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Julia/Limit of series - Experiment 1 BigFloat.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ある種の級数の極限を調べよう"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# 後でグラフを描く準備\n",
"\n",
"using PyPlot"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a = 0.8\n",
"n = 200\n"
]
},
{
"data": {
"text/plain": [
"176-element Array{Float64,1}:\n",
" 1.0 \n",
" -1.0 \n",
" 1.0 \n",
" -1.0 \n",
" 1.0 \n",
" -1.0 \n",
" 1.0 \n",
" -1.0 \n",
" 1.0 \n",
" -1.0 \n",
" 1.0 \n",
" -1.0 \n",
" 1.0 \n",
" ⋮ \n",
" 2.45898e-31 \n",
" -4.16644e-38 \n",
" 2.30161e-46 \n",
" -1.96543e-56 \n",
" 1.04663e-68 \n",
" -1.15229e-83 \n",
" 6.85088e-102\n",
" -4.30136e-124\n",
" 3.92402e-151\n",
" -4.67081e-184\n",
" 3.88087e-224\n",
" -6.42315e-273"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# パラメーター\n",
"\n",
"const a = 0.8\n",
"const n = 200\n",
"\n",
"println(\"a = $a\")\n",
"println(\"n = $n\")\n",
"\n",
"# 級数を準備\n",
"\n",
"x = 0.9999999999999999\n",
"[(-1)^k*x^(2^(k^a)) for k in 0:n if 0 < abs(x^(2^(k^a))) < 1]"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"$f(x)=x^{2^{0^{0.8}}}-x^{2^{1^{0.8}}}+x^{2^{2^{0.8}}}-x^{2^{3^{0.8}}}+\\cdots$\n"
]
},
{
"data": {
"text/plain": [
"f (generic function with 1 method)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 級数の計算 (n まで和を取る)\n",
"\n",
"ftitle = \"\\$f(x)=x^{2^{0^{$a}}}-x^{2^{1^{$a}}}+x^{2^{2^{$a}}}-x^{2^{3^{$a}}}+\\\\cdots\\$\"\n",
"println(ftitle)\n",
"\n",
"f(x::Float64) = sum([(-1)^k*x^(2^(k^a)) for k in 0:n if 0 < abs(x^(2^(k^a))) < 1])"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" "
]
},
{
"data": {
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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x00000000204AEBE0>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" 4.677026 seconds (489.59 k allocations: 27.907 MiB, 0.37% gc time)\n"
]
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.text.Text object at 0x000000002709BB38>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# x=0~1でのグラフ\n",
"\n",
"x = [linspace(0.0,0.9999999999999999,10000);]\n",
"@time plot(x, f.(x))\n",
"title(ftitle, fontsize=16)\n",
"xlabel(\"\\$x\\$\", fontsize=12)\n",
"ylabel(\"\\$f(x)\\$\", fontsize=12)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"10-element Array{Float64,1}:\n",
" 0.5\n",
" 0.5\n",
" 0.5\n",
" 0.5\n",
" 0.5\n",
" 0.5\n",
" 0.5\n",
" 0.5\n",
" 0.5\n",
" 0.5"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# x->1 で f(x)->0.5 と収束している?\n",
"\n",
"(x->f(x)).([0.9999990:0.0000001:0.9999999;])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000026AB77F0>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.text.Text object at 0x000000002BB5C0B8>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# x=1 の近くの様子\n",
"\n",
"x = [linspace(0.999,0.9999999999999999,1000);]\n",
"plot(x, f.(x))\n",
"title(ftitle, fontsize=16)\n",
"xlabel(\"\\$x\\$\", fontsize=12)\n",
"ylabel(\"\\$f(x)\\$\", fontsize=12)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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F165dmzk7IiKqDSfybQGcnZ3h7Oysf29jY4P27dvD19fXIG7hwoWYPXu2/n1ubi6ioqKwYsUKhIeH37QdR0dHAMDx48exb98+vPPOOzfEuLi4AAC2bduGCxcuYNCgQTfEuLm5AQA+//xzWFtbo3///gCAkJAQrF69Gl5eXrC0rPlX09XVVT95JTVdU58v9PHxwZtvvtk8yRARUb2xgGtFunTpYvDe3t4eANC1a1d06tRJv93Pzw/x8fEYMmQIAGDVqlVwdXVFly5dkJmZiYkTJ2Lw4MEYMGCAfp+EhAT07NkTrq6uSE5OxsSJE/Hqq6+iR48e+phPPvkE9957L+zt7bFlyxZMnToVc+fO1S/pNGHCBHz22WeIiYnBtGnT4OzsjBMnTiAxMRH//ve/YWFh0eA+nzlzBoWFhThz5gy0Wq1+dQJfX199/4mIiMwNCzi6wbFjx6DRaPTvz58/j8mTJyM/Px8eHh549tlnMWvWrBv2mTlzJgoLC+Hl5YXXX38dr776qkHM3r17ERcXhytXrsDPzw9Lly5FbGys/vMOHTpg9+7dmD59OgYMGICKigp4enri4YcfNhi92hBvvPGGwVfD1+dFa2lr4hERUevCZ+CIiIiIzAxHoRIRERGZGX6FasZ0Oh1yc3PRpk0bg5GlREREZLpEBCUlJejQoUOjHxFiAWfGcnNz0blzZ2OnQURERI2Qk5NjMIiwIVjAmbE2bdoAuPYL4ODgYORsiIiIqD6Ki4vRuXNn/XW8MVjAmbHrX5s6ODiwgCMiIjIzTXn8iYMYiIiIiMwMCzgiIiIiM8MCjoiIiMjMsIAjIiIiMjMs4IiIiIjMDAs4IiIiIjPDAo6IiIjIzLCAIyIiIjIzLOCIiIiIzAwLOCIiIiIzY7IF3OLFi+Hl5QVra2uEh4dj7969dcZv374dISEhUKvV8PX1xbJly26IWbVqFfz8/GBtbY1evXph48aNDW73+++/x4ABA9CuXTsoFAqkp6ffcIzy8nJMmDAB7dq1g729PZ588knk5+cbxBQWFmL48OFwcHCAk5MTRo8ejStXrtTjzBAREVFrZ5IF3IoVKzB58mTExcVh//79CAwMRFRUFC5cuFBj/KlTpzBw4ED07dsX6enpmDRpEp5//nls3rxZH7Nnzx7ExMRg9OjRSEtLw+DBgzF48GAcPHiwQe2Wlpaid+/eeO+992rN/9VXX8W6deuwatUq7NixA7m5uXjiiScMYoYPH45Dhw5hy5YtWL9+PX755ReMGTOmsaeMiIiIWhMxQWFhYTJhwgT9e61WKx06dJD4+Pga46dNmyb+/v4G24YNGyZRUVH699HR0TJw4ECDmPDwcBk7dmyj2j116pQAkLS0NIPtRUVFYmVlJatWrdJvO3LkiACQ5ORkERE5fPiwAJDffvtNH/PTTz+JQqGQc+fO1djHmmg0GgEgGo2m3vsQERHRzZWUV8nu4xdvybGb4/ptcnfgKisrkZqaisjISP02pVKJyMhIJCcn17hPcnKyQTwAREVFGcTfLKYx7dYkNTUVVVVVBsfx8/NDly5d9MdJTk6Gk5MT7rrrLn1MZGQklEolUlJSaj12RUUFiouLDV5ERETUvA6e0+Cpf+3Bs5/vxc+H82++gxGYXAFXUFAArVYLNzc3g+1ubm7Iy8urcZ+8vLwa44uLi1FWVlZnzPVjNqbd2nJRqVRwcnKq9Th5eXlo3769weeWlpZwdnaus634+Hg4OjrqX507d653XkRERFQ3EcE3KWcwdEkyjuaVwE5tCTcHa2OnVSOTK+CodjNnzoRGo9G/cnJyjJ0SERFRi3DpSgWmrDqA//shE2VVWoR7O+PHl+5Dr06Oxk6tRpbGTuCvXFxcYGFhccOozfz8fLi7u9e4j7u7e43xDg4OsLGxqTPm+jEb025tuVRWVqKoqMjgLtyfj+Pu7n7DgIzq6moUFhbW2ZZarYZara53LkRERHRz5zVleOKfe3BeUw4AmBrVA+P7dIVSqTByZrUzuTtwKpUKoaGh2Lp1q36bTqfD1q1bERERUeM+ERERBvEAsGXLFoP4m8U0pt2ahIaGwsrKyuA4x44dw5kzZ/THiYiIQFFREVJTU/Ux27Ztg06nQ3h4eL3bIiIiosarqNbqvzI9rylHB0drLHg6CBP6+pp08QbANEehJiYmilqtlmXLlsnhw4dlzJgx4uTkJHl5eSIiMmPGDImNjdXHZ2Vlia2trUydOlWOHDkiixcvFgsLC9m0aZM+Zvfu3WJpaSnz5s2TI0eOSFxcnFhZWUlmZma92xURuXTpkqSlpcmGDRsEgCQmJkpaWpqcP39eHzNu3Djp0qWLbNu2Tfbt2ycRERESERFh0MeHH35YgoODJSUlRXbt2iXdunWTmJiYBp0njkIlIiJqnLLKahn+2a/iOX29eE5fL/fGb5Uzl0pvS9vNcf02yQJORGTRokXSpUsXUalUEhYWJr/++qv+s+eee0769OljEJ+UlCRBQUGiUqnEx8dHEhISbjjmypUrpXv37qJSqcTf3182bNjQoHZFRBISEgTADa+4uDh9TFlZmbz44ovStm1bsbW1lSFDhhgUeCLXCsGYmBixt7cXBwcH+fvf/y4lJSUNOkcs4IiIiBqupLxKRvz7WvHWc9ZPsnTHCSm6Wnnb2m+O67dCRMRYd/+oaYqLi+Ho6AiNRgMHBwdjp0NERGTSKqt1+CblNJb+koXzmnJYWymx7O9huMen3W3Nozmu3yY3iIGIiIiouZ0rKsPfE/bi9/xry1a6O1hjSWwogjo73WRP08QCjoiIiFq0UwWlGP7Zr8jVlMPFXoVJkd3xVGgnWFtZGDu1RmMBR0RERC3WwXMajEz4DQVXKuDjaoevnw+Hh6ONsdNqMhZwRERE1OLodILvUs8i7sdDKKvSoqeHA74cHQYX+5YxnyoLOCIiImpR9p+5jLd+PIQDZzUAgAe6u+KTZ4LhYG1l5MyaDws4IiIiahGKy6vw5tpD+D7tHADAXm2Jl/r54vne3rC0MLm1C5qEBRwRERGZvdyiMvw94Tccyy+BQgEMDe2E16J6oH0b01yMvqlYwBEREZFZO5SrwahlvyG/uAKubdRYGhuKkC5tjZ3WLcUCjoiIiMzWjt8v4sWvUlFaqUW39vZI+Pvd6NTW1thp3XIs4IiIiMgsfZNyBrPWHoRWJ4jwaYclsaFwtGk5AxXqwgKOiIiIzEpltQ5vrz+Er349AwB4Irgj5j4ZAJVlyxqoUBcWcERERGQ2Dp7TYOp3GThyvhgKBTA5sjte6ucLhUJh7NRuKxZwREREZPJKK6qxcOtx/HvXKWh1AidbK3w4NBAP9XQzdmpGwQKOiIiITJaIYNPBPLy9/jDOa8oBAI8GeODNQf4tZlWFxmABR0RERCbpQkk5pn+XgaRjFwEAndra4K1B/q32rtufsYAjIiIik7PtaD6mrsrApdJKqCyUGNfHBy/29YW1lYWxUzMJLOCIiIjIZIgIFmw9jo9/Pg4A6OnhgIVPB6GbWxsjZ2ZaWMARERGRSSiv0mLadxn48UAuAGDkvV6Y8Ygf77rVgAUcERERGV3BlQq8sHwf0s4UwVKpwOzBd+LpsC7GTstksYAjIiIiozpxoQQjE37D2ctlcLSxwr9GhODeri7GTsuksYAjIiIio9lzsgDjvkxFcXk1PNvZImHk3fBxtTd2WiaPBRwREREZxXepZzHz+wxUaQWhnm3xaWwo2rXiud0aggUcERER3VaV1Tq8u+Ewvkg+DQAYGOCBD4cGcrBCA7CAIyIiotsmt6gME77Zj7QzRQCAl/v54tXI7lAqW9dapk3FAo6IiIhuORHByn05mL3+CEoqquFgbYn5w4K4qkIjsYAjIiKiWyqn8Cpmfp+JXScKAABBnZ2w8OlgdGlna+TMzBcLOCIiIroldDrB1ymnMfenoyit1EJtqcRrA3pgVG9vWPAr0yZhAUdERETNLrugFNNWZ2DvqUIAQJiXM957KgDeLnZGzqxlYAFHREREzUanEyzbk433Nx9FeZUOtioLzHjEDyPCPTlQoRmxgCMiIqJmkVN4Fa+tOoCUP+669fZ1QfwTvdDZmc+6NTcWcERERNQkIoLE33LwzvrDuFqpha3KAq8P7IlnwrpAoeBdt1uBBRwRERE1WnmVFq//cBCr958FAIR5O2PeU4EcYXqLsYAjIiKiRsnTlGPsV6k4kFMEC6UC06J64IX7ffis223AAo6IiIgaLPV0IcZ9tR8XSyrgZGuFxc+E4D5fF2On1WqwgCMiIqIGSdx7BrPWHkSVVuDn3gafxt7Fr0xvMxZwREREVC9VWh3eWX8Yy/9YhP6RO90xb2gg7NQsJ243nnEiIiK6qUtXKvDi1/v1U4RM6d8dL/Xz5ShTI2EBR0RERHU6eE6DsV+m4lxRGezV1xah738HF6E3JhZwREREVKu16ecwfXUGyqt08Haxw2fPhsK3fRtjp9XqsYAjIiKiG2h1gvc3H8XSHVkAgD7dXbEwJhiONlZGzowAFnBERET0F5qrVXglMQ07fr8IABjXpyumRvWABed3Mxks4IiIiEjvaF4xxn2ZiuxLV2FtpcR7Twbg8aCOxk6L/oIFHBEREQG49rzbjNWZKKvSoqOTDZbGhuLOjo7GTotqwAKOiIiolavS6vDuhiNYticbAHB/NxcseDoYznYq4yZGtWIBR0RE1IrlFpVhYmIafsu+DACY0LcrJvfn826mjgUcERFRKyQi+CHtHOJ+PISS8mq0UVviw+hADPB3N3ZqVA8s4IiIiFqZwtJKvP5DJn46mAcACOrshPnDguDtYmfkzKi+WMARERG1IluP5GP66kwUXKmApVKBSZHdMK5PV1haKI2dGjUACzgiIqJW4EpFNWavP4zE33IAAN3a22P+sCCOMjVTLOCIiIhauN+yCzF5ZTpyCsugUACj7/PGa1E9YG1lYezUqJFYwBEREbVQFdVafLTld3z6SxZEgI5ONpg3NBARXdsZOzVqIpP9wnvx4sXw8vKCtbU1wsPDsXfv3jrjt2/fjpCQEKjVavj6+mLZsmU3xKxatQp+fn6wtrZGr169sHHjxga3KyJ444034OHhARsbG0RGRuL48eMGMSdPnsSQIUPg6uoKBwcHREdHIz8/3yDGy8sLCoXC4DV37tx6nh0iIqK6Hc4txuOf7MbSHdeKt6dCO2HTpPtZvLUQJlnArVixApMnT0ZcXBz279+PwMBAREVF4cKFCzXGnzp1CgMHDkTfvn2Rnp6OSZMm4fnnn8fmzZv1MXv27EFMTAxGjx6NtLQ0DB48GIMHD8bBgwcb1O7777+PhQsXYsmSJUhJSYGdnR2ioqJQXl4OACgtLcWAAQOgUCiwbds27N69G5WVlXjssceg0+kM8n777bdx/vx5/evll19uztNIREStkFYn+Of2E3h88S4czStBOzsVlsaGYt7QQLSx5kL0LYaYoLCwMJkwYYL+vVarlQ4dOkh8fHyN8dOmTRN/f3+DbcOGDZOoqCj9++joaBk4cKBBTHh4uIwdO7be7ep0OnF3d5cPPvhAH1NUVCRqtVq+/fZbERHZvHmzKJVK0Wg0BjEKhUK2bNmi3+bp6Snz58+/+cmog0ajEQAGbRERUeuVXXBFnvznbvGcvl48p6+X57/4TS6WlBs7LfqL5rh+m9wduMrKSqSmpiIyMlK/TalUIjIyEsnJyTXuk5ycbBAPAFFRUQbxN4upT7unTp1CXl6eQYyjoyPCw8P1MRUVFVAoFFCr1foYa2trKJVK7Nq1y6D9uXPnol27dggODsYHH3yA6urqOs9NRUUFiouLDV5EREQighW/ncEjC3Zi3+nLsFdb4oOnAvBpbChc7NU3PwCZHZMr4AoKCqDVauHm5maw3c3NDXl5eTXuk5eXV2N8cXExysrK6oy5fsz6tHv9z7pi7rnnHtjZ2WH69Om4evUqSktL8dprr0Gr1eL8+fP6fV555RUkJiYiKSkJY8eOxZw5czBt2rQ6z018fDwcHR31r86dO9cZT0RELV9haSUf50BBAAAgAElEQVTGfpmK6aszcbVSi3BvZ/w08X4MvaszFAouh9VSmVwBZ+5cXV2xatUqrFu3Dvb29nB0dERRURFCQkKgVP7vdE+ePBkPPvggAgICMG7cOHz00UdYtGgRKioqaj32zJkzodFo9K+cnJzb0SUiIjJR249dQNTHv+C/h/NhZaHAzEf88O0L96Czs62xU6NbzOSmEXFxcYGFhcUNozbz8/Ph7l7z+mzu7u41xjs4OMDGxqbOmOvHrE+71//Mz8+Hh4eHQUxQUJD+/YABA3Dy5EkUFBTA0tISTk5OcHd3h4+PT639DgsLQ3V1NbKzs9GjR48aY9RqtcFXs0RE1DqVV2kRv/EIvkg+DeDapLwfPx0E/w6clLe1MLk7cCqVCqGhodi6dat+m06nw9atWxEREVHjPhEREQbxALBlyxaD+JvF1Kddb29vuLu7G8QUFxcjJSWlxtxcXFzg5OSEbdu24cKFCxg0aFCt/U5PT4dSqUT79u1rjSEiIjpz6SqG/HOPvngbea8X1r3cm8Vba9N8YyqaT2JioqjValm2bJkcPnxYxowZI05OTpKXlyciIjNmzJDY2Fh9fFZWltja2srUqVPlyJEjsnjxYrGwsJBNmzbpY3bv3i2WlpYyb948OXLkiMTFxYmVlZVkZmbWu10Rkblz54qTk5OsXbtWMjIy5PHHHxdvb28pKyvTx3z++eeSnJwsJ06ckC+//FKcnZ1l8uTJ+s/37Nkj8+fPl/T0dDl58qR89dVX4urqKs8++2yDzhNHoRIRtS5JR/Ml4M3N4jl9vYS+819JOppv7JSoEZrj+m2SBZyIyKJFi6RLly6iUqkkLCxMfv31V/1nzz33nPTp08cgPikpSYKCgkSlUomPj48kJCTccMyVK1dK9+7dRaVSib+/v2zYsKFB7Ypcm0pk1qxZ4ubmJmq1Wh566CE5duyYQcz06dPFzc1NrKyspFu3bvLhhx+KTqfTf56amirh4eHi6Ogo1tbW0rNnT5kzZ46UlzdsqDcLOCKi1kGr1ckn246L14xr04M8/skuyS26auy0qJGa4/qtEBEx7j1Aaqzi4mI4OjpCo9HAwcHB2OkQEdEtUFJehSkrD+C/h689ox0T1gVvDroDakuuY2qumuP6bXKDGIiIiOiaExdKMObLVGRdLIXKQom3H/fH02FdjJ0WmQAWcERERCZo08E8TFmZjtJKLTwcrfGvEaEI6uxk7LTIRLCAIyIiMiFaneCjLcewOOkkACDc2xmLh4dwRQUywAKOiIjIRBRdrcQrien45feLAIDRvb0x4xE/WFmY3KxfZGQs4IiIiEzAoVwNxn2VipzCMlhbKfHekwF4PKijsdMiE8UCjoiIyMjWpJ3DjO8zUF6lQxdnWyyNDUVPD84uQLVjAUdERGQkVVod5mw8goTd2QCAPt1dseDpIDjZqoybGJk8FnBERERGcLGkAhO+2Y+9pwoBAC/388WkyO6wUCqMnBmZAxZwREREt9n+M5cx/qtU5BdXwF5tiQ+jAxHl727stMiMsIAjIiK6jb5JOYO4Hw+iSivo6mqHpbF3wbe9vbHTIjPDAo6IiOg2KK/S4s0fDyHxtxwAwMP+7pgXHQh7NS/F1HD8rSEiIrrFcovKMP6rVBw4q4FCAUyN6oHxfbpCoeDzbtQ4LOCIiIhuoeSTl/DSN/txqbQSTrZWWPh0MB7o7mrstMjMsYAjIiK6BUQEn/6Shfc3H4NWJ7jDwwFLY0PR2dnW2KlRC8ACjoiIqJmVlFdh6qoMbDqUBwB4Irgj3h3SCzYqCyNnRi0FCzgiIqJm9Ht+CcZ9mYqsglJYWSjwxmP+GBHehc+7UbNiAUdERNRM1qafw4zVmSir0sLD0Rr/HB6C4C5tjZ0WtUAs4IiIiJqosvrakljL9mQDAHr7umDB00FoZ682bmLUYrGAIyIiaoJTBaWYlJiGA2c1AIAJfbticv8eXBKLbikWcERERI0gIli5LwdvrTuMq5VaOFhb4sPoIPS/w83YqVErwAKOiIiogS6XVmLG9xnYfCgfAHCPjzM+ig5CBycbI2dGrQULOCIiogbYefwipqw8gAslFbCyUGDKgB544X4ffmVKtxULOCIionoor9Lig83H8J9dpwAAPq52WPh0MO7s6GjkzKg1YgFHRER0E7/nl+CVb9NwNK8EADDini54/W93cGJeMhoWcERERLUQEXyxJxtzfjqKymod2tmp8N6TAYjkQAUyMhZwRERENbhQUo6pqzKw4/eLAIAHe7ji/acC0L6NtZEzI2IBR0REdIOfD+dj2uoMFJZWQm2pxP/9rSeejfDkclhkMljAERER/eFqZTVmbziCb1LOAAD83NtgYUwwuru1MXJmRIZYwBEREQHIPKvBxBVpyLpYCgB44X5vvBbVA2pLDlQg08MCjoiIWjWtTvDpL1n48L/HUK0TuDmo8eHQIPTu5mLs1IhqxQKOiIhardyiMry6Ih0ppwoBAA/7uyP+iV5oa6cycmZEdWMBR0RErdK6A7l4/YdMFJdXw1ZlgTcf88fQuzpxoAKZBRZwRETUqpSUVyFu7SF8n3YOABDY2QkLhgXBy8XOyJkR1R8LOCIiajVSTxdi0op05BSWQakAXurri5cf6gYrC6WxUyNqEBZwRETU4lVrdVi47QQ+2XYcOgE6tbXB/GFBuNvL2dipETUKCzgiImrRTl8qxcTEdKTnFAEAhgR3xFuP+8PB2srImRE1Hgs4IiJqkUQE36WexZs/HkJppRZtrC3x7pBeGBTYwdipETUZCzgiImpxNGVVeP2HTKzPOA8ACPN2xvxhQejoZGPkzIiaBws4IiJqUX7LLsSkxHScKyqDpVKBV/t3x7g+XWGh5PQg1HKwgCMiohahWqvDom0nsOiPgQqe7Wyx4OlgBHV2MnZqRM2OBRwREZm9nMKrmLQiHamnLwMAngjpiLcfvxP2al7mqGXibzYREZm1Hw/k4vXvM1FSUY02akvMHnInHg/qaOy0iG4pFnBERGSWSiuqEffjIXyXehYAENLFCQueDkZnZ1sjZ0Z067GAIyIis3PkfDEmfLMfWRdLr62o0K8bXunnC0uuqECtBAs4IiIyGyKCFb/lIO7HQ6io1sHdwRoLng5CuE87Y6dGdFuxgCMiIrNQWlGNf6w5iB/+WIS+T3dXzB8WBGc7lZEzI7r9WMAREZHJO5ZXghe/TsXJi6WwUCowZUB3jHugK5Sc241aKRZwRERkskQEq/adxRs/HkR5lQ5uDmosiglBmDcXoafWjQUcERGZpKuV1fjHDwfx/R9fmT7Q3RXzowPRzl5t5MyIjI8FHBERmZwTF65g3FepOHHhCpQKYMqAHhjfh1+ZEl1nsuOtFy9eDC8vL1hbWyM8PBx79+6tM3779u0ICQmBWq2Gr68vli1bdkPMqlWr4OfnB2tra/Tq1QsbN25scLsigjfeeAMeHh6wsbFBZGQkjh8/bhBz8uRJDBkyBK6urnBwcEB0dDTy8/MNYgoLCzF8+HA4ODjAyckJo0ePxpUrV+p5doiIWq5NB89j8OLdOHHhCtq3UeObF+7BhL6+LN6I/sQkC7gVK1Zg8uTJiIuLw/79+xEYGIioqChcuHChxvhTp05h4MCB6Nu3L9LT0zFp0iQ8//zz2Lx5sz5mz549iImJwejRo5GWlobBgwdj8ODBOHjwYIPaff/997Fw4UIsWbIEKSkpsLOzQ1RUFMrLywEApaWlGDBgABQKBbZt24bdu3ejsrISjz32GHQ6nf44w4cPx6FDh7BlyxasX78ev/zyC8aMGdPcp5KIyGxUa3WI/+kIxn21H1cqqhHm7Yz1r/TGPZwihOhGYoLCwsJkwoQJ+vdarVY6dOgg8fHxNcZPmzZN/P39DbYNGzZMoqKi9O+jo6Nl4MCBBjHh4eEyduzYerer0+nE3d1dPvjgA31MUVGRqNVq+fbbb0VEZPPmzaJUKkWj0RjEKBQK2bJli4iIHD58WADIb7/9po/56aefRKFQyLlz525ydv5Ho9EIAIO2iIjMUUFJucR8miye09eL5/T18s66Q1JZrTV2WkS3RHNcv03uDlxlZSVSU1MRGRmp36ZUKhEZGYnk5OQa90lOTjaIB4CoqCiD+JvF1KfdU6dOIS8vzyDG0dER4eHh+piKigooFAqo1f97yNba2hpKpRK7du3S5+Lk5IS77rpLHxMZGQmlUomUlJRaz01FRQWKi4sNXkRE5i49pwiPLtqFPScvwVZlgUUxwfjHo3fAiqsqENXK5P7vKCgogFarhZubm8F2Nzc35OXl1bhPXl5ejfHFxcUoKyurM+b6MevT7vU/64q55557YGdnh+nTp+Pq1asoLS3Fa6+9Bq1Wi/Pnz+uP0759e4NjWFpawtnZudY+AkB8fDwcHR31r86dO9caS0Rk6kQE36ScQfSSZJzXlMPHxQ5rJtyHxwI7GDs1IpNncgWcuXN1dcWqVauwbt062Nvbw9HREUVFRQgJCYFS2bTTPXPmTGg0Gv0rJyenmbImIrq9yqu0mL46A//3QyYqtToMuMMNa166D93d2hg7NSKzYHLTiLi4uMDCwuKGUZv5+flwd3evcR93d/ca4x0cHGBjY1NnzPVj1qfd63/m5+fDw8PDICYoKEj/fsCAATh58iQKCgpgaWkJJycnuLu7w8fHR3+cvw7IqK6uRmFhYa19BAC1Wm3w1SwRkTnKKbyKF7/ej8xzGigVwGtR16YIUSg4ypSovkzuDpxKpUJoaCi2bt2q36bT6bB161ZERETUuE9ERIRBPABs2bLFIP5mMfVp19vbG+7u7gYxxcXFSElJqTE3FxcXODk5Ydu2bbhw4QIGDRqkz6WoqAipqan62G3btkGn0yE8PLzuE0REZMZ++f0iHvtkFzLPadDW1grLR4XjxQd9WbwRNVTzjaloPomJiaJWq2XZsmVy+PBhGTNmjDg5OUleXp6IiMyYMUNiY2P18VlZWWJraytTp06VI0eOyOLFi8XCwkI2bdqkj9m9e7dYWlrKvHnz5MiRIxIXFydWVlaSmZlZ73ZFRObOnStOTk6ydu1aycjIkMcff1y8vb2lrKxMH/P5559LcnKynDhxQr788ktxdnaWyZMnG/Tx4YcfluDgYElJSZFdu3ZJt27dJCYmpkHniaNQichcaLU6+WTbcfGacW2U6WOLdsrZy1eNnRaRUTTH9dskCzgRkUWLFkmXLl1EpVJJWFiY/Prrr/rPnnvuOenTp49BfFJSkgQFBYlKpRIfHx9JSEi44ZgrV66U7t27i0qlEn9/f9mwYUOD2hW5NpXIrFmzxM3NTdRqtTz00ENy7Ngxg5jp06eLm5ubWFlZSbdu3eTDDz8UnU5nEHPp0iWJiYkRe3t7cXBwkL///e9SUlLSoHPEAo6IzIGmrFKe/+I3/RQh0787IGWV1cZOi8homuP6rRARMe49QGqs4uJiODo6QqPRwMHBwdjpEBHd4Pf8Eoz9MhWnCkqhslTi7UH+eDqsi7HTIjKq5rh+m9wgBiIiahk2ZJzH1O8O4GqlFh2dbPCvESEI6ORk7LSIWgQWcERE1KyqtTp88N9jWLojCwBwn287LHw6GO3sOYqeqLmwgCMiomZz6UoFXklMw+4TlwAAY/v4YOqAHrDkqgpEzYoFHBERNYuMs0UY/9V+nCsqg63KAh88FYiBAR4335GIGowFHBERNdnKfTn4x5qDqKzWwdvFDktjQ7mqAtEtxAKOiIgarbJah7fWHcLXKWcAAJE93fDRsEA4WFsZOTOilo0FHBERNUqephzjv05F2pkiKBTA5MjumNDXF0olV1UgutVYwBERUYOlZF3ChG/SUHClAg7WlljwdDD6+rU3dlpErQYLOCIiqjcRwbI92Xh3wxFU6wR+7m2wNDYUnu3sjJ0aUavCAo6IiOqlrFKLmd9nYE16LgBgUGAHzH2yF2xVvJQQ3W78v46IiG7q9KVSjPtqP46cL4aFUoH/+1tPjLrPCwoFn3cjMgYWcEREVKf/HsrDlFUHUFJeDRd7FT55JgT3+LQzdlpErRoLOCIiqtFfl8QK6eKExcND4OFoY+TMiIgFHBER3eBCcTle+jYNe08VAgBG3eeNGY/4QWXJJbGITAELOCIiMvBr1iW89McUIXYqC7zPJbGITA4LOCIiAgDodIKlv2Thg81HoROgh1sb/HNECLq62hs7NSL6CxZwREQEzdUqTFl1AD8fyQcAPBHcEbOH3MkpQohMFP/PJCJq5Q6e02D816nIKSyDykKJNwf5IyasM6cIITJhLOCIiFopEUHibzmI+/EQKqt16NTWBv8aHopenRyNnRoR3QQLOCKiVuhKRTX+8UOmflWFh/za46PoIDjaWhk5MyKqDxZwREStzMFzGrz8bRpOFZTCQqnAlAHdMe6BrlAq+ZUpkblgAUdE1EqICL789TRmrz+CSq0OHRytsTAmGHd5ORs7NSJqIBZwREStgKasCtO/y8CmQ3kAgMie7fHBU4Foa6cycmZE1Bgs4IiIWri0M5fx8rdpOHu5DFYWCsx4hAvRE5k7FnBERC2UTif4964svL/pGKp1gi7OtvjkmWAEdHIydmpE1ETNVsCVl5dDoVBArVY31yGJiKiRCksrMWVlOpKOXQQADAzwQPwTveBgzVGmRC1Bowu47du3Y+3atdi9ezcOHz6MsrIyAICtrS169uyJe++9F4MHD8aDDz7YXLkSEVE9/Jp1CRMT05BfXAG1pRJxj3FiXqKWRiEiUt/gqqoqLF26FB999BGys7Ph7OyMkJAQ+Pj4oG3bthARXL58GadOncL+/ftRWFgIT09PTJkyBWPHjoWVFf/l15yKi4vh6OgIjUYDBwcHY6dDREZWrdVh0bYTWLTtOHQCdHW1w+LhIfBz598PRKakOa7fDSrgPD09UVlZieeeew7R0dEICQmpMz41NRWrVq3C8uXLoVKpkJ2d3agkqWYs4IjoupzCq5i0Ih2ppy8DAJ4M6YR3BvtzLVMiE3TbC7ilS5di5MiRDX7OrbKyEgkJCRg7dmyDE6TasYAjIgBYk3YOs9YcRElFNdqoLTF7yJ14PKijsdMiolrc9gKOTAsLOKLWrbi8Cm+sOahfDusuz7aYPywInZ1tjZwZEdWlOa7fyqYkMGXKlKbsTkREjZR6uhB/W7ATa9JzYaFUYHL/7kgccw+LN6JWokkF3KJFizBkyBD9CNSanD59uilNEBHRn1RrdZi/5XcMXZKMs5fL0NnZBivHRuCVh7rB0qJJf6UTkRlp0v/tGzduxI4dO3D//fcjLy/P4LPTp09jzJgx6NGjR5MSJCKia3IKr2LYp79iwdZro0yfCO6Ija/cj1DPtsZOjYhusyYNT4qMjMSePXvw6KOP4u6778a6devQtm1bvPvuu1i+fDkUCgVGjx7dXLkSEbVaHKhARH/W5PHlfn5+2Lt3LwYOHIjevXujuroaFhYWGD9+PKZNmwYPD4/myJOIqFXiQAUiqkmTC7icnBy89957SE9PR0VFBRQKBebPn4/x48c3R35ERK1W6ulCTExMx9nLZbBQKvBKv26Y0Lcrn3UjoqY9A/f888+jW7du+M9//oMXXngB2dnZGD16NF5++WXMnTu3uXIkImpVahuoMDGSAxWI6Jom3YH7+uuv8cILL2DmzJno0KEDAODTTz9Ft27dMHPmTBw7dgyffvopl9AiIqqnv66o8ERwR7z1uD/acBF6IvqTJhVwJ0+e1BdufzZ16lR069YNI0aMQFZWFnbs2NGUZoiIWgUOVCCi+mpSAVdT8Xbd4MGDsWPHDgwaNKgpTRARtXgcqEBEDXVLVzkODQ3F3r17b2UTRERm7c8DFZQK4JWHuuGlvr581o2I6nRLCzgA6NiRt/+JiP6qWqvDJ0knsPCPSXk7O9vg42FBCPV0NnZqRGQGGvRPvJ49e2L58uWorKys9z4VFRVISEjAHXfc0eDkiIhaopzCq4hemoyPf75WvA3Rr6jA4o2I6qdBd+BGjRqFyZMnY+LEiRg0aBAiIyMREhICb29v2Npee1ajtLQUp06dwr59+/Dzzz9j3bp1UKlUmDp16i3pABGROfkh7SxmrTmEKxyoQERNoBARqW9wt27d8NFHH+HkyZNYtmwZMjMz9Z9ZWl6rBaurqwEAIoI777wTo0aNwqhRo+Dg4NDMqVNxcTEcHR2h0Wh4folMXHF5FWatOYi1HKhA1Oo1x/W7QXfgTp8+jeLiYkyaNAmTJk1Chw4dMG7cOFRXV+PSpUsAgHbt2sHPzw8RERHw9vZuVFJERC3JvuxrAxXOFV1bUWHiQ93w4oNcUYGIGq9BBVyXLl0M7rrl5eXB19cXzzzzTLMnRkRk7qq1OizcdgKfbPvzQIVghHq2NXZqRGTmGlTAjRw5EnFxccjIyMD9998PALh8+fItSYyIyJyduXQVE1ekIe1MEQCuqEBEzatBz8CJCBYvXoxly5bhwIED0Ol0AAA7Ozv4+/sjICAAvXr1QkBAAAICAuDk5HTLEic+A0dkikQEP6Sdwxtr/xioYG2J2YM5UIGI/qc5rt8NKuD+rLy8HLa2thg7dizatWuHjIwMHDhwADk5OVAoFACuzQEXGBiIdevWNSo5qhsLOCLToimrwj/WHMS6A9cGKtztdW2gQqe2HKhARP/THNfvRj9Ba21tjVGjRmHYsGGYPXs2fvzxR5w+fRqXL1/G9u3bsWDBAkRFReHixYuNOv7ixYvh5eUFa2trhIeH33RFh+3btyMkJARqtRq+vr5YtmzZDTGrVq2Cn58frK2t0atXL2zcuLHB7YoI3njjDXh4eMDGxgaRkZE4fvy4QUxeXh5iY2Ph7u4OOzs7hISEYPXq1QYxXl5eUCgUBq+5c+fW8+wQkanZe6oQf1uwE+sO5MJCqcCU/t2ROCaCxRsR3RpighITE0WlUsnnn38uhw4dkhdeeEGcnJwkPz+/xvisrCyxtbWVyZMny+HDh2XRokViYWEhmzZt0sfs3r1bLCws5P3335fDhw/LP/7xD7GyspLMzMwGtTt37lxxdHSUNWvWyIEDB2TQoEHi7e0tZWVl+pj+/fvL3XffLSkpKXLy5El55513RKlUyv79+/Uxnp6e8vbbb8v58+f1rytXrjToPGk0GgEgGo2mQfsRUfOprNbKvM1HxXvGevGcvl7uf2+b7D9daOy0iMiENcf12yQLuLCwMJkwYYL+vVarlQ4dOkh8fHyN8dOmTRN/f3+DbcOGDZOoqCj9++joaBk4cKBBTHh4uIwdO7be7ep0OnF3d5cPPvhAH1NUVCRqtVq+/fZb/TY7OztZvny5QVvOzs7y2Wef6d97enrK/Pnzaz8J9cACjsi4sguuyOOf7BLP6deKt8kr0qWkvMrYaRGRiWuO67fJTUJUWVmJ1NRUREZG6rcplUpERkYiOTm5xn2Sk5MN4gEgKirKIP5mMfVp99SpU8jLyzOIcXR0RHh4uEFb9957L1asWIHCwkLodDokJiaivLwcDz74oEH7c+fORbt27RAcHIwPPvhAPwlybSoqKlBcXGzwIiLjWJN2Dn9bsBPpOUVoY22JRTHB+DA6EPbqW77ENBHRrV/MvqEKCgqg1Wrh5uZmsN3NzQ1Hjx6tcZ+8vLwa44uLi1FWVgYbG5taY/Ly8urd7vXYuo4DACtXrsSwYcPQrl07WFpawtbWFj/88AN8fX31Ma+88gpCQkLg7OyMPXv2YObMmTh//jw++uijWs9NfHw83nrrrVo/J6Jbr7SiGm+sPYTV+88CAMK8nDH/6SB0dLIxcmZE1JqYXAHXEsyaNQtFRUX4+eef4eLigjVr1iA6Oho7d+5Er169AACTJ0/WxwcEBECtVmPMmDGIj4+HWq2u8bgzZ8402K+4uBidO3e+tZ0hIr2D5zR45ds0ZBWUQqkAXnmoG17u1w0WSoWxUyOiVsbkCjgXFxdYWFggPz/fYHt+fj7c3d1r3Mfd3b3GeAcHB9jY2NQZc/2Y9Wn3+p/5+fnw8PAwiAkKCgIAnDx5Ep988gkyMzNx5513AgACAwOxc+dOLF68GEuWLKmxD2FhYaiurkZ2djZ69OhRY4xara61uCOiW0