{ "cells": [ { "cell_type": "markdown", "id": "c2e46f4f", "metadata": {}, "source": [ "# Appendix: Implicit Method" ] }, { "cell_type": "markdown", "id": "194049e3", "metadata": {}, "source": [ "**강좌**: *기초전산 유체역학*" ] }, { "cell_type": "markdown", "id": "b7432f24", "metadata": {}, "source": [ "## Implicit Time Advancement\n", "\n", "FTCS 에서 Implicit Method를 적용해보자\n", " \n", "- Backward Euler\n", "\n", "$$\n", "\\frac{T_i^{n+1}- T_i^n}{\\Delta t} \n", "=\n", "\\alpha \\frac {T_{i+1}^{n+1} -2 T_i^{n+1} + T_{i-1}^{n+1}}{\\Delta x^2} + O((\\Delta t), (\\Delta x)^2)\n", "$$\n", "\n", "- Crank-Nicolson\n", " - Trapezoial (사다리꼴) 기법을 적용하여 시간 정확도가 2차이다.\n", " \n", "$$\n", "\\frac{T_i^{n+1}- T_i^n}{\\Delta t} \n", "=\n", "\\frac{\\alpha}{2}\n", "\\left [\n", "\\frac {T_{i+1}^{n} -2 T_i^{n} + T_{i-1}^{n}}{\\Delta x^2} +\n", "\\frac {T_{i+1}^{n+1} -2 T_i^{n+1} + T_{i-1}^{n+1}}{\\Delta x^2}\n", "\\right]\n", "+ O((\\Delta t)^2, (\\Delta x)^2)\n", "$$\n", "\n", "이들 기법은 Unconditionally stable 하다.\n", "\n", "\n", "### 구현\n", "#### Backward Euler \n", "이 기법을 정리하면 다음과 같다.\n", "\n", "$$\n", "-\\beta T_{j+1}^{n+1} + (1+2\\beta) T_j^{n+1} - \\beta T_{j-1}^{n+1}\n", "=\n", "T_j^n\n", "$$\n", "\n", "여기서 $\\beta=\\alpha \\Delta t / \\Delta x^2$ 이다.\n", "\n", "Matrix 형태로 표현하면\n", "\n", "$$\n", "\\left [\n", "\\begin{matrix}\n", "1+2\\beta & -\\beta & 0 & ... & 0 \\\\\n", "-\\beta & 1+2\\beta & -\\beta & ....& 0 \\\\\n", "0 & -\\beta & 1+2\\beta & ... & 0 \\\\\n", "... & ... & ... & ... & ... \\\\\n", "0 & 0 & 0 & ... &1+2\\beta \\\\\n", "\\end{matrix}\n", "\\right ]\n", "\\left [\n", "\\begin{matrix}\n", "T_2^{n+1} \\\\ T_3^{n+1} \\\\ T_4^{n+1} \\\\ ... \\\\T_N^{n+1}\n", "\\end{matrix}\n", "\\right ]\n", "=\n", "\\left [\n", "\\begin{matrix}\n", "T_2^{n} \\\\\n", "T_3^{n} \\\\\n", "T_4^{n} \\\\\n", "...\\\\\n", "T_N^{n}\n", "\\end{matrix}\n", "\\right ]\n", "+\n", "\\left [ \n", "\\begin{matrix}\n", "\\beta T_{1} \\\\\n", "0\\\\\n", "0\\\\\n", "...\\\\\n", "\\beta T_{N+1}\n", "\\end{matrix}\n", "\\right ].\n", "$$\n", "\n", "#### Crank Nicolson \n", "이 기법을 정리하면 다음과 같다.\n", "\n", "$$\n", "-\\beta T_{j+1}^{n+1} + (1+2\\beta) T_j^{n+1} - \\beta T_{j-1}^{n+1}\n", "=\n", "\\beta T_{j+1}^{n} + (1-2\\beta) T_j^{n} + \\beta T_{j-1}^{n}\n", "$$\n", "\n", "여기서 $\\beta=\\alpha \\Delta t / 2 \\Delta x^2$ 이다.\n", "\n", "Matrix 형태로 표현하면\n", "\n", "$$\n", "\\left [\n", "\\begin{matrix}\n", "1+2\\beta & -\\beta & 0 & ... & 0 \\\\\n", "-\\beta & 1+2\\beta & -\\beta & ....& 0 \\\\\n", "0 & -\\beta & 1+2\\beta & ... & 0 \\\\\n", "... & ... & ... & ... & ... \\\\\n", "0 & 0 & 0 & ... &1+2\\beta \\\\\n", "\\end{matrix}\n", "\\right ]\n", "\\left [\n", "\\begin{matrix}\n", "T_2^{n+1} \\\\ T_3^{n+1} \\\\ T_4^{n+1} \\\\ ... \\\\T_N^{n+1}\n", "\\end{matrix}\n", "\\right ]\n", "=\n", "\\left [\n", "\\begin{matrix}\n", "\\beta T_{3}^{n} + (1-2\\beta) T_2^{n} + \\beta T_{1} \\\\\n", "\\beta T_{4}^{n} + (1-2\\beta) T_3^{n} + \\beta T_{2}^{n} \\\\\n", "\\beta T_{5}^{n} + (1-2\\beta) T_4^{n} + \\beta T_{3}^{n} \\\\\n", "...\\\\\n", "\\beta T_{N+1} + (1-2\\beta) T_N^{n} + \\beta T_{N-1}^{n}\n", "\\end{matrix}\n", "\\right ]\n", "+\n", "\\left [ \n", "\\begin{matrix}\n", "\\beta T_{1} \\\\\n", "0\\\\\n", "0\\\\\n", "...\\\\\n", "\\beta T_{N+1}\n", "\\end{matrix}\n", "\\right ].\n", "$$\n", "\n", "$N \\times N$ 행렬의 역행렬을 계산해야 한다. 이 행렬의 특징을 보면\n", "- 0 이 매우 많다 : Sparse Matrix\n", "- 대각 포함 3개의 Band로만 구성되어 있다. : Tri-diagonal Matrix\n", "\n", "역행렬을 직접 구하지 않고 Tri-diagonal matrix Solver로 계산할 수 있다." ] }, { "cell_type": "markdown", "id": "26d8040b", "metadata": {}, "source": [ "### Tri-diagonal matrix solver\n", "다음과 같은 Tri-diagonal matrix를 생각하자.\n", "\n", "$$\n", "a_i x_{i-1} + b_i x_i + c_i x_{i+1} = d_i\n", "$$\n", "\n", "Matrix 형태로 표현하면\n", "\n", "$$\n", "\\left [\n", "\\begin{matrix}\n", "b_1 & c_1 & 0 & ... & 0 \\\\\n", "a_2 & b_2 & c_2 & ....& 0 \\\\\n", "0 & a_3 & b_3 & ... & 0 \\\\\n", "... & ... & ... & ... & ... \\\\\n", "0 & 0 & 0 & ... & b_n \\\\\n", "\\end{matrix}\n", "\\right ]\n", "\\left [\n", "\\begin{matrix}\n", "x_1 \\\\ x_2 \\\\ x_3 \\\\...\\\\x_n\n", "\\end{matrix}\n", "\\right ]\n", "=\n", "\\left [\n", "\\begin{matrix}\n", "d_1 \\\\ d_2 \\\\ d_3 \\\\...\\\\d_n\n", "\\end{matrix}\n", "\\right ].\n", "$$\n", "\n", "#### Thomas Alogorithm\n", "##### Forward Sweep\n", "For i=2,..., n\n", "\n", "$$\n", "\\begin{align}\n", "w &= \\frac{a_i}{b_{i-1}} \\\\\n", "b_i &\\leftarrow b_i - wc_{i-1} \\\\\n", "d_i &\\leftarrow d_i - wd_{i-1}\n", "\\end{align}\n", "$$\n", "##### Back substitution\n", "$$\n", "\\begin{align}\n", "x_n &= \\frac{d_n}{b_n} & \\\\\n", "x_i &= \\frac{d_i - c_i x_{i+1}}{b_i} & i=n-1,n-2,...1\n", "\\end{align}\n", "$$" ] }, { "cell_type": "markdown", "id": "8ae47bb5", "metadata": {}, "source": [ "### 예제\n", "$n=10$ 일 때 $(a_i, b_i, c_i)=(1, -2, 1)$ 이고 $d_1=1$ 이고 나머지 $d_i=0$ 일 때 $x$ 를 구하시오." ] }, { "cell_type": "code", "execution_count": 1, "id": "c550184d", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "from matplotlib import pyplot as plt\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": "be20b4a7", "metadata": {}, "outputs": [], "source": [ "def solve_tdiag(a, b, c, d):\n", " \"\"\"\n", " Tri-diagonal matrix solver\n", " \n", " Parameters\n", " ----------\n", " a : array\n", " lower off-diagonal array\n", " b : array\n", " diagonal array\n", " c : array\n", " upper off-diagonal array\n", " d : array\n", " combination\n", " \n", " Returns\n", " -------\n", " s : array\n", " solution\n", " \"\"\"\n", " n = len(b)\n", " \n", " # Forward sweep\n", " for i in range(1, n):\n", " w = a[i-1] / b[i-1]\n", " b[i] = b[i] - w * c[i-1]\n", " d[i] = d[i] - w * d[i-1]\n", " \n", " x = np.empty_like(b)\n", " \n", " # Back substitution\n", " x[-1] = d[-1] / b[-1]\n", " \n", " for i in range(n-1)[::-1]:\n", " x[i] = (d[i] - c[i] * x[i+1]) /b[i]\n", " \n", " return x" ] }, { "cell_type": "code", "execution_count": 3, "id": "b509c4d7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-0.90909091, -0.81818182, -0.72727273, -0.63636364, -0.54545455,\n", " -0.45454545, -0.36363636, -0.27272727, -0.18181818, -0.09090909])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = 10\n", "a = np.ones(n-1)\n", "b = np.ones(n)*-2\n", "c = np.ones(n-1)\n", "d = np.zeros(n)\n", "d[0] = 1\n", "\n", "solve_tdiag(a,b,c,d)" ] }, { "cell_type": "markdown", "id": "42d31d9b", "metadata": {}, "source": [ "### Computational Costs\n", "\n", "- Tri-diagonal algorithm의 계산 시간은 $O(n)$ 으로 매우 빠름" ] }, { "cell_type": "code", "execution_count": 4, "id": "ddc46916", "metadata": {}, "outputs": [], "source": [ "def test(n):\n", " a = np.ones(n-1)\n", " b = np.ones(n)*-2\n", " c = np.ones(n-1)\n", " d = np.zeros(n)\n", " d[0] = 1\n", "\n", " solve_tdiag(a,b,c,d)" ] }, { "cell_type": "code", "execution_count": 5, "id": "1c1fbe16", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Size of matrix : 3\n", "5.25 µs ± 90.9 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n", "Size of matrix : 4\n", "6.06 µs ± 58.7 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n", "Size of matrix : 5\n", "6.82 µs ± 71.1 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n", "Size of matrix : 6\n", "7.62 µs ± 87.5 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n", "Size of matrix : 7\n", "8.29 µs ± 97.1 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n", "Size of matrix : 8\n", "9.13 µs ± 56.1 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n", "Size of matrix : 9\n", "9.91 µs ± 105 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n", "Size of matrix : 10\n", "10.5 µs ± 91.3 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n", "Size of matrix : 11\n", "11.3 µs ± 90.6 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n", "Size of matrix : 12\n", "12.1 µs ± 128 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n", "Size of matrix : 13\n", "12.9 µs ± 123 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n", "Size of matrix : 14\n", "13.5 µs ± 134 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n" ] } ], "source": [ "size = np.arange(3, 15)\n", "elapsed = []\n", "\n", "for n in size: \n", " print(\"Size of matrix : \", n)\n", " t = %timeit -o test(n)\n", " elapsed.append(t.average)" ] }, { "cell_type": "code", "execution_count": 6, "id": "b6337446", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Elapsed