{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Image of an accretion disk around a Schwarzschild black hole\n", "\n", "This [Jupyter/SageMath](https://www.sagemath.org/) notebook is relative to the lectures\n", "[Geometry and physics of black holes](https://relativite.obspm.fr/blackholes/)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.1.beta8, Release Date: 2020-03-18'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Function $\\Phi_b(u)$\n", "\n", "We evaluate $\\Phi_b(u)$ via the functions [elliptic_f](https://doc.sagemath.org/html/en/reference/functions/sage/functions/special.html?highlight=elliptic_f#sage.functions.special.EllipticF) and [elliptic_kc](https://doc.sagemath.org/html/en/reference/functions/sage/functions/special.html?highlight=elliptic_f#sage.functions.special.EllipticKC) of SageMath, taking into account that the second argument of `elliptic_f` and the argument of `elliptic_kc` is $m = k^2$ and not $k$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def Phi(u, b):\n", " u = RDF(u)\n", " b = RDF(b)\n", " bc = RDF(3*sqrt(3))\n", " if b > bc: \n", " xi = 2*arcsin(bc/b)/3\n", " un = RDF(1/3*cos(xi + 2*pi/3) + 1/6)\n", " up = RDF(1/3*cos(xi + 4*pi/3) + 1/6)\n", " ua = RDF(1/3*cos(xi) + 1/6)\n", " k2 = (up - un)/(ua - un)\n", " phi = arcsin(sqrt((u - un)/(up - un)))\n", " # NB: elliptic_kc() and elliptic_f() takes m=k^2 as argument\n", " aa = elliptic_kc(k2) - elliptic_f(phi, k2)\n", " return sqrt(2/(ua - un)) * aa\n", " else:\n", " xi = bc/b - sqrt((bc/b)^2 - 1)\n", " un = (1 - xi^(2/3) - xi^(-2/3))/6\n", " us = sqrt(un*(3*un - 1)) + un\n", " k2 = (us - 2.5*un + 0.25)/(2*(us - un))\n", " phi = arccos(abs(us - u)/(us + u - 2*un))\n", " # NB: elliptic_kc() take m=k^2 as argument\n", " aa = elliptic_kc(k2) - elliptic_f(phi, k2)\n", " if u > us:\n", " aa = - aa\n", " return aa / sqrt(2*(us - un)) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Asymptotic direction $\\varphi_\\infty$ from some emission point" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def phi_infinity(r_em, b, phi_em=0, pre_periastron=True, eps_L=1):\n", " # print(\"r_em: {}, b: {}\".format(r_em, b))\n", " u_em = RDF(1)/RDF(r_em)\n", " b = RDF(b)\n", " bc = RDF(3*sqrt(3))\n", " phi_em = RDF(phi_em)\n", " if b > bc: \n", " if pre_periastron:\n", " return phi_em + eps_L*(Phi(0, b) + Phi(u_em, b))\n", " return phi_em + eps_L*(Phi(0, b) - Phi(u_em, b))\n", " return phi_em + eps_L*(Phi(0, b) - Phi(u_em, b))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "2.5472182273726496" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "phi_infinity(6., 5.2, phi_em=pi/2, pre_periastron=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Value of $b$ for a given $(\\varphi_\\infty, r_{\\rm em}, \\varphi_{\\rm em})$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def find_b(phi_inf, r_em, phi_em, pre_periastron=True):\n", " phi_inf = RDF(phi_inf)\n", " r_em = RDF(r_em)\n", " phi_em = RDF(phi_em)\n", " bmax = 0.999*sqrt(r_em**3 / (r_em - RDF(2)))\n", " eps_L = 1 if phi_inf > phi_em else -1\n", " bc1 = 1.0000001*RDF(3*sqrt(3))\n", " def delta_phi(b):\n", " return phi_infinity(r_em, b, phi_em=phi_em, \n", " pre_periastron=pre_periastron, \n", " eps_L=eps_L) - phi_inf\n", " return find_root(delta_phi, bc1, bmax)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "6.932148479189469" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "find_b(0, 6., pi/2, pre_periastron=False)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "5.478913722083879" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "find_b(2*pi, 6., pi/2, pre_periastron=True)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "5.207989587554517" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "find_b(-2*pi, 6., pi/2, pre_periastron=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $\\varphi$ as a function of $r$ along a null geodesic parametrized by $(r_{\\rm em}, \\varphi_{\\rm em}, b)$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def phi_sol(r, r_em, phi_em, b, em_pre_periastron=True, \n", " pre_periastron=True, eps_L=1):\n", " u = RDF(1)/RDF(r)\n", " u_em = RDF(1)/RDF(r_em)\n", " phi_em = RDF(phi_em)\n", " if em_pre_periastron:\n", " if pre_periastron:\n", " return phi_em + eps_L*(Phi(u_em, b) - Phi(u, b))\n", " return phi_em + eps_L*(Phi(u_em, b) + Phi(u, b))\n", " return phi_em + eps_L*(Phi(u, b) - Phi(u_em, b))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1.1962212307131173" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "phi_sol(7, 6, pi/2, 6.93)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Periastron as a function of $b$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def r_periastron(b):\n", " return RDF(2/sqrt(3)*b*cos(pi/3 - arccos(3*sqrt(3)/b)/3))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "3.0" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r_periastron(3*sqrt(3))" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(4.453363193811356, 8.78885066249973)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r_periastron(6), r_periastron(10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computation of null geodesics" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def geod(r_em, phi_em, b, eps_L, em_pre_periastron=True, rmax=25, np=500):\n", " resu = []\n", " if em_pre_periastron:\n", " rp = 1.001*r_periastron(b)\n", " if r_em < rp:\n", " raise ValueError(\"r_em < r_per(b)\")\n", " dr = RDF(r_em - rp)/RDF(np - 1)\n", " for i in range(np):\n", " r = r_em - i*dr\n", " phi = phi_sol(r, r_em, phi_em, b, em_pre_periastron=True,\n", " pre_periastron=True, eps_L=eps_L)\n", " resu.append((RDF(r)*cos(phi), RDF(r)*sin(phi)))\n", " #\n", " np = 2*np\n", " dr = RDF(rmax - rp)/RDF(np - 1)\n", " for i in range(np):\n", " r = rp + i*dr\n", " phi = phi_sol(r, r_em, phi_em, b, em_pre_periastron=True,\n", " pre_periastron=False, eps_L=eps_L)\n", " resu.append((RDF(r)*cos(phi), RDF(r)*sin(phi)))\n", " else:\n", " dr = RDF(rmax - r_em)/RDF(np - 1)\n", " for i in range(np):\n", " r = r_em + i*dr\n", " phi = phi_sol(r, r_em, phi_em, b, em_pre_periastron=False,\n", " pre_periastron=False, eps_L=eps_L)\n", " resu.append((RDF(r)*cos(phi), RDF(r)*sin(phi)))\n", " return resu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inner and outer radii of the accretion disk:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "r_disk_in = 6\n", "r_disk_out = 9" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Colors of the various images:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "color1 = 'orange'\n", "color2 = 'peru'\n", "color3 = 'red'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Emission from the upper part of the disk ($\\varphi_{\\rm em} = \\pi/2$)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "phi_em = pi/2" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "r_em = r_disk_in" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "em_pre_periastron = False" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "6.932148479189469" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b1_in = find_b(0, r_em, phi_em, pre_periastron=em_pre_periastron)\n", "b1_in" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "eps_L = -1" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = circle((0, 0), 2, edgecolor='black', fill=True, facecolor='grey', alpha=0.5)\n", "graph += circle((0, 0), 3, color='lightgreen', thickness=1., linestyle='--', zorder=1)\n", "graph += line([(0, r_disk_in), (0, r_disk_out)], color='darkorange', \n", " thickness=4, zorder=50)\n", "graph += line(geod(r_em, phi_em, b1_in, eps_L, em_pre_periastron=em_pre_periastron), \n", " color=color1)\n", "graph" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "em_pre_periastron = True" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "5.478913722083879" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b2_in = find_b(2*pi, r_em, phi_em, pre_periastron=em_pre_periastron)\n", "b2_in" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "eps_L = 1" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph += line(geod(r_em, phi_em, b2_in, eps_L, em_pre_periastron=em_pre_periastron),\n", " color=color2)\n", "graph" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "eps_L = -1" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "5.207989587554517" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b3_in = find_b(-2*pi, r_em, phi_em, pre_periastron=em_pre_periastron)\n", "b3_in" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 6 graphics primitives" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph += line(geod(r_em, phi_em, b3_in, eps_L, em_pre_periastron=em_pre_periastron,\n", " np=4000), color=color3)\n", "graph" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "r_em = r_disk_out" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "em_pre_periastron = False\n", "b1_out = find_b(0, r_em, phi_em, pre_periastron=em_pre_periastron)\n", "eps_L = -1\n", "graph += line(geod(r_em, phi_em, b1_out, eps_L, em_pre_periastron=em_pre_periastron), \n", " color=color1)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "em_pre_periastron = True\n", "eps_L = 1\n", "b2_out = find_b(2*pi, r_em, phi_em, pre_periastron=em_pre_periastron)\n", "graph += line(geod(r_em, phi_em, b2_out, eps_L, em_pre_periastron=em_pre_periastron),\n", " color=color2)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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7Cg4IgA8/lOFnIYRoQyT4eojdbufxxx8nMTGRgIAAPnxoIsVFBcRPeqz+9JEtMXKkDD8LIUQbIsHXQ1588UX++9//8sYbb/DH/Fc5LT6AJ+Zu460Pv/BMhVXDzzL7WQghWj0Jvh6ydu1apkyZwlmn9aLsz6+JHn4ZYd1HsmHDBs9UWDX8vHEj/POfnqlDCCGEW0jw9ZAxY8bwy8qf2Tn3cfw7dCUnahS//PILF1xwQYP3WK1WCgsLsTsczat05Eh46CF46inYsaN5ZQghhPA4Cb4eMmPGDJ67djilR9OZ9PhXDB02nPvvv5+rr244qcbMmTMJCwsjeX1y8yt++mmIj4ebb4bmBnEhhBAeJcHXQxa99zzdzFkUdDqb+Ut/5aOPPuKf//wnH330UYP3PProoxQUFDB8xPDmVxwQAO++C2vWwH/+0/xyhBBCeIzJ1w04GVkLMgk9uJic4K6cf+tTaJrGwIEDOXDgADNnzuT666+v9z6LxYLFYgFjC2dDjx0Ld90Fjz4KkyapNJRCCCFaDen5upnutLN/wbOUWB3sDxxea5lAo9GI0+n0TkNmzoTISLjtNtB179QphBDCJdLzdbOMXz6h5PA2VuXH88mcl+mc0IP+/fvzxx9/MGvWLG666SbvNCQ0FN5+G84/X82CvvFG79QrhBDihCT4ulFx2mYyf/2EuDHX89g9l1Dm/wR33XUXWVlZdOrUidtvv50nn3zSew067zyYPl0l4DjvPIiL817dQgghGqTpuoxJuoO9rIjt792MJSyWnte80rIsVp+Ngox1tY/FjYRpa5te1tGj0K8fnHEGzJsHNYbBhRBC+IY883UDXddJ+/5lnLZSEib/zf3pI1siKgpmz4Zvv4Wvv/Z1a4QQQiDB1y2OblpE/s5VxF/wf5jDYnzdnLouuwwuuQTuuUf1hIUQQviUBN8WKss5wMFlrxN16kVE9Bnn6+Y07I03wGaDBx7wdUuEEKLdk+DbAk67lf3fPoMlLJYuE+5xW7mZmZluK+uYuDh45RX45BP44Qf3ly+EEMJlEnxbIH3Fe5QfTSNh6hMY/PzdVm5sbKzbyqrl+ushKQluvx0KCz1ThxBCiBOS4NtMhakbyVr/FZ3G30pgTA9fN8c1mgZvvQW5ufDII75ujRBCtFsSfJvBXlbEgYUzCek6lOgRl/m6OU2TkAAvvABvvgmrVvm6NUII0S5J8G0iXdc5uHgWzopyuk56BE1rg3+Ed90Fo0erlY/KynzdGiGEaHfaYOTwrbytP5K3fTldJj6AOTTa181pHoMB3nsP0tLgH//wdWuEEKLdkeDbBNaCTNKWvEpE/3OJ7H+Or5vTMr17w+OPw8svQ0qKr1sjhBDtigRfF+lOBwf+NxOTJZguE//i6+a4x4wZ0LOnWvnIW6stCSGEkODrqiO/fUVx2ma6TnoUk3+Ir5vjHmazWvlo3Tr473993RohhGg3JPi6oDRzNxkr3yNm5FWEdD3V181xrzFjVM/3kUfg8GFft0YIIdoFWVLwBJwVVvZ/9xz+HboSN9Y7a+JmZmbioTQb9XvxRfjuO7j3XrXykRCiddB10J3A8XunOldr38Cx4++tc0xXe/TqOl39fmxRvJrluPA9+ky3/jG1RRJ8T+Dw8rex5h2mz01vYzCZvVJnbGwsZOz3Sl0AhIfDv/8NV16pVj+aOtV7dYu2TXeC0w56hdo7K0BvbH+Ca2qWVfOc7gTdcdxW37GmHm9mGQ0GskYC47F7mhAYT1bTTuKfzUUSfBtRuC+Z7A3fcMq59xDQMdHXzfGsyy+Hjz9WKx+dfTaEhvq6ReJ4ug6OcnCUqc1eWv251lYOThs4rGrvtB73uXJ/7Bpr49fXOmerHSw9GSA0ExhMaq8ZQDMet7l4DAMY6jlW9dlgAs1S+5hmVPccf+xYHZUb2nF7Q+Wa2TX3DRw7/l5Xjx1fR2P1nrA8Te1rfabuOaj+7up1x87RQB3tmwTfBqgsVi8SkjiMjsMv8XVzPE/T1Lq//fqpV5Bee83XLWqbnHawF0NFkdpXbTW/1/u5nkBqLwNHae2g2hSaAQwWMJjBWLk3WGp/rnnO6A/msPrPHbvPDzQ/ta8KjAa/hvcGU+X19Vxb89zx92rGGv9wC3HykeDbgEPLXsNZUUbXC//aNrNYNUfXrvDss/DQQ3DNNXD66b5ukXc5K8BWABX5YMuv3tvyoaKg/mMV+dUBtKJI9RQbpYEpGPyC1d4UAqYgMAWCMRDMkWAKAGPVFnjc94DKaxs75l8ZMOV/byFaK/m/sx75O1eTu2UZXSc92nazWDXXvffCnDlw662wcSP4+fm6Rc3jKAdrTvVWngO2o7WP1dpyVS+zIX6h4BeueoZ+4WAOh6CEyu+hlYG0cvMLaeBzsAqm0qMTot2T4Hsce2k+aT/MIqznaCIHJPm6Od5nMsE778Dw4TBrlkrE0Vo47VCeBeUZUJYJ5ZlQVvW5cl+WAdYssJfUvd/gB5aOYIkCSwe1hfRUe3OE2qoCq1+Y2pvDwRRa+fxPCCHcQ4LvcdIWv4quO4g//0G09tpDGToU7r8fnnoKLrsMunf3fJ2Ocig5CKWVW0la9eeydBVoy7OpPcFHA/+O4B+rtpCe6hUG/5jq4FpzMwVLr1MI0SpI8K0hd9vP5O9YQcLUJ/ELjvJ1c3zr6afh66/V7Ofvv2950LKXQvG+ym0vFO+H0rTqQGvNrn29fzQEdlFbxzMhIBYC4lSQDYgF/zgVeA1tdFhcCNGuSfCtVFF8lINLXiW871lE9jvb183xveBgNeN56lSYPx8ucWHGty0PCnZA8R4VZIv2Qknlvjyz+jpjgHpeGhQPEUOh8xT1ObBL5f4UNWlICCFOUhJ8UWv0pv3wLzTNSHwrWDTB6xmuGjJ5Mlx0EfzlL5CUpAKy7lS91YIdULgdCndUbtvV89gq/jEQ3A2Cu0PMOWof3A1Cuqveqwz/CiHaMQm+QG7KEgp2r6HbZc9iCgz3dXO8n+GqPrqueqt/uwTGL4bbR8C1/lC4s3pWsMECob0htC9Ej4ewvup7cA81s1cIIUS92n3wtRVmcWjZ60QOSCK81xhfN8c3nBWq95r3J+Rtgvw/1eeq57BTzPDlDrjoEjj1GhVsw/pAYFeZBSyEEM3QroOvruukff8yBr8ATplwr6+b4x1OBxTthKPrq7f8FJU2ECAoESIGQ8+71D5iMFwSB38Mhv9mw4oHZchYCCFaqF0H39yUxRTuS6b7lS9iCjhJ1ug9XulhOPpbjWC7AexFgAZh/SBqOCTeoIJs+CCVNKI+s2er576ffgrXXuvNn0AIIU467Tb4VhQf5dCPs4kcOJGw7idJGkVdh6JdkLUaslZB9moo2a/OBXaBqBEw4HG1jzxNZV9y1YQJcMUVKvXkRReplZCEEEI0S7sNvgeX/BvN4Mcp59zlsToOHz7MjBkz+OGHHygrK6NXr1689957nHbaae6pwOmA/M0qyFYF2/IslVA/YgiccrFKOtFhpHpHtqVmzYI+feCJJ+D111tenhBCtFPtMvjm7VhJ/s5VJF78FKbABoZZW1pHXh6jR4/mrLPO4ocffiA6Opq9e/cS3pIeo66rBBWZyyBjKRxZrpL7G8yqN9v9Fug4FjqOUvmG3a1zZ3jmGXj4YbjhBnDXLxFCCNHOaLqut6tVje1lhWx7+3qCOven26X/8FgKyUceeYRff/2V1atXN/3mz0ZBxrrax0KiISYISlLVkmsdRkHsuRAzXgVebyWlsNtV0PX3h7VrwdBOVnwSQgg3anf/ch766T/odhtdJt7v0dzN3333HcOGDePyyy8nOjqaIUOG8M477zR6j9VqpbCwELvDUfdkRSF0vhDGfgeX5cKEVTDwSYge691sUCYT/Oc/sH49vP++9+oVQoiTSLsKvoX7ksndvJjO59yFOaSDR+vat28fb775Jj179mTJkiXccccd3HfffXz88ccN3jNz5kzCwsLYvvn3uidDB8Kw1+GUSU2bKOUJo0erGc+PPQb5+b5tixBCtEHtZtjZYStl+zs3YonoTI+r/+XxFYvMZjPDhg1jzZo1x47dd999JCcns3bt2nrvKS8rJWP1h3T881GCDYW1T2YFwJ3bICHBg61ugvR06NULbrtNTcQSQgjhsnbT801f8S720gLiz3/YK0sFxsXF0a9fv1rH+vbtS1paWr3X24pySPv6UfI2fo0hdih63Ejs0cNZux/sIQMgx6TW2P3lF4+33SWdOsHf/qZmPW/f7uvWCCFEm9Iugm/J4W1kb5hP3LibsUR08kqdo0ePZufOnbWO7dq1i65du9a5tnDfena8dwvWvMP0vOYVAq9bjjZtLaVTfuSMN6D0ql/hpVQYMADOPhs++MArP8MJPfAAxMerffsYQBFCCLc46YOv7rST9sO/CIztSfQwF5bFc5MHHniAdevW8fzzz7Nnzx4+++wz3n77be6+++5abTu84h32fPFXAmN70ufmdwmJH1x/gVFRsGQJ3Hgj3HSTSnZR38Qsb/L3V0POS5bAwoW+bYsQQrQhJ/0z3yO/fcXhn/9L7xv+Q1BcH6/WvXDhQh599FF2795NYmIiDz74ILfeeisAFcW5pM5/muJDKXQadzMxo65G02r/LlRYWEhYWBgFBQWEhla+t6vraqj3gQfgvPPgs88gzDPvKrtE12HiRNi3D7ZuBYvFd20RQog24qQOvraCI2x7+3qiBl9Al6T7fN2cY4oPbSV13t/RdSfdLn6K4PhB9V5Xb/CtsnSpSvcYHw+LFkGXLl5oeQO2bYNBg+DZZ+GRR3zXDiGEaCNO6mHng8tew2gJotPYm3zdFECtopS9cQG75/wFc3gsfW9+p8HAe0JJSbBmDRQWwsiRsGmTexvbFP36wT33qOCbnu67dgghRBtx0gbf/F2/ULDrV06ZcC9Gf98v7O6ssHJg4QscXPIKHYZOpuc1r+AXHNWyQvv1g3XrIC4OzjwTFi92T2Ob46mnICBAer5CCOGCkzL4OmylHFz6GqHdRhDeZ5yvm4M1P4OdH99D3vYVdJ38GF2S7sNg9HNP4bGxsHIlnHWWWm3oBFm0PCY8HJ57Dj75BJKTfdMGIYRoI07K4Jux+iPspfkeTyHpisLUDez44HYc1hJ6Xz+bqAFJJ7xn9uzZ9OvXj+HDh7tWSVAQzJ8Pd9yhkl489hg4nS1seTPcfDP0768WXjh5pxIIIUSLnXQTrkqz9rLjvVvpNO5mYs+4xmft0HWd7A3zOPTjbEK7DSdh8uOYApqWFrLRCVf1V6pe/Xn4Ybj6avU+sLdnH//wA1xwASxYAJMne7duIYRoI06q4KvrOrs+uQ97WQF9b3nPfUO7TeR0VHBwyb85umkh0adfQeezbkczGJtcTpODb5Wvv1a5l884A779Fppyb0vpupoMdvAgpKSAn2/+DoQQojU7qYad87b9TMmhFPc+U20ie2k+ez5/mNzNi+l64QxOOeeuZgXeFrnsMvjxR/j9d/UsOCvLe3VrGrz8Muza5bvnz0II0cqdNMHXYSvl8E9vEtbrTEITh/mkDWXZqez48E7Kcw7Q85pXiBp8vk/aAcCYMbBqlXr1Z/Ro2L/fe3Wfeipcf72aAV1YeMLLhRCivTlphp0Pr3iHrPVz6XfbR1jC47xef8GetaR++w/MYbF0v/w5t7Sh2cPONe3bp4aBS0tVYo4BA1rcLpccOqRWPXrgATULWrQ9uq5SmNrtal/zs92uNqsVbLaGt4qK6mtr3ltVnsOhJgfW/H788Zrnnc6636vaWfP64z9Xfa95bdWm62qr+lzzWNWfQ0PfGzvX2PeGPrt67vi9q8fq29f8+67vv4HGzjfnOMhSpIDJ1w1wh/LcQ2T99hUxo6b5JPBmb/yWg0tfI6znKBIm/w2jOdDrbWhQt25qJaTzzlPvAi9apJ4Fe9opp8CDD8K//qVmYfsyA1dr4HSqQFVern4RKixUW0EBFBVVb8XFaisvh7IydU/VdnxQq7nZ7bUDXUNB7viA01AAaS9qvg1x/JsR9b0pcaJrGiqvoeuO37vyuaV7g6HpdZ/o52jqNeLk6PnunfsYZUf20u/2jzD4+XutXl13kr78HY6s+5zo4ZfR+Zw73fp81y093yrQBQgXAAAgAElEQVQFBWr2cXKympB1wQXuaWRjioqgRw8V+D/6yPP1tYSuq4CXnw9HjkB2Nhw9Cnl5kJurjhcUqIBZFSBLSlQgLStT9x7f06sZ7NxJ06o3g0FtmgZGo/psNNbeTCa11fxc9b3mNTW/+/nV/lzznqrv9e39/MBsrv39+Pvrq79mG2qeq6/dVT/z8VvNP4+GjksgEK1Em+/5Fuz9jYLda0i8+CmvBl6n3caBhS+Qt205p5x7N9EjLvda3c0SFqYyYF11FUydCl98AZd4eJWnkBD13Pfuu+H//s/zQ95OpwqWBw+q4fYDB9Qz76wsdTw/vzp4lpRU9yyrgmVTVAW7qiBjNqstJESt9mSxqM3fX20BAWoLDFTvZdfcgoPVjPSQELWv+hwYqMqoGcQkeAhxUmjTPV+no4Lt79yIX0hHek6b5bWEGvayIvZ9/Tgl6dtImPI4ER7KouXWnm+Vigq47jrV+50zRwVjT7LZoG9ftfDC/PlNu1fXVe95zx7Yvl3NoE5NhYwM1SvNz1fnS0tVPScKoAaDCpZmc3VADA5WgS4sDCIj1dahA0REqGUcIyPVvupYUJC6V4KgEKIF2nTPN3vjt1jz0ul2yTNeC7zWgkz2fjGDitI8ek6bRXCXgW6vY/bs2cyePRuHJ9br9fODTz9VPaprrlE9v+uvd389VcxmePppFfDXr4cRI9Rxp1NNyvr9d/jzT9ixQ/VYq3qpxcWqbQ39bujnp4JgUJB6vhweDh07QnQ0dO6sjiUkQGKiSsEZHFz9rEsIIXyszfZ87WVFbH1zGhF9xxN//kNeqbMsO5U9n/8fmsmPHle+iH9UvEfr80jPt4rTCbffDu+9B2+9BZXrDLuNrkNmplp5ae1aNfEKICZGPTstL697j8GgAmpoqOplxsRUB9GePVXqyu7dVS9Vep5CiDaszfZ8M9d8gu6oIO7MG7xSX0n6DvZ8+VfMIR3pcdVLLV+RyNcMBhV0/f1VPmirVS0L2FQFBep94jVrVEarPXtU0C0qqn+i0dGjKpB26aImY/XrB6edpgJrSNPSbwohRFvVJoOvNT+D7A3ziR19nVeCYNH+P9j79WMEdOxG9yteaHKO5lbLYIDXXlND0Pfeq56Z3n9//ddarSrALlumZkzv2qVmBVutta/z91fPR/v3V896hw1Trzj16qWSfRiNqhzpuQoh2rE2GXzTV7yDKSDMKzOM83f9Sur8pwiOP5Vulz6D0Rzg8Tq9qiodpMmkEmJYLOr57A8/wPffq0C7f7+aHVxTaKgaAh4wAEaNgnHj1OfGcjk//zxMmAALF8KkSR79sYQQojVrc898S9K3s/PDO4m/8K90GOzZd1WPblnKgf+9QHivMSRMeRyDyezR+o7n0We+VRwOWL4cvvqq/lzMfn5qAlP//irITpyo0keamvF7m67DOedATg5s2iQToIQQ7Vab6vnqus7hn97Ev2M3ogZO9GhdOZsWkfb9y0QNvoD48x9EM7SpP6qGlZTA3LlqtaPkZPXaTtXvX35+6lUkUIkx3nlHTXhyF01TqSbPOEO96nTFFe4rWwgh2pA21fUo2P0rxQc3c4qbM0kdL+ePhaR9/zIdhk4h/oL/a9uB12pVrxadf756ZzU4GG68Ua23W1wMI0eqRBi7d6t3ZR0OuOkmlQd6zRr3t2fUKJVr+tln3Z/5SQgh2og2E1V03Un6yvcI6TqU0G7DPVZPzh//I+2Hf9Fh6FS6TPyL194fdhtdh19/hbffVsPJhw9X92w7dFBBeOpU1esMD697v8Gg7rXZYNo09Qx4yhT3tvGJJ9QkrO++U20RQoh2ps08883d+hP7F/yD3tfPJqhzf4/Ukf37dxxcPIuOp03llCTfB16Xn/nabPDJJ/D++7BxY/UM5KAg9Xz28svhhhvU+7GusttV9quFC1UveOzYFv0sdZx9tspQtXGjzHwWQrQ7baLnqzvtZKz+gNAeo7wQeC/mlKT7fBp4XcpwlZ8Pr7wCX36phoydThXEEhJUb/Luu9Vs5OYymdRw9QUXqAUZVq6EwYObX97xnnwSzjpLzai+8EL3lSuEEG1Am+j55vz5PWmLXqLPze8QGNPT7eUf3byYAwtfaBWBt6Y6Pd+yMvj3v1UPd/dudZHJpILi9Olwyy0qGb97G6GCZHq6Gs7u1s095eq66k3bbLBunfR+hRDtSqufcOW028hc/RHhfcZ7JPDm7VjFgUUvETX4glYVeGv54AMYOFANIz/6qFpc4Iwz4Jtv1BDzhg1w333uD7yg3uf94Qc1UWviRJV72R00TfV+169Xw9pCCNGOtPqeb/aG+Rxc9jp9b/2AgA5d3Vp2YeoG9n71KGG9xpA45XGPzqBusi1bKHz4YcKWLKEACDUY1PPb++6Da69VmaK8qSrgd+oEK1a4JxWkrqvZzyYT/PJLy8sTQog2olX3fJ0VVjJ+/YTIARPcHniLD21h39ePE5IwlITJj7WOwGu1wj/+oZJaDBwIS5ao408+qZbN27hRrUDk7cALanWgJUtU7uarrmr6+rf10TT429/UcLYnXmsSQohWqlUH35xNi7CX5hM3Zrpbyy3N2sveL2cQGNubbpc8jcHYSEpEb0hLUwvbBwerQHv0KFx8sRpOBnjoIfXKj68NGqQyYS1ZotrkDhdeCH36qBSXQgjRTrTa4Ot0VHBk3edE9j8HS0Rnt5VrK8xi7xczMId3ovsVz2Pw83db2U22bJkaSu7aVS00HxcH//2v6uXOm6dW/2ltJk6E119XCzK88UbLyzMYVCBfsEAt1iCEEO1Aqw2+uSlLqCjKIWbUNW4r01FezJ4vZ6AZjfS48gWMliC3lX0iM2fORNM07r//fvjsMzW0nJQEmzerZ6m//aZ6wLff3vpzHt95p1qE4S9/Ua8KtdS110J0NMya1fKyhBCiDWiVE650p51tb00nILoH3S59xi1lOh0V7P1yBqWZu+g1fbbbnyE3Jjk5mSsuv5yb7Hbuz80lpKxMTTK68kr16lBU/csiemVhheZyONTQ+PLl6nntwIEtK+/55+GZZ9QvINHR7mmjEEK0Uq2yi5W3fQXWvHRiR1/nlvJ0XSft+39SfDCFbpc959XAW1xUxP8uvJBdR4/yxOHDBFitcMcd6v3ZOXNqBV6r1UphYWGtrdUyGlUPvnt3ldQjL69l5d1xh/qFxB1D2UII0cq1uuCr604yf51DaPeRBMa655ln5i8fk5uyhK4XPUJIvBuzNJ3IggXYo6N5Jjsbv4oKPj/lFP56553w5psQUHdd4JkzZxIWFnZs69Kli/fa2hzBwepZdX4+XHON6g03V2Qk3HwzzJ6tnnkLIcRJrNUF34LdayjP2U/s6GvdUl7+ztVkrP6AuLE3Edn/HLeUeULr1qnJUlOnElxejv2WW6CggLe6d8fZyDq4jz76KAUFBce2gwcPeqe9LZGYCJ9/DosXq9WRWuL++1UP+rPP3NI0IYRorVpd8M367SuCThlA8CkDWlxWWdY+9n/3HOF9xrttCLtRubkqFeOoUeh797LQbGb76tWY3nnHpVeFLBYLoaGhtbY2ISlJrdP77LNqneDmSkxUrx7Nnl29EpMQQpyEWlXwLUnfQfHBzcScfmWLy7KXFrD3679hiehM14tmeDZtpNOp0j7GxKjsT8OHs+Stt5hkszFk/HhMJhMmk4mVK1fy2muvYTKZGl80oS165BE1AWv6dNi5s/nl3HMPbNokSTeEECe1VrWqUdb6uZjDOxHW84wWlaM77aTOfxqntZSe02ZhNNd9vuo2y5erJfuOHlWTpz7+GC64gNFFRaSMGlXr0htvvJE+ffowY8YMjL7IUuVJmgYffQTDh6sMWGvXgn8z3qGeMAF69FC939Gj3d9OIYRoBVpNz9dWmEXe9uVED7+sxakeD694l6KDf5J4ydNYwuPc1MLjWK1qlm/VurSPPALZ2WoJPiAkJIQBAwbU2oKCgoiKimLAgJYPqbdKISHwxRewbRv89a/NK8NgUMshfv01ZGa6t31CCNFKtJrgm7VhHkZzAFGDz2tROQW715C17gs6n3UbIV1PdVPrjvPtt6qXu2CBer81LQ1mzpRl8UBl7PrXv1QWrAULmlfGDTeAnx+8845bmyaEEK1Fq0iy4bCVsuX1y4kaMolTzr6j2eXYCo6w/f1bCT5lAN0ue879z3ltNpWDedEiFRxeeUX10jykVSfZaIyuq+e/q1er57fNeWXq9tth4UI4cEC9/yuEECeRVtHzzd3yIw5bGdGnXdzsMpyOClK/fRqjOYCuFz3i/sC7cSPExqrAO3SoGhL1YOBt0zQN3n9frT/c3Pd/b7sN0tNlrV8hxEnJ58FX13Vyfl9AWI9RmMNiml1O+op3KM3YReLUv2MKcGMvUdfVTObhw6GgQKVB3LhRJYUQDYuMVBm8fvlFpdBsqqFD1SpK77/v/rYJIYSP+Tz4lqZvpyxrLx2GTm52GYWpG8j67Ss6nX07QZ37ubFxpSrovvCCyje8ZYsKxB42e/Zs+vXrx/Dhwz1el0eNHasWX3jsMdixo2n3ahrcdBN8952ayCaEECcRnz/z3b/wBYoPbKL/nZ82a5azvayI7e/eiH9UPD2u/iea5qbfJ7ZsgTFjVG938mS1xJ+XXw9qs898ayorU5OwwsPh11+b9vw2Jwc6dYIXX1SrKAkhxEnCpz1fe1kRedt+psOQSc1+vejg0n/jtJVVPud104/z3nsqYBQWqklVCxZ4PfCeNAIC1Pu/GzbAyy837d4OHWDKFPX34ft5gUII4TY+Db65KUvQnQ6iBp3frPvzti0nb+uPdJl4P+ZQNy1Dd889cMstKmisW6fyDYuWGTkS/u//4O9/h+3bm3bvTTfB1q2QnOyZtgkhhA/4LPjquk7OpoWE9zoTv+CmT16qKD5K2pJXCO97FhH9z215g5xOlaN49mxISIBDh2DEiJaXK5SnnlJ/rnfe2bRebFISxMXBp596qmVCCOF1Pgu+ZZm7KM/ZT9Tg5vV6Dy59DU0zEj/x/pa/VlRSAn37wrJl6jnv7t0QFtayMkVt/v7wn//AypVqGNpVRiNccQV89VXLliwUQohWxGfB92jKUkxBkYQmntbke/N3/Ur+jpWcMuEeTIEtDJJHj0K3brBrlxriXLVKkjp4yrnnwrRp8PDD6s/dVVddpd6rXrXKc20TQggv8knw1R128rb+SOSAc9EMTQt0DmsJB5e8Smj3kUT0O7tlDcnIUEn8s7LgmWfUxB5JEelZs2aB3d603M+nn66GrL/4wmPNEkIIb/JJ8C3Y+xv2sgKiBjY9j3P6yvdwlBfR5bwWDjfv3w+9e6tFEV59FZ54ovllCdfFxKg82O+/D+vXu3aPpqne79dfQ0WFZ9snhBBe4JPgm5uyhICYHgREd2vSfaUZO8neMJ+4cTdjCYttfgNSU6F/fyguVr3dv/yl+WW5gVN3UuIsIcueRWpFKrtsuzjqqB6W3WXbxS7bLg5UHCDHkUO5s9yHrXWD225TC1I8+KDrk6+uugpyc+HHHz3bNiGE8AKvP9x0lBdTsGctncbf2qT7dF3n4LLX8e+YSPSw5ueAJiNDpS0sK1MzaK++uvllNVG5s5wjjiNkObLItmczPnA8gYZAfij5gT0Ve45dt/rd1fz+/u/4Of0A+KnkJ/yN1WvjRhoiuS7sOgDmF80n2BBMtDGaGFMMHYwdMGmt/Jm10aiGnydMUL3Zyy8/8T2DBqmRirlz4fzmTdITQojWwuv/SufvWYPuqCCi7/gm3Ze37SdKDm2h57RZTX5OfExubnWP9913PR54y53l+Bv80XWdTwo/Ic+ZB4AZMx1NHXGgZu8O8R9CX3NfggxBBBmCuPPhOzE+bKSkqISwsDBuCb+F4NBgyp3llOglVCUlc+pOggxBZDuy2WHbgRMnGho3hN1AqCGUHEcOIYYQLJrFoz9ns5x7Llx0EcyYAZMmqdnQjdE0lXDjgw/UrGdJeiKEaMO8H3x3rCSoc78mJcVw2Mo4/PN/Ce89lpCEoc2ruLQU+vWDvDyVtermm5tXTiN0XSfLkcW+in3sq9hHkbOIW8NuxagZGWAZQKAhkBhjDOGG8FrPqzuZOjVarp/mh0WzYDFaCKN6drdBM5AUlASAXbdz1HGUbEc2IVoIAEtKlpDryKWzqTPd/LrRza8bocZWlKby5ZfV8PNrr7k2AWvyZHjpJfWseNQoz7dPCCE8xKvPfB3WUgr3rie8z7gm3Xdk7efYSwvo3Ny1fp1OGDYMjhxRyR48kLWq3FnO+wXv80XRF/xp/ZMoYxRnB1bPxh7qP5Q+5j5EGCPcv9whYNJMxJhiGGAZcKz8ScGTGBswFgMGVpet5oPCD8iwZ7i97mbr00c9/33hBZXK80RGjlQpJ7/7zvNtE0IID/Jqz7dgz1p0R0WTgm9F8VGO/PYl0SMuxxLReA+xQZMmqbSG116rUhy6ga7rpNnT2Fexj/EB4/E3+DPEfwjRxmg6mTphcFee6RYINYQy2H8wg/0HY9WtpFWkEW1UIw6LihcRaAhkkGUQUcYo3zXyscfUpLdXX4Unn2z8WqNRDVV/952aMS2EEG2UV4Nv/o6VBMb1adJM5cxf52Aw+REzqpnPZx98EL7/XvWaPv64eWXU4NAdbLFu4Q/rHxQ4C+hg7ECpXkqQFsRQ/2YOiXuBRbPQ09wTUL84RBoj2WLdwmbrZjqbOjPcfzjxpniP9Mob1bmzSjk5axbcey9ERDR+/eTJ8OGHsGePekdbCCHaIK91z5x2K4X71hPe+0yX77HmZ5Dzx/+IGXk1Jv+Qplf65Zfq+W6XLio7UgsDi67rfFP0DSvKVhBjjOHykMuZFjKNIENQi8r1Nk3TGBUwipvCbuL8oPNx6A4WFS/Cqlt906AZM8BmUwH4RCZMAD8/+OEHz7dLCCE8xGs93+K0P3FWlBPW8wyX78n45SOMASF0HHZJ0yvcu1cNM/v7w8aN6h/sZtB1nQP2A3QwdiDYEMyIgBEEG4LpYOzQrPJaE6NmpJe5Fz39elLgLMDf4I/VaWVF2QqG+w8n0tj0BS+aJTYW7r5bDT0/+GDjvd/gYDjjDPjpJ9VTFkKINshrPd+CPeswh8bg3yHBpevLcw6Qm7KUuNHTMZoDmlaZzab+gbbbYeFC6Nix6Q0GChwFzC+ez4LiBWy3qaXwEvwSTorAW5OmaYQbwwEocBZw2H6YOYVzWFG6Aptu804jHnpI/b299daJrz33XFixQv39CiFEG+SV4KvrOgV71hHa/XSXnylmrvscv+BIok69sOkVTpqk8jU/8QScc06Tb9d1nT/L/2RO4RwKnAVMCprEMMuwprejDYo2RTM9dDpjAsaw1bqVTws/Jd2e7vmKY2Nh+nT497/BeoLh73PPhYICNaIhhBBtkFeCrzX3ELb8dEJ7jHTpelthFrlblhF9+pUYTOamVfbhh7B0qUrG/8wzTW8skOfMY1XZKvpZ+nFN6DV0M3fz6kSk2bNn069fP4YPH+61OmsyaSaG+g/lmtBrCDWEouGln/3BB9XqRZ991vh1w4ZBaKikmhRCtFmarjdlZfPmyVo/l8PL32bQA9+5NIR8aNkbHE1ZwoB7vsRoDnS9oiNH1OQqk0l9DnF9kpau6+yq2EUPvx4YNSOFzkJCDb5NSFFYWEhYWBgFBQWEhvqmLbquo2kaTt3JkpIlDPYffMKkIC0yebJ6Xp+SAoZGfjecMkW9G7x8uefaIoQQHuKVnm9h6kaCuwx0KfDaS/PJ2bSQjsMuaVrg1XU4+2y16s1XXzUp8Np1Oz+V/sTiksUcqDgA4PPA21pU9fitupVivZhvir5hi3WL5yp8+GHYtk1NqGrM+PGwbp2sciSEaJM8Hnx1p53ig5sJ7jrEpeuzNy5A1/WmL57w8svqH+0rrlCJGFxU4ixhXtE8dth2MCFwAt3MTVtpqb0IMARwSfAl9Lf056fSn1hRugKH7nB/RWeeqdKAvv1249eNGgXl5bBpk/vbIIQQHubx4FuauQenrZSQ+FNPeK3usJPzx3dEDUzCFBjueiU5OfC3v6nngHPmuN42ZylfFH5BgbOAS0MupZ+ln+t1tkNGzcjZgWdzVuBZpFhT2Fexz/2VaBrcfjt8+616/tuQIUPAbIa1a93fBiGE8DCPB9/itE1oJguBnfqc8Nr8naupKD5Kx9Oa2OudPFm9djJnTpPe5w3QAhjkP4irQq8izhTXtDrbsUGWQVwbei09/FSGKbe/jnTddeq5/QcfNHyNxaImXq1Z4966hRDCCzwefIsObCL4lAEYjCcOitkbvyW4yyACopsw9Ltgger9jBunXjFywS7bLnbbdqNpGsP9hxNiaEb2rHauaoGIXbZdfFLwCbmOXDcWHgFXXqmGnp3Ohq8bNUp6vkKINsmjwVd3Oiqf9554yLksax/FB/+kw2lTXa/A6YSbblK9pPnzXbplh3UHi0sWk1qR6no9zTBz5kyGDx9OSEgI0dHRTJ06lZ07d3q0Tl/obOqMRbPwddHXHHUcdV/BN98M+/c33rMdNQrS0iCjFa3UJIQQLvBo8C0/mobTVkpw5wEnvPbon99jCoxoUu5nnn0WcnPhgQdOnJAf2G3bzdLSpfQx9+HcwHNdr6cZVq5cyd133826detYtmwZdrudpKQkSkpKPFqvtwUZgrg05FKCDEHMK5pHniPPPQWPHq1eG2vsnd9TK3+p+/NP99QphBBe4tHgW5q+A9AIjOvV6HW6w07u1h+JHDDBpeFpVXgpPPecmmTlwvJyqRWpLC5ZTC9zL84NPNfjS/4tXryYG264gf79+zN48GA++OAD0tLS2NhIVqby8nKys7NJTU1l586dx3rKmZmZ5OXlYW+l6RQDDAFcHHwx/po/q0pXuadQgwGuvlq9NtbQ60SJiSrX8+bN7qlTCCG8xKMLK5Skb8e/Q1eMlsZX/Snctx57aT6RA5NcL/z226tzARuNJ7w8yhjFEMsQzgg4wydr7RYUFAAQGRmp0m0WFJCenk56ejqHDx8mOzub77//nvXr12M0GtE0TeVcDg/n1Vdfxd/fH6PRSHBwMKGhocTFxdG5c2c6depEXFwcgYFNeCfaAwINgVwScglGTvx34bJp0+Cll2DZMrjggrrnDQYYNEh6vkKINsejGa62v38bAdHdSLjokUav2zfvKay5B+l7y3uuFVxUpIaZY2Lg8OFGLy1zlqGh4W/wd7XZbqfrOpMmTSIzM5Onn36alJQUsrKysNlsmEwmQkNDCQkJwWKxYLFY8Pf3x8/PD7vdzltvvcXdd9+NruuUlZVRVlZGSUkJhYWFFBUVoWkaZrOZhIQE+vfvT+/evYmLi/P+urw15DvySbGmMCZgTMvaoevQv7+a1dzQWsx33aWWi9ziwcQfQgjhZh7r+TrtVsqy9tJhcOMLIzjKiynY/Sudxt/ieuH33gsOh1qrt7GydQeLShbh1J1cHnK5TwJSeno6t9xyCxs3bmTSpEn8+OOPxMbGMmTIEDp06EBAQMNZv6xWK2azmaioKCwWS53zuq5TWFhITk4Ohw4dYt68eRiNRmJjYzn99NM57bTTfJKWMs+Zx+/W3zFpJkYFjGp+QZoGF1+sRjccjvpHOAYNUrOiy8vV8pFCCNEGeCz4lmWngtNBYGzPRq8r2LsO3VFBRN+zXCu4pAQ+/RTi4lQ2q0asKF1Bhj2DS0Mu9WrgdTqdpKSksHbtWj788EPy8/O599576d+/P+Hh4W5ri6ZphIWFERYWRvfu3XE4HGRlZbF//37mzZvH4sWLOfXUUznjjDPo2rWrW+p0RaJfImcEnMGasjV0MHagp7nx/wYaddFF8PzzKpXk6NF1z/frpwLzvn3qsxBCtAEeC77l2epVHv+OCY1el79jFYFxfTCHRrtW8EMPqYQa//xno5dttW5li20L5wSe49mFAGrQdZ3t27ezdOlS9uzZQ2pqKoGBgTz00EN0bOaawk1hNBqJi4sjLi4Om83Gvn372LBhA+vXr2fIkCEkJSURGxvr8XYADLMMI8eew9KSpUQZo4g0RjavoBEj1HrMCxfWH3x7qEQf7N0rwVcI0WZ4sOe7H3N4XKOLIzgryinct57Y0de5VqjTCZ98op73Xn11g5dZdataEtDcjwGWE7/m5A4HDx5k0aJFbN++nZCQEBwOBw6Hg+nTpxMQEEBxcTEAFosFvyZk4Wous9lMnz596N27NwcOHGDTpk38+eefjBo1iqSkJI8PR2uaxrlB5zKvaB4FzoLmB1+jUU22+t//6p/VHhcHAQGwZ0/LGiyEEF7k0Z5vQMfERq8p3JeMs6Kc8N5jXSv0nXfUK0YPPqieBzbAolmYHDSZDqYOTWlys1RUVLB8+XKWLl2KwWBg5MiRxMXF8fTTTwPw0Ucf1bp+ypQpnHrqiZOOuIumaSQkJBAfH8/u3btZvXo1W7ZsYerUqQwePNijw/F+mh9XhFzR8jrOPx8++kgl04g7Lg2opqnerwRfIUQb4tFnvid6dahg729YIrvgH9XFtUKff15ls3rssQYvyXHkEGWIorNf56Y0t1kOHTrE3Llz2bt3L71796Z///4YKteg/fvf/+7x+pvCYDDQu3dvEhISSE5O5v3332fEiBFMmTKFkCYsv9hUmqapkYjSVQz1H0qUMarphYwbp/YrV8JVV9U93727GnYWQog2wiMvvDpspVQUZeMf1fAkH13XKUpNJrTbCNcKTUlRqQTPP18NM9aj0FnI3MK5bLQ2nMjCXTZs2MDrr79OZmYm5557LgMHDjwWeFszi8XCmDFjGDZsGOvXr+eNN97g0KFDHq3TiJEMewbLSpbh1BvJ1dyQ2Fjo0wdWrKj/fLdukOrZdKFCCOFOHokWtny1FJwlouGJTta8w9gKjhCaeJprhVb1JBvJZrW8dDlmzcxAy0CX29pUDoeDhQsXMmfOHCIiIku7QekAACAASURBVEhKSiI8vAnLH7YS8fHxnH/++eTn5/Of//yHPz2YqMKkmZgQNIEsRxabrM1cf3f8eNXzrU9cnOR3FkK0KR4JvtZ89Q+hJbzhZfqK9iWjGUwuLbqA0wk//ADR0SrpQj0OVRxif8V+xgaOxaLVfSfWHaxWKx9//DGLFy+mb9++jBw5EqML2bVaq4CAAJKSkggMDOTDDz/kp59+wlM5V+JMcfQ39ye5PBmrbm16AePGwY4dkJVVT+FxKvHKSZY3Wwhx8vLIM19bfjqayYwpqOEZroX7NxDUuX+js6GPWbBAJVG45556T+u6zq9lvxJtjD62xqy7lZeX8/HHH7N582bGjBnj0Vd21q9fT3JysscCYU1Go5HRo0ezdetWFixYQEVFBRMnTvTIRKzTA05nl20XBysO0sPcxL+nEZWPJzZuVI8eaqqahJWZqZ7/CiFEK+eR4GvNz8AS3qnBf8B1Xac4bTMdh13iWoGzZqn9o482eEk/Sz8iDZEeCRpVPd6UlBTGjRvn8Xd2R4wYwYgRI7BarbzwwgserQvUpKgBAwZgMplYtGgRmqaRlJTk9j/LYEMwN4bd2LxUn4mJEB5ef/Ct+kUoI0OCrxCiTfBY8DWHN9wztOYewlFeRPAp9Q8h16LrkJwM8fEQWX9PWtM0jz3ndTqdfP7552zevNkrgdeX+vTpg67rLFq0iICAAMaOdfEVsCbwN/jj0B1k2jObNiNd02DoUPj997rnqoLvkSPuaaQQQniYR575VhQfxRzccJAqSd8GQGBc3xMXtmIFWK0qx289tlu3N38WrQuWLFnChg0bGD169EkdeKv07duXbt26sWDBAnbs2OGROrZYtzCveB4FjoKm3Xjaaarne7yqhCGFhS1vnBBCeIFHgq+9JBdTUMOL25cc3oYlKh5TgAvvl77+utrff3+dU7qu87v1d8r0Mo8sE/j777+zZMkSBgwYQNzxyR1OYoMHDyYkJIRPP/2UIx7oTfa39MesmdlsbeI6vIMGqdfNjg+yJpN6/ayoyH2NFEIID3J7xNJ1HXtJPn4nCL7BnV0Ycgb1eklEBCQk1DmV4cggx5HDYMvgZra2Yenp6cydO5eYmBj69Onj9vJbM03TGD16NOXl5XzyySdYrc2YndwIk2ain7kfW21bset212/s1Uvt68tmFRoqPV8hRJvh9uDrKC9Cd9ob7PnqDrtKPXmC1Y4AyMuD3FwYPrze05utmwkzhBFvim9Jk+uw2+3MnTsXu93OiBEuJgE5yfj5+TF27FgOHDjA0qVL3V7+QMtArLqVXbZdrt/Us/K/mV313BMSIj1fIUSb4fbgW1GSB4BfA68ZleceQnfaT5j3GYC5c9W+nqUDbbqNvba9DLIMcvus3JUrV7J7925GjRrVpt/jbamQkBD69+/P8uXL2bdvn1vLDjeGM8QyBH+tCTOfIyLUCkf1Bd/gYAm+Qog2wwM9X7V6j9E/uN7z5Tn7AfDv4ELw/eYbtb/ssjqnzJqZ60Kvo7/FxeFrF6Wnp7N48WJ69uxJZAOzq9uT3r174+/vzzfffIPNZnNr2WMDx9LN3K1pN/XsWf+ws8mk1vUVQog2wO3B11lRpgq21J88oyw7FVNgBH5BLqRk/OMP9W5nWFidU7quE2oMdWs2K13X+f7779F1nQEDvLMUYWunaRqjRo3iwIEDrF271u3lZ9gz2G3b7foNnTvD4cN1jxsM6rU0IYRoA9z+nq/TpoKv0a/+xQ/Kc/bj3zHhxAXZ7ZCTU53ZqIY8Rx7ziuYxJWQKHYzuWzZwz549bNmyhWHDhvl0uNmbGa5cERISQnx8PD///DPDhg0jKCjIbWXvsu1ij20PPfx6uPb4IC4Otmype9xgUGlIhRCiDXD/sHNl8DWY6w++1vwMLBEuJFfYulX1ZE4/vc6pfRX7KNfLCTPU7RE3l67rLF68mICAADp39vxyhI0ZMWIEd999N7feeqtP21HToEGDyM3NZfXq1W4tN9EvkWK9mBxHjms3xMWpNJLHk+ArhGhD3D/sbCsDgxHN6FfveVtBJuawmBMXtHCh2l9wQZ1T+yr20cWvC35a/XU0x/bt29m9ezdDhgzx6ALzbZW/vz/du3dn5cqVFBcXu63czqbOmDUz+ypcnNAVF6dmwZeX1z6uaRJ8hRBthkee+Rr9/OsNYA5bGY6yQteC75o1aj96dK3DZc4yMuwZdPNr4kSdE/jtt98IDAwkOjrareWeTPr27UtRURF//PGH28o0akYSTAmuB98OlY8Z8v6/vTuPj6q6Gz/+ubNP9n2DbBD2TQQCIpsoyCIugAJairQiFqw/26pPW6212qcutX20FduKWm3FivogPiqyqIDsm7IvCZBAIAnZM8kkmfX+/jiZSYYEEmCSDOG8X6+87sy9d849w4R855x7zveU++6vq7vgOs+SJEmBpg2SbLhB0/z9UrtFLAdnCGtF8D1xAgwGMYWkkVxHLioq6fpWjJZupeLiYg4ePEhPTxIHqVlGo5GEhAS2bduG24+tzL7GvqTr01t3j9vz+3B+67umRgZfSZJa7SPPVNYO4v+cjBf5A+rwBt9WtC7PnWt2IYXeht7cH3Y/wRr/DfrZvXs3TqeT1NRUv5XZWfXu3ZszZ86Q1dxc28uUqk9lhHlE67r7LxZ8g1qxPKUkSde8rVu38u6773ZoHdokt/OFOGtFIn1dUAvTjFRVJExoZuCToiiEa/030MrtdrN79266du16TSfUaK2YmBiMRiP7919iXuYWFDmLyHfmt3yiDL6SJF2hZcuWcd9993VoHdqk5avQfAvGWWNB0erR6FvIalReLhImnJfP2ak6+dDyIWcdzczzvExnz56ltLRUtnovQZcuXTh06BAuPya12Fm3k221rZhH7Olarqnx3V9dDX6cAiVJUufkdDpZtWoVd9xxR4fWo91bvjpzeMvdi56pJMnJPrtLXCUUuArQKv5roR47dgxVVYmJ8d984c4uJSWF8vJyTp065bcy47RxFLmKLm9us9UKtbUi9aQkSdJFrF69mlGjRhHUwT1lfg++is6A29V8GkJXXRXa1iwjePq02J4XfItcRSgofk2scejQIWJjY9Fo2vV7yFUtMjISrVbLsWPH/FZmvC4eu2qn0t3CGr+e4Nz4C1yRGEuAHKkuSVILAqHLGdogw5VGb8Jtr0NV1SYtXLejruUuZ4DcXLE9r9u5yFlEtDYaneKfatfW1pKXl0efPn38Up6/BFqGq/MpikJ0dLRfF1uI04rAec51jgjtRcYEeP5NGn9ZksFXkqRWqK6uZvv27fz73//u6Kq0QfA1mAAV1WlH0fvmXVZdDjRaQ8uFFBSIbdeuPrstbgsRmlbkhG6lgoIC7HZ7wHU5Z2ZmkpmZic1m44UXXujo6jQrOjqa06dP43Q60emu/NfIrDHTVdcVTUudMbLlK0nXrPLycn73u9/hdDo5fvw499xzD/feey+PP/44qqpSXl7Ok08+Sd++fZt9/YoVK5g2bVqTv1mbN2/mjTfeIDs7m6eeeorJkyfzt7/9jaNHj+JwODh48CAvv/wyI0aM4P333/dm+jtw4ADPPvss48ePv+T34v/gqxMtW9HK9Q2+bqcDRdeKrFSV9V2Pob5d1MNNw9Eo/usezs/PFws0hIX5rcxrRUxMDMeOHaOoqIikpCS/lDkjdEbLJ1mtYtt4cNWZM2JVowD7EiVJkv/Y7XYWLVrEn/70J5KSkjh16hTp6el8+umnvPLKK2RnZzN16lQiIyN57bXXmi1j2bJlPPvssz773G43b7zxBu+++y6PP/448+fPZ9asWUyfPp3FixcDsHDhQu69917uv/9++vfvz9/+9jcAnn76ae6++26Ki4sv+dal3290ag0Nwfd8qtuBom1FvLfZxNbk20XdRd+FRF3iFdfRIz8/n5CQEJlO8jJERkbicDgo8PRS+IGqqtjVFpYttFjEtvEXppMnITVVBGBJkjqlv//978yfP9/7Zd9kMqGqKmlpaaSnp+NyuejRowdz5sxp9vXnzp3j1KlTDD9vvYBdu3Z50wrn5+dTXFzM1KlTuemmm7znhIWFkZOTQ3x8PNOnT/fuj4+Pp6ysjOLi4kt+P34PvhqDGEHmslmbHFNdThRNK1q+nuBraOiidqpOdtbupMJV4Zd6ApSWlhIS0vy6w9LF6XQ6jEYjFRX++zzW1axjZdXKi590oeDbzb/pRiVJCiyRkZFMnDjR+3z37t0ATJo0CYDJkydz+PBhbjwvJbHHBx98wKxZs5rst9ls3HXXXQBs2rSJW2+91Vumx/79+0lPT+fBBx/02X/kyBHMZjPR0dGX/H78Hnw9CTScNc2MWlUUoBWDiDz39RoNOLK6rWyr29byaNhLUFFRgVmmJLxsBoOBqqoqv5UXpARRo9Zc/CRP8G28xrMMvpLU6c2dO9fn+fr169FqtYwaNapVr1+2bBn33ntvk/1jxowhLS2N48ePc+bMGSZMmOBz3Ol0snXrVsaNG9ekl3Tt2rWMHj36ssa9+D346oMjAXBYy5ocUzR6VJez5UI8b8Th8O6yqqIl7a+0kqqqUllZ2eFzva5mBoOBykr/fRkK1gRjdTftMfFRVOSb81tVRR5wGXwl6ZryzTffMGTIEEJDW56+mpWVhaqq9OrV66LlAYwbN85n/65du6iurm6y/8CBA2RnZzNz5sxLrju0UbezojPgtJY3PabVoboczbzqPJ7BNPaG+39OVQRtA60YLd0KNTU1OBwO2fK9Amaz2a/BV6/oceK8+BSrM2dE2lHPN9DTp0Uq0n79/FYPSZICW3l5Ofv27WsSEN98881mz2/N3N7169cTERHB4MGDffZv2LABaBqU33//fYxGozf4vvXWW61/A7RFkg1FQR8ciaOmafBVtK1s+XqCb6MUgm7c3vL9weFwoKqqX6bJXKv0ej02z/15P/BMM1Ivdmvi7FnfnN+eHNMDB/qtHpIkBZbi4mIyMzP53e9+B4gsVW63m8zMTJ9ztnqWoj3P8uXLmT179kWvsWHDBsaMGdNk1PL69evp1q0bKSkpPvtXrFjB7bffTmRkJAcOHODMmTOX9J4uOfKoqtrifT6bNpSyc2cI9dyfq1dtd1NXVYXlvP1NeLoUT56E7t0BcDldJNUlUavUomquPPlERUUFdrsdp9Pp1wByJZxOp0++ZE+9AqV+53O5XNhstpY/z1aKV+O5R7mHKkvVhb9k5eaK+byea+7YARERYgCWn+ohSVLbCw0NbXVjauPGjezatYspU6ZQW1vL8uXLSUpKorp+gRWr1cojjzzCiy++2OS127dvJyUlhYSEhAuWf+TIEQoLC5u0bh0OB1u3bm12oFZJSQljx47F7Xbz4osv8uqrr7bqvXgo6iWmUbJYLISH+29VoY4UGhpK3759ZdfzZSovL+fIkSPY7S1MD5IkSTpPZWVlq3MsVFVV8bOf/QyDwUB1dTW/+tWvsFgs/PrXvyY1NRW73c4TTzzBwGZ6wH76058ydOhQ5s2bd8HyN2/ezKxZs9i6davPIjvFxcX079+fDz74wGfqEYiu7DfffJOYmBgeeughbr755la+c+GSg29rWr4Fm/9F2cG13P/WMXbt2uXdf27Hcop2r2DA4uUXv8iePTB+PPzsZ/DMM4C45zs8czi7du7yS6KNyspKXnrpJbKzs/nZz352xeV5LF26lAULFlzWa89v+VZVVfHmm2+yaNEivyUCuZL6nW/Pnj289tprHD161C/l5TnyuHXErRzafaj5b8RWKyQlweuvg+f+zcCBMHUqPP/8BcsdNmyYz+/hlbBYLCQnJ5OXl+e3z8Sf9bvWymuLzwMC+z0Henmt/UwupeV7uZxOJxkZGRw4cKBVA7Pa0yV3OyuK0uIvuaNrd6x7LZgNWp9zbdHxVGEjNDQE5WIB1DMi7dw573zOPEceVVRBCIRpr/w/mclkwmQy4XK5MBqNLb+glRRFuezyLvQ6o9HotzpeSf3O53a7W/X70OrybG6cGueFe1aOHxfb668Xvxdnz8KpU+KL2kXqoNVq/Z7FLCwszG9l+rt+11p54N/PAwL/PQd6eeD/z+RyrF27luHDhwdc4IU2WlLQGCEGxDyy4Ac++3VBEaC6cdW2cG/Ok6PXs7oRYFJMjHpgFHVq08xZl8NgMGAymejRo4dfyvMYNmyYX8vzN3/Wr7a21mfS+xWX567lpgduuvAJhw+Lbe/eYrtli9heYFK9hydFXKDyd/2utfLaQqC/50AvL1AEygpGzWmT4GuIFOm/pk8a67s/TARVu6WFVFw6nVg0vVHwDdYEM/qB0S3PA70EERERpJ23ctKVajz6LhD5s352u/2y57g1p0atYeqDUy98wsGDYrENT8t4yxbIyICLDKSAwP/DEuh/SAO9vLYQ6O850MsLBFarlc2bNzN58uSOrkqz2iT46kOi0RiCqCvJ9dlvCBOLndstRS0XEh8PjfJlmhUzGjTeZBv+EBkZSU1NCxmVOpBWq/XZBhq73e7X7pxqd/XFk6js2AGNW+4bN7bY6vU3o9HIb3/7W7/eqpAun/w8Ak+gfCaffPIJU6ZMQa9vRUrjDtAmwVdRFMxx3agtOuGzXxcciaLRYbeca7mQ9HSorfXO9VUUhSAliFp3rd/qGR8f7x2qHog8c5ADcS5yTU0NLpeL2NhYv5XZ19CXgcYLzNd1uWD3bvAkRS8ogH374LxUcG3NaDTyzDPPdPgfFkmQn0fgCZTPZOPGjfzwhz/s0DpcTJv9VTfHZVB96nuffYqiQR8Wh6OlbmcQg2rWr4fvv/e2buaFz0On+K/KSUlJ1NbW4nA4AvbbUaAqKSnBaDT6bTlBgG6Gi6SIPHwYqqsbgu/q1SLL1a23+u36kiR1HkuXLu3oKlxUm7R8AYLiu1NXlofb4ZsgwhiegK38bMsFeFaVWL3au8ufgRcgMTERvV5PWVnTPNTSxZWVlREeHu6/kc6qm8O2w1hcFxiMt2ULaLUwdKh4/uWXkJkp1/CVJOmq1GbB1xzfA1R3k65nU0wKdaWnL/CqRkaMENuNG727jtmP8aHlQ7/VMTY2luDg4Mtai/FaV1JSQlpamt/m6ZW7y1lXs44K9wWWKFy3TvxOhISIBTfWrYMAHUghSZLUkjYMvt1RdAaqzx7y2W+KScNWdqblHM8hISJtoGd6CSL3b4GrwG8jnrVaLb179yY/P98v5fnLzp07WbJkScB2mzgcDioqKvw6TavIKQbhxWnjmh50OuHrr8Ezremrr6CiAu64w2/XlyRJak9tFnw1Wj3BiX2w5h3w2W+KSUV1O6kra0US6gEDoLQU6ruF47XxAJxztmLAViv16dOHysrKgMqfnJmZyeLFi/2WicrfCgoKMBgM9OzZ029lFrmKCNeEY9KYmh7cvRsqKxuC7/LlIhHLoEF+u/7FPPPMMyiK4vNzsTyxkv99++23TJs2jaSkJBRFYeXKlT7HVVXlmWeeISkpCbPZzLhx4zh06NAFSpP8oaXP5P7772/y/2aEp0dTarvgCxCc3J/qMwd8logLSugJiobqvP0tFzBtmth+/jkAoZpQTIqJIlcrpiq1Us+ePTGbzZw924r70BIAp0+fJjU1lejoaL+VWeQqar7VC7BqlegFGToUbDZYuRJmzWpYVrAd9OvXj4KCAu/PgQMHWn6R5DdWq5VBgwbx2muvNXv8pZde4s9//jOvvfYau3btIiEhgQkTJrSYCle6fC19JgCTJk3y+X+zatWqdqxhYGvTOSwhXQdwbusy7BX5GCNF1iutMZjgLn2pyt1D7PW3X7yA2bPhiSfgP/+BH/4QRVGI08b5NfiGhYWRkZFBTk4O3eSC7C1yOp2cO3fO799gozRRJOgu0Jr8+GO4/XaRfOWLL0QruJlVRtqSTqeTrd0ONHny5AsmS1BVlVdeeYUnn3yS6dOnA/Duu+8SHx/P+++/z8KFC9uzqteMi30mHkajUf6/uYC2bfl26QcoVJ/X9RyaNoSq3O9Q3a7mX+iRnCyyGW3b5t010jySG83+TawwbNgwysvLA3rOb6DIzc3FYDBw/fXX+7Xcm4Nvpp+xX9MDhw7BkSNw993i+dtvw+DB0LevX6/fkuzsbJKSkkhPT2f27NmcPHmyXa8vXVhOTg6FhYU+qU6NRiNjx4694PquUvvYsGEDcXFx9OzZkwULFlBU5L+G09WuTYOvzhyKOT6Dqtw9PvvD0ofiqquipjC75UJGjRItnfqVc+J18URr/dfdCTBgwACio6M5duyYX8vtjLKyshg0aBBRUVF+K7PEVXLh5CkffSQWTZgwQSyk8Pnn8OCDfrt2awwfPpx//etfrFmzhqVLl1JYWMjIkSMpLS1t13pIzSssLARE0pzG4uPjvcek9jd58mSWLVvGN998w5/+9Cd27drF+PHjA2p8TUdq0+ALENZtGJac3aiq27svOKkPGkNQk6DcrIcfFtu//tW7a2ftTvbV7fNbHQ0GAyNGjOD06dM+S/pJvoqLi6mrq2O4J9GFn3xt/Zpvar5pekBVxS2HO+8Eo1G0ek0muPdev16/JZMnT2bGjBkMGDCAW265hS+++AIQXZtS4Dh/2puqqm2+ZJ10YbNmzWLq1Kn079+fadOm8eWXX5KVleX9/3Ota/vgmz4Mp7XcZ76votURmnodlpzdLRcwYYL4w7tihXdXubucA3b/DnjJzMzEZDL5bW3azmj//v2kpqb6dYqR1W2l0FVIN30z99s3bYKsLJg/X6SXfPNNmDPnossHtofg4GAGDBhAdnYrem6kNue5p3h+K7eoqKhJa1jqOImJiaSmpsr/N/XaPPgGJ/dHYwiiMnubz/7QtCFYzxzE7WhhiUCtFkaPhsJCqO8W7qbvRqmr9MLZkC5DdHQ0N954I8eOHcNut/ut3M6isLCQyspKJk2ahEbjv1+bHEcOCgpp+rSmB5cuFasWjR0Ln3wiVrn6yU/8du3LZbPZOHLkCImJiR1dFQlIT08nISGBdevWeffZ7XY2btzIyJEjO7BmUmOlpaXk5eXJ/zf12jz4arR6wrsPpyJrs8/+0PShqC5H66YcPfGE2D73HAAp+hQ0aDjp8O+gl3HjxhESEsLBgwf9Wu7VTlVVvv/+e/r06UNfPw90ynHkkKhLxKwx+x4oLxejnB94QDx/6SUYPx6GDPHr9VvjscceY+PGjeTk5LBjxw5mzpyJxWJh3rx57V6Xa1V1dTV79+5l7969gBhktXfvXk6fPo2iKDz66KP84Q9/4JNPPuHgwYPcf//9BAUFcW8736K4llzsM6muruaxxx5j27Zt5ObmsmHDBqZNm0ZMTAx33XVXB9c8MLTLcjnhPUdR/ulz2CoLMYaLLiJTdAr6kBgsObsJ69bCGrO33CK6GlesAJcLo9ZIii6FI/YjXGe6zm/1DAsLY/z48axcuZKMjAy/5S2+VDt37mTXrl0+86M70smTJ7Hb7UycONGv99BUVUWLlh76Zrqxly4Ftxvuv1+kGN21S+Rz7gBnzpxhzpw5lJSUEBsby4gRI9i+fTupqakdUp9r0e7du7npppu8z3/+858DMG/ePN555x2eeOIJamtrWbRoEeXl5QwfPpy1a9f6dclLydfFPpO//e1vHDhwgH/9619UVFSQmJjITTfdxPLly+VnUk9R2+EvvMtmZf//3EGX8Q8Rl9mw+HruZ89Te+44fR54q+VCHn4YliwRA3Bmz6bIWYSKSrzOv/d07HY7f/nLXygtLfV7sLlUNpuNF154gV/+8pcdtjxXTU0NX375JWPHjmXmzJktv8Af7HaxpOSkSfDWWyKH89mzYglBOYBGkqROoM27nUEk1gjtNpTyI74jWkPTh1BbdAJHdStWFXrySfGH9+mnAYjTxfk98IIY+Txjxgzvfb1rmaqqbN++nYSEBKZMmeLXst2qm5P2k7gbjYL3ev99yM+Hxx4TqxmtXg2//rUMvJIkdRrtEnwBovvfivXsYZ8VjcLSxP27qvPW/W1WYiLccANkZ4tcv0Cxs5jlluUXniN6mdLT0xk/fjyHDx+mvLzcr2VfTbKzs7FYLEyfPp2goCC/lp3ryOUz62cUu85bUcrthpdfFqlFe/cWQXfQILjnHr9eX5IkqSO1W/AN7zkSrTGYsgNrvfv0IdGYYtOpas2UI4BXXxXb+nsLwZpgil3FHLH7v4U6ceJEevXqxcaNG6mra2FEdidUVFTE/v37GT9+PH369PF7+ftt+4nXxjftvVi+XGS1+tWvxLKB334L//3f4McR1pIkSR2t3f6iaXRGIvuMp+zgOp+EG2HpQ7Hk7mnd4KKhQ0VraNMmOH6cIE0QGYYM9tn24VL9mxzDYDDwgx/8gOjoaL799ttrKvlGdXU1W7ZsYdCgQUydOtXv5Ze6SjnlPMUA4wDfAw4H/OY3otWbmSkC8MiR4Ocub0mSpI7Wrs2JqAETsVvOUX2qITtVaPpQHJYias+1cuL1K6+Ibf1ye0NNQ7G4LRy0+X96UGRkJHPnzsXlcrFjx46AGX3cljzzI7t06cK9996LVqv1+zW21W4jTBNGL0Mv3wNvvw0nT4qW7ltvwXffwR//KO/1SpLU6bRr8A3u2h9jZBKlB1Z794WlD0EfFkfx7k9aV8jEidC9O2zYAAcOEKONoY+hD0fsR9okOKalpTF79mxKSkoCavpPW7Db7Xz99dcEBwczb948goOD/X4NVVVJ06cxxjwGndJoppvFAs88I1JHJiWJVu+8eaLlK0mS1Mm0a/BVFIXoQVMpP/wN9qoSsU+jI3bInZQd+gqHtaI1hYhWEYi0g8AY8xhmhs5ss2lBgwcPZvbs2RQWFrJz585OGYA9gddkMrFgwYI2S8unKAr9jf3pbujue+B3vxMB+Pnn4amnwOmEF19skzpIkiR1tHYfxRJ7/R1o9EaKtn/g3RczaCooCiV7P2tdIWPHikxHm9fM+AAAIABJREFUe/bAmjWYNCZ0io4KVwV17rYZHJWZmcmcOXMoKipi8+bNneoecHV1NevWrSM4OJgHH3yQLl26tMl1TjlOsda6Fqfq9D1w8KAYTPeb34gUkv/4Bzz7LMi8vJIkdVLtHny1phBih86g+PvPcFjFNB5dUDhR/SdQsudTVJezhRLq/fvfohU8dy44HDhVJ8urlrO9bnub1X3YsGHMnz+f2tpa1qxZQ01NTZtcZ+fOnSxZsoSlS5e2SfmNFRYWsnbtWuLi4li4cGGbBV6X6mJz7WYq3ZVoaXQf2e2GxYvFrYSHHhK9GcOHN6xmJUmS1Al1yPyNuGEzUDQainZ+2LBv6Awc1SWUH/u2dYX06QM/+hEUF8PTT6NTdAw1DWWfbR/5zvw2qjn079+fhx9+mKioKNasWdMmi0NnZmayePFiFtQPKmsLqqpy7NgxNm/ezHXXXcfixYvbdAWYPXV7KHWVMsY8xvf2wOuvi+lEr78uWrt5efDOO2JBDUmSpE6qQ4KvzhxG7JA7Kd6zEmetWJnIHNeNkNTBFO9e0cKrG/nrX0XO55deguxsBhsHk6BNYJ11HQ7V0Ua1h6SkJBYvXky/fv3YtGkTu3btwulsZYs9AFitVr7++muOHj3KpEmTmDdvnt+TaDRW4iphR90OhpiG+M7rzc4Wi2YsWgR6vRjJ/vvfQ69eFy5MkiSpE+iwzAVxmfegut0U7frfhn1Dp2M9cxBrQSvX1DWbRSvJ7YYpU9CoMCF4AlXuKnbU7mibitcLDQ3lgQceYNasWZSVlbFq1ao2aQX7k6qqZGVl8eWXXxIcHMyiRYu47bbb2mQ6UWNnHWeJ0kYx3DS8YafLJRZNSEoSaSTnzBFLRz76aJvWRZIkKRBon3nmmWc65MIGM66aSkr2fkbs4NvR6AwYo7pSdmANTmsFEb1Gt66gPn1EuskdO8DhwDzhNqK0UXQ3dMeotO1iBIqikJKSwqBBgygqKmL37t0UFRURGRmJyWS64vJdLhebN29m1KhR6HSXvwCVqqrk5+ezadMmiouLGTduHHPnzm23hcYTdAn0NfT1nVr0zDNikYxPPoFf/lIsnPDVVxAe3i51kiRJ6kgdmrMvbsRs3A4bxXtWAqBotMQOuYvyw9+0brEFjw8+EH+0X3gBtm4lw5BBqCaUGncNNretjWrfIDY2lgcffJAf//jHBAUFsW7dOrZs2UJlZWWbX/tiVFWlsLCQdevWsXPnTnr27Mmjjz7KXXfd5ZcvBy0pdBayu243btXtG3jXrBHdy88+C5s3w9q18N57ohUsSZJ0DWiX9XwvxBAaQ/SgKZzb+SGxw2agNZiJHjSVgk3vUPL9ZySObuVi5SEh8NlnMGaMSEWYk4MaEcHK6pUEKUHcHnI7GqVtv2doNBquu+46+vfvz/bt23nqqad4++23MRqNxMfHM2DAACZMmNAua1na7XZOnDjB8ePHcTqdZGRkcOutt9KjR492WyLR6rbyefXnhGpCuc54HRrP97y8PLjvPrFc4MCBcMcdYsWqiRPbpV6SJEmBoEODL0D8DXMo2fs5Jd//H/HDZ6EzhxLVfyLFez4hLvNutMZWDgQaPRoef1ykI7z1VpTt27nRfCOfVn/KltotjA5qZTf2FdLpdAwYMACtVsvChQupra0lOzubjRs3sm/fPhYsWEBiYqLf77PW1dVx5swZzpw5Q2lpKUFBQWRmZpKZmUlaWlq7rkvsVJ18Xv05ALeF3NbQ6rVa4c47IShIZLCaMgVuv10k2JAkSbqGdHjwNYYnED3gVs5tX07s9Xei0RtJGHkfpQdWc277BySN/VHrC3vxRdi6VawBu2ABqW+9xWjzaL6t/VakoTT6f3We5oSHh/P11197n+fn5/Pxxx/z2GOP0atXL4xGI+Hh4URFRRETE0N0dDRBQUGtDpButxuLxUJJSQllZWWUlZVRVVWF2WymR48e3HzzzQwaNIiwsLC2eosXpKoqX9d8TbGrmJmhMwnW1KeodLlEi/fYMfj0U/jBD8Tc3vfekysWSZJ0zenw4AsQf8O9lO5fTcm+L4gbOh1DeDxxmXdzbsdyYq6fhiE0tnUFKYpYeL1nT5Gkf+BArnvkEUpcJayvWU+aPg2zxty2b6YZSUlJ9O3bF4fDwS9/+Uvy8/PJycnh1KlT7Nu3D5tN3JfW6/VotVqMRiN6vR6Xy0VJSQnbtm3D7XZjs9mw2+3YbDZ0Op23S3vIkCF0796dnj17EhIS0u7vrzEXLmyqjVuCbyFBl9Bw4IknxK2BDz4QA6zsdvG8g+srSZLUERQ1QBIV53z6e6pP76PfT5ah0Rlw2awc+tt9hGfcQOpt/3WJheVA375gs8EXX+CcNIFiVzGJusS2qXwL6urqGDVqFL179+a9997z7ldVlaqqKvLz86moqGDJkiW89957KIqCplFr8OWXXyY6Oprw8HBCQkIIDQ0lJiaGxMTEdhk41Vo21YZRMaKqqm8r/o9/FMH35Zfh//4P9u0TC2Ncd12H1VWSJKkjBUzwrSs5xeE3f0TCDfd5u5qL96wkb82r9P7xUoLiMy6twG++gVtuEZmSNmyAG29EVVW2122nt6E3kdpIv9V92bJlLFy40Pv8yy+/ZPRocY/Z4XBw9913c/r0aTZs2HDRrmCbzeZtBQNYLBaSk5OprKzskC7kS5Ftz2Z9zXruCb2HCG1Ew4ElS0SqyF/9CvbuhY0bYd06uVqRJEnXtIAJvgD53/6Twq3v0edHSzHHdUN1OTm8dD6GsDgy5rx86YOG3n9f3GfU62HTJmyZ1/Gh5UNsqo3podOJ0kb5pd5VVVWcO3fO+7xLly6YzWYcDgf33HMPJ0+e5JtvviE6OvqSyrVYLISHhwd88M2yZ7HGuoYehh5MDJrYMLL87bfhxz+GRx4RCyasWgWffw4TJnRshSVJkjpYQI10SRh5H6bIrpxa9UdUtwtFq6PL+Ieoyt1DZfbWSy/w3ntFy8vhgDFjMO7cy/TQ6ZgUEx9XfUyJq8Qv9Q4NDSUjI8P70zjwZmdn89VXX11y4L1aHLUdZbV1NT0NPX0D7+uvwwMPiOB75Ah8+SWsWCEDryRJEgEWfDU6AylTn6Am/yhF9Tmew3uMJKz7CPLWvILLZr30Qhctgr/8RQzwGTOG4J0HmBE6gxBNCB9XfUyZ6xKSebSS0+lk5syZ7N69m2XLluFyuSgsLKSwsBC73e7363UUu2pnY+1G+hr6MiFoggi8qioSaCxeLFYpOnZMjED/8kuYOrWjqyxJkhQQAqrb2SNv7V8o3beKPgv+iTEiEXvlOQ6/MY+oAbeSMulnl1fo3/8OP/kJ6HSwYgW2qRP5zvYdw03D/Z6AIzc3l/T09GaPrV+/nnHjxrWqnEDtdnaqTty4MSgGyl3lRGgixC0Blwt+8QuxNu8vfiEyV+XlicA7YkRHV1uSJClgBFTL1yNp3APozOGcXvUyqqpiCI8nadyDlHz3KdV5+y+v0IcealiE4fbbMS55gxvMN6BRNJx1nOUb6ze4VJdf6p+Wloaqqs3+tDbwBqpqdzUfVX3E11YxjzlSGykCr8UiEmb89a9iZPN770FVlUgfKQOvJEmSj4AMvlpDEMmTf05V7h7KDqwGIHbIHQR36cepL/6I23mZ+ZrnzRPJ+41GMQjoRz8Cp5NqtZrD9sOsqF6B1X0ZXdvXiEJnIR9YPqDGXcMQ05CGAydPwg03iOQm//Vfopu/Wzex2EW/fh1XYUmSpAAVkMEXILz7cKL6T+DMV0twVJeiaLSkTHkce2Uh+euXXn7BN90k5pnGxsI//wnXXUevikhmhM6gwlXBMssysu3Z/nsjncSO2h18WPUhYZowZofNJk4XJw6sWAFDhog51bfdBs8/D9Oni6lecXEdW2lJkqQAFbDBF6DrLYtRFC15a/8CgDk2jS43LaRo18dUnriC9Xp79YLDh0V36KFD0KULiS++zX2h99JF14VNtZtwqk4/vYvOQUEh05TJjNAZImVkXR389KcwYwYMHw5hYfDRR2J0+XvvQQAl/5AkSQo0AR18dUERdL31/1FxdCMl+1YBEDtsBmHdh3PqsxcubdnB88XEwLZtouUWEgJPPUVQSk+mbNUzO3Q2OkWHxWXpkFbwkiVL6Nu3L8OGDWv3a3u4VBfbarexs3YnAJnmTEaYR6BVtPDddyLg/uMfIkfz9u1QUSFGNS9aJNJ8SpIkSRcUkKOdz3dq1R8pO7iOXvOWEBTfA0d1GUfe/DFBCT3oPusFlCsdrexyiQFZb70lpsoMGwavvcbOAbCtbhupulRuNN9IrK6VOab9pCNGO6uqygnHCbbWbqXSXclw03AyzZnioM0Gzz0n1k3u2VN8gdm0CebOFfd5IyIuXrgkSZIEXCXB1+20cezdh3HbrfSe/wZaUwiWkzs5/sF/kTj6/tav+9uS776Du+8WA4gAdfJk8n6/mPXdS6hwV9DL0IsbzTcSqmn7NXmh/YOvQ3WwomoFha5CUnQpjDKPavjC8fXXops5OxsmTxZB12SCN96AadPavG6SJEmdSUB3O3todEa6Tf8dzppKcj9/EVVVCeuWSeLo+ynY9A6Vx7f750LXXw9ZWaIVZzKhrFlDytBpzF24ikkFGRQ4C1AR31U60z3hUlcpqqqiV/R00XXhrpC7uCv0LhF4T56Eu+4SebL1eujRQ6xGdOed4n65DLySJEmX7Kpo+XpUZG3h5MdP0uXmnxA/fBaq6ubER09iPXOA3vP/gTGyi/8uVlAA/+//iUFE9fcw1bFjUP7yV1z9+/JO5Tsk6ZIYaBpIkjapTRarb8uWr0t1cdxxnP22/eQ787k95HbS9Y0SgxQUiO7lv/8doqLE2rtbtogvKK+9JqYWSZIkSZflqgq+AGe/+QfndiwnY9YLhHXLxFlXxbF3foKiaOk57zV0Jj93CR84AB9/LKYl5eUBoHbpQsH829g+vRt5aUaitdEMNA6kv6G/X7NltVXw3Ve3jx11O6hVa+mq68pA40C667uLuhcWiqX/liwBg0Hc2/3+e4iPh9/+VuRq1mr9VhdJkqRr0VUXfFW3ixMfP0n16f30+uFrmOO6UVd6mmPvLiYooScZs15E0era5uJZWfD442J1Hqfodrb3SOf0tCHkTB7ALeN+DVot2Y5sknXJmDXmK7qcv4JvhauCk46TpOpTidZGs9+2nzJXGQOMA4jW1i/4sHcvvPIK/Oc/IgVn796iWzkkRCwHuGgRmK/s/UiSJEnCVRd8AVy2GrL+/VNcddX0uv919CHRVJ36nuz/PEb0wEmkTH6sTbqBvcrKxOIBS5aI5zod1NRAXBy2qRNYe7OJvLG9iAtPp5u+Gyn6FGK0MZd8mSsJvsXOYo7Zj5HjyKHMXYYWLeODxtPX2LfhJKsVVq6EN98Uax7HxooRzEeOQGKiGGC1eLGYwytJkiT5zVUZfAHsliKOvfMT9KGx9PzBK2j0Jkr3r+bU5y8Qf8O9dLnpwbavREEB/OEPYr5rSAgMHgxnzkBWFm6TkaJxAzl8a3fOTR7GnF4/B2B77XbCNGHE6+KJ0ESIebMX0Jrga1ftlLpKKXIWcc51jqGmoURpo/i25luO2o+Srk8nXZ9Oij4Fg2IQLfZvvxWJMD76CKqrISUFamuhuBj69xeLIsyZI9JwSpIkSX531QZfgJrCLLL+/QghKYPoNvP3aLR6zu38iLNfLSFp3AISRt7XPhU5dQqefVYs3NClCyxcKFrDX3yBumULitsNw4fjmnYbn49XyO0V7B3EZVbMzAmbQ6gmlIO2g1jcFvSKHg0arBYrY+PHsuHcBsyhZmyqjTq1jgnBYk3c5ZblFLoKAdCgIUYbw9igsSTpkrCpNvToxX3cigpYs0aMUl61CsrLIToaQkNF3YOCYNYscT/3hhtkkgxJkqQ2dlUHXwBLzm5OfPgrInqNJu32J1E0WvK//SeFm98l+dZHiR1yZ/tV5tgxMShp+XIxOnjWLMjMhNJSEfRWrwarFTU9jerbbqZ0ykiKR/ZmcGgmOkXHhpoNnHScZN0b69jw1gbcTjdFJ4r486k/ExwWjFExEqwJ5q6Qu9AqWrLt2bhUF5HaSKK10egUnUgSkpsLu3eLubjffityWYMYNKXRiBa7Xg833wz33CPmNoeEtN+/kyRJ0jXuqg++AOVHvyXnk2eIue42kuvX+z371RKKdn1M6u2/Jrr/xPat0N69YsTwmjVQUiKSUVx/vViAICQETp+G9eshP19khZoyRSzHN2ECREZ6W57NdjurqugiLi+Hs2dFoM3NhZwcMUBq3z6xvB9AeLgYJFVaCg6HaO2OHy/m6E6dKo5LkiRJ7a5TBF+Akn2rOP3FS8QOuYuuE38KKJxe9UdK968m/Y7fENn3pvavlNstguHGjWJ5ve3bRaAE0dXbtatogRYXQ1FRw+uCgiAkBIvZTPipU1SmphLmdotBXRaLCKSNGQwiyCqKOMduF/tTUkTAHzVKBN2BA0XLV5IkSepQbTQnp/3FDJoCbhenv/wzbpeDlMk/J2XyL3A77eR8+hxuRx3Rgya3b6U0GjEIa/Dghn3nzsGePXD0qOimPnpUBEyjUeROBvG8pqbhNadOXfgaBgMkJIhu7h49xE///iLoxrZvLmpJkiSpdTpNy9ejdP9qTn3xElH9J5A69QlQFPJW/w8l339G1wk/JW7YjI6uYvNUVbRqCwtFS7i2FktZGeGzZ1P51luERUaKAG00im7smBhxDzc8XA6QkiRJusp0mpavR/TASShaPbn/99+oLgdp035N8qSfozEEcWbdX3HZa0gY+YO2nQd8ORRFBNLwcLHeMDTcu505U861lSRJ6kQ6XfAFiOp3swjAK5/lpNNB+l1P02X8Q2iNwRRsfAtXTSVdbv4JikamSZQkSZLaX6cdfRPZewzdZj6H5cR2TnzwX7hs1SSO+iHJtz5K0e4VnPzfp3HZazu6mpIkSdI1qNMGX4DwjBvImPMyNUXHyXr3YWwVBcQOuZPud/+BqlPfkfXe/8NeVdLR1ZQkSZKuMZ06+AKEpgyi1w+XoLodHHtnEdb8I4RnjKDn3L/itJZx7J2fUFOY1dHVlCRJkq4hnT74Apiik+n5w9cxRiaR9d6jVBzbRFB8Br3u/zv64EiO/ethSvd/2dHV9FqyZAl9+/Zl2LBhHV0VSZIkqQ10uqlGF+N22Mj97Hkqjm4gYdQ8Ekf9ENXtJG/Nq5TuW0XM4NvpOuFhNDpDR1cVaLv1fCVJkqSOdU0FXwBVdVO4dRkFG98mrNsw0u54Cp05jJLvPydv7auY4zNIv/NpjBGJHV1VGXwlSZI6qWsu+HpYTu4i59Pn0BqC6DbjOYISemDNP0rOJ8/grKsiZdLPiep3c8fWUQZfSZKkTumaDb4AtooCTq74LXUluXS9eTEx19+O22bl9Or/ofzw10QNnETyxEfQGoI6pH4y+EqSJHVO13TwBXA7bZz56nVKvvuU8B43kjr1cbTmcMoOrCFvzSvogiNJnfI4oWnXt3vdZPCVJEnqnK754OtRkbWZU1+8hEarJ3XarwlLH4Kt/CynvniJ6tP7iBk8zZslq73I4CtJktQ5XRNTjVojouco+jzwNqaYVI7/5xecXv0KuqBIetz3PyTf+ihlB9dxeOl8LCd3XnLZCxcuRFEUXnnllTaouSRJknS1kcG3EUNoDBlzXqbrhEcoO7CaI0vnU5Wzm9ghd9JnwT8xRSVz/IMnyP2//8ZRXdqqMleuXMmOHTtISkpq49pLkiRJVwsZfM+jKBrihk2nz4J/YozqKoLtZ8+jNQaTMedlUqY8TuWJHRz6+1zO7fgQ1eW8YFlnz57l4YcfZtmyZej1+havbbPZsFgsPj+SJElS5yOD7wUYIxJFsJ36BJVZmzn8xjzKj6wnetAU+j30HlH9J3L2m79z5K0HqMr9vsnr3W43c+fO5fHHH6dfv36tuubzzz9PeHi49yc5Odnfb0uSJEkKAHLAVSvYq0rIW/MqlVmbCEkZRNeJjxAU152awmzy1r6K9cxBwnvcSNK4BZhj0wARSNevX8+aNWtQFIW0tDQeffRRHn300Qtex2azYbPZvM8tFgvJyclywJUkSVIn0ynX8/U3Q2gM3Wc+h+XkLvLW/oWjby0g9vo7SBwzn55z/8rnS58lf+dqyo5tZtW+Em5a8AKvvvoq3333HYqitPo6RqMRo9HYhu9EkiRJCgSy5XuJ3C4HxbtXULDpXRStjqTR8zFmjOXcuXPYT2zEfvhznPYalm06xbKt+ZRbHQC4XC40Gg3Jycnk5ua26lpyqpEkSVLnJIPvZXJUl3J2w1LK9q/BEJFI0tgfE9n3Jty2GnLW/xPLgS9AdaFJHYU24xYm3XEPc+fOZf78+fTq1atV15DBV5IkqXOSwfcK1RadJH/jm1Rmb8Uc34MuNy0gNH0Yrroqinb9L8W7PsbttPP5vlKih97Nop//qtVly+ArSZLUOcng6yfVefs5u/4NrGcOEtylLwk3ziWs+whctmqKd39C1tqlBJt0xAyYSFzmTILie7RYpgy+kiRJnZMMvn6kqiqWkzsp3PJvrGcOYo7PIGHkD4joPQa3vZaS7z+jePcn2C3nCEm5jrjMuwnPGIGi0TZbngy+kiRJnZMMvm1AVVWqT++lcMu/qcr9DlN0KvEj7yOy700oikLF0U0U7foI69nDGCO7EHP97UT1vxV9cIRPOTL4SpIkdU4y+LYx69lDFGx5D8vxbehDoom5/g5iBk9DHxyJ9ewhinb9LxXHNoGqEt5rNDHXTSU07XoURSODryRJUiclg287qS3OoXjXCkoPrgXVTWS/m4kbNoOg+B44ayooPbiO0u8/p670FIaIRKIHTUGfOpLY5AwZfCVJkjoZGXzbmbPWQsnezynesxKHpYjgLv2Ivm4qkX3GodGbsZ45yOYP/kR4bQ42h5Obfr+Vk99+QPKQSeiCwju6+pIkSZIfyODbQVS3k4pjmynd9wWWk7vRGExE9h1PzKCpBCX1wW2vIW/PatJvnMnGp0cTYtYT1i2TqH63EJ5xA1pjUEe/BUmSJOkyyeAbAGyVhZTtX03pvi+xW85hikkjetBktF2GEpucQcnZHFxnv6P88NdYzx5C0eoJTR1MeM9RRPS8EX1IdEe/BUmSJOkSyOAbQFS3i6rc7yjZ+wWV2VuostYx9rnNnNjwPslDJ6MPjsBWUUBl1hYqsjZTnbcfVDdBSX2I6DmK8IwbMMWmX1I+aUmSJKn9yeAboFx11eR9t6ah29mkIyx9CBG9xxHeYyT64EicNZVUnthBZdZmLCd34nbUoQ+JIbTbUMLShxGWPgRdUETLF5MkSZLalQy+Acwz1agk/xTugu8pP/SNaO0CwV37Ed7jRiJ6jMQUk4rbYaPq9F6qcvZgydlFXXEOoBCU0IPQ9KGEpAwipGt/tMbgjn1TkiRJkgy+gay5eb4OazmW49upyN6M5eRuVKcNY1Qy4T1vJLzbcIK79kOjM2CvKqEqZzeWnN1U5e7BaS0HRYM5PoOQ5AGEJA8iJHlgk8QekiRJUtuTwTeAtZRkw+2wYcndQ2X2Fiqzt+K0lqPRmwhJHkhot2GEpQ3BFJsOgK38LNWn91Gdt5/qvP3YKwoAMEYlE5zUm6DE3gQn9cYcn4FGJ9cUliRJaksy+AawS8lwpapuaotOelu71af3oboc6EOiCUkdTEjyQEKSB2KKSUVRFOyWIqrz9mM9cwhrwVFqzx1HdTlAo8Uc153gxF4EJfbGHN8dc0w6Gr0MyJIkSf4ig28Au5L0km6HjeozB7Cc3EX16X3UFGaB6kZrDvMG4pDkgQTFZ6BodbhdDmqLTlCTf4yagqNY849QV3IKUEHRYIzsgjk+A3NcN8xx3THHdcMQFi9HVkuSJF0GGXwD0JIlS1iyZAkul4usrCy/pJd02Wuwnj1M9WnR7WzNP4zqtKPoDATFZxCU2IegpF4EJ/bGGNUVRdHgstdSV5JLbdEJaotOereuuioANIYgTFFdMUanYIpKxhidjCk6GVNUMhq9yR//FJIkSZ2SDL4BrC0XVnC7HNQUZFGTfxhrgWjt2srOAKA1BhOU2IugxF6ilRvbDVN0CopWh6qqOKqKRTAuzsFWlkdd6WlspXk4ayu95RvC4jFGdcUQkYgxPEFsIxIwhCeiC46ULWZJkq5pMvgGsPZe1chZW0VN4TFq8o9iLThCTWE2DksRAIpGhykm1dvlbI7rjikmFX1orDeQOmst1JXmYSs7Xb89g62yEHtFgbe1DKDRmzCEJ2AIT8AYkYA+NBZ9aAz6kBgMoTHoQ2Nl+kxJkjo1GXwDWCAsKeisraKuOKeh67lYbN2OOkAEUmOU6G4W25T6x13RGhoCqKuu2huIPVt7ZSG2ikIc1SW4ai0+19UYgtCHNgRjfUg0+uBIdMGR6IIi0AVFiOfmcBStrl3/TSRJkq6UDL4BLBCCb3NU1Y2tPL++u/k0dWV52ErzqCvNw1lT7j1PHxqDMbKLT9ezaO0mog+JRtFovee6HTYc1SXYq0pwVJXgqCrGUVX/vLp+n7Uc1WlrUh+tKdQ3IAeFozWFiv2mULSmEPHYHFq/PwStMRhF0bTLv5ckSdL5ZPANYIEafC/GWVclAnGZCMb2inxs9a1cp7UhMCsaHYbwOAzhiRjC49GHxPi2dENj0AWFNwmQLnstzpoK8WMtx+F9XIGzphyHVTx31VWJH5u1+YoqGrTG4PoAHYLWFILGEITWECS2RrP3udhnRmsManSOGa1BnKNo9fIetiRJl0QG3wB2NQbfi3E76rBVnhNdzo27n6uKRUu3ugxUt/d8RaMT3c2hMfX3hKMbtW5FS1fnaekaQ5oNgKrbhctmxVVXhbOuClddNa5az2Px3FkfpN32Gly2GrG119Zva1Cd9ou/MUWDRm9EozOh0RtQdEY0ehManaF+a6zEUnyIAAAFLUlEQVQ/bqw/ZvTZp9EbUXQGFK0ejVYvgrlWh0ZrQNHqUHR6FI0ejc5zrNF5Or1swUvSVUgG3wDW2YJvS1S3C4e13Lfb2dPlXFWCo7oUZ02lGFXdKEiDCNS64PqAHCQCss4c1qhle143tFk8VnTGFlutqtuJy1aL21HbKDjX4LbXiq2jDrfTjttRh+qw4XbacJ+39e73OVaHWv+6K6Jo0OjqA3Wj4IxGi6LRoWi0jX7EczRaFG39PqV+q9XVv6Z+n7bRuU3K0TY6phVfABSN2Go0oCgoirZ+qxHn1j9G0aBoGp3vOVejEZ+FohXbRudc8HUaLaDU769/naIASn25DY9RFBQUUMS/GSiyx0LqMDL4BrBrLfi2lup24aqrqu9iLhcB2acLun5fncXbur1QgFO0+vp7wCHozKHndSsHoTGe99wQhNYY5O1y9uzTGEwiQF3GH3NVVVHdTlSnA9XlwO0SW/HjxO2y1x+rf+xyeo+7XY5mX+d2OcDtQvX+OFHdroZ9Lieq6mrY56rfr9Yfczc65nY2Kkc89y3b1eTL0NXFE7DxBnXxRNPweXqCfaPH3vM9AR3Pl4umj0VZDY/rX9zQa3HeYxQN3t8k7++Uct5zGv2+NT3m2df0nGbe90WONZTjW673S875r/Nes/ljoNB95nNc6+QwUemqo2i03m5nSGvVa9wuB67aqvru52rvPWFvV7RnaxctW4e1rEkrV3U5WqqYT/ezRmdCadzF7H0suqSV87qkNfVdz4pW79OS9XQ/awwmdFoDGm8L11DfFV3/vIO7n1VVBdUltm43quoGtX7rdvseV931QVttOM/d6HxVRVXrj/vsrz8P1Rv0xfUaykVVUVFBVaF+631ev09Vzzve6PEFz7+Uc5u7duNjFyiv4XH9lxnVs/G0kTw7GrWZ6h+rFznmeZ16kWMN5Vz4mM9n3aRO3qONjqvejfck2d4DZPANSI0zXEn+odHq0YREoQ+Juuwy3C4Hbtt5Xc6e+8T13chNu58b9rmdNu+IbbfD5t3nedxicG+BotHV3yM21N8T1tV3FzfqTtY27T7G26Ws8z1HEV3TTbudG86jUbe16AbWeLubafS4SdezxtNF3Oicxl3HntdqFDS6887XnFdmk25nTX3DzdMqbdzl3NAtLbucpY4ku50DmOx2vrb4dj/bcXu6l5123I32i+5nsd/7uL5rWpxnb+iG9nYrOy/Srdyoa7n+GOed16Tr2tNt7S1XtG4bNXGuDs12+3ruPTd/71ihIcD7dC8rmuYDvE85zV+vyTVa3Z3c2q7k88tRfLuRm+2abqbbupku5CZfYnzqpTSc3aic9Dt/w7VOtnwlKUAoioKi1YNWD1ydGb68XcrerubmupSbP37+Mc9jn9eef15zx326ed2eftT6LmkxT93THdrwuJkuYO9+t897E4/dDd2nnq7vZrqoG8ppqIe3TvXXVn0eN+pybvhHbbFLuaXuZNXnWNOyVJ/XXKQbWVV9u5C9r/U89r2u97zG3eeyvQfI4CtJkh95RyujBW3L50vStUpOEJQkSZKkdiaDryRJkiS1Mxl8JUmSJKmdyeArSZIkSe1MBl9JkiRJamcy+EqSJElSO5NJNgKYqqpUVVURGhoqs/FIkiR1IjL4SpIkSVI7k93OkiRJktTOZPCVJEmSpHYmg68kSZIktTMZfCVJkiSpncngK0mSJEntTAZfSZIkSWpnMvhKkiRJUjuTwVeSJEmS2pkMvpIkSZLUzmTwlSRJkqR29v8Bw1R6AMreEZYAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 9 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "eps_L = -1\n", "b3_out = find_b(-2*pi, r_em, phi_em, pre_periastron=em_pre_periastron)\n", "graph += line(geod(r_em, phi_em, b3_out, eps_L, em_pre_periastron=em_pre_periastron,\n", " np=4000), color=color3)\n", "show(graph, xmax=15, axes_labels=[r'$x/m$', r'$y/m$'])" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "graph.save(\"gis_disk_image_detail.pdf\", xmax=15, \n", " axes_labels=[r'$x/m$', r'$y/m$'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inner radius and width of primary image:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(6.932148479189469, 3.0197242048926336)" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b1_in, b1_out - b1_in" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inner radius and width of secondary image:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(5.478913722083879, 0.15113581710277924)" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b2_in, b2_out - b2_in" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inner radius and width of tertiary image:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(5.207989587554517, 0.005314937250211926)" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b3_in, b3_out - b3_in" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Emission from the lower part of the disk ($\\varphi_{\\rm em} = 3\\pi/2$)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "phi_em = 3*pi/2" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "r_em = r_disk_in" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "em_pre_periastron = False\n", "b = find_b(2*pi, r_em, phi_em, pre_periastron=em_pre_periastron)\n", "eps_L = 1\n", "graph += line([(0, -r_disk_in), (0, -r_disk_out)], color='darkorange', \n", " thickness=4, zorder=50)\n", "graph += line(geod(r_em, phi_em, b, eps_L, em_pre_periastron=em_pre_periastron), \n", " color=color1)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "em_pre_periastron = True\n", "eps_L = -1\n", "b = find_b(0, r_em, phi_em, pre_periastron=em_pre_periastron)\n", "graph += line(geod(r_em, phi_em, b, eps_L, em_pre_periastron=em_pre_periastron),\n", " color=color2)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "eps_L = 1\n", "b = find_b(4*pi, r_em, phi_em, pre_periastron=em_pre_periastron)\n", "graph += line(geod(r_em, phi_em, b, eps_L, em_pre_periastron=em_pre_periastron,\n", " np=1000), color=color3)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "r_em = r_disk_out" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "em_pre_periastron = False\n", "b = find_b(2*pi, r_em, phi_em, pre_periastron=em_pre_periastron)\n", "eps_L = 1\n", "graph += line(geod(r_em, phi_em, b, eps_L, em_pre_periastron=em_pre_periastron), \n", " color=color1)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "em_pre_periastron = True\n", "eps_L = -1\n", "b = find_b(0, r_em, phi_em, pre_periastron=em_pre_periastron)\n", "graph += line(geod(r_em, phi_em, b, eps_L, em_pre_periastron=em_pre_periastron),\n", " color=color2)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps_L = 1\n", "b = find_b(4*pi, r_em, phi_em, pre_periastron=em_pre_periastron)\n", "graph += line(geod(r_em, phi_em, b, eps_L, em_pre_periastron=em_pre_periastron,\n", " np=1000), color=color3)\n", "graph" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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gIlOllTl1Alkjlo786jk5HwwBEBAHlj7K2guIhbDB6t4SBebo6jRKCaQ5CswRyiUpCILQDRyTAqppGoeWPIUhIJTEKTd393A6j2eegSVL4M47lSV6pLisUL4fyveB/RBUZoE9U6UVWVBxWK22rMEQAAF9lTAGxkH0GAiIV8++V2AcGEPFAhQEoVdxTApo4YbF2A6sJ/2SpzAEhHT3cDqP2FgVK/e66+DKK2HKlObra14lhOX7qq+9Pvf7wFFYV9cQAIGJENwfglMhdqKaI6zJC0xUlqKIoiAIRynHnIA6SnM4/O0rRI88u+cHiu8IrrlGWZ833QSbN0NAgNpAbNsN1u1g3QFl1altp9pSAYBOCWJIKoQPg37nqPuayxIj4igIwjHNMSWgmubl4JdPYgwMJ3HKn7p7OJ2P1w22XfDgOTD9Hrj5eDjPo9ywNXsCLTEQPgT6jIPUqyE0A0LTIDhZWZmCIAhCoxxTAlq4fjHlBzeQfunTGCzB3T2cjsVlhZKNUPKbSkt/g7KtdRblOaHwwV6YdS2MO0kt0AkbrNysgiAIQps5ZgTUUZLN4e9epc8J5xKWMqa7h3NkeJxQugmKfq27rDsATW2sDx8GkSNgwB8gciREHA/nmmHIEPh3Pnx2XXd/AkEQhF7PMSGgynX7BMagcPpNvqm7h9N2qvKh4GfI/xEKV0PJBhUCTmdUQhk3CYbeDVGjlVXZ2NYOC/Dcc3DRRfDFF3D22V39KQRBEI4qjgkBLVj3KeWHfmPgZc9isAR193Baxn5IiWXBTyq17lD5wQOgz8kw4FKIPlFZl22Zp7zgAhVc4dZb1YrcwMBOGb4gCMKxwFEvoI7SHLK/f40+o2YSOmBUdw+ncSrzIPcbyF0G+T+A/aDKDx8KsZPguAcgZoLaHnIk6HTw4oswfDg8+aQEmxcEQTgCjmoB1TSNzP89iyEglH6n3djdw2mI/SAsGakW/ABEjIDE8yH2dxBzKgT06fh3DhqkAis8/jhccQWkpnb8OwRBEI4BdJqmdeMZR51L8ZZlHFj8GGkXzen+cH3zx0POKv88iwlGXwrxp0P8VBWRpyuw29WCohEj4PPPu+adgiAIRxlH7XEQ7opSspbNJWLIad0vnkBebk7DTFcijH8HUi7vOvEECA6Gf/1LLSYSARUEQWgXR62AZn3zMprmpf+0W7p7KNgPbyWU8oYF+/bDLbeA292wrLOZNQvOOEMtKKqs7Pr3C4Ig9HKOSgG17ltD8Zav6TflT5hCorptHJqmkbf6P+x871ac5li8saNxx45l5QFwx46F9FPUsWMzZkBJSdcOTqeDF16Aw4dV0HlBEAShTRx1c6AeZyXbX78GS0QC6Zc9022HZLsrrRz84p+U7V5B7EmX0G/iH9EZjFitVsLDwykrKyMsLAy+/15tL4mJUe7UjIyuHeidd8Irr8CuXdCvX9e+WxAEoRdz1FmgOT+9hcteTP8z7+g28bQf3saON66nPGsLab9/nMTJN6EzNLHg+bTT4NdfQa+HcePg22+7drAPPKDmRP/2t659ryAIQi/nqNrGUpGzk/xfPyZh0h8JiErs8vdrmkbhhs/J+voFgvoOImPW3zGHxbbcMD0dVq6ESy5R85Ivvww33ND5AwYID4dHHlGntfz5z3DiiV3zXuGYQtM0dVyepqHVS9G8deVoKJ+YpsqqDz2oc5TV5KP6qPes2mu+L65to9V7Vr35tEerfp3m07f/WOq69hmf5ttPXRvNZ/xNjq8236ffJsq0JvKba+Of3fY2/u9vZZsGn9m3RGu0WnNtaKKN1o42vg/1/x1iRp1LWzlqXLia18POd/6M1+1kyLWvNW3xdRJet4PMpc9T9NsS+ow6j8Rpf0ZvaBhSr4EL1xe3G26/HebOhXvvhUcfVZZpZ+PxwKhRyhL95Rc5pqwNaJqG5nWjeVxonurU60HzuPB6fPLr1fHW5tW0caN5PeD1oGne6nuV1j170DRPvbLW1vP69+0rWprWUODwF7bWCmCdEOJXLgjdi89vWhO/b6Pu/a7NvR41Fmjhxi+pyNlBxhUvdrl4Osvy2PfJg1Tm7yP57HuIPv7M9nVkNKqFPQMGqLnJgwfhzTfBYunQ8TbAYFDbWiZPhg8/hEsv7dz3dSKapimBclbicVXidarL46zE66zA46pEcznxup143Q40t6Pu3uXE63HidTmqy5w+qdM/z+PG63GB19MxA9fp0ekN6PQG0BvQVT/75uv0etAZ6ur5tqm91/v0YUBnMvuV1fatM6gfEp1eTXXUprqG+agUnQ5dvbRh+5br1ebTSDlU/8Cpcehqn6nNU1k6v2fVl289fPrwf675MdXVz9NRXbeuToN+GhtfvbxGx1eT30iez4t82jb5H8Xntqn2bavfoFpr2jTxjoZjb7mN7zt0ranfzLi6etruqLBAXfZSts27gvCMUxhw9l+79N22AxvYv+gh9KYAUi94mKC+g5qt36wF6svChSpS0PjxsGgRRER08MgbYdYsWLcOduyAoK6PGaxpmhK5qnLcVTY8VeV4HOV4qu/dVeU+eeV4nBV1AumqEcqKVomazmhGb7SgN1qq783oTRZ0BpX65VfX1Zks6A1mlW8woTOY0BmMKtUb0BlM6GufjXVlBmPts97vuaa9sVpQ2vp9eZu0RKm2NGutTa8HzVudX2Od1lqNNLAulavR1yKllVZrc/k1FmldHY3m+qv9oLTomlWZ9dyo9Vyr1CQ+Ltp6eTX1GnMj17pqa5/ruZLr5dX11TDP36Xs+66GrsUG7tYGrtSmy5rtq8Evf0suWq3poja0bTj8tri0m39vs27qBk39ywdd9VLz9RvhqLBAs394DdC6NFyfpmnk/7qQw9+9SmjySFLOexBjUAeK3EUXQd++MHMmnHIKLFkCyckd139jPP00DB2q0gcfPOLuNK8bd0UZropS3PZS3BWluCvKcFeU+NyX4rKX4K4sw1NV3qS7T28KwGAJwRBQd5mCo9BHBmIwB6I3BaI3B2IwB1Wn6llvqruvqaczmv3+Uq2xWmusS6/b6WN1Ov3zqy3UGres11VZ67LVPG68XjfUlPm5ad1oXheax1Pnsq1frlWLXK0L1sftWuOC9XHH9ipqLM8aC6yBRVrf2oXmrMrq0gZ5qk3DPJU0ZwX6vKuexduUFayy61vCvn3pqDOO6lvDvn01YRH7fX8NvlD/pyYsv7rP1Hz7NllxzVmZjZQ3fHVzVmrz727Wwm1F+4ZjOzKLtddboOVZW9j17v/R/4zbiRk9s0ve6fW4yPzqWYo2faW2qEz6Izp96/4WabUFWsPOnXDmmSrYwZdfqrnKzuSee9Qc7M6dkNj0QiyPw47TWoCrvBCXrQCXrQinrRBXeQEuWyEuWxEue3EDQdQZTBiDImovU3D1fWA4hsBQDAGhGANCMASE+gmm3mBC07x4HRW4qy1Qr7MCr6uq2j1bY4lWqXtXZV1+dV6tS9ft9HHdKoFs8a/V+uj0tRakvtba9LEsqy1SX+uzfrnez1I1KvdqtYu1UfesTg/6mnuDz31j9X1cwLoa17C+zjWsr3bj1nyWRsSsztXqX6dOHBprVy/fTwQF4eiiVwuo5nWz480b0RmMDLrqZfXD0Mm4K0rZ998HsWdvJ2nGXUQPP71N7dssoAB5eXDOObB9OyxerLa+dBZWK6Sn4515Ns7H/46jLBdnaQ6O0hycpTk4y3JxlOXiqbT6NTMEhmEOjcEU2gdTSDSm0BjMoX0wBkfViWRQJHpzIJrHhbuyzMcKVfe1rtoaF62vu9ZRjqfKTnNCpzOYqq3OAAzVFmmd5RlQW6Y3BdS5Ymvcsz7uWp1faml4Xy2AgiAc2/RqAc1f81+yls1l0DWvENx3cKe/r7LgAHsX3ovXWUnqhY8Sknhcm/tol4CCCgB//vmwfLla6HPeeW1+d300TcNlK6CqKBNH0SGqig5RVZxJ1YGtuDSf8H56A+awOCwR8Zgj+mIJ74s5oi/msBhMoTGYQqLQ6Q24yotxlRdVW6CFOMuLcJcXKRdujVhWluF12BuMRWc0YwwIq3PRWvxTo29eQAgGSzB6c5CP+zag0VXPgtAhVM/d+l3N5fu2a+y+LWUd1U9jZTV5Xq9/naY+Y2vKmnq/19v2ssb6ba6sqbr1x91Yu3Zs4eu1AuoqL2brvCuIGjqFpDPv6PT3le1dzf5PH6a0Ei575ltySh21ZXFxceTm5raqn3YLKIDTqRYWffwxvPEGXH11q5u6K21U5u+hMm8vFfl7qMrfR1VxJl6nEkqd3oglKhFLVH8CIvsR8NTLmKMTsbz8FsaQaLyO8mprNFdZoaU5uGwFym1rK8RtL8HXOtTpjZhCozEGRylXba3bNtzPhVvzrDcF9G5Xn6ap7UBOZ91VWQkVFSqtuRwOVVaT1r9crob3bre6d7nUvdut3lWT1r/3qAVFTV6a1nSeb1n9vLaISFM/sDV5vmlTeU3Vae1zU3nN5QvHLu34P9FrFxFl//gmOp2ehEl/7PR3FaxdROayFwlLO5EvthmJ6neQ9du/qS03GLrInWc2w/z5akXuNddAcTHc0fCPB6etAPvh7VTm7aYyfy8VeXtwWfMB5eYMjE0lMC6dyKGTCYhOwhKdhDk8Hre9mKqiQziKMqk4+3eUrv4Bx1u34HTbaoUWQG8OwhLRF1NYDMHxgzANPLnaddunNjUGhbVrZekRoWnKUrdaobBQXaWlUFam8qxWsNmgvFxddrsSuIoKqKpSolYjbL6CVSNQXq+/OPkKS0+g/iKYmjnJpu5be+n1/qnB0HhfNeUtXc2NwbesZg90W