{ "cells": [ { "cell_type": "markdown", "id": "66419b7d", "metadata": {}, "source": [ "We are looking at the problem Max $k$XOR, where each variable is involved in $D+1$ clauses and has no overlapping constraints.\n", "\n", "This is code comparing one-local algorithms: Hirvonen's threshold algorithm and Farhi's QAOA at depth 1." ] }, { "cell_type": "code", "execution_count": 1, "id": "538e24e5", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_78203/3810261615.py:3: MatplotlibDeprecationWarning: \n", "The mpl_toolkits.axes_grid module was deprecated in Matplotlib 2.1 and will be removed two minor releases later. Use mpl_toolkits.axes_grid1 and mpl_toolkits.axisartist, which provide the same functionality instead.\n", " from mpl_toolkits.axes_grid.inset_locator import (inset_axes, InsetPosition, mark_inset)\n" ] } ], "source": [ "from functools import lru_cache\n", "from matplotlib.ticker import StrMethodFormatter\n", "from mpl_toolkits.axes_grid.inset_locator import (inset_axes, InsetPosition, mark_inset)\n", "from numpy import cos, sin, tan, arctan as atan\n", "from scipy.optimize import minimize\n", "from scipy.special import binom, erf\n", "from sympy import exp, simplify, expand, expand_trig, trigsimp\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import sympy\n", "import time\n", "plt.rc('axes', axisbelow=True)" ] }, { "cell_type": "code", "execution_count": 2, "id": "478adeea", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Starting time: Sat Sep 11 18:13:44 2021\n" ] } ], "source": [ "print(\"Starting time:\", time.ctime())" ] }, { "cell_type": "markdown", "id": "57557cb9", "metadata": {}, "source": [ "# QAOA for Max 3XOR" ] }, { "cell_type": "code", "execution_count": 3, "id": "a16babfd", "metadata": {}, "outputs": [], "source": [ "def qaoa_perf_3xor(s, D):\n", " return s/ ( 1 + 3/(1 - s*s)**D)**0.5" ] }, { "cell_type": "code", "execution_count": 4, "id": "b2d3a947", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{\\sin{\\left(\\gamma \\right)}}{\\left(1 + 3 \\left(1 - \\sin^{2}{\\left(\\gamma \\right)}\\right)^{- D}\\right)^{0.5}}$" ], "text/plain": [ "(1 + 3*(1 - sin(gamma)**2)**(-D))**(-0.5)*sin(gamma)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gamma = sympy.Symbol('gamma')\n", "D_symbol = sympy.Symbol('D')\n", "qaoa_perf_3xor(sympy.sin(gamma), D_symbol)" ] }, { "cell_type": "code", "execution_count": 5, "id": "6c1f7305", "metadata": {}, "outputs": [], "source": [ "Ds = [5, 10, 20, 50, 100, 500, 1000, 5000, 10000, 50000, 500000]\n", "inps = np.linspace(0, 3, 100000)" ] }, { "cell_type": "code", "execution_count": 6, "id": "d8aeff7f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for D in Ds:\n", " outs = [qaoa_perf_3xor(np.sin(i*D**-0.5), D)*D**0.5 for i in inps]\n", " plt.plot(inps, outs, label=\"$D$=\" + str(D))\n", "plt.grid()\n", "plt.legend()\n", "plt.title(\"QAOA performance for $k=3$\")\n", "plt.xlabel(\"$\\gamma \\sqrt{D}$\")\n", "plt.ylabel(\"$C_{3,D}$: performance is $1/2 + C_{3,D}/\\sqrt{D}$\")\n", "plt.savefig(\"images/QAOA_max3xor.png\", dpi=300)" ] }, { "cell_type": "markdown", "id": "f98151a6", "metadata": {}, "source": [ "We can also look at the derivative of performance with respect to $\\gamma$:" ] }, { "cell_type": "code", "execution_count": 7, "id": "5daba25f", "metadata": {}, "outputs": [], "source": [ "qaoa_perf_derivative = sympy.lambdify((gamma, D_symbol), sympy.Derivative(qaoa_perf_3xor(sympy.sin(gamma), D_symbol), gamma, evaluate=True))" ] }, { "cell_type": "code", "execution_count": 8, "id": "60969f78", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5 0.9889298892988929 -7.89382122379223e-06\n", "10 1.019440194401944 -5.557421224877679e-07\n", "20 1.035970359703597 9.036765468040109e-06\n", "50 1.0463804638046381 -6.05624229221835e-06\n", "100 1.049920499204992 -3.116431702476774e-06\n", "500 1.052770527705277 7.448490694839105e-06\n", "1000 1.053130531305313 7.55082733017165e-06\n", "5000 1.053430534305343 -1.179938904916078e-07\n", "10000 1.053460534605346 3.909266844126513e-06\n", "50000 1.053490534905349 3.155058544646039e-06\n", "500000 1.053490534905349 7.4604497740105025e-06\n" ] }, { "data": { "text/plain": [ "Text(0.5, 1.0, 'first derivative')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for D in Ds:\n", " outs = [qaoa_perf_derivative(i*D**-0.5, D) for i in inps]\n", " plt.plot(inps, outs, label=\"$D$=\" + str(D))\n", " pt = np.argmin(np.abs(outs))\n", " print(D, inps[pt], outs[pt])\n", "plt.grid()\n", "plt.plot(inps, [0]*inps, color='black')\n", "plt.legend()\n", "plt.title(\"first derivative\")" ] }, { "cell_type": "markdown", "id": "fe68ddf6", "metadata": {}, "source": [ "Let's check to make sure this works given $\\gamma$ and $\\beta$. Using the asymptotic values:" ] }, { "cell_type": "code", "execution_count": 9, "id": "2ce2fc66", "metadata": {}, "outputs": [], "source": [ "def qaoa_perf_2var_3xor(beta, gamma, D):\n", " p, q = np.cos(2*beta), np.sin(2*beta)\n", " c, s = np.cos(gamma), np.sin(gamma)\n", " return 0.5*q*s*(3*p*p*c**D - q*q*c**(3*D))" ] }, { "cell_type": "code", "execution_count": 10, "id": "4e8203b4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.29003649304891665 0.10535000000000001\n", "0.3305431427004284\n" ] } ], "source": [ "D = 100\n", "gamma = 1.0535/D**0.5\n", "beta = np.arcsin((1/(np.cos(gamma)**(2*D) + 3))**0.5)/2\n", "print(beta, gamma)\n", "print(qaoa_perf_2var_3xor(beta, gamma, D)*D**0.5)" ] }, { "cell_type": "code", "execution_count": 11, "id": "508ad519", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'QAOA for Max 3XOR')" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Ds = range(3, 500, 1)\n", "plt.plot(Ds, [qaoa_perf_2var_3xor(0.29, 1.0535/D**0.5, D)*D**0.5 for D in Ds])\n", "plt.grid()\n", "plt.xlabel(\"degree $D$\")\n", "plt.ylabel(\"$C_{3,D}$: performance is $1/2 + C_{3,D}/\\sqrt{D}$\")\n", "plt.title(\"QAOA for Max 3XOR\")" ] }, { "cell_type": "code", "execution_count": 12, "id": "352ee4f3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'QAOA for Max 3XOR')" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Ds = range(3000000, 1000000000, 100000)\n", "plt.plot(Ds, [qaoa_perf_2var_3xor(0.29, 1.0535/D**0.5, D)*D**0.5 for D in Ds])\n", "plt.grid()\n", "\n", "plt.xlabel(\"degree $D$\")\n", "plt.ylabel(\"$C_{3,D}$: performance is $1/2 + C_{3,D}/\\sqrt{D}$\")\n", "plt.title(\"QAOA for Max 3XOR\")" ] }, { "cell_type": "markdown", "id": "edc567cb", "metadata": {}, "source": [ "What's the asymptotic value of QAOA on Max 3XOR?" ] }, { "cell_type": "code", "execution_count": 13, "id": "d0647c96", "metadata": {}, "outputs": [], "source": [ "def v(k):\n", " return k / (1 + 3*exp(k*k))**0.5" ] }, { "cell_type": "code", "execution_count": 14, "id": "3e31c4b5", "metadata": {}, "outputs": [], "source": [ "k = sympy.Symbol('k')\n", "der = sympy.lambdify(k, sympy.Derivative(v(k), k, evaluate=True))" ] }, { "cell_type": "code", "execution_count": 15, "id": "596987c2", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - \\frac{3.0 k^{2} e^{k^{2}}}{\\left(3 e^{k^{2}} + 1\\right)^{1.5}} + \\left(3 e^{k^{2}} + 1\\right)^{-0.5}$" ], "text/plain": [ "-3.0*k**2*(3*exp(k**2) + 1)**(-1.5)*exp(k**2) + (3*exp(k**2) + 1)**(-0.5)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.Derivative(v(k), k, evaluate=True)" ] }, { "cell_type": "code", "execution_count": 16, "id": "3a5c2ec8", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "inps = np.linspace(0, 2, 10000000)\n", "plt.plot(inps, der(inps))\n", "plt.plot(inps, [0]*inps, color='black')\n", "plt.grid()" ] }, { "cell_type": "code", "execution_count": 17, "id": "cd6497e6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1.0535025053502505, 3.2796303450766118e-09)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pt = np.argmin(np.abs(der(inps)))\n", "inps[pt], der(inps)[pt]" ] }, { "cell_type": "code", "execution_count": 18, "id": "3203de86", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 0.331462726717571$" ], "text/plain": [ "0.331462726717571" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v(inps[pt])" ] }, { "cell_type": "markdown", "id": "b592f03b", "metadata": {}, "source": [ "What are the optimal values of QAOA for every degree?" ] }, { "cell_type": "code", "execution_count": 19, "id": "9c9cbfbb", "metadata": {}, "outputs": [], "source": [ "fmaker = lambda D: lambda i: -qaoa_perf_3xor(np.sin(i*D**-0.5), D)*D**0.5" ] }, { "cell_type": "code", "execution_count": 20, "id": "d1d72563", "metadata": {}, "outputs": [], "source": [ "Ds = range(2, 10000)" ] }, { "cell_type": "code", "execution_count": 21, "id": "550a1065", "metadata": {}, "outputs": [], "source": [ "optimized_vals = [-minimize(fmaker(D), 1).fun for D in Ds]" ] }, { "cell_type": "code", "execution_count": 22, "id": "a137a45b", "metadata": {}, "outputs": [], "source": [ "comparison = [qaoa_perf_2var_3xor(0.29, 1.0535/D**0.5, D)*D**0.5 for D in Ds]\n", "assert np.all(np.array([o-c for o,c in zip(optimized_vals, comparison)]) > 0)" ] }, { "cell_type": "code", "execution_count": 23, "id": "0d5c9ad3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(Ds, optimized_vals)\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "e2b4c3f4", "metadata": {}, "source": [ "# The threshold algorithm for Max 3XOR" ] }, { "cell_type": "code", "execution_count": 24, "id": "af5a63df", "metadata": {}, "outputs": [], "source": [ "@lru_cache(maxsize=int(1e7))\n", "def g(D, t):\n", " return 2**(-D) * sum([binom(D,i) for i in range(0, t+1)])" ] }, { "cell_type": "code", "execution_count": 25, "id": "3dcb327c", "metadata": {}, "outputs": [], "source": [ "@lru_cache(maxsize=int(1e7))\n", "def Delta(D, t):\n", " return 2**(-D)* binom(D, t)" ] }, { "cell_type": "code", "execution_count": 26, "id": "fdff9222", "metadata": {}, "outputs": [], "source": [ "@lru_cache(maxsize=int(1e7))\n", "def general_improvement(D, t, k):\n", " val_delta = Delta(D, t)\n", " val_g = g(D, t)\n", " return 0.25 * ( (1-2*val_g + 2*val_delta)**k - (1 - 2*val_g)**k )" ] }, { "cell_type": "markdown", "id": "3ec4ec8c", "metadata": {}, "source": [ "What's the performance at $k=3$?" ] }, { "cell_type": "code", "execution_count": 27, "id": "d9ef701d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for D in [5, 10, 20, 30, 40, 80, 100, 300, 1000]:\n", " inps = np.array(list(range(-1, D+2)))\n", " plt.plot((inps/D - 1/2)*D**0.5, [general_improvement(D, t, 3)*D**0.5 for t in inps], label=\"$D$=\" + str(D))\n", "\n", "plt.legend()\n", "plt.ylabel(\"$C_{3,D}$: performance is $1/2 + C_{3,D}/\\sqrt{D}$\")\n", "plt.xlabel(\"a: threshold is $D/2 + a/\\sqrt{D}$\")\n", "plt.xlim(-2, 2)\n", "plt.title(\"Performance of threshold algorithm for Max 3XOR\")\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "e0e3b5b0", "metadata": {}, "source": [ "Finding the optimal threshold:" ] }, { "cell_type": "code", "execution_count": 28, "id": "e055851b", "metadata": {}, "outputs": [], "source": [ "def get_argmax(D, k, negative_only=False):\n", " if negative_only:\n", " inps = range(-1, int(D/2))\n", " else:\n", " inps = range(-1, D+2)\n", " return inps[np.argmax([general_improvement(D, t, k) for t in inps])]" ] }, { "cell_type": "code", "execution_count": 29, "id": "7be50499", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "inps = range(1, 500)\n", "plt.scatter(inps, [(get_argmax(D, 3) - D/2)/D**0.5 for D in inps], s=3)\n", "plt.xlabel(\"degree $D$\")\n", "plt.ylabel(\"a: threshold is $D/2 + a/\\sqrt{D}$\")\n", "plt.title(\"Optimal threshold for Max 3XOR\")\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "f45e7cc9", "metadata": {}, "source": [ "If we only look at thresholds below $D/2$, we get a clearer pattern:" ] }, { "cell_type": "code", "execution_count": 30, "id": "5c868596", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "inps = range(1, 500)\n", "plt.scatter(inps, [(get_argmax(D, 3, True) - D/2)/D**0.5 for D in inps], s=3)\n", "plt.xlabel(\"degree $D$\")\n", "plt.ylabel(\"a: threshold is $D/2 + a/\\sqrt{D}$\")\n", "plt.title(\"Optimal (negative) threshold for Max 3XOR\")\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "74d37d45", "metadata": {}, "source": [ "# Comparison for Max 3XOR" ] }, { "cell_type": "code", "execution_count": 31, "id": "df1579ac", "metadata": {}, "outputs": [], "source": [ "def get_max(D, k):\n", " inps = range(-1, D+2)\n", " return max([general_improvement(D, t, k) for t in inps])" ] }, { "cell_type": "code", "execution_count": 32, "id": "c2bcc4bf", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$C_{3,D}$: performance is $1/2 + C_{3,D}/\\\\sqrt{D}$')" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { 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bz8Y9xQ1eO7hbO+bNGMzwnplkJCfU7K+qUpbnFfDSkjye/+L7eq8f26c9V07sx4kDO9epSYLT1r+vuJzXV+zgtWXbWJ5Xd1nzyUd34topRzG0eybt0xIDvk7133ZxWSVfbXYC1Ctf135vL5/QhzOGdWNMn/Y1TYSNUVVWbjvApxv28tbKnXyz8yD9OqUxc2QPTh7UhUFdM0LqU9q67xDrdxWybGsBewrLmNC/Iyce05l2yQm1+i0a4v//rKpUKSzPK2Dz3mKG9cikW1ZKwPc9FGWVTp/LwdJKevgEyyMpzLm2LJBUi7ZAsmTLPs77+0IA7jhnKJcc3weAZVsL+MHfPqt17pg+7Xn5+hMA6Dv33/Wm+c5/T2HqfR9HNJ/BOmlgZzJTEvjXsuC+Kef+KofeHVJZtDGfix/7otHzfz11ID89aUDN9sHSCua+vII3V+6s95oZw7oxd/qgmnZ8X/O//J65AWptACce05mbzhjEoK51+3Oq7TxQyu3/XsMbK3bU2j9rbC9mnzwg4Gv6KyqrZNF3+dz8r5U1NYL/yunPFSf0pUu75Eaurm3jniI+XLeHnQdKODo7g5kjuwfVyR7ob7s62CUneDgmO6PBzvXWyCZtbBoLJD5aMpAs2piPAMcf1RFwRsj8ZsFKXvLpc1gy71Q6pifVGyimHpvN5r2HWLer4Q7aSPryN6cw/s4PGq01zJsxmCsn9iNO4PUVO/jZP5fWe64nTlh+y+m1vu1Vequ4/Ikv6/RLVHvhJxMY169DwGPvr9nFNc/U/b3+66cTGdkrq8F87y8u53+//J4/v7OuZt9rsycyvGfD1/nKLyrjnvfW06djKpMGdGZI9/qDT328VUpRaSWZqQmNnxxh9qEaG5orkNh9JEfI1n2HuPDRRcx6dFHNvjkvLa8VRADG3P5+g+m8s3pXRILI5KM78fiPAv5N1PK78cl0aZfMot+c0uB5vz1zCFdN7IfHHWp59ojuPHLZmIDndkxLZOnvTqvTZBDvieN/fzyeqyb2q7X/qM5pLLzp5HqDCMCpQ7JZdNMpjO6dBcCZw7ux6vdTGw0iAO3TEvnpSQNYf/t05s0YzD9OT21SEAHomJ7EHecM49op/UMKIuAE15YIIsaEywLJETL57g9rnv/tww2A8609kEc++i6s1+qUHrgdvFr71AT+eM4wphzTmXNH96j3vLNHdOeoLKdZpEtGMm/dODngeRnJ8Vw9qV+dtumpx3blbxePrrWvW2Yyb944mXbJ9X9g/u6sIfx66kASPXFMGtCJN26YRLfMxtuUu2YmM//aCSyedyoPXjy6yW3bifFxXDP5KBLaWBOOMc3NAkkz2H2wlPP+/jl73LH9Xr82oT+/s46qKq2zv9qdb30T8mv3yErhg1/m8JMpR9V7zj2zRtKrQyoJnjju+eHIgOecPiSbv/5wRK19g7u149EAtYyVt06t97VmDO/GvBmDASfAPXv1uJoBAw356UkDWH/HdJ675nhSE4MPCInxcQ3e12KMiTwLJM3guUVbWLJlP//rjsYJNGa9qLzuDWzB+PmpxzRY43j5+hPITEkIeMNftaF+Q4nvv3BknXOmHts14Mic04/tyovXTWjwWn9XT+rHutunsXjeaQzoktHo+caY1sUCSXNwhzN+u7uQ0gpvwEDygwc/q7MvGCcP6kKXjPq/0Xdwh3fOHNmdv14wos7xb++YTueM2t/YZ46s3bz1xBVjG2zyGtUri+SEOO4+b3idawMRCW56DmNM62SBpBlUt7C/sWIH/z1/GWWVdac42Li34fsP6tMpI5GHLx1Du+S6zT2XHN+7Zm4mEeHEgZ3rnFPf+P+nrxpX87xPx7QGx/bHe+L45rbp/PC4Xk3NvjGmDWo0kIhI5CZ6qf81ponIOhHZICJzAxyfKSIrRGSZiCwWkUl+xz0islRE3mjuvDbmQEkFX39/+M7bt1fv5MJ/LGrgiqbpkJZI746p/Hpa3bkO7jhnWK3trJQEMnw6nH88uZ//JTVOPKYzC286mbnTB3FUp7SI5dcY0/YFUyNp1iEsIuIB/gZMB4YAF4nIEL/TPgBGqOpI4CrgMb/jNwLB3abcDBZv3sdf3HsQrnn6qzrzODV297Ovqyf145az/IvvWPX7qTVNRMH8UuI9caz8/eGO8JtnBE63WrfMFK47sX/Is9caY2JTMIGkue9YHAdsUNWNqloOzAdm1sqAapEevnMyzTdPItITmEHd4HLEnP/wQh50h/QuC2EOJV8n9O/IFSf05Y9+tQug1nDWYO6PMMaYIyHkSWTcD/D2wEZVDa3B39ED2OqznQccH+D1zgHuBLrgBI5q9wFzgHqHA4nItcC1ANnZ2eTm5oaU0aKiogavzc3NpbKJ03D7+3btKjy7POzaXXdUl/9r3z0lhTkfOzO5zjkuud68TeweT/tkCancjZW5LbIyxwYrc+Q0OZCISF/gFSAbKAW6ish/gF+q6voQ8hCoHaXOp7GqLgAWiMgU4DbgVBE5E9itqktEJKe+F1DVR4FHwZkiJdQpAuqdXuBtZzqTE088EX37zZDSrjZx3FiG9cykcs0u+Lr2lB/+r11UVsmcj98B4L/Oq//O83BmgbBpJGKDlTk2NFeZQxm1dRfwiKr2UNX+QCbwOvCWiBwdQnp5gO/wn55AvTP+qerHQH8R6QRMBM4Wkc04TWIni8hzIeQhIpoyg219khKcX0lcEL+Z5CBXzzPGmOYUyifRMar6SPWGqla63/ivB34XQnpfAUeLSD8RSQQuBF7zPUFEBojbAywio4FEIF9Vb1LVnqra173uP6p6aQh5iIjKquAXy3nhJxMC7q+eYdV//ZG1f6i7rFn1eggN3cVujDHNLZRAEvB7t6q+CwxucmKqlcBs4B2ckVcvqOpqEblORK5zTzsPWCUiy3BGeM3SKJy2eOC8t4M6b9KATozr14Hlvzu91v4rTuhbM/Q2u10yK289fDwlMfANfZv/NIObzmjy226MMRETSmd7VxG5GlgFrFZV32W/QvpwV9U3gTf99j3s8/wunCa1htLIBXJDef2WUt2MVW3OtIG1ht7a3eDGmNYglEByKzAKuBwYKiIHgdU4gaVr5LLWdlXHikS/u8z9txM8dj+HMSb6NTmQuP0hNdxhwMOBYcBHEcpXTPCfdt1/DWi7MdAY0xoEE0ga/DRT1TyckVfhjXs1xhjTKgUTSBJFZJiqBl7YOkYdKq+kqLSSrfsPNXje5RP68MzCLbX2NaWm8cQVY+nXKT2kPBpjzJHQaCBR1UoRKRaRc91d+cBn7mirmHXuQ5/zzc5CxvWtf/lXgAuP6103kDThdU4elB1C7owx5sgJqo9EVTcCGwFEJAuYLiLxQDlOUClorgxGq292Ouuml1Q0PDlyYx3mL19/Auf9/fOI5csYY460UDrbC3DuZMcNJhNFpAOQBCxS1c2RzGC0C7TWiC//DnQ4PGoLYEyf9hyTnc76XUV1zjPGmNYg5EkbXX2B43BuRNwDrAc2h5lmqxJo9UNfgWokU46uveDU6zdMCnuyR2OMaSkhT9YkIr/HueP8DVW9WlXnqurXkcta69B4IInj3Z9Pqdm+9awhXDmxb61zkuI9pCWFG9ONMaZlNDmQiMgEd96ru4A/q+o3kc9W61HWSCCJjxOOyc5g/FFOp3zXzBS7P8QY06aEUiP5EbAEeAK4XERi+m72xmok/n0k8XEWRIwxbUsone3XAYjIIJzlcZ8SkUzgQ+BtnFFczb7Oe7QobaSz3b+PJN6mPQmeKlR5QatA3Z812z6PWvuqz/PbbvTaw8c65C+DdaW1r615uH1ZNc/V+alVh5+j9RynCeeq3756jtebVjCvdThPx+zYAQdfPnxt9bR5NV13GuCYNnIswHkNHfOfh7XR9MN77RH798PmrAbOa85y1ypogDI3z/5+aaPCW6CoHiE3zLtNWt8A94pICnAScAFwDzA2MtmLfhWNdJLHuwuLiHv3SHwwC400N1XwlkN5MVQcgvJDUF4ElaVQWeYcc3923bEcFm+EynLwljk/K0sPP6/5WQ5VlbUf3grng7pmn992reMV7k/v4WMt9H1kOEDU334rIHHuEEBxfkrc4ed1jhPgePU10LG8HAqTDh8Dn+GFvttSa1fgYz7XBUyjoWP1vXY9aYTx2qJe5++tVhrV7wuHBf2ehFjuWsf91Npf3/nB7y8trz3QJ1Ii0sOrqiUi8pY7i6/x4V8jiUj3SFUVlOyDol1QvBdKC6D0AJQU+D0/AGUHnUBRUez+POQEkCA/pAcBrPPfKxCfBJ4k52d8EngSIC4B4uLBE+/8rH7EJ0Fc2uHtWscTIM7jc8x3230ucc6j5rnvvrgA+3ye19n2+F3nu8/5uWTpUsaMOa72tb4fzLU+kGniB3qcz3WNnRvouO8HUeQsjMHVApfFYJl35OYysBnSjUggEZErgMtEpBj4HvifMNdxb7X++ePxXPSPRTXbTe5YV4VD+6BgM+zfDPu3QMEWOLjdCRxFu51HfYFA4iA5E5KzICULkjIgpQMkpkJCKiSmHf7p+zwhFRKSIT7ZDRCJ4Eli0eKljJ84xQ0WiW5QiG+WD7NoUfjdIegxuqWzYUyrEakxpzmqegqAiAwHbgHmRCjtVqVn+5TgT1aFvd9C3pewcxXsWgW7Vju1DV+pnSCzB6R3ha7DIT0b0rs4j9ROTsBIznICSFJGRD/kS1O2Q7tuEUvPGNP2RCqQHKx+oqor3DveY5L/1PD+Ekr2wpJ/w7fvwvcL4VC+eyAVugyGwWdC50HQvq/zyOoDSTZpozEmekXqA3+8iDyAMyx4Cc6a6jEp4PDeynLGl+Tys4RXOe7ltYBCZi84eir0Hg+9J0DHAU67vTHGtDKR6mwf5y5wNQb4IdAvEum2Rh6fQJJIBSx8CD69hxuL9/C9dGbr8J/R+4QLIHtom+5nMMbEjog1QfkscPVqpNJsjaprJONkLX9OeATe2Q39pvCngzfyyLa+PDd8Ar27dmrhXBpjTOQ0S1+GiFwJbFLV3OZIP5p5RPll/Av81PMqW7QLXLYA+p/MJfsOsfv99RzXyPolxhjT2jRXo/y/caaVjykevKS8fj03xP+LF70nsvWCd6D/yQD06pDKPT8cSWK89YMYY9qWZqmRqOpu4J3mSDt6KbfFP0H8mg+5u2IWD3nPZvOwmO0qMsbEkIh8PRaR60TkHyJyoYi8ISLXRyLd1uQSzwdcHP8hVRN/wUPemdSeY8EYY9quSLWznAxcC8xW1TOBERFKt1XoLbv4TfzzfOwdhpzy25bOjjHGHFGRCiT5qqo4a5QAlEUo3ai0dd+hWtvz4p/DSxxzKq5F7F4QY0yMidSn3v0Aqvq6u/1KhNKNSpPv/rDm+VDZyOmeJfyjcgY76diCuTLGmJYRygqJvxWRX/ru818lUVU/CjdjrcXs+Fcp0DSe9E5r6awYY0yLCGXU1mXASP+dInIN0FlV7ww3U61Few5yStzXPO6dThGpLZ0dY4xpEaE0bZWo6qEA+58FLg0zP63KDM8XJIiXV70TWzorxhjTYkIKJCJSZ15xVS0DKsPPUusx0/MZ66p6slZ7t3RWjDGmxYQSSP4KvCoifXx3ikgXoCoiuWoFOnCQ4+LW84Z3PHbPiDEmljU5kKjqi8DfgCXuzYe3i8gfgc+Av4SSCRGZJiLrRGSDiMwNcHymiKwQkWUislhEJrn7e4nIhyKyVkRWi8iNobx+KE6IWw3AJ1XDj9RLGmNMVAppihRVfVpEXgHOAY4FioGLVHVxU9MSEQ9OYDoNZ/bgr0TkNVVd43PaB8BrqqruCowv4CwnXgn8UlW/FpEMnOD2nt+1zWJC3BoOagorte40KA9ePIoeWU1YKdEYY1qxkOfaUtVC4JkI5GEcsEFVNwKIyHxgJlATDFS1yOf8NEDd/TuAHdX5EZG1QA/fa5vLiLjvWF7VHy+eOsfOHN69uV/eGGOiRjQsidsD2OqznQcc73+SiJwD3Al0AWYEON4XGAV8EeDYtThTuJCdnU1ubm5IGS0qKiI3N5ckyhkoW3m0qk42Qk47WlWXOZZYmWODlTlywg4kInKaqr4XThIB9mmdHaoLgAUiMgW4DTjVJw/pwMvAf6vqwQDXPgo8CjB27FjNyckJKaO5ublMnnIiA9/5fySIlxVVR9U5J9S0o1Vubm6bK1NjrMyxwcocOZGYIuWuxk9pUB7Qy2e7J7C9vpNV9WOgv4h0AhCRBJwg8ryqNvvULBXeKgbINgDWa69ax168bkJzv7wxxkSdaJhh8CvgaBHpJyKJwIXAa74niMgAEWeBcxEZDSQC+e6+x4G1qnrPkchsZZUyIG475erhe+1Ss/+MYV1t9UNjTEwKqWlLRJ7EaX4SoLeIPFF9TFWvakpaqlopIrNxFsLyAE+o6moRuc49/jBwHnC5iFQAJcAsdwTXJJwpW1aKyDI3yd+o6puhlCsYlW6NZLN2DdjRbowxsSbUPpKnfJ5PAp4OJxPuB/+bfvse9nl+FwGa0FT1U47w3YAVXqWv7GST1r65X+v06hhjTGwI9T6Smtl9RaQwlmb7rfR66S75diOiMca4ItFHUh6BNFoN76EC0qWU7er0h3jibHoUY0xsCzuQqOr4SGSk1TiQB8B27QRASoLTT2JNW8aYWBUNo7ZalbiDztDfHeqshphcHUjq3vpijDExwQJJE0mhE0i2u4EkKd55C61GYoyJVSEFEhEZJCKnuHeU++5v8+vNyqG9AOwjA4CURBsCbIyJbaGs2f4z4FXgBmCViMz0OfzHSGUsWsWV7KNA06h0B7xdcrwtamWMiW2hDP/9MTBGVYvciRJfEpG+qno/MbDCk6ckn33q1EZOHdyFbpnOdPHWsmWMiVWhBBJP9bTuqrpZRHJwgkkfYiGQlO5jH+3cLUHafImNMaZhofSR7BSRkdUbblA5E+gEDItQvqJWfOk+9rs1Et8gYp3txphYFUoguRXY5btDVStV9XJgSiQyFc3iy/aR7waSOImBKpgxxjQilKati4HjRWQd8DbwtqruBFDVzyKZuaijSmLZfva7I7bEwogxxjQ9kKjqdeAMAQamA0+JSCbwIU5g+UxVvRHNZZTweEuJq6qgQJ1Rz7X7R6xtyxgTm0K+IVFVv1HVe1V1GnAy8ClwAQGWum0rPN4SAIpwRmqJgLtMivWRGGNiVkTWbFfVEpxp4JttHZBoUFJyCIAiTQacIGKNW8aYWBfRKVJE5MpIphdt7v9yPwDF1TWSlsyMMcZEiUjPtfX7CKcXVVIpBaCYwzWSatayZYyJVU1u2hKRFfUdArLDy050S8PtI9HDNRK7IdEYE+tC6SPJBqYC+/32C/B52DmKYml+NZK4WjckWp3EGBObQgkkbwDpqrrM/4CI5IaboWiWLk4gqamRiDCyVxYA10w+qqWyZYwxLSqU+0iubuDYxeFlJ7pVN23V9JEAHdOT2PynGS2YK2OMaVm2sFUTVNdIDpHk7LD+EWOMsUDSFGmUUKxJqPu2xVlPuzHGWCBpijRKa+4hAauQGGMMhBFIROQCEclwn88TkVdEZHTkshZ9UqWMYk2q2bYKiTHGhFcj+a2qForIJJzhwE8Df49MtqJTEhWUkVizbROkGGNMeIGkeobfGcDfVfVV8PmUbYMSqaDcZ6BbnDUMGmNMWIFkm4g8AvwQeFNEksJML+o5gSTBZ4/VSIwxJpwP/h8C7wDTVLUA6AD8OhKZilaJUkm5Hq6RWB+JMcaEMY28qh4CXvHZ3gHsiESmolUSFRxyb0YEq48YYwyENmnjp6o6SUQKqT3prQCqqu0ilrsoU6ePxKokxhjT9KYtVZ3k/sxQ1XY+j4xQg4iITBORdSKyQUTmBjg+U0RWiMgyEVnsjhQL6tpISqSSMp8+EosjxhgTBZ3jIuIB/oaz/vsQ4CIRGeJ32gfACFUdCVwFPNaEayMmSWp3tlscMcaYKAgkwDhgg6puVNVyYD4w0/cEVS3Sw/O0p3G4Sa3RayMpkUrKanW2WygxxpiIrNkeph7AVp/tPOB4/5NE5BzgTqALzr0rTbn2WuBagOzsbHJzc0PK6Ei/4b/btuWRm7snpLRai6KiopDfr9bKyhwbrMyRE3IgEefr+CXAUar6BxHpDXRV1S+bmlSAfXVWiVLVBcACEZkC3Aac2oRrHwUeBRg7dqzm5OQ0MYuOQx9W1gokvXr2Iien2VrSokJubi6hvl+tlZU5NliZIyecpq2HgAnARe52IU5/RVPlAb18tnsC2+s7WVU/BvqLSKemXhsu/1Fb1rJljDHhBZLjVfWn4Kw/q6r7CW2KlK+Ao0Wkn4gkAhcCr/meICID3BoQ7sSQiUB+MNdGjLeSeKmiXK2z3RhjfIXTR1LhjppSABHpDFQ1NRFVrRSR2Th3yXuAJ1R1tYhc5x5/GDgPuFxEKoASYJbb+R7w2jDKVD9vGYDVSIwxxk84geQBYAHQRUTuAM4H5oWSkKq+Cbzpt+9hn+d3AXcFe22zqHQCSVmtubaMMcaEM0XK8yKyBDgFp5XnB6q6NmI5izbecgC/SRuNMcaENfxXVb8BvolQXqJbZd2mLa0zPswYY2JPOCskPi0iWT7b7UXkiYjkKhq5NZIytRqJMcb4CmfU1nB3+nigZtTWqLBzFK1qaiQWSIwxxlc4gSRORNpXb4hIB6LjTvnmEWDUljHGmPA++P8KLBSRF93tC4A/hp+lKBWgRmJdJMYYE96orWdEZDFwsrvrXFVdE5lsRaHqQKJWIzHGGF/hzLWVBIwE2rnpnC8iqOofIpS36NJ7ApPK7mePZrZ0TowxJqqE8/X6VeAAsAQoi0x2olhCMnnauaVzYYwxUSecQNJTVadFLCetkN1HYowx4Y3a+lxEhkUsJ8YYY1qlcGokk4ArRGQTTtOWAKqqwyOSM2OMMa1COIFkesRyYYwxptUKZ/jvFveGxKOBZJ9DW8LOVSuhdieJMcaENfz3GuBGnFUJlwHjgYUcvq/EGGNMDAins/1G4Dhgi6qehDPP1p6I5MoYY0yrEU4gKVXVUnBuTnSnlB8YmWwZY4xpLcLpbM9zp5H/F/CeiOwHtkciU62F3UdijDHhdbaf4z69VUQ+BDKBtyOSK2OMMa1GRGYgVNWPIpGOMcaY1iecUVtjgZuBPr7p2A2JxhgTW8KpkTwP/BpYCVRFJjvGGGNam3ACyR5VfS1iOTHGGNMqhRNIbhGRx4AP8JlGXlVfCTtXxhhjWo1wAsmVwCAggcNNWwrETCBRG/9rjDFhBZIRqmrTyBtjTIwL5872RSIyJGI5McYY0yqFux7Jj2w9EmOMiW0hBRIREeAnxNCU8YFYD4kxxoQYSFRVReReVR0T6QwZY4xpXcLtIzkuYjkxxhjTKoXTR3IScJ2IbAaKsT4SY4yJSVGxZruITAPuBzzAY6r6J7/jlwD/424WAder6nL32M+Ba3C6LFYCV1avk9Lc7DYSY4wJo2lLVbcAWcBZ7iPL3dckIuIB/oYTmIYAFwUYVrwJONGt7dwGPOpe2wP4GTBWVYfiBKILQyqQMcaYkIQcSETkRpyJG7u4j+dE5IYQkhoHbFDVjapaDswHZvqeoKqfq+p+d3MRzjrx1eKBFBGJB1KJscW1jDGmpYXTtHU1cLyqFgOIyF3AQuD/NTGdHsBWn+084PhGXvctAFXdJiJ/Ab4HSoB3VfVd/wtE5FrgWoDs7Gxyc3ObmMXAtm3fRm7u3oikFa2Kiooi9n61Flbm2GBljpxwAokAXp9tr7svlHT8Bex9EJGTcALJJHe7PU7tpR9QALwoIpeq6nO1ElN9FLc5bOzYsZqTkxNCNoG3/11rs3v37uTktO1ZYnJzcwn5/WqlrMyxwcocOeEEkieBL0Rkgbv9A+DxENLJA3r5bPckQPOUiAwHHgOmq2q+u/tUYJOq7nHPeQU4AXjO/3pjjDHNI5w12+8RkVyc2oHgjJZaGkJSXwFHi0g/YBtOZ/nFvieISG+cWYUvU9X1Poe+B8aLSCpO09YpwOIQ8mCMMSZETQ4kIvKsql4mIjeq6v3A1+FkQFUrRWQ28A7OqKsnVHW1iFznHn8Y+B3QEXjImZ2FSlUdq6pfiMhLbh4qgaW4TVjGGGOOjFBqJGNEpA9wlYg8g18fh6rua2qCqvom8Kbfvod9nl+Dc69IoGtvAW5p6mtGgt1HYowxoQWSh4G3gaOAJdQOJOruN8YYEyOaHEhU9QEReRDnDvSrmiFPxhhjWpGQbkhU1SpgRITz0upYy5Yxxtjsv8YYY8Jks/8GSQP0rFtnuzHGRMnsv62BBQ1jjAksnKat74HJwI/cWX8VyI5IrqJQlUUSY4wJKJxA8hAwAbjI3S7EmQ6+TQoURgZmpx/xfBhjTLQJp2nreFUdLSJLAVR1v4gkRihfUce3QtIuOZ5nrz6e4T0zWy5DxhgTJcIJJBXuolQKICKdgaqI5CoK+TdtjeiV1TIZMcaYKBNO09YDwAIgW0TuAD4F/hiRXEU5d74vY4wxhDf77/MisgRnxl2AH6jq2shkK/r4VkgCDQU2xphYFXIgEZFk4AyckVtVQKKIbFLV0khlLprYqC1jjAksnD6SZ3BGaj3gbl8EPAtcEG6mopFvGLGmLWOMOSycQDJQVX3n2/pQRJaHm6FoZc1ZxhgTWDid7UtFZHz1hogcD3wWfpaiU5XFEWOMCSis+0iAy0Xke3e7N7BWRFbSFufcskBijDEBhRNIpkUsF62AWiQxxpiAwhn+uyWSGYl21kVijDGBhdNHElNs+K8xxgRmgSRIFkaMMSYwCyRBsgqJMcYEFlYgEZGuDW23JXYfiTHGBBZujeTxRrbbDAsjxhgTWFiBRFVnVD8XEfHdbmusQmKMMYGFcx9JDRG5ArhMRIpxluD9H1UtjkTa0cJGbRljTGARCSRAjqqeAiAiw4FbgDkRSjsqWBgxxpjAIhVIDlY/UdUVIhKpdKOGdbYbE90qKirIy8ujtDS4lSwyMzNZu7bNLqEUUDBlTk5OpmfPniQkJASdbqQ+8MeLyAPAEvfR5tZutzhiTHTLy8sjIyODvn37BrXUQ2FhIRkZGUcgZ9GjsTKrKvn5+eTl5dGvX7+g043IfSSqOg64GygAfgj0jUS60cQCiTHRrbS0lI4dO9p6QWEQETp27Bh0ra5axJqgVDUPyANejVSa0cQmbTQm+lkQCV8o72FU3NkuItNEZJ2IbBCRuQGOXyIiK9zH5yIywudYloi8JCLfiMhaEZnQHHm0GokxxgTWLIFERK4SkZwgz/UAfwOmA0OAi0RkiN9pm4AT3TVObgMe9Tl2P/C2qg4CRgDN0ntmw3+NMQ0pKCjgoYceAiA3N5czzzwz4q9xxRVX8NJLLwV9/ubNmxk6dGjAYzk5OSxevDgi+WquGskbQFKQ544DNqjqRlUtB+YDM31PUNXPVXW/u7kI6AkgIu2AKbh31KtquaoWhJ/9uiyMGGMa4htIguX1epspN0dWswzTVdXdwDtBnt4D2OqznYez+mJ9rgbecp8fBewBnnSbu5YANzbHzZC+FRJrhjUmuv3+9dWs2X6wwXO8Xi8ejyfoNId0b8ctZx1b7/G5c+fy3XffMXLkSBISEkhLS+P8889n1apVjBkzhueeew4RoW/fvlx11VW8++67zJ49mw4dOnDLLbdQVlZG//79efLJJ0lPT2fu3Lm89tprxMfHc/rpp/OXv/wFgI8//ph77rmHnTt3cvfdd3P++eejqsyZM4e33noLEWHevHnMmjWrVv5KSkq44oor+Pbbbxk8eDAlJSVBl70xkbqz/TpgDPABcCnwb1X9e7CXB9gXsAIgIifhBJJJ7q54YDRwg6p+ISL3A3OB3/pddy1wLUB2dja5ublBZu2wbUVVNc8rKipCSqM1KioqipmyVrMyt06ZmZkUFhYCUFFe0ei3fVVtUo2goryiJv1A5s2bx4oVK/jkk0/45JNPuOiii/jiiy/o1q0bp512Gu+99x4TJkxAVRER3nrrLfLz87nkkktYsGABaWlp3Hvvvdx5551ce+21vPzyyyxZsgQRoaCggMLCQioqKti6dStvvfUW69evZ9asWUydOpVXX32VJUuW8Omnn5Kfn09OTg6jR4+mrKyMqqoqCgsLefDBB0lJSeGzzz5j1apVTJ48meLi4oBlKi0tbdLfQ6RqJCcDs4BPVHWSiDzchGvzgF4+2z2B7f4nuXfMPwZMV9V8n2vzVPULd/slnEBSi6o+ituvMnbsWM3JyWlC9hzrdxXCpx8DEB+fQChptEa5ubkxU9ZqVubWae3atTX3SNx+3shGz4/0fSTp6enExcWRkZFBamoq48aNY9CgQQCMGTOG3bt3k5GRgYhw+eWXk5GRwUcffcS6deuYNs1Zuby8vJwJEybQo0cPUlNT+fnPf86MGTM488wzSUxMJCEhgfPPP5/MzEyOO+449uzZQ0ZGBkuWLOHSSy8lKyuLrKwscnJyWLt2LcOHD6/J0xdffME111xDRkYGEyZMYPjw4aSlpQV8D5KTkxk1alTQZY9UIMlXVRWRu9ztsiZc+xVwtIj0A7YBFwIX+54gIr2BV4DLVHV99X5V3SkiW0VkoKquA04B1oRTkPpY05YxpimSkg53E3s8HiorK2u209LSAKdWdNppp/HPf/6zzvVffvklH3zwAfPnz+fBBx/kP//5T510q2fcCHbmjeYaHt3kznYR+a2I/NJv9/0Aqvq6u/1KsOmpaiUwG6dPZS3wgqquFpHr3CYzgN8BHYGHRGSZiPgONbgBeF5EVgAjgT82tUxB5dOntc0GcBlj/GVkZDTY9BXI+PHj+eyzz9iwYQMAhw4dYv369RQVFXHgwAHOOOMM7rvvPpYtW9ZgOlOmTOH//u//8Hq97Nmzh48//phx48bVOeeFF14AYNWqVaxYsaJJeW1IKDWSy3A+sGuo6jcicg3QWVXvVNWPmpKgqr4JvOm372Gf59cA19Rz7TJgbFNeLxRVVY2fY4yJXR07dmTixIkMHTqUlJQUsrOzG72mc+fOPPXUU1x00UWUlTkNObfffjsZGRnMnDmT0tJSVJV77723wXTOOeccFi5cyIgRIxAR7r77brp27crmzZtrzrn++uu59NJLGT58OCNHjqwTaMIhTZ2MUESWq+qIAPuTgK9Vtf5hDVFg7NixGsrY6dXbDzDjgU8ByEpNYNnvTo901qJSW2g7byorc+u0du1aBg8eHPT5NtdW/QK9lyKyRFUDfmkP5T6SEhHp5r9TVcuAygDntwm+8daatowx5rBQAslfgVdFpI/vThHpArTZBiALHsYYE1iT+0hU9UURSQWWiMgiYBlOQLoAuDWiuYsivp3tNmrLGGMOC2mKFFV9GugHvAAkAKXARar6fATzFlWsRmKMMYGFfB+JqhYCz0QwL1HNJm00xpjAomIa+dbAwogxxgRmgSRIViExxpjALJAEqan32xhjTKxolmnk2yILI8a0Im/NhZ0rGzwlxVsJniZ8BHYdBtP/1OApd9xxB8888wy9evWic+fOjBkzhszMTB599FHKy8sZMGAAzz77LKmpqWzZsoWrrrqKPXv20LlzZ5588kl69+7N66+/zu233055eTkdO3bk+eefD+ou+ZZkNZIgWYXEGNOQJUuWMH/+fJYuXcorr7zCV199BcC5557LV199xfLlyxk8eDCPP/44ALNnz+byyy9nxYoVXHLJJfzsZz8DYNKkSSxatIilS5dy4YUXcvfdd7dYmYJlNZIgWdOWMa1IIzUHgJIIT5HyySefcM4555CamgrA2WefDTgTJM6bN4+CggKKioqYOnUqAAsXLuSVV5z5bS+77DLmzJkDQF5eHrNmzWLHjh2Ul5fTr1+/iOWxuViNJEhVFkeMMY0INE37FVdcwYMPPsjKlSu55ZZbKC0tbfDaG264gdmzZ7Ny5UoeeeSRes+PJhZIgqTWS2KMacCUKVNYsGABJSUlFBYW8vrrzqoahYWFdOvWjYqKCp5//vA92yeccALz588H4Pnnn2fSJGfh1wMHDtCjRw8Ann766SNcitBY01awfOLInKmDWi4fxpioNHr0aGbNmsXIkSPp06cPkydPBuC2227j+OOPp0+fPgwbNqxmzZIHHniAq666ij//+c81ne0At956KxdccAE9evRg/PjxbNq0qcXKFCwLJEHqkJ7I2GwPf7pkIgO6xNbU08aY4Nx8883cfPPNgBMQwFkH5Prrr69zbt++fWtWPfQ1c+ZMZs6c2az5jDRr2grSoK7tmD0q2YKIMcb4sRqJMcY0g+oaSSywGokxps2wYfrhC+U9tEBijGkTkpOTyc/Pt2ASBlUlPz+f5OTkJl1nTVvGmDahZ8+e5OXlsWfPnqDOLy0tbfIHZmsXTJmTk5Pp2bNnk9K1QGKMaRMSEhKadBd4bm4uo0aNasYcRZ/mKrM1bRljjAmLBRJjjDFhsUBijDEmLBJrIxxEZA+wJcTLOwF7I5id1sDKHBuszLEhnDL3UdXOgQ7EXCAJh4gsVtWxLZ2PI8nKHBuszLGhucpsTVvGGGPCYoHEGGNMWCyQNM2jLZ2BFmBljg1W5tjQLGW2PhJjjDFhsRqJMcaYsFggMcYYExYLJEEQkWkisk5ENojI3JbOTySJyBMisltEVvns6yAi74nIt+7P9j7HbnLfh3UiMrVlch06EeklIh+KyFoRWS0iN7r723KZk0XkSxFZ7pb59+7+NlvmaiLiEZGlIvKGux0LZd4sIitFZJmILHb3NW+5VdUeDTwAD/AdcBSQCCwHhrR0viJYvinAaGCVz767gbnu87nAXe7zIW75k4B+7vviaekyNLG83YDR7vMMYL1brrZcZgHS3ecJwBfA+LZcZp+y/wL4X+ANdzsWyrwZ6OS3r1nLbTWSxo0DNqjqRlUtB+YDrWtB5Qao6sfAPr/dM4Gn3edPAz/w2T9fVctUdROwAef9aTVUdYeqfu0+LwTWAj1o22VWVS1yNxPch9KGywwgIj2BGcBjPrvbdJkb0KzltkDSuB7AVp/tPHdfW5atqjvA+eAFurj729R7ISJ9gVE439DbdJndJp5lwG7gPVVt82UG7gPmAFU++9p6mcH5kvCuiCwRkWvdfc1abluPpHESYF+sjpluM++FiKQDLwP/raoHRQIVzTk1wL5WV2ZV9QIjRSQLWCAiQxs4vdWXWUTOBHar6hIRyQnmkgD7WlWZfUxU1e0i0gV4T0S+aeDciJTbaiSNywN6+Wz3BLa3UF6OlF0i0g3A/bnb3d8m3gsRScAJIs+r6ivu7jZd5mqqWgDkAtNo22WeCJwtIptxmqNPFpHnaNtlBkBVt7s/dwMLcJqqmrXcFkga9xVwtIj0E5FE4ELgtRbOU3N7DfiR+/xHwKs++y8UkSQR6QccDXzZAvkLmThVj8eBtap6j8+htlzmzm5NBBFJAU4FvqENl1lVb1LVnqraF+d/9j+qeiltuMwAIpImIhnVz4HTgVU0d7lbeoRBa3gAZ+CM7vkOuLml8xPhsv0T2AFU4Hw7uRroCHwAfOv+7OBz/s3u+7AOmN7S+Q+hvJNwqu4rgGXu44w2XubhwFK3zKuA37n722yZ/cqfw+FRW226zDijS5e7j9XVn1fNXW6bIsUYY0xYrGnLGGNMWCyQGGOMCYsFEmOMMWGxQGKMMSYsFkiMMcaExQKJMcaYsFggMcYYExYLJMaESURuFZFftXQ+AETkJyKyw12LYrmIvOjesWxMs7FAYkwUEEck/h+H49y5PlJVR+DcxfyKNDArpTHhskBiTAhE5GZ3Rbn3gYE++y91VyNcJiKPiIjH3f9bEfnGXZ3unyLyKxHpK85KjQ8BXwO96ru+obT9DMOZBgUAVX0Y6ErtifmMiSgLJMY0kYiMwZkIcBRwLnCcu38wMAtnGu+RgBe4RETGAuf5nD/WJ7mBwDOqOgpIDXR9Q2kHyN5QnDmWfJUA7QOca0xE2HokxjTdZGCBqh4CEJHq2aBPAcYAX7ktSSk403V3AF5V1RL3/Nd90tqiqosaub6xY7jp9gIKVfWgz74EnOWFN4ZdamPqYYHEmNAEmu1UgKdV9aZaO0V+3kA6xY1dH8SxasOpWxu5EmcK9cIGrjMmLNa0ZUzTfQycIyIp7toPZ7n7PwDOd1emQ0Q6iEgf4FPgLBFJdldmnFFPuvVd39ixarX6R0TkdOAmICpGlJm2y2okxjSRqn4tIv+Hs5bJFuATd/8aEZmHs152HM4aLz9V1UVu89dy9/zFwIEA6Qa8Hqf5q95jPkkMA3JE5BScGsxaYJqqrov8u2DMYbYeiTFHgIikq2qRiKTi1GiuVdWvWzpfxkSC1UiMOTIeFZEhQDJOX4cFEdNmWI3EGGNMWKyz3RhjTFgskBhjjAmLBRJjjDFhsUBijDEmLBZIjDHGhMUCiTHGmLBYIDHGGBOW/w8iz7UnU8i5iAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "inps = range(1, 500)\n", "plt.plot(inps, [get_max(D, 3)*D**0.5 for D in inps], label='threshold')\n", "plt.plot(inps, optimized_vals[:len(inps)], label='qaoa')\n", "plt.legend()\n", "plt.grid()\n", "plt.title(\"Performance on Max 3XOR\")\n", "plt.xlabel(\"degree $D$\")\n", "plt.ylabel(\"$C_{3,D}$: performance is $1/2 + C_{3,D}/\\sqrt{D}$\")" ] }, { "cell_type": "markdown", "id": "94a93403", "metadata": {}, "source": [ "Zooming in at small degree:" ] }, { "cell_type": "code", "execution_count": 33, "id": "acf171e2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$C_{3,D}$: performance is $1/2 + C_{3,D}/\\\\sqrt{D}$')" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "inps = range(1, 100)\n", "plt.plot(inps, [get_max(D, 3)*D**0.5 for D in inps], label='threshold')\n", "plt.plot(inps, optimized_vals[:len(inps)], label='qaoa')\n", "plt.legend()\n", "plt.grid()\n", "plt.title(\"Performance on Max 3XOR\")\n", "plt.xlabel(\"degree $D$\")\n", "plt.ylabel(\"$C_{3,D}$: performance is $1/2 + C_{3,D}/\\sqrt{D}$\")" ] }, { "cell_type": "markdown", "id": "8770c552", "metadata": {}, "source": [ "When does QAOA win?" ] }, { "cell_type": "code", "execution_count": 34, "id": "9364220a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1, 3, 4, 6, 8, 11, 13, 18, 20, 27])" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.array(inps)[[get_max(D, 3)*D**0.5 - o < 0 for D, o in zip(inps, optimized_vals[:len(inps)])]]" ] }, { "cell_type": "markdown", "id": "8068dc52", "metadata": {}, "source": [ "# Threshold algorithm for Max $k$XOR" ] }, { "cell_type": "markdown", "id": "f93cc36a", "metadata": {}, "source": [ "The performance increases with $k$." ] }, { "cell_type": "code", "execution_count": 35, "id": "22047e46", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$C_{k,D}$: performance is $1/2 + C_{k,D}/\\\\sqrt{D}$')" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "inps = range(1, 200)\n", "for k in range(2, 4):\n", " plt.plot(inps, [get_max(D, k)*D**0.5 for D in inps],label=\"threshold $k$=\" + str(k))\n", "plt.grid()\n", "plt.legend()\n", "plt.title(\"Performance on Max $k$XOR\")\n", "plt.xlabel(\"degree $D$\")\n", "plt.ylabel(\"$C_{k,D}$: performance is $1/2 + C_{k,D}/\\sqrt{D}$\")" ] }, { "cell_type": "code", "execution_count": 36, "id": "da877b7c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$C_{k,D}$: performance is $1/2 + C_{k,D}/\\\\sqrt{D}$')" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "inps = range(20, 300)\n", "for k in range(2, 10):\n", " plt.plot(inps, [get_max(D, k)*D**0.5 for D in inps],label=\"threshold $k$=\" + str(k))\n", "plt.grid()\n", "plt.legend()\n", "plt.title(\"Performance on Max $k$XOR\")\n", "plt.xlabel(\"degree $D$\")\n", "plt.ylabel(\"$C_{k,D}$: performance is $1/2 + C_{k,D}/\\sqrt{D}$\")" ] }, { "cell_type": "code", "execution_count": 37, "id": "b924701c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$C_{k,D}$: performance is $1/2 + C_{k,D}/\\\\sqrt{D}$')" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Xf2BHX5VKSNOnZ6rrG3/BhYu/RBCcN/U0WCZXaDPPI+6+56totz9Z9h0gTp4eLJ+MkmR7x9xcXvnfPPLoP7tivW73boLgHFF0GYB+/0H6/Qfo9z/7tPWkzDj12I8yGp0DCi17RBBcKMvkeVBqu09Hl1f+N0p9tPx8afm/8/jp/3BFAFdKEU+ARq//AFG0zHD4OKDX78SJH7wiKEqZcc+9X8vm5vvNc3MuX/5fbGw8e0B/NrQHJM+S8kxrEruZ8W4fSZIUzHjnkZhSI5FjtfnixYtcvnz5CW09a9PWFRn/MzRtPYmP5JFHvo/V1T/ZUa6QxOVEuTwPUSp5ApOMoks7nvdcTVv9wWc5ffo/PMmL0Tbt7wTBJH16Zp3nQ5TKdphusnxAHK8+AayWlv4b99z7tU/oWzGGNO2wsvIHT2AaBUPKTOh40daV+lYwxPHeilAqf0Lo+ZPXXdkBjsX8XQmEwnDJtNnf8fdKbY5GjzMYPEzPgGWxNyYl6uXl36HTeaKp8eLSr7G8/D/Lz2myTZZ1kTIDoL39MdbX33tF81oUrexou1iXYkxPRcPRKS5f/h22trTUXqzLJAjefc87OPcMTLZ6zcb9TJM2eT66omaxuvZHfPKTbxrPmxGIij50u/eyuvZHbF3BHBqGF+j3H6DbvUe3n3YASRg9kb+8kLQHJM+SMmOSknKn9L9bIymARLDzxR2bq8ZA8jd/8zd86EMf2lFOKVmCUmaYYhzH9HpPlH5L09YVXrSy7QlfSq/XewLjy0uNZFxuY/OvuXz5D3aUK17USe0qL/u6Mww6DJdRKi2luudq2spSzdgGg53HhVQJJDvB8kpSf9F+ng/KeSiY524GtLn1Afr9z5ba1rhPek3W1t/LyVM/RH/w0I56Y+a8U7u6Ut/GQDLc8TdJtp42AEPKhDjZIMuGE2PSbV8ZSC4BYx9g8TdOdD2lFOvrf/GEQIHh6HFTvqv/lkCyWdY7c/bHOHf+PTvqKZVz4cIvsrr2R+azLBl5sb80E1YMR489ob+Tmm9cAElWALvuQxhdetoxDwcndTtFu2ZdCvDM84ggOM/W9oeeUHdz829KLSzPYzPeUbk+idEAg/ACoDWG4izaJLXbH0fKuJz/Yr4L82dk3qfde+sJYzHrUABXsceiPSB5aVGWaQDYlc7rCRpJmmpGJqwhaTp2xuYyMPXTUuJK05Qw3Cn9Tr6ohcT/8Y9/nN/4jd94Qp8KjaQwba2srPALv/ALRNFOZ+FuH8lgMOA973kPp0+f3jmWfLCjvFIpSqV0ew/uYGBjJhxOfKeZXSEd6u/6paljDKRPrZFMguxu5lsw+Sec5FdPDiRp2nlaplu0r1ReaolFm4V5p/h9MHgYkCXAlqatkuFpprnbcR+EF80YzLzuMm3lecAnP/nmJ0SYFVJkXgY/FIKCLOuORmefAHhRtAoo09dizXcCSRCcNz6TnSbIEvTS3RqJrtfvP8Ajj/5TlpZ27sPR6PSOucgMoBSmxiwbkOeBCU4Ya0qD4UmyrF8y7Szro4+WjRl7kmqmuFt4uHjxV/nEJ7+wFN4KZjvWSLo7xpSmHT770PcyMMAx2QeYYL6G+RdjLoSi0ej0DvNTkmzxyKPfz7nzP2PKFXteTWipxhRutNILF3+JT3zyTTvMZqA1Dv2MNf3sXRrJeP4f3lFPqZx+/6GSl4yMKSw2e7EYUxyvPyPT3HOlPSB5lpTnetMqtdM8NHa2698LIAGtbo7rj5luwbhmZj9Oq/WhHZrBZLlCIxkOh/T7fXq9EzvMTPkuE9ja2hqbm5tsba2wtX1X+dzdmstgsMXNt3yAra1P7hzjLh+JUrqeEHFps4Wx9KlNLnJHnUkgiSYkwgJIpdypkfT7fT796U9z8eKv89GP3THBkHYy335fv2j9waM7mKBizJR3zt/4pe50OoxGHc6e/Sm2tz+6o33d1k6wmgSS0ejsBDgVJqrBjs9JrPvQbn+cSQoLIHmCRrJl2rlAGC1x+vR/2LHupUaSPzHgoGAwjz76/dx9z1czHD72hHo76+40bS1f/p+cPv0fOHf+Z8uySslyrZ7KtBUEeixLl/5b6UvT87MTSIo5yfMheR6WzFipnO2J+el0Pl3OhVJyh5ZWaAbFPA0ngGQ0OsPZcz9DHK8RhpdQSl3RtNXufIqtrQ/w4Ge/Ywf4Dk1oedF20W6abiNlaoBZU9f0F7SpU8qo3CeT5qMkaaOULPtQCBO97r3k+ZBHHv1nYwCMVsr5iQyQ7AaQAmCGw1PmSIDi0qX/zic/9RbuuferWVn53/r3p9BIQD4j39pzpT0geZZU+Egg2aE1PFEjGTOESYa000+ggaTZPMPCvnu4fHlsJ570ociSOebU620eePBbOHnqh8YAke8EiCzL8LyA8xf+IZ/97HeVL/luaX0UnGd2doUw+ilGo7PjsZQ+Es0oJrWvwgaux9idGFeIlBlCaOk/mjBtheHyxFhMYEA21hgATpw4wcc//jucPfsTSBmXTKFkaKZPg+GGmZ+gZNCadmsk4z4XL9Pv/u7P8alPvZMLF3+RZTPXO4FkgJRx+YIHEwJAvz82KRQAOna268/bbV2+139gx34Yj2UnIKRG4h4OjTkjXmNp6dfLdp7KtAXa5KGUYjA8Q5Z1uf+Bby2dxZMgvrvNgiH1+3pPXLjw86ytFVF23YkDtwWQ7ASgMFo2fe/s2K+jYQEk3R1zApqpFe0CbG/fVf6/29E565RKSdPODl9CkmyT53HZ98HwhCkrOXnqXwJ6rwXBObKsX675GMx0HwqgGQ5OIoSNlAkPPPgPjLaqGJrn7tZI9HebRKWmIeiYHHtp2mH58u9gWT5p2iFNO0QT+zxN20a70n0MgwtmvU5Qqx1nMHi49LkU2oieZwMk8cauv4VpMWU4fIx25xM8fvrf4fuLeN487c4nAEqBYgwk4/l8Mc1bVwQSUXCGPQIgnzi5PikhFpLf+EUcA8YkkEweRCxMUpal6zx++t+XEtqTaSRSrfKyl32APNfq/9ixr1/2wqyUpGu8/BV/SZLslBJ3m7aSuAuAUhEPfva7yoiQfOIciY4UGo9lMvR0B5DIsNQyYCczm7RRF21HkYkGMn2L4x433vRxEGLH92NGaMaYjO3LO81bu4Fk3JcCSI4e/TMUbSqVI6UZapLh5flwx5oW63bx4kXOnH3/eAxpDymzCcbVLdvJcwelsnIdw/Ay2sz0RO0qzwNj7tEAIMT1XFz61ZJ57AaSyQCPOF43Y4gZDF4NKB57/Ed31NNtDXT4sRFMCtt7r3ua7e1DTE29mpOnftj0bbOsV0SilVFbySZKSTqdx4njGpXKHVxc+nXyPCTLhiWzTZOdTLyoW0j1rnMj29sfQSnJaNSn070b150zfdvcEYCQpu2SEbruDKPR4yiV8dDDv0yvdx/XXvvD5TrtNKV2zV/dFykjkmSTXu8R0nSe6659D2F4kcsrv18GJQjhPYkUr+e5SHs0M/P6cl0fefTnyPMRx49/30QfJjSStL0jwioILxDHa6Rpm3rtKzl48Bu4uPRrDIeP0+vdj23X8P39xNEaSuXjvpRAskazeSughZq11T9BiDq3vew3mZu7k273bvJcC1eW5ZGmbaRMXzpAAogXrfW/hSSfCkh2ayTZM9FIdBnLStlYP47nLXL+ws/v+A3GGonvfQLLzpie+hrzrJFpUzOJNC2cv5/F90M879v159KUMtxRrmAWUfROougSG5vvM+ULTSRHyqQ04+W5v0MjySaYhcx3pnMpHJ/nzp1j6eK4TsHglTJ9TgrA+BjV6oDpqXeb79vm+51RW2nWJ009wCmBRK9Jf8f8xvHYL5UkWyTJgGqtR7f7GmamX10y690aScnsc6e0Y9977710Ow/gefNlHyaZejEPUvbodA4gRIXt9sdQSrG9fXLH8/X8TmgWyTZhuIKUFln6LeR5WJ47KJhjvss8BZrpFuaZbucwi4tfYQIB8p2mrWzwBACSMkOxRTCaZnHfdyJlRK/3AKoEEvEEH4lSGWnaJgyWiKIGjvNVpOk2a2t/ysmT2gldqRx6gqO76GsUr6KUoNu9hSTZZDA8wZ/8yc+R58MyDU8Sb+xg4kmyPeEfOWzWeZXNzd9hMJhj38I34bpzBMH5ieAOsSOKznVnAW3e6g9O0N6u0W7PMjV1B+trf8bjp3UU1PT0q0jTwhzVRl/cqjWCKF5F5nXC8GqC4Bzr6+9la+t/EkW3sm/hSwEYBeeIohUsq6rbTtqlf6RWu5YwvFju1w99+AxXH/8BbLvOyVM/xqXlD9NqvZxK5TBxvGbmQGLbdeJEa55xvMbU1Ctw3Vk6nU+zsfE+VlYOcurUWWamX0uadtjY+CtAMTWlM0Yl6TZJul3OwecbSD6/N1+9xEjmTwUk+mVVpUZS+C08gnASSCYBYgwkcVKlWrl2IqR2wuFcMGgxIo5rII6aZ41QSiKESdtShL5KE3GTHNOfS/PETnNF0dZoeMyU395RvmhDGr/GYHCEMFwqpZydpq2ANC18K3Ypod53332sbzxKIY+MQ4VNdFsZ+bVGntso9XLzbG12KM06hbktG5CmFZQ6yGBwAikl73//H1BK/aXZbsI8kW4zHOo1GA6reP6+UsKedPZn2VgjGQ3nSNNtsmxAHA+p1tq0Wq/T5dLujtPs43kYkMQ1fO822u2PceHCBd73vt82v82Tm2cnySTIbRPFq8RxjSBoUK9fS69/P0tLj5OmHWy7gZTajFoCkLKI4/US6Pr9Cq3my8jzEZ3OKUbBpTIvmQZHszeVqyXseBUhcsKoiRBXI4TN2trH6XZOI7CpVo+W0VpZ2se29QVIcbxOmq4SRQ2S+Cj1+nVcWv59Pv5xDXzT06825sGULO3hOC09xniT0egySVJhMDgOCJaXfwchtON4/+JXmudvmL0lcN1ZzQjNXltenjZjeB9CrHP58o30+31qteMlEweo1a4ea4hpF8FxM0cPkedbDEczjEYjFhffwXD0GCdP/iYgmJ15A0rlxrzWpla7WvcpWScMVxgFPpubWnN65NHvI46bXFr6IiqVIwjhEATnCaNlmo0bTdudUruanrqDPA/Ybn8EpQT9Xossq3D0yHfS798FLON5N+P7i0TxWukfaTZuRsqIOF4jywZ86lOnqFRuZGPzr5AqYmP9ajqdDtPTrwXg/gd+CoDZmS8we2uLJNmiUjmA583v0NpeaHrOPhIhxGEhxMuEEPUXskMvddqtkcg4Y/Wn7ikluCIZYwEkQTBDYOyjANGEpJzLGClzbDtH5i4Kv3R0F0wZxoAjRECWeWSpbdoY7fDTFHWlHCClRRR5ZT/138J5HhkmXTiVbWy7MTYnTfgX8jxAGo2k2zkIQK+nD7oV0qcuFxLFWsMJgymSZAspY+I4xvcG+P7hspyUCUKYEFrz0iu1TRQ1CAKLQqrUGlcRamuARA7JMo88P8xg+ChbW1ucOKGdt76/v9TSwqCLUqCURZpsMzBA0u95+N4+I2F3SNMuQrhm3APiRPenP5g1c3MeqZawLIXrvNyMuz8hRPikWdeMKSRJK1j2ywjDJTY3H6JaHQBVYF9ZJwzbJLGWXJNkizRZI47rBEHAVOsV9HoP8vu//0sANOrXlWsdhcX6zJEkmwxH542Ub9No3ALARz/2P9jefpxG/cZy7UtwHLVI007pkI3CFmGoaDRuZn3jE8TJMo67D8+dHTvZky6dTsX0exmp2kRhgyAIOHDgaxiNHmJufgmlHFrN28z89EizLrXaNYBFnGwSBJeJ4xrDocX+xXewuvoH7D9wL0EwRa1mmG+yQZps47oz+N4CaTI2bbXbc1iWj+LT5HmDrc2r6PV61GtXMxqd48KF+xHCpV7Xwpj2dQWcOZMAgs3NvzFzMMNwOGRx39sBi4WFJaScp1o9Ml6PdJt67VqEcIjjDYJgmTiuMxxM4zgtXHeehx96M+12hBAaeDfWH2I4uEi1dhVQI023S6364Yf1+7Ox8T7SdAYpXYbDIUePfidK1RACsvQYFX+/1kiMttxsGVOWCfkdjTzyTPfTshbp9xfo9/tUq4fw3INUKuso5TA9bTSSeJMk2cLz5qlUDn3eNZIdJIQ4JoS4H/gM8KfAhhDi/wghrn+hO/dSJKnGIXRp1ifvJ6TbPRQ6/K7QSHITJjwcTJsDSdpsEARj5ivzEEVxKt1BqUopdQZBtyxXMHYhIvLMI060dJ/no52nyovQYjkkTX2CoLDNF6fCi7ISKSPybIBSgiDINfMobf1jP4TWevRzt7bmEcIdA0naxbJ8Uy4gCnW9INSSaBStEccRfmWIZR0pyxXhvWnqkcshUqYItg0zDXHdaZK0MyH1VyfGMCLLPJJ4kTTtMBhcxPP1/NRr15bzEUU98txFyjpJsk0wugDAYFDBsjVIxPEGadqhUjlo5mlQpr4ZDubMOlzAtpbMvBxHCM9oJAVzrpCmvdJBm6YVlHyFkVLfT6U6QMo5PYa80AT7hJHWGJJ0myzfNBpJwNTUHWRZj6kp/dI3GmNA6Pc3kNIiTVvE8Tqj0QWiqI6UAiEOYNs18uw0tt3H968xe2ccfh6M9LoUDu4wbBIEAdPTr0LKs9SqffJ8FsedKh3FSgUEwRRQ+MeUAfyA/YvvBCzm5i4Tx7Nj01/SJkk6rK70EaJFkmySxGskcZ0wDLnllp/m9tt+j7XVa1laupXhMMZxWsTJBkm6jefN4XpaI4kizVSTuEa1ei0A/d4rUMo2GskxsqzN6to92PYCrjtTCgh6zapY1jzdnnZoj4YaSDxvHte93azhuO/6VH0b15vH8xaMqakA+ojbb/s1br7pvxHHDZIkIQxDarWr6fVPkuVbeO5BoEmStImNhn/xom3Wvc1oNGvaHOE4TYaDN5OmHt3uDH7lAFJGDE1wzNgn8nA5B2l6CAAhXg8I+n29tq53q9n30/j+fjMWrZE49iy+f/BFPZT4XDSSHwN+RSl1SCl1DTAF/B/gr4QQ172gvXsJkpIpUuppy7I+KlNIp2DQotRICmY5HE4DYz9J4WQGEzZbZgN2kdIr7dnD0aS0rxm5JULDRMdAUmguUopxlBVDsswnCBKEcCds8jF5brSZfESeD8gyjzCMDPNumz72jB+iOKmu+xjHHtXqcZ1ifqNHEnfw/QPlWAptq2A8UbxClnWw7Zw02Vc+L4qKy8G0MptmPYTVJooaDIdDwwzaE8zaR8rAMLaR6bN+8QeDB6kYIKnVrh77SJIBMneQeY0kbROGF0lTjyzzkbk21STJBmnapVox2lI2HAPJcA4QDAaP0Jp6kCiq0+9buG6LNOuVYBtFTbKsX8b9p0mFKPKZn38LWf4xarUeQdBAUJ3wv4wIQwMk8QZKdcYayZS+4HNh4QIAnn+1qTNkONoiz1ziuEISbxKGF4kMIAVBRLNxC9XaGSxLMhy1AIssG9Drre1Yl073M+S5Q5JUGY1GTE+9CiFSGs02o2EVx2mRpX3GOasMkHTvK8ccBAG+vw/HaGn9fgPL0kCVpl2CYJPBELKspqX8bJM40WAJYNvXcvr069ncuJrt7W08bx9huMZotIoQUzjOLEnSZjhYIctclLLxvesBh40NDa69Xq80QU1NrROGVVx3hizrlY7uNPWBBUAhZZM01WPW9BoA2ts1LHvG7Mk1sqzH3XefIMsaBKOzKBWWQD89/SqU2kdB3W6XavUYntdBCMX2tgKapGmbTmeJLHMYjRql1tvttMz+0u/k5ubL+Mynv5aNjX4JAPffrw9nVnzNTgcmYjCOa4xGR7jqqncTBq8z826OHeQGZPtNksQ35TeI4y3uv/8Mm5s5cbzyrDNVP1N6LkByvVLqV4oPSqlMKfWrwP8P+JEXrGcvUZIqJU21qp9lA8gkW65mIq47i1JFri0NJKOR3qBBcJ7Bx5aJRt2Smes08YUvxTFgkiBlUmoumvnpjW9ZkWaiUeEPGDEcjiXhwpeBHJKlHmEQ4TgNdJ4liWWlJIk2qeTZEGnMRGGotYA07RI8vEmWDcbl8hGoEKUEUjr4/hGC8AL//Vd+k+FoHccpACIgjsamLdAOd5VpiXI4bJXPGwyKQ1IaSKLwEpYVEkd1RqNRKVUWZqY4rpn5HiFESJ55DIfzeN4+BoMP4vsj0sQny6solSBlSpoMyaVDlteMH2KZyDDvNNNAsrl1hsFgjZXVIeCTZQOiqDhcWMF197N06b/h+x0ef/z1dDodHGeaLO2ztaUj0aKoAahSUEjTCmEYcvDgNyDEkEplRLfroaiYdVAIEZEmFZSqmHDNvASSWu04QjRotraR0qLfq5qxDwnDNlnuEoU+cbJJHF8qxxQEAY3GLfi+ZlAb63m59lvby6aMXpfB4IQBIMFoNGJqenydz/a2hWO3SLM+/b52YGepDzTpm9s6o6hRMmMpX2f2+RTDoTLrtUWW9bXQk1TN3GhmnCQJWZbtOIDbbrfx/X2srp5ie/sC585tce7sBmm6zShYLfdiq/UuLPEvGQ4129IaiQYS287ptEGpGkplbG2dMvPmk2XTpl/7zF4cmn16Ixsbx9jcPMrAyHenT3/EzJVDELjlYcVifYq5LqjT6WCJA+XnM2c6QIM0adPpXDK8wsJxDpi2Z3b0YTAYoJTNxsYGFQMkvr9Kkvj81m/9HwB6BkiSpMZgEHHtNf8CU70EkjA8glIwGs6yvLyBbTc4ceJDQEaS+Gxs6MCZZ5LE9LnQcwGSJ3W+K6X+Brjp+XXnbwGpjCz1UEqQZX36gz4fqWlJrduVFCffi79h2EIIlzC8SP9Dl0jjYQlEuQyRqsiT5ZBljvn/iDAs8jhVyLIRSiksO9aM35is8ixgMNguy2nfh0SpEWnmMxqOcOwmeTZktGkc5CVABEhV+BtybGeaNOmw/T9PAuEEkARARJa5gMBxDhKGlxjIPrYdc/FCES0VEifFifDCtLWKZWmg29xyy3L9vgGSSANJEc0SxY0SSJLRNo/87gd3lNNhmiFZ5hJFCQf2fxVJeh+NZps4rjPoJ2UbWTYizx3StEKabJMkl8fmpFjP/wOf/hBZ1qXdjskyhywfEkdtlII8d3Gcg4Di3NlX0+seoNPpaI0k7bK2qs/dRGHDjLlI+FchiiLmZr+QPNeMOxjVSVPXOMPXsCxZmt36A222iOMaURQhpcK2rzPf1VlbGx9+TGJtrhuNXLR5ckgY6fZHoxGeN7YuX7w4wHGaZNmAbnfV9HHK/CoJg2ZZz/fmieNpsxYVktQhy/pcvHjStO0h85bJxmAbcNDMNAyuY/nSzWxuHKPdTkzbD2HbKZbVJArdcm4SIxCEYbiDGW9vb+O580jZwfcTms2DtNupCXRYJU0qZj484GgJQr1ej2r1CEoJs99qrKzo/bi6qhM15rJKHBVj3cnEh8OUM6fvJAxbrK8PAJv1dW22XZg/znBgU9w/FEf1EgQn+97tdomiqfLz8nJIllZI0jaj0TpKFS7kAsRmyz7oMyxDhBBsb29j21rLrlQCGvVD9HoRUCXPB6SphxA+g4E5UzMo/G0hSZLQ7dqcfvxr2Ny8maWlJYSYIsv1Oaurr345mxvSzNGLY956LkCyXwjxXUKI1wohGrt+e04RXkKItwkhHhNCnBFC/NBTlLlTCPGgEOJRIcRHdv1mCyEeEEK897m0/2yoeJmk9MmyPsFohO3ozaZVylSfvUjHmoZtG7NRJsmJSiCR+di0lecuqQGS4allgq0iMqqimb6MsCxpgMQ4oOMBvbVV0/aY8VtWQJb6hFGI7TRIhl1O/7y+3yEptKl8hDL+BgBBgzTtsGV1saycJKmVz0NE5Lnum2UdQKkUp76BEBBG43aL8OIs87GsaaJoBdvrArC2mmFZFXIZMBoVZ0f0S1ZIuoVG4rmzJGmbZXVpR7kk2UQISZZ7xHHM/gN/H5A0m9q/0u2O0+nr2yUdktgnTjbI841Seh+NEhxnCmm3cZyUubmryDKXLBuSpH3yXINmvfZOjh/7QVZWNIPudDq4zjRxb4uNS4WpUr8Cw9EZ00etkQhhM+i9zJRpEkea2Z2/pziA55NlNSJzwK/UzqIImR8zm22WS5eKNCF9snxInnvEBgiBiTGNgKvK7zsdC6WqZOmAQX9jog1t9gh31IN+TzO6MGrQ72eA5PIFLQk3GgulFpckWpMpmOloFNPrvRUpZ1hf1+u/dEEnDDx44FqGI7vsUzHGSSDxPI/t7W2yrIHnjbCsmMXF60jSwvd2iSStlvXyPC8DV/r9Plk2XoN6/Qhnz2ozXq+nAwrm544xGum93OuOx6yUYjAYcODAATzPY319A6Wa1OpdABYWjtMfjPueJLrvQRA8AUgGw3G8kZTTdHu5Ma31aTS0JpKl1+O5t5Fleu2GwyFhGCKl5NChQyilWF0NSlBsNA9x+PBh4iIoI65x/PjxUgMZDAYIc+ZqMBjQ6/WoVG7i4MFjLC0tMRza1GpaCFncfx1RVOyvlw6Q/BvgFcCPAxeFEOeFEO8VQvwXYP+zfZjQAdu/ALwduBn4JiHEzbvKTAO/CLxDKXUL8HW7HvN96PveX3RSZEhlIXPPmIBSHLtIi6I3iVIJeVrk5LKwLB0tk2YpWLGx2+qT7YX/Ic9d0kQvx+DBi0S9rnmmT54FEwfEPEYj7dgPL66xdc+ZHW3n+QhhR6SZR5ql2FaNLOkzcIqQ4LFpSxkTmO5nnVyOWPY1Y7ONQ1o7+iPDXAFjH261NNDV60fKsRQHIvPcwbLm2W5/lAMHHyeNq0SR1ECSh4xGRS4j/YIPdplMHGeKTHYZusUcaAZQhBRnmUcURTTq15GnOhTaymbY3jaBCuubKBUhpUMUe+acjSw1Et3GHFXDNCqVOdLEJk37pGlvDK7iZczPfxMgqAmfXq+HbTdJsi6JPQTll/M+HJ5FSos8d0uJefXSzXTOvpHR8ABhqF/6y4/oMzVTU/vLujDWuoIgIAq0Q7WSL7KxYSTs9z+IZaV4XqsUGmAMCEEQEMdTWnPM6kjpkiQ20eYmo8EWStlIaSOElsrDaFwvTVPW1w8jw1kc6xDtbd3/9qZmxpXqXAleYVhHCEGSJKRpymg0ol6rs3//ftbW2oAP9obZG4tldJreF+M2C2Z86NAh2u02w6GNZWmAmJs9VmohQsTYxn8RhiFpqoW2arVKr9ej3W6XGvA117yGTicx87lU9mFzc46F+bezsbFAtVolz3OiKGI4HNJsNtm/fz8rKyuEoUOlooF1Yd81pTCllGBm5ljZ92J95+bm6Ha7tLcTsszDcxd4/eu/kH5PAjmVyoCZ6SO0Wi16vTuwrH9e1huNRqVmdM01OjDinnvuIzHj9r1FbrvtNsJQv3dStlhcXGQwGCCl1JFni4sAJm1Sj6mpKa666ipWV1cZDASWpQXOQwdvHL9DLxUgUUr9qlLqHyulvkgpNQd8IZrJd4CPPH3tJ6XXAGeUUueUdjD8HvDOXWW+GfhjpdSS6UOZ31kIcRj4cuDX+ZxQhlIWuQGSNE5wjEaSGclJygSZRcYpL7BEgzTp0iPAtjNkbsrlISIbm7aSxPhO5JCUkDy3yXOHXAYTB8S8sRM9GRILc0rdbMAk2cayMrJMg5UQNXI5ZOgUuY/q5u8ITDgxgFT6pdmu6xfQ88a+DyFi8qKc1Op3s6mBxHMXjCkoICvPkThY1hHieJ0wbNJ//K0AKOURr23TOaHbKCTU0eg0UtrGPKeABkpkeH4h+RlHqDlhrB3OMVJKor6OvHGzBdpt3f6l37sb285A+USRW65cYYYajUYIMU29rjWjWm0fWe6SJD3yfEieuaZ/cZn4ck42zdpUyRjgOAmO3URKPW9RdIE09RHCKuuMAkV28Y0sziwyMlrkqKK3ru9PE8e+mVMXIfSeCIKAfmcGmTtMqWtLAO8n2zhOSq02WzI43W6DSqViGNOIfn8BLzzAwsICo2FGnPbAjrCsGpZlI804wrBFs9ksGVqncwj7k/+cQ4vH2djQDE5U9fxUK7MEgWfq1ZmZmSn7OhwMcS7FzPvTrK2tkSYe9erQ7JH9pTahFLRaV5lnhCUzPnToEJ1Oh62trBxTs3kQ358vP1cr+7BtmyAIyDJdbnFxkSzLuHz5MqGJErzu8Ku4/bY3AOBVuqA8ms1Zut2cI0f+PVnms3+/lnWHwyHD4ZBGVYPg8vJyGS4PcPDADSUIxnGVI0euKsccBAGO47CwsEC322V7u00SzOEOFnjzm9/MgYNag3WcjHpjP9PT03Q6Hfr9Pp7nMT8/z3A4LM1TR48exbZtHn/8cVKj+TjZNLfcckupCbnWAq1WCykl3W6XNE05eFBHG3a7Xfr9PlNTUxw9WpwxG2tJtdp+9u8/Tp759E7sTHz5QpHzDMoIIcTLlFIPP9mPSqllYBnYfUHEM6VDwGSe52XgtbvKXA+4Qoi7gCbws0qp4qTXe4AfNN8/KQkhvgf4HtAb8K677nqOXQVUhpQeSSrY2rpEeOYstlNoJHrjfexjHyYYdam4Ghj6fYnnreCIEZaVIUQVKW0uXDhNFlfxGpr5bmz0OHYchqNt8maMlNoBH8eb3HOPxugs8xgFAUp59AYbxE6FOmNN49579e1smdF6trZHeHQYOUN8IMv0Bnv0xP3G36BfngsXNmk0YFQxyeEGglYLzp59FAjJDEN75JEl9i36NI1G0u3m+BWHCxceo9sd0GpZgMXFC29kdvbLePihR3ldeh24p4kixSDcJE4FDbS2pZQDZMRRC1+5xCLj7Nl1XA/qlSFIp5TcT5/Rd1lkuR7bhz70IVaXDnHAOog/uJEs0xJ0IPpYVgb4xBPMIYya1Cyf8+fPc/QqSbWqBYCN9SF55tHvbxBFDrnU7Z04cYKVFa0FzeZ1LjlbLF/aplKNqDk5eeqiVCG1JqTpDL7v0+/3+fCHP0yYRlRwCbOU/sCkFa/qeev1EvLcZm5OA6rva1/Y3Xffzfpqh8HFb+FA43XY9t1IaRHaXVw7JY5EKTRkWQPLqiKE4MKFC2xubnJ5+Q28XL2WS9dEDEc5drONY88hMw/HcRgMHFotrcnUazqE9qMf1Qksq8qDKGQw1H0tpPNOJyJObPbv18BVmFQ++tGP0uv2WMj3odoJSZIQxy6NhgagS5fa5b5MkypKabn1gQce0CG4wmH42BZKKS5caPMyfQyFRx5ZQohWuW5B4GDbNufOnaPZLA5aakD5zGc+Q5oe4Ph0j4fvXsaqt1CA74eQTbOxsUGWZeU1DYVG89GPflSbEe9ukx41563M+4uyuP/+UyCmAb0+STww79e9tNttLMtiOByyvb1Nv9/HWXk719vXcVftLiwx4TO50CWOp+h2usQ9DUD9fp92u80992gT4GOnHiuFAdJpYIv1pZCV9j04UoO2DBosLWkB7AMf0PemFBrN3XffjVKK8N4NVroKy7KoOvuAE6AEn/jEQwghWFq6hSn/CHfddRfD4fD58cFddEWNROnVHwkh/r7590VCiGcCQM+UniwFy25fiwO8Eq15fBnwr4UQ1wshvgLYUEo97cXQRot6lVLqVYcPH+bOO+98Tv/e9KY3IYREKQuZ+zQaFouLizh2CkoghN7kr3/9q/A8Cyk1kLRaB3DdmK6lNZJWc548dzh0aAHX1i+tzF0qlWkA3IpE2jEoz0j3GTfffEwPJquilML3W1RrgtQusuhq5nLttXrjYV6KmZmDWE5C4OgXochrdPXxeYQlUcZme2C/dvBWqrrc7NwRpHQ4cmQftpUgDeAcO3Yc1z5oDtrBsaM3k+c2i4vT1Go2UmrAOXr0am6/XUuHTVWlXq1hWVU8X5E4Yy2smLM4btBUus+Hj+iYjXp1hEODqSktRc7prlOr6v+86lWvQog6aw9+LYvxy8il3pahPcS2U5rNudInpJRHFteY8prUajUq3jiE8/Zbv4Asd3HsFNdJcZwGlmVx6NAhbr5ZW1nnpWZsxWnthh9R9+aYmtpf2rXTpMLBgwfJsozXvU5HM/nK5cYj15KaQ6S2r+ftyJHrSo0kieulJHn11VeDELjRPPtbB/mWb3kXee7S89o4dsrBQ9eglI0QU6DmaTQaLCwsUKvVmJuZxU5bVIMFvukbv4n9+6/GsmMcJ6VemWNmZgZLHEaIWdKkynXXXYeUkmPH9N6qKZ+/9wVv5a1fog0C+w0G33DDK0rpPAqb3HTTTeb7G0jzlAoeNx3Q4aeCBgj9+r7xC7+sFK7ipMbtt99uxn6EmekZqtLjGqXNM1E0NvO95o63cOutry8/H124ienpaaanp3Ecp1x7MNpN9zhXf/I/8cqbX82b3/zlYNajas9xxx06nLpl9kFRrzAL1ZXP7Qf1eKaq2qTo5C3e/Oa3cHBehxnHcZ23vlVr1ceOHaPVajEzM8Ott96KlJI4jmkOjtAMj3DnnXdSrS6Ufb/28G3ceOONxElM2o3Yv2+R66+/nizLOHRIt3fz/S2uPnbc9Efv9WMLt3LnnXdysKG1mwOV63j96/WcNIyg87rXva401QHM96rc1riW7//+7+eOa9+4YyxvfPUbWF6+hfrUG7nzzjtpNBrPmv89HT0j05YxO/2xUuqPgc8CbxdCfLUQ4suN/+L50DJwZOLzYWD3Wf5l4H1KqZFSagv4KHA78AXAO4QQF9AmsbcIIa582fZzoO3Ll3j/b/wywspR0iJNXbK0T5qmOE6CyKoIqzBVxCiZlEAiVY0069EVA2w7x0ZrJLmMwERtuVmNIiIyVD2tueCRSwelIqKRCTFOtXlGiCq5CkltXb9gmEUaBMfYRGXukRMQOUXsfGtHOSvVEnWSaADwK1rKcZymNqvlAZZIEHkRmx6DHL8oNXcBKR2SeIiUIUp5WJZFkiREIz0gF5v56TmSBKSKyOwi9NMro1rCqEZDFeY5zcG8Sh9b1vB9LeHpBIhQq82XfYmSGA+HmvTZv6jND5EzxLYzKtXp0tausllcHKp4jEYjguHY5NXyF8kzF5kPQQZYoo7v+8RxTNjX5rVpVcOxHc6d16Ypu9LDzmvUag2k9Ms1mJ2dRSlFt9sFoKJcjrUOUa/Pm7a09lqpTJfgH4RVZqbG5qIgCqkqDxlmHDt2DN+dwnViLDvHs/S6OvYdBMF1VLwKNb9qTGJ9qsoHBSrKOHLkehwnY8qysGWdWq3G1tYrcez/CAjm53Wf1td1Iseq8rBSuOYaHSSQV7exZJVWa4pebxHVeT3d7n4WFvT6b5mAkKrymKPJtddey1zjcDmvFX8O3wB2HNeYaU1j2zZhGDJq9/GVSyM0czfh93HiJocPX1+e16pn81Sr1R2mrepDet8PBgNaGFNxkCKEjW32lJ02Sg3m0qM6OKIwba2trZV9n8lqvOUtb+GIYdq2eXfmW0eI4yrpaI6WN/ZhhWGInzk0jNYPMKVqyDBD5QrU2DhiBXWmp6cB6DCknvnU63WUUmxsbOBgYY8kc3W9/s1YA5xjIsEO2BpgZkYHnjCWRqNBq9ViY0PvyYaqkLUjms0mTqzr24l+3w809iGU4HIwTsz5QtJz8ZF0lVL/Ryn1J8BfA7cbUPlGIcSx59CHe4DrhBDHhRAe8I3An+8q82fAFwohHCFEDW36OqmU+mGl1GGl1DFT70NKqXc9hz5ckcJ+j4c+/Dc6tYe0NZDkA9I0xXZSrKxanvKWMkGRoIyErH0iOSNfR+BY0tf+jywApQ8JVlWFINR29FB2sewcS/lltFQ00v4B32xyQZVcBWRWkfzQOEONM81NChOAiyIld4uzKA2Usss073ZaRyCIY81YKwZIPLuhQ2LTIcJOIKvgCocoisgSoxooQd2ZMf6dMZAUTDge6L55ymHf9AJhKMkIyC19aNO2ayjjY4ijsUbS7WhmYbkxVlajWp1GqXGKbWdZA3QURURZjK9crAxuuEHbRra9bWw7x6VWBjZk0TQONhWlgWQwHEfk+PkUwqqBFWM5MVZWHQNJZ1iOYbo1RZLo9VBuiJXWqNfrpT8qTSvMNKd1H7b1WldwqSmPG298BQAznmGEtbG2lMR15Me3cG2HwWBAlMUaSCJT1pth0dNStmcOUyr1rWyuvAJ7I8Fe107v4WBATRlfVpTj2E2ElVPxEqy0Qq1WYzQMGVwKsC0bf1k/f319HaGgggavQuuSboCd12k0GuS5y+qDbyTPPeamdCDG5qZmSlXlQSh517vexZRj4m2kjaWqNCtzJly7gd+FWk0f7BsNRlSUizuQVCoVLFHFyiqIzIfQZf/i/nLtWkOtcYVhCH1tmvJPRFiWZl9No1VLE4RiG6e+HdVptfRYtqwBKJj1WgghWF3V+7+mfOQg5U1vehN1IyDZJhBhsTLL/fd9JaOl15CvhlQqFYLBiMFaF3sjxXpwnGtvStVAGTCT42BWe1QrfUpKgN/VAACwunSZqvQRCG5duI6v/MqvZGbzBqy0jhtoQKn1b6a59mr85aNlvS3LnGZfy8rxgQaSvGMyig/NHIQtlFI4keIauUh9aneg7QtDz/c+kmPAq4GvAF4OzD7bByh9Hdo/RoPSSeD3lVKPCiHeLYR4tylzEngf8BBwN/DrSqlHnmffnxX59QaW5WBZEks5pEW4aBLi2Al2VsUWhUM61gcT8+JciN7oaUVLcCL3kdIhy0MgRuYOVeURjDSQxAywrAxbVpDmGWGgN34l0xtH4RHnfSw7AyVKyb6IyvDT4pSxZpi+V5woriFzr3Rci6yGb3tEkS5XNXZxV9WRuUOSDrDtBHIfT2gnd2qkJTttULcr5LlD3OkgowCVOrjYRiPRbbo43HToWvLMJlQDLEebAh3HJy+c1XGduqogECxdGidctNIq1WqdPHfJc+P8HRbmsJgoS/ApgESbThITcmylPlK6OM4+4v4+XGVTzV2CIKDTNdZTaSMiD9dtIQQ4boIY+VQq+jxIoZF4OEw3pkrfE4CVaOacGm0uSyqoD2rpsAASX7moKAfMocqKyQjrz4zPVUQNfOlQsf0xczZMHcBWNSxjErOjCr7vM1jpMNro4eUOlVA7ogejITUT3ivDDNuul21aSYV6vc6oP6R3ch0/d5D36vlcX1ungoeFQIW5TvhozENWUi0ZWFsYJ/wHthBClJJwVbnIQDN424QJ22kdOUqZ8ps8/NBbWb50K86FmGq1qsN/wxBfuZAoFhf2cXjhIHY8jZO0kMMUK1Eooy17a3WtkYwC3NUcV9k42DRruq2W8VPt7oMIxn0PREwFj+H7L9FoNMr1qSqP3Jw/sgLT96iBSnMW7GmyzGcqb5JcGlCtVmk/skKYRFSrVaob41PiU0UfRilO4iNyE/nXrzFVHWsolY4BXmC716Em9Hp5fXjFLbdTW7+e6z78C1gDLVRZ/RoHH/pH0HERqaJmV0hFjo1F8KcXaJk5qCgXx3HI2gZI+kYri1vIUUreS7gzvYXXv2FsMnwh6fkkbfy3wNcA71VKfZdS6oeUUvdfqd6TkVLqL5VS1yulrlFK/Ufz3S8rpX55osxPKKVuVkrdqpR6z5M84y6l1Fc8x+Fckfxanaa/DyEklnRNZI8iCPVZBDutY5VAkoDIUNLBEXYZO25XNDMQmadNW3kIIiaXDjU8oijBsiqkToBt5di5X0btJMkaWeZQlyYKRvpkItBAkntl1E9kzD9O2sCzXZJUA5HnaXOSrSrk0h1f1pNV8C2XMMyR0sX3CyDRUuigZy6Pynw8tEZShJzaaZ0qFaR0iMMeWDGkHnasw0OjoTHbKZvF2hyu1yCzQiwrh9zDdb0SZOOogYtN1atwaWmr9DtYcZVarVbOg5QWDSPxDQYDJBJfOVgZNBpa8nM93a5tHO2HDv4q7Yt34GJTMcBcnG+w0zoqzPDdsYPUGnh4wtFANQgQChxs5luzOO5YArSiKvV6naQIoZYNPHMWqL1lgAQXGWUI4SKUg3QikDZ+XtOpRu77drY2j1FpVKkIb4I5e8hQ274tVSPzu7rRkatDX09vkFgZ9fkWnjmjMoxGY40kTLFN5I6yE0SoQS/OE+KapD7doIpn5mJITY0BSAgLy+wzK6nSqOrn9KwRjuUgzwyoepUS9Cp4yMCAXjIGkryX0LTqDIdzZGkV8fiImgGEKI+p+nrtv/pL3sFX3PoW3HAeJ5olHybkg5RqPIvKfORqpgEoCIlJqTY00246+m9LFqatog+6v1ZQw5KCqnkvG/U6wQMb1FxdXihBY7aF7MVm3U3fkxb5IMWLBC+Xx7ipeYxkeUDV9nWYtUiZOr6Am9pU/ApNp4aDibgcptgJ2MYiQKdCNXIQxfkQVcG+aI4GoGjOtLCnfbLNoASB4jkAcpAiXJOSaTMs16nRbEKqcC4k5XNrty0ghykyzrG2K1pYS6bI+wl5PwYBVmMcfPJC0vPRSH4c+Aml1KkXqjMvZao0GrQqi1ojkW4Z7ZTmfRxbm7ZsI12M+lsgUpAOLk6Zt8o30r6V+sjcIc9Ck4jRpWIYgG3XyJwIy85w0rFpK8k2yDKv3Ei5dFF2hG3liNzDEkbrydrkuY0tfSqOXx6E8wvmKivkuVvmfbLSGhVLp0nJ0grCxJ67eZ1cOoQDfa7Eyip4aOY6GtRMXS1Jy9xBWSnYKZZdwZXaRxIbp4+Hg0okc3OHsOwU28oQuYdrO6VZKIrqOMqi7lXJc1maNay4QrVSNSfrddRa09LtF36IQiMRwgNl47kmPb+JwR9uhyRJrk1bxjRV2OTttIEcZVScMZA4eQN7pLRpKwhxcRAI3nDDq/m2b313WU6E2t5daCmWNY2v9PO3DZBUlIuMDCBIIyVmVfxYv3qd/jxKWdSmG1SkUx4QrCoPMolKJXZeA8vcL9d3qXoVwjQmJqM226CSj/091QlAsPKx30GMXGpVPW99EVJr1qmoyXpjANJ9rJf7w440kEoU9WYdu+5SwSNJNBOrNxqlNmAVTDytk/cTmsZ/1KjWIZb4uUuv0yUXkuYhDfyVxMZLLPaf+A4OPPLdmhkOEqaGV1FXx1BJjhdaSCQ9P6LWrGPVXeroPd9SVXAs5Mj0wYSV20mDbDuiZvrQWpzBanl4xiJVxaN2yzz5IEHlCrtfM3uiSd6PyXsJr23cwlXHNZB4oUXf0nuruU/vl7naNHM0cRYMmI0S7AScpIXIXVQb8nZc+v+mD8whPz1OUzJ1eA5noUq6FY7NUk0POTBZGgYJ3jEtvMQX+9RSvWbNqSZTX341/qbWrJtOjcoNej7zTkTeyzl07h8xfektGkh6CXbTQ9gvzvVSzyX77+uFEMI4vl+cDGAvQXL9Cq1CI1FOCSQ5QxzHmLaMWeGvf/mnQWQgHTzhlM7jQtoXqUteONtFQp67JUBYok7uBDhWjojdMhIplVvkmVe+8FnmoOwYy86wpIctXJQaM1tbWVRtH3OkgboXg7SwpVuCE2hG4Qt9iC4xm1TkHm7mkOcOjgmRFaKGp2x9kGtkITMPO61DJBGiAnaCZadYooojbS3NhxFCCWwsVJyxb+EwlpXpPuc+jrLpd45gtV9BkmipruoUzvFa2b+K7ZUaSZZ5pUmj09GmGc9oJCiwqVJ3jY9loOt85n//IRk5fsWnKgvNxkGkVQ0kQUrFHgNJbXoBe6DKMXgmSt7JBa364nhTjDxt2jJ7wXJa+Eb6bXc6CCXwhIOKCtu9kfKzKl6kX70e2nRWn2ngZ+N1qRb+tmgXIPRsfFxGIkIqSW2qXmoWAHXb+AvCDCubqBf4eOZQZDfuU2vW8WoVHHOBU015ZL4ag54xK9lZjbwTl/uuVqtRuX62BEJLCZrHZpGBzuhgh4VG0kD2YxomMq0108KqOVgrMf2R5uRTx7RPIu8nmmGyiMcBo5EkLDz+Ddy6+It6PzxmUoMQUK1WcRdr1Ixfr2nVcBequg9SYYe1sg/xmU4JJM1Wk6m3H6cS6jHX3SrOXFX7NoYJdKrs2/gmWquvIx9oKd5ueXiHm8hBittXDIV+oerzejxvm3sdbwxuwD+u948cptiJwE6aOGqKvJ2QbQY0Degd+OLraFwzj2vptZ7aN4MzXyXbCMnaWjPyjzbJhwkqzVFxjn9VCyxB8MAGdcMnms0m9dfuZ/YqPYfTczM4syYv23ZI3o1ZaLwdL9yHNBqJNTU2y77Q9Fw0km8H7hNC/J4Q4h8IIZ71afa/laSg4c1iWblhxiZ3FCPjbK9hFS+0TBFWqk1b2ESR3jRFllor9swZkRAsbdoqXlSokNshtpVjZX7pI5FCn7h2sfEdjyyzwY5xhTaB2VioEmR8bGwqlkfbqMueF2DlPnZmkaUTQJJpINne3i41Jyur4qaCPHcR5rSx6zXxcg0QQRwRXH4FzfVXaUZngMS2M2yriqtskkjfReJhIxDIOKfitcy9Hgl27uPkgq21Kv2PvQEQOJZDzQCJSOtlXyrKLQ8JZplHs9nEQuzQSAQCleRYskLLMcywb5tnuKTk+I0qVcYvkxsu4Caz5KOUmjVdfl+fX8RNBaP+gGGvi28b8IlzSG3tEAbsuEpFuqVWZYkp6jPGJh8F+Di4s9XSaW4V4JhXEP0MC0FPaCCpzjbx03EAQGPWOLzDDHsCEFTHxkts+kJLxvWZZqnNArRmNUNTYYaVjutZWRV7VQsFCn0y3DtQp2KAr+ZWySq6PaUUdjIG8vh8rzSZeY5D5caZUguq4OEfboEEFeVYI6PpZQ3yQUI90Hut2Wox/x23UnHG899YMIk8+4lmwE0Xu+kihyn5IMFSLvXrD4ElcDvGf5gmGkj217l2tMBrmjfSnG5hNVxkkGkATcfmtehku2S+jUaD2u0L1I1prOJ72C3zznRj1CjjsP/teOGiYb4J9pSPe3jshyj3SL2Od6QJjw2oSBfvaAsE5KMUO4WplTeyaH0tKspIlodMe02q1SpTN+9n/ttvoVLzy+e4CzVUkpMs9RG+jbOvpv0axndjT/k48xXSy2MTZLPZRAjBgS/TkWaN/U3sWRO8sTSAXOEdNodojXZVjPXFoOcStfVupdQd6FQpM8BvCSE+JYT4T0KIN4nijsq/Y5RtBCjLQgiJo7xSI7H8TWwn0S+qWWTPdRFWjpAOrrKJYwulxNi0FXnI3CZNRwgrIc+dUqpUuYd0Imwrw5beDu0hyzxsLKpuhTCQCEtStcbSfQFuaepjCwvf8uh2jbrsjRC5j5MJ0qy4GMvF9Xx9EDCOy3BUK6vgJGJH247XxJVaIwnTmPTsFzO18SbNsKyqNmtZGbZTw8UmjhOSONZmIc9CxZrJA9RFhEUFOxVkeY7jaObjOm5pzy7Cl+2shqfc8kBknrl4zSqecEsgKWzmMtJmvtw3US2hbs9z6qQiw29WS2bg2x6HH/4+Dqx9BzLIqJmDXwCtA4fwcEjzjFTm+J5eVxVrCdGeADlnK2c4mCMIWliqRWW+gTBHoyrKxVmoTUj5hsmqOnk7pqJcMmNKbCy0SkBwlU1t0YRvRxkiGZ+xoGvjjSA3F4PVZppUJ5hzc24KLIEMc+yJnFx2VkWcH+eI8hwHd3+ditGC6pUq0tEApFI5oZFUiU93SkHHkhmV62bwMUAiXKyGAdogRZi8Vo7VIu8leD2wlSDtdfCONFl40/GyD/VWA1FxNKMbJlgND6vukhvTlvBsrJqLu1jTjnlDlYqPs7/GVFLl+rUZrGkPq+aSBykySLENkDiqRXyhVwKJrSTCEviHjc/SUdhGSk9Xh6DA3V8HS5AP0pL5egcaYAvq0+OIp2q1inekibmcFHexhlVzkSPtI2luv5Yji/8AgOR8j9fuv413vWscUCpSDRK+65Rmsf5DK9jTHnbTAwnpurk+ounhLhi/kAkBrtUM0Fsp/tpFKtYIq+YgfJvOg/rgojNXwWq4pY/EeYlpJAAopU4ppX5GKfU24C3Ax4GvR1949XeOVCbpWdsIAbbyGI2mqfg3MH/sIwihsLMaTim1uQgrA1wTwZShZHVs2gocpHRIoz5YhY9EvyhhqLDtFGHMP7uBxFIWFcdnc1Or+p4bIpSHJQV5CRAerq/t2GWOLDvHkj5Wwg4zkVvzy5e0sPULWcGORakNATh2ExdH5zvKU3xc7IYJF6WifR92huPUtEaSJMRJgoeDVXG0A9BEsjheiGVXsBPIc4ljzDGe61ItolhM/LuV1vCzMUjmuY/T8vCUU57srZmQRhVliMxDmQg1Jy8AqkZKjufrgAHbspnyGvgs4vnzyCClno0ja6YPH8GzXBSQiBzP80CAjDNknI/9B1kdezWl3T7Mffe+E0e4uPPV0k/i42JP+6VpyzKAYFt1osc65bwLoLLQKJlzVXk4+8yJ+TAr6+n5qOKGYzt3tValPjPue2tmCqtqI8MUMQEkVlbFG1+Fg2MJDSRmz/quQ+4qrZGEWak92baOWCokYUcIrJpLpWL2urCw6mZtRinWoALKwrNmSTcCiCXXbSqmU70mfmUsFVerVeyWx/bpi4TrXaOReMhhQj5MEXWbzuplvKtaVOtj7cq1LNxFvQYVu0bqJlg1BznKkEGGPziKLepUKkdAQtU1ZujQCHJFhhkrLqX003/5MT3epofdcHXfM4nd8hGuxezXXU/zlonzU7Wa1kiK+VyoaqZdONvrLs6MMdOmkjjs8KnfKmOHsPJCS81KIHGFR+qmJTCnq7q/dsMt94NfM1GcWzooY9Rp43U2ibsdhBAaVLu6DXumgt30SDdDrS2+lDSSp6CvB34AnX70M38Xr9/1DjdZregIJhcfpWz27/8xInPjmZXWxozSdbRGgodjmKrMKriuUVVD7SMRdo6wU5T0Sjv8YJhiOwnCzrHzCSBAM37HsqnaXply3vIDhPCwczE2/6Q+btWjItzSSQ0glIcdU4JTlnl4VR9PmRvcivxcuY8TsQPEXKeJp5wy86qnbMJkoE0vsqKDECyJbddwcUjShDiJcS0X4duoOEeYCC3hx1h2BSuCXEpsAySu5zJtN7Btm0o0rceXVbUEbsYhcw+r4eHJseJbnzPSe5yXZicAJ69gY+G6DeMj8RAIGtU6046Whgsp0h+M81d5fovqtMkDJmJsWyA8PQaV5DukdXVhhFVEmKFw5qslQHjCgGiUg9QRUKC1ThVlJXDYAty5sbZUxcPdV2hZGSIyY1J6bXZK5xW8+Tqe0tqvVbWwqq6OvgrHjMNSdSqM69ko3P1j/4otFNLVpi0ZZthmjI43BQp8k8zClloTchrGbCgllmFuMshg6HBD/lPM51+upXxAhH3SoQlfZky1Wg17yiPe6OuQ37qLVdfrIQcJvf46f/Jj/46pv3ecw999x3gsaA2goCDvY9VcVJQhhym17nW84dpPUGlpf5ZnFftBM2+RmYioKNQgaIE7MO9Ty8NqeSTLur/33fXnPP7pj1N7+T6syjjhRq1WwzlkwrezAXEaYNdd4vYQBjFW3cWeGQP5peUTXHzoATKTokXFxnmZxtgtH2k0zEAOsE1kVbpmgKQ5FiwcK8GKQipKj2XY1o77wbaOoJNVhSX0gJ1pH7vlkV42h4xfihrJLnqzUuqLlVJfCfwK8KMv0HNfUuR4+jVwilh9WeHsw2+nd+k2atu3lBqJ49pYVo4QHq7UQDJ5/sDO9PkQDSQJMnfxjBQbxuC5JhzRqoAa18syD9uxqVjjsGC8WANJNmb8aebjuC6+1DfLKXORFsrFCtUOjcRxHPwCMAqbeu7hjOQOEHPsWgl2AE4GUTLUTCefkHydCq6yyWVOf9jDsx2E0UiEceZbbo6oVXCkNvlhaUbsei7H3f38s3/yfVQTbWqy8hrZ8qhM5ZJn2o5ezJdQUJvTGomMMqx0wvF82xE84dDNOygBtsl99s5Xfxmvn34Zlm9rSTbIoCswGEmeOtSM/T4VORYS4dvI0rSl27PSGrIT45t5sZTUQFI455VAVGyQSkupha+j0FzLegpRdUpfTFV52PNjp3k+0POjcg2Ek4Dgui7OnE9V6Yi+QdhGVB0NCEGOMPPm1VtYWFhSD1LkOc5irQSvPAuQjp5DOaGRuCargI009Ywtp67NdVk6wq7pZ5z4i/eDgqnqK/Gbc5gqjLI+YV8nDbXkRHxOlmI3PSqqhmv5BEkf2/g60k5It79Bd30V7LGwoPdEhlVxiEygQi/YxDZaUWYyF1s1B8f4DNw4oHb+JL4BEidNIc9Rwx7CEqgKtMxVu6Jua63I+Ccunn6Q03d/Ss9RaEyDSuJ5HnEW0k+26aXbtFcuYzVcgrVt0s0u0lWlqQlgZU3ngRsYTUIO+4gsJRsNEZYgNMlXu6N1rKaJNjyrwcFquPjHWziLNTa6p6mffxRlAhYGbX02rb+lyyaO5h2pjElkjD3loxK9VmtrZ1l5/MVJkv5CAUmpNCulHuKZJYP8W0fCAIkriqR5GXHq0n3sTVjJNHY2BhJh5Qjh4phQ2DQZMzgnr5iU3iDsfIdGkmdueb+J5VYQuzUS16FijX0n2hnuYqWUWkqWerjO2O9SaAJIFyuaAJLUx3UcPBMZVtj+yV3UKEfJcdsWlZJ5A7gKEhlr01Y2ASSWi2uk14gMBwvLaCT5iDE5PpW5OrlSpOiN7noeKpXU3ErJrG1qxEuDkiHK1MFueLhmvjxcrCnjX4oyxARgz375LTg1l7XMnJkxUt++ygyVyGJ7/RIbq+eNBJyZGyoFWZRT2z8+LyJlUo5htNkupXVbGGZrUnmQpTs0EivTDA/ADcfO9iJ1jmOqiTxDCIHnG7+DchlkOiJNhjmYdC4ytcEWePUJLTNLUXXBlKoxrep0eitYBkj6lzewzHw4tamyfNFXy7OpKhtX2YTDLXIXyBXDle1yL+Smr8rcr6OMbV9a+m+/t4yomuSkZ/Qh1253bYcZJch6BOYeDYxETp4RdDtIX+Hbel42Ny+W5xzyTkyUDVFSMmxvkwQjMECAGcMgN5emdZZKreizf6SvJPqLX/lJaOp+bXQuYkcjwkHPzOmI5uMPkG1rpp7aaSnFb6xe2OGUDvIB7RUdAp8MumYOM2SeEfR7fGrzz7h/+/10Vpaxag527uBbVVYvPY5SEmdGz//AXGPd29wgz1LU6hL1sw8TdPU6D81h282ti9pHAlgjiPOA3/8P/5LUTlj8Z3dw4dyD+nkmPU2pkRggCZW5XC7rs3bmsdJMBvD+3/lFHnjfi3Nl0wsFJK8TQvycEOLbhRC3Ai+eMe7zSJY5GORYhUSfkSGxlCAXOY4xv1iOvgtAKbs85R2X936ALf0yrBdAZjrqyHd3mrKE62PjIPOx78NxXF42dS2vuf0LynLKcrCVNRHZ5GO7DkdZ4Ku/+qtxDANT0sGR1ti0lbsIAZ6JFnJiI9lnjj4XkBeXC9kI2KmRSIizEBlluBP3agjp4vl6rImVo5LEmIUy8tHYNKCkTf2aOZRQJEIzCK/ioxJJd2WNxsYdRPffjh0fRA4SLAOGWeJgNb0S1HzlsN3VL7qMcuwJULPtKo5toRzXtKkZUG95jfb5JQb9bbY2llCphKHESnxkYpGEIbWD43DgJBqUGsnqiVPYSQuZC4RfmLjMGY9UR/l4xoAjkwjpaPBSnaAMx00z4+MQOxmjbdKguLlg89I5cIQ+WGgSJuaJoHb7AswVk6iQcUTqZ7w5vYU705vZWL+AVXVQUU5/ZR2K+WjWENMuKktMX7XkuhBbfEP8BbS3LlLIDZ/94/eWoJekpv/9Nu72Gr65Z4ek+BszinooFA1Xm3k/+ee/yzDUjDMnI5ZhqZEoU0/kGcP2NrEYX7l7+cJJ7EbhNxJE5uro3uY6g+0thElOKBPd906kc4Strj6OZbSihj2NQnHms59hO7gMAtZ6+obGwARnBH39d9Ruk2cZsdLtJHnIuc/eXTJyAFF3aK8so6QkNkxf5Blhv0/Q7dJNNhmkbdqrl4lliGdVqDoNOp1V7v/LP8eeqSBFToweZ39znWG7jVAKYUASoBtqUFvbOEuqEiS59nk0XJZPPMIjH34/ndXLRCNzRa8xZRX1w0GfNI7ox3reg3zA5cdO0B2sl2P58h/+Ib70e/4JLwa9IECilHoN+oBiF+0vOfZCPPelRkU8mk0RZpuRI7GVICfFyR2ktLB8veFVbuMqR2cINSG3KtMSoJyw8RdA4Ts+2YRfQng+thQ7fBqO4zBFjavmx9EvuSWwlVVqJGnqIwA7g9tvvx3bmKxyaeFg7dBIkBm+ad8tgcTWNv2sABIXKbMdGomdK+JshAozvAmnrsgt/MpYK8ijiDSPkHFOPhzPpcosqgu6vYgElMLxHVSSs3nmLHZeJThxDdJkRy40kjwS2A23BDUflzMndHyHHKblmQuVCyzLxbbGQCKTCBzBuU99BtfycJtVBuaSLZGDSh3y2CIeDXH88asRDbulRrJx5hwzS29l6a+uRbkGGA1zVkmMsAS2KsYYMxzo58v1XgkkUZxgNVwSOSjrKaWwrIzrs4PsS6usnTuDVXWINnu4JndUGsHM111PNGUmMs+JhgMSWx+adHFYWX4cq2KTjxLSflgCcHKVjfryOsJI9XmkGVsnWMVXDpvtJVIMoIWC+tatdE7sJ+jqteyNVqlsLJOOihD2EH/lAs6gS39zA2lLWt6s2Y85Zx7VKf+DrI8QFmkckSYxeRSAUiWQhNl4U6yvniWcUFtbV+mTBf3NDYad7XHfw4AsSTi5/Snu6b2PbnuNzIRPTfkL2HUPt1Ll/OpDZF9TZ5h1sB2HwIBZ0DOgpiSjTptRYi6Nc3PO3vsZLAMksQx51Tu+miyOGbS3GW1tln0f9boEPQ0sjuvRvrxc7iVbONT3z/Hx3/tt5NU2j4f3c/Udr8KybfqbGyUIAAw7bdIk5mLnEbZYZZC0WX38VDkvjYPzHLj+Rh79yAdZeVyf/T54w80MtrVGMmiPDzcOtrfpDLVWKKtw+eSjnH9MJxsRVZvDt96CW5mIAHwB6YXSSFBKLSul/kwp9SMvZqqSzycVQGKJIsw2JRcKS0FGhp3qFB54xqGWUqZOKG9FTPUBvcmIqCwxp89tD5WPmbD0taYhszGQICQqk+TjSE4yJXAcZ4fvQ6YxKpUkYYSVa+kylQrP93acyVBZRk35uK5L09zpnaXGeZwVJjwXmSc7NBJbCKJkiEolfjiOqJGpwKtO5KNSiq21i6g4R06YtmRm4bq6H+vpCsgcZesQ263zOqghFzmpZQ5EGo0ujXQ4ZNEXTzmceOBjKBRZJ8Iy81eAsyVA2QZgowDh2+Rhiu/Vqcw06Q/GL7VMbPLEJg4ChMzL76NuB+HbpMOQqNPHSabpX/ZJbeO0zbSEnBU2dKkZnkpjum0jEfZibCPlB2HMwX/1OqK4a8qlZHFMpIa8KbuJKbfC+rkzWBWHYKVbrkOeCKLhoIw+EjIjHPQJ5IBc5aQiob1yCeUJZJjhCR/XniJPBcNul9Gwi2V8HFkwIk1iTrU/zcP2J0hlTBRp89Ns6yBO2iK89Cou98/ifvEsG9ESCN0+QByMaGYhQkl662skKqJma3Pg4k3XlQxsmHTZd/xqQCc+jYYDbcrLcwbtbYZRZzzPecDS6c+Wn4+/Vqd8722sM2yPgSQbDQn6XaJ8hHWN3ntLZ/V1Sa7ysOoOR26+laWHH2B7XV91dOD6GxmZW0fDfg+/Zq553t6kH2im7LR82ivLfPzP/oee34bD4nF9e2F7ZZn+5jpCSa2R9LolMO2/7no6K8t0O6tl36//ojfiVqr8+R/8JJ9d/RDHX/4qmnPz9DbWSxBozi8w6mwzarfpJOvErwVJzj3/54+JMgPYTY9bv+hL2F5e4sG//gv8ep1jt72CoNclS1OG7W1mD+qMy4OtTba2l8hEirtYY+X0qXId7NaL52iHFxBI/q7T6pkuHXNznGUk80G/+AwZCXYqUNJGeMaOnOoU6jCOiJKpwHbs0vYMmkEATFebNKwJ27znGNAZM/48SZCJJA/GIaAqF3jNyg5nexqFqFQSdXulkzfPFPNffeMODSdLY3xcvvGtX8+h8DCit0Bi7rYW+VgjyZKwZN6usqlNtwjNZT/VcBykl0YSbyLEs95ssr2+rB3Vo3GfZSp0WC0wsEYIJUnzGJnkbJ3TL7/l2SQmzX7aW2Br6wjDjRrKkrhm6/qWSxoF5JYkbQdjIEn17zaAuYgpHQ1RjsKzKljSxqlXiLMxuoUXFumebRIHI1ThS0ADhLQk6SDEtT2w9AufGHNFbq4YzoKR+awBRZHS3tJmNzcS5TmS2Dhys8BENcmMcNhnkGqmajU9Ni6cQ1QcVD8tNZk8sRh1OyTDgZGMc21i6fcZpV1E3UYpyWCwhUBQ96fxvGlkYjPY3mTU7WBFIXaaEA8HRIMBqUqo36yjmwZt7Utq+LMIz2b20GG2V5YYzenxzB44RGRCrqPhgH1X6btTehvrhMn4DvGjd9xemlRGWY/DN+u09GG/Tzjo46YxFZUzbG/TmzC9VOZbfOQPf6v8PHfDcRozs/S3NjSQGHBPBv3STHXkFp2o88G7/qKsZ9Vcjt76cjqrK5x74B6qrSnmjxwjNEAS9HvsMwAx2Nyg0zOZgPfPghBsb+n91zyyj9lD+oaL9vIS/c119vkuTr/DqNdl1Oti2Q4Hrr2B7voa6+vnyz5UF6Z463f/Q3rrOmP1Vbe9nNbCotFINJAcuPYGhu3t0mG+eM111KamWXr4QRJMSqOGx/WvfyOO67F+7jQHrr2B5rwOQ+6trxH2exy4Xt+b0t/aoLu5xvmrz9B43X7yNC21LftFjNiCFwlIhBDfKYS488V49ueLlFIoE4ZimaiZe/9Gq5qWUqQy0RqJssFEXeWpwjWhtUXUlsws3Lq3UyMx5z/eds0Xcn3l6Ph7B31ifQJIkniEyiRyAkjyVOBNVYlTH5QgTSokodYWwm5/zIhSQfVAc4fmkhkTx4d/4wFcVaXy4e9itGYidcwBwjx3SeIRrgHQinJw6xWS3Gz2iaitNMyx3YlzDvU6QdCDXKEmUrfnmSg1EsuvgJQkWYiMcwLjSLR8h1gaZh0KTp64kzyyiIZDLBNiVXErOJ5PphLS7bEpJzdalVBjv0wyGJCR4ts1hASvVSPOxzb64MI1bHx2njgYIY1TWS9aTpJFyDijNbWIVXGoNJp0nC3kQQvVXaU57JAOB+RZShpqZlufrrO5ckHPg6jjDw9DPEf/skIpRWqYsshzwsGAXqjHXZlvkkYhve46nvSxlItQLtIASTToY6FNLOFAR0SdG3yW2h367o9HP6lvA3TxWFBfQefUMfpbGkgq/W2utTOiwYBwoDWQ/ddcj+04rBttwE0drKoGkv7mBtuXNWNdOHZ1qZFEgwH1mVkas3OsnztNEI8PqRx95StQjmI5PM1KcIYjBkiCfo+w32d/3OeAZzHsbNPurKKUDiH+ku/5h7zma74OZbIpOE1vzHzb2/i2jVCSaNAbawPXXIdbqbJ6/nFyZQ5+1lyuuu3lACw9/CDzR66iNjVFNBqSxhHRcMDi1foirtUzjzNKunre97X4pn/347zzR35Etz/lU5uaxq/XWXr0YfIs45W33ow76BD0ewS9LrWpKWYPHUHmGSsXx2kHrbrL9a97I7e++a3sv+Y6pvbtp7Wwj77x9/i1OrMHDzHqdktHeXN2vtSA3Gnjf2u6VOoNrn2Nztp74Lobac7Nm74/pr+79noQgq2lCyRhQHP/PIduuhWAxZuuBUu8qKfa4QUEEnOXSEHvBV5cCPwck+3YYJsQSGUhgBzNbIRUpDLGSoT2fZjzInmUjzWSCSCxD1VRE0CSp6CEwpYWVjzhX8gUjuugpEmol3mEoz6kOVmQl6m+80Thz9TY3DxGfv93kaZVomEfpOL0J5ZKIMkSheu6BMEUnY399Pv7SKJCKh5hCxen4hEkJkuxKHxBLknYL53IFeVh+Q6J1IBZpMwGSEYZ1jhegFqrQaaMD6E/qYWVUb9Iy0FISRyPEAo8k2fKrnqlrTiLJ/0CQzDSqe947L/mOpIsIu8mpV9HpoI8SxET6eDiYZ8kC6mbBI3+dGMHkPgmxDQORhpgTaiqkBlba0s68CGZRng2talpttJlBrdHWGnC0ak68XCgAWHrUb5o/83MHp1n5YJ+2WvONE4yTbX/ffTXU+LRSNvpoASEzmCVwBnSvEn7BjZXLyBMNFHLewPD1TpBVzOximXhqlybtvpdLuYnWXj7Tfj1OoPBVjmmaf/V0L+NwfYWo26H2tQ0tVaLcDgomXF9Zobp/QcJRsbMJMGqOswZafzsvfdh2Q5zh4+QxhFZmhINB1QaTaYWFll6+LMk0oylYuPXa1z1spfzibU/pud1mD2obwIMel3CQZ9Ks0Vjdo5he5v+9gaplWI1PI7eejuv/7pvwmlVTKZat2S+w/Y2+zyL/Soh6PUYGf9EfXqGucO6n7JIjVNzmDt8lPqM9tnMHT5K3Vwc1r6sNcSpffup1BtcOvEwgdljdsPj4PU3UT8wr8OHF2sIIZg9eJilRzTILhw9huN6BL2uAZLpcnzxhL25OKT5pd/7T/nm//jTus2FRYadNt31VZpz89Rn5lBKsn7+LADNubkS4BqHtNZRRLG97C1fBsDRW2+jOad/WzU+k6mFRRrTMyyfelTvlX2L1KdneNO3fAdvetd3Mv2Oq2m87gAvJr2QGsm/nfj/dUqpv34Bn/15J9sVCOP4VcrCxkaZEEhbCFIZYccKKS2Uo5lTGmalRjJp2uKgCxOhtYgKOTlkEuIJgIn14UYpPZS0QHlE0RCZSGSYTtjOFZW5uk7n3i1eWu34u3D38lgjiTWQ5LnHiQe/iDiuEw+1JGmrCFs4OLUKQdTTJ7Kt4j4Vl2Q4wHJsLHMBkuU7pIZ5WBN+nThIUfaYeTdmpkhlcRDTgcI/EyuEOdOQSolQitCAmm/u0XBqPoHxIyRJAXg50WiINFFHjnI5cN0NxOkIW1ilOU6mOvpq0tcRdtuEyZCaowGjOjdFYjQepRTeTB3XrxCPRsSjUVlXSMnqhcewhYMrmgjfpj49w6jbLaX66f0HiYZDokEfqVIO3n6QhWPHiaKBvhrZ9lG2oDY9DUrRXrmESGJuXpzD6WstI+h3uHT1RRbecD0Hb7iZqcPjl/+moz9B5/QUg3absN/jlvkW82logKRPtTWFEILFq69DVCZyqVUdmnPzdNbWWTu7Sn16hkqjpTUZ0/dqs8Xc4aOkRjAAwLNLs87lU49Qm5ql2jQ3VQ56RMFIA8m+RbI0KZloET119R2vAcCt7KM2Na3r9XuEgz7VZovGjAGSzQ1yP8eemgi5TSSZEAjbYmrfIv2tLTYvrjA9M0u9WiXodUrTVm16mrnDR3e0bdVchBAsXKWvSa5PH6A6pfu+uXRB12u1aM4vsLV0gVHWxf2CWR0RBwhbkH3FNVi3aMl/9uARUqO5t/YtUpue3gEkM8ZHkcio5KjFuZblxzo8fJe+2qG1oDXGyydP0pibpzGrw+/WzjyOV63iVWtc88rXsnDsauau1WMqIsj2X3szt33pv2Lh2I00zc2Wy6f0mZDG7BzN+QU2L2jT2tSCNlW++h1fw+LV19J43cEy79aLRS8kkPy1EOJ7hBDfArz9BXzuS4Jsx0JYxf3q2uQkjSPYtR3iPMIx0VjCHArK0hynOB+SjDUSuSAQk2c07Cq5SlGpREXj7/NUYfsmTXvmY1s2uUzJwpT1s50yQimLwa2bK0tNSGluIolcIccaiQESAGXrpQ9NbLyFBhK37pPGEQd+6DVkJiopz13CQQ9pSSq5RVNVsSteKYXuAJJRglRj/8LUvnkyAyQVu4Iw2lUWq1LiB3Bsu4xwqroH9Xc1n7XwPPW/f5RRpMMjC+k9M34I1/Y4cN0NJRMsfSSZIAlDyMdAEnTaBKMuloma8Fp1bN8jUSmxDKlOtfBrNeIgIB4Ny7qtmRnSXD+/ImxwLGpT0/TWt7j3L08hLIupffuReUbfRORUm02ufuWrueENb0I55kChY2kgAT78259EADfdcANCSW2yGg2ptaawbJtv+nc/zuKNN5d992caOJ7Pg+8/ybDbozE1Ta1pAMGYWAC+7N3/lLe8e5zq3qo6pVO3vbJBbWqaarNJNBgfEqw2W8weOoJCkRuzUm4JpvcfNP6lHL8+Q8VcEtVbXwOlqDYaTO3T2lNx2F6aNOUHb9A3QrqVfXjVGpbt0Fnf1qBnNJJoOCAJA4Y3Rcx81bVln4dJTmCEjNbCPpTMCXrrNGbmcKs18iyjs7qCV63ien5pmrMb5p4Rc66ltXCd7kN1kboBs1Of1Pfh1VrTpa8BIZh/+/WlHyGJMt77a4/w6Mc0AMwYjQM0k661pgyQ9KhPTVNtNKm2pnB8X5+wF/qAKcDDH17m7veeK+sCpHFAY2aOhtGYNs6fpTGrwWH/tdfzbT/2c1RNiv0iEePlxzo8fk/A5VMdXM+n0mjRvqxzajVm52nOLVAkYy8A63NJLwiQCCF+A3gH+rrbW5RS/+qFeO5LiSaBROXgKAtlPruuR5KFuNja2W6ARKWiNG0J42iVqUVuZ6W5CvQdJLlM2bzQI26P/QtppLA9m+216xhefC2WZZPLDBlnDNaHpRkniyWOrdtJ0EAiTeSQL9T4/EIocRwThlyUD4qAgRjHchGuTWrCUckFaeqRxFXCfo9MZbymv59XZdfg1LzSRyImgaQfk8ixil+fapWH8mxhl2awLMrHB8wAx3VZOafNQFXPAEm9QhQMUYcd7GDAzQcXsYMBvfU1rDjkcD7HnDfHgWsngaTwkVgkUYjKxm1kUcgo6JafrYpDc26BJNeH36qtKfx6gyQYEU1oJDML+8dgaGlmWZ+eIRz2iAZ9/FqTSkNLfJ0V7bA+9ekOjZl5vuL7fhDpmHMllqDWKiRjzQRm9uuxdlY10+q3ISic8YzJrrrUp6cJeluoPKXabFFttYxG0iu1hdb8PqaPHBxX9C2ac/MomaHyNq7fotpskWcZ/c11EIJKo8GNb/hC5m+6DWn2hbQtHNel1tLM1vGmyjF218xtnUYjAUomHmXGHGg1cBtfQ33u9QghqLVaPPbp8wS9Xgkk5R65ak6nczf0cCy5J8hRStGaHzNFtzqFY+5U2bp0odR0XvaWL+U7fuaXCY1bK840CE0tvhy38TV4tcPUWrrspUdPA1BtTdEyQNKcm8d2xgJcdz1AKRiZdWgt6Pm0nAaO52khYmObUbdD1aznvmNXc/C6G6DqkDmUgQf9rZB4lJGnkta+8Vgcf6oEkixNdswHQNB0ObGvjjSaTX9Lv2vDrhFomjOAwrJd/Hq9BEW3Ui3XCbSm/ec/+wAnPrHCi0kvyAl0pdR3CX1F3x3Aq4UQv6KU+t5nWl8I8TbgZ9FBNr+ulPovT1LmTuA9gAtsKaW+SAhxBPhtYD86IcOvKqV+9nkO50nJdi2EbcIPc2U0Ev3S+J5HLwtxsJDKQggj1WXgFtJvpq/flJlFGsdjEQ5wnDpZnpJ2Y/LhhBM+lgjPord+CL89hdMYkqkUIXVupPKQXpxjmY0bm3j63By+c4UqD+mlkdT3XEsJ5r5rmRfljBnHtUEp8jRFZTkPPvD3yKIKzf4p0qmIaXtGJz6s+qVpC2Xr9CLKJh4FjIIurrJJRY5T8anMtqBQDAyQpGGOmgASz/NIMy0h+7aWfP1GjWg05MTHzyOAW2+8gUsf/AvaK5dIs4C3pW+ibzdozM6VkrQqcnJllolcSwAH29J+rVSNzTcaSObpb26T5iNsZx9erUYUjIiDwqHvcOjG6+gPtMPZFwYQpqaRWYzlDHC8GtUCSNb0C/v43T1e8WUjFo40yYV+0XJL0DK2epXr+P/a9Ax+rV46tB/7dI/5oyu88m3HSJWW9HJAuBbV1jT9LR0FVG1oQNhcukCWJFSaV/HIRy9z65sOjZNLASliLHmTI6waFZNBtr1ymUqjiWXZzB0+ylV3finpB/QLlplHVJqLBL0NhN0qx3j57DK3f923kk/pKKc3/qN/gefW6CgHZQlOnjxJlkpe9x0vx7L15zu+7XuRuQL1Zfj1BspxeOM/+hcADEWNB+97CL/mopTi+nfq9T958iTKdstyXq1BXUkO33QrCIHtOJw8OU75kbzRJVIOVPpsnzyJeyDldd/xcvJqm5V20Z4AFOu9PnO3v4Y3Xnsztuvy6CMnEJYGgDTOefW7ZnC8WI+l0dR1hc3Jkye56s1v42AUAwq/3uDkyZPc/FXfiAI2+ylCNct+Xf0Wj6uVx6nHTyEE47FUGyytrZef3Uplx1jiIGX6NYLHT5/CcW3kVMqr3zWDrLY5eXLAbV//LmSWgLA4deoUM7e8nDdedS2WbXPq1Njpn2eS/a+EyN3k5Mle+f3U1NSO9iapUqlw+PDh0nrxTOhZA4kQ4l8DgVLqpya/V0qFwCfMv2fzPBv4BeCtwDJwjxDiz5VSJybKTAO/CLxNKbUkhCigPQN+QCl1vxCiib4n5f2TdV8o2mHaSnNsZZf6nOf7JGmAhbXjoKHKFK7J7+Qrm9b5L+fxx+8nuyNBGd9Jntt4flVLvLl+bpo7KCsjizLwFbmQ5EpiOy65CrEQ2IwP6aWhBKPWrqc9bNfBb5psoZZVnlJOAwMWSlHEMuXGDOWZ9CGWSQOTJjFZkBDRxJaCLImJ4iEVWzMTq+IhkeRCkskElTsI4RCHAb1BGweblBzb96nNz0IR5SkngGQiMsp1fTLTl4oQSAv8ep08Tbn/r/WL0ZybByHorFzW1xQDhRFNeRNpRBj7SGSagOPgGk0sySeBxKYxO8cnH/lDAF4jvxe/Vica9IkGQ5AgpM0XfP23ENy2Tfu3TiCEQAqtkQBIuY2wFvDrmvl114p0LFXCUrMQ+OjNWpigpDR3hjebVJut0gksRI1RV9eLc0UVMAI2lcY0Sj5m6leoNFuEvR5ZlrJxMS2BJEwkSinNFCW05sZZa6WsUm3oEPPOymUq9SYrpzscvG7GzI+kxlgb8mu6rszrpaTrzCxw1Q1XceSaa3A9n82lC1Qrc1Rym8y2qB2oE41S+luh9lUcbbJ9eZk0igFJY3aBSr3K1iWtlVn2ArbnMHewQZbmtFd0GPXswQa2TemMrk0vokRG2DHXGNfqzBzQ2oJSiuHlIT4gGx6VaZ/eRkAcZlTqLs25ChvnvTLp6OLV1xKNhvTW1/BqDbKkTnO2QrXpMezGBL0Y17eZ2V8niTLal88jRIWFqw4x6rYZmVPujdkFGjPTei/GOf21EQiYPdJESsX2stb4Z/bXcH2H9XPnUCqn2trH1MIU6+fPoWSOV20xe3CxHMv2ygiZSRqzFWpNb8dYWvNVti+vkUYDhOWx79hRwsGQ/uYall1h/uhhLBPJMuzGBK0Yx7WYPThOgz8YDMqU9JOklGJ7e5vl5WWOHz/+hN+fip6LaetbgV/a/aUQ4ruFED/8HJ73GuCMUuqcUioBfg94564y3wz8sVJqCUAptWH+rhb3xCulBsBJ4BAvAlmOMKnhC9/HeOoc2yFKzXmEidQnQlrlgcSqdKlf/mJGazWyJCZXhUbg4noVcpVBnmELCyuvoHKbNI5RUpKRk5HjOF7J+H1rbCZKwqz0NyRCYlk29TmtNnvCota+CX/wVoarHnmWlRFPtuVQn5sx5YxJzSSAyuKYdGRMV6avcRpQtY0JwimuGs4I00ADifKIRyOCXhdHWWW5xr4Jtd2YweJRSjwY31Fda85Sn581YwMpRMmclTkB7tXqVGp12quXywNbiWGy0i9CnCeAJApJhiYqywB8yhi8pGtRbc6Rq4xcZWSJh1+rEwcjuhtd3H6EPzpAnkmUMxYQMiht7sgBMvdL/4EGBA2qgbkuNVVFUIHCr9URlgNmTAiPSrNJYM44YFUJzB3ihZkokTpc2K2MX/wocKg2W2SpzgqgVJWhucQs6CekZl5iKctwUYA0qVBtaiDpbqwx2IY/+ekHCAcJSilCkxKlqG/7um4S10ogqS9MUa/4KGlh2Tb7jh1HmpB4acYqc6MhKoWUykSfSfObwDKHRHXCOUvPsVLIAjUBJaXx0Vjmsyg1ad0nRRpnZXuFy63sgxz3RZh2zCQjc4VdHFQ1skUa6/ciT2VZT7erEFYTrBp5Jplkm2k87m84TMiBXOmIS5mNfYDFs4r8xzIvTNiWWZdx+1kiy7pFX/Ks8FeapJvFWJQeS/E8pSz6m2EJmIm5xz7LVPnd05EQgrm5OaIoumLZSXoupq1QKRU8yff/A7gf+M/P8nmHgEsTn5eB1+4qcz3gCiHuAprAzyqlfnuygBDiGPAKnuQ+FCHE9wDfA7C4uMhdd931LLsIWZqV95kP+oMyYR/AcDAkyfTEq0mNxPZ1ttaswoysESUaBE488ghpnKOUIMsd+v0huapi5zm2sCDzkFbM+uoKwYxFTk6GJAwjlHFmepZTJigMBhEnH9ZORGUplFSE5qX1LAdL+mycuREll7nrQx8cO7mV4MCdb4XPgGdp7WZtQzuLP/GxjxENQqj7JZBkMsE2prrHzp5D2DZxHhPmI/LEQjkWWRKzuXIZe/EGbGVx72fuJ+l3OISWHLNEQ/CwO+Khux/WyceEIEzguje/FT6uzUexlJy7eNHMqY4u+tRHHkLZDqNOmxCbc1HMajdldNdd5HYFcsjSwrQluPejDxD1RzA9p8+tANIeq+sf+8Qn2dgcn6y+cG4blfcYdLsM++DFNp51lA/9zUfwhnCNeV022x22z6yV9eLI5oGH9cnqwfYmWJrhPvLAKdaix6jFgmkshlHCRz7yEYRTQSVDEBU++BefIkjGwQlC1Fi5tMldd93F8JJiBodEKT70/rtod8av3emTa1Ra45PUwqoRBxkffP+HGW3ADUon8rn/wUeobyo0A8vZXk94uDBpKIVw/v/svXeYXVd57/9Zu5196jTNjDSjalmWLTfZsi13yzZgbIzpYBNiQi7tBggkIT/gchMgoSZAIKGTQEJCLzbVDrFBuBsXSe6yep3R9Dl91/X7Y629zzmjkVy518nN+zx6dM6ZvfZee5193u96v29zQcLNP7+d0KzjRAWwYGRsgkMbN1L3+jCdU2jWF3D7XXehqmApxVyZauJHGix9kKYgimMqlQpBo6W0KuUKUdyWz9MMqdZqCCGQmAnbRHm2QtxaCmrVOoaFKikhYwI/ps2VgcBg+lAdt0sVE4ikqvLQ9HyiSkCo0TDwQyqVCilRKAzKM1UMS4IwEMLGsMBrBlQqIb6XKG11L2FTInQTk2qlThy0KNnAk5Rn1fPZrOqpRlAtV2nX2/VaAy9skABJGEjK5TLo35YQBjPjNTIlCBvJdwpe00eWfRJXXxioe0ljSIRJZbZK6KnftOmYyoI6VMFyVRk3YSgwrMxW0p7tURTpNZlfms3mU9KTT8ciaQghDgtKllJ6dPoHn6zM141+LnRawDrgRcBlwF8IIY5LTyBEAfgh8C4pZXnOWKSUX5FSniGlPGPx4sVs2LDhKf87+5yzMTT9Ywq7teMGuordaQRTWrId6FmgIlpOnDmB44IBTFsp/mOWL8MyVTHGKLIZWryUKA4wkCqENXQR2JTyeUr5AjGS2SikWCimlJVjOKCrDUtPcsxSZYZKQ2JbDitPPlEfp+a5ZLkqU7Fu7do0t8IybS667PkAuI4a3z+ovtqT15yE1JVahVagST4IwIqVx5LNF9g08zAPzdxFFFhY2rcRNSsYUmBLi5NPPJUzL76o9WVESbMfSdEppdZR/4JB1p+vkq4MIZDC4LQzz9Lfr6IHnMYwPf2aaiHigQZku3vZsGEDZr5bzTHsoui8jPKeIjM7QoR2klsig+1msbVTOpKSdevWs/rEVp+LUm4xK1atQoYBkedj2srKOfXEdZxw4inpcYVSFxde+rz0vYyznHlG6x4NI4tpGSzqV89alOyohcmGDRtwdGl2IbIMdR/D4mXL9UhBaaAHG5cNGzZQ6lLWQCBh3dr1LBpe2ZqDM8SpZ5yRvl96ojLE1645k2OWHEcgIZSSlcesZv0Z56kdNSDDEhdccmk6btUZ6ntf0n8sNrnUeip09bBhwwaKhUHs/PNA2qw//TxMO0fy85SxgYVLzs0jgaoEXwqKxSJWm8bPujnMNgCXsalaxRoWApOi7tuRzeSw7VbgRibjksvlEyIXpIHAIFFb2ZICQctwsQyHSEDDEJimRaFQSPOskEK915sggYEpbNXozeynZ2EPbj6DjCCfL0CcjINCvoDjtObkWBkssy1FThqI0E7ZgVKf/n3aGZy2zpWOnSGXzYORwTCzyFjgOrl0ToWeHDKCuGEhIwPbNXFcGyENCvlCSyPGan2TMk1gYFsZiC0y+QF6Fw2QKzlEHkidSlDoVuvrZnIUi0WKxSKmaaav5/vnuu5hOvBo8nSA5FPAj4UQy9o/1H6LeP4hR5X9wJK294uBuSEG+4EbpZQ1KeUEcAtwqr6ujQKRb0opf/Q0rv+kJAiC1CLxPQ9TL52QEEtBM6qSv3IJUdsK5LuVIjCIMYRJqKu+hr4PcUwUmUSRhe1kiWSIgYpsIlAPRuB7xGEEQhCIGIGBrTvFZQwbdNRW0Azx6hrIDHWtrqGF+jgd0qhLhsyMTKYWiYGZlsZ3LTXXUOP62K4plSkJGEkHRdkKpQ3CGDubZ9wbpSxHkWEGr5bkiNSJoxhDmgTNiK7BRYR6qxnqMGiv6lOemE1BTcQmRpuTOJQyrYdkCLVz2v1AGUtX3EW4qhig7j4YJMmZZCjwxzQmXYJGE6GjuWQouOQP3kxh4GR9fkUJJv02ACrTkkw2RxQExFGVnkWK9quXfZp+6979SOLkWzSTMLLMHPIxtR/GzRfJlRzqmi7yfHWPTU1TGEbSNCrP2J4KrqaahJHlmLX91GbUuFojuTdoVoO0tZ8wLCYP+riFVjmd489RG4XKZJParEcgpRpXC2hWgxRIAi+DV29tdoq93WRLDhMHqgTVFqXV1C+8eoijQ1nLk02kzjM2DAPLMWlUfUJ9f5ZrIWNlEctIpqVpFF3V+m5lLKjP+kARJ9ednj8MFaUjNL+vKBsJRh7b7VHvA1KKys7YWI5JsxoQ+JHqA2QJ4kgipaLVDFOoqhSxTIHFsEz8Rkij4uMWbOyMia2fPV/3rE96D8WxTKkxw1QUXHtLFdu1aVQDGhUfyzHJZC0QEAYxURhjmAaGIYijWJ8ng1tQVK9XC9N1yeQzFPtc/KaK8MpkbUxLEIWxptPAzpgpVRhLE8NyMK0MXj0kjmLcfBbDMMh3Z7C0ZWLaRrq+Ufh01POTk6fTs/37KOf4fUKInwkhPiyE+CjKyf7JpzGHe4BVQogVOjv+auAnc475MXCBEMISQuRQ1NejQsXY/RPwqJTy00/j2k9afN9PLRK/6WGSNLkyifUOxlpTII5aS1paoJxnhvQwhIXnA0I5rolj4ljliNhOjpgIE1U5FK9IHGQIPY846agmIgQGTiFxoruIRjcydIlDg8ZswrmrHVf3sKKSHCOrynFoY2J6dBKRZGxjgCmQgK6QT6TvZWzPVKuJkXaQC6cVsuyFEsvJgvSIAo/K9guZeOAFrfWa9RD1hQRehGnlUmsmDLIqYk1CZXIaNOUhI9GaBBBEkkxeAUkcljEtGykN4lh3cRQ5EODrfuhaRxNISb0SIYSBlI20ZlYcCE648FIiu18fp5SkZStlbNp5KpM+tg4vRTbpX6rAdS6QeEFM6AFC+4sMl8kDNZycssgKfT1kSw6NslKyvua1m35MHMVITYu6hSLje8tk9LhMrkShO0MUxnj1kGotSO+pWQ2Qsd7tZgs0qyH7Hmtl5fctUfdVmWpSn/VpWgZ1CY1qoEGoiGFlEMLh0dtHQbc0zpa6WDCcZ3J/Fb/WApKGvt9mLaB/qZrfxL4KMll/0yRbtImCWPmChMBx25RvLLH09xlFsfJvgOIfhKA262FlXLr6CximQAhBFMSq9bJtqKCGKFHiFq72l0W+fm4BwzRxCzahHxE0I2zHxDQTn4EGNw0ICux0/TXLSsEh353pOK6p19zOJL4MNQfDFG2KXaTX7x7M0TdcoGdRnu6BrP5c+TaiMMa0NAAloAg4Ohy+WQ8wrBxdgwsxTYtswaHQ42JYBpmchanXL3nGkzlFYYyMId+1EDuTIfQ7/y6EoGtBFmEI3Lydrm8YPIeABEBK+S/ACuB7qGjBJnCNlPKbT+NcIfB24N9RzvLvSSkfFkK8VQjxVn3Mo8CNwAPAb1Ehwg8B56Gc/5cIITbrf1c8nXt6IlEWifrCvHoDU1NbFiZh4ggLwjanl6B7UMefyyamMAlCsJwMge8jo1gVVwxc9cOwDEwhVFLggy9lcsv5BF6TSPOx0ggR0iRTUsrVMV2cPecy+8BbQQqa5RbfKTDI9XYDkDGzRDLGa6p5zY5NIrRlITAVT220nO2BBsLxvdMYOpRYSAs74yIyrZpavh9j2S5S1pFxhM0KyiMtxtNt5MnVlhA0QwIvItAUVmXHxZgzr1bnaJTTmllEBlHccpT6kSSTVfca+hUy+TymZRBpHwhGjlKfS5ACiXasmgb12QDDyoCstUBTmtRnfWqJ81EDSRRaIDJk8kVkLPEarZ9EsU9ZK/WyT7MeEum5eUFMo+orMAMK3d2M760gdTfL3kW9yiIpBzSqLcd3EEu9e1TrmO/pojzR5LG7ZtT1FvSQ0xne9VmfRjVkyjGZCCWNakCka58luQtbbtKVi4Wgd2EfpmVQnmxSn/XYV3TYYho0awGNaoDlruPMq/4HAI/cPpJy/ioZscDUSA2/KvGyJr4pKDcjtR61gAW6N/mehycRhlaWhkkmZyMMQehHWLaBYXZaEqbVAgSZWAOGqSyAjFLChqmOMS292w+l+swUSA1IAHYCUqECsdlymS9/9au4OYu9+/dy4QvOxsqoObQrbTuJQvQiEnVnOUqR57ocTDMBFzXWbyS9cUz27tvD2tNP1c52gWkbhEGcsLEYppnO3XZMDH2u5ccNpRZJct6PfeLDfPrvPtVxLzKW2Bmb2++6m9///d9Xcyo59A2pZ920EiBRc0qAIgGO//mOt3Dsicu58AVnY+j5JfIfN/+S8593BqeuO5FPfOIT6freeOONrF69mlNPPZWPf/ywLIunLU87IVFKWZFSfkNK+R4p5V9JKe99Buf6hZTyOCnlSinlR/RnX5JSfqntmL+VUq6RUp4kpfyM/uw2KaWQUp4ipVyr//3i6c7jaJJYJFJCEAZp1JYtTfwUSHykVsRxbNI1uJBYxgjZwBAWEgPTtAk9D6KIxx69gF27TofYQNgmhjAwhYUpe6lPFQnmWCRIQaakftSmsMCwqE0qhdBMOtChoqwM/WMxhEmEpKmDyqYf3dqqIZVEjgmBo+mExI84M1rGSDLUI5Mr3vHn5BasSq/R9CMMy00jqnLdhVSRQkvZ+c0IvxkRagrLrw4RVdaqe4prrXpbgfoRJ0E7kQSM5HySTC5H33Aev6nuS4gc3YN5fB21E+gft3AtajMewnAwrUYaFi2kSXXao1rxkUCIxG+ENOshwihS0OG8Oze1Yu2zxSKOa9Io+zSqQTq3ph9pukgBXe+iPnY9MJFSRt0L+8gVbRoVX9EuSdQWCpQiHbbd1Z9QZ4Y+zwLyOru6VvZoVHwmV/cyEiiLJNR9X4p6kxBFDiBwC0VM26LQm9HUlk+2y8UpODSrAc2qj2H2s/YFl2I5Bn4jTK2gbKnEguECURBTOwRyQY5dq/uoN0J8L0JKKHRnyJYcDjw2Dbo7qNCUjasT5toVaRzFxLHaxRtmYll07uJ7FubTEFVQJYgSi8S0hKaDNEVGCxAATNOkXC7z5S9/BcM00h1+Ogcp02gnS1NWgRchEcRxjOXY9CzMk5tTyDCxSoRoU8qy3SIxFEWGAkTDNDmSyLgFpopeozVWnwsUOGzZsoXTTjstHZskMyYWXdCMUiBL7gXg2mtfz0+vVx0PbddKx0VRxNve9jZuuOEGHnnkEb797W+zbedW/GaQfn7PPffw7W9/m0ceeXYyJZ6VhMT/F6Svr4+80QPSJJKtYowWJoGOQT3w4Y8Sn6p3ZbFJvrefabkfAxXtFCFBWIS+j4wimk3NcUsDw7YwIxMpLCzXIJgVRL6HEQSq36SmrDLFAonnzXAMalPqB1N9fCssVVSasnBEmksQG9CoquNmHnkUsVyXfY8TJ7DA0UmUfpA8jD4y8igKC+F3seSkdUzd/iCgy4j7EUJkQCp6pdBTaIUkAvnuEv6YeuiDZkikFVAgIWjqH6CsYRoLCFAl9/1m2MpblNAoxyTRRk42R/+yEod2at+UkaVnMMf+x1RZlWYIoQBZsKnOeMjYRph1BNCVyxPN5qlON2nUQuKiRSBBNkL8ekimeAkXXHMaP//SOFMHW/Eibj5PriujfB2xJInYbDSiDp/FwIoBDu6o0LOwl6kDB8kWS5gZR3PnQWqRhBJmxuoITYktWNJPYcEQXQtcfvW1n5ItdaVAMjvWIAxiuhZkMSxBs+bTrEWYdp5CTw9BlMPJWoxtK6TZ8sVel8qU8pEsWFIgCmOaVWWRAGSLNt2DOSb2VSn0dNGs7CNbLFHUPe/DBhT7XNycRbMW4GmaJ5OzKfW5HNpVxjRbFgnAp27ZzgN7Z5TCNASBH6W7X9MSyqLQSlQSaN/K4VnWURinVsSJw1382QUrW9SWIZQi1ed1slk+9unPsGPHDtauXcuxK49Fypi3/tFbuOP2OxjoX8h3v/UDBBb7D+7j8hdeznnnXsC9993N1774D/z7LbfyxS9/Bd/3Wb9+PV/4whdoNptc/bpXsm/ffmIZ8Zcf+EtWLTmRKIp457vfxr33/5bh4WH+6Qv/RtbNYjkZvvxP/8Q3v/s9AN74xjfyrne9C/0DBODvPve3/PD67zI8vJjuUi/r1q1rWWC2uhfbUUDyhje8Ac/zeMtb3sLQ0BAf+chH0vuWcQJIOnpS+6Q2XHQhe/aqyEYn2wK13/72txx77LEcc4zym1199dXc8Mufc+bac9LPK5UKV199NT/+8Y9Zs6ZViufpyjMukSKEeP4znsV/Aunq6iJn5pGxRSzD1NluYeLpcMHZe+9Hhol5b+JkCkQywhRSWRqODVg0du3s6HdBDMKxMYWJZTgYrk3oGwSNJmGSX4ByUtpt5Q9M1ybQvUyaukijOp/mnJPYB1PQqGigsIy28N/EImk9CM0kX08GxFHIynwfGW8BfiPE17xzDHiNkPaOyqW+rpR3B8iVurAzytnuexGhPtYq2JQnNF0XVzB1VFnkC/xGlO76QyRTI7V0B+xkc/QvKRDpSDXLzuMWbeJI7T6DCB4aLBAszDFzqE4cW4SBspZedNGFZBtDjG3aQRTESNfE0852rx6Q6zqG5WtPJpO3Ou4hk8+TLdqKZqoFxHoHXW+GNKoBQihAPvXSVbzqfWew6FgF5NmicrbLWDJzqM5kKDm4IGYqlEyP1EFbMrmuLjb83vEsPn5RumYJtTWhE9myRYds3k5Baekpr+TMq17Bi99xKle+7RSyxVIKJKU+l/JEg0bZJ9+Vwc3bqbPdcU1My6Bnobp292CfPn8XPYtyqYO7tCBLJm8T+jG1pBxH3qLUp2m1Lp2Qqr83YQptCYhUgbbyFYQKFpakjvf5gzRbu3BQvvTEIonjOKXMkh15tlTi05/9LCtXrmTz5s188lOfZMfO7bz97W9n86YH6Cp1cd3116l5moLtO7fxqpddw69uuB3hZPjhdddz++23s3nzZkzT5Jvf/CY33ngjQ8ND/PrG27n7tvu4/PIXghBs37GdN7zujdxz5/1093Tz8xuU+3bnwRG+9b3vc/fdd3PXXXfx1a9+lU2bNqX3sOXBTVz/0x9xz2/v5dv/9j02P3B/atlAy/qxtEUyMDDAZZddxvOe9zw++tGPIoTgwgsv5JIXnscll5/PRc8/h9NPP41Lrjifm391U3pvpmVgWUZqGQIcOHCAJUta8UuLFy9m9NBBRg8dZHh4ccfnBw4cmPf7eKrybFgknwD+41k4z3NehBmlFkkS/mtJk2ZTJ3FZmZQ/jWNLOcWExNLl2E3XBCzqjz+OXHJc68SxgbBtaKqoLTtrImNLdf1r1oFudf3YwM6XkCgay8rZoBPBIiNOczISSyOSYAkwHJvahKZXDFK/AZqGa7mRoVHX1k6kkwCzulVrI8QP24EkQrYDSX8JRIsWynd34YyF+F5I0NQAYQoK3S6j2xMncYypFVjka4tEaR0iCdMjNYTIIGWNTC7HwLISQgNLxs6kzl3fC4lCsHIW+R4XvxEihEOky7TnSnmsTJMDv94EpRNonjPEjhv3sKIe4tVDMjn1M+gZzCMo4GuWMJPLkytJxh8dwd8xzZLexRDGNJsR9VkPw1rM4LIG+a4ShR4DR4e8ZgtFLA14+350ExHLmFwZE2+HqZEawuhGGAa9i1TIbqG3D8O0KA0M4rgWVsZk5LYHgV6yRRu34NCoqMig1etPo39ZK+P4xIsuTZMhi32uspRQXHtTO9ob1QBX90JfeVo/cRjjZnv0cSUs26Srx2JmMqDQ46T+jNkJ9T1l8jZFXQurqLO4E1rnAy8+kXYZ31vBtFSeRFd/lsCL0tphQkzh5gsdCZKJ+M2QmUMqT6ZnUR6vFhDHsUpe1M+I45oEfohpHQ5GK1asYO3atYRBzCknrWX37t1q9y8FSxYv5YzTz8SwDO669z7uv/9+zjzzTAAajQYDAwO89rWv5d3vfjd//bG/5MUveTEvuPxSDOMAy5Yu56QTT8EwBWesW8fe/XsxLYPb77idl73sZeR1QMjLX/5ybr311pSiuvueO7nisisplApknIjLnndFB5DkSg6ZrEkUhezevZtrrrmGL3/5y5xzzjnpPd16663MjjfUZqekHPGTB6tEQYwQIgV/RCcQz5d4aJpGK3qtTdrHPRP5b2rrKYhhRkhpE8sotUhsjDRZKLCcpMsqMjZVhioSW3P9lmshpan8BW2htDISGG3x83Y+A0IXV4xbVIuMBXa+kOZmO0UHoePJQxEpf4AwkbGitZL8BTPrgG5KFRoKDIE0Xr792arrnDfLG8cXkMkpxd2cradhrLGh/BlxWx+SbDFPodsjmLaJCcj3dmO7M8oiaYZ4sUTkbUoLXEZ3tMZZhgExhPWI6Zt+Q4wuZCfRFolaFyebo3dRHkOvpWvb2JmkhW6kulG6FgUdhYNo7dCcbI5Cd5VyWYVEuwvzGFkLrxHgNUIyuvz4Ra9djV9fwrf/Qo3L5AvkSj6NRkxc9WDAgDAmBGbGGril47jmr9/UWrx9Kq/W9nzsbnWPM1MhohscXZ1ierSGYXZx9V99haFVaj5OLLlo5yiL9frmihazozmwlEXiFmzKEw3iSJItdvL6p515LsJWnxV7W8EQ+a4M9bKPV1cAlIxbefoAK08fYPdmn/LEGLarASKaZoYCOWqEuW4Axu9+BBC4OfW9AXQNKAAS2iKRUYS3Ywf28DBmPq+c3X6oEv0MkdIxAN0Lh7Gs+f0K7Y7ixK+AVNFPiXM6V8oQCf8w5SfDkIyuC2WaAtM0aTabaRJ8PpdLzyul5PWvfz0f+9jhedP33nsv1//rN/nQX/0Fd91zO1e98JU4SfM1w8CyLaIoxLKNJ8wSF0gECgQT8ACJaSZBBwIjY7FlyxbOPPNMpqamMOf4XC644AJmZ2aJI1J/UxTG/OX7/ppLNlx6RBBYvHgx+/a1crz379/P8PAwixYOs2/37o7Ph4aG5jnDU5enRW0JIb4uhPiaEOLrwFL9+mtCiK89K7N6joqySBxe8Zd/nTrbLcy03EloOen2XlErMbINSOycRRybatcdtwMJYLYw3S25KZDEbUmAMkIHCSvJ5B0MvQuOCdL+HsQ6TFG/tbJW63wEqUUiNenfnkVaq4SAiRnOqGtoINn3/g9Rn1SfSUPg1QMV8aTFcbNK2YgMYJHPOTiuid9UoZlbvZju31/D0LHddA208h+sJFqs7DPxw590ONunR+vKDwPYwsC0DXq7+7Hcc+hxF7QskmZEHIKTMdNwTrM9GczNUuiy8TJKCWYLDk7Wwp9jkSxYXGDRqn6SlGRlkdgEOHhOV4q/oVQVYrOFzqJ2ts7lcSRktSO3ll+EY8WYtsCyDWZG9a57YW86ztu5k+zMLMGuXQDkcgaRpamkgk22YKe79blAsv+P/5hDH/5rQFkkieS6bNy8jZQwO1ZPLZJElp16Oi/+k/elyqgkFTWaiyvpsaMb71PrkLco9SvA6RlS804skrjpIX0f2VDWi2GAFEl4brsSVb11RFuJk7jeIPZ01WZDqEx7KTGM1m47jmVKo7VLsVhMM7PDmRlkECCDoLVLR+VvASmtZpoGl156KT/4wQ8YG1NtCaamptizZw8HDx4ka1m89nmX8CdveTP333+/SozVVFySEZ7JWeS7M1x44YVcf/311Ot1arUa1113HRdccEF67fPPOIMb/v0nNJtNavUqv7z5BnUeo1P5b9myhXPPPZfvfOc7vOENb+DQoUMpSN16663cdfMt/OqG27h7461s3ryZ226+nYvOvziNvJxPzjzzTLZt28auXbvwfZ/vfOc7XPWSqzj9lLVs37mz8/OrrjrieZ6KPF2L5J/bXp8P/Mszn8pzXwwzhNiksKCvlUciTTz9wwlNJ60VFMcmYRAhaXX8s3M6mx1AtlkakaFKRWhxu3OppUEHkAjCUKYss+WYFPtKNKcBIRHKr4mMDEKvBSSOGXDsGYt4+CaQsgk6ukqG2nJJcjmErk8kLERUBRtcnQDZmKrQHPTBzSFNgVcPCZqtH7iTzVHqqyONHEiBI5vYrknghfjNkEBCdijPyUuKrDy9yBff9Dl1D/pmgtAiNN10ziGS2fFGCiSGVlQ9uYDp7Dlko93pTtWresShCqtMgMTN2ASNZG5ZcoXWXLNFm0zOwtM+kp6FrXI3SIkdxwSmqZztJZ3L4RQRIkIaKu9mZqxOz2DbOGDYizh1zyFyhpm2Ng2tHFnDAyzcgk112kMIRRclEuxXBRtjHcKddVu73cQiSRzR7eAlfR/v8W0I7fgutFkkrtmisyqTTYaO6+mY68x3v8vEV77CsTfdhDAMlniPEm29lax/TdogqpFVuSmZnMXi43q47E0n0T3osWPnzrTsuvR1wqeu2dG+SW7fjSdO5tYyS/y9ezGyLs4yldtsqGxDnUjY+r6Satrt0tfXx3nnncdJJ53Eaj1ehiHCthE6GEWk+dH6vQxZs2YNH/7wh3nBC15AHMfYlsXnPv95yuUyf/5nfwZhiOO6fOkf/zE9j5q/BiMhMUXM6aefzh/8wR9w1lmq+sIbXvMaTmrrW7J+1RJe9YLnsXbtWpYuXcb6M89V55kDAFu2bGH9+vUcd9xxfOITn+BVr3gFP/v85ymeeCLCsrBiH9sPsXD1+BgQGDLimmuuYePGjUxMTLB48WI+9KEP8T/+x//Asiz+4e//nhdccgkx8IdvfCNrjjuO6s4DfOYTf8Nll11GEAS88Y1v5MQTO6nJpytPC0iklL9JXgshKu3v/yuLMCLi2EJYRppHYmPS0K8Dy0bq2kMysoj8GInA0kDi5B3AIjQtRBtlFYekjm+AbE+exPfRXrBHRoIgiLFkrEKFHYOewRLj2/X89LEyhMCPVJQYAmTAhmtO4+GbLMBv+Uik0WG5JAUbwUbKGmCRyWWBiMjM4CXJlpaBN+MRtXVztLNZin2u9mEI7KCKnXGpTjfxm0megRrvZFsK2NaFlmRsEdiF1CIxHBPph5iGTQToHlt0mxWgQMabTsM+d7ztz2DVtTiu1QIS2yDJrLFdl3xLx+JmIJO1mRmra4ukrZnY1BRWGBMYBpbtpJYFgGd7dK8ahLvHCJoRbqHTOhCHxhieqRKXy+RyFoIYiYEdNYBsCiRuwe4IffV1b5JIh3Bnbd0yNvaxM2aHNdFukXi7dkEYEk0payJftBEyQgoTpzmDW9BWjxA4ushlIrM/+SnhwRGiyUms/n7MiQMMjdxHNHWZCjpAAYmJyhgHOHadKrp9aGYW29Wlbnz9vGt+12hT+qIdSNqLaOlxMgyQfpIJG5HxZ1Fp4aUOK0REIfPJt771LbUO27YRe146h3e85W2E0kLEAcuXL+eejbdTa4Jo1oECr3nNa3jNa15DXK/j7dyJs2QJZlcXl65bRzA6ilks4ixbRmWsyi2/vEvN3xD82Z/9Gd7Wrfh79+Iccwx/+qd/yp/+6Z8iw5Dm1q1EszPYgwOMHDiA3LeP97z5zfzlJz+JsG3G95RBiPRewpkZwvFxPvnxjyv/KHDllVfygpNPJqpUiBtNzGIBAg/Xm4VQd2+UEWAhooBvf/vbyDDE274da2AAq7dl5b7wwgt54Kc/xezqwlmyhKhaxQ5rvPiqF/HSa159xOq/T1eecdQWtJVT/S8uwgh1B0Sjg9pKTPnAtFJDo0VtiZTayhRsEBaBaab5DaAUv4xaisXOWdgZnU3edlwcCrxyjUh/ZpoGPYtaJT5SIIlUT4UEIGQcqlIQWpG3J+mFfkyYUGIaSAzDItT9PVxd2ys0s3iGVmK2QeBFhGFLqTmuAhIreyF27hJsr4ydSaitEMuG8n+omAzLttO59gs4ZugEhDRpuj1ppJmRSSw+HeWiI8b6GAcZk6scSBO0mnq3ZmdMciWHUy5ZTI/VUpyWkyGb0You8qEyjZOzaM7UO6gtgGBkFCuOsaMYWauRa1PcoZgmf2Wr3tVcaisYUUUUo3IFIQSZpIOmpyDN1QradTvpjWDffj1OBSu4htrlO14Z6ftk20I7HbOlkL3HVZOmULedlbUKjjeLHVSRk+MdkTziwK70dTQ7S2PzZnXtUVV8MhxXyY3h5EQ6LrRzGgRbMvVv3yQ6NJZSWQmQJFUEEytAxBFI2dqB+15KYwHEVRWVltRzk2GIFTawwjoyDDsoMRG2qRjfxz9wEH/fPu08jonnglmScKs3a2bkK6OkVu7wbQSa3oq1Y3AuKIq2ik8iDpGh+hc3GsRtBQ+jchmkVOAYx9DWTI0wVOVVknUI1RrE5TLS8/APHEjnJKOIKFkXvVbpnHSCl6HvSQSq+VxcqyHDkGBkhLjR+q6i5JnQVXyT87VXp3g25RkDiZTy7GdjIv8ZRBihKpduGS1nuzTJdet+H6aZAomMLcIgIpYipbYyRQeBRWjSASRxKGj/rQhDki0muR5tFkkIzYmZNMpKiIieRS1/Q6KckQZNXdJavU96jqi3ZltCojddIdRKWmieyTQMAu0UzeQygMR3isTCRCLT+lzoaDQjlpiWRbHLwrAGMKxFWLVpFWXTDGlOlRHT44y8/3/r6QQpMHTLmPWnXoRA0Mz0pM2ukq6Klq6Ma+kfUsEb5/w73kfX5OMpteU7CkxFeRIhBBe8+jjyDaWULakiU7JaAdtBlWh8nEzWol7TWfH33JEqj2B0BDtSQBJVKmk4LoBZmUzBAMC7+Rcc+tjH1A/a84gmJtRXpnuhZ3SOjVVXFoOl58T2hzn0ib9Jlai/XzlG49lkXDOdazA2hu23lFb1n7/cuv7jj6v1rNeJm02imRmyzUkcb5ZgbIxMrq0S9faH09e1229PQ8BbQKLmHk1MYmfMVmHPZlkpUCkZ+7vPcOjDHwYkUVUBdUv5aisqTQCNlN/C8zEiHzPyCLXiBohrenwcI6MoVZTqXGHHBgpfrUc4OYk1MkI0PUU0O6sUt++3rPYEABJQ0yH2RtCkWN2HETRT0IiqtRTMEoCbC0hpHTgZd/iBMAzCNl9GorST9RBtQCKDABnHrWoSXlMDQB1hWcTVKtGk6q+SAJKayxwg0feSlC0yQh8ZBOp+hIEwTQWuUYQMQ6JKBYQg1uAmfR9hGAjrdxNf9WxYJP/PiDAiVd3XEh21tkqDSpkHpmhZJJGKxY+lSHuEZ4rKIpGClmMc1Zs99Fo7TdX4Jqn51PpBRSH4k2XixJ8SB/QuLJAwlEbcApLKzgMtyko/fIlaMdPdo8GOV76GICnmpsNlbQFhQkNlXEwzxst0q0sSp9ZC4r+wYtVLopBrzdUsj2O7FkEzonzvFky/RlwuK4U3O5uCmRVGqUXgub2q6xsqlBdaAGJqpRtXKjhBlWi6RW15uvCif2+rg4CYTYBELULO0I7woEIwNobjCJLif96tN3Poox8FIBwZJe/55D2fuFLBzbZFE80cwsla6U7VEQFT//INwrExwtFWWflI+zoykVJa1uw4xDF2Y0bNpTfH1Ne/TvkG5YBtWSQaSJLQ66BCODKCUR7X6+xR/ua/0XhYgUICJKAouWh6hpU7r+e47d8nHBvH8avp39m1NbU6qrfcishm0/uNqjWkVrDhpAJjW1eztvwq/q5d1G69lckvf5nuV70STLO1000tkkT5Js3TtPL1muTro2QLFtHsLHGzme6khXbYyyDoyKuSQaDqnyfPflP11wgnJ5FOBmeFSrSLazXitr4ZKQC07doBYs/HKOSVYp2dVecaO4SwbMyursPuJQHO9DwyQnpeei170SK1cZieJvY84nodUzcsk57XCSRhqIIAkuCaZkOtSxRiDQxglkoEhw4RlctEs7MI28bIZpGep0BB/1aTTYcRNCk0RjGjJrLZJK7VMHJZ7CVLkL6Pv3sP4dQUSKmoLm0pxZ6HcJxnLdx3rvw3kDwVEYraQkqMpFAjJl1DimuMTCMN/41jS5V8aAOMbMlJo6c6LJIAfL/NHI4Ccl3KIhFtpngcgDdbS2s+EYV0D+bSUFcjAQhpUNnRAhKplbOp35vJgy4NglCkFX9F7HHJtceTFy3zyLQsTCNKgaTijSCO0XSaBhIzUkojZ4cIGWGGDZiewHFNwiDG9yWZbrVG4cQE0ewsll4XMwhUxVTQFom6tq2BxEmARWdKRlWlZKOZGSxtYnnaIvHuvCXdVYrJqXRuAG6sS9H7VcLxccw2JVtcs4rqrbcBip46cf8E63aNElUqGF4dK1RKVkwcQAiBpXvV9z3/QnXdxx9PaS1oAYKtEyJtr4xRqWDOKkXee/6ZGPk8jc2biZtNwkOHOsZlNBVm+1WCkRHMSZUJnusrYHZ3M/H5L6j12vY4hs4hCaemiWZm6Crvpmdmm9r9T46mCswOqlR+/WtkHFO99VaKF1+McByCQ6OE4y1LIdkd27pRmx3WaD76KDPXXYfZ08PCv/xLhG0TNxtKSSaKLnn24uQZjFoKzDSxBwcRpklw4CCy0UBGEUaifHXEVSIJhZRYN4S+ooJ8n7hYwMhl1W6+VtOUjUBYdgoAZtDAiENE6GlF7mO4LmaxSFQu4+/eTVyvYw30K6UdhsRBkO7akRLiuA1IpFLszSbCcTC7uzFyOYKDB/F1OK2l+7HHnqfoLMMAIZCBvpc4wCBChkFKixm5HPbwMIbr4u/bR1yrYXZ1ITIZdb3kWbZsSCjAIMTSATAJkBr5PGY+j7NkCXGzQTg2hpFxMbu71Rh9LpFpK3//LMt/A8lTEGGEyNAkmp3F0M5xR5r0LCoABr5lJSwSMrIJg6gDSMyshaX7MrSb7pHfCSRSBuRLurLsHF9Kc7aeAomMVRnspF+ImZrkBtX948RJ3wjddMvU45xmA9uyMcMcgZ1P2TMZ+pxw7hBW1PpRm3GMKcIUSGZ334lzrM4lEAZGLLHiWJnYzQaZ5jR2UCPUFAlAUBwgO6jzQ8bHiWZmUgVvNH0cDRrSsIj0XC3tyO7yBQu9kKIuphVXNADEMVQrGET4OR2SOjNB9dcbiZtNxIy2SDTlYnpVjMjHDiqEY2OY1en0Hgsrhgn27SOq1ghGR9KOF3G1SlSt4ugMRWNkL3Gzmfo8iitUDL73+OMEBzWQmCaxBgSnOaPmENQwpqYwJlQWcbaUwT3pJBpbHiDQmcVGqUSsrSinqebmBBWCkVHEqCqDkevJ0vXSl1K95Rb8ffsID46Q0z1Joulpomk1TmSzhIcOEY6MYgc6Q74nz+xPfkLlP24impykcNGFWAsXEo6MppZKnMuqXX8QYHkaDOMmtd/+lurNv6L0ohepqCjbVkpd79BFJqN2z227eEPGCiCaHiLjIiwLe2iIuFHH1zkOVqLogkApX9NEmGZrF99m3QSjoyAMZC6nfA75vAKSZhORcRCOAhKiCCPyKMbTCKmfSykRmQxGqaTO3WhgL1qE2dOD0EEDiXIXOudEhmHqGBeGoi7jRgMjm0UIgbN8OdbgoALEQgEjk1Hr4ilqSzgOwrJUQEEQkPFn6crpDohTU+peMxmEaeIsW4aRyYCULSAJw3R9jXxO0VNhiAwDdW4nk1Jqhm63YHZ14SxfjrBtzAV9KXDEjaYCkt+RfwSefh7J8UKIS3VDqfbPX/jsTOs5KiIkji2CsXFKMs+FwQksiXrpGVL0UmCaaZ6hjCxCvy0iChCWga2LKbY3NYgCie+3HRj65It699Ce+CQNGlWV8ZscJ4TA0BZFamlgUB8vpxFQUlNWCZ3keE2uvez3sMMCgV1o+VI0FWCGrRBFI4wwCdJdvzy0H1u0QM9OgKRWJ240yNcP4XrThJMtIPGMPE5B3U/LIkk4eC+1SABmymNYvTuwdLOjru4i55oFTM2px5UKaEokmp7GkkHqI7GzNtVbfkNwcCQ9vxlprr5W49gd17G4vJlwfBxDWwcA+ZWqnIT3+ONK+eokrahcVlSa9lGIQ/vwtm7F0rv13GA31sCAtkiU1eAsW6b4acCuKavICapYExOIgwoQskWH7Cmn0Ny6FW+bCrlzT1xDVKkg4xizOsWy6d+ysLGdYHQEsW9nOq7rqhdDGDL+2b9Xczh7vV6LKSLdRzyzahXh2BjByAi2jtbqv/JSGvfex4F3vhOEIH/++dgLFxIcOtRytC9eQjg5STg1nVokbtFl9vofI32frpeonIMkyigBTCObbe3ioxCQKp9EU1uGqy3Xri6s3l4FEk4mpdcUtRUiLCvdfctA+UlU6RWBDALMUjFttWvk80rZ1moYGqhos5AMDQiJ81o4DmZXF/bQEM6qVVh9feq3o5VtYg0m42QQKnoNFbElG01kEGBo4BGGgd3fj7t6NY4uR5JYEgTtQBKmlVBNXXBV+j5CAyKAsCyc5ctxli3HyGbTOaWWS9JOQftoFP3lqnsVAiOXTZ9lM58nc9xxWD09yifiOKnP7jllkQgh/hjVH+QdwENCiJe0/fmjz9bEnpMilLPdH58kloLjoiFMUHkIwkQSpBZJHNmEQUwo26JPLAMnAZK2ekShH6cVhEE51gpa8QpAJM5wDJpNiGVCJ2jFn1BWUcsiqZdbznbpqQcwAQgzlhi+omuCTLFFgfk6qayNZjB8Hyv2kYb2WYRNxOhefZ0IxzCxIklcrxHX6xy/9ZucNPZTookJTD2/CJOM9vmE4+NE0zMptWU0G9hmC1QtRxDu35RGDhWG+jBKxdQRHVWrLUU/PY0VewS6TXDx1DXU7riT4MD+1JlvRTFRtUpcrbJ4/E4GuiPCsXHE5KH0msXjVSSWt/UxgtFRMqtUleO4UiXSQGITYMiI6m23pcrZLdhkVq+m+fg2RUEtWIC1YIGiYaTEqioHth3UcB57DFtbKLmiQ/bUUyAMqfzylwBkTzpJ9aipKV/SmuC39HVFyoexewcWIbmSg3v88WSOO47yz1TV1/x6BSTh1BTRzAzCtsmsWE4wPkZw8CB21EAIWPg/38gxP/8ZCz/0IRZ97KNYfX1YCwcJR0fTIIFg8WLicplw5GBK52X7Syq34phjcE86SX3vGkiidiBB+yjCkBKzZKyQuF5XjuY2BWYtXIhRKGD2dKsyH7bdorZsG2wr3XnbcYNs0UkVa0LVQJvCj2OEmwHLSikxIAWpxKFuaP+A1duLYbdF21kWwjSJdfBAorSJFJBYhNi2QCaUXbaltIHUigIwMhli30NEGkiSewuDVKmnx7aFwIMCE7Oo9uWJ5RBXqwjTarMsWkCSWFJGNtuR5Al0+EGMjNtK+nyOWSRvAtZJKV8KbEC1vX2n/tvvxpPznJEQGVt4Y1OtwEAZky04CGEipYdMzQCbsBkQdSxJhKNLQSTUloGhgCRuOy5sks8ZJMvZHmXVDFUNLgCpo1ksDSBWEtkhBR6ZFmXlKaVgJEASxTqmHqKugZQqi/VnhtfykRiejxm3HJpm1CTercJObb/Kqf3DHDM2rSKH6g1lwi/sIpycxJidSMc5XTkwDCJtkaTUVq2B0aymNEamK4u3bRuuoebQtXIRZqkrVVpxuZzuAKPpaUy/FfJYWr+OcGSE2m23pWtmJsq5WsXM57EGBtQO/FCrhER++RBGqUTzkUcIx8bIHKeBpFohrlZZeOhuVi9Su8PqLbdgax9JtuCQOW4V/o4dBPv2Yy9ahFEqKsui2aRvbAvHD07TxTTOQw9TKu/muDVZho7rxj1Fte6t/PrXGLkczvLl6p5my0TlMmaxhL1wId6unYSjo5y94hBrn7dUrclVL1Zrl8+TWb0aTJNoappwehqzuxtrYJBwfILgwAEydkwmb2OaBpmVK+l5zavpfulL1fe3cBHB2BjBoTGEbRMtVCVbmlsfTy2S3NACfc2rWjvoNgpKWFaLMokiZBSqroC23VLqbX1shGGQWb4cW7dMbgFJiLBstYsPFLXliJB8VwYjn1e78EKLABGZTBqBZOjXUlufgLIcDKPl9zhCtJIQQitliTDNFLQSuq3oeLht4eGJRTLvuRxHMQ1SphYJYaisG0uVeU/Wwsjnjn4ehAJJx25ZgDogQth2Oo8U+I50LrcF4s81asuUUlYBpJS7UWByuRDi0/xXBxIRIGOT5vhUCyC0AjSEAbFH7EG12kOzuoig2iASbSGYUYibJP3JJPtWNQby49ZXIQOPnK0Sj6DlREcaeGTSVtRof0JOc+pWEkMsDUVZJUCim5Ek1JcZS0RTl5co9KaWS9zQu7ck5lxKaDSx2nIJbNcmeHAzQigH7spTTqOvpsIqkwfdWbKYuFolHtmfjnOyNmZvL+H4hHKUJ0tarRJXKlihLhDYU8Tfswf7a3/NqQ98nsHTV2KWSkSVsko6CwLspQpIwokJDL+VL9J1vtqdz17/Y2yd7W3FMXGlQlyrYhQKCkjGxhAHdqvrC3CyFu5xxymHexxjL1mCcF2iiprbgsmHOP1CVS23+cCDaVZ6Jq/GSd+nsXmz4t2LJRWBU65ghw1OPyEks2gQc3YWK/a59E1rcfM29sAA1qJFiq9fsgSjpCL/4vIscaWMWSphLVpIsEdZfytO7VeBFUDpRS8CIcisWoUwDMyeHk1tzWD29CjHbxDQfOQRht1xTjx//npK1sJBCAK8xx7D7F9ArOfgbX0stUi6Tj2B/Lnn0PXyl3WMTXbm7btsGUUQRQpo2pSW4R6ZUkn8LSor3VLvwxCCIFWg1uAgmWOP7dhpz87O8pUf/BCAPaOjnHbRRWoOOihDmGZqeTxRtFJKVzmOok01lbZ73z7WXnJJahEI2z5q+GxyXP9ZZ6lz2bYCN9/jw5//PJ/85Ccxsq6io9osm5tuuiltbAVo6yWZewswk/BjYVkcmJzkhW96E6dcdBEnnngin/3sZzvmkjSwOuGcc/jkP/6j+k4s6znV2GpUCLE2eaNB5UpgAXDyszSv56goi6Q8NpF28kvCtCzDAHxEJOEHJ8DYxfjVBmH7Eoc+rp1ESCV0lerhEBp2KzEp9HDtMI3GMhOzGoPAykPSic5vIuMYS+/CEseywMB3SsjkuIY22/0keivGqGkgcbs6ACeqVDCCFuDEtRpW0AKSrovOofLvN+KYEU5QIXOsooXiep24oZSPvUTtnKPHW01zHNfE6u9X1NbsLHZSDK9SJZotp0CSP2YJZk8PcmqS5euXkl27NqW2Es7Y0ef3tu/A0mAqTHCXL8NevJhodhZ3UO2urUhqp3lNAUl/P9HUFHK/StBzcmqnmFm9Og3htRctwigWiCuVVijvKl2tWUqW99dZ/5Jj1C7/OPW59DwFJKWiCnPWvLRZKqZUnLN0aYcCyWqrxF6yGFP3bVdhoGWMUhF7YavjZGKxJPPrfcMb6HrFy9U99vQQTk8TTc9oi0RFEIWjoyxfFHL2S1tJlO2SnL/x0ENY/f3EmsNvPvpYapHkFw+w9Gtfw9bnTKSlfDOpzyrJmaANSBIFdiRJLBKQ2kdiAVJF3yVAYBgpWCUyMzPDV771TWWtOA5pf3hPW89tllKi4FW/88PbzaZAoQFHmFYrkICWhXA0a6T9POm59H3HnpeWsbH6+8kcc0wHHTW3sRWQWkbCsfX9K4sLwwDTxM5k+LvPf55HH3uMu+66i89//vNpk6r2xlYPbd7M92+4gcf27u34/LnQ2OqDwKH2D3S73GuFEF+ed8QTiHbSfxaV6vCPUsrDoFIIsQH4DKp2yISU8qInO/bZEqmB5JZHbubc4dPVh0n2bNuGZ/H2HZSXZhkZH2VQl4AHFRWVSRwaCbUlIQ4lsekqyioKkc2m8kVgImkP19UXsVXF3NhT4Y+tnIyWjySwc2kPdNmoIKMozcUwYwm1MlAgcAqtwLAowN+9W/0dMOKYuFrF8utp65GB113D3h99l0x5hGxzAmfFZWoZGo00F8FZonoeBA9vghWqxpDjWlgLFhBOTCAyGRZYLo1SD2LbCHGlDUhWLuO422/rWHez1IX0fUIdmmr1L0DkcniPP44ZKd5eB8ORP+ccZr7/fdzhYQpmk/y+MWVZVKsYhXyqZE2vBsi0PErm+NXp9eyFCzELiqKKdbixNdCP2d1NNDPDwhMGWXD5cnVfK1cqRRpF2EOL1LVqtTSCyiiWsBcphZ1QZolkTzmFyr//O87iJZhdbUBSqWCWurAXLUyPdZYu7Rg7+P/9eWt9enuJpqaJZmfJHHss1kB/617a6j/NFXuh6p8Sl8sKSHTJDO/xx8n0KZDLluanQxKO3vzt3yBmt+HU6gjbxgkCjIwDhonTaCBMA+7KznsOUHRsQqWmlou7hGDtu44KQO9973vZsWsX61/2MlatWkUUx/zRBz/I3Vu2MDQwwE9vugnLttlz4AAvffnLueR5z+POO+/k+uuv59Zbb+Xv//7v08ZWn/vkJ6nV61z7rndxYHycsNHgvW99K2eeeCJRHPPmt7yF22+5heHhYX7y85+T1ZuBT3/603zta6pO7Rvf+Ebe+c53pgAhLIuPfeYz/Os3vsHiwUH6Fy3izOGhNrBsyXyNrT74jneo8yRgaFvISNN/QrBo0SIW6eeqWCxywgkncODAAdasWdPR2ErGMa+8/HJ+9utf0yiVnlONrV4L/EII8R0hxB8IIdKnXUp5+1M9mRDCBD4PXA6sAa4RQqyZc0w38AXgKinlicCrnuzYZ1cUtZX33Jb/QQOJ3VbgTVTKGJZgZHKso0S7DD2yZkJTJcpaHyAMhRORinSRnoeRlGFJaLCkHpdjIUMPdJJU4ri2E/NdGiAMAssAGRNVJlTtHn2cFccwrR2sRratlIqPv2sXZlKCJZbEtSqWzrkwLEF+zWpy69dzyqa/5/jKHRha+SRRWwB20lSnjdqyXTMFkmhmhsWFLp536tnE9Trh9HQKJE72cOWRKNk0VLZQxOru1kCiQyT1sPx5GriWLOH17/0rlkwpWkv5SJRFAiCQOI5I+W/3+OPT61na1xFXKkSVqgoddRysBBBWtQDBcJzUWrAWLcLU9FCSV2KWitjDQ3pcWw8aUA53tEWix0WTk8hGA7OrhKV9FtbChalzeT4xe3t0QqLykbRbDwmIzSdW29+s/n6ihF6r1VhkjfOit51C31Bh3rFGLgdCINrLwic7EiFIeyjPU7m3Q9opJyE63ot2p/gc+fjHP542tvrbv/1btm3fzluuvpr7rruO7q4ufvjDH6ZK+PHt27n22mvZtGkT9Xqd7373ux2Nrb71wx9y8/33M7RkCVu2bOH+//gPnq/7gmzbsYO3ve1tPLJ1Kz0LFvDDHyo67b777uPrX/96R2OrzZs3K6tECO7ftInv/fCH3Pm97/Htz3yG+zZvOeK9zNfYynBdnvf613PGRRexdu1azrrqKta/8pWsf+lLuOmmmzrG7969m02bNrFeB160N7YShsHS449nZGZm3oZX/9caW0kp3woqBBilwP9ZCNEF/Bq4EbhdyqPUOD5czgK2Syl36vN+B3gJ0G5