{ "cells": [ { "cell_type": "markdown", "id": "cb2065bf", "metadata": {}, "source": [ "# Boundary Value Problem\n", "**강좌**: *수치해석*" ] }, { "cell_type": "markdown", "id": "6efe8fa0", "metadata": {}, "source": [ "## Boundary Value Problem\n", "IVP와 달리 미분 방정식의 양끝단에서 값이 주어진 문제가 있다.\n", "\n", "$$\n", "\\frac{dy}{dt}=f(x, y(x)), x \\in (a,b), g(y(a), y(b)) = 0.\n", "$$\n", "\n", "IVP와 같이 미분방정식을 적분해야 하나, 양끝단에 조건이 만족할 수 있어야 한다.\n", "\n", "크게 2가지 방법으로 'Shooting method' 와 'Finite Difference method' 가 사용된다.\n", "\n", "### 예제\n", "\n", "다음 예제에 대해서 이들 방법을 설명하고자 한다.\n", "\n", "금속 막대에 열전달이 발생하는 경우 Fick's Law에 의해 다음 방정식이 만족한다.\n", "\n", "$$\n", "\\frac{dT^2}{dx^2} + h(T_a - T) = 0.\n", "$$\n", "\n", "이때 경계조건은 \n", "\n", "$$\n", "T(0) = T_1, T(L) = T_2.\n", "$$\n", "\n", "10m 막대에 대해 다음 변수들로 생각하자. $T_a=20, T_1= 40, T_2=200, h=0.01$.\n", "\n", "이때 이론해는 다음과 같다.\n", "\n", "$$\n", "T=73.4523e^{0.1x} - 53.4523e^{-0.1x} + 20.\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "id": "a514f51b", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "from matplotlib import pyplot as plt\n", "from scipy.integrate import solve_ivp\n", "\n", "import numpy as np\n", "\n", "plt.style.use('ggplot')\n", "plt.rcParams['figure.dpi'] = 150" ] }, { "cell_type": "code", "execution_count": 2, "id": "ecea538d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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jIY7ABQAAAIQ4u2GNnPn3SiXF5YXIKHmm/1GmZ193GwsDBC4AAAAghNmvPpPz2F+l0tLyQnS0PNfdIdOtt7uNhQkCFwAAABCi7JpP5Dxxn1RWVl6IiZPnd3fIpPRwt7EwQuACAAAAQpCTtlL2qQck65QX4hLkuf4umU5d3W0szBC4AAAAgBDjfPQv2YXzJWvLC/GJ8sz8k0z7zu42FoYIXAAAAEAIcd5fLPvSE75CUsPysNW2o3tNhTECFwAAABAinHdel0191ldIbizPzHtkWrV1r6kwR+ACAAAA6jlrrezbL8oueclXbNJcnpl3yzRv5V5jIHABAAAA9Zm1Vva1Z2TffcNXbN6q/MpWk2buNQZJBC4AAACg3rKOI/vi47IfLvMVW51UfmUrubF7jcGLwAUAAADUQ7asTPbZh2Q//cBXPKmjPDf+SSapoXuNwQ+BCwAAAKhnbGmJ7IK5sms+8RU7pshz/SyZhET3GkMlIRO4tm7dqvXr12vz5s3KzMzUgQMHFBUVpRdeeKHac7Kzs/X6669r3bp1ys7OVkREhFq3bq0zzzxTF1xwgaKioqo8b9OmTUpNTVVGRoZKS0vVtm1bDR8+XIMGDQrQuwMAAADK2ZJiOY/OkdJX+4opPeSZcbtMbLx7jaFKIRO4XnvtNa1evfroB/5o9+7duuOOO3T48GG1aNFCffv2VVFRkb799lstXLhQq1ev1p133qnISP8/os8//1xz586VtVbdunVTUlKSNmzYoPnz52v79u2aMmVKbb81AAAAQJJkCwvkPPJn6dv1vmKPPvJc/QeZmBj3GkO1QiZwpaSkqEOHDurUqZM6deqkadOm1Xj8okWLdPjwYZ1//vm64oor5PF4JEmHDh3SnXfeqW+//Vb//ve/NXjwYO85ubm5mj9/vhzH0U033aQBAwZIkg4ePKg777xTS5cuVd++fdWjR4/AvVEAAACEJZufK+fBP0lbvvUV+5whz9SbZaq5Mwvu87jdQG0ZO3asJkyYoL59+yo5Ofmox2/cuFGSNG7cOG/YkqSGDRtq2LBhkqQtW7b4nfPBBx8oPz9f/fr184YtSUpOTtakSZMkSUuWLPmpbwUAAADwYw/nyPnH7X5hywwcJM+0WwhbQS5krnAdr/+9VbAqiYn+DxyuWbNGkjRw4MBKx/bp00dRUVFKT09XcXGxoqOja6dRAAAAhDV7cL+cuXdKe77z1szZ58tcdrWMJ2Sun4SssP0/1KtXL0lSamqqHMfx1g8dOqR3331XEREROuuss/zO2bFjhyTp5JNPrvR6kZGRateunUpKSrR79+4Adg4AAIBwYfd9L+dvf/APW+eNkZl0DWGrngjbK1yXXnqptm7dquXLl+vLL79Ux44dVVRUpI0bNyopKUm///3v1bZtW+/x+fn5ysvLkyQ1blz1JnKNGzfWli1blJWVpQ4dOtTF2wAAAECIsnt2ypl7h3Rwv7dmRl8sM/oSGWNc7AzHI2wDV6NGjTRr1iw98MADWr9+vX744QdJkjFGAwYM8AtbklRYWOj9dUw1K8BU1I88tiYzZ86sVIuOjtacOXMkSU2bNj2m1wmEilsumzVr5loPCF7MD1SHuYHqMDdQE+ZHZSVbNyn7vj9KOQe9taQrZihh7KXuNeWCUJgbYRu4tm/frjlz5sjj8eiWW25Rt27dVFRUpLS0NC1atEhfffWV7r77brVs2dLtVgEAABBGir9N14E/zZTNzy0vGKMGV9+i+OFjXe0LJyYsA1dpaanmzp2r7OxszZkzRx07dpQkJSQkaMSIEXIcR88995xefvllXX/99ZKk2NhY7/lFRUWKj6+8qVxRUVGlY2syd+7cGsezsrJkrT2m16ptFT9F2LdvnytfH8GN+YHqMDdQHeYGasL88LEb15Xvs1X04x1THo/MlTcqr8+ZygvDP59gmBvGGLVq1eqEzw/LJ+0yMzO1Z88etWjRwhu2jnTGGWdIkr755htvLT4+3huysrOzq3zdirqbtwICAACgfrJfpZXvs1URtiIj5bnmVnkGnONuY/hJwjJw7d9f/uBhXFxcleMV9dzcXL96+/btJUlbt26tdE5paal27NihqKgotW7dujbbBQAAQIhz0lbKeXSOVFpSXoiOkWfGnTKnVt6OCPVLWAauio2Rd+/erYKCgkrjFRse/+/DeX369JEkpaWlVTpn7dq1KikpUY8ePdiDCwAAAMfMWblM9sn7pYqtiuIS5Llxtkz3U13tC7UjLANXSkqKGjZsqKKiIj355JMqKSnxjmVnZ+vZZ5+VVHmD4yFDhiguLk6rV6/WZ5995q0fOnRICxculCSNGjWqDt4BAAAAQoGz7FXZRf/0FZIaynPzn2U6d3evKdSqkFk0Y+3atXr99df9aqWlpbrtttu8vx8/frz69Omj6Oho/eY3v9H999+vjz76SBs2bNDJJ5+skpISZWRkqKCgQB07dtTYsWP9Xi8xMVHXXHON7r//fs2dO1fdu3dXUlKS0tPTlZeXpwsuuEA9e/asi7cLAACAesxaK5v6nOzyIz6/Nm4qz41/kmnZtvoTUe+ETODKyclRZmamX81a61fLycnx/rp///76y1/+osWLF2vjxo368ssvFRkZqVatWumMM87QyJEjq7w1cODAgZo9e7ZSU1OVmZmp0tJStWnTRsOHD9fgwYMD9wYBAAAQEqxTJvvCY7IfLfcVm7eWZ+bdMk3q735TqJqxbq07jqPas2cPy8IjKDE/UB3mBqrD3EBNwml+2NJS2afnyX7+ka/YtkP5M1sNGrnXWJAKhrnxU5eFD5krXAAAAEAws0VFch77q5S+2lfs1LV8NcKERPcaQ0ARuAAAAIAAs/l5ch6+W8r07fOqbr3lmf5HmdiqtypCaCBwAQAAAAFkcw7KeWCWtOOIvVz7nCHP1JtloqJc6wt1g8AFAAAABIjdv0/O/XdKP+zy1syZQ2QmXycTEeFiZ6grBC4AAAAgAOz3O8vDVnaWt2aGjpG56EoZY1zsDHWJwAUAAADUMrt9i5x5d0m5vm2JzNhJMiMuImyFGQIXAAAAUIvspg3lC2QUFpQXjJG55LfyDB7hbmNwBYELAAAAqCX2q8/kPPY3qbSkvBARIfPrG+QZcI67jcE1BC4AAACgFjj/+UD22QclxykvREXLc/X/yfQ63d3G4CoCFwAAAPATOe+9JfvKk75CXLw8190hk3KKe00hKBC4AAAAgBNkrZV98wXZZa/4ig2S5bl+lky7k91rDEGDwAUAAACcAOuUyS56THbVcl+xSXN5Zv5Jpnlr9xpDUCFwAQAAAMfJlpbIPjVP9ot/+4qt28lzw2yZRk3cawxBh8AFAAAAHAdbWCDn0Xulb77yFTumyHP9XTIJSa71heBE4AIAAACOkT2cI+fB2dJ/M33F7qfJc82tMrFx7jWGoEXgAgAAAI6B3b9Pzry7pO93emvm9F/IXHmDTGSUi50hmBG4AAAAgKOwe76Tc/9d0oEsb80MHiFz8TQZj8fFzhDsCFwAAABADey2jPLbCHMPe2tm9CUyoy+WMcbFzlAfELgAAACAativvyxfIKOosLxgjMwlv5Vn8Ah3G0O9QeACAAAAquB8tkr26XlSWVl5ISJS5qob5Tn9F672hfqFwAUAAAD8D+f9xbIvPeErxMTKc80fZE45zb2mUC8RuAAAAIAfWWtl31wou+xVXzGxgTy/u0um48/cawz1FoELAAAAkGTLymQXzpf9+D1fsUlzeW6YJdOyrXuNoV4jcAEAACDs2eIiOU/cJ331ma/Ypr0818+SadTEvcZQ7xG4AAAAENZsfq6ch++RMr/xFTt3k+e6O2QSEt1rDCGBwAUAAICwZQ/sl/PALGnXdl+xd395fvN7mZgY1/pC6CBwAQAAICzZPTvlzLtLyt7nrZkzh8hMvk4mIsLFzhBKCFwAAAAIO3bLt3IeulvKO+ytmQt+JXPhZBljXOwMoYbABQAAgLBi138h57G/SsXF5QVjZCZOlWfIaHcbQ0gicAEAACBsOJ+8L/vcQ5LjlBciImWuulGe03/hbmMIWQQuAAAAhDxrrezyVNnUZ33F2Dh5pv9Rpltv9xpDyCNwAQAAIKRZp0z25SdlP1jiKzZIluf6u2TadXKvMYQFAhcAAABCli0pln3yftk1n/iKzVrKc+OfZJq1dK8xhA0CFwAAAEKSzc+V88hfpIwNvmL7zvL87k6ZBsmu9YXwQuACAABAyKlyQ+MefeT57f/JxMa51hfCD4ELAAAAIcXu+e7HDY2zvDVzxmCZy2fIRPLxF3WLGQcAAICQYTdvLN/QOD/XW2NDY7iJwAUAAICQYL9Mk/PEfVLJERsaX/wbec4d5W5jCGsELgAAANR7zsplsi8+LtkfNzSOjJRn6k0yfc90tzGEPQIXAAAA6i1rrewbz8u+85qvGJ8gz/TbZLr0cK8x4EcELgAAANRLtrRE9rmHZT9d6Ss2airP9bNk2rRzrzHgCAQuAAAA1Du2MF/Oo3+VvvnSV2zTXp7f3SXTuKl7jQH/g8AFAACAesUezJbz0J+kHVt9xS495Zn+B5n4RPcaA6pA4AIAAEC9Yfd8J+eB2dL+vd6a6XeWzJU3ykRFudgZUDUCFwAAAOoFm/mNnIfv8d9j67wxMhf9WsbjcbEzoHoELgAAAAQ9u+YTOQvmSqUl5QVjZC66Up6hY9xtDDiKkAlcW7du1fr167V582ZlZmbqwIEDioqK0gsvvFDjeSUlJXrnnXf0n//8R3v27JHjOGrcuLG6du2qiRMnqnHjxpXO2bRpk1JTU5WRkaHS0lK1bdtWw4cP16BBgwL07gAAAMKXs+It2VeekqwtL0RGyXPVjTL9znK3MeAYhEzgeu2117R69erjOufQoUO6++67tWPHDiUnJ6tnz56SpO+//14rV67U4MGDKwWuzz//XHPnzpW1Vt26dVNSUpI2bNig+fPna/v27ZoyZUqtvScAAIBwZh1H9tWnZVe85SvGJ8pz7W0yKae41xhwHEImcKWkpKhDhw7q1KmTOnXqpGnTptV4vOM4+tvf/qYdO3Zo3LhxuuiiixQREeEd/+GHHxQXF+d3Tm5urubPny/HcXTTTTdpwIABkqSDBw/qzjvv1NKlS9W3b1/16MEmewAAAD+FLSmWfWqe7OqPfcUmzeW5/i6ZVie51xhwnEImcI0dO/a4jv/www+VmZmpAQMG6OKLL6403qJFi0q1Dz74QPn5+erXr583bElScnKyJk2apPvuu09LliwhcAEAAPwENjdHziN/kTZ/4yu2O1meGXfKJFd+3AMIZiETuI7XihUrJEmjR48+5nPWrFkjSRo4cGClsT59+igqKkrp6ekqLi5WdHR07TQKAAAQRuy+7+U8OFv6fpeveMpp8lz9fzKx8e41BpygsAxcBQUF2rJli+Li4tS5c2dlZGRo9erVys3NVdOmTdWvXz+1a9eu0nk7duyQJJ188smVxiIjI9WuXTtt2bJFu3fvVocOHQL9NgAAAEKK3ZZZvqHx4UPemjnzPJlJ02Uiw/JjK0JAWM7cnTt3ylqrli1b6umnn9a//vUvv/GXX35Zo0eP1qRJk7y1/Px85eXlSVKVKxdW1Lds2aKsrCwCFwAAwHEo/Pzfcu67Qyou8tbMmEtlRk6UMcbFzoCfJiwDV0Vw2rFjh7Zt26bRo0dr+PDhio2N1RdffKFnnnlGb7/9tpo3b65hw4ZJkgoLC73nx8TEVPm6FfUjj63JzJkzK9Wio6M1Z84cSVLTpk2P/U3Vssgff4rUrFkz13pA8GJ+oDrMDVSHuYGaFL77pg7+8++S45QXIiLU8No/KO7cke42BteFwveOsNyS2/nxL3NZWZnOPPNMTZ48Wc2bN1eDBg00ZMgQXXbZZZKkN954w802AQAAQpp1HB1+9hEdnP9Xb9gy8QlqdOf9hC2EjLC8whUbG+v99eDBgyuNDx48WE8//bT279+v77//Xi1btvQ7p6ioSPHxlR/aLCoqqvT6NZk7d26N41lZWbIVG/zVsYqfIuzbt8+Vr4/gxvxAdZgbqA5zA/+rymXfk5vIXH+Xclp3kJgrUHB87zDGqFWrVid8flhe4WrevLn311VdnoyJiVGDBg0klW+OLEnx8fHekJWdnV3l61bU3bwVEAAAINjZ3Bw5c+/wC1uRHTrL84e/y7Tt4F5jQACEZeBq2rSpkpKSJJVvZvy/HMfxPud15NWq9u3bS5K2bt1a6ZzS0lLt2LFDUVFRat26dSDaBgAAqPfs3j1y7r1F2rzRW4s+dYAa/+WfMo35oTVCT1gGLknq27evJOnrr7+uNJaRkaHS0lJFR0erTZs23nqfPn0kSWlpaZXOWbt2rUpKStSjRw/24AIAAKiC3fKtnHt/L+3d7a2Zs4aq0e33yROf4GJnQOCEbeD65S9/KY/Ho7ffflvbtm3z1g8dOqSnn35aUvmzXJFH7PkwZMgQxcXFafXq1frss8/8zlm4cKEkadSoUXX0DgAAAOoPu+Y/cv5xu5Sb462ZsZNkLr+OPbYQ0kJmdq9du1avv/66X620tFS33Xab9/fjx4/3XqVq27atpkyZoqefflq33367UlJSFBMTo02bNikvL08dO3bUpZde6vd6iYmJuuaaa3T//fdr7ty56t69u5KSkpSenq68vDxdcMEF6tmzZ+DfLAAAQD1hrZV97y3Z156WKhYDi4yUueJ6eQac425zQB0ImcCVk5OjzMxMv5q11q+Wk5PjN37BBReodevWWrx4sTZv3qySkhK1aNFCI0eO1OjRo6vcb2vgwIGaPXu2UlNTlZmZqdLSUrVp00bDhw+vcsVDAACAcGXLymRfekL2w2W+YnyCPNNvk+nSw73GgDpkrFvrjuOo9uzZw7LwCErMD1SHuYHqMDfCjy0skPP436X01b5ik+byXH+XTKuT/I5lfqA6wTA3fuqy8CFzhQsAAADBwR7YL+ehP0nf+Z6TV8cUea67TaZBI/caA1xA4AIAAECtsd9tk/Pgn6SD+33FPmfIc+VMmSoe1wBCHYELAAAAtcJuWCPnn3+Tigq8NTNsrMz4K2Q8Ybs4NsIcgQsAAAA/mfPhO7IvPiY5TnnBeGQumSbP4BHuNga4jMAFAACAE2adMtnXn5V9901fMSZWnmm/l+l1umt9AcGCwAUAAIATYosK5SyYK32V5ismN5Znxh0y7Tq51xgQRAhcAAAAOG72YLach++Rtm/2FU/qKM91d8g0bupeY0CQIXABAADguNid/y1f9j07y1fs2U+eaTfLxMa71xgQhAhcAAAAOGZ2w1o5j/1VKjxiJcJzR8lMuEomIsLFzoDgROACAADAMXE+XCb74uP+KxFOvEqeIaPdbQwIYgQuAAAA1Mg6ZbKvPi274m1fMSZWnt/cLNO7v3uNAfUAgQsAAADVsoUFcp64T1r/ha+Y3Lh8cYz2rEQIHA2BCwAAAFWy2VlyHr5b+m6br9ju5PKw1aiJe40B9QiBCwAAAJXY7ZvlPHSPdCjbV+zdX56pN8nExrnXGFDPELgAAADgx36ZJmfBP6TiIm/NDBsrM36KjIeVCIHjQeACAACAJMlaK/vuG7KvPytZW170eGQuu1qes893tzmgniJwAQAAQLa0RHbho7KfrPAV4xLkufoWme6nudcYUM8RuAAAAMKczTss59E50qZ0X7FpC3lm3CHTup17jQEhgMAFAAAQxuz3u+Q8dLe0d7ev2Lm7PNP/IJPU0L3GgBBB4AIAAAhTduM6Of/8q5Sf662ZgYNlLr9OJirKxc6A0EHgAgAACEPOv9+VfeFRqazMWzNjJ8mMuEjGGBc7A0ILgQsAACCMWKdM9tVnZFe85StGRctz5Q0y/c5yrzEgRBG4AAAAwoQtyJfzxH1S+mpfsWEjea69TaZjinuNASGMwAUAABAGbNYPch6+R9q13Vc8qaM8190u07iZe40BIY7ABQAAEOLs5m/kzL9XOnzIVzx1oDxX3SgTG+deY0AYIHABAACEMOfTlbLPPSSVlnpr5oLxMmMny3g8LnYGhAcCFwAAQAiyjiP75kLZd17zFSMiZS6/Vp6fD3GvMSDMELgAAABCjC0skPPk/dJXab5iYgN5pv9R5mfd3WsMCEMELgAAgBBi9+8rXxxj5zZfsXW78sUxmrV0rzEgTBG4AAAAQoTd8q2cR/7svzhGz37y/OZmmbh49xoDwhiBCwAAIARUuTjGsLEy46fIeCJc7AwIbwQuAACAeqx8cYznZd953VeMiJSZPF2eM89zrzEAkghcAAAA9ZYtzJezYK607nNfMbGBPNf8QSblFPcaA+BF4AIAAKiH7L7vy5/X2rXdV2zTXp5rb2NxDCCIELgAAADqGZuxQc6jc6TcHF+x1+nyTL2JxTGAIEPgAgAAqEecf78r+8KjUlmZt2bOHy9z4SQWxwCCEIELAACgHrBlZbKvPiX7/mJfMTJS5vIZ8pwx2L3GANSIwAUAABDkbF6unMf/Ln3zpa/YIFme6X+U6dTVvcYAHBWBCwAAIIjZPTvlPHyPtHe3r9ju5PLFMRo3c68xAMeEwAUAABCkbPoaOU/8XSrI9xX7/lyeX98gExPrXmMAjhmBCwAAIMhYa2Xfe1P2tWcl63jrZsylMiMnyhjjYncAjgeBCwAAIIjYkmLZ5x+R/XSlrxgTK8+VN8r0OcO9xgCcEAIXAABAkLAHs+XM/4u0LcNXbNJcnutuk2nb0b3GAJwwAhcAAEAQsNsy5cz/s3Qw21dMOUWeq2+VSWroXmMAfhICFwAAgMuctJWyzz4slZZ4a+bs82Uu+Y1MZJSLnQH4qQhcAAAALrFOmezrz8m++4avGBEhM/E38gwe4V5jAGpNyASurVu3av369dq8ebMyMzN14MABRUVF6YUXXjjm17j77ruVnp4uSXr88ceVnJxc5XGbNm1SamqqMjIyVFpaqrZt22r48OEaNGhQLbwTAAAQDmxebvmS718fsZlxYlL5LYRderrXGIBaFTKB67XXXtPq1atP+PwPP/xQ6enpMsbIWlvtcZ9//rnmzp0ra626deumpKQkbdiwQfPnz9f27ds1ZcqUE+4BAACEhyo3M27boXwz46Yt3GsMQK0LmcCVkpKiDh06qFOnTurUqZOmTZt2zOfm5OTo+eefV+/evbV7927t27evyuNyc3M1f/58OY6jm266SQMGDJAkHTx4UHfeeaeWLl2qvn37qkePHrXyngAAQOix67+Qs+Af/psZ9/m5PL++XiY2zr3GAASEx+0GasvYsWM1YcIE9e3bt9pbAavzzDPPqLCwUFdddVWNx33wwQfKz89Xv379vGFLkpKTkzVp0iRJ0pIlS467dwAAEPqstXKWvlJ+ZeuIsGXGXCrPb28hbAEhKmSucJ2or776Sh9//LEmTpyoli1b1njsmjVrJEkDBw6sNNanTx9FRUUpPT1dxcXFio6ODki/AACg/rFFhbJPPyC75hNfkc2MgbAQMle4TkRRUZGeeOIJtWnTRmPGjDnq8Tt27JAknXzyyZXGIiMj1a5dO5WUlGj37t2VxgEAQHiy+76XM+cW/7DVrKU8f/g7YQsIA2EduF5++WXt27dPU6dOVWRkzRf78vPzlZeXJ0lq3LhxlcdU1LOysmq3UQAAUC/Zb9fL+ctN0s7/+ordT5Xntn/ItGnvWl8A6k7Y3lK4detWLVu2TOecc45OOeWUox5fWFjo/XVMTEyVx1TUjzy2JjNnzqxUi46O1pw5cyRJTZs2PabXCYSKANqsWTPXekDwYn6gOswNVCfc5oa1VvlLX9Phpx6QnDJvPX7MJUq6fLpMRNh+BKtSuM0PHLtQmBth+bfdcRw99thjSkhI0OTJk91uBwAAhBBbXKScf/5dBR8s9RWjotXw2j8obtD57jUGwBVhGbiWLl2qbdu26eqrr1aDBg2O6ZzY2Fjvr4uKihQfH1/pmKKiokrH1mTu3Lk1jmdlZdW4J1ggVfwUobol8hHemB+oDnMD1QmXuWGzs+Q8eq/030xfsVFTeab/QbkdfqbcEH//Jypc5geOXzDMDWOMWrVqdcLnh2XgWrNmjYwxWrVqlT766CO/sYMHD0qS7rvvPkVGRuriiy9W165dFR8fr/j4eOXn5ys7O7vKwJWdnS3J3VsBAQCAO+zmb+Q8OkfKOegrdu4mz9W3yjRs5FpfANwVloFLKr+3euPGjdWOZ2RkSCrfFLlC+/bttXHjRm3dulVt27b1O760tFQ7duxQVFSUWrduHZimAQBAUHJWLZd98XGprNRbM4MukJk4VSYyyr3GALguLAPXrFmzqh279tprtW/fPj3++OOVNlDu06ePNm7cqLS0NJ199tl+Y2vXrlVJSYlOO+009uACACBM2JIS2Zcel/3oX75iRKTMpb+V5+zh7jUGIGiE9bLwx2vIkCGKi4vT6tWr9dlnn3nrhw4d0sKFCyVJo0aNcqs9AABQh+zBbDn/uM0/bDVsJM/NfyZsAfAKmStca9eu1euvv+5XKy0t1W233eb9/fjx49WnT58T/hqJiYm65pprdP/992vu3Lnq3r27kpKSlJ6erry8PF1wwQXq2bPnCb8+AACoH+zmjXL++VfpULav2DFFnul/kElu4l5jAIJOyASunJwcZWZm+tWstX61I5/HOlEDBw7U7NmzlZqaqszMTJWWlqpNmzYaPny4Bg8e/JNfHwAABDfno+Wyi/7nea0zz5O57BqZKJ7XAuDPWLfWHcdR7dmzh2XhEZSYH6gOcwPVCYW5YUtKZF98TPbf7/qKEREyF/9G5pwLZIxxr7l6LhTmBwIjGOYGy8IDAAAEmD24v3zJ962bfMUGyeVLvv+su3uNAQh6BC4AAIAalD+vNUc6dMBXPLlLedhqxPNaAGpG4AIAAKiCtVb2w3dkX17g/7zWL4bJXPJbntcCcEwIXAAAAP/DlhTLLnxU9j/v+4oRkTKXTpPn7PPdawxAvUPgAgAAOILdv0/Oo/dK2zf7ig0by3P1/8l07uZeYwDqJQIXAADAj+zGdXIe/7uUe8RWMp27yfPb/5NJbuxeYwDqLQIXAAAIe9Za2ffelH3tWck63roZPEJmwlUykTyvBeDEELgAAEBYs4UFss89LPvFv33FyCiZSdPlOXOIe40BCAkELgAAELbsD7vlzP+LtHuHr9i4qTzX/EGmw8/cawxAyCBwAQCAsGTXfS7nyblSQb6v2LWXPNN+L5PU0L3GAIQUAhcAAAgr1nFkF78ku+Qlv7oZfqHMhZfLRES41BmAUETgAgAAYcPm5ZZf1Upf7SvGxMpzxe9k+p3lXmMAQhaBCwAAhAX73bby/bX2fe8rtmgjz/Q/yLRu515jAEIagQsAAIQ8J22l7POPSMXFvuKpA+T59Q0y8QnuNQYg5BG4AABAyLKlJbKvPCm7cpmvaIzMmMtkLviVjMfjXnMAwgKBCwAAhCR7YL+cx/4qbfnWV0xIkuc3N8uccpp7jQEIKwQuAAAQcuymDeVh6/AhX7F9Z3mu/j+Zpi3cawxA2CFwAQCAkGGtlX3vLdnXn5Ecx1s3Z54nc9nVMlHR7jUHICwRuAAAQEiwhflynnlQWvMfXzEyUuaS38pz9nD3GgMQ1ghcAACg3rO7d5Qv+f79Ll+xcVN5rv6DTMefudcYgLBH4AIAAPWa88W/ZZ99SCoq9BW79S5fHCOpoXuNAYAIXAAAoJ6ypaWyrz0t+/5iv7oZMUFmzCUyngiXOgMAHwIXAACod+zB/XIe+5u0eaOvGJcgz1U3yvTu715jAPA/CFwAAKBesZvSy8PWkUu+t+0ozzW3yjRv5V5jAFAFAhcAAKgXrLWy/0qVTX1eskcs+X7GuTKXXSMTE+NidwBQNQIXAAAIejY/T87TD0hfpfmKkZEyF0+TOXu4jDHuNQcANSBwAQCAoGa/2ybnn3OkvXt8xSbN5bn6/2Q6sOQ7gOBG4AIAAEHL+c/7sgsflUqKfcUefeS5aqZMYgP3GgOAY0TgAgAAQceWFMu+9ITsR//yFY2R+eUl5cu+ezzuNQcAx4HABQAAgord9335LYQ7tvqKiUnyTL1Z5pTT3GsMAE4AgQsAAAQN+9Vncp6eJ+Xn+YodU+T57f/JNGnmWl8AcKIIXAAAwHW2rEz2zYWyy1/3q5vBI2UuulImKsqlzgDgpyFwAQAAV9lDB+Q8/ncpY4OvGBMrc/l18vQ/273GAKAWELgAAIBr7KYNcp74u3TogK/Y6iR5rrlVptVJ7jUGALWEwAUAAOqcdRzZ5a/LvvmCZB1v3Qw4R2bytTIxsS52BwC1h8AFAADqlM07LOfJ+6X01b5iZKTMxKky51wgY4x7zQFALSNwAQCAOmO3Zch57G/S/r2+YpPm8lz9fzIdfuZeYwAQIAQuAAAQcNZa5S97Tc5TD0plpb6B3v3l+fUNMgmJ7jUHAAFE4AIAAAFlC/N16B93qvDjFb6ixyNz4WSZYRfKeDzuNQcAAUbgAgAAAWN3bpPzz7+p8IddvmLDxvJMu1kmpYd7jQFAHSFwAQCAWmetlf1kheyix6SSYt9Al57lYatBI/eaA4A6ROACAAC1yhYVyr7wT9lPP/AVjVHCRVeoYMgvZTwR7jUHAHWMwAUAAGqN3fOdnH/+Vdq9w1dMbKBGN/1JMacNUOG+fe41BwAuIHABAIBa4aR9KLtwvlRU6Ct27i7PtN8rJqWre40BgIsIXAAA4CexxUWyLz0h++93/epm+DiZsZNkIvm4ASB88R0QAACcMPv9LjmP/VXa+V9fMT5RnitvlOl9umt9AUCwCJnAtXXrVq1fv16bN29WZmamDhw4oKioKL3wwguVjnUcR5s2bdKaNWv0zTffaO/evcrPz1eTJk3Us2dPjR07Vs2bN6/2a23atEmpqanKyMhQaWmp2rZtq+HDh2vQoEEBfIcAAAQX5/OPZJ97RCoq8BU7psjz21tkmlT/7ygAhJOQCVyvvfaaVq9efUzH7t27V3fddZckqXHjxkpJSZHH49HmzZu1YsUKffLJJ/rDH/6grl0r32/++eefa+7cubLWqlu3bkpKStKGDRs0f/58bd++XVOmTKnV9wUAQLCxJcWyLy+QXbXcr27OGyMz/nKZyCiXOgOA4BMygSslJUUdOnRQp06d1KlTJ02bNq3G43v37q0LL7xQ3bt399ZKSkr0xBNP6MMPP9SDDz6oBx98UJFH3Heem5ur+fPny3Ec3XTTTRowYIAk6eDBg7rzzju1dOlS9e3bVz16sJEjACA02b27y1ch/G6brxiXIM+vr5c5baB7jQFAkPLU9gvOmDFDb775pg4dOlTbL12jsWPHasKECerbt6+Sk5NrPLZly5a67bbb/MKWJEVFRWnq1KmKj49XVlaWMjIy/MY/+OAD5efnq1+/ft6wJUnJycmaNGmSJGnJkiW184YAAAgyzhf/lnP3jf5hq31nee64n7AFANWo9Stce/fu1YsvvqhXXnlF/fr103nnnadevXrV9pcJmOjoaLVq1UpbtmxRdna239iaNWskSQMHVv5HpU+fPoqKilJ6erqKi4sVHR1dJ/0CABBo1d5COGS0zPgrZKK4hRAAqlPrgevCCy/UqlWrlJ2drc8++0yfffaZmjdvrvPOO0+DBg1Sw4YNa/tL1irHcZSVlSVJla6U7dhRvonjySefXOm8yMhItWvXTlu2bNHu3bvVoUOHQLcKAEDAla9C+Ddp5//cQjhlhkzfn7vXGADUE7UeuC6++GJNmDBBX375pd577z2tW7dOe/fu1aJFi/Tyyy/r9NNP15AhQ4L2qtcnn3yiQ4cOqUGDBurSpYu3np+fr7y8PEnlC21UpXHjxtqyZYuysrIIXACAes/5bJXs8/P9VyFs37l8FcJmLd1rDADqkYAsmuHxeNS3b1/17dtX2dnZ+uCDD7Ry5UplZWUpLS1NaWlpQXnVKysrS88884wkacKECYo64haJwsJC769jYmKqPL+ifuSxNZk5c2alWnR0tObMmSNJatq06TG9TiBULBbSrFkz13pA8GJ+oDrMjdBgiwqVs2CeCt57y68eP2qCkqZcKxN1/LfNMzdQE+YHqhMKcyPgqxQ2btxYv/rVrzR+/HitW7dOK1as0Nq1a4PuqldhYaHuu+8+HT58WKeffrqGDRvmWi8AALil9Lv/6uB9t6t0+xZvzSQkqeGM2xQ78BwXOwOA+qnOloU3xujUU0/VqaeequzsbD344IPauHGjysrKvFe9WrZsqdGjR+vcc8+Vx1PrCyhWq7S0VP/4xz+0detWde3aVddff32lY2JjY72/LioqUnx8fKVjioqKKh1bk7lz59Y4npWVJWvtMb1Wbav4KcK+fftc+foIbswPVIe5Ub85/3lf9oV/SsVFvmLHFJlpv9fhpi10+Cf8f2VuoCbMD1QnGOaGMUatWrU64fPrdB+urKws7+2FR64A2KFDB+3YsUPff/+9nnjiCb3//vv6wx/+oAYNGgS8J8dx9NBDD2ndunVq3769/u///q/KFQbj4+MVHx+v/Px8ZWdnVxm4Kt6Tm7cCAgBwvGxhgeyif8p+utKvzkbGAPDTBTxwOY6j1atX6/3339f69evlOI4kKTExUYMGDdLQoUPVsmVLHTx4UO+++66WLl2qrVu3atGiRbr66qsD3Z4WLFigTz/9VK1atdLtt9+uhISEao9t3769Nm7cqK1bt6pt27Z+Y6WlpdqxY4eioqLUunXrQLcNAECtsDu3yXns79L3O33F+ER5rrxBpnd/9xoDgBARsMC1d+9evf/++/rwww918OBBbz0lJUXDhg3TGWec4X0ITipfgr1i4+I//vGP+vLLLwPVmteiRYu0YsUKNW3aVHfcccdRF+/o06ePNm7cqLS0NJ199tl+Y2vXrlVJSYlOO+009uACAAQ9a63sv/8l+9ICqaTYN9Cpqzy/+b1Mk/r7gDoABJNaD1xpaWlasWKFNmzY4H3+KC4uTmeddZaGDRumdu3a1Xh+p06dlJyc7BfSAmHJkiV68803lZycrDvuuOOYbgMcMmSIUlNTtXr1an322WcaMGCAJOnQoUNauHChJGnUqFEB7RsAgJ/K5ufJPv+I7OqP/ermgl/J/PJSmcg6feIAAEJarX9Hvf/++72/7tChg4YOHaqzzjrrmBeSkOR35etYrV27Vq+//rpfrbS0VLfddpv39+PHj1efPn303//+V88//7wkqXnz5kpNTa3yNYcMGaKuXbt6f5+YmKhrrrlG999/v+bOnavu3bsrKSlJ6enpysvL0wUXXKCePXsed+8AANQV+99MOY//Xdr3va+Y1FCeK2+U6dHHvcYAIETVeuCKiorSz3/+cw0bNkydO3c+odd45JFHjvucnJwcZWZm+tWstX61nJwcSVJeXp736ltGRoYyMjKqfM1TTjnFL3BJ0sCBAzV79mylpqYqMzNTpaWlatOmjYYPH67Bgwcfd98AANQFa63sirdlX39WKiv1DXTpKc/UmTLJTdxrDgBCmLG1vO54Xl5ejQtP4Njt2bOHZeERlJgfqA5zIzjZ3Bw5Tz8grf/CVzQemdEXy4y8SMYTEfAemBuoCfMD1QmGuRF0y8ITtgAACB4242s5C/4hHcjyFZMbyzP1ZpkuPdxrDADCBE/FAgAQgqxTJrvsVdm3X5Ks4xvo2U+eX18vk1TzyrwAgNpB4AIAIMTYg/vlLJgrbUr3FSMiZMZNkTnvlzIej3vNAUCYIXABABBC7Povyp/Xys3xFZu1lOc3N8t0THGvMQAIUwQuAABCgC0tkU19Tva9t/zq5vRfyEyaLhPPM9YA4AYCFwAA9Zzdu6d8b63tm33F6GiZi6fJnDVUxhj3mgOAMEfgAgCgHnPSPpRd+KhUVOArtmkvz7Tfy7Ru515jAABJBC4AAOolW1ggu+gx2U8/8Kubc86XmXCVTHSMS50BAI5E4AIAoJ6xO7bIefw+6YddvmJcgjxTrpPpe6Z7jQEAKiFwAQBQT1hrZd9fLPv6M1JpqW+gU1d5pt4k07SFa70BAKpG4AIAoB6wh3PkPPOAtP4LX9EYmQt+JTP6EplI/kkHgGDEd2cAAIKc3bhOzpP3S4eyfcWGjeW56kaZbr3dawwAcFQELgAAgpQtLZV9+wXZ5amStb6Bnv3k+fX1MkkN3WsOAHBMCFwAAAQhu+97OU/cJ23L8BUjI2XGT5EZ8kv21gKAeoLABQBAkHE+WyW7cL5UeMTeWi3ayDPtZpl2ndxrDABw3AhcAAAECVuYL7vo8cp7a515nszFv5GJjXOpMwDAiSJwAQAQBOy2TDkL7pP27vEV4+JlJl8rz+m/cK8xAMBPQuACAMBF1nFk331D9s2FUlmZb+DkLuV7azVr6V5zAICfjMAFAIBL7MFsOU/dL21c5ysaIzPiIplRF7O3FgCEAL6TAwDgArvui/KNjHNzfMVGTeW5aqZMlx7uNQYAqFUELgAA6pAtKZZ97RnZD5b4D/Q5Q57Lr5NJSHKnMQBAQBC4AACoI3bX9vK9tXZt9xWjo2Um/kbmF8PYWwsAQhCBCwCAALPWyq5cKvvq01JpiW+gbcfyvbVaneRecwCAgCJwAQAQQDbnoJxnH5LWf+FXN+eNkRl3uUxUlEudAQDqAoELAIAAsRvWynl6npRz0FdskCzPr6+X6dHXrbYAAHWIwAUAQC2zJSWyqc/JrnjLf6BnP3mu+J1Mg2RX+gIA1D0CFwAAtcju2iFnwX3Szv/6ipFRMhf9WmbwSBbGAIAwQ+ACAKAWWGtlP1xWvjBGSbFvoE17eabeJNO2g2u9AQDcQ+ACAOAnsjkH5TzzoJS+2q9uzh0lM36KTHSMS50BANxG4AIA4Cew6WvKF8Y4fMhXTGpYvjBGz36u9QUACA4ELgAAToAtLpJ9/VnZD5b4D/TsJ88VM2QaNHKnMQBAUCFwAQBwnOx32+Qs+Ie0e4evGBkl86tfy5zLwhgAAB8CFwAAx8g6juz7i2VTn5VKS30DLIwBAKgGgQsAgGNgD+6X89Q8aeM6v7o575cy4y6XiYp2pzEAQFAjcAEAcBR27adynntYyjvsKzZsJM+vb5A55TT3GgMABD0CFwAA1bCFBbIvL5D9+D3/gVMHyHP5DJmkBu40BgCoNwhcAABUwW7dVL4wxr7vfcXoGJmJU2V+MYyFMQAAx4TABQDAEWxZmeyyV2WXvCQ5jm+gfWd5ps6UadnWveYAAPUOgQsAgB/ZvXvkPDlX2rrJVzQemQt+JTP6YplI/tkEABwf/uUAAIQ9a63sf96XffEJqajAN9CkuTxXzZT5WXf3mgMA1GsELgBAWLOHc+Q8/7D0ZZpf3ZwxWObiaTLxCS51BgAIBQQuAEDYshvWyHnmQenQAV8xPlFm0nR5Tj/LvcYAACGDwAUACDu2qEj29WdkVy71H+jWW54rrpdp3NSdxgAAIYfABQAIK3b7lvLl3r/f6StGRsmMu1xmyGgZj8e95gAAIYfABQAIC9Ypk12eKvv2IqmszDfQpr08U2+SadvBtd4AAKGLwAUACHl23/dynrpf2rzRVzRGZuhYmbGTZKKi3GsOABDSQiZwbd26VevXr9fmzZuVmZmpAwcOKCoqSi+88EKN561atUrLly/Xzp07FRkZqZSUFI0bN05dunSp9pxNmzYpNTVVGRkZKi0tVdu2bTV8+HANGjSolt8VAOCnsNbKfrJC9qUF/su9N2oqz5U3yHTt5V5zAICwEDKB67XXXtPq1auP65xnn31WS5cuVXR0tHr16qWSkhKtX79e69at08yZM9W/f/9K53z++eeaO3eurLXq1q2bkpKStGHDBs2fP1/bt2/XlClTaustAQB+Anv4kJznHpG++p/l3gecI3Ppb2XiE13qDAAQTkImcKWkpKhDhw7q1KmTOnXqpGnTptV4/IYNG7R06VIlJSXpnnvuUatWrSRJGRkZmjVrlubPn6/u3bsrMdH3D3Jubq7mz58vx3F00003acCAAZKkgwcP6s4779TSpUvVt29f9ejRI3BvFABwVHb9F3KefUjKOegrxif8uNz7L1zrCwAQfkJmKaaxY8dqwoQJ6tu3r5KTk496/OLFiyVJ48aN84YtqTy4DR06VPn5+Vq5cqXfOR988IHy8/PVr18/b9iSpOTkZE2aNEmStGTJklp4NwCAE2ELC+Q8P1/OQ3f7h61uveW56yHCFgCgzoVM4DoexcXF2rBhgyRp4MCBlcYramvWrPGrV/y+qnP69OmjqKgopaenq7i4uLZbBgAchd3yrZy7b5D9aLmvGBklM3GqPDfMZm8tAIArQuaWwuOxe/dulZSUqEGDBmrSpEml8Y4dO0qStm/f7lffsWOHJOnkk0+udE5kZKTatWunLVu2aPfu3erQoUPtNw4AqMSWlsgufln2ndck6/gGTupYvtx763buNQcACHthGbiysrIkqcqwJUmxsbFKSEhQXl6eCgoKFBcXp/z8fOXl5UmSGjduXOV5jRs31pYtW5SVlUXgAoA6YHfvkPPk/dKOLb6i8chcMF5m9MUykSz3DgBwV1gGrsLCQklSdHR0tcfExMQoLy9PhYWFiouL855TMVbdOUe+/tHMnDmzUi06Olpz5syRJDVt6t7tL5GR5VOjWbNmrvWA4MX8QHXqam5Yx1H+0ld1+Ln5UonvNu6IFm3U8MY7Fc1y70GH7xuoCfMD1QmFuRGWgctaK0kyxhz1GABAcCnb970OPXiPitP9n7ONGzZGSb/+nTxx8S51BgBAZWEZuOLi4iRJRUVF1R5TsfBFbGys338rzouPr/wPesXrHXlsTebOnVvjeFZWlmvBr+KnCPv27XPl6yO4MT9QnUDODWutbNqHsi8+JhXk+wYaJMtz+QwV9z5d+3PzpNy8Wv/a+On4voGaMD9QnWCYG8YYv1XNj1dYBq6KW/X2799f5XhhYaHy8vKUkJDgDWfx8fGKj49Xfn6+srOzqwxc2dnZfq8PAKgd9nCOnIWPSGs/9R84baA8k6+VSWroTmMAABxFWC4L37p1a0VFRSknJ6fK0LVt2zZJUrt2/itbtW/fXpK0devWSueUlpZqx44dioqKUuvWrQPQNQCEJ7vuCzmzrvMPW3HxMlfeKM81fyBsAQCCWlgGrujoaPXo0UOSlJaWVmm8ota3b1+/ep8+fao9Z+3atSopKVGPHj1qXIwDAHBsbGG+nOcelvPw/2xi3LVX+SbGZwyu8VlcAACCQVgGLkkaOXKkJCk1NVV79uzx1jMyMrRixQrFxcXp3HPP9TtnyJAhiouL0+rVq/XZZ59564cOHdLChQslSaNGjaqD7gEgtNmMDXJm/U723+/6ilHR5ZsY3/gnmSb1d7UqAEB4CZlnuNauXavXX3/dr1ZaWqrbbrvN+/vx48d7r1L16tVLI0aM0LJly3TLLbeoZ8+eKisr0/r16+U4jmbMmKHExES/10tMTNQ111yj+++/X3PnzlX37t2VlJSk9PR05eXl6YILLlDPnj0D/2YBIETZkmLZNxfKvveWdOSiQe07y3PVjTKtTnKvOQAATkDIBK6cnBxlZmb61ay1frWcnBy/8SuuuEIdOnTQ8uXLlZ6eroiICPXo0UPjx49X165dq/w6AwcO1OzZs5WamqrMzEyVlpaqTZs2Gj58uAYPHlz7bwwAwoTdvkXOk3OlPd/5ih6PzMgJMiMmyESGzD9ZAIAwYiwbTgWtPXv2sCw8ghLzA9U5kblhy8pk33lVdsnLUlmZb6Bl2/KrWh1+VtttwgV830BNmB+oTjDMDZaFBwDUW3bPTjlP3S/91/8OBXPeL2UunCwTHeNSZwAA1A4CFwCgzlnHkf1gsWzq81JJsW+gcTN5fn29TNde7jUHAEAtInABAOqUzfpBztMPSBkb/Orm50NkJk6ViU9wqTMAAGofgQsAUCestbIfvyf78pNSUYFvoEGyPJOvlTl1gHvNAQAQIAQuAEDA2YPZcp57WEpf7T/Q9+fyXDZdJqmBO40BABBgBC4AQMBYa2U//0h20WNSfq5vID5R5tLfyvQ/W8YY9xoEACDACFwAgICwhw/JWfiotPY//gM9+soz5TqZ5CbuNAYAQB0icAEAap39Mk3O849Ihw/5ijFxMhOulPnFMK5qAQDCBoELAFBrnNwc5Sy4X86Hy/0HuvSU54rfyTRt4U5jAAC4hMAFAKgVdsMaZS2cL2f/Pl8xOlpm3BSZwSNlPB73mgMAwCUELgDAT2IL82VfeUr23+/6D5zcRZ5f3yDTso07jQEAEAQIXACAE2Y3rpPz7EPS/r2+YmSUzC8vlRk+VsYT4V5zAAAEAQIXAOC42aJC2defkV25zK8eeXKKGl5/pw7Gs68WAAASgQsAcJxs5jdynp4n7fveV4yIkBkxQU2mTJeJjJT27av2fAAAwgmBCwBwTGxxkeybC2VXvC1Z6xto0778Wa32ncrDFgAA8OJfRgDAUdkt38p5+gHph12+ovHInD9OZvQlMlFR7jUHAEAQI3ABAKplS4pl31ok++6bknV8Ay3byvPr62VO7uJabwAA1AcELgBAley2zPJntfZ85ysaIzN0rMyYS2WiY1zrDQCA+oLABQDwY0tKZJe8JLv8dck54qpW89blV7U6d3OvOQAA6hkCFwDAy27fXP6s1q7tvqIxMkNGy4ydLBPDVS0AAI4HgQsA8ONVrZdll7/mf1WrWUt5rvidTEoP95oDAKAeI3ABQJiz27eUP6t15FUtSWbwSJlxl8vExrnTGAAAIYDABQBhypaWyC59RXbZq/5XtZq2KL+q1aWne80BABAiCFwAEIbsji3lz2rt/K9f3QweITNuCle1AACoJQQuAAgj3qta77wmlZX5Bpo0L7+q1bWXe80BABCCCFwAECaqfVZr0AUy46/gqhYAAAFA4AKAEFfts1pNmsszZYZMt97uNQcAQIgjcAFACKtyXy1JZtAImfE8qwUAQKARuAAgBJXvq/WS7PLXK1/V4lktAADqDIELAEKM3ZYp55kHpN07/OqsQAgAQN0jcAFAiLAlxbJvvyj7rzcky75aAAAEAwIXAIQAu+VbOc88KH2/069uzh0lM+5ymZhYlzoDACC8EbgAoB6zRUWyb78g+97b/le1mrUsv6qV0sO95gAAAIELAOorm/G1nGcflPbu8RWNkRnyS5mxk2RiYtxrDgAASCJwAUC9YwsLZN94XnblUsla30CLNvJcMUOmc3f3mgMAAH4IXABQj9iN6+Q897CU9YOvaDwyQ8fIjLlUJpqrWgAABBMCFwDUA7YgX/a1Z2Q/Wu4/0Oqk8me1Tu7iTmMAAKBGBC4ACHI2fY2chY9I2Vm+oscjc/54mVEXy0RFudccAACoEYELAIKUzTss+/KTsp9+4D/Qpr08v75epn1ndxoDAADHjMAFAEHIfpkm54VHpUMHfMWISJmRE2QuGC8TyVUtAADqAwIXAAQRe/iQ7IuPy37xb/+B9p3Ln9Vq28GVvgAAwIkhcAFAELDWyn7+kexLT0i5Ob6ByKjy1QeHjpWJiHCvQQAAcEIIXADgMntgf/ntg+s+9x/o3E2eKTNkWrZ1pzEAAPCTEbgAwCXWWtmP35N99WmpIM83EBMrc+FkmcEjZTwe9xoEAAA/GYELAFxg930v5/lHpI3r/Ae69ZZn8rUyzVq60xgAAKhVBC4AqEPWcWRXLpN94zmpqNA3EJcgc9GvZc4aKmOMew0CAIBaFfaBKyMjQ2+//bY2bdqk3NxcxcbGqmPHjho2bJgGDhxY5TmrVq3S8uXLtXPnTkVGRiolJUXjxo1Tly5d6rh7APWJ3fOdnGcfkrZ86z/Qu788l10j06iJO40BAICACevA9emnn2revHmy1qpTp0465ZRTdODAAX399dfasGGDxowZo8suu8zvnGeffVZLly5VdHS0evXqpZKSEq1fv17r1q3TzJkz1b9/f5feDYBgZUtLZf+VKrvkJam01DeQmCRz8TSZ/mdzVQsAgBAVtoGrrKxMTz75pKy1uuGGG/Tzn//cO5aRkaHZs2fr7bff1pAhQ9SyZfmzFBs2bNDSpUuVlJSke+65R61atfIeP2vWLM2fP1/du3dXYmKiK+8JQPCxO7bIeeZB6bttfnVz+i9kLpkmk9TQpc4AAEBdCNvlr3bt2qWcnBy1adPGL2xJUkpKinr37i1rrbZu3eqtL168WJI0btw4b9iqOH7o0KHKz8/XypUr6+YNAAhqtqRYTupzcv58k3/YSm4sz7W3yTPt94QtAADCQNgGrqioqGM6ruJqVXFxsTZs2CBJVT7bVVFbs2ZNLXUIoL6ymd/I+dP1su+8JjmOt25+MUye2Q/LnDrAxe4AAEBdCttbClu0aKEWLVpo165d+s9//lPplsJ169apefPm6t69uyRp9+7dKikpUYMGDdSkSeUH2zt27ChJ2r59e928AQBBxxbmy6Y+J7tymf9A0xbyXH6dTLfe7jQGAABcE7aBy+PxaPr06frrX/+qefPmafHixWrRooUOHDigb7/9Vp07d9aMGTMUGVn+R5SVlSVJVYYtSYqNjVVCQoLy8vJUUFCguLi4OnsvANxn09fIWfiIlJ3lKxqPzJDRMmMvk4mJda85AADgmrANXJLUrVs3zZo1S/fdd5+2bNmiLVu2SJLi4uLUs2dPNWrUyHtsYWH5fjnR0dHVvl5MTIzy8vJUWFh4TIFr5syZlWrR0dGaM2eOJKlp06bH9X5qU0XQbNasmWs9IHgxP3ycnIPKefIBFa5a7lePbHeyGlz3R0WnnOJSZ+5gbqA6zA3UhPmB6oTC3AjrwPXxxx/r0Ucf1c9+9jPdcMMNatu2rQ4cOKDFixcrNTVVGzZs0KxZsxQZGSlrrSTVuHRzxTEAQp+1VoX/fk+Hn5wn59AB30BkpBJ/dYUSxl8uc4zPigIAgNAVtoFrz549euSRR5ScnKxbb71VsbHlt/u0atVK06ZN04EDB7RmzRp9+OGHOu+887xXrIqKiqp9zeLiYknyvtbRzJ07t8bxrKws10JcxU8R9u3b58rXR3AL9/lhs/fJeeGf0vov/Ac6psgz5XcqaNNOBQcPutKb28J9bqB6zA3UhPmB6gTD3DDG+K1QfrzCdpXCTz75RGVlZerdu3eVAemMM86QJH399deSfLf37d+/v8rXKywsVF5enhISEnh+CwhR1nHkfLhMzl3X+Yet6BiZCVfJc+tfZdq0c69BAAAQdML2Cld2drYkKT4+vsrxinpubq4kqXXr1oqKilJOTo72799fafGMbdvK99lp144PW0Aost/vlPPcw1LmN/4D3XrLM/lamWYt3WkMAAAEtbC9wpWcnCxJ3oUy/tfmzZsl+S5jRkdHq0ePHpKktLS0SsdX1Pr27VvbrQJwkS0tlbP0FTmzr/cPW/GJMldcL8+NfyJsAQCAaoVt4OrXr58kaePGjXr33Xf9xjIyMrR06VJJ/pscjxw5UpKUmpqqPXv2+B2/YsUKxcXF6dxzzw106wDqiN2WKefPM2XfXCiVlnjrpu+Z8vzpEXnOHFLjQjoAAABhe0vhySefrNGjR2vx4sVasGCB/vWvf6lNmzY6cOCAMjIyZK3Veeedp169ennP6dWrl0aMGKFly5bplltuUc+ePVVWVqb169fLcRzNmDFDiYmJLr4rALXBFhXKvvWC7IrFknV8A8mN5bnsaplTB1Z/MgAAwBHCNnBJ0uTJk9WlSxe999572rp1q3bv3q3Y2Fh1795dQ4YM0VlnnVXpnCuuuEIdOnTQ8uXLlZ6eroiICPXo0UPjx49X165dXXgXAGqT/fpLOc8/Iu3f61c3Z58vM36KTHyCS50BAID6KKwDlyT1799f/fv3P65zBg0apEGDBgWmIQCusLk5sq88JfvpB/4DzVvLc/l1Ml16uNMYAACo18I+cAEIb9Za2S/+LfvSE9LhQ74Bj0dm+DiZ0RfLREW71yAAAKjXCFwAwpbdv0/OC49K6av9B9p3lmfKDJmTOrrTGAAACBkELgBhxzplsivfkX3jOamo0DcQHS3zy8tkzvulTESEew0CAICQQeACEFbsru1ynn1I2pbhP9D9VHkmTWdPLQAAUKsIXADCgi0pll36iuzyVKms1DeQkCQz4SqZMwazpxYAAKh1BC4AIc9mbChf6v37XX510/8cmYlXyTRIdqcxAAAQ8ghcAEKWzc+Vfe0Z2X+/6z/QuJk8k66R6dnPncYAAEDYIHABCDnWWmntf+S8+Lh06IBvwHhkhoySGXOZTGycew0CAICwQeACEFJsdpacRf+U1n3uP9C2gzyXz5Dp+DN3GgMAAGGJwAUgJFinTPbDd2RTn5eKCnwDUdHlmxcPHSsTybc8AABQt/j0AaDeszv/K+e5hysv9d6lpzyXXyvTvLU7jQEAgLBH4AJQb9niovKl3v+VKpWV+QbiE8uXev/5uSz1DgAAXEXgAlAv2W/Xly/1vnePX52l3gEAQDAhcAGoV2xujuyrT8v+533/gSbN5bnsGpmefd1pDAAAoAoELgD1grVW9rNVsi8vkHJzfAPGIzP0lzK/vFQmJta9BgEAAKpA4AIQ9Oy+7+UsfFT65kv/gXYny3P5dTLtO7vTGAAAwFEQuAAELVtWJrviLdm3F0nFxb6B6BiZMZfKDPmlTESEew0CAAAcBYELQFCy2zLLl3rfuc1/oEef8me1mrZwpzEAAIDjQOACEFRsYb7smy/IfrBEstY3kNRQ5uLfyJz+C5Z6BwAA9QaBC0DQsF+lyVn0uHQgy69uzhoq86srZBKSXOoMAADgxBC4ALjOHtgv58XHpC/T/AdatpFn8rUyKT3caQwAAOAnInABcI11ymRXLZdNfU4qLPANREbKXHCRzAW/komKcq9BAACAn4jABcAV9rttcp5/RNqW4T+Qcoo8k66VadXWncYAAABqEYELQJ2yRYWyi1+Ufe8tyXF8A/GJ5c9pnXmejMfjXoMAAAC1iMAFoM7Y9NVyXvintH+vX90MOEdmwlUyDZLdaQwAACBACFwAAs4ezJZ9eYHs6o/9B5q1lGfSNTLdT3OnMQAAgAAjcAEIGOs4sh/9uChGQb5vICJCZvg4mZETZKJj3GsQAAAgwAhcAALC7twm5/n50tZN/gOdupYv9d6mvTuNAQAA1CECF4BaVb4oxkuy773pvyhGXILM+CkyvxjGohgAACBsELgA1BqbvkbOC49WXhTj9F/ITJwq07CRS50BAAC4g8AF4CezB/fLvrRAds0n/gNNW8hz2dUyPfq60xgAAIDLCFwATph1ymRXLZd94/nKi2IMGysz8mKZGBbFAAAA4YvABeCElGzNkPPQn6VtGf4DnbrKM2m6TNsOrvQFAAAQTAhcAI6LLSxQztMPKn/xK5JT5huI/3FRjLNYFAMAAKACgQvAMbNffSbnxceUn53lVzf9z5GZeKVMAxbFAAAAOBKBC8BR2ex9cl58XPrqM/+B5q3KF8Xofpo7jQEAAAQ5AheAatmyMtn3F8u+vUgqKvQNREYq4cJJKhg0UiaaRTEAAACqQ+ACUCW7LUPO849I323zH0jpoaYzblPkSR1UuG+fO80BAADUEwQuAH5sfq7sGwtlV70jWesbSEySuehKmTPOVWTz5u41CAAAUI8QuABIkqy1sp9/JPvKk1LOQb8xc+Z5Mr+6QiaxgTvNAQAA1FMELgCye3fLeeGf0jdf+Q+0OkmeSdfIpPRwpS8AAID6jsAFhDFbUiK7/HXZZa9KpSW+gahomVETZYaNlYmMcq9BAACAeo7ABYQpu3GdnEX/lL7f5T/Qo688l/5WpllLdxoDAAAIIQQuIMzYnAOyrz4tm/ah/0ByY3ku/o3U5+cyxrjSGwAAQKghcAFhwjqO7Ef/kn3jOSk/zzdgPDLnjpQZc5lMXLx7DQIAAIQgAhcQBuyOrXIWzpe2ZfgPdPiZPJOmy7Tv5E5jAAAAIY7AJengwYN688039eWXXyorK0vR0dFq3ry5evbsqUmTJlU6ftWqVVq+fLl27typyMhIpaSkaNy4cerSpYsL3QPVs4X5sm8tkn1/iWQd30BcvMyFl8ucM1zGE+FegwAAACEu7ANXRkaG7r33XuXl5alt27bq16+fCgsLtXPnTi1ZsqRS4Hr22We1dOlSRUdHq1evXiopKdH69eu1bt06zZw5U/3793fpnQA+1lpp7X/kvLRAOrjfb8z0P0dmwpUyDRu51B0AAED4COvAlZ2drXvvvVclJSW6+eabK4WlzZs3+/1+w4YNWrp0qZKSknTPPfeoVatWkspD26xZszR//nx1795diYmJdfYegP9l9+6R8+Jj0oa1/gPNW8tz2dUy3U91pS8AAIBw5HG7ATctWrRIeXl5mjRpUpVXpjp37uz3+8WLF0uSxo0b5w1bkpSSkqKhQ4cqPz9fK1euDGzTQDVsSYmcJS/LmTXDP2xFRsqMvkSeWQ8StgAAAOpY2Aau3Nxcffrpp4qPj9e555571OOLi4u1YcMGSdLAgQMrjVfU1qxZU7uNAsfAblwn50+/k33rBamk2DfQ/VR5Zj0szy8vkYmKdq0/AACAcBW2txRu2rRJJSUl6tmzpyIjI5WWlqZvv/1WpaWlatOmjc444wwlJyd7j9+9e7dKSkrUoEEDNWnSpNLrdezYUZK0ffv2unoLgOyhA7KvPCX7+Sr/gYaNZCZOlel3FntqAQAAuChsA9d3330nSWrYsKHuvPNOZWT4L5e9aNEiTZ8+XWeccYYkKSsrS5KqDFuSFBsbq4SEBOXl5amgoEBxcXEB7B7hzjplsquWy76xUCr4nz21Bo8o31MrPsG9BgEAACApjANXXl75h9SPPvpIkZGRuvrqq70rFC5fvlxLlizRQw89pNatW6t9+/YqLCyUJEVHV39bVkxMjPLy8lRYWHhMgWvmzJmVatHR0ZozZ44kqWnTpify1mpFZGT51GjWrJlrPaBqJZs36tCjf1Pplm/96pGdu6nh1bcoqnPXgPfA/EB1mBuoDnMDNWF+oDqhMDfCNnA5TvmeRGVlZbrqqqu8z3E1aNBAl19+ubKyspSWlqa33npLv/vd78qX2ZZqvD2r4hggEJzcw8p94Z/KX/6GdMRcM/GJSpp8jeKGjZGJYE8tAACAYBK2gaviCpQxRuecc06l8cGDBystLU3ffPON3/FFRUXVvmZxcfliBbGxscfUw9y5c2scz8rKci3EVfwUYd++fa58ffhYa2U/+1D2laekw4f8xszAQTIX/Vp5DRopLzu7znpifqA6zA1Uh7mBmjA/UJ1gmBvGGL8Vyo9X2Aauiv95ycnJioqKqnb80KHyD7gVt/ft37+/0rGSVFhYqLy8PCUkJPD8FmqN3fOdnBf+KW1K9x9o2bZ8T62uvdxpDAAAAMckbANXxaqCeXl5stZWulUwNzdXku9qVevWrRUVFaWcnBzt37+/0uIZ27ZtkyS1a9cu0K0jDNiiQtmlL8u++6ZUVuYbiI6WGTFBZviFMpGVf1AAAACA4BK2+3C1a9dOzZs3V3FxsTIzMyuNf/3115Kkk08+WVL5YhY9evSQJKWlpVU6vqLWt2/fQLWMMGG/+kzOXdfJvvO6f9jq3V+e2Y/IM3ICYQsAAKCeCNvAJUljxoyRJD399NPKycnx1rdu3aolS5ZIkoYOHeqtjxw5UpKUmpqqPXv2eOsZGRlasWKF4uLijmkTZaAqNusHlT18j5xH/izt3+sbaNJcnmtvU8R1t8s0beFegwAAADhuYXtLoSQNGTJE6enpSktL0w033KCUlBQVFRVp06ZNKi0t1ZAhQzRw4EDv8b169dKIESO0bNky3XLLLerZs6fKysq0fv16OY6jGTNmKDEx0cV3hPrIlpTIvvuG7LJXpB8XXpEkRUTKDBsrM3KCTMyxLcQCAACA4BLWgcvj8eiGG27Qe++9pw8++MB7G2GnTp00dOhQnX322ZXOueKKK9ShQwctX75c6enpioiIUI8ePTR+/Hh17Rr4/Y8QWuzGdXIW/VP6fpf/QJee5YtitDrJncYAAABQK8I6cEnloWv48OEaPnz4MZ8zaNAgDRo0KHBNIeTZg9myrz4l+/lH/gMNkmUmXCXT/+wa93wDAABA/RD2gQuoS7asTHblUtm3XpAKC3wDxiMzeITMmEtl4rktFQAAIFQQuIA6Yrd8K2fho9LObf4DHVPkuewamfad3GkMAAAAAUPgAgLMHs6Rff0Z2U9W+A/EJ8qMu1zmF8NkPGG9YCgAAEDIInABAWIdR/bjd2VTn5fyDvuNmTPPkxk/RSapoUvdAQAAoC4QuIAAsNu3yHnhUWlbhv9A2w7lqw927u5OYwAAAKhTBC6gFtm8XNk3F8quekey1jcQG1e+IMbgUTIREe41CAAAgDpF4AJqgbVW9tOVsq89LR0+5DdmTv+FzIQrZZKbuNQdAAAA3ELgAn4iu/O/5ZsXZ37jP9CyjTyXXi3Trbc7jQEAAMB1BC7gBNmCfNnFL8q+v1hyHN9AdIzMqIkyQ8fIREa51yAAAABcR+ACjpO1VvaLf8u+8pR0KNt/8NSB8lw8VaZJc3eaAwAAQFAhcAHHwe75Ts6ix6Rv1/sPNGspzyXTZHr2c6cxAAAABCUCF3AMbGGB7JKXZVe8JZWV+QYio2Qu+JXM+eNkomPcaxAAAABBicAF1MBaK639j5yXn5QOZPkP9uwnz8W/kWneyp3mAAAAEPQIXEA17Pe75Lz4uPTNl/4DTZrLc/FUqfcAGWPcaQ4AAAD1AoEL+B+2qEh22Suy/3pDKiv1DUREygy/UGbEBJkYbh8EAADA0RG4gB9Za6WvPpPz0hNS9j7/we6nynPJb2VatnGnOQAAANRLBC5Akt27W86LT0gb1vgPNGoqz8SpUp8zuH0QAAAAx43AhbBmi4pkl78mu/x1qfTI2wcjZIaOlRk5QSY2zr0GAQAAUK8RuBCWrLXSus/Lbx/cv9d/sGsveS79rUyrk9xpDgAAACGDwIWwY/fuKQ9a6av9B5Iby0y4SqbfWdw+CAAAgFpB4ELYsMVFsstfl33ndam0xDcQESFz3i9lRk2UiY13r0EAAACEHAIXwoKtuH0w6wf/gS49y28fbN3OncYAAAAQ0ghcCGnV3j7YsLHMhCtlTv8Ftw8CAAAgYAhcCEm2uEj2ndd/XH3wf24fHDJaZvTF3D4IAACAgCNwIaTUuPogtw8CAACgjhG4EDLs3t1yXlpQ9eqDF3H7IAAAAOoegQv1ni0qkn3nVdl/pVbevJjVBwEAAOAiAhfqLWut9NVncl5eUPXmxZdM4/ZBAAAAuIrAhXrJ/rBbzkuPSxvW+g8kNylffZDNiwEAABAECFyoV2xRoeyyV2XffaOK2wfH/Hj7YJx7DQIAAABHIHChXrDWSms/lfPKAik7y3+wW+/y2wdbneROcwAAAEA1CFwIenbPzvLbB7/5yn+gUVN5Jlwp9T2T2wcBAAAQlAhcCFq2sEB26Suy770llR15+2CkzLCxMiMnyMTEutcgAAAAcBQELgQda63sF/+WffVp6eB+/8FTTpPn4mkyLdu40xwAAABwHAhcCCp213Y5Lz4ubUr3H2jcTJ6JU6XTBnL7IAAAAOoNAheCgs3Pk138kuwHiyXH8Q1ERsmcP07m/F/JxMS41yAAAABwAghccJV1HNm0D2Vff0bKOeg/2Ot0eSZOlWneyo3WAAAAgJ+MwAXX2B1b5Sz6p7TlW/+BZi3lmfgbmd6nu9MYAAAAUEsIXKhzNu+w7JsvyK5aLtkjbh+MipYZ8SuZ4eNkoqLdaxAAAACoJQQu1BnrOLIfvyf7xnNS7mH/wT5nyHPRlTJNW7jTHAAAABAABC7UCbstQ86ix6T/ZvoPtGxTvsz7Kae50xgAAAAQQAQuBJQ9fEg29TnZj9/zH4iJlRk1Uea8X8pERrnTHAAAABBgBC4EhC0rk131juxbL0j5eX5jpv/ZMr/6tUyjJi51BwAAANQNAhdqnc34Ws6Lj0k7/+s/0Ka9PJdMk+nS05W+AAAAgLpG4EKtsQf3y772jOxnq/wH4uJlxlwmM2iETESEK70BAAAAbiBw4SezpSWy7y+WXfyyVFTgN2bOHCIz7nKZBo1c6g4AAABwD4HrCLm5ubrhhhuUk5Oj1q1ba968edUeu2rVKi1fvlw7d+5UZGSkUlJSNG7cOHXp0qXuGg4C9usv5bz0uPT9Lv+Bdp3kufS3Mp26utMYAAAAEAQIXEd49tlndfjw4WM6bunSpYqOjlavXr1UUlKi9evXa926dZo5c6b69+9fB926y2b9IOeVJ6Uv0/wHEpJkLpws84uhMh5uHwQAAEB4I3D9KD09XatWrdJ5552nFStWVHvchg0btHTpUiUlJemee+5Rq1atJEkZGRmaNWuW5s+fr+7duysxMbGuWq9TtrhI9l9vyL7zmlRS7BswHplzhpc/q5XYwL0GAQAAgCDicbuBYFBcXKwnnnhCbdu21ejRo2s8dvHixZKkcePGecOWJKWkpGjo0KHKz8/XypUrA9qvG6y1sl+lybnzWtm3F/mHrU5d5bn9H/Jcdg1hCwAAADgCgUvSq6++qh9++EFTp05VRA2r6BUXF2vDhg2SpIEDB1Yar6itWbMmMI26xH6/U84Ds+Q88hdp/17fQMNGMlfeKM///VWmXSf3GgQAAACCVNjfUrh9+3YtWbJEgwYNUvfu3bV3795qj929e7dKSkrUoEEDNWlSedPejh07el8zFDgFeXJee1p2xWKprNQ3EBEhM2S0zKiLZeLi3WsQAAAACHJhHbgcx9Fjjz2m+Ph4TZo06ajHZ2VlSVKVYUuSYmNjlZCQoLy8PBUUFCguLq5W+60r1loVrPqXDj/zsOyBLP/Bbr3LNy9udZI7zQEAAAD1SFgHruXLl2vz5s2aPn26kpKSjnp8YWGhJCk6OrraY2JiYpSXl6fCwsKjBq6ZM2dWqkVHR2vOnDmSpKZNmx61p0DIW/yyDj05z6/madZSDa68XjEDz5ExxpW+EDwiI8u/dTRr1szlThBsmBuoDnMDNWF+oDqhMDfC9hmurKwsvfTSS+revbsGDRp0TOdYayWpxsBRcUx9FnfuSHmSG5f/JipaCROvVLOHX1TsGYMIWwAAAMBxCNsrXAsWLFBpaammTp16zOdUXLEqKiqq9pji4vLV+2JjY4/6enPnzq1xPCsry7UAlzj5GhV99m+VjJ2kwmYtVZhzWNLR9yhDeKj4KdO+fftc7gTBhrmB6jA3UBPmB6oTDHPDGOO3OvnxCtvAtXbtWiUkJGjBggV+9ZKSEknlYWfWrFmSpFtvvVWxsbHeW/z2799f5WsWFhYqLy9PCQkJ9fb5rQpx545U/JBRfOMDAAAAfoKwDVySlJeXp2+++abKseLiYu9YWVmZJKl169aKiopSTk6O9u/fX2nxjG3btkmS2rVrF8Cu6wa3DgIAAAA/XdgGrldeeaXK+t69e3XdddepdevWmjdvnt9YdHS0evTooS+//FJpaWkaOXKk33haWpokqW/fvgHpGQAAAED9EraLZpyoipCVmpqqPXv2eOsZGRlasWKF4uLidO6557rVHgAAAIAgErZXuE5Ur169NGLECC1btky33HKLevbsqbKyMq1fv16O42jGjBlKTEx0u00AAAAAQYDAdQKuuOIKdejQQcuXL1d6eroiIiLUo0cPjR8/Xl27dnW7PQAAAABBgsD1P5o3b17t811HGjRo0DHv3wUAAAAgPPEMFwAAAAAECIELAAAAAAKEwAUAAAAAAULgAgAAAIAAIXABAAAAQIAQuAAAAAAgQAhcAAAAABAgBC4AAAAACBACFwAAAAAECIELAAAAAAKEwAUAAAAAAULgAgAAAIAAIXABAAAAQIAQuAAAAAAgQCLdbgDVM8a43UJQ9IDgxfxAdZgbqA5zAzVhfqA6bs6Nn/q1jbXW1lIvAAAAAIAjcEshAAAAAAQIgQtVuvXWW3Xrrbe63QaCFPMD1WFuoDrMDdSE+YHqhMLc4BkuVKm4uNjtFhDEmB+oDnMD1WFuoCbMD1QnFOYGV7gAAAAAIEAIXAAAAAAQIAQuAAAAAAgQAhcAAAAABAj7cAEAAABAgHCFCwAAAAAChMAFAAAAAAFC4AIAAACAACFwAQAAAECAELgAAAAAIEAIXAAAAAAQIAQuAAAAAAiQSLcbQHApLi7Wm2++qU8++URZWVlKTExU7969NXHiRDVp0sTt9uCSoqIirVu3TmvWrNGWLVu0b98+OY6jli1basCAARo1apRiY2PdbhNBIDc3VzfccINycnLUunVrzZs3z+2WEAQOHjyoN998U19++aWysrIUHR2t5s2bq2fPnpo0aZLb7cElGRkZevvtt7Vp0ybl5uYqNjZWHTt21LBhwzRw4EC320OAbd26VevXr9fmzZuVmZmpAwcOKCoqSi+88EKN561atUrLly/Xzp07FRkZqZSUFI0bN05dunSpo86PHxsfw6u4uFh33323Nm3apEaNGqlr167at2+fNm/erAYNGuiee+5Ry5Yt3W4TLnj//ff12GOPSZJOOukktWnTRgUFBcrIyFBBQYHatGmjWbNmqWHDhi53Crc98sgj+uijj2StJXBBUvmH6nvvvVd5eXlq27atTjrpJBUWFmrnzp3av3+/XnrpJbdbhAs+/fRTzZs3T9ZaderUSS1atNCBAwf07bffylqrMWPG6LLLLnO7TQTQ3/72N61evdqvdrTA9eyzz2rp0qWKjo5Wr169VFJSog0bNshaq5kzZ6p///6BbvuEcIULXm+88YY2bdqklJQU3X777d4rFkuWLNFzzz2nRx99VLNnz3a5S7ghMjJSw4YN08iRI9WqVStv/cCBA5ozZ462bdumZ555Rtdff72LXcJt6enpWrVqlc477zytWLHC7XYQBLKzs3XvvfeqpKREN998c6UPQ5s3b3apM7iprKxMTz75pKy1uuGGG/Tzn//cO5aRkaHZs2fr7bff1pAhQ/hBbwhLSUlRhw4d1KlTJ3Xq1EnTpk2r8fgNGzZo6dKlSkpK0j333OP9PJKRkaFZs2Zp/vz56t69uxITE+ui/ePCM1yQJJWWlmr58uWSpKuuusrv9rBRo0apffv22rhxo7Zu3epWi3DROeeco6lTp/qFLUlq1KiRrrrqKknS559/rtLSUjfaQxAoLi7WE088obZt22r06NFut4MgsWjRIuXl5WnSpElV/uS5c+fOLnQFt+3atUs5OTlq06aNX9iSyj+E9+7dW9ZaPnOEuLFjx2rChAnq27evkpOTj3r84sWLJUnjxo3z+zySkpKioUOHKj8/XytXrgxUuz8JgQuSpG+//VZ5eXlq0aKFOnbsWGl8wIABklTp0i/Qvn17SVJJSYkOHz7scjdwy6uvvqoffvhBU6dOVUREhNvtIAjk5ubq008/VXx8vM4991y320EQiYqKOqbjgvFKBdxRXFysDRs2SFKVz/dV1NasWVOnfR0rbimEJGn79u2SVGXYkqSTTz7Z7zigwg8//CBJioiI4B/HMLV9+3YtWbJEgwYNUvfu3bV37163W0IQ2LRpk0pKStSzZ09FRkYqLS1N3377rUpLS9WmTRudccYZx/RTbYSeFi1aqEWLFtq1a5f+85//VLqlcN26dWrevLm6d+/uYpcIJrt371ZJSYkaNGhQ5SJuFZ9fg/VzKoELkqSsrCxJqnYlwsaNG/sdB1RYtmyZJOnUU0895p9aInQ4jqPHHntM8fHxrDYHP999950kqWHDhrrzzjuVkZHhN75o0SJNnz5dZ5xxhhvtwUUej0fTp0/XX//6V82bN0+LFy/2WzSjc+fOmjFjhiIj+ZiKckf7nBobG6uEhATl5eWpoKBAcXFxddneUTGTIUkqLCyUJMXExFQ5XvFMV8VxgCStXbtWK1euVEREhCZOnOh2O3DB8uXLtXnzZk2fPl1JSUlut4MgkpeXJ0n66KOPFBkZqauvvlr9+vVTYWGhli9friVLluihhx5S69atvbcmI3x069ZNs2bN0n333actW7Zoy5YtkqS4uDj17NlTjRo1crlDBJOKz5/R0dHVHhMTE6O8vDwVFhYGXeDiGS5Iko62OwC7B+B/7dy5Uw899JCstZo8ebI6dOjgdkuoY1lZWXrppZfUvXt3DRo0yO12EGQcx5FUviLdlClTdO6556pBgwZq3ry5Lr/8cg0cOFClpaV66623XO4Ubvj444912223qWnTpvrLX/6i5557Tg888IDOPPNMpaam6u6772YhJnhVfA41xhz1mGBE4IIkeX8SUFRUVOV4RZ3NbSFJ+/fv11/+8hfl5eVp1KhRGjFihNstwQULFixQaWmppk6d6nYrCEIV/64YY3TOOedUGh88eLAk6ZtvvqnTvuC+PXv26JFHHlGDBg106623qnPnzoqNjVWrVq00bdo09e3bVxkZGfrwww/dbhVB4mifU6XyhTWk4Pysyi2FkCQ1bdpUUvkH6apkZ2f7HYfwlZOTo3vuuUdZWVkaNGiQJk+e7HZLcMnatWuVkJCgBQsW+NVLSkoklV8BmzVrliTp1ltvDcp/BBE4zZo1kyQlJydX+XxnxfihQ4fqtC+475NPPlFZWZl69+5d5feFM844Q2vWrNHXX3+t8847z4UOEWyO9jm1sLBQeXl5SkhICLrbCSUCF35Ucf/8tm3bqhyv2AuD++zDW0FBge69917t2rVL/fv319VXX13j5X2Evry8vGqvUBQXF3vHysrK6rItBIGKVcPy8vJkra30vSI3N1dScP40GoFV8UPc+Pj4Kscr6hVzBGjdurWioqKUk5Oj/fv3V1o8o+Lza7t27dxo76gIXJAkde3aVfHx8frhhx+0bdu2SsvDf/bZZ5KkPn36uNEegkBJSYn+9re/acuWLerdu7duuOEGeTzclRzOXnnllSrre/fu1XXXXafWrVtr3rx5ddsUgka7du3UvHlz7d27V5mZmUpJSfEb//rrryX5th1B+KjYDqBioYz/tXnzZkm+q6BAdHS0evTooS+//FJpaWkaOXKk33haWpokqW/fvm60d1R8WoIkKTIyUueff74k6amnnvJbjXDJkiXavn27unbtqs6dO7vVIlzkOI4eeOABff311+rWrZtuvvlmlusFcFRjxoyRJD399NPKycnx1rdu3aolS5ZIkoYOHepKb3BPv379JEkbN27Uu+++6zeWkZGhpUuXSqp6g1uEr4qQlZqaqj179njrGRkZWrFiheLi4oJ2k3Vjg3lJD9Sp4uJizZ49W5mZmWrUqJG6du2qrKwsZWZmKikpSX/+85/VsmVLt9uEC5YtW6ZnnnlGktS/f/9q74+ePHmyGjRoUIedIRhxhQsVHMfRvHnzlJaWpsTERKWkpKioqEibNm1SaWmphgwZot/+9rdutwkXPP/881q8eLEk6aSTTlKbNm104MABZWRkyFqr8847T9OmTXO5SwTS2rVr9frrr3t/n5mZKWOM3w/3x48f73d31TPPPKNly5YpJiZGPXv2VFlZmdavXy/HcXTjjTcGbUjnR9Twio6O1l133aU33nhDH3/8sb744gslJCTonHPO0cSJE1kwI4wdeR/9559/Xu1xF110EYELgJfH49ENN9yg9957Tx988IH3NsJOnTpp6NChOvvss13uEG6ZPHmyunTpovfee09bt27V7t27FRsbq+7du2vIkCE666yz3G4RAZaTk6PMzEy/mrXWr3bklXFJuuKKK9ShQwctX75c6enpioiIUI8ePTR+/Hh17dq1Tvo+EVzhAgAAAIAA4RkuAAAAAAgQAhcAAAAABAiBCwAAAAAChMAFAAAAAAFC4AIAAACAACFwAQAAAECAELgAAAAAIEAIXAAAAAAQIAQuAAAAAAgQAhcAAAAABAiBCwAAAAAChMAFAAAAAAFC4AIAAACAACFwAQAAAECAELgAAAAAIEAIXAAAAAAQIAQuAABqwZtvvqkJEybokksu0ebNm6s8Zu3atZo4caImTJigjz/+uI47BAC4gcAFAEAtGDNmjHr27KmysjI98MADKigo8Bs/cOCA5s+fL2utzj77bJ111lkudQoAqEsELgAAaoExRjNmzFDDhg31ww8/6IknnvCOWWv18MMPKycnRy1bttTUqVNd7BQAUJcIXAAA1JLk5GRNnz5dxhh9/PHH+vDDDyVJb731ltLT0xUREaHrr79esbGx7jYKAKgzBC4AAGrRaaedppEjR0qSnnrqKX300Ud6+eWXJUmXXHKJOnXq5GZ7AIA6Zqy11u0mAAAIJaWlpbr99tu1detWb61379764x//KGOMi50BAOoaV7gAAKhlkZGRmj59uvf38fHxuvbaawlbABCGCFwAAATAihUrvL8uKCjQf//7X/eaAQC4hsAFAEAtW7NmjZYvXy5Jat++vay1euSRR3Tw4EF3GwMA1DkCFwAAtahivy1JGjRokGbPnq1mzZrp0KFDeuSRR8Sj0wAQXghcAADUEsdx9PDDD+vw4cNq1aqVrrzySsXHx+v6669XRESE1q1bpyVLlrjdJgCgDhG4AACoJW+//XaV+22lpKToV7/6lSTpxRdf9Fu9EAAQ2ghcAADUgs2bN/vtt3XyySf7jV944YU65ZRTVFpaqgceeECFhYVutAkAqGMELgAAfqKCggI98MADKisrU69evTR69OhKx3g8Hl133XVKTEzUnj179NRTT7nQKQCgrrHxMQAAAAAECFe4AAAAACBACFwAAAAAECAELgAAAAAIEAIXAAAAAAQIgQsAAAAAAoTABQAAAAABQuACAAAAgAAhcAEAAABAgBC4AAAAACBACFwAAAAAECAELgAAAAAIEAIXAAAAAAQIgQsAAAAAAoTABQAAAAABQuACAAAAgAAhcAEAAABAgBC4AAAAACBACFwAAAAAECAELgAAAAAIkP8HEDaGdadGk9kAAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Exact solution\n", "def exact(x):\n", " return 73.4523*np.exp(0.1*x) - 53.4523*np.exp(-0.1*x) + 20\n", "\n", "x = np.linspace(0, 10, 101)\n", "\n", "# Plot Exact solution\n", "plt.plot(x, exact(x))\n", "plt.legend('Exact')\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "markdown", "id": "cc9d1e4c", "metadata": {}, "source": [ "## Shooting method\n", "Shooting method는 IVP를 푸는데, 안주어진 초기 조건을 가정해서 경계조건을 만족하도록 shooting 하는 방법이다.\n", "\n", "위 예제를 IVP로 풀 경우 다음과 같이 고차 미분항을 보조변수를 이용해 표현한다.\n", "\n", "$$\n", "\\begin{align}\n", "\\frac{dT}{dx} &= z \\\\\n", "\\frac{dz}{dz} &= h(T-T_a)\n", "\\end{align}\n", "$$\n", "\n", "초기조건으로 $T(0)=T_1$ 주어졌으나 $z(0)$는 주어지지 않아서 이를 가정해서 푼다. \n", "\n", "`solve_ivp`를 이용해서 이를 구현하면 다음과 같다. " ] }, { "cell_type": "code", "execution_count": 3, "id": "d906dd3c", "metadata": {}, "outputs": [], "source": [ "# Constants\n", "Ta, T1, T2 = 20, 40, 200\n", "h = 0.01\n", "\n", "# derivative function\n", "def dydx(t, y):\n", " # y[0], y[1] : T and z\n", " return np.array([y[1], h*(y[0] - Ta)])" ] }, { "cell_type": "code", "execution_count": 4, "id": "405e7a2a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " message: The solver successfully reached the end of the integration interval.\n", " success: True\n", " status: 0\n", " t: [ 0.000e+00 1.000e-01 ... 9.900e+00 1.000e+01]\n", " y: [[ 4.000e+01 4.000e+01 ... 5.063e+01 5.086e+01]\n", " [ 0.000e+00 2.000e-02 ... 2.320e+00 2.350e+00]]\n", " sol: None\n", " t_events: None\n", " y_events: None\n", " nfev: 32\n", " njev: 0\n", " nlu: 0\n", "T(L) for guess z0=0.000: 50.862\n" ] } ], "source": [ "# z(0)가 0일 때 해석\n", "z1 = 0\n", "sol1 = solve_ivp(dydx, t_span=(0, 10), y0=[T1, z1], t_eval=x)\n", "\n", "# Print result\n", "print(sol1)\n", "\n", "# T2\n", "print(\"T(L) for guess z0={:.3f}: {:.3f}\".format(z1, sol1.y[0][-1]))" ] }, { "cell_type": "code", "execution_count": 5, "id": "5c880e71", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T(L) for guess z0=20.000: 285.897\n" ] } ], "source": [ "# z(0)가 0일 때 해석\n", "z1 = 20\n", "sol2 = solve_ivp(dydx, t_span=(0, 10), y0=[T1, z1], t_eval=x)\n", "\n", "# T2\n", "print(\"T(L) for guess z0={:.3f}: {:.3f}\".format(z1, sol2.y[0][-1]))" ] }, { "cell_type": "markdown", "id": "232cc9b0", "metadata": {}, "source": [ "초기 추측값으로 실험한 결과 $z_0 \\in (0, 20)$ 일 때 해가 존재한다. \n", "\n", "$z_0$ 값을 바꿔도 되지만, 이를 root finding 기법으로 찾아보자.\n", "\n", "`root_scalar` 함수를 활용하자." ] }, { "cell_type": "code", "execution_count": 6, "id": "98bc7bc6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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GDRqE1NRUPPPMM2hubsYtt9yC2NhYnDhx4mJ/nO1KCIFPPvkEERERXmF6165dsp9Pa/9r7yWI2dnZaGhoQHx8PEaNGuXVP2fOHADAN99849V30003AQA++uijdh0TERFRR6gotyJvlxHix7ClUgOZk8MQFcNVGheDPyUKKn369AEArF+/Hg8//PAlB6+HHnoImzdvRnJyMhISEpCdnY3ly5fj9OnTWLZsmezYkpIS3HrrraitrUViYiJmzZqFiooKbNiwAd988w1effVVzJs3T3bOypUr8dvf/hZOpxNpaWno27cv9u3bh/fffx8bNmzA559/jsTERADAlClTYLfbkZOTgxEjRmDkyJHuxxk4cOBFvZ4TJ05g9uzZCA0NRXp6OqqqqpCXl4f77rsPH3zwASZPniw7/k9/+hPeeusthIaGYuLEidBoNFi5ciXy8vKgVCov6WfZ3kpLS1FeXo5rr73Wa0loTEwMFixY0Op5OTk5OHbsWLuP/8CBAwDQatgCgKSkJNlx5xowYAD69u2L77//HmazGRqNpl3HRkRE1F5OHLWiMMcI/LinsVotIXOyHpFRjBEXiz8pCio33XQTXn31VVRUVGDixImYMWMGMjIykJqaiiFDhkCSpDbPPXnyJLRaLbZs2YL+/fsDAMrLyzFr1iysWrUKixcvRnx8PADXbMvDDz+M2tpaPPTQQ/j973/vfuy1a9figQcewOOPP47MzExER0cD8MyGSZKEd955B9OmTQMAOJ1OPPfcc3jzzTfx6KOPYt26dQBc4S86Oho5OTmYOXMmFi9efMk/j88++wz33nsv/vSnP7nvFXrzzTfxpz/9Ca+88ooscGVnZ+Ott95Cjx49sGrVKgwePBgAUF9fj4ULF15w1q4zZGVlAQDGjBnj1ZeYmIh//OMfXu15eXlYvXo1IiIiZFUNd+3a1WZAa8v48ePx+eefu/9cUVEBwBPyz9fS3nLc+ZKTk7F+/XoUFBRg/PjxlzQWIiKiznC8zIK9uZ6iV+oQCeOn6BHRnRHiUvCnFaSEEDDYLr/stMrpCg92u6O9hnRR9GrFBUPRT4mPj8fbb7+NRYsW4fTp0/j888/dX5J79uyJBQsW4OGHH0ZERESr5//v//6vO2wBQFxcHG6++Wa8/fbbyMrKcgeuXbt2oaSkBHFxce4Q1WLu3Ln46quvsH79eqxYsQIPPfQQAODjjz+G2WzG/Pnz3WELABQKBf7whz9g7dq1KCwsRF5eHlJTUy/7Z3CuAQMG4JlnnpEVZrj77ruxdOlS5Ofnw2q1umeL/vvf/wJw3X/UErYAIDIyEk8//TRuvfXWdhnT5SopKQEAJCQkXNTxp06dwv333w+73Y7XX39ddt6FZsTa0jLz2MJoNAJAmwVLdDodAMBgMFzw8Q4cOMDARUREfufoIQuK8z1hK1QjIXNyGLpF+nbFSyBi4ApSBpsTd3x2yNfDuGQfLhiMsJAr+4c8efJk7Nq1C5s2bcKOHTuQn5+PgwcPorq6Gq+//jo2bNiA1atXey03VKvVmDBhgtfjDRo0CABw9uxZd1t2djYA4Prrr291qdr8+fOxfv16ZGVluQNXywzNzTff7HV8aGgo5syZg7feegvZ2dntFrjGjx8PtVp+M6tKpUJcXBz27t2Luro69OrVC4Dr3jLAFRjPN3HiRHTv3h11dXXtMq7LUV1dDQBthuVzmUwm3HfffTh79iyee+45r6WTbc2IXQohXGsr2voFQUt/W1oKt9TU1FzROIiIiNpb2UEzDhSa3X/WaCVkTglDeDeGrcvBohkUlEJDQzFv3jy8+OKL2Lx5MwoLC/H0009Dq9Xi2LFjeOGFF7zOiYmJaTU8tcxUnLtZckuBi379+rX6/C3tZ86ccbe1/Hdb57TMrJ1fPONKtLXcraWi3rmv6cyZM5Akqc1zfF0JsampCQAQFhb2k8f+9re/xd69e7Fw4ULcf//9HTKelp9hy0zX+Vr2HTu3euG5wsPDAXheFxERkT8o3S8PW1qdhAnXMmxdCc5wUZcQFRWFBx54ABqNBk8//TS+/fZbr2MuZynjT53TWv/lnHO52vOxfmrGpqNdbEBZunQp1qxZg/T0dPz1r39t9ZjDhw/j1VdfvaTnT0xMdM9WAp4AWllZ2erxLe1tBdXGxkYAntdFRETkS0II/LDPjMMlnsrMOr0C46/RQ6dn2LoSDFxBSq9W4MMFg3/6wDa03PNjt9vba0gXRa/u2EnXlntlWsrHX67evXsDQJsl0lsKJcTExLjbevXqhbKyMpw4caLV+5BOnjzpPs4XYmJicOLECVRWVrrvVTtXW8Gis/Ts2ROAq4hHWzZs2ICXX34Z/fr1w5tvvtnmBtdnz57FZ599dknPP378eFngGjFiBACguLi41eP37dsHABg+fHir/Q0NDQAufwsDIiKi9iKEwIFCM46UesKWPlyB8VPCoNVxQdyVYuAKUpIkXdG9UCqV61y7wrezGpdKCHHBWZ3jx48DuPJQk56eDgBYvXo1nnzySa+liCtXrgQAZGRkuNsyMjKwa9curFq1ClOmTJEdb7VasXbtWtljA3AHhs4IvmlpaThx4gTWrVuHBx98UNa3a9euKw6pV6ol4Bw+fLjV/gMHDuCRRx6BVqvF22+/fcEgM2HChDarB16scePGoVu3bjh27BiKi4u9ysO3VJu87rrrWj2/5XWcW+6fiIioswkhsC/PhONlntsMwiNcYStUw7DVHvhTpKDy4osv4vnnn0d5eblX35EjR/DnP/8ZADBr1qwrep4JEyZg+PDhKC8vx9///nfZcruNGzdiw4YN0Ov1ssp+CxcuhEajwVdffYXNmze7251OJ1544QWcPn0aycnJsoIZLcGwrKzsisZ7Me644w4AwBtvvCELNQ0NDfjLX/7S4c//U1rCa2vl6WtqanDPPffAZDLhlVde6ZQQExISgrvvvhsA8Mc//lF2L9cbb7yBkpISpKenIzk5udXzCwoKEBIS0mY/ERFRRxNOgaJsediK6K7EhGsYttoTZ7goqBgMBrz11lv417/+hYSEBAwePBgqlQoVFRUoLCyE0+nE6NGjsWjRoit6HkmSsGzZMixYsADLli3Dxo0bMXLkSFRUVCAnJwcqlQovv/yybElhbGwsXnzxRfz2t7/F3XffjXHjxrk3Pi4rK0N0dDReeeUV2fOkpKSgZ8+eWLduHW655RbExcVBoVDgtttuw7hx467oNZxv/PjxuPvuu/Huu+9ixowZ7o2Pd+3ahf79+yMlJQX5+fleVQ8v5KmnnnIvrWuZIdu4cSP279/vPqZlZu+nDB48GHFxccjPz/faLPj999/HyZMnERMTg02bNmHTpk1e56enp+P222+/6LFfjEcffRQ7duxAbm4uJk2ahPT0dJw8eRIFBQXo3r07lixZ0up5x44dQ2VlJa655hpuekxERD7hdAoUZBlxqtzmbusepUTG1XqoQxi22hMDFwWVxx57DKNHj8a2bdtw4MAB7N69G83NzejWrRsyMzMxZ84c3H777W3e23Mphg8fjq+//hqvvPIKtm7dinXr1iE8PBwzZ87EQw89hLFjx3qdM3/+fMTFxeG1115Dbm4uCgoKEBMTg5///Od45JFHvCoEajQavP/++3jhhRdQWFiIPXv2QAiBcePGtXvgAoDnn38eiYmJeO+997Bjxw706NEDN9xwA37/+99j5syZkCTposqytzh06BAKCgpkbdXV1e4S75dCkiQsXLgQ//d//4dvvvkG8+bNc/c5na49537q3qz2DlwajQafffYZXn31VXz55Zf4+uuvERERgQULFuCJJ55os2DGF1980SHjISIiuhgOh0DebgPOVHhuWYiKViL9qjCo1O1XcItcJOHr0mPUpsrKygtWhhNCoKamBlFRUe1ajQ7wXdEM8k+VlZXIzMxEfHw8tm3b5rPr4+zZsxg/fjyuuuoqvPvuu5363O1FCIHJkyfDYDAgKytLtil1RzxXR71HtCU6OhoAUFVV1SnPR4GD1wZdCK+PzmO3C+R+b0DVac9neHRvFdIm6qFS+V/Y8odr40Lb5lwMzhcSkdvhw4fd+0e1qKmpwaJFi2C323HjjTf6ZmA/iomJwT333IPNmzfj4MGDPh3L5dq4cSPKysrwxBNPdGjYIiIiOp/dJpC1vVkWtnr1VWHcJP8MW8GCn/ZE5Paf//wHX375JUaNGoWYmBhUVVWhuLgYTU1NSEpKwm9+8xtfDxEPP/wwPv74Y/zjH//A66+/7uvhXBIhBJYuXYphw4bJCqoQERF1NKvViaxtBtTXOtxtffurMTZTB4WCYasjMXARkdvs2bNx5swZ7Nu3DwUFBVAoFIiPj8fs2bPx61//Glqt1tdDREREhKzoRiCRJKnVgh5EREQdyWJ2Ys+2ZjTWO91t/QeGYEyaFhLDVodj4CIit8mTJ2Py5Mm+HgYRERG1E5PRiT3fNaO5yRO24hNDMCpF22n393Z1DFxEREREREHI2OzA7u8MMBo8YSthWCiGj9YwbHUiBi4iIiIioiDT1OjAnu+aYTZ5Kl4PHaXB4BGhDFudjIGLiIiIiCiINNTZsWebAVaLJ2yNGKNBwjCND0fVdTFwEREREREFidpqO7K3G2CzecLW6DQtBiSE+nBUXRsDFxERERFREKg+Y0P2TgMcP26zJUlAcroO/eJDfDuwLo6Bi4iIiIgowJ05ZUPu9wY4f6yPoVAAKeN16NOPYcvXGLiIiIiIiALYqXIr8vcYIX5cRahUAuMm6RHdW+3bgREABi4iIiIiooB1vMyCvbkm959VaiD9qjBERfNrvr/g3wQRERERUQAqO2jGgUKz+8/qEAmZk/WI7MGv+P6EfxtERERERAFECIHS/WaU7re420I1EsZPCUN4hNKHI6PWKHw9AKKOsH37dtx7771ITk5GfHw8Ro4ciSlTpuChhx7Chx9+CKvVKjs+NjYWGRkZPhrt5Ttx4gRiY2Nxyy23+HooXhwOB1avXo0///nPuOmmm5CYmIjY2Fj87ne/u6LHbWhowMiRI/E///M/7TTSy2MymbBx40YsXrwY1113HYYOHYrExERcd911WLp0KQwGwwXP/+yzzzBnzhwMHjwYI0eOxF133YWcnJxWj33mmWeQkJCAioqKjngpREQUQIQQ2F9gkoUtnV6BiVMZtvwVAxcFnZdeegkLFy7E119/jaioKEybNg2TJk2CSqXCl19+iSeffBL19fW+HuZFWbFiBWJjY/Hyyy/7eiiXrLm5GQ888ADeeOMNZGdnw2Qy/fRJF+Gf//wnGhsb8dhjj7XL412uL774Avfddx8++eQTOJ1OTJkyBRkZGThx4gReeuklzJ49G9XV1a2e++yzz+Kxxx7DDz/8gKuuugrJycnYvn075s+fjw0bNngd/+CDDwIA/u///q9DXxMREfk34RQoyjHh6CHPL47Duikw4dow6MMYtvwVlxRSUCkqKsLSpUsREhKCN998E1OnTpX1V1ZW4qOPPkJISHCUSO3duze2bdsGrVbr66F4UavVmD9/PpKTkzFmzBjs378fTz311BU95pkzZ/DOO+9g+vTpGDJkSDuN9PKo1Wr8/Oc/xy9/+UsMGjTI3X7mzBn8/Oc/R3FxMf70pz/htddek523c+dO/Oc//0H37t2xevVq97m5ublYsGABFi1ahPHjxyMyMtJ9Tq9evXDLLbfgww8/xIMPPoihQ4d2ymskIiL/4XQI5GcZUXnC5m6L6K5ExmQ9QkM5h+LP+LdDQaVldmDu3LleYQsA+vTpg8WLF8u+zAYytVrtXqrnb3Q6Hf75z3/i3nvvRWpqKkJDr3yH+08++QQWi8UvllAuWLAAf/vb32RhC3CFo7/85S8AXNfj+ctX33jjDQDAo48+Kjs3LS0Nd911FxobG/HJJ594Pd/8+fMhhMAHH3zQ3i+FiIj8nN0ukL3TIAtbPaKVGH9NGMNWAODfEAWV2tpaAEBUVNRlne9wOLB8+XJMmjQJAwcORFpaGv7yl7/AYrG0enxFRQWefPJJpKenY+DAgRg9ejTuv/9+FBYWtvkcubm5uOeee5CUlISBAwciIyMDTz31FE6fPi077pZbbsGiRYsAAEuWLEFsbKz7fytWrADQ9j1c5y5FrKiowIMPPoikpCQkJCRg1qxZ2LRpU6tjE0Lgvffew7XXXotBgwYhNTUVzzzzDJqbm3HLLbcgNjYWJ06cuNgfZ7sSQuCTTz5BRESEV5jetWuX7OfT2v86cwniyJEjAQAWiwV1dXXudrPZjO+//x4AMGfOHK/zWto2b97s1Tdu3DjExsZi1apVMJvNXv1ERBScbFYn9mxrRtVpu7stpo8KGVeHQa2WfDgyulhcUkhBpU+fPgCA9evX4+GHH77k4PXQQw9h8+bNSE5ORkJCArKzs7F8+XKcPn0ay5Ytkx1bUlKCW2+9FbW1tUhMTMSsWbNQUVGBDRs24JtvvsGrr76KefPmyc5ZuXIlfvvb38LpdCItLQ19+/bFvn378P7772PDhg34/PPPkZiYCACYMmUK7HY7cnJyMGLECPeXeAAYOHDgRb2eEydOYPbs2QgNDUV6ejqqqqqQl5eH++67Dx988AEmT54sO/5Pf/oT3nrrLYSGhmLixInQaDRYuXIl8vLyoFT6dm14aWkpysvLce2113otCY2JicGCBQtaPS8nJwfHjh3r1PEfP34cgGsG8tzZ1MOHD8NisSAqKgp9+/b1Oi8pKQmA69o6nyRJyMzMxMqVK5Gbm4tJkyZ1zOCJiMhvWMxO7NlmQGO9w93Wp78aKRk6KJQMW4GCgStICSFgt4nLPt/pdAIAHHZnew3poqjUEiTp8t9AbrrpJrz66quoqKjAxIkTMWPGDGRkZCA1NRVDhgy54GOfPHkSWq0WW7ZsQf/+/QEA5eXlmDVrFlatWoXFixcjPj4egOvn+/DDD6O2thYPPfQQfv/737sfe+3atXjggQfw+OOPIzMzE9HR0QA8s2GSJOGdd97BtGnTALh+1s899xzefPNNPProo1i3bh0AV/iLjo5GTk4OZs6cicWLF1/yz+Ozzz7Dvffeiz/96U9QqVz/3N9880386U9/wiuvvCILXNnZ2XjrrbfQo0cPrFq1CoMHDwYA1NfXY+HChRectesMWVlZAIAxY8Z49SUmJuIf//iHV3teXh5Wr16NiIgIWVXDXbt2tRnQ2jJ+/Hh8/vnnF3XsW2+9BcAVms9dSnnq1CkAnl8MnE+n0yEiIgL19fVobm5GWFiYrH/s2LFYuXIlsrOzGbiIiIKc0eDEnu+aYWj2fBeLGxSC0alaSAqGrUDCwBWk7DaBjV80+noYl2zmTd2gDrn8N5H4+Hi8/fbbWLRoEU6fPo3PP//c/SW5Z8+eWLBgAR5++GFERES0ev7//u//usMWAMTFxeHmm2/G22+/jaysLHfg2rVrF0pKShAXF+cOUS3mzp2Lr776CuvXr8eKFSvw0EMPAQA+/vhjmM1mzJ8/3x22AEChUOAPf/gD1q5di8LCQuTl5SE1NfWyfwbnGjBgAJ555hl32AKAu+++G0uXLkV+fj6sVqt7tui///0vAODXv/61O2wBQGRkJJ5++mnceuut7TKmy9Uy65OQkHBRx586dQr3338/7HY7Xn/9ddl5F5oRa0vLzONP+fbbb/Hxxx9DrVbjiSeekPW1lIq/UJETrVaLhoYGGAwGr8DV8hoOHDhwKUMnIqIA09TowJ7vmmE2eX55njAsFMNHa67oF9PkGwxcFHQmT56MXbt2YdOmTdixYwfy8/Nx8OBBVFdX4/XXX8eGDRuwevVqr+WGarUaEyZM8Hq8lsIGZ8+edbdlZ2cDAK6//vpWl6rNnz8f69evR1ZWljtwtczQ3HzzzV7Hh4aGYs6cOXjrrbeQnZ3dboFr/PjxUKvVsjaVSoW4uDjs3bsXdXV16NWrFwDXvWWAKzCeb+LEiejevbvsfqTO1lJiva2wfC6TyYT77rsPZ8+exXPPPee1dLKtGbErdejQITzyyCMQQuDpp5+WLQMFXDOjAC77w7J79+4AgJqamisbKBER+a36WjuythtgtXjC1rAkDRKHhzJsBSgWzaCgFBoainnz5uHFF1/E5s2bUVhYiKeffhparRbHjh3DCy+84HVOTExMq+FJp9MBgKzaXEuBi379+rX6/C3tZ86ccbe1/Hdb57TMrJ1fPONKtLV0Ta/XA5C/pjNnzkCSpDbP8XUlxKamJgDwmvVpzW9/+1vs3bsXCxcuxP3339/RQwPgmlG74447UF9fj1/96letPm/L2I1GY5uP07JfWcvfUWvnt/wsiIgouNSctWP3d82ysJWUqsXgEZzZCmSc4QpSKrWEmTd1u+zzlT8uQXPY7T9xZPtSdVC1naioKDzwwAPQaDR4+umn8e2333odczlvZD91Tmv9l3PO5WrPx2qZnfGV8PBwAD8dNpYuXYo1a9YgPT0df/3rX1s95vDhw3j11Vcv6fkTExPds5Xnq62txcKFC1FRUYHbbrsNzzzzTKvHtRTKqKysbLXfaDSioaEBERERrQbLltfe8rMgIqLgceaUDbm7DHD+WB9DkoDkDB36DQiOvUO7sqAIXBaLBUVFRcjLy0NZWRmqqqrgdDrRu3dvZGRkYO7cudBoNLJzPv300wveAH/DDTfgjjvuaLXv4MGDWLVqFUpLS2G329GvXz/MmDEDU6ZMac+XdUUkSbqie6FUKtfkp10RXJOg48ePB+ApH3+5evfuDQBtlkivqKgA4Jo1a9GrVy+UlZXhxIkTrd6HdPLkSfdxvhATE4MTJ06gsrLSfa/audoKCZ2lZ8+eAFxFPNqyYcMGvPzyy+jXrx/efPPNNje4Pnv2LD777LNLev7x48e3Griam5tx55134vDhw5g9ezb+/ve/txl0ExISEBoaipqaGpw6dcqrUuG+ffsAAMOHD2/1/JbXfrnbHhARkX86ecyKwmwjWn63qVACqeP16B2rvvCJFBCCInDt3LnTvZlo//79MWbMGJhMJpSWluLTTz/F999/j2effbbVez+GDh3q/vJ8rvM3M22RnZ2NJUuWQAiB4cOHIzw8HMXFxVi+fDmOHz+OX/ziF+374uiSCCEuOKvTUq77SkNNeno6AGD16tV48sknvZYirly5EgCQkZHhbsvIyMCuXbuwatUqr3ButVqxdu1a2WMDcAcGeyfMNKalpeHEiRNYt24dHnzwQVnfrl27rjikXqkRI0YAcM1OtebAgQN45JFHoNVq8fbbb18wlEyYMMEdiq+ExWLBPffcg6KiIkyZMgWvvfbaBcvPa7VaTJw4EVu2bMG6devwy1/+UtbfUqHyuuuua/X8ltd+/r1hREQUuI6WWlBcYHL/WaUG0ieFISomKL6mE4IkcKlUKkyfPh1z5syR3X9SV1eHF154AUePHsW7776LRx991OvcqVOnXvTMVHNzM5YvXw6n04nFixe7v0zX19fjmWeewbp165CamopRo0a1y+uiS/fiiy/CZrPh5z//OeLi4mR9R44cwZ///GcAwKxZs67oeSZMmIDhw4ejpKQEf//73/G73/3OHfQ2btyIDRs2QK/Xyyr7LVy4EK+//jq++uorXH/99e4v1U6nEy+88AJOnz6N5ORkWcGMlmBYVlZ2ReO9GHfccQe++OILvPHGG5gxY4a7Kl9DQwP+8pe/dPjz/5SWf2+tlaevqanBPffcA5PJhH//+9+dEkgcDgcefPBB7Nq1CxkZGRecUTvXL3/5S2zZsgWvvPIKpk6d6v7lTm5uLj744AOEh4fjZz/7WavnFhQUAJCHciIiCkxCCJTut6B0v2cz+5BQCRlX6xHZIyi+otOPguJvc/LkyV5VyABXRa/77rsPTz/9NLKzs2G322XlsS/Vli1bYDQakZaWJpu5iIyMxJ133omXXnoJa9euZeDyIYPBgLfeegv/+te/kJCQgMGDB0OlUqGiogKFhYVwOp0YPXo0Fi1adEXPI0kSli1bhgULFmDZsmXYuHEjRo4ciYqKCuTk5EClUuHll1+WLSmMjY3Fiy++iN/+9re4++67MW7cOPfGx2VlZYiOjsYrr7wie56UlBT07NkT69atwy233IK4uDgoFArcdtttGDdu3BW9hvONHz8ed999N959913MmDHDvfHxrl270L9/f6SkpCA/P9+r6uGFPPXUU+5lci0zZBs3bsT+/fvdx7TM7P2UwYMHIy4uDvn5+TCbzbJlwu+//z5OnjyJmJgYbNq0CZs2bfI6Pz09HbfffvtFj/2nvPPOO9iwYQMAoEePHnjqqadaPe6ZZ55Bjx493H+++uqrcd999+Gtt97C9OnTcfXVV8Nms2H79u1wOp1YtmyZuxrhuYQQ2LNnDyIiItqtiiUREfmGEAL7C0w4eshTvEqrk5A5JQxh4W2vlKDAFBSB60IGDBgAALDZbGhqamr1i8zFysvLAwBkZmZ69aWkpECtVmPfvn2yvY2ocz322GMYPXo0tm3bhgMHDmD37t1obm5Gt27dkJmZiTlz5uD2229vl7+f4cOH4+uvv8Yrr7yCrVu3Yt26dQgPD8fMmTPx0EMPYezYsV7nzJ8/H3FxcXjttdeQm5uLgoICxMTE4Oc//zkeeeQRrwqBGo0G77//Pl544QUUFhZiz549EEJg3Lhx7R64AOD5559HYmIi3nvvPezYsQM9evTADTfcgN///veYOXMmJEm6qLLsLQ4dOuSelWlRXV3tLvF+KSRJwsKFC/F///d/+OabbzBv3jx3X8tG3T91b1Z7Bq6Ghgb3f7cEr9YsXrxYFrgA4M9//jNGjhyJd999F9u3b4darcakSZPw6KOPtjl7lZ2djVOnTuHee+/1uieViIgCh9MpUJRtxMnjNndbWLgCmVPCoNUF173z5CIJX5ce62Dl5eV4/PHHoVQq8f7777t/O99SNOPqq69GWFgYrFYroqKiMHbs2Dbv37rnnntgMBiwZMmSVkt7P/XUUygrK8OLL77YatGBS1VZWXnBynBCCNTU1CAqKqrdS4W2zAR2xr1D5P8qKyuRmZmJ+Ph4bNu2zWfXx9mzZzF+/HhcddVVePfddzv1uX3tySefxEcffYRvv/0WQ4cOvahzOvI9oi3R0dEAgKqqqk55PgocvDboQrrK9WG3C+TtMuBspefzM6K7EhmT9QgNZdhqjT9cGxfaNudiBP0M1/r16wEAycnJrS6F2r59u+zPK1asQEZGBh588EHZb5GNRiMMBgMAeP22ukWPHj1QVlaG6urqiwpcrS1rCwkJce8R1VKVrS1CCNTV1UGlUrX7l6mWx7uSJZgUeA4dOoR+/fpBq9W626qrq7F48WLY7XbMnz9fdr119vXRt29f3HfffVi+fDkOHz6MYcOGderz+8qZM2ewcuVK3HLLLZd0f5oQAgqFAtHR0Z0WuFquiZYPSKIWvDboQrrC9WGxOLB57SlZ2OoTq8V1c/pCHcKw1ZZguDaC+tt0fn4+tm7dCqVSidtuu03W17t3b9x1110YO3YsevbsCYPBgJKSEnzwwQfIysqC0+nEE0884T7ebPbc0BgaGtrq87W0n3ssUSD597//jVWrViEpKQkxMTGoqqrCvn370NTUhNGjR+OBBx7w9RDx6KOP4qOPPsKSJUvw73//29fD6RTLli0DAPz+97/38UiIiOhyGA12fL26AnU1nnu2BgzSY/L03u6teCh4BW3gOnnyJJYtWwYhBO666y6vGaerr75a9meNRoNJkyZh5MiRePzxx5GTk4ODBw9e9NKdy7FkyZIL9ldXV//kkkKn0wm73c4lhdQuZs6cicrKSuzbtw/5+flQKBSIj4/H7Nmz8etf/xpqtVpWfMYX14der0dxcbHPnt8Xnn32WTz77LMALu01t7xHVFVVcUkh+RyvDbqQYL4+DM0O7PnOAKPB6W6LGxiCUakq1NXV+HBkgcEfrg0uKWxFTU0N/vrXv8JgMGDu3LmYPXv2RZ/bvXt3TJkyBWvWrEFRUZE7cJ27vNBisUCn03mda7FYvI4lCiRtVfwkIiKiS9dQ50DW9mZYzJ5foCcOC8Ww0ZpO+0UY+V7QzWE2Njbi+eefR3V1NaZMmYK77rrrkh+jJcHW1dW523Q6nTtktbUBbEv7T917RURERETBrabKjl1bm2Rha8QYDYaP0TJsdTFBFbhMJhP+9re/oaKiAunp6fjNb35zWRd0c3MzAO+ZqpYS80eOHPE6x263o7y8HGq1Gn379r2M0RMRERFRMDhdYcOebc2w/1j5XZKAMeO0SBjGVVBdUdAELpvNhhdffBFlZWUYM2YMHnvsMSgUl/7yhBDIyckBAK/y8CkpKQCAPXv2eJ2Xn58Pm82GUaNGcQ8uIiIioi7qxFELcr83wOlw/VmhANIm6hE3qPWiaxT8giJwOZ1OvPLKK9i/fz+GDx+Oxx9//ILlqhsbG7Ft2zbYbDZZu9lsxn/+8x8cOnQIkZGRXhuQTp06FVqtFrm5ucjKynK3NzQ04IMPPgAAzJ07tx1f2YW1zN4F+VZqRHSZWt4buHSFiKhzHP7BjMJsE1q+mqnUQMbkMPSO9d6aiLqOoCiasXHjRmRnZwMAwsPD8eabb7Z63F133YVu3brBbDbjtddew9tvv41+/fohKioKRqMRR48eRVNTE/R6PRYtWuRV/j0sLAwPPPAAli5diiVLlmDEiBEIDw/Hvn37YDAYMGvWLCQlJXX46z2XSqWCzWZrs1Q9EXVdNpuNe+kREXUCIQRKiswoO2hxt4VqJGRcrUdEd74Pd3VBcQW03HMFwB28WrNgwQJ069YN4eHhuOGGG3Do0CGcPn0ax44dg0KhQExMDCZPnoy5c+e2ublxZmYmnnvuOaxatQqHDh2C3W5HbGwsZsyYgWuuuabdX9tPCQkJgdlsRkhICH+LTURuQgj3ewMREXUcp1OgKMeIk8c8K6d0YQpkTtZDH6b04cjIX0iC69H8VmVl5U8uFxRCoL6+HiqVClqtFkpl+/zD5j5cdCG8Pvybw+GAyWSC3W5HZGRkp/4yxh/2SyH/xGuDLiRQrw+7XSB/twFnTnk+D7tFKpFxtR4abVDcueNz/nBtcB+uLk6SJERERMBkMqGhoaHd7udqKTjidDp/4kjqinh9+DdJkqDRaBAREcGZbyKiDmK1OJG9w4C6Goe7LSpGhXET9VCH8L2XPBi4goBCoYBer4der2+3wOUPv00g/8Xrw78xZBERdSyT0Yk925rR3Oj5xWPvWDVSxuugVPI9mOQYuIJMe33RankcfnGj1vD6ICKirqqp0YE925phNnp+yR03KASjU7WQFPxcJG8MXEREREREF6G22o7sHQbYrJ6wNWRkKIaM1PCXkNQmBi4iIiIiop9w5pQNubs8GxoDQFKKFvGDuTUPXRgDFxERERHRBZw4akVRjtG9obFCAYzN1KFvf269QT+NgYuIiIiIqBVCCBz+wYIf9prdbSoVMG6SHj17qX04MgokDFxEREREROcRQmB/gQlHD1ndbaEaCRlX6xHRnV+h6eLxaiEiIiIiOofDIVCYZcSpEzZ3mz5MgYzJeujDlD4cGQUiBi4iIiIioh/ZrAI53xtQc9bubovorkTG1XqEahQ+HBkFKgYuIiIiIiIAZpMTWdub0Vjv2dA4urcKaRP0UKlZ9p0uDwMXEREREXV5zU0O7NlmgMngCVuxA9RIHqeDQsmwRZePgYuIiIiIurS6GteGxlaLZ0PjhGGhGD6aGxrTlWPgIiIiIqIuq7UNjUcka5AwVOO7QVFQYeAiIiIioi7peJkFe/NMwI8TW5ICGJuuQ+wAbmhM7YeBi4iIiIi6FCEEDh2w4GAxNzSmjsfARURERERdhtMpsC/PhPIj529oHIaI7txji9ofAxcRERERdQl2u0D+bgPOnPLssaUPVyBzchh0eu6xRR2DgYuIiIiIgp7F4kTODgPqajzVMbpHKZF+lR4hoQxb1HEYuIiIiIgoqBmaHcjaZoCh2bPHVq9YFVIz9VCqWPadOhYDFxEREREFrfpaO7K2y/fYGpAQgqQULSQFwxZ1PAYuIiIiIgpKZyptyNtlgMNzyxaGJWmQODyUGxpTp2HgIiIiIqKgU37Egr25JoiWPbYkYMw4HfoP5B5b1LkYuIiIiIgoaAghULrfgtL9nj22lCogbaIeMb25xxZ1PgYuIiIiIgoKTqfAvlwTyo+ev8eWHhHd+bWXfINXHhEREREFPLtNIHeXAVWnPTdshYUrkDFZD52eGxqT7zBwEREREVFAM5ucyNpuQGP9OXts9VQifRL32CLfY+AiIiIiooDV1OhA1rZmmIyesu99+qkxNlMHpZKVCMn3GLiIiIiIKCDVVNmRs9MAm9UTtgYNCcWIZA3LvpPfYOAiIiIiooBzqtyKgiwjnE5P28ixWgwaEuq7QRG1goGLiIiIiAKGEAJHDlpwoMhT9l2hBMZm6NC3P/fYIv/DwEVEREREAUE4BYoLTDh22FP2XR0iIf0qPXr05Nda8k+8MomIiIjI79ntAvm7DThzylP2XadXIONqPcK6sew7+S8GLiIiIiLya2aTE9k7DGio85R9j+yhRPpVeoRqWPad/BsDFxERERH5raZGB7K2G2AyeKpj9IpVISVTD5WKlQjJ/zFwEREREZFfqjlrR8738rLv8YkhGDVWC0nBsEWBgYGLiIiIiPzOyeNWFGXLy76PSNZg0JBQ7rFFAYWBi4iIiIj8hhACh0ss+GHfOWXfFcDYTJZ9p8DEwEVEREREfsHpFNiXa0L50fPKvk/So0c0v7ZSYOKVS0REREQ+Z7W4imNUn/GUfdeHKZB+tR5h4Sz7ToGLgYuIiIiIfKq5yYZv1p5CXY0nbHXvqcS4SXqEhrLsOwU2Bi4iIiIi8pmGOjs27zwBk9Gzx1bf/mokZ+igVLI4BgU+Bi4iIiIi8okzp2zI222AwzOxhcRhoRg2WsNKhBQ0GLiIiIiIqNMdPWRBcYEJ+HGLLUkCRqVoEZ8Y6tuBEbUzBi4iIiIi6jTCKXCgyIwjpRZ3m0ot4ZqZfaDRGX04MqKOwcBFRERERJ3CbhfI32PAmQrPGkKNVsKMG/ojqmcoqqoYuCj4MHARERERUYczm5zI3mFAQ52nOEa3SCUyrtYjqieXEVLwYuAiIiIiog7VWO9A9o5mmIzC3darrwopmXqo1CyOQcGNgYuIiIiIOszZSlclQrvN0zZwcAhGJmshKRi2KPgxcBERERFRhzh22ILifBOEZ2ILI8dqMWgIlxBS18HARURERETtSjgFDuw148hBTyVCpRJIGa9H71i1D0dG1PkYuIiIiIio3djtAgV7jDhd4VlDqNFKGDdJj8ge/OpJXQ+veiIiIiJqF21VIky/Sg+tTuHDkRH5DgMXEREREV2xhjoHsnc2w8xKhEQyDFxEREREdEXOnHJVInR49jNmJUKiHzFwEREREdFlEULg6CEr9heagJaJLQkYNVaLgYNZiZAIYOAiIiIiosvgdArsLzDh2GGru02pAlLH69GrLysRErVg4CIiIiKiS2KzCuTtNqDqtGcNoVYnIf2qMHSLVPpwZET+h4GLiIiIiC6a0eBA1nYDmhud7rbIHkqMm6SHRstKhETnY+AiIiIiootSW21Hzk4DrBZPJcI+/dUYm66DUsXiGEStYeAiIiIiop908rgVRdlGOD0TWxg8IhRDR2kgSQxbRG1h4CIiIiKiNgkhcLDYjEMHLO42SQGMSdOh/8AQH46MKDAwcBERERFRqxx2gcJsI06dsLnb1CESxk3SIyqaXyOJLgb/pRARERGRF7PJiZydBtTXOtxtYeEKpF+thz6MlQiJLhYDFxERERHJNNQ5kL2zGWajpzhGz14qpE3QQR3CSoREl4KBi4iIiIjcTlfYkL/HAIdniy0MSAjBqBQtFAoWxyC6VAxcRERERAQhBMp+sKBkr9nTKAGjkrWIHxzCSoREl4mBi4iIiKiLczgE9uWacOKY1d2mUgEpE/To1Uftw5ERBT4GLiIiIqIuzGJ2Ivd7A2qrPcUxdHoF0q/SIzyCxTGIrhQDFxEREVEX1dTgQPYOA4wGz27GPaKVSJuoR2goi2MQtQcGLiIiIqIu6EylDfm7DLCfUxyj/8AQJKVqoVTyfi2i9sLARURERNSFCCFwpNSCA0VmwFP1HSPGaDBoaCiLYxC1MwYuIiIioi7C6RDYm2fCiaOe4hhKFZCSqUfvWBbHIOoIDFxEREREXYDF7ETuLgNqqzzFMbQ6CelXhaFbJItjEHUUBi4iIiKiINdY70D2TgNM5xTH6N5TiXET9QjVsDgGUUdi4CIiIiIKYmdO2ZC32wDHOcUx+sWrMTpNx+IYRJ2AgYuIiIgoCAkhUHbQgpIis6ydxTGIOhcDFxEREVGQcTgE9uYYcfK4zd2mVAGp4/Xo1ZfFMYg6EwMXERERURAxm5zI/d6AuppzimPoFUifpGdxDCIfYOAiIiIiChL1tXbk7DTAbPJssNUjWom0CSyOQeQrDFxEREREQeDUCSsKsoxweia2EDcoBEkpWihYHIPIZxi4iIiIiAKYEAKl+80o3W9xt0kSMHKsFvGJISyOQeRjDFxEREREAcpuEyjINuL0SU9xDLVaQuoEHaJ7szgGkT9g4CIiIiIKQEaDAzk7DGhs8GxmHBauwLir9AgLZ3EMIn/BwEVEREQUYGrO2pG7ywCrxVMcI6aPCimZeqhDuISQyJ8EReCyWCwoKipCXl4eysrKUFVVBafTid69eyMjIwNz586FRqNp9dxt27Zh48aNOHnyJFQqFYYMGYKbb74ZQ4cObfP5Dh48iFWrVqG0tBR2ux39+vXDjBkzMGXKlA56hUREREQux8ss2JdngvBkLSQMC8XwJA0kBcMWkb8JisC1c+dOvPHGGwCA/v37Y8yYMTCZTCgtLcWnn36K77//Hs8++ywiIiJk57333ntYt24dQkJCMHr0aNhsNuzduxdFRUVYtGgR0tPTvZ4rOzsbS5YsgRACw4cPR3h4OIqLi7F8+XIcP34cv/jFLzrlNRMREVHX4nQK7C8w4dhhq7tNoQBGj9Ohf3yID0dGRBcSFIFLpVJh+vTpmDNnDvr06eNur6urwwsvvICjR4/i3XffxaOPPuruKy4uxrp16xAeHo7nn3/efV5paSmeffZZLF++HCNGjEBYWJj7nObmZixfvhxOpxOLFy9GRkYGAKC+vh7PPPMM1q1bh9TUVIwaNaqTXjkRERF1BRaLE3m7jKg5a3e3hWokjJukR/eooPg6RxS0gmIHvMmTJ+P++++XhS0A6N69O+677z4Arpkpu93zJrVmzRoAwM033yw7b8iQIZg2bRqMRiO2bt0qe7wtW7bAaDQiLS3NHbYAIDIyEnfeeScAYO3ate374oiIiKhLa6x3YMc3zbKwFdFdiaumhTNsEQWAoAhcFzJgwAAAgM1mQ1NTEwDAarWiuLgYAJCZmel1TktbXl6erL3lz62dk5KSArVajX379sFqtXr1ExEREV2qUyes2Lm5CSaDpxJhbJwaE68Ng1YX9F/jiIJC0P9LPXPmDABAqVS6lweeOnUKNpsN3bp1Q1RUlNc5AwcOBAAcP35c1l5eXg4AGDRokNc5KpUKcXFxsNlsOHXqVLu+BiIiIupahBA4WGxC3i4jHA5P+/AxGozN1EGpYnEM6hqEEHAamn09jCsS9IFr/fr1AIDk5GSo1a4NAKurqwGg1bAFABqNBnq9HgaDASaTCQBgNBphMBgAAD169Gj1vJb2lscnIiIiulR2m0Du90aU7re421RqIP1qPRKHaSBJDFvUNYjaatQ//zjqnn8cwun86RP8VFAv/M3Pz8fWrVuhVCpx2223udvNZjMAICSk7Yo+oaGhMBgMMJvN0Gq17nNa+to659zH/ymLFi3yagsJCcELL7wAAOjZs+dFPU5HUKlcl0Z0dLTPxkD+i9cHtYXXBrWF18bFaWywYcc3p1Bfa3O3RUSqcd2cvojoHryVCHl90LmEEDB9uxZNb78Ci9E14RGesw36ubf6eGSXJ2gD18mTJ7Fs2TIIIXDXXXchPj7e3Sd+3LjiQr8hEudubkFERETUwSpOGLF1YyWsFs9v8vsN0GHK9N4ICVX6cGREncdRdRoNy1+AtSBL1m4tzoduzoKAnOENysBVU1ODv/71rzAYDJg7dy5mz54t69dqtQBcGya3paXwRcuGyedunGyxWKDT6bzOaXm8tjZZPt+SJUsu2F9dXe2z4NfyG6aqqiqfPD/5N14f1BZeG9QWXhttE0LgSKkFB4rMwDkf+4nDQjEsSY2GxlrfDa6T8PogIQTEjk0Qn70NmE3udkmnR/i9j6J5dIbPbtuRJMmrGvqlCLrA1djYiOeffx7V1dWYMmUK7rrrLq9jWpbq1dTUtPoYZrMZBoMBer3eHc50Oh10Oh2MRiNqa2tbDVy1tbWyxyciIiK6EIddYG+uESePe5YQKpTAmHE69BsQvEsIic4lqs/A+f6rQEmRvCMpDT0f/X9Q9oyBIYDDeFAFLpPJhL/97W+oqKhAeno6fvOb37Q67di3b1+o1Wo0NjaipqbGq3jG0aNHAQBxcXGy9gEDBqCkpARHjhxBv379ZH12ux3l5eVQq9Xo27dvO78yIiIiCjYmoxM5Ow1oqPOUIdTqJKRN1COyR1B9RSNqlXA6IbZvhPj8PcDimdWCTg/ptl9CGn8NlD1jfDfAdhI0VQptNhtefPFFlJWVYcyYMXjsscegULT+8kJCQjBq1CgAwJ49e7z6W9pSU1Nl7SkpKW2ek5+fD5vNhlGjRl2wGAcRERFRbZUdO75pkoWtHtGuzYwZtqgrEGdPwfny0xAf/ksetsakQ/Hcq1BMuDYg79dqTVAELqfTiVdeeQX79+/H8OHD8fjjj7ur3bRlzpw5AIBVq1ahsrLS3V5aWorNmzdDq9Xi2muvlZ0zdepUaLVa5ObmIivLcyNfQ0MDPvjgAwDA3Llz2+tlERERURA6XmbBru+aYTF7btiKTwzB+ClhCNUExVczojYJpwPOTV/C+dwjQGmxp0MfDun+xVA8+EdIka1v3RSoguJXKBs3bkR2djYAIDw8HG+++Warx911113o1q0bAGD06NGYPXs21q9fjyeffBJJSUlwOBzYu3cvnE4nHn74YfdGyS3CwsLwwAMPYOnSpViyZAlGjBiB8PBw7Nu3DwaDAbNmzUJSUlLHvlgiIiIKSE6HQHGBCcfLrO42SQEkpWgxIKH1LWeIgok4VQ7nu/8EjpbKO1ImQHHHryF16+6bgXWwoAhczc2e3adbgldrFixY4A5cAHD33XcjPj4eGzduxL59+6BUKjFq1CjMnz8fw4YNa/UxMjMz8dxzz2HVqlU4dOgQ7HY7YmNjMWPGDFxzzTXt96KIiIgoaJhNTuTuMqCu2rOEMFTjul+rR8+g+DpG1CZht0N8vQpi7SeA3e7pCI+A4o7fQEqd6LvBdQJJcMMpv1VZWcmy8OSXeH1QW3htUFu68rVRV2NH7vcGmE2ez/TIHkqkTdRDq+MSQqBrXx/BTpSXuWa1ThyVtUsZk12FMcK7tXGmiz9cGywLT0REROSnyo9YsC/PBKdnL2P0HxiCpFQtlMrgKAhA1Bphs0Ks+QTi61WQ/QOI7AHFnf8DaUy67wbXyRi4iIiIiNqZ0ymwv8CEY4fPuV9LAkaO1SI+MSRoqq8RtUYcLoHzvWXA6ZOydumq6ZBuuRuSLqyNM4MTAxcRERFRO7KYXfdr1VZ57tcKCZWQNkGPqBh+9aLgJcwmiC8/gNiyFjj3tpievaD4+UOQho/x3eB8iP/qiYiIiNpJa/drRXRXYtwk3q9FwU3sL4Dzv68BNWc9jZIEaeo8SDfeCSlU47vB+RgDFxEREVE7aO1+rX7xaoxO1UGp4hJCCk7C0ASx4i2I3VvkHX36Q/GLhyEltF75uyth4CIiIiK6Ak6HwP7CVu7XStYifjDv16LgJISAyP0e4uM3gKYGT4dSCWnmfEhzboOkVvtugH6EgYuIiIjoMrW2v1ZIqITUCXr05P1aFKREXQ2cH74OFJ23/+2ARCjufhhSv4G+GZif4jsBERER0WWorbYjbxfv16KuQzidEDs3QXz+LmAyejpCQiDdcAekqddDUip9Nj5/xcBFREREdImOl1mwL98Ece7+WvEhSErj/loUnMTpk66iGKX75R1Dk1wVCGMuf2PgYMfARURERHSRHA6B4nwTyo9wfy3qGoTdDvH1Koi1KwC7zdOh1UNacA+kSdN43f8EBi4iIiKii2AyOpH7vQH1tZ77tUI1rvu1oqL5lYqCjzh6CM73lwEnj8k7UiZAsfBXkCJ7+GRcgYbvDkREREQ/ofqs634tq8Vzv1b3KCVSJ/B+LQo+wmKG+PJDiG/XQLZuNqIHFLf/GlLKeN8NLgAxcBERERG1QQiBo4esOFBogvBkLQxICMHIsbxfi4KPKM6D84PX5RsYA5Cunglp/s8h6cJ8NLLAxcBFRERE1Aq7XWBvjhEV5Z77VhQKIClVi7hBoT4cGVH7E431rg2Ms7fJO3rFQvHzByENGeWbgQUBBi4iIiKi8xiaHcjZaUBTg2c5lUYrIW2iHt2j+PWJgocQAmLXFojP3gYMTZ4OpRLSjPmQ5t4KSR3iuwEGAb5jEBEREZ3jzCkbCvYYYbN51hBGRbvu1wrV8H4tCh7i7CnX8sGSInnHwCGuUu/94n0yrmDDwEVEREQE12/6Dx2w4GCxWdY+aEgoho/RQKHg/VoUHITdDrHpC1epd5tniwOEaiHdfBekKbMgKbiBcXth4CIiIqIuz2Z1oiDLiDOn7O42pRIYk65DbByXU1HwEGU/uDYwrjgu7xiT7qpA2CPaNwMLYgxcRERE1KU11juQ870BxmbP/Vr6MAXSJurRLZK/5afgIIwGiC/+C7FtA2QlNyO6Q/GzXwKpE7mBcQdh4CIiIqIu6+QxK4pyjXB69jJGr74qjM3QQR3C+7UoOIj83XB+/AZQXytrZ6n3zsHARURERF2O0yFwoMiEo4essvahozQYPCKUv+mnoCBqq+D8+N9AYZa8o09/KO56ENLgEb4ZWBfDwEVERERditnkRO4uA+qqPdNa6hAJKZk6xPRR+3BkRO1DOBwQW9dCfPkhYDmnCIxKDWnOrZBm3gxJxWu9szBwERERUZdRU2VH3i4DLGbPPSzdIpUYN1EHXRjv16LAJ44fhvP914DyMnnH0CQo7vwfSL1jfTOwLoyBi4iIiIKeEAJHSi0oKTLL6gX0jw9BUqoWShWXEFJgE2YjxJcfQmxZBwhPARiEhUNacC+k8ddyqayPMHARERFRULPbBIpyjDh1wuZukxTAqLFaDEgI4ZdQCniiYI/rXq26alm7NGEqpFvugRTezUcjI4CBi4iIiIJYU6MDud8b0Nzo+Y2/RishbaIe3aP4NYgCm6g56wpaRdnyjl6xUNz5AKRho30zMJLhOw0REREFpVMnrCjMNsLh2csYPXupkJKpQ6iGJd8pcAm7HeLbNRCrPwKsFk+HSgVp1i2u/6m5Ybe/YOAiIiKioOJ0CpQUmXGk1CJrTxweimGjNJAUXEJIgUuU/QDnB8uBk8fkHUOToLjjAUh9+vlkXNQ2Bi4iIiIKGmaTE3m7Dait8pR8V6mBsRl69I5lGWwKXMLQDPHF+xDbv4as8ktYtx+LYlzD+xH9FAMXERERBYWas3bk7ZaXfA+PUGDcRD304Sz5ToFJCAGRtQ3i07eApgZZnzRpGqT5v4AUxqIY/oyBi4iIiAKaEAJHDlpQslde8j12gBqj03RQseQ7BShx+iScH/4L+GGvvKNPf9eeWkNG+mZgdEkYuIiIiChg2WwChdlGnD7Jku8UPITVArHhc4iNKwH7OVVfQkIgzbkN0vQbIam4RDZQMHARERFRQGqsd5V8NzSfU/JdJyFtAku+U+ASxflwfvQvoOq0vCMpDYqFv4IU3ds3A6PLxncjIiIiCjgnj1mxN9cIh6c2BqJ7qzA2U4fQUJZ8p8Aj6mogVrwJkfe9vKN7Tyh+9ktgbCZnbAMUAxcREREFDIdDYH+BCcfLrLL2ISNDMWQES75T4BEOB8SWtRBffQRYTJ4OhQLSdddDmrcQkkbruwHSFWPgIiIiooBgNDiQ+70RDXWeaS11iISxGTr06sv7WSjwiMMlcH74uveeWgnDXHtq9R/ok3FR+2LgIiIiIr935pQNBVlG2KyeMoQR3ZVIm6iDTs+S7xRYRHMjxMr3IHZ+I+/Qh7vKvE+8DpKCS2ODBQMXERER+S3hFDi434xDByyy9gEJIRg5VgulkksIKXAIpxNi5zcQq94HDE2yPmnSNEg3/wJSOPfUCjYMXEREROSXLGYn8vcYUX3GUxZbqQRGp+nQLz7EhyMjunTieJlr+eDRUnlH7AAo7nwAUuII3wyMOhwDFxEREfmdmio78ncbYDZ5lhDqwxUYN1GP8AguIaTAIYzNEF9+CPHdBkB4tjBAqBbS9QshTZ0HSclrOpgxcBEREZHfEELgyEELSvaaITxZC337qzFmnA4qNZcQUmAQQkBkfQfx2TtAY72sTxp3FaQF90LqHuWbwVGnYuAiIiIiv2CzOlGYbcLpCpu7TVIAI8ZoMXBwCPcgooAhKo67Ni8u3S/v6B0LxcJfQxqR7JNxkW8wcBEREZHP1dfakbfLCKPBs+RKo5OQNkGP7lH8ukKBQZiMEKs/htiyBnCes3wwJATS7FshTb8JkppbGHQ1fAcjIiIinxFCoPyIFcX5Jtn30+jeKqRk6hASytLY5P+EEBDZ2yE+extoqJN3jkmH4me/hNSzl28GRz7HwEVEREQ+YbcJ7M0zouK4ZwkhJGDoKA0GDw/lEkIKCK7lg28ApcXyjujerqA1epxvBkZ+g4GLiIiIOl1TgwO5uwxobvRMa4WESkgdr0PPXlxyRf6vzeWD6hBIs26BNPNmSGpuX0AMXERERNTJThyzYl+uEQ6Hp61HtBKp4/XQaLmEkPybu/rg5++2vnzwtvshRff2ydjIPzFwERERUaew250oyjGi/IhV1p44PBRDR2mgUHAJIfk3ceKoa/ng4QPyjp69oPjZryCN4fJB8sbARURERB2usd6KLRtPo7baE7bUIRLGZujQqy+XEJJ/E8ZmiK8+gti6Xr55ccvywRk3QQoJ9d0Aya8xcBEREVGHOnXCir25J2Czer6oRvZQInWCHjo9lxCS/xJOJ8TuLRAr3wOaGuSdyRlQ3Hoflw/ST2LgIiIiog7hcAgcKDTh2GH5EsKBg0MwYowWCiWXEJL/EscOuZYPHi2Vd8T0cS0fTEr1zcAo4DBwERERUbszNjuQu8uIhjpPZQy1WoHR4zTo25+V28h/iaZGiC/eh9j5DSCEp8O9efGNrD5Il4SBi4iIiNpV5UkrCrONsJ+zvVaPnqG4dmZvWGwNbZ9I5EPC6YDY9jXElx8AxmZZn5Q6EdKCeyFFRftodBTIGLiIiIioXTgdAiV7zThSapG1D0gIweRp/aBSKVBV5aPBEV2AKN0P58f/Bk4elXf06Q/Fwl9BGj7GNwOjoMDARURERFfMaHAif7cBdTWeJYRKFTAmTYfYASFQqVgcg/yPqKuB+PwdiOzt8g6NFtL1t0O6Zg4kFb8u05XhFURERERX5HSFDYXZRtisnvtdwiMUSJugR1g3pQ9HRtQ6YbNBfPMlxPrPAItZ1ieNvwbS/LshRXT30ego2DBwERER0WVpawlh3MAQjEzRQqViFULyL0IIYG8unCv+A1SdlncOSHQtH0wY5pvBUdBi4CIiIqJLZjQ4kbfLgPpa+RLC0ak69ItnBTfyP+L0SThXvAUU58k7wiMg3XQXpInXQVJw6Su1PwYuIiIiuiRtLSFMnaBHOJcQkp8RJiPE2k8gvl0DODy/IIBC4bpH6/qFkHRhvhsgBT0GLiIiIrooXEJIgUQ4nRC7t0Cseh9orJd3Dk1yLR+MHeCTsVHXwsBFREREP8nY7EDebiOXEFJAEGU/wPnJf4Bjh+QdUTFQLLgXSBkPSeIvCKhzMHARERHRBbW2kTGXEJI/EvU1EKveh9i9Vd4REgJp1i2Qpt8EKSTUN4OjLqvdA9fDDz+MqVOn4pprrkFERER7PzwRERF1EodD4EChCccOW2XtcYNCMHIslxCS/xA2K8Q3X7Ve5n3cVa4y71HRPhoddXXtHrjOnj2Ljz/+GJ9++inS0tJw3XXXYfTo0e39NERERNSBDE2uJYQNdectIUzTod8ALiEk/yCEAAr2wPnZ20D1GXlnv3gofvYrSENH+WZwRD9q98B10003Ydu2baitrUVWVhaysrIQExOD6667DlOmTOGsFxERkZ87VW5FUY4RdrunrVukawlhWDiXEJJ/EBXH4VzxJlBSJO8IC4d0412QrpoGScHrlXxPEkKInz7s0jidThQUFOCbb75BUVERnE4nAECpVGLcuHGYOnUqZ70uQmVlJTrgr+eiREe7pt2rqqp88vzk33h9UFt4bQQ2h11gf6EJx8vkSwgHJLiWECqVl7+EkNcGXcilXB+iqRFi9UcQ2zYCwunpUCpdZd7n/gySnmXeg4U/vHdIkoQ+ffpc9vkdUjRDoVAgNTUVqampqK2txZYtW7B161ZUV1djz5492LNnD2e9iIiI/EhTowN5uwxoavB8gVWpgTFpOvSN4xJC8j1ht0N8tx5izceA0SDvHDEWip/dD6lPf98MjugCOmSGqzVCCBQVFWHz5s3Iz8+H48eN5zjr1TbOcJG/4vVBbeG1EZhOHLViX55RtidsRHclUifooA9rnyVZvDboQn7q+hD78uD89C3g9El5R0wfKG69HxidxjLvQcof3jv8coarNZIkITk5GcnJyaitrcU///lPlJSUwOFwuGe9evfujXnz5uHaa6+FQqHorKERERF1SXabwL58I04es8naBw0JxfDRGiiuYAkhUXsQlSddQas4T96h1UGaexuka+dCUql9Mziii9Sp+3BVV1e7lxfW1ta62+Pj41FeXo7Tp0/jP//5D7799ls89dRT6NatW2cOj4iIqMtoqHMgb7cBhibPEkJ1iITkdB16x/ILLPmWMDRBrPkE4rv1kE29ShKkq6ZDuuEOSN0ifTY+okvR4YHL6XQiNzcX3377Lfbu3esuoBEWFoYpU6Zg2rRp6N27N+rr67Fp0yasW7cOR44cwUcffYTf/OY3HT08IiKiLkUIgeOHrdhfaILznHoD3XsqkTpeD62OK0zId4TdDrFtI8TqjwBjs7xzyCgobrsfUtwg3wyO6DJ1WOA6e/Ysvv32W3z33Xeor693tw8ZMgTTp0/H+PHjoVJ5nj4yMhK33norUlNT8Yc//AEFBQUdNTQiIqIuyWp1Ym+OCZUn5UsIE4eHYugoDRQKLiEk37Hk74bzP0uByhPyjqgYKBbcA6RM4H1aFJDaPXDt2bMHmzdvRnFxsbvgg1arxaRJkzB9+nTExcVd8PyEhARERkbKQhoRERFdmdpqO/J3G2AyeooxhWokjM3QIbo3lxCS74jKE6h9/W+w5u+Wd4RqIc25FdJ18yCpWSmTAle7B66lS5e6/zs+Ph7Tpk3DpEmToNFoLn5Qqk69tYyIiChoCSFQ9oMFP+wz49zCtz17qTA2QweNlksIyTdEUyPEGtd+WtZz17dKEqRJ01z3aUV0990AidpJuycbtVqNCRMmYPr06UhMTLysx3jttdfaeVRERERdj8XsREGWEVWn7e42SQKGJmmQOCyUy7PIJ4TdBrFlHcTaFYDpvP20eJ8WBaF2D1xvvPEG9Hp9ez8sERERXYKq0zYUZBlhMXumtbQ6CSnj9ejRkytJqPMJIYDCLDg/fwc4WynrU/aKRfjdD6ExYQR/EUBBp93fcRm2iIiIfMfpFDhYbMbhEousvXesGmPGaRESyiWE1PlEeRmcn74NHNwn79DqIc29FT1vvRuSOgRN3BibghB/xUVERBQkjAYH8ncbUVfj2bdIoQBGJmsxIDGEMwfU6URdDcSXH0Ds3gLZTYQKBaTJMyHNWwgpPIJFMSioMXAREREFgVMnrCjKMcJ+TsV3fbgCqeP1iOiu9N3AqEsSFjPE119AfL0KsMpnWzEqFYoF90Dqe+HK1UTBgoGLiIgogNntAvsLTCg/YpW19x8YglEpWqhUnNWiziOcTojdWyG+/C9QXyvv7BvnClqjUn0zOCIfYeAiIiIKUI31DuTtNqC50VNSW6UCktJ06DeAS7Soc4kf9sL52dtA+RF5R3gEpBvvgDRxGiQlZ1up62HgIiIiCjBCCBwvs2J/oQlOz+1aiOiuROp4HfTh/FJLnUdUnoRz5btAUba8Q6WGNO16SLMWQNLqfDI2In/AwEVERBRArBYninJMOF1hk7UnDA3FsCQNFEouIaTOIZoaIFZ/DLF9I3DuxsUApPSrId10F6SevXw0OiL/wcBFREQUIGrO2pG/xwCzyVPtLSRUwtgMHWL6qH04MupKhM0KsXkNxIbPAJNR3pkwDIoF90JKGOabwRH5IQYuIiIiP+d0Chw6YEbpAQtwTmXt6N4qJKfroNFyby3qeMLphMjZAfHFf4Gas/LO6N5QzP8FkDKB2w8QnYeBi4iIyI8ZDU7k7zGgrtpzs5YkAcNGa5AwNJRfbqlTiIP74PzsHeD4YXmHLgzS3NsgTZkNSc1ZVqLWBE3gOnLkCPbu3YvDhw/j0KFDqKurg1qtxocfftjq8Z9++ik+//zzNh/vhhtuwB133NFq38GDB7Fq1SqUlpbCbrejX79+mDFjBqZMmdIeL4WIiAiAa2+tvTkm2GyeaS2dXoHU8TpERgXNRzj5sTYLYihVkK6Z7Qpb+nCfjI0oUATNu/Xnn3+O3NzcSz5v6NCh6N27t1f7oEGDWj0+OzsbS5YsgRACw4cPR3h4OIqLi7F8+XIcP34cv/jFLy55DEREROdqa2+t2AFqJKXqoFZzVos6lmish1jzMcT2r70LYqROhHTzzyHF9PHR6IgCS9AEriFDhiA+Ph4JCQlISEjAr371q4s6b+rUqRc9M9Xc3Izly5fD6XRi8eLFyMjIAADU19fjmWeewbp165CamopRo0Zd7ssgIqIurqHOgfzdBjQ3eb7kKlXA6FQd+sVzby3qWMJigfjmS4iNqwCLSd6ZMAyKW+6BlDjcN4MjClBBE7huvPHGDn+OLVu2wGg0Ii0tzR22ACAyMhJ33nknXnrpJaxdu5aBi4iILpkQAkcPWVFSZJJNKET2UCIlk3trUccSTgfEri0QX30I1NfKO1kQg+iKBE3g6gx5eXkAgMzMTK++lJQUqNVq7Nu3D1arFSEh/C0kERFdHIvZicJsI85W2mXtCcNCMWwU99aijiOEAIrzXfdpVRyXd+rDIc251XWvlooFMYguV5cPXMXFxTh27BisViuioqIwduzYNu/fKi8vB9D6/V0qlQpxcXEoKyvDqVOnEB8f35HDJiKiIHG20obCbCMsZk9hjFCNa2+t6N78kksdR5SXwfn5u0BJkbxDpYY0dS6kWQsg6cN8MjaiYNLlA9f27dtlf16xYgUyMjLw4IMPQqPRuNuNRiMMBgMAoEePHq0+Vo8ePVBWVobq6uqLClyLFi3yagsJCcELL7wAAOjZs+fFvox2p1K5Lo3o6GifjYH8F68PaguvjYvncDiRu7sG+wsNsvb+8XpMmhoDrTa4PqJ5bfgPx9lKNH34b5i3bfTq00yeifA7fgVlJxfE4PVBbQmGayO43s0vQe/evXHXXXdh7Nix6NmzJwwGA0pKSvDBBx8gKysLTqcTTzzxhPt4s9ns/u/Q0NBWH7Ol/dxjiYiIztdQZ8V3m06jpsriblMqJYyb2BPDkyJ4nwx1CGdTA5o/fw/GdZ8DdpusLyQpFeF3Pwx1wlAfjY4oeHXZwHX11VfL/qzRaDBp0iSMHDkSjz/+OHJycnDw4EEMHdpxbzxLliy5YH91dbVrbbUPtPwWoaqqyifPT/6N1we1hdfGhQkhUH7Eiv0FJjg8+xgjrJsCqeP16BZpQ3V1te8G2IF4bfiOsFkhtqyFWP8ZYJTPqCJ2ABTz74Z9VArqJQnw0d8Prw9qiz9cG5IkoU+fy5/17bKBqy3du3fHlClTsGbNGhQVFbkD17nLCy0WC3Q6nde5FovF61giIiIAsFqc2JtrQuVJ+czCgIQQjEzWQqnirBa1L+F0QOzZ5qo8WHvel9XIKEg33glp/BRIClbAJOpIDFytaEmwdXV17jadTgedTgej0Yja2tpWA1dtrauMqi/vvSIiIv9TfdaGgj1GmE2eVQvqEAljxmnRpx+r2lL7umDlQa0O0qxbIE2dBymk9VskiKh9MXC1orm5GYD3TNWAAQNQUlKCI0eOoF+/frI+u92O8vJyqNVq9O3bt9PGSkRE/svpFDhYbMbhEousvWeMCskZOmh1Ch+NjIKVOHbIVXnw4D55h1LlKu8++1ZI4d18MjairoqB6zxCCOTk5ADwLv+ekpKCkpIS7Nmzx+sesPz8fNhsNowdO5Z7cBEREQxNDuTvMaK+1nOzliQBw0ZrkDA0lIUxqF2Js5UQX/wXInenV5+UfrVr+WB0bx+MjIi6ZOBqbGxEQUEBJkyYALXas8eJ2WzG+++/j0OHDiEyMhLp6emy86ZOnYpVq1YhNzcXWVlZyMjIAAA0NDTggw8+AADMnTu3814IERH5HSEETh6zYl++CY5z9jHWhyuQkqlDZI8u+dFLHUQ01kGsXQGx/WvIKrEAwPAxUMy/G9KABN8MjogABFHgys/Px8qVK2Vtdrsdf/zjH91/nj9/PlJSUmA2m/Haa6/h7bffRr9+/RAVFQWj0YijR4+iqakJer0eixYt8ir/HhYWhgceeABLly7FkiVLMGLECISHh2Pfvn0wGAyYNWsWkpKSOuX1EhGR/7FafyyMcUJeGCNuUAhGjtVCxcIY1E6E2Qjx9ZcQ33wJWM7bjqb/QFfQGjnWJ2MjIrmgCVyNjY04dOiQrE0IIWtrbGwEAISHh+OGG27AoUOHcPr0aRw7dgwKhQIxMTGYPHky5s6d2+bmxpmZmXjuueewatUqHDp0CHa7HbGxsZgxYwauueaajnuBRETk19oqjDE6TYu+/bnUnNqHsNsgtn0NsW4F0NQg74yKgXTjHZDSJ0NS8P5AIn8hCV9t9EQ/qbKykvtwkV/i9UFt6YrXhtMhcHC/d2GMqBgVxrIwhltXvDbak3A6IXJ2QHz5AVB9Rt4ZFg5pzm2QJs+CdM6tEoGE1we1xR+uDe7DRURE5CPNTQ7k7zaioe68whhJPxbGUHAJIV0Zd4n3Ve8DJ4/KO0NCIU2/EdL0myBpvberISL/wMBFRER0iYQQKD9ixf4Ck6xOAQtjUHsSZT+4glZpsbxDqYR01XRIc38GKaK7bwZHRBeNnwhERESXwGJxYm+OCacrWBiDOoaoPAHnqv8ChXu8+qS0Sa4S77245ydRoGDgIiIiukhVp20oyDLCYpYXxhgzTos+/VgYg66MqKmCWPMxxK4tgHDKO0ckQ3HzzyENSPTN4IjosjFwERER/QSHQ+CHvWYcKZUXxujZy1UYQ6NlYQy6fKKpEWL9ZxDfrQfs8plTDEiEYv4vIA0f45vBEdEVY+AiIiK6gMZ6Bwr2GNDY4JlxUCiAYaM1GDQkFJLEJYR0eYTZCPHNaohNXwBmk7yzVywUN90JpEzgNUYU4Bi4iIiIWiGEwNFDVpQUmeA8Z3VXeDcFxmbqEdFd6bvBUUATNhvE9o0Q6z713ksrMgrS9QshTZgKSclrjCgYMHARERGdx2xyoiDLiOozdln7wMEhGD5aCyULY9BlEE4HxO7vINZ8DNSclXfqwiDNXgDpmtmQQkJ9M0Ai6hAMXEREROeoPGlFUY4JNqunMEaoRkJyug4xfQJzU1nyLSEEkL8bzq8+BCpPyDtDQiFddwOkGTdC0oX5ZoBE1KEYuIiIiADYbQLFBSacOGqVtfeKVWFMmg6hGhbGoEsjhABKCl0l3o8flncqVZCung5pzm3cS4soyDFwERFRl1dbbUdBlhHGZs/NWkolMHKsFnGDQli0gC6ZKPsBzi/+CxzcJ++QJEiZUyDNWwgpurdvBkdEnYqBi4iIuiynU+DQATNKD1gAzwpCRPZQYmymDmHhLFpAl0acPArnlx8CRdnencmZUNx4J6TYuM4fGBH5DAMXERF1Sc1NDhTsMaK+1uFplIDBw0MxZKQGCgVntejiiTOnIFZ/BJGzAxBC3jlsNBQ33QVp0FDfDI6IfIqBi4iIuhQhBMqPWLG/wATHOVlLp1dgbKYOPXryo5Eunqitgli7AuL7zZDtHwAAA4e4ZrRGJPtkbETkH/ipQkREXYbF7ERRjhFnTsnLvfcfGIJRY7VQqTmrRRdHNNZDbPgc4rsNgN0m7+wb59q0eEwG7/8jIgYuIiLqGs6csqEw2wirxbPcSx0iYcw4Lfr0C/HhyCiQCEMzxKYvIL5dA1jM8s7o3pCuvx1S+lWQFLz/j4hcGLiIiCio2W0C+wtNKD8iL/ce3VuF5HQdNFqWe6efJswmiG/XQHz9BWAyyDsje7jKu0+aBknFr1ZEJMd3BSIiClp1NXYU7DHCcE65d4USGDFGi/hElnunnyasFohtGyE2fA40Ncg7w7pBmnULpCmzIIWE+mR8ROT/GLiIiCjotJR7P3TAIisYF9HdVe49vBuXe9GFCbsNYuc3EOs+Bepr5Z1aPaTpN0K6bh4kjc43AySigMHARUREQeWC5d5HaKBQclaL2iYcDog9WyHWfALUnJV3hoRCmjoP0oybIOnDfTNAIgo4DFxERBQUhBA4XmbFgcJWyr1n6NAjmh951DbhdELk7oRY/TFwpkLeqVJDmjIL0qz5kLp198n4iChw8dOHiIgCntnkKvd+tpLl3unSCCGAgt1wrv4YqDgu71QqXYUwZt8KqUdP3wyQiAIeAxcREQW0Uyes2Jtrgs3quVkrJFTC6DSWe6e2CSGAvblwrv4QKD8i75QUkMZfA2nubZCie/tmgEQUNBi4iIgoINmsAsUFRpw8Jt90tldfFcaM0yFUw3Lv5E0IAZQUwvnlh8DRUq9+adxVkK5fCKl3Px+MjoiCEQMXEREFnOqzNhRmGWEyema1lCpgZLIWcYNY7p1aJw4Wu2a0Svd7d47NhOL62yH1i+/0cRFRcGPgIiKigOFwCPyw14wjpRZZe/coJcZm6KAPZ7l38iYOH4Dzq4+AH/Z6dyalQXHDHZAGJHT+wIioS2DgIiKigNBQ59rEuKnRs4mxJAFDRmmQOCwUCgVntUhOHC2F86sPgf0F3p3Dx7iCVsKwzh8YEXUpDFxEROTXnE6Bsh8sOLjfDOHJWgjr5ir3HtmDH2UkJ46Xwbn6I2BvjnfnkJFQXH8HpKGjOn9gRNQl8VOKiIj8lqHJgYIsI+pqHLL2gUNCMTxJA6WKs1rkIcqPwLnmY6Awy7szYRgUN9wBDBvNe/yIqFMxcBERkd9xb2JcZILjnK21NDoJY9N16NlL7bvBkd8RJ4+5glb+bu/O+MFQ3HA7MDKFQYuIfIKBi4iI/IrZ5ERhthFVp+WbGPcboMaoFC3UISz3Ti7iVDnEmk8gcnd6d8YNguL624HR4xi0iMinGLiIiMhvVJRbsS9PvomxOsS1iXHf/tzEmFxE5QlP0BJC3tkv3hW0kjMYtIjILzBwERGRz1ktTuzLN+FUufcmxqPTdNBoOatFgKg8CbH2E4icHd5BK3YAFPMWAmMzISl4vRCR/2DgIiIinzpbaUNRjhFmk3wT41Fjteg/kJsYEyBOn4RYswIiZ7t30OrTH9K8hZBSJzBoEZFfYuAiIiKfsNsEDhSZcLzMKmvvEa1EcroO+jBuYtzVidMnIdaugMjeAdmeAADQux+keT+DlDYRkoLXChH5LwYuIiLqdDVVdhRmGWE0eL5EKxTAsCQNBg0JhcRNjLs0cfokxLpPIbK2txK0YiHN/RmkcZMYtIgoIDBwERFRp3E4BA4Wm1H2g0XW3i1SibEZOnSL5BforuyCM1q9YiHNvQ1S+lUMWkQUUBi4iIioUzTU2VGQZURTwzlfpCVg8PBQDBmhgULJWa2u6oJBK6bvj0HrakhKBi0iCjwMXERE1KGcToHDJRaU7jfL6h3owxUYm6FD9yh+FHVVovKEK2i1VnWwVyykubdCGsegRUSBjZ9yRETUYZoaHSjMMqK+1iFrHzg4BMNGa6FScVarKxIV5RDrVrS+jxaXDhJRkGHgIiKidieEwNFSC0r2meE8J2tpdBKS03WI7qX23eDIZ2zHy+D8778g8r5n0CKiLoOBi4iI2lVTow27tzajpko+q9U/PgQjx2qhDuGsVlcjTh5F3TtLYdm11buzdz9X0GLVQSIKUgxcRETULoQQOLi/AVk7q2C3eWYvQjUSRqfp0DuWs1pdjSgvg3PNCqBwDyznd/bp7wpa3EeLiIIcAxcREV0xk9GJvblGnK1skLX36adGUpoWoaEKH42MfEEcPQTnuhVAUbZ3Z9841z5aqRMgKXhdEFHwY+AiIqLLJoRAxXEbivNNsJ0zq6UOkZCUokXfODUkiUsIuwpR9gOca1cAxXlefar4RITdeg8aE0YyaBFRl8LARUREl8VidmJvngmnT9pk7f0G6DB8jAoaLb9UdxWitNgVtEqKvDvjEqCYdxuips6BpFCgqaqq8wdIRORDDFxERHTJKk9asTfXBKvFM6ulUgGZV8dg8PBuqK6u9uHoqDMIIYAf9rqCVmmx9wHxg6GY+zNgdBokSeKsFhF1WQxcRER00awWJ4oLTKg4Lp/ViopRITldhwHxET4aGXUWIQSwP98VtMp+8D4gYRgUc24DRqVwOSkRERi4iIjoIp05ZUNRjhEWs2dWS6EERozRIj4xhF+ug5wQAijKgnPtp8Dxw94HDBkFxdzbgGGjeS0QEZ2DgYuIiC7IZhXYX2jCiaNWWXv3KCWSM3QIC2dJ72AmnA4gfzec6z4FTh7zPmD4GCjm3gZpyKhOHxsRUSBg4CIiojZVnbahMMcIs/GcWS0FMDRJg4QhoZAUnMkIVsLhgMjZDrHuM+D0Se8DRqW6glbCsM4fHBFRAGHgIiIiL3abwIEiE46XyWe1IrorMTZDh/AIzmoFK2G3QezeCrHhc6DqtPcByZlQzFkAKX5w5w+OiCgAMXAREZFM9Vk7irKNMBqc7jZJAQwZoUHi8FAoOKsVlITVArHzG4ivVwG151WZlCRIqRMhzVkAqd9A3wyQiChAMXAREREAwG4X+GGvCUcPyWe1ukUqkJyuR0R3zmoFI2E2QWzbCLHpC6CxXt6pUEBKnwxp9gJIffr5ZHxERIGOgYuIiFBT5ZrVMjSfM6slAYnDQzFkhAYKJWe1go0wNkNsWQexeTVgaJJ3KlWQJlwLaeZ8SDF9fDNAIqIgwcBFRNSFOewCP+wz40ipRdYe3k2B5AwdInvwYyLYiMZ6iM1fQWxdD5hN8k51CKSrpkOacROkHtG+GSARUZDhJykRURdVV21HQbYRhibPrBYkIHFYKIaM1EDJWa2gImqrITZ9AbHja8AqXzaKUA2kKbMhTb8BUrfuPhkfEVGwYuAiIupiHA6Bg8VmlB20AJ5q79CHKzA2Q4fuUfxoCCbibCXExpUQu7YADru8U6eHdO08SFPnQgrr5psBEhEFOX6qEhF1IXU1dhRmG9Hc6JS1DxoaimGjNFCqOKsVLETFcYj1n0Pk7ACE/O8b4RGQpt0IacosSFqdT8ZHRNRVMHAREXUBDodA6X4zDv9w3qxWmALJ6Tr0iObHQbAQR0vhXP8ZUJjl3dm9J6QZN0OaNA1SaGjnD46IqAviJywRUZCrr3Hdq3X+rNbAIaEYlqSBirNaAU8IARzc5wpaJUXeB8T0cVUcHH8NJJW68wdIRNSFMXAREQWpllmtsh8sEOfMaul+nNWK4qxWwBNOJ7A3B84NnwNHDnofEDvAtYdW2kRICu6jRkTkC/y0JSIKQvW1rnu1mhrOm9UaHIJho7Wc1QpwwuGAyN0JseFzoOK49wGDhkIx+1ZgdBokiX/XRES+xMBFRBRE2pzV0iswJl2HnjF82w9kwmaF2LUF4utVQNVp7wOGj4Fi9gJgaBKDFhGRn+AnLxFRkGhrVis+MQTDR2uhUvMLeKASZiPEto0Q36wGGmq9D0jOhGL2LZAGDun8wRER0QUxcBERBTiHQ+DQATMOl7Q2q6VFzxgWSQhUoqkB4ts1EFvXAUaDvFOhgJQ+2VUMIzbONwMkIqKfxMBFRBTA6mvtKMwyoqmRs1rBRNRUQXzzJcSOrwGrVd6pUrvKuk+/EVJ0b98MkIiILhoDFxFRALrwvVqc1QpUovIExIaVENnbAIdD3qnRQpoyG9J110OK6O6T8RER0aVj4CIiCjB1Na57tc7fV4uzWoFLHDkI54aVQOEe787wCFfImjILki6s08dGRERXhoGLiChAOBwCpcVmHD5oAViBMOAJIYD9BXBuXAkc3Od9QFQMpBk3QZp4HaSQ0M4fIBERtQt+OhMRBYC66h9ntZq4r1agEw4HRP4uiI0rgfIj3gf0jXMVwhh3FSQVP6aJiAId38mJiPyYwy7wQ7EZR0rls1r6MNesVlQ038YDhbBaXHtobfqi9T20EoZBMesWICkNkkLR+QMkIqIOwU9qIiI/VVtlR2GOEYbzZ7WGhGJYkoazWgFCGJshtq6H+HYN0NTgfUBSGhQz5wODR3CzYiKiIMTARUTkZ+x2gR/2mnD0kLwcuD5cgeRxOvTgrFZAEHU1EJtXQ2zfCJhN8k5JAWncJNfSwf4DfTNAIiLqFPzUJiLyI9Vn7SjKMcLYfM6slgQkDAnF0FEaKDmr5fdE5UmIr1dB7PkOcNjlneoQSJOugzSNe2gREXUVDFxERH7AbhMo2WvCscPyWa2wbgokp+vQPYpv1/5OlP3gqjhYmOXdqQuDdM1sSNfOhdQtstPHRkREvsNPcCIiH6s6bUNRjhEmo6cqhiQBCcNCMWSkBkolZ7X8lXA6geI8V9A6dMD7gMgoSNNugHT1dEgaXecPkIiIfI6Bi4jIR2xWgQNFJpQfkc9qhUe4ZrUie/At2l8Juw0iewfE16uAU+XeB/TpD2nmzZDSr4akUnf+AImIyG/w05yIyAfOnLJhb64RZpN8VmvwiFAMHq6BgrNafkmYjRDbN0FsXg3UVXsfkDjCVXEwKZWl3YmICAADFxFRp7JanNhfaMLJYzZZe7dIJZLTdYjorvTRyOhCRGMdxLdrIb5bDxgN3geMSYdi5nxIicM7f3BEROTXGLiIiDpJ5Ukr9uWZYDF7ZrUUCmDwSA0Sh4VCoeCslr8Rp09CbPoSYvdWwC4PyVCqII2/BtL0GyH16e+bARIRkd9j4CIi6mAWsxP78k2oPCH/wh7ZwzWrFR7BWS1/Iw6XwPn1KqAoGxBC3qnVQbp6JqTr5kGKjPLNAImIKGAwcBERdRAhBCrKbSjON8FmPWdWSwkMG6XBwCGc1fInwukEirJdQavsB+8DInpAmnY9pKtmQNLpO3+AREQUkBi4iIg6gMnoxL48I86ckm982yNaiTHjdAgL56yWvxA2K8TuLRCbvgLOVHgf0Kc/pBk3QUqfDEnNioNERHRpGLiIiNqREALlR6w4UGSS3fKjVAHDR2sRnxgCSeKslj8QzY0Q322A2LIWaGrwPmDISChm3AyMYsVBIiK6fEETuI4cOYK9e/fi8OHDOHToEOrq6qBWq/Hhhx9e8Lxt27Zh48aNOHnyJFQqFYYMGYKbb74ZQ4cObfOcgwcPYtWqVSgtLYXdbke/fv0wY8YMTJkypZ1fFREFEmOzA0W5JlSfkc9q9eylwphxWuj0nNXyB6LqNMTm1RA7vwGsFnmnJAFjM6GYcTOkQW1/DhAREV2soAlcn3/+OXJzcy/pnPfeew/r1q1DSEgIRo8eDZvNhr1796KoqAiLFi1Cenq61znZ2dlYsmQJhBAYPnw4wsPDUVxcjOXLl+P48eP4xS9+0V4viYgChBACxw5ZUbLXBIfD065SAyOTteg/kLNa/kAcPQSx6QuIvF2AcMo71SGQJk6FNO0GSDF9fTNAIiIKSkETuIYMGYL4+HgkJCQgISEBv/rVry54fHFxMdatW4fw8HA8//zz6NOnDwCgtLQUzz77LJYvX44RI0YgLCzMfU5zczOWL18Op9OJxYsXIyMjAwBQX1+PZ555BuvWrUNqaipGjRrVcS+UiPxKc6MDhTlG1FU7ZO29+qqQlKqDVselaL4knE5gXy6cm74ASvd7HxDWDdI1cyBdMxtSeETnD5CIiIJe0ASuG2+88ZKOX7NmDQDg5ptvdoctwBXcpk2bhg0bNmDr1q2YN2+eu2/Lli0wGo1IS0tzhy0AiIyMxJ133omXXnoJa9euZeAi6gKcToGygxaUFpvhPGeyRB0iISlFi75xas5q+ZCwWSH2fAex6Uvg9EnvA6J7u/bPGj8VUmhop4+PiIi6jqAJXJfCarWiuLgYAJCZmenVn5mZiQ0bNiAvL08WuPLy8to8JyUlBWq1Gvv27YPVakVISEgHjZ6IfK2hzo6iHBMa6uSzWn37qzEqRYtQDWe1fEU0NUJsWw+xZV3rhTAShkEx/SYgOR2SgvfUERFRx+uSgevUqVOw2Wzo1q0boqK8N60cOHAgAOD48eOy9vLycgDAoEGDvM5RqVSIi4tDWVkZTp06hfj4+PYfOBH5lMMhcOiAGYdLLLK9cEM1EpJStejTj79o8RVx5hTE5q8gdn0LWK3yTkkCkjOgmH4TpMThvhkgERF1WV0ycFVXVwNAq2ELADQaDfR6PQwGA0wmE7RaLYxGIwwGAwCgR48erZ7Xo0cPlJWVobq6moGLKMjUVttRlG1Ec5O82ELcwBAMT9YgJISzWp1NCAGUlcD59ZdAURZkKRjwFMK47gZIvVgIg4iIfKNLBi6z2QwAF1z2FxoaCoPBALPZDK1W6z6npa+tc859/J+yaNEir7aQkBC88MILAICePXte1ON0BJXKdWlER0f7bAzkv7rS9WGzOpG3pwYH9jbL2sPCVZh4bS/E9tf5aGT+qTOuDeGww5K1HYavPobtYLFXvyKiO3Sz50M382YoIrp32Djo0nSl9w26dLw+qC3BcG10ycAlfvwt6IVuaBfn/6aUiLqcinIDvt96Fs1N8n21RoyJRGpGFNSc1epUTpMBps1rYVyzAo6zlV79yn4DoL9+IbSTZ0AK1fhghERERN66ZODSarUAAIvF0uYx1h/vAdBoNLL/bzlPp/P+rXbL45177IUsWbLkgv3V1dU+C34tv0WoqqryyfOTfwv268NqceJAoRknjsnvBQoLV2BMug49egL1DTU+Gp1/64hrQ9RWQ2xZA7F9E2AyeB8wNAmKaTdCJKXCoFDA0NgEoKndnp/aR7C/b9CV4fVBbfGHa0OSJFlV80vVJQNXy1K9mprWvzCZzWYYDAbo9Xp3ONPpdNDpdDAajaitrW01cNXW1soen4gCz6kTVhTnm2Axe37ZIUlA4vBQDB6hgVLJUu+dRRwvg/jmS4jcnZDtKA0ACgWktEmujYrjB/tmgERERBehSwauvn37Qq1Wo7GxETU1NV7FM44ePQoAiIuLk7UPGDAAJSUlOHLkCPr16yfrs9vtKC8vh1qtRt++vDmbKNCYTU4U55tQedIma4/orsSYcTpEdGcJ8c7g3qj4m6+Ag/u8D9DqIF01HdK18yBFBe56fiIi6jq6ZOAKCQnBqFGjUFBQgD179mDOnDmy/j179gAAUlNTZe0pKSkoKSnBnj17cPXVV8v68vPzYbPZMHbsWO7BRRRAhBA4cdSKA4Vm2GyeWS2FEhg6SoNBQ0KhUHBWq6MJiwVi9xaIzauBMxXeB/SIhjR1nitsaVmohIiIAkeXDFwAMGfOHBQUFGDVqlVISUlxr8ssLS3F5s2bodVqce2118rOmTp1KlatWoXc3FxkZWUhIyMDANDQ0IAPPvgAADB37tzOfSFEdNkMzQ7szTWh+oy8KEaPaNesVlg4Z7U6mqivhdi6HmL7BqC5lfuu4ge7lg2mToSk5N8HEREFnqAJXPn5+Vi5cqWszW63449//KP7z/Pnz0dKSgoAYPTo0Zg9ezbWr1+PJ598EklJSXA4HNi7dy+cTicefvhhhIWFyR4vLCwMDzzwAJYuXYolS5ZgxIgRCA8Px759+2AwGDBr1iwkJSV1/IsloisinAJHDllwcJ9ZdmuQSgUMH6PFgISQC1YxpSsnThyF+OYriOztgEMeeD0bFd8IJAzn3wUREQW0oAlcjY2NOHTokKxNCCFra2xslPXffffdiI+Px8aNG7Fv3z4olUqMGjUK8+fPx7Bhw1p9nszMTDz33HNYtWoVDh06BLvdjtjYWMyYMQPXXHNN+78wImpXjfUOFOUYUV8rL8LQq68KSak6aHUs9d5RhNMJFOe57s/6Ya/3AaEaSBOvcy0djLn8alBERET+RBLccMpvVVZWsiw8+aVAvD4cDoHDJWYcKrFAOD3tIaESRqVo0be/mjMp7aC1a0NYzBC7t0J8uxo43cr9WZFRkKbOhXTVDEj6MO9+CgqB+L5BnYfXB7XFH64NloUnIvoJtdV2FOUY0dzolLXHDlBj5FgtQkM5q9URRF0NxNa1ENu+BozN3gcMSPTcn6XixxEREQUnfsIRUdCy2wR+2GfC0UPyDYw1Ogmj03To1Ufto5EFN9vhEjg/fQ8ir5X9s1ruz7ruBmDwCM4qEhFR0GPgIqKgdLbShr25RpiM8mW5AweHYFiSFio1v+i3J+F0AIVZqNm2EbYDhd4HuO/PmgsphnsVEhFR18HARURBxWJxYn+BCRXH5RsYh3VTYMw4HXr05NteexImI8TObyC+XQPUnIXz/AN6REO6di6kq6ZB0vH+LCIi6nr4zYOIgoIQAhXlNuwvMMFq8cxqSRKQODwUg0dooFRyVqu9iKrTEFvWQuz8BjCbvA8YNBTSdTdAShnP/bOIiKhLY+AiooBnNDixL8+Is5Xy/Zwie7g2MO4WyS/87UEIARzaD+fm1UBhNmTlHgFAoYBmwrXQzbsNDT16+WaQREREfoaBi4gClnAKHDtsRck+k2zvXKUSGJakwcDBoZAUnNW6UsJmg8jZ4SrrXn7E+wCd3lXS/Zo5iBw2wtXG0s5EREQAGLiIKEA1Nbg2MK6rkVfBi+6twug0LXR6zmpdKdFYD7FtI8R364HGeu8DYvpCum4epPHXQtJoO318REREgYCBi4gCSlsbGKtDJIwaq0XsAG5gfKVE+RGIb9dAZG8D7HbvA4aPgWLq9UBSKiQF9zAjIiK6EAYuIgoYtVU/bmDcdN4GxnE/bmCs4Zf/y+Uq654N57drgNJi7wNUakjjr3FVHOwX3+njIyIiClQMXETk92w2gZIiE46XyTcw1uokJKXq0KsvNzC+XMJocJV137IWqDnrfUBED0jXzIZ09QxI4RGdP0AiIqIAx8BFRH7tdIUN+/KMMJu4gXF7EqcrILasgdi1FbC0UtZ9QCKk666HlDYRkoqBloiI6HIxcBGRXzKbnCjON6HypHwD4/AI1wbG3aP49nWphBDA/gLXssHiPO8DFApIKRMgTZ0HJAzjvXBERETtgN9YiMivCCFQfsSKA0Um2M/JWgoFMHiEBonDQqHgBsaXRFjMELu3QHy7Fjh90vsAXZhryeA1syH1iO78ARIREQUxBi4i8hvNTQ7szTGipkpe6r1HTyVGj9MhvBtLvV8KUX0GYut6iJ2bAKPB+4A+/V1l3TOmQArVdP4AiYiIugAGLiLyOadD4PBBCw7tN8N5TgFClRoYPlqLAQkhXN52kYQQQGkxnJvXAEXZkNXOBwBJApLSoJg6Dxg+hj9XIiKiDsbARUQ+VVfjKvXe1CAPBv+/vXsPjrO67z/+efamXd1s+SrfDTayLVu+Y2ww2BjbAQylhRQm09BmGoZkaBgok+kwaaaFCQlpptOBIdBmklKSTNOE/koI2GDAYGMbYy6yseSrfMPgC7blm6TV3p/z+2Mv2tWubGO8F0nv14xG+5zn7O4RsxbPR+c831M72q2G2T55fZR6vxgmHJL54F2Zt1+VjhzK7uD1ybpuqawlK2QNG1n4AQIA0E8RuAAURTRitLs5oIN7M0u9l3ktNczxacRoT5FG1ruYUydl1r0ms+FNyd+e3WHYyPjeWdcukeUrL/wAAQDo5whcAAru+NGImho7FezMLPU+boJHU6b75PawzO184ssGd8h+Z6W0dXP2skFJqp8lx9LbpamzZTmYJQQAoFgIXAAKJhiwtX1rQMc+zyz1Xlnl0PSryzV4KL+Szie1bPCdldLhT7M7eMriM1lLbpM1YkzBxwcAALJxdQMg75Kl3ndtCyoS6ZrVshzSVVO8mjilTE5KvffogssGh9bKunGFrOtuklVeWfgBAgCAHhG4AORVe1tMTR936nS3Uu81Q5yaQan3HqWqDb6zUtr6Qe5lg1NmxKsNNsyR5eC/IwAApYjABSAv7JjRvt0h7d1Jqfcvw4RCMh+ep9qgp0zWghvjywZHji38AAEAwJdC4AJw2Z0+GdW2jzvV0ZY5KzNitFvTKPWekzn5hcy612U2viV1dmR3YNkgAAC9EoELwGUTCRvtagro0P7MUu9en6WGOeWqHeUu0shKkzFG2vWJ7HdWSU0fScZkd6qfKceS26WG2SwbBACgFyJwAfjKjDE6djii7VsCCgUzQ8P4iR5Nnu6T283ywSQT7JR5f63MO6ukLw5ndyjzylqwJL5JMdUGAQDo1QhcAL6SQKet5sZOHT8azWivGuDQjLnlqhnCr5kk88VhmXdWybz/jhQMZHcYNjIeshYskVVeUfgBAgCAy44rIQCXxLaNDrSEtLs5oFha1nI4pKumejVxUpkclHqXsWNSc2O82uDOT7I7WJY0bY4cS1ZI9bPYpBgAgD6GwAXgSzvVGtJ77xxX64lQRvuQYS41zPWpsop7jYy/XWbjGpl1r0mtx7M7+CpkXbdU1o23yBo2svADBAAABUHgAnDRolGjlh1BHdhzNqO+g9tjaepMn0aPd/f7Uu/ms/3xZYMfrpci4ewOo8bFlw1es1hWmbfwAwQAAAVF4AJwUU4ci6i5MaBOf2ap99Hj3Kqf6VOZt/8uhTPRiEzjJpm1q6T9u7M7OBzSrPly3HibVDe134dSAAD6EwIXgPMKBW3t2BrQkc8iGe1V1W5NneXR0Nr+W+rdnDkls361zPo3pLaz2R2qBsi6frmsRTfLGjS04OMDAADFR+ACkJMxRp8dCGtXU1CRcNf6QcuSGmbVaObVg3Tm7KkijrA4jDFSy3bZa1dJWzdLtp3d6Yq6+LLBOQtluftvIAUAAAQuADm0t8XU9HGnTp+MZbTXDHZq+txyTbhqSJFGVjwm2CmzeZ3M2teko59ld3C5Zc27QdaNt8oaf1XhBwgAAEoSgQtASixmtG9XUHt3hWTSJm5cLmnKdJ/GTfDIcvSv+4/MscMya1fJbF4rBTqzOwweFl8yuHCZrKoBhR8gAAAoaQQuAJKk1uMRNTUG5G/PXCJXO9qtabN88pX3n6IYJhaTtn0ge93r0q5tuTvVz5Ljxlul6XNlOSiDDwAAciNwAf1cOGRr5ydBff5pZglzr89Sw5xy1Y7qP/cgmbYzMuvfjBfBONOa3cFXIevaJbIW3yqrdlTBxwcAAHofAhfQTxljdPhQRDs/CSgcSttUy5KuuKpMk6d55XL3/eWDxhhp/y6Zta/LNL4nxaLZnUaPj9+bNW+RLK+v8IMEAAC9FoEL6Ic62mNq/jig1hOZ4aJ6oFMzrvZp4KC+/6vBhIIyH6yTWfu6dPhgdgenU9bsa2XduEKaOIW9swAAwCXp+1dVAFLsmNG+3SHt3RnMqGbudEqTGry64qoyOfp4UQzzxWGZda/LbHo7dxGMgYPiRTCu/5qsATWFHyAAAOhTCFxAP3HqZFRNH3eqoy2zKMawES41zClXeUXfLYpxUUUwJk+XY/Gt0ox5slz8agQAAJcHVxVAHxcO2drVFNRnBzKLYpR5LU2b7dOI0e4+u1zOnD0tsyFRBCPXJs1en6wFS+L3Z40YU/gBAgCAPo/ABfRRxhgdORTRju5FMSSNn+jR5Aaf3J6+F7SMMVLLdpm1r8l8slmKxbI7jRona/GtsuYvpggGAADIKwIX0Af522Nqagyo9Xi3ohgDHJo+t1w1Q/reP33T6Zd5f63Mu69Lxz7P7uB0yZpzrazFt1IEAwAAFEzfu+oC+rGeimI4nNKkqV5dOanvFcUwnx2Qefd1mc3rpHAou8OgIbJuuFnW9ctkVVMEAwAAFBaBC+gjzlsUY7ZP5ZXOIo3s8jORsEzjezLrXpf2787dqX6WHDfeKk2fK8vRd352AADQuxC4gF4uHLK1a1tQnx3s+0UxzIljMutXy7y3Rupoz+5QUSXruqWyFn1N1rCRhR8gAABANwQuoJcyxujwoYh29vGiGCYWk5o/ipd037E1d6cr6mQtvkXW3IWyPGUFHR8AAMD5ELiAXqijPabmjwNqPdF3i2KYs6dlNr4ps+FN6XRrdgePR9a8RbIW3yJr3MSCjw8AAOBi9P6rMqAficWM9ucoiuF0SpOmeXVFXe8uimGMkXY3yX73demTD3KXdK8dLWvxLbIW3CirvLLgYwQAAPgyCFxAL9F6IqKmjwPyt+coijGnXOUVjiKN7Ksz/g6Z99+WeXe19MWR7A5Op6yZ82UtvkWa1NBn7kkDAAB9H4ELKHGhoK2d2wI6/Gkko93rszR1Vu8timGMkT7dK7PudZmPNkiRcHanmiGyblgua+FyWQMHFX6QAAAAXxGBCyhRxhh9fjCsnduCioQzi2JccZVHkxp8crt7YdAKBmQ+XB/foPizA9kdLEuaOkuORbdIDXNlOSnpDgAAei8CF1CC2s/F1PRxp063Zt7DNKDGqelzfRo4qPf90zVHDnVtUBzozO5QWZ0o6X6zrKG1BR8fAABAPvS+qzagD4tGjfbuDGr/7pBM2qSW0yVNbvBp/ERPryqKEd+geFP83qx9O3N3uqpe1qJbZM2+VpbbXdgBAgAA5BmBCygRJ45F1NwYUKc/syhG7Wi3ps3yyVfee4pimONHZda/IbOphw2KfeWy5t8Yn80aNa7wAwQAACgQAhdQZMGArR1bAzr6eWZRDF+5pYY55Ro+snfM+phoVNr2Ybyk+65tuTuNnSBr8S2yrr5eltdX0PEBAAAUA4ELKBJjG326P6zdzQFF07KWZUlXTipT3VSvXK7SXz5oTp2Q2fCmzMa3pHNnsjskNyhedLOs8VcVfoAAAABFROACiuDs6aiaPg7o3JnMohg1g52aPrdc1QNLuzKficUU2vK+Yq/8QdreqIwbzpJGjJG1+BZZ8xezQTEAAOi3CFxAAUUiRnuaAzq4LyylZRS329KUGV6NvdJT0ntqmTOnZDa+pZOb3pbdejy7g8sla/Z1shbdHC+GUcI/CwAAQCEQuIACMMbo2OGIdmwNKBjInA0aNc6tqTN9KvOWZlEMY9vSzk9kv7taavpQsm1lzWcNGyHrhptlXXuTrKrqYgwTAACgJBG4gDzr7IipeUtAJ45FM9orKh1qmOPT0NrSLIph2s7IbFwjs+FNKddsltMpzbxGjhtuliZPl+UozcAIAABQTAQuIE/smNH+lpBadgRlp92q5XBIE6d4NXFKmZzO0lpyZ2xb2tMs8+5qmU82S7FYdqfBw1R581/Id9NtOh3Lce8WAAAAUghcQB6cOhlV08ed6mjL3FNryHCXGub4VFlVWkUxTPs5mU1vy6x/QzpxLLuD5ZCmz5Vj0S3S1JmqHF4bbz95srADBQAA6GUIXMBlFArZ2rUtqM8PhjPaPWWWps7yadRYd8kUkjDGSC3b47NZW9+XotHsTgMHy7p+uayFy2QNGlL4QQIAAPRyBC7gMjDG6PODYe3cFlQknLnMbtwEjyZP98rjKY17nEx7m8z7b8usf1M6fiS7g2VJ0+bIccPXpIa5spylNRsHAADQmxC4gK+o7WxMzY2dOt2aeb9T9UCnps/1qWZw8f+ZxWezdsisf0Nmy3u5Z7MGDJK1cGl8RmvwsMIPEgAAoA8q/pUg0EtFo0YtO4I6sCeUse+v0yVNnubV+KvK5HAUd/mg6WiTeX9t/N6sLw5nd7AsqX5mvNLg9KtlufiVAAAAcDlxdQVcgi+ORLR9S6cCnZnLB0eMdmvqLJ985cVbPmiMkfbukHn3fLNZNbKuWxq/N2tobeEHCQAA0E8QuIAvodNva/vWTh0/khlifBUONcz2afjI4u2pdcHZLEmqnxW/N2vGPGazAAAACoArLuAi2LbRgZaQWrYHM7amshzShElluqreK5er8MsHM+/N2iRFI9mdqgd2zWYNG1HwMQIAAPRnBC7gAk6fjKqpsVPt5zL31Bo01Knpc8pVNaDwVfzilQbfkdnwhvRFjkqDErNZAAAAJYCrMKAH59tTq36GT6PHF3ZPrdS+WanZrBz3ZiVns65fzr1ZAAAAJYDABXRzvj21xl7p0ZTpXnnKClcUw7Sfk9n0jsyG8+ybVT8zPps1ndksAACAUsKVGZCm7WxMTY2dOtNtT62qAQ5Nn1uuQUMK80/G2La0pzk+m7V1sxSj0iAAAEBvROACJEUjRi07c++pNWmqV1fUFWZPLXPujMymt+OzWSe/yO7AvlkAAAC9Cldr6NeMMfE9tbYGFOy2p1btaLemFWBPLWPHpJ2fyN7wprTtQ2WUQUwaOCg+k3XdUllDhud1PAAAALh8CFzotzr9MW3fEtDxo5nL9corHJpWgD21zJlTMu+9JbNxjXTqRHYHyyFNmx2/N6thrixn4ashAgAA4KshcKHfsWNG+/eE1LIzKLvAe2qZWEza3hifzWr6WDJ2dqeaIbIWJu7NGjQ0L+MAAABAYRC40K+0noiqubFTHW2ZQWfwMJca5vhUVZ2fWSTTelxm41sy770tnT2V3cHhkKZfHZ/NmjpLloPZLAAAgL6AwIV+IRS0tfOTgA4fimS0e8osTZ3p06hxl39PLRONSts+lL3hDWnnJ8qoxpE0eFh8z6zrbpI1cPBlfX8AAAAUH4ELfZqxjQ4dCGt3U1CRSGbgGTfBo8nTvfJ4Lm9RDHP8qMyGN2U2vS21n8vu4HRJM+fJcf3XpCkzZDkKt6cXAAAACovAhT7r7OmomhsDOns6s+rfgBqnGub4VDP48n38TSQs07gpXs69ZXvuTsNGyrphuawFS2RVD7xs7w0AAIDSReBCnxMJG+3ZHtDBfWEpbVLL5ZYmN/g0foJH1mXaU8scORSfzXp/rdTZkd3B5ZY1+1pZN3xNqpt62ZctAgAAoLQRuNBnGGN09LOIdnwSUCiYuXxw1Fi36mf65PV99eV7JhiQ+WhDfDbrYEvuTqPGxe/Nmr9YVkXVV35PAAAA9E4ELvQJHW0xNW8JqPV45p5aFVUONcz2aWjtV9tTyxgjfbpPZsMbMh9ukEKB7E6eMllXXy/r+uXSlZOYzQIAAED/DlyPPfaYdu7c2eP5H/zgB5o5c2ZW+7vvvqvVq1fr8OHDcrlcqqur05133qlJkyblcbTIJRY12rsrqP27Q7LTKr07nNJVU7yaMLlMTuelBx/j75D5YF18Nuvwp7k7jZsYn82ad4MsX/klvxcAAAD6nn4duJKuueYaeb3erPZBgwZltf3617/WqlWr5PF4NH36dEUiETU1NWnbtm165JFHNG/evEIMGZKOH41o+5aAOv2Ze2oNG+HStNk+VVRe2l5WxhipZUd8NqtxkxSNZHfyVciav0jWwuWyxl55Se8DAACAvo/AJenee+/VsGHDLthv+/btWrVqlaqqqvTEE09oxIgRkqSWlhY99thjeu6551RfX6/Kysp8D7lfC3Ta2r41oC8OZwYhr8/StNk+1Y66tD21TNsZmU3vyGx4SzpxNHenq+plXf+1eCGMsrJLGT4AAAD6EQLXl/Dqq69Kku68885U2JKkuro6LVu2TK+//rrWrl2r22+/vVhD7NNs2+hAS0gtO4KKpd2qZVnSlZPKVFfvlcv95YKWsWPSjq2yN7wpNX0kxWLZnaoGxEu5L1wma8Tor/hTAAAA4MuwjVHMNnJepirThUbgukjhcFjbt8f3V5o/f37W+fnz5+v1119XY2MjgSsPTp2IqrmxU+1tmcsHBw1xqmFOuaoHfrnlg6b1uMx7a2Tee1s605rdwbKk+plyXL9cmjFPluurFd0AAADo72K2UUc4po6wrY5wTO2hWOb3sK2Obm3+yD61h6L6/nUjdd246mL/CJeEwCXpnXfeUUdHhyzL0ogRIzRv3jwNGTIko8/Ro0cViURUXV2twYMHZ73GFVdcIUk6dOhQQcbcX4SCtnZuC+jwp5nLBz1llupn+DR6/MUvHzSRiLTtA9kb3pJ2fSIZk92pZois65bKuu4mWUOGX4afAAAAoO8wxigQtdURshPhKZYRouKBKRGowjH5wzG1J/p2RuwLv0EP2sM5ViH1EgQuSS+99FLG8W9/+1vddddd+vrXv55qa22Nz4LkCluS5PV6VVFRIb/fr0AgIJ/Pd8H3feSRR7LaPB6PfvrTn0pSVugrJJcr/tEYOnRoUd7fto327Dinxs2nFA5l/uOcNLVacxcMUZn34ma1op8fVOdbryqw7nWZtrPZHZxOlV19vcqX/Zk8M+fJcl5asY3+pNifD5QuPhvoCZ8NnA+fj8IyxqgzHFNbKKr2YFTtocRX4nFbMPO4q09E7cGoYjn+Zp33Mbt8vfbz0a8D15QpU7RkyRJNmjRJNTU1am1t1ebNm/XSSy/pxRdfVHl5uW699VZJUjAYlBQPRD0pKyuT3+9XMBi8qMCF3FqPB7Xp3RNqPRHKaB88tEwLFg3TsNrsipLd2YFOBTe9o8Cbf1Jkz/acfZwjx8i39M/ku/EWOWtyB2kAAIBSFInZag9F1RGKqiMU6xaM4o87QmnHaec7QlHZRQhNSU5LqvK6Ve11Jb7cqipzaUDacfJcTYVX1V6XBpT13j+I9+vAdc8992Qcjxw5UnfeeacmTJigH//4x3rxxRe1dOlSeTyeeKlw6bzL10yuJWrn8W//9m/nPd/a2vqlX/NySf4F4eTJkwV7z0jY1u7moD7dF85od7mlydN8Gj/RI8vRrpMn23M+P7458V6ZDW/KfLRBCubYnNjtkTXnOlkLl8nUTVXAshSI2lIBf86+oBifD/QOfDbQEz4bOJ/++PmIxIz8kZj8YVudie/+cEz+SHz5XfqxP9zVryPRHirGNFM3PpdDlR6HKsucqvQ4VelxqMLjVJXHqcqyxPfE+SqPUxUeh6rKnPK5HBd5S0hMQ4fG9zg9efKk/Pn9cXqUvO3oUvXrwNWTGTNmaMKECdq/f79aWlo0bdq01IxVKBTq8XnhcDwo5NrTCz0zxujwoYh2fhJQOJT5y2PUWLfqZ/rk9Tl6fn5Hm8zmdTIb35KO9HAP3dgr43tmXXODrHLK9gMAgEtnG6NAxO4KS4lQ1Jlo80di6gzb6ox03bvkT/vuj9gKl0BgkiRvMjSlBabKRDiq9HQFqcpEiErv5+qlVQMLjcDVg9raWu3fv19nz56V1HU/1alTp3L2DwaD8vv9qqioYDnhl9B+Lqbmxk6dOpl5I2RFlUPT5/g0ZHju6oDGtqXdTTIb35LZ+r4UjWZ38lXIumZRvJz7uAn5GD4AAOhlYnYiLEXiAagzYqsznHZ8EY8DEVulEZckhyVVepwqd+cOTRUepyrc6YHJoQp3V7/eWmq9NyFw9cDvj09aJmerRo4cKbfbrba2Np06dSqreMbBgwclSWPHji3sQHupaMSoZWdQB/aEMooFOpxSXb1XEyaVyeHM/gVgTp+U2fS2zMY10qkTuV+8bmp8NovNiQEA6DOSs0rJwBMPS12hKdDtOB6Suh1HYgpGSyUqxTkspUJRRTIkuR052roCVGVam9dlXXTFZhQHgSuHtrY27dq1S1JXuXePx6Np06Zp69at2rx5s1asWJHxnM2bN0uS5syZU9jB9jLGGH1xJKLtWwMKdmb+whs+0qVps30qr8i8KdJEI9K2j2RvfFPasTV3OffqgbKuvSle0r12VD5/BAAAcJGMMQrH4mXEA2lBKT0cBaK2LLdf/nBMp9v8ifPdg1S8Xykqc1oqT4WjeAgqTw9IqePMEFWeWKZX5iQw9XX9NnC1tLQoHA5r6tSpGR/yEydO6JlnnlEoFNLcuXMzZrJWrFihrVu36qWXXtLs2bNTN8+1tLRozZo18vl8WrJkScF/lt7C3xHT9i0BnTiWufzPV25p2uxy1Y7KXD5ojn0eXzL4/lqp/Vz2C1oOqWGOHNcvk6bNleXqtx9nAAAuG9sYBdMCUuACjzu7PQ5GbAWiXUvvSuRWpZy8rngQ8iXCks8dD0TlyVDUw+MKt0PliTbuY8KF9Nsr1KNHj+q5555TTU2NRowYoYEDB+rUqVM6cOCAIpGIxowZo+985zsZz5k+fbpuvfVWvfbaa/qHf/gHNTQ0KBaLqampSbZt68EHH1RlJQUZuovFjPbvDmnvrqDstFu1LIc0cXKZJk7xyuWK/7IywYDMxxvjBTD27879gkNr4zNZ194ki3LuAIB+LmqbRMixU0EpFZjSj7uf6/acruMSTkgJHqel8kRQKnd3haHkVyo4eXKdj88u+VwO7l9CQfTbwDVx4kQtX75ce/fu1eHDh7Vnzx6VlZVp/PjxWrBggZYvX55zz61vfetbGj9+vFavXq3m5mY5nU5NmzZNd911lyZPnlyEn6S0nTgW0fYtAfk7MpcBDBnuUsNsnyqrnTLGyOzfLfPeGpkPN0ihHOXcXW5Zc66VtXCZVDdNlqPnqoUAAJQiY4wiiXAUjJpUCApG7YzAFD82FzgXUyAaf61IMTdU+hIsSeVuh7zdgpHP5VBNVbkqPU4pGkqEqK6g5HMlg1NXf3eO+7yBUtVvA9fo0aN13333XdJzFy9erMWLF1/eAfUxgU5bO7YGdOxwJKO9zGtp6iyfRo5xSx1tst9cG5/NOvZ57hcac0W8yuA1i2VVMHsIAMi/mG0UisVDUSgt6ISi8RCU3haMJgOUrVDMViBiss+nHfeSbJTicsT3WvK5HfK5nPK6k48dqWCUOp/z2JlqP9+9Sv1xHy70H/02cCE/bNvoYEtIe3YEFUu7VcuypPFXlamu3i13yyeyV62Rtn2ojE5JlHMHAJxHzI4XYgjF4uEnlAg18eP0wJN43EN791AVSpzrLTNGubgdlnxuh7yuePDxuh3yuazE966w5O0WjHyuHMduh9xOVpQAXxWBC5fNqRNRNTd2qr0tc/lgzWCnGq7sVNW2lTK/e1v22dx7malumqzrl8maRTl3AOiNjDGK2iYebmLxjV3jwcbos+BZBaO2Tp5qUyjWFXhC0a4+Ob8nHgejtsKJx6WyYexX5XFaqfDjdTnkdVmJ746M9lRIcjlU5rIyAlH3/hRwAEoPgQtfWShoa+cnAR0+lLl80O2RplR9plGf/EHWH5pzbxA4YJCsa5fIWrhU1rCRBRkvAPQndqIsd3pYCaeFoeRMUTjadS49MCWPw7HE81Ovk9ae1r8XTw7l5LCkMmc8DJUlQk7y2Ot2yOt0dLWnBabuASr15U68lpOCDUB/QeDCJTO20af7w9rdHFA0I2sZjbX3q27jf8jTlmNzYqdTarhajoXLpGmzZTmd2X0AoI+xjVEkFv8K2/HgEv9uFIl1PQ7b8fATseOBKFf/cCoM9fA4FaTiM059XZkzHoa8LkseZ9dMkNflSBxbibZ4e1m3PumPy1zxEJUMWB72SALwFRG4cEnOnIqquTGgc2diGe3VwaOa2vRL1bTtz35S7aj4fVkLbpRVXVOgkQJA/J6fqJ0IPHY8mERso2giqETs9DBkdz1OBJZkkImk9U21Je4niqT1SR3bma/T3zgsyeOMh5lyj0tlLodcMqnQ40l8L+sWlJJtye9elyPVP/m4LC0QOQhEAEoYgQtfSjhka1dTUJ8dCGe0u6Kdqtv3/zTu8Nuy0hcPlnllzV0YL+c+YTJ/JQT6OGOMYkYKRm1FE2EkGXSiduZxMvBEkgEn57nM50Yy2uyM4x6/x0p749VCcyZCUDzsxIOOx9kVXjxpASh+vodzydCUOF+W1i8ZiFyOrtkhqtAB6K8IXLgoxhh9fjCsXU1BhUOZVy6jjm3U5L2/V1m4ratxwuT45sRXL5TlLS/waIG+JTk7EzNGUTu+yWmyrftXLHG+p6/k+UjqOC0IpYWe1Fes63Ekx2tHYt2Pd+e+XxM5eRKBxp0IN+7ksaMrELmdjlQ/T87Hie+JAJR8jbL0866uNu4bAoDCInDhgs6dian5Y7/OnM6sPljZcVhTd/9ag8/uiTdUDZC1IFEAY8SYIowU/ZUx8Rv17cTsSsxO/x4PFTFbqce2USrA2LYUzdEes9Of3/XcaNprJQNL8r26Pzeaek7u4/TXyNUneY4Akx8uh+R2xAOK22nJ7cgMPKnHGeccqeNkUEo+9nQLR+5kcEo7Tg9E6bM/AIC+i8CFHoXDMW1f/4UOHvVIVtc+HM5oUFcdfFnjP3tDDhlpeqIARsNcWS4+UudjGyNjJNtIRpmPbSMZkwgPSrSbtHYlQ0VmwIg/v+tx+nvY3fultykeNrr3yfW87t+9vk7Zxqi9w5/RHksPPnZ2ezLUJIORbZuux2nBpnvf9HPJ56X3Y7lY6XNYkisRWlyOrgCTfJw819UeDzKutLb079ntjqw+GecSoSj9edz3AwAoBK6OkaXj7Dn9x0t7NSw0QG6HV0q7JjkXOK6jbXu0dfBoWXWPSoOGxuu/t0l67wtJSv013qQugk23Y2X9xd6YtOclGjKP49+zziUe2Knnm8zXukC7SbxW13G8r532usnjVL+s58QDknKFp7T36If3yyPPLMVDTPxLcqYeZ345E+eTwcbltOS04sHDmRZ8kl/u1POUfS55bKUFprQ+w4cOlsvhUNvZ013vl3gfAAD6IwIXshz68KhGRUZIaZvLnzNRbbLbdMRtpMF18caIpONhSeFcLwOUFKcVDyQOy0o9djrSHluSw+oKGk7LyuxjdQWXeFvacepx5mu7rPhrdYWervOuHH2690s/Tg9OrrT3LzVDB/gkSY4g/3sBAEAicCGH2qvHaccbAfksp6LG6BO7Q83Gr9iFn4o8c1jxL0uWrERAcFiKP1bXscPKPO/I6GtlHGc+vrhz5T6vHJalSDiY0e5M6xcPN/Ewkurj6Dp2OrKf40oEoq5+aSHIkhyJoJH++i5H17HT6uqXPOdM+7kBAAAKjcCFLJVVXpV79slEqmWNMpo9ZIBmq+K8z+l+Ldv90jZ53so6k34usy0ZKtJfM71v+gW0I0e7lXqd+IGVfH8r81zyfVJtlpV5PjmW5PskQkD6+zqt9NewUgFIicCRfB1Ht36ORL/UczLCVKJ/4n1KKTBQ3hkAAODiELiQpczl0LfuXyJJam1tLfJoAAAAgN6LwIWcSmk2BQAAAOitHBfuAgAAAAC4FAQuAAAAAMgTAhcAAAAA5AmBCwAAAADyhMAFAAAAAHlC4AIAAACAPCFwAQAAAECeELgAAAAAIE8IXAAAAACQJwQuAAAAAMgTAhcAAAAA5AmBCwAAAADyhMAFAAAAAHlC4AIAAACAPCFwAQAAAECeELgAAAAAIE8IXAAAAACQJwQuAAAAAMgTAhcAAAAA5Imr2ANAzyzLKvYQSmIMKF18PtATPhvoCZ8NnA+fD/SkmJ+Nr/reljHGXKaxAAAAAADSsKQQAAAAAPKEwIWcHn30UT366KPFHgZKFJ8P9ITPBnrCZwPnw+cDPekLnw3u4UJO4XC42ENACePzgZ7w2UBP+GzgfPh8oCd94bPBDBcAAAAA5AmBCwAAAADyhMAFAAAAAHlC4AIAAACAPGEfLgAAAADIE2a4AAAAACBPCFwAAAAAkCcELgAAAADIEwIXAAAAAOQJgQsAAAAA8oTABQAAAAB5QuACAAAAgDxxFXsAKC3hcFgvv/yy3nvvPbW2tqqyslIzZszQPffco8GDBxd7eCiSUCikbdu2qbGxUfv379fJkydl27Zqa2t1zTXX6LbbbpPX6y32MFECOjo69PDDD6utrU0jR47UU089VewhoQScPXtWL7/8srZu3arW1lZ5PB4NGzZMDQ0N+uY3v1ns4aFIWlpa9Morr2jPnj3q6OiQ1+vVFVdcoeXLl2v+/PnFHh7y7MCBA2pqatK+ffu0d+9enTlzRm63W//93/993ue9++67Wr16tQ4fPiyXy6W6ujrdeeedmjRpUoFG/uWx8TFSwuGwfvSjH2nPnj2qqanR5MmTdfLkSe3bt0/V1dV64oknVFtbW+xhogjefvtt/eIXv5AkjRkzRqNGjVIgEFBLS4sCgYBGjRqlxx57TAMGDCjySFFszz77rNavXy9jDIELkuIX1U8++aT8fr9Gjx6tMWPGKBgM6vDhwzp16pR+//vfF3uIKIL3339fTz31lIwxmjBhgoYPH64zZ85o9+7dMsbojjvu0F/91V8Ve5jIo5/97Gf6+OOPM9ouFLh+/etfa9WqVfJ4PJo+fboikYi2b98uY4weeeQRzZs3L9/DviTMcCHlj3/8o/bs2aO6ujr98Ic/TM1YrFy5Ur/5zW/07//+73r88ceLPEoUg8vl0vLly7VixQqNGDEi1X7mzBn99Kc/1cGDB/XCCy/ooYceKuIoUWzNzc169913tXTpUq1Zs6bYw0EJOH36tJ588klFIhF9//vfz7oY2rdvX5FGhmKKxWL6z//8Txlj9PDDD+vaa69NnWtpadHjjz+uV155RTfddBN/6O3D6urqNH78eE2YMEETJkzQ/ffff97+27dv16pVq1RVVaUnnngidT3S0tKixx57TM8995zq6+tVWVlZiOF/KdzDBUlSNBrV6tWrJUnf/va3M5aH3XbbbRo3bpx27dqlAwcOFGuIKKJFixbpvvvuywhbklRTU6Nvf/vbkqQPP/xQ0Wi0GMNDCQiHw/rlL3+p0aNH6/bbby/2cFAifve738nv9+ub3/xmzr88T5w4sQijQrEdOXJEbW1tGjVqVEbYkuIX4TNmzJAxhmuOPu7P//zPdffdd2vOnDkaOHDgBfu/+uqrkqQ777wz43qkrq5Oy5YtU2dnp9auXZuv4X4lBC5Iknbv3i2/36/hw4friiuuyDp/zTXXSFLW1C8wbtw4SVIkElF7e3uRR4Ni+d///V8dP35c9913n5xOZ7GHgxLQ0dGh999/X+Xl5VqyZEmxh4MS4na7L6pfKc5UoDjC4bC2b98uSTnv70u2NTY2FnRcF4slhZAkHTp0SJJyhi1JuvLKKzP6AUnHjx+XJDmdTv7n2E8dOnRIK1eu1OLFi1VfX68TJ04Ue0goAXv27FEkElFDQ4NcLpc2b96s3bt3KxqNatSoUVqwYMFF/VUbfc/w4cM1fPhwHTlyRJs2bcpaUrht2zYNGzZM9fX1RRwlSsnRo0cViURUXV2ds4hb8vq1VK9TCVyQJLW2tkpSj5UIBw0alNEPSHrttdckSTNnzrzov1qi77BtW7/4xS9UXl5OtTlk+PzzzyVJAwYM0D/90z+ppaUl4/zvfvc7PfDAA1qwYEExhocicjgceuCBB/Qv//Iveuqpp/Tqq69mFM2YOHGiHnzwQblcXKYi7kLXqV6vVxUVFfL7/QoEAvL5fIUc3gXxSYYkKRgMSpLKyspynk/e05XsB0jSli1btHbtWjmdTt1zzz3FHg6KYPXq1dq3b58eeOABVVVVFXs4KCF+v1+StH79erlcLn33u9/V3LlzFQwGtXr1aq1cuVLPPPOMRo4cmVqajP5jypQpeuyxx/Sv//qv2r9/v/bv3y9J8vl8amhoUE1NTZFHiFKSvP70eDw99ikrK5Pf71cwGCy5wMU9XJAkXWh3AHYPQHeHDx/WM888I2OM7r33Xo0fP77YQ0KBtba26ve//73q6+u1ePHiYg8HJca2bUnxinR/8zd/oyVLlqi6ulrDhg3TX//1X2v+/PmKRqP605/+VOSRohg2btyof/zHf9SQIUP0k5/8RL/5zW/09NNP67rrrtNLL72kH/3oRxRiQkryOtSyrAv2KUUELkhS6i8BoVAo5/lkO5vbQpJOnTqln/zkJ/L7/brtttt06623FntIKIJf/epXikajuu+++4o9FJSg5P9XLMvSokWLss7feOONkqSdO3cWdFwovmPHjunZZ59VdXW1Hn30UU2cOFFer1cjRozQ/fffrzlz5qilpUXr1q0r9lBRIi50nSrFC2tIpXmtypJCSJKGDBkiKX4hncvp06cz+qH/amtr0xNPPKHW1lYtXrxY9957b7GHhCLZsmWLKioq9Ktf/SqjPRKJSIrPgD322GOSpEcffbQk/yeI/Bk6dKgkaeDAgTnv70yeP3fuXEHHheJ77733FIvFNGPGjJy/FxYsWKDGxkbt2LFDS5cuLcIIUWoudJ0aDAbl9/tVUVFRcssJJQIXEpLr5w8ePJjzfHIvDNbZ92+BQEBPPvmkjhw5onnz5um73/3ueaf30ff5/f4eZyjC4XDqXCwWK+SwUAKSVcP8fr+MMVm/Kzo6OiSV5l+jkV/JP+KWl5fnPJ9sT35GgJEjR8rtdqutrU2nTp3KKp6RvH4dO3ZsMYZ3QQQuSJImT56s8vJyHT9+XAcPHswqD//BBx9IkmbPnl2M4aEERCIR/exnP9P+/fs1Y8YMPfzww3I4WJXcn7344os520+cOKHvfe97GjlypJ566qnCDgolY+zYsRo2bJhOnDihvXv3qq6uLuP8jh07JHVtO4L+I7kdQLJQRnf79u2T1DULCng8Hk2bNk1bt27V5s2btWLFiozzmzdvliTNmTOnGMO7IK6WIElyuVy6+eabJUnPP/98RjXClStX6tChQ5o8ebImTpxYrCGiiGzb1tNPP60dO3ZoypQp+v73v0+5XgAXdMcdd0iS/uu//kttbW2p9gMHDmjlypWSpGXLlhVlbCieuXPnSpJ27dqlN998M+NcS0uLVq1aJSn3Brfov5Ih66WXXtKxY8dS7S0tLVqzZo18Pl/JbrJumVIu6YGCCofDevzxx7V3717V1NRo8uTJam1t1d69e1VVVaUf//jHqq2tLfYwUQSvvfaaXnjhBUnSvHnzelwffe+996q6urqAI0MpYoYLSbZt66mnntLmzZtVWVmpuro6hUIh7dmzR9FoVDfddJO+853vFHuYKILf/va3evXVVyVJY8aM0ahRo3TmzBm1tLTIGKOlS5fq/vvvL/IokU9btmzR//3f/6WO9+7dK8uyMv64f9ddd2WsrnrhhRf02muvqaysTA0NDYrFYmpqapJt2/r7v//7kg3p/IkaKR6PR//8z/+sP/7xj9q4caM++ugjVVRUaNGiRbrnnnsomNGPpa+j//DDD3vs95d/+ZcELgApDodDDz/8sN566y298847qWWEEyZM0LJly3TDDTcUeYQolnvvvVeTJk3SW2+9pQMHDujo0aPyer2qr6/XTTfdpIULFxZ7iMiztrY27d27N6PNGJPRlj4zLknf+ta3NH78eK1evVrNzc1yOp2aNm2a7rrrLk2ePLkg474UzHABAAAAQJ5wDxcAAAAA5AmBCwAAAADyhMAFAAAAAHlC4AIAAACAPCFwAQAAAECeELgAAAAAIE8IXAAAAACQJwQuAAAAAMgTAhcAAAAA5AmBCwAAAADyhMAFAAAAAHlC4AIAAACAPCFwAQAAAECeELgAAAAAIE8IXAAAAACQJwQuAAAAAMgTAhcAAJfByy+/rLvvvlvf+MY3tG/fvpx9tmzZonvuuUd33323Nm7cWOARAgCKgcAFAMBlcMcdd6ihoUGxWExPP/20AoFAxvkzZ87oueeekzFGN9xwgxYuXFikkQIAConABQDAZWBZlh588EENGDBAx48f1y9/+cvUOWOMfv7zn6utrU21tbW67777ijhSAEAhEbgAALhMBg4cqAceeECWZWnjxo1at26dJOlPf/qTmpub5XQ69dBDD8nr9RZ3oACAgiFwAQBwGc2aNUsrVqyQJD3//PNav369/vCHP0iSvvGNb2jChAnFHB4AoMAsY4wp9iAAAOhLotGofvjDH+rAgQOpthkzZugHP/iBLMsq4sgAAIXGDBcAAJeZy+XSAw88kDouLy/X3/3d3xG2AKAfInABAJAHa9asST0OBAL69NNPizcYAEDRELgAALjMGhsbtXr1aknSuHHjZIzRs88+q7NnzxZ3YACAgiNwAQBwGSX325KkxYsX6/HHH9fQoUN17tw5Pfvss+LWaQDoXwhcAABcJrZt6+c//7na29s1YsQI/e3f/q3Ky8v10EMPyel0atu2bVq5cmWxhwkAKCACFwAAl8krr7ySc7+turo6ff3rX5ck/c///E9G9UIAQN9G4AIA4DLYt29fxn5bV155Zcb5v/iLv9DUqVMVjUb19NNPKxgMFmOYAIACI3ABAPAVBQIBPf3004rFYpo+fbpuv/32rD4Oh0Pf+973VFlZqWPHjun5558vwkgBAIXGxscAAAAAkCfMcAEAAABAnhC4AAAAACBPCFwAAAAAkCcELgAAAADIEwIXAAAAAOQJgQsAAAAA8oTABQAAAAB5QuACAAAAgDwhcAEAAABAnhC4AAAAACBPCFwAAAAAkCcELgAAAADIEwIXAAAAAOQJgQsAAAAA8oTABQAAAAB5QuACAAAAgDwhcAEAAABAnhC4AAAAACBPCFwAAAAAkCf/H6tM6or5Of7VAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot results of initial guess\n", "plt.plot(x, exact(x))\n", "plt.plot(sol1.t, sol1.y[0])\n", "plt.plot(sol2.t, sol2.y[0])\n", "\n", "plt.legend(['Exact', 'Shooting 1 (z=0)', 'Shooting 1 (z=20)'])\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "code", "execution_count": 7, "id": "f6d62950", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " converged: True\n", " flag: 'converged'\n", " function_calls: 6\n", " iterations: 5\n", " root: 12.690853836888637\n" ] } ], "source": [ "from scipy.optimize import root_scalar\n", "\n", "\n", "# Root finding function\n", "def obj(z):\n", " sol = solve_ivp(dydx, t_span=(0, 10), y0=[T1, z])\n", " return sol.y[0][-1] - T2\n", "\n", "\n", "# root finding (Bracketing method)\n", "root = root_scalar(obj, bracket=[0, 20])\n", "print(root)" ] }, { "cell_type": "code", "execution_count": 8, "id": "83a92ac3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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h8xf9KO5b8cryst/5KxAeaZXCe+65R1JeSL/kkktUpUoVffvtt36LqEyaNElPP/20unXrpvfee8/773zvvffq/fffV0REhM4++2xFRERo8eLFys3N1QUXXKBPPvlEEydO9Ntwe+fOnRo6dKg2btyoypUrq2PHjgoJCdHff/+tP//8U88884z3+F27dunss89Wdna2zjvvPNWoUUPGGI0aNcobytxUlucHSlZxLQtfUl/b4B6W/cbhMD+Ci01LlfPsQ9KmOG/N9Bggc9nIAl/3S8PcYFl4oAiffvppkWMtWrTQPffco4MHD+q2225Tbm6unnnmmQIrVt52221auHChFi5cqLfeekvXXXedJOnxxx9X48aN9dFHH+nnn39WTEyMzj33XP3rX//Sxx9/XOjHrFWrlmbPnq3XX39ds2bN0vfff6+QkBDVrl1bI0eO1DnnnOM9tmbNmnrzzTc1adIkLV68WKmpeZtYDx48uFQELgAAgONh09PkPDfeP2x1719o2AoUXOEqxbjChdKK+YGicIULRSkNv6VG6cX8CA42I03Os+Ol+L+8NdO1r8wVNxX9zFYpmBsneoUrIFYpBAAAAFB62Yw0Oc89/I+w1eewYStQELgAAAAAlBibkS7n+UekDWu9NXNeb5nLAz9sSQQuAAAAACXEZqTLeeERaf2f3po5t5fMlTfLeIIjigTHuwQAAABwUnnDVtwf3po5+wKZ4bcETdiSCFwAAAAAilnhYauHzNWjgypsSQQuAAAAAMWo6LA1JujClkTgAgAAAFBMCFsFBee7BgAAAFCsCFuFC3G7AQAAAABlW97S7w/7r0ZI2JJE4AIAAABwAvI2NX5E2kDYKgyBCwAAAMBxyQtbD/tvakzY8kPgAgAAAHDMbHqanOfGS/F/eWvmnJ4yV91K2DoEgQsAAADAMbFpqXlha+M6b82c2yvoNjU+GgQuBKQffvhBb7/9tpYtW6b9+/crOjpa1atXV8uWLdWlSxddeumlCgsL8x5fp04d1a1bV7/99puLXR+7rVu3qnPnzurSpYs+++wzt9vxk5ubq1mzZmnFihVavny5Vq9erfT0dA0fPlxPPPHEcb/ugQMHdNZZZ+n888/X5MmTi7HjY7dq1Sr98MMP3ve4a9cuhYeHa+PGjYUe7ziOfv/9d33zzTdatGiRtmzZooMHD6pWrVo699xzdeutt6pevXrH1cvBgwf1yiuvaM6cOdqyZYtCQkJUu3Ztde7cWQ888ICio6P9jt+3b59efPFFzZ07Vzt27FBMTIw6deqkO+64Q6effnqB1z+ez+eaNWvUu3dvPfjgg7r55puP630BAEofm5Yq59mHpE1x3po5r7fMlTcTtgpB4ELAefrppzVp0iRJUrNmzXTmmWfK4/EoPj5eX3zxhT7//HP17NlTsbGxLnd6ZB9//LHGjh2rsWPH6q677nK7nWOSkpJSIj9kP//880pOTtYdd9xR7K99rJ599ll9/fXXR3385s2bNXjwYElSzZo11aFDB3k8Hi1fvlxTp07VF198offee08dO3Y8pj7i4+M1bNgw7dixQ/Xq1VP37t2VlZWl+Ph4vfPOOxo9erRf4Nq9e7cuvvhibd68WTVq1FD37t21e/duzZkzR/Pnz9c777yj8847z+9jHM/ns2XLlurVq5deeOEFDRs2TJUrVz6m8wEApY9NS5Hz7Hj/sHX+hTJXjCJsFYHAhSJ9+WeiOtaJVvXo0MMel5CarUVbD2pAsyonqbOirVy5UpMmTVJYWJimTJmiHj16+I3v3LlTH3zwgd/VrbKsZs2a+v777xUZGel2KwWEhoZqyJAhatu2rdq0aaM//vhD999//wm95u7du/XWW2+pV69eatq0aTF1evzat2+vFi1aqE2bNmrbtq3atm172OONMeratavGjBmjzp07e+uZmZm677779Mknn2j06NH6+eefFRp6+P/f5UtLS9Pw4cO1a9cu/fe//9WIESNkjPGO//XXXwWCzr333qvNmzere/fuevXVVxUVFSVJmjVrlm666SaNHj1av/76q19IO97P5+jRozVv3jxNnjxZDzzwwFG9JwBA6WRTU+RMGidt3uCtma59Za64ye97D/wRuFCoL/9M1Gu/79JXa0P12AX1igxdCanZenD+Fu1KyZYk10PXnDlzJEn9+/cvELYkqVatWmXuStHhhIaGqkmTJm63UaioqCg9//zz3r9v2LDhMEcfnY8++kiZmZm65JJLTvi1isOtt956TMc3aNBA77//foF6eHi4Hn/8cc2dO1fbt2/XkiVL1KVLl6N6zZdeeklbtmzRTTfdpGuuuabAeLNmzfz+vn37ds2fP18hISF6/PHHvWFLkvr166e+fftq1qxZ+uijj3T99dd7x47389m+fXs1aNBAH330ke65556A+WUHAAQbm3pQzsRx0pZ4b8106ydz+Y2ErSPguh8K1aVeBdUsH6pdKXmBKiE1u8Axh4atmuVD1fmUGBc69ZeUlCRJqlq16nGdn5ubq8mTJ+ucc85Rw4YN1aFDB/33v/9VZmZmocdv375d9957rzp27KiGDRuqdevWGjlypFasWFHkx1iyZImuvfZatWrVSg0bNlSnTp10//33a9euXX7HXXLJJRo7dqwkaeLEiapTp473v48//lhS3jNcderUKRBAPv74Y9WpU0fPPPOMtm/frltvvVWtWrVS48aN1adPH82bN6/Q3qy1euedd9S9e3c1atRI7du317hx45SSkqJLLrlEderU0datW4/2n7NYWWv10UcfqWLFigXC9C+//OL371PYf6XhFsTDiYiIUKNGjSTlXck7Go7j6MMPP5QxRjfccMNRnbNmzRpJ0imnnKK6desWGD/rrLMk6ZhulTySQYMGKSkpyfsLEQBA2WIPJst55kH/sNVjAGHrKHGFC4WKLR+mx3s31P1fb/KGrkOvdP0zbB3uKtjJVKtWLUnS7NmzNWbMmGMOXqNHj9b8+fPVtm1bNW7cWIsXL9bkyZO1a9cuvfDCC37Hrl27VkOHDlVSUpKaNGmiPn36aPv27ZozZ46++eYbvfjiixowYIDfOdOmTdOdd94px3HUoUMH1a5dW6tXr9a7776rOXPm6LPPPvNeseratatycnL0+++/q0WLFn4LGTRs2PCo3s/WrVvVt29fhYeHq2PHjkpISNDSpUt1/fXXa+rUqTr//PP9jn/ooYf0xhtvKDw8XGeffbYiIiI0bdo0LV26VOXKlTumf8viFhcXpy1btqh79+4FrpLExsbq0ksvLfS833//XX///bfr/R9Jbm6utm3bJkmqXr36UZ0TFxen3bt367TTTlOtWrX03Xff6YcfflBaWpoaNGigvn37FliEIy0tTZJUqVKlQl8zv/7nn38WOn48unTpomeffVbffvutBg4cWGyvCwAoefbggbywtX2zt2Z6DpS59DrC1lEicKFIseXD9NgF9bzBKj90SSqVYUuSLr74Yr344ovavn27zj77bPXu3VudOnVS+/bt1bRp08N+Ydi2bZsiIyO1YMECnXLKKZKkLVu2qE+fPpo+fbruuusuNWjQQFLe1ZYxY8YoKSlJo0eP1n333ed97ZkzZ+rmm2/W3Xffrc6dO3t/eM6/GmaM0VtvvaWePXtKyrtK8fDDD2vKlCm6/fbbNWvWLEl54a969er6/fffdeGFFx7XrZCffvqprrvuOj300EMKCcn7v/uUKVP00EMP6bnnnvMLXIsXL9Ybb7yhKlWqaPr06Tr11FMlSfv379fll19+2Kt2J0P+CpJt2rQpMNakSRM9++yzBepLly7VV199pYoVK+qWW27x1n/55ZciA1pRSnolyC+//FKJiYmqWrWqOnTocFTnrFuXtxTvKaecouuuu67AVakJEybowQcf1MiRI721/F9C5Ie7f8qv79u3T6mpqQVWNzwebdu2lcfj0eLFi0/4tQAAJ49N3ifnmf9IO7Z4a6b3YJkhIwhbx4DAhcOqHh3qF7pGfZV3KTnHUakLW1LeMzJvvvmmxo4dq127dumzzz7z/pBcrVo1XXrppRozZowqVqxY6PmPPvqoN2xJUr169TR48GC9+eab+u2337yB65dfftHatWtVr149b4jK179/f3355ZeaPXu2Pv74Y40ePVqS9OGHHyojI0NDhgzxhi1J8ng8+ve//62ZM2dqxYoVWrp0qdq3b18s/x7169fXuHHjvGFLkq655hpNmjRJy5YtU1ZWlvdq0XvvvSdJuummm7xhS8q74vHggw9q6NChxdLT8Vq7Nm8H+8aNGx/V8Tt27NDIkSOVk5Ojl19+2e+8w10RK0pJPiu3fft2PfTQQ5Kku+++W+Hh4Ud13oEDByRJ3333nSTpwQcf1ODBg2Wt1bRp0/Tkk0/qoYceUqNGjdS9e3dJ0hlnnKGIiAglJCRo4cKF6tatm/f1HMfxC5UpKSnFErjKly+v2NhYbd26VQcPHlRMjPu3HwMADs/uT8q7srXL9ws60+cSmYuvImwdIwIXjig/dI36Kl45Tl4txKNSF7bynX/++frll180b948/fjjj1q2bJnWrVunxMREvfzyy5ozZ46++uqrArcbhoaGep9fOVT+czV79uzx1vJ/U3/RRRcVeqvakCFDNHv2bP3222/ewJV/hSZ/WfBDhYeHq1+/fnrjjTe0ePHiYgtcXbp0KbDaXUhIiOrVq6dVq1Zp3759qlGjhqS8Z8ukvMD4T2effbYqV66sffv2FUtfxyMxMVGSigzLh0pPT9f111+vPXv26OGHHy5w62RRV8TckJaWppEjRyopKUkXXnihrr766qM+13Hy/g+Zk5Oj0aNH+y3bfuuttyopKUmvvPKKnn/+eW/giomJ0YgRI/Tqq6/qjjvu0BNPPKGzzz5bu3fv1hNPPKH4+Hh5PB45jiNPMS7vW7lyZe3atUt79+4lcAFAKWf375Xz9IPS7u3emul/mcxFVxC2jgOLZiAghYeHa8CAAXryySc1f/58rVixQg8++KAiIyP1999/a8KECQXOiY2NLTQ85a/ilpWV5a3lL3BR2KIDh9YPXfwg/89FnZN/Ze2fi2eciPxn2v4p/6rFoe9p9+7dMsYUeU6dOnWKra/jcfDgQUl5V0uO5M4779SqVat0+eWX+91OV9pkZ2frhhtu0KpVq9SxY0e9+OKLx3T+oVefhg0bVmA8v7Zs2TK/hV/uu+8+XXTRRUpMTNT111+vZs2a6fzzz9e8efM0btw4WWslSRUqVDiet1Wo/M9b/ucRAFA62b0Jcp683z9sXXSFPAOvJGwdJ65w4YjyF8jIcfKubEl5txT+cyGN0qxq1aq6+eabFRERoQcffFDffvttgWOO54vIkc4pbPx4zjlexfla+T+EuyX/qsiRfmCfNGmSZsyYoY4dO+r//u//Cj1mw4YNxxxumjRp4r1aWRwcx9GYMWP03XffqUWLFnr77bePeT+1Q29/LSzI59dyc3O1b98+1axZU5IUFhaml19+Wdddd50WLFigvXv3qkaNGhowYICMMRo/frwaNGhw1Lc2Ho38zxtXtwCg9LKJu+U8/YC013dXjxk0XJ5+7j5WUNYRuHBYha1GKKnAQhplIXRJ8u5tlL98/PHK/8G1qCXSt2/P+61QbGyst1ajRg3Fx8dr69athT6HlL9YQf4tfidb/jM2O3fu9D6rdqidO3ee/KYOUa1aNUl5i3gUZc6cOXrmmWdUt25dTZkypcg9n/bs2aNPP/30mD5+ly5dijVw3X///ZoxY4YaNWqkDz/88Khulfyn5s2bq1y5csrNzdX+/fsLrG546C2ghT2LdeaZZ+rMM8/0q7355puSVOjttSci//N2vFs2AABKlt2zI++ZraREb80MGSHPhUNc7CowcEshirQnJavQ1Qjzn+k60j5dbjjSVZjNm/OWND3RUNOxY0dJ0ldffaXc3NwC49OmTZMkderUyVvL//P06dMLHJ+VlaWZM2f6vbYkb2DIyck5oX6PRv7KePmrJB7ql19+OeGQeqJatGghqegNd//880/ddtttioyM1JtvvnnYH+zPOussbd++/Zj+K84VCh9//HFNnTpVderU0UcffeQNk8eqYsWK3vnyyy+/FBj/9ddfJeUtJnM0V5aysrL09ttvS5KuuOKK4+qpMAcPHtTu3btVr149rnABQClkd22T89S//cPWZdcTtooJgQuF2pOS5d2Dq7DVCEtr6HryySf12GOPacuWLQXGNm7cqEceeUSS1KdPnxP6OGeddZaaN2+uLVu26KmnnvILenPnztWcOXMUHR3tt7Lf5ZdfroiICH355ZeaP3++t+44jiZMmKBdu3apbdu2fgtm5AfD+HjfRoMl5corr5Qkvfrqq36h5sCBA/rvf/9b4h//SPIDa2HL0+/du1fXXnut0tPT9dxzz/ntWVbavPrqq3rxxRcVGxurjz766KiejVu+fLnOO++8QleKzL/q9sQTT/jN+7///ltPPfWUJOmqq67yO2f79u3au3evXy0lJUVjxoxRfHy8hg4dqjPOOOOY31tRVqxYIWut3y8TAAClg92xJS9s7ff9YtVcMUqeC9g3sbhwSyEK9euW5CPus/XPJeMXbT2oAc2quNCtT2pqqt544w298soraty4sU499VSFhIRo+/btWrFihRzHUevWrTV27NgT+jjGGL3wwgu69NJL9cILL2ju3Lk6/fTTtX37dv3+++8KCQnRM88843dLYZ06dfTkk0/qzjvv1DXXXKMzzzzTu/FxfHy8qlevrueee87v47Rr107VqlXTrFmzdMkll6hevXryeDy67LLLCtwKdqK6dOmia665Rm+//bZ69+7t3fj4l19+0SmnnKJ27dpp2bJlBVY9PJz7779fq1evluS7jXPu3Ln6448/vMfkX9k7klNPPVX16tXTsmXLlJGRoYiICO/Yu+++q23btik2Nlbz5s3TvHnzCpzfsWPHYr1qI0nz588vsNphVlaW30qPd9xxhy644AJJ0po1a/Too49Kynv+6vnnny/0da+44gq/cJKenq74+Hi/hS/yde3aVTfddJNeffVVXXDBBTrzzDNlrdXvv/+utLQ0de/eXTfccIPfOT/99JPuvfdetW7dWnXq1FF6eroWL16s5ORkde3aVY8//nihfR3N53Pu3LkFzsu/0pa/UiIAoHSw2zbJmThOOpi3zYiMkbnqVnnO7eVuYwGGwIVCDWyRd4tTxzrRh30+Kz90lYawJeX9cNu6dWt9//33+vPPP/Xrr78qJSVFFSpUUOfOndWvXz9dccUVRT7bcyyaN2+ur7/+Ws8995wWLlyoWbNmKSYmRhdeeKFGjx5d6BWCIUOGqF69enrppZe0ZMkSLV++XLGxsbr66qt12223FVghMCIiQu+++64mTJigFStWaNGiRbLWFvrsTXF47LHH1KRJE73zzjv68ccfVaVKFQ0cOFD33XefLrzwQhljjulZo/Xr12v58uV+tcTERO8S78fCGKPLL79cTzzxhL755hsNGDDAO5a/PPqRns0q7sC1d+/eAu/PWutXO/RKUnJysvdq6NKlS7V06dJCX7dLly7HdDVo3LhxatOmjd588039/vvvys3NVZMmTTR06FCNGDGiwOqbrVu3Vr9+/bRs2TL9+eefCgsLU7NmzXTZZZfpsssuK3KxleP9fH755ZeqUqXKCV9ZBgAUH7s5Xs6kcVLq/xajMkbmmtvkOauHu40FIGPdXnoMRdq5c+dhn0my1mrv3r2qWrVqsS/Tmb9R7sl4dgil386dO9W5c2c1aNBA33//vWvzY8+ePerSpYvOPfdc77NGKF3+OTeWLFmigQMH6pZbbtEDDzxwVK9Rkl/b4J78RV0SEhJc7gSlEfPj5LIb18l5dryUnppXMB6Z6++Up9P5hz3PDaVhbhxu25yjwTNcALw2bNig9PR0v9revXs1duxY5eTkaNCgQe409j+xsbG69tprNX/+fK1bt87VXnB0XnrpJVWsWNFvU2YAgHts3B95txHmh61y5WRuuLtUhq1AwS2FALxef/11ffHFF2rZsqViY2OVkJCgNWvW6ODBg2rVqpVGjRrldosaM2aMPvzwQz377LN6+eWX3W4Hh7FmzRrNmzdPDzzwgKpUcf+WYwAIdnbtSjkvPiZl/e+Z4HIh8oy6V6ZtZ3cbC3AELgBeffv21e7du7V69WotX75cHo9HDRo0UN++fXXTTTcd88a8JaFixYp+izSg9GrZsqV3TzoAgLvsmqVyJj8uZWflFUJC5bnl3zKt2h/+RJwwAhcAr/PPP1/nn88tBQAABBK74jc5rz4h5T97HRYmz+j/yDRv425jQYLABQAAAAQou/RnOa8/LeXm5hXCI+W57T8yTVu621gQIXABAAAAAchZtFD2zeckm7d9iiKj5bn9IZnGzdxtLMgQuAAAAIAA4/zwtezUyVL+FkNR5eUZ+4hM/SbuNhaECFwAAABAAHG+nSH70eu+QkzFvLBVt6F7TQUxAlcZZoyRMUaO46hcuXJutwMAxSI3N9f79Q0AcGycOdNkp7/jK1SqIs/Yx2Rq1XWvqSDHxsdlXFhYmDIyMtxuAwCKTWZmpsLCwtxuAwDKFGutnC8/8A9bVWPluedxwpbLuMJVxkVGRurAgQOSpPDw8GK70mX/d79v/v8Ch2J+oCgnMjdyc3OVmZmpjIwMVaxYsbhbA4CAZa2V/ext2Xmf+4qxtfKubFWt7l5jkETgKvNCQkJUsWJFpaen68CBA8X2A7DHk3fx03GcYnk9BBbmB4pyInPDGKOwsDBVrFhRISF8ewKAo2EdR/bD12S/m+0r1jpFnrGPylSq4l5j8OI7WgAICQlRTEyMpOK74lC9et5vQxISEorl9RBYmB8oyonMDZ7ZAoBjY3NzZd95QfbXBb7iKQ3lufMRmRjuFCgtCFwBprh+YMl/HX4AQmGYHygKcwMATg6bky07ZaLs0p99xYZN5bl9vEx0efcaQwEBE7g2btyoVatWacOGDVq/fr327dun0NBQvf/++0Wek5SUpGnTpmnlypVKSkpSuXLlVLt2bZ199tnq06ePQkNDCz1v3bp1mj59uuLi4pSTk6O6deuqd+/e6tq1awm9OwAAACCPzc6S8/IEafUSX7FpS3nGPCgTEeVeYyhUwASuzz77TEuWLDnygf+zY8cO/ec//9HBgwdVo0YNtW/fXpmZmfrrr780depULVmyROPGjSvwHMHixYs1ceJEWWvVvHlzxcTEaM2aNZo8ebI2b96sESNGFPdbAwAAACRJNiNdzkv/lf5a5Su2bCfPqPtlwsPdawxFCpjA1bRpUzVo0ECNGzdW48aNdeONNx72+A8++EAHDx7UhRdeqGuuucb7oPeBAwc0btw4/fXXX/rxxx/VrVs37zkpKSmaPHmyHMfRXXfdpU6dOkmS9u/fr3HjxmnWrFlq3769WrZsWXJvFAAAAEHJpqXIef4RKf4vX7FdF3lG3i1TxJ1ZcF/A7MM1aNAgDR06VO3bt1elSpWOePzatWslSYMHD/aGLUmqWLGievXqJUmKj4/3O2fBggVKS0tThw4dvGFLkipVqqThw4dLkmbOnHmibwUAAADwYw8my3nmQb+wZTp3lefGewlbpVzAXOE6Vkez5HD58v4PHC5dulSS1Llz5wLHtmvXTqGhoVq9erWysrLYtBMAAADFwu7fK2fiOGnnVm/NnHehzJWjZDwBc/0kYAXtZ6h169aSpOnTp/vtF3PgwAHNmzdP5cqV0znnnON3zpYtWyRJjRo1KvB6ISEhqlevnrKzs7Vjx44S7BwAAADBwibskvPk/f5h64KBMsNvJmyVEUF7heuKK67Qxo0bNXfuXC1fvlwNGzZUZmam1q5dq5iYGN1zzz2qW7eu9/i0tDSlpqZKkqpUKXwTuSpVqig+Pl6JiYlq0KDByXgbAAAACFB25zY5E/8j7d/rrZkBw2QGXM72G2VI0AauypUra/z48Xruuee0atUq7d69W1Le3jGdOnXyC1uSlJGR4f1zeBErwOTXDz32cMaOHVugFhYWpgkTJkiSqlWrdlSvUxLyb7nM38QUOBTzA0VhbqAozA0cDvOjoOyN65T09L+l5P3eWsw1YxQ96Ar3mnJBIMyNoA1cmzdv1oQJE+TxeHTvvfeqefPmyszM1KJFi/TBBx9oxYoVevTRR1WzZk23WwUAAEAQyfprtfY9MlY2LSWvYIwqjLpXUb0HudoXjk9QBq6cnBxNnDhRSUlJmjBhgho2bChJio6OVt++feU4jt599119/PHHuv322yVJERER3vMzMzMVFVVwU7nMzMwCxx7OxIkTDzuemJgoa+1RvVZxy/8tQkJCgisfH6Ub8wNFYW6gKMwNHA7zw8euXZm3z1bm/+6Y8nhkrrtTqe3OVmoQ/vuUhrlhjFGtWrWO+/ygfNJu/fr12rlzp2rUqOENW4fq0qWLJOnPP//01qKiorwhKykpqdDXza+7eSsgAAAAyia7YlHePlv5YSskRJ6b75On0/nuNoYTEpSBa+/evAcPIyMjCx3Pr6ekpPjV69evL0nauHFjgXNycnK0ZcsWhYaGqnbt2sXZLgAAAAKcs2ihnJcnSDnZeYWwcHnGjJNpW3A7IpQtQRm48jdG3rFjh9LT0wuM5294/M+H89q1aydJWrRoUYFzli1bpuzsbLVs2ZI9uAAAAHDUnIWzZd+YJOVvVRQZLc+dD8u0aOtqXygeQRm4mjZtqooVKyozM1NvvPGGsrOzvWNJSUl65513JBXc4LhHjx6KjIzUkiVL9Ntvv3nrBw4c0NSpUyVJ/fv3PwnvAAAAAIHAmf2p7Aev+AoxFeW5+78yTVq41xSKVcAsmrFs2TJNmzbNr5aTk6MHHnjA+/chQ4aoXbt2CgsL0w033KBJkybphx9+0Jo1a9SoUSNlZ2crLi5O6enpatiwoQYNGuT3euXLl9fNN9+sSZMmaeLEiWrRooViYmK0evVqpaamqk+fPmrVqtXJeLsAAAAow6y1stPflZ17yM+vVarJc+cjMjXrFn0iypyACVzJyclav369X81a61dLTk72/rljx476v//7P82YMUNr167V8uXLFRISolq1aqlLly7q169fobcGdu7cWQ8//LCmT5+u9evXKycnR3Xq1FHv3r3VrVu3knuDAAAACAjWyZV9/1XZH+b6irG15Rn7qEzVsrvfFApnrFvrjuOIdu7cybLwKJWYHygKcwNFYW7gcIJpfticHNm3npVd/IOvWLdB3jNbFSq711gpVRrmxokuCx8wV7gAAACA0sxmZsp59Qlp9RJfsXGzvNUIo8u71xhKFIELAAAAKGE2LVXOi49K6337vKp5G3lu+bdMROFbFSEwELgAAACAEmST98t5bry05ZC9XNt1kWfk3TKhoa71hZODwAUAAACUELs3Qc6kcdLu7d6aObuHzFWjZcqVc7EznCwELgAAAKAE2F3b8sJWUqK3ZnoOlLn0OhljXOwMJxOBCwAAAChmdnO8nGcfklJ82xKZQcNl+l5K2AoyBC4AAACgGNl1a/IWyMhIzysYI3P5TfJ06+tuY3AFgQsAAAAoJnbFb3JefVLKyc4rlCsnc+0d8nQ6393G4BoCFwAAAFAMnF8WyL7zvOQ4eYXQMHlG/Uum9ZnuNgZXEbgAAACAE+R886XsJ2/4CpFR8oz+j0zT091rCqUCgQsAAAA4TtZa2S/el539ia9YoZI8t4+XqdfIvcZQahC4AAAAgONgnVzZD16V/X6ur1g1Vp6xj8jE1navMZQqBC4AAADgGNmcbNk3n5X9/UdfsXY9ee54WKZyVfcaQ6lD4AIAAACOgc1Il/Py49KfK3zFhk3luf0hmegY1/pC6UTgAgAAAI6SPZgs5/mHpb/X+4otzpDn5vtkIiLdawylFoELAAAAOAp2b4KcZx+Sdm3z1syZ58pcd4dMSKiLnaE0I3ABAAAAR2B3bpUz6SFpX6K3Zrr1lRl2o4zH42JnKO0IXAAAAMBh2E1xebcRphz01syAy2UGDJMxxsXOUBYQuAAAAIAi2D+W5y2QkZmRVzBG5vKb5OnW193GUGYQuAAAAIBCOL99L/vWs1Jubl6hXIjM9XfKc+a5rvaFsoXABQAAAPyD8+0M2Y9e9xXCI+S5+X6Z089wrymUSQQuAAAA4H+stbJfTJWd/amvWL6CPLc9JNPwVPcaQ5lF4AIAAAAk2dxc2amTZX/6xlesGivPHeNlatZ1rzGUaQQuAAAABD2blSnn9aelFb/5inXqy3P7eJnKVd1rDGUegQsAAABBzaalyHnxMWn9n75ik+byjP6PTHR59xpDQCBwAQAAIGjZfXvlPDde2r7ZV2zTUZ4b7pEJD3etLwQOAhcAAACCkt25Tc6zD0lJCd6aObuHzFWjZcqVc7EzBBICFwAAAIKOjf9LzguPSqkHvTXT5xKZi6+SMcbFzhBoCFwAAAAIKnbV73JefULKysorGCNz2Uh5egxwtzEEJAIXAAAAgobz87ey774gOU5eoVyIzPV3ynPmue42hoBF4AIAAEDAs9bKzp0uO/0dXzEiUp5b/i3TvI17jSHgEbgAAAAQ0KyTK/vxG7ILZvqKFSrJc/tDMvUau9cYggKBCwAAAAHLZmfJvjFJdunPvmL1mvLc+YhM9ZruNYagQeACAABAQLJpKXJe+j8pbo2vWL+JPLeNk6lQybW+EFwIXAAAAAg4hW5o3LKdPDf9SyYi0rW+EHwIXAAAAAgodufW/21onOitmS7dZK4eIxPCj784uZhxAAAACBh2w9q8DY3TUrw1NjSGmwhcAAAACAh2+SI5rz8tZR+yofGwG+Tp3t/dxhDUCFwAAAAo85yFs2U/fE2y/9vQOCREnpF3ybQ/293GEPQIXAAAACizrLWyn78nO+czXzEqWp5bHpA5raV7jQH/Q+ACAABAmWRzsmXffVH214W+YuVq8tw+XqZOPfcaAw5B4AIAAECZYzPS5Lz8hPTncl+xTn15bntIpko19xoD/oHABQAAgDLF7k+S88Ij0paNvuJpreS55X6ZqPLuNQYUgsAFAACAMsPu3CrnuYelvXu8NdPhHJnr7pQJDXWxM6BwBC4AAACUCXb9n3JefMx/j60LBspceq2Mx+NiZ0DRCFwAAAAo9ezSn+VMmSjlZOcVjJG59Dp5eg50tzHgCAImcG3cuFGrVq3Shg0btH79eu3bt0+hoaF6//33D3tedna25syZo19++UU7d+6U4ziqUqWKmjVrpssuu0xVqlQpcM66des0ffp0xcXFKScnR3Xr1lXv3r3VtWvXEnp3AAAAwcuZ/6XsJ29K1uYVQkLluf5OmQ7nuNsYcBQCJnB99tlnWrJkyTGdc+DAAT366KPasmWLKlWqpFatWkmSdu3apYULF6pbt24FAtfixYs1ceJEWWvVvHlzxcTEaM2aNZo8ebI2b96sESNGFNt7AgAACGbWcWQ/fUt2/pe+YlR5eW59QKbp6e41BhyDgAlcTZs2VYMGDdS4cWM1btxYN95442GPdxxHTz75pLZs2aLBgwfr0ksvVbly5bzju3fvVmRkpN85KSkpmjx5shzH0V133aVOnTpJkvbv369x48Zp1qxZat++vVq2ZJM9AACAE2Gzs2TffFZ2yU++YtVYeW5/SKbWKe41BhyjgAlcgwYNOqbjv/vuO61fv16dOnXSsGHDCozXqFGjQG3BggVKS0tThw4dvGFLkipVqqThw4fr6aef1syZMwlcAAAAJ8CmJMt56f+kDX/6ivUayTNmnEylgo97AKVZwASuYzV//nxJ0oABA476nKVLl0qSOnfuXGCsXbt2Cg0N1erVq5WVlaWwsLDiaRQAACCI2IRdcp5/WNq13Vc8/Qx5Rv1LJiLKvcaA4xSUgSs9PV3x8fGKjIxUkyZNFBcXpyVLliglJUXVqlVThw4dVK9evQLnbdmyRZLUqFGjAmMhISGqV6+e4uPjtWPHDjVo0KCk3wYAAEBAsZvW521ofPCAt2bOvkBm+C0yIUH5YysCQFDO3G3btslaq5o1a+qtt97S119/7Tf+8ccfa8CAARo+fLi3lpaWptTUVEkqdOXC/Hp8fLwSExMJXAAAAMcgY/GPcp7+j5SV6a2ZgVfI9LtMxhgXOwNOTFAGrvzgtGXLFm3atEkDBgxQ7969FRERod9//11vv/22vvrqK8XGxqpXr16SpIyMDO/54eHhhb5ufv3QYw9n7NixBWphYWGaMGGCJKlatWpH/6aKWcj/fotUvXp113pA6cX8QFGYGygKcwOHkzHvC+1/5SnJcfIK5cqp4q33K7J7P3cbg+sC4WtHUG7J7fzv/8y5ubk6++yzddVVVyk2NlYVKlRQjx49dOWVV0qSPv/8czfbBAAACGjWcXTwnZe0f/IT3rBloqJVedwkwhYCRlBe4YqIiPD+uVu3bgXGu3Xrprfeekt79+7Vrl27VLNmTb9zMjMzFRVV8KHNzMzMAq9/OBMnTjzseGJiomz+Bn8nWf5vERISElz5+CjdmB8oCnMDRWFu4J8KXfa9UlWZ2x9Scu0GEnMFKh1fO4wxqlWr1nGfH5RXuGJjY71/LuzyZHh4uCpUqCApb3NkSYqKivKGrKSkpEJfN7/u5q2AAAAApZ1NSZYz8T9+YSukQRN57n9Kpm4D9xoDSkBQBq5q1aopJiZGUt5mxv/kOI73Oa9Dr1bVr19fkrRx48YC5+Tk5GjLli0KDQ1V7dq1S6JtAACAMs/u2Snn8XulDWu9tbC2nVTl/16RqcIvrRF4gjJwSVL79u0lSX/88UeBsbi4OOXk5CgsLEx16tTx1tu1aydJWrRoUYFzli1bpuzsbLVs2ZI9uAAAAAph4/+S8/g90p4d3po5p6cqP/i0PFHRLnYGlJygDVwXXXSRPB6PvvrqK23atMlbP3DggN566y1Jec9yhRyy50OPHj0UGRmpJUuW6LfffvM7Z+rUqZKk/v37n6R3AAAAUHbYpb/IeeZBKSXZWzODhstcPZo9thDQAmZ2L1u2TNOmTfOr5eTk6IEHHvD+fciQId6rVHXr1tWIESP01ltv6cEHH1TTpk0VHh6udevWKTU1VQ0bNtQVV1zh93rly5fXzTffrEmTJmnixIlq0aKFYmJitHr1aqWmpqpPnz5q1apVyb9ZAACAMsJaK/vNl7KfvSXlLwYWEiJzze3ydDrf3eaAkyBgAldycrLWr1/vV7PW+tWSk5P9xvv06aPatWtrxowZ2rBhg7Kzs1WjRg3169dPAwYMKHS/rc6dO+vhhx/W9OnTtX79euXk5KhOnTrq3bt3oSseAgAABCubmyv70euy3832FaOi5bnlAZnTWrrXGHASGevWuuM4op07d7IsPEol5geKwtxAUZgbwcdmpMt57Slp9RJfsWqsPLc/JFPrFL9jmR8oSmmYGye6LHzAXOECAABA6WD37ZXzwiPSVt9z8mrYVJ7RD8hUqOxeY4ALCFwAAAAoNnbrJjnPPyLt3+srtusiz3VjZQp5XAMIdAQuAAAAFAu7ZqmcV56UMtO9NdNrkMyQa2Q8Qbs4NoIcgQsAAAAnzPlujuyHr0qOk1cwHpnLb5SnW193GwNcRuACAADAcbNOruy0d2TnfeErhkfIc+M9Mq3PdK0voLQgcAEAAOC42MwMOVMmSisW+YqVqsgz5j8y9Rq71xhQihC4AAAAcMzs/iQ5Lz4mbd7gK57SUJ7R/5GpUs29xoBShsAFAACAY2K3/Z237HtSoq/YqoM8N94tExHlXmNAKUTgAgAAwFGza5bJefUJKeOQlQi795cZer1MuXIudgaUTgQuAAAAHBXnu9myH77mvxLhZdfL02OAu40BpRiBCwAAAIdlnVzZT9+Snf+VrxgeIc8Nd8u06eheY0AZQOACAABAkWxGupzXn5ZW/e4rVqqStzhGfVYiBI6EwAUAAIBC2aREOS8+Km3d5CvWa5QXtipXda8xoAwhcAEAAKAAu3mDnBcekw4k+YptOsoz8i6ZiEj3GgPKGAIXAAAA/Njli+RMeUbKyvTWTK9BMkNGyHhYiRA4FgQuAAAASJKstbLzPped9o5kbV7R45G5cpQ8513obnNAGUXgAgAAgGxOtuzUl2V/nu8rRkbLM+pemRZnuNcYUMYRuAAAAIKcTT0o5+UJ0rrVvmK1GvKM+Y9M7XruNQYEAAIXAABAELO7tst54VFpzw5fsUkLeW65XyamonuNAQGCwAUAABCk7NqVcl55QkpL8dZM524yV4+WCQ11sTMgcBC4AAAAgpDz4zzZ91+WcnO9NTNouEzfS2WMcbEzILAQuAAAAIKIdXJlP31bdv6XvmJomDzX3SHT4Rz3GgMCFIELAAAgSNj0NDmvPy2tXuIrVqwsz60PyDRs6l5jQAAjcAEAAAQBm7hbzouPSds3+4qnNJRn9IMyVaq71xgQ4AhcAAAAAc5u+FPO5Melgwd8xbad5bn+TpmISPcaA4IAgQsAACCAOb8ulH33BSknx1szfYbIDLpKxuNxsTMgOBC4AAAAApB1HNkvpsrO+cxXLBcic/Wt8pzVw73GgCBD4AIAAAgwNiNdzhuTpBWLfMXyFeS55d8yp7ZwrzEgCBG4AAAAAojdm5C3OMa2Tb5i7Xp5i2NUr+leY0CQInABAAAECBv/l5yX/uu/OEarDvLccLdMZJR7jQFBjMAFAAAQAApdHKPXIJkhI2Q85VzsDAhuBC4AAIAyLG9xjPdk50zzFcuFyFx1izxnX+BeYwAkEbgAAADKLJuRJmfKRGnlYl+xfAV5br5fpunp7jUGwIvABQAAUAbZhF15z2tt3+wr1qkvz60PsDgGUIoQuAAAAMoYG7dGzssTpJRkX7H1mfKMvIvFMYBShsAFAABQhjg/zpN9/2UpN9dbMxcOkbl4OItjAKUQgQsAAKAMsLm5sp++KfvtDF8xJETm6jHydOnmXmMADovABQAAUMrZ1BQ5rz0l/bncV6xQSZ5b/i3TuJl7jQE4IgIXAABAKWZ3bpPz4mPSnh2+Yr1GeYtjVKnuXmMAjgqBCwAAoJSyq5fKef0pKT3NV2x/ljzX3iETHuFeYwCOGoELAACglLHWyn7zhexn70jW8dbNwCtk+l0mY4yL3QE4FgQuAACAUsRmZ8m+95Lsrwt9xfAIea67U6ZdF/caA3BcCFwAAAClhN2fJGfy/0mb4nzFqrHyjH5Apm5D9xoDcNwIXAAAAKWA3bRezuT/SvuTfMWmp8sz6j6ZmIruNQbghBC4AAAAXOYsWij7zotSTra3Zs67UObyG2RCQl3sDMCJInABAAC4xDq5stPelZ33ua9YrpzMZTfI062ve40BKDYBE7g2btyoVatWacOGDVq/fr327dun0NBQvf/++0f9Go8++qhWr14tSXrttddUqVKlQo9bt26dpk+frri4OOXk5Khu3brq3bu3unbtWgzvBAAABAObmpK35Psfh2xmXD4m7xbC01q51xiAYhUwgeuzzz7TkiVLjvv87777TqtXr5YxRtbaIo9bvHixJk6cKGutmjdvrpiYGK1Zs0aTJ0/W5s2bNWLEiOPuAQAABIdCNzOu2yBvM+NqNdxrDECxC5jA1bRpUzVo0ECNGzdW48aNdeONNx71ucnJyXrvvffUpk0b7dixQwkJCYUel5KSosmTJ8txHN11113q1KmTJGn//v0aN26cZs2apfbt26tly5bF8p4AAEDgsat+lzPlGf/NjNudJc+1t8tERLrXGIAS4XG7geIyaNAgDR06VO3bty/yVsCivP3228rIyND1119/2OMWLFigtLQ0dejQwRu2JKlSpUoaPny4JGnmzJnH3DsAAAh81lo5sz7Ju7J1SNgyA6+Q56Z7CVtAgAqYK1zHa8WKFfrpp5902WWXqWbNmoc9dunSpZKkzp07Fxhr166dQkNDtXr1amVlZSksLKxE+gUAAGWPzcyQfes52aU/+4psZgwEhYC5wnU8MjMz9frrr6tOnToaOHDgEY/fsmWLJKlRo0YFxkJCQlSvXj1lZ2drx44dBcYBAEBwsgm75Ey41z9sVa8pz/1PEbaAIBDUgevjjz9WQkKCRo4cqZCQw1/sS0tLU2pqqiSpSpUqhR6TX09MTCzeRgEAQJlk/1ol5//ukrb97Su2aCvPA8/I1KnvWl8ATp6gvaVw48aNmj17ts4//3ydfvrpRzw+IyPD++fw8PBCj8mvH3rs4YwdO7ZALSwsTBMmTJAkVatW7ahepyTkB9Dq1au71gNKL+YHisLcQFGCbW5Ya5U26zMdfPM5ycn11qMGXq6Yq2+RKRe0P4IVKtjmB45eIMyNoPx/u+M4evXVVxUdHa2rrrrK7XYAAEAAsVmZSn7lKaUvmOUrhoap4q33K7Lrhe41BsAVQRm4Zs2apU2bNmnUqFGqUKHCUZ0TERHh/XNmZqaioqIKHJOZmVng2MOZOHHiYccTExMPuydYScr/LUJRS+QjuDE/UBTmBooSLHPDJiXKeflx6e/1vmLlavLccr9SGpyqlAB//8crWOYHjl1pmBvGGNWqVeu4zw/KwLV06VIZY/T999/rhx9+8Bvbv3+/JOnpp59WSEiIhg0bpmbNmikqKkpRUVFKS0tTUlJSoYErKSlJkru3AgIAAHfYDX/KeXmClLzfV2zSXJ5R98lUrOxaXwDcFZSBS8q7t3rt2rVFjsfFxUnK2xQ5X/369bV27Vpt3LhRdevW9Ts+JydHW7ZsUWhoqGrXrl0yTQMAgFLJ+X6u7IevSbk53prp2kfmspEyIaHuNQbAdUEZuMaPH1/k2K233qqEhAS99tprBTZQbteundauXatFixbpvPPO8xtbtmyZsrOzdcYZZ7AHFwAAQcJmZ8t+9JrsD1/7iuVCZK64SZ7zervXGIBSI6iXhT9WPXr0UGRkpJYsWaLffvvNWz9w4ICmTp0qSerfv79b7QEAgJPI7k+S88wD/mGrYmV57v4vYQuAV8Bc4Vq2bJmmTZvmV8vJydEDDzzg/fuQIUPUrl274/4Y5cuX180336xJkyZp4sSJatGihWJiYrR69WqlpqaqT58+atWq1XG/PgAAKBvshrVyXnlCOpDkKzZsKs8t98tUqupeYwBKnYAJXMnJyVq/fr1fzVrrVzv0eazj1blzZz388MOaPn261q9fr5ycHNWpU0e9e/dWt27dTvj1AQBA6eb8MFf2g388r3X2BTJX3iwTyvNaAPwZ69a64ziinTt3siw8SiXmB4rC3EBRAmFu2Oxs2Q9flf1xnq9YrpzMsBtkzu8jY4x7zZVxgTA/UDJKw9xgWXgAAIASZvfvzVvyfeM6X7FCpbwl309t4V5jAEo9AhcAAMBh5D2vNUE6sM9XbHRaXtiqzPNaAA6PwAUAAFAIa63sd3NkP57i/7zWub1kLr+J57UAHBUCFwAAwD/Y7CzZqS/L/vKtr1guROaKG+U570L3GgNQ5hC4AAAADmH3Jsh5+XFp8wZfsWIVeUb9S6ZJc/caA1AmEbgAAAD+x65dKee1p6SUQ7aSadJcnpv+JVOpinuNASizCFwAACDoWWtlv/lC9rN3JOt466ZbX5mh18uE8LwWgOND4AIAAEHNZqTLvvui7O8/+oohoTLDb5Hn7B7uNQYgIBC4AABA0LK7d8iZ/H/Sji2+YpVq8tx8v0yDU91rDEDAIHABAICgZFculvPGRCk9zVds1lqeG++RianoXmMAAgqBCwAABBXrOLIzPpKd+ZFf3fS+WObiq2XKlXOpMwCBiMAFAACChk1NybuqtXqJrxgeIc81t8l0OMe9xgAELAIXAAAICnbrprz9tRJ2+Yo16shzy/0yteu51xiAgEbgAgAAAc9ZtFD2vZekrCxfsW0nea69QyYq2r3GAAQ8AhcAAAhYNidb9pM3ZBfO9hWNkRl4pUyfS2Q8HveaAxAUCFwAACAg2X175bz6hBT/l68YHSPPDXfLnH6Ge40BCCoELgAAEHDsujV5YevgAV+xfhN5Rv1LploN9xoDEHQIXAAAIGBYa2W/+VJ22tuS43jr5uwLZK4cJRMa5l5zAIISgQsAAAQEm5Em5+3npaW/+IohITKX3yTPeb3dawxAUCNwAQCAMs/u2JK35Puu7b5ilWryjLpfpuGp7jUGIOgRuAAAQJnm/P6j7DsvSJkZvmLzNnmLY8RUdK8xABCBCwAAlFE2J0f2s7dkv53hVzd9h8oMvFzGU86lzgDAh8AFAADKHLt/r5xXn5Q2rPUVI6Pluf5OmTYd3WsMAP6BwAUAAMoUu251Xtg6dMn3ug3lufk+mdha7jUGAIUgcAEAgDLBWiv79XTZ6e9J9pAl37t0l7nyZpnwcBe7A4DCEbgAAECpZ9NS5bz1nLRika8YEiIz7EaZ83rLGONecwBwGAQuAABQqtmtm+S8MkHas9NXrBorz6h/yTRgyXcApRuBCwAAlFrOL9/KTn1Zys7yFVu2k+f6sTLlK7jXGAAcJQIXAAAodWx2luxHr8v+8LWvaIzMRZfnLfvu8bjXHAAcAwIXAAAoVWzCrrxbCLds9BXLx8gz8m6Z089wrzEAOA4ELgAAUGrYFb/JeetZKS3VV2zYVJ6b/iVTtbprfQHA8SJwAQAA19ncXNkvpsrOneZXN936yVx6nUxoqEudAcCJIXABAABX2QP75Lz2lBS3xlcMj5C5erQ8Hc9zrzEAKAYELgAA4Bq7bo2c15+SDuzzFWudIs/N98nUOsW9xgCgmBC4AADASWcdR3buNNkv3pes462bTufLXHWrTHiEi90BQPEhcAEAgJPKph6U88YkafUSXzEkROaykTLn95Exxr3mAKCYEbgAAMBJYzfFyXn1SWnvHl+xaqw8o/4l0+BU9xoDgBJC4AIAACXOWqu02Z/JefN5KTfHN9CmozzX3iETXd695gCgBBG4AABAibIZaTrwzDhl/DTfV/R4ZC6+SqbXxTIej3vNAUAJI3ABAIASY7dtkvPKk8rYvd1XrFhFnhvvlmna0r3GAOAkIXABAIBiZ62V/Xm+7AevStlZvoHTWuWFrQqV3WsOAE4iAhcAAChWNjND9v1XZH9d4Csao+hLr1F6j4tkPOXcaw4ATjICFwAAKDZ251Y5rzwh7djiK5avoMp3PaLwMzopIyHBveYAwAUELgAAUCycRd/JTp0sZWb4ik1ayHPjPQpv2sy9xgDARQQuAABwQmxWpuxHr8v+OM+vbnoPlhk0XCaEHzcABC++AgIAgONmd22X8+oT0ra/fcWo8vJcd6dMmzNd6wsASouACVwbN27UqlWrtGHDBq1fv1779u1TaGio3n///QLHOo6jdevWaenSpfrzzz+1Z88epaWlqWrVqmrVqpUGDRqk2NjYIj/WunXrNH36dMXFxSknJ0d169ZV79691bVr1xJ8hwAAlC7O4h9k331Jykz3FRs2leeme2WqFv19FACCScAErs8++0xLliw5qmP37Nmjhx56SJJUpUoVNW3aVB6PRxs2bND8+fP1888/6/7771ezZgXvN1+8eLEmTpwoa62aN2+umJgYrVmzRpMnT9bmzZs1YsSIYn1fAACUNjY7S/bjKbLfz/WrmwsGygy5WiYk1KXOAKD0CZjA1bRpUzVo0ECNGzdW48aNdeONNx72+DZt2ujiiy9WixYtvLXs7Gy9/vrr+u677/T888/r+eefV8gh952npKRo8uTJchxHd911lzp16iRJ2r9/v8aNG6dZs2apffv2atmSjRwBAIHJ7tmRtwrh1k2+YmS0PNfeLnNGZ/caA4BSylPcLzhmzBh98cUXOnDgQHG/9GENGjRIQ4cOVfv27VWpUqXDHluzZk098MADfmFLkkJDQzVy5EhFRUUpMTFRcXFxfuMLFixQWlqaOnTo4A1bklSpUiUNHz5ckjRz5szieUMAAJQyzu8/ynn0Tv+wVb+JPP+ZRNgCgCIU+xWuPXv26MMPP9Qnn3yiDh066IILLlDr1q2L+8OUmLCwMNWqVUvx8fFKSkryG1u6dKkkqXPngt9U2rVrp9DQUK1evVpZWVkKCws7Kf0CAFDSiryFsMcAmSHXyIRyCyEAFKXYA9fFF1+s77//XklJSfrtt9/022+/KTY2VhdccIG6du2qihUrFveHLFaO4ygxMVGSClwp27IlbxPHRo0aFTgvJCRE9erVU3x8vHbs2KEGDRqUdKsAAJS4vFUIn5S2/eMWwhFjZNqf5V5jAFBGFHvgGjZsmIYOHarly5frm2++0cqVK7Vnzx598MEH+vjjj3XmmWeqR48epfaq188//6wDBw6oQoUKOu2007z1tLQ0paamSspbaKMwVapUUXx8vBITEwlcAIAyz/nte9n3JvuvQli/Sd4qhNVrutcYAJQhJbJohsfjUfv27dW+fXslJSVpwYIFWrhwoRITE7Vo0SItWrSoVF71SkxM1Ntvvy1JGjp0qEIPuUUiIyPD++fw8PBCz8+vH3rs4YwdO7ZALSwsTBMmTJAkVatW7ahepyTkLxZSvXp113pA6cX8QFGYG4HBZmYoecqzSv/mS796VP+hihlxq0zosd82z9zA4TA/UJRAmBslvkphlSpVdMkll2jIkCFauXKl5s+fr2XLlpW6q14ZGRl6+umndfDgQZ155pnq1auXa70AAOCWnK1/a//TDypnc7y3ZqJjVHHMA4rofL6LnQFA2XTSloU3xqht27Zq27atkpKS9Pzzz2vt2rXKzc31XvWqWbOmBgwYoO7du8vjKfYFFIuUk5OjZ555Rhs3blSzZs10++23FzgmIiLC++fMzExFRUUVOCYzM7PAsYczceLEw44nJibKWntUr1Xc8n+LkJCQ4MrHR+nG/EBRmBtlm/PLt7LvvyJlZfqKDZvK3HiPDlaroYMn8HllbuBwmB8oSmmYG8YY1apV67jPP6n7cCUmJnpvLzx0BcAGDRpoy5Yt2rVrl15//XV9++23uv/++1WhQoUS78lxHL3wwgtauXKl6tevr3/961+FrjAYFRWlqKgopaWlKSkpqdDAlf+e3LwVEACAY2Uz0mU/eEX214V+dTYyBoATV+KBy3EcLVmyRN9++61WrVolx3EkSeXLl1fXrl3Vs2dP1axZU/v379e8efM0a9Ysbdy4UR988IFGjRpV0u1pypQp+vXXX1WrVi09+OCDio6OLvLY+vXra+3atdq4caPq1q3rN5aTk6MtW7YoNDRUtWvXLum2AQAoFnbbJjmvPiXt2uYrRpWX57o7ZNp0dK8xAAgQJRa49uzZo2+//Vbfffed9u/f7603bdpUvXr1UpcuXbwPwUl5S7Dnb1z873//W8uXLy+p1rw++OADzZ8/X9WqVdN//vOfIy7e0a5dO61du1aLFi3Seeed5ze2bNkyZWdn64wzzmAPLgBAqWetlf3xa9mPpkjZWb6Bxs3kueEemapl9wF1AChNij1wLVq0SPPnz9eaNWu8zx9FRkbqnHPOUa9evVSvXr3Dnt+4cWNVqlTJL6SVhJkzZ+qLL75QpUqV9J///OeobgPs0aOHpk+friVLlui3335Tp06dJEkHDhzQ1KlTJUn9+/cv0b4BADhRNi1V9r2XZJf85Fc3fS6RuegKmZCT+sQBAAS0Yv+KOmnSJO+fGzRooJ49e+qcc8456oUkJPld+Tpay5Yt07Rp0/xqOTk5euCBB7x/HzJkiNq1a6e///5b7733niQpNjZW06dPL/Q1e/TooWbNmnn/Xr58ed18882aNGmSJk6cqBYtWigmJkarV69Wamqq+vTpo1atWh1z7wAAnCz27/VyXntKStjlK8ZUlOe6O2VatnOvMQAIUMUeuEJDQ3XWWWepV69eatKkyXG9xksvvXTM5yQnJ2v9+vV+NWutXy05OVmSlJqa6r36FhcXp7i4uEJf8/TTT/cLXJLUuXNnPfzww5o+fbrWr1+vnJwc1alTR71791a3bt2OuW8AAE4Ga63s/K9kp70j5eb4Bk5rJc/IsTKVqrrXHAAEMGOLed3x1NTUwy48gaO3c+dOloVHqcT8QFGYG6WTTUmW89Zz0qrffUXjkRkwTKbfpTKeciXeA3MDh8P8QFFKw9wodcvCE7YAACg9bNwfcqY8I+1L9BUrVZFn5N0yp7V0rzEACBI8FQsAQACyTq7s7E9lv/pIso5voFUHea69XSbm8CvzAgCKB4ELAIAAY/fvlTNlorRuta9YrpzM4BEyF1wk4/G41xwABBkCFwAAAcSu+j3vea2UZF+xek15brhbpmFT9xoDgCBF4AIAIADYnGzZ6e/KfvOlX92cea7M8FtkonjGGgDcQOACAKCMs3t25u2ttXmDrxgWJjPsRplzesoY415zABDkCFwAAJRhzqLvZKe+LGWm+4p16stz4z0yteu51xgAQBKBCwCAMslmpMt+8Krsrwv86ub8C2WGXi8TFu5SZwCAQxG4AAAoY+yWeDmvPS3t3u4rRkbLM2K0TPuz3WsMAFAAgQsAgDLCWiv77QzZaW9LOTm+gcbN5Bl5l0y1Gq71BgAoHIELAIAywB5MlvP2c9Kq331FY2T6XCIz4HKZEL6lA0BpxFdnAABKObt2pZw3JkkHknzFilXkuf5OmeZt3GsMAHBEBC4AAEopm5Mj+9X7snOnS9b6Blp1kOfa22ViKrrXHADgqBC4AAAohWzCLjmvPy1tivMVQ0JkhoyQ6XERe2sBQBlB4AIAoJRxfvtedupkKeOQvbVq1JHnxrtl6jV2rzEAwDEjcAEAUErYjDTZD14ruLfW2RfIDLtBJiLSpc4AAMeLwAUAQClgN62XM+Vpac9OXzEySuaqW+U581z3GgMAnBACFwAALrKOIzvvc9kvpkq5ub6BRqfl7a1VvaZ7zQEAThiBCwAAl9j9SXLenCStXekrGiPT91KZ/sPYWwsAAgBfyQEAcIFd+XveRsYpyb5i5WryXD9W5rSW7jUGAChWBC4AAE4im50l+9nbsgtm+g+06yLP1aNlomPcaQwAUCIIXAAAnCR2++a8vbW2b/YVw8JkLrtB5txe7K0FAAGIwAUAQAmz1sounCX76VtSTrZvoG7DvL21ap3iXnMAgBJF4AIAoATZ5P1y3nlBWvW7X91cMFBm8NUyoaEudQYAOBkIXAAAlBC7Zpmct56Vkvf7ihUqyXPt7TIt27vVFgDgJCJwAQBQzGx2tuz0d2Xnf+k/0KqDPNfcJlOhkit9AQBOPgIXAADFyG7fImfK09K2v33FkFCZS6+V6daPhTEAIMgQuAAAKAbWWtnvZuctjJGd5RuoU1+ekXfJ1G3gWm8AAPcQuAAAOEE2eb+ct5+XVi/xq5vu/WWGjJAJC3epMwCA2whcAACcALt6ad7CGAcP+IoxFfMWxmjVwbW+AAClA4ELAIDjYLMyZae9I7tgpv9Aqw7yXDNGpkJldxoDAJQqBC4AAI6R3bpJzpRnpB1bfMWQUJlLrpXpzsIYAAAfAhcAAEfJOo7stzNkp78j5eT4BlgYAwBQBAIXAABHwe7fK+fNZ6W1K/3q5oKLZAZfLRMa5k5jAIBSjcAFAMAR2GW/ynn3RSn1oK9YsbI8194hc/oZ7jUGACj1CFwAABTBZqTLfjxF9qdv/AfadpLn6jEyMRXcaQwAUGYQuAAAKITduC5vYYyEXb5iWLjMZSNlzu3FwhgAgKNC4AIA4BA2N1d29qeyMz+SHMc3UL+JPCPHytSs615zAIAyh8AFAMD/2D075bwxUdq4zlc0Hpk+l8gMGCYTwrdNAMCx4TsHACDoWWtlf/lW9sPXpcx030DVWHmuHytzagv3mgMAlGkELgBAULMHk+W896K0fJFf3XTpJjPsRpmoaJc6AwAEAgIXACBo2TVL5bz9vHRgn68YVV5m+C3ynHmOe40BAAIGgQsAEHRsZqbstLdlF87yH2jeRp5rbpepUs2dxgAAAYfABQAIKnZzfN5y77u2+YohoTKDr5bpMUDG43GvOQBAwCFwAQCCgnVyZedOl/3qAyk31zdQp748I++SqdvAtd4AAIGLwAUACHg2YZecNydJG9b6isbI9BwkM2i4TGioe80BAAJawASujRs3atWqVdqwYYPWr1+vffv2KTQ0VO+///5hz/v+++81d+5cbdu2TSEhIWratKkGDx6s0047rchz1q1bp+nTpysuLk45OTmqW7euevfura5duxbzuwIAnAhrrezP82U/muK/3HvlavJcd4dMs9buNQcACAoBE7g+++wzLVmy5JjOeeeddzRr1iyFhYWpdevWys7O1qpVq7Ry5UqNHTtWHTt2LHDO4sWLNXHiRFlr1bx5c8XExGjNmjWaPHmyNm/erBEjRhTXWwIAnAB78ICcd1+SVvxjufdO58tccZNMVHmXOgMABJOACVxNmzZVgwYN1LhxYzVu3Fg33njjYY9fs2aNZs2apZiYGD322GOqVauWJCkuLk7jx4/X5MmT1aJFC5Uv7/uGnJKSosmTJ8txHN11113q1KmTJGn//v0aN26cZs2apfbt26tly5Yl90YBAEdkV/0u550XpOT9vmJU9P+Wez/Xtb4AAMEnYJZiGjRokIYOHar27durUqVKRzx+xowZkqTBgwd7w5aUF9x69uyptLQ0LVy40O+cBQsWKC0tTR06dPCGLUmqVKmShg8fLkmaOXNmMbwbAMDxsBnpct6bLOeFR/3DVvM28jz0AmELAHDSBUzgOhZZWVlas2aNJKlz584FxvNrS5cu9avn/72wc9q1a6fQ0FCtXr1aWVlZxd0yAOAIbPxfch69Q/aHub5iSKjMZSPlueNh9tYCALgiYG4pPBY7duxQdna2KlSooKpVqxYYb9iwoSRp8+bNfvUtW7ZIkho1alTgnJCQENWrV0/x8fHasWOHGjRoUPyNAwAKsDnZsjM+lp3zmWQd38ApDfOWe69dz73mAABBLygDV2JioiQVGrYkKSIiQtHR0UpNTVV6eroiIyOVlpam1NRUSVKVKlUKPa9KlSqKj49XYmIigQsATgK7Y4ucNyZJW+J9ReOR6TNEZsAwmRCWewcAuCsoA1dGRoYkKSwsrMhjwsPDlZqaqoyMDEVGRnrPyR8r6pxDX/9Ixo4dW6AWFhamCRMmSJKqVXPv9peQkLypUb16ddd6QOnF/EBRTtbcsI6jtFmf6uC7k6Vs323c5WrUUcU7xymM5d5LHb5u4HCYHyhKIMyNoAxc1lpJkjHmiMcAAEqX3IRdOvD8Y8pa7f+cbWSvgYq59jZ5IqNc6gwAgIKCMnBFRkZKkjIzM4s8Jn/hi4iICL//zT8vKqrgN/T81zv02MOZOHHiYccTExNdC375v0VISEhw5eOjdGN+oCglOTestbKLvpP98FUpPc03UKGSPFePUVabM7U3JVVKSS32j40Tx9cNHA7zA0UpDXPDGOO3qvmxCsrAlX+r3t69ewsdz8jIUGpqqqKjo73hLCoqSlFRUUpLS1NSUlKhgSspKcnv9QEAxcMeTJYz9SVp2a/+A2d0lueqW2ViKrrTGAAARxCUy8LXrl1boaGhSk5OLjR0bdq0SZJUr57/ylb169eXJG3cuLHAOTk5OdqyZYtCQ0NVu3btEugaAIKTXfm7nPGj/cNWZJTMdXfKc/P9hC0AQKkWlIErLCxMLVu2lCQtWrSowHh+rX379n71du3aFXnOsmXLlJ2drZYtWx52MQ4AwNGxGWly3n1Rzov/2MS4Weu8TYy7dDvss7gAAJQGQRm4JKlfv36SpOnTp2vnzp3eelxcnObPn6/IyEh1797d75wePXooMjJSS5Ys0W+//eatHzhwQFOnTpUk9e/f/yR0DwCBzcatkTP+Ntkf5/mKoWF5mxjf+YhM1bK7WhUAILgEzDNcy5Yt07Rp0/xqOTk5euCBB7x/HzJkiPcqVevWrdW3b1/Nnj1b9957r1q1aqXc3FytWrVKjuNozJgxKl++vN/rlS9fXjfffLMmTZqkiRMnqkWLFoqJidHq1auVmpqqPn36qFWrViX/ZgEgQNnsLNkvpsp+86V06KJB9ZvIc/2dMrVOca85AACOQ8AEruTkZK1fv96vZq31qyUnJ/uNX3PNNWrQoIHmzp2r1atXq1y5cmrZsqWGDBmiZs2aFfpxOnfurIcffljTp0/X+vXrlZOTozp16qh3797q1q1b8b8xAAgSdnO8nDcmSju3+ooej0y/oTJ9h8qEBMy3LABAEDGWDadKrZ07d7IsPEol5geKcjxzw+bmys75VHbmx1Jurm+gZt28q1oNTi3uNuECvm7gcJgfKEppmBssCw8AKLPszm1y3pwk/e1/h4K54CKZi6+SCQt3qTMAAIoHgQsAcNJZx5FdMEN2+ntSdpZvoEp1ea69XaZZa/eaAwCgGBG4AAAnlU3cLeet56S4NX51c1YPmctGykRFu9QZAADFj8AFADgprLWyP30j+/EbUma6b6BCJXmuulWmbSf3mgMAoIQQuAAAJc7uT5Lz7ovS6iX+A+3PkufKW2RiKrjTGAAAJYzABQAoMdZa2cU/yH7wqpSW4huIKi9zxU0yHc+TMca9BgEAKGEELgBAibAHD8iZ+rK07Bf/gZbt5RkxWqZSVXcaAwDgJCJwAQCKnV2+SM57L0kHD/iK4ZEyQ6+TObcXV7UAAEGDwAUAKDZOSrKSp0yS891c/4HTWslzzW0y1Wq40xgAAC4hcAEAioVds1SJUyfL2ZvgK4aFyQweIdOtn4zH415zAAC4hMAFADghNiNN9pM3ZX+c5z/Q6DR5rr1DpmYddxoDAKAUIHABAI6bXbtSzjsvSHv3+IohoTIXXSHTe5CMp5x7zQEAUAoQuAAAx8xmZshOe1t24Wy/ekijpqp4+zjtj2JfLQAAJAIXAOAY2fV/ynnrWSlhl69YrpxM36GqOuIWmZAQKSGhyPMBAAgmBC4AwFGxWZmyX0yVnf+VZK1voE79vGe16jfOC1sAAMCL74wAgCOy8X/Jees5afd2X9F4ZC4cLDPgcpnQUPeaAwCgFCNwAQCKZLOzZL/8QHbeF5J1fAM168pz7e0yjU5zrTcAAMoCAhcAoFB20/q8Z7V2bvUVjZHpOUhm4BUyYeGu9QYAQFlB4AIA+LHZ2bIzP5KdO01yDrmqFVs776pWk+buNQcAQBlD4AIAeNnNG/Ke1dq+2Vc0RqbHAJlBV8mEc1ULAIBjQeACAPzvqtbHsnM/87+qVb2mPNfcJtO0pXvNAQBQhhG4ACDI2c3xec9qHXpVS5Lp1k9m8NUyEZHuNAYAQAAgcAFAkLI52bKzPpGd/an/Va1qNfKuap3Wyr3mAAAIEAQuAAhCdkt83rNa2/72q5tufWUGj+CqFgAAxYTABQBBxHtVa85nUm6ub6BqbN5VrWat3WsOAIAAROACgCBR5LNaXfvIDLmGq1oAAJQAAhcABLgin9WqGivPiDEyzdu41xwAAAGOwAUAAazQfbUkma59ZYbwrBYAACWNwAUAAShvX62PZOdOK3hVi2e1AAA4aQhcABBg7Kb1ct5+Ttqxxa/OCoQAAJx8BC4ACBA2O0v2qw9lv/5csuyrBQBAaUDgAoAAYOP/kvP289KubX51072/zOCrZcIjXOoMAIDgRuACgDLMZmbKfvW+7Ddf+V/Vql4z76pW05buNQcAAAhcAFBW2bg/5LzzvLRnp69ojEyPi2QGDZcJD3evOQAAIInABQBljs1Il/38PdmFsyRrfQM16shzzRiZJi3caw4AAPghcAFAGWLXrpTz7otS4m5f0Xhkeg6UGXiFTBhXtQAAKE0IXABQBtj0NNnP3pb9Ya7/QK1T8p7VanSaO40BAIDDInABQClnVy+VM/UlKSnRV/R4ZC4cItN/mExoqHvNAQCAwyJwAUApZVMPyn78huyvC/wH6tSX59rbZeo3cacxAABw1AhcAFAK2eWL5Lz/snRgn69YLkSm31CZPkNkQriqBQBAWUDgAoBSxB48IPvha7K//+g/UL9J3rNadRu40hcAADg+BC4AKAWstbKLf5D96HUpJdk3EBKat/pgz0Ey5cq51yAAADguBC4AcJndtzfv9sGVi/0HmjSXZ8QYmZp13WkMAACcMAIXALjEWiv70zeyn74lpaf6BsIjZC6+SqZbPxmPx70GAQDACSNwAYALbMIuOe+9JK1d6T/QvI08V90qU72mO40BAIBiReACgJPIOo7swtmyn78rZWb4BiKjZS69VuacnjLGuNcgAAAoVkEfuOLi4vTVV19p3bp1SklJUUREhBo2bKhevXqpc+fOhZ7z/fffa+7cudq2bZtCQkLUtGlTDR48WKeddtpJ7h5AWWJ3bpXzzgtS/F/+A206ynPlzTKVq7rTGAAAKDFBHbh+/fVXPfvss7LWqnHjxjr99NO1b98+/fHHH1qzZo0GDhyoK6+80u+cd955R7NmzVJYWJhat26t7OxsrVq1SitXrtTYsWPVsWNHl94NgNLK5uTIfj1dduZHUk6Ob6B8jMywG2U6nsdVLQAAAlTQBq7c3Fy98cYbstbqjjvu0FlnneUdi4uL08MPP6yvvvpKPXr0UM2aec9SrFmzRrNmzVJMTIwee+wx1apVy3v8+PHjNXnyZLVo0ULly5d35T0BKH3slng5bz8vbd3kVzdnnitz+Y0yMRVd6gwAAJwMQbv81fbt25WcnKw6der4hS1Jatq0qdq0aSNrrTZu3Oitz5gxQ5I0ePBgb9jKP75nz55KS0vTwoULT84bAFCq2ewsOdPflfPfu/zDVqUq8tz6gDw33kPYAgAgCARt4AoNDT2q4/KvVmVlZWnNmjWSVOizXfm1pUuXFlOHAMoqu/5POY/cLjvnM8lxvHVzbi95Hn5Rpm0nF7sDAAAnU9DeUlijRg3VqFFD27dv1y+//FLglsKVK1cqNjZWLVq0kCTt2LFD2dnZqlChgqpWLfhge8OGDSVJmzdvPjlvAECpYzPSZKe/K7twtv9AtRryXD1apnkbdxoDAACuCdrA5fF4dMstt+iJJ57Qs88+qxkzZqhGjRrat2+f/vrrLzVp0kRjxoxRSEjeP1FiYqIkFRq2JCkiIkLR0dFKTU1Venq6IiMjT9p7AeA+u3qpnKkvSUmJvqLxyPQYIDPoSpnwCPeaAwAArgnawCVJzZs31/jx4/X0008rPj5e8fHxkqTIyEi1atVKlStX9h6bkZG3X05YWFiRrxceHq7U1FRlZGQcVeAaO3ZsgVpYWJgmTJggSapWrdoxvZ/ilB80q1ev7loPKL2YHz5O8n4lv/GcMr6f61cPqddIFUb/W2FNT3epM3cwN1AU5gYOh/mBogTC3AjqwPXTTz/p5Zdf1qmnnqo77rhDdevW1b59+zRjxgxNnz5da9as0fjx4xUSEiJrrSQddunm/GMABD5rrTJ+/EYH33hWzoF9voGQEJW/5BpFD7la5iifFQUAAIEraAPXzp079dJLL6lSpUq67777FBGRd7tPrVq1dOONN2rfvn1aunSpvvvuO11wwQXeK1aZmZlFvmZWVpYkeV/rSCZOnHjY8cTERNdCXP5vERISElz5+Cjdgn1+2KQEOe+/Iq363X+gYVN5Rtym9Dr1lL5/vyu9uS3Y5waKxtzA4TA/UJTSMDeMMX4rlB+roF2l8Oeff1Zubq7atGlTaEDq0qWLJOmPP/6Q5Lu9b+/evYW+XkZGhlJTUxUdHc3zW0CAso4j57vZch4a7R+2wsJlhl4vz31PyNSp516DAACg1AnaK1xJSUmSpKioqELH8+spKSmSpNq1ays0NFTJycnau3dvgcUzNm3K22enXj1+2AICkd21Tc67L0rr//QfaN5Gnqtulale053GAABAqRa0V7gqVaokSd6FMv5pw4YNknyXMcPCwtSyZUtJ0qJFiwocn19r3759cbcKwEU2J0fOrE/kPHy7f9iKKi9zze3y3PkIYQsAABQpaANXhw4dJElr167VvHnz/Mbi4uI0a9YsSf6bHPfr10+SNH36dO3cudPv+Pnz5ysyMlLdu3cv6dYBnCR203o5/x0r+8VUKSfbWzftz5bnkZfkObvHYRfSAQAACNpbChs1aqQBAwZoxowZmjJlir7++mvVqVNH+/btU1xcnKy1uuCCC9S6dWvvOa1bt1bfvn01e/Zs3XvvvWrVqpVyc3O1atUqOY6jMWPGqHz58i6+KwDFwWZmyH75vuz8GZJ1fAOVqshz5SiZtp2LPhkAAOAQQRu4JOmqq67Saaedpm+++UYbN27Ujh07FBERoRYtWqhHjx4655xzCpxzzTXXqEGDBpo7d65Wr16tcuXKqWXLlhoyZIiaNWvmwrsAUJzsH8vlvPeStHePX92cd6HMkBEyUdEudQYAAMqioA5cktSxY0d17NjxmM7p2rWrunbtWjINAXCFTUmW/eRN2V8X+A/E1pbn6tEyp7V0pzEAAFCmBX3gAhDcrLWyv/8o+9Hr0sEDvgGPR6b3YJkBw2RCw9xrEAAAlGkELgBBy+5NkPP+y9LqJf4D9ZvIM2KMzCkN3WkMAAAEDAIXgKBjnVzZhXNkP39XyszwDYSFyVx0pcwFF8mUK+degwAAIGAQuAAEFbt9s5x3XpA2xfkPtGgrz/Bb2FMLAAAUKwIXgKBgs7NkZ30iO3e6lJvjG4iOkRl6vUyXbuypBQAAih2BC0DAs3Fr8pZ637Xdr246ni9z2fUyFSq50xgAAAh4BC4AAcumpch+9rbsj/P8B6pUl2f4zTKtOrjTGAAACBoELgABx1orLftFzoevSQf2+QaMR6ZHf5mBV8pERLrXIAAACBoELgABxSYlyvngFWnlYv+Bug3kuXqMTMNT3WkMAAAEJQIXgIBgnVzZ7+bITn9Pykz3DYSG5W1e3HOQTAhf8gAAwMnFTx8Ayjy77W85775YcKn301rJc/WtMrG13WkMAAAEPQIXgDLLZmXmLfX+9XQpN9c3EFU+b6n3s7qz1DsAAHAVgQtAmWT/WpW31PuenX51lnoHAAClCYELQJliU5JlP31L9pdv/Qeqxspz5c0yrdq70xgAAEAhCFwAygRrrexv38t+PEVKSfYNGI9Mz4tkLrpCJjzCvQYBAAAKQeACUOrZhF1ypr4s/bncf6BeI3muHi1Tv4k7jQEAABwBgQtAqWVzc2Xnfyn71QdSVpZvICxcZuAVMj0ukilXzr0GAQAAjoDABaBUspvW5y31vm2T/0DLdnnPalWr4U5jAAAAx4DABaBUsRlpsl+8L7tgpmStbyCmosywG2TOPJel3gEAQJlB4AJQatgVi+R88Jq0L9Gvbs7pKXPJNTLRMS51BgAAcHwIXABcZ/ftlfPhq9LyRf4DNevIc9WtMk1butMYAADACSJwAXCNdXJlv58rO/1dKSPdNxASItPnUpk+l8iEhrrXIAAAwAkicAFwhd26Sc57L0mb4vwHmp4uz/BbZWrVdacxAACAYkTgAnBS2cwM2Rkfyn7zpeQ4voGo8nnPaZ19gYzH416DAAAAxYjABeCksauXyHn/FWnvHr+66XS+zNDrZSpUcqcxAACAEkLgAlDi7P4k2Y+nyC75yX+gek15ht8s0+IMdxoDAAAoYQQuACXGOo7sD/9bFCM9zTdQrpxM78Ey/YbKhIW71yAAAEAJI3ABKBF22yY5702WNq7zH2jcLG+p9zr13WkMAADgJCJwAShWeYtifCT7zRf+i2JERssMGSFzbi8WxQAAAEGDwAWg2NjVS+W8/3LBRTHOPFfmspEyFSu71BkAAIA7CFwATpjdv1f2oymyS3/2H6hWQ54rR8m0bO9OYwAAAC4jcAE4btbJlf1+ruzn7xVcFKPXIJl+w2TCWRQDAAAELwIXgOOSvTFOzgv/lTbF+Q80bibP8Ftk6jZwpS8AAIDShMAF4JjYjHQlv/W80mZ8Ijm5voGo/y2KcQ6LYgAAAOQjcAE4anbFb3I+fFVpSYl+ddPxfJnLrpOpwKIYAAAAhyJwATgim5Qg58PXpBW/+Q/E1spbFKPFGe40BgAAUMoRuAAUyebmyn47Q/arD6TMDN9ASIiiLx6u9K79ZMJYFAMAAKAoBC4AhbKb4uS895K0dZP/QNOWqjbmAYWc0kAZCQnuNAcAAFBGELgA+LFpKbKfT5X9fo5krW+gfIzMpdfJdOmukNhY9xoEAAAoQwhcACRJ1lrZxT/IfvKGlLzfb8ycfYHMJdfIlK/gTnMAAABlFIELgOyeHXLef0X6c4X/QK1T5Bl+s0zTlq70BQAAUNYRuIAgZrOzZedOk539qZST7RsIDZPpf5lMr0EyIaHuNQgAAFDGEbiAIGXXrpTzwSvSru3+Ay3by3PFTTLVa7rTGAAAQAAhcAFBxibvk/30LdlF3/kPVKoiz7AbpHZnyRjjSm8AAACBhsAFBAnrOLI/fC37+btSWqpvwHhkuveTGXilTGSUew0CAAAEIAIXEATslo1ypk6WNsX5DzQ4VZ7ht8jUb+xOYwAAAAGOwCVp//79+uKLL7R8+XIlJiYqLCxMsbGxatWqlYYPH17g+O+//15z587Vtm3bFBISoqZNm2rw4ME67bTTXOgeKJrNSJP98gPZb2dK1vENREbJXHy1zPm9ZTzl3GsQAAAgwAV94IqLi9Pjjz+u1NRU1a1bVx06dFBGRoa2bdummTNnFghc77zzjmbNmqWwsDC1bt1a2dnZWrVqlVauXKmxY8eqY8eOLr0TwMdaKy37Rc5HU6T9e/3GTMfzZYZeJ1OxskvdAQAABI+gDlxJSUl6/PHHlZ2drbvvvrtAWNqwYYPf39esWaNZs2YpJiZGjz32mGrVqiUpL7SNHz9ekydPVosWLVS+fPmT9h6Af7J7dsr58FVpzTL/gdja8lw5SqZFW1f6AgAACEYetxtw0wcffKDU1FQNHz680CtTTZo08fv7jBkzJEmDBw/2hi1Jatq0qXr27Km0tDQtXLiwZJsGimCzs+XM/FjO+DH+YSskRGbA5fKMf56wBQAAcJIFbeBKSUnRr7/+qqioKHXv3v2Ix2dlZWnNmjWSpM6dOxcYz68tXbq0eBtFUJrxV5ISUrOPeFxCarZm/JWUt6fWI7fJfvm+lJ3lO6BFW3nGvyjPRZfLhIaVXMMAAAAoVNDeUrhu3TplZ2erVatWCgkJ0aJFi/TXX38pJydHderUUZcuXVSpUiXv8Tt27FB2drYqVKigqlWrFni9hg0bSpI2b958st4CAtSMv5I0ZekezVy3T49dUE/Vo0MLPS4hNVsPzPtbu9Ny5ayfq/6HbmBcsbLMZSNlOpzDnloAAAAuCtrAtXXrVklSxYoVNW7cOMXF+S+X/cEHH+iWW25Rly5dJEmJiYmSVGjYkqSIiAhFR0crNTVV6enpioyMLMHuEcg6nxKjmev2aVdKth6cv6XQ0LXnYIYenLVeu3NDVSN9rzol/pE3YDwy3frm7akVFe1C9wAAADhU0Aau1NS8jV9/+OEHhYSEaNSoUd4VCufOnauZM2fqhRdeUO3atVW/fn1lZGRIksLCir4tKzw8XKmpqcrIyDiqwDV27NgCtbCwME2YMEGSVK1ateN5a8UiJCRvalSvXt21HoJV9erS5KFVNHraau04kKFxC7frxSGtVLNChCRp2+o1+s/Xm7U7pIJqpO/VIyteVfXM/Qpp0lwVR92r0CbNSrxH5geKwtxAUZgbOBzmB4oSCHMjaJ/hcpy8PYlyc3M1YsQIde/eXRUqVFBsbKyuvvpqde7cWTk5Ofryyy8l/W+Zbemwt2flHwOcqJoVIvTikFaqXTFCOw5k5IWvXXu14eXnNGbmBu06JGzFlstRhZvuUdUnXj8pYQsAAABHL2ivcOVfgTLG6Pzzzy8w3q1bNy1atEh//vmn3/GZmZlFvmZWVt5iBREREUfVw8SJEw87npiY6FqIy/8tQkJCgisfH1I5SY90q6MH5m/RjgMZGvbBakmtlRMZ4gtbZ7SVufRapVaorNSkpJPWG/MDRWFuoCjMDRwO8wNFKQ1zwxjjt0L5sQraK1z5n7xKlSopNLTgogT54wcOHJDku71v7969BY6VpIyMDKWmpio6Oprnt1BsqiXv0iPxHynEyVGOp5xyPCEKcXL0yPYvVWP03fJcP1amAhsYAwAAlFZBe4Urf1XB1NRUWWsL3CqYkpIiyXe1qnbt2goNDVVycrL27t1bYPGMTZs2SZLq1atX0q0jCNjMDNlZH8vO+0IKiZEOvW3Z45HnjvEyFaPcag8AAABHKWivcNWrV0+xsbHKysrS+vXrC4z/8Ufeqm+NGjWSlLeYRcuWLSVJixYtKnB8fq19+/Yl1TKChF3xm5yHRsvOmaaEkBiNa3tT3pUt6yjESDny6D/f7TyqfboAAADgrqANXJI0cOBASdJbb72l5ORkb33jxo2aOXOmJKlnz57eer9+/SRJ06dP186dO731uLg4zZ8/X5GRkUe1iTJQGJu4W7kvPibnpf9Ke/coIbySxrW9Sbsjq6pGaK5eufhUvTKwsWqWD/UuGU/oAgAAKN2C9pZCSerRo4dWr16tRYsW6Y477lDTpk2VmZmpdevWKScnRz169FDnzp29x7du3Vp9+/bV7Nmzde+996pVq1bKzc3VqlWr5DiOxowZo/Lly7v4jlAW2exs2Xmfy87+RPrfwit+YSs6RP/t2di7F9djF9TTg/O3HHafLgAAAJQOxgb5WuaO4+ibb77RggULtGPHDklSgwYN1LNnT5133nmFnvPdd99p7ty52r59u8qVK6dTTz1VQ4YMUbNmxbsk986dO1mlMMDZtSvlfPCKtGu7t5YQXknjzhyj3SExqlk+tNBAlZCa7Q1dRR1TkpgfKApzA0VhbuBwmB8oSmmYGye6SmFQX+GSJI/Ho969e6t3795HfU7Xrl3VtWvXkmsKAc/uT5L99E3ZxT/4D1SopN96jdbuxKLDliRVjw71u9K1aOtBDWhW5SR1DwAAgKMV9IELOJlsbq7swlmyX74vZaT7BoxHpltfmYFXaGBUeXn+SlLnU2IOe9UqP3QRtgAAAEovAhdwktj4v+RMfVnatsl/oGFTea68WaZ+Y2/paANU9ehQwhYAAEApRuACSpg9mCw77W3Zn+f7D0SVlxl8tcy5vWQ8Qb1gKAAAQMAicAElxDqO7E/zZKe/J6Ue9BszZ18gM2SETExFl7oDAADAyUDgAkqA3Rwv5/2XpU1x/gN1G8hz5SiZJi3caQwAAAAnFYELKEY2NUX2i6my38+RDl3SPyJSZuAVMt36y5Qr516DAAAAOKkIXEAxsNbK/rpQ9rO3pIMH/MbMmefKDL1OplJVl7oDAACAWwhcwAmy2/7O27x4/Z/+AzXryHPFKJnmbdxpDAAAAK4jcAHHyaanyc74UPbbGZLj+AbCwmX6XybTc6BMSNH7aAEAACDwEbiAY2Stlf39R9lP3pQOJPkPtu0sz7CRMlVj3WkOAAAApQqBCzgGdudWOR+8Kv21yn+gek15Lr9RplUHdxoDAABAqUTgAo6CzUiXnfmx7Pwvpdxc30BIqEyfS2QuHCwTFu5egwAAACiVCFzAYVhrpWW/yPn4DWlfov9gqw7yDLtBJraWO80BAACg1CNwAUWwu7bL+fA16c/l/gNVY+UZNlJq00nGGHeaAwAAQJlA4AL+wWZmys7+RPbrz6XcHN9AuRCZ3hfL9B0qE87tgwAAADgyAhfwP9ZaacVvcj56XUpK8B9s0Vaey2+SqVnHneYAAABQJhG4AEl2zw45H74urVnqP1C5mjyXjZTadeH2QQAAABwzAheCms3MlJ37mezcaVLOobcPlpPpOUim31CZiEj3GgQAAECZRuBCULLWSisX590+uHeP/2Cz1vJccZNMrVPcaQ4AAAABg8CFoGP37MwLWquX+A9UqiIz9HqZDudw+yAAAACKBYELQcNmZcrOnSY7Z5qUk+0bKFdO5oKLZPpfJhMR5V6DAAAACDgELgQFm3/7YOJu/4HTWuXdPli7njuNAQAAIKARuBDQirx9sGIVmaHXyZx5LrcPAgAAoMQQuBCQbFam7Jxp/1t98B+3D/YYIDNgGLcPAgAAoMQRuBBQDrv6ILcPAgAA4CQjcCFg2D075Hw0pfDVBy/l9kEAAACcfAQulHk2M1N2zqeyX08vuHkxqw8CAADARQQulFnWWmnFb3I+nlL45sWX38jtgwAAAHAVgQtlkt29Q85Hr0lrlvkPVKqat/ogmxcDAACgFCBwoUyxmRmysz+Vnfd5IbcPDvzf7YOR7jUIAAAAHILAhTLBWist+1XOJ1OkpET/weZt8m4frHWKO80BAAAARSBwodSzO7fl3T745wr/gcrV5Bl6ndT+bG4fBAAAQKlE4EKpZTPSZWd9IvvNl1LuobcPhsj0GiTTb6hMeIR7DQIAAABHQOBCqWOtlf39R9lP35L27/UfPP0MeYbdKFOzjjvNAQAAAMeAwIVSxW7fLOfD16R1q/0HqlSX57KR0hmduX0QAAAAZQaBC6WCTUuVnfGR7IIZkuP4BkJCZS4cLHPhJTLh4e41CAAAABwHAhdcZR1HdtF3stPelpL3+w+2PlOey0bKxNZyozUAAADghBG44Bq7ZaOcD16R4v/yH6heU57LbpBpc6Y7jQEAAADFhMCFk86mHpT94n3Z7+dK9pDbB0PDZPpeItN7sExomHsNAgAAAMWEwIWTxjqO7E/fyH7+rpRy0H+wXRd5Lr1OploNd5oDAAAASgCBCyeF3RQn54NXpb//v727D46qPPQ4/ttks+QdEAgh4dXQECMhVRxeWq+kEJyOwMWCQrmF1qspelMYIsPtMNVrwzWKdTqdMAoOA0W0rVIdESEwqaZFGNSUmlBIQLIJoVx5aSAhELIk2d3s3j/Sjax5RXP2rOT7+UvO8yT+MjwTzm/POc+p9B+IT2zb5v3Ou8wJBgAAABiIwoVe23PysqaNitGwqLBu511yuFT8+TXNS7lN3mtX5d35uryHPvCfNCBclrmLZcn8d1ms3X8/AAAA4JuKwoVe2XPysraWXFRBRb3yMkd3WbouOVx6uuj/9M9GlzyVxzW3aJN03eE3xzLlPlke+k9ZBg8JRHQAAADANCFmB8A3w7RRMYqPDtM/G9sK1SWHq8OcG8vWcNdVTf3TFv+ylThGIWueU8hP11C2AAAA0C9QuNArw6LClJc5usvSdcnh0lPvn24rW011+t9PN2pYy5W2wYhIWX74U4X8T74sE9LM+QEAAAAAE1C40Gtdla6LV6/rqd2fqea6p61s/X1ze9myfHeWQvJeUcisebKEhpr7AwAAAAABxjNcN2hsbFROTo4aGhqUkJCg/Pz8LuceOHBAhYWFOnv2rKxWq5KTk7VgwQJNmDAhcIFN4CtdvlsHn3ivSvJ45LbY/MvW6CSF/MfjsiSlmB0ZAAAAMA2F6wavvfaarl271qt5e/fulc1m06RJk+RyuXTs2DEdPXpUq1ev1pQpUwKQtu98ld0Hn707Uv91oF5uhUiWUFk97rayZW2V5eFsWf5ttiwhXNECAABA/0bh+peysjIdOHBAmZmZKioq6nJeeXm59u7dq5iYGOXl5WnEiBGSJLvdrtzcXG3atEmpqamKjo4OVPSv5SvtPlheqqmH3pQmPylZvrgr1TI9QyHzH5IlOjZQ8QEAAICgxjNckpxOp7Zs2aKRI0dq3rx53c7ds2ePJGnBggXtZUuSkpOTNXv2bF2/fl379+83NG9f6u3ug0/5dh9suaJvfbxLz0x8VO4Qq6wet6zeVrlDrHomeoZqLREm/BQAAABAcKJwSXr77bdVU1OjrKwshXazsYPT6VR5ebkkadq0aR3GfcdKSkqMCWqAXu0++Kdq1fxr98Gc8t8rP3WJaiKGaHhLvTaNrdMrD36rx9IGAAAA9Ef9vnCdOXNGBQUFysjIUGpqardzz58/L5fLpdjYWA0Z0vE9UuPGjWv/nt8knZWufzY06/zFej2167hqmrxtZevEm1+ULTUrb/6dGv5vMxQXbeu2tAEAAAD9Vb8uXB6PR5s3b1ZkZKSWLl3a4/za2lpJ6rRsSVJ4eLiioqLkcDjU1NTUp1mN9uXStejVw/rh74+qRuEdy1a4Rc89eKfihsR2+fWULgAAAKCfb5pRWFioqqoqZWdnKyYmpsf5zc3NkiSbzdblnAEDBsjhcKi5uVkREd0/z7R69eoOx2w2m1544QVJ0tChQ3vM1JeGDZM2LbpNi7YdlttrkUK+2H3w8NjpqokYooSB4Xp5YZriY8O7/PoV75Tp/NVmldV7tXjssID+DAgMq7XtV8ewYfz9wh9rA11hbaA7rA905VZYG/22cNXW1mrHjh1KTU1VRkZGr77G6/VKkiwWS49zvtFCQiTPFz9H5LxFevThJYo+UacZSUM6LVs+8bFthezAqTotvisxEGkBAACAoNVvC9fWrVvldruVlZXV66/xXbFqaWnpco7T6ZTUdnthT37zm990O15bWxvQAufb+t3t8cpq8Uoer9whVv138x3Ku3BZM0fapJZrunSp+3eVhUqaOdKmS5cuBSY4As73KRN/x/gy1ga6wtpAd1gf6EowrA2LxeK3O/nN6reFq7S0VFFRUdq6davfcZer7bmj2tpa5ebmSpLWrl2r8PDw9lv86urqOv2ezc3NcjgcioqK6vF2wmBz43u24qPDtPHhdFksFmW/9ff2Z7K6e08XAAAAgI76beGSJIfDoRMnTnQ65nQ628daW1slSQkJCQoLC1NDQ4Pq6uo6bJ5x+vRpSdLo0aMNTN33vly28jJHa8TAtsKYlzm6fYzSBQAAANycflu43nrrrU6PX7x4UStWrFBCQoLy8/P9xmw2myZOnKgjR46ouLhYc+bM8RsvLi6WJE2ePNmQzEborGzdWKh8uw9SugAAAICb16+3hf8qfCVr586dunDhQvtxu92uoqIiRUREaObMmWbFu2nFn1/rsmz5fHnL9+LPu3+GCwAAAECbfnuF66uaNGmSHnjgAe3bt08///nPlZaWptbWVh07dkwej0crV65UdHS02TF7bV7KbZKkaaNiur1q5StdxZ9fa/8aAAAAAN2jcH0FjzzyiMaOHavCwkKVlZUpNDRUEydO1MKFC5WSkmJ2vJvW2wI1LCqMsgUAAADcBArXl8TFxXX5fNeNMjIyev3+LgAAAAD9E89wAQAAAIBBKFwAAAAAYBAKFwAAAAAYhMIFAAAAAAahcAEAAACAQShcAAAAAGAQChcAAAAAGITCBQAAAAAGoXABAAAAgEEoXAAAAABgEAoXAAAAABiEwgUAAAAABqFwAQAAAIBBKFwAAAAAYBCr2QHQNYvFYnaEoMiA4MX6QFdYG+gKawPdYX2gK2auja/7/7Z4vV5vH2UBAAAAANyAWwoBAAAAwCAULnRq7dq1Wrt2rdkxEKRYH+gKawNdYW2gO6wPdOVWWBs8w4VOOZ1OsyMgiLE+0BXWBrrC2kB3WB/oyq2wNrjCBQAAAAAGoXABAAAAgEEoXAAAAABgEAoXAAAAABiE93ABAAAAgEG4wgUAAAAABqFwAQAAAIBBKFwAAAAAYBAKFwAAAAAYhMIFAAAAAAahcAEAAACAQShcAAAAAGAQq9kBEFycTqd27dqljz76SLW1tYqOjlZ6eroWL16sIUOGmB0PJmlpadHRo0dVUlKiU6dO6dKlS/J4PIqPj9fUqVM1d+5chYeHmx0TQaCxsVE5OTlqaGhQQkKC8vPzzY6EIHDlyhXt2rVLR44cUW1trWw2m+Li4pSWlqalS5eaHQ8msdvt2r17tyoqKtTY2Kjw8HCNGzdO999/v6ZNm2Z2PBisurpax44dU1VVlSorK1VfX6+wsDD94Q9/6PbrDhw4oMLCQp09e1ZWq1XJyclasGCBJkyYEKDkN48XH6Od0+nUs88+q4qKCg0ePFgpKSm6dOmSqqqqFBsbq7y8PMXHx5sdEyb485//rM2bN0uSRo0apcTERDU1Nclut6upqUmJiYnKzc3VwIEDTU4Ks23cuFEHDx6U1+ulcEFS20n1+vXr5XA4NHLkSI0aNUrNzc06e/as6urqtGPHDrMjwgSffPKJ8vPz5fV6lZSUpOHDh6u+vl4nT56U1+vV/Pnz9aMf/cjsmDDQiy++qE8//dTvWE+F67XXXtPevXtls9k0adIkuVwulZeXy+v1avXq1ZoyZYrRsb8SrnCh3bvvvquKigolJyfr6aefbr9iUVBQoNdff12vvPKK1q1bZ3JKmMFqter+++/XnDlzNGLEiPbj9fX1euGFF3T69Glt375dq1atMjElzFZWVqYDBw4oMzNTRUVFZsdBELh8+bLWr18vl8ulNWvWdDgZqqqqMikZzNTa2qrf/va38nq9ysnJ0Xe+8532MbvdrnXr1mn37t2aNWsWH/TewpKTkzV27FglJSUpKSlJy5cv73Z+eXm59u7dq5iYGOXl5bWfj9jtduXm5mrTpk1KTU1VdHR0IOLfFJ7hgiTJ7XarsLBQkvTYY4/53R42d+5cjRkzRp999pmqq6vNiggTzZgxQ1lZWX5lS5IGDx6sxx57TJJ0+PBhud1uM+IhCDidTm3ZskUjR47UvHnzzI6DIPHGG2/I4XBo6dKlnX7yPH78eBNSwWznzp1TQ0ODEhMT/cqW1HYSnp6eLq/XyznHLe7BBx/UokWLNHnyZA0aNKjH+Xv27JEkLViwwO98JDk5WbNnz9b169e1f/9+o+J+LRQuSJJOnjwph8Oh4cOHa9y4cR3Gp06dKkkdLv0CY8aMkSS5XC5du3bN5DQwy9tvv62amhplZWUpNDTU7DgIAo2Njfrkk08UGRmpmTNnmh0HQSQsLKxX84LxSgXM4XQ6VV5eLkmdPt/nO1ZSUhLQXL3FLYWQJJ05c0aSOi1bknT77bf7zQN8ampqJEmhoaH849hPnTlzRgUFBcrIyFBqaqouXrxodiQEgYqKCrlcLqWlpclqtaq4uFgnT56U2+1WYmKipk+f3qtPtXHrGT58uIYPH65z587p448/7nBL4dGjRxUXF6fU1FQTUyKYnD9/Xi6XS7GxsZ1u4uY7fw3W81QKFyRJtbW1ktTlToS33Xab3zzAZ9++fZKkb3/7273+1BK3Do/Ho82bNysyMpLd5uDn888/lyQNHDhQzzzzjOx2u9/4G2+8oezsbE2fPt2MeDBRSEiIsrOz9atf/Ur5+fnas2eP36YZ48eP18qVK2W1cpqKNj2dp4aHhysqKkoOh0NNTU2KiIgIZLwesZIhSWpubpYkDRgwoNNx3zNdvnmAJJWWlmr//v0KDQ3V4sWLzY4DExQWFqqqqkrZ2dmKiYkxOw6CiMPhkCQdPHhQVqtVTzzxhO655x41NzersLBQBQUFeumll5SQkNB+azL6jzvuuEO5ubn69a9/rVOnTunUqVOSpIiICKWlpWnw4MEmJ0Qw8Z1/2my2LucMGDBADodDzc3NQVe4eIYLkqSe3g7A2wPwZWfPntVLL70kr9erZcuWaezYsWZHQoDV1tZqx44dSk1NVUZGhtlxEGQ8Ho+kth3pfvKTn2jmzJmKjY1VXFycfvzjH2vatGlyu9167733TE4KMxw6dEhPPfWUhg4dqueff16vv/66NmzYoO9+97vauXOnnn32WTZiQjvfeajFYulxTjCicEGS2j8JaGlp6XTcd5yX20KS6urq9Pzzz8vhcGju3Ll64IEHzI4EE2zdulVut1tZWVlmR0EQ8v27YrFYNGPGjA7j3/ve9yRJJ06cCGgumO/ChQvauHGjYmNjtXbtWo0fP17h4eEaMWKEli9frsmTJ8tut+vDDz80OyqCRE/nqVLbxhpScJ6rckshJElDhw6V1HYi3ZnLly/7zUP/1dDQoLy8PNXW1iojI0PLli0zOxJMUlpaqqioKG3dutXvuMvlktR2BSw3N1eStHbt2qD8RxDGGTZsmCRp0KBBnT7f6Ru/evVqQHPBfB999JFaW1uVnp7e6e+F6dOnq6SkRMePH1dmZqYJCRFsejpPbW5ulsPhUFRUVNDdTihRuPAvvvvnT58+3em4710Y3GffvzU1NWn9+vU6d+6cpkyZoieeeKLby/u49Tkcji6vUDidzvax1tbWQMZCEPDtGuZwOOT1ejv8rmhsbJQUnJ9Gw1i+D3EjIyM7Hfcd960RICEhQWFhYWpoaFBdXV2HzTN856+jR482I16PKFyQJKWkpCgyMlI1NTU6ffp0h+3h//rXv0qS7r77bjPiIQi4XC69+OKLOnXqlNLT05WTk6OQEO5K7s/eeuutTo9fvHhRK1asUEJCgvLz8wMbCkFj9OjRiouL08WLF1VZWank5GS/8ePHj0v64rUj6D98rwPwbZTxZVVVVZK+uAoK2Gw2TZw4UUeOHFFxcbHmzJnjN15cXCxJmjx5shnxesTZEiRJVqtV3//+9yVJ27Zt89uNsKCgQGfOnFFKSorGjx9vVkSYyOPxaMOGDTp+/LjuuOMOrVmzhu16AfRo/vz5kqRXX31VDQ0N7cerq6tVUFAgSZo9e7Yp2WCee+65R5L02Wef6f333/cbs9vt2rt3r6TOX3CL/stXsnbu3KkLFy60H7fb7SoqKlJERETQvmTd4g3mLT0QUE6nU+vWrVNlZaUGDx6slJQU1dbWqrKyUjExMXruuecUHx9vdkyYYN++fdq+fbskacqUKV3eH71s2TLFxsYGMBmCEVe44OPxeJSfn6/i4mJFR0crOTlZLS0tqqiokNvt1qxZs/T444+bHRMm+N3vfqc9e/ZIkkaNGqXExETV19fLbrfL6/UqMzNTy5cvNzkljFRaWqp33nmn/c+VlZWyWCx+H+4vXLjQ7+6q7du3a9++fRowYIDS0tLU2tqqY8eOyePx6Mknnwzaks5H1Ghns9n0y1/+Uu+++64OHTqkv/3tb4qKitKMGTO0ePFiNszox268j/7w4cNdznv44YcpXADahYSEKCcnRx988IH+8pe/tN9GmJSUpNmzZ+u+++4zOSHMsmzZMk2YMEEffPCBqqurdf78eYWHhys1NVWzZs3Svffea3ZEGKyhoUGVlZV+x7xer9+xG6+MS9IjjzyisWPHqrCwUGVlZQoNDdXEiRO1cOFCpaSkBCT3V8EVLgAAAAAwCM9wAQAAAIBBKFwAAAAAYBAKFwAAAAAYhMIFAAAAAAahcAEAAACAQShcAAAAAGAQChcAAAAAGITCBQAAAAAGoXABAAAAgEEoXAAAAABgEAoXAAAAABiEwgUAAAAABqFwAQAAAIBBKFwAAAAAYBAKFwAAAAAYhMIFAAAAAAahcAEA0Ad27dqlRYsWacmSJaqqqup0TmlpqRYvXqxFixbp0KFDAU4IADADhQsAgD4wf/58paWlqbW1VRs2bFBTU5PfeH19vTZt2iSv16v77rtP9957r0lJAQCBROECAKAPWCwWrVy5UgMHDlRNTY22bNnSPub1evXyyy+roaFB8fHxysrKMjEpACCQKFwAAPSRQYMGKTs7WxaLRYcOHdKHH34oSXrvvfdUVlam0NBQrVq1SuHh4eYGBQAEDIULAIA+dNddd2nOnDmSpG3btungwYP64x//KElasmSJkpKSzIwHAAgwi9fr9ZodAgCAW4nb7dbTTz+t6urq9mPp6en6xS9+IYvFYmIyAECgcYULAIA+ZrValZ2d3f7nyMhI/exnP6NsAUA/ROECAMAARUVF7f/d1NSkf/zjH+aFAQCYhsIFAEAfKykpUWFhoSRpzJgx8nq92rhxo65cuWJuMABAwFG4AADoQ773bUlSRkaG1q1bp2HDhunq1avauHGjeHQaAPoXChcAAH3E4/Ho5Zdf1rVr1zRixAg9+uijioyM1KpVqxQaGqqjR4+qoKDA7JgAgACicAEA0Ed2797d6fu2kpOT9dBDD0mS3nzzTb/dCwEAtzYKFwAAfaCqqsrvfVu333673/gPfvAD3XnnnXK73dqwYYOam5vNiAkACDAKFwAAX1NTU5M2bNig1tZWTZo0SfPmzeswJyQkRCtWrFB0dLQuXLigbdu2mZAUABBovPgYAAAAAAzCFS4AAAAAMAiFCwAAAAAMQuECAAAAAINQuAAAAADAIBQuAAAAADAIhQsAAAAADELhAgAAAACDULgAAAAAwCAULgAAAAAwCIULAAAAAAxC4QIAAAAAg1C4AAAAAMAgFC4AAAAAMAiFCwAAAAAMQuECAAAAAINQuAAAAADAIBQuAAAAADAIhQsAAAAADELhAgAAAACD/D8N+3syDOfPyAAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Solve IVP with the root z\n", "sol = solve_ivp(dydx, t_span=(0, 10), y0=[T1, root.root])\n", "\n", "# Plot the result of shooting method\n", "plt.plot(x, exact(x))\n", "plt.plot(sol.t, sol.y[0], marker='x', linestyle='none')\n", "\n", "# Legend and labels\n", "plt.legend(['Exact', 'Shooting 1 (z={:.3f})'.format(root.root)])\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "markdown", "id": "e5e8ccd3", "metadata": {}, "source": [ "## Finite Differenece Method\n", "Finite Difference 를 적용하면 양 끝점 사이 $x$ 를 *n* 등분 한다.. 이 때 미분을 Finite difference로 표현하면 다음과 같다.\n", "\n", "$$\n", "\\frac{T_{i+1} - 2 T_i + T_{i-1}}{\\Delta x^2} - h(T_i - T_a) = 0.\n", "$$\n", "\n", "이를 정리하면 다음과 같다\n", "\n", "$$\n", "-T_{i-1} + (2 + h \\Delta x^2) T_i - T_{i+1} = h \\Delta x^2 T_a\n", "$$\n", "\n", "양 끝점의 값은 $T_0$, $T_{n}$ 이다. \n", "\n", "각 점에서 이 식을 전개하면 다음과 같다.\n", "\n", "$$\n", "\\begin{align}\n", "&+ (2 + h \\Delta x^2) T_1 &- T_{2} &= h \\Delta x^2 T_a + T_0 \\\\\n", "-T_{1} &+ (2 + h \\Delta x^2) T_2 &- T_{3} &= h \\Delta x^2 T_a \\\\\n", "& & ... & & \\\\\n", "-T_{n-3} &+ (2 + h \\Delta x^2) T_{n-2} &- T_{n-1} &= h \\Delta x^2 T_a \\\\\n", "-T_{n-2} &+ (2 + h \\Delta x^2) T_{n-1} & &= h \\Delta x^2 T_a + T_{n}\n", "\\end{align}\n", "$$\n", "\n", "*n-1* 개의 연립방정식을 해석한다. 위 예제를 적용하면 다음과 같다.\n", "\n", "$$\n", "\\left [\n", "\\begin{array}{cccc}\n", "(2 + h \\Delta x^2) & -1 & 0 & 0 & ... & 0 \\\\\n", "-1 & (2 + h \\Delta x^2) & -1 & 0 & ... \\\\\n", "0 & & ... & & \\\\\n", "0 & & ... & -1 &(2 + h \\Delta x^2) & -1 \\\\\n", "0 & & ... & & -1 & (2 + h \\Delta x^2)\n", "\\end{array}\n", "\\right ]\n", "\\left [\n", "\\begin{array}{c}\n", "T_1 \\\\ T_2 \\\\ ...\\\\ T_{n-2} \\\\ T_{n-1}\n", "\\end{array}\n", "\\right ]\n", "=\n", "\\left [\n", "\\begin{array}{c}\n", "h \\Delta x^2 T_a + T_0 \\\\ h \\Delta x^2 T_a \\\\ ... \\\\h \\Delta x^2 T_a \\\\h \\Delta x^2 T_a + T_n\n", "\\end{array}\n", "\\right ]\n", "$$\n", "\n", "`linalg.solve` 함수를 활용해서 해석하는 코드는 다음과 같다." ] }, { "cell_type": "code", "execution_count": 9, "id": "7cafb27c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 40. 65.96983437 93.77846211 124.53822833 159.47952369\n", " 200. ]\n" ] } ], "source": [ "# Number of division\n", "n = 5\n", "\n", "# Array x\n", "x = np.linspace(0, 10, n+1)\n", "dx = np.diff(x)[0]\n", "\n", "# Array y\n", "y = np.empty_like(x)\n", "y[0], y[-1] = T1, T2\n", "\n", "# Operator\n", "A = np.zeros((n-1, n-1))\n", "\n", "for i in range(n-1):\n", " A[i, i] = 2 + h*dx**2\n", " if i > 0:\n", " A[i, i-1] = -1\n", " if i < n-2:\n", " A[i, i+1] = -1\n", "\n", "# Forcing term\n", "b = np.ones(n-1)\n", "b *= h*dx**2*Ta\n", "b[0] += T1\n", "b[-1] += T2\n", "\n", "# Solve system\n", "y[1:-1] = np.linalg.solve(A, b)\n", "print(y)" ] }, { "cell_type": "code", "execution_count": 10, "id": "911c2f2e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot numerical results\n", "plt.plot(x, exact(x))\n", "plt.plot(sol.t, sol.y[0], marker='x', linestyle='none')\n", "plt.plot(x, y, marker='d', linestyle='none')\n", "\n", "# Legend and Labels\n", "plt.legend(['Exact', 'Shooting 1 (z={:.3f})'.format(root.root), 'Finite Difference'])\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "markdown", "id": "25ad0d36", "metadata": {}, "source": [ "## Scipy 활용\n", "\n", "`scipy.integrate` 모듈 내 BVP 해석 함수도 제공한다.\n", "\n", "### boundary value problem\n", "`solve_bvp` 함수는 경계 조건에 맞게 미분 방정식을 수치적으로 해석한다" ] }, { "cell_type": "code", "execution_count": 11, "id": "2c5fb9ce", "metadata": {}, "outputs": [], "source": [ "from scipy.integrate import solve_bvp" ] }, { "cell_type": "code", "execution_count": 12, "id": "ef555e02", "metadata": {}, "outputs": [], "source": [ "# derivative function\n", "def dydx(t, y):\n", " # y[0], y[1] : T and z\n", " return np.array([y[1], h*(y[0] - Ta)])\n", "\n", "# Boundary condition\n", "def bc(ya, yb):\n", " # both ends point as ya and yb\n", " return np.array([ya[0] - T1, yb[0] - T2])\n", "\n", "# Array x\n", "n = 10\n", "x = np.linspace(0, 10, n)\n", "y = np.zeros((2, n))\n", "\n", "sol = solve_bvp(dydx, bc, x ,y)" ] }, { "cell_type": "code", "execution_count": 13, "id": "04585190", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot numerical results\n", "x = np.linspace(0, 10, 101)\n", "plt.plot(x, exact(x))\n", "plt.plot(sol.x, sol.y[0], marker='x', linestyle='none')\n", "\n", "# Legend and Labels\n", "plt.legend(['Exact', 'Scipy'])\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] } ], "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": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 5 }