{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 10wk-1: 중간고사\n",
"\n",
"최규빈 \n",
"2023-05-08\n",
"\n",
"
\n",
"\n",
"**제출은 `*.ipynb`, `*.html`, `*.pdf` 파일로 제출할 것**\n",
"\n",
"- `ipynb` 파일형태제출을 권장함.\n",
"\n",
"# Imports"
],
"id": "1d56922c-ce1f-40e9-a367-a221ab61a7b4"
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import yfinance as yf\n",
"import PIL\n",
"import io \n",
"import requests"
],
"id": "57a11f55-3e57-4fb5-b03d-038ef3bdcd03"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 1. Numpy and Pandas (35점)\n",
"\n",
"## FIFA23\n",
"\n",
"`(1)--(3)` 아래는 FIFA23 자료를 불러오는 코드이다."
],
"id": "12c0f64f-858c-4660-b09d-77187becd86e"
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"df=pd.read_csv('https://raw.githubusercontent.com/guebin/DV2022/master/posts/FIFA23_official_data.csv').drop(columns=['Loaned From', 'Best Overall Rating']).dropna().reset_index(drop=True)\n",
"df.head()"
],
"id": "59745b07-8533-47ea-ac3f-b88f893391c6"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(1)` 공백이 포함된 column이름이 총 몇개인지 count하는 코드를 작성하라.\n",
"\n",
"**hint** 모두 11개의 column name에 공백이 포함되어있음\n",
"\n",
"`(풀이)`"
],
"id": "17e64173-03dd-4776-9374-25ef29df2573"
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"sum([' ' in name for name in df.columns])"
],
"id": "d563d4d0-100a-40a7-8bbb-06e346f7b95b"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(2)` column name에 공백이 포함된 열을 출력하라.\n",
"\n",
"`(풀이)`"
],
"id": "1209a818-810a-4f8c-b4fc-1470fb8917eb"
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"df.loc[:,[' ' in name for name in df.columns]]"
],
"id": "88490ceb-420a-4224-b39a-f9601a158ed9"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(3)` 데이터프레임을 올바르게 해석한 사람을 모두 고르시오 (모두\n",
"맞출경우만 정답으로 인정)\n",
"\n",
"- 세민: 데이터프레임에는 모두 27개의 열이 있다.\n",
"- 성재: 한국선수(`Nationality==Korea Republic`)와\n",
" 일본선수(`Nationality==Japan`)의 `Overall`의 평균값은 일본이 더\n",
" 높다.\n",
"- 민정: 총 159개의 나라선수들이 포함되어 있다.\n",
"- 슬기: 선수들의 연령이 25세이상(\\>=)인 선수들은 그렇지 않은\n",
" 선수들보다 평균적으로 키(`Height`)가크다.\n",
"\n",
"`(풀이)`\n",
"\n",
"**세민**: 데이터프레임에는 모두 27개의 열이 있다 -\\> True"
],
"id": "b72fab48-63d9-4f5d-ad9a-7c1a5d5f8266"
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"len(df.columns) == 27"
],
"id": "f6b78e34-6e14-4532-b64b-39c53e4c8615"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**성재**: 한국선수(Nationality==Korea Republic)와\n",
"일본선수(Nationality==Japan)의 Overall의 평균값은 일본이 더 높다. -\\>\n",
"True"
],
"id": "965a8411-ac9c-4f55-be6b-07ed276fa962"
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"df.query('Nationality == \"Korea Republic\"').Overall.mean() < df.query('Nationality == \"Japan\"').Overall.mean()"
],
"id": "94e2ff81-7044-43d8-b2cc-478c9ada91bb"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**민정**: 총 159개의 나라선수들이 포함되어 있다. -\\> True"
],
"id": "e072bf1d-ac90-4526-9f31-35ae8e3bb169"
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"len(set(df.Nationality))==159"
],
"id": "8016e847-1752-4e13-8ee4-3f5e6b4e350d"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**슬기**: 선수들의 연령이 25세이상(\\>=)인 선수들은 그렇지 않은\n",
"선수들보다 평균적으로 키(`Height`)가크다. -\\> True"
],
"id": "32cb2392-8c25-404f-9f5f-d3454260b81d"
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"_old = np.mean([int(height[:3]) for height in df.query('Age>=25').Height.tolist()]) \n",
"_young = np.mean([int(height[:3]) for height in df.query('Age<25').Height.tolist()]) \n",
"_old > _young"
],
"id": "d6f2925d-0862-46e8-b017-315b61ce05ec"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 삼성전자의 주가\n",
"\n",
"`(4)--(5)` 다음은 삼성전자의 주가를 크롤링하는 코드이다."
],
"id": "b5b0b517-c798-4567-b2cc-9d4365703023"
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[*********************100%***********************] 1 of 1 completed"
]
}
],
"source": [
"start_date = \"2023-01-01\"\n",
"end_date = \"2023-05-02\"\n",
"y = yf.download(\"005930.KS\", start=start_date, end=end_date)['Adj Close'].to_numpy()"
],
"id": "ac8f0da9-e17e-45ed-9d34-afa3ca784df3"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"삼성전자의 주가 ${\\boldsymbol y}$를 시각화하면 아래와 같다."
],
"id": "d24addd6-6bb9-41f1-a0f4-2f8cfd3a4925"
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
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c1UdqXBS2iNk1Kr3A2uTmsX1nmJ8cyztWZoesLpGBHGSMOQiUjHJ/kc/PBvj4CMc9DDzs\np3w/sDqQuqjxe73MTmSEsGmhew/VJfMS6e5zUdvS7b0yUWq6nW3tptzeyS2bC5mXHMsju6o4drad\nNfkpg44rrWvlf/5ygmtXz+d9Jfnc+9eyYS0DxyybfeyRmRhNXJSN7j4Xt2wuDOmKqzoDOQzsPG3n\nwsJUEmLcsX9pdiKAdhWpkNpR5h7UsHVJJhutnbyGdhU5+wf47GMHSYuP5lvvWYOIUJA2eDgmuLuJ\nZtO6RB4iQkF6HFE24aZNBWOfMIU0GMxxrV19HKltHbRT0pIsKxjo8FIVQjvL7GQkRLM8O4mclDjy\nUuPYX9k86JjnS89xsr6Db2xf7b3y97f0s6PTSeosDAYAN27I5+OXL2FeUmxI6xFQN5GavXaV2zFm\n8LZ5aQnRZCZG67IUKmSMMew4beeixRlEWP38JUVp1ugi4519+8tdlSzIiOdqn770gvQ4HJ1OOnr7\nSbRau81dTtYO6V6aLW6/bHGoqwBoy2DO21HWRHy0jeL81EHli7MSOdWgw0tVaJxu7KS+rZeLF5+/\nSClZkEZDey81VhfQsbNt7Kts5oObF3gDBpxf4M3TOjDG0NzZNytzBjOJBoM5rKfPxbOH67hsaRbR\nkYP/1EuzEylr6PA7m1OpqbbztHvRxK1Lzi/GVlLkHuDgmW/wyK4qYqMieF9J/qBzPSNwPMGg0+nC\n6RqYlTmDmUSDwRz2p1GWwl2SlUhbTz+N7b1+zpw9TtW3c9P9u2jr6Qt1VdQ4vH7KTl5qnPcqH2BZ\ndhJJMZHsq2ymtbuPP75Zy/bivGG5gKFLPzfP0qUoZhoNBnPYI6MshbvUmuU42/MGfzvZyO5yBweG\nJB7VzOUaMOwub2LrkoxBK3PaIoT1C9I4UOXgiQM1dPe5/C7NkBofRWJMpLc7ybMUhbYMJkeDwRzl\nWQr31ov8L4W7ZJ57RNGpWR4MKps6AfdYdDU7vFXbSltP/6BBDR4bi9I4Wd/Bw69XsL4wldV5w5PC\n7uGY8YMWeANIm0XLV89EOppojnpkZyWJMZG8d32+3/vnJcWQFBs5rpbBqfp2KpvOD+mLiYzg4sUZ\nIZ0oU2XVp7SuLWR1UOOzu9w9v8Bfi3XDAnfeoLalmzu2LR92v0dBWhwVdveFwGxdpG6m0WAwB9k7\nenn28Flu3lTgHXo3lIiwZF7iuILBzQ/sGbZa5E8+uJ5tq3MmVd/JON8y0GAwW+ypcLAoK8HvuPp1\nBalERgip8VFsWz1/xMcoTI/ntVONGGNwdLrzRbNtkbqZRoPBHPTYvmqcrgE+NMaiV0vnJfLK8cD2\nhXD2D2Dv6OVDWxbw/o0F9PS5uPEnu7xX5qHg7B+gtrmb+GgbZxxdtPX0kRyCdeBV4FwDhn2VDq5f\n6/8CIi7axkcuXcjirERiIm0jPk5hRjw9fQM0dvTS3OkkQtC//SRpzmCO6XcN8KvdVVyyJNObFxjJ\nknmJ2Dt6abGa2aPxNMWXz09idV4KJUXpJMZEcra1Jyj1nojalm4GDFxxwTwAjmrrYMY7fq6N9p5+\n7zpZ/nzp2hX8Y8noSzP4Di91dDlJi48eNBdBjZ8Ggznm5eMNnG3t8TucdKil8wIfUeTpHspMPN8U\nz0mJ5Wxr90injOhcaw///rtDk95gx9NF9M417qtM7Sqa+faUu+cQbF44uc3eC7wTz7pp7pydi9TN\nNBoM5pj9lQ5iIiO8V8ujWZBh/UM1j93V4xmxkZEY4y2bnxLLuXG2DKodXbzvpzv53YEavv7M0XGd\nO1SVlUDcuDCdzMQYHVE0C+ytcJCfFkduatykHic/zX3+GUcXjlm6SN1Mo8Fgjqls6mJBRnxAI3xy\nUtz/UHUtY3+gN3UM30kqNyWOunEEg7KGDt73k120dffzvg35vHay0TuyZCTO/gE+9NAe7vvr6WH3\nVTZ1kRgTSUZCNKtyk7WbaIYzxrC30jFqF1GgYqNsZCfHUO3ooqWrj9R4zRdMlgaDOaaqqZMFGQkB\nHRsXbSM1Piqgq3tvN1HC4JaBvaPXu/vUaErrWnn/T3fRPzDAo7dv4ZvvXs385Fi+9/zxUZfEuPul\nk/z9lJ0/Hakbdp/7tcYjIqzKTeZUQwc9fa4x66JC43RjB45OJ5uDEAzAnTc4Y+UMdCTR5GkwmEMG\nBgxVTV0UZQS+Yc385MD6/R2dTiIjhOS48wPQclJiMQYa2scOJh/79RtER0bw+L9exIqcZGKjbHzq\nyqW8caaFV443+D1nT3kTP/nbaZJiIjl+tn3YB737tboD3+q8FFwDhpO6t/OMtTtI+QKPQmspa80Z\nBIcGgzmkvr2H3v6BgFsGALmpcQGNCGrqcF99+c5mzrH6fcc6397RS1VTFx+5ZCGLss6PcHpfST5F\nGfF8/4UTw7bgbOvp43OPH6IwPZ5vvns1/QNmUIK43zVAdXOXN++xKjcZ0CTydOnpc3kXmwvU3goH\n85JivH+zycpPj6eutYf+AaM5gyDQYDCHVNrdieCicQSDQJPATZ3Dm+I5Ke5JQ2MFA88H9ErrA9sj\nyhbB565ezvFz7TxzeHA30NeeKuVcWw93v38dF1szVQ9Vt3jvP9vaQ5/LeF9rQVo8STGRmkSeJg+9\nXsEtD+yh0krij8UYw94Kd77A3/IoE+G7yJ22DCZPJ53NIWcc7n/M8Vx55abE0tTppKfPRWzUyJN8\nmjp7yfQZSQTuQAJwboxuJs8H9Kqc4evMXL8mh5/89TTffu44u067k8kdvf08e/gsn75yKesL3dsh\n5qTEcqimxXueZ1ip57VGRAgrcpO1ZTBN/nK0HoC9lQ6KModffDx1sJaspBjvfgVnHF2ca+th86Lg\ndBGBe0kKj3Rdl2jStGUwh1Q2dRFlk3EN25tvjSiqbxv96t7R6SQjcfDVV3Kse/XIsUYjlda1kZ8W\nR4qfER8REcJ/Xr8CW4Tw6okGXj3RwL5KB9euns8nrljiPW5tfgqHa85f9XvWSPL9IFqVm8zxs+24\nBnSPhqnU0N7jbaXtr3QMu7/L2c+//+4wtz60l2cOuVt8eyo8+YLgJI/BPQvZQ9clmjxtGcwhVU2d\nFKTHYxvHTExPV09dS8+ouQZPzmCoQLqZjta1efv0/bl4cSY77rxi1McoLkjlhdJ6Wrrce91W2TuJ\njYpgXtL51sqq3BS6+yqpsHewxJpQp4LvVSvhX5QRP2zPYoB9lc04XQPkpcbxqUffpMvZz77KZtLi\no7z7bwdDdlIs0bYInK4BDQZBoC2DOaTS3jWufAGcDwbn2kbu6unpc9HR2z+sm8hz/mijkTp6+6mw\nd7Iqd3L7066ztu30tA4qm7pYkJ4wqP9Zk8jT46VjDeSlxvH+jYWU2zuHLV64s8xOlE145pOXcOnS\nLL745BH+dPgsmxamB3XJiIgI8U4+05zB5GkwmCOMMd5x9+MxP4AksGf2sb+WgTsYjHzusbPuD+bR\nWgaBWJ2fgsj5JLK/17pkXiLRkRGU1rXR2dvPA6+Vc9G3X+ZrT5dO6rnVeT19Lv5+qpErV8xj00J3\nPmdo6+D1MjvrC9NIT4jmgVs3cM2qbLr7XGwK0pBSX/lWSzg5Vjs5JkuDwRxh73DS6XSNu2UQHx1J\nSlwUZ0fp9/fMPs7w200UR2NHL30u/xPPSmut5PEkWwbJsVEszkrkUE2Lez6Fo2tY4jLKFsHy7CSe\nPljH1u++wl3PHaO7z8Xj+6vpdupktGDYedpOT98AV67IZnVeCtGREYPyBs2dTo6ebfNuXBMTaePe\nW9Zz7y3r+cDmwqDXZ01eMosyE4I2QimcaTCYI6qaxj+SyGOsq/umTnc3wNAEMrhHIxkzcgK6tK6N\njIRospOHdzGNV3F+KgerWznb1oOzf8Dva92wII1zbT2ULEjn9x+7mPs+sIEup4uXj9dP+vmVu4so\nIdrGlkXpxETaKM5PYX/V+ZbBrvImjGHQLmaRtgjeuTZn1NFqE/WZq5bx1Ce2Bv1xw5EGgznCO7pm\nnC0DGLvf/3zLYPgH+vnhpf6DwVt1bazMTQ7Kldu6ghTsHb3eIaj+Xusd25az484rePC2EtYXprFp\nYTrzk2N56uDw5SzU+BhjeOVYA5cuzfLuNVBSlM5bta3eltfrZXYSYyIpzp9cSzBQUbYI4qO1iygY\nAgoGIpIqIk+IyHEROSYiF4nI963bh0XkDyKS6nP8l0SkTEROiMg1PuXbrLIyEbnTp3yhiOyxyh8T\nEc0GjVNVUye2CCEvbfyrQc5PiRt1RND5FUv9tAysYaz+Fqzr7Xdxqr590l1EHsUFqYB7DDv4bwXF\nR0eS5zO01hYhvKs4h7+eaKC1qy8o9QhXpXVtnGvr4coV51fE3ViURv+A4aCVy9lZZmfLovSQboWq\nJibQv9g9wPPGmAuAYuAY8CKw2hizFjgJfAlARFYCNwGrgG3A/4mITURswL3AtcBK4GbrWIDvAncb\nY5YAzcBHgvHiwkllUxd5qXFETeCf0HfimT/2zl6ibRF+t9AcbeLZqfoO+gfMpJPHHhfMTybaFsGO\nMjvRtgjvqqtj2b4ujz6X4c9vnQ1KPcLVS8fqEYHLfZZH31Donjewv9JBTXMXlU1d3olmanYZ85ND\nRFKAy4CHAIwxTmNMizHmL8aYfuuw3YBn5/XtwKPGmF5jTAVQBmyyvsqMMeXGGCfwKLBd3P0HVwBP\nWOf/Anh3UF5dGJnISCIPzwf6SP3+jg73hDN/XT1JMZEkRNv85hy8M4+DFAyiIyNYkZvMgIGC9LiA\n51OsynUnGbWraHJePtbAhQWpg4YYp8RHsTw7iX1Vzewsc3ffXbJUg8FsFMhl5EKgEfiZiLwpIg+K\nyNDO2n8G/mz9nAdU+9xXY5WNVJ4BtPgEFk/5MCJyu4jsF5H9jY2B7d0bDowxVNg7J5QvgPNdPSMl\nkf2tS+QhIuSkxvkdjVRa10ZCtG3C9fJnndUXPZ7HFBFuWJfL7oqmcW/Go9wa2ns4UtvKlSuyh91X\nUpTGG1XNvHaqkaykGJaOsd2qmpkCCQaRwHrgPmPMhUAn4Nvf/x9AP/DrKamhD2PM/caYEmNMSVZW\n1lQ/3azR0tVHe0//pFsGIyWRmzqdg3Y4GyonJZazfloVpVbyOJgTjTx5g/GszApwQ3EuxsCzh7V1\nMBFvWUOE/S0nsbEonY7efl4oPcfWxRk6zHOWCiQY1AA1xpg91u0ncAcHROSfgOuBD5jzO5TUAr67\nWedbZSOVNwGpIhI5pFwFyLNo20SvwMdafbSpo9fvHAOP+cmxw3IGrgHDsbNtQUsee1xoLVy3eN74\nXuuirETW5qdoV9EEHT/n3idi2fzhy3yUFLn/Jn0uw8VLtItothozGBhjzgHVIrLcKroSOCoi24A7\ngBuMMb6b6D4N3CQiMSKyEFgK7AX2AUutkUPRuJPMT1tB5FXgRuv824CngvDawkaVd9G2ibUMPBPP\nRupCaepwjhoMclLjaGgfPPGssqmTLqdr2LLVk7UwM4HHbt/CP6zPH/vgIW4ozuVIbSvljR1BrVM4\nOHGunbzUOJJjhy82mJca572g2KrBYNYKdOjJJ4Ffi8hhYB3wLeDHQBLwoogcFJGfABhjSoHHgaPA\n88DHjTEuKyfwCeAF3KORHreOBfgi8DkRKcOdQ3goGC8uXFQ1dSEC+WkT3zQkJyXW7+qjXc5+uvtc\nY3YTuXc8O79GjWd9oGAlj31tXpQxoQlM16/NBeDFozoBbbxOnGtnuZ9WAbhzMm9blsXKnORBw3rV\n7BLQbA1jzEGgZEjxEj+Heo6/C7jLT/lzwHN+ystxjzZSE1DV1EluStykZnjOT4n1u1jdaEtReHi7\nmVq6vR8GpXWtRNmEpTNo9dD5KbEUpscP2hfBV1lDO6V1bWxf53f8Qtjqcw1wurFj0JDSob6+fZUu\nHT7L6cyQOaByEsNKPXJS/I8IGm3Cme+5cD7n0NPn4pmDdVxYmEZ05Mx6ixUXpHKo2v9uaPe8XMZn\nHzvofc3Krbyxkz6XYXn2yIE9JtKmM4FnuZn1n6ompKqpa9yja4bKGWHimWddopGGlsLwJSl+vecM\nda09fObKpZOq01Qozk+htqWbhvbBgc8Yw74KBwPm/Hr9yu34OXeX30jdRGpu0GAwy7X19NHU6aRo\n0i0D9wd6Q9vgtek93UT+9jLwSI51Tzyra+2mo7ef/3u1jK1LMmbkyJJ11tDUw0NaB7Ut3Zyzhsfq\nonaDnTjXTmSEsDiIG9OomUeDwSznWd9/8i0DzxpDg/MGTaPsZeAhIt4dzx5+vYKmTif/fs0Fk6rP\nVFmVm4ItQoblDTxr8hcXpPLaSTvOfv9LcoejE+faWZSVMOO6/FRw6V93Fuvo7ec///gW+Wlxk14C\nYKTVRx2dTmKjIoiPHj05nZsax4lz7TzwWjlXr8z2XoHPNHHRNpZnJ3kXVvPYX+UgMSaSj719MR29\n/eypaApNBWeg4+faWT4/+KPC1MyiwWAW++YzR6l2dHH3+9f5XURuPLx7IQ9pGdg7eslIiBlzVun8\n5FjK7Z10OPv5wjXLRz021NxJ5BbOz5N0twzWL0jjsqVZxERG8PIxzRsAtPf0UdvSzQWaL5jzNBjM\nUs+/dY7H9lfzsbcvYWPR8CUCxishJpLk2MhhLYMma5G6sXiCyXsuzGPZKKNOZoLi/BTaevq9e0C0\ndvVxor6djQvSiIu2ccmSTF46Vj8oWISrk/XumcejjSRSc4MGg1mooa2HL/3+MGvyUvj0VcEbsZOT\nEjds4pmjc/TZxx6r81JIjo3ks1ctC1p9popnfSNPvuWNM80Y496oBeDKFdnUNHdzsl5nKnuWodCR\nRHOfBoNZ6M7fH6G7z8Xd7183of0LRpKTOnziWVNHL+l+djgb6upV83njv95BQfrkRjVNh6XzEomL\nsnnzBvsqHURGiDfP4dm85aVjwRlVZIzhp387TVlDe1AebzqdONdOYkwk+RPYNEnNLhoMZpnmTiev\nHG/gXy9bzJIgLxWcY40I8jDG0NTpJDOAbiJg1uxuFWmLYE1eindE0f7KZlbnpRBnJcmzk2NZk5fC\ny0EKBmdbe/j2n49z/2vlQXm86XT8XDvLshN1JdIwMDv+e5WXZ82fYOQJhspJicPe4aSj1721RKfT\nRW//wKjDSmer4oIUSuva6Ozt52BNCxutlTc9rlwxjzerW7B39I7wCIHzdEftKGuaVXkIY4y1JpGO\nJAoHGgxmmWDvHubLMzz1FzsrAfcOZ8Coi9TNVsUFqTj7B/jd/mqc/QPefIHHVSuyMUGajXyoxv03\nq23p5oyja4yjZ476tl5au/t0JFGY0GAwy5TWtZGbEkvaFFytry9M46oV8/jJ307T0uXEbi1FEcho\notmmOD8VgId3VAJQsmBwy2BVbjLzk2N5JRjBoLrF29X2epl90o83UTXNXaz6yvPD5liMRJehCC8a\nDGaZ0rpWVgZ5wxhfn796OR29/fzkb+XnWwZzsJsoPy2OjIRozji6WJSZMKz1IyJctiyTnaebJrUa\np2vAcKS2lWtX5zA/Oda7T3AoHKpupdPpYkeAAemENZJIWwbhQYPBLNLl7Kfc3jklXUQeK3KSuaE4\nl5/vrODYWfeV4VzsJhIR7xDTkiH5Ao+tSzJp7e7zds1NRHljBx29/awrSGXrkkx2nrYzEKKlnivs\n7qGygb6eE/XtZCfHkBo/9y4G1HAaDGaAbqeLX+6qpKZ59P7kY2fbMWZq8gW+PveOZfS7DD/522lg\nbrYM4HxX0dB8gcdFizMAd+J3ojxdMsUFqWxdkkFzVx9HrSA73cob3dujegYhjEWTx+FFg8EM8I1n\nS/mvp0p5+/f/yuceP8ipev/j0Y96ksd5U9dNBO5F796/sYBOp4uEaNukNs2Zya64YB65KbFcOsK6\nTvOSYlmenRRwt4o/h2paSIqJZFFmgndLyMk83mSU293BoKqpi7aevlGP7XL2c7K+fcovPNTMocEg\nxF48Ws9v91bzwS2F3HpREX8+co533P0aX/jdoWHDEEvr2kiNjyLXWvphKn3qyqXERkWQPgeTxx5r\n8lPY+aUrvSu2+nPxkgz2VTqG7fMQqEPVrawtSCEiQshOjmXJvER2nJ7+vIExhvLGDu9OdMfGaB3s\nrXC4N7i3Wkdq7tNgEEIN7T188cnDrMxJ5ivXr+Ir71rJjjuv4OZNhTxxoMY7JNGjtK6NVbnJ0zIB\nKDs5lq9cv4qbNxVO+XPNZJcsyaS3f4A3zjSP+9yePhfHzrZ5u6M8j7e3oone/okFl4lydDpp6+nn\n+uIcYOyuop2nm4i2RVCyIPjzWdTMpMEgRIwxfPGJw3T29nPPTeu8a8WnJ0Rz57UXEG2L4KmDtd7j\n+1wDnDjXzqopHEk01C2bC/nY20fc6josbFqYji1CJtS1c/RsG/0DxpuoBrh4cQY9fQO8eaYleJUM\ngKeLaMvCDDITY8YMBq+fsrN+Qap3Vraa+zQYhMiv9pzh1RONfOnaC1g6ZEXIlLgoLr8gi2cPn/UO\nayxr6MDpGtA+3GmWFBtFcX7KmElkYwyd1sxtD8/MY9+9HbYsziBCYOc05w0qrOTxoqwEVuUmjzqi\nyNHp5OjZNi6ZgTvVqamjwSAETjd2cNefjnLZsixuvajI7zHb1+XR2N7L7nL3h5DnSk6DwfS7ZEkm\nh2taRky6djn7ufXhvVz8nVeo9plhfKi6hfnJsWQnn8/xJMdGsTY/ddonn522dxBlE/LT4lmVm0xZ\nQ8eIXVW7rJzGTNy2VE0dDQaTsL/S4V3HJ1B9rgE+8+hB4qJsfP/GtURE+O//v+KCeSTGRHq7ikrr\nWomLsrEwU/ehnW4XL8lkwMBuP4nftp4+bnt4LzvK3Ftlfv7xQ97W3KGaVooLhnfrXbIkk0M1rbSP\nMaInmCoaO1mQkYAtQliVm0L/gOHkOf9LdL9eZicpJpK1UzxqTc0sGgwmqLW7j3/86S4+9ds3x7X4\n2D0vneJIbSvffu+aQVeMQ8VG2bhm1Xz+/NY5evpclNa1cUFOErYRgoeaOhcWphIXZWPnkGDg6HTy\ngQf28OaZFn5083r++92r2Vvp4KevuZfzqLB3DsoXeFy2LAvXgOGpg3XT9ArcOYNFme59sj2ty5G6\ninaetrN5UcasWYVWBYf+tSeo2tHFgIFXjjfw6z1nAjpnf6WD//trGe/bkM+21TljHr99XS7tPf28\neryBY9ZIIjX9YiJtbFyYPiiJfKi6hZvu38WJ+nbuv3UD71ybw3vX5/HONTn8719O8pu97vfEOp+R\nRB4bi9LYsCCNH71yasJDVsfDNWCoaupkYZY7GBSmx5MYE+k3iVzt6KKqqYutS3RIabjRYDBBNc3u\nTWAWZMTz3386yunG0XfFau/p47OPHyQ/LZ6v3rAqoOe4eHEGmYnR3PvXMtp7+6d1JJEabOviDE41\ndPD0oTo+8OButt+7g/q2Xn7+Txu54oJswL3ExV3vWU1GYjTfe/4EIrA6f/jfTES445rl1Lf1eleI\nnUo1zV30uQyLrS7GiAhhZY7/JPLO0+6At1XzBWFHg8EE1ba4g8FPP7SB2Cgbn33sIH2uAcC9LeW3\nnzvGDT9+nXf9yP113Q//Tm1zN3e/vzjgzesjbRG8c00Ob9Vq8jjUPB+On/rtm5ys7+DL113Ajjuv\nGJZkTY2P5n/etw6AxVmJJMdG+X28zYsyeNuyLO772+kxZwNPlmdYqadlALAyN5ljZ9uHLcK3o6yJ\nrKQYlgZ54yQ18wUUDEQkVUSeEJHjInJMRC4SkXQReVFETlnf06xjRUR+KCJlInJYRNb7PM5t1vGn\nROQ2n/INInLEOueHMgu2Vapp7iIh2sby7CS+/Z41HK5p5ZvPHuU//3iES773Kg/8vZyE6EiykmKs\nf64kvndjMRvGOYnnhnV5ANgiZMZvND+XrcxJ5vbLFvHf717N3++4nNsvWzxiUL9kaSbf2L6KT14x\n+hyNf79mOS1dfTw4xTugedYk8uQMwH1h0d3nosIKFOAeHrvztJ2tizN0Z7MwFNglKtwDPG+MuVFE\nooF44MvAy8aY74jIncCdwBeBa4Gl1tdm4D5gs4ikA18FSgADHBCRp40xzdYxHwX2AM8B24A/B+k1\nToma5m7y0uIQEa5dk8ONG/J5ZFcV0bYI/mFDPv962SKKfP75Jmp9YSoF6XEkREfO2TWCZoOICOHL\n160I+PiRhgz7Wp2XwjvX5PDg6xXcenERmVO0Omx5YwfJsZGDdqzzdDmW1rV6t089Ud+OvcOpQ0rD\n1JjBQERSgMuAfwIwxjgBp4hsB95uHfYL4K+4g8F24BHjHmKz22pV5FjHvmiMcViP+yKwTUT+CiQb\nY3Zb5Y8A72aGB4Pa5m7y085v/v6N7au4sDCVq1ZkjzpKaLxEhB/fvH7sA9Ws9Lmrl/F86TnufbWM\nr74rsFzSeFXYO1mUNXgf46XZiUTbIjha18Z2q/X5+inNF4SzQLqJFgKNwM9E5E0ReVBEEoBsY8xZ\n65hzQLb1cx5Q7XN+jVU2WnmNn/JhROR2EdkvIvsbGxsDqPrUqWnuIj/t/AJn8dGRfGDzgqAGAo/i\nglS/QxTV7Lc4K5H3Wa3KZw5NzVDT8sbOQV1EAFG2CJbNT6S0ro3alm6+9nQpP/jLCZZlJ3oXs1Ph\nJZBgEAmsB+4zxlwIdOLuEvKyWgFTvmOHMeZ+Y0yJMaYkKytrqp9uRK3dfbT19A8KBkpN1H+8cwUb\nFqTxqUff5LF9gQ1TDlRnbz/n2npYlDW8y3JVTgp7Kxy87Xuv8qvdVVy/NpcHb90Y1OdXs0cgwaAG\nqDHG7LFuP4E7ONRb3T9Y3z2bxdYCBT7n51tlo5Xn+ymfsWqtYaV5qfFjHKnU2JJio/jFhzdx6dIs\nvvjkER5+vSJoj+1JEPubuX7ZsiyibMIHtyzgb3dczg/eV0xhhr6nw9WYwcAYcw6oFpHlVtGVwFHg\nacAzIug24Cnr56eBW61RRVuAVqs76QXgahFJs0YeXQ28YN3XJiJbrFFEt/o81ozkGVaqLQMVLHHR\nNh64dQPbVs3nG88e5aEgBQRPMPDXMnjn2hxKv7GNr92wSruGVMDzDD4J/FpEDgPrgG8B3wHeISKn\ngKus2+AeDVQOlAEPAB8DsBLH3wT2WV/f8CSTrWMetM45zQxPHnu2p9RgoIIpJtLGj2+5kMuWZfGj\nV07h7B+Y9GN6hpUWZUx+ZJua2wIaWmqMOYh7SOhQV/o51gAfH+FxHgYe9lO+H1gdSF1mgprmbuKi\nbIOG6ikVDJG2CD58cREf/vk+/n6qkStXZA+6v9rRxacffZN7brqQgvSxu3Qq7O7dzXRfAjUWnYE8\nATXNXd45BkoF2yVLM0mLj/K7kN3PdlTyxpkWXjne4OfM4crtnSwMwnwXNfdpMJiA2pZu7SJSUybK\nFsF1a3J48Wj9oA1zupz9/O6Ae3S2Z+OckdS1dPP1Z0o5WtfG0mxdWkKNTYPBBNQ0azBQU2v7ujy6\n+1y8dKzeW/bHN+to7+knLzWOgzUtfs+ra+nmjicO8bbvv8ovd1WxfV0eH788vLcuVYEJdDkKZeno\n7aelq2/Q7GOlgq1kQRq5KbE8dbCO7evyMMbwyK5KVuYkc+3q+fzPiydp7e4jJW7wQnhf+N0hDlQ1\n84HNC/iXSxfq+1QFTFsG43R+joG2DNTUiYgQ3rUul9dONuLodLK3wsHxc+3cdvEC1hWmAnCkZvAS\n1J29/eyrdPBPW4v42g2rNBCocdFgME46rFRNl+3FefQPGJ47cpZHdlWREhfFDcV5rM1LBeDQkK6i\nvZUO+lxGN7JXE6LdROPk2dRGr7rUVFuRk8SSeYk8squS8sZO/vmShcRF24iLtrEoM4GDQ5LIO8vs\nRNsiKBnnMulKgbYMxq2muYuYyAgyE3WOgZpaIsL24lxO1nfgMoYPbl7gva+4IJXDQ1oGO8qaWL8g\nVecUqAnRYDBOtS3dOsdATZsb1uUCcMXyeYPWDSrOT6G+rZdzrT0ANHX0cvRsm3YRqQnTbqJxqhmy\nj4FSU2lBRgL/+4/FrC9MG1TuWdL8YHUL21Lms6u8CUA3plETpi2DcdI5Bmq6vXd9/rBd81bkJBNl\nE28SeUdZE0kxkazNSwlBDdVcoMFgHLqc/Tg6nTqsVIVcbJSNFTnJ3pnIO8rsbF6UQaRN/6XVxOg7\nZxxqm3XpajVzFOencrimlTNNXZxxdLF1SUaoq6RmMQ0G46DDStVMsjY/hY7efh7ZVQmgyWM1KRoM\nxsEz4axAWwZqBlhnJZF/s/cM85JiWDJPF6RTE6fBYBxqWrqJtkWQmRgT6qooxaKsRBJjIulyuti6\nJFOHO6tJ0WAwDjXN7jkGERH6T6dCzxYhrLFGD128WPMFanI0GIzDmaYuTR6rGcWzaN1WzReoSdJJ\nZwFq7+nj6Nk2Pvb2xaGuilJeH710ERuL0sjV4c5qkrRlEKA95Q5cA4aLF+sVmJo50hOiueKC7LEP\nVGoMGgwC9HqZndioCNYvSA11VZRSKug0GARo52k7G4vSiYnUFSGVUnOPBoMANLT1cLK+Q5N0Sqk5\nS4NBAHaedq8IuVXzBUqpOUqDQQB2lNlJjY9iZW5yqKuilFJTQoPBGIwx7Cizc9GiDGw62UwpNUcF\nFAxEpFJEjojIQRHZb5WtE5HdnjIR2WSVi4j8UETKROSwiKz3eZzbROSU9XWbT/kG6/HLrHNnzKdu\nZVMXda09ummIUmpOG0/L4HJjzDpjTIl1+3vA140x64CvWLcBrgWWWl+3A/cBiEg68FVgM7AJ+KqI\neLZvug/4qM952yb6goLt9TI7oCtCKqXmtsl0ExnA04meAtRZP28HHjFuu4FUEckBrgFeNMY4jDHN\nwIvANuu+ZGPMbmOMAR4B3j2JegXVzjI7uSmxFGXostVKqbkr0OUoDPAXETHAT40x9wOfAV4QkR/g\nDioXW8fmAdU+59ZYZaOV1/gpDznXgGFXeRNXrcjWFSGVUnNaoMHgEmNMrYjMA14UkePAjcBnjTFP\nisg/Ag8BV01VRQFE5HbcXU8UFhZO5VMBcLSujZauPu0iUkrNeQF1Exljaq3vDcAfcPf53wb83jrk\nd1YZQC1Q4HN6vlU2Wnm+n3J/9bjfGFNijCnJysoKpOqT8tqpRkCXB1ZKzX1jBgMRSRCRJM/PwNXA\nW7hzBG+zDrsCOGX9/DRwqzWqaAvQaow5C7wAXC0iaVbi+GrgBeu+NhHZYo0iuhV4KngvcWK6nS5+\nsbOSTQvTmZccG+rqKKXUlAqkmygb+IPVZx4J/MYY87yIdAD3iEgk0IPVfQM8B1wHlAFdwIcBjDEO\nEfkmsM867hvGGIf188eAnwNxwJ+tr5D6xa5KGtp7+fEt68c+WCmlZjlxD+CZfUpKSsz+/fun5LFb\nu/u47HuvcmFhKj//8KaxT1BKqVlCRA74TBHw0hnIfjzwWjmt3X184erloa6KUkpNCw0GQzS29/Lw\njgquX5vDamt/WaWUmus0GAxx76tl9PYP8HltFSilwogGAx+1Ld38ek8V/1iSz8LMhFBXRymlpo0G\nAx/7Khz0uQy3XVwU6qoopdS00mDgw97RC0BOSlyIa6KUUtNLg4EPe4eTaFsEybGBrtKhlFJzgwYD\nH00dvWQkRuuidEqpsKPBwIfdCgZKKRVuNBj4aOp0kpkYE+pqKKXUtNNg4MPe3ktGggYDpVT40WBg\nMcZg73SSmaTdREqp8KPBwNLe24+zf4BMbRkopcKQBgNLU4cTQFsGSqmwpMHA4plwpjkDpVQ40mBg\nabKCgY4mUkqFIw0GlkZPN5HOM1BKhSENBhZPyyAtQYOBUir8aDCw2Dt6SYuPIsqmvxKlVPjRTz5L\nU4eTDM0XKKXClAYDi72jV/MFSqmwpcHAoi0DpVQ402BgaezoJUuDgVIqTGkwAHr7XbT39JOhI4mU\nUmFKgwG+S1Foy0ApFZ40GHA+GGjLQCkVrjQYAPZOaykKbRkopcJUQMFARCpF5IiIHBSR/T7lnxSR\n4yJSKiLf8yn/koiUicgJEbnGp3ybVVYmInf6lC8UkT1W+WMiMq2X6PZ2KxjoInVKqTA1npbB5caY\ndcaYEgARuRzYDhQbY1YBP7DKVwI3AauAbcD/iYhNRGzAvcC1wErgZutYgO8CdxtjlgDNwEcm/9IC\n19Spy1crpcLbZLqJ/g34jjGmF8AY02CVbwceNcb0GmMqgDJgk/VVZowpN8Y4gUeB7SIiwBXAE9b5\nvwDePYl6jZu9vZe4KBvx0ZHT+bRKKTVjBBoMDPAXETkgIrdbZcuAS63unb+JyEarPA+o9jm3xiob\nqTwDaDHG9A8pH0ZEbheR/SKyv7GxMcCqj61Jt7tUSoW5QC+FLzHG1IrIPOBFETlunZsObAE2Ao+L\nyKIpqicAxpj7gfsBSkpKTLAe197Rq5vaKKXCWkDBwBhTa31vEJE/4O7yqQF+b4wxwF4RGQAygVqg\nwOf0fKuMEcqbgFQRibRaB77HTwt7h5O81LjpfEqllJpRxuwmEpEEEUny/AxcDbwF/BG43CpfBkQD\nduBp4CYRiRGRhcBSYC+wD1hqjRyKxp1kftoKJq8CN1pPeRvwVNBeYQB0kTqlVLgLpGWQDfzBnecl\nEviNMeZ56wP9YRF5C3ACt1kf7KUi8jhwFOgHPm6McQGIyCeAFwAb8LAxptR6ji8Cj4rIfwNvAg8F\n7RWOYWDA4Oh06naXSqmwNmYwMMaUA8V+yp3AB0c45y7gLj/lzwHPjfAcmwKob9C1dPfhGjBkaMtA\nKRXGwn4Gsme7S20ZKKXCWdgHg0YrGGjLQCkVzsI+GHgWqdO9DJRS4Szsg4Hd2zLQYKCUCl9hHwya\nOpzYIoTUuKhQV0UppUIm7IOBvaOX9IRoIiIk1FVRSqmQ0WDQoXMMlFJKg4HOPlZKqfALBj944QQ/\n31FBt9MFQFNnr253qZQKe2G1gL9rwHCgqpld5U386JUy/vmShdjbtZtIKaXCKhjYIoTf3r6FvRUO\n7n21jO+/cALQYaVKKRVWwcBj08J0Ni3cxFu1rfzhzVquX5sT6ioppVRIhWUw8Fidl8LqvJRQV0Mp\npUIu7BLISimlhtNgoJRSSoOBUkopDQZKKaXQYKCUUgoNBkoppdBgoJRSCg0GSimlADHGhLoOEyIi\njUDVBE/PBOxBrE4wzMQ6gdZrPGZinWBm1msm1gnCo14LjDFZQwtnbTCYDBHZb4wpCXU9fM3EOoHW\nazxmYp1gZtZrJtYJwrte2k2klFJKg4FSSqnwDQb3h7oCfszEOoHWazxmYp1gZtZrJtYJwrheYZkz\nUEopNVi4tgyUUkr50GCglFIqvIKBiGwTkRMiUiYid4awHg+LSIOIvOVTli4iL4rIKet7WgjqVSAi\nr4rIUREpFZFPh7puIhIrIntF5JBVp69b5QtFZI/1t3xMRKKnq04+dbOJyJsi8uwMqlOliBwRkYMi\nst8qmwnvrVQReUJEjovIMRG5KMTvq+XW78jz1SYin5khv6vPWu/1t0Tkt9b/wJS/t8ImGIiIDbgX\nuBZYCdwsIitDVJ2fA9uGlN0JvGyMWQq8bN2ebv3A540xK4EtwMet31Eo69YLXGGMKQbWAdtEZAvw\nXeBuY8wSoBn4yDTWyePTwDGf2zOhTgCXG2PW+YxLnwnvrXuA540xFwDFuH9vIauXMeaE9TtaB2wA\nuoA/hLJOACKSB3wKKDHGrAZswE1Mx3vLGBMWX8BFwAs+t78EfCmE9SkC3vK5fQLIsX7OAU7MgN/Z\nU8A7ZkrdgHjgDWAz7tmYkf7+ttNUl3zcHxZXAM8CEuo6Wc9bCWQOKQvp3w9IASqwBqzMlHr51ONq\nYMdMqBOQB1QD6bi3JX4WuGY63lth0zLg/C/Zo8YqmymyjTFnrZ/PAdmhrIyIFAEXAnsIcd2s7piD\nQAPwInAaaDHG9FuHhOJv+f+AO4AB63bGDKgTgAH+IiIHROR2qyzU762FQCPwM6tb7UERSZgB9fK4\nCfit9XNI62SMqQV+AJwBzgKtwAGm4b0VTsFg1jDu8B+yMb8ikgg8CXzGGNPme18o6maMcRl3cz4f\n2ARcMJ3PP5SIXA80GGMOhLIeI7jEGLMed3fox0XkMt87Q/TeigTWA/cZYy4EOhnS/RKq97zV934D\n8Luh94WiTlaOYjvuAJoLJDC8S3lKhFMwqAUKfG7nW2UzRb2I5ABY3xtCUQkRicIdCH5tjPn9TKqb\nMaYFeBV3MzlVRCKtu6b7b7kVuEFEKoFHcXcV3RPiOgHeK0uMMQ24+8A3Efq/Xw1QY4zZY91+Andw\nCHW9wB003zDG1Fu3Q12nq4AKY0yjMaYP+D3u99uUv7fCKRjsA5ZaWflo3E3Dp0NcJ19PA7dZP9+G\nu79+WomIAA8Bx4wx/zsT6iYiWSKSav0chzuHcQx3ULgxFHUyxnzJGJNvjCnC/T56xRjzgVDWCUBE\nEkQkyfMz7r7wtwjxe8sYcw6oFpHlVtGVwNFQ18tyM+e7iCD0dToDbBGReOv/0fO7mvr3VigSNqH6\nAq4DTuLuc/6PENbjt7j7A/twXzV9BHef88vAKeAlID0E9boEd7P4MHDQ+roulHUD1gJvWnV6C/iK\nVb4I2AuU4W7ix4Tob/l24NmZUCfr+Q9ZX6We9/gMeW+tA/Zbf8c/AmmhrhfuLpgmIMWnbCb8rr4O\nHLfe778EYqbjvaXLUSillAqrbiKllFIj0GCglFJKg4FSSikNBkoppdBgoJRSCg0GSiml0GCglFIK\n+P8BCQeapiSGrA4AAAAASUVORK5CYII=\n"