zvRb4kZRyr57D2FMY+6yJJEDGFm7gtpztuhid3dYeyoglBiF2lE96TKmoj8DHRTvEERhRhNHuGzFBRgFxo6li1qUgwkj7FCRAUl3gUrrrq1jnrOqwSBzb6Tiu7loI7ybimRFko94CEtMm2LUTIz4BX9pYCQhGAY9uujk9zpRSRUl5CkiScN7ea3+f+t1vJ7twdRrDHtfrxLU6WBZ2ogDDlpPezrSAxCyVsBcvTsMhg4MHW0DiHt6vIgGr4IAKsTVLRcyeHjWuT0ekaJ2TW78e4bpkVq3C6upCgLYsqhjLl6cWCYCTs1Pgyhx7LBiGSu4qFJRFUq0QVyrp9e2FC/EefRR3Vadl4a4+Dn/HDuxFQ6mfqD0/JKG2DrNI1q6l/51/TOnyy1Ol5+tKwEaxjRJro7XmE6unh9rUlEpo6+lOwRLAHjoykJjd3WnIqtXfDxkVkisbDZz+PpadfHgDqkQMx8FdvRrWfAohBMFjj6XObWf5CsxCHjk5icjn4SiUkGw08HfsUOuzejVISaAz9o8GJHNlxYoVnKo3A6edfDK7d+9OqaZlS5dy9tmqktPNN9/MfffdN29jq/d+4hO85z3v4bL16znnuOOYKZfThlkA69atY7dOQLztttvmbWx1yutfD6gS8C996UvJaevlyisun3feQRDM29jKLJX4zY3/rvJBhMA/eJBoagqzuxtncavLYbVa5RWveAWf+cxnKOmNwNxeKWY+r4If5umh8n+9sZWU8jHgMeDvhGpCfTHKUvg0cMZTONUwsK/t/X5g/ZxjjgNsIcRGoAh8Vkr5jSc5FiHEm4E3AwwODrJx48anMD0lUsZAhIxNskFrFx8HPhs3bkxDZ0Ep4Hp1BivO6wq8QBxy35134unkMmHYGFKmkVQAoYxx4oDtjzxCfPAgdtAkzLT/mBRAjDRn6J3dSXm3w/bf3JIq/mK9xqKDB5VfxoCGV2Nkeoxsucxnf/Y3nJzww6bJ9IMPYqx8Pg0/Sz6NGwh4ZNPNLI3Vj8OQkj2PPoZVV4lysQzV2glB76KF1IoFdv/2bgaBnY88jFGr4To2tz/8MIOo6rXoCsQPP/YgC2ZnKIUh1V3bCRf0cWD/AbqAfffehxWqrn+PPPYQe6Y7H25n9x56gLtv+ynLgfsfe4wCkgykFokUUfq9Gh/4S0ZLJbj/fgaB7Q88SG56mplymR07ttMPSNvGKAY0jel0XF9/P9I02bhxI12NBtahMWYsG8s02LhxIwXLIlsscPvjj8O2ben8ck6GghD8dvcunD176Ab23nMvWeCuBx8EwyB72mlsiiLk3GfvhBPggQdASgYMg4ObNuMCjx84QPOxxxgQggnHZtdRntn8bJmCjmrbPTHJI3fcQX+xgFGpcu+ePR0FBudKX6mENT7OzqkpqtUqQT6H1WgwGUdHvGZXV1faCyQRUwiE9sHVvaayThxHZWS3hZMfJlGUKqGatmiT93XP68yjQvH/lUqFarVKHMfpa9u2QSgLXBgm1VqNupSE/f1kc7l0vo1Gg2uuuYYPfvCDh01l48aN/PKXv+R/f+xjXHrWWfzeVVdh23ar70kYUqvVqFQqNBoNPM9L/+Z5Hs1mk7rOaG82mwRhqCwsKQnjuOP4RB588EFOP/10pqenaTabHX+/7CVXUdXhy+hABkyTD3/sY1x88cUEQcCrXvUqXvnKV/L85z8/HdvT08OuXbvS9zt27KCvr6/j8yiK0s/nzgmg2Ww+JT35rFTwklI2UHTXoJTyHU9x+HyQOBc6LWAdcCmQBe4UQtz1JMcipfwK8BWAM844Q27YsOEpThHi2OPXG0HGFnbcskhEHLJhwwa+89XPQVK4LpbkXZtGpUWBEYesXbOGkT172DS5G9PKYJsmVqVt155zkTM+K4aHsQb6eXzjDRj9izHzeUQcI/TtrjhhFdmuLnp6uulbeyobwwjDMDi2p58lG3/DLRe8hBDo6iuybHA1E7/6FRvHbmBtrHZH2WIRa+tOzBU+ocy3GluFHkNl2fK5GCbDvb3sbCisLnbn2bBB4fQbq19n9cAK/vzsS3gsm8Wzy1hWg1KxxIbnP5+tRUUN2bYgCGD9OWfgFJoc+N73sYOYgdWrya9bx/5vfIO+OOaAttTOOucM+pd2lrdu9Pay+x/+gdHRB1kOrL/4YsYeeIDyw49g6+AFO2My93uVUvKYbfNo9V7O8BosPm4VA1deyWPv+1+4K1bw+++/pOP4mT9+BzKKOGXDBkZu/hWTu7fjxdN0Dwxy8oYNxGeeSTQ7y4lzuspFZ5xJ86UvYc3ZZ1O/5x72fPFL1GZ2kwUueOELMRyHjYXCYfObK4+XStRnlCVz0vr1FC66iJkPf5jsaWvJHHPMEcdNHTjAoZ//HIDVZ55B14YN7BxejLdtGxdcddVRfQ17VqygPj7OmvPP5z6gMLyY5sQkw2tO5PQjzPfRRx89rAS5Z9vEGjDypVJnrsZRREpJ88ABhGlS1Dvqpmkio4hCd/dhTvak/PmiRYuo1WoUi0UKhQKGYSg/gu9j2hYZw6BYKlHo7cUwjHS+L3rRi3jJS17Ce97zHgYGBpiamqJSqWDbNoODg7zpTW+iN+Pyz//8dV73spd1jM1kMgRBQLFY5AUveAF/8Ad/wAc+8AGklPziF7/gX//1X9Njk7+/57WvJWg0+Pf/+A/e8ta3HrZu27dv54ILLuB1r3sdL3vZy/jVr37F4KDyXd1xxx3pceH0NMGBA9hDQyqpU3d6PPnkk3nf+97Xcc4NGzbw5je/mYmJCYaHh7nuuuv41re+xerVq9PPS6VS+vl85eRd1z0sAOBo8myXgvwQ8PWnOGY/sKTt/WLg4DzHTEjVJKMmhLgFOPVJjn1WJE76KcQWsWl0lBWBlq9DCKXuRdhEiFKrtU4UEDebLYe37WDncpiTrZpPRsYijkNks4FsemSCCNHVjblyJVZbi0zhSEQ2q0ofNJssnqpwwp++G3vTFjwAQ5diMIM0zryr3gIIJ5uDMFQl1YGmhNLLjqVy04MsasKsbqxkGgbR7CxOQ5f8aKOdHqntwK2pjHIjm2XX6CO49ZB+Xa7EWrAAv1JRhRuDEDujnO2JRMUcRiGhrA5gl9TXaB+F2hqYlel7q0eVaVE9XlrUlpSST937KV688sWs7l2Nmc9TnjiA4UnMQgFhquixpJlSu/zypIhIRlyjrxFXqkyONxhaqgxsI5+fN26/mYEHl8HZkIbxhgcPIjPOU0sCKxaQBzW1pc/TrSOzjibtfSiSpL2wtwj9vU9Y7VUOqLBma0E/TIxTzgscwOs+sk9mXmlT+InyD6IA0zBVaPwRJElKbAeMyBSIWBzVv9Le2OqEE05Q57IUkCTjwjhktDbaMe6wxla2zec//3lmZ2f58z//cwzDwDYM/u497+m4p4pfIWzrITS3sdUb3/jGDsV7+umn85rXvIb1L30pSxcu5HzdPTGIA/zIJ2+r52huY6tXv/rV3HTTTWlUY7pOqdNd/X/77bfzr//6r5x88skp9fbRj36UK664Asuy+NznPsdll11GFEX84R/+YdrAKvn8/3pjKyHEA0f6EzD4NOZwD7BKCLECOABcjfKJtMuPgc8JISxU/NB64O9Q1NoTjX1WROqUdRmbhFYmpaxk6KtCcUkCnO0ohTU9CaLUKpESh6oyqAaSYm+Bci7XEQYocjYyqhM3lRP9hJFJlv/J+7jx1tuwMhkkMQKD2AoxMhnGpvfz8V++k7dLyYLhpdT2KCUk7Vj1z7XiVPF1V0kpMFt/ZrY1GyqetZC4aONUWzW5LNMiPHQo9V+k/T/CJhW/Qk2HiBq5HKIxi6x7aXir1ddHcOgQTs6hXglxsiZmG3fv5x0MncnrHzxItle1SU0y2h+ZfIT33PIe/u2KfyOvi/v1z6ixRj6P2aOUp1PQiVn6ST5UP8S/PPIv5J08q3tXQz5Hr+7zYeTV9YY+/rEOP0Ii39n6HWzD5prjr8EsFrCDmGwthidI+vru1u/ymfs+w61X30pOg96CMsTdR45WAqXovvzAl7l69dX0ZfuIClkKmqhNnO+jtVF63B4y5pFzMcyensNeX3euweQKwd8cdQaw1RpnKeB1Z2ECZnKSAWAyF7H0Cca2S6zDFqUQCEP1NN8+s50F2QX05w5f63Zp5m0wDJI7DAyJYbb4+zAOiWR02Bokja0Sqe7egQm86x1vJ9O3gBlvhuJgkbvuv6vjuKSx1Vy57DIVgRhWKwS79xBlHR566CEA9lf287r/+ToWF1v+iaSx1VwZ0YEW73//+3n7a1+F2fAprFHRhaO1UaaaUxzfezyGMPjUpz6Vjrvyyiu58sor510jP2NwqEcw6JpkgTPPPpOHxh9iqDBEj9tz2PFXXHEFV1xxxRE/fy40thoErgVePM+/yad6Mh06/Hbg34FHge9JKR8WQrxVCPFWfcyjKEf+A8BvUWG+Dx1p7NO4pyeUxCKRsUVoZjsoKxkEaQ8Ey3Hovfb3MXVOQmqRxMoiSUId7YzLueeeywK3FRVjXbyYYOePVWXVZhM7iikuXIRlWViWRah7akRmgMi6eLUy5Yqqk2S4Gaw+pVyDjO7JbkUtIKlB3gvIFop0d6sHzxQJ+Kk2qFGXmkvSm9yyLILR0RaQ6LLtk031NbcDien5GJ6P1D3e3ZNOInfmGakV42QszAUthdLIW6myFFHEQmMPr3rvGSmQ3HHwDnaXd7OnvAdTP/DFJoSu2r0mCjPTldP3oM67r6I0cSXp4ZHP0VfRlozOjM6fc45yrreJlJL9lf2UdbHCxFrqK4M/TyRZu+yY2YFEMuPNYJQU6FkxBLmj0ztbxrfwpS1f4lf7fgVAmG8pSrNUIpYxr/zpK/nC5i8cNnZ/ZT+TDfU9GD3drXHaInlgUcANS6fS7+iIczje5TcnCWYKSmlXCur7msiq3XcUR9x58M7DHLVRHLG/sh9fW7WxjtJKcpdCGRLLmLpObDySSCkZzXpMZlu7/ZmiwXhJEusosLH6GLtmd83rLG6XUHdnjPTzm1gQXlKqJ44YqY10WBbt80gk0L+LpCFoFEfEMk7PA9AIG+m9t0sUK6s2vZeCYKxbpOcP4kC1GdZjgyhgpjkz7721f9YIGtQyrXvxY7/j3mIZs2t2F9X21gH/B+XpAMnPgIKUcs+cf7uBjU9nElLKX0gpj5NSrpRSfkR/9iUp5ZfajvlbKeUaKeVJUsrPHG3s70LagaTuuq0YrThE+j5G4lewbXqvvRbDUO87AKfpge8hJNhuhnXr1mGtaSWLxV0grJCo0SCoVxGuixCCM844g0suuYTQVA9PZAUYGRc8n4w2KoTrUrzsMvrf9U7q+kNptoCkpyrJBiFv/MAn6F6gIpeE2QIcAD9p0KXLs1u2Qzh2KK2Z5WiLZKKhQofbgcTyQlwfAp27Mvje97D0y1+mHM+AITFtAyOfw9M+jVpWdJS8qGfCDt/I9hlVzLDslxG2TZjRvUe0UhfduqFXUSc2al0/F0iiXIY+jSlG4ciWxWRzkkbYoKJLvycRZU4EDd3RUErZoUwS2TWrkhtnvBlVqVXvpJu6s+HOmZ28b9/72Dq1tWPcwxNqz5MAgtfW0dAolZhuTjPrzXLbgc68mjAOef0Nr+dv7lH2RiXXFvnXVUzvB1rreCS5p2+Gz7/YZMZXVtuMXqKRjPLd3XbgNt78H2/mpr2dIacVv8KsN5sqrkgr8QRQEmXdbIvcm0+COCCKo/R4KSV1K6LpCAJdhdqLPKI4ohF2dmsM47BDcQZGJwAk50yUbj2sM9WYYqo51XEeP/LZOrU13UT4QlPDc88T+aly31fZx97K3g5lL6VkT2UP4+F4+r5mBDSc1jnmgttUc4oD1QOHAW7Fr7B1emu6Bk0dVBJoPTT3PF7kUQ/q6W+zfU5lrzwv6D2b8pSBREr5P6SUtx3hb78TWum5IFLqpjexyWwh25FHIj2vVcdK9ysIVqjddxomHIUqP6TpYQrV/hWg0dVSHoHhYWRcHjm4iZu23ZCGLy5dupRTTj0FXzTT44TrIvwAR2+uRCaDvXAhC976VppC19GywjQ8t1tvTI1sFlPvmmNT/3g1oHglZU14lqa2bBuiGIEkkyHtHT4XSEQuh+1FZAJotrkEpJTsbuzCM3VpB9G2882C2QYkU1angt4xo0JCE0DwtS+k6apHdp+pfvSPxkqJGxqgEiBJFEyYcyhoXRZm1Tk+cMcH+OKWL3Zcrx2ApJSpXwag6qj1+dIDX+KKH17R8WOVUrJ7djcAs94sQgg8nZtS0wbGlvEtVOMq33jkGx3XfHiyE0gauomWb6mqtIfqKu/38enH02MAfjvyW8YaY+wuq+tOOmrtQgPKturJkRy/fboTSPZX9qfAF8s4nXuiXLcel+M3Jwm2l9QztG1GRad9d+t3O86TAG6ipBOlmwBKu+JMlF89qFPxKwRRkCrgBGjCWM07lnHH7h1IlWA1aIFGLGP2lPewp7wnvVbDUIRzqC2SSFeESMYn15prAYzXx4lklJ6/KQMqWajrqOVQd6uLZUwQB+qeogAv9DrmVA2qNIIGfuynxybXSeaY3FMCAAlAtD9TsYwZqY4QxVH6G5sLJOl5dOve5N5qQS29XyklY/Ux9lX2pc/S70r+ux/Jk5S5FkkrjyQBEl0qRTvDaqvUrr/VOyQgbqrmOJYwsHXxNt9o7bI8o4lwXcJGnWplgijT6ewLtEUSmJ5q1OOHKZC0l95ooB6+qM3Z3l3V9E4ul3Zz83RvcKmTJOu6P3ldU2PCaVE6515hc9oLlIM6UVLJLkpmM7g+uD7UrVYJiocnH2ZaTNCwKsQyJoojpvPq7+VMjLBtfEeHNBttPbDjKFV2yS4xsUTqWjmP9xgEJvzGUMr4SBZJmG0BddlSP+xf7PwFX9j8BW7ec3P6t/0V5V+KZUwtqKn8By2ztlrkhyYeYqwxxgfv+GCqICabk6lSnfXUrr6p6byKXscDVRWJdcOuGzoA4ZHJR9JzQAt4ahmJlJJDtdaP/57Re9LXP9upKv8erKq4kjF/iqoL1awChHpYTxVPAgS/HfktV11/FZf/6HKu/tnVBFHAaG00PW5a12vbW/L5/ItN9nmKmt1TVuHqd4/cnYKOlDIF6mTHHGo6KAGUoM3/5oVeqvj3lvfy+PTjjDfUrr3dygjjsIN2CuKAWMbpZ8k1pZQcqB5IlWcjbBDGIZVMzN4BkVJTCQAkijVR3kEctEAjbDLjzajXei382Ge8S1Cz43Re6b1EXnpdgUgBQEqZ3lNyXLv1moBKakmEqud6I2wghKDqV9PzjtfHCeIAIQT1sK4sYQ0Ycy2bxKJrhs3UpzTjKaA8VD/ERGMC0zCp+tWUKvxdyH8DyZOUlrPdIjazbU70gD/75R8T6jwSU0db+Flt6icniEN+/Mj32Tm2lZyQ9OqoIc9omf6+aGC4LsLzcQKotHUqrPgVQl0R1zMaCDeD4Yc4CbWlrZdm2EwtktD00yqj3XrjJLLZNFO8KjQtoS2TmubHa1pxYreA7G55KzldLiP58TTChuKEXRs3ADeAitVSIDfsuoF7lv6cfz/ua4oGCarM6KSVKU2/JUp3L5Ppj2N/dX/6IyzrplLJbr3sKNAbyXn84btM7lo+inXGDEVdCWRveW/HOK8tCmzKbDLeGKcZNbEMi7+4/S/YV1bAkwBQstZem19kymqm5y7YBX6z/zf8cJvKcE4AD0gVUrKTnbb99H4yIkMQB+m4il9JLYrEGihr4Km5av7JLtIyLO4aUQ7jelDnpr034RgOM94MtaDGofohylkoayBpB6tt0wpIvrjli9T8GletvIp6WOfRqUc75j7tTXfMJQGp3bO7OabrGCxh8f3Hv6/WNFLAYAgjtUgCTQdFQnYoTFDPST2oE8uYwfwgeTvPVHNKhf5Gred/LpD4sZ8ClWM66nmTERONCcpeOXXi18N6yw9izKNstQXkRR55O49pmKlVMl4fxxAGXZmuVLm3+1SklJ2gGHnpnBfkFlAP6lT9KhW/QiNo0JfVxT3DZgeQJAEDqSUWNVMQWJBdgCEMxhvjTDYmmWxO0pXpImflaISNFFDhcIskWadm1MS1XPJ2nhlvhtH6KJONSXrdXobyQ8QyPowafDblv4HkSUqkHwoZmzhRttV9MArZMf5YWuiwGuvMZqF3EKnjLWJqdhQ8j6i5g1uGdwPgCfXlBoZPPaq3ACKEaerpLrfsl1MfiWc0MNwsth+nFkmgqZ3xxngKOKHhdzjbPQvqUSMNLW1oOinSTvyyBpKqKzn1xVfRs6A7vf/vH7wh3TG1m+H1sE7oWqlFUtbXjmXMjbtvJMp6TOdGU75/sghNG2ZQ65RYGLN2mNJZ7bx+Agg1NzkuSHfrseuwftFZfK/r8xhunDrMoWWRJFQYwKRRTwHjfWep2Pu/u//vgE4gKfvl1C8CMGGoHe/+yn5etfpVrF+0nk/e+0m8yOtQxsl3VdX3NGmq9dpf2c9SZynnDp3Ldx/7LkEcpNZIySmlin9Gf5k1V+1KD9UPYQmL84bO47ejvwXg1/t+TSNs8LJVqhrvwepBxupjTJYEU0WhgERbOAPZAbbPbKfiV9g0tomXHPsS3nm66viwaWxTCmSGMFIAScDwUP0QYRyyu7yb0wZO45Kll3D99uupBTWaYTNVvsluP+l+ExmSUCpAMA0T27DxIkUBCSHodXvpcXuI4oh6WKcRNshYasGCOCCQLQUZREEKVL2uCiSpRBXG6+OUMiX6s/24lksjaKRK2xBGB5AIIZAo57YXebiWS3emm4pfYcfMDsp+mb5sH3k7nzrU/chPQ5YTcBNCYBomfuTTCBvYps2C7AJMw2RPeQ/7KvuwDZuB3AACkQKJqYs1BjJI5+WYTnoegIJdoDvTTdkrM1obxTEcBvOD5OwczbBJPVC/lYyV6bg3x1QbOy9UVpJrunS73QRRwFRjit5sLwvzC8nbeYQQrQCU34E8bSARQrxKCFHUr/+3EOJHQojTn72pPbfE264cpXEscEK3I6zXDpVTFsDX3QMTIPHNZIcVYwYRvSJPJl9Kd3weHqEICA2fWlDDcLOYfsSAKOGZMT/d8VNAKbdAK+mmUIBjBTFZ7Vnc01Qhh+P18fQ432imQJLzlf9irD6W1mKqZVqAAyr0E6CRgdVXXY7R3SptcZBpfr5TJb21A0ktqBFmLPJNFak0ram6TWObGKuPccUKFYI41Zxi1pvlJ2cbfOJVBmX9UFfbduFbxlU9ooTXL9rFFEgqWjlXHRUJNFofZTA3yLUnXstYfYwH6g8w681SCSqYwkzppkamBQiHqKSAsX7Rei5ddin3jN5DLGP2VfZhaX6s7JepOi0O/ZBRYaQ6QihDVpRWcO2aa6kFNe4dvZfd5d24pkvJKaVKuJxRD8OME1ALahyoHqDP6uP3Tvg9xhpj/HTHT1P/yHlD56WKf8r29FoIxhvjHKodYiA3wNmLzmZfZR/bprfx3a3fZVF+EVceo8JEEyD5+lU5vny5oXa0GpjWL1rPVHOKn+38GZGMuGDxBQzkBhguDLNlfAu7ZndRckoszC1kujlNLGNmvVkGsgNEMmLr9FZmvBlWdK3g9074Pcp+mSuvu5Jm1KToFHFMJ6UsPRESG+BbLeVrG7ZS9GGDil8hb+cxhEHBLiCEAr0ojijayh/VbpFkrEyacwEKcE3DpByVMQ2TRflFCCHIWlkaYQMv9DCEQdbKEsowtYpylrLIq0EVKSUZM0OP25MCw6LCohSQoOUjS/I8kjlZwiJjZlJqyzVdDGGwtLiUhfmFLCosYmlpKYYwcAyHRqTm5JoulmF1+IoKtvINJhsP13IZyA0wVBji2O5jWdm9EtuwyVqKrk6sxYJdIIzD1P+Ss3MIBNVA0VaupZ5D13JZkF3AwtzC9D5zVu53GtH1TCySv5BSVoQQ5wOXAf8CfPEJxvznlaL6UiMEBmYHZeUGMm3UFBlKAfkJkGh6SqKsB9OPMV23xafHTULTJzA9amENMg52ENMtcti5QsqHl/1yqvDr1DBcF0PCYtGLb8L2strNjzfGW5aLaHYU+/NsBQKZVav4/p+spb6o0DHX6ay6h6oLs/4sFVspxNi2GSgNcffI3QAd1EktqOE7BolrZEr7Z27cdSOu6fLyVSqhbtqbpuyXmS4KHl5mKGCMAirakS1KxRRIdszsYLgwTH+uP91FVTRS1zMw1ZjiUO0Qg/lBzhs6j+5MNw82HkxB4pjuY6j6SnHUnBbFeEjOsK+yD0MYDOWHWDe4jhlvhp0zO9lf2c+qblULq+JXqNgtimWEWfZUlK9gaWkpZy08i4yZ4dYDt7JrdhfLSsvocXsoe2XCOGQ2sSwyig6baEywwF7ABcMXcEr/KfzDpn/gntF7GC4Mc0z3MVT8Cn7kM2bW03ETjQkO1dU9rl+kqgm85mevYfPYZv7wpD9M8xkOVA8wVh+jtGwls912B7V19pCqL/UvD/8LJafEyQtUl4dT+09l09gmds7uZHnXcnrcHqab09TiGhLJiQtUktqdB+8EYHlpOacPns43Lv8GS4tLiWVMV6YLx1A74kbYIEIytbiLmitSpWkZFq7l4kc+fuSnCtQ0TAp2IfV/FRz1eeLIFkLgmm5qkRjCwDKsVLkPF4ZT0M9aWWIZU/bLZMxMqrSTENycnUu/UwDXdMmYGY7vPZ4VXSvodXtVGwEzgxCCWR29llwrmZNlKiBphk38yE+VfM7O0Zfto9ftTcHIEU5qkTimg23YHSCZ3G/Vr5KxMhjCwDRMlS9kZVJfR3KNelDHMZ00jyaIFCVmGzaO6XTcmyEMVnavZDA/2FFHq+gUU2vrdyHPBEgSzuZFwBellD8mLTb+X08WHPtCzjn7ZqplVR4jTJ3oITlP1aUCCHUIYlNTVqlDW8Q4ARh+iOFmWxy+9AgNn8BQ4XuRY+IEYAcSN9/V4TwOTXVcI6qnZbwXRgUCuxXlNNGY6PSlGEbq0E4skjAO+UVxF4u6VXHFJBpsLB/imzBZEpS9MrOWBsFcllU9q9gx27pGd6YbUEDiOa0HdkyqHd2tB27lnKFzGC4o58VUYyoFz55MD7PeLDPeTEptLVp4LA+Mq1zX7bPbWdm9kpJTSpXNjHYG1TOCyeakUrK5QUzD5Nyhc3m08Wiq7Nf0riGSKlw0ibjyXMFYY5x9lX0syi/CNm3WDa4DVIjrZHOSNX2qcHTZL1OJajT003xAzqQU1rLSMlzL5ayFZ3HL/lvYPbub5V3L6XK6mPFmqPiV9J7qLtw/dj8AfZYqvvf/nfn/MdGY4LYDt3Fi34kppz7VnGLMUiBcc9WGILnHY7uP5ZiuYziu5zi+ecU3ufr4q+lz+8iYGQ5WD6bH9bq9TDVb4a1nLVRZ1weqBzhv6LxU+Z42cBoTjQkeGH+AFaUV9Lg9TDWnqMXq+ictUMlztx9QxbyXdy1Px/3zC/+ZwdwgRaeIrZN3kqCLrK0UX7qLNyxcs2XVFp3ivK+zVlYBgGyNsw07tUhsU5VOH8wNssBeQMEpMDMzwxe+8AVyVo4Dew9w5XlXdgBJatmYSlEn0U8JHTS3WKEhDGVxaKd23s5zYO8B1p++vsMiSXwVCWjMJycsOSGNQEvm9KmPforPflo1n0qsJIkka2YPa2yViGVY6Xxdy02/v0bUwGt6XH7h5Vx14VW8+LwX87lPfK4jYTNpYHXsscfy8Y9/PAXxH//sx8+ZxlaJHND9R16NqrOVeYbne06LabrkcssJdWXdUDsXiUNyTdI8ksTp6KGAxDe0k15bJMIPsNxsqiCbcVMBielRC2oEtkEmBMuPsbJ5yn6ZZtik7Jc5WNrOvp5H1Y9Cl0zI12Mi20rpoLH6GJGlY/i1093LaCDRFsljU49RC2os7V2sj1NznbF8Pv7HC/nNyUJZD6YGwWyOlV0r2TW7izAOmWhMsLSk8p7nAknNCtkyvoUD1QOcM3QO3W43AFPeVAqeS4pLKPtlBST697hi+CR2l3erRMTZ3QpIMiXKfplYxkxpx3U9oyyisfoYg3lVSOH84fOpxlV+uVv1Pz+hT5XMKPtlKnotfNdmvDHO/sr+dDe/uLCYgdwAP97xY4AUSCp+RWXu699lJROxaWwTOStHn6sU/4WLL2RfZR/7q/tZ0bWCrowCkllvlpr2r9QyiuIDBSSgrIHLV6hKsCcuODE930RjglFDUQ9+zlY+kpoCCCEE173kOr5z5Xc4uV9ZFUIIhgpDHKwpamsgN0Bvtjf1kXRluhjMDdKTUYmbFyy+IP2O1g6sVc9F5KW78mlvmmqkrn987/EIBJvHNmMJi6FCq7ZYQpUA2LouTaKkkx10uovXFgkoBZ4oRWgBSbIjb9+1W4bVAqmgnlo+jumQM5QSToDEMZ3Un5GxlNJuT/hrV8aWYaX16uaTZK6mYaZjEorMMqwORd0OkHOl/RoJkMQyJpYxpmF2nN+13HkbWyWSWFQZM5OudyNo4GQcfv7Ln7Px7o384Nc/4I5f3cE9v1WRfe0NrB555BG+/e1vs+PxHZiY/Pmf/PlzprFVIq8GXgh8Uko5I4RYBPz5E4z5Ty+h0FETIgBciEPyTdWgCsA3tBLXQBIaPrEpiY2InKfa11rZPLO+ii7yYo/YighNn1oQ4dvgBCD8EEeX9Bivj1PxK+wa2Exl+X7OCs8i0FZGpuYTZ5w0zHOiMUFWR3A1tEO7mREUKxA4JmP1Me4dvReAFX3LmWA/TX1cNajSvXQp0diEcowb6vM467Kye2XqJPZjn+Wl5Tww/gD1oE5gt/wJng3Xbb8OgHMWnYNt2BSdItPN6bS/ynBxmM1jmzsskstOfjnf3XQXb7/57QRxwLHdxzJeH2fHzA4VGaN/t/WMcsYHccBgTgHJuUOqB8lv9v+GgewAC7KqplfFrzBrq+8rzmUYr48z483wvGXPA5RSXDewjht23wDACb0nIFAgKhC4GaCirnnP6D0sKy1Ld7IXLL4AFNPH8tJy9lf2s3N2J2W/3ArjdQX3H1IWyQKrVWfsT07/E0Zro2xYvCH15eya3cVMNiZ2LPy+EvtmdtCMmilYzlevaqgwxM4Zdc12i8Q2bPpcZQGt6lnFPaP3pGsEcGz3seSsHPWwzoquFUw3p5luTlPNKSAZyA0wkBvgUP0Qy0vLUwU2VyzD4huPfIPds7uRyDTKyDRMwjhMlWjyWQIIifiRjxAidcgnu/1ju4/lvWe9V31vMu4AoETe+973smPHDk477TSGlg8RRRHvfvu7ufvOu+kZ7OFbP1DlU/bv3c+VV1zJuvPW8eC9D/KLn/7isMZWX/jCF2g2m/zBK/+Avfv3Qgx/9YG/YsHqBURRxP9+1//mofseYsnwEj7+tY9TyBewTfuwxlbvete70vkJIfjSp77EjT+8kYVDCyn0FCidXkqtCtd0U4psvsZWH/nIR1If0Awzqa8FSEOGu0vdeJFHGITEUZw+m+2NrYC0gdX5F57P6lWrnzONrQCQUtallD+SUm7T70eklL98xjN6DksUR21AoiwPGYcUfCOttZU42xtS7dJC02ffeXVq1QcoNJXCdXKF1GnXlE12Lr+XbYvvVhExlsSKwWh4uDkVXTXWGKPslSllSuStvCrPoLcAds3DdLMcqB6g7JcZr49j9kYETpOqo5x0SZKgzGYYb4xzz6F7WF5aTndBR2+hQjOrQTXdfZb9MuM6PFhmc6zsVhn4iZ9kaVFbJGGNut2KT286yj+yKL+IZSUV4tzr9qqoLX+WrJWlz+1j1ptlujmtwoFNk+7+xXzp+V9KqZ52aqviV1LLpZ6BR6ceBWBhTlFzfdk+ljqKu19cXJzudit+hWkdmSZzLvur+5nxZlhSbNX5TOgtUP6Pgl1ILZJ6BqRjE5mCGW8mtcJA8fQru9SarOhaQXemO7VIJrpAGoKgt8B4Y5yslaVgtJIvFxUW8Y3Lv8Ex3cekFsm2mW14jmD/F9/NzvOXp874BCznk+H8cEo3DuQGUiCZbE6m6/iSY1/C753we+l7UABwSv8p6dx73B68yGMqVJRYT6YnpSQTWutIYggDiUQgVAFGIVJASHbmWSt7GIgAqf8gOVaiQocTCyWR+YCsvbHVhz72Ifbu3Mvb/uht3LP5HkqlEtf/6Hp1r8Jix7YdXPXqq/jVnb+at7HVN7/5TW688UYWDy/mRxt/xK9/+2te+MIXYhkWu3bs4po/vIY777+Tnp4ebvrZTbiWO29jq02bNqXz2/bgNm68/kY23b+Jf/3uv/LQpofSAARQlkhCp83X2EoIwQUXXMDFZ1/Mqy95NReuv5AzTj+DV1z8Cn79q1+rtZcGF551IReecCEbLtkwb2MraDWwOjRy6LnT2EoIcZuU8nwhRIXOku0CkFLK0rMys+egNMIGkbY4EsAg8ukObAz94/F0OfS6djqHRsDeY6ZZEU9S0GHcTlYplbJfxos96kv2UPbK1MNleKYkC4hqnWyhG1B0VdkvU3SK5Owc9aDeyj6vNLGHFgKz3H7gdsYb4yxbkuPhhdel4YV1bTGIbJZDtUM8Pv04L1zxQiydJxIIRavVgho9bg9ZK8usN8sh1G5ZZrMc06V2N3ePKiBJQKLqV4nbkhA9WyVRvXDFC9MdUk9GOXMzZoauTBddmS7qYZ3xxjg3nyp4x+v+HiOXYyE5vvr8r/KTHT/h+J7j2ZjZSDWoUvbL7BkQBEMLmBr2GZ1UQJLs1gHWZNew19/L0tJSSo7OkwmqTOk8HaNQIIwVsM4HJEWnSFemi1KmRMWvIBD0Zi1d50tRcgl4JrJhyQb2VPawvLScUqZELagx2Zzk/mMF7ve+irPjb2FmO8OF4SM2EErCWtNItRWr6AsfpDy1GYCF+YXzjgM6KKd2IDGFmdJ0V628iqtWXnXY2POGzuOxqcdYXFyczuFQoPJWut1uhgvD3D92PytKK454fYA/OvWPKPtlbMPmuN7j2D27O6W6VnStSKmZJ5Lx+jhj9bH0XhJqC5jXImmXnkwPy5Yv48x1Z9IMm6w5dQ27d+1GCIEhDJYsXcKpZ5xKxswctbHVu9/9bsy/Mnn5VS/niuddgSlMhpcOc/zJx2MZFuvWraN8qMyC7AKuv+36eRtbJRTVI/c8wotf8mLy+TzSllz8wouJZZxaFX3ZProyXcRRPG9jK1DNsebKtultaXiybdls3ryZbSPbePNr38xDDz3ESSeddMQGVs+pxlZSyvP1/89e6cj/JNIIG0QaQCZp4l1oE/7kQUqLMhg6SqSZAEmsM391WK9nybRURyavlm7Wm6Upm+TtPGEcUgtqNCxDdXmXknxB8dtj9TEqfoWSU0opiaYlsQCjWidX6KHXrfDrfb9mvDHOusF1yq+gna5Jhq6Zy/HAxAOEccgZg2dgNxWQhGaguP2gRsEuUHRU2O0IuqFVNkvOzjGUH2Lz2GaAdHdeD+sEbUmIMpsBfM4Zav0getwe9lf3k7WzdDldqaLfV9lHMyPoP+v89NjlXcv549P/GFDhvxLJSG2EiS5B7d/+Bu7+KAd1/kP7bn1Ndg03zt7IkuKS1LFY9stMWrpZUqH1uLYDyTHdx9Cd6U6VctEpUvYUtTXV75IpLcc2HiWIgxQ8E3nzKW/msuWXkbNzafDBvso+pBD0HHsCgyODbJ/Z3lExdq7k7BxZK5vmzvS6vfRnW8Utj2qRFIY7jut1e2mEDUZqIx0+kfnk99f8Pq847hXYhp1Wjx0NRslZOTJmJl2Pufc8VxKFn/yfKEqY35I4krSPswwrjWSK4mhea2bu2KybbY01DZpNlXQqhKBQKKTJekkfj4997GOHnee+++7jZz/7GR/94Ee59457ecErXoCTaflXTNPExk7PczTJ2tk0Omu+NTGEgWM6bHloC2eeeSZTU1NpJ9RELrjggsOaTvmRz59+8E+56JKLUhA4bug4Lr74Ym688UZOOukkFi9ezL59rbyo/fv3MzQ0dMTPnw35L+sc/12Iskh0BV4jpLIGiAMKnpH2I2micwFkkjUepBZETkfeZfOqRElikeTtPHk7Ty2oUTdaYaeZfAnXdBmvjx9mkdR1foqIJYbrcuHiC7l1/63MerP0Z/vT+Poojqg7Sfn4YhrNcsbgGVjazxIZQZpFnbfzKkmuOcmELBObBlJnx6/sXpkmfg0XhjGFSS2oUTFbcy51qYSssxeenX6WUFsJPdeVUfe/p7yHvJ0/4o6zlFGAk5QYKTrFdPdsCSt9DbDMWcbb1r6NFx3zog5qa0Ko3XGm1Cq13Q4khjD4n6f+T645/pr0GmVf0Wm/evFilv7TP6bKfK5Szdm51LHf5ah7SjLli06RgZzK11lcODKQAPS5fYzUVB5QT6Yn9fGYwkxfzyftFslgfjBdjyAOUsrsSGIaZrpO7UCSvH6y1FaiGJP/25Vm4pR/MtIOOsk50nObhwNSsVict7OfKcyUUrOELvCJULkZps2ll17KD37wA8bGlPUzNTXFnj17OHjwILlcjmuvvZZ3v/vd3H///ZiiNf/2+wK48MILuf7666nX69RqNa677jouuOCCjr9fd911NBoNGrUGG/9947zn2bJlC+eeey7f+c53eMMb3sChQ62yOLfeeiubN2/u+PfLO37JORedQ3mqzMzMDKCsqptuuonjdavhM888k23btrFr1y583+c73/kOV1111RE/fzbk2W5s9V9a2qmtyAhomCEZIO+JtIdHA+U0TIBEWFJZGmaL/snmu2FGWSSe9FKLpB7UqbX9aAzXpT/Xn1okw4VhTEMp70YhJuEQhZthw5INXL/9ekBRAyO1ERphQ/3TetrRPpGlxaUM5gcZd3Q9KsNPFVnBLtCV6VI1loRg7/teQz6n8gpWdq/k1gO3Yhu2so7snL63lkUy3H8M0upPo7WANE+hy+liRdeK1CLZU96T7uTnk+S4JFu9HUj6c/0disoQBm899a1Aq7bSTHOGimwQ5DNk+xUY9Lq9aY5AIq89oVVrtOSU2FvZq5K4siWMbJbB/CD7q/s7fCRzJbmPPZU9FOwClmG1gKS4GI5STb0v28f+6v50rRLwSDKnjyQJkCQbkXY/SPvrJ5LejFrTelznmIyiMC9ZegkjtZHUl3IkaY+Imvv/0RpazZW5FgmoSKVIRvOeZ77GVkDqp0nOE7cyvoAn2djKtvniF7/YsfYJKCXyZBtbrV27lmXLlrHuHEWhzrXSnmxjq0SS8VNjU7zxlW8kiiLiOObVr3512svkP0Vjq/+XpR7WU2orEiEN6VMSkGvK1CKJDEk1qFKNFa8uLKlKQZitHgX5fA/MtCySnJUjiANGqiPUjFbxRcPNMpAbUM52bZEk86i3WQFGxuWcRefgGA5+7LMguyC1SBphI3W2Z4tqt3nmQsUPZ3SVWs9qpJ3kEoskobDsC84h3qWOSxzuC7ILFGVgF7RF0qop9L6L/grpdv4Iet1eIhlxoHqAUwdOTS2Sg9WDHN97/BHXOwGSpApAwS6kCvJolI9jOrimy2hd3dPjf/U6LjvrtfCLH3VYI/NJQm2Zwkyd+QvzCyk6xTSUdj5J7mlfeV/6OgGS4cIwHKX4amI9FOwCjumk1Fa7D+hI4zJmJr1Ou4X2RBZJu7Q3Rkped2W6+KO1f/SEYxPaaa5FMnfn/UQyH5AM5gY7envMlbmNrRJ5yx+/hWaoqK2h5UNpc6pEnqixVSJlr8z1t16fUmTvfve7O/7+ZBpbvf/97wdavo256/JkG1slkow/+ZSTO5z7c+U/Q2Or/2elEbRbJKH2DwjcZkQmjOg9eQX7BhpMNibTpEDDFodRVoWi+sG3+0gSaqtitDJPhZthIDuQOtsTH0kjbFCdc1zOzqWZzP25/nmBJF9SyiVxMJcWZDnnTcPs7nmQkap6+PN2nq5MV/oDbldOSZRSsmPO23nqQZ0ZndCIEBSKvSkAJJIop2bU7PCRRDLqsFzmSkJtHawpIGm3SJ5IyRacQgpA1upjKfYPUbSLhznMD7umU0qjthLgfvMpb+ZvL/zbozomE/CoBJX0/k5ecDI9mR5O6D3hiOOgZT0k67Qgp9b3aGAJavc9XBhOj+sAkqdgkeTtfAoE83XbO5o4psNwYTi1yJKd+1MFElOYLUtCn8M27aMm/h1Jni6Y/a7O03Eu8czONZdKfK7I074rob713wOOkVL+lRBiKbBQSvnbZ212zzHppLZCVZnTAqcZIoBlF51FdedGxupjxEZM9oIKM+Ze7CCmZrTon1yhB0MYitqK26itsE5ZtHb3iUUyskfVeUrKHDTCRudxuiT9lcdcyb2j9zJcGCZn59LSEQ1HAJJlA8fx/pPez2XLWzuvlSctJH4oalFbTqEDCHrdXso6aumYbkV7JEoqZ+dUVJWsExsCy83Oq2wT6gTo8JEAR93lJ/M4UD1AxszgmE4LSJ5AyRadYnpPSS2nj13wMZaUntgiqYd1aLZKWRzTdUwatXYkab+n5PUJfSdwy9W3APAojx5x7FwgSS2SJ7hHgL84+y/SjPKna5EIIejJ9DDWGDsq1Xikse2bgaer6IQQaTLhM40keraU9lxfzTOR+XxIT0cSKvGJItn+T8szsUi+AJwDXKPfV4DPP50TCSFeKITYKoTYLoR47zx/3yCEmBVCbNb//rLtb38ihHhYCPGQEOLbQoinvoV5kqKoLe1sFwE1v4ZvSuy6+iynnehJGGPveonoUVFb1TbFb2azlJwS441xYmJydi61SMrJ7h5lafTn+tO+CqVMKeX3x6PZtuPULV++4nJuvfpWik4xzTKeak6lPhK7UOTq46/ueAiT8yU0UGKRJNKb7e04dk3fGlb3rFbvLWWR1KI6YcZC5OcP9Wzf5ZacUkd5jCfjI2m3Dp4MtQUaSKotcAS4aMlFTwgIyTXrYb1jnk8kBbuQOmfnWmRPJAkAJIDbnenmBctewIWLL3zCsWcsPIMT+xTPnUQmQef39mQk+Y6eqkUyV57JLt427GdFaT9dq+iw8zyLFknie3ymIOlaLiu6VqSRic8VeSYrtF5KeboQYhOAlHJaCPGUYVIIYaIA6PnAfuAeIcRPpJRzc/dvlVJeOWfsMPDHwBopZUMI8T3gauCfn/rtPLF0WiSRytmwwNAFG/PZboA0Aipn5cjZOSabk3MsiAwlp5TumBOLxIs8JuNWhc7EIkmk6BTTsMND4XTbca3SDQlIJEAy2ZhMqa325leJJMXwRqsKSAp2yyKxDCvdzSfyrSu+lTo/83aesfoYNb9G5NoY2ScGkq5MF5ZhUbALVIPqURVX1spiCSu1xqC1034iaqvoFNMS5AmQPBlpB4+nAghCCLoyXUw1pzqA+MlIck/JWggh+NSGTx1tyBGl1+3FwOgo5/FkJAWSo1iIT0ZMw2S4MHxYQMOTkYX5hU8YVvtk5NkCAEMYdLvdT2lDcSTpdruPSuM+FXmyuTn/J+WZWCSBBgEJIITohzkhEk9OzgK2Syl3StXP9jvAS57CeAvICiEsIAccfBpzeFLSnkcijYjx+nja1hMgrxMIx+uqU1rWypK384w3xtMEQlAWRFemq8MvkfzwDgatEu1G1u0AkiRSCmC8OYFvCX2+wwGi3SJJypC0VwJul6JTTEt1tFskSWXUdjGNFpedt/PUwhq1sEbsOkc8fzvlkijn5P+jWSRCiNRPkgDaKf2n8Gfr/uwJd+sluwUCc8HwqOPawOOpKpBk3Z4ykMyhtp6J9Lq9T9kaab/2s6Hsut3ueUN2n0iyVvZZUZJJEchng/4ZLgw/K0DyX12eCWT/PXAdMCCE+AjwSuAvnsZ5hoF9be/3A+vnOe4cIcQWFFC8W0r5sJTygBDik8BeoAH8cr4yLUKINwNvBhgcHGTjxo1PeZLd0w9Q2/MpIuNqAKQR8/jI41zUtoIPP6TqXT22S0VTbH1oKzM1VTbDbzvu9nvuIayGHGwqzNu1dRf1SMWHltsioO578EFGxlo7y20PbmNWU1r7pvcRWAInlOzYt4+H5tzT9rpKcNuybQsPLROMXHkJh8plmOfeDb+1n7j3jnvZ3dwNgBM6bNy4kWq1Ou+azUzNMFGbICamaUDF94+4tq5wacom2x/cjve4hxGoax7YfoCNI/OPAbBCtXBBNUjPvZzl3H3b3R3HzZ1jebKcvn7gngfYae484jXaZWezddzex/ey8cCR53aYaFZyfN84G8ud4460hgBjgc5pODDFxspTuN48sjRYygADT/kZr0+p52/PI3vYuPPoY7u6uubN4fg/IVEUPalrD9lDNGq/u46AR5MnO8f/m/JEc2w2m0/pGXraQCKl/KYQ4j7gUlR5lJdKKY/sUTyyzEcazrVv7weWSSmrQogrgOuBVUKIHpT1sgKYAb4vhHidlPLf5sz1K8BXAM444wy5YcOGpz7LvS6/2gvoMvGWY+LZHkHbCj7v0sv5X9/+IGH5AcjYnHvmuZR3l7ntods6gOTC5z2Pn9/xKx7dpZbrrLVnMevP8q3ffKvjuLMuuIB4eJC/+uZfAXDxORdzsHaQr/7yq1Tisurp3ow57qST6JlzT+6Iy1d++RXyuTpBRbDmQ39xxHIbX7/h6xwcO0jWynLpxZcyMD7AF37xBZYtWMaGDRvYuHEj863ZA/c/wG8e/A0A4bknMzRwCqceYW0X/HAB+6v7ufjci1lcXMy//fLf2D+yn/PXnZ+GI88nX/35VxmbGGPpwqVsuGj+cwOHzXHTfZu4/SFVBv2yiy970tz74unF/N1PVNfEs08/m7MXnf0EI1ryw5t/yK79uzh9zelsWNU51yOtIaiy6w/f9TCvP/H1T+jDeSLZwPzXeCLZumUrv9n8Gy4+52JWdB29LMqjjz76rIaOPhV5tsNWfxfyX2GOrusesSLxfPJMOiT+CzAqpfy8lPJzwKgQ4mtP41T7gfZQmsXMoaeklGUpVYaflPIXgC2EWAA8D9glpRyXqqn6j4Bz+V2InaNuCAydWGhYqotdoOklbBvXzmIbFmNmq1hd3lKUlZ/oMctCWFaaCQ2a2kqOawMS4bpp1zNQVEtyXCgjYkcd3O4jSSSltnZt7Hg/nyTnT+i1lNoSR1e+7TRE5Q9eTP873n7EYxO6JTl3yVBzfqIooYRW6KAXpnYd4ejDx7mm+5QcuAmVdtg1n8LY9u/2yYhlWHzo3A89YxB5JrKmbw3dZveTihT7b/lvmSvPxEdyipRyJnkjpZwGnjyEteQelHWxQjvrrwZ+0n6AEGKhDjdGCHEWat6TKErrbCFETv/9UjhKnOUzESdPQwhMUxlLpmWojmPaR2I4DkIIilaOCV0zJ2flUuWcAIShS7y3K6z246QhkJYab+horMRPkpRISSRy1HEic3igWtqmU8/lqECi55JEgpQ0gPTOHt3d1O5QTV/HMcSHJ5H1ZnoxhZleo2tGZXJ3W0d3hKcgmvg5xrfC36+F3bc/qXEdjvZvvATu/MJRx3U42xM/y87fwF1fOuo4aIFi+3dLFHYeVB55wvPMKzt/AzN7n97YJyEXLL6Av17810f3UTSmj/y3/8OS9CMB2L17NyeddNKzfo2ne95FixYd9tkHP/hBPvnJT857/JEaWz0ZiaKI00477bBExrmNreZ+/lxqbGVoagkAIUQvT68IZAi8Hfh3FAh8T0r5sBDirUKIt+rDXgk8pH0kfw9cLZXcDfwARX09qO/nK8/gno4sdo6GYbSAxFZWR0JtCQ0QBdMlTFpl2tk2IEkc40rpH2aRtCllqS2M5NgBK0/OUL0dku5qAFJX7xVHsUgmTQMT46i78qKO8MnriJkicILnc2p89FpJ8wLJT94B37v2sGP7c/1pr2yA7ihESEn3E0TppM72RMFP79H/H90qOcySkVKBz/6jpzm1931Ix973ddjYVuRvcgds+c5hY1NrK3HY7/stfHQIZhVoMvYofPp42Hv3YWOfUL77Orj100993G1/B9/5vdb7h6/rfP9kZfQh+JtjYGRL67O5IHkkmfsdT2yH8tOIiYljhK4VNzMzwxc+/zmY2Hb4+Y84DUms2z0Qt81dxjC1E/yj1LF5slKf4nBm/ugyb2OrOITKaOe9hU3mymc/+9mOEjEwX2Orb/HIQw92fP5camz1KeBOIcT39ftXAR99OifSdNUv5nz2pbbXnwM+d4SxHwA+8HSu+5TEzlIXAifxkVhJ5Vz1Z6E7FhbaFHbWyqbJYnMtkq62iqY5O5fmigCIjAO1RnrOY6YPMu4302Nbc+q0XNolpbZMk6yhWpUSR7DpX+HU14LV1q0uUGGyea0YTL/O9w6OQv7odZbyZsvKSYFkYuu81NObT3kzLz32pen7V8Y5Vo1PYnva4bfjV3Dj++CNN0OmZUUcZlnUdb/4mo5ui2O45W9xvFUd10ssn9SSac5CHLTGAfzi/4PSEJz/rvQjIQQlp8RUc6p1zcooNGcgCsC04d6vwZ2fg+NfBJmWBbMwvxBDGK1Ciwfug8hTwAOtdRl9AJbOF0+iJQrhn54H570LTnwpeFXwyi1AAth6A+T7YfEZRz4PwPab4eDmzveP/UwpvNxRoruCBjx8PZx6NQgBY48ohTv2KDinQujD2COM/uP1eNueIJAhqINhQRJF5VdBmKB/G6lST2psnXA8C//X/zr8PJURcvVJ6OpRja127mTtRVey6oSTiKKIN73xjdxxx20ML17Kj3/8Y7LZLLt37+byyy/n4osv5s477+T666/n1o2/4u8/8yn82GD92efwhc9+iubUKK++5s3sHx0niiL+4s/fyfrzLlTnfdObuOOOOxgeHk7PC6jGVv+o9q1vfPNbVWOr2niq/D/ykY/wjX/5OkuGFtK/aAnr1q07/J5QQPKG11+LNzvOW97556qx1f/6E0RlBJyC+j34NZh4HPqOTZ+5/fv38/Of/5z3v//9fPrTrU1GR2MrKbn6RRfz4+9/iw0vvCr9/LnU2OobwMtRVYQOAS/Xn/3XFCdPwxBYGkhsbWFEtlpCoctNF5PyDqjOb3ltQcR2p0VSils7jbkWicg4CNdNd+/vrHp8fUxFa7VbJDjJtQ+3SJLjQiHIJlVM994JP30nPPbTjmOLvopuyUvt7/F1Lkv1KAWigHyyu6MNSBozUJ9QirtNFrp9nNLW22K4UeGKWl3v4ID998L4YzCyuWNcqaGir4qBrgyQAEldA8LkNtj4URaN/EfnPWmQKzR19FYCILXx1kGP/hQ2f/Ow+yqZWXJtlgmVkc5rJ+sy1smiXr7icr535fda5Ummd8+Zs/5/6gkU7/ijcHAT7L1Lz1lFdVFua0L08z9TwDtXpOzcxU7vAb+igAFa9z+x7ehz2PRvcP1b1TygBWLJHMImICHy5x3emk/c+qc+aH2eSOQrwH0i8WuqXUMcqcZWy5ex+T++w99+5INs27aNt/3ha3n4pm/TXSrwwx/+MB22detWrr32WjZt2qQbW32H26//Gptvv6nV2OrXdzA0uIAtW7bw0JbNvHD9aqiNq/O+7W08/PDDdHd3p+dNG1v99P9v77zj7KrKvf9dp5c501uSmUx6I4EUUigJAUKoghTpXYSL6ItyUUCu5XpFUMSCgIrtXhUpUgUpUhIINZAyIaT3TJLp7czpZb1/rF3OmUzNTMgE9m8+8znn7LL2s9vzW09Z6/lf3v/XI2ZhK+16rPjoQx577DFWvfYMT//ubj788MNuT6u6uprSgINTTz+dRSeeoApbpeLMP/daps8+hunTpzP96HlMP+Vips+ex2uvvQbAN75+Ez+95x5stgw1LiV7tn5C5QhtZuhkjIryYvbsqem24NVgYCBTpLiB6UCu1s4FWvGUHw6KZEMNdicRYcelVUZ0oB4YqRGKzaW5ttBiEloyml/77dZq8epuqLyUasctpTEo0DiUywG6lSElnqbteBJhkBKn3YlDQlKogD90bZFkzlHk0WdP1RVZzQqYer6xPhAPabJrRBLTiaS+x0viT5imtiG/TiBNW2HETHPjV74D25bC1z7MliWiEYmu6PeuglFmfZKApvBywy3Z++nba0o9ry3bRM/VXGA5urtCV6D6ZzqtFHRwr/L9ezNG3wdriehDoqSEYJ15zEC52UbdWqicY+zntDmZmD/OFEJ3w0WagULzXHXLREpY+ReYdBb4M6Y02bNSO7da7VM7nqHE48o1FKxVxK0NhAXgH1epdi/6q7ZdjXne+SMziGSjsoq2L4N374fzfp91/dj6hvps3anuo37s9r1QjKEwy792FZRMpFuEm1UbTj+UTFCE1rBBrRt2FCA0d5mEksngzHiWE1FFOC6fOiedDA3yksbv0aNHM33KOAg3MWvaJHbs2GE0U1U1knlTR0M6rQpbrVrN7DOuAJuDSDxJaX4Ol55+LLf+6JfcdtttnLX4JOZPLqWlpla1O306ALNmzmTH1s2QSvL2229z7tln4ve6Qdg579xzWfbWm8z40gkALHtzKeeeey4+tw0cOZx9+mJN1iQkI+Dyg7CRSCRUYaurb+B399zBMYvP1e5xlGXP/Ek9b4Fh6rp31IErAMXjeOGZJynNdTNrXClLqzM8ANFWZKjZdIMl1PMvZHpoFbbKwHNAG7AC6EN34vBHxG7DaVME4NJiJUL/1KyCgNar92r3TO/le0gCAps2eDA3oS6ZT7NMXDYXDilJCoHdYSOtk0NHHWgV50hEwOXDj6ANiegUdyHaDrs/gPGnYBM2PAiiSLy64RlpizqM0QAAb0dJREFUVZ812b2j3LBa7tetpHgGkWRYHZ3hz/Ap+7UsLINImreZRJKMQfXjqmecToHNbhKBbpGEM4gkU7aGLeCEHJ209iMSRXa57RvUS2rX4ht7VDuBpOY20RVouFltF201XSp7VsC4Rep77VoC0Q7CTqdSXtE29eJntqEr9roM8pISXrkTPn4Cblqu3EaGRaKfYyeLZN9qeP7/KavoqufBoV3DvRqRBHUiqTOvbaxDs1AkyBTsWAaTv6DWb10C654DT56Sp3WX2fPv0IhEl71xk/pc+yRs/reSo+QatSyVUAQDZoDfsEj2mtuAeiZlGhBKzmRM/c4pUwSgKTLSiez9QCMENQ8coNx3To+SPdSgjmWzQ9lUTTGms9vQFWMyjtvtVscG7OkEEf14sRB+t0Nry6kKW33pHO6+/UZ1nQrHqASIjlpWvPQoL67YwR3f/R6Lj5vJlRechduluaojLdijzUSCbdC2SynlpEZoMqVkyUwySScRmRab/tleozouwg7+YtZtq2f20bNort+nClslIkquZIz5515LMBxTLsFUXGtf8LNf/pp33n6Tf/77TV488hii8RTtwSCXX3YZf/v5d6gYVmoWsEqEqdlXz/CyIipGjBiSha0qpJQXSSl/KqW8T/8fFKmGKMLChksb2a7HSmyahWLESLQX16c94z7tYffo2+sWida70t1DQkp86TQOKbHbpWllZLpBNMtBb1MP/Ns8HqXwn7wWHrnAUEA6memfRtbNvmrzJQACmlLO0UlDj1vIlKn8GjbCBw/D89+AHW8rOWIhQ3ZvKqFeAt1FoccFALa8BrE2pWDCTeqF0GWJdFKymUQSbWPe3vVc09rOVOnI3i6cbZE4UlGo/8TYNWencgsFDALSYyNSHTPTbVfzkfm9+lH+o7WNW5uaFdnoyjzz2IZFoh0vnVKK+P0H1bp91UqxdOfaatmh7lftx+r37g/ghVtMxbinGyIB5WZrzRi/u3WJKcO/v2tcN4K12QkJoXpNQWtWZsMm81gOL6x7juF7X9aWrVCkD6ZV1aZZJDqhZFoFiYh6NoP7FBlE20xrVu9spBKass0gkmTcUP6A2lc/RvsepUDTSUVGCbPTQipOICeHYEdHtizJKAgbyKTaLxZU1hBCKe5oOyefeCJPPv8y9Y3NkIqrwlY7trG3tgGfx8nll17MrTddz8qPN6j9ZEodu2WHOle7C6LtLDjuWJ594UXCkQihcIRnnn2G+ceY46EWHDObZ555lkgkSjAU4fmXX1X3PNIK7lwV++ioo/rDdzn26Ok89tDdXHPLD6jbu1u9J6kYy575E6uXPKuKWr3xDKtffYzVrz7KooXHc/ftX6dmzZvsWLmExx76MSedMJ+//eZeSMWZPXcem7ftYPuWzcQ7WnnsuVc4+5QFzJ41c0gWtnpXCDFNSvnxoEhyGCBiE7hsigBc9iSkwSbSgM2MkWguK6+mlP1aL8VnSwN2I1U3NxrS1qfVA5aM4JcSezqN3Z5C6tONZCrkeAdQgi+dBpvNiNcIjwfe+SVs0eIEwVoIlOOVkhYBXr1XqivvVEy5ZTSLIdBeB7lmsN2wSEApMSnhT6eZSj/SDKOOJ0eLX/ikxBYLZmfCNGfI/fE/stszZ9Yxe+uhjN667mra+R6BdIpbWlozevWdXGEddRi92p3vKXdJtA3PnpWcXFLAbN3KygyyhxpM5SxspoWWSsCax5mOByLtSmHryl9vI502SanuE3VtPvyjclHNvg4+/IMKTJdOMS2ZcBN4M2RPxZRLrfZj5aqY9x/w1r0w9kTl5qpfh9HD13vnOtr3mMq8ZJLpglrzONR9DLOuUVlm9euykx466pVi1V0ejZuU66h+HRz7ddi3hnFb/giN12nkJCC/0rRI2jtbJHGzpxwPmUq8dIqSMdKiyC0RVvdbphSJ7GeRaPfHk69ZXEF1ff0lyqqpW6uWpZMgbEiZRqQSFBUUc9zs6Uw96UtMnqDKG5BOgl+bUigRUSRodypLz5MH0TamjB/Dj779VRZfepMqbOUN8OBdt9PWXM+3fvRLbE4vThv85iffU+6ndFqRqLArmVJtgGTmlNFc/aWzmHPW1SDTXHfttcyYOtm4TjOnTuSi889h+uJLqKoayfw50zWilCrBw+GBxk1Ur/iAubOOYsKkKfzk+7dz4TVf5bXX3sCpP5vJDIvGlaPezVi78lLklIOvAMQ76jp31IEnD4e/lAd+dBunnn46qUSMay85lyMmjgWRHpKFrY4HrhZCbEe5tgQgpZQ9p/ocxogAbu9eTr9hGu/UPQN14LArIjFiJEltJmCDSNRnjkirjpFmkbgjLXjSafwyrfW4IvjTaZxCULygCDlfC6RmWSQdGW3bcGgTSNqa1sEbP1I+5ob1htL0ppQbSSc1oq1gc6oXes8KRSSpBIH2WsgtN2Q3YiQAHXU4E0FFHov+G7ab4xl8GjH502n1cGcGXpu2aG0FYePLUDZNKbqOOsicUNCwSBoht0K9iPuqYcxC5baxuxWp6D3c/VxbDZBXQTQaxbPrPaWUd7yNkCl+6RylMqQ6K+NQg9le1XHKIkmnVUZTqAEWfBve+im07TatM32/SLPqMRZPVHGG9j2w5jEoPxLOvE8F8Os+gYqM0frhJihCEYl+/Zu3KSIpnwoLvwPr/gnvPQj5VUohVs5VlkosmG2RtO3Rrr+AGZfDv/9LXd+XbocRR8OJdyoiadigtrW7FXGF6s1rkD9S9dT3fKSONWIWzL2R1K9mYHv+ZqXsh89QCq9xs7IqIi1KkYUb1fVMJUDPIIx1qGfTk6dcUZ58dc4dmgvOk6euWyqhnhFh13rdcc0KE+ArUs9n83Z1jQLDVFsOr7oGUoLTi0xEERoh/f3BH2vnF1fZTE2bwZ3DrV+/USnadJJRRx6nCluFm5UMoUYuOudULrrkMnUu5Uepa2WbxqkLj1XXJlirYjruHNa+8YQ6t7wKbv3Wt5UcDeshWMst11/GLd+6A9p2KXlTMcBG29aPIBXjzv/8Gndef74ifD0u5PSZ2Wp5Fdz3vW+o7958zjrzDM5aOBs0rweuHO29Sqj75M5VBKk/u+4AODwsPPcaFp51kdIjnnyw2Tnj5PmccfrpyrL0l6r7n4oPycJWpwPjgcXAF4CztM/PJBKpBEkBXplkzIwSfFov32HPzpwKaD0Ir9Y7dyWiOKQkF4FwCKN2COFGctNpFSNJhCERwpeWBNJpvP4WfHqqYGbPPh4CKfFploMrJ4GjtBSxQ+uVnvc79RlqgHQar2YNeXVLI9IChaNVT0/vhbfVMCIR5z+bWlgU03y8WRZJPb6w1gstO0IpOs3dYQs14k2nVWwl2mbGR/JHmpbUhhdVz/yYm9TvYF12Lz/crCn6Rhh3slqmu7e2v6WC2XkVGTEObd+k5k7pqIOcUtryJqssJylVUN/pU7GDVFydd6hBs4RQx9LdRpPOUgqscaNK6fUVw9HXGNfGyNjSlagux9gTzfPbswKmnqd+l05RRKK7tfKrsmMkw7R+VtMWNTajfBrYbMqa2bsSPvqjWj9Rq24XrFVkWaj1utv3KkspMAzGa3VlHrtUKacv/S/klKhzqF+nXFtFY5UCCjWaCmjUfKXIP35S/R4+EwJlbB17LezUxtqMPVHJ3rrLtIBGaM+kTJkWidOnuS1ToE8W6c5R11p3o3nU+BpFJAm1n92l3FrJmLIYXDkYrqRcjUQAPAF1nxMRcPqQwqFleSXMYyFNt5jDYyYfBIapOA2oawAQbVFE5dKSQ1Jxs7eP0NyzcRWr0eV2eNU1BZUK7S00rW9PQLWXjKn9HC7S+u9kTK1zes3UZ7/WDigZ9BRsT56WaCBVrBPAo8msv48Ol2YlJdX11c9BCPXdX6IsMGFTv3X3pH49+pIZd4AYSPrvzq7+B1O4oYRwUvlodaWsK3OHNuOvESPRUmm9ySRIiYh3cFtTC+f5RmF3pbDnaw9nqIFJ8QTj4gn1osRDnBEKcWY0rXrCOpq2qV4GqAcqGTOsHd/oCOPeeB3RukMp28IxRtvEg4Yl4tUtDd1lNOJoMy7QuhMBXC1zKNb92bGgqXQ76vBGNCIpHKNIItKstgnV45dSWVXRNjOYP2KWUs7hZuVyyas0A8IdGUTiCiiZYu2ql140DgpGKSIJN6se++gFkFNqkCORZggMN8+zox5yymjLm6KynLa+DptfVZZGfqV5zFAjFI/P3s/pNwnh8SuUBXTSfykF5PAqJRqsVXLmj8xWxqNVdg7LtNHKR2jZNmVHqN6nTqTDZ2QTSfk0pVS2LlEvevk0te6oi5Q81Y8qotcTFTpqlfz5I1WvvV2zSPJHqvPJrVDK87InzPMtnQz1G1TvvmC0UjAd9aZirzpOfX7ytDpWrrqeteUnm+c15kR1jGTEHISoZ6jpLim7y1RmNoc5pkbYtIB/Wi3Xx+PoBGB3mm6xlEYkNpt6zl05JiGBRgASSIPTR9rm0HromvWrtx1tB4Rq11ekSDDHnDkbu0NdX1Dkoiv2RNg8F7vL7Aw53ErO/Cr1TGZmN+kZfna32sfhUueRVOSatjnVuSUiZgKFJ09di86zK+dWKuvW4VbPHCgZbE7zt24V293m9XbnZMvUGfp1ETZF9sLee6r2ADCgUrtCiAIhxBwhxAL9f7AEG2qIaP5un6aUdUJx5apqdkIzR3NiShn7ZFoLQnZwcbCDiZXHM/KERoouPUc1GGriwboG/rOlVT3M8TCXtXdwhW90RvaLVC4QXdlohKMH23MizQi7XfV+C0aph8fh0VwwrXi17by6nzXSql6CiqOVpRNuNnvOZVPNBzbeoV5GLSDojexTL0F+FRRUqW1ad0NHPX7h2N8iGa4pwe1vKh/+UZeoB98VUApNjzEUj1My6G4qf7FSvLs+gGf+A5CKSPzFar9oq1JOJROMa2haJNqgqr+dr3rik85UPmRQZBBqVERlc5gxkpxSKBoP7jzlFjnuZmWNCKGIuW23EW/CX6za0C2SorGQN1K1M2KWuv6giCQZhW1LFCHlVSgCkVqCgb9UXcfNWjxLv7eePEUm+vUzZK8zyJLcEcoiadulSEMIuPgRuO5VLZVWQ+lkRWb6c6ETseHOOwYQ6n4Nn2kqJCHgi7+BE/8LRh5j3utd76rPCo1I9AC5PaNn7y3opGzz1afTp1kXNo0ANCJxZFgkuquzoErdo8x2tDRZ1ZZXs0gyYi26wkxG1LMvhDqer3B/Rav38J0+JQMYCSyKENymstXT532F2SnJoLbzFprWhN2tSCSVQSSZMoHq/JRMMi0tHTabaTXppCNTGrFov/X30pFB3JnT8HQFfVCv06eug92VlWAz2BjIpI3XAW+hpjb5b+3zB4Mj1tCDTiS6UvZpD7IrX/XmbAkVL8jV4gte3WWlP6gj5+HOTeKIaW6CcKNSNKCZ7tp2upJs32Om/upKQtvOiL8kompZy3blshJCmeChRoi2ZlgkUUVKkVbVI9JHQ+98Rykbm0ONBdBjI7EO9SDmlJpEkj9S9erydSLZCaEGpjnymBKLqx5htFWt010gS+4GJMy4TP3W2jMskqLxysLQf/s0IumoVbIt+oGKFfhLs91Kxdq4hY46LTBbSsg/Ek7/KZzzIHxthSKEQLm5XahB9cx9xRlEUqZe5BmXw6yr4eQfmDc8r0JzbWlEou9nkF6JIg2AI84z99OX7V6urpWvEBIh3LEWdS18hcqyS0ZUL7EkY3qL2V9RnxVHQ0CbPDG4T1kSOSWKSFp3qdhH/ki1fvh085g6SiZp1mtEPReGRdIACEWAuvUyvNPUHHkj4IRvafdaO8bO90y5wFRIumsrp9wMcutwB9R6T66myDR3TzppWiQypa6JrjCF2F/5C5siC2EDh4e0cKj9klHVa7c7MdSY3k538OSp83cHuiASp6n0+9JWQZX5fDnciiBlynRtdW7HZjOP2R1sdtNScni0kf42M66kW3f5I3uelQA0ArGZxKNbgAcJAwm23wzMBt6XUp4ohJiEIpTPJAzXltYb0wnFrRGJSIUhnSYnGgRyVKZUvMNUznpvru4TNWYh1KgUbnCfRhCaW6lkkvps3W0+eOWaXz3WAfEQgXQaFwK3nmIabjJ7xP7i/S2SVEpZR9FW1XOsnKd6SMsfVgoyf6SWux5RYyziHeqBdfmho165tsq1gXY6kbTsgFADd5dfCFt/pXq32hgOhh2pHuLGjcqi0GXLKdMskmb1oOcO72SRFEHFFWrfIy8yXRM5pcoS0Udj6wPgGtZrYxZKISxg7g3ZN03fv32vukb+EvUfalREol/r07qY2Se/UgWxnV7l0vEWaGRWr15qT74i+M2vqGlMdBRPNLOUCkYZbhpvREuf9RWZLsiSidm93bIpcO0rihhcOeoaNW1WSjOnTAW9N7+izjnPHKG8H0qnmN8LRqsR+DuWqWvvK1T3qXiCIqXMQaOdoR+jYb0iCl+hst5SGUQihIppdIaewaUTg91pPuM2Z3bPvDelnTtcU6YCqc82EA9r8QChWTfRbCLoCk6vume6TDanmVmnu6hAWRiiH33szAJadrfiRx29ydQZDq8Wa3F3OrcMsvUV9dwGqOtbMlGdI6h24lrSwiANQsw63AD2jUopo6BGuUspNwA9DHE9vBHRxn34tHEJIxJJStKC4SVKwYp0GGJt5OjpvlKqhz0eVA+Tv0i9mLVrzHmfdNeB5toCTOXWVmP62fUAbbwD4mEube/g14Hpahz6Hi3WUTBaffpLFJFEW5VVBIpQwo0qFuEtUA/V3OtVMHv7m0rh6f7teFCzSAJKEQdrlUVSpAV7/cVKwe1bo3qXgWHKZaW7thxeta+uhGZcaV7ETIvEV6QUUzqh5fqjSM1XqNJRM/3bfuU+pEGbkkQnEn1AYE5Z1zfNHVB+8fr1gNSIpJNF0h3yRirSaN+rubZK1Pm171XfbTY45qvw5VeV9aLD6VHuGVDXVXvpfWGdSAqVlQDKndgZI+cpuYVQ8u1bo12DUqVQ9VRu3VroCqWTzO+Fo9W1jLRosmvXVbfqOlskmfDkmvGAvBEZnxKw7e+m6YxMhWV3mWNI9HiEsa4XInF6jcC31KYgMlxkYCrZzi6ovsikFqrevq70+9JOJjKJ0O5CCpsZY+yNJDtDP7Yuiz2D3PoLh8e8R3aXena6mJl7MDAQIqkRQuSjiky9KoR4joNY5vZQI+AKsMhbQWksBOk0hYkob8jhVGkBXJHsgGgb+ek0J9rzODoSM2Iahh93+HQVSNZ74LoyiIfNzIyicYBQ/vnmreoBLxqvHkzNtVWWSnFsqdaT1IPmhkWi9bgjrcb4EW86bQ5i033Xs65WSjbcpKwMXcZYUJGJK0e5LJq3qcF+ei9aCCW3TmD+EiNHn2ibmelSPF59n3yWeRENi6RJKVQ9qKqPss7MaMmETir1WgplXqV6Sep7IRJQLiJ94KC/SMnbVqNkDfREJBo5pBOKLPVeYMMGk9g8eV1PmlimWQRdEkmGRaLHR7qVvdyczyunNJuweiISb4G6d8KmrpUub/165SIDZb2d+7vur7lxHK2zk6sRiRaYN6yBviLTraO7tgAVIO/F5ZOBdGYddsMN5M7+7LNMupLWzkVX1v21IjKVvMNlWhJ68L8/0N14eoqwcW79bGc/GbX9D1Lm1kCyts6VUrZKKX+AKrH7B/pXa/2wwsTCifxi+KmMSSS11NMOcPmNgYi2VBCibdiB+0tOYFYspuIberwBVO+veZuZ0qu/pIkM15a3QCnGLa/D6r8rC8Wu+UZ1YgJTkexHJMWmRSIzLBK916/3ML0FMPMKc1/dIol1ZMdIdDtdTz/Vj20of41I9BHNOlGd8j9wyePmCwGqvVib8vHr1gcol5XDa/pzO0PvRTdsNM/RX2LKkGm9dEZOuXKx6bL6S8yU3p4IKD/DdZRTZirc+g2mMu4OesyioCqDSLTYmLdQuTSHz4QJp/bcTk6Z+eLnlJpKHLJJpUsZpmiE6zKvT9su81oWVKmZfXuD/pzpxzOIpJ+KLcsCcaoOkrCZLpw+wrBI9HZABZ6d/gNwI+lEkkEoucP75jrKhM2uOnp6HAOUPC5f/91InlzlytbPbSAWSSb0cz1IcZKBBNuPFkI8I4RYCfwaNYX8ikGTbChCV3TxsGFp6NPCi0RG1lJmEF2PN4CZzaRn7GRZJGHzGHkVKpff6VO9Rn15vCODSDQSatigSEFX4P4SpXxad+M15v2SZnZWZvrhvBuVoq2ca5JdLGjKnKloi8aY3/Vjg1JSnlwz/Ve3SMqmaNlBGdCDk42b1MvqzSCSnnrGuuJu3KSUhdOn9tdz+XsikkCZuZ3u2jLa7ckiySCSwDCzV5+MmN+7w4TTVRyqbGrXFomvEK5f0vNkh2BeL11W3Srwl2YTdFdY/COVgaVvb7TTw7XqCvozalgk2md/e8gGkWhuHyFU56G38+gMIcDmpLUtyEN/+AsAO/Y1MfXE8/oX14D9lbXuTtSsgD4XttKzorRrMmzYMOUCLBxnbNKvwlaZ5KOTYxfW1qhRo5g2bRrTp0/n6KOzLeP9Cltp53iwClsNJNj+CPAtVEGp9OCIM8ShP/S6peHKMcaPiFTIrH6n99p0l1WmawvUJHmQQSQa4dhd6uE+6mLl5158l0kQnYkkp9QctaxbI2AquabNeLWH0JNOm3MmZcxyS8EouFXrre9ersmSGSNRijYt7NjyMlwpmW4Vf6kij/Y9SkH0aB1oijudMBUqqCytzPTVzvDkq6BhKqYUmRAmIbgC3VsyYKbRgmmRGOt6kDV3uDZvU1op9Ezfcm9EUj4VvvyK+q6liXtiDdnjAPoCnUiEXZGuPpI801rqDpmZXJnk2ZvsnaF3GjItkhj9ckdBxvaZLrHCMQcW+LU7aW0P8tDv/8xXv/GtPu8mpURKaU67nmmJDBSZ1iKoZ6ePp9ZlYSsd7oDyBnTz3CxZsoTi4uxOmF7A6tVXX6WiooLZs2dz9tlnMzEXbrrldl59fQl5eXmcdNJJnH322YNSj2QgRNIgpfzngCU4nKC/yDpBuHOw5+eDTeDwpM1JA/Vem561lelOKhhtTqaXO1wpad21pbc/5yv7H9vlz87ucvmVgmjf0w2RbMXr8QGprl1b+7WvD+xqU0TpyjEUbdRThs+e8ajoSQLCrtrz5Cn/u7CpbKDukKm4My0SMEcOdwUhNJfUXpN89PPszc1kHFMoWbOIpAeLxO7Upu/eoxR65uSC/VHGdocZQ/IV9U9x6iSoB/ddPnXNeoqPdNnOACwS3WrSB3PmjoCGpKGElz2xicbdHd3snAmpnl8RBufKHrcsrsxh/oU9PEd2J7f/+H62btvO9OnTGT9+fLcFqLosbLVsGffffz/xWJS508bz0EMPEQ2FuPDCC6mpqVGFrb77XebOndt7Yas//QmA6667ThW2ysBdd93FX/7yFyorKykpKem5sNU11xCLxbjhhhtUYau77lJTvAthjn/pI7IKW4FRwGrhnCOHXmEr4PtCiD8IIS4RQpyn/x9IQ0KI04QQG4UQW4QQt3exfqEQok0IsVr7/17GunwhxJNCiA1CiPVCiGM67z9o0HsFibARI3EUFzP2j3eRMyJqZhHpvZOESTgG9CwZdy443KTsnixXWbdwB0zLRZdF9+XqGVtg9j7bdjPKGcBlczEsmcqwSPK7bx/M2hvuHKNHHPF2Su/UFZmu4Nyaayvaarq2ukKm4vYVZpNab0FfnTD0c9Y/eyIDMHv1viLlyzZIQPROCHmV2kytfmUV6Zk4/e3VGzL3kvvfGXoyQKbyP+dBmH9r/9px5ZijpDuP9+gNoxfAVz8wEwOGz1Dulp6e1S6RMehxoLC7uOc7/4+xY8eyevVq7r333m4LUEFXha0e55133mH16mrs3jweefolXn75ZYYPH64KW61dy2mnnQbQe2GrDz7g/fffNwtbaVixYoUqbLVqFU8//XTvha1KSzn11FNZtGiRKmwlBPPnz1dFrTr964WthBAsXryYWbNm8fDDDxvtdVfAak9LhMqq0fstHwwMxCK5BpgEODFdWxJ4uj+NCCHswIPAKUAN8KEQ4p9SynWdNl0mpTxrvwbgV8DLUsoLhBAuwNef4/cLusUQbtIK7qiXyTVxuhqOqc/aqis3gyAyJkcbMVNNTaEpl7TNoyyAeMgc4doVXH5tzEnYLFuqK9+uLBJgmruEDy59HMddw8wAc+cpGnToZJc5t5SvWBX/8XYy23V3h67c9WA7omci8RWDPlOvr0j11t15KgDfk0UCpgLUlbJ+7r31sPV7oV8XfT9fUe8ujUx3m82m9gnV979X7ytSSRb9JRLdIsk83qQz+tcGaL7/EjVupDfC7mrfzHRiX6GSR/PZ92g5dEa4SSOhfrj3uoKvKNtlCdkFqGbN6lTYqop58+YBqMJWK1Ywe/ZsACKRCKUjRnLppZdy6623qsJWZ53F/PnzaWlp6bbdt99+m3PPPRe/X53Leeedx7JlywwX1bJly1RhK20W7+6mazcKW11yCb/73e845hizH7xs2bIeL8M777zD8OHDqa+v55RTTmHSpEksWLCg2wJWQ7Ww1VFSyl7yF/uEOcAWKeU2ACHEY6jsr85Esh+EELnAAuBqACllHDh4wzd1RZ85+yaYFkj7HqWoHVqevO7aynxxdItEe6FTdrcih0zXVpfHznBtOf3mKHboRCQZisKbj8PuVMo93Kh61/ZubrlOdjqRuANq24v/zu5tQbJyhLwFantduevzKunfu4PdYWaVGb30AkUkmRUCu0JOZyLRXVt9tEj062IQUC/7AZx61/6xkVB9/5VxZyuqr9Bl74usvcFfqoikvyQ4mOjv+XcHp3e/58WdUW7abrcTiUSM37qyBxUnueqqq7j77rv3a3bFihW8+OKL3HHHHSxevJgrr7yy23a7Usqd0RclvW7dOmbPnk1zc7MqbJWB+fPnEwwG99vnZz/7GYsWLTKKUpWWlnLuueeyfPlyFixYQEVFRZcFrLpbPhgYCJG8L4SY0oXl0F+MADJmKaQGmNvFdscIIapRY1VulVJ+AowBGoA/CyGOQmWN3SylDGXuKIS4HrgeoKysjKVLlx6QoL7QLuYA2z7+gDHA+m27qQurto515uNKtBLBzQdLl3KccFO/fRPDY0F21TaxXTumPRnmeARNEcHapUuZIVw01u7GkQwDgtXdyDahqZ2iYBPNO7dQKB28t3QpY1siVALvbaojtsvc73i7H0cqxJ7mMJuXLmWOdOEDonh4v4dzn29z0b57PQXAxxu309S0FHDTkUzsd80mFcwiJCvYvXQpw/bWGiNRN+yqozbR/TGOxk8ODSxft53wzhQzk05ygY27m9jXg2xjmiKMBLbXB9m5dClFjfuYBmxrCLFr6VI6Ojq6vK/OeDvHAfWhNOu09fNtHtoSTtb08zk4Km6nAHhvzVZim9r6vN+ktjjlwJ6WKJv7c0wpOdaZR02bjV0H+MzqmBq1UQy8uWI90raly226u4adkZeX16WC+zSQSqWMY7e3txMMBuno6CCdThvLY7EYsVisy3Xz5s3j4osv5itf+QolJSU0NzfT0dGB0+mkoKCAc845x6jjft5553Xb7qxZs7jxxhu56aabkFLy1FNP8fDDDxvbZq5PJpM899xzXHvttftdt/fff59Zs2Zx0UUXcdlll/HCCy9QWqrI/sUXX+z2OtTW1pJOpwkEAoRCIV566SVuu+02gsEgkyZNYtOmTXz88ccMHz6cv//97/zxj39k/PjxxvKysjJjeVf3MhqN9ktPDoRIjgeuGoR6JF3Rdme6XwlUSSk7hBBnoAZBjkfJPxP4upTyAyHEr4DbUeNazMakfBh4GODoo4+WCxcu7KeIGlp3wYcwptQP22HykUczeYrW1qbRsHcV3vwyFi5cCCvzGFHggb1pqsYfQdX8jGPWn0rxyGNYePxCWlf5KA54IJaAnFK6lS36CjS9z7CiXEgUqO0KGyC6kWMWn589ynhNOTRvZcTYKYxYuBA2lUFkL56C8u7bB/gwnwKtcNe0WfNg9HwAli5duv9+2u+xAJ+0gDakY9JRc5g0pdO2mdg9BrbuYM4Jp6necU0VBDczceZxTJzUw36utbD7aUZPmcXoOQuhJgfW/ogx0+YxZubCrmUENSXEB25KR0+lVF+/aTKFlfN6vhZdoWEctK7hmEVf6N/gt9irUPcGI8ZNU/ejP5j9EWM8eYzp72C7zgi9ANHtnHDSKd1u0u017IT169cPai2L/kCvoxEIBDj++OM55phjmDx5MjabzZDJ7XaTSCQIBALk5ORkrZs9ezY//vGPDZJwOp08+OCDtLW1ccEFF2Cz2XA6nfzmN7/Zb9/MdufPn8+1117LySefDMD111/P8ccfb8g5f/58LrnkEubPn09VVRUnnHACbrd7v+u2adMm5s6dy8yZM7n33nu59tpree2113A6e3a7NjQ0cO655wKQTCa59NJLOe88M0T94IMPcv7555NKpbj22muZM2dO1nK9sJW+vDM8Hk/3mWRd4ICIRCib7QZg54Hs3wk1QGY+YwWdRshLKdszvr8ohHhICFGs7VsjpfxAW/0kikgODvRpqHXXVqbLKq9CjVrXXTvaPFXqe6fA5KWPG1/TNrfpsurJd2yk/3aYLrAjv6T+O8NfogY96vEQXabuAu063DkZrq1+BFMz3Vk9ubbAdNMYmWxa3KA3t4fh2tK2L52ipm4fs7Dn/YRQdTrKMjJTrnq+/wPqQE03kjui/yOoD9S1BYPnijrh2zDzyt63O4zw97//vcvlt95qJiOMGjVKFbbKwEUXXcRFF120336nnrr/ANHMfTPbBbjlllu45ZZb9ttn3z71Dt15553ceeedPZwB3Hfffcb3s846i7PO6ioMvD/GjBlDdXV1t+v1AlbdLR/swlYHRCRSSimE+IWUsut8tv7hQ2C8EGI0sAe4GLg0cwMhRDlQpx13DirbrEn7vVsIMVFKuRE4mT7EVg4Y3cVIQNWFgIxxHz6zsl0PSjll90CiRZGJsyci0Qr4hJt6z5jRffi6LPqU092l/upwB8yKjK5+PGRZRJLf87Yj56k6GXqgWyeG3oLt+gBBPbXa5VME0Rd0DlC7D/AFmn+rOUNvfzAQIhks5JQe2viIhc80BhojmS2l7D6vrQ+QUiaFEF9D5T3ZgT9JKT8RQvyHtv63wAXAjUIV/YgAF0sz2vV14BEtY2sbKpvs4MDhAb2WNnSySDQFZ1gkOaoolf69G6TsHoiG+5a1BYrEehsRbcwFlZ8tU29Ekkke/bJI8jO+92KRzLpa/eswgue9KNmR8+Cal9Qo/EMFl6/ne9QdDjT914KFwwQDIZITgRuEEDuBEAceI0FK+SLwYqdlv834/gDwQDf7rga6mDnvIEAvaRnqwmWl95R1paqXIIUeXVbKItHTf3uzSFBE0tPU32ASiW6R6Mq9N2shs6fen3ECmUV2eiOSzph+mRr41xvJCQFVx/av7aGCkfOoLzmO0hGDYcBbsDD0MBAiOX3QpDic4PSZRJKpePUpJHRlnUkKPbhSUna3KgqVTvTi2tLWpWI9bwcHbpEYVojoX66/ZwBEkjfCnDzyswp/MeuO+DalvcWoLFg4THHARPJZrs/eI1w+ZX9BtrItGKWmCNH90JkukB5692mbx6zT0FuwvavvXaFyjpowUB9f0udgu0Z4rl7qQXeGXm/a7uy9RoUFCxY+cxiIRYI2dmO+9nOZlLL7NILPCnRrwObMzt7JKYXrXjer0zn7pvhTmdND9xgjyenbdqAmh7zxHfN3X4Pt+jH6Ex/R4ck9sEwoCxYsHPYYyDTyN6NmAC7V/v8mhPj6YAk2ZKEr8a7IYcRMs8JZn11bGTUUenJZZSr3/s5z1OcYSe6Bta8fo79uLQsWLHwmMBCL5MvAXH0UuRDiJ8B7qNokn13oYzh6SyHto2sri0j66trqaSqVrjDqOJhzA1TM7nk79wAsEl/xwKu4WbBg4bDEQGb/FUBmAeAUfZ6B/zCGsweLJBM6edicPSrYtO0guLY6w5MHZ/y09/0yYyT9xRd+CWd0XbjHgoXBRmtrKw899BDQjwJU/cSBtjts2LD9lvWrsFUf0draygUXXMCkSZOYPHky7733nrFuv8JWnZYPdmGrgRDJn4APhBA/EEL8AHgf+OOgSDWUYbi2elG2huXS83Ype0aFuJ7azAq2H4Ci7wuMGMkBDNgrmWjWrLBg4SAjk0j6Cikl6fTQq8HXY2GrHnDzzTdz2mmnsWHDBqqrq5k8eTJgFrZ66aWXWLduHY8++ijr1q3LWv7hhx8aywcD/XZtCSH+KqW8AjV1/DWoObcEcI2UclWPO38W0EeCMBR/LyPEs4LtPbmsHB6zYl9/XVt9xUAsEgufSyz534ep37ltUNssrRrDiVdf3+M2t99+O1u3bh1YYat4nLlz56rCVtHo0Cxs1Q3a29t56623+N///V8AXC4XLq1aa7eFrRYuHFKFrWYJIaqAa4HtwN+AvwI7hRCf/aG7BkH0lUh6doH1OUYihHnMgdZz6A46kRxIjMSChU8R99xzzyAUtlptzPR7uBW22rZtGyUlJVxzzTXMmDGD6667jlBIjUvotrBVN8sHAwcSbP8t8DJqCvcVGcu1ikWMGQS5hi6cfXRt6cq+V9dWZoykD3GXWPvBJxLLIrHQR/RmOXxaGFBhq9LSw66w1UcffcTKlSv59a9/zdy5c7n55pu55557+J//+Z/Do7CVlPJ+IcQDwB+klNcOihSHE3pK/82Es28WSdqWmf7bi8uqj1bOAWMgMRILFg4hPm+FraZOnUpFRQVz56q55y644AIjeH4oClsdULBdSpkGjup1w88inH2zNPrqAjNdW0JVfutLmwcrRuIrVG3nDs7DZcHCwUIgEDig4lonn3wyTz75JPX1apqj5uZmdu7cyd69e/H5fFx++eXceuutrFy5ssd2FixYwLPPPks4HCYUCvHMM88wf/78rPXPPPMMkUiEYDDI888/32U71dXVHHvssTz22GNcc8011NXVGeuWLVvG6tWr9/tftGgR5eXlVFZWsnHjRkBZWnqsY/bs2WzevJnt27cTj8d57LHHOPvss7tdPhg45LP/Hnboa9aWq2/jTQzXlsvf+7QkRozkYGVt+eFrHw1OaVcLFg4iioqKOO6445g6daqRrdQXTJkyhR/96EcsXrx4v8JW3/rWt7IKW/WEmTNncvXVVxuFoa677rqszKuZM2dy0UUXMX36dKqqqrJIJhPV1dXMnTuXCRMm8JOf/IQLL7ywT4WtAH79619z2WWXEY/HGTNmDH/+858BcDgcPPDAA5x66qlGYasjjjgCwFiuF7bSlw8YUsoD+kfV/UgBW4E1wMfAmgNt79P6nzVrlhwQqp+Q8vu5Ur77YM/bdTSq7V64pcfNlixZIuV/F0l57/jej/23L6k2Yx19l3cQsGTJkk/1eAeCoS7jUJdPyr7LuG7duoMrSA9ob28/ZMfuKz4LMnZ1j4GPZDd61Zr9t79w9Tf9tw/Wg8vXN3eVyw8INUGiBQsWLAwRDGRA4i7UhI1XSTUTsAQ++z6Rvo5sd7hh2oUw9sQ+tOnvWwDdnaOObxvIbbNgwYKFwcVALJKHUIMSTwJ+CASBp4BeJnQ6zKHX+vD3UrZUCDj/931r0+XrG5GMX2zNsGvBgoUhh4F0bedKKW8CogBSyhbggLScEOI0IcRGIcQWIcTtXaxfKIRoE0Ks1v6/12m9XQixSgjxwoEcv18on6qmix91/OC16crpG5FM/gKced/gHdeCBQsWBgEDsUgSQgg7yqWFEKIEZaH0C1obDwKnADXAh0KIf0opO08Cs0xKeVY3zdwMrAdyu1k/uKjIruy7vTHEyEIfdtsBDu5Z9IODl9JrwYIFCwcZA7FI7geeAUqFEHcBbwM/PoB25gBbpJTbpJRx4DHgnL7uLISoAM4E/nAAxx4w6tqjLPr5m7y6rvbAGxl7Ioyc2+3qNzc18IdlgzufkQULFiwMFg6YSKSUjwDfBu4G9gFflFL+4wCaGgHszvhdoy3rjGOEENVCiJeEEJnJz7/U5Dgk03rWtUdJpSW1bdFet63e3Updu7ndLY+v5tkt8V73e3JFDQ8t3dpv2dbUtDL1+6/0Sbb3tjYRTZhVATbVBYnEUz3sobB+Xzs7GkO9btcZUkqSqXTW745Yst/tALy/rYlEuveRxp1R0xKmsSN2QMe0YMGCiQGV2pVSbgA2DFCGrvxBnbXCSqBKStkhhDgDeBYYL4Q4C6iXUq4QQizs9gBCXA9cD1BWVsbSpUsHKLKJtY1K2a7ZsJmliZ7L2H/t9RDzhjm4fIoahLhsQ5g8Z7pXebbvidISSvHGkiXYepoRNCb5YF+SRVUOhBC8vSdBRyzJk6++w9Ti7mupN0XS/OebEa6d6mJBhZNkWnLja2HOGefkrDEuOjo6upXxu+9EKPYKbp6pRuj/bV2MUFJyw5GeLrfX8cauBC9sS3DfCV6EEHywL8mf18a4b6EPv7P7c5RS8lFdipmlduw2Ych+2TiJ09a1jN3h++9GKPMJvjrdlFVK2evUFns70mxqSbGwUg0aW12f5NENcf7nOC8ue9f7dnUNQwnJPcujfHmqi1F56v6sqEsyscBOjqt/btInNsaxCbhgggpTpqUkLcHRD3drR0cHjzz/Bk9sivPV6W7c3ZxLXl5en0aVt0TT+BwCt0O1k0pLhKDHZ7grJFKSZBq8TkEqlaK1rZ14GryO/ruSM++vlJJgHPwusA9wzql4Sqksl92UUdK/69+dvOEk+BwDnxcrLaVx7VOpVI/3MBqN9k9PdjfApLd/wAPcAjyNytb6JuA5gHaOAV7J+H0HcEcv++wAilHWUI32uxYIA3/rad8BD0jshOer98iq216QP37RHMCzqykk48lU1nbtkbisuu0FefOjK41lM3/4bzn7v//V6zHO/vUyWXXbC7I1HO9xu98s3SKrbntB1rSEpZRS/vntbbLqthfkPz7a3eN+729tlFW3vSAfXLJZSillfXtUVt32gvzm46uklD0PVDviey/Lcx542/h9zgNvy6N/9Gqv53TL46tl1W0vyLaIOqdfvrpJVt32gly5s7lPsr62rlZKKeXKnc2y6rYX5E2/e6XXY9a1R2Q4ljR+T/3ey/LsXy8zft/6xGr51UdW9NrOd55eI0fd/oJxj3/2ygZZddsLct3etm736eoa6ufyh2XbpJRSNgbVdb/v3xt7leGN9XVyze5W4/fCe5fIRfctNX7f+cwaef5D7/TazoZ97fLuF9fLdDotlyxZIn+rPUP6ffhkT5uc+v2X5db6oLFPV4PV0um0bOqIGdckkUzJ6t0tsqY5nHWsPS3h/fbtqq10Om383tnYIdfuUefa3t4u97aG5dtrd8hfP/CAlFLK7du3yyOOOKLXdiPxpFxT0yrDsYSUUspwLCmrd7fIhmDUOO6elrDxjPTUbjSRzHrHN9cF5eY6dY38fr/c2RSSG/aZg/6+//3vy3vvvbfLtl599VV5+eWXGzLuaOyQqZQ6/9ZwXFbvbpFB7T2JJVJy3d42uWrNWnnUUUcZ/4FAQP7iF78w2nzppZfkhAkT5NixY+Xdd98tpVTX/6//eFZOmDBBjh492ljeFfo7IHEgMZK/AEegSus+AExGTSffX3yIsi5GCyFcwMXAPzM3EEKUC42OhRBzUC65JinlHVLKCinlKG2/N6SUlx/oCR0I2iIJADqiyi0Tiac45Rdv8n/v7sjaTndpdcRMd1EonqQ5apBjr8doC6vPFTtb+Pm/N+63ne5iate2D2oyZbrTusI+zfVlHEf73N0c7nG/9qiyePTtAVrDcRqCsV7dVLtbVNutIbVvS1i5+HY29XzMDbWqF1UfVC6p5pDarzFiusleWLOX+mD2OafSkrPuf5v7tOvWEUsSjCWpzbg2q3a3smRDfZbLrStsru9Ayoxjd6jP7dr1bwnF+c3SrSQ6tVPTEuaLD75jXNdd2qd+f/T78Mmeth6Pn0il+X+PruLnr6pzSacle1oi1LREjGdpTU0bH+1sMZ6Z7vCnt7fz2ze3GsfW74su28pdLQSjSZZsbOixnWgiRU1LmBbtmsS1c9c/U2lJLJkynknofuLDmpYIOzKeg0giTSotSWpFqeLJNO3tbTz0kJrGJBRLEE+mSXUqWiWlJJ4037f2SIJUKkVYc9nq63SXbjyZprEjRkMv7s60lGxtCLGnJWL8jiRSxDKOFdV+689AKJakIRgj3cU5r1692phepTkUpy2SIJzIli2aUO2E40kSqTSllWNYvXo1q1at4tW33sXn83HuuecCZmGrvz/5LKvWfMyjjz5K9ZqPCcfi/Ne3vjk0CltlYKKUMnPixiVCiOr+NiKlTAohvga8AtiBP0kpPxFC/Ie2/rfABcCNQogkEAEulr1p308JrdqLqivO1kicaCLN8u3NXDffnFFff1HDcbVdKi2Nh6M1nKDAb2ZOL9lQTzie4swjVclOXVG3RuKMxMc/V+/h/97byZeOrqSy0Mz22tGkFJn+sgY1mep7IZK9beqFaI+o7dujOpFEut0HYF+ralcnASWj2ndHY4ipI/K63Vd/CVvCcUYW+WjtI5FsqlNEoivxJoNI1OPQ1BHja39fxXkzRvDzi6Yb+1XXtFIfjLG5vgPAiBs1BGOk0hK7TVDbFiUcT7GxLsgRw03ZQ7EkoXiS0oBygW3R2mgIxijL9RhxFp1Inlu9h5+8vIEiv4sLZ5v1Hx5bvpvVu1t5b2sTlYU+Q1nrz4b+uXavSSTPrtrD6GI/R1XmG8tW7WolGEsa16o+GFMKOwUt4QSFfpdBVit2NXPSpDJiyRSt4QRludluvGWbFUHoz84u7Z7r++/Ulr+3tYkvHz8aqSnNRDKN02Gj9fmtxPeGiKfSBJJpYnZBvcNOMp0mkEhjE1DvcpCWkoCmwOvcdgTCUJIepw3dwy2lJJbnJLJghFK60lT4iaRJJL+6+wds36YKW1VUjSGZSnHlNdex+qMPGDFiBM8++yytcUH1+s1845qLOPmkE3lz2Tvc9/u/suylj/jrH39LOBpj0pEzuOveXxEKhTj3/AvYuWs36XSaH37/exxzzDziiSRXXH0tK5Z/QEWFKmwVl3aSqTQP/fYBXnzq70gJZ37pMi6/7kajExJPpvn9/T/j5WefoGrkSDyBfCYecRRNHXFKAsq1nUylqWmJsOz9FXz9P64jGo1y0w3XUVRSxt13/5gct8Mkkk6kp7/jHbEkTz3/MsNHjmJEhXrWli9fzshRY3AWDKM5kubiiy/myaefZcKMuYwfP3QKW+lYJYSYp/8QQswF3jmQhqSUL0opJ0gpx0op79KW/VYjEaSUD0gpj5BSHiWlnCelfLeLNpbK7tODBwVdcVd7J4tEV8ZrarJ7lbqSCGkvUyie3G8dqN7lnc98zC9f22T8NohEIy1deS7b3Jh1jB2N4SyZTIvE7GG1hRP7nYdOCPp++mdtezQrAA/KGtJ7+zoBtUUSpNOSVIas2zsF4NfUtPLRjmZA9aj3tZlEoj7Vfrri2t0c5oa/fsS7W7PPUSeCJs0K0HvATRqR6Md9Yc0+GoLmeb+p9aj3tka0a6LOIS2hsSNGULOuAFbuajX2+2RvG4t/8RbnPvguUkqaOmL7kViTRiS6RbhRI7vfvrWVlJYEkJaSp1bWALC1QZ2DYZFo97+2TZctRkNQ/X/j8dVc8Nt3eXT5LkOmpRvVzLW7W8Kk0tKwIkBZPR2xpHE9l29vAeB/XljH3B+/zuJfvMmf3t6uyRFir3Zs/dnpbC3plsHy7U2k0pJX19XR1BFnQ61KstB72Lo1oP/Wcx/U0myrO51Wv1PaMxNNpJFaWDShtSOlJKb16vU9M62cm+/4ASNHjWb16tV887/+m13bt3LuZdewes3H5Ofn87+PPG4Q/OZNG7niiiv4xytvEY1EePbpJ3nnnXd4+c33sNvsPPXEo7z00kuUlJXzj3+/zVOvvcvxJy4iHEuybesWvnDJNTz273dw+wI89dRTNIXirFuzmmce/xvL3nmXl994i6ce/Qvr164hppHd2upVvPzPp3l56Xs8/o8nWbNqJQhBfTBKMpWmI5pgc30HwViSDes+xp1bwOJTT2X2cQv4f7d/j1gizfz58znthGO48NT5nDJ/HtOnT+ek4+by/rKlxJIpo3PwyvNPc9rZ57OzKUwkkWLTtp0UlA7DLgTt0STDhw9n5+4amutrGTmEClvpmAtcKYTQn/CRwHohxMeAlFIeOWDphhA21LbzzcerefDSGYwpMefP0hWn3vsPRk0lXN8epVTrAeo94LC2XTjDxVXbHmHKcDUEZvmOZva2RSnSLJSOeNJ4KXWl22wQSQOXzh0JKJea7qYJxnQiUZ91muLfWBvktF+9xfHjivmvM6cwsVzNTKwrV90SyXRV7dHW7W2N8IN/fsK/19Vx/swK7rvwKIOApFSklZYSXV/oSnVzXZDv//MT3t3aRMDtoPr7i9nbGjHOSSdH3SLRe8b/+ngfr3xSxyuf1HHezBH85PwjcdgEmzUl3RTKdm21xiTxZJpt2nHjqTSPLt/F/ztZ1ZF/c1ODcT5SZmfZ1bVH8TrNZIRVO1u4Yl4VSzbUc+MjK0iklMLb1RzOIv1Gjah015Yu+4baIF6nnW0NIf79SS2nTxvG+qY0+9qiCKEUOJjKuraTawsUgenXZnxpgDue/phgNMH1C8Ya55JISfa2RqjJIpIITrvZP/xoRzPRRIrnVu1lumbV/PCFdcwZXWgQu00oAi/3SmpadItEfe5sCuGy22iPJlm/r50nV9Rw8QQ7JQE3jR1xbMcNpyzPTW1tELsQSGDk8Fx2N0cIRtR1GVGeS1skTrAtihACt9+F3WEj2BqhPM9DXXsMt8NGVaGPLQ0duBw2iCsXVGaAOZ6UODUCAkVWiVSaeFJSWTWKiVOOZG9rhHGTp7Fu01bOPM9Jq8vO8IqRzDh6Dpvqgix/5y0+rl7F7NmziSfThCMRCotLOPuUE3jrP2/Fd89/M//kxZx4wgk0dtQxorKKs086lsaOGGOnTOOTjVs4cmGS9auWc9JpZyGcHuwyxcmnncXK5e+xeP48JLBy+XucfNpZSIcbu9vFCaecTp7XQSqt3GKxZAq3w05VvpO9Nbu57uor+fn9D1A5aToep51IMsWbb73FJ3vakagg+RHDc9lYG8RuF0TiKdojCRrbQrz56sv85O67CcWTbK4L0hCMYrcJqop8bGsMEdZcg26Hbb+A/WAVthqIRXIaMBo4QfsfDZwBnAV8YeCiDS047Tbq26Nc8cflRm8a9o+R6MoYoDrDKjEsEo1IMi2S2jaz5/zsKtVDaAnHlTWS4ePWj6X3xt/e0miY0jubTQvAcG1FddeWan9NTStSKqvijPuXsVbzxe/tFCNpz/Bj72oOI6Xkwt+9x1ubGygNuNlcH9TkNq9DayRuuLUAtmtK9a4X17N2TxsnTyolGEuyuyWc5TLb3yJRSvHjPW0Mz/PwlfmjeXrlHl5fX09jR9zYTicQ/VMC+9oibG8M4bQLjhtXxN/e30k8maYlFGdNTSuFfhfheIq2SCIrNlLbFjXuT3GOi5W7WkilJd/751pGFvr489Vq1p+Vu1oMiwgwerxNGa6tdFqyqTbI+bNGMKrIx0NLlVXy9p4EuR4HJ04sZZtukTSZRKKTW75PZYJ9sredZZsbyfc5ee5rx3HKlDJ+8epmPq5p45O97cwfX2zcn8zruaclYlgV88YUsqamjZfW7iMYS3Lr4on85ctzCLgd/ObNrSzb3MioIh9jS3LY3hiiJSpJpJSbb1dzmLRGnqccoabQe2ntPpZsrMfnslOe56U4x01rJG5YVIU5LtJSkkiliSVTRoZQPJkmlkzjsAl8LjvheJL2SAK3w05pwMOoIh+JZJpN9R2k0pJheV7sNkEkkSKaUO3YhSCeSqN1+PE6bUgpDevZ6/FQ6HfSFkkQTwtcNkllgY8cjwOP12s8J26H4OwLLmHVqlU89erbvPzOCm685XZGjh7HEy8tZerUqTzwk//hnh//iFA8hc/rweO0Mzzfi8flpDUURQABjwMBhoxOu0CAski0TpLH5dAUfhKbAK/TTqHPRTyZpiTgZnxpDtu3bGLWrFnY7HaCsTQ+l4Mct8OwSL506vFcfNoCLlh8PEdNn8EXFx3H6veX4XLYqG+P8dYbrzJjxgwmjK5kfGmAqkIf0yaMoa1hH363A5fdxqZtOyguK2fs6JFDq7AVgJRyZ0//gyLdEMLYkhz+79o5tEcSXP6HD4zevkEksWzXFqhxIzp0pau7trIsEm1dNJHiXx/vw2W3kZaq7exAtunaKvS7CEaTBllljuXI9J8C1AejpNOSnU1h7DbBK99YQCoteWeLchvtM2Ik2a4tgJrmMPVh1VP93llHcMa0YWyt70BKaRAQKCLQScEmlFJNptJ8tKOFLxw1nK9rlsH6fcGsHrRODC1hlb7aFIoTjCZYu6eNIyvy+fZpk8hxO3hrc4NhjeS4HQaZ6goClBLd3hCistDHdcePoT4Y4/EPd/H2lkbSEr40q0KdU0uEuvYoemZmXTBmXIPTppazoynMPz7aze7mCN9YNIHjxhXjd9lZubOVLXVBctwOPE4bjR0xIvEUoXiKPK+Txo44G2qDhOIppgzL48aFY/l4TxsLfrqEj+pSnD19OFOG5bKzOUxrOE5TKE5pwK3ILpxgX1uUsSU5jCry8XFNG29vaeC4scU47Ta+d9YUUlJy3V9U+Z8rjxml7ntTiJqWMCUBNwGPg5qWsGHpnDezgngqzb0vb6Q04OaYsUXkepxcfkwVL368j7e3NDJ/fAlVRX52NoVp0NyD0yvz2dcWYU9rhGgizbwxRYwq8vH7t7aTSEl8LmW9lQTcOOw2WiMJPE47uR5FglGNOHLcyuERT6WJJ9O4HHb8LgeReJpQLEWuV60PeJyMKckxiMbvsuN12onElZJ2O2w4HTYSSZNIhhUXEA510NgRxy7UM1ee52VkoY/SXDe5Xic2myDH7TTeGafdximLFvHqv55j995aEqk06UiQvTW72LJjFw6Xh0svu5xv3HIL6z+uxmETxmwVNiHI9zo1EnFy0okLWfrvF2lqDdLU1s5rL73AnGOONeI5R887ltdeep5IJMzehmbeeu0VhBAML/AyaViAYXlebDZBdXU1848/jvse+jN33nIT0fYmPE67coW++BpPvLKMZe9/yBOvLOOVt97jiVeWceoppxDwOElJySv/fIrLLr0EAK/LTp7PxckLjmXLli3s2LEDr0Py4rNPsfCUM1hw7LyDVtjKmka2H5g6Io9fXDSdrQ0h3tnSBOxPJDrBlAbcVNe0Gvt2DrZnWSRa7/iNDfUEo0nOma56CU2heJZSbw2rWERLOM7pU8uxCXhrkx4sVcrDJjJjJOozkVL7bG8KUVngpbLQR1mum421atChTlDtRpwngcthw+2wsas5zNY29fbOqipgbImfUDxFXbtSvnqefGs4blhPE8tz2dEYYv2+IB2xJHNGFzKhLAchlItwd4sitIDbQWs4TjKVJhhNMqFMudo+3tPGzqYw0yrycNptHDu2iDc3NhiB9tmjCkzXVjjOSC3hoKY1wo6mEGOK/ZwwoYQ5owv57nOfcO8rG8nzOjltajmg3HS1bVHGlORgtwnqMiyS06eqBIe7/rWeEfleFk8pw24THFWZb1gk40pzKM5Rrh3dKjm6qgCAVz6p1a5BgAuPruShy2YyutiPlHDJnJGMLfWTSksjvjVndKF6Btqi1LZHKc/zcMSIPN7c1EBde4zjNcujstDHl48fTV17jOIcNydNKsXlsLGzSVkklQVeRuR7qdGyt3LcDk6ZrCyJvW1Rzj5quKEUrzluFE67jVgyzfzxxYwq8rGjKURdWN3n48YWkZYY8alRRT6OGVtEPJXmiOG5huvMbhOUa67bXI8Tt0MtD8WUm9PvdiAQxJMpjUhs+N12pPaX5zGLN3lddiaWBRhdnIMQilCiiTSRRAqP047LbsuySEZVlDP96LmcecIcfvnj7xvy5PtcWeNUXA4bNq1euc9l58hpU7npW3dyxumnccEpx3HpeV+gtbGBj1ZXc9kXTubk4+fwi3t/wtdu+TYlgeypAx12G0U5bioLfapw1WVX8MXFC7nkzJO58uprmTFjphEjmT5jJhddeBEXnraAb15/Jcced5z2foos12N1dTXTpk1jxpGT+cYd3+fGa6/AgSKjtnAcgSDP69R+q/fL47QT8DiIRMK8v2wp559/fracGYWtTpw7k8VnfZEjp03F7XIZy48++mguvPDCQStsNaABiZ9HHFmpsnn0gPP+ri31efy4Yl7fUG8MgNIVVSKlfPk6odiFSTL/XL2X0oCbM48cxj9W1NAcynYXtYbjtEcTpNKSMSU5HFmRz7LNDXzzlAnsaAxR5HchtAAbKMskx+2gI5akrj3GjsYQVUVqcsiJ5blsqA0aAfMR+V7DxdIWSZDvdZLrdbK7OUIimCLH7WBcaY7hxtna0MG+1ijjSnPYUBukLZIwfNczRubz9w/ajWlj5owuxOdyMKrIz4Z9QVwOG8PyPDhsgpZwwjjH6ZX5bKgN8q81+wCMrK8TJpbw73V1vLS2ljyvk4nluby9pREpJc2hOFNH5LK7Oczu5jDbG0PMH1+MzSb4y7Vz+NaTa3i+ei9nHjnMyHDb0xqhtj3K8HwvHdEkde3Kp1yc42ZWVQEOmyAYS/K1k8bh0F76WVUFPLR0KwGPg0Wagm7siJlEMqqQ1zfU8/Jak0iEEJwxbRhnTBvGkiVLOGJ4Hklt4NpSLfg/Z3QhL6zZR227IreTJ5VSlOM2rsHx44qN+//VhWN5emUNJ01S5Day0MfOphA1rWFmVBYQjqcMa6+iwEuB38X40hw213fwxRnmZBGlAQ8Xz67kiY92c8zYIuqDMWLJNJtbVJbVvDFF3P/GFt7arBOJn3ljinh0+W7On1mBNk8rAAU+J1J6yfM6cdhtOGw2wyr3OG04HYJYMk0ilcZltxnWjNNuw+vKHiRryxi853UpwkmlleJMpNJ0xJK4hBo86LLb+MVv/0wsmaI812PEIgFuvfVW4/uoUaNYtnwlde1R/G4HboeN084+jy9deBHBaIJxJTnUB2O0RxM8+epJTBmWa9xzgLVr13bZLsA3vvFNzr/qBkB5LNoiCcKxJB9t3oPbYeO73/0vLvzKzcSSKSaWB3A79h8UfN99ahLWVFpy9cXn8/WrLyYtJaIlTiyZxuO047DbcGpEarcJnHaBw+5gVFkhdQ0NWcSk44wzzuCMM85ASuVNCHgcWcuDwSCBQM/VW/uDAVkkQojynn5/FlHkd6uURi3uoBNJXPMLt0dVb3726ELaIgl2NoUJx9VYCz3tLxRLEtJcW6U+lXYqpeT97U0snFhibNccihntF/ldtEYSRqZQcY6LEyaUsHp3K7VtUbY3hhhV7CfX4zAskY5okrGlKjGgrj3KjsYQo4sVkUwuD7ClvsNwg0wsD5BKS8JxdQ65XicjtRTVra1pjqzIw24TRntbGzrY2xZh8jCVJNAaThiWzQwtqPuPFTWMLPQxLE8V4po8LMCG2nZqWsJUFvjI97loDceNQLue4qor42kakSwYr6bu/2B7MxPKcijOcZFISYKxJM0dcUoDHvLdgo92tBBLphldrGT0OO386qLp/PKi6dx+2iSK/C7cDpthkZTnuinLdVPbriySYXnKHz5leC5ep52LZ4807vvMkQWk0pLWcILxmkXSEIwZgfZZmkWysS5IZaHXcOvo0IOaY0rU9X9zk8q8mj1KWSQbazuIJFKU53mYOkJd01FFvqz07oDHyb+/eQI/OHuKsX5bQ4i9rVEqC71UFCiLZHdL2NjvjGnDmDO6kCOGZ89neueZk3n55gUEPE5GaZ2LTxpTDM/3Gskk72xpxGkXDMvzcOoR5fznKRO4KCOdWT+vohy3oXzdTpsxnsLtsOGy2+iIJZHab7vNRr7XaXR6uoPX6cj4bsPlsJGWklgKnFrQWE+Q8Lt77g/ne514nXZyPQ4cNoFNCMOD4HLYcDuV7E67LYtEekMmEXqcdlwOGykpSWiBbVCxFN2i6gl2myCgWWg2IQyZPFo7Hu1cPU47QqhzKMv1dEkimRBCUFmo3rWDiYG6tv7Yy+/PHPSea31QzbEVjCaNAGlHNEl7JEmux8mRFUoJVte0GhlCYzUlEoonjaD7ML+N2vYoWxtCtIYTHF1VSKGWsdUcMmMk+lgLPSZQ6Hdx/swK0hIeXb6LnU1hRhX5CXgctEeTpNOSjniScZpS+GRvG6F4ilFFSsFMLA8QT6V5b6ty0U3SMrj0uEye10llgZcdTSF2B9PMGJkPKJddjtvByp0tRBNpY78WjRCEMAlhX1vUcN2oY6j4wJb6DioLvRT4nLSEzQD6iHwVwG0KxRmR7zWuQ2Whz7h248sCxvLatijBWJJCv4sir2DFTpXqqpMlqF7uF2eMoLLQhxCCEfledjapObb0nmx9e4xajUgAbj99Er+46CjyfKbrRT9/JYMis8aOuGGhjSjwMlzbf2JZ95NQBzxOynKVWyzXo6w8IWD1biX7sDyvMYZFd2tlIs/rNHq2VUV+NmsB6soCHxUFXjpiSbY1hKgsUPf5m6dM4IkbjtlPabsddkZp12lUsdq2JabaKQ24cTlstIYTVBb4cNhteJx2vn7y+F6Vtq5AhebCcTlshqXq0taNLPJnWRBdwWkXOGw6OZmKOJaSxvdcrwOPw76fZbOfTE4748sCuBxKCbscKlBv12IgupLOzNzrCxQxCtwOu/ZpqlOXdo+G5Xm0e9y/7CiPtr/bIJBsQhlqGBCRSCnP7On3ZxWluW7qgzGj5z8iX/W4O2JJrTfvYEJZAJ/Lzgfbmw0iGaf15sNagBag3G8jGE0aA8NmVhVkEEmM1nACl93G8Dyvskg0xVXodzGyyMeCCSU88sEuatujjCryket1qjER8SRSmj3gD7arVE9deeipv0s21CMERnyiPZrQyNBBZaGPcDxFSsKMStXjFkIwtsTP21qMqLLQp8U6lIsqz6t6uLqXIptIAkip3H+VBT4KfC5aQgljLEiBz2UQ3bROgxlPmKAKiU0ozTGuz1Ytg6rQ76LYK4xxBvo5d4URBV6qa1pJSyjL81Ce66EuGGVfW8QgkmPHFnOaFivRke9zGe2OLw1QnOOmORQzRtgX+V3GtdXJtTuM1ci9qsiP026jJMfNKm3sSnmeh0K/i4cum8nXThzfYztVRaa1UlHgM57DZFpSWdj3cszD8ryGch5Z6MNmE1QWqP1HZhyjL9AVnctuM5S2jszvvUGPk+huna7ayfe5mFAe6PfcXbrCd2mWja60+6ukhRAU+V0U+p1ZcmUeQ7ce+guPq5MlosvYj2v4aWLQpBKDlZB8GKA0oHqxurWgv8DBaJJgNEnA48Rpt7FgfAmvr68zxmLoCiQUSxrjSYb51WX715p95PucjC3x43bYVWaSNl1CrtdJvs9Ja9h0bRX5lfvr8rkjDT/9qGJlkQSjSSNmox5013699XGlKtC8ub6D4hw3xTmqvbZwwnBtZbpVpmf0yMeU5BjHHJbnIV9Lu2wJq9iKy2FjhKaI5mYQie4GA6go9JLvc9EWMWMk+T6nEcOZVpFNJKdMUXGJIyvzDVk3ZxGJepR9LjulmmuwKwzP8xoDNIfleSjLddMaTtAeTVKe17PynV1VSI7boVlOLtJSyRBwK/dFZ5LuDjoh6UkC5Xkeg5B0Mjtj2jDK83rutevXCtBcW+b9GlnYdwKw24RBPDpx6PuPKuqelLuCrkCNT42gbEL0ewLD8jwPVZocmS6c/hBSjzLadWWtguj5GRZo32X0UqLNeKCTZ+YxDhQBtwO3w27ElPzaM5bjGZph7UEhEiHE1cBrQoh/CiEeEEL07+k7zFAaUBaJHhPQlWZHTOXH52o3+5QpZdS1x3h1XR2A4XsOxZRF4rLbDAX40c4WZo0sMB7EQr+LZi1rK8/r0IgkbqS9Fmi9oJMmlRrKZ3Sxn4DbSXskYaQABzxOSgNuwvEUDpswSM/tsDNGU3zD8zxGZkh7NGm4tnRlUuIVhvIG00UHqjeb7zVjHbovdmxJDmW57iyFVlFgxg6UReKkQ5uDCBSR6BZJ5+lVjhlbxLJvn8jMkabFlkkkRR513UYV+Xt0I+j3CqCsU5B2WC+K+1unTeTvX5mLzSYo1shqY2278X1MPy0Snaj1aUtsAiM+1hfo10oIdR8yz62yH0QCZgejQrdEtP2r+mmRuA2XjNnr1z/77d5x2g1Xmt1murp6izf0Bt3tpH/qLs+Buo2ElgRgExx4kTsNXpeDieUBg0BdDhsTyroO2A8FDJZFslBKebKU8mzgYeD7g9TukERpwE1TKEazFiQ2XFvRJMFowsinP2lSKXab4LX1deT7nMZo9VA8STiexO+2U+gxH7hZowqM7wUakehKPd+resA7m8JGbwVUSuJVx47C51I94lyvQ7OMFMnleByGohpZ6MsKJuo952F5XiOnvy2S0MjQtEjG5mc/JroidNgEJQHVk2vRgu16r+7OMybz0GWzspSHEMJQspWFPvK167GjMYTDJshxOzhufDFHDM/Nikno0OUxiERLB9ZjJACje3BrAQzPN5Vtea7HSF9V16FnIinOcXNkRb7xHdQodf2+XjCrgp+ef6ThwuwOpmvLZ8gBikR6C552Phe7TTAs14PLYaPA5zR6sBUFfXdtKVmyraTKA7RInHYVBC7QOhTOThbKQODSpo0fLItkoO10BZ/LjtsuBm3E+OGCwbqS7foXKeUaPuNpxSW5HqSEbdpUF7pLQcVIkoZSLvC7OLqqgLRUykLvjYfjKmvL53JQkEkkI00iKdKIpDUSV0SiKehtjR0U5mRnYFw/fwxvfftEctwOAh4nkUTKCGAHPA7KcpXSG1WcrRR0pT4s32OQ3z5t+pI8r5Mct4OvLhzLySOzTX49c6ss14PdpvLclYsqbiiQ8WUBI5MpE1NH5OF32SnJcVOgndP2xhD5PpXFM3NkAf/6f/MNebqCx6lcf/p0KJmurTHFPSs+nfRddhuFflfWJIbDenFtZUInklRaGt/zfWqSxt6UyKyqAs46chgnTFDZaLoLqzfXWmc47TYqCkyXlt6zLs5x4XP17xU8siIPtx3GaBlvs6oKyPc598v26g1CyybSe/cOmwrU91eerqCTbH/Itiv4XHaGZVjhg4mKAi9lvs8XicDgKfx5Qoj7gRXa/8HNNTvEKNPcD3qPuGI/15b5gJ4ypYwPtjczLM+Dz61erlAsZVgkLrsk3+ekI5rMmuG10O9i/b52HHbB+NKA4TLaqg2Iy4TNZrqe9HxxfaR2boZF0tlNMbFcKYkR+V5jP30CQJ0Mv33aJJYuzS4jXFXk00YSq3YLtDTeZEr2+nLefPJ4zp9Zgc0mDNLZ3hgyrIy+otDvYldzGCFUemepT/CFo4Zz6hE9Z6DrRFKa69aUnulKKs3tu1upJMPVV5TTP9n9bgcPXDrT+K1bJMN6yWTqCrdpI/91TB2RlzUbc19x9lHDcTRsMjLVZowsYPX3Fve7na6gJ3IMFAGPg3giOWC3kRDCiGsMNoT4/FkjMEgWiZRyDvBToBW4EDXv1mcWul9d99Hryqk5pAYRBTICYnqQuDzPi1/rlYViSTpiSaOXNjzPyxEj8rJ8tEV+lwq2hxNZFkl7NEmhv3uFp5OYHuDPcTsNeUd36q1P1wLX0yvzcdht5LgdxrxNPRGC22FnYnku4zVCy/c5aY0kCMaSBjl0hwK/ywik6+fUFIr3ul9n6MRjDoQT/PqSGT1OXQ+K/FRMwWPs73bYKPK7+uUjz/U6DF99ZvzoQGBaJP1XbmdMG8YCzbIB+Mn5R/K7K2b1ux0hRI+VKYcCCv1uyv3qmre2tvLQQw8BsGPHDqZOnTroxzvQdocNG7bfsh/84Af87Gc/63L71157jSuuuKLfx/nFL37BEUccwdSpU7nkkkuIRs2Boi+//DITJ05k3Lhx3HPPPfstP+qoo7KWDxSD5iSUUtZIKZ+TUn7vs54GXJphkbgcNvJ9Tuw2YVoBGUq4qsjPNxdN4IJZFUaeekib2dSvWSh3nzeNe86blnWMAr+a3E25ypzkZ7RZ1EPvXSexvdrMvAGPw+jpdiaSkoCbj/5rEUdrg+LyvE7TIunBtQTw9+vm8t2zphj76bP+6kkAfUEmefQ3Y6ZYswL6a8m4HCqVWid/3RUzLL9/SlwNxHNlyXKg0C3G3mI0fYGa2mZoBmQHE5lE0ldIKUl3Kn41FFBdXW0Utuor9uzZw/33389HH33E2rVrSaVSPPbYY4BZ2Oqll15i3bp1RgGrzOVDqbBVtxBCXANsl1IuPRjtH2roPdD2aJKSgHKR5LgdWco7EzcvMscD+F12wjE1ILHQr1xNmS4tHZkKUlkk5u/OMZJM6KNj97ZGsAnlD14woYQffXEqx47df4Bb9r4Ow8rK7cVFlVmIK5MQ+uN3ziSPA7VICg9gxO5Dl83Mur4LJ5bsNxK9LyjOcbOvLTpgi2RUkY+rjx3Vq1tuKOKll16itra29w37gfLyck4//fQet7n99tvZulUVtho/fjypVIqvfOUrvPvuu4wYoQpQeb1eduzYwemnn86JJ57Ie++9x7PPPsuyZcu4//77icfjzJ07l4ceeohoNMqFF15ITU0NqVSK7373u8ydO7fbdgF+/vOf86c//QmA6667jm984xtZMt5111385S9/obKykpKSEmbN6tpSrK6u5pprriEWi3HDDTcwfPhw7rrrrl5dZMlkkkgkgtPpJBwOGzP5Ll++nHHjVAErwChgtXDhQmP5UCps1RP+BQzs7RrCcDlsWa4VQCMSPS7RvTL1uR2mRdLDiNxMqyPf68xS0H2zSNTEffqgsMvnVfXqW871Oo1RyJ8GIXi1aSUA8vthyQCGe6+/Fgko4s5Mj/3hOVP59mmT+t2ObokUDZBIHHYbPzj7iP2SISx0j3vuuYexY8eyevVq7r33XjZv3sxNN93EJ598Qn5+Pk899ZSx7caNG7nyyitZtWoV4XCYxx9/nHfeeYfVq1djt9t55JFHePnllxk+fDjV1dWsXbuW0047DaDbdlesWMGf//xnPvjgA95//31+//vfs2rVKuOYK1as4LHHHmPVqlU8/fTTfPjhh92eS3V1NaWlpZx66qksWrSIH//4xwghmD9/PtOnT9/v/7XXXmPEiBHceuutjBw5kmHDhpGXl8fixSqmtWfPHiq7KGDV3fLBwKBZJEIIl5QyDiClrEeVzv3MojTgpjkUzyKSGiNQ3b1S9LvsakBiPImvh15wZ4vE5bCpfeOpHpWnLk9de7RfWUiZ+0Lvrq1MZBJJf1xUQggKfE7q2mP9tkgO1LU1mNAtkYG6tg5n9GY5fFoYPXo006dPB2DWrFns2LHDWFdVVcW8eaqY6+uvv86KFSuYPVvVmIlEIpSWlnLppZdy6623ctttt3HWWWcxf/58Wlpaum337bff5txzz8XvV+R/3nnnsWzZMsNFtWzZMs4991x8PtVh6W669kQiwY4dO7jkkkv43e9+xzHHHGOsW7ZsWbfn29LSwnPPPcf27dvJz8/nS1/6En/729+4/PLLu6zkKrQZkLtaPhgYTNfWfwN3AAghjpNS9rnsrhDiNOBXqJrtf5BS3tNp/ULgOWC7tuhpKeUPhRCVwF+AclRVz4ellL8a4Hn0CSUBNxtqgyaReBzGtCedXVuZ8LsdRvpvT+6ULCLRlHO+z0UoHumxB6wfOy17lqMr6OQhRP/2zXS79ZcQCnwu6tpjWTGgvsBwbR1KItFiZQO1SCwMHG63eQ/sdjuRiFnsS1f2oOIkV111FXffffd+baxYsYIXX3yRO+64g8WLF3PllVd2225XSrkz+qKk161bx+zZs2lubsZuz/ZQzJ8/n2AwuN8+P/vZzwySKylRiRbnnXce7777LpdffjkVFRVdFrDqbvlgYDBdW68IIa4XQlwG9LmbIoSwAw9q+0wBLhFCdOW0WyalnK79/1BblgT+U0o5GZgH3NTNvoOO0oCZ9QNkkUJPvXm/S02qGEmkjMFjXaGzRQJmb78n11amHP0lksxzsfUjxTKTBPL6GTTPzyDJ/mAoEMnZRw3n6yeNM2YysPDpIRAIdKlke8PJJ5/Mk08+SX29mn25ubmZnTt3snfvXnw+H5dffjm33norK1eu7LGdBQsW8OyzzxIOhwmFQjzzzDPMnz8/a/0zzzxDJBIhGAzy/PPPd9lOdXU1xx57LI899hjXXHMNdXV1xrply5axevXq/f4XLVrEyJEjef/99wmHVQXT119/ncmTJwMwe/bsLgtYdbd8MDAob4AQ4o9AGzAdeF9K+Z1+7D4H2CKl3Ka19RhwDtBrOoGUch+wT/seFEKsB0b0Zd+BQh9zkGmR6OhJgfvcdqMUqt/lUHZUF8jRymTGU2lDUetKtyfl6bCbLrBAP9xTYI4d6e9ALX17h1asqj/QLZiCfmdtHXiMZLAweVhu1vxhFj49FBUVcdxxxzF16lRDgfYFU6ZM4Uc/+hGLFy8mnU7jdDp58MEHaWtr41vf+hY2mw2n08lvfvObHtuZOXMmV199NXPmzAFUsD0z82rmzJlcdNFFTJ8+naqqqiySyUR1dTVz585lwoQJ/OQnP+HCCy/ktddew+ns+X2YO3cuF1xwATNnzsThcDBjxgyuv/56ILuwVSqV4tprrzUKWOnLE4kE11133aAVthJ9MdGydhDiu0BYSnlfp+VeYCYwG5gspbyhj+1dAJwmpbxO+30FMFdK+bWMbRYCTwE1wF7gVinlJ53aGQW8BUyVUrZ3Wnc9cD1AWVnZLD1NbiB4dUeCRzbEOWesk3PHu/jT2hhv1SQRwB9P9XU74+eDq6OsbUwRScJVU1zMLoyRk9P1lBrfXBKmJSZ5+BQfLrvgwdVRPqxNGb+7g77fvGF2/uOovqeU6uc0MmDjh8eZ8ZWOjo5uZdRx42shnDa4/6T+BYz/d22MpTVJ7jrOy4hA3w3ktJS8vCPBiZVOvA7RJxkPJYa6fNB3GfPy8hg3btynINH+SKVS+7mAhho+CzJu2bKFtra2rGUnnnjiCinl0V1tfyAWyRUoy6MzLgNKpJT7Ox97RlcasTO7rQSqpJQdQogzgGcBI6dWCJGDIppvdCYRACnlw6g5wDj66KPlwoUL+yni/git2ccjG1Zy1OTxLDx+NG93rOOtmu3kep2cdOKJ3e73YmM1H9bWADBj2hRy2jbTnTzl1csIN3Sw+GTV3pK2tWxs3WP87g7FK9+kpb6DsSNHsHDhtB63zUTTihoe2VDNiJICFi6cZyxfunRptzIax1z+Bi67rdftOmN5dANLa7ZyysJjDXdhX3FSxve+yHgoMdTlg77LuH79+kGtrtcfDHZlv4OBz4KMHo+nX2NbDiRGEpFShrtY/lfg8gNorwbILLtWgbI6DEgp26WUHdr3FwGnEKIYQAjhRJHII1LKpw/g+AeEsm5cW73FJTLnHOopRgIqFpLpZrrhhLE8fGWXHYIs6Flj/XdtObXP/vcv8r2uA6rCNmNkAUcMzz2g8SAWLFgYGjgQiyQihBimxScMSCljQojkAbT3ITBeCDEa2ANcDFyauYFWwrdOSimFEHNQBNik1UD5I7BeSvnzAzj2AWPK8FzOnDaMeWOLADPI3VvarD6aXX13kOhh2yMr8rJmTR2e782avbY7BPpIap2hk9aBTGb3tZPG9bveBKgpZPRpZCxYsHB44kCI5D7gOSHEl6SUO/WFQohSug0ddw8pZVII8TXUuBM78Ccp5SdCiP/Q1v8WuAC4USOqCHCxRirHo1xtHwshVmtNfkezWg4qfC4HD15mTrzXV+Xd2SJp62HbAxkkp2TQLZJ+pv96+0aGXeFwHJVtwYKFwUG/iURK+Q8hhA9YIYR4H1iNshC+BPzgQITQFP+LnZb9NuP7A8ADXez3Nl3HWD515Lh1t1DPSjgzPTfH7eiRSA4Uh8IisWDBwucXBzSOREr5f6gZfp8AnEAUuERK+cggynZYQY+R9Nabz4yL9DSyfSDQZQi4+0cIRX43U0fkdjn3lwULFix0hwPWZFLKIGpUuQVMS6M3K8CfQR49zbU1EOgy9Le+s8th44Wvd53vbsGCBQvd4WBN2vi5g668e3NtZRLJYFSN6wq5B+jasmDBgoUDgUUkgwQza6sXi0SzQpx2cVBqRoMacV0ScFOR7+t9YwsWDkNYha3gV7/6FVOnTuWII47gl7/8Zda6w7aw1ecd5bkerl8wptdUVt0KOVjWCMDRowr58M5F/Z73yoKFwwWf98JWa9eu5fe//z3Lly+nurqaF154gc2bNwOfocJWn0fYbILvnNH7nD/6OJKDFR+xYOHTxKZN/0OwY/2gthnImcyECd/tcZvPe2Gr9evXM2/ePGOa+hNOOIFnnnmGb3/725+pwlYWuoEeIzlYGVsWLHwe8HkvbDV16lTeeustmpqaCIfDvPjii8YU8Yd1YSsLfYNfc2n5LSKx8BlAb5bDp4XPW2ErgNtuu41TTjmFnJwcjjrqKBwOpVMO98JWFvoAj9OGTViuLQsWBhOft8JWixYt4stf/jJf/vKXAfjOd75DRUUFwGFf2MpCHyCEwO9yHNRguwULn3V83gtbAcY57Nq1i6effppLLrkEOIwLW1noH3xue68z/1qwYKF7fN4LWwGcf/75NDU1GedQUFAAHJrCVkgpP1f/s2bNkocajy/fJd/f2iillHLJkiWHVpg+wJJx4Bjq8knZdxnXrVt3cAXpAe3t7Yfs2H3FZ0HGru4x8JHsRq9aFskhwIWzK3vfyIIFCxYOE1gxEgsWLFiwMCBYRGLBgoV+Q/Yha8nC4YkDubcWkViwYKFf8Hg8NDU1WWTyGYSUkqamJjweT7/2s2IkFixY6BcqKiqoqamhoaHhUz92NBrtt5L7tHG4y+jxeIwxKX3FkCASIcRpwK9QpXb/IKW8p9P6hcBzwHZt0dNSyh/2ZV8LFiwMLpxOJ6NHjz4kx166dGm/Jzj8tPF5lPGQE4kQwg48CJwC1AAfCiH+KaXsPC3lMinlWQe4rwULFixYOEgYCjGSOcAWKeU2KWUceAw451PY14IFCxYsDAIOuUUCjAB2Z/yuAeZ2sd0xQohqYC9wq5Tyk77uK4S4HrgeoKysjKVLlw6O5IOAjo6OISVPV7BkHDiGunxgyThY+DzKOBSIpKuZzTqng6wEqqSUHUKIM4BngfF93Bcp5cPAwwBCiIYTTzxx54AkHlwUA42HWoheYMk4cAx1+cCScbDwWZWxqrsVQ4FIaoDMod4VKKvDgJSyPeP7i0KIh4QQxX3ZtzOklCUDlngQIYT4SEp59KGWoydYMg4cQ10+sGQcLHweZRwKMZIPgfFCiNFCCBdwMfDPzA2EEOVCm5NZCDEHJXdTX/a1YMGCBQsHF4fcIpFSJoUQXwNeQaXw/klK+YkQ4j+09b8FLgBuFEIkgQhwsTaJWJf7HpITsWDBgoXPKQ45kYByVwEvdlr224zvDwAP9HXfwwwPH2oB+gBLxoFjqMsHloyDhc+djMKa5sCCBQsWLAwEQyFGYsGCBQsWDmNYRGLBggULFgYEi0g+RQgh8oUQTwohNggh1gshjhFCFAohXhVCbNY+Cw6xjN8UQnwihFgrhHhUCOE51DIKIf4khKgXQqzNWNatTEKIO4QQW4QQG4UQpx5CGe/V7vUaIcQzQoj8oSZjxrpbhRBSS6sfcjIKIb6uyfGJEOKnQ01GIcR0IcT7QojVQoiPtOzSQyKjEKJSCLFE0zGfCCFu1pYfvHemu9KJ1v/g/wP/B1ynfXcB+cBPgdu1ZbcDPzmE8o1ATYzp1X4/AVx9qGUEFgAzgbUZy7qUCZgCVANuYDSwFbAfIhkXAw7t+0+Gooza8kpU5uNOoHioyQicCLwGuLXfpUNQxn8Dp2vfzwCWHioZgWHATO17ANikyXHQ3hnLIvmUIITIRT2AfwSQUsallK2oucH+T9vs/4AvHgr5MuAAvEIIB+BDDfA8pDJKKd8Cmjst7k6mc4DHpJQxKeV2YAtqTrZPXUYp5b+llEnt5/uoAbNDSkYNvwC+TfasEENJxhuBe6SUMW2b+iEoowRyte95mAOjP3UZpZT7pJQrte9BYD2qk3jQ3hmLSD49jAEagD8LIVYJIf4ghPADZVLKfaAeAKD0UAkopdwD/AzYBewD2qSU/x5KMmagO5m6mn9txKcsW1e4FnhJ+z5kZBRCnA3skVJWd1o1ZGQEJgDzhRAfCCHeFELM1pYPJRm/AdwrhNiNeofu0JYfUhmFEKOAGcAHHMR3xiKSTw8OlDn8GynlDCCEMi+HDDSf6Tko83Y44BdCXH5opeo3+jT/2qcJIcSdQBJ4RF/UxWafuoxCCB9wJ/C9rlZ3sexQXUcHUADMA74FPKHNdDGUZLwR+KaUshL4JprngUMooxAiB3gK+IbMmGaqq027WNYvGS0i+fRQA9RIKT/Qfj+JIpY6IcQwAO2zvpv9Pw0sArZLKRuklAngaeDYISajju5k6vf8awcTQoirgLOAy6TmkGboyDgW1WmoFkLs0ORYKYQoZ+jIiCbL01JhOZBGTTo4lGS8CvW+APwD0zV0SGQUQjhRJPKIlFKX66C9MxaRfEqQUtYCu4UQE7VFJwPrUHODXaUtuwpVCfJQYRcwTwjh03p8J6P8q0NJRh3dyfRP4GIhhFsIMRo1S/TyQyCfXr3zNuBsKWU4Y9WQkFFK+bGUslRKOUpKOQqlUGZqz+qQkFHDs8BJAEKICahElcYhJuNe4ATt+0nAZu37py6j9u7+EVgvpfx5xqqD984c7AwH6z8rm2I68BGwBvVyFABFwOuoB+91oPAQy/jfwAZgLfBXVCbHIZUReBQVs0mglN2Xe5IJ5a7ZCmxEy6Q5RDJuQfmeV2v/vx1qMnZavwMta2soyYgijr9pz+RK4KQhKOPxwApU9tMHwKxDJaMmi9T0jP7snXEw3xlrihQLFixYsDAgWK4tCxYsWLAwIFhEYsGCBQsWBgSLSCxYsGDBwoBgEYkFCxYsWBgQLCKxYMGCBQsDgkUkFixYsGBhQLCIxIIFCxYsDAgWkViwMEAIIX4ghLj1UMsBIIS4QQixT6uLUS2E+Ic2WtmChYMGi0gsWBgCEAqD8T4eCXxPSjldSnkUagTz09q0GRYsHBRYRGLBwgFACHGnVk3uNWBixvLLhRDLNYvgd0IIu7b8u0JVS3xVqMqTtwohRmlV7B5CTf1R2d3+PbXdCdNQU4kAIKX8LVBO9qR8FiwMKiwisWChnxBCzAIuRtV5OA+YrS2fDFwEHCelnA6kgMuEEEcD52dsf3RGcxOBv0hVWsDX1f49td2FeFOBTzoti6DmdbNg4aDAcagFsGDhMMR84BmpzegrhPintvxkYBbwoeZJ8qKm6i4EnpNSRrTtn89oa6eU8v1e9u9tHVq7lUBQZtSe0KYTHwZsG/BZW7DQDSwisWDhwNDVbKcC+D8p5R1ZC4X4Zg/thHrbvw/rdBzJ/tbINcAbUpVctWDhoMBybVmw0H+8BZwrhPAKIQLAF7TlrwMXCCFKAYQQhUKIKuBt4AtCCI9Wte7Mbtrtbv/e1unIio8IIRajSr4OiYwyC59dWBaJBQv9hJRypRDicVSdh53AMm35OiHEfwH/1jKwEsBNUsr3NfdXtbb9R0BbF+12uT/K/dXtuowmpgELhRAnoyyY9cBpUsqNg38VLFgwYdUjsWDhU4AQIkdK2aHVSX8LuF5KufJQy2XBwmDAskgsWPh08LAQYgrgQcU6LBKx8JmBZZFYsGDBgoUBwQq2W7BgwYKFAcEiEgsWLFiwMCBYRGLBggULFgYEi0gsWLBgwcKAYBGJBQsWLFgYECwisWDBggULA4JFJBYsWLBgYUD4/zt0yWQ9YjePAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "inps = range(50, 200)\n", "for k in range(100, 1000, 100):\n", " plt.plot(inps, [get_max(D, k)*D**0.5 for D in inps],label=\"threshold $k$=\" + str(k))\n", "plt.grid()\n", "plt.legend()\n", "plt.title(\"Performance on Max $k$XOR\")\n", "plt.xlabel(\"degree $D$\")\n", "plt.ylabel(\"$C_{k,D}$: performance is $1/2 + C_{k,D}/\\sqrt{D}$\")" ] }, { "cell_type": "markdown", "id": "903b0e50", "metadata": {}, "source": [ "What about the optimal threshold?" ] }, { "cell_type": "code", "execution_count": 38, "id": "45104b00", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'a: threshold is $D/2 + a/\\\\sqrt{D}$')" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "inps = range(50, 500)\n", "for k in range(2,10):\n", " plt.plot(inps, [abs(get_argmax(D, k) - D/2)/D**0.5 for D in inps], label='$k$=' + str(k))\n", "plt.grid()\n", "plt.legend()\n", "plt.title(\"Optimal threshold for Max $k$XOR\")\n", "plt.xlabel(\"degree $D$\")\n", "plt.ylabel(\"a: threshold is $D/2 + a/\\sqrt{D}$\")" ] }, { "cell_type": "markdown", "id": "1bcc26f7", "metadata": {}, "source": [ "### Large degree approximation" ] }, { "cell_type": "code", "execution_count": 39, "id": "2e84c9cc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "alpha (k=2): -0.4384483844838448\n", "improvement*rtD: 0.33648925802613555\n", "alpha (k=3): -0.5661056610566105\n", "improvement*rtD: 0.34753464968074316\n", "alpha (k=4): -0.6461164611646116\n", "improvement*rtD: 0.35948123367974816\n", "alpha (k=5): -0.7040770407704077\n", "improvement*rtD: 0.37007481521513996\n", "alpha (k=6): -0.7493114931149312\n", "improvement*rtD: 0.37934716987803424\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f(alpha):\n", " return -erf(2**0.5 * alpha)\n", "\n", "def grtD(alpha):\n", " return (2/np.pi)**0.5 * np.e**(-2*alpha*alpha)\n", "\n", "def large_degree_improvement(alpha, k):\n", " return f(alpha)**k * (k/2) * (-2*alpha)/(k-1)\n", "\n", "inps = np.linspace(-1, -0.1, 100000)\n", "plt.plot(inps, [grtD(i)/f(i) for i in inps])\n", "for k in range(2, 7):\n", " plt.plot(inps, -2*inps/(k-1), label='$k$=' + str(k))\n", " alpha = inps[[(grtD(i)/f(i)+2*i/(k-1) > 0) for i in inps]][0]\n", " print('alpha (k=' + str(k) + '):', alpha)\n", " print('improvement*rtD:', large_degree_improvement(alpha, k))\n", "plt.legend()\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "a38f698e", "metadata": {}, "source": [ "We can use SciPy to find the optimal threshold and value." ] }, { "cell_type": "code", "execution_count": 40, "id": "320caecf", "metadata": {}, "outputs": [], "source": [ "fmaker = lambda k: lambda i: abs(grtD(i)/f(i)+2*i/(k-1))" ] }, { "cell_type": "code", "execution_count": 41, "id": "1a500269", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for k in [2,3,4]:\n", " plt.plot(inps, fmaker(k)(inps), label='$k$=' + str(k))\n", "plt.xlabel(\"alpha\")\n", "plt.ylabel(\"difference (optimal at zero)\")\n", "plt.grid()\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 42, "id": "e30a2247", "metadata": {}, "outputs": [], "source": [ "ks = range(2, 200)\n", "best_alphas = [minimize(fmaker(k), -1, method='Nelder-Mead', options={\"ftol\":1e-10}).x[0] for k in ks]\n", "best_threshold_perf = [large_degree_improvement(a, k) for a,k in zip(best_alphas, ks)]" ] }, { "cell_type": "code", "execution_count": 43, "id": "e75241c9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k: 2 alpha: -0.4384504927322263 perf: 0.33649336434608373\n", "k: 3 alpha: -0.566110652685165 perf: 0.34754360662427763\n", "k: 4 alpha: -0.646119719278067 perf: 0.35948708249696404\n", "k: 5 alpha: -0.7040850546211003 perf: 0.37008946845499674\n", "k: 6 alpha: -0.7493118736892935 perf: 0.37934788180340984\n", "k: 7 alpha: -0.7862569719552992 perf: 0.3874867747324553\n", "k: 8 alpha: -0.817399865761399 perf: 0.39471621046350674\n", "k: 9 alpha: -0.8442601535469293 perf: 0.40120335548614106\n", "k: 10 alpha: -0.8678350865840913 perf: 0.4070774997450675\n", "k: 11 alpha: -0.8888135105371475 perf: 0.4124388540093239\n", "k: 12 alpha: -0.9076905906200408 perf: 0.41736591797938943\n", "k: 13 alpha: -0.924833858758211 perf: 0.4219210415038646\n", "k: 14 alpha: -0.9405233614146706 perf: 0.4261543840769254\n", "k: 15 alpha: -0.9549772322177886 perf: 0.43010682728185895\n", "k: 16 alpha: -0.9683685787022114 perf: 0.43381207871486654\n", "k: 17 alpha: -0.9808370001614093 perf: 0.4372982310985033\n", "k: 18 alpha: -0.9924966532737016 perf: 0.4405889197979946\n", "k: 19 alpha: -1.0034420400857929 perf: 0.44370420750299183\n" ] } ], "source": [ "for i in range(18):\n", " print(\"k:\", ks[i], \"alpha:\", best_alphas[i], \"perf:\", best_threshold_perf[i])" ] }, { "cell_type": "code", "execution_count": 44, "id": "2a6db7b6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Best asymptotic performance of threshold algorithm for Max $k$XOR')" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(ks, best_threshold_perf)\n", "plt.grid()\n", "plt.xlabel(\"$k$\")\n", "plt.ylabel(\"$C_{k}$: performance is $1/2 + C_{k}/\\sqrt{D}$\")\n", "plt.title(\"Best asymptotic performance of threshold algorithm for Max $k$XOR\")" ] }, { "cell_type": "markdown", "id": "c66a4c08", "metadata": {}, "source": [ "Comparing the expression with its large-degree asymptotic form:" ] }, { "cell_type": "code", "execution_count": 45, "id": "799e0ad7", "metadata": {}, "outputs": [], "source": [ "@lru_cache(maxsize=int(1e7))\n", "def long_range_improvement(D, t, k):\n", " alpha = (t - D/2)*D**-0.5\n", " val_delta = (2/np.pi/D)**0.5 * np.e**(-2*alpha*alpha)\n", " val_g = 0.5 + 0.5*erf(2**0.5 * alpha) + 0.5 * val_delta\n", " return 0.25 * ( (1-2*val_g + 2*val_delta)**k - (1 - 2*val_g)**k )" ] }, { "cell_type": "code", "execution_count": 46, "id": "29bd461a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'asymptotic (large-degree) vs generic performance of threshold algorithm; $D$=1000')" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "D = 1000\n", "k = 8\n", "inps = np.array(list(range(-1, D+2)))\n", "plt.plot((inps/D - 1/2)*D**0.5, [long_range_improvement(D, t, k)*D**0.5 for t in inps], label='asymptotic')\n", "plt.plot((inps/D - 1/2)*D**0.5, [general_improvement(D, t, k)*D**0.5 for t in inps], label='generic')\n", "plt.xlim(-2, 2)\n", "plt.grid()\n", "plt.xlabel(\"$a$: threshold is $D/2 + a/\\sqrt{D}$\")\n", "plt.ylabel(\"$C_{k}$: performance is $1/2 + C_{k}/\\sqrt{D}$\")\n", "plt.legend()\n", "plt.title(\"asymptotic (large-degree) vs generic performance of threshold algorithm; $D$=\" +str(D))" ] }, { "cell_type": "markdown", "id": "528c69fe", "metadata": {}, "source": [ "# QAOA for Max $k$XOR" ] }, { "cell_type": "markdown", "id": "97e97ee6", "metadata": {}, "source": [ "We have a relationship from $\\gamma$ to $\\beta$. So let's plot performance as a single-variable function:" ] }, { "cell_type": "code", "execution_count": 47, "id": "7601cbf1", "metadata": {}, "outputs": [], "source": [ "# @lru_cache(maxsize=int(1e7))\n", "def gamma_from_beta(b, k, D):\n", " return atan( ((tan(2*b)**(-2) + 1)/k/D)**0.5 )" ] }, { "cell_type": "code", "execution_count": 48, "id": "b825a5b3", "metadata": {}, "outputs": [], "source": [ "def f(b, k, D):\n", " p, q = cos(2*b), sin(2*b)\n", " g = gamma_from_beta(b, k, D)\n", " c, s = cos(g), sin(g)\n", " return -0.25*s*1j*( (p + 1j*q*c**D)**k - (p - 1j*q*c**D)**k )" ] }, { "cell_type": "code", "execution_count": 49, "id": "ceeabd1f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k: 3 D: 2 beta/pi: 0.09113411341134134 gamma: 0.6457133550969802 perf: 0.29410412861806556\n", "k: 3 D: 5 beta/pi: 0.09178417841784199 gamma: 0.4422524799948612 perf: 0.3146569554910147\n", "k: 3 D: 10 beta/pi: 0.09203420342034223 gamma: 0.3223806563933743 perf: 0.32268419004512405\n", "k: 3 D: 20 beta/pi: 0.09215921592159236 gamma: 0.23167755729751552 perf: 0.32697175492210245\n", "k: 3 D: 100 beta/pi: 0.09228422842284248 gamma: 0.10498972786802262 perf: 0.33054742740112547\n", "k: 3 D: 500 beta/pi: 0.09230923092309251 gamma: 0.04707999959190555 perf: 0.33127896219847697\n", "k: 3 D: 1000 beta/pi: 0.09230923092309251 gamma: 0.033302887938561315 perf: 0.33137080088961723\n", "k: 3 D: 10000 beta/pi: 0.09230923092309251 gamma: 0.010534803199471842 perf: 0.3314535299965894\n", "k: 4 D: 2 beta/pi: 0.07350735073507372 gamma: 0.6707077469306936 perf: 0.31273335595182417\n", "k: 4 D: 5 beta/pi: 0.0744824482448247 gamma: 0.460203752247109 perf: 0.33641563218166026\n", "k: 4 D: 10 beta/pi: 0.07485748574857508 gamma: 0.33568475060518954 perf: 0.34572486409324354\n", "k: 4 D: 20 beta/pi: 0.07505750575057528 gamma: 0.2412987329831272 perf: 0.35071041090831745\n", "k: 4 D: 100 beta/pi: 0.07523252325232545 gamma: 0.10938136825980022 perf: 0.3548750224898438\n", "k: 4 D: 500 beta/pi: 0.07525752575257547 gamma: 0.04905838095594313 perf: 0.35572784016109366\n", "k: 4 D: 1000 beta/pi: 0.07525752575257547 gamma: 0.034703431880728046 perf: 0.35583491989138766\n", "k: 4 D: 10000 beta/pi: 0.07525752575257547 gamma: 0.010978155318363525 perf: 0.3559313779605138\n", "k: 5 D: 2 beta/pi: 0.06238123812381262 gamma: 0.6914843004927927 perf: 0.3281876209826412\n", "k: 5 D: 5 beta/pi: 0.06355635563556379 gamma: 0.4750964091162255 perf: 0.3546963040752536\n", "k: 5 D: 10 beta/pi: 0.06398139813981421 gamma: 0.3468346065582889 perf: 0.36517453657251486\n", "k: 5 D: 20 beta/pi: 0.06423142314231446 gamma: 0.2493408953847929 perf: 0.370799005813208\n", "k: 5 D: 100 beta/pi: 0.06443144314431466 gamma: 0.11306015754691891 perf: 0.3755040521630587\n", "k: 5 D: 500 beta/pi: 0.06445644564456468 gamma: 0.050716447902231246 perf: 0.37646827287224693\n", "k: 5 D: 1000 beta/pi: 0.06445644564456468 gamma: 0.0358773219470221 perf: 0.37658933555084917\n", "k: 5 D: 10000 beta/pi: 0.06448144814481471 gamma: 0.011345631207865314 perf: 0.3766984221260389\n", "k: 7 D: 2 beta/pi: 0.04885488548854911 gamma: 0.7241763672015993 perf: 0.3524320255598121\n", "k: 7 D: 5 beta/pi: 0.05020502050205046 gamma: 0.49886966247200565 perf: 0.38384779513791106\n", "k: 7 D: 10 beta/pi: 0.050705070507050955 gamma: 0.364531438704665 perf: 0.39638119437081776\n", "k: 7 D: 20 beta/pi: 0.05098009800980123 gamma: 0.2622344618087329 perf: 0.4031346410999332\n", "k: 7 D: 100 beta/pi: 0.05120512051205146 gamma: 0.11896535473529471 perf: 0.40879767143215534\n", "k: 7 D: 500 beta/pi: 0.0512551255125515 gamma: 0.05335431842602078 perf: 0.4099596976860411\n", "k: 7 D: 1000 beta/pi: 0.0512551255125515 gamma: 0.0377451050228159 perf: 0.4101056478639212\n", "k: 7 D: 10000 beta/pi: 0.0512551255125515 gamma: 0.011941154273739346 perf: 0.4102371058046652\n", "k: 10 D: 2 beta/pi: 0.037803780378038075 gamma: 0.7599211884000758 perf: 0.3786286364946791\n", "k: 10 D: 5 beta/pi: 0.03922892289228949 gamma: 0.5252912290279241 perf: 0.4160734614929132\n", "k: 10 D: 10 beta/pi: 0.039778977897790044 gamma: 0.38420289214024267 perf: 0.4311762570138485\n", "k: 10 D: 20 beta/pi: 0.040079007900790345 gamma: 0.2765142408952303 perf: 0.4393511679241211\n", "k: 10 D: 100 beta/pi: 0.04030403040304057 gamma: 0.125554693219044 perf: 0.44622581933117295\n", "k: 10 D: 500 beta/pi: 0.040354035403540614 gamma: 0.0563186231943233 perf: 0.4476386226442099\n", "k: 10 D: 1000 beta/pi: 0.040379037903790646 gamma: 0.03982022411775004 perf: 0.447816050716899\n", "k: 10 D: 10000 beta/pi: 0.040379037903790646 gamma: 0.01259825382237099 perf: 0.44797610429101614\n", "k: 100 D: 2 beta/pi: 0.007475747574757784 gamma: 0.9846191191253346 perf: 0.528330274340077\n", "k: 100 D: 5 beta/pi: 0.008450845084508758 gamma: 0.7002022674161685 perf: 0.621413963206732\n", "k: 100 D: 10 beta/pi: 0.008825882588259133 gamma: 0.5184745277920191 perf: 0.6625250178308172\n", "k: 100 D: 20 beta/pi: 0.009050905090509357 gamma: 0.3748139084978714 perf: 0.6856606454079309\n", "k: 100 D: 100 beta/pi: 0.009225922592259532 gamma: 0.17092097273305687 perf: 0.7055912953067912\n", "k: 100 D: 500 beta/pi: 0.009250925092509557 gamma: 0.07683141025610506 perf: 0.7097254589486673\n", "k: 100 D: 1000 beta/pi: 0.009275927592759583 gamma: 0.05423536485283009 perf: 0.710256965197822\n", "k: 100 D: 10000 beta/pi: 0.009275927592759583 gamma: 0.017165877947379102 perf: 0.7107338122175934\n" ] }, { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for k in [3, 4, 5, 7, 10, 100]:\n", " plt.figure()\n", " Ds = [2, 5, 10, 20, 100, 500, 1000, 10000]\n", " for D in Ds:\n", " inps = np.linspace(1e-15, np.pi/4, 10000)\n", " outs = [complex(f(i, k, D)).real*D**0.5 for i in inps]\n", " plt.plot(inps/np.pi, outs, label=\"$D$=\" + str(D))\n", " print('k:', k, \"D:\", D, 'beta/pi:', inps[np.argmax(outs)]/np.pi, 'gamma:', gamma_from_beta(inps[np.argmax(outs)], k, D), 'perf:', np.max(outs))\n", " plt.title(\"QAOA for Max $k$XOR, $k$=\" + str(k))\n", " plt.grid()\n", " plt.ylabel(\"$C_{\" + str(k) + \",D}$: performance is $1/2 + C_{\" + str(k) + \",D}/\\sqrt{D}$\")\n", " plt.xlabel(\"$ beta / \\pi$\")\n", " plt.legend()" ] }, { "cell_type": "markdown", "id": "7bbabd1b", "metadata": {}, "source": [ "Find the maximum performance of QAOA for any k and D:" ] }, { "cell_type": "code", "execution_count": 50, "id": "a99a657e", "metadata": {}, "outputs": [], "source": [ "fmaker = lambda k, D: lambda i: -complex(f(i, k, D)).real*D**0.5" ] }, { "cell_type": "code", "execution_count": 51, "id": "102fc7f8", "metadata": {}, "outputs": [], "source": [ "def get_qaoa_max(k,D):\n", " # do pass to find approximate optimum\n", " inps = np.linspace(1e-15, np.pi/4, 100)\n", " outs = [complex(f(i, k, D)).real*D**0.5 for i in inps]\n", " return -minimize(fmaker(k, D), inps[np.argmax(outs)]).fun" ] }, { "cell_type": "code", "execution_count": 52, "id": "00b7ad1e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 7.26 s, sys: 15.8 ms, total: 7.28 s\n", "Wall time: 7.28 s\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%%time\n", "for k in range(2, 10):\n", " Ds = range(2, 300)\n", " qaoa_kxor = [get_qaoa_max(k,D) for D in Ds]\n", " plt.plot(Ds, qaoa_kxor, label=\"$k$=\" + str(k))\n", "plt.grid()\n", "plt.xlabel('degree $D$')\n", "plt.legend()\n", "plt.ylabel(\"$C_{k,D}$: performance is $1/2 + C_{k,D}/\\sqrt{D}$\")\n", "plt.title(\"Best QAOA performance for Max $k$XOR\")\n", "plt.savefig('images/qaoa_best_maxkxor.png', dpi=300)" ] }, { "cell_type": "markdown", "id": "0d445944", "metadata": {}, "source": [ "### Limiting behavior for QAOA on Max $k$XOR" ] }, { "cell_type": "code", "execution_count": 53, "id": "45fd9130", "metadata": {}, "outputs": [], "source": [ "def qaoa_asymptotic_kxor(k,t):\n", " if t*t*k < 1:\n", " return 0\n", " term_1 = (t*t*k - 1)**0.5 + 1j*np.e**(-t*t/2)\n", " term_2 = (t*t*k - 1)**0.5 - 1j*np.e**(-t*t/2)\n", " return -0.25*1j * t**(1-k) * k**(-k/2) * (term_1**k - term_2**k)" ] }, { "cell_type": "code", "execution_count": 54, "id": "c5d8294a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k= 2 Max: 0.30326532976533727 at t= 1.000010000100001 beta= 0.3926940817237238\n", "k= 3 Max: 0.33146272666069077 at t= 1.053510535105351 beta= 0.2900007252938392\n", "k= 4 Max: 0.3559421057897224 at t= 1.097790977909779 beta= 0.2364444875259528\n", "k= 5 Max: 0.3767105761875506 at t= 1.134771347713477 beta= 0.20254429534400661\n", "k= 6 Max: 0.3945945274726129 at t= 1.1663716637166373 beta= 0.1787938843543141\n", "k= 7 Max: 0.41025178270098717 at t= 1.1939319393193932 beta= 0.16105629649069836\n", "k= 8 Max: 0.42415677803753304 at t= 1.2183321833218332 beta= 0.14721507819709934\n", "k= 9 Max: 0.436652898412887 at t= 1.2402124021240213 beta= 0.1360585132329121\n", "k= 10 Max: 0.4479939244835788 at t= 1.2600526005260053 beta= 0.12683796844261103\n", "k= 11 Max: 0.45837176828801823 at t= 1.2781727817278172 beta= 0.1190684308018922\n", "k= 12 Max: 0.46793469585178904 at t= 1.2948529485294853 beta= 0.1124149146297139\n", "k= 13 Max: 0.4767994633283053 at t= 1.3103131031310313 beta= 0.10664016752303325\n", "k= 14 Max: 0.48505957497866997 at t= 1.3246932469324693 beta= 0.10157385452874085\n", "k= 15 Max: 0.4927910317504684 at t= 1.3381533815338154 beta= 0.09708471535533157\n", "k= 16 Max: 0.500056421040816 at t= 1.3508135081350814 beta= 0.09307340836387287\n", "k= 17 Max: 0.5069078845008667 at t= 1.3627336273362733 beta= 0.0894652652894109\n", "k= 18 Max: 0.5133893126807297 at t= 1.3739937399373994 beta= 0.08619903774779461\n", "k= 19 Max: 0.5195379937755544 at t= 1.3846938469384693 beta= 0.08322362503779358\n", "k= 20 Max: 0.5253858710444761 at t= 1.3948539485394853 beta= 0.08050154038452571\n", "k= 25 Max: 0.5509636811068565 at t= 1.4392943929439295 beta= 0.06970404853736062\n", "k= 30 Max: 0.5719838963056846 at t= 1.4758147581475813 beta= 0.06201425968054553\n", "k= 35 Max: 0.5898068021689621 at t= 1.5067750677506775 beta= 0.05620858907729072\n", "k= 40 Max: 0.6052637696458998 at t= 1.5336353363533635 beta= 0.05164048078066199\n", "k= 45 Max: 0.6188999875431959 at t= 1.5573355733557335 beta= 0.0479343674408014\n", "k= 50 Max: 0.6310922401449064 at t= 1.5785357853578537 beta= 0.04485524761360049\n", "k= 55 Max: 0.6421117416978646 at t= 1.5976959769597696 beta= 0.04224851351195602\n", "k= 60 Max: 0.6521601660819848 at t= 1.6151761517615175 beta= 0.04000718536146906\n", "k= 65 Max: 0.6613915200872363 at t= 1.6312563125631256 beta= 0.03805489178122506\n", "k= 70 Max: 0.669926043626932 at t= 1.6461164611646115 beta= 0.03633647307704454\n", "k= 75 Max: 0.6778593942828799 at t= 1.6599565995659957 beta= 0.03480915754390776\n", "k= 80 Max: 0.6852689052875331 at t= 1.6728767287672877 beta= 0.03344143529528098\n", "k= 85 Max: 0.6922179770576518 at t= 1.6849968499684997 beta= 0.03220785721108846\n", "k= 90 Max: 0.6987592263249378 at t= 1.6964169641696416 beta= 0.031088230478568527\n", "k= 95 Max: 0.704936794282571 at t= 1.7072170721707216 beta= 0.03006638535265316\n", "k= 100 Max: 0.710788070882332 at t= 1.7174371743717436 beta= 0.029129622001118922\n", "k= 105 Max: 0.716344998965084 at t= 1.7271372713727138 beta= 0.02826700946054821\n", "k= 110 Max: 0.7216350829403267 at t= 1.7363973639736396 beta= 0.0274690113931174\n", "k= 115 Max: 0.7266821696568858 at t= 1.7452374523745238 beta= 0.026728428316747342\n", "k= 120 Max: 0.7315070703718496 at t= 1.7536775367753676 beta= 0.026039100103206533\n", "k= 125 Max: 0.7361280503094398 at t= 1.7617776177761777 beta= 0.025395142091060568\n", "k= 130 Max: 0.7405612298183664 at t= 1.7695376953769537 beta= 0.024792281002654782\n", "k= 135 Max: 0.7448209028950489 at t= 1.7769977699776998 beta= 0.02422624911952744\n", "k= 140 Max: 0.7489198045223782 at t= 1.7841978419784197 beta= 0.02369329833341943\n", "k= 145 Max: 0.752869329028446 at t= 1.7911179111791118 beta= 0.023190897250129763\n", "k= 150 Max: 0.7566797084358322 at t= 1.7977979779797797 beta= 0.02271605441273773\n", "k= 155 Max: 0.7603601678121659 at t= 1.8042580425804258 beta= 0.022266351514169155\n", "k= 160 Max: 0.7639190512095958 at t= 1.8105181051810517 beta= 0.02183962849299841\n", "k= 165 Max: 0.7673639301990055 at t= 1.8165581655816558 beta= 0.02143442076825826\n", "k= 170 Max: 0.7707016962498999 at t= 1.822438224382244 beta= 0.0210484930497432\n", "k= 175 Max: 0.7739386396084962 at t= 1.8281182811828118 beta= 0.02068095205508028\n", "k= 180 Max: 0.7770805158690821 at t= 1.8336383363833637 beta= 0.02033011075323807\n", "k= 185 Max: 0.7801326069422092 at t= 1.839018390183902 beta= 0.01999465081359408\n", "k= 190 Max: 0.7830997688198661 at t= 1.8442384423844238 beta= 0.019673797821672293\n", "k= 195 Max: 0.7859864778822064 at t= 1.8493184931849318 beta= 0.019366430518416054\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, '$C_{k}$: performance is $1/2 + C_{k}/\\\\sqrt{D}$')" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "qaoa_asymptotic_maxes = []\n", "for k in range(2, 200):\n", " inps = np.linspace(0, 2, 100000)\n", " outs = [qaoa_asymptotic_kxor(k,i).real for i in inps]\n", " plt.plot(inps, outs, label=\"$k$=\" + str(k))\n", " if k < 20 or k % 5 == 0:\n", " t = inps[np.nanargmax(outs)]\n", " print(\"k=\", str(k), \"Max:\", np.nanmax(outs), \"at t=\", t, 'beta=', np.arcsin(1/t/k**0.5)/2)\n", " qaoa_asymptotic_maxes.append(np.nanmax(outs))\n", "plt.grid()\n", "plt.xlabel(\"$t$: gamma = $t/\\sqrt{D}$\")\n", "plt.ylabel(\"$C_{k}$: performance is $1/2 + C_{k}/\\sqrt{D}$\")\n", "# plt.legend()" ] }, { "cell_type": "markdown", "id": "55f50a61", "metadata": {}, "source": [ "# Comparison for Max $k$XOR" ] }, { "cell_type": "code", "execution_count": 55, "id": "dbb2a7c3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 7.64 s, sys: 208 ms, total: 7.85 s\n", "Wall time: 7.54 s\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%%time\n", "fig, axs = plt.subplots(3, 2, sharey=True, figsize=(10, 14))\n", "axs = axs.reshape(-1,)\n", "ks = [3, 4, 5, 7, 10, 20]\n", "for i in range(len(ks)):\n", " ax = axs[i]\n", " k = ks[i]\n", " Ds = range(2,300)\n", " ax.plot(Ds, [get_max(D, k)*D**0.5 for D in Ds], label='threshold')\n", " ax.plot(Ds, [get_qaoa_max(k,D) for D in Ds], label='qaoa')\n", " ax.grid()\n", " ax.set_xlabel('degree $D$')\n", " ax.legend(loc='lower right')\n", " ax.set_ylabel(\"$C_{\" + str(k) + \",D}$: performance is $1/2 + C_{\" + str(k) + \",D}/\\sqrt{D}$\")\n", " ax.set_title(\"Best performance for Max $\" + str(k) + \"$XOR\")\n", "fig.tight_layout()\n", "plt.savefig('images/comparison.png', dpi=300)" ] }, { "cell_type": "markdown", "id": "ea187ea9", "metadata": {}, "source": [ "So for $k > 4$, the QAOA does better than the threshold algorithm." ] }, { "cell_type": "markdown", "id": "2399eb63", "metadata": {}, "source": [ "This is true even in the large-degree limit." ] }, { "cell_type": "code", "execution_count": 56, "id": "1eb7694d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.7882407077057314" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max([q for q in qaoa_asymptotic_maxes if q != np.inf])" ] }, { "cell_type": "code", "execution_count": null, "id": "b3e5bd24", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 57, "id": "6432b97f", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_78203/1739955069.py:21: UserWarning: FixedFormatter should only be used together with FixedLocator\n", " ax2.set_yticklabels(ax2.get_yticks(), backgroundcolor='w', fontsize=9)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax1 = plt.subplots()\n", "ks = range(2, 200)\n", "ax1.scatter(ks[:len(best_threshold_perf)], best_threshold_perf, label='threshold', s=3)\n", "ax1.scatter(ks[:len(qaoa_asymptotic_maxes)], qaoa_asymptotic_maxes, label='qaoa', s=3)\n", "ax1.grid()\n", "ax1.set_xlabel(\"$k$\")\n", "ax1.set_ylabel(\"$C_{k}$: performance is $1/2 + C_{k}/\\sqrt{D}$\")\n", "ax1.legend(loc=0)\n", "ax1.set_title(\"Asymptotic performance of algorithms for Max $k$XOR\")\n", "\n", "# Following https://scipython.com/blog/inset-plots-in-matplotlib/\n", "ax2 = plt.axes([0,0,1,1])\n", "ip = InsetPosition(ax1, [0.69,0.095,0.25,0.3])\n", "ax2.set_axes_locator(ip)\n", "max_k_vals_inset = 8\n", "ax2.grid()\n", "ax2.scatter(ks[:max_k_vals_inset], best_threshold_perf[:max_k_vals_inset], s=30, label='threshold')\n", "ax2.scatter(ks[:max_k_vals_inset], qaoa_asymptotic_maxes[:max_k_vals_inset], s=30, label='qaoa')\n", "ax2.set_xticks(np.arange(2, max_k_vals_inset+2, 2))\n", "ax2.set_xticklabels(ax2.get_xticks(), backgroundcolor='w', fontsize=9)\n", "ax2.set_yticklabels(ax2.get_yticks(), backgroundcolor='w', fontsize=9)\n", "ax2.yaxis.set_major_formatter(StrMethodFormatter('{x:,.2f}')) # 2 decimal places\n", "\n", "plt.savefig('images/asymptotic_comparison.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 58, "id": "4efb9b73", "metadata": {}, "outputs": [], "source": [ "def logfit(x, y, deg=1):\n", " logx = np.log(x)\n", " logy = np.log(y)\n", " return np.polyfit(logx,logy,deg=deg)\n", "\n", "# poly = np.poly1d(coeffs)\n", "# yfit = lambda x: np.exp(poly(np.log(x)))\n", "# plt.loglog(inps, yfit(inps))\n", "# plt.loglog(inps, dataset)" ] }, { "cell_type": "code", "execution_count": 59, "id": "40e3d49f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.1917382 -1.23055679]\n", "[ 0.11544326 -1.15496742]\n" ] } ], "source": [ "dataset = qaoa_asymptotic_maxes\n", "inps = ks[:len(dataset)]\n", "\n", "qaoa_coeffs = logfit(inps, dataset, deg=1)\n", "print(qaoa_coeffs)\n", "\n", "dataset = best_threshold_perf\n", "inps = ks[:len(dataset)]\n", "\n", "threshold_coeffs = logfit(inps, dataset, deg=1)\n", "print(threshold_coeffs)" ] }, { "cell_type": "code", "execution_count": 60, "id": "9c9f5971", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.loglog(ks, best_threshold_perf, label='threshold')\n", "plt.loglog(ks[:len(qaoa_asymptotic_maxes)], qaoa_asymptotic_maxes, label='qaoa')\n", "plt.loglog(ks, [(np.e**threshold_coeffs[1])*k**threshold_coeffs[0] for k in ks], label='threshold fit')\n", "plt.loglog(ks, [(np.e**qaoa_coeffs[1])*k**qaoa_coeffs[0] for k in ks], label='qaoa fit')\n", "plt.legend()\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "a7fccf50", "metadata": {}, "source": [ "This suggests that QAOA's performance scales as $k^{0.2}$ and the threshold algorithm's performance scales as $k^{0.1}$." ] }, { "cell_type": "markdown", "id": "cd55f7ce", "metadata": {}, "source": [ "# Comparison with the Parisi constant (upper bound at large degree)" ] }, { "cell_type": "code", "execution_count": 61, "id": "edd09ca3", "metadata": {}, "outputs": [], "source": [ "# %%time\n", "# %run parisi.ipynb\n", "ps = range(2, 35)\n", "outs_scaled = np.array([1.0799048 , 1.15044002, 1.16740424, 1.17328777, 1.17560844,\n", " 1.17659504, 1.1770332 , 1.17723326, 1.17732629, 1.17737008,\n", " 1.17739087, 1.17740081, 1.17740557, 1.17740787, 1.17740898,\n", " 1.17740952, 1.17740978, 1.1774099 , 1.17740996, 1.17740999,\n", " 1.17741001, 1.17741002, 1.17741002, 1.17741002, 1.17741002,\n", " 1.17741002, 1.17741002, 1.17741002, 1.17741002, 1.17741002,\n", " 1.17741002, 1.17741002, 1.17741002])" ] }, { "cell_type": "code", "execution_count": 62, "id": "3727ee90", "metadata": {}, "outputs": [], "source": [ "parisi_clean_data = np.array([[p, x * p**0.5 / 2] for p,x in zip(ps, outs_scaled)])" ] }, { "cell_type": "code", "execution_count": 63, "id": "390b5919", "metadata": {}, "outputs": [], "source": [ "parisi_estimate = lambda x: (x*np.log(2)/2)**0.5" ] }, { "cell_type": "code", "execution_count": 64, "id": "f4f441b3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "size = len(parisi_clean_data)\n", "ks = np.array(list(range(2, 200)))\n", "assert np.allclose(ks[:size], parisi_clean_data[:, 0])\n", "\n", "plt.plot(ks[:len(best_threshold_perf)], best_threshold_perf, label='threshold', linewidth=3)\n", "plt.plot(ks[:len(qaoa_asymptotic_maxes)], qaoa_asymptotic_maxes, label='qaoa', linewidth=3)\n", "plt.plot(parisi_clean_data[:, 0], parisi_clean_data[:,1], label='optimal (parisi value)', color='green', linewidth=3)\n", "plt.plot(ks, parisi_estimate(ks), label='parisi limit at high $k$', color='gray', alpha=0.3, linewidth=6)\n", "\n", "plt.grid()\n", "plt.xlabel(\"$k$\")\n", "plt.ylabel(\"$C_{k}$: performance is $1/2 + C_{k}/\\sqrt{D}$\")\n", "plt.legend()\n", "plt.title(\"Upper and lower bounds for Max $k$XOR\")\n", "plt.savefig('images/parisi_comparison.png', dpi=300)" ] }, { "cell_type": "code", "execution_count": 65, "id": "45f12691", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ending time: Sat Sep 11 18:18:08 2021\n" ] } ], "source": [ "print(\"Ending time:\", time.ctime())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 5 }