time')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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q1SoWL16Ml5eX3cQaX3zxRZFXwH7++WfA/j6okSNH4unpyX//+1+WL19eaJ9Tp07x+eefk56ebmu74447AHjppZc4e/asrX379u3MmDGj2OchIiIi4ihp2blMWhvDtA2xZOUWfLYadORnJkS/T/WMU3kNQdWxPDsFS7Xqtj7l/Qt9DQWs5Cy9BmIlbyXs4i635r/QzegoLL0Gll6BFzB69OjzbgsPD2f8+PHF7n/fffcxd+5cZsyYQVRUFE2aNCE2NpaNGzcycuRI2/C8ogwePJglS5YQFRVF69atOXnyJOvXr7dNiBEWFmbr++WXX/L000/TsGFD6tevj6urK/v372fHjh14enry1FNP2frWq1ePd955h8cff5x7772XyMhIGjRogGmaHDt2jL1795KVlcXNN9+Ml5cXkDc5xsqVK/n999/p0qULXbp0ITU1lbVr13LrrbfapmMXERERuVL2JqYzaU0MsSnZtrYqWSk8sXsObZL25N2+kpZyUV/o225FiY7CKEOfPYtjmJd6Z7441IkTJ4qdHME0TRITEwkKCtIkBOe4mJnumjZtyooVK2z/7tixI8eOHbPN1pd/pWnv3r1MmDCB6OhoUlNTiYyM5K677uL2228nPDycmjVrsmHDBttx5syZw5gxYxgzZgwDBw5k4sSJbNiwgYyMDJo1a8bjjz9e6H6t5cuXs2zZMqKjo4mNjSUrK4uwsDA6d+7MI488QkRERKH6Dxw4wIcffshvv/1GbGwsHh4ehISE0KZNG/r168d1111n95pITU1lypQpfPfddyQlJVGzZk1GjBjByJEjqVWrVqHnURnkrzF27lVFqZh0riuP0j7X+jvsPMHBeR+64+PLzxWLyso0TRbtOcWM6JOcM+kfzU/tZ/SuWQRmp2BcdyPGTSMw16wo9IV+UefaTIwv1S/0DcOw+1L8so6hYOVcClalr6R/lM8NVmPHjnVkaeJg+rBdeehcVx4KVpWHglX5kJyZyzvrT7DxWMHyNBbTyi2HVjL08CpcwmtjuftxjIiG5z1GWTjXjghWGgooIiIiIiKXbOfJNCatjSExreCLjsDMMzy1cxbNUo9gDLod4/qbMVzdnFhl6VGwEhERERGRi5ZrNflmZyKz/kzAes7AqzaJu3l89xz869bBcufbGGE1nVekEyhYiYiIiIjIRTmVnsPUtcfZGlcwO7GLNZfbDy5hYPxmXIbdjdH9egxL5Zt8XMFK5BINHz6c4cOHO7sMERERkVL1x4lUpvx2lDMFk/5RPT2JMTu/pmG9MCyPT8OoGuS8Ap1MwUpERERERM4r12oyMzqWb3afxqRgEpdO8X8yKmYFfrffA226VPoJXhSsRERERESkSPGp2UxesZddqRb4O1S5WbO5d98i+tbzw/LgVAwfX+cWWUYoWImIiIiISCEb9sXz9vpYUoyCWf1qpMUzNmYJkbcOx2jS0onVlT0KViIiIiIiYpOVk8uM5X+y+JQXnBOqron7nYdq5eJ91wsYHh5OrLBsUrASEREREREAYo6d5I1V+zngWtXW5pGbxUOJa7huyPUYdSKdWF3ZpmAlIiIiIlLJmVYrvy5dw/sJ/qSfE6rqpJ5gXHgKtW4fieHi4sQKyz4FKxERERGRSizj+FE+/iGalT4N4ZzsdH3qHu67sR2eYeHOK64cUbASEREREamEzJxsDv/4I5NiAzjq09DW7p2TwajQFLqOGFjpp1C/FApWIiIiIiKVjPXAHlZ8t4pPqnUjy8fd1t4gN4lxvRsQWiPYidWVTxZnFyBSUlu2bCE8PJzw8HDeeecdZ5dTZowePZrw8HDWrVvn7FLKvXXr1hEeHs7o0aMvab85c+YQHh7O5MmTHVJHWloa8+fP57nnnqN///5EREQQHh7Ou+++65DjlyeXe07Kq8mTJxMeHs6cOXOcXYpTHD16lPDwcIYOHVriY1X2n6WImZlByuzPmfJdNO+F9CTLpSBU3RSYwcTbOytUXSYFKyn3vvnmmyL/v5RdHTt2JDy8/I/XLu0PaAcOHODJJ5/ks88+448//iArK8uhx9cHThGRis3cvoW9E19i3Nn6/BbSytbuZ2bxXOdq3HdDK9xcNPTvcmkooJRr2dnZLFy4EMMwCA4OZu/evWzbto0WLVo4uzSne/rpp3nssccqRIBxttatW7N69Wr8/PycWoevry+33XYbrVq1olWrVvzwww+8/fbbTq1JpDSEhoayevVqvLy8nF2KSLlkpiRjnfMpPxzNYkbkCHIsBRGgmZ/J2F5NCPJ2K+YIcjEUrKRc+/nnn0lKSqJz58506tSJqVOnMn/+fAUrICQkhJCQEGeXUSF4eXlRv359Z5dB3bp1mTRpku3fy5Ytc2I1IqXHzc2tTPwOipQ3pmlibvyV5PlfMa3m9Wxs0Ny2zcBkWNOqDG8ZgotFV6kcQUMBpVybP38+AIMHD2bw4MEAfP/99+Tm5hbZv2PHjoSEhGCaJp988gnXXHMN9erVo23btvzf//0fZ86cKbTPufcq/fTTTwwaNIgGDRrQtGlTHnjgAfbt21don3Pvrdm/fz+PPPIILVu2pGbNmixdutTWb9WqVdx66600bdqUevXqcfXVV/Pqq68WquPhhx8mPDycCRMmFHqsffv2ERkZSaNGjTh8+HCRdf/zZ5B/Fevzzz+nZ8+eREZG0qlTJ9577z1M0wRg27Zt3HXXXTRr1oyGDRty3333cezYsUKPHxcXx3vvvceQIUNo27YtdevWpVWrVjzwwAP88ccfdn3z74vJP07+vXHh4eF07NjRrm9WVhaffPIJ/fr1o2HDhtSvX5/+/fsza9YsW40XsmbNGkJCQnjqqafs2nNzc2ncuDHh4eFMmTLFbltiYiI1a9akX79+heo+936ejh072vYdM2aM3XMp6r6248ePM2rUKFq0aEFkZCQ33HADy5cvv6jnUVK//PILI0aMoG3btkRERNCmTRsGDRpk99wv9fkUJSkpiZdffpmuXbtSr149mjVrxu23387q1auL7J9/3rOyspg6dSrdu3cnIiKC++67z9bn6NGjPProozRr1owGDRowcOBAVq5cWWwdpmkyd+5cBg8eTJMmTYiMjKRXr1588MEHZGdnF+qf/zthmibTp0+nV69eREZG0rt37ws+58t5f8g3f/58Bg0aRKNGjWw1vvPOO2RkZFzwcQF69uxJeHg4+/fvL3L70aNHqVmzJl27drX9zpz73nSpr8mLfb8C+2Glf/75J3fccQdNmjShWbNmjBw5kpiYGCDvvsGXX36Zjh07Uq9ePXr27MnixYuLfC5F3WOVkZHBrFmzuPfee+ncuTORkZE0adKEwYMH8/3331/Uz1GkojIT47G+8zK75s5nbOP72FitIFRVdYeXrqvNiNahClUOpGAl5VZycjKrVq3Cw8OD/v37U69ePVq3bk18fDy//vprsfs+88wzvPLKK4SFhdGnTx9yc3OZPn06Q4YMISUlpch9Fi9ezF133UV2dja9e/cmJCSEJUuWcOONN7Jjx44i99m/fz/9+/fnjz/+oEuXLnTv3h1X17wLxe+88w533XUXUVFRtGjRguuvv5709HSmTZvGgAEDiI+Ptx3ntddeIywsjA8++MDuQ252djajRo0iIyODl156iTp16lz0z++FF17g5ZdfJjAwkG7dunHq1CkmTJjA5MmT2bRpEzfffDNHjx6lS5cuBAcHs2zZMoYPH056errdcZYtW8aECROIjY2lcePGXH/99bafzaBBg+w+VFevXp1bbrkFb29vAG655Rbbf/3797f1S0tL49Zbb+WFF17g6NGjdOjQgc6dO3Po0CHGjRvHf/7zn4t6ju3atcPDw6NQMNi+fTtnz54FKLQtKioK0zTp1KlTscfu378/TZs2BaB9+/Z2z6V69ep2fY8ePUq/fv3YtGkTHTp0oFmzZvz555/cf//95w0djvLFF19w++23s379eho0aGALqkePHrWbVONSnk9RTpw4wYABA2zh5frrr6dZs2b89ttvjBgxgo8++qjI/axWK/fffz/vvfcederUoU+fPrbHO3ToEAMGDOD7778nMDCQ3r17Y7Vaueeee1i0aNF5j/fwww/z1FNPsXPnTq666ip69OhBYmIiL7/8Mvfddx9Wq7XIff/973/z0ksvUa1aNfr06XNJv0+X+v7wr3/9iyeffJJt27bRoUMHrrvuOuLi4njttdcYNmxYod+zotxxxx0AzJo1q8jt+V9CjBgxotB0yZf6mryU96tzRUdHM2jQIGJiYujWrRsBAQEsXryY4cOHk5yczC233MKcOXNo3Lgxbdq04a+//uLhhx/ml19+ueDzBzh27Bjjxo0jOjqa8PBw+vTpQ7NmzdiyZQuPPvqowyaOESlPTGsu1lWLyXnhMb4548dzrR8mwbNgwd/Wod68eWN9rgr1cWKVFZOGAkq5tWjRIjIyMujXrx/+/v5A3pWr6OhoFixYwLXXXnvefefNm8fChQu56qqrAEhNTeXee+9l7dq1TJo0if/+97+F9pkxYwavv/46t99+O5D3rfjEiROZNm0aY8eOtbsSle/777/n3nvv5cUXX8TlnNXK//jjD15//XV8fX2ZPXs2rVu3BiAzM5MnnniCxYsX89xzz/Hhhx8CEBAQwFtvvcWtt97Kk08+ycqVK/H39+f1119n+/bt9O/fn+HDh1/Sz2/x4sX8+OOPNGrUCMi78tWnTx8++OAD5s+fz7///W8efPBBIO/q0R133MHatWtZuHCh3WO1b9+eFStW2D6U5/vll1+49957eeaZZ1izZg2GYVC/fn3efPNNoqKiSEtL48033yyytpdffpkNGzYwZMgQJk6ciI9P3pt/YmIid999N1999RW9e/emV69exT5HT09P2rRpQ1RUFEePHqVWrVpAXngCaNSoEVu2bCEjIwNPT0+7bZ07dy722M8//zyTJ09m586d3HbbbcX+/OfNm8d9993HCy+8YAvWn3zyCS+88AJvvfUWPXr0KPaxSmLatGn4+fmxYsUK2/OHvNfvuaHyUp5PUf7zn/9w+PBhhgwZwuTJk3Fzyxurv3HjRkaMGMErr7xCt27dCr1OYmJicHd359dffyUsLMxu2zPPPENCQgJ33303r7zyChZL3neBM2fOZPz48UXW8cEHH7B48WK6d+/Ou+++S1BQEJAX1h999FFWrFjBF198wT333FNo3yVLlrBs2TLb78SluJT3hx9++IGvv/6a0NBQ5s+fT0REBABnz57lrrvuYuPGjUyePJnnnnuu2MccOnQor776KvPmzePf//637WcOeVdl58yZg6urK8OGDSu076W8Ji/1/epcX375Jf/9739t7yXZ2dnceeed/Pbbb9x0000EBQWxZs0aAgICgLwwOG7cON555x2uueaaC/3YCQwMZObMmVx99dW21wfAkSNHGDZsGG+++SbDhg2ze+2LVGTm8SNYv3iH00eP83aTEfwRWPB+5mLAHS2DGdQ0EIvWproidMWqnDNNk5Ss3HL138UO47qQ/BkAhwwZYmu76aabcHV1ZcmSJaSmpp533/vuu88WqgB8fHyYMGEChmEwe/ZsMjMzC+3Trl0724cmAMMwGD9+PDVq1GDbtm1s3ry50D5BQUE8++yzdqEK4LPPPsNqtfLAAw/YPqQAeHh4MGHCBDw9Pfnxxx85ceKEbVvXrl1tQ2ieeeYZ1q1bxwcffEBoaCj/+9//ivtRFelf//qX3QfI+vXrc91115Genk54eLjtgxCAu7s7DzzwAFAQPPI1adKk0IdlgGuuuYYBAwZw6NAhdu/efdF1JSQkMGvWLGrXrs0bb7xhC1WQ9/PMf65fffXVRR0vPyCdGyKioqLw9/fnvvvuIzMzky1btti2rV+/HovFUmhoYknUqVOH559/3vYBFuCee+4hICCALVu2OHx2v3MlJCRQq1atQh8sDcOga9euDnmMw4cPs3LlSvz8/Hj55ZftPuB36NCBO++8k9zcXGbMmFHk/k8//XShUHXo0CFWr15NQEAAzz33nN2H5hEjRtCuXbtCx8nJyeH999/H19eXadOm2UIVgLe3N2+88QYeHh7nfe2MGjXqskIVXNr7w/Tp0wEYP368LVQB+Pn58eqrr2IYBl9++eUFXxdVqlRh4MCBJCQkFBrC99NPPxEbG0ufPn0IDi48bfKlvCYv5/0qX6dOnezeS9zc3GxDPffv388bb7xhC1UAw4YNIzAwkN9//73IYZv/FBgYSI8ePexeHwC1a9fmiSeewGq1smLFigseR6S8M7OzsS6cifXl0fyZlMuYdqPtQlWwjysT+9RhcLMghaorSFesyrnUbCu3z9vr7DIuyde3NMDX3eXCHYtx9OhRNm7cSEBAAD179rS1BwUF0aNHD1atWsWSJUvOu+bJoEGDCrXl3xexY8cOdu3aRatWrey233TTTYX2cXNzo1+/fnzyySds2rSp0Ie9q6++ushZrDZu3AjAzTffXGhbtWrV6NGjB8uWLWPz5s3ceOONtm3/+te/+O233/juu+9YtWoVpmkydepUqlatWug4F3L11VcXaqtdu/Z5t+UPizp58mShbZmZmfzyyy9ER0eTlJRk+1C2a9cuAA4ePEiTJk0uqq6oqCiys7O55ppr8PDwKLS9WbNm+Pr6snXr1os6XpcuXZgyZQpRUVEMHz4cq9VqG/6UHyyioqLo0qULSUlJ7Nmzh+bNm1OlSpWLOv7F6Ny5s13YAHB1daV27dr8+eefnDp16opNNHLVVVexceNGXn31VUaMGEHdunUd/hj5r+eePXvarh6fa8iQIXz00Ue2fucyDKPIe5k2bdpkO2b+0NFz3XTTTYW+zNi2bRtJSUn07NmTwMDAQvsEBwcTERHB7t27SU9PL/S7eTH3VJ3Pxb4/ZGdns2XLFgzDKPJ9qEmTJjRp0oSdO3eyc+fOQu9D/3TnnXcyZ84cZs6caTecdubMmUBeCC3KpbwmL/f9Cop/L6lVq5ZdsARwcXGhVq1abN26laSkpIv+vdi4cSPr1q0jNjaWzMxMTNO0vVcdPHjwoo4hUl6Z+3Zh/eJdcmOPM6dub76pfS2mUfBlQ6davjzeMQxfj5J99pILU7CScumbb77BNE1uvPFG3N3d7bYNGTKEVatW8c0335w3WJ1vWEitWrXYsWMHcXFxhbbVrFmz2GPFxsYW2na+qc7j4uIwDOO8x8xv/2cd7u7uTJ06ld69e3P27Fnuu+8+unfvXuQxLuSfVwgA2wfY4rb981v0Xbt2ce+993L06NHzPtb57lsrSv7EFl988QVffPHFeftd7A3+7dq1w93d3Xalbfv27Zw5c4YuXboQERFBWFiYbVv+/VUXGgZ4qYr6eQK2q3FX8orVhAkTuP/++5k2bRrTpk0jNDSUDh060L9/f/r161fom/7Lkf86Le736tx+56pWrVqRATq/b40aNYo8ZlG/W/mvwZ9++umCywycPn26ULAqydIEF/v+cOrUKbKysqhevbpt+GlR++zcubPIn9c/tW7dmubNm/Prr79y7NgxatasSVxcnO1ncL5hppfymrzc96vzPU7+e0loaGiRxzvfe01RkpOTeeCBB1i7du15+1zK+49IeWJmpGEu+ALzlyUkuFdhasuR7Aoo+LLC1WJwX5vq9GsYUOg+S7kyFKykXFqwYAGQN+vbP7/1zf9jvGbNGuLi4i7pSsDlDFMsbp+iPjBeiqLeCBcuXGj7/9u3b8dqtV7Wh2NHvMmapsnDDz/M0aNHufPOO7nzzjupU6cOPj4+GIbBxIkTeffddy/p55o/o2Pz5s0v+ipXcby8vGjVqhUbN27k6NGjthDVpUsXIO+b+x9++IGMjAzWr19va3MkZ/5Ba9q0KT///DO//PILP/30E1FRUSxcuJCFCxfSoUMH5syZU+jLCUfLf/5F/RzO9zuS/5q5lJ9d/msnIiKiyKGCF3rc8wWdkjjfa/9intfFPvc77riD//znP8yePZtx48YxZ84ccnJyuO2228773nAlXpOXekxH1DBhwgTWrl1Lp06dGDduHI0aNcLf3x8XFxdWr17NiBEjHDb8XKQsMf/chPWr9+FUApuCmvBO42GkuBUMna/h58b4buHUC3T8+5qcn4JVOefjZuHrWxo4u4xL4uNWsm/Io6OjbdMLHzx48LzDPKxWK99++y0PP/xwoW1Hjx6lYcOGhdqPHz8OUGQYK2qq8XP3Od+3r0UJCQnhyJEjHDt2rMi1WfKP+c/Z2DZs2GC76hAZGcnatWt59913eeKJJy76sR1p37597Nu3j5YtW/Laa68V2n7kyJFLPmb+N9ydO3cuchKRy9G5c2fbUKGoqCgCAgJs94V17tyZBQsWsGXLFqKiohx+f1VZ4OnpSd++fenbty8Af/31F48++igbN25k1qxZ3H333SU6fv7vy/muWua3X8zsgv88Zv7vwj8V1Z5/datx48bnnRjlSrnY94eqVavi7u7OyZMnixyOeO6xLvbnNXjwYF555RVmz57N6NGjmT17NhaL5ZInIDmfy32/Kg1Lly7FxcWFzz77rNDw3XOXnxApq6wrF2K07owRVPheyHOZifGY0VEYHbpjzv4Yc9NvZBsufBU5gEW17EeuXFO3CiM7hODtpqF/pU2TV5RzhmHg6+5Srv4r6beU+ZNWPPLIIxw/frzI//KnH86/svVPRa1vsm/fPnbs2IGvr2+RV0rOvVKULycnhx9//BHggt+Qn6tDhw4AfPvtt4W2JSYmsnr1aiwWi90xz549yxNPPIFpmkyZMoV33nmHqlWrMmXKlIu+38jRTp8+DRQ93Of06dPnnfY+/96OnJycQtu6dOmCi4sLK1euPO96ZJcq/wrU2rVr2bhxIx07drR9k5+/7ccff2T37t00bdq0yPuEipL/PBxVZ2lp2LChbVa8cycWudznk/96XrVqVZFrGuX/Hub3uxjt27cH8ob1paWlFdpe1O9wq1atqFKlCuvWrbNNp19aLvb9wc3NjTZt2mCaZpHPYffu3ezcuRNfX98iJ4Upio+PD4MGDeLEiRO8/PLLHD58mGuvvfa8wygv1eW8X5WWM2fO4OvrW+Q9keebkl+krLCuXIg55xOsk5/FTCx6yQL4ez2qSc/m9X36QcxNvxHrGcgzrR+1C1UeLgZPdApldJcwhSonUbCSciUnJ8f2AaaoG7/zde3alWrVqrFjx44iZ6SbPn0627dvt/07LS2N5557DtM0GT58eJHDhDZt2sTs2bNt/zZNk0mTJnH8+HGaNm1q+yB4Me655x4sFguffvqpXSjKysriueeeIz09nRtuuMEusDzzzDMcO3aM++67jx49ehASEsIbb7xBdnY2jz322EWte+NoERERWCwW1q5dy4EDB2ztGRkZ/Oc//7EFr3/K//a+qIVNw8LCGDZsGAcPHuSJJ54gKSmpUJ9NmzaxatWqi64z/z6rH374gTNnztgN9cu/zyp/zZ9LGQaYf1XlfAu0Olt6ejqffvppobBjtVptaxWde1/R5T6fOnXqcN1115GSksLzzz9vN5vb5s2b+eKLL3BxcbmkK2MRERF069aN06dP8+qrr9qtPTVnzpwiZ+H08PBg5MiRnDlzhgcffLDIq0g7d+68IgvHXsr7w7333gvApEmT7K6qpKSk2N6H7rjjjksaonnnnXcCeVOmA3YzFJbU5bxflZZ69epx5syZQuf0o48+uuiFrUWcxWjdGYJDIT72vOHKTIzH+vq/IeHv+7izMlkT3JKx7Uazv0rBfa11/D2YfENdrovU/VTOpKGAUq789NNPJCYmEhkZSfPmzc/bz8XFhf79+zNjxgwWLFjAM888Y7d96NChDBgwgK5du+Ln58eGDRs4efIkjRo1Yty4cUUe86677mLcuHF89dVX1KlTh127drFnzx58fX2ZOnXqJT2P1q1bM378eP73v/8xcOBAOnfuTGBgIJs2bSImJoaIiAgmTJhg6//999+zYMECGjVqZPdcbrjhBoYPH86cOXP473//e1nTrpdEtWrVuO222/j666/p3bs3Xbt2xdPTk40bN5Kbm8uwYcOYO3duof169+5tm6WvS5cueHt7ExgYaHtu+d+6f/fdd6xcuZJmzZoREhJCfHw8Bw8eJDY2lvvvv5/rrrvuour08vKiZcuWtpnm/hme8ocDFrWtOD169MDT05OPP/6YPXv2EBISgmEYPPzww0UOmXKE+++/3zZJQP701jNmzLCtkxQSEsKnn34K5H3wff7553nllVdo3rw5tWrVIjs7m61bt3L8+HHq1KljW2S2pM/nf//7H4MHD2b+/PmsX7+etm3bkpiYSFRUFLm5uTz//PMXfQUm38SJExk0aBCfffYZv/76Ky1atODIkSNER0dz55138uWXXxba54knnmDv3r189913dO/enebNmxMeHk5SUhJHjhzhyJEjXH/99UXO4lcSl/L+MGDAAG6//Xa+/vprevbsSdeuXfHy8iIqKorExETatGlz3veh82nevDmtW7cmOjqakJCQi/7duBiX+n5Vmh577DEef/xxHn30UWbMmEFYWBg7d+5k3759PPjgg3z88cdOqUvkYhhBwVjGTsA6+VlbuLKMnWAbFmhNiMV8ZSyk5l2Bz7S4Mr3+QFbUsF/A/vr6Adzftjoerrpe4mw6A1Ku5A8DvJgPRflXtBYsWGD3bTfAq6++yn/+8x+OHTvG8uXLMQyDe+65hwULFpx3mu0bb7yRzz77DIvFwrJlyzhx4gTXX389ixYtKjbknc8TTzzBjBkz6NSpE1u3bmXJkiW4u7vz6KOPsnjxYtvaM8ePH+fpp5/G3d2dt99+u9AN9i+//DJ16tThq6++KrSWTWmYOHEizz//PLVr17YNtbv66qtZsmTJeWcRu//++3nyySfx8fHhxx9/ZNasWXbfOHt5eTFr1iwmTZpEixYt2LNnD0uXLuXQoUPUrVuX5557rsh754qTH5jOvb/qn9sMw7ik+6tCQ0OZPn06bdq0YePGjcyePZtZs2YVOSW9o2zfvp3o6Giio6NtM83FxMTY2s69Epu/PluvXr1ISkpi+fLlrF27Fn9/f8aPH8+SJUvs1hAqyfMJCwvjhx9+YOTIkba15LZt20a3bt2YOXMmI0eOvOTnWq9ePRYtWsSNN95IYmIiy5YtwzRNpk+fzsCBA4vcx2KxMG3aND766CO6dOnCwYMHWbJkCXv37qVatWqMHTu20BctjnCp7w+vv/46b731Fs2bN2f9+vWsXLmSatWq8e9//5u5c+cWee/VheQvHzBs2DC79akc4WLfr0rb4MGD+eKLL2jTpg07duzg559/JiQkhLlz59KnTx+n1CRyKfLD1T+vXFl3/I75f6Nsoeqod3X+3eZxu1Dl7WZhfLcaPNoxVKGqjDBMTZfjVCdOnCh2xiLTNElMTCQoKEiXdh2gY8eOHDt2jLi4uCLv7ynK6NGjmTdvHvPmzbPNJCflQ/6Hy4s911J+Oetcl5X3B9M06d69OwcPHmTt2rW2taIqotI+1/o77Dz5gT0+/vz3H1UUZmK87coVhgF/fzY0gZ9C2/FJg0FkuhQMD64f6Mn4bjUI9buys7qWlrJwrg3DKPGQZsVbERGRcm7x4sUcOHCAnj17VuhQJVJRGUHBGPePyfvH36Eq3cWDt5rcyrTGw+xC1U2Nq/JanzoVJlRVJLrHSkREpJwaN24cZ86cYdWqVbi4uDB+/HhnlyQil8H8awfme6/a/n3AtwaTm97OCe+CYbZ+7hae7FyD9jV9nVGiXAQFKxERkXJq1qxZuLq6Uq9ePcaPH0+LFi2cXZKIXALTNDFXL8Wc9SFYrZjAkvAufB45gBxLwcf0psFejO1Wg2rebs4rVi5I91g5me6xKn2676by0LmuPHSuKw/dY1V5lIX7bq4kMzsbc9aHmL/lTTyV4urFtEZD2RBc8AWJYVoZkrCR227vh2tw6S/CXVrKwrl2xD1WumIlIiIiIlKKzNNJWD94DfbnrbW5p0ptpjS9nXjPqrY+VT0MntzzDVcd2gRT12GeMxW7lE2avEJEREREpJSYB/ZgnTAG9u/GisGCWtfwbOtH7EJVq1Bv3uwfSauHH77gIsJSdihYiYiIiIiUAuvalVjfeBpOJ3HazYdXrrqPryL7YTVcALAYcGerYF7oWYsAL9dC61yZ0VFOfgZSHA0FFBERERG5gsycHMx50zF/WgzAtoBIpja9jdPuVWx9gr1dGdutBk2Cve32zQ9XZnQUll5FL44uZYOCVRlnGAaGYZCbm2u7YVdERERKR25uru1vscjlMM+ewfrB/+Cv7eQaFubW6cX8OtdhnvOa6ljTl8c7heHn4VLkMYygYAyFqjJPn9TLAU9PT9LT0/H19dUbu4iISCnKzMzE3V0LscrlMY/sxzrtVUiKJ9G9ClObjmBnQD3bdleLwb1tgunfsKo+41UAClblgJeXF2fOnCE5ORlPT0/c3Nz0y1cC+dPba6WBik/nuvLQua48Sutc5+bmkpmZSUZGBv7+/lf0saRism5YjfnFO5CVxebAxrzTZDhn3Xxs28P83BjfLZzIQE8nVimOpGBVDlgsFgICAkhPTyc9PZ2zZ886u6RyzWLJm7PFarU6uRK50nSuKw+d68qjtM61YRi4u7vj7++vofhySUxrLuaCLzCXfUu24cJXkQNYVKu7XZ/udavwSIcQvN2KHvon5ZPeKcoJwzDw9vbG2zvvhkZ9K3v5ysIidFI6dK4rD53ryqO0zrVGhsjlMFPPYv1oEuyMJtYzkClNR7CvSm3bdncXg5HtQ7iunr9eYxWQglU5pV/Gy5f/s9PPsOLTua48dK4rD51rKavM44exTpsA8bGsC27Be42GkubqZdte29+d8d3CqR3g4cQq5UpSsBIRERERKQFzyzqs098kMzuHzxvczLLwznbb+9T354G2IXi4agnZikzBSkRERETkMphWK+bCmZg/zOWYdzCTW9zOYd8atu1erhYe7RhK97pVijmKVBQKViIiIiIil8hMS8X66RT4cxM/h7Tlo4Y3k+lSMDV/ZKAn47vVIMxP0/VXFgpWIiIiIiKXwIw9hnXaBNLj4/mo8XBWh7a1235j46rc3SoYNxcN/atMFKxERERERC6S+ecmrJ9M5qCLP5PbPkmMd7Btm5+7hcc7h9Gxpp8TKxRnUbASEREREbkA0zQxf5yH9fuvWRrWic/rDyDb4mbb3iTYi7FdaxDs41bMUaQiU7ASERERESmGmZGO9bO3SP1zC9Oa3s764Kts2wxgaLMgbruqGi4WLQNQmSlYiYiIiIich3nyBNb3XmXPWZMp7UYT7xlo2xbg6cJTXWrQKszHiRVKWaFgJSIiIiJSBHNnNDkfvsHCoLZ83aovuRYX27ZWod6M7lKDql76OC159EoQERERETmHaZqYK77j9PfzeafRMLYENbZtsxhw+1XBDG4WiMXQ0D8poGAlIiIiIvI3MysT84t32bbnKG+2fYIkD3/btmrerozrWoMm1b2dWKGUVQpWIiIiIiKAmRhP9nsTmWeJYH7Lh7AaBetQdajpyxOdwvDzcCnmCFKZKViJiIiISKVn7tlO/PT3eLN2f3YERNraXQ24p011BjSqiqGhf1IMBSsRERERqbRM08T85Ud+X/4rbze+j2R3X9u2UF83xncLp36QpxMrlPJCwUpEREREKiUzO5vsrz/g6xNufNf8XrttV9fx49GOoXi7aeifXBwFKxERERGpdMzTicR++A6Tq3Rmb+06tnZ3CzzYPpTekf4a+ieXRMFKRERERCoVc/9u1s5cwLTaN5Hm6mVrr+XrwvgetakT4OHE6qS8UrASERERkUoj49flfLYhhqX1Btu194rw46EOYXi4Ws6zp0jxFKxEREREpMIzc7I5Nmcmk1JqcahGJ1u7p2FlVJeadK9bxYnVSUWgYCUiIiIiFZqZfJqfZszlI/+OZPgWDPOr523yr171CfNzd2J1UlEoWImIiIhIhZV2YC8f/fAHPwd2t2sfUMeTezrXxs1FQ//EMRSsRERERKRCOrD6Nyb9ZXI8sIWtzdfM4rGuNekcEejEyqQiUrASERERkQrFmpPD0nnLmJ5Tm2xvN1t7Y7d0xvZrRnVfDf0Tx1OwEhEREZEK4+yp00xbsIEoz0j4e5SfYZoMDs1lRM9WuFq0NpVcGQpWIiIiIlIh7Nm5n0kbEjjpWbDgr39OGqM7BNOmSS0nViaVgYKViIiIiJRrVtPk+xVb+DLOk1x3f1v7VTnxPDWoNYH+vk6sTioLBSsRERERKbfOpGfx1ndb+N0aYBv6ZzGt3Oodz5CbrsZVs/5JKVGwEhEREZFyafuRRCb/cpgklwBbW1DmGcY2dadZpx7OK0wqJQUrERERESlXcq0m89YfYM6BTKwu3rb2dikHeaJfC/xr1XRidVJZKViJiIiISLmRlJ7DlGW72ZbqCkbeMD9Xaw53Zu5g4J0DsHj7OLlCqawUrERERETEqawrF2K07owRFFxsv993H+PNTQkkWzxtbSHpiYwLiqfB7bdgWHQ/lTiPXn0iIiIi4jTWlQsx53yCdfKzmInxRfbJsZp8/ts+Xvo9xS5UdU3YxpTWLjS8eZBClTidXoEiIiIi4jRG684QHArxsUWGq5Mp2TyzcDffHsmxtbnnZvNIzArGDe2Ab9tOpV2ySJEqzFDAAwcO8Oeff7Jv3z727t3LqVOncHNz4+uvv76k46SmphIdHc3vv//OoUOHSEhIwDAMatasSbdu3ejTpw+urhXmxyYiIiLiVEZQMJaxE7BOftYWrixjJ0BwMKv3JfDKj3tJtRZcC6iZGsfYrC1EjHoQw1vrU0nZUWESwvz589m8eXOJj7No0SIWLFiAYRhERETQtm1bkpOT2bNnD/v27WP9+vU8++yzeHh4OKBqEREREflnuMqY8jyTBj3Pgr/OcO4Aq+tObOSBCAOvm5/AsLg4r2CRIlSYYNWwYUPq1q1LZGQkkZGRPPTQQ5d1HE9PT26++Wauv/56AgMDbe0nTpzg5ZdfZvfu3XzzzTeMGDHCUaWLiIiIVHr54erYO28wOfR6Dv51xrbNMyeTkQcWcs2Aa7G07+bEKkXOr8IEq0GDBl3R44SFhTFixAjefvtt1q5dq2AlIiIi4mCrk915v9G9ZFgNW1vE2eOMPfoDNR9+HKNWhBOrEylehQlWpaFu3boAnDp1yrmFiIiIiFQgGTlWPtoYy6qDyUBBqLrh2FruPvAjHs++oVAlZZ5mBbwEcXFxAAQEBDi3EBEREZEK4tCpDMYu3v93qMrjk53Gv7bP4MEDi3C3ZmN+8Np5p2IXKSt0xeoS/PjjjwC0a9fuovcZM2ZMoTZ3d3dee+01AKpVq+aY4uSi5c/qGBxc/CKEUv7pXFceOteVh851xWGaJt9vj+XNnw6SZRZcpWp45jBjds+m8eh/4d6gKfFPP0xu3HGMqc8T+Mq7uASHOrFquRIqyu+1rlhdpOXLl7Nt2zZ8fHwcdj+XiIiISGWUkpnD/y3eweur9tmFqpuP/MyE3Z/TZOJbeHftiWv10LwwFRJObtxxkp57jNz4WCdWLnJ+umJ1EXbu3Mnnn3+OYRg88sgjdrMFXsiUKVOK3Z6QkIBpmiUtUS5B/rch8fEaUlDR6VxXHjrXlYfOdfm3NzGdN345TFxGQVuVrBSe3DWb1jlxGM+/xWmfKrjl5C0InIQL5lMvweRnyY07Tvwzj2AZOwEjqHxf3ZACZeH32jAMwsLCSnQMXbG6gMOHD/PGG2+Qk5PDPffcQ4cOHZxdkoiIiEi5Y5om3+9M5D9LD9mFqhan9jJl81Rak4Tl2SlYqlUvtG/+VOwEh0J8LGZ0VClWLnJxdMWqGLGxsUyYMIHU1FRuueUWbrjhBmeXJCIiIlLuJGfm8tavh9l8Mov8Wf8sppVhh1YytIk/Lg2HYrTtVuxVqPxwZUZHYek1sJQqF7l4ClbnkZSUxCuvvMLp06fp168ft9xyi7NLEhERESl3dpxMY/Ivh0jMLhgoFZh5hqeOLKbF8KEYTVpe9LGMoGAMhSopoxSsipCSksKECRM4efIk11xzDXfffbezSxIREREpV3KtJvO3nWT29iSs59x90jZxF4+77iNg7HgMvypOrFDEsSptsFq6dClLly6lQ4cOjBgxwtaemZnJxIkTOXr0KJ07d+bhhx/GMIxijiQiIiIi5zqVnsOUnw7w52kr+UP/XK053HF4OTd2bYLLNeP0+UoqnAoTrLZs2cI333xj15aTk8Ozzz5r+/eQIUNo06YNAMnJycTExHDq1Cm7fWbNmsXevXuxWCy4uLjw/vvvF/l4o0aNcvAzEBERESn/omNSmLr6EGesBR8zQ9ITGZPwM43uuwujRm0nVidy5VSYYJWcnMzevXvt2kzTtGtLTk7+526FpKamAmC1WlmzZs15+ylYiYiIiBTIsZrM3HycBX+dxTQKPmJ2ObmVR8PS8L37Xxhu7k6sUOTKMkwtouRUJ06c0DpWpawsrJUgpUPnuvLQua48dK7LpvjUbCat2Mvu1IJ7qdys2dx3dAV9B/TAclXbSz6mznXlURbOtSPWsaowV6xEREREpPStP3yad9YcI+Wcj5XhqXGMzdpCvcfuxahS1YnViZQeBSsRERERuWTZuVY+X3OQxceyOfcj5bVxv/Ngcz+8ez2JYbGc/wAiFYyClYiIiIhckpjkTN5YtocDWQX3THnmZvJQ3Gp6Dh+AUbueE6sTcQ4FKxERERG5aKv3nOT9TXGkGwWhqm5KDOO8j1DziZEYHh5OrE7EeRSsREREROSCMnOsfLRqNysTLGC42dr7xm3ivu718Wh3j/OKEykDFKxEREREpFiHk9J4Y9kejlq9bG3eOemMOruRrvcOxaga5MTqRMoGBSsRERERKZJpmqz44wgfbz9LlqUgVDVIPsLYWumE3vkAhsXFiRWKlB0KViIiIiJSSFp2LtN+3MaaFE+wFHxkHJSwiTsGdMAtspETqxMpexSsRERERMTO3hOnmbRqP7GGj62tSlYKTxi7aTdyCIantxOrEymbFKxEREREBMgb+rdo3V/MOJBDjqUgVDVPPshTV/lSresdTqxOpGxTsBIRERERktOzeHvRH2zKrgJ/3zdlMa3ckvwHw27piWtwqJMrFCnbFKxEREREKrmd+08weW0MCS5VbG1VM5MZExBLi9uGY7hoggqRC1GwEhEREamkrKbJNyuimXnSE6tLwdC/NskHeLJHXQKaDnRidSLli4KViIiISCV06kwqUxf9wVYjCIy8NhdrLrdn72bQXX1w8fFzboEi5YyClYiIiEgl88fWfUz94wynXQsW9q2ecYoxdbNp3HMwhmE4sTqR8knBSkRERKSSyMnJZdai9XyTWhXTtWDoX6fUAzzWryV+NcOdWJ1I+aZgJSIiIlIJnIxNYMrSnexyq24b+udmzeZe92PccG8vLG7uzi1QpJxTsBIRERGp4DasjebtfSYpbtVtbTUyEhnXyo/Itjc4sTKRikPBSkRERKSCysrI5IsFa1hkhtt96uuReZiHB3fEu2qA02oTqWgUrEREREQqoJh9h5i0+gj7PQvum/LIzeKhoNNc16+PJqgQcTAFKxEREZEKxDRNfl3yK+/H+5PuWTD0r05mAuO61aR2w6ucWJ1IxaVgJSIiIlJBZJw6zSffrmOFRz27T3nXGye477bOeHp5Oq84kQpOwUpERESkAjiy5U9e33KGo171bG3euRmMijDpdvW1TqxMpHJQsBIREREpx6zZWaxcsJKPM2uS5RVsa6+fnci4Pg0JqxFczN4i4igKViIiIiJliHXlQozWnTGCig9EZmI8aauX8358FX7zbQAuBdtu8k7ijgGdcHdzOf8BRMShLM4uQERERETyWFcuxJzzCdbJz2Imxp+/X8JJ9k55nbGJdfJC1d/8ctJ5rpkL993cRaFKpJQpWImIiIiUEUbrzhAcCvGx5w1XuUcPsviDL3m68d2c8K5ma29qnmLqwAa0b9Wg0D4icuUpWImIiIiUEUZQMJaxE84brpI3RvHagi18GtGfHEveHR2GaTK8WjqvjOhEcFVfZ5UuUukpWImIiIiUIUWFK2t8LDtnzeapbbCxWjNb34DcNF7s6M+I61vjYtGCvyLOpGAlIiIiUsacG66s8XF888FMns1tQYJnVVufVq5neXNoM1o2qOHESkUkn2YFFBERESmDjKBgzgx5kLfWxfBHYCNbu8W0ckcdCzd3a4fF0FUqkbJCwUpERESkDNq6ZjNT9sLpc0JVtYxTjO0SStMmEU6sTESKomAlIiIiUobk5FqZvWgd81MCMd0L7trokLCDx3bPxXe/P+bYCRdc50pESpfusRIREREpI+LPZvB/szcyL7UappH3Mc3VmsOD1ZJ5+var8a3qX+xU7CLiPApWIiIiImXAxoOJPPXdHnYSYGsLS0/gf41zGXB9ByzVqhc7FbuIOJeClYiIiIgTZeeafLruMBPWxXPW4mFr737yDyZfE0L99i1tbRda50pEnEfBSkRERMRJYs9m8fQPf7HwYLqtzT03i1H7FjB6eFd86jcotM8/w5UZHVWaJYvIeWjyChEREREnWHM4mWnrjpNmLZgyvXbKCcamb6T2qPuwVAs977754cqMjsLSa2BplCsiF6BgJSIiIlKKMnOsfPr7SZbtOw0UhKreMRu4v211vHr++6KOYwQFYyhUiZQZClYiIiIipeTomUze+O04h89k2dq8cjJ45MBCug/th9GinROrE5GSULASERERucJM0+SnA2f4cFMcmbmmrT3y7DHGHv2BGiMfx6hdz4kVikhJKViJiIiIXEFp2bl8uDGOXw4l27UPOPobd2buxGPssxiB1ZxUnYg4ioKViIiIyBVyICmDN9bEEHO2YOifb3Yqj++eS/saPlhGT8Dw9HZihSLiKApWIiIiIg5mmiY//nWaz7acJNtaMPSvyemDPLVrJsGdu2Lc+iCGi4sTqxQRR1KwEhEREXGglMxc3t1wgqijKbY2w7Qy5PBPDD+8Ctehd2P0vgnDMIo5ioiUNwpWIiIiIg6yJyGdSWuOczI1x9YWkHWWJ3fNomXqESwP/wujTWcnVigiV4qClYiIiEgJWU2T73Ym8dXWeM6Z9I+WSX/x5K7ZBHi6YBn3KkZEQ+cVKSJXlIKViIiISAmcycjhzXUn2HIi1dZmMXO57eBybj7yC5awmlieeB6jWogTqxSRK03BSkREROQybYtLZfLaE5xKLxj6Vy3jFE/tnEmT5MPQpCWWh/+N4e3rxCpFpDQoWImIiIhcolyryZztCczdlsg5I/9on7CDx3bPxS8nHaNrL4w7HsVw1cctkcpAv+kiIiIilyAxLZspa2PYfjLd1uZqzeHu/T/Q7/haDMC4+U6MG4Zq5j+RSkTBSkREROQibT6ewltRJ0jOzLW1haYnMHbH10SmHAdXN4x7n8TSobsTqxQRZ1CwEhEREbmA7FyTr7bG892uJLv2q+OiGfnXArxzM8HXD8uoZzHqN3VSlSLiTApWIiIiIsWIS8nijTUx7E3MsLW5mzk8sOdbrovdhAFQvQaWJ5/HqF7DaXWKiHMpWImIiIicx9ojyUxbH0tqttXWViszkbFbP6d2WlxeQ4OmWB59BsO3ipOqFJGyQMFKRERE5B+ycq1M//0kS/aetmvvFR/N/bvm42HNBsDo0APjnicw3NycUKWIlCUKViIiIiLnOHYmkzfWxHDodKatzdNi8siueVx9YrOtzRgwHGPgCM38JyKAgpWIiIiIzU8HzvDhplgycgpWp6rnms7Yte8Qlp6Q1+DiinHXKCxdrnNSlSJSFilYiYiISKWXnm3lw02x/Hww2a59gHmUO1e9h5v59/Tq3j5YHnkao/FVTqhSRMoyBSsRERGp1A6dyuD1NTEcT86ytfm6WXgscTUdtiwq6FgtBMsTz2OE1XJClSJS1ilYiYiISKVkmiZL957m099Pkm0tGPrXOMCVp/6YTvCh7QWdIxpieew5jCoBpV+oiJQLClYiIiJS6aRk5fLu+liijp61tRnA4FoWhi96FdfTCQWd23TBcv9TGO4epV+oiJQbClYiIiJSqfyVkM4ba2I4mZpta/P3dOGp0LNcNes1yCxYCNi4/maMwXdjWCzOKFVEyhEFKxEREakUrKbJwt1JfBEdT27ByD+uCvVmtHUHATM+BPPvhYAtFowRD2Pp0dc5xYpIuaNgJSIiIhVeckYOb0ad4PeYVFubxYDbWgRx847vsaxaWNDZ0wvLyH9hNG/rhEpFpLxSsBIREZEKbXtcGpPXxpCUnmNrC/J2ZWyHajT+bhr8saGgc9VqWJ74P4yaEU6oVETKMwUrERERqZByrSbzticyZ3sC50z6R/twHx5v5o3vhy/B4X0FG2rXw/L4/2EEBJV+sSJS7ilYiYiISIWTmJbN1HUn2BaXZmtztcDdraszwDcZc9K/ICm+YIeWHbA8MBbD08sJ1YpIRXDFgtXmzZv5448/SEhIICsri+eff962LSMjg8OHD2MYBg0bNrxSJYiIiEgltCUmhTfXneBMZq6tLdTXjXHdalA/bjfW1/8H6QWBy+g5AGP4/RgWF2eUKyIVhMODVUJCApMnT+bAgQPn7ePm5sZbb71FYmIib7zxBrVr13Z0GSIiIlLJ5FhNvt4az4KdSXbt3er48WiHULw2rML61Xtg/XvmP8PAGP4AlutudEK1IlLROHRRhszMTCZMmMCBAwcIDAzk+uuvx8Oj8GJ6Li4u9OzZE4BNmzY5sgQRERGphOJSsnhmxWG7UOXuYjCqYyhjO4fitfgrzC/eLQhV7h5YHn1GoUpEHMahwWrZsmXExMQQERHB1KlTue+++/D09Cyyb/v27QH4888/HVmCiIiIVDJRR87y1JJD7EkoWNi3ZhV33ri+Dr1re8EnkzGXfFOwg39VLP+aiNGqoxOqFZGKyqFDAdevXw/AXXfddd5Ala9WrVpYLBZiYmIcWYKIiIhUElm5Vj7bcpIf/zpt194r0p8H24XgkX4W65QJsH93wcbwOlgefx4jKLh0ixWRCs+hwSomJgaLxULjxo0v2NdiseDt7U1qauoF+4qIiIic63hyFm+sOc7BU5m2Nk9XC490COGaCH/M2GNY334J4mMLdmraCsvIf2N4+zihYhGp6BwarLKzs3F3d8diubgRhpmZmbi5uTmyBBEREanglu46yeurDpKRU7A4Vb2qHozvFk6NKu6Ye7Zjfe9VSEuxbTeu7oMx4mEMV600IyJXhkPfXfz9/UlMTCQ1NRUfn+K/DTp06BDZ2dkEB+tSvIiIiFxYRo6VV5b/xY874+za+zeqyr2tg3FzsWBd/zPm5+9Abo5tuzHkbozrB2MYRmmXLCKViEMnr8hfkyoqKuqCfRcsWABA06ZNHVmCiIiIVECHTmUwdskhu1Dl427hP93DeahdCK4WA+vCWZifTi0IVa5uWEb+C0vfIQpVInLFOfSKVZ8+fYiKimLevHk0btyYmjVrFuqTmZnJl19+yYYNGwDo3bu3I0sQERGRCsK6ciG06sTyU258+vtJsnILhv41qubJuK7hVPd1wxoXg/nxJDi8r2BnP38so57FiLzwfd8iIo7g0GDVtGlTrr32Wn7++WeeeeYZ2rRpQ2Zm3k2lCxcu5MiRI2zZssU2YUX//v2pW7euI0sQERGRCsC6ciEp87/i/b9M1vk3stt2R7ua3NzAJ+8q1bGDmK+Og+zsgg6h4VieeAEjOLSUqxaRyszhd3A+9NBDeHp6smTJErshgV9//bVdv/79+3PnnXc6+uFFRESkAthXrz2TOlYnzj3A1ubv4cILNzShU92qxMfHY/1rB+aU5yA3t2DHhs2xPPo0ho9f6RctIpWaw4OVxWLhnnvu4brrrmPVqlXs2bOHU6dOYbVaCQgIoFGjRlx33XW6UiUiIiKFmKbJwt2n+OKPM+ScE6papBzhqWta0rhuVQCsW6IwP3gNzILhgUanazHufgzDVTMOi0jpu2JzjtaqVYt77rnnSh1eREREKpjkjBzeijrB5piCNS4twLCTaxmycyEuh0PIffV9Mjevxfxwkt2+xo23Ydx4qyapEBGn0WIOIiIi4nQ7TqYxeU0MiekF06QHerkyrmsNmroGYZ28AeJjiR85BKzWgh0tLhj3PoGl07VOqFpEpICClYiIiDhNrtXkmx2JzNqWgLVgVB/tavjwZOcwqni6Ylo94bobYfbH9qHK0xvLY89hNGpe+oWLiPzDFQtWe/bs4fDhw6SmppJ77k2lRRg6dOiVKkNERETKqKT0HKaujeHPuDRbm6sF7mpVnYGN8+6lMrdvwbpgBhw9WGh/Y9QzClUiUmY4PFhFR0fzySefkJCQcNH7KFiJiIhULltiUngz6gRnMgq+fA3xdWNc1xo0rOaFeXBvXqDa/WfhnQ0DTBPzi3cxx07ACAouxcpFRIrm0GC1fft2Xn/9dax/X6YPDQ3F398fFxcXRz6MiIiIlFM5VpOZW+P5ZmeSXXvX2n6M6hiKd1Is1g++wvx9beGdPTyp+n9TcA0JI/6ZRyA+FuvkZ7EoXIlIGeDQYDVv3jysViuRkZE8+eSThISEOPLwIiIiUo6dTMlm0toY9iSk29rcLAYPtKtOn2pWmPsh1t+W299HlS8gCMt/XsejcVMALGMnYJ38rMKViJQZFkce7ODBvPHPTzzxhEKViIiI2Kw/epbRSw7ahaqaVdx545rq9Nn+A+ZzD2OuXmofqlz//v63WiiW/7xuF5yMoGAsYydAcKgtXJmJ8aX1dERECnFosHJxccHLy4vQ0FBHHlZERETKqexcKx9tjmPir8dJzSoITT3r+vGGx3Zqv/4Y5o9zISuzYKfgUOh8LeTkQHAolnFFX436Z7gyo6NK4ymJiBTJoUMBa9asyf79+8nKysLd3d2RhxYREZFyJiY5izfWHOfAqYLQ5OlqMDIgiR4L34Ckf1xh8vPHGDAco/v1GK5uWGtHYrTuXOwQv/xwZUZHYek18Eo9FRGRC3JosOrduzd//fUXv/32G9ddd50jDy0iIiLlyOqDZ3hvYxwZOQVXqep65jJ292zCD2217+zhhdFnEEafmzA8vW3NFxuUjKBgDIUqEXEyhwar7t27s23bNj7//HM8PT3p2rWrIw8vIiIiZVxGjpWPN8excv8Zu/a+qbu559cvcLfmFDS6uGL06IvRfxhGlYDSLVRExMEcvo7VqFGjCA4O5u2332bmzJlERkbi6el53v6GYfDII484ugwREREpZYdPZ/LGmuMcPZNla/M2sxi1YzadE7bb9TU69MAYdDtGsO7LFpGKweHBauXKlfz4448AJCQkXNRCwQpWIiIi5ZdpmqzYf4aPN8eRlWva2hskH2Hszq+pnnGqoHOz1lgG34VRO9IJlYqIXDkODVabNm3i448/BsDDw4OGDRtqgWAREZEKLC07l/c2xPLb4bN27YOO/MyIg8twNf++x6pOfSxD7sZo0tIJVYqIXHkODVYLFy4EoFWrVowePRovLy9HHl5ERETKkL2J6UxaE0NsSratrUpWCk/snkObpD15DdVrYLn5DmjbFcMwnFSpiMiV59BgdeTIEQAefvhhhSoREZEKyjRNFu05xYzok5wz6R/NT+1n9K5ZBGYlg39VjAG3YnTrjeHq8DsPRETKHIe+07m6uuLt7U3VqlUdeVgREREpI5Izc3kn6gQbj6fY2iymlVsOrWTo4VW4eHpiDLoDo9dADI/zT14lIlLRODRY1alTh127dpGenq4rViIiIhXMzpNpTFp9mMSsgiF9gZlneGrnLJqlHskLU/1uwfCr4sQqRUScw+LIg/Xr1w+r1cqyZcsceVgRERFxIqtpMnfdPp5dfsguVLVJ3M3k39+iedM6WF75AMvw+xWqRKTScugVq3bt2jFkyBDmzJkD5AUtd3d3Rz6EiIiIlKKkmDjeXLWXrZZqYOR9H+tizeX2g0sYGJCG69MTMGpGOLlKERHnc2iwevHFFwHw9PRk1qxZfPPNN9SsWfOCCwQ///zzjixDRERESshMSSb6hxW8mVaHM+7VbO3V05MYc2YNjW/th9GwuRMrFBEpWxwarHbu3Gn376ysLA4cOODIhxAREZEryMzMJGflQmbtOMWCGt0w3QvuGuiUvI/H2lXDt914TZ0uIvIPDg1WQ4cOdeThLsmBAwf4888/2bdvH3v37uXUqVO4ubnx9ddfX9bxUlNTmTdvHhs3buT06dMEBATQvn17hg0bho+Pj4OrFxERcS4zNxdz7Qril/zAlFr92B3ewrbNzZrDfUHJ9B3eF4umThcRKZJD3x1vueUWRx7uksyfP5/Nmzc75Fhnz57lueee48SJE4SEhNC+fXuOHTvGkiVLiI6OZsKECfj5+TnksURERJzJNE3YEoX12y/ZmOPPu43vIcWt4AvEGpZMxveKoF6IJqUQESlOhfnaqWHDhtStW5fIyEgiIyN56KGHLvtYM2bM4MSJE3To0IGnnnoKFxcXAKZPn87SpUuZMWMGjz32mKNKFxERcQpzzzas38wg+9B+vojsxw81r7bbfm0tL0Z2boiXm0MnERYRqZAqTLAaNGiQQ45z+vRpfvvtN1xcXHjggQdsoQrgzjvvZN26daxZs4Y77riDgIAAhzymiIhIaTKPHsS64AvY/jsnvIKY3GYUB/xq2rZ7uMDDHcLoWc/fiVWKiJQvFSZYOUp0dDSmadK0adNCwcnNzY22bdvy888/88cff3DNNdc4pUYREZHLYcbHYi6ciblhNZgma6q35P2GQ0h3LZi9t26AB+O71aCmv4cTKxURKX8uO1jlD4ULDQ3lueees2u7FIZh8M4771xuGQ53+PBhACIiil6TIyIigp9//plDhw6VYlUiIiKXzzx7BvOHuZi/LIHcHDItbnzaYCAra3S063dDgwDubVMdD1cN/RMRuVSXHazi4+OBvKs4/2wrzxISEgAIDAwscntQUJBdvwsZM2ZMoTZ3d3dee+01AKpVq1Zou1xZrn/PaBUcHOzkSuRK07muPCrDuU5dNAfPTj1wCQ4ttl9ufCwZ61fjc+NwrOlppC2cTep3X2OmpwFw1Ls6k5rdwVGfguP4uLvwdO8G9GxQ9n9+leFcSx6d68qjopzryw5WjzzyCADe3t6F2sqzjIwMADw8ih4Ckd+emZlZajWJiEjllrpoDmc/fZO0xfMIfOXd84ar3PhYkp57jNy442Tt3Er2rq1YTycBYAKrQtvzScNBZFkKvhRtGuLHS/0aU8Pfs8hjiojIxbnsYFXU/UUV4Z4j0zQBHLbw4ZQpU4rdnpCQYHtMKR3534ZUhCusUjyd68qjop9rs0ELCA4lN+448c88gmXsBIwg+292zcR4rJOegYQ4sLiQGfWzbVuaiwcfNh3Ob0HN7fYZ1CSQO1oG45Z1lvj4s6XyXEqqop9rKaBzXXmUhXNtGAZhYWElOoYGUf+Dl5cXUHDl6p/yr1Sd74qWiIiIoxlBwVjGToDgUIiPxTr5WczEgg8gZmI81onj8kIVgDXXtm1/1TqM7/6sXajy83Dh/66pyb1tquPm4pgvEkVEKjuHBqv33nuPGTNmXHT/r776ivfff9+RJZRY/j1PSUlJRW5PTEy06yciIlIazheurH9uxvp/j8CZU3b9TYuFH7rfz9OtR3HCLBjm16y6F2/2q0u7cN/SfgoiIhWaQ4PV6tWrWbdu3UX3j4qK4pdffnFkCSVWp04dAA4ePFjk9vz2/H4iIiKlpVC4evoBzHdeguwsu35n2/Tg9SFv8KmlETnWv/cFhrcI4uXralPN263wwUVEpES0jtU/tGrVCsMw2LVrF2fOnMHfv2BxxOzsbH7//XcMw6B169ZOrFJERCorIygYY+AIzE+nwD/v0W3YnL/63MXkA67Ex+fYmqt6uTKmSxhXhfqUcrUiIpWHU++xSk5Odtq9SkuXLmX06NHMnDnTrr1q1ap07dqVnJwcPvnkE3JzC8apf/XVVyQnJ9OtW7dCiweLiIhcaaY1F+vCWXmh6p/b7hnNghvG8MwOiE8rCFWtw3x4s19dhSoRkSvMKVes0tLSWLVqFVlZWdSuXdshx9yyZQvffPONXVtOTg7PPvus7d9DhgyhTZs2QF6oi4mJ4dQp+zHpAPfccw979+5lw4YNjB49msjISI4ePcrRo0cJCQnh7rvvdkjNIiIiF8s8ewbrJ1NgZ7T9BouF0y7evL09iz98C9ZYtBhwZ8tgBjUNxOKgmW5FROT8ShSs5s2bx/z58+3aTp8+zfDhwy/6GB07drxwp4uQnJzM3r177dpM07RrS05OvqhjValShYkTJzJ37lw2bdrExo0b8ff3p2/fvgwbNgxfX93wKyIipcfctwvrh6/D6cSCRosLxmPP8adHGFPXxXDareBvU3UfV8Z2DadxsJcTqhURqZwMswSLKBUVrC6Wq6srV199NQ888IBtteXK6MSJE1rHqpSVhbUSpHToXFceFfVcm6aJueJ7zAUz4Jyh6bh7YP3PG8xN8mHe9kTO/SvSMXkvj9/cAb/QkFKvtzRU1HMthelcVx5l4Vw7Yh2rEiWaa665hmbNmgF5b/4vvfQSvr6+jB079rz7GIaBl5cXNWrUwN3dvSQPLyIiUmGZaSlYP38botfbb/DxI3HcZKbuzGRnfMEVLFcD7o1ZRd89yzCOLsIsYhFhERG5ckoUrIKDg20JE/LWdvL396dp06YlLkxERKSyMo8cwPrBaxAfa78hIJDN903gnahkzmZZbc01/NwY3y2cCHMY1slbIT4WMzoKo9fAUq5cRKTycugYvGnTpjnycCIiIpWKaZqYvy3HnPUR5GQXbGjWmpz6zfkqoD0Lt5y126dH3So83CEEbzcXwBPL2AmY0VFYFKpEREpV5b25SUREpAwxMzMwv3ofc/3PBY2GgTHwNmKvHsTkdbHsO5xh2+ThYvBQ+xCuq+ePcc6sf0ZQsK5UiYg4gYKViIiIk5knjuUN/Ys5UtDo54/lgbGs9anHtGVHSMsuGPpXx9+D8VfXoJa/c9aCFBGRwhSsREREnMi68VfML6ZBZnpBY/2mZN8/jun7c1gWHWPX//r6AdzftjoerpZSrlRERIqjYCUiIuIEZnY25txPMX/50a7duP5mjvUczqSoOA6fzrS1e7tZGNUxlG51qpR2qSIichEUrEREREqZmRCH9YP/weF9BY1ePhj3juanKo34aPlRMnMLVqeqH+jJ+G41CPXTMiUiImWVgpWIiEgpMrduwjp9KqSlFDTWjiTzgX/xwQGT1Tvtp1gf2Lgqd7WqjpuLgYiIlF0KViIiIqXAzM3F/O4rzKXf2LUbPfpysM+dTFp/kpizBVOs+7lbeLJzDdrX9C3tUkVE5DIoWImIiFxh5ukkrB+/AX/tKGh094A7H2NJ1auYviqGHGvB0L+mwV6M7VaDat5uTqhWREQuh4KViIjIFWTu/hPrx5Mg+XRBY1gt0u7/F+8edmH95jhbswHc0jyIW1tUw8WioX8iIuXJZQernTt3OqyIpk2bOuxYIiIiZYFptWIumY/5/UwwC9agMjr2YM8N9zNlUwInUwumWA/wdGFM1xq0DPVxRrkiIlJClx2sXnzxRYcUYBgGs2fPdsixREREygIzJRnrp1Nh++8Fja6umMMf4rvgdny1OpZzRv7RKtSbp7rUIMBLA0lERMorp7+Dm6Z54U4iIiLlhLl/N9aPXoekhILGaiEk3/dv3jrqQfQfBe0WA25vGczgpoFYDA39ExEpzy47WM2ZM6fI9s2bNzNt2jT8/PwYOHAgzZs3JygoCMMwSExMZNu2bSxatIjk5GQee+wx2rZte9nFi4iIlBWmaWL+tBhz3meQm1OwoVVHdvQfyZQtpzmVnmprDvZ2ZWy3GjQJ9nZCtSIi4mgOvWJ14MABpk6dSoMGDXjmmWdwd7dfyDAkJISQkBC6d+/Oq6++ypQpU5gwYQJ169Z1ZBkiIiKlykxPw5zxDubvawsaLRasN9/NvLBuzF2bwLnjMzrW9OXxTmH4ebiUeq0iInJlWBx5sO+++46cnBwefPDBQqHqXO7u7jzwwAPk5OTw3XffObIEERGRUmUeO4j1lTH2oSogkFNPvMoLLm2Ysz3RFqpcLQYPtqvO093DFapERCoYh16x2rNnD97e3oSHh1+wb82aNfH29mbXrl2OLEFERKTUWNeuxPz6A8jOKmhs0pItN47ira1nOZtZMOtfmJ8b47uFExno6YRKRUTkSnNosEpJSQHAarVisRR/McxqtZKVlUVWVlax/URERMoaMzMTc9YHmGtXFTQaBjn9buXrWtfy/cbTdv27163CIx1C8HbTVSoRkYrKocEqMDCQkydPsmnTJjp27Fhs302bNpGTk0P16tUdWYKIiMgVZcYex/rBa3D8cEGjbxXi7xzHpJMB7N192tbs7mIwsn0I19Xzx9CsfyIiFZpD77Hq0KEDAB999BE7duw4b7+dO3fy0Ucf2e0jIiJS1pmb12CdMMY+VEU2Zv0D/2PMPm/2JmbYmmv7uzO5b116RQYoVImIVAIOvWI1ePBg1q9fT0JCAi+99BKNGzemWbNmBAYG2qZb37FjB7t37wagWrVqDB482JEliIiIOJyZk405/3PMVYvs2rOuu5nP617P0j+S7dr71PfngbYheLg69PtLEREpwxwarHx8fHjhhReYOnUqBw4cYPfu3bYQ9U8RERGMGTMGHx8fR5YgIiLiUGZiPNYP/wcH/ypo9PIm5rbRTEoK4dD+glDl5Wrh0Y6hdK9bxQmVioiIMzk0WAFUr16dCRMmsGHDBtauXcuBAwc4c+YMAP7+/tSrV48uXbrQqVOnC05wISIi4kzmtt+xfjoFUs8WNNaK4JeBT/Hh7kwyczNtzZGBnozvVoMwv/MvNyIiIhWXw4MVgMVioXPnznTu3PlKHF5EROSKMq25mN/Pwvxxrl17xtU38HG9G/l5R4pd+42Nq3J3q2DcXPSFoYhIZXVFgpWIiEh5ZZ45hfXjSbBnW0GjuzuHhj7B5JSaHD9cEKp83S080TmMjjX9nFCpiIiUJVc0WCUnJxMfH09mZiZNmza9kg8lIiJSYuae7Vg/fgPOnCpoCw1n2Y3j+Gx/DtnWgrUXmwR7MbZrDYJ93JxRqoiIlDFXJFht3ryZefPmcejQIQAMw2D27Nm27SkpKbz11lsAjB07Fk9PrUIvIiLOY1qtmMsWYH77FZhWW3ta+2uZ1nAwUXvTbW0GMKRZECOuqoaLRdOoi4hIHocHq++++45Zs2bZtZmmafdvX19fPDw82LRpE9HR0boXS0REnMZMPYt1+pvw56aCRhdX9t78KJPTIzh5vCBUBXi68FSXGrQK04y2IiJiz6F32e7du5dZs2bh4uLC3Xffzaeffoq/v3+Rfa+++mog7+qWiIiIM5gH92J9+Sm7UGUNqs7COybyTGJNTqZm29pbhnrzZr8IhSoRESmSQ69Y/fjjjwAMGjSIfv36Fds3/56r/fv3O7IEERGRCzJNE/OXHzHnfgo5Obb2My278k7jYWw5XDCNusWAEVdVY0izICyGhv6JiEjRHBqs8hcD7tu37wX7+vn54enpSVJSkiNLEBERKZaZkYb5xTTMTb8VNBoWdgwYydSc+iTFFYSqIG9XxnWtQdPq3k6oVEREyhOHBqvk5GS8vLyoUuXiVpx3cXEhIyPDkSWIiIicl3n8MNYPXoPY47a2XP9Avuk/nrknXLCaubb29uG+PNE5jCoeLs4oVUREyhmHBit3d3cyMjKwWq1YLMXfvpWWlkZqaupFhzAREZGSsK77CfPr9yCrYMr0pCYdeLPpbWyPKbiXytUC97SuzoBGVTE09E9ERC6SQ4NVjRo12LdvH0eOHKFu3brF9t2wYQPABfuJiIiUhJmdhTnrI8zfltu1R1//AG/RhOTEglAV6uvGuG41aBDkVdpliohIOefQWQHbtm0L5E25XpzY2FhmzpwJQPv27R1ZgoiIVHDWlQsxE+Mv2M9MjMf63VdYJ463C1U5vv58ccsrvJzZkOTMgqF/V9fxY2q/ugpVIiJyWRx6xapv374sWbKEqKgo3N3duemmm+y2x8XFsXbtWhYtWkRaWhrVq1fn2muvdWQJIiJSgVlXLsSc8wnmT4uxjJ2AERRcZD8zMR7rq2Mh+bRd+8n6bZjS7A7+ii+YCdDdxeDBdiH0jvTX0D8REblshvnP1XtLaO/evbz66qukpaXZtbu7u5N1zrh2X19f/u///q/SDwU8ceJEoQWU5coKDs77IBYff+FvvKV807mueMzEeKyTn4X4WAgOtYWrc8+19eQJzFeegnT7v0Pre97Duy7NScu22tpq+bszvls4dQI8SvV5yOXT73XloXNdeZSFc20YBmFhYSU6hkOHAgI0aNCA119/nY4dO9p983duqGrfvj0TJ06s9KFKREQujREUjGXsBAgOhfhYrJOftRsWaN2/B/OFx+xCVZaXHx8PepHXrU3tQlWvSH8m9a2rUCUiIg7h8CtW50pJSeGvv/7i1KlTWK1WAgICaNSokWYCPIeuWJW+svCtiJQOneuK659XroJffZ+sHX9w5q2X4Jz31Ji6VzGp+V0cSikIVJ6uFh7tEEKPCH9nlC4lpN/rykPnuvIoC+faEVesHHqP1T/5+vrSpk2bK/kQIiJSCeVfucoPV/Ejh4DVatdndbc7+NCjJRnnhKp6VT0Y3y2cGlXcS7tkERGp4Bw+FFBERKQ0GEHBGI/9HxiGXahKd/fhnf4v8JbrVWTkFly96t+oKq9fX0ehSkRErgiHXrHKycnh9OnTuLq6EhAQYLctIyODuXPnsm3bNiwWC61bt2bw4MG4u+sPnIiIXDozIQ7zvVfthv4d8gllcrfRHE8t+N7Qx93CE53C6FTLzxlliohIJeHQYLVq1SqmT59Ojx49ePTRR+22TZw4kd27d9v+fejQIXbv3s0LL7yg6W1FROSSmH9txzrtVUhLyfs3sLxGJ6bXv5HszIJQ1aiaF+O61qC6r5uTKhURkcrCocFq69atAHTr1s2uffPmzezevRvDMOjatSvu7u78+uuv7Nq1i19//ZUePXo4sgwREanArL8tx/zqfbDmLe6b6uLJRz2e4DdrNbt+QyI8GdGpNq4WfXknIiJXnkOD1fHjxwGoV6+eXfuaNWsAuOmmm7jtttsAiIiI4NNPP2XNmjUKViIickFmbi7mvOmYqxbZ2vb61WRK+4eJsxYMK/fPSeXJHTNpteMslkYT4DyLCIuIiDiSQyevSE5OxsPDA19fX7v2HTt2AHDdddfZ2rp37w7A4cOHHVmCiIhUQGZqCta3X7SFKisG39fqwTNtH7cLVVeFeDO1V01auZ4tcp0rERGRK8WhwSojI6PQ/VInT54kOTmZatWqUb16dVu7p6cn3t7epKSkOLIEERGpYMwTx7C+Og52/gFAsps3E6+6lxmR/ckl72+OxYAHO9fhvz1rERQeYreIsBkd5cTqRUSksnDoUEBfX1+Sk5NJTU3Fx8cHgO3btwPQsGHDQv2tViuenp6OLEFERCoQc/vvWD+aBOmpAOzwj2BqiztJci0YGRHk5cpL/ZvSuqa/bXHJ/HWuzOgoLL0GOqV2ERGpXBx6xSr/3qqffvoJyAtOP//8MwDNmjWz65ucnExGRkahadlFRERM08S6/Dusb78M6ankYjC3znW80Pphu1DVPtyHN/vVpXVN/0LHMIKCFapERKTUOPSKVY8ePfjjjz+YOXMm27ZtIzk5mYMHD+Lp6Unnzp3t+u7atQuA8PBwR5YgIiLlnJmdjfnVe5jrVgGQ5O7HW01HsC0g0tbH1QJ3tarOwMZVtWSHiIiUCQ4NVl26dGHr1q388ssvtqnX3dzcePDBB21DA/OtW7cOKHwlS0REKi8z+RTW9ybC/rx1D6OrNuStZreR7FrwNyTE143x3WrQIMjLWWWKiIgU4tBgBfDII49w7bXX8tdff+Ht7c1VV11lN2kFQE5ODt7e3vTo0YM2bdo4ugQRESmHzCP7sU6bAEkJ5BgWZkVcz7e1r7Xr07W2H6M6huLj7uKkKkVERIrm8GAF0LhxYxo3bnz+B3V1ZeTIkVfioUVEpBwyf1+HdfpUyMrkpEcAU5uOYI9/Xdt2dxeD+9tW5/r6ARr6JyIiZdIVCVYiIiIXw7RaMRfPwVw0C4AN1ZrxbqNhpLoVDPOrWcWd8d1qULeqZpEVEZGy64oFq5ycHP7880/279/PmTNnAPD39ycyMpKrrroKV1dlOhGRyszMzMD62Zvw+zqyLK7MqNefJTW72vW5rp4/D7UPwdPVoZPYioiIONwVSTdLly5l3rx5513819fXl6FDh3LDDTdciYcXEZEyzkyMxzrtFTh6kBivakxuejsH/QpmifV0NXikQyjXRBSeRl1ERKQscniw+uCDD2xrVwEEBgYSGBgIQFJSEklJSaSkpPD5559z8OBBHn30UUeXICIiZZi5bxfW916Fs2dYXb01HzYcTIarh217RFUPxncLJ7yKuxOrFBERuTQODVZr1qyxhaqrr76aoUOHEhoaatcnNjaWb775hl9//ZXVq1dz1VVX0a1bN0eWISIiZZR17SrMr6aRYTX4pNEt/BTW3m57v4YB3NumOu4uGvonIiLli0OD1fLlywHo27cv9957b5F9QkNDGTVqFN7e3ixdupRly5YpWImIVHCmNRdz/ueYK77nsE8Ik5vewTGfENt2H3cLj3cMo3NtPydWKSIicvkcGqwOHz6MYRgMHTr0gn2HDh3K0qVLOXLkiCNLEBGRMsZMS8X68RuY27ewMqwDn9a/iSwXN9v2RtU8Gdu1BiG+GvonIiLll0ODlWEY+Pj44Od34W8c/fz88PHxwWq1OrIEEREpQ8y4GKzvvkxqfCIfNB3B2uqt7LYPbhrI7S2DcbVobSoRESnfHBqswsLCOHToEBkZGXh6Fr/eSEZGBunp6URERDiyBBERKSPMndFYP3ydfS5VmdzuSeK8gmzb/D1cGN0ljDY1fJ1YoYiIiOM49O7ga6+9FqvVypIlSy7Yd+nSpVitVnr27OnIEkRExMlM08S6ahG5b73IosA2PNP6UbtQ1TzEm6n96ipUiYhIheLQK1Z9+vRh586dzJkzh5ycHG688cZCV64yMjJYvHgx33zzDV26dKFXr16OLEFERJzIzMnGnPkhyVFreKfpXWyu1tS2zWLA8BbVuKVZEC4a+iciIhWMQ4PVe++9h7u7O15eXsyfP5+FCxcSGRlpt47V/v37ycrKwtvbGzc3N957771CxzEMg0ceecSRpYmIyBVmnj2D9f2J7DqZxpR2o0n0DLBtC/RyZWzXGjQP8XZegSIiIleQQ4PV6tWr7f6dlZXFrl27iuyblpZWqP+5FKxERMoP89hBst99lW99mjG7VW+shottW9saPjzZOQx/T4evSS8iIlJmOPSvXPfu3TEMDe8QEalMzOj1JH7xEW9F3syfVRvY2l0MuKt1MAMbB2LR3wYREangHBqsRo0a5cjDiYhIGWaaJuaP84hevYG3rnqEM+4FS21U93FjXLcaNKrm5cQKRURESo/GZYiIyCUzMzPJmfEOMxO8+faq+zGNgklmu9T2Y1THUHzdXYo5goiISMWiYCUiIpfEPJVI3AdvMsW/K3vq1LW1u1ng/rYh9G0QoGHhIiJS6ShYiYjIRTMP7GH91/N4t9bNpLgVzPAX7uvK+O41iaha/OLwIiIiFdUVCVanT5/mp59+Ys+ePSQmJpKZmYlpmkX2NQyDd95550qUISIiDpQZ9TMz1hzkh3pD7dqvrevHyA5heLk5dM15ERGRcsXhwWrjxo1MmzaNjIwMRx9aREScwLTmEvPNXCYlBnOgRhdbu6dhZWSncHrW83didSIiImWDQ4PVsWPHeOutt8jJyaF169a0adOGTz/9FG9vb+68805Onz7Ntm3b2LlzJ35+ftxyyy14eHg4sgQREXEgMz2N1TPm8IFXa9L9Cob51fUyGd8rkppV9B4uIiICDg5WixcvJicnh6uvvprHHnsMgE8//RR3d3d69uwJwODBg4mOjmbKlCmsXr2al156yZEliIiIg2SciOHjBVGsDOhs135DLXfu61oXdxcN/RMREcnn0L+KO3fuBGDQoEHF9mvdujV33XUX+/fv58cff3RkCSIi4gCHo7cxbvE+VgY0s7V5W7P4V6dqPNy9nkKViIjIPzj0L2NSUhIuLi7UrFnTrj07O7tQ3+7du2OxWFi7dq0jSxARkRIwTZNlP/zGuG0mR72r29obWFKYelMjukZWc2J1IiIiZZdDhwK6uroWWrvE09OTtLQ0cnNzcXEpWCzSw8MDT09P4uLiHFmCiIhcptT0LN5bEMUaQuCctX1vCkjlzr5tcXPR2lQiIiLn49ArVlWrViUtLY2srCxbW/Xq1TFNk8OHD9v1TUlJIS0tjZycHEeWICIil2HvsQTGzP0jL1T9zS8njeeaWLivv0KViIjIhTg0WIWHhwNw4sQJW1ujRo0AWLhwoV3f2bNnA1CjRg1HliAiIpfANE0WbdjPf36OI9a1iq29WUYMb15fk/ZtGjqxOhERkfLDoUMB27Rpw6ZNm9iwYQN16tQBoHfv3qxcuZKoqCiOHj1KnTp1OHLkCEePHgXg2muvdWQJIiJykc5m5vL2sp1sPOsGlryxf4ZpZVjOPobd0QdXD88LHEFERETyOTRYtWvXjt27d2OxFFwIq1OnDvfccw8zZszg2LFjHDt2zLata9eu3HDDDY4sQURELsLOk6lMXrWfBKu7ra1qZjJPVUvkqhtvLHS/rIiIiBTPocGqSpUqPProo4Xa+/btS4sWLVi/fj2JiYl4e3vTqlUrmjdv7siHFxGRC7CaJt9sO8nMPxOxGgWhqvWpvTzZOZSqbfVll4iIyOVwaLAqTnh4OEOGDCmthxMRkX84nZ7DlF8PszUhG4y8kQUu1lxuP7mGQcOvx6VmXecWKCIiUo6VWrASERHn+eNEKlN/O8rpc5YVDM5IYkzKBpo8dD+GX5Xz7ywiIiIXpGAlIlKOWVcuxGjdGSMouMjtuVaTWX8mMH9HAiYF9011it/GqGqn8Lv7cQxX/SkQEREpqcv+azp//nyHFTF06FCHHUtEpLKwrlyIOecTzJ8WYxk7oVC4ik/NZvLaGHbFp8PfocrVmsO9+xdzQ/ercOl5ixOqFhERqZguO1jNmzfPYUUoWImIXDqjdWfMnxZDfCzWyc/ahauNx87ydtQJzmZZbf1rpMUzdt83RN5zL0aTls4qW0REpEK67GDVpEkTTccrIuJERlAwlrETsE5+1haucp96hS+OmCzafcqub4/Y33nodBQ+Y5/FqB7mpIpFREQqrssOVv/9738dWIaIiFyOc8NV7NksJn+/k/1eobbtHrlZPLj3W671z8LlmdcxvLydWK2IiEjFpTuWRUTKOSMomLUjnue9LYmku3jY2uuknGDszq+p2a4NlttHYlhcnFiliIhIxaZgJSJSjmXmWPnk9ziW70uBc0JVn5j13LtvIR5D78al901OrFBERKRycGqw+uuvv8jJyaFp06bOLENEpFw6ciaTN347zpEzWbY275x0Ht0zny7x28DigqVNFydWKCIiUnlYSrLz8OHDGTlyZJHbPv/8c95///1i9580aRIvvfRSSUoQEal0TNNk5f7TjP3xoF2oikw+yqTNb9ElYTu4uIA1F+vkZzET451YrYiISOVQomBVnHXr1vHLL79csJ9pmleqBBGRCictO5epa4/zzvpYzplJnRuP/sqr0e8R6m5imfgJlgkfQXCobbZAhSsREZEr64oFKxERcawDSRmMXbSX1YdTbG1+2ak88+d07t2/GLfAICzPTMIICrbNFqhwJSIiUjoUrEREyjjTNFm0M4HxSw4Qk17Q3vT0ASb//hbtknZDcCiW8RNtCwQDClciIiKlSMFKRKQMS8nMZeLSv/gkOoGcv9+yDdPKLYdW8mLyL1TLOJ0XqsZOsAtV+f4ZrszoqFJ+BiIiIpWDplsXESmjdp04y+SfDxBvFkyjHpCZzFPHltBy6ECMpo9hXbkQo3XnIkNVvvxwZUZHYek1sDRKFxERqXQUrEREyhirafLtmr/46nAuVqMgVLVK2sOTgfFU/dd4DE9vgIsOSkZQMIZClYiIyBWjYCUiUoacOpvOW4u2Em0GgJE39M9i5jIibi2D+3XCpYkW+xURESmLFKxERMqIrVt2M2VbKqddA2xt1TJOMdbrME1G3Ynh6eW84kRERKRYJQ5Wp0+fZvjw4efdXtw2R8vKyuK7775j7dq1JCQk4OvrS8uWLRk+fDhBQUGXdKw//viDH3/8kf3795OWloaPjw/169enf//+tGjR4go9AxGpjHLSM5j93W/Mzw3HdPWxtXdI3sfjPepSpemtTqxORERELkaFuWKVlZXFyy+/zJ49e6hatSrt2rUjPj6eX375hS1btvDKK68QGhp6UcdavHgxX3zxBYZh0KhRIwIDA4mLi2PLli1s2bKFBx54gD59+lzhZyQilUH89h1MWXeCnT61wMhrc7XmcK/rYfrd2wuLp6dzCxQREZGLUqJgNXToUEfVUWLffvste/bsoWHDhjz33HN4/v1hJD8kvf/++7z44osXPE5ycjIzZ87E1dWV559/nsaNG9u2rV+/nqlTp/Lll1/SvXt322OIiFwqMzODTQsW83ZmBGd9atraw7JOM76NP5Et+zuxOhEREblUJQpWt9xyi6PqKJGcnByWLl0KwP33328XeAYMGMDq1avZtWsXBw4coF69esUea+/eveTk5NCqVSu7UAXQqVMnateuzeHDhzl27Bj169d3/JMRkQova9c2vli+lUXV2oFbQXt3SzyPDGuHt4/upRIRESlvKsRQwN27d5OamkpISAgRERGFtnfs2JHDhw+zefPmCwYrNze3Yrfn8/X1vaxaRaTyMjPSOfHNHCYn12BftXa2dndrNiMbuHFdx24YhuHECkVERORyVYhgdfjwYYAiQxVgC1P5/YoTGRmJt7c327dvZ/fu3XZXrTZs2MCRI0do1KjRRd+vJSICYO7aym/fLef9Gr1Iq1JwRaq2kcb4GxpRu5pPMXuLiIhIWVchglVCQgLAeWf+CwwMtOtXHB8fHx5++GHefvttXnjhBdvkFSdPnmT//v20atWKRx999KJrGzNmTKE2d3d3XnvtNQCqVat20ccSx3B1zXvZBwcHO7kSudLKwrm2pqWS8Nk03jtssLz2jXbbbqztyZiBXfBwdXFSdRVHWTjXUjp0risPnevKo6Kc6woRrDIyMgDw8PAocnv+PVf5/S6kU6dO+Pr6MnXqVHbv3m1r9/f3p1mzZvj5+ZWwYhGpDDKj17Pj4494o0ZfDtcIs7V7G7n8u3cjejcNK2ZvERERKU8qRLAyTbNE2/9p0aJFfPXVV7Rv355hw4ZRvXp1Tp48yZw5c/jqq6/Yu3cvY8eOvahjTZkypdjtCQkJl1yflEz+tyHx8fFOrkSuNGedazMtBevc6fy0/xQfN7idTBd327ZIX4PxPRsQ5ueq16AD6fe68tC5rjx0riuPsnCuDcMgLKxkX3haHFSLU3l55d2vkJmZWeT2/PaLmR59586dfPnll9StW5cxY8ZQu3ZtPD09qV27NmPHjiUiIoINGzawdetWxz0BEakwzD83kfriWN5KDOLdxsPtQtWNDf3534AGhPm5F3MEERERKY8qxBWr/PuUEhMTi9yelJRk1684q1evBvJmErRY7HOnxWKhQ4cOHDx4kB07dtCyZcuSlC0iFYiZmoI552MObNvN5KZ3EONdME7czxWe6BpOh5oaRiwiIlJRVYhgVadOHQAOHjxY5PYDBw7Y9StOfgjLvwr2T/ntKSkpl1yniFRM5h8byP3qPZb6NObzNo+RbSlYtqFJNU/Gdgsn2OfilnIQERGR8qlCBKvGjRvj7e1NXFwcBw8eLDTt+oYNGwBo06bNBY/l7+8PwP79+4vcnt9evXr1kpQsIhWAmZKMOetjUrZsYFqjW1gf3MK2zQBuaR7ErS2q4WLR2lQiIiIVXYW4x8rV1ZW+ffsCMH36dLvZ/xYvXszhw4dp3Lgx9evXt7UvXbqU0aNHM3PmTLtjdejQAYA1a9awefNmu22bNm1izZo1GIZh6ycilZP5+zqsz49i9+6DjGk32i5UBXi68N+etbi9ZbBClYiISCVRIa5YAQwePJht27axZ88ennzySRo3bkxCQgJ79+7Fz8+v0NpTycnJxMTEcOrUKbv29u3b06lTJ9avX8/rr79OZGQkwcHBxMfH265W3XrrrdSoUaPUnpuIlB1m8mnMmR+S+/s6vq/VnZkRfcm1FKxD1SrUm6e61CDAq8K8vYqIiMhFqDB/+d3d3XnhhRf49ttvWbNmDZs2bcLHx4cePXowfPjwi16I1zAMnnrqKX7++WdWr17NkSNHOHToEN7e3rRu3ZobbriBVq1aXdknIyJljmmamJvXYM78kDOZubzd4l6igxrbtlsMuL1lMIObBmIxdJVKRESksjFMLaLkVCdOnNA6VqWsLKyVIKXDUefaTD6F9esPYEsU2wPqMbXJCE55VLFtr+btyriuNWhS3btEjyOXT7/XlYfOdeWhc115lIVz7Yh1rCrMFSsREUczTRNzw2rM2R+Tm5rCvLq9mV/nOqxGwe2pHWr68kSnMPw8XIo5koiIiFR0ClYiIkUwTydh/eo92LqRRPcqvNnqIXYERNq2u1oM7mkdzIBGVTE09E9ERKTSU7ASETmHaZqYUT9hzvkE0lL5PbAx7zQeRrK7r61PmJ8b47qGUz/I04mVioiISFmiYCUi8jczKSHvKtW2zWQbLsys15/va/ew69O9ThUe6RiCt5uG/omIiEgBBSsRqfRM08RcswJz3nRITyPOsypTmt7O3iq1bX3cXQweahdCr0h/Df0TERGRQhSsRKRSMxPjsX7xLuyMBiCqWnOmNb6FNFcvW59a/u78q1s4tQM8nFWmiIiIlHEKViJSIVhXLsRo3RkjKLjYfmZiPGZ0FMZ1N2L+ugxz/meQkU6WxZXPIgewLLyLXf/ekf482C4ED1fLeY4oIiIiomAlIhWAdeVCzDmfYP60GMvYCecNV2ZiPNbJz0J8LOYvP0JcDADHvYKZ3Ox2DvnWsPX1crXwaMdQutetUuSxRERERM6lr2BFpNwzWneG4FCIj8U6+VnMxMILDJqJ8VgnPQPxsYBhC1U/h7RhfLsn7UJVZKAHU/vVVagSERGRi6ZgJSLlnhEUjGXshPOGKzMxHuvr/4aEuPwW0l3cebvxMN5pcisZLu62vjc2qsr/+tQhzM8dERERkYulYCUiFUJR4So3PpacuBisL4+GpARb30M+ofyr3Wh+CW1na/N1t/BMj3AeaBeCm4veGkVEROTS6B4rEakw8sNV/n1U8Q8PhVwrYMLf/7u8RiemN7iJbKNgHaomwV6M7VqDYB835xQuIiIi5Z6ClYhUKLZw9cyDkJtra0919eS9prcSFdi0oC8wpFkQI66qhotFa1OJiIjI5VOwEpEKxczNxfrDXLBabW17/WoxudV9nHTxsbX5e7owpksNWoX5FHUYERERkUuiYCUiFYZ59gzWd1+BA3sAsGKwqObVfFXvhv9v774DoyrTt49fM+mFJJBGQichdJCiArKgFHdXRV30J6yuuq6s66IIAiq7uIqvdaXbFWzoYgVZDIqKCEiXXgIECISShFRSJqTMzHn/YDMhUsMkmWTm+/kr3s+ZkzseM86V8zzPkc1cOfWvW9NAje8Xq8YBvAUCAICawacKAG7BOLRf9tefk/LzJEkFPoF69Yo/a3NQa8cxZsOuPyYE6bbeLZj6BwAAahTBCkCDZ//5exn/edOxpmp3aFvN7H6vcs0BjmPCyws1ftdH6phUInPc89J5HiIMAABwOQhWABoso7xcxqfvyFj1nSTJJpMWtBqsz9sMlV2Vd6SubBasMe0bKzi5xLEVu3nC8zIRrgAAQA0hWAFokIzcbNnfekk6lCxJyvUN0ayOf9SuxnGOY7zNJj3Uv42ua+4jk8kk44yt2I2t62QacrOr2gcAAG6GYAWgwTH27ZT97ZelwnxJ0pYmCXql0x9V4F25w1/TYB89P6yzOkY3UlZWlqTKrdiNretkJlQBAIAaRLAC0GAYhiFj2WIZX74v2e2ymsya3+a3WtTyuirH9W/VSKOvaqrW0Y3OOocpPJI7VQAAoMYRrAA0CEZpiYwPX5Xxy8+SpEz/xprR6S4lh7R0HOPrZdJfe0draFyoTCZ2/QMAAHWHYAWg3jMy02R/40XpeKokaX1EF73e4Q5ZvP0dx7QI9dVj/ZupVZifq9oEAAAejGAFoF4zdvwi+9wZ0imLysze+jDuRn3b7JoqxwyJC9Vfe0fL39vsoi4BAICnI1gBqJcMu11G4mcyvv5EkpQWEKHpne7SoUbNHMf4e5s1+qpoDWwT6qo2AQAAJBGsANRDRnHR6btUOzdJklZG99DbCcNV4lU5za9tYz891r+ZYkN8XdUmAACAA8EKQL1iHDss+xsvSFkZKjH7aG67W7U85soqx9zYvrHu6xEpHy+m/gEAgPqBYAWg3rBvXCXjw1elslKlBjXV9E536VhQtGM8yNesR/rEqE+Ls7dRBwAAcCWCFQCXM6xWGQs+lLHsvzIkfR9ztd6Pv1llXj6OY9pHBGjiNbGKCvY5/4kAAABchGAFwKWMgjzZ354qJe+Sxctfb7a/TWujulc55rZOTXRn90h5m3k2FQAAqJ8IVgBcxkjZJ/ubL0knc7S/UXPN6HSXTgSEO8ZD/bw0rl+MesYGu7BLAACAiyNYAXAJ+6qlMj55R4bVqsTmv9FHbX8vq7nyLalbdKAevSZWTQJ4mwIAAPUfn1gA1CmjvEzG/LdlrP5BBT6Beq3Ln7QpopNj3GySRnaN0O2dw+XF1D8AANBAEKwA1BkjJ0v2N1+UUg8oKbS1ZnS6U7l+YY7x8ABvTbgmVp2jA13XJAAAwGUgWAGoE8ae7bK/M1W2okItbDVIn7W+XnZT5XOoescGaWzfGIX487YEAAAaHj7BAKhVhmHI+H6RjAUfKtcnSLO7j9LOxu0c495m6Z4ronRzh8YymZj6BwAAGiaCFYBaY5SckvHhqzI2rda2xu00u+NI5ftWPtw3OthHE6+JVUJEgAu7BAAAcB7BCkCtMDKOy/7mi7KmH9OnbX6nha0GVRm/pmUjPXR1UwX5ermoQwAAgJpDsAJQ44xtG2R/b6Yy7b6aecWD2hfa2jHm62XS/b2i9Nv4MKb+AQAAt0GwAlBjDLtNxtefykj8TBsiOuu19v8ni0/lDn/NQ3z1WP9YtW7s78IuAQAAah7BCkCNMCxFss+drvLd2/Rh/M36pnn/KuOD2obqb1dGy9/bfJ4zAAAANFwEKwBOM44ekv3NF5VWZNWMng8ppVFzx5i/t0kPXtlU17UNdWGHAAAAtYtgBcAp9g0rZcx7VavCOumtXrepxNvPMdamsZ8m9o9V8xC/C5wBAACg4SNYAbgshtUq48v3deqnpXq33S36MeaqKuM3JITpvp5R8vVi6h8AAHB/BCsA1Wbk58n+9r+VmpajGb3G6GhQU8dYkI9ZY/rEqG/LRhc4AwAAgHshWAGoFuPgXtneeknLAuL1bs+7VObl4xhLCPfXxP6xig72dWGHAAAAdY9gBeCSGIYhY+VSWb6Yp7fibtHq6CuqjA/v1ER3dY+Ut5lnUwEAAM9DsAJwUUZZqYz5b+nA9r2a3uMhZQREOMZC/Lw0rm+MejULdmGHAAAArkWwAnBBRk6mbG++pERbU33U8yFZzZVvG12iAzW+X4zCA30ucAYAAAD3R7ACcF5G0jblv/eaXmvxe/0S0dlRN0sa0TVC/9clXF5M/QMAACBYATibYRgyvluopGWrNKPjKOX4hznGmgR4acI1zdQlOtB1DQIAANQzBCsAVRglxbK+/4oWZvvp0ysekN3k5RjrFRuksX1jFOrPWwcAAMCZ+HQEwMHIOKact2drdpPfaEfbBEfdyyTdfUWkbunYRGYTU/8AAAB+jWAFQJJkbF2vLQv+q1fi7tBJ38qH+0YFemnib5qrfUSAC7sDAACo3whWgIcz7DZZF83XJ3sLtLDD3TJMZsdY3xbBerhPjIJ9vS5wBgAAABCsADdkX7ZYph59ZQqPvPBxR1OU9d6bmhE5SHtbXemo+5gM3d+7qX7XLkwmpv4BAABcFMEKcDP2ZYtlfDZXxvJEmSc8f95wZd+5SRvmL9Br7UeqyCfIUY8NNOnxa1urTWP/umoZAACgwTNf/BAADYmpR18psqmUlSH79MkycrLOOqbk+8Wa+81WvdTl3iqh6rqWQZpxUztCFQAAQDURrAA3YwqPlHnC8+cMV4a1XMfee0f/TAnUkua/cbzGT3Y90qepxv2mhQJ8eFsAAACoLj5BAW7oXOHKfmi/Vr36jiZ6XaWDjZo7jm3tb9eMm+I0OC7MdQ0DAAA0cAQrwE2dGa5Kc3L0xpdrNSNqsE55V07z+10LP718Swc1D/VzYacAAAANH5tXAO6scbiOXjFI00421dGgpo5yoFGuh/o2U/+4Ji5sDgAAwH0QrAA3Zc/P07L5izUnqIfKgnwd9XYFRzThxq6KaUmoAgAAqCkEK8ANWZJ26c0f9+nnJldXqd98dJXuSvlWPkcjZVxgK3YAAABUD2usADdi2G3a/9/FmrDmpH5u0tlRb1Ru0eQuPvrLX/8gn4jIC27FDgAAgOojWAFuwp6fq6/f/kSTCtoqPTDCUe9UkKoZQ5rpqu5xF9yKHQAAAJePYAW4gYKd2/Xixz/r3ZDesppPz/A1GXbdkbFGz97eQ1HNKzeuIFwBAADUPIIV0IAZdpuSvlqsRzcWa2NYe0e9cWmBphz6Qnf++WZ5R0ad9bpfhytj67q6bBsAAMDtsHkF0EDZTuZq4affaX5wN9n9vRz1Hn7FeiQyS41vGX3BzSkqwpWxdZ3MQ26ui5YBAADcFsEKaIDytm/TrDXHtS20h6NmNuz6Uxtv/aFfD5lNPS/pPKbwSJkIVQAAAE4jWAENiGG3aftXSzQzv6lOhsY56pH2Yk24ro06Nm/swu4AAAA8F8EKaCCsudn65PPlWhDcRYZf5fLIq/0tGnNTdzXy49cZAADAVfgkBjQAWVu3asaGLCU16uaoedut+ks7P91wdU+ZTCYXdgcAAACCFVCPGTabNn71jV4tilVho5aOeoy9SI8NjVdc0zDXNQcAAAAHghVQT5XlZGvelyv1dXBnyaeyPiCwSH+/sYcCfb3O/2IAAADUKYIVUA+lbd6iaZtP6mBwZ0fNz16uBzoGaHCvXkz9AwAAqGcIVkA9YthsWr3gG71xqrmKg2Id9Zb2Qj322/ZqGRXiwu4AAABwPgQroJ4oycrUuwvX6vvgDlV+M68PLtL9N/SUvw9T/wAAAOorghVQDxzZuFnTthcpNbiDoxZoK9XorsH6TY/eLuwMAAAAl4JgBbiQvbxcPy78TnNKW6o0MNpRj7fna+KNnRQT3siF3QEAAOBSEawAFyk+kak3/7tRq4LipTNm+Q0LKdK9N1wlHy82qAAAAGgoCFaACxxcv0lTd5cqPSjeUQu2ndIjV4Tq6m5M/QMAAGhoCFZAHbKXl+mbL3/Q+9ZWsvoHO+od7XkaP6yrohoHX+DVAAAAqK8IVkAdKUxP16uJ27UhME4yn66ZDLtub2zRH3/fR15mpv4BAAA0VAQroA7sWfOLpu+zKSuwtaMWZi3Wo72b6IrOnVzXGAAAAGoEwQqoRbbyMi364kd9bG8pu1/lDhXdjRw9emsPNQ4NdGF3AAAAqCkEK6CW5B1L06ylu7UtoI30v1l+ZsOmOyOKddtv+8lsYuofAACAuyBYAbVgx88bNeOASXkBLRy1iPJCTegTpU4dOruwMwAAANQGghVQg6ylZfrsy+X6wmgpw9fsqF9lZGnM7b0UEszUPwAAAHdEsAJqSPaR45r+/T4lBbR2TP3ztlv15+hTumlof5mY+gcAAOC2CFZADfhlxQbNPuyjwoBYRy2m7KQm9m+m+HZdXNgZAAAA6gLBCnBCWUmpPl6wSv9VC8mnsv4bndDfR1ytoEB/1zUHAACAOkOwAi5TxuFjmvbjQe33r9ygwtdWpr/Glmro4AFM/QMAAPAgBCvgMqz+cYNeP+arYv9oR61FWa4eG9hCrdq2uMArAQAA4I4IVkA1lJw6pfcWrNF3puZVfnuGKk2jRl4j/wA/1zUHAAAAlyFYAZfo6MEjmrryiFL9mjtqAbZSjW5RrgHXDXJhZwAAAHA1ghVwCZZ9v17vZASq1C/CUWtbmqXHBrdVbKtmLuwMAAAA9QHBCriA4uJTenvBOq0wx0pelfWbTMd1752/ka+/r+uaAwAAQL1BsALOIyU5VdPWpOm4b+WzqYKtp/RIa5uuHjjYhZ0BAACgviFYAb9iGIa++W6j3s8KVLlvY0e9Q0mGJlzfXlEtYlzYHQAAAOojghVwhsLCYr2+aKPWmZtK5tM1k2HXcPNx3Xn3QHn7MvUPAAAAZyNYwa3Zly2WqUdfmcIjL3ickZOlfctXarqlpTJ9mjrqoeVFejTepB79h9Z2qwAAAGjAzK5uAKgt9mWLZXw2V/bpk2XkZJ33OFt2phbO/Uz/LOmoTJ8QR73bqeOadX1z9ejfqy7aBQAAQANGsILbMvXoK0U2lbIyzhuu8lKP6rlP12te8yGymU9v+2c2bLrL64im3DtATWKbnvUaAAAA4NfcaipgWVmZFi1apDVr1ig7O1vBwcHq3r27RowYofDw8GqfLyMjQ4sWLdLOnTt18uRJ+fv7KyYmRldddZVuvvnmWvgJUJNM4ZEyT3he9umTHeHKPOF5KfL0tMAdG7Zr5u4S5TZOcLwmvCxfEzr4qHPf613VNgAAABogt7ljVVZWpmeffVZffvmlSkpK1Lt3b4WHh2vFihV64oknlJGRUa3zbdy4URMmTNBPP/2k4OBgXXnllWrTpo0yMzP1ww8/1NJPgZpWEa7OvHNVmpGmN99frKf3+yjXL9RxbO9TRzTz963VuW9PF3YMAACAhsht7lh99dVX2rdvnxISEvTkk0/K399fkpSYmKh58+bpzTff1DPPPHNJ5zp8+LBmzZqlgIAAPfbYY+rQoYNjzG6369ChQ7XyM6B2nHnnKje/WE+99b12hcVJptPj3nar7vE9rmH3DpLZx8e1zQIAAKBBcotgZbVatXTpUknS/fff7whVknTTTTdp5cqV2rNnj1JSUtS2bduLnu/999+X1WrV6NGjq4QqSTKbzYqLi6vZHwC1zhQeqa3Dx2n2zmIV+AY76k1LcjWxi7/aXf1bF3YHAACAhs4tpgLu3btXFotF0dHRatOmzVnjV199tSRp06ZNFz3XsWPHtGfPHsXExKhXL3aDcwdWu6H3f9ilZ/eZq4SqazK3aXr/Jmp3NVP/AAAA4By3uGOVmpoqSecMVZIcd6kqjruQXbt2SZK6deumsrIyrV27VikpKZKkVq1aqW/fvgoMDKyJtlEHMgrLNP2b3Uq2BjhqvrZy3X9gsYakb5Apa7mMCc9f9DlXAAAAwIW4RbDKzs6WpPPu/NekSZMqx13I0aNHJUm+vr56/PHHlZaWVmV8/vz5mjBhgjp16nRJvY0fP/6smq+vr1566SVJUkRExCWdB9X30540vbh0n4pMlaGqhSVDT7c3q9N9TyrrHw/KduK4TDOfUpPnXpNXJFuruxtv79NvcZGRBGd3x7X2HFxrz8G19hzucq3dYipgSUmJJMnPz++c4xVrriqOuxCLxSJJ+uabb1RUVKSJEyfqgw8+0KxZs9S/f38VFhZq6tSpysvLq6HuUdNKrXZNXbJDk787qCJT5WYUgzN+0VuDY9Rt5Ah5RzU9Haaim8l24rhyn3xYtqzq7RwJAAAAVHCLO1aGYTg1fia73S5JstlsGjNmjLp37y5JCgwM1COPPKL09HQdPHhQ3333nUaOHHnR882YMeOC49nZ2dXqDxd2vKBMLy87oMOnKv9m4G8t1YMHF2ng/XfJ2ipeVqtVkpQrLxmP/j9p+mTZThxX1j//LjPTAt1KxV++srLOfjg03AvX2nNwrT0H19pz1IdrbTKZFBMT49Q53OKOVUDA6alepaWl5xyvqJ+5W+D5VBzTpEkTR6g603XXXSdJ2r1792X1itqzPOWkxidWDVVtCo9r2q63NfDhB2RuFX/Wa379nCtj67q6bBkAAABuwi3uWFWsU8rJyTnneG5ubpXjLiQqKkrS+ed4VtQLCgqq3SdqR4nVrrfXp2l5apHO/FvBDWlrdW9YvvwmPXPBu1AV4crYuk7mITfXQccAAABwN24RrFq1aiVJ531w75m7+l1M69atJUlFRUXnHC8sLJR0aXe/UPsO55Vo6sojOmaxO2pB5cV6+PhS9f3THTKd4y7VuZjCI2UiVAEAAOAyuUWw6tChgwIDA3XixAkdOnTorG3XN2zYIEnq2fPizyvq2rWr/Pz8lJGRoezs7LPuciUlJUk6/9buqBuGYei7Ayf17i8ZKjNMjnr7/MN6tGSzmo55SKaQMNc1CAAAAI/iFmusvL299bvf/U6S9N5771XZ/S8xMVGpqanq0KGD4uMr714sXbpU48aN0/z586ucy8/PT7///e9ls9k0d+7cKufatm2bVq5cKZPJpCFDhtTyT4XzsZTZ9PLqNL258USVUDU8dbmea3xMTR95glAFAACAOuUWd6wkafjw4dq5c6f27dunsWPHqkOHDsrOztb+/fvVqFEjjR49usrxBQUFSktLO+e26bfffrv27NmjLVu2aOzYsYqPj1dBQYGSk5NlGIZGjhxZJaSh7uzPOaWpPx/XCYvVUQspK9LY5C/Uc9hvZe43yIXdAQAAwFO5TbDy9fXV008/ra+++kqrV6/WL7/8oqCgIA0cOFAjRoyo1oN4K861ePFi/fzzz9q2bZt8fHzUpUsX3XjjjZc0pRA1yzAMLd6bp3lbM2U9Y3f6rnn7NTb9e0U8OPaS11MBAAAANc1k8BAll0pPT+c5VhdRUGLV7HXp2pRmcdTMhl0jDn+v4X5Z8vnbY9Wa+lcfnpWAusG19hxca8/BtfYcXGvPUR+udU08x8pt7ljBPe3OLNb01WnKOVU59a9J6Uk9mvSJuvTuItPtD8vkzX/GAAAAcC0+kaJestkNfbk7R5/uyJb9jHqvnD0as3+hQv94H+upAAAAUG8QrFDv5J6yauaaNO04Ueyoedut+lPKtxpWvEdeE59mPRUAAADqFYIV6pUtaUWatTZd+aU2Ry36VI7GJ/1H7WLCZH50BlupAwAAoN4hWKFesNoNzd+epQVJuVXq/TK36+/7Fij42qEy3X4f66kAAABQL/EpFS6XWVSuaWvStC/7lKPmayvXfQcW6/qsLTLf8xDrqQAAAFCvEazgUuuPFuqV9emylFVuUdHMckITk/6jVn5WmSf9m/VUAAAAqPcIVnCJMptdH2zJ1JLkk1Xq16X/or/uXyT/+PYy/+1x1lMBAACgQSBYoc6lFZRp6urjSskrddT8baX6W/JCDTyxVabBw1hPBQAAgAaFT66oUysP5euNjSdUYq2c+tem8LgmJP1HseX5Mt03jvVUAAAAaHAIVqgTJVa75mw6oWUH86vUf398je49uES+YWEyT2A9FQAAABomghVqXerJUk1dfVxH88sctUDrKT289wv1yd4lJXRhPRUAAAAaNIIVao1hGPrhYL7mbDqhMpvhqCfkp2r8nvmKKsljPRUAAADcAp9mUSuKy216fUOGVqcWVqnfeuQn3XnoO3l7ecl031iZ+w12UYcAAABAzSFYocbtzzmlaavTlFFU7qiFlBXpkb2fqmdustQ4QubR/5CpdTsXdgkAAADUHIIVaoxhGPp6X54+3JqpMzb9U5e8gxq35xM1KSuQEjrL/LcnWE8FAAAAt0KwQo0oKLXp1fXp2nisyFEzG3bdcXiZbkv9UV4yZBp0k0z/9xfWUwEAAMDt8AkXTkvKLNa0NWnKKbY6ak1K8/Vo0ifqnJ8iefvIdPdo1lMBAADAbRGscNlsdkMLknL0yY5s2Ss3/VPPnD0as/dzhZZbWE8FAAAAj0CwwmXJO2XVzLVp2p5R7Kh52W36U8q3GnbsZ5llsJ4KAAAAHoNghWrblm7RjLVpyi+xOWpRJbkav/s/Sig8KkmspwIAAIBH4VMvLpnNbmj+jmwt2J2jM2b+qW/mDo1O/lJB1hLWUwEAAMAjEaxwSbIs5Zq+Jk17sk45aj52q+47sFi/TVsvk8R6KgAAAHgsghUuasOxQr2yLl1FZZUPp2p2Klvjd32kNpb00wXWUwEAAMCDEaxwXuU2uz7cmqWv9+VVqV+XsVmj9n+lAFuZJNZTAQAAAHwSxjmlF5Zp6urjOphb6qj5G1b9de+Xuu7EltMF1lMBAAAAkghWOIdVhwv0xoYMnbJWTv1rVZqjCdvfU/PirNMF1lMBAAAADgQrOJRa7Zqz6YR+OJhfpf7bzE36896F8rNbTxdYTwUAAABUQbCCJOlIfqmm/nxcR/LLHLVAk00P7f5EfTN3OGqspwIAAADOxqdjD2JftlimHn1lCo901AzD0LKD+Xpn0wmV2SqfTtWuJFPjt72r6JL/bVzBeioAAADgvAhWHsK+bLGMz+bKWJ4o84TnZQqPVHG5TW9uOKFVqQVVjr3l2CrdefBb+Ri20wXWUwEAAAAXZHZ1A6gbph59pcimUlaG7NMnK/t4hsZ/e7hKqGpktmvyzvd074HEylCV0FnmJ2cQqgAAAIALIFh5CFN4pMwTnneEq5DXn1akb+V4Z3OhZqx+Qb1y9la+ZtBNMj/6LJtUAAAAABdBsPIgZ4Yrr6x0jV37qhr7mnRHyR5NWf6cwsv+d/fKy1um+8bK/McH2KQCAAAAuAR8avYwFeHKPn2yGqen6LXMJxVgq3wIsEIby/zwk0z9AwAAAKqBO1YeyBQeKdP94yWpaqhq007mp2YTqgAAAIBqIlh5qtAmkslU+c8mk0yjJrKeCgAAALgMBCsPZORkyZjxpGT877lVZrNkGDJmPS0jJ8u1zQEAAAANEMHKwxg5WbJPnyxlZUiRTWV6cY7ML8ypshU74QoAAACoHoKVB/l1qDJPeF7miOiztmInXAEAAADVQ7DyEOcKVabwSMc44QoAAAC4fAQrD2FsXXfeUFXh1+HK2LrOBZ0CAAAADQ/PsfIQ5iE3yy7J1KPvOUNVhYpwZWxdJ/OQm+uuQQAAAKABI1h5kEsNSqbwSJkIVQAAAMAlYyogAAAAADiJYAUAAAAATiJYAQAAAICTCFYAAAAA4CSCFQAAAAA4iWAFAAAAAE4iWAEAAACAkwhWAAAAAOAkghUAAAAAOIlgBQAAAABOIlgBAAAAgJMIVgAAAADgJIIVAAAAADiJYAUAAAAATiJYAQAAAICTvF3dgKczmUyubsFj8e/ec3CtPQfX2nNwrT0H19pzuPJa18T3NhmGYdRALwAAAADgsZgKCAAAAABOIljB40yaNEmTJk1ydRuoA1xrz8G19hxca8/BtfYc7nKtWWMFj1NWVubqFlBHuNaeg2vtObjWnoNr7Tnc5VpzxwoAAAAAnESwAgAAAAAnEawAAAAAwEkEKwAAAABwEs+xAgAAAAAncccKAAAAAJxEsAIAAAAAJxGsAAAAAMBJBCsAAAAAcBLBCgAAAACcRLACAAAAACcRrAAAAADASd6ubgBwhaKiIo0bN04FBQWKjY3VrFmzXN0SatjJkye1aNEibd26VdnZ2fL19VVUVJS6du2qP/3pT65uDzUkOTlZixcv1r59+1RUVCR/f3+1adNG119/vfr06ePq9lANKSkp2rFjhw4cOKD9+/crLy9PPj4++s9//nPB161cuVJLly7VsWPH5O3trYSEBA0fPlzt27evo85RXdW51na7Xfv27dPmzZuVlJSkzMxMFRcXKzw8XF27dtWtt96qqKgoF/wUuBSX+3t9pmeffVY7d+6UJL3zzjsKCwurpW6dR7CCR/rwww9VWFjo6jZQS5KTk/Xiiy/KYrGoefPm6t27t0pKSnTs2DElJiYSrNzEunXrNGvWLBmGobi4OHXu3Fl5eXnavXu3du3apVtuuUV33XWXq9vEJfryyy+1adOmar3mww8/1JIlS+Tr66tu3bqpvLxcO3bs0Pbt2zV+/HhdddVVtdQtnFGda52Zmamnn35aktSkSRMlJCTIbDbrwIEDWrZsmdasWaN//OMf6tChQ222jMt0Ob/XZ1qxYoV27twpk8kkwzBqsLPaQbCCx9m5c6dWrlypIUOGaNmyZa5uBzUsNzdXL774osrLyzVx4sSzPlgdOHDARZ2hJtlsNr377rsyDEPjxo1Tv379HGPJycl65plntHjxYg0ePFhNmzZ1Yae4VAkJCWrdurXi4uIUFxenBx544ILH79q1S0uWLFGjRo303HPPKSYmRtLp6z9lyhS98cYb6tSpk4KDg+uifVRDda919+7d9Yc//EGdOnVy1MrLyzVnzhytWLFCr7zyil555RV5e/Oxtr6p7rU+U0FBgT766CN1795daWlpysrKqsVOawb/BcKjlJWVac6cOWrevLmGDRtGsHJD8+fPl8Vi0V/+8pdz/rU6Pj7eBV2hph0/flwFBQVq1qxZlVAlnf4feffu3bVp0yalpKQQrBqIW2+9tVrHf/3115Kk4cOHO0KVdPr6Dx06VN9++61++uknDRs2rCbbRA2ozrVu2rSpJk+efFbdx8dHo0aN0saNG5Wdna3k5OQqwQv1Q3V/r8/0wQcfqKSkRPfff7+effbZmmuqFrF5BTzKF198oRMnTmjUqFHy8vJydTuoYUVFRVq3bp0CAwM1aNAgV7eDWuTj43NJx3G3wj2VlZVp165dknTOtXQVtc2bN9dpX6hbvr6+jlCdm5vr4m5Qk7Zt26bVq1dr+PDhDeqPY9yxgsdITU1VYmKirr32WnXq1EmZmZmubgk1bN++fSovL1fXrl3l7e2t9evXa+/evbJarWrWrJn69u1brxe94tJFR0crOjpax48f19q1a8+aCrh9+3ZFRUXxF2w3lZaWpvLycoWEhCg8PPys8TZt2kg6/b4P92W325WdnS1JvLe7kdLSUs2ZM0fNmjXTLbfc4up2qoVgBY9gt9v19ttvKzAwkI0L3NjRo0clSaGhoXrqqaeUnJxcZXz+/PkaPXq0+vbt64r2UIPMZrNGjx6tf//735o1a5a+/vprRUdHKy8vT3v37lV8fLzGjBnDmgs3VfFh+lyhSpL8/f0VFBQki8WiU6dOKSAgoC7bQx1Zs2aN8vPzFRISwi6QbuSzzz5TVlaWnn766Qb3Ht6wugUu09KlS3XgwAGNHj1ajRo1cnU7qCUWi0WStGrVKnl7e+vBBx907Ai4dOlSJSYm6tVXX1VsbKxatWrl4m7hrI4dO2rKlCmaNm2aDh48qIMHD0qSAgIC1LVrVzVu3NjFHaK2lJSUSDo9Fex8/Pz8ZLFYVFJSQrByQ9nZ2frggw8kSXfcccclTw9G/ZaSkqJvvvlGAwcOVOfOnV3dTrWxxgpuLzs7W59++qk6deqka6+91tXtoBbZ7XZJp3eMu/feezVo0CCFhIQoKipK99xzj/r06SOr1ar//ve/Lu4UNWH16tWaPHmyIiIi9MILL2jevHmaPXu2rrnmGi1cuFDPPvusrFarq9tELajYdtlkMl30GLifkpISTZs2TYWFhbryyit1/fXXu7ol1ICK2UVBQUG6++67Xd3OZSFYwe3NnTtXVqtVo0aNcnUrqGUVf5U2mUwaOHDgWePXXXedJCkpKalO+0LNS09P1+uvv66QkBBNmjRJ8fHx8vf3V0xMjB544AH16tVLycnJWrFihatbRS2o+F0vLS097zFlZWWSTk8LhPuwWq2aPn26UlJS1KFDB40dO9bVLaGGLFmyRIcOHdJdd92lkJAQV7dzWZgKCLe3ZcsWBQUFae7cuVXq5eXlkk7f0ZoyZYokadKkSfxPuAGLjIyUdHoR87mmhVSM5+fn12lfqHlr1qyRzWZT9+7dz/k727dvX23evFm7d+/WkCFDXNAhalNERIQkKScn55zjJSUlslgsCgoKYhqgG7Hb7Xr11Ve1fft2tWrVSk888cQFp4OiYdm8ebNMJpNWrlypVatWVRk7efKkJGnatGny9vbWyJEj6+VDoQlW8AgWi+W8dynKysocYzabrS7bQg2r2AnMYrHIMIyzpgkVFRVJ4i/Y7qBia+XAwMBzjlfUK6453EtsbKx8fHxUUFCgnJycszaxOHTokCSpZcuWrmgPtWTu3Llat26dYmJi9OSTTyooKMjVLaGGGYahPXv2nHe8YlOqgoKCumqpWghWcHuff/75OeuZmZl6+OGHFRsbq1mzZtVtU6gVLVu2VFRUlDIzM7V//34lJCRUGd+9e7ckqW3btq5oDzWoYmvlig0rfu3AgQOSKu9Swr34+vqqS5cu2rp1q9avX68bb7yxyvj69eslSb169XJFe6gF8+fP17JlyxQREaF//etfCg0NdXVLqGEVs4fO5aGHHlJWVpbeeeeder21PmusALiVimdevP/++1X+opWSkqLExERJ0tChQ13SG2pO7969JUl79uzR999/X2UsOTlZS5YskXTuh8fCPVSEqYULFyo9Pd1RT05O1rJlyxQQEMCDwt1EYmKiFi1apLCwMP3rX/9yTAUF6hvuWAFwK4MHD9bOnTu1fv16jRs3TgkJCSotLdW+fftktVo1ePBgPmy7gbZt22rYsGH6+uuvNXfuXH333Xdq1qyZ8vLylJycLMMwNGTIEHXr1s3VreISbdmyRQsWLKhSs1qtmjx5suOfb7vtNvXs2VOS1K1bN91www365ptv9Pjjj6tr166y2WzasWOH7Ha7xowZo+Dg4Dr9GXBpqnOtDx8+rI8++kiSFBUVpYULF57znIMHD66Xa248XXV/rxs6ghUAt2I2mzVu3Dj98MMPWr58uWP6X1xcnIYOHaoBAwa4uEPUlLvvvlvt27fXDz/8oJSUFKWlpcnf31+dOnXS4MGD1b9/f1e3iGooKCjQ/v37q9QMw6hS+/W6ij//+c9q3bq1li5dqp07d8rLy0tdunTRbbfdxofseqw617pizax0+m7krx/8XqFz585c83rocn6vGzKTwYMeAAAAAMAprLECAAAAACcRrAAAAADASQQrAAAAAHASwQoAAAAAnESwAgAAAAAnEawAAAAAwEkEKwAAAABwEsEKAAAAAJxEsAIAAAAAJxGsAAAAAMBJBCsAAAAAcBLBCgAAAACcRLACAOAipkyZojvuuEOff/65q1sBANRT3q5uAACAumIYhtavX6/Vq1fr0KFDys/Pl9lsVlhYmMLCwhQfH6+OHTuqS5cuCgwMdHW7AIAGhGAFAPAIFotFU6dOVVJSkqPm5eUlPz8/ZWdn68SJE9q3b5+WLFmi0aNH69prr3UcFxERodjYWIWEhLigcwBAQ0CwAgB4hNdee01JSUkym8264YYbNHToUEVHR8tsNstms+nYsWPatm2bVq9efdZrH374YRd0DABoSEyGYRiubgIAgNqUnp6usWPHSpLuvPNO3XrrrRc8vqysTL6+vnXQGQDAXXDHCgDg9g4fPuz4unfv3hc9/tehasqUKUpKStLtt9+uO+64w1F//fXXtXLlykvq4VwbXxQXF2vp0qXatGmT0tPTVVpaqtDQULVv31433HCDEhISLuncAADXI1gBADxKbm6umjdvXiPnCgwMVGho6HnHS0pKVFpaes6x/fv36+WXX1Z+fr4kyWw2y8/PTzk5OVq7dq3WrVunkSNH6g9/+EON9AoAqF0EKwCA24uLi5PJZJJhGJo3b57Gjx+v2NhYp89733336b777jvnWHZ2tv75z3+qtLRUPXr0qDKWmZmpF154QRaLRX369NGtt96qVq1aycvLS/n5+Vq6dKkWLVqkTz75RM2aNdNVV13ldK8AgNpFsAIAuL2oqCgNGjRIP/74o44cOaJHH31UrVu3Vrt27dS2bVvFx8erRYsWMplMNfL9iouL9dJLL+nkyZNq2bKlxo0bV2X8448/lsVi0YABA87aGCM0NFQjRoxQUFCQ5s2bpy+++IJgBQANAMEKAOARRo0apbCwMCUmJqq0tFSHDh3SoUOHHOOhoaHq37+/brnlFoWFhV3297Hb7Zo5c6aOHDmi0NBQTZo0SQEBAY7xoqIibdiwQZIuuInGwIEDNW/ePKWmpurkyZNO9QQAqH0EKwCAR/Dy8tKIESM0bNgwbdq0SUlJSTp48KCOHz8uq9Wq/Px8LVmyRKtWrdI//vEPxcfHX9b3ee+997R9+3b5+Pjo8ccfV0RERJXx5ORkVWzI+8wzz1zSObOzswlWAFDPEawAAB4lMDBQAwYM0IABAySd3lp97969+vbbb7V582YVFhZq+vTpmj17drW3XE9MTNT3338vk8mkhx56SO3atTvrmNzcXMfXFRtXXMz5NsAAANQfBCsAgEfz9fVVt27d1K1bN8f26Tk5Odq2bVu11jZt2rRJH330kSRpxIgR6tev3zmPs9vtju/78ccfO/8DAADqBbOrGwAAoL4YMmSI4+u0tLRLfl1KSopmz54twzA0YMAADR8+/LzHVkzpKysrU0ZGxmX3CgCoXwhWAAD8j7+/v+NrHx+fS3pNTk6O/v3vf6u0tFQdOnTQgw8+eMHj27dv79h9cM2aNZffLACgXiFYAQDcXmZm5iXdgVq5cqXj6zZt2lz0+JKSEr300kvKy8tTdHS0Jk6cKG/vC8+yDw0NVe/evSVJixcvvmhfRUVFF+0DAOB6rLECALi9o0eP6uWXX9YVV1yhfv36qWPHjoqKipIkWa1WHT16VN9++61WrFghSYqPj1eHDh0uet6ZM2cqNTVVQUFBeuKJJxQSEnJJ/dxzzz3au3evCgsL9dRTT+nOO+9Unz59FBgYKEkqKCjQnj179PPPP6u0tFSTJ0++vB8cAFBnCFYAALfn5eUlwzC0detWbd26VZLk7e0tf39/WSwWx/bn0uk7VRMnTpTZfPFJHRXnKisru+jW6XPmzHF8HR0drSeffFLTpk1TVlaW3nrrLb399tsKDAyUzWZTSUmJ49iuXbtW62cFALgGwQoA4PauuOIKvfLKK9qyZYv27t2ro0ePKjc3VxaLRb6+vmrSpIlat26tq6++Wn369LmkUHWm8vLyS946vUKbNm00c+ZMLV++XL/88otSU1NlsVjk7e2tmJgYxcXFqXfv3urRo0e1zgsAcA2Tceaf6QAAAAAA1cbmFQAAAADgJIIVAAAAADiJYAUAAAAATiJYAQAAAICTCFYAAAAA4CSCFQAAAAA4iWAFAAAAAE4iWAEAAACAkwhWAAAAAOAkghUAAAAAOIlgBQAAAABOIlgBAAAAgJMIVgAAAADgJIIVAAAAADiJYAUAAAAATiJYAQAAAICTCFYAAAAA4CSCFQAAAAA46f8DVGGpJThP2bEAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(size, elapsed, marker='x')\n", "\n", "# Approximate elapsed time with 1st order polynomial\n", "z = np.polyfit(size, elapsed, 1)\n", "appxf = np.poly1d(z)\n", "\n", "ax.plot(size, appxf(size))\n", "ax.legend(['Elapsed', 'Approximate with 1st order polynomial'])\n", "ax.set_xlabel('Size')\n", "ax.set_ylabel('Elapsed time')" ] }, { "cell_type": "markdown", "id": "ca1a2955", "metadata": {}, "source": [ "### 예제\n", "$\\alpha=0.1$ 이고 $x\\in [0, 1]$ 에 대해서 해석한다.\n", "\n", "- 초기 조건 : $T(x,0) = 100$\n", "- 경계 조건 : $T(0, t) = 0$, $T(1, t) = 300$\n", "\n", "$\\Delta x = 0.1$ 일 때 Backward Euler 기법으로 계산하면 다음과 같다." ] }, { "cell_type": "code", "execution_count": 9, "id": "3047fde9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error: 1.67398\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Conditions\n", "alpha = 0.1\n", "ti = 100\n", "ts = 300\n", "\n", "t_target = 1.0\n", "dt = 0.1\n", "\n", "# Make grid\n", "nx = 11\n", "x = np.linspace(0, 1, nx)\n", "dx = np.diff(x)[0]\n", "\n", "# Const\n", "beta = alpha*dt/dx**2\n", "\n", "# Solution array\n", "u = np.ones_like(x)*ti\n", "d = np.empty_like(u[1:-1])\n", "\n", "# Calculation\n", "t = 0\n", "while abs(t - t_target) > 1e-10:\n", " # Adjust time step to reach target time\n", " dt = min(dt, t_target - t)\n", " \n", " # right hand side\n", " d[:] = u[1:-1]\n", " \n", " # Apply bc\n", " u[0] = ti\n", " u[-1] = ts\n", " d[0] += beta*u[0]\n", " d[-1] += beta*u[-1]\n", " \n", " # Operation matrix\n", " a = c = -beta*np.ones(nx-3)\n", " b = (1+2*beta)*np.ones(nx-2)\n", " \n", " # Solve\n", " u[1:-1] = solve_tdiag(a, b, c, d)\n", " \n", " # Update solution and time\n", " t += dt\n", "\n", "# Exact solution\n", "dts = ts - ti\n", "u_exact = ti + dts*x + np.sum([\n", " 2*dts*(-1)**n / (n*np.pi) *np.exp(-n**2*np.pi**2*alpha*t)*np.sin(n*np.pi*x) \n", " for n in range(1, 10)\n", "], axis=0)\n", "\n", "# Visualization\n", "plt.plot(x, u, marker='x')\n", "plt.plot(x, u_exact)\n", "plt.legend(['Computation', 'Exact'])\n", "\n", "# Compute Error\n", "err = np.linalg.norm(u[1:-1] - u_exact[1:-1])\n", "err = u - u_exact\n", "err = np.sqrt(np.sum(err**2) / nx)\n", "print('Error: {:.5f}'.format(err))" ] }, { "cell_type": "markdown", "id": "38494378", "metadata": {}, "source": [ "### (Optional) 실습\n", "\n", "$\\Delta x = 0.1$ 일 때 Crank Nicolson 방법으로 해석해보자." ] } ], "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": "3.12.2" } }, "nbformat": 4, "nbformat_minor": 5 }