}
}
],
"source": [
"plt.plot(y)"
],
"id": "3c45a2bd-6684-4493-86ba-6da6de2b674f"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(4)` 아래와 같은 변환을 이용하여 ${\\boldsymbol y}$를\n",
"$\\tilde {\\boldsymbol y}$로 변환하고 결과를 시각화하라.\n",
"\n",
"- $\\tilde{y}_1= \\frac{1}{4}(3y_1 + y_2)$\n",
"- $\\tilde{y}_i= \\frac{1}{4}(y_{i-1}+2y_i+y_{i+1})$, for\n",
" $i=2,3,\\dots,n-1$\n",
"- $\\tilde{y}_n= \\frac{1}{4}(y_{n-1}+3y_{n})$\n",
"\n",
"**hint**: 아래의 코드를 관찰"
],
"id": "01092eb4-6be7-49f2-bde2-eb8192d4626d"
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"np.eye(4) + np.array([abs(i-j)<2 for i in range(4) for j in range(4)]).reshape(4,4) "
],
"id": "f7f724a2-4374-48f4-9f29-fe6925c492d2"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(풀이)`"
],
"id": "b639d4ea-76dc-4b9a-905c-3eb9d8ce1690"
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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SibUeAFpPBkfeoOcU/Q9Sv4Vzn4TIJFzMJi6dPZWVtkTUT/+Et+fBf5Lg8TDe\nee9/HC6v5dkrxzLVWFtpW1bp0XseKq3hj2ohI4q+gWEX4HngG+5zWyqdyN3k9dUHuPrV9WQYnfgt\nstvQGT/xlZ7G+ITQTlslN6bRlq1SM+g4mYHchxwsrqJSRzJ2aNuH7VX5xBNTtZraBhvuLs1P8imq\nqmOUWwEsnAO5W2DcdYTqIq43f83hsmEtPsau3DIUdsIrU2DMlTD+xqPHzhk/jAvW/pHXKrM5L6oe\n/4bDuNQW89S+UO6ePYiknPfhkJmBvhFsyy49el1OzkHONG8hd+SviLj8KdShbXz7aRGVueVgt4NJ\nPud0pW92O/qZNmQUExd88qi1z7bmEOLjxtSBwWAyk3PZF/z3lTXcnNA5TUTgWJLiiEBZl6jD5H9M\nH5JRVM0T+nq8z/lDm6+xBgwiTJWSX1jQ4nnFlXU8XPQwFB+AK96Gef/FM3s1f7C8R35xy5/Gd+WW\nExnghcs1H8Av/n3cejQmk+KRC4ZTYA7j9ZxIns4fzxPlZ3PuqHB+M2ugo+noqwdYUX89d+y7Cb56\nCNK/Z3+1JxfU/R3zHGMuRXgig6LCqD20F/3SNMja0ObfgWif/Irao7W05IyTBypU11v53Ufbuf71\nDXy7Lhm0Zm2RF5l6AJPjAzstjphGzU2yLlHHSc2gDzlUUEh0gAfmdszEbBg0l7u313N1WQMxLSwx\nZK7KI0jlwdlPwYh5jsK46bit+y/u+VuBpGavzcs+wJnBJsenddPJ+7xOHRjMmofObPriaxZB1gY2\nffshDelrGbzpTZStnkxuptrFn1DfY/cbGeHHhw1+2CqLsCx/GG7+9qSF0ETHrdqTD0BckCfJTSwd\nvjGjhHqbneF+DSQuv4S9+y5kg+ctBHi6MCjEu9PiCPNxx9Vsot5ml2TQCaRm0IfMzXqO92rvgBaG\nap7IP3Y0n9mnk1vT/JtmbYONzDovPhz/Hoy46NiBmNOwo4goTW722so6KzPKv+AvWb+E6taHuzYp\nehINMx7m6oZHWH3pJjjzETKKqokN9Dqu/XlkhC/VuLNj6J2Qkww7l5za44kWfZuST6S/B1dOjCG9\nsOqkxQvXphbiYlZ8mrCUAFXJPXtG8OX2Q0yKD+zUJSNMJnV08pn0GXScJIM+QmvNwLrdVHjGtOvT\n8AA/dxJVKg3ZW5s9p7iqHhtm7GGjj1/4zsOfQ+6DGFyzvdlrUw6VM9u0mfLgsY4tCk/RqCg/lIKt\nudXgGXh0jkFjg0K9cbWYWG6ZhS1sNBVfPsLMv3/FX5buOuXHFcerbbDx0/4CZg8PZVJ8AMBJtYPV\nqYXcGpqCW8oSOP13xIyYRE2DjUmdNKS0sahAT8wmha+7NHJ0lCSDPqKoqJCB5FAZMq5d13m6WviP\n2/OMSHu9+XtX1nOJ6UeGl/5w0rHDAROIsB+iwWpt8toDafsYZcrAPOy8dsV1Il93FwaGeLMtuxS7\nXZNZXH1Sx6WL2cTQMB8+25bHr/Mvxqf2EHMavmVRchY19TIZrTOsTSuktsHO7KHBjLZk42Y5vt+g\npKqe+LxvuLvsnzBgNJaZv+X5q5N4/uokrpkc0+nxjI70JSHYS/bx7gSSDPqI4n1rMSmNKXpiu689\nZInGrzqj2eNFVXXcbllKXNanJx1LH3Mv0+qeI6+i6ZVPzanfAOA95oJ2x3WixCh/tmaVcai8lnqr\nvcnx6uNjAzhcXouOm0nqWa9z5tUPUF1vY+We1mdZi9Z9m5KPl6uZaYfexPXVGaxxvZsRu56GvF1g\nrWddehH77JFURZ0O8z8AswsWs4nzx4S3OFrtVN1z1hA++820Tr9vfyR1qz6iIXM9dq3wH9KGyWYn\nKPGIZWzF9maHZJaUlTNDHaJiwBUnHQsJDAAUh8tqiQo4+c05qvBH8iwRhIW0PPy0LcZG+7Fkczbr\n0hzrGcUFnTyk8YG5Q7nl9AQi/T2ACcTbNQN83Phsay4XjOmcZRD6K60136XkM2NwCJax8+HwNsry\nSrmw5GN4cTEMu4DVbg+R6xqPz4IPoBt2wHMxm3Bx4k57fUmbfotKKX+l1GKl1B6lVIpS6jSl1D+N\nn7crpT5RSvk3Ov9hpVSqUmqvUuqcRuVzjbJUpdRDjcrjlVLrjfIPlVLSG9RO213G8aTtaiLCQtt9\nbbVvAm7UQ1kzk8/yUzArjVtk4kmHIvw9+I35E0K/u/+kY3VWG7+u+hXLhj3RKaN6EqP9AccYdqDJ\nmoGnq8VIBA7mvV/yufl+Nuw9SFm1bH7TEbtyyzlcXsvs4aEQEAvz3ydz7ptMqnuB9EmPwsBZrN1f\nwJSEQKduhSpOTVv/Ys8By7XWw4BEIAVYAYzSWo8B9gEPAyilRgBXASOBucALSimzUsoMPA+cC4wA\n5hvnAjwJPKu1HgSUADd1xpPrT9Y2DOIr38tP6VOSDhwEQH1e02sEuRY5lpp2jz45GQzwcydIlROR\nvcwxO7mR/XmVlNg9CR7c/qarpgwb4Iur2cSa1EJczSbC/dqwDLJXCCG1GZzLGr7aeahT4uivvk3J\nw0dVc+G+hyHP8ZoYHxNIMb586XY+2YOuJqO4xjHRTPQ6rb5zKKX8gNOB1wG01vVa61Kt9Tda6yO9\nhj8DUcb384APtNZ1WusDQCowyfhK1Vqna63rgQ+AecrR83MmsNi4/i3gok55dv1FVSEehzeSEHhq\nszBV5DiurPsjh/3GNHncoyKTKtxRAfEnHfNxs7DVNBKLvRZyNx93zLr631xj/paREb6nFNeJXC0m\nhkf4YtcQHdjG+RTRk9ChI7jRbRWfbT155VPRditT8nko8Efc9n0ONsdwUj9PF4aG+bAxs4S1qY7m\nu+mDJRn0Rm35GBkPFABvKKW2KKVeU0qd2Fj7S+Ar4/tIoHF7Q7ZR1lx5EFDaKLEcKT+JUupWpVSy\nUiq5oKDlGbP9id77FU+V/Y4k79JTuj4sOIj1eji5NU0nk3e8b+RG/zeb7E9QSpHla0w4y1h97IDd\nzsD9C5lmSWmybf9UjY3yA5ruL2iSUqjxNzLUnkZlxsZ2b8YjHPIraknPOcyldZ/BkLkQcWzU2oS4\nADZnlvDj/gJCfNwYHNp5E8tE92lLMrDgmF76otZ6HFAFNG7v/wNgBd7tkggb0Vq/orWeoLWeEBIS\n0tUP12vUZ2ygTHviGXFqnbQD/Nw5zbQLy85FTR4vqqrH3bf5MeJeAaFkmGOPTwa5W/CxFrPff3qn\nTjQ60m8Q254EM+YK7BZ35pu+44vtUjs4FTtzylhg/gZ3axnMfPC4YxPjAqmss/L1rsNMGxgkwzx7\nqbYkg2wgW2u93vh5McbaA0qpG4ALgGv0sR1KcoDGu1lHGWXNlRcB/kopywnloo3sWRvYYh9MXLDP\nKV0f7ufOZeYfGLbzmZMPluVwV/HjJJoymr1+gK87XzEVgoc4Ctb+B/3F3Vi1idrY2acUU3PGxTgm\nOg0MbUcy8PDHNOcxdgfOlqaiU5Sak8/Nli9pGHgWRB6/9MiEOMffpMGmmTpImoh6q1aTgdb6MJCl\nlBpqFM0Gdiul5gIPABdqrRtvorsUuEop5aaUigcGAxuAjcBgY+SQK45O5qVGElkFXGZcvwD4rBOe\nW/9QW457yV622AcRF3xq68R7ulrINUfhXZ8PdSdsUn9oG7Ntawhyb343s3B/D56q/gUN5zzhKCg/\nREN9Pf+znU18TFSz152K+GAvPrx1CpcmtfO+k24hbuJ57MgpI72gsvXzxXEOHC5mkctFuMx+5KRj\nkf4ehPs51oiaJsmg12rr0JM7gXeVUtuBscDfgf8CPsAKpdRWpdRLAFrrXcAiYDewHLhDa20z+gR+\nA3yNYzTSIuNcgAeB+5RSqTj6EJqfDiuOl70BhWazHtLkOP+2KvOMc3xTlHpceX2uY6kJa/AImnNs\nxzNjjZq5f2f5zE951Lqg0zqPG5ucEHRKE5jmxdRzk/lLVuyWCWjttaVAsSHqhuP6Co5QSjFzSAgj\nwn2PG9Yrepc2TTrTWm8FJpxQPKiF8x8HHm+ifBmwrInydByjjUR7xc3g+ZjnyMkL69AMzxq/BKjG\nkQwixh4tt+ZsJ9cehq9fQLPXHvlUeKi05uibwa7cMlzMisGhp9Z01RVC8n7ijy7v8kTqdJg58KTj\nqfkV7MotZ97YJscv9FsNNjuehdsYO7D5IcKPzhuJzd72BRJFzyMzQ3o7ixsrawczILj5N+u2MAUN\nxI6Cwv3HlZsLdpGiYwjybn4e4JHx/kd2PKttsPH51lzGxQTgaulBL7ExV1Bj8mRizjtNHn5uZSr3\nfriV4qqml9bor9LzK3nd/ATzCl5u9hw3ixlPV1nQoDfrQf9TRbtVF8M3f8RWmNa+0TVNCAnwY0bt\n/1E7tdFMYpuVOrM32+wDHVteNmOAUTM4Mmzz3fUHyS2r5Z7ZgzsUU6dz92NvzHxm2dZSlLHtuENa\nazYeKMauj63XLxyy0nYQoCpxjZXKe18myaA3O/ADrP035poi4jq4yXi4nzs5hJBf2Wj1UbOFr6d9\nwEu2Cwn2dmv2Wl93C16uZnLLaqiss/LCqlSmDQrqkSNL9JQ7qMGVhpVPHleeU1rD4XJHMpNF7Y5X\ne8Cxa1zwMFkQri+TZNCbpf+A1eLFdp3Q4ZpBuJ8Hk1UK3p9cB/tXQK1jE/sio8mkpZqBUooBfu4c\nLqtl4eoDFFXV87tzOr4wXVcYlhDHG/bzyK+zOBbmMxxZkz8x2p8f9xVSb21+9FR/45G/hRrccQkf\n6exQRBeSZNCL2dN/YIMezoAAnw4vATDAzx0vVYN/zvfw7mXwZCz8xY85m36Nu4sJT9eWO6cj/D3Y\ne7iCV39MZ86IMMYak8N6Gg9XM8uCfsk/3e44bkZ1cmYx3m4Wbj9jIJV1VtYfKHJilD1LeOUusj2G\ngqnzl6AWPYckg96q9CCmknS+rRvOs1eOxdutY5134X7ufGdP4rVpq+D6z+D0ByD+dDJcBhLk5dbq\nrNIBvu6kF1ZRWW/lt+cMbfFcZ0uMCWBbVik6exOUZACOmkFSbACnDw7BzWJiZYr0GwBU1DZwd+2t\nbB128qq0om+RZNBLbdi0iTLtScz485gYd+rbSR7h5WbB191CdpUJEs6AWQ/Dgs95y+uXLY4kOuLI\n8NKLx0UyJKznDCdtSmKUH7q2HP3m+fDd45TnHcQrfxMX+mfi4Wpm+qBgvk3JQ7djL+m+al9eBft1\nFAGDpzg7FNHFZCxYL5RfXsuv1ngRE/QBi38xvdPuG+7nQW7p8Qu5FVfVE9yGZDAq0g9fdwv3njWk\n0+LpKonR/lTgSVrslQze8Sa+OxaxxBUqc8YAlzN7eBgr9+SzL6+SoQN6dmLraiW7VnKpKZmhYTOd\nHYroYlIz6IUe+ngHNQ02nr5qPC6WzmvHDfd353B5zXFlRZV1BHo1P5LoiDkjB7D5j2cTHdixUU3d\nYXCoNx4uZpZ4zYczH+Gb+Ae5qeEBLJe+AsCckGJcsPJtSueMKtJa8/IPaaTmV3TK/bpT6L4P+K3L\nR0QFdt7Ks6JnkmTQy5RU1ZO9dxNrvR9kUF1Kp9473BgRdITWmqI21gyAXrO7lcVsYnSkH+sP2+D0\n3/FazSyKIs7APWI4FKYS/M5s/hzwDSs7KRkcKqvlH1/t4ZUf0zvlft0prGInB9yHy0qk/UDv+N8r\njtqVW850004CazLBZ0Cn3jvcz4PCynoq6xxzDarqbdRZ7S0OK+2tEqP92JVbTlWdla3ZpUw0Vt4k\neBCMmMf82g+oyN5JYWVdhx9rW1YpAGtSi3pVP4SuzCfMdpjSwKY3PRJ9iySDXmZXbhlTTTuxBSSA\nf3TrF7TDkeGpb63NAKC40jHHIKiFCWe9VWK0P/VWOx8lZ1FvtTOhcSf83CfRrj48aXmFVSkd3ypz\nW3YZ4JjYdrC4upWze47SfesAUFGds22p6NkkGfQy+7PzOM2cgnngGZ1+76SYAM4aHspLP6RRWl1P\nYZXjU3FbRhP1NolR/gAsXJMBwITYRms7eYdgPu9Jkkyp6PWvdvixtmWVHm1qW51a2OH7narskmpG\n/mk5W42aSmtKMrfToM0EDZZlKPoDSQa9TMzBT/CiFhLnd8n9758zlMo6Ky/9kH6sZtAHm4miAjwI\n8nLlYHE1CcFeJ9V+1Jgr2OF7OoWF+R1ajdNm1+zIKePcUeEM8HU/uk+wM2zLKqOq3saaNiakFYFX\nM7HuBYZEhXZxZKInkGTQi1TXW/m+IoLkiGsgums+rQ0P9+XCxAjeXHuAlEOOJSn6YjORUuroFppH\nduo64QTSz3yJp2ovYldu2Sk/TnpBJZV1VsZG+zNtUDBr0wqxO2mp5wOFjk192vp89uZV4OYbjL9n\n3/swIE4myaAHqKm38b91GWSXtNyenHKogs32IRRP+1OXxnPf2UOw2jQv/ZAG9M2aARxrKprQzKS9\n0wYGAZpd2zed8mMcaZJJjPZn2qAgSqob2G0k2e6WXlAFOAYhtCpzLZfuf5ipwbWtnyv6BEkGPcBf\nv9jFHz/bxRn//J77Fm1lf17T49Ht614gSuUzMtKvS+OJDfLiyonRVNXb8HI1d2jTnJ7szGGhRPi5\nM6OZdZ1Cfdz5q9+XXLbhSsdy4adgW3Yp/m6KhL2vMtPPMVS1rc00nS290JEMMouqKa9taPHcht1f\nMLF+A9GREd0RmugBJBk42YrdeXy9YRefhL/FI6NK+GrHYc5+9kd++9G244ch5m5l4p6nuNh9MxHG\n0g9d6a7Zg3F3MRHYBzuPjxgd5cfah2cf3ZynKdUJ5+BCAw1bPzylx9h2sJTnvBZiWvkXgj6+iqnB\nNaxJ6/5+A6016QWVR3eiS2mldlCfspyf7cOZOKRzR6yJnkuSgRPlV9Ty4JLtDBgQSaJvNTfsu52t\noxbxq3EeLN6UfXRIIgA/v0A1HqSEX9QtE4DCfN350wUjmT8ppssfqycbPOY0dtjjqNv4druvrW2w\nkXK4grqwJJhwE1hrecb2D3YdyKbOauuCaJtXXFVPea2VCxLDgVaaikoy8CpP40fGMSG24+teid5B\nkoGTaK156d1FhNcd4Ln54zBdswhmPojbvi94KPVa7ndZwvLkPY6Ty3PRO5ewyHYGCVHdV22/enIM\nt5/R7FbX/cKk+EAW22fhXbIbDm1r/YJG9qfuxWrX6Am/hAuegcvfIKwmnev152w5WNo1ATfjSBPR\nlPgggr3dWk4G+1cAUBg+E49Wli4XfYckAydZsWwJ9x36HQuD32NwqDe4esKs38Md61EJM7nD/AnL\nd+U5hjV+/XuU3crr1jmMjPB1duj9io+7CwcGzKUeF9i+qNnztNZUGTO30Rp+epphH81imDp4bG+H\nQWdRfdViXrBdxNpu7jc4YHQeJ4R4MTLCt8URRZV48I1tPIOGJXZXeKIHkGTgBDnbVjJjw22UuoYR\ncuN70LjZJzAe5r/PygvWkFFp4ef0IvAMYn/8tWTpMEkGTjB2SDxX1T9C+bSHmzxeXW/l+oUbmPrE\nd+RkZ8K7l8PKv7LDayoV3gMJ8z3Wx+M1bDbDo4LZsu8AFKV111MgrbASF7MiKsCTkRG+pOZXNttU\n9YP7bG5tuL9Hblsquo4kgw5Izig+uo5PWzVkb8H/02s5pEJwvWkZJr+mm31mJA7F283CZ1tz4Pyn\neS/wdjxczMQHe3dG6KIdpg4KZrN9MD9nVsLe5VB17FN9eW0DCxZuYE1qIadZk/FeOAOd8ROc9y/u\nt9/FqJiT29ynDwzizwX3Yv3srm57DgcKqogN8sJsUoyM8MNq1+w7XHnyidXFrNuXi4+bhTFdPGpN\n9CySDE5RWU0DV7y8jrve39KuxccOfPxXSuyeZJ73LqEDopo9z93FzDkjB/DVzsPUNtjYlVvOsHAf\nzCZZPbK7jYvxx8PFTPK+g7D4l/DsKPjqQUozd/B/z/+HtIPZ/Gd+EvcOKSDX6scH496mdNQCDhRV\nH53Y1tjpQ0P5wDoLy8HVkH3qcxjaI72wihGBwOvnMKn8G6CZyWerHue+nRczJd6/16xCKzqH/LVP\nUVZxNXYN3+3J5931B1u/QGuSM4qZd+h63hryArMmjWv1knljI6iotbJqTz4pueXSROQkbhYzE+MD\nWXWgBm79HkZdgt7wGv5vTOdPFY/y1qxazh8TzpD5T/DS4Ff54xob721wvCbGGhPbGpsYF0BKxCWU\n44Xtp2e6PH6bXZNZVEV4WCjEnkbIt3fxiNuH7M4pPf5ErbHuWc4m2yCmDpYlKPobSQanKLvEsQlM\nbJAnj325m7SCJqrc4GhSWPk3bC9O57cfJhMS4M/dl81u02NMHRhEsLcrz3+fSkWdlZERUm13lmkD\ng9ifX8nSXG+uKbye6TVP8zg3s/Ps9xh9xuUAKIsbj16aRJC3K08t34tSMCrq5L+ZUoq7zh3Hm9az\nMe39Egr2dWns2SXV2G1WBgZ7wxm/h/E3cLP6jF+k/BbqGk1wLNiLpSKbVfaxTJP+gn5HksEpyil1\nJIOXrxuPu4uZp95bRkO5YxP1gvzDfPv6H/n8iWup++cI7D89zU9FPlSWFvHslYlt3rzeYjZx/uhw\nduY4hgFKzcB5jrw53vX+FvblVbLgvBnc/fCTjJp2Prgcm7Tm7+nK05ePBWBgiDe+7i5N3m9yQhD7\nYq+hFhdq93zdpbGnF1Zxn+Uj5ibf5BiscMH/sSzqXpLqNqA/uPbYict+C8B2j0mOEW6iX2nTu5JS\nyh94DRgFaOCXwF7gQyAOyACu0FqXKMeMqOeA84Bq4Aat9WbjPguAR4zbPqa1fssoHw+8CXgAy4C7\ndQ/fBSS7pBovVzNDw3x48sKhxHx8AUUvPMl/h77B3k3f85Hl31gx87P3WSzzvZLDrjE8NDqc8e2c\nxHPh2EjeWpeJ2aR6/EbzfdmIcF9uPT2BmEBPLhsf1eISHdMHB/PXeSPx82g6ERzx6/Mmc/p//o/5\nNRO4r7MDbiTr0GGuM6/Aze9sMDtiqhp7E9enu/Pv4AaCjPN03k52M4hBg4bKzmb9UNs+ojre3Jdr\nrS9TSrkCnsDvgZVa6yeUUg8BDwEPAucCg42vycCLwGSlVCDwZ2ACjoSySSm1VGtdYpxzC7AeRzKY\nC3zVSc+xS2SX1BAZ4IFSinPyXwXTQX5Z/ltWJ+dwadIZHJy8m5hAD6Z7BtKRLeuTYvyJDvTAy9XS\nZ9cI6g1MJsXvzxve5vOvPy2u1XNGRfoxafRwXlt9gAUTggkKDGr1mlMRuvc9fFUNeuaxlDMywo/f\n2UezOnIs84yy1Cu+49KXt/JXaSLql1pNBkopP+B04AYArXU9UK+UmgecYZz2FvA9jmQwD3jb+GT/\ns1LKXykVbpy7QmtdbNx3BTBXKfU94Ku1/tkofxu4iB6eDHJKaogK8IT0H2Dtf2kYdwOzB1zPP4aH\nHTeuvKOUUvx3flKn3U/0LPfNGUJAyjt4PX8T3L0RfDt5hnlDLZPzPmSryzjGRh4btDA4zBtXs4nd\nueXMGxsJwA/ZUIub9Bf0U23pM4gHCoA3lFJblFKvKaW8gDCt9ZE9AQ8DYcb3kUBWo+uzjbKWyrOb\nKD+JUupWpVSyUiq5oKCgDaF3neySagb5NMCnt0FgAi7n/p1rJsd2aiI4IjHav8khiqL3Gxjije/I\nOShrHdmLftv5D7D9QwLsxawNv/64YheziSEDvNmVW05OaQ1/WbqLf32zlyFh3kcXsxP9S1uSgQVI\nAl7UWo8DqnA0CR1l1AK6vI1fa/2K1nqC1npCSEhIVz9cs8pqGiivtRLp5wqRSXDpq+Dq5bR4RO92\n28WzWepzBVHZX7Lqq8Wdeu+qIRdxb/1t2GNPbqwcGe7HhgPFzHxqFe/8nMkFYyJ47XrZ77i/aksy\nyAaytdbrjZ8X40gOeUbzD8a/+cbxHKDxurdRRllL5VFNlPdYOcaw0uDQSLjyHYgc7+SIRG/m4+7C\nBbc9Rb55AFHr/sQbP3beUNMD5fCJfQbxIScPPjh9SAguZsW1U2L54YFZ/OvyRGKCPDvtsUXv0moy\n0FofBrKUUkONotnAbmApsMAoWwB8Zny/FLheOUwByozmpK+BOUqpAKVUADAH+No4Vq6UmmKMRLq+\n0b16pJzSGgaqHIZVbwJby5uECNEWHl7eBFz2LHHmfL746gteX32g4zdd9wK2jW8AjgXqTnT+mHB2\n/XUuf7lwpDQNiTaPJroTeNcYSZQO3IgjkSxSSt0EZAJXGOcuwzGsNBXH0NIbAbTWxUqpvwEbjfP+\neqQzGbidY0NLv6KHdx5nl1RzufkHElZ8AxOyW79AiDZwGX4e1ru34/VxNv/5bj/XTYnF1XKKU4Fs\nVvjpaTw8xwKDiQuSZkzRsjYlA631VhxDQk900lRao//gjmbusxBY2ER5Mo45DL1CdkkNc81pMGAM\nWPreZvHCeSz+Edw41cJ7b7/I6r0jOXPk8WMpsoqrufuDLTx31TiiA1to0jnwPVQX8lPATCL9PWRf\nAtEqmYF8CnKLKxil0lFRTeVHITpmhscBXnV9Bs+v7wO7/bhjb6zJYPPBUr7bk9/M1YYdi8HNjy9r\nRxMfLLUC0TpJBqfAUrQHD+ogSkZeiM5niZ3MyrBfMqV8OQ3LHnJsloNj34SPNjlGZ2/LKm3+Bg01\n2HcvZbP36Ww/VMPgMFlaQrROksEpCC3f6fhGRhGJLuJzziO8bj0Xl+SX4YcnAfh0Sy4VtVYi/T3Y\nml3a5HW5pTX846Pv2VgXwzOHE5k3NpI7ZvXvrUtF27S1A1kYKuusvFUzneHTZ3JZQJyzwxF91IS4\nQO71vIkhrnZmfP8EesyVvL0uixHhvpw7agBPr9hHWU3DSesf/fajbWzKhLpJr/PEjHjHLHkh2kBq\nBu2UU1KDFQtu0UnHb1cpRCcymRQXjIvi5uLrqLj4bTaU+rLncAU3TwxgbIw/ADuyj9+cpqrOys6M\nXG6b5M9fLhwpiUC0iySDdjqUl8efLW8xiDZsaCNEB8xLjKTObuKzmkTeXpfJ2e57uPj7cxhfvAzQ\nbDuhqWhDRjFzWctdWy7o1v2VRd8gyaCd6g9u5EbL14SbmtgyUIhONDzch0Gh3ry9LoOvdx1mzNgJ\nqIhxeH51F897v8mOg8evz5W2fS33WpZAQBwEJjgnaNFrSTJoJ9fDmwHwGzTJyZGIvk4pxbzECPbl\nVWLTmnkzJsL1S2HGbznfuoJbM+6DqiLHybuXcu2uW3E1mzBdvlCaMEW7STJop6DS7WSYolAeAc4O\nRfQDF451LGl95tBQx7pBJhPM/iM/jPo7I+37Kdv0ERzeAYuuI8UezWcT34HwRCdHLXojGU3UHloT\nU72bbZ5TiHN2LKJfiA3y4pkrEkmKOf7Dh++kq5mzyZ2HA85j7oBwNk/8J/N/CuH9kcOcFKno7aRm\n0B7VRdRrE8UBY5wdiehHLkmKIu6EWcTDw33JNYWzLcfRd/VR3Wm4unkyJtLPGSGKPkCSQTtUu/gz\nsfZ5chOuaP1kIbqQu4uZ4eG+R2cir0ktZHJCEBaz/JcWp0ZeOe3g2MdAERko0/uF8yVG+bM9u4yD\nRdUcLK5m2qCu2UNZ9A+SDNrB74tb+I35E5nMI3qEMVF+VNZZeXtdBgDTZe9i0QGSDNqqoYag7BV4\nqVqiA2QjEOF8Y419sd/bcJBQHzcGhUqNVZw6SQZtlbsVs7ayjaEEe8seBsL5EkK88XazUF1vY9qg\nYJTMLRAdIMmgrbIcW0Af9huDyST/6YTzmU2K0cbooakDpb9AdIwkg7bK2kC2KRKfwAHOjkSIo44s\nWjdN+gtEB8mkszaqCxjExw1uR9tphegJbpmRwMS4ACJkQ3vRQVIzaKOfYu7gmYbLmDpQPoGJniPQ\ny5Uzh4U5OwzRB0gyaIu6Ctbsz8fdxURSrL+zoxFCiE4nyaAtvv4Dv9p6CRNjA3CzmJ0djRBCdDpJ\nBm1gzfyZFGs40waHODsUIYToEpIMWlNTiqVoL5vsQ5gm/QVCiD5KkkFrspMB2Os6nBERvk4ORggh\nuoYMLW2FPrgOGya84idjlslmQog+qk01A6VUhlJqh1Jqq1Iq2Sgbq5T6+UiZUmqSUa6UUv9WSqUq\npbYrpZIa3WeBUmq/8bWgUfl44/6pxrU95l33UNhMHmu4lvFDop0dihBCdJn2NBPN0lqP1VpPMH5+\nCnhUaz0W+JPxM8C5wGDj61bgRQClVCDwZ2AyMAn4s1LqyPZNLwK3NLpu7qk+oc62sjKWN21zZUVI\nIUSf1pE+Aw0caUT3A3KN7+cBb2uHnwF/pVQ4cA6wQmtdrLUuAVYAc41jvlrrn7XWGngbuKgDcXWe\n8kMU7FhJrK+ZuCBZtloI0Xe1tc9AA98opTTwstb6FeAe4Gul1L9wJJWpxrmRQFaja7ONspbKs5so\ndzr77s+4L+dBqgd/JCtCCiH6tLYmg+la6xylVCiwQim1B7gMuFdrvUQpdQXwOnBWVwUKoJS6FUfT\nEzExMV35UACU719HrQ5g1IiRXf5YQgjhTG1qJtJa5xj/5gOf4GjzXwB8bJzykVEGkAM07m2NMspa\nKo9qorypOF7RWk/QWk8ICemGCWC5m9hqHyTLAwsh+rxWk4FSyksp5XPke2AOsBNHH8FM47Qzgf3G\n90uB641RRVOAMq31IeBrYI5SKsDoOJ4DfG0cK1dKTTFGEV0PfNZ5T/HU1JQV4l+TRZH/KEJ93Z0d\njhBCdKm2NBOFAZ8YbeYW4D2t9XKlVCXwnFLKAtRiNN8Ay4DzgFSgGrgRQGtdrJT6G7DROO+vWuti\n4/vbgTcBD+Ar48upVn63nAuApNO6tOVLCCF6BOUYwNP7TJgwQScnJ3fJvctqGpj95DdcOKCQP/3y\ncnCVkURCiL5BKbWp0RSBo2Q5iia8+mM6hbVwyS8ukkQghOgXJBmcoKCijoVr0nkx4itG6VRnhyOE\nEN1CksEJnl+VSqC1gHOL/we5m50djhBCdAtJBo3klNbw7vpMbhtU4iiITGr5AiGE6CMkGTSy8UAx\nDTbN3IBcMLtC2ChnhySEEN1CkkEjhZV1APgVb4cBo8Hi5uSIhBCie0gyaKSwsh5Xs8JckQ2R450d\njhBCdBvZ3KaRoso6grzdUHdvB2uts8MRQohuIzWDRgor6wjydgWlwMXD2eEIIUS3kWTQSFFVPb+0\nfgTLfufsUIQQoltJM1EjhRV1TFJrobBHbKcghBDdRmoGBq01FVWVRNSmS+exEKLfkWRgqKizMtiW\njgkbRMhkMyFE/yLJwFBUWc8IU6bjh/BE5wYjhBDdTJKBobCyjlpcKQ9KBL+o1i8QQog+RJKBoaiy\njsW2mWRf+oVjaKkQQvQjkgwMBZX1AAR7uzo5EiGE6H6SDAyVJflscvsVgQeWOjsUIYTodjLPwGAp\n2kuQqgAPf2eHIoQQ3U5qBgbPsjTHN6HDnBuIEEI4gSQDg39VGrXKHXxlJJEQov+RZGAIq8skzzUW\nTPIrEUL0P9JnYFhtG86wASHEOjsQIYRwAvkYDNRZbfxf7S/Yn3C9s0MRQginkGQAFJeU4kY9wT6y\nzaUQon+SZADYtn1EituNRKpCZ4cihBBOIckA0AV7qMMF71DpMRBC9E9tSgZKqQyl1A6l1FalVHKj\n8juVUnuUUruUUk81Kn9YKZWqlNqrlDqnUflcoyxVKfVQo/J4pdR6o/xDpVS3rgnhUryPVB1BsLds\ndSmE6J/aUzOYpbUeq7WeAKCUmgXMAxK11iOBfxnlI4CrgJHAXOAFpZRZKWUGngfOBUYA841zAZ4E\nntVaDwJKgJs6/tTazrs8lf06imAfWZdICNE/daSZ6DbgCa11HYDWOt8onwd8oLWu01ofAFKBScZX\nqtY6XWtdD3wAzFNKKeBMYLFx/VvARR2Iq31qy/GuyyNDReHpKiNthRD9U1uTgQa+UUptUkrdapQN\nAWYYzTs/KKUmGuWRQFaja7ONsubKg4BSrbX1hPKTKKVuVUolK6WSCwoK2hh66z4Ju5MdnpM67X5C\nCNHbtPWj8HStdY5SKhRYoZTaY1wbCEwBJgKLlFIJXRQnAFrrV4BXACZMmKA75abuvnzs+gsqfKyt\nnyuEEH1Um2oGWusc49984BMcTT7ZwMfaYQNgB4KBHCC60eVRRllz5UWAv1LKckJ59yjYi6ksi2Bv\nmWMghOi/Wk0GSikvpZTPke+BOcBO4FNgllE+BHAFCoGlwFVKKTelVDwwGNgAbAQGGyOHXHF0Mi/V\nWmtgFXCZ8ZALgM867Rm25us/8Pvyx2RTGyFEv9aWZqIw4BNHPy8W4D2t9XLjDX2hUmonUA8sMN7Y\ndymlFgG7AStwh9baBqCU+g3wNWAGFmqtdxmP8SDwgVLqMWAL8HqnPcNW6II97LHFSM1ACNGvtZoM\ntNbpQGIT5fXAtc1c8zjweBPly4BlzTxG9/fg1pSgyrLYZz9NagZCiH6tf89A3rkEgB/sY6RmIITo\n1/p3Mtj2IVUBw9mp4wmSmoEQoh/r37Os5n9AcvJWOFRLiNQMhBD9WP+uGXgFkW5xTI0IkmQghOjH\n+mcysNbDe1fCgR8pqqzHbFL4e7g4OyohhHCa/pkM9n0F+5aDtY7CyjoCvVwxmZSzoxJCCKfpn8lg\nyzvgEwEDz6Swsl5GEgkh+r3+lwzKcyH1Wxh7NZjMFFbWyRwDIUS/1++SwY+L/wPaTu3IqwAoqqoj\nyEuSgRCif+tXQ0ttds3WCj8OWmfz7KsZ/HK6orBCmomEEKJfJQOzSXHX3Q+x4UAxo1al8s+v9wIy\nrFQIIfpVMjhiUnwgk+InsTOnjE+25HDBmHBnhySEEE7VL5PBEaMi/RgV6efsMIQQwun6XQeyEEKI\nk0kyEEIIIclACCGEJAMhhBBIMhBCCIEkAyGEEEgyEEIIgSQDIYQQgNJaOzuGU6KUKgAyT/HyYKCw\nE8PpDD0xJpC42qMnxgQ9M66eGBP0j7hitdYhJxb22mTQEUqpZK31BGfH0VhPjAkkrvboiTFBz4yr\nJ8YE/TsuaSYSQgghyUAIIUT/TQavODuAJvTEmEDiao+eGBP0zLh6YkzQj+Pql30GQgghjtdfawZC\nCCEakWQghBCifyUDpdRcpdRepVSqUuohJ8axUCmVr5Ta2agsUCm1Qim13/g3wAlxRSulVimldiul\ndiml7nZ2bEopd6XUBqXUNiOmR43yeKXUeuNv+aFSyrW7YmoUm1kptUUp9UUPiilDKbVDKbVVKZVs\nlPWE15a/UmqxUmqPUipFKXWak19XQ43f0ZGvcqXUPT3kd3Wv8VrfqZR63/g/0OWvrX6TDJRSZuB5\n4FxgBDBfKTXCSeG8Ccw9oewhYKXWejCw0vi5u1mB+7XWI4ApwB3G78iZsdUBZ2qtE4GxwFyl1BTg\nSeBZrfUgoAS4qRtjOuJuIKXRzz0hJoBZWuuxjcal94TX1nPAcq31MCARx+/NaXFprfcav6OxwHig\nGvjEmTEBKKUigbuACVrrUYAZuIrueG1prfvFF3Aa8HWjnx8GHnZiPHHAzkY/7wXCje/Dgb094Hf2\nGXB2T4kN8AQ2A5NxzMa0NPW37aZYonC8WZwJfAEoZ8dkPG4GEHxCmVP/foAfcABjwEpPiatRHHOA\nNT0hJiASyAICcWxL/AVwTne8tvpNzYBjv+Qjso2yniJMa33I+P4wEObMYJRSccA4YD1Ojs1ojtkK\n5AMrgDSgVGttNU5xxt/y/4AHALvxc1APiAlAA98opTYppW41ypz92ooHCoA3jGa115RSXj0griOu\nAt43vndqTFrrHOBfwEHgEFAGbKIbXlv9KRn0GtqR/p025lcp5Q0sAe7RWpc3PuaM2LTWNu2ozkcB\nk4Bh3fn4J1JKXQDka603OTOOZkzXWifhaA69Qyl1euODTnptWYAk4EWt9TigihOaX5z1mjfa3i8E\nPjrxmDNiMvoo5uFIoBGAFyc3KXeJ/pQMcoDoRj9HGWU9RZ5SKhzA+DffGUEopVxwJIJ3tdYf96TY\ntNalwCoc1WR/pZTFONTdf8tpwIVKqQzgAxxNRc85OSbg6CdLtNb5ONrAJ+H8v182kK21Xm/8vBhH\ncnB2XOBImpu11nnGz86O6SzggNa6QGvdAHyM4/XW5a+t/pQMNgKDjV55VxxVw6VOjqmxpcAC4/sF\nONrru5VSSgGvAyla62d6QmxKqRCllL/xvQeOPowUHEnhMmfEpLV+WGsdpbWOw/E6+k5rfY0zYwJQ\nSnkppXyOfI+jLXwnTn5taa0PA1lKqaFG0Wxgt7PjMsznWBMROD+mg8AUpZSn8f/xyO+q619bzuiw\ncdYXcB6wD0eb8x+cGMf7ONoDG3B8aroJR5vzSmA/8C0Q6IS4puOoFm8Hthpf5zkzNmAMsMWIaSfw\nJ6M8AdgApOKo4rs56W95BvBFT4jJePxtxteuI6/xHvLaGgskG3/HT4EAZ8eFowmmCPBrVNYTfleP\nAnuM1/v/ALfueG3JchRCCCH6VTOREEKIZkgyEEIIIclACCGEJAMhhBBIMhBCCIEkAyGEEEgyEEII\nAfw/0jdvL7F8kK0AAAAASUVORK5CYII=\n"
}
}
],
"source": [
"T = len(y)\n",
"M = (np.eye(T) + np.array([abs(i-j)<2 for i in range(T) for j in range(T)]).reshape(T,T))/4\n",
"M[0,0] = 3/4; M[-1,-1]= 3/4 \n",
"plt.plot(y,label=r'$y$')\n",
"plt.plot(M@y,'--',label=r'$M@y$')\n",
"plt.legend()"
],
"id": "dc45c446-b9d2-43c2-abe1-6e3b1858cc23"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(5)` `(4)`의 변환을 50회 반복적용하고 결과를 시각화하라."