/qqPwZoflyNfV/1y5sra6pt/X+XBguUmilrS92W2rXUt2/d+nvOm/oOGuu7uX6aat/UGOvnN/Zcv6yj3tlGeqWAVuTtpmjjlyROuwVjYButuDagaV6yv3+dvFULiD3xIvpNvgn3w49gNBqJj4/vtPc2i8GgAtBHR8Nf/oKnuICK6y+mImcH9sPbsGdvx2UrAMAYHElQXDpRQ6cQGJdOYGwalsgEnGW5VObtparoEMVbv6WqWLlwva4qQFmP5sgELJERhG7NwXzdn6tdt8qFawgI7XhrsaoK8vPhwAE4dAhyc9Xcb2EhFBXViV+N6NUIXo2F5vG0X8j0+rrLYFCX0Vh3BQaq1GRSl9lcl1osdZfZDAEBdfm+5TX5vldNnfrtaur79m0y1Y3Ld7y92WoXhF5OrxNQTdPIWvYSluj+7Qq91Fq8HhcHv3iCkq3fkDj1z8SeeFFt2e7du0lISMBisTBu3DjmzJlDampqo/04HA4cjjp3r9VqbbRea/E47JRnbaF8ajK20JlUuFfAByvRmwII6juIqGFTCUoYQnC/IRjMQVTm76Uyby+2gxvIX/Mxlfn70NxqPMagSAKi+xMUn0HUsCkERPXHEp2EJSJerSr+9luYOhVm3AEnTWz9IDVNWcd79qgg9Xv3qqAQOTlKEEtKlCBWVtYJYEvip9PViViN4ERHq/2qISEQGlp3hYWpEIW+V0SEuiIj1RUcrProikhPgiAclfS6OdDSnT+x778PkHbxE4SnjeuUd3gcFez77wOUZ24i+Zx7iRo6ubbsq6++oqKigoyMDPLy8nj00UfZsWMHW7duJTo6ukFfDz30EP/4xz8a5Ld2DtTrdlKeuQnr/rWUH9xIRe4u0LyYQqIJSRpJSKaN4MdfIeDcS6l68A7sOTuxZ2/DfngbjuJMQFmUAX2Sa63QoLh0AmNTW7dv9YwzlPht2aIEzOGAfftg/XrYuhV271YWY36+cpfa7cr12RQmkxKuoCAlduHhStBiYtSVkKBOhenXT22jiY1VAtlVbnJBEIRW0qsE1Ot2sv31q7FE9iP9kqc65R2u8iL2fPRXHKXZpF3wKKEDTmi2vt1uJy0tjbvvvps7GpmPbMwC7d+/f7MC6ijLxbp3Nda9v2I7sA6vq0oJZvIJhCaNJCR5JMagCOxZW7Ad2oh9/XdUlOegmVUIt6DYNIL7DSWo72AC49IJ6JPc+hWqmgZZWSom7po18PXXSjxBCWhjh38bjUoQw8OhTx+Ii1MCOGAApKXB4MEqYH5oaOvGIAiC0AvoVS7cgrWf4CjNJfXCxzqlf0fEJRhuAAAgAElEQVTJYXYvuBPN7SLjihcIik1rsU1wcDDDhw9n9+7djZZbLBYsLcSy1TSNiuztlOz8EevulVQVHQSdnpDE4cSfeiVhaeMwh8XVCmbhxi98LNE+BKcNJyEnheAn5xE0eSb6u15p2WJzOmH1avjmG1i7VlmSublqcU1Tf1MNGwapqTBwoLo/4QQYNEi5VAVBEI4xeo2Auuwl5PzyHjGjziUwJqXD+68sPMie+X9Bbw5g4FXPYQlv3SIhh8PB9u3bmTBhQpvep2leyjM3U7pjOSU7f8RlzccYFEH4wJPpO/FaQpNH4bIVULZ3NVlfv0h51mbwejCF9CEkeSR9TjibkKSRWCL71S3oiRihtrm4NXjrrToR3bcPPvtM7SHduhWys9VCHF8CA5W7dNQoGDIExoyBU09VYrlrlxLM669XR54JgiAIvceFm/n1ixRt/h/H/emDjo05i1rVu2f+nRhDohh46dOYQhrOZdZw5513cs4555CUlER+fj6PPvooy5cvZ/PmzSS3EKtW0zTy9mygb8ZoVjxxDha3FVNINBGDfkfE4IkExWdgO7gB695VlO1djcuaj85oIXTAKMLTxhGaMsZfMBtj7ly45RZ1n5iorEpft2tgoJpnHDxYHeA9bRqMHduyxXrllWpR0Z49qg9BEIRjnF5hgTpKcyhc/xl9J1zd4eJpP7yVPR/do+ZVL34SY1B4s/WzsrK49NJLKSwsJCYmhpNOOolVq1Y1K56u8iKKtyyjaNP/KMzaA0BExgT6j55OYFwa1n1rKFz/GWV7VuJ1VWGJSiQiYwLh6eMISRqB3tiEC9jrhZ9/hgULlHW5b59a5FM3WBg5Up3oMmOGOq6svaesPPCA2oP62mtw223t60MQBOEooldYoAcWz8G6fy3D/vQBBnPHWT+2gxvYu/BvBMamk/77xzEEhHRY35rXQ9meVRRuWIx13xp0egMRGadiTJlA0glTOPDrF3gy12Dduwqvq4rA2DQihkwicvBEAqKTmuhUU4L5xhtKMA8dqguBZTZDSooSy1mz1JaRm25SgRaefrpj9gtecw189ZUS6m447kwQBKEn0eMt0Mr8fRRvWUb/M2Z3sHhuZM9HfyUk8ThSL3y0w/p22Usp+u1LCjcsxlmWR1DfwSRNv53wwZNwlmRxYOWnABz8/HFikocQf8oVRAyeSEBUEyefHD4ML70En3+uTkip2SISFKTmK08/Xc17Dm4kFrDHo+YsQ0PhoYeO/MM98AC8954K5NDIimNBEIRjiR4voId/eB1LZF/6jDyrw/osz9zM3v8o8Uy7aA56U/OrZFuDPWcHBWsXUbLtOwAih04mZvQszOFxFG36H7vf/T+qig7iMCoX8eBr5xE7YFjjna1aBc8+q+Yci4tVntEIGRlw9tnKskxpxUKqm29W0Xv++le1l/LOO4/sQ6amKiv0n/+EG25QfQqCIByj9GgXbnnmJna9dysDZj5A1LApHdKn/fA2di+4k6D4DNIv/id6U0C7+9I0DduBdeStmI/t4HrM4fH0GTWTPiPOxFGaS8HaTyjZ/j3odERkTCD6+OloUelEREb57wPVNLXf8umn1f7Lyuq4s1FRMGmSEswpU9ofNef+++Gxx+D11+GPRxg7+MABtTL3ySfh9tuPrC9BEIReTI8VUE3T2P3+bXicFQy+9rUOCUxekbOT3fPvICAmhfRLnsRgbt88nub1ULrzJ/JWzqcidxeBcQOJP/lywtLGUbbrZ/LXfkJF9nbM4fHEjD6P6BEzamP2+p3GsnMnPPywsjRrRDMxEWbOhL/8pXVWZqsGrClX7muvqfNEZ8w4sv6uvlrtH927V8VpFQRBOAbpsQJqO7Ce3fPvIO2iOYQPPPmI+6vM38euD2ZjiezHwEufxmAJbnMfmqZRuvNHcpa/SVXRQUKSTyB+/GUE9RtK0cYvyF/9H1zlRYQOGE3MmPMJTz+pwcHL1r17CU9PpywigrDSUpWZkACXXgr33KPC2XUGHg9ccAEsWwY//KC2rrSXbdvUvtA33oBrr+2wIQqCIPQmeqyA7nr/NrzOSgZdM++IT/5wlOWy653/wxgcwcDLn8MY0PaQctb9a8n+4XUqcnYSmjKGhN9dgyWqPwVrPyF/zX/xOiuJGn46seMuJrBPvS0tmqbO8Hz4YaxbthAOlIWFETZrllrcM2DAEX2+VlNRoVzBe/fCypUqzF57mTVLCem2bRKnVhCEY5IeKaC2gxvZ/cFsUi98jIiMU46oL3dFKTvfvQXN62HQlS82GyShMezZ28n+/nVsB9cTlDCEfpNuIDA+nbxVH1Kw5r9omkafE84mbtzFmMNi/RuXl6sFPO+8o+71eqxjxhD+66/tO1C7IygshJNPVqK+YkX7Ld7Vq+Gkk9QfBhdc0LFjFARB6AX0SAHd9cHteKpsDL729SOyPj3OSnbPvwNnaS4ZV77Y9FaRRnDaCsn+fh7FW5YR0GcACZP+SOiAMRSu/5TcFR+geVzEjDmf2BMvwhQc6d943z74v/+DpUvVPs2ICLjuOnjoIaxeb90caHcIaM34xo9Xi4G++679sWwnT1bHkq1ZI+dSCoJwzNHjtrGUH9pE+cENpF7wyBGJp+Zxs/+Tv1NVeICMPzzfavH0up3kr/kvub+8i95gJmnGnUQdN43iLd+wbd4VuOzF9Bl5Nn1PvbKhNbtundresX69eh44EB5/3N9CO8LzQDuE1FT49FO1wvfmm9Xq3PZ81/feq/ahfvONCgkoCIJwDNHjBDTnl3cJjE0j/Ahct5qmcWjpv7AdWE/axf8kKD6jVe2s+9eRufQ5HCXZxIyeRd8JV1OZv5cdb/2JqoJ9RA45jb4Tr2soxmvXqsU0mzer5/HjVfCDE5o/Cq1bGT8e5s1T+zpHjKiLn9sWpk5VoQKfe04EVBCEY44eJaAVOTux7V9Lynl/P6JtKwVrPqZo4xckn30PYSljWqzvqSon67tXKNr4JSH9R5B6/sMYAsPIXPovSrZ9S3C/oQy65lWC+9aL9rNli4oCtHGjsuCmToV//xtaCCrfY7j6aiX6t9+uTmCZOrVt7XU6FRf3mmvUiS0ZrftDRRAE4WigR82B7v/0YezZ2xl20/sNtn+0lrI9q9i78G/EjbuYfpNvbLF+6e4VZH71LB5nBf0m30j0iBkUrPuUnB/fRG+00O+0G4k6/gx/QS8ogIsvhu+/V8+TJsHbbzcrnC+99BIvvfQSHo+HXbt2de8cqC9ut4putHq1mstMT29b+6oqSEpS38eLL3bOGAVBEHogPUZAHaU5bH3lchKn/R+xY85vVx+V+fvY+e7/EZp8AqkXPNysCLsrbWR+/TwlW78hLG0cSWf+BY+zkkNfPoH98HZiRs+k78Tr/Le8OJ1w663KyvR4YPRo+OADdah0K/ELpNATBBSgtFTtCw0JUdtbAtoYnenBB5UbNysLwps/zUYQBOFo4cjD+3QQ+Ws+xhAQQvTxZ7arvbuijL0L/4Yloi8DZt7XrHjaDv3G9jeuw7p3Fcnn/I3UCx+leMsydrzxR9yVNjKueIH+Z8z2F8/334foaDVvGBenogetXdsm8eyxRETAwoWwfTvMnt329jfdpCzRt97q+LEJgiD0UHqEgLorbRRt/JKYUTPbdSqKpnk58PkcPM4KUi96rMkQfZrHTfbyN9j9we1Ywvsy5I9vEtxvKLvevYXs5W8QM+Z8hlz3b0L6D69rlJ2tTj254gp1EkqNpTV5cns/bs9k5Ejlgp03T1nVbSEhAX7/e9Xe4+mc8QmCIPQweoSAFm5YjOb1EDN6Vrva5/7yPta9v5Iy8wEs4fGN1nGVF7F7/h3krviAvr+7hoGXP0t55mZ2vHkDniorg66cS+KUP/mfzPLQQ2p+b8MGOOssdTLK7NlH757HP/5R/aFw443KGm0Lt96q9pcuXdo5YxMEQehhdPscqOZ1s+WlSwhLG0fyjLva3N66bw17PrybvhOuou+EqxutU565mf2LHkLTNFLPf4ig+Awyv36Bot+WEDlsKknTb/ePjXvokAp5t2ePOhHlk09g4sR2fsJ64+2Jc6C+2O1w4onq5Jc1a1o/H6ppattOaqr6vgRBEI5yut0CLd21ApetkJjR57W5rdOaz/7PHiEsdQzxp17ZoFzTNPLXfsKuD2ZjjkhgyHWvYwgIY8dbN1G89VuSzrqbAefe5y+eL7ygRGDPHrjqKsjP7zDx7BUEB8OCBWpbygMPtL6dTqcs2M8/h9zczhufIAhCD6HbBbRw/acEJx5HUNzANrXTvB4OLH4MvdHCgHPva7BvVPO6yfzfc2R9/QIxo88j4/LnsGdvZ+c7fwJg8DXz6DNiRl20o6oqmDBB7WsMDlYnlrz99rEZKP3449X5oc88o76H1nL55erg73fe6bShCYIg9BS6VUCrCg9iO7CemFEz29w2b/VHlB/axIBz78MYFOFX5nFUsHfhfRRu/IKkGXeSOPX/yF21gH0f309YylgGXf0ygTED6hps2gR9+8LPP6vFQXl5x5bV2Ri33w6/+x1ceSWUlbWuTWQkXHih2ubTM3ZHCYIgdBrdKqAFGxZjDAwnYnDbxKoiZyfZy98gbvwlhCaP9CtzWvPZ9d4tlGdtIf2SJ4k6bhoHPnuEnOVv0HfC1aSc/5D/Kt2akHtWq1ph++23bd8HeTRiMChLsqysbWH+rr9eub+XL++8sQmCIPQAuk1APc5Kijf9j+iRZ6E3tv40EK+riv2fPUpgbBp9f+d/mHNV4UF2vnMz7iobg654keC+g9nz4T2U7vyJlFkP0XfC1XWuXk2DP/xBnZoSEqIWzLRnD+TRTHIyPP88vPde61fXTpigQvq9+Wbnjk0QBKGb6TYBLd35Ix6HnT4nnNOmdod/eB2nNZ+Uc+9DbzDV5lfm72PX+7MxBIQy+OpXMASGsev926jM38PAy54hcsikuk4cDhV554MPYNgwOHxY7fUUGnLVVWpF8k03qRW6LaHTqT9MFi1SB3gLgiAcpXSbgBZvWkpI0kgsEX1b3aY8aysFaz4hYeK1BPSpiztbkbuLXR/MxhTah4zLn8PjrGTXu3/GXWkl44oXCel/fF0nBQUwYIA6emzWLBVMPSSkAz/ZUYZOB6++qlbW/v3vrWtz6aXqAPEvvujcsQmCIHQj3XIai6MsF9vB9SSffU+r23jdTg4teYqgvoOIHVt3vqb98Db2fHQ3lqj+pF/8JO7KMnZ/MBu9KZCMK57BHBZb18m+fSrijs0G990Hjz7akR/LH02DkhIVtejwYZUWFtadB3rffWqvZWCgWvUbEqLiyCYkQL9+kJioFuX0BNLTlXjedx9cdlnL1np6utpLOn++ilAkCIJwFNItgRRyfn6XvJXzGX7bJ02G3atP9o9vkbvifYZc+zqBsakAlGdtYc+HdxMYm0r6xU/gspfUiecf/uV/4PXmzepH3eFQq0SvvbaJN7UDTVP7JleuVNeqVeq5qsq/ntGIVdMI93goMxgIq9kio2ng9TYMgxcdDUOHqqPGRo9W4z/uOLVVpKtxuWDMGCX4K1Yo8W+O55+Hu+5SK5p7yh8CgiAIHUiXC6imaWx79Q8EJx7HgHPubVWbysKDbP/3tcSPv5yEiUr4KnJ3s+uD2QTFpZP2+8dxlRc3LZ6rV6vFLR4PfPyxct0eCV6vWmX6yy91gllcrNydKSkQFqYCMGRnq9WsY8eqkIAhIViNRsJfe42yv/yFME2Dykp1FRWp+tnZyl1a888SEAAmk3KJapqyVE89VW23OeccGDy4+bF2JMuXq6Pb3ntPzXM2R06OsqLnzVMBFgRBEI4yulxAy7O2suvdPzPwsmcJHdDywh1N09jz4d04Sw8z5Pq30BstVBVlsuu9WzCHxzPwsmfxOMrZ+c6f0ZsCGornunUwfrwSva++gmnT2j94TYPFi+H++9Vh2uHhyiqMjVXu2vXrITcXLTISx4yp2M6ahHn6OYRH9uew6zDbnduxWW2cn3A+n2R/Qr+IfpwYeCIAu5y7CNQFEqIPIcRlwnTwMOzYoU58+fVXdZWWKpEOD1cLelwuZZ3OmqWu0aM7P07vRRcpC3TnzpbnjqdMUX9AfP11545JEAShG+hyX2Dp9u8xBkcRkjSiVfXLdv+Cbf8aUi+ag95owWkrZM+COzEGhpN+8T/RNA97PrwbnV7PwMuf8xfPbdvg5JOVeH7zjbKe2oOmqfb336+EbMIE+NvfYNs2tGXL0NntkJpK9kUT+e30ZPacGIfXZABcTAgsYBT9efOVN5n38jy8Hq/6XJ4yQr3quDS35uYr+1e1r9OhIyo+ivMGnkfIzJlYPVYCdQGY9h5Uh3gvWQLLlikBzcpS+1fnzFHbR264Qa2c7dOnfZ+1JZ56Slm9TzwBjzzSfN1Zs+COO9ReUjknVBCEo4wutUA1zcuWuRcTkXEK/c9oec+l1+1g22tXExDVn7SLn8DrqmL3+7fhshcz6KqXMQZFsOeje6jM20PGlXMJ9FmZy4EDav6wqgq+/BLObN85o6xYoRbP/PADJCWhhYUpYdY0isYOZOf0DIZdeC8Rx43nN8cmyrxlxBpiCTOEEaILIUgfhFFX93dKU8HknZoTu9dOhbeCEm8JBZ4CJgZORK/Ts9C2kDx3Hv1N/Uk1pZJiSiHEZVIu1Q8/VGd5lpcr0SwtVfOT55+vogmdeGL7Pndz3HcfPPusmuft37/peocOqb2kCxbAJZd0/DgEQRC6kS4V0Fr37eX/ahBBqDFyfnmPnJ/eZuj1b2GJ7Me+T/6Obf9aMq58kcDYdA4sfozSHcsZeOkzhCT5bFUpK1M/3GVl8NFH7VsJum6disCzciWYzeB0QkAA2ZOPY+v0dDJPP56YfseRYkoh3ZROgL510YvacxpLgbuATHcm+1z7yHZno6FxQcgFJJoS0TQNXWWlci2/9pqyUEND1ZiLipQb9W9/g9NO6zj3rs2m5novvFBtcWmOUaPUoeMLFnTMuwVBEHoKWheSuWyu9tu/ztO8HneLdV32Em3DU2dqmcvmqrbfvKytm3OaVrp7haZpmpb1/WvauscmasVbv/Nv6HZrWkqKpoGmvfhi2wZos2na889rWnKyag+aOzxU23/lVK3y0/9omt2uba/aru117NVcXlfb+q6mrKxMA7SysrJ2ta/0VGrbq7bXvn+JbYn2v/L/admubM3r9Wra5s2adsMNmmY2a1pQkKbFx6vPcsopmrZiRbve2ShPPaVpRqOm7d3bfL1//EPTwsI0zeHouHcLgiD0ALoskIKmeSnZsZyIQRPR6Vs+4SR3xXwA4k++nOKt35K/+iMSp9xMePp4ircsI2/FB/SbfBORQ0/zbzh1KuzfD3/+swrT1xpWrFDzo+HhcNttaNnZlE0/lS+W3svcvf9g1YvXYTtrEgQFMdgymFRzqp9btisJ0Acw2DK49v1xxjhy3Dn8x/YfFtgWsCvDjPbqq+o7uPFG5dINC4ODB9V88IUXwt69Rz6Qm2+GmBh4+OHm682cqfa+SmxcQRCOMrpMQCvz9uCy5hM5+Hct1nVa8ylYt4i4cb/HVVHGoSVPETlsKjFjL6Aibw8HlzxN1PAziB13sX/Du+5Sc5WTJsHcuS0PyuOBe+5R20J+/BGCguDBB/km9xPemX8R5lMmcUn4ZVwSdgkxxph2fe7OZlTAKK4Ku4qZITMJ0gXxtf1r7JpdBWR49lkV2H3WLLXYqF8/9TmHDVMLgByO9r84KEjNhb73nlot3BTHH69Oulm2rP3vEgRB6IF02Rxozs/vkrfqQ46//TO/GLaNcXDJ05Tt/InB17/Fnvl3gKYx6JpX0Lwedrx5IwZLEIOufAm9yVLX6KuvYMYMJRIHDrQcbGDLFjjrLDh0CC0ggOJ7b6bi1uvpHzGYEk8JAJGGjg8A0J450Db177USpg/DpblYZl/GqIBRxBvj1Zzu7bfDTz/B8OGwfbuKGPTGG8oybQ8OB6SlwemnNx88/sor1fe9fn373iMIgtAD6TIL1LrvV8JSxrQono7SHIp+W0Ls+Ms4/O3LOMtySbngYfSmQA599SyeyjJSL3jEXzzz85WVZTKpoAnNiafVqg5+Pv54yMzEdfkl/G/3m7x/SxK7zdmAEs7OEM+uIEyvRLncW06xp5iPbB/xY8WPuEYdr9yo//63Wh0bEaFmeSdMUJak09n2l1ksSpTff1+FK2yKqVNhwwYVh1gQBOEooUsE1F1Rhv3wNsLSWt5Skb/6I4wBoRgtQZRs/YakGXcS2CeZ4s3/o3T79ySdead/AHpNUy5Yh0Nt6ejXr/GOKyvV3sW4OJg/H23AAPZt/Jw3504iM8TGWcFnMTlocgd94u4n0hDJZWGXMSFwApscm5hvnU+OJxeuuw62boWTTlLBEE48EZ58UgWb2L+/7S+6/noV3u+FF5quM3WqSr/7rn0fRhAEoQfSJQJq3b8WNC9haeOareeyl1D42xKiRpzJ4e/nEXXcNKKGTaWqOIvMpc8TffyZDRcN3X037N6t3ITnn994x9u2KVfjX/+qLK2HHsKzZyfLk/NJMiZxRdgVpJvTO+jT9hz0Oj2jAkZxedjlBOoCcWkuVdCvn9r28tJLyq2alqasw9GjlSu8LYSFqaPOXn21LlB+fRIS1J5cmQcVBOEoomsEdO9qAmPTMIc2vxAnf81/0ekNOIoy0emNJE79PzTNy8Ev/okpJJrE02/xb7B5MzzzDMTHw1tvNd5pjbWVlwfJyZSs/BrbA3dg1Ju4JPQSzgw5k0B9YAd90p5JpCGSi0IvIsmUhFfz8kvlL9i1CrWSdvVqFanJZlP7Nc86S62s9Xpb/4LbblNnf779dtN1Jk1S86+CIAhHCZ0uoJqmYTu4gdABo5ut53FWUrj+U0KTR1G2+xcSp92CMSicgnWfYs/aQtJZd/uf3KJpcMYZ6n7p0sZPB1m9WllVNhtcdBF71n/K/IE7WFW5CuCoF05fdNVBFMq95Wx3bOdD64fkufPU8W4139PatWrbyUMPKYu+tfOiCQlw3nkqcHxTa9JOPllFLioq6pgPJAiC0M10uoA6y3Jx2QpajH1bsvVbPFV2NVeaPp7IoZNxluWR/cPr9DnhXELrt7/7bnXix623qgVB9Vm8WP1ou1xoL7/Myrdu40vdclJNqZwWdFrD+scIYYYwLgm7hGB9MAttC9nh3KGOG/vqKzU/+umnSgwXLlSrmsvKWtfxjTcqV/kvvzRePn68Slet6pgPIgiC0M10uoCWZ24CIKT/8CbraJpGwfpPMYXF4nU7SJp+OwCH/vccBksw/U67wb9BTo4KoB4bq9L6LF1atyp31Sq+uTKdX6t+5eTAk5kePL3bgiD0FEL0IVwYeiEDzQNZal9KpitTfVevvKKCxS9aBGefrba+TJzYutWzkyerudR58xovT0lR/14rV3bshxEEQegmOl9AD/1GQEwqxsCm9zzaD2+tDrSQR7/JN2IOi6Vs9y9Y966i/xmzMQTUOzZr5kwVBOGjjxrGd/3+ezWPZzQqARg7lmRTMtODpzM2YGytK/NYx6gzcnrQ6ZwTfA6JxkSVqdPBnXcqIf3kExVHNzdXiWN+fvMd6vXqJJiFC1X0o/rodMoKFQEVBOEooQss0M2EJjXiYvWhZvFQSP/j6XPCOWgeN4e/m0doylgiMk71r/z117BmjVqUUv94sp9/Vud96nR4f/mZnQONaJpGhjmDQeZBHfq5jgZ0Oh2p5lR0Oh37nPtYW7VWFdx0k1oQtGiR+o4LClonon/4g5o3XbSo8fJx49Q8a9ceQSsIgtApdKqAuuylOIozCU5s2n3rcdgp3fkjmgZJM+5Ep9NTuOFzHMVZ9JtyU8MG11yjDmleuNA/f+VKdeIIoH33Hd8MKWGpfSmFnsKO/Ejtwu12Y7VaKSoqIr9ahAoKCiguLsZms+Fty4rXTqLAU8Avlb+woWqDyrjqKnW6y0cfqTnRoiJ1JJzN1nQnCQnK5fvhh42XH3+82uqSmdnxH0AQBKGL6dTJwMq8XQAEJwxusk7xlmXg9RA9YgYB0Ul4qsrJ+eltokecSVBsmn/lt96C7Gy12MX3wOhff1U/3B4PLFnC6jEmtletZ3rw9C6PYetyucjLyyM7O5ucnBwOHTrE4cOH2bhxI9u2bQMgPDycZ599FrPZjF6vJzAwkP79+9O/f3/69u1LQkICMTEx6BtbWdxJnBhwIi7NxY+VPxKmDyPNnKa+5+JitWDrrrvUXs+LLoLPP1dzpo1xySUqkH9+vprz9KVmsdemTZCU1LkfSBAEoZPpVAGtyN2NwRKMOSKhyTp5q/8D6Oj7u2sByF05H6/bQd/fXeNfUdPU/JzZDC++6NNBnhJPtxsWLmT35DRW25cwPmB8l7ltrVYr69evZ/PmzRw+fJjKykrcbjfBwcFERESQkpLC8OHDMRgMuN1uXn75ZcaPH1/7bLVaycvLY9euXVRVVWE2mwkKCiI5OZmRI0cyYsQILBZLywM5AnQ6HacEnkKZt4yl9qX83vB7+hj6KOHMzVX7bR97DB58UEUfeuutxs8XveACdQrOxx+rfaa+JCaqEIKbNqlFSoIgCL2YThbQXQTGDWxy4U5VcSbO0mxCkkZiDu2Dq7yI/F8XEjf+soZBF15/XVlDs2er0HGgRHXaNKiqgpdfhgsuYHf5EjJMGYwNGNuZHw1N0zhw4AC//vor69evp6Kigri4OFJSUoiOjiYyMhKDoeGxbQ6HA4vFQkxMTKOi6HQ6KS4upqioiKysLDZt2kRkZCTjxo1j7NixxMXFddpn0ul0nB58Ot/Yv8GEj4X55JMq+PwTT8CcOUpUMzLUQd316dNHzZsuXtxQQHU6Fch+8+ZO+wyCIAhdRadboA0WAflw+Du15aEmwlDB+sXo9AZiT7ywYeUHH1TW5z//WZf397+rH+Pp0+FPfwJgevB0vHg7bbVtVZ9T49wAACAASURBVFUVv/32GytXrmT//v0YjUbS09NJS0vDbDYfcf9ms5n4+Hji4+MZNmwYdrud3bt3s2zZMr777juGDBnCSSedxNChQxsV6CPFpDNxZsiZADg0ByZM6A0GWLBALQL697+VS/f++2HMGHUSS31mzIB77wW7HYKD/cuGDVPnrwqCIPRyOk1A3VU2nKXZBMUPbLTc63Jg3bsKU2gfgmLT8LqdFK5fTPTx0zEGhPpX/vxz5aq9+mp1AgjAb7/Bo49CRATaxx+zvOIHUkwpJJuS0XfS2qjt27fzySefkJ2dTWxsLOPHjycuLq5Tt8YEBwczcuRIhg8fTmZmJrt27WLTpk0MHDiQCy+8kISEpt3jR4JH87DQupBB5kGMDRyrDhtfvFhFLMrOVlGgLr1UbRUaMMC/8VlnwR13qC1F9V21aWnq9BZNa9wFLAiC0EvotFUqVYWHAAiISWm0PH/tIjSPm+gR5wBQsv0H3BUlxIye1bDyPfeoH9tnn1XPDoeyfDQNvvyS3abD/Ob4DYd2BAdEN0NFRQULFy5k3rx5OBwOZsyYwcSJE4mPj++yfaUGg4EBAwZw+umnM2nSJDIzM/nXv/7Ft99+i9vt7vj36QwMMA1gddXqupXMGRkqAP3776tAFWFhalGRy+XfeOBAJZRfftmw49RUKC+XkH6CIPR6Ok1AHcXVAhqV2KDM63GRt2o+AH1GnqkiEa35mLDUsQT0SfavfPCgmn+bMEGFnAMVpzU/H2bPxn7SCL6v+J50UzoZ5owO/xzbt2/nueee48cff2T48OGcdtppBNd3S3Yx0dHRTJ8+nYSEBBYtWsTLL79MdnZ2h7/npMCTCNeHs8y+DK9WvdXmiivgssvUPOgLL8DGjcoT4ItOp9zq337bsNPUVJXu29fh4xUEQehKOs8CLc7CFBaL3hTQoKx481I8lVYs0UmYw2KxH95KRe4uYsZc0LCjv/5VpU89pdIffoD//AfS09GefprvK75Hh67D49tWVlby8ccf+1mdaWlpPSaSkcFgYOTIkUyePNnPGvV4PB32DqPOyLTgaRR4ClhXtU5l6nRqwVZYmNrWcv/9anVu/Ri3EyaoY+by8vzzU6o9EiKggiD0cjrPAi3KJCCqf4N8zesmd8V8dAYTEYMmAFCw5r9YohIbHritafDZZxATow5+1jS1wR/giy+o1Dko9BQyKWgSQfogOgqbzcbrr7/O8uXLa63OwMCeeXJLVFQU06dPp1+/fixatIgPP/ywQ1268cZ4Tg48mWhDdF1meDjMnQtLlii37ujRyitQVVVX55RTVPrzz/4dhoer69ChDhujIAhCd9CpFqilEQEt3vodztJsNI+L0KSROK35lOxYTszo89Hp6g3niy+gslL9OAO8+ab64b3gAhg0iCB9EFeGXclAU+MLldpDSUkJr732Gnv37mXKlCk9yupsCoPBwIgRIzjppJNYuXIl7733Hg5Hx80HjwkYQ6o51T9z5kx1gPnttytX7oEDaptLDYmJanFRfQEFiItrOSygIAhCD6dTBFTTNJyl2VgiExrk5634gICYVNAbCE4cRuH6xehNAUQff0bDjp5+WqV/+5taqPKXv6gIOK+/TpYri2JPMXqdvsMErrS0lHnz5pGVlcW0adOIiIjokH67isTERE499VTWrVvHO++8g7O153m2ggpvBV+Uf+EfGvGFF9RB2gsWqDnRxx+HPXvqyk85pfHg8bGxIqCCIPR6OkVAvQ47XldVg2AI9qzNVBUdxBAYRnDfwej0Bgo3fE708WdisNRbmOP1qnm1AQMgKkrt+SwrgzvuwB0RyrKKZayo7Lj9hDabjTfeeIO8vDymTZtGSEhIy416IPHx8UycOJFNmzaxYMGCDnPnWnQWCj2F/t95v35qjvrll9XCovh4FYWoJlj8yJFqn279WL8ioIIgHAV0ioA6y9UWBVNotF9+0eavMYfH4SjOJCTpeKz71+GuLKPPqHMbdvLVV+pkj4svVhvyn31WLVx55BG2OrZi89oYHzi+Q8ZbVVXF22+/zaFDh5gyZQpBQR03n9odxMTEcOqpp7JmzRoWLlzYIcHqDToD4wPHs9+1n2y3z4rf2bPVHPWjjyqLdOlS5XoHGDFCWaj1FwzFxjZcXCQIgtDL6BQBddmUm88UUhfw3etyULL9e8IzJuAuLyIofhC2/eswh8cTEN1IYPGag5lvu02twHU4/p+98w6Pqkr/+OdOTZkUkpAeSui9SUdRVIoKCtiwgb1gwbZFd5XVdfenrmVXXXsv4CqCgiCiCIr00EInISQhvc4kk0y/vz8O6QkkmQyQcD7Pc5/J3HvPuedehnnnPed9vy/8+c+oOh077Tvppe9VN7DFC77//nsOHz7MRRdd1G49z/pER0czatQoNm7cyNatW9ukz9763oRpwmoqtgAEBMCzz4oKLPHxoiLOE08IYf8q8fjdu+t2FBoqqrJIJBJJO8Y3BrTKAzXVGLjSI7/jsVurhRUContTlradoO4jGl/D3LhRTN1GR8O//y0UiBYsIMOVgdljZojfkDYZ66FDh9iwYQNDhgxpd2uep6JLly7Ex8ezfPlyitpAuEBRFAYbB5PuTK8rWnHLLSK/8/nnxTro3r1iXTQqSnibe/fW7SggQHimEolE0o7xmQHVGgPR6GvE0ouTVxMYNwBXeRFaPxNodNiK0gnudl7DDoqKxDZqlKjqUVoqEvj9/Oik6cR4//HEaGO8HmdlZSVLlizBZDLRo0ePUzdohwwfPhyr1co333zTJlO5/Yz9mBcyD6NSSwhfpxNBRF9/LX70zJwJf/2rmILv0aPhFK40oBKJpAPgEwPqtluFkTyBq7IMS9p2wgZcQkXuEfyjelGevgNQCOo2rGEHX34pXq+/XiTqK0q1iHywNpjz/M5rk8jblStXkpOTw5gxY876VJXWotfrGTNmDLt3726TqVyDYiBAE4BLddWoE4HQKe7cWUROP/OMSGtZtEgIJ6Sl1e3E318aUIlE0u7xURRuOVpjjQE1p24Cj5uQ3uOxF2fiH9ENS9p2/KN7oQtoZNp0+XLxOmwYHD4MY8dCeDi7bbvZbdvd8PxWUHvq9kxL8/ma6OhoEhIS2mwqt8JTwfvm90lz1jKMfn5ivfrjjyEmRojIv/gidO0qjGlt/P1F/db6GroSiUTSjvCRB1qBxlATyWo+tIGAmL7ogyKwl2Rh6BRH2bEkgruPaLyDPXtqpOIAnnwSgGR7Mnlu76M3HQ7HaZ+63bp1K2+88QbvvvvuablefaqmcpctW+Z1XwGaAAKVQFKdqXUP3H67SFn59FNR8mzfPigrg+PHGzeWHdTrl0gk5wY+nMIVXp3H7cRydCuhvSfgtBSgup0oGh0uawlB3RoxoB4P5OZCz57w1VfCW5k6FbPbTJGniO76xqu7tIQ9e/aQnZ3N6NGjT9vU7ahRo5g/fz533nnnableffR6PcOHD2fv3r1kZWV53V93Q3fSnGl1p3EjI+Gqq+Cdd4SIwpgx8OuvIi+0tudbtRbrg3qmEolEcrrwzRSusxKNXmjHVmQdwOO0EZw4ElvxcQCcZfkoOgOmhEENGx89Kr5ge/SAwkJRd1KjIc2ZhhYtXfVdG7ZpAaqqsmnTJsLCwjpMykpziY+PR1VVtm3b5nVfifpEbKqNHHdO3QN33SWq52zaBPfdJ2YTAIqLa86pEryXHqhEImnH+EbKz+NG0QjvwnIsCa2fCf+onjjMuYBCRd4RTPGD0OiMDRuvXy9eCwrE6yOPAHDUeZR4XTwGxeDV2DIzM0lNTaVPnz5e9dMe0Wg0JCYmsnXrViorK73qK0obhb/iT64rt+6BSZOEQtGXX8LVV4upeGjogUrvUyKRtHN8bkDL03di6jIMRaPFaS1G6xeENTOZoO6NpK8AbN8uXg8dAoOhuqrHeX7nMdJvpNdj27p1K4qiEBsbe+qTOyC9evXCYrGwa9cur/rRKBrmBs9lhF+9aXiNRoj9L1kicnevu07sz61laG028W8rkUgk7RjfVGNRPSgaLW5HJdas/QR3Gw6Ay1qC1hggpnSbCiA6cEC85uYKLVWNGGIXfRfi9HFeDctqtZKUlETPnj07bNrKqfD396dz585s3LgRtUqztpUYNY3MIABccw1kZ4tp3NtvF/u2bKk5bjaLkmYSiUTSjvGRB+oBRcF6PBnV48J0woA6rSUAaP2D8Y/q2Xjj7GxRcUVVxRQgkO5MZ499j9fj2rFjB2VlZfTs2cS1zxH69u1LRkYGqamppz75JFg8Fj40f0iWq15Q0rhxIpVlyRLxIwjqVmWRBlQikXQAfGJAFa0O1e3CmrUfrX9wtdaty1qCx+0kMLZ/w9qfVRQXV3udVdN/Bx0H2W/f7/W49u/fT+fOnTEam/CczhEiIyPR6XQcOnTIq34ClUCsHiv5rnqVVTQamDoV1qwRP4YAduyoKbgtDahEIukA+MSAanQGVJcDa84hAmP6VE+XepyVeBwV+HXu1nTjigoRpennB12E4c135ROpi/RqTG63m/T0dDp37nzqkzs4iqIQEhJCZmamV/1oFS0R2gjy3Y2UJrv0UqGBW1W2zGYTlVpASDN2MN1hiURy7uEbD1RnwO2yU5FzkIDommhXt6MSj6MS/4iTpKLYbEKl5oTAgUt1UeIpIVLrnQEtKCigoqKCsLAwr/rpKERERJCRkYG7KqWklURqIylwFTQ8cPHF4vXHH8VrdHRNmbPsbDhHg7gkEknHwTceqNaAx27FZS0hILZv9X633QqAsVN84w1VtaYY83kiStfqsaKiEqwJ9mpMOTk5OJ1OwsPbpgRaeyc8PJyKigoKChoxfi0gWBtMmVrW8EBkJAwcCL/8It4PHSo8UFUVykTxTXwGJBKJpJ3gGwOqN+KqMAPUCRbyOEUJLENIVOMNa8u9XXCB6EvRMNAwkFCNd1N+2dnZ+Pv7o69akzvHCQsLw+l0kp2dfeqTT0JfQ1+uNl3d+MFRo2rSkkaOhMxMSE6GnBxpQCUSSbvHJwZU6xeMq8KMxuCPIbiWsfS4AAW9qYlp1KogE4DzzwcgSBPExYEXE6z1zgM9fvw4wcHe9dGR0Ov1+Pv7k5OTc+qTT4JJY6Kzrol15ZEja9KSRowQeaFLlog1bmlAJRJJO8cnBlTnH4zbYcUvvGudfEtVBY0xAEWja7yhw1Hzd3eheWvxWChye1dBxOPxkJ6eTkREhFf9dDSCg4O9DiSq9FSytmJt4/9GI0fWyPbFxor0lp9/Fu8TE726rkQikZxpfGZAVZejOn2lBg/aWlVaGlClTqPRiCLNiAos35V/59V47HY7Doejw5ctaymBgYFYLBav+lBQSLYnN25ABw2qSUmKjhZl6ZKThYzfOZ6LK5FI2j++mcINEDl+OlO9gB1VROg2iZ+feNXVeKgu1YUe79YtXS4XqqqilfqrddBqtThqe/2tQK+IfxuX6mp40GCAKq8/MlJUZ7FYxOyCXIuWSCTtnCbmUk+OqqqUlTUSeXmCCo+ecpsLk1Ot4+GU290YbK6mvZ6qCFyNRnzRApYKCzaXDYvSek+ppKQEu92O2+3Gbre3up/W4HK56qSKVF3/dI+jMVRVxWq1euWFqqqKzWLD4rJgMTbST1CQEJK326F/f7EvJKT631cikUjOFoKCglok86qorRBEtVgshLQzJZng4GD69++PX5WXK8FsNnPgwAFstYO3JBKJ5BzFbDa3KNi0VQb0VB6oJW0HR5f8haixNzJjwavV9Sd3vzoTQ1AE/W5/t/GGbjeEhYmp3Lw8ADZWbOS282/jYNLBlg6zmtLSUl544QVSUlJ4+OGHW90PwLvvvtuiotj1PdCysjLee+897rvvPq+jgls6lvrs3buXl156iYMHW/9sVVVlU+Um5k+cz85tOxueMHQopKdDSQmkpsLw4TBsGKxb1+DUkSNHel2r1GKxkJCQQGZmplfPty3G0hZ9nE1jOZuebVv1c7b0IZ+t7/ppybNtqQfaqilcRVFOOhCnxoHJT0eg3oNWq60+1+SnRW/UNN3WKoQWcLur60hODZ5KqD7Uqw+VRqOp1r/1VgdXUZQW9dHUuUaj8bSPpT5arfaU/5bNYWrIVIxaY+P9FBeL+p8aDezbJ/YVFNTUCa03nrZKNQoODvaqr7YYS1vdz9k0Fjg7nm1b9XO29FGFfLa+68fbZ9sYPgkiclWaQdHgMOcxf/78WkcUPM6TBK1UrQvWFlSAen20HJ1Oh6Io9K9ag/OCkSO9r0naVng7FpfLxZgxY7zqw6k6yXJmcfd9dzc8aDaLDcSMwpYtEBUllIgamcHw9t+5LWmLsbTV/ZxNY2kLOtpzkc/Wd320ZT++oFVTuKcie9175G9bgiE4kv53f1y9f9eLU0FVGfqH1Y03LCur8UzKysBkIsWRwobKDdwSfAuapiq4nAJVVXnmmWcICQlhaFV5rTOExWLhlVde4eGHHz7jwg5r164lMTGRefPmtbqPfFc+i8oWcV3QdUTrouse/OUXmDRJ/P3773DffRAXBytXwrZt1XKNbUnV+nxL1zIkp0Y+W98hn63v8OWz9Y0HaitD62fCVnIc1V07vUHB47JXS/o1oHaAz+HDJwaowewxU6lWtno8iqLQrVs3iouLW91HW1GVSnM2pNRYLBbivVQEsqpi2j1Q00iO7bZtEHAi7zc1FXbvhiuuEO+9FHBoCqPRyNNPP33Ol6zzBfLZ+g75bH2HL5+tTwyo21aGLiAUPG5sxTVflIpO5P45ypoQMK+V/8natQAEaMQXsNVj9WpMcXFxXosGtAW6E/eo07Vq+bnNqKysxOVyEetlVZSqf5cApRGBjK1bawpqV2nizpwpfij50IAuXLhQfhH5APlsfYd8tr7Dl8/WJwbU43KgOyGmUJF7uHq/Vu8PgMOc23hDRREbwIYNgNBahRpPp7XExsbicrmorGy9J9uRKCwsxGAwEBMT41U/Vo8Vf8UfrVLPo1ZV2LwZRo8W73fsEMY0Olro4PrIgEokEsnpwicGVHU70ej9MYYlUJFzqOZixgBQNNiKMppurNUKI7pnDyA8Gx06StwlXo0pJiYGg8FAYWGhV/10FIqKiggJCSHUy8LWKirh2kZKxB06BFlZcMkl4v2uXTBlivhbGlCJRNIB8Mk8osflQG80ERDTh4qcmhxDjd4PrTEAW2F60439/ERVlowMcLvRaLXMMM0gTOtdIezQ0FBCQkIoKioiISHBq746AsXFxSQmJrYo56kxxviPodE4tDVrhJTfxIniB1F5OcyeLY5FRYH8ISORSNo5vvFAXQ4UnZ7AmD5U5KVUBxJpjSY0en9sBWlNNw4JETmDbrfwWoAEfULjQSotQFEUunfvTn5+vlf9dATcbjelpaVe/5DwqB48qqdxI7xmjai+4ucnpnPDw2uibkNCoLTUq2tLJBLJmcY3BtTjRtFoCYwfhOpyYM0WNSH1gZ1QNDqs2QeajsSNiBCJ9wBffAFAsbuYNdY1OFTvhM+HDh2KxWLBXJWbeI6SkZGBTqdj8ODBXvWT48rhzdI3KXXXM4YVFaJs2ZQpNTVeR42qWd8OCanJD20DFi5ciKIodbbo6OhTN5Q04Ndff2X69OnExsaiKArLli2rc1xVVRYuXEhsbCz+/v5ceOGF7KsSyJCcklM933nz5jX4LHubq30u8M9//pORI0cSFBREZGQkV111FYcOHapzjt1u54EHHiAiIoLAwEBmzJjB8ePHvbquTwyootGCx0NAdC+0xkDKju0AQBfYCVV1o7qdlB9PbrxxXBy4XGItdMUKANyqm/2O/RS4mojebSb9+/cnKiqqwYM91zh8+DADBw6kc+cmCmE3k3x3PioqwZp6uVWrVgkjevXV8MMPYt+ECTXHQ0Pb3AMdMGAAOTk51VtychOfL8lJsVqtDBkyhNdff73R4y+88AIvv/wyr7/+Otu2bSM6OppLL730pNKekhpO9XwBpk6dWuezvHLlytM4wvbJ+vXrmT9/Pps3b2bNmjW4XC4mT56M1VoTfLpgwQKWLl3K4sWL2bBhA+Xl5VxxxRV1pFZbim9yKRRNtRdq6jqUsvQdxJw/F31gJ9y2cnSBYZSlJRHcvZFE+n79RKJ9YiIcOQIVFYT7h2NQDGS6MonTx7V6WDqdjrFjx/Ltt98ybNgw9OdgSa3i4mLKy8sZXRUd6wWZrkyiddENBS6++kpE3PbsCQ8+KPYNGVJzPDi4zaux6HQ66XW2AdOmTWPatGmNHlNVlVdffZUnn3ySWbNmAfDxxx8TFRXFF198wd13N6JGJanDyZ5vFUajUX6WW8gPVT/UT/Dhhx8SGRlJUlISF1xwAWazmffff59PP/2US04ENn722WckJCTw008/MaUqwLGF+MwDVT3Cqgd1HYE1az8epw29KRyPo4KgLkOwpG1vvPEFF4jXHj3E2tmSJWgUDd103TjqPOr12EaMGIGfnx9paSdZh+3AHDp0iJiYGPr27etVP07VSYYzg+767nUPVFSImYNrrhHyfT/+KPaH14rU1enEGncbcuTIEWJjY+nevTvXX389R496/1mR1CUtLY3c3FwmT55cvc9oNDJx4kQ2btx4BkfWsVi3bh2RkZH07t2bO++8U8ZttIKqZbqwMBF8mpSUhNPprPPZjY2NZeDAgV59dn1jQLU6VI8IHArqNlxM2WYmY+wkkvb9OnenMu8IropGpvEmThSvVUo9b74JQKIhkQJ3AWUe76aKOnXqxJAhQzhy5Ejj0aMdGIfDQVZWFmPHjvVaCSnPlYcbN4n6xLoH/vc/URRgzhz46CMREAaiyk4VVUFibcTo0aP55JNPWL16Ne+++y65ubmMGzeOoqKiNruGBHJzRf52VFRUnf1RUVHVxyTeMW3aND7//HPWrl3LSy+9xLZt25g0adJZUT+4vaCqKo888ggTJkxg4MCBgPjsGgwGOnXqVOdcbz+7PjGgWkMAHkcFAH4RXdEHRWBJ3YKxk5h+1QWK3EPLibXROoSEgNEopm8TE4Wajc1GN103JvpPRI/3066jR4/G4XCcc//pDx8+TGBgICNGjPC6r3h9PHeG3Eknbd0PJO+8A5Mni7Xs116D888X+2sb0CrjXRUs5iXTpk1j9uzZDBo0iEsuuYTvv/8eENOLkranftS1qqpep0NJBNdddx2XX345AwcOZPr06axatYrDhw9Xf6Ylp+b+++9nz549LFq06JTnevvZ9Y0BNQbitovFW0VRCOk1gdLDv6HxCxbHKsvwi+hG2bGkxjtISBA1JO+6S3gq77+PUWNkqN9Q/DTeF8Tu2bMnAwYMYOvWrbhcrlM36ABYLBYOHjzI+eef77Wgskf14Fbd1TKL1ezdC5s2iX+3RYuEkMLo0eIHkQ8NaH0CAwMZNGgQR44c8Un/5ypV63L1f3jm5+c38EolbUNMTAxdu3aVn+Vm8sADD/Ddd9/xyy+/1NH5jo6OxuFwUFJSV5DH28+uTwyoxhiA215R/T60zwQc5jxsBakYw+KxFx8nqNsIytK2Nz6NOmaMKG02bZqY7nvlFQAqPBWsq1iHxeNdAIqiKMyaNQt/f3927GjEC/YBW7du5Y033uDdd5soJu5DVFVl8+bNdO3atc4aQGs55jzGh+YPG+oTv/66EEm44gr417/g8stFGkvXrjVTuVBjOH3ktdjtdg4cOOC1TKGkLt27dyc6Opo1a9ZU73M4HKxfv55x48adwZF1XIqKisjMzJSf5VOgqir3338/33zzDWvXrqV797qxGSNGjECv19f57Obk5LB3716vPrs+8kBNuO3l1e9NXYagNQZSemA9fhHdqCw4SnD3ETjMedhLshp2cP314nX5cjEFmJoK+/ahU3QcsB9gn937vLOIiAiuuOIKMjMzycvL87q/UzFq1Cjmz5/PnXfe6fNr1efgwYPYbDauvvpqDAaD1/3tse8hUBNYV9wiJwc+/BAeeghWrxbe6OOPw7Fj0L2RQCOjscYT9ZLHHnuM9evXk5aWxpYtW7j66quxWCzMnTu3Tfo/lygvL2fXrl3sOiFikpaWxq5du8jIyEBRFBYsWMA//vEPli5dyt69e5k3bx4BAQHccMMNZ3jk7YOTPd/y8nIee+wxNm3axLFjx1i3bh3Tp08nIiKCmTNnnuGRn93Mnz+fzz77jC+++IKgoCByc3PJzc2t1j4PCQnh9ttv59FHH+Xnn39m586d3HTTTdXLPq3FJwZU52fCVWmp9i41Wj2hfSdSvO8n/KN6UZl/lMC4gaDRUpbWyDTu5MnCO1mxAl54Qex79FEMioG+xr7ste/FrXofhDJmzBgGDRrE5s2bO+xUrsViYd++fUyaNKnBr7LWUOouJd2VzmBjPRGGf/9bGMW77oInn4SLLhIR1ceOQbdudc+tqKgpc9YGHD9+nDlz5tCnTx9mzZqFwWCo9rglLWP79u0MGzaMYcOGAfDII48wbNgwnnrqKQD+8Ic/sGDBAu677z7OO+88srKy+PHHHwkKCjqTw243nOz5arVakpOTufLKK+nduzdz586ld+/ebNq0ST7fU/Dmm29iNpu58MILiYmJqd6+/PLL6nNeeeUVrrrqKq699lrGjx9PQEAAy5cv9yqg0id5oHpTBKrLgdtejs5P/MOHD5pK0e6VIsXF7cRRlkdgbH8sadvpPOLKeh3oheD4rl0wciR06SKk4YqKGBw6mD32PaQ6U+lt6O3VODUaDbNmzeLll19mx44djBo1yqv+zjbaeuoWYK99L0bFWPfZFxeLaOl77hEiClVroaoq6rrW907a2IAuXry4zfo617nwwgtPGp2uKAoLFy5k4cKFp29QHYhTPd/Vq1efxtF0HJqTUeHn58drr73Ga6+91mbX9YkHqg8SOX/Ospo0gsCEgRhCY6jIPgAoVOQeIbj7eZSn76jOGa3DtGli/WzbNvi//xPrZg89P3r5AwAAIABJREFURLg2nDhdHLvtu9tkrFVTucePH+9QuYOqqrJ9+3bsdnubTd2CUB/qb+iPXqkVDf3Pf4pgr/vvh6eegquuEuvYaWkipaW2iAIIA+rv3ybjkUgkkjOFbwyoKQIAZ3lNxQ1F0RA2cDKlhzfgF55ARfYBghPPw223Upa+q2EnDz8sXv/zH7EmGh0tIjvz8znf/3wuDri4zcY7duxYLrroInbs2EFmBymzlZycTFZWFtdcc02bTN1WMdM0kzH+tbQ5MzJEuspjj8Hnn4v3zz0nju0+8SOnvuZuUVHdqFyJRCJph/jIgJ7wQMvrJrKHD5qCx1GBzhROWfouAmL74xfRjYKkbxp20revyAldtUqsh770kvBC588nShdFmDYMt+rGo3qfCqEoCldeeSXjx49ny5YtZGdne93nmWT//v2kpKQwc+bMNhOirvBUkOvKRVEUDEotb/app4Q037XXwrPPwoIF0L+/OLZnD0RGisjc2uTnN9wnkUgk7QzfpLHojWj9g3FY6kpQGTvFEpw4CnvxcezFmbisxUSOnI358EbspTkNO5o8Wayv7dkjlG1iY2HJEkhLw6E6+MzyGYccbSMMr9FouOaaaxg1ahQbN24kI+MkRb/PUlRVZffu3Rw8eJArrriCC6pkEduAbbZtLC1fWrcizoYN8PHH8Mwz8Ne/QqdO8PTTNceTkoQmbn3y84VhlUgkknaMTwwogLFTHPbihqViosffjLNMVFUpS99F2MBL0fqZKEha2rCTqi/jZ54RXuhHH4nAlFmzMCgGwrXhbLJtwqW2TQStTqfjxhtv5IILLmDr1q2kpKS0Sb+ng6o1z2PHjjF79mwuvfTSNlOHMbvN7LHvYYRxRI336XCIoKFRo0QJum++EbMEVdGCHg/8/juMH9+ww7w8aUAlEkm7x2cG1C+8S6MG1JQwCFPXYShaA2XpO9Ho/YgYegVFu77H7aioe/KAAWKqb+VK8YV86aXiC3nXLvj8c8b5j8PqsbLVtrXNxq3Varn66qu59NJLSU5O5rfffjvrdSjNZjOrV68mLy+P66+/nokTJ7aZ8VRVlV8qfsFf8WeY37CaAy+/DAcOiACie+8VgUPXXVdzfP9+KCmpW8ZMdCgMqJzClUgk7RzfeaBh8diKGw/IiRl/M6rbgfnwb6iqSsSIK3E7Kineu6bhybfdBpWV8Omn4v2iRSIB/+67CbMZGeU3iu227eS52k4MQaPRMGPGDG677Tbcbjfff//9WTmlq6oq+/fvZ82aNURERHD//fe3SZmy2hxyHCLdlc7FgRfXRN4mJ4vZgQULRAARwNtv11UW2rBBVF2pP578/Bp1IolEImnH+M4DDUvAXWnBVWFucMzUdRh+Ed1wVZipyD2CMSSa0N4TKNj2TcN8nr/8RRjMZ58V7xMS4G9/E+kRN9zAeX7n0V3fHafqbNPxK4rCkCFDePTRRxk1ahRJSUlnlTda5XWmpqZy+eWX8+CDD9KtvmBBG9Dd0J1LAi6pKVtms8GNN0KfPqLe57JlwnjWn5Jdvx6GD4fAwLr7q1KFEutVcZFIJJJ2hk89UKBRL1RRFGIvuguAgm1fA9D5vFnYitIbCswHBIip29RUMXUL8MQT0Ls3fPcd2iVLmW6aTrw+Hl8QFBTEjTfeyK233lrtjaakpHhVxdwb7HY7ycnJ1V7nAw88wLRp09osz7MKVVWxeqwYFSMDjANqDjzxBBw6JNSGHn5YKA+dKK5cjdst5PwaE2+oMqBtmFojkUgkZwKfroGi0VKZl9ro8ZCeY9H6BVF66DdA6OX6R/Ygf9uShie/8YZ4vfde8aooIr1Fp4ObboLcXGweG9+Wf0uGs+2nWhVFYejQoTzyyCOMGTOGAwcO8O2335KUlER5efmpO2gDioqK+P3331m+fDnZ2dk+9ToBdtp38on5E8o9te7v66+FsP/TT8Of/gQDBwoJv/ps3izWPy+/vOGxo0ehc+eaYCOJRCJpp/jMgGp0Bvw7d6ci73CjxxVFIXzwVDzOSor3r0VRFDqPnI0lZTO2onpea2IiDBsmvpjT02v2vf22qNoyYQIGl4Kqqqy0rqTU3Uih7jYgODiYG264gT//+c9cdtlllJWV8cMPP/Dzzz9z/PjxNi/Q7Xa7SUlJYdWqVaxfvx6dTse1117Lk08+6ROvs4pjzmNsqNzAYL/BmDQmsXPvXpg3T+R7btgAZrMwqH6NlJdbuVJE5o4c2fBYSgr06OGTcUskEsnpxCdauFUERPemIrfpOnbR588jf+vX5Kx/n7D+kwjrfzE5v35A9q8fkDjz6bonv/EGjBsHd9whdHFBBBj98AN89RWam25m2uJPWVy2mOXly7k2+FqMitEn9xUREcHUqVOZNGkSe/fuZePGjSQlJbF9+3aCg4MJDw+v3vybKVmnqipWq5XCwkKKioooLi6mrKwMvV7P4MGDGT16NL1790aj8dlvHgBK3CWssq6im74bY/3Gip3FxSLKNjFReI7ffCOMZFPe74oVMHVq49VWkpOhDQp6SyQSyZnGtwY0qhfFyT/icTvRaPUNjuuMgQQmDMKauYfyrP2Y4voTO/F20lc8T/nIqzHF11p7GztWTBn+/LOYBqwKQvnsM5Gw/9VXGIcNY8Yf7mFx2WJ+sP7AjMAZbZbO0RgGg4Hhw4czbNgwsrKyOHDgAMePHyc9PZ309HQcDgc6nY7g4GACAwPR6XS43W5KS0vZvXs3Go0Gl8tFWVkZZWVlqKqKwWAgPDyc/v37Ex8fz8CBAwkPD/fZPdRGVVVWW1djUkxMCZyCRtEI3dorrhAe5+zZojrO+++LdenGOHhQCF88/XTDYy6XSG+59Vbf3ohEIpGcBnxqQP2je6N6XNgKjhEQ3avRc6LH3Ujql3vI+vlN+tzyGmEDJ5O/9Wuy1r5J75tfq2sAP/1UTOXOmQNbtoh9BoOo/NG7NzzxBJ3i4pg2Zxol7pJGr+cLFEUhPj6+ugK6qqqUlJSQk5NDdnY2WVlZrFy5ko0bN+LxeCguLsZqtWIymfD396dLly7ExsYSGxtLTEzMGStdpCgKkwMno0EjvHeXS+R27t4NjzwCf/+7iIq+7bamO1m8WHipl13W8NiRI2LKfdAg392ERCKRnC5UH+J2VKpJ/5yk5icta/Icj9ul7vrX5WrScxPV0sO/q6qqquaj29Sk5yaqxQfWNWwwfryqgqr+/nvd/QcPqqrRqKqKoqqrVlXvPu48rno8nja5n7bAbDargGo2m8/0UKpxepzqxoqNqsPjqNnpcqnqLbeoqk6nqo8/Lp7r3Xer6smepcejqr17i3aNsXix+LcrLGzbG5BIJJIzgE8X1DR6PwKie1OemdzkOYpGS8TwGaDRkr7qZdx2K8HdzyO4x2iyf3kbj7tefueiRaDRiAottenTB376SUToTp8Ov/9OobuQr8u+Zn3l+jYP8OkoOFUn35V/xw7bDordxWKnywVz54rqKvfdJyT6br0V/vvfumIJ9dm1S9T/nDOn6eNxcXCapqQlEonEl/g2IgWRnlKeseukBixi+AzweHBXmsn65R0A4i66G3tpLnmb6xVLTkgQ0aCZmWI9rjYTJsD//ifyECdOJOLHbUwKmMRu+25+rvi5TSq3dCRsHhvLypeR68rlKtNVROmiwOkUqUGLF8Ptt8Prr4v377wjfricjA8+EIIKFzdRam7TpobKRBKJRNJO8b0BTRiMs6wQhzm3yXOMIdGE9BqLLiCEwh3fUp6xB//IRKLGXE/uhk+wFabXbfDWW6KE1l/+IvINazN7tkivUFW4/HIGLd3H5IDJHHAcYFn5Mmwemw/usv3hUB18WfYlRe4iZgbNJE4fBxaLyN1csgSuuUYYzfvugw8/bDyitjYVFWKN+rbbQN8wYAyXSxRHHzvWNzckkUgkpxnfG9D4QYBCecbuk54XMfxKnGWF+HVOJH3li3hcdmImzMUQEkX6yn+h1vYe9Xrxpe50iuna+syaBcuXC49pzhz6/fcHZppmoqCgVU5hCM4RDIqBwcbBXB90PTG6GOHRT5gggrOmTBEe6LPPioLmzUmd+d//RKTunXc2fnzPHmFkpQGVSCQdBJ8bUJ1/EP6Riac0oMGJIzGGJaAPDMNhziVnwydo9Ea6THsM6/FkCnd8V7fBrFkwcaIomfXJJw07vOwycSwgAB55hPh7FzIzYAZ6RU+xu5ijjqNteJftA1VVSbIlkWwXa9LD/IYRqg0Vz2n0aOHN9+wJP/4oUlX+8peTr3nW5u23hXRfUxq3mzaJHz4yB1QikXQQfG5AAYK6DceStu2k66CKoiFqzPWUHUsiYth08jYtoiLvCEFdhxIxbDpZa99qqFC0YgX4+wuvp6CgYaejR8O+fRAdLQzC4MGQm0uyPZnl1uX8bP0Zu3p2iMP7GovbwtLypWyo3FAjz6eqQprvwgvF2qXHA1lZsG7dyVNV6rN9u1CJuueeps/ZuFGkIDWmXCSRSCTtkNNiQIN7jMZZVkhlwcm9vrCBl6I3heO2W/GL6Er69y/icTuJu/he9EERHPv22bpRuSaTmGp0OIQ32piB7tZNJPdffLFI4o+P54Jnf2CScSKHHIf43PI56c70hu06CKqqkmxP5nPL55S4S7jKdBVj/ceKHxyzZon8zrFjxQ+NhARhDMeNa9lFXnxReK4zZjQ1CCGAcdFF3t+QRCKRnCWcFgNqShiMRu+HJWXzyQejMxA5+hqK9/1E7IV3Yss/Svbat9EaAuh25V+oyE8l59cP6jaaMUOkTRw4AA8+2HjHISEixWXNGujUCeX//o9BXS9l3g8BhCoh/GD9AYfqaKO7Pfs47DhML0Mvbgq5ia76rkKKb8AA4WkOHCi0bf/wB/jtN4hvYVWbo0dF0NYjjzQdaLRvnyii3ZR6kUQikbRDTosB1egMBHUbgSV1yynPjRg6Ha0xEEvKZuIuvo/8bV9TcmAdgTF9iZ14B3mbFmOu389nn4kCza+/DkuXNt35JZeIL/L586GoiIAbbmXmyCe4cVNnDOixeqxsq9zW5rVFTzdWj5W1FWs55jyGoihcabqSSwIvwZhdKPJnZ8+GqCihClRaCmvXwnPPNR49eypefhnCwkRqUVOsWSOmbsePb/U9SSQSydnGaTGgIKZxy4/vxWUrO+l5WmMA0WNvoHD39wT3GEVov4tI//55bEUZRI25juCeYzj27bPYS7JrGmk0InrUaBTSc+knmZLVaISh3b8fhgxBOXwY02WzYfx4in9dzmbbZj4yf8Ru227c6pmp+dla7KqdjZUb+cj8EYcdh6tTdnRODzz/vBCb+PFHUYtz3z4hzL9vn1gDbQ25uSL38/77xVp0U/z0k4jwleufEomkA3HaDGhIj9GgerCkbj3luZ1HzEQf0Imc3z6i62WPozdFcPSbp/E47XSb8QQ6/2COLvkrHmetnM6oKPj2W5HaMnIk2E6R79m3L+zcKSJ4g4Nh82YSLprDfRP+y/B1+ayrXMdH5o/aTbRutiubD8wfsNO2k6F+Q7k1+Fb66nqJ3Mz+/UUh7Lg4EWkbHCyCev7zH/F3a/m//xNaxE1NnYNYn16/Xk7fSiSSDsdpM6CGkCgCYvpQenD9Kc/V6I1ET7iFkn0/4zDnkjj7GRylOaSveB6tMZDE2X/HXpJF2rd/R/XU8hKnTBG5iwUFcN55Iqr0ZCgK3HwzHDsmpiIHDkS7/yAjZv6FBxKf5tI/fkfI7qOgqmQ6M8lyZp01koAe1UOKI4Wdtp0ARGgjGGIcwtyQuYzXj8b41TIh2n7LLSKIR6uF8nKRP5uUBGPGeDeAzEx480147DHo1Knp89avB6tVpLhIJBJJB0JRT6NFyN20iJzfPmTwgmVoDQEnPVd1u9j/zi0YwxLoed3zlB76jaNLniJq3I3EXXgH5iMbSf36L3QefiXxkx+sW7Xl5pvFuuiUKaJeaEsoLIQnnxTtKyrEvuhojk0fwc7J8ZgvGEZXU28S9YnE6eLQKS0raGOxWAgJCcFsNhPcQu/PqTo55jzGUedRjjmPYVNtJOgShEiEooj1zPfeg9deg4wM4XHm5YnqKI88IraAkz/3ZnP33UKxKC1N9N8U998v0o3S0pqfUyqRSCTtgdOpXG8rzhJVVvatbdb5JQd/FVVajmxUVVVVczctUpOem6gW7lqpqqqq5id9qyY9N1HN3bSobkOPp6Zqy223tXKwNlV95RVV7dRJVTUa1RMUpKqgOk3+6tErR6ir3rpJPZqzXVVVVc1z5qlZzqy61UyaoCXVWCrcFeoxxzE1xZ6iqqqqWtwW9dXiV9XPzJ+pGys2qvnOfFV1u1X1559Vde5cVQ0IENVTYmPFvUdHq+q//qWqFkvrnkFTpKSI67z44snP83hUNT5eVR98sG2vL5FIJGcBp9UDBTjwwV0YQ2NInPW3U56rqiopix7DYc6l350fomj1ZKx6iaI9q+h53fMEdz+PrHXvkbfxM7pd+VfCBtQSMXe5RKrG4cOwYIEQDGgNVqsIOnr+eeGRjhyJarWi7NyJqtWiTJjAwam92XxpJJbESDppOhGpi6SfoR9d9F2o9FRi9pgJ1ARiwEBZWRmdQztTUFqAKciEQ3VQrpbjr/jTSduJQnchWyq3kO/Ox+KxABCpjWROsKhwUu4px+Q2itST774TKSTHj0NoqBDRLysT07N33y0ibn0RuDNrltC1PXTo5B5tUpKYSv/5Z5g0qe3HIZFIJGcQnxbUboxOfSeSs+ET3I5KtIaTRG5yolD1pQ9w4L3byN/2NdFjb6DLlAU4ywo5+vVf6HXDS8ROvB2nJY/0Ff+HLiCU4O4npOJ0OkhOFoW2X31VpGjUr97SHAID4Y9/FAbp5ZfhlVfEdOlDD6GYTLBzJ30WfkLfP9ux9U0k77JRHJnaD+v4ONBDuiud1dbV1d3ZLCK46f3S9/Hz1Bi34cbhnB9wPm7VjU210VPfk0hdJJHaSEI9JiFwsGEDpg0bRFSr2SzGVjUtajQKAfg77oAhQ1p+n83ll19EqtDnn596OnjZMrE+ev75vhuPRCKRnCFOuwdqL81h33/n0HXGE4QPbF5gyfE1r1O4awX97/kUQ1BnPE4bRxY9jq3wGL1v+jfG8ASOfvUEZRl76HntPwnqNrymcUWFSN84flysAb70knc3UFAgvNE33xR9h4aKFI3ISJHWsWULFBWJ91dcgXP6NEouGsGbH3/Cp29+isftIe1IGkkFSQQFB2FQDARqAgkiEGNxOeTkiLEePChSTPbtE0LslZUiECgwUAQDeTxijfPKK+Haa8UYTlUxxVvcbhg+XIzh999PvqapqkKkYfhwEQkskUgkHYzTbkABDn/6EIpWR68bmmfMXLYy9r89l8C4fiTO/juKouCylXHk84dxlhXR64aXMIbFcfTrvzRuRK1WkcqRkSGiUj/+2PubsNuFsVy3TnhlmzaJfQCxsWLqtLhYBPZoNEINyd8fi8FAyLFjmPv2JdjlEuk2lZXiPHetiGKtVvThctX0GxUlZPcuuURIE/bpc3oDc95+W+jdbt0qUoVOxp49whNesUKUSJNIJJIOxhkxoIW7V5Lx/YsMvP9LDMGRzWpTcnA9ad88TfeZC+nU70IAnNZSUhY9iqOsgF5zXsIvokvTRtThEGLm+/fD1KmwcmXbGh+HQ8gJ7t4tttRUYbDT0oRxPIEFCAHMQJMxuJ07C+PYo4fYhgwRVUxiY89cJGt+PvTrJ8rHffTRqc//059ERHBOTusUjiQSieQs54wYULe9guT/zCJ63E1Ej7+p2e2OLnmK8sxk+t/1EbqAEABclRZSFj+OvSSLntf/C//I7tVGNHHm04T0qiWM7vHABReI6cdhw0QFEYOhrW+vIeXlIj2mrAxLTg4hU6ZgXrpUpLFotcLAhIVBeLhYM9Sd9qXpU3PjjbB6tfiR0Lnzyc/1eITa0WWXialuiUQi6YCcEQMKcOy757BmH6T/3Z/UzeE8Cc7yIva/M5eQXuPpNv3P1fvdtnJSvvwjlQVp9LzueQJiepO27O+Yj/xOl8seI2LIZTWdqKoItlmyREyJJiWJtcTThDd5oGeMVauEMfz4YzEFfio2bBCBQ7/+KgOIJBJJh+W0KRHVJ2zQVOzFmViPJze7jd4UTvzF8ylOXk3pod+q92v9TPS8/kUConuRsvhxyjP2kDhrIRFDLyfj+xfI+f3TGgUhRRGpHwsXCpGBHj3EOqakcaxWuPdese56883Na/PFF6I0mhSPl0gkHZgzZkCDug3D2CmOgh3ftahd2OCphPSeQPrKF3GUFVbv1xoD6Hnd85i6DiXlyz9StHsVCVMfIeaC28hZ/z4Zq16qW0v06aeFdq7bLXIUn322rW6tY/HEE2L98623mrf+arOJGq1z5ojgKYlEIumgnLFvOEXREDH8SkoPrsdpLWlBO4Wulz2GRqsnfcXzqGqN3q1G70ePq/9OxLAZZKz6F9nr3iF6/E10veKPFCevJuWLR+tea8YMEVQUHg5PPSUiXKvk+yQi3/Q//4F//EN46s3hm2+EYP3tt/t2bBKJRHKGOaMuQvjgqaAoFO1e2aJ2uoBQul7xJ8rStlGwbUmdY4pGR8KUh4i7+D7yNi0mbekzdOo3iV43voKtOJNDH95DRd6Rmga9ekF2tojM3bwZoqPF67lOSYmo8XnxxSevtlKf994TgVq9e/tsaBKJRHI2cEYNqM4/mLD+F1O487u6VVWaQXDiSCJHXk3WL+9gzTlY55iiKESNvpbE2c9gTtnEoU/mozeF0/fWt9EGhHDo4/kU7PiuZl1UrxeBMv/9r/BAx40TIuhnSeWVM8L8+WL986OPmj8Vm5IicmLvvNOnQ5NIJJKzgTO+SBUx4koc5jwsqVta3Db2orvwj+xB2jdP46q0NDge2ud8+sx9A7e9goMf3EVlQRp9bn6N8EFTyfzhZdKW/g23rbymwb33ijSNuDh44w3xmtz8IKcOw6JFYnvjDYiPb367998XykyzZ/tubBKJRHKWcMYNaGBMXwJi+pJfbyq2OWh0BrrPWojbUcmx7/5RZz20ioConvS99W0C4weQ+uWfyNu8iIQpD9F95kIsads48MGdWLMP1DTo1UsIIDz8sJDmGzJEeGOnqi3aUTh8uEaIfs6c5rdzOkWt0ZtuAv+TaxxLJBJJR+CMG1CAyFHXUHYsiYq8lBa3NYZE023Gk1hSt5C78fNGz9H5B9Hjmn8Qc/48cjZ8wpHPHyEwrj/9bn8PXUAohz65n5wNn6C6XaKBogjh+D17hBf63/9CRAR8/703t3n2U1kpcmRjYuCdd1qmerRsmUgLktO3EonkHOGsMKCd+k3EEBJF/pYvW9U+pMdooifcQs6vH2I5uq3RcxRFQ8z5c+l14yvYS7M58N5tVOQcovfN/yFqzPXk/PYRBz+6t64RHzhQeKMLF4oyYVdcAaNHC3m6jshDDwkP9KuvTl4kuzH+/W8RPDR4sG/GJpFIJGcZZ4UBVTQ6IkdeQ/H+tTgs+a3qI2bCLQQnjiJt6UJshelNnhfUZQj97viAoG4jSFu6kPQVzxM16hr6zPsvqsfFwQ/vJvvXD2tyRhVF5Izm5cFFFwkh9fh4kaZRJfLeEfj0U3j3XbHu2VIjmJQk5BEfesg3Y5NIJJKzkDMm5Vcft72CvW9cS/iQy4i/+L5W9mHl0MfzUd0O+sx9s1ovtzFUVaV47xqOr3kNRaMlYfJDBPcaR97Gz8nd9Dl+neJJmPJQXUF6gPXrxTrf8eOiBufjj8Pf/tbsSNWzUspv924ReXzNNWIds6WC9XPniueSmur7kmoSiURylnBWeKAglIQihs2gcOeKupGxLeojkB7X/hO3zcrRb56qqzxUD0VRCB80mf53fYQpYTBpy/7GsW+fJWL4DJHu4h/EkS8e4ejSv9X1iidOhMxM+OADESzz97+LyNOXXmqfaS/5+UJQok8fsdbbUuOZlyeUh+6/XxpPiURyTnHWGFCAyJGzUd1OCnZ82+o+jKExJF79LNas/WT+8AqncrD1pnASZz9D95kLsR7fx/535lKevpNeN7xC1+l/pjxjF/vfvoXc3z/D47TVNLz1VlE4+5lnRM3Oxx4TNT+ffbZuXc8TvPHGG/Tv35+Rp6qjeTpxOODqq4X83rffQkBAy/t46y1RPUYqD0kkknOMs2YKt4qMVS9RevBXBsxfhNbQii/0ExQlryZ9+T+JueA2YiY0o4II4Kowk73+PQp3rsAvoisJkx8kILo3ORs+pmD7UnQBIURPmEvEkMtQtLVKjrlcwpC+8oooXebvD3fdBf/8Z4OUjrNmCldVRbrKRx8JMf1x407VoiE2G3TrBrNmCe9VIpFIziHOKg8UIGrcjbjtVgpbKDJfn/BBU4ideAc5v35A4c7lzWqjCwihy7RH6XvbO2j9TBz54hHSv3+BziOuov/dn2DqOozMH15h/7vzKNn/S03eqU4nDKjZDM8/L9ZG//1vEcl62WVw5MjJL3wmeOMNETT01lutM54gypvl58OCBW07NolEImkHnHUeKED6yn9hPvw7A+cvQqP3a3U/qqpy/Mf/ULDjWxJn/Y3QPs2vTamqKiX7fiJr7ds4K0qIGHI50RNuwVVRSva6d7GkbsE/qhfR424ktO8FKIqmdmOh5PPUUyKwBsQa41NPYbn8ckJCQ8+sB7p8OVx1ldC4feWV1vXhcol7GjEC/ve/th2fRCKRtAPOSgNqL81h31s3ETfpHqJGXeNVX6rHTdq3f8d8eAM95/yLoC5DWtTe47RRkLSM3I2f43E5iDxvFlFj51CZf5TcDZ9Qlr4DY3gXosfeQNiAS+pO7YKQAlywQEyTejxY/PwIsdkw79hB8LBhXt1bq9iyRaTjTJsmDF9rA3+qSpYlJcHw4ac+XyKRSDoYZ6UBBUj//gXMKZsZeN8iNHqjV315XA5Sv/wTFbmczxe6AAAgAElEQVSH6HXjKwREt7xSiNtWTt6WL8nf+hWKRkvkqGvofN4s7MWZ5G78AvOR3zGERBE58mrCB09D62eq20FFBTz3HJb33iMkPx8zEBwfL4KRHn+85cIFreHIETFd26cPrFnTesk9VYVhwyAqClavbtsxSiQSSTvhrDWg9pIs9r11M/EX30ukl14oiBzRI4sew16SJYxoZDPrW9bDWV5M7qbPKdy5AkVRiBg2nchR1+C2lZO76QtKDvyCRqsnbNAUOo+YiX/nbnXaVwcRTZ5M8Pr1NWIMvXqJfMqHHgKTqeGFvSU/XxhPnU6IHoSHt76vVavE2u4vv8CFF7bZECUSiaQ9cdYaUDjhhR7ZyIB7v0BrbH1EbhUuWxlHvngUpzmPXje9in/n7q3uy2ktoWDbEgp2LMPjsBE2aDKRo65F5x9EwY7vKNy5HJe1mKCuw+l83kxCeo5F0erqRuEGBcGSJfDqq0LhyOkUeZg9eojI1ocegthYr++bsjJR1zMzEzZtEpGz3nDBBWKsGze2PG9UIpFIOghntQF1mPPY99ZNRI+7iZjz57ZJn65KC0c+fxintZjeN/0bv/AuXvXntlsp3Lmc/K1f4SwvwtR1GJ1HXEVwj9GYD/9OwfZvsGbtQxcQStjAS9F1H09Mz2ENg4g8HrGu+NprsGOHyNEECAsTXt78+WLtsqUGq7JSeIs7doh1WG/XXX/7TRjQZcvgyiu960sikUjaMWe1AQU4/tN/Kdy1nAH3LkIfGNomfTqtpRz5fAFuWzm9bnoVv7AW1LxsAo/bSenBXylIWor1+F70QRFEDJtBxNDLcVpLKE5eTfHeNZQWFzLx2d9JWfsJXUZeht7UyFSqqsLatSLVZP16KC4W+3U66NkTLr0U7rjj1Jq1DoeItl2/Hn78EcaP9/o+mTQJSkpE8FBzC21LJBJJB+SsN6CuCjN737yBiMHTiL/0/jbr11lexOHPH8Zjt9JzzksN1iq9oSLvCAVJyyje+xN43AT3HEv44CkEdRtB1t7f6DpiCuufvgCTQYMpYTCh/SbSqe/Exo0piKnXN96AFStEIFCVd2owiICgSZNE/c5Ro2qMmsslomS/+06UYbvkEu9v7JdfxLW+/VbI/0kkEsk5zFlvQAFyNnxC7u+f0v+eTzGGRLdZv87yYo4segxXeRE957zYqujck+GqLKM4eTVFyaupzDuCzj8EXbfxDJj1Rwqz01Hz91J6YB2WY0ng8RAYP5BOfScS0mscxk5NrH2qKuzcCe+/Dz/9BEePCmMJwnhGR8PQoSJdpaio7aZaVVXoAFdUwLZtcu1TIpGc87QLA+p2VLDvvzcS3GMU3ab/uU37dlVaSFn8B+zFmfS47gVM8QPatP8qKvOPUpT8AxnbVzH+TyvY8sr1xA+7hNC+E9EHRWJJ+Z2SA+spS9uO6nFhDEsgpMdognuOwZQwGI3O0HjHqioKfy9eLDzEAwfAYqk5bjCIQKQBA+D880VN0/79W24Af/pJTB2vWAGXX976ByGRSCQdhHZhQAHyt3/D8R9fo+8d77U6BaUp3HYrqf/7MxW5h+lxzT8aljCrxbx58/j444/r7Bs9ejSbN29u1rXMpcWEdgpnz5dP4zm+HbetHGOnOEL7TiS07wUYOyVQnr4Dc+oWLKlbcJYVoNH7EdRtOEHdziOo61D8Onerq3xUhccD99wjJPpuuEEYyV27ID1daPRWodFAp07QpQv06yemfidNEoa1MWEFVRXrp243bN4svU+JRCKhHRlQj9vJgXdvwxDcmZ5zXkJp4y9xj9NG6td/pTxjF91nLiS0d+MBN/PmzSMvL48PP/ywep/BYCAsLKxZ16mdxmIK9Kc8fSclB9dTeug33JUW9EERBPcYTXDiaIK6DcdpycecuhlL6hasWftR3U50/iGYugzB1HUoQV1OGFQVuPNOUc/zww9FTmltbDYRTPTDD2J69+hREZzkrFfyzWSCyEiR6tKnjwhUcjhESs0PP8CUKS14qhKJRNJxaTcGFMB8ZCOpXz1B4tXPNWngvMHjcnDs279TengDXaY+TMSw6Q3OmTdvHqWlpSxbtqxV12iqGovqcVGesQdzyibMqVuwF2WARospfpAwqD1GYQyNoSL7IGXpuyjP2CUMqseFVh9A9xUZBG3YT+ULf8Vw78PoApoZsWw2w6+/im3XLqHdm58v1jrrfzT0elGyLTIS4uOha1chANG/PwwaBHFxsiaoRCI5Z2hXBlRVVVIWP46jNId+d32ERqtv+2t43Bxf8xoFScuInjCXmPPn1fF2582bx7JlyzAYDISGhjJx4kSee+45IiMjm9V/c8uZ2UtzsKRuwZy6hfL0nXicNrT+wQR1GVrtfRpDY6jI3Id2/gL8f9xE5k3DKewrVIyMnWIJiOmLf1RP/CN7EBDVE11gWPM9d1WFrCxYuFAELPXrJ9ZTc3OhtLRGQak+er2oKxoaKtSOIiNFYFNcnDC43buLVJyYGFG1RiKRSNop7cqAggjGOfD+HUJofvS1PrmGqqrkbfqC7HXvEj7kMrpMewRFI0Tiv/zyS0wmE127diUtLY2//vWvuFwukpKSMDZiEOx2O/ZaxsZisZCQkNCiaiwelx3r8X0nPM/dWLNPTOXqTXRfdhTTlkPY/v0P9Hc8gLuiFGv2AaxZ+6nIPURl/lE8jgoAdAGh+Ef2EEY1qgf+Ed0whsU3XXfV6RTeZa9esHJl/YcEBQVCLH//fjh8WKy1ZmWJ/WazEHGoP0VcG0URRtnfXxhdk0loAgcHCwGJsDDo3FkY4OhoEQwVHy/2m0xyLVYikZxR2p0BBcj44VVK9q2h/z2ft5m4QmOsePtpIvN/YetRCwuXHWXpd99z/vl1S6Ll5OTQtWtXFi9ezKxZsxr0sXDhQv72t7812O9NOTOP0441JQn9rfdgSNpP+g2DKOkTAooGv4huBMb1JzC2HwExfTCGJ+AqK6QiL5XK/FQq81OozEvFYc6t7k8f1Bm/8C74hSdgDO8i/g5LQP/ZVygPPCimdk8l2tAUqiqkBI8eFdPDaWkirzU7W0wVFxWJ41arWKd1OERaTnM+looipoy1WuH56vXCq/XzqzHKVYbZZILAQGGcAwPFVmWwaxvukJCac/z8RH863anHIpFIzjnapQF1VZSy780b6TTgErpMfdhn1ykrKyNr989UbHwTTVA0iVc/R3DnhqpFvXr14o477uCPf/xjg2Nt4YE2oLRUpKPs2gXLlqFOughbYTrW7P3V3qet4Bigomh0+EV0rZ7KFdO5PVA0OmzFmdiKMrAVZWIvysBWlIG9JAvV7URjdzPg5S1YB8RR8OBMDKExGEKiMdZ61QV2ajwauC1wucR9ZmcLrzY7W0wfFxQIJaTSUhFZbLWK9drKSmGAq4yw0yn6cLtFdLK3KIqIXq4y2hpNzVZlxGtvOp3Yqv6uMvA6nfC6q97X3l/779pb1Q+EqnOq9jfWtvZW+zpV163dtvZr7Xuqfa/NfZVIzkHapQEFyNv6FVk/v0m/29/DPzLRp9eqyD1C6ldPgKrS49p/1BFcKCoqIi4ujnfeeYdbbrnllH01dw20SXJzYepU4cWtXAmjRzd6mtteccLjTKUiL+XE30dRXcKY64MiTnidXWq8zvAu6AJDcVoKUBcuxPjWx+R++DSVfg4cpTnYzbm4K2tyTBWNDr0pHH1QOHpTBPqgE5spAr0pHENQBDpTGFqjqc2jpluEqgqDarMJo2s2i62sTLyWl4utyhOu2qoMc5VxttuFca5voF2umr9rbx5Pw01V624dmdr/5vX//ave139t7rGT9Xmqc9vi79Ycb+mx5vTdnPct2dfSftvius35bmhJm9aOY9euU4+jfhft1YBWpbXoA8PoddOrPv+CdpYXcfjLP2HNTUUdOIeoIZdy7NgxnnjiCTIyMjhw4ABBzajp6ZUBTUsTYgaVlULbdkDLRB9Ujxt7SdYJg3q0gdcJoNH7EaANp+eTX2OdPhH7nx+o9j4NIVGoLgcOcx720hycZQU4ygpxlhfiLCvCWVaAs7wIt62sznUVjQ5dQAi6gNBar6F13/uHoPMPRutnQms0oTH4n1mje7pQVWFYq4xubUPsdNYYbZerrvGu/1p/c7ka/l27b5er5rpVU+ZV76v+buoHQNWPg8bOq9pXdV7t9/XPqZoZONmPi6r9Vc+q9rHGXmt/nTX2/mT7W9pHY22b2tfctrWpv68557T18Zae29z+Wmp22nqcjbVpKjDyJLRbAwpgSUsiZdGjdJ3+BOGDJvv8etayUr766ywGR3p46+d0Vqd4uOiii3j22WdJSEhoVh+tNqB798LkyWJtbs0a70uS1UL1uHGYc6unc/3//m8C127n8NPTqHRbQK2aAlXQB0WIadzQGAxBndEHdT7heYZjCOqMLiAU1e3EWV4kjGp5Ea6KUpwVpbgqzPx/e2ceJVdV5/HPe7X2Ut1Jd5LuhKSzmhBIJJlARDAjB9CgkRCVbVxQNldUJHHiAs5hOWxugyASBYYJqCgCSsAogSjKIAEjUTEhQehspDtr7921vjd/3FdVr7au6upaurt+n3Puuff97lrdffpbv9+7777wQBfh/k5b6rKNb0PTcXhqYoIazZ3eeFn3VONwedHdVeiuKhzuqjRlL5rDVRliLAhCSRnVAgrQ+vj19OzZxgmfWY/Tm90DHC6madL2pwdof/5/GX/i2Uxf8RV0Z+6PY+QloJs3q/eDzpihDjNoLtx5wCns2qU825tugrVrMSNhgt2HCHS2Eexqj4Vyg51tBC2PEyMS76/puGoblLBaoVxndT2u6nE4a8YneqBVdaBpRPy9hPu7iAR6ifitFOglbOV2W7Qc9vdghAYwgn4gy5+w7lCC6rJE1elBd7rRnG50pxvd6bGVLbvDyl2ehLLmsNo4nGi6U4mzw6Fy3Ykes6epL9b9YkEQysKoF9Bgz2G2r7uExoXLmbb86pLNe+yfz7LnyVupaprDrA9dj7uusM+BxnjoIbjsMvUu0EceUTtEi8nKleps3R071E7WLJimQbivg1DvURXO7TlMqOeI5YEeJtR7LOaBJggtABrOqrqYoDqqanF4fTg9KndEvc2YLZ50lwrxmqaJGQ4QCQ5gBAeIhFRuBAcwQv6Y3QgNxMvhIGY4gBEOJpTNSBAjZC8HMSJBzHAwFuIeFppuE1anJbhKYNGdaLpDJU2H5LKmo+nRskONpTuULVa22a0cXVftU8aw6qPr0jTQdECLl7VoWYu3QUtsr2loJLXRktqA+hyaZn2J0OLlWFtsc0bbqL8RawA1j1WO/v0oe6pNmVJtCWOl3F/UkiIVms2eaotdprHFx0q0JX6O5LUlzy+MdEa9gAIc3PIL3tp8D8dfek/B36gyGH1tr/Hmo9/EDAeZ+cH/wjc9+8uqcxZQ04Sbb4Zrr4VLL4V169SOyWKyaZMKE//853BhYZ+xNU1TeZX9XYT7OmLhWyWuHcoD9fcS8ffEPMxIoBczHEw/oO7A4a5Gd1fhiHqW7qoMNlvZVRX3JF2eJO/TE/c0k7xF04hgRkKW6AYwI2ErhWJ1pmHZrNywlVUewoxEMI1QvL9hG8c0MA0DjAimGcE0rbJhxMtmxNZG3Ts0LTumVTYMW9lmj7Y3o3ZT1akPCKap2lj3/WLlbB6+UATy38CjDaVvSp2WVJ1/3+R6bZC6oXze7J9PS1tMZ7B/voVffDTjnBnXMhYE1IyE2XH/leguL/M+8YOShspCfZ3s/tUN9OzdxnFnfoZJSy8Y9I8uJwENheBzn4N774UbblAiWuxvpuGweg1aQ4M6M3eEfBM2woHUsG5UaNN4l5Fgf6rHGRogEuhPf681A5rDlRTW9cRCv7rTozxIhyue6ypMq8eunYltrGs94Tqpv2Z5kZZnmeBRJpUz1+mgOQruyZiW2CYLq5lWeK22ZBbkaJuEcUmeIza7rV+qLdrOTGOLzWX/EmBfQ5ItOoGZxhb7OcQmjOdmsi1hrOh6zKR6kvrZ2iX/7BMtg1wOvvHITPg5JA2bpa+9PrVrtjVmlplBP98QN0GZefc1mbzsk4O3T8OYeEJcczhpWf5ldj30RY5u+w0TFn+gZHO7asYx5z9u560/3Mtbz95Nf9trtLz/Kzjc2cOfaenpUd7fM8/AAw+kHgpfLH70I3Wi0Ah716fu9KDXejK/bDxHTNNUYVkrhBvzJEOBeDnZboV0E+w2D9SIhDCD/crTjIRSPdJoG7uXWYhQcC5kCOvGxFlzpIZa04Zjk+qT8mztYAjj2MO2CaFTe+hWSw2bJoVC046T0N/mrSXbcgnv2vrY/b6s60uYz/a50n02kqrs86StSPbK7MUc+2SYNHP/zH3sY+fuxWaeJ7P3mtvaUkLzOfTJhTHhgUbZveEWuv71Z0741PqinlCUiY4df2DPk7fiHjeF2effiGf8cSltBvVA9+9X9yD/9S947DE4++wSLbxDHde3ciXcf39p5qxQlMcViYVwVZjXEl8jEgvNJoReoyHbWAjXXhexhWXtYd5MdbaxB/X+Ej3EdB5oxnYYlrOVWp/Sn3SeKKkeYRrPLr7u5LponyRb1ONL8vYSx473SfUObf5N2vUNtjYS1iaMPP7t638Ycp8xJaChvg62/+gT1M1ayszzri3LGgYOt/Lmo9cR7uugZcVaxh//7wn1GQV0yxZYtUqdFrNhQ/5H5+XDl7+swsWvv17cHb6CIADJYcvBwo7pQ66DhyozhWmTQ9FD65N7ODi3tZl59EmwZvoZph0j1Z78M/SMm5y+zyCMKQEFOPr337LnyVuZfdFt1M9Of0pPsYn4e9nz1O107vwjE0/+EMed+Rl0pxvIIKA//anaabtkifI8m5pKt9jXXlOvIrvxRvjqV0s3ryAIwihnzD2Y1rBwOb4ZS9j32+8Ssd5CUmoc3lpmfuh6pr33Sxx5ZQO71l9FoONAakPDUBuEPvpRuOgi9bxnKcUTYM0amDYNri7dI0CCIAhjgTHngQIEOg6w/ceXMnHxuUx9z1VlXUt/207efPx6Jg88T/04H7hrePmllzllyRKc/zwC39kLt94KX/lK6TfvbNwI738//PKX8OEPl3ZuQRCEUc6YFFCAgy8+zFub1zHvk3dTM2V+WdcS8fcSunc+3sD+xIp9Opz5uNq8U2r8fliwQJ1utGnTiNp5KwiCMBoYcyHcKJOWnk9V89vY89S3MCPhsq7F4a3F05D6GjTmz4Fzzy39ggC+9S3YuxfuukvEUxAEIQ/GrIBqupPp71+D/8huDr74cLmXw8H29lRjYBc8Phle+Di8uR4G2kqzmNZWdcrRNdfA8ceXZk5BEIQxxpgN4UbZv/keDr/8KPOvuB9vY25vTCkKP30ntL2YaJswH05aCW2boOOvylZ/AkxcBpP+XeU1RVjzeefBX/+qzrutrS38+IIgCBXAmBdQI+Rn+48vw1XbyNyP31HSY/4SSCegk0+Fj/xZlf2Hof0ZOPQcHPojdO9Q9poZcUGdtAx8c4cXcn3ySRU2fuQROP/8/McRBEGocMa8gAL07NnG6z+5mqlnf55JSy8ozyKyCWgy/sNw+Hklpof+CJ3b1EktnkZoWAqN0XQKeCfmtoaBAfWqsjlz4He/k3ufgiAIw2BMnIWbDd/0RUw8+cO89YcfUzf71PKGcnPFOxGmfVAlgFA3HH4Bjm6BI1vg9bvg1aOqrmamJaYnw7iTYPxJ4E3zerXbb1fHBW7cKOIpCIIwTCpCQAGmnHEF3W/8mT1P3cbcj90RfxfiaMFVB1POUQnUkVR9rXDkJTj6khLWtzZAxDo8wtushHTcSTB+EXQ1wC23wOrVMG9e+T6HIAjCGKEiQrhRevf+nV0PfYnjzvosTe8o7PsuszLUEG4+GBHofQM6/wYdVur8G/Tvg28De4F182HSiVA/H+qOh7r5UDcXnDWFW4cgCEIFUDEeKEBty9uZdMqHOfDcvdTPORVvY0u5l1RYdIcSw7q50GK71/vLh+CVj8N/XwotVWqD0hv3Jj42UzNdCapvHtTOUsk3W21iclaX/KMIgiCMdCrKAwW1K3fHfVfgrKpn7se/X7pQbik80HT09MAJJ6i3uzz5ZOK9z2AndO9Ugtr9mpV2Qm8rGIF4u6rJSlBrZsXFtWY6VE9VyeEp7mcQBEEYgVSUBwqgu7xMX7GWXQ9+kUMvPULTqReXe0nF5brr4OhR+MEPUjcOucfBhHeoZMc0lHfa+2ZSegPaN4E/6VAIz0SonhYX1Fh5mhJfb5O6hysblwRBGENUnIAC1E5byKSlF3Dgufuom/NOqiZML/eSisNf/gJ33qkOq58xI/d+mg7Vx6k0aVlqfbgP+vdbaV9i+fDzqhw8ltjH4QXPJKhqVoKaKXkmKGHXK/JPUxCEUUTFhXCjGKEAO+67Aoe3lnmX3IlW7H/YpQ7hhsOwdKl6ZdrLL4PLVZx5Ms5viexAO/gPKq/Vf1ClgYPxsv9gYrg4imsceBrA3aCefXVHyw3gbkysc9UrD9dVpzZDleuwDEEQKoqK/ZqvuzzMOPer7Fz/Bdpf+CmT33VJuZdUWO68E7ZtgxdfLL14ghKyunkqDYZpqmdcowIbOAbBo1ZupcBRVd+1PX4dyfSuVw1cPktQbcIaE1j7dS04atQmKWcNOKzcmWTT3RJ+FgQhhYoVUICa406k+bSP0fanB6ibtZSaKWPkYPW9e9W9z89/XnmhIxlNA3e9StnE1k7ED8EOJaahLiXCKclmD3ZC316brUt5yTmt0ZEksNVx4XVUq/C0w6NyPSl3eEDPUu/wxtvobtBdoLlUHk2aU0RcEEYYFRvCjWJGwuxc/3kigX7mX/5jdJe3OBOVKoRrmuqw+K1b1WHxdXWFHX8sYZoQGYBwP0T6VB7uU95tOMO1vV24T/U3AkrQIwEwrDziTy2bxvDWqzmTRNUVF9wEW5ZrzaEeedKcqpyc9HT2NLZM7fRsfXUrzK5ZuXWtabZy1J5kS9svi81uT7Bp8qVEGBYV7YECaA4nM1Z+gx33Xcn+Z++h5Zyry72k4fH447BhAzz6qIhnNjTNCtVWAxOKP58RHkRso3kQjJBKZiheNkLxumS7maZNsj0SgHCvZY/EkxFOvDYjYKazZWobKf7PrdgMKsaauo6JrV10k+xY9nR9hlKX0qaAcw02Xs5zYctJ6kdiWcvRlrV+GPPl2ve09QyVihdQAG9jC1PP/Az7nr6D+re9k/rZ78jeaSTS1QVf+IJ628oHP1ju1QjJ6E6VxtKpT6apPOtsAmwXX6J9jHgZI9UWs5tJ9UZ83nT9Bh0rh/FTxjLVNaZVJul6EHu+dbE2FGa85LoUe45zRX/n8T+A1HKm+mgEJmO9mWorVX2egVgRUIsJS1bR9a8X2PPkbZxw5f/grK4v6Pjt7e00F3TENFx7rRLRu+6S0JRQGjRNhWUZZWdLC0IBkP3+Fpqm0bJiLaYRZu/G71DoW8PNzUWWz5deUocl3HgjtIyxIwoFQRBGICKgNty+CbS8bzWdO//IsVefLvdycicYhCuugMWLVQhXEARBKDoSwk1i/PHvpmvhcvb97g5qp70dz7jJ5V5Sdm67DbZvVycPOeVXKgiCUArEA03DtPd8AWeVjz0bbsE0Rvguw+3bVdh27VpYtKjcqxEEQagYREDT4PDWMv3cr9O77x8c3PKLci8nM5EIXH45zJqlDk4QBEEQSoYIaAZ8LSfRdOrFHHjuXvraXiv3ctJz112wZQvcdx94i3QAhCAIgpAWEdBBmPzuy6humsPuX99EJJjp7NUy0doKX/+6Oq7v9NPLvRpBEISKQwR0EHSHixnnXUeo5wj7nv5+uZcTxzThU5+CCRPg5pvLvRpBEISKRAQ0C96GqUxbfjXH/v5bjv3z2XIvR/HAA/DMM7BuHfh85V6NIAhCRSICmgMNC5cz/oQz2fvb7xLobCvvYtra4Jpr4JJL4JxzyrsWQRCECkYENAc0TaPlnGtwen3s/vVNmEa4fIu56ipwu+G73y3fGgRBEAQR0FxxeGuZcd619B3YQdvzD5ZnEY8+Co89pnbfNjaWZw2CIAgCIAI6JGqnLmDysk/S/n8P0rv376Wd/NgxteN21So4//zSzi0IgiCkIAI6RJpP+yi1UxfQ+sRNhAd6Sjfx6tXg96sD4+VNK4IgCGVHBHSIaLqDGSu/gRHsZ+/Gbxf8rS1pefpptfP2O9+BKVOKP58gCIKQFRHQPHDXN9HyvjV0vvYcR//2VHEn6+lRz3yeeSZcdllx5xIEQRByRl7dkSfj559Bd+sK9m+6i9qpC/FOmF6cidauhSNHYPNmCd0KgiCMIMQDHQZTz74KV90kWn99I0Y4OGjb9vb2oU+weTP88IfqdWWzZuW5SkEQBKEYiIAOA4e7ipmrrsN/ZA9vbb5n0LbNzc1DG7ynR4VszzgDPvvZ/BcpCIIgFAUR0GFS3fQ2pp71OQ7/5TE6d/6pcANHQ7f33w+6/JoEQRBGGvKfuQBMWLKK+rnL2PPUbQS68gjVJmMP3c6cOfzxBEEQhIIjAloANE1j+or/xOGpYfevbsCMDOOoPwndCoIgjApEQAuEs8rHzFXfpK9tJweeuy//gSR0KwiCMCqQ/9AFpOa4EznujCs5+OLP6Hpjy9AHkNCtIAjCqEEEtMBMeseF1M0+lT1P3Eyw53DuHSV0KwiCMKoQAS0wmqYz49yvojlc1qvPIrl1lNCtIAjCqEL+UxcBZ/U4Zpx3Lb37/kHb8+uzd5DQrSAIwqhDBLRI+KYvUq8+e349Pbv/mrmhhG4FQRBGJXIWbhFpPu2j9O7ZRuuvb2JBYzj9t5Vo6Pb3v5fQrSAIwihC/mMXEU13MOO8b4BpEjj2VmqDri4J3QqCIIxSNLMkL7SsbLpb/4L+y7Oo1bsTK9rcsPU0ePZZ8T4FQRBGGfJfuwTUzTwZt29CakU4LB4TkCsAAAb2SURBVLtuBUEQRinyn7tEuOomphpbWiR0KwiCMEoRAS0RGmlehj0pjagKgiAIowLZhVsi2tvbSXkj6LGXYcNcGL/YSotUXtVUjiUKgiAIQ0AEtEQ0NzdD2+5EY+1smPw+6NwG22+BkLXJyNscF9RxC6B+AdTNA4en1MsWBEEQMiACWiomLAAgHInw8ksvc8rSU3A2nQQn36HqTQP6dsOxV6DjFejYBq3rYcB6/EVzgG+OEtP6E1UatwB8bwPdVZ7PJAiCUMHIYywlpru7m/r6erq6uqirq8veIdgJXf9UqfPVeNl/UNXrLvDNhfoTwDcP6uaq67p54B5X3A8jCIJQwYiAlpghC2gm/EfiYtr1KnS/Bt274h4rgGeiJahJwlo7Cxze4X8YQRCECkYEtMQUTEAzEeqFntehZxd077TyXdCzM36PFaBqCtTOhJpZKq+dCTUzlbhWTQHdUfi1CYIgjCFEQEtM0QU0E6YJ/kNKSHvegL5W6G2F3jdVeaAt3lZ3QfV0S1gtga1ugeqpUD1NCazDXbq1C4IgjEBEQEtM2QQ0G+EBtYmptzVVXHtbIdRla6yBtykuqAm5iKwgCJWB7MIVFM4qqJ+vUjpC3dC/30r7EvODz6o8lHTWr6dRPZLjbYaqyVDVbLu2bN5mcI8HLc1BE4IgCCMY8UBLzIj1QAtBgsjuB387DLSn5uGexH66Ky6s3ibwTgDPIMk9HjQ5REsQhPIiAlpixrSA5kq4L72w+tvAfxgCR+IpeCy1v6aDuyGNsDaoR3fc48A13ipbucsqS1hZEIQCISFcofQ4a8A3W6VsGGElonZRjSa/rdyxDYIdEOpUz86akfTjOariwuoal1SuB1cdOH3g8qXm0bKzVnYpC4IgAiqMcHQneCeplCumCeFeJaShTiWsQUtY7SIbLffvh+A/lC3cA6EeMMODz+GoTi+uLktgnTWqjbM6Q16TuU7EWRBGBSKgNh577DHWrVvH1q1bOXr0KK+88gqLFi1KaBMIBFizZg0/+9nPGBgY4KyzzuLuu+9m6tSpZVq1kIKmxUWNaUPvb5pgBJSQRgU1Wg73Jl4n5/5DEHoDIgMQ6Vfh6nA/RPrUcY25oLuTBLhKHXzh8ILuSS3HbB7QvfFy2jZJ7R1eNZ/uVveidTdoLlWWjV2CMCgioDb6+vo4/fTTueCCC7jyyivTtrn66qvZsGEDDz/8MI2NjaxevZoPfOADbN26FYdDPIcxgabFxYYCvXLONMEIWaLaH8/Dfam2dG2MAET88TzYBYYfIlG7vWzlET8wjC0OmjMuqrorUWAdNqG1i29O7VxqbM2pvO1oWXOoiENKOcd2unWddTx7WVfXaPKFQRgysokoDbt372bmzJkpHmhXVxcTJ07kwQcf5KKLLgLgwIEDTJs2jd/85jcsX74869iyiUgoGaapQtERS1wziawRUOJuhMAIqty0lVPyJJsZgoiVp21vGzPazoyo+9tmOLVshnP31guKZgmwbhNWWzlqR8+t3VDsObfTbLlm1WuJ9pQ2+fRJ0ybXvgn24c6npZZh8OvYFyF7v+TrNP0mvWvIfzHigQ6BrVu3EgqFeO973xuzTZkyhQULFvDCCy/kJKCCUDI0jZj35/KVezVDwzTjYmqE05fNMBi28mCinCzQsWvDEmvDqrOuo+VB7bm2y9EeHdMIZWgXAUzrZ2OoMrayaVrtk+wpbfLpk6bNUOYbDXxk6OsUAR0C7e3tuN1uxo8fn2Bvamqivb09bZ9AIEAgEIhdd3d3p20nCIINTVMhVpwgd0ZGPzGRzUewzXgb+1gpAj2EthnHGBoVK6A/+clP+PSnPx273rhxI8uWLctrLNM00TLcP7nlllu4/vrr8xpXEARhTBALz8JY+kZUsce5rFy5km3btsXSySefnLVPc3MzwWCQjo6OBPuhQ4doampK2+drX/saXV1dsbRv376CrF8QBEEoLxXrgfp8Pny+od0XWrJkCS6Xi02bNnHhhRcC0NbWxquvvsrtt9+eto/H48Hj8Qx7vYIgCMLIomIFNB3Hjh1j7969HDhwAICdO3cCyvNsbm6mvr6eyy+/nNWrV9PY2EhDQwNr1qxh4cKFnH322eVcuiAIglBiKjaEm44nnniCxYsXs2LFCgAuvvhiFi9ezD333BNr873vfY9Vq1Zx4YUXcvrpp1NdXc2GDRvkGVBBEIQKQ54DLTHyHKggCMLYQDxQQRAEQcgD8UBLjGma9PT04PP5Mj76IgiCIIx8REAFQRAEIQ8khCsIgiAIeSACKgiCIAh5IAIqCIIgCHkgAioIgiAIeSACKgiCIAh5IAIqCIIgCHkgAioIgiAIeSACKgiCIAh5IAIqCIIgCHkgAioIgiAIefD/claEa7og3k4AAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph, xmax=20)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "image/png": 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Kl/oCkpq96lroYIg5GYbcB1HjwDrIux5JOwwbBnfdBU8+CVddBSkpnf8dhBBCiA7QaZrW55fD1Nwutr91CwCDr30ZnaEHY7L3T4T8nxueizsBJt0HBd9B/ncqcRk6iBgFsaeogCT2ZJUfpDNUVcHgwTB+vFogUAghhOhFjomWk8LVHx1KttajgUlLStfAiishbDgkXw7xZ0LMRDCHdc37rFZ4/nmYMQPmz4dzzuma9wghhBBHoBf+UneuutJc8n96k9hxl/aKZGuapjVdID1kAFy4FIISuq8il1+ukrPdfjts3gwBAd33biGEEKIV+p6uQFfSNI3985/HFBLVK9bOqTuYQ23xnmauWLs3MAHf4NicHPjb37r33UIIIUQr+nRwUrrxW6py1pJ8zr0YzD2bVKx080K2v3kzdl0YnujR0G+CGlNSGACLtsKiRd1fqSFDVDr7P/8ZsrO7//1CCCFEM/rsgFhndSlbX7mGsIwTSZ3ec1NmPU47+xe+QMn6r4kcPpWks+/CYPZbd6asDK64AhYvVi0ZN9/cvRWsrobMTDj5ZJg7t3vfLYQQQjSjz7ac5C58EZ1OT+KZv+uxOtQdzGH7W7dSuvl7Us77P1Km/bFhYAIQEQHffAO33KK2O+4Al6v7KhkSAk8/DR9+CMuWdd97hRBCiBb0yZaTip0r2P3Rn0id/iCRw6f0SB1Kty5i39fPYA6NI+3iRwmMSTv8TS+/rBbomzxZtWKEh3d9RQE8HjWtWNNg9WrQ99mYVQghxFGgzwUnboeNra9cS2B0CgOueAZdN6do1zwuDix+haJVHxIx7Mz2j3dZtAguvRTi4tQ039TULqtrA8uXw6RJ8OabcO213fNO0ak0zQMeD5rmRvN4QPN49+qzptWfcx+6pu5x+11rWh5NU8egymiaCmQ1D5r3nCqjAfXXmrkHzVvWW1c0332Hnud3P77zh75fS8/2e7f6D5pW/4fidwxaC+f9y2stnK8/1lo43+D59XX3/eV4zzZ/vie7noXojfpccHJg0X8p+nUeQ296G0t4v259t7OmnL2fPUb1/o0kTr6NmDEXHVlwlJWlco/YbPDVV3DCCZ1f2ebMmAE//qjeb7V2zzt7GU3T0NwONJcTj8uBp/7Y7UBz+Y49LvW58XnN5UTzuNDcLjSP2+/Y+7n+uM3XfWXqg4gGAYV/EHFU0qmZYzodOp23xU6nV/+/0enUsfccOh26JuX9Ptcfg3ev8x3S9LyvCt57fYWbeUbz59W9zZ/3na4/1jV8vt+zM2e9cLg/KCGOKX0qOKktzmbb69fTb9I19Jv0m259d03edvZ88giay0naxY9iTT6uYw8sKoJp02DLFjUe5NxzO6eircnJUZlj77lHzeDpxTSPG7fdhttejdteg9teg8deg9tRi8dZ59u8n92HztXicfhdd9bidtThcdlVkOF2HlF9dAaTdzOiN5jQ6Y3oDAbQG73HRnR6g9+xun7oXKtlvMd6A+j16kdZb1B7nQ6dzoBOr1c/5Ho9+H/W6dV9h66pz+rehuXVc/XodI3Ke9/TbABB/XkVSED9se7Qj3XD++vv0dPdrZrdoUHrUeMWFc2/VUXt6//z29OzCYXobfpMcKJpGjvfuxtnVTFDbnwDvdHSbe8+uP5r9i/4B4FxGaRf8jhma0znPNhmg5kzVevJv/8NN93UOc9tzcMPw7PPwrZtkNaGcTIdoGke3LVVuGorcdVW4LJV4PY/rqtuEHyoTX32OGpbfbbOaEZvCsBgCkRvCkBvDlB7v88G/88mi7rHYFZ7oxmdwaT2RrMKOJo9b0ZnNPl+tJt8Rw08bjxuZ8NWEnej4/q9X6uI5nH7Hfud17znPb5uGl93jP+9Ht9xfVeP//M0t/d30q/rxr/bpNmuG//uGL8yWqMy3h9nTWupW8ivK6ilMv4/8s11yRz6L5dflxL1O7+uId9fhl8Z75VG5w79neF7hv/9zXfLdPw/ocf/aUmHnyFEX9JngpPSLd+T/fmTZMx4htD0cd3yTs3tYv/CFzm49nOiR08jccrt6I3mzn2J2w133gkvvaRWEX7yyZZXHe4M1dUwaBBMnKhabNpJ87hx2cpxVpfirC7x29Rnl60MV20lblsFrrqqZrsjDJZgDIFhGANCMFhC0FuCMQQEq/OWEO/euwU0/KyCDYtqLfDWx+OsUy0qjlrVcuKsU1029V0z3lYTT6vHjkPHmsuugg2309f90krw0bV0TVtUGrSMGPxaRwx+rSP1rS+6ZlpB6ls69H7dKPoGLSKHytCoC6aZ5zRoOcHv2Tp83TV+XTSqvPda/XeEZrtNdM2cO3StSTeP92wz53zdM426f3Q0epbvnO9ZDc/5upganvN7WMPnAZHDJrftr1uIY0SfSF/vrqsm9/t/Ez7olG4LTFy1Vez9dDZV+zaQfM59RI8+v2teZDDAiy+qVoz77lNdL2+8AeZODoLq1U8tvuYaNbV40qRDlzRNw11bgaOiEHtFIY7KQhwVBTgqCnFUFuGqLsFZU9Yk4DAGhWMKicIUEoklPIHghKEYA0MxBoWpIMR7bPQeozeguRy47dW46qp9LSh+x/bSXHWuPuBw1PoFIKo7x+2sRXM52vjFdd7WFkuD1pNDLSRGMzqjBYMlCH1wuK8bp74LxuDrmlHdOoZG1/3ONShbf2xqGFjo/btkvN0uft0zh873wa4RIYToEy0n+xe+SMn6rxl68zuYQztp5d5W1JXmsvvDP+KqrSD94sexpozq8ncCqiVj1iw44wyYNw+Cgg5/TztpHjeO8gLsV19EXbgZ+zWXYS/Pw1FegKOyEI+z7lBZvSkAc2gc5rA4TKGx3gDEf4vEFByJ5nHhtJXjtlXgtJXjslXgspX7bd7PtZWHgo8Wx37oDRgtIRgCvC0q5kD05kDVfeM91psC1fn6vbm+K8f72WhB5w1C6rtzdHqj/NALIUQvcdQHJ7bCXWx/4yYSTruR+BOv7PL3VWWvZc8nszEGRzDgsqcIiEzs8nc28P33cOGFcNxxaixKRMQRPcbjsqu1fop2U1eyj7qSXOyl+7GXHTgUGOhcHixB0VhShmAOi8ccFndos4TFozMH4aopxVl1UG3VJd79QZxVJTiqinFWl+Bx2Jq8X28KwBgU7replhNDoPVQ8GHwduv4H+tNARJEtJemqVw29fvWNrcaq4LLBU6n+tz42OVSx/Vl/ff+5xtf89/718n/2O32nWuu3q1dg+af3bis//nmtvo/s7acb3yuvg71/I8b/6fW//MHH3Te37cQfcBRHZxomsbOd+/CZStn8A2voTeYuvR9B9d9yb4F/8CaMpq0i2ZjDOih6barVqnZO4mJsGABxMe3WFTTNBwVBdQW7aG2aLfaF+/BXpp7qPvFHBaHJTKZgMhELJFJBESpvenyWThL8nB89A6O6mLs5QU4yvNxVBRgL8/HWXUQ/8GAOoMJkzUGU0gUZms0Jms0ppAojCGRmPwDkcAw9KbuG7DcZpoGdXVQW6vG3lRVQWUl1NSowcn1+9patdUf19X5NrtdbU6n2hwO37HT2fCHvfGPeeO9/9bSD3RzP5L1x+LoIX9fQjRwVAcnZdt/ZO8ns8mY8Syh6WO77D2a5uHAopcpWvUh0cdfSNLU36PT9/BwnS1bYOpUCAyEhQsPzaxx1pRjy99GTd52bPnbqcnbhru2EgBDgJXA2HQCYwcQGJNOYGw6ATGpaC6naj0p3U9dyT7sJd592YEG40dMIVGYw/thDovHEhaPOTwec2ic6sKxRmMIsHZtq4amqYCgokJNta7fDh6EkhIoLVXBRFWV2mpqfMGD3a4ChfpgofG//v3/hdtZ/Ade6nQq827jfXObweDbNz42GMBobFjWf9Prfdf9zzV+bkvPb+6Zzb2j8bMb10ena/7d9d+9vkxLfyaN/3yaK1v/zJb+TJsr09KfPfiuNclpQvvPtbd8QMCR/W9MiD7qqA1OPC47W1+5loDoFDIu/0sXvsdBzld/pWzrIhKn/J7YsZd02bvaS9u7h9orzqM6Ukf1jLOx1eThqCgAwBgYRlDCEIL6DSI4YTCBcRkYLCHUHcymtnA3tsJd3i6dnEPBC+gwh8cTEJlEQFQylshEzK/MwfLTr5hXrkMfFtk5FbfZYP9+2LUL9u2D/HwoKIDiYhVglJX5gou6Ol9A0Z4Aov4HyGj0bSaT2iwWtQUEqC0oSAV5/sdBQWoLDvadCwz0fQ4OVoOHg4N95wIC1EBlo7FrZ1QJIUQfd9QGJwUr3yfvx9cZesMbBESndMk73PYa9nz8MNW5m0id/iARQ07rkve0leZxU1u0m6p9G6jet57q/Ztw11aic2sEFdgInnQeQcedQnDCEPSWYGoLsrDl76C2cBe2wl2+lhCdnoCoZAJjBxAQnUJAVLIKRiL6N+1u2btXTS1+9FE1lbkldXWwcyds2gQ7dqhZRXl5qmWjtFQFGzabCjJa+5+cXu8LIOqDgZAQCA2FsDC13lBYGERFqS0mRm3x8Srlf2iouleCAyGEOGodlcGJs7qELS/PIuq4c0iacnuXvWPXBw/gqCgg/dI/d9+MnEYcVQep3LOayt2rqNr7K257DTqDieD+wwhJPg5r8iiCAmOxX3UxNa4San57Eba6IupKcgCVMyQwNoPAuAGqOyduAIHRae0b83HnnfDCC/DKK5CdrdLb79unWjvKylTQ4XY3f6/ZrFoVQkMhMlIFEnFx0K8fJCWpcTMpKeo4MlI1wwshhDimHZXBSc43z1K+4yeG3fKuyovRyepK9rHrg/vRPG4yrniGwNj0Tn9HSzSPi+rcLVTuXkXl7lXUFu0GdAQlDCZswHisKccTGJ9BXXE2VfvWU52znurcTSpjqkcjsKiW4DGTCR59GsEJQ7BEJraYvbThizXYvVstPLhmjcoQu2+fGs9RU9O0vMGgWjUiI1WgkZwM6emqlWXoUMjIUK0c0oIhhBCinY664MRWuJPtr99E4tTbiR1zcec/v2Anu/53H8bgCDJmPNMteVM8bidV2Wsp3/4j5VnLcNdWYgwKJzR9LKEDxmNNHYPLVk7l7p+pyl57KBjRmwIIThyBNWUUIYkjCAqKRz/tAhVYLFgA48c3fZmmwfbt8N13sHIlbN4MublqIKn//xR0OtWdEhurVkbOylLjRBYsgJNPVl0uQgghRBc4qoITTdPY9f69OKtLGHLD6+gMnTtjpubAFnbN/T8sEYlkzHimS1pl6nlcDir3/kr59h+pyFqG216DJaI/4UNOIzxzEpaoZKr3baBy189U7l6Fo7IQndFMSNJIrCmjCUkeRXC/QU3/DCor1YrGmzbBN9+oFo7PPlPZXnfuVLNa/AeWms0qAMnIgBEj4MQT4ZRTICGhYatHebmaEfSb38A//9llfy5CCCHEUZW+vmrvr1TlrCX9sqc6PTCpylnH7o/+RGBsBhlX/AWDJbhTnw8quLLlbaNk0wLKti7CXVdFQFQKMWMuIXzIqRiDIqncuYz8pW9QlbMeze3EEpFAWOZE1YKSPKr1sSLZ2fDuu94vVKVaOOrp9WoA6fjxMHasyjJ7+ulqLEhbhIf7Vit+4AHo3/+I/xyEEEKI1hw1LSea5mH7m7egN5rJnPVip+bTqNi9ij3zHiYkaSTplzzR6cuXOyqLKN28kJKN32Iv3Y/JGk3k8ClEDp+KMSic8h1LKd/+I1U56wGwJo8ibOBJhGZMaDkDrabB+vXw5puweLGallvnTS2v06kZLeXl6vOcOXDVVR0f/1FZqbp4Zs6Ef/2rY88SQgghWnDUBCelWxeR/dnjZF79AiHJIzvtueVZy9j7yaOEDhhH2kWz0Rs7J3OppmlUZa+leM1nVOxcjs5gInzQyUSNPJugfoOp2LmC0k3f+gKS1OOJGHwqYZknYwoOb/6hubnw8svwxRdquq7Du6id0aiChkmTYMYMmDxZnSsrU60jhYWwdCkMHNjxL/bUU/DYYyoYSkrq+POEEEKIRo6K4ERzu9j6yjVYopI6NeFaxc4V7Jn3CGGZE0m74OFO6Spy22so2bSA4jWfYS/ZR0B0KjEnXEjEsDOpK9pDyaZvKdu2GI+jlpDkUUQOP5PwzEkYg5oJSDweNV7klVfU4NXAsuLJAAAgAElEQVRKb7I0g0EFGlOmwG9/C6NGtdwqUlSkxpDU1sJPP6lZNR1RVaXGnlx2GfznPx17lhBCCNGMoyI4KV77Ofu//QeDb3iNoNgBnfLMyj2r2f3Rg4QOmED6RbM7HJg4KgopXPUhJRu/weO0Ez7oZGJOuJCAmAGUbvqWg2s/x152AHNYPFEjzyZyxFlYwvs1fVBtLbz2Grz9NmzYoNKsgxq0etppcP31cOaZvpTbbZGbq8afmEyqBaWVtXja5Jln4KGH1ADblK5JgCeEEOLY1euDE4+zjs3/nok19XjSLnioU55Zlb2WXR/+AWvq8aRf8kSHFgysLc6m8Of/UbrlewyWYGKOv4Do46fjrq2i+NdPKd2yEM3tInzIaUSPOo+Q5OOa5h1xOlUrxCuvwNatajyJXq9yhsycCbfddsSrDx+ye7cKUPr1gyVLwNqBRQtralQLzMyZ8OKLHauXEEII0UivD04Kf/6AA0teZdjNc7BEJHT4edX7NrJr7gMEJ45gwGVPHvEYE1vBTvKXvU1F1jJM1mhix19B1HHnUp2znqLVH1G9bz2mkCiiR08nevT5mEKiGj5A0+DTT1UrxK+/qgyrBoPqorn5ZjVl19LJK/du2KAClIkT1bgVUwdWcX7sMfjLX1Sa+tiuzwUjhBDi2NGrgxOPs47NL11J2MATSTnvgQ4/z1aQRda7dxHcbzADLn+6fSncvepK9pG39E3Kty3GEplI3IkziRh6OhVZyylY8R51xXsJThxOzJiLiRh0StPuotxcNRX3889V2nedDgYPVq0jN9+sBrJ2pR9+gLPPhlmz4PXXj3wGT0mJ6tK5+2544onOraMQQohjWq8OTgpXf8SBH/7DsFve7XCrib3sADve/j3m8HgGznwOgzmoXfc7KovI/+ktSjZ+i8kaTb+TryVi6BmUbf6ewp/fx16WR2j6OOJPurrpbCJNg/fegyefVLNsQLU2XHstPPhg23ONdJY5c1TLzOzZakG/I3XPPWoqc05O938HIYQQfVavDU48Tjub/30lYQPGk3L+/3XoWc7qUrLm/B50Bgb95sXmZ8a0wG2vIX/5HIp/mYfBHET8xKuJGj2Niqxl5P34Bo7yfMIHn0L8SVcRFJ/Z8Ga7Xa3k++qrapaLXq+6Vf761+ZTy3enp59WdXv9dbjuuiN7Rm6uWk/nqafgvvs6t35CCCGOWb02OCn6ZR6537/E0JvfaTkRWRu47Tay3rsLV3UJmb/5V/MzZJqhaR5KNy/kwKL/4nHYiJswg5ixl1FzYDN5S16ltnAXYQMnknDq9U0XBiwogN//XnXduFwqIdpNN6lWiqD2tdh0GU2DW2+FN95QXT3+2WTb47rr4NtvYe/ezh8jI4QQ4pjUK4MTj8vOln9fhTXtBFKn/fGIn6O5Xeya+3/U5G8nc9YLbZ6GbMvfwf7vXqDmwBYihpxO/8m34qqtIPf7f1Ods47gxBH0P/0mQpJGNLwxN1f9WH//vfrxT05W4zFmzeqdq/M6nTB1KmzZAr/8cmTTgrdvV6sQv/qqmuYshBBCdFCvDE6K13zO/u/+ydCb3iYg6siykGqaxv75z1OycT4ZVz6LNWX0Ye/xOOvI+/F1ilZ/TEBMGklT7yAwdgB5P77OwXVfEBCVTP/TbyI048SG6fPz89X4kYULVVAydCi89JLKS9LbHTyo1toJC4PlyyH4CNYUmj5dreuzYUPvDMKEEEIcVXrdwn+ax03R6g8JH3TKEQcmAMW/fsLB9V+SfN4DbQpMqrLXkfPNszirD9L/jJuJGXsJpZu+Y+8ns/G4nfSffCuxJ1zUcPZNVZXK0PrJJyooGTZMdZOMG3fE9e520dFqWvGJJ8I118CHH7YvwRvAHXeobLU//nh0BGRCCCF6tXb+CnW98qzl2MsOEDfhiiN+RsXuVeR+/xKx4y8n+rhzWy3rttewb/5z7Hz/bszWaIbc8AZhmZPY9f597PvmWUIHjGPYLXOIG3eZLzDxeOCPf1Sr/M6bBwMGqNTwmzcfXYFJvREj1AyeefPUYN32mjxZtRa98ELn100IIcQxp9e1nBStmktI0nEEJww5ovtrD+aw97PHCR0wjv6n39xq2er9m8j+4klctZUknXU3UaPOpfjXT8n78XVMIZEMnPk81tTjG970ySdqbEV5OURGqrEWF198RHXtVS66SE1rfughOOkkOPXUtt+r06nWk9/9TnXvpKZ2VS2FEEIcA3rVmJPq/ZvImnM76Zc9RfjAk9p9v9tew/Y3b0anNzLompcwWJofP6F5XOQvm0PB8jkE9x9K6vQH0dxOcr76KzUHthIz5mISTrsBgznQd1NBAZx/PqxZozKrPvggPPJI3xpj4XKp7pkdO2DdOoiLa/u9NTWQmAg33ADPPtt1dRRCCNHn9apuncJVc7FEJROWMaHd92qaRs5Xf8VZU0b6pU+2GJg4qorJevcuCpbPod+ka8i8+h9U79vA9jduwlVbQeasf5I09XZfYKJpKllZYqIKTM46S2VHnT27bwUmoLLTvv++6ra66iqVUr+tgoPhxhvVooU1NV1XRyGEEH1erwlO6kpzqchaTtz4y5sujNcGRb98TPmOpaSe/4cW86JU5axj++s34agoJPPqfxI7/jJyvnqGnK/+QviQ0xh83auEJPlld929WyUZe/xxNZtl0SKV06Mji+b1dv36qQBl0SKV0bY9br0VKirgo4+6pm5CCCGOCb0mODm47gsMgVYih09p973V+zdxYNHLxI6/nPBBTZOJaZpG4aq57Hz/XgJj0hh83avozQFsf+NmyncsJWX6n0g9/w8Nu3H+8hfIzFRjKK6/HoqK4PTTO/ANjyJnnKFahh5/HH7+ue33paXBmWeq1hMhhBDiCPWKMScep51NL15K1HHnkjj51nbd67KVs+21GzCH9yPzqr83WWjP47KT89VfKdu6iLgTryTh1Osp3fID+775GwHRKaRdOLvhlOXychWErF8PERGqpeRonIHTUS4XTJqkurDWr297/pMPP4QrrlCJ3YYO7do6CiGE6JN6RctJ2bZFuOuqiDl+ervu0zSNffOfx+N2kHbRI00CE5etnJ3v30t51jLSLnqUhFNv4MDiV8j58mkih09h0DUvNQxMFi+GhAT1Y3zBBWoQ7LEYmIAafzJnDuTltW/dnAsuULlTXn+96+omhBCiT+sVwUnxms8JTR+HJaJ/u+4r2Tif8h1LST7nPszWmAbX6kpz2fH2bdhLc8m86u9Y005g94d/pGj1xyROuYPkc+9Hb/RbC+bBB1V3htMJ774Ln30GZnNnfL2j18CB8Nxz8PLL8M03bbvHYlErHr/zjlr4UAghhGinHg9OavK2Y8vfTvQJF7brPnvZAXK/e4GokecQMfiUBteqczez4+3fgd7AoGv+jSk0lqw5d1CTt42MGc8SO/ZiX/p5pxNOOUWtrBsfD1lZaqaKUG6+Gc49V00RLi9v2z3XX6/S4n/+edfWTQghRJ/U48HJwfVfYg6NI2zA+Dbfo3ncZH/xZ4zBkSROub3Btarstez6330ERqcx6Dcv4XE72fH2bXjsNjJ/8y9C007wFS4uVoM4f/pJDeTct099Fj46Hfz3v1BdrbLitsXQoTB+vGqBEkIIIdqpR4MTj7OOsq2LiRx5Njq9oc33Ff0yj5oD20id/icMlqBD5yt2r2LXh38gJGkEGTOeoa5kH1lzbsdgCSbzmn8RGO236u6GDSoQOXBA/eguXKiSq4mmEhPh6adV986yZW27Z+ZMmD9fDagVQggh2qFHg5PyHT/hcdiIGjG1zffYy/LI+/F1YsZcTEjicN+zspaz5+OHCE0bQ/qlT1KTv51d/7uXwOhUMme90HBMyrffwpgxUFurxkY89VRnfq2WOZ1qgOmePbBtmwqQfvkFNm5UOVUKC8Fm6566tNctt6jWkJtuattYkssvV8nc5s3r+roJIYToU3p0KvHO/92H5nKQOattC8Zpmsau/92HvTSXITe9icGsWk3Kti1h7+dPED5wIqkXPkzNga3snvt/BPcfyoDLnkJvCvA95IMP1L/qTSaVaGzixM79Um63WgBw5Uq1z81V3UXZ2WrMRlv+uK1WlQwtOVkNSh0yRG3HH6/W8+kpGzfCCSeoHCgPPXT48lOnqoBs8eKur5sQQog+o8cW/nNUFlG1dw3J593f5ntKNy2gKnsNA67466HApDxrGXs/e5yIIaeTOv2PVOduaTkweeUVNcAzMBDWroXBgzv+RQ4ehFWrVDCyciWsXq3GZxgMaoCt06m6NupTwRuNakZLQIAKkFwu1RJRV6fKAlRVqS07G5YvV9c9HnUtPR1OPFH98E+ZooKY7jJyJNx9t+riufZa1d3Tmpkz4brrVIB2uLJCCCGEV4+1nBSseI+C5XMYcccnDcaNtMRVW8WWl68iNH0caReof7VXZa9j19wHCBt4EmkXPkLNga3s+uD+5gOTl19W6dWtVti0CVJSWnhTG3g8anXiP/9Z5UQBiI2FYcPU9ON9+1S3jV6vWmamT8d5/tmUpIbjMHjw4MGjeTDqjCSbkgGo8dRgsWsYi0ogPx9ycmDnTrUI35o16nmgApqAABW8gAoYpk6FCy9Uqwl39Xo/lZWqNWfqVJUHpTUVFWrxwKeegnvu6dp6CSGE6DN6LDjZ+up1BMakkXbhw20qv/+7FynZ+A3DbnkXU0gUNfnb2fne3QT3H86Ay/6MvSyPrDm/JzA2g4wr/tIwMHn7bfUv/bAw2L5dtWgcCU1T41Ueeki1vEyZAmPHqmBiyRLYuxdPcBDlZ44j59zR7J6SSVL8aMYHjifflc+HVR82eFygLpCbwm8C4K2Kt6jwVGDRWQjWBWPVW5kYOJEYYwwuzYWhsgbdunWqZWbJEtUlZbdDSIiqV02NGuB71VVq64xWoZa89ppa5O/nn9U4lNZMm6aClKVLu64+Qggh+pQeCU7qSvax9b+/If2SJ5pdC6ex2uK9bHvtehJOu4H4E2diryhgx1u3YgnvR8aVz+Fx2Njx1u/QW4IZNOsFDAEhvpvnzYPLLoOgINUScaTdIEuXqkRty5bBoEGQmIi2Zg268nI8Cf3QT7+ArWdlsGi8hiEwmFhDLBH6CJJNyWSYM3BqTsrd5Zh1ZvQ6PXrvWORgvUoLv9+5n2pPNTVaDTWeGio8FZwceDIRhgiW2Jaww7GDOEMcaaY00s3pWOsMKkj5+mu10F5xMYSHq+6hujrVYnPXXapFxdjJvXdutxp7EhgIK1a03lrz2muqK62wUGWOFUIIIQ6jR4KT/OVzKFz5PiPv/Ay9ydJq2fpBsI6KAobc+Caay8GOd36Px+Vg0DX/Rm80k/XunbhsZQy65t+YQ2N9N//0E5x2mupq2bJFjddor19/hXvvVcGJ1Ypms6FzuykfmUrWWYPZfc4wRpx4DcMDRlDlqcKtuQnTh/mSvHWCPFce+5z7OOA6QJ4rDw8eTg86nZGWkWiahs7thu+/V90s8+ap4CEqSgUEKSlwxx0qQGjr+jhtsWSJWoNo3jy4+OKWyxUWqoDwjTdU65UQQghxGD0SnGx77XrvonuPHLZs+c4V7PnoT6Rf9hRh6ePY9eEfseVtZdA1/8YS0Z/dH/2R6gNbyZz1AkGxA3w37t2rujY8HjVmY+TItlfQ41GtEbNnqzEfgGYwoDv9dLadncnqKXGEpY0k3ZxOmikNq97a3j+CI2b32Ml2ZRNniCPcEM7q2tVkO7MZGTCSDFMGxtIK1Vrx0kuwf78aiFpQoGb5/OEPakpwYODhX9QWU6eqqdEbNqgBwC056STVlfbJJ53zXiGEEH1at+c5qSvNpbZoN+GDTz1sWU3zkLfkNUKSRxGWcSIHFv+Xqpy1pF38OAHRKexf+CKV2WtJv/jxhoFJdbXqdnA6VQr1tgYmixbBlVeqcRwzZqDt3En1+BH8+PotbMv7CRYuJPnuZ5gx4v+40HohIy0juzUwAbDoLQwyDyLcEA5AnDEOo87IgpoFvFHxBsuDtlN9/20ql8o776jWEpdLBST33w8ZGWoMTv3sn4544gnVIvXhh62Xmz4dFixQeWWEEEKIw+j24KR8x1L0poA2pasv27qYuuI9JJx2I+Xbf6Ro9UckTr6N0LQTKNk4n4NrPyf5rLsbpqTXNDVIs6wM/vY3tS7M4VRXwxVXwOTJ8MEHaHo9RbfN5M19/+DN+TdSc/k0oiJVl1CwPhiLrvWuqO6UYkrhYuvFzAqdxSDzIDbaN1LmLlPjTGbNUsHDnDkqGNHpVOB17bWqNeOXXzr28vHj4fzz4dFHVQDUkunTVXK5H3/s2PuEEEIcE7o9OKnctQpr6gkNZ9M0Q3O7yF/6BqEZJ2IMDCXn62cIH3I6MWMuwlaQxb75zxN13LlEjz6/4Y3XXQdbt6oZK22ZvrpokUp29uGHqpXhmWfYlbuc/z0xjsTwQVwTeg3nhpxLnDGuA9+660UaIjk16FRuCLuBJFMSmqbxZfWX/Opch/OqK9QspdmzVbr+8HDV1TN+vBpP05EWjccfV4sl/u9/LZcZMgQSEuCHH478PUIIIY4Z3RqcuOqqqM7dROiAcYctW7LpW+xlB4ifeDV7PpmNKSSKlHPvx+OwseeTRwmMTSfprDsb3vTBB/DWW5CZefgcHOXlcPbZqrWkooLa225g7Z6v4P77GRA2gqtDr2Zq8FRCDaFH/oV7gEmn1gdy48aqt7KydiXvVLxDtqlITYHOylIDWXNyYPhwNTbl+ONVIrkjMXo0nHMOPPtsy9lvdTq1sOL33x/htxJCCHEs6dbgpGrvGtA8hB6mS0fzuChY8T7hg0+lZP3XOMrzSL/4MQyWIPYv+CcuWzlpF85Gb/TrXtm/X3VjBASoTK0tzZapqYGHH1ZJ0xYsQDv+eNbt+pLXnziOLZb9ODQHep2eKENUJ37z7mfUGTkt6DRmhc4iyhDF59Wfs8S2RLVgzJunWooKCtRYFLdbdfM89FDr3TMtuf9+ldhu4cKWy5x5pkpYV1x8xN9JCCHEsaFbg5PK3asIiE7FEtZ6ErSy7UtxlOcRknwcJRu+IXHK7QTGplO6eSGlm78j+ey7sUQk+G7QNDVl2OVSA2BbWn/mo48gKQmefBL0eqpef5G5i+/np/BdjLKM4srQKzHrzJ33hXuBcEM4F4RcwJlBZxJtUHlGNFC5X7ZsUUHJzp0qJf7TT8NZZ0FRUftectppagDys8+2XGbyZLWXdXaEEEIcRrcFJ5qmUbF71eFbTTSNwpX/IyR5FEU/z8WaegJRx52Lo7KIfd/+ncjhU4gcPqXhTX/4g5qdcv31anprc954Q62UW1amxlrs3s2aGcNxaA4us17GpKBJGHU9ttRQl9LpdAyzDGO4Ra3i/GPtjyyzLcMTHQVffqkGDq9apbp56hf3a083j04H992num3q0/k3lpCgxp7IuBMhhBCH0W3BSd3BHFw1pYSmj221XFX2GmoLd2IICMFVW0HyOfcCsO/bv2MwB5E0tdE4ky1b1L/Y4+LUwn7Nee45FbgAntmzKfrxU+jfn5MDT2Zm6Ez6Gbtx8bxeIFQfylr7Wr6s/hK7zqkGxS5erHKWhISoBG6nnKLG8LTVpZeqAOS//225zKRJqstNCCGEaEW3BSfV+zaA3kBw/2Gtlita/THmiEQqspbT75TrsEQkULZ1EZW7VpJ09l0NU9Nrmm+q8IIFaqG9xu64Q/2rPjgYx5KFfHnvaD62fYrNY8OgM/TZ1pLWHB9wPBeEXECeO4+5lXPV1ONJk1RrSWCgWg351FNVzpfnnmt5oKs/o1EFgO+9p6ZmN2fCBNi82bdooRBCCNGM7gtO9m8gKD4Tg7nl7KT28nwqd/+M5qwlqN8gYsdegstWQe7CFwkffCrhmZMa3vDXv6oVgK+/Ho47rukDf/c7ePFFSE2les9m5o7KJ8+dx7kh5xKkP/xKyH1ZiimFGdYZAGy0b1Qn09NVy8bYsSonyWWXqcDunnvaFqBcf70KTObObf76hAnqOatXd9K3EEII0Rd1S3CiaRrV+zYSktxMAOHn4Lov0RlMOG3lJJ93Pzq9gQOL/4vmcZM09Y6GhSsq4JFHIDQU/vOfpg+7+251fsAAKrev4WPLEhyagyusV5BqSu28L3cUizBEcEXoFUwMnAiAQ3OolZu/+kpND/7sM7jhBvjHP+C22w6fVTYlRU3PbqlrZ/Bg9fyff+7kbyKEEKIv6ZbgxFGeh7P6INakltPIe1wODq77Es3jIv7EmQTFDsBWtJuSDfPpd/JvMYU0mtp75ZUqPf3rrzdddfcPf1A/qElJakyK0YhVb+Uy62VEGlqYyXOMsugsGHVGilxFvFnxJrnOXLBY1MymSy6BN9+EW29VgV5bApTrr1eZZ71rEjWg16vByBKcCCGEaEW3BCfV+zcCOoITR7RYpnzHMtx1VZjD4omfOAuAAz+8jCWyPzHHT29YeOtWmD9fzS659NKG1x55RHX3xMdTs/kX7CYINYRyifWSoy6hWneKNEQSa4jli+ovyHPlgckE776rApTXX1eDZv/7X9XN05pzzwWrteWundGj1UKBQgghRAu6ZTSoLT8LS2QixsCWF8kr+uVjAJLPvge90UzlntVU7f2F9EueQGdoVM2rr1b7xgvOPfGE2qKicG5ez+f8gNVmZVrItM78Om2iaRqlpaXk5+eTl5fHgQMHKCoqwuFw4HQ6cblcGAwGTCYTZrOZ8PBwEhMTSUhIICEhgZiYGAytrfTbyYw6I+eHnM/n1Z/zRfUXXGG9gghDhMq0O326LzB59lm10nFLSwMEBsIFF6iZPg8/3DQZ3ogRKmFeeblKoy+EEEI00j3BSeFOguIzW7zutFVgy9uKOSwOa9oYNI+b3B/+Q0jSSMIaD4JdsQLWrVOzSYYM8Z1/5ZVDY1C0DRtYaFlDubOcKUGNcqJ0oaKiIjZu3Mj+/fvJycmhsrISu92O2WzGarUSFhZGQEAABoMBvV6Ppmm43W7cbjfFxcXs2rWL2tpaTCYTQUFBJCcnk5SUxJAhQ0hLS0PXUtbbTmLSmZgWPI0Pqj7ge9v3XBpyKTqzWWWUnTxZzcS57TbVipKQADNmNP+gGTNUq8vmzSoY8Vf/efNmNUNICCGEaKTLgxPN46a2cFfTmTZ+Cpa/C0C/U65Hp9NRsuk76or3Muja/zT9Qb75ZvWv8Xfe8Z3bu1fNzAkIgLVr+SXyADvrdnJe8HnEGGO64msd4na72b59OytXrmTr1q243W7CwsKIjo5m4MCBREVFERDQ+iKH/pxOJ6WlpZSUlFBcXExWVhbfffcdaWlpTJgwgVGjRrXree1l0VuYHjIdPXrfn31wsBocO3asmmlz5ZVwzTVqTM/EiU0fMmWKahX5+OOmwcngwWqM0KZNEpwIIYRoVpcHJ3WluXicda22nJRunI/eHETk8CkqQ+zPcwnLnEhwwpCGBTdsUP/iPuMMtZIwqHVhJk9W+08/pSw1kp8rv2ZCwAQyzBld9r0qKytZs2YNK1euJD8/n5CQEEaMGEFycnKHumNMJhNxcXHExalVkDVNo7CwkB07djBnzhy++uorxo0bx7hx44iPb30ZgCMVYYgAwK7Z2ePYwxDLEIiPVwHKpEkwcKAa2HrZZbB2rbrmz2xWafDnz4fHHmt6bdAgFZwIIYQQzejy4KS2IAuAwLiBzV4v3/Uzbns10aOno9PpqMpeS93B7KaZYEG1jkDDTLB33aVaTq68EqZNIwK41Hop/Qxdk/XV4XDwww8/sGTJEmw2G/379+eMM84gIiKiS96n0+mIj48nPj4em81GVlYWixYtYsmSJYwePZrp06cTFhbWJe/e6djJD7YfCNQHqunXJ5yglgGYOROef16NP7niCpW23mRqePM558C116p1emJjG14bOBB27+6SOgshhDj6dflsndriPZhD41ocDJu/5FUA4if9BoCiX+YREJNGSMqohgWLilSCsJEjYcAAdW7ZMvjXvyA+Hu3NN9nj2IOmaSQYE7pkfEZOTg4vvvgiX3/9NYmJiUybNo0JEyZ0WWDSWFBQEKNGjWL69OmMGDGCX375heeff561a9eitSVJWjsNMw8j2ZjMDzU/YNfs6uSVV6rcJw89pNbkWbEC/vjHpjeffbbaL1jQ9Fp6ugoohRBCiGZ0eXBSV5KLJSqp2Wu2/B3UFu3GHJ6A2RqNvSyPip0riB17SdPg4oEHVHbR555Tn2tq4PzzVe6M775jCzv5suZL8t35nf4dHA4H8+fP54UXXqC4uJgpU6YwYsQIzOaeWcFYr9eTlpbG+eefj8lk4q233mLOnDlUVFR06nt0Oh2Tgyfj0Bz8ZPvJd+Ef/1Azdp57Tq3w/NxzTRf0i4tTLS3fftv0wWlpKkW+292p9RVCCNE3dHlwYi/dT0BkYrPX8pe/A+iIHKFWEi5e8xmGQCuRw85sWFDT1ODK6Gg403vtyitVlthHH6VqWCo/2X5iiHkICcaETq2/f2vJgAEDOOuss7qsG6W9zGYzkyZNYty4cfz6669d0ooSqg9lUtAktjq2qjV4QA2Q/d//1BgghwNOP1114ZSXN7z5tNNU61ZjaWkqgV5eXqfVUwghRN/RpcGJ5nFjLzuAJbJpy0lt0R4qspYDGuEDJ+J22CjZ8DXRo85Db2o0G+Xjj1VLyW9/qz5v2ABffqm6dx56iCW2JZh1Zk4NPLVT679u3Tr+9a9/HWotGTp0aJdP5z0SiYmJh1pR3n77bb766qtODVCGm4dzpfXKQwNlATj+eDWl+M9/htmz1WJ+t9/e8MaJE9XaR/v2NTyflqb22dmdVkchhBB9R5cGJ47KIjS3E0szLScFK97FYAlBH2AlMG4ApZsW4nbUEnP8hU0f9Oyzavrwgw+qz/VJ2N5/nwJ3IXuce5gYNBGL3tJpdV+5ciVz5swhMjKSqVOn9prWkjW1VKIAACAASURBVJbUt6IMHz6cBQsWMG/ePNyd1G2i0+mIMcbg0TyUuEt8F2bPVvlOHn8c/v53ldvEv3unfprx8uUNH1g/u6ewsFPqJ4QQom/p0uDEXnYAoEm3Tl3Jfsq2LsYYHIE1Wa23U/TrPMIzJ2EOi2v4EKdTTVcdOtS3KN3mzarLYNw4Yg2xnBN8DoNMgzqt3kuXLmXu3Ln079+fCRMmoNd32+LNHTZw4EDGjBnDkiVL+OCDDzotQAFYXbeaj6o+wu7xDo4NClJr7ixapNbjOflklaTN7r0eG6tm5jQOTsLDVa6T4uJOq5sQQoi+o0t/dZ1VBwEwWRsmQju44WsMgVbsFQWEJI+iau8a7CX7iBl7SdOHvPWWGjh5441q7MmNN6pBsO++i0tzodfpyTRndlp3y6pVq/jkk09IS0vjhBNO6JXdOIeTmprKhAkTWLlyJZ9++imewy3W10bDLcNxa27W2Nf4Tp51lkpv/+CDaqDs7t2+QcsAY8bA+vUNH6TXq/FDRUWdUi8hhBB9S9cGJ9UlGAJD0Rt9s1o0j4uyzQuxJo8GtxNr0khKNs5X04ebW7X4lVdUl86NN6rjggK45hq0hATmVs1lTd2apvccofXr1zN37lwSExMZObLlFZSPBomJiYdaUL7++utOGYMSog9hVMAo1tWto8ZT47vwl7+ocSU//gh3363WN8rNVddGjFAJ1xq/PyZGWk6EEEI0q8tbTkwh0Q3OVe5dg7O6BFNYLDqjhYDYNKr2riFs4ElNWyk0TQ1+zchQC8rNng0GA/z97+S4cjjoPki8sXOypBYWFjJ37lyioqKO2haTxlJTUxk5ciTff/89GzppJeAxljHo0bPRvtF3csgQlfvkiSfgjjsgJESNQwGVl6aysumg2OhoKClBCCGEaKzLW07M1qgG50o3LSAgOhWXrYLA2HTqinNw1VYQmjqm6QNWrFBjTqZNg4UL1QDKCy+EsDA22jcSY4ghwdDxqcNut5t58+bhdDqZMGFCnwhM6mVmZhITE8Nnn31GZWVlh59n0VsYGziWcH2jFYUfeUTNqHrvPdXF88YbsGOHCk4ANm5sWD4oCGprO1wfIYQQfU+XByfGEF9w4q6rpjxrGZEjplJbuIuguAyqstegM1oIThzW9AGvv672N96okrABPP88le5K9jr3MtIyslMCieXLl7N161YmTJjQoXVxequxY8dSVlbG559/3indO2MCxqj1dvz1768WA/z739W+f394+GGVrC0wEHbtalg+MBBstg7XRQghRN/TpcGJu64aY4AvbX35rhVoLgfhg0+hriSHwLgMKvf+ijV5ZINxKYcsXqxWGrZYVPfOuHGQnEy+O59AXSCDzB2foVNYWMj8+fNJS0sjOjr68DcchSwWC2PGjOGXX37ptO6dUndp0/E+DzygxpF88IFqSfnoI9i+HVJTm+Y0CQyUlhMhhBDN6trgxF6DwRJ86HPFjmUEJQzBY68Fj5uA6BSq92/EmtZMl46mwf79agXbhx5S555+GoBB5kFcF3YdJp2p6X3tqZ9fd86oUaMOf8NRLCkpidjY2E7r3jnoPsiy2mWUukt9JzMy4OKL1XpHV12lcqD87W8qOMnJafgACU6EEEK0oGuDE0cNem9w4nHaqdyzmvDMSYfyn7hqq9BcjuaDk23b1BTiiRPhiy8gNBROP506Tx0uzYVR1/EFlVesWNGnu3Maq+/e+eKLLzr8rHRTOiZM7HI06q659VbYuhVWr1Yzd+bMUTNzGrecGI3gcnW4HkIIIfqeLgtONI8bj6MWgzkIgKqctXicdYRlTsJenochIARb3jaMQREExqQ1fcAnn6h9aipUV6t/ket0rKpbxfuV73e4fi6XiyVLlpCYmNhnu3Mas1gsHHfccaxdu5bCDmZnNeqMpJhS2PP/7J13eFRV/v9fd2qSySQhPYQWIKEjRWmCqKig665iXVQsWHd1Lbjr7rrVdV13115+fnXtDV0XFQuKgiKCUlSQXkICSSC9TzL93vv742Qyk2QChMlQwnk9z33uzLnnnHsn4WHe+VRfYdsLZ5wBeXnw7LNw003CQrJ3b8c+On6/ECgSiUQikbQjauJE87nFDSyxADj2/IAlIYOYlH546kqxJPXGsed77DnjUZQwjxGoKhooh/6HP6DrOoW+QvqYwzcS7Apbt26loqKCYcOGHXxyD6J///6oqsr3338f8V4DzQOpUCva1jxRFCFKFi4Ulq+rr4YNG6C2tm2tE1WV4kQikUgkYYmq5QRAMYgvoMa964kfMBZFUfDWl2K2p+IszydhwPjwG+zaJf7qXrlSuAUGD6ZWq6VRa2SgeWDEz7dmzRoSEhKO+Z453Y3RaGTAgAGsWbMGT6DM/GEywDyAU2JO6XhhzhxhGVm0SGRaORxCjDQ1BeeoqqhZI5FIJBJJO46AODHia67DXVWIfcA4ALyNVS1/RevYczoRJ5WVopeO0wnnnAPAHt8ezJjpY4rMclJWVsbOnTsZMqT7+vEcT+Tl5VFXV8em9rVHukisIZYpsVOwGWxtL/TuLfrsvPOOqHMydKgYr6sLzvH5pOVEIpFIJGGJXkCsLvq5KAYDjqINANj7C3HidzXgb67DmtIPS0J6x7V+vyjoFWi4d+ONADRrzWSaMiMOhl23bh2qqtK3b9+I9jlesdlspKSksHr16ojrnjSoDWx0h0lPvuwyWLZMVIGdPVuM5ecHrzc2CvEpkUgkEkk7om45QTHQtHeDECL2VHTNj+py4Kkv69ylU1EhLCtNTeKv62nTAJgeN53Z8bMjei632813331HTk7OcdVtuLsZMmQIhYWFFLcvK99FqtQqvnJ9RZPW1PbCxRcLkbl4McyYIcY+/zx4vb5edCeWSCQSiaQdUft2DsSa6JpK0/6txPcdBYj0YdBRXQ3Y+owMvzhQTbSpCQYNAoMBXdfRdT3iirC7d++mvr6e3NzciPY53snKykJRFLZt2xbRPulGYfmq9LfrMJyZCWPHirYDycli7LPPgtelOJFIJBJJJ0RNnAQqvqruJtzVe7FlibgDv7OhdU5M2oDwiwsKxFnTYOpUAIr9xTzf8HzbzJDDoKysDLPZjM1mO/jkHoyiKCQlJbEv0D34MLEb7MQoMVSqlR0vnnOOECcBC9XGjcFuxVKcSCQSiaQTomc5MYnqre7aEtA14lrEieZ3t0xQiEnuJLC1pCT4+oILAOE+UHWVOCUuoufat28fCQkJEe3RU0hJSaGoqAhN0w57D0VRSDemU6VWdbw4c6Zw0e3aJd4bjcLNo2liPD1MvJFEIpFITniiJ06MwnLiqd2HYjS3FlrTVVEV1GxLxmCyhl9cG1ISffp0AByagwRjQkRuHV3XKSoqIjngZjjBSUlJobm5merq6oj2GWAeQKoxTCG7yZNFzNC6deL96NHCtVNVBV4vnKAByRKJRCI5MNETJ4qCYrLgrS8nNi0HxdgSg+L3AWC2p3W+uLnFdRMTI8rWIzJ1bEpkrpi6ujoaGxtPmIqwByMlJQWv10tZWVlE+4yNGcvk2MkdL8TEwEknCXcOwOmniwyewpaqslKcSCQSiSQMUU1XMcUk4GuqIiakPL2megEw2w8gELxiDmlBAdOsNXesp9FFSktL8Xg8pKSkRLRPT8FisWC1WiltX1q+i6i6SoPagKaHcQ9NnCh67YCIQXE4glV/pTiRSCQSSRiiKk4MMXb8zfXEpPbvcO2A4iRQuTTky2umbSYTYiZE9DxlZWVYLBZiYmIi2qcnkZiYGHFQbLG/mFcaX8GpOztenDgR9otGj0ybJmqbfPMNxMWBtGBJJBKJJAxRLdFptMSha35iUkLEiSJKlpvienW+MGA5GTCgdSjJGHlmR1NTkxQm7bDZbDQ0NBx84oH2aHG3NWvNxBvi214c2ZIuHhcHNpsQK1u3wrBhog+PRCKRSCTtiK7lpCWd2JqU1TqmtJj+jeYDiISA5aRFnGi6xhfNX1Dmjyw2wu/3n9CF18JhNBrx+XwR7WFWRGaWX/d3vJiXJ86BDKlJk6CsTIgTiUQikUjCEF1xYhbZOJbEjNYxze9puXYAcdIu5kRDY4t3Cw1qZH/h+3w+KU7aYTKZIhYnhpZ/RhphYk7i40UDR4sQqkycKCrHZmZGdE+JRCKR9Fyi+03dYrY3WIK1SVrL2h+oI63aMqfFBaOjt2wXmRtAVdWI9+hpKIqC3x/G4tGVPRA/07DiBILCBERTQIlEIpFIDkB0xUmLEPE761uHlBZXj64e4K/1QLfaJtGvpfXLL1w2SBcwm80RFRzriaiqitlsjmgPu8HOr5J+RT9Tv44XdR1cruD7nTsDN47onhKJRCLpuURVnARcON6GiuANW4qzaT535wsDQastTekO6DboAiaTSYqTdnSHOFEUBYNiCG+VChRcc7f8vlevFm6eoqKI7imRSCSSnkuUxYmIHfHU7Q8Otnx/qe4D9MixtlSO3bsXAINiYJx1HCnGyOqTSHHSEb/fH7E4qfRX8k7jOzRqjR0vBiwljY3CirJ6tUgRj7DhoEQikUh6LlEVJ6qnGYM5Bnf13taxQPl6f3Nd5wvjW9JRWywnANPippFpiiyIMjk5GafTia7rEe3Tk2hsbCQ9wh43DVoDZWoZZsKInA0bRHyR2y366WzYILoV5+eLwFiJRCKRSNoRXXHiasRk64W7OmjCVwwiENbnCNMoLkDAchJSubRWraXCX9HJgkMjKysLXddpaollOdHRdR2Hw0F2dnZE+zg1J0aMxChhMrDWrYPBg8XrpUvB54MzzhAxJxFWppVIJBJJzyS64sTdhCUhHVfVntYxxSj+uvY6DtBsLiBOamuFKwBY61rLKteqiJ6nd+/eWK3WiBvd9RScTieqqtI7wgyaZr2ZOENc+JiTtWthxAjxetky4dKZMkW8j7AyrUQikUh6JlETJ7qmomt+rEm98dTuQ/WI0uYBceI7kDiJa0k9VlUoKQHAZrDRrB0gTuUQsNlspKWlUVNTE9E+PYWamhqsVmvE4qRJawrflLG6GnbvFs3/AFasgJkzg20JWn63EolEIpGEEj1x0pIqbE3uC+g4y0VgpMEkxInqbsTvcoRfHNqYb+lSABINiTRoDeGrkHaBfv36UVtbG9EePYXq6mp69eqF3W6PaJ8x1jFMiA3T92j5cnGe3NKxuKhIiJPERBFXJMWJRCKRSMIQNXGi+VvESVImBnMMzrIWcRJSkM1d00k6aUhPHT7+GIB0UzoaGjVqZFaP7OxsHA6HDIoFamtr6d+/f8SF6dJN6eSYczpe+OwzUaY+o6VCsMUixImiQHq6sKxIJBKJRNKOKFpORBqxwRJLbEYuzaU7ADDFJbbMUHCHxKK0IRCjYDKJmAUgzZhGoiERt36A+iiHQHZ2NoqinPDWE7/fT0NDA31DOj8fDg1qA+tc63Br7X4vui7EycyZwaycqVMhYKVJTIQIGw5KJBKJpGcS1ZgTABQD8X1H0VS8EV3XMVrjQTFgTkjDUfRj+MX9W7oYJySIJnEuFybFxLWJ19Lf3D/8mkMkJyeH3r17szNQf+MEZe/evVitVkaPHh3RPvv9+1ntXo1BafdPaetWEfA6cybsaRGhs2YFrycmQn09EolEIpG0J2riJJAyjKZiHzAOv7MOd9UeFEXBFJeIJSEDx94f0MOVpLfZRG2MQGDs+++3XvLq3oiey2AwMHnyZEpLS/F6I9vreGbXrl2MHj2a5OTkiPapVCvpZeiFRbG0vfC//wkBcsYZ8MknYuyMM4LXk5Kk5UQikUgkYYleKrEixImua8T3GYliNOMo2gCAKa4XptgE/M56XJWF4dfb7cHuxC+8AMAu7y6erX8Wl+YKv+YQGTduHDabjd27d0e0z/FKVVUVbrebiRMnRrxXsa+YLFNW20Fdh//+Fy68ULjmPvpIjIfWU7HbRdVYiUQikUjaEXXLia6pGMwx2LJH4Ni7HhBBsrrqQzFZcez5PvwGffuKOicZGaLkuaaRbcpGR2evb29Ez2a32xk/fjwFBQUnZGDszp076dOnD7m5uRHtU6fWUafVMdA8sO2FTZtE2frLLxdxJ1UtBfd69QrOMZlAthKQSCQSSRiiJ06MorNwoFy9fcA4HMU/omt+LElZeBrKie87GsfeH8JvMHq0CKScMUOUPl+5EpvBRqYxk0JfJ9aWLjBhwgRUVaW8vDzivY4nPB4P5eXlTJ48GYMhsl+/ESNjrGPoZ27XjfiVVyAtDc46C/7zH+jdW7joYkIqyBqNsjOxRCKRSMISNXFiMMeAYkD1iMJpCQNPQfM001SyBWtSb7z1ZS2CZVNr9+I2nHaaOI8ZI87//CcAOeYcinxFEdc76d+/Pzk5OWzZsuWEsp5s374du93OuHHjIt4rwZjA9LjpmJWQnjoulxAn110neiN99JH4HbaPbTEYpOVEIpFIJGGJnuVEUTBa49C8ojJsXNYQzPGpNOxahTUpC131EZsxEN3voXnf1o4b/OQn4rx+PWRlwZdfgtfLQMtAFBTqtcgyPRRFYdasWTidTgoKCiLa63ihtraW3bt3M2PGDGy2MBVdu4BLc7HRvRGP1k5YvvOOyMK56SZ4+GFRUC85Gfr0aTvPaJTiRCKRSCRhiWpvHaPF1mo5URQDiXmnUr9rFZbkQG0NBVNcEo3hXDvZ2RAbC2vWwPXXi+DYV18lxZDC9UnXk2pMjfj5hgwZwrRp09i4cSPNzZGVxj/WUVWV1atXk5uby+mnnx7xftu821jpWolKiGtG1+H//T84+2xRAfbll+H220VKcWhhPfFAwnoikUgkEkk7ovrtYLAGxQlA0pBpeBvK0TxNGCyxuCsLhWuns6DYoUNFifNf/1r8pf3AAyiKgkWx4NE8HQt/HQbnnnsuvXv3Zs2aNT3avbNlyxYUReGSSy7BZDJFtJeu62z2bCbXkkucIVjxly+/hO++g7vvhsceE0Gvv/wl7N3bUZw4nSJlXCKRSCSSdkRVnJhi7fidwVoW9v5jMNmSqd2yjNj0QTgrdmPPORln2S78rjBppeecI/7C3rBBBFcWFcG6dai6ymuNr7HBsyHiZ4yNjeWiiy6iqampx7p3amtryc/PZ+bMmWSHpvMeJkX+Ihq0BkZb2xVwe/BBGDsWRo6EJ58UVpOEBCEww4mTuDgkEolEImlPVMWJOT4VX1OwF45iMJE88izqtgpx4irPJ2HAeEBvTTNuw/XXi/N//gMPPSRe33EHRsXIIMsgtni2oOqRZ3z0ZPdOqDtn+vTp3bLnJs8m0oxpZBozg4Nr18IXX8C998L994vMnHvugfx8ITDz8tpu0twsxYlEIpFIwhJdcWJPaSNOAFJGzcLvagBFwV1bgjHWjjW5L449YeJOcnNFsa5ly2DUKJFevGYNbN/OaOtonLqTXd5d3fKs5557LtnZ2Xz11Vc9pnKsrut8++23GI3GbnHnBBhpGcmU2CnBhoG6Dr/7HQwfLqwmL7wgREpSkqh5AuJ3F0pzs4gpkkgkEomkHdG3nDiq2sRyxKYPJDZjMJ6aEtA1mvdvI2HQBOp3rULzhxEFp50miniVlQkLCsC8eaQaUxlkHsQa95qI04pBuHeuu+467HY7X375JX5/5HseTXRdZ+3atTQ0NHDVVVd1izsnwEDLQAaYBwQHFi+Gr76Cf/1LxJtkZ8Ntt4lrmzaJ9ykpbTepqek4JpFIJBIJURcnKWg+d2s6cYCUUTNxFG/EGJNAU/FGUsf+DL+zjrodX3Xc5Pbbxfnf/4aJE0XNjDVrYMMGpsROIcmQFHGn4gAZGRnMmzcPs9nM8uXLj1uBous6P/zwAxUVFcyZM4eRI0d2y77l/nLec7yHUwv5ffr98Nvfir45Pp/oo/PEE8GCa5s2dbSaAFRWiuq/EolEIpG0I6rixJKQDoC3oaLNePLoWRjMVkxxCTQVbyI2tT/2nFOo+u7djhkzZ58tvujeflu8b+mzw5VXkmzoxWz7bOIN8d32zH369GHevHkYDAaWLVt23Ll4NE1jzZo1lJaWcvnllzN+/Phu2VfXdb5xfYNTcxKjhFR6ffpp2L4d/vY3uOMOUZ/mggsCi2DdOhEkG4rPJywn6end8mwSiUQi6VlEVZxYk0XhLXftvjbjphg7aeNn460vp7l0G5rfQ/opF+Es20nz/m1tN1EUkbVTXi6CK8ePF++3b4dXXwWgyFfEFs+WbnvunJwcbr75ZuLi4li6dClNTU3dtnc08fl8rFy5ktraWubOncukSZO6be9ifzH7/PuYEjsFg9Lyz6a4GP74R7j1Vnj3XeF+e/JJ8TsD8fuqrIRp09puVl0tzlKcSCQSiSQM0U0ljkvCGBOPp7akw7WMCZeAwYCu+mgq2UzCoIlYe2VT9f27HTe67z5xvvdecX7jDVFD47bbwOFgn38fXzm/olqt7rZn79OnDzfffDOpqaksWbKE/Pz8Y7oOSnl5OZ988gler5frrruOse2tFRHg1b186fySPqY+5JhzxKCuC1GSlCTE4uOPwz/+AQNDmgCuWiWEyuTJ7R9WnKVbRyKRSCRhiKo4URQFa3Jf3GHEiSkuidRxFwAKdTtWoCgG0k6+iLodK/A6qtpOHjMGMjNFnxZVFU3l/vIXkfExbx4TYyaSaEhkafNSNL37SqJnZGRwxx13MGPGDLZt28YXX3xxzKUa+3w+1q5dy6pVqxg+fDjz589n+PDh3XqPKn8Vft3PjLgZwQyd116Djz8WQbC33ipiTu64o+3ClSvhpJMgMbHt+J494pyT063PKZFIJJKeQdTrh8ck98HTzq0TIHPSz0FRqN++HF3XSRk9C4PJQvX6DztOnj8fPB7hNgBhRcnJgYULMS1bztm2s6lSq/jB3UmX48N9/pgYZs+ezS9/+UtsNhuffvrpMWNFCVhLGhoauPLKK7n++utJiUIGTLY5m+sSryPJmCQGdu8WVqtrrhGZOg0NotlfaDl6XRcZPO1dOgCFhaK8fWrkLQgkEolE0vOIujixJvfFXVMc9svcHJ9CwqCJqO4mnKU7MFptpIw+l+oNH3XsVDx/Plitrd2JMRjg00/F+aKLyGyOZZx1HNu827qlMFt7cnNzueuuu1qtKEuXLmX//v1HRaTU1tayatWqVmvJ3XffzeTJkzF0c68ar+7lG9c3eHUvJqWlRorPB1dcIVwyI0fCW2+JFO9+/dou3rFDlK0/99yOGxcUCPdPwAojkUgkEkkIURcnsRmDUV2N+Nq7alroc9atAJStfBmAtPGz8Tvrqdv2ZduJRiNceaUIsFy0SIwNGSKyRJqa4LzzmBQzkTkJczAqxqh8llArSlZWFt999x0ffvghW7duxePxHHyDCFBVlYKCApYsWcLy5csxGo3MnTs3atYSXddZ2ryUje6NbVOH588X7QR+9zv4/e/hzjvh8ss7brB4sciyCtdksLCwbWyKRCKRSCQhKHqU//T3OqrY8tSlDLz4fpKGhDHxA1ueuQJvQwVjfr0YgzmG3f/9HT5HFUOvfx5FCdFPDQ2QnCz6tAT64Og6nHoqrF4tvjAffBCH5uBH94+cGntqMLOkm9F1nX379rFu3Tq+//57HA4HmZmZDBkyhNTU1GBsRoT3cDgc5OfnU1xcjMlkYtSoUUycOJG8vDyMxuiIMIA1rjWsda/lfNv5DLIMEoMvvgg33AAPPCBSiAcPFiXrzeaOG5x5pqgAu3hxx2sDBsCllwZbEkgkEolEEkLUxYmu62x+4iJSx/6U3tPnhZ1Ttf4jSpY8QsakOWSfeTNNJZvY9frt9P/ZvaSMPKft5AsvhA8+gM8/FzVQABobxRdeXR189BHFM0ezqGkR46zjmBo3NZofD4Dm5mY2bNjA6tWr2bdvH5qmER8fT69evUhJSSElJYWEhIQDul10Xae5uZna2lqqq6upqamhqakJTdNITk5m0qRJnHLKKaQegTiN3d7dLG5ezOSYyUyInSAGv/1WWEGuvBK+/x4cDlEMLzOz4wZ1dSJN+PHHRbBsKI2NIkD2tddg7tyofxaJRCKRHH9EXZwA7H77HjAYGHzZP8Ne11QfGx8+D8VoYvSdH2AwWSh89880l+1gxM2vYzBbg5Orq0W8Q9++IqYhwPr1MGGCiEH54Qc25Pr52vU158SdwzDrsOh+wMDn0DSKioooLS1l//79FBUVUVFRgdfrRdd1YmNjMRqNKIqCwWBA13U0TUPTNNxuN6qqYrVaSU5Opl+/fvTp04esrCwGDhyIxWI5Ip8BhNWkTq1jlm2WsABt3w5Tp8KwYcJK8uOPQqwM6+Tn+uKLcOONsH8/ZGW1vfbtt8LStWGDyMKSSCQSiaQd3dMJ7iDEZuZRs/GTTq8bjGaS8qZSt305VRs+IuOUi+l9xk1s+881VH63kMwpVwYnp6bCnDnw5pui3slVV4nxcePgv/+FSy6ByZMZs3UrNakjWOZchkWxBF0TUcRgMJCTk0NOSIqsy+WirKyMsrIy6urq8Pl8+P1+/H4/RqMRk8mE2WwmPj6erKwsevfujd1u7xa3UFfx6T7MiplJsZPQdE08Q3GxqGPSu7fohbNkCSxd2rkwAVHN9/TTOwoTEOXsjcYDr5dIJBLJCc0RsZzU71pF4cI/MuLWt7EmhnEDAE0lm9n1+q9QzDGMuOV1LPY0Sj5/ippNnzLiFwsw25KCk5uboVcvsNlEGfRQd8kTT4ggzZQUtO3b+DxuPYPMg8i15Eb5Ux7f1Kv1vOt4l9PiTgv+rMrKRP0St1tYORYvhoULg+Xpw1FRIYTMs88K60l7br1VpBhv3RqVzyGRSCSS45+oZ+sAxPcZBUBT8aZO59j6jCQmpT9oKiVLHkfXdbKmzkVRFMpWvtJusg3uuQfq60XGSCh33AF33QU1NRjGn8ws18nkWnLRdZ0qf/iMoROdWrWWhY6FmBUzvU29xWBJiegI7XCIQmoffywsIgcSSKB1dQAAIABJREFUJgDvvNOa3h2W9evFfhKJRCKRdMIRESemuERi0nJoKtnY6RxFUUg7eTa6ptKQ/w3127/CFJdE5rRrqV7/QceeO/ffLyrFPvKI+As/lEceEcGWJSUwYgTs28dO707edrzNNk+7fU5wyv3lLHQsJEaJ4WL7xdgMNlHB9bTTwOuF4cOFxWTBArj44gNvpuvw/PNw/vnCBdQetxt++KFjOXuJRCKRSEI4IuIEIL7vSQe0nAAkjzwbg8mCNaUfJZ8/id/ZQPrJs4nLyqPok4fQVF9wsqKIGBNVhZ/+tO1GiiKaAt54o6iLMnIkeXt0hlmGsdS5lJXOld1a5v54Rdd1VjhXkGRICgqT774T4kFRRMbNt9+KtgGXXXbwDdeuhc2b4eabw19fv14UcZPiRCKRSCQH4MiJk36j8dSW4Guq6XSO0WojeeQ5qK5GNNXLvi+eQTGY6Hfeb3BXF1Gx+q22C844QwRr/vADvPRS22uKAs89B3ffDQ0NGMaOY8YmG6fFnsYGzwY+bPoQn+7jRETTNZq1ZhRF4fz487nIfhGxhljRWXj6dBHIajIJC8qXX4av8hqO554TKd3nnBP++urVovaJdOtIJBKJ5AAcMXFi7ye+kBxFPx5wXvqES/E7G0jKPZXazZ/RWPgdcRmDyZg8h/JvXsdVtbftgvfeg7g4+MUvRJpxKIoCDz8MTz0FHg/K1KmMfWUtF8RfQKwhFtORSVY6pnBqTj5s+pB3He+i6Ro2gw2TpojOz5dcAqecIiq4Go3CajJx4qFtXF8vLFk33tg2QDmU1avh5JPDF22TSCQSiaSFIyZOzPEpxKTl0Fi47oDzYlL6kjRkGs37txHfbyzFnz6C6nWSNfVqrEm92fvB/Wh+b3CBzSbiIbxemDEj/Ka33Sb68JhM8Itf0P/c65nJVBRFYa9vL+tc66LSj+dYI9+bzxuNb1ChVjA9brqonltRAbNmwV//KtJ/V64U57VrIS/v0Dd/7jnhYpsXvtAeug7ffANTpnTDJ5FIJBJJT+aIiROAxEGTaCxch36QeI+MyXPw1O2j19DT8DXXsf/L5zCYrAy48E+4a4op/er5tgsuuABmzxY1NP70p/Cbzpwp0lfHjhUl11NS4JFHqPVVs8a9hncc71CtVodf2wP4yvkVnzR/QrYpm7kJc+lv7g+ffSZShDdsEIHDX38Nf/kLvP8+JCQc+uYej0jhnjs3fMVYED/78vLOBaREIpFIJC0cUXGSMGgC/uY6XOX5B5xn6z2M+H5jqN70Kdln/oLq9R9Qu/UL4jIGk33GzVSu+x8NBWvbLnrnHVE59oEHYMWK8BsPHiyCMt9+W7gWfv1rxuVewNwv7fg1H281vsW3rm97TCyKpmu4NBcAA8wDONd2LufZziOu0SssHLNmCZHm9YraMStWCHHS1e7GCxaIjKlf/7rzOUuXiq7SU6PfTkAikUgkxzdHVJzE9xmFwRLXUViEIWvatbjKd2GO70WvEWdR/MlDuKqLSDvlYhIGTWTvhw/gaSgPLjCZRIyE0SgCOGs6D7zl8suFO+Pii6G0lF6XzOOqaf/mzDVQ6C3E0PJjOQL16aKCruutLpwvnF8AQpzkmXNR/vc/GDlSiLkhQ4RF48ILRUn6wxEOmiYa+P3sZzB0aOfzli0T+8fGHuankkgkEsmJwhEVJ4rRRELOyTQWrDnoXHv/MdhzTqZsxUv0nXkHloQM9rz3FzSfiwE/vRejJY497/4Zze8JLho4UDSUc7lEnx3tAO6juDhR7XTNGhg8GGXLVkacdztXnvsMxnXfU6fW8Wrjq2z1bMWv+7vh00cfXdcp8hXxX8d/+aT5ExIMCUyIaWnct2GDyMS5/HIRp+PzieOzz8TPLDHx8G76/vui984993Q+x+sVVpmzzjq8e0gkEonkhOKIihOAxMGTad6//YApxQF6T78Bd00RDfnfknPx3/A2lFP86aMYYxMYePHfcFXvpXjJY20tHHPmiDobhYUd65+EY+JE2LFDxEzExqKsXg2TJpEw5GTG/HcTXzg+56WGl/jG9Q2NamMEnzx6BGq2uHU3HzV9BMBF8Rdxof1C0nfXik7C48ZBfj4kJUFRkUix3ry587TfQ0FV4c9/Fnucemrn81avFm4jKU4kEolEcggY//rXv/71SN7QkphBxbp3sCZmYut9ADcAYLGn4qzYTd325WSdOhdrSl/KV76MwWim1/AzsCRkUL7yZRSDsTVVGYCf/AQ+/xyWL4fa2oPX6TAYhEi56y4YPx4qKjBs3ETmR6uZ8ORy+m2pY6+yn6reMeTY8vDpPjQ0jIqxG34ih4ema5SqpXzn+o6vnF8x2joaq8FKriWXk2NOJnFrkfg8t9wC+/aB3Q5VVcJy8t57orx8pCm9b70lsnQWLIDs7M7nPfWUqJny8MMivVsikUgkkgNwRBr/tWf3279B8/vIu+rxg851Ve1l+wvz6H36jWROnkPp1y9TvupVci78C72Gn0HZqtco+/ol+v/096SMmhlc6PdDbi7s3QuPPy567nQFt1uk1z7zjOgvA+gWC8rZZ1Ny7liWnRFDSr9RDDQPJMecI6qrHgE0XWOZcxl7fHtw627ilXhGWkcyNmYsFr8CixbB00+LzJuAq6axUWQ03XcfjB7dPQ/i84nS9sOHwwcfdD5P18XvYcYMIWQkEolEIjkIR0WcVP+4mOJPH2HUrxZijk8+6HzRnfgTRtzyBiZbMns/fID6HSvIu+px4noPp/jTh6nZtITBl/+LhJyTgwsbGkTF0vp6ePNNuOKKrj+s2y067N5/v9gvMxO9rAxF06gdN4ids4ZQcN5IBo29gMlxU3Brbuq0OlKNqZiVw7dMaLpGjVpDpVpJpVpJvVrPhfEXoigKS5qXYDfYGWgeSKYhA+X774X14q23RLn+9HTxmXVdpPf+5jcHDlY9HJ57TlhlfvzxwBVft24VAbiLF8N553XvM0gkEomkR3JUxInf2cCmJ2bTd+YdpI07SJdbwO9ysPXZK0kcPJkBP/09mt9L/oK7cdcUkTf3KWJ6ZVOw8A80lWwmb+6TxGUMDi4uKRFfzC6XyFC55JLDe+imJhGX8tBDwmowYwYYDOhffIHS1IR/QF9MP5vNvnPH8f64GnSzCbvBjk2xkWHKYHrcdAC2eLa02VZDw6f7aNaaiTfEMy5mHG7NzQsNL6AiCsP1MvQi3ZTOjLgZQvC43SLAdMkS+PBDEV9jswk3TX29CAy+4Qa49lpRir67qa8X1pDzzhM9jA7EP/4BDz4oXEoxMd3/LBKJRCLpcRwVcQKQ/9av0VX/Ibl2AKrWf0jJkkcZcs0z2LKH43c1suuNO1DdTeRd/RSm2AR2vXEnPkc1eVc9TkxKv+DiggIYNUp8qb/3nkidPVxqa0XsxBNPCDFwwQWivkplpehDU1KClphA4zlTKD9vIqVnj8bcK41pcdNQdZVn6p9BI5hFpKBgwoTNYKOvqS9n2s5E13V+9PxIujGdNGMqlqp60ZBvzRoRXPrtt+Kz2GwihqOpCZKTRSG6OXNEz6Gu1irpCnffLSwnu3ZB794HnjtxIvTrB//7X/SeRyKRSCQ9iqMmTmo2LaHo438y4ta3sSZ2UlU0BF1T2fHyzYDC0Ov+D8VgwtdUw87XfoWiKOTNfRIUA/lv3oXqdpB75WNtBcqOHaI6rMcDr78uMlgiobwcHntMlMXfvFmMDR4saod4vSIAdPduUXdl+nRRB2TYMLDb0S0WdKsFxWRG8XqF0HC5hPApK4PSUnHs3CncIg0NYn+rVQiipibxftgwYcH52c9Eyfkj0bNm1y5RTfa+++Deew88d+9eyMk5fJeaRCKRSE5Ijpo4Ub1ONj9xERmTryBr6tWHtKa5dAc7X/0l2WfcRMaknwPgqStl1+u3Y7DEknvloygGU+cCZdcukVLb3CyExZ13ds+Hqa4Wbpbly+H774VYcTrFNaMRLBYhQA7lR60oYr6iCJETqNVitQpxdfLJoobLjBkHt1p0N7ou0rO3bhW1TQ7mpvnnP0WsTkUFxMcfmWeUSCQSyXHPURMnAHs/epDmfZsZfsubKIeYYrpv2TNUrV/EsBteIia5DwDu2n3kL5iPYjCRe+WjGIwW8hfMDy9QSktFgGZdHfz2t+ILtLtRVeFK2rFDxLwUFwtLSlGRyPxxOIRAAiFejEZR4TYpSbiIUlKE8Bg0qO1hOspdlBcuhEsvFYXXDsU1Nnq0+FkvWBD9Z5NIJBJJj+GoihNH0Qby37yLvLlPEt/30FJcVa+L7S/Mw5KYSe4Vj7aKGk99GfkL5oOmCYFijiV/wXz8zXUMuvyf2HoPC25SXy9cE6WlIkD2nXdk/Y2DUVcn0oYnTxZxOwdj82YhTj76CM4/P/rPJ5FIJJIewxGvEBtKfL+TsCRmULNpySGvMVpi6Xfu3TQVbaB6w4et49akLPKuegLFZBaBsp4m8uY+iTWlL/lv3tW2n09SkshwGTtWWANGjgxaMiTh+d3vxM/oqacObf5bb4kg3Ugq0EokEonkhOSoihNFMZA8ahZ125ejeg5dHCTknEzq2J+xb9kzuGuKW8ctCenkXfUERms8u177Fe6aEnLnPIJ9wHgK3vk9NZs+DW5itcIPP4g6INu2QZ8+Io5C0pGvv4b//Ee4wA5UCTaApglXzqWXivgZiUQikUi6wFEVJwCpY89H83mo3bK0S+uyZ/wCS0I6ez98AF0NNuYzx6eQd9UTWFP6kb/gLhp2r2bgxfeRctJ5FH38L/Yvfw5dE/VDUBTR9O7xx0VGzKhRouCaJEhTE8ybJ9w5t9xyaGu+/FLE18ydG91nk0gkEkmP5KiLE4s9jaS8qVT9sIiuhL8YLbEMuOAPOCt2U7bylTbXTHGJ5F7xMEl509jz/l+pXLeQvrPmkz3jl1Ss+S8FC/+A6m4KLrjjDlE7JC4OfvEL0YvH5+umT3icc/fdIr35tdcOvXbK88+LNOcpU6L7bBKJRCLpkRx1cQKQOu4C3NV7aSrZ1KV1tqyhZE27lvLVC3AUb2xzzWCyMuCCP5A55Sr2f/ksJUseIW38hQy67EGaSzaz49Vf4qraG1wwaZKoXTJxoqi82rt3sH7JicrHHwt3zmOPiRouh0J1tcjmufFGGWQskUgkksPimBAn9gHjsCb3pfqHRV1emzn5CuL7jmLP+/fha6ppc01RDPQ+/Qb6n/9bajd/zq7Xbyc2LYch1/4fCgo7X7mF6o2fBC02cXGiCut990FNjegZM3/+odUn6WlUVcH114sOzzfeeOjrXntNiBLp0pFIJBLJYXJMiBNFUUgbdwF1O7/uIDAOutZgJOfCPwOwZ9H96Jq/w5yU0eeSd/VT+Jvr2PHijXgbqxhy3bP0Gn4mxYv/zd4PH0D1OIML/vxn2LhR9KV57DFRfv1ECpbVNBFnomnwwguHbgHRdTF/9mxITY3uM0okEomkx3JMiBOA5NEzMZgsVH3/fpfXmuNTyJn9F5pKNlG64qWwc2xZQxk67zliM3PZ/fZvqFz7Dv3Onc+AC/5EQ/437Hj5Jpzlu4ILRo2Cffvgtttg/35RF+Wmm8DfUfz0OB55RLh0XnkFMg/eWqCVb78VIq4rlhaJRCKRSNpxVIuwtWff0qep2fwZI297B6Mltsvry1e/Reny5xh4yQMk5Z0ado6uqZR/8zplq17Dlj2CARf8AV31s2fR33BVFpA5+Uoyp87FYAzpU7NpkygkVlICCQnCOnDppYf7MY9tVq0SfXp+8xvRTbgr/PznIj17587oNh6USCQSSY/mmPoGSZtwCaqnmZqNnx58chgyJv2cxLyp7P3wAVxVe8LOUQxGsqZdS95Vj+NrrGTHC9fjLNtJ3tVPkznlKspXv8mOl26iuWxHcNHo0aIE/b//LXrkXHYZjBkjStL3JKqq4PLLRZbN/fd3be2+faKg3e23S2EikUgkkog4piwnIOJGmvdvZcQv3kAxdL2XjOpxsvO129B8LoZe+3+Y4pI6net3OyhZ8hh1274kMfdU+s66C7+zjqKP/42rsoCMSZeTNfUaDOaQBncOhxAnS5aIWIyf/EQEgfbqdTgf99hBVeG882DDBvjxx643Fbz3Xnj6aeECs9uj84wSiUQiOSE45v7EzZh0Od6Gcup3rDys9UZrHIMu+wea103hu39GUzuvV2KKsZNz4Z8ZePH9NJduZ/t/rsFZtosh1zxD1mnXUbluIdueu4a6HV8HM3rsdvj0U1i/HoYOFbEZaWlwww3CqnK8cu+9sGyZqOzaVWHicomU43nzpDCRSCQSScQcc5YTgPw356N6mxly7bOH3K24PU37tpD/5l0kjziLfj+556D7+F0O9n3x/6jdtAT7gHH0nTUfEHEwjQVrsOecQt9zbicmpW/bhYsXiwDQsjJRqv2660SGT2zXY2aOGm+8IVJ/H30U7rqr6+tfeEEEC+fni+7JEolEIpFEwDEpThoL17H77XsY/POHSBh4ymHvU7P5M4o+epDep99I5pQrD/nexZ8+gq+plvQJl5J56lU4in5k39Kn8DZWkjb2p2SeejXm+OTgIl2HV1+Fe+4RcRsmkwgOffppSEw87Oc/IqxbB6edBnPmwEsvdb1wmq6LmJycHPjww4PPl0gkEonkIByT4kTXdXa+8gsUo4m8uU8dtvUEoPTrlylf9Sr9z/8tKaPPPaQ1ms9N+eq3qFjzFqaYBLJn3EJi3lSqvn+PitUL0FU/6RMuI2PS5RittraLFywQmS6lpSIw9Kyz4MknYciQw/4MUaO0FE4+GQYMgOXLRTPErvL55zBzpnAJzZjR7Y8okUgkkhOPY1KcADTsXk3BO79n8JxHSMgZf9j76LpOyaePUr1xMYMufYDEwZMPea2nvoz9X/wf9Tu/xpY9nN6n30hs+mAqVi+g8vt3MZhjyDx1Lmljf9o2aBbgo4/g17+GXS21U/LyRAbMpZceG2Xdm5tFynB5OXz3XdfqmYRyxhkiSPi7746NzyWRSCSS455jVpzous7Ol2/GYI4h96onIrKe6Jqfwvf+SmPhd+Rd+Si27BFdWt+45wdKlz+Hs3wX9pxTyD79BkzxyZStfJWajZ9gik0gfcKlpI27AGNMfNvFO3aI9NovvhAVV+12ke3z978fviCIFL8fLrwQVqyAr7+GsWMPb581a0S34oUL4eKLu/cZJRKJRHLCcsyKE4D6Xd9QuPAP5F75GPb+h/kF2oLm87D77d/gqt5L3lVPEps2oEvrdV2nfufXlK54EU9NMUlDT6f39HkoBhMVa96iZtMSDCYLaeNnk3bKJZht7VKYm5rgT38SsSl1dWIsN1f07rnxRjAaI/p8XfggcPPN8PLLIpj3nHMOf68LLxTia9s2WdtEIpFIJN3GMS1OdF1nx0s3YrTGk3fV4xHv53c52PXGHfid9eRd9UTHzJtDeSbNT83mzylb+Qq+xiqShk4nc8oVmGzJVK57h+r1H6JrKr1GzCD95IuIy8zruMnXXwuh8s03or6IySS6Id95p7BARNM98ve/i3u//DJce+3h77Ntmyjp/+KLIoVYIpFIJJJu4pgWJwD1O1dS+O6fyL3iUewDxkW8n6+5jvw37kT1NpN31ZNYe3WxpkcLmt9DzabPqFjzNt76Uuw5p5A55QpiUnOo2biYqvUf4GusxJY9grSTLyJp6GltS+IDeDwiWPb550UaLoDZLFwlt98uGuh1p0XilVdEqvP998Mf/xjZXtdcA19+CQUFIoVaIpFIJJJu4pgXJ4HMHRSFIdc8E1HsSQBfUw273rgDXfWRe9UTWBMPP/ZD1/zUbV9BxeoFuCoLiMsaStrJs0kaMg3Hnh+o/P49moo2YLIlkzJ6JimjZhGT2r/jRo2NouHe668Hy+KbTDBsmCgpf+utkNR5tduD8sEHwipz/fXw7LORWWeKimDwYHjoIWHtkUgkEomkGznmxQmAY+968hfMJ+eiv9Fr6Gndsqe3sZJdb4gv1ryrHseSkB7Rfrqu01i4jsp1C3Hs+Q5TbCIpY84jdezP0Hxuqn74gLpty1DdTdiyh5M8aha9hp+BKSZMRdX6emFReecdEdOhqmI8IwPOPFO4Y84669CtKkuXisaFF1wgUp1NXW8L0Iabb4b33oO9e8FmO+h0iUQikUi6wnEhTgDy3/oN3sYKht/40mH13AmHp6Gc/NfvQDGayL3iUSyJGd2yr7umhKr1i6jdtATV6yJx8CRSx/6U+H4n0ViwjppNS2gsXIdiNJE4aBJJw04ncfAkjJa4jptpGrz/vigPv3q1SNsFIUz69xfpwNddB1OnhreGrFolgl7PPFMIikhdMHv2iLToBx8UqdISiUQikXQzx404cZbvYsdLN9HvJ/eQetJ53bavp76M/DfvAl1n8BWPEJPcp9v2Vr0u6rYuo+qHRbgqCzDZepE84mySR8/EHJdE7Zal1G1fjrNsJ4rJIoTK0OkkDp6M0RpGqIDo/vvCC6Knz7Ztoq8NiGyfrCwYP140I7zkEigsFKJk/HiRmdMdJfWvv17sVVgIcZ08o0QikUgkEXDciBOAPe/fR9O+LYy45Q0M5sOoZtoJ3sZK8hfcjeZ1MnjOI11OMz4Yuq7jqthNzeYl1G39Ar+zntj0QSSPOoekodNB16nfsYK6HStwlm5HMZqx9x9LwqBJJAyacGDBtGuXKDv/xRewc2fQshLKFVcIt85550VWTn/3btHs8OGHZayJRCKRSKLGcSVO3LX72Pbc1WSfcRMZk37erXv7mmrJf+vX+JtqGDznYeIyc7t1/wC66qehYC21mz+jYfdqdNVHXNZQkoZOF/E0BiP1O1fSuHsNTcUb0TU/1uQ+JAyaSOKgicT3PenAwqyxUYiH++8X743GYMwKQEyM6Do8apTICjrrLDjppEOLQ7nmGhG/UlBwfDU2lEgkEslxxXElTgCKlzxG3bYvGHHLG5jiIsheCYPf1cjut+/BU7ePQZf9i/g+Xask21VUTzMNu9dQv2MFDQVr0f0eYjNySRoyjYRBE7Am96Gp6Ecad6+loWANPkcVitGMLXs48f3GYO8/Blv2cAymELGycaPocdO3r+h3k5ICJSXCDfTVV/Djj8I15HS2fZi4OBFwO2iQqBg7ZQpMmybWg7DQDBsGTzwBt90W1Z+LRCKRSE5sjjtx4muuZ+uzV5I84mz6zep+14Lqaabgnd/TXLaTgbP/QmLulG6/R9j7el00FqylbscKGgvWonmdmOJ6kTDwFBIGTcQ+YDz+5loce9fjKP6RpuKNqG5Hq1ix9RlFQoOJ+HnzUXIGioZ8ycmd37C5GVauFAXhNmwQLpvyclHJNhSDQQiXwPiVVwrxMm6cOEeS3iyRSCQSSRiOO3ECULH2v+z/8jmGXf8CsekDu31/zedhzwd/pyH/G/qdO5/UMed3+z0OhK76adq3hcbCtTQWrMNVWQCKAVvvocT3H4e930nEZQ/HW19GU9GPOIp/RFu9ipxnvsGTEkvRnWcTO3gMtt7DiOs9jNj0gRgth+iGUVXYulUIlw0bRHG4jRuhoSH8fEUR3YztdiGGMjOF1WbQINGJedgwGDhQXJeNASUSiURyCByX4kRTfWz/z7VYkrIY/POHuqUwW3t0TaXk86eoXr+IrGnXkTn16qjc51DwOqpoLFhHY+F3NBVvxO+sA8VAXNYQ7P3GkFhnwnb93eh5g2l46s80O0po3r8NZ/kudNUHKFiTs4lNH0Rs+iDiMgYTmzEYsz3t0D7TeecJy8rWrSLg9ocfxLFzJxQXC4tLTY2Id3G7Rf+ecJjNQsjYbJCQIFxGqalC0GRliViYrCzIzoY+faBXLzFfIpFIJCcUx6U4AajftYrChX9k0GUPkjh4clTuoes6Fd++SemKF0gd81P6zrqj22qsRPJMnppiHMUbRcDssqX0f/5bXJk29s3/CTGDRmPLGoat91AsKX3x1u7HVbkbZ8VuXBUFuCoLUN0io8cYYycmtT8xKf2ISemHNbmvOCdloRhbPufy5SId+X//E+nJh0JDgxAu27aJ4Nl9+4SAqa4WTQ8bG4VbyeNpG6zbGSZTUNjExgpxY7NBfHzwsNuFiylwJCeLIzUV0tNFlpLNJuq8SAuORCKRHNMct+JE13V2L7gbr6OK4Te+HPwyjQI1mz6laPFDJA6exIAL/hi+WNrRYNEi9MsvRzt1EvX/uJPm+r04S7fjrCwATUUxmonNGIwtayixGYOJTR9ETGp/VLejRazsxl1TjKe2BHdNMZq3pWaKwYi1VzYxvfrQ909vopgtNL/7EpZevbEmZmK0dmNVWFWF2lohYIqKhIipqICqKnHU1Qmx09go4l6cTvB6xaGqokhdV/8JK4qIpTEYRDaT0SgEUEAEBQ6LRQgiq1VkOcXEtH0fej30CJ0bGxt8Hxsrjri44GuLpe09TaYj16FaIpFIjlGOW3EC4KwsYMeLN9Jnxi9Jn3CIf9UfJg0Fa9nz/n1Yk7IYdOk/uq2a7GHz8stwww3CmvH6620qv2p+D66K3TSX7qC5dDvOsp14avcBOq0unrSBxKYPJCZtILFpAzAnZqK6GvHUFOOuEWLF/MkyMp/4kPybx+PoF9+6vzE2AUtiJtbETCwJ6ZjtqeKIT8EcL14fcoxLd6CqwhJTXy+sM1VVws1UWyvETX29EDgBceN0iuJ1Ho84AmLH6wWfD/z+4BEQQIHjaKAoQWtP4HW49wZDx9eh58DR2fUD7QXh1wTGO7t3Z/cxGjvOD4wd7Fnaf/7Ac4T7mQTGAus6+xmG7hFu7aFc62zegY7AHnffHdm/EYmkh3FcixOA4k8eoW77lwy/+XXM8QfITukGXJWFFPzvXjS/h0GXPIAte3hU79cpjz4q/jO76SZ45plD+ktb87lxVe/FVVmIu7IQV2UhrsoC/K6WQFfFgDUpS7h2kvtgTcgi5fI7YchQ+HQJqrP+h2DgAAAYK0lEQVQeT3053oYyvPXleBrK8NaX4XVU43NUo3nbpiYbrDYs8amY7SmYbMmY45IwtR6JLYd4b4yJR1G6sftytFHVoJDxeoNix+Vq+9rtFkdACIUKIrdbrPV4xD6hh6oGj4BACndoWsfXoefODl0/8AEHft2Vc/vX4d5L5M9EImnHcS9O/M56tj53NYmDJzPgp7+P+v18zXUUvvsnnGU76X/+70geMSPq92xF1+FPf4IHHoDf/16cI4if0HUdf3Nti2tnH+7aEnGuKcH+6Tr6frSL7beNx5PdC0tiBpaEDCxJmeKcmIklMQNrYiZmewqaz4uvqQafoxpfUzW+phq8jip8jmr8zXX4nPWozgb8rkaEBScExSDESmwixhg7xph4TDHxGK02jNZ4jDEtR/vX1niMllgUk+WoBStLuoFQYRTqpgsnkA5FPB3KvMB9QsVawDIWaiULJ+baX2s/53D2OPPM7vt5SiQ9gONenABUb/iY4k8fJu+qJ4nvNzrq99P8Xoo/eZjaLZ+TOfUasqZdG/0vR58PfvlL0VfnoYei23TP4UAfPBjtzNNoun8+ntr9eBsr8DZU4G0ox9tQEbS4ACgGLPY0TPHJLa6dwNH2faBont/lwO+sDzkaxNnVgOppRnU3icMjzn5PE5qnufPnVQwYLLEYzbEYLLFtX5tjMFrajZtjUEwWDCYLBpO19bXS8j742tLm9dEOhpZIJJIThR4hTnRdY+ert6L53Ayb93xUg2OD99SpWL2A0q+eJ2nodPqf/9voBco6HHDZZaLi64svwtVXR+c+Ae69Fx57TGTc9OsXdorqdeFtrGwVK97GSvxNNcJ60lSDr6kWv7OeNlYSxYAptsWlE5uAMeR1wHISeG2MTWyxnsSjGE3omorqcbYKllbx4nOhecWhel1oPrd472t53zKmtowF3ms+T9tnOxQMRiFYjBYUkxnFaEYxmFCMpjZng9GMYjS2vW40oxjajwXXGYxmMBhRFCOKwQCKAcVgQDEYoWVMUYxgMKAoLeMGY/B1y3wxN3QPMQeDMeR1y16KQYjq1rM4FCUQ12FAQQm+ltYpiURyhOgR4gRauha/fAvZZ95CxsTLjth963euZO9H/8CSkMHAS/7erV2NASgtFV2GCwvhvfdEafposmePKJx2zz3wt79FtJWu+vE564JipakGX3MdqqsRv6tBWExcwtXjdzZ0iFsJoJisLS4eW4tLxxZyhLyPsWFosYwYzDEYLDEYzLEYQ94rRuEC0nUdNBXN70Xze9D93gO+bh1Tveg+jxjT/OJQVXTV1/La3+7sQ1dVtE6vh7zW/OiaBpqKrmugH6UA3AMSRsAo7QRMS/xQYI6IJwq3jpa5oeMhrwkGrCot59Axceo4Fnjfek2h3V4dx8QzdByjVY8p7fYLzFXairbWOUrItOBYcKjt2JFwSUskxxM9RpwAlHz2ODWbP2P4za9hsacdsfu6qosoXPhHfM21DPjZH0jqrpL3W7fCuecKv/Snn4pmfdHm0kvh22+F1SQ+/uDzuxHN70V1O1rcPA3CMuJpQnU3C3ePp7llLOS9O/he93sOfhPF0CpejC3iRbxvce8YQ9w4RnPQrWM0h1xvGTeGuH0C40YzBCwiBmPQOmIwCWtKqKXlIJYIXddBV4Vg0TV0LfBaFa91EdcQfK22fa1rIWIndK1YExA/QgjprWcIea1roLebIwbazNGhZW7ouN5unZijt+6ro6O3WxeYE5ivt9wPMVcMdgi41cOMic/RcSy4puNY6889cJ+Wewfe63rHsdA9xFK93b60e77A+uDzDbn6qQP9U5BITjh6lDjxux1se/Zq7P3HkDP7L0f03qqnmb0fPUjDrlUtcSjXRJaBsnw5zJ4N/fvD4sWiYmq0WbECTj8dXnsN5s6N/v26GV31CzePz43mdbe4bwJunbbvQ6+rLW4eXQ1aSHTV12I9Ea/bj3eLVUMxtAgVY+cCpo3Aae++CVgmguOtLpxW901bdxDt3UPh5gfuEzLW1vJBO5dPyLVWq0EYN1HAyhDGuhK0nrTfu72FJfSeIfNCr4mdw1gqOo63XERpYzEh5HWoFab1Qpv7BC+1u39gqL01pvVycG+DOebA/1YkkhOMHiVOAGo2f0bRRw8yeM7DJOScfETvresaFd8uoHTFiyQMnsiAn/0BU4y96xu98QbMmyeEwsKFotR7tFFVOOUUUQhs9epgzQZJB1pdQmHEjHDjhLh7tFA3jtrOpRPmeqiLR1WDazR/i2VEa2MZIWAdCVgbNC3EStJ2bqgFpivz21s+JN3PuHu/OtqPIJEcU/Q4caLrOvlv3onPUcWwG17GYD7yvVkaC9exZ9H9mGITyJn9V+Iycw9toaaJVOF//AOuuw6ee06IhSPBiy+Kom7ffguTo9MOQNIzCLo2Qlw+ra6eoEujrZsmZA1BN1Ebl0yryyfEJaO3W9PGpUTLtcDcgIAKcQG1c68E3S8h463zCO4VZrzV7dPJeHDfjuPBte3GW54hecRZnf68JZITkR4nTgDcNcVsf+F60idcQvYZNx+VZ/DUlVL4/l9xV+2hz1m3kTruZweOMWhqElk4ixbBv/4lUoWPVHZEYyPk5Ylg2zffPDL3lEgkEomkE3qk7T4mpR+ZU6+mYs1/cZbnH5VnsPbqzZCrnyZ1zPmUfPYYexb9DbWzWh3FxTB1KixdCh98AL/5zZETJiAsNY2N8M9/Hrl7SiQSiUTSCT3ScgKgqT52vHQzBqOJIdc+c1QLaNVt/4qiTx7CHJfIkCw/JmdJ8KLDAd8UwsoM+PDDI5ORE0pBAQwfLirO/vWvR/beEolEIpGEoceKE4Dm/dvY+eqtZM+4hYyJlx/VZ/HU7WfP+/fRt/YdbEpD24u1drizANKOXPozIHzf558PW7bAtm1g68ZuwxKJRCKRHCY90q0TwJY9nLRTLqJ0xUt46kqP6rNYe2WTd/XTmOJ6dbw4bPiRFyYAH30En3wCjz8uhYlEIpFIjhl6tDgB6D39esxxSRQveZSjbSQymCxYkzI7XmjeDQUvg3PfkXsYpxNuvx1mzYILLzxy95VIJBKJ5CD0eHFitMTR99z5OPZ8T+2WpUf7ccKjumHt9bCoL3w8HL6/HYoXgqsievf85z+hrAyefPLIBt9KJBKJRHIQTog2q4mDJtJrxFnsW/Y0CTknY45PPtqP1JakUXDxx1D+BZR/DqWLYVdLOWt7HqSfBmnTxNnWP3IxsXu3SFe+5x7IPcQaLBKJRCKRHCF6dEBsKL7merY/fy22PqMYePHfjl6H1QWToWxN27GsSXDF6rZjzv1QuRKqvhbnhi1iPK4PpJ4KKadAygRIHgemLsSL6LpoJLhtmzjiotRJWSKRSCSSw+SEsJwAmG1J9J11F3ve+wt1274keUSUu/tGSlw2DPi5OAA8NVD1DVR+DTVrYNOHoLpEz5GE4UKopJwijsRRYLSE3/eDD0QTwUWLpDCRSCQSyTHJCWM5CbDn/fto3PsDw298GXN8ypF/gEO1nBwMzQ8N26BmHdR+BzXfQf0m0FUwWCFpJCSNbjlGibNmg2HDYORI+PhjGWsikUgkkmOSE06c+J31bPvPddj6DGfgxX8/8u6d7hIn4fC7oO5HIVbqNgqx0rBFBNwCvG+DD5zwv+tg5KmQMBQShoD1KIg0iUQikUg64YRx6wQwxSXR79z5FL77J+q2LiN55NlH+5G6D1MspE0WRwBNhabdsP4z+GA+zMkFlsPal2ltfGZNEULFPiQoWBKGgG0AGI9840SJRPL/27v74DjKw47jv927k05vpxfbwi8SkoxjUvPSYJgMMTBMQoeXxgmk085kSCYkkCFQZtohDnGoW5OhvCQUkkwztDSyM0AySSbT6fDiwvBSKKQJdAoh6QA2xkWybMe2bGRZryfdy/aPZ0/3opN0ku5uV7rvZ+aZ59ndZ3ef0z/+eZ99ASpbxYUTSWo6+zI1b7pCh57/RzV0bvZmeqdc7IB54ufuW6X2Dumf3zL3msTHpeH3paF90tB70vB70uDvpb5fSvERd2fL3PtS1yXVd0n167PbNWvMPS8AABRRRYYTSWq/8q/0bveX1ffsQ1r/5/d69/ROOTz+uPTyy9Jzz6Vvgg3WSM3nm5LJcaTxoyasjHwgjfSYMrRfOvqcFM1494pdLdW2myeIateZuiajXdsmVbeagAQAQIEqNpwEaxt15jXb9MG//q0G3n5eK867yushlcbJk9K2bdL110tXXjl3f8uSateacsYnp2+Pj0ojvdKoG1rG+sybbUf7pBO/kcaPSMnJjOMFpJq15ipL+Ay3tJq6ulWqOSPdrm7hSgwAoHLDiSQ1bbzUvJzthR+qoXOzqho8+L5NqX3jG1IyKX3/+8U5XrBOajrHlHwcR5o4aQLL2GETVsYOSePHpGi/uVE3etyU5ET2vlZQCq9yg8oKqarFBJaqlpx2c/ZyoIYnjwBgGanocCKZ6Z293W/p4J4HtOHz35W1nP7n/vLL0mOPSd3dUmtrec5pWSZghFdJLRfM3M9xpPiweUX/RL8bWDLqyQFpYkAa7U23Y4P5j2VXu4GlUQpGpFCqNGS03ZJve7BOCtRKwVrJDpXkzwIAKFzFh5NgTUQdW7frwC++qRNvPqHWi/7M6yEVRzQqfe1r0qWXSjfe6PVoprOsdEhQga/QTyZMQJkYMIElFVpS7diwFBtKl4l+t51af9q8B2Y2digdVAJ1bl1rAsxsbbtaCoTdOqdth93aXZ/ZtqvNObnyAwBTKj6cSFJk/ce16sLrdOSlRxTpvFDhlR1eD2nx7r9f6u01b4K1l8nVIDtgpnsW+l4WxzHvfEmFl3iqHpMSY6aOj87enjgpjR5Mr0+Mmjo5kX6fzELkhhk7lC5WaOZlK1h439z+VtDcEzRbsQvok9V/pm35jmMTygDkRThxrfvULRrqeVO9T92rjTc8LDuwhC/v79tnwsn27dKmTV6Pxj8syzylFKwxN+IWm+NIyZiUjEqJiXRgyWzPuC5nezJmihNLt3OXExOSMzp3v6zleLrtF5YtyXZryw0tGe3UNssqrF++bVPb5zhGIf1kudvdYDXVTq1X/n5Zyzn7bvlJSf60wFJFOHHZobA6r92h9x67Tcf+63Gtvfwmr4e0MMmkmc7p6JB27PB6NJXFssw3jQJVkt+zreNITtJMc81a4qZOztVvjpKM518vdxypeqa2Ztk2td1ZXL9p55vteI6pU+2pZU3fnvp7Z/ZP9ctaBpBCOMlQt+ajWnPpDTr6q0cVOeti1bfN8ESKnz36qPTqq9KLL0rhsNejgV9ZlplaEe+gAeA/y+RmhOJZveV61a39qA4+fa8Sk2NeD2d++vvNo8Nf+pJ0hc+/ugwAwAwIJzksO6iOz/yNYiMDOvziP3k9nPm5/XbzP+IHH/R6JAAALBjhJI9wS5va/uQ2ffi7PRp8/zdeD6cwe/ZIP/uZ9IMfSKuW4cvkAAAVg3AygxUf26rIhk+o79//QbHRU14PZ3ZDQ9Itt0hXXy198YtejwYAgEUhnMzAsix1/OkdkpNU3zMPyvHzHfXbt0unT0uPPMJ7IwAASx7hZBah+had+elv6vT7v9bJ3z7l9XDye+UVE0q+8x3z+DAAAEsc4WQOTRsv0crN1+rwfzys8RM9Xg8n2/i49NWvSpdcIt16q9ejAQCgKAgnBWi74i9V3bRWPU/8vZLxibl3KJdvf1s6dEjavXv5vKIeAFDx+BetAHaoWl3X7dTEwCEdeelfvB6O8cYb5pHhu+6Szj7b69EAAFA0hJMC1bSu17orbtWJN/5Np71+vDgWk266STr/fPPSNQAAlhHCyTysuvBzimz4hA7u+a5iIx96N5AHHpDeecdM54T8/hEXAADmh3AyD5ZlqePT22UFgup96j45TrL8g9i7V7r7bumOO6TNm8t/fgAASoxwMk+huiZ1fOZODfe+qf7//mV5T55ImOmczk5p587ynhsAgDIhnCxApOsitV78eR35z26NHt1XvhM//LD02mvSrl1STU35zgsAQBkRThZo7eU3qbb1LPU+eU95vl7c2yvdead0223SZZeV/nwAAHiEcLJAdiCkzut2KjZ8Uoef/2FpT+Y40s03SytWSPffX9pzAQDgMcLJIoRb2tR+1V/rw/99VgPvvlS6E+3aJb3wgvSjH0kNDaU7DwAAPkA4WaSW865W86ZPqe/ZhzQxeLT4J+jrk7Ztk2680Xx1GACAZY5wskiWZan96tsVDDeo54m75STixTu445hv5zQ2St/7XvGOCwCAjxFOiiAYblDX5+7S2LH9OvLKruIdOHM6p7GxeMcFAMDHCCdFUrf2j7Tukzer//Vf6PSB1xd/wMzpnGuuWfzxAABYIggnRdT68b9QZMPF6n36Pk0O9S/8QKnpnEhEeuih4g0QAIAlgHBSRJZlq3Prt2QHq9T75D1ykgu8/2T3bjOd090tNTUVd5AAAPgc4aTIgrVN6rp2p0YOv62jv3p8/gfo65O+/nWmcwAAFYtwUgL1Z56vNZd9Wcd+/RMN9/628B2ZzgEAgHBSKqu3fEENnReo58l7FBsZKGwnpnMAACCclIplB9T52R2S46j36fvkOMnZd0hN53zlK0znAAAqGuGkhEL1K9R57Q4N97yp46/9fPbOqekcXrYGAKhwQa8HsNxFui7S6i1f0B9e2a369vNUn69Tf7/0wuvSM88wnQMAqHiW4ziO14NY7pxkXPt/ersmTx/Tuc0HZR3/n+wOh2xp6Abpxz/2ZoAAAPgI0zplYNlBdV33d0rGJzRx6sj0DoEA0zkAALgIJ2VSFWlVx9ZvKR4dnr7xrLOYzgEAwEU4KaOmj2xRqH5lng0EEwAAUggnZVYVafV6CAAA+BpP65SZZVnTVw68Ib10ldT8Man5AlM3fESyA+UfIAAAHiOc+EH4DClQLR38ubT3AbMuUCs1/7EJKk3nSY3nmFK9wtuxAgBQYoSTclt5bv51l3ebdvSkNPh76dRb0qnfSf2vSge6Jcf9wnF4tQkpTeemA0vjOVJVY/l+AwAAJcR7TpaCxKQ0vF86/Y4pg2+beuSAlHotfm2bFNkkRc6WGjZKkY2mXdsuWdxaBABYOggnS1kiKg3tkwbd0DL0rjT8vjR8QEpOmj6BsFS/ITu0NGw097RUr5Ty3QMDAICHCCfLUTIhjR2UhvZLQ++Zqy7DbnvsULpfsE6q65Lqu6T69RntLtMO5X3ZPgAAJUU4qTTxMXN1ZeT/pJEet3wgjfZIo73makxK9ap0UKnvkurOlGrapLp2M11U1cKVFwBA0RFOkOYkpehxE1ZSwWW0J708/of0jbmSFKgx97rUtpmwUtue0W6TataZp4sIMACAeSCcoHDJhAkvY4fN9FC+evyI5CTS+9gh86h0eLUpNal6TUbbrYO13v02AIBvEE5QXFMB5pAJKtHj0vhRafyYFD2WrqPHpGQse99ggxtUWs3NunOVUCNXZQBgGSKcwBuOI00OTA8t40eliZM55YQUG5p+DCtopo2mAssKqarZlFCTVNU0vV3VZJaDNeX/zQCAghBOsDQkJqXJD6cHl2jOcmxQmjwlTbp15j0ymezq/OEl1GCu4IQapFAk3Z5a15C9LhDm6g0AFBnhBMuX40iJMTeouGElltGeHJweZuLDUmzYrYek+Ojs57ACMwSXOvMJgmCtW2csT63LU+fuZ/MSZwCVh3ACzMZJSvERE1imQkueOnddfMwEo3x1fHTmKzq57JAJKYGwKXZ1dh2oluxwup21bR797ZBkV5naCkmBKlOn1k1tC3ClCEDJEU4ALyRjsweYrHrUvH8mMSElo+l2Iiolc+qsdqp/qk80/bmDxcgNLHYqyOQJM3kDT8hcEbKCbtgJustztFP97QLa0/bN1zfgFtvUstNtyzbLdub6fP0IakApEE6ASpKM5w8zyZhbJrNrJ8+6qTpnnRMz9wY5Mxwr85hOwozFibt1YnrbiWf3y237RcHhJmP9VChy21v3evsbAJ9hQhuoJHZQsuslLfFPEziOuQpUSIjJbE8FoNRyMqNOSspZdhLuugL65VtfcD8AmbhyAgAAfMX2egAAAACZCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBXCCcAAMBX/h+IKsdxTq4kCwAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 17 graphics primitives" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph1 = graph + polygon([(15,-10), (15,10), (25,10), (25,-10)], color='white', \n", " zorder=100, axes=False)\n", "graph1" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "graph1 += circle((25, 0), b1_out, color=color1, fill=True, zorder=101)\n", "graph1 += circle((25, 0), b1_in, color='white', fill=True, thickness=0.1, zorder=102)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "graph1 += circle((25, 0), b2_out, color=color2, fill=True, zorder=103)\n", "graph1 += circle((25, 0), b2_in, color='white', fill=True, thickness=0.1, zorder=104)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 22 graphics primitives" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph1 += circle((25, 0), b3_out, color=color3, zorder=105)\n", "graph1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Slight reajustment to take into account that the null geodesics are cut at finite $r$:" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "a = 0.995\n", "b1_in *= a\n", "b1_out *= a\n", "b2_in *= a\n", "b2_out *= a\n", "b3_in *= a\n", "b3_out *= a" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 32 graphics primitives" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph1 += line([(15, b1_out), (25, b1_out)], linestyle='dashed', \n", " color=color1, zorder=106)\n", "graph1 += line([(15, b1_in), (25, b1_in)], linestyle='dashed', \n", " color=color1, zorder=107)\n", "graph1 += line([(15, b2_out), (25, b2_out)], linestyle='dashed', \n", " color=color2, zorder=108)\n", "graph1 += line([(15, b2_in), (25, b2_in)], linestyle='dashed', \n", " color=color2, zorder=109)\n", "graph1 += line([(15, b3_out), (25, b3_out)], linestyle='dashed', \n", " color=color3, zorder=110)\n", "graph1 += line([(15, -b1_out), (25, -b1_out)], linestyle='dashed', \n", " color=color1, zorder=106)\n", "graph1 += line([(15, -b1_in), (25, -b1_in)], linestyle='dashed', \n", " color=color1, zorder=107)\n", "graph1 += line([(15, -b2_out), (25, -b2_out)], linestyle='dashed', \n", " color=color2, zorder=108)\n", "graph1 += line([(15, -b2_in), (25, -b2_in)], linestyle='dashed', \n", " color=color2, zorder=109)\n", "graph1 += line([(15, -b3_out), (25, -b3_out)], linestyle='dashed', \n", " color=color3, zorder=110)\n", "graph1" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "graph1.save(\"gis_disk_image.pdf\")" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.1.beta8", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }