnZzNq1Kj296loJwUFBSxbtoz58+dfl34TNwtmsxmdTockSXzzzTccOHCAX/7yl155gdwMdGSGwdOQ8zvgF8CvhBB3CSFWAwOBLGCHJEl/6ojBqKioOKelQLGqMROg0WgwmUyKAKstrFYr7733HtmHdmM0W7FKWjRabau19NzcXJYuXcq5c+cA6NKli0d3qGazmerqao/GY7PZqKmpASA9PZ05c+a4DHp0Oh3V1dVUVVV59D6b4RA0PvWUbOH83XewZo1TQaOj7FGymSk8f5b6mjIC9FpKTK3Flk0xGAwsXbqU7777DoDu3bszYcKEaxIsONw7Hd1Au3fvzgsvvKAGC264cOECr7zyiqLtyMjI4Oc///ktFyx0NJ5mGH4AHhBCHHXy2i+B/xFC3MAtttQMg8rNS0uzH5PFxsWCC0wYkkZ4oK/S58FTMjMziYqKIigi2uVautVqZfv27YwZM6bN7nn5+fkYjUalv4Sn4/nwww+pq6vjqaeecrp/bm4u586dY8qUKV6dV+H4cdnKecsWOTj4619hzhynDo0gZznOXKxgwODhSJKEuaEeva+sQag0mhmXGt1sf5vNRnFxsZIR2bdvH8nJydfMGdFoNCrVDevWrSM4OLj9mo5bHKvVyqFDh4iOjiYpKYmGhga2bNlCRkbGLV9Kej0yDIOdBQsAQohXgZEdMRgVFZXWOO56A/RaJEmi9vJFTuzcxLcHMgH3d74gf1lu2rSJ/Px8QL6bj42NbVxLD2dcajTpceHUlBWzevVqrFYrWq2WKVOmtBksCCHYvn07u3btcnSvdTseq9Wq7Dds2DDGjRvncv+CggKysrIwmUwevU+FoiJ48kk5q3DwIPz973D6NMyd6zJYAFmkWVd2SakG0fvKxlAmi81p2eO2bdtYvnw5dXV1AIwcOfKaBQuHDx/mH//4B7W1tQAeV6DcTgghlM/Hx8eH/fv3k5WVBchVO3ffffctHyx0NB6JHoUQSn5RkqQgoBNQ5BA8ugomVFRUrpwak4XwAL0ibozuFseQcVMJ6Jzg0fFWq5Xc3FwiIiLcirdMJhOXL1+mtra2Tbe/y5cvExoail6v57777sPX17fN8rza2lqWL1/OqFGjGDRoEMnJyc1eF0Jw4sQJwsPD6d69O6NGjWLkyJEemUIBsqDxlVdkUaPFAj//uSxodKF5qKioYPPmzdx1112EhYUxY8YM6sx2jhZUIUlSMxvs1C7y55Gfn09oaCihoaEMGzaM+Ph4AgOvXklkU4qKiggICCAsLIykpCSGDx+ulHOqpZGtWbduHZcuXeK5557Dx8eHhQsXqn4TV4jH+T1JkmZIknQEqAZygH6N29+VJOlBD8/xviRJpZIknWyyLUKSpK2SJJ1r/De8cbskSdJSSZKyJUk6LknSoCbHPNa4/zlJkh7z9D2oqNyMhPjrKC0tYfcXn1BvMiBJEpFxyYQFul9vLSgowG634+fnx9NPP01GRkarfWpra8nJyQEgNTWVZ599ts1goa6ujn/961/s2LFDHl9IiNu1X0dGISgoiO7du7s8v2MZ5PDhw4Csz/AoWLDZ4L33ICUF/vQnuOsu+OEHuZukG4GkRqOhtLSUsrIyQNZJhAf6kh4Xjl7rQ6XRrIhAwwL0GI1GPvjgA/bu3QtAWFgYqamp12Syrq+vZ9myZXz7rawvDw8PZ9KkSW1mgG4nLl26xLp167BY5MK9AQMGMGbMGOXvTw0WOgAhRJsPYCZgA7YAvwLswKDG134LfO3hecYCg4CTTba9hOzlAPAb4G+Nz6cDmwEJ2TTq+8btEcD5xn/DG5+Ht3XtwYMHCxWVm5FKQ4PY8N1J8dKr/xC7j54V+3PKxPYfikWlocHlMUVFReLFF18U33//vdtzr1mzRrz00kvCbDa3OY6m+xw7dkzU1dW1eUxubq549913hclkcvq6zWYTmZmZwm63CyGEqKioEDabrc3zKnz1lRD9+gkBQowYIcTevUII+TM7klchdp4pEUfyKpTPas+ePWL9+vXNru+OmpoacfjwYeXn8+fPi4YG1597R3LhwgWxY8cO5eecnBxRX19/Ta59s1BVVSUMBoMQQv7dvPTSS6KoqOg6j+rGAjgkPJifPXl4mmH4I7BMCDEFuZyyKSeBNA+Dk91ARYvN9wIrGp+vQA5OHNv/3fie9wNhkiR1BaYCW4UQFUKISmArMM3D96GictMghODChQuEBegZMyCZifc9gt0vtNldr7NjQK5quOeee5x2zLPZbMpd2LRp03jsscfavJPPzc1lyZIllJSUANC/f3+PUvE6nQ6LxaLY6rbk7NmzrF+/nrNnzwLynbNHWoUTJ2DaNPlhMMDHH8vVDxkZrVwsGyw2pbLEYrFgNptd2ky35NChQ3z55ZfKWnhiYuJVrXxw/P5A/syPHDmiuGUmJSWpKv4m1NXV8dprr+EQsyckJPCLX/xCsTRX6Xg8rZKoB+4WQmxt9GSwAEOEEEckSRoLbBFCOO812/pcCcAmIURa489VQoiwJq9XCiHCJUnaBPxVNHo8SJK0DfhPYDzgJ4T4n8btvwdMQohXnFxrIbAQIC4ubnBeXp4nQ1RRuSFwtEp++umn6dKlS5v7FxcXs3HjRu6//37FP6EldrudFStWEBYWxqxZszwei8Fg4IsvvmDKlCltdqQ8ceIEtbW1yhKIaNG62mw2U1ZWRrdu3RBCkJeX53FzLC5d+tGhMTT0x5bTTSZSR7AQoNdSV1PFvm82EZI8FJ/gTgzsHu7WpdJms3Ho0CFiY2OJiYmhoaEBo9F4TTo4OiyIp06dSnx8PGazGR8fn+vS6vpGZdeuXVgsFsVA7MiRIyQlJXncJfV25HpUSdQAruS/CcDljhhMC5wtDAo321tvFOJfQoghQoghUVFRHTo4FZWrzeDBg7nvvvtcOh62RKvVYrVa3Xog+Pj4kJqa6lGN/rlz5/j0s885klfBoUIDySMmg77tdeDs7GyysrKUu/iWa/yff/45H330EVarFUmSPAsWDAZZn9CzJ/z73/DCC5CdLQsbW9x115gs+Grka1okHQ12CexWfPDBYhPNfCxaYrVa2bNnj9I3wNfX96oGC3a7XfGiCA4ORqvVKtkfvV5/2wcLVquV8+fPKz/X1NQonxfAoEGD1GDhGuJphuFDZJHjWKAWOcMwGDgN7AGOCiEWenTB1hmGLGC8EOJS45LDTiFEqiRJ7zQ+/6jpfo6HEOLpxu3N9nOF6sOgcjOQk5PD999/z7x58zyaLCwWC2fPnqVv375A67t5kL90t27dyoABAzx2gwTYsftbDh/JZPjUWYQGBSkVAy2XQ4QQHDlyhJ49exIaGorZbEar1TZL99fV1aHX69Hr9ZSWllJfX++Z3a7NBitWwO9+J2cX5s6VHRp79HB5yOoNX1F6MZ/xM+ZxtqQWi80OSOg0EqldQlo5Wubl5XH8+HFmzJiBJEnU1NQQHBx8TcSMH374IUajkQULFqiVDk7YvXs3O3bsYPHixYSFhTn9+1Zxz/XIMPwW6ILs7Pgu8h39b4CjQCzw4hWMYQPgqHR4DFjfZPujjdUSI4BqIcQlZGvqKZIkhTdWVExp3KaictNTX19PTU2N27bUTdm/fz+ffvoply/LST5nX6YWi4UzZ85w4cKFNs9XUFCg+DWExvdh1F33E9Y4eTq8IHLLmusRamtr+frrr5XqBr1e3yxYMBqNvPnmm4oTYXR0tGfBwtatMGiQ7KmQkAB798paBSfBQlN/h/guUfgFh1NnaqC23oIQUG+x0S1Mrijw12moMf3YAqe8vJzs7GxFpxASEuL0c3TltukNVquVY8eOKdmXwYMHM2rUKK/Pc6tSUVHBe++9h2P5OD09nUceeUTp66AGC9cXT30YLjSWNf4JWXRoQ842fAX8QQhR5Ml5JEn6CDlDEClJUiGymPKvwMeSJD0J5AOOxvJfIldKZANG4InGsVRIkvRn4GDjfv+fEKKlkFJF5abBYrFQWlpKTEwMffv2pXfv3m2K8cpqjBRUNWDt1JOMaWHoAkNb7ZOTk0NSUhL+/v48++yzbQrm7HY7GzZsIDAwkMcff5zaeivhLdb6HQ2q7HY72dnZpKSkEBISwlNPPdXKtKihoQFfX18CAgIYN25cK98Fl5w8KTs0fvWV7ND48cduHRqrqqpYsWIFEydOpF+/fowcNpjeaf3ILTNgx4AdQWqXYIL9ZGFnrdFEzqE9RFr70rdvXwYOHEj//v3dZnSaum2GB+gxNQopXYlPXZGdnc3nn39OQEAAycnJijvm7YoQgkuXLmGz2ejevbvSMtqxLBMcHHxbtpG+UfG4vfXNjrokoXKjsmHDBk6fPs3ixYs9qqv/Zscujh0/ycg75xDk7+t0qSAnJ4eVK1dy33330a9fP7fnKy8vV6oTysrKCA4OxtfXt5l40IEjnW++dJavvvqKhQsXOlWlnz59mg0bNrBw4ULPm0VdugR//KPsqeBC0NiUpu2jP//8cwYNGkR8fHyzfZpO9H5aH+qtdgz1Zs5+u5EB/foxcqRnJrXuPouW7cCbYrfb2bdvH8HBwfTv318RecbHx9/Wd8sOm28hBG+88QZhYWE88sgj13tYtyTXpb21iorK1WH8+PH06tXLYxMeqz6YsMhoxSraMYnllhnoH6NBo9GQlJTEfffdp2gbXFFRUcFbb73F+PHjGT16dLMsQWJkIJn5lYCcWairb6C6ppaRveMI6jaYsLCwVsGCYyLo3r07vXv39qwM0GCQTZZeegnMZli8WNYsuAk0duzYwbFjx3juuefQ6XQuKz4c9td7Dhzh7PHDjJsxj0EJnRjfa4FXfSkcbptNcdUOHH78HCRJ4syZM0RGRtK/f3/PRZ63MN999x1Hjx7lmWeeQZIk5syZc02qUFSuHLVBuorKdeDIkSNs2rQJIQQhISFtVi1cvHiR06dPA+AfGcvQsZPRNEmh++s0nDtzmjfeeAODQXaD7Nevn8tJ0WazARAREcGkSZMYOHBgq30ck63D9TBzxybOf7+VED8tWq2W1NTUZvt/9dVXrFu3DpBTyffee697rwZHy+mUFDmzMG2a3PPh7393GizU19djtcp9HhITExkwYICbT0yetG02G2EBevrGRdOlUxipUX6EBei9a2KF7LZpstiabXPVY+L48eO88cYbmM1mJEnikUce4d577/XqercSRqORffv20dDQAKBYlJvNcrDVtWtX/Pw8qspXuc6oGQYVleuAo1WzzWbzqBpix44d1NTU0KtXL2XyapoeN1lsREdHISq7tJnqzs7O5osvvuCJJ54gJCSEESNGuNw3QAsDu4chSRIxmnGAa7OjoKAgJEnyrKvk1q3wq1/JHSVHjIBPPgEn1tUODAYD//znPxkxYgRjxowhISHB7Z16Q0MDy5Yto1+/fowaNYqkpCSSnLSz9pSW2ZaWPSbq6urQaDT4+/sTHh5O165daWhoUCpDbjeEEFitVnQ6HRUVFWzZsoWwsDB69+5Nr169bnvtxs2KqmFQUblGGI1GTCYTnTp1otLQQO7lOmobbK1aSzuwWCwIIdDr9RgMBnx8fPD392+2Lm+qLKWkuIjoHmkeC/AqKir48ssvmTFjhtsa9urqapYtW8bYsWMZNGhQq9cNBgMbN24kIyPDs6oHkAWN//EfsHkzJCbKLadddJEUQlBVVaWkq3fu3ElqaqpbJ7+mLZ+/+OILkpKS6N27t2dja4Mqo9lpO3Cj0ciSJUsYMWIEEydO7JBr3cxYrVbeeust+vbty8SJExFCUF5efs06eao053qUVaqoqFwBQgg++ugj1qxZQ6WhgaMFVVjsEB6gx2y1tyrTs+DUUcoAACAASURBVNlsvP/++2zcuBGAwMBARePQdKng7OkT5GcdJ62LPHm5Kv07d+4c27dvB+SU8MMPP+wyWHDcRISEhNCjRw9cmZ457h4rKyvb/gCKi2HhQhgwAPbtkzULP/wA8+a5rH7YvXs3b7/9ttI+evz48W6Dhf3797N06VLFhvquu+7qsGABaNYOPD5IUJAjt0oOCAhgypQpTpd1bhdycnLYv38/IBuI9e3bl5iYGEAuhVSDhVsDdUlCReUq0fKONGPcREIDfLlQblQ8DYBmosX0ODlDoNFoGDhwIJ06dWp1XoPBgGSVqyL63j9T6UjprvQvNzeXnJwcRo8e7TZFnp2dzbZt23jsscfw8/Pj7rvvbvZ6cXExhw4dYvr06ej1ehYtWuR++cFgkDUJf/ubLGh8/nlZ0OjkfYHs6eDj40NgYCBpaWn4+fm5FYM6XC0DAgLo2bMnBoPhmrgj7t27l1OnTpGamoper2fIkA65gbupqK2tVUoez5w5Q3Z2NkOHDkWj0aiZllsUl0sSkiT9wYvzCCHEnztmSFcHdUlC5VpSZTRzJK+Ci6cPExQYSLeUfkrp47GCKsID9M20BkIIyuvqsRedolevXsrdWUvsdjv//Oc/CQ4O5rHHmnd2b1n6V1F6CQs+dIqMol83+Yu9rcn04sWLbN68mdmzZztVrh8/fpwtW7bwxBNPOA1mFGw22cL5d7+DoiKYPVtefujZ0+UhDQ0NLFmyhD59+rQKVJxhNpuV/WfMmNHm/ldCdXU1W7duZcKECXTq1EkxebpdPQJOnjzJ2rVrefbZZ4mKiqK+vh6dTodGo7neQ1NpwbUqq3yxxc9t9XG4oQMGFZVrSW6ZQdYY1FYirA3NsgiuRIsBWsG+Eyfw8fFpFTA4LHF9fHyYMmWK4nzXlKalfzarlf3bNhEW2RldxlS3gcKRI0cwGo2MHj2amJgYnnzyyWbBTE5ODlarldTUVPr160dKSop7Vfs338iCxmPHYPhw2XjJhZuhEIKCggLi4uLw9fVl2rRpdO/e3eWp7XY7BQUFxMfHo9frmTRpktv93eFKk9AUq9WKVitXheTl5VFaWkqnTp1uu0Chvr6e3bt3k5KSoghOx48fr+hF1CqH2wOXuUQhhI/jgdy+OhfZDjoB8G/8978at7sv9lZRuY0oLy+nvKqWAL2W4ROmMzBDTs9abXaO5FdSVGXixMVqSmvqEUJQUlqCocFCakwnFi5cyIQJE5qdz2g0snz5cqUhUkpKitOGVCH+OioqKxFCoNFqGTnpHtJGTnJa+teUvLw8cnNzFe1Cy8zHjh07+O6775SgxeXkcPIkTJ8OkydDdTWsXi3rFdxYH3/33XcsW7ZMsbYeMGCAW6Onb7/9lhUrVlBeXg7IzYfa01iuZQtsZzqStWvX8umnnwKyhuSFF17oUE3EjY7FYlE+Z61Wy4kTJygqkk19g4KCGDdunEctzlVuHTxd7HsDeFcI8VKTbfnA3yRJ8gHeBO7o6MGpqNxsWCwWli1bRmhUV4LHTFOyCLX1Fk5crCLIT0f38AD8tBpyy+uoKL/MDzs/Y+yEOwjr3QVorS/w9fX1aF0+0FbLxvUfkjZiPD17peEb2gmj2UrfyOZf6na7nQMHDtCrVy/CwsKYMWMGWq1WCRSEEJw6dYqUlBT0ej3z5s0jICDAdblmcTH84Q+yQ2NwMLzyCvz0py4dGsvKypAkiU6dOjFo0CBCQ0PdiuIKCgrw8/MjKiqKIUOGEBUV5bl7pAscGaCmOhIhBEd+yGHiYDkoiImJwWazKYHS7ZZu/+CDD7DZbDz11FNotVoWL15823fPvN3xtEpiOOBKAHAQcF3IraJyG6HT6ZgxYwZTp0zGaLZiNMtNkc5frkMgkRQpexVEh/jRLyaMHnHdmDJ5MsMHpzc7j6PNssViQaPR8PDDD7t0bXRkBpITujN0+HC6xiVSaTQrtsUt0+x1dXVs376dY8eOKWNuGgwUFxezdu1aMjMzAblawulEYTDAn/8s6xKWLZODhJwc+OUvXQYLNpuN5cuXs3XrVgD8/f1JS0tzGYxYLBZWrVrFnj17AFnc2Lt37yu2Va4xWfDXNQ8Ayguy2bPpY6Xx0YgRIxg1atRtY+GcnZ3NqlWrlMZY48aNY/LkycrflxosqHj6F1ANTAa+cfLalMbXVVRuSywWC1988QX9+vWjR48eiilNSKi8Rl5pNGO22egfE0qwn4666kqOfreDwWOnUGvRMc6JcdLFixfZvn074eHhbifUM2fOsHPnTh5//HH8/Py4c8pk5bUf1+irCNRLUF3MkIH9CAkJYdGiRc1EjTabjUuXLhEbG0vXrl157LHHWvVlaLIzfPAB/Pa3sqDxvvtkQaOL5lJWq5UzZ87Qt29fNBoNs2fPJjo62uXnWVdXx8mTJxk+fDg6nY4HH3zQ6RLMlRDir8NotlJVdAG9nx9RXbsT3i2BAaMmuhSc3moIISgsLCQyMhJ/f3+sVivV1dXU1NQQFhZGDzctxFVuTzzNMLwP/EqSpDclSRovSVLvxn//CfwCueW1isptid1up7i4mNLS0mbbm9btp8dFoNXI/91sNhu11ZVUVFW20hc4PA3i4+N59tlnSUtLc3vtoKAg/Pz8FJtdBy3X6HNOH+eL9es4d6EAkL0YmgYh27ZtY8WKFYr6PyEhwXmQ8s03MHgwPPEExMbCnj2wdq3LYAHg2LFjrF27lsLCQkC2dXa39n3q1Cm2bt2qrJ937969w90SEyMDMTZYOH5gD+d/OI7RbKXBLjE+Y/htcyd9+fJl3n//fY4fPw5A6v/P3nvHx1WfafvXmd5npBn1ZhUX2SpWMe7d4IYxJWB6idmEwJuwpLzZXzbZZHezeUM2G0g2bGgJJBBYCARsMKa6gAuucrdly5LVuzTS9Hp+f4w0SNbIFrZcORcff7A1Z2a+OirnOc/3fu57/HgeeuihM5p5SXy1GZHTY59O4V+BfwR0/R8GXMATwM9EUQxfqEWOBtJYpcRo09LSQkJCAnK5PKqmH44up5eNuw6RnpWNVinH5fPjDYqDtgx27NjBxx9/zDe/+c0z7ulXVVXR1dXFNddcA3wxQTGQirpu3B4f8pAfvclMKBSksb6O1Mwx0XRFn89HKBRCp9PhcDhobGyMadlrd/tp3rabxJ//FOvmjwlnZiF7/JewalXUdOn0iQON345OKSMrK4tQKERdXR3Z2dkxP59wOMyePXuIj48nNzeXUChET0/PeesUYlFZWcnu3bu544476PUGOVTTRFCmwaxXx5ySuJoQRZE1a9ZgNBpZuDAiOTty5Ai5ubkjCwmTuCK56E6PoiiGRVH8CZABzAfuAOYC6aIo/svlXixISIw2XV1dPPfcc2zZsgU4+/7usQN7OfTpOry9XXS7/WhUyiH6gkmTJjF79uyzJvft37+fioqK6F5zrE5ArydAxcZ3+PyTdyJTE3IFGVnZ9HoCQKTL8eyzz7Ju3Tog4icQq1joqanH9cCDTFg8G0vFTmr/6Wd8tnYz9htuHlQsDOxm+AIh3lm7lo8/iThLyuXyYYsFiFzIduzYEQ3Xksvlo1osBIPBaNhWKBTC5XLhdDqx6FTMmjSGefnJI7bVvtJwOp0cPXoUIDqWO9Boa+LEiVKxIDFipCwJCYlzZO/eveTn55/RibA/iCkQCHDy5MkhF+WKigpOnTrFjTfeeEZxXUNDAyaTCZPJhM/nQy6XxyxSvF4varWaffV2mupOoVOrsKWkA+D2B5GJQabkJkXfOyEhgfT09KFv6HbDb35D6JePI/i8dN3zddr+8YeE4iOTF/2CSoh0M1xuDy0njzC2sBSZTE5bWxsmsyn6XrE+nx07dnDTTTchk8lwuVxnnsQ4RxwOB8899xyzZ89mypQpMUdHrzYGdpw+/PBDduzYwfe///0Rx6dLXF1ckiwJQRBSBEH4tSAIuwRBOCkIwk5BEH4lCELyaCxEQuJyx+Vy8dprr9HV1QVEPADO9Et49+7dvPjii9HUvlh38G63G6fTSSAQGPZ1vF4vL730Ehs3bgSGH7O02+089dRT7N27l2ybHp0tFZ01GVEUcfuDNDc18MnfXqSurg6AkpKSocVCOAx//nMkcvonP6FrxlyOf/I5zf/2K0LxEWdHrVIe7VRApJvh7mrl8O6ttDdFdAoJCQm0uUIxcy36z2VtbW30XOr1+lG7iPt8PurrI1oNg8FAfn5+VDQpCMJVXSw0NDTw5JNP0tLSAkQmPb71rW9ddcXCcJkpEheWEal7BEEYB3wGxAFbgSogGXgUuFcQhNmiKJ64YKuUkLgM6OhxcaqugY0VJ8gZO+6se956vR6dTjckwrqpqYlwOEx6ejozZsxgxowZMS9iLpcLvV6PRqNh1apVpKamxnyf/jtKs9lMfn4+qampUcFlTYeLLqcXs17NjIJcxPZxGAyG2AvesCEyErlvH0yZAq++SkNWQcRuesBhnkAIo0bBiRMn8Hq9mMzp+JIyuPaWezFaIlsJ7Q4fzT1ebAY1cToVTq+P/33jQ/JzM5k7czrjxo0jNzf3gggM33nnHWpqanjsscdQKBQsXbp01N/jciEcDlNZWYnBYCAjIwOr1UpSUlJ0u8pkMl3iFY4+Z8pMuRq3lS4nRtpheBzoBcaJojhfFMU7RFGcD4wjMlL5+IVaoITEpaa5uRm72091r8jsG+9m7LjxMZ0BIWJKdOJEpHbOz89n1apVg/aIw+Ewb731Fh999FH0Qh+rWKitreXJJ5+kqqoKgJycnJgOi8ePH+fpp5/G6/UiCALLli2LJjpadCq8jceo+Xw9xelmEi0GbrrppqH6gCNH4PrrYeFC6O6GV1+Fzz+H2bMj0wQD/CT6/55t07N9+3Z27tzJGKsOTyCEXGeKHlPT6STbqkerlCMIAgaNmpDPTUtnLxC50x+tYsHtdrNhw4ZoENWcOXO46667rupph4Edqffee4/+7VatVsudd945bHF5NTDQdEsQhOjfazpcl3ppVz0j/YmaDzwkiuKpgR8URbFWEISfAf8zyuuSkLgsOHHiBK+88gpTFizHmpZ9xoRJgPfff5+uri5ycnKQy+XRYsDj8aBWq5HJZNx2220YDIaYhUJ/EZGWlkZJSQnJyWfe8TMYDGi1Wnw+X8yCQq/XY7FYCAaDQ0cTW1vhpz+F554DgwF+9Sv49rdhwOsM7FS0dNpprqxg8bULiNOrufnmm9Fqtcjl8ugx3W4/Jq2SFLOWQFcDH324lXkrVqFSa5i1+EbsnuG3Xs4Vl8vFli1bSExMpKCg4IweD1cD7733HrW1tdGk0Pvvv/+sQtmriYGZKf1olXK6pW2JC85ICwYV4BjmMQex/GwlJK4CcnNzWbx4MR5T2hBnwP5fUqFQiHA4jFKpZOXKlX1TCV8c63Q6efbZZ5kyZQqzZ88eNvvgyJEj7N69O3p3vGzZsiHHiKLIzp078fv9zJ49m9TUVO67775o8REIBFi/fj3Z2dkUFhZSVFREUVHR4Bdxu+GJJyJmS14vPPJIxNp5mFHOSNGgolXtZ9e6I/RMnkhyvHnQ1kb/MaIoEgwGAejw69EZjAT9flRqDd5g+Ky5FiNBFEU++OADBEFg8eLFJCQk8Nhjj121gVBdXV3s2bOH+fPno1AoGDNmDEajkXA4jFwuP3Nq6FXIcOFto/G9JXFmRrolsQ/4dp8fQxQh8lvq4b7HJSSuCjo7O3nttdfw+XzIZDKmTZuGxaDBEwgNOs4TCGFQy3n55ZcHjSeevm+s1+spKioi7wzRzgAymYxgMIjH4xn2GEEQaG5upqGhIabiXy6X09HRgd1uH/rkgYLGH/8YFi2Cw4fhd78bUiz07xO/9v5nvP7uh9jdfpKSknjssccYP358zLWFQiGef/55Nm7cSLZNj8IQR+mCG9AajIO2Ms4Vl8sV/XzD4XB0nx6uvphpv9+Pz+cDIgXDjh07aG5uBiKjkLNnz/7KZVv0c6ZtMokLy0iNm5YA7wIngdeAZiKix1uBscByURQ/vIDrPG+ksUqJkXLq1CnefPNN7rzzzqgeYKDQSquU4wmEcPuD5CQY2LF9Gyi1jM2fFBVCOhwO3n//fZYsWXLGi1lVVRU+ny+aEyGKIj2ewCATpMw4DUf27aawsDC6vTBwu8Nut/Ppp5+yZMkSVCpVdJRzEAMFjeXl8F//BXPmxFzTwM/16I6N9HR3UThvBaVjrDFFZU6nM9pt2LBhQ3RrYCTx0SPl4MGDvP322zz88MNYrdaYZlX9ax+t97xUuFwufve73zFnzhxmzpyJKIp4PJ5olLTE1fF1vliM5ljliLYkRFF8XxCE64GfA/9MxOVRBPYA11/uxYKExNkQRZG2tjaSkpIYM2YM3/nOd1Aqv2hxDpo6cPnoqDlMTnY21e2QNbE0WkT0q7WDPh+1tbW0tLQMWzCIosiWLVsIhUJMnDgRQRDo8QSGKMB3nmii4rMtyGQyZs6cOUTM19PTw+HDhykuLiYrK2twsXD0KPzgB7BuHWRmwl//CrffDqcXFANe6/W33iFv8nR0BhvF0+chlyvwBEJD9BoQ8XJYt24djzzyCHFxcSxYsOC0c3buv8Sbm5tRKpXYbDays7OZNm1aVKcxXLFwparn9+7di8fjYebMmej1embOnBk1uxIEQSoWTuN8v7ckzo0vbdwkCIKOyHhltyiK7guyqguA1GG4+hjNu4zt27dHbZljieYGvpdGFmLL2ldJzMxlXNms6F5qOByi7lQ16WNyKcmMIxAIDCo6+mlsbMRms6FWq3E6nWg0mmgR0O+YqJKJNNdWk5E7Hrc/SNDrYubEzOhrNDc309bWRnFxMRDxahgkemxthZ/9LCJo1OvhRz+CRx8dJGiMhdPp5L//52lKps8jLfuLfAhRFOl2+5k7PhG3200wGMRkMuFwONi5cyczZ86MKbo8VwKBAL/5zW/Iy8vjlltuGdFz+s/dwL3t002mLhdEUaS9vT36vfb3v/8dh8PBvffee1X7REhcfC6JcdNpz5ER6TJISFwSTrcjHm7McaRMnjw5KqAb7r167HYsWiXIVUyav5K4ceWDhJBVhyrYu3EdTc0R05xYxYLD4eCFF15g8+bNQGTKYWDHoD92ueboAXZtWk9PVwdapZygfPDFeOvWrWzatClqeRy9WLvd8ItfRMKgnnsOvvUtqKqCH/5w2GJh165drFmzBrvbz4muAInTbqBDYcPh/WKioV9UFgqFeOaZZ3j//fcBorkEo1Es1NfX8+GHkWalUqnk9ttvZ/ny5SN+fqzI6tNNpi4Xtm/fztNPP01PTyTod8WKFYPEqxISlyMjHlQWBGEx8B/AZPq2JARB2Av8syiKH12g9UlIxGTgLDYMP+Z4Jurq6qioqGDFihVotVrGFUxmX719UMeixxPgtV31dHV2oK3ezJjCqZSWTwGLhVMdLjyBECqZiEKhJHfiZMJqI05Bz+bKtkFdj/4OgNFoZPHyGxCNiTGPkfldeJRyciYWE5eQjDnehtsfxKRVUlVVRVJSEkajkaVLlyKTyb4QvoXD8PLLkcjphgZYuRIefxyGESgO1AB4vV66e3rZU9OOQathQkocBxp7ONDQTWGaBbkAjQ21LLymCLlcznXXXTfspMeXZaBws6mpiQMHDjBjxgwMBsPw8drDcDmr53t6evjwww+ZPn066enpTJw4EZ1OF91qiFVcSkhcboyow9BXLKwDDMC/E5mM+DlgBN4TBOHaC7ZCCYkYjMbdZGtrK3V1dbhcrpgdi/cPNfO/O2rp8QRItFmRJY2j0mug2e5Bq5Rj0Cg4vHsrm955nWAwQKc7SFPYjM2gRiETONzUw1+21fDW5t088cSTUQMopzYJUaYc1Bnpdvl4+eWXObjlA1y+AL4QWJNSowrwRC289tprbN26FYhMXkTtfjdujAgZ77sPkpJg0yZ4++1hi4Wenh5eeOEFTp06BcCsWbMonnc9Bq0GnUqBSauiON2CQaPkWKuDpuojHNq8Dld3OxAJyRoNr4Pe3l6ef/55jh8/DkBZWRmPPvro8E6UZ+FyU8/39vZGI881Gg2NjY3R6RWLxcLkyZOlQkHiimKkHYafAR8SEThGZ5kEQfg3ItMT/wqcV5dBEITHgAeJiCkPAg8AKcD/AvHAXuAeURT9giCogb8AZUAnsOp0UymJq5tzvZsMhUJ0d3djs9koLy+nuLgYlUoVFcsN7FhUN3UQqN2HdWw5YVGGOWcycm+Ag412zLoEUi1aUibkckQuYHcH6HAGKEizoFXJqWxxoFHKI5MG3QoESyqH2ryoHfZB7yMPB9AqFZzqdLNw4UJUKhX6uPiouDLk6KRsUh4WnYq7776btLS0Lz6Zo0cjWw3vvAMZGZEOwx13DCto7O8q6HQ6wuEwXq8XiNzdn26GE3B0kqESIS6eGTkzmJCeMCrugeFwGIfDgdkc8XEYuJVxvs6MA4Wp/QZS45MvjeBRFEVefPFFLBYL9957L2q1mkcffVTacpC4ohmphqEYeOr0GOu+f/8PkW2Kc0YQhDTgO0C5KIoFgBy4nYjl9BOiKI4FuoHVfU9ZTUR0mQc8gWRN/ZXjXO8m3333XV588cWolXK/+2GsjoXb5QJnGwbRjS8Ywh8Mo1EKdNYd59SJo2Tb9JQWTeLuW1Ywf2IKyWYNCUY1TXYPgY46mvZtornHg19QkFUyl1aPwL46O8FQ5MfI2Wvnozf+TGv1UXo9AbKzs0lLS4te+PSOOra89zfc9g4AzAkpHGxysG3bYdrvWY1YWAibN0cMmCor4a67hi0Wtm/fzp/+9CdEUUSpVLJ69epBYVj9BRhELuo7N6zj0J7tmLRKlEpldIrjfHnzzTd56aWXoqOf99xzz7C+DudC/7mbOz7xok9HVFRU8OKLL0YLsxUrVnD99ddHH5eKBYkrnZEWDD5guBQTY9/j54sC0AqCoAB0RLweFgBv9D3+Z+DGvr+v7Ps3fY8vFKSfxq8U/RcGlUJGt9sfVcKf7QIxc+ZMFi9ePESk13/BFEWRztYmAPRxNoRJy0hIySTLpkchh05XAK2jAV97LebTuhn9r+H0hSDow+PsRRYKYNEq0SjlBEMQr1dR3RExTdUbzWTm5aO3JkU7I6FQCIcj8nhxcTErV64kJSUFu9vP/uNN2P77N0xdPB3bq3+m8fb76DlwJNJliJFGONDcyGg0Eh8fj98fEYWe/uOSpIVj+3bg8gUQBIHJc5cxbtqi827nh0Ih9u3bF3V/LCsrY/78+VfFxTMYDHL48OHoOVUoFKhUqmjnJjs7e2huh4TEFcxIe4CbgH8XBOFzURRr+j8oCEImke2KjeezCFEUGwVB+DVQB3iIbH/sAeyiKAb7DmsA+vuxaUB933ODgiD0AFagY+DrCoLwDeAbAJmZmUhcXYx0Fvvw4cO0t7czb948bDYbthgWyNk2PRV13dQe28/RXZ8xfdltZNv01Ha46HH7UPh7MSm1CEY1S1etIi8lbshFT+ZopanDjUIdjzJtHEFlCgq5DJtRgy8YxqCWI+tp5PCebWTfcDsmvY680pmDOiN//etf8fv9rF69GpVKxeTJkyEcxv7sC0z71b+jbm6k57pltPzoX7FnZKMSZJTE+JwdDgcvvfQS06dPp6SkhIKCAgoKCoY9R50tDdQe2k1GVjY+gxVbYtKomOHU19ezZs0aFAoFBQUF5OTknNfrXQ70dxAaGxt54403uPnmmyksLIz+kZC4WhlpwfBDIrHWlYIgfM4XTo/TAHvf4+eMIAhxRLoG2X2v9zcgViZtv2lErNuTIYYSoig+CzwLER+G81mjxJVLTU0NbW1tZ7TTNWuVlGTGcUJZQFiQY0tM4poEAz2eAFuONFC19V3iMsZx44rlZFmH3nWHw2G2bt6AVqcnd8ZS9tXZUSsUJBhVyAUBbyBEltWIUzRjNFk41daLPeAkwaihLMMY7VZcc801gxMsN22C732PMXv34i4qofq3z+CaPgsAbZ83wkD8fj8qlQqDwUBycvKwplHhcJi9e/ei1WqZNGkSBQUFpKWlnfcdsSiKfP755ygUCqZMmUJWVhYPPPAAGRkZ5/W6lwOhUIiXXnqJ7Oxs5s6dS2ZmJvfeey9jxoy51EuTkLgojNTp8bggCEXA94DZQCnQBfyWiMag+TzXsQioEUWxHUAQhL8DMwCLIAiKvi5DOtDUd3wDkAE09G1hmPvWIyEBgM/no93upN0nQ59TRtEkBQ5fCItuaMFw6NAh9u3bxx133MGU3ESm5EYmAMLhMBadiqzZ4zkUdyM5OTlDHPdaWlpISEhALpez/Mav0e4VcAVEJmdacPlCHG/pobf2EHJEDoYKCQTlJJcuJNtmQKuU09nVxd9eep75CxYxrbzkC13BsWORrYa1ayEzk1NPPkPr8pvQab644z9d5Llt2zZ27NjBI488gkql4uabbx72/PR4AmzbuRuF1ojfmEq2TX9exUK/JkEQBGpqalCpVEyZMgVBEK7o7l5LSwttbW0UFRVFg576s0IEQYi6MUpIfBUYsSy5ryj4/gVaRx0wrc9F0gMsBHYT2er4GpFJifuANX3Hr+379/a+xzeIX9ayUuKqRRRFXvzzX3D5AsxYdhtWo/asNsGBQACfzxctCFpbW3n99de55ZZbSE1NjdnO7+jo4Nlnn2VC6XT0mZNo7vGQbTWQYFTjCYQIhUUW5CfzfvVuAqEAKVoFdq9ItztARiiMoFJgjYsjITULj6xPg9DeHnFofOaZiEPjL38J3/kOFlFOTV03+IODsyyshqijZEZGBg6Hg+F+FJqbm/n0009ZsHg5h1pclMxfgUmvw9s32nmuIsGjR4+yfv16HnroIXQ6HbfeeusVPS440KFz586dHDt2jEmTJiGXy1mxYsUlXp2ExKVjWNGjIAgLBEE4t4HoL4koijuIiBf3EhmplBHZSvgh8F1BEKqIlJmihgAAIABJREFUaBT+2PeUPwLWvo9/F/ini7FOiSsDQRAYU1DOhLKZ6NXKyChh3yhjTUck8bC3t5eamogcp6CggPvvv39Q96A/dTKWOC8QiHg9KHQm8spmk5o3CbcviEIQqOty0+P2UnNwJ25HL+sPtWAcN4XcaxaRHq9HJZcj627gs3deJRgIIMhkXDP3OhRybaQ4yM2NFAsPPfSFQ6NWG1PkOTFJy8t/epYtW7YAkJGRweLFi1Gr1THPSzAYpLGxkUPVjehUCixGAzKZbMi5GQlOpzOaHmmz2UhLS4uK/67kYqGyspJf//rXdHVFGpbz58/n29/+9lc2GVJCYiDDZkkIghACpouiuLPv3zIi4sfVoiieuGgrHCWkLIlLw8VKlRNFkW3btmEymSgsLGRzZRtxOtWgC/7APIRXXnmFlpYWvvOd70Tn/51OJ3v27GHOnDnDqviPHTvGunXrePDBB6nuCUezC/bUdmHSKPEFw+B3cfLTtzBmF9OkSueaMfH4Q2G8gRAymUCwp42OqgPMX7wcrUaL9s3XyPyv/0DVeHaHRogYL5nNZgA2bdpEdnZ2TFfEcDjMe++9h9FoZO7cuUBkH35LVecZz83Z8Pv9/OY3v6GwsPBLWTdfjgQCAfbs2UN6ejrp6en09vayadMmZs+eTVzc5ZU/ISFxLlysLInTf2MKwCwiY5QSEmdltPMezoQoipw4cYKTJ08Cg30F+nH7gxhUMuxuP1mTZzJh9nIONjmi6zl27BhbtmyJuvPFIikpiczMTGQy2SDvBq1cpK22ErVChk+mJXfuLZgz80k0qvEFw9hP7sPdcBSAgDaetCnXYt1fQfby+eR991vIEhMjjo1ncGiEiJ/C73//+2gGwbx584YUC/2jlDKZjEAgEB1pBJDL5THPzdlMr7q7u9m7dy8AKpWKJUuWMG3atGGPv5wRRTHaHQHYvHlz1G3SZDJxww03SMWChEQMzs9aTULiDIxG3sPZ6O3tRaPRoFKpuOOOO6JGTP1jkhCxjHb7Auze9B5Ws4newhnoNAbSjWZcvgDbDtcwY1I2ZWVl5ObmDrlYHDp0iKamJq677jri4uK49dZbATBpg1G3yVBrFa0HtyPXx2OJt9LlVqCUiRSmWWi0e3A77ChVaryBEON7min8919g2/AB/tQ0Ov7neeqX3kivL4SprntIF8btdiOKInq9nvz8fILB4LBxxydPnmTt2rWsXr0ak8nEjTfeOKRbcvq56ddDjE+OfZEURZHdu3ezc+dOJkyYgE6ni4x7XqG8+uqreL1evv71r6NUKnnkkUfO2Y5aQuKrxLmkVUpIjIgLnR7o8/l4/vnnWb9+PQBqtTp6cTx9z1+tUpCbmUZYY6Shy83R5l6Otzo4uH0DBzau5URzN4IgxLyzbGlpob6+Pqpd6CdZL9DR0Y7bHyS/uJTihTch6Mzo1AqM8jCB2r1YlCHGJxvJLJmHOT6HBb//d+bdsgDbrm3w//4f7gOHOTj/evxhYnZhgsEgf/jDH6IpjhaLhdmzZw/SCYiiGNUPWK1WEhMTo2uNtbUyEtMrh8PBm2++SVNTE4IgMHPmTL797W8PW6hczjQ0NLB27dpo56W4uJjy8vKoOFQqFiQkRsbZOgxpgiD0O63IB3zMfvqBoihWj+rKJK54LnR6oFqtZt68eYNm/E/XTPhaa8jPSicxMQ67bQ5/2VaDTSagU8jxh8KItlzGJmfgDg6+sJ48eRK9Xk9ycnLUmVA2wHZZFEXeefN1QmGRlKW30usNkZWZwbw+A6bPj7o4UXOcPXorxWPHMvXNP5H6P08g97gRvvlN+OlPITGRmhgZFqIosvfoSRaU5aNQKFi0aBEpKSkxz8HAzIKbbroJi8XCXXfdddZzN5zpVf+EgEqlor6+nrFjx5KamnrFFQo9PT1otVpUKhU9PT1UVlYyc+ZMrFYrkyZNutTLk5C4IjmT6DHMUDMkIcbHABBF8bKWEUuix4tPv4ZBp1IMan2PdHwvlmDSqJbz0UcfUVRUNCQM6fT3c7g8bF7zEuPGjuNrN99IRV03hxrtdFXuQqVSkzyhHG8gSCgsMinNTElmpLsQCAT43e9+R2ZmZnT7oR+n04ler0cQBE6dOoVWqyUpKQmI7PMfOHyMsC0HnUqBx+lE8fe3KPrDf2JqayKw/HqUv/5PGJDhEEucefLIfvZv38g3vvGNYQuFgcLHbdu2odfrKS4uHsFXZXjWrl1LV1cX999/P/CFt8KVRkdHB0899RTLly+nvLyccDiMKIrSpIPEV5LRFD2eqcPwwGi8gcRXl/NJDxx48Y/TqaI+ChNsao4dO4bBYBhSMPRrJuQhPyi1mAw6pi2+BbPFAkS2SHJsBloPBQBZ34UEulx+sm16Ojo6sFqtKJVK7r777iFGRp2dnTz33HMsWrSI8vLyIQ5/e/bsYcfOncxemU7Cnt0k//wn6A5U4JpUxInf/oGxt98w5POMChD9bkLBIEZLPAmZYymWyaKFyOkcOXKEN954gwcffJDU1FRmzJhx1vMZC1EUaWhoID09HUEQyMjIIC4uLloofJli4WJNw8RCFEU2bNiARqOJdhGWLFnC2LFjAa7IokdC4nJk2A7D1YbUYbiy6J+u6G/VO3vtCGo9aqWc/ETtkPAoiNytK4NuNr/zGhPLppOTXxwdF4z3t9IrM6HQGgiGwjT3eHH6QijkkBmvI1cf4I9//CMrVqygpGRwOkMoFEIulyOKIp988gmlpaXRYqKpqQmFQkFiYiJ+v58d735K0TNPYP7wPfwpabT+8Cd033gr3d5gzJFFu9vP3lOd7HrvVUzmOEoX3hCzC+PxePB4PMTHx+Pz+di6dSvTp09HGyN0aqQcP36cV199ldtvv/28EiPPt5N0LgSDQZqamqIukq+//jparVYyVpKQOI2LNVYpIXHJGCiYdNi7+OTvL9N0/AC9nkDMYgEid+syjYHMvHwSUiMXEk8ghFoIsG7dOtqrD+L2B1HIZYxLMpKfYiTVpKYo3UJqaioLFiwYFPkMcPDgQZ566ik8Hg+CILBo0aJosRAMBnn11VfZsGEDtLej+u53mXXbEgzbPqXlh//C8c27sd9yO56QOES30eX0su7TXeyr60ahkDPhmnnklM2NKUAURZEXXniBtWvXAhHtxoIFC750sSCKIseOHePEiYiNSl5eHitWrCA3N/dLvc7pDJyGiWWSdSHYsGEDf/nLX3C73QDceuutUrEgIXGBkQoGicuSgV4BBnMcE0quwZY5NqZg0uPx8M4775Cil+EJhMgrnYmo0rPlaC1vVzSwu8FN0fyVzJm/aNB0QHtdFYc+eQONLEyPJ4A+cxI76xyDphRsNhtJSUmEQl/4FtTX1yOKIgqFglUrV3JLVRXk5cHTT+P/+mq2v7+d2m98h7BGg9sfHJRGCZE78o+27mb3xvcI2ltRK+SYEtOYOiE9WiyEw2EqKyujyYjXXnstS5fGymP7cmzatImdO3cCkVZ9aWlp1LjqXLnQ0zAQser+4x//GPXIKC8v584774wWTVdDXLaExOWO5MMgcVmSapTz9jsfMqF0OnFmExn5pUMuvNDXDj9Wy/4DB1HEpzFxwnhqO11s3V+J7+gmUifNIl5nps4D4ZOdzBqbEBU3NhmDOJqr6XR4ON7pj9gla5Uc3LOdfaEwNy27jpSUFFatWhV9vxMnTvDKK69w29e+Rv6+faT/6EdQVwfXXw+/+hXq/HwK+vbzT9dttLa24vV66RJMZOWOJ95kIDEtM3qxG+hPceTIEd58803uuusu8vLyovvxwzGchuDkyZNs2bKFu+66C4VCwR133DFsguW5ciGmYURRjG73JCUlYTAYCAaD0Y5CfHz8eSdrSkhIfDmkgkHi8sTvoaupBueYHFBqBl14+y+OJ+sasYtasq1xLL7tAcJyFdXtTuQygfS0VLrd+SSnZqBQRfIk7O4AW3ZVEK8MMWPGDFJTU7njjjui++/9F7ygx0UoLFLd7qQ0Kx5RFOnt7cVsNpObm8vtqank3HMvVOzFMbGQllfeJmHl0ug2QqyRRVEUefvttxEEgXFzVhKvV6PP+CLpUKuUU9fQiCVkJzs7m4kTJ6JQKEa0XXC6QNTl9bO7up3ynAQEQcDj8dDb20t8fHx0smI0+bJGUGeiv6MSDod55ZVXyM7O5mtf+xp6vZ5vfvObo710CQmJL4EkepS4LKjtdPH5yU5a2jtITrAxLddKok42ZJ++/+LYWVvJ4c83kTxlKSqTjfHJRgKOTg7v/RxV3nQUciUmrTJ69y6KIj0eP76qHajCHu6///6oev6TQ420VO4ld2IxeqOZcDiMIAjRbIW1a9dSXV3Nw4sWofrxj2HNGrzJqTR+/8e4vrYKT0iMKfLrzykoLy9HoVDQ1taG0WjkWLt3kKATwOULsP291zBq1Tz44INf6twNFIj6fV4+eetl0scWkF9yDZMzIhMio9GyP9MkxGhMSWzevJnq6moeeCAyoNXQ0IDNZhtWsyIhIXF2LtZYpYTERaG208XbextQudqwH9iIqngBb/d4uLE0nazTdH39Ajvz2HyaOnuxJSbhD0GT3YMl6MVl70LudaIxx+MLhtEo5TjaG0FtQKnWUTB7IWXZtkGjdlpZiFOVhzCYzOTkFyOTyXB6fBjUkWNKMzOZ9sorKH/wA9BoaPrBj2m87xtozCYEQCf/Ym0DOwv19fV88MEHmM1m8vPzSUyMTElk2+SRi7zXQ+OJg2ROLMUXgpU33kxqwpe/K+/qdYO7G11qBiq1JiL6TEmj1xMYtb394cZc+4uk4YygzoTb7ebAgQNMmTIlknFhMpGQkEAwGEShUJCenj4qa5eQkBgdpIJB4pIw8I50R00XBpWcxLRMcBeTmJKOwx/m85OdZFm/0CxUVVWxbfN2cqcs4HCzk+OhJGorm8jS+lHGp4IhHmPpclRKBUqZQJfbj8EfpnbXx6gTMpk4bT5jUyzIZDI8Hg9Hjx6ltLSUiWOScSy7A4vJGNl+cLnZvv4NSvInwOv7SP+P/wCXC/7hH+BnP+OEXSDutLtnrVJOt9tPbW0tvb29FBYWkpOTw0MPPTTET6Hfn2LngWNU7t9FXGIKU4snnvMIYv3B7TRUH2fZHQ+iVKmZVD4Ttz+ISjF6mubRygURRZFQKIRCoaChoYEPPviApKQksrOzKSkpGTLSKiEhcfkgFQwSF52Bd6vqsI/e45/jyyrFpFWRPCHSOTPKwjT3eAY9z+l04nLY2XCoDovJRLZVT/fRrXS42nCPvRZthg2VQk5mvB57j50sq5GWHg/WyQvIz8mgZExC9KK8Z88eNmzYQFZWFlarlanjUqlud0aEiho18xsbKP7149DUFBE0Pv44TJwIgMnXPazIb+uWj+np6aGgoABBEAYVC6IoUlFRQTgcpry8nOumFXHNhEwsfcZSI8Xj8bB9+3bKysowm83MmzOb/Znj6PaKdHX20OUOIJfBtROTz+nrE4teT2DYIunLrPvZZ59l6tSpTJs2jby8PB5++GESEhJGbZ0SEhIXDqlgkLjoDLxbbWpqQ9nbRMiVQ7tDg14d+ZZ0eAMkGDW43W66urpIT09nzLiJeGrltHW4CMvc2MwG9DllVNW3o/SCQaMk1aLF09XM4Y/e5pqF1/P1WSVARDjodDppa7OTmJjI9OnTGTt2LFarFQB7WxPb163jgdxcdP/yL7BrF0yeDH/5CyxcOGj9A0V+8nCAIxU7SRpbxNRxqYy94YZBIVgDEQSByspKwuEwZWVlCILwpYqFfkGg3+9n27ZtWCwWSktLGZOWhKAx8NGRVkLhMPE6FfF6NdXtTsxa5aiYJ53rJMSJEydwOByUlpai1WoZN24cNpsNiIx1SsWChMSVg1QwSFx0ej0B1GEvqMykjsmjfLmVLSftdDo9ZMZrcXgD9HgCzM9PYu3atTQ2NnLfgw9xsNmJ2x8ip7cCf4+cU/7JZNmMZKYnAwLjkowR46CkVMYWlqIw2aLvKYoiL7/8MnK5nAcffBC5XD7o7t/S1sb1f/wjuooKSEuDF1/Efssqaro89Fa2DRLyDbS8bm7tofbYfsZlZ2DRjQEGX5zb2tr46KOPuPHGG9Hr9dx8882oVKovrS345JNPcDqdrFy5ErPZzD/+4z8OSlnscvkpTDMPuqC7/cFRixL/MpMQLpcLvT6ylbR//37a2tooKSlBEIRR8ZKQkJC4NEgFg8QF53QFfUPlfmoO7mLhTXdhMFnITIhjuqDkWIuD5h4PCUYNc8cnkGXVY7zuOjweD/U9EZ+ERJMGtzkNs0aNJd6EQi4QDCkQuuvY/O7nzF52C3K5gpziaagUMnp7ezEaI4XEsmXL0Ol00Yv1rl27cNTUsGDLFix/+AMWjQZ+/nN47DHsKIYV+bXUVdPW1sacOXMoyYxjTv5jQyKS+7sBMpmMtrY2Ojs70ev1qNXqEZ83h8MR9Uzof61ul49Tne6+cxmIFjGjsWVwJkaaC7J7927Wr1/PY49FzsnSpUvRarWSsZKExFWA5PQocUHp1yv4g2HidCr8wTCaxCwS8woRVDp6PX7213dzqsPFtJx47pqWhbZlH8d2bwEiBj3JyclUbN+Mu6uVwjQLHvMYAqZM5DJod/pQyQWS440IcgUBvz/qrmgWPPz+979nz549AGRmZkbb4Xi9mJ95hln334/41FOwejVUVcE//zPodGe0O66urubIkSNR98eBxYIoiqxfv57169cDEafIRx99NJp5MFIqKyt54oknaGpqAmDBggXMXriYffX2Qeey35VyoDNmP6MZJQ5fFA1zxydGpyNcLhcffPABzc3NAGRnZzNnzpxoMqRer5fCnyQkrhKkDoPEBaX/wut3dFFdc4JJZTNIT7SSED8Vf1hkX1038QY1ZVlxKOQy9tXbEeRK1Gp19C49EAjQ2ViDWq0muyCRTKuOI029iN312PQKbl8xD7M2j+r2iTi8QfTyMCWZcZi1yqhWASK+CJ9u2kRZVRWWxx9nXG0t4vLlCL/6VVTQ2M/AO3avx8WhnVsYW1iGV21k0aJFKBSKQRfC/oCq/k6AKIqDugwjobW1lXA4TEpKCmPGjGH69OmYTKYh5zLWpMJomiedjUAggNvtxmw2I5fLqaiowGazkZKSgtVqZe7cuaP+nhISEpceqfSXuKD05ww019VQX3UUn9eNVilHFMGoUTI1x0ZxehzujkZC7l50KgVpBVNZsGABNTU1hMNhNBoN9z6wGnN2EQcaujFpFEzNjicl2IzR1YRJo8CiU1GaFY/J3ciWtX/F6/Wwr96OLHUS1T1h7G4/4c2bmbh6NZaHHwaLBT7+GOHdd4cUCzA4y0IQZLQ21tLW1oJJq0SlUg0qAurq6njyySejOQfXXXcdS5Ys+VJt+H5nww0bNgCRgKlrr712UPfiTJkN/Xf//TkZsUKsRgNRFHnuued49913AdBoNHz3u9+lrKxsVN9HQkLi8kPqMEhcMMLhMMqwD09AzoTJ15CTX4Rao8XtD2LSKmmye3D7gjjcPpq2fUBCSgbTFy6j2+2nrq6Ol156ieKZC4nLGBdJopQJyN2deInHZNAyY9H1qNUqTnW6idNHtAHJyckkp6ZxoN6O2WhAJwvRuP490t54HcvH60lKTYUXX4S77wa5fNi1e1ur2X/kOCWzr0Or1jDnpnvxhYhmWXS7fJxo6sYTlqERFCQkfTHCONJCobGxkX379rFs2TJkMhm33nprdGojFmebVDgX86SRcOzYMQ4dOsQtt9yCIAjMnz8fnU4XfVylujAR1hISEpcXUsEgccF49913OXGyGuPkpYgyed+4n4BMBslmA58dbabNFcTpCxJOmorXYCaxrZcxCUaMVjMTpi0kacw49OqI6PBgdTPe/R9hyszHVDAVv6igrctDzYGNHLUaWbZ4ESkpKYyftgh/MIzR2YP6p/+X0rVvIao1NH3vR6T+W0SjcDbEgA9ZwI1MDNLtDmHSqpjYJzC0u/28/NdXkAkwe8lNeAJyMsoXoTKcfUSy34pdEAQ6Ojo4cuQIM2bMIC4u7qzOhhdr20EURRoaGkhJSUGhUOB2u+no6MDtdqPX68nPzx/V95OQkLgykLIkJC4Yx6pq2HawikBcNu0OH/5QmASjmhsmp1FZ18L29/9OlyEbwZaDQi7gba8n3n6MO+6+D6+giuYj+Dxu/IKS9QebULrbmDg2jx5fiJNtTtLjdQSqd2HUqRkzeSalWfHsrDhOzt/+TPYLzyJzOqladjN7Hvw+LmsCt5Smx2zTO51O1qxZw9SpU8nLy4vmSQzsFnR3d2OxWNhXb6f62CFUCjlZYyciCELUWbE/CTMWbrebV199lbKyMiZPnkw4HCYUCqFUjlyYOBqZDWejtraWF198kZtvvpnCwsKY50JCQuLKQMqSkLhsqaqqoru7mylTptAW1mPXZxL0BJEJAga1kkBIpLbTRb0zDIYEZPo4uj0BAMw6I/hM2D0B/ELEfrmp9iS7Nq4na9oysqxGdjss1BxoQNN2lDZNJi6/jWXXzMfhC3Ki1Ynmzb8x9Yl/xdzVSdfcRWxe/T284/IRRVAjDso/gC/GH7VaLW63OxqffLpQsbq6mpdffpk777yT3pCJsfmFgy6gw40wiqKI3W4nLi4OrVaLXq+PFggymexLTxBciG2HcDjM22+/TUpKCtOnTyczM5ObbrqJ8ePHR9cpISEhIRUMEqNKRUUF3d3dlJaWcrDBTmuvl2BIJBQWkRNC23Wc/RQhKFTUGfKxyTxkeBvwxefh8skJZ0/HL6gwahR4AiFsyWlkjZtET1hFTZODY629xKuCpAfa8KqMHG3RkGjsZvLx7XztT/+N9fB+7Lnj+Oynv6Z2yjxkAggI+IIhxicbkcuEqJnR3r17qaio4IEHHogaOg0sArxeL729vSQmJpKVlcWcOXNITU3F0eEbsevhO++8w4kTJ3j00UdRKBTcfvvtF+XrcDacTictLS3k5eUhk8kIBALRMVFBECgqKrrEK5SQkLjckAoGifMmEAgQDAbRarWsXLkSALlcTpPdS4/bj0mrQq2QEXb1oOg4SZvWQva48chlMuT2euSuZjBnRYoKmQx7wwnqWmpJK12AXq0kp2Qm7+87RWftCazGTGSo2ambilqlJr21jiV/+TFl+7bgjItn109+TfieexBF8Lc5kCHDoBHIshoxapSEw2G6XT4AtFotBoMBn88X01zolVdewev18q1vfQuHL4Q5p5hd9U4EAXo8ARKNmiFaglAoxMGDB5kwYQIajYaSkhKys7Mvi7v0/m4KwMcff8yxY8f4/ve/j0KhYNWqVZd4dRISEpc7UsEgcV4MtFy+5557Binmxb7/hIAbNHrC2jhaM+YQZ9BhUQQZn2zkpDAOmSUPtSDHopOhUymI1ynoDYeYlKynyRHkcJOdOG8jMm8Vh1VWBK2RhJCXW17/PSu2v0tAoWLXqns5ct+jjB2biUGtwOv2U5IZH9VBAPh9Xj5d/3fGjJsE+cnk5+cPEvCJosjRo0cZP348crmchQsXolKp6PEEhrg+CgTwBUN4+zoL/a6Hzc3NrFmzhmAwSHl5ORkZGWRkZFz0r8vp1NTUsGbNGu6//34sFgtz5sxh9uzZKBTSrwAJCYmRcdn8thAEwQI8DxQAIvB1oBJ4DRgDnAJuE0WxW4jcJv0WWAa4gftFUdx7CZb9lUcQBMrLy2PmI6RadAjd9Shr9uLInIWgj8dsMqE79RkNHWqK564kwaimrsuNv70eQaHAEJ+JPnUs1xdNRhb0kqr205tgxJw+m985DAS9cOOHr3Db+y+g8Xr4cOpSXl7+IDcuKWesRYtRo4yObfZPFYSCQQxaNQHkqPUm0hNiTzPU1NTwt7/9LSr2y8rKAogWCwMNkxKMmqjIcefOnRyq8zNr1ixSUlJYvXo1aWlpF/bEn4VQKERlZSVWq5WkpCTi4uKw2Wz4/RGdRXx8/CVdn4SExJXHZVMwECkA3hdF8WuCIKgAHfAj4BNRFH8pCMI/Af8E/BBYCozt+zMV+EPf/yUuEnv27MFsNpOXl0dhYWHMY4rSzfh9WXhCbizxVtQqFUqFjOwpM8nPsNHkFxifbCLbquPTYx8h0xiYPK2YQCgiTjz48RsgU2AoWoRaLmfJyb3M+fOTJHc2c7DgGt5ZchOHcmeRnWgkI16HVimP2kL33/Eruk/x2ZbPKF+yinizgTtX3TpoquB4TR0nG9vRJWRg1FhYecttFEyaMOjziJXToJZHtiUAGhoa8Hq90Zb/2cYjLyTBYBCFQkEoFGLNmjVMnjyZpUuXYrFYuPvuuy/ZuiQkJK58LouCQRAEEzAHuB9AFEU/4BcEYSUwr++wPwObiBQMK4G/iJGZ0M8FQbAIgpAiimLzRV76V5JgMMiuXbtISEggLy9vyOMNDQ1s37mLxInTcQQE2tQZGI9+RpshDZVtDGm5CbgVRgzudgR1HMfbXaSVX0teqg2Ps5fuoJJGu4c2yyTSE+OIq9jNlN//gowTB2lJzeA/v/tbPhszmTE2PStybKTFaaMOhyatkrwEE3plpNuRNyaT7vZxTM+1DjIbgsiI4voPPiTgcXHtLffiDYZxK+KjhUD/+GJLT0S4mWjSANDScIrdmz9kzorIvv8NN9xwWbT23377bXp6erjvvvtQqVSsXr36i+wMCQkJifPk0v+Wi5ADtAMvCIJQDOwBHgWS+osAURSbBUFI7Ds+Dagf8PyGvo8NKhgEQfgG8A3gS4f/SAzF7XajVqtRKBTcc889aLXamMedqm+iuroGfWYRBrWCRlFAFAQEUQQB2h0+tCE3ez94jZlz5pOXOgGFzMjRmnoaPl+HKmsyXtMYgvWdzPvDL5i4/WNctiTeuPshds+4loLJpfzQpkchl+H2BylKt0S7BoFAgGeeeYbx48dz7bXXkpKSwg033BBdm8fjYeukqq5bAAAgAElEQVTWrcyaNYuaDg9FMxZi0uuQyWToVBFh4oEGO6GwGNUsBEMiB061MD7RQHqSFaXejNGaRJo58p6Xqljo7OzkwIEDzJs3D0EQyMzMxO12RzsdiYmJZ38RCQkJiRFyuRQMCqAU+LYoijsEQfgtke2H4YjlIDPEgUoUxWeBZyFi3DQaC70aGYkZkNfr5dlnn2XChAksWbIEvV4/6HG/309tUytOmYFjQSvJU5dTdfwIQVMWmTYjJ8NlBEKQFArS4fSRZDJTNOtazJl5OH0BDjR76A1qUKVNxCA3UvT7n7Nk898Jy2Vsvf1BOv/P/8UvV5LuDjApzUyvJ4BOLYtuPTidTgwGA0qlkoKCgmG3BXp6eti+fTspKSn0KhKwxsUN8VM41NRDQao5qlmw6ZV4DnzAYUsSLQWzEBEomrMES9zZnR1HG7/fj0wmQ6FQ0NTUxNatW5k0aRKJiYmUlpZe9PVISEh8dbhcCoYGoEEUxR19/36DSMHQ2r/VIAhCCtA24PiB0vN0oOmirfYqoj9+euAEwOnmRhAJGSovLycnJyfm67zx97epOXWKjJk3UdPuxhB04juxF3+qiNuYQSAsYva2YGw9SlvqLBKMGmaNm8jhAxXUHt6DqWQJfo+fuTt3cs0rT6NyOdk2dwW75lyDK38Wk7Q68AfRqYa6Ke7du5f169fz8MMPExcXx7x58wY9vn//fhwOB7NmzSI5OZlHH30Uk8lERV13TD8FARHR5+JkVQ25Eycjk8uZUD6bWreCSamW6ChlrPN0Ienu7ubpp59myZIllJSUkJ+fT25u7pCtFgkJCYkLwWVRMIii2CIIQr0gCONFUawEFgJH+v7cB/yy7/9r+p6yFvg/giD8LxGxY4+kXzg3zhSZXJyu4NNPP6WwsBCr1cqsWbOGPL+//R2XV0y7KhmCPmwGDR6/gs70OXSFNCQCaoWcgDaeYDgFlVKN2xfAEwiRkppGb2crsw58Rtqvf4GlpYGqiYV88A8/ZW9cJjnxOvRqOd5AiB5vgEmpkbhnn89HR6+bNg90CBayJ07GP8y386lTp+jq6mLGjBnIZLJoZPRw2Qx5iUZqju3jxP4dpGTmojMYcetTSDAQ8zxdiMCnfnbt2oVMJqOsrAyLxcKUKVNISUkBIlshl4N2QkJC4qvB5fTb5tvAX/smJKqBB4jEb78uCMJqoA64te/Y94iMVFYRGat84OIv98qmfxti64l2kkwa0uJ0GDURp8J+m2OXy8XOnTsRBIG5c+cOer4oinz88ccAXHvttTR5lajCPk5teYu0adfjRo0lLh5n9TGUTjcy6yRQaumwTCLRfoygT4N7zFzKu5uZ8uR/oa/YjWvCJN564CEqE8xYC/OxdvnxBkPEGVSExDDpcVqK0i2Ew2H+8PTTKI3xlM9bRrItHrN5GkdaIxqLkMfBe++9x/Lly4mPj2fp0qUolcohY5/9kdA1HS5au3uoO7CdKWWlZKaPwefLJyV7HFq9Abc/SJfLT1nW4M7GcHbQ54MoinR1dUVTK48fP45cLqesrAxBEFi0aNGovp+EhITESLlsCgZRFPcBsQIyFsY4VgQeueCLukoZuA2RZNLg8gWpbOllfLIJo0aJvdeByWjAaDTy0EMPYTQah7yGIAgEAgHC4XCky4CIITETAh4scVbUQZHGLjcWWQCd6EFlVCIICjRKOTKPjJTuNmb+fw+jevvv+KxWdv/gJ4T+4f+QIIKz3Um3J8i8CRYMagWiGIl2NoSc0fZ/TuEU1AbLoDt+URSp6XCRF6eiq6uLrq4u4uPjzxi/rFNASWYcwVQjT3/aQcDtwKJTMSU3iZoOV3TyYnKmBYV8sFvjcHbQ58PGjRvZvn073/ve99BoNNx6661SfLSEhMRlgZRW+RWkoq476oDo8AaobHEgIKJXK4hX+Ni+/g3mLVjErGlThjy3vr4eg8FAXFwcoihy6NAhjh8/jq1gFnvr7ASCYXwd9Si1BtRmK+MS9SjEIPWHdjKx5BpUviCJv/0VGa++iKBSEf7+93nGaEKRnIE8qxQRgbGJhkGTDwAHDhzgrbfe4utf/zoZGRlsrmwjTveFWdSh3Vtx9fYwdupC5o5PJBwOn9WO+f333+fUqVN885vfRBCEMz5nYJE1cPvifDUMXV1dfPLJJyxYsACr1UpbWxtNTU0UFBRI2w0SEhLnjZRWKXFeDDQiMmqUjE820tjtprXXS26ulaKiYgomjB3yvEAgwGuvvUZmZia33XZbJNbZ7aa3t5cio5LPAyH8fv//3959x8d5nYee/53pvWDQQQAESAIk2AAWiU2NogopWt2OZMst8tVGiZLIsZPYm43Xm+sUa9dJNq43bpJtOVZxbMmSLJqqFFUokWKvIAESIHqZgunt3D9mAJEUm0hKpMTn+/nMB++ceTlz5pmXmAenku/eQtpVinIsYtYkP4Zsgq1PtWNft47Zj/wCY3SMgRtuoOx732OspJwp7X14XE4cFtPEFzEUNkgaDI4R1ja6s14qWi5lyzAM6yBKQTSZwm0vrI1gNpsxmC24rUbgxDssdnV1UVNTg9FopK6uDrvdTi6Xw2QynTTBOLL7YrzVYXyGxnuOfyRCNpulpKQEs9lMV1cXIyMjBAIBysvLZTqkEOKCJC0MF6EjWxgActks2za+xvTWhVwytXLivPFxDqFoEp/LRkOpk+joIPl8HiisbaG1RmvNy1vayVm9hBIZgqOjOG1msqM9zG6bT9ubz6P/9m9RnZ1w/fV03XcfP924kTvvvJOYreyougDE01nMRsWrv/slWUzMWX4Lh0ZjGIC81tQHXAwP9bP/9TXMu+J6aibVkcjkGBpL4rGbJ7owjp0eeujQIR588EFuueWW87YbYz6f51vf+hYNDQ3cfvvtE2UXwuZUQoiPnnPZwiC/pS5CDaXOiSWUtdYMDPRzcPcW1NjAxDnjTfCRyBib1z5O575dbO4K4vSX8fvf/55nn312YoZET08P6373KxL9B2iu9LCoZTLmSA/5Zx5n8o0r4BOfQDsc9D34IPz+99TdcAP33nsvTU1NRBIZ7OZCq4DWmr6uDmwmA2PJLM0LLmfushUE42nsZhMeuwULWYLxNLVVFfjLq7DbrATjaVLZHJrCbAy/w0I6m+ftQ6O8vX0nO3fuBAoJzs0333zUhlNnajw+L+8dZHNXkNBJBj++9dZbPPLII0Ch5eOmm25i+fLlE49LsiCE+DCQLomL0Hjz+p7DwwQzJsqrqvn8/7iX2sp3lhEen25pc1jw+AM4bTZsJgMHR+LcdtttRzXlT5o0idmLrsDmLSU0MkT5WJRrfvBdfE8/Qaa8En70I37tcnGwq4vPhWMcDqeJJKAnWehaGF8Loa+rgzee+x1tV66itmEqESrxOyx0dYXw2Ex0vf0iqViY8gWrcFW4mbn0OubW+ugcjvF2VxCryUDAaUUpNdFi8dq613GYDcycOROlFHPnzj3r+J1q7YpsNsu+ffuYPn06BoOBfD5PLpcjk8lgNptpamo66zoIIcQHTbokLlLt7e089thjfPrTn37X9sv5fJ6Hn1xLy5w2UnkDe3uGOfTq70i4ashWtnBTazXGYBdvvb6ee+65B4fDQTCW4uf/9i2WvfgCra+sQ5vMHLjrj/H+X1+hoq6GYDDI6FiCrrjxqIGD3f2DZBIxGhsaCglJRzvuijrm1ZcUxguMjjKSMZHNK1LD3SQScUrrmyhx2jg0GiWazFLishKJZ/A5LISHekl1bePylbdgMlvoHwly9ew6jEbjOYvdsV068E43yrz6Enbv3s2jjz7Kpz71qePutSGEEB8UGfQozlptbS1z5sw57uZEfX19dGzbgNFiI2Srpms0Sd5VQ8pRRjqVZdOhIDUWMxXVNYyOjmI3GLB959v8yQPfxBwdY9+qjzP4V1/mlTeeo3XHVlbV1eD3+zk4Bg5L/qipkD1b1pFOJWme2kgokaGucdrE2AN7ppcnn3yYutbL2Z/1MzxmIY+ZacNxOoZi+J0WSl1W0JrhSAyr2YDNaiWcSpGIRTE5vZSV+M5psgDv3r0yk07x5prfEqidyrz65TQ1NXHXXXfR0NBwTl9XCCHOJ+k8vYjEYjFeeOEF8vk8NpuN1atXH7WBVDweB8DpL6Nt+Y3s2dvO3q4Boqk8mfIZWLMxqpIHSWfzpC1eqqbO4Y0vfYnklKnYv/I3xFvns/03awj9x/fIVtex/NrrueyyyyaeP5LIYDVAx+5tZLOFHSHnL1vB1KU3TEyPzKRTDPQXFu1sbqxn/uLLiFhKiKbyOKwmAk4rHUNR8kBOg8UAh9b/Bmewnd5QAqunhIqFqzE5vcTTWRpKj97z4lzw2M0MDPTTc3A/AGaLFYvdidtZiKXRaGTKlCkyNkEI8ZEiLQwXkfb2dl5//XVmzJgxsbwwFPrkX9u0jU3r1tC2/Ca0w4/b7cGUGMFgD3E4pqkPOPHkI6hUgnQqiW/rTtr+1zfxbtlIvGk6e376KB0NdWxc9weumjwZh7sES/nkoxZ98tjN9Pf2sOW1FzCaTNRPayFlcjGSilGdzeN3WFi/5reER4e5594/I+C2U9PcSqg3TLnfgK04OHLroSF0uJ+4sYaM3UxJXTM2bylxm428Bq00FpPhXdMeT2eTrZPJZrOYTCYaSp28+ocNxEIjVNU1kszmaVq04l17XAghxEeJJAwXgUQigd1up7W1lcmTJ+Pz+Sa+PHtDCfrCSSa5yqibMoPu/iHw25g7ycf0qz/Bgf0HUFmFwaBwT70E8+aXueLvP8vMHdvJlFXAj37EGwuvodTvwRmJEmiYRXsI3OkYDquJtjo/fX19DA0N0TB1OqF4GYtXfZyKiiri6Swdw2N4EoNYlBulTMxesJREJkNXMEnAbSeSyJDNahz2d/5atw7tJdW3F+/iW0hmzHgmz0JrcKOp8dmPu5jS6W6ydSLbt2/nmWee4b777sPndHLjDSvpi+YIFZOPM12TQQghPiwkYfiI27BhA+vWreOee+7B6/VOJAubu4JEQ0G2bX2beNlM+sIm6u0eBreso3z+9bx+IItV5Uh1bMDmriEarmLBL37Jpc/8krzRwIZP3UvVP/7fbN7yBoc3PEfzklV0BzOUTJuP1WQgkkgTTmYJxdOsX7+e3t5e7ps5s7j4kWXii9ZHnF1vrCU0Noa1qgmX1UaVz0ckUeiy8NjNGMjQs3sbpbVTsLn9BBpb6HZW4HW7aSh10jkcYzSWprXO964VIsedbJOt420elUql2Lx5M1OmTKGsrIzKykpaWlrI5XIA1FWVU/d+fWhCCHEBkoThI27q1KmMjo7idL7Tl985HCOfh87OTjLDXZRUTCWFiYOqAu/MK+iL5jA4cjTUeDHNvpK6B7/NlWufwpaIs+mqm+n48y9T2jSFAwkIVFTh8PjoHBnDbDBiNRlIJJMEO7bTPHMuncMxVq5ciclkwmg04nMYqbYGMYYGmNM8h7Fkhr45y3FXTcJmNpPK5tjeE6Kl2ovWmoZSJwcHRjl4cAcGkxm/1UXeZGPWtAaqfHayec3MGu8puxeOHagI7948SmtNMpmcmDL63HPPkcvlKCsro6ysjI997GPn/gMSQogPCUkYPoJGRkZob29n0aJFBAIBVq5cOfFYLpejf2CIKDZKG2YQi44R2/canrnXEkoZGEvlMOxfi3XaUqqfW8813/ln3IcPcWjmXMIP/Ad66lQGn38Kf7kDfFX0GCqprLaR6gljsUIkmcGSTTF2aAeZqlIiLhcu19F9++vXr6erq4uZM2cCYPZXoZSRWDpLXyjBcDRFsnsnXRuT3PXJO7hqZi1u2110hbMksnlaqr0nbEk4EY/dPLHew7hjN4/66U9/isPh4I477sDhcPAXf/EXE1thCyHExU4Sho+gTZs2sXXrVuqnTqc/ro8a5PfSH55hz752vPNXU+FzE6icRH82w2g0STidp3vEzOUjOW598P+g7mAH4SnN7Pjhf/FSwzwubyrHWlzGOJZMERyNkcnlmVHlwRIfYqh7kCVLl+G2lTCl8vNgtmMxGUgmk6xfv56FCxfi9Xq59tprJ1octIY5NV4ODEXZ2z2Ax+1hdo2XoQNGohkYGUsQcNtZMbv+rGLSUOpkc1cQYGINiL6eblS4h9baVSilaG1tPWpnSEkWhBDiHTLv6yNivDkd4Oqrr+aOT3+ePcMp0sXZB+lsns1dQWa1LaR5+gzSI4eJJNKUVtfhcPvJ7n0JQ2cHf/vzf+D+b/9P/MND/OGev2Ln0y9zeNYsUvteJZZMYzAauWzV7eQ81RhgYmVFS3yIZP8B9vcH0VqD2T4xrTGZTLJhwwYOHDgAgNvtnpjO6bGbMRkN6MgQlr1/wBgb4sBQHF0+jWkLr6IrmDwn8Rlf3TKbjDIylsBiMlBiSNK+ZzfRaBSAefPmMWvWrHPyekII8VEjLQwfQsebHvjqi2vp7u7m7rvvxmw2M5w24rAo7GYj7TveJptJM3nWQiKYiYaD2DM5MvkGhqIpjKksq9c8w6WvvkTebGHdnffyxk2fRbs91AQT2ONxVCpCMBTCYAxgNxsZCo0RO7iVyjmtgIe5C5cyZc6l7BuOE4ynGevrhEQI3/TrwGHh/vvvP2ocBcDg4CC2VJRQzsmowQ3lTaSMLkxGhc9h4dBojGQ2d86mK8aCQzz32IN8/OMfp6WuhWz1ApYuWnjOF3YSQoiPIkkYPmRC8TSvtA8RLk43TOdzrG8fImApxV9jJprO4ze/M8hPKUU0FCQeG6Mxl2EsY+D2229n586dpBKD1D//EqX/9gCWaIStbW28cu//JFpVT360m1TfICnPTFYvasV9xXzGUrmJ7Z29djPBkcOkwjVQXY3JbMaiFdPKXbhtZg4MDjA21MtwJE6px/GuZEFrzWOPPYbdbufWO+7irYNBMuUz8LjslLmtOK0mwvEU0WT2jGOVz+d5/vnnCQQCzJs3j6qqKq6++momTZoEgMkkl78QQpwu+Y35IbPtcIjDwQQ+u4VEpI+eoSAZdzXuijJmTJnKlu5Q4S/yZITRtImA30/LgsWsefRBXnn5BbzTF+G2Ghl78CHmP/YonsFBgksu58e3/RmhyQ24PF7MmRyxwU4cZgNttUsnBhf2d7VzcPdubr75ZsK1PjZ678TtsKO1ZjQY5O31z1HdspCGulraLllCKgfbe8doM5nwOSz09/ezYcMGVq9ejdFo5NZbb8Xr9eJwWJhZ7WEgnMBuMWE1GUlmsuS1xmV7b5doJpNhaGiI6upqDAYDPT09E9txGwwGli1bds4/EyGEuBjIGIYPmW2Hw0TiGTqGxujetQnDwB58dhOHg4mJdQb294d5a+0TbH/9ReLpLGnMOJsWoZwB2g5tZ9ptq7jqu98hbTDwhy9+ke0/eZTUrNmkR3pIJRKgFJlJC3C2XEljmWvitSORCIODgyQSCXwOCwsayzEbFcF4GofDTi6VwEEGh8WEyWTGaTVjNxvpGBwDIBwOs3fvXoaHhwGoqqrC4XAAUO2zUx9wYTYaiCQzmI0G6gMuqn32dwfhJJ555hl+/vOfk8kU1nH4zGc+w3XXXXcuQi+EEBc12a3yQyQUT/MvT+/EZVG4nQ4O9I5gMCgCXjdKwY1zawAKXQaJXl56+WVmL7mGQykr7kPtzPiXv2bWjh1kysrpvv8rdK24loUzJ7PxcIxkJMgbv38ENWkuaX8jdrPCTB7fyHbmt85l/txZ5PN5lFIT+z6sW7eOgwcP8ulPfxqlFC/tGaCkOAgSIJNO8+qa3+CvaeCuG69Ba00mkzlqJsKR7218JcbxWQzxdPaUKzH29PSwZs0abr/9djweDwMDA8TjcSZPnjxRDyGEuFjJbpUXmfFBjpsOjWDrep20wUx6+mU4nA6iyQx94SRTS8w88ejDRNz15Hw1XFLrRlkcxHp6aP3lr5j721+gDYqXL7+c6Jf+jtq2S8iFY/T09OCxl5HN+Zhy2c2EtZ2RaAq/00qpw0zPwQh7uoeYMi2Nz2Ehk8lgMplQSuFyufD7/WSzWcxmM16HhXg6Sz4Zxe31Y7ZYsDrdeFyF8QtKqeMmC/DOLIbxMRInWm5Za01vby82m41AIIDdbieZTBKJRPB4PFRUVLzvn4cQQlyMpIXhAnfkX967esOEu3bTF8vjrGggk9OMRFOkczm8ViPOng2ktAnD5EvIptJc8+yDLPvvh7Ank+xfeRub7r4frCmaZswimNTs2rie4MFdzLn+DvYMZ6j02Bg4tJ9E717GapcwrdKL1WTAbDRQF3AwM2DkoYce4vrrr6elpeW4dX38iacYOLiP6z/xebLKdFqtBKdDa41SilQqxbe+9S3mzJnD6tWrj3pMCCHE0aSF4SLSORwj3NuJwe/HbXNgmzILdzpHKJ6mxGklkOphPyXYrWaynlocfVtofetZlvz8+5T1d3OwaTprrrmGgas/R1ob8eadGPuD9MZg+pyFmGdMpydrwmLKogyKaBbMRiNmsgxEUritRsJjUXb0mqm9vJHGxsajFjTK5/Ns376dKVOm4HO5uGLxJeyuqCSS1vic794x8kysXbuWkZER7rjjDqxWK3feeedRu21KsiCEEO8/SRgucMGxBO2bX8dfVkHLkmvZ2x/BbjZgdFqptibo2ruBqpqZTJ9xKZHO3az4xX9Ru38PfTUNfPtL/47hisV0HtiLOavI6hxje55nl91D65WrqS51kUnbefOp/8ZdXouzZDZzWqbTMTQJldP0hBKYonswhvtxzriWp7b1M7dlCQdiMNQVpKHUST4Z5YknnuDqq69m6dKlTJs8iWmTJ530PZ1qm+lYLMbu3buZP3/+RNdHJpOZaEloaGh4v8MuhBDiGJIwXKDS6TRmsxm/286Ca26mxOvFYDTSXOlhf1+QvDJQVlFF/ZRphDdvYOpPf8jc1/5A1OPjqZtv5bXLVhMpn0M+rLGWTKXW72QkmiJW2oK2utjXH6LMbcVlNWOzOzCaLURTWZoq3GzZ3000Z8FpMWMqqSNv81LmsdExHMPvMOOOHaYrHCY0cwFtdX6+8IUvHPUX/8mcaJvp1lofXrsZg8FAe3s7Tz/9NDU1NVRVVbF48eL3OdpCCCFORRKGC0wonmZvzwjrnnqU2inNLF56GaG4g2ROYzdogv3ddK9fw8fv+CQVpgyeZ5+n/pGfkVcGnlj9eX591R9Ra+hHm22YTIpkcBDf0EYihkUM5n2Ul9eRGT5E7O032GW7kZbaMi65aiVbD4cwGRQkx7Dsex78zTjrWrA4Kqmpq6dndIyA00okmSV4uJd4JAjVMzAaFJc3VZ/2+zveNtOJ2Bg//MHDXLfiaubOncvMmTOpqamhrKzs/QqzEEKI90gShgvI+F/fdrOZqtrJeMuq6RiK0ljmYjSWJhhPU1JahtdmI/3P38D52ON4wiG2zVvACytW0D97FfmEkfa0k9mTPKSTOSyeUrL5RtJGNzUeCx6HlcG4D+UuQ+Xz9ATjVHvM+PJhagK1ZDRMm7+MIWMpXrcTj91CcLCHxOYX8M5ZwUjUwZTmhdRYzCQzObZ0hd7TzpHjK1D2dXWQy2aZ1NiE3+vFU1o1MTbCbDZLsiCEEBcYSRguEMFYil89/SLaV0N5iY/G1qW4bWbi6Sw9AyOkBg5w5RVXoJ54gjn/3/+Ls7eX0UXL2Hjf/8kBfymRLS/g1klaqqoJd27D1D7ApctuZDiW5bClBVvHOvCU0uFrIZm10jbnckxmAwORJJG9rzN4uJPblv1VYdpj83L2Hh7mxV09pHJOPB4/dn8lo7EUkycFsFsLyYFSUOK00Dkco63u1AlDIpGY2GZ6/47N5HKFhCGZzXPpVdfTcI72jBBCCHHuXVAJg1LKCGwEerTWq5VSDcCvgBLgbeDTWuu0UsoK/AyYD4wAf6S1Pnieqn3WQvE0b+zpZmjvJsqmpMl4W9nSHcRlNZHLa8Ldu/Gue4rk3/wN9o0bsTQ18fAnP0nv4ivoMVaQD0Fpy0pcDiudIzGU2YPRpghYIZYxEfDYOWQOEIrbyBgTXFpfgiHcS9RewpzJ5cxsXUEymZxYI0FrzbO/fhivv4S5V64mkshQc80NvNExgt1sQGtNKpsjmcnRVOGmN5QAOOEgRoDXXnuNl19+mbvvvY+d/XFmLlmB1+0ins4ST2dprpRkQQghLmQX2tLQfwnsPuL+N4F/01pPA4LA3cXyu4Gg1noq8G/F8z6U0unCjIESv58pl92It3EOOa0ZCCXoHRylZKiXG3/8fT7/gx+g2tvhBz8g9tZmItesIhkeYSQUondkjOjeVxk9tJtUNo+7vJa83c9rTz1MiTFFLJUh5J2Gq6KOaeVuxqIR+ra+RKJ3HwCBQAC3282rr76K1ppwIkPT/GWUT18IwNxaH5c3lbOoMUBeM7F0c3Olh2QmT1848a5ttHsGR1mzZg3BYBCAyZMns2TJEjw2M211fjweN+FkFovJcE7WaRBCCPH+umBaGJRSk4AbgH8E/koVJtcvBz5ZPOUh4OvA94GbiscAjwPfUUop/SFbhWpoaIiHHnqIyW3LaGqaTsOkKvb2RxgcS+HqeJ3FT/wXl77xOloZeHnlrbzW1sI1ly7BGEoxdcFVmGtDhEZSDIYT5GKa0ViSEk8OpcBdVo3POoeENlJXYkGlxijRITLOyYQSBhwtV7No9lRyxYjt27ePF154gaq6Bg7FjJRUT55YonlzV5C2Oj9zJvnI5fVRyzd3jsRoCLhwWExksxlUNo3DYmVnT4g333qLsHIxbXoLDaWlXHFFYXCkDU6rC0MIIcSF40JqYfh34G+AfPF+AAhprcf3Nz4M1BSPa4BugOLj4eL5R1FK3aOU2qiU2jg0NPR+1v20jA9qfHnvIJu7giirk8bGRsrLykhkcrhtZqYH7Mz97c/506//NUteWcf2Bcv48Y+e4fV7vkrKZuPl9a/RG0owMDRMaO8b1C/nEykAABfRSURBVLiMNFd5MTcuxhvvxda3FbvFSCRrIFM5m12DSWLpHK6xbkb3b2aS18KcGi+lZaXsfvMlogOHCMXTEKhn4ao7easvSz5fmL0QTWXpHo2zb2CMNTv6AWir82MxGQjG01hMBqq8NsrcVnQ+z9rHf8aON18hm8uzZyTD8tvvZvqMmROtDqF4+jx/AkIIIc7UBdHCoJRaDQxqrTcppa4cLz7Oqfo0HnunQOv/BP4TCktDn4OqnrHxZMFmVAzt34a5aTbbe9Msv76wvPHmQ6Pkf/a/mPXD7+Hu7eHA7Et4bsVVDNbW46msxpQDW8tynF4fO3sjjA4FcYSG8EYHUI5qPA4L+ZrpxLSZgdE4pQ4Dg/07sXpqSecsNLcuojc8h1Qmj8oX9n4IBoepqa6aWBehuryUQx0jxFIZclrTE4xjMxspdVoZjqUnWhraioMTd+7cydCuvZRecgUOi4mW+YtxeXyFLhaXFY+rsBPl+BTK0x0cKYQQ4sJzQSQMwFLgRqXUKgot1h4KLQ4+pZSp2IowCegtnn8YqAUOK6VMgBcY/eCrffrG1x+IDfexc+OrGG0uYs5KOoZjLAt2svifvobtjdcYLivnwHd/wprJlxA/sBHD6EFive0kPPUY4nF6D3dhr2nG5PSTr55DaPdreGYvZ0R5GbNUglK0VXuwqRydu/dT6/eSNAcYTWvMI/s52LEPV+sq2iYHWH33Fzg4EiedzU98qQecFqLJDNsPh6n22bCZTSQzOQJOC3azkU279rN8/gyUUgSDQWKjA4zFE4CduqkzSGRyjHaMML/+6EGMdrORoLQwCCHEh9YF0SWhtf6q1nqS1noycAfwgtb6U8CLwO3F0z4LPFE8frJ4n+LjL1zo4xeCY3HsZiNl1bUsvuEOQtYKXH09XPG1P6f5xhUY2vfR/bWv85P7/5LMwlksnlqGZfIC9KQ2VEkdGCA93IUv1o2PBCVOC1l3JdnKWWStfupKnDSYQlRHdlHitOJ0Omm4/HYMzhJaKpyksnk8pVU0NrfwyUvruLypHL/TSiSRwW42TtSz2mcnDwyOJbAYDSQzhdkQ1T474f4u1j/9GB0dHQAsWbKEP733T1jQWH5UN0VrnQ+T8ehLK5HJ4bGbP8iQCyGEOIculBaGE/lb4FdKqW8Am4EfF8t/DPxcKbWfQsvCHeepfqflwIEDbHjq1yxccRMVFZXEo1ku/fG/0/zoT8jn87x53fWoB74PTjvZR37Cs2vWMPu6T+Kxm4jbLOQzSVB2DlgamJoIkel8k7JLV1PmtmKvW8jBkTj94SSOZJR0eJiRcJRSnxuVjdP5+tPYspcxb1YbbXWN76rb+LoI4y0MbpuZ+hInw9E0g+EYyY43qa1vxG2bjSqfROuyFdTW1gJgMBSSgsLW1O90NYx3vwATgyNl6qQQQny4XXAJg9b6JeCl4nEHcMlxzkkCH/9AK3YWysvLqaurJ59TuH/0A67/929ijYTYf90trL9yMd3pBNdZTAzHcjQtXkEyOMTkMi820xgb3niblC3AcGkr5V43Nn8rVqud/nASnzVPsONN7JVNVFXWokpnE3T5ONSxD0PzLOx2H+VzLqOkromGUudx69ZQ6mR9+xCheIZMLo/KJrHm4vzRwhkcGBxjx74UhnyGeDpLMqe5YvHCifUaTqSQQPjpHI4RjKfx2M3nZNdKIYQQ588FlzB8VCSTSbZs2cKll16K2+XiUw4bubtWY2xv5+C06az90j+Qvex6LGN96Ldf4K1X/oBjxhWYLQHGVJz9w3GqfS5mLlzGzjdeZO7kKN5JUzk0bMNgVKSSOfZHU3gjMUpKUpS7bPSEEqQGDuCIjTEQnorLZqJ15qxTLt2c1xoUKBRDu14nMzbKdZfOYl59Cb5VtzFWXC/hvXzpH9vqIIQQ4sNNEob3ybZt21i7di1TQyFK//mfYd06jDNmEH7kcX7Rvg8sWRqsRrDWYvZVYnBXMBRN444cYmj3BsgmGauaxrSG6bQPJ7GV12NUCnuog9HD+9lqb6PCa6eqoY3E4W10BaqpqyjBPnspiZwBbVDcOq/2lF/wb2zewd4N61h+051YrDbCnitJ5zWHRhO01fmZV1/yAUVMCCHEheyCGPT4UZLJZABYWF7Ol7dupXTlSti9m76vfY3s22/TsWg5/ooqcokI2bERMnnNpHnLMZZUU+Oz46ttxuYJEOrcgdWoODgSZ3LjVOpKHGRyOUYzZrTVS2ullWkVHlLKQj6XxZhLEklmmFlfQcskP211JcdNFnK5HLt27WJ0tDCpJGu04fL4SKeSAHhLSikNlBJJZD64oAkhhLjgSQvDObRx40Y2Pv88dw8OYvrud7GiaP8ff8GbK29j/7YXqf/tM5S1LKJ59jxCA71U2DU19SW88OQjjAaDuFpX0hXO4qlopcRlI5HJMzY2RmbPC+SbWzGUNjKjuZn2V3ZhGNpHTf2VpFxWeqxXY/W4iCazJ9ybIZfLYTQaSSQS/PrXv2bZsmVcddVV1FRXUVb+sYlBjyAzGoQQQrybJAznSibD1DVrmP3AA5gjEfpu+jjt9/01+60l6FwWDCZ6Dx4gWzOXhkAFK27/LHa7g7FkhpyvFsNQH9G+DvyBRkJxO/lYmlAuxqIpZWjdhNVhpCubxwBYK6bi9vpxWkw4zEbSuTx5DXny7xprEIqnefTRR8nmNYtXrKah1MkXvvAFKioqgMKgR5nRIIQQ4lQkYThL4VCI4EMPMfl738O3bx9cdRV7vvQ1DgYCbHzxGWoWXIs/UM6g00M6GqLaDu3d/Qxvepqa+imYGy/FXj2NnNVDZ9yCMZ7FPboHa6SL0ktvxm0zg8fDiy++yNW3fQazw0Nz5RL29o+RzOTQOo/baqLGb5/YxGloaIj1b+9l1rxL2NwVxFNaidlgmFiiua0ucMyUSJnRIIQQ4uQkYTgbnZ1kbryRyTt2kG9uxvC738ENNzCwb4hkfxe5dJKuXZsIt1xG9cKVpFMpJlUEyJttxJ1uers6qZjUSmOph3V9igqXiVASBpUfjwrii44ylvRy1YIF1NfX4y17ZxnnpgoXnSMxRqMpWuv8TC934LEVPs6Ojg5eeuklDCV1OGxOZrYuPLraxyzRLDMahBBCnIokDGfD5yOQzRJ94AFcX/wi8XSaza+9BqVT6UkWxwDERsnmoGPfLoz9Oxjw3UpNeQVX3v15lFLsG0mztbMfS/vzUD4N7WvGXVKOO7SV8GAvfYEq0pior68HmGgNSGZyzKz20lDqJBkZ5cff/za33norzc3NtLW1MXv2bN7qjuI6YhVHkCWahRBCnBlJGM6G34/auRNXsXn/hWefZdOmTcy5woLB6icw+wpGcBNJpAnnTPizGbbt2s3tDbVYLGa6u7tpqKrllX0GbKW1RMJDZJ1TMZkNGGdeR0obaQg42XY4hNtmJpLI4LGbmRxw0L5zK5asE1/dTHLWMlpbW/H7C+MOLBYLFosFjz111CqOIAMahRBCnBmZVnmWtFLE43GAiRUQD3e2YzcpRrraye1/jYGxJI5ADYaZ19O6YAkdQ1F++8waHv7lL3lzbw8umwmrvxJldeCwKLx2CzabneZKDzazgS1dQVKZHJZcknQ2z5buEJs2b2bv3r0AGI1GVq5cSXl5+VF1ayh1Tsya0FpPHJ9o1UchhBDiRKSF4Sw9+eST7N69m/vvv5/ly5czGgoTKZ0NKGykSKYiVDoM1Ja5MEQiOEgSz9sY0F601kRH+8may9iXK4VAGR6jCafFhMtqYmq5m46hKDaLkbdeeYFQbwfNV99BwG1n/tU3ccnUypPWTQY0CiGEOFckYThL7e3tpFIpRkdHsVgsHO7pZZK3hoSlkpoF13FoJAEGA70jYdTOl8mNNOBruQyzv4rGWfMZ0S6MyoDHbiYYy9AXTmAyGrDmomx++XXGymbhdrlwVjXi8JWRzWsOjcao8NhOq34yoFEIIcS5IF0SZ+nKK6+kvLyckpISlFLEImH6ug6QzObpGw6R6m/HZDRS5vfg8vgZC40yEksRcFqx183B5fYwlswQcFipcyuW1DnxOyyYDIrgQA8e4jgtRvxlVZTUNWG3WjAA0WT2fL91IYQQFxFpYThLWmuUUlitVpJ5A5XLbsVqdeCxW0h1dmAc2IuxajJua4DZV16PNlnZO5KmxGmlOxjHYzMTT+cxkSO741nStdMITFvIvLopjDRUE89oBsIJkpksVpORVDZHXmtcNvnohBBCfHDkW+cshOJp3t6xh4HBQV7e0o62OjGPdJKwl2I11+CvqifScwBjPk1dwEFOg8du5poKPx1DUaJduwjGwphq2oiloWrWUuy+UpxWE4lMDp/Thg+wmQpTISPJDC6rifKAixKXdDMIIYT44EjCcIZC8TSbu4LMXnINbSqHNtl4fW8vkb1b8ZVWYK6aRMpdSfOKO3A5bFzeVE42m+XAgQPU1TbhtZvp2qnpGY4TsJtwWk3YLHXktMbvsBy1PHMonqa2xHHU0s0y00EIIcQHSRKGM9Q5HMNhMRHu7+LAri0sve4WSv1u0hX12EuriKayuKwm/A47fqeZUDzNS6+9ydZXn+ey1Z9g3owpfObWGwgnMnQOx+gNJYgms7hsJkpcFhpKnROzGWSmgxBCiPNNEoYzFElk8DssbN23k8GeLsKjw5S5nGxyz6S83IfbaiIUjrBn3UvMX7CQcKKestopLL3OjcNXVtzTwT8xi6Gt7sSbPclMByGEEOebzJI4Qx67mUQmx6yFy5i3bAUefwlD0RRT3VkYG2QwmiKYMaAMRrZ0h8nnweN0UDFpMk6rGYfFROdw7Hy/DSGEEOK0SAvDGRrfFtphd1M7dTrJrGY0mkJ3bWEkk6Zk/ip8fgeWZTfw5sFRDo1EsVsK+zqMdz/kyR/V9SCEEEJcqCRhOEPjqyg+8dx6Du54i2TTCuxWC9NnL0WbrOQNRmxmE8lMjnK3FYNS7B8cI5cHm9mIxaTIa+NRXRNCCCHEhUq6JM5COJFhOGPBVVZLa5WbUqeN1w6n6AxmsBgNJDM5kpkcs2t85IH9g1GsJgOgSWXzNJa5pGtCCCHEh4K0MJyFNw6MEKioxtvQAECVvVC+fziK32kh4LRQH3DjtpkxGhSHRxOksjncNjP1ASdumxmttWw3LYQQ4oInCcNZGBpLUuW1H1VW4bERS+doqii0HtjNRuLpLAYDXDm9DKvJKNtNCyGE+NBRWuvzXYcPhFJqCDh0Lp/T4PAGUAYD+VzunUKjEZ3P55PRkDJZrEoZTFrnszqbTgEYzHan1vk8Op9HGQxKGQz5TCJ21HNAKTB8Lut6kZH4nT2J4dmTGJ49ieHZa9Zau8/FE100LQxa67LzXYfTpZTaqLVecL7r8WEl8Tt7EsOzJzE8exLDs6eU2niunksGPQohhBDilCRhEEIIIcQpScJwYfrP812BDzmJ39mTGJ49ieHZkxievXMWw4tm0KMQQgghzpy0MAghhBDilCRhOA+UUgeVUtuVUlvGR7AqpUqUUmuVUu3Fn/5iuVJK/YdSar9SaptSat75rf35oZT6iVJqUCm144iy9xwzpdRni+e3K6U+ez7ey/lyghh+XSnVU7wWtyilVh3x2FeLMdyrlLruiPLri2X7lVJf+aDfx/milKpVSr2olNqtlNqplPrLYrlch6fpJDGU6/A0KaVsSqk3lVJbizH8f4rlDUqpDcVr6hGllKVYbi3e3198fPIRz3Xc2J6Q1lpuH/ANOAiUHlP2APCV4vFXgG8Wj1cBvwcUsAjYcL7rf55idjkwD9hxpjEDSoCO4k9/8dh/vt/beY7h14EvH+fcFmArYAUagAOAsXg7ADQCluI5Lef7vX1A8asC5hWP3cC+YpzkOjz7GMp1ePoxVICreGwGNhSvr0eBO4rlPwDuLR7/KfCD4vEdwCMni+3JXltaGC4cNwEPFY8fAm4+ovxnuuANwKeUqjofFTyftNbrgNFjit9rzK4D1mqtR7XWQWAtcP37X/sLwwlieCI3Ab/SWqe01p3AfuCS4m2/1rpDa50GflU89yNPa92ntX67eDwG7AZqkOvwtJ0khici1+ExitdTtHjXXLxpYDnweLH82Otw/Pp8HLhaKaU4cWxPSBKG80MDf1BKbVJK3VMsq9Ba90HhPxVQXiyvAbqP+LeHOfl/sIvJe42ZxPL47is2mf9kvDkdieFJFZt12yj8dSfX4Rk4JoYg1+FpU0oZlVJbgEEKCecBIKS1zhZPOTIeE7EqPh4GApxBDCVhOD+Waq3nASuBP1NKXX6Sc9VxymRqy8mdKGYSy3f7PjAFaAX6gG8VyyWGJ6CUcgG/Bu7XWkdOdupxyiSGHDeGch2+B1rrnNa6FZhEoVVgxvFOK/48ZzGUhOE80Fr3Fn8OAr+h8IEPjHc1FH8OFk8/DNQe8c8nAb0fXG0vaO81ZhLLY2itB4q/fPLAD3mnSVJieBxKKTOFL7qHtdb/XSyW6/A9OF4M5To8M1rrEPAShTEMPqXU+HYPR8ZjIlbFx70UuibfcwwlYfiAKaWcSin3+DFwLbADeBIYHy39WeCJ4vGTwGeKI64XAeHx5k/xnmO2BrhWKeUvNnleWyy7aB0zHuYWCtciFGJ4R3GEdQMwDXgTeAuYVhyRbaEwiOrJD7LO50ux3/fHwG6t9b8e8ZBch6fpRDGU6/D0KaXKlFK+4rEdWEFhLMiLwO3F0469Dsevz9uBF3Rh1OOJYnti53vE58V2ozCqd2vxthP4u2J5AHgeaC/+LNHvjIj9LoU+qu3AgvP9Hs5T3P6LQlNlhkJmfPeZxAz4YwqDe/YDnz/f7+sCiOHPizHaVvwFUnXE+X9XjOFeYOUR5asojG4/MH79Xgw3YBmFJtttwJbibZVch+ckhnIdnn4M5wCbi7HaAXytWN5I4Qt/P/AYYC2W24r39xcfbzxVbE90k5UehRBCCHFK0iUhhBBCiFOShEEIIYQQpyQJgxBCCCFOSRIGIYQQQpySJAxCCCGEOCVJGIS4CCmlPqeU0kqpqee7LkKIDwdJGIQQQghxSpIwCCGEEOKUJGEQQqCUekkptV4ptUIp9bZSKq6U2qGUuvk4585VSv1GKTWilEoopfYqpb56xONKKfXFYnlaKdWnlPqOUspzzPNopdQ3lFJfUkodUkrFlFJPK6XKi7dHlVJhpVS3Uupvj1OPBqXUw0qpIaVUSim1RSl1y/sTISGEJAxCiHFTgP8f+FfgVgrLSD9+5DgHpdQlwOvFc78I3FA8f9IRz/OPxbK1wMeAB4DPAU8rpY79nfNpYDnwp8CfA5cBP6OwKds24DbgGeBflFKrjqhHLYVtkecW63Ej8Dbwa6XUjWcXBiHE8cjS0EJchJRSnwN+CkzTWu9XSr0ELAVatNbtxXPKKSQNf6+1/qdi2TqgAWjWWseP87wlFHa8+5XW+nNHlN9FYb+Am7TWTxbLNIX9F1q01tli2b9SSAD+Xmv9jWKZqficT2utP18s+zGFJGG61nrkiNdZC5Tpwta/QohzSFoYhBDj2seTBZjYfn0QqANQSjkoJBUPHy9ZKFoEWIFfHFP+KyALXHFM+drxZKFoT/HnxO6Nxcf3c/RWvNdTaHkIK6VM47fiv5t7bPeHEOLsmU59ihDiIjF6nLIUhd3uAPwU/sg4fJLnKCn+PGoLdq11Vik1csTj44LH3E+fpNx2xP1y4DPF2/EEgMhJ6imEeI8kYRBCnK4gkAdqTnLOeNJRSWH7dmCiWyEAjBzvH52BEeAV4JsneLz3HL2OEKJIEgYhxGnRWseVUuuBu5RS/6C1ThzntDcotErcATx/RPkfUfh98/I5qs6zwGJg5wnqIYQ4xyRhEEK8F1+m8KX/ulLqWxS6JxqBVq31n2utR4sDF7+qlIpRGGcwA/gGsB54+hzV42vAm8A6pdR3gIMUukxmAY1a6z8+R68jhCiShEEIcdq01m8ppZYC/wB8m8IAx0MUZlyM+ztgCPgTCtMlRyhMlfyq1jp/jurRpZRaAHwd+CegrPg6O4CHzsVrCCGOJtMqhRBCCHFKMq1SCCGEEKckCYMQQgghTkkSBiGEEEKckiQMQgghhDglSRiEEEIIcUqSMAghhBDilCRhEEIIIcQpScIghBBCiFOShEEIIYQQp/S/AXJAJC0fnHbVAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.arange(data.income.min(), data.income.max(), 50)\n", "get_y = lambda a, b: a + b * x\n", "\n", "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "for i in range(models.shape[0]):\n", " y = get_y(models.a[i], models.b[i])\n", " ax.plot(x, y, linestyle='dotted', color='grey')\n", " \n", "y = get_y(ols['a'], ols['b'])\n", "\n", "ax.plot(x, y, color='red', label='OLS')\n", "ax.scatter(data.income, data.foodexp, alpha=.2)\n", "ax.set_xlim((240, 3000))\n", "ax.set_ylim((240, 2000))\n", "legend = ax.legend()\n", "ax.set_xlabel('Income', fontsize=16)\n", "ax.set_ylabel('Food expenditure', fontsize=16);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Second plot\n", "\n", "The dotted black lines form 95% point-wise confidence band around 10 quantile regression estimates (solid black line). The red lines represent OLS regression results along with their 95% confidence interval.\n", "\n", "In most cases, the quantile regression point estimates lie outside the OLS confidence interval, which suggests that the effect of income on food expenditure may not be constant across the distribution." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n = models.shape[0]\n", "p1 = plt.plot(models.q, models.b, color='black', label='Quantile Reg.')\n", "p2 = plt.plot(models.q, models.ub, linestyle='dotted', color='black')\n", "p3 = plt.plot(models.q, models.lb, linestyle='dotted', color='black')\n", "p4 = plt.plot(models.q, [ols['b']] * n, color='red', label='OLS')\n", "p5 = plt.plot(models.q, [ols['lb']] * n, linestyle='dotted', color='red')\n", "p6 = plt.plot(models.q, [ols['ub']] * n, linestyle='dotted', color='red')\n", "plt.ylabel(r'$\\beta_{income}$')\n", "plt.xlabel('Quantiles of the conditional food expenditure distribution')\n", "plt.legend()\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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 1 }