{ "cells": [ { "cell_type": "markdown", "id": "ccaceccf", "metadata": {}, "source": [ "# 수치해석 실습 101\n", "**강좌**: *수치해석*" ] }, { "cell_type": "markdown", "id": "1ba3bb3f", "metadata": {}, "source": [ "## 낙하산병 문제\n", "\n", "낙하산을 맨 병사는 중력과 공기에 의한 항력을 받는다.\n", "\n", ":::{figure-md} parachute\n", "\"parachute-fig\"\n", "\n", "낙하산병 (From pxhere.com)\n", ":::\n", "\n", "이 때 사람에 작용하는 힘은 다음과 같다.\n", "\n", "$$\n", "F = F_D + F_U\n", "$$\n", "\n", "여기서 $F_D$ 중력에 의해 아래 방향으로 작용하는 힘이고 $F_U$ 는 공기 저항에 의해 위로 작용하는 힘이다. 각각은 다음과 같이 표현할 수 있다.\n", "\n", "$$\n", "\\begin{align}\n", "F_D &= mg, \\\\\n", "F_U &= -c v.\n", "\\end{align}\n", "$$\n", "\n", "여기서 $m$ 은 질량, $g$ 는 중력 가속도이다. $c$는 항력 계수이고, $v$ 는 속도이다.\n", "\n", "뉴턴의 제2법칙을 적용하면 지배방정식 (Governing Equation)은 다음과 같다.\n", "\n", "$$\n", "\\begin{align}\n", "F &= ma = m \\frac{dv}{dt} \\\\\n", "\\frac{dv}{dt} &= \\frac{mg - cv}{m} = g - \\frac{c}{m} v\n", "\\end{align}\n", "$$" ] }, { "cell_type": "markdown", "id": "d72d290b", "metadata": {}, "source": [ "## 엄밀해 결과 가시화\n", "\n", "낙하산병이 처음에 정지하고 있었다면 ($t=0$ 일 때 $v=0$), 이 미분방정식의 엄밀해 (Exact Solution) 은 다음과 같다.\n", "\n", "$$\n", "v(t) = \\frac{gm}{c} (1 - e^{-(c/m)t})\n", "$$\n", "\n", "낙하산 병의 몸무게 $m=68.1 kg$, 항력계수 $c=12.5 kg/s$로 생각하자. 중력 가속도는 $9.81 kg/s$으로 가정하자.\n", "\n", "파이썬에서는 `matplotlib` 패키지로 그래프를 그린다. 아래와 같이 불러온다.\n", "\n", "- Jupyter 노트북 내 실행을 위한 매직 커맨드 \n", " - `%matplotlib inline` 또는 `%matplotlib notebook`\n", "- `pyplot` 모듈 불러오기\n", " - Matlab과 비슷하게 그래프를 그릴 수 있는 interface\n", "- 그래프 스타일 로드\n", " - 참고 : https://matplotlib.org/stable/gallery/style_sheets/style_sheets_reference.html\n", "- 그림 DPI 조절" ] }, { "cell_type": "code", "execution_count": 1, "id": "301a799b", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "from matplotlib import pyplot as plt\n", "\n", "plt.style.use('ggplot')\n", "plt.rcParams['figure.dpi'] = 150" ] }, { "cell_type": "markdown", "id": "7df04e16", "metadata": {}, "source": [ "엄밀해를 계산하는 함수를 만들어보자." ] }, { "cell_type": "code", "execution_count": 2, "id": "d1c78377", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# 주요 상수\n", "m = 68.1\n", "c = 12.5\n", "g = 9.81\n", "\n", "# 엄밀해 계산 함수\n", "def exact(t):\n", " return g*m/c*(1-np.exp(-(c/m)*t))" ] }, { "cell_type": "code", "execution_count": 3, "id": "3e767a80", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "44.91892648723751" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "exact(10)" ] }, { "cell_type": "markdown", "id": "b8822b04", "metadata": {}, "source": [ "시간에 따른 엄밀해를 30초 까지 연속적으로 계산해보자. \n", "`np.linspace` 를 이용하면 등간격으로 시간을 구할 수 있다." ] }, { "cell_type": "code", "execution_count": 4, "id": "d1ba4f77", "metadata": {}, "outputs": [], "source": [ "# 0~30 까지를 100 등분 함\n", "t = np.linspace(0, 30, 101)" ] }, { "cell_type": "markdown", "id": "8a54362b", "metadata": {}, "source": [ "For Loop를 이용하면 연속적인 계산이 가능하다." ] }, { "cell_type": "code", "execution_count": 5, "id": "8394c98d", "metadata": {}, "outputs": [], "source": [ "v = []\n", "\n", "for ti in t:\n", " v.append(exact(ti))" ] }, { "cell_type": "markdown", "id": "d6150944", "metadata": {}, "source": [ "Pythoniac 코딩으로 List Comprehension을 사용하면 좀 더 빠르게 계산할 수 있다." ] }, { "cell_type": "code", "execution_count": 6, "id": "cc4b9317", "metadata": {}, "outputs": [], "source": [ "v = [exact(ti) for ti in t]" ] }, { "cell_type": "markdown", "id": "e493d847", "metadata": {}, "source": [ "`numpy` 는 벡터 연산이 가능하므로 다음과 같이 빠르게 계산할 수 있다." ] }, { "cell_type": "code", "execution_count": 7, "id": "1b836bb4", "metadata": {}, "outputs": [], "source": [ "v = exact(t)" ] }, { "cell_type": "markdown", "id": "7df0fd5b", "metadata": {}, "source": [ "`plt.plot` 을 이용해서 그래프를 그리자" ] }, { "cell_type": "code", "execution_count": 8, "id": "138e4a14", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t, v)" ] }, { "cell_type": "markdown", "id": "5a1a739d", "metadata": {}, "source": [ ":::{note}\n", "엔지니어는 그래프의 축과 선의 의미를 꼭 표기해야 한다. (무조건 오답 처리)\n", "::: " ] }, { "cell_type": "code", "execution_count": 9, "id": "3e3b1428", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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z7oCUlSmVMaKhVjidUmSMO/hERUuRUbIi3Y/6waMVGXW+HeUORJHng1EFww5QFxGeUOc8++yz2rhxo6666irdfLN7lcIXXnhBEyZM0IMPPqg+ffp4rmC0a9dODodDy5cv9wobubm5evjhhz3h6kK9e/fW4MGDtWLFCj300EN6+umnvQLUnj17VFRUpI4dO0oqCTa7du2q1M+RmpqqJ554Qvfcc49GjBghh8Ph2ZaTk6PHHntMp0+fVnx8vPr27StJioqK0pQpU/TWW2/pD3/4g15//XXPUMVdu3bp+eeflyTdcccdl3x/p9OpPn36aNWqVXrrrbd01113SZIKCgo0ffr0cq9uJSQkaM+ePdq1a5c6depUoZ918ODB6tKli7Zu3apnnnlGv/vd7zz/MM+fP1/z5s1TdHS0Jk+eXKHjAUB1GVeRO/CcPS1lnJY5e1rKOOP5Yy54rqxztRuGIqPcI1KioqXoWCkqRlZ0jLuv+DEqWlbxPsWPkVGyQsNqr06gDiI8ISA88MAD5W5r0aKFHnzwQUnuVdtefPFFNWnSRM8884xnn969e+uBBx7Q//7v/2ratGl65513ZFmWGjdurB//+Md69913NXr0aA0ZMkQRERFavXq1ioqKNHnyZM2YMaPUe/7zn//U5MmTNXv2bC1evFgDBgzw3CQ3NTVVzz77rCc8DR8+XBEREXr11Ve1fft2NW3aVJZl6Z577vHsUxZjjJYuXaqlS5eqYcOG6tGjhxo0aKBTp05p06ZNOnPmjCIiIvT8888rPDzc87pHHnlE69ev1zfffKNBgwZp4MCBys7O1ooVK5Sbm6s777xTV155ZYX/u99yyy3685//rM8++0zx8fFKSUlRTk6ObrzxRn300UelXjN69Gh99913uummmzR48GBFRUWpYcOG+v3vf1/u+1iWpRdeeEE33nijXnjhBc2fP19du3bVoUOHtGbNGoWGhurZZ59l2B6AajOFhe7Ac/aUdPaUzJlT0plT0tnT7udnT50PRWdrfoGEkFApJk6KifU8WtFx7ufRMefbse6AFB3r3i8y2jMcH0Dt49OHgFDWl/RiSUlJevDBB3Xu3Dn96le/UlFRkZ599lk1atTIa7/i+yUtXrxYb775pv7f//t/kqS//vWv6tChgz744AMtX75csbGxuvzyy/W73/1OH374YZnv2axZM82dO1evvvqq5syZo6VLlyo0NFTNmzfXXXfdpaFDh3r2TUhI0BtvvKG///3vWr16tWcO0cSJEy8anjp37qwPP/xQS5Ys0erVq7V9+3alp6fL6XSqVatWmjRpku666y61bt3a63UxMTGaNWuWXnnlFX322Wf6+uuvFRYWph49euj222/XhAkTLvrf+kLDhg3Tm2++qb///e/asmWLIiMjdfnll+sPf/hDmaFSku68806dPXvWc2+mgoICtWzZ8qLhSXLfb+vLL7/U888/r8WLF2vOnDmKjY3V1VdfrXvvvVe9e/eucN0AgpPJy5NOp0un02VOn3Q/P3NK5sxJpZ87K9epE3KdOVVzV4nCnFJcfXf4iasvK7aeFBsnxdaTYurJiolzt2PO90VEMvwNCDCWKWsZMfjUkSNHylyt7ULGGJ08eVKNGjXy+V+ktq22B5/hHNasmvz8FWtyfqLzCSY6ByTOn/1MUZH7qtCpEzInT0in3H/MqXTpVLp0Jt292IKvOcOleg2keg3dgSiuvjsgXfg8tp77MTyCMFSD+BwGPrvPoWVZ5d7ipKK48gQAAGxnCgvdV4rSj8mcPC6dPCGdvOD56XTfLrcdFe0ORPUbyjr/WBySrHoNzj9v4F49DgDOIzwBAIAaZ4xxr0B34qhM+jEp/VjJ8xNHpdMnfTPHyHK4g1CDRlKDRrLqux/jWrVVSKMmOmOFSPUaybpgrigAVBThCQAA+IRxudyLL5w4InP8SMnj8SPS8aPum7xWV2w9qWETqWFjWY3ipQaNZTVsLDU4/6deA1k/uN2BJEWeHy5kMeQLQDUQngAAQKWYcxnSsUMyxw67H48flo4dlo4flvLzq3fw+g2lRvGyGjWVGseffx4vNWoiNWjCFSMAtiI8AQCAUkxRkXto3dGDMkcPnX88KB09WL2FGSKjpSZNpcYJspo0lRo3ldU4QWrcVGrURFaY03c/BAD4GOEJAIAgZgoL3MPqjhyQOXzg/ON+6dghqaorfMbVl+KbyWrSTIpPkJo0kxXfTGqS4F6uGwACFOEJAIAgYFwu6eRx6dA+mUP7Sh6PHZKKiip/wKhoqWkLWU2bS02bu5/HN5eaNpMVEeX7HwAA/ADhCQCAOsbkZEsH98oc3CMd2CNzcK90+EDlF2ywLPdwuoSWshJaSAktZCW0lBJaSrH1uKcRgKBDePITlmXJsiy5XC6FlLFKEICaU1RU5PkMAoHEGONe4nv/Lpn9u2UO7JEO7nHPVaoMh0OKby41byWrWSupWStZzVtLTZvLcrJAAwAUIzz5EafTqdzcXEVHR9tdChBU8vLy5HQySR3+zRjjDkX7dsrs3yWzb7d0YLf73kmV0bip1KKNrBZtpOat3Y8JLWSFhtVM4QBQhxCe/EhkZKTOnnX/IxgeHu6zK1DGGK9HBB7OYc0oKipSXl6ecnNzVa9ePbvLATw8V5T27pDZt1Nm7w5p704pO7PiB4mMklq0ldWqrdSynTsktWjNfCQAqAbCkx8JDQ1VvXr1lJOTo7Nnz/rsi7LD4ZAkuVw+uHM7bME5rBmWZcnpdKpevXoKDeWvQ9jH5GS7g9Lu7TJ70qQ9aVLGmYofoGETqXV7Wa3ay2rVTmrZ1r0EOENRAcCn6sy3henTpys1NbXc7b///e/Vq1evUv1Lly7V/PnzdfDgQYWGhioxMVETJ05Up06darDa8oWGhio2NlaS764yNDl/V/UT3FU9YHEOawZfLGEH43JJRw7K7NoqFYelIwekiv6dH99MVpuO7rDUur3UqoOsWJb/BoDaUGfCU7Hk5GRFRESU6m/YsGGpvrfffltz5syR0+lUjx49VFBQoJSUFG3atEnTpk3TgAEDaqPkcvnqi13xcfiiGLg4h0DgMnm57qtKO7fK7Nwq7d4mZWdV7MWN4qW2HWW1uUxW245Smw6yomJqtmAAQLnqXHi67bbbFB8ff8n9tmzZojlz5ig2NlaPP/64mjVrJklKS0vT9OnT9dJLLykpKUkxMfwjBQCoOJOZIe1MlUn7XmZHqntRh4rcRykqWmqbKKt9J1ntE6U2HWXF1a/xegEAFVfnwlNFff7555KkiRMneoKTJCUmJmr06NGaN2+eFi9erGuvvdauEgEAAcCcOSWTtkXakSqz43vp0L5Lv8hyuFe869BJat9JVrtO7mXBz89vBAD4p6AMT/n5+dqyZYskaeDAgaW2Dxw4UPPmzdO6desITwAAL+bcWWn7Zpntm2W2pUhHD136RRGR7pDUoYusjp2ldp1kRbLqHQAEmjoXnhYtWqTMzExZlqVmzZppwIABaty4sdc+hw8fVkFBgeLi4tSoUaNSx2jXrp0kad++Cvz2EABQp5ncbOWuXqb8lLUq2rCqYleW4urLuqyrlNhVVsckqWUbWQ5ugA4Aga7OhafZs2d7td955x1NmjRJN9xwg6cvPT1dksoMTpIUERGh6OhoZWVlKScnR5GRkRd9z2nTppXqczqdeuqppySpVHirbcVLMBev2IbAwzkMfJzDwGGKClWwY6vyN61W3sY1KkjbojOXmLPkaJIgZ9decnbtLWdSL4U0b8UCL36Gz2Dg4xwGvrpwDutMeOrSpYtGjhypTp06qUGDBkpPT9fKlSs1e/ZszZgxQ1FRURo7dqwkKTc3V5I74JQnPDxcWVlZys3NvWR4AgAEtqITx5S3/jvlbVip/JR1Mpe4Ga2jQWM5u/eRs3tfObv3VUjT5oQlAAgCdSY83XTTTV7t5s2ba+LEierQoYOeeOIJzZgxQ1deeaWcTqfn/kkX+4euMvdYeu655y66PT093Wf3bKoK7hEU+DiHgY9z6F9MQYF7Rbwt62Q2r3PfZ+kirJhYObv3U377TrI695CatlCBZalAUpYknR/RAP/FZzDwcQ4Dn93nsHhaT3XUmfBUnp49e6pDhw7atWuX0tLS1K1bN8+VpLy8vHJfl5+fL0ll3jMKABB4zNnTMilrZFLWSFs3SXm55e8cEip17CKrS09ZSb3VpG+yrJAQvrQBQJCr8+FJkhISErRr1y6dOXNGUskcpJMnT5a5f25urrKyshQdHc2QPQAIUMYY6cAemZTVMpvWSHt3XPwF8c1lde8rq2sf90IP4SW/PLNCWOwBABAk4Skry30n9+KrSM2bN1dYWJgyMjJ08uTJUgtH7NmzR5LUunXr2i0UAFAtprBQ2vG9zIbvZDatlk5dZDid0yl16iGrWx9Z3frKiq/eUA4AQN1X58NTRkaGtm7dKqlkCXKn06lu3bppw4YNWrlypcaNG+f1mpUrV0qS+vbtW7vFAgAqzeTnSakbZdZ/5x6Sl3Wu/J0bNpHVs7+sHv2lxG6ynOG1VygAIODVifCUlpam/Px8de3a1WsRiOPHj+uFF15QXl6e+vXr53WFady4cdqwYYNmz56tPn36eCaPpaWlacGCBYqMjNTIkSNr/WcBAFyayc2R2bxWZt1yacv6i89fapcoq+cAWT37Sy3asioeAKDK6kR4Onz4sF566SU1aNBAzZo1U/369XXy5Ent3r1bBQUFatWqlX72s595vaZHjx4aO3as5s6dq4ceekjdu3dXUVGRUlJS5HK5dN999ykmJsamnwgA8EMmL1favFauNd9KW9ZK5xf2KSU0VOrSS1bvgbJ69JdVr0HtFgoAqLPqRHjq2LGjxowZox07dujgwYPavn27wsPD1bZtWw0aNEhjxowp855OU6dOVdu2bTV//nxt3rxZISEh6tatmyZNmqTOnTvb8JMAAC5k8vOkzetk1n7rHpKXX84qqeGRsrr3lfoMcs9fioyq3UIBAEGhToSnli1b6q677qrSa0eMGKERI0b4tiAAQJUZV5G0LUVm5VKZDd9JuTll7xgVLavXQFl9BktJPWWFlX/jcwAAfKFOhCcAQGAzxkj7dsqsWiqzZpl09nTZO0ZGy+qVLKv/UKlLT1mhYbVbKAAgqBGeAAC2MafSZVYulvlukXT0UNk7hUfK6jVAVv/LpaTessIITAAAexCeAAC1yuTnyWxYKbNikbR1o2RM6Z1CQqRufWUlD5fVY4CscJYUBwDYj/AEAKhxxhhpT5rM8oXuYXk5WWXv2DHJHZj6DZEVE1e7RQIAcAmEJwBAjTFZmTIrl8gs+1I6tK/snZokyBo8UtbAK2Q1blq7BQIAUAmEJwCATxljpB2pMsu+ct/EtqCM+zGFR7ivLg2+UrosiRvXAgACAuEJAOATJitT5ruFMku/lI4eLHunxG6yhlwpq88gWRGRtVsgAADVRHgCAFSLObBHZvEcmVVLy76JbUycrCGjZA0dIyuhRe0XCACAjxCeAACVZgoLZNZ/J7N4rrQzteyduvSUY9hVUq9k7scEAKgTCE8AgAozGWdklsyT+WZ+2TeyjYmVNWS0rGFXyYpvVvsFAgBQgwhPAIBLMof2yyz4VGblEqmwoPQObTrKGjlOVv/LZYU5a70+AABqA+EJAFAmY4z0/Qa5vv5USt1QeofQMFn9h8q6Ypysdom1XyAAALWM8AQA8GIKC2RWfSPz5WzpyIHSO9RrIGvEWFnDr5YVW6/W6wMAwC6EJwCAJMnk5sh8+5XMV59Kp9NL79CynazR18nqP0xWGAtAAACCD+EJAIKcOZchs+gLmUVfSNmZpXfo0V+OK6+TOvfgZrYAgKBGeAKAIGVOn5T5crbMsi+l/HzvjSGhsgZdIWvMj2Q1a2lPgQAA+BnCEwAEGXPqhMy8WTLffiUVFnpvDI+UNfwqWVdeL6tBI3sKBADATxGeACBImJPHZebOlFm+QCr6QWiKrSdr1LWyRoyVFR1jS30AAPg7whMA1HHmxFGZeTNlViyUioq8N9ZvJOvqSbKGjpYVHm5PgQAABAjCEwDUUebMSZk5M2SWfVU6NDVsLOuaG2QNGc3KeQAAVBDhCQDqGHMuQ2b+LJnFc6SCHywE0She1tgbZA0aRWgCAKCSCE8AUEeYnGyZrz+V+foTKTfHe2OjeFnjJrtX0AslNAEAUBWEJwAIcKagQGbJXJm5M6TMc94b4+rLGn+TrKFjuNIEAEA1EZ4AIEAZY2TWfisz+z9S+jHvjVEx7oUgRo6TFR5hT4EAANQxhCcACEAm7Xu5Zr4p7Unz3hAeIWv09e4/USw5DgCALxGeACCAmKOH5Jr1trRxpfeGkBBZw66SNX6KrLj6ttQGAEBdR3gCgABgsjNlPntfZsnc0suO9x4ox8TbZSW0sKc4AACCBOEJAPyYcRXJfPu1zMf/lTIzvDe2S5Tjxv8n67Ike4oDACDIEJ4AwE+Znalyvf9/0v7d3hsaN5U18XZZ/YbIsix7igMAIAgRngDAz5hT6TKz3pZZvdR7Q3iErLE3uheDCHPaUxwAAEGM8AQAfsIUFsos/Ezm8w+kvFyvbdbAEe6rTQ0a2VQdAAAgPAGAHzA7U+X677+lQ/u8N7TpKMeUn8rq2MWewgAAgAfhCQBsZDIz3EP0vv3ae0NMnKyJP5E1ZJQsR4g9xQEAAC+EJwCwgTFGZsUimZlvSJnnvLZZw65yB6foWJuqAwAAZSE8AUAtM0cPyfXOv6S07703tGwrxy0/Z4geAAB+ivAEALXEFBXKNW+WzGfvSYUFJRvCI2Rdd7OsUdfKCmGIHgAA/orwBAC1oGDPDp3915Myu7Z5b+g1UI4f/1RWwyb2FAYAACqM8AQANcgUFMjM+VAn58+SiopKNtRrIMfN98jqM8i+4gAAQKUQngCghpjd2+V665/SkQNe/daQUbJuvFNWdIxNlQEAgKogPAGAj5nCApnPP5SZN1MyLk+/o0mCdMvPZXXtbWN1AACgqghPAOBD5tA+uV5/Tjqwp6TTshQ19gbF3HqPTmZm2VccAACoFsITAPiAcRXJLPhM5uN3pMLCkg1NEuS44wHFDR7ubhOeAAAIWIQnAKgmk35Mrjf/Ueq+Tdbwq2XdcIesiEh7CgMAAD5FeAKAKjLGyKxYJPP+/0l5OSUb6jWU4/b7ZHXva19xAADA5whPAFAFJidb5r8vyaz+xqvf6jdU1i33yIqJs6kyAABQUwhPAFBJZvd2uV79Xyn9WElnVLSsW34ux4Bh9hUGAABqFOEJACrIuFwyX34s8+l/vW94m9hVjjunyWrYxL7iAABAjSM8AUAFmDOn5Hrj79LWTSWdlkPWdVNkjb1RliPEvuIAAECtIDwBwCWY7zfI9dqzUmZGSWfDxnLc9VtZlyXZVxgAAKhVhCcAKIdxFcl88aHMFx9KxpRs6DNYjp/cKys6xr7iAABArSM8AUAZzLkM99Wm1A0lnWFOWVPuknX5VbIsy77iAACALQhPAPADZvd2uV75m3QqvaQzvpkcP39YVst29hUGAABsRXgCgPOMMTKL5sh89IZUVFiyoc8gOW7/layoaPuKAwAAtiM8AYAkk5cr8/YLMmuWlXQ6HLImTZU1+nqG6QEAAMITAJgTR+V66Unp4N6SznoN5fjZQ6ymBwAAPAhPAIKa2Zbint+Uea6ks1N3Oe7+ray4BvYVBgAA/A7hCUBQMsbILJ4j8+Frksvl6bfGTJA18XZZIdz0FgAAeCM8AQg6pqBA5r2XZb79uqQzNEzW7ffKMfAK+woDAAB+jfAEIKiYM6fkevkpade2ks76jeT4xe9ltbvMvsIAAIDfIzwBCBrmwB65XviLdPqC+zd16CzHzx+RVY/5TQAA4OIITwCCgtm8Vq5XnpHycjx91tDRsm6+R1ZYmI2VAQCAQEF4AlDnuRbPkXn/VcmcXxjCcsi66S5ZI8dx/yYAAFBhhCcAdZZxFcnMeENm4eclneGR7vs3de9rX2EAACAgEZ4A1EkmN0eu156VNq0u6WzQWI77HpXVqp19hQEAgIBFeAJQ55gzJ+V64XFp/66SztYd5Ljvj7LqN7KvMAAAENAITwDqFHPkoFz/+LN06kRJZ88Bcvz0t7LCI+wrDAAABDzCE4A6w+zeLtcL/yNlnvP0WVdeL+vGqbIcITZWBgAA6gLCE4A6wWxe5775bX6eu8OyZN10lxyjrrW3MAAAUGcQngAEPNd3i2Xe/qdUVOTuCAmVdec0OfoPtbcwAABQpxCeAAQ011cfy3z0ZklHeKQcv/y9rC497SsKAADUSYQnAAHJuFwys96W+erjks7YenLcP11Wmw72FQYAAOoswhOAgGNcRTL/+ZfM8oUlnU0S5Hhguqz45vYVBgAA6jTCE4CAYgoLZd74u8yaZSWdrdq5rzjVa2BfYQAAoM4jPAEIGKYgX65XnpY2rS7pTOwqx72PyoqMsq8wAAAQFAhPAAKCycuT66UnpNSNJZ1JveX4xe9lhYfbVhcAAAgehCcAfs/kZLtvfrsjtaSzV7Icdz8kKyzMvsIAAEBQITwB8Gsm65xczz8m7Unz9Fn9L5f1/34tK5S/wgAAQO2pk988MjMz9cADDygjI0PNmzfXP/7xj3L3Xbp0qebPn6+DBw8qNDRUiYmJmjhxojp16lR7BQMokzl3Vq7n/iQd3OPps4aMkvWTe2U5QmysDAAABKM6GZ7efvttnTt3rkL7zZkzR06nUz169FBBQYFSUlK0adMmTZs2TQMGDKiFagGUxZzLkOu5R6WDez191hVjZU25W5bDYV9hAAAgaNW58LR582YtXbpUV155pRYsWFDuflu2bNGcOXMUGxurxx9/XM2aNZMkpaWlafr06XrppZeUlJSkmJiY2iodwHkm65xcf/9BcBrzI1k3TJVlWfYVBgAAglqd+vVtfn6+Xn31VbVs2VLXXnvtRff9/PPPJUkTJ070BCdJSkxM1OjRo5Wdna3FixfXaL0ASjNZme4rTgcuGKp31USCEwAAsF2dCk8fffSRjh07prvuukshIeXPh8jPz9eWLVskSQMHDiy1vbhv3bp1NVMogDKZ7Ey5/v4naf9uT581ZoKsSbcTnAAAgO3qTHjat2+fvvjiC40YMUJJSUkX3ffw4cMqKChQXFycGjVqVGp7u3btPMcEUDtMdpZcf/+ztG+np8+68jpZN9xBcAIAAH6hToQnl8ulV155RVFRUbr11lsvuX96eroklRmcJCkiIkLR0dHKyspSTk6OT2sFUJrJyZbr+enS3h2ePmvUtbIm30lwAgAAfqNOLBgxf/587dy5U7/4xS8UGxt7yf1zc3MlSU6ns9x9wsPDlZWVpdzcXEVGRl70eNOmTSvV53Q69dRTT0mSGjdufMmaalLo+XvhNGnSxNY6UHV1+Ry6crJ1+tk/yLV7u6cvauwkxf70N3UqONXlcxgMOH+Bj3MY+DiHga8unMOAv/KUnp6uDz74QElJSRoxYkSFXmOMkaSLfjEr3gdAzTEF+Trz1CMq2LbZ0xd59Y/qXHACAAB1Q8BfeXrttddUWFiou+66q8KvKb6SlJeXV+4++fn5ktxD+C7lueeeu+j29PR0W8NYcbo/ceKEbTWgeuriOTRFRXL939PSptWePuvyMcr70e2eobV1SV08h8GE8xf4OIeBj3MY+Ow+h5Zlea2yXRUBH57Wr1+v6Ohovfbaa179BQUFktzBZfr06ZKkhx9+WBEREZ5hdCdPnizzmLm5ucrKylJ0dPQlh+wBqDzjcsn851/S+u88fVb/y2Xd+nNugAsAAPxWwIcnScrKylJqamqZ2/Lz8z3bioqKJEnNmzdXWFiYMjIydPLkyVILR+zZ476/TOvWrWuwaiA4GWNkZrwus2JhSWf3frL+369lOcq/xQAAAIDdAj48zZgxo8z+48eP695771Xz5s31j3/8w2ub0+lUt27dtGHDBq1cuVLjxo3z2r5y5UpJUt++fWukZiCYmc8/kFn4eUlHYlc57vmdrNCA/+sIAADUcUE7PqY4MM2ePVtHjhzx9KelpWnBggWKjIzUyJEj7SoPqJNcCz6T+fz9ko42HeW491FZznD7igIAAKigoP1Vb48ePTR27FjNnTtXDz30kLp3766ioiKlpKTI5XLpvvvuU0xMjN1lAnWGa8VCmQ8vmJuY0FKO+6fLioyyrygAAIBKCNrwJElTp05V27ZtNX/+fG3evFkhISHq1q2bJk2apM6dO9tdHlBnmM3rZN5+oaSjUbwcv/4fWbFx9hUFAABQSXU2PMXHx5c7H+pCI0aMqPD9oQBUntm3U65X/ia5XO6OuPpyTPsfWQ3tvXk0AABAZQXtnCcANc+cOCrXP/9Hyst1d4RHyvGrP8uKb25vYQAAAFVAeAJQI0xmhlzPPyZlnHF3OBzuVfXadLC1LgAAgKoiPAHwOZOfJ9e/HpeOHfL0WT+5T1a3PjZWBQAAUD2EJwA+ZVxFcr32rLRrm6fPuv5mOYaMsrEqAACA6iM8AfAZY4zMB69JG1Z6+qzLx8gad5ONVQEAAPgG4QmAz5ivP5FZPKeko3s/Wbf8XJZl2VcUAACAjxCeAPiE2bhKZuZbJR1tOsrxs4dkhYTYVhMAAIAvEZ4AVJs5uMc9z8kYd0ejeDl+9ais8Ah7CwMAAPAhwhOAajEZp+V64fGSezlFRMpx359kxTWwtzAAAAAfIzwBqDJTkC/Xi09Kp064OyyHHHc/JKtFa3sLAwAAqAGEJwBVYoyReesFafd2T581+Q5Z3fvaWBUAAEDNITwBqBIz9yOZ1Us9bWvYVbJGXWdjRQAAADWL8ASg0sy6FTKf/Leko1N3WT/+GUuSAwCAOo3wBKBSzP5dcr3xXElHfHM5fv6wrNBQ+4oCAACoBYQnABVmzmXI9dJfpfx8d0dUtBz3/VFWdKy9hQEAANQCwhOACjFFRXK9+ox08ri7w3LI8bPfyUpoaW9hAAAAtYTwBKBCzMfvSFs3edrWpNtlJfWyryAAAIBaRngCcElm7bcyX872tK3+l8saM8G+ggAAAGxAeAJwUebQPrne+mdJR4s2sm6/j5X1AABA0CE8ASiXyc6U66Unpbxcd0dUtBy/eERWeIS9hQEAANiA8ASgTMblkuv1v0vHj7g7LEuOu34jK765vYUBAADYhPAEoEzmiw+klDWetnXdj2V172djRQAAAPYiPAEoxWxZJ/P5ByUdPQfIGjvZvoIAAAD8AOEJgBdzKt09XK9Y0xZy/L9fy3Lw1wUAAAhufBsC4OG+Ee7/SpkZ7g6nU46fPywrKtrewgAAAPwA4QmAh/n0v9LOVE/buvkeWS3a2FgRAACA/yA8AZAkmc3rZObN8rStQVfIGjzKxooAAAD8C+EJgHue0xvPlXQ0ayXrlp9zI1wAAIALEJ6AIOee5/SMlHnO3eF0yvGzh7gRLgAAwA8QnoAg557ntNXTZp4TAABA2QhPQBBjnhMAAEDFEZ6AIGXOnJLrjQvu58Q8JwAAgIsiPAFByLhccr35vPf9nJjnBAAAcFGEJyAImUVfSKkbPG3rpruY5wQAAHAJhCcgyJiDe2RmvVXS0StZ1uVX2VYPAABAoAitqQOfOHFCp0+fVkZGhvLz8xUbG6u4uDg1a9ZMTqezpt4WwEWY/Dy5XntOKix0d9RrIMdP7mOeEwAAQAX4LDzl5+drxYoV2rhxo7Zu3aozZ86UuV9ISIjat2+vpKQkDR06VK1bt/ZVCQAuwcz+j3Ron6ftmHq/rNg4GysCAAAIHNUOT8eOHdOcOXO0bNkyZWdnX3L/oqIi7dixQzt27NCnn36qxMREjRkzRkOHDuW330ANMpvXySz83NO2rrxOVrc+NlYEAAAQWKocnjIzMzVz5kx9/fXXKjw/BCghIUFdunTRZZddpnbt2ik2NlYxMTFyOp3KzMxUZmamjh8/rh07dmjnzp1KTU1VWlqa0tLS9Nlnn+mWW25Rr169fPWzATjPZJyR663nSzpatJE18Sf2FQQAABCAqhyefvWrXykrK0uxsbEaOnSohg0bpvbt25e7f7169VSvXj21aNFCvXv3liTl5ORo5cqV+uabb5Samqq//vWvmjp1qq655pqqlgXgB4wxcr39gpRxxt0RGibHT38rK4y5hwAAAJVR5fBkWZZ+/OMf6+qrr1ZERNXuDRMZGakrrrhCV1xxhXbu3KmPPvpIWVlZVS0JQBnM0nlSyhpP27phKsuSAwAAVEGVw9OLL75Y5dBUlo4dO+qRRx5Rbm6uz44JBDtz/IjMR2+WdHTrI2vkePsKAgAACGBVvs+TL4NTbRwXCDbG5XLPc8rPc3fExLpX12NhFgAAgCrhJrlAHWUWfSHtSPW0rZt/LqteAxsrAgAACGw1dpPcsuzfv18pKSlyOBzq1auXmjdvXptvDwQNc/SQzMf/8bStvkPk6D/UxooAAAACn0/D05YtWzRr1ixddtlluvnmm722ffHFF/rvf/8rY4wk6Z133tFPfvITVtYDfMy4is4P18t3d8TWk3XLPfYWBQAAUAf4dNjed999p9TUVMXHx3v1HzlyRO+++66MMQoNDZXT6ZTL5dLbb7+tPXv2+LIEIOiZBZ9Ju7Z52o5bfi4rtp6NFQEAANQNPg1PaWlpklTqRrcLFy6Uy+VSUlKSXn/9db355ptKTk6WMUZffvmlL0sAgpo5clDm4/962taAYbL6DraxIgAAgLrDp+Hp7NmzcjgcatSokVf/xo0bJUmTJk1SRESEQkNDPcP6tm7d6ssSgKBliorkevMfUmGBuyOuvqwf321rTQAAAHWJT8NTZmamoqKivJZCzsnJ0YEDBxQREaGkpCRPf0JCgsLCwnTq1ClflgAELfPVJ9KeNE/bcdsvZMXE2VcQAABAHePT8BQWFqbs7GzPohCStH37dknum+A6HN5v53Q6ffn2QNAyh/bLfPaup20NvEJWr4E2VgQAAFD3+DQ8JSQkyOVyKTW15N4yq1evliR17tzZa9/CwkJlZ2erXj0msgPVYVxFcv3nBamw0N1Rr6GsKT+1tygAAIA6yKfhqU+fPpKkl19+WStWrNCcOXO0ZMkSSVJycrLXvnv27JExRo0bN/ZlCUDQMUvmSbu3e9qO234pKzrGxooAAADqJp/e52n8+PFaunSpjh8/rueff97TP2jQILVu3dpr3zVr1kgqfUUKQMWZUydkZr/jaVv9L5fVs7+NFQEAANRdPg1P0dHRevzxxzVjxgylpaUpOjpaffr00XXXXee1X2FhoRYvXixJ6tq1qy9LAIKGMUau916R8nLcHVExsqbcZW9RAAAAdZhPw5MkNWzYUPfcc8/F3zQ0VK+++qqv3xoILutXSJtWe5rW5P8nK66BjQUBAADUbdWa8zRjxgzt2bPHV7UAqCCTlSnX+/9X0tGpu6zBo+wrCAAAIAhU68rTrFmzNGvWLDVs2FD9+/dXv3791LVrV4WEhPiqPgBlMLPeks6edjdCw9yLRFxwfzUAAAD4XrXC0zXXXKN169bp+PHj+vLLL/Xll18qKipKvXv3Vr9+/dS7d29FRkb6qlYAksz2LTLLvvK0rWunyGra3MaKAAAAgkO1wtPUqVM1depU7d+/X6tXr9aaNWu0d+9eLV++XMuXL1doaKiSkpI8V6UaNmzoq7qBoGQK8uV658WSjpZtZY35kX0FAQAABBGfLBjRunVrtW7dWjfccINOnTqlNWvWaM2aNUpNTVVKSopSUlL0+uuvq3379p4g9cOlywFcmpkzQzp2yN2wLDl+cq+sUJ+v+wIAAIAy1Mhqe1dddZWuuuoqZWdna8OGDVqzZo02btyo3bt3a/fu3frwww8VHx/vCVKdO3eWw+HT+/UCdU7hgT0y82d52tbI8bLaJdpYEQAAQHCp0V9ZR0VFaciQIRoyZIiKior0/fffa/Xq1Z55UnPmzNGcOXMUExOjvn376pprrlG7du1qsiQgIBljlPHK/0pFRe6Ohk1kTbjV3qIAAACCTK2N9wkJCVGPHj3Uo0cP3XXXXdq9e7cnSO3fv19Lly5VfHw84QkoQ+6yr5W/Zb2n7fjx3bIiWIwFAACgNtk2WaJ9+/Zq3769pkyZouPHj2vNmjUsKAGUweRk69ybL5R09Ogvq1eyfQUBAAAEKb+YaR4fH69x48bZXQbgl8zn78ucTnc3QsPkmPJTewsCAAAIUjUanvLz85WVlaWi4nka5WjcuHFNlgEELHNon8zCzz1t65obZDVJsLEiAACA4OXz8JSbm6tPP/1UK1as0NGjRy+5v2VZ+uCDD3xdBhDwjDFyvfey5HJJkkKatpC5eqLNVQEAAAQvn4ans2fP6s9//rOOHDlS4dcYY3xZAlBnmFVLpbTvPe3Yn/5a55zhNlYEAAAQ3Hwant5//30dOXJETqdT1157rXr27Kl69eopJCTEl28D1HkmO0vmozc87fABlyui3xCdO3HCxqoAAACCm0/D0/r17qWUf/nLX2rgwIG+PDQQVMxn70kZZ9yNMKdi7/y1rfUAAABAcvjyYNnZ2QoNDdWAAQN8eVggqJgDe2QWzfG0rbE3KrRpMxsrAgAAgOTj8NSoUSOFhITI4fDpYYGg4V4k4hXJuBeJUHwzWVf9yN6iAAAAIMnH4al///7Ky8vTzp07fXlYIGiYNcuknametuPHd8sKc9pYEQAAAIr5NDxdf/31atKkiV599VVlZWX58tBAnWfy82RmvV3S0StZVre+9hUEAAAALz5dMCI2NlaPPvqo/vnPf2ratGm68sor1aFDB0VERFz0dUlJSb4sAwhI5utPpVPnV9MLCZXjxjvsLQgAAABefH6T3JCQEDVp0kQ7d+7UzJkzL7k/N8kFJHPmpMy8ks+LNWq8rPjmNlYEAACAH/JpeDp+/Lj+9Kc/6fTp0xV+DTfJBSTz8X+lvFx3IyZO1rjJ9hYEAACAUnwanmbMmKHTp08rNjZWt9xyi3r27Kn69evXyup7X3zxhbZt26b9+/fr7NmzKigoUP369ZWUlKTrr79erVq1KvN1S5cu1fz583Xw4EGFhoYqMTFREydOVKdOnWq8ZkCSzL6dMisWetrW9bfIioqxsSIAAACUxafhafPmzZKk+++/X927d/floS/p448/Vm5urtq0aaPWrVtLkg4cOKBvvvlGK1as0IMPPqjevXt7vebtt9/WnDlz5HQ61aNHDxUUFCglJUWbNm3StGnTuF8VapwxRq4PXivpaNFG1uVj7CsIAAAA5fJpeMrOzpbT6VS3bt18edgKefDBB9W+fXs5nd7LOn/11Vd67bXX9PLLL+vf//635yrYli1bNGfOHMXGxurxxx9Xs2bum5CmpaVp+vTpeumll5SUlKSYGK4AoAatX+G9NPnk/ycrJMTGggAAAFAen46na9y4sST3IhC1rXPnzqWCkySNGTNGCQkJOn36tA4fPuzp//zzzyVJEydO9AQnSUpMTNTo0aOVnZ2txYsX13zhCFqmIF+uj94s6eg5QFZS7/JfAAAAAFv5NDwNGjRI+fn52rJliy8PW23FV5tCQ90X2i6sceDAgaX2L+5bt25dLVWIYGQWfCadPO5uhITIcQNLkwMAAPgzn4anCRMmqHXr1nrllVd0/PhxXx66ypYuXarDhw+rWbNmio+PlyQdPnxYBQUFiouLU6NGjUq9pl27dpKkffv21WqtCB7m7GmZOR952tYV42UltLCxIgAAAFyKT+c8fffdd7riiiv00Ucf6Te/+Y2Sk5PVsWNHRUZGXvR1w4cP91kNn332mQ4cOKC8vDwdOnRIBw4cUIMGDXT//fd7rkClp6dLUpnBSZIiIiIUHR2trKws5eTkXLJ+oLLMJ/+V8nLcjZhYWeNvsrcgAAAAXJJPw9NLL73k1V62bJmWLVt20ddYluXT8LRp0ybPqn+SOyDdd999at++vacvN9d9P52y5kgVCw8PV1ZWlnJzcy8ZnqZNm1aqz+l06qmnnpJUMhfMLsXDFZs0aWJrHXAr2L9bJy9Ymjzu5p8pqm27i76Gcxj4OIeBjfMX+DiHgY9zGPjqwjn0aXiyOyRI0qOPPipJysrK0v79+zVz5kxNnz5dU6ZM0cSJEyWV3Jj3YgtbcPNe1JTM/74suVySpJAWrRV51fU2VwQAAICK8Gl4evHFF315uGqJjo5Wly5d9Mgjj+iPf/yjPvzwQ/Xo0cNrGGFeXl65r8/Pz5fkHsJ3Kc8999xFt6enp9saxorT/YkTJ2yrAW5mR6pcq0uuxprrblH6qdOXfB3nMPBxDgMb5y/wcQ4DH+cw8Nl9Di3L8lpluyp8umCEPwoNDdXgwYNljPGsnld8hezkyZNlviY3N1dZWVmKjo5mvhN8xhgj16y3Sjrad5J6l17tEQAAAP6pzocnSYqNjZUkZWRkSJKaN2+usLAwZWRklBmg9uzZI0lq3bp17RWJum/TKmnXNk/TMel2W+6JBgAAgKoJivCUmpoqSWratKkk92IO3bp1kyStXLmy1P7FfX379q2lClHXmaIiuWa/U9LRo7+sxG72FQQAAIBKq3J4ev3113X69KXnalTGypUr9e2331b6dVu3btWKFStUVFTk1V9YWKh58+bpm2++kdPp1ODBgz3bxo0bJ0maPXu2jhw54ulPS0vTggULFBkZqZEjR1bxJwG8mRULpSMH3A3LkmPiT+wtCAAAAJVW5QUjvvrqKy1evFijRo3S6NGj1bJlyyodJz8/XytXrvTcn+nGG2+s9DGOHTuml156SbGxsWrfvr1iY2N17tw57d+/X6dPn1ZYWJh+8YtfeK0G2KNHD40dO1Zz587VQw89pO7du6uoqEgpKSlyuVy67777FBMTU6WfCbiQycuT+ex9T9saNFJWizY2VgQAAICqqHJ4uvvuu/Xhhx9q/vz5mj9/vtq1a6chQ4aoS5cuatu2rWcd97Kkp6drx44dWrt2rdauXeu571JycrJGjBhR6VqSkpL0ox/9SKmpqdq/f78yMjIUGhqq+Ph4JScna+zYsUpISCj1uqlTp6pt27aaP3++Nm/erJCQEHXr1k2TJk1S586dK10HUBaz6AvpzPm5daFhsq672d6CAAAAUCVVDk+jRo3S0KFD9emnn2r+/Pnas2ePZ6GF0NBQNW/eXHFxcYqOjlZYWJiysrKUmZmpY8eOeRZuKNa1a1dNmTJFiYmJVaolPj5eP/7xj6v02hEjRlQpsAEVYbLOycyb6WlbI8fLahS4N4YDAAAIZtW6z1N4eLgmT56sCRMmaMWKFVq4cKF27NihwsJC7d+//6KvjYuL05AhQzR69Gi1aNGiOmUAfsvMnSnlZLkbkdGyxt5gb0EAAACoMp/cJNfpdHqu4GRnZ2vbtm3auXOnTp06pYyMDBUUFCg2NlZxcXFq2bKlunTpQmBCnWdOnnAP2TvPuuYGWdGxNlYEAACA6vBJeLpQVFSU+vTpoz59+vj60EBAMZ+/JxUWuBv1G8kaNd7eggAAAFAtQXGfJ6C2mWOHZb5b7Glb1/1YljPcxooAAABQXYQnoAaYLz6QXC53o0mCrEHcMwwAACDQEZ4AHzNHDsisWuppW9f+WNZFlu4HAABAYCA8AT5mPv9AMsbdSGghK3mYvQUBAADAJwhPgA+Zg3tl1izztK1rfyzLEWJjRQAAAPAVwhPgQ67P3itpNG8tq99Q+4oBAACATxGeAB8x+3ZJG1Z62o7rbpbl4CMGAABQV/DNDvARr6tOrdpJvQfaVwwAAAB8jvAE+IDZvV1KWeNpO66/hatOAAAAdYxPv92lpqb68nBAwPC66tT2MqlHf/uKAQAAQI3w6c1nHnvsMTVv3lxXXnmlhg8frpiYGF8eHvBLZmeq9P0GT9tx/c2yLMvGigAAAFATfD6u6PDhw/rPf/6jn/3sZ3rhhRe4GoU6z/XJuyWNDp2lrn3sKwYAAAA1xqdXnp5//nktXLhQS5cu1dmzZ/Xtt9/q22+/5WoU6iyzfbO0fbOn7bj+Fq46AQAA1FE+DU8JCQm65ZZbNGXKFK1du1YLFizQ5s2bPVej3n//fSUnJ2vUqFFKSkry5VsDtnDNmVHSSOwmde5hXzEAAACoUT4NT8VCQkKUnJys5ORkpaena8GCBVq6dKlOnTrF1SjUGWbXNmnrJk/bMf4mrjoBAADUYTUSni7UuHFjTZkyRZMnT9b69eu1aNEibdiwodTVqNGjR6tz5841XQ7gM665H5U0OnTmqhMAAEAdV+PhqZjD4VC/fv0UGhqqc+fOKS0tTZJUUFDguRqVmJio22+/XR07dqytsoAqMft3e9/XadxkrjoBAADUcbUSnk6fPq1FixZp0aJFSk9P9/R37txZAwcO1KZNm7Rx40alpaXpT3/6k/7whz+oa9eutVEaUCXmwqtOrdtL3fraVwwAAABqRY2FJ2OMNmzYoAULFmjDhg1yuVySpMjISA0bNkyjR49Wq1atJEnXXHONjh07ptdee00pKSn68MMP9T//8z81VRpQLebIAZn1Kzxtx1iuOgEAAAQDn4enkydPatGiRVq8eLFOnjzp6W/Xrp1Gjx6toUOHKjw8vNTrmjZtql//+tf66U9/qn379vm6LMBnzNyZkjHuRrNWUu+B9hYEAACAWuHT8PTUU09p06ZNnqtMTqdTgwcP1ujRoys0jykqKkr169f3GtoH+BNz4qjM6qWetjX2BlkOn99rGgAAAH7Ip+Fpw4YNkqQWLVroyiuv1IgRIxQVFVWpYyQnJyszM9OXZQE+Y+bPks7/ckBNEmT1H2ZvQQAAAKg1Pg1PgwYN0pgxY6p1A9yf/OQnPqwI8B1zKl1m+UJP27rmBlkhITZWBAAAgNrk0/D0wAMP+PJwgF8xX30sFRW6Gw0ayxp0hb0FAQAAoFb5dLLGY489pueee67C+//jH/9gVT0EBJNxWmbZl562ddVEWaFhNlYEAACA2ubTK0+pqamqX79+hfffsWMHi0MgIJivP5Py892N2HqyLh9tb0EAAACodbYuE2aM4f448HsmK1NmyVxP27rqR7KcpZfbBwAAQN1mW3hyuVw6e/Zsmfd8AvyJWTpPys1xN6JiZA2/2t6CAAAAYItqDdvLzs5Wdna2V5/L5broUDxjjLKysrRkyRIVFhaqTZs21SkBqFGmoEBm0ReetnXFWFkRlVt+HwAAAHVDtcLTnDlzNHPmTK++jIwM/fKXv6zwMYYN4z458F9m5WLp7Gl3IzRM1shx9hYEAAAA2/h0wYjKaNiwoUaPHq2rr2YIFPyTcblkvvrE07YGj5QV18C+ggAAAGCraoWncePGacSIEZLcw/Huu+8+xcXF6cknnyz3NZZlKSoqSlFRDH2Cn9u8Vjp60P3csmSNnmBrOQAAALBXtcLTD0NQly5dFBsbqyZNmlS7MMBuri9nlzR6JstKaGFfMQAAALCdT4ftTZ8+3ZeHA2xjdm+XdqR62o6rfmRjNQAAAPAHtt7nCfBXri8/Lml06CyrYxf7igEAAIBfqPKVp9RU92/lw8PD1aFDB6++ykpKSqpqGYDPmeOHpQ3fedqOqybaWA0AAAD8RZXD02OPPSZJatGihZ577jmvvsqwLEsffPBBVcsAfM58/alkjLvRtIXUc4C9BQEAAMAvVHvYnin+kmnT6wFfMufOyixf6GlbYybIcjC6FQAAANW48vThhx9WqA8IJGbxHKkg392Iqy9r0BX2FgQAAAC/wa/UgfNMXp47PJ1njRwvK8xpY0UAAADwJ4Qn4DyzYqGUec7dCI+QNeIaW+sBAACAf/F5eMrOzlZubu4l98vNzVV2drav3x6oEuMqkvn6E0/bGjpaVnSsfQUBAADA7/g0PK1atUp33HGHXnnllUvu+89//lN33HGH1q5d68sSgKrZvE46cdT93HLIGnWtvfUAAADA7/g0PH33nfveOCNHjrzkvldeeaUkacWKFb4sAagS18LPSxq9k2U1SbCvGAAAAPgln4anvXv3SpLat29/yX07deokSdqzZ48vSwAqzRzaL23d5Gk7uOoEAACAMvg0PJ06dUqRkZGKjo6+5L7R0dGKiIjQqVOnfFkCUGlm0QVXnVq1ky7ral8xAAAA8FtVvs9TWSzLUlFRUYX3d7lcvnx7oNJM1jmZlYs9bWvUtbIsy8aKAAAA4K98euWpUaNGys/P1/79+y+57969e5Wfn6+GDRv6sgSgUsw3X0n552+KG1tP1oBh9hYEAAAAv+XT8JSUlCRJmjFjxiX3/eijjyRJXbsyRAr2MEVFMksuuCnusKu4KS4AAADK5dPwdM0118iyLK1Zs0b//Oc/debMmVL7nDlzRs8//7zWrl0rh8OhsWPH+rIEoOI2rpROpbufh4SIm+ICAADgYnw656lFixaaMmWK3n//fS1fvlyrVq1S+/bt1bhxY1mWpRMnTmjXrl2eeVE33XSTWrZs6csSgApzLShZKMLqO0RW/UY2VgMAAAB/59PwJEkTJkxQVFSU3n33XeXm5iotLU1paWle+0RGRurWW2/13OsJqG1m3y5pZ6qnzU1xAQAAcCk+D0+SNGbMGA0ZMkQrV67U9u3bdfbsWUlS/fr11alTJw0cOFBRUVE18dZAhZiFn5U02iXKat/JvmIAAAAQEGokPEnu+ziNGjVKo0aNqqm3AKrEZJyWWbPM0+aqEwAAACrCpwtGAIHALP1SKix0N+o1lNV3sL0FAQAAICDU2JUnSTpw4IB27dqljIwMSVJcXJw6duzIIhGwjSkskFk6z9O2RlwjKzTMvoIAAAAQMGokPG3cuFHvvvtuuTfLbd26tW699Vb17NmzJt4eKJdZ+6109rS7ERoma/jV9hYEAACAgOHzYXvz58/XX//6V09wcjgcqlevnurVqyeHw/12+/fv15NPPqn58+f7+u2BizKLLrgp7oBhsmLr2VgNAAAAAolPrzzt3btXb731liSpY8eOuvHGG9W1a1eFhbmHRRUUFOj777/XrFmzlJaWprfffltdunRRmzZtfFkGUCazf5e0p2TZfGvkeBurAQAAQKDx6ZWnL774QsYY9e3bV3/5y1/Uq1cvT3CSpLCwMPXq1UuPPfaY+vbtK5fLpTlz5lzkiIDvmKUXXOlslyirTQf7igEAAEDA8Wl42rp1qyRp6tSpniF6Zb6pw6GpU6dKkr7//ntflgCUyeRky6xa6mlbw6+xsRoAAAAEIp+GpzNnzigqKkrx8fGX3Dc+Pl5RUVE6c+aML0sAymRWLpbyct2NqBhZ/YfaWxAAAAACjk/Dk9PpVH5+voqKii65b1FRkfLz8+V0On1ZAlCKMUZmyQXLkw8eJcsZbmNFAAAACEQ+DU8tW7ZUYWGhVq5cecl9v/vuOxUWFnLPJ9S8nVulwyXL5rM8OQAAAKrCp+Fp4MCBkqTXXntNKSkp5e6XkpKi119/XZI0aNAgX5YAlHLhVSd16SkroYV9xQAAACBg+XSp8jFjxmjRokU6ePCgnnjiCSUmJqp79+5q2LChLMvSyZMntXnzZqWluZeLbtWqlcaMGePLEgAv5txZmfXLPW0HV50AAABQRT4NT2FhYfrDH/6gZ599Vjt37lRaWponKP1Qx44d9Zvf/EahoT4tAfBivl0gFRa6G/UaSj2T7S0IAAAAAcvnyaVhw4b6y1/+opUrV2rFihXavXu3zp49K0mqV6+e2rdvryFDhig5Ofmiy5kD1WVcLplvSu7tZF0+WhZhHQAAAFVUI98kHQ6HBg8erMGDB9fE4YGKSd0gpR9zP7ccsi5niCgAAACqjks/qLNcFy4U0bO/rIZN7CsGAAAAAY/whDrJnDwhpaz1tB3Dr7GxGgAAANQFVR62l5qa6rMikpKSfHYsQJLMsi8l43I3miRISb1srQcAAACBr8rh6bHHHvNJAZZl6YMPPvDJsQBJMoWFMt9+7Wlbw66SxeIkAAAAqCbbv1EaY+wuAXXNplXS2dPu56GhsoZcaW89AAAAqBOqfOXpww8/9GUdgM+4ln3leW71GSIrtp6N1QAAAKCuqBM3vcnLy9OmTZu0bt067dq1SydOnJDL5VJCQoKSk5M1fvx4RURElPnapUuXav78+Tp48KBCQ0OVmJioiRMnqlOnTrX8U8AXzMkTUupGT9sadpV9xQAAAKBOqRPh6dtvv9Urr7wiSWrVqpV69uypnJwcpaWlacaMGVq+fLmmT5+uevW8r0C8/fbbmjNnjpxOp3r06KGCggKlpKRo06ZNmjZtmgYMGGDHj4NqMCsWSsVDQeObSYld7S0IAAAAdUaNhqeMjAydOHFCeXl5NbqiXmhoqMaMGaNx48apWbNmnv7Tp0/rqaee0p49e/TWW2/p/vvv92zbsmWL5syZo9jYWD3++OOe16WlpWn69Ol66aWXlJSUpJiYmBqrG75lXC6Z5Qs8bWvIlbIsy8aKAAAAUJfUSHhau3atPvroI+3du1dS6RX1MjMz9fzzz0uSfvOb35Q7pK6ihg8fruHDh5fqb9Cgge6880798Y9/1OrVq1VYWKjQUPeP/Pnnn0uSJk6c6BW4EhMTNXr0aM2bN0+LFy/WtddeW63aUIu2bZJOHnc/txyyBo+0tx4AAADUKT5fbe+TTz7RM8884wlOUukV9WJiYhQeHq6UlBRt2LDB1yV4adOmjSSpoKBA586dkyTl5+dry5YtkqSBAweWek1x37p162q0NviW+bbkqpO695VVv5F9xQAAAKDO8Wl42rFjh95//32FhITo9ttv1+uvv15qnlGxyy+/XJL7KlVNOnbsmCQpJCTEMwTv8OHDKigoUFxcnBo1Kv0Fu127dpKkffv21Wht8B2TmSGz4TtP23H5aBurAQAAQF3k02F7c+fOlSRNmDBBY8eOvei+xXOgdu3a5csSyq2pV69eCgsLkySlp6dLUpnBSZIiIiIUHR2trKws5eTkKDIyskZrRPWZVUulwkJ3I66+1K2frfUAAACg7vFpeNq2bZsk6eqrr77kvrGxsYqIiNCpU6d8WYKX9evXa/HixQoJCdFNN93k6c/NzZUkOZ3Ocl8bHh6urKws5ebmXjI8TZs2rVSf0+nUU089JUlq3LhxVcr3meJ5Xk2aNLG1jppijNHJ7xbpfHRS9Kjxir1gHltdUNfPYTDgHAY2zl/g4xwGPs5h4KsL59Cnw/YyMjIUGRmpuLi4Cu0fEhKiwuKrBT528OBBvfDCCzLG6LbbblPbtm0924rnYF1sJbYfztOC/yrcuVWF+0quYEZeOd7GagAAAFBX+fTKk9PpVG5urlwulxyOi+ey7OxsZWVlVThoVcbJkyf15JNPKisrS+PHjy81hLD4SlJeXl65x8jPz5ekCq0E+Nxzz110e3p6uq1hrDjdnzhxwrYaapLr849KGpcl6bQzSqpjP2tdP4fBgHMY2Dh/gY9zGPg4h4HP7nNoWZbXKttV4dMrT82bN5fL5dL+/fsvue+qVaskyeuKkC9kZGTo8ccfV3p6ukaMGKHbbrut1D7Fw+hOnjxZ5jFyc3OVlZWl6Oho5jv5OZOXJ7PmG0/bGspCEQAAAKgZPg1Pffv2leRervxijh49qvfee0+S1L9/f5+9f05Ojv7617/q0KFDGjBggO65554yh+Y1b95cYWFhysjIKDNA7dmzR5LUunVrn9WGmmHWLZdyst2NiEhZfYfYWxAAAADqLJ+Gp6uvvlpxcXH67rvv9NJLL+nQoUNe248dO6bZs2frkUceUUZGhuLj43XFFVf45L0LCgr09NNPa9euXerZs6ceeOCBcocOOp1OdevWTZK0cuXKUtuL+4rDIPyXWf6157k1YJis8OrdcBkAAAAoj0/nPEVFRemhhx7Sk08+qaVLl2rp0qWebbfddptnHpHkvlHub37zG8/y4dXhcrn0/PPP6/vvv1eXLl3029/+1rOaR3nGjRunDRs2aPbs2erTp49n/GNaWpoWLFigyMhIjRw5stq1oeaYo4ektO89bYbsAQAAoCb5NDxJ0mWXXaann35a77zzjlavXu1ZKOHC4NS/f3/95Cc/UXx8vE/ec/78+Vq9erUk9xLor732Wpn73XbbbZ4FKnr06KGxY8dq7ty5euihh9S9e3cVFRUpJSVFLpdL9913n+emuvBPZvmCkkaLNlLby+wrBgAAAHVetcLT008/rVGjRql3795eQ+SaNGmiadOmKTMzU2lpaTp9+rRcLpfq16+vTp06+XyFvczMTM/z4hBVlhtvvNHrvadOnaq2bdtq/vz52rx5s0JCQtStWzdNmjRJnTt39mmN8C1TVCTz3SJP2xo6+qJLzwMAAADVVa3wtG7dOq1bt07169fX8OHDNWLECDVv3tyzPSYmRn369Kl2kZcyefJkTZ48uUqvHTFihEaMGOHbglDzvl8vnT3tfh4aKmvgCFvLAQAAQN1XrfAUHx+v48eP68yZM/r000/16aefqnPnzrriiis0aNAghYeH+6pOwIv5bnFJo+cAWTG+v18YAAAAcKFqhacXXnhBqampWrx4sVatWqW8vDxt27ZN27Zt05tvvqkhQ4ZoxIgRSkxM9FW9gEx2pszGVZ62Y9AoG6sBAABAsKj2ghFJSUlKSkrSnXfeqeXLl2vJkiVKS0tTbm6uFi5cqIULF6pFixYaOXKkhg0b5vP5Tgg+Zu1yqbDA3YitJ3XtbW9BAAAACAo+W20vIiJCo0aN0qhRo3T48GEtWrRIy5Yt05kzZ3To0CG98847eu+999S3b19dccUV6t27NxP8USUXDtmzBgyTdYll6QEAAABfqJFvnc2bN9ett96qm2++WRs3btSiRYu0fv16FRUVafXq1Vq9erUaNGjgWawhISGhJspAHWSOH5F2pnra1iDf3GQZAAAAuJQa/ZW9w+FQnz591KdPH507d05Lly7VkiVLdODAAZ0+fVoff/yxPvnkE33wwQc1WQbqELNySUmjWSupdQfbagEAAEBwcVx6F9+IjY3V+PHj9fTTT+uGG27wDNkrvokucCnGGJmVFwzZGzSSoZ8AAACoNbU2WeTIkSNavHixvvnmG50+fdrT73Q6a6sEBLpdW6UTR93PLUtW8nB76wEAAEBQqdHwlJeXpxUrVmjx4sXavn2717a2bdvqiiuu0OWXX16TJaAOMd8tKWl07iGrYWPbagEAAEDwqZHwtG3bNi1atEirVq1Sbm6upz8qKkpDhw7VyJEj1a5du5p4a9RRpiBfZu0yT9saNNLGagAAABCMfBaeTp065VkQ4ujRo17bunbtqpEjRyo5OVlhYWG+eksEk5Q1UnaW+3l4hKzeA+2tBwAAAEGnWuGpsLBQa9eu1eLFi5WSkiKXy+XZ1rBhQw0fPlwjR45UfHx8tQtFcHNdeG+nPoNkRUTaWA0AAACCUbXC089+9jNlZmZ62iEhIerXr59Gjhypnj17shIafMJknJG2rPO0rYHc2wkAAAC1r1rhqTg4tWzZUldccYWGDRumuLg4nxQGFDNrlklFRe5G/UZS5+72FgQAAICgVK3wNHLkSI0cOVKXXXaZr+oBSjEXDtkbOEKWI8TGagAAABCsqj1sD6hJ5tB+ad9OT5shewAAALCLw+4CgIsxK0uuOqlNR1ktWttXDAAAAIIa4Ql+y7hcMiuXeNrWIK46AQAAwD6EJ/ivHanSmZPu5w6HrP6X21sPAAAAghrhCX7LrP6mpNGlp6y4+rbVAgAAABCe4JdMYaHM+uWetjVgmI3VAAAAAIQn+Kutm6TMc+7noWGyeg+ytx4AAAAEPcIT/JLXkL0e/WRFRtlXDAAAACDCE/yQyc+T2bDS03YwZA8AAAB+gPAE/7N5rZSX434eESl172dvPQAAAIAIT/BDrguG7Fm9BspyhttYDQAAAOBGeIJfMdlZUspaT9sawL2dAAAA4B8IT/ArZuNKqbDA3YiJlbr0srUeAAAAoBjhCX7lwlX2rD5DZIWG2lgNAAAAUILwBL9hzp1139/pPG6MCwAAAH9CeILfMOuWSy6Xu1G/kXRZkr0FAQAAABcgPMFveA3Z6z9UloP/PQEAAOA/+HYKv2BOnZB2pHraVn+G7AEAAMC/EJ7gF8yab0saTRKkth3tKwYAAAAoA+EJfsFryN6AYbIsy8ZqAAAAgNIIT7CdOXpI2r/L02aVPQAAAPgjwhNsZ9YsK2m0bCureWv7igEAAADKQXiC7S4MT1x1AgAAgL8iPMFW5vB+6cgBT9vqN9TGagAAAIDyEZ5gK7N+RUmjdQdZTRLsKwYAAAC4CMITbGXWlYQnq+9gGysBAAAALo7wBNuYo4ekg3s9basP4QkAAAD+i/AE23gN2WvZVlZCC/uKAQAAAC6B8ATbMGQPAAAAgYTwBFuYE0e9b4zbd4iN1QAAAACXRniCLbyG7DVrJatZK/uKAQAAACqA8ARbeA/Z46oTAAAA/B/hCbXOnDwu7UnztJnvBAAAgEBAeEKtu/Cqk5q2kFq0sa8YAAAAoIIIT6h1F853svoOlmVZNlYDAAAAVAzhCbXKnEqXdm3ztJnvBAAAgEBBeEKtMhu+K2k0SZBatbOvGAAAAKASCE+oVWbdcs9zq+8QhuwBAAAgYBCeUGvMmVPSzq2eNqvsAQAAIJAQnlBrzIaVkjHuRqN4qU1HewsCAAAAKoHwhFrjPWSPVfYAAAAQWAhPqBUm44yU9r2nbfVhyB4AAAACC+EJtcJsXCkZl7vRoLHULtHeggAAAIBKIjyhVpgNKz3PrT6DZDn4Xw8AAACBhW+wqHEmJ1valuJpW70H2lgNAAAAUDWEJ9Q4s2W9VFjobkTHSh2T7C0IAAAAqALCE2rexlWep1aPfrJCQmwsBgAAAKgawhNqlCkskNm81tO2ejFkDwAAAIGJ8ISalbZFyslyPw9zSl1721sPAAAAUEWEJ9Qoc8GQPSX1khUeYV8xAAAAQDUQnlBjjDEyGy6Y79Qr2cZqAAAAgOohPKHm7NspnTnpfm5Zsnr0t7ceAAAAoBoIT6gxXkP2OnSRFVfftloAAACA6iI8ocZcGJ4YsgcAAIBAR3hCjTDHj0iH9nnahCcAAAAEOsITaoTXkL3mrWU1bW5fMQAAAIAPEJ5QI8zGlZ7nXHUCAABAXUB4gs+Zc2elnds8bavXQBurAQAAAHyD8ASfMylrJONyN+o3ktp0sLcgAAAAwAcIT/A5s+HCIXsDZDn43wwAAACBj2+18CmTlydt3ehpM2QPAAAAdQXhCb6VukHKz3c/j4ySOnWztx4AAADARwhP8CmvG+N26ysrNMzGagAAAADfCbW7AF/ZvXu3UlJStHPnTu3YsUOnT59WWFiY3n333Yu+bunSpZo/f74OHjyo0NBQJSYmauLEierUqVMtVV53mKIimZTVJR29GbIHAACAuqPOhKeZM2dq7dq1lXrN22+/rTlz5sjpdKpHjx4qKChQSkqKNm3apGnTpmnAgAE1VG0dtWurlHnO/TwkVFa3vvbWAwAAAPhQnQlPiYmJatu2rTp06KAOHTro7rvvvuj+W7Zs0Zw5cxQbG6vHH39czZo1kySlpaVp+vTpeumll5SUlKSYmJjaKL9OMClrShqdusmKjLKvGAAAAMDH6kx4mjBhQqX2//zzzyVJEydO9AQnyR3CRo8erXnz5mnx4sW69tprfVlmnWZSSq78WT3621gJAAAA4HtBuWBEfn6+tmzZIkkaOLD0vJzivnXr1tVqXYHMnDgqHTngaVvd+9lYDQAAAOB7QRmeDh8+rIKCAsXFxalRo0altrdr106StG/fvtouLWCZzRfMN0toKSu+Wfk7AwAAAAGozgzbq4z09HRJKjM4SVJERISio6OVlZWlnJwcRUZGXvR406ZNK9XndDr11FNPSZIaN25czYqrJzTUfZqbNGlSY+9xanuKzt/dSVHJlyuuBt8rGNXGOUTN4hwGNs5f4OMcBj7OYeCrC+cwKK885ebmSnIHnPKEh4d77YvyuXJzlL95vacd3m+IjdUAAAAANSMorzwZYyRJlmVdcp+KeO655y66PT09vVLH87XidH/ixIkaOb7ZuEoqOH/dKTJKZxs3l1VD7xWsavocouZxDgMb5y/wcQ4DH+cw8Nl9Di3L8looriqC8spT8TC8vLy8cvfJz3eHgYiIiFqpKZBdON/JSuotKzQoMzkAAADquKAMT8VzkE6ePFnm9tzcXGVlZSk6OvqS852CnTHGa4lysUQ5AAAA6qigDE/NmzdXWFiYMjIyygxQe/bskSS1bt26tksLPAf2SGfO/ze0LFnd+9pbDwAAAFBDgjI8OZ1OdevWTZK0cuXKUtuL+/r2JQhcitcS5W0vkxVbz75iAAAAgBoUlOFJksaNGydJmj17to4cOeLpT0tL04IFCxQZGamRI0faVV7A8JrvxJA9AAAA1GF1Zmb/+vXrNWvWLK++wsJC/eEPf/C0J02apD59+kiSevToobFjx2ru3Ll66KGH1L17dxUVFSklJUUul0v33XefYmJiavVnCDTm3Flp93ZP2+rRz8ZqAAAAgJpVZ8JTRkaGduzY4dVnjPHqy8jI8No+depUtW3bVvPnz9fmzZsVEhKibt26adKkSercuXOt1B3IzJb1UvES7PUbSq3a21sQAAAAUIPqTHgaMWKERowYUWuvg6QLh+x173fR+2YBAAAAgS5o5zyhekxhofvK03kM2QMAAEBdR3hC1ezaJuVkuZ+Hhkqde9pbDwAAAFDDCE+oErN5TUmjU3dZEdxMGAAAAHUb4QlVYlIunO/EEuUAAACo+whPqDRz4qh05ICnzXwnAAAABAPCEyrtwhvjqlkrWU0S7CsGAAAAqCWEJ1Sa+cES5QAAAEAwIDyhUkxenrRts6fNkD0AAAAEC8ITKidts1RY4H4eGSV16GJvPQAAAEAtITyhUsz3G0oanXvICg21rxgAAACgFhGeUCnm+/We51bXPjZWAgAAANQuwhMqzKQfk44e8rStrr1trAYAAACoXYQnVJjXkL2EFrIaN7WvGAAAAKCWEZ5QYQzZAwAAQDAjPKFCTGGhtC3F02bIHgAAAIIN4QkVs3u7lJPtfh4aJiV2s7ceAAAAoJYRnlAhXvOdLkuSFR5hXzEAAACADQhPqBDmOwEAACDYEZ5wSebcWWn/Lk/b6kZ4AgAAQPAhPOGSTOpGyRh3o34jqXlrW+sBAAAA7EB4wqV5DdnrJcuybCwGAAAAsAfhCRdlXC7vxSK69rWvGAAAAMBGhCdc3MG9UsYZ93PLISupp53VAAAAALYhPOGivK46te0oKzrWvmIAAAAAGxGecFEsUQ4AAAC4EZ5QLpObI+3c6mmzRDkAAACCGeEJ5du+WSoqdD+PipbaXmZvPQAAAICNCE8o14VD9tSlp6yQEPuKAQAAAGxGeEK5zBbmOwEAAADFCE8okzl+RDpx1NMmPAEAACDYEZ5QJq8lypu1ktWwsX3FAAAAAH6A8IQysUQ5AAAA4I3whFJMUZF7pb3zrK69bawGAAAA8A+EJ5S2d4eUm+N+HhoqXdbV3noAAAAAP0B4Qilm68aSRocussLDbasFAAAA8BeEJ5RitqZ4nlude9hYCQAAAOA/CE/wYvJypV3bPG2rS08bqwEAAAD8B+EJ3nakSkWF7ueRUVLby+ytBwAAAPAThCd4MVs3lTQSu8kKCbGvGAAAAMCPEJ7gxWwrCU8M2QMAAABKEJ7gYc5lSPt3e9qEJwAAAKAE4Qkltpessqd6DaVmreyrBQAAAPAzhCd4XDjfyerSQ5Zl2VgNAAAA4F8IT/DwWiyiM0P2AAAAgAsRniBJMunHpBNHPW2rCzfHBQAAAC5EeIKkH1x1atpCVsMm9hUDAAAA+CHCE9y2lSwWwSp7AAAAQGmEJ8gYU2qxCAAAAADeCE+QDu2Tzp11P7csqVN3e+sBAAAA/BDhCd7znVp3kBUda18xAAAAgJ8iPOEHQ/aY7wQAAACUhfAU5ExhoZT2vadNeAIAAADKRngKdnvTpLwc9/PQMKljF3vrAQAAAPwU4SnImdQL5jt17CLLGW5fMQAAAIAfIzwFObPtgvlOnVmiHAAAACgP4SmImdwcafd2T9tK6mVfMQAAAICfIzwFsx2pUlGR+3lktNSmg731AAAAAH6M8BTELhyyp07dZTlC7CsGAAAA8HOEpyBmtm/xPLc6d7exEgAAAMD/EZ6ClMnOlPbv9rStToQnAAAA4GIIT8Fqx1bJuNzPY2Kl5q3trQcAAADwc4SnIGXSNpc0ErvJcvC/AgAAAHAxfGMOUl7znRIZsgcAAABcCuEpCJnsrB/Md+pmYzUAAABAYCA8BaOdqSXznaKZ7wQAAABUBOEpCF04ZE+JXZnvBAAAAFQA35qDkNleslgES5QDAAAAFUN4CjLMdwIAAACqhvAUbErNd2pjbz0AAABAgCA8BRmTxnwnAAAAoCr45hxkvO7vxHwnAAAAoMIIT0HE5GRL+3Z52sx3AgAAACqO8BRMmO8EAAAAVBnhKYhcuES5LmO+EwAAAFAZfHsOIt7znRiyBwAAAFQG4SlIuLKzfjDficUiAAAAgMogPAWJgtRNJfOdomKkFsx3AgAAACoj1O4C7Jafn69PPvlEy5cvV3p6umJiYtSzZ0/ddNNNatSokd3l+Uz+9xtKGondmO8EAAAAVFJQf4POz8/XX/7yF82cOVO5ubnq16+fGjVqpCVLluh3v/udjh49aneJPpO/Zb3nOfOdAAAAgMoL6itPH3/8sbZv367ExET98Y9/VEREhCTpiy++0H/+8x/9+9//1mOPPWZzldXnys5Swa7tnjbznQAAAIDKC9orT4WFhZo/f74k6c477/QEJ0kaP3682rRpo61bt2r37t12legzBVtTJFeRu8F8JwAAAKBKgjY8bdu2TVlZWWratKnatWtXantycrIkae3atbVdms9dOGRPidzfCQAAAKiKoP0WvW/fPkkqMzhJUvv27b32C2TMdwIAAACqL2jDU3p6uiSVu6Jew4YNvfYLVCYn23u+UyLznQAAAICqCNoFI3JzcyVJ4eHhZW4vngNVvN/FTJs2rVSf0+nUU089JUlq3LhxVcustrx13+n0+flOVkysmvTuz7C9ABQa6v6oNmnSxOZKUFWcw8DG+Qt8nMPAxzkMfHXhHAbtt2hjTLW2B4oL7+/kTOpNcAIAAACqKGivPEVGRkqS8vLyytxe3H/hKnzlee655y66PT093bYwZoZdrfqduil/y3rlNG2pEydO2FIHqqf4NzScv8DFOQxsnL/AxzkMfJzDwGf3ObQsS82aNavWMYI2PBUPpTt58mSZ20+dOuW1X6CyomMVkTxMEcnDlMdfNgAAAECVBe0YrjZt3Pc62rNnT5nbi+/vVLwfAAAAgOAWtOGpc+fOioqK0rFjx8oMUKtWrZIk9enTp7ZLAwAAAOCHgjY8hYaG6uqrr5YkvfHGG16r6n3xxRfat2+fOnfurI4dO9pVIgAAAAA/ErRzniRp4sSJ2rx5s7Zv3677779fnTt3Vnp6unbs2KHY2Fj94he/sLtEAAAAAH4iaK88Se57Mf35z3/WpEmT5HQ6tWbNGh0/flzDhw/X3/72NyUkJNhdIgAAAAA/EdRXniR3gLrpppt000032V0KAAAAAD8W1FeeAAAAAKCiCE8AAAAAUAGEJwAAAACoAMITAAAAAFQA4QkAAAAAKoDwBAAAAAAVQHgCAAAAgAogPAEAAABABRCeAAAAAKACCE8AAAAAUAGEJwAAAACoAMITAAAAAFQA4QkAAAAAKoDwBAAAAAAVEGp3AcHAsiy7S5DkP3Wg6jiHgY9zGNg4f4GPcxj4OIeBz65z6Iv3tYwxxge1AAAAAECdxrA9AAAAAKgAwlMQePjhh/Xwww/bXQaqgXMY+DiHgY3zF/g4h4GPcxj46sI5ZM5TEMjPz7e7BFQT5zDwcQ4DG+cv8HEOAx/nMPDVhXPIlScAAAAAqADCEwAAAABUAOEJAAAAACqA8AQAAAAAFcB9ngAAAACgArjyBAAAAAAVQHgCAAAAgAogPAEAAABABRCeAAAAAKACCE8AAAAAUAGEJwAAAACoAMITAAAAAFRAqN0FoObk5+frk08+0fLly5Wenq6YmBj17NlTN910kxo1amR3ebiE6dOnKzU1tdztv//979WrV6/aKwhl2r17t1JSUrRz507t2LFDp0+fVlhYmN59992Lvm7p0qWaP3++Dh48qNDQUCUmJmrixInq1KlTLVUOqfLnb8aMGZo5c2a5x7v++ut1yy231FS5+IG8vDxt2rRJ69at065du3TixAm5XC4lJCQoOTlZ48ePV0RERJmv5TPoH6pyDvkc+p8vvvhC27Zt0/79+3X27FkVFBSofv36SkpK0vXXX69WrVqV+bpA/BwSnuqo/Px8/eUvf9H27dvVoEED9evXTydOnNCSJUu0fv16Pf7440pISLC7TFRAcnJymf/4N2zY0IZq8EMzZ87U2rVrK/Wat99+W3PmzJHT6VSPHj1UUFCglJQUbdq0SdOmTdOAAQNqqFr8UFXOnyR16tSpzL9D27dv74uyUEHffvutXnnlFUlSq1at1LNnT+Xk5CgtLU0zZszQ8uXLNX36dNWrV8/rdXwG/UdVz6HE59CffPzxx8rNzVWbNm3UunVrSdKBAwf0zTffaMWKFXrwwQfVu3dvr9cE6ueQ8FRHffzxx9q+fbsSExP1xz/+0fPl+4svvtB//vMf/fvf/9Zjjz1mc5WoiNtuu03x8fF2l4FyJCYmqm3bturQoYM6dOigu++++6L7b9myRXPmzFFsbKwef/xxNWvWTJKUlpam6dOn66WXXlJSUpJiYmJqo/ygV9nzV2zUqFEaMWJEzRaHSwoNDdWYMWM0btw4z2dJkk6fPq2nnnpKe/bs0VtvvaX777/fs43PoH+pyjksxufQfzz44INq3769nE6nV/9XX32l1157TS+//LL+/e9/y+FwzxgK5M8hc57qoMLCQs2fP1+SdOedd3pdtRg/frzatGmjrVu3avfu3XaVCNQZEyZM0OTJk9W3b1/Vr1//kvt//vnnkqSJEyd6fVFITEzU6NGjlZ2drcWLF9dUufiByp4/+Jfhw4frrrvu8vosSVKDBg105513SpJWr16twsJCzzY+g/6lKucQ/qdz586lgpMkjRkzRgkJCTp9+rQOHz7s6Q/kzyHhqQ7atm2bsrKy1LRpU7Vr167U9uTkZEmq0lAVAFWXn5+vLVu2SJIGDhxYantx37p162q1LqAuatOmjSSpoKBA586dk8RnMNCUdQ4ReIqvNoWGuge8BfrnkGF7ddC+ffskqczgJJWMBS7eD/5t0aJFyszMlGVZatasmQYMGKDGjRvbXRaq4PDhwyooKFBcXFyZi7YUf2b5bPq/LVu2aO/evcrPz1ejRo3Uu3dv5ln4mWPHjkmSQkJCPEN/+AwGlrLO4YX4HPq/pUuX6vDhw2rWrJlnCkKgfw4JT3VQenq6JJW7ol7xQgPF+8G/zZ4926v9zjvvaNKkSbrhhhtsqghVdanPZkREhKKjo5WVlaWcnBxFRkbWZnmohG+++car/eGHHyo5OVm//OUvy13dDbVr7ty5kqRevXopLCxMEp/BQFPWObwQn0P/89lnn+nAgQPKy8vToUOHdODAATVo0ED333+/5wpUoH8OCU91UG5uriQpPDy8zO3Ff6EU7wf/1KVLF40cOVKdOnVSgwYNlJ6erpUrV2r27NmaMWOGoqKiNHbsWLvLRCUUf+bKGhdeLDw8XFlZWcrNzfW7fzAgJSQk6LbbblPv3r3VuHFjZWVlaevWrfrvf/+rVatWyeVy6cEHH7S7zKC3fv16LV68WCEhIbrppps8/XwGA0d551Dic+jPNm3apM2bN3vajRo10n333ed1RTDQP4eEpzrIGFOt7fAPP/zHonnz5po4caI6dOigJ554QjNmzNCVV1550b984F+KP3uWZV1yH/inYcOGebUjIiI0dOhQde3aVb/97W+1Zs0abd++3a/vUVLXHTx4UC+88IKMMbrtttvUtm1bzzY+g4HhYudQ4nPozx599FFJUlZWlvbv36+ZM2dq+vTpmjJliiZOnCgp8D+HLBhRBxUn9Ly8vDK3F/dzSTsw9ezZUx06dFB2drbS0tLsLgeVcKnPpuSeSCvx+Qw0DRo08CyZvGnTJnuLCWInT57Uk08+qaysLI0fP77U1Xk+g/7vUufwYvgc+o/o6Gh16dJFjzzyiNq3b68PP/xQO3fulBT4n0PCUx1UvJjAyZMny9x+6tQpr/0QeIpvCnjmzBl7C0GlXOqzmZubq6ysLEVHR/vdMAVcWvFyu6dPn7a5kuCUkZGhxx9/XOnp6RoxYoRuu+22UvvwGfRvFTmHl8Ln0L+EhoZq8ODBMsZ4Vs8L9M8h4akOKl7ac8+ePWVuL76/U/F+CDxZWVmS/PM3Mihf8+bNFRYWpoyMjDL/0Sj+zBbfnR2BJTMzUxKfSzvk5OTor3/9qw4dOqQBAwbonnvuKXNIEJ9B/1XRc3gpfA79T2xsrCR3OJYC/3NIeKqDOnfurKioKB07dqzMALVq1SpJUp8+fWq7NPhARkaGtm7dKqn85ejhn5xOp7p16yZJWrlyZantxX19+/at1bpQfcYYrVmzRpJYKrmWFRQU6Omnn9auXbvUs2dPPfDAA55VvX6Iz6B/qsw5vBg+h/4pNTVVktS0aVNJgf85JDzVQaGhobr66qslSW+88YbXqnpffPGF9u3bp86dO6tjx452lYhLSEtL05YtW0pNmDx+/LieeeYZ5eXlqV+/fuUu8wn/NW7cOEnuJeiPHDni6U9LS9OCBQsUGRmpkSNH2lUeLiIjI0NLly5VQUGBV39ubq5effVV7dixQ/Xr19eAAQNsqjD4uFwuPf/88/r+++/VpUsX/fa3v/XciLM8fAb9S2XPIZ9D/7N161atWLFCRUVFXv2FhYWaN2+evvnmGzmdTg0ePNizLZA/h5bx5+UsUGX5+fl67LHHtGPHDjVo0ECdO3dWenq6duzYodjYWD3xxBOeeTPwP0uWLNFLL72kBg0aqFmzZqpfv75Onjyp3bt3q6CgQK1atdKf/vQn1atXz+5Sg9769es1a9YsT3vHjh2yLMvrlxOTJk3yutL71ltvae7cuQoPD1f37t1VVFSklJQUuVwu/frXvy7zjuuoGZU5f8ePH9e9996ryMhItWzZUo0aNVJ2drb27Nmjc+fOKTo6Wr/73e/UuXNnO36UoDR37ly99dZbkqQBAwaUOz/itttuU1xcnKfNZ9B/VPYc8jn0P8XfWWJjY9W+fXvFxsbq3Llz2r9/v06fPq2wsDD98pe/9ApPUuB+DlmqvI5yOp3685//rI8//ljffvut1qxZo+joaA0fPlw33XQTi0X4uY4dO2rMmDHasWOHDh48qO3btys8PFxt27bVoEGDNGbMGJYo9xMZGRnasWOHV58xxquveJx3salTp6pt27aaP3++Nm/erJCQEHXr1k2TJk3iH/xaVpnzFxsbq+uvv147duzQ0aNHtXfvXjkcDsXHx2v48OEaP3685ybkqB3F81skafXq1eXud+ONN3qFJz6D/qOy55DPof9JSkrSj370I6Wmpmr//v3KyMhQaGio4uPjlZycrLFjx5b5C/tA/Rxy5QkAAAAAKoA5TwAAAABQAYQnAAAAAKgAwhMAAAAAVADhCQAAAAAqgPAEAAAAABVAeAIAAACACiA8AQAAAEAFEJ4AAAAAoAIITwAAAABQAYQnAAAAAKgAwhMAAAAAVADhCQAAAAAqgPAEAPBrkydP1uTJk/X999/bXUqNOXfunKZOnao777xTubm51T7e8uXLNXnyZP3rX//yQXUAgGKhdhcAAKi7Jk+eXOXX/uIXv9CIESN8V4wf++ijj5Sdna1bb71VERER1T7eoEGDNGvWLC1btkxjx45V+/btfVAlAIArTwCAGlOvXr0y/4SHh19yH6fTKUlq3ry5mjdv7vWauuTw4cP6+uuvFRcXp6uuusonx3Q4HJo0aZKMMXrnnXd8ckwAgGQZY4zdRQAAgsuMGTM0c+ZMz/Ng9n//939asGCBrr32Wt12220+O25RUZF+9rOfKSMjQ3/961/VoUMHnx0bAIIVV54AALBJbm6uli9fLkm6/PLLfXrskJAQDRo0SJL09ddf+/TYABCsmPMEAPBrxfOm/vznP6tr166e/uPHj+vee++VJP3rX/+SZVmaNWuWNm3apIyMDDVs2FBDhgzRhAkTPPOI9u/fr08++URbt25VRkaGGjVqpOHDh+v6669XaGj5/ySeOXNGc+bM0caNG3X8+HEVFhaqQYMG6tatm8aPH6+WLVtW6Wf79ttvlZOToxYtWqht27bl7rdjxw7NmzdP27dv15kzZ+RwOBQbG6smTZqoe/fuuuKKK9SoUaNSrxs6dKi+/PJLLV++XFOnTvXJfCoACGaEJwBAwNuzZ49efvllZWVlKTIyUkVFRTp27Jhmz56trVu36tFHH1VKSor+/ve/Ky8vT1FRUSosLNTRo0f14Ycf6sCBA3rggQfKPPa6dev0/PPPe1bBCwkJUWhoqI4fP65Fixbpm2++0c9+9jMNHz680nVv3LhRktSlS5dy91myZIn+/e9/q3iUfVhYmBwOh9LT05Wenq6tW7eqcePGZS6u0aFDB4WFhSkvL09bt25V7969K10jAKAE4QkAEPBefvlltW/fXnfccYdatmyp/Px8LVy4UG+//ba2bt2qmTNnav78+erbt69uueUWNWnSRLm5ufrkk080e/ZsrVixQiNHjlSPHj28jrtz5049++yzKiws1JVXXqlx48apWbNmnvDyySef6KuvvtLLL7+sli1bVnpe0fbt2yVJHTt2LHN7Xl6e3nzzTRljdPnll+vGG29UQkKCJPeQv8OHD2vFihWKi4sr8/WhoaFq3769tm/frtTUVMITAFQTc54AAAGvYcOGevjhhz3D55xOp6655hoNHTpUkjR79mx17NhR999/v5o0aSJJioiI0JQpUzxXfVasWFHquK+//roKCws1adIk3X333WrRooUcDvc/nY0bN9Zdd92la665RkVFRZo1a1alaj527JjOnj0rSeUO2Ttw4IBycnIUHh6uX/ziF57gVFx/+/btdeutt6pPnz7lvk/xsdPS0ipVHwCgNMITACDgjRs3TmFhYaX6e/bs6Xk+YcIEWZZV7j779u3z6t+7d6927dqlkJAQXXvtteW+d/Fwvc2bN8vlclW45tOnT3uel3flKCoqSpJUWFioc+fOVfjYF4qNjS31fgCAqmHYHgAg4JU37K1evXqe5+UNqSveJysry6t/27ZtkiRjjO6///5y37s4MOXl5encuXNe73kxGRkZnucxMTFl7pOQkKAWLVro0KFD+sMf/qDRo0erV69eat26tecK2KUUH/vC9wMAVA3hCQAQ8MpbRS4kJMTzPDIy8qL7FBUVefUXX6lxuVye4XWXkpeXV6H9JCk/P9/zvLyV/hwOh+6//3797//+r44fP6733ntP7733nsLDw5WYmKjk5GQNHz78ojcQLr7ZcEFBQYVrAwCUjfAEAEAZiq8otWjRQn//+999fvzi4XSS+6pXeVes2rZtq3/84x9at26dNm3apO3bt+vgwYPavHmzNm/erI8//liPPPKIWrduXebrMzMzJZV/dQsAUHGEJwAAylC/fn1J7oUdcnNzfX6PpAvnOWVmZl50uF9oaKiSk5OVnJwsSTp37pxWrlyp999/XydPntSLL76ov/3tb2W+tjg8lTevCgBQcSwYAQBAGTp16iTJvVjD6tWrfX78Zs2aeYYMHjt2rFKvjY2N1ejRo3XLLbdIct/nqrwFJY4fPy7JfQUNAFA9hCcAAMrQoUMHtWvXTpL0wQcfXHLBheIrPBUVERHhOf7OnTvL3OdS85SK5zNJKncBieJjJyUlVao+AEBphCcAAMpgWZZ++tOfKiwsTOnp6fr973+vlStXei0KcerUKX3zzTf6y1/+ov/+97+Vfo/iQFNeeFq+fLkeffRRff31115Xp1wulzZu3Kj33ntPkpSYmKjo6OhSrz9z5ozS09O93gsAUHXMeQIAoBwdO3bU7373Oz3//PM6fvy4nnvuOTkcDkVHRys/P98rSI0cObLSxx86dKg+++wzpaamKjs723Nfpwtt375d27dvlySFhYUpIiJCmZmZMsZIkho0aKCf//znZR5/7dq1ktyLThTfQBgAUHWEJwAALqJHjx765z//qa+//lrr16/XwYMHlZWVJafTqZYtWyoxMVH9+vVTjx49Kn3stm3bqmPHjtq5c6dWr16tESNGeG3v16+f7r33Xm3ZskV79uzRmTNnlJmZqcjISDVv3lx9+/bV1VdfXeZVJ0latmyZJOnKK6+sdG0AgNIsU/yrKwAAUOuWLl2qF198UV27dtWf//xnnx33+PHjuu+++xQREaGXX3653PtcAQAqjjlPAADY6PLLL1fLli31/ffflzv3qSo+/fRTGWP0ox/9iOAEAD5CeAIAwEYOh0O33nqrJOmjjz7yyTHT09O1ePFiNW7cWGPHjvXJMQEAzHkCAMB2ffr00dSpU5WVleWTG/Kmp6drwoQJ6tatm9dy5gDw/9u3gxIAAAAEYv1bW+HA79biQPn4PAEAAARmewAAAIF4AgAACMQTAABAIJ4AAAAC8QQAABCIJwAAgEA8AQAABOIJAAAgEE8AAACBeAIAAAjEEwAAQCCeAAAAAvEEAAAQiCcAAIBg7SRbW6/RyUEAAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t, v)\n", "\n", "# x,y 축 이름\n", "plt.xlabel('Time (s)')\n", "plt.ylabel('Velocity (m/s)')\n", "\n", "# 그래프 선 이름\n", "plt.legend(['Exact Solution'])" ] }, { "cell_type": "markdown", "id": "07b4daf8", "metadata": {}, "source": [ "## 수치해석\n", "이를 수치적으로 풀어보자. `scipy` 패키지에는 다양한 과학함수와 수치해석 기법을 제공한다.\n", "\n", "`scipy.integrate` 에 있는 `solve_ivp` 함수로 계산해보자." ] }, { "cell_type": "code", "execution_count": 10, "id": "8e7c75cc", "metadata": {}, "outputs": [], "source": [ "# solve_ivp 함수 호출\n", "from scipy.integrate import solve_ivp\n", "\n", "#solve_ivp?" ] }, { "cell_type": "code", "execution_count": 11, "id": "7301ede1", "metadata": {}, "outputs": [], "source": [ "# 우변 함수 작성\n", "def f(t, v):\n", " return g - c/m*v" ] }, { "cell_type": "code", "execution_count": 12, "id": "a92e6a03", "metadata": {}, "outputs": [], "source": [ "sol = solve_ivp(f, [0, 30], [0])" ] }, { "cell_type": "code", "execution_count": 13, "id": "cef610a2", "metadata": {}, "outputs": [ { "data": { "image/png": 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u379fZCw9e/YsdtzXrl3Dhg0bcOLECdy6dQvx8fG5Eo+SHrskco5AmJ+cydqAAQMKravRaNC7d29s27YN6enpuHTpkvzPFiU/jznZ2dmhY8eOhe6rb9++WLVqFQDg7NmzmDBhgrzu2LFjcuw3b97EzZs3C92XYaj99PR0BAcHo2XLlvnWK8n5JyLlMHkiokpn4sSJmDt3LlJTU/HXX3/h22+/lRMcIPfcTlOmTMl1s3dISAh0Oh0AfStBzolLi2IYqKG4Hj58KD9u2rRpkfWbNWsmP845NHRiYiISEhIAAC1atFCsNUEJM2fOxJo1awAAa9aswTfffCOvCwsLw65duwDoL5ALazEojFKvozGYmprC3t4eLVu2RJ8+ffDCCy+gXr16eept2rQJL7/8MuLj44u1X8P7oTCGFtPCCCHw3nvv4auvvpI/F0ocuySKilOp819e76PGjRsX+ZnMOUjKgwcPcq0zTCuQkZFRou8joPDvpOKcfyJSHpMnIqp07OzsMGrUKPzxxx9ITk7G1q1b5dYF8djcTo+PkFfci9P8aLXaEtVPSkqSHxdndKucdXJOApzzYjVnklgZdOzYER07dsT58+fx22+/4YsvvoC5uTkAfaug4TV78cUXS30MpV7HirBu3boSj8p47NgxTJo0CVlZWQCADh06oH///mjcuDHs7OxydXU0XFwb6hbGwsKiyDpLlizBF198AQAwMTFB//790b17d9SvXx9WVlZy68zVq1cxf/78Yh+7JIqKU6nzX17vI0tLyxLtK2ccQNm+kzIzMwtcV5zzT0TKY/JERJXS9OnT8ccffwDQX6QbkqejR4/KQzF369YNLVq0yLVdzuRj2rRpWLduXbnFmPNYBXW/yskwbDqAXENs5xza+PELr8pg5syZePHFFxEbG4u//voLzz33HIQQWLt2LQB9sjt27NhS71+p17Gy+vjjj+WE5Mcffyww0cz5vJSQmpqKzz//HID+dfLx8Smw+1lRXdzKk1Lnv7zeRyXd1+P/ALG2tkZcXBwaNmyI4ODgIvdFRJWb8e9IJiLKR9++fVG/fn0AgK+vr9z1pbCBIoDcXVmuXr1arjHWqVNHfmyYv6UwOevk3NbGxgZ2dnYA9PddGbokVhYTJ06UEzxDF74jR44gKCgIgH5gieL8d74gSr2OlVFGRoZ8z8sTTzxRaAvdf//9p+ixT548KV/Uv/zyy4Xet6P0sUtCqfNfXu+j27dvF/mZNHwWgLzd6dzd3QEA9+7dU7xLJBFVPCZPRFQpqVSqPF31kpOT8ddffwHQd1kZP358nu2cnZ3lG6zPnz9frheF7dq1k0dUO3LkSJHd/g4ePCg/fnwiUsPN3/Hx8QWOMFhWOUfwK0mCZmVlJY8m5uvri8DAwFwDRZSlyx6gH63MkChfunQJUVFRhdYv7HWsbKKjo+X3RePGjQutu3//fkWPHR4eLj9W4tiG+36UTu5znsOc5zY/mZmZ8ufDzMwMXl5e8jolP485xcfH48KFC4Xuy8fHR37cqVOnXOsMA8BkZWXhn3/+KXQ/RFT5MXkiokpr2rRp8gXbhg0bsGXLFrlb25gxY3J1d8tpypQpALJvli8vZmZm8rDCkZGRue7FelxAQAB2794NAHB1dc01NDQAOTkBgPnz5xf75v6SyNmdqKRdxGbOnCk//uKLL7Bt2zYA+gvFnBewpTV69GgA+ovjnINSPC4iIgIbNmwAkPv1r6xytsjdvn27wHqJiYn4+uuvjXLsCxcuyO/NwhjeP0p3L+zRowdq164NANi1a1eho9GtW7dOTq6HDRuWazh4JT+Pj1u+fHmB6yIjI/Hbb78B0P9TZ/DgwbnWG76PAGDRokUVfp8eESmLyRMRVVoeHh7yf23v3LmDDz74QF5X2Bwus2bNkkc827hxI15//XV5+N/8xMfHY8WKFUX+1zs/b7/9tpzgvfnmm/nOzxMWFoaxY8fK/wl/880388wBNHbsWHkY8OPHj2PKlCkF3muh1WqLdbH7OAcHB7l74KVLl0rUgtCmTRt0794dALB27Vr59Sxrq5PB7Nmz5YEoli5dmu8Q84mJiRg/fjzi4uIA6Of8KWpYc2Ozs7OTR3U7d+5crrmgDJKSkjBu3Dh5uHaldOrUSX5vrlmzJt/7bYKCgjBmzJhiDRLRqFEjAPqupampqYrFqdFoMGfOHAD65Hns2LHyvE85+fn5yfMkqVQqvPPOO3nqKPV5fNwff/yBH374IU95cnIyJk6cKA8K8cILL8De3j5Xna5du2LkyJEA9F0FR4wYUejofpmZmdi2bRu+++67QmMiIuPggBFEVKlNnz5d7qZjGIq4QYMG6NOnT4HbWFtb4++//4a3tzcSExOxcuVK/PXXXxg3bhy8vLxga2uLxMREBAcH48yZMzh8+DAyMjLw66+/lji+Hj164K233sJXX32FhIQE9OzZE8899xy8vb2h0Whw6dIlrFmzRh5yuGfPnvlOuGliYoItW7agW7duiImJwe+//47Dhw9jwoQJ8PLygqWlJaKionDhwgXs3LkT5ubmhU48WpC+ffti+/btuH37NsaPH4/Ro0fnutjr3bt3gaN4vfzyy/Dz85OXra2tMXHixBLHkB8PDw989dVXmDVrFjIzMzFy5EiMHj0agwcPho2NDa5fv461a9fKcxA1a9YM//d//6fIscvb66+/jlmzZgEAnnnmGUyaNAk9e/aEjY0Nrl27hnXr1uHBgweYPHlyqd6DBXFzc8OYMWPw119/IS4uDl5eXnj55ZfRtm1b6HQ6+Pn54ddff0Vqamqxjt2vXz/4+/sjOTkZI0aMwNSpU+Hk5CQnK507d4aDg0OpYn3nnXewc+dOnDx5EleuXIGnpydmzJgBLy8vpKen48iRI/j999/lhOfdd99F165d8+xHqc9jTu3atUNcXBxeeeUV/P333xg1ahTs7e0RGBiItWvXyl2DGzVqhM8++yzffaxbtw6BgYEICAiAr68vGjdujDFjxqB79+5wcnJCWloaHj58iAsXLuDAgQOIiYnBCy+8UKrXkojKmSAiqsSSkpKEjY2NACD/fPzxx8XaNiAgQHh5eeXatqAfMzMzsXfv3jz7+Pjjj+U6Pj4++R5Hp9OJ999/X6hUqkKPMWzYMJGYmFhozIGBgaJNmzZFxtuoUaM8265bt05ev27dunz3f/HiRWFhYVHgfoODgwuMLTU1VTg4OMh1X3zxxUKfS2msXLlSmJmZFfrcu3TpIh4+fFjgPopzzkpi6tSpRb6uhdHpdGLKlCmFPqennnpKpKSkyMu9e/fOd1+9e/eW6xRHdHR0oZ8BlUolPvnkE+Hj41Pk5+v+/fvC2dm5wH3lfK2Ls7/HxcfHi8GDBxf6OpmYmIiPPvqo0P0o9XnMeS4uXLgg3NzcCtxX48aNxe3btwuNKy4uTowdO7ZY30cAxPz58/PsozifcSIqX+y2R0SVmpWVVa5hsCVJkgeSKErLli1x8eJF/P3335gyZQqaNm0KW1tbmJiYwN7eHl5eXpgyZQrWr1+Phw8f5rlXobgkScKSJUtw6dIlvPrqq2jRogWsra1hbm6OBg0aYMKECdi9ezd27dpV5DxOTZs2xaVLl7Bx40Y888wzqF+/PiwsLKDRaODm5oYBAwbg//7v/3D8+PFSxdquXTucP38eM2bMQPPmzUs0Sp65uTl69OghLyvVZS+nWbNm4caNG3j77bfRtm1b2NnZQaPRwN3dHU8//TT+/PNPnDx5Eq6uroofu7xIkoQNGzZg48aN6Nu3L+zt7aHRaFC3bl0MGzYMmzZtwj///FMu8/Y4ODjAz88PS5cuRYcOHWBlZQULCwt4eHhg2rRp8PPzw4IFC4q1L3d3d1y4cAFz5sxB69atYW1treiEzra2tti7dy927dqF8ePHo379+jAzM4O1tTVatGiBV199FZcvX8aiRYsK3Y+Sn0eD9u3b49KlS/joo4/QunVr2NjYwNraGu3bt8eSJUvg7+8PDw+PQvdhZ2eHzZs34/z585gzZw7at28PR0dHqNVqWFtbo2nTphg5ciSWL1+O27dv49NPPy32a0dEFUcSopKNiUtERJVSfHw83NzckJKSAi8vL1y6dMnYIRGVG0Ni2Lt3bxw5csS4wRBRpcGWJyIiKpZffvlFHsTi5ZdfNnI0REREFY/JExERFSkpKQlffPEFAMDe3h6TJ082ckREREQVj6PtERFRvs6cOYOYmBiEhYXh22+/lUe6e/vtt4t9rwgREVF1wuSJiIjyNW/ePHmYeINOnTrlO78OERFRTcBue0REVCiNRoNmzZrhgw8+wMGDB4ucUJSIiKi64mh7RERERERExcCWJyIiIiIiomJg8kRERERERFQMTJ6IiIiIiIiKgckTERERERFRMTB5IiIiIiIiKgYmT0RERERERMXASXIrQFhYGIw5IryTkxMAICoqymgxUNnwHFZ9PIdVG89f1cdzWPXxHFZ9xj6HkiTB1dW1TPtg8lQBhBBGTZ5yxkFVG89h1cdzWLXx/FV9PIdVH89h1VeVzyG77RERERERERUDkyciIiIiIqJiYPJERERERERUDEyeiIiIiIiIioHJExERERERUTEweSIiIiIiIioGDlVeiSk1jKNhP1V5WMiajuew6iuPcyhJkmL7IiIioqIxeapktFotUlNTkZGRodhFVmxsLABAp9Mpsj+qeDyHVV95nENJkqDRaGBhYQG1ml/nRERE5Y1/bSsRrVaL+Ph4mJubw97eHiqVMr0qDRdVWq1Wkf1RxeM5rPrK4xzqdDqkpaUhPj4ednZ2TKCIiIjKGf/SViKpqakwNzeHlZWVovs1dO1hF5+qi+ew6iuPc2hiYiJ/X6SmpsLGxkaxfRMREVFeHDCiEsnIyIC5ubmxwyCiKsbMzAwZGRnGDoOIiKjaY/JUSQghIIRQrKseEdUcJiYm8ncIERERlR9eqRMRERERERUDkyciIiIiIqJiYPJERERERERUDEyeiIiIiIgoj503YhCZnFlkvcjkTOy8EaPYtpUZhyqnSs3d3b3IOmPHjsXXX39d/sEYycOHD/Hjjz/Cx8cH9+7dgyRJcHJyQoMGDdC1a1eMHDkSjRo1KtMxnnnmGZw8eRKnTp1CvXr1FIo8f2+88Qa2bNmCLVu2oHv37uV6LCIiIiqdnTdisOZ8BHbdjMXi/vXhbGWab73I5Ex8dDAEYUn6RGlEC4cybVvZMXmiKmHs2LEFruvcuXMFRlJyy5Ytw/Lly7F8+XKMHz++RNteuXIFEyZMQFxcHBwdHdG1a1fY29sjIiICFy9exPHjx2FqaopZs2aVU/Ql16VLF9y/fx+hoaHGDoWIiIhKqWs9G+y6GYuwJH2Ck18SlDP5cbU2Rdd6NmXetrJj8kRVQnVuWSrMG2+8gbi4ODz33HP47LPPoFZnf2TT09Oxf/9+mJmZGTHCknv//fcxa9asYrUqEhERkXE4W5licf/6coLzeBL0ePKTc12B2zqjyG0rO97zRFRJ3blzBzdu3ICpqSk+++yzPBMom5mZ4amnnsKgQYOMFGHp1K5dG02aNIGFhYWxQyEiIqJCGJIgV2tTOQmKTM4sVvKT37ZhCWkIS0irsokTwOSJqpnFixfD3d0dM2fOzLMuKioK7dq1Q/369XHu3Dm5PDw8HKtWrcKYMWPQsWNHNGzYEO3atcOMGTNw6dKlAo+VkpKClStXYtCgQWjWrBmaNm0Kb29vLFiwAPfv3weg78K2fPlyAMDcuXPh7u4u//j5+RX6XKKjowEAVlZWeRKnoqSmpuJ///sf+vbti8aNG6NFixYYPXo0/vnnn2Lv4969e3B3d8czzzyT7/ply5bB3d0dmzZtAgD4+fnB3d1dfu45n2uXLl3k7d54440Cn39oaCjmzZuHzp07o1GjRmjbtm2B5yFnfKmpqViyZIm8XY8ePfDdd99x0lgiIqrxhBAQ2kyItFSI5CSIhFiImCiIyDCIsPsQ9+9C/Hcb4s5NiFsBENcvQ1y9AHH5LMSFk3AMOI1PHUJRW61FWFImZv4dhJl/ByEsKRO1VRn4VLoEx4Obodv2C3Rb1kG3aQ10f/wA3a+r4Ljle3wafQC1dckIS8rEuLWnMW7t6SqbOAHstkfVzLx583Ds2DHs3LkT/fr1y3Wv1FtvvYXIyEjMnTsXTzzxhFy+f/9+fPbZZ2jYsCFatGgBa2tr3L17F3v37sXBgwexYcMG9O7dO9dxwsPDMWHCBAQGBsLe3h49evSAWq3G3bt38fPPP6NVq1YYP348hg0bhmPHjiEgIACdOnVCw4YN5X24uLgU+lzc3NwAAHFxcfjnn3/w9NNPF+s1SEpKwtixY+Hv7w9HR0f069cPqampOHHiBE6fPo3z58/j008/Lda+SsLFxQVjx47F7t27kZKSkuu1d3Ao+gbQ69evY9y4cYiJiUGTJk0wZMgQhIaGYu/evfj333/x7bffYsSIEXm2y8jIwLPPPovAwEC0a9cOTZs2xalTp7BkyRIkJSXh3XffVfR5EhER5UfosoBMLaDNADIzgMxMQJuZ9/ejHyHX0T4q0+Zan7tcC6HNBLIer6t9VPbYsqEsSwtkZZX5uTkB+NTMHq91mQetSp8+qHVafHryKzilx6Gwf1Xqtz2Ze1sJVTJxApg8VQlCCCA1ufTbP7pPRmi1SoVUPBZWkCSpQg+p0Wjw3XffYdCgQZg/fz66du2KevXqYcOGDTh48CA6dOiAOXPm5NqmU6dO+Pfff+Hp6Zmr/MiRI5g+fTo++OADHD9+PNdzef311xEYGIiRI0fiyy+/hKWlpbzuzp070Ol0AIAFCxZg2bJlCAgIwMSJE0s0YIS7uzt69eqFo0eP4qWXXsL69evRq1cvdOjQAR06dCiw29vSpUvh7++PJ598EmvXroWVlRUAICgoCGPGjMHatWvRu3dv9OvXr9ixFEeTJk3w9ddf4+TJk0hJSSnRfWpCCMyePRsxMTGYNWsW3nvvPfn13rVrF1555RW8/fbb6Nq1K5wNHaYfOX/+PLp06YJjx47JSdrly5fx1FNP4aeffsKsWbPk14CIiGoGodUCGen6JCYjHcgw/E4HMvW/RcajJCcj41GZIenJ+WNIcjKy12szs5MjOQHKUCRJocqPyVNVkJoM3ZxnS715hoKhlIRqxR+ApbUi+ypscIG1a9di8ODB8nKTJk0wf/58fPjhh3j99dexdOlSLFq0CFZWVli5cmWuQRcAoGXLlvnu19vbG8OHD8e2bdtw48YNuZ5hlDsXF5c8iRMAeHh4lPZp5vHdd9/h9ddfh4+PD/z8/OSubqampujVqxfmzp2Ldu3ayfVTUlLw559/QqVSYcmSJbmShiZNmmDOnDmYP38+fv75Z8WTp7Lw8/PD9evXUb9+fcybNy9Xojp8+HD8888/2LNnDzZt2pRnZEGVSoUvv/wyV+uWl5cX+vTpg3///ReXL1/mkOhEVCF23ohB13o2Rf43PTI5E6fuJVaJYZnLi9Dp9IlMelqOn1QgXV8mDGUZaXJZgokEkZ4GXXw8hGFbQ0L0+A8TmeIxUQMmJoBanf3Y5PHHJog0s8MCl6HQqtRQiywAErQqNRZ0mYNFGafgrNI+qm8CqEyyt1WZIFIyw4LUZtDq1FA/aqPSCqnAUfgqOyZPVCUUNlR5fonVtGnTcPjwYRw6dAhPP/00UlNTsWzZslzd5nJKT0/HkSNHcPHiRcTExCAjQ59yXr9+HQAQHBwsJ0/Hjh0DAIwaNSpP4qQ0BwcH/Pbbb7h27Rr27t2LM2fOwN/fH4mJiTh06BB8fX2xcuVKPPXUUwAAf39/pKWloUOHDvkmcWPGjMH8+fNx9uxZCCEqvGWwIGfOnAEAPPXUUzAxMcmzfsyYMdizZw9Onz6dJ3mqV68eGjdunGcbw/OPiIgoh4iJiHKrzvPaAI96wWSkA6kpQFoKkJqq/52eCpGaCqTl+El/tC4tDSI9FUhLyy7PmSyVUEo5PK9ypzYFTE0f+63R/1arc5VLJursOvKPOu9vQz0TNSS1+lGZYZ2Jvp6JOrturt8m+rqPEp3iXAdEJmfi44MhCJfvU9L/zdW/j62wwGlwge/5yORMLDgYgnCdfttV49oBAF7dfKnQYcwrMyZPVCWUZqjyZcuWoWvXrkhMTMSAAQMwYcKEfOtdv34d06dPx7179wrcV1JSkvz4wYMHAIAGDRqUOKbS8vLygpeXF7RaLTIzM3HixAksWrQIN27cwHvvvYd+/frBysoK4eHhAFDgRLd2dnawtbVFQkICEhMTYWtrW2HPoTBhYWEAgLp16+a73lBueH451alTJ99tDK1u6enpSoRIRFSoyjyvjRBCn7ikpOhvA0hJBlKTIR791i+nyImRSH1UL0cZUlMBoauQeMuFRgNozABTM33yojHTlxkem2og5VxWmz5ab6ZPVDQaQJ2jjqkpoM752DTvY7W60vyTsrQKG1WvsGHMC9rW1da8WNtWZkyeqgILK30XuFIydFPTGuGeJ2M6cOAA0tL0/9kKCgpCSkpKnpYiIQRmzpyJe/fuYfLkyZg8eTIaNGgAKyv9/Vqff/45vv3223xHbTPWF6KpqSm8vb3RqlUrdO/eHfHx8Th37lyuQS2KE1tZ4zfc16WkomLKb31V/8NERNVDWebEKQ45AUpOApIT9b9TkiCSk+THSNE/FqnJ2WWG5KgcvrMVI6kAMzPAzEL/W2Oea1kyMwc05rCwrwXJzAwpWbpHyY/+R7/eLJ8fDWBmrm/V4d+KEivqPVvYe74s21Z2TJ6qAEmSynTvkPQoeZIqOnkyojt37mDhwoWwtLREr169sG/fPixcuBBffPFFrnpBQUEICgqCl5cXli5dmmc/ISEhecoMo+DdvXu3XGIvLmdnZzRp0gT+/v6IiYkBoJ9DCcg/bgBISEhAQkICLC0tYW1d+HvK1FT/BZacnP9gJYYWOCW4uroCQIGtf6GhoQCKHqGQiMiYCrogBJDrQnJRX3c4ZSVDPEgAkhKBpASIZP3vXMuGJMnwO6uS/B03MdEnNhaWgLlFrh/J3AIwt9SvN7cAzM0BMwtI5ub6ZTMLfUJjZlg217f6FCO5sX00YFBaZGR5P0MCcOpeYpHJ/uPvecO9fGXZtrJj8kTVjlarxezZs5GSkoIvv/wSI0eOxMCBA/H777+jb9++uQaXiIuLA5B/16+4uDgcPXo0T/mTTz6J//u//8P27dvxzjvvFDnZqyEJySrhzatF3ZOUlZUlJxuGpKlt27YwNzfHpUuXcOfOnTz3PW3btg0A0Llz5yL/UDk4OMDU1BQhISHQarW5BtrIyMjAqVOn8t3O8Hwf36YwnTt3BgDs2LED8+bNy3Pf09atWwEg13xRRESVhcjKApITgIR4OCXG41OnRMxPtUVYEjBz+y0AgFZSoXZGHD7x2wDH3Q+gM9Y8dBoNYGGtT3wsrQALS0gW+t947LdkYflo2VKfEFk8SoyKmexQ1WZIZIoaBMWQBOVMfsqybWXH5ImqnWXLluHSpUsYNGgQnn1WP0rhypUrMXLkSLzzzjvo0KGD3ILRqFEjqFQqnDhxIleykZaWhvfee09OrnJq3749unfvDj8/P8ybNw9ffPFFrgQqODgYWVlZaNKkCYDsxOb27dsleh4BAQH47LPPMHPmTHh7e0Olyp7TOjU1FZ988gliY2Ph4uKCjh07AgAsLS0xYcIErF+/Hh9++CHWrl0rd1W8ffs2VqxYAQCYPn16kcfXaDTo0KEDTp8+jfXr12PGjBkAgMzMTCxcuLDA1i1XV1cEBwfj9u3baN68ebGea/fu3dGyZUtcv34dX375Jd599135D/O+ffuwd+9eWFlZYdy4ccXaHxFRWQldFpCYAMTHAgmxEPGxQEKc/CNyPEZyIpAjGSpwTpzzq+CcHlf24Cws9T1SLK0AKxvA0hqSlbW+zPDb0gqSoY7ht4UlJHXl7xZFlUdxExpnK9M8dcuybWXG5ImqhDfeeKPAde7u7njnnXcA6Edt++677+Ds7Iwvv/xSrtO+fXu88cYb+OqrrzB37lz8+uuvkCQJTk5OmDhxIn7//XcMGDAAPXr0gLm5Oc6cOYOsrCyMGzcOmzdvznPMb775BuPGjcO2bdvg4+ODzp07y5PkBgQEYNmyZXLy1Lt3b5ibm+Onn37CzZs3Ubt2bUiShJkzZ8p18iOEgK+vL3x9feHg4IC2bduiVq1aiImJweXLlxEXFwdzc3OsWLECZmZm8nbvv/8+Lly4gKNHj6Jbt27o2rUrUlJS4Ofnh7S0NLzwwgvo379/sV/3SZMm4eOPP8aOHTvg4uICf39/pKamYuzYsdiyZUuebQYMGICTJ09i/Pjx6N69OywtLeHg4IAPPvigwONIkoSVK1di7NixWLlyJfbt24dWrVohNDQUZ8+ehVqtxrJly9htj4jKTGi1+oQnPgaIj4GIiwHiYoD4WP3j+JhHSVF8+Q+QYKIGrG0Baxv5t2Rlq39sZf1o2UafIFnZ6OtZWMnd8Ymo4vHTR1VCfhfpBp6ennjnnXeQmJiI119/HVlZWVi2bBkcHR1z1TPMl+Tj44N169bh+eefBwB8/vnnaNy4MTZu3IgTJ07AxsYGTz75JN59911s2rQp32PWqVMHe/bswU8//YTdu3fD19cXarUabm5umDFjBnr27CnXdXV1xc8//4z//e9/OHPmjHwP0ejRowtNnlq0aIFNmzbhyJEjOHPmDG7evImoqChoNBrUq1cPY8aMwYwZM1C/fv1c21lbW2Pr1q1YvXo1duzYgX///RempqZo27Ytpk6dipEjRxb6WufUq1cvrFu3Dv/73/9w9epVWFhY4Mknn8SHH36Yb1IJAC+88ALi4+PluZkyMzNRt27dQpMnQD/f1v79+7FixQr4+Phg9+7dsLGxweDBgzFr1iy0b9++2HETUc0k0tOB2CggNgoiNlr/OC4GIi4aUYnx0MVEQhcXk6uVSFGmGsDWHpF2dbDA/Wn9nDjQQZ4Tp9d7WNxGBWdHO8DGTn+PELu/EVUpkshvGDFS1MOHD/MdrS0nIQSio6Ph6Oio+Bep0UbbI8XwHFZ95XkOy/P7g/ScH92oHskb1Y1GZGXpW4ViIiGiI4EY/Y+IiQJiooC4KP1gC0rTmAF2tQA7B8DWHpKtPfDoR35sY6f/bWaOqBRtnlHGAJRppD3S4+ew6jP2OZQkqcApToqLLU9ERERkdEKr1bcURYVDREcA0ZFAdI7HsVHKDrdtaaVPiOwdID36bUiSJLtajx7X0o8eV0xlmROHiKoGJk9ERERU7oQQQGI8EBkGERUORIVnP44MA2KjlbnHSFLpE6FajkAtR0j2+t+29RrCxNEZcZIJYOcIKce9okqozvPaEFE2Jk9ERESkCKHT6QdfiHwIEfEw+3fEQyAiTD/Ja1nZ2AEOzoCDEyRHF6CWEyQHJ6DWox+7WpAem+4AACwedReSyqm7UHWe14aIsjF5IiIiohIRiQlAeChE+AP974gHQPgDIOIBkJFRtp3bOwCOLpAcawNOLo8euwCOzkAtZ8VbjJRSnee1IaJsTJ6IiIgoD5GVpe9aF3YfIiz00e/7QNj9sg3MYGEFONcGnFwhOdcGnGpDcnIFnGoDjs6QTDXKPYkKVl3ntSGibEyeiIiIajChzdR3q3t4D+LBvUe/Q4DwUKC0o0Pa2gMudSA51wFcXAHnOpBc6gDOrpCsbRWNn4ioIjF5IiIiqgGETgdERwCh/0GE/pf9OzwUyMoq+Q4trYDa7pBquwG13fSPXdyA2nUgmVsq/wSIiCoBJk9ERETVjEhNAe7fhbgfDNwLhrh/F3hwr+QDNkiSvjuda11Iru6Aqzsk17qAa13Axo7zihFRjcPkiYiIqIoSQuiH+A65DRFyB+JeMHA/WH+vUkmoVICLG+BWD1KdekCdepDc6gO13SBpKucADURExsDkiYiIqAoQQuiTov+CIEJuQ/x3B7h3Rz93Ukk41QbcG0BybwC41df/dnWHpOZ8Q0RERWHyREREVMnILUp3b0H8FwRx9xZwNwhISSr+TiwsAfeGkOo1BOo20idJ7vV5PxIRURkweSIiIjIykZqiT5Tu3IQIDgSCA4GEuOLvwMEZqO8BqZ4HpHqNgLoN9UOA854kIiJFVZvkaeHChQgICChw/QcffIB27drlKff19cW+fftw//59qNVqNGvWDKNHj0bz5s3LMVoiIqqphE4HPLwPcfs6YEiWHt4DhCjeDlzqQGrQRJ8s1fcA6jWGZMPhv4mIKkK1SZ4MunTpAnNz8zzlDg55J6PbsGEDdu/eDY1Gg7Zt2yIzMxP+/v64fPky5s6di86dO1dEyEREVI2J9DR9q1LQdYig68CdG0BKcvE2dnQBGjaB1KAppIZNgAaNIVlal2/ARERUoGqXPE2ePBkuLi5F1rt69Sp2794NGxsbLF68GHXq1AEABAYGYuHChVi1ahU8PT1hbc0/Usbk7u4OALCzs8PJkydhZ2eXp86yZcuwfPlyvP/++5g1a1ZFh2gUzzzzDE6ePIlTp06hXr16lfq4WVlZ2LhxI7Zu3YobN24gJSUFtWrVQu3atdGhQwf06dMHAwYMKFNcmzZtwty5czF37ly89dZbZdpXUfz8/DB27FiMHTsWX3/9dbkei8rfzhsx6FrPBs5WhQ+WEJaQBt/b0ehbV1PkPkVSAhAUABF4DeJWgH5Qh+LMo2RpBTRsBsmjOSSPZkCDJpBs7Yv5TIiIqCJUu+SpuHbu3AkAGD16tJw4AUCzZs0wYMAA7N27Fz4+PhgxYoSxQlTUPwFR6OxuVeQFQmRyJk7dS8SIFnlb6owpPj4eP/30E95++21jh0IlkJGRgWnTpsHX1xcmJiZo37493NzckJ6ejmvXrmHDhg04fvx4mZMnJRmS8eXLl2P8+PHGDofK0c4bMVhzPgK7bsZicf/6BX4/RiZnYsGuK3gQn4bkji55vh9FXAxE4FXgVgDErWtA6H9FH1xS6Ue8a9wc8GgOqVFz/bDgKpUST42IiMpJjUyeMjIycPXqVQBA165d86zv2rUr9u7di/Pnz1eL5OmfgCj8eDYMO66bFnmB8NHBEIQlZQJApUmgVCoV1Go11qxZgxkzZsDe3t7YIRndihUrkJqaCldXV2OHUqiff/4Zvr6+qFevHjZu3IiGDRvmWn/16lUcPHjQOMGVUvv27eHr6wsbGxtjh0Jl1LWeDXbdjEVYkv67L7/vx5zfi2525uhazwYiMR64eQXi5hWIG/5AWGjRBzO30CdJjVtCatICaNQckgVHvSMiqmqqXfJ0+PBhJCUlQZIk1KlTB507d4aTk1OuOg8ePEBmZiZsbW3h6OiYZx+NGjUCAPz3XzH+e1gFdKtvix3Xo4t9geBqbYqu9SrPhaGpqSkmTJiADRs24Mcff8S8efOMHZLRGbozVnZ79+4FAMyZMydP4gQArVu3RuvWrSs4qrKxsLBAkyZNjB0GKcDZSv8PJcN33+Pfjzm/F+uYAUszz8D6y2PQFadlydYeUtNWQLNWkJp4AnUbQFKZlPMzIiKi8lbtkqdt27blWv71118xZswYPPPMM3JZVFQUAOSbOAGAubk5rKyskJycjNTUVFhYWBR6zLlz5+Yp02g0WLp0KQDkSd7yI4RAbGws1Gq14kPL1raRsHSwB97bd0e+QPh8UCO4WOv77kckZeRKnHKuqyzefPNNbNy4EWvXrsUrr7yCWrVqyetUj7q5GFqoDEaNGgU/Pz+cPXsW9evXz7W/kJAQdOrUCd27d8f27dvl8i+//BJfffUVVqxYgZYtW2Lp0qU4d+4cVCoVevXqhU8++QRubm5ITk7GV199hZ07dyIiIgINGzbEO++8U2BLZUBAAFauXAk/Pz/ExMSgVq1a6NOnD9566608seWMoVmzZli2bBnOnz+P2NhYHDp0CK1bty70uUVHR+P777/HgQMHEBISAlNTU9SrVw/9+/fHzJkz5cFTwsPDsWXLFhw8eBDBwcGIjo6Gvb09OnXqhNdffx3t27fP8zwM700TE5Ncr3VBYmJiAADOzs7Fqp/TwYMHsXr1aly+fBlpaWmoW7cuhgwZgtdffz3PvW8mJvqL0rK+B5544gncu3cPAOR7qAy2bduGHj164MSJExg9ejTGjx+Pb775Jtc+tVot1q9fj02bNiEoKAiAvivwxIkTMWXKlDyvW874rl69ipUrV+L69eswMzODt7c3Pv74Y7i5uRX5WgkhoFKp4OzszKGpS8jZGVg1zgGztuq75S3wCcXKUZ7QBgdh/vEohGVpUDs1GgtProZ1elyB+1E5u0LTqh00rdpD49kOJm71eC4qGcNnz9nZ2ciRUGnxHFZ91eEcVpvO1S1btsSsWbOwcuVK/Pbbb/j6668xYcIEmJiYYPPmzdizZ49cNy0tDYA+wSmImZlZrrpVnYu1Bp8PagRXa1OEJWXi/f3BiEjKQERSBt7fH1ypEycAqFOnDiZNmoSkpCR8//335X68CxcuYMSIEQgNDUWvXr1Qq1Yt7NixA8888wwSEhIwevRobNy4ES1atEDHjh0RGBiIF198ET4+Pnn2tWvXLgwaNAjbtm1D7dq1MWjQILi4uGDjxo0YNGgQbty4kW8MJ0+exFNPPYV79+7B29sb3bp1K/Ji7ObNm+jXrx9WrlyJuLg49O3bF927d0dGRgZWrFiB69evy3X37duHRYsWISwsDC1btsSQIUPg6uqKPXv2YMSIEThy5EiZXkMA8v2Ef/zxB7RabbG3W7FiBSZNmgQ/Pz+0bdsWgwcPRmpqKr799lsMGTIEERERZY4tP8OHD0erVq0AAJ07d8b48ePln6IGosnKysLUqVPx4YcfIjg4GL169UKvXr0QFBSEd999Fy+88AJ0Ol2+265fvx4vvPAChBDo27cvrKys8Pfff2PMmDFITU1V/HlSbq625vimTx3UMc3Cg/g0jP/5LCb5xODho8Tp00ur4fxY4qSq5QTzXgNh+9r7cPrhLzj/uA32b3wMywFPQe1en4kTEVE1VW1anh6/sdvNzQ2jR49G48aN8dlnn2Hz5s3o378/NBqNfuZ2oNA/bqK4820AWL58eaHro6KiityfEAI6nQ5arVbxP7qGLN/BXJWri8qL2wMBAFod4Gqt777iYK4q0UVuRdFqtXjttdfwxx9/YO3atZgxY4bcgmK4IDW8fgaG1zwrKyvPc8p6NPKVECLXOsO+NmzYgIULF+LFF18EAGRmZmLy5Mk4duwYhg0bBkdHRxw7dky+/+rPP//E22+/ja+//hpPPvmkvL+QkBDMmjUL5ubm+PPPP3PdY7dlyxa88cYbmDNnDnbv3p0nho0bN+LDDz/Eq6++Kp9DrVYLrVab73PTarV4/vnn8fDhQ7z88st4//33YWqa3T3z6tWrcHBwkOt36NAB//77Lzw9PXO9NkeOHMH06dPx7rvv4vjx47nej4W9pvmZOHEiTpw4gf3796Nz584YPHgwnnjiCTzxxBMFtqhcunQJS5cuhbW1NTZu3Ci3gKWnp+P111/Hrl278P7772P16tXyNobzWdb3wEcffYRly5bh2rVrmDBhQp7vFa1WW+CxfvjhBxw8eBAtW7bExo0b5Rbn8PBwjB07Fnv27MH69esxefLkPPGtW7cOf/75J3r27AkASE1NxYQJE3Du3Dls3boVEyZMKPR1Nnx/REZG8qK9mERmpn5EvKvnIa6ch+rhPSw0s8drXeZBq9J/3tQ6rZw4SdY20LR5AhkezSG1aAvUdkemJCETQDIAPOrRQJWX4T/dkZGRRo6ESovnsOoz9jk03NZTFtWm5akgXl5eaNy4MVJSUhAYqE8WDN3w0tPTC9wuIyMDAPKdM6oqM/TxV6v0SZNWB6hVKHQgicrC1dVVbn3KeeFcHrp27SonToD+vqvnn38eAHD79m18+eWXuQauGDduHBwcHHD+/HlkZmbK5WvWrEFqaio+/PDDPIOTjB07FoMHD8alS5dw5cqVPDG0aNECr7zySrFj3rNnD4KCgtCyZUt89NFHuRInQH9/Uc6EpWXLlnkSJwDw9vbG8OHDcffu3QJbxYpr1KhR+Oijj2Bubo7Q0FC522WnTp3g7e2N9evXy8mIwbp166DT6TBjxoxcXQfNzMzw2WefwdzcHHv27MHDhw/LFJvSfv75ZwD6CbtzdtWtXbs2PvroIwD690N+XnzxRTlxAvTfUS+//DIA4NSpU+UVco0j4mOhO3YAWd99Bt2bk6BbPh/iwN/6CWrzI0mQBo2C6oNlcNmwF7XeXQKV91BIrnWZpBIR1VDVPnkCII9IFhcXByD7HqTo6Oh866elpSE5ORlWVlZF3u9EFeu1116Dubk51q1bJ99PUx5yth4ZNGjQAABQr149eVARAxMTE9SrVw+ZmZm54jp27BgAYNCgQfkep1OnTgD0rS2P69+/f4ku0I4fPw4AmDRpknwfWFHS09Oxf/9+LF26FPPmzcMbb7yBN954Q+7eFxwcXOzjF+SVV17B2bNn8fnnn2PEiBHy/FC3bt3Chx9+iJdeeilXd7YzZ84A0Cdej3NyckLv3r2h0+lw7ty5MsemlNDQUISGhsLFxSVXEmQwYMAA2NnZISgoKN/vnd69e+cp8/DwAIBy66JYEwghIELuQLdrI7I+ewu6t6dC/PItcOk0kJ67S3akmT0WdHwVWpUaaklALQFayQQLdG0R5dIQkgkHeyAiomrUba8wycn6mdwNrUhubm4wNTVFQkICoqOj8wwcYbhgfPwG8+rAMHqUocUJ0Lc+FTQKX2VTu3ZtPPfcc1izZg2+//57fPjhh+VynPyadC0t9cMKFzQ8uGG9odUSgDz4QLt27Qo9Xn6JYElH1Hvw4AGA7CSvKNevX8f06dPlGPOTlJRUohgK4uDggClTpmDKlCkA9K13q1evxu+//459+/bh77//xujRowHou7lJkoS6devmuy9DeXh4uCKxKSEsLAwACozZ8Hzi4+MRFhaW5zsnv/eblZUVgNzvJyqa0GqBW9cgLp6EuHwGiCmkO51GAzRvi6iWnbEg0QPhqTq5CzOAXKPwrRrnAFfb6tUTgYiISq7aJ08JCQnyf9ENrQUajQatW7fGxYsXcerUKQwbNizXNoZuMh07dqzYYMvZ48OR53eBUBUSqNdeew2//fYb1q9fj5kzZ5ZqHwXduF8cJWkN0ul0kCQp12iP+WnevHmeMsOgJSVVnPiEEJg5cybu3buHyZMnY/LkyWjQoAGsrKwgSRI+//xzfPvttyW6968kGjdujC+++AKxsbHYs2cPDh06JCdPxVXWblNleQ8UpDgx5VeHXcDKRmSkAwGXIC6chPA/CyQnFlzZwRmSVydIbTsBzVojKlOFBQdDEJ6a/b1o+A7MeY/orK1X8O2YNmD7ExFRzVYtkqfAwEBkZGSgVatWuS5CIiIisHLlSqSnp+OJJ57I9d/eYcOG4eLFi9i2bRs6dOgg/+c3MDAQBw8ehIWFBfr27Vvhz6W8PD4ceUEXCFUhgXJxccGUKVPw448/YtWqVXKLz+MM9/wYWh5zMrTSlLc6derg7t27WLRoUblPqmq4n+nu3btF1g0KCkJQUBC8vLzkIfVzCgkJUTq8fHXv3h179uzJ1fJWu3ZthISE4P79+/nOpxQaqp+QtKjR74CKew8YWiMLa8UzxF27dm3FjluTibRUiCvnIM6fAK5eyNMNL5dGzSB5dYbk1Qlwbyj/ncjvH0o5v/tyzgP1ID4Ns7Zewad93Cv19yMREZWvapE8PXjwAKtWrUKtWrVQp04d2NvbIzo6Gnfu3EFmZibq1asn33xt0LZtWwwdOhR79uzBvHnz0KZNG2RlZcHf3x86nQ6zZ8+GtbW1kZ6Rsh4fjrywC4SqkkC99tpr+PXXX7Fhw4YCW3UMF9d37txBixYtcq3z9fUt9xgBoGfPnrh79y727duHsWPHlvuxfv/9d/zxxx+YNm1aoa0Zhvv/8usuFhcXh6NHjyoSkxCi0DgMiV7OhKJz584ICQnB9u3b8c477+SqHx0dDV9fX6hUKjzxxBNFHr807wFDwvX4QBaFcXd3h7u7O0JDQ3H8+PE89z0dPHgQcXFxaNKkSYHzy1HRRHoacOUcdGePA1fPAQV1aVSrgZbtILXvCqltJ0h2tfKtdupeYoHfiwaG78cFPqF4EJ+GU/cSMaKFg5JPi4iIqpBqMWBEkyZNMHDgQNjb2+P+/fs4ffo07t27h4YNG2LKlCn4/PPP80yqCQDTpk3Dq6++Cnd3d1y5cgU3b95E69at8cknn+QZGa0qOxmSUOwLBMM8UKfuFdLtpRJwcnLC1KlTkZqaii1btuRbp1u3bgCA1atX55or5+jRowWOeqa0l19+Gebm5li4cCEOHDiQZ31sbCzWr1+vyFw+Q4cOhYeHBwICArBkyZI8Q3NfvXpVbm1p1KgRVCoVTpw4gTt37sh10tLS8N5778nJVVlNmzYNP//8M+Lj4/OsO3z4MH777Tc59pzbqFQqrF27FpcvX5bLMzIy8NFHHyE1NRVDhgwp1lCjpXkPGBK527dvF+MZZjOMxrhw4cJcg0JERERg8eLFAIAXXnihRPskfZc8cd4PutVfQDd3MnSrvwAu+OVNnMwsID3RE9JL70C1/DeYvL4AqicHFpg4AcCIFg6Y0dGlyH8WOVuZ4tsxbTCntwcTJyKiGq5atDzVrVsXM2bMKNW23t7e8Pb2VjagSuZpT/3ogp3drYq8QFjcv36V+c/qq6++il9++QUpKSn5rn/66aexatUqnDt3Dr1794aXlxcePnyIy5cv46WXXsIPP/xQ7jF6eHhg5cqVmD17NqZPn47GjRujadOmEELg/v37uHXrFjIyMjBq1Kgyj+yoVqvx008/YeLEiVi1ahW2bduGjh07IisrC7dv38atW7ewZcsWuLm5wcnJCRMnTsTvv/+OAQMGoEePHjA3N8eZM2eQlZWFcePGYfPmzWV+/g8ePMD8+fPx6aefonXr1qhbty60Wi2CgoJw69YtAMCzzz6LgQMHytu0b98e77zzDv7v//4PTz31FLp16wYHBwecPXsWDx48QKNGjfDZZ58V6/ileQ/07t0b5ubm+Omnn3Dz5k3Url0bkiRh5syZ+XYjNHjxxRdx4sQJHD58GD179kSPHj0ghMDx48eRlJSEIUOGYNq0aeVyr1V1I3RZwA1/iFO+EBdPAmkF/HPB0gpSu66QOnQHPL0gmZZ8gu/ifte52ppjfHt3zi9DRFTDVYvkiYr2tKdTsSY1dbYyrRKJEwA4Ojpi2rRpWLVqVb7rLSwssGnTJixevBhHjhzB4cOH0bx5c3z//ffw8vKqkOQJ0LeqtGjRAqtXr8axY8fg4+MDMzMz1K5dG6NGjcLQoUNha2uryLFatGiBAwcO4Pvvv8eBAwfk+/fc3d0xZ84ctGzZUq77+eefo3Hjxti4cSNOnDgBGxsbPPnkk3j33XexadMmReL58ccfcejQIRw9ehR37txBYGAgMjMz4ejoiCFDhmDcuHG5EieD119/HZ6envjpp59w+fJlpKWlwc3NDa+++ipee+21XHNsFaY07wFXV1f8/PPP+N///oczZ87I90uNHj260OTJxMQE69atw4YNG7B582YcOXIEANCsWTOMGzcO06dPh0qlYvJUACEE8F8QxGlfiLPHgPjY/CtaWEFq1wVSp55ASy9I6srbvZiIiKofSZTXcFoke/jwYZGjlgkh5GHTlR55S63W58jFSZ6ocuI5rPrK8xyW5/dHeRMxURCnfCBOHgbCQvOvZGYBqV1nSJ2eBDzbQzKt+ITJ2dkZANjyVIXxHFZ9PIdVn7HPoSRJxer2Xxi2PBERUYUSGekQF09B+B0Grl8C8vvnkokJ0LojpC69IbXtDKmUQ/cTEREpickTERGVOyEEEBwIceKQvlteat7h4wEATTz1CdMTPSBZK9OdlYiISClMnoiIqNyI5CSIU0cgju0HQv/Lv5KzK6TufSF17QPJifNgERFR5cXkiYiIFCWEAG4FQBw7oJ/ENjOf+ZjMzPWtS937A009q9y9WkREVDMxeSIiIkWI5CSIk4cgfPcDYffzr9SsNaQe/SF16AbJvGzD8xMREVU0Jk9ERFQm4l4whM9uiNO+QEZ63grWtpB69IPUcyAkV/eKD5CIiEghTJ6IiKjEhDYT4sJJCJ89QFBA/pVaekHVaxDQrgvnYyIiomqByVMlIUkSJEmCTqeDiYmJscMhoiokKytL/g4pbyIhDuLIXoij+/KfyNbaBlKPAZB6DYLkUra5NIiIiCobJk+ViEajQVpaGqysrIwdChFVIenp6dBoNOV6DBEaAnHwH4hTRwBtZt4KDZpA6jsMUqcnIZmWbyxERETGwuSpErGwsEB8fDwAwMzMTLEWKPFoAkqR30SUVCXwHFZ95XEOs7KykJ6ejrS0NNjZ2Sm2XwMhBHDtInT//gMEXMxbQW0KqVNPSH2GQWrUTPHjExERVTZMnioRtVoNOzs7pKamIj4+XrGLLJVKBQDQ6XSK7I8qHs9h1Vce51CSJGg0GtjZ2UGtVu7rXGgzIU4fhdi/DXh4L28Fu1qQvIdC6j0Yko3ySRsREVFlxeSpklGr1bCxsQGg3H+onZ2dAQCRkZGK7I8qHs9h1Vce51Dpe5xEWirE8QMQB/4BYqPyVqjbCNKApyB16gXJlANAEBFRzcPkqRJT6sLIsB9OQll18RxWfZX5HIrEBIjDuyAO7wJSkvJWaNsJqv5PAS3aVsr4iYiIKgqTJyKiGkrERkPs3wZxbD+QkZF7pYkaUrc+kAaOglSnrnECJCIiqmSYPBER1TAiJhJi71aI4wcArTb3SjMLSL0HQer/NKRajsYJkIiIqJJi8kREVEOI6AiIPX9BnDgIZD2WNNnYQeo3ApL3UEhW1kaJj4iIqLJj8kREVM2JyDCIvX9B+B0CsrJyr7R3hDR4DKSeAyCZmRknQCIioiqCyRMRUTUl4qIhdm+GOHYgb9Lk4ARpyDOQegzgyHlERETFxOSJiKiaEYkJEPu2QvjsBjIfGwjC0QXS0GcgdevHpImIiKiEmDwREVUTIjUF4t9/IP79G0hLzb3S0QXSsHH6EfTUTJqIiIhKg8kTEVEVJzIzIY7sgdizGUhKzL3S1h7S8PGQeg5kSxMREVEZMXkiIqqihBAQ545DbPsFiArPvdLSWj8QRN9hkMzMjRMgERFRNcPkiYioChKB16D7ax0QHJh7hZk5pAFP638sOeQ4ERGRkpg8ERFVISIsFLqtG4BLp3KvMDGB1GsQpOETINnaGyU2IiKi6o7JExFRFSBSkiB2/AlxZE/eYcfbd4Vq9FRIru7GCY6IiKiGYPJERFSJCV0WxPF/Ibb/BiQl5F7ZqBlUY5+H1NTTOMERERHVMEyeiIgqKREUAN2fPwIhd3KvcKoNafRUSE/0gCRJxgmOiIioBmLyRERUyYiYKIitGyDO+OZeYWYOaehY/WAQphrjBEdERFSDMXkiIqokhFYLcWgHxM6NQHparnVSV299a1MtRyNFR0REREyeiIgqAREUAN1v3wOh/+Ve0aAJVBNehNSkpXECIyIiIhmTJyIiIxJJCfouesf/zb3C2hbS6CmQevSDpDIxTnBERESUC5MnIiIjEEJA+B2G+OtnICkx1zqp1yB94mRlY6ToiIiIKD9MnoiIKpgIC4Xu12+BwGu5V9RtCNWkV9hFj4iIqJJi8kREVEFElha6vVshdvwBaDOzV5iZQ3rqWUj9RkAyYRc9IiKiyorJExFRBcgMvoX4b5dA3L6Re0W7rlBNfBGSg7NxAiMiIqJiY/JERFSORGYmxO5NiN63FcjKyl5hVwuqZ2dC6tDNeMERERFRiTB5IiIqJ+LOTejWfwM8vJerXOrRD9LYFyBZWRspMiIiIioNJk9ERAoT2kyInZsg9v4FCJ1crnJ2BSa9AqlVeyNGR0RERKXF5ImISEEi9D/o1i4H7gVnF0oSLIc+A+vnZiI6Kdl4wREREVGZMHkiIlKA0GVBHNwBsf1XQKvNXuHsCtX0N2Dbvbd+mckTERFRlcXkiYiojERUOHTrvs4zb5PUezCkZ6ZDMrcwTmBERESkKCZPREQ57LwRg671bOBsZVpovcjkTJwMScTwmIsQf/4IpKdmr7RzgGrqbEhtOpZztERERFSRmDwRET2y80YM1pyPwK6bsVjcv36BCVRkciY+/Pc/hCdrIW6dw/AciZP0RE9Ik2ZCsratqLCJiIiogqiMHQARUWXRtZ4NXK1NEZaUiY8OhiAyOTNPncjkTHy49zbCk7WonRqNLlGPuupZWkF68W2oXp7HxImIiKiaYvJERPSIs5UpFvevX2ACFZGYjg93XEd4OlA7NRqfXloN5/Q4oFkrqD7+BqrOvYwXPBEREZU7Jk9ERDkUlEBFPIzER9v8Ea7TZCdOGQmQnn4WqrcWQ3JwNnboREREVM54zxMR0WMMCdRHB0MQlpSJmf8EAVk6aNU22YmTlRqqOUsgNfU0drhERERUQdjyRESUD2crUyzq6w41dNAKCVqVCdQ6rT5xauUJ1YJvmDgRERHVMGx5IiLKh0hMgO7n7wGHYYAq+/9M0ujJUPXpD0mSjBgdERERGQNbnoiIHiPu3ET4/83HAque0KrUUOu0UIssaFVqLEj0QFSK1tghEhERkREweSIiekQIAd2hXQhfsRQLGo5DuIUjaqdG47vkg/h+cN0ihzEnIiKi6o3JExERAJGeBvHTV4jYvhkL2syQE6dF7rGo/fIcuDjZFTqMOREREVV/TJ6IqMYTkWHQLZ2HCP8rWNDuZX3ilB6LxV1rofaQ4fL9TUXNA0VERETVG5MnIqrRxA1/6Ja8Bdy/i9NOrfSJkzYRi4c2hUvrvKPpPZ5AnbqXaISoiYiIyBg42h4R1UhCCAif3RCb1gA6HQBgeOgJoEVbdBvRBy625gVua0igTt1LxIgWDhUVMhERERkZkyciqnFEZibEHz9AHP83u1BtCmnqLDzdtU+x9uFsZcrEiYiIqIZh8kRENYqIi4Huh6XA7RvZhfaOUL36AaRGTY0XGBEREVV6TJ6IqMYQ94KhW7kIiI3KLmzcAqpX3odkV8t4gREREVGVwOSJiGoEceUcdKu/BNJT5TKp5wBIz86EZGpqxMiIiIioqmDyRETVns5nN8SfPwFCPzAEJBWk8TMg9R0mD0NOREREVBQmT0RUbQldFsTmnyEO7cwuNLOA6uV5kNp0NF5gREREVCUxeSKiakmkpUK3Zhlw+Ux2YS0nqGbPh1SvkfECIyIioiqLyRMRVTsiLhq6lYuBkNvZhfUbQzX7I0j2jsYLjIiIiKo0Jk9EVK2Ih/eh+/pjICYyu9CrM1Qvvg3JrOCJb4mIiIiKwuSJiKoNcecmdCs/BZIS5TKp/9OQxk6DpDIxYmRERERUHTB5IqJqQVw5r5/8NiNdXyBJkMbPgKrfCOMGRkRERNUGkyciqvJ0J30gNnwDZGXpC0zUkF6YC1WnnsYNjIiIiKoVJk9EVKXpDmyH2LIuu8DMAqrXPoDU0st4QREREVG1xOSJiKokodNBbN0AcWB7dqGNHVRzFkJq0Nh4gREREVG1xeSJiKococuC+OVbiBOHsgudXaF6YyEkFzfjBUZERETVGpMnIqpShFYL8fP/IM4eyy6s10jf4mRXy3iBERERUbXH5ImIqgyRmQHd6i+Ay2eyC5u1gmrWfEgWlsYLjIiIiGoEJk9EVCWI9HToVn0GBFzKLvRsD9WrH0AyMzNaXERERFRzMHkiokpPpKboJ7+9FZBd2K4LVC/Ng2RqarzAiIiIqEZh8kRElZpIToRuxSdAcKBcJnV6EtLzb0JS8yuMiIiIKg6vPIio0hKJ8dAtXwDcD5bLpB79IE2ZBUllYsTIiIiIqCaqlslTUlIS3njjDSQkJMDNzQ1ff/11gXV9fX2xb98+3L9/H2q1Gs2aNcPo0aPRvHnziguYiPIQiQnQLZ8P3L8rl0l9hkKa8BIklcp4gREREVGNVS2Tpw0bNiAxMbFY9Xbv3g2NRoO2bdsiMzMT/v7+uHz5MubOnYvOnTtXQLRE9DiRnAjd/x5LnAaOgvTMNEiSZLzAiIiIqEardsnTlStX4Ovri/79++PgwYMF1rt69Sp2794NGxsbLF68GHXq1AEABAYGYuHChVi1ahU8PT1hbW1dUaETEQCRnKRvcbqXo6veoNGQxkxl4kRERERGVa36vmRkZOCnn35C3bp1MWLEiELr7ty5EwAwevRoOXECgGbNmmHAgAFISUmBj49PucZLRLmJlCTo/rcACLkjl0kDRzJxIiIiokqhWiVPW7ZsQXh4OGbMmAETk4JvJs/IyMDVq1cBAF27ds2z3lB2/vz58gmUiPIQKcnQ/e9j4L8guUzq/xSkZ6YzcSIiIqJKodokT//99x927doFb29veHp6Flr3wYMHyMzMhK2tLRwdHfOsb9SokbxPIip/IjUFuhULgbu35DKp3whI415g4kRERESVRrW450mn02H16tWwtLTEc889V2T9qKgoAMg3cQIAc3NzWFlZITk5GampqbCwsCh0f3Pnzs1TptFosHTpUgCAk5NTkTGVJ/WjuXCcnZ2NGgeVXnU+h7rUFMQu+xC6OzflMsuhY2Dz4lvVKnGqzuewJuD5q/p4Dqs+nsOqrzqcw2rR8rRv3z4EBQVh8uTJsLGxKbJ+WloaAH2CUxAzM7NcdYlIeSIzA3FL30fmjStymcXgUdUucSIiIqLqocq3PEVFRWHjxo3w9PSEt7d3sbYRQgBAoRdnhjrFsXz58iJjLMn+lGbI7iMjI40WA5VNdTyHIisLuh+/AC6fkcukJwcifdRUuXW4OqmO57Am4fmr+ngOqz6ew6rP2OdQkqRcA8WVRpVveVqzZg20Wi1mzJhR7G0M3fDS09MLrJORkQFA34WPiJQldDqIX74FLpyUy6ROT0J67hVOgEtERESVVpVvebpw4QKsrKywZs2aXOWZmZkA9K0+CxcuBAC89957MDc3l+9Bio6OznefaWlpSE5OhpWVVZH3OxFRyQghIDavhfA7lF3Y5glIz78JSVXwKJlERERExlblkycASE5ORkBAQL7rMjIy5HVZWVkAADc3N5iamiIhIQHR0dF5Bo4IDtZPzlm/fv1yjJqoZhI7N0Ic2pld0KwVVDPfhaSuFl9HREREVI1V+auVzZs351seERGBWbNmwc3NDV9//XWudRqNBq1bt8bFixdx6tQpDBs2LNf6U6dOAQA6duxYLjET1VS6gzsgdv6ZXdCgCVSz5kPSmBkvKCIiIqJiqrE3FxgSpm3btuHhw4dyeWBgIA4ePAgLCwv07dvXWOERVTs6v0MQm3J0r3WtC9WchZAsLI0XFBEREVEJVPmWp9Jq27Ythg4dij179mDevHlo06YNsrKy4O/vD51Oh9mzZ8Pa2trYYRJVC+LKeYgNK7MLHF2gevNTSDa2xguKiIiIqIRqbPIEANOmTUPDhg2xb98+XLlyBSYmJmjdujXGjBmDFi1aGDs8ompB/BcE3er/A3Q6fYGtPVRzP4XkYNzJo4mIiIhKqtomTy4uLgXeD5WTt7d3seeHIqKSEZFh0H3zKZD+aLJpMwuoXv8YkoubcQMjIiIiKoUae88TEZUvkZQA3YpPgIQ4fYFKpR9Vr0Fjo8ZFREREVFpMnohIcSIjHbpvFwPhoXKZNGU2pNYdjBgVERERUdkweSIiRQldFnRrlgG3b8hl0tPPQtWjnxGjIiIiIio7Jk9EpBghBMTGNcDFU3KZ9ORASMPGGzEqIiIiImUweSIixYh//4bw2Z1d0OYJSJNegSRJxguKiIiISCFMnohIEeLSaYi/1mcXNGgC1cvzIJmYGC0mIiIiIiUxeSKiMhP3g/X3OQmhL3B0ger1+ZDMzI0bGBEREZGCmDwRUZmIhFjoVi7OnsvJ3AKq2Qsg2dYybmBERERECmPyRESlJjIzoPtuCRATqS+QVFC9NA+Se33jBkZERERUDpg8EVGpCCEg1q8E7tyUy6Rx0yG16WjEqIiIiIjKD5MnIioVsWcLxBlfeVnqNQhSv6eMGBERERFR+WLyREQlJs77Qfz9W3ZB8zaQJr7MIcmJiIioWmPyREQlIkJuQ/fz8uwCFzeoXnkPklptvKCIiIiIKgCTJyIqNpGYAN2qz4GMDH2BpRVUsz+CZGVj3MCIiIiIKgCTJyIqFpGVBd1PXwLREfoCSQXVy+9Ccq1r3MCIiIiIKgiTJyIqFrH9V+D6ZXlZGjMVkmc74wVEREREVMGYPBFRkcS54xD7t8nLUqcnIQ0cabyAiIiIiIyAyRMRFUqE/gfd+m+yC9wbQJo6myPrERERUY3D5ImICiRSkqBbtQRIT9MXWFpB9er7kMzMjRsYERERkREweSKifAmdDrq1/wMiHuoLJAmqGW9BcnEzbmBERERERsLkiYjyJXZtBPzPysvSUxMhtXnCiBERERERGReTJyLKQ1w9D7FzY3aBV2dIQ8cZLyAiIiKiSoDJExHlImKi9N31DGq7Q/X8m5BU/LogIiKimo1XQ0Qk00+E+xWQlKAv0GigeuU9SJZWxg2MiIiIqBJg8kREMvHPb0BQgLwsPTsTknsDI0ZEREREVHkweSIiAIC4ch5i71Z5WerWB1L3fkaMiIiIiKhyYfJERPr7nH5enl1Qpx6kSa9wIlwiIiKiHJg8EdVw+vucvgSSEvUFGg1UL8/jRLhEREREj2HyRFTD6e9zui4v8z4nIiIiovwxeSKqwXifExEREVHxMXkiqqFEXAx0P+eYz4n3OREREREViskTUQ0kdDro1q3IPZ8T73MiIiIiKhSTJ6IaSBzeBQRclJel8TN4nxMRERFREZg8EdUw4n4wxNb12QXtukB6cpDR4iEiIiKqKtTltePIyEjExsYiISEBGRkZsLGxga2tLerUqQONRlNehyWiQoiMdOjWLAe0Wn2BXS2opszmfU5ERERExaBY8pSRkQE/Pz9cunQJ169fR1xcXL71TExM4OHhAU9PT/Ts2RP169dXKgQiKoLY9gsQ+p+8rJo2B5KNrREjIiIiIqo6ypw8hYeHY/fu3Th27BhSUlKKrJ+VlYVbt27h1q1b+Oeff9CsWTMMHDgQPXv25H+/icqRuHIe4tBOeVnq/xSk1h2MGBERERFR1VLq5CkpKQl//fUX/v33X2gfdQFydXVFy5Yt0bRpUzRq1Ag2NjawtraGRqNBUlISkpKSEBERgVu3biEoKAgBAQEIDAxEYGAgduzYgUmTJqFdu3ZKPTciekQkxEG3fkV2gXsDSKOnGC8gIiIioiqo1MnT66+/juTkZNjY2KBnz57o1asXPDw8CqxvZ2cHOzs7uLu7o3379gCA1NRUnDp1CkePHkVAQAA+//xzTJs2DUOGDCltWET0GCEEdBtWAglx+gK1KVQvvg3JlPceEhEREZVEqZMnSZIwceJEDB48GObmpZsbxsLCAn369EGfPn0QFBSELVu2IDk5ubQhEVE+hO9ewP+svCw9M43DkhMRERGVQqmTp++++67USVN+mjRpgvfffx9paWmK7ZOophMRDyG2rMsuaN0BUt/hxguIiIiIqAor9TxPSiZOFbFfoppG6HT6+5wy0vUF1jb60fU4MAsRERFRqXCSXKJqShzeBdwKkJelZ1+BZFfLiBERERERVW3lNklufkJCQuDv7w+VSoV27drBzc2tIg9PVGOIsFCI7b/Iy1LHHlB16mnEiIiIiIiqPkWTp6tXr2Lr1q1o2rQpnn322Vzrdu3ahd9++w1CCADAr7/+iilTpnBkPSKFCV3Wo+56GfoCGztIk2YaNygiIiKiakDRbnsnT55EQEAAXFxccpU/fPgQv//+O4QQUKvV0Gg00Ol02LBhA4KDg5UMgajGEwd3ALdvyMuqSa9AsrEzYkRERERE1YOiyVNgYCAA5Jno9tChQ9DpdPD09MTatWuxbt06dOnSBUII7N+/X8kQiGo08fA+xPbf5GWpcy9IHbsbMSIiIiKi6kPR5Ck+Ph4qlQqOjo65yi9dugQAGDNmDMzNzaFWq+VufdevX1cyBKIaS2RlQbfua0CbqS+wtYc08SWjxkRERERUnSiaPCUlJcHS0jLXUMipqam4d+8ezM3N4enpKZe7urrC1NQUMTExSoZAVGOJA38DwYHysmryq5CsbY0XEBEREVE1o2jyZGpqipSUFHlQCAC4efMmAP0kuCpV7sNpNBolD09UY4nQEIgdv8vLUtc+kNp1NWJERERERNWPosmTq6srdDodAgKy55Y5c+YMAKBFixa56mq1WqSkpMDOjjeyE5WF0GVB98tKQKvVF9g5QJrwonGDIiIiIqqGFE2eOnToAAD44Ycf4Ofnh927d+PIkSMAgC5duuSqGxwcDCEEnJyclAyBqMYRR/YCd27Ky6rJr0GysjZiRERERETVk6LzPA0fPhy+vr6IiIjAihUr5PJu3bqhfv36ueqePXsWQN4WKSIqPhETCbHtV3lZ6vQkJK9ORoyIiIiIqPpSNHmysrLC4sWLsXnzZgQGBsLKygodOnTAU089laueVquFj48PAKBVq1ZKhkBUYwghoPtjNZCeqi+wtIY0YYZxgyIiIiKqxhRNngDAwcEBM2fOLPygajV++uknpQ9NVLNc8AMun5EXpXHPQ7KtZcSAiIiIiKq3Mt3ztHnzZgQHBysVCxEVk0hOgu7PH7MLmreB1L2f8QIiIiIiqgHK1PK0detWbN26FQ4ODujUqROeeOIJtGrVCiYmJkrFR0T5EFvXA/Gx+gW1qX6QiBzzqxERERGR8sqUPA0ZMgTnz59HREQE9u/fj/3798PS0hLt27fHE088gfbt28PCwkKpWIkIgLh5FeLYAXlZGjEBUm03I0ZEREREVDOUKXmaNm0apk2bhpCQEJw5cwZnz57F3bt3ceLECZw4cQJqtRqenp5yq5SDg4NScRPVSCIzA7pfv8suqNsQ0sBRxguIiIiIqAZRZMCI+vXro379+njmmWcQExODs2fP4uzZswgICIC/vz/8/f2xdu1aeHh4yInU40OXE1HRxO7NQHiofkGSoJoyC5Ja8XFfiIiIiCgf5TLa3qBBgzBo0CCkpKTg4sWLOHv2LC5duoQ7d+7gzp072LRpE1xcXOREqkWLFlCpFJ2vl6ja0d4Lhti3VV6W+g6H1KiZESMiIiIiqlnK9V/WlpaW6NGjB3r06IGsrCxcu3YNZ86cke+T2r17N3bv3g1ra2t07NgRQ4YMQaNGjcozJKIqSQiBhNVfAVlZ+gIHZ0gjnzNuUEREREQ1TIX19zExMUHbtm3Rtm1bzJgxA3fu3JETqZCQEPj6+sLFxYXJE1E+0o79i4yrF+Rl1cSXIJlzMBYiIiKiimS0myU8PDzg4eGBCRMmICIiAmfPnuWAEkT5EKkpSFy3MrugbSdI7boYLyAiIiKiGqpS3Gnu4uKCYcOGGTsMokpJ7PwTIjZKv6A2hWrCi8YNiIiIiKiGKtfkKSMjA8nJycgy3KdRACcnp/IMg6jKEqH/QRzaKS9LQ56B5OxqxIiIiIiIai7Fk6e0tDT8888/8PPzQ1hYWJH1JUnCxo0blQ6DqMoTQkD3xw+ATgcAMKntDjF4tJGjIiIiIqq5FE2e4uPj8fHHH+Phw4fF3kYIoWQIRNWGOO0LBF6Tl21efBOJGjMjRkRERERUsymaPP355594+PAhNBoNRowYAS8vL9jZ2cHExETJwxBVeyIlGWLLz/KyWecnYf5EDyRGRhoxKiIiIqKaTdHk6cIF/VDKr732Grp27arkromqnZ03YtC1ng2crUzzrBM7/gAS4gAAkVbOuNpzOiZWcHxERERElJtKyZ2lpKRArVajc+fOSu6WqNrZeSMGa85H4KODIYhMzsy1TtwLhji8GwAQaWaPBV1ex8oLUdh0MdQYoRIRERHRI4omT46OjjAxMYFKpehuiaqdrvVs4GptirCkzFwJlH6QiNWA0OkTp46vIlxnBjc7c/Ru7GjkqImIiIhqNkWznE6dOiE9PR1BQUFK7pao2nG2MsXi/vXzJFDi7DEgKECfOLV7GeEae7ham+LbMW3gamtu7LCJiIiIajRFk6enn34azs7O+Omnn5CcnKzkromqnccTqA///Q8RO7ZlJ04WjnC1flSHiRMRERGR0UlC4bHCw8PD8c033yAqKgr9+/dH48aNYW5e+IWfp6enkiFUOg8fPjTqkOzOzs4AgEiO1FYpRSbrW57CkjKh1mkBAFqVGrUtJHw2yAPOVqY8h9UAz2HVxvNX9fEcVn08h1Wfsc+hJEmoU6dOmfah+CS5JiYmcHZ2RlBQEP76668i63OSXKrpnK1MsaizDV45GAGtSv+RVEOHzwY1zXckPiIiIiIyDkWTp4iICCxYsACxsbHF3oaT5BIBYt92QN0ju0DioCtERERElY2iydPmzZsRGxsLGxsbTJo0CV5eXrC3t+foe0SFiLh5C/OzWkOrUeu77alMoBUSPjoYgsX967P1iYiIiKiSUDR5unLlCgBgzpw5aNOmjZK7LtKuXbtw48YNhISEID4+HpmZmbC3t4enpyeefvpp1KtXL9/tfH19sW/fPty/fx9qtRrNmjXD6NGj0bx58wqNn2qmiKQMfHQqFuEWjqidGo1Pw3ZB9frHmO8TKo/Ct7h/fTzqIkxERERERqT4JLkajQatW7dWcrfFsn37dly8eBHW1tZo06YNOnToAFNTUxw9ehTvvvsuLl68mGebDRs24LvvvsO9e/fQpk0bNGnSBP7+/vj4449x5syZCn8OVLNEJmfioz23EK621SdOl1aj9uhxcLE1zzOMeVhCmrHDJSIiIqrxFG15cnJyQlRUFCRJUnK3xfLOO+/Aw8MDGo0mV/mBAwewZs0a/PDDD/j+++/lLoRXr17F7t27YWNjg8WLF8sjbwQGBmLhwoVYtWoVPD09YW1tXeHPhaq/yGT90OThmSZy4uTcohkkz/YAsocxN4zCN2vrFXw7pg1MjBw3ERERUU2maMtTt27dkJGRgatXryq522Jp0aJFnsQJAAYOHAhXV1fExsbiwYMHcvnOnTsBAKNHj841ZGGzZs0wYMAApKSkwMfHp/wDpxrp1L1EhCdrsxMnbSJUz0zPVSfnPFAP4tPgezvaSNESEREREaBw8jRy5EjUr18fq1evRkREhJK7LhNDa5NarW9oy5ngde3aNU99Q9n58+crKEKqaYbXkfB88F594pQeB6nPcEiu7nnqGRKoOb09ML593vVEREREVHEU7bZ38uRJ9OnTB1u2bMFbb72FLl26oEmTJrCwsCh0u969eysZRi6+vr548OAB6tSpAxcXFwDAgwcPkJmZCVtbWzg6OubZplGjRgCA//77r9zioppN/P0bhv/3qGXT2gbS8PEF1nW2MsX4hhwxgoiIiMjYFE2eVq1alWv52LFjOHbsWKHbSJKkaPK0Y8cO3Lt3D+np6QgNDcW9e/dQq1YtzJkzR26BioqKAoB8EycAMDc3h5WVFZKTk5Gamlpk8jd37tw8ZRqNBkuXLgWgvxfMmAwtbs4csq1SyAy5g2i/Q/Ky7bMvw7Jho0K34Tms+ngOqzaev6qP57Dq4zms+qrDOVR8wAhju3z5sjxkOqBPkGbPng0PDw+5LC1NP3JZfvdIGZiZmSE5ORlpaWlFJk9EJZH02w+ATgcAMHGvD4tBTxs5IiIiIiIqDkWTp++++07J3ZXK/PnzAQDJyckICQnBX3/9hYULF2LChAkYPXo0AEAIAQCFjgpoqFMcy5cvL3R9VFRUifanNEN2HxkZabQYSE/cCoDuTHZrrHhqEqJiYovcjuew6uM5rNp4/qo+nsOqj+ew6jP2OZQkKddAcaWh6IARlYmVlRVatmyJ999/Hx4eHti0aROCgoIAQG5JSk9PL3D7jIwMAPoufERKEEJAt3V9doFHc6B93gFLiIiIiKhyqrbJk4FarUb37t0hhJBHzzN0L4yOzn/o57S0NCQnJ8PKyopd9kg5l08Dt2/Ii6oxU40yJxoRERERlU61T54AwMbGBgCQkJAAAHBzc4OpqSkSEhLyTaCCg4MBAPXr16+4IKlaE1lZ0G37NbugbSdIzVobLyAiIiIiKrFSJ09r165FbGzR92qUxKlTp3D8+HFF9wkAAQEBAIDatWsD0A8U0bp1a/mY+cUBAB07dlQ8FqqZhN8h4OE9/YIkQTV6inEDIiIiIqISK3XydODAAcyePRvr1q3D/fv3Sx1ARkYGjh49irfffhv/+9//EBYWVuJ9XL9+HX5+fsjKyspVrtVqsXfvXhw9ehQajQbdu3eX1w0bNgwAsG3bNjx8+FAuDwwMxMGDB2FhYYG+ffuW8lkRZRPp6RA7/pSXpW59Ibk3MGJERERERFQapR5t76WXXsKmTZuwb98+7Nu3D40aNUKPHj3QsmVLNGzYUB7HPT9RUVG4desWzp07h3PnzslDh3fp0gXe3t4ljiU8PByrVq2CjY0NPDw8YGNjg8TERISEhCA2NhampqZ49dVXcw2l3rZtWwwdOhR79uzBvHnz0KZNG2RlZcHf3x86nQ6zZ8+GtbV1iWMhepw4vAuIe9Q9VG0K6alnjRsQEREREZVKqZOnfv36oWfPnvjnn3+wb98+BAcHy/cKqdVquLm5wdbWFlZWVjA1NUVycjKSkpIQHh4u33tk0KpVK0yYMAHNmjUrVSyenp4YNWoUAgICEBISgoSEBKjVari4uKBLly4YOnQoXF1d82w3bdo0NGzYEPv27cOVK1dgYmKC1q1bY8yYMWjRokWpYiHKSSQnQuz9S16W+g6H5Fh1J4YjIiIiqskkocAERBkZGfDz88OhQ4dw69atYs1pZGtrix49emDAgAFwd3cvawiV2sOHDznPUw2