],
"id": "176d12df-4f85-4084-be18-d3e622e57aa6"
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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yD7H/cAoh/r4MnrygS2KIDvEhq7gKu1NLn0EXkGTQj6TmGR3BcZ1IBh3tBM4v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\nAAAAAElFTkSuQmCC\n"
}
}
],
"source": [
"plt.plot(y,label=r'$y$')\n",
"plt.plot(np.linalg.matrix_power(M,50)@y,'--',label=r'$M^{50}@y$')\n",
"plt.legend()"
],
"id": "6ee43144-cb63-41b9-8dbd-9d0bf0dd54bc"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 회귀모형\n",
"\n",
"`(6)--(7)` $(x_i,y_i)$가 아래와 같이 주어졌다고 가정하자."
],
"id": "6dbd188a-ff79-4b9a-b736-81d3268fc076"
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"x = np.array([0.00983, 0.01098, 0.02951, 0.0384 , 0.03973, 0.04178, 0.0533 ,\n",
" 0.058 , 0.09454, 0.1103 , 0.1328 , 0.1412 , 0.1497 , 0.1664 ,\n",
" 0.1906 , 0.1923 , 0.198 , 0.2141 , 0.2393 , 0.2433 , 0.3157 ,\n",
" 0.3228 , 0.3418 , 0.3552 , 0.3918 , 0.3962 , 0.4 , 0.4482 ,\n",
" 0.496 , 0.507 , 0.53 , 0.5654 , 0.582 , 0.5854 , 0.5854 ,\n",
" 0.6606 , 0.7007 , 0.723 , 0.7305 , 0.7383 , 0.7656 , 0.7725 ,\n",
" 0.831 , 0.8896 , 0.9053 , 0.914 , 0.949 , 0.952 , 0.9727 ,\n",
" 0.982 ])\n",
"y = np.array([0.7381, 0.7043, 0.3937, 0.1365, 0.3784, 0.3028, 0.1037, 0.3846,\n",
" 0.706 , 0.7572, 0.2421, 0.232 , 0.9855, 1.162 , 0.4653, 0.6791,\n",
" 0.6905, 0.6865, 0.9757, 0.7665, 0.9522, 0.4641, 0.5498, 1.1509,\n",
" 0.5288, 1.1195, 1.1659, 1.4341, 1.2779, 1.1648, 1.4002, 0.7472,\n",
" 0.9142, 0.9658, 1.0707, 1.4501, 1.6758, 0.8778, 1.3384, 0.7476,\n",
" 1.3086, 1.7537, 1.5559, 1.2928, 1.3832, 1.3115, 1.3382, 1.536 , \n",
" 1.9177, 1.2069])"
],
"id": "ebd83cce-1ef4-4cd6-a0a1-e060734a99bf"
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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}
}
],
"source": [
"plt.plot(x,y,'o')"
],
"id": "bcbdbb67-f82f-429e-8818-d6ae04f20ea5"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`6`. 아래의 수식을 이용하여 적절한 추세선\n",
"$\\hat{y}_i= \\hat{\\beta}_0 +\\hat{\\beta}_1 x_i$를 구하고 시각화하라.\n",
"\n",
"$$\\begin{bmatrix} \\hat{\\beta}_0 \\\\ \\hat{\\beta}_1 \\end{bmatrix} = ({\\bf X}^T {\\bf X})^{-1}{\\bf X}^T {\\boldsymbol y}, \\quad {\\bf X}=\\begin{bmatrix} 1 & x_1 \\\\ 1 & x_2 \\\\ \\dots \\\\ 1 & x_n \\end{bmatrix}$$\n",
"\n",
"(풀이)"
],
"id": "a4e03aeb-4c03-49ea-aabb-cf816a1b93dc"
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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5aNaYEm45ZyQlvYowoKRXUdJz5be32UdEkmi6MbMC4DZgClAJrDazpe6+odGh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\nAAAASUVORK5CYII=\n"
}
}
],
"source": [
"n = len(x)\n",
"X = np.stack([np.ones(n),x],axis=1)\n",
"b,a = np.linalg.inv(X.T@X)@X.T@y \n",
"yhat = b+a*x \n",
"plt.plot(x,y,'o')\n",
"plt.plot(x,yhat,'--')"
],
"id": "fa401e25-41dd-40ad-8375-a6755ca5f734"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`7`. $\\frac{1}{n}\\sum_{i=1}^{n}(y_i-\\hat{y}_i)^2$을 계산하라.\n",
"\n",
"`(풀이)`"
],
"id": "3430526a-c8d7-4bde-a9c7-3330e0ab8558"
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"np.mean((y-yhat)**2)"
],
"id": "a03f7393-7261-4934-9c2b-992cc896e2ed"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 2. fashion MNIST data (60점)\n",
"\n",
"아래는 9가지의 의류이미지가 저장된 이미지데이터를 불러오는 코드이다."
],
"id": "5bcb9d5e-4046-4a93-9303-e856026c3c66"
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
"df_train=pd.read_csv('https://media.githubusercontent.com/media/guebin/PP2023/main/posts/fashion-mnist_train.csv')\n",
"df_test=pd.read_csv('https://media.githubusercontent.com/media/guebin/PP2023/main/posts/fashion-mnist_test.csv')"
],
"id": "7dc4f14c-0b68-4fc6-8617-ae782da323c3"
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [],
"source": [
"def rshp(row):\n",
" return row.reshape(28,28)"
],
"id": "fce74000-08c4-462d-acd8-70e821df0f48"
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"xtrain = np.apply_along_axis(rshp,axis=1,arr=np.array(df_train.iloc[:,1:]))\n",
"xtest = np.apply_along_axis(rshp,axis=1,arr=np.array(df_test.iloc[:,1:]))\n",
"ytrain = np.array(df_train.label)\n",
"ytest = np.array(df_test.label)"
],
"id": "084d6540-4f85-4817-9043-33406de63270"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"아래는 데이터에 대한 설명이다.\n",
"\n",
"- 전체의 이미지의 수는 70000개이며, 60000개의 이미지 ${\\tt xtrain}$에\n",
" 10000개의 이미지는 ${\\tt xtest}$에 저장되어 있다.\n",
"- 이미지에 대한 라벨은 각각 ${\\tt ytrain}$과 $\\tt ytest$에 저장되어\n",
" 있다. 따라서 $\\tt ytrain$에는 60000개의 이미지에 해당하는 라벨이,\n",
" $\\tt ytest$에는 10000개의 이미지에 해당하는 라벨이 기록되어 있다.\n",
"- 보통 분석에서는 60000개의 이미지를 가지고 라벨을 맞추는 “훈련”을\n",
" 하고 (${\\tt xtrain}$을 이용하여 ${\\tt ytrain}$을 맞추는 방법을\n",
" 학습하고), 그러한 훈련이 잘 되었는지 10000개의 이미지를 이용하여\n",
" “테스트”한다.\n",
"- 위와 같은 의미로 $({\\tt xtrain}, {\\tt ytrain})$ 을 training data\n",
" set, $({\\tt xtest},{\\tt ytest})$ 를 test data set 이라고 부른다.\n",
" (ref:\n",
" [위키참고](https://en.wikipedia.org/wiki/Training,_validation,_and_test_data_sets))\n",
"\n",
"아래는 이미지자료와 시각화에 대한 설명이다.\n",
"\n",
"- 각 이미지는 (28,28) 픽셀의 흑백이미지이다. 따라서 각 이미지는\n",
" (28,28,3) 이 아니라 (28,28) 의 shape을 가진 텐서로 구성되어있다.\n",
"- 흑백이미지를 시각화 하기 위해서는 `plt.imshow(img, cmap='gray')`를\n",
" 이용한다. 여기에서 ${\\tt img}$은 임의의 2차원 텐서이며 이 예제의\n",
" 경우 (28,28)의 shape을 가진다.\n",
"\n",
"아래는 ${\\tt xtrain}$의 두번째 이미지, 즉 ${\\tt xtrain[1,:,:]}$를\n",
"확인하는 코드의 예시이다."
],
"id": "3274e1c6-ff42-41ae-b8c6-3d77203eeb16"
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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}
}
],
"source": [
"# plt.imshow(xtrain[1,:,:],cmap='gray')\n",
"plt.imshow(xtrain[1],cmap='gray') ## 같은코드임"
],
"id": "c0adfcce-30b0-4b0d-a8e7-cf1f5928103f"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"이 이미지에 대한 label은 ${\\tt ytrain[1]}$의 값으로 확인가능하다."
],
"id": "9fbaff16-6dae-4ae4-9be1-5c00e1dce69f"
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"ytrain[1]"
],
"id": "b5a3bad7-c9c1-479d-85b9-2e6c802ddfee"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"이미지와 라벨을 한번에 표현하는 코드는 아래와 같이 작성가능하다."
],
"id": "697a12e6-69eb-4d22-a338-7ec5f9311e8c"
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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}
}
],
"source": [
"plt.imshow(xtrain[1],cmap='gray')\n",
"plt.title('label={}'.format(ytrain[1]));"
],
"id": "0c116c43-1ed7-4421-80a5-94f940211821"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"여기에서 9가 의미하는 것은 ’Ankel boot’이며, 다른 숫자가 의미하는 것은\n",
"각각 아래와 같다."
],
"id": "50a02811-b886-4706-a34e-1b069fdd42df"
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [],
"source": [
"labels= {0:'T-shirt/top', \n",
" 1:'Trouser', \n",
" 2:'Pullover', \n",
" 3:'Dress', \n",
" 4:'Coat', \n",
" 5:'Sandal', \n",
" 6:'Shirt', \n",
" 7:'Sneaker', \n",
" 8:'Bag', \n",
" 9:'Ankel boot'} "
],
"id": "2e6f9679-cb03-4e19-871c-93fd5cb46ef6"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"아래는 ${\\tt xtrain}$의 처음 10개의 이미지를 라벨과 함께 출력하는\n",
"코드이다."
],
"id": "07e7059c-38f9-4157-8349-d3d86d91ab07"
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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DBgxwesSIEU5z1r2h0B1kIYQQQgghMmiALIQQQgghRAYNkIUQQgghhMhQ1gwy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\nRU5ErkJggg==\n"
}
}
],
"source": [
"fig, ax = plt.subplots(2,5,figsize=(10,5))\n",
"\n",
"ax[0][0].imshow(xtrain[0],cmap='gray'); ax[0][0].set_title('label={}'.format(labels[ytest[0]]));\n",
"ax[0][1].imshow(xtrain[1],cmap='gray'); ax[0][1].set_title('label={}'.format(labels[ytest[1]]));\n",
"ax[0][2].imshow(xtrain[2],cmap='gray'); ax[0][2].set_title('label={}'.format(labels[ytest[2]]));\n",
"ax[0][3].imshow(xtrain[3],cmap='gray'); ax[0][3].set_title('label={}'.format(labels[ytest[3]]));\n",
"ax[0][4].imshow(xtrain[4],cmap='gray'); ax[0][4].set_title('label={}'.format(labels[ytest[4]]));\n",
"\n",
"ax[1][0].imshow(xtrain[5],cmap='gray'); ax[1][0].set_title('label={}'.format(labels[ytest[5]]));\n",
"ax[1][1].imshow(xtrain[6],cmap='gray'); ax[1][1].set_title('label={}'.format(labels[ytest[6]]));\n",
"ax[1][2].imshow(xtrain[7],cmap='gray'); ax[1][2].set_title('label={}'.format(labels[ytest[7]]));\n",
"ax[1][3].imshow(xtrain[8],cmap='gray'); ax[1][3].set_title('label={}'.format(labels[ytest[8]]));\n",
"ax[1][4].imshow(xtrain[9],cmap='gray'); ax[1][4].set_title('label={}'.format(labels[ytest[9]]));\n",
"\n",
"fig.tight_layout()"
],
"id": "30c5af65-e6a8-46a6-aa37-21521761ae84"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"------------------------------------------------------------------------\n",
"\n",
"`(1)` ${\\tt xtrain}$에서 각 라벨에 대한 평균이미지를 계산하고 계산결과를\n",
"${\\tt imgmean}$에 길이가 10인 `list`로 저장하라. 즉 ${\\tt imgmean}$은\n",
"아래와 같은 자료구조를 가지고 있어야 한다.\n",
"\n",
"- ${\\tt imgmean}=\\big[{\\tt imgmean[0]},\\dots, {\\tt imgmean[9]}\\big]$\n",
"- ${\\tt imgmean[0]}, \\dots, {\\tt imgmean[9]}$ 는 각각 (28,28)의\n",
" shape을 가진 numpy array\n",
"- ${\\tt imgmean[0]}, \\dots, {\\tt imgmean[9]}$ 는 각각 숫자 0,1, …, 9의\n",
" 평균이미지를 의미\n",
"\n",
"${\\tt imgmean[0]},\\dots, {\\tt imgmean[9]}$를 시각화 하라.\n",
"\n",
"`(풀이)`"
],
"id": "1e97ed45-7e9b-4f66-89dd-0ea2b32bd571"
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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IEaEBshBCCCGEEBG19iCzj4Z9Mxyz3yk3j6jnq8n1T+X6YLi8DPvLvOP36mNY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\nCCGEiNAAWQghhBBCiIj/B7fGK7RHXiA4AAAAAElFTkSuQmCC\n"
}
}
],
"source": [
"imgmean = [xtrain[ytrain==i].mean(axis=0) for i in range(10)] \n",
"\n",
"fig, ax = plt.subplots(2,5,figsize=(10,5))\n",
"ax[0][0].imshow(imgmean[0],cmap='gray'); ax[0][0].set_title('label={}'.format(labels[0]));\n",
"ax[0][1].imshow(imgmean[1],cmap='gray'); ax[0][1].set_title('label={}'.format(labels[1]));\n",
"ax[0][2].imshow(imgmean[2],cmap='gray'); ax[0][2].set_title('label={}'.format(labels[2]));\n",
"ax[0][3].imshow(imgmean[3],cmap='gray'); ax[0][3].set_title('label={}'.format(labels[3]));\n",
"ax[0][4].imshow(imgmean[4],cmap='gray'); ax[0][4].set_title('label={}'.format(labels[4]));\n",
"ax[1][0].imshow(imgmean[5],cmap='gray'); ax[1][0].set_title('label={}'.format(labels[5]));\n",
"ax[1][1].imshow(imgmean[6],cmap='gray'); ax[1][1].set_title('label={}'.format(labels[6]));\n",
"ax[1][2].imshow(imgmean[7],cmap='gray'); ax[1][2].set_title('label={}'.format(labels[7]));\n",
"ax[1][3].imshow(imgmean[8],cmap='gray'); ax[1][3].set_title('label={}'.format(labels[8]));\n",
"ax[1][4].imshow(imgmean[9],cmap='gray'); ax[1][4].set_title('label={}'.format(labels[9]));\n",
"fig.tight_layout()"
],
"id": "21b7a672-aadc-4e0f-9172-ab00e833e1a1"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(2)` 아래와 같은 numpy array 를 생성하라.\n",
"\n",
"$${\\tt loss}= \n",
"\\begin{bmatrix} \n",
"{\\tt loss[0,0]} & \\dots & {\\tt loss[0,9]} \\\\ \n",
"{\\tt loss[1,0]} & \\dots & {\\tt loss[1,9]} \\\\ \n",
"\\dots & \\dots & \\dots \\\\ \n",
"{\\tt loss[59999,0]}& \\dots &{\\tt loss[59999,9]} \\\\ \n",
"\\end{bmatrix}$$\n",
"\n",
"여기에서\n",
"\n",
"$${\\tt loss[i,j]} = \\frac{1}{28\\times 28} \\sum_{p=0}^{27}\\sum_{q=0}^{27}\\big({\\tt xtrain[i,p,q]}-{\\tt imgmean[j][p,q]}\\big)^2$$\n",
"\n",
"이다. 이제 ${\\tt loss}$에서 “최소값을 가지는 원소의 인덱스를 출력”하는\n",
"함수를 행별로 적용해 이미지를 분류하라. 예를들어 모든 $j=0,1,\\dots,9$ 에\n",
"대하여 아래를 계산한 결과\n",
"\n",
"$$\\frac{1}{28\\times 28} \\sum_{p=0}^{27}\\sum_{q=0}^{27}\\big({\\tt xtrain[1,p,q]}-{\\tt imgmean[j][p,q]}\\big)^2$$\n",
"\n",
"$j=9$일 경우 그 값이 가장 작다면 ${\\tt xtrain[1]}$ 이미지는 9번으로\n",
"분류한다. 분류한 결과와 실제 라벨 ${\\tt ytrain}$을 비교하라. 얼마나 많은\n",
"결과가 일치하는지 비율을 계산하라.\n",
"\n",
"`(풀이)`"
],
"id": "29c2ba3a-ff7c-46bd-8934-1ae77ce9e866"
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [],
"source": [
"training_loss = np.array([[np.mean((xtrain[j,:,:]- imgmean[i])**2) for i in range(10)] for j in range(60000)])\n",
"ytrain_hat = training_loss.argmin(axis=1)\n",
"np.mean(ytrain_hat == ytrain)"
],
"id": "70e15fa0-1c83-40f3-8c9a-3e833712c2f9"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(3)` ${\\tt xtrain}$에서 학습한 평균이미지 ${\\tt imgmean}$를 바탕으로\n",
"${\\tt xtest}$의 1번라벨에 해당하는 이미지만을 분류하라. 아래의 물음에\n",
"답하라.\n",
"\n",
"- 1번라벨에 해당하는 이미지를 0번라벨로 분류한 경우는 모두 몇건인가?\n",
" (잘못된 분류)\n",
"- 1번라벨에 해당하는 이미지를 1번라벨로 분류한 경우는 모두 몇건인가?\n",
" (올바른 분류)\n",
"- $\\dots$\n",
"- 1번라벨에 해당하는 이미지를 9번라벨로 분류한 경우는 모두 몇건인가?\n",
" (잘못된 분류)\n",
"\n",
"**hint**: 아래와 같은 결과를 주는 dictionary를 만들면 된다.\n",
"\n",
" {0: 28, 1: 895, 2: 11, 3: 36, 4: 8, 5: 12, 6: 10, 7: 0, 8: 0, 9: 0}\n",
"\n",
"- 1번라벨에 해당하는 이미지를 0번라벨로 분류한 경우는 모두 28건\n",
"- 1번라벨에 해당하는 이미지를 1번라벨로 분류한 경우는 모두 895건\n",
"- $\\dots$\n",
"- 1번라벨에 해당하는 이미지를 9번라벨로 분류한 경우는 모두 0건\n",
"\n",
"`(풀이)`"
],
"id": "3a0780d2-ad55-46bf-9c26-d3643cf9edc7"
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [],
"source": [
"test_loss = np.array([[np.mean((xtest[j,:,:]- imgmean[i])**2) for i in range(10)] for j in range(10000)])\n",
"ytest_hat = test_loss.argmin(axis=1)\n",
"{j: ytest_hat[ytest==1].tolist().count(j) for j in range(10)}"
],
"id": "c58047f6-250d-4796-8c27-a927bd2679ba"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(4)` ${\\tt xtest}$의 이미지를 올바르게 분류한 비율을 카테고리별로\n",
"정리하라.\n",
"\n",
"`(풀이)`"
],
"id": "7877f39b-d5e7-4880-a8aa-0886bdbddc96"
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [],
"source": [
"{labels[j]:ytest_hat[ytest==j].tolist().count(j)/sum(ytest==j) for j in range(10)}"
],
"id": "809aa45a-3741-4435-a7d4-6d3a77ad2725"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3. 파이썬의 설치 (5점)\n",
"\n",
"다음을 읽고 파이썬과 가상환경에 대하여 올바른 진술을 한 사람을 모두\n",
"골라라. (모두 맞출 경우만 정답으로 인정함)\n",
"\n",
"**민정**: 구글코랩은 사용자의 컴퓨터에 설치된 아나콘다를 기반으로\n",
"동작하며, 실제적으로는 사용자의 ipython과 크롬과의 통신만을 담당한다.\n",
"따라서 구글코랩은 반드시 파이썬만 연결하여 사용가능하지 않으며 실제로\n",
"구글코랩에 R을 연결하여 사용하기도 한다.\n",
"\n",
"**구환**: 아래와 같이 스크립트로 구성된 `mysum.py`와 같은 파이썬파일을\n",
"실행하기 위해서는 반드시 ipython 이나 주피터랩이 설치된 상태이어야 한다.\n",
"\n",
"``` python\n",
"## mysum.py\n",
"total = 0 \n",
"for i in range(1,11): \n",
" total = total + i\n",
"print(total)\n",
"```\n",
"\n",
"**슬기**: 아나콘다를 이용하여 가상환경을 만들 경우 두 가지버전 이상의\n",
"python을 동시에 관리할 수 있다.\n",
"\n",
"**승민**: 아래와 같이 `myfuns.py` 파일을 구성하였다고 하자.\n",
"\n",
"``` python\n",
"# myfuns.py\n",
"def vec2_add(a,b): \n",
" return [a[0]+b[0], a[1]+b[1]]\n",
"```\n",
"\n",
"이 경우 아래와 같이 임의의 주피터 노트북에서 `myfuns`를 임포트하면\n",
"`vec2_add` 함수를 사용할 수 있다.\n",
"\n",
"``` python\n",
"import myfuns\n",
"```\n",
"\n",
"단, 여기에서 `myfuns.py`는 현재 실행중인 노트북과 같은 폴더에 있다고\n",
"가정한다.\n",
"\n",
"`(풀이)` 슬기, 승민\n",
"\n",
"- 민정: 코랩은 사용자의 컴퓨터에 설치된 아나콘다를 기반으로 동작하며\n",
" (X)\n",
"- 구환: 반드시 ipython 이나 주피터랩이 설치된 상태이어야 한다. (X)\n",
"\n",
"------------------------------------------------------------------------\n",
"\n",
"# 4. 삼성전자의 주가 추가문제 (30점)\n",
"\n",
"다음은 삼성전자의 주가를 크롤링하는 코드이다."
],
"id": "e5feda89-ed42-48b4-9ab1-97f454eaca38"
},
{
"cell_type": "code",
"execution_count": 231,
"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[*********************100%***********************] 1 of 1 completed"
]
}
],
"source": [
"start_date = \"2023-01-01\"\n",
"end_date = \"2023-05-02\"\n",
"y = yf.download(\"005930.KS\", start=start_date, end=end_date)['Adj Close'].to_numpy()"
],
"id": "b41ff245-9cb3-455c-849f-c0cd860ee686"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"삼성전자의 주가 ${\\boldsymbol y}$를 시각화하면 아래와 같다."
],
"id": "ed0ca177-28ff-4142-8e22-07a580945df3"
},
{
"cell_type": "code",
"execution_count": 232,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
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c1UdqXBS2iNk1Kr3A2uTmsX1nmJ8cyztWZoesLpGBHGSMOQiUjHJ/kc/PBvj4CMc9DDzs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\n+P8BCQeapiSGrA4AAAAASUVORK5CYII=\n"
}
}
],
"source": [
"plt.plot(y)"
],
"id": "8223019c-07a8-44e0-8cfa-f4d795e92e03"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(1)` 아래와 같은 ${\\bf x}$를 설정하라.\n",
"\n",
"$${\\bf x}=(x_1,x_2,\\dots,x_n)=\\big(\\frac{1}{n},\\frac{2}{n},\\dots,1\\big)$$\n",
"\n",
"${\\bf x}=(x_1,\\dots,x_n)$을 바탕으로 아래와 같은 매트릭스 ${\\bf X}$를\n",
"생성하라. 단, $n={\\tt len}({\\boldsymbol y})$.\n",
"\n",
"$${\\bf X}=\\begin{bmatrix} 1 & x_1 \\\\ 1 & x_2\\\\ \\dots & \\dots \\\\ 1 & x_n \\end{bmatrix}$$\n",
"\n",
"**hint**: ${\\bf X}$를 아래와 같이 해석해도 무방하다.\n",
"\n",
"$${\\bf X}=\\begin{bmatrix} x_1^0 & x_1^1 \\\\ x_2^0 & x_2^1\\\\ \\dots & \\dots \\\\ x_n^0 & x_n^1 \\end{bmatrix}$$"
],
"id": "df501db7-0b93-4bfc-90b7-f12e83d92157"
},
{
"cell_type": "code",
"execution_count": 363,
"metadata": {},
"outputs": [],
"source": [
"x = np.arange(1,83)/82 # x = np.arange(0,82)/82 정도의 실수는 정답으로 인정..\n",
"X = np.stack([x**k for k in range(2)],axis=1)"
],
"id": "ef4005d8-ce01-4355-b7f7-45f4ddc4e9de"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(2)` `(1)`에서 계산된 ${\\bf X}$에 대하여 아래를 계산하라.\n",
"\n",
"$$\\hat{\\bf y}= {\\bf X}({\\bf X}^T {\\bf X})^{-1}{\\bf X}^T {\\bf y}$$\n",
"\n",
"$(x_i,y_i)$와 $(x_i,\\hat{y}_i)$을 겹쳐서 시각화하라. 단,\n",
"$\\hat{\\bf y}=(\\hat{y}_1,\\dots,\\hat{y}_n)$.\n",
"\n",
"**hint:** 계산의 편의를 위하여 ${\\bf y}$와 $\\hat{\\bf y}$은 모두\n",
"$n\\times 1$ col-vector가 아닌 길이가 $n$인 벡터로 해석해도 무방하다.\n",
"\n",
"`(풀이)`"
],
"id": "3c140c2d-28c5-4bc9-b0bf-30a6a41a9261"
},
{
"cell_type": "code",
"execution_count": 235,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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wKb2o03N2ZZXy5CeZhPr7kH6qmoYme7vXjXs1At+MxHDsDs0x2du597SGv58F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\n"
}
}
],
"source": [
"yhat= X@np.linalg.inv(X.T@ X)@ X.T @ y\n",
"plt.plot(x,y, label=r'$(x_i,y_i)$')\n",
"plt.plot(x,yhat,'--',label=r'$(x_i,\\hat{y}_i)$')\n",
"plt.legend()"
],
"id": "22cd565e-253e-40c4-beea-593d8ba601f6"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`3`. 아래와 같이 ${\\bf X}$를 수정하라.\n",
"\n",
"$${\\bf X}=\\begin{bmatrix} 1 & x_1 & x_1^2 & x_1^3 & \\dots & x_1^{10} \\\\ 1 & x_2 & x_2^2 & x_2^3 & \\dots & x_2^{10} \\\\ \\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\ 1 & x_n & x_n^2 & x_n^3 & \\dots & x_n^{10} \\end{bmatrix}$$\n",
"\n",
"수정된 ${\\bf X}$에 대하여 아래의 수식으로 $\\hat{\\bf y}$을 구하라.\n",
"\n",
"$$\\hat{\\bf y}= {\\bf X}({\\bf X}^T {\\bf X})^{-1}{\\bf X}^T {\\bf y}$$\n",
"\n",
"$(x_i,y_i)$와 $(x_i,\\hat{y}_i)$을 겹쳐서 시각화하라. 단,\n",
"$\\hat{\\bf y}=(\\hat{y}_1,\\dots,\\hat{y}_n)$.\n",
"\n",
"`(풀이)`"
],
"id": "8433978e-0119-48e0-ae52-8377af71346b"
},
{
"cell_type": "code",
"execution_count": 244,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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MsYVf8azXv4h5awrYzIBSa4WAKJj8Czj7MViwmPxTHqK40sZlk+LxnHw9zP4L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\n"
}
}
],
"source": [
"X = np.stack([x**k for k in range(11)],axis=1)\n",
"plt.plot(x,y, label=r'$(x_i,y_i)$')\n",
"plt.plot(x, X@np.linalg.inv(X.T@ X)@ X.T @ y,'--',label=r'$(x_i,\\hat{y}_i)$')\n",
"plt.legend()"
],
"id": "f0efce4b-ae50-4ed1-8389-7507915459fa"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 5. fashin MNIST data 추가문제 (30점)\n",
"\n",
"이 문제는 2번문항의 추가문항입니다."
