{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Demystifying the Beigel-Reingold-Spielman construction" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from math import *\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import numpy as np\n", "\n", "plt.rcParams['font.size'] = '16'\n", "color_palette = sns.color_palette()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "### A helper to plot the graph of a function\n", "def plot_func(f, xs=None, label=None, title=None):\n", " if xs is None:\n", " xs = np.arange(-100,100,0.5)\n", " if label is None:\n", " label=\"(unknown)\"\n", " \n", " ys = np.array(list(map(f, xs)))\n", " \n", " plt.figure(figsize=(12,8))\n", " plt.grid()\n", " plt.axvline(x=0, color=\"black\", linewidth=\"1\")\n", " plt.axhline(y=0, color=\"black\", linewidth=\"1\")\n", "\n", " if title is not None:\n", " plt.title(title)\n", " \n", " plt.plot(xs, ys, label=label, linewidth=2)\n", " plt.legend()\n", " plt.show() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The hyperbolic tangent\n", "\n", "$$\\tanh(x) = \\frac{e^x - e^{-x}}{e^x + e^{-x}}$$\n", "\n", "Often, this function is used as a smooth approximation for the sign function. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_func(tanh, np.arange(-100,100, 0.1), label=\"tanh\", title=\"Hyperbolic tangent (tanh)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Trying the same with truncated exponentials" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def trunc_exp(x, t=20):\n", " s = 0.0\n", " for i in range(t+1):\n", " s += x**i / factorial(i)\n", " return s\n", "\n", "def tanh_trunc(x, t):\n", " a = trunc_exp(x,t)\n", " b = trunc_exp(-x,t)\n", " return (a-b)/(a+b)\n", "\n", "def tanh_proxy(x, f):\n", " return (f(x) - f(-x))/(f(x) + f(-x))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12,9))\n", "plt.grid()\n", "plt.axvline(x=0, color=\"black\", linewidth=\"1\")\n", "plt.axhline(y=0, color=\"black\", linewidth=\"1\")\n", "\n", "xs = np.arange(-100, 100, 0.5)\n", "ys = np.array(list(map(tanh, xs)))\n", "plt.plot(xs,ys,color=\"red\",label=\"Actual tanh\", linestyle=\"dashed\")\n", "\n", "colors = iter(color_palette)\n", "for i in range(21,25):\n", " ys = np.array(list(map(lambda x: tanh_trunc(x,i), xs)))\n", " plt.plot(xs,ys, color=next(colors), label=f\"tanh truncated at {i} terms\")\n", "\n", "plt.legend()\n", "plt.ylim(top=5, bottom=-5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Doesn't quite work :-(" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Why doesn't it work?\n", "\n", "\n", "$$\n", "\\begin{align*}\n", "\\operatorname{tanh-proxy}(f,x) &= \\frac{f(x) - f(-x)}{f(x) + f(-x)}\\\\\n", "& = \\frac{f(x) + f(-x)}{f(x) + f(-x)} - \\frac{2f(-x)}{f(x) + f(-x)}\\\\\n", "& = 1 + \\frac{2}{\\left(\\frac{f(x)}{-f(-x)}\\right) - 1}\n", "\\end{align*}\n", "$$\n", "\n", "If we can somehow ensure that $f(x) > 10 \\cdot (- f(-x)) > 0$ for all $x > 0$, then we will have that $1 \\leq\\operatorname{tanh-proxy}(f,x) \\leq 1.22..$ for all $x > 0$. \n", "\n", "One issue is that, for any odd-degree polynomial, for large enough $x$ we will always have $f(x) \\approx -f(-x)$.\n", "Therefore, $\\operatorname{tanh-proxy}(f,x)$ shoots to $\\infty$ as $x$ grows. Similarly, if $f$ is an even-degree polynomial, then $f(x) \\approx f(-x)$ for large $x$ and this means that $\\operatorname{tanh-proxy}(f,x)$ goes to $0$ in this case as $x$ grows. \n", "\n", "\n", "If we wish to somehow ensure that $f(x) > 10 \\cdot (- f(-x))$, we want to choose an odd-degree polynomial f, and also figure out a way to keep giving some advantage to the positive side, at least until $x \\leq 2^n$.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Beigel-Reingold-Spielman function\n", "\n", "$$\n", "\\begin{align*}\n", "\\operatorname{BRS}_n(x) &= (x+1) \\prod_{i=1}^n (x + 2^i)^2\\\\\n", "\\operatorname{BRS-tanh}_n(x) &= \\frac{\\operatorname{BRS}_n(x)-\\operatorname{BRS}_n(-x)}{\\operatorname{BRS}_n(x)+\\operatorname{BRS}_n(-x)}\n", "\\end{align*}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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MHTsWgGeffZa2trYBe96WlhaampoG7PmqXTn0V0NDA01NTey///6Z1yJJkoq3Y0rGqPL8C3HFB2bIh+bO4DxQFi1axDHHHDOgz1nN7C9JkrSn1nSe9OeUDEmSJGl3qzfnR5ineNKfJEmStLs1hSkZk8cYmCVJkqTdrHGEWZIkSepZS1sHm1raaagLxo1ozLqcHhmYJUmSlJnOq/xNHj2currIuJqeGZglSZKUmc4T/iaPKc8VMsDALEmSpAx1zl+eXKbzl8HALEmSpAx1rpBRrif8gYFZkiRJGdo5JcPALEmSJO3GEWZJkiSpD6vL/KIlYGCWJElShtZs7lxWzlUyJEmSpN10TsmY6gizJEmStLvVLisnSZIk9aylrYPNre001pfvZbHBwCxJkqSMdE7HmDx6OBHleVlsMDBLkiQpI5UwHQMMzJIkScrImub8ChlTyviEPzAwS5IkKSM7R5jLd0k5MDBLkiQpIzuu8ucIsyRJkrS7rif9lTMDsyRJkjLROSXDEWZJkiSpB44wS5IkSX1wWTlJkiSpDy4rJ0mSJPVi2/YOmlvbGVZfx9imhqzL6ZOBWZIkSUOu65Jy5XxZbDAwS5IkKQOrmyvjoiVgYJYkSVIG1lTICX9gYJYkSVIGVlfIVf7AwCxJkqQMrNmcXyHDEWZJkiSpB6ubW4AqGWGOiHMi4sqIeCYitkXEYxHx+YgYU8S+qZfb0QNSvSRJkipSJY0wF7Po3UeBpcAngOXAMcBFwIKIeGlKKdfP/j8G/rPbtsdLK1OSJEnVZNXmyhlhLiYwvzaltLrL9zdGxDrgJ8B84E/97L8ipXT7HtYnSZKkKrSqsErGtLHlH5j7nZLRLSx3+mvhfsbAliNJkqRql1Ji1aZ8YJ46pinjavq3pyf9nVS4f6SItv8YEa0RsTUi/hQRL9/D15QkSVIV2LC1je0dOcY0NTBiWH3W5fSr5MAcETOAi4EbUkp39tP8MuC9wCnA+cAk4E8RMb/U15UkSVJ12Dkdo/xHlwEipVR844jRwCJgOnB8Sml5SS+WX1njQWBZSullfbQ7n3zAZtq0acdefvnlpbzMgGhubmb06NFD/rqVyv4qnX1WGvurNAsWLGDhwoVZl1FRPMZKY3+Vxv7a1YNr2vnyna0cMamOfzluxG6PZ9FfCxYsuCulNK+nx4o56Q+AiBgBXAPMAU4qNSwDpJQ2R8RvgXf20+5S4FKAefPmpfnz55f6Untt0aJFZPG6lcr+Kp19Vhr7q3T2V2k8xkpjf5XG/trV6juXwZ33c+j++zJ//tG7PV5u/VVUYI6IRuBXwDzg1JTSA3v5usUPa0uSJKmqdE7JmFoBK2RAEYE5IuqAnwEnA2fuzRJxETEWOBP4y54+hyRJkirbqk35NZinVcAKGVDcCPN/AOcCnwO2RMQJXR5bnlJaHhEHAE8BF6eULgaIiI8ChwILgWeBA8hfBGUf4C0D9xYkSZJUSZ7fVGUjzMAZhftPFm5d/Rv5q/4FUM+uq248Bry+cBsHbAL+DLwzpeQIsyRJUo3qvMpfpayS0W9gTinNKqLNEvKhueu2a8ifJChJkiTtsGOEuQIuiw17fuESSZIkqWQpJVZvrpyr/IGBWZIkSUOo8yp/YyvkKn9gYJYkSdIQer4wf3lqhcxfBgOzJEmShtCqTZ2Xxa6M+ctgYJYkSdIQer7C1mAGA7MkSZKGUOdV/qY4wixJkiTtrtKu8gcGZkmSJA2h53fMYTYwS5IkSbvZuUqGUzIkSZKk3exYJcMpGZIkSdKuUkqscoRZkiRJ6tn6rW20dSTGNjXQ1FgZV/kDA7MkSZKGSOfociWd8AcGZkmSJA2RzhUyKmk6BhiYJUmSNEQq8Sp/YGCWJEnSEFm9uXOE2cAsSZIk7aZzhHnqGKdkSJIkSbvZMSXDEWZJkiRpd570J0mSJPXhuY35EeZ9xznCLEmSJO2ivSPHqs0tRMBUV8mQJEmSdrW6uZVcgsmjhzOsobIiaGVVK0mSpIq0skKnY4CBWZIkSUOgc/7yPhW2QgYYmCVJkjQEOkeYp48fkXElpTMwS5IkadCt3LANgH2ckiFJkiTtbuUm5zBLkiRJvXIOsyRJktSHnRctcQ6zJEmStIuOXOL5wpSMaeMq67LYYGCWJEnSIFvb3Ep7LjF59DCGN9RnXU7JDMySJEkaVM92zl+uwBP+wMAsSZKkQfbcxsKScmMrb/4yGJglSZI0yCr5sthgYJYkSdIge84pGZIkSVLvHGGWJEmS+lDJazCDgVmSJEmDbOWm/El/jjBLkiRJ3eRyyTnMkiRJUm/WbtlOW0diwshGmhor76IlYGCWJEnSINo5ulyZ85fBwCxJkqRBtHJjZc9fBgOzJEmSBtFzmyp7STkwMEuSJGkQVfoazGBgliRJ0iBauSE/JcM5zJIkSVIPHGGWJEmS+rCywtdgBgOzJEmSBkkul3askjFjvFMyJEmSpF2s2txKW0di8uhhFXvREigiMEfEORFxZUQ8ExHbIuKxiPh8RIwpYt+miPhSRKws7HtbRLxiYEqXJElSOVuxYStQ2aPLUNwI80eBDuATwKuA7wD/CFwfEf3t/wPg3cCngTOBlcAfIuLoPS1YkiRJlWH5+sJ0jAmVHZgbimjz2pTS6i7f3xgR64CfAPOBP/W0U0S8EHgz8PcppR8Vtt0IPARcDJy1F3VLkiSpzK3YUPnzl6GIEeZuYbnTXwv3M/rY9SygDfhll+dqBy4HTo+I4SXUKUmSpAqzYn2NBOZenFS4f6SPNkcCi1NKW7ttfwgYBhy0h68tSZKkCrBjhHnCyIwr2TslB+aImEF+SsUNKaU7+2g6EVjfw/Z1XR6XJElSlaqWEeZIKRXfOGI0sAiYDhyfUlreR9vrgLEppRO6bT8FuB54RUrp5l72PR84H2DatGnHXn755UXXOFCam5sZPXr0kL9upbK/Smeflcb+Ks2CBQtYuHBh1mVUFI+x0thfpanF/kop8Q83bKW1A/7jlSMZ1RhF75tFfy1YsOCulNK8nh4r5qQ/ACJiBHANMAc4qa+wXLAeOKCH7Z0jy+t6eAyAlNKlwKUA8+bNS/Pnzy+2zAGzaNEisnjdSmV/lc4+K439VTr7qzQeY6Wxv0pTi/21fst2Wv9wPaOHN/DqU+YTUXxgLrf+KmpKRkQ0Ar8C5gGvTik9UMRuDwGzI6L7pJUjgO3Ak6UUKkmSpMrRdYWMUsJyOSrmwiV1wM+Ak4HXpZRuL/K5rwEagXO7PFcDcB5wXUqptfRyJUmSVAmqZQ1mKG5Kxn+QD72fA7ZERNc5yctTSssj4gDgKeDilNLFACmleyLil8DXCiPUi8lf8GQ28JaBfBOSJEkqL9WyBjMUNyXjjML9J4Hbut3eVXgsgPoenu/vgB8BnwV+C+wHvCqldPfelS1JkqRy9uyGGhphTinNKqLNEvKhufv2bcCHCzdJkiTViGpZUg72/MIlkiRJUq9WVNEIs4FZkiRJA64zMM90hFmSJEna1dbt7azbsp1h9XVMHj0863L2moFZkiRJA6rzhL/p45uoq6vsNZjBwCxJkqQB1rkG8/QqmI4BBmZJkiQNsGpagxkMzJIkSRpgK6roKn9gYJYkSdIAc4RZkiRJ6oMjzJIkSVIfdq7BPDLjSgaGgVmSJEkDpqWtg+c2tVBfF+w7vinrcgaEgVmSJEkDZsWGbaSUX4O5sb46omZ1vAtJkiSVhaXrtgKw/8TqmI4BBmZJkiQNoGUGZkmSJKl3S9fmA/N+BmZJkiRpd07JkCRJkvpgYJYkSZJ6kVJyDrMkSZLUm3VbtrNlewdjmhoYN6Ix63IGjIFZkiRJA6LrdIyIyLiagWNgliRJ0oCoxvnLYGCWJEnSAKnG+ctgYJYkSdIA6RxhrqY1mMHALEmSpAHilAxJkiSpD8vWbQMMzJIkSdJutrfneHbjNuoCpo8fkXU5A8rALEmSpL22YsM2UoJ9x41gWEN1RczqejeSJEnKRLXOXwYDsyRJkgaAgVmSJEnqw441mCcZmCVJkqTdLF1bnWswg4FZkiRJA8ApGZIkSVIvUkoGZkmSJKk3a5q309zaztimBiaMbMy6nAFnYJYkSdJeWbxmCwCzp4wmIjKuZuAZmCVJkrRXlnQG5ipcIQMMzJIkSdpLT3cG5smjM65kcBiYJUmStFc6R5hnTXaEWZIkSdrNkrWdI8yjMq5kcBiYJUmStMdyubTjpL9ZBmZJkiRpV89taqG1Pcfk0cMY21R9S8qBgVmSJEl7Ycf85UnVOboMBmZJkiTthZ0rZBiYJUmSpN0sqfL5y2BgliRJ0l7oPOFvjoFZkiRJ2t3itY4wS5IkST1q78ixbN1WwJP+JEmSpN2s2LCNto7EvuOaGDGsPutyBo2BWZIkSXtkcQ0sKQdFBuaImBkR34yI2yJia0SkiJhV5L5LCu273163N4VLkiQpW50rZMyeUt2BuaHIdgcBbwTuAm4GTivxdf4AXNRt22MlPockSZLKSOcI8+wqH2EuNjDflFKaBhAR76L0wLwmpXR7iftIkiSpjC1eWzjhr4pXyIAip2SklHKDXYgkSZIqy+I1zUB1X+UPhu6kv9cW5j63RsTtzl+WJEmqbC1tHaxYv426gP0mjsi6nEE1FIH5GuADwOnAW4AW4KqIeOsQvLYkSZIGweI1W8glOGDSKIY3VO+ScgCRUipth/wc5u8Bs1NKS0p+wYh64HZgn5TSfr20OR84H2DatGnHXn755aW+zF5rbm5m9OjRQ/66lcr+Kp19Vhr7qzQLFixg4cKFWZdRUTzGSmN/laYa++uOle18575Wjplaz4de1DSgz51Ffy1YsOCulNK8nh4r9qS/AZNS6oiIK4AvRsS+KaWVPbS5FLgUYN68eWn+/PlDXCUsWrSILF63UtlfpbPPSmN/lc7+Ko3HWGnsr9JUY3/dc/3jwBOccMQs5s8/bECfu9z6K+sLl5Q2vC1JkqSy8OTq/Al/B02prpHzngx5YI6IBuA8YGlK6bmhfn1JkiTtvSefLwTmqdUfmIuekhER5xS+PLZwf0ZErAZWp5RuLLRpB36SUnpn4fs3AWcDvwOWAdOA9wEvAt40IO9AkiRJQ6q9I7fjoiUHGph3cUW3779duL8RmF/4ur5w67QYmAp8CZgIbAHuBF6VUvpDqcVKkiQpe8vWb2N7R47p45oYPXzIT4kbckW/w5RSlNqmcHW/k/egLkmSJJWpJ1flp2PUwugyZH/SnyRJkirME6s2A7UxfxkMzJIkSSpR5wizgVmSJEnqwVOFwHzw1DEZVzI0DMySJEkqWkrJEWZJkiSpNys3trBlewcTRw1j4qhhWZczJAzMkiRJKtqO0eUauMJfJwOzJEmSilZrS8qBgVmSJEkleHJ15wl/BmZJkiRpN7V2wh8YmCVJklQCA7MkSZLUizXNrazbsp3RwxvYd1xT1uUMGQOzJEmSivLYc/lLYh8ybTQRkXE1Q8fALEmSpKI8WgjMh+07NuNKhpaBWZIkSUV5dOUmAA7bpzYuid3JwCxJkqSiPPZ8YYR5H0eYJUmSpF105NKOOcyHTnOEWZIkSdrFM2u30NqeY99xTYwb2Zh1OUPKwCxJkqR+dY4u19r8ZTAwS5IkqQiPdE7HqLH5y2BgliRJUhEeey6/Qsbh+zrCLEmSJO3m0R0jzAZmSZIkaRdbWttZum4rjfXBnMmjsy5nyBmYJUmS1KfHn99MSnDglNEMa6i9+Fh771iSJEklqeUVMsDALEmSpH48WsMrZICBWZIkSf14tLBChiPMkiRJUjcp7bwk9mE1uKQcGJglSZLUh+c3tbJ+axvjRjSyz9imrMvJhIFZkiRJvXpwxUYAjpw+lojIuJpsGJglSZLUqwefzQfmuTPGZVxJdgzMkiRJ6tWDK/In/B05vTZXyAADsyRJkvrwUGGE+ShHmCVJkqRdrWluZeXGFkYNq2fWpFFZl5MZA7MkSZJ69NCzndMxxlFXV5sn/IGBWZIkSb3YsULGjNqdvwwGZkmSJPWiMzDPnV6785fBwCxJkqReuKRcnoFZkiRJu9m4tY1l67YxvKGOA6fU7gl/YGCWJElSDzqXkzt837E01Nd2ZKztdy9JkqQePej6yzsYmCVJkrSbziv8za3xFTLAwCxJkqQedI4wH1njK2SAgVmSJEndNLe2s3jNFhrrg0Omjcm6nMwZmCVJkrSLB5ZvJCU4bJ+xDGswLtoDkiRJ2sU9y9YDcMz+47MtpEwYmCVJkrSLe5duAODo/cZnWke5MDBLkiRph5QS9yzbABiYOxmYJUmStMOzG1tYvbmVcSMamT25tq/w18nALEmSpB26TseIiGyLKRNFBeaImBkR34yI2yJia0SkiJhV5L51EXFhRCyJiJaIuC8i3rBXVUuSJGlQ3LPUE/66K3aE+SDgjcB64OYSX+MzwEXAt4AzgNuBKyLi1SU+jyRJkgbZvc5f3k1Dke1uSilNA4iIdwGnFbNTREwFPgp8IaX05cLmhRFxEPAF4Hcl1itJkqRB0taR44EV+Sv8GZh3KmqEOaWU28PnPx0YBlzWbftlwFERMXsPn1eSJEkD7NGVm2ltzzFn8ijGjxyWdTllY7BP+jsSaAWe7Lb9ocL9EYP8+pIkSSrSvYULlji6vKvBDswTgQ0ppdRt+7ouj0uSJKkM3NO5QoYn/O2i2DnMQyoizgfOB5g2bRqLFi0a8hqam5szed1KZX+Vzj4rjf1VOvurNB5jpbG/SlMp/XXrY1sByK16ikWLlmRWR7n112AH5vXA+IiIbqPMnSPL63rYh5TSpcClAPPmzUvz588f1CJ7smjRIrJ43Uplf5XOPiuN/VU6+6s0HmOlsb9KUwn9tWHrdp77/fUMb6jjLWcuoLE+u8t1lFt/DXZPPAQMBw7str1z7vLDg/z6kiRJKsLdhfWXj5oxLtOwXI4Guzd+D7QBb+m2/a3AgymlxYP8+pIkSSrCHYvzf/g/franmHVX9JSMiDin8OWxhfszImI1sDqldGOhTTvwk5TSOwFSSqsi4hLgwojYDNwNnAecDJw1QO9BkiRJe+mvhcB8nIF5N6XMYb6i2/ffLtzfCMwvfF1fuHX1SaAZ+BCwD/AY8MaU0rUlVSpJkqRBsW17Bw+s2EgEHHvAhKzLKTtFB+aUUuxJm5RSB/DZwk2SJEll5p5l62nrSBw5fSxjmxqzLqfsOKNbkiSpxv11cf6Ev+NmOR2jJwZmSZKkGvfXJZ7w1xcDsyRJUg1r68jtWFLOEeaeGZglSZJq2EPPbmLr9g7mTB7FlDHDsy6nLBmYJUmSatiO5eQcXe6VgVmSJKmG/WWJ6y/3x8AsSZJUo3K5xJ2FwPxiA3OvDMySJEk16snVzazf2sY+Y5uYOWFE1uWULQOzJElSjbr1yTUAvHjORCL6vUZdzTIwS5Ik1ahbnlwLwMsOmpxxJeXNwCxJklSD2jty3P50PjCfaGDuk4FZkiSpBt23fCPNre3MmTyK6eOdv9wXA7MkSVIN+nNh/rKjy/0zMEuSJNWgWwzMRTMwS5Ik1Zgtre3cs3Q9dQEvmTMp63LKnoFZkiSpxvxlyTraOhJHzRjHuJGNWZdT9gzMkiRJNeZWp2OUxMAsSZJUY1x/uTQGZkmSpBqyprmVR1ZuYnhDHS86YELW5VQEA7MkSVINueWJ/HSM42ZNpKmxPuNqKoOBWZIkqYb86dFVAMw/dErGlVQOA7MkSVKNaO/IcePjqwE4+bCpGVdTOQzMkiRJNeLupRvYuK2NWZNGMmfK6KzLqRgGZkmSpBrROR1jgaPLJTEwS5Ik1YiFhcDsdIzSGJglSZJqwIoN23js+c2MGlbP8bMnZl1ORTEwS5Ik1YDO6RgvO3gywxtcTq4UBmZJkqQa4HSMPWdgliRJqnLbtnfw5yfzFyxZcKiBuVQGZkmSpCp361NraG3PMXfGWKaObcq6nIpjYJYkSapyv3/wOQBOOXxaxpVUJgOzJElSFWvryHH9I88D8Oqj9s24mspkYJYkSapidzy9jg1b2zhwyigOnurV/faEgVmSJKmK/e7BlQCcMXdfIiLjaiqTgVmSJKlKdeQS1z2Un7/8qrn7ZFxN5TIwS5IkVak7l6xjTfN29p84kiOnj826nIplYJYkSapS/1tYHeOMufs4HWMvGJglSZKqUC6Xdiwnd4arY+wVA7MkSVIVunf5Bp7b1ML0cU28cOa4rMupaAZmSZKkKnT1vc8C8CpXx9hrBmZJkqQq09aR45r78oH59cfMyLiaymdgliRJqjI3P7GatVu2c9DU0cyd4eoYe8vALEmSVGV+ffcKID+67HSMvWdgliRJqiKbW9q4/uHnATj76OkZV1MdDMySJElV5H8ffI7W9hwvnj2RmRNGZl1OVTAwS5IkVZGrukzH0MAwMEuSJFWJZzds4/bFaxnWUOfFSgaQgVmSJKlKXHXPClKCUw6fyrgRjVmXUzUMzJIkSVUgl0v84i9LATh33n4ZV1NdigrMEbFfRPwqIjZGxKaI+HVE7F/kvqmX29F7VbkkSZJ2uOmJ1Sxfv40Z40fwioOnZF1OVWnor0FEjAT+BLQCbwcS8FlgYUS8IKW0pYjX+THwn922PV5aqZIkSepN5+jym47fj/o6114eSP0GZuDdwBzg0JTSkwARcT/wBPAe4JIinmNFSun2Pa5SkiRJvXp+Uws3PLKKhrrgjU7HGHDFTMk4C7i9MywDpJQWA38Gzh6swiRJklSc//7rMjpyiVMOn8bUsU1Zl1N1ignMRwIP9rD9IeCIIl/nHyOiNSK2RsSfIuLlRVcoSZKkXnXkEpf/dRkAb35xUaeYqUSRUuq7QcR24JKU0gXdtn8WuCCl1Oe0joj4KXAt8CxwAPAx8kH71JTSol72OR84H2DatGnHXn755UW9mYHU3NzM6NGjh/x1K5X9VTr7rDT2V2kWLFjAwoULsy6joniMlcb+Ks1g9td9q9v56l2tTBkRfPEVI6iLyp+/nMXxtWDBgrtSSvN6eqyYOcx7JaX0f7p8e3NE/Ib8iPVngZf1ss+lwKUA8+bNS/Pnzx/sMnezaNEisnjdSmV/lc4+K439VTr7qzQeY6Wxv0ozmP31gx/cAbTy9ycdysnzDxyU1xhq5XZ8FTMlYz0woYftEwuPlSSltBn4LXBcqftKkiRpp8ee28zNT6xhRGM9bzrek/0GSzGB+SHy85i7OwJ4eC9eu++5IJIkSerT929+GoA3zpvJ+JHDMq6mehUTmK8GToiIOZ0bImIWcGLhsZJExFjgTOAvpe4rSZKkvFWbW/jNvc8SAX934uysy6lqxQTm7wFLgN9ExNkRcRbwG2AZXS5GEhEHRER7RHy6y7aPRsT3IuLNETE/It5Ofjm6fYBPDuQbkSRJqiU/ve0ZtnfkOO2IacyaPCrrcqpavyf9pZS2RMTJwFeBnwIB/BH4p5RSc5emAdSzawh/DHh94TYO2EQ+ML8zpeQIsyRJ0h7Ytr2Dy25/BoB3vXxOP621t4paJSOltBR4Qz9tlpAPzV23XQNcs6fFSZIkaXe/umsZ67e28cL9xjPvgJ7WZtBAKmZKhiRJksrE9vYc31n0FADnv3wOUQXrLpc7A7MkSVIFueKuZTy7sYWDp47mjLn7ZF1OTTAwS5IkVYjt7Tm+vTA/uvyhUw6mrs7R5aFgYJYkSaoQv7prOSs2bOPgqaN59dx9sy6nZhiYJUmSKsD29hz/sfBJAD74SkeXh5KBWZIkqQLsMrp8lKPLQ8nALEmSVOa2tLbz1RseB/Kjy/WOLg8pA7MkSVKZu/Smp1m9uZUXzhzHaxxdHnIGZkmSpDL2/KYWLr3paQA++ZojnLucAQOzJElSGfvyHx5jW1sHpx85jeNnT8y6nJpkYJYkSSpTDz+7iV/dvZyGuuCCMw7PupyaZWCWJEkqQyklLrrmIVKCt55wALMnj8q6pJplYJYkSSpDV9y1nL8sXsekUcP4p1MOzrqcmmZgliRJKjPrtmzn8797BIBPvuZwxo8clnFFtc3ALEmSVGb+/XePsH5rGy89cBKvP2ZG1uXUPAOzJElSGbn96bX86q7lDKuv4zOvm0uEy8hlzcAsSZJUJra0tnPBlfcD8N4FB3LglNEZVyQwMEuSJJWNz/3uEZas3cph+4zhH+cfmHU5KjAwS5IklYE/Pfo8P79jKcPq6/ja3x7N8Ib6rEtSgYFZkiQpY2ubW/mXXz0AwMdOP5TD9hmbcUXqysAsSZKUoVwu8S+/up81za2cMGci73zZ7KxLUjcGZkmSpAx958an+OOjqxg3opEvn/tC6upcFaPcGJglSZIycvMTq/nydY8RAV8772hmThiZdUnqgYFZkiQpAys2bOODv7iHlOCDJx/MgsOmZl2SemFgliRJGmJbWtt5z0/vZP3WNk46ZAofeuXBWZekPhiYJUmShlB7R473//xuHlyxiQMmjeRr5x3tvOUyZ2CWJEkaIikl/vXqh1j42GomjGzkx393PBNGDcu6LPXDwCxJkjREvnPjU/zsjqUMa6jj+2+fx+zJo7IuSUUwMEuSJA2BH96ymP/3+8cA+Oobj+bYAyZmXJGK1ZB1AZIkSdXuj0vb+OnDDwPw768/ite8YN+MK1IpHGGWJEkaRD+74xl++vB2AC4++0je/OL9M65IpXKEWZIkaRCklPj2oqf40h/y0zA+feYRvO0ls7ItSnvEwCxJkjTAcrnExdc+zI9vXUIEvOWwYfz9y2ZnXZb2kIFZkiRpAG3b3sFHf3Ufv71/JcPq6/jqeUczat1jWZelveAcZkmSpAGyfP1W3vCdW/nt/SsZPbyBH//dcZ7gVwUcYZYkSRoAtz21lvf9/G7WbdnOrEkjufRt8zhk2pisy9IAMDBLkiTthbaOHN/44xP8x8InySU46ZApfONvj2HcyMasS9MAMTBLkiTtoWfWbuFDl9/Lvcs2EAHvX3AQ/3zqIdTXRdalaQAZmCVJkkrU3pHjx7cu4SvXPc62tg72HdfEV887mhPmTMq6NA0CA7MkSVIJHlyxkQt//QAPrNgIwJkv2JfPve4op2BUMQOzJElSEVZtauEr1z3OFXctI5dg+rgmPvO6ubzy8GlZl6ZBZmCWJEnqw6aWNn54y2Iuvelptm7voKEueMdLZ/GR0w5h1HCjVC3wX1mSJKkHG7e18eM/L+EHtzzNppZ2AE47YhoXnHEYc6aMzrg6DSUDsyRJUhdL127lx7cu4Yo7l7G5NR+UXzx7Ih8+9RBe7El9NcnALEmSat729hwLH1vFFXcu44+PriKl/PaXHjiJD77yYFe/qHEGZkmSVJNSSjy4YhNX3r2cq+97lnVbtgMwrL6Os46ezjteOou5M8ZlXKXKgYFZkiTVjPaOHHcv3cANjzzPDQ8/z9Nrtux47NBpY3jDsTN4/TEzmTJmeIZVqtwYmCVJUlVbvn4rdzy9jj8/uYaFj61i/da2HY9NHDWMs144nXOOncmR08cS4RX6tLuiAnNE7Ad8FTgVCOAG4J9SSkuL2LcJ+AzwVmA8cC/w8ZTSTXtWsiRJUs/aO3I8saqZB5Zv5K9L1nH74rUsW7dtlzazJo3k1COmccrh0zj2gAk01NdlVK0qRb+BOSJGAn8CWoG3Awn4LLAwIl6QUtrS1/7AD4DXAB8DngbeB/whIl6SUrp3L2qXJEk1bG1zK0+uaubJ1c08/txmHlixkYdXbqKlLbdLu7FNDRw/eyInzJnE/EOncOCU0Y4kqyTFjDC/G5gDHJpSehIgIu4HngDeA1zS244R8ULgzcDfp5R+VNh2I/AQcDFw1l5VL0mSqlZHLrFqcwsr1m9jxYb8bdm6rfmQvKp5l6kVXR0waSRHzRjH0fuN54Q5kzh837HU1xmQteeKCcxnAbd3hmWAlNLiiPgzcDZ9BObCvm3AL7vs2x4RlwMXRMTwlFLrnpUuSZIqSS6X2NrWweaWNja3tLO2eTtrt7Tm75tbWbOlcN+8nVWbW1i5oYX2XOr1+UYNq+egqaM5cOpoDp46hrkzxnLUjHGMHzlsCN+VakExgflI4Dc9bH8IOLeIfRenlLb2sO8w4KDC15IkaYCllMglaM/l6Mil3W7tXb9PhW0diVza9bH2jhyt7Tla2jpobc/R2t7BA8+08fhNT9HSlv++tS1HS+F+W1sHza3tNLe0s7mlnebWdja1tNHc2r5jfeNiTR49jOnjRzCjcJs5YQQHTh3NQVNHs8/YJqdWaEgUE5gnAut72L4OmLAX+3Y+rgq1vT3H5pY2tm7v4NnmHA+u2EhrewctbTs/VFvadv2+vSNHWy7RkcvR3pH/QG7vyBXuC9/ncju2d36g51L+gz8lSCRyOcilRGLn9lzhB0P3bV3vE12eq6c31csHeW+f76mPT/7e98nfb9u2jRF/Wdilfc979PYSpf7Q2XXf/ncu5umLqaG391Xq87Ru386wP9+w189TzDsr7n319xxD2Mc9NJr5oct5wUV/KOm1imlUXM2Vd3wlIJfLUXfD//bdaAjr6fs5iuvjvfmcKMojj5a8y4jGesY0NTCmqYFJo4YzafSw/G3UcCaPHsak0cOZNGoYk8cMZ8b4ETQ11g9C4VJpynJZuYg4Hzi/y/cZVlMD6huoHzme+lHjqSvc7/h++Chi+Ejqho+irvN+2Mj8tsZua1Tecks29Veybd3/+KI+tTqDq1j1TaPZ1NKedRmVJ5frv02FSbkOSLn8fS5HSjnY8XUH5DpIufy2/Pe5Hfvs+DrXQWrfnr91bN/5dXsbqb01f9+xnVzbdijcp+1bybV23rbs+J5UfX2s6ldMYF5PzyPJvY0ed9/3gF72hZ0jzbtIKV0KXAowb968dOeddxZR5sBatGgR8+fPH/LXHQxrm1tZsnZr/oSJ9dtYvn7n189tamHzHv5QbagLRjc1MGpYAx1tLUwYO4amxjqaGuppaqxjeOG+qbGepsZ6hjXU0VgfNNTV0VAXNNR33seO7+vrYrc29XX5X5rqIgigLoK6AIKd2+oK28jfR6FNEERnuy73Qe+/iPX2+1lvv7b19Qtd7/vAHXfcwYtf/OJu7UurqdfXLaJ9Mb+IFvOyRb1WEc/U3/PceuutnPjSlxbzYkNSTzEvlWUfT5w4gXXr1ndvNECvVczzVNbxBXDTTTfxile8omzqGYh+7vw8HAzV9HNyKNhfpcmiv/r6v1JMYH6I/Fzk7o4AHi5i39dHxMhu85iPALYDT/a8m/bE6s2tPPbcZp5YtZknVjXz5PP5pXY6L/XZm4a62PnnsDHDmVz4U9jEUcMYP6KRMU2NO/58NqapkbGF+6bGuh0HV/7AfvlQvM2qsXhkHQdMGpV1GRVjQlMdU8c2ZV1Gxci1bmHcyMasy6gow+rDP/9L6lExgflq4MsRMSel9DRARMwCTgQu6Gffa4B/I39y4E8K+zYA5wHXuULGntvS2s69yzZw3/IN3LdsA/cv38jKjS09th09vIHZk0ftOFlixoTOEydGsu+4JsaNaKTO5XYkSZJ6VExg/h7wfuA3EfEp8ucRfAZYBvxnZ6OIOAB4Crg4pXQxQErpnoj4JfC1iGgEFgP/CMwG3jKQb6TatbR1cNcz67ntqbXc+tQa7l++cbeldkYPb+Dwfcdw0NQxHDx1NAdPyy+zM23scOeBS5Ik7aF+A3NKaUtEnEz+0tg/JT+t6o/kL43d3KVpAPVA9+tL/h3wOfJXBxwP3Ae8KqV0915XX+XWNLfyx0ee57qHnueWJ9fQ2r7zRIn6uuCFM/OLsr9wv/G8YOZ45kwe5UixJEnSACtqlYyU0lLgDf20WUIP5yiklLYBHy7c1I91W7bzm3tX8Nv7V3LX0vW7LAl05PSxvPTASbzkwEkcN2siY5qcnyhJkjTYynJZuVrT3pHjxsdXc8Wdy/njo8/T1pFPycPq6zjxoEmcesQ+nHL4VE94kiRJyoCBOUNrm1v52R1Luez2Z1i1OX/+Y13A/EOn8IYXzWTBYVMZPdx/IkmSpCyZxjLwzNotfPfGp/j13St2zEueM3kU58ybyd8cM5N9xjmSLEmSVC4MzENo6dqtfPNPT/Dre1bQUVjh4pWHTeWdL5vNSw6c5EoWkiRJZcjAPATWb9nO1//4BJfd/gztuUR9XXDusTP5h/kHcuCU0VmXJ0mSpD4YmAdRW0eOy25/hq/d8AQbt7VRF/CGF83kAycfxKzJXuFNkiSpEhiYB8kDyzfy8Svv5+GVmwA48aBJ/N8zj+CwfcZmXJkkSZJKYWAeYC1tHXz1hsf5/s2L6cglZk4YwUWvPZJXHj7VOcqSJEkVyMA8gB57bjMf+MXdPP58M3UB73zZbD5y2iGMHGY3S5IkVSqT3ABIKfGzO5bymWsfprU9x5wpo/jKuS/kmP0nZF2aJEmS9pKBeS9t297Bx6+8n6vvexaAN86byUVnHemosiRJUpUw1e2FlRu3cf5/3cUDKzYyalg9n3/DCzjrhdOzLkuSJEkDyMC8h+5dtoF3/9edrN7cyv4TR/L9t8/jkGljsi5LkiRJA8zAvAduenw17/npXWxr6+Alcybx7be8iAmjhmVdliRJkgaBgblEv71/Jf/0y3to60i84UUz+cIbjqKxvi7rsiRJkjRIDMwl+O+/LuPjv76flPJLxn3y1YdTV+faypIkSdXMwFykX9+9fEdY/uhph/C+BQd5IRJJkqQaYGAuwm/vX8lHr7iPlOCCMw7jH046MOuSJEmSNEScfNuPPz7yPB+6/B5yCT70yoMNy5IkSTXGwNyH+5Zt4H0/v5v2XOI9r5jDP51ycNYlSZIkaYgZmHuxdluOd/3XnbS05Tj32JlccMZhzlmWJEmqQc5h7sHmlja+elcLq5sTL5kzic+9/ijDsiRJUo1yhLmb9o4c7//5PSxvThw4ZRTffeuxDGuwmyRJkmqVSbCbLds72NzSxphG+NE7jmfcyMasS5IkSVKGDMzdjBvRyM/ffQIXHD+C/SeNzLocSZIkZczA3IOmxnpmjLFrJEmSZGCWJEmS+mRgliRJkvpgYJYkSZL6YGCWJEmS+mBgliRJkvpgYJYkSZL6YGCWJEmS+mBgliRJkvpgYJYkSZL6YGCWJEmS+mBgliRJkvpgYJYkSZL6YGCWJEmS+mBgliRJkvpgYJYkSZL6YGCWJEmS+mBgliRJkvoQKaWsa+hTRKwGnsngpScDazJ43Uplf5XOPiuN/VUa+6t09llp7K/S2F+lyaK/DkgpTenpgbIPzFmJiDtTSvOyrqNS2F+ls89KY3+Vxv4qnX1WGvurNPZXacqtv5ySIUmSJPXBwCxJkiT1wcDcu0uzLqDC2F+ls89KY3+Vxv4qnX1WGvurNPZXacqqv5zDLEmSJPXBEWZJkiSpDzUdmCPiwxFxTUSsjIgUERf10fZ1EXFPRLRExDMR8amIqO+h3csi4taI2BYRz0XEJRExYlDfSEYi4h2Ffuvttk+Xtot6afNPGb6FTETEkl764nU9tH13RDwaEa0R8VhE/EMGJWcmIg6JiK9HxP0R0Vz4v3p1RLywh7Y1f4xFxH4R8auI2BgRmyLi1xGxf9Z1lYOIOCcirix8fm8r/H/6fESM6dJmVh+fZ+MzLH/IRcT8XvphQ7d2EyLi+xGxJiK2RMQNEXFURmVnpo/PnxQRvy+0qdnjKyJmRsQ3I+K2iNhaeM+zemjXFBFfKnzWbyu0f0UP7eoi4sLCz9OWiLgvIt4wmO+hYTCfvAK8G9gE/A/QaxCJiNOBK4EfAB8GjgH+HRgDfLxLuxcA1wN/AM4EZgNfAmYA5w3GG8jYb4GXdNsWwDXA0yml57o9dj/wnm7blgxOaWXvD8BF3bY91vWbiHg38J/A54EbgFcC346ISCl9ZyiKLAOnAQuAnwB3A+OBfwFuj4iXpZTu6ta+Zo+xiBgJ/AloBd4OJOCzwMKIeEFKaUuW9ZWBjwJLgU8Ay8l/jl8ELIiIl6aUcl3afh64utv+m4eiyDL0QeCvXb5v7/wiIjo/72cBHwDWAxeSP+aOTiktH8I6s/ZeYGy3bS8BLmH3Y6kWj6+DgDcCdwE3k/9s78kPgNcAHwOeBt4H/CEiXpJSurdLu8+Q/z/9ycJz/i1wRUScmVL63aC8g5RSzd6AusJ9A/kfLhf10u4e4MZu2z4NbAf26bLtKuAJoLHLtrcVnvtFWb/fIerTlxfe7/u6bV8E3JJ1feVwIx/gLuunTQOwCvhJt+0/JL+Qe+Ng1VdON/IL10e3bePI/2D+r27ba/oYAz4EdAAHddk2m3zA+XDW9WV9A6b0sK3z8/nkwvezCt+/K+t6s74B8wt9cUofbc4utFnQZds4YB3wjazfQ9Y38uGvFZhY+L5mj6/OvFX4+l2FfpjVrc0LC9v/rsu2BvKDSVd32Ta10K//1m3/PwL3D9Z7qOkpGWnXEYUeRcR+wNHAZd0e+inQCJxRaNcIvAr475RSW5d2/00+WJ89ACVXgreTf7+/yLqQCvcSYAo9H3eTgJcNeUUZSCmtSYVPwi7bNgKPk//LjXY6C7g9pfRk54aU0mLgz9TO50+vUkqre9jcOXLqsbRnzgKeTSkt7NxQ+P95DTV+zBX+4nMucE1KaV3W9WStmLxF/nhqA37ZZb924HLg9IgYXth8OjCM3X8+XgYcFRGz977i3dV0YC7SkYX7B7tuLPwg2gocUdh0INDUQ7sW4Kku7apW5Odqnwtc28sHxDGFuZVthTmp7xziEsvJawvzuFoj4vYe5i/3eNwBDxXuq/546k1ETATmAo/08HAtH2NHsvvxAvljpmaPl36cVLjvfix9PiLaC8fS1bU4J7eLn0VER0SsjYifd5sT39cxt39EjB6aEsvS68lP2/xJD495fPXsSGBxSmlrt+0PkQ/IB3Vp1wo82UM7GKTPu1qfw1yMiYX79T08tr7L4321W9fl8Wr2OvJzuHr6gLgJ+Bn5kcHx5P8U+v2I2Del9NmhKrBMXEN+ZGsxMA14P3BVRPyflFLnb8y9HU/ruj1ei75Jfq7817ptr/VjbCK9f/5MGOJayl5EzAAuBm5IKd1Z2NxK/ryB64DVwGHk5zzfGhHHp5R6+iWtWm0EvgLcSP5cn2PI98VtEXFMSmkV+WNuSQ/7dn5OTQCaB7/UsvQ28tPq/rfLNo+vvvX1Gdb5eOf9hu5/feyh3YCqmsAcEaeQP+GuPzemlOYPcjkVaQD68O3kPyB2m3CfUvp0t02/iYirgE9GxNdSShX5obonfZZS+kC357gKuJ38iSDd/8RUVfb2GIuIC4E3A+/sOvUAqvcY08ArjHz+hvz87r/r3J5SWsmuJ4DfXFjh4CHyJxe9dSjrzFJK6R7y5+90ujEibgL+Qv5EwE9lUlgFiIjpwCnA1wtTCgCPr0pXNYEZuBU4vIh23Yf6+9P5205PIzQT2PkbTV/tJrLzTwXlbI/7MCL2Jf8B8c2uHxD9+AX5UemjgNuK3Kfc7PVxl1LqiIgrgC8WRkNXsuvxtLJL887fnCt1TtzeHGP/QH51mk+llH5Y5OtVwzFWrPX0/vnT06hNTSpMHbsGmAOclPpZySGltCwibgGOG4r6yllK6e6IeJydfdHXMdf5eC16K/kprz39tXUXHl+7WA8c0MP27j/31gPjCytGpT7aDaiqCcyFOS+PDsJTdwbdI+nyA7ewfuBI4OHCpqfI/7nlyK47R0QT+Q/mKwahtgG1l334VqCeIj4genrpPXzNzA3CcdfZF12Pu66BuXNu1sNUoD3tr4j4P8C3ga+klD63Jy+9B/tUmofo9vlTcAQVerwMtMLJ2b8C5gGnppQeKGH3WjiGitX1c6qn5cGOAJbW8F913g7cl1K6r4R9PL7yx9PrI2Jkt3nMR5BfTODJLu2Gkz937Mlu7WCQPu886a8fKaWlwH3AW7o99FbyZ3P+b6HdduD3wBsjousvIueQ/4ftvuZitXkb+eVc7i1hn7cA24BSfmhVncLxch75HzCda1ffRn75uJ6Ou3XkVz6oCRHxeuBHwPdTSh8tcfdaOsauBk6IiDmdGwq/2J9I9X/+9Csi6sjPcT8ZeF1K6fYi99uf/Ko0fxnE8ipCRMwDDmVnX1wNzIiIk7q0GQu8lho95gp9dARFDh55fO3iGvKrj53buaHLz8frUkqthc2/J5+/evr5+GBhUYYBVzUjzHuicGDPYucvDkdExDmFr3/X5TecTwDXRsR/kv8T7zHk5299Pe16cY6LyM9F/e+I+I/Cc38J+FXa/QILVSMiXkR+1YKP9PL4y4ELgF+TP0FkHPnfwM8CLkg1dEGFiHgT+eWWfgcsI3/S3/uAFwFv6myXUmqLiP9L/kIlK8hfuORk4O+BDxR+Qat6hSs8/YL8L60/jogTujzcWphn6TGW9z3yJ5D+JiI+RX7E6jPkj7P/zLKwMvEf5H8Qfw7Y0u1YWp5SWh4RXyH/8+A28idlHUr+Qhy5wn41IyJ+Rv7E5LuBDeR/7l0IrAC+UWh2Nfm+uiwiPsbOC5cE8P+GuORy8Tbyc+N/1v2BWj++uuSrYwv3Z0TEamB1SunGlNI9EfFL4GuFvwYtBv6R/HryO8JxSmlVRFwCXBgRm8kfo+eR/xl51qC9gcFa4LkSbsCPyf9Q6enWfUHtvyH/Q7uV/NWiPg3U9/CcryD/n6EFeJ78mfwjs36vg9yPXyf/2960Xh4/iPxI/IpC/zWTn8v6pqxrz6CvTiB/NbbnC322gXwYPr2X9u8hv+pDK/mL4rw36/cwxP11UR//R5d4jO3WX/uTvyrpJvJXDvuf7p9ltXoj/4tUb8fSRYU2f09+BZv1hf+fzwE/Bw7Nuv4M+utC8lfO3Fjoi2XApcC+3dpNJH9BpXXkzz34I/DCrOvPqM8ayQfha3p5vKaPrz7+/y3q0mYE+asjPlfIUXcA83t4rnryA5fPFD7z7wfOGcz6o/DCkiRJknrgHGZJkiSpDwZmSZIkqQ8GZkmSJKkPBmZJkiSpDwZmSZIkqQ8GZkmSJKkPBmZJkiSpDwZmSZIkqQ8GZkmSJKkP/x+OdBRYj5xnjAAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def