{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Empirical Test Statistics\n", "\n", "In this notebook we will compute test statistics empirically from pseudo-experiment and establish that they behave\n", "as assumed in the asymptotic approximation." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pyhf\n", "\n", "np.random.seed(0)\n", "plt.rcParams.update({\"font.size\": 14})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we define the statistical model we will study.\n", "\n", "* the signal expected event rate is 10 events\n", "* the background expected event rate is 100 events\n", "* a 10% uncertainty is assigned to the background\n", "\n", "The expected event rates are chosen to lie comfortably in the asymptotic regime." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "model = pyhf.simplemodels.uncorrelated_background(\n", " signal=[10.0], bkg=[100.0], bkg_uncertainty=[10.0]\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The test statistics based on the profile likelihood described in [arXiv:1007.1727](https://arxiv.org/abs/1007.1727) cover scanarios for both\n", "\n", "* POI allowed to float to negative values (unbounded; $\\mu \\in [-10, 10]$)\n", "* POI constrained to non-negative values (bounded; $\\mu \\in [0,10]$)\n", "\n", "For consistency, test statistics ($t_\\mu, q_\\mu$) associated with bounded POIs are usually denoted with a tilde ($\\tilde{t}_\\mu, \\tilde{q}_\\mu$).\n", "\n", "We set up the bounds for the fit as follows" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "unbounded_bounds = model.config.suggested_bounds()\n", "unbounded_bounds[model.config.poi_index] = (-10, 10)\n", "\n", "bounded_bounds = model.config.suggested_bounds()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we draw some synthetic datasets (also referrerd to as \"toys\" or pseudo-experiments). We will \"throw\" 300 toys:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "true_poi = 1.0\n", "n_toys = 300\n", "toys = model.make_pdf(pyhf.tensorlib.astensor([true_poi, 1.0])).sample((n_toys,))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the asymptotic treatment the test statistics are described as a function of the data's best-fit POI value $\\hat\\mu$. \n", "\n", "So let's run some fits so we can plots the empirical test statistics against $\\hat\\mu$ to observed the emergence of the asymptotic behavior." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "pars = np.asarray(\n", " [pyhf.infer.mle.fit(toy, model, par_bounds=unbounded_bounds) for toy in toys]\n", ")\n", "fixed_params = model.config.suggested_fixed()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now calculate all four test statistics described in `arXiv:1007.1727`" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "test_poi = 1.0\n", "tmu = np.asarray(\n", " [\n", " pyhf.infer.test_statistics.tmu(\n", " test_poi,\n", " toy,\n", " model,\n", " init_pars=model.config.suggested_init(),\n", " par_bounds=unbounded_bounds,\n", " fixed_params=fixed_params,\n", " )\n", " for toy in toys\n", " ]\n", ")" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "tmu_tilde = np.asarray(\n", " [\n", " pyhf.infer.test_statistics.tmu_tilde(\n", " test_poi,\n", " toy,\n", " model,\n", " init_pars=model.config.suggested_init(),\n", " par_bounds=bounded_bounds,\n", " fixed_params=fixed_params,\n", " )\n", " for toy in toys\n", " ]\n", ")" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "qmu = np.asarray(\n", " [\n", " pyhf.infer.test_statistics.qmu(\n", " test_poi,\n", " toy,\n", " model,\n", " init_pars=model.config.suggested_init(),\n", " par_bounds=unbounded_bounds,\n", " fixed_params=fixed_params,\n", " )\n", " for toy in toys\n", " ]\n", ")" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "qmu_tilde = np.asarray(\n", " [\n", " pyhf.infer.test_statistics.qmu_tilde(\n", " test_poi,\n", " toy,\n", " model,\n", " init_pars=model.config.suggested_init(),\n", " par_bounds=bounded_bounds,\n", " fixed_params=fixed_params,\n", " )\n", " for toy in toys\n", " ]\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot all the test statistics we have computed" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "muhat = pars[:, model.config.poi_index]\n", "muhat_sigma = np.std(muhat)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check the asymptotic assumption that $\\hat{\\mu}$ is distributed normally around it's true value $\\mu' = 1$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "fig.set_size_inches(7, 5)\n", "\n", "ax.set_xlabel(r\"$\\hat{\\mu}$\")\n", "ax.set_ylabel(\"Density\")\n", "ax.set_ylim(top=0.5)\n", "\n", "ax.hist(muhat, bins=np.linspace(-4, 5, 31), density=True)\n", "ax.axvline(true_poi, label=\"true poi\", color=\"black\", linestyle=\"dashed\")\n", "ax.axvline(np.mean(muhat), label=\"empirical mean\", color=\"red\", linestyle=\"dashed\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we define the asymptotic profile likelihood test statistics:\n", "$$t_\\mu = \\frac{(\\mu-\\hat\\mu)^2}{\\sigma^2}$$\n", "\n", "$$\\tilde{t}_\\mu =\n", "\\begin{cases}\n", "t_\\mu,\\;\\text{$\\hat{\\mu}>0$}\\\\\n", "t_\\mu - t_0,\\; \\text{else}\n", "\\end{cases}\n", "$$\n", "\n", "\n", "\n", "$$q_\\mu =\n", "\\begin{cases}\n", "t_\\mu,\\;\\text{$\\hat{\\mu}<\\mu$}\\\\\n", "0,\\; \\text{else}\n", "\\end{cases}\n", "$$\n", "\n", "$$\\tilde{q}_\\mu =\n", "\\begin{cases}\n", "\\tilde{t}_\\mu,\\;\\text{$\\hat{\\mu}<\\mu$}\\\\\n", "0,\\; \\text{else}\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def tmu_asymp(mutest, muhat, sigma):\n", " return (mutest - muhat) ** 2 / sigma**2\n", "\n", "\n", "def tmu_tilde_asymp(mutest, muhat, sigma):\n", " a = tmu_asymp(mutest, muhat, sigma)\n", " b = tmu_asymp(mutest, muhat, sigma) - tmu_asymp(0.0, muhat, sigma)\n", " return np.where(muhat > 0, a, b)\n", "\n", "\n", "def qmu_asymp(mutest, muhat, sigma):\n", " return np.where(\n", " muhat < mutest, tmu_asymp(mutest, muhat, sigma), np.zeros_like(muhat)\n", " )\n", "\n", "\n", "def qmu_tilde_asymp(mutest, muhat, sigma):\n", " return np.where(\n", " muhat < mutest, tmu_tilde_asymp(mutest, muhat, sigma), np.zeros_like(muhat)\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now we can compare them to the empirical values:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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x/aOPPtpp39rPB1R9KKkuJiaGxx9/nMcff7zO5+zWrVvVhc/VTZs2reoC4T293+zZs2v8HBUVxc0338zNN9+8y8cRkdBWe6Q8JSVlj6cLa6RcI+UiuzRvHjRvDief3GhPqZEgkd+xYsUKCgoK6N27N88//zytW7dm7ty5DfZ8eXl5vPXWW7z//vtVF/KKiISC2iPlP/30007ThTVSrpFykb1SVARvvglnnw2e+u0Atzum+tBvU9G3b1+7ePFit2PIbqxZs4YePXq4HaNe9OjRg6VLlxIXF9coz9exY0e2bt3KxIkTaxz499fAgQPp1avXLkeBQlE4/R2FI2PM19bavm7nCEW7O06F09/166+/zieffMLUqVMB+MMf/sDTTz9N165dG/R5/+///o+2bdsya9asenm8pvj+COH1tyQR7JVXnGlwH34IAwfW+8Pv6lil6XAiu1FUVER0dHSjFUAAP//8c4M8bl3T6ERE9seKFSv2arrw/srLy+PTTz/l/fffZ/ny5Q32PCLSiObOhQMOgOOPb9SnVREkshsJCQl1Xm8jIiJOERQXF0fv3r059thjq6YLX3jhhQ3yfH369GHr1q3cc8899OrVq0GeQ0QaUU4O/POfzlpp0dGN+tQqgkRERGSfrF69ulGnC2ukXCTM/P3vUFYGF13U6E+txggiIiKy19yYLiwiYebFF+GQQ2AXXSUbkoogERER2WuaLiwi++XHH+GLL6CBps/+HhVBIiIiIiLSuF58EYyBCy5w5elVBImIiIiISOOx1imCBg6Edu1ciaAiSEREREREGs+iRbB2rSsNESqpCBIRERERkcbz4osQFwdnnulaBBVBIiIiIiLSOIJBmDcPTj8dUlJci6EiSEREREREGsd77zmLpLrUFa6SiiAREREREWkcL74IzZvDoEGuxlARJFKHG2+8kUEuvzhFREREwkpBAbz5Jpx/Pni9rkZRESRSh0WLFnHUUUe5HUNEREQkfMyfDyUlrk+FA5eLIGNMtDFmsjEm0xhTsuO/dxtjYtzMJZErEAjg9Xr55JNPuPvuuzHG0LNnT7djiYiEhAULFtCzZ0+GDRvGSy+9xPnnn+92JBFpSl58ETp3hqOPdjuJ6yNB44FRwGjgIGDMjp8nuBlKQkd+cYCl6/L4+Lsslq7LI7840KDPFxMTwxdffAHAwoUL2bRpE59//nmDPqeISFMxd+5c3nzzTQ488EAmTJjAxRdf7HYkEWkq1q+HDz90RoGMcTsNbo+4HAMssNYu2PHzz8aYtwD3y0NxXWUB5PPGkObz4g+Ws3RdHn3ap5Hqa5h5pFFRUWzatImkpCSOPPJITAi8SEVEQsXLL78MwB133MEdd9zhchoRaVJefhmshaFD3U4CuD8S9BlwojHmIABjTE/gJOCfrqaSkJCZU4TPG4PPG4Mxpur7zJyiBn3epUuX0rt3bxVAIiIiIvXBWnjhBWcaXNeubqcB3C+C7gf+Bqw2xgSBb4A51tona+9ojBlhjFlsjFmcnZ3d2DnFBQX+IPGe6Brb4j3RFPiDDfq8y5Yto0+fPjW29e/fn82bNwOwZMkSzjrrrAbNICISqtQ9U0T22tdfw6pVMHy420mquF0EnQdcDAwBDt/x/UhjzGW1d7TWzrTW9rXW9s3IyGjkmOKG5HgP/mB5jW3+YDnJ8Z4Gfd7ly5dz6KGHVv1srSUrK4tWrVoBsHLlyhq3i4hEEnXPFJG9Nns2xMY6rbFDhNtF0IPAQ9baedbaldbavwGPoMYIAnRKT6A4UEZxoAxrbdX3ndITGvR5y8rK+Pbbb9m4cSP5+fn89NNPdOrUqer2lStXcsghhzRoBhGRUKPumSKyT0pKYO5c+OtfITXV7TRV3C6CfEB5rW3luJ9LQkCqz0uf9ml4Y6LIKw7gjYlq0KYIlaZMmcK8efNo27YtEyZMYMWKFTWKnqVLl6oIEhHXqXumiDQJCxZAXh5cconbSWpwuzvcAuBmY0wmzvVAfYBxwAuuppKQ4RRCjbui8NChQxlarXPJpEmTKCkpAeCrr75i4cKFdO7cuVEziYhUp+6ZItJkzJ4NbdvCH/7gdpIa3B5xuRZ4DXgSWAM8DMwCJroZSqS6FStWUFBQQO/evXn++edp3bo1c+fOdTuWiEQwdc8UkSZh40Z49124+GKIjv79/RuRqyNB1tpCYOyOL5GQtHr1apYuXUpcXJzbUUREAKd7ZlqtEZ94TzR5DTwlrq7umSIiu/Tii1BRAcOGuZ1kJ26PBDVta9bABRdAbq7bSaSBFBUVER0drQJIws9XX8FVV0FWlttJZB+ESvdM0BICIrIL1jpT4Y45Brp1czvNTlQE7Y+yMpg3D5591u0k0kASEhJYtWqV2zFE6t/06c7q3fHxbieRfRAq3TO1hICI7NKiRc6AQYg1RKikImh/HHIInHgiPPGEUxCJiDQFmzbB3/8Ol14KSUlupwl5xpjWxpg5xphsY0yJMWa1MWaAm5lCpXumlhAQkV2aPds50XbuuW4nqZOKoP01ejSsWwdvveV2EhGRPTNjhnPiZtQot5OEPGNMKvA5YIBTgR44TX1cn0dYWQgN6N6iUQogcLpnrl+/noqKCp566iktISAidfP7ndkGZ50Fyclup6mT2y2ym77Bg6FDB3j0UTjzTLfTiIjsXmkpPP00/PnP0KWL22magpuATdbai6tty3QrTKhZsWKFlhAQkZ29+SZs2wbDh7udZJc0ErS/oqPhmmvg449h+XK304iI7N6rr8KWLaw9/5JGW2SziTsDWGiMecUYk2WMWWaMucaoRzSgJQREZBdmz4b27Z3LRkKURoLqw2WXwR13wGOPwTPPuJ0mZFhrtZaE7DNrrdsRwo+1lE2dRumBXcntP4A0b0yjLLLZxB0IjASmAvcBhwGP7bjt8eo7GmNGACMA2rdv34gR3aMlBEQiW35xgMycIgr8QZLjPXRKTyB1axa8/z7ceitEhe54S+gma0rS0uDCC+GllyAnx+00IcHj8eD3+92OIU2Y3+/H42nYdr8RZ+FCYpZ8TdawK/DFehp1kc0mLApYYq2dYK1daq19HngU2OmCKmvtTGttX2tt34yMjEYP2ti0hIBIZMsvDrB0XR6BsgrSfF4CZRUsXZeH/9nZTnvsEFwbqDoVQfXl2muhpEQjQTu0aNGCDRs2UFxcrDP6slestRQXF7NhwwZatGjhdpzw8uijlCUmUXTuBTU2x3uiKfAHXQoV8jYBq2ttWwNExlDPbmgJAZHIlplTVHUireqkmica88IcOOEECPHrAzUdrr706gUnneS0y77hBoiJ7F9t8o5OIBs3biQY1Icr2Tsej4eWLVtW/R1JPdi4EV59la3DrqDIG4+v2k2NschmE/Y50L3Wtm7ALy5kEREJGQX+IGm1plGnL11I3E9r4fZbXUq15yL7k3p9Gz0azjgD3ngDzj7b7TSuS05O1odYkVDx9NNQXk7c2GspDjjrmsV7ovEHyykOlNG9VZrLAUPWVOB/xpiJwCtAH2A0cIurqUREXJYc78EfLMfn/a2cSHlpDmXJycScc46LyfaMpsPVp9NOg44dnXbZIiKhorIt9qmnktyrhyuLbDZV1tqvcDrEnQusAqYAtwFPuplLRMRtndITKA6UURwow1pLaXYOaf9aQPn5F4DP9/sP4DKNBNWnynbZN9wAy5bBYYe5nUhEBF55BbKzndFqKhfZVNGzp6y17wDv1PNjqnum7Bddbytuq1ywOTOniLziAAe+9RrRpSVEX32V29H2iEaC6tullzrV72OP/f6+IiINzVpndLpHDzj5ZLfTCOqeKfVDHTQlFFQWQgO6ZdBu/kvQt2+TGQRQEVTf0tLg4ovVLltEQsOXX8LXXzsdLDXyEBLUPVP2hzpoSkhatAhWroQrrnA7yR7TdLiGcO21zvz7GTNg4kS304hIJJs2DVJS4KKL3E4iO6h7puwvddCUkDNrFiQkwAUX/P6+IUJFUEPo2RNOOQUef9y5Pig21u1EIhKJfv4ZXnsNxo2DxES300g16p4pImGjsBDmzYPzz4ekJLfT7DFNh2so118PmzfDyy+7nUREItWjj0JUVFVDBBERkXr38stQVNSkpsKBiqCG88c/OguoPvKIc2GyiEhj2rYNnnkGzj0X2rVzO42IiISrWbPgkEPgqKPcTrJXVAQ1FGOcKSgrV8J//uN2GhGJNM8840xRGDfO7SQiIhKuli2DxYudUaAm1nxHRVBDGjIEWrWChx92O4mIRJJgEKZPhwED4Igj3E4jIiLhatYs59r3oUPdTrLXVAQ1pNhYZ/HU996DVavcTiMikWL+fPj1V+faRBERkYZQXOwsCXP22dCsmdtp9pqKoIZ21VUQHw9Tp7qdREQigbXO6HO3bnDqqW6nERGRcPXqq871p02sIUIlFUENrXlzGD4cXnzR6RYnItKQPv3UmZ993XVOZzgREZGGMGuWc8LthBPcTrJPdIRsDGPHOnP0n3zS7SQiEu4eecQ5+XLxxW4nERGRcPXNN/D553D55U2uIUIlFUGNoVs3GDzYKYKKi91OIyLh6ocf4K234OqrwedzO42IiISrp55yrn2/5BK3k+wzFUGN5frrITcX/vY3t5OISLiaNg08Hhg1yu0kIiISrgoL4YUXnHXo0tPdTrPPVAQ1kPziAEvX5fHxd1ksXZdH/hFHQ9++zlSVigq344lIuMnNheefhwsvdFrzi4iINISXXnIKoZEj3U6yX1QENYDKAihQVkGaz0ugrIKlv+ZTNGo0fP89vPOO2xFFJNw8/TT4/U5DBBERkYZgrXN5R58+cPTRbqfZLyqCGkBmThE+bww+bwzGmKrvvz9+ELRvDw8+6HZEEQknJSXw2GMwaBD06uV2GhERCVeffw4rVzqjQE20IUIlFUENoMAfJN4TXWNbvCeagjJg3Dinhe3//udOOBEJP3PmwJYtMH6820lERCScPfkkpKTAkCFuJ9lvKoIaQHK8B3+wvMY2f7Cc5HiP00qwWTO4/36X0olIWCkrgwcegKOOgoED3U4jIiLhassWeO01pyNcGHQgVRHUADqlJ1AcKKM4UIa1tur7TukJkJAA117rtLH95hu3o4pIUzd/Pvz0E9x8c5OfmiAiIiHs2WeddS+vusrtJPVCRVADSPV56dM+DW9MFHnFAbwxUfRpn0aqz+vscM01TgX9wAPuBhWRps1auO8+6N4d/vIXt9OIiEi4Ki93GvCcfLJzzAkDMW4HCFdOIeSt+8b0dLjiCnjiCZg82WmWICKyt/79b1i2zDk7F6VzWiIi0kDeeQd+/RWmT3c7Sb3RUdMt48Y5/33kkZ3XFCoOuJtNRJqG++6DNm1g6FC3k4iISDh78knneDN4sNtJ6o3rRZAxprUxZo4xJtsYU2KMWW2MGeB2rgbXvj0MHYqdNYtVy9fWXFNIhZCI/J6FC+HDD50TKrGxbqcREZFwtXYtvPceXHklxITPJDJXiyBjTCrwOWCAU4EewLVAlpu5Gs1NN2GKi+k4b/ZOawpl5hS5nU5EQtn990NamjO1VkREpKE8/bRT/Fx+udtJ6pXbI0E3AZustRdbaxdZazOttR9Ya9e4nKtx9OxJzkmDaPXCM0QVba/aHO+JpsAfdDGYiIS0NWvg9dedJitJSW6nERGRcOX3w3PPwZlnQuvWbqepV24XQWcAC40xrxhjsowxy4wx1xgTOX1ec6+5jpj8PNJefqFqW9WaQiIS0XZ5veCDD0J8vNNuX0REpKG8/DLk5cHVV7udpN65XQQdCIwEfgIGAdOB+4BRtXc0xowwxiw2xizOzs5u3JQNqOWgE8nv24/mMx6H0tKaawqJSMSqLIBqXy+47fsf4cUXnWkJGRluxxQRkXBlLUybBoceCgPC73J9t4ugKGCJtXaCtXaptfZ54FHqKIKstTOttX2ttX0zwujAn+rzEnPLBGI3b8Tz93k7rykkIhEpM6eo6hrB6tcLlj7wMFRUwPXXux1RRETC2UcfwcqVMHZsWC7G7XYRtAlYXWvbGiCiFs5JPGMwHHooB73wFH3aJKsAEhEK/EHiPdE1tiVu30bzl+fAkCHQoYNLyUREJCJMm+bMOLjgAreTNAi3i6DPgdrLznAe0YoAACAASURBVHYDfnEhi3uMgVtugW+/hfnz3U4jIiEgOd6DP1heY1vqjCeI8vth/HiXUomISET48UdYsACuugri4txO0yDcLoKmAv2MMRONMV2MMecAo4EnXM7V+M4+Gw46CCZPdqa6iEhE65SeUHWNoLWW0uwcWs6ZSfCvZ8LBB7sdT0REwtljjzltscOwIUIlV4sga+1XOB3izgVWAVOA24An3czliuhomDgRVq2CN990O42IuCzV56VP+zS8MVHkFQdo87dZxBRtx3vH7W5HExGRcFZQ4LTFPu+8sGuLXZ3bI0FYa9+x1va21sZZa7tZax+11lq3c7ni/POhSxdnNChCfwUi8pvKQmhA6zhaPz8DzjjD6dIjIiLSUJ57DgoLnYYIYcz1IkiqiYlxrg1auhTeecftNCISKh5/HPLz4dZb3U4iIiLhrLzcmQp37LFwxBFup2lQKoJCzYUXQseOcNddGg0SEdi+HR55BE49NewPSCIi4rK334affgr7USBQERR6PB5nNOirr+D9991OIyJue+opyM2F225zO4mIiIS76dOhfXtn+nWYUxEUioYNg3btYNIkjQaJRLLiYnjwQTjlFDj6aLfTiIhIOFu+HD78EK65xrlEI8ypCApFXi/cfDN88QX8979upxERt8yYAdnZcLs6womISAObPh18Prj88qpN+cUBlq7L4+Pvsli6Lo/84oCLAeuXiqBQdemlTlvCyZPdTiIibvD74YEH4MQTnQtURUREGkpWFsydC8OHQ1oa8FsBFCirIM3nJVBWEVaFkIqgEJRfHGBplp+1l4yEjz+m8P0P3I4kIo3t2Wdh82aNAomISMN7+mkoLYXRo6s2ZeYU4fPG4PPGYIyp+j4zp8jFoPVHRVCIqV51+4ddSiC9BcE7JoVN1S0ie6C0FO6/H44/HgYMcDuNiIiEM7/faYt96qnQvXvV5gJ/kHhPdI1d4z3RFPiDjZ2wQagICjHVq258CeRedS3NvvyUrH/+x+1oItJYnn0W1q93OsIZ43YaEREJZ7NnQ04OjB9fY3NyvAd/sLzGNn+wnOR4TyOGazgqgkJM7ao79+LLCGa0oMX9d6tTnEgk8Pvh7rudUaCTT3Y7jYiIhLPycnjoIacD6XHH1bipU3oCxYEyigNlWGurvu+UnuBS2PqlIijE1K66bbyPDVdfR+riL+ADXRskEvaeego2bXIKIY0CiYhIQ/rHP5zFUW+6aadjTqrPS5/2aXhjosgrDuCNiaJP+zRSfV6XwtYvY5vg6ELfvn3t4sWL3Y7RICqvCfJ5Y4j3ROMPluPfXsQJpx5HVJsDnLbZ+mAkEp62b4dOnaBPnyaxWLIx5mtrbV+3c4SicD5OiUiYsBaOOgq2bYM1ayA6+vfv0wTt6lilkaAQU1fVfViXVkTdfhssXAj//KfbEUWkoTz2mDMvW63xRUSkoX38MSxeDDfcELYF0O5oJKipCAbhoIMgJcX5g41S/SoSVvLznVGg446DBQvcTrNHNBK0axF5nBKRJiG/OEBmThHtLzqH5NUrKPpuLanNkt2O1WA0EtTUeTxw552wdCm8/rrbaUSkvk2d6hRCd93ldhLZBWPMBGOMNcY87nYWEZF9UXnZRfSqlTT/5AM2DxvB0ix/RC7FoiKoKRkyxBkNuv12p5uHiISHnBynCDr7bOd6IAk5xph+wAhghdtZRET2VeVSLO2ee5JyXwIFw68IqwVQ94aKoKYkOto5S7x6Ncyb53YaEakvDz7oNEWYNMntJFIHY0wK8BJwKZDnchwRkX1W4A+SnLWR1Dfnk3fBxVSkpobVAqh7Q0VQU3PWWXDooc7UuLIyt9OIyP7avNlpiDB0KPTs6XYaqdtM4DVr7Ye728kYM8IYs9gYszg7O7uRoomI7LnkeA+ps54Ea8m5YiQQXgug7g0VQU1NVJTTOWrtWnjhBbfTiMj+uu8+CATgjjvcTiJ1MMZcAXQBbv29fa21M621fa21fTMyMho+nIjIXjowOkDGvBfIHXwmgQPaht0CqHtjn4sgY8xrxpjbjDFnGGM679g2pP6iyS4NHgxHHulMnSktdTuNiOyrX391FkcdPhy6dHE7TVjan2OVMaY7cA8wxFobeXNFRCTspLzwHDHFxWRfNTosF0DdG/szEjQF+AU4FphhjCkEdCqzMRjjrCa/bh3MmOF2GhHZV5MmOYvV3Xab20nC2f4cq/oD6cA3xpgyY0wZMAAYuePn2AZJLCLSEIqKnCY8f/oTPQYdx4DuLSK2AAKI2dc7WmuXAksrfzbGHAkMq49Qsnv5xQEyu/elY7/jSJx0F0XnDiG1VbrbsURkb6xeDc8/D6NHQ4cObqcJW/t5rHoDqL3Yz/PADzgjRJHXU1ZEmq6ZMyE7m8IbxrN2XZ7TJCHeQ6f0hIgshPa5CDLGtLDWZlX+bK39yhgzs35iya5U9nf3eWPIuXUyaaedSP6ke+Dh+yLyD1ikyZowARITYeJEt5OEtf05Vllr84H8Wo9XBGy11q6q36S/+SW3iC9/zCW7sISMpDj6dW5Oh+aRN19fROpRSQk8+CDBEwbyUXpXtm3cRlmZJSbGsD6vmOO7ZkTc58h9LoKAN4wxGUAmsBKIA1YZYzyaO91wKvu7+7wxlPTuQ/7pZ9FuztO8PfgCUjt3iOiKXqTJ+OwzeOstuOceSNcobgNrUseqX3KLeGPJelLiPbROiaewJMgbS9ZzxuFtVQiJyL577jnYtIk19z7G+jw/qfFefPFRlJZVsD7Pz4r1+ZzQrYXbKRvVHl8TZIxZtWOtBACstcdYa7sCVwGfAluAeGC5MUaLyTWQAn+QeE901c8/jh4PwTK6Pj2VNJ+XQFkFS9flReTKvyJNgrVw001wwAEwZozbaZokY8zLxphBdWyvcZyC+j9WWWsHWmuv2cfov+vLH3NJifeQ4oslKiqKFF8sKfEevvwxt6GeUkTCXSDgdCI95hgWH9iblDgPcZ5ojDHEeaJJifOwNqvQ7ZSNbm9GgnoCdV0Emgv80Vo7qnKDMca3v8GkbsnxHvzBcnxe539dZkor4v9yAQe98RI//DQO07mrsz2niD7tNRokEnLeeAO++AJmzQKf3ir30QJgBtCx1vY6j1M7CqPrdxyn3qi2PeT+B2QXltA6Jb7GtqQ4D5u2+V1KJCJN3gsvON1IZ87EmijA1trBYjFuJHPV744EGWP+ZYyZhPMba1fHLj7gyuobrLXF9RNPauuUnlDV091aS25RKcuGXUNFXDyt7nNWm4/UlX9FQl5ZmXMtUI8eTlts2Vd/BJ6r/GFfjlMQmseqjKQ4Cktqvn8XlgTJSIpzKZGINGllZXDvvdC3LwwaRNcWiRSUBCkJOp8jS4JlFJQE6doi0e2kjW5PRoJW4rQENcCiHe1Fl+N021kBHARsarCEUkOqz0uf9mlk5hSRVxwgNd5LekZ7cq4eQ6uHpuBbvJCcQ4+IyJV/RULes8/Cd9/Bm29CzP5ckhnxjgLurvZz2Byn+nVuzhtL1gPOCFBhSZBt/iAn9mjpcjIRaZJefhl++gkeeQSM4dC2qWzK9/NTdhHbS4Mkxno4MCOBQ9umup200Rlraw+J7WJHY0px1kw4ADhsx1dvnELqFmvtyw0Vsra+ffvaxYtrdy2NTJXd4hLLSjnspKPwd+jE1y+8Tp8OzdQcQSSUFBU5C6J26QKffOKs99XEGWO+ttb2deF5BwPnW2uH1toeFscpdYcTkXpRXg4HHwyxsbBsGRhDfnGAz37IJr84SLC8Ak90FKk+D8eFcXe4XR2r9uZUZOKOTjpLgLfrLZnsl+ojQ5mjbqDbnTdy5KrPSexxltvRRKS6qVNh82aYP7+qAMovDpCZUxTxazXsLWvtApzrgmoLi+NUh+YJKnpEZP/Nn+/MPvj736uOO5k5RWQkxdGh+W/T34oDZRF5Lfked4cLxVai4qgshLpNHAvdu5N4x23OHFARCQ3Z2fDAA/DXv8IxxwC/jeIGyirU2bGe6DglIrJDRQXcfTccdBCceWbV5tpdhiFyryXf4yJImoCYGIrunAxr1vDdvdP1gUokVNx1FxQXOxen7lB9zS9jTNX3mTlFLgYVEZGw8NZbsHKlsyB39G9FT2WX4er8wfKIvJZcRVAYyS8OsKj38RT07ceBj95Ped42FUIiblu9Gp56CkaMgO7dqzbrbJyIiDQIa2HyZOjcGc4/v8ZNtbsMV37fKT3ypuCqCAojmTlF+GI9bJl0HzG5OXSYMU1nlkXcdv31kJTkjAZVo7NxIiLSIN58E5YscUaBanUirbyEwhsTRV5xAG9MFH3ap0Xk9ajq0RpGCvxB0nxeSg49jLxzhtD82afIvWAYW1q0cTuaSGT65z/h3Xedpgjp6TVu6pSewNJ1eYAzAuQPllMcKKN7qzQ3koqISDgoL4fbboNu3eCii+rcxSmEIq/oqU0jQWGk+pnlLTfdhvV4aXH3bTqzLOKGYBDGjXMORCNH7nSzzsZJo3n/feeDkYiEv1degVWrYNIkrUf3O1QEhZHq8zyDLVqy8eqxNHv/Hbp+85Xb0UQiRmXXt7V33g/ffcf2e+8Hb92FTWUhNKB7CxVA0jC++goGDYI//clp0S4i4ausDO64Aw49FM491+00IS9kiiBjzARjjDXGPO52lqaq9pnl3CtGUt6hA4k336izgCKNoLIAqsjKpuPjD5F//Il81aOfmpOIe/r2hVmz4PPPoXdv+Pe/3U4kIg1lzhxYu9ZpihAVMh/xQ1ZI/IaMMf2AEcAKt7M0ddXPLB/WrTXRDz0EK1bAs88Cv31I+/i7LHWOE6lnlW2vOz7+ENFF28m64x58sR41JxH3GAOXX+6MCKWnO6NCt9yiteREwk1pqdOA56ijYPBgt9M0Ca4XQcaYFOAl4FIgz+U44eess+D44+HWW8nflK3FGUUaUIE/SOpP39PsxefYeuGllHbvobbXEhoOPtgphC67zFmvasAAWLfO7VQiUg/yiwP8ev90WLeOtaPHk69jzh5xvQgCZgKvWWs/3N1OxpgRxpjFxpjF2dnZjRQtDBgD06ZBTg6ld96lxRlFGlByXAytJt1CRWIiW66fAKjttYQQn8+ZGjd3rjND4LDDnFa6ItJk5RcHWP7dBlo+/jDbjz6G3H4n6AT3HnK1CDLGXAF0AW79vX2ttTOttX2ttX0zMjIaPlw4OfxwuOQSMp6fQcqGX2rcpLPUIvWn6+KPSfnsI3699ibKUtMiehE6CWEXXABLl0KnTnDGGTB2rDOVRkSanMycIjq9MgdvdhZbbroNX6yHigp4b9VmXfrwO1wrgowx3YF7gCHWWn0Kb2hTpmC9sbS8c0KNzTpLLVJPSktJnDCe8m7dyBt+udpeS2jr0gX+9z8YMwamT4djjnEuqBaRJqUoeysHzHyMwoEnU3xUfwpLgvyytYh8f0CXPvwON0eC+gPpwDfGmDJjTBkwABi54+dYF7OFn1atCNwykbT/vo/3X29jrdVZapH69OCD8MMP+B98BDw6sSBNQGysM136jTcgM9OZNTBvntupRGQvdJ77DDF5W9lyw0QANub7iQKaJ8Tq0off4WYR9AZwCHBYta/FwLwd36tkrWfxN15PeY+edLzrFrbl5usstUh9ycyEKVMI/PVMPuxwGN9s3EZmdhHfbNzGpz9k6wychLa//AWWLXPWFrngArjiCigudjuViOxCZaffz7/8loyZT7DppD+R2+MQrLXkFgWosJYDUuOr9telD3VzbSlZa20+kF99mzGmCNhqrV3lTqrwk18cIDOniAJ/kOR4D12mTifpT3/k+PnPOn3kRWT/jRkD0dEsGXsb6/P8pMZ78cVHUVpWwfo8PyvW53NCtxZupxTZtfbt4aOPnIUW770XvvjCWXn+4IOrdql9POmUnqCTaCKNrLIA8nlj6DZrOtHFRXw78kaiy8opCZaTGu8h3hvNxnw/20sLSYyNIc3npVmiXqu1hUJ3OGkglS+U6i2xF3c4hMD5Q+CBB+D7792OKNL0LVjgfN15J6ujkkiJ8xDnicYYQ5wnmpQ4D2uzCt1OKbKTndaNC1TAlCnw3nuQnQ1HHumsMWdtnccTXWcg0vgq16NL3fgrzf/2LHnnX4SvT2+S4jwM6N6Cfp2bk5m9ne0lQZJiY9heEmTVhnyaJagIqi2kiiBr7UBr7TVu5wgXlS+U6i2xKyrgXxdfR5k3loLLryS/SB2BRPZZcTGMHu2cLR8zBosBbK2d7I7tIqFjt0XNH/8Iy5c7zRIuvxyGDuWXzE1aYkEkBBT4g8R7oml5/ySsx8uWcRNqTHfbWhSgV5tUEuM8FJaWkxjnoVebVLYW6YRFbSFVBEn9qnyhVCosCfJL7nY2+9LYcuOtJH/6EetnvaAzeSL76t574eef4YknwOOha4tEthSU8MOWAtZs3MYPWwrYUlBC1xaJbicVqaGuk2Q1ippWrZwRobvvhldeodufB9Jszcoaj6HrDEQaX3K8h+iFX5L69hvkXHkNZS1b1ej0W+APkpEUS/dWyRzRIY3urZLJSIrVa7UOKoLCWHK8B3+wvOrnjfl+ooyheYKXrRdfhv/gQ+h2/x388vPmqn12mh6hAkmkbj/84EwrvfBCGDAAgA7NEwiUVVBaVkGFdf4bKKugQ3N1YJTQUvskGdRR1ERHw8SJ8PHHRAcDdP7rKTR/9imwzminllgQaXydmvtoe8/tBDJakD3imp06/db+7Ad6re6KiqAw1ik9oerF4XQMKaUCnI4hMTFsnPIw3s2biJo8mY+/y+KT77P47IdszfkW+T3WwjXXQFyc0xp7h61FAfp2bE6P1sm0bZZAj9bJ9O3YXNMQJOTs1Qel447Dv3AxW487kQPunED7y4ZQmpWtJRZEXJD63jukLP2KzddPINd4d+r0W/uzn5ZD2TUVQWEs1eelT/s0vDFR5BUHSI330qFZAklxzkFuy8F9WPPnczj41dm0+vVH1m0tZn1eMeUVVnO+RXZn/nx4/31nqlCrVlWba05DaKZpCBKy9vaDUkq71sQseIv1t08h6aP/cOjggfTdsEbd4UQaUyAA48dDz560v/4aBnRvsdNSJ7U/+2k5lF1TERTmKl8MA7q3YFCvVkRFUXXQ+ylnOwtHXE95UhJtJ15PWbCC5DgPG/P9VffXnG+RWgoL4brr4LDD4Oqra9ykaQjSVOzLB6XUhFjaTrqFqP/9D29cLEmDTnaui6uoaMTkIhFsxgxYu9aZgRCz61Vuqn/2UwG0ayqCIkjtg15pWQVdex7IlomTSFj0BYf86++AYXtpWdV99AFOpJYJE2DDBnj66Z0OQpqGIE3JPn9Q6tuX/M++JO/Pp8Mtt1Aw8A9sy/y1YcOKRLr8fJg0CU46Cf7v/9xOExZUBEWY6ge9w9unERMdRd55F7H92BPo/dg9lP36KzFRRh/gROry+efw5JPO4qhHH73TzZqGIJEgvzjA0m0VfD91Juvvm0bioi+JO+oItr/9L7ejiYSv++6D3FxnFMho2YX6oCIoglWdtQ6Ws/7eqUQFg5zy5N20bxavD3AitZWUOGumtG8PkyfvcjdNQ5BwV9VeO9ZD3tDhrH37v5SnNSPh9FPh1luhrOz3H0RE9ty6ddhp09h65nl8nNBWTavqiYqgCJbq83JgRiI/5xTxn0AiK664jlYfvccJKz7RBziR2qZMgW+/hZkzIVHr/kjkqt1eu/Sgnvy44AM2n3m+8zo58UT4VdPjRPbG7pYoCVw3jgoMv1w3Qd1765GKoAiWXxzgp+ztdExP4IRuLSi9dgwFBx9KxahrYOtWt+OJhIT84gBr3vuMivvuI/es88k/bqDbkURcVVcDkGJPHJsfeQJeegmWLXMah7z1lksJRZqWygKoziVKPvgA7z/ms/HqscR07KjuvfVIRVAE22nFcF8cv9w3HbM1F66/XgunSsTLLw6wNDOHdjeNpiIllZ8n3KXXgkS83TYAGTIEliyBDh3gL3+BsWOhtNTtyCIhbafPY5VFzqZ8GD0af9v25I8cU+M+6t67/1QERbC6Vgy3vQ/j18tGwezZ/PzyG1o4VSJaZk4RB859lsQVS9k46X68LVtQUQHvrdqskwMSsX63AUjXruR/8DFZw0fA9OkUH9mPDYtX6qSayC7U9Xks3hNN0jNPw+rVbLzzXoqja3bqVffe/aciKIIlx3vILizlu80FfP1LHt9tLiC7sJSt199MyYFdOGjSTSSUlWroVSJW4PsfaPfIvRScPIhtp59JYUmQX7YWke8P6OSARLTdNQDJLw6wdEsxmbfdw8+zXsTzSybpA/rj+fvf9boRqUNdU0zLNm6k0xMPwZ/+RPPzz9LyCw1ARVAEa5bgZdWGfLaXBEmKjWZ7SZDFP+eyqRT+ec2dxP36C83uv7tqfw29SiSomgb67RY6TLyeiuhoNtzzCBjDxnw/UUDzhFidHBDZhepTewr/dBr/fvFfbDuwG71uvIq2N48loTyg141INXVNMc2YciempIRFY24nM7eYAzMStfxCPdv1crMS9rYWBejVJpW84gCFpWVERRm8nmhyt5cSe9zxrBp8AT1nz+DLwwZS0b8/aT4vzRL1gpPwVVkA+bwxdH7rFVot+oz/XnsHNqE5GdaSWxQgWF6OiTJ8/ctWEmNjaJ0SR0mtM3gikazAHySt2oezrGat+GzWa3R54iEOffEpfIsXsXraTJYmtabAHyQ53kOn9AR9oJOIVTmymplTRF5xgORlX9FuwatsvHI0cQf3wB8s56fs7Sp86plGgiJYgT9IRlIs3Vslc0SHZvi8MbRMiqOswpLi8/LaudewLb0VJ917IyVb81m1IZ9mCXrxSfiqPIOdsmk9re+ayPZjT8COuJKc7aXkFQfwREOw3OKNjiI5zkOwvIKVG/K1bp1INbWn9iTGxlBQBt+PmUDm3+YTnZPNIX/9Iz3+NZ+0eM9O0+PUlEciUdUU0y7N6X73RAItW5F33U2addCAVARFsNoHqu2l5YB1Dlj+IO06tOLfN95L8uZf6T/zQXq1SWVrkQ5GEr4K/EHio6DduKshKor1Dz9BRko8rVLiGNC9BV1aJBHniQYqqx6DRRWQSHW1p/ak+bxs2zE6VDjgJN6a8w5beh5G/3vG037MlSSWFld9wNttq2CRSPDss/hWLWfzrZOpSPhtTTpdklD/VARFsNoHqphoKCgJckBqPNtLy0jzeSk/fiBrh1xB5/l/o9OSz/QClLCWHO8hZcbjJCz6go133U+wTbsaHXishUPbpOCJNhSUlOGJNhzaJgVrXQ4uEkJqd49rlujljMPb0izRS15xgPzUdH6Z+zqbb5hIylvz6fLngTT7dhUF/uCuWwXrDLhEgq1b4ZZbKDz6GH448bSdGlepG1z90jVBEaz2HNT2zXwU+INERxkSvNEU+ANYDLkTbqPkq09oe8M1bH//c6CF29FFGkTnLT+T+PA9bD3lVPLOPA//jpME3VulAU6RFCiroHur5Kr7FAfK8MXqfJJIdc7xpeb06Q7NnU5Wla+j7DE3UtTvWNpfczmd/3oK8bdM4sfzLiEtIbbG/eI90eRpJEgiwYQJkJdH4QOPsGrjNlLiPSTFeSgsCbIhr5gzDm/rdsKwoiN3hKve5vSEbi04rmsG3pgofLExFJaWEawo57u8IP+95UFicnM46O5b3I4s0jACAZJHXAqpqWy4byp5/uBOHXh2u0ikiOyR6q+joqP6s2LBh2w9ZgBt75xA7zGXEsjOqbG/1kORiPDJJzBzJlx3HVs6dqNXm1QS4zwUlpaRGOfRJQkNQCNBUkPl2btO6QlYa8kvDhIsr2Brt178MGIs3Z98CP5+Jpx7rttRRerX5MmwbBlRb7zBIX261rnLTh184j10b6VuPSJ7Y6fXUYsMYt5eADOfJGX8eHqdNpAfp82kvP8x+IPlNUZjwWmckJlTpM5yEj5KSmDECOjYESZNomB9ERlJsbRIjqvaxVqrEdF6piJI6pSZU0RGUhwdmv92Ud6GK8eS/vF/SB5xFd92OoR2B3fWgUfCw5dfwj33wPDh8Je/7HbXuqb5iMjeqfN1dN11mOOPx3PuufQccjqZo8dTPnoc3auNxlZvY5/m8+IPlrN0XZ5aB0vTds898N138N57kJBAcnwAf7Acn/e3j+kaEa1/mg4ndSrwB4n3RFf9XFgSZHVOES+NnITxF9Ns7Cg+/T5LHXuk6Ssupvyiiwi0PoDPRk1UJyqRRlajJXaLzmz44DPy/28wB069h87DzsFs2VK1rxonSNj55hu47z648EI45RRAU68bi4ogqVPt9tk/ZBWyMb+Ekk7dWDV6Im3+9yEpzz/DivX5LqYU2TO7W3ekdPQYoteu5cf7HyO5Zbpa8oo0ototsbduD/D62kKW3PcU6++dSuLCL4g9qi8r5rzGx99lsWRdHmXlFTUeQ62DpckqL4fLL4fkZHjkkarNtTss1r4+VeqHiiCpU+2zED9mbccTbTggNZ7M84az+dgTOfbpe9n6v0VuRxXZrd2uO/Lqq8Q++wwbR1xL2YATdWZZdmKMmWCM+coYU2CMyTbGLDDG9HI7V7ioPbKTVxwgJd5Dnj9I3oWXsGL+e/h9iRxyybkc9OSDxOEsUFxY8lvRo2lC0hTlFwf4dcrD8OWX/HzrFPITUmrcXr1xlQqghqEiSOpU+yxEdLShXVo8CbExEBXF15OmUZqcysA7xsD27W7HFdmlXU2f2bBkNVx+OQW9Dydn/G017qMzy1LNQOBJ4BjgJKAM+I8xppmbocJF7anX20vLSIrz7Fi8G9a27MT7s99m7f+dRctHH+K06y7Cl72Zn7K3V00Tyi4sobAkWOdIr0goyi8OsHrhKg544C4KB/yBLYPP0t+uC1QEyS5VPwtxYvcWlFVYSoLOyFBBYgrv3PgAKb9msvniK/TilZBV+0MWQHlJKRkjhlNm4ZM75trzbwAAIABJREFUp5NdUnN6jc4sSyVr7SBr7fPW2lXW2pXARUAGcKzL0cJC7anXibExFJYESYx1XrPbS8spj49n+aRH+HX6DBLXrOKCEWfQ8pN/k1ccoLSsHAvExkTvPNIrEmIqZybM//pX2tx6IxXlFbw36g5+zfNTUYFmIDQyFUGyRw5tm0rbNB/lFZZt/gCFJUF+6nUkP185llavzyPptXk68EhIqv0hq7AkSPzkO2mxZjkbHniU+G5dWbUhn6yCEl2AKnsiCefYmed2kHBQe+p1ms/LNn+QNJ8Xay0x0bCloITiQBkfHHEK/57zNiWtDuCPN49gwIz7SI6ytEiKU6MECXnVp2a3/c87dPjff/nv+aPwt21HsNzyy9YiNub73Y4ZUVQEyR5J9Xk5rmsGB7dJ4cCMRFLivfTt2Jzt4ydSdFR/Ot1+E2kbftGBR0JO7Q9Z/gXv0GfeLDZfMJyC086gRXIcvdqkkrO9VBegyp6YDiwDvqh9gzFmhDFmsTFmcXZ2duMna4JqT71ulujljMPb0izR6/yc4IzuVFRYkmKj2dyyHXMeeomCy6+EqVM58P/Zu+/wKKvsgePfO72kd9Ig9C4gAirV3ruLfS3outh/6iquXeyKYkFFXXvBXtcuovSm0gQSSiBAeplMb/f3RwgbURQUM0nmfJ4nD/hmBs+8z8yc97z33HtPPALThnWsKXexpLSWNeUuwpGotLOKNqe5NTvRVceoqbexrXtfVpxyLtWNQWxmIwbA7Q/HOsy4orTWsY5hjw0dOlQvXrw41mHEtVlrKkl1WFBKYd5aRvfDR+HtlMcjk18gJTmBzEQbfXOTCEe1bGgnYq55c0V/aRmDjhtLNCubDR99jbbbgf9tQjemV1aMI21flFJLtNZDYx1Ha1FKTQFOA0Zqrdf/1mMlT+0d32+qo9YdpM4bxB0Ik2A1YTYa8Ici9Fv4NT0mXQHRKIsn3U3FkScQCEdo8AXpm5vM6J7yeRZtx6w1laTazXSZcCaOb77iiftfY2NOEd5ghKIMJ06LkS6ZCRw9MDfWoXY4u8pVMhIk/pCWLUah3HyW3/4QST+t4MCnH6DBG2L5lnqmzSxhc61X+rRFzKU4LAzOS2L/W6/E6vex/P4nWd0QYklpHWvKXVQ1BmQOkPhNSqmHgNOBg36vABJ7j8sXwmZuvlRReINhyuq81PuCRI8/gbef/YBt+V058KbLGHzn9Rj9ATQqpjEL8WuUAs9TT5P0xSfMPOcKNuQUEY5qLMam93cwqkm0mX7nXxF7kxRB4g/ZucXovYIhfHLw3xj36WvkfPMpW+p91PtCfPlTOUs31bG51iuT/kRs3X03fP01tfc+yAJ7Nm5/iESrEbc/xIot9aQ5ZZRS/Dql1FT+VwCtjnU88UQpWLalgVBEk2QzUd4QYEu9D5vZiFKKYF4hXz8xg4V/m0DRu69w+AXHMdxXTjtschEdUPM8oI+XbWXDwuXs+9BtVAwZwdyjz6LW7cduNjK0KI2CNAd2s1yStzY54+IP2bmPe1Otl7dOvYQNXfpwxrSbsZQUU9XoZ3OtjySbmVAkSmmNWyb9idj45BO4+WY480w2Hz+e/nkpJNjMNAbCJNjM9M9LodYjo5Til5RSjwPnAWcAdUqpnO0/CTEOLW4oNNBU1XhDYVpeKyZYTURNZj4/+0o+f/B5LDXVDDjpMNTzz/F9aa10H4iYqfcGmV1cxcotDXy/voqx91yPVorZ/76fEIouGQkk2sxEohqz0cCAvBQp3luZFEHiD2u5hLbZqHBFjTxx6b2EzRZuePZGDO5GQuEISilsZhMGpWTSn2h969bBGWfAwIEwfTouf5jMRCu9cpLYt3MavXKSyEy0ykRqsSsTaVoR7itgW4ufa2IZVLzQGgbkpWA2GnD5QyRaTRSmOXdcLCbZzawpd4HWVIwYzb13v0pxl36Mvud6Ui46n7k/bJBCSMTEsrJ6yuq8GA2KER+8ROeVi/nvBdfjycljUEEKPbOTyEu178hDJqNB2rJbmRRBYq9IspuJRqNUpmQxfeJd5FeVMemN+wiGo6zaWk9xhQtPMEKC9LuK1uTxwIknNvXUvPMOOBy/WDIbZF8gsWtaa7WLn1tjHVs8SLKbMRkNO25a7N8tg2BUYzIotNZUuvzkpjooTHeytrKRyoR0Zkx+mrnnXE7nLz/kgPFHsO7z72L9MkScaG5/m7WmkplrKjEZFJmlJYx9+RGK9z+YkiNOZlOtl9wUOw3+0I73sWzNEBtSBIm9oktGAgXpTpSCxUWDeP64ixm3ag5//24Gavsk1WA4smPSX8svClkwQfwltIYLL4QVK+C116BrV+CX89kk+QjRdu38eTUaFPmpdgrTHdR5gwQjEYZ1SWNwYRpWk5GiDCdpSQ6++dvFzH7qDcx+H/uceiTFN939q+1xkovE3tJyH6BUh4VIRLO10sWQGy8jlJDMRxNvJhiNguYX72PZmiE2YnpbXik1CTgJ6AUEgPnAJK31iljGJfbcwPxkQuEIoWRNOKL5/uRzmbtlDad/+DRzDx3F5qGjqPc1JZfmLwqHxUSqw4IvFOH7TXXyBSD2mnpvEPc995P/2mts/ddNOEaNI2X775rbODdUe6jzBkmym+mVI+89IdqiX/u8juqRuePzmmQ3EwxHWzxDE4po7GYjm/oNZd6UNzhh6k30mnwDtQvn8PW1d1Fvc+INRHBamy6BzEYDoUgUs9HAljovI1v8+0Lsrg3VHqJR2FzrxR0IYzUZGP7CY6QV/8S8B58lqXM+tTUecpKsWEyGn72PRWzEujdpLDANWAQo4HbgS6VUX611bSwDE3tmYH4KLl+Iem+IUCRKIBxh0b/voc/VZ7LfpEtwvfQxhX17Eo7qHRuGOSxNb7/mPzdUexhcKF8IYs817wPk8oVQCsJffsXYu26hdPRhfHfCeSQXV/0s4TRdWMl7TYj24Lc+r0UZTr7fVAdAfqqd4opGTEYD3bMS2VrvxeVMZv7D/yHp89fJvvtWxixdyvOX3ol/yDCWb2mg3htiVM9McpPtBMIRyuq8LCurZ3TPrJ99r8hed+L3bK338dNWF1vr/XhDIfquXMRB7z/PonEnsGbYOKwmxbCiNCl+2pCYtsNprQ/XWj+ntV6htV4OnA1kAgfGMi6x51IcFkb2yKRfXjJdMxPom5tM/x75VD7/OiYDjLvhYixBP0l2My5fCLvZ+LPn281GmZgu/pCdWxA2L1vDsEmX4Mrrwo+3P4zRYKSszseysvpYhyqE2MtarlSamWijU7KdvBQ74UgUTyBMboqdHjnJVF90KS/c+xIRFFfefiEDX3uK8novgXCYksrGHQv4JNnMFFe6f/G9Invdid9TWuNlxZY6NFEKAw2c98RNbM3pzMcXXkdRppN+uclSALUxsR4J2lkiTYVZXawDEXuu5d265gRSn1vApkeepsu540m7YiKrH3wSdyBCOKLJSrLteK5MTBd/VMuRReXzMm7SxZhDQd66+TGSE5OwAcnaTEllo+wgL0QH1Jx7Bhem/mz0xmExkZFgJdHWlFu+S+3K19c9zT9fe4BjX3uUnKXzue+061kT1mQl2nBYjCRaTSgD0rEg9tiWWi9WkxErmtMenoQ14OWZ6x4nZHEwppfknraorS2MMBX4AZi38y+UUhcppRYrpRZXVVW1fmRij7S8O7dq0IEsuuhaun31EUOfm0pGgpUVW+qpdPllYrr401y+EOFIlDVb6kiccC45637ijSvu4gdHNj9tc7Gx2oM3GJJd5IWIAy23bji8fw4GAzsWVXD5gpQrB9P/eRevnDuJfdb9yBMPTqDXqkU4LEa8gQirK1zkJNulY0H8AZq8VAeHvfUUXVcu5v0L/42hf3+a97gSbU+bKYKUUlOAkcDJWuvIzr/XWk/XWg/VWg/NzMxs/QDFHmtORrkpdhovu4oNx59G9tT7SXrjFYoyE6h2B2RVFPGnKQXLt9TT75G76Pzt53x87rW80WkQgXAEh8WALxhmTUUjnZJtv/+PCSE6jJ039U60mbCbDaAU3449kWuufhK3PYEpz/yLoc8+jJkonZIdJFhNspS+2C0tVxe0Wkxkz/+Wce88w8rDT6L06FMJhCJ0z06MdZhiF9pEO5xS6iHgNGCc1np9rOMRe9fWeh8bq90svWASp2zcyJA7r+PDxAwSDj1EhojFH1Za42H+uhoWbKxh6H9n0OfVpykZfx7fn3A2iRWNGJUBTyCMyWggN6XpwkYIEV9atmkv39JASWUjDd4QLn8YT243br/5P0yYMZWRM56k19qlrLxvGiWVJrKT7Gxr8FGUnkBmohVfKII3GKZXTmqMX5FoK3Ze6XaE1cf+j/2bioJufDRhEqFQ04IaB/XJjnWoYhdiPhKklJoKnA4cpLVeHet4xN5X4fKxtd6HMlv49NZHqcvtzGG3XMrGOYtlbwbxh5TWeHhvaRm+YJihqxYw/qUHWLbPgXx4zjUYDAbG9MgkJ8VKXqqDbpkJDOuStmOHeSFEfBqYn0znNAd9OiUxIC+Z7tmJpGWlU3zvI2x++EnS1qxg+MmHUjT/GwpSHRSlJ7ChxsPmOq90LIhf+Nl81EiEA2+6HHs4yEc3TsWZmkSP7CROG96ZzunS6t9WxXqfoMdpWhHuBKBOKZWz/VdurbU7dpGJvckbjGIyGgBF0JnEazdN45yrT+O02y6hfP+ZuM2psk+Q+F0tJzwv2FBLgsVIwZZ1jLz/Gqq79OSzfz+MwWigd5YTtz9E75wkeuUkAU1zAhzWmN/zEULE0M5bOWQkWqjzBMlPcVB30ni+z+nOiBsuZdy1E1ixeB71V0yiKD2BtISmtjohWnL5QqRuv2bJfuAunAvnsWnqU/QYPVS6XNqJWPeHTNz+51c7Hb8NuLV1QxF/FYfFQEGqg0Z/BE8wQkNKFq/f8Cjn33wBtglnsuH1D3BH4bMV5eQk22Q/BvEL9d4gs4urdly8rC1voGekkRE3/J2II4EZNz2KTnBQ5wkyqCCVLXVeCtKcaK2ljUUIAfxvK4eWe/+kOS3UeoLUeYNsyixg3UOvM/rp+9h3xrOkLl3Aa1feg+7aDWDHY2XfIAHsmDeW8/WnZD0+hdoz/s62Y04mySQ33NqLWO8TpHbxc2ss4xJ7V/esREJRTU6yjd45idjNZrb2Hsicmx/EuWQhOZdfxKbKBuq331WR/RjEzpaV1VNc6WZLfVNrpcnj4dTbL8Xsqmf+1BdI692dQFhjMSvSEiycMCSftASLLLwhhPiZlqvHDS5MpXO6c8d/OyxGqsMw85KbePffU0ndspGJ14yn28yPqHUHeW9pGbXuoOSpONZyIYRGf4ht386n02UXsrlHf5455Uo2Vntkpdt2JNYjQSIODMxPocEXosEXwuWLYDUrbCYzlvHj2earo9OdN3GAxcnyf9+DUkr2YxC/sKysnvIGHxENBp+Pqx77F4VlxTxy2f0U9uxL2B8iyWbihCH5O/qvpQ9bCLEnWrZuLxg0muX3vM7ZU6/npPuuZV3JD2ydeAN13iBZSTbJU3Fo546E8LZyTrr6AnyORN658VGCJhMbq900+EJy062dkCJI/OVSHBZGtWhB6JrlxOULYTQoqv5xKeUbyhj86lM4szOou+kOoGk/hjq5wya221bvo94TItWi+Pujk+ixZilPnn8z83sNw9zgIzPRxrg+2VL4CCH+sJat2w3+COTm8+r9LzHulUc54O3/kLFsCV/f+ijk7Af8Mk+1nLco7XIdz7KyesrqvCTbLSSg2efGiSS463n05mcJpmfjNBuxmhTz19VILmonpAgSraLlMqXwv2RR5w1SfvkkMiM+8qc/iiktjapLrpL9GMRONEprxk+7hT6LZ/HuBZP4cfQxdE8wcenBPWMdnBCiA+ielcjKrS5ykm1AFF9QE4iEKfm/G4mMHsvQW67k2AnHse3OB6g/9QyqGgNUuwPMWlOJUtDgC5GVaCPVYcEXisiCPx1Ay8L2m7WV5CXbsJmMDL7tX3Re+yNTL7qD77O6McxiJBTR1HpCeILhWIctdpMUQSImWhZF9d4g3103mVBdA0X33EZpxMyGU84iN8XOrDWVckctTrVMPlrDma8+wODZn/DR+EuZc9jfSDVApxS52yaE2Dtatm5bzUZqPX7SnGa6ZSbgP+Qwnk19m5OmXE/B1Zfg//RzFpx/PRm5GXiDYcobAtgsBtKdVmnr7iDqvUE+W7GN9VUe3IEQ66vd1HtCnDXneTp/+AYfHD+BeUPGYTUolFJYTAq3P4rFbIx16GI3SREk2gRlMDD3xvsxuhsZ9sBNVGAmdO7fd2xSN7u4iiS7Ga2RoigO7LwJ3anvTWfwF28y58RzWXbmxWSZDJiNioH5ybEOVQjRQezcut0/r+n7JRzVmE2KzF5FzHz0Ffo89xiDnn+ECcu/Z86dj6P3GURprRefJ0xJZSODC9MAaetu7+auq2bOuhoUABqtDSR+/TmDn7mLsoOP5tvxF+Or9pDmsBDVUbyBMIFwhH4ZkpfaCymCRMxtqPaQmWijc3oCrudfofq0EznmwRt4PyGJzQcfjlJQ6wmSmWhlYF6KtBnEgZab0GU8+QidXn6C5UeeyrfnX0OnFDtmo4EUh5mB+SmxDlUI0YHs3Lrd7PtNdVgzjE0jPLfdysvd9+GEB/7Fsf84ia8mXIfvoJOwGA1sqvXuKIJatsvJzbv2Z05xFY2+IAaDgUhUU1S+jutfvJ2N+d2Ze929pIcUTrsVi0lR7Q6Q6rDSPz+FgjRHrEMXu0mKIBFzLTcc03Y7798+jSOuOItjJl/BO9GpzO8zHItRYTMbpc2gA2vZ/rauqpEUu4WUZ55kwJN3sXrMURTfeh9ZwShdMxPkgkII0apa5imAtb335c47XuHs6bdx+JOT6fzjfB4/4184cjLRWlPVGGDxxhpSnVZ8wQgmk6KszsuoHpnyvdVObK334/KFMBgNZFRu5dqHrsRvtXP3hXdxVmEmharpfZGZaMNuNu7Yk06WyG4/ZEcnEXPNG441q9AW7rviISryu3LKnZfTe8HX1HvD1LoDOx5jNxtx+UKxCFf8BZqXHl25pYH1VW6KKzz4J9/FQU/eRfHIQ3nvijuZt7GO3GT7jv095EJCCNFads5TdrOBGnsSL1z/CN9edB09Fn7Drbf9HduSRbwwdwPv/lCGNxQh0WYmyW7GqAyU1flYVlYfw1ch9ojSuPwREutqueWxqzCHglx34f2E8/MZ0yuL0T2zGNkjE4vJIHvStVNSBImYK8pw4g2G8QbDaK1x+cN4nMm8dtd/qOzelwmPXM++C7/AF4oC0OgPsaysnnVVjbJZXQfRvPSo0aBItpk58NVpnPHek8wddihPXHwn1SHQGsobfLEOVQgRh3bOU06riWS7mQSHldnHnsP0yc8R0XDz/RM5d86bhINhymq9uP0hlGrqZEi2mSmpbIz1SxG7Kd1pJT3i46bH/4+Uhhru/Od9VHTuTrrTuuMxO2++KwVQ+yLtcCLmmr9EmpfMdlpM5BemEtGaV25/mvG3XcyEaTfyhNfPC+ETqXUHSbKb6JmdyMqtDdJi0E4tL6vnkxXlVDT4KHcF2Cc/mexEO32n3Uevd55i5ogjeXj8vygymFCapt3cW4wGCiFEa9k5T3VKttM1M4FgOIo7EGZFtwE8fN/rnPb0HQx89G4m9pvJ0xNuYsEG6JqZhMNiIMFqQhlUrF+K+B3NuamktJrbn7qegm0beOCS+6noN5iuNjNdpN2tw5AiSLQJLSejKgWrtjaQYbdiTXPy8b3/YeT/nc8/n7+Dlw1RPhhyGOFoFJNSP2sxGN0zK8avQuyu5WX1PDGzBBSYDVC7ffLwIc/eT6+3n2PWmBOYPv7/SLFY6JqZAECt249GLiCEELGx89YOzStY2s1Gfthcj8to44NJD1H91duMeuIubrn5HO4+8wYqx4wFrdEajhiQG9sXIX7T8rJ6ps0swajD3PjybfTfsJw7T7uBmgPG0DvZjsVkkAV5OhBphxNtzsD8FPJTHUSimgZfkJ8ao/xn0iNsHHwA5zw7mePmfUii1cy6ao+0GLRT736/GXcwRCAcpcEfwWZUTHhjCkPefo6S8efxwcU34Q1rnBYDUR3F7Q8SCEcoypBVd4QQsdc8MtQ8H8RggASrCU8oyof7H89N1z2Nx2rn/qeuYeTLj7Gtxk1JlYePl29lxsJNLC+r5/tNdcxaUylt3W3Iu99vxucPctr0yQxdNocnT76CWUMOZlu9j7wUOz2yEqQI6kBkJEi0OSkOCyNb7NWwYmsDBoeD6Vc9wIn3XM05L99PuKqalw8+G4D8FDsOm7yV25M1FW6CoQg+FcUQDHHFy/cwdtFnzBjzN3yX3EhGo58Em0WWHhVCtFktR4Y2VLv5enUlSTZIsBr4PrWQv//zMW767ElO+fg5evy0lHvOuoFt5lyWb6nni5XlDMhPIdlulpXjYqxla/b84iqu/+wJRs75mNeOPp8vxpyMORTGFYjQLy9ZViXtYOTKUbRJLZPLrLVVlFa7SU+w8/DFd3L2M5M5/7Pn6FRXwSf/vJkFdV5OGJwX44jFngiHIrh8ETrh59rpN9BvzVKeO+IC3jjsTK7PSqBrdoIsPSqEaDfsZhOD8lOpaPTT4A8T0ZCclcrrE29j3YDhnP3SvUx74CJuP+Valu07Gm8ojDcUoV9uEmajgarGAMl2s7R1t7LlZfXc/fEqyhv8hEIhLn9rCsf++DnvjBvPB8dcgBnwBSHZYmRwYWqswxV7mRRBos2zW4wAhCIavzYw+dTr2JKcxYXfvka+t5YXr7iXRn84xlGK3VFa42H+uhrqAhEsWzZx2ys3k1ddxkNn38jHA8fRNzuJMb2aLgKa9w2q8wZJspvplSMr7wgh2qYEm4kUh4lOKSlYTUbC4Qj13iAGpXir71i+/GcBk9+4i4devJHXN/6Nh8c0dTIMt6UTCkep8wRZVtYgRVAre+bb9aytdONUmhvffoDDf/ySR/Yfz39GnUtvNMFwlFAkSlayLdahir+AFEGizUtzWhhUkEpZvY+GQASbxcg7J/0DX24Bl7zxIJffMYHbL7yXFVsayE62M7J7OnaLCZcvJJtqtiGlNR6em72eGk+IrqWrmfzMDVjDAa6bcC8bBg6jZ6KNnjmJOx6/q53bhRCirclNsWMzGanzBnH5Q3TJSKDc5cdsVDT6gjRmFXLFZdO44tOnOO3bN+i//kduPPUGNualYjMrItEoq7c1MmtNpeStv1jL9rev1pTj0FFue/8Bxi6bxWMH/Z1Hh52KDkao94dxWEz0zk2kV05SrMMWfwEpgkSb1yMrgVVbGxhUkEKVO4A3EMFkhI0nnM6L3bsw/r6rmfzAP3jw8gdYlNOVb9dUMLpnFlmJNum1jrHm0RyXL8QXK7exptLNiJ8WMvHJf9PgSOSK8+4l0LsXw4vSZdUdIUS7VZThpN4bpCDNgd1spCDVweKNNaQ6rawpb6TRGwS7jRnnXsecggFc+9aDvDhtIg9UXs2cQWNRStM/P5VUhwVfKML3m+pk35m/wPKyep79bj0pdjP5qXbwBbnrvXsYW7yAJ46dyKsjTsTqDRDSMKp7BmajAbPJwMD85FiHLv4CsjqcaPNarhaXYDERjoSxGAxkJlqYkd6X8857AKPW3PbARPoun0eVO8DMtZVsqfeytc5HSaVbdumOgXpvkFfnb+Shz9fw4Odr+HDZFob993WufOxatmblc+mlj7OpUxcaPCFZdUcI0a7tvFpcWoKF04Z3Zr+iNAYVpFCQ6STdaSUQivJ131GcNGEqpZkF3P7K7Vzy5hQ8dW42VjbyxuJNzC6uptEfZkO1J9Yvq8P5ZEU53mCEhRtr+Wj+Op54+w4OKV7A5CMv4c1RJ6MUaKVIT7CSl+IgN9VOd8lNHZaMBIk2r+VqcYFIlG6ZCbgDITyBMHWeALpnX265fjqTnriOW566jtxxZ/HUqNOodidhNCqMBlhWZpBe61b2/g9lvLO0jGgUrCE/t771ACeunMnc3sOZfvGdaJMNo8dP1KBk1R0hRLv3ay28ndOdpDktvL6glGBEo9CU1XppyCngpqsf59yPn+WkL1+lX+lKJp16A+ssfTAZfWyoamRM7yyZjL8XtOxImF1SxbY6L1kBDw+9cgv9N67k2iMv5719DiMtGMa4vQA6rF8ORZlOaU3s4KQIEu1Cc3IpynD+bIO6xaV1KK3xd8rn3puf4+hpt/KPr1+iT+kq7j/7RkJJKTitBurcQem1bgUte62/K6kmHInSu7GCO16+laLyjUwZeSbPjD6NgTY7RDRmo4H8VIckeiFEh9U53clpwzszf10NVY1+bGYDPbKcmExG3jv9Cmbn9+eGN+7hlacu5fVzr2PWiKMoq/fxw6Y6Th1aGOvw27V6b5B3l27mx80NNPhClFS4KKrazPS37iCzoYrbz7yRD7sMx6ghO8lOisPM8KI0zhzRRa4T4oAUQaJdaW45aF41rH9uEiu3uAiEIhgtFm44/mrmZPbk5i+n8/Qj/+Tms25hfnJnqp0hPl+5jQSrha6ZTg7vnyNfcHvZzr3Wjb4QY1fP4/6PphA1mrjkzNv5PH8wRMAdCGEyGkhPtNI3T3qthRAdW+d0J53Tm5b4r/UG2FTjI9luwWRUfNV9KOMveox7P3iQ856+nV4rF/Hg8Zfx7dogV8/4nuxkO0f2z2GAtGTtsS9WlfP6ojJq3H6CEc3g4h944r27CZnMXPWPKSwv7IPTF8ZqNXL1Yb3kRmmckTlBot1pLoTG9MrisoN7MrgwBa30ji+5d4cfw1WXTMUYjfDotMs5fumnuAIRPIEw5S4fc0uqmLeuJtYvo8P5ZEU59d4g3xRX8fq8DVz+1XM88fZkNqbncfGVT7G07wjMJrCYID/VQdeMBPbJT2F4UVqsQxdCiFZz4uACzEYD7mAIjz98xNzdAAAgAElEQVSE1hpXehb3XfMY7x13ISPmfcaU+y6kcNNawpEoG2vcTJtZwnKZ27rHXl9QyqZqN75ghJMXfcwLb9zM1sQMTvr7FJbm9sakFLmpdorSExjTK0sWo4gzMhIk2rXO6U7+Mbb7jjaDBn8Yu1lRkbsP/7r+P1w8/Wbu+PgRhm1eyScXXk8gIRGtNd8VV3LkgE6xDr/da9n+NnddDW5/iB7+Om56+z4Gr/+RV/c5gsmHXkRmYhIGrTEbjeSlWRlRlIHJpEi2m2XCqRAirgzIT2HiuO47vjuL0p0Eo1E6pSaw4JxLmJXbm0mv3MVzT1/JJ+FrmHPIqZQ3+nhqVgmnDi2U0Yrf0bwfXVWjn5VlLrSOcMNXz3H2gveY1XVfLjnuOtxWB4fmJtIYjODyhji8X3aswxYxIEWQaPd2bjMoqXRjNhqJWDK55OzJXDDzZS6cPYMDb1nO8+ffxFf5Aymp8EibwZ+0vKye2z9cyZY6L4FwlBpPiPHLvuDmmc+g0Nx+0jU832MsGoigSTAb6ZLmYGSPDJlwKoSIawPyU3bknf/toRakzhNlUW4/Nl41ncnvT+H4p++i6McFPHTq/7FG2dlQ5SEYjTC7uIqumQnkptjle7SF0hoPry8oJRSJopTC4WngwY+nMG79El4ZfgJTDrsQT1ADUNEYJMVu4ZiBmRw3KC/GkYtYUFrrWMewx4YOHaoXL14c6zBEG7S8rJ5pM0tQBjArxdx1NQSjUY7ybebyF++i07aNzBh6NNMOn8CgvgWEtEZHYeK47lII7aF/vriY70oqiWrIctVw80ePcND6xczvPJCpp1/H5uRsGjx+MBg4fp88nDYTRRlOjujfSRJ2B6GUWqK1HhrrONoiyVNiT7QcvfhsZQUZCRbykmwc+OGLHPrKVOoS05hy1o30PeM4FqyrYV2NB7NR0TU9gX0KkjlxSH5cf682dyXMLq4iHInSLy+ZERt+ZOTkq0nxNnDnoRfx/vBj0RoCoQiJNhMPjh8sN+PixK5ylRRBosNp2aK1ocZDNBIl2WHFEvRz0KuPMn72O5Snd+KjK+9kVfeBbKn1keY0c/G4HvJl+DtaJurHZxYTjmhOXvMdkz6ZhiUc4p6x5/LikKPJSbZjNxswmxROq5krDu4pyaYDkiJo1yRPiT/qzcWbeP+HLaTYLSRYjXjmL+RfL9xBXs0WZp1wHncNG0/UaEYTpVOqg3A4yqlDCzllaEGsQ4+J5WX1TP1iLd5QiOIKNzatueibFznzm9fZnJHPJUdfy+qcrjjMBpRBoYBj98njjhMHxDp00Up2laukHU50OC3bDL5dW8ns4mqq3QF8QSNTDr+IhQNGMumtB5hw8/l8dtCpvHTYuazzWlm5tYE15S5yU+xojVy0b9dc+BRXNlJc0UhWopUUh4WU2ipu+eppjlg7l2X5fbj+2KtYlZQLQL9Oibh8YVyBEBeP7saYXrJHkxBC7I5D++bg9of4cXMDFa4AVQW9mXL3q0z8cBrj3v0POYvmcMdp/2ZTeieCYY0/GOHNxaVkJlrjMm/NWFjKqm0u6nwBMqrKeeSD+xm8bQ0fDzuKr/8xiZpyLxZvCJvZQJLDSp9OiUwY3TXWYYs2QEaCRIdW7w0yu7iKem+IUCTK20u3YDZAnyQjBz8/hXHfvEODM4WXjr0I5z8mMKukilpPCIOCZIeV/YvSOGNE57hKKC2V1nh4cmYxm+t8bKz24A9HSDNEmLj4fQ7/6AUUmsdGns6ro/9GGAPuQASA3jkJZCXbOGO/Qg7rLwtQdFQyErRrkqfEn9Fyg891VY00+MLkJNlY8ch/uO7dKZgiYZ486QpmjzyGjTVuPMEInZJtJNutjO6RwQWjunbovNWyK+GZ2etp8IY5ec0sbv3kcaLKwPVHXMbM/iM5on8uFQ1eHFYzmUlWBuWnMqJb+o55xCI+yEiQiEspDgsje2TuSCZje2WyaGMNLqOVx068gg/3PZwL35rK5a/dy6YFHzL34AlUFfYjN8VOvcfP20s3U+sNMqpHZlzeYXtz8Wa+WVNFnS+IP6Q5Yu1cbpr5LHkNlXzdfxQ3jzyPbclZ2KKA0tjNilE9MnnynP1iHboQQrRbzRuEA+xTkLLjZt53A0fxY25P7nznfv7v9XsZtehzJo27CHdmARalcHmDvL2kDKfVyMVje8T4Vfw1Sms8PD97PdXuIMFIhOStm3noy6cYt34JSwv6ctWx11CamAVhUAr27ZLBiK5phKNauhLEz8hIkIgrLXePXrGlHqfVTFGGg1PWzqb3lDvIcNXw2eBDeH/8ZZQnprO+0kUwHCUrju6wtZxT9dmqbbgDmoE1G7n+8+kcsGkZP2V24b7DLsJ62KHM31CNLxjBaTViMxvJT3Vw0zH9ZJGJOCEjQbsmeUrsTc0jQ09+s461FS4SzHDs3I847YPp2EIBXtz/JN468hz8VjuhUIQkh5lPrhgb67D3mpYjP8u3NFDV6CddRTn605c48r8vEjSamDrqLN7c/3j8UQhGmjbCvPeUgeSm2DEaFBaTgcGFqbF+KSIGZGEEIbZrTiZzSqqpcPnpku4k1WHhoXeWcMGc1zlz9ttEjEbeG3YMD+1zHJUJaXRKMqNRgObvBxR12Dtsy8vqeWJmCUppTEYDK79ayCXz3uC4n77FZXPy0MizeGXQEUQMRk4clMvmGjdRpShKd8py43FIiqBdkzwl/grfrq3kq58q2Fjjxe0PsXl1KZO+eY4Tl39FRUoW046dyFuF++IJK5KsRlIcZs4a0ZmLxnSPdeh/WGmNh1s/WMHysgZ8oTCBoObw0oXc9MXT5NRs44O+Y5g89nyqEtOxmhRKQSSiSXWaefqcYfhCEbzBsGyEGsekCBJiJzvPF3puzkZC0QiDgnWc9unzHLjgMyIGI2/ucxgfH3EW25KzqPP4wWjgkF7ZHeaif/qsEl6eX0q9N0QkGiXNaWW4azMnfPICB/wwC5/ZymuDj+TZA/9GlS2RcLTpeScNziUz0cqB3TMY3VNaDOKRFEG7JnlK/BV2zltTv15LJKwZU1XMVe9Ppdu29cwqGsI9Y8/F26sPvmAEdyDM2F5Z9M1NJjPR1i7mxLQc+fliVTlryhtxWIz0rtnE+Z88yyElC1mfUcgrZ1/Ll9l9Ka3zAZDuMBGNaiJoTt+vkAO6x2cru/g5KYKE+BUtJ59+V1zFN6srsFmMmJWB2hVruHjBW5yy4iuU1nwy5DAeGnIi61NzyXCYsJiNpDstjOmVhc1kaDfJpeVr/vqnct5YshmrwYjZpMgrXskl82ZwaMlCvDYn/xl8DM8OPY46RzI2kyIa1YSjkGg3cO3hfUi2mxnVI1OSS5ySImjXJE+Jv0rL7/Dn527gx031WM1GbNEIY795m6u+e4WkoJe5fQ/ghXGn81VCEWHAagSbycjAgmQmnziwzeaq0hoP1731A8vLGgiENWENA8pL+L/FbzFu5Ww8ZhtTDzydF4Yex+DuWYQimtKaRjzBCE6LmfQEC2eP6MxZ+xfF+qWINkKKICF+R703yKvzS5m/vpZ6X5DV21yYDNA36uaMb2dw1IKPMUfCzCoawjcHHs0X3YZR4Wv6/JjbSXKp9wa5esb3zCmpJhiBKJAY8HL6xnkct+RT+m/+iTpbIs/vdzwrTjqH9SEjG2qa7rAlWgxEdZSoVpw6NJ8ThxTI3bU4J0XQrkmeEq3h27WVvLO0jJ+2unD5w2xzBcgOuLlgxSecNvddkrwuvus8iMcOGE9Jz30IaPAEoiRYDaTYLWQmWTl7eGdO3De2ewzNLaniiZklrN7motYbJkLTyl37bV3FP2bPYOyGJbisTt4+8ESeGXIs24xOosCA3CRMRoXVpBjaJZ1rDu8d09ch2iYpgoTYDS3vsL22YBMLN9RgNRsxK/BtKefspR8xfsWXZDfWUO1M4e1+B/HGwEOpz+9Coz9CUINZQdcsZ5u5E9Wy3S0QihCIggnNfttWc8L3n3PM6u9whvxsyOrMa/scxsv9D8NrsTO8SwqBsGZzXSP+YBS73GETO5EiaNckT4nWsHN73MNfrSUajZKeYCcx6Gf/L9/kwkXvkump54fCfrw07Dg+6rwfAZOFHpkO6n0hGn0h8lMdDCxM4ZQh+RzQPbNVYm9ueVtcWsN3a6vxBkIk2MxU13oYt34R5y75kP03LafGnsSz+53AS0OOJikrHW8oTKMvjMUIo3tl4bCYpDVb/CYpgoTYQ6U1Hu7/dDU/bXPhDUbY5gpgUZCXbGH/kqWM/u59Di5ZiDka4fv8PnzQayRfd9uP0tRcClOsVDYGsJoNaK1afXJq8wpv366tZPXWRhJtRpJsRhLW/MS4dYs4YdUsutdsxmO28WGf0cwYeBhVfQfhDoZx+cIooEdOAg6zkcwEG8O7pXL+yG6tErtoP6QI2jXJU6K1/KzFeVUFby0tw2kxYLcYKa0LYA0FOHvlF0yY/zY5DVW4rE4+7nUgc/c/gs9TuhPAgAHITrJiMxs5pE8WyXbzXm/xbjnPRynYUufDbjHxzZpKttV5GLJ1Daf+9A1jfvyGFL+b8oQ0nh1+Em8OPoJ6ow1omvMTjmqC4QiH9M5h3y5pmExKWrPFb2rTRZBSaiJwLdAJWAlcqbX+blePl+QiWkvLL+03Fm2i3hcmxW7BbIR1NT4yPHWcsuJrTlr+FT1rNgGwLi2Phb2H8VHBvizK70enzAR8wQi13jBmI4AiyW5iUF4KVd4gVa7AHrck3PvfVby+eBMefwSnzUjXNAdlDX5cvjA2s4GsJBv7F6Xzybw17FfyPWPXL2HsusVkNNYAsDivDx8MOZz3ux9Ag8UBQE6iGW8wgjsQpWe2k5HdM9AoLEbFacM7t9kWPxE78VQESZ4S7UXL0X9XIIIJSHaaMUUj9Fi1hBNXfs0Ra+fhDPkpS8ri/X5j+W+vA6nt2pMKTwQF2CwKu9lEeoIVgwHcvvCfylNWs4Ekm5lAOIIvGAWiJFtNnOFoxPHxBxyy9AsK68vxm6182mME7/Y7iNldBhE1GHFYDHiCTSvyZDibOhJOHpLPfkXpuHwhWfhA/K42WwQppcYDLwMTgdnb/zwP6Ku13vRrz5HkImLh8xXbmPzxT4TCEaI6SoU7DECCVeEOaArqyzlo3SIOWreYEZuWYY2EcFvsrO7Sn2WZRSxJL2JFTjcCefk0BKL4IpDmMNItI4FGf5iyOi8YNJGIwmExMqgghcGFqWQm2vhxUy2frCrH44+AhqAGpwksJgMuf5QIYItGGOLdSt7GtfQtX8f+DRvpun4VlmiYRquDed325bMuQ5nVdQjVzlQSrUa0BncwAoDDpHDaTAztnMawojQ8gXC7WexBxEa8FEGSp0R7NX1WCQ9/sQaDUhgN0BBouubrbI0wZOm3nLhyJgdu/AGjjuKyOlmc14eFBf1Z12sfFqYX0RA14bQo+uYk/SJPJdlNHNW/E707JVPV6Gfhhhp+2NyAP/TLPFXvj2KMhBlUuY6xFT/RZ/0yhm5aSXLAQ1Qp5nfZh4/6j+PLPiPxWm24g/+7NjUriGo4dd887jl1UKxOpWjH2nIRtABYprW+sMWxYuAtrfWkX3uOJBcRK5+v2MarizZR2eDHF4qwpcaHxaxwh/73OcpOtNBY42LEpmUcvH4xwyqL6bxtA5ZoU9HktjpZmV3E2vRCqp2pOIsKKcbBT4ZEKp2pGNJTaQhqIlE4qFcGjYEQCzY24DREyA24sNbUkOWuJddXR57fRWJtJb2rNtK7aiO2cBAAr9nKmuyu/FDQl5ndhrKqywD8yohBaVyBpjtqVgNEok2LIxzZP5u/7Vcod9TEHomjIkjylGi3Wo4MaR0lHNVkJ9oorfOjgUx3HYduXU7/9csYtnkF3WvLAPCZrKzI7saW5Cx0586staSy0pLKluQsojnZNEbAG9Ds3y0No4JvS2ox6yhFwTqSqirIc1XSubGSLu4a0mu2MaCiBEcoAMCGtDwW5fdjSef+OI86jA8qocEXxmSAJIeJmsYwYcCkwGkzMrZnJrcdP0Byk/hD2mQRpJSyAF7gdK31my2OPw7011qP+bXnSXIRbUVzcilv8BOMQpJVkZfiYHWFBw1kOEykOG2UltfRs3oT/cvXMbx+I102raGodiup/sY/9f+PKkWNI5ni9EJWZHdjW9c+LE7tTElKDiGM7N89jXnrajECZpPCYTZS7QljBDRgtypOGVLALccP2AtnQ8SbeCiCJE+JjqTeG+Txr4v5Zm0V6ys9RACn2UBmooWNtX4Acnz1HFRTQo/VS+lbuZ68hko6uWswRiN7/P+LKANVSelsSsxkVVZXFhb0p6zfvpRZknAHQkSicNnB3SmucLNwYy2+YAi7yUS37ASOGpBD5/QEuTkn/rRd5SpTLIJpIQMwAhU7Ha8ADml5QCl1EXARQGFhYasEJ8TvuWhM9x2LHbw8bwMvzS+lyh0k1WHC7QtjUBAKhwgZzazM7sbmwp7MsVsob/QRjoA9HOLgDChbtZ4sdy2dvHVkBN0YgGg0SliD1mBQgNGIJymNEnMSVc5UKp2pGLOy2eYL74gnP8VOMBwl5A5gMsKQglS8gQgrtzYQjYLNYuL60d3a9e7hQrQyyVOiw0hxWLjkoB4cNTCXeetqmLFoE75gFHcgtOMxgbR0vs3J4Y2CoYQ1WAywX0EyG5YXk9dQSWFjFV3DjQSDIbRu6lqIajAZQBkMVDpT2eDMYEtyFuUJ6aQlO6lyB2i+5Z6XYMUU1aggOKwGqhsD5KfZGdWzJ0f07yTFjmg1sS6CdpvWejowHZrusMU4HCF+4az9i362dHTzKFGdN0SiReEOagxoQuEQZiAM2JNsVCQl8GOuGQ2k2ps+khoIBMOYTIpIVBMMgd1qxG420egP0Fz3pOooRiACmGkquIKhKAZgQF4yZXU+hnfN4Nbj+jMgP6U1T4cQcUfylGgPUhwWBhdaGFyYyqCCZN5aWkZFg5+8QIi15U3dCf5QCLMRwmFIcZgJatiWlMXWpCxK7CYWWM14AiG8gTAWc1OeCofBYjGigHAksiNPhcIhjDTlPAsQCEUIo7GYFGcMK+SA7pky2iNiItZFUDVN12/ZOx3PBspbPxwh9p6Wo0QAU79Yw6sLS3H5wiQ5zIzevjpcuStAVoKFancQHY1iMipc/giRKIzq0TQnaP6GesKRCCGlMWz/98wKPMEoSY6frw6XZDdx3siuXHFor9i8cCE6FslTosM6oHvmz/YFau5oqHEHKUy30b9TEhtqvb/IU6FwiHA0QjgKwwtSMSrFN8U1RAIREqzqF3kq0WGkX04SVZ4gNe4g2QlW2XNOxFxMiyCtdVAptQQ4FHizxa8OBd6OTVRC/DWuOLTXbxYmLYukRJuJQQUpDCxIITPRRlG6c8fqcE6bkXMOKOS6o/q2YvRCxCfJUyKe7NzRsLOf3cyzmzhlyP9Wh4tozQ+bG/CFJE+J9qEtrA43HniJpiVH5wAXAxcA/bTWpb/2HJlwKoQQsRcPCyOA5CkhhGjP2urCCGitZyil0oEbadqEbgVw1K4SixBCCNGaJE8JIUTHE/MiCEBrPQ2YFus4hBBCiF8jeUoIIToWw+8/RAghhBBCCCE6DimChBBCCCGEEHFFiiAhhBBCCCFEXJEiSAghhBBCCBFXYr5E9h+hlKoCZFWe35ZB0yZ/YvfI+dozcr72TEc9X5211pm//7D4I3lqt3XUz8ZfRc7X7pNztWc68vn61VzVLosg8fuUUovjYf+OvUXO156R87Vn5HwJ8evks7Fn5HztPjlXeyYez5e0wwkhhBBCCCHiihRBQgghhBBCiLgiRVDHNT3WAbQzcr72jJyvPSPnS4hfJ5+NPSPna/fJudozcXe+ZE6QEEIIIYQQIq7ISJAQQgghhBAirkgRJIQQQgghhIgrUgQJIYQQQggh4ooUQR2cUipNKfWoUmq1UsqnlNqslHpCKZUe69jaCqXURKXUBqWUXym1RCk1KtYxtUVKqUlKqUVKKZdSqkop9aFSqn+s42ovtp8/rZR6LNaxCNGWSJ76fZKndo/kqT8n3vKUFEEdXy6QB/wLGACcBYwGXotlUG2FUmo8MBW4CxgMzAU+UUoVxjSwtmksMA04ADgICANfKqXSYhlUe6CUGgFcBCyLdSxCtEGSp36D5Kk9MhbJU39IPOYpWR0uDimljgI+AlK01q5YxxNLSqkFwDKt9YUtjhUDb2mtJ8UusrZPKZUANAAnaK0/jHU8bZVSKhlYCkwAbgFWaK0vjW1UQrRtkqf+R/LUHyd5avfEa56SkaD4lAQEAG+sA4klpZQF2Bf4fKdffU7TXSTx2xJp+g6pi3Ugbdx0mi5WZsY6ECHaEclTSJ7aCyRP7Z64zFNSBMUZpVQKcAfwtNY6HOt4YiwDMAIVOx2vAHJaP5x2ZyrwAzAv1oG0VUqpC4HuwI2xjkWI9kLy1M9InvpzJE/9jnjOU1IEtVNKqcnbJ6/91s/YnZ6TAHwIbKGp91qIP0QpNQUYCZystY7EOp62SCnVi6Ye/jO01qFYxyNEa5M8JWJJ8tTvi/c8ZYp1AOIPexh4+Xces6n5L9sTy3+3/+cxWmv/XxVYO1INRIDsnY5nA+WtH077oJR6CDgNGKe1Xh/reNqw/Wm6i7tSKdV8zAiMVkpdDDi11oFYBSdEK5A89edJnvoDJE/ttrjOU1IEtVNa62qavhx/l1IqEfgEUMARWmv3Xxlbe6G1DiqllgCHAm+2+NWhwNuxiaptU0pNBcbTlFhWxzqeNu49YPFOx54Dimm68xZs9YiEaEWSp/48yVN7TvLUHonrPCVFUAe3PbF8TtMk0xMAp1LKuf3XtVrrDv0G3w1TgJeUUguBOcDFNC3X+mRMo2qDlFKPA2fT9D6qU0o196O75YLll7TW9UB9y2NKKQ9Nn7sVsYlKiLZH8tTvkjy1myRP7Zl4z1NSBHV8+wIjtv997U6/Gwd806rRtDFa6xnbN+S7EegErACO0lqXxjayNmni9j+/2un4bcCtrRuKEKIDkTz1GyRP7RHJU2K3yT5BQgghhBBCiLgiq8MJIYQQQggh4ooUQUIIIYQQQoi4IkWQEEIIIYQQIq5IESSEEEIIIYSIK1IECSGEEEIIIeKKFEFCCCGEEEKIuCJFkBAxopTKVErdqpTKjHUsQgghxM4kT4mOTPYJEiJGlFJvA1bAq7X+W6zjEUIIIVqSPCU6MhkJEiIGlFJnAD6t9TFASCklyUUIIUSbIXlKdHQyEiSEEEIIIYSIKzISJIQQQgghhIgrUgQJIYQQQggh4ooUQUK0IqXUCKVUVCmV2OJYqlJKK6X2iWVsQgghhOQpES+kCBKidQ0CirXWjS2ODQaCwKrYhCSEEELsIHlKxAUpgoRoXYOApTsdGwys0lqHYhCPEEII0ZLkKREXpAgSonUNAr7f6dgQ4IcYxCKEEELsTPKUiAtSBAnRSpRSBmAAv7zDNhRJLkIIIWJM8pSIJ1IECdF6egIOYGvzAaXUgO3HJbkIIYSINclTIm5IESRE6xm0/c9LlVI9lFKHAq9vP2aNUUxCCCFEM8lTIm5IESRE6xkEfAHkAyuAKcDtQB1wWQzjEkIIIUDylIgjSmsd6xiEiAtKqU+B77XWk2IdixBCCLEzyVMinshIkBCtZxCwLNZBCCGEELsgeUrEDSmChGgFSqkcIBtJLkIIIdogyVMi3kg7nBBCCCGEECKuyEiQEEIIIYQQIq5IESSEEEIIIYSIK1IECSGEEEIIIeKKFEFCCCGEEEKIuCJFkBBCCCGEECKumGIdwB+RkZGhu3TpEuswhBAiri1ZsqRaa50Z6zjaIslTQgjRNuwqV7XLIqhLly4sXrw41mEIIURcU0qVxjqGtkrylBBCtA27ylXSDieEEEIIIYSIK1IECSGEEEIIIeKKFEFCCCGEEEKIuCJFkBBCCCGEECKuSBEkhBBCCCGEiCvtcnU4IcSuuVwuKisrCYVCsQ5FtHNOp5P8/HwMBrlfJoTYeyRPib3FbDaTlZVFUlLSHj9XiiAhOhCXy0VFRQV5eXnY7XaUUrEOSbRT0WiULVu2UF1dTVZWVqzDEUJ0EJKnxN6itcb3/+zdd3iUVd7/8feZlsykhyS0EKUrRYqsgg3XsujP8uha1rqgYgMVsNAsYENdxd4b2B9XXUXdtTy6VqwoEhCkCwLBJJCQnpnJnN8fAzEJqCBJ7mTyeV1XLjN3ZjKfcGEO33Of8z2Vlaxfvx5glwuhNlcErdlUzhcrN1FQWkVmUjxDu7djj3YJTscSaRT5+fl07tyZQCDgdBRp5VwuF+3bt2fNmjUqgpqZximJZRqnpLEYYwgEAnTu3JkNGzbschHUptY4rNlUzmvfrqMyGKZjip/KYJjXvl3Hmk3lTkcTaRShUAi/3+90DIkRXq+XcDjsdIw2ReOUxDqNU9LY/H7/H1pa2aaKoC9WbiLF7yUlEIfL5SIlEEeK38sXKzc5HU2k0WhpgTQW/V1qfhqnpC3Q7xZpTH/071ObKoIKSqtIivfWu5YU76WgtMqhRCIiIr/QOCUi0jzaVBGUmRRPaVX922WlVSEyk+IdSiQiIvILjVMiIs2jTRVBQ7u3Y0tliC0V1UQiEbZUVLOlMsTQ7u2cjiYiIqJxSkSkmbSpImiPdgmcMDgbv89D3pZK/D4PJwzOVtcdEYlZo0aN4thjj3U6huwkjVMiLdsbb7xBnz59GDlyJM899xynnXaa05HkD2pzLbL3aJegwUREWqxDDz2Ufv36cf/99zfK6+655x6stY0ZUZqYximRluv5559nzpw5PP/880yZMoWHH37Y6Uit3qhRoygsLOTNN99s1vdtc0WQiEhbkpKS4nQEEZGY8cILLwAwbdo0pk2b5nAaZ8TKZF2bWg4nIi3bsmXLOPLII4mPj6d79+689dZbxMfH89577+3S93n77bc5+OCDSUtLI5VzCToAACAASURBVD09nREjRrBkyZJ6z/n4448ZOnQoiYmJpKSksN9++7Fo0SKefvpp2rVrR3V1db3nn3nmmRx//PG1jw899FAuvvhirrjiCtLT08nMzOSee+6hurqasWPHkpqaSk5ODs8880y911x00UWMGzeOtLQ00tLSuOqqq4hEIkB0Nuyjjz7igQcewBiDMYYff/wRgOrqasaPH0/79u2Jj49n6NChfPrpp7/7uobL4ay1zJw5k549exIXF0d2djZTpkzZpT9fERGRxpKSkkJqamqzv6+KIBFpEZYvX85+++3HkCFDWLRoEffeey+jR4+murqagQMH7tL3Ki8vZ/z48Xz11Vd8+OGHpKSkcNxxxxEMBgEIh8P8z//8DwcddBALFizgyy+/ZPz48bjdbk455RQikQhz5syp/X5btmzh1Vdf5bzzzqv3Ps899xxJSUl8+eWXTJ48mfHjx3PCCSfQq1cv5s2bx8iRIxk9ejR5eXn1XhOJRPj888955JFHePTRR7n77ruB6GzYsGHDOOecc8jLyyMvL48uXboAMHHiRF588UWefPJJ5s+fT//+/TnqqKPIy8v7zdc1NHXqVG688UamTJnC999/z0svvfSrzxURkfoaa7IOfn/CTpN1TTxZZ61tdR/77ruvFZHtLV68ePuL48ZZO3x4836MG7fL2f/yl7/Ys88+u961c88913bu3HmXv1dDZWVl1uVy2U8++cRaa+2mTZssYD/88MMdPn/s2LF2xIgRtY8ffPBB2759exsKhWqvDR8+3A4dOrT2cSQSsRkZGfa4446rvRYMBq3X67UvvfRS7Wt69uxpI5FI7XNuvPHGej/j8OHD7dixY7fL7/V67VNPPVV7LRwO227dutmrr776V19nrbUjR460xxxzjLXW2tLSUhsXF2cfeuihX/uj2s4O/05tBcyzLWBMaIkfGqdEduy3fqe0dMuWLbMpKSl28uTJdvny5fbNN9+0nTp1soAtKCjY5e/38ssv25dfftkuW7bMLliwwJ5yyim2e/futrq62oZCIZuammqvuOIKu2LFCrtkyRL73HPP2cWLF9uKigqbmppqX3zxxdrvVVxcbP1+v33ttddqrw0fPtwmJSXZadOm2WXLltk77rjDAvaoo46yd999t12+fLm95pprrM/nsxs2bKh9TWJior3kkkvskiVL7IsvvmiTk5PtzJkza99n2LBh9pxzzrF5eXk2Ly/PhsNha621l112me3QoYN988037eLFi+3o0aNtQkKC3bBhw2++ru44Za21kydPtikpKfaJJ56wy5cvt5999pl94IEHfvPP8o+MVdoTJCKO++mnn3j33Xf55ptv6l33+XwMGDBgl7/fypUrufbaa/nyyy8pKCggEokQiURYu3YtAOnp6YwaNYoRI0Zw+OGHc/jhh3PyySeTk5MDwPnnn8/gwYNZt24d2dnZPPnkk4wcORKPp/6vzH322af2c2MMWVlZ9O/fv/aa1+slLS2N/Pz82mtDhw6td7r1sGHDuPbaaykpKSE5OflXf55QKMSBBx5Ye83tdjNs2DAWL168038uixcvprq6msMPP3ynXyMi0uTGj4fvvmve9xw4ELbehd9Zl1xyCccffzy33HILAD169OCoo47inXfeISMjY5cjnHTSSfUez5o1i+TkZL766iv69OlDcXExxx13HN27dwdgr732qn3umWeeyZNPPsmpp54KRBs2JCcnc8wxx9T7nn379mX69OkAXH755dx66614vV7GjRsHwHXXXcdtt93G3LlzOfnkkwHo2LEj9957L8YY9tprL5YtW8add97J5ZdfTkpKCj6fj0AgQIcOHWrfp7y8nIceeojHH3+8NsPDDz/Mf//7Xx544AFuuummHb6uobKyMu666y7uvvtuzj333No/52HDhu3yn+/vUREkEut28Ze8E+bPn4/b7aZfv371rufm5nLooYcC0WLh1VdfpUOHDnz77bfcfPPNvPLKKzv8fsceeyzZ2dk88sgjdO7cGY/HQ58+fWqXw0F0sBk/fjxvv/02r7/+OldffTWvvfYaI0aMYMCAAQwePJjZs2dzwgknMG/ePJ599tnt3sfr9dZ7bIzZ4bVtywiaQt2CSkREmkZjT9bBb0/YHXTQQZqsa2IqgkTEcdsKhVAohM/nA2Du3Ll89tlnjB8/Hmst+fn5tbNHCxcurPeLva5Nmzbxww8/8OCDD/LnP/8ZgG+//ZZwOLzdcwcMGMCAAQOYNGkSRx99NE899RQjRowAogPMP/7xDwoLCznwwAPp3bt3o/ysX375Jdba2gHmiy++oFOnTrUDi8/no6ampt5runfvjs/nY+7cubUzgjU1NXz++eecccYZv/q6hvbee2/i4uJ4//336dmzZ6P8PCIiuy1GJut21e9N2GmyrmmpMYKIOG7ffffF5/MxefJkVq1axZw5c2qbEAwYMIBVq1bRtWvX2ucvXLiw3kxWXWlpaWRkZPDYY4+xYsUKPvroIy666KJ6s2OrV69m8uTJfPbZZ6xZs4YPPviA3Nxc+vTpU/uc008/nY0bN/LQQw9t1xBhd2zYsIHx48ezdOlSXn75ZW6//XYmTJhQ+/U999yTr776ih9//JHCwkIikQgJCQlcfPHFTJo0if/85z8sWbKEiy++mJ9//pkxY8b86usaSkpKYty4cUyZMoVZs2axcuVKvvrqKx566KFG+/lERGJR3cm6bbZN1tVt3jNs2DA2btwIRCfgGi5522bbhN3UqVM54ogj2HvvvSktLd1uwm7bRN2HH37IoYceylNPPVX7tfPPP5/Zs2fz+OOPN8lk3Ta7Olm3zbbJum1j665O1jU1FUEi4rhOnTrxxBNPMGfOHPbZZx9mz57NmDFjSExMpEePHuTm5tYrerZ1R9sRl8vFiy++SG5uLv369WPs2LHceOONxMXF1T4nEAiwbNkyTjnlFHr16sXIkSM588wzmTRpUu1zkpKSOPXUU4mLi6tdc90YzjzzTGpqath///05//zzOe+88+oVQVdeeSU+n48+ffqQmZlZu4/ptttu429/+xvnnHMOAwcOJDc3l7fffpuOHTv+5usauuWWW5g0aRI33ngje++9NyeddBLr1q1rtJ9PRCQW/d5kHbBLqxZ+b8JOk3XNMFm3o24JLf1DXXdEdqw1d91paNq0aXbYsGHWWmunT59uL7roImuttV999ZVNSEiwNTU1TZ7hqKOOsqNHj2607/drHdxaMnWH0zgl0pha8zj17LPP2i5dutiEhAR7wgkn2HvuuccmJibWjkcrVqywhx9+eO3zr7jiCvvKK6/86vd7//33bd++fW1cXJzt27evffvtt21CQoKdNWuW3bhxoz3xxBNtp06drM/ns126dLFXXXWVDQaD9b7HOeecY5OSkmxZWdl2339HY07fvn3ttGnT6l1r3769ve+++2pfc+GFF9qxY8falJQUm5qaai+//PLaTm7WWrt06VI7dOhQ6/f7LWBXr15trbW2qqrKjhs3zmZlZVmfz2f333//2q6sv/W6ht3hampq7C233GK7du1qvV6vzc7OtlOnTv3VP0dr1R1ORGJIbm5u7exabm4u8fHxDBgwgAMPPJCOHTvy/PPPc9ZZZzXJexcVFfHJJ5/w7rvvsmDBgiZ5DxERaV3OPPNMzjzzzNrH06dPp3///rhc0YVVO1q1cOGFF/7q9zvssMNYtGhRvWtlZWW1n//rX//63Ux5eXn87W9/IyEhYbuvffjhh9tda/h+QO3yvW08Hg/3338/999//w7fs1evXnz++efbXY+Li+Puu++uPftuZ183e/bseo9dLheTJ09m8uTJO/w+jUVFkIi0SAsWLGDixIlAtFvM/PnziY+Pb5b3HjRoEJs3b2bGjBnbbYIVERGB+pN12x5XVVUB8PXXX/Pll1/WNrNpbJqs230qgkSkRVq5ciUQPXvA7XY3WwEE1J5i3dh2NCsnIiKtU93JOmjeVQuarNt9KoJEpEVLSEjY4e17ERERJ22brNumOVctaLJu96k7nIiIiIjIbnBi1YLsHhVBIiIiIiK7QasWWh8VQSIiIiIi0qaoCBIREYlVeXlw8smwYoXTSUREWhQVQSIiIrEqEoH33oPzzot+LiIigIogERGR2NW5M9x5J3z8MTz0kNNpRERaDBVBIiIiseycc2DECJg0CVavdjqNiEiLoCJIREQklhkDjz4KLhecfz5Y63QiERHHqQgSERGJdTk5cPvt8P778NhjTqcREXGciiAREZG24IIL4LDD4MorYe1ap9OIiDhKRZCIiEhbYAw8/ni0S9wFF2hZnIi0aSqCRKTFWLZsGUceeSTx8fF0796dt956i/j4eN577z2no4nEhq5d4bbb4J13YPZsp9OItDpvvPEGffr0YeTIkTz33HOcdtppTkeSP0hFkIi0CMuXL2e//fZjyJAhLFq0iHvvvZfRo0dTXV3NwIEDnY4nEjsuvhiGD4cJE2D9eqfTiLQqzz//PHPmzKFbt25MmTKFv//9705Hkj/I0SLIGOM2xtxojFltjKna+t+bjDEeJ3OJtHXFFUHmry3io6X5zF9bRHFFsMnf85JLLuH444/nlltuoUePHhxzzDEcddRRdO7cmYyMjCZ/f5E2w+WCJ56AYBAuvFDL4kR2wQsvvEDPnj2ZNm0aa9eu5f/9v//ndCT5g5y+EzQJGAtcBuwFjNv6eIqToUTasm0FUDAcIS3gIxiONHkh9NNPP/Huu+8yfvz4etd9Ph8DBgxosvcVabO6d4cZM+Df/4Znn3U6jYhIs3O6CDoAeMNa+4a19kdr7evA68D+DucSabNWF5YT8HkI+DwYY2o/X11Y3mTvOX/+fNxuN/369at3PTc3t3Yp3LBhw9i4cSMA3377LSeddFKT5RFpEy69FA44AMaNg7w8p9OItArauxo7nC6CPgX+bIzZC8AY0wc4DPhPwycaYy4wxswzxswrKCho5pgibUdJZQi/113vmt/rpqQy1GTvaYwhEokQCv3yHnPnzuWzzz5j4MCBWGvJz8+nQ4cOACxcuJB99tmnyfKItAluNzz5JFRWwpgxWhYnrYoTy7a1dzW2OF0E3QY8Ayw2xoSA74GnrLUPNnyitfZRa+0Qa+2QzMzM5s4p0mYk+71UhmrqXasM1ZDs9zbZe+677774fD4mT57MqlWrmDNnDueddx4AAwYMYNWqVXTt2rX2+QsXLqR///5NlkekzejdG264AV57DV580ek0IjvFiWXboL2rscbpIuhvwN+BM4DBWz8fY4w5z9FUIm1Y14wEKoJhKoJhrLW1n3fNSGiy9+zUqRNPPPEEc+bMYZ999mH27NmMGTOGxMREevToQW5ubr2iZ/78+SqCRBrL5ZfDfvvBJZdAfr7TaUR+lxPLtrV3NfY4XQTdDtxhrf1fa+1Ca+0zwJ2oMYKIY1IDPgblpOHzuCiqCOLzuBiUk0ZqwNek73vmmWeydu1aysrKePXVV9m8eTP9+/fH5XKRm5tLVVUVAF9//TVffvkl3bt3b9I8Im2G2w2zZkFpabQQEmnhnFi2vTN7V6V1cboICgA1Da7V4HwukTZtWyE0vHdWsxRAO5Kbm1s7u5abm0tJSQkDBgxg1qxZdOzYkeeff77ZM4nErD59YPp0eOkleOUVp9OI/CYnlm3/3t7VbdTEp/Vw+jyeN4DJxpjVRPcDDQIuB552NJWIOG7BggVMnDgRgMWLFzN//nzi4+MdTiVtjTFmLHAhsOfWS98DN1lr/+1YqKZy1VXRAmjMmOhhqtrjIC1U14wE5q8tAqJ3gCpDNVQEw/TukNZk71l37+qECRNYuHAhkyZNAqidsFMTn9bF6TsulwIvAw8CS4CZwGPA1U6GEhHnrVy5kgsvvJDy8nLcbrcKIHHKOqJn2g0GhgD/BV4zxsTev2w8nuiyuKKiaNtskRbKiWXbv7d3FVATn1bG0SLIWltqrR1vrd3DWuu31naz1k611lY5mWuXLFumtqIiTSghIYFFixY5HUPaKGvtHGvtW9baFdbaZdbaq4FSYJjT2ZpE//5wzTXw/PMwZ47TaUR+lRPLtn9r7yqgJj6tjNN3glq3N9+Mthf9+GOnk4iISBMzxriNMacBicBnTudpMlOmwIABcNFFsHlz7WUnzmURacnq7l3d9lhNfFoPFUG747DDID0d7rvP6SQiItJEjDH9jTFlQDXwMHCitXbhDp4XG4d6e73RZXGFhTBhAuDcuSwiLdmCBQvqNUVQE5/WxenGCK1bIADnnw+33w5r10JOjtOJRESk8S0FBgIpwMnAU8aYQ6219dZpWmsfBR4FGDJkSItfJ11cEWR1YTkllSGS/V66ZiT8sqRo0CCYPBluuglOPZXV/Q+oPYsFqP3v6sJyBuU0f/dIkZZg5cqV9R6riU/rojtBu2vMmOh/H3zQ2RwiItIkrLXBrXuCvrHWTgG+AyY4nWt37NSdnWuugb594cILKf+5sNnPZRFpTdTEp/VREbS7cnLgxBPhscegosLpNCIi0vRcQJzTIXbH6sLy2js7xpjaz1cXlv/ypLi46LK4vDz2vuP6Zj+XRaQ1UROf1kdFUGO47LLo5lGt+5QWIBKJOB1BYoRV50uMMbcaYw42xuy5dW/QLcChwHMOR9stJZWhnbuz86c/wVVX0e6fzxH/3/+jIhjGWktFMExFMEzXjIRmTC0i0nhUBDWGgw+OdtK59161yxZHJSQksH79eoLBoP4BK7vFWsumTZu0tAM6AM8S3Rf0PvAn4Ghr7VuOptpNyX7vzt/ZmT4d9tqL/tdPJL6yrNnOZRERaUpqjNAYjIneDTrvPPjoIzj0UKcTSRuVnZ1NYWEha9asIRwOOx1HWrn4+Hiys7OdjuEoa+0opzM0ha4ZCcxfWwRE7wBVhmqoCIbp3SFt+yfHx8OsWbgOPJAB986ARx5p5rQiIo1PRVBjOf10mDgxejdIRZA4xOVykZWVRVZWltNRRKQF23bQ5OrCcooqgiT7vfTu8Bt3doYOjbbLnjkTTj0VDj+8eQNLTLHWYoxxOobEiD+68kXL4RqL3x9tlz1nDqxZ43QaERGR37StEBreO2vnlrbdeCP07AmjR0NZWfOElJjj9XqprKx0OobEkMrKSrzeXW/SoiKoMV18cXRpnNpli4hIrPH74cknoxN9kyc7nUZaqaysLNavX09FRYX2rspusdZSUVHB+vXr/9AKGC2Ha0x122VPmxY9TFVERCRWHHQQXHppdOn3KafA8OFOJ5JWJjk5GYANGzYQCumcKdk9Xq+X9u3b1/692hUqghrbZZfByy/Dc89Fl8eJiIjEkhkz4M03o82AcnM14Se7LDk5+Q/9o1WkMWk5XGM76CAYOFDtskVEJDYlJMATT8DKlXD11U6nERH5Q1QENbZt7bIXLYIPPnA6jYiISOM79FAYMwbuuQfmznU6jYjILlMR1BROPx0yM+Guu5xOIiIi0jRuuy26F/bcc0HdvkSklVER1BTi46MzZG++CUuXOp1GRESk8SUmwuOPw7Jl0WZAIiKtiIqgpjJmDMTF6W6QiIjEriOOiDYBmjkTvvzS6TQiIjtNRVBTycqCs8+Gp56CggKn04iIiDSa4oog89cW8dHSfBaMu5pIx07RZXHV1U5HExHZKSqCmtKECVBVBQ8/7HQSERGRRrGtAAqGI6QFfFT5E1k47R+weDHccIPT8UREdoqKoKbUpw8cfTTcf3+0GBIREWnlVheWE/B5CPg8GGMI+DxUHf4XNp1yRrRZwjffOB1RROR3qQhqaldcAfn50cNTRUREWrmSyhB+r7veNb/XzZKrpkP79nDOORAMOhNORGQnqQhqaocdBgMGwJ136vBUERFp9ZL9XipDNfWuVYZqSGifAY88AgsXws03O5RORGTnqAhqasbA5ZdH10q/847TaURERHZL14wEKoJhKoJhrLW1n3fNSIBjj4WzzoIZM+C775yOKiLyq1QENYfTToNOnaItREVERFqx1ICPQTlp+DwuiiqC+DwuBuWkkRrwRZ9wzz3Qrl10WVwo5GxYEZFfoSKoOfh8cOml8N57kJvrdBoREZHdsq0QGt47q34BBJCeDg89FL0TdNttzoUUEfkNKoKaSN0zFOavLWLLWaMgEIjuDRIREYllJ54YXQVxww2waJHTaUREtqMiqAk0PEMhGI7wbZmh+u8j4fnnIS/P6YgiIiJN6777IDU1uiwuHHY6jYhIPSqCmsCOzlAI+DysOGN0dCC47z6nI4qIiDStjAx44AGYN097YkWkxVER1AR+7QyFwqxs+Otfo2ulS0ocSiciItJMTjkFTjoJO20ai9//onaJeHGFzhESEWepCGoCv3aGQrLfC5MmQXExPPqoQ+lERESaVt19sZ9fPp2QP0CXqy4lLc5NMBxRISQijlMR1AR+8wyFP/0JDj882iChutrpqCIiIo2q4b7YlSaRj8deQ9L8eWQ+8VDtEvHVheVORxWRNkxFUBP43TMUJk2KNkd45hlng4qIiDSyhvtiwxFL/jF/ZcMhR9L+9pvxrVqB3+umpFJnCImIc1QENZHfPEPhiCNg8GD4xz+gpubXv4mIiEgr03BfbGKcBwx8cvlN2Pg4sq+8hMqqYHSJuIiIQ1QEOcEYmDwZli+H115zOo2IiEijabgvtlOqn5KqEKH2WWy47hYSvv6C9FmPRpeIi4g4REWQU/76V+jRA269leLy6noHq2qzqIiItFYN98W6XYbstAA56QFW/b+/suXQI+hx9wxS835yOqqItGGOF0HGmI7GmKeMMQXGmCpjzGJjzHCnczU5txsmToR58/jxn2/UO1hVhZCIiLRWO9oXe1DPTA7plcXwvdqT8sws8HopPWskHy3ZqDFPRBzhaBFkjEkF5gIGOAbYG7gUyHcyV7M5+2xCme3p+sT92x2sqq45IiLSWv3Wvtji9CyWXjWdpC/m0uNfz2ryT0Qc4fSdoIlAnrX279bar6y1q62171trlzicq3nEx/PTyAtImfsR/gXzay+ra46IiMSq1YXlbDn9bEoPOYwOM6aT8vP6epN/dc8YUnEkIk3F6SLoBOBLY8yLxph8Y8x3xphLjDHG4VzNpnTUeYSTksl86O7aa7UHq4qIiMSYksoQfp+H9f+4B4yh86Rx+D0uSipD250xpLtEItJUnC6CugFjgFXACOAe4FZgbMMnGmMuMMbMM8bMKygoaN6UTWiPrh1Zf/ookv/zOt6Vy+sfrCoiIhJjtnWPC3XuwsarbyDpkw9JfHY2yX7vdmcMaYm4iDQVp4sgF/CttXaKtXa+tXYWcC87KIKstY9aa4dYa4dkZmY2e9CmkhrwkTr5SqzPR8oDd29/sKqIiEgMqds9btMZI9ky7GByZlxHt8pN250xBFoiLiJNw+kiKA9Y3ODaEiDHgSyOSenaBde559LxtX8yyJSpABIRkZhVr3tcVZh1/7gXN5aUcZeQHO+pd8YQaIm4iDQNp4uguUDvBtd6AWscyOKsSZPAWrjtNqeTiIiINKm63eP6HjQQc+ut8M479H7rlXpnDGmJuIg0FaeLoLuAocaYq40xPYwxpwCXAQ84nKv57bEHjBwJjz8OGzY4nUZERKT5jBkDhxxCYPJVDPZU1DtjSEvERaQpOFoEWWu/Jtoh7lRgEXAzcC3woJO5HDNlCoTDcPvtTicRERFpPi4XPPEEBIOkTLiMQV1Sd3jGkIhIY3H6ThDW2n9bawdYa+Ottb2stfdaa63TuRzRvTucdRY8/DD8/LPTaURERJpPjx4wYwa8+SY895zTaUQkxjleBEkDU6dCMAgzZzqdREREpHldeikccABcdhls3LjDp+gwVRFpDCqCWppeveC00+DBB6Gw0Ok0IiIizcfthiefhMrK6D6hBgtDdJiqiDQWFUEt0dVXQ0UF3HWX00lERESaV+/ecMMN8Oqr8M9/1vuSDlMVkcaiIqgl6tMHTj4Z7rsPNm92Oo2IiEjzuvxy2G8/uOQSyM+vvazDVEWksagIaqmuuQZKS+Hee51OIiIi0rzcbpg1C0pKooXQVsl+rw5TFZFGoSKoBSquCDI/tQuFRxxN+K67KM4rcDqSiIhIs6htfODOYMO4ifDSS/DKKwB0zUjQYaoi0ihUBLUwdTd9Fo2fiKekhM23ztSmTxERiUl1u719vCyfT5YX1DY+WHfeWIr37k/wwouY+8USVheW0y0zUYepishuUxHUwtTd9Fk1YBAlh4+gy9OPsmZ1ntPRREREGlXDbm9rN1WwrqiSmojFGEPY7eGdK2bg3rKFPrddRzAcYVVBGV0zEnSYqojsFhVBLUzDTZ/54yfhLS4i+dGHHEwlIiLS+Bp2ewtHLCnxXjYUVwKwobiSmr79yf37GNJee5n2H76rbnAi0ihUBLUwDTd9Vg4czOYjjqbL7IegqMjBZCIiIo2r4cRfYpwHsJRVR8fB6H8tq0ZfSuXefek8ZQKJ5SXqBiciu01FUAuzo02fKy65Ck9JCcyc6XQ8EZE2xRgzxRjztTGmxBhTYIx5wxjTz+lcsaLhxF+nVD8lVSE8brDW4nFDSVWIjpkprJv5AJ5NhWRNm6JucCKy21QEtTCpAR+DctLqbfrsdeSB8Le/wd13Q4E6xYmINKNDgQeBA4DDgDDwnjEm3clQsaLhxJ/bZchOC5CTHqCoIkhOeoDstABul6Gy3wA2XDiOzFdfpOe8j2q/R93GCvPXFqmRkIjsFGOtdTrDLhsyZIidN2+e0zGa1w8/QN++MGEC3HGH02lERDDGfGOtHeJ0juZkjEkEtgAnWGvf+LXntclx6g8qrgiyurCcksoQyX4vXTMS6jU7qPv1FFeE/v9zOO6SLfD99xR7/cxfW0TA58HvdVMZqqEiGFbDBBGp9Wtjle4EtRZ77QVnnQUPPAAbNjidRkSkrUoiOnZqk2Yj2bYC4te6vdX9JjJtzwAAIABJREFU+sCeHXA/NRvy8uCKK7ZrrLDtczVOEJHfoyKoNbnuOgiHYcYMp5OIiLRV9wDfAZ83/IIx5gJjzDxjzLwCLV1uOn/6E1x1FTzxBO7/+796jRUA/F63GieIyO9SEdSadO8O554Ljz4Ka9Y4nUZEpE0xxtwJHAScZK2tafh1a+2j1toh1tohmZmZzR8wRu1wz8/06bDXXuw17QqCm4vrPb8yVKPGCSLyu1QEtTbXXAPGwE03OZ1ERKTFM8a8bIy51hhzgjGm+9ZrZ/yB73MXcDpwmLV2VWPnlB1reJhqMByJFkIRFzz5JN4N6+l4y7R6HVUrgmG6ZiQ4HV1EWrg/XAQ11sAiu6hLF7joIpg1C1ascDqNiEhLdzOwBjgQeMQYUwpM25VvYIy5h18KoB8aP6L8mt/c8zNsGGbCBDq/+DTpX35a21FVTRFEZGfszp2g3R5Y5A+aMgV8Prj+eqeTiIi0aNba+dbap621V1lrjyDa5vr/dvb1xpgHgHOAM4AiY0yHrR+JTRRZ6mh4mCo02PNz443UdO9OzsTLcJWrGYKI7Lw/XATt7sAiu6FDB7j0UnjuOfj+e6fTiIi0WMaYrLqPrbVfE52821ljiHaEex/Iq/NxZWNllF/X8DBVqL/npxgPC6bPxLf+J/a+75ZflsvprCAR+R27sxxudwcW2R0TJ0JSEkyd6nQSEZGW7DVjzHJjzLvGmJlb7+wsMsbs1M55a635lY/pTRtbYPvDVCuCYfJLqyitCvHR0nzeWbSRosFD2XTOBWTMfoyMb79Ui2wR2Sm7sxxutwYW+eOKK4LML3ex6rxL4PXXKX3vA6cjiYi0SNbaA6y1PYGLgE+AnwE/sMAYk+toOPldqQEf3TIT+bGwnI+X5bN4wxYqqmuI87hJC/gorgyyZnM5K8ZNoTpnT7KvvIRAuFotskXkd+10EWSMOcwYk77tsQYWZ9TtlFN+0ViCHToSufIqisurnY4mIuKohuNUXdbaVdba16y1N1hrT7bW9gGGNnNE2UXFFUFWFZSxZ0YCh/TKwutxUVRRTU3EYoyhXUIcLmBd0MX6O+4jbs1qMm67US2yReR37cqdoH8DBcaYtcaYN4wxNxpj/gq4NLA0n7qdcggkkH/FFFIWfMOi+2fXP0NBRKTt2dE4dZIxpseOnmytrWjmfLKLGnaHC9dAcryXDcWVAHRK9ROxlk3lQcqGHsTPZ55Dh1mP0GOF5mJF5LftShF0ItHNoO8CPwF/Bl4GlhpjthhjPjXGPGCMGa2Bpek07JSz9thTKNqzB/0euI00n0ubQkWkzTDGvGCMGVHn0o7GqZfYfpw634G48gc0HPMS49yAoaw6DEBSvJc92iWS6vdSVBFk49Tp2C45JI25ECorHUotIq3BrhRB9wHnW2tHW2vHWGsPAg4GlgHXEO0M1wGY1PgxZZuGnXI2lIX49sKrSP1pNe1efLb+GQoiIrHtDeCROo93dpya2OxJ5Q9pOOZ1SvWzpSqEx2VqGyW4XDCiXweG985iQJ8cXE88DkuXwvTpzgUXkRbPswvPzQaW1r1grZ1rjJkEjLTWntSoyWSHumYkMH9tERA9K2FTeTUlBx5OyZD9ybrrVor+eip+f4Ai3QkSkdh3JPBknccap2JMwzHP7TJkp/lJ2XrnJ9nvpUNKIqsLyympLMYYIGcfepxyFh3vuIOyY44n6RA1rhWR7e3KnaBPgHN3cH0h0YFImkFqwMegnDR8HhdFFUFS/T72aJdIwTU34s3/mcxHH6h3hoKISAzbD3iuzmONUzGm4Zjn87g4uGcmh/TKYnjvLLpmJLCqoIxgOILHZVi8YQvfbyhh7ZTrCWZ1wHXuuRQXlTr9Y4hIC7QrRdAlwFhjzCxjzABjjMcY4wcmAJubJp7syLZBYXjvLEb064DLBYX9B7Pl6OPIePgeQnl5dM1IcDqmiEhTmwzcUOexxqkYVHfMG5STRmrAV/u1uo0T8rZU4XW7Ka0M8d76Kr6acisJK5dRde1058KLSIu100WQtXYZ0Vm3TsB8oAIoBUYDU5oknfyuurNkSy+djKuqij8991C9QUJEJBZZa9+w1p5Z57HGqTambuOEgrJq8rZUYjDRttn7D2fZ0SeR9fA98M03zgYVkRZnV/YEYa1dDowwxmQDgwALfGOtzWuKcLJzooWQD3IOoHrUOXgff4wvTxyJr3dPumYkqCASkTZD41Tbsq1xQsDnoaK6BhdgjMHv8xDvdTPv0qvp8vUn+M85B+bNA5/GQxGJ2pXlcLWsteu2zsC9qYGl5SiuCDLv75divT5633Wz2mWLSJulcapt6JqRQEUwTEUwjN/noiocobQ6SEaSj6pQmCJfAu+PuwEWLiRv0rXbjYfbDiDXOXsibc8fKoKkZVpdWI4nuzMFY8aT+tbrZH7zhdpli4hIzKq7JDzO6yY7LUD3zERqIpZQTYRgxFJ8+AiKTjyV9vffybJ3P60tdLYVQMFwhLSATxOHIm2MiqAYsm1tdOEFlxDsnE3H66fgd0Wvi4iIxKJthdBJg7Pp2T6R3h2SGZyThstl8HtddMtMJO/626hJS6fvNeNZnVcMRCcOIxH4aXMF364t4qfNFUQiaOJQpI1QERRDtq2Ntn4/G6fegP/7hST+77Nqly0iIjGvYTvt6nCE/p1TSYr3UpOWxoabZ5Lw/UKKpt/E/e8v4+V5a5m/tohQTYTkeC+hmghrNpWxobjS6R9FRJqBiqAYUndtdPGxJ1C67/5k33ETXX01v/9iERGRVq5uO+3BOWl43L/8M2fpsCP47oC/MPx/H6J3wVpKK8MsWl9EWXUYYwzxXg8uYyirCgPaLyQS61pMEWSMmWKMscaY+53O0lrVmwWrDLF++gx8mwpJvfsOp6OJiIg0q7oTg9ZavlmzmX+NmkRVQjJ9r5tAJBzCZVwsySvBWktVqIYIkBjv0X4hkTagRRRBxpihwAVArtNZWru6s2B7HXsYjBoFd90FK1cCmtkSEZG2oeHyuE3l1VSlpvOvcybRafkihr/5DBEsxZUhSqrCeN2GPdIT6JTqr3cIqzGm9nPtFxKJHY4XQcaYFOA54FygyOE4sefmm8HrhYkTNbMlIiJtSt2JwWS/h83l1Swc9hcW7X84J8x5nMCqFcR7DINzUumSHsDlit5BqnsI6zZ+r1uNhkRiiONFEPAo8LK19gOng8SkTp1g6lT4178oeOMdzWyJiEib5Pd5CIYtP5dW8cipl1Pti2fc87dSVR3i42X5/FhYTrfMRFIDvtpGQ3VVhmrUaEgkhjhaBBljzgd6ANfsxHMvMMbMM8bMKygoaPpwsWTCBNhjDzpOj7bMrkszWyIi0hb4vR7aJcXhcrnYlJjG06ddTu/V3/PXT/7FIb2y2DMjgVUFZRRXBLfbT7Tt864ZCU7/GCLSSBwrgowxvYEZwBnW2t/9V7i19lFr7RBr7ZDMzMymDxhL/H64/XYSf/iexOefrvclzWyJiEhbkOBzE/C46Nsxhf27tmPlEcfz3cCDGPHC/cStXllvdUTD/UQ+j4tBOWmkBnxO/xgi0kicvBM0DMgAvjfGhI0xYWA4MGbr4zgHs8Wek08mfNDBZN9+E8Gf8zWzJSIibUpWcjydUv1EbITy6jBVNRHeGXsdEV8c2VdeCpFIvdURdfcTqQASiT1OFkGvAf2BgXU+5gH/u/Vz7dZvTMbgefABvKVb2OPOmzWzJSIibUqnVD97dUyhW2YindL8dMtIIKn7nuRePo2Erz+n3exHtTpCpA1xrAiy1hZbaxfV/QDKgc1bH1unssWs/v0x48aR8cLTDN/yowogERFpM7pmJOByQZf0AINz0hjYJY1QOELJqWdQ8ucjaH/rDURWrNDqCJE2oiV0h5MmtN25QBOnQseOcPHFUFPz+99AREQkBjTc55Oe6OOEwdmkJ8Wx+Lp/gNvFkJsnkRrvcTqqiDSDFvV/urX2UKczxJJtBVDA5yEt4KMyVMP8ijD73fIPEkaeBQ8/DGPHOh1TRESkWUQLoforIPZolwA5aXDXXbjPP5+fbrmLVSefTbLfS9eMBK2YEIlRuhMUw3Z04nUkAm/2PoiiAw4hPHUqW1b/5HRMERERxxWffjabDxhOpxnTyNq0UQeKi8Q4FUExrOGJ16VVIdZsKqO4Kkz+zXfgqqykYsIV9X7Bb7d8Tr/8RUSkDVi9qYI1t94NxpA9eRwBr1sHiovEMBVBMazhidcbiitxGUO7BB/BHr0ovOBSOs55ifz/vAf8UgAFwxHSAj7NgomISJtRUhnCveeebJx6PUmffEjaC0/rQHGRGKYiKIY1PPF6U3k1EaJtQgHyL7uCqk7ZZEyawMeL1vPOoo1EItRbPqdZMBERaQuS/V4KSqv5/IiTyBs8jPY3XE3JslVqmS0So1QExbCGnXBS/T72SE8gKT76C73E5eODi6eSvmoZPV6cRXFldLlcadUvs16aBRMRkbYgPcHHvB83seTnMl656FpsOEy7Ky5l+cYSrYoQiUEqgmJc3ROvR/TrgMtF7Z2hVYVlrDnwcDYfeiTt77yVLiX5uIxhQ3Fl7et1cJyIiLQFazaV4/O4iPO4KMjM5rVTL2HvBZ/Rac6LBMMRPl1ewMfL8rVnViRGqAhqQxreGaoOR+ifnUb+LTMBGHb71US2Lpuz1tYupdPBcSIiEuuW55fRPjmenu2TSUvwsfa0c/mp777se8/NuPLyWFdUwdrNFdozKxIjVAS1MXXvDA3OScPjdhHKzuHnSdeS9skH7P/Z26T6fRRVBPF5XAzKSdMZCSIiEvMMFjAAVAQjeH1u3p5wE55QkM5TJpAc5yFcg/bMisQIFUFtWN3GCYV/H03poCH0vPU6jmrvZnjvLBVAIiLSZvTISmJLVYiqUA1+r6G8qoZ1GZ357sIr6PTJe+z57uskxv1y7IT2zIq0biqC2rDUgI9umYn8WFjOxys38enEW/CWl5Iy5Sqno4mIiDSrfbJTyU7zU2MjxHndVIbCpPq9BMdcQkG/wQy+czp7hEpqn689syKtm4qgNqy4IsiqgjL2zEjgkF5ZpO83iB8vHAcvvAD//rcOThURkTYjNeDj4J6Z9O2UQt9OKRzZtz377plO2Lj48R/34q2qpPv0SdhIRHtmRWKAx+kA4pzVheW165ohej5QwdjL6fDum8RdeBG5r31AXHoaaQEflaEa5q8t0hI5ERGJWdF9szsY43pnUXntdaRfezUbX3kJ30mn0LuDxkOR1kx3gtqwksoQ4ZoISzeW8M2aIpZuLCHk9rDkhpmYDevpfc8tOjhVREQE8E+eCH/6E31mXM0gf3i7AkirJ0RaFxVBbZgxkLt+C6EaS3K8h1CNJXf9FsoGDWH9WefR/tknCXz1ee3ztQlURETaLI8HZs2CkhK45JJ6Rc/Hy/L5ZHkBwXBELbRFWgkVQW1ctCWo3frIUhUMsyK/lPfPuozS9p3JmDCW75ZtYOnGEgpKq7UJVERE2q6+feG66+Cf/2Td48/UFj1rN1WwrqiSmojV6gmRVkJFUBtmLfTvnIrX7aKkKkSoJoLP4yZUY+nQKYP/PW8qKWtXse9jMymrCrFofTHpCVr/LCIibc+2Oz8f/88oinr3pdcNk0kq24IxhnDEkhLvZUNxZe3ztXpCpGVTEdSGJfu9eNwuendIZt890gn4PCT43LRLiKO0KozrqKOYf8xp7P3ik+z5/Tf065zK5nLd2hcRkbZlWwEUDEdITUngvatuxV1cTPyVE/hmzWY2lQWpCIYpq66pfY1aaIu0bCqC2rC6h6Vaa9lUHiRiLZ1S/ZRVh6O3+CdfT2mnHA64+UraU61ZLRERaXPqdlM1xlC5d18+PGk03f7vdXp/8V9SA16WbiwhGK7BWqsW2iKtgIqgNizaCjQNn8dFUUWQVL+XPdolkhTvJTHOQ3W4hgpvPN9cfxfe9evIun6qZrVERKTNKakM4fe6612be8r5bNyzFwNvnUpKVTmd0gJ43YaiiiA+j0tHSoi0cCqC2rhthdDw3lmM6NcBlwsqgmE6psSzsaSKxRu3sKRrf74/6yKy/vkcPb/6wOnIIiIizSrZ76Uy9MtSt4g1pKUm8L8XTsO3eRN7/eM6+nRMpltmIsN7Z6kAEmkFVARJrbp3hoorQ3hdhi6pfvw+F7nnjWNLrz4ExlwMBQVORxUREWk2DZePB2vCrC2qIOnAoSwfNYZ+771G+I03MeaX1+jcIJGWTUWQ1LOtEOqU6udPXdsxrHsmQ/ZsR/9u7fnh1vuxxcUUnHUu89ds1i90ERFpExouH/e4DJ1SAwR8bn4YPY7ibr0Yfue1uEtLgPqNFHRukEjLpCJIdqjh+ufSqhDfZ+Tw9bnjyXz3TZL+9U/9QhcRkTaj7vLx7plJ7LdnOl63i+KIi2+um0nC5gK63ToNiDZSiETgp80VfLu2mJ82VxCJoHODRFoQFUGyQw3XP28orqQqHOGz4//Oz/2HkHPdJLzr1ukXuojENGPMIcaY140x640x1hgzyulM4ryGR0xkHX4wa0ZdTMeXnyf3iX/y2YoCfthYQqjGkhzvIVRjWbO5vN45QiLiLBVBskMN1z+vK67kp80VpCT5+e7GuzCRGnpccRF5haVORxURaUqJwCJgHKB/wQqw/RiZX1LFS8edR3FON7pdPYG1P/7MqoIyaqzFGEO8140LKKsKOx1dRLZSESQ71HD9czAcoUtagPSEOCq6dOW7qbfSIXceezww0+moIiJNxlr7H2vtVGvty0DE6TzSMjQcI9dsLsMdCPDVtXeQkJ/HiS/eR3FFNSsLSrHWUhUKE7GWxHiP09FFZCv93yi/KvpLPtris6w6zM9bKqkKhYnzuFlxxHEkfvIBfWbdx4JDDiHy58PompGglqAiItIm1B0jVxaU0iE5nvLB+7HijPMZ+tyjLDnwL3wbP4iSqhCJcR6y2iWSnqgxUqSl0J0g2SmdUv3s0S4Rr9tFSVWIUE2E98ZcQ0lON/pcNZbIxp/VKEFE2jRjzAXGmHnGmHkFOkqgTbEYKoJh1mwq49UTL2BzpxyOv386nrLyrXeCaqgMhemakeB0VBHZSkWQ7JSuGQm4XNAlPcDgnDRcLoM3OZHV9z+Bu6SYXpMvI+BxqVGCiLRZ1tpHrbVDrLVDMjMznY4jzahTip+lG0uoqA7jS07k1bHXk1a4gVNefRiDAQPW6ZAiUo+KINkpDdc/V4cj9O+cinvgQPKum0HSB/9Hl9kPU1IZcjqqiIhIs0qIc9MpLYDH7aK8uobvuw/g4yNP5YC3XiAr92viPW4CXo8mCkVaEO0Jkp1Wd/1zst9LMBzdI7z57HNJnPsRHW67gfcye3P/uoFkJsXTp1My4YilpDJEst+rPUMiIhKTrIX99kwnb0sVZdU1VIZq+HjUeAYs+JRDbp3Ef555mzVVIarCNQzKSXM6roigO0HyB9VrDwrMnTiDzSkZHH3zBJYvX8d/l/zMHW//wMfLClhVUMb367fw6fIC7RkSkVbFGJNojBlojBlIdMzM2fo4x+ls0nIk+71UhX5pHlgdClPp8/P+FTeT+NOPDH5splpki7QwKoLkD2m4PG7upjD3nXc96Zt+5oJZN1FWGeSnzeV8v2ELKX4fbpdhXVEFueuKnY4uIrIrhgDzt374geu3fn6Dk6GkZUlP8LFofTFlVSGS4txYY1hTWM633QbxzdF/o9vzj/Pz2//lk+UFvPjVWhauK2b+2iI+WpqvpkIiDlERJH/YtkJoeO8s8suqye83mFdOu4y+X33Aka/Pwu/zsKG4YutBcR6S470szy9zOraIyE6z1n5orTU7+BjldDZpOTaXB+nXOZXEeC+l1WHS/F7aJcZTFarhtdMvozCtPWc+diOmsoKF64t56IMVrN1UQVrARzAcUSEk4gAVQdIowjWWzeVB3j3iNL4aNoK/v/0ke+fOpayqhiV5W1izqYzKYA1G/XFERCTGlFSGyEyKo3eHZPbdI50u6QHSE70k+32UeOJ45IxJZOev5YTXn6AqFKE8GOK/S37m27XF/LS5gkgENU0QaWYqgqRRdE6JzniFI5anR13N6o7duO6FW+hanEfA56aiuoYffi6hQ4rf6agiIiKNKtnvpTJUU/s4YqFLWoCkeDfriipZus/+fHTI8fz5zWfwz/+GimANeSWVJMd7CNVY1mwuZ0NxpYM/gUjb42gRZIyZYoz52hhTYowpMMa8YYzp52Qm+WP26ZJGlzQ/NdayybqZcd6NYAw3PDON0JZSPG4XHVMCJMZFGxIWVwS1HlpERGJCvWZB1uJxGUIRy7DuGWQmxlMVivDYsRezOaUdo2fdRElRGRXBGn7YWMLPJZVUhWrUNEGkmTl9J+hQ4EHgAOAwIAy8Z4xJdzKU7Lqe7ZM4sm9HBnZJpXtWIgl79ebtqTPJXr+Kkx6+gW4ZAfbvmo61vxRAwXBE66FFRKTVa9gsKKddgOw0P26XIdnvZlN5NZs9fp4aNYU9fv6Rk95+Cq9h60qJMD9tKsfl9L/IRNoYR88JstaOqPvYGHM2sAU4EHjDkVDyh3TNSKC4IshBPTPxe93kri9mc6dDWXv5VLrNvBn/G/uzdtRFBOJcrC4sJ+DzEPBF//pt++/qwvLac4hERERak7pn6UF0wm91YTk1FrqkB4hE4Ju9h/LukBGcN/ef/HjwkVR0yyQQ5yE1wUck8hvfXEQaXUubd0gimqnI6SCya7abBUsPkJ0WYOPF49ly1LF0mDEN38cf0jUjgZLKEH6vu97r/V43JZUhh9KLiIg0rm3jYp9OKRzSM5Mhe6bRr3MK74yeSElSOhc9NQMTrCYYjmAtJMbr/HqR5tTSiqB7gO+Azxt+wRhzgTFmnjFmXkFBQfMnk99Vt2X2Ib2yOKhnJj6vm4U33UPFnt3pN340yz7+ho1bqigora732spQDcl+r0PJRUREmkbPrETCkQjtk+PZq0MyyZ2yePzMieSsX8lBLz0GGKrDEZJUBIk0qxZTBBlj7gQOAk6y1tY0/Lq19lFr7RBr7ZDMzMzmDyi7bFtR1G/vbHIfegbcHgZcfBYdQ2UsWl9MfkkV1trazaRdMxKcjiwiItKo9slOJTstQE3EsqUySE2N5acDD2PFkcdz4D8fpf+m1RgsK/JL1SxIpBm1iCLIGHMXcDpwmLV2ldN5pHGtLiynILMzL11zH6716+h+wdl0iIPCsmqKKoL4PC4G5aSRGtB+IBERiS2pAR8H9cykb+cUumUmsmdGgL6dU7jnuLFsCSSz99TxFG0pJ1Rj1SxIpBk5XgQZY+7hlwLoB6fzSONbkV/K5ysK+LFnf96deBudF39L76sn4DKW4b2zVACJiEhMq7tcPCneyyfLC7Dp7Xjzwqns+dMyes5+kIrqGowxtY2DdHiqSNNy+pygB4BzgDOAImNMh60fiU7mksa1urCCOI+bxHgfKw89hs/OvZyBn75F8m0369a/iIi0KUvythDvcRPweVgy7Ei+GHI4p73zNCs/+JwXv17Du99vpLgiqGZBIk3M6TtBY4h2hHsfyKvzcaWToaRxGSwet2trBxzL+yecy6cHH8eIVx6j63/+RTAc4dPlBXy8LF9FkYiIxLQtFWG6ZybgdkFlMMJTp19BeXwCY5+5hYryStZuLuc/uRuoCG63PVpEGpGjRZC11vzKx3Qnc0njyklPID3Bh9tlKA/WUFYd4q0x17Jm4FCyJ11Gwuefsq6ogrWbK7QeWkREYlr7FD/VoQgdUwLRYyOSUpl53Fj2Xr+MI99+AZcxbKkKsaqg1OmoIjHN6TtB0gYM7d6OUE2EtICH3u0T8bjdRDw+Vj4wm+Ce3eh10d/JWbuccA1aDy0iIjHt6H4dKK4MsbmsippIDfml1Xz0/9u78/i46nr/46/vObNPJplsTZum6UahLaWUtkCpslREAVEpoqAX8SqCiIB6Re7lXmVR1OtFRFywcn8uV0RFxAWVpUBBWQttgW60TbqkTZfs6+zL+f2RtE0rJU2BzCTzfj4efbRzJnPymfOY5N3POd/v9xz/LpbPOY0z7/sxRVvrGV/io7EzlutSRUY1NUHytptYHuT8uTX4PS52d8Uo8btZMLWCytqxbLvn9yQDQRZ94ROM3dOw7zW6eaqIiIxGx9WEuezUKQR8bho7Yrgsw/iwj0evupG0z8+nf34rbT0JLJxclyoyqqkJkmExsTzIRSfVcvWZR3PFaVMo9ruIJtMkq2tYduc94GRZdO0luHc1Arp5qoiIjF7H1YS5/uzp3H7RCZx3fDUet01HqJy/fOp6Jtat5h1/uxcwmicr8jZSEyTDbu9SoR6XRUc0SXjucfz9+7/EdHUx7sMfYMPqOpp74rp5qoiIjHqTyoPMGl+CMQ5PzTuLNSecykV//gnZTXUsXbebR9bs4dG1e9QIibzF1ARJTgy8Z8LsmjDp2XN48js/Jdi0izO/8AlSrW2sbuzcdxasoS3Cy9s7dFZMRERGleqwn7m1ZSycWsHJUyt4+OqbSLm9fPoX36Ay6MFxsqzY1sbzm9tyXarIqKImSHJua2uEypCP6vPew47//RXhbXWc/IVPsXxNI1taenlpWxu/Wd5Ae29Sq8eJiMioMrkiiGXBhLIAc2tL2eYu4f6PfoGpG1/hhAd/TZHPQ9jv5qWt7bkuVWRUURMkOdcdS+F32wD0Lno3T994B+PWvcz7brma5uYuXtvdQ0tvgp2dUa0eJyIio8rBQ8QzmSx1Z1/AxhPewYKffofExo1kHEik0rkuVWRUURMkOVfsdxNL7b8p3GPHnso9n7yBmWue5+JvXguRKPFkhk1N+++ZoNXjRERktDhgiHhtmMbuBL+97L9wLJvz77qFLc09VJf6c12myKiiJkhybnJFkGgyTTSZxnEc2nqTPHfaB3noi9+gdtWzXH3HF/EmonTH9p8F0+pxIiIyGk2uLCLsd9FRWsUoi5z7AAAeuUlEQVSfLvki09av4JynHgDQvFiRt5CaIMm5g4cClAXdhINu1r/nQzz6H7cxef0qPvPf15Dt6uybHLqlhRe3trGrM6YwEBGRUSXocXHucdVMKA+w9uwLqZ93Khfc/0PKd27TvFiRt5Ar1wWIwN5GyAOAMbCyoYNkJsuqhefQfZ3FBbd/mS9951p+9pW72ImXYp8b2zJ0RJM0dkQ5dVol4YAnx+9CRETkzSn2u/G5bd5z7DgANnz9dmouOovTvvllHqt9AOO2iaeybGmNMLe2lMkVQeWfyBHQlSDJO7NrwkwbU8T4Ej/jwj7WnvJu7r7m20zYvonLb7kCq72d7liKrmgS21g0dsRY3diZ67JFRETetIOHiNe7SvjjZTdQvWE1s3/zE9bv6uaVHe28tqubdTu7eKauRVeFRI6AmiDJO+GAh3dOq+TY8SVMqSwik3VoeMeZ/OmmHzF211ZuvOMaMrt2sXJHJ03dMTyWob65Z/Adi4iI5LmDh4gnM1k63r+Yxnefx+yffg/PujXs6Ijx2u4uVm7vYM3OLp0IFDkCaoIkLw1cKcfrsvFYhpUzTuamT3+LypadfPv2KynevInGjjibmnqIJjOD71RERGQEGJiBx1YX43PbLL/ua/QGivnXn9yEK5Uk7PeAA/VNPSzfqhupigyVmiDJe36vza6uOPFUhrXT53PZJ2/DTqe484fXUP7Ss+zoiGGMyXWZIiIib7nqsJ+J5UU45RXccdF1TNm9hY89+kvi6SzRZBrbsmhojea6TJERR02Q5L3yoJtw0INtGeLpLPU10/jUZ+6kraSCL9/xeU589iGWrdvDl+57mf95ZANrNCxARERGickVQSwLJpQFqD/pDB4+8WwueOxeptSvoaUnSXNPHHQeUGTI1ARJ3qsq9jO5IkhlsRevbVFZ5IPaidx8/RI2TzueL/7yVs7+6y/IZDI0tPTynUc2cPujG/jhE5u478XtNLRFcv0WREREjsjAOUJu2+JH511FW7iSL/7qG/gSUWKpDKlUVvcQEhkiNUGS96rDfmaMLWFqRRFjSnyUBD3UlgUZWzuO/7z82zxy/Lu4/NGfsXjJ1+nsiVLf0svjG5rpjCbZ1NTDb5c3qBESEZERa28jNLO6hLLqSn562VcZ27qLz9/7LYyTJZ7OsKWlV6vFiQyBmiDJewOHApw+rYJxJT4cHNy2xe64w60f/g/uf++lnP70g1z/3Wspam+htSdGWyRFVzxFc2+CJ17bk+u3ISIi8qaUBT2cOKmMzpPfwR8uvoaTVz3Jx574NfXNvdy7vIE/rGzkmbpWrRYnchjUBEneGzgUoCLkY1J5kDkTSplaWYTPY+P32jxy8dX8/DO3cMz2DfxqydXMbliP32NjYYglMqzb1Z3rtyEiIvKmTBtThNtlmDOhFOvfvsQ/Tn4vlzz0M07dtJzygJtUNsvyrW0sXdeU61JF8p6aIBkR9jZC75tdzcdPmcSJk8uYXBnk2OpiPC6bRCrD86ecwycuu4OY28uSn32Zcf/3E9bu7KAtkmBPV0zjpUVEZESbXROmpjRAJuvQFU9x49nXsLH6KL76m2/iqtvUt1oc8OoOXQkSGYyaIBlxBt4/4cPzJzB/Uhm2bWiPJNhaM5UPfeoOnjv6JK558C6+9PNb2LJ1Dw1tUX7x7BZ+8dw2/riqUY2QiIiMOAffTDzt9fKli75Kwu3h2/fciLenl854klgynetSRfKemiAZ0WbXhDlxchlnzajifbOrqQz5cJeX883LbuWn53yaM9b8g9/87N+o2rkNx4G27jiPrN3D4+s1R0hEREaegScCS4NeOsrHcvPHb2Js+x5uvO8beAG/x5XrMkXynpogGdEOPisWDriZMbaImooinr7w01x96Tcpi3Zx75LPce6y3+F3WSTSGX63YoeGx4mIyIg2fWwRHrfN+klzuGvxtSzY+CKfefwXJDIZ3TtPZBA6VSAjXt9ZMQ8Ay7e20xFJABBPOTw9ZQ7/cs2PufHB7/ORX9/B7JV/5xsXXMdr/nKWrttNkdfDlMog7501lnDAk8u3ISIiMiTzJ5Xjd7tYv7uLB0/5AEftrOPSf9zHlpKx/HX+OXjcNi9tbeXG98/iuJpwrssVySu6EiSjyjmzxhJLZvDaFrVlPvxemz3+Ur57zW3832VfpXbbBpbcfhkfWvkQkXiaPT0xnq1v4fnNbbkuXUREZEgWTC2nvMjDebOr+ezpU/nRBdfy9ynzuPkvd/LRVx8BYFNTL3ctq8txpSL5R02QjCrH1YS57NQpBHxuGjtiHDUmRHWJH49ts2zB+7j46iWsHX80N/z5Tq667VoCzXuob+7lx0/Vc9+L23VTVRERGTEmlgc5f24Nfo+L3V0xtvWm+c9/uZHl0xfwpT98j4tWPITbhqfrW/jhE5uUcyIDGMdxcl3DkM2fP99ZsWJFrsuQEaAzmuSPqxp5pbGL7miCdXu6Get3869rl/K+e79HBovfvvdS/nzqBSxeMJXVjZ1Ekhl6E2mqSnxcOLeGhUdV5vptiOQlY8xKx3Hm57qOfKScklyY/7VH8botii346i9vZuH657jlPVfy8xPOY2yxhyK3ixnjQ1z33hlMLA/mulyRYXGorNKcIBnVwgEPi+fWMKe2lO5Yintf2EYq6/DC2RezrPYEPnH/nXzqwSWc88LfeOaq/+RF7zQ8lqGm1M/Ozhi3L90IoEZIRETyXm1FkG2tvdgeD7dcciPX/+Jmblq6hGzW4Q8LP0A0kaFtU5yw38PXF8/OdbkiOaXhcDLqDVxO9Py5NRT7XCRTGeqLq/jGZ/6br111Gy63zYdv/iy3/fwGxuxpIJLKks1CJJ7mWw9t0DACERHJe1eeNpUir4dUJkNnBq78wL/zyNGncMvjP+GTLz2I22WIpbI8tGa3VkiVgqcrQVJQFk6toCeWYktLhN3dUSzLJrLoLB67+IO0fOt2Llt2D/d8/wqWLrqQ+971MTbELOIpaO2NE/C4eKauhevOnq5hBCIiknfeM2scAL9+aTvNXXGaetNct/jfcf/1dv7t4Z8QivVy24kfoS0DNz24hhK/m9OmjeGyU6dohVQpOJoTJAWnM5pka2uEuqYeVjZ0MLE8QFXIx3eWbqCoq43rn76XM1/4G0mXh3uPP5v/d9IFuGuqSTuQSGU4d/Y4DSMQQXOC3ohySvLBvK89SjyVociG/3rwTj7w8lKerz2Oz593HeEpE0imHZKZLJcunMiVZ0zLdbkib4tDZZWaICloDW0RXtjcRktPnKfrm9nZHqc06GFqeyOnPvAzPrjuSbKWxcMnnctvF13MalNMJA3FXptwwM0lCyZyxelH5fptiOSEmqBDU05JPvjsL1fwTH0LlmUwDpy5Yilff+wuYm4fd176FZ6ZPI/m3jjGOHz8lCmcM2us7icko46aIJFB/GNTMw+t3sXGpl564im2tESZ3LOHz634E+9f+Qg4Dn+auYj/m3cePdNnEktlaY+mCXgNOJaaIik4aoIOTTkl+WBNYydfe3AtOztiJDJZ2qJpZrTt4K6//g+T92zl7oUX8j8LLyFtu6gu8TI+7OXG9x+nRkhGFTVBIoPojCZ5pq6FzmiKVCbLj/9eTySRpizopbqnjbMfuZeLX30UfzpBffVRPHD8e7j36NPo9hVR7DWk0g6JDMwcW8Rp06t0Rk1GPTVBh6acknyxprGTh9fuoakrxpMbm3FZMN5r8dHf3sFHVj3MyurpfPEDXyZdW0skmeaUyeUsufTEXJct8pZREyRyGPbOF+qOpXh8/W6WrtuDZSwsAzu7kxTHe7m4/hkufGUpR+/cRMJ28/AxC/nb/HNYNnYmGdO34OKUigA+l0VVsY9kJqt7DsmopCbo0JRTko+WPFnPL1/Yisey2NYR57zX/sG3HvkBnmyah096Hz+Y90E2ByrxuwzFfhcfO2kinz/rmFyXLfKmqAkSGaLOaJKfPr2Ff9S10hVL0NgWx21DVTiAy7Lwrn2Vj6xeyuJ1T1GciNAaKOHvU+bx5JT5bDr+FOqSbjwWFAfcuCyLRCpFxjEk01mFi4wKaoIOTTkl+Whvrj1d38orO7qwgGPirXzu+d/x3hWPkjWG+487i9+d+VG2ByvoSWYpD7rxumwqi718/OSJLJ43IddvQ2RI8roJMsZcBXwZGAesA77gOM7Th/p6hYsMl4FXhpatb+L3qxoJeiz8HpuGjgQApSR55/rnOXPzi5y+ZRWl8R7SxmLl+Bk8OfVEts+axwuhatodLwBVRS4Sqew/hUtlwMMrOzvpjqUJeGzmTAhzQm0plSEfr25v5+H1e4jEMwR9NrVhP9s7Y/seTykL0NgVpzuWptjv4sxjxhAu8tHUFWNnZ5TNLRESqSzhgJtSv4u6ll7iKfC5YXJ5kNZIct9r54wP0xJN0tKdoLLYi9vAml1dxFNgG6gO+6gpC1BV4iMSTfHc1lZiCQe/13B0ZREtkRSd0RThgJupFUE2t0b2PT5+fAk7u+O0dCcwxsFxDACVxV7OPnYsJX4PLT1xKkM+PLbh6c2tNHXFqSrxMb0qxIamnn2PT51aQTLj0NITxxjAGJysQ2XIR2nAzSuNXTR1xagq8fPOo8rxe1x0x1IU+924LMP6Xd37vtfM6mLSWYfuWKpvX4DjQLHfTVnQQ3skecjXLphafsCS6c/Vt/D7VY376nyjK4ADP1/FfjeTK4IHLFM72PNvxef6zey3kJog5ZSMFnt//q+7/xWau+OU+D14XYb45gaueuF3fHj14xgDDx5/Ft+fv5iG0mpOrC2hJ56msSMKlkMm03el6NxZ45g+roSWnjgvbm3jlR1dxFNDz6l0JktDW5SdHVHAYIxDRzRNxjmCnLJhUlmA8aUBirwuOiJxXtnRRSKV25wKeG1CPjc98RQOBrcF29pidEWTyqkj+L5DkbdNkDHmIuBXwFXAM/1/fxKY6TjO9td7jcJFcuXuv9fzqxca6IymSKQyJLIQ8lr0JLIAWNkMC1vrWLDhJRZtfoljm7cAkDYWm8trWFs1lcZJM1hdOZlVoWo6/MWcODHM5tZe2qMZ/DYEvTbd8QyZLJw5vZKeRIoXtnbic4HPZdEdz5Kh707HJb79j91AWZGLSCJNJAXH1xQT8Ni8uKUDy4KygJv2SIpk/4+8z4Z4pu/fNlBR5KI7liaWgTK/xdTKEBv2dNHTfx89F5DuPw6Ty3yks7CjM46LvpDqTfU957VhbLGX1p4EkTQEXFAZ8tIWSdCbhPKgTZHHxY7+JnJi2IuxLVq6E5w5s4pTp1XyamMny15rYkplkHElfja3Rti4q5tjxoWYWlnEru4YW5sjLJpeRU2pn+e3tOI4ffeBau1N8nRdMzOrS5hQ6qe5J8G21gjvP348s8aXsK0twrLXmji6KkRVsY+mnjib9vSwaHoVFUUeVu/swuBw3Pgw8VSWtTs7mTU+TGXIy9bWCE9uaOLosSGqQj564im6YinOn1vDxPIgz9W38IMn6ijxuSkJuOmKpuiKp7jmzGn/FDCd0SQvb+8g4HHhd9vEUhmiyTQn1JYSDngGff5IvZX7LZQmSDklo9HStbu59W+vkUpnyGazNEX6fsPPSHVw+XP3c95LD+HJpGkIj2XrzHk8M24mj1ROp7GkiqoiF9FUhmjC4R1HlWEbw1N1bVhAkdfQm3AOO6cmVwRZtqGF3niacMCmN96XrXBg7hxOTnkM+zKuttQLjsX2zhgW4HdB/1sc9pw6uqqIVxs72d2dYMHkMmLJDE9tbKYi5GXG2BDd8bRyagjfd6jyuQlaDqx2HOfyAdvqgN87jnPD671G4SL5oKEtwn/98VXWNHbT1d9N+GyYUB5gc3OULFAba+eM7gbKN61jVtNmZjVtpqq3fd8+kpaL7pJydvqKaQ6W0RoqpTdUStqySWbBcdmkjUUya2F5XLhsm95Eet/ri7yuAx6H/W5iyTSpjIPLNlgGso6DZVkYIJbK7vtar8sikc4e8NqeeIqM0xdctRVBtrVGAOi/0AJA1ul/DGTpuzrkddlEU5l9+6oo8tLemyDb/3XlRV46IgkyDtgWuCxD1gEcB2MZQj43iVQat21zxjFjWNnQTiKVwed2URnysqW1l2Q6g8dtM6W8iJaeOPFUBq/LpjzkIdP/NmzLEE2kiCez+Dw21eEA3bEk0WQGr9vipMnlbNjd3bdvj4uyoIeOSIJYMoPXbVMW3LsvB9vqe8OJdN/3GVPs2/dav8emNNh3ZS/eX/fciaX88eVGkqksQe/++1BHEmk8bovFJ9Qc8Plp7IiSzjh4XNb+z0M6i8s21JQGBn3+SB283/aPfoKI7cbjsjihtnRI+yqgJkg5JaPS0rW7991Yta6pF5eB8mI/AJkdOzhnw7Ms2LGGhTvXURTtAWBncSWvTTqWTneAiHGR9niI225iloe014tjDsyWwXKqNOihI9LXxdiWOSCn+jKMA177RjllGXB4/Zxy2QfWNZw5NaUySGcsRar/d280kSKRcvC4+vYLKKfe4Pt2fvBCekLhI8opyNMmyBjjAaLARx3HuX/A9h8BsxzHOX3AtiuAKwBqa2vnNTQ0DHe5Iv9k732GVmxr45n6VixjsC1o7koQz0JF0E2J38Xm1hgAHgummxgVm9YysWMXYyIdzDRRzO7djIl0UNnbTmmsB4vcD1OVwrB+9RbS4VI6oklOP2bMkF5bCE2QckoKxZ2PbWTJU/V4XRZet0VTb1/jUl3sZVJZgPYXV3HyjrWcsmMNs5u34knG8aST+NIJPJn0IHsXOXJ1jz5NbMasI8opOHRWuV7vi4dRBX1XOJsO2t4EvHvgBsdx7gbuhr4zbMNSncggJpYHmVge5KKTag8YYzuxPMi21ijprENXLEmw/zK8y0CTP8TqqX3Lj1YXe5lYUcRLW9pIA26r76wZ2SzpRBKP7UA6QyaZIeg2+F02Lf1nzAAqg54DHleX+OiKJkmksnjdBssyZDJZbJeNhaErfuirSNUlPlp64qSyfT+UcyeV8tK2DqDvjJtl9Y0/zvSfYbOgb3iDBUGPi84B+55SEaShNbJvOMSkiiA72iOksuCxwW1bZLMOjuNg24bKkI9ILIXXY/PZM6bx+5U76I2nCPk8TK0sYvnWVmKJNH6/i5MnVrCltYfuWIqQ18XEiiCpjAMY3LahIxKnO5ah2O9iZnWYpu4YnZEkRX4XF584iSc3NtEbSxHye6gtD7CjPUJ3NEWR30VNaZB0xgEcXHbfGahIIkXQ62bamBBPbtxDbyxNccDNhLK+8dXdsSR+t4vF82r4yp9WE42lKSvy7TsW7b1xAn4Xt54/+4DPzurGTpLpLAH3/l/D0VQaj8tidk140OeP1MH7zZSUEEtlKPa7j3ifo5xySgrC3oV6fv1iA92xNCGvIZt1KPa5SGWzbBwzmQ1jJvPgOxcT9LqJJFJEE2k8bkM2k8GKpwhZGQzQm9g/MmCwnBpfFmBnewwHB7dtH5BTLgsGXLwZNKdsq+8q0OvllNdtH1DXcObUSVPK2dUVI5FyCHhsOiJxIoksAY9FRcgPOMqpN/i+mVDobcmpXDdBIqPGwqMqDxhPe/DEQ5N1eGZz6z+FSzqdpjhg0x7N4DJgG4fuVJYMLk6Ztn9OUKJ/TlBv1rvvl7bl2f/YDbR7XEQcNxHX688Jiln75wQlbIj3X8G297424N431rrLGyRbkj6sOUFxN/T2D5fz2tDu8ZIIWfvGWrd7vMRD1r6x1u6Dxlr32BYtqQRnTq8iESqh9iiHZa81EQgH6Qn48VYZtu3q5piKED2BIlJhmz3JCDOOqmLcwDlBkytw9ybZWNdMaWUJ0SI/McfD7kSE988cTzpcwoSj3Cx7rYlQWYhEyIeDl93JHhZNff2x1tt2dlI1Lkw65KVmqpsnN+x/bU88RVfazflza6AsyLmnHcsPnqgjyoCx1i6La06bBmVlB3xean1FvLy9g8zrjHkm4Bn0+SN1qP0eM3boQwxEZHT5/FnHHLBq6R9X7uCe5Q3s6U4wpshDa28SJ5sllU6RzmZIZ+HkCaX75gRF6Z8TZDmHnVM1FUE2JffPCYrbh54TNFhODTonqD/zhjuniqqKiGX65wTVlhHYOyco4GVcZd+cIOXU4N/3rc6pETMcbiCNtZbRYG+47F3dRqvDaXW4kbbqjobDKaeksNz52MZ9V4q0OpxWhzuc549UoawOtxx41XGcKwZs2wQ8oAmnIiL5qxCaIFBOiYiMZPk6Jwjgu8A9xpgXgWeBK4FqYElOqxIREemjnBIRGWVy3gQ5jnOfMaYc+Ap9N6FbC5zrOI6W1RERkZxTTomIjD45b4IAHMe5C7gr13WIiIi8HuWUiMjoYg3+JSIiIiIiIqOHmiARERERESkoaoJERERERKSgqAkSEREREZGCkvP7BB0JY0wLoFV53lgF0JrrIkYQHa+h0fEamtF6vCY6jvP6d9grcMqpwzZafzbeLjpeh0/HamhG8/F63awakU2QDM4Ys6IQbmL4VtHxGhodr6HR8RJ5ffrZGBodr8OnYzU0hXi8NBxOREREREQKipogEREREREpKGqCRq+7c13ACKPjNTQ6XkOj4yXy+vSzMTQ6XodPx2poCu54aU6QiIiIiIgUFF0JEhERERGRgqImSERERERECoqaoFHOGFNmjPmBMWaDMSZmjNlhjPmxMaY817XlC2PMVcaYrcaYuDFmpTHm1FzXlI+MMTcYY14yxnQbY1qMMX8xxszKdV0jRf/xc4wxP8x1LSL5RDk1OOXU4VFOvTmFllNqgka/amA8cD1wHHAJcBrwm1wWlS+MMRcBdwLfBE4AngMeNsbU5rSw/HQGcBewEHgXkAYeN8aU5bKokcAYswC4Alid61pE8pBy6g0op4bkDJRTR6QQc0oLIxQgY8y5wF+BsOM43bmuJ5eMMcuB1Y7jXD5gWx3we8dxbshdZfnPGFMEdAHnO47zl1zXk6+MMSXAKuDTwE3AWsdxrs5tVSL5TTm1n3LqyCmnDk+h5pSuBBWmYiABRHNdSC4ZYzzAPGDpQU8tpe8skryxEH2/QzpyXUieu5u+/6w8metCREYQ5RTKqbeAcurwFGROqQkqMMaYMPB14H8dx0nnup4cqwBsoOmg7U3A2OEvZ8S5E3gFeD7XheQrY8zlwFHAV3Jdi8hIoZw6gHLqzVFODaKQc0pN0AhljLm1f/LaG/0546DXFAF/AXbSN/Za5IgYY74LvBP4kOM4mVzXk4+MMcfQN4b/Y47jpHJdj8hwU05JLimnBlfoOeXKdQFyxL4H/GqQr9m+9x/9wfJQ/8PzHMeJv12FjSCtQAaoOmh7FbBn+MsZGYwxdwAXA4scx9mS63ry2Cn0ncVdZ4zZu80GTjPGXAkEHcdJ5Ko4kWGgnHrzlFNHQDl12Ao6p9QEjVCO47TS98txUMaYEPAwYICzHcfpfTtrGykcx0kaY1YCZwH3D3jqLOCB3FSV34wxdwIX0RcsG3JdT577E7DioG0/B+roO/OWHPaKRIaRcurNU04NnXJqSAo6p9QEjXL9wbKUvkmm5wNBY0yw/+l2x3FG9Qf8MHwXuMcY8yLwLHAlfcu1LslpVXnIGPMj4OP0fY46jDF7x6P36j8s/8xxnE6gc+A2Y0yEvp+7tbmpSiT/KKcGpZw6TMqpoSn0nFITNPrNAxb0/3vTQc8tAp4a1mryjOM49/XfkO8rwDhgLXCu4zgNua0sL13V//cTB22/Bbh5eEsRkVFEOfUGlFNDopySw6b7BImIiIiISEHR6nAiIiIiIlJQ1ASJiIiIiEhBURMkIiIiIiIFRU2QiIiIiIgUFDVBIiIiIiJSUNQEiYiIiIhIQVETJCIiIiIiBUVNkEiOGGMqjTE3G2Mqc12LiIjIwZRTMprpZqkiOWKMeQDwAlHHcT6S63pEREQGUk7JaKYrQSI5YIz5GBBzHOc8IGWMUbiIiEjeUE7JaKcrQSIiIiIiUlB0JUhERERERAqKmiARERERESkoaoJEhpExZoExJmuMCQ3YVmqMcYwxx+eyNhEREeWUFAo1QSLDaw5Q5zhOz4BtJwBJYH1uShIREdlHOSUFQU2QyPCaA6w6aNsJwHrHcVI5qEdERGQg5ZQUBDVBIsNrDvDyQdvmAq/koBYREZGDKaekIKgJEhkmxhgLOI5/PsM2H4WLiIjkmHJKComaIJHhczQQAHbt3WCMOa5/u8JFRERyTTklBUNNkMjwmdP/99XGmGnGmLOA3/Zv8+aoJhERkb2UU1Iw1ASJDJ85wGNADbAW+C7wNaADuCaHdYmIiIBySgqIcRwn1zWIFARjzCPAy47j3JDrWkRERA6mnJJCoitBIsNnDrA610WIiIgcgnJKCoaaIJFhYIwZC1ShcBERkTyknJJCo+FwIiIiIiJSUHQlSERERERECoqaIBERERERKShqgkREREREpKCoCRIRERERkYKiJkhERERERAqKmiARERERESkoaoJERERERKSgqAkSEREREZGC8v8BgjZiSrLL3psAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "muhat_asymp = np.linspace(-3, 5)\n", "fig, axarr = plt.subplots(2, 2)\n", "fig.set_size_inches(14, 10)\n", "\n", "labels = [r\"$t_{\\mu}$\", \"$\\\\tilde{t}_{\\\\mu}$\", r\"$q_{\\mu}$\", \"$\\\\tilde{q}_{\\\\mu}$\"]\n", "data = [\n", " (tmu, tmu_asymp),\n", " (tmu_tilde, tmu_tilde_asymp),\n", " (qmu, qmu_asymp),\n", " (qmu_tilde, qmu_tilde_asymp),\n", "]\n", "\n", "for ax, (label, d) in zip(axarr.ravel(), zip(labels, data)):\n", " empirical, asymp_func = d\n", " ax.scatter(muhat, empirical, alpha=0.2, label=label)\n", " ax.plot(\n", " muhat_asymp,\n", " asymp_func(1.0, muhat_asymp, muhat_sigma),\n", " label=f\"{label} asymptotic\",\n", " c=\"r\",\n", " )\n", " ax.set_xlabel(r\"$\\hat{\\mu}$\")\n", " ax.set_ylabel(f\"{label}\")\n", " ax.legend(loc=\"best\")" ] } ], "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": "3.8.6" } }, "nbformat": 4, "nbformat_minor": 4 }