dEkLA7G3N/OopKrQ7uDtZY8HQQwn3aGTs1ImqlTO4ZOJVKhdDQUGzdulW/TafTYevWrYiIiKhxn4iICIN4ANiyZYtB/M1i6tOut7c33N3dDWKKi4uRkpKij7l69SoAwNLSsDa2sLDQT3xck/T0dCiVSrRv377WGCK6/QpLK/HC8n14e/1hVGp1iOzphp8m3s/ijYiMq/nGVDSfxMREUavVsmzZMjl8+LCMGTNGnJycJC8vT0REZsyYIbGxsfr469OITJ06VY4cOSKLFy+ucRoRS0tLmTdvnhw5ckTi4uJqnEakrnZFrk0j4uTkJGvXrpWMjAx5/PHHDaYRqaysFF9fX7n//vslJSVFTpw4IfPmzROFQiEbNmwQEZE9e/bI/PnzJT09XU6ePClfffWVuLq6yrPPPtug88RRqES31p4TBRL27hbxnL5euv3fRlm2+5TodDpjp0VEZq7FTiMiIrJo0SLp0qWLqFQqCQsLk19//VX/2XPPPSd9+vQxiE9KSpKgoCBRqVTi4+MjCQkJNxxz5cqV0r17d1GpVOLv768vqOrbrsi1qURmzZolbm5uolar5aGHHpJjx44ZxPz+++/yxBNPSPv27cXW1lYCAgIMphVJTU2V8PBwcXR0FGtra+nZs6fMmTNHysvLG3SOWMAR3RpV1Vr5cPNR8fpjbre+85Lk4LkiY6dFRC1Ec1y/G72UFhkfl9Iian65RWWYmJiG37IvAwCi7+qENwf5w1Zlco8ME5GZao7rN/9GIiL6w+ZDeZj2XQY0ZVWwV1vi3SFchJ6ITBMLOCJq9cqrtJiz8QiWJ58GAAR2csTCmGB4trMzcmZERDVjAUdErdrpS6V48QwTNzUAACAASURBVOv9OJR7bWWTsQ/4YMqAHlBZmtwgfSIiPRZwRNRqbcg4jxmrM1BSUQ1nOxU+ig7Egz04lQ8RmT4WcETU6lRUa/Huhv99ZXq3V1ssjAmGhyOXwyIi88ACjohalTOXrmLCN/uReU4DABj/YFdM6d8dlhb8ypSIzAcLOCJqNX7KPI9p3137ytTJ1grzo4PQ149fmRKR+WEBR0QtXkW1FvEbj2LZnmwAQKhnWyyKCUYHJ35lSkTmiQUcEbVoOYVX8dI3+3Hg7LWvTMc+4IPXonrAil+ZEpEZYwFHRC3W5kN5mLrqAIrLq+FoY4WPogPxUE83Y6dFRNRkLOCIqMWprNbhvU1H8Z9dpwAAwV2c8MkzIejIr0yJqIVgAUdELUpO4VW89O3/t3fnYVHW6//A3zMMM2wOiKwaKoSoobLYF8JS60hhWVmaGpmZWVqZHrOjSSe15ZimdiqVjmUdOR4LlBb3pXIpU0RFUJQlFMwVTJFFZZ25f394nF+TqKADzwy8X9c1V80z9zyfe26UeTszzzPp2H+8BADw/D3+mNK/C0/MS0TNCgMcETUbW3POYOLyDJRW1EDvoMG8ISF4INhH6baIiCyOAY6IbJ7BKPj4x18xf8thAJe/y3ThU+Hwc3dSuDMiosbBAEdENq34YjX+mpSO7XlnAQAj7uqANx/uCp3GTuHOiIgaDwMcEdmsjOMleHlZGk6VVsLBXo1Zg7rj8bDblG6LiKjRMcARkc0REXyZegzvrMlCtcGIjm2csGhET3Tx0SvdGhFRk2CAIyKbUlFtwN9XZuLbfScBADHB3pg7JAR6B3uFOyMiajoMcERkMwrOXsRLy9KQU1gOtQp4vX8XjOkTAJVKpXRrRERNigGOiGzC94cK8dqK/SivqoWHixYLYsMRdXsbpdsiIlIEAxwRWbVagxHzvv8Vi346AgC4s0NrxA8Ph7feQeHOiIiUwwBHRFbr9/IqTEhMR0r+OQDAc3f7I+6hLvwieiJq8RjgiMgqpf1WjJe/3Ieisio4ae0w54keeLhHW6XbIiKyCgxwRGRVRAQJO49i5rps1BoFt3s649MRPRHo1Urp1oiIrAYDHBFZjYtVtZj6bSbW7D8FABjQwxfvD+4BFx1/VRER/RF/KxKRVTh85gJeWpaGvDMXoFGr8MZDXTHq7o48RQgRUR0Y4IhIceszT2Ny8n5crDbAW69D/FPhuLOju9JtERFZLQY4IlJMjcGI9zfk4PNfCgAAdwW4Y0FsODxb6RTujIjIujHAEZEizpRVYtxX+7Dn6HkAwNi+AZj8QGdoeIoQIqIbYoAjoiaXmn8O475Kx9kLVWil02DukBD07+ajdFtERDaDAY6ImoyIYPH2fLy/MRcGo6CzdyssGtET/h7OSrdGRGRTGOCIqEmUV9ZgytcHsOFgIQDg8bB2mPl4Nzhp+WuIiKih+JuTiBpdbmE5XlqWhvyzF2Fvp8L0R4LxdGR7niKEiOgmMcARUaNalXESU7/JREWNAb6uDvhkeDjC2rdWui0iIpvGAEdEjaK61oiZ67Lwn5TfAAC9O3ngo2GhaOPCU4QQEd0qBjgisrjTpRV4+ct9SD9WAgAY/5dATIwOgp2ab5kSEVkCAxwRWdSOw2cxPjEdxReroXfQ4KMnQ/GXLt5Kt0VE1KwwwBGRRRiNgn/9dAQffJ8LowB3+Oqx6OmeaN/GSenWiIiaHQY4IrplpZdq8FpyBn7MPgMAGNLzNrz7WDc42Nsp3BkRUfPEAEdEt+TQqVK8tGwfjhVfglajxrsDgzHs/9or3RYRUbPGAEdENy1573G8ufIgqmqNuK21IxY93RPd2rkq3RYRUbPHAEdEDVZZY8Dbaw4hcfdxAMB9nT3x4bBQuDlpFe6MiKhlYIAjogY5XnwJL32ZhoMny6BSAZOigzDuvkCoeYoQIqImwwBHRPW2NfcMJiZloLSiBq2d7PHxk2HoE+SpdFtERC0OAxwR3ZDBKPh4cx4WbMmDCBDi54ZPhoejnZuj0q0REbVIDHBEdF3FF6vx16R0bM87CwB4+q72mPbwHdBpeIoQIiKlMMAR0TXtP16Cl7/ch5MlFXCwV+O9x7tjUPhtSrdFRNTiMcAR0VVEBF+mHsM7a7JQbTCiYxsnLBrRE1189Eq3RkREYIAjoj+pqDbg7ysz8e2+kwCAmGBvzB0SAr2DvcKdERHRFQxwRGRScPYiXlqWhpzCcqhVwOv9u2BMnwCoVDxFCBGRNWGAIyIAwKZDhfjbiv0or6qFh4sWC2LDEXV7G6XbIiKiOqiVbuBa4uPj0bFjRzg4OCAyMhK7d+++bv22bdsQHh4OnU6HwMBAJCQkXFWTnJyMLl26wMHBAd27d8f69esbvK6IYPr06fD19YWjoyOio6ORl5dnVlNYWIgRI0bAx8cHzs7OCA8PxzfffGNWU1xcjOHDh0Ov18PNzQ2jR4/GhQsX6jkdIsupNRgxa0M2xv43DeVVtbizQ2usm9Cb4Y2IyIpZZYBbvnw5Jk2ahBkzZmDfvn0ICQlBTEwMzpw5U2d9QUEBBgwYgPvuuw8ZGRmYOHEinn/+eWzatMlUs3PnTsTGxmL06NFIT0/HY489hsceewwHDx5s0Lpz5szB/PnzsWjRIqSmpsLZ2RkxMTGorKw01TzzzDPIzc3F6tWrkZmZiUGDBmHo0KFIT0831QwfPhyHDh3CDz/8gLVr1+Lnn3/GmDFjLDlGohs6U16Jp79Ixac/5QMAnrvbH4lj7oK33kHhzoiI6LrECkVERMi4ceNM1w0Gg7Rt21ZmzZpVZ/2UKVMkODjYbNuwYcMkJibGdH3o0KEyYMAAs5rIyEgZO3Zsvdc1Go3i4+Mjc+fONdWUlJSITqeTxMRE0zZnZ2dZunSp2Vru7u6yePFiERHJysoSALJnzx7T7Rs2bBCVSiUnT568xlSuVlpaKgCktLS03vchumLn4bPS890fpMPra+WOaRtkzf76/9kjIqKbZ4nnb6t7Ba66uhppaWmIjo42bVOr1YiOjkZKSkqd90lJSTGrB4CYmBiz+hvV1GfdgoICFBYWmtW4uroiMjLSbK1evXph+fLlKC4uhtFoRFJSEiorK3HvvfeaenFzc8Odd95puk90dDTUajVSU1OvOZuqqiqUlZWZXYgaymgUxG89jOGf78LZC1UI8nbBqlfuwcM92irdGhER1ZPVBbizZ8/CYDDA29vbbLu3tzcKCwvrvE9hYWGd9WVlZaioqLhuzZV91mfdK/+9UW8rVqxATU0N2rRpA51Oh7Fjx+K7775DYGCgaT9eXl5m+9BoNHB3d7/mYwSAWbNmwdXV1XTx8/O7Zi1RXc5frMZz/9mDuZtyYRRgcPhtWDXuHgR6uSjdGhERNYDVBbjmYNq0aSgpKcGPP/6IvXv3YtKkSRg6dCgyMzNvab9xcXEoLS01XY4fP26hjqklSPvtPAbM345tub9Dp1FjzuAe+GBoCBy1/EosIiJbY3WnEfHw8ICdnR2KiorMthcVFcHHx6fO+/j4+NRZr9fr4ejoeN2aK/usz7pX/ltUVARfX1+zmtDQUADAkSNHsHDhQmRmZqJbt24AgJCQEGzfvh3x8fFYtGgRfHx8rjogo7a2FsXFxdd8jACg0+mg0+mueTtRXUQEX/xSgNkbclBrFPh7OOOT4eHo6stvVSAislVW9wqcVqtFz549sXnzZtM2o9GIzZs3Iyoqqs77REVFmdUDwA8//GBWf6Oa+qzr7+8PHx8fs5qysjKkpqaaai5dugTg8luif2RnZwej0WjqpaSkBGlpaabbt2zZAqPRiMjIyOuNh6hBSitq8OKyNPxjXTZqjYIB3X2x+pW7Gd6IiGyd5Y6psJykpCTR6XSSkJAgWVlZMmbMGHFzc5PCwkIREZk6daqMGDHCVJ+fny9OTk4yefJkyc7Olvj4eLGzs5ONGzeaanbs2CEajUbmzZsn2dnZMmPGDLG3t5fMzMx6rysiMnv2bHFzc5NVq1bJgQMHZODAgeLv7y8VFRUiIlJdXS2BgYHSu3dvSU1NlcOHD8u8efNEpVLJunXrTPvp37+/hIWFSWpqqvzyyy/SqVMniY2NbdCceBQqXU/miRLp/f4W6fD6Wgl8Y50k7CgQo9GodFtERC2eJZ6/rTLAiYgsWLBA2rdvL1qtViIiImTXrl2m20aOHCl9+/Y1q9+6dauEhoaKVquVgIAAWbJkyVX7XLFihQQFBYlWq5Xg4GCzQFWfdUUun0pk2rRp4u3tLTqdTvr16ye5ublmNb/++qsMGjRIvLy8xMnJSXr06HHVaUXOnTsnsbGx4uLiInq9XkaNGiXl5eUNmhEDHNXFaDTKsl1HpdPf10uH19dKr1mbJePYeaXbIiKi/7HE87dKRETZ1wDpZpWVlcHV1RWlpaXQ6/mWGAEXq2rxxneZWJVxCgAQ3dULHwwJhasTv4ieiMhaWOL52+oOYiCim/NrUTleWpaGI79fhJ1ahSkxnflF9EREzRQDHFEz8O2+E/j7dwdRUWOAt16HhU+F4/86uivdFhERNRIGOCIbVlljwFurDyFpz+VzAt4T6IGPngyFhwtPN0NE1JwxwBHZqMNnLuCVr/Yhp7AcKhXw136dMP4vnWCn5lumRETNHQMckQ36dt8JvLnyIC5VG9DGWYuPnwzDPZ08lG6LiIiaCAMckQ25VF2L6asO4eu0EwCAqIA2+PjJUHjpHRTujIiImhIDHJGNyCkswytfpePwmQtQq4C/9gvCK38J5FumREQtEAMckZUTESTtOY63Vh9CVa0RXq10+PjJMETd3kbp1oiISCEMcERWrLyyBm98dxBr9l8+MW/fIE/8c2gI2vAoUyKiFo0BjshKHTxZinFf7cNv5y7BTq3C5JjOGNM7AGq+ZUpE1OIxwBFZGRHBf3YexXvrc1BtMKKdmyPmx4ahZ4fWSrdGRERWggGOyIqUXqrBlG/2Y9OhIgDAA3d4Y84TPeDmpFW4MyIisiYMcERWYt+x8xj/VTpOllRAa6fGGw91wcheHfldpkREdBUGOCKFGY2Cz3/Jx5yNuag1Ctq7OyH+qXB0v81V6daIiMhKMcARKaj4YjVeW5GBrbm/AwAG9PDFrEHdoXewV7gzIiKyZgxwRApJzT+HCUnpKCqrgk6jxoxHghEb4ce3TImI6IYY4IiaWK3BiIVbD2P+5jwYBbjd0xkLnwpHV1+90q0REZGNYIAjakInSyowMSkde46eBwAMCm+Hdwd2g7OOfxWJiKj++KxB1ETWZ57G1G8OoKyyFi46DWY+3g0DQ9sp3RYREdkgBjiiRnapuhbvrs1C4u7jAIAQPzcseDIM7ds4KdwZERHZKgY4okaUdaoM4xP34cjvF6FSAS/1vR2v3h8Eezu10q0REZENY4AjagQigoSdRzHrf1+H5dVKh4+GhaJXoIfSrRERUTPAAEdkYecuVGHy1wewJecMACC6qxfmPBECd2d+HRYREVkGAxyRBf2SdxavrsjA7+VV0GrUeHNAV4y4qwPP7UZERBbFAEdkAdW1RnzwQy4++zkfIkAnLxfMjw3jud2IiKhRMMAR3aKjZy9iQlI6DpwoBQAMj2yPNwfcAUetncKdERFRc8UAR3QLvt13AtNWHsTFagNcHe3x/uAe6N/NR+m2iIiomWOAI7oJ5ZU1mLbyIFZmnAIARPi746NhoWjr5qhwZ0RE1BIwwBE1UPqx8/hrUgaOFV+CnVqFif064eX7AmGn5oEKRETUNBjgiOrJaBQs+vkI/vn9r6g1Ctq5OWJ+bCh6dnBXujUiImphGOCI6qGorBKvLs/AziPnAAAP9/DFzMe7w9XRXuHOiIioJWKAI7qBH7OKMPnr/Th/qQaO9nZ4e2AwhvS8jed2IyIixTDAEV1DZY0Bs9Zn4z8pvwEAgtvqMT82DLd7uijcGRERtXQMcER1yCsqx/jEdOQUlgMAnr/HH5P7d4ZOw3O7ERGR8hjgiP5ARPDV7mN4Z00WqmqN8HDRYt6QENzb2Uvp1oiIiEwY4Ij+p+RSNaZ+k4mNhwoBAH2CPPHBkBB4ttIp3BkREZE5BjgiALvyz+HV5Rk4XVoJezsVXu/fBc/d7Q81z+1GRERWiAGOWrRagxHzN+dh4dbDMAoQ4OGM+bFh6NbOVenWiIiIrokBjlqs48WXMHF5BtJ+Ow8AGNLzNrz1aDCcdfxrQURE1o3PVNQirT1wCnHfZqK8shatdBrMHNQdj4a0VbotIiKiemGAoxblUnUt3lp9CCv2ngAAhLd3w8dPhsHP3UnhzoiIiOqPAY5ajIMnSzEhMR35Zy9CpQJeuS8Qf+3XCRo7tdKtERERNQgDHDV7RqPg3zsKMGdjLqoNRvjoHfDhsFBE3d5G6daIiIhuCgMcNWu/l1fhb8n78dOvvwMAHrjDG+8P7oHWzlqFOyMiIrp5DHDUbP386++YtGI/zl6ogk6jxrSH78DwyPb8EnoiIrJ5DHDU7FTXGjF3Uw4Wby8AAHTxaYX5sWEI8m6lcGdERESWwQBHzUr+7xcwISkdB0+WAQCeieqANx7qCgd7fgk9ERE1Hwxw1CyICL5OO4EZqw/hUrUBrZ3sMeeJENx/h7fSrREREVkcAxzZvLLKGvz9u4NYs/8UACAqoA0+HBYKH1cHhTsjIiJqHAxwZNP2HTuPCYnpOHG+AnZqFSbdH4QX+94OO34JPRERNWMMcGSTDEbBop+O4J8//AqDUeDn7oiPnwxDePvWSrdGRETU6Kz2FPTx8fHo2LEjHBwcEBkZid27d1+3ftu2bQgPD4dOp0NgYCASEhKuqklOTkaXLl3g4OCA7t27Y/369Q1eV0Qwffp0+Pr6wtHREdHR0cjLyzPdfvToUahUqjovycnJprqOHTtedfvs2bMbOKWWqbC0Ek9/noq5m3JhMAoeDWmLdRN6M7wREVGLYZUBbvny5Zg0aRJmzJiBffv2ISQkBDExMThz5kyd9QUFBRgwYADuu+8+ZGRkYOLEiXj++eexadMmU83OnTsRGxuL0aNHIz09HY899hgee+wxHDx4sEHrzpkzB/Pnz8eiRYuQmpoKZ2dnxMTEoLKyEgDg5+eH06dPm13efvttuLi44MEHHzTr+5133jGrGz9+vCXH2Cz9mFWEBz/+GSn55+CktcO8ISH4+MlQ6B3slW6NiIio6YgVioiIkHHjxpmuGwwGadu2rcyaNavO+ilTpkhwcLDZtmHDhklMTIzp+tChQ2XAgAFmNZGRkTJ27Nh6r2s0GsXHx0fmzp1rqikpKRGdTieJiYnXfDyhoaHy3HPPmW3r0KGDfPjhh9e8T32UlpYKACktLb2l/diCiupamb4yUzq8vlY6vL5WBsz/WY6cKVe6LSIiogazxPO31b0CV11djbS0NERHR5u2qdVqREdHIyUlpc77pKSkmNUDQExMjFn9jWrqs25BQQEKCwvNalxdXREZGXnN3tLS0pCRkYHRo0dfddvs2bPRpk0bhIWFYe7cuaitra1zH1dUVVWhrKzM7NIS5BWV47H4HfhPym8AgBd6++Pbl+5GgKeLwp0REREpw+oOYjh79iwMBgO8vc3P3+Xt7Y2cnJw671NYWFhnfVlZGSoqKuDo6HjNmsLCwnqve6X2evv5sy+++AJdu3ZFr169zLZPmDAB4eHhcHd3x86dOxEXF4fTp0/jn//8Z537AYBZs2bh7bffvubtzY2IIHH3cbyz9hAqa4zwcNHig6Gh6BvkqXRrREREirK6ANecVFRU4KuvvsK0adOuum3SpEmm/+/Rowd0Oh3GjBmDWbNmQafT1bm/uLg4s/uVlZXBz8/P8o1bgZJL1Zj6TSY2HrocjPsEeeKDISHwbFX3bIiIiFoSqwtwHh4esLOzQ1FRkdn2oqIi+Pj41HkfHx+fOuv1ej0cHR2vW3Nln/VZ98p/i4qK4Ovra1YTGhp6VV9ff/01Ll26hGeeeeaGjzsiIgK1tbU4evQoOnfuXGeNTqe7ZrhrTlLzz2Hi8gycLq2EvZ0Kr/fvgufu9oea53YjIiICYIVHoWq1WvTs2RObN282bTMajdi8eTOioqLqvE9UVJRZPQD88MMPZvU3qqnPuv7+/vDx8TGrKSsrQ2pqap29ffHFF3j00Ufh6Xnjt/wyMjKgVqvh5eV1w9rmqtZgxIc//IrYxbtwurQS/h7O+Palu/F87wCGNyIioj+y3DEVlpOUlCQ6nU4SEhIkKytLxowZI25ublJYWCgiIlOnTpURI0aY6vPz88XJyUkmT54s2dnZEh8fL3Z2drJx40ZTzY4dO0Sj0ci8efMkOztbZsyYIfb29pKZmVnvdUVEZs+eLW5ubrJq1So5cOCADBw4UPz9/aWiosLsMeTl5YlKpZINGzZc9fh27twpH374oWRkZMiRI0dk2bJl4unpKc8880yD5tScjkI9XnxRBn+yw3SU6WsrMuRCZY3SbREREVmcJZ6/rTLAiYgsWLBA2rdvL1qtViIiImTXrl2m20aOHCl9+/Y1q9+6dauEhoaKVquVgIAAWbJkyVX7XLFihQQFBYlWq5Xg4GBZt25dg9YVuXwqkWnTpom3t7fodDrp16+f5ObmXrWfuLg48fPzE4PBcNVtaWlpEhkZKa6uruLg4CBdu3aV9957TyorK+s5ncuaS4Bbd+CUdJ+xUTq8vlaCp2+UleknlG6JiIio0Vji+VslIqLsa4B0s8rKyuDq6orS0lLo9Xql22mwimoD3ll7CIm7jwMAQv3cMP/JMLRv46RwZ0RERI3HEs/fVncQA7UMWafKMCEpHYfPXIBKBbzU93a8en8Q7O2s7mOZREREVocBjpqUiOA/O4/ivQ05qK41wquVDh8NC0WvQA+lWyMiIrIZDHDUZIovVmPK1/vxY/bl75bt18ULc4eEwN1Zq3BnREREtoUBjprEzsNnMXF5Bs6UV0GrUePvD3XFM1EdoFLx9CBEREQNxQBHjarWYMRHP+YhftthiAC3ezpjQWw47mhrewddEBERWQsGOGo0p0oq8NekdOw5eh4A8OT/+WH6I3fAScs/dkRERLeCz6TUKH7IKsLfkvejtKIGLjoNZg3qjkdC2irdFhERUbPAAEcWVVVrwKz1OUjYeRQA0OM2VyyIDUOHNs7KNkZERNSMMMCRxRScvYjxiftw8GQZAOD5e/wxpX8XaDU8txsREZElMcCRRazKOIk3vs3ExWoDWjvZ44OhIfhLF2+l2yIiImqWGODollyqrsVbqw9hxd4TAIAIf3d8/GQofF0dFe6MiIio+WKAo5uWU1iGV766/HVYahUw/i+dMKFfJ9ipeW43IiKixsQARw0mIvhq9zG8syYLVbVGeOt1+GhYGKJub6N0a0RERC0CAxw1SGlFDd74NhPrMk8DAO7r7Il5Q0LQxkWncGdEREQtBwMc1Vv6sfMYn5iOE+croFGr8Hr/Lhh9jz/UfMuUiIioSTHA0Q0ZjYLF2/Mxd1Muao0CP3dHLIgNR6ifm9KtERERtUgMcHRd5y5U4bXk/diW+zsAYEAPX8wa1B16B3uFOyMiImq5GODomnYeOYuJSRk4U14FnUaNGY8EIzbCDyoV3zIlIiJSEgMcXaXWYMT8LYexYEseRIBALxcsfCoMXXz0SrdGREREYICjP6kxGPH056lILSgGAAy70w8zHr0DTlr+USEiIrIWfFYmM/Z2anRv54pDp8ow8/FuGBjaTumWiIiI6E9UIiJKN0E3p6ysDK6urigtLYVeb7m3N6trjSgqq4Sfu5PF9klERESXWeL5W23hnqgZ0GrUDG9ERERWjAGOiIiIyMYwwBERERHZGAY4IiIiIhvDAEdERERkYxjgiIiIiGwMAxwRERGRjWGAIyIiIrIxDHBERERENoYBjoiIiMjGMMARERER2RgGOCIiIiIbwwBHREREZGMY4IiIiIhsjEbpBujmiQgAoKysTOFOiIiIqL6uPG9feR6/GQxwNqy8vBwA4Ofnp3AnRERE1FDl5eVwdXW9qfuq5FbiHynKaDTi1KlTaNWqFVQqlcX2W1ZWBj8/Pxw/fhx6vd5i+6WrcdZNg3NuGpxz0+Ccm0ZjzllEUF5ejrZt20KtvrlPs/EVOBumVqtx2223Ndr+9Xo9fzk0Ec66aXDOTYNzbhqcc9NorDnf7CtvV/AgBiIiIiIbwwBHREREZGPs3nrrrbeUboKsj52dHe69915oNHyXvbFx1k2Dc24anHPT4JybhjXPmQcxEBEREdkYvoVKREREZGMY4IiIiIhsDAMcERERkY1hgCMiIiKyMQxwNq64uBjDhw+HXq+Hm5sbRo8ejQsXLlz3PiKC6dOnw9fXF46OjoiOjkZeXp5ZTWVlJcaNG4c2bdrAxcUFgwcPRlFRUYPXnjBhAnr27AmdTofQ0NA6+zlw4AB69+4NBwcH+Pn5Yc6cOTcxicZl7XM+duwYBgwYACcnJ3h5eWHy5Mmora01q9m0aRPuuusutGrVCp6enhg8eDCOHj1680NpJM1h1iKCefPmISgoCDqdDu3atcPMmTNvYSqW1xzmfMXhw4fRqlUruLm53cQkGpetz3nbtm0YOHAgfH194ezsjNDQUHz55Ze3OJVbFx8fj44dO8LBwQGRkZHYvXv3deu3bduG8PBw6HQ6BAYGIiEh4aqa5ORkdOnSBQ4ODujevTvWr1/f4HUt9bOrFyGb1r9/fwkJCZFdu3bJ9u3bJTAwUGJjY697n9mzZ4urq6usXLlS9u/fL48++qj4+/tLRUWFqebFF18UPz8/2bx5s+zdu1fuuusu6dWrV4PXHj9+vCxcuFBGjBghISEhV/VSWloq3t7eMnz4cDl48KAkJiaKo6OjfPrpp7cwFcuz5jnX1tZKt27dJDo6WtLT02X9+vXi4eEhcXFxppr8/HzR6XQSFxcnhw8flrS0NOnTp4+EhYVZaEKWY+uzFrn8575z586yatUqyc/Pl71798r3OPfOzAAAC0FJREFU339vgelYTnOYs4hIdXW13HnnnfLggw+Kq6vrLU7F8mx9zjNnzpQ333xTduzYIYcPH5aPPvpI1Gq1rFmzxkITarikpCTRarXy73//Ww4dOiQvvPCCuLm5SVFRUZ31+fn54uTkJJMmTZKsrCxZsGCB2NnZycaNG001O3bsEDs7O5kzZ45kZWXJm2++Kfb29pKZmdmgdS31s6sPBjgblpWVJQBkz549pm0bNmwQlUolJ0+erPM+RqNRfHx8ZO7cuaZtJSUlotPpJDEx0XTd3t5ekpOTTTXZ2dkCQFJSUm5q7RkzZtQZ4D755BNp3bq1VFVVmba9/vrr0rlz5/qOodFZ+5zXr18varVaCgsLTTX/+te/RK/Xm+aanJwsGo1GDAaDqWb16tWiUqmkurr6pmdjac1h1llZWaLRaCQnJ+dWx9FomsOcr5gyZYo8/fTTsmTJEqsLcM1pzn/00EMPyahRoxoyCouKiIiQcePGma4bDAZp27atzJo1q876KVOmSHBwsNm2YcOGSUxMjOn60KFDZcCAAWY1kZGRMnbs2Hqva6mfXX3xLVQblpKSAjc3N9x5552mbdHR0VCr1UhNTa3zPgUFBSgsLER0dLRpm6urKyIjI5GSkgIASEtLQ01NjVlNly5d0L59e1PNzax9rcfQp08faLVa07aYmBjk5ubi/Pnz9d5PY7L2OaekpKB79+7w9vY21cTExKCsrAyHDh0CAPTs2RNqtRpLliyBwWBAaWkp/vvf/yI6Ohr29va3OiKLaQ6zXrNmDQICArB27Vr4+/ujY8eOeP7551FcXHyr47GY5jBnANiyZQuSk5MRHx9/K+NoNM1lzn9WWloKd3f3hozCYqqrq5GWlmb22NVqNaKjo02P/c9SUlLM6oHLj/OP9Teqqc+6lvrZ1RcDnA0rLCyEl5eX2TaNRgN3d3cUFhZe8z4AzP7CXrl+5bbCwkJotdqrPk/y55qGrn2tfurq5Y+9Ks3a51yfGfr7++P777/HG2+8AZ1OBzc3N5w4cQIrVqyo3xCaSHOYdX5+Pn777TckJydj6dKlSEhIQFpaGp544on6DaEJNIc5nzt3Ds8++ywSEhKs9gvdm8Oc/2zFihXYs2cPRo0aVfeDbmRnz56FwWC47nz+7FqPs6ysDBUVFdetubLP+qxrqZ9dfTHAWaGpU6dCpVJd95KTk6N0mzavJc25sLAQL7zwAkaOHIk9e/bgp59+glarxRNPPAFpgi9jaUmzNhqNqKqqwtKlS9G7d2/ce++9+OKLL7B161bk5uY26totac4vvPACnnrqKfTp06fJ125Jc/6jrVu3YtSoUVi8eDGCg4OVbqfFs74v9yK89tprePbZZ69bExAQAB8fH5w5c8Zse21tLYqLi+Hj41Pn/a5sLyoqgq+vr2l7UVGR6ShRHx8fVFdXo6SkxOxfCUVFRab738za1+rnz0ffXLnekP3cjOYyZx8fn6uOhPrzDOPj46HX682O8F22bBn8/PyQmpqKu+6667pzuFUtada+vr7QaDQICgoy1XTt2hXA5SP+OnfufN053IqWNOctW7Zg9erVmDdvHoDLR/8ZjUZoNBp89tlneO655647h1vRkuZ8xU8//YRHHnkEH374IZ555pnrPvbG5OHhATs7uzqfN64307rq9Xo9HB0dr1tzZZ/1WddSP7t6a9An5siqXPmQ6t69e03bNm3aVK8PyM6bN8+0rbS0tM4PWX799demmpycnDo/IFvftW90EMMfP0gfFxdnlQcxWOucr3wQ+Y9HQn366aei1+ulsrJSREQmTZokkZGRZj2eOnVKAMiOHTtuai6NoTnMetOmTQJADh8+bKrJyMgQAJKbm3vTs7Gk5jDnrKwsyczMNF3+8Y9/SKtWrSQzM1OKi4tvdUQW0RzmLCKydetWcXZ2loULF97KOCwmIiJCXnnlFdN1g8Eg7dq1u+5BDN26dTPbFhsbe9VBDA8//LBZTVRU1FUHMVxvXUv97OqLAc7G9e/fX8LCwiQ1NVV++eUX6dSp01WHqHfu3Fm+/fZb0/XZs2eLm5ubrFq1Sg4cOCADBw6s8zDn9u3by5YtW2Tv3r0SFRUlUVFRDV47Ly9P0tPTZezYsRIUFCTp6emSnp5uOsKppKREvL29ZcSIEXLw4EFJSkoSJycnqzyNiLXO+cqpAB544AHJyMiQjRs3iqenp9mpADZv3iwqlUrefvtt+fXXXyUtLU1iYmKkQ4cOcunSJUuP65bY+qwNBoOEh4dLnz59ZN++fbJ3716JjIyU+++/39KjuiW2Puc/s8ajUEVsf85btmwRJycniYuLk9OnT5su586ds/So6i0pKUl0Op0kJCRIVlaWjBkzRtzc3ExH006dOlVGjBhhqr9yGpHJkydLdna2xMfH13kaEY1GI/PmzZPs7GyZMWNGnacRud66Ipb72dUHA5yNO3funMTGxoqLi4vo9XoZNWqUlJeXm9UAkCVLlpiuG41GmTZtmnh7e4tOp5N+/fpd9cpARUWFvPzyy9K6dWtxcnKSxx9/XE6fPt3gtfv27SsArroUFBSYavbv3y/33HOP6HQ6adeuncyePdsyw7Ega5/z0aNH5cEHHxRHR0fx8PCQ1157TWpqasxqEhMTJSwsTJydncXT01MeffRRyc7OtsB0LKs5zPrkyZMyaNAgcXFxEW9vb3n22WcVfcKrS3OY8x9Za4Cz9TmPHDmyzt/hffv2tcyAbtKCBQukffv2otVqJSIiQnbt2mW6beTIkVf1t3XrVgkNDRWtVisBAQFm875ixYoVEhQUJFqtVoKDg2XdunUNWlfEcj+7+lCJNMEnmImIiIjIYngUKhEREZGNYYAjIiIisjEMcEREREQ2hgGOiIiIyMYwwBERERHZGAY4IiIiIhvDAEdERERkYxjgiIiIiCxs5syZ6NWrF5ycnMy+99RSGOCIiIiIbsK9996LhISEOm+rrq7GkCFD8NJLLzXK2ppG2SsRERFRC/b2228DwDUD3q3iK3BERERENoYBjoiIiMjGMMAREVmJkydPwsHBAc8995zZ9h9//BH29vZ49dVXFeqMiADgvffeg4uLi+myfft2vPjii2bbjh071iS9qEREmmQlIiK6oVdeeQWfffYZ8vLy0KFDB+Tk5CAqKgq9e/fGypUroVbz391ESikuLkZxcbHp+vDhwzF48GAMGjTItK1jx47QaP7/IQYJCQmYOHEiSkpKLNoLfxMQEVmRuLg4qNVqvP/++zh37hwefvhhdOzYEYmJiQxvRApzd3dHYGCg6eLo6AgvLy+zbX8Mb42JR6ESEVmRdu3a4YUXXsDixYuxb98+VFRU4KeffoKzs7PSrRFRAxw7dgzFxcU4duwYDAYDMjIyAACBgYFwcXG55f3zn3NERFbmb3/7G6qqqnDgwAGsXr0a7dq1U7olImqg6dOnIywsDDNmzMCFCxcQFhaGsLAw7N271yL752fgiIiszJgxY7B48WLY29sjNzcX/v7+SrdERFaGr8AREVmRuXPn4vPPP8fChQuh0Wgwc+ZMpVsiIivEAEdEZCVWrlyJqVOn4t1338W4ceMwZswYLF26FAUFBUq3RkRWhm+hEhFZgbS0NPTp0weDBw/G0qVLAQCnTp1CQEAAnn76aXz++ecKd0hE1oQBjohIYSdOnEBERAQCAgKwefNm6HQ6020vv/wyPv/8c34WjojMMMARERER2Rh+Bo6IiIjIxjDAEREREdkYBjgiIiIiG8MAR0RERGRjGOCIiIiIbAwDHBEREZGNYYAjIiIisjEMcEREREQ2hgGOiIiIyMYwwBERERHZGAY4IiIiIhvDAEdERERkY/4fbYpDy4g/XWUAAAAASUVORK5CYII=",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000002709BEF0>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.text.Text object at 0x000000002C16DF28>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# x=1 の近くの様子\n",
"\n",
"x = [linspace(0.9999,0.9999999999999999,1000);]\n",
"plot(x, f.(x))\n",
"title(\" \"*ftitle, fontsize=14)\n",
"xlabel(\"\\$x\\$\", fontsize=12)\n",
"ylabel(\"\\$f(x)\\$\", fontsize=12)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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OVlZWeO6557Bu3bpq96PRaFBaWoqWLVsiNDQUvXr1qjA31JUrV2BtbQ0XFxd4enritddew8yZM41q8vLy4ODgAIVCAScnJ2zcuBHDhg0zvC4iyMnJQfPmzZGZmYmuXbvi8OHD6N27N7p06YKBAwfipZdeqtCfj48PVCoVsrOzodVqqx1L586dK0wM+uabb2LLli2G+e0swebNm5GXl4fp06ff1frnzp3D+vXrMWrUKLRv376euyMiopri5MwWwtXVFa6urobndnZ2cHd3R4cOHYzqPvroI7z77ruG59nZ2YiIiMCmTZsQGhp6x/04OzsDAM6ePYsjR47gnXfeqVDj5uYGANi9ezcuX76MwYMHV6jx8PAAAKxZswa2trYYOHCg0esKhcLw3bANGzbA29sbQUFBAICgoCCkpqZWGNsftWrV6p58t6wpGD58eJ3Wb9euHd588836aYaIiO4aQx8Z8fHxMXru6OgIAGjfvj1at25tWO7n54dFixZhyJAhAICYmBi0bNkSPj4+OHHiBF5++WVERUXhkUceMayzdu1adOnSBS1btkRCQgJefvllvPrqq+jcubOhZsWKFbj//vvh6OiI2NhYzJw5E4sXLza6HdjSpUsxaNAgKJVKfPPNN1i8eDE2b94MKysrAMDs2bPxl7/8BdOmTcP48ePh4OCA1NRUxMbGYsWKFXd1XH799VcUFhYiNzcXRUVFhjN9Xbt2hUqluqttEhER3UsMfXRX0tPTodFoDM9zcnIwY8YM5OXlwcvLCy+88ALmzZtXYZ25c+fi2rVraNu2Ld544w28+uqrRjWHDx/GggULUFhYCD8/P6xevRqjRo0yqvnhhx/w97//HSUlJQgICMDWrVvx6KOPGl739/fH3r178cYbb6Bv374QEbRv375Oc+yNHz8ee/fuNTy/PbddRkYG2rZte9fbJSIiulf4nT4iIiIiC8Crd4mIiIgsAD/ebeL0ej2ys7PRrFmzCleiEhERkXkSEVy/fh2tWrUyumlBXTD0NXHZ2dnw9vY2dRtERER0Fy5cuGB0IWVdMPQ1cc2aNQNw64/GycnJxN0QERFRTWi1Wnh7exvex+sDQ18Td/sjXScnJ4Y+IiKiRqY+v5rFCzmIiIiILABDHxEREZEFYOgjIiIisgAMfUREREQWgKGPiIiIyAIw9BERERFZAIY+IiIiIgvA0EdERERkARj6iIiIiCwAQx8RERGRBTDb0Ldy5Uq0bdsWtra2CA0NxeHDh6ut37NnD4KCgqBWq9GhQwdER0dXqImJiYGfnx9sbW3Ro0cP7Nixo9b7FRHMnz8fXl5esLOzQ3h4OM6ePWtU8+mnn+Khhx6Ck5MTFAoFCgoKKuzn2rVreO655+Dk5AQXFxeMGzcOhYWFRjVZWVmIjIyEvb093N3dMXPmTJSXl1d7HIiIiIgqY5ahb9OmTZgxYwYWLFiAo0ePIiAgABEREbh8+XKl9RkZGYiMjET//v2RnJyMV155BePHj8euXbsMNYcOHcLIkSMxbtw4HDt2DFFRUYiKisLJkydrtd8lS5bgo48+wqpVq5CYmAgHBwdERESguLjYUHPz5k0MGjQIr7/+epVjfO6553Dq1CnExsZi+/bt2LdvHyZMmGB4XafTITIyEqWlpTh06BDWrVuH6OhozJ8//66OKREREVk4MUMhISEydepUw3OdTietWrWSRYsWVVo/a9Ys6datm9GyESNGSEREhOH58OHDJTIy0qgmNDRUJk6cWOP96vV68fT0lKVLlxpqCgoKRK1Wy4YNGyr0FR8fLwAkPz/faHlqaqoAkF9++cWw7IcffhCFQiGXLl0SEZEdO3aIUqmU3NxcQ80nn3wiTk5OUlJSUulxqIxGoxEAotFoarwOERER3VmepkiOZeXfufAuNMT7t9md6SstLUVSUhLCw8MNy5RKJcLDw5GQkFDpOgkJCUb1ABAREWFUf6eamuw3IyMDubm5RjXOzs4IDQ2tsreq+nVxcUGvXr0My8LDw6FUKpGYmGio6dGjBzw8PIz61Wq1OHXqVJXbLikpgVarNXoQERFR/Tmdq8XD7+1ByMI4PP95IpIvVPwalzkyu9B35coV6HQ6o7ADAB4eHsjNza10ndzc3ErrtVotioqKqq25vc2a7Pf2z9r0VlW/7u7uRsusra3h6upqtK/K9vPHPiqzaNEiODs7Gx7e3t417ouIiIiqdqOkHJ/vP4dBH+zHb7/fAAA429mghYPKxJ3VjNmFPqqbuXPnQqPRGB4XLlwwdUtERERNwor4X/Hu92mG555Otvh26v3wdrU3YVc1Z23qBv7Mzc0NVlZWyMvLM1qel5cHT0/PStfx9PSstN7JyQl2dnbV1tzeZk32e/tnXl4evLy8jGoCAwNrPEZPT88KF6WUl5fj2rVrRvv685XDt3ur6jgAgFqthlqtrnEvREREVL11hzKx6Ic0FJfpjZZ/N+0BuDezNVFXtWd2Z/pUKhWCg4MRFxdnWKbX6xEXF4ewsLBK1wkLCzOqB4DY2Fij+jvV1GS/vr6+8PT0NKrRarVITEyssreq+i0oKEBSUpJh2e7du6HX6xEaGmqoOXHihFE4jI2NhZOTE7p27VrjfREREdHdu1lajre2nTIKfPe52OGnGf3g7tR4Ah8A87x6d+PGjaJWqyU6OlpSU1NlwoQJ4uLiYriSdc6cOTJq1ChD/blz58Te3l5mzpwpaWlpsnLlSrGyspKdO3caag4ePCjW1taybNkySUtLkwULFoiNjY2cOHGixvsVEVm8eLG4uLjI1q1bJSUlRZ588knx9fWVoqIiQ01OTo4cO3ZMPvvsMwEg+/btk2PHjsnVq1cNNYMGDZKePXtKYmKiHDhwQDp27CgjR440vF5eXi7du3eXRx55RJKTk2Xnzp3SsmVLmTt3bq2OJa/eJSIiqp3Scp0sjzsjb287Jf/af07azN5ueLy04eg96aEh3r/NMvSJiCxfvlx8fHxEpVJJSEiI/Pzzz4bXRo8eLf369TOqj4+Pl8DAQFGpVNKuXTtZu3ZthW1u3rxZOnXqJCqVSrp16ybff/99rfYrcmvalnnz5omHh4eo1Wp5+OGHJT093ahmwYIFAqDC4489Xb16VUaOHCmOjo7i5OQkf/3rX+X69etG28nMzJRHH31U7OzsxM3NTV577TUpKyur4RG8haGPiIiodpbsTDMKem1mb5elO09LXFquaItK70kPDfH+rRARMdVZRmp4Wq0Wzs7O0Gg0cHJyMnU7REREZq3gZin+sijO6ONctbUSe2f2h6fzvfs4tyHev83uQg4iIiIiU/l3YhaKy/To6uWED54JxJc/n8eTga3uaeBrKAx9REREZLF+Ss3D7vTL6HGfM54IaIXoQ5kAgBcf9EUnj2Z4+8nupm2wHjH0ERERkUXafOQCZv0nxfB87jcnANyafy+yRytTtdVgzG7KFiIiIqKGlnHlBv625SQAYICfO9wcb91Vw0qpwMKnukNl3fQiEs/0ERERkcVZuus0Ssv16NPBDZ+/0As3Sstx4OwVdPZshnYtHU3dXoNg6CMiIiKLciwrHztO5EKhAN6I7AKlUoFmtjZ4tIfXnVduxJreuUsiIiKiKuj1gre2pQIAnurZGl28LGc6M4Y+IiIishj/OpCB5AsFcFBZYdagzqZu557ix7tERETU5KTlaLFsVzqSsvJha22Fdi0dYK+yQtzpW/e0nzXIDx6N7d65dcTQR0RERE1KXFoeJn95FKW623fVKEOuttjw+tgHfPFCWBvTNGdCDH1ERETUZJzJu47J/74V+Pp3bomXwztBRPDr5UJcvVGKEF9XBPk0N3WbJsHQR0RERE1CmU6PGZuTUVquR9+Obvj0hV6wsbp1+UJPCw16f8QLOYiIiKhJWLH7V5y8pIWznQ3eGxZgCHx0C48GERERNXonLmqwIv5XAMA7Ud3hbmEXadQEQx8RERE1asVlOszYnAydXhDp74XBAU3vvrn1gaGPiIiIGrV3tqfi7OVCuDmq8c6T3U3djtli6CMiIqJG65ujF/HvxCwoFMD7wwPg6qAydUtmi6GPiIiIGqWYIxcw8z8pAIBp/TvgwU4tTdyReeOULURERGTWRAQFN8twqaAIl68X41J+EXacyEXCuasAgKeC7sOr4Z1M3KX5Y+gjIiIis3QqW4N1hzKx+/RlXCksrfC6jZUC0/p3xPQBHaBUKkzQYePC0EdERERmpbhMh3e2p+Krw1kQ+d9yN0c1PJ3VcG9mC//Wzhga1Brervama7SRYegjIiIis3HtRinGRv+C5AsFAIDH/b3wbIgPevo0h53KysTdNW4MfURERGQWNDfL8PzniUjNuXVXjRXP9kTfjrw4o74w9BEREZHJlen0mPDFEaTmaOHmqMamiX9B+5aOpm6rSeGULURERGRyf/8+DYkZ1+CotsaX40MY+BoAQx8RERGZVMyRC4g+lAkA+OeIQPh5Opm2oSaKoY+IiIhM5viFAryx5SQA4OWHO2JgVw8Td9R0MfQRERGRSVwtLMHkL5NQWq5HeBd3vPxwR1O31KQx9BEREdE9V67TY/qGY8jWFMPXzQHvjwjkBMsNjKGPiIiI7rmlP6bj0G9XYa+ywupRwXCytTF1S00eQx8RERHdUxsPZ2H13nMAgKVPB6CTRzMTd2QZGPqIiIjontl1Khevf3sCADCtfwdE+nuZuCPLwdBHRERE98S249mY9tVR6AUY0csbrz3SydQtWRTekYOIiIgalE4v+PCnM1ge/ytEgCcCWuHvQ7pDoeCFG/cSQx8RERE1mKTz1/DWtlSkXNQAAMbc3xbzHu8KK16pe88x9BEREVG9+v16CeJPX8amIxeQdD4fANBMbY13orojqud9Ju7OcjH0ERERUZ2ICE5laxGXdhm7T+fh+H/P6gGAjZUCT/VsjdciOsG9ma0JuySGPiIiIrorZ/Ku46vELOw6lYscTbHRa/6tnRHexQPP9PaGuxPDnjlg6CMiIqJaOXFRgyW7TmP/2SuGZXY2VujT0Q3hXdzRv7M7g54ZYugjIiKiGrleXIa/f5+Gjb9cAABYKRUY2MUDw3q1xgMd3GBrY2XiDqk6DH1ERER0R0ez8jH9q2O4VFAEABjS8z7MGNgJ3q72Ju6Maoqhj4iIiKq1NfkSZv4nBaXleni72mHZ0wEIbdfC1G1RLTH0ERERUaVEBCt2/4r3Ys8AAMK7eOCDZwLhqGZ8aIz4WyMiIqIKRATv/XgGK+J/BQBMfLAdZg3y46TKjRhDHxERERkRESzZlY5P9vwGAPhbZBeM79vOxF1RXTH0ERERkZHV+84ZAt+bT3TFmAd8TdwR1QelqRsgIiIi8/F10kUs/uE0gFtn+Bj4mg6GPiIiIgIAxKdfxqyvUwAAEx5sx490mxiGPiIiIsKxrHxM+fIodHrBkJ73Yc4gP1O3RPWMoY+IiMjCnfu9EGOjf0FRmQ4PdmqJJU/7Q8mrdJscsw19K1euRNu2bWFra4vQ0FAcPny42vo9e/YgKCgIarUaHTp0QHR0dIWamJgY+Pn5wdbWFj169MCOHTtqvV8Rwfz58+Hl5QU7OzuEh4fj7NmzRjXFxcWYOnUqWrRoAUdHRwwdOhR5eXlGNUePHsXAgQPh4uKCFi1aYMKECSgsLDSqUSgUFR4bN26s9jgQERHVxmVtMV5Ycxj5N8vg39oZnzwXBBsrs40HVAdm+VvdtGkTZsyYgQULFuDo0aMICAhAREQELl++XGl9RkYGIiMj0b9/fyQnJ+OVV17B+PHjsWvXLkPNoUOHMHLkSIwbNw7Hjh1DVFQUoqKicPLkyVrtd8mSJfjoo4+watUqJCYmwsHBARERESguLjbUvPrqq9i2bRtiYmKwd+9eZGdn46mnnjK8np2djfDwcHTo0AGJiYnYuXMnTp06hTFjxlQY29q1a5GTk2N4REVF1eXQEhERGWiLyzB67S+4mF+Eti3ssWZMbzhw4uWmS8xQSEiITJ061fBcp9NJq1atZNGiRZXWz5o1S7p162a0bMSIERLJLfqDAAAgAElEQVQREWF4Pnz4cImMjDSqCQ0NlYkTJ9Z4v3q9Xjw9PWXp0qWGmoKCAlGr1bJhwwbDcxsbG4mJiTHUpKWlCQBJSEgQEZHVq1eLu7u76HQ6Q01KSooAkLNnzxqWAZBvv/22qsNUIxqNRgCIRqOp03aIiKhpKS4rlxGrD0mb2dsl+J1YOX/lhqlboj9oiPdvszvTV1paiqSkJISHhxuWKZVKhIeHIyEhodJ1EhISjOoBICIiwqj+TjU12W9GRgZyc3ONapydnREaGmqoSUpKQllZmVGNn58ffHx8DDUlJSVQqVRQKv93+O3s7AAABw4cMOpx6tSpcHNzQ0hICNasWQMRqfQY3FZSUgKtVmv0ICIi+iOdXjBj03H8fO4aHNXWiP5rb/i0sDd1W9TAzC70XblyBTqdDh4eHkbLPTw8kJubW+k6ubm5ldZrtVoUFRVVW3N7mzXZ7+2fd6pRqVRwcXGpsmbAgAHIzc3F0qVLUVpaivz8fMyZMwcAkJOTY1jn7bffxubNmxEbG4uhQ4diypQpWL58eaXH4LZFixbB2dnZ8PD29q62noiILItOL5gZcxzfn8iBjZUCn44KRvf7nE3dFt0DZhf6LEG3bt2wbt06vPfee7C3t4enpyd8fX3h4eFhdPZv3rx5eOCBB9CzZ0/Mnj0bs2fPxtKlS6vd9ty5c6HRaAyPCxcuNPRwiIiokdDrBbO/TsE3xy7BSqnA8pE9cX8HN1O3RfeI2YU+Nzc3WFlZVbjaNS8vD56enpWu4+npWWm9k5OT4WPTqmpub7Mm+7398041paWlKCgoqLb/Z599Frm5ubh06RKuXr2KN998E7///jvatat6IsyQkBBcvHgRJSUlVdao1Wo4OTkZPYiIiMp1esz+OgX/SboIK6UCHz3TE4O6e5m6LbqHzC70qVQqBAcHIy4uzrBMr9cjLi4OYWFhla4TFhZmVA8AsbGxRvV3qqnJfn19feHp6WlUo9VqkZiYaKgJDg6GjY2NUU16ejqysrIq7d/DwwOOjo7YtGkTbG1tMXDgwCqPTXJyMpo3bw61Wl1lDRER0Z8Vleow6cskxCRdhFIBvD88AJH+DHwWp94uCalHGzduFLVaLdHR0ZKamioTJkwQFxcXyc3NFRGROXPmyKhRowz1586dE3t7e5k5c6akpaXJypUrxcrKSnbu3GmoOXjwoFhbW8uyZcskLS1NFixYIDY2NnLixIka71dEZPHixeLi4iJbt26VlJQUefLJJ8XX11eKiooMNZMmTRIfHx/ZvXu3HDlyRMLCwiQsLMxojMuXL5ekpCRJT0+XFStWiJ2dnXz44YeG17/77jv57LPP5MSJE3L27Fn5+OOPxd7eXubPn1+rY8mrd4mILFuetkiGrDwgbWZvl05v7JCdJ3NM3RLVQEO8f5tl6BO5FYp8fHxEpVJJSEiI/Pzzz4bXRo8eLf369TOqj4+Pl8DAQFGpVNKuXTtZu3ZthW1u3rxZOnXqJCqVSrp16ybff/99rfYrcmvalnnz5omHh4eo1Wp5+OGHJT093aimqKhIpkyZIs2bNxd7e3sZMmSI5OQY/yMbNWqUuLq6ikqlEn9/f1m/fr3R6z/88IMEBgaKo6OjODg4SEBAgKxatcpompeaYOgjIrJcv2Rcld7vxkqb2dulx4KdcjjjqqlbohpqiPdvhcgd5gChRk2r1cLZ2RkajYbf7yMishBlOj0+2fMbPoo7i3K9oJOHI1Y9H4x2LR1N3RrVUEO8f3PabSIioibk5CUN5nyTgpOXbs3T+ri/F/4x1J932iCGPiIioqYgT1uMpbvS8fXRixABnO1s8NbgbngysBUUCoWp2yMzwNBHRETUiP16uRDRhzLwddIlFJXpAACDA1rhb5Fd4O5ka+LuyJww9BERETUyIoJ9Z69gzYEM7D3zu2F5kI8L/vZ4VwT5NDdhd2SuGPqIiIgaiZul5fjm6CWsPZiB336/AQBQKICH/Tww9oG2CGvfgh/lUpUY+oiIiMzcpYIirE/IxIbELGiLywEAjmprDOvVGmPub4s2LRxM2yA1Cgx9REREZupUtgaf7juH7Sk50OlvzbDWpoU9Roe1xbBerdHM1sbEHVJjwtBHRERkZhJ+u4qP9/yK/WevGJaFtWuBsX18McDPHVZKfoRLtcfQR0REZCZSs7VYvPM09v334gwrpQKRPbww4cF26H6fs4m7o8aOoY+IiMjErhaWYNEPpw1z7FkrFRgZ4oMJD7aDt6u9qdujJoKhj4iIyEREBF8fvYR3v09Fwc0yALfuoDEzojMvzqB6x9BHRERkAr9fL8H/xRw3zLPXxcsJC4d0R0/OsUcNhKGPiIjoHtuTfhn/F3McVwpLobZW4pXwThjf1xc2VkpTt0ZNGEMfERHRPaLXC96LTcfK+N8AAH6ezbB8ZE909Ghm4s7IEjD0ERER3QPXi8vw6qZk/JR2GQDwQlgbvP5YF9jaWJm4M7IUDH1EREQN7PzVGxi/7gjOXi6EylqJfwztgSE9W5u6LbIwDH1EREQN6MRFDcasPYyrN0rh4aTG6lG9EOjtYuq2yAIx9BERETWQA2evYOIXR3CjVIdurZywZkxveDjZmrotslAMfURERA1g2/FszNicjDKd4P72LbB6VDDvlUsmxdBHRERUzzYezsLcb09ABIjs4YX3RwRAbc0LNsi0GPqIiIjq0b8Tz+ONb08CAJ7/iw/eGtwdVkqFibsiYugjIiKqN1/8fB7zttwKfGMf8MW8x7tAoWDgI/PA0EdERFQP1idkYv7WUwCAF/v64vXHGPjIvDD0ERER1dHagxl4a1sqAGBiv3aYM8iPgY/MDkMfERFRHXy+/xze/T4NADD5ofaYFdGZgY/MEkMfERHRXfpj4JvWvwNee6QTAx+ZLYY+IiKiu7DmQIYh8E0f0AEzBjLwkXlTmroBIiKixib6YAbe3n7rO3zT+jPwUePA0EdERFQL6xMy8eZ/L9qY8lB7fqRLjQZDHxERUQ19kfC/aVkm9WuPmbxogxoRhj4iIqIa+PLn85j338A38cF2mD2IgY8aF4Y+IiKiO/gqMQt/+++dNl7s64s5j3IePmp8ePUuERFRNdYc+N9FG+P68E4b1Hgx9BEREVVCRLAy/lcs+/EMAN5ajRo/hj4iIqI/ERH8Y2c6Vu39DQDwSnhHvPxwRwY+atQY+oiIiP5Arxe8ue0U1iecBwC88VgXvPhgOxN3RVR3DH1ERET/VVKuw8yYFHx3PBsKBfD3qB54NtTH1G0R1QuGPiIiIgCam2WY8MURJGZcg7VSgWXDAhDV8z5Tt0VUbxj6iIjI4l3Mv4kxa3/Br5cL4ai2xqrng9Gno5up2yKqVwx9RERk0ZLOX8OkL4/i9+sl8HSyxdq/9kYXLydTt0VU7xj6iIjIYn2VmIUF351EmU7g59kMa//aG17OdqZui6hBMPQREZHFKS3X481tp/BVYhYA4NHunlg2LAAOar4tUtPFv24iIrIo56/ewEsbk3H8QgEUCuD/HumMKQ+15xx81OQx9BERkcXYmnwJb3x7EoUl5XCytcaHz/REfz93U7dFdE8w9BERUZOnLS7DW9+l4uujFwEAvds2xwfP9MR9Lvz+HlkOhj4iImrS4tLy8Ma3J5GrLYZSAUwf0BHTB3SAtZXS1K0R3VMMfURE1CRdu1GKt7adwtbkbABAmxb2WPp0AEJ8XU3cGZFpMPQREVGTotcL/pN0Ef/YeRpXb5RCqQDG922HV8M7wU5lZer2iEyGoY+IiJqMo1n5eOu7Uzh+UQMA6OzRDEue9keAt4uJOyMyPYY+IiJq9PK0xfjHD6fxzbFLAABHtTVefrgjRt/fFiprfnePCADM9l/CypUr0bZtW9ja2iI0NBSHDx+utn7Pnj0ICgqCWq1Ghw4dEB0dXaEmJiYGfn5+sLW1RY8ePbBjx45a71dEMH/+fHh5ecHOzg7h4eE4e/asUU1xcTGmTp2KFi1awNHREUOHDkVeXp5RzdGjRzFw4EC4uLigRYsWmDBhAgoLC41qsrKyEBkZCXt7e7i7u2PmzJkoLy+v9jgQEVmSgpulWPzDafRbGm8IfMN7tUb8/z2EFx9sx8BH9Adm+a9h06ZNmDFjBhYsWICjR48iICAAERERuHz5cqX1GRkZiIyMRP/+/ZGcnIxXXnkF48ePx65duww1hw4dwsiRIzFu3DgcO3YMUVFRiIqKwsmTJ2u13yVLluCjjz7CqlWrkJiYCAcHB0RERKC4uNhQ8+qrr2Lbtm2IiYnB3r17kZ2djaeeesrwenZ2NsLDw9GhQwckJiZi586dOHXqFMaMGWOo0el0iIyMRGlpKQ4dOoR169YhOjoa8+fPr49DTETUqN0oKceK3WfRd0k8Vu39DcVlegS3aY6tUx/AkqcD0LKZ2tQtEpkfMUMhISEydepUw3OdTietWrWSRYsWVVo/a9Ys6datm9GyESNGSEREhOH58OHDJTIy0qgmNDRUJk6cWOP96vV68fT0lKVLlxpqCgoKRK1Wy4YNGwzPbWxsJCYmxlCTlpYmACQhIUFERFavXi3u7u6i0+kMNSkpKQJAzp49KyIiO3bsEKVSKbm5uYaaTz75RJycnKSkpKTS41AZjUYjAESj0dR4HSIic1VcVi5rDpyT4Hd+lDazt0ub2dsl4p97JfZUruj1elO3R1RvGuL92+zO9JWWliIpKQnh4eGGZUqlEuHh4UhISKh0nYSEBKN6AIiIiDCqv1NNTfabkZGB3NxcoxpnZ2eEhoYaapKSklBWVmZU4+fnBx8fH0NNSUkJVCoVlMr/HX47u1sThB44cMDQb48ePeDh4WHUr1arxalTpyo/eP/dtlarNXoQETV25To9Yo5cwIBle/HWtlRcKSxFmxb2+PCZQOx4qS/Cu3rwNmpEd2B2oe/KlSvQ6XRGYQcAPDw8kJubW+k6ubm5ldZrtVoUFRVVW3N7mzXZ7+2fd6pRqVRwcXGpsmbAgAHIzc3F0qVLUVpaivz8fMyZMwcAkJOTU22/f+yjMosWLYKzs7Ph4e3tXWUtEZG50+sF245n45EP9mHmf1JwqaAIHk5q/H1Id/w0ox+eDLwPSiXDHlFNmF3oswTdunXDunXr8N5778He3h6enp7w9fWFh4eH0dm/uzF37lxoNBrD48KFC/XUNRHRvSMiiE3Nw2Mf7cf0Dcdw7vcbcLG3wdxH/bB3Zn88F9oGNryjBlGtmN2ULW5ubrCysqpwtWteXh48PT0rXcfT07PSeicnJ8PHplXV3N5mTfZ7+2deXh68vLyMagIDAw01paWlKCgoMDrb9+f+n332WTz77LPIy8uDg4MDFAoF3n//fbRr186wnT9fOXy7t6qOAwCo1Wqo1fwCMxE1TiKCA79ewbIfz+D4hQIAQDO1Ncb3bYexfdqima2NiTskarzM7j+TVCoVgoODERcXZ1im1+sRFxeHsLCwStcJCwszqgeA2NhYo/o71dRkv76+vvD09DSq0Wq1SExMNNQEBwfDxsbGqCY9PR1ZWVmV9u/h4QFHR0ds2rQJtra2GDhwoKHfEydOGF05HBsbCycnJ3Tt2rXS40BE1Jglnb+GEZ/+jFH/OozjFwpgZ2OFyQ+1x75Z/fFyeEcGPqK6qrdLQurRxo0bRa1WS3R0tKSmpsqECRPExcXFcCXrnDlzZNSoUYb6c+fOib29vcycOVPS0tJk5cqVYmVlJTt37jTUHDx4UKytrWXZsmWSlpYmCxYsEBsbGzlx4kSN9ysisnjxYnFxcZGtW7dKSkqKPPnkk+Lr6ytFRUWGmkmTJomPj4/s3r1bjhw5ImFhYRIWFmY0xuXLl0tSUpKkp6fLihUrxM7OTj788EPD6+Xl5dK9e3d55JFHJDk5WXbu3CktW7aUuXPn1upY8updIjJ3mVcKZfKXRwxX43Z8fYe8+d1JydMW3XlloiaqId6/zTL0idwKRT4+PqJSqSQkJER+/vlnw2ujR4+Wfv36GdXHx8dLYGCgqFQqadeunaxdu7bCNjdv3iydOnUSlUol3bp1k++//75W+xW5NW3LvHnzxMPDQ9RqtTz88MOSnp5uVFNUVCRTpkyR5s2bi729vQwZMkRycnKMakaNGiWurq6iUqnE399f1q9fX6GXzMxMefTRR8XOzk7c3Nzktddek7KysjsdOiMMfURkrgpulMo7205Jh9e/lzazt0vbOdtlZkyyXMq/aerWiEyuId6/FSIipj3XSA1Jq9XC2dkZGo0GTk5Opm6HiAg6veDLn8/j/dgz0BSVAQD6dnTD6491QRcv/v8UEdAw799mdyEHERE1Xcey8vG3LSdxKvvWHKKdPBzx+mNd8FBndxN3RtT0MfQREVGDy79RiiW70rHxlyyIAE621pgZ0RkjQ3xgzalXiO4Jhj4iImowIoLtKTlY8N0pXLtRCgAYGtQacx/zg5sjp5ciupcY+oiIqEFcKSzBvC0n8cPJW3cR6uThiHee7I7Qdi1M3BmRZWLoIyKierc9JRvzt946u2etVGBq/w6Y2r8DVNb8KJfIVBj6iIio3miLy/DGtyex7Xg2AMDPsxmWDQtA9/ucTdwZETH0ERFRvTialY+XNhzDxfwiWCkVmPpQe0wb0JFn94jMBEMfERHViV4vWLXvN7z/4xmU6wWtm9vho5E9EeTT3NStEdEfMPQREdFdu1JYglc3JWP/2SsAgMf9vbDwqR5w4n1yicwOQx8REd2V4xcKMOnLJORoimFnY4W3BnfDsF6toVAoTN0aEVWCoY+IiGpt0y9ZmLflFEp1erRr6YDVzwejo0czU7dFRNVg6CMiohorKdfhrW2p+CoxCwAwsKsH3h8egGb8OJfI7DH0ERFRjVy+XoyJXyThWFYBFArgtYGdMOWhDlAq+XEuUWPA0EdERHd0OleLcdFHcKmgCE621vhwZE/07+xu6raIqBYY+oiIqFrx6Zcx/atjKCwpRzs3B6wZ0xtt3RxM3RYR1RJDHxERVWndoUy8te0U9AKEtWuBVc8Hw9me398jaowY+oiIqIJynR7vfp+G6EOZAIARvbzxTlR33l2DqBFj6CMiIiPFZTpM++oYfkrLAwDMedQPEx9sx/n3iBo5hj4iIjLQFpdhfPQRHM68BrW1Eh+MCMSjPbxM3RYR1QOGPiIiAnBrSpbRa35BWo4WzWyt8a/RvRHi62rqtoionjD0ERERsq7exKg1iTh/9SbcHNVYPzYEXVs5mbotIqpHDH1ERBYuLUeLF9Ycxu/XS+Djao8vxoWgTQtOyULU1DD0ERFZsF8yr2Fs9C+4XlwOP89mWD82BO5OtqZui4gaAEMfEZGF2n06D5O/PIqScj16t22Oz0f3hrMd5+AjaqoY+oiILNA3Ry9i5n9SoNMLHvZzx4png2CnsjJ1W0TUgBj6iIgszL8OZOCd7akAgKeC7sM/hvrDxoqTLhM1dfUW+oqLi6FQKKBWq+trk0REVI9EBMt+TMfK+N8AAOP7+OL1x7pAqeSky0SW4K5D3549e7B161YcPHgQqampKCoqAgDY29ujS5cuuP/++xEVFYWHHnqovnolIqK7pNML/rblJDYczgIAzBrUGZP7teddNogsiEJEpKbFZWVlWL16Nd5//31kZmbC1dUVQUFBaNeuHZo3bw4RQX5+PjIyMnD06FFcu3YNbdq0wWuvvYaJEyfCxoZfEL7XtFotnJ2dodFo4OTEObeILFFJuQ6vbEzGDydzoVQAfx/SAyNDfEzdFhFVoyHev2sV+tq0aYPS0lKMHj0aw4cPR1BQULX1SUlJiImJwfr166FSqZCZmVnXfqmWGPqILFthSTkmrD+CQ79dhcpKiQ+f4W3ViBoDk4e+1atXY8yYMbX+3l5paSnWrl2LiRMn1rpBqhuGPiLLdbWwBH+N/gUpFzVwUFnhsxd64f4ObqZui4hqwOShjxofhj4iy3SpoAij/pWIc7/fgKuDCtF/7Q3/1i6mbouIaqgh3r/rdI3+a6+9Vi9NEBFR/Tmbdx1DPz6Ec7/fwH0udoiZFMbAR0R1C33Lly/HkCFDDFfuVub8+fN12QUREdXCsax8DFudgFxtMTq4O+I/k8PQvqWjqdsiIjNQp9C3Y8cO7N27F3379kVubq7Ra+fPn8eECRPQuXPnOjVIREQ1syf9Mp79LBEFN8sQ6O2CmIlh8HK2M3VbRGQm6hT6wsPDcejQIRQUFKB3795ITk42CntffPEFxo0bV1+9EhFRFbYmX8L4dUdQVKZD345u+Pf4UDR3UJm6LSIyI3W+I4efnx8OHz6MyMhI9OnTB+Xl5bCyssLkyZMxa9YseHlxagAiooa05kAG3v7vbdUGB7TCsmEBUFnztmpEZKzOoe/ChQv4xz/+geTkZJSUlEChUOCf//wnJk+eXB/9ERFRFUQES3el4+M9t26r9tcH2mJeZFfeVo2IKlWn/xQcP348OnbsiH/961948cUXkZmZiXHjxmH69OlYvHhxffVIRER/Uq7TY87XJwyBb2ZEZ8x/nIGPiKpWpzN9//73v/Hiiy9i7ty5aNWqFQDg008/RceOHTF37lykp6fj008/5e3XiIjqUXGZDtM3HENsah6UCmDhkB54hrdVI6I7qFPo++233wxh749mzpyJjh074vnnn8e5c+ewd+/euuyGiIj+S1NUhhfXHcHhzGtQWSuxfGRPRHTzNHVbRNQI1Onj3coC321RUVHYu3cvfv3117rsgoiI/uvCtZsY+skhHM68hma21vhibAgDHxHVWJ0v5KhOcHAwDh8+3JC7ICKyCCkXCzA2+giuFJbA08kWa//aG128eGtFIqq5Bg19AHDfffc19C6IiJq02NQ8vLThGIrKdOji5YS1Y3rD09nW1G0RUSNTq493u3TpgvXr16O0tLTG65SUlGDt2rXo2rVrrZsjIrJ00QczMOGLW5Mu9+vUEjGTwhj4iOiu1OpM39ixYzFjxgy8/PLLGDx4MMLDwxEUFARfX1/Y29sDAG7cuIGMjAwcOXIEP/30E7Zt2waVSoWZM2c2yACIiJoinV7w9+/TsOZgBgBgZIg33n6yO2ysOOkyEd0dhYhITYs7duyI999/H7/99huio6Nx4sQJw2vW1rfyY3l5OYBbk4Z2794dY8eOxdixY+HkxO+emIJWq4WzszM0Gg1/B0SNRGFJOV7ZmIyf0vIAALMH+WFSv3ZQKDgHH5GlaIj371qd6Tt//jy0Wi1eeeUVvPLKK2jVqhUmTZqE8vJyXL16FQDQokUL+Pn5ISwsDL6+vvXSJBGRpci6ehPj1/+CM3mFUFkrsWxYAAYHVD1TAhFRTdUq9Pn4+Bid3cvNzUWHDh3w7LPP1ntjRESW5tBvVzDl30dRcLMM7s3UWD0qGD19mpu6LSJqImoV+saMGYMFCxYgJSUFffv2BQDk5+c3SGNERJZCRPDlz+fx5rZU6PQC/9bO+HRUL16wQUT1qlbf6RMRrFy5EtHR0Th+/Dj0ej0AwMHBAd26dYO/vz969OgBf39/+Pv7w8XFpcEap5rhd/qIzFtpuR5vbjuFrxKzAABPBrbCP4b6w9bGysSdEZEpNcT7d60uA1MoFJg2bRqOHDmC69evQ0QwYcIEvPTSS2jZsiV27tyJl156Cf3790eLFi3g4+ODJ5544q4aW7lyJdq2bQtbW1uEhobecZLnPXv2ICgoCGq1Gh06dEB0dHSFmpiYGPj5+cHW1hY
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