],
"id": "d99dbacf-cff2-4877-988e-50032da91aaf"
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [],
"source": [
"# read data \n",
"df_train=pd.read_csv('https://media.githubusercontent.com/media/guebin/PP2023/main/posts/fashion-mnist_train.csv')\n",
"df_test=pd.read_csv('https://media.githubusercontent.com/media/guebin/PP2023/main/posts/fashion-mnist_test.csv')\n",
"\n",
"# rshp 함수정의 \n",
"def rshp(row):\n",
" return row.reshape(28,28)\n",
"\n",
"# cleaning data \n",
"xtrain = np.apply_along_axis(rshp,axis=1,arr=np.array(df_train.iloc[:,1:]))\n",
"xtest = np.apply_along_axis(rshp,axis=1,arr=np.array(df_test.iloc[:,1:]))\n",
"ytrain = np.array(df_train.label)\n",
"ytest = np.array(df_test.label)"
],
"id": "424153c1-03e3-4dcb-b567-b3f0c799b513"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(1)` ${\\tt xtrain}$에서 각 라벨에 대한 평균이미지를 계산하고 계산결과를\n",
"${\\tt imgmean}$에 길이가 10인 `list`로 저장하라. 즉 ${\\tt imgmean}$은\n",
"아래와 같은 자료구조를 가지고 있어야 한다.\n",
"\n",
"- ${\\tt imgmean}=\\big[{\\tt imgmean[0]},\\dots, {\\tt imgmean[9]}\\big]$\n",
"- ${\\tt imgmean[0]}, \\dots, {\\tt imgmean[9]}$ 는 각각 (28,28)의\n",
" shape을 가진 numpy array\n",
"- ${\\tt imgmean[0]}, \\dots, {\\tt imgmean[9]}$ 는 각각 숫자 0,1, …, 9의\n",
" 평균이미지를 의미\n",
"\n",
"모든 $i=0,\\dots,9$에 대하여 아래를 계산하고\n",
"\n",
"$${\\tt dist}[i] = \\frac{1}{28\\times 28} \\sum_{p=0}^{27}\\sum_{q=0}^{27}\\big({\\tt imgmean}[2][p,q]-{\\tt imgmean}[i][p,q]\\big)^2$$\n",
"\n",
"${\\tt dist}[i]$의 값이 가장 작은 $i$를 찾아라. 단 ${\\tt dist}[i]=0$ 인\n",
"경우는 제외한다. (즉 2번 라벨과 평균이미지가 가장 비슷한 카테고리를\n",
"찾아라)\n",
"\n",
"**hint:** 4번라벨이 2번라벨과 가장 비슷하다.\n",
"\n",
"`(풀이1)`"
],
"id": "5acafc8f-c838-48c2-87be-27a4e58e99ed"
},
{
"cell_type": "code",
"execution_count": 247,
"metadata": {},
"outputs": [],
"source": [
"imgmean = [xtrain[ytrain==i].mean(axis=0) for i in range(10)] \n",
"[np.mean((imgmean[i] - imgmean[2])**2) for i in range(10)]"
],
"id": "619981f9-2137-44ee-8baf-64c4c8c06be6"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(풀이2)`"
],
"id": "d2071450-f5a0-4511-8a5b-190b72644001"
},
{
"cell_type": "code",
"execution_count": 362,
"metadata": {},
"outputs": [],
"source": [
"imgmean = [xtrain[ytrain==i].mean(axis=0) for i in range(10)] \n",
"np.mean((imgmean - imgmean[2])**2,axis=(1,2))"
],
"id": "922cee53-ee6f-4eb8-ba40-48ca07e73953"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(2)` `(1)`의 과정을 반복하여 아래의 평균이미지를 비슷한 카테고리로 묶는\n",
"작업을 하였다고 하자."
],
"id": "fec69e80-2cc3-4373-b5b6-7dc7acd2d250"
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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h6v8l6VyT1eG4rn9YTBeLkPQhSd8tpfxh46Y7JN3U//4mSbcPtQZYlqgbDIO6\nQVvUDIZB3SCzmHeQXyvpXZLuiYi7+z/7gKQPSvrLiHiPpEcl/eJE1hBLFXWDYVA3aIuawTCoGwyU\nniCXUr4saaH3p18/3tXBckHdYBjUDdqiZjAM6gaZVl0sJi3L0Lqs/6xndNtqm1vJMshZH+Ust+O9\n/rLnl2W2s4wyeny7eAY56w/bNmvq+aysd6jn09iPw8lev1me1DPIfv8sj9k2N9c2g9y2B62vn9d5\nlnOcB9k2zLKaWbZy1F7TWR9l13auypafPf95mavavrazHuR79+6txitXrqzGPtdk6zOqtucWft3O\nwYMHq7FnrP3cJzuXmlofZAAAAGCecIIMAAAANHCCDAAAADTMNIOc5Y+yfJePvRfgWWedNcLate8J\nOe48VZaz8eeX9VKc8efeT03Wn9q1zXp6vuvo0aPVOMvdZT0wPdua9Tn2PNdy3a+T1jY/6plj793p\ndXHkyJFq7HXUNk/a9vWd5QL9ds89eq9SX/+2/bep0/b9cN2omeVsrmx7/7brP6+yY44fA3xu2bdv\n38Df99fuqMfArA6ybH02txw4cKAaeyZ51apVA5c3qc8+4B1kAAAAoIETZAAAAKCBE2QAAACgoVN9\nkF2WqfPciWeQR81zZbdPOl+VLT97vtnyyIctjm8nz4d51tRvz7Lyvt88c+zLyzLIbbOg8yrL4PrY\n94vnAr13586dO6txljVv27O27TUcbfui+/PxOve68+3DfPNi2T7OeuOP+7XdNruZPX42t00qK7rU\ntO2x7tcv7N69e+Dvr1u3rhr7Z0SMer2Da5tB9oyx93Ves2ZNNfY+yFkP+XHhHWQAAACggRNkAAAA\noIETZAAAAKBhSWWQM1nOxnMrLvsc+rb9crO+o1kvwez+/nxH7UE5rxnBts/b+79m/WGzfre+H/3+\nWcbY+/FmdTev2ub+fLtnucD9+/dX423btlXjrE6yfGrbXOCo88+uXbuq8fr166ux153/vm+/bH6b\nB75P216PkPXmdl4zWYY4W362D/35ZMfkeeXb0eeCbE736xv8+oAzzzyzGmf7YdRznbZ14tc3PP74\n49V49erV1XjFihXVOJubxzW38A4yAAAA0MAJMgAAANDACTIAAADQ0KkMctbnOJP1RT7rrLOqseda\nzj777GrsuZ22fUfb9gE9ceJENfYcUttcUbZ+8yKrq7Zjz2tlnwvvdXfuuedWY+/x6PvZx57vyrLo\nWT/deZFlkEftP+29Pfft21eNV65cOXD5Pl9ldeiy+SbrTeo5SM9Yb9myZeDvZ71QR50fl4K2+8C1\nnUu8prIsafb4vg99eT5Xjfu6nOUq2w7ZdSd+buB9g5944omByz/nnHOqcZYVz/h+97rxudSfz549\ne6qxZ5A3bdo08Pd9e02qrjhyAgAAAA2cIAMAAAANnCADAAAADZ3KILus157nUrZv316NP/7xj1fj\nhx56qBr755V7nsuzolmOx/n6eubQM8beG9DHO3bsqMZ33XXXwPt7Dmg5Zv4WY9T+1D72vNSXvvSl\naux5Lu9/+7Wvfa0aex7Ll3fRRRdVY88FfvnLX67GXifHjh2rxm3rYrnUiT8Pnz98v37uc5+rxt7X\n2HOA99xzTzU+fvx4Nc563o67N2nbvsfZ68Jv94zygQMHqvG999478P5ZX/qlyLeZP0fvV/vII49U\nY5/DH3744Wp85513VuNLLrmkGvt1NX79gsv68XqN+/ref//91dhfQ9k+Xy5zi/Pn5cd+n/P/9m//\nthp7n2PPIP/d3/1dNfa68v2SXW/l2fa2161kPeR9LvS6yDLXjz32WDX26zsefPDBapz1aF8s3kEG\nAAAAGjhBBgAAABo4QQYAAAAaYpoZoIjYI+lRSesl7U3uPktdXr9ZrdvmUsoFM3jcpVI3XV43aX7r\n5pjYL6OYq7pZInONxPothLoZjPU7tVPWzVRPkF940IhvlFJunPoDL1KX16/L6zZpXX7uXV43qfvr\nNyldf96sXzd1/Xmzft3U9efN+rVDxAIAAABo4AQZAAAAaJjVCfKtM3rcxery+nV53Saty8+9y+sm\ndX/9JqXrz5v166auP2/Wr5u6/rxZvxZmkkEGAAAAuoqIBQAAANDACTIAAADQMNUT5Ih4U0Q8EBEP\nR8Qt03zsBdbnwxGxOyLubfxsbUR8PiIe6v+7ZobrtykivhAR90fEfRHx3q6t4zRQN63Xj7oRdTPE\n+lE3om5arhs100fdtFq3JVE3UztBjojTJf2JpDdLukbSOyLimmk9/gJuk/Qm+9ktku4spWyVdGd/\nPCvPSvqtUso1kl4t6df726xL6zhR1M1QqBvqZhjUDXXT1tzXjETdDGFp1E0pZSpfkl4j6bON8fsl\nvX9ajz9gvS6XdG9j/ICkjf3vN0p6YNbr2Fi32yW9scvrSN10b59QN9QNdUPdUDPUTVf3S1frZpoR\ni0skPd4Yb+//rGs2lFJ29L/fKWnDLFfmeRFxuaSXS/q6OrqOE0LdjIC6eQF10wJ18wLqZpHmuGYk\n6mZoXa4bLtIboPT+GzPzPngRcZ6kT0h6XynlcPO2rqwj/kFX9gl1s7R0ZZ9QN0tLF/YJNbP0dGG/\ndL1upnmC/ISkTY3xpf2fdc2uiNgoSf1/d89yZSLiDPUK6KOllE/2f9ypdZww6mYI1A11Mwzqhrpp\ni5qRRN20thTqZponyHdJ2hoRWyLiTElvl3THFB9/se6QdFP/+5vUy8bMRESEpA9J+m4p5Q8bN3Vm\nHaeAummJupFE3bRG3UiiblqhZl5A3bSwZOpmykHst0h6UNL3Jf3LWYav++vzMUk7JD2jXmboPZLW\nqXf15EOS/oektTNcv59Q708M35F0d//rLV1aR+qGuunqF3VD3VA31Ax1Q90M+8VHTQMAAAANXKQH\nAAAANHCCDAAAADRwggwAAAA0cIIMAAAANHCCDAAAADRwggwAAAA0cIIMAAAANHCCDAAAADRwggwA\nAAA0cIIMAAAANHCCDAAAADRwggwAAAA0cIIMAAAANHCCDAAAADRwggwAAAA0cIIMAAAANHCCDAAA\nADRwggwAAAA0cIIMAAAANHCCDAAAADRwggwAAAA0cIIMAAAANHCCDAAAADRwggwAAAA0cIIMAAAA\nNHCCDAAAADRwggwAAAA0cIIMAAAANHCCDAAAADRwggwAAAA0cIIMAAAANMzdCXJEbIuINyzifiUi\nrhzyMYb+XXQTdYNhUDcYBnWDYVA34zV3J8hdFRH/KiKeiYijja+Xznq90H0R8YqI+GK/ZnZFxHtn\nvU7otoj4jM01P4iIe2a9Xui2iDgrIv60P8/sj4i/iohLZr1e6LaIWB0RH4mI3f2vfzXrdVoMTpC7\n5eOllPMaX4/MeoXQbRGxXtLfSPozSeskXSnpczNdKXReKeXNzblG0lck/ddZrxc6772SXiPpekkX\nSzog6T/NdI2wFPwHSedKulzSqyS9KyL+t5mu0SLM7QlyRLwqIr4aEQcjYkdE/HFEnGl3e0tEPBIR\neyPi30XEaY3f/5WI+G5EHIiIz0bE5ik/BcxAB+vmX0j6bCnlo6WUp0spR0op3x1xmRizDtZNc90u\nl/STkv58XMvEeHSwbraoN9/sKqWckPRxSdeOuEyMWQfr5q2S/qCUcryUsk3ShyT9yojLnLi5PUGW\n9Jyk35S0Xr3/Eb9e0q/ZfX5B0o2SXiHpberv0Ih4m6QPSPrHki6Q9CVJHzvVg0TELf0iPeWX3f2t\n/T9b3RcR/2wszxLj1rW6ebWk/RHxlf6frv4qIi4b15PF2HStbpreLelL/QMXuqVrdfMhSa+NiIsj\n4lxJ75T0mfE8VYxR1+pGksK+v26E5zcdpZS5+pK0TdIbTvHz90n6VGNcJL2pMf41SXf2v/+MpPc0\nbjtN0nFJmxu/e2XL9bpGvT9ZnS7pxyXtkPSOWW8vvjpfNw9KOijplZLOlvQfJf3trLcXX92uG1uX\nhyX98qy3FV/drxtJ50v6i/7vPivp25LWznp78dX5uvl/JH1S0kr1YoDfl/T0rLdX9jW37yBHxFUR\n8d8jYmdEHJb0e+r9b6vp8cb3j6p3AitJmyX9UeN/SfvV+x/R0BcrlFLuL6U8WUp5rpTyFUl/JOl/\nGXZ5mIyu1Y2kp9Sb+O4qvT95/mtJPx4R54+wTIxZB+vm+fX6CUkXSfpvoy4L49fBuvkTSWepd73D\nCvVOengHuWM6WDf/XL1j1UOSblfvHentIyxvKub2BFnSf5b0PUlbSymr1PuTQth9NjW+v0zSk/3v\nH5f0q6WU1Y2vc/ontpWI+EDUV4tXXwPWr5xifTB7Xaub76hXK88rQhd1rW6ed5OkT5ZSBs1FmJ2u\n1c0Nkm4rpewvpTyt3gV6r4rexcLojk7VTb9e3llKuaiUcq16557/c4zPdyLm+QR5paTDko5GxNWS\nTpX5/Z2IWBMRm9S7evfj/Z//qaT3R8S1khQR50fEPznVg5RSfq/UnSmqr+fvFxFv6z9WRMSr1Psf\n1+3je7oYk07VjaT/S9IvRMQNEXGGpP9d0pdLKYfG83QxJl2rG0XEOZJ+UdJtY3mGmISu1c1dkt7d\nX9YZ6v1p/slSyt7xPF2MSafqJiKuiIh1EXF6RLxZ0s2S/s34nu5kzPMJ8m9L+iVJRyT9F/1DcTTd\nLumbku6W9NfqXaCgUsqnJP2+pL/o//niXklvHnF93q5eFvCIeleT/34p5SMjLhPj16m6KaX8v+q9\nO/DXknarl+/6pVGWiYnoVN30/bx6+fUvjGFZmIyu1c1vSzqh3p/K90h6i3oXe6FbulY3Pyrpnv76\n/FtJ7yyl3DfiMicuSuEvsgAAAMDz5vkdZAAAAOBFOEEGAAAAGjhBBgAAABpGOkGOiDdFxAMR8XBE\n3DKulcLyRt1gGNQNhkHdYBjUDYa+SC8iTlfvU7zeqF7D57vU++S3+wf8DlcELmGllJH7Mi+Fuomo\nn+bpp59ejU877bSBY7//ihUrqrG/5nzsv//0009X4xMnTgz8/ZMnT1bj5557buDtkzYvdYPxmkXd\nLPWa8bnjjDPOGHi7zw3PPPNMNfa5Yglc1L+3lHLBqAuZt7rJ+DFx1iZQh6esm5eMsMBXSXq4lPKI\nJEXEX6j3ed4LHrDmzahFlf1+2+V3ZLKbet1k28lPcM8888xq7Ce4q1atGnj/88+vP8Tu1a9+dTX+\nwQ9+UI39oOS/v23btmp83311d5xnn322Gh87dqwaHz58uBr7CXdWFx05KDLfYBgzrZtxHwOy8Xnn\nVa2udemll1Zjn1sOHjxYjXfu3FmNjx6tPz/G55pxzxVjmGseHXUBfXM133gdZW/6ZHXYVrbf2x6j\nhjjXOWXdjBKxuET1RxVu1yk+ijAibo6Ib0TEN0Z4LCwf1A2GQd1gGGndUDM4BeoGI72DvCillFsl\n3Sot/z9DYHyoGwyDukFb1AyGQd0sf6OcID+h+rO8L+3/bNlo++etSY/b/tnD/8zgf1r3P5dNKZs6\n8brJtptHItavX1+NL7vssmp84YUXVmP/M+UFF9TRpde97nXV+Kd+6qeq8ZEjR6qxRy7WrVtXjbdv\n316NP/GJT1Rjj2AcOlR/yvTevfWnwD7++OPVeMeOHdX4qaeeqsZeF9POMPct+/kGEzHRusnmmnEf\nAzxTvHbt2mq8adOmauzr43Ern/tWrlxZjffs2VONDxw4UI2zuSL70/aofyqfYPxrWc83XlcveUl9\nKnjWWWcNHPv9/VykrWy/+tiz834u4+c6foz131/IKBGLuyRtjYgtEXGmeh+VfMcIy8N8oG4wDOoG\nw6BuMAzqBsO/g1xKeTYifkPSZyWdLunDS+GztTFb1A2GQd1gGNQNhkHdQBoxg1xK+bSkT49pXTAn\nqBsMg7rBMKgbDIO6wcQv0ltKsjxZlgGe9v39ds8FeX7Ls6/eDqyj7b1ay3J7nhm+4oorqvHmzZur\n8ZYtW6rx1q1bq/FVV11VjT3Xd/z48YG3+370XJ9npt/61rdW48cee6waP/jgg9X44YcfrsbnnHNO\nNfa68Yyyr89yqROgrVF7pGcZZb/dX5veYnLDhg0Df9+vP8jatnmbOL/ewtfX28RlWc9Rs6ZZj3cs\nTlbHZ599djX2uvDbvU7bGjWL7q1Svc597J8lsNB1NXzUNAAAANDACTIAAADQwAkyAAAA0DDXGeS2\nPSg9p+PZ0Kw3YJYZzn7f1yd7/Gz9PbezVPNd2fM899xzq7FnkK+++upq/MY3vrEae0bZe0L6dvLM\nbpZD9DxV1q/aXX755QPHN9xwQzX+2te+Vo09j5XlCjvykeVoyV8n7Ldc9trN5my/ve3yPOvpPdJ9\nbsvmdH+87LXs1294Jtnv79e1ZOuTjdses6jpxcn6IPt1KqtXr67Gnkn2Y2LWF7ntuUZ2fz9Get36\n/bNj2vN4BxkAAABo4AQZAAAAaOAEGQAAAGiY6wxyJsu2es7FM8F+e5Y5zvJo2eelZ4/nt3t/3mE/\nr3zW2maQL7300mr8ute9rhp732Nfvmd2Pffm2z3ruei/73kqz9357VnO0HODP/ZjP1aN9+/fX423\nb99ejQ8dOlSN2/Y2xXR4nWa3jzuTvFz2e3O7ZHNodgxoe12K//7KlSur8dq1awfe3+d0v9357Z49\nzWoqOyb63Jf1Nfa5ze/vc5vfvlSOWdPW9voqP2auWbOmGvt1PF6nXldtM8TZ/X3s1+34685vz/qB\nP493kAEAAIAGTpABAACABk6QAQAAgAYyyAN43snzVZ4B9txNlhEetU+yL997Zvrj+e3Z55U3czld\nyhdmeaqsl+hLX/rSarx+/fpq7PmmLEeY5eg82+05P68z76Oc5fCy/teeYfa6ufLKK6uxb4/du3dX\nY38+mI22uUKvG79/lg/N5oAsr5r9flfmmOZ28teKv3Y9q+lzjR8Tsoyyjz1z7P1ofZsfOHCgGmfX\nL/jz8+sV/Hbn9/ft4xlkXx+vOb/d55q2y8OptT1met1t2rSpGl944YXV2F8XPpdk+znLomfX6Xif\nZj+m+jFtIbyDDAAAADRwggwAAAA0cIIMAAAANJBBbvBcTpZB9pxOlkfLsqxZLih7fM9/+f09p5Nl\nTZt5r67kA08ly+R6HmnDhg3V2Ldjlh3P+gBndeSybeu/n2VJs7ryPJjny7wuPDeZPX6Xa2Upy+qq\n7TUKXidt855t97Pfv23GeRoiotouPqeuWrWqGvtrx+eabE5u23/WM7+excyOWb7N/fH9+Xh/W+dz\noW+fY8eODVxfr7msBn15R44cGXh/nFp2zPC69bq45JJLqrF/doDXTda3OPsMhiyT7HOTP7739l8s\n3kEGAAAAGjhBBgAAABo4QQYAAAAayCA3ZLkcz2J63szzYp4ny7KoWT7M82S+/Czf5rd7j00fN/Nd\nXcgHLiTLbvt+8hyfbxfPL/lz956K2fpkfPleJ1nG2fnve916nXnezOu4bQYZ45HNR17nPh/469nr\n3nm+0/uiZ3lSl9XFoBziLOeb5nb2bepZzHXr1lVj38YrVqyoxj7X+GurbQbZ56Ksz3E21/jyvYb8\n/p4F9efrNeRZUR97TXjNHTx4sBo/+eSTQi7rmZ59xoPXhV/Hs3nz5mrsWXSvu1H7Hme3ex1+5Stf\nGbg+C+EdZAAAAKCBE2QAAACggRNkAAAAoGGuM8ht+x57rsXzYd4/1nM4vnzPzXguJssQZ5ljH3tu\nx5//RRddVI137Nix4O/OUtt+sL7fPJPsy/Pbsx6OWday7e3+fDwz3DZP5s/Hc3+eg/S69dt9+3qe\nDMPJMseeC/T95L1JX/ayl1Vjz8/u3LmzGu/atasaex72+PHj1TjLIHuduP3791fjffv2vfD9rOab\niKjWO7vOJLuOw38/67Hu1wP48nyfeybX+wD7PvS5xOcaX98LLrigGvs+zeYSX17W99jHhw8frsbZ\nawKLkx0zs+y914XXqV/H4/vNZT3Ss77HPnbZZxkshHeQAQAAgAZOkAEAAIAGTpABAACAhrnKILfN\nHLfN4WzcuLEae17NH8/zYp7p8/XJMn1Zrsh5Ntczhg8++OAL33vudpba7kfP9XluzfNOWU9I7+2Z\n5aVc2wx1lvXM+h77fm5mPU+1Pl739EEejyw77jk9r1u/RuD666+vxq95zWuq8XXXXTdwfb7+9a9X\nY68zXx/Pk7qsn7bf/u1vf7saN/O0/pqaliyD7K8lzwRnfZHPPvvsapzNNb78rL9sls3Mrmfw9fN9\n6OvnxzB/Pn67Z4z9uOL397nQn6/PTehpO9f4fvUMsde1j/114fslu17K18/3c5ZB9rry112WgV4I\n7yADAAAADZwgAwAAAA3pCXJEfDgidkfEvY2frY2Iz0fEQ/1/1wxaBuYPdYNhUDcYBnWDYVA3GGQx\nGeTbJP2xpD9v/OwWSXeWUj4YEbf0x787/tUbLMvZZFlPz8l47sYzxp4B9LHncjy/luWlsn62WX9c\nv91zRZ7n8h6TnkFs5t0OHTq00Gov5DZNqG6y/ep5I8/V+XbwfFPWj7pt1jvLf2X3zzK/bW9vm0Oc\ncgb5NnV0vmmr7fzj1zhcddVV1fjHf/zHB44vv/zyauy5QK/rp556qhr7a/yxxx6rxp7z8zq58MIL\nq/GWLVuqsfdp9vX53ve+pxHcpjHUTURUr08/JniO2rOO3g/W96nn+7PrTDxz7L+fXe/gWc3s/r5P\ns/X361b8mJP1OfYa9OU5//1hs6UNt2mZzDeDtO2V7+cyGzZsqMZeFz6XZZ/JkGWQM17H2dzqdbvY\nx0vfQS6lfFHSfvvx2yR9pP/9RyT9/KIeDXODusEwqBsMg7rBMKgbDDJsF4sNpZTnP2Ztp6QNC90x\nIm6WdPOQj4PlhbrBMKgbDGNRddOsGX8nCnOpdd1geRp5Nii9v5OVAbffWkq5sZRy46iPheWDusEw\nqBsMY1DdNGuGE2Q0LbZuprxamJJh30HeFREbSyk7ImKjpN3jXKmFtO1/63koz4957sZzNp6Z80xy\n288bz7KxPvYckD+/rFdolnn2zKH3pGyuz5hypp2oG+c5Pc9iZwfNUTPBzrOZbZef9YzMPvfel9/2\n+TfH/lhDmknduKyO/HZ//Xle1TPDr3jFK6rxK1/5yoH3z655yHru3nDDDdXY50vPBPt84fPpxRdf\nXI0vvfTSgeNm32NJ+uQnP/nC9541HVLruomIajt5jtvHfgzwbKZnkrN+sT72bZxdP5H1UM/mlrYZ\naF9fr7msX61njn15vv6eWZ7Qf2g6Md+MIjtm+H5av359NfbXqn/Gg9dxdsxoe/7gdZods7L+2F7H\ni82uD1tdd0i6qf/9TZJuH3I5mC/UDYZB3WAY1A2GQd1A0uLavH1M0lcl/VBEbI+I90j6oKQ3RsRD\nkt7QHwMvoG4wDOoGw6BuMAzqBoOkEYtSyjsWuOn1Y14XLCPUDYZB3WAY1A2GQd1gkGEzyGPRNtPn\nuRHPQ/nnxnvmL/t8cf99v3+W6fU8mOensrHngjw347f743kuxzOHnt/yvJnnipYrz1r7+OjRo9XY\nt0v2ufEuuz3r350tL8sge87P6+DEiRMDl59l3ZeKtts5u3/WR90zw575vf7666uxZ3j99e9jr0uf\nH3x+9Iyxz49+DYavr/dNd778rBepP//m8/ManRbPIHsG2Me+z32b+jEly4n7nOxz+KnWd9D6ZT3e\nswyyL8/X1/e516Qf43yu8eV5dtXv77l1LqrsyTLHvp/83Gfz5s3V+KUvfWk19uuvsrocNZM86lzt\n69d2/Z9HdQEAAAANnCADAAAADZwgAwAAAA1TzyA3syLZ53F7bsXzUJ6T8V59nnlr24PS18ezmFkv\nviw348/Pt0fWA9Mf338/y9Z6vqttn+VpGqUPs28Xz8X5djp27FirdfH96Nstu3/bjLLz5fnzO3Lk\nSDX2XqTeqzTLJY6pJ/bU+fPw17vf7rk9z496r9CXvexl1fjqq68eeH+fn3zs+VbPIPv6Z/NpxvOg\nF110UTW+8MILq7HXeXaNha+fb49mL9Z9+/YtYo0no1kH2TbOasT3YZYb9xrMMra+Pr5PsutUsmOQ\nHxOy7GbWg91/32t0UC9+KT8Gzou2nwnh/bmvuOKKanzttddWY88kT7rvscv6IGf8+ftnWnhdeY/3\n5/EOMgAAANDACTIAAADQwAkyAAAA0DDVDHLWYzLre+yZuFe+8pXV2DN8nlfKPsc+y2u5LJPsy/Pn\n55lC79Xn+bWsP61n/jz/5b/vOR3fH12V9UjMcnTZfvNstt/uvU7brl/b+2d9l/32LGOc1alvvyyD\n3NVMckRUGVLP3fnrzeePZiZWenEG1zO0fru/fn35nlfN8qltM8a+n7P5wOvAZddk+PKyrL3nIpvb\n+/vf//7AdZmUiKjqPctWZscYn3s809x2H2fbOMsAt+2DnI2dr3+WofbMcfb7XZ1rMm2PAdnt2THO\nj1E+93mP8x/6oR+qxt6/O9vv494v2dzisteF95hf7LkO7yADAAAADZwgAwAAAA2cIAMAAAANU80g\nn3766VXu1jPFznMvW7ZsqcbXXHNNq8f3/JfnszwP5be37SnpPTI9F7Rhw4Zq7JnGtWvXVmPPGB84\ncKAaP/XUU9XYczlZ3s37JDdzOl36zPssj5Tls7Iei9l+9+ykGzWjO2oG2W/3vs7Z9vN97a+bLtXC\nIGeccUbV//Itb3lLdbu/vvz14ZngrK961sfY7+/zg4+9brNep9l+yrLlbfOe2TURWR7Wn29ze/m6\nTlPzefs28vXKxlkmuW3G12X9aH19fJ9k9/fb266f82NYtv5t168rRr2OI3ve/lr36xkuu+yyavzy\nl7+8Gl933XXV2K+f8Lkw2y+Zthni7Powl21PP9fyuXoh3awuAAAAYEY4QQYAAAAaOEEGAAAAGqae\nQW7mN703n+eTPAdz1VVXVWP/vPC2+TDPHHtW02/39csyyJ5B3Lhx48Cx92X1Xn379++vxp7L8e3l\nORvPLfny9+zZs+Dts856Dcowtf1cet9uWQbZZVnNbFtl/WFH7Znpy8t6jWb9vn37LZVepGeeeWaV\n6/f5wjOw/vrxsb9ePPfnrzcf++O17Zmb7Ye2+Uyfz7Icn79usr7r3o/br5Hw59P8/SyzOEnNx862\ncdue7Nk4y3pm2yXrVZ3NXdn6ZM8/e7xJZ1lnqflcsp7nbfe7z0W+PD932Lp1azW+/vrrq7H3Bc4+\nQ6Lt3JIdU7K6yTLIbevAP3PC59aF8A4yAAAA0MAJMgAAANDACTIAAADQMNUM8mmnnVZlXbwPsudQ\nPGfjfYK9r7BnBD3z57kXz8h5Btlvz3IxnhPyfrnr16+vxr7+nuHbu3dvNT548KAG8cfz7eeZP88d\n+fNvPp8u5U5Hzf1lPRV9P7Tta5z1Jc5yhdn92+a7vI69TrPtkfXw7KpSSpW/9vp2Wc9X306+XZ1n\ndP31l/XEzXJ+WSbY68Tr2sd+/+z3/fF8nGWQPQfYnN+ympyk5mNn1xe0zQS3zQCPOtdk2c1s/bL1\nzdYvy6623b5Z7+1ZiYjq9evXF/mxP+tx7q8Nn7M9U+t9jP36Lj938nOD7HqHtpnprC6zzHHb672y\nOlxs5tjxDjIAAADQwAkyAAAA0MAJMgAAANAw1QzyyZMndfz48RfGze+lF+dsPDfiOZMTJ05U46x3\nn+dYsj7HWZ9PX54/nq/fvn37qrFnjHfu3FmNve+xP97atWurseeevA+zb1/PaG/btq0adyUTKLXL\nvWa5viyH59nJLL/k+6VtX2Q3ah9kv93r1uvA+fbJMshdzSQ/88wz1Wvq3nvvrW733qH+evGcXnaN\ng9eJ113bLHd2zYOPs4xwlgNs21s0y7v64/t8u2LFigWXN6t+t6WU6nn4c2qbfcyymtkxq+3ys7kt\nu71tJnncshx8lvufFb++yj+zwY/N2Xb1OvC5xzPIPpdt2rSpGvu5gl9/5MeE7PqIrE6z7Hh2PYSP\n/fF8rs0ez8c+Ny2Ed5ABAACABk6QAQAAgAZOkAEAAICGqWeQm71Id+zYUd0+KJMmvTg34/f3Pqee\nEfQ8k2eEvU9n1ovPeU7n0KFDA5fnmeQnn3yyGmcZbe996I/nmUrPMfnyvvOd71Tj3bt3L7jus9Q2\nN+c8V5hldrN+2tn6Zbe37aWa5auyvs9te4dmeblJ5xKH9dxzz1Wvibvvvru63fuG+zjL8GeZ/qyX\naKbtfnej5nizOm7b29Tzo7785nw4q2sePIOcXXfi2vb5zbKnbfP94+653vbxR13ftr27Z5VVd6ef\nfnqVC966dWt1e5ZBzq6b8bnG5ybPGK9bt64a+/UU2fVebeeu7HqErCe6n4v58vzcJTvGZT3ZF1s3\n3TyyAQAAADOSniBHxKaI+EJE3B8R90XEe/s/XxsRn4+Ih/r/rpn86mKpoG4wDOoGbVEzGAZ1g8xi\n3kF+VtJvlVKukfRqSb8eEddIukXSnaWUrZLu7I+B51E3GAZ1g7aoGQyDusFAaQa5lLJD0o7+90ci\n4ruSLpH0Nkn/qH+3j0j6/yT9brKsKhty9OjR6vYsX5RlHbPMrfMcjI+z/FnWI9MdOHCgGm/fvr0a\nZ32PPUe0YcOGgb9//vnnV+Osj+s999xTjQ8fPvzC920zgeOsm1Msu9W6OH8uWY/GLH81ah/gUXN+\nbTPIWZ48y1lOMvc3zro5efJklW1rZuqlus+39OLXQ5Yx9teT5/hG7XHrsh6x2f0zWba/bebZ685z\nhp4L3LVr1wvf+2swedyxzjXN14evs29Tfy1lef+sl7XXSNsM8ajjUbXt3e3bL7suyK8zGuXamHHW\nTURU88WaNfWbzj7OMsA+9rknux4ru37CM8ZZnWXXY/nr1febn/v4uZ/PNb6+WUbb68p7rvvjLfZ6\nkFYZ5Ii4XNLLJX1d0oZ+gUnSTkkbFvo9zDfqBsOgbtAWNYNhUDc4lUV3sYiI8yR9QtL7SimHm2f0\npZQSEaf8r2hE3CzpZqm7V7tjcsZRN5g/1A3aGkfNtO00gqVvHHXjfy3C8rCoM9aIOEO9AvpoKeWT\n/R/vioiN/ds3Stp9qt8tpdxaSrmxlHIjJ8jzZVx1M521RVeMq266+hHYGD+OURjGuOqG/1gtT+l/\ne6J3lPmQpO+WUv6wcdMdkm6S9MH+v7cv5gGb2ZYsz+V5pGYmVnpxLsczbdn/6rzPcNYHOcvh+uTq\neamdO3cOHPvjew7Iczl+f3/+/nnt2eevex/m5vLaZtXGXTeDZNnMtrlAzy/55Jfl+CZ9Yta2b7I/\nX39+bfNmk8wxjrNuSilVNs5zaD4/ZJnhbJz1uG3bV3jSfZDHXbfZ+mWv0+Z81iY/Pe6aada/z7F+\nzPA5Pht7jfk299deduKVvTbb5tZd25rM5lLffn7djI/9swL8dj/mtTHJY1RWN1mfYc8gZ9dD+P19\nP/l+ya6v8nMv349e10eOHKnGe/bsqcZ+buH8Mx28J32WOfaxb++9e/dW48W+Dhbzd4HXSnqXpHsi\n4u7+zz6gXvH8ZUS8R9Kjkn5xUY+IeUHdYBjUDdqiZjAM6gYDLaaLxZclLfTWwuvHuzpYLqgbDIO6\nQVvUDIZB3SBD4AoAAABomOqll57vyvJDnnvxnIvnubL8ludyfPlZpjfjj+/5Ke/D6nkq/31fX88F\necbRt4c/H++j7DkoX99mrqcrn3l/KlmG1vNWWbbc97tv5yzT7Npe+DNqL9Mst+h1kfUmzZ5vl2uj\nue7+es/2czbO5pds3Na4M8jjNmrdjnLNw7h4bt3nRO8363OqZyd9jvU5PJuTs9dy2+sr/LU97hy7\nL99fY55d9azqE088MXDsWVJ/Tc9KKaV6rjt27KhuH5S3l/LPLPDrh/z2rK+y11WWJff95ude3kPe\nr6fyzLHvN6/7zZs3V+MLLrigGvv1I749vO48g+zr49t/IbyDDAAAADRwggwAAAA0cIIMAAAANEw9\ng9zM4mQZQM+Oen7r0KFD1dhzKFnPyaw/rK9fljX1nIznbvzzyP35+PKz9fVckPdGzLK4nlPy9W/b\nM3Na2mYbs56Pvp+zPsG+PM/5jdoPNuvxmOX+XJZ/y5aX5Ra7nEFuyuo5uz3LEHftg0lmnUFue/8u\n1NHJkyer179nkLPsp2cjnWdw/f5ZBrntXNJ23Lb3dts+yFkG2bOift2O74+uZJBPnjxZPbdHH320\nut3X0z/TwT+zwOvMx1kf5Kyne1ZH2bnWrl27qrFnrj2T7Pt93bp1rW5fv359Nfbt4XXnxzhfP3+8\nhfAOMgAAANDACTIAAADQwAkyAAAA0DDVDLJU5xk985plL7Oejp4l9RyOZ5zbZi+zzzP33oCeOfbn\nm2VHXZYTyrbnKBnkLuQDn9c2B5dlhn07ej7Jfz/LqnveK+ufO2of4mzs6+v72esgex10NZueadvT\nNctjLnfz9nyf16x3z4r6dSWeIc76Gvtc432V2/ZBHjVz3HYfZ699nyvaZpCzzLEfY31unpWTJ09W\nvXe9f7NnYleuXFmNvW48256Ns7rJMshZH2Gve99vfrtfH+XHMF++bx9fvmeS/flnx3SvK3/8hfAO\nMgAAANDACTIAAADQwAkyAAAA0DD1PsjNzFCWyfX8kudKPHeT9QL0LOip1q8py4b6+nhezXsHelZ1\n1PyXZyT9+fn6ee7Gt4/nw7qUQRy0Llmeyre7j/15e+7Ns+Tnn39+Nfb8VLZfsoxxNs7qwO3fv78a\n+/P15+PbJ+sj3aU6Gafl+rywMO/V769tn0N9jvcsps+x/lry5fsxrO0xq22f5LZ9jrPXRHYM92N+\nljn2udezrW2v45mUkydPVsfbLPPq2fOsz7Gf62TjLLvufDt6Xfq5TbZfvM69brwufPt4JtvrIrtu\nxh/fX6eL7Z/NO8gAAABAAyfIAAAAQAMnyAAAAEDD1DPIg/ogZxljH3u+Kxt7nivLd3leK8sg+/Px\nnMu4M42eFXX++J4r8pyS397VDGaWs/PMrmduPZPr9/celp4H8/GqVauqcZb/GjXnl+W5HnvssWr8\n4IMPVuMsF+l5s7Z9mbtaN8BiNOvZ53jPWno/1myu8Neev3Z8eVn/2mzuG/V6B9e257wfUzwLumvX\nrmrs/W+973E2N81Sc1v4enrG1jO0vt/99uz6Kh973WQ93dt+NkD2WQFt+2VndePbr+1nWvjvL7Z/\nNu8gAwAAAA2cIAMAAAANnCADAAAADTHNvGBEtHowz81kY8+lZJ9Hni2vbd7Kbx/3ts2eb5apzm7P\n8mqllMENdyckqxvfLp77889xX7NmzcDH89yb579Wr15djS+88MKBj+cZZe/x6LLsuK+f99z0HJ/n\nJrPn41l6X57nCBeRW+xk3aDbZlE3XjM+t3jW07Oj3t/We4z72O/vy/Prbpwfg9qOs2NW2yyp39+v\nk/G5zOcav92Xnz2epG+WUm4ctM6TMOpcM+5zm3FfbzXuXvhtz2X8ddf2XG0RWftT1g3vIAMAAAAN\nnCADAAAADZwgAwAAAA3TziDvkfSopPWS9iZ3n6Uur9+s1m1zKeWCGTzuUqmbLq+bNL91c0zsl1HM\nVd0skblGYv0WQt0Mxvqd2inrZqonyC88aMQ3ZhGkX6wur1+X123Suvzcu7xuUvfXb1K6/rxZv27q\n+vNm/bqp68+b9WuHiAUAAADQwAkyAAAA0DCrE+RbZ/S4i9Xl9evyuk1al597l9dN6v76TUrXnzfr\n101df96sXzd1/Xmzfi3MJIMMAAAAdBURCwAAAKBhqifIEfGmiHggIh6OiFum+dgLrM+HI2J3RNzb\n+NnaiPh8RDzU/3fw5xJPdv02RcQXIuL+iLgvIt7btXWcBuqm9fpRN6Juhlg/6kbUTct1o2b6qJtW\n67Yk6mZqJ8gRcbqkP5H0ZknXSHpHRFwzrcdfwG2S3mQ/u0XSnaWUrZLu7I9n5VlJv1VKuUbSqyX9\nen+bdWkdJ4q6GQp1Q90Mg7qhbtqa+5qRqJshLI26KaVM5UvSayR9tjF+v6T3T+vxB6zX5ZLubYwf\nkLSx//1GSQ/Meh0b63a7pDd2eR2pm+7tE+qGuqFuqBtqhrrp6n7pat1MM2JxiaTHG+Pt/Z91zYZS\nyo7+9zslbZjlyjwvIi6X9HJJX1dH13FCqJsRUDcvoG5aoG5eQN0s0hzXjETdDK3LdcNFegOU3n9j\nZt7mIyLOk/QJSe8rpRxu3taVdcQ/6Mo+oW6Wlq7sE+pmaenCPqFmlp4u7Jeu1800T5CfkLSpMb60\n/7Ou2RURGyWp/+/uWa5MRJyhXgF9tJTyyf6PO7WOE0bdDIG6oW6GQd1QN21RM5Kom9aWQt1M8wT5\nLklbI2JLRJwp6e2S7pji4y/WHZJu6n9/k3rZmJmIiJD0IUnfLaX8YeOmzqzjFFA3LVE3kqib1qgb\nSdRNK9TMC6ibFpZM3Uw5iP0WSQ9K+r6kfznL8HV/fT4maYekZ9TLDL1H0jr1rp58SNL/kLR2huv3\nE+r9ieE7ku7uf72lS+tI3VA3Xf2ibqgb6oaaoW6om2G/+CQ9AAAAoIGL9AAAAIAGTpABAACABk6Q\nAQAAgAZOkAEAAIAGTpABAACABk6QAQAAgAZOkAEAAIAGTpABAACAhv8fUEWS41UOBnoAAAAASUVO\nRK5CYII=\n"
}
}
],
"source": [
"# 평균이미지"
],
"id": "6b8bd159-0a8a-41f5-94b1-17cf902215d1"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"작업결과 아래와 같이 비슷한 카테고리를 생각하였다고 하자."