BRS(x,n):\n", " out = (x+1)\n", " for i in range(1,n+1):\n", " out *= (x + (2**i))**2\n", " return out\n", "\n", "def BRS_tanh(x,n=5):\n", " return (BRS(x,n) - BRS(-x,n))/(BRS(x,n) + BRS(-x,n))\n", "\n", "plot_func(lambda x: BRS(x,5), label=\"BRS, n=5\")" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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L+ec//4m1tTUAbm5uDB48mIULFxIYGFgl8QghhBDlsf9cClM3/0pGTh5zh7Zj7DNNTXKJx4HMKNdw9vb2AOTl5ZVat2PHjmRlZXHz5k1jmVarxcXFpcgPdkEyXZz169fj5+eHra0t9vb2+Pj4sGrVqmLrT5gwgbVr13Lt2jXjspBmzZoBkJOTQ0hICN7e3tja2uLq6srgwYM5c+aMSRsFy0piY2MZM2YM9vb2uLu7M3ny5CKXleh0OmbNmoWbmxuOjo4MHjyYhISEEq8L4PDhw5w4cYLRo0eXKf6KMDc3N0mSC3Ts2JHc3FyTvyeAUaNGsXv3bq5evVrhPoUQQoiHlZuvY97OU4xf8xMN61vwzaRneaVLs8cuSYY6NqP8wY7fOJV4+6Ha0Ol0mJubV/j8tu72zB7c7qH6z8/PR6fTcenSJUJDQ3FxcaFXr16lnhsfH4+DgwNOTk7Gsk6dOrF27VpmzJjBiBEj8PHxKfKD3qtXL1RVNb4/cOAAY8eOZfLkySxcuBC9Xs+ZM2dIT08vtv+ZM2eSkpJCXFwc33zzDQBWVlYA5ObmkpGRwYwZM3Bzc0Or1bJy5Uq6dOnC6dOncXV1NWnrlVde4eWXX2bbtm0cOnSIOXPm0KBBAz744AOTegsWLKBr166sWbOG5ORkpk6dytixY4mOji5xrKKiorCzs6NDhw5lih8gPz+/xDYL1KtX8j+rAwcO4OjoiJubm0l59+7d0ev17Nmzh1dffbVMfQkhhBCV6WJKJpM3HOW3xNu88kxT3n+uDRqLiudFtV2dSpTrgtatW5u8d3d3Z+fOncaZ5fsVJNUZGRlERESwdetWlixZYpLof/TRR1y4cIH58+czf/587O3tCQwMZPTo0YwYMaLYOGJjY3F0dGTJkiXGsv79+5cYe4sWLXB2dsbS0pJnnnnG5JiDg4PJjXc6nY4BAwbQuHFjNmzYQEhIiEn90aNHG5Pivn37cvjwYTZs2FAoUW7WrBnr1683vk9JSWHatGkkJibi7u5e4vX5+PiYzKqXFD+AhUXZNlG//wvHg3bv3k1ERARz584tlFA7Ozvj4eFBbGysJMpCCCEeKVVV2XIkgdnf/IaVhRmfv/I0/du5ln5iHVenEuWHmcktkJGRgZ2dXSVEUzERERF4eHigqiqJiYmsWLGC4OBgYmJiaNOmjUndB5PqiRMnMmnSJJMyFxcXYmJiiIuLIyoqisOHD7N37162b9/Onj17+OKLL4qMIyAggLS0NMaOHcuoUaN49tlncXR0fKhr27x5M4sXL+bs2bMmNyc+uKsHwHPPPWfy3sfHh7179xaq9+BOET4+PgBcuXKlxEQ5MTERLy+vcsUfFxdXrvoPOnXqFC+//DI9evQodDNfAWdnZxITEx+qHyGEEKI8bmXnERpxgm+PJ9GluROfjPTF1UFT3WHVCHUqUa4LvL29jTfogWEW19PTkzlz5rBp0yaTugVJdUpKCmFhYaxcuZLOnTszbty4Qu0GBAQQEBAAQHp6OsOHD2f16tVMmTIFb2/vQvV79uzJli1bWL58OS+88IKxLCwsjPbt25f7unbs2MHIkSMZP348s2fPplGjRpiZmREcHFzk2uMH1/ZaWVmRm5tbpnpAkW3eLycnx2RZRVn4+vqWq/79Ll26RL9+/fDy8uLrr78udnmGtbU12dnZFe5HCCGEKI8j8VqmbDzGjds5/COoFW/0aIG52eO3Frk4kijXcNbW1jRv3pzjx48XOnZ/Ut27d2/at2/PtGnTGDZsGPXrF/+UHEdHRyZPnsx3333HqVOnikyUAYYPH87w4cPJzMwkOjqa6dOnExQUREJCQqk3Aj5o48aNtGzZkvDwcGNZXl4eWq22XO1UFicnJ9LS0sp1TkWXXiQkJNCnTx/s7e3ZvXt3iQm6Vqut0BcRIYQQojzydXr+376LLP3uHB4NbPjPm13x9XSs7rBqHEmUa7isrCwuXrxIu3YlLyuxsrJi4cKFDB06lJUrVxr3U05KSip00xhg3G2iqGMPsrW1ZdCgQVy6dIkpU6aQmpqKs7NzsXEUNSOalZVVaBb1q6++QqfTldp/VWjdujUxMTGFyouLHyq29CIlJYW+ffsCsGfPHho1akRGRkaRdXU6HVeuXOGll14qdz9CCCFEWV1Lz+adjUeJi0/jeV935j7vjZ2mbJNBjxtJlGuYY8eOcfPmTVRVJSkpiRUrVqDVann77bdLPXfIkCEEBASwePFiJk2ahLW1NUFBQXh6ejJkyBBatWpFdnY2+/fvJywsjC5dutCtW7ci25o1axY3btwgMDAQd3d3EhISWLZsGb6+vsUmyQBt27ZFq9Xy6aef4u/vj0ajwcfHh6CgICIjIwkJCWHQoEEcOXKE5cuXP/S654rq0aMHX375JampqSa7hBQXP4C/v3+5+sjOzmbAgAHEx8ezZs0aEhISSEhI4M6dO9SvX5+2bdua3KR58uRJsrKy6NGjR+VcpBBCCPGAb48n8e6246gqfDKyAy/4eVR3SDWaJMo1zP2zic7Oznh7exMVFcWAAQPKdP68efMYMGAAn332GSEhIYSGhrJ161Y+/vhjkpKSUFUVLy8vpk6dynvvvVfsEorOnTuzbNkyQkJCjHsx9+/fn7lz55bY/2uvvUZsbCyhoaGkp6fTtGlT4uPjef3117l69Spr1qxh1apVBAQEsGPHDuP650dt6NChaDQadu7cyfjx40uNvyJu3LjB0aNHARgzZkyh4/v27TPZ9m/nzp24urqWaStAIYQQojzu5ObzwY7f2HwkgQ6ejiwb5UtTp+KXaQoDpaStrKqTv7+/euTIkWKPnz59utAuEJWhune9qI1q65hNmDCBhISEInfTqErFjVfbtm0ZNmxYqV9GoOo+/zVRdHS0fHkoBxmv8pMxKx8Zr/KpCeN18totJm84yu+pd5jYqwXv9H0KC/Oa+8y5Rz1miqL8rKpqkb82lhll8diaPXs2bdq04ciRI+VeVlHZtm/fzo0bN5g6dWq1xiGEEKLu0OtV/u/A7/xr9xmc6lux/rVn6NLCqfQThZEkyuKx5eXlRXh4OMnJydUdCtnZ2axbt67a1mwLIYSoW5Jv5zB1y6/8cP4mA9o15qMX29OgvmV1h1XrSKIsHmujRo2q7hCAmhOHEEKI2u/7Mzf4+5bjZN3N58MXfHi5kyeKInsjV4QkykIIIYQQdUBOno6P/nuG8IPxtHa1Y/nLz/Bk49p3D1FNIomyEEIIIUQtd+5GBpM3HOXM9Qxe7ebFP4JaobEwr+6waj1JlIUQQgghailVVVl3+Arzdp7C1qoeX04IILC1S3WHVWdIoiyEEEIIUQtp79xl+tbj7Dl1gx5PObPopfa42GmqO6w6RRJlIYQQQoha5uCFm4RsPob2zl1mPNeGV7t5YWYmN+xVNkmUhRBCCCFqiTydnrA95/hs/0W8GtXn/8YH4N3EobrDqrMkURZCCCGEqAXib95hysaj/Jpwi5c7eTJzUFtsLCWVq0o19/mFj5nw8HAURTG+zM3NadKkCSNGjODs2bMl1rW0tKRFixaEhoaSk5NTqO39+/cTFBSEu7s7Go0GDw8PgoKC+Prrr411oqOjURSF+Pj4h7qOyMhIwsLCHqqNsoiPj0dRFFavXl3hNvR6Pb6+vixatMhYVtnxf/LJJwQEBODk5IRGo6Fly5aEhoaSmppqUu/5559n4sSJldavEEKIukNVVbb+nMBzy37g95t3WDmmIwtebC9J8iMgiXINs2XLFg4dOkRMTAwLFizg6NGj9OnTh1u3bhVb99tvv2XAgAEsWLCAadOmmdSJjIwkMDAQjUbDihUriIqKYv78+TRq1Ihdu3ZVevyPKlGuDOvWrSMpKckkQa3s+LVaLS+++CLh4eFERUXx1ltvsW7dOvr164derzfWmz17Nl988QXnzp2rtL6FEELUfrdz8nhn0zGmbvmVdk0ciHqnB8E+btUd1mNDvorUML6+vrRs2RKAbt264e7uTr9+/Th48CADBw4stm6/fv04f/48a9asYenSpZiZGb4DhYWF4efnR0REhMlTecaPH2+SqD2OFi1axLhx47CxsamyPubOnWvyvlevXpiZmfHOO+9w9OhRnn76aQD8/Pzw8/NjyZIlrFy5ssriEUIIUXv8fDmNKRuPknQrh6n9nmJiYEvM5Ya9R0pmlGs4e3t7APLy8kqt27FjR7Kysrh586axTKvV4uLiUuSjKwuS6eKsX78ePz8/bG1tsbe3x8fHh1WrVhVbf8KECaxdu5Zr164Zl4U0a9YMgJycHEJCQvD29sbW1hZXV1cGDx7MmTNnTNooWFYSGxvLmDFjsLe3x93dncmTJxe5rESn0zFr1izc3NxwdHRk8ODBJCQklHhdAIcPH+bEiROMHj26TPFXpoYNGwJQr57p99RRo0bx9ddfk52dXel9CiGEqD10epXl351nxKpDAGx+owtv93lSkuRqUOUzyoqiBAPvAh0BPXAO+Ieqqt9Xemf/fReun3ioJqx1+WD+EMPi6gMDP6rw6Tqdjvz8fHQ6HZcuXSI0NBQXFxd69epV6rnx8fE4ODjg5ORkLOvUqRNr165lxowZjBgxAh8fnyKT5l69eqGqqvH9gQMHGDt2LJMnT2bhwoXo9XrOnDlDenp6sf3PnDmTlJQU4uLi+OabbwCwsrICIDc3l4yMDGbMmIGbmxtarZaVK1fSpUsXTp8+jaurq0lbr7zyCi+//DLbtm3j0KFDzJkzhwYNGvDBBx+Y1FuwYAFdu3ZlzZo1JCcnM3XqVMaOHUt0dHSJYxUVFYWdnR0dOnQoU/wA+fn5JbZZ4MEEuODcu3fvcvz4cT788EP69Olj0jdAjx49uH37NocOHaJ3795l6ksIIUTdci09m5CNx/gpXsuQDu7Me8Ebe41FdYf12KrSRFlRlDeAFfdeczHMYPsCVfe77lqudevWJu/d3d3ZuXOncWb5fgVJdUZGBhEREWzdupUlS5Zgbv7HIys/+ugjLly4wPz585k/fz729vYEBgYyevRoRowYUWwcsbGxODo6smTJEmNZ//79S4y9RYsWODs7Y2lpyTPPPGNyzMHBweTGO51Ox4ABA2jcuDEbNmwgJCTEpP7o0aONSXHfvn05fPgwGzZsKJQoN2vWjPXr1xvfp6SkMG3aNBITE3F3dy/x+nx8fExm1UuKH8DComz/obr/CwdAZmYmdnZ2xvd9+vQhIiKi0HkdOnTAzMyM2NhYSZSFEOIx9N8TSUzfehydXmXxSx14sWOTIie3xKNTZYmyoijNgCXANFVVl9x3aHdV9fkwM7kFsjMyTJKaRy0iIgIPDw9UVSUxMZEVK1YQHBxMTEwMbdq0Man7YFI9ceJEJk2aZFLm4uJCTEwMcXFxREVFcfjwYfbu3cv27dvZs2cPX3zxRZFxBAQEkJaWxtixYxk1ahTPPvssjo6OD3VtmzdvZvHixZw9e9bk5sQHd/UAeO6550ze+/j4sHfv3kL1goODC9UDuHLlSomJcmJiIl5eXuWKPy4urlz1C9jY2BAXF0dOTg5Hjx5l3rx5DB48mL1795rMPltYWODg4EBiYmKF+hFCCFE7Zd3NZ+7OU2z46SodPBxYOsqPZo3qV3dYgqqdUX4Vw1KLz6qwjzrH29vbeIMeGGZxPT09mTNnDps2bTKpW5BUp6SkEBYWxsqVK+ncuTPjxo0r1G5AQAABAQEApKenM3z4cFavXs2UKVPw9vYuVL9nz55s2bKF5cuX88ILLxjLwsLCaN++fbmva8eOHYwcOZLx48cze/ZsGjVqhJmZGcHBwUWuPS5Yx1vAysqK3NzcMtUDimzzfjk5OSbLKsrC19e3XPULmJmZ4e/vD8Czzz5LixYteO655/jPf/7DqFGjTOpaW1vLGmUhhHiMnLx2i8kbj/L7zTu82asFf+v3FBbmcgtZTVGVfxPPAmeAUYqiXFQUJV9RlAuKorxVhX3WOdbW1jRv3pzjx48XOubt7Y2/vz8DBw5k586dPPXUU0ybNo07d+6U2KajoyOTJ08G4NSpU8XWGz58OPv37yctLY2IiAiSkpIICgqq0G4ZGzdupGXLloSHhxMcHEynTp3o0KEDWq223G1VBicnJ9LS0sp1joWFRZlepfHz8wPgwoULhY5ptVoaNWpUrriEEELUPnq9yuofLvHiyoPcyc3n6z93ZnpQa0mSa5iqnFF2v/daCIQCF4GXgBWKotRTVXVpFfZdZ2RlZXHx4kXatWtXYj0rKysWLlzI0KFDWblypXE/5aSkJNzcCu+3WLDbRFHHHmRra8ugQYO4dOkSU6ZMITU1FWdn52LjKGpGNCsrq9BNbl999RU6na7U/qtC69atiYmJKVReXPxQ8aUXDzpw4ABgWBN9v+vXr5OTk0OrVq0qpR8hhBA1U3JGDn/fcpyYcyn0a9uYj4e1p2F9y+oOSxShKhNlM8AOmKCq6rZ7Zd/fW7v8nqIoy9QH7npSFOUvwF8AGjduXOLOBQ4ODmRkZFR60DqdrkraLU3BUoFDhw5x+fJlVFXlxo0bfP7552i1Wl577TVjXAV1MzMzTWINDAykY8eOLFq0iPHjx2NtbU3//v1p0qQJwcHBPPnkk2RnZ/Pjjz+yYsUKOnXqRPv27Yu83nnz5pGSkkL37t1xc3Pj2rVrLFmyhPbt26PRaEzOuX/Mmjdvjlar5ZNPPsHPzw+NRkO7du3o1asXkZGRvPXWWwQFBXH06FFWrVqFo6MjeXl5pV5bwbKLgrLMzExj/fvrZWVlGX+W9PfYqVMnvvzyS+Lj4012CSkufqDMCWxBv7du3eLFF19kxIgRtGjRAkVR+Pnnn1mxYgU+Pj7069fPJMaCz3vHjh1L/Qzm5OSUurNHXZGZmfnYXGtlkPEqPxmz8pHxKp8Hx+t4Sj6rT+SSnQ/j2loS6JnB8biD1RdgDVSjPmOqqlbJCzgEqIDdA+Uh98rdSzr/6aefVkty6tSpEo9X1O3bt6uk3dJ8+eWX6r1xMb6cnZ3VwMBANSoqqsi658+fL9TO7t27VUANCwtTVVVVN27cqL700ktq8+bNVWtra1Wj0aht2rRR33vvvRKvdefOnWr//v1VV1dX1dLSUvXw8FBfffVV9dq1a4Xq3t9OZmamOmrUKNXR0VEF1KZNm6qqqqo6nU59//33VTc3N9Xa2lrt0aOH+ssvv6hNmzZVx48fX+q1zZ49WzV8XA1+//13FVC/+OILk3r79u1TAXXfvn3FXpuqqqpWq1U1Go0aHh5uUl5c/BWRk5Oj/ulPf1KffPJJ1cbGRrW3t1fbt2+vzpw5s8ixf+2119TSPvcFqurzXxOV9ncpTMl4lZ+MWfnIeJVPwXhl381X53xzUm06fac64JP96tnr1ZNv1AaP+jMGHFGLyUcV9YGtrCqLoiirgT8D9qqqZtxXHgKEAW6qql4v7nx/f3/1yJEjxbZ/+vTpQrtAVIaMat71ojaqrWM2YcIEEhISitxNoyoVNV45OTm4ubmxaNEi/vznP5faRlV9/mui6OjoMu0jLgxkvMpPxqx8ZLzKJzo6Go+2T/P2hmOcTrrNhK7NeHdgazQW5qWf/Jh61J8xRVF+VlXVv6hjVblivGCj2AEPlAcBCSUlyUI8CrNnz+bAgQOU9IXsUVm1ahUuLi6MHz++ukMRQghRSVRVJfpqHoOWH+DG7RzWTPBnzpB2kiTXIlW5RnkXsA9YpShKI+AShpv5+gN/qsJ+hSgTLy8vwsPDSU5Oru5QsLKyIjw8vMin+gkhhKh90u7c5d1tx9n92126P9mIxS91wMVeU91hiXKqsv8rq6qqKoryPLAA+ABogGG7uDGqqq4v6VwhHpUH9zGuLn/961+rOwQhhBCV5NDFVEI2HSP1Ti4jW1myYHwnzMzkCXu1UZVOX6mqeht4695LCCGEEKLOytPpWbL3HCujL+LlVJ/V47tx8/xRSZJrMfk9rxBCCCHEQ7qSmsXkjUc5djWdkf6ezBrclvpW9Yg+X92RiYchibIQQgghxEOIOJrAzMjfUBRYMdqPQe3dqzskUUkkURZCCCGEqICMnDxmbf+NiKPXCGjWgE9G+uLRwKa6wxKVSBJlIYQQQohy+uVKGlM2HuVaWjYhfZ/ircAW1DOvyl13RXWQRFkIIYQQoox0epXP9l8kbM85XO01bH6jC/7NGlZ3WKKKSKIshBBCCFEGSbeyCdl0jNhLWgZ3cGfe8944WFtUd1iiCsnvCGqI8PBwFEUxvszNzWnSpAkjRozg7NmzJda1tLSkRYsWhIaGkpOTU6jt/fv3ExQUhLu7OxqNBg8PD4KCgvj666+NdaKjo1EUhfj4+Ie6jsjISMLCwh6qjbKIj49HURRWr15d4Tb0ej2+vr4sWrTIWFaV8aenp+Pm5oa9vX2hx2a/8847BAcHV0m/QgghHl7UyesELfmB4wm3WDi8PctG+UqS/BiQRLmG2bJlC4cOHSImJoYFCxZw9OhR+vTpw61bt4qt++233zJgwAAWLFjAtGnTTOpERkYSGBiIRqNhxYoVREVFMX/+fBo1asSuXbsqPf5HlShXhnXr1pGUlMTEiRONZVUZ//Tp00s8tm/fPvbt21clfQshhKiY7Ls6QiNO8Nd1P9PUyYZvJ3fnJX9PFEX2Rn4cyNKLGsbX15eWLVsC0K1bN9zd3enXrx8HDx5k4MCBxdbt168f58+fZ82aNSxduhQzM8N3oLCwMPz8/IiIiDD5Rz1+/Hj0ev0juqqaadGiRYwbNw4bm6q/Q/nHH39k3bp1LF++nD//+c+Fjru5uTF48GAWLlxIYGBglccjhBCidKcSb/P2hl+4mHKHN3o2Z2q/VljWkznGx4n8bddw9vb2AOTl5ZVat2PHjmRlZXHz5k1jmVarxcXFpchvvgXJdHHWr1+Pn58ftra22Nvb4+Pjw6pVq4qtP2HCBNauXcu1a9eMy0KaNWsGQE5ODiEhIXh7e2Nra4urqyuDBw/mzJkzJm0ULCuJjY1lzJgx2Nvb4+7uzuTJk4tcVqLT6Zg1axZubm44OjoyePBgEhISSrwugMOHD3PixAlGjx5dpvgfRl5eHm+88QbvvvsuzZs3L7beqFGj2L17N1evXn3oPoUQQlScqqqsOfA7z/+/H8nIyWfdnzvz3sA2kiQ/hurUjPLHP33MGe2Z0iuWQKfTYW5uXuHzWzdszfROxf+KvSz95+fno9PpuHTpEqGhobi4uNCrV69Sz42Pj8fBwQEnJydjWadOnVi7di0zZsxgxIgR+Pj4FJk09+rVC1VVje8PHDjA2LFjmTx5MgsXLkSv13PmzBnS09OL7X/mzJmkpKQQFxfHN998A4CVlRUAubm5ZGRkMGPGDNzc3NBqtaxcuZIuXbpw+vRpXF1dTdp65ZVXePnll9m2bRuHDh1izpw5NGjQgA8++MCk3oIFC+jatStr1qwhOTmZqVOnMnbsWKKjo0scq6ioKOzs7OjQoUOZ4gfIz88vsc0C9eqZ/rP617/+xd27d/nHP/7BoUOHij2ve/fu6PV69uzZw6uvvlqmvoQQQlSulIxcpv3nV6LPptC3jQv/Gt6BhvUtqzssUU3qVKJcF7Ru3drkvbu7Ozt37jTOLN+vIKnOyMggIiKCrVu3smTJEpNE/6OPPuLChQvMnz+f+fPnY29vT2BgIKNHj2bEiBHFxhEbG4ujoyNLliwxlvXv37/E2Fu0aIGzszOWlpY888wzJsccHBxMbrzT6XQMGDCAxo0bs2HDBkJCQkzqjx492pgU9+3bl8OHD7Nhw4ZCiXKzZs1Yv3698X1KSgrTpk0jMTERd/fin4wUGxuLj4+Pyax6SfEDWFiU7aaN+79wXLhwgXnz5rFjxw6TpLsozs7OeHh4EBsbK4myEEJUg/3nUpi6+Vdu5+Txz6HteOWZprIW+TFXpxLlh5nJLZCRkYGdnV0lRFMxEREReHh4oKoqiYmJrFixguDgYGJiYmjTpo1J3QeT6okTJzJp0iSTMhcXF2JiYoiLiyMqKorDhw+zd+9etm/fzp49e/jiiy+KjCMgIIC0tDTGjh3LqFGjePbZZ3F0dHyoa9u8eTOLFy/m7NmzJjcnPrirB8Bzzz1n8t7Hx6fQThFAoZ0ifHx8ALhy5UqJiXJiYiJeXl7lij8uLq5c9QHefPNNhg4dSt++fctU39nZmcTExHL3I4QQouJy83UsjDrL6gO/06qxHV+/1plWrtWXC4iao04lynWBt7e38QY9MMzienp6MmfOHDZt2mRStyCpTklJISwsjJUrV9K5c2fGjRtXqN2AgAACAgIAwzZlw4cPZ/Xq1UyZMgVvb+9C9Xv27MmWLVtYvnw5L7zwgrEsLCyM9u3bl/u6duzYwciRIxk/fjyzZ8+mUaNGmJmZERwcXOTa44YNTTdvt7KyIjc3t0z1gCLbvF9OTk6pM7wP8vX1LVf9zZs3c/DgQeLi4oxLVjIzMwG4c+cOt27dwsHBweQca2trsrOzy9WPEEKIiruQnMnkDUc5lXSbcV2aEhrcBo1FxZdgirpFEuUaztramubNm3P8+PFCx+5Pqnv37k379u2ZNm0aw4YNo379+sW26ejoyOTJk/nuu+84depUkYkywPDhwxk+fDiZmZlER0czffp0goKCSEhIKPVGwAdt3LiRli1bEh4ebizLy8tDq9WWq53K4uTkRFpaWrnOKe/Si1OnTpGVlUW7du0K1Xn++edxcHAotOZbq9VW6IuIEEKI8lFVlU1xV/lgxyk0FmasHudP37aNqzssUcNIolzDZWVlcfHixSKTrftZWVmxcOFChg4dysqVK437KSclJeHm5laofsFuE0Ude5CtrS2DBg3i0qVLTJkyhdTUVJydnYuNo6gZ0aysrEI3uX311VfodLpS+68KrVu3JiYmplB5cfFD+ZdeTJgwodBNmMeOHSMkJIRFixbRuXNnk2M6nY4rV67w0ksvlasfIYQQ5ZOedZf3tp3gvyev82zLRiwe0YHG9prqDkvUQJIo1zDHjh3j5s2bqKpKUlISK1asQKvV8vbbb5d67pAhQwgICGDx4sVMmjQJa2trgoKC8PT0ZMiQIbRq1Yrs7Gz2799PWFgYXbp0oVu3bkW2NWvWLG7cuEFgYCDu7u4kJCSwbNkyfH19i02SAdq2bYtWq+XTTz/F398fjUaDj48PQUFBREZGEhISwqBBgzhy5AjLly9/6HXPFdWjRw++/PJLUlNTTXYJKS5+AH9//3L10axZs2K3l+vQoQPPPvusSdnJkyfJysqiR48e5bsYIYQQZXboYip/23yMlIxc3hvYmte7N8fMTG7YE0WTRLmGuX820dnZGW9vb6KiohgwYECZzp83bx4DBgzgs88+IyQkhNDQULZu3crHH39MUlISqqri5eXF1KlTee+994pdQtG5c2eWLVtGSEiIcS/m/v37M3fu3BL7f+2114iNjSU0NJT09HSaNm1KfHw8r7/+OlevXmXNmjWsWrWKgIAAduzYYVz//KgNHToUjUbDzp07GT9+fKnxPwo7d+7E1dW1TFsBCiGEKJ88nZ5P9pzj0/0XaeZUn20Tu9Lew7G6wxI1nHL/VlY1ib+/v3rkyJFij58+fbrQLhCVobp3vaiNauuYTZgwgYSEhCJ306hKxY1X27ZtGTZsWKlfRqDqPv81UXR0tHx5KAcZr/KTMSuf2jhe8TfvMGXjUX5NuMVIf09mDW5LfatHM1dYG8eruj3qMVMU5WdVVYv8tbHMKIvH1uzZs2nTpg1Hjhwp97KKyrZ9+3Zu3LjB1KlTqzUOIYSoS1RV5T8/JzDnm9+oZ27Gp2M6MtCn9HtzhCggibJ4bHl5eREeHk5ycnJ1h0J2djbr1q2rtjXbQghR19zKyiM08gTfHk+is1dDPhnpi7ujdXWHJWoZSZTFY23UqFHVHQJQc+IQQoi64Kfftbyz8SjJGblMG9CKv/ZsgbncsCcqQBJlIYQQQtQJeTo9y747z//bdwHPhjb8582u+Ho6VndYohaTRFkIIYQQtd7l1DtM2XiMY1fTGf60B3OGtMP2Ed2wJ+ou+QQJIYQQotZSVZWIo9eYGXkSMzOFFaP9GNTevbrDEnWEJMpCCCGEqJVu5+QxI+Ik3/yaSKdmDQkb2QGPBjbVHZaoQyRRFkIIIUStcyRey5SNx7h+O4ep/Z5iYmBLuWFPVDpJlIUQQghRa+Tr9Cz//gLLvz+PRwMbtvy1Cx2faFDdYYk6ShJlIYQQQtQKV7VZvLPpGD9fTuNFvyZ8MLQddhqL6g5L1GFm1R2AMAgPD0dRFOPL3NycJk2aMGLECM6ePVtiXUtLS1q0aEFoaCg5OTmF2t6/fz9BQUG4u7uj0Wjw8PAgKCiIr7/+2lgnOjoaRVGIj49/qOuIjIwkLCzsodooi/j4eBRFYfXq1RVuQ6/X4+vry6JFi4xllR3/nDlzTP6uFEXB3t6e559/3qTeO++8Q3BwcKX1K4QQdU3k0WsEL/2Bc9czWDrKl7CRvpIkiyonM8o1zJYtW/Dw8ECn03Hx4kXmzp1Lnz59+O2333BwcCiybkZGBhERESxYsICMjAyWL19urBMZGcmLL77IkCFDWLFiBQ0bNuTy5cvs2bOHXbt2MWbMmEqNPzIykr179/K3v/2tUtutCuvWrSMpKYmJEycay6oq/gMHDmBubg7AnTt38PT0NDk+ffp0mjdvzr59+wgMDKzUvoUQojbLyMlj1vbfiDh6Df+mDfhkpC+eDeWGPfFoSKJcw/j6+tKyZUsAunXrhru7O/369ePgwYMMHDiw2Lr9+vXj/PnzrFmzhqVLl2JmZvhlQVhYGH5+fkRERKAof9zkMH78ePR6/SO6qppp0aJFjBs3Dhubqv8PbufOnalXz/DPLSMjAzs7O5Pjbm5uDB48mIULF0qiLIQQ9/x8OY13Nh3lWlo27/R9kkmBLalnLr8MF4+OfNpqOHt7ewDy8vJKrduxY0eysrK4efOmsUyr1eLi4mKSJBcoSKaLs379evz8/LC1tcXe3h4fHx9WrVpVbP0JEyawdu1arl27Zlxm0KxZMwBycnIICQnB29sbW1tbXF1dGTx4MGfOnDFpo2BZSWxsLGPGjMHe3h53d3cmT55c5LISnU7HrFmzcHNzw9HRkcGDB5OQkFDidQEcPnyYEydOMHr06DLF/yiMGjWK3bt3c/Xq1UfWpxBC1ET5Oj1L955nxKpDqCps+WsX3un7lCTJ4pGrUzPK1z/8kNzTZ0qvWIJ8nQ7tvV+RV4RVm9a4hoZW+HydTkd+fj46nY5Lly4RGhqKi4sLvXr1KvXc+Ph4HBwccHJyMpZ16tSJtWvXMmPGDEaMGIGPj0+RSXOvXr1QVdX4/sCBA4wdO5bJkyezcOFC9Ho9Z86cIT09vdj+Z86cSUpKCnFxcXzzzTcAWFlZAZCbm0tGRgYzZszAzc0NrVbLypUr6dKlC6dPn8bV1dWkrVdeeYWXX36Zbdu2cejQIebMmUODBg344IMPTOotWLCArl27smbNGpKTk5k6dSpjx44lOjq6xLGKiorCzs6ODh06lCl+gPz8/BLbLFAwc3w/T09PkpOT8fDw4MUXX+TDDz/E2trapE737t3R6/Xs2bOHV199tUx9CSFEXZOQlsU7G49x5HIaz/u688/nvbGXtciimtSpRLkuaN26tcl7d3d3du7caZxZvl9BUl2wRnnr1q0sWbLEuBYW4KOPPuLChQvMnz+f+fPnY29vT2BgIKNHj2bEiBHFxhEbG4ujoyNLliwxlvXv37/E2Fu0aIGzszOWlpY888wzJsccHBxMbrzT6XQMGDCAxo0bs2HDBkJCQkzqjx492pgU9+3bl8OHD7Nhw4ZCiXKzZs1Yv3698X1KSgrTpk0jMTERd/fin8wUGxuLj4+Pyax6SfEDWFiU7T/U93/haNmyJR999BF+fn4oisL//vc/li5dysmTJ9mzZ4/Jec7Oznh4eBAbGyuJshDisfTNr4m8H3ECVYVPRnbgBT+P6g5JPObqVKL8MDO5BYpaP/ooRURE4OHhgaqqJCYmsmLFCoKDg4mJiaFNmzYmdR9MqidOnMikSZNMylxcXIiJiSEuLo6oqCgOHz7M3r172b59O3v27OGLL74oMo6AgADS0tIYO3Yso0aN4tlnn8XR0fGhrm3z5s0sXryYs2fPcuvWLWP5g7t6ADz33HMm7318fNi7d2+heg/uFOHj4wPAlStXSkyUExMT8fLyKlf8cXFx5aoPMHbsWJP3/fr1o1GjRrz77rvs3buXvn37mhx3dnYmMTGx3P0IIURtlpmbz6ztJ9n2yzX8nnBk6Ug/nnCSG/ZE9atTiXJd4O3tbbxBDwyzuJ6ensyZM4dNmzaZ1C1IqlNSUggLC2PlypV07tyZcePGFWo3ICCAgIAAANLT0xk+fDirV69mypQpeHt7F6rfs2dPtmzZwvLly3nhhReMZWFhYbRv377c17Vjxw5GjhzJ+PHjmT17No0aNcLMzIzg4OAi1x43bNjQ5L2VlRW5ubllqgcU2eb9cnJyTJZVlIWvr2+56hfnpZde4t133yUuLq5QomxtbU12dnal9COEELXB0StpTNl4jIS0LCb3eZLJveWGPVFzSKJcw1lbW9O8eXOOHz9e6Nj9SXXv3r1p374906ZNY9iwYdSvX7/YNh0dHZk8eTLfffcdp06dKjJRBhg+fDjDhw8nMzOT6Ohopk+fTlBQEAkJCaXeCPigjRs30rJlS8LDw41leXl5aLXacrVTWZycnEhLSyvXORVZelGSotaKa7XaCn0REUKI2kanV/k0+gKf7D2Pq72GTW90IaBZw9JPFOIRkkS5hsvKyuLixYu0a9euxHpWVlYsXLiQoUOHsnLlSqZNmwZAUlISbm5uheoX7DZR1LEH2draMmjQIC5dusSUKVNITU3F2dm52DiKmhHNysoqdJPbV199hU6nK7X/qtC6dWtiYmIKlRcXP1Rs6UVRCn4z0KlTJ5NynU7HlStXeOmllyqlHyGEqKmupWcTsukYP/2uZXAHd+Y9742DtdywJ2oeSZRrmGPHjnHz5k1UVSUpKYkVK1ag1Wp5++23Sz13yJAhBAQEsHjxYiZNmoS1tTVBQUF4enoyZMgQWrVqRXZ2Nvv37ycsLIwuXbrQrVu3ItuaNWsWN27cIDAwEHd3dxISEli2bBm+vr7FJskAbdu2RavV8umnn+Lv749Go8HHx4egoCAiIyMJCQlh0KBBHDlyhOXLlz/0uueK6tGjB19++SWpqakmu4QUFz+Av79/ufvx8/Nj3LhxtGrVCkVR2LNnD8uXLycoKIjevXub1D158iRZWVn06NHj4S5OCCFqsG+PJ/HetuPo9CqLX+rAix2bFPkbNiFqAkmUa5j7ZxOdnZ3x9vYmKiqKAQMGlOn8efPmMWDAAD777DNCQkIIDQ1l69atfPzxxyQlJaGqKl5eXkydOpX33nuv2CUUnTt3ZtmyZYSEhBj3Yu7fvz9z584tsf/XXnuN2NhYQkNDSU9Pp2nTpsTHx/P6669z9epV1qxZw6pVqwgICGDHjh3G9c+P2tChQ9FoNOzcuZPx48eXGn9FtWrVihUrVpCUlIRer6d58+ZMnz6dmTNnFqq7c+dOXF1dy7QVoBBC1DZ3cvOZ881vbPk5AV9PR5aO8qWpU/HLBIWoCZSyrqd81Pz9/dUjR44Ue/z06dOFdoGoDNW960VtVFvHbMKECSQkJBS5m0ZVKm682rZty7Bhw0r9MgJV9/mviaKjo+XLQznIeJWfjFn5VGS8fr2azpSNR7mszeKtXi2Z0vdJLB6TG/bk81V+j3rMFEX5WVXVIn9tLDPK4rE1e/Zs2rRpw5EjRyq0rKIybd++nRs3bjB16tRqjUMIISqTTq+yKuYiYf87h4udFRtff4bOzZ1KP1GIGkISZfHY8vLyIjw8nOTk5OoOhezsbNatW1dta7aFEKKyJd0y3LAXe0nLcz5ufPiCDw42csOeqF0kURaPtVGjRlV3CEDNiUMIISrDf08k8e62E+Tp9PxreHteetpDbtgTtdIjWyCkKEqUoiiqoijzHlWfQgghhHh0su7m8+7W47z59S80dbLh28ndGeHvKUmyqLUeyYyyoigvAx0eRV9CCCGEePROJNxiysaj/J56hzd7tSCk71NY1ns8btgTdVeVJ8qKojQAPgFCgPVV3Z8QQgghHh29XuXzHy6x+H9ncapvxdevdaZri0bVHZYQleJRzCh/DJxUVXWDoiiSKAshhBB1RGJ6NlM3/8qhS6kEtXPlo2E+ONpYVndYQlSaKk2UFUV5FhiHLLsQQggh6pSCJ+zl61X+Naw9L/nLDXui7qmyB44oimIJHAUiVFWdca9MBeYXvC/inL8AfwFo3Ljx0xs3biy2fQcHB1q2bFnpcet0OszNzSu93bpMxqx8KmO8Lly4wK1btyopopotMzMTW1vb6g6j1pDxKj8Zs/K5mZ5JxBULfkzMp7mDGW+0t6JxfVmLXBz5fJXfox6zwMDAanngyD8Aa2B+WU9QVfVz4HMwPJmvpKeynD59ukqeBldbnzJXnWTMyqcyxkuj0eDn51dJEdVs8lSr8pHxKj8Zs7L7+XIa08IPkZqTz9u9WzK5z+PzhL2Kks9X+dWkMauST7eiKE8A7wMzAStFURwVRXG8d7jgvUxB3ic8PBxFUYwvc3NzmjRpwogRIzh79myJdS0tLWnRogWhoaHk5OQUanv//v0EBQXh7u6ORqPBw8ODoKAgvv76a2Od6OhoFEUhPj7+oa4jMjKSsLCwh2qjLOLj41EUhdWrV1e4Db1ej6+vL4sWLTKWVUX8Op2OJUuW4O3tjUajoWnTpvTt25ekpCRjnXfeeYfg4OBK7VcIISpLvk7Pkr3nGLHqEHoVNr3Rhan9W0mSLOq8qppRbg5ogHVFHPv7vZcfcKyK+q+1tmzZgoeHBzqdjosXLzJ37lz69OnDb7/9hoODQ5F1MzIyiIiIYMGCBWRkZLB8+XJjncjISF588UWGDBnCihUraNiwIZcvX2bPnj3s2rWLMWPGVGr8kZGR7N27l7/97W+V2m5VWLduHUlJSUycONFYVhXxv/LKK+zevZvQ0FD8/f25fv06P/30k8mXmunTp9O8eXP27dtHYGBgpfUthBAP60pqFu9sOsovV9J53ted/k7pBDRrWN1hCfFIVFWifAwo6v/2+zAkz/8HXKiivms1X19f49rrbt264e7uTr9+/Th48CADBw4stm6/fv04f/48a9asYenSpZiZGb7lh4WF4efnR0REhMlNFuPHj0ev1z+iq6qZFi1axLhx47CxsamyPjZu3MjmzZs5fPgwTz/9NGBYejFy5EiTem5ubgwePJiFCxdKoiyEqBFUVWXbL9eY/c1vKMDSUb4M9W1CdHR0dYcmxCNTJb8zUVU1XVXV6Adf9w5fvvc+syr6rmvs7e0ByMvLK7Vux44dycrK4ubNm8YyrVaLi4tLkXciFyTTxVm/fj1+fn7Y2tpib2+Pj48Pq1atKrb+hAkTWLt2LdeuXTMuC2nWrBkAOTk5hISE4O3tja2tLa6urgwePJgzZ86YtFGwrCQ2NpYxY8Zgb2+Pu7s7kydPLnJZiU6nY9asWbi5ueHo6MjgwYNJSEgo8boADh8+zIkTJxg9enSZ4q+olStX0rNnT2OSXJJRo0axe/durl69+lB9CiHEw7qVlcfbG44ydcuvtHWz57/vdGeob5PqDkuIR+6RPJnvUflh8zluXn24/PthdyRo5GlL9xFPPVT/+fn56HQ6Ll26RGhoKC4uLmVa1B4fH4+DgwNOTk7Gsk6dOrF27VpmzJjBiBEj8PHxKTJp7tWrF/fvgHLgwAHGjh3L5MmTWbhwIXq9njNnzpCenl5s/zNnziQlJYW4uDi++eYbAKysrADIzc0lIyODGTNm4ObmhlarZeXKlXTp0oXTp0/j6upq0tYrr7zCyy+/zLZt2zh06BBz5syhQYMGfPDBByb1FixYQNeuXVmzZg3JyclMnTqVsWPHljrjERUVhZ2dHR06/LFzYUnxA+Tn55fYZoF69Qz/rPLy8jh8+DBvvPEG//jHP1izZg23bt2iQ4cO/Otf/6J3794m53Xv3h29Xs+ePXt49dVXy9SXEEJUtkMXU5m6+RjJGblMG9CKv/ZsgbmZbPsmHk+PNFFWVVX+pZWidevWJu/d3d3ZuXOncWb5fgVJdcEa5a1bt7JkyRKTRP+jjz7iwoULzJ8/n/nz52Nvb09gYCCjR49mxIgRxcYRGxuLo6MjS5YsMZb179+/xNhbtGiBs7MzlpaWPPPMMybHHBwcTG680+l0DBgwgMaNG7NhwwZCQkJM6o8ePdqYFPft25fDhw+zYcOGQolys2bNWL/+j+fYpKSkMG3aNBITE3F3dy/x+nx8fExm1UuKH8DCwqLE6y9Q8IUjNTWVu3fvEh4eTvPmzfniiy+wsrLio48+IigoiIMHD+Lv/8duNM7Oznh4eBAbGyuJshDikbubr+eTvef4bP9FmjnVZ+ubXeng6VjdYQlRrerUjPLDzOQWqO6tziIiIvDw8EBVVRITE1mxYgXBwcHExMTQpk0bk7oPJtUTJ05k0qRJJmUuLi7ExMQQFxdHVFQUhw8fZu/evWzfvp09e/bwxRdfFBlHQEAAaWlpjB07llGjRvHss8/i6Oj4UNe2efNmFi9ezNmzZ032AH5wVw+A5557zuS9j48Pe/fuLVTvwZ0ifHx8ALhy5UqJiXJiYiJeXl7lij8uLq5c9QvWgOfl5bFr1y5jPH5+fnTo0IGFCxeyadMmk3OcnZ1JTEwsVz9CCPGwLqZkMmXjUU5eu83LnTyZ8Vxb6lvVqRRBiAqRfwU1jLe3t8mDVPr374+npydz5swplFQVJNUpKSmEhYWxcuVKOnfuzLhx4wq1GxAQQEBAAADp6ekMHz6c1atXM2XKFLy9vQvV79mzJ1u2bGH58uW88MILxrKwsDDat29f7uvasWMHI0eOZPz48cyePZtGjRphZmZGcHBwkWuPGzY0vaPaysqK3NzcMtUDimzzfjk5OSbLKsrC19e3XPUbNGiAoii0bdvWJGm3tbWlS5cuHD16tNA51tbWZGdnl6sfIYSoKFVVWf/TFebuPIW1hTmfjX2aIG/X0k8U4jEhiXINZ21tTfPmzTl+/HihY/cn1b1796Z9+/ZMmzaNYcOGUb9+/WLbdHR0ZPLkyXz33XecOnWqyEQZYPjw4QwfPpzMzEyio6OZPn06QUFBJCQklHoj4IM2btxIy5YtCQ8PN5bl5eWh1WrL1U5lcXJyIi0trVznlHfpRcHfXXGKGkOtVluhLyJCCFFeqZm5TN96gr2nb9D9yUYseqkDje011R2WEDWKJMo1XFZWFhcvXqRdu3Yl1rOysmLhwoUMHTqUlStXMm3aNACSkpJwc3MrVL9gt4mijj3I1taWQYMGcenSJaZMmUJqairOzs7FxlHUjGhWVpbxJrcCX331FTqdrtT+q0Lr1q2JiYkpVF5c/FD+pRcAL7zwAsuXL+fatWs0aWK4YzwjI4ODBw8SFBRkUlen03HlyhVeeumlcvcjhBDlEX02mWn/Oc6trDxmPNeGV7t5YSY37AlRiCTKNcyxY8e4efMmqqqSlJTEihUr0Gq1vP3226WeO2TIEAICAli8eDGTJk3C2tqaoKAgPD09GTJkCK1atSI7O5v9+/cTFhZGly5d6NatW5FtzZo1ixs3bhAYGIi7uzsJCQksW7YMX1/fYpNkgLZt26LVavn000/x9/dHo9Hg4+NDUFAQkZGRhISEMGjQII4cOcLy5csfet1zRfXo0YMvv/yS1NRUk11CiosfMLnxrqz+/ve/89VXXzFw4EBmzZqFpaUlH3/8MVlZWbz77rsmdU+ePElWVhY9evR4uIsTQohi5OTp+Oi/Zwg/GM9TjW1Z+6dOtHUvfLO4EMJAEuUa5v7ZRGdnZ7y9vYmKimLAgAFlOn/evHkMGDCAzz77jJCQEEJDQ9m6dSsff/wxSUlJqKqKl5cXU6dO5b333it2CUXnzp1ZtmwZISEhxr2Y+/fvz9y5c0vs/7XXXiM2NpbQ0FDS09Np2rQp8fHxvP7661y9epU1a9awatUqAgIC2LFjh3H986M2dOhQNBoNO3fuZPz48aXGX1GNGzcmJiaGqVOn8qc//Qm9Xk+nTp3Yv39/od8S7Ny5E1dX1xrzfHshRN1y5vptpmw4xtkbGUzo2ox3B7ZGY1Hx7VCFqBS6PLj8I5zeCdYNoPf71R2RCeX+vXNrEn9/f/XIkSPFHj99+nShXSAqQ3XvelEb1dYxmzBhAgkJCUXuplGVihuvtm3bMmzYsFK/jEDVff5roujoaPnyUA4yXuVX18dMr1f58mA8H//3DPbWFix8qT2BrVwq3F5dH6/KJuNVhLtZcPF7OLMTzv4XctKhnjV0GAmDlz7yMVMU5WdVVYv8tbHMKIvH1uzZs2nTpg1Hjhyp0LKKyrR9+3Zu3LjB1KlTqzUOIUTdcuN2Dn/f8is/nL9J3zYufDSsPY1sy7fjjxCVIjsNzu2G0zsMSXJeFmgc4KmB0GYQtOgDljbVHWUhkiiLx5aXlxfh4eEkJydXdyhkZ2ezbt26aluzLYSoe3b/dp13tx4nO0/HvOe9GdP5iSKfzCpElbmdBGe/NSyriP8B9Plg5wa+o6H1IGj2LJiXbUep6iKJsnisjRo1qrpDAGpOHEKI2i/rbj5zd55mw09XaOduz9JRfrR0sa3usMTjIvWiYdb4zE5IuLdblFNL6DIJ2gwG945Qzi1mq5MkykIIIUQdcTwhnXc2HuP31Du80bM5U/u1wrJe7UlKRC2kqpB4FM58a0iOUwzbz+LmC71nQOvB4NwKaulvMyRRFkIIIWo5nV7ls/0X+WTPOZztrPj6tc50bdGousMSdZUuDy4fNCTGZ76F29dAMYemXeHpP0HrYHB8orqjrBSSKAshhBC1WEJaFn/b/Cs//a7lOR83PnzBBwebmr3uU9RCd7Pg4neGxNi4U4XGcBNe7xnwVBDYNKzuKCudJMpCCCFELaSqKhFHrzF7+2+owMLh7Rn+tIfcsCcqT5YWzkUZbsa7+D3kZ4PGEVoNhNbPQYveYFm/uqOsUpIoCyGEELVMetZd3o84ybcnkvBv2oBPRvri2bDmba0laqH0q3+sN758EFQd2DeBjq8Ydqpo2rXG71RRmSRRFkIIIWqRA+dvMnXLMVIz7zJtQCv+2rMF5mYyiywqSFUh+fS95HgHJP1qKHduDc+GGGaO3f1q7c14D0sSZSGEEKIWyMnT8XHUGb78MZ4WzvVZPS4AHw+H6g5L1EZ6vWHrtjM7DAmy9pKh3KMT9PsntHoOGrWs3hhrCNkzpoYIDw9HURTjy9zcnCZNmjBixAjOnj1bYl1LS0tatGhBaGgoOTk5hdrev38/QUFBuLu7o9Fo8PDwICgoiK+//tpYJzo6GkVRiI+Pf6jriIyMJCws7KHaKIv4+HgURWH16tUVbkOv1+Pr68uiRYuMZZUd//1/TwUve3t7FEXho48+MtZ75513CA4OrrR+hRB1y2+Jtxi8/ABf/hjP+C5N2fl2d0mSRfnk58L5PbBjCixuBWv6Q+xn0LA5DPoEpp6F1/ZAtymSJN9HZpRrmC1btuDh4YFOp+PixYvMnTuXPn368Ntvv+Hg4FBk3YyMDCIiIliwYAEZGRksX77cWCcyMpIXX3yRIUOGsGLFCho2bMjly5fZs2cPu3btYsyYMZUaf2RkJHv37uVvf/tbpbZbFdatW0dSUhITJ040llV2/IcOHSpUtmTJEjZt2sSQIUOMZdOnT6d58+bs27ePwMDASulbCFH76fQqX/xwicX/O4ujjSVrX+1Ez6ecqzssUVvk3Ibz/zPMGp/fA3czwNIWnuxnWG/8ZD/DY6RFsSRRrmF8fX1p2dLwTa5bt264u7vTr18/Dh48yMCBA4ut269fP86fP8+aNWtYunQpZveeehMWFoafnx8REREmd0KPHz8evV7/iK6qZlq0aBHjxo3DxqbqboB55plnCpX99NNP+Pv707ZtW2OZm5sbgwcPZuHChZIoCyEA023fgtq58uGLPjSsb1ndYYmaLuMGnN1luBnv0n7Q50F9Z/B+0ZAcN+8J9ayqO8paQ5Ze1HD29vYA5OXllVq3Y8eOZGVlcfPmTWOZVqvFxcWlyO2CzEp5hOT69evx8/PD1tYWe3t7fHx8WLVqVbH1J0yYwNq1a7l27ZpxmUGzZs0AyMnJISQkBG9vb2xtbXF1dWXw4MGcOXPGpI2CZSWxsbGMGTMGe3t73N3dmTx5cpHLSnQ6HbNmzcLNzQ1HR0cGDx5MQkJCidcFcPjwYU6cOMHo0aPLFH9lOXDgAL///jvjx48vdGzUqFHs3r2bq1evVmqfQojaRVVVtv2SwMAlP3Aq8TYLh7fn07EdJUkWxUu9CD8ug//rb1hWsfMdSL0And+AV3cbllUMWQZP9ZckuZzq1IzyvvDPSb586aHa0OXrMK9nXuHzXZo2J3DCXyrev05Hfn4+Op2OS5cuERoaiouLC7169Sr13Pj4eBwcHHBycjKWderUibVr1zJjxgxGjBiBj49PkUlzr169UFXV+P7AgQOMHTuWyZMns3DhQvR6PWfOnCE9Pb3Y/mfOnElKSgpxcXF88803AFhZGf5B5ubmkpGRwYwZM3Bzc0Or1bJy5Uq6dOnC6dOncXV1NWnrlVde4eWXX2bbtm0cOnSIOXPm0KBBAz744AOTegsWLKBr166sWbOG5ORkpk6dytixY4mOji5xrKKiorCzs6NDhw5lih8gPz+/xDYL1KtX/D+rtWvXYmlpycsvv1zoWPfu3dHr9ezZs4dXX321TH0JIeoW2fZNlImqQtKxeztVfAvJpwzlru0hMNSwU4VL28d2p4rKVKcS5bqgdevWJu/d3d3ZuXOncWb5fgVJdcEa5a1bt7JkyRLMzf9I9D/66CMuXLjA/PnzmT9/Pvb29gQGBjJ69GhGjBhRbByxsbE4OjqyZMkSY1n//v1LjL1FixY4OztjaWlZaMmBg4ODyY13Op2OAQMG0LhxYzZs2EBISIhJ/dGjRxuT4r59+3L48GE2bNhQKFFu1qwZ69evN75PSUlh2rRpJCYm4u7uXuL1+fj4mMyqlxQ/gIVF2faNvP8Lx/1ycnLYsmULAwYMMPkyU8DZ2RkPDw9iY2MlURbiMSTbvokS6fLhykHDwz/OfAu3E0Axg6bdIOgjQ3JcRx4bXZPUqUT5YWZyC2RkZGBnZ1cJ0VRMREQEHh4eqKpKYmIiK1asIDg4mJiYGNq0aWNS98GkeuLEiUyaNMmkzMXFhZiYGOLi4oiKiuLw4cPs3buX7du3s2fPHr744osi4wgICCAtLY2xY8cyatQonn32WRwdHR/q2jZv3szixYs5e/Yst27dMpY/uKsHwHPPPWfy3sfHh7179xaq9+BOET4+PgBcuXKlxEQ5MTERLy+vcsUfFxdXrvoPioyM5NatWyXeQOns7ExiYuJD9SOEqF1k2zdRrLtZhifinfkWzv0XstPuPTa6t2Hm+KkgqF944kVUnjqVKNcF3t7exhv0wDCL6+npyZw5c9i0aZNJ3YKkOiUlhbCwMFauXEnnzp0ZN25coXYDAgIICAgAID09neHDh7N69WqmTJmCt7d3ofo9e/Zky5YtLF++nBdeeMFYFhYWRvv27ct9XTt27GDkyJGMHz+e2bNn06hRI8zMzAgODi5y7XHDhqbPi7eysiI3N7dM9YAi27xfTk6OybKKsvD19S1X/Qf9+9//xtnZmX79+hVbx9ramuzs7IfqRwhRe5xKvM07m45y7kYm47o05b2BbbC2rPjyP1EHZGnh3G7DzXgXvrv32GgHeOreY6Nb9qnzj42uSSRRruGsra1p3rw5x48fL3Ts/qS6d+/etG/fnmnTpjFs2DDq1y/+H5GjoyOTJ0/mu+++49SpU0UmygDDhw9n+PDhZGZmEh0dzfTp0wkKCiIhIaHUGwEftHHjRlq2bEl4eLixLC8vD61WW652KouTkxNpaWnlOudhll5cv36d//3vf0yaNKnEdrRabYW+iAghapcHt30L/1MAvVq5VHdYorqkX/1jp4r4Hx94bPRzhuUVj9Fjo2sSSZRruKysLC5evEi7du1KrGdlZcXChQsZOnQoK1euZNq0aQAkJSXh5uZWqH7BbhNFHXuQra0tgwYN4tKlS0yZMoXU1FScnYvex9PKyqrIGdGsrKxCN7l99dVX6HS6UvuvCq1btyYmJqZQeXHxw8MtvVi3bh06na7I3S4K6HQ6rly5wksvvVThfoQQNZ9s+yZQVbh+4o/k+PoJQ3mjVvDsO4Zt3B7jx0bXJJIo1zDHjh3j5s2bqKpKUlISK1asQKvV8vbbb5d67pAhQwgICGDx4sVMmjQJa2trgoKC8PT0ZMiQIbRq1Yrs7Gz2799PWFgYXbp0oVu3bkW2NWvWLG7cuEFgYCDu7u4kJCSwbNkyfH19i02SAdq2bYtWq+XTTz/F398fjUaDj48PQUFBREZGEhISwqBBgzhy5AjLly9/6HXPFdWjRw++/PJLUlNTTW6sKy5+AH9//wr39+9//xsfHx/8/PzIyMgoss7JkyfJysqiR48eFe5HCFFzqapK5LFrzIr8Db2qsnB4e4Y/7VHkTkSiDtLlweUf4cwuOPtfuHUFUMCzM/Sba5g5dmpR3VGKB0iiXMPcP5vo7OyMt7c3UVFRDBgwoEznz5s3jwEDBvDZZ58REhJCaGgoW7du5eOPPyYpKQlVVfHy8mLq1Km89957xS6h6Ny5M8uWLSMkJMS4F3P//v2ZO3duif2/9tprxMbGEhoaSnp6Ok2bNiU+Pp7XX3+dq1evsmbNGlatWkVAQAA7duwwrn9+1IYOHYpGo2Hnzp0ms7zFxf8wjh49yokTJ0welV2UnTt34urqWqatAIUQtUvanbvM2H6Sb48btn0LG+HLE06y7Vudl5uBc/KPsPVrOL8bcm79cTNez38YbsazlSct1mRKcVtZVTd/f3/1yJEjxR4/ffp0oV0gKkN173pRG9XWMZswYQIJCQlF7qZRlYobr7Zt2zJs2LBSv4xA1X3+a6Lo6Gj58lAOMl7lV9Vjtu9MMv/Yepz0rLu80/epWr/tm3zGSpFx/d6Sim/h9xjQ3QXrhtBqILQKhhaBcjNeKR71Z0xRlJ9VVS3y18YyoyweW7Nnz6ZNmzYcOXLkoZZVVIbt27dz48YNpk6dWq1xCCEqz53cfOZ9e5oNP12hVWM7wv8UQDt32fatzlFVSDljSIzP7oJrPxvKG3hBp79wNNsdvyF/BTPZzaQ2kkRZPLa8vLwIDw8nOTm5ukMhOzubdevWVduabSFE5YqL1zJ1869cTcvijR7NCen3FBoLSZTqDL0Orh7+IznW3nsqsHtH6D3TsN7YuTUoCreioyVJrsUkURaPtVGjRlV3CEDNiUMI8XBy83WE7TnH5zGX8Ghgzaa/dKGTV8PSTxQ1390suLTPcDPeuf9CViqYW4JXD+gyybCswr70naRE7SKJshBCCFEJTiXe5m+bj3HmegYvd/Lk/efaYmsl/5ut1e7cNOxQcXYXXNxnePiHlQM81d+QGLfsCxr76o5SVCH5FyyEEEI8hHydnlUxl1iy9xwO1pasmeBP79aNqzssUVGpF/9YUnElFlDB3kMe/vGYkkRZCCGEqKD4m3f42+Zj/HIlnWAfV+Y9Lw8PqXX0ekj8xZAcn/kWbp41lDf2gZ7ToXUwuLaXh388piRRFkIIIcpJVVW+PnyF+d+exsJcYekoX4Z0cJeHh9QW+bmGrdvO7ISzUZB5HRRzaNYN/F81bOXWoGl1RylqAEmUhRBCiHK4fiuHf2w9Tsy5FLo/2Yh/DW+Pm4N1dYclSpOlhfP/MyypuPAd3M0ES1to2QdaPQdP9gMbufFSmJJEWQghhCijb35NZGbkSXLzdcwd2o6xzzSVWeSa7Ob5ezfj/ReuxoKqB1tX8BkOrQdBs+5goanuKEUNJomyEEIIUYq0O3eZuf0kO48n4evpSNiIDjR3tq3usMSDdPmG/Y3P7oJzUZB6wVDe2Ae6/92wpMLNF8zMqjVMUXvIJ6WGCA8PR1EU48vc3JwmTZowYsQIzp49W2JdS0tLWrRoQWhoKDk5OYXa3r9/P0FBQbi7u6PRaPDw8CAoKIivv/7aWCc6OhpFUYiPj3+o64iMjCQsLOyh2iiL+Ph4FEVh9erVFW5Dr9fj6+vLokWLjGVVEf/atWt5+umnsbe3x9nZmaFDh/LDDz+Y1FmyZAk+Pj7o9fpK7VsI8fD2nU1mwJIYok5e5+/9n+I/f+0iSXJNknMbfouAbX+BRS0hPBgOrwLHphC8CN45CW8egN7vQ5OOkiSLcpFPSw2zZcsWDh06RExMDAsWLODo0aP06dOHW7duFVv322+/ZcCAASxYsIBp06aZ1ImMjCQwMBCNRsOKFSuIiopi/vz5NGrUiF27dlV6/I8qUa4M69atIykpiYkTJxrLKjv+zz//nAkTJtCpUye2bt3K6tWruXv3Lv369ePo0aPGem+88QYpKSmsXbu20voWQjyc2zl5TP/Pcf70ZRyONhZEvtWNSb2fpJ65/K+z2qVfgcOfw7+fh381hy0T4PweeCoIRvwbpv8Or2yDTq+Do2d1RytqMVl6UcP4+vrSsmVLALp164a7uzv9+vXj4MGDDBw4sNi6/fr14/z586xZs4alS5didu8bc1hYGH5+fkRERJisoxs/fvxjP3u5aNEixo0bh42NTZX1ER4eTpcuXfj000+NZQEBATRr1ozNmzfj5+cHgLW1NePGjWPRokX86U9/qrJ4hBBl88P5FKb/5zjXb+fw154teKfvk/II6uqk10PiUcMT8c7+F26cNJQ3egqeedPw8A/PTvKoaFHp5GtxDWdvb3jiT15eXql1O3bsSFZWFjdv3jSWabVaXFxcirzZxKyUXz+tX78ePz8/bG1tsbe3x8fHh1WrVhVbf8KECaxdu5Zr164Zl4U0a9YMgJycHEJCQvD29sbW1hZXV1cGDx7MmTNnTNooWFYSGxvLmDFjsLe3x93dncmTJxe5rESn0zFr1izc3NxwdHRk8ODBJCQklHhdAIcPH+bEiROMHj26TPFX1N27d41/hwVsbGywsLAo9EVl1KhRnDp1ioMHDz5Un0KIisvMzee9bSd45f9+wtrSnK1vduXdga0lSa4Od7MMSfE3kyGsNazuDT+EgcYR+s+DST/DpDjoPxeadpEkWVSJOjWjnL7jIncT7zxUGzpdPtnmFR8WS/f6OA5u8RD968jPz0en03Hp0iVCQ0NxcXGhV69epZ4bHx+Pg4MDTk5OxrJOnTqxdu1aZsyYwYgRI/Dx8Skyae7VqxeqqhrfHzhwgLFjxzJ58mQWLlyIXq/nzJkzpKenF9v/zJkzSUlJIS4ujm+++QYAKysrAHJzc8nIyGDGjBm4ubmh1WpZuXIlXbp04fTp07i6upq09corr/Dyyy+zbds2Dh06xJw5c2jQoAEffPCBSb0FCxbQtWtX1qxZQ3JyMlOnTmXs2LFER0eXOFZRUVHY2dnRoUOHMsUPkJ+fX2KbBerV++PzM3HiRP7yl7/wf//3fwwbNow7d+4we/ZsLCws+POf/2xynq+vL3Z2dkRFRdG1a9cy9SWEqDw/XrjJP/5znMRb2fylR3P+1u8pSZAftYwbhpvwzv4XLkUbHhltaQdP9v3jkdGyhZt4hKosUVYUZTjwMuAPuABXgG3Ah6qqZlRVv7Vd69atTd67u7uzc+fOQrOS8EdSnZGRQUREBFu3bmXJkiWYm//xH/aPPvqICxcuMH/+fObPn4+9vT2BgYGMHj2aESNGFBtHbGwsjo6OLFmyxFjWv3//EmNv0aIFzs7OWFpa8swzz5gcc3BwMLnxTqfTMWDAABo3bsyGDRsICQkxqT969GhjUty3b18OHz7Mhg0bCiXKzZo1Y/369cb3KSkpTJs2jcTERNzd3Uu8Ph8fH5NZ9ZLiB7CwKNsjS+//wvHqq68ChoT5tddeA6Bx48bs2bOHp556yuQ8MzMzOnToQGxsbJn6EUJUjpx8lZmRJ/kq9jJejerzn7924emmkow9EqoKN377Y0nFtZ8N5Y5PQMdxhl0qmnaDevK0Q1E9qnJG+e8YkuNQIAHwA+YAgYqidFVVtdIXyD7MTG6BjIwM7OzsKiGaiomIiMDDwwNVVUlMTGTFihUEBwcTExNDmzZtTOo+mFRPnDiRSZMmmZS5uLgQExNDXFwcUVFRHD58mL1797J9+3b27NnDF198UWQcAQEBpKWlMXbsWEaNGsWzzz6Lo6PjQ13b5s2bWbx4MWfPnjW5OfHBXT0AnnvuOZP3Pj4+7N27t1C94ODgQvUArly5UmKinJiYiJeXV7nij4uLK1d9gO3bt/PWW2/xxhtvMGTIELKzswkLCyM4OJh9+/bh7e1tUt/Z2Zlz586Vux8hRMUcupjKzB+zuZlzmT8/68Xf+7fC2lJmkatUfi7EH4Bzuw3J8a0rhvIm/tB7piE5dmkrj4wWNUJVJsqDVVVNue/9fkVRtMBaoBfwfRX2XWt5e3sbb9ADwyyup6cnc+bMYdOmTSZ1C5LqlJQUwsLCWLlyJZ07d2bcuHGF2g0ICCAgIACA9PR0hg8fzurVq5kyZUqhZA2gZ8+ebNmyheXLl/PCCy8Yy8LCwmjfvn25r2vHjh2MHDmS8ePHM3v2bBo1aoSZmRnBwcFFrj1u2NB0NsfKyorc3Nwy1QOKbPN+OTk5JssqysLX17dc9VVV5S9/+QvDhw9n6dKlxvIuXboQEBDAzJkziYiIMDnH2tqa7OzscvUjhCi/rLv5/CvqLOEH43GxUdj8RhcCmskscpXJuG54Kt653XBxH+TdgXrW0CIQek6DJweAXePqjlKIQqosUX4gSS5QMCXXpKr6rWusra1p3rw5x48fL3Ts/qS6d+/etG/fnmnTpjFs2DDq169fbJuOjo5MnjyZ7777jlOnThWZKAMMHz6c4cOHk5mZSXR0NNOnTycoKIiEhIRSbwR80MaNG2nZsiXh4eHGsry8PLRabbnaqSxOTk6kpaWV65zyLr24ceMGycnJxi8oBSwtLenQoQOnT58udK5Wq6VRo0bliksIUT4//a5l2n9+5XJqFhO6NqOLTbIkyZVNr4eko4bE+NxuSDpmKHfwhA6jDNu4eXUHC3n0t6jZHvXNfD3v/SycIYgiZWVlcfHiRdq1a1diPSsrKxYuXMjQoUNZuXKlcT/lpKQk3NzcCtUv2G2iqGMPsrW1ZdCgQVy6dIkpU6aQmpqKs7NzsXEUNSOalZVlcpMbwFdffYVOpyu1/6rQunVrYmJiCpUXFz+Uf+lFgwYNsLKy4qeffjIpv3v3LseOHaN58+aFzvn999/p1KlTufoRQpRN9l0dC3ef5cuDv+PRwJqNf3mGZ5o7ER1d1LyOKLec23BpH5z7n2H2+E4yKGbg0Qn6zIanBsiSClHrPLJEWVGUJsA/gb2qqh4pps5fgL+A4YanknYucHBwICOj8u8J1Ol0VdJuaQqWChw6dIjLly+jqio3btzg888/R6vV8tprrxnjKqibmZlpEmtgYCAdO3Zk0aJFjB8/Hmtra/r370+TJk0IDg7mySefJDs7mx9//JEVK1bQqVMn2rdvX+T1zps3j5SUFLp3746bmxvXrl1jyZIltG/fHo1GY3LO/WPWvHlztFotn3zyCX5+fmg0Gtq1a0evXr2IjIzkrbfeIigoiKNHj7Jq1SocHR3Jy8sr9doKll0UlGVmZhrr318vKyvL+LOkv8dOnTrx5ZdfEh8fb7JLSHHxA7Rq1arY9u53f7/jx4/n888/x9bWlqCgIHJycli1ahXx8fEsWLDApG56ejrnzp1j0qRJpX4Gc3JySt3Zo64o+I2GKBsZr6Kd0er48mQuN7JU+jxRj5eeUsi5coLoKzJm5XX/eFlnJeGUGodTahwOt05hpuaTV68+2oYdSX1iDNqGHcm3sAcdcDoFTu+v1tirg3y+yq9GjZmqqlX+AmyBI0Ai4FGWc55++mm1JKdOnSrxeEXdvn27StotzZdffqkCJi9nZ2c1MDBQjYqKKrLu+fPnC7Wze/duFVDDwsJUVVXVjRs3qi+99JLavHlz1draWtVoNGqbNm3U9957r8Rr3blzp9q/f3/V1dVVtbS0VD08PNRXX31VvXbtWqG697eTmZmpjho1SnV0dFQBtWnTpqqqqqpOp1Pff/991c3NTbW2tlZ79Oih/vLLL2rTpk3V8ePHl3pts2fPVg0fV4Pff/9dBdQvvvjCpN6+fftUQN23b1+x16aqqqrValWNRqOGh4eblBcXf0Xl5eWpy5cvVzt06KDa2tqqjRo1Up999ll19+7dhequW7dOtbKyUm/evFlqu1X1+a+JSvu7FKZkvEzdzr6rhm47rjadvlPt/vH36o/nUwrVkTErh7xc9ei2paoaFaqqyzqq6mx7w2tFJ1X930xV/f2AqubnVXeUNYp8vsrvUY8ZcEQtJh9V1Pu2sqoKiqJYA7uADkBPVVVPlOU8f39/9ciRIieeATh9+nShXSAqQ3XvelEb1dYxmzBhAgkJCUXuplGVihuvgQMH0qhRI7766qtS26iqz39NFB0dXaZ9xIWBjNcfvj9zg/cjTnLjdg6vdvNiajE7WsiYlSIzBS7sMexvfHEf5N4Gc0to1t2w1vip/tCgWXVHWWPJ56v8HvWYKYrys6qq/kUdq9KlF4qiWAD/wbCXcr+yJslCPAqzZ8+mTZs2HDlyBH//Iv99PDLHjh3j+++/57fffqvWOISoC7R37vLPHb8ReSyRpxrbsnJMV/yeaFDdYdUeej1cP/7HLhXXfgZUsHWFdi9w4m4TfAa/BVa21R2pEFWuKh84YgZ8DfQGBqmqKk9REDWKl5cX4eHhJCcnV3coXL9+nfDwcJOtAYUQ5aOqKjuOJzHnm9/IyMljSp8neSuwJZb1yrdLz2MpOw0ufg/n98KFvYYb8VCgSUcIDIUn+4NbB1AUUqOjJUkWD0VVVdJy00jISOBqxlXjy93Wnbd836ru8ExU5Yzy/wNeAuYDdxRFuf9RZwmqqiZUYd9ClMmoUaOqOwQAgoKCqjsEIWq1G7dzeD/iJHtP36CDhwMfD+9Ma9fCTzQV9+j1cP3Xe4nxHkiIA1UPGkdo0Rue7Gd4XLStS3VHKmqpfH0+1+9cNybBCRkJJGT+kRjfybtjUt/FxoXuTbpXU7TFq8pEeeC9n+/fe93vAwxP6RNCCCEqTFVVNsVdZf6u0+Tp9Lwf3IZXn/XC3Ey2ICskS2uYNb5QMGt8b1s8N1/oPhVa9oMmT4P5o945VtRWWXlZxiT4asZVk0Q4KTOJfDXfWNfCzIImtk3wtPOko0tHPO088bTzxMPOgya2TdDU01TjlRSvKh840qyq2hZCCCEuJGcQGnGSn37X8kzzhnz0YnuaNSr+YUuPHb3e8KCPC3vh/B64dsQwa2zdAFr0Mcwat+gts8aiWKqqkpqTajIrfP9SCW2O6UPD7C3t8bTzpJ1TO4KaBeFh52FMiF1sXDBTat8yKPnaKIQQolbJydPx//Zd4LP9F7GxrMdHL/owwt8TM5lF/mPW+PweuPjdvVljBdz9oMe0e7PGHcGs8O4f4vGUlZdFYmYiCZkJJGQkcC3zmnGZxLXMa2Tn//EQLgUF1/queNh50Muzl3FG2NPOEw9bDxysHKrxSqqGJMpCCCFqjR/OpzAj8iSXU7N40a8Joc+1oZGtVXWHVX10+ZD4yx9LKq79fG/WuCG07GNIjFv2gfqNqjtSUU10eh03sm6YJMDGRDjjGqk5qSb1retZG5PfZ9yeMUmGm9g2wdLcspqupHpIoiyEEKLGS8nIZd63p9h+LBGvRvX5+rXOdGv5mCZ/2t8NifHF7+H3HyD3FsYdKnr8w7Ckwt1PZo0fE6qqcvvu7T8S4Ptmha9lXiPxTiL5+j/WCpsr5oZZYVsPenr2xMPWw7hO2MPOgwZWDVDkMeNGkigLIYSosfR6lQ1xV/j4v2fIydMzpc+TvNmrBRqLxygJzLkFv8fcS473QdrvhnIHT2g31LDO2Ksn2DSs3jhFlbmru8u1zGsmCfD9s8IZeRkm9R2tHPGw9aCtU1v6Ne1nkgi71nfFwsyimq6k9pFEWQghRI10KvE2MyJP8MuVdJ5p3pD5L/jQwvkx2L9Xl29YQnHxe7i0DxKOgKoDS1vD0/CemQgtAsGpJcjMX52g0+tIyU4xzABnJposkbiWeY3krGRU/niSsqWZJU3smuBh64Gvsy8edoZZYQ9bQ0Jsa/kY/Dt5RCRRriHCw8P505/+ZHxvZmaGq6sr3bp1Y+7cubRq1arYuhYWFnh6ejJy5EhmzZqFRmO6xcr+/ftZsGABx48fR6vV0qhRI7y9vXnllVcYM2YMYHhcZGBgIL///jvNmjWr8HVERkZy6dIl/va3v1W4jbKIj4/Hy8uLL774gtdee61Cbej1ejp27MjYsWP5+9//DlRN/J9++ilLly7l999/p3HjxowaNYr58+djYfHHN/p33nmHc+fOsWvXrkrrV4jaKu3OXcL2nOPrw5dxtLFk8UsdeLFjk7r962DtJcNs8cXvDbPHubcxLqd4NsQwa+wRAPUer/WhdcWDiXDBz4I/X79z3WQrNQUFFxsXmtg2obNb50LLIxpZN6qVO0jURpIo1zBbtmzBw8MDnU7HxYsXmTt3Ln369OG3337DwcGhyLoZGRlERESwYMECMjIyWL58ubFOZGQkL774IkOGDGHFihU0bNiQy5cvs2fPHnbt2mVMlCtLZGQke/furfJEuTKsW7eOpKQkJk6caCyr7PgXLFjA+++/T0hICEFBQRw7dozZs2ej1WpZvXq1sd706dNp3rw5+/btIzAwsFL6FqK20elV1v90hcX/O0tGTj7jujQjpO9TONjUwV8T306C+B/g9/2GxDj9iqHcwRPaPS/LKWoZnV5HclaycU3w/YnwpZuXSF+XbpIIAzhbO+Nu646Psw9BXkG427rTpH4T3GzdcLd1x8r8Mb5JtQaRRLmG8fX1NT7GuFu3bri7u9OvXz8OHjzIwIEDi63br18/zp8/z5o1a1i6dClmZoZvmmFhYfj5+REREWEyGzN+/Hj0ev0juqqaadGiRYwbNw4bG5sqaT8nJ4cPP/yQcePGsXjxYsDw93T37l1mzpxJSEgI7dq1A8DNzY3BgwezcOFCSZTFY+nwpVTm7DjF6aTbPNO8IXOGtKtbT9bL0t5LjGMMr5vnDOUaB8Nyii6TDMmxLKeokfL1+aRkpRSZCF/LvMaNOzcKJcIu1i6427rT1LIpz7d43pgIu9u642brJolwLSGJcg1nb2/4H0VeXl6pdTt27MjevXu5efMmLi6GDeS1Wi2enp5F/sqyIJkuzvr161m4cCHnz5/HzMyMpk2bMmnSJN54440i60+YMIG1a9cCGPtr2rQp8fHx5OTk8N5777Fnzx7i4+OxtbUlICCAhQsX0rp1a2MbBctKDh06xPLly9mxYwe2trYMHz6cf/3rX4WWleh0OmbNmsUXX3xBdnY23bt359NPP8XDw6PEazt8+DAnTpwwxlta/BVx8uRJMjMzC33B6du3LzNmzCAyMtKYKIPhcdovvfQSV69exdPTs0J9ClHbJN3K5sNdZ9jxayJNHK1ZOaYjA71da/8yi5zbcOXQvcR4P1w/YSi3qA9Nu4LfK+DVA1x9ZHeKGiAnP4frd66TdCfJ+DMxM5HEO4Zk+Pqd6+hUnck5BYlwB+cONPEyJMDutu40sW2Ca31XYyIcHR1Nr469quGqRGWoU4nyf//7X65fv/5Qbeh0OszNK/4fLVdX10KJUXn7z8/PR6fTcenSJUJDQ3FxcaFXr16lnhsfH4+DgwNOTk7Gsk6dOrF27VpmzJjBiBEj8PHxKfJ/QL169UJV/7hR4MCBA4wdO5bJkyezcOFC9Ho9Z86cIT09vdj+Z86cSUpKCnFxcXzzzTcAWFkZ/kORm5tLRkYGM2bMwM3NDa1Wy8qVK+nSpQunT5/G1dXVpK1XXnmFl19+mW3btnHo0CHmzJlDgwYN+OCDD0zqLViwgK5du7JmzRqSk5OZOnUqY8eOJTo6usSxioqKws7Ojg4dOpQpfoD8/PxC7RSlXj3DP6uCz5GlpemawoL3J0+eNCnv3r07er2ePXv28Oqrr5apLyFqq4ycPD6PucTqH35Hp6pM7vMkb/ZsgbVlLU0ac27D1Z/g8o+GmeNrvxhuwDO3As9OEDjDkBg36QjmdXApSQ2mV/WkZqeSdCfJmAgXJMMF7x98wpyCgrO1M03smuDr4ot7fUMCXJAMu9V3e+z2E35c1alEuS64f3YVwN3dnZ07dxpnlu9XkFQXrFHeunUrS5YsMUn0P/roIy5cuMD8+fOZP38+9vb2BAYGMnr0aEaMGFFsHLGxsTg6OrJkyRJjWf/+/UuMvUWLFjg7O2NpackzzzxjcszBwcFkTa5Op2PAgAE0btyYDRs2EBISYlJ/9OjRxqS4b9++HD58mA0bNhRKlJs1a8b69euN71NSUpg2bRqJiYm4u7uXeH0+Pj4ms+olxQ+Y3HxXkoIvHE8++SRmZmbExsbywgsvGI//9NNPgGG2/37Ozs54eHgQGxsribKos+7m61l/+DLLvr+A9s5dBrV3Y3pQazwbVs0SqCpz5yZcPmiYNb78o2HGWNWDYg5NnjbcgOfVw5AkW1hXd7R1WlZeljHpLZQIZyZxPeu6yT7CADb1bHC3dce1vivtnNrhWt8Vt/puxp+NbRpjIV9oBHUsUX6YmdwCGRkZ2NnZVUI0FRMREYGHhweqqpKYmMiKFSsIDg4mJiaGNm3amNR9MKmeOHEikyZNMilzcXEhJiaGuLg4oqKiOHz4MHv37mX79u3s2bOHL774osg4AgICSEtLY+zYsYwaNYpnn30WR0fHh7q2zZs3s3jxYs6ePcutW7eM5WfPni1U97nnnjN57+Pjw969ewvVCw4OLlQP4MqVKyUmyomJiXh5eZUr/ri4uHLVt7W15dVXX2XFihX4+fkRFBTE0aNH+ec//4m5uXmRS1+cnZ1JTEwsVz9C1AZ6vcq3J5JY9L+zXE7NoktzJ94d2JoOno7VHVrZpF+By4fgykFDglywxriexrAbRfe/G5ZUeASAlWzNVVmy87NJzkomOSuZ63eucyPrBjfu3DCZEb5997bJOeaKOc42zrjVd8PH2Yf+9fvjVt/tj0TY1g07C7vav7xHPBJ1KlGuC7y9vY036IFhFtfT05M5c+awadMmk7oFSXVKSgphYWGsXLmSzp07M27cuELtBgQEEBAQAEB6ejrDhw9n9erVTJkyBW9v70L1e/bsyZYtW1i+fLlxNrRnz56EhYXRvn37cl/Xjh07GDlyJOPHj2f27Nk0atQIMzMzgoODycnJKVS/YUPTO72trKzIzc0tUz2gyDbvl5OTY7Ksoix8fX3LVR9g8eLFpKamMnr0aFRVRaPR8P7777N06VLc3NwK1be2tiY7O7vc/QhRU6mqSvS5FD7Zc47jCbdo7WrHl38KoNdTzjU3UdHlwY3fICHOsJziyiG4ddVwzMoBnugMvqPhia7g7gv15Kas8ip4mtyNrBskZyVz4869n1k3/njduVEoCQaws7DDzdaQ+Pq6+BqT4IKyRtaNqGcm6Y2oHPJJquGsra1p3rw5x48fL3Ts/qS6d+/etG/fnmnTpjFs2DDq169fbJuOjo5MnjyZ7777jlOnThWZKAMMHz6c4cOHk5mZSXR0NNOnTycoKIiEhIRSbwR80MaNG2nZsiXh4eHGsry8vELLDx4VJycn0tLSynVOeZdegOFmzG3btpGSksL169dp1qwZycnJzJw5k2effbbQuVqttkJfRISoaVRV5bvTySz7/jzHE27RxNGaRS914AW/Jpib1awE2TI3FU5tNyTGCUcg8Rjk3/vCWt/FMFPc9W3DT5e2cvNdKfL0eaRmp3Iz+6ZJImz8872f2fmFJwWcNE40rt+YJrZN6OjSkcY2jWlcvzEuNi6GP9s0xsaili3TEbWaJMo1XFZWFhcvXjTZHaEoVlZWLFy4kKFDh7Jy5UqmTZsGQFJSUpEzl2fOnAEo8tiDbG1tGTRoEJcuXWLKlCmkpqbi7OxcbBxFzYhmZWUZb3Ir8NVXX6HT6QrVfRRat25NTExMofLi4ofyL724n7Ozs3HMCmbUX3rpJZM6Op2OK1euFCoXojbR6VX2nLrO8u8v8FvibTwbWvPxMB9e8PPAsl4NeEBCboZhPXHCEWNi3DUjEQ4B5pbg1gH8/wQe/oZlFA6esl3bPVl5WdzMvsnFnIvkxudyM/smKVkppGSnkJqdSkp2Cjezb5KWk2byFDmAeko9XGxccLFxoXXD1vT06GlIfus3NibAztbOsi5Y1DiSKNcwx44d4+bNm6iqSlJSEitWrECr1fL222+Xeu6QIUMICAhg8eLFTJo0CWtra4KCgvD09GTIkCG0atWK7Oxs9u/fT1hYGF26dKFbt25FtjVr1ixu3LhBYGAg7u7uJCQksGzZMnx9fYtNkgHatm2LVqvl008/xd/fH41Gg4+PD0FBQURGRhISEsKgQYM4cuQIy5cvf+h1zxXVo0cPvvzyS1JTU012CSkufgB/f/9y97Np0ya0Wi2tWrUiLS2Nbdu2sXnzZrZu3VpoLfzJkyfJysqiR48eD3dxQlSD2zl5bI67SvjBeBLSsmnqZMPC4e153q8JFubVlCDfuQlJvxpe149D0nHDE/AKkjjHptC0K+dzHHmy18uGrdoes2UUefo80nPS0eZoSc1JNSa8KVmmyW9Kdgp38u78ceINw496Sj2crJ2MD89o79weZ2tnGlk3wtnaGZf6hpnghpqG8iS5OkxVVdS8PNSsLPQ5OeizslFzstFnZ6PPykKfde9ndpahjvG9abnVk0/R+L13q/tyTEiiXMPcP5vo7OyMt7c3UVFRDBgwoEznz5s3jwEDBvDZZ58REhJCaGgoW7du5eOPPyYpKQlVVfHy8mLq1Km89957xS6h6Ny5M8uWLSMkJAStVouLiwv9+/dn7ty5Jfb/2muvERsbS2hoKOnp6cZ9iF9//XWuXr3KmjVrWLVqFQEBAezYscNkN4hHaejQoWg0Gnbu3Mn48eNLjb+iFEVh5cqVXLx4kXr16vHMM8+wa9cu+vXrV6juzp07cXV1LdNWgELUFGevZ7DhpytsOXKVO3d1dPJqyIzn2tKvbeNHt8Qi/y5oL0LKGUg+bUiIk36FjPtujHV4AtzaQ4dR4NresE2brWG/+WvR0TzpUf4vwjWRXtVzK/cW2hxt4Ve2lrTcNFKzU41lRa0BBrCuZ21Mdp9q8BTdmnQzvk88n0jvzr1xtnHG0cpREuBaQNXpUHNyDIlpTg76rCzD+6xs9DnZpn/OzkafnWNIXrMLzslGzbp3bva9Ovf/OTsbyvMQM0XBzNoaxcYGMxsbzKytMauih389LOX+9ZQ1ib+/v3rkyJFij58+fbrQLhCVobp3vaiNauuYTZgwgYSEhCJ306hKxY1X27ZtGTZsWKlfRqDqPv81UXR0tHx5KIdHMV7JGTnsOp7E1l+uceLaLSzMFQZ3cOfVbl54N3Gouo5zbkNavGHHiZSzkHLa8DP1omHPYgAUaPSUISl2bW9YSuHqU+KjoGviZ0xVVbLzs7l99zbpuencyr3FrdxbpOemc/vubZP3t3JvcfvubdJy0kjLTUOvFk5YFBQcrRxpqGlIA00DGmoamr6sG9LAqoEhGbZxpr5F8fe51MTxqsmKGi9Vrzckp7m5qDk5qLm5xj/rc3JR7+aiz8lBzclFzb1XlpuLPrcMZfclxAUzvGoRN8OXRrGyMiSz1taGRFajQbGxxkxjfa9cg5m1zQPlGkN9jTVmNtbGBFixtsGs/h8JsaLRlHgz76P+jCmK8rOqqkV+W5YZZfHYmj17Nm3atOHIkSMVWlZRmbZv386NGzeYOnVqtcYhRFF0epXTSbf54fxN9py6ztGr6agqtHO3Z/bgtgzp4I6TbSUsWcjNhMwbcCvBkBA/+Mq+7+ZfxQwaNgfn1tBmsOGncytwehIsq39mKk+fR+bdTDLzMgv/fKAsIy+DO3l3yLybaUyC03PTydMX/0RWjbkGBysH48vLwQtfF19j4uukcTJJiB2tHDF/zG9CVFUV8vLQ381DzbuLerfol97457w/yvNKO573QBu595LXXJy0Wi6YzzNJitUyPG23WPXqYWZpaUg2NVaYWWlQNBpjmbmdXdEJ7QNJrKL5o7xQQmxtjVLOm/brKkmUxWPLy8uL8PBwkpOTqzsUsrOzWbduXbWt2RaPD1VVyder5OtU8vR68nUq+To9eXqVvHw9+Xo96Vl5XEq5w6WbdziVdJtfLqeRmWt4YINPEwdC+j7FgHautHK1u79hw7Zq+TmoedmGnwV/vpuJmp2GmpMO2emQkw7Zt1CzUlEzb0DmddSMZNS8TENTBW2a1UO1bwKOTVHbPAeOT6A6eKI6tYCGzVHvu/Gr4Lejel0O6r0bclVVRb1vdjVPl0ee7i55+jzD6977s5mnMb8Md/V375WZHs/WZZOTn0N2fjY5edmGn/m55ORnk6PLMfzMzyErP5vce/UKktwH58yU+36Ja2lmia1Ffepb2FLfwob6lrY0tvTA3rYt9lb22Fs54GBhh4OlA3ZW9thb2eNgYY+9pR1W9TR/jLvpX3Dh97lAbgY6THflMVbR6VB1OsOvznU6VL0e9HpUnR70ukI/6128xB07O0PdouqoKvp77an3/9TpQTW0q+bnQX4+an4+at69nwVlefmGmPLzUPN1YDx+76XLe6DMULdwvfw/yu4lsA/8bRQai+KohaoqKJaW970sUCwtMLOwRLG4V6axwcy+Abma+jh6NEGx0qBYWmKmsQIrDWZWVoYyKwtDcmqpwUxjiWJlhWJpZSizsrr3srx33AqlXtGpW2WsENDfe3H33p/Ue/8eVfWPj5aK4WZN9Y+Pm7FvY5lqeuy+P6sqJu/vNQ8q1LMyw96pZj2gRxJl8VgbNWpUdYcA1Jw4RN2xcfa/iFfzyFcebmeZp+69KJgwvgm3Y2BL4U1jysn+3quEB//oAe29FwA5wPl7r8q1Py6lTPXMsKA+FhS/MKFy3CaX2ySTQPV/kS9K9JWER9CLGdQzg3q1fCcM18Z//Dk/DzLzIDOz+uKpwRrqbJg47+/VHYYJSZSFEKKOSb+eQoKqwxyFRtma+47cP+NU2mxaQV3lvppFzVjd345aRBl/bK9W5IyXct/xom4GesjjinIvHrVQ/wqAYoZa8GdVb7wE4xWYmRvaUNWib1YyNzMc1xd33NzQWBmOK0Udr3dvuURx5xuP6w11HrxA83IcL/T3o/zRvk5nPK6qqmF9qaJAwexmvu6B8b933OLe8bz8wu2bmYFFPcNY382j0OfLzAwK9q/PvVv4uPl9SXRRa3DNze/Fp947v5jjqgqFZpsxHDM3L/24XoW8oo5bgLkZuvw8zHVF/N1ZWBiuUa+HopZiFBzX6Q0JdrHHdZCfX/i4paXh76DU4/mGv78HWVkCiuHcorZytbIyfIbyijmuufftOi/P5Ljh353yx/G7fxy3vW8XqpqiVifKxn+sQjxGauoNuKLm2PZJOJnWuTTN0PGnP78MjRqBiwvcvg12drIv8APk5rTykfEqHxmv2q3WJsoWFhZkZ2djU0O3ExGiqmRnZ5f78dvi8aK1ysc5rz4Bk8bA8wPB0RH27wd7++oOTQghapVae0uji4sL165dIysrS2bYRJ2nqqrxkd8JCQkmD0kR4kF5ig7LfPBOuw7Hj8PLL1d3SEIIUSvV2hll+3szI4mJieQ9zDYrD8jJyUGj0ZReURjJmJVPRcerXr16aDQannjiCRlvUaI8dCiqCv/+t2Ed4siR1R2SEELUSrU2UQZDsmxfyb9KjI6Oxs/Pr1LbrOtkzMpHxktUpZz02+gVFTO9HtavhyFDoEGD6g5LCCFqpVq79EIIIURh2deTAAw7KKSkwLhx1RyREELUXrV6RlkIIYSpHO1tABRFhcuXoXHjUs4QQghRHEmUhRCiDsnPyoV6YGamwhNPVHc4QghRq8nSCyGEqEP0dw27AJnlZkFkZPUGI4QQtZwkykIIUYfo7z0Ay1J7A376qXqDEUKIWk4SZSGEqEtUw1P3rNNTwcenmoMRQojaTRJlIYSoSxRzAJySEyVRFkKIhySJshBC1CF6xfCf9SeuXoVWrao5GiGEqN0kURZCiDpENVOop5rh5u4OFhbVHY4QQtRqkigLIUQdojdTsFDNMY+Lq+5QhBCi1pNEWQgh6hCdAvVUMzCT/7wLIcTDkv+SCiFEHaI3Uw2J8r591R2KEELUepIoCyFEHZKvqNRTFcjMrO5QhBCi1pNEWQgh6pB8RY+ZXgFPz+oORQghaj1JlIUQog7JV/SY61V44onqDkUIIWo9SZSFEKIOyVN0mKlAgwbVHYoQQtR6kigLIUQdkZmqJV/Ro+j1oCjVHY4QQtR6VZooK4riqSjKfxRFuaUoym1FUbYpiiK/DxRCiCpw8cQJAMxUtZojEUKIuqHKEmVFUWyA74HWwHjgFeBJYJ+iKPWrql8hhHhcpVyIB0BRJFEWQojKUK8K234daA60UlX1AoCiKMeB88AbQFgV9i2EEI+d2ze1AJjp8qo5EiH+f3v3HR5Hdbd9/HtWq14sS7ZlW7Jxw73iTrXpvQUCpJBAgLQntNADPCSBJCQhCaQ8vCQhISHBGFNCNd0EMNW4YVsuuMq2ZEmWrF5297x/zMpeyStba2s1Wu39ua69RpqZ3fnpaLS6dXTmjEjPEM2hF+cCH7aEZABr7SbgfeC8KB5XRCQuNe6pA8CL3+VKRER6hmgG5XHA52HWrwLGRvG4IiJxydfkBOTElGj+s1BEJH5EMyjnABVh1u8GNG+RiEgnCwScmS7SczJdrkREpGcwNkpXRxtjmoDfWGtva7P+XuA2a+1+XR7GmGuAawDy8vKmzps3Lyq1HUhNTQ0ZGRldftxYpjaLjNorMmqvjtv0/PtsyWpmbFY2/Y6a7HY5MUPnWGTUXpFRe0Wuq9ts7ty5S6y108Jti+b/5yoI33PcXk8z1tpHgEcApk2bZufMmRO14tqzaNEi3DhuLFObRUbtFRm1V8dtfOFDoJljzz2HgSOGu11OzNA5Fhm1V2TUXpHrTm0WzaEXq3DGKbc1FlgdxeOKiMQl6/HgsUYhWUSkk0QzKD8PzDLGDGtZYYwZAhwT3CYiIp0o4DEkkuB2GSIiPUY0g/Kfgc3Af4wx5xljzgX+A2wD/l8UjysiEpf8Hki0CsoiIp0lakHZWlsLnAisA/4J/AvYBJxora2J1nFFROJSTQ1+A95ANPs/RETiS1Qn27TWbgW+FM1jiIgIsG0bfo/Fa43blYiI9BjqehAR6Qm2bcNvAiQoKIuIdBoFZRGRnmDbNppNAE/A7UJERHoOBWURkZ7giCNoNn48gejcREpEJB4pKIuI9ACVU6fSjB9PlO62KiISjxSURUR6gE2ffQYGjHqURUQ6jYKyiEgPUPqnhwEwaJCyiEhnUVAWEYl1TU1UJ6YEP/G7WoqISE+ioCwiEuvWrqUxNQsAYzT0QkSksygoi4jEupUr8SenA+BJ1DzKIiKdRUFZRCTWrVhBwJsMgCc10eViRER6DgVlEZFYd8opBBKdoJycleFyMSIiPYeCsohIrDvpJGyCF4C0/n1cLkZEpOfwul2AiIgchro6KCzEGoOxhuQcBWURkc6iHmURkVi2ZAlMnUrAY0gkAW+S+j9ERDqLgrKISCz7+GMAAsaQaPWWLiLSmfSuKiISy/71r2CPMngVlEVEOpXeVUVEYtXKlbB0KXzjG/iMVVAWEelkelcVEYlV8+eD10vzxV/G7wmQENDNRkREOpOCsohIrLr7bnj/fd7YsJVmEyBBd68WEelUCsoiIrFm+3YoLITERJgxg+IFL1HraSLNqkdZRKQzaR6hEGsXL6Pyzc94+4PC1hsSvZAbnJu0vBzb3NxmeyL0znE+LivH+nyttycnQXbv4PZS8Ado1fGTnAy9ejkf7yoF26ZbKCUV23K3rV2l+57b8kFqKmRkgA04xw99rgXSUiEtuL28vNVTAUhPd17D74eKiv3ahYwMSEkBnw8qK/fbXBXws3BVGfiaYc+e/Z+fmQlJSdDcDHuq9t/eK8tpw8YmqK7ef3t2NngToKERasJs790bEhKgvgFqa/bfnpMDHo8z32xd3f7bc3PBGKhtZ3vf4Pe+psY5RpAF53l9cp0V1dVOjaE8Huf41kJVFTQ1UltTxytvfh7cbpxzw1qoqsb6mlt//70JkJnlfFxVBT5fyPfOQoIXMjKD2/cEzy27b7s30fn+gtP2NhDcFNwnMck5P1pev+25l5TknBsQ/nubnAQpqU5jVIXbngIpyc5xq9p+76zz3ORkCASgOsy5kZpKTXMzz7+zBhv83jpfn1NnIDkFEr1Yvx/q6oJr97UAKclOG/l9e783rb7ClGTn3PH59v/eAaSmONubm53zM9x2D872pqY27Wed18c4Pxtt3xdajg/Q7Ae/jwAQwHkZC873B5z6/X4IWGfZ3OycW5mZBIBdWYn08idw0V3f56NPPtr/OCIickgUlEN88upiNiRUQWObX9iNQE1R+09sBGq2tb+9GajZepDtByisJsrbq4OP9lQFHwdSWtr+tj3FB35u5UG2Vxxk++6SA28vP8j2soNsLz3AdguUHqC+AFC2c9/nBsgEqN23bk9I24X7iawJbvcASWG215c5y8Tgo61G548jUtqpseXvvtSDbE87lO3VB9lec/DtSQT/4Au3vd5pYwOkh9seDL8JB9nuBcLe+TkYjttr25btSYT/3tCw7/lhNR5ke2g4N8GHJ+QJTuN5rGFkWiap6e19E0VE5FAoKIeYMuc4kt5cTK+MDEL/gWkSEiAr2GtXXYMJBHuGWnYK9uoZcHrFAoHWL5yUCC2vuWdP6+0GSErCpAd/S++pBBtodXySk51eQWNg9+5WL23Mvu0GoKJle8grpKZAehomEIDdlWBCthqcHsXUVPAHYPduAoGA87H1Y/0BbHISJHixTc1QUwUBiw0EnKX1U13fSGavLGhuxtbXY60f/BZrLdYfgITgCB9fM7bJF3xdi7XB49Dyei2fH652Bmp6DMZ4nF5c43Eaz2MwXi+YBDwtPZUt+7Q0cFKSsy7gtInBea4xTkOalBRnu98HAT8G4/T2GeM80tKcZVMTJhCgpraOjEzn+20SEoLbcXo0/f6Qb59x2i4t3TlOXQNYf+vvbYIX0oMJsq5uX49xMFSZRG+wx9g4ve0BG6wLAtbiS4DmpET81kdzbTU+68MX8OO3fprx4TMWH+C3Pny+RnwBHz78+Kwff3vjYcP89z/BePBi8JBAgsfgMR48ePB4vBhPAh4MCYEAHjwY48GDcfb2JlLf1ERmWjqmuRnjtC5g8BgDiUkYrxdPwEJjk/MsA+BxfjaSksHrdXpzm4KhM9CM8TeAvxlMABNoguYGaK6HwP69vqalnY0XPInBc8frLJOCPc4BnLbd+8MV/P4nt5wbfvzNPmp9AaqbAtQ0BWgOfqsSPJDi9ZDsAa/HkGQMCQk4X0tyovNafp/TzZyQ4LxeG7lD+nPS17/azjdEREQOlYJyiHFzJ1BqypkzZ47bpexlrcU2NWEbGgg0NASXjdiG+tbLxgYC9Q3Y3s3OsjFkv5LGNs8PLhsbsfX1rZZ7g9ohMklJziM5GZOUhKfN5yY5Kbi+5fNUTFIinpbtSW33Cz4/MRG8XkxiIsab6CwTWz5vvcSbiElqvZ6EBCfYdgOLFi3q9HOsyd9EZWMlFQ0VVDZWOo+GSioaK6hs3LZ3fej2el996xfJbf1pckIymUmZrR5ZiVl7P85IyiDNm0ZaYtoBlyneFDxhwl1HHVJ7+X1QsQnK1kHpWmdZtg7K1kNz8N8jCTihs3c+ZA8OPoZC9hGQNRAy8pxHam/nD59DEAhY3ttQxnNLt/Pa6hJqfD6y0rwcO6kPxx/Zl5nDcjkiJw2Pp3ucmyIi0pqCciewgYATPOvrnUddnRM86+sJ1NUTqA9+Xudsc/YLWdfy+d6PnYetqyPQ0LB/D3UHmZQUPCkpzjI5GZOauneZkJnZentKMiYltfUyOQVPaoqzTEkOht1gAE7eF4Df//hjjjvpJCeUdpMwGuustVQ1VVFeX05ZfRnlDeWU15fvXZbVl1HRUBEMwpXUNte2+1qZiZlkp2TTO7k3fdP6cmTvI8lOziY7OZteyb3ISsraLxBnJmWSnJDchV/xYWiogpJVULwSilc4y11rwB8y5jhzAPQ5EiZeAn1HQe4I6D0EehVAQrvjHg5ZRW0TC5YU8fhHW9hSXkdWipezJgzgnEkDmTUsB2/Cof/hICIiXUdBOUT9ypWkvfkmZYWFbQJsXcjn9dj6tp/XH/zFQ3k8eFJTMWmpeFLT8KSmOo/0NBL69Nn3eVqqE25T0w4cYEMCsCc5GZOS4oTaLgqtNjUVT1LYAZoSoiX87mzaycc7P243AJc3lLO7YTe+MMMAvMZLTmoOuSm55KTmMKTXELKTs+md0rv1Mrk32SlOEE70dH4QdE1tGWz/DIqXO4F45wqn57hFag4MmAgzroa8cdBnFPQZASm9uqS8NTur+Mu7m3hhxQ6afAFmDMnhxlNGcvr4/iR7E7qkBhER6TwKyiFq33uPzKcWUArg9e4LrKmpmDQn0CZkZuLJ67cvwLYNtMHA60kNWZeWuu/ztDSnJ1Y9rz1KXXMdu+p2UVpfyq66XXsfpfWllNaVUlJXQmldKU2B4DjZkOv7QsNvbmouI3uPpE9qH3JTc8lNyW31cVZy1mENY4gpzQ1QvIKCbc/Dgn/C9k+hYvO+7TnDnFA85avQfyL0n+D0HLvws7VkSwV/ensDbxbuIi0pgS9PK+Brs45gdP+sLq9FREQ6j4JyiJzLL2fV4MEcf8opGPWQCtDsb24Vfls+Lq0Lrqt3Pq5p3n9akVRvKv3S+tE3tS+T+k6iX1o/+qT2oXRzKccddZwTgOMt/LbHWij/wgnDRZ86y+LPIdDMCICsfMifCtOuhPxpTihOcTeEWmt5f0M5f3h7PR9u3E3vtER+eMpILp89hF5pPagXX0Qkjikoh/Ckp2PT0xWS40Szv5mSuhKKa4sprit2lrXFlNSW7F1f0bj/vNJej5d+qf3om9aXEdkjOHrg0fRN7euE4rS+9EvtR7+0fqQnpof9z8Gi0kXMHDCzK77E7svfDDuXw5bFsPUD2Poh1AdnbEnKgIFT4Oj/gfxpLN7ayNGnfcndettYurWCXy5cywcby8nLSubOs8bwlZmDSUvSW6qISE+id3XpkXwBH6V1pXsDcEltSaswXFxbTHlD+X7Py0zKpH96f/qn9Wdcn3H0S+tHXlpeqyCcnZytHuBINdZA0SdOKN6y2Ok1bpl1I2c4jD4TBs10eov7jgLPvvG8TSWL3Kk5jPUl1fzq1bW8trqE3PQk7jlnLJfNHKzxxyIiPZSCssScgA1QXl/Oztqd+4JvSyAO9gSX1ZcRsK1nC0nzpjkhOL0/o3JG0T/N+TgvPW9vOE5LbO+uGhKR2rJgb/GHsHWxc9Gd9TvTsfWfAFO/AYNnO4/MPLerPaiiijp+98Z6nvmsiLQkLzeeMpIrjx1KRrLeQkVEejK9y0u30xxopqS2hJ21O9lRs4MdtTvYWbNz73Jn7U6aA61vI56SkLI39M4aMGtvIG4Jw/3T+5OZlOnSVxQH6itg8/uw+V3Y9F/YtdpZ701xeomPvQGOmA0FM1wfWxyJ2kYff1q0gT+/68ys8a1jh/LdOSPISdfwLBGReKCgLF2u3lfPztqdrcLv9prte4NxaX3pfr3BfVL7MDB9IGNyx3DS4JMYkDGAAekD9obhXsm9NJNIV2qshi0fwOb/OsF45wrAgjcVBs+CCRfBEcfCwMngjZH5mEMEApZnl27n/oWF7Kpu5IIp+dx82igGZusW0SIi8URBWTpdVVOV0xNcs2Nv+A1d7m5ofRvuBJNAXloeAzIGMHPATAakD2BgxsC9y/7p/WPn5hc9VVMdbPtoX4/x9s+coRQJSU4v8ZzbYOjxzswUMRiMQy3dWsE9L6xm+bZKJg3K5uGvT+Wowb3dLktERFygoCwRq26qZnvNdrZXb6eopoiPd3/MgjcX7O0dbjtVWnJC8t7QOzpndKsQPDB9IH3T+uL16FTsVvw+2LEUvngLNr3jXIjnbwKT4IThY2+Aocc5F+Al9oxe1pKqBu5/pZBnlm6nb2YyD1w8iQum5Ov20iIicUzpRPbT4GtgR80OimqK9gbi7TX7HlVNVa32TzEpDPYOJj8jn+l501sF4QHpA8hJydGwiFiweyN88XYwHL8LjXsA49zUY+Z3nB7jwbMguWeN9W7yBfjLexv5w1sb8Pkt35sznO/NHaEL9UREREE5HvkCPopri/cG36LqolZBuKy+rNX+SZ4kBmYMJD8zn4l9J5Kfke88MvMpyCjgs8WfMXfuXJe+Gjlk9ZXOMIov3oKNb++7612vQTDuPBg2F4bNgbQcF4uMro82lnPnc5+zflcNp4zN466zxjI4VzOfiIiIQ0G5B7LWUlZf5oTgmqL9eoSLa4vxW//e/RNMAv3T+5Ofkc9x+ce1CsEDMwbSJ7XPAecNVm9xjPA3O/MXtwTj7UvABpwbfAw9HmZ9H4afCLnDXbkNdFfaXdvEz19ew1NLisjPTuWv35jGSWO6/zR1IiLStRSUY1RVU9W+nuDgWOGWILyjZgeN/sZW+/dJ7UN+Rj6T+k7izKFnUpBZsLdnOC89j0SPbrnb47TcFrolGG96F5qqnbmM86fCcTc5wbhgGiTEx/c/ELA8tWQbP3+lkJoGH9+dM5wfnDhCd9QTEZGw9Nuhm/IH/JTUlVBUXcS26m0U1QSXwc/bjhPOTMqkIKOA4b2Gc3z+8eRnOiG4pVc4xZvi0lciXaqxxhlOseF12PAGVG511vceAhMvdoZTDD0OUuNvFoe1xdX86NmVfLqlgulDenPfBRMYmdezxluLiEjnUlB2UV1zHUU1RfvCcHUR22q27e0p9gV8e/f1Gi8DMwZSkFnA+D7jKcgo2NcrnJlPVlLs3MRBOpG1UFoI64PBeOsHzuwUiekw7AQ45jqn1zhnmNuVuqauyceDb67nr+9uIjPFyy8vmshFRxVoNgsRETkoBeUostZS3lDeqic49OPyhvJW+2cmZlKQWcDI3iM5afBJDMocREFmAYMyB5GXlqcp1MTRWA0b3wn2Gr8Je7Y56/uOgZnfhhGnOLeG9urucf9dV8odz66kqKKeL08r4LYzxuiueiIi0mFKXoepyd/Ejpod+0JwyBCJ7TXbqffV793XYOif3p+CzAJOGHQCBRkFrcJwVlKWLoyT/Vnr3BI6tNc44IOkTKfX+PibYPhJkD3I7Uq7jcq6Jn764hqe/qyIYX3Tmf/t2cwY2nNn7xARkehQUO6APY17WvUEh4bh4tpiLHbvvqneVGdscGYBswfOdoJwMBAPzBhIUoJ6s6QDGvbAxkXBcPwmVO9w1ueNh9n/AyNOdm72oV7jVqy1vLyymP99/nMq65r5n7kj+J8TR5CSmOB2aSIiEoMUlEN8UfkF71e/z9IlS1uF4uqm6lb79UntQ0FGAdPypu3tDW5Z5qbkqldYImctlKyC9a85vcbbPnJ6jZN7wfA5TjAecTJkDXS70m6rpKqBO5/7nNdXlzAhvxf/uHImYwdq7L6IiBy6qARlY8xI4PvAXGAYUA18AtxlrV0ejWN2hje2vMG83fPwVnopyCggP9OZTq0lBA/KHER+Rj5pibohgXSCpjrY/C6sWwjrXoOqImd9/wlw9LVw5ClQMD1upm47VNZa5n2yjZ+9vIYmX4A7zhzNlccMxZvQ/tzfIiIiHRGtHuVTcULyY8BnQDZwC/ChMeZYa+2SKB33sFw08iL6lvblvBPPI8Gjf9VKFFRuY+D2V+Bff4JN74CvwZmhYvhcmHOrcyFe1gC3q4wZm8tquf2ZlXywsZxZw3L4xYUTGdIn3e2yRESkh4hWUJ4H/NFau3fwrjHmLWAzcB1weZSOe1hyU3PJ8eYoJEvnCfih6JN9vca7VjESnHmNp34TRp4GRxwD3mR364wxPn+AR9/fxAOvrSPJ6+HnF07g0umDNOxJREQ6VVSCsrW2LMy6PcaYdUB+NI4p0m3U7XbuhrduoTPeuL4CPF5nyrZT7+Xjit7MOPOrPf420dGyvqSam55azvKiPZw6No+fnj+evCzdUEdERDpfl13MZ4zJAcYDf+uqY4p0CWth1xpY/6rTa7ztQ7ABSMuFkafDkac6N/1IzQagbtEiheRD4PMH+PO7m/jt6+vISPHyh69M4awJA9SLLCIiUWNCRkdE90DG/Au4AJhord3Qzj7XANcA5OXlTZ03b16X1BaqpqaGjIyMLj9uLIvHNvP4m8iuXElu+Sfkli8hpXEXANUZQynPnc7unGlUZY0As/8wnnhsr8NRU1NDFWn8ZWUjG/cEmJaXwOVjk8lKVkAOR+dX5NRmkVF7RUbtFbmubrO5c+cusdZOC7etQ0HZGHMy8HoHjvWOtXZOmOffDvwM+Ja19tEOvA7Tpk2zn376aUd27VSLFi1izpw5XX7cWBY3bbZn+75e442LwFcPiWkwbI7Ta3zkqdDr4COL4qa9OoE/YLn9sdd57gs/6UkJ/OS88Zw9Ub3IB6LzK3Jqs8iovSKj9opcV7eZMabdoNzRoReLgTEd2K8uzMG/gxOS7+xoSBbpFgIB2LkU1i6Eta9AyUpnffZgOOrrcORpMORYSNT42GjYsKuGmxcsZ+nWZk4bl8e950+gb6YuehQRka7ToaBsra0DCiN9cWPM14E/AQ9Ya++L9PkiXa65Hja+A2tfhnWvQk0xGA8MmgUn/9gZc9x3lMYYR5E/YPnrexv59WvrSEtK4DsTk7n1sqnqRRYRkS4XtYv5jDEX4Fy49xdr7U3ROo7IYavZ5cxQsXahM1uFrx6SMmHESTDqDGdIRVqO21XGhS9Ka7j5qeV8trWSU8bmcd8F41m95EOFZBERcUW07sx3PPAEsBz4uzFmVsjmRmvt0mgcV6RDWmapWPuyE5CLPgUs9BoEU77mhOMhx2pu4y7kD1j+9v4mfvXqWlISE/jdJZM5b/JAjDGsdrs4ERGJW9HqUT4RSAaOAt5vs20LMCRKxxUJz98MW953xhqvfQUqtzjrBx4Fc+9wwnHeeA2pcMHG0hpuWbCCT7dUcPKYPH52wXj6aV5kERHpBqJ1w5F7gHui8doiHVZfAevfgHWvOMvGPeBNcWapOPYGZ7yxbhftmkDA8tgHm7l/YSHJ3gR+e8kkzp+cr2EWIiLSbXTZDUdEusTujft6jbcsBuuH9L4w9lyn13jYHEhKd7vKuLe9sp6bn1rO4i/KmTuqL7/40kTdXU9ERLodBWWJbQG/M8a4ZbxxaXByln5j4djrYeQZkD8VPB5XyxSHtZanP9vOj59fRcBafnHhBC6ZPki9yCIi0i0pKEvsaayBjW87vcbrXoW6MvB44YhjYOoVMOp06D3E7SqljbKaRu54ZiWvrS5hxpAcHvjyJAblpLldloiISLsUlCU2VO0IBuOFzjzH/kZI6eVM3TbydBhxMqRmu12ltOPVVcXc8cxKqht8/OjMMVx57FASPOpFFhGR7k1BWbona6Hkcyh82RlWsXOZs773UJh+ldNrPHg2JCS6WqYcWFVDMz9+fjVPf1bEuIFZ/PvqyYzqn+l2WSIiIh2ioCzdh98HWxcHw/FLULkVMFAwHU6+xxlvrLvixYzFG8q46anllFQ38oMTR/CDE48kyaux4iIiEjsUlMVdjTXO3fAKX4L1rzpTuiUkw/C5cPzNzrCKjH5uVykRqG/yc//CQv6+eDPD+qSz4DuzmTK4t9tliYiIRExBWbpezS5nvHHhS7BxkTPeOLW3E4pHnQnDT4TkDLerlEOwbFslN85fxsbSWr559BBuPX00qUkJbpclIiJySBSUpWuUbYDCF53xxts+BixkD4bp33LC8eDZkKDTMVY1+wP8/s31/HHRF/TLTOZfV83kmBF93C5LRETksCiZSHQEArB9yb5wXLbOWT9gEsy5HUafBXnjNN64B1hXUs2N85fx+fYqLjwqn/89Zxy9UnWRpYiIxD4FZek8zQ2w6b/OhXhrX4GaEmd+4yHHwvSrnTvjZQ9yu0rpJP6A5dH3NvGr19aSkezl4a9N5fTx/d0uS0REpNMoKMvhqa8gr3gRzH8UNrwJTTWQlOHMazz6bDjyFM1v3ANt213HD59azsebdnPK2Dx+dsEE+mYmu12WiIhIp1JQlshVbnOGUxS+CJvfZ4z1Q0Z/mHCxE46HHgdehaaeqOUW1Pc8vwqAX100kYumFugW1CIi0iMpKMvBWQvFK/eF4+KVzvq+o+GY61hS15+pZ18NHs2R25NV1DZxx7MreeXzYmYMzeE3X55EQW/dglpERHouBWUJz98MWxYHw/HLsCd4849BM+GUnzoX4+UOB6B60SKF5B7unXWl3PzUcirqmrjtjNFcfdww3YJaRER6PAVl2aexBr5405nfeN2r0FAJ3hQYNhdOuCV484++blcpXai+yc8vXlnDYx9s4ch+GfztiumMG9jL7bJERES6hIJyvKsugXWvOL3GoTf/GHUmjA7e/CMp3e0qxQWfb9/DdfOW8kVpLVcc49w8JCVRNw8REZH4oaAcj8rWO2ONC1+Gok9wbv5xhHPzj9FnwaBZuvlHHPMHLA+/8wW/fX0duRlJ/PNbMzjuSP0nQURE4o/SUDywFnZ85gypWPMilK111g+YDHPvcMJxv7G6+YewbXcdN85fxiebKzhr4gDuO3882WlJbpclIiLiCgXlnqrlYrzCF52AXLUdTAIMOQamX+UMq+hV4HaV0k1Ya1mwpIgfv7AaA/z2kkmcPzlf076JiEhcU1DuSZrq4Iu3greNfiV4MV4qjDgJTrwLRp4GaTluVyndzO7aJu54ZiULVxUzc2gOD2jaNxEREUBBOfbV7XZmqCh80bkznq8eUrKd20WPPguGnwRJCj0S3qK1u7h5wQoq65q4/YzRXKVp30RERPZSUI5Fe4qcC/EKX4DN74P1Q1Y+HPV1JxwfcQwkJLpdpXRjodO+jczL4O+a9k1ERGQ/CsqxwFooXRscb/wi7FjqrO8zCo65DsacDQOP0sV40iGh075decxQbjl9lKZ9ExERCUNBubsKBJyZKta84ITj8g3O+vxpcNL/wphzoM+R7tYoMSV02rc+Gck8/q2ZHHtkH7fLEhER6bYUlLsTXxNsec+Zwm3ty1C9EzxeGHIczPyOM6wia6DbVUoM2ra7jhueXManWzTtm4iISEcpKLut5bbRa150Lspr3AOJac5MFaPPgZGnOnfKEzkE1lqeWlLEj59fhccYTfsmIiISAQVlN9SWO7eNXvMibHwbfA2QmuOMNR59NgyfC4mpblcpMU7TvomIiBweBeWuUrl1353xti4GG4Beg2DqN51wPHi2bhstnUbTvomIiBw+JbNosRZ2rXEuxFvzAhSvcNb3HQPH/dAJxwMmaaYK6VQNzX5+8Uohf1+8WdO+iYiIHCYF5c4UCEDRJ878xmtehIpNzvqCGXDKT5xwnDvc3Rqlx1qzs4rr5i1lXUkNVxwzhFtPH61p30RERA6DgvLh8jXBpv864bjwZajdBZ5EGHo8HP0DZ6aKzP5uVyk9WCBgefT9Tfxy4Vp6pSXy2JUzOGFkX7fLEhERiXkKyoeisRrWv+4Mq1j/OjRWQWI6HHmK02t85CmQmu12lRIHSqoauOmp5by7voyTx+Rx/5cmkJuR7HZZIiIiPYKCckfVlDpzGxe+CBsXgb8J0nJh7LnONG7D5kBiittVShx5dVUxtz29gvpmP/ddMJ6vzBisad9EREQ6kYLygVRsdsYaF74IWz8ELPQaDNOvCs5UMQs8GgMqXauuycdPX1zNEx9vY3x+Fr+7ZAoj+mW4XZaIiEiPo6AcylrSazbB2x844bjkc2d9v3Fwwi1OOO4/QTNViGtWFFVy/bxlbCqv5TsnDOfGU0aS5PW4XZaIiEiPpKAc6q2fMv3TBwADg2bCqfc6F+PlDHO7Molz/oDl4Xe+4Levr6NvZjL/vmoWs4fnul2WiIhIj6agHGrMOawtaWDUuddDRj+3qxEBYHtlPTc8uYyPN+3mrIkD+Nn5E+iVluh2WSIiIj2egnKogVPYOXAPoxSSpZt4fvkOfvTsSgIBywMXT+LCo/J1wZ6IiEgXUVAW6YaqG5r53/+s4pml25kyOJvfXTKZI3LT3S5LREQkrigoi3Qzn27ezfVPLmNHZT3Xn3wk/zN3BN4EXbAnIiLS1RSURboJnz/AQ29t4A9vrSe/dypPfedoph7R2+2yRERE4paCskg3sKW8luvmLWPZtkq+dFQB95w7lswUXbAnIiLiJgVlERdZa1mwpIh7nl9Fgsfw+8umcM6kgW6XJSIiIigoi7imsq6JO55dycsri5k5NIffXjKZgdmpbpclIiIiQV0SlI0xlwJPANuttQVdcUyR7mzxhjJunL+csppGbj19NNccP4wEj6Z9ExER6U6iHpSNMdnA74DiaB9LpLtr8gV4cm0TC1/9iKG56Tz7vWOYUNDL7bJEREQkjK7oUf4lsBzYCZzcBccT6ZY27KrmunnLWLWjma/MHMydZ40hLUmjn0RERLqrqP6WNsYcA3wNmAjcGc1jiXRX1loe/2gr9720mrQkL9dOSebGCya4XZaIiIgcRNSCsjEmEXgE+JW1doNuuyvxqKymkVsXrODNwl0cP7Ivv75oIqs/+9DtskRERKQDjLU2Oi9szJ3AN4Hx1toGY8zfgZMPdDGfMeYa4BqAvLy8qfPmzYtKbQdSU1NDRkZGlx83lqnNwltR6uMvKxup88ElI5M46QgvHmPUXhFSe0VG7RU5tVlk1F6RUXtFrqvbbO7cuUustdPCbetQj7Ix5mTg9Q7s+o61do4xZgTwI+ACa21DRwu11j6C0wvNtGnT7Jw5czr61E6zaNEi3DhuLFObtdbQ7OcXrxTy9yWbGZWXyYOXTWZ0/6y929VekVF7RUbtFTm1WWTUXpFRe0WuO7VZR4deLAbGdGC/uuDyIeAt4MPgrBcASYAJft5ora2PoE6RmLB6RxXXP7mUdSU1XHHMEG49fTQpiQlulyUiIiKHoENB2VpbBxRG8LpjgSOAijDbKoAHgesjeD2Rbi0QsDz6/iZ+uXAtvdISeezKGZwwsq/bZYmIiMhhiNbFfJcCKW3W3QZMBS4GiqJ0XJEut6uqgR8+tZx315dx8pg87v/SBHIzkt0uS0RERA5TVIKytXa/y/qNMd/EGXKxKBrHFHHDm2tKuHnBCuqafNx7/ni+OnMwmuFFRESkZ9DdDkQOQUOzn5+9vIZ/fLCFMQOy+P1lkxnRL9PtskRERKQTdVlQttZ+s6uOJRJNhcVVXPuEc8Het44dyi2njyLZqwv2REREehr1KIt0kLWWvy/ezM9fKSQrRRfsiYiI9HQKyiIdUFbTyM1PLefttaWcOLofv7xoIn10wZ6IiEiPpqAschCL1u7ipqeWU9Xg48fnjuPy2Ufogj0REZE4oKAs0o6GZj+/XLiWR9/fxKi8TB6/amarO+yJiIhIz6agLBLG+pJqfvDEUgqLq/nm0UO47QzdYU9ERCTeKCiLhLDW8vhHW7n3xdVkJHt59JvTOHF0nttliYiIiAsUlEWCdtc2ccuCFbyxpoTjR/bl1xdPpF9m2xtMioiISLxQUBYB3ltfxo3zl1FZ18xdZ4/liqOH4PHogj0REZF4pqAsca3R5+fXr67lz+9uYkS/DP52xXTGDezldlkiIiLSDSgoS9zasKuG6+YtZdWOKr42azA/OnMsqUm6YE9EREQcCsoSd6y1zPtkGz9+YRWpiQk88vWpnDquv9tliYiISDejoCxxpaK2idueWcGrq0o4ZkQuv/nyZPKydMGeiIiI7E9BWeLG4i/KuPHJ5ZTXNnL7GaO5+rhhumBPRERE2qWgLD1eky/Ab99Yx8PvfMHQ3HT+fPkxTCjQBXsiIiJyYArK0qNtKqvlunlLWVG0h0unD+Luc8aSlqTTXkRERA5OiUF6JGstTy0p4p7nV5GY4OH/vnoUZ0wY4HZZIiIiEkMUlKXH2VPXzB3PreSlFTuZNSyH33x5MgOzU90uS0RERGKMgrL0KB9v2s3185ayq7qRm08bxXdOGE6CLtgTERGRQ6CgLD1Csz/AQ2+u549vb2BQThoLvns0kwdlu12WiIiIxDAFZYl5W8vruHbeUpZtq+SiqQXcc+44MpJ1aouIiMjhUZqQmPbs0iLuem4VxsDvL5vCOZMGul2SiIiI9BAKyhKTqhqaueu5z/nPsh1MH9Kb314ymYLeaW6XJSIiIj2IgrLEnCVbdnPdvGXs3NPAjaeM5HtzhuNN8LhdloiIiPQwCsoSM3z+AH94ewMPvbme/N6pzP/2bKYe0dvtskRERKSHUlCWmLBtdx03PLmMT7dUcMGUfH5y3jgyUxLdLktERER6MAVl6faeX76DHz2zEgv87pLJnD8l3+2SREREJA4oKEu3VdPo4+7/fM4zn21nyuBsHrxkCoNzdcGeiIiIdA0FZemWlm6t4Ponl7Ftdx3XnjiCa086UhfsiYiISJdSUJZuxR+w/N+iDfz2jfX0z0ph3jWzmTE0x+2yREREJA4pKEu3saOynuufXMbHm3Zz9sQB3HfBBHql6oI9ERERcYeCsnQLL6/cyW1Pr8AXsPz64kl86ah8jDFulyUiIiJxTEFZXFXb6OMnL6zmyU+3MamgFw9eOoUhfdLdLktEREREQVncs6KokuvmLWNzeS3fmzOcG04ZSaIu2BMREZFuQkFZulwgYHnk3Y38+tW19MlI5t9XzWL28Fy3yxIRERFpRUFZulTxngZunL+MxV+Uc8b4/vz8wglkpyW5XZaIiIjIfhSUpcu8tqqYW55eQWNzgPu/NIEvTxukC/ZERESk21JQlqhraPZz70urefzDrYwbmMVDl01heN8Mt8sSEREROSAFZYmqwuIqfvDvpazfVcPVxw3lptNGkexNcLssERERkYNSUJaosNbyjw+2cN/La8hKSeSxK2dwwsi+bpclIiIi0mEKytLpymsauWXBCt4s3MWcUX359cWT6JOR7HZZIiIiIhFRUJZO9d76Mm6cv4zKumbuPnssVxwzRBfsiYiISExSUJZO0eQL8MDra3nkvxsZ1iedv18xg7EDs9wuS0REROSQKSjLYSuuDXDRw4tZUbSHy2YM5u6zx5KapAv2REREJLYpKMshs9by9Gfb+d/F9aQk+Xj4a0dx+vgBbpclIiIi0imiGpSNMfnAT4Ezgd7ADmCetfb2aB5Xoq+qoZkfPfs5LyzfwajeHv727eMYmJ3qdlkiIiIinSZqQdkYMwR4H9gEXAuUAEOAEdE6pnSNJVsquG7eUnbuaeCHp4xknKdIIVlERER6nGj2KD8MbAfmWmubg+veieLxJMr8Acsf397Ag2+uZ0CvFOZ/ezZTj+jNokXb3S5NREREpNNFJSgbY4YDpwGXh4RkiWE7Kuu5/sllfLxpN+dOGsi9F4wnKyXR7bJEREREoiZaPcrHBJf1xpjXgeOBOuAF4AZrbXmUjitRsPDzndz69Ep8/gAPXDyJC4/K19zIIiIi0uNFKygPDC4fBf4J/BxnbPLPgbHGmBnW2kCUji2dpK7Jx09fXM0TH29jYkEvHrp0CkP6pLtdloiIiEiXMNbag+9kzMnA6x14vXestXOMMXcA9wEvWGvPDXmdS4B5wJnW2lfCHOca4BqAvLy8qfPmzevYV9GJampqyMjI6PLjdjdbqvw8vLyRnbWWM4cmcuGRiXg94XuR1WaRUXtFRu0VGbVX5NRmkVF7RUbtFbmubrO5c+cusdZOC7etoz3Ki4ExHdivLrhsGVrRNly/FlxOAfYLytbaR4BHAKZNm2bnzJnTwfI6z6JFi3DjuN2FtZZH39/M/R8Vkp2WxOPfmsyxR/Y54HPivc0ipfaKjNorMmqvyKnNIqP2iozaK3Ldqc06FJSttXVAYQSvu+og2zXsohsqq2nkpqeWs2htKSeP6cf9X5pIbkay22WJiIiIuCJaY5Q/BIpxZr74fcj604PLT6J0XDlE76wr5Yfzl1PV0MxPzhvH12cdoQv2REREJK5FJShba33GmNuAvxtjHgaewbmY7z5gEfBWNI4rkWv0+fnVwrX85b1NjMzL4PGrZjC6f5bbZYmIiIi4Lmo3HLHWPmaMCQC3AlcAu4HHgdttR64glKj7orSGa59YyqodVXxt1mDuPGssKYkJbpclIiIi0i1E8858WGv/iTM9nHQj1lrmf7qNe55fTXKih0e+PpVTx/V3uywRERGRbiWqQVm6nz11zdzx7EpeWrmT2cNy+e0lk+nfK8XtskRERES6HQXlOPLJ5t1cP28ZJVUN3HL6KL59/HAS2pkbWURERCTeKSjHAZ8/wO/f2sDv31pPQe80Fnz3aCYPyna7LBEREZFuTUG5hyuqqOP6ecv4dEsFF07J58fnjSMzJdHtskRERES6PQXlHuzFFTu4/ZmVWAu/u2Qy50/Jd7skERERkZihoNwD1Tb6+PELq5j/aRGTBmXz0KWTOSI33e2yRERERGKKgnIP8/n2PVz7xFI2ldfy/bnDuf7kkSQmeNwuS0RERCTmKCj3EIGA5a/vbeKXrxaSm57Mv66aydHD+7hdloiIiEjMUlDuAXZVN/DD+ct5d30Zp47N4/4vTaR3epLbZYmIiIjENAXlGPd24S5uemo5NY0+7j1/PF+dORhjNDeyiIiIyOFSUI5RDc1+7l9YyN/e38zo/pk8cc0sRuZlul2WiIiISI+hoByDNuyq5gdPLGPNziq+efQQbjtjNCmJCW6XJSIiItKjKCjHEGstT3y8jZ+8uIq0JC9//cY0ThqT53ZZIiIiIj2SgnKMqKxr4ranV7JwVTHHjujDb748iX5ZKW6XJSIiItJjKSjHgA83lnPDk8sorW7k9jNGc/Vxw/B4dMGeiIiISDQpKHdjzf4AD725nj+8vYEhuek8872jmViQ7XZZIiIiInFBQbmb2ra7jmvnLWXp1kounlrAPeeOIz1Z3y4RERGRrqLk1Q39Z9l27nz2cwAeumwK504a6HJFIiIiIvFHQbkbqWn0cfd/PueZz7Zz1OBsHrx0CoNy0twuS0RERCQuKSh3E8u3VXLdvKVs3V3HtSeO4NqTjsSb4HG7LBEREZG4paDsskDA8si7G/n1q2vpl5nME1fPYuawXLfLEhEREYl7CsouKqlq4Mb5y3h/QzlnjO/PLy6cSK+0RLfLEhEREREUlF3zxuoSbl6wnIbmAL+4cAKXTB+EMZobWURERKS7UFDuYg3Nfn728hr+8cEWxg7I4qHLpjCiX4bbZYmIiIhIGwrKXWhtcTXXPrGUtSXVXHnMUG49YxTJ3gS3yxIRERGRMBSUu4C1lsc/3MK9L60hM8XL366YztxR/dwuS0REREQOQEE5ynbXNnHr0yt4fXUJx4/sywMXT6JvZrLbZYmIiIjIQSgoR9HiDWXcMH8Zu2ubuPOsMVx5zFA8Hl2wJyIiIhILFJSjoNkf4Devr+Phd75gaJ90/vqN6YzP7+V2WSIiIiISAQXlTralvJZrn1jK8qI9XDp9EHefM5a0JDWziIiISKxRgutEz3xWxF3PfU6Cx/DHrxzFWRMHuF2SiIiIiBwiBeVOUN3QzF3Pfc5zy3YwfUhvfnfpFPKzU90uS0REREQOg4LyYfpsawXXzVvK9op6bjh5JN+fOxxvgsftskRERETkMCkoHyJ/wPLwO1/wm9fX0T8rhfnfns20ITlulyUiIiIinURB+RDs3FPPDU8u48ONuzl74gDuu2ACvVIT3S5LRERERDqRgnKEXl1VzK1Pr6DJF+CXF03k4qkFGKO5kUVERER6GgXlDqpv8vPTl1bz74+2Mj4/i4cuncKwvhlulyUiIiIiUaKg3AFrdlZx7RNLWb+rhmuOH8ZNp44iyasL9kRERER6MgXlA7DW8tjizfzslUKyUhL5x5UzOH5kX7fLEhEREZEuoKDcjvKaRm5esIK3Cndx4uh+/PKiifTJSHa7LBERERHpIgrKYby7vpQb5y9nT30z95wzlm8cPUQX7ImIiIjEGQXlEE2+APMKm1i48GNG9MvgH1fOYMyALLfLEhEREREXKCiH+NWrhSzc3MxXZg7mrrPGkpqU4HZJIiIiIuISBeUQ3z5hOKk1O7jxgglulyIiIiIiLtMcZyH6ZCRzVJ7+dhARERGRKAZlY0yuMeZBY8xGY0y9MWaTMeYPxhjNryYiIiIi3V5Uuk+NM0XE88BI4G5gDTAW+AkwzRgz21pro3FsEREREZHOEK1xBkcCRwPfttY+Ely3yBgTAP4PJ0CvjdKxRUREREQOW7SGXiQFl1Vt1ldG+bgiIiIiIp0iWj3Kq4D/AncZYzYAhThDL+4GXrHWronScUVEREREOoWJ1lBhY0w68E/ggpDVLwEXW2vr23nONcA1AHl5eVPnzZsXldoOpKamhoyMjC4/bixTm0VG7RUZtVdk1F6RU5tFRu0VGbVX5Lq6zebOnbvEWjst3LYOBWVjzMnA6x041jvW2jnB5/wbmAP8GOdivjHBj5cA51hrAwd6oWnTptlPP/20A4fsXIsWLWLOnDldftxYpjaLjNorMmqvyKi9Iqc2i4zaKzJqr8h1dZsZY9oNyh0derEYJ+geTF3wgGcBlwEnW2vfDG77rzFmI/AacA7wnw4eW0RERESky3UoKFtr63DGGXdUy63tPmmz/uPgcgwKyiIiIiLSjUVr9oni4HJGm/Uzg8vtUTquiIiIiEiniFZQfgbYAfzDGPNdY8xcY8x3gX8A24Bno3RcEREREZFOEZXp4ay1VcaYWcA9wC3AAGAn8AJwj7W2JhrHFRERERHpLNGaRxlr7TbgW9F6fRERERGRaNId8kREREREwlBQFhEREREJQ0FZRERERCQMBWURERERkTAUlEVEREREwlBQFhEREREJQ0FZRERERCQMY611u4awjDGlwBYXDt0HKHPhuLFMbRYZtVdk1F6RUXtFTm0WGbVXZNRekevqNjvCWts33IZuG5TdYoz51Fo7ze06YonaLDJqr8iovSKj9oqc2iwyaq/IqL0i153aTEMvRERERETCUFAWEREREQlDQXl/j7hdQAxSm0VG7RUZtVdk1F6RU5tFRu0VGbVX5LpNm2mMsoiIiIhIGOpRFhEREREJIy6DsjHmRmPMC8aYncYYa4y55wD7nm+MWWqMaTDGbDHG3GmMSQiz37HGmMXGmHpjTLEx5jfGmNSofiEuMcZ8M9hu7T36h+y7qJ19rnfxS3CFMWZzO21xfph9rzbGFBpjGo0xa40x33GhZNcYY0YaYx40xqwwxtQEf1afN8ZMCrNv3J9jxphBxpgFxpg9xpgqY8wzxpjBbtfVHRhjLjLGPB18/64P/jz93BiTGbLPkAO8n2W7WH6XM8bMaacdKtvs19sY8xdjTJkxptYY84YxZoJLZbvmAO8/1hizMLhP3J5fxpgCY8zvjTEfGGPqgl/zkDD7pRhjfhV8r68P7n98mP08xpjbg79PG4wxy40xX4rm1+CN5ot3Y1cDVcBzQLsBxBhzGvA08FfgRmAK8DMgE7g1ZL+JwOvAq8DZwFDgV0A+cEk0vgCXvQTMbrPOAC8AG621xW22rQC+3Wbd5uiU1u29CtzTZt3a0E+MMVcD/w/4OfAGcBLwJ2OMsdb+X1cU2Q2cCswFHgM+A7KBW4APjTHHWmuXtNk/bs8xY0wa8BbQCHwDsMC9wNvGmInW2lo36+sGbgK2AncARTjv4/cAc40xR1trAyH7/hx4vs3zq7uiyG7oWuCTkM99LR8YY1re74cAPwAqgNtxzrnJ1tqiLqzTbd8Dstqsmw38hv3PpXg8v0YAXwaWAO/ivLeH81fgLOBmYCPwfeBVY8xsa+2ykP1+ivMz/aPga14KPGWMOdta+3JUvgJrbdw9AE9w6cX5pXJPO/stBd5ps+5uoAnoH7LuWWA9kBiy7vLgax/l9tfbRW16XPDr/X6b9YuA99yurzs8cILb4wfZxwvsAh5rs/5RnMnXE6NVX3d64Ew2b9qs64XzC/kfbdbH9TkGXAf4gREh64biBJsb3a7P7QfQN8y6lvfnE4OfDwl+fpXb9br9AOYE2+LkA+xzXnCfuSHregG7gYfc/hrcfuCEvkYgJ/h53J5fLXkr+PFVwXYY0mafScH1V4Ss8+J0Ij0fsq5fsF1/3Ob5bwIrovU1xOXQC9u6ByEsY8wgYDLweJtN/wQSgTOC+yUCpwPzrbXNIfvNxwnU53VCybHgGzhf7xNuFxLjZgN9CX/e5QLHdnlFLrDWltngO2DIuj3AOpz/1Mg+5wIfWms3tKyw1m4C3id+3n/aZa0tDbO6padU59KhORfYYa19u2VF8OfzBeL8nAv+h+di4AVr7W6363FbR/IWzvnUDDwZ8jwfMA84zRiTHFx9GpDE/r8fHwcmGGOGHn7F+4vLoNxB44LLz0NXBn8B1QFjg6uGAylh9msAvgjZr8cyzljsi4EX23ljmBIcO9kcHHP6rS4usTs5JzhOq9EY82GY8clhzztgVXDZ48+n9hhjcoDxwJowm+P5HBvH/ucLOOdM3J4vB3FCcNn2XPq5McYXPJeej8cxtyH+ZYzxG2PKjTH/bjPm/UDn3GBjTEbXlNgtXYAzPPOxMNt0foU3Dthkra1rs34VTjAeEbJfI7AhzH4Qpfe7eB2j3BE5wWVFmG0VIdsPtN/ukO092fk4Y7TCvTH8F/gXTk9gNs6/PP9ijBlgrb23qwrsJl7A6cnaBOQB/wM8a4z5urW25S/k9s6n3W22x6Pf44yF/12b9fF+juXQ/vtP7y6updszxuQDPwHesNZ+GlzdiHNdwGtAKTAaZ0zzYmPMDGttuD/Oeqo9wAPAOzjX8kzBaYsPjDFTrLW7cM65zWGe2/I+1RuoiX6p3dLlOMPnXglZp/PrwA70HtayvWVZ2fa/jWH261QxH5SNMSfjXEh3MO9Ya+dEuZyY1Alt+A2cN4b9BtJba+9us+o/xphngR8ZY35nrY3JN9NDaTNr7Q/avMazwIc4F3i0/VdSj3K455gx5nbgK8C3QocYQM89x6TzBXs6/4MzfvuKlvXW2p20vrD73eCMBatwLhr6WlfW6SZr7VKc63NavGOM+S/wMc4Ffne6UlgMMMYMBE4GHgwOHQB0fsW6mA/KwGJgTAf2a9ulfzAtf92E65Hpzb6/YA60Xw77/iXQnR1yGxpjBuC8Mfw+9I3hIJ7A6YWeAHzQwed0N4d93llr/caYp4D7g72fO2l9Pu0M2b3lL+VYHfN2OOfYd3Bmm7nTWvtoB4/XE86xjqqg/fefcL00cSk4ROwFYBhwgj3IzAzW2m3GmPeA6V1RX3dmrf3MGLOOfW1xoHOuZXs8+hrOkNZw/11tRedXKxXAEWHWt/29VwFkB2eAsgfYr1PFfFAOjmkpjMJLtwTccYT8og3O/5cGrA6u+gLn3yrjQp9sjEnBeUN+Kgq1darDbMOvAQl04I0h3KEP8Ziui8J519IWoeddaFBuGXu1mhh0qO1ljPk68CfgAWvtfYdy6EN4TqxZRZv3n6CxxOj50tmCF10vAKYBp1hrV0bw9Hg4hzoq9H0q3DRfY4GtcfxfnG8Ay621yyN4js4v53y6wBiT1mac8licSQI2hOyXjHNt2IY2+0GU3u90MV87rLVbgeXAV9ts+hrO1ZmvBPdrAhYCXzbGhP7hcRHON7TtnIk9zeU407Isi+A5XwXqgUh+WfU4wfPlEpxfLC1zT3+AMw1cuPNuN85MBnHBGHMB8DfgL9bamyJ8ejydY88Ds4wxw1pWBP+gP4ae//5zUMYYD84Y9hOB8621H3bweYNxZpn5OIrlxQRjzDRgFPva4nkg3xhzQsg+WcA5xOk5F2yjsXSw00jnVysv4MwmdnHLipDfj69ZaxuDqxfi5K9wvx8/D0620Olivkf5UARP6CHs+0NhrDHmouDHL4f8RXMH8KIx5v/h/Ct3Cs74rAdt65tq3IMz1nS+MeaPwdf+FbDA7n9jhB7DGHMUziwEP2xn+3HAbcAzOBd+9ML5i/tc4DYbRzdCMMZchjNt0svANpyL+b4PHAVc1rKftbbZGHMXzg1GtuPccORE4ErgB8E/zHq84B2ZnsD5Y/XvxphZIZsbg+ModY45/oxzYeh/jDF34vRQ/RTnPPt/bhbWTfwR5xfwfUBtm3OpyFpbZIx5AOf3wQc4F1uNwrmBRiD4vLhhjPkXzgXHnwGVOL/3bge2Aw8Fd3sep60eN8bczL4bjhjgl11ccndxOc7Y93+13RDv51dIvpoaXJ5hjCkFSq2171hrlxpjngR+F/zvzybguzjzwe8NxdbaXcaY3wC3G2Oqcc7RS3B+R54btS8gWhM0d+cH8HecXybhHm0nwr4Q55d1I87dne4GEsK85vE4PwQNQAnOlflpbn+tUW7HB3H+ustrZ/sInJ737cH2q8EZq3qZ27W70FazcO6eVhJss0qcEHxaO/t/G2cWh0acm9l8z+2voYvb654D/Ixu1jm2X3sNxrmLaBXOnb6ea/teFq8PnD+g2juX7gnucyXOjDQVwZ/PYuDfwCi363ehvW7HudPlnmBbbAMeAQa02S8H50ZIu3GuLXgTmOR2/S61WSJOAH6hne1xfX4d4OdvUcg+qTh3MywO5qiPgDlhXisBp8NyS/A9fwVwUTTrN8EDi4iIiIhICI1RFhEREREJQ0FZRERERCQMBWURERERkTAUlEVEREREwlBQFhEREREJQ0FZRERERCQMBWURERERkTAUlEVEREREwlBQFhEREREJ4/8D/is0P/RuNzwAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12,9))\n", "plt.grid()\n", "xs = np.arange(-100, 100, 0.5)\n", "ys = np.array(list(map(lambda x: tanh(x),xs)))\n", "plt.plot(xs,ys,color=\"red\",label=\"Actual tanh\", linestyle=\"dashed\")\n", "\n", "colors = iter(color_palette)\n", "for t in range(2,10):\n", " ys = np.array(list(map(lambda x: BRS_tanh(x,t), xs)))\n", " plt.plot(xs,ys,color=next(colors),label=f\"BRS's tanh (t={t})\")\n", "\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## That's awesome!\n", "\n", "\n", "Reference: [\"PP is closed under intersection\" by Richard Beigel, Nick Reingold and Daniel Spielman](https://www.sciencedirect.com/science/article/pii/S0022000085710173)" ] } ], "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": "3.8.2" } }, "nbformat": 4, "nbformat_minor": 4 }