{ "cells": [ { "cell_type": "markdown", "id": "5a846a36", "metadata": {}, "source": [ "# Burgers 방정식" ] }, { "cell_type": "markdown", "id": "2a2f5242", "metadata": {}, "source": [ "**강좌**: *기초 전산유체역학*" ] }, { "cell_type": "code", "execution_count": 1, "id": "8edd8c60", "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": "markdown", "id": "bd674b5a", "metadata": {}, "source": [ "## Burgers 방정식\n", "Burgers 방정식은 다음과 같이 표현된다.\n", "\n", "$$\n", "u_t + \\left ( \\frac{u^2}{2} \\right )_x = 0.\n", "$$\n", "\n", "비 보존형의 경우 다음과 같이 표현할 수 있다.\n", "\n", "$$\n", "u_t + u u_x = 0.\n", "$$\n", "\n", "이 방정식은 운동량 보존식에서 비선형 항만 표현한 식이다.\n", "\n", "선형 파동 방정식과 비교했을 때, 각 지점에서 교란의 전파 속도는 $u$ 이다. 즉 $x-t$ 그래프에서 Characteristic의 기울기가 해 $u$ 에 따라 달라진다." ] }, { "cell_type": "code", "execution_count": 2, "id": "448f8c1c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'x')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 3, 151)\n", "u = 1+ 0.25*np.sin(np.pi*x)\n", "t = np.linspace(0, 1, 101)\n", "\n", "fig, axs = plt.subplots(2, 1, sharex=True)\n", "axs[0].plot(x, u)\n", "axs[0].set_xlim(-0.1, 3)\n", "axs[0].set_ylabel('u')\n", "axs[0].set_ylim(-0.1, 1.3)\n", "axs[0].set_xlabel('x')\n", "\n", "for i in range(15):\n", " xi, ui = x[10*i], u[10*i]\n", " \n", " # Characteristics with the wave speed u\n", " xx = xi + ui*t\n", " axs[1].plot(xx,t, color='gray')\n", "\n", "axs[1].set_ylabel('t')\n", "axs[1].set_xlabel('x')" ] }, { "cell_type": "markdown", "id": "f27a1ef7", "metadata": {}, "source": [ "## Riemann Problem의 해\n", "다음 Riemann Problem를 생각하자.\n", "\n", "$$\n", "u(x,t) = \\left \\{\n", "\\begin{array}{cc} \n", "u_L & x \\le 0 \\\\\n", "u_R & else \n", "\\end{array}\n", "\\right.\n", "$$\n", "\n", "2가지 해가 존재한다.\n", "\n", "### Shock\n", "$u_L > u_R$ 인 경우 불연속 충격파가 발생한다. 충격파의 속도는 Rankine-Hugoniot Jump 조건을 통해 구할 수 있다.\n", "\n", "$$\n", "s = \\frac{f(u_r) - f(u_l)}{u_r - u_L}\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "id": "35b366b4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'x')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-1, 2, 151)\n", "u = -np.tanh(1e8*x) + 1.5\n", "t = np.linspace(0, 0.5, 101)\n", "\n", "fig, axs = plt.subplots(2, 1, sharex=True)\n", "axs[0].plot(x, u)\n", "axs[0].set_xlim(-1.1, 2)\n", "axs[0].set_ylabel('u')\n", "axs[0].set_xlabel('x')\n", "\n", "xs = 1.5*t\n", "\n", "for i in range(15):\n", " xi, ui = x[10*i], u[10*i]\n", " \n", " # Characteristics with the wave speed u\n", " xx = xi + ui*t\n", " \n", " # Do not draw characteristics after shcok\n", " idx1 = np.argmin(xx < xs)\n", " idx2 = np.argmax(xx < xs)\n", " \n", " if idx1 + idx2 == 0:\n", " if xi != 0:\n", " axs[1].plot(xx, t, color='gray') \n", " else:\n", " if idx1 > 0:\n", " axs[1].plot(xx[:idx1], t[:idx1], color='gray') \n", " else:\n", " axs[1].plot(xx[:idx2], t[:idx2], color='gray') \n", " \n", "# Rankine Hugoniot condtion\n", "axs[1].plot(xs, t, color='blue')\n", "\n", "axs[1].set_ylabel('t')\n", "axs[1].set_xlabel('x')" ] }, { "cell_type": "markdown", "id": "6f069840", "metadata": {}, "source": [ "### Rarefaction\n", "$u_L < u_R$ 인 경우 해는 연속적으로 팽창한다. 이 때 해는 $x/t$ 에 Self-similar 하다. 현재 시간과 경계에 대한 국소 좌표계를 $\\hat{t}$, $\\hat{x}$ 에 대해서 Self-similar 한 해 $\\hat{u}$는 다음과 같다.\n", "\n", "$$\n", "\\hat{u} \\left (\n", "\\frac{\\hat{x}}{\\hat{t}}\n", "\\right )\n", "= \\left \\{\n", "\\begin{array}[cc]\n", "1u_L & \\hat{x}/\\hat{t} < u_L \\\\\n", "\\frac{\\hat{x}}{\\hat{t}} & u_L < \\hat{x}/\\hat{t} < u_R \\\\\n", "u_R & \\hat{x}/\\hat{t} > u_R \\\\\n", "\\end{array}\n", "\\right.\n", "$$" ] }, { "cell_type": "code", "execution_count": 4, "id": "613ad9ea", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'x')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2YAAAKLCAYAAACdeJsWAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/P9b71AAAACXBIWXMAABcSAAAXEgFnn9JSAADUKElEQVR4nOzdaWBTVd4G8CdNuq9J2TvKKpZ9KYuOoOA2DDrjMjNFGdnEBVqkiCwqKpvKKohIwRFBdsXdYbDOOAoCjlAKsu+FskOXpG26N7nvh7zNbYBCU5Kce2+e3ydu2tw+vbel+eec8z86SZIkEBERERERkTABogMQERERERH5OxZmREREREREgrEwIyIiIiIiEoyFGRERERERkWAszIiIiIiIiARjYUZERERERCQYCzMiIiIiIiLBWJgREREREREJxsKMiIiIiIhIMBZmREREREREgrEwIyIiIiIiEoyFGRERERERkWAszIiIiIiIiARjYUZERERERCQYCzMiIiIiIiLBDKID+LuLFy9CkiSPn7devXoAgJycHI+fm8Tj/dU23l9t4/3VNt5fbeP91S6dTodGjRoJzcDCTDBJkrxSmFU/P2kX76+28f5qG++vtvH+ahvvL3mDZgqzDRs24PDhwzh9+jTy8/NRUVGBmJgYtG3bFo888ghuueUWt85XVFSEzz77DDt27IDFYkFMTAy6d++OxMREhIeHe+m7ICIiIiIif6SZNWZfffUVdu/ejYiICHTo0AFdu3ZFYGAgfv75Z0ycOBG7d++u9bkKCwvx6quvYuPGjdDr9ejevTtCQ0Px3Xff4ZVXXkFhYaEXvxMiIiIiIvI3mhkxGz9+PFq0aIGgoCCXx//9739j6dKlWLJkCRYvXoyAgBvXoitWrMCFCxfQo0cPvPjii9Dr9QCAZcuWIS0tDStWrMCoUaO88n0QEREREZH/0cyIWXx8/FVFGQA8+OCDaNSoEcxmM86fP3/D81gsFmzZsgV6vR7PPPOMsygDgEGDBiEqKgpbt26FxWLxZHwiIiIiIvJjminMrqdqlMxguPEA4e7duyFJEtq2bYuYmBiXjwUGBiIhIQF2ux2//fabF5ISEREREZE/0nxhtnnzZpw/fx6NGzdGgwYNbvj5WVlZAIDmzZtf8+NVj586dcpjGYmIiIiIyL9pZo1ZlW+//RZnzpxBWVkZzp07hzNnzsBoNCIlJaVW68uq9qUwmUzX/HhsbKzL5xEReZtktwEHfoN0+YLoKOQBRRERAAC71So4CXkD76+28f5ql85gAJ58WmgGzRVme/bswb59+5zHsbGxeOGFF9CiRYtaPb+0tBQAEBwcfM2PVz1eVlZWq/ONHTv2qseCgoIwc+ZMAPJGhZ5WNW2zfv36Xjk/icX7q21X3l/rl6thXblIZCTyIPb11TbeX23j/dWw4BAWZp72+uuvA3DsQ3b69Gl8/vnnmDJlCp544gk8/vjjN3x+1YaBOp3OqzmJiGqrfPevoiMQERGRl2muMKsSHh6ONm3a4JVXXsFrr72GTz/9FB07dkSrVq2u+7zQ0FAA8sjZlapGymoaUbvSvHnzrvvxnJwcr+weX/VOe3Z2tsfPTeLx/mrblffXZq32Hu2tLYGYa0+1JnUI/v8OwmXl5YKTkDfw/mob76+GBV7d3d3XNFuYVTEYDPj973+PzMxMZGRk3LAwq5pamJeXd82P5+bmunweEZHXlctTpwP+9AR0nXsKDEM3y8g3VjSN91fbeH+1Swmz5TTflREAIiMjAQAFBQU3/NymTZsCAE6ePHnNj1c9XvV5REReV1ZtBD+odqP1REREpC5+UZgdPHgQANCwYcMbfm7nzp2h0+lw6NAh5Ofnu3ysoqICGRkZ0Ol06NKli1eyEhFdpdqIGYJDxOUgIiIir9FEYXbo0CH88ssvsNlsLo9XVlbiu+++w88//4ygoCD8/ve/d34sLS0NY8aMwdq1a12eYzQacdddd6GyshJLly51Oefq1atRUFCAXr16XbX5NBGR11TvAlvL9a1ERESkLppYY3bp0iWkpqYiMjISLVq0QGRkJAoLC3H69GmYzWYEBgYiKSnJZV1YQUEBzp8/D7PZfNX5hg4dimPHjmH79u0YM2YMWrZsiTNnzuDMmTNo2LAhhgwZ4stvj4j8mCRJQHn1qYwcMSMiItIiTRRmbdu2xWOPPYaDBw/i9OnTKCgogMFgQIMGDdCzZ0/0798fjRo1qvX5oqKiMGPGDKxfvx7p6enYsWMHoqOj0a9fPyQmJiLi/zcXJCLyuopyoHrnVq4xIyIi0iSd5I1e7VRrFy5cYLt8chvvr7ZVv7+StQD2F59yfizgvU+gCw0TFY08gL+/2sb7q228v9ql0+nQuHFjoRk0scaMiEizqq8vA7jGjIiISKNYmBERKVn19WWGQOgC9OKyEBERkdewMCMiUrLqrfK5voyIiEizWJgRESlZ9c2luYcZERGRZrEwIyJSMu5hRkRE5BdYmBERKZnLHmYszIiIiLSKhRkRkYJJ1UfMuLk0ERGRZrEwIyJSsuojZpzKSEREpFkszIiIlMxljRlHzIiIiLSKhRkRkZJV68qo4xozIiIizWJhRkSkZOVcY0ZEROQPWJgRESkZ15gRERH5BRZmRERKxjVmREREfoGFGRGRkrlMZeSIGRERkVaxMCMiUjCprPoG0xwxIyIi0ioWZkRESlZ9xIxrzIiIiDSLhRkRkZK5jJixMCMiItIqFmZEREpWbcRMx+YfREREmsXCjIhIyThiRkRE5BdYmBERKVk52+UTERH5AxZmRERKxhEzIiIiv8DCjIhIoSRJ4ogZERGRn2BhRkSkVOXlrsdsl09ERKRZLMyIiJSqvNT1mFMZiYiINIuFGRGRUpWxMCMiIvIXLMyIiJSq+vqywCDoAvTishAREZFXsTAjIlKqsuqNPzhaRkREpGUszIiIlKqcrfKJiIj8BQszIiKlqj6VMYit8omIiLSMhRkRkVJVb/7BPcyIiIg0jYUZEZFCSVxjRkRE5DdYmBERKRXXmBEREfkNFmZERErFNWZERER+g4UZEZFSVVtjpuNURiIiIk1jYUZEpFTV15hxKiMREZGmsTAjIlKqcnZlJCIi8hcszIiIlKqMa8yIiIj8BQszIiKFklxGzDiVkYiISMtYmBERKRXXmBEREfkNFmZEREpVvV0+15gRERFpGgszIiKlKqu+wTQLMyIiIi0ziA7gCWVlZdizZw8yMjJw4sQJZGdnw263o1GjRujZsycefvhhhITU/kVNcnIysrOza/z4/PnzERcX54noREQ1qzZixn3MiIiItE0ThdnWrVvxwQcfAABuueUWdOrUCSUlJTh69CjWr1+Pbdu2YcqUKYiOjnbrvPfcc881Hw8LC7vpzEREN+QyYsbCjIiISMs0UZgZDAY8+OCDeOihh9C4cWPn42azGTNnzsTJkyfx8ccfIyUlxa3zJicnezoqEVHtcY0ZERGR39DEGrN77rkHzzzzjEtRBgBGoxHDhw8HAOzYsQOVlZUi4hER1U0515gRERH5C00UZtfTtGlTAEBFRQUKCwsFpyEiqh3JbgfKy+UHgoLEhSEiIiKv08RUxuu5dOkSAECv1yMiIsKt53777be4ePEiAgMDccstt6BHjx6IioryRkwiIhdS9fVlAKcyEhERaZzmC7ONGzcCADp37ozAwEC3nrt69WqX4xUrVmDYsGG49957a32OsWPHXvVYUFAQZs6cCQCoV6+eW5lqy2Bw3Nr69et75fwkFu+vthkMBthsrlOv68X9DgEhoYISkSfx91fbeH+1jfeXvEnThdmuXbvw008/Qa/XY8CAAbV+XkJCAtq3b48WLVogKioKly5dwk8//YSNGzdiyZIliIiIQI8ePbyYnIj8nVRa4nKsY1dGIiIiTdNJkiSJDuENZ8+exeuvv46ioiIMHToU/fv3v+lz/vDDD/jHP/6Bxo0bY8GCBR5ICVy4cAHeuAVV7+Rcbz82Ui/eX22rX78+KrJOIDflKccDQUHQL/pcbCjyGP7+ahvvr7bx/mqXTqe7qpGgr2my+Udubi7efvttFBUV4eGHH/ZIUQYA9957L6Kjo3HhwgVcvnzZI+ckIroWlzVm7MhIRESkeZorzAoKCvDmm28iJycHffr0waBBgzx27oCAADRs2BCAY480IiJvcSnM2PiDiIhI8zRVmJWUlGDGjBk4d+4cevTogREjRkCn03n0axQVFQEAQkL4QomIvMdljRnXlxEREWmeZgqziooKzJ49GydOnECnTp0wZswYBAR49ts7c+YMzp8/j+DgYMTFxXn03ERE1blOZWRhRkREpHWaKMzsdjsWLFiAAwcOoE2bNhg3bpyznWlN0tLSMGbMGKxdu9bl8d9++w2ZmZlXfX5WVhbmzZsHSZJw77333vD8REQ3g1MZiYiI/Ismqou0tDTs2LEDABAZGYmlS5de8/MGDRrk3CC6oKAA58+fv2qt2NGjR/H555+jfv36aNiwIaKionD58mWcPHkSNpsNbdu2xcCBA737DRGR33OZysjCjIiISPM0UZhZrVbnv6sKtGv529/+5izMatK5c2fk5ubixIkTyMrKQnFxMUJDQxEfH49evXqhb9++Hp8iSUR0JdepjEHighAREZFPaKIwS0xMRGJiokee07p1a7Ru3dpT0YiI6qT6iJmO7fKJiIg0j0M/REQKxDVmRERE/oWFGRGRArkWZuzKSEREpHUszIiIFIj7mBEREfkXFmZERAoklXIqIxERkT9hYUZEpEBSefWujCzMiIiItI6FGRGRArmMmHEqIxERkeaxMCMiUiCXdvls/kFERKR5LMyIiBTIZSoj15gRERFpHgszIiIFcp3KyMKMiIhI61iYEREpkFTGdvlERET+hIUZEZECubbLZ2FGRESkdSzMiIgURrLZgIpy+QGuMSMiItI8FmZERArj0vgD4BozIiIiP8DCjIhIYVymMQJcY0ZEROQHWJgRESlM9T3MoNMBQUHiwhAREZFPsDAjIlIYqax6q/xg6HQ6cWGIiIjIJ1iYEREpzJWFGREREWkfCzMiIoVxmcrIwoyIiMgvsDAjIlIYlxEztsonIiLyCyzMiIgUhoUZERGR/2FhRkSkMJzKSERE5H9YmBERKQybfxAREfkfFmZERApTvTDTcSojERGRX2BhRkSkMC5TGYM5YkZEROQPWJgRESkMpzISERH5HxZmREQK49r8g1MZiYiI/AELMyIihZHKyuQDrjEjIiLyCyzMiIgURipju3wiIiJ/w8KMiEhhpNLqG0yzMCMiIvIHLMyIiBTGtfkHpzISERH5AxZmREQKU30qI/cxIyIi8g8szIiIFMZlKiPXmBEREfkFFmZERArj0vyDa8yIiIj8AgszIiKFcVljxqmMREREfoGFGRGRwrhOZWRhRkRE5A9YmBERKYhkswGVFfIDXGNGRETkF1iYEREpSfVpjADXmBEREfkJFmZEREpSXuZ6zDVmREREfoGFGRGRkpRXGzHT6QBDoLgsRERE5DMszIiIlKSs2ohZUAh0Op24LEREROQzBtEBPKGsrAx79uxBRkYGTpw4gezsbNjtdjRq1Ag9e/bEww8/jJAQ96YDFRUV4bPPPsOOHTtgsVgQExOD7t27IzExEeHh4V76TojI77m0yuf6MiIiIn+hiRGzrVu3Yu7cufjpp58gSRI6deqE+Ph4XL58GevXr8crr7yC/Pz8Wp+vsLAQr776KjZu3Ai9Xo/u3bsjNDQU3333HV555RUUFhZ68bshIr9WfY0Z15cRERH5DU2MmBkMBjz44IN46KGH0LhxY+fjZrMZM2fOxMmTJ/Hxxx8jJSWlVudbsWIFLly4gB49euDFF1+EXq8HACxbtgxpaWlYsWIFRo0a5ZXvhYj8XPU1ZmyVT0RE5Dc0MWJ2zz334JlnnnEpygDAaDRi+PDhAIAdO3agsrLyhueyWCzYsmUL9Ho9nnnmGWdRBgCDBg1CVFQUtm7dCovF4tHvgYgIACSXNWYszIiIiPyFJgqz62natCkAoKKiolZTEHfv3g1JktC2bVvExMS4fCwwMBAJCQmw2+347bffvJCWiPwepzISERH5Ja9MZUxNTXX7OTqdDiNHjvR4lkuXLgEA9Ho9IiIibvj5WVlZAIDmzZtf8+PNmzfHTz/9hFOnTnksIxGRk0vzDxZmRERE/sIrhdnmzZvr9DxvFGYbN24EAHTu3BmBgTfeDygnJwcAYDKZrvnx2NhYl88jIvKoaoWZjlMZiYiI/IZXCrO77777unvvFBcX48SJE8jLy0NERAQSEhK8EQO7du3CTz/9BL1ejwEDBtTqOaWljhdFwTW0qa56vKz6OpDrGDt27FWPBQUFYebMmQCAevXq1eo87jIYHLe2fv36Xjk/icX7q12FBj2K/v/fIVHRiOY91hz+/mob76+28f6SN3mlMEtOTr7h50iShE2bNmHp0qUIDQ3FsGHDPJrh7NmzWLhwISRJwqBBg9CsWbNaPU+SJADgpq5EJIRUfcQsJFRgEiIiIvIlYe3ydTod+vbti6KiIqxatQpt2rTBHXfc4ZFz5+bm4u2330ZRUREefvhh9O/fv9bPDQ11vBCqGjm7UtVIWU0jaleaN2/edT+ek5PjLAY9qeqdnOzsbI+fm8Tj/dUuu8Xs/HeJzY4y3mPN4e+vtvH+ahvvr3bpdLqrOrz7mvCujPfddx90Oh2+//57j5yvoKAAb775JnJyctCnTx8MGjTIredXTS3My8u75sdzc3NdPo+IyKOqT5Ou5RtAREREpH7CC7PQ0FCEhoZ6pMthSUkJZsyYgXPnzqFHjx4YMWKE21MSq9rrnzx58pofr3q86vOIiDxJctlgml0ZiYiI/IXwwsxqtaK4uLhWmz9fT0VFBWbPno0TJ06gU6dOGDNmDAIC3P/2OnfuDJ1Oh0OHDiE/P/+qr5GRkQGdTocuXbrcVF4iomviPmZERER+SXhhtmbNGgBAkyZN6nwOu92OBQsW4MCBA2jTpg3GjRvn7JpTk7S0NIwZMwZr1651edxoNOKuu+5CZWUlli5dCpvN5vzY6tWrUVBQgF69el21+TQRkUdU38eM7fKJiIj8hpB9zCoqKpCTk4P09HScPXsWANC3b986f720tDTs2LEDABAZGYmlS5de8/MGDRqEqKgoAI61aOfPn4fZbL7q84YOHYpjx45h+/btGDNmDFq2bIkzZ87gzJkzaNiwIYYMGVLnrERE11VtjZmOa8yIiIj8hlcKs9TUVLc+/+6778Yf/vCHOn89q9Xq/HdVgXYtf/vb35yF2fVERUVhxowZWL9+PdLT07Fjxw5ER0ejX79+SExMRERERJ2zEhFdV/WpjFxjRkRE5Dd0khd6td9oHzO9Xo/w8HA0bdoUvXr1Qvv27T0dQTUuXLjAdvnkNt5f7bKNHwpYHF1hA8bPgK51O7GByOP4+6ttvL/axvurXUpol++VEbNFixZ547RERNpXxuYfRERE/kh48w8iIqqmert8rjEjIiLyGyzMiIgUQqqsBKp1guUaMyIiIv/BwoyISCmqj5YBHDEjIiLyIyzMiIiUovr6MoAjZkRERH6EhRkRkVJU31w6QA8YvNKfiYiIiBSIhRkRkVJU28NMFxICnU4nMAwRERH5EgszIiKlqLbGTMdW+URERH6FhRkRkVJUW2PGwoyIiMi/sDAjIlIKl6mMoQKDEBERka+xMCMiUgipjFMZiYiI/BULMyIipeAaMyIiIr/FwoyISCnKOJWRiIjIX7EwIyJSinI2/yAiIvJXLMyIiJSCa8yIiIj8FgszIiKlYFdGIiIiv8XCjIhIKThiRkRE5LdYmBERKQVHzIiIiPwWCzMiIoVw3ccsWGASIiIi8jUWZkRESuHSlZEjZkRERP6EhRkRkVJUHzHjVEYiIiK/wsKMiEgpXEbMOJWRiIjIn7AwIyJSCpc1ZhwxIyIi8icszIiIlMKlKyPb5RMREfkTFmZERErB5h9ERER+i4UZEZECSJLEDaaJiIj8GAszIiIlqKwE7HbnIacyEhER+RcWZkRESlBe6nLIqYxERET+hYUZEZESlJW5HHIfMyIiIv/CwoyISAmqj5jp9dAZDOKyEBERkc+xMCMiUoIydmQkIiLyZyzMiIiUoHpHRjb+ICIi8jsszIiIlMBlDzMWZkRERP6GhRkRkRKUV9/DjFMZiYiI/A0LMyIiBZCqrzHjVEYiIiK/w8KMiEgJytn8g4iIyJ+xMCMiUoLqzT+4xoyIiMjvsDAjIlKCcnZlJCIi8mcszIiIlID7mBEREfk1FmZERErgssYsWGAQIiIiEsEgOoCnZGZmYu/evTh+/DiOHTsGs9mMwMBArFmzxu1zJScnIzs7u8aPz58/H3FxcTcTl4jIlcsG0xwxIyIi8jeaKcw+//xz7Ny506PnvOeee675eFhYmEe/DhERN5gmIiLyb5opzFq3bo1mzZqhZcuWaNmyJZ577rmbPmdycrIHkhER3ZjEETMiIiK/ppnC7NFHHxUdgYio7jhiRkRE5NfY/IOISAm4jxkREZFf08yImTd8++23uHjxIgIDA3HLLbegR48eiIqKEh2LiLSo+ogZpzISERH5HRZm17F69WqX4xUrVmDYsGG49957BSUiIs1yKcw4YkZERORvWJhdQ0JCAtq3b48WLVogKioKly5dwk8//YSNGzdiyZIliIiIQI8ePWp1rrFjx171WFBQEGbOnAkAqFevnkezVzEYHLe2fv36Xjk/icX7qz2XK8ph//9/G8LCYTAYeH81ir+/2sb7q228v+RNXGN2DU8//TR69OiBevXqISgoCLfccgsGDx6MZ555BgDqtDcaEdH1SKXV15hxKiMREZG/4YiZG+699158+umnuHDhAi5fvowGDRrc8Dnz5s277sdzcnIgSZKnIjpVvZNzvY2ySb14f7VFkiRIZSXOY3tgICorK3l/NYq/v9rG+6ttvL/apdPp0LhxY6EZOGLmhoCAADRs2BAAYDabBachIs2orACqvUHDroxERET+h4WZm4qKigAAIVycT0SeUq1VPsCpjERERP6IhZkbzpw5g/PnzyM4OBhxcXGi4xCRVpSVuRyyKyMREZH/8dvCLC0tDWPGjMHatWtdHv/tt9+QmZl51ednZWVh3rx5kCQJ9957r7MrDxHRTSuvNmJmMECn5/8vRERE/kYzf/137dqFL774wuWxyspKTJo0yXn8l7/8BV27dgUAFBQU4Pz581etFTt69Cg+//xz1K9fHw0bNkRUVBQuX76MkydPwmazoW3bthg4cKD3vyEi8h/V9jBDULC4HERERCSMZgqzgoICHDt2zOUxSZJcHisoKLjheTp37ozc3FycOHECWVlZKC4uRmhoKOLj49GrVy/07dsXAQF+O9BIRN5QfY1ZEKcxEhER+SPNFGZ9+vRBnz59av35iYmJSExMvOrx1q1bo3Xr1h5MRkR0A9XXmLEjIxERkV/i0A8RkWjVpzIGcyojERGRP2JhRkQkmOQylZGFGRERkT9iYUZEJFo515gRERH5OxZmRESilXEqIxERkb9jYUZEJFq1NWY6TmUkIiLySyzMiIhEq77GjF0ZiYiI/BILMyIi0bjGjIiIyO+xMCMiEo1rzIiIiPweCzMiItGq72PGNWZERER+iYUZEZFgEteYERER+T0WZkREonHEjIiIyO+xMCMiEo0jZkRERH6PhRkRkWjcx4yIiMjvsTAjIhKNI2ZERER+j4UZEZFoXGNGRETk91iYERGJVs59zIiIiPwdCzMiIoEkSbpixIxTGYmIiPwRCzMiIpHKywFJko+5xoyIiMgvsTAjIhKpvNT1mFMZiYiI/BILMyIikapPYwTY/IOIiMhPsTAjIhKpeqt8QyB0AXpxWYiIiEgYFmZERCKVVe/IyPVlRERE/oqFGRGRSNXXmHF9GRERkd9iYUZEJBI3lyYiIiKwMCMiEqv6GjPuYUZEROS3WJgREQkkuawx44gZERGRv2JhRkQkEqcyEhEREViYERGJ5dL8g1MZiYiI/BULMyIikaqtMdNxjRkREZHfYmFGRCQS15gRERERWJgREYnFNWZEREQEFmZERGKVcY0ZERERsTAjIhJKKuc+ZkRERMTCjIhIrDJOZSQiIiIWZkREYpWz+QcRERGxMCMiEotrzIiIiAgszIiIxKo2YsZ9zIiIiPwXCzMiIpFc2uUHictBREREQrEwIyISiVMZiYiICCzMiIjEKmdhRkRERCzMiIiEkex2oLxcfoDt8omIiPyWQXQAT8nMzMTevXtx/PhxHDt2DGazGYGBgVizZk2dzldUVITPPvsMO3bsgMViQUxMDLp3747ExESEh4d7OD0R+aWKctdjtssnIiLyW5opzD7//HPs3LnTI+cqLCzEa6+9hgsXLqBhw4bo3r07zp49i++++w67d+/GW2+9hcjISI98LSLyY9XXlwEAuzISERH5Lc0UZq1bt0azZs3QsmVLtGzZEs8991ydz7VixQpcuHABPXr0wIsvvgi9Xg8AWLZsGdLS0rBixQqMGjXKU9GJyF9dVZhxxIyIiMhfaaYwe/TRRz1yHovFgi1btkCv1+OZZ55xFmUAMGjQIPzyyy/YunUrnnrqKcTExHjkaxKRn6reKj8wCLoALvslIiLyV3wVcIXdu3dDkiS0bdv2qsIrMDAQCQkJsNvt+O2334TkIyINqV6YcX0ZERGRX9PMiJmnZGVlAQCaN29+zY83b94cP/30E06dOuXDVO6Rzp5C6dG9jn8XFAhOQ95QGhUFgPdX7aTzZ+QDri8jIiLyayzMrpCTkwMAMJlM1/x4bGysy+fdyNixY696LCgoCDNnzgQA1KtXry4xr6vw+y9g+XyFx89LymERHYA8Th8Wjvr16wMADAbHf81Vx6QtvL/axvurbby/5E2cyniF0lLHYvzgGqYVVT1eVlZ2zY8TEdWFofHvREcgIiIigThidgVJkgAAOp3OI+ebN2/edT+ek5Pj/JqeYg8KhaFVGwBAZUWFR89NymAIDATA+6sZpnqoeOgJZGdnA5Dfia06Jm3h/dU23l9t4/3VLp1Oh8aNGwvNwMLsCqGhoQDkkbMrVY2U1TSipgQBffujXuIQAPyPQ6vq8Q8DERERkaZwKuMVqtZ85eXlXfPjubm5Lp9HRERERER0s1iYXaFp06YAgJMnT17z41WPV30eERERERHRzWJhdoXOnTtDp9Ph0KFDyM/Pd/lYRUUFMjIyoNPp0KVLF0EJiYiIiIhIa/y2MEtLS8OYMWOwdu1al8eNRiPuuusuVFZWYunSpbDZbM6PrV69GgUFBejVq9dVm08TERERERHVlWaaf+zatQtffPGFy2OVlZWYNGmS8/gvf/kLunbtCgAoKCjA+fPnYTabrzrX0KFDcezYMWzfvh1jxoxBy5YtcebMGZw5cwYNGzbEkCFDvPvNEBERERGRX9FMYVZQUIBjx465PCZJkstjBQUFtTpXVFQUZsyYgfXr1yM9PR07duxAdHQ0+vXrh8TERERERHg0OxERERER+Ted5OlNtMgtFy5c8Pg+ZgD32dA63l9t4/3VNt5fbeP91TbeX+3iPmbksY2sRZ2fxOL91TbeX23j/dU23l9t4/3VHiXcU46YERERERERCea3XRmJiIiIiIiUgoWZRr388st4+eWXRccgL+H91TbeX23j/dU23l9t4/3Vttdffx2vv/66sK/PNWYaVV5eLjoCeRHvr7bx/mob76+28f5qG++vthUVFQn9+hwxIyIiIiIiEoyFGRERERERkWAszIiIiIiIiARjYUZERERERCQY9zEjIiIiIiISjCNmREREREREgrEwIyIiIiIiEoyFGRERERERkWAszIiIiIiIiARjYUZERERERCQYCzMiIiIiIiLBWJgREREREREJxsKMiIiIiIhIMBZmREREREREgrEwIyIiIiIiEoyFGRERERERkWAszIiIiIiIiARjYUZERERERCQYCzMiIqJa+vrrr5GYmIgnn3wSx48fv+bn7Nq1CwMGDEBiYiK2bt3q44RERKRWLMyIiIhq6ZFHHkGHDh1gs9mwYMEClJSUuHzcbDYjNTUVkiTh7rvvRq9evQQlJSIitWFhRkREVEs6nQ4vvPACoqOjcenSJXz44YfOj0mShPfffx8FBQVo1KgRnnnmGYFJiYhIbViYERERuSEmJgZJSUnQ6XTYunUrNm3aBAD45ptvsG/fPuj1eqSkpCAkJERsUCIiUhUWZkRERG7q0qULHnroIQDAsmXL8PPPP+PTTz8FADz55JNo2bKlyHhERKRCOkmSJNEhiIiI1KayshKvvfYaMjMznY916tQJr776KnQ6ncBkRESkRhwxIyIiqgODwYCkpCTncVhYGJKTk1mUERFRnbAwIyIiqqMffvjB+e+SkhKcOnVKXBgiIlI1FmZERER1kJGRgbS0NABA06ZNIUkSFi1aBIvFIjYYERGpEgszIiIiN1XtVwYAffr0wdSpU1G/fn3k5+dj0aJF4PJtIiJyFwszIiIiN9jtdrz//vsoLCxE48aN8fTTTyMsLAwpKSnQ6/XYs2cPNmzYIDomERGpDAszIiIiN3z77bfX3K+sdevW+Otf/woAWLdunUu3RiIiohthYUZERFRLx48fd9mvrEWLFi4ff+yxx9CuXTtUVlZiwYIFKC0tFRGTiIhUiIUZERFRLZSUlGDBggWw2Wzo2LEj/vSnP131OQEBARg1ahQiIiJw4cIFLFu2TEBSIiJSI24wTUREREREJBhHzIiIiIiIiARjYUZERERERCQYCzMiIiIiIiLBWJgREREREREJxsKMiIiIiIhIMBZmREREREREgrEwIyIiIiIiEoyFGRERERERkWAszIiIiIiIiARjYUZERERERCQYCzMiIiIiIiLBWJgREREREREJxsKMiIiIiIhIMBZmREREREREgrEwIyIiIiIiEswgOoC/u3jxIiRJ8vh569WrBwDIycnx+LlJPN5fbeP91TbeX23j/dU23l/t0ul0aNSokdAMLMwEkyTJK4VZ9fOTdvH+ahvvr7bx/mob76+28f6SN3AqIxERERERkWCaGjErLy/H119/jW3btiEnJwcRERHo1KkTBgwYgNjY2FqfJzk5GdnZ2TV+fP78+YiLi/NEZCIiIiIiIu0UZuXl5Zg+fTqOHDkCo9GIbt26ITs7G5s2bcKuXbvw5ptvuj1v9J577rnm42FhYZ6ITEREREREBEBDhdlXX32FI0eOoHXr1njttdcQEhICANiwYQNWrlyJxYsXY+rUqW6dMzk52RtRiYiIiIiIXGhijVllZSXS0tIAAMOHD3cWZQDw8MMPo2nTpjh06BAyMzNFRSQiIiIiIqqRJgqzw4cPo6ioCA0bNkTz5s2v+njPnj0BADt37vR1NCIiIiIiohvSRGGWlZUFANcsygCgRYsWLp9XW99++y3+8Y9/YPny5fjhhx9QUFBwc0GJPOTgwYMoLS0VHaPOTpw4gbKyMtEx6oz5xVJ7/vXrdbBYRKeou7S0EJw+rRcdo87S04OQnh4oOkadZWbqkZYWcuNPVKjLlwPwzTfqza92paWlOHbsmOgYdab2/DeiiTVmVZv81dR50WQyuXxeba1evdrleMWKFRg2bBjuvffeOqQk8ozc3Fx8/fXXCAkJQYcOHdChQwfo9ep5kZSbm4sff/wRwcHB6NixI/P7GPOLtX+/AU89ZYDRKGHkyAg8+6wVQUGiU9Xe4cMGJCcbERgoYc4cC/70J3W9QbRvXyAGDTKhshJYtiwPd99dLjqSW9LTgzBsmBFFRQH45JNc9OyprvybNgUjJSUGZnMAGjfORY8e6sqvZpIkITMzE//73/9QUlKCiIgING7cWHSsWlN7/trSRGFWNXIQHBx8zY9XrTmr7QhDQkIC2rdvjxYtWiAqKgqXLl3CTz/9hI0bN2LJkiWIiIhAjx49anWusWPHXvVYUFAQZs6cCUDeQd7TDAbHra1fv75Xzk/i/PTTTwAcP8+nTp3C/fffD51OJzhV7VXlLysrY/4aePP3l9dfrAULHEWk2azDt99G4o03QhGgkrkrxcXAqFEGlJbqUFqqw+uvG/HXv1YiKkp0sto5dAh46ikDCgsdPy8jRsTi2LFKxMR49ut46/f3s890ePppPcrKHPmffTYWhw55Pr83lJcDb7wRgHnz5DdRRo+Oxe7d6vn5qaLG11f5+fn4/vvvcfz4cedjv/zyC5555hnn96Nkas/vDk18Nzfafd3d3dmffvppl+NbbrkFgwcPRpMmTfCPf/wDa9asqXVhRuRJZ86ccfmPqU+fPqp6Ucr8YjG/WL/8osPGjXIVNm2aTTVFGQC89JIehw7J13vZMptqXlSfOgX0729ATo4jv8EgYflymyqKGkkC3nknAK++Khc1QUES5s9XR/6TJ4GnntIjPV3+YQ8JkfDyy3ZERgoM5gfsdjsyMjKwefNmlJfLo5MGgwGdOnVCgML/A1J7/rrQRGEWGhoKADWuOah6vHq3xrq499578emnn+LChQu4fPkyGjRocMPnzJs377ofz8nJcbtwrI2qd3Kut1E2qYskSfjhhx+cx3FxcYiOjlbNPb4yf4MGDZi/Bt74/eX1F0uSgFdeiUXVn92ePe3o0eMyVBIf33wTgo8+MjmPR460omvXAlXkv3gxAI8/Xg/nzjmKMp1OwoIFFvTsWeKV/J78/a2sBCZNisbq1eHOx2Ji7Fi2LA89e5Yr/vp/800IJk6MQWGh/AL6ttsqsHixGW3aVMLNFSaKoJbXV3l5ediyZQsuX77s8niTJk3Qu3dvREVFITc3V1C6GxORX6fTCZ8eqYnCrGo6YE03KC8vz+Xz6iogIAANGzZEfn4+zGZzrQozIk85e/YsLly44Dy+5557VDVacGX+bt26Mb8PMb9YmzcH43//k6fbT5tmh1riZ2XpMXFijPO4c+dyTJigjmZYeXk6DBwYi6ws+eXOjBn5ePTREoGpasdq1WHkSCN+/FF+U7lp00qsXJmLVq1sApPdWEmJDpMnR2HNmnCXx598sgjTphUgLMzzb0iTQ2VlJXbv3o09e/a4vPEfHByMO+64A7fddpui/+9Ue/6bpYnCrGnTpgCAkydPXvPjVfuXVX3ezSgqKgJw86NvRO6QJMllu4dmzZqhWbNmin/HrsqV+ePi4hAXFycwkXuYXyz15wdmzZLnbN13nx19+0qKH+0AHGuDkpONzhGPyEg7UlPNqmhYUliow1NPxeLIEbkD4+uv52PQoGKBqWrnwoUADB4ci4MH5exdu5bj44/zEBtrF5jsxg4fNmDkSCOOHpWzR0TYMXu2BY88oq5mMWpz/vx5bNmy5aou4i1btsSdd97pnGGmVGrP7wmaKMzi4+MRFhaGS5cu4eTJk1e1zd++fTsAoGvXrjf1dc6cOYPz588jODhYVS8KSP1OnTrl0lW0T58+4sLUwZX5u3XrJjCN+5hfLLXn37gxBHv3ypXMtGnKfmFd3ezZUdi9W84+a5YFTZsqe7QGcIzYDB1qwp49cvaUlEKMGFEkMFXtHDxowKBBsbh4UV5T1r9/Cd57zwwlvy6VJGDt2jC88UY0SkvlEY3OncuxaJEZzZop/+dGrcrKyrB9+3YcOXLE5fGIiAj06tULt9xyi6BktaP2/J6kicLMYDCgX79++PLLL7Fs2TJMmjTJOaK1YcMGZGVlIT4+Hq1atXI+Jy0tDWlpaejRowcGDhzofPy3335DVFSUc++zKllZWXj33XchSRLuvfdezXWBIeWy2+0uowVNmzZFkyZNBCZyz7Xyq2kaMPOLpfb8Nhswe7Y8WtavXwm6d1fH349Nm4KxeHGE8/jJJ4tUMeJRXg4895wRv/4qTx0dPtyK8eMLBaaqnc2bg/Hcc0ZYrfKarOeft+K11woU3SimoECHCRNi8M9/ulaOzz9vxcsvF6hihFWNrmwhX0Wn06F9+/ZISEhAYKBy9+xTe35vUMdfh1p4/PHHsW/fPhw5cgQpKSmIj49HTk4Ojh07hsjISCQlJbl8fkFBAc6fPw+z2ezy+NGjR/H555+jfv36aNiwIaKionD58mWcPHkSNpsNbdu2dSnkiLzt+PHjsFTbjVZtowXMLxbzi/XFF6E4ftzxwkKnkzBhQiEAo9hQtXDpUgBGj45xHt92WwWmT1f+ujKbDXjhBdd1WYmJxZgypUDxa/rWrg3Dyy9Hw2ZzBA0IkDB9ej6GDlX21MtduwKRlGTEmTPyS0qTyYYFCyy49171bgSvdFarFdu2bcPp06ddHo+NjUXv3r0V385f7fm9RTOFWVBQECZPnoyvvvoKW7duRXp6OsLDw3HPPfdgwIABtW780blzZ+Tm5uLEiRPIyspCcXExQkNDER8fj169eqFv376abM9JymSz2ZCRkeE8btWqlXPDdDVgfrGYX6yyMuCdd+TRsscfL8Htt1cKTFQ7djuQkmJEbq5jKl1IiITFi80IDVV2wwa7HZgwIRobNsijNv37l2DOHIuiR5vsdseo6sKF8s9KaKgdixeb8cADyi1s7HZgyZIIzJoVicpKuer9/e/LsHChGY0aqWfKrprY7XYcPHgQO3fuREVFhfNxvV6Prl27omPHjop+nar2/N6mmcIMcBRnAwYMwIABA274uYmJiUhMTLzq8datW6N169beiEfktsOHD8NqtQJwDO0nJCQITuQe5heL+cVaty4MZ886/swaDBJeekn5U+kAIDU1Alu2yNMA33gjH23aKLuglCRg6tQofPKJ3AWwb99SvP++GUpeeVBWBowdG4Ovvw5zPtaggQ0rVuShY8eK6zxTrOzsAKSkxGDzZnlkUq93/IyPGmWFXn+dJ1Od1aaFvJKpPb8vKPi/KyL/VlFRgd27dzuP4+PjVfWfFvOLxfxiFRfr8O678gjIwIHFqmiasXNnoMuauP79SzB4sLKn0gHAvHmRWLpUXg/Xs2cZPvzQjODg6zxJMLNZh+HDTdi+XQ55++0VWLUqD3Fxyv1Z+fnnIIwebUR2tlx9NWlSiUWLLOjRo/w6z6S6UnsLebXn9yUWZkQKdeDAAediWL1ejy5dughO5B7mF4v5xVq2LNz5wjUkREJKivJHy/LzdUhONjrXOMXFVWLOHIvi12Z98EE45s2Ti8mOHR1t5ZU89fLUKT0GDYpFZqb8MqxXrzJ8+GEeoqKUmbuiApg7NxKLFkVAkuQfin79SjB3rgVGozJzq11NLeRbtWqFO+64Q/Et5NWe39dYmBEpUFlZGfbs2eM8bteuHcLDw6/zDGVhfrGYX6z8fB1SU+XRm6FDixS/3kaSgHHjYpxTL/V6CYsWmRETo+wX22vWhGHatGjncevWFVizRrnFDeAYlRw2zIS8PHnEKTGxGLNmWRTbvfDsWT2SkozIyJADBgdLeOONfAwZUqz44l2N1N5CXu35RWFhRqRAe/fuRXm5Y0pIYGAgOnXqJDiRe5hfLOYXa8mSCOTnOxavR0TYkZys/NGy1avDsHGj/M71+PGF6N5duWucAOCbb0IwcaJclDVtWol163JhMim3CP7Xv0IwerTRZZ+vceMKMGaMVbHFzb/+FYLx42OcP9MA0LJlBRYvNqNdO2WvPVSj67WQb9euHbp166boFvJqzy8aCzMihSkuLsb+/fudxx07dnTuy6cGzC8W84uVnR2ApUvl0b0RI6wwmZQ7egMAhw4ZMGWKXOD07l2G5GSrwEQ39sMPwRg92uicUteokQ2ffJKr2JFJSQL+8Y9wTJ8e5cwcGCjhnXcs+MtfSm7wbDFKSoBp06KxcqXraHViYjHeeisfYWHK/rlWI7W3kNdCftFYmBEpzJ49e1BZ6XgXMiQkBO3btxecyD3MLxbzi7VwYQSKix0jCyaTDc8+WyQ40fUVF+swcqQ8ghMba8OCBWZFt5f/5ZcgPP+8ydmi3Wi0Yd26XNx6qzIbZthswOTJUVi+XJ7eGh1tx4cf5uGuu5TZLOPYMQNGjjTi0CF5ZCM83I4ZM/IVW0iq2fVayCckJKBDhw6KbiGvlfx79uzB+PHjhWZhYUakIFarFQcPHnQed+rUCUFKXXRwDcwvFvOLde6cHqtWyaMLo0ZZERGh7FGFyZOjcOyY/OJ7wQILGjZU5qgTAOzeHYihQ03OQjIy0o61a/PQurUyp9QVFemQlGTEDz/Io7633FKJVavycNttysssScCnn4bitdeiUVIiv5Du0KEcqalmtGihzOJXzWpqIR8XF4devXopvhutlvIrYYolCzMiBdm1axfsdseLovDwcLRt21ZwIvcwv1jML9b8+REoL5en1g0erOzRsm++CcHatXIhOXKkFX37KndD40OHDHjqqVgUFTkKhpAQu6L3+7p0KQBDhpiwb5/85kLnzo6OkfXrK6/4LSzU4eWXo132VAOAZ56x4tVXCxS99YAaqb2FvFbzi8bCjEghLBYLjh496jzu2rUrDEreGfUKzC8W84t14oQe69fLL2jHji2EkrtAZ2XpMWFCjPO4c+dyTJhQUPMTBMvM1OPJJ2NhsTiKssBACR99ZEbPnsqcCnjgAPCnP9XDuXPyz/Af/lCCRYssimzjv2dPIEaONCIrS85rNNowf74FDzyg3GJdrdTeQl6r+Vu0aCEokUw9f/WINC4jI8P5rk1UVBRat24tOJF7mF8s5hdr7two5/5fzZpVIjFRuZsyl5cDyclGWK1y58jUVLNiW7WfOxeAJ5+Mde4LFxDgaOXfp48yC4Yff9QhMVGPggJ5tGD4cCsmTy6AXn+dJwpgtwMffhiOGTOiUFEh573zzjIsXGhG48bKG9lTM7W3kNd6/ltvvVVQMhkLMyIFyM3NRWZmpvM4ISFB0Qtlr8T8YjG/WPv3G/Dtt66t5hWwVKFGs2dHYffuoGrHFjRtqsy1Qzk5AXjiiXrO/dUAYO5cCx56qFRgqpqtXx+K8eP1zsYkOp2EKVMK8MwzypvWmpsbgDFjYvDjj/L6t4AACS++WIiUFKviikg1U3sLeeb3HRZmRAqQnp7u/LfJZELLli0FpnEf84vF/GLNni0vbm/TpgJ//rNyu9Zt2hSMxYvl7oADBxbhkUeUWeRYLDo8+WQsMjPllyrTp+djwADlXV9JAt55JxLz50c6HwsJsSM11YI//EF513fbtiC88IIRly7J1VejRjYsWmTGHXcoc3qoWmmhhTzz+w4LMyLBLl68iDNnzjiPu3XrpugFs1difrGYX6z09CD897/yiMOECQWKbTV/+XIAUlJinMe33VaBqVOVua6sqEiHwYNjcfCg/C72+PEFePpp5Y08lZcD48bF4Isv5DWGDRpIWLYsF126KKsxSWUlMH9+JBYsiHDupwYADzxQinnzzIrfc09NtNJCnvl9i4UZkUCSJLmMFjRo0EARc5xri/nFYn6xJAmYMUMeIenatVyxjRLsdmD0aCNychwjJCEhEhYvNityk+DSUuDpp03IyJCnW44caUVKivjNX69ksejw7LMm/PKL3LIwPl7CN99UIiJCWUXZuXN6jBoVgx075KxBQRJee81R8Kro/RDFq6mFfJMmTdC7d29VtZCvjvm9j4UZkUBnz57FxYsXncfdu3dX1WgB84vF/GJt3hyM7dvlF7kvv1yg2Be3qakR2LJFzjp5cj7atFHePloVFUBSkhFbt8pZn3qqCJMmKe/anjmjx+DBJhw9Ko/q3XlnGb7+OgBGI5CdLTDcFdLSQvDSSzHOrpaAo0nNkiVmdOigrAJSzbTaQp75fYeFGZEgkiRh586dzuO4uDg0adJEYCL3ML9YzC+WJAGzZsmjZXffXYq77lLm2pydOwMxe7actX//EgwapLyukXY7MHZsDL7/Xm6k8thjxZgxI19xRdlvvzk2uq7qFAkAjz9ejLlzLTAalbNmpbQUePPNKCxfHuHy+F/+Uoy3385X/AboaqLVFvLM71sszIgEOXXqFHJycpzH3bp1E5jGfcwvFvOLtXFjCPbulafaTZhQKDBNzSwWHZKTjc5W/nFxlZgzx6K4QkeSgEmTovHll/I6rQcfLMH8+RbFrdn7/vsQJCXFoLRUDvbii4V46aVCRV3X48f1GDnS5LJOLyzMjrffzsff/qa8BipqpfUW8szvWyzMiASw2+0uowXNmjVDgwYNBCZyD/OLxfxi2WxwGYH64x9LFNfkAXAUO+PHxzhbzev1jv2/YmKUNUoiScDbb0di5cpw52N33VWGxYvNitt24KOPwjF5cpSzcYbBIGH2bIviOkWuXx+KSZOiUVwsF4/t2lVg8eI8tGypzK0R1OZ6Ldjbt2+PhIQExbRgvxbmVyYWZkQCHD9+HBaLxXmckJAgLkwdML9YzC/WF1+E4vhxxx98nU7C+PHKHC1bvToMGze67q/WvbvyCsiFCyOQmuraRGX58jyEhFznST5mswFTp0bho4/kKYGRkXZ8+GEeevdWzhRWq1WHV15xHXkEgKeftmLSpAJFXVM1y8/Px/fff+/SURZQbgv2K1mtVmzdupX5FYiFGZGP2Ww2ZGRkOI9btWoFk8kkMJF7mF8s5herrMyxX1WVxx4rwe23K6+JxqFDBkyZEu087tWrDMnJyutq+PHHYZg1y3UfuFWrchEerpxRvZISHV54IQbffScXuXFxlVi5Mg/x8cq59/v2BWLkSCNOnpRf2sXE2PHOOxb066e8vdTUyG63Iz09HZs3b0Z5uVyQK70FexW1tpCvovb8tcHCjMjHDh8+DKvV8QJJp9OpbrSA+cVifrHWrQtzTg00GCSMG6e80bKSEh1GjjSitNQx3a5ePRsWLjQrbq3WZ5+FYtKkGOdx8+aVWLcuV1FTLbOzAzBsmAm7d8vrCTt0KMeKFXlo2NAuMJlMkhxTLN98MwoVFfIitx49yvD++2bExSkjp9qpuQU7wPxqwcKMyIeqWrlWiY+PV9V/JswvFvOLVVKiw4IF8mjZwIHFaNpUeet1Jk+OwrFj8tqKBQssaNBAWS/Ov/suBGPHxjiPmzSpxKef5qJ+feXkPHbMgEGDTDhzRn6pdN99pVi82KyYEb28vACMHRuD//xHnqOo00lISbHixRcLYeCrvJum9hbszK8u/JUl8qH9+/c7F6nq9Xp07dpVcCL3ML9YzC/WsmXhuHy5aoNmO8aMUd5o2TffhGDNGrmJxogRVvTpo6xNrzdvDkZSkhF2u+PFVP36Nnz6aS7i4pRT5P7vf0EYPtyE/Hx5mHHIkCJMm5avmGLnf/8LwqhRRly8KLfsb9jQMTqq1K0b1KamFuzt2rVDly5dFN+CXe0t5NWevy4U8t8LkfaVlZVh7969zuN27dohLCzsOs9QFuYXi/nFys/XITVVbvwwbFixYqayVcnK0mPixBjncefO5Zg4saDmJwiQnh6E4cONKC93FGXR0XasXZuLFi2UU5R9+WUoxo6NcU4L1OkkvPZaAZ5/vkgR7fBtNmDBggjMnx/pLG4B4N57S/HuuxbExirr51KNSktLsWPHjmu2YH/ooYfQsmVLZCtpB/ErXC+/GlrIqz3/zWBhRuQje/fuRVmZ453rwMBAdOrUSXAi9zC/WMwv1pIlEbBYHKMnkZF2JCUpa7SsogJITjaisFDOmJpqRlDQDZ7oQ/v2BWLQIBNKShwZw8LsWLUqF23bKqOBhiQ5Cp45c+TptSEhEhYuNKN/f2U0zzh/PgAvvGDEr78GOx8LDJTwyisFePbZIsWtI1Sb2rRgb9KkicCE16f2FvJqz+8JLMyIfKCkpAT79+93Hnfs2BEhKupbXFxczPwCMb9Y2dkBWLpUnh74/PNWmEzKWGNUZfbsSJcGFbNmWRS1/u3YMQMGDjQ5C8fgYAnLl+chIUEZ7fsrKoCJE2Pw6afyKK7JZMPHHysn43/+E4wXX4yB2SxPXWzatBKpqWZ07qyMjGqm9hbszK8NLMyIfOC3335DZaXjXeGQkBC0b99ecCL37Nmzh/kFYn6xFi6McG7UazLZ8OyzRYITudq0KdhlH7CBA4vwyCPKGOEBgNOn9XjiiVjk5TkKCr1ewpIleejVSxnroAoKdHjuORO2bJFHoVq0qMSqVblo1kx8cVtWBrz9dhSWLo1wefyRR4oxa1Y+IiOV9SaB2qi9BTvzawsLMyIvs1qtOHjwoPO4c+fOCFLS/KIbuDJ/p06dmN+HmF+sc+f0WLVKHi0bNcqKiAjlvBC+dCkAo0fHOI9vu60C06YpZ13ZxYsBeOKJWGeDCp1OwnvvWfDgg8poSHLunB6DBplw5Ig8PapnzzJ89FEejEbx9zkzU4+kJCP27ZN/Z0JC7HjrrXwMGFCiiDVvaqb2FuzMrz0szIi8bNeuXbDbHYuxw8PD0aZNG8GJ3HNl/rZt2wpO5B7mF0vt+efPj3A2qmjc2IYhQ5QzWma3AykpRuTmOoqe4GAJixebERoqvqAAHK3cBw6MRVaW/FJj5sx8PPpoyXWe5Tv79gViyBATLl2SpwY++mgx5s2zIDj4Ok/0kS+/DMXLL0ejqEgeLWjTpgKpqWa0bq2MdXlqpfYW7MyvXZoqzMrLy/H1119j27ZtyMnJQUREBDp16oQBAwYgNja2zue9cOECxo0bh4qKCnTq1AmTJk3yYGrSMovFgqNHjzqPu3TpAoNSei3XwpX5u3btyvw+xPxiHT+ux/r18pqjF18shJKWxqWmRrhMv5syJR9t2ijjBXthoQ5//7vrSNTrr+fjqaeKBaaS/ec/jpb9VVNUAeCFFwoxYUKh8AYaRUU6vPZatMvPHgAMHlyEN97IhwY7hPuU2luwX7hwAT///DPza5R6/kLeQHl5OaZPn44jR47AaDSiW7duyM7OxqZNm7Br1y68+eabaNSoUZ3O/Y9//MO5PoLIHRkZGc53g6KionD77bcLTuSeK/O3bt1acCL3ML9Yas//zjtRsNkc79o2a1aJxERlFBUAsHNnIGbPlteV9e9fgkGDlJGvpESHoUNN2LtXnn6XklKIESOUMdr48cdheP31aGereb1ewowZ+fj738VfvwMHDBg50ogTJ+SCNjrajjlzLHjoIeWsG1SjsrIybN++XbUt2JnfP2imMPvqq69w5MgRtG7dGq+99pqz49eGDRuwcuVKLF68GFOnTnX7vD/++CMOHDiA+++/Hz/88IOnY5OG5ebmIjMz03mckJCgqgWszC/WpUuXVJ1f7dd//34Dvv1Wfud2/PhCKKVLc36+DsnJRmfRGBdXiTlzLIpYb1ReDjz3nGs79+HDrRg/Xvz2AnY78NZbUViyRG6iERFhxwcfmIVvwi1JjoJx+vRolJXJNzIhoRypqWb87nfim5ColdpbsDO/f9FEYVZZWYm0tDQAwPDhw13aMD/88MPYvHkzDh06hMzMTLRo0aLW583Pz8eqVavQoUMH3HXXXSzMyC3p6enOf5tMJrRs2VJgGvcxv1ibN292/luN+dV+/WfNkhedt2lTgT//WRnroiQJGDcuBmfPOv586/USFi0yIyZG/Loymw144QUjfvxR/hucmFiMKVMKhBeNJSWO9Xj/+pdcbDdqZMPKlblo107sjBizWYdx42KQliZn0+kkJCdbMW6cct4QUCOr1Ypt27bh9OnTLo+rpQU78/sfTRRmhw8fRlFRERo2bIjmzZtf9fGePXsiKysLO3fudKswW758OcrLy/Hss88iNzfXk5FJ4y5evOiyF0e3bt1UtZCV+cU6c+YMjh8/7jxWW361X/8dO4JciouJEwuErzuqsnp1GDZudB3J695d/B5WdjswfnwMNmyQsz30UAnmzLEIv3a5uQEYNsyEjAx5amXbthVYuTIXjRvbBSYD0tODkJQUg/Pn5Zdj9evb8N57Ztx9tzK2E1AjtbdgZ37/pYnCLCsrCwCuWZQBcBZjVZ9XG7t27cIvv/yCxMRENGrUiIUZ1ZokSS6jBQ0aNMCtt94qMJF7mF8sSZKwadMm57Ea86v7+gOzZslrtxISynH//cpo7X7okAFTpkQ7j3v3LkNyslVgIgdJAqZMiXLZnLlv31K8/74Zonu9nDihx+DBsTh1Sg7St28pliwxC932wGYD3n8/Au+8E+mckgoA99xTigULLKhfX2zBqGY1tWCPi4tDr169FN+Cnfn9myYKs5ycHACosfOiyWRy+bwbKS0txUcffYQmTZrg0UcfvalsY8eOveqxoKAgzJw5EwBQr169mzp/Tao6n3GY2PcyMzNx8eJF5/EDDzyABg0aePRrePP+Xpn//vvv93h+b9JC/uqjTWrMr+br/+9/6/Drr/KfxhkzAtCggWd/z+ry+1tUBIwaZUBpqeNFfIMGEtasCUDDhuL/j586NQAffSS3nO/Vy46vvtIjLExstm3bdPjLX/TIy5MLn2eeseG99/QwGLzztxe48f29cAEYOlSPn34KqPYcCVOn2vHSS3oEBNS9i7Q/q6ysxNatW/Hrr786t+gAgNDQUNx///1o3769R0buvfX311f5vUUL+X/55Rc0btxYaA5NFGalpY5ORcE1bDxSteas6vNu5JNPPkF2djbeeOMNVbV2JvGuHO1o3rw5mjZtKi6Qm66Vv1mzZsLyuIv5xVJ/fuD11+UC4/777ejTR/zaLQB46SU9Dh+WX9R89JENdWw07FHz5wfgrbfka9ali4SvvrIhLOw6T/KB9et1ePppvXMPOgB4+20bXnrJLnS9W1qaDsOH65GdLYdo1kzCqlU29OypjJ81NcrKysJ3332HvLw8l8fbtWuH+++/H+Hh4TU8UxmYX6yq/IWFhbjvvvuEZtFE1VF9c7q6fLy6EydOIC0tDXfffTfat29/s9Ewb9686348JyfHrXy1VfVOTnZ2tsfPTTU7efKky2hBx44dvXIPvHV/r8zfqVMnVf0MMb9Yas//r3+FYPduk/P4xRdzkZ3t+fVb7v7+fvNNCJYtk3ONHGlF164FEH1p16wJw8SJMc7j225zrNsqL7cLyyZJjv3d3n5bni4VHCxh/nwzHnmkFLWcOHNTrnV/y8uBmTOj8MEHES6fW7UOLzpaEn4/1aisrAy//vqry36JgGsL9uLiYhQXe24rBE/+/a1NC3lP5/ckreVXQndITRRmVZvRlZVdex1A1eMhN9gZ1Gaz4YMPPkBYWBgGDx7s2ZCkeXa7HTt37nQeN2vWTFVTuK7M37RpU1VNhdVa/tatW6s6v9quv80Gl33B+vUrQefO4ptqZGXpXYqfzp3LMWFCQc1P8JFvvgnBxInyerdbb63EunW5MJnErY2qqAAmTYrGmjXyu/NGow3Ll5vRvbu4RhpZWXokJRnx229y85GQEAlTpzr2TlPw7C7FUnsLduYX63r5RdNEYVa1TqumBh1VQ6s3Ws+Vm5uLU6dOISYm5qqRrqIix8aYx48fx5QpUxASEoKXX375ZqOThhw/fhwWi8V5nJCQIC5MHVyZv1u3buLC1IHW8t9zzz3iwtSB2q//F1+E4vhxxwsJnU7ChAni990qLweSk40oLHSsRYqMtCM11YygoBs80ct++CEYo0cbIUmOFzENG9rwySdiOxwWFuowYoQRmzbJb8A2a1aJVaty0aKFuD3AvvkmBBMmxMBqldeTtW5dgcWLzYiPF9umX63U3oKd+cW6Xn4l/N3VRGFWtYbn5MmT1/x41SantV3rY7FYXF5gVFdUVISDBw8iTPQEelIUm82GjIwM53GrVq2cTWfUgPnFujJ/+/btUb9+fdVMA1T79S8rA955Rx4te/zxEtx+u/gXzbNnR2H3brkKmzXLgqZNxW40/MsvQXj+eRMqKx1FmdHoKMpE5jp/PgCDB8fi0CH5Hfpu3cqxbFkeYmPFFIvFxcD48dFYu9Z1bc3f/16EqVMLEBrK9WTuUnsLduYXqzb59Xr9dc7gG5oozOLj4xEWFoZLly7h5MmTV7XN3759OwCga9eu1z1PgwYNsH79+mt+7MCBA5g6dSo6deqESZMmeSY4acbhw4dhtTraVut0OtWNljG/WFfm7927t+BE7lH79V+3Lsy5YbPBIGHsWPGjZT/9FIzFi+X1SAMHFuGRR2rXwMpbdu8OxNChJmdnyMhIO9auzUPr1uKK2P37DRgyJBYXL8ovqB5+uAQLFphxg9ULXrNvH/D3vxtw+LBcKEZG2jFrlkX4PVSrmlqwN2nSBL1791Z8C3bmF0tN+TVRmBkMBvTr1w9ffvklli1bhkmTJjnXk23YsAFZWVmIj49Hq1atnM9JS0tDWloaevTogYEDB4qKThpQUVGB3bt3O4/j4+MV9Ut+I8wv1rXyG41GgYnco/brX1ysw4IF8mjZwIHFaNZM7KjUpUsBGDMmxnl8220VmDZN7LqyQ4cMeOqpWBQVOd4RDwmxY8WKPHTsKG4d3k8/BeP5543OTICjMcqrr4rZEFySgFWrwjB1qrytAQB06VKORYvMwkc71aiyshK7d+/Gnj17XBqlBQcH44477sBtt92miHVBNWF+sdSYXxOFGQA8/vjj2LdvH44cOYKUlBTEx8cjJycHx44dQ2RkJJKSklw+v6CgAOfPn4fZbBaUmLTiwIEDzsWjer0eXbp0EZzIPcwvFvOLtXx5OC5fdoy2hIRISEkRO1pmtwOjRxuRkyNnWrzYLHTq28mTejz5ZCwsFke1Exgo4aOPzOjZU1xDjdWrw/Dqq9HOzZkDAiS8+WY+hgwR0/0tP1+H8eNj8K9/hbo8PnKkFRMmFAhfF6hG58+fx5YtW1BQ4PqmRMuWLXHnnXc6G78pldrzX7hwAT///DPz+5hmCrOgoCBMnjwZX331FbZu3Yr09HSEh4fjnnvuwYABA7y2kTP5t7KyMuzdu9d53K5dO8Xv11Ed84vF/GLl5+uQmipPF3z6aSsaNRLXwAIAFi2KwNat8p6ckyfno00bcVMFz50LwBNPxCI721EoBgRIeP99M/r0uXYXZG+z24FZsyLx/vvyKGdYmB2LF5tx//1iMmVkBCI52YgzZ+SXVPXrS5g/Pw99+4rJpGa1acGuZMwvltrza6YwAxzF2YABAzBgwIAbfm5iYiISExNrfe527drVuP6M/NfevXud2zEEBgaiU6dOghO5h/nFYn6xliyJcI4CRUbaMXKkVWie9PRAzJkjFxz9+5dg0CBx+//k5ATgiSfqOdffAcDcuRY8/LCYdVKlpcCLLxrx7bfyO90NG9qwcmUu2rf3ffFqtwOLF0dg1qxI58gdANx7rx3Ll9tgMLAoc4eWW7Azv/epPX8VTRVmRL5UXFyM/fv3O487dux4w73ylIT5xWJ+sbKzA7B0qTy69/zzVphM4qYLWiw6jBpldL7Aj4urxJw5FmF7XOXn6zBwYCwyM+WXCdOn52PAgJLrPMt78vJ0GD7chB075NHE+HjHhtZxcb4f5bx8OQApKTH4+Wf5Z16vlzBuXCGmTg1FQAC4YbQbamphbjKZcPfdd6u2Bbva82uhBb4a8lfHwoyojvbs2YPKSse7tCEhIWjfvr3gRO5hfrGYX6yFCyNQXOwYLTOZbHj22SJhWSQJGD8+xjkypddLSE01IyZGTKFYVKTDoEGxOHBAfnd5woQCPP20mGt08qQegwbF4uRJ+SXL3XeX4oMPzIiK8v012rw5GKNHxzjXAQLA735XifffN6N79woEBChz7YoS+UMLdub3HrXnvxYWZkR1YLVacfDgQedxp06dEKSi1d3MLxbzi3XunB6rVsmjZaNGWRERIW60bNWqMGzcKL+YnzChEN26iel2WFoKDB9uQkaGfD9HjrRi9Ggx0zx37gzEsGEm5OXJRdCAAcWYNcsCX89KqqgA5s51Xd8GOKaczpljEVZIq1VNLczj4uLQq1cvxXd3ZX6x1J6/JizMiOpg165dsNsd02fCw8PRtm1bwYncw/xiMb9Y8+dHoLzcMUewcWMbhgwRN1p26JABU6dGO4979y5DUpKYIqiiAkhONmLLFnm64N//XoRJkwqETKncsCEEo0cbUVYmf/EJEwowerTV53lOn9YjOdmIXbvkgjU4WMLkyfkYPLhY2JRTNVJjC/PqKisrsXXrVvzvf/9TbX61X381578RFmZEbrJYLDh69KjzuEuXLjAY1POrxPxiMb9Yx4/rsX59mPN4zJhCYRsRFxfrMHKk0bnnVb16Nrz3nlnIHlx2OzB2bAzS0uSRu8ceK8aMGfk+LzokCfjgg3BMny4XrEFBEt55x4LHH/f9Grd//jMEEybEoKBAvjGtWlVg8WIz2rYV1zFTjWpqId+qVSvccccdim1hXuX8+fP44osvkJeX5/K4mvKr/fqrOX9tqOevKZFCZGRkON+liYqKwu233y44kXuYXyzmF+udd6KcDTaaNavEgAHiuh5OnhyFY8fk+XgLFljQoIHvG1lIEjBpUjS+/FIuWB94oBTz51ug11/niV5QWQm8/no0Vq6Up5rGxNixdGke7rzTt/umlZQAU6ZEY/Vq1y0gnniiCNOnFyAsjFMXa0vtLcyZXyy153cHCzMiN+Tm5iIzM9N5nJCQoKqFpcwvFvOLtX+/waXV+vjxhT5fp1Rl/Xod1q6VX/CPHGkVtjfYzJmRLoXQXXeVYcmSPJ9fm6IiHUaMMOLHH+UhzFtvrcSqVXlo1cq3I1NHjxowcqQRhw/LFyEiwo5Zs/Lx6KNiOlOqkdpbmDO/WGrPXxcszIjckJ6e7vy3yWRCy5YtBaZxH/OLxfxizZ4tLwZv06YCf/6zmBfYmZlAUpI8FNW5czkmTCi4zjO8Z+HCCJdmFl26lGP58jyfT++8eDEAQ4aYsH+/vIarKkv9+r4bRZQkYN26MLz+ehRKS+U3HTp2LEdqqhnNm9t8lkXt1N7CvKb8DRs2RP/+/RU/hVur118t+etK2T9VRApy8eJFnDlzxnncrVs3VS0wZX6xmF+s9PQg/Pe/crUxYUKBkLVcFRXAoEF6FBQ4rl1kpB2pqWaIaGr58cdhmDnTtVhdvToX4eG+naJ36JABgwebcP68/JLkj38swcKFFoSG+i5LQYEOEyfGuIyqAo497l5+uUDIPVIjtbcwv1H+vn37Qq/XI1uhG9Vp/forPf/NYmFGVAuSJLmMFjRo0AC33nqrwETuYX6xmF8sSXJM16vStWs5HnhAzLTB2bMjkZ4uv6iYNcuCpk19Pwrz2WehmDQpxnncvHkl1q3L9XnL959/DsZzzxlRWChfk2efteL11wt8ur5t9+5AJCUZcfq0/LLIZLLh3XctuO8+MT8ralRTC/MmTZqgd+/eim9hXpv8el8vvHSDP1x/rWNhRlQL586dw8WLF53H3bt3V9VoAfOLxfxi/fxzMH79VW4B/8orYtq/b9oUjNRUuUAcOLAIjzxS6vMcGzeGYOzYGOdxkyaV+PTTXJ9OGQSATz4JxcSJMaisdNyMgAAJ06blY9gw3zVksdsdHSBnzoxy5gCA3/++DAsXmtGoke+bsaiR2luYM79Yas/vSSzMiG7gytGCuLg4NGnSRGAi9zC/WMwv1pWjZb17l+H3v/dtdz8AuHQpAKNHxziP4+MlTJvm+3VlmzcHIynJCLtdbtH/ySe5iIvz3aidJAFz5kRiwQL5voSGOqZ0Pvig70ancnICkJISg02b5CmuAQESxo4txOjRVp93pFQrtbcwZ36x1J7f01iYEd3AqVOnkJOT4zzu1q2bwDTuuzJ/9+7dBaZxH/OLpfb8GzeGYO9eeXHQyy/7vhiy24GUFCNycx2v9ENCJKxZU+nT9VMAsGNHEIYPN6KiwlGURUfbsW5dLlq29F1RVlYGjBsX49Kav359G1asyEOnThXXeaZnbdkShNGjjbh8Wa6+Gje24f33zbjjDt8X7mpUWlqKHTt2qLaFOfOLpfb83sLCjOg67HY7du7c6Txu2rQpGjRoIDCRe66VX02djJhfLLXnt9kcIzNV+vUrQefOvnvxXyU1NQJbtshTKefOtaNDB8CXvQP27QvE4MEmlJQ41nKFhdmxalWuTzdINpt1eOYZk8u00ttuq8CqVXm45RbfFIeVlcA770Ri4cIISJI8NeoPfyjB3LkWmEzcm+xG1N7CnPnFUnt+b2NhRnQdx48fh8VicR6rbbSM+cVifrG++CLUuYGzTidhwoRCn2fYuTMQs2fLxWH//iV49lnf/uk9dsyAgQNNzgYbwcESli/PQ0KC74rU06f1eOopE06ckF9w/f73ZVi6NA/R0b4phs6d0yM5OQbp6XJhGBQk4fXXCzBsWJGQdYdqo/YW5swvltrz+wILM6Ia2Gw2ZGRkOI9btWoFk8kkMJF7mF8s5hervByYN08uiB5/vAS33+7bTYrz83VITjbCZnO84o+Lq8ScORbodPV8luH0aT2eeCIWeXmOKXt6vYQlS/LQq5fvpuvt3h2IoUNNyMmRpw3+9a/FmDPH4rMW9N99F4KXXopBfr7c/bFFi0osXpyH9u19+3OhRmpvYc78Yqk9vy+xMCOqweHDh2G1WgE4htgTEhIEJ3IP84vF/GKtXRuGM2ccf+IMBgkvveTb0TJJcqylOnvWkUGvl7Bokdmn7egvXgzAE0/E4uJFR0Gk00l47z2LTxtspKWFIDk5xmWz5pdeKsCLL1p9MkJVWgpMmxaNFSvCXR7/61+L8fbb+T7fs02N1N7CnPnFUnt+X2NhRnQNFRUV2L17t/M4Pj5eVf95ML9YzC9WcbEO774rj5Y9+WSxz/cKW706DBs3yt3Exo8vRPfuvps6mJenw8CBscjKkv/Mz5yZj0cfLbnOszzrww/DMXVqlHMtV2CghDlzLPjb33yT4fhxA0aMMOLQIXn6ZFiYHTNm5OOvf/XddVArtbcwZ36x1J5fFBZmRNdw4MAB56JUvV6PLl26CE7kHuYXi/nFWr48HNnZcgfEMWN8O1p26JABU6ZEO4979SpDcrLVZ1+/sFCHp56KxZEjckHy+uv5eOop3+wPZrMBU6dG4aOPIpyPRUXZ8eGHvplCKUnA+vWhmDQp2tnsBADaty9HaqrZp10o1UrtLcyZXyy15xeJhRnRFcrKyrBnzx7ncbt27RAeHn6dZyhLWVkZ9u7d6zxmft9ifrHy83VITZULgmHDiny6SXBJiQ5JSUaUljreCY6NteG998zw1fKJkhIdhg41Yc8eefFWSkohRowo8snXLy7WITk5Bv/+t/zC63e/q8TKlXk+WeNXWKjDK69E46uvwlweHz7cikmTChAcXMMTCYDj93/79u2qbWHO/GKpPX9paanoCCzMiK60b98+lJc73tUNDAxEp06dBCdyz759+1BW5lhDosb8e/fuVXV+Xn+xliyJgMXiqIIiI+1ISvLtaNkbb0Th6FF5pGrBAgsaNvRNYVheDjz3nNGlHf3w4VaMH++ba3D5csBVRWGnTuX4+OM8NGjg/WuwZ08gkpKMOHVKfmkTE2PH/Pm+3bhajdTewpz5xdJK/p07d+LFF18UmoWFGVE1JSUl2Ldvn/O4Y8eOCAkJEZjIPcXFxarPv3//fuexGvPz+ouTnR2ApUvl0b3nn7f6dF+qb74Jwdq18tcfMcKKvn19UxDYbMALLxjx44/y/UpMLMaUKQU+abJx9KgBgwaZnM1OAOCBB0qRmmpGWJh374EkOdazvf12lHPzbADo2bMMCxeaERfnuxFTNVJ7C3PmF0sL+bdu3YozZ84oonhkYUZUzW+//YbKSsd0m5CQELRv315wIvfs2bOH+QVifrEWLoxAcbFjtMxksuHZZ30zfQ8AsrL0mDAhxnncpUs5Jk4sqPkJHmS3AxMmRGPDBnn64EMPlWDOHItPplBu2xaEZ54xoaBA/mJPP23FlCkF0Ouv80QPyMsLwJgxMfjvf+WCNCBAQkqKFWPGFMLAVzk1UnsLc+YXS6v5ReN/WUT/z2q14uDBg87jTp06IchXm+x4wJX5O3furOr8vP6+pfbrf+6cHqtWyaNVo0ZZERHhm9Gy8nIgOdkIq1WeQrlokdkne3RJkqPRxiefyN97376leP99s0+Kks8/D8W4cTHOkSqdTsLkyQU+KYr/978gjBpldG4HAACNGtmwcKEZv/+97/ZpU6OaWpjHxcWhV69eiu/CyvxiaTV/48aNBSWSsTAj+n+7du2C3e6Y8hIeHo62bdsKTuSeK/O3adNGcCL38PqLpfbrP39+BMrLHcVB48Y2DBniu9Gy2bOjsHu3XIXNmmXxWXv+efMisXSp3OykZ88yfPih94tCSQLefTcCc+fKL8BCQux4/30L/vhH7y6gr6wE3n03Eu++G+FsxQ8A991XinfftcBk4tTFmqi9hTnzi6X1/K1btxaYzoGFGREAi8WCo0ePOo+7dOkCg4rmwFyZv2vXrszvQ8wv1vHjeqxfL3fhe/HFQvhqadxPPwVj8WK5MBo4sAiPPOKbzl4ffBCOefPk/do6dnQ02ggN9e5IYXk5MGFCDD77TL7msbE2fPxxHrp29e6UoPPnAzBqlBHbt8sNTgIDJUyaVIBnninyyXo6taqphXnLli1x5513Kr6FudpbsGs1v9p/fqrnV0JRqZ6/vERelJGR4Xz3JCoqCrfffrvgRO65Mr8S3vVxB/OLpfb877wTBZvN8Qe1WbNKJCb6Zr+uS5cCkJIS4zy+7bYKTJvmm3Vla9aEYdo0ea+01q0rsGZNHqKivFuU5efr8OyzJmzbJhdGLVtWYNWqPK+PEv7738F48UWjs+sm4Ljfixeb0bGjctaIKI0WWphv377d5c0jQD351X79md+3WJiR38vNzUVmZqbzOCEhQdELVq/E/GIxv1j79xvw7bfyO7XjxhXCF4217HYgJcWI3Fx5I+vFi81eH60CHN0fJ06Ui7KmTSuxbl2u16fwnT2rx6BBJpftAO64owxLl+bBaPTe911WBrz1luuG1QDw2GPFmDEjH5GRvuu8qSZaaWHO/GIwvxiaKszKy8vx9ddfY9u2bcjJyUFERAQ6deqEAQMGIDY2tlbnsNls+OKLL3DixAmcO3cOBQUFsNlsiI2NRceOHfHoo4+iXr16Xv5OyJfS09Od/zaZTGjZsqXANO5jfrGYX6zZs+U1Tm3aVOCRR0qu89mek5oagS1b5FGjyZPz0aaN9zdQ/s9/gjF6tNG5tqpRIxvWrcv1+ibae/YEYsgQE7Kz5UYbjz1WjHfesXh10+YTJ/RISjJi/3550VxoqB1vvZWPxMQSTl2sgZZamFenpvxqv/7ML4ZmCrPy8nJMnz4dR44cgdFoRLdu3ZCdnY1NmzZh165dePPNN9GoUaMbnqeiogKff/45QkJC0LRpU7Ro0QKVlZU4deoU/v3vf2Pr1q1444030KJFCx98V+RtFy9edPmPv1u3boqYY1xbzC8W84uVnh7k0iZ9woQCn7SH37kzELNny2u7+vcvwaBB3p8+uW1bEJ5/3oTKSsc9MhodRZkvphAmJRlRUiJf3JSUQowfX+jVwujzz0PxyivRzi0QAEfxvWSJGa1aeb8IViOttDBPT093bt0BOPJ37doVHTt2VEV+tV9/5hdHM4XZV199hSNHjqB169Z47bXXnJuibtiwAStXrsTixYsxderUG54nMDAQ06ZNw2233QZ9tQ1Y7HY7PvnkE3z99df46KOP8NZbb3nteyHfkCTJZbSgQYMGuPXWWwUmco8kSdi5c6fzmPl9iz8/YkkSMGuWXBx17VqOBx7w/mbO+fk6JCcbnWva4uIqMWeOxesjN7t2BWLYMBPKyhxfKDLSjrVr89C6tXcLlI8/DsPrr0fDbnd8XYNBwqxZFjzxhPdGJouKdHj11Wh8/nmYy+NDhhThjTfyfdbYRW1qagHepEkT9O7dW7UtzJnfN5hfGTRRmFVWViItLQ0AMHz4cGdRBgAPP/wwNm/ejEOHDiEzM/OGI116vR7x8fFXPR4QEIABAwbgX//6F44dO4bS0lKXr0Pqc+7cOVy8eNF53L17d1WNFpw8eRIXLlxwHqst/7lz51SfX80/P2q//j//HIz//U+eQ/fyywVeL44kCRg3LgZnzzr+dOr1EhYtMiMmxrtrnA4dMmDQoFgUFTne6Q0JsWPFijyvNryw24Hp06Pwj3/I67oiIuz48EMz7r7bewXw/v0GjBxpQmam/PIkOtqOd97xfht+tdJ6C3Pm9y7mVxZNFGaHDx9GUVERGjZsiObNm1/18Z49eyIrKws7d+68qSmIOp0OAQEB0Ol0LqNppD5XjnbExcWhSZMmAhO5R5IkbNq0yXmsxvxqv/7ML44kATNnyqNlvXuX4a67vL+h8OrVYdi40bXRSPfu3u0GePKkHk8+GevsRBgYKOGjj8zo2dN7329JiQ6jR8e4fK+NG9uwalWu19bRSRKwfHk4pk+Pcu5HBwDdupVj0SIzfvc73+wLpzYXLlzAli1bkJ+f7/K4llqYK5narz/zK48mCrOsrCwAuGZRBsBZjFV9Xl1IkoSvv/4aZWVl6NChgyI7uVDtnTp1Cjk5Oc7jbt26CUzjviNHjlw1WqMmar/+V+bn9fetjRtDsHev3Azi5Ze936L+0CEDpkyROyH27l2GUaOsXv2a584FYMCAWGfDjYAAxwhdnz7eG7HKyQnA0KEmlw2z27cvx4oVeV5rMJKXp8O4cTH4/nv5RZROJ+GFF6x46aVCqGhLPZ9RWwvwK6k9f0lJCX7++WfV5lf79Vd7/uvRxH93VS8wauq8aDKZXD6vtlavXo38/HyUlJQgKysLly5dQlxcHJ5//vmbC0xC2e12l7U1TZs2RYMGDQQmco/dbsfmzZudx02bNlV0h6EraeH6X5mf1993bDa4NN7o168EnTt7d9SquFiHkSONKC11jOTExtqwYIHZq41GcnIC8MQT9XDunPxneu5cCx56yHvT+Y4fN2DQIBNOn5a/5r33lmLJEjPCw70zXXP79iAkJxtx4YI8C6VBAxvee8+M3r29PwqqNmptAV5FC/kPHjyI//znPygqKnI+rqb8ar/+as5fG5oozEpLHX+ogmvo2Vu1Fqzq82pr+/btuHTpkvP4lltuwejRo916ETN27NirHgsKCsLMmTMBwGut9w3//xajml4w+srevXthsVicxw8++KCqrtPevXuRm5vrPFZjfrVff2/n9+bvr9qv/8qVOhw/7rg+Op2EGTMMXs8/YoQex47JVdjHH0to3752W7Bcy43ur9kMDBpkQGamPKVv/nwbkpMjAERc8zk3a8sWHf76Vz3MZvlrPvecDe++q4fB4Pm/UzYbMHNmAKZPD3A2FgGAP/zBjo8+sqNBg+jrPFvZvPX7m5+fj++//x7Hjx93ebxBgwZ46KGH0LhxY49+PU+rKX/Dhg3Rv39/1eZX+/VnfmXRRGFWfbFfXT5ek4ULFwIACgoKkJmZiU8++QQvv/wynn/+efTp06dO5ySxKisrsWXLFudx+/btVfWilPnFYn6xysqA6dPlkZUnn5TQrp13v+b69TosWyYXZWPH2vCHP3iv2YfVCjzyiB5798rFytSpNiQne2+fsnXrdHj2Wb3L2q6ZM2148UW7VxqqnD8PDBmix+bN8nU1GCS8+aYdY8bYfbLlgZrY7XZkZGRg8+bNKC+XRxENBgN69+6NHj16KHrdO/OLxfzqoonCrGpxX1nZtefdVz1e1y6KUVFR6Ny5M1q3bo1x48Zh6dKlaN++fa1Gu+bNm3fdj+fk5NS5cLyeqhdb2dnZHj+3mh04cMC5SFSn06Fdu3aqukbV8wcEBKg6v9qvvzfze+v3V+3Xf/nyMGRlxQBwvJAfNSob2dneawpx+rQeI0fKhWuXLuV44YUc3Owlq+n+lpYCQ4fG4tdf5ak4I0daMXx4wU1/zWuRJOC99yJcNukODpawYIEZf/pTKdyc/V8rP/wQjBdfjEFenlx93XprJVJTzejSpQLVJgOolid/f2vTAjwvL++mv463aDV/s2bN0LNnT9XmV/v191Z+nU4nfORNE4VZVYGUW8P/6FU37WanDYaFhaFr167497//jb179+Lee++9qfORb1VUVGD37t3O4/j4eNXsawFcnb9z586qzq/268/8vlVcrMOCBfLasoEDi726sXJFBZCUZERhoaOAiIy0Y9EiM4KCbvDEm/x6W7bIU/IHDSrCpEne2QagogJ4+eVofPJJuPMxk8mGZcvyvNJpsrwcmDHDtf0+APz5zyWYNcuCqCjvbjmgNmpvAa7l/A888AA6dOjgdt8CX9Ly9VdD/puhicKsadOmABz7Ol1LZmamy+fdjKoXMle2diXlO3DggHOxqF6vR5cuXQQnck/1/AaDAXfddZfb6yZF0tL1Z37fW7483NmdMCREQkpKoVe/3uzZkS6dCWfNsnitELTbgbFjXbsSPvZYMd5+O98rRVlBgQ7PP2/Ezz/Ls0iaN6/EqlW5aN7c89/jyZN6JCcbsWePfD1DQuyYPr0ATz5Z7PX959RG7S3ktZ7/1ltvFZSsdrR+/ZWe/2ZpojCLj49HWFgYLl26hJMnT17VNn/79u0AgK5du9701zp48CAAoFGjRjd9LvKdsrIy7N2713ncrl07hIeHX+cZynJl/m7duiEyMlI1hZnWrj/z+1Z+vg6pqfJIy7BhRV5r3Q4AmzYFIzW1+uhcER55xDu/a5IEvPpqNL78Msz52B/+UIL58y1eWWt17lwAhgyJxaFD8nTJ7t3LsGxZHkwmz49aff11KCZOjIbVKn8z8fEVWLzYjNatvbMnmlqpvQU484vF/NqgicLMYDCgX79++PLLL7Fs2TJMmjTJuZ5sw4YNyMrKQnx8PFq1auV8TlpaGtLS0tCjRw8MHDjQ+fjOnTuh1+vRuXNnl2HSsrIyfPnllzh48CBiYmLQuXNnn31/dPP27t3rXGsYGBiITp06CU7knivz33HHHYITuUdr15/5fWvJkgjnBssREXYkJXlvtOzSpQCMHh3jPL7ttgpMm+a9GRIzZkRi1Sq5SL7rrjKkpprhjY7P+/cbMHhwLC5dkhfK/+lPJXj3XTPquAS7RsXFOrz+epTLVEnAMT1z8uR8aPxNb7eovQU484vF/NqiicIMAB5//HHs27cPR44cQUpKCuLj45GTk4Njx44hMjISSUlJLp9fUFCA8+fPw2w2uzyemZmJzz//HEajEc2bN0dYWBgsFgtOnToFq9WKsLAwvPjii3VuJEK+V1JSgv379zuPO3bsqKr7d638YWFh13mGshQXF2vu+jO/72RnB2DpUvnF/YgRVq+M7ACOKYUpKUbk5spTJhcvNiM01Dtfb+HCCCxaJI/Mde1ajuXL8zxeJAHAf/8bjBEjjCgulkeukpML8fLLhR4fmTt40ICRI404flx+MRUVZcecORY8/LA6Rvl9xWq1Ytu2bTh9+rTL47Gxsejdu7fiu6Yyv1jMrz2aKcyCgoIwefJkfPXVV9i6dSvS09MRHh6Oe+65BwMGDKh144+ePXuitLQUhw4dwokTJ2C1WhEUFIRGjRrh/vvvxx//+EcYjUYvfzfkSb/99hsqKx1TZkJCQtC+fXvBidyj9vx79uxRdX61X3+151+4MMJZTJhMNjz7bNENnlF3qakRLs033ngjH23aeGe6XWpqAGbOlJuvtG1bgVWrcr2ykfPKlWGYNCnauV+YXi/h7bfz8dRTxR79OpIErFgRhmnTolFWJs846dq1HKmpZtxyi/eataiN3W7HwYMHsXPnTlRUyM1W9Ho9EhIS0KFDBwQoeN8A5heL+bVLM4UZ4CjOBgwYgAEDBtzwcxMTE5GYmHjV402bNsXgwYO9EY8EsFqtznWBgKOTYZC32qp5gdbyd+rUSdX51X791Zb/3Dm9yzS/UaOsiIjwzujVzp2BmD1bHr3q378Egwd7tnCpsmqVDmPGyNMJW7SoxNq1uYiJ8ez3Zrc7pkpWXy8XHm7HkiVm3HvvtbeXqSuLRYfx42OwcaPrHMXk5EKMH1/olamZalVTC/C4uDj06tVL8d1SmV8s5tc2TRVmRFfatWsX7HZHk4Dw8HC0adNGcCL3aC1/27ZtBSdyj9auv9ryz58f4dz0uHFjG4YM8c5omcWiQ3KyETab42v97neVmDPH4pVugRs3huD55+WiLC6uEp98kov69T3bzKS01DEtc8MGuVBq1MiGFSty0b69Z0cB09MDkZxsxLlz8kuKevVseO89C+65x7MFoJqpvQU484vF/P6BhRlplsViwdGjR53HXbp0gcGgnh955heL+cU6flyP9evltZRjxhR6Ze2VJAHjx8fg7FnHtdHrJSxaZPb46BUAbN4cjKQko3NKYf36NnzySS7i4jw7xS8vLwBPP21Eero8LbNNmwqsWJGLuDjPFYB2O7BoUQTmzIl0FrUA0Lt3Gd57z4wGDbzXOVNtLly4gC1btjg3eK+ilhbgzC8W8/sP9fyVJnJTRkaG812ZqKgo3H777YITuYf5xWJ+sebOjXK+2G/WrBIDBnhnWuHq1WEu0+/Gjy9Et26e32B5x44gPP20ERUVju8pJkbC2rW5aNHCs0VZZqYegwbF4tQp+c97nz6lWLLEjMhIzxWbly8HYPRo1w2x9XoJEycWYuRIq1da/auR2luAM79YzO9/WJiRJuXm5jo3FgeAhIQEVS0kZX6xmF+s/fsN+Oc/5WJp3DjvrFE6dMiAKVOince9e5chOdnq8a+zb18gBg82obTUcQ/CwyX88582tGjh6SmFQRg2zAizWZ4qOXBgEd5+O9+j12/TpmCkpMQgJ0f+Or/7XSUWLTJ7pahVI0mScOLECdW2AFd7C3PmF0vt+UViYUaalJ6e7vy3yWRCy5YtBaZxH/OLxfxizZ4tL/5u06YCjzxScp3PrpuSEh2SkowoLXWMYNWrZ8OCBWaPj/QcO2bAwIEmFBY6ThwcLOHLL23o2VNCdrbnvs6334ZgzBijSzfEV14pQHKy1WNr5crLHfdm8eIIl8f79y/B3LkWREd7pzGL2uTn5+P777/H8ePHXR5XSwtwq9WKrVu34syZMy6PM79vML9/Y2FGmnPx4kWX/xC6deumqgWlzC8W84uVnh6E//5XXkw2YUKBV6bFvfFGFI4eld+xXbDAgoYNPbsm6swZPZ54IhZ5eY6RJb1ewpIleejb13NdxyQJWLw4Am+9JZ8zKEjCu++a8cgjntszLCtLj+RkI3bvlrt6hoRImDLF0XZfRT9iXlPVAjwjIwPl5eXOx9XSAlztLcyZXywt5D9y5AgaN24sNAcLM9IUSZJcRgsaNGiAW2+9VWAi9zC/WMwvliQBM2e6brj8wAOe7+r3zTchWLtWbsM/cqQVffp49utcuhSAJ56IxcWLjqJMp5OwYIEFDz7oua9TWQlMmhSN1avl7yUmxo5ly/LQs2f5dZ7pnm++CcHEiTHOUT8AuO22CixebPbaPm9qU1ML8CZNmqB3796KbwHO/GIxv1hV+c1mM+677z6hWViYkaacPXsWFy9edB6rbbSA+cVifrE2bw7Gr7/KzSQmTizw+EhMVpYeEyfGOI+7dCnHhAkFHv0aeXk6PPmkawOOmTPz8dhjnpuSabXqMGKEET/9JI8uNm1aiZUrc9GqlWcaipSU6DB5chTWrAl3eXzgwCJMnVqAsDBOXaypBXhoaCh69Oih+Bbgam9hzvxiaS2/Eta9sTAjzZAkCTt37nQex8XFIS4uTmAi9zC/WMwvliQBs2bJo2W9e5ehVy/PjfoAjjVSyclG58hPZKQdixaZ4ck9twsLdXjqqVgcOSL/gX/9dcd0P0+5cCEAQ4bE4sAB+Wt07VqOjz/OQ2ysZ6ZjHj5swMiRRpfpnhERdsyebfHoFEk1O3/+PLZs2YKCAtfCvl27drj//vtRXOydTqKeUlP+Vq1a4Y477lB8C3PmF0ur+UVjYUaacerUKeTk5DiPu3XrJjCN+5hfLOYX67vvQrB3r1whTZzo+T+Ws2dHuayRmjXLgqZNPdeuvqREh6FDTdizR/4aKSmFGDHCcxtjHzxowKBB8hRJwNF84733zPDE6yBJAtasCcPkydHOxigA0LlzOVJTzR69Xmp1oxbgXbt2BQDFFmZqb2HO/GJpOf/dd98tKJXM44VZTk4OAgICYDKZavX5eXl5sNvtqFevnqejkB+x2+0uowVNmzZFgwYNBCZyD/OLxfxi2WzA7NnyaFm/fiXo0sWzbdd/+inYpZvgk08WeXTkp7wceO45o8tUzKeftmL8+EKPfY3Nm4Px3HNGWK3yWq/nn7fitdc80yAlP1+HCRNisGGDa4X3/PNWvPxygUdHFtXoei3A27Vrh27duiliKlRN1N7CnPnF0vLPf1X+IAX8J+fxwiw5ORkxMTH44IMPavX5r7/+OnJzc/HJJ594Ogr5kePHj8NisTiP1TZawPxiMb9YX3wRimPHHH/QdToJEyZ4rpgBHI04UlJinMe33VaB6dM9NyJnswEvvGDEjz/K670SE4sxdarn1sitWxeGiROjnZtuBwRImD49H0OHemZUZteuQCQlGXHmjPyyIDbWhnffteDeez3fgEVt1N4C3Gq1Ytu2bTh9+rTL4yaTCXfffTfze5kW8qv9518t+RUxlbH6gkEid9lsNmRkZDiPW7VqVesRWyVgfrGYX6yyMuCdd+TRssceK8Htt3uu05/dDqSkGJGb65j6FxIiYfFiM0JDPfN3x24HJkyIdhll6t+/BHPmWDwyiiVJjtHE996Tr1FoqB2LF5s90rHSbgeWLInArFmRqKyUq8i77irDwoVmj28hoDZaaAHO/OIwv1hqzC+8MKuoqIBer7/xJxLV4PDhw7BarQAcQ9IJCQmCE7mH+cVifrHWrQvD2bOOP0UGg4Rx4zw7WpaaGoEtW+TphVOm5HusxbskAVOnRuGTT+SuhX37luL9980weOCva1kZ8NJLMfjqqzDnYw0a2LBiRR46drz5qZ7Z2Y6RxM2b5ZE+vV7CSy8VYtQoK/z9T3NNLcDj4uLQq1cv1bQAV3sLc+YXQ6s//0rPL7Qwy8vLQ0FBAaKjo0XGIBWrqKjA7t27ncfx8fGK/WW7FuYXi/nFKi7W4d135ZGgJ58s9mhziZ07A13WrvXvX+LR7ojz5kVi6VJ53VrPnmX48EMzgoOv86RaMpt1GD7chO3b5ZPdfnsFVq3KQ1zczV+jn38OxujRMcjOlquvJk0qkZpqQffunu2GqTZaawFehfl9g/nFUnv+my7MDh48iIMHD7o8Vlpais8//7zG50iShKKiIuzevRuSJKFVq1Y3G4P81IEDB5yLOPV6Pbp06SI4kXuYXyzmF2vZsnBnYRASImHMGM+NllksOiQnG51rsn73u0rMmWPx2JqvDz4Ix7x5ctHXoYOjXb0npkhmZekxaJAJJ07IC+l79SrDhx/mISrq5s5fUQHMnRuJRYsiIEnyxejXrwRz51pgNPr30oKaWmi3bNkSd955p2pbgDO/bzC/WGrPD3igMDtw4MBVRVhpaSk+++yzWj0/MDAQjz322M3GID9UVlaGPXv2OI/btWuH8PDw6zxDWZhfLOYXKz9fh9RUebRp2LAiNGrkmfVMkgSMHx/jnCKp10tYtMiMmBjPFB1r14Zh2jR5pkfr1hVYu/bmiyYAyMgIxLBhJueaOMDRSGTWLMtNd0U8c0aP5GQjMjLkEwUHS3jjjXwMGVLs8c281UTLLcCZ3/uYXyy156/upguz+vXro23bts7jgwcPwmAwoHXr1jU+R6fTITQ0FLfccgv69OmDRo0a3WwM8kP79u1Debljyk1gYCA6deokOJF7mF8s5hdryZII5OfLGz0nJXlutGz16jBs3Ci/Mzp+fCG6dfNM+/1vvgnBhAlyUXbrrZVYuzYXJtPNF5UbN4bghReMLvuHjRtXgDFjrDddNG3cGIJx42Kc1xwAWrasQGqqGe3be67ZitpouYU583sf84ul9vzXctOFWZ8+fdCnTx/n8YABAxAREYHJkyff7KmJalRSUoJ9+/Y5jzt27IiQkJDrPENZmF8s5hcrOzsAS5fKo3vPP2+FyeSZ0axDhwyYMkUunHr3LkNystUj5/7hh2CMHm10TgFs1MiGTz7JRePGN1eUSRLwj3+EY/r0KOe5AwMlvPOOBX/5S8kNnn19JSXAtGnRWLnSdTQ1MbEYb76Zj/Bw/526WFMLcyW20L4W5heL+cVSe/6aeLz5x8iRIxWxQRtp22+//YbKSse7vMHBwWjfvr3gRO5hfrGYX6yFCyNQXOwYuTGZbHj22SKPnLekRIekJHnEKTbWhgULzB5pW//LL0F4/nmTs6W80WjDunW5N92sxGYDJk+OwvLl8rTO6Gg7li7Nw+9/f3NNOI4dM2DkSCMOHZLfMQ4Pt2PGjPybLvjUTI0ttKtjfrHsdjsyMjKwadMm1eZX+/VXc/4b8XhhVn30jMgbrFarS8OZzp07q+rNAOYXi/nFOndOj1Wr5NGbUaOsiIjwzKjNG29E4ehRuQhZsMDikX24du0KxNChJmfBFxlpx9q1eWjd+uamABYVOQrJH36QRztvuaUSq1bl4bbb6n5uSQI+/TQUkyZFo7RUfoHSoUM5UlPNaNHCc50v1UarLcyZ3zfy8vLwr3/9C+fPn3d5XE351X791Zy/NoTvY0bkrl27dsFud7zYCg8Pd1njqAbMLxbzizV/fgTKyx0FTuPGNgwZ4pnRsm++CcHatXLBN3KkFX373vwGzIcOGTBoUCyKihwFTkiIHStX3vw+YhcuAH/5Syz27ZOL6s6dHZ0d69evezFZWKjDyy9H4+uvw1wef+YZK159tcAjrfzVSO0ttJlfLOYXS+353cHCjFTFYrHg6NGjzuOuXbvC4ImdXH2E+cVifrFOnNBj/Xq5YBgzphCeWBqXlaXHxIkxzuPOncsxYUJBzU+opZMn9Rg4MBYWi6MoCwyUsHSpGT163NwUwwMHgEceMeD0afmFxB/+UIL337cgLKzuo4e//RaIpCQjsrLknwmj0Yb58y144IGbL1LVqqYW2q1atcIdd9yh+BbazC8W84ul9vzuUs9fdCIAGRkZzndLoqKirtv9U4mYXyzmF2vu3CjnvmLNmlViwICb3+y5ogJITjaisFDu8Jiaar7p1vLnzgXgiSdicfmyo219QICj5f7NjsJt2RKE554zoKBALsqeecaKN94ogF5/nSdeh93uaB4yY0aUcw0cANx5ZxkWLjTfdHMStVJ7C23mF6um/NHR0ejXr5/ip81p9fqrJX9dsTAj1cjNzUVmZqbzOCEhQVULPJlfLOYXa/9+A7791rWFvSe6GM+aFYXdu4OqHVtuuiFHTk4AnniinnMfNACYO9eChx4qvanzrl8fivHjY5zFk04nYerUAgwfXvfpnLm5ARgzJgY//igPPQYESBgzxooxYwrrXOyp2fVaaLdr1w7dunVTdAtt5hfrRvn79euHoKAgZGdnC0xZM61ff6Xnv1kszEg10tPTnf82mUxo2bKlwDTuY36xmF+sWbPkd5fbtKnAn/98810BN20KxuLFcjfDgQOL8MgjN1c85efrMHBgLDIz5T+P06fnY8CAuueVJOCddyIxf36k87HQUMcI3B/+UPe827YF4YUXjLh0Sa6+GjWy4f33zbjzzpubbqlWVqsVW7duxZkzZ1weV0sLbeYXqzb5ldxsyR+uv9axMCNVuHjxossvardu3VS10JP5xWJ+sdLTg1xGdCZMKLjpFvaXLgVg9OgY5/Ftt1Vg2rSbW1dWXKzD4MGxOHBAfjd2/PgCPP103Ue0ysuBceNi8MUX8tq6Bg0kfPWVDc2a1a0oq6wE5s+PxIIFEc59zwDg/vtLMX++xSObXauN2ltoM79YzC+W2vN7EgszUjxJkrBz507ncYMGDXDrrbcKTOQe5heL+cWSJGDWLHmkqGvX8ptuRGG3AykpRuTmOkaKQkIkLF5sRmho3RtnlJYCw4aZsHOn/G74yJFWpKTUfXNqi0WHZ54x4X//k1sh3nZbBTZsAJo3B+oyE+rcuQCMGmXEjh3yOYOCJLz2mqOAVFG97jE1tdCOi4tDr169FL8WiPnFYn6x1J7f01iYkeKdPXsWFy5ccB6rbbSA+cVifrE2bw52KUwmTiy46eIhNTUCW7bI55w8OR9t2tR936+KCiApyYitW+VzDhpUhEmT6p71zBk9Bg0y4dgxefTtzjvLsHRpHpo3r1enc6alheCll2KcXSIBRxOVJUvM6NDh5tr3q5HaW2gzv1jML5ba83uLpgqz8vJyfP3119i2bRtycnIQERGBTp06YcCAAYiNja3VOYqKirB7925kZGTg1KlTyMnJgU6nw+9+9zv06tULDz74oKraU6vdlaMFcXFxiIuLE5jIPcwvFvOLdeVoWe/eZejV6+bWPu3cGYjZs+Vz9u9fgkGD6t7d0W4Hxo6Nwfffy41JHnusGG+/nV/nomzPnkAMGWJCdra89uvxx4sxd66lTvuIlZYCb74ZheXLI1wef/zxYsyYke+xDbrVpKYW2i1btsSdd96p+BbazC8W84ul9vzepJkKo7y8HNOnT8eRI0dgNBrRrVs3ZGdnY9OmTdi1axfefPNNNGrU6Ibn+ec//4kvv/wSOp0OzZs3R0JCAgoKCnDkyBEcP34cv/76KyZNmoRgf92l08eqiuMq3bp1E5jGfcwvFvOLtXFjCPbulacGTpx4c2vALBYdkpONzpb7cXGVmDPHUucCSpKASZOi8eWX8vqvBx8swfz5ljqvgfv3v4ORlGRESYl8ghdfLMRLLxXWKefx43okJZlc1r2Fhdnx9tv5+Nvfbr6BitqovYU284vF/GKpPb8vaKYw++qrr3DkyBG0bt0ar732GkL+f9fSDRs2YOXKlVi8eDGmTp16w/OEhITgsccewx/+8AeYTCbn4xcuXMD06dNx+PBhfPHFFxg4cKDXvhdysNvtLqMFTZs2RYMGDQQmcg/zi8X8YtlswJw58shWv34l6NKl7tPtJAkYPz7G2cJer3d0NYyJqfto0YwZkVi5Mtx5fNddZVi82FznNv7LloXjjTeinA05DAYJs2db6tzR8bPPQvHqq9EoLpaLvHbtKpCamodWrW5uSwC1uV4L7fbt2yMhIUHRLbSZXyzmF0vt+X1JE4VZZWUl0tLSAADDhw93FmUA8PDDD2Pz5s04dOgQMjMz0aJFi+ue69FHH73m440bN8bAgQPx3nvvYdu2bSzMfOD48eOwWCzOY7WNFjC/WGrPv3//flXn/+KLUOf6Kp1OwoQJhTd1vlWrwrBxo+s+aN27173QW7gwAosWuTYlWb48D9X+fNSazQZMnRqFjz6SpxpGRtrx4Yd56N3b/ambVqsOr7ziOpIHAE8/bcWkSQV1yqhmVqsV27Ztw+nTp10eV0sLbeYXi/nFUnt+X9NEYXb48GEUFRWhYcOGaN68+VUf79mzJ7KysrBz584bFmbX06xZMwCA2Wyu8zmodmw2GzIyMpzHrVq1chnBVDrmF0sL+bds2eI8Vlv+8nJg3jy56HnssRLcfnvdm3McOmTA1KnRzuNevcqQnFz3bokffxyGmTNd91VbtSoX4eHuj76VlOgwalQM0tLkorFJk0qsWpWH+Hj3v+d9+wIxcqQRJ0/Kf55jYux45x0L+vW7uT3a1OZ6LbS7du2Kjh07KrqFNvOLxfxiqT2/KJoozLKysgDgmkUZAGcxVvV5dXXp0iUAQExMzE2dh27s8OHDsFodL7x0Oh0SEhIEJ3IP84ul9vy7d+9Gfn4+AHXmX7s2DGfOOP68GAwSxo2r+2hZcbEOI0caUVrqmB4YG2vDe++Z67wG7LPPQjFpUozzuEWLSqxbl1unKZHZ2QEYOtSE336T19F16FCOFSvy0LChe3uJSRLw0UfhePPNKFRUyIvRevQow/vvWxAX519TF2tqod2kSRP07t1b8S20L1++jH/+85+qza/268/8Yqk9v0iaKMyqFsfX1Hmx6p3m6ovo62Ljxo0A1DelSG0qKiqwe/du53F8fLyqfomvzN+mTRtV51f79Vdj/m3btjmP1Za/uFiHd9+VR8uefLIYTZvWvaiYPDnKpeX8ggUWt4ueKhs3hmDs2BjncZMmlfjkk1zUr+/++Y4dM2DQIJOzAAWA++4rxeLFZrdH3vLydBg71oj//Eeeo6jTSUhJseLFFwvhT42A1d5Cu7KyEps2bcKvv/4Ku13+uVJTfrVff+YXRwv5RdPEf/elpY7pHTV1Sqxac1b1eXXx73//G/v27UN4eHiN69CuZezYsVc9FhQUhJkzZwIA6tWr2342N1LV0l+Nc3d/+eUX5+JQg8GA+++/H5GRkTd4lnJcmf++++7zeH5v3l+tXX815i8qKgKgzvyzZwc428SHhEiYPj2ozj+n69frsHat/Gdq7FgbEhPrVqT+5z86JCXpYbc7XhQ0aCDh3/+W0Lq1+1NEN2/W4W9/08NikV9gjBhhw7x5ehgMN/4/vfrv75YtOgwerMe5c/K5GjeWsGKFDX36hADwnwVlp06dQlpaGvLy8lweb9euHe6//36Eh4fX8ExlyMrKwnfffcf8gvjq58dbf3/58y/WqVOn8MMPP2DkyJFCc2iiMKteldfl4zdy8OBBfPzxx9DpdBg5cqSq1nqoTWlpKX799VfncUJCgqpelDK/WMwvlsUCzJ0rzzFMSrKjSZO6nSszE0hKkvcB69bNjmnT6jZStm2bo5CqmiIYEyNh48ZKtG7t/rnWrNHhuefkc+l0EmbNsiMlxe5WO3ybDZg+PQBvvRXgLBYB4I9/tGPpUhtU+J5anZWUlODHH3/Enj17XB6Pjo5Gv3790LJlS0HJaof5xWJ+sbSUXwmdITVRmFVtRFdWVnbNj1c9HlKHVlZZWVmYM2cOKisrMWzYMPTo0cOt58+bN++6H8/JybnpwvFaqt7Jyc7O9vi5vSk9Pd05shkYGIjWrVur6nvwVX5v3V9ef7Gq5w8KClJd/lmzImGxOArJiAg7hg27jOxs9/9/q6gAnnyyHgoKHAVLZKQd772Xjfx896dE7tsXiL/9LRbFxY5zhYXZsXJlLho3roA7l1aSgHffjcDcufKIXUiIhPfeM+Ohh0rhzkz5srL6GDpUj59/lgvPwEAJr7xSgGefdYyWqui211ltW2gr9Xfgevm7d++Otm3bqjZ/u3bt0K1bN9Xm9+bPj6f+/mr551/NPz+iaaIwq5oOmJube82PVw2rujtt8OLFi3jrrbdQVFSEv/3tb/jjH/94c0HpuoqLi7F//37ncceOHetUTIvC/GJpLX/Pnj1VlT87OwBLl8pTVUaMsMJkqtubTrNnR2L3brmhxqxZljqtUzt2zICBA00oLHSM4gUHS1i+PA8JCe612a+oACZOjMGnn8rt600mGz7+2P1z/ec/wXjpJQNyc+VRsmbNKpGaakanTnVv/682am+hfb38f/7zn9G4cWPFviAFtH39md/7tJpfCTPiNFGYNW3aFABw8uTJa348MzPT5fNqIy8vD2+++SYsFgv69++Pv/3tbzcflK5rz549zoWXISEhaN++veBE7mF+sbSUPzQ0FD169EBBQYHgVLW3cGGEcyNkk8nmHPlx16ZNwUhNladvDhxYhEcecX998OnTejzxRCzy8hyjUnq9hCVL8tCrl3v7ihUU6PDccyZs2SKvYW7evBKrV+eiWbPaF4tlZcDbb0dh6dIIl8cffbQYM2fmIzLS8zMnlOh6LbQTEhLQoUMHRbfQrk3+hg0bCkx4ff5w/Znfe7Sev2PHjgLTOWiiMIuPj0dYWBguXbqEkydPXtU2f/v27QCArl271up8VqsVb731Fi5fvow+ffpgyJAhHs9MrqxWKw4ePOg87tSpE4KCgq7zDGW5Mn/nzp1VnV/t11/t+X//+9/X2MxIic6d02PVKnm0bNQoKyIi3C80Ll8OQEpKjPP4ttsqMG2a+8XpxYsBeOKJWFy86CjKdDoJ771nwYMPXnu6e03OndNj0CATjhyR1x306FGGjz7Kc2s0MDNTj6QkI/btk38mQ0MlvPmmBQMGlLi1Nk3NamqhHRcXh169eim++yjzi8X8YvlDfiV0jNREYWYwGNCvXz98+eWXWLZsGSZNmuScArRhwwZkZWUhPj4erVq1cj4nLS0NaWlp6NGjBwYOHOh8vKysDDNmzMCZM2dw5513YsSIEYq4UVq3a9cuZ2vh8PBwtG3bVnAi91yZv02bNoITuUdr11/t+Wv7JpJSzJ8fgfJyx/+TjRrZMHiw+6NldjswerQROTlyR8fFi80IDXW/9fzAgbHIypL/vM2cmY9HH3VvDcG+fYEYPNiEy5fldWCPPFKMefMscGeG6ZdfhuLll6NRVCS/i9y+vYQ1aypRr55y1jV4kxZaaDO/OMwvFvP7liYKMwB4/PHHsW/fPhw5cgQpKSmIj49HTk4Ojh07hsjISCQlJbl8fkFBAc6fPw+z2ezy+Lp163Ds2DEEBARAr9dj8eLF1/x6ycnJXvte/I3FYsHRo0edx127dnW2o1WDK/N36dJF1fnVfv21kF8JnaFq68QJPdavl9dejR1biP/vx+SW1NQIl+mCkyfno00b9/aUKSzU4amnYl1GuF5/PR9PPVXs1nn+859gJCUZnVMzAeCFFwoxYUJhrTe2Li7WYdKkaJdrAwCDBxdh4cIghIb6R4OP8+fPY8uWLVdNy23VqhXuuOMOZ/MupWJ+sZhfLOb3PfW8ermBoKAgTJ48GV999RW2bt2K9PR0hIeH45577sGAAQNq3fijav8gu92OrVu31vh5LMw8JyMjw/kuRlRUFFrXpYe1QFfmv/322wUnco/Wrj/z+9bcuVGw2RzvNjZrVonERPeKIADYuTMQs2fL68r69y/BoEHunaekRIehQ03Ys0eeLjhmTCFGjHBv9G7FijC89lq0s4W9Xi9h5sx8DBxY+zwHDhgwcqQRJ07IBWJ0tB1z5ljw0EOlCA1V9sJ4TygrK8P27dtx5MgRl8cjIiLQq1cv3HLLLYKS1Q7zi8X8YjG/OJopzABHcTZgwAAMGDDghp+bmJiIxMTEqx5PTk5m0eVDubm5zuYsgGPfJiUvHL0S84vF/GLt32/At9/K7ziOH18Idwf7LBYdkpONzuLud7+rxJw5FrfWXZWXA889Z8Svv8ojbsOHWzFuXGGtz2G3A2+9FYUlS+TmHBERdnzwgRl9+tRubZokOQq7adOiUVYmfwMJCeVYtMiMW25xv7Ok2tS2BbhSMb9YzC9WbVvgK5Xarz+gscKM1Cc9Pd35b5PJpPiNCK/E/GIxv1izZ8uLvdu0qcCf/+zemilJAsaPj8HZs44/RXq9hEWLzIiJqf26MpsNeOEFI378UV74NWBAMaZMKah1cVdS4ljftnGjXGQ2amTDypW5aNeudtMpzWYdxo2LQVqafA6dTsKoUVa89JL7BasaWa1WbN26FWfOnHF5XE0ttJlfHOYXSwst8NV8/auwMCNhLl686PIL1K1bN0UtwLwR5heL+cVKTw/Cf/8rF0MTJhTUev1VldWrw1yKofHjC9GtW+338rLbgQkTorFhg3yOhx4qwZw5llpnyc0NwLBhJmRkyFMg27at+P9NqO21OseOHUFITo7B+fPyn9T69W147z0z7r7bvfb8aqT1FtrM713MLxbzKwsLMxJCkiSX0YIGDRrg1ltvFZjIPcwvFvOLJUnAjBnymrCuXcvxwAPutaI/dMiAKVOince9e5chOdnqVoYpU6LwySdym/6+fUvx/vtm6PXXeWI1J07oMWiQawfHvn1LsWSJuVbt/m02x/5t77wT6VyTBgD33FOKBQssqF+/doWdmvlDC20lY36xtJq/SZMm6N27t2rzq+X6XwsLMxLi7NmzuHjxovO4e/fuqhotYH6xmF+szZuDsX27vJ7r5ZdrP20QcDTqGDnSiNJSx5NiY21YsMDs1ojbO+9E4qOP5PVgPXuW4cMPzajt9nU7dgRh2DATLBb5i/7970V4++181Kap58WLAXjhBSN++UW+DgaDhAkTCjFypNXt0UO1UVsL6isxv1hayJ+enq7q/Gq//mrOfz0szMjnJEnCzp07ncdxcXFo0qSJwETuYX6xmF8sSQJmzZJHy+6+uxR33eXedL033ojCsWPyoqv33rOgYcPajy4tWRKO+fPlDB07lmPFirxa73n2zTchGDPG6Nx7DQAmTSrAyJHWWhWYP/4YjJSUGOTlyUNzt9xSidRUM7p2rf1UTLVSYwvq6phfLLXnz8rKwnfffYe8vDyXx9WSX+3XX+35b4SFGfncqVOnkJOT4zzu1q2bwDTuY36xmF+sjRtDsHevPCw1YULtOx8CjqJo7Vp5+uGIEdZadz0EgDVrwjB9ujwFsnXrCqxZk4fIyBsXZZIELFoUgRkz5OktwcES5s8345FHSm/4/PJyYObMKHzwQYTL4w8/XILZsy2IjnZvM2y1UXMLaoD5RWN+sZhfHViYkU/Z7XaX0YJmzZqhQYMGAhO5h/nFYn6xbDZgzhx5pOqPfyxBly61HyHKytJj4sQY53GXLuWYOLGg5idc4ZtvQjBxolyUNW1aiXXrcmEy3Xi0raICmDQpGmvWyEWh0WjD8uVmdO9+4xG/rCw9kpKM+O03uSgNCZEwbZpjjzOVzpqpFbW3oGZ+sZhfLOZXFxZm5FPHjx+HxWJxHickJIgLUwfMLxbzi/XFF6HOKYg6neTWPmEVFUByshGFhY7FV5GRdixaVPs1Yf/5TzBGjzZCkhwVUKNGNnzySS4aNbpxUVZYqMOIEUZs2iR3kWzWrBKrVuWiRYsb7y32zTchmDAhBlarvHDs9tsrkJpqRnx87drpq5XaW1Azv1hazd+wYUPceeedqs2v9uuvlvx1wcKMfMZmsyEjI8N53KpVK5hMJoGJ3MP8YjG/WOXlwLx58mjZ44+XuFWUzJ4did275Sps1iwLmjat3YbL27YF4fnnTaisdBRlJpMN69bl4tZbb/z88+cDMGRILA4elN9RTUgox/LleYiNvX5RV1yswxtvRGHdunCXx//+9yJMnVpQ6zVtaqT2FtTML5aW8999993o0aPHVWvMlETL118N+W8GCzPymcOHD8NqdbTD1ul0qhstYH6xmF+stf/X3p0HNlHm/wN/p0kPejflKIdcRSyHlNIWPBBQdxWRZRVdUL4gCOpCQUBXwANEBOUSFIWCisih+PXEdfkhurty1QNKC5RKOWqhHG2hR9L7SjK/P/LNDKFnIO2TSd+vv5hkMn1npkP6yTPPZ7b74sIF60eGTifhH/9o/GjZ3r3eiI9Xirpx40obNacLAJKTPfHkk3pUVlqLsoAAC7ZvL0DPng0XhampOkycGIqcHKVJx8iR5XjnHQMamh+elqbDtGkhdk1KAgIsWLnSiL/8pXHZ1cpdW2gzf/Nw9/zh4eGCkjWOu+9/V89/o1iYUbOwtTa1iYiIUNXJxfxiMb9Y5eUarFlzdWFV1ujRritXPDBrVrC8fPPN1Xj99cbNK0tL02HChFCUllq/GfXxsWDr1gLcemvD89r27vXGM8+EyK8FgGnTSvDyy/XfCFuSgG3bfLFoUZDczh+wzoeLjzc0apROrdTegpr5xWJ+sZjfPbAwo2aRmpoqT9rUarUYMGCA4ESOYX6xmF+sTZv8cOWKddTJx8eC2bMbN1pmsQAzZ4YgL8/2Wgnr1xsadQlgRoYWjz8eKt9nzNNTwkcfGTBwYMONOj791BcvvRQEs9n6Ie7hIWHJkkJMnFhW7+sKCzV44YVg7NplP5wWF1eMuXOL4Ubzy2tQewtq5heL+cVifvfBwoyaXGVlJVJSUuTlPn36wNfXV2AixzC/WMwvVmGhBvHxSnv4J58sa/Q9x+Lj/XHggHID5ldfLUSvXg1fgnjpkgceeywUubnWgs7DQ8K6dYYG2+pbLNZ7rK1dq4zu+fpasGGDAffeW/9rk5I8ERcXgosXlY9F642vjbj77sa381ebiooKHDp0SLUtqJlfLOYXi/ndDwszanIpKSmorLT+YePp6YnIyEjBiRzD/GIxv1gbNvjLo1YBARbExTVutOzwYU+sWKEUSCNGlOOJJ+ofsQKA3FwPPPZYa1y6pHw8rVplxIMP1j+vq6ICeO65EHz3nfLNaliYGVu25KNv37qLQYvFWkCuWBEgj7ABwODBlXj3XYNDN75WE7W3oGZ+sZhfLOZ3XyzMqEmVlZUhNTVVXu7Xrx98fHzqeYVrYX6xmF+s3FwPbNyodCT8+99LoNc3fBmi0ajB9OkhcqHTsaMJK1caG7zXl9GowbhxocjIUD6aFi8uxJgx5fW8Cigo0GDyZD0SE5XRuYiIamzdmo+OHesurHJzPTBzZjD271eOiVYrYc6cYkyfXlLvXDQ1U3sLauYXi/nFYn73xsKMmtSxY8dgMlm/rfbx8UHfvn0FJ3IM84vF/GK9954/ysqs1Yleb8bTT5c2+BpJAubMCZYvCdRqJcTHGxAcXH9BV1qqwRNP2Le1nzOnCJMn1/8zz57VYsKEUJw9q3ycDRlSgfffNyAwsO6fuW+fN2bODJbnvwHWAnLdOgNiYxt/02w1UXsLauYXi/nFYv6WgYUZNZmSkhKcOHFCXo6MjIRXY+8m6wKYXyzmF+vSJS22bVNGy2bMKIG/f8OjZdu2+do1z5gzpxgxMfUXOhUVwOTJeiQlKftn6tQSzJpVUu/rDh+2ttIvKFCKq8cfL8XSpYV1NuqorgZWrgzAunUBdo+PGFGOlSuNDRaQaqX2FtTMLxbzi8X8LQcLM2oyycnJsFislxH5+fmhd+/eghM5hvnFYn6x3n7bH1VV1msP27c3Y+LEhkfL0tJ0WLQoSF6+665KTJ9ef3FVXQ3ExYUgIUG5DPF//qcU8+cX1Xvp486dPpg5M0S+vxkAzJ1bhJkzS+p83fnzWsTFhdjd6NrbW8Krr1o7NrpjJ2a1t6BmfrGYXyzmb3lYmFGTMBqNOH36tLw8YMAA6HTq+XVjfrGYX6z0dC2++ELpHPncc8VoaGpcWZkG06aFyPf+snY0NNQ7T8tiAZ5/Phg//KCMsD30UBmWLi2ss0iSJOD99/2weLFSAHp5SVi92oiHH657Ltq//uWDuXODUVSkBOrRoxrr1xvQu3fDnSLVqK4W1OHh4bj99ttdvgW12ltoM79YzC+W2vOLop6/FEhVkpKS5G9HAgMD0bNnT8GJHMP8YjG/WKtWBcqNO7p2NWHMmIa7KS5cGIgzZ5TrB99911hvR0NJAl5+OQjffKMUgPfdV4533jFCq639NSYTsGBBELZuVS6xDA624KOPCnDbbbXf36y8HHjttSB88omf3eNjx5ZhyZJC+Pq636WLlZWVOHjwoGpbUKs9f3l5OX766SccO3bM7nG15Ff7/md+sdSeXzQWZuR0+fn5yMjIkJejo6NVNaGT+cVifrFSU3V2LefnzGn4xsr//KcPtm9XCp9p00rqveeYJAFLlwbYzWG7885KrF9vqPNnlZZqMHVqCH76SRm669zZhG3bCtCjR+0jXqdO6RAXF4KTJ5WN+vtbsGxZYb2ja2ql9hbU7pL/4MGDKC1VLv1VW36173/mF8Md8p89exbt27cXmoOFGTldYmKi/G+9Xo/w8HCBaRzH/GIxv1grViiTsHv1qsaoUfUXMJmZWsybFywvR0VVYd68orpfAGDtWn+75htRUVX4+OOCOi+XzMnxwMSJeqSmetm9ZvPmArRuXXNUTpKAzz7zxYIFgaioUIrifv2qEB9vQLdu5nrzqVFJSQl+/vlnnD9/3u5xtbSgZn6xmF8s5hfLlj87Oxt33nmn0CwszMipcnJy7O5NERMTo6qJncwvFvOLlZjohf/+V6mO5s0rqneOWFUVMH16CIqLlRtQr1tX96gXAGze7Itly+yLv23b8uHnV/slhWlpOjzxhB5ZWcrH1QMPlOO994xo1arma4qKNJg3L9hu1A8AnnmmBC++WARv7xovUTW1t6B21/w6nQ4DBgxQbX6173/mbx7ult8VRvRYmJHTSJJkN1rQtm1bdO7cWWAixzC/WMwvliQBy5Ypo1gDBlThT3+q+3JEwDq6dnWHw+XLjejSpe7RqC+/bIVXXgmWl7t1M+Gzz/IRElJ7UbZ/vxeeeUYvF34A8PTTJViwoKjWeWhHjngiLi4E588rH216vRlvv21s8L2okdpbULtr/q5du+KBBx6Q72Hoqtx1/zN/83DX/KKxMCOnuXjxInJycuTl2NhYVY0WML9YzC/Wvn3e+O03ZTjppZfqb1e/d6831q/3l5fHjSvFX/9aUef633/vg3/8I1he7tDBhM8/z0ebNrU3CPn881aYOzcYJpM1hIeHhEWLar/htMUCfPCBH5YuDZTXB4Dbb6/Ee+8Z0L593U1I1EjtLajdPf8dd9wBjUaD3NxcgSnr5u77n/mbljvnv+OOOwQms2JhRk4hSRIOHz4sL3fs2BEdOnQQmMgxzC8W84t17WjZkCEVuOOO2rscAsDlyx6YOTNYXr755mq8/nrd88r27fNGXFyI3OmxdWsz/vd/89GxY83RNUkC3norAO+8o+Rp1cqC+HgD7ruv5qhXXp4HZs8Oxp49yiWYHh4Snn++GDNnltTZ4VGt2AJfrMbkd+U/SlvC/ndlzC9WQ/l9fX3reGXzYWFGTnHu3Dnk5eXJyzExMQLTOI75xWJ+sXbt8sHx48oliXPnFte5rsUCzJoVgvx8a8Xj4yNh/XpDrfO9AOu8tcmTQ+SbVQcFWbB9ez7Cw2sWZZWVwAsvBNu10G/TxowtWwoQGVldY/0DB7wwc2YIrlxRqq/27c1Yt86AQYPqLizVSO0tqJlfLHfI/9tvv9ndHxJQV37uf3HUlJ+FGd0wi8ViN1rQtWtXtG3bVmAixzC/WMwvltkMrFihjE498EA5oqJqFkE269b548AB5ZLHhQsL0atX7XNpUlN1mDBBL3dG9PW1YNu2fPTpU3N9o1GDp57S49dflW337FmNbdsK0KmTfRFnMllH1dau9YckKaMT999fjrfeMkKvd597k7lDC2rmF4f5xWJ+sdSYn4UZ3bD09HQYjUZ5OTo6WlyY68D8YjG/WF9/3Qrp6dYPJo1Gwpw5dY+WHT7siZUrlSJuxIhyTJhQ+82n09N1ePzxULlxh7e3hI8/LkB0dM2i7/x5LSZM0Ms5AOCOOyqxcWMBgoLsi6xLl7SIiwvB4cPKCJ+Xl4QFC4rw5JOl9c6LUxt3aUHN/GIwv1jML5Za87tVYVZVVYVvv/0WP//8M/Ly8uDv74/IyEiMHTsWoaGhjd7OiRMn8PvvvyM9PR3p6ekoLi5Ghw4d8M477zRdeJUym81ISkqSl3v06AG9Xi8wkWOYXyzmF6uyEli1Sim0Ro8uxy231D76VViowfTpyjyxTp1MWLnSWGshdOGCFmPHhqKgwHqJoVYrYcOGAgweXPPywiNHPDFpkh55ecrliI8+WoaVK43w8rJf19ZApLBQ6dLYvbsJ69cXoG9f1+6A5wh3a0Ftw/zNg/nFYn6x1J7fbQqzqqoqLF68GKdOnUJISAhiYmKQm5uLvXv3Ijk5GUuWLEFYWFijtvXxxx8jMzOziRO7h5MnT6KkpASAdWhYbaMFzC8W84v12We+uHjR+jGg01kbZtRGkqxzv2zrarUS1q41IDi45iWDOTkeGDs2FDk51kJLo5Hw7rvGWht3fP+9D2bMCLa7CfQLLxRh9uwSu4KvogJ4/fUgbNniZ/f6Rx8tw5tvFtZ5DzQ1ctcW1MzfPJhfLOYXS+35ATcqzHbs2IFTp06hZ8+emD9/Pnx8rB26du7cia1bt2L9+vVYtGhRo7YVGRmJ22+/HT169EBAQADmzZvXlNFVq7q6GkeOHJGXIyIiVPFLb6P2/FVVVarOr/b9r/b8ZWUarFmjjJaNG1eGrl1rvwfZJ5/4YtcupdvWnDnFiI2teUliQYEG48aFIjNT+WhZtqwQDz1UXmPdDz/0w6JFgfIcMU9PCStXGvG3v9mvm56uw9SpIUhLUy5z9PW14M03C2usq2bu3IKa+Zse84vF/GKpPf/V3KIwM5lM2L17NwBgypQpclEGACNHjsS+ffuQlpaGjIwMdO/evcHtjR8/Xv63q914zpX8/vvv8mRKrVaLqKgowYkco/b8SUlJqs6v9v2v9vwff+wndzP08ZEwa1bto2VpaTq89lqQvHzXXZWYPr2kxnrFxRqMHx+KU6eUAmrBgkKMH28/B81sBhYtCsRHHyn3QAsMtODDD+0vdZQk4IsvWuGVV4JQXq6MqPXtW4X4eEOtXR3VSu0t8LOzs7F//37mF4T5xVJ7fv7/41rcojA7efIkSktL0a5dO3Tr1q3G84MGDUJmZiYOHz7cqMKMGlZZWYmUlBR5uU+fPvDz86vnFa5F7fkrKirw66+/ystqy6/2/a/2/IWFGsTHK4XR5MklCAureRPm8nIN4uJCUFFh/aYxNNSMNWsMuPby/PJy4Mkn9Th2TJkUNmtWMaZOtb8ZdFmZBtOnB+PHH5UPyk6dTNi6tcBubltJiQYvvRRk1zYfAKZMKcErrxTB2xtuwR1aaDO/OMwvFvOLpfb8dXGLwsw2H6y2ogyAXIxx3pjzpKSkoLLSOmfE09MTkZGRghM5Ru35f/vtN1RUVABQZ36173+159+wwR9Go7W6CgiwYNq0miNgAPDqq4E4fVoZAVuzxoh27ewLuKoq4Jln7NvcT5lSUqO745UrHpg0yb54i4yswubNBWjbVtlmSoonpk0LwblzysdTcLAFb79d+w2m1UiSJKSlpeGHH35QTQvnq6mxBfXVmF8sd8jP81cctedviFsUZrYbu9bVedHWJe3qG8DS9SsrK0Nqaqq83K9fP7vLR12dO+RPTEyUl9WYX+37X835c3M9sHGjMrr397+X1Hrfr3/+0wfbtyvrTZ1agrvvti+MzGbg2WdD8NNPyvsfM6YMr71WZNe84/Rp6/3MbM1DAOC++8qxbp0Rvr7Wny1J1nlnb74ZiOpq5cWDBlVi7VoDOnSoOaKnRiUlJdizZw/S09PtHnf1Fs42am1BbcP8YrlDfnc8f/V6PYYMGaLa/GrZ/43hFoWZbeTAu47rW2x/NNnWa07PP/98jce8vLywbNkyAEDr1q2b5OfqdNZD2xS/pP/+979hMlkvO2rVqhWGDRtW5753Re6Q39YCVq351b7/mzp/U56/y5Z5oKzMOlrWurWEl15qhYAA+2vwMzKAF19UPh5iYy146y1veHkpeSwWYOpULXbuVK5rHD3ags2bPaHTKevt2aPBmDFaFBYqxdb06Wa89ZYOWq31/7+8PODpp7XYtUvZloeHhJdftuDllz2g0zX+dieuymKxICkpCfv27UNVlTKXTqfT4a677sLAgQOh1Wrr2YJYzN94TXH+cv+LxfxiqT2/I9yiMLu6A8v1PE+NV1hYiOTkZHn5jjvuUNUf1cwvFvOLdf488P77SvEzd64FAQH261RVARMmaFFUZC2kAgIkbNtmtrunmCQBc+d6YPNmZVv332/B1q1m6K76VNm2TYOpU7XyCJhGI2HFCgtmzrTII2r792vwxBNaZGUphVuHDhK2bDFj6FD3+L/7ypUr2LVrF7Kysuwe79q1Kx544AGEhIQIStY4zC8W84vF/GKpPb+j3KIws3Vcsc35uJbtcRGXG61evbre5/Py8pqkcLR9U5ebm+vU7e7fvx9ms7Ubmp+fHzp37uz0n9GU3Cl/QECAqvOrff83Zf6mOn8XLAhCVZX12vv27c145JHLuPZHLFkSiMREpTHI8uUGBARU2K23alUA3n1XqegGDarEunUFKCxULkt8+21/rFql3D7Ax0fCe+8ZMGJEBfLyAJMJWLMmAO+84w+LRSnK7r23Au+8Y4Reb6mRTW3qauHcqlUr3HvvvQgLC4PJZHLZc6AxLaiZvyZnnb/c/2Lx/BVLRH6NRoP27ds7bXvXwy0KM9vlgPn5+bU+X1BQYLceXR+j0YjTp0/Ly1FRUfIlG2rgbvkHDx6s6vxq3/9qy5+ersUXXyhdDmfPLsa131Xt3euN9euVouzxx0vx17/aXwL+/vt+WL1aKcpuvdXawKNVK+sHZ1UVMHduML78UvlZoaFmbN5cgAEDrJfgZmV54NlnQ/Dbb8poo6enhFdeKcJTT5VCJbebqVddLah79OiBBx98EH5+fi77BxFQf/7bbrvN5VtQM79Y7pyf52/TU3v+G6Gevyrq0aVLFwDA2bNna30+IyPDbj26PklJSfK3FoGBgbjlllsEJ3KMO+UPCQlBv3795C8d1MCd9r8a869aFQiz2VrxdO1qwtix9vcXu3LFA7NmBcvLN99cjddft/9Q3L7dF6+/rtzTrGfPamzfXoDAQOt+KSzU4Omn9fj5Z6XgCg+vxrZtBejSxTrS+OOP3njuuRC5K6Qtz/r1BvTrV/Om1WrTmBbOrnxrBbW3oGZ+sVpCfp6/TUft+Z3BLQqziIgI+Pr64vLlyzh79myNtvkHDx4EAAwYMEBEPLeQn58vF7gAEB0dDY9rb2bkwtwt/5AhQ1Q10dXd9r/a8qem6vDdd8o3jHPmFOPqbsIWi7W7Yl6e9XfK21vC+vUGuWMiYO3SOHeuUpR17mzCZ5/lQ6+3dku8eFGLCRP0du31b7utEhs3FiAkREJlJfDGG/Y3lgaA0aPLsHRpIfz91T2fTO0tnJlfLOYXi/nFUnt+Z3KLwkyn02H48OH45ptvsGnTJrzyyivyfLKdO3ciMzMTERER6NGjh/ya3bt3Y/fu3Rg4cCDGjRsnKrpqXN2eXa/XIzw8XGAax7lb/t69ewtM4zh32/9qy79ihTLXq1evaowaVW73/Lp1/khIUEa5Fi4sRK9eyg2f//Mfb8ycGQJJso64hYWZ8b//my/flPrYMU9MmqTHlSvKlwUPP1yGVauM8PYG/vhDi7i4EKSmKh1EWrWy4I03CjFmTLnqL11kC2qxmF8s5heL+d2LWxRmADB69GgcP34cp06dwqxZsxAREYG8vDycOXMGAQEBiIuLs1u/qKgIWVlZMBgMNbb13//+Fz/99BMAyG3Jc3Nz8corr8jrTJkyRb5xtbvLycnBhQsX5OWYmBhoVPSXFPOLxfxiJSZ64b//VSaTzZ1bhKsH+xITPbFypTJnbMSIcjzxhHKZ4y+/eOHvf9fDZLK+55AQMz77LF++NPHf//bGtGkhKC9XNjpzZjHmzi2GRgN89VUrvPRSkNyiH7AWhxs2GNCjh1L8qZHFYsGJEydw+PBh+bMCALRaLaKjo3Hrrbe69Mgq84vF/GIxv1hqz99U3KYw8/LywsKFC7Fjxw4kJCQgMTERfn5+GDp0KMaOHetQ44/8/HycOXPG7rHq6mq7x64eanVnkiTZjRa0bdsWnTt3FpjIMcwvFvOLJUnAsmVK0TVgQBX+/Gele63RqMGMGSHy3LOOHU1YudIoj2AdOWIdCauosLXOt2D79gL07GktqDZv9sWCBUFyV0WdTsLy5UY89lg5Sks1ePnlIHz1ldIEBAAmTizFq68W1mg8ojYFBQU4cOAArly5Yvd4x44dMXjwYAQGBtbxStdQUFCA/fv312hg0KFDB9x1112qyF/b/mf+5sH8YjG/+3KbwgywFmdjx47F2LFjG1x3zJgxGDNmjMPPtTSXLl1CTk6OvBwbG6uq0QLmF4v5xdq/39uu8+FLLxXJRZckAXPmBOPiRevHgFYrYd06A4KDrXO90tJ0GD8+FKWl1m8sfXws2Lq1AP36VcNstrbV/+ADZb5YQIAFH3xgwJAhlUhN1WHqVD3OnlU+YoKCLFi1yogHHrDv8qg2jWnh7Mq/I8wvFvOLxfxiqT1/c3Crwoyc69rRgo4dO6JDhw4CEzmG+cVifrGuHS27665K3HFHlby8bZsvdu1SGoK88EIxYmOtl5NkZGjx+OOhcudET08JH31kwMCBVSgv1+DZZ4Px/ffKazt0MGHr1gJERJjw0Ud+WLIkEFVVyodrTEwV1q0zoFMnc5O93+ag9hbOzC8W84vF/GKpPX9zYWFGdTp37hzy8vLk5djYWIFpHMf8YjG/WLt2+SAlRWm28eKLyodhWpoOixYpHRbvuqsSM2aUAAAuXfLAY4+FIjfX2sjDw8M6kjZsWCXy8jwwaZIeR44o2+3btwpbthTAy0vC5Mkh+PFH5cNVo5EwY0YJXnihGCq65VsNam/hrPb8FRUVOHToEPMLwvxiMX/LouKPSmpKFosFhw8flpe7dOmiqs44zC8W84tlNgMrViijZcOHl6N/f+toWFmZBtOmhcjzxlq3NuPddw3w8ABycz3w2GOtcemS8tGwapURDz5YgfR0HSZM0OP8eeW5e+6pwIYNBqSmemL69BBkZytdGdu2NeO99wwYPFgZpVMbtbdwri9/nz59EBMTo9r8at//zN/0mF8stecXhYUZ1So9PR1Go1FejomJERfmOjC/WMwv1tdft0J6uvUDT6ORMHdusfzcwoWBOHNG+TBcs8aItm0tMBo1GDcuFBkZysfC4sXWdva//eaFKVP0djeFnjChFIsWFSI+3h+rVwfIDUAA4O67K/DOO0a0bm1pyrfZpNTewpn5xSosLMSPP/6o2vwlJSVISEiw60gLqCu/mn9/uP9bLhZmVIPZbEZSUpK83KNHD+j1eoGJHMP8YjG/WJWVwKpVymjZ6NHluOUWaxfFf/7TB9u3+8nPTZtWgmHDKlFWpsETT4TixAmlYJszpwiTJ5dix45WeP75YLs5YwsWFGLUqHL8z/+E4tdfleYiOp2El14qwjPPlEKtXY7V3sKZ+cWyWCxITEzEvn37UFWljBarKb/a9z/zi+MO+UVjYUY1nDx5EiUl1vkmGo0G0dHRghM5hvnFYn6xPvvMV+60qNNJ+Mc/rKNlmZlazJsXLK8XFVWFuXOLUFEBPPmkHklJyryxadNKMHNmCdas8be7ObW3t4Q1awxo1UrCffe1gcGgXLrYubMJ8fEGREUpH8Zqo/YWzswvFvOLxfxiuUP+X3/9FU8//bTQHCzMyE51dTWOHDkiL0dERLj8yXQ15heL+cUqK9NgzRpltGzcuDJ06WJGVRUwfXoIiout31QGBFiwbp0BGg0QFxeChARl1GvChFLMnVuEuXOD8NlnyuhaSIgZH3xQgB9/bIUPP1Ta5APAqFHlWL7ciMBACWqk9hbOzC8W84vF/GK5U36dC3SpEp+AXMrvv/8uT9LUarWIiooSnMgxzC8W84v18cd+uHLFOorl4yNh1izraNmKFYF2nRSXLzfippvMmDUrGD/8oHRRfPjhMrz0UhEmTdJj3z7lDtDdupmwbJkRixcH2XV69PGxYMmSIjz2WBlc+HO3XnW1cA4PD8ftt9/u8i2c3TW/Wlpo15W/T58+iIqKUm1+/v40D+5/serKLxILM5JVVlYiJSVFXu7Tpw/8/PzqeYVrYX6xmF+swkIN4uOVkawnnyxFWJgFe/d6Y/165fFx40oxalQFXn45CN984ys/ft995ZgzpwiPPNIaaWnKXLPY2Eo8+mgZpkzRo6REmRtwyy3VWL/eIM9fUxu1t5BnfrHqy//ggw8iPDwcubm5gtI1zJ33P/M3PXfN7wqf+SzMSHb8+HFUVlYCADw9PREZGSk4kWOYXyzmF+v99/3lrokBARbExRXj8mUPzJwZLK9z883VeP31IixdGoCtW5UPoDvvrMSzzxZj9Og2yMlR5o2NGFEOX18J8+aF2P2sCRNKsXBhIVz8y9Baqb2FM1vgi9WY/K58I/qWsP+Zv+m4e35X6MDMwowAAOXl5Th+/Li83K9fP/j4+NTzCtfC/GIxv1h5eR748EOl0Pr730sQHCxh3Dg98vOVSxvXrzdg40Y/rFunzEMbMKAKkyaV4rHHWqO0VBkRGzu2FElJXnLbfQAIDLRgxQoj/vKXimZ4V85XVwtqvV6PIUOGuHwLZ7W3oHaH/c/84tT1+8/8zaMl/P64wlw4FmYEADh69ChMJuslST4+Pujbt6/gRI5hfrGYX6x33/VHWZm1qNLrzXj66VKsW+ePAweUph4LFxbi4EEvLFumNDPp1asaf/lLOaZODYHZbP1A8vCQMGpUOb791heVlcqH1IABVYiPN+Cmm8zN9K6cxx1aODO/OMwvFvOLxfzNi4UZoaSkBCdOnJCXIyMj4eXlVc8rXAvzi8X8Yl26pMW2bcpo2YwZJTh5UoeVK5VRsREjytGqlYTZs5VLErt1M2HQoEosWhQkP+bra0Hv3tX49ltl7hkATJ9ejDlziuHCV6jUqa4Wzh07dsTgwYNdvuumO7SgZn5xCgoKsH///hrz3dSUX+37n/nFUWN+FmaE5ORk+aZ6fn5+6N27t+BEjmF+sZhfrLff9pdv/ty+vRkPPVSGUaPayCNgnTqZcP/95XjuOaUoa9/ehO7dTdi8WWkKotebodMBhw8ro2ytW5vx7rtGDB1a2UzvxnncqYUz8zc/5heL+cVifnFYmLVwRqMRp0+flpejoqJc4j4OjcX8YjG/WOnpWnzxhTK6NWtWMebPD5ZvMK3VSpgypQQvvBACi8X6IRQaakZoqAX//a8yh65NGzMKCjzkYg4A7rqrEu++a0DbtpZmejfO464tqNWeX+0ttNWen78/zYP5xVJ7fvX8BUJNIikpSf42ITAwELfccovgRI5hfrGYX6xVqwLlYqprVxPMZmDXLuVD57HHyrB8eSCqq63r+Ptb4O0tITVVuVQzONiM3FylE6NWK2Hu3GLExZXAhS67b5SKigocPHjQrtgG1NPCWe353bWFNvM3D/7+i6X2/a/2/DYszFqw/Px8ZGRkyMvR0dEuNQGyIcwvFvOLlZqqw3ffKUXYuHGlWLxYmS/Wv38VvvuuFSoqrO/J29sCjQbIylL+2/f2lmA0KkVZp04mrFtnQEyMMkFaDdy9hTPzNy3mF4v5xWJ+18LCrAVLTEyU/63X6xEeHi4wjeOYXyzmF2vFCmXS8i23VOOrr3xRUWEdGQsKMuPcOR2Ki61FmU4nwWLRoLjY/pr6q7sujhhRjpUrjQgOlqAmdbVwVnsLeTXlV3sLf+YXh7//YrnD/ldz/tqwMGuhcnJy7H6RY2JiXHYiZG2YXyzmFysx0ctujlhYmBn79inLHh6AweDxf/+WYDIp702jkSBJyrKPj4TXXivE+PFlUNEuUF0L5GtZLBakpqYiMTFRvlUDoK78at//zC+OLX9tv/8DBgxAv379XD5/amoq978gav/9rw8LsxZIkiQcPnxYXm7bti06d+4sMJFjmF8sSZLsRpvUmF/d+x9Yvlxphd+1q8muKAsMtMBgsF2eKMlNP2zLVxdlN99cjfXrDejVywQ1UXsL8CtXrmDXrl3Iysqye1wt+dXYgvpqzC+W2vPz/BVL7bdAaQgLsxbo0qVLyM7OlpdjY2NVNVrA/GJdvHgROTk58rLa8qt9/+/f741ff1Va2l++rHwr6ONjQVHR1d8SXvu+lOVx40qxaFERfH3Vc+mimlsgA0r+lJQU+RYNgPryq33/M78Y7pKf568Yas/fWCzMWphrRzs6duyIDh06CEzkGOYX69rRJjXmV/f+B5YtU0bLAgIs8jwyDw9JbvRRH39/C1asMOKvf61ospxNITs7GwcOHEBhYaHd42ppgeyu+dXSgp35xeLvv1juml8tvz+OYGHWwpw7dw55eXnyckxMjMA0jrs2f2xsrMA0jnO3/Pz9aV67dvkgJUVpdW8rygBcc8li7fr3r0J8vAFdupibJF9TUHsL6rryBwUF4fbbb1dtfrXvf+ZvHu6an+dv81B7/uvBwqwFsVgsdqMdXbt2Rdu2bQUmcsy1+bt06aKqjjvumJ+/P83HbAZWrAhoeMU6TJ1agnnziuDl1fC6rkDtLZDryx8bG4shQ4bU+PbXlbjz/mf+pufO+Xn+Nj21578RLMxakPT0dBiNRnk5OjpaXJjrcG1+tY3WML9Yas//9detkJ5u+yCSUHP+WO30ejPeeceIe++tbLJszlZXC2q9Xo8hQ4a4fEHdUP7evXsLStY4dbWgVtP+Z35x3D0/z9+mpfZbENwoFmYthNlsRlJSkrzco0cP6PV6gYkcw/xiMb9YlZXAqlVXj5Y1rii7885KvPuuAWFhloZXdgH1tUBWewtntedXQwtq5heL+cVifvfAwqyFOHnyJEpKSgBYh4LVNlrG/GIxv1jbt/vi4sXG/3et1Up4/vliPPtsCbTahtd3BWzhLJa77n/mbx7ML5a75lfL/5/OxMKsBaiursaRI0fk5YiICFX9kjO/WMwvVlmZBmvWNH5uWYcOJsTHGxEbW9WEqZxH7S2QmV8s5heL+cVifvfDwqwF+P333+XJk1qtFlFRUYITOYb5xWJ+sT7+2A+5uY0b9ho+vBxvvWVESIg67k2WlZWFAwcOoKioyO5xtbRAdtf8ammhzfxiMb9Y7ppfLf9/NhW3Ksyqqqrw7bff4ueff0ZeXh78/f0RGRmJsWPHIjQ01KFtlZaW4ssvv8ShQ4dgNBoRHByM2NhYjBkzBn5+fk30DpyvsrISx44dk5f79OmjuvwpKSnyMvM3L+YXq7BQg3Xr/Btcz8tLwsKFhZg4sQxq+HJR7S2QmV8s5heL+cVifvfmNoVZVVUVFi9ejFOnTiEkJAQxMTHIzc3F3r17kZycjCVLliAsLKxR2youLsb8+fORnZ2Ndu3aITY2FhcvXsT333+PI0eO4I033kBAwPW3rW5OKSkpqKqyXtLk6emJyMhIwYkck5KSgspKazc55m9+zC/Whg3+KCysf7JzeHg14uMN6NvX1Eyprp/aWyAzv1jMLxbzi8X8LYPbFGY7duzAqVOn0LNnT8yfPx8+Pj4AgJ07d2Lr1q1Yv349Fi1a1KhtbdmyBdnZ2Rg4cCCee+45aP9v9vymTZuwe/dubNmyBTNmzGiy9+IspaWlSE1NlZf79esn7xc1KC8vZ36BmF+sK1eADz6of3RvzJgyLFlSCD8/1790Ue0tkJlfLOYXi/nFYv6Wwy0KM5PJhN27dwMApkyZYvfH18iRI7Fv3z6kpaUhIyMD3bt3r3dbRqMRBw4cgFarxVNPPSUXZQAwYcIE/PLLL0hISMD48eMRHBzcJO/HWX755ReYTNZv0X18fNC3b1/BiRxz9OhR5heI+cVassQDFRW1j5b5+FiwcmUhRo8ur/V5V6L2FsjMLxbzi8X8YjF/y+MWhdnJkydRWlqKdu3aoVu3bjWeHzRoEDIzM3H48OEGC7MjR45AkiT07t27RuHl6emJ6Oho7NmzB0ePHsWwYcOc+C6cq6ioCMnJyfJy//794eXlJTCRY0pKSnDixAl5mfmbF/OLdeECsGFD7R9WPXtW46OPCtC9u7mZUzlO7S2QCwoKsH//fuTm5to9rvYW1GrPr6bfH+YXh/nFUnt+UdyiMMvMzASAWosyAHIxZlvvRrbVrVs37NmzB+fOnbuOpM0nISEBZrP1Dzc/Pz/06tVLcCLHJCcnw2Kx3hSX+Zsf84s1apQWtd1Eevz4Urz+eiG8vZs/kyPU3gKZ+cVyh/wJCQn49ddfVZtf7fuf+cVRe37R3KIwy8vLA4A6Oy/q9Xq79RqzLdtrrmX7GY3ZlihGo9GuE2NUVBR0OvUcaqPRiNOnT8vLzN+8mF+sF18MxO+/239oabUS4uMNGDmyQlCqxlN7C2TmF8sdWoB//fXXKCgosHtcTfnVvv+ZXxy153cF6vlrpR4VFdY/Vrzr+BrZNufMtt6NbMv2uK3TW0Oef/75Go95eXlh2bJlAIDWrVs3ajuOSEhIkL+lCAkJwZ133mk3V87VMX/DbIVGU0yY5f4XJysL2LZNh6tHy4KCJCQlmdC5cwAA1+4Ga7FY8NVXX9l9KAcFBWH48OEIDw8XmKxxmit/U52/3P9i2fIbDAb5MTXmV/v+5/krhtrzuwq3mHF39VDp9Txf27pqHWaVJAm+vr7yZMohQ4ao5o9SgPlFY36x2rUDQkMlANb/h/R6C3JyTOjcWWyuxvLw8MDw4cMBWP8PHThwIJ5++mnVfCgzv1jMLxbzi8X8BLjJiJltaLSuUSzb441plW3bVl2ja7Zt1TWidq3Vq1fX+3xeXp5DhWNjDBgwAAMHDsTRo0fRpk2bGhPXXd2AAQPQo0cPnDx5kvnrYPumrim2zf0vVkoKcO+9YcjJkXDsWA6uuSLK5fn7+yMmJgadOnVCmzZtUFhYKDqSQ5ojf1Oev9z/Yvn7+2Po0KHo3r07dDqdKvOrff/z/BVH7fk1Gg3at28vNINbFGa2ywHz8/Nrfd52rXdjLhu0rXPt9eE2tp/RFJcgOlNISAjuvvtu1f1RahMYGIiBAweKjnHdmF8stedPSbE27lHp6YuoqCjREW4I84ul9vx33nkngKb5w705qH3/M79Yas8vmltcytilSxcAwNmzZ2t9PiMjw269G9mW7fHGbIuIiIiIiKgx3KIwi4iIgK+vLy5fvlxrQXXw4EEA1kucGtK/f39oNBqkpaXVGIKtrq5GUlISNBoNvxEgIiIiIiKncYvCTKfTyRMON23aZDc/bOfOncjMzERERAR69OghP757927Mnj0b27dvt9uWrYubyWTCxo0b5XuBAcAnn3yCoqIiDB48uMbNp4mIiIiIiK6XW8wxA4DRo0fj+PHjOHXqFGbNmoWIiAjk5eXhzJkzCAgIQFxcnN36RUVFyMrKsmtrazNp0iScOXMGBw8exOzZsxEeHo4LFy7gwoULaNeuHSZOnNhcb4uIiIiIiFoAtxgxA6z3Blu4cCEeeeQReHl5ITExEVeuXMHQoUOxfPlyhIWFNXpbgYGBWLp0KYYPHw6TyYRDhw6hrKwMw4cPx9KlSxEYGNiE74SIiIiIiFoajeTsXu3kkOzsbKe3yweatp0ricfj6954fN0bj6974/F1bzy+7ovt8qnJb2St1htlU+Pw+Lo3Hl/3xuPr3nh83RuPr/txhWPKETMiIiIiIiLB3GaOGRERERERkVqxMHNTL774Il588UXRMaiJ8Pi6Nx5f98bj6954fN0bj697W7BgARYsWCDs53OOmZuqqqoSHYGaEI+ve+PxdW88vu6Nx9e98fi6t9LSUqE/nyNmREREREREgrEwIyIiIiIiEoyFGRERERERkWAszIiIiIiIiATjfcyIiIiIiIgE44gZERERERGRYCzMiIiIiIiIBGNhRkREREREJBgLMyIiIiIiIsFYmBEREREREQnGwoyIiIiIiEgwFmZERERERESC6UQHoBtTUVGBQ4cOIT09HWfOnEFmZiZMJhPGjRuHhx566Lq3m5SUhO+++w7nzp0DAHTt2hWjRo1CdHS0c4KTQ06dOoVvvvkGp0+fhslkQqdOnXD//fdj2LBhDm1n7969iI+Pr/P5O+64A7Nnz76xsFRDVVUVvv32W/z888/Iy8uDv78/IiMjMXbsWISGhjq0rdLSUnz55Zc4dOgQjEYjgoODERsbizFjxsDPz6+J3gHVx1nHd/r06cjNza3z+bfffhsdO3Z0RmRqpIyMDKSkpMifsQaDAZ6envj000+va3s8f12LM48vz1/XUllZiWPHjiEpKQl//PEHcnNzYbFYEBYWhkGDBmHkyJHw8fFxaJvNcf6yMFO5nJwcrF271qnb3LVrFzZv3gytVotbb70VOp0OKSkpWL58OSZNmoQRI0Y49edR/Q4dOoTVq1dDkiT06tULAQEBSE1NRXx8PDIzMzFx4kSHt9mlSxd07dq1xuM333yzExLT1aqqqrB48WKcOnUKISEhiImJQW5uLvbu3Yvk5GQsWbIEYWFhjdpWcXEx5s+fj+zsbLRr1w6xsbG4ePEivv/+exw5cgRvvPEGAgICmvgd0dWceXxthg4dWuvjvr6+zohMDvjqq69w+PBhp2yL56/rcebxteH56xoSEhLw/vvvAwBuuukmREZGory8HKdPn8YXX3yBn3/+Ga+99hqCgoIatb3mOn9ZmKmcj48P7rnnHvTo0QPh4eE4ePAgvvnmm+veXlZWFrZt2wZPT08sXLgQPXv2lB9fsGABtm3bhqioKLRv395Zb4HqUVJSgvj4eFgsFvzjH//AoEGDAABGoxGvvvoq/t//+3+Ijo5G3759Hdqu7Rseano7duzAqVOn0LNnT8yfP1/+hm7nzp3YunUr1q9fj0WLFjVqW1u2bEF2djYGDhyI5557DlqtFgCwadMm7N69G1u2bMGMGTOa7L1QTc48vjbTp09viqh0HXr27ImuXbsiPDwc4eHheOaZZ657Wzx/XY8zj68Nz1/XoNPpcN999+HBBx+0+5vVYDBg2bJlOHv2LDZv3oxZs2Y1anvNdf5yjpnKhYWFYerUqfjTn/6Ebt26wcPjxg7prl27YDab8ec//1kuygCgQ4cOePjhh2E2m/H999/faGxqpJ9++gllZWWIiYmRizIACA4Oxvjx4wFY/wAk12QymbB7924AwJQpU+wumxg5ciS6dOmCtLQ0ZGRkNLgto9GIAwcOQKvV4qmnnpI/FABgwoQJCAwMREJCAoxGo9PfB9XOmceXXNNDDz2EMWPGIDo6GsHBwde9HZ6/rslZx5dcz9ChQ/HUU0/VGEgICQnBlClTAFivSDKZTA1uqznPXxZmZCc5ORkAcNttt9V47vbbbwdgnX9GzcO2r2s7HgMGDICnpyeOHz+Oqqqq5o5GjXDy5EmUlpaiXbt26NatW43nbcV2Yy6lOXLkCCRJQu/evWv8AeHp6Yno6GhYLBYcPXrUGdGpEZx5fMm98fwlch1dunQBAFRXV6O4uLjB9Zvz/OWljCQrLS1FXl4eANQ6/yg0NBQBAQHIzc1FWVkZr5duBufPnwcAdO/evcZzOp0OnTt3xh9//IGsrKxaj1ldMjIysG3bNpSXlyM4OBh9+/ZF7969nRWb/k9mZiYA1PpHO6AcV9t6N7Ktbt26Yc+ePXLDHmp6zjy+V/vuu++Qk5MDT09P3HTTTRg4cCACAwNvLCwJxfO35eD56/ouX74MANBqtfD3929w/eY8f1mYkcxWlPn5+dXZqSY0NBTFxcXIy8tD586dmzNei1NWVobS0lIAgF6vr3UdvV6PP/74A3l5eQ4VZsnJyfLoKGCdAN27d2/Mnj2bl3M4ke2cqqszn+242tZrzLbq+l2w/YzGbIucw5nH92qffPKJ3fKWLVvw5JNP4p577rmOlOQKeP62HDx/Xd+uXbsAAP3794enp2eD6zfn+cvCjGQVFRUAAG9v7zrXsT1nW5eaztX7uK5j4ujxCA4Oxt/+9jfExsaibdu2qKqqQnp6Oj799FOcOHECy5Ytw5tvvnnDcxXJqqFzyvYFSGOOX0Pbsj1eWVnpcE66Ps48vgDkRj7du3dHYGAgLl++jD179mDXrl3YsGED/P39MXDgQOeEp2bF89f98fxVh+TkZOzZswdarRZjx45t1Gua8/xlYSbYqlWrcOHCBYdeM2PGDPTo0cPpWSRJAgBoNBqnb7ulcqXjC1i/Herfv7+87Ovri5iYGPTt2xfz5s1DRkYGfvnlFwwePLhJfn5LYzunrvf52tbl+ek6nHl8AWDy5Ml2yzfddBOeeOIJdOjQAR988AE+/fRT/mGnUjx/3R/PX9d38eJFvPfee5AkCRMmTGj0lUbNef6yMBMsNzcXWVlZDr2mqb5Ra9WqFYD6v921/WxHb8rXUt3I8b16H1dWVtY6p89Zx8PHxwcPPPAANm3ahKNHj7IwcxLbOVXXOevI8Wvo/LRtq74Rb3IuZx7f+txzzz34/PPPkZ2djStXrqBt27Y3tD1qfjx/Wy6ev64hPz8fb775JkpLSzFy5EiH7snbnOcvCzPBli1bJjqCrHXr1gCsTUAqKipq/WMiPz/fbl2q340cX19fX/j6+qKsrAwFBQW1FmYFBQUAnHM8bC1l2a7ZeWzHxXbeXMuR42dbx/aaa/HcbH7OPL718fDwQLt27VBYWAiDwcA/7FSI52/LxfNXvKKiIixZsgR5eXkYNmwYJkyY4NDrm/P85UQSkvn5+cm/VLV1lsnPz0dxcTFat27NjozNxNbStbb7IJlMJpw/fx6enp7o0KHDDf8sW6MRjoY6j+34nT17ttbnbcfVtt6NbMv2eGO2Rc7hzOPbEJ6f6sbzt2Xj+StOeXk5li5dikuXLmHgwIGYOnWqw5ckNuf5y8KM7AwYMAAA8Ntvv9V47tdff7Vbh5pefccjOTkZ1dXV6Nu3L7y8vG74Z9l+Rm2t+en6REREwNfXF5cvX671P/SDBw8CaNw51b9/f2g0GqSlpaGwsNDuuerqaiQlJUGj0SAqKso54alBzjy+9blw4QKysrLg7e2Njh073tC2SAyevy0Xz19xqqursWLFCvzxxx+IjIzE7Nmzr6u5WXOevyzMWqjZs2dj9uzZNYZlR4wYAQ8PD/z73//G6dOn5cezs7OxY8cOeHh4OHRdLt2Ye++9F61atcLhw4flP/IAoLCwUG7JO3LkyBqvq+v47tq1q8Y10iaTCV9++SV+++03eHl5YdiwYc5/Iy2UTqfD8OHDAQCbNm2y2/c7d+5EZmYmIiIi7Jq97N69G7Nnz8b27dvtthUSEoI777wTJpMJGzduhNlslp/75JNPUFRUhMGDB/N2B83Imcf36NGjtY6MZ2ZmYvXq1ZAkCffccw90Os5AcGU8f90bz1/1sFgsWLNmDX7//Xf06tULL7zwQoP73xXOX/6GuIGVK1fK84Js17n+8MMPSExMBGBtkT5nzhy719gaUphMJrvHO3TogPHjx2Pr1q1YuHAh+vXrB61Wi5SUFFRVVckdhqh5+Pv7Y9q0aXj77bexevVq9O7dGwEBATh+/DhKS0vxwAMP4NZbb63xurqO7+bNm7F9+3Z06tQJrVu3RnV1Nc6dOweDwQBPT088++yzdd6ng67P6NGjcfz4cZw6dQqzZs1CREQE8vLycObMGQQEBCAuLs5u/aKiImRlZcFgMNTY1qRJk3DmzBkcPHgQs2fPRnh4OC5cuIALFy6gXbt2mDhxYnO9Lfo/zjq+p0+fxldffYU2bdqgXbt2CAwMxJUrV3D27FmYzWb07t0b48aNa863RrBemfD111/bPWYymfDKK6/Iy4888og8KsrzV12cdXx5/rqe3bt349ChQwCAgIAAbNy4sdb1JkyYIN8A3BXOXxZmbuDcuXPIzc21eyw/P18u0tq0aePQ9kaOHImwsDD861//QlpaGgDr5W2jRo1CTEyMc0JTo912221YtGgRvvnmG5w5cwYmkwkdO3bE/fffj7vvvtuhbT366KM4ffo0Ll26hIsXL0KSJISGhuJPf/oTRo4cyaK7CXh5eWHhwoXYsWMHEhISkJiYCD8/PwwdOhRjx451aLJwYGAgli5dii+++AKJiYk4dOgQgoKCMHz4cIwZMwb+/v5N+E6oNs46vv3790d+fj7++OMPZGZmoqysDK1atUJERAQGDx6Mu+++m/cXFKCoqAhnzpyxe0ySJLvHioqKGrUtnr+ux1nHl+ev6ykpKZH/bSvQavO3v/1NLszq01znr0Zy9EYrRERERERE5FQs34mIiIiIiARjYUZERERERCQYCzMiIiIiIiLBWJgREREREREJxsKMiIiIiIhIMBZmREREREREgrEwIyIiIiIiEoyFGRERERERkWAszIiIiIiIiARjYUZERERERCQYCzMiIiIiIiLBWJgREREREREJxsKMiIiIiIhIMBZmREREREREgrEwIyIiIiIiEoyFGRERERERkWAszIiIiBrp22+/xZgxY/D4448jPT291nWSk5MxduxYjBkzBgkJCc2ckIiI1IqFGRERUSP99a9/xa233gqz2Yw1a9agvLzc7nmDwYD4+HhIkoQhQ4Zg8ODBgpISEZHasDAjIiJqJI1Gg2effRZBQUG4fPkyPvzwQ/k5SZKwdu1aFBUVISwsDE899ZTApEREpDYszIiIiBwQHByMuLg4aDQaJCQkYO/evQCAf/7znzh+/Di0Wi1mzZoFHx8fsUGJiEhVWJgRERE5KCoqCg8++CAAYNOmTdi/fz8+//xzAMDjjz+O8PBwkfGIiEiFNJIkSaJDEBERqY3JZML8+fORkZEhPxYZGYmXX34ZGo1GYDIiIlIjjpgRERFdB51Oh7i4OHnZ19cX06dPZ1FGRETXhYUZERHRdfrPf/4j/7u8vBznzp0TF4aIiFSNhRkREdF1SEpKwu7duwEAXbp0gSRJWLduHYxGo9hgRESkSizMiIiIHGS7XxkADBs2DIsWLUKbNm1QWFiIdevWgdO3iYjIUSzMiIiIHGCxWLB27VoUFxejffv2mDx5Mnx9fTFr1ixotVocO3YMO3fuFB2TiIhUhoUZERGRA7777rta71fWs2dPPProowCAzz77zK5bIxERUUNYmBERETVSenq63f3Kunfvbvf8ww8/jD59+sBkMmHNmjWoqKgQEZOIiFSIhRkREVEjlJeXY82aNTCbzejXrx/+8pe/1FjHw8MDM2bMgL+/P7Kzs7Fp0yYBSYmISI14g2kiIiIiIiLBOGJGREREREQkGAszIiIiIiIiwViYERERERERCcbCjIiIiIiISDAWZkRERERERIKxMCMiIiIiIhKMhRkREREREZFgLMyIiIiIiIgEY2FGREREREQkGAszIiIiIiIiwViYERERERERCcbCjIiIiIiISDAWZkRERERERIKxMCMiIiIiIhKMhRkREREREZFgLMyIiIiIiIgEY2FGREREREQkGAszIiIiIiIiwViYERERERERCfb/AVTjciNY33+NAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-1, 