],
"id": "a47b2cb1-b599-48ab-bc8c-c4f2848bda1a"
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [],
"source": [
"mapping_rule = {0:[0,2,3,4,6], 1:[1], 2:[5,7,9], 3:[8]}\n",
"mapping_rule"
],
"id": "29ac2ed1-2c30-4365-a7d3-c7086cc8bfb6"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"즉 기존의 0,2,3,4,6번에 해당하는 이미지는 모두 비슷하다고 판단하였다.\n",
"위에 제시된 mapping_rule에 의거하여 아래와 같이 라벨의 수정하는 변환을\n",
"수행하라.\n",
"\n",
"| Before | After |\n",
"|:------:|:-----:|\n",
"| 0 | 0 |\n",
"| 1 | 1 |\n",
"| 2 | 0 |\n",
"| 3 | 0 |\n",
"| 4 | 0 |\n",
"| 5 | 2 |\n",
"| 6 | 0 |\n",
"| 7 | 2 |\n",
"| 8 | 3 |\n",
"| 9 | 2 |\n",
"\n",
"수정된 라벨에 대하여 평균이미지를 다시 계산하여 `imgmean2`에 저장하고\n",
"아래의 코드를 이용하여 시각화하라.\n",
"\n",
"``` python\n",
"fig, ax = plt.subplots(1,4,figsize=(10,5))\n",
"for i in range(4):\n",
" ax[i].imshow(imgmean2[i],cmap='gray')\n",
"```\n",
"\n",
"`(풀이1)`"
],
"id": "b9ec6f40-e9f3-4042-9d66-51fc8a342ba5"
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [],
"source": [
"ytrain2 = np.array([m for y in ytrain for m in mapping_rule if y in mapping_rule[m]])"
],
"id": "18021832-e98b-469a-a2b2-fe8159587668"
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [],
"source": [
"imgmean2 = [xtrain[ytrain2==i].mean(axis=0) for i in range(4)] "
],
"id": "72d0695c-476e-4a3e-9249-59ccac18901a"
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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ZqxeGz+0F6ByvhwlaLqqj8Try7jGuZ+6rvcVsuT64Tr3zsP+ujY7aLHYfCYrZ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\nTkSuQmCC\n"
}
}
],
"source": [
"fig, ax = plt.subplots(1,4,figsize=(10,5))\n",
"for i in range(4):\n",
" ax[i].imshow(imgmean2[i],cmap='gray')"
],
"id": "4c826279-fd5c-4ea4-9a11-2faeb5fc33d0"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(풀이2)`"
],
"id": "6ec1a723-eb1c-4b09-8d64-e044117b0130"
},
{
"cell_type": "code",
"execution_count": 347,
"metadata": {},
"outputs": [],
"source": [
"inv = {v:k for k in mapping_rule for v in mapping_rule[k]}\n",
"inv"
],
"id": "26076d39-58de-477c-b648-22dd7fdea34b"
},
{
"cell_type": "code",
"execution_count": 355,
"metadata": {},
"outputs": [],
"source": [
"ytrain2 = np.array([inv[y] for y in ytrain])"
],
"id": "bfa8b65e-831f-460f-920e-91a37aa709fe"
},
{
"cell_type": "code",
"execution_count": 356,
"metadata": {},
"outputs": [],
"source": [
"imgmean2 = [xtrain[ytrain2==i].mean(axis=0) for i in range(4)] "
],
"id": "a4755305-905e-4536-b45c-c9cc0612deb1"
},
{
"cell_type": "code",
"execution_count": 357,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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ZqxeGz+0F6ByvhwlaLqqj8Try7jGuZ+6rvcVsuT64Tr3zsP+ujY7aLHYfCYrZ\n5jkS8UDxfct+J6D+bOdnZ87/OKmsWdWmlBYALIx+XzSzJwFszeUTYhzpSHRFGhIlkI5EKRp5oMzs\nOgC3APj1aNMXzex3ZnaPmV2xRJ7dZrbPzPZ1K6pYLkhHoivSkCiBdCS6EB5AmdkaAD8G8OWU0hkA\n3wNwA4CbcWE0/y0vX0ppT0ppV0ppV/fiiqEjHYmuSEOiBNKR6EooDpSZXYwLQvthSuknAJBSOjr2\n9+8D+I8SBcp5hjzfDvtB2A/gzXHyAoPr1q2r7bNhw4ZKmhcG9eaY2yyimLvGSPl5ntfzRHDZPD/Z\nFD1QM9VRDu86uH5yaW+bpwluX87DugLqsWLYb+MtvsrbuC29uDBt/DfzpKSGxuvH85RwvxLxM+U8\nUJE2iOgs4q3Mebg8H53Xb+TIeTgj/qxIzCK+5i5xzUrqaPycnl+V+2/2onr3P29jHXnXycdts5iw\n11b8PIq0b05HXv/LeSK+L/aTHT16tLYPx4biuE9e7K6oByryFZ4BuBvAkymlb49t3zK222cAHMgd\nS6xcpCPRFWlIlEA6EqWIvIH6EIDbAew3s8dG274O4DYzuxlAAvAHAF+YQvnE8kE6El2RhkQJpCNR\nhMhXeA8D8NYW+Hn54ojlinQkuiINiRJIR6IU/TY8CCGEEEL0kN4tJsyGNTZ8PfXUU7U8HBSTj8FG\nMwD47W9/W0mzYRwANm7cWEmz0fyyyy6r5fGC640TMVRycDBv0UwOvsbX6Blc169fP/E8ALCwsFBJ\n5wLrDZWImT9ioOdthw4dqu3zy1/+spJmc6dnYvzVr35VSbMRko8JAJs3b66k2Zz88MMP1/Jwe3Nw\nQu+jjTb10nciAW75Po0s+hsxiEeM/G0+TsmZfafVRpEFar0PWHJEjPPz0N34OT0TOffVkeCPzz33\nXCV9+eWXV9LeYsK5wM8e3A5eu+T28Z5pkbZiuK/hPN5HD2ws955pvA+fx+vjos85vYESQgghhGiI\nBlBCCCGEEA3RAEoIIYQQoiE2yzljM3sRwHMANgKor6DYT4ZUVmD+5b02pXTVNE8gHU2dPpR1qjoa\nqIaAYZV33mVVX+SjsjZjSR3NdAD15knN9g0lDP6QygoMr7xdGNK1qqz9ZGjXOqTyDqmsXRnStaqs\n5dAUnhBCCCFEQzSAEkIIIYRoyLwGUHvmdN42DKmswPDK24UhXavK2k+Gdq1DKu+QytqVIV2rylqI\nuXighBBCCCGGjKbwhBBCCCEaMvMBlJl93MyeMrPfm9mdsz7/JMzsHjM7ZmYHxrZtMLMHzOyZ0b9X\nzLOMb2Bm283sF2b2hJk9bmZfGm3vZXlL0mcNAdLRUOizjqShYdBnDQHS0bSZ6QDKzFYB+FcAfw/g\nJgC3mdlNsyxDhr0APk7b7gTwYErpHQAeHKX7wHkAX0kp3QTgrwD806gu+1reIgxAQ4B01HsGoKO9\nkIZ6zQA0BEhH0yWlNLMfAH8N4L/G0l8D8LVZliFQxusAHBhLPwVgy+j3LQCemncZlyj3zwB8bCjl\n7XCdvdfQqFzSUY9/hqAjaajfP0PQ0Khc0tGUfmY9hbcVwPhy9c+PtvWZTSmlN5asfwHApnkWxsPM\nrgNwC4BfYwDl7cgQNQQMoF2ko97rqPdtIg31XkPAANplKDqSibwB6cIQuFefLZrZGgA/BvDllNKZ\n8b/1sbyin+0iHQ2LPraJNDQ8+tguQ9LRrAdQhwFsH0tvG23rM0fNbAsAjP49NufyvImZXYwLQvth\nSukno829LW8hhqghoMftIh0BGIaOetsm0hCAYWgI6HG7DE1Hsx5A/QbAO8xsh5ldAuCzAO6fcRma\ncj+AO0a/34EL87Jzx8wMwN0AnkwpfXvsT70sb0GGqCGgp+0iHQ1KR71sE2loUBoCetoug9TRHIxh\ntwJ4GsCzAP553iYwKtuPACwAeBUX5rM/D+BKXHD+PwPgfwBsmHc5R2X9MC68yvwdgMdGP7f2tbwr\nRUPS0XB++qwjaWgYP33WkHQ0/R9FIhdCCCGEaIhM5EIIIYQQDdEASgghhBCiIRpACSGEEEI0RAMo\nIYQQQoiGaAAlhBBCCNEQDaCEEEIIIRqiAZQQQgghREM0gBJCCCGEaMj/A24chSCfJFy5AAAAAElF\nTkSuQmCC\n"
}
}
],
"source": [
"fig, ax = plt.subplots(1,4,figsize=(10,5))\n",
"for i in range(4):\n",
" ax[i].imshow(imgmean2[i],cmap='gray')"
],
"id": "35404b19-69e6-4319-b0b3-26b24cf5ccb2"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(3)` 수정된 라벨에 대하여 xtrain의 이미지를 분류하고 분류결과를\n",
"카테고리별로 제시하라.\n",
"\n",
"`(풀이1)`"
],
"id": "041cfe23-2b69-4859-a1dd-0bca55cacc87"
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"training_loss2 = np.array([[np.mean((xtrain[j,:,:]- imgmean2[i])**2) for i in range(4)] for j in range(60000)])\n",
"ytrain2_hat = training_loss2.argmin(axis=1)\n",
"{i:ytrain2_hat[ytrain2==i].tolist().count(i)/sum(ytrain2==i) for i in range(4)}"
],
"id": "6a12009e-2dc4-43c6-92fd-5aa038c73e31"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(풀이2)`"
],
"id": "7cf40517-0893-405c-9d98-8391b54a087b"
},
{
"cell_type": "code",
"execution_count": 365,
"metadata": {},
"outputs": [],
"source": [
"training_loss2 = np.array([[np.mean((xtrain[j,:,:]- imgmean2[i])**2) for i in range(4)] for j in range(60000)])\n",
"ytrain2_hat = training_loss2.argmin(axis=1)"
],
"id": "450b991e-5988-4a84-874e-a60ec2b2f7bd"
},
{
"cell_type": "code",
"execution_count": 371,
"metadata": {},
"outputs": [],
"source": [
"[np.mean(ytrain2_hat[ytrain2==i]==i) for i in range(4)]"
],
"id": "53d5ed20-76d3-4784-ae68-6b7944418b86"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 6. 동물명: 최하니 (20점)\n",
"\n",
"아래는 동물명 “최하니”의 이미지이다."
],
"id": "76c92602-54e2-4d40-af76-f15f26c14649"
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [],
"source": [
"url = 'https://raw.githubusercontent.com/guebin/SC2022/main/hani.jpeg'\n",
"hani = np.einsum('ijk->jik',np.array(PIL.Image.open(io.BytesIO(requests.get(url).content))),dtype=np.int64)/255"
],
"id": "2ce1c331-b321-44d4-8cef-460075a66edf"
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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S6kApdTeE8OFHnq0XENiZlrERvnP4ECgwWSblLIBzI4h7dKa2adlWFWWecevO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SRWOzKjuijyKZ+mwvgICEi4aob/dh2z2SznZRkZQ67dlFVuYZFBFciYXmSOttxnVKLSu+rMSivJ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\nH6+P1zdxfWxwH6+P1zdx/f8BcjoCBTxXkpIAAAAASUVORK5CYII=\n"
}
}
],
"source": [
"plt.imshow(hani)"
],
"id": "65f67dba-736f-41fa-a90f-503269d9e6ef"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"아래는 하니를 적당히 분리하여 아래와 같이 `hani_left`와 `hini_right`를\n",
"만들고 시각화한 것이다."
],
"id": "31dfb341-b519-43b8-aebc-960a63a69fc3"
},
{
"cell_type": "code",
"execution_count": 330,
"metadata": {},
"outputs": [],
"source": [
"hani_left = hani[:,:1512,:].copy()\n",
"hani_right = hani[:,1512:,:].copy()"
],
"id": "d7ad3036-32d5-40ee-8d7e-921454d985d5"
},
{
"cell_type": "code",
"execution_count": 331,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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S2K6jrhZkWlMUGd47trZn4KGNSq1eLcmLkrIo6Eyw5hACrTPyLENIiTEGax2j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1uISp1Bg1EFfd/mPpYOEqhUlNkOkCEVoHJDNi0p38TZyScvAmMQQxaD7W0MrMOb7b2L0s0iB6O9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\nRU5ErkJggg==\n"
}
}
],
"source": [
"fig, ax = plt.subplots(1,2)\n",
"ax[0].imshow(hani_left)\n",
"ax[1].imshow(hani_right)"
],
"id": "e5975ba9-f3a7-42d5-983f-02008361430f"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(1)` `hani_right[:,:,2]`의 모든 원소에 아래와 같은 변환을 수행하라.\n",
"\n",
"- $f(x)=\\begin{cases} x & 1.15x >1.0 \\\\ 1.15x & 1.15x \\leq 1.0 \\end{cases}$\n",
"\n",
"`(풀이1)`"
],
"id": "54354ad1-4a4e-4c9a-a037-eca846249717"
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [],
"source": [
"_a = hani_right[:,:,2] * (hani_right[:,:,2]*1.15 > 1.0)\n",
"_b = hani_right[:,:,2]*1.15 * (hani_right[:,:,2]*1.15 < 1.0)\n",
"hani_right[:,:,2] = _a + _b"
],
"id": "2127b208-4c04-4c3e-bee5-6356ccab6d43"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(풀이2)`"
],
"id": "3101ff43-b569-49ed-93cd-7d7a78acaa12"
},
{
"cell_type": "code",
"execution_count": 336,
"metadata": {},
"outputs": [],
"source": [
"def f(x): \n",
" if 1.15*x > 1.0:\n",
" return x \n",
" else: \n",
" return 1.15*x "
],
"id": "74094a52-21f4-4114-8529-3416cee66f59"
},
{
"cell_type": "code",
"execution_count": 333,
"metadata": {},
"outputs": [],
"source": [
"for i in range(4023):\n",
" for j in range(1512):\n",
" hani_right[i,j,2] = f(hani_right[i,j,2])"
],
"id": "8409bdf8-f131-4b50-b878-7580d553de08"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(2)` `hani_left`와 `(1)`에서 변환된 `hani_right`를 `np.concatenate`을\n",
"이용하여 합치고 결과를 시각화하라.\n",
"\n",
"`(풀이)`"
],
"id": "8593ea8f-550e-4ff6-a1c2-2d776082629f"
},
{
"cell_type": "code",
"execution_count": 334,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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Od77zDllWYvKSo+NDbl6/Rdd3eGs5WFTocEzwsJjPmFUzyiLDGI3re5p6Q55l\nlGVOCJ6DwxUE6KKwNbstRVlRlSW9Fe2HUmRZTpHnKK2x1uKcZzarcNZSVRVN00iCcJCwh1aBerfB\nWikufe7Fl8hMwWp5JFkYeC6379CqD7n72Ru8+vLP80e+8gs8utjy8muvo1F8441v40PADISo+4je\n6KtNM0US8pgWsRo01Dj2NcgYXxuLWvcn8QpYkszS9GgP9NAEFct9QiDLcvp+6sOFGBXIUCoRCI3C\nZHS2d77xOsbrGUGU72/8nTApfxH4Svz7LwK/ggjcLwJ/Kcgs/apS6kgpdSeE8MF3PdsgILA3CQka\ne+xwNRxnskzKWQDnJhD35Exd27Gra8o84+btVzg+vs3RyQ3yPOPo+k0++/qX+PD+u/za3/zb2L5h\nvVlz78P3qaqSw8MDtFLMq5JMK8pCiFPLqkKrQNc2GKOxmxZFoO9qjMnw9pA8z1lfroXly1psNDMx\nGV3b0tQ7irLA6IzFYjF8v+12Q9t0GK04XB1greXy8hLvA7bv6dqWXV2jgCyDzGRsd5c03ZZq6emy\nh1x7fs5LN3+Cf/AX/ikenW34+b/3DxO04hu/+53I4zlucsOiNBnWdo9pt1HwkqA9eYP8SJPsMXtt\ntFBC2NcwOiH0j5074Nx8eLfJwHs7bBQpRKAjf4vzo/CHEEMjKeitUu6uiv8CcA5h9RFf4JON71fg\nAvCfKRH//1sQ1uRbEyG6B9yKfz+J5vw5YE/g1ITq/PDwkLEu6jFPeTRfVAJRpgtlSiIqj7VWsRZt\n1HI6y0FrfvV/+BXuPTrl1dd+nE3boXtLOasoV0dcfOt3mc8KvvRTP83F2UP+1m/+Leq65tbNG8xn\nM5TSLOYzyiIX0CMzQmHQbsnzgr7v2K7PMVpTliWXZ0uKqsLkJQqNtS1d23H91l207tmsL3C2xzrL\n0cl1bC+COlushI2rKoS6Oy9QCrquhrBifXmG9562adisL3jzm99GKcvDs/eo+w/4kR+/zueOX+Ha\nwRcowuf5iS9/GRUcBwcZu9qzbZtB88DgtskidZapMMjr+xUFU1j9ypw+wTWI0Hv4bnjE45ruSSP5\np+n0xpioxabrQzYNpZQwng1rJGCybFxOykefMiW69yiVEdh+z+v4OOP7Fbg/HEJ4Tyl1E/hlpdTv\nTl8MIQT1CXVxmFCd3717NyjYY9QdMkyI03HV3odhjnwI4hsFsfOn2SmD0GlN7zxvfvubLBbXWDcO\nVTh224esjq5BCHz9O9/hN3/tv6NaLmjqhuXhIYvFkqosKIsMQiA3WrRUIQLWt+24+C/PaNbn4mvk\nGbPZnDzPmR3doCxyLk5PObl+h3vvfYfFcsn56SOOr11jtz5nfXqfoswls2VxyPHJLdq2x1qLtT1G\nG2xbs704o96u6XtLXs05ODriS1/8Ed745m/x3gcfcnyyY3nQsDyEo9VNnrvx01y/vsAocA7cRcOj\nDz/g+PodLi+3e85U33cxTzGFCkYf7Mk+9v7GN44pNV068go484QxgBvJerny2BgjpXVB1F+eGZzt\n04ICVKz21nHzGJm5QLhER/85btzKpW8ff/YLUj/t+L4ELoTwXvx9Xyn1l5HuOB8mU1EpdQe4Hw//\nRDTnaUhx5FieM/wOYZiIPb9hog1TDGn63jSGdB4vcaUvfOEPYLI53lvatue//C//PX7uK/84ZTHj\n3e98m9XBAZv1mtl8yXJ5wOFqQaYD1lrKIsP2rWRjZHB+dobvauaLJdv1BRcPPqBrdjjXM5sJWpmX\nJbPTRzR1w/G1m3R9TzVbcHn2kCwveP/tb7NarWi7jnfeepOyyLh59xWauos+nWO7uSTPC9q2pm02\n9H1P27YcmoyD1QEHixV/4o//SX71//erfO2N/xraa4T2gJuv/Aw/93M/RZFpicdlcHFZ86Nf+hG+\n894DVosZ2hTkueb+w0fkeYFNC3gQjlGzDYjicIsfp6V/HJSI55hYIR+1Asbfo7ANn0Mkh5r4mVmm\npeYwjIH3FPQG8M5OtK4nM9m+IlWp8qEVTaeOIfweazil1ALQIYR1/PuPAv8q8FeAPw38hfj7P45v\n+SvAn1VK/bsIWHLxPf03UobD4wKTXh9iavHx9MYZY9BKE5QbSzcmYYU8z9ldXtLVW159+XVAcXl5\nyvryjNNH93n/vTdYLm7wW7/13/MTP/az9NZy52ApiczK412PVgrbtajg0Eqx3Wypdxvwjq4/ZXf2\ngN12LdXj7Za+k8k2WcbZo1Oq+ZzL9RrbW1YHR3R9x8uvvsrZo0fsdjW2bTk7fcR8OWdxfIf33nsb\n73tmiyVlOWc2m2OMpql39F0L2lCUBR54/oUXuH7zJu/ft9y4/QVefu3zHB3N+eLnv8TJtTmEgHOW\n3a5DK02eZ5ycnHC4yAim4P6HslfO53PatsF7G+c+mZ1Xg1RXzYwnCdJE+yWf7InypgZT8EnzngRQ\nA1lWxLpHCQ2JxpuEJQCJw+2blCNKmcW1E7Uh0a5SCqJpOZqY39/4fjTcLeAvxwWcAf92COE/VUr9\nGvDvK6X+eeA7wJ+Mx/9VJCTwBhIW+Gc/zodIvdZ+4nGQaCzT0PcIqoz0Z965SWrRflpXCMLK3PaO\n7WbNanVIWebUm0e88+1v8vkv/BSvv/LjdO2OL3/5D2D7noNDMTF1COC80GN7S9s1keNfsatr2nqH\n7S31+hTXbNFa03YNtrNsdw/jBIPJK9brNc5JVsvF2RnXbt7kd3/nt7m4OAcUF6enUpmQ3earv/W3\nODt9QGY0q9WK5cERy+UBZZXTdX3UthVaG1YBZvMDDpYL/uDPfIWgDauDOYu54ebNHKM1TdPQNDVd\nZ5jNcjZbxxc+d4zrWnY1vN3Jomub+omNUOQ+7iOSU0h9qulGofooIZyee3z+KgI6lM8M0qjI84KU\n1qVgCG5fPWeC/8dE9giaJIFLwW4Vz6Ry+UzlCJRPuO5PPj61wIUQ3gS+/ITnHwH/wBOeD8Cf+aSf\nIzflSrxN7UNVA2hyBcHai/V8xILJsoyqKum6juSfvPHmb3LjzmuUJvDBvW+Tm4L3PniHLIO2bShn\nGQqNdxbbbAjB0XTyWZ2z1Lsdtuu5PD2lLHPa7Ybddk3fNunCaOqG1fE1dpstpshZHRzTtB3+w3s4\n79lcXOC8Y7vZsjo85v6H93n/vXcl9rZcUu92bDY7FquNhDbynBACXWml2tl7mrrm6OQmN64/x+JA\nTOw8h9mswjqLtZa28fig6HrPjRtzqtJjTcF7H57Tdj3L5QGLSnPvfjfZsDTgmGbwP+neTsd0LoZw\ngoJU9/mEmZ8Ichjli6jX4t9BaYqY9zp5Z/Q5/QisaSP08Si8c6SY7KgR968vhGNCCGi9RioHjp90\nkZ94PPOZJgmmvSp0V2mp07GEUZslc0WhImvx/rlNzDwoqoLFbMlmfQkhcPe513j99Z9mvd7wu1//\nTfq+4ad/6g/w/rvf4frxMUfz61Lg6Dqa7Zp2tyafHbFrGtqmgQC9teRlxfr8Eb1tsF0rgev1Bu8s\nBEV3/0Oq+QqtDOvLC1BIZYLztG1D27b0XUfb9bSXazyeLMswsZK8t46mbSmriiLL0ZmhbS1tLwjn\nbNbG3b9mdVhRLfIYJgls1lvqTUCbEmsdi0VOWcJmDZcbT5EXvPryi2x3F9i+jcSpGmPkJkpgOTwx\ne2fq18G+sKV5CiGlfqnhPdO53D9+AmiohG6qYb7LssK7fni7UrHHw2RdCEot4Ii13XB9itRSbEyy\nkPWmo6w6lNoRwu8TgSMQJ1vtPZnMgavPw2QHDSPn4TSZNb3mYx6itZaLy3OKvKQq51xbnbCY5RiT\n87lXv8B3sjdZLQ+oioKyLOhtj9HQ1FtA0TUNzl/Q20C9vgQtO6ZSGT5oNOI39G1Ls6slPmgMtuvA\nNFhn6fue45MTrJW/u04aSmoj6V9tUwsBkRJavHrXUJR+COJ2dORFQdN0zKzFWUe/suRFjrOPmC1e\nIMsDJvPsdjWEgHWwmCvQsN0IZ0rdKPI8sFjOuH9/R55r6iawOlzhLBjt2NY1NIHlcslmsx45Z4CE\nXE1DMk8ujVLDHDK+e29+YeQaScJ2dfgI4fuhQ04gkBH8yNeCmqT2qf31FII0NCH2hhvR17SZf28U\n9ZOMZ17gZKrG5DcVIjAy0XhPyhJQSo2kQUqyC6YomY6zvdmcUuiaXd3j/SHWK4pqzntvf4si0/i+\n5fb162itKfM5RklqUFWUbK2n71qC0jS7SxwFzjm2Z2eAYr5a0TuFRpo3tk1HXkgWSd8J2kgQrdXU\nO5qmJgTouw7vA33vyIuc4Dx5XqCzPMaYJM3JWod1DUEJxXkArJXCyb6TlrpaKfruQ6r5EsIB84Wh\nmlnAYAz0naVtpfGGkIcpFBkEz9HhDO9zymLByXGg3u1o254sy/HLJaenp9J9B3n//ixMwwbTdLC4\neK9Q3cXpjSOm4H2MiJJGgTZRo40U92PydaRJ1LG5YghDb7j0edpkaD2tmxyH96vojlwt3vt045kX\nuDHOpiZPPD4Re7tgKsf3VwOz8dh0nhD48N2v8+GDjkX5JS7Wglw+evSAWZnjtKZZX5AXBaacYYwm\nMxLj2W235Mawa3YiMLsdQfW4vqfe7tit1/Sdo5gtUATa3TlVtcDkBRdnpxFjC7i+p1UN8/mCvm4I\n2hCCppxVoDJ6awnBkheFEA8ZLVUEStO1HdV8Rtt2UmLTddKeK242fW+lsYh7SDVbRIvgSM6hJa1q\nvfYUucL2nsUii+2ARRirFbSdYj7LsS6w3lRsdzUHhzPeeeeDgShoj6d/ApaMgfGpRcJE+6Vq7r2Z\n3Jv3j1oHw3oIAWNynLfxczTOjZXbKn620VqIoAL71eCktL+raymd3uD9wdNScM++wEHapWI2nRrx\nqsfBlOSzyfDeS22UGnMqxcyINzlIk9ldM+P+vW9gilc4Pr7Lwcld3nzjb/H6K5+HuWe3OaOrdxxd\nu06eZ9iuoW0bmnpD19von8Fuu6ZterI85+yDDzl/+z2u3bxJsVwxmxdk1ZICJ/mVbcN8uUIBTb2j\nqiqB9b2i7RylznDOU5QVWVYQEC4RZx3lLMd7MYVl7Qacd7RtOxD4VFXFQOvBKUppur6L2RYLdOYp\nS9nluy5QFpG9yzu01mSZ9A43SIss1wV2u4Z5obj3cMN2u7niWycBetIMjkKyV2A6WBzjcfuxvOn7\nn3hiAIlFukjnoDRdN108xJCAEU0V71W6Hggo8yTOnEQq+xEM0J9yPPMCl3bQeOeQvJN9yHkc+0im\n0kKd5kOgqmYURRGLLeW4oixZzg948ME533n/OxwfrOna3VAB3PQNShvmqxOa7Tn333ubxcEhh0cH\ntLVju93SNQ2+68FZ+npHs23ZrRsOrl3n4s1vcfHO2ywWMyhnHH7x83R9x/H1u2y3a7KixAePKWZC\nIJvNBnTNWk85mxMCFGVF73qqfEbf9zhr0cZQlCV921HO5qA0fdehjaHvxezrehHQEB7Rdg3r9SVG\nGUJ4gYOjJc5IHKuaa9rW09QdzgeqEi7XnjzXEmjPM7x3VIXm7PKMrpf6u+Vixnq9iRtdKnF5smk2\n+kExvkayRJ68oPdDDVz5PfXnNHleUHeCAGutxrxZEsItge8QPC7oPSJcRUBpHxFJPdlApibk40js\npx3PvMAZY2Jaljx+DNMabn7ipBwL+xO9nrduAEekwLMYhM87+M7b7xEoeec7b7Hb9qxWhzjruLw8\n5/rJdeEyyQuyLOfy9AHrs4ccHh2jlKFpOkLfYbuW9dkF3aal6T2zxZyDO8+htxIEt80Od+8eOs8x\n125wdPN5TJbjgyCStu/RTU2z2zJbzggIS3MIAZNn5GWBD4HSZHRtg7OWvCjZbbbkFWRqzK5wzuNK\nT9e2cSHt6GzHdrtFa0XXNYTwGtVszmJp2Gx6do1lt11zcHjAxcUa19fUdcvq4ATjA9Y6nO2ZzVbU\nzTmHhytOT88nWShjrOyq/TVafxMCoAlCOdVqT9aS6srv0TxVKmCyHOc3sl60xjobQ+KMa8Fk5Jl0\nlXUxgM8AqKRQwOh3ar3DuYPhc5+OuP1dIHBjUvJkm5tAuOOBw38xs0B2zsPDQ7zSHJ9ck/zHqsSY\njKIoZHF6z8m16wSvOH/0Fk2z5bk7z1EYyUyQjdhjjGZ1cpvMZFyePeTBg/tkJqMoZ2y7Hhcy0BWz\ngxm59XR9x+z4hPLomObRI3Sw1PdPWRzMMR7Mi68QTE6eZeRFRdc2aGPIiyICH6Mv4ZyFYDBZTp4L\nfV/ftlhrYyPI2GfcRJoBlVBY4Ym03oOzbDdrAOp6x7Ze88JLX+DiwtJ3Aec7VoeHNF1P37bcf3Cf\nxWxGlnnqeovSmu3lGcvDQ1bzinq3ZT5f0HYtIcjnDNn5gcfmZxoQl/whhR5QzHESH9cu47RPzzOG\nCmSe0ucLt0kY14MPg0lpJO31MQ2nhw1hiqo6jLmQI0LFM5FL+YMYKkY8B3ubfe02/T19TyIx3W63\nnFy/yXJ1yHK5ZLk6pCxLdOyE6XzPo4t7HB8c8LnXX2VWHVPkBtcbZrMFhTF421EUJXjLbLkkL3J2\nmw3b9SUmD6yO53Rty+LwJrbtUEEKRbE9WmmKwyP6s1OKLCM3GcVqyeadd5i99lrM5ZQfFZBK8LgZ\nWGsHtNVa6SDa+SCIpda0tfSya5qaRV7IYus6VAxLeO8pygWrwxPuvfutmFVhqNsd55dn1PWO2fyA\nk2u3KMqS+/cf8uoXX+Pbv/s+RTWnnJVsNht2u5qLs1OMKXCux+QLnrvzPE3X8fDhfbzrrvTrniYr\npMcTYp4BoPzuAEl89MT5ndo6RqesIuEzmTryA+eJyVDa473ey0JJLYj3104gBOmgqvWaENYEf/d7\nrNSPN555gZPx5MBp+jv9Tik/affz3mOd4/zslM3169R1jc5yMmOoDg4oi5Jr10/o++cpcvC+5+Dg\ngHprKfMKfMB2rSS3up48NygfQCuOjw8o8oxt3eI95F0vSUdK4fqe4vCQ5vwC3/egRPuAgqpE5QXV\nakVX1+giQ2lNbjIoXBQsP3CLpEB+nkvpT55prHdiynUtWmv6rkdrRd8Jw5Yx4oscntygqmbce+/b\nwqDsoetadvWWsmx545u/w81bzzMrF2y2Fzz32uewbU+9u6StO+zhiuODFe+8/W3msyXOb3jjG7/F\ncnXAredeY3V4k6qsqNsSY3J2uw2pNu4q4DEBFZn634+bavv+0tUMoz33Ic43KpdMkSAuiDCLJeGW\nDkaS5KAiLfv4URIuiBQMespLGYADYAOUhKdEUv5sC9zVnW0Iln4E9UIK8aSHcQLQit729L2lLAsW\nB0cUZYW1lvPLNTduHKGDQPSbs4YQJPXH2YbOWZz3ZFpRRR6SPDP0fUtZaGyv6bxiUVTYXvIZTZFT\nZoa8LLFti+07uk2Gdz02Ags6Fyp0hcJ5t7frBgLNrpGUI+vIS6n6zrJMdnEFJmo+7z15kdM1Inxk\nGVprZtWceruh3V6Cn0uGvBahbduGLCtZX17gnGO33fLSa1/g7