l27IO4sB2/YKFFVSf/wjJyqbE++E5rPp4Dqs2nr+qj+ew6uM5rPqMfQ6VmOdJkUlyNRoNvL294e3tjZSUFNy4cQNBQUGIiYlBQkICMjMzYWNjA1tbW9StWxctW7as9gkTkYiO1HfZe0Qa8kypEiciIiIiqhwUSZ5ysrS0RIcOHdChQweld01UpYidfwDaTP2CvSOkfsONGxARERERlUmNmOeJqKKJ8AcQJ33kZempiZA0ZkaMiIiIiIjKiskTUTkQuzYCOp1+wdkVUjcOe09ERERU1TF5IlKYeHgP4rSvvCyNmAipkKH7iYiIiKhqYPJEpDCxcyNgGF3R1R1Sl17GDYiIiIiIFMHkiUhB4v5diLPH5GVpxERIKhMjRkRERERESmHyRKQg3Y4/shfc6kN6oqfxgiEiIiIiRTF5IlKI+O82cPGUvKx66llIKn7EiIiIiKoLXtkRKSRXq1O9RkD7rsYLhoiIiIgUx+SJSAHizk3A/6y8rHp6EludiIiIiKoZRa/uAgIClNwdUZWRq9WpYVOgbSfjBUNERERE5ULRyWc++eQTuLm5oX///ujduzesra2V3D1RpSSCAoBrF+Vl1dPPQpIkI0ZEREREROVB8X5FDx48wC+//IKXX34ZK1euZGsUVXu6v3/PXmjcAmjVwXjBEBEREVG5UbTlacWKFTh06BB8fX0RHx+P48eP4/jx42yNompL3LwC3LwiL6uensRWJyIiIqJqStHkydXVFZMmTcKECRNw7tw5HDx4EFeuXJFbo/7880906dIF/fr1g6enp5KHJjIK3e7N2QvNWgMt2hovGCIiIiIqV4omTwYmJibo0qULunTpgqioKBw8eBC+vr6IiYlhaxRVG+L2DeD6ZXlZNXw8W52IiIiIqrFySZ5ycnJywoQJEzBu3DhcuHABhw8fxsWLF/O0Rg0YMAAtWrQo73CIFKPbsyV7oXELtjoRERERVXPlnjwZqFQqPPHEE1Cr1UhMTERgYCAAIDMzU26NatasGaZOnYomTZpUVFhEpSJC7uSe12nYOLY6EREREVVzFZI8xcbG4vDhwzh8+DCioqLk8hYtWqBr1664fPkyLl26hMDAQCxYsAAffvghWrVqVRGhEZWKyNnqVN8DaN3ReMEQERERUYUot+RJCIGLFy/i4MGDuHjxInQ6HQDAwsICvXr1woABA1CvXj0AwJAhQxAeHo41a9bA398fmzZtwqefflpeoRGViXh4D+KCn7ysGspWJyIiIqKaQPHkKTo6GocPH4aPjw+io6Pl8kaNGmHAgAHo2bMnzMzM8mxXu3ZtvPnmm3jxxRfx33//KR0WkWLEnr8AIfQLdeoB7bsaNyAiIiIiqhCKJk9Lly7F5cuX5VYmjUaD7t27Y8CAAcW6j8nS0hL29va5uvYRVSYiMgzijK+8LA19BpJK8bmmiYiIiKgSUjR5unjxIgDA3d0d/fv3h7e3NywtLUu0jy5duiApKUnJsIgUI/ZtBR79cwDOrpA69TJuQERERERUYRRNnrp164aBAweWaQLcKVOmKBgRkXJETBTEiUPysjTkGUgmJkaMiIiIiIgqkqLJ0xtvvKHk7ogqFXFgO5Cl1S/UcoLUrY9xAyIiIiKiCqXozRqffPIJli9fXuz6X3/9NUfVoypBJMRCHNsvL0uDRkNSmxoxIiIiIiKqaIq2PAUEBMDe3r7Y9W/dusXBIahKEP/uADIy9As2dpCeHGDcgIiIiIiowhl1mDAhBOfHoUpPJCdBHNkjL0uDRkHS5B1un4iIiIiqN6MlTzqdDvHx8fnO+URUmQjfvUBaqn7B0hpS78HGDYiIiIiIjKJM3fZSUlKQkpKSq0yn0xXaFU8IgeTkZBw5cgRarRYNGjQoSwhE5UpkZkIc3iUvS32GQjIv2fD7RERERFQ9lCl52r17N/76669cZQkJCXjttdeKvY9evThPDlVe4pQPEB+rX1CbQuo7zLgBEREREZHRKDpgREk4ODhgwIABGDyYXaCochI6HcSBv+VlqXtfSLa1jBcQERERERlVmZKnYcOGwdvbG4C+O97s2bNha2uLJUuWFLiNJEmwtLSEpSW7PlEld+UcEHZf/1iSIA0YadRwiIiIiMi4ypQ8PZ4EtWzZEjY2NnB2di5zYETGptu/LXvBqwskV3fjBUNERERERqdot72FCxcquTsioxF3bgK3AuRl1aBRRoyGiIiIiCoDo87zRFRZ6fZvz15o3AJSk5bGC4aIiIiIKoVStzwFBOj/K29mZobGjRvnKispT0/P0oZBpDgR8QC4eFJeVg0abcRoiIiIiKiyKHXy9MknnwAA3N3dsXz58lxlJSFJEjZu3FjaMIgUJ/79BxBCv1DbHfDqbNyAiIiIiKhSKHO3PWG4yDTS9kRKEonxECcOycvSwJGQVOzdSkRERERlaHnatGlTscqIqhLhsxvIzNAv2NpD6tbHuAERERERUaXBf6kTPSLS0/XJ0yNS3+GQTDVGjIiIiIiIKhMmT0SPCL9DQFKifsHMHJL3EKPGQ0RERESVi+LJU0pKCtLS0oqsl5aWhpSUFKUPT1QqQpcF8e/f8rLUcwAkKxvjBURERERElY6iydPp06cxffp0rF69usi633zzDaZPn45z584pGQJR6Vw5D0SG6R9LKkj9Rhg3HiIiIiKqdBRNnk6e1M+N07dv3yLr9u/fHwDg5+enZAhEpaI7tDN7oX0XSM6uxguGiIiIiColRZOnu3fvAgA8PDyKrNu8eXMAQHBwsJIhEJWYCA0Brl+Wl1VsdSIiIiKifCiaPMXExMDCwgJWVlZF1rWysoK5uTliYmKUDIGoxMThHK1O9RoBTVsZLxgiIiIiqrRKPc9TfiRJQlZWVrHr63Q6JQ9PVGIiORHilI+8LPUbAUmSjBgREREREVVWirY8OTo6IiMjAyEhIUXWvXv3LjIyMuDg4KBkCEQlIo4eADIeTYprYwepcy/jBkRERERElZaiyZOnpycAYPPmzUXW3bJlCwCgVSt2kSLjEFlZEEdyTIrbaxAnxSUiIiKiAimaPA0ZMgSSJOHs2bP45ptvEBcXl6dOXFwcVqxYgXPnzkGlUmHo0KFKhkBUfJdOATFR+scmJuCkuERERERUGEXveXJ3d8eECRPw559/4sSJEzh9+jQ8PDzg5OQESZIQGRmJ27dvy/dFjR8/HnXr1lUyBKJi0x3MHihC6tgDkr2jEaMhIiIiospO0eQJAEaOHAlLS0v8/vvvSEtLQ2BgIAIDA3PVsbCwwHPPPSfP9URU0cR/t4GgAHmZk+ISERERUVEUT54AYODAgejRowdOnTqFmzdvIj4+HgBgb2+P5s2bo2vXrrC0tCyPQxMVizi0I3uhUTNIHs2NFwwRERERVQnlkjwB+nmc+vXrh379+pXXIYhKRSTEQpw9Ji+z1YmIiIiIikPRASOIqgLhux/QavULdg6QOnY3bkBEREREVCWUW8sTANy7dw+3b99GQkICAMDW1hZNmjThIBFkNEKbCeG7V16WvIdAUpsaLyAiIiIiqjLKJXm6dOkSfv/99wIny61fvz6ee+45eHl5lcfhiQokzh0H4mP1C2pTSL0HGzcgIiIiIqoyFO+2t2/fPnz++edy4qRSqWBnZwc7OzuoVPrDhYSEYMmSJdi3b5/ShycqlDicY1Lczr0g2dgZMRoiIiIiqkoUbXm6e/cu1q9fDwBo0qQJxo4di1atWsHUVN8tKjMzE9euXcPWrVsRGBiIDRs2oGXLlmjQoIGSYRDlS4TcBoKzh82X+g43YjREREREVNUo2vK0a9cuCCHQsWNHLFq0CO3atZMTJwAwNTVFu3bt8Mknn6Bjx47Q6XTYvXt3IXskUo7wzdHS2agZpAaNjRcMEREREVU5iiZP169fBwBMmzZN7qKX70FVKkybNg0AcO3aNSVDIMqXSE2BOO0rL0u9hxgxGiIiIiKqihRNnuLi4mBpaQkXF5ci67q4uMDS0hJxcXFKhkCUL3HKB0hP0y9YWkPq1NO4ARERERFRlaNo8qTRaJCRkYGsrKwi62ZlZSEjIwMajUbJEIjyEEJAHMkxPHn3fpA0ZkaMiIiIiIiqIkWTp7p160Kr1eLUqVNF1j158iS0Wi3nfKLyF3QdeJA9bD6HJyciIiKi0lA0eeratSsAYM2aNfD39y+wnr+/P9auXQsA6Natm5IhEOWRs9UJLb0gubobLxgiIiIiqrIUHap84MCBOHz4MO7fv4/PPvsMzZo1Q5s2beDg4ABJkhAdHY0rV64gMFA/XHS9evUwcOBAJUMgykUkxkNcOCEvq9jqRERERESlpGjyZGpqig8//BDLli1DUFAQAgMD5UTpcU2aNMFbb70FtVrREIhyEccPAlqtfsHOAfDqYtyAiIiIiKjKUjxzcXBwwKJFi3Dq1Cn4+fnhzp07iI+PBwDY2dnBw8MDPXr0QJcuXQodzpyorIROB3E0e24n6ckBkJisExEREVEplcuVpEqlQvfu3dG9e/fy2D1R8QRcBKLC9Y8lFaQn2UWUiIiIiEqPTT9UbelyDhTh1QmSg7PxgiEiIiKiKo/JE1VLIjoS8D8nL6t6DzFiNERERERUHZS6215AQIBiQXh6eiq2LyIAEMf2A0KnX3B2BTzbGTUeIiIiIqr6Sp08ffLJJ4oEIEkSNm7cqMi+iABAaLUQx/+Vl6VegyBxcBIiIiIiKiOjX1EKIYwdAlU3l08D8bH6x2o1pB79jRsPEREREVULpW552rRpk5JxEClGd+yA/Fjq0AOSjZ0RoyEiIiKi6qJaTHqTnp6Oy5cv4/z587h9+zYiIyOh0+ng6uqKLl26YPjw4TA3N893W19fX+zbtw/379+HWq1Gs2bNMHr0aDRv3ryCnwUpQURHAgGX5GWp1yDjBUNERERE1Uq1SJ6OHz+O1atXAwDq1asHLy8vpKamIjAwEJs3b8aJEyewcOFC2NnlboHYsGEDdu/eDY1Gg7Zt2yIzMxP+/v64fPky5s6di86dOxvj6VAZCL9DgKErqEsdoFkr4wZERERERNVGuSZPCQkJiIyMRHp6ermOqKdWqzFw4EAMGzYMderUkctjY2OxdOlSBAcHY/369ZgzZ4687urVq9i9ezdsbGywePFiebvAwEAsXLgQq1atgqenJ6ytrcstblKW0OkgThyUl6Ue/SFJkhEjIiIiIqLqpFySp3PnzmHLli24e/cugLwj6iUlJWHFihUAgLfeeqvALnXF1bt3b/Tu3TtPea1atfDCCy/go48+wpkzZ6DVaqFW65/yzp07AQCjR4/OlXA1a9YMAwYMwN69e+Hj44MRI0aUKTaqQDcuA9ER+seSClL3vsaNh4iIiIiqFcVH2/v777/x5ZdfyokTkHdEPWtra5iZmcHf3x8XL15UOoRcGjRoAADIzMxEYmIiACAjIwNXr14FAHTt2jXPNoay8+fPl2tspCxxPLvVCW06QrJ3NF4wRERERFTtKJo83bp1C3/++SdMTEwwdepUrF27Ns99RgZPPvkkAH0rVXkKDw8HAJiYmMhd8B48eIDMzEzY2trC0THvBXajRo0AAP/991+5xkbKEUkJEBdPysuqJwcYMRoiIiIiqo4U7ba3Z88eAMDIkSMxdOjQQusa7oG6ffu2kiEUGFO7du1gamoKAIiKigKAfBMnADA3N4eVlRWSk5ORmpoKCwuLco2Ryk6c9gW0Wv2CrT3Q+gmjxkNERERE1Y+iydONGzcAAIMHDy6yro2NDczNzRETE6NkCLlcuHABPj4+MDExwfjx4+XytLQ0AIBGoylwWzMzMyQnJyMtLa3I5Gnu3Ll5yjQaDZYuXQoAcHJyKk34ijHc5+Xs7GzUOMqLEALRJw/jUeoEq37DYZPjPrbqoLqfw5qA57Bq4/mr+ngOqz6ew6qvOpxDRbvtJSQkwMLCAra2tsWqb2JiAq2htUBh9+/fx8qVKyGEwOTJk9GwYUN5neEerMJGYnv8Pi2qvLRB16H9L7sF06L/cCNGQ0RERETVlaItTxqNBmlpadDpdFCpCs/LUlJSkJycXOxEqySio6OxZMkSJCcnY/jw4Xm6EBpaktLT0wvcR0ZGBgAUayTA5cuXF7o+KirKqMmYIbuPjIw0WgzlSbdzS/ZCU0/EaiyBavZcq/s5rAl4Dqs2nr+qj+ew6uM5rPqMfQ4lSco1ynZpKNry5ObmBp1Oh5CQkCLrnj59GgBytQgpISEhAYsXL0ZUVBS8vb0xefLkPHUM3eiio6Pz3UdaWhqSk5NhZWXF+50qOZGeDnH2qLws9eRAEURERERUPhRNnjp27AhAP1x5YcLCwvDHH38AADp16qTY8VNTU/H5558jNDQUnTt3xsyZM/Ptmufm5gZTU1MkJCTkm0AFBwcDAOrXr69YbFQ+xPkTQGqKfsHcAlLHHsYNiIiIiIiqLUWTp8GDB8PW1hYnT57EqlWrEBoammt9eHg4tm3bhvfffx8JCQlwcXFBnz59FDl2ZmYmvvjiC9y+fRteXl544403Cuw6qNFo0Lp1awDAqVOn8qw3lBmSQaq8xIl/5cdS516QzMo24TIRERERUUEUvefJ0tIS8+bNw5IlS+Dr6wtfX1953eTJk+X7iAD9RLlvvfWWPHx4Weh0OqxYsQLXrl1Dy5Yt8fbbb8ujeRRk2LBhuHjxIrZt24YOHTrI/R8DAwNx8OBBWFhYoG/fvmWOjcqPCAsFAq/Jy+yyR0RERETlSdHkCQCaNm2KL774Ar/++ivOnDkjD5SQM3Hq1KkTpkyZAhcXF0WOuW/fPpw5cwaAfgj0NWvW5Ftv8uTJ8gAVbdu2xdChQ7Fnzx7MmzcPbdq0QVZWFvz9/aHT6TB79mx5Ul2qnMSJg9kL7g2Ahk2NFwwRERERVXtlSp6++OIL9OvXD+3bt8/VRc7Z2Rlz585FUlISAgMDERsbC51OB3t7ezRv3lzxEfaSkpLkx4YkKj9jx47Ndexp06ahYcOG2LdvH65cuQITExO0bt0aY8aMQYsWLRSNkZQlsrIgTh6Wl6WeAwodep6IiIiIqKzKlDydP38e58+fh729PXr37g1vb2+4ubnJ662trdGhQ4cyB1mUcePGYdy4caXa1tvbG97e3soGROXv2gUgPlb/WK2G1NXbqOEQERERUfVXpuTJxcUFERERiIuLwz///IN//vkHLVq0QJ8+fdCtWzeYmZkpFSdRLuKkT/aCV2dI1srPF0ZERERElFOZkqeVK1ciICAAPj4+OH36NNLT03Hjxg3cuHED69atQ48ePeDt7Y1mzZopFS8RREoSxKXT8rKqWz8jRkNERERENUWZB4zw9PSEp6cnXnjhBZw4cQJHjhxBYGAg0tLScOjQIRw6dAju7u7o27cvevXqpfj9TlTziHMnAG2mfsHGDmjV3rgBEREREVGNoNhoe+bm5ujXrx/69euHBw8e4PDhwzh27Bji4uIQGhqKX3/9FX/88Qc6duyIPn36oH379rzBn0olZ5c9qXMvSEUMS09EREREpIRyuep0c3PDc889h2effRaXLl3C4cOHceHCBWRlZeHMmTM4c+YMatWqJQ/W4OrqWh5hUDUkIh4CQQHystRNmUmWiYiIiIiKUq7/slepVOjQoQM6dOiAxMRE+Pr64siRI7h37x5iY2Oxfft2/P3339i4cWN5hkHViDh1JHuhTj2gfmOjxUJERERENYuq6CrKsLGxwfDhw/HFF1/gmWeekbvsGSbRJSqKEALiVI4ue936susnEREREVWYCrtZ5OHDh/Dx8cHRo0cRGxsrl2s0mooKgaq629eByDD9Y0mC1KW3ceMhIiIiohqlXJOn9PR0+Pn5wcfHBzdv3sy1rmHDhujTpw+efPLJ8gyBqhFx8kj2Qou2kBycjBYLEREREdU85ZI83bhxA4cPH8bp06eRlpYml1taWqJnz57o27cvGjVqVB6HpmpKZGZAnDsmL0vd/r+9e4+Pqr7zP/4+yUwuJIGEEEjCLSQxhPu1BKwKpupawJXCFvp4KPtjf7raellaH17bqrhi1bZr164Xuu12ddvalXJrFWXVFUHhF7kJSSQk4X4zJAOEXMgkmeT8/pjOJEMSMgkhZybzej4ePh7ne86ZMx8eX74mb873fE+uhdUAAAAgFPVYeDp37px3QYiysjKfY+PGjVNubq5ycnJkt9t76isRSvJ3Shdr3duRUTKmzLS2HgAAAIScKwpPLpdLu3bt0ubNm5Wfn6/m5mbvsYEDB2r27NnKzc3V4MGDr7hQhLbm1u92mjpLRlS0hdUAAAAgFF1ReLr33ntVU1PjbYeHh2v69OnKzc3VpEmTWAkNPcKsqpQKd3vbxkze7QQAAIDed0XhyROchg0bphtvvFE33HCD+vfv3yOFAR7mzk+lpiZ3Iz5Ryp5gbUEAAAAISVcUnnJzc5Wbm6trrrmmp+oB2jBbT9mbOUdGWLiF1QAAACBUXfG0PeBqMk8dl44d9LaZsgcAAACrhFldAHA5Zl7LXSeNzJQxdIR1xQAAACCkEZ4QsMzmZpl5n3jbxizuOgEAAMA6hCcErtL9UuVZ93ZYmIyvXW9tPQAAAAhphCcELHPH1pbGmEky+sdbVgsAAABAeEJAMl0umXu2edvGjBssrAYAAAAgPCFQFe2Taqrd2za7jCmzrK0HAAAAIY/whIDkM2Vv4nQZ0f2sKwYAAAAQ4QkByGyol/lFnrcdxpQ9AAAABADCEwJPwS6pvs69HRUtTZhubT0AAACACE8IQM2tpuwZk2fKiIi0sBoAAADAjfCEgGJerJXyd3nbxgze7QQAAIDAQHhCQDH35kmuRncjNk4aM9nSegAAAAAPwhMCSutV9oypX5dhs1lYDQAAANCC8ISAYVZfcL/f6a94MS4AAAACCeEJAcPcvU1qbnY34hOla8ZaWxAAAADQCuEJAcNnyt7XrpMRxl9PAAAABA5+O0VAMM9VSKX7vW3ja0zZAwAAQGAhPCEgmDs/a2kkJUtpmdYVAwAAALSD8ISA4DNlb8YNMgzDwmoAAACAtghPsJxZdko6fsjbZpU9AAAABCLCEyxn7vy0pTEsTUbqCOuKAQAAADpAeILlWocn7joBAAAgUBGeYCnz9HHpqxPetjH9OgurAQAAADpGeIKlzD3bWxojMmQkJVtXDAAAAHAZhCdYytzdEp6MaddaWAkAAABweYQnWMYsOyWdPOptG1MJTwAAAAhchCdYxmfK3rA0GclDrSsGAAAA6AThCZZhyh4AAACCCeEJljArynxfjDvt6xZWAwAAAHSO8ARL+EzZSxkuI2W4dcUAAAAAfiA8wRK+U/a46wQAAIDAR3hCrzPPlktHSrxtnncCAABAMCA8ode1vuukIUOloSOtKwYAAADwE+EJva71807GtGtlGIaF1QAAAAD+ITyhV5nnHNKhA942zzsBAAAgWBCe0KvML/5fSyMpWRo+yrpiAAAAgC4gPKFXmbu3ebeNaV9nyh4AAACCBuEJvcasPCcdLPK2WWUPAAAAwYTwhF5jfpEnmaa7kThYGplpbUEAAABAFxCe0Gt8p+yxyh4AAACCC+EJvcKsqpRKvvS2jalM2QMAAEBwITyhV5h78ySz2d1IGCSNyrK2IAAAAKCLCE/oFeYXed5tY+osGWH81QMAAEBw4TdYXHVm3UXpQL63bUyZaWE1AAAAQPcQnnDVmYV7JJfL3YiJkzLHWlsQAAAA0A2EJ1x9ez/3bhoTp8sID7ewGAAAAKB7CE+4qkxXo8yCXd62MZkpewAAAAhOhCdcXSWFUl2te9seIY2bYm09AAAAQDcRnnBVma2m7GnsZBmRUdYVAwAAAFwBwhOuGtM0ZX7R6nmnyTkWVgMAAABcGcITrp5jB6XKs+5tw5Ax8WvW1gMAAABcAcITrhqfKXsZY2T0j7esFgAAAOBKEZ5w1bQOT0zZAwAAQLAjPOGqMMu/kk4d87YJTwAAAAh2hCdcFT5T9lJHyBiSal0xAAAAQA8gPOGqMPfmebe56wQAAIC+gPCEHmdWX5AOHvC2jckzLawGAAAA6BmEJ/Q4M3+nZDa7G/GJ0sgMawsCAAAAegDhCT3O/KL1lL0ZMsL4awYAAIDgx2+16FFmfb1UtNfbZsoeAAAA+grCE3rW/i+khgb3dnQ/afR4a+sBAAAAegjhCT3K58W446fJsNktrAYAAADoOTarC+gphw8fVn5+vg4ePKjS0lKdP39edrtdf/jDHy77uS1btmjTpk06efKkbDabsrKytHDhQo0ePbqXKu87zKYmmfk7WnZMYcoeAAAA+o4+E57WrFmjXbt2dekzb775pjZu3KiIiAhNnDhRjY2Nys/P1759+/TQQw9pxowZV6naPupQkVRT7d4Ot8kYP83aegAAAIAe1GfCU1ZWltLS0pSRkaGMjAzdc889lz2/sLBQGzduVFxcnFauXKmUlBRJUklJiVasWKHXXntNY8eOVWxsbG+UH1TeOXBOM4fHKSnGd0qemb+zpTF6vBzNduUdOKfbsgf2coUAAABAz+sz4WnBggVdOv+dd96RJC1cuNAbnCR3CLv55pv1/vvva/Pmzbrtttt6ssyg986Bc/rN7nK9W3xeK28a4ROgzPyWO3+OcbP01EfHVVbTKEkEKAAAAAS9kFwwoqGhQYWFhZKkmTPbPpfj2bd79+5erSsYzBwep+RYu8pqGvXjj46rotYdjsyKMumrE5Kkish4PVmTobKaRiXH2jVzeJyVJQMAAAA9IiTD0+nTp9XY2Kj+/fsrMTGxzfFRo0ZJko4dO9bbpQW8pBi7Vt40ok2AMgvcd50qIuP11LT7daauWcmx9jZ3pwAAAIBg1Wem7XWFw+GQpHaDkyRFRUUpJiZGtbW1qqurU3R09GWv99BDD7XZFxERoRdeeEGSNGjQoCus+MrYbO5uTkpK6pHrJSVJry0eqAfWFuj0Baee2nxKK0+WqjEyXk9NvldnIgYodUCUXlk0Qcn9o3rkO0NdT/cheh99GNzov+BHHwY/+jD49YU+DMk7T06nU5I74HQkMjLS51z4Su7vDkepA6J0+oJT98TcrPtzHtWZ6ESlRhsEJwAAAPQ5IXnnyTRNSZJhGJ2e44+XXnrpsscdDkeXrtfTPOm+oqKiR68bLumfbxyq7/75oFxh7r9KtuYmPfONdIXXV6uiorpHvy+UXa0+RO+hD4Mb/Rf86MPgRx8GP6v70DAMn4XiuiMk7zx5puHV19d3eE5DQ4Mk9xQ+dKK5VTA0DBm2kMzkAAAA6ONCMjx5nkE6e/Zsu8edTqdqa2sVExPT6fNOoayitlE/+ui4XEaYbM0u2ZpdchlhPqvwAQAAAH1FSIan1NRU2e12VVVVtRugjhw5IkkaMWJEb5cWNCpq3Svtnalp1JC6s3r185/q1R0/05B+4W2WMQcAAAD6gpAMTxERERo/frwkKS8vr81xz75p06b1al3BwhOcymoaNSSsXv+891dKqq9UUkqSnrslrd33QAEAAADBLiTDkyTNmzdPkrRu3Tp99dVX3v0lJSX66KOPFB0drdzcXKvKC1itg1NyrF3/fHKDkuorJUnGxK91+B4oAAAAINj1mSf79+zZo7Vr1/rsc7lc+tGPfuRtL1q0SFOnTpUkTZw4UXPnztV7772nRx99VBMmTFBTU5Py8/PV3NysBx98ULGxsb36ZwgGeSeqvcHp2ZkJSty4x3vMmDhdUsuLdD0hK+9EtW7LHmhVyQAAAECP6DPhqaqqSqWlpT77TNP02VdVVeVzfNmyZUpLS9OmTZtUUFCg8PBwjR8/XosWLVJ2dnav1B1sPCFo5vA4JeZ/1rIEe/xAaXi69zxPgCI4AQAAoK/oM+Fpzpw5mjNnTq99LpR5wlBzwS7vPmPC9DbvzUqKsROcAAAA0GeE7DNPuDKmyyWzsO2UPQAAAKCvIjyhew4dkOpq3ds2m5Q9ydp6AAAAgKuM8IRuMQt2tjRGT5ARxcuEAQAA0LcRntAtZn7r552+ZmElAAAAQO8gPKHLzIoy6asT3jbPOwEAACAUEJ7QZWarVfaUMlxGUrJ1xQAAAAC9hPCELjMvWaIcAAAACAWEJ3SJWV8vHSjwtpmyBwAAgFBBeELXlBRIrkb3dnQ/KWOMtfUAAAAAvYTwhC4xv/yipZE9UYbNZl0xAAAAQC8iPKFLzC/3eLeNcVMtrAQAAADoXYQn+M10nJHKTnnbxrgpFlYDAAAA9C7CE/zmM2UveaiMQUOsKwYAAADoZYQn+I0pewAAAAhlhCf4xXS5pAP53jZT9gAAABBqCE/wz+Fiqe6ie9tml7LGW1sPAAAA0MsIT/CLz/NO14yVERllXTEAAACABQhP8AvPOwEAACDUEZ7QKbP6gnT8kLdtjCc8AQAAIPQQntApc/9eyTTdjfhEKXWEpfUAAAAAViA8oXM+U/YmyzAMC4sBAAAArEF4wmWZzc2+i0WMm2ZdMQAAAICFCE+4vJNHpapK97YRJmPsJCurAQAAACxDeMJl+dx1SsuUERNnXTEAAACAhQhPuCyWKAcAAADcCE/okOmskw4WedssUQ4AAIBQRnhCx4oLpCaXe7tfjJR2jbX1AAAAABYiPKFDrafsacwkGeHh1hUDAAAAWIzwhA6ZhTzvBAAAAHgQntAus/wrqaLM2yY8AQAAINQRntAunyXKU4bLGDjIumIAAACAAEB4QrtYohwAAADwRXhCG2ZTk3ulvb8yxk2xsBoAAAAgMBCe0NbRUslZ59622aRrxllbDwAAABAACE9owyza29LIGCMjMtKyWgAAAIBAQXhCG2ZRvnfbyJ5oYSUAAABA4CA8wYdZ75QOHfC2jTGTLKwGAAAACByEJ/gq3S81udzb0f2ktGusrQcAAAAIEIQn+DCL9rU0ssbLCA+3rhgAAAAggBCe4MM80BKemLIHAAAAtCA8wcusrpKOH/a2CU8AAABAC8ITWhS3rLKnAQOllOHW1QIAAAAEGMITvFo/72SMmSjDMCysBgAAAAgshCd4+SwWkc2UPQAAAKA1whMkSabjjFRR5m0bY3g5LgAAANAa4QmSLrnrNGSojIFJ1hUDAAAABCDCE9wOtCwWwSp7AAAAQFuEJ8g0zTaLRQAAAADwRXiCdOqYVH3BvW0Y0ugJ1tYDAAAABCDCE3yfdxqRISMmzrpiAAAAgABFeMIlU/Z43gkAAABoD+EpxJkul1TypbdNeAIAAADaR3gKdUdLpPo697bNLmWOsbYeAAAAIEARnkKcub/V806ZY2RERFpXDAAAABDACE8hzjzQ6nmnbJYoBwAAADpCeAphprNOOlzsbRtjJ1tXDAAAABDgCE+hrHS/1NTk3o6OkUZmWFsPAAAAEMAITyGs9ZQ9jZ4gIyzcumIAAACAAEd4CmFmcaF328ieYGElAAAAQOAjPIUo82KNdPywt22MJjwBAAAAl0N4ClWlRZLZ7N6OjZNSR1hbDwAAABDgCE8hyiwpaGlkjZcRxl8FAAAA4HL4jTlE+TzvlMWUPQAAAKAzhKcQZF6sveR5p/EWVgMAAAAEB8JTKDq4v+V5pxiedwIAAAD8QXgKQa2n7ClrHM87AQAAAH7gt+YQZBa3LBbBEuUAAACAfwhPIYbnnQAAAIDuITz1Ye8cOKeK2kbfnW2edxqpitpGvXPgXO8XCAAAAAQRm9UF4Op458A5/WZ3ud4tPq/XFg9Ucv8oSZJZ4vu8k6OuST/+6LjKatwh67bsgVaUCwAAAAQ87jz1UTOHxyk51q6ymkY9sLZAZVVOSb6LRTgyp3iDU3KsXTOHx1lVLgAAABDwCE99VFKMXStvGqHkWLtOX3DqgbUFKj9bJR07JEmqiIzXk9WjvMFp5U0jlBRjt7hqAAAAIHARnvowT4BKHRCl0xec+vHHJ1UR0V8VkfF6asp3dcYpghMAAADgJ5556uOSYux6ZdEEPbC2QKcvOHV/zqOSJFeYjeAEAAAAdAF3nkJAcv8ovbJogmxmk1xhNrnCbLLJJDgBAAAAXUB4ChHNzjrJNFt2GIZ1xQAAAABBiPAUAsqqnPqndYXuO07NLtmam+QypR9/dLzte6AAAAAAtIvw1Mdc+mLcilr3UuWnndKQurN69fOf6tXqD5TUz6aymkYCFAAAAOCnkF8woqGhQRs2bNC2bdvkcDgUGxurSZMmacmSJUpMTLS6vC7xvBh3zZdn9fNb0ySp5T1Orio9s/dXSqqvlCNjtOqrmyXJG6B4/gkAAAC4vJC+89TQ0KBnn31Wa9askdPp1PTp05WYmKhPPvlEjz32mMrKyqwusUveLzkvSap0Numh94/oiQ+OqaymUalxEXpm92tKqq9URWS8Hr2Qrqp6d3gKN8QdKAAAAMAPIR2e1q9fr+LiYmVlZenll1/WD37wA/3kJz/R3//936uqqkqvv/661SV2ydLJSd7tqvpmVVx0KamfTS9lNymp7pwqIuP12LR/UmWrjHTP9MFKjrWrrKZReSeqLagaAAAACA4hG55cLpc2bdokSbrrrrsUFRXlPTZ//nyNHDlSRUVFOnz4sFUldtmsEf31+PWpPvvqm5rVWFLoDk5TH1BlRKz32OPXp+rWrIFaedMI3T1tsG7LHtjbJQMAAABBI2TD04EDB1RbW6shQ4Zo1KhRbY7n5ORIknbt2tXbpV2RSwNUVX2z/k/laH0v5zFVRvb37n/8+lTNGuFuJ8XYCU4AAABAJ0I2PB07dkyS2g1OkpSenu5zXjC5NEA1G2FqDgv3tlsHJwAAAAD+CdnV9hwOhyR1uKLewIEDfc67nIceeqjNvoiICL3wwguSpEGDBnW3zG7726QkmfZovfjxoZadpqlHv5Ghv504tNfrwZWx2dxDNSkpqZMzEajow+BG/wU/+jD40YfBry/0YcjeeXI6nZKkyMjIdo97noHynBdsyqqc+nXecd+dhqHf5J1QWVVw/pkAAAAAK4XsnSfTNK/oeGsvvfTSZY87HI4uXe9KVdQ26uFNR1XpbPrrHs93Gzp3sVH/9609+vmtabzXKYh4/oWmoqLC4krQXfRhcKP/gh99GPzow+BndR8ahqGUlJQrukbI3nmKjo6WJNXX17d73LO/9Sp8waBtcJKenzdGz88b421XOpv08KajvNcJAAAA6IKQDU+e55DOnj3b7vFz5875nBcM2gtOj1+fqtnXJGn2NUk+i0gQoAAAAICuCdnwNHLkSEnSkSNH2j3ueb+T57xg8Mf8ijbBqfWqepeuwlfpbNIf87n1DQAAAPgjZMNTdna2+vXrpzNnzrQboD7//HNJ0tSpU3u7tG47eLZlIYiOliO/NEC1/gwAAACAjoVseLLZbLr11lslSb/97W99VtV79913dezYMWVnZyszM9OqErvsl/PTNXJARKfvcfIEqJEDIvTL+em9WCEAAAAQvEJ2tT1JWrhwoQoKClRcXKzly5crOztbDodDpaWliouL03333Wd1iV3mbxiaNaI/L8oFAAAAuiBk7zxJ7hfZPv3001q0aJEiIiK0c+dOlZeXa/bs2XrxxReVnJxsdYkAAAAAAkRI33mS3AFqyZIlWrJkidWlAAAAAAhgIX3nCQAAAAD8RXgCAAAAAD8QngAAAADAD4QnAAAAAPAD4QkAAAAA/EB4AgAAAAA/EJ4AAAAAwA+EJwAAAADwA+EJAAAAAPxAeAIAAAAAPxCeAAAAAMAPhCcAAAAA8APhCQAAAAD8YLO6gFBgGIbVJUgKnDrQffRh8KMPgxv9F/zow+BHHwY/q/qwJ77XME3T7IFaAAAAAKBPY9oeAAAAAPiB8BQCHn/8cT3++ONWl4ErQB8GP/owuNF/wY8+DH70YfDrC33IM08hoKGhweoScIXow+BHHwY3+i/40YfBjz4Mfn2hD7nzBAAAAAB+IDwBAAAAgB8ITwAAAADgB8ITAAAAAPiB9zwBAAAAgB+48wQAAAAAfiA8AQAAAIAfCE8AAAAA4AfCEwAAAAD4gfAEAAAAAH4gPAEAAACAHwhPAAAAAOAHm9UF4OppaGjQhg0btG3bNjkcDsXGxmrSpElasmSJEhMTrS4PnVixYoX279/f4fEf/vCHmjx5cu8VhHYdPnxY+fn5OnjwoEpLS3X+/HnZ7Xb94Q9/uOzntmzZok2bNunkyZOy2WzKysrSwoULNXr06F6qHFLX+2/16tVas2ZNh9e7/fbbdccdd1ytcnGJ+vp67du3T7t379ahQ4dUUVGh5uZmJScnKycnR/Pnz1dUVFS7n2UMBobu9CHjMPC8++67OnDggI4fP64LFy6osbFR8fHxGjt2rG6//XYNHz683c8F4zgkPPVRDQ0NevbZZ1VcXKyEhARNnz5dFRUV+uSTT7Rnzx6tXLlSycnJVpcJP+Tk5LT7w3/gwIEWVINLrVmzRrt27erSZ958801t3LhRERERmjhxohobG5Wfn699+/bpoYce0owZM65StbhUd/pPkkaPHt3u/0PT09N7oiz46bPPPtOvfvUrSdLw4cM1adIk1dXVqaSkRKtXr9a2bdu0YsUKDRgwwOdzjMHA0d0+lBiHgWT9+vVyOp0aOXKkRowYIUk6ceKEtm7dqu3bt+uRRx7RlClTfD4TrOOQ8NRHrV+/XsXFxcrKytKPf/xj7y/f7777rv7rv/5Lr7/+up555hmLq4Q/li5dqsGDB1tdBjqQlZWltLQ0ZWRkKCMjQ/fcc89lzy8sLNTGjRsVFxenlStXKiUlRZJUUlKiFStW6LXXXtPYsWMVGxvbG+WHvK72n8c3vvENzZkz5+oWh07ZbDbdcsstmjdvnncsSdL58+f1wgsv6MiRI3rjjTe0fPly7zHGYGDpTh96MA4DxyOPPKL09HRFRET47P/ggw/0m9/8RqtWrdLrr7+usDD3E0PBPA555qkPcrlc2rRpkyTprrvu8rlrMX/+fI0cOVJFRUU6fPiwVSUCfcaCBQu0ePFiTZs2TfHx8Z2e/84770iSFi5c6POLQlZWlm6++WZdvHhRmzdvvlrl4hJd7T8EltmzZ+vuu+/2GUuSlJCQoLvuukuStGPHDrlcLu8xxmBg6U4fIvBkZ2e3CU6SdMsttyg5OVnnz5/X6dOnvfuDeRwSnvqgAwcOqLa2VkOGDNGoUaPaHM/JyZGkbk1VAdB9DQ0NKiwslCTNnDmzzXHPvt27d/dqXUBfNHLkSElSY2OjqqurJTEGg017fYjg47nbZLO5J7wF+zhk2l4fdOzYMUlqNzhJLXOBPechsH388ceqqamRYRhKSUnRjBkzNGjQIKvLQjecPn1ajY2N6t+/f7uLtnjGLGMz8BUWFuro0aNqaGhQYmKipkyZwnMWAebMmTOSpPDwcO/UH8ZgcGmvD1tjHAa+LVu26PTp00pJSfE+ghDs45Dw1Ac5HA5J6nBFPc9CA57zENjWrVvn0/7d736nRYsW6e/+7u8sqgjd1dnYjIqKUkxMjGpra1VXV6fo6OjeLA9dsHXrVp/222+/rZycHN1///0dru6G3vXee+9JkiZPniy73S6JMRhs2uvD1hiHgecvf/mLTpw4ofr6ep06dUonTpxQQkKCli9f7r0DFezjkPDUBzmdTklSZGRku8c9/0PxnIfANGbMGOXm5mr06NFKSEiQw+FQXl6e1q1bp9WrV6tfv36aO3eu1WWiCzxjrr154R6RkZGqra2V0+kMuB8YkJKTk7V06VJNmTJFgwYNUm1trYqKivT73/9en3/+uZqbm/XII49YXWbI27NnjzZv3qzw8HAtWbLEu58xGDw66kOJcRjI9u3bp4KCAm87MTFRDz74oM8dwWAfh4SnPsg0zSs6jsBw6Q+L1NRULVy4UBkZGXruuee0evVq3XTTTZf9nw8Ci2fsGYbR6TkITDfccINPOyoqStddd53GjRunhx9+WDt37lRxcXFAv6Okrzt58qT+7d/+TaZpaunSpUpLS/MeYwwGh8v1ocQ4DGRPPvmkJKm2tlbHjx/XmjVrtGLFCn3nO9/RwoULJQX/OGTBiD7Ik9Dr6+vbPe7Zzy3t4DRp0iRlZGTo4sWLKikpsbocdEFnY1NyP0grMT6DTUJCgnfJ5H379llbTAg7e/asfvKTn6i2tlbz589vc3eeMRj4OuvDy2EcBo6YmBiNGTNGTzzxhNLT0/X222/r4MGDkoJ/HBKe+iDPYgJnz55t9/i5c+d8zkPw8bwUsLKy0tpC0CWdjU2n06na2lrFxMQE3DQFdM6z3O758+ctriQ0VVVVaeXKlXI4HJozZ46WLl3a5hzGYGDzpw87wzgMLDabTddee61M0/Sunhfs45Dw1Ad5lvY8cuRIu8c973fynIfgU1tbKykw/0UGHUtNTZXdbldVVVW7PzQ8Y9bzdnYEl5qaGkmMSyvU1dXp+eef16lTpzRjxgx997vfbXdKEGMwcPnbh51hHAaeuLg4Se5wLAX/OCQ89UHZ2dnq16+fzpw5026A+vzzzyVJU6dO7e3S0AOqqqpUVFQkqePl6BGYIiIiNH78eElSXl5em+OefdOmTevVunDlTNPUzp07JYmlkntZY2OjfvrTn+rQoUOaNGmSvv/973tX9boUYzAwdaUPL4dxGJj2798vSRoyZIik4B+HhKc+yGaz6dZbb5Uk/fa3v/VZVe/dd9/VsWPHlJ2drczMTKtKRCdKSkpUWFjY5oHJ8vJy/exnP1N9fb2mT5/e4TKfCFzz5s2T5F6C/quvvvLuLykp0UcffaTo6Gjl5uZaVR4uo6qqSlu2bFFjY6PPfqfTqV//+tcqLS1VfHy8ZsyYYVGFoae5uVkvv/yyvvzyS40ZM0YPP/yw90WcHWEMBpau9iHjMPAUFRVp+/btampq8tnvcrn0/vvva+vWrYqIiNC1117rPRbM49AwA3k5C3RbQ0ODnnnmGZWWliohIUHZ2dlyOBwqLS1VXFycnnvuOe9zMwg8n3zyiV577TUlJCQoJSVF8fHxOnv2rA4fPqzGxkYNHz5cTz31lAYMGGB1qSFvz549Wrt2rbddWloqwzB8/nFi0aJFPnd633jjDb333nuKjIzUhAkT1NTUpPz8fDU3N+sHP/hBu29cx9XRlf4rLy/XAw88oOjoaA0bNkyJiYm6ePGijhw5ourqasXExOixxx5Tdna2FX+UkPTee+/pjTfekCTNmDGjw+cjli5dqv79+3vbjMHA0dU+ZBwGHs/vLHFxcUpPT1dcXJyqq6t1/PhxnT9/Xna7Xffff79PeJKCdxyyVHkfFRERoaefflrr16/XZ599pp07dyomJkazZ8/WkiVLWCwiwGVmZuqWW25RaWmpTp48qeLiYkVGRiotLU2zZs3SLbfcwhLlAaKqqkqlpaU++0zT9NnnmeftsWzZMqWlpWnTpk0qKChQeHi4xo8fr0WLFvEDv5d1pf/i4uJ0++23q7S0VGVlZTp69KjCwsI0ePBgzZ49W/Pnz/e+hBy9w/N8iyTt2LGjw/O+/e1v+4QnxmDg6GofMg4Dz9ixY/Wtb31L+/fv1/Hjx1VVVSWbzabBgwcrJydHc+fObfcf7IN1HHLnCQAAAAD8wDNPAAAAAOAHwhMAAAAA+IHwBAAAAAB+IDwBAAAAgB8ITwAAAADgB8ITAAAAAPiB8AQAAAAAfiA8AQAAAIAfCE8AAAAA4AfCEwAAAAD4gfAEAAAAAH4gPAEAAACAHwhPAICAtnjxYi1evFhffvml1aVcNdXV1Vq2bJnuuusuOZ3OK77etm3btHjxYr3yyis9UB0AwMNmdQEAgL5r8eLF3f7sfffdpzlz5vRcMQHsT3/6ky5evKg777xTUVFRV3y9WbNmae3atfr00081d+5cpaen90CVAADuPAEArpoBAwa0+19kZGSn50REREiSUlNTlZqa6vOZvuT06dP68MMP1b9/f/3N3/xNj1wzLCxMixYtkmma+t3vftcj1wQASIZpmqbVRQAAQsvq1au1Zs0a73Yo+/d//3d99NFHuu2227R06dIeu25TU5PuvfdeVVVV6fnnn1dGRkaPXRsAQhV3ngAAsIjT6dS2bdskSddff32PXjs8PFyzZs2SJH344Yc9em0ACFU88wQACGie56aefvppjRs3zru/vLxcDzzwgCTplVdekWEYWrt2rfbt26eqqioNHDhQX//617VgwQLvc0THjx/Xhg0bVFRUpKqqKiUmJmr27Nm6/fbbZbN1/COxsrJSGzdu1N69e1VeXi6Xy6WEhASNHz9e8+fP17Bhw7r1Z/vss89UV1enoUOHKi0trcPzSktL9f7776u4uFiVlZUKCwtTXFyckpKSNGHCBN14441KTExs87nrrrtO//M//6Nt27Zp2bJlPfI8FQCEMsITACDoHTlyRKtWrVJtba2io6PV1NSkM2fOaN26dSoqKtKTTz6p/Px8/eIXv1B9fb369esnl8ulsrIyvf322zpx4oS+//3vt3vt3bt36+WXX/aughceHi6bzaby8nJ9/PHH2rp1q+69917Nnj27y3Xv3btXkjRmzJgOz/nkk0/0+uuvyzPL3m63KywsTA6HQw6HQ0VFRRo0aFC7i2tkZGTIbrervr5eRUVFmjJlSpdrBAC0IDwBAILeqlWrlJ6ern/4h3/QsGHD1NDQoP/93//Vm2++qaKiIq1Zs0abNm3StGnTdMcddygpKUlOp1MbNmzQunXrtH37duXm5mrixIk+1z148KD+5V/+RS6XSzfddJPmzZunlJQUb3jZsGGDPvjgA61atUrDhg3r8nNFxcXFkqTMzMx2j9fX1+s///M/ZZqmrr/+en37299WcnKyJPeUv9OnT2v79u3q379/u5+32WxKT09XcXGx9u/fT3gCgCvEM08AgKA3cOBAPf74497pcxEREfrmN7+p6667TpK0bt06ZWZmavny5UpKSpIkRUVF6Tvf+Y73rs/27dvbXPc//uM/5HK5tGjRIt1zzz0aOnSowsLcPzoHDRqku+++W9/85jfV1NSktWvXdqnmM2fO6MKFC5LU4ZS9EydOqK6uTpGRkbrvvvu8wclTf3p6uu68805NnTq1w+/xXLukpKRL9QEA2iI8AQCC3rx582S329vsnzRpknd7wYIFMgyjw3OOHTvms//o0aM6dOiQwsPDddttt3X43Z7pegUFBWpubva75vPnz3u3O7pz1K9fP0mSy+VSdXW139duLS4urs33AQC6h2l7AICg19G0twEDBni3O5pS5zmntrbWZ/+BAwckSaZpavny5R1+tycw1dfXq7q62uc7L6eqqsq7HRsb2+45ycnJGjp0qE6dOqUf/ehHuvnmmzV58mSNGDHCewesM55rt/4+AED3EJ4AAEGvo1XkwsPDvdvR0dGXPaepqclnv+dOTXNzs3d6XWfq6+v9Ok+SGhoavNsdrfQXFham5cuX6+c//7nKy8v11ltv6a233lJkZKSysrKUk5Oj2bNnX/YFwp6XDTc2NvpdGwCgfYQnAADa4bmjNHToUP3iF7/o8et7ptNJ7rteHd2xSktL07/+679q9+7d2rdvn4qLi3Xy5EkVFBSooKBA69ev1xNPPKERI0a0+/mamhpJHd/dAgD4j/AEAEA74uPjJbkXdnA6nT3+jqTWzznV1NRcdrqfzWZTTk6OcnJyJEnV1dXKy8vTH//4R509e1avvvqqXnzxxXY/6wlPHT1XBQDwHwtGAADQjtGjR0tyL9awY8eOHr9+SkqKd8rgmTNnuvTZuLg43Xzzzbrjjjskud9z1dGCEuXl5ZLcd9AAAFeG8AQAQDsyMjI0atQoSdJ///d/d7rggucOj7+ioqK81z948GC753T2nJLneSZJHS4g4bn22LFju1QfAKAtwhMAAO0wDEP/+I//KLvdLofDoR/+8IfKy8vzWRTi3Llz2rp1q5599ln9/ve/7/J3eAJNR+Fp27ZtevLJJ/Xhhx/63J1qbm7W3r179dZbb0mSsrKyFBMT0+bzlZWVcjgcPt8FAOg+nnkCAKADmZmZeuyxx/Tyyy+rvLxcL730ksLCwhQTE6OGhgafIJWbm9vl61933XX6y1/+ov379+vixYve9zq1VlxcrOLiYkmS3W5XVFSUampqZJqmJCkhIUHf+9732r3+rl27JLkXnfC8QBgA0H2EJwAALmPixIn65S9/qQ8//FB79uzRyZMnVVtbq4iICA0bNkxZWVmaPn26Jk6c2OVrp6WlKTMzUwcPHtSOHTs0Z84cn+PTp0/XAw88oMLCQh05ckSVlZWqqalRdHS0UlNTNW3aNN16663t3nWSpE8//VSSdNNNN3W5NgBAW4bp+acrAADQ67Zs2aJXX31V48aN09NPP91j1y0vL9eDDz6oqKgorVq1qsP3XAEA/MczTwAAWOj666/XsGHD9OWXX3b47FN3/PnPf5ZpmvrWt75FcAKAHkJ4AgDAQmFhYbrzzjslSX/605965JoOh0ObN2/WoEGDNHfu3B65JgCAZ54AALDc1KlTtWzZMtXW1vbIC3kdDocWLFig8ePH+yxnDgC4MjzzBAAAAAB+YNoeAAAAAPiB8AQAAAAAfiA8AQAAAIAfCE8AAAAA4AfCEwAAAAD4gfAEAAAAAH4gPAEAAACAHwhPAAAAAOAHwhMAAAAA+IHwBAAAAAB+IDwBAAAAgB8ITwAAAADgB8ITAAAAAPiB8AQAAAAAfvj/kBQLqvgJLN4AAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t, v)\n", "\n", "# 수치해 결과 그리기 (Marker만 그리기)\n", "plt.plot(sol.t, sol.y[0], linestyle='None', marker='x')\n", "\n", "# x,y 축 이름\n", "plt.xlabel('Time (s)')\n", "plt.ylabel('Velocity (m/s)')\n", "\n", "# 그래프 선 이름\n", "plt.legend(['Exact Solution', 'Numerical Solution'])\n", "\n", "# 그래프 이름\n", "plt.title('Velocity of Paratrooper')\n", "\n", "# 그래프 저장\n", "plt.savefig('velocity.png', dpi=200)" ] }, { "cell_type": "markdown", "id": "8a59313e", "metadata": {}, "source": [ ":::{note}\n", "수치해석은 모든 답을 줄까?\n", "No !!! (No free lunch!!!)\n", "::: " ] }, { "cell_type": "markdown", "id": "6b25427d", "metadata": {}, "source": [ "계산 결과를 저장하자.\n", "\n", "ASCII 방식과 Binary 방식이 있다.\n", "\n", "- ASCII data: 사람이 읽을 수 있도록 숫자, 문자, 기호로 표기\n", "- Binary data: 컴퓨터가 저장하는 2진수 방식으로 기록\n", "\n", "행렬 (Array)를 어떻게 구분할까?\n", "\n", "- Whitespace (띄어쓰기, Tab)\n", "- CSV 파일: https://ko.wikipedia.org/wiki/CSV_(%ED%8C%8C%EC%9D%BC_%ED%98%95%EC%8B%9D)" ] }, { "cell_type": "code", "execution_count": 14, "id": "ceaf6498", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0.00000000e+00, 0.00000000e+00],\n", " [1.00000000e-04, 9.80990997e-04],\n", " [1.10000000e-03, 1.07899107e-02],\n", " [1.11000000e-02, 1.08780146e-01],\n", " [1.11100000e-01, 1.07885319e+00],\n", " [1.11110000e+00, 9.86025483e+00],\n", " [4.72197940e+00, 3.09793935e+01],\n", " [9.26404220e+00, 4.36818913e+01],\n", " [1.47507404e+01, 4.98740638e+01],\n", " [2.13260752e+01, 5.23714367e+01],\n", " [2.93351884e+01, 5.31924207e+01],\n", " [3.00000000e+01, 5.32214224e+01]])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 데이터: (시간, 값) 으로 기록\n", "arr = np.array([sol.t, sol.y[0]]).T\n", "arr" ] }, { "cell_type": "markdown", "id": "d3cd10b4", "metadata": {}, "source": [ "`numpy` 에 `savetxt`, `loadtxt` 함수를 활용하자." ] }, { "cell_type": "code", "execution_count": 15, "id": "f945bcc3", "metadata": {}, "outputs": [], "source": [ "# sol.csv 파일로 기록\n", "np.savetxt('sol.csv', arr, delimiter=',', header='t,v', comments='')" ] }, { "cell_type": "code", "execution_count": 16, "id": "1ea73d1f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "t,v\n", "0.000000000000000000e+00,0.000000000000000000e+00\n", "9.999999999999999124e-05,9.809909967511212543e-04\n", "1.100000000000000066e-03,1.078991067353642086e-02\n", "1.110000000000000049e-02,1.087801455912157239e-01\n", "1.111000000000000043e-01,1.078853190808823914e+00\n", "1.111099999999999977e+00,9.860254828888242784e+00\n", "4.721979401067658344e+00,3.097939353875368340e+01\n", "9.264042202257618541e+00,4.368189129769811530e+01\n", "1.475074044342309776e+01,4.987406378138719276e+01\n", "2.132607522137336886e+01,5.237143665039166507e+01\n", "2.933518837367320486e+01,5.319242067027523291e+01\n", "3.000000000000000000e+01,5.322142241925892847e+01\n", "\n" ] } ], "source": [ "# 확인 (Excel 에서도 읽기 가능)\n", "with open('sol.csv') as f:\n", " print(f.read())" ] } ], "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 }