2, 151)\n", "u = np.tanh(1e8*x) + 2\n", "t = np.linspace(0, 0.5, 101)\n", "\n", "fig, axs = plt.subplots(2, 1, sharex=True)\n", "axs[0].plot(x, u)\n", "axs[0].set_xlim(-1.1, 2)\n", "axs[0].set_ylabel('u')\n", "axs[0].set_xlabel('x')\n", "\n", "for i in range(15):\n", " xi, ui = x[10*i], u[10*i]\n", " \n", " # Characteristics with the wave speed u\n", " xx = xi + ui*t\n", " \n", " if xi != 0:\n", " axs[1].plot(xx, t, color='gray') \n", "\n", "# Expansion fan \n", "for i in range(5):\n", " axs[1].plot((1+2/5*i)*t, t, color='blue')\n", "\n", "axs[1].set_ylabel('t')\n", "axs[1].set_xlabel('x')" ] }, { "cell_type": "markdown", "id": "70521423", "metadata": {}, "source": [ "### Entropy Condition\n", "쌍곡 보존식의 해는 팽창파 뿐 아니라 팽창충격파도 존재할 수 있다. 그러나 자연 현상에서는 점성에 의해 팽창파만 존재한다. 즉 엔트로피가 증가하는 방향으로만 해가 존재한다.\n", "\n", "Burgers 방정식에서도 Entropy 조건을 만족해야 한다.\n", "\n", "볼연속 충격파의 전파 속도는 다음 조건을 만족한다.\n", "\n", "$$\n", "f'(u_L) > s > f'(u_R).\n", "$$" ] }, { "cell_type": "markdown", "id": "d7f984e8", "metadata": {}, "source": [ "## 수치해석\n", "- 앞선 선형 방정식과 같이 다음 Finite Volume Method 식으로 계산한다.\n", "\n", " $$\n", " U_i^{n+1} = U_i^n - \\frac{\\Delta t}{\\Delta x} \\left (\n", " F^n_{i+1/2} - F^n_{i-1/2}\n", " \\right )\n", " $$\n", " \n", " * $F^n_{i+1/2} = \\frac{1}{\\Delta t} \\int_{t^n}^{t^{n+1}} f(u(x_{i+1/2}, t) dt$\n", " - $F^n_{i+1/2} \\approx \\mathcal{F} (U_i^n, U_{i+1}^n)$\n", "\n", "- Flux를 제외한 수치 방법은 동일하다.\n", "\n", "- 시간 간격 계산시 Wave speed $f'(u)=u$가 위치별로 다르므로, 최대값을 사용한다.\n", "\n", "- Runge Kutta 등의 다양한 시간 적분 기법을 적용하기 위해 다음과 같이 Semi-discrete form으로 계산할 수 있다.\n", "\n", " $$\n", " \\frac{dU_i}{dt} = - \\frac{1}{\\Delta x} (F_{i+1/2} - F_{i-1/2})\n", " $$\n", "\n", "### Godunov Method\n", "- Exact Riemann Prolbem을 해석해서 계산한다.\n", "\n", " $F^n_{i+1/2} \\approx f(u^n_{i+1/2})$\n", " \n", " - $u^n_{i+1/2}$ 는 Exact Riemann Problem으로 Shock wave 와 Expansion Wave 결과로 계산한다.\n", " \n", "### Approximate Riemann solver\n", "- 간단한 Burgers 방정식의 경우 Exact Riemann Problem 계산이 가능하나, Euler 등의 System 방정식에서 Riemann Problem을 해석하는 것은 어렵다.\n", "\n", "- 수치 안정적인 Upwind 기법 적용이 가능하다.\n", "\n", " $$\n", " F^n_{i+1/2} = \\mathcal{F} (U_i^n, U_{i+1}^n) = \\frac{1}{2} \n", " \\left [\n", " f(U_i^n) + f(U_{i+1}^n)\n", " \\right ]\n", " - \\frac{1}{2} |a_{i+1/2}| \\left (\n", " U_{i+1}^n - U_i^n\n", " \\right )\n", " $$\n", "\n", " 여기서 Intercell에서 Wavespeed는 $|a_{i+1/2}|=S$ 로 한다. " ] }, { "cell_type": "markdown", "id": "94967d2d", "metadata": {}, "source": [ "## Converavtive vs Non-conservative\n", "- Finite Volume method for conservative form\n", "\n", "$$\n", "\\frac{\\partial u}{\\partial t} + \\frac{\\partial }{\\partial x} \\left ( \\frac{u^2}{2} \\right )= 0.\n", "$$\n", "\n", "- Finite Difference method for non-conservative form\n", "\n", "$$\n", "u_t + uu_x=0.\n", "$$\n", "\n", "- (Lax and Wendroff) 수치해가 수렴하기 위해서는 weak form 을 만족해야 한다. 즉 jump condition을 만족해야 한다." ] }, { "cell_type": "code", "execution_count": 5, "id": "047572d4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0IAAAJqCAYAAAAG1vCbAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/P9b71AAAACXBIWXMAABcSAAAXEgFnn9JSAABqCElEQVR4nO3de3yU9Z33//c1kxPkwDkhIGdFQLxBAoiWFqQVLObeRS1ha5d6YvuzpdZI2113tbWsWlitEbXaw7re0gq1itIqN6Z2b7EVtiRAULEohFMKBnIikBBCTnP9/sAZrkkmmWOYuWZez8fDhzPXXHPNd/hmkrzz+R4M0zRNAQAAAEACcUS7AQAAAABwsRGEAAAAACQcghAAAACAhEMQAgAAAJBwCEIAAAAAEg5BCAAAAEDCIQgBAAAASDgEIQAAAAAJhyAEAAAAIOEQhAAAAAAkHIIQAAAAgIRDEAIAAACQcAhCAAAAABIOQQgAAABAwkmKdgPs6MSJEzJNM2qvP3jwYElSbW1t1NqA8NCH9kb/2R99aH/0ob3Rf/YXC31oGIaGDh0a8vMJQiEwTTOqQcjaDtgbfWhv9J/90Yf2Rx/aG/1nf3buQ4bGAQAAAEg4BCEAAAAACYcgBAAAACDhEIQAAAAAJByCEAAAAICEQxACAAAAkHBYPhsAAAAxx87LMicCd/9Esp8Mw4jYtQJBEAIAAEBMcLlcam5u1rlz5whCMa6+vl7S+T6LFMMwlJycrJSUFKWmpvZ6MCIIAQAAIOpM09Tp06eVlJSkfv36yel0RrtJ6EFS0vkY0d7eHrFrulwutba2qrm5We3t7UpPT+/VMEQQAgAAQNQ1NzfL4XAoIyPjog+RQvDcfRTJvnI6nerTp49SU1N1+vRptbS0KC0tLWLX74zFEgAAABB1ra2tSktLIwRBDodDaWlpam1t7d3X6dWrAwAAAAFob29XcnJytJuBGJGSkqK2trZefQ2CEAAAAKLKvTAC1SC4ORwOmabZq4tmEIQAAAAAJByCEAAAAICEE/aqcS0tLfrggw+0a9cuHTx4UDU1NXK5XBo6dKiuvvpq5efnB7Xaw/Lly1VTU9Pt408++aSGDx/e5bjL5dJbb72ld955RydOnFBaWpquuOIKFRQU6JJLLgnpvQEAAACIT2EHoa1bt+oXv/iFJGnEiBGaMmWKmpubtX//fr3yyivatm2bfvSjH6lfv35BXXfOnDk+j/ft27fLMdM0tWbNGm3fvl3p6emaNm2aGhsbVVJSorKyMj300EO67LLLgn9zAAAAAOJS2EEoKSlJ8+fP14033qjc3FzP8fr6eq1evVqHDx/Wiy++qHvvvTeo6y5fvjzgc7ds2aLt27crNzdXK1euVP/+/SVJ27dvV1FRkZ5++mmtWbOGjbkAAABgC75GQFldc8012rBhQ7fnJyUlKTMzUzk5Obryyit1/fXXa8GCBZ6NUHt6vd///veaPn26z/PeeOMNffOb35R0vgiyffv2gN5PLAo7CM2ZM8dn9WbAgAG666679OCDD6q0tFTt7e3d/sOHa9OmTZKkr33ta54QJEmzZs3S9OnTtXPnTu3YsUOzZs3qldcHAAAAesPixYt9Hr/00kt7PN/lcqmxsVGHDh3Shg0b9Oqrr2r06NH66U9/qquuuqrH19y4cWO3Qej1118PovWxrXeSyWdGjRolSWpra1NjY6MGDBgQ8deorq7WsWPHlJKSomnTpnV5fNasWdq5c6d27dpFEAIAAICtrFmzJuzzjxw5otWrV+vNN9/U4sWL9bvf/U6TJ0/ucl5qaqpGjRqlN954QytXruxSxDh58qTeffddXXnlldqzZ09Q7YpFvRqEqqqqJElOp1MZGRlBPfeNN97QiRMnlJycrBEjRmjmzJnKysrqct6RI0cknS/N+ao4jRkzRpJUUVERZOtj07tr/0vnzjRKks42N0e5NQhV3z59JNGHdkX/RZHR9Y7hdErZw2T0TQ/4MpmZmZKkxsbGCDbu4ktOTtY111yjgQMHRrspAGLY6NGj9fOf/1wZGRn6zW9+o+9+97v6wx/+4PPcm266Sf/xH/+hd999V1/60pe8HnvjjTfU1tamm2++mSDkz+bNmyVJU6dODXqn4Jdeesnr/tq1a3XHHXdo3rx5Xsdra2slSYMGDfJ5Hfdx93mBWLFiRZdjKSkpWr16tSRp8ODBAV8r0n7y1FPaXVUXtdcHAMSWSy+9VHv27Em4ebDuP34OGTIkyi1BKDr3n2maqq+vV1JSEpuqdhLs1JKezv/3f/93/f73v9dHH32kXbt26eqrr+5yzuLFi/XYY49p48aNuuGGG7we27hxo9LT07Vw4UKtXLkypPYFyjRNORwODRkypNe+JnotCJWVlWnLli1yOp1asmRJwM/Ly8vT5MmTNXbsWGVlZamqqkpbtmzR5s2bPUl25syZnvPPnTsn6XxQ8SU1NdXrPAAA4smBAwd07Ngxz3B0IN6Ypik1N0W7GcHrkx5zoS4rK0tf/OIX9eabb2rbtm0+g5B7JNYf/vAHNTU1KT39fLW9oqJCO3fuVEFBgc9VnO2oV4LQsWPH9Mwzz8g0TS1dulSjR48O+Ll33nmn1/0RI0bo61//uoYNG6Zf/vKXWrdunVcQcovkF1pRUVGPj9fW1p7/UEbB+EuGyeE4vw+u6XJFpQ0In0Ef2hr9F2M62qX29u4fdzikPunSgMHSZ380c49SaGtruxgt7BVlZWWe2ydOnIibX0wC5a4k9LT3IGJX5/4zTVMul0vt7e1dfqczz56R695bL3obw+V4ar2MvsFNDfGlvafvbyGcP3HiRL355pvat2+fz3Pb29t10003qaSkRG+88YZn8YVXXnlFkrRo0SKv5wXbvkC5vyZqamq6/T3fMAyvVauDFfEgVFdXpx//+MdqampSfn6+Fi5cGJHrzps3T7/97W91/PhxVVdXKzs7W5I8m7W2tLT4fJ77eDCbusayojeK+eYfB+hDe6P/YotpmtKxIzI/KJX5Qal0pNz3iYNz5PjxL2UYRlz04bhx4zyjHTo6OqLcGgC9pbtltPfu3Rv0Pp2SPHMKT58+3e05//t//2/98Ic/1MaNGz1BaOPGjcrOztbs2bNVVxcf0zQiGoQaGhr0yCOPqLa2VnPnztXSpUsjdm2Hw6GcnBydPn1a9fX1niDknq/TXYe4j0dzXg8AoPcYhiGNGCNjxBgpf4nMUydlfrhD5oc7pI/fl1pbz59YWyWda5b6xEflxDonyM6VLQA962757O6mhfjjHtXU02iq/v37a968efrjH/+o6upqVVZW6uDBg/qnf/qnuJqPGLEg1NzcrFWrVunTTz/VzJkzdffdd0d8XGRT0/nxodbqjnvY3dGjR33uVXT48GFJ0siRIyPaFgBAbDL6D5TxhQXSFxbIPNcs1z2WeapnGuImCFkXIeqtoSlATOiTLsdT66PdiuD1CXwly54Eu3y2PydPnpQkr703fbn55ptVXFys3//+9zp69Kgk6ZZbboloW6ItIkGora1Njz32mA4ePKgpU6aosLDQM48lUo4eParKykqlpqZ6lQizs7M1fPhwffrppyorK+syf8i9221eXl5E2wMAiH1GWh+pb7p09rOJ1k2N0pCh0W1UhFj/KksQQjwzDEOKwFwbnPfXv/5VknTZZZf1eN6XvvQl9evXTxs2bFBVVZUuu+wyXXnllRejiRdN2GnF5XLpqaee0l//+ldNnDhR3/ve9/wuo1dcXKzCwkKtX++d7t9//30dOnSoy/kVFRUqKiqSaZqaN29el+vn5+dLktatW+c13rGkpEQ7d+5Udna2ZsyYEepbBADYWXrmhdtn7L1vkBUVIQDBamho0LvvvitJuvbaa3s8NzU1VTfeeKM++ugj1dTU6Oabb74ILby4wq4IFRcXq7S0VNL5Deqef/55n+ctXbrUsyFqQ0ODKisrVV9f73XO/v37tWHDBg0ZMkQ5OTnKyspSdXW1Dh8+rI6ODk2aNEm33tp11ZDrrrtOu3fvVmlpqQoLC3XllVeqsbFRe/fuVXJysu65555eW+McABDjMrKkmhOSJLOpUbG1mG3oqAgBCNa///u/6+zZs5o6daqmT5/u9/yvfOUreuutt2QYBkHIlzNnznhuuwORL4sXL/YEoe5MnTpVdXV1OnjwoCoqKnT27Fn16dNHEyZM0OzZs3Xdddf5HHLncDi0YsUKbd68WVu2bNGuXbuUlpamGTNmaMmSJRoxYkTobxAAYG9UhAAkuIqKCq1atUpvvvmm+vbtq5/85CcBPe/qq6/WRx991Muti56wg1BBQYEKCgoi8pzx48dr/PjxIbXD4XAoPz/fM0wOAABJMjIy5dn5rakhmk2JKOtIB4IQALfCwkJJ56evnDlzRocOHdKBAwdkmqbGjBmjZ599VhMnToxuI2ME48UAAPEtTitCBCEAvrz66quSzn+PyMjI0NChQ/WVr3xF8+fP1/z585kuYsG/BAAgvmVYglBTfAYh9hEC4s+nn37aq+eH8/zs7GxVVVVJsvcfYiK7xjUAALEm/cL8VJOKEADgMwQhAEB8S4CKEEEIAIJHEAIAxDXDa44QiyUAAM4jCAEA4hsVIQCADwQhAEB8s8wR0rlmme3xsbAA+wgBQHgIQgCA+GatCElS0xnf59mM0+n03CYIAUDwCEIAgPiWkiolXaiexMteQtaKEMtnA0DwCEIAgLhmGIb3pqpN8bFggrUi1NHREcWWAIA9EYQAAPHPOjyOihAAQAQhAEAisFSEzDhZOc66ahwVIQAIHkEIABD/4rAiZA1CVIQAIHgEIQBA3DPicI4Q+wgBQHgIQgCA+BfnFSGCEAAEL8n/KQAA2JxlU9V4nCNEEALiz/Dhw/2es3jxYq1Zs6b3GxOnCEIAgPhHRQiATS1evLjbx2bOnHkRWxK8J554QkVFRSoqKtKSJUui3ZwuCEIAgLhnpGfKdN+hIgTARqj49B7mCAEA4p9XRSg+Fkuw7iNEEAKA4BGEAADxzzJHSGfPyDTN7s+1CafT6blNEALwyCOPaPjw4br77ru7PFZbW6upU6dq5MiR2rlzp+d4VVWVnnvuOd1yyy3Ky8vT6NGjNXXqVC1btkzvv/9+t6919uxZPfXUU/rSl76k8ePH67LLLtPcuXP1wx/+UMeOHZMkXX311SoqKpIkrVixQsOHD/f89z//8z+RffMhYmgcACD+WStCHR0yzzbJSM+IXnsiwFoRYh8hAP/8z/+s9957T2+++aa++MUves0t+u53v6uamhqtWLFC06dP9xz/wx/+oEcffVSjR4/WhAkTlJGRoSNHjuitt97Sf//3f2vt2rWaM2eO1+tUVVXpH/7hH7R//34NGDBAn/vc55SUlKQjR47ohRde0BVXXKElS5boxhtv1Hvvvae9e/dqxowZGj16tOca2dnZvf7vEQiCEAAg/vX1Dj2uxtNy2DwIWStCHR0dUWwJ0LtM01RDg/2GtGZlZckwjIv2eikpKXr22We1YMEC/eAHP9CsWbM0YsQIrV27Vv/93/+tadOm6d577/V6zowZM/THP/5RkyZN8jr+7rvv6o477tC//du/aevWrV7v4zvf+Y7279+vm266SU888YRSU1M9jx06dEgul0uS9MMf/lBPPPGE9u7dq69+9asslgAAQDQYTqfUN1062yRJMhtPS0P9L00by6gIIVE0NDR0+UXdDvbu3at+/fqFfZ2eltH+r//6L91www2e+5deeql+8IMf6IEHHtB3vvMdrV69Wg8//LDS09P1zDPPeC2yIkkTJ070ed25c+cqPz9fr7/+uj755BPPebt379bWrVuVnZ2tJ554Qunp6V5Dc8eOHRvOW73oCEIAgMSQnukJQq7G01FuTPisv9BQEQLiV0/LZ/sKSbfffrveeecd/b//9//093//92pubtYTTzzhNTTNqqWlRe+++652796tkydPqrW1VZL08ccfS5IOHz7sCULvvfeeJOmmm25Senp6OG8rJhCEAACJISNLqjkhSXI12m+YTWfWIERFCIhfoSyf/cQTT2jWrFlqbGzU9ddfr3/4h3/wed7HH3+sO+64Q0ePHu32WmfOnPHcrqyslCSNGjUq6DbFIoIQACAxpF9YMCHeKkKsGod4lpWVpb1790a7GUHLysryf1Ivefvtt3Xu3DlJ0oEDB3T27Fn17dvX6xzTNHX33Xfr6NGjWrp0qZYuXapRo0YpPT1dhmFo1apV+ulPf+pzlc2LOfepNxGEAAAJwci4sKkqQQiwD8MwIjLXJlEcOnRIP/rRj9S3b1994QtfUHFxsX70ox/pscce8zrvwIEDOnDggKZMmaLVq1d3uc7f/va3LseGDRsmSTpy5EivtP1iYx8hAEBisFSEzDgbGkcQAiCd/15wzz336OzZs1q5cqWeeeYZjRkzRuvWrVNxcbHXuadOnZIk5ebmdrnOqVOn9Oc//7nL8c9//vOSpI0bN+rs2bN+2+Ne1CVW5zEShAAAiSGDoXEA4tsTTzyh999/XwsWLNCtt96qvn37elaL+/73v6/q6mrPuWPGjJHD4dC2bdt06NAhz/Fz587p/vvv9wQlq6uuukrXXnutqqur9f3vf79LGDp8+LAOHDjguZ+TkyNJOnjwYITfaWQwNA4AkBjSL4zXj4fFEqzLZxOEgPhVWFjY7WPDhw/X97//fUlSaWmpnn32WQ0ZMkSPP/6455yrrrpKhYWF+slPfqIVK1bo17/+tQzD0ODBg/XVr35V69at0/XXX6/Pfe5zSktLU2lpqTo6OlRQUKBXXnmly2s+/fTTKigo0IYNG/TOO+9oxowZng1V9+7dqyeeeEKXXnqpJGnOnDlKS0vTf/7nf2rfvn3KycmRYRi6++67PedEE0EIAJAYqAgBsKFXX32128cmTZqk73//+2psbNR3vvMddXR06IknntCgQYO8zvvOd76jLVu2aMuWLfo//+f/6M4775QkrVq1SuPGjdPLL7+sbdu2KTMzU5///Of1L//yL/rtb3/r8zVzc3O1efNm/dd//ZfefPNN/elPf1JSUpKGDRumZcuWafbs2Z5zhw4dqhdeeEFPPvmkSktL1dR0fguDm2++OSaCkGH6WgoCPTp+/LjPFTQuliFDhkiSampqotYGhIc+tDf6z57Mve/L9eQPJUnO7FwN+eXrtu7DP//5z/rqV78qSRo9erS2bdsW5RZdXHwO7a1z/5mmqbq6Og0aNChuViSLd+4/xvTWH2IC+ZowDMPnHKdAMUcIAJAY4rgixD5CABA8ghAAIDFY5giZzWdl2jw8WINQrK7IBACxjCAEAEgMloqQJLnO2HvBBCpCABAeghAAIDGkpEpJF1Zas/vwOOuqcVSEACB4BCEAQEIwDMOrKmTaPAg5nU7PbSpCABA8ghAAIHGkx8+CCVSEACA8BCEAQOLIiJ9NVakIAUB4CEIAgMQRxxUhtgWEnbn3ieHrGG4ul0uGYfTqvlIEIQBAwjCsc4Qa7B2ErBUhqfc2NQQulqSkJKqb8GhtbfX6g09vIAgBABJHnFaEJIIQ7C8lJUXnzp2jKgS5XC6dO3dOKSkpvfo6Sf5PAQAgTmRYg5C95whZ9xGSCEKwvz59+qilpUVnzpxRnz59ulQ9EVvcgTWSwdXlcqm1tVXnzp1TcnKyUlNTI3ZtXwhCAIDEkW5dLMHeFaHOQYghRbA7wzDUr18/NTc36/Tp01SGYpzDcX5gmcvlitg1DcNQcnKy+vTpo9TU1F6dHyQRhAAACcTIyJT7V6t4C0JUhBAPHA6H0tPTlZ6eThCKcUOGDJEk1dTUROyavR18OiMIAQASR7r3hqoX90duZBGEEO8u9i/FCI67f+zcT2EHoZaWFn3wwQfatWuXDh48qJqaGrlcLg0dOlRXX3218vPzlZaWFtC1mpqatHv3bu3atUtHjhxRbW2tDMPQJZdcotmzZ2v+/PldvvFL0rPPPqs//elP3V532bJlmj9/fsjvEQAQJ6xzhM40yGGatv0hThACgPCEHYS2bt2qX/ziF5KkESNGaMqUKWpubtb+/fv1yiuvaNu2bfrRj36kfv36+b3Wm2++qddff12GYWjMmDHKy8tTQ0OD9u3bpwMHDmj79u164IEHup04NWXKFPXv37/L8WHDhoX1HgEAccIyR0gdHVLzWalvevTaEwbDMOR0OtXR0SGJIAQAwQo7CCUlJWn+/Pm68cYblZub6zleX1+v1atX6/Dhw3rxxRd17733+r1WWlqabrrpJi1YsEADBw70HD9+/LgefvhhffLJJ3rttdd06623+nz+okWLdMUVV4T7lgAA8So9XTIMyT33oKnRtkFIOr+ENkEIAEIT9j5Cc+bM0bJly7xCkCQNGDBAd911lySptLQ0oG/QixYt0le/+lWvECRJubm5nvCzbdu2cJsMAEhQhsMp9bEEnzON0WtMBFiHxxGEACA4vbqh6qhRoySdX9KzsTG8HzajR4+WdL7SBABAyCzzhNQUP3sJEYQAIDi9umpcVVWVJMnpdCojIyMi1/I1B8itpKREJSUlcrlcys7OVl5enoYPHx7W6wIA4kx6pqTjkiTzTGPcrBzHPkIAEJxeDUKbN2+WJE2dOlXJyckRudb06dO7Pae4uNjr/rp163T99dfrjjvuCGp34hUrVnQ5lpKSotWrV0uSBg8eHPC1eoP7B597/XbYD31ob/SfvZ0cMEith8/fzjBMpdu4H1NSUjy3MzMzE+prks+hvdF/9hcPfdhrQaisrExbtmyR0+nUkiVLwrrW22+/rT179ig9PV2LFi3q8viYMWM0fvx4TZ48WYMGDdKpU6e0e/duvfzyy3r77beVlJSk22+/Paw2AADigyPzwiqmdt9U1fpHRipCABCcXglCx44d0zPPPCPTNLV06VLP/J5Q7N27Vy+++KIMw9A3v/nNLgspSNLChQu97mdnZ2vBggWaOHGi7r//fhUXFys/Pz/gSk5RUVGPj9fW1kZ1t+Pe2MkXFxd9aG/0n725ki6Eh7PVJ3TOxv1o3QOprq4uob4m+RzaG/1nf7HQh4ZhdFmwLRgRXyyhrq5OP/7xj9XU1KT8/PwuISUYFRUVevzxx9Xe3q7bb79dM2fODOr5I0eO1PTp0+VyubRnz56Q2wEAiCPWxRLiaNU4KkIAEJyIBqGGhgY98sgjqq2t1dy5c7V06dKQr3XixAk9+uijampq0uLFi/XlL385pOsMHTpUEqvNAQA+Y9lU1WyydxCyDo1z7ycEAAhMxIJQc3OzVq1apU8//VQzZ87U3Xff7VWyD8bJkyf1yCOP6NSpU1q4cKEWL14ccruampoknd+sFQCAeKoIWRcCoiIEAMGJSBBqa2vTY489poMHD2rKlCkqLCyUwxHapc+cOaNHH31U1dXVmjt3rm677baw2lVWViZJGjt2bMjXAQDEDyPduo+QvYOQtSLEPkIAEJywg5DL5dJTTz2lv/71r5o4caK+973veY1Z9qW4uFiFhYVav3691/GWlhatWrVKR48e1TXXXBNQVamyslI7duyQy+XyOt7Q0KA1a9aorq5Oo0aN0uWXXx7aGwQAxJc4rQgRhAAgOGGvGldcXKzS0lJJ5/cweP75532et3TpUmVlnR+X3dDQoMrKyi7zdn7zm9+ovLxcDodDTqdTP/vZz3xea/ny5Z7b9fX1evzxx5WZmalhw4Zp4MCBamho0KFDh9Tc3KxBgwbpvvvuC3mYHgAgzljmCKmlWWZ7m4yk8Pa6ixYqQgAQurCD0JkzZzy33YHIl8WLF3uCUHfc83lcLpe2bt3a7XnWIJSbm6uFCxeqvLxcVVVVOnDggJKTk5Wbm6u8vDwtXLhQGRkZgb4dAEC8s1aEpPNVof5dt2awA+sIDIIQAAQn7CBUUFCggoKCiDxn+fLlXiEnEAMHDmSzVABA4FJSpeQUqa31/P2m+AhCLJYAAMGJ+D5CAADEMsMw5Mi0jFCw8TwhKkIAEDqCEAAg4Tgy+124Y+OV4whCABA6ghAAIOFYg5CdN1UlCAFA6AhCAICEY1grQjYeGseqcQAQOoIQACDheM0RamqIXkPCxD5CABA6ghAAIOE4qAgBQMIjCAEAEk68zBGiIgQAoSMIAQASTjzOEWIfIQAIDkEIAJBwvOcI2TcIWStCHR0dUWwJANgPQQgAkHAcWdaKkH0XS6AiBAChIwgBABKO12IJZ8/INM3oNSYM1n2EqAgBQHAIQgCAhOMVhDo6pOaz0WtMGKxBiIoQAASHIAQASDhGeqZkGBcO2HSeEBUhAAgdQQgAkHAMp1NGesaFAzZdOY6KEACEjiAEAEhIXsPjmuy5YII1CLGPEAAEhyAEAEhIXpuq2rQiZF01jiAEAMEhCAEAEpJ3RcieQci6jxBBCACCQxACACQkw7qpKhUhAEg4BCEAQEKKhzlCVIQAIHQEIQBAQvIKQnFQEWLVOAAIDkEIAJCQvBZLiIM5QuwjBADBIQgBABJSvM0RoiIEAMEhCAEAElI8rBpn3UeIihAABIcgBABISPEwR8gahKgIAUBwCEIAgITkFYRammW22y9IUBECgNARhAAACcmR1c/7gA2rQlSEACB0BCEAQEIyUtOk5JQLB2w4T4gNVQEgdAQhAEDiSs+8cNuGFSE2VAWA0BGEAACJK8MShJoaoteOEFERAoDQEYQAAInLUhEybVgRss4RIggBQHAIQgCAxOVVESIIAUAiIQgBABKWYfM5QgQhAAgdQQgAkLjS7T1HqPM+QqZpRrE1AGAvBCEAQOLKiJ85QhJ7CQFAMAhCAIDElZ514bYN5whZV42TzleFAACBIQgBABKWkWHvOULWfYQkKkIAEAyCEAAgcaXbe9W4zhUhFkwAgMARhAAAiavT8tl2W2ygc0WIIAQAgSMIAQASl3WOkMslNZ+NXltC0LkixNA4AAgcQQgAkLjS0yXDuHDfZsPjOleEWCwBAAJHEAIAJCzD4ZT6pF84YLMFEwzD8FpCm4oQAASOIAQASGwZ8bWpKgAgMAQhAEBiS4+fTVWpCAFA4AhCAIDElmHvTVWpCAFAaAhCAICEZqTbe1NVKkIAEBqCEAAgscXRHCH2EQKAwCX5P6VnLS0t+uCDD7Rr1y4dPHhQNTU1crlcGjp0qK6++mrl5+crLS0tqGs2NTXp1VdfVWlpqU6dOqX+/ftrxowZKigoUHp6us/nuFwuvfXWW3rnnXd04sQJpaWl6YorrlBBQYEuueSScN8mACBe2bwiZN1LiCAEAIELuyK0detW/eQnP9GWLVtkmqamTJmiCRMmqLq6Wq+88or+9V//VadPnw74eo2Njfq3f/s3bd68WU6nUzNmzFCfPn301ltv6V//9V/V2Nj1h5RpmlqzZo3Wrl2rkydPatq0aRoxYoRKSkp0//33q7y8PNy3CQCIV5aKkGnDOULWvYQIQgAQuLArQklJSZo/f75uvPFG5ebmeo7X19dr9erVOnz4sF588UXde++9AV1v7dq1On78uGbOnKn77rvP8w3+hRdeUHFxsdauXatvf/vbXs/ZsmWLtm/frtzcXK1cuVL9+/eXJG3fvl1FRUV6+umntWbNmi4bzwEAoHTLYglUhAAgYYRdEZozZ46WLVvmFYIkacCAAbrrrrskSaWlpQF9cz516pTee+89OZ1OLVu2zCu4LF26VFlZWdq6datOnTrl9bxNmzZJkr72ta95QpAkzZo1S9OnT1dVVZV27NgR4jsEAMQzw2uOkP2CEHOEACA0vbpYwqhRoySdX8XG15C2znbv3i3TNDVp0iSvQCOd/4tXXl6eXC6X3n//fc/x6upqHTt2TCkpKZo2bVqXa86aNUuStGvXrtDfCAAgftl8jhBBCABC06tBqKqqStL58csZGRl+z6+oqJAkjRkzxufj7uNHjhzxHHPfHjFihNcPg87PcV8bAAAv1opQS7PMdnstQU0QAoDQhD1HqCebN2+WJE2dOtVrDHN3amtrJUkDBw70+figQYO8zrPedj8WyHP8WbFiRZdjKSkpWr16tSRp8ODBAV+rN7h/6A0ZMiSq7UDo6EN7o//sz9qHrrQUVVseG5yVJUe6/z/exYo+ffp4bqelpSXM1yWfQ3uj/+wvHvqw1ypCZWVl2rJli5xOp5YsWRLQc86dOydJSk1N9fm4+3hLS0uX56SkpPT4HPd5AABYGSneP3PMttYotSQ01j80dnR0RLElAGAvvVIROnbsmJ555hmZpqmlS5dq9OjRAT3PNE1JkmEYQb9mKM/pTlFRUY+P19bWetoaDe7kXVNTE7U2IDz0ob3Rf/Zn7UPT5fJ6rO7EcRlt9gkULkv7T548mTBfl3wO7Y3+s79Y6EPDMLos2BaMiFeE6urq9OMf/1hNTU3Kz8/XwoULA36uu7zfXfXGXQmyVozcm7Vaq0S+nhPspq4AgMRgOBySdY6pjStCzBECgMBFNAg1NDTokUceUW1trebOnaulS5cG9Xz33JuTJ0/6fLyurs7rPOtt92OBPAcAAC/JluHVrfYKQmyoCgChiVgQam5u1qpVq/Tpp59q5syZuvvuu4MeruZebvvw4cM+H3cfd58nyTPs7ujRoz5/ALifM3LkyKDaAgBIIEmWBX2oCAFAQohIEGpra9Njjz2mgwcPasqUKSosLJTDEfylp06dKsMw9PHHH+v06dNdXmPXrl0yDENXXXWV53h2draGDx+u1tZWlZWVdbnm9u3bJUl5eXlBtwcAkCCsCyawfDYAJISwg5DL5dJTTz2lv/71r5o4caK+973v+dzPx6q4uFiFhYVav3691/EBAwboc5/7nNrb2/X88897rX7z0ksvqaGhQbNnz+6y2Wp+fr4kad26dV4BqqSkRDt37lR2drZmzJgR5jsFAMQt6xYPNhsaZ/2Z29ZmrxAHANEU9qpxxcXFKi0tlSRlZmbq+eef93ne0qVLlZWVJen8XKLKykrV19d3Oe/2229XeXm5SkpKVFhYqHHjxuno0aM6evSocnJydNttt3V5znXXXafdu3ertLRUhYWFuvLKK9XY2Ki9e/cqOTlZ99xzj99wBgBIYEmWOUI2Gxpn/fnG8tkAELiw08GZM2c8t92ByJfFixd7glBPsrKytGrVKr3yyivasWOHSktL1a9fP91www0qKChQRkbXTe4cDodWrFihzZs3a8uWLdq1a5fS0tI0Y8YMLVmyRCNGjAjtzQEAEoNlLzqzrVWR25Ch91ERAoDQhB2ECgoKVFBQENHnZGRk6M4779Sdd94Z8DUdDofy8/M9w+QAAAhYMhUhAEg0Ed9HCAAA27HOEbJZVYWKEACEhiAEAECcVIRYNQ4AAkcQAgAkPMPGQYh9hAAgNAQhAACS7buhqtPp9NwmCAFA4AhCAAAkWzZUtdk8GypCABAaghAAAF4VoZbotSMEVIQAIDQEIQAAvOYIURECgERAEAIAgDlCAJBwCEIAAFjmCJk2rgixjxAABI4gBACAjStC1n2EOjo6otgSALAXghAAADbeR8gahKgIAUDgCEIAAMRJEKIiBACBIwgBABKeESdBiIoQAASOIAQAgNccIXuFCWsQYtU4AAgcQQgAABtXhNhHCABCQxACAMDGQYh9hAAgNAQhAABsHISoCAFAaAhCAADYeI4QFSEACA1BCACAThUh0zSj15YgURECgNAQhAAAsAYhSWq3T1WIVeMAIDQEIQAAOgchG80TYh8hAAgNQQgAgJTOQcg+gcI6NK6joyOKLQEAeyEIAQCQlOx9v7UlOu0IgXWxBCpCABA4ghAAIOEZhuEdhmw0R4iKEACEhiAEAIDkPTzORnOEqAgBQGgIQgAASN4LJrTaJwhZK0Iul0sulyuKrQEA+yAIAQAgeQ+Ns1FFyLpqnMQS2gAQKIIQAACSlJJ64baN5ggRhAAgNAQhAAAkyTLEzE5D4whCABAaghAAAJLXHCGToXEAEPcIQgAASMwRAoAEQxACAEDyniNk4yDEEtoAEBiCEAAAkvccIRuFCes+QhIVIQAIFEEIAABJRpI9N1Q1DMNrLyGCEAAEhiAEAIAkpViDkH0qQpJ3VYggBACBIQgBACB1GhrXEr12hICKEAAEjyAEAIDktXw2FSEAiH8EIQAApE5ByD5zhCQqQgAQCoIQAACSrYOQdQltghAABIYgBACA5DVHyLRxEGIfIQAIDEEIAABJSrZuqGqvMGENQh0dHVFsCQDYB0EIAACp06pxVIQAIN4RhAAAkOJmjhAVIQAIDEEIAABJBhUhAEgoBCEAAKROc4TsG4RYNQ4AAkMQAgBA6jRHyF5VFfYRAoDgJfk/xb9Dhw7pww8/1IEDB1ReXq76+nolJydr3bp1QV3n3Xff1XPPPef3vOXLl2vOnDme+88++6z+9Kc/dXv+smXLNH/+/KDaAgBIMDaeI+R0Oj23CUIAEJiIBKENGzZo586dYV9n6NChXgHH6uzZs9qxY4ckacKECT7PmTJlivr379/l+LBhw8JuGwAgznkFISpCABDvIhKExo8fr9GjR2vcuHEaN26cvvGNb4R0nQkTJnQbct5++23t2LFDl19+uXJycnyes2jRIl1xxRUhvTYAIMF5BaGW6LUjBMwRAoDgRSQILVq0KBKX6dF7770nSfrCF77Q668FAEhA1jlC7e0yXS4ZDntMpSUIAUDwbPEdvrq6Wvv27VNSUpKuueaaaDcHABCPUlK877fbZ3gcQQgAgheRilBv+/Of/yxJmjZtmjIyMro9r6SkRCUlJXK5XMrOzlZeXp6GDx9+sZoJALCzpE5BqK1VSkn1fW6MYR8hAAieLYLQ1q1bJfkfFldcXOx1f926dbr++ut1xx13eK2o48+KFSu6HEtJSdHq1aslSYMHDw74Wr3B/QNvyJAhUW0HQkcf2hv9Z3+++tBs66cqyzmDsjLlHGiPPrb+kTA1NTUhvjb5HNob/Wd/8dCHMR+EDhw4oMrKSqWnp2vatGk+zxkzZozGjx+vyZMna9CgQTp16pR2796tl19+WW+//baSkpJ0++23X9yGAwDsJSlZMgzJNCVJZqt9ltCmIgQAwYv5IOQeFnfttdd6faO3Wrhwodf97OxsLViwQBMnTtT999+v4uJi5efnB1zJKSoq6vHx2tpamZ/9oIwGd/KuqamJWhsQHvrQ3ug/++u2D5OTpc8C0MkTJ2Q4Uzo/NSZ1dHR4bjc0NCTE1yafQ3uj/+wvFvrQMAzl5uaG/PyYXiyho6NDf/nLXySFtlrcyJEjNX36dLlcLu3ZsyfSzQMAxBvrPKF2+1SE2FAVAIIX00Hogw8+0OnTp5WTk6PLL788pGsMHTpUklRfXx/JpgEA4pHXXkL2CUJsqAoAwYvpIOTeO+jzn/98yNdoamqSJKWlpUWkTQCAOGZdQtumc4QIQgAQmJgNQufOndPOnTslhR6E2traVFZWJkkaO3ZsxNoGAIhTSZZNVW206ACLJQBA8KIShIqLi1VYWKj169d3e05JSYlaWlp02WWX9TgJqrKyUjt27JDL5fI63tDQoDVr1qiurk6jRo0KeWgdACCBJNtzjpA1CFkXTgAAdC8iq8aVlZXptdde8zrW3t6uBx54wHP/lltu8Sx/3dDQoMrKyh7n7biHxflbJKG+vl6PP/64MjMzNWzYMA0cOFANDQ06dOiQmpubNWjQIN13330yDCPUtwcASBSWoXFmW6vs8pODihAABC8iQaihoUHl5eVex0zT9DrW0NAQ8PXq6+v10Ucfyel06tprr+3x3NzcXC1cuFDl5eWqqqrSgQMHlJycrNzcXOXl5WnhwoVeG80BANCtZPvPEaIiBACBiUgQmjt3rubOnRvw+QUFBSooKOj28QEDBujll18O6FoDBw5ks1QAQGQwRwgAEkbMLpYAAMBFl2L/OUKsGgcAgSEIAQDwGcOmQ+PYRwgAgkcQAgDAzaYbqjqdTs9tghAABIYgBACAm1cQss9cGypCABA8ghAAAG7J1sUSWqLXjiBREQKA4BGEAABwoyIEAAmDIAQAgJvX8tn2mSPEqnEAEDyCEAAAbimpnpumTYMQ+wgBQGAIQgAAuCXbvyLU0dERxZYAgH0QhAAAcLPpHCEqQgAQPIIQAABuNt1HiIoQAASPIAQAwGeMOAhCVIQAIDAEIQAA3LzmCNknUFARAoDgEYQAAHBLvrBqnJ0qQtZ9hKgIAUBgCEIAALjFwapx7CMEAIEhCAEA4BYHc4QIQgAQGIIQAABucbB8NkEIAAJDEAIAwM0ahDraZbrssfAAQQgAgkcQAgDAzTpHSLJNVci6WILL5ZLL5YpiawDAHghCAAC4WStCkm3mCTmdTq/7rBwHAP4RhAAAcOschFrtEYSSO1Wy2EsIAPwjCAEA4OZ0SoblR2O7PYIQFSEACB5BCACAzxiG0WkvIXsECipCABA8ghAAAFYp9ttLiIoQAASPIAQAgFWSJQjZdI4QS2gDgH8EIQAArKyhwkZzhAzD8NwnCAGAfwQhAACsUlIv3LbREDPrpqoMjQMA/whCAABYJV2oCJk2GRoneQchFksAAP8IQgAAWCXbb7EEiYoQAASLIAQAgJV11TibzBGSqAgBQLAIQgAAWCXbb9U4iYoQAASLIAQAgIWRZL8NVSUqQgAQLIIQAABWNp0jZN1LiIoQAPhHEAIAwCrFnkHI6XR6brOPEAD4RxACAMAqDipCBCEA8I8gBACAlU3nCFERAoDgEIQAALCy6dA4KkIAEByCEAAAVjYdGmddNY4gBAD+EYQAALCyVFZMmwYhVo0DAP8IQgAAWCWnXrhto0DBPkIAEByCEAAAVsnWxRJaoteOIFERAoDgEIQAALDymiNkn0BBRQgAgkMQAgDAwvCqCDFHCADiFUEIAAArrzlC9gxCVIQAwD+CEAAAVsn23FDVuo8QFSEA8I8gBACAlU33EXI6nZ7b7CMEAP4l+T/Fv0OHDunDDz/UgQMHVF5ervr6eiUnJ2vdunVBX2v58uWqqanp9vEnn3xSw4cP73Lc5XLprbfe0jvvvKMTJ04oLS1NV1xxhQoKCnTJJZcE3Q4AQIKyaRCyVoQIQgDgX0SC0IYNG7Rz585IXMpjzpw5Po/37du3yzHTNLVmzRpt375d6enpmjZtmhobG1VSUqKysjI99NBDuuyyyyLaPgBAnLJpELLOESIIAYB/EQlC48eP1+jRozVu3DiNGzdO3/jGN8K+5vLlywM+d8uWLdq+fbtyc3O1cuVK9e/fX5K0fft2FRUV6emnn9aaNWu8hg0AAOCTdY6QyyWzo0OGDX5+EIQAIDgRCUKLFi2KxGVCtmnTJknS1772NU8IkqRZs2Zp+vTp2rlzp3bs2KFZs2ZFqYUAANuwrhonna8KOftEpy1BYPlsAAiO7RdLqK6u1rFjx5SSkqJp06Z1edwdfnbt2nWxmwYAsCNrRUiyzfA4ls8GgOBEpCLUG9544w2dOHFCycnJGjFihGbOnKmsrKwu5x05ckSSNGLECK8fAm5jxoyRJFVUVPRqewEAccI6R0iyTRBi+WwACE7MBqGXXnrJ6/7atWt1xx13aN68eV7Ha2trJUmDBg3yeR33cfd5gVixYkWXYykpKVq9erUkafDgwQFfqze4A9+QIUOi2g6Ejj60N/rP/vz14QmnU/qsqjIwM1NJNujrzMxMz+2kpKS4//rkc2hv9J/9xUMfxlwQysvL0+TJkzV27FhlZWWpqqpKW7Zs0ebNm/Xzn/9cGRkZmjlzpuf8c+fOSTofVHxJTU31Og8AAH+M5FSZHWclSWZrS5RbExiWzwaA4MRcELrzzju97o8YMUJf//rXNWzYMP3yl7/UunXrvIKQm2EYEWtDUVFRj4/X1tbKNM2IvV6w3Mm7p/2WENvoQ3uj/+zPXx+alqHW9dVVMtL7XZR2haOl5UJgO3PmTNx/ffI5tDf6z/5ioQ8Nw1Bubm7Iz7fNYgnz5s1Tv379dPz4cVVXV3uOp6WlSfL+AWDlPu4+DwAAv2y4lxAVIQAIjm2CkMPhUE5OjiSpvr7ec9w9X6eurs7n89zHoz2vBwBgI9Yg1GqPIMQ+QgAQHNsEIUlqamqS5F3dGT16tCTp6NGjPr/xHz58WJI0cuTI3m8gACA+WJfQbrdfEGLVOADwzzZB6OjRo6qsrFRqaqqGDx/uOZ6dna3hw4ertbVVZWVlXZ63fft2SecXYQAAICCWipBpk1DBPkIAEJyoBKHi4mIVFhZq/fr1Xsfff/99HTp0qMv5FRUVKioqkmmamjdvXpf9gvLz8yVJ69at0+nTpz3HS0pKtHPnTmVnZ2vGjBm98E4AAHEpxd5D46gIAYB/EVk1rqysTK+99prXsfb2dj3wwAOe+7fccoumTZsmSWpoaFBlZaXXXB9J2r9/vzZs2KAhQ4YoJydHWVlZqq6u1uHDh9XR0aFJkybp1ltv7fL61113nXbv3q3S0lIVFhbqyiuvVGNjo/bu3avk5GTdc889PjdbBQDApyT7LZZARQgAghORdNDQ0KDy8nKvY6Zpeh1raGjwe52pU6eqrq5OBw8eVEVFhc6ePas+ffpowoQJmj17tq677jo5HF2LWA6HQytWrNDmzZu1ZcsW7dq1S2lpaZoxY4aWLFmiESNGhP8mAQCJw4ZzhKyrxlERAgD/IhKE5s6dq7lz5wZ8fkFBgQoKCrocHz9+vMaPHx9SGxwOh/Lz8z3D5AAACJWRkirPbnE2CRVOp9Nzm4oQAPhnm8USAAC4aJIsFSGbzBGiIgQAwSEIAQDQmQ03VLVWhNhHCAD8IwgBANCZddW4dntUV6wVIYIQAPhHEAIAoDPrYgmtLdFrRxCoCAFAcAhCAAB05rV8NhUhAIhHBCEAADqz4Rwh6z5CBCEA8I8gBABAZ5Y5QqYNgxCrxgGAfwQhAAA6s84RsmEQYh8hAPCPIAQAQGc2nCNERQgAgkMQAgCgEyPF3nOEqAgBgH8EIQAAOrP5YglUhADAP4IQAACd2XCOkHX5bNM05XK5otgaAIh9BCEAADpLTr1w2ybVFWtFSKIqBAD+EIQAAOjMhhWhzkGIvYQAoGcEIQAAOrP5HCGJIAQA/hCEAADoLNl7+WzTNKPXlgARhAAgOAQhAAA6swYh0yV1xH6oIAgBQHAIQgAAdGadIyTZYsGE5E5tJggBQM8IQgAAdGatCEm2mCfkcDhkGIbnPkEIAHpGEAIAoLMuFaHYD0KSd1WI5bMBoGcEIQAAOjEcTslpmXNjkyDkdDo9t6kIAUDPCEIAAPjitZeQPaor1ooQQQgAekYQAgDAF+s8odaW6LUjCFSEACBwBCEAAHyxBqF2KkIAEG8IQgAA+OK1qao95ghZ9xIiCAFAzwhCAAD44jU0zn5BiFXjAKBnBCEAAHyxDDMzbVgR6ujoiGJLACD2EYQAAPDFhnOEqAgBQOAIQgAA+JJi7zlCVIQAoGcEIQAAfEmy3xwh66pxVIQAoGcEIQAAfDC8NlS1RxCy7iNERQgAekYQAgDAFxvOEaIiBACBIwgBAOBLiv2GxlkrQuwjBAA9IwgBAOBLkv0WS7BWhAhCANAzghAAAL5Y5wjZZGgcFSEACBxBCAAAX7yGxrVErx1BoCIEAIEjCAEA4ItlsQTTJgsPWPcRIggBQM8IQgAA+GLDOUIEIQAIHEEIAABfUghCABDPCEIAAPhiww1VrUGIfYQAoGcEIQAAfDCsG6raJFRYg1BHR0cUWwIAsY8gBACAL8n2GxpnXTWOihAA9IwgBACALzYMQuwjBACBIwgBAOCL1xwhe1RX2EcIAAJHEAIAwBcbVoRYNQ4AAkcQAgDAF4IQAMS1JP+n+Hfo0CF9+OGHOnDggMrLy1VfX6/k5GStW7cuqOs0NTVp9+7d2rVrl44cOaLa2loZhqFLLrlEs2fP1vz5872+ybs9++yz+tOf/tTtdZctW6b58+cH/b4AAAmsUxAyTVOGYUSvPQFg+WwACFxEgtCGDRu0c+fOsK/z5ptv6vXXX5dhGBozZozy8vLU0NCgffv26cCBA9q+fbseeOABpaam+nz+lClT1L9//y7Hhw0bFnbbAAAJxjpHSJLa27seizEsnw0AgYtIEBo/frxGjx6tcePGady4cfrGN74R0nXS0tJ00003acGCBRo4cKDn+PHjx/Xwww/rk08+0WuvvaZbb73V5/MXLVqkK664IqTXBgDAS3KnP7q1tcR8EGL5bAAIXESC0KJFiyJxmW6vk5ubq1tvvVVPP/20tm3b1m0QAgAgYjqHHhsEC+vy2VSEAKBntlksYfTo0ZKk+vr66DYEAJAYkjoHodhfMIGKEAAELiIVoYuhqqpKknzOAXIrKSlRSUmJXC6XsrOzlZeXp+HDh1+kFgIA4onhcJwPQ+2fBQobBCE2VAWAwNkmCG3evFmSNH369G7PKS4u9rq/bt06XX/99brjjju8fjj4s2LFii7HUlJStHr1aknS4MGDA75Wb3BPhh0yZEhU24HQ0Yf2Rv/ZX6B9WJWSKvOzIDQgI13JMd7n1vm1Docjrr9G+RzaG/1nf/HQh7YIQm+//bb27Nmj9PR0n/OIxowZo/Hjx2vy5MkaNGiQTp06pd27d+vll1/W22+/raSkJN1+++0Xvd0AAHszUlJknj1/22y1V0WIoXEA0LOYD0J79+7Viy++KMMw9M1vftPrr11uCxcu9LqfnZ2tBQsWaOLEibr//vtVXFys/Pz8gCs5RUVFPT5eW1sr0zQDfxMR5k7eNTU1UWsDwkMf2hv9Z3+B9qHLeeHH5KmaahmDYrvPz50757nd3Nwc11+jfA7tjf6zv1joQ8MwlJubG/LzY3qxhIqKCj3++ONqb2/X7bffrpkzZwb1/JEjR2r69OlyuVzas2dPL7USABC3Om2qGuus+wgxRwgAehazQejEiRN69NFH1dTUpMWLF+vLX/5ySNcZOnSoJFabAwCEwLqENkEIAOJKTAahkydP6pFHHtGpU6e0cOFCLV68OORrNTU1STq/WSsAAEGxVIRMG8y5IQgBQOBiLgidOXNGjz76qKqrqzV37lzddtttIV+rra1NZWVlkqSxY8dGqokAgERhHRrX2hK9dgTIGoRYLAEAehaVIFRcXKzCwkKtX7/e63hLS4tWrVqlo0eP6pprrtHdd98twzB6vFZlZaV27Nghl8vldbyhoUFr1qxRXV2dRo0apcsvvzzi7wMAEOesQag99oOFNQh1dHREsSUAEPsismpcWVmZXnvtNa9j7e3teuCBBzz3b7nlFk2bNk3S+ZBSWVnZZd7Ob37zG5WXl8vhcMjpdOpnP/uZz9dbvny553Z9fb0ef/xxZWZmatiwYRo4cKAaGhp06NAhNTc3a9CgQbrvvvv8BioAALqw2RyhZEt7qQgBQM8iEoQaGhpUXl7udcw0Ta9jDQ0Nfq/jns/jcrm0devWbs+zBqHc3FwtXLhQ5eXlqqqq0oEDB5ScnKzc3Fzl5eVp4cKFysjICPYtAQAgIzlVns0SbLaPEBUhAOhZRILQ3LlzNXfu3IDPLygoUEFBQZfjy5cv9wo5gRg4cCCbpQIAeodXRSj2KyxUhAAgcDG3WAIAADHDa46QvSpCrBoHAD0jCAEA0J0U66pxsR+ErBUhghAA9IwgBABAd5IsQcgGiyVQEQKAwBGEAADojo3nCBGEAKBnBCEAALpjmSNk2mCOkHUfIdM0WTkOAHpAEAIAoDs2myNkDUISVSEA6AlBCACA7iTZd0NViSAEAD0hCAEA0B2v5bNjf46QdbEEib2EAKAnBCEAALpheA2Na4leQwLUuSLEHCEA6B5BCACA7lgrQjaornSeI0RFCAC6RxACAKA7Npsj1DkIURECgO4RhAAA6E5K6oXbNghCDodDDseFH+1UhACgewQhAAC6Y7MNVSXvqhCrxgFA9whCAAB0x2uOUOxXhCSCEAAEiiAEAEB3Oi2fbbpc0WtLgAhCABAYghAAAN2xBiHJFnsJEYQAIDAEIQAAutNpXx47zBOy7iXEYgkA0D2CEAAA3elcEbLBPCGn0+m5zfLZANA9ghAAAN1J6lwRiv0gREUIAAJDEAIAoBuGYdhu5ThrRYg5QgDQPYIQAAA9sdleQtaKEEEIALpHEAIAoCfJqRdut7VErx0BYtU4AAgMQQgAgJ7YrCJEEAKAwBCEAADoic3mCBGEACAwBCEAAHpCEAKAuEQQAgCgJ5ahcSZBCADiBkEIAICeeFWE7DVHiH2EAKB7BCEAAHpiDUKt9qoIdXR0RLElABDbCEIAAPTEGoTaYz8IWfcRoiIEAN0jCAEA0APDa/ns2A9CTqfTc5uKEAB0jyAEAEBPbDZHiIoQAASGIAQAQE9sNkeIihAABIYgBABAT5gjBABxiSAEAEBPbDxHiH2EAKB7BCEAAHpis6Fx1ooQQQgAukcQAgCgJ5YgZNpgqJl1HyGCEAB0jyAEAEBPbDZHiCAEAIEhCAEA0JMUew2NIwgBQGAIQgAA9CTJXoslWIMQq8YBQPcIQgAA9MCw2YaqVIQAIDAEIQAAemIdGmeDihCrxgFAYAhCAAD0JNleQYiKEAAEhiAEAEBPbDxHiCAEAN0jCAEA0BOv5bOZIwQA8YIgBABAT1g+GwDiEkEIAICeWCtCHe0yXR3Ra0sAWD4bAAKT5P8U/w4dOqQPP/xQBw4cUHl5uerr65WcnKx169aFdL2mpia9+uqrKi0t1alTp9S/f3/NmDFDBQUFSk9P9/kcl8ult956S++8845OnDihtLQ0XXHFFSooKNAll1wSztsDACQyyypskqS2dinVGZ22BMAahDo6Yju0AUA0RSQIbdiwQTt37ozEpdTY2KgHH3xQx48fV05OjmbMmKFjx47prbfe0u7du/Xoo48qMzPT6zmmaWrNmjXavn270tPTNW3aNDU2NqqkpERlZWV66KGHdNlll0WkfQCABJOc6n2/rUVKTfV9bgywLp9NRQgAuheRIDR+/HiNHj1a48aN07hx4/SNb3wj5GutXbtWx48f18yZM3XffffJ6Tz/V7cXXnhBxcXFWrt2rb797W97PWfLli3avn27cnNztXLlSvXv31+StH37dhUVFenpp5/WmjVrPNcCACBgXSpCsR0urD/rqAgBQPciMkdo0aJFKigoUF5enieEhOLUqVN677335HQ6tWzZMq9v5kuXLlVWVpa2bt2qU6dOeT1v06ZNkqSvfe1rXq8/a9YsTZ8+XVVVVdqxY0fI7QIAJDBnkmQYF+7H+BLaVIQAIDAxtVjC7t27ZZqmJk2a1CVQJScnKy8vTy6XS++//77neHV1tY4dO6aUlBRNmzatyzVnzZolSdq1a1dvNh0AEKcMw7DVpqrWPyKyahwAdC+mglBFRYUkacyYMT4fdx8/cuSI55j79ogRI7wmiHZ+jvvaAAAEzUZByFoRIggBQPciMkcoUmprayVJAwcO9Pn4oEGDvM6z3nY/Fshz/FmxYkWXYykpKVq9erUkafDgwQFfqze4A9+QIUOi2g6Ejj60N/rP/oLtw+rUVLmaGiVJ/dPTlRLDfW/9GWWaZtx+nfI5tDf6z/7ioQ9jqiJ07tw5SVJqN6vxuI+3tLR0eU6KdcM7H89xnwcAQLCMlAs/l8zWlh7OjD42VAWAwMRURcg0TUmfjccOUijP6U5RUVGPj9fW1nraGg3u5F1TUxO1NiA89KG90X/2F2wfdjguzLs5XVsjI4b7/syZM57bLS0tcft1yufQ3ug/+4uFPjQMQ7m5uSE/P6YqQn369JHUffXGXQmyVozS0tK8HuvuOe7zAAAImo3mCFERAoDAxFQQco9rPnnypM/H6+rqvM6z3nY/FshzAAAIimUBAjPGl6QmCAFAYGIqCI0aNUqSdPjwYZ+Pu4+7z5Ok0aNHS5KOHj3q8xu++zkjR46MZFMBAInEqyJknzlC7CMEAN2LqSA0depUGYahjz/+WKdPn/Z6rK2tTbt27ZJhGLrqqqs8x7OzszV8+HC1traqrKysyzW3b98uScrLy+vdxgMA4pdXEIrtcGENQh0dHVFsCQDEtqgEoeLiYhUWFmr9+vVexwcMGKDPfe5zam9v1/PPP+/1Dfyll15SQ0ODZs+e3WWz1fz8fEnSunXrvAJUSUmJdu7cqezsbM2YMaP33hAAIL5ZhsbF+hwh6z5CbW1tUV3cBwBiWURWjSsrK9Nrr73mday9vV0PPPCA5/4tt9yiadOmSZIaGhpUWVmp+vr6Lte6/fbbVV5erpKSEhUWFmrcuHE6evSojh49qpycHN12221dnnPddddp9+7dKi0tVWFhoa688ko1NjZq7969Sk5O1j333ONzs1UAAAJhJKfKEydaYzsIOZ1Or/sul6vLMQBAhIJQQ0ODysvLvY6Zpul1rKGhIaBrZWVladWqVXrllVe0Y8cOlZaWql+/frrhhhtUUFCgjIyMLs9xOBxasWKFNm/erC1btmjXrl1KS0vTjBkztGTJEo0YMSK8NwgASGzWilB7bAcha0VIOl8VIggBQFcRCUJz587V3LlzAz6/oKBABQUF3T6ekZGhO++8U3feeWfA13Q4HMrPz/cMkwMAIGJsOkdIYp4QAHQnphZLAAAgJlmDUIwPjeschFg5DgB8IwgBAOCPjTZU7Tw0jr2EAMA3ghAAAP54zRGK7QpL5/lABCEA8I0gBACAPykXKkJmq302VJUIQgDQHYIQAAD+JNlnsQSHwyGH48KPd4IQAPhGEAIAwB/rHKEYXz5b8p4nRBACAN8IQgAA+GOdIxTjFSHJe54Qq8YBgG8EIQAA/DBSrMtnx/YcIcm7IsQ+QgDgG0EIAAB/bDRHSPJeMIGKEAD4RhACAMAfm80RsgYh5ggBgG8EIQAA/PEaGkcQAoB4QBACAMAfmy2WQBACAP8IQgAA+JPE0DgAiDcEIQAA/LEOjevokBnjK7GxWAIA+EcQAgDAn+RU7/st56LTjgBZgxDLZwOAbwQhAAD8SU+XHJYfmQ310WtLAKz7CFERAgDfCEIAAPhhOJxSv4EXDtTXRa8xAXA6nZ7bVIQAwDeCEAAAgeh/IQiZp09GsSH+URECAP8IQgAABKK/tSIU20GIihAA+EcQAgAgAIY1CFERAgDbIwgBABAIyxwhM8bnCLGPEAD4RxACACAQAwZduB3jFSGCEAD4RxACACAAXkPjThGEAMDuCEIAAASiv6UidOqkTJcrem3xgyAEAP4RhAAACIS1ItTRLjU1Rq8tfhCEAMA/ghAAAIHoky6lpF64H8MLJliDEKvGAYBvBCEAAAJgGIZ3VSiGF0ywBiH2EQIA3whCAAAEyjJPKJaX0GYfIQDwjyAEAECA7LJynNPp9NymIgQAvhGEAAAIlNfKcVSEAMDOCEIAAATKUhEyqQgBgK0RhAAACBQVIQCIGwQhAAACZJc5QuwjBAD+EYQAAAiUNQg1npbZHpvVFoIQAPhHEAIAIFDWICRJp09FpRn+EIQAwD+CEAAAATKSU6SMzAsHYnSeEEEIAPwjCAEAEIx+sT9PiCAEAP4RhAAACMaACyvHmVSEAMC2CEIAAATBsEFFiOWzAcA/ghAAAMGwwRLaVIQAwD+CEAAAwejP0DgAiAcEIQAAgmCHTVUJQgDgH0EIAIBgWBZLYPlsALAvghAAAMGwLpZwrlnmubPRa0s3CEIA4B9BCACAYGT1kxyWH58xODyOVeMAwD+CEAAAQTAcTilrwIUDMRiEnE6n53ZHR0cUWwIAsSvJ/ymBaW1t1e9+9ztt27ZNtbW1ysjI0JQpU7RkyRINGjTI/wUkvfvuu3ruuef8nrd8+XLNmTPHc//ZZ5/Vn/70p27PX7ZsmebPnx9QGwAA8GvAIM/8IPNUnYwoN6czKkIA4F9EglBra6sefvhh7du3TwMGDND06dNVU1Ojd999V2VlZXrkkUc0dOhQv9cZOnSoV8CxOnv2rHbs2CFJmjBhgs9zpkyZov79+3c5PmzYsMDfDAAA/sT4pqpUhADAv4gEoY0bN2rfvn0aP368HnzwQaWlpUmSNm3apF/96lf62c9+ppUrV/q9zoQJE7oNOW+//bZ27Nihyy+/XDk5OT7PWbRoka644orQ3wgAAAEwBgyU6b4Tg0GIihAA+Bf2HKH29nYVFxdLku666y5PCJKk/Px8jRo1Sh9//LEOHToU1uu89957kqQvfOELYV0HAICwWSpCsbipKhUhAPAv7CD0ySefqKmpSTk5ORozZkyXx6+++mpJ0s6dO0N+jerqau3bt09JSUm65pprQr4OAAAR4bWXEBUhALCjsIfGVVRUSJLPECRJY8eO9TovFH/+858lSdOmTVNGRka355WUlKikpEQul0vZ2dnKy8vT8OHDQ35dAAB8MfrH9tA49hECAP/CDkK1tbWS1O3KcAMHDvQ6LxRbt26V5H9YnHuIntu6det0/fXX64477vAaJuDPihUruhxLSUnR6tWrJUmDBw8O+Fq9wf0DbsiQIVFtB0JHH9ob/Wd/4fZh+9jL5PmpdvqkBg8aJMMROztSnDlzxnO7vb1dgwcPlmHE2tp24eFzaG/0n/3FQx+GHYTOnTsnSUpNTfX5uHvOkPu8YB04cECVlZVKT0/XtGnTfJ4zZswYjR8/XpMnT9agQYN06tQp7d69Wy+//LLefvttJSUl6fbbbw/p9QEA6MwxwPIHsfZ2mY2nZfQb0P0TLjLr0Djp/Dwha5UIABCBIGSaZliP++MeFnfttdd2+0184cKFXvezs7O1YMECTZw4Uffff7+Ki4uVn58fcCWnqKiox8dra2vDfl/hcCfvmpqaqLUB4aEP7Y3+s79w+9A0TSklVWptkSTVHtgvY+TYiLUvXKdPn/a6f/z4ca/FjOIBn0N7o//sLxb60DAM5ebmhvz8sOv4ffr0kSS1tLT4fNx9PJRvwB0dHfrLX/4iKbTV4kaOHKnp06fL5XJpz549QT8fAABfDMOQ+lv2EjodW/OEOv/hkHlCANBV2EHIXWWpq/O9fOjJkye9zgvGBx98oNOnTysnJ0eXX355SO1zb+RaX18f0vMBAPCp/4W5sWZ9bC2hTRACAP/CDkKjRo2SJB0+fNjn4+79g9znBcO9d9DnP//5EFsnNTU1SQqtIgUAQHcMa0UoxlaO6zxHiCAEAF2FHYQmTJigvn37qqqqymcYKikpkaRuFzrozrlz5zx7D4UahNra2lRWVibpwjLeAABEhKUiFOtD49hLCAC6CjsIJSUl6YYbbpAkvfDCC16rw23atEkVFRWaMGGCLr30Us/x4uJiFRYWav369d1et6SkRC0tLbrssst6nARVWVmpHTt2yOVyeR1vaGjQmjVrVFdXp1GjRoU8tA4AAJ8sFaFYHxrX0dERpZYAQOyKyFqaN998s/bs2aN9+/bp3nvv1YQJE1RbW6vy8nJlZmbqW9/6ltf5DQ0Nqqys7HHejntYnL9FEurr6/X4448rMzNTw4YN08CBA9XQ0KBDhw6publZgwYN0n333Rd3+ycAAKIshhdLMAxDTqfTE4CoCAFAVxEJQikpKXrooYe0ceNGbd26VTt27FB6errmzJmjJUuWBL1QQn19vT766CM5nU5de+21PZ6bm5urhQsXqry8XFVVVTpw4ICSk5OVm5urvLw8LVy4UBkZGeG8PQAAujD6D5JnI4UYqwhJ56tC7iBERQgAuorY7mopKSlasmSJlixZ4vfcgoICFRQUdPv4gAED9PLLLwf0ugMHDmSzVADAxWetCDWeltneLiOGNi1NSkrybGFBRQgAugp7jhAAAAnJGoQk6XRsbdNgXTmOVeMAoCuCEAAAITCSU6T0zAsHTsXW8Din0+m5TRACgK4IQgAAhMomewkRhACgK4IQAAChsi6hHWNBiIoQAPSMIAQAQIgM66aqMTY0zloRYrEEAOiKIAQAQKhieGictSLE8tkA0BVBCACAUFkqQiYVIQCwFYIQAAAhMmK4IpRk2dOIOUIA0BVBCACAUA2I3TlCBCEA6BlBCACAUPWzVITONcs8dzZ6bemEIAQAPSMIAQAQqqx+ksPyozSGhscRhACgZwQhAABCZDicUtaACwcIQgBgGwQhAADCMSA2V46zrhpHEAKArghCAACEo19srhxn3UeIIAQAXRGEAAAIgzEgNoMQ+wgBQM8IQgAAhMNSEYqloXHWilBHR0cUWwIAsYkgBABAOLz2EqIiBAB2QRACACAMRv/YHBpHRQgAekYQAgAgHP28K0KmaUavLRZUhACgZwQhAADCYV0soaNdOtMQvbZYsI8QAPSMIAQAQDj6pEspKRfux8jwOIIQAPSMIAQAQBgMw5D6W4fHxcbKcQQhAOgZQQgAgHD1ty6hTUUIAOyAIAQAQJgMa0WonooQANgBQQgAgHBZl9A+HRsVIeuqcQQhAOiKIAQAQLgsFSEzRipC1n2ECEIA0BVBCACAcMV4RYh9hACgK4IQAABhisU5QtaKUEdHRxRbAgCxiSAEAEC4rBWhxtMyY2AoGhUhAOgZQQgAgHBZg5Akna6PTjssqAgBQM8IQgAAhMlITpHSMy8ciIFNVakIAUDPCEIAAERCjC2YwD5CANAzghAAAJFgCUJmPUEIAGIdQQgAgAjwWjnudPSHxhGEAKBnBCEAACLBOjSOihAAxDyCEAAAkWCpCJkxMEfIulgCQQgAuiIIAQAQAYZXRSj6Q+Osy2cThACgK4IQAACRMMA6Ryi2KkIsnw0AXRGEAACIhH6WilDzWZn7PopeW8QcIQDwhyAEAEAk9BsgXTLac9f1QpHMpjNRaw5BCAB6RhACACACDMOQ4+v3SO65OSdrZb70nEzTjEp7CEIA0DOCEAAAEWKMuUzG33/Nc9/cuVXmX96JSlsIQgDQM4IQAAARZCy4Sbr8Ss99c/0vZVZXXvR2EIQAoGcEIQAAIshwOOW4s1Dqm3H+QEuzXM8XybzIYYR9hACgZwQhAAAizBg4RI6vL79w4PB+mZtevqhtYB8hAOgZQQgAgF5g5H1Oxue+5Llvbt4gc/9fL9rrd64IRWvRBgCIVUn+TwlMa2urfve732nbtm2qra1VRkaGpkyZoiVLlmjQoEH+L/CZ5cuXq6amptvHn3zySQ0fPrzLcZfLpbfeekvvvPOOTpw4obS0NF1xxRUqKCjQJZdcEtJ7AgAgHMY//JPM8r9K1ccl0yXXfxXJ8dBTMtzD5nqRtSIkSR0dHV7zhgAg0UXkO2Jra6sefvhh7du3TwMGDND06dNVU1Ojd999V2VlZXrkkUc0dOjQoK45Z84cn8f79u3b5ZhpmlqzZo22b9+u9PR0TZs2TY2NjSopKVFZWZkeeughXXbZZSG9NwAAQmWk9ZFj2ffk+o9/ljo6pJM1Ml/6mfRP35NhGL362taKkCS1tbURhADAIiLfETdu3Kh9+/Zp/PjxevDBB5WWliZJ2rRpk371q1/pZz/7mVauXBnUNZcvX+7/pM9s2bJF27dvV25urlauXKn+/ftLkrZv366ioiI9/fTTWrNmTZe/jgEA0NuMMZfJ+LtbZW78tSTJ3PGedOV0Gddc16uv66siBAC4IOw5Qu3t7SouLpYk3XXXXZ4QJEn5+fkaNWqUPv74Yx06dCjcl+rWpk2bJElf+9rXPCFIkmbNmqXp06erqqpKO3bs6LXXBwCgJ8YNN0vjJ3vum+t/LrP6eK++pq+KEADggrCD0CeffKKmpibl5ORozJgxXR6/+uqrJUk7d+4M96V8qq6u1rFjx5SSkqJp06Z1eXzWrFmSpF27dvXK6wMA4I/hcMpx131S3/TzB841y/WDb6rjh8vl+uXjcm36rcz3t8usOSHT5YrIa3YeBsfKcQDgLeyhcRUVFZLkMwRJ0tixY73OC9Qbb7yhEydOKDk5WSNGjNDMmTOVlZXV5bwjR45IkkaMGOFz7LO7XcG+PgAAkWQMHCLH0uVy/eKx8wdcLun4UZnHj0qSPGu6pfaRho2QMXyU1Kev5EySkpLO/999OylJcjrP3/fMNTIu3DYkR7v3ULg3n12j/hm9v0jDxdK3Tx9J0tnm5ii3BKGg/+zP3YdZQ7J1bcGtUW5NaMIOQrW1tZLU7cpwAwcO9DovUC+99JLX/bVr1+qOO+7QvHnzgnp99/FgXn/FihVdjqWkpGj16tWSpMGDBwd8rd7gDnxDhgyJajsQOvrQ3ug/+4taH375JjWerFbT79ZLba2+z2lpPr/v0OH9Yb2Us9Ny2T/4zxfDuh4A+PKly0br75ffG+1mhCTsIHTu3DlJUmpqqs/H3XOG3Of5k5eXp8mTJ2vs2LHKyspSVVWVtmzZos2bN+vnP/+5MjIyNHPmzC6vn5KS4vN67nYF+voAAPSmzK/9f8pYcpc6jh9V25EDaq846PmvI4LzhgzD0JCUJNW0MiQOAHwJOwj526At2A3c7rzzTq/7I0aM0Ne//nUNGzZMv/zlL7Vu3TqvIOQWyWVIi4qKeny8trY2qhvTuf+C2dN+S4ht9KG90X/2FxN9mJYhTZh6/r/POJrPSpV/k/npEamq8nzVqL39/NLb7e1SR7vMDvf9Nqnjs5Bjmpaxdeb5+5Ied2bqP3d/rOa2+AtDhuP8NOdIzanCxUX/2Z+7D8deMjxq30sNw1Bubm7Izw87CPX5bHxgS0uLz8fdx62ryYVi3rx5+u1vf6vjx4+rurpa2dnZXtft7dcHAKC3GX36SuMmyBg3ISLXu/6z/+JRTIRZhIz+s7946MOwV41zz5epq6vz+fjJkye9zguVw+FQTk6OJKm+vj7g13cfj/a8HgAAAACxI+wgNGrUKEnS4cOHfT7u3j/IfV44mpqaJHlXd0aPHi1JOnr0qM+lQd3tGjlyZNivDwAAACA+hB2EJkyYoL59+6qqqspnGCopKZEkn3v8BOPo0aOqrKxUamqqhg8f7jmenZ2t4cOHq7W1VWVlZV2et337dknnF2EAAAAAACkCQSgpKUk33HCDJOmFF17wWp1t06ZNqqio0IQJE3TppZd6jhcXF6uwsFDr16/3utb777/vqSBZVVRUqKioSKZpat68eV32C8rPz5ckrVu3TqdPn/YcLykp0c6dO5Wdna0ZM2aE+1YBAAAAxImwF0uQpJtvvll79uzRvn37dO+992rChAmqra1VeXm5MjMz9a1vfcvr/IaGBlVWVnrN9ZGk/fv3a8OGDRoyZIhycnKUlZWl6upqHT58WB0dHZo0aZJuvbXrhk3XXXeddu/erdLSUhUWFurKK69UY2Oj9u7dq+TkZN1zzz0+N1sFAAAAkJgikg5SUlL00EMPaePGjdq6dat27Nih9PR0zZkzR0uWLAl4oYKpU6eqrq5OBw8eVEVFhc6ePas+ffpowoQJmj17tq677jo5HF2LWA6HQytWrNDmzZu1ZcsW7dq1S2lpaZoxY4aWLFmiESNGROJtAgAAAIgThhnNDXFs6vjx4+wjhLDQh/ZG/9kffWh/9KG90X/2Fwt9GO4+QmHPEQIAAAAAuyEIAQAAAEg4BCEAAAAACYcgBAAAACDhEIQAAAAAJByCEAAAAICEQxACAAAAkHAIQgAAAAASDkEIAAAAQMIhCAEAAABIOAQhAAAAAAmHIAQAAAAg4RCEAAAAACScpGg3wI4Mw4h2EyTFTjsQOvrQ3ug/+6MP7Y8+tDf6z/6i2YfhvrZhmqYZobYAAAAAgC0wNA4AAABAwiEI2dD999+v+++/P9rNQBjoQ3uj/+yPPrQ/+tDe6D/7i4c+ZI6QDbW2tka7CQgTfWhv9J/90Yf2Rx/aG/1nf/HQh1SEAAAAACQcghAAAACAhEMQAgAAAJBwCEIAAAAAEg77CAEAAABIOFSEAAAAACQcghAAAACAhEMQAgAAAJBwCEIAAAAAEg5BCAAAAEDCIQgBAAAASDgEIQAAAAAJhyAEAAAAIOEkRbsB6N65c+dUWlqqAwcOqLy8XBUVFWpvb9ett96qRYsWhXzdXbt26Y033tCRI0ckSaNHj9bf/d3fKS8vLzINh5d9+/bp9ddf1/79+9Xe3q5LLrlECxYs0Ny5c4O6zrvvvqvnnnuu28evvfZaFRYWhtfYBNXa2qrf/e532rZtm2pra5WRkaEpU6ZoyZIlGjRoUFDXampq0quvvqrS0lKdOnVK/fv314wZM1RQUKD09PReegeIVB8uX75cNTU13T7+5JNPavjw4ZFoMj5z6NAhffjhh56fdfX19UpOTta6detCuh6fwYsvkn3IZ/Dia2lp0QcffKBdu3bp4MGDqqmpkcvl0tChQ3X11VcrPz9faWlpQV3TLp9DglAMO3HihH76059G9JqbN2/Wiy++KKfTqSuvvFJJSUn68MMP9R//8R+6/fbbtXDhwoi+XqIrLS1VUVGRTNPUxIkTlZmZqY8++kjPPfecKioqdNtttwV9zVGjRmn06NFdjl922WURaHHiaW1t1cMPP6x9+/ZpwIABmj59umpqavTuu++qrKxMjzzyiIYOHRrQtRobG/Xggw/q+PHjysnJ0YwZM3Ts2DG99dZb2r17tx599FFlZmb28jtKPJHsQ7c5c+b4PN63b99INBkWGzZs0M6dOyNyLT6D0RHJPnTjM3jxbN26Vb/4xS8kSSNGjNCUKVPU3Nys/fv365VXXtG2bdv0ox/9SP369Qvoenb6HBKEYlhaWprmzZunSy+9VOPGjVNJSYlef/31kK9XWVmpX//610pOTtZDDz2k8ePHe47/4Ac/0K9//WtdddVVys3NjdRbSGhnzpzRc889J5fLpe9+97u6+uqrJUmnTp3SD3/4Q/3f//t/lZeXp8mTJwd1XfdfVBAZGzdu1L59+zR+/Hg9+OCDnr96bdq0Sb/61a/0s5/9TCtXrgzoWmvXrtXx48c1c+ZM3XfffXI6nZKkF154QcXFxVq7dq2+/e1v99p7SVSR7EO35cuX90ZT4cP48eM1evRojRs3TuPGjdM3vvGNkK/FZzA6ItmHbnwGL56kpCTNnz9fN954o9fvgPX19Vq9erUOHz6sF198Uffee29A17PT55A5QjFs6NChuvvuu/WlL31JY8aMkcMRXndt3rxZHR0duv766z0hSJKGDRumm266SR0dHXrrrbfCbTY+88477+js2bOaPn26JwRJUv/+/fWP//iPks7/ooboaW9vV3FxsSTprrvu8ir95+fna9SoUfr444916NAhv9c6deqU3nvvPTmdTi1btszzjV+Sli5dqqysLG3dulWnTp2K+PtIZJHsQ0THokWLVFBQoLy8PPXv3z/k6/AZjJ5I9SGiY86cOVq2bFmXP4QPGDBAd911l6TzI1za29v9Xstun0OCUAIpKyuTJM2aNavLY9dcc42k8/OHEBnuf0tf/97Tpk1TcnKy9uzZo9bW1ovdNHzmk08+UVNTk3JycjRmzJguj7sDbCBDPnbv3i3TNDVp0qQuvwgkJycrLy9PLpdL77//fiSajs9Esg9hb3wGgcgbNWqUJKmtrU2NjY1+z7fb55ChcQmiqalJtbW1kuRzfsmgQYOUmZmpmpoanT17ljG4EfC3v/1NkjR27NgujyUlJWnkyJE6ePCgKisrffZJdw4dOqRf//rXam5uVv/+/TV58mRNmjQpUs1OKBUVFZLk8xdo6ULfuc8L51pjxozRli1bPIuUIDIi2YdWb7zxhk6cOKHk5GSNGDFCM2fOVFZWVniNRa/iMxhf+AzGhqqqKkmS0+lURkaG3/Pt9jkkCCUIdwhKT0/vduWPQYMGqbGxUbW1tRo5cuTFbF7cOXv2rJqamiRJAwcO9HnOwIEDdfDgQdXW1gYVhMrKyjzVPen8JNVJkyapsLCQIQlBcn8uultVzN137vMCuVZ3/e1+jUCuhcBFsg+tXnrpJa/7a9eu1R133KF58+aF0EpcDHwG4wufwdiwefNmSdLUqVOVnJzs93y7fQ4JQgni3LlzkqTU1NRuz3E/5j4XobP+G3b3bx7sv3f//v21ePFizZgxQ9nZ2WptbdWBAwe0bt067d27V6tXr9aPf/zjsOeSJRJ/nwv3Hw0C6SN/13Ifb2lpCbqd6F4k+1CSZwGTsWPHKisrS1VVVdqyZYs2b96sn//858rIyNDMmTMj03hEFJ/B+MBnMHaUlZVpy5YtcjqdWrJkSUDPsdvnkCDUi5544gkdPXo0qOd8+9vf1qWXXhrxtpimKUkyDCPi145XsdR/0vm/xkydOtVzv2/fvpo+fbomT56sf/mXf9GhQ4f0P//zP5o9e3avvH48cn8uQn3c17l8xi6uSPahJN15551e90eMGKGvf/3rGjZsmH75y19q3bp1/BIWo/gMxgc+g7Hh2LFjeuaZZ2SappYuXRrwyBW7fQ4JQr2opqZGlZWVQT2ntxJynz59JPX8V1H3awe7aVa8Cqf/rP+GLS0tPudcRerfOy0tTV/+8pf1wgsv6P333ycIBcH9uejucxdMH/n7jLmv1VNVFsGLZB/2ZN68efrtb3+r48ePq7q6WtnZ2WFdD5HHZzC+8Rm8eOrq6vTjH/9YTU1Nys/PD2qPSbt9DglCvWj16tXRboLH4MGDJZ1fNOHcuXM+fymoq6vzOjfRhdN/ffv2Vd++fXX27FmdPHnSZxA6efKkpMj8e7uXvIyV5Sjtwv1v7/7a7yyYPnKf435OZ3y+ekck+7AnDodDOTk5On36tOrr6/klLAbxGYxvfAYvjoaGBj3yyCOqra3V3LlztXTp0qCeb7fPIZMJEkR6errni87XSh11dXVqbGzU4MGDWTEuQtxLTvrav6S9vV1/+9vflJycrGHDhoX9Wu6FGajmBcfdR4cPH/b5uLvv3OeFcy338UCuhcBFsg/94XMW2/gMxj8+g72rublZq1at0qeffqqZM2fq7rvvDnqIm90+hwShBDJt2jRJ0vbt27s89pe//MXrHISvp3/vsrIytbW1afLkyUpJSQn7tdyv4WupbnRvwoQJ6tu3r6qqqnx+0y4pKZEU2Odi6tSpMgxDH3/8sU6fPu31WFtbm3bt2iXDMHTVVVdFpvGQFNk+7MnRo0dVWVmp1NRUDR8+PKxroXfwGYxvfAZ7V1tbmx577DEdPHhQU6ZMUWFhYUiLL9ntc0gQikOFhYUqLCzsUpZcuHChHA6H/vjHP2r//v2e48ePH9fGjRvlcDiCGgeKnn3xi19Unz59tHPnTs8vY5J0+vRpz7Kg+fn5XZ7XXf9t3ry5y5jb9vZ2vfrqq9q+fbtSUlI0d+7cyL+ROJaUlKQbbrhBkvTCCy94/ftu2rRJFRUVmjBhgtcCGMXFxSosLNT69eu9rjVgwAB97nOfU3t7u55//nl1dHR4HnvppZfU0NCg2bNns8R5hEWyD99//32fFdyKigoVFRXJNE3NmzdPSUmMKo8mPoP2x2cwtrhcLj311FP661//qokTJ+p73/ue33/jePkc8pUU4x5//HHPvA/3uMo//OEP2rFjh6TzSyp///vf93qOe4J/e3u71/Fhw4bpH//xH/WrX/1KDz30kP7X//pfcjqd+vDDD9Xa2upZlQWRkZGRoW9+85t68sknVVRUpEmTJikzM1N79uxRU1OTvvzlL+vKK6/s8rzu+u/FF1/U+vXrdckll2jw4MFqa2vTkSNHVF9fr+TkZN1zzz3drtuP7t18883as2eP9u3bp3vvvVcTJkxQbW2tysvLlZmZqW9961te5zc0NKiyslL19fVdrnX77bervLxcJSUlKiws1Lhx43T06FEdPXpUOTk5uu222y7W20ookerD/fv3a8OGDRoyZIhycnKUlZWl6upqHT58WB0dHZo0aZJuvfXWi/nWEkJZWZlee+01r2Pt7e164IEHPPdvueUWT1WPz2DsiVQf8hmMjuLiYpWWlkqSMjMz9fzzz/s8b+nSpZ5NbePlc0gQinFHjhxRTU2N17G6ujpPKBoyZEhQ18vPz9fQoUP15ptv6uOPP5Z0fjjV3/3d32n69OmRaTQ8Zs2apZUrV+r1119XeXm52tvbNXz4cC1YsEDXXXddUNf6yle+ov379+vTTz/VsWPHZJqmBg0apC996UvKz88nxIYoJSVFDz30kDZu3KitW7dqx44dSk9P15w5c7RkyZKgJnRmZWVp1apVeuWVV7Rjxw6VlpaqX79+uuGGG1RQUBDQrtwIXqT6cOrUqaqrq9PBgwdVUVGhs2fPqk+fPpowYYJmz56t6667jn26ekFDQ4PKy8u9jpmm6XWsoaEhoGvxGYyOSPUhn8HoOHPmjOe2OxD5snjxYk8Q6omdPoeGGewmCwAAAABgc8RqAAAAAAmHIAQAAAAg4RCEAAAAACQcghAAAACAhEMQAgAAAJBwCEIAAAAAEg5BCAAAAEDCIQgBAAAASDgEIQAAAAAJhyAEAAAAIOEQhAAAAAAkHIIQAAAAgIRDEAIAAACQcAhCAAAAABIOQQgAAABAwiEIAQAAAEg4BCEAAAAACef/ByVdk6dbx8oDAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Finite Difference Method\n", "t_target = 0.5\n", "cfl = 0.9\n", "\n", "# Make grid\n", "nx = 75\n", "x = np.linspace(-1, 2, nx+1)\n", "dx = np.diff(x)[0]\n", "\n", "# Solution array\n", "u = np.empty(nx+3)\n", "du = np.zeros_like(u)\n", "\n", "# Upwind scheme\n", "def upwind(nx, u, du, dt, dx):\n", " for i in range(1, nx+2):\n", " du[i] = -u[i] * (u[i] - u[i-1])*dt/dx\n", "\n", "# Transparent BC\n", "def bc_transparent(u):\n", " u[0] = u[1]\n", " u[-1] = u[-2]\n", "\n", "# Initialize\n", "u[1:-1] = -np.tanh(1e8*x) + 1.5\n", "bc_transparent(u)\n", "\n", "# Calculation\n", "t = 0\n", "while abs(t - t_target) > 1e-8: \n", " # Adjust time step to reach target time\n", " dt = cfl*dx / abs(u[1:-1]).max()\n", " dt = min(dt, t_target - t)\n", " \n", " # Periodic BC\n", " bc_transparent(u)\n", " \n", " # Non-conservative Upwind\n", " upwind(nx, u, du, dt, dx)\n", " \n", " # Update\n", " u += du\n", " t += dt\n", "\n", "# Plot solution\n", "plt.plot(x, u[1:-1])\n", "\n", "# Plot exact\n", "s = 0.5*(u[0] + u[-1])\n", "plt.plot(x, -np.tanh(1e8*(x - s*t)) + 1.5, color='k')\n", "\n", "plt.legend(['FDM', 'Exact'])" ] }, { "cell_type": "code", "execution_count": 6, "id": "92aa0f53", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Finite Volume Method\n", "t_target = 0.5\n", "cfl = 0.9\n", "\n", "# Make grid\n", "nx = 75\n", "x = np.linspace(-1, 2, nx+1)\n", "dx = np.diff(x)[0]\n", "xc = x[:-1] + 0.5*dx \n", "\n", "# Solution and flux array\n", "u = np.empty(nx+2)\n", "f = np.empty(nx+1)\n", "\n", "# Upwind flux\n", "eps = 1e-10\n", "\n", "def upwind(nx, u, f):\n", " for j in range(nx+1):\n", " ul, ur = u[j], u[j+1]\n", " \n", " fl = 0.5*ul**2\n", " fr = 0.5*ur**2\n", " \n", " s = (fr - fl + eps) / (ur - ul + eps)\n", " \n", " f[j] = (fl + fr)/2 - abs(s)/2*(ur - ul)\n", "\n", "# Initialize\n", "u[1:-1] = -np.tanh(1e8*xc) + 1.5\n", "\n", "# Calculation\n", "t = 0\n", "while abs(t - t_target) > 1e-8: \n", " # Adjust time step to reach target time\n", " dt = cfl*dx / abs(u[1:-1]).max()\n", " dt = min(dt, t_target - t)\n", " \n", " # Periodic BC\n", " bc_transparent(u)\n", " \n", " # Compute Flux\n", " upwind(nx, u, f)\n", " \n", " # Update solution and time\n", " u[1:-1] -= dt/dx * (f[1:] - f[:-1])\n", " t += dt\n", "\n", "# Plot solution\n", "plt.plot(xc, u[1:-1])\n", "\n", "# Plot exact\n", "s = 0.5*(u[0] + u[-1])\n", "plt.plot(x, -np.tanh(1e8*(x - s*t)) + 1.5, color='k')\n", "\n", "plt.legend(['FVM', 'Exact'])" ] }, { "cell_type": "markdown", "id": "a8edb923", "metadata": {}, "source": [ "## 예제\n", "Burgers 방정식을 생각하자.\n", "\n", "$$\n", "\\frac{\\partial u}{\\partial t} + \\frac{\\partial }{\\partial x} \\left ( \\frac{u^2}{2} \\right )= 0.\n", "$$\n", "\n", "계산 영역은 $[-1,1]$ 이다. 아래 유동을 유한체적법으로 계산하시오. Flux 기법은 Upwind를 사용하시오.\n", "\n", "1) 아래 초기 조건에 대해서 Tranparent 경계 조건이고 $t=0.5$ 일 때 계산하시오. Rankine-Hugoniot 조건을 이용해서 충격파의 Wave speed를 예측하는지 확인하시오.\n", "\n", " $$\n", " u(x,0) = \\left \\{\n", " \\begin{array}{cc} \n", " 1.5 & x \\le 0 \\\\\n", " 0.5 & else \n", " \\end{array}\n", " \\right.\n", " $$\n", "\n", "2) 아래 초기 조건에 대해서 Tranparent 경계 조건이고 $t=0.5$ 일 때 계산하시오. Entropy 조건을 만족하는지 확인하시오.\n", "\n", " $$\n", " u(x,0) = \\left \\{\n", " \\begin{array}{cc} \n", " 0.5 & x \\le 0 \\\\\n", " 1.5 & else \n", " \\end{array}\n", " \\right.\n", " $$\n", "\n", "3) 초기 조건이 $u(x,0) = 1 + 0.5 \\sin(\\pi x)$ Periodic 경계조건 인 경우 $t=0.5, 1.0, 1.5$ 일 때 계산하시오. $x-t$ 그래프를 그려보고 수치해와 이론해를 비교 분석하시오.\n", "\n", "\n", "다음과 같이 조건을 변경하면서 계산하시오.\n", "\n", "- CFL 수를 바꿔가면서 계산하시오.\n", "\n", "- 격자 개수 ($nx=50, 100, 200, 400$)를 다르게 하면서 변화를 확인하시오." ] } ], "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 }