MN3+Np779E0Em/bbi95/50ePNz/\n4B3avubi7CHuHcuDB+/xmc/9JNfvvILHc3p2GqdsBEfGPMjpPKbHam++ZCpjPuQe6jl97yhsQakx\nvKMgBOnommXZyNmiICBzqbVBq4C1Cd2WaxHaBT8I81i+5QhBuqqGcPj7JyxwNel4GuO5alImyH94\nH+BsT900eO+kesAYttsN1jlpmuEDqihwfUsxXxCKgt3lGXVMaVLEbjnesb28oO9qNJIqpo2RQLR1\ndBiq2QHeK7qmG5x6nWlylaMWczFzXS/axlqpwzIKozQ+ODRjcWxZlQL7K6lKz4uCvJCsE6UUbduw\nXB7QNA3r9QXlTGrteh/o24aagLM9XpthRWutCdaSRWZia3vWF2e0rbT0+sbvitAWeU7wcH76oZig\n2w1d1+J9T991NPWGvu9AK1zwZMUSRSDLsmgGMxG2qUVyRXMNGMt+YxZ5fezPtqcto7Al3EVrhVZ2\naFCS5ZlUDkw0HEh1htZS+zclXJcwyT7ivb+RB1LbqqcxnmmBS+DH9HHaFh9LZp78PZgvCOf9rKyo\nqkoWOHB+9pDl8pBmt+Xkxg0CsNs+4J3Th9y8dpusnLMqKwiOZlezWZ/hbU9VzdB6jo0FmV3ToLMM\nb6X8p69rlsc3UD6jjdkiwTuhSQ89wU6ABYSDo+/tsOOmuFZmBIYv8gKreimSbTthdp7N2O12aKPZ\n7Tbkecl8Psc5J4KTgtBqvC/GFHShoTCG1lrm8yW7piYzhqapQSse3P8ApRRFUdJEgU4AjNGGvu9i\n/FHSwtqm4dvf/B2a7ZbPfPFnODq8ycPTU7QeG2pMs00eQy+nNmbcHKeUCnsgi4qZs5ONN70spmIR\nT+UoSkXX7afxaQPa5CgVEEB1XC+CgH+U+jKE8PssDgeTfVGNVDJXfTit9ETDxdSuLCPLC2bzOdY6\nPNLH4eDgOMaxCrqu5/L8lEwplssjtnXNvCzIqhnO9qxOrjNbHYDzbC9P8c6Slytpj2Q72u2arAio\nvqdtWnbrS+aLJdb2MX/TD40vpiCCUmpoWKiVQilNpg2mMHjnsPH7lUURK7sVu81GCGDzgrprUUBv\nuyG22HZdzAuMt0vrwQfUKiPLctq2QWvFYrZgW28kGdpkcr0h0HUtSfVIYSdDrzzbyzF91wxa64P3\n3uLGnZeZzY/QWg+UEjL0cK7UH2CUIzVEBhLGodgXplH6xjnd9w0TH4keZDnPcuq63z9GKYzJUQqs\n9VFRxs0oyxkykyYopffLeP1jw8qnMZ5pgQs8blKGKHR7mSZ7EzHOk1aag4NDrt24w4/++E/zhR/9\ncVQQDZCayed5gbcWb8QvO1xdJ9MZ2hRU1YIsyygOM7SCo5MTXN/StzVdb2k7h9Y59fqcoAJZqWh2\nG/K8IMsynO1QwUGw4mNIex7J6AgxgB+8NHNxsfF8SJpuLJgt8pwsy2jblrapKYqSKs/pnRvAIRDh\nzEyB872EAkhCJ8imUoqynKFQkh6GMFwlRNeYjC7S8hmTxbZUHd6m7BMJk3jv6bsGgqfpO+7fe5sv\n/ugfolp2nJ09oixn7HYbvLfjvE0sPKW8zOAghGLk6Sigg/KLpmPy1ZIPH2cZiD760ApLkWcZ1tWD\n1RBCGFLilFL005BLgCJL2vEqLrBAKgUSxfvj8M6nGc+0wO1ptmG3C9Ln+QlI1yiY8lqWF/zcH/4H\nWa6W1LsL3v7WVzk8PCIvK4qyYj5fiJ+lCg4PbnLtmjjcWkFwfVxwDmc1DuG4yMoZ3vWUSnp0G60I\n3tLstigrk9i1DVVVCY99EPLVzGhpDeUdzkui71XN5wahk+n18VjbJ6Qyw1pH17UYYzBKknZVRNcO\nD46o64YQhIfThtSAw4vm80F6l1shis2zXMAh74d6OildSdwfLj5WUnRre3or1IDC+NzhbM+De98B\nbzlcHZKbjPPLc3a70bxP/uwTZnb/OQVME9Unh+6HAkbLJsvySaUAaKNwNmX+p2NNpMKT5O6EJocg\nG046cB+gEXArTAL0T2M80wIHCfy4ilQ9jlLu+XHasDo84uT6Xf7T//yXuffB+zz/3PMcLubMZgs8\nmoOjE46u3WC5XELsVW20EToG20lcxzmaeketpO5LRe3j+i5eg5SDzOYzCB7b93grnXZ8cENJiLMe\nIw4p6Ayt3NBKS+rJRDDKIo9+XS/gCMBQWCnxNtFI03ZcnhArmN2gGT1lXuG8l1JRazE6Ugb6KOA+\nIXRCkGu0YbfbxsUnMbwu1vDJog4420nDRdvJhuR6vHPsNudo5bl755j79w2b3XZPQPaFLUIWcSEn\ngRymNjkNH+mjp/clDZfh/egPGqOHiu7kR2qtJac2SMbMFJHM8vwjDMaE6MTKgt8PJuUwpo5yuvdh\n39xMKr+aLVkd3eJyfcGbb3yNtm64dedFXvvs5/iRn/oZTq7fiqxZGc5b2t0WRWA+KyVTwwbQBmUC\naEEiu3pHXe9QKMpKjuu6FhvRT+8dKVbWeYvrOoIfd9Iiz2O3UDdoL60URFh/T4Am3Cvpb+scOjNk\nmQTAQxAS2aIqoXP0fY8xhnq3w2RazG6lyCS6j7WiPWezghBcrAO0FHlB17ZkRUnbtWLqeh9JivpB\n2JSCvuuxthdek+AH8iWQa+m6mlnpWG/WXK7PSZviPkI5DYLHaQxXAbD0e1+rJEGLj4bfUq0dhUJr\ntB6zTtIxWpkhlzKZlKNJmg+oZRoj6PPk7kLfz/ieAqeU+iXgTwD3Qwg/Ep/7xHTmSqk/Dfyv42n/\ntyGEv/hJLnQvLMCELCaaQ2VZMqsq8qLg9NE9drsdWZ6zWh3xEz/7h/jSj36Z5aIkEDh7dI/FYsVi\nteL4xk0ypQlBtJozBjLpvmL7FrqearGkKDLaekez20pCtOsJ0YcyxkQ7P8SAtQTMiY0NVQiC1ngf\nO8+McTeF0Pm5GPAW6oOk/aTPdJ7leAXWBbQWoduH4MPQN1zpHIaSmYmf4zV931IUJdoJgCSpYRrn\n7FB9QLy3yY8D8bN0ZshVgdYVTb3Buh7v/JCvevbwHh/ce45tvR0YsqSJxj5CGZBaRIlvPZnda3++\nH18D09dMXgzlNiJkeiy/CWKBJDCtbRG/euKiZPkU8g+TnxxogQoeE8lPPz6Ohvt/Af8X4C9NnvtE\ndOZRQP8V4A8g3+Z/UEr9lRDC2ff68BRPS38nW198nEg5YAzOWdE6fYezVrg4Dq5z97Uvs1wdcvro\nIb6rUEqT53lsS+vp6obGtZR5hh7oC+Qis7wk05qubeVm5YbgpaMNDmxwuN4NKJd3Hm87MSudjUJk\nxxhYSMe5SF0ufqEb2j8FfDRzcjOT1RfZopzzuOjfGWXorZVAfiUATV03ZF2HyWRK+16QuqGFU2ai\nudqJX5llsYd5QdO0MfF5BHCS/6UnqCfa4L3FZDmhmOP6neBAWpMXJXXTs91t6Z0dCmWnfpxodz3c\nL0GbR5NZZOBJQqgmr4/HyqaQ4yIQJlYCeJewakCp+B0U3imskzim1loq2LOcUfNOWaQNT+LR/H7H\n9xS4EMJfV0q9fOXpXwS+Ev/+i3wPOvN47C+HEE4BlFK/DPwx4N/5rh8+bnd7gjd9LYuZFTqif11X\ng8o4vH6boprz7gf3eHS/RmuY5zeZL5csVgesVgcDx0XqFya1ZA49LA5pPGiMJjhFogaVGNdwhwYT\nJsSAdvAOhhxJWfDO+WGiM5OhlcYqIXPVSkhxtNECgKBQppCFEosjbTQv67rBq0DX28Gs9t6TZ0IJ\nkZmM3jm6rpcAdkhdbiw6xvd09AO11kKeNCCnAa00Lm4MiXip77vBD1JkkJeiRbzFa0+eV2x3W5SK\nmfoqkvBOBGVPm0203kDm84SsFAFv9iZ9z+dTSvovDMnICpwvBtLapGHFV5V4nh9IYGUYnQHd3ueO\n/psGZvHUv7c+3CelM/+o5x8bakp1fnS4p/4TNDyNlyQOkMxoikwAgONrN8myjIf33uPb33qTo6Pr\nvPaZz7A4OI7+WylNCY2ACpnwiEqCcggEa7FIqpezluBHn0AAxVEjBWK9nh+zSBTgghoKHm1vB46N\nZOrtmaLxxzmPCpCXM8oYknDO0fU9SsU+cLGDZ5bn1Nsdbu2oqhJB7BUqKLIso2st5MkPtDhnKUuB\n9pNW1UimiHfJBNX4CKaAGmoRTcwDTVn4slEl+nO4dftFnnvxdZTyVGXFrt4R8Kgh/1DOOaSvqRSf\nm847jDG7fZDsKtI5fV2bPIIkY1X5XkhACcW9jtSEY7U3oIQ6L13jKHQ6+pkFTzPLBJ4CaBLCJ6cz\n/x7nG6jOn3v+uZBMEom3AaSshBFY0FqjUGR5Jja9C3z43tvUdc3p/Q85WB5xcXHJzVt3KKsZWV5Q\nlqWUxuQ53tuIuPX0fYfyFvCScOwtnU2vd+B7VHAoYvgAwHtcMiOdx8dONiGIlsgLQcK881GwHKP5\nEodSkr5VVszmQofgrKNtGpq6ZrfdUu9qetuz3u5isFsaD9Z1zWq1GjSSVgaTZ4KWOvEZk3ZzTiHx\nbOldDmrQ0M5ZlM6iCRai8Jl9YYmCqLUhK6XZ5Mm1mxwcnrDd7YYKB9CiscJIKLSv4YYvjviJT/LR\nku83Vhpc9QmzrMD7DoKkeUlmyCg8aWMTQmA/CJycxw89zvdRbxMvMZXkPD2z8tMK3CelM3+P0QRN\nz//K9/qQJFjJMZcn4wSQmJgMxujYqCOjKEp2uzVZZsjLGXdffJWDk2tcv3mH1eERy9WKrCgwSkts\njABBxQVpUThsW0unGG/xVrIsnO3xvVDY4YXiTUXE0WgNRkvpR2Ts9XER+xAIzg/fJWkNuXY9bBhZ\nLnVxJs/FrPOevm2pNxvOT0+5/+AB5+sNnfXUuwYb/a3bt29SZIa+d1y7djwW7GpN7xy97cFbtJNA\nu8QWRTCdd3gX2wp7O6CnIYygi9bJl0tASEDlhcQBTUFZzbhx8znOzk453+5kgWthPhaN6Icmi+PE\n7vtoSXtNBW3qr8kxV0GU6FKYPLIuT4Um+l7RpFRaCx9NZmX+1GhWGvN4hXoISSwsTxvI/7Rn+0R0\n5kqpvwb875RSx/G4Pwr8yx/ngx7f9QTq1kby/oqyoqxKgvcC2SuFMhXV/ID54QkvNi3LwxNu3b6D\nyUQ4Z7M5BOHsCN6KdgoBoxRBK0ImDr+zFtt1WNcR+p7gPc4LEOKcJXihViDWsqUFSphA/m7cUZM/\nkUzJpJGG1zLx76z31Nstjx485P79+9x/eMrZekNQcHa5pe0t251kU6zbjqPFnGvHB2R5PrS2sr0V\njWY91rZD264sz4Wkwmj6rkGrfOBB0SbDOhuD5eP1JRNy8HlDwDl5vFwdMlse0/WS+9n13YDpyZwZ\n2SSDoLXeewKax2normq2q+tg+nui4UxO3wuBkI7hjDQCow/Xti3LoOPGMvqWicH8alxXnmsnwvd0\nxscJC/w7iHa6rpR6F0Eb/wKfgM48hHCqlPrzwK/F4/7VBKB8nLEvdBLvyrKc+WLBfHkoib5FweG1\nW9y4fZfdZkM5P2C2XLLbbTk4OJJE4uAEsjYZs2pG19ZY68iLkuB6rO8IQUyQPCvAezQB1fZ0SkCR\nEIXNez/kSuroXwcvpTMqZaVHs3EaL0zDxBiZiSlHOvaW7pod68sNH3zwgK9+/Zt8eHrO6WZH5xxN\n29HbaWJuQOU5j07PCSjm8zkXmwWHqxUBodHr+h7bK3TUUqJdFa7x6MxIjqRzZFmOdR4f73NRFHuf\nI/5yP1gbxmRonbFaHVOWc05OrmG9ox/M00TCkyZRRz82Uc49jkSOZTMwFaonCWB6zpgM37YDGum8\nHUCVZKZqY8jzAqOsaF5EcLXSGD3iAePvZfyManqBT7iGTz4+Dkr5T3zES5+IzjyE8EvAL32iq4vj\n6mL13jNfLFksD5gtFgSlODg44faLr3Bxel+Yp4x40GVZ0fcdVVURgsFow6yaY/sWFzuYetvj+hrX\nt9Fs0qT0JtSI3vnkiBPQweOig56M3CzLCUoNJmOq1LZdL4FlGDQEQcy3LM8pspxgNH3Tst1s+c6b\nb/EbX/sW715sONtsmS8PBIhIi4LpclSsdzXf/M47lEVOXpQYLWBL07bsmkbiZREJzeLic85Jiy0r\n6KXSWvol6MQhMynynAwRODHlF4sV127e5eT6Hdq2YbPbEpwf4qPj3CdgUmrPfFBD8HvKc/J47G2K\nWE6fG6n1tM5irBOMzglukvUYfGxTZaK2n4QmUHHTi2cN02ibjz8XiFH25LbXn2Y885kmU2FLu6Bz\njkcP77PZXDBfHHDn+Rdxrudr/8N/Tb1bc3B8i7puuHb7BaEBL0uyrIgN6qFra8Ikm5/gY/aEx9uW\nvquxXYPtG1zbxL+jKWl7vO0IIbIex2B2MstSYD7lYQrLVo9zEjeTTHqF0hIAnpUVZi7AijOaLMbL\n8jyLQXGoZnOCc/TOYRTsmgZlNMG6Qbibruet9+4xqyqKPMdkkgq2q2tSorQPniLPsdbHXuC9BNZN\nNiCHZVFE/8vDkEw8rbTWaJNTFCUvv/I5Xnr1i3gisa0yzOcLLtbnkznTSLpZEhod3fAnLeCPq0Wm\nVQcSYA8xrcsnSkWlIpCi0Tqn7zucS3wn0anUGh19TIVsggpQ6hKYI9XeBzxNMXnmBS7dtDSS0Blj\naNtauPfrDZkxlLMZt+6+xPU7L1ItDsiLGdVMqOfKsqTvBbYnkd54j4uaTvIn+yFPcEwsZmBI9l7M\nSduLAAUnMbYEhKQ8yJAC2T6ITxPCIJDSf1roGCS5WTSBMYb5YkHbtCyXS24eLul9oHOehw8+5Pb1\na9RWoX1PkRdcbC5RStF1/SB0Zxdr3v3gHsvljKoq2O120ZQGa1vJtugts7IkC56cQjRF35EVpZTW\ndO1gVhqjHvMzRfNrFqtDdFHSuUBX13QRnXTODt2BEpqZiGITnjEijVfHGC64Wn71URpGaS18MBGN\ndM7unVppMSlNniFUfqOw6shzIoo8SBA/QAglKjiCyuN7nt549gWOfcABoCgKuq6jKudUszkHh0fM\nliuOr93k8OQmymRkJqeq5pRlRZZJAWUyk5y9gkyFpKkk+4OpLxF9A5PnBAXWOwmixvxEP8mRNEZj\nsgzXW3yQ9CzxdVKOn6PrW+kREPsJyKJsyLKcsiyoikI2j9ywKgyv3brON96/z9l6w2p5DEaxPj8l\npbe1bTSDfcArT9tJgnHbB/KywDhP1ymUMVLdHhy+bijLAus9mSnISxMFU0IBAkrpKCTJ7xrvR5Ie\n52G9XZPPloNfFwDXt4PvOr4/9c2Wx2IYXu338NGu0lUEM81d8n1B8iL3Yf+AVgalNYvFgkAtsUoE\nKclMgv9TJB1BrNPjUMFTC3nLeLYFboi9MfErRPBOrt8kL0qu3biNdZbrt26jtRRZmqIgzyuKUoo3\nlQpDPZl3MuHOe4H7uwZvWyk16XtC1HIJifSx4b21QmOeko+zRMcWh3MirEaLpvVRCFPmutYZ8zzH\n42nrVopKjZiqfd+z2+1wTugPTq6dsL1c07Qd7Dpev3uLb35wn9PT+yQAI+VuBh84Ojrk/PyCRVmy\nmlUcHSxRsctN1/doU5E5C9F3sbanbjsKD6HQ0DTkRRnjfWuqasZ8uaQoqwHdlOmIhbJZhmSV9HTN\nDpOXmLwY7gGM/bTHVsUS90IJ5fgYmwtD7Gy6+Kf+3H5cjf3X1UipbrKMvt8Ha5SOoQ2CFJ9OzpGZ\n/Io4KVCL6M81KBwhbhT6sbDEpxvPtMCNsTY9xLCS0NXbNUrBW9/6XVYHRxydXGOxWpAXFTrTg6+U\nFwXeOdqmjiiZmFfeWfHFYgqWd6KVQhh9spDQyOCHNCqtMoLxqODIM41TFm8c2gvhjwAigbysICAm\no48Flsag0ZiFkLlmmcH2PX3XR0oGR6Y0JtMsD1astls669Be8dL1I94/PWfddEM1uEI2pASAHB/M\n+dznXmE2K1BZzBrJMjJXSUA+aoOZOsDanq5tqNuO1jrY7bi4OGO9XlNkGddv3OT6zTvMZ9WkEw1D\nitd8sWQ+X5FFNjGlTUzrSgszCVXy/5KG25vdqAGns55yGJkI5RPCBJNAeQI7jMloG6k2T69prQcq\nc2fFw55u4rIJJCGX+rfAUXxuhgqizcNTyu14pgUOrsK18juZYqZpuHH7OV545bMcHF7Du47N5pQ8\nqyiqeWyWrmjq3QBnp1o373tJ2fJ2ELjg3ACMONvhum7QbAnm9rGeTBsd41VmyMwIufSP9t5JG2It\nxK7JJHPOoSN4UZblZKfNYtlNYNe25AqKqmQxn9O2HZvtjsNCU9w4YttaHq0lTOCDI8sKZrnh81/4\nDC8+d5OTk0OpCQPyTGGygPMzrPW4uMs7GyR+OVvQti1d23L/wQe8+967nF+KptxuNxRZQXXnjvQB\nj0ht0gi97bBdRzVbYXJJAB5TwKaditJMRr9taESjkwU3mdv0nkQ5HuL5htUwnEsoyvXkfal6ZGzU\nkYLpWhmM9rH4VC4qeCTRW43uhQTX8+H9+6GJpzOeeYG7ilKC7Fqz+YIXXvkcq2PJrvjgnTcI3oLS\n3Hr+tUgI6umaekQ3fSwQjUnFIYIdzttY1xYBkb7D9V3MMJHeBJI1Es2VlKMXuQ5BhEkpMKYcYnTO\n9sIdmeUYbchjBojtexSB2WyGMYbddkvKszRZxna3g6Jgce0aIc8xF5eoi3NoOqqsZF4YWusJWvHC\niy/wwot3mFeFNEtUgoA6L5koBoXzJWWpY4lKT9sJG7N3wmRWlDOOr93kYr3j4ekjHrUNF9sNRVlw\ndHLMYrFiWmoTQqBvW7abM0xuKP0KTC5tn0zqiT3M4N5cBiIg6pEAOPuxShmCrowCuJ/6FaMqkhUz\nlNMIzO8HYY8+npZQEEoKgUXBxRBJrBQYBX5JCPMnrEGemtw98wIHU4RMfvKi4M7zL9F1O976xnsE\n7zm+doP5YsWt519lvjgQqLypcdZFenAEHIkTlFBCjMb3MZ1pSOPqsH0XSVmjmUmkPQiT337UulOz\nR7JGchFIGECNEILE/aIWJL6W5TltLTyUKMVitRLkU2n6EFiajHy15Mg66l3NbrcjrypObpzwwvN3\nKUvJ/i+rKuYyaqxzOA9oTW9nBCLzVu8wmaY0M9q+Z7vdsNntQMGP/OiXeeHFl3j7nbd4//13+dbb\n3+Fzn/sii8WKlLmfBM+YLKZwBRIF4ehfMtkkx3kcnxfwJElfAqFHnzhpFxfPOeZSxiNj8FozFWht\nsrgp7qOqkiEjhbzJRBXC3GyiPYmf93hidQhw5cBPPf6uEThjDEcn1zg8OkFnGW3TsL44o29rbtx5\njvnBETfvvEg1X2CtUG8rHROaswhte0VQ8kPwBBfbGXsf4f4W33e4PvEcjpotBXK99xDzKdO1OWcR\n2jupVdNG6uoCqQXUCP2ngtkQzJDoO5/PB7MthIApCkCzOjxiV9e0bUfTtHR9R5Zl5IWYo7MqYzGf\nSwee2I7JRZM3KKF4a7uWXV3Qxvo4YwzKOepmx73793n/g/eo25bgpbXXzZu3efGFl3nxhVd4442v\nSo+5aCFIoq8aUqjaZke1PBB4PeVIMU00fnweQ4rBaQEiRjxkBEbGBX+1rXRCUiVNLITANPtfay15\nrsN1xEoBLZuFc7LRKq3A+aGafZQl8f+uhiSGj38K45kXuLRTHR5fo6xmfPj+u6A1B4fHrA6PWSxe\n4Obdl5ktVsyXC5pGOtEYYyiyCq0zlA6yoJ3He2K+YNROPnKY2H4k8UH4LJ1PrbLEDwgEYsXNAK4k\nU5C46JUSUqE+lvToIWDMsHi9lzKbxWKB1LjVLJZLhFtEQSpWDVAUGbu6YbmcD2SmKTO+LIuBQAgU\nWZGzXm8oyjl5WdK2PQFF2xtc07BZrwFF07R87etf5+HpQ3phRpVCWjzn56fC9lwUHB4e0iUgiKjJ\ntRHWsGqG0ord5gKT5ZTzg+SVTeJsaSWPuTGyhlXKQedxKr1peGBaOjP6amljsr2wYqt4vFaGVNCa\n5EPHuKFCGMimgiPFutPQhAbsY5qTvTN+f+OZFziA1fKQi3XD6YP7FIU0regjZdzxtVvSiijP2K7X\naC1UaXk1k5iK1pRlPmmyHolmOofrGknvignJwowsra18kLSDVEGN0lLO4mFogUwK7mqyvIzEQyMN\nmyLtllJomedC5OMj8GOtJc9zbt68iXQeFZPXOYeNnUzzfE5VlTjr5Lq98FgmxDYvy+g/GrKyYqEM\nTdMzywq6zgo7WZhTtx1BaXZ1zdvvvsMb3/oms/mCsppj2ybGE8cgfdu3bHcbHj16yB/+e/4wL7/w\nYtwEHE27RWlBYPOqom+lN1s5O8DksYB2WLR+8nsyompJAphQzfGx/Jbnpu8dewB0VmguAkjOK9F0\nB5LgC0ppyLJu7EoUzy9m8FTg5owbxb5J/JQsymdf4LTSONtzcfYwkpwG+q6jPJxz+/lXuX7rDrZv\neXDvbWbzA7K8IC+lpqvIi9iJJsK9SopEu7aOwVkfNZVUevvE9hRtf6OFnCi9lvyTMExCbI/koWtq\ntBqrAeQ0+4S1PhL0VIXwr/ggLY6dc7G+zcRFneOKXDSPdxQw7OrpXENMMs8xRSnuqdagM4JvaeqO\ni4sNs/mcspxTFXNms47driXLcm7cvC3B8vi9vO+HbJhUYmNdT93U/PX/5v/L7X/0T1KVZcz4dzF7\npyIzxaBVvOsEsTVJ2BLS+ITV+j0X8JhjKeGDwFXwxCezPv2nkj+dBCSW5mipTvA+NfM0oPo90lwZ\nG2DFqImfnqCl8YwLXGz2boUuYDZf4YNntVzx0qufR5mMs4f30MZwdHyNci6xIaX0UBcmQyMFlxGo\nUIpgDN6bQSiCkGEMIIk49qP/pTV4J3mB0pwlATAe20luZYg7b6pxm4IpktwsDej7viMrYq83wsAb\nMsQcvcdghr028UiqlKmfCSOy955ysQAMIRajKpUzny3Z7Gqs92w2G9r2EVpngKYoKhazJYvZnIuL\nc7xz5NqwdY4mdhFVSlEW1aBxrHO88ea3+NLnvzDcq+ClkWQxW1CUsyFRQGdefDOkMmM6pos39rcf\nUMYkII+XyEzDAiMQ4pxltjgYUdG9BoyjaZv8uCEIj0fpFLdL15cDfYzDuXgdo9Z9mkL3TAucwOwS\n56pmC6y1HBwdc/P2czx8cE94SUzGweEJq4NjTFFI3tykSnkMJRhpWG8i6VCXEEPJi/QxyI1imNDx\n5qcQQuQpSdoOaQ2sNKgwibVdCdQLT4ilVxJzK4oiOYJUsxllWUUNFivCQ4imreQIjhtHBD2M+CpG\nS4xvVzegDHXTEoLGGNGmVTWj7x1dZ+itJ89LQKoayqqiaArOTk9p2nrgTBFTeGTuUkphreXRo4dR\nw7ixX4KTzq8uL6kWK9TePVd4FUA/zkuSkMerzz1Js0yFLfl7WivatuPazVdQEaySg+NPPE8CTET1\nIT53PJtGXh9HTkipXGH0J39fxeEEjY0VyUEoALTWbLdrVofHlFXFanVENZ8PO5GeaLdkhvW9gCLe\nSYyt71rJKokaTcGQuRCi5pC/ZccVmoJYVaCIKNeYFKSzDNwo3GkMIIpLWlIWnw8Oo4Q5zFmLz11E\nMEeTdEyInsSo4m6dl1KnpbIMrTJMVmF9oOsdzgXW6y3buhmEviwrzs/vsdlt8N7RNDXeWuqmjteo\nCWEs3Ex+a9o4UjZIMtckS6eXxG8r8cq+rSnnB/FcDMfr0TEj5YXsreGEWn7ESObh+FsEqLeWo6Mj\noYWI92bsC6fieZNrkIGaWC7xasak+MRVWUZhG9HS31cmpfDZ53G30tx98RWOr92kms8E2HBeTKmA\nZLsXBWVRDu/3QeB+10tupFAmtMKo5Sw+9nr2QxbJSC3gYqxsuOFB8hZDTPUKQ/qRSPpY/xUGrRbi\ndzC5dOXUxqC1mlD7uchqLAshy8yQXQ8MTr9Oxaq5+KYmyyOSKTma2ni0dRysVmy29UCs1HWSNrZY\nHFHkJcGv2WzW7LaX9G0jYecgvJfWxap3k5GZbAhBSC+5nNc/9yN7vqNcoABJKgQp4O0a8ipHm5Ed\neg/u39NWySdNZttV7TZd6fvoZzr3YlmxXrck2vv9ZovjPOhJjDBdilKKqcWbTNqrYz9s8P2Pp1t7\n8JRH8B5rHVpn3Lr7PLP5gvXFKW987bep6x2L1SFlWbFYHg59Amxsf+tjJgUxA0SIXftY4o/kN0bT\nzTm3x4uR0MKkkZKQpbzIFEBPiy8JiNTIxfO5kYohaSquAB9FUZDK/YuiGBpugGRBCH+mwZgsNgiR\nSneVjRkdWsvn97FkyBjN4eEhJ8fHGKM5P79gvRbNdrg6JDjHrJxLaCEE8EJPMCvnKKWpymowyZO2\nev75l3n9cz9KVsyimS8VEEWWMStmQtGX5QQnzUu0icBRWtzhqhK7quJG2P9Ji3sfuRSzfTZfYcxc\nahKD+MhjorScVyuF0ol1WQ/gjpxTo7SdfIpB2gxPTNS/A+OZ1nAA8+WSg8MT3vjGN8myS8pqzvMv\nv8rh8Q1Wq0NmiwXeB3a7NSbLyPMKrUzktvCx0rcfYmYDwhU1mHdWwBG177BrbR6jzFY65hJGAUok\nq8LTr5jM5yCEiYE4y/JIxjpWEAg4kcVONvIea+3AeZLKiSQH1KIib6WYQwZTSGFl10kDDmvFPM6z\nDJc75tWMF55/jnfePadpdmP8b76gLEpmRRVJbtUANCUTvCxLeiutjF9++bMUZYl3K9anm4HjxBhD\nWVVU1QxTVITgMFqxWiwxWrPZ7QZC2r0xDdEpIuz75EU+artR4Pq+Y3V4k67tx3IcrfaC4MRsIhV9\n8qhMh5CAaLgroQo0kjz9+LU8pbj399ZwSqlfUkrdV0r99uS5/41S6j2l1G/Enz8+ee1fVkq9oZT6\nulLqH5o8/8fic28oYWv+nsNkOXmWc3r/XgQ3HEU1YzZbSelIllHXO2zfMSsrFotFZMKKPpuN3UZ9\n+i3C5510Fg3J/g9BGLgGgEWPWinepZRJMv1RSg1BV2sTaY+la1u6rhuacvR9Tx2p7mzX463E+gjg\ngqdtWpqmpa5r+t7Sth19b6nrOvL2d+gsw/aOtmsxWpOZPF4jFEVOHglxu66lbVtsL7t3Xe+YzeZo\nbajrHRcX55yfP6LZbQjek2kJV7vEluzdUGHhnaMoSp577gWc85i8IIQQv6uUOeVlSTlbkOUlxWxJ\nNZtDDMOIxtbRnRp9J6UCqH32rNH9fXIYYRoW6fue5epIeoqnKntthg1vzGiJxEdmtFpSVovWsTnW\nxMwVLRiGz2P6+tW0mU85Pi3VOcD/MYTwv58+oZT6IvCngC8Bd4H/XCn1enz5/wr8AkIC+2tKqM6/\n+t0+2HvH5fmpZNxrzeHxCcvVAXlRUERO+SzWn2VFEQPWPlZiy49UcAsHY3A9qKhJ+i76IKMZIg65\ni6bJCILIXAXUJBdvoC5XaohfpTSxEKQfWzIxhShWPqNTQi9exELTLMuli6ofTaFUOT50xxH8nKKa\nsTo8oC8czrXRJ9Sxps6Schx76yJgIFrb9j0XF2fsdhu6rmOzuaRpW2zfS75nRFarbEYdNSEIMe7L\nL77GspoRvCPTmfBAJjQ1sZeFQBlpLCTFS9FZNwT2pR9Ch3WWBAxOE5FHDbYvaE9CCWWjM+SZVDRI\nnqxH6yL61eN9lDxKhVYB51PTRgHDjJlSrieEdAwF/J0an5bq/KPGLwL/bgihBb6tlHoD+Jn42hsh\nhDcBlNDo/SLwXQWOIL7M6uCIXW1BGxaHx5TVXBx8JT3giiyP5Kuym/a2QxGwfSclN5GpyoYQS2+E\nNq7rpS5Oa40LssunxZQ4I733KB+ZlcOIGoYgfJMCkY/aT2up+ra9kJNKFoiOZKRRUIGEtKmuk/zH\niE4652jqmkenpzw6O+fewwupzM5yXn35BQ4PDijLkqOjI5aLBSYztHXLervl7OKCtu0lSybAxfkF\n211N11fCxtx11LsdNvqxOiK5RhuhDFQKPVvQtA2z2YLjgyNefOEFqqoij36bJwygj6wPAae6rqPt\nevE3y5mkXCnpiOqDw7VWIHwx9OI9nPpLY9bJd/WhQmA+X9K1DU1bk+eHqCBJChJnG0cC25QGSTQa\nwx6p38BUQKfve2wDeEpS+P34cH9WKfVPA38T+F8GaczxHPCrk2OmlOZXqc5/9kknVROq85OTE4py\nhs5Kjm/e5tqNW2hTkuc5VVWRZUJmk+i4+8hNQvCCug3aSNF1qYK7RytF0wuLlsly+tYNCJZCyXOx\nfVPinZw65Om3Vop+YnqWMc0qTLSd9JxTEn6Ii9SYTOjLY5C7axuKoqC3PU3TcHZ2znsffMBXf/fb\nfHB2wfl6y43r1/iN3/4a292Og9WSF+7e5cXn7/Liiy9Sb3e8f/9D3n73fd5//wOuHR9zuFryrTff\nZFu3dJ1ntRDeyqKcgcnQRxl1vZUiVWOGWra6bSiLktXqgJOjY65fvy390U1GokvwPrFHQ9c1cq9M\nickMLnhsuxP2L1NIxYaX5O5ZOcOHEBFR/13W8P5iT5ou+c0HRzc5O71PNV9EICq6ASEwMG8Fj1JG\n+t9pjbVjfmeIc6CGo5O5KNUCYyQjaeGn1f/00wvcvwH8eeSu/Hng/wD8c0/jgsKE6vzVV18Li+UB\nxWJJ2O1QSnN8/RoG6SZTTagMhJWpHyBmrY2ghEHaTqkQIjGQp+t2mMxgUyvq4dYLQ6/QMkjqkApB\nuoxOTLTk9yWi0WRiJmHrmoZkoiQ/SylF10k/bms3lNVsQiyUDWCKkBA5yjzj+Ts3aHqL0ZrzszMu\n1huUUmzWGx58+IBvv/ltXnrlXR7c+5Cm7Xh4fo4Kmvv3HohmDz4CPZp7243cAxRlNWOxWElVgwks\n5jMyk3F2cU5VFORFyfHhMScn1zlYHVBEavhHjz6U8ITJ6J20Gy7blq5r0PlcNpBkxlpLrzoyU8ji\nVZGDpWsZk5Qfh/6nPtVVc1IpydKZLw5445tf5bVXvzAYo8ZkQ2reEL7Qosm09jHeOmpWQVHd5JOS\nQCaSoRGouYqSfj/jUwlcCOHD9LdS6v8O/Cfx4UdRnfNdnv/IoY2mmM3wfcvi4IiT6zdpdjVlUVDN\nZzjbxbiVHbMI4s3q2xo/9GfzdO2OxLyVZSXN9hKjNa6XWJ1MmtmD7gUidkMcLERN6tyYbRJvCNoI\nXYL4huJC+uAhZqv4aHo2zU5gdWMoy3IQtGneZTWbcffuXe7cucNLLz5H1/d4H6i3O3b1jkdnFxgF\ny6WARLc/8wL3zzeUZc755QbDbCA4aruWIp/Ddhtjcw1aaS66nqZvaHrLwWLB7Zt3uX3zLk1Xo7Vm\nPptx7eQ6J8fXmC8WdH1L2+xwfY9RhryQWFvbNtT1DkzBLDsixOrStOlJhr4s9Kat+V4Ldxr3elIM\nLJ33wf33+NzrPxa1GrE0KSaohzFYLoFvT8SohmGMQbojEX25FCJIgvbRyOn3Mz6VwKnYVyA+/EeB\nhGD+FeDfVkr96who8lngv0eu/rNKqVcQQftTwD/5cT5ru95w/fYd5gfHQiG3mFNVM3ywGF3QNjXe\nWXHmXU8bKwDwscym77F9I5qrl5he2+wwWU5b73Cxo6cADjl9VwMxwG2l2UUyVxKxK3tAiwSykx9n\njI45eqLxrO0jCdEYj3PO0bYNJsvIMkn1SlqyLEuqqpJEJq05jtkU0h5KwB7b9/TWURQVddOwa3u8\nfoRHc3RwTNdJ/VzbNlR9xWYjGtcYibMF7yN7WEaupLXwvQ/f54XnXuAzr36Wsppxcnydo5PrzFcr\nsqzg4vwUowR57F2PDhkmmc4gIYSmIS9nJPJcoaMQM30vYyYZch8R6E5ZKvHR3mvXr9/BOcv5xaM9\nIietNX2kqRgSTTAxk8bHnnFjJ54sNrskfrQKScjG8XcCPPm0VOdfUUr9OPK93gL+Z3KB4XeUUv8+\nAoZY4M8ESUhEKfVngb+GBDp+KYTwO9/78hQ37j7PbHWI0RlVmQ/N34OHtm+HLIKuq8V0jI5yapmr\ntCIvKrqIvjnnyExG0zYCrMQG9RiDi00Sg3fgpI+39GgzwrTctRGyTFXcLgpG7OJDGJBP57uBkSuh\nfgmxy4qcoiyl71yc1eSHZlkWY1cCTuR5NoAxecxYsRFVtFa+z/l6hy4XLA4P6XvL+fkFH3xwb6jC\ntlbJdVmLcz1N2w/N5IvYvoqorYzWHB4ecXh8wny5QqG4vDil3l2QmZw8rwi2kXihzujannq3pZgt\nh6oLk+nBdBsrxZ88vzKehFJOKy3EvNda88JLr/LWW29T77aYLMd66YUg1d7deDpEuwmS6wZ6BUI0\nKbOcaT86+axU8T3G6uR59T308scfn5bq/P/xXY7/14B/7QnP/1Wk98DHHnlekOclru/QuSYvCrJM\nD8xMZVnSNjvhIUntc20/0G2HAH3f4qwb4HqTGZptDd7TtrsIVtgx0O0DIZLEKm1IjMRJuMR8UTGD\nP7GAjRkL3rsh2yUgzFAmonrSbZPYecYQYnWyc1Y4T3LxQ4o8G7u0TjSp1kJTPs8ynHdDCtft5QFH\nJyfcudPy6OyC7Y1rvPrqy9y//5AHDx6SFwdsdlvq7YbtZo3OcmxvadsGHX0ynRkOj084Ojzk8OCQ\nqiyxXUvdbllfnEk1fGYpywVVtsB5G0MAga5rWF884vD4FtplKJ0zdjxKNW2jJrsa0trXdE9+PmX7\nQ8aDhx9EinZpJ6ZgoDOP7yC1Gk4U7zbyjaahJ3wmSeuKl6mHz/490XC/l0PSoxyL5YL5bCU8/cGL\nkPQtu80FgPQSSDuqIOLi2HdtBEqkuBSgq3e4vqVptigUzoW4U7dDgnOC+rXJkWx56ZIjxY6BrpNJ\nnpb2BC/o25SrJKVIZUW5F7sLQdKO8iyPwXJFOS8GM3Ja4jMtM8qLgrwo5JzklPEaRNsonPPcvnmd\ng4MDfPA8fHjK2fma83PNe++/wzvvvsV8sWS7WbPdbqVmsChYLpfkZcErL73KyckJ3rY0u0t612Od\nxdkWEBOx62qyooh+Zw/EPnXOUe/WAsRk2Z52+/jjSbG4EUgxJqOuWz784J2YNWNGdFmnCo8wnCpt\nUgppdjk5a6yFs4xaVqPoUSp/sqA9JRX3TAucMZmYNoslfW+H3Maua+jamtxkw8KUntk+9oqTjAtr\n24ECT9KjemniYW2crJRRYgmuo7ctqbuplJrIcalODlIRo4wQQuzj7QT69qAYe9klgdEqUYRLYWdm\nDNpIIHbavqrv++G9ScON9yK2aVUMGjN9hnNOClvnc/KiioLRU5UFRWZ48YUXCSiOj69xcXHG5eaS\n8/NTmqbm1q07Q+D6tVc/i1Keut4KWITEOqVINprjmVgCeUw88EF6mVNW8Z7JvTI6H77L6LeNftm+\nBvnoMEB8BoDbd15EhcCD+x9ExHE0/4RvxU89wbE8R0khbwhIpQcq0rHbvQyXwNhJNdoy4/WHq2lg\nn2482wKXGfIyF35+n0w54YwsyxJrLVme0bVCk5AXWexWIw05Et2BZFt0dM02QvEWtJL2UsbQtS19\nLL5MeY6JOqHvI1nsBL1MC8laK00NY4skmfQwWPxJYIL3pHapiVA0+DD0J0++5VXS277ryYt88O98\n8EKxFz8/tZRSSrGYS/Jx0/XS06CVFLBbt27gWfHyK6/inaNpG+rdlvXmEu8dN27eiRkbGVpB1wkK\nLJuWi35ejlVOfNUQKIyYvNKKTQ3ZO6lpyKgM9jviJNNw33e7Oqa1aCMq+dzzd7h+/YS3v/OAy8tz\nyT+N5n5iYAsRpElSpDQMnKE+lebE481+VqNSGhVaQmxVFfbyO8PvDw3nQ8DGDjFlWYrTb7tJzCvQ\nR6GSvt0NwQqjslbglaJt24G63Hvp6e2VlqRloLftkOblnVQED0CGE2QwpWWFuPsppaSbjnVxko18\nng8Ik6/ZW2gQhS5mntiuF9Zl28dqAIPt+kHgpJJAKgOC1Xgd8Er6AySAw0ba9TSkUFeKao0xLJcL\nZrMK5wO7uooaSTJC3MERy+0BZVkNCdi73SWub4ZC287a2AAjtunVYJRGefFybN9jonYuihKTFYCK\nG5BUz4vfJTR4YzBZ7uRHr+D91CqtDV/40uf47Gdu8e23Lvjw/gc0zY75YkEi2FXxOO9i55woH1IR\noFDKxyYfsSOQCleKT9M1FdGne5y86Op8ftrxTAucBDp75vM53jnq3S7WjGm6LvZ1VkoQRi89toX4\n1ccON9JQ3nsxe0JMLhbzzNP37UCRp2MSr3cjPV4CWhTTolQ/ybQYE57HTBUzmFDii40ZEvvfTUdE\nVTI8lFIYlRZwgXclZRmGsEMIDNdlrZvU02WDL+mcEA0pExnGlJAlaaWZV3lMy9JstzWr5Yqmrdls\nLujahu3mlEybwczt2h2FnuFsH8EHQTq1AY8n10XU4PLdpJK9ItFFEAPbo7YatVp4rDrgqqYbA3Gr\no1ssD0q+9e01Dx+1fPD+O3Rdx8nJ9YnJmu5n0q7TJphScpO6FCXr1uiphkvXo4YQxmhSPl3k5JkW\nOEKQRore08TsjWxSjSwTrnF9Q9/UQ9BZAs1CGGR7QTQTPUJZzai3a0LwsW+30KKFIBn8UVTi4o6V\nzn686QK0iLM9CpsndYIJQQohhc05xB7aY/4ljGaVlLmM9Ho6Fx58T8B6B32HI1BSYvKMPCYGp8Uy\nDZpPd2BrLW00LZ1XA2clXhK7eysU7uvLM7y32K7B2w4X6Smsc5jYn07FdsHeBpSRsAYxJhkCkhje\ni2/s3ZyizKJ59thkDoInAjKNv40+XgJJlFIUswOq5Q16pzm76FHA/fvv4b1jdXgy+c6a1O99UKMq\nUSxkEMQtYDhasSdvBEKIFAshxMLUaYrX0xvPtMAlZ7VumkH4BlYpI7Cu7Tv6tok9woR/0HaNVHe7\nHq20HNO15FnBbruGIL27pTYg8nbEVKg090MAdVLykXbzYaEo0YjJDE0VA5DQtalQppy/yXPeScIw\nEKIvl76fD0GSkGGMH8ZAbx95N5mcW65RauJCCPRdL9pVKXxoaGIPgd1uy3Z3Gc9pYzpZQ57lBMRU\n9CTQaNrWKxV4SgJy37exENUM89A2WwF0ZssBQLm6GUwFT84d7+Xwtwjk6vg2s+V1inLB/YeWutlg\nm5qz84cQFMvV0bhO2I+UDbpKpU1ZEcPBwxvGGFxAQsNSCyeXaglkTGNyj9H8fcrxTAtcCIHddkMI\nMJ8LiZDWCTWTfth9Ezt8KkVwAusrJcnCBCQzo+so8kJSk6zw+hNkUSfYX+D8mH8YUoaEISjJQFcx\nFzDVX4Wwr/lkN4xZ6yECJ9HUGZx4FGGSsR6SLx4kjW1aZzcVsCmwMphRiGuZKxUTkDVN00bE1tF3\nPZ219NbT9adcXJzhvKVrm8E0FjCpjXFHaQziM/luvbM4/BBjFN8yFcYGeitJBlIiJUW2PravUkpR\nzpboWHA7vUeQbsfVMphkxinycsWLL99g18zpbcD2Qs13evohu+0WlKYs56P2UcIvM2KUydfWexse\nw+EapUeBCiGJgQUKpE2VZr9c9OmQIzzzAqe1Ybk8oGlqoZlTCms9tquxXS03Vhu6th92MZv8NSe5\ndcpo+q6lj5koBFCZgVgI6qxkrxM1kgjYvgAAuL2G9sl0UaigB9o3FBi1/x1CPG6684rPZgb/KIEx\nUyg9ac2maYbQQdtKY8m8yAcTSmvDbldLPLHrsb2AHm3X03Y9m41nt72MZTUZiX7Cey9lNwScY6iS\nV9owr2b01sXQi8WFMIBGRktVQAjgvUVbizM93ktuaN/WAFTzJSrT0bc0o4BwNagctb/SlMtrLA9v\nkRlN2zratmWzOWc1L7n/4H3atiHPy8g3KkKqdHQD0k9IyKUkMIegGcsNFQxWhoBCApbM5DFAMDBQ\ntz/d8UwLnNY6Ur21Mf4jE9e3W0mijXG44P1Qse1j2GDM6hcfw8dS/4E+L5pv1nZR08SCxDAS5aTQ\ngAqMwqsmeYEm5vIFeZ/Matjf1ScwePo/eB9LJffJgsYas7GqXEhiBQFs225P46E0Xe9jlowjy8T8\n7Jyl7TqapmOz3bJeS8tkxRjPU0pD6KNW1hhdUOQM98M7CaaX2QwfHNY5rPc4LzTwCkbLIlZkmD4X\nkzJfSv+5Zkc5W2JirukA0Q+3Z4zLaZNx4+6LLA8PuLxUfPAAnG3Z7TZs1g85WAg1onWW2eyAIq+i\nr41sZiEkWYunVMN8+Qg4pc80CHIp4I1ouuRTyqZoCE+pAePV8UwLHMgOmkAQpZTwIMYgeApC97Yj\nMQdLAnFOMAHb7GQBeYcLozkmxaMu7ugR5o+maFDJ0Y7HJ5BApVKb/dZKye8IYWydFBh9QHMV/g4M\npuk0Zjc9t7V2QB+NyQbt2EZkFqWkqhtFoCbPywG51VqzaxqarqWuW9brNV03w/YtWabJjYQbZJGK\nVsuynLE+TUUAKbbpYlK6pEWT25gwQEjpbzEu2YlfZ7KSsprhvRW0kwqdjQzNo88m3z8rKhbHdzDl\nEdttIntyNLtLLi/P0Mpj25bTRw/wLpBlxWTjEKshMZ9NTh99eoV3IyoqWjqZixWJPCiEmhAOUAT8\noN0mTM/7KvlTj2de4JyVQs0sK3DWYiN9G0jcy9pu4CYJIQxsVm3kXkywPyCmpFYD3O9iP4GRkVkT\nYqb7lGwmyIfJjVeJzWofeQQIekIsdDVkAINfJwhazHLxCRENUcDMUFGdgJNUJ5dl2RBmMCZlxKhI\n9jNyejR9R9tZttutxCGd0JY7p2hCQ6ZTRYOEJeTcZu9affD01tE5QTslD1ThldC/hxg+0BFyTARH\nzlr6rsZkGWU5A8SP1iFgssRKNgrA4uAa+fyErJjTdwL2NM2Grq3ZXJ6yvjzlxRde5eLilPX6LM6J\nZOL4iCQn5rLEkj3UKWqN0oFEZ0KcBTHFPQzAyJUQQPSth+3hKQkbPOMCF2I9W6JQ6LqGLM/FdPOj\n76VjHp2JgEHXNVjbwRD/khtWFBV9NJmclYx82XU9WUwmBidZIT71oo5xtGjKofXAiDwdUxN0yvg8\nnawUC/LO772WKBG0YihKdc5hshyt3XDepmmi/xfpH4KYd0KZ3mNtzOkMnl3d0ve9EApNUgaDdfSA\nHlpKSWPJzEjDSKIvqZWmyBR1rIzvbUdqmZHM5BCkfVUGeJ2hlFwz3tG1ETwpZwSl8baPYIUZMnDK\n+SHPv/oim11J34kl0tRr2mZHU2/ZXJ5T7zYslwd84xtvUdcNAeidQ5vkfwHoCJJNNafEaEXDXckq\n0SqajUW8MZITOoI6gck2Ot68pzCeaYHz3pNnRYwnjUFeZaR6WkeTz0fI3dqevmuEUk6BCyk2BtVs\nLr6cd+R5JtU3iJbMszwWq7roF47Z/0lwTCalMd65QYvCJJw7nWw1Nnqf/p1eT77ZdCilhNtk8DtE\nq6RWxImNOUH/MUg2+HQhBLpWyF8dgbazwvjVtjgnqUwKyeUk+Jj7KVu5co4W+Yw8lyYixkitXpYJ\nFZ+PGiCxF4eJWe29RwcHmJhYIEzUbb0DoKoWKJNeCwQyquUJq6O7XFyCcw3e9TS7DZuLR5H6r6au\nN2SZVEjcv/+eUDkoM5RYSUWGxNTcHidlrNpWKTA/udEBxiBcQilLroYnwgRJVd+FGfqTjmda4FJ3\nk972cRcXobKtpG6Jpxuhd0LMJvFkmaFt7WDWLZYrSalK6VyJrwQxTVSQMELaeY3O8MqhXKxT0xko\nIQ1SKsSfEQhJaOIAZsSRnk++5ZS+HEZUcloTl0IGWkkCdjJfE0q520nOZ15KqlaRF4NQps/Z1TXO\nB+rdjtQhKBVgBmfRRpPFVK+E9AUfIpmsfA/tHXVbo3RkLvZq0CjpPd47VAwoe2vRRrq+eu/BSflO\nW+8EfZzNpX+bD2TzFbPVDZTJCV7huobt9oJ6e0nb7mibmqbdUdc7bt2+g7Udjx58iLOWYjbHxY0x\nOsToGEaJd12C3JkalJOQrY3CpLWGoKNZqUjdefbH/uOnZVU+0wIXgpS8FIX4D9ZaaZ4ZTchEsmpt\nJ1kiSpHnBV0ngXJjMmazRdzptwB42w30CAkZTHmMyRRxHlTkA8mMkZxJpKOqYSRplWsU4GbI2p9o\nNDf5nMFP1HrvmKvHpdeE1HUU3r7vI4Oyj6il3J9MG7quw3spym0ie1bbiHYJMYitUFJmo2SBCQFu\nAmU0JtMYJf6t7XuyCJFba9HOESb5odoYoTNXo8aWUIME0ouiRJt8MMPr3VaqGWY5s8MbZMUsfscO\n27fUu0t22w31dkPX1VxcnLLbbWnbmpPjH2Nzec7Fxan0xotIpwA948aV+k+MSdSpsNYPJny6H1ob\ngjIQDEqNgjoONZR5yX1+GqtZxjMtcCgGWgPpnxZjbCFxiwgKJtaDtHHqW+HWL6sKYwzNbhP9u2zg\nLlHKIIkaCuftUBntvRf3LYImZvATHFrFrjXRVxhMxgSEMNayAYMAwcjCnDTaVACT9kpjTJyWnM2k\nFbuup653MQl5NCONkZiYLPhA23eDSdz3fdz9WzIjdWGJNXnUuN0Qy1ORorw0mZiRzokWCtKARDFm\n2ygf0FlGFrWaigF/74XmXWel+MVRw3ZtQ14umS2O2NUbdqf3yLJSYojbS6nY6BupzgiBzeaCtms4\nPDzm3bffZLvZDr3etJJW0kkkdCw+9cHH/g8O75UwhjkGoEmG38ujHMlfA6OImcmjEUh5GuPZFjhk\nsQ6sVlZ48IX8tKfvW4pM6q7a0Aqjnfcslys80O52o58RUpBGoXSI7WnTgk3ckUCQHIMslyJLJpoH\nIGg/EAYnDeucH8o9rjbimGrDlNM4BVUS2AIM2i7xnzg7mqACmKhYYeDp+ywKbaCczaQsyXrJmoma\nRs6JhECCnfinCS1N4IfHW49yYBEQRaWaPR/9RKLpKzi8oL8xtplpjVaxHwFeLAwURbUctaLWuL7j\n9MH7rI5v0tQ76t02ki91rM8lG8Z66TtX73aUVUVZzvjww3eo65qiqAgqsNlu9gAxFQmEgpckZR88\n292aD++/x607L0kpVlxPIfjogzeEkA3aMS2PlAUj5ujjebDf7/g4VOcvKKX+K6XUV5VSv6OU+p/H\n50+UUr+slPpm/H0cn1dKqf+zEkrz31RK/eTkXH86Hv9NpdSf/t6Xp4bE3sRRnzSe+C85Kstp+y4u\ncCOtq1C0TRN9l9SjDQjScdQYE32T/QLPZKZMyWkSVJ+aUyQtlYRn5ORHQgaTmrYkqEqNHXPgycCJ\nEAu1NE0zCF26hmllQggjM7NQqO9oa3lPH3vdSS+F2DcheLJMvmfXtRPT1pDKUITeIceYXHIgQ2RV\ntnYwC5WWKoToPCN5irJp2V7a+brILqYQOjvb7dBakxclRTljNl/Qbs5otxc429G1NfV2Q73bsqt3\nXF6ec++Dd7h/7112m0tu3bpL8I4HDz7AOWGJ3m03vPntb0nuqx/Zwbyze3hiWVQcHV7DZDrmu44C\no1UGYTXMhYxkmaQGkFeArqek4j5OgphFiF6/CPwc8GeUUJr/OeC/CCF8Fvgv4mOAfxhh6/osQuj6\nb4AIKEJA9LMIG/O/koT0o4ZSkGfFAEjkRYFHgI6yqsjLKjrBMW0oSNFmbztpFxxicFlJ8DYrCoYy\nDh1vbGBYUBDRyInpp81ogglAI/6LMtke6DFWL6jhnDpC4MlXTNosTaSYyZNg/HCeUfittRFeLwfB\n997Tx6B9Z3vW2w1dLEdyThpqJKp3n0h2tB4C3EmYpmZvEmRthDlamwKTyWemQP7gD2oxIdO9ler5\nGPKIJmUIjr5vaeptjNVJfeG1G7cJfcOirCgyzeFqhQqeRw/v0TU7gus5Pjrm9t3neOGl19hsLjk7\nfUiRFxwdX2N1cMCLL71EVUmPvMAk84ZxQyyrihdf+gyLZSFafSJXWSwUHse+/5aeEa03VjA8jfFx\nSIQ+AD6If6+VUl9D2JR/EfhKPOwvAr8C/Evx+b8UZFX9qlLqSCl1Jx77yyGEUwCl1C8Dfwz4dz7q\nsyUDJBWY5hKgzXMJAFtLs1kLlB99Iq01eZbRW0tnuyF4HYLwlnjf0/tIydDbwVxMxwQvELDSYjJJ\nRxw3wMhTygMg0nmrQXMNCGVKYp68fhWtBAZGL2Hkku9XVTMJgzhH4wWRzPI8pkdJdkm9q6XwNVfg\nNH3fY2OyMyHg/MifKdfgo/ArPJqh5it4vB9LnXwyuWOsLwX9x1B12mCI2l6+rg8eo0xs5+Ulfumd\ncGBpS1OvJXbYSwegPCvZXp6yW6/xXcuj++9z7/1vYztLMZtx4/pNDo6ucfvmc3zw3lus15coo1lU\nc+ZlxfWTa8znC/HJgxQAp6r86WaZ5TlGh7EShCigydJIpiNRuJLnFsIQFphIwkct0080PpEPp6TH\nwE8A/x1wK4zclPeAW/Hv53ic1vy57/L81c8YqM7vPvcckNKdhFOyyHOsi1nvWpEhwiMthR3Whtgv\nQPpeF1qL+eKcZDxElEspJUF0hKwoEAYBCqQ2v35gw7/qm9nI9JUqBtJuCAwxL6JJJq+HQbtZm/hZ\nRtM0RHM3M4agY2xLaXQpBalajwKnl4a6rglKDeavUDJ0extIlkvCgKSKxd3fZMP3EDMViAKotILI\nRSJrNxIm6OTrjXFJ9PhYazMEmUMETrTOURFZBsVud0mel+zqDfhAZ8UcrusdDx895OLsEfcf3qfp\nGn7rt/4mr73+JX72Z/8+7t9/n7rZ8cYbX+Nv/8Z/S2YyDo6O+ON/4k8N2lcrjQ+PxzWlUkMEbv81\n6YceAyUDaDImQI+aLY2n5cN9bIFTSi2B/xD4X4QQLqeZFiGEoJ5SdDBMqM5/5Ee/HEAaQjhnyWKy\ncqKVC0rhbMwg6duYfeHJcmHAcs7St00suOykxVPc6crK4PoILsR8PFn4kQNRKbwHk8UMEvYBEIhm\nRyoBCQ4cQ7wMpFxEq9Q+OApFTNGanicRyaZsfhU1tskysshLKUxlku/ZWxu7BQl1X1VV9Db6XJON\nIfFX5kUZM2uk+FK0k55cQxgySIwau86EeKzWo/k8qDVSnEsNi9tkWRToiGRGxqxU/uSsZIhYa6MP\nJilr5+ePeO+9t8TMVYqL3ZaT42uE4Ll//32auuH+vfdo6zXaFHHjiaYeY/1gCuukHMpUfe5id1el\nFCqM/CfDHDLVX3Iv/k6NjyVwSqkcEbZ/K4Tw/4lPf6giA3M0Ge/H5z+K7vw9RhM0Pf8r3/VztWI2\nnwOijVzswSZxLyMUdyajb1vJGCkqoWjzQp+Qiiy1Et4NWaBRY3ataEiVERDHX6lkfuoYx4vN+YLw\nQU2FZNQkiSpvTGpOgIjR0vgCxgB50pDpHENFQtKcrqfIKrIiZ6EXgzbMsrhQUwsoayWvMYSYoS8m\nqY3B/0TLHu8kWSFpTKkodIq8xjmOmSujAA0XDtE8VwzlRUlwBw2NIJWxajyEMKSeSQOQmAzdtdjg\n2azXZEUhjVVqCeV88MG7tG1DWS147TNfomlqHj78kN1uK5SHQUxVk2XCN5kEW6mRQGhYO2PzSunR\nPtqOKqGWyfogXaeaWCqj5TKglk9hfByUUiHEr18LIfzrk5f+CpCQxj8N/MeT5//piFb+HHARTc+/\nBvxRpdRxBEv+aHzuu4705RP65p0dSH1UzDBQRlNUs9gDWw98lsJ2lZEXZayhEjIdrTR5bPaYwg3J\n3zOZaJhRcOxgbk1ZtdLnj/dJ7wlT8n9iUp8gmIM2GEMCSdvleR5NR01wPrIuC1VeVc1xzlHOKppm\nF+vn1JDEbWPZUlVVVFVFWVUUVUVRlgMzmCTsMkFXJ6CQ0bEJ6aTNMmGCyo7fafjOSqGHc6eWyFm8\nNkOeVxR5NaTNOefou4aua9hszmnbht1mjbM9s2pGVVUUxQxjCk5u3OSVl15nfXE69LUbM3jC0Jo5\nID4jCmlUktD8dK3ChT0UDaf3Ewlsk5Ie0ch9zTYVvKc1Po6G+0PAPwX8llLqN+Jz/yvgLwD/vlLq\nnwe+A/zJ+NpfBf448AawA/5ZgBDCqVLqzwO/Fo/7VxOA8lEjLQxrLbbvISYqE4jpPQYQyu4U1J4m\nNItWM8Proqw8PRIc7hNBjo6Z4kp2yZSYMCTHDotM6M2TZhqJhaIARvQrCWVCAacJ1FOB1VqTmREV\nzTIhVe07yYnMskw4XWJDkdyMuY0hMAho23Uxv9BQFgXWObq+x6hYSe6LqL0iIBD9LEEvo2ZTEkuT\nOKWO1zTVgvF3GMMiokGSpkf6sIUgbMhK4nm5ks9uWwGArG2p8oKmbqibFmsdj04f8OjRQ2lwUkkT\nyJPj63zzjd+m7ztm1ZwsL+hb8QeLMnZWjbmlpJbC6UKAkR907PuQvB4dOVf2gRE1noN9VPJpCt7H\nQSn/BmN44+r4B55wfAD+zEec65eAX/q4FxeizwMMAEByzDU51knZR981MQbkyfISpZUQ21hLQGJw\nWWI5jt1QnXMDDbbSSshitcbbkctSBG6f2BUtHClTYRPzidEMi4RCCdCYxtBSHDH4wGw2l504CqWJ\nCKvODDr6N1VVRcBE7sVyueLi4owQGGJ78/mc3W5HggaMMWTeY2OqWcoYTP5lih/KpiHVEVqNYMoA\njSc4kkjIYzK5/15o+oimrtbSkkqpWC9npbFlRg5aYHhrDF1nQWvavqGaldRtTd3s6GOb5L7vqWZz\nXnz5VUxmePTww9ioJZ/c20BZVtFvDqSWqoOWkm+xt5Hu9/4e5ynB/ennqhk5jdH9wMICv5cjfcdp\npnyICz21jOoigZDWYxGomtzwVKgo/eMcXVujEuQf/S+Fmpge46eLf7RfQpp6VifTcZoHmUY6jdY6\nJgQLv4rRRkAU16O0cFsulktQTHrH2VjlnQ/nGF/zw+LxXsqQZrMFWinm8/kQHgixgNUoRRO1eFo8\nY7qaoKLBG0IEjYhJvYLN6uh3/v/b+/Og3bfsrg/77L1/0zO84xnvufPU3epuIVkokjCGEIwxxlRE\nqkhZpCoQm4qTGJedfxKjOBXHAapCKjEmVQ6YGBJwJRaEJGWFgqJEICZOWWhAUkvqQX1v39t3PNM7\nPtNv2EP+WHvv3+893bf7tu6h+7T67q7T932f95l+z7PXXmt913d9lzh47z2eAZ0m0iDe3DpRJ1NK\nY0JAGZOJxdYOBCMNwUVRYoce5yWy2PVblPbUTUXV1HJfJbqWL778GYa+5/TsIXawbHebPLOPICAZ\n6b3FZCB9c4lAM+bTVa65ZeR1okkpTzkeLNNid94JjzGqfKINDsZTORVetdZR8NVFoEMEUn2crijN\npRLelUbqUm2ca+athZRAB/Fs+FgW8KMeJbE4nMKiaI1XKFiKr+VIpsI2mSp0tTPAmFFDUqFou5b5\nciFs+rpmu91KY2UEPMQbOoYI6FjrmM8XbLdbUYzuewEZZjPRlCwK6QlMxXWV5heY8fBSGvSoL2JM\nGXM2JC/TsiVcOvVV4paKfB8hIZBjZ0XyKM5aVPDiCaNi1jhroYzUrGj0QCgVpug5vnaNazduslpt\nuHb9BnfuPMfl6pT16kLQ6cKwv3/ExZmMJazrhivYYnjk52hw4QoIElf6nhIQkhK/iRebGl0OqR+T\n1T0eKaJ/iuuKBwmxEdJFDl088rKkuZONnmha3nu6dhfnfIvEG1pFtrvJm0YkD1zOcVKDadUsUMrk\ngFo0UGyGydMaa1ojKTiFbfICY872KNK5urwEyKAHQYZ21E3DbD6nrmuqqo5Fcnlfi8WSuq7jQEeP\nt2OTalVV1GWZu9rjBcoc7yiXrrXK3nYMnQJaFxNAJYFEJrNvdITatUmF8eLKPhzLKj4SXeT+3kt4\nboyhKhuU0tSVzAEvdMnx8Q1eeOElFosZt24+xfVrMlL48vKMYRioq4pr166TvoimbpAKWjoAx2mL\n2VspURnzXuda6LhnEstI0OcpcJLWo57ucVG7nmwPF0L0CsSO4PiBGYMfxIBEvDUKv8a5X8H7PB8u\n8ezEYA3S1+Zy02oyaFQMTeKxbooKXRR4azO0D+TcwU1Ov2nIFvLjS1wn3dJKa/DhazxiCEFm1bUt\nWmt2ux19K+WMqqmZzWaUZUHXjerM6/U6I5feh9iONOaUIBt/PpuJBgoQtAxRLFQhsukJ2Uv5mooa\nmJPJP9nbMyJ/8tl4ghfWSip651gvFw9G5o1SRr6f4FAhyriXNcMgXR/WJpFfzYsvvMonP/X9NFXN\nycl9VpcXnJ09oKpq1us18WiULnIZMZvLLdOllMpIro0SgCk0RgvIMmZ7U2MaQ8uUIk624mNZT7TB\nJSKwi8wRG2d4O2fFoLyjKIsMdBQxHBNUyhEykTfk/Ex072NjqJVh7ynES7O80TrOD5PTMyGlUw+m\nogdzsRg9/RdQuaCevHOICsZJAKksStq2JVTyTVpr6bteWmqiN0/fclEY2hZk/riblAtmsTtiyW63\nywaX3qtWisE5jFEsZss4kpeI6MqmM0bjESlUUY2OorYEfFB4FzJamUsdgcx6CSEIyGNK8ZgTICmF\n3UrpseAeoDQly9mCpm4YBkfbdSxne3gCz92+wer0XS7OTthuN/HANaxW5yRmTDOb5wNTaZVzZlkp\nhNc5xJ/aSvp+rmZx8ZGT0PSqgYXHZnFPtMFByq8Ss97jrcwQ0NqgdJGHdKTNJjoo44y3KZzrvL0S\nNk6/ibS/RezUZr5dZvRPYvlEaM7tIdP6FNKgKTPHpSF29LYaG8aGVBEFcqhBYb2oVaWygfeefhio\ntQj+VFV5BVjZbjccHh6xi0Xjpmky4KKUygpew2Dpug3GtMzmArAkepfPnj0hk5HepLUwa+LB5YOL\n+V0KJQFUBJ483il8GCjMWFA3se4n45E7Qu/zZ5h68lQI1IVmr1ni9+cEAk/fvMbp3dfodqs8R2K7\n3dLuVqQ8a9bMJ/mxyqFhWkrprD2ZRJ1GUFNlMCifHozd7F+LSI74weNYT3YOF0Kkcg34IAMRIWTP\n52M3QI7ffcD2PRGrykGDTzPfVBzYkZG+CIRkXqB8HGUcoJgAmBTOpYJq9lrTpDquHGbmLgHZ3FPO\nZC7YK6EkiT6LzqhoUZWZKZLqeIn2NTavhhyKTmuC40GAjJaqykwVk4ZM6f1L4EFmY+QIQEocPkhX\ndVVVhPiZZfBqik9EyXXFOEjSx1ahru/wCBPGRuWxJIBkhw6tYOhl9PN2u+HBg3uUhcENHSr03Lh+\nE2MMq9VZnnZEgFmzECMLY4f9FDNJ4WQqU0xRSaOLlLWRAuEP2Hz5r98zKOWYzIpXClqJyrEWDRIV\nw0KlZWiGD17g51j8vhqfqxhaxl40L9NMk5chgR6IsQTnZVRxgpKVkTA1naw6SZirmIvY3IJTFEUm\nEicO49Q4kxfw3qELI8/tffZgVdQrSf+k1iXG33VdZKcEuq7LsnpJknzKJPFBCNlN3cQRxQPWBwJ2\nLGtYhwtx0o53KF3KZ0R67Yq6qiM1a4wiclFcSXlF0EsJM60XAaPBW1IndlmULGdLmVtnpDZ3fn7K\nxeUF+3v7vPTCy2w2a7wPPHx4n3lVcP1wj/X6Bnfvvn8lqZrNZhFlTN4q5sYASgRy1eQzUIw1PPF8\nUTwoPmiUrP9apDI/7nshhwMIfixEA9E72DgeWNglPoZ96QOeFjpHMCOVAwQxK+Kc7JBBE/ngddRn\ndOEqwAFgnUWjKFMdKOYHISDd6GGsxxWRItZ3bTY2a23eCEopnPeEfmDvaJ/V+Rmz2SwWf5tMmxqG\nUUDJmLGvLgTRBEnPm65zOqpYA4VSeF9RBE9hqpibQXAyjwClMBlA0RFRDJGhQi6PWCftNplHGUIO\nm1XkjCZaWKKcuV6my3pv6a1ns4HCGBazGW+981XeffcdtCnZbjY8/+yLvPziK3T9ltPTE04vLvjE\nK59mvdnywgsvM9ies5O7BOeom4Vcb8wPXQwbAVQIoCObRCm8nYo6xcM0ASjwAYb0CEL5GEPKJ9vg\nJlB7AgGmEgI+ODRR6zDmCyOFK2TS6hXuo9FoL3C4UZoh6lAqr0HHsMq6XBrIIImScKtumghGjwaZ\nIHmCTB5VShogE7s/MUwSJ3NaKE9QfWLUaK3p2o7ZYp6L3mnSaZKxS8rMqYF1u93m9yKGGAnOkeki\nFLgCpTzOOzF0ZGZ3UaT3VUjdEuLfPBhpixIASKNDyG04BDmUgkvCPuI5XHAYJQyURtc4ZzCDxnvF\njes3KbRi6Fr6weECrFeXXK43/NKv/jJP3brFbrvi+Pg688UB682aeW24cXyNzZ1nMdrw8P670jMY\nxqhhiqZmw4gRSPK6EWfF5BqkIqiUMsSrDuTv+dHCt/teAU2mOYm1gjqm/jUpAYjXEgWofpJnxI8/\nwt3p9xTySctIvE/UZ3TWg3O5ZtX3XQYyTFFQVbUIwQ49ScNSXlMMLpCYDNP8Lly5hhTC6knoMkQ5\nCOssVVkD0LUts/k8t+4IBB8hb62zV1NK5WL5tPXHeZm3IMZmsNZTVbXkT35s4yEItB/UVGtFIfPS\niwk9ygsTJIj4udbCR/STOl7Xt3g8zg8yLrqs4kFT0nc9i6bk+PCIsqw4OrrGru25WF1yfnmB0SJU\ndHL6gC9++YusW8e27XjlhRdo6oqjg6PY29czm82zR5vyVlN1Igs7qRF1TZ91Ohym62pe+giPkuk1\nfvT1ZBucYjQg77G9bG6lDUYnFG3A9T3OjXMCQMLMMAkL08b1QXqxElfSBzE472NfXBxTa/sB2ydZ\nuZABkAT3E0Ie5pEYKdNxUtY5qrJk6NsrX1YWRIqgxND1Mkp5ws1MfMtkQFOPWBQmd4qn+6af67qO\nwJsAFXLtmhC0lE8i4VsXhq7rSEmMs46goqdH5/1o7TDRc9EMCThh7HaXfj/Z7LvdBoxi8D0lBWVd\nCXjkDLPSYDdvsrHvUVYly2ofFQwHN27xmVc+RVmX1E1N373AyfmO+ydnDCcPWG+3lMawt9xjs91w\n8+Yd5vO9DGDpGDEk+XVIIInklwlgSmuk4D2KTsZbs3HKfTwpR71qpL/Z9WQbXAwbgvNx4GJsdIwb\n3/YdPuZ4ksQnZS9hyfvoebSpoyCOvxJmymeqYi5tItvdYwdpXPXeo2NT5VgmsOM0zTACC9YKZzIb\nwCPk5jG0G3MceaMKNyQV5KucTBdDR21MDKdFUXosgYQctqbfE9BkMqdRNmJRGEwhdLDCFDT1Ipcr\npJZW5OZcHRtHnR/RXa1BB02awibzDKVeKNcsMudBBQpd4p1lvbmgNCX9Zsv+vGBebFgWnkp3tKcb\n3v5Hp2zXiubaTfbvPMXNl17kxrO3+d0/9mP0Fi5Wa1arFW+/+1UGfxpDycBisYxGFTUmw7T8I8aW\ncjg5IEcjyiOR+dpaW0jltgAhjKqgKXx9HOvJNjjklM3jFjJh2MYZZHFTazCqkJndMU/SQQxIRbmC\nABl6Fxj8apggYZgoXfmkNWKMUJm0wQ42Gvzodb13AqtrkRLXXvKGEHM6qXPJF991XaRiXZXdS+Fm\nOpXTJtFa2nSquibJK8jfxppjCk9HA4tK1W40nIRy9l1HUcXJOYApNCEYBmfRCZRRSTBIoohi0kok\n3evi0ZIXDfHnBFLZOBwF47HeojwMXU8YNmjbUbodC3NKVQTalcfcu8CcDWxff5ONt7h/9piD3/U0\n5ew2ZXmbW8sXePr6Uzi34WJ1yWwuxfuqnpFIyFonucBxZRICKYeberiYpz5iQMmjyf8rfKaNpczw\ne8DgQoZpR3duncUNIl6qgskQ91QnhCATt5XRItdmpZDdR2AiuBHe19pgGQjWxzYdkXBQ2mBSo2Os\niQlgk7RRRk+UPG/Kr1wsLwiYMsL0U2ObhoLxYlF6PFTKUgrdiXamTSGz2fBXnivlXT4EVAgUZU1T\njrmLtDVJ75yKnqhtW4Yh9vWRZgpUI2gQUs/hGG4lFr6INMQ3C7HrXGqOy9mSzXbNrtvRh40QnlvL\nwpxz0HhKtcMoi8KzfeeMqq/xBIqqIbg1t+8ojpf3MOYufa+xlwe0p4fos4Ha1uzv3aSJCgCgKcoG\nax3WJxnBCaqcRlUFN3qycLUfEcbDM/45Rzzyt/E+3xNlgRBRsZAK1EF4kJlJ3/ep9UxOd21Q+DgD\nWyD14MaCcAhB6k7OEYLMCZdxV2nUUUS8tGxA2VRS10ksjtTvlbq/k1cxRVQr9l+bE0h7iuVRjwqj\ngSV2xjTc1Fpj+4HZIjax6pGu9DWP1zr31U1zORfniMvdA2VZM/SOXjkcAedtDh2NKdFaUZiCYbCJ\nfBIPMWL/4NWCv3djqKy1oq5q1t0Kj0IHjw4De03HwaylKbegZ9hdy+5uj7+00LYoazn4xD7XbtXM\nZ566NgzugMHcovLP8vT8gMNPPAfz56hnc+p6TtsNtO2Od957N3+HRWkojc75uqCtLh/aIYegX996\nQojjyghx9NeYDjwme3uyDS4VuZKxiWpwwDkfjWnIcHsq+A5xhrVLbThxs/R9HxsjR2Sv61rs0IMC\nUxZxpLC00RRlFcNGeQrXS+7mJyhhguhTnaysalxsGXLWSi9dCv/KOhr1mENOjSb3v5nYFRFzs1Hq\nbpR4yJ40hp7WWlQqkEeQpajk+bAK3BjCplC5KiusdygKrLfiJVAoNyKUiljzDCPAkNpukoc1wTFE\nSQjnhEx9tHeNwfZsd+cETljWZ8xrS1X0aAp2l1v6k4GhC3FWBNx6YcneXkE1O2Rb/jMUN34cVd/B\nuIrFrqOyA127o2t3PLh8Xz73qkYB70UBovS97u0dsN51WBdimkH0XGkY4wesTD1RKPUIxet7IYdT\niiwcZIchI0qpTaYq0yhbnUOwTGty47zvBA4IxahDJVg9kZXDWLOT19WYssD2A4GA7a00Wkb+Y8qL\n0msbMyKHpqxwbkcAYfK3reSCSPgFMitNXudqaJg0RkII9Fuhewnc31/ppdMTT5d+zx0DzqP1DGeV\ntPnUDUNfMtghjvOy+ZpLU+CUH9WW4+ERgG7ogEBZVPFzjHktPorgJhn6EmIHQsoPy1ImrM5nc7Rf\nslzso/U7oDaEoOnPauxuBwygFAcvHXP01DVYfpp3zH+DNc+izpeEsKLvO/quxQ4tIIyY09OHbDer\n3A1uh4Gh7/DOsXaWy/NTvLOcPLhLYQpm8yWz+YKiLNjsNgQllLWsmB2935i6pB75Sej5eEDKb25w\nSqlngb+O6E4G4C+HEP6CUup/Cfz3gQfxrv+zEMLfiY/5SeBPIAHfvxVC+Hvx9j8A/AWEnP6fhBD+\n19/otUMgyn7LYIkhSnVb55nNZjgf0Ioroqdp8wVUHrqYPEJvBzm17YD3lpF9kljtYArp/5JTPg6J\niPzAhAomAzPGMPQ98/k852UZGUPeuylFdwQlcu2Co8T2FTeyaExhMqk3a3BohTI6yrVHFn8MLRNV\nIpcl4iFCrL/Vs7moeRlNXc9B7cRQEXDJaIN14oWDlYJw6nIoSlHeGuxA27ZZiCgEmWZUF0UsBYjX\nK4sqzmcbcySlFPPZEucKqBZcckygY2HPaS8f0PsdpikwBbzwI5+l+Ozv5+TaD2CLJaYouXn9iGZW\nsFoJB9R7USzzdsf68gEPN5e0uw193+bpQFICcWw2gl7fuH6LVd/x4P67zOZ7HB3fpO8s6+2GqqxY\n7B9Q6CKG/BXNrKGu55R1Mynmx734bQRNktT5P1FK7QG/qEQ1GeDPhxD+t9M7K5FB/wngM8Ad4O8r\npT4R//wfAf8CIgL780qpnw4hfP6DXljk66T4vF5dsNmsKauaw6Nrko85UfKdbvLUu5ZoV/E9Zag+\nHWJpUyilCGoM5QDqZs7Q93kjDxEsAfGY6XQUQ7Rs1iv2Do5od9tIzB0oyoLVxTmH127EnBGUTZN6\nCplM6uKoqnhopOswxogGp/eUppaQLsrfZW+olPQFRuOsqortdoeJAwvbdis8yllDVXmaekHXbyFI\nL9swDDKtNNYehZo1HjDayKSawYkOjI/NpHKgdVRVnRFfKfzLNKPUrZ5QWmMa1q3HuwUEjfKGi80W\nfXCTcg9u/NiPoX7097G59gJeaYJ11HWDLmGz62i7DheFm+q6xhWaw+OnUMWcdrfl7OQu69V5HFMs\nQ0RQcHqywbuOupYWpq7dcH52j1u3nqcsa95/90080NQzlJL8dG9vj/39Q3yA5cExB4fXmc2W2aAf\nx/ooUucftH4c+KkQQge8oZR6DZklAPBaCOErAEqpn4r3/UCDc3bg9OQ+ZVGy2+0wpuDo+AY2hmRV\nVVKW4+ANHzu+pSDuoz7jOLttDBFCRuhUQEIiZ6V2o0VSwRSlCBE5i2Ls4k7h3NDLUMiMjCpFVc9Y\nX5wSvKNvhQ1TxDwvGRQInN/3fQ5RUw9cQjuTEbn4OB1RyMwk0WIMynuUc/SdFOh1ZOVXVYn38vi+\n7fBOJs809QJrLG0HKEWfCc8FIYjWyDh/QIyoLMVzekKkmTWAoL+JuaJRUhrRSfQ2ooaxM9zTcN4G\n1i1c+JK+uoY5rrjxg/8shz/y+xiahRSuY66+3a6pa8NsVnFwsERRsVg4uq7i7OyColowmwea2T77\nB9dxdhD5vdUZpyfvs7o8pW23PHh4j+V8yWw2p6pqrHV85fVf4/DwOgdH13n3/Xewsz2aZsH+3oKj\n45vM50suzx/y4P2vcnr/HfYOrtEsDmma+TczlQ+1PorU+e8E/k2l1B8DfgHxgmeIMf7s5GFTSfNH\npc5/9Ou8RpY6v37jBn3XSv1Ha67dvIUdXEbitDYxxwg412WAJbt/FZEpTJ4mo0JCqkZ9/eTp5MRP\n02MGun6HjbnRFJUcul6AaV3gvAWl2W427O0fZE5kQrhs9JSpIJ28WFlGUR3rJ8amIl2si55OQjcd\nZ9mZCIhYa6nqmqT0pSMpWkLrZCwp/xsYhjW73YbFYp+ybqhnc5HaUx3D0KO1krKB1TFfNNG4SzFG\nZXM42/YtZVFmsdc0p0/H0gWM4fkY7hbU9QHWLVnZDnej4s5nXuD2b/99VHvHnJ4+TN8+piy5ffsa\nt58Sw7cOzs8Vd+9v6fpz6kJmBiRxWR1JCaasaOZLnn/p+9BKcX7+gIf33+Xi9B7BW5yTdKLrdty9\n+xbnFydU1ZyT++/w6id/iJdf+QwhOLp2Q93MQAXadsfq/CGbi1POzk++FVP5wPVRpM7/IvCnEbfx\np4H/HfCvfdQ3FCZS56984hNhsdhjvlhyXNXs2lZkzqO3qCqRQejj7LQUZkoLTlQ2Bqzrs8hQ2tje\nx2KmUhDnVhcReGnqmu36EjuIdBtq1GEc+j53FGhjMErAk65rWfh9MfqAdB5oI7J3ie8HV4AOHee1\nJQ0W6WxXMSxWeXyvtTYauJZ5ApE7GSITxhQFeb4dwxWKmWz+gLMDZ6cPaBZ7LJYyqimRn1OPmpQk\nBAVO+pcoRVM1bNstSslcPo2ibMqMko7josb2HWtlEo8wdGIBOgR0UXPwzFPcfPG34ZTn7PR9QjBg\nCmZNzZ2nDljuSeH97CxwetKyWZ8xX1S8/NIRVeG5/3DJa19uUUOPtaJXI4eiYn//GK01bdfxzPMH\n3LrzEniPtR3tbs3i7D7nZw/Y7bZs1pc479lszmnbltde+xxNXTObzQU3SJL31nL57TQ49XWkzkMI\n9yZ//z8Cfzv++kFS53yD27/u0kozW+xRlBXr9TrnB0mlOE2cUVoms8iJqxncINSkVEZIGora4HKt\nTMVic9Rk9D56FanfibdM8gJyWtvovVJIl+pPfRQ53W1WuV0o8SvLqoKAdF0XJS7K9YUg21Mrg4+b\nPs1s80EK/GhFEQJlVdG1rUz/jEYvGiSpflZkI4E2e+QrBGotIrab9QVKqThwUkLKtGFBNFbAEoII\n03Z9B5UoZe1aGXBp7UDbCQrpnEMXkUYXpJyQQn5nI8MnMvRDCDTzPW7eeYlmvsf68pyABl2wWFzj\n+eeP6PvA/fuB7W4TDyPN088ccnxsqOuC3abnwcOzK+RtYwqKQlPXDQ8f3hOV7phC7O3tUxYVm80l\nZTVjb/86t5/uCN5zcfGAk4fvc356lzfe+CJnpycyaNIPsZok4lLWOWzbfRhT+abrw6CUiq8jda7i\nXIH4638L+LX4808D/1el1H+AgCavAj+HwBWvKqVeRAztJ4D/zjd7/aHv8W7ARz2ToirRahwRpbWO\nQpCRjBxPOm+RQnmqu5lRbCfldEoZYBwjRWTjJw1LpZLuR0HbbiGCE1qNLUOp2TUEMTgXn9/agbIS\nWpY2hrBZxxA3fX5i2GYSTk49TRFZLsMwUForo5cmo4BBCNKDixNffZc9f2KxTAdLFkWJ8x7XO3bb\nDWVtqevZyMSJfWKJOylhrygct53kgHXVsLVrQDinbdcyny3orcUH4kTU1OvnriKuSqhrh0e3uHHz\nebbtDuKYKa3guWcPefhw4OJ8TVFqnnl6n9ksoE38XKzC6sBX39pxeXEpFC2lkMNBPHnbbuPPLhO1\nX3750xK5DFI2uLw4iwalsfZVCIGL8xPWqwuMNux2a9brc9p2G/eBlKVcThU+2vooUud/VCn1g0hI\n+SbwPwAIIfy6UupvImCIBf5kCDJLSCn1byLzBAzwV0MIv/6NXth5R9duaZqG7XbLYi6S15JbmOh9\nfJ6GGV8fUoNkkJM9dURPOXejJIHBDUPOj3xEGVXsbxsBF6lrmajkZXK45yKFyOexxgkESd5yVpYU\nVY0deoa+p5nP86D3RwvgXddhrWU+n2dql3eOsp5BBG/EP0d5hAlKGT/j7N0GO1BWFUrJAMWiMHgn\nCtbSYd7mOpQAO1EOQhuGYHP9Txg5Q44u+r7HW8sQAtt2S1k2FIV0OPR9Jz2DvY8hWeqXE6MP3nP3\n/TcxRYkuKsqywdRLLlea87MLvA/cun3EzZszrLMUxrBrd4Dh9a+sefjwDJBw3A6jolqe+eZc5sla\na7m4OOPWrTtS6rGWy8szmnqeh8Noo5nNFwx9x3q1outanLe07ZaHD96n6zZopbk4S3nmR1sfRer8\n73yDx/xZ4M9+ndv/zjd63KMryZpb55gvFsyXB2ht5PSPSXueqBNDJ62kOzmNMUr5WmradFbymaKQ\ntpKkaaKNEY2QWNCVoR+Wtt3FDR2ngUaisTJiqC7C9WkJjO7y6CYfvW5ZVjL5JWpi2kHGS6mo+ZgL\nPnFN9TiHwdLMDcPQkYR8Uh1ssDL/rZ41uTaYQBmf0Fg/8XIWejfIjDbXUVUNxqQir3xOJtPLxnah\nvrfRE466KalkglJZDRnADhZTFqhMlxNkdjbfo+9bdLtmvjhg1szY7XaUsz26rkcpzf5Bzc0bNVpr\nmqJhtVqx3cG771xycXEp5RUlDJgQYmd6+p7dmM8lNs9XvvIlNpsVx8c3KMqK5fKQvu/oupZ2t6Vt\nd+y2a9brSzbrFYOVw3Jvb5/9/UN2uwrvLdev3/mw2/YbriecaaLyaKJmvgQEKKmqKiKAXS5uJ+FT\nH5W50hfjvTR2lnGeWu/EEzVVTR91GzN1So3CQdMyZ+Juqgi9K6CLfW4+DnM3hcHZNGg+iCeOI6JG\nErLOTbNp4+YidkQvpzw/ay2z2SxvnlQWSCwIEWUtsgfWWoRgN5tNNnqRaNA5/zVGo4OWcodStO2W\nsqzHsDYaqDEiQWG9pS5rILDdbjPVLQSP7TsxYqXoQqAqZ3jfMwwdtZH3PZ/PAU3TLCjqxciYYSyS\n992W4cRS1DUvvrjPbCZljc2m5cEDx917F3Rth9aGp+5c4/79cy4vW4qyjHlWyK1Faea6c+BcT9ta\n3nrrK9y79y4y0VYOM+d7+f7jZB8XjTV97g8f3mW5PKAsa7wvabtvUw73nVwp1Jot9tCmYDabjYyH\nfpclwFMUeeWxESTwcYc47wXMiGwLO+mLK4qSthUqk9CzCkxVypTVbPQqb1oQbmYRCcM5jI3gRFU3\nmKoCdDbWrmvZrVYslvt0/U7C4UnnAMRwWGuIoe9INVP0fTfhMIJSZlKCkBqkSAeOgyq0MVnTQ+aS\nGKrK0DsrxfaiiH1/lrKsCSFJy48EbZHbExQ18U9TfpjCdE+QuQJIb5qJnr2uG/b3j3nq9jPsHd7k\nwfmKoqoZokT72el90AXGObzd8eyzN3DW88abF9jBs1r37La7fJ3PPX+Tp54q2N+/xfvv18znFcZo\ntpuO9967J7lknDEuWiyaohhbnpyLSm3OEYIdy0gxrH/hxVdo6gUPH97l/v13sypa4r8+jvVEGxwE\nmtmSoqxyjpIkFmwMrxIrPtXqnJ22Xkxa8CetMGmzKG1EUsEU9F2fvY5zjqGL7S1FkSewJkZ+u9sI\nGumFzFuUJnY0yLDI2XxO1cwITjiaRSFDI1PtCJA6GJBOikfbfRLjRClphEw0NDEGn7sKpvPFjZK8\ncexAiGGkc2gl3k1YKjr3sRljYhglo7DEQAXgCEFmoycuaioVyCCRLhqnj0TDkI0NYLnc57nnXkEp\nzSc/+X3cO11Rz/Z48eXn+dIXv4xxHlM2DN0W5x11s8feXs077244O70kKZa52ErVzBquXZMD7No1\nODg4JkIDqNBgdMFrr702Ft0no7bSf1Ou2zQNq8sLvN/FqKDm2vWbPPPMK5Rlxc1bz7BcHvD221+J\nBokY6GNYT7jBqZxPDEOiV8kXm+aCFUWBtwNdRiALKYLDlRMsFW5TjpO9Si9qx1VV0bW7XDgvlKCL\nhUlIn8KYpKko6OK0+bPretwwxORdU8/m7NbrmJw7hq6jrGup/YWAsx4ZpDHqQqYDQeqJYycAsWQQ\nLwkY1bnSPymCp6J9nL4TUleEiOCC0LHqqqbtW5SKNC8rsnZFWQneFHPiwUpZBcZitkD8NufGAFqH\nWCs0WeBnt9vRti2LxR7nqwsu1zua2RHnFx1FtUTpCo9iXi2wLqpXF4rdrqdp5my3m/iZeKq64vnn\nb+CcZr2C+cLTtoaicDx8OHD9es18UaNQNM2Mtt3lz3GMPqTr/bOf/WHqumazXdNuNxKRVBVFIXS9\nppnjg+ell76Pi8sz1quLPI/vcawn2uBSwm+tZeg7ilhITd0BphDgIgn5ALn9xgWfoenEDkmhXVlW\ncQOL8WYx1YhqlkWR86M05CMxKmxsm0mz10JI+UM0yqJgeXQNiGN+lcocy3lR0bbbLEwqHtlRzhph\nTUQDszGnSF5MmyTtpjILBMYivjIyPD5J1SUEddTSiW0+8qIUqEyUlmtA+KKR8d/3cSZC/DwFlAqg\nUmPsSDRQaowg+qFFt4bD41sobXjrna9wsH9M5zRls8+d52/x1bfe5tr1fc7Pd3RdF3O5Amsd77/X\n4Z3IAZZlwbPPHrHdOo6OhcKnQqCqQiSWe955p+Ptt9/h4cNjjK4oq4rlYo9huBc9ZOxAjwY3WMts\nNscYw/7eYWyD6uNU2R37B9fle0fjy5Knn36RL3z+FyNxun88e/qxPMs/xeWco9/thOKVmkpDEBRM\nmzxIfvQOkaTsRAA0b76JBn1IXEnnswe1tqdIwIgxVHWdSwuJepWSa+ckdExk4hROBqWoZ3OaZib8\nQx+iV7SUVZlLFwm6r2rJZ8YQSE/EkcaSxKi+NeaRUzpYykFSfS55b9F3iY/RojBm9HiN004DOXS+\nVqogKClzOudF2TqWD67kNArSDIB2t+Hi/IQQpNn18uKMs9P7HN98hrv37mOM4c6dJYeHRyhTIQ0/\nUuw/P78AAuv1JbduH3P7Vsnzz1bsL8C5gsVc09SaopDD8v79E5xz3Lt3l812RVGWXF6eZzArIZYp\nzJTvWcCXvu8IwXN4eMy1a7cxRcG9e2+ThnU659huN3TdLtdlH8d6og3Oe8fq/AwXHFVds1qtY1G4\nxGhRxPLZi0VVLucFIFGgCkM/TLuztfRQlWU0tBBrOXESixIdjLKshLYVhVdNnAXed5I3Gm1yDjet\no5VlxWL/aCIKKzxC79yk+DqRLVBQNXX2sKBy4Twpd5WlFKyVVmPOBFc2fGqfIZY0TFlMDFAMV0oC\nQhFLxpy8apINtBF0SO9FJNJD7gToui4/Jr+H2G0AUJiCsqzpug1nJ3fRgI7NvOdnDzk7vcds3qCM\nYXlQ5UqI95bZfIH3ntXlBbvNJYrUC2mjF5UoYrMVFPreXUvXteztHbBY7LHbbtmspH8ugSapZSux\naJ55+nlmsxqtYT6fcXh4LR4UmsXikItIeh6GXjiX77+dw9Krwzp/8+uJNjiRYpMNKOOKiGilMLdF\nilxCuSmknkKxxOJP8L8AFZom9q8JJSvlduNgQZniWQoTRSnqZoa1w7ixs4HIpuu6TkLJgyOUUqwu\nz3OdyNqekEsVPk8+TUTjsiwnxpNEZ8fQMbcRxWK+szYSjsfOhXSt+T35q7MPlJKiN8oz2B6vRH+/\nKMpMJ0t1zNQHGILPGv0he9hAF/OjVA9kcuCoWPY4OLzJ/v51zs8e0Pctu3bL2cn7KOBg/whtHIVR\nkWgtkcB6vaLdbbFDi7U9Jw8v6HoVgSrY7QKrDVivOT+zvPvu/dxfaLSh3W4IcZCmTFeycdCLlExu\n3HyKV169Q1Gdc35+hrURTfWO3W7Nw4d3mc/m9H1L2+748mufZ72+GHO3x9SA+kQbHMiJvV2vAHIX\ndYixt1bibRI4AuPGS5IFwTkKU2TYvJnPKaua1eW5yCvExxANyZQyC3ywA33fRZqTjYCBjmN644ZO\nnEmgns2l08DLSCqQcHi3FQ4lRFaJVhK66nFGWdu2GShJK4WN6XEg+iREilS63uTN0v1CZLukorDk\nsVpUqrWJzazyHOnaBYmt88SdNHBSqVFQx2XP7Ona7STU1jFP1Pm12+0aZQy37rwkB9D5PS7P7gkt\nzsQ567luOiqgte0aa4VOdffuO3R9LerOCvb3vYzP8pbXXn/IdrvGW8v5yQNWF2c5hLR2ECTbDtnY\nyrLg5Vc+SVl1hFDFEFi89jB0rNfn1FXBwf51Li7O+PVf/wXuvv9WzAHlIJ9GJh9lPdGgSfAyIaau\nwZSKvf2DyIyP4ZJKswTGdpC0cYtCQjkT58oZIzOpZ4sl6/UK17dXVI0hhYiSjwxtJ8TmCLQQb3eR\nxSJULkehK0zMxRZ7h2y3G6qmpqwqUceK9TNgzJWsi4wVTW87MQzn8ly3lGMJV9NS1nWki4mhmEn+\nNc0xs6ecslZCoCor+qGjrhphdJDKEPJZmhhuW5ekEiqMEcKAmXhKYfyPXEUJuyuCDxSFjqinlE52\nm3MInhu3n2O+OKLtdmxXJ5w+PGL/4JCTB9sMRCTygNDNJCSk7zh5sKJpDLrWLBZwfjbw1bdOWa9W\nOCsE9aqu2e22JCqXi7VBec+gFRweHjKra4buiItLCRnTRFnnArNmyfnZQ957901Ozx5cmaMXvMc/\nwib6KOuJNjjihmtmuU1bOgT6XlA5F4fMK9EKAeHUVVp4i9466RJuHUUhfMK6rlmfnUrtLdeSxj61\nWeQ52mHIY6tEmEig+WFoBUXwIksAxLYUIfsS1phYCugjuz6VIpQSmH7XRxg8XlNRVQxdT3InKlLI\n0vtK45OFwV+MJQEzRRpHSfWU7/kQlTq0ziFzXTfioWNNbjRyndkuRTHyE5W10bvFkkokG2R0Ms53\ncF54j1obdFFSVTVlUbG+eEg92+Pp57+PzeUZm9U568tj2t2God8JT3NoY6g80He7OOqr4L333qaZ\nv8iR9zx4uOPevTPhmg4dwTuef+EVDg8rfvmXP5/rgyOZPGRPXRQVIRRcXm745V/6r+i6HYvFHrNm\nQde1bNYXXJyfCFqpRTA3jxNzaVz190DhO3hP2+1omoZZ2cQCdEQJVYFSEw6l0Sh3NfcxpXRAN3VD\n1/cs9g64OD0BZMRuAie0LoTjFxvp7TBQ1kIFG4ZhDGW9zJIO8b2FSKfyVjxpu9vK/AECgxsgeLSp\n8vWoSB2r6kq4lJF+RfTKKsrypfup7KlU9LyjpxRPZLLkuB3kFDYpfDRS1JdudZcPFsI4yXRqrMYY\nERXyDmtdBlXkLYytSkVZMQzS7CvRxgiapCEgOt6/qGpu3XyZxd4x7731Gyz2jjjau83F+Zbzswci\nphRGz2Zj50JVN2it2WzWvPnmO7z9lqHtO4lirBDajVbcuHGTZn7Ks88+x+npQ4wu6LuW84vTOD1V\nWDObzUoElIZe8kQ78GD1XjYi7x1dt8tASwglxF7JsfD9PeDhvPcZIKnqOor7CGJpY8IcgtS+8jw2\nN4Y7AmEL5FzWJZvVBf1OQr6+a2MoZihr8YjWi7KVwgsNyEoCvlgs6XsRHiKkudJgYgNnUCKRZwr5\ngvuulZMWRVmV9F13JXRNdDDvfRRqTbO1FRIpqzwIXsAPmf6q1KgarCJdTaFQUVbCO48pxesmuD9J\n3RVFmY0rBFBxvLB4TPFyRSlDN+TxWlqiSN7MZ5pcWYy9dOg4EVWJQKxSIytGcmBDUc+pZvu07Zb1\n6gwfPNu1dAbsHR7zwgsv8sUvfp7dVmhkSbxJPHug260FKcUzdC273Ya95QJTbim04rkXFty8+UzW\noen7jt/4jV/j4uIUgNXqkvXqMrbv+GxYKdRPIWjKlRNAlj5//5jCSXjCQRPnHZvVGm0KFss9rHOU\ndX0lRymr2DngEwHVZ115gfQLirLA9r0wRMoyegsZhFg3jfTc+RHx9M7naasyIHGWKR4+9r6lPIvU\niBpgt17nepkKsjn9BAhJRkIYvUtC1YSxP4oJTdG/sV9tnD2QRY+UvKdsgOm6zWTiahjLCCEN2/KJ\nrym8TJCGX62LvPmUjoavU+F/kJHPhDhIUmHyNFUgG3TqFexZXZ5y/vB9+m7D4dFtbt15jrPTE7p2\ni3NSiL5+fcZTd54jDVRJPWhlPcPGXMvaHtt3dN0W7yy3b9+hLHsGpwiuFmTSCdNnsdzj+z79A5md\nM/Q9n/vcz/Jrn/u5eFCPs/Xk803fvxzyTVPz/POv8OKLn8iHTeB7oA5nh46z04c082UuUicRnTTo\nwkcEKW20ES7Xmbkh0noSHhVFJW0/KOqmjh7GQhj5iTKZtIjPUUQxn+iVImKptEZD1EjRsZDq2G1W\nmZ1SlWXOBVJJIYEPqQ3G+xBJ2JM5c5M1bSrNvNBUsI6AR0ISp3SzKdAhDZxjD5+OQknp+WSpK+9P\nJsgqjFJxQqiiLMocNooHlUNLxbDc6FRmiPJ5kYMavGNotwzdFu8Vh8e3KKtZ1Lp0BFVx+9adLNQz\nDq7U9H0ba4RD1Mz07O3v8fwLtzg7Kbj7vqNtG05O7gLQdS1937NczlgulxhjODw4lpxtviAQBANA\naojWDQxRQ0a8uOP5517ipVc+ywsvfZr9g6OMVD6O9UQbXGEKmtmC3XaLMppFLI5674UJwrgBdVFK\nkTWGTtOZ1G7oBW1jpGKVVUVZN4ToTbTWMSSUzSQQ9jgAUWuTR9OaKJ2QEcUpShh87E4fN+ZYxxJP\nM8SygdJJTyXB8yWJNJw6CZxzmFiHE72TyA2dFOqBHB5O2SM5fFRcQdkSYpsMQ15/5Gnm3CYV2RXx\ns5G2o0wanxipYhrKipcPQAiOqllA9JyrywvpTECDMtTVDGeFy3jn6efjOwwURcVgxaMNgxjIK698\nhk998gf4oR/6QZwrmM/3OD46putaZrMFxpR86Uuf4/O//gtsNl2kqbW89/5XefedN3HOcuvW09hB\nQt1E4JaoRa61LAua2RytFXU944UXPylG8r1Q+K7qmvliyXK5jG0tkeOnRjZ7ah1JKJyAKkmrQ5A1\nhaau6thiM7LJy7LC9kMca2VyCCjolBhL13eYwuSZcijpNk6eJxtF9B5JojwXtMPIVs/F6TAWpseu\nahNh/5FonYYralPEcM1nbwnk10zPnWtncaXaIaS8ccwJ81y1JKsQDXqa5xktTbom0s6KspZSSxat\n1aLpqXV+7Hit5JnqSimaZs75+QknJ3d5752vcH7+gL7vaJo9djvxMNeu3crvx2hNv9vGkc1SpN7b\n2+PatVscHhdstg6thfMaAhweXmOz2fD+e2/y8OE9fu5n/wFdu2W7vhBSeYwI2pgPLhYLXn35+2ia\nJr5fTd3UvPzKpwQ8cgNlWXHr1jM89/wr3Lh++7Hs6ScaNAkBbty6zcHxDYahp2nq6V8lh1Iib4BP\nYIaLnmAMx0KCeePjlBLBmWEYGPo2GqXCRsg7zWPz8dhPLAti0yeTdo2kOZmS8GSARWyc9V5oXXI9\n0dBSsh5DyKqu88CS5BWdc7nRNosLeZtR2eTF+r7P4WoKX6cbP2mVmMg/FIQyiTSIt1fxfyk3VTGP\nUlpGQomX1QRTUDUznO0xuojNszEs1XyNwTsnzagP7r5JMz+g7Xas3n0Daz2DHQhoPve5n2Vv74CX\nXv408/keWptYvHbstmuStwvBs9vtWO7Jlm13O/aWPjse5wbefft1Th+8x9PPvsq9u29z69YzLBb7\nhBC4dv02bbulazcopfjkJ38bx9duU5Ylp6eihzVrGqqqot3tYlmoYhharl+/xa2bj6fj+5t6OKVU\no5T6OaXUryilfl0p9e/H219USv1jpdRrSqm/oZSq4u11/P21+PcXJs/1k/H2Lyml/sVv+ua0Zv/w\nGNkcmrpqxnwmzrDWWolEWyDG2nwN60RH1AukeF0UhShh7dYxJ1OZWW9MSQgighPiZM9MVibp5pMB\ngkeh9RTy2VgsVfqR3Cu14iAoaBFl7qbE4XSNolxcRlZKypsS6ni1aD/NMUZjSyRnMHqcgOq96J2Y\njJCqCIGP3h+EOpeUwkJIPYeGoogd4lqU0GSAYxoTNZYyvPcoDGVZ4/yAcwNDnMPunAWlODu9z5e/\n9Cv88j/5//HgwXv5cGu7bRRianL/4sOHdymKlqEXEvt2s2a7WbFZX3B+fs5vfOHnpUYXEdLkLctS\n8va+2/HgwV3hvC736bst8/mC55//JDdu3CZ4y3vvfpV7997h5OQe282afujjtX2z3frh1ocJKTvg\n94YQfgD4QeAPKKV+DPhziNT5K8AZMkuA+N+zePufj/dDXZVA/wPA/0EleOwDVllWlJXUZA4ODkj9\nVwqZcAmyKVLf1PSEH2He6UgoUVYuYu8bk/uAeLaiKiRkiopdVV1nlDAZlKCI5OEVOY/Uk6EcKgm7\njiWAKflYvLGnqJtMc0rPlRBKo2VU8PQ9psNEvLjNxjUFXKa5ZbxhHMNLGs2bRvVeNdaMwMTPTYCT\nUTVax5BaxSjAaB2N0mSDG8sfBlSgbhaiDxnHfg3xgFRo+nZDUVRcXJzyuV/5WbabS5wd6NotZVll\nqfK+73jn7dexg2G3Lajrmje+8uu89eYXmDULXvvir3Dy8H3KqhZji9HCbreibXe8/fbrvPnGF+j7\nlqKs6NotXbeLQIml73ZcXJzhnePZZ1/ixRe/j6qqRVxofX6lu/6jrG9qcEHWOv5axn8B+L3A34q3\n/zXgD8effzz+Tvz7P6/kG/hxogR6COENYCqB/kGvTVlWomhsLdvtmrYV/Xjbd9i+I4geHiGNWJps\ntEcNrqxKyqrMcHwqD0wNIgm+Ou8wZUlZNSgSR1Hel5K4k8Bo3FNJumR46kr39bjBx8dUgjI6m+8z\nDQVNRkq58vdUp0qvlzxfZqqokfJF9N4jFUxUv7TRMkMgcjpH8ESTBXIRAzNRJyR9tkbrrL4c44JM\n6ZL3GAGU2Hdnh46u65jN9xiGVqB5As5JY2ddN6KWZgdWqzP6foe1A02zyIhuu1uz2axZrzvOTs/k\nO+y3LPYOGQbLr/7Kf8nQ7VgsD2l3GwiOd995jdOTu7gQYlF9oKpmBAJ3777NbntJ120j+uxYXZ4z\nn8+YzZc082XOt+fLg6y1+VHXhwJNlFJGiUTefeBngNeB8zD2nU/lzJ8mSprHv18A16a3f53HTF/r\nX1dK/YJS6hcuLy9Z7O2xurzk4vRU8pqywUX2fZJVUNrE8DJO5fTjWKtRmlw6q4E8S0xpgymqzM9M\nSGRiWWQa1SRsS+FV0zSk5lUYjUy6h8eRVo8+jiCGr1CTueFjM6vkWKI3kgRU03PEz2dEROPv0/xx\nmkPFB5LmFUwfFyJ7YhzDPOZv0pnA5DlBozHJkNJs76ihIs87gllyn5F50nVb3v3ql3j7q1+KsH2L\n7Xv6dgcqkRVEa8T2vfyt22GtZbfbiLzg0AOKi4stD++/Tb/boLXm+Pg2v/iL/wVnp/cIwGJ5xHZ7\nCcD68oS6kYmpQowoqKqGrm159503Wa/Osb1o2aAUbbvGOxlyopSmbTeUZU3TLIW29xjWhwJNglAd\nflApdQj8P4FPPZZX//qvlaXOP/3Z7w+nDx/G1veGpmlivgO6bnDDQOc9pqjwtsd6n4WDJF+Cvu1Q\nkFWatdbY6NGIm1vpAmOk9ScxzItSFLe0Hkfv5s2XQii5MRuYtZY6av6njTwFMUYYviAg6B9+9IrJ\n8EbK2QjbT/PAacnBWpc3ehK8iZ9jhCkfDbFH5FQKukmCPXm5KRk6RQcqgyj4dDDE51BmYuhXuxAI\nYIcdu+2K+w8f8P69d6lne+wd3EJrGZSS+I/CbHHxmgaCUrS7DSE4eiS3BviNL32O9dm7fOJTP8xm\ns+Ldd97kq1/5VezQslgeUtVzhn4X6XKWvYMbDN0Oa7usyWKHnna3YnPtOJYAisjYcbS7DcvlEdvN\nSmpzXkLOzWb1WPb3t4RShhDOlVL/EPgdwKFSqohebCpbnqTO31HCRToATvjGEugf9IJUZSm5VSnh\nYGEKrJWEfAg9ZVkxxO5d711mUhAL4tbaCfSrRBt/UjdLYIfz0ogZKOh227jBPXawuQaTEELha/Y5\ntMshpBpLBHFHjmyPSRljaogyT0C8ZApvU/E+tetMgZEQ6WzTUsTYYBsFhYLo+k/zsbTSDDUV4XRF\nHH1FyFQxMdoCpZKUuCZEab0kRJSMa+rVQjZkeS6tHN5LWFtVEj7fe++r7B/cjPnVNr+nw8NrHEVp\nimHoOTl9KG02wWL7jrKesVzu89Ybv8r9u2+y2bYMfctTzzrWl6d465jNFmilePqpZ9lu15iipO92\nDK0ok3ln2W0vYsExcHF6ws1bz1BWDev1BU094+z8hK7vuff2myyXS2azJdY63n77K99wq37Y9WFQ\nyhvRs6GUmiHz3b4A/EPgj8S7/XHgP48//3T8nfj3fxDkaP1p4CciivkiowT6By5rbRzG52Nvl6dt\nd1g3YO244b0dYj4nyKJPJOMwMuhT0mtjw+PoIUZAxMbxTYnHCAJOJFZ+YnskGN5EOfL0Oqk8ILla\noJwUolPLR2aHAGOpIXm3Md9LxpZ7zqLHGd/aKOJz1YNOyyUjFSwDGY+EndKVHg+MiYdK5ZPxfuOw\nSBJmm0JJrfIs+qSklbymc8JrvXnzKV588ROUZcHrr32O2WyGHXr6voUQeP6FV3nuhU/x4iuf4dVP\n/gCvvvpZaYNyDusGDvcPePnlz+Btx2y2YLO+wIfA6vKMbrchEGjm+4TgODw84tatOzz77KusLh7S\nRcSz71va3Zph6CnLkrOLk6zlsjp/AAFefPmznDy8y3Kx4ODwOsPQ8c47b3Lv3jf2DR92fRgP9xTw\n1yKiqIG/GUL420qpzwM/pZT6M8AvIfMHiP/9T5XMhTtFkEnCN5BA/6CltNSMtFb0bcdmWFHVFWUp\nG37oBuwwjMMj/HjqTyfIWDego46jivA3RN7crMlGl3K7ohjFg7QpCJEYHYwBTAYbRM6ginnAmDsm\nBeR43VcRyMh9nHZki1crxPNEY5saxmhoo+JwIj2HiVHB1xbA5XpTDgnBp6k8Yy6HmpIJfDbusRCv\nUEoMWQUV23UUzgeMUfgwCj4551HKoUyJMYoQpDVovjzmmec/zY1bL/KP/ov/F++8/WWOj5/i/OwB\nRotac+pkL4qSp+48x2p9yf1776K0ZrncZ744YN7UvPzy72TXbml7y8mD9+m7VjoMTMl2fc6gevb3\nj7l9+2l+44u/RFGKd00Nx8ZUOA+ry3Nef+3z1PWS7eYSYzQ377xM37bMZnNWq3Ne+41f5a2vfikP\ncvmo68NInX8OmQn36O1f4eugjCGEFvhvf8BzfV0J9A98bSen7vnpKdYOHBweYqNGfprdnYiuSXHK\n9h0+tpekzei8QxlPiD1dQwzHut1OkMtI30qFZ60UYQLxJ/QyFbSdmkzI0QYfX8uHQGFGGT5nXQY0\nRjhfchWfjW0aiqWcTZC+VBNLzJlkvNZaimpk/6fnTddrv8ZgRVBJ7poMLQ1ASfmYJskPpvxslBOM\n+puFjuAFGdyR50uqYvL7MFiU94RQxgOs5PDoOov9a3z21vO88PJn+cLnf4Hzi3NOT+5xcX7KFz//\ni3zm+38EdXCMD/Jd3r71NA/uvYdGcXb2EGsFPNnbO+D6jduU9T4//7N/F2s75st9IUAEz3Zzyc1b\nz0xKOS5GMENk9RRx8CRcnJ/xc//Vz3B5do/rN25x972vsr48x3nP+cUZl+cPZE/5x0NefsKZJoGL\n8zPKUpC/EJGvFLYlJn5RFFnTP+lsSOHYZ4KsFMgdKqjMKpG54UL7CQj5VyH1tRSyhjiko1BX61qC\njqrYei+eYKy9mSvgRgoZR683vUZInkV+1ig1esRpbggjoqlilSKBLNm4FAQnj79SN8zFWwXBMdbh\nAoQYTE4NVCXvKPeVHjudPaXzARkfO3rUNAgywJUoYIgNo009o6waDo8qfvtv/11cXJ5xfHjMr/7q\nz/Puu19h7+CY555/lbbdUjdzbt16lqIUIOv84pT7d7/KcnHAdrtGG0M9N8ybKpZyDMF59vcPebB+\nQFE1WNtzsH/EeruOqYbFFCVFNeb0Whvef+8NVpcPsMDZxf+XoqypmkXURPGZU/o41pNtcAQ2q0v6\nYeDW7afky4uCQE3ToOoK20mzpy4KjHf0VqQLfIyVgofCCGvfWUc1r9ltt1LbiuGjiy0b6dT3XjZ4\n0zRZ2mAq7uO9TOwpKiEby3COMYSdrpT3JBvzMayUP5LToSkCOfVcCXHNHciPlBumrxNCyATr9Dzy\nt/GgQIHyUtsb7x9f07sI6vjIZqkYXBKDlZHDImOeriF9Ljp7N1H50ln6wnuPs5b15anMBUe88Wy2\n5OjggB/5kX+OF1/8BG+++WXee+8t6qrm2vVbNM2ctt3RNAva3ZaiKHnvnS9zeHRTRkptL3n18Cl2\nu5VEGbEb5N13Xufuu69zdONZnn7mFa5fv4m7nwCaRNWTKbPGGPpORhWDsHH6CNCk+e0iuzjWYD/q\neqINzg4D7XbL0fUbtO2Ovus5vnFdSL1IUq5NIXr17S6CBAZ0yGGY8475bM56s6IsS9rthqLQtLFr\nOHgRTG1jh7Dw50bRzxC/IB/VjF32qmWctCoeLoEp6TFpYCCQ6WUS0YUofRCTJ3FT+X4wepp0sj7q\n5abvLYeOSjaT1go/XH1cBkN0qqlJ+JqWc3YUXQojXczaIYrQJpFZQ9/3KFNEzUtRXRavF1W8iFJ8\n3sWDT4yu3a1ZXTzg8PAmdTPPs8Tt4Lh27To3btzm8vKCs4uz+JFo1qsLlst9Tk+E63h++pCnn3qK\n20+/jC4K6rrK10wsA7339ms8uP8OX/nKF+k6ix12DLaPUUkxRhxexKUuzh/I8JG6kc83CEDkbB8F\njVwsHz0ei3uiDQ4F9WzGyckDjDE8dedZZvN5niBTRu0Q76YJbRIB9XlIuygmW2ZNw3a1iw2jArG3\n2030Mh47SNvPGCLFsEgbQszHkhGl7nOCi3ajULoALwyK5I2m3iqRlYP30hYE+JhHuUeIywIYyZp2\nJycju9I3Fz0XWuFi/nrFOCcAivxXSgbTPC+9to/5norgTop/U8ioYi6U3qfU8hTBFOllSBJ7qRZK\n8HgvCtmbzYVINCjZ2LP5HlU9wyvLfFYxn9/BB9i1gmA2zSyqa0FwPWVVUc0WlGXNbrfKBqKN0OmG\nQTr5h2Hgrbd+g4f33+H2nZcxhcl5XHyTBBSX5w/lMK3mOUcnCBk6jR1O4ffjWE+0wXkf+Oobr3Pt\n+nWefeFT7O8fyRjb0EvLiInNnFFABsheRwayS90oTRrdbbeCPho58521sWUnXAnV0gef4X5tcLGt\nxbtU44oASCyCex29WapxRTZMklNIhegMzCTDS6FX8Mnnyd8ZhV2nXM0p/J89nB5zr4S4pt+lu8GM\nRf6MYvoM62ud2nxU3IgiyTedxBOCfB82z9Mer8u6NvbJTZgoEifHxznRAFXys60bmmZOPd/D2Z5N\nu8EHEWEq6wVFNWc5r5nV1+j6gbPbd3jw4H2MMcwW+3jb47VhdX6f1eoiX2cKvRNTyNkhI5NjrVai\nDaM1XStFeWNM1suR4ngr8hBAVVWSxnwvGJwdesrSsDw4wjkv1X4vzaNFYWjqOrt8jSKO+riySWUQ\nvAAgfbvNKsoApNN50lyYZBjSrGqtNdqI/qVzAaXkMQlkeBSCj/5gDF2sJajJ75OO7FS+kFzKxxN6\nyJ0ChKtTf5LBaa2v8DThqmGOMnGpG1xO82mHt8jicaVwL8KoqWY/bfeJ73ti6H3fy2a0onsi47RM\nFu4xpoj3F0KC8zLxqAsBoxyt37Fb3xd5CW2YLw/Rao/getr1AwIKU1ToouZTr36KZ59+ltPTB1Iw\n364IwXF+ep+Tk/ux7ioAWYgHhxs6lCmjjmmgHzrKouT69Rv88A//bn7ji7/E3XdfwxMoi9SRIYf1\nMPQcHBxy68ZT1M2CL37hl8UrP4b1RBucIF6Boe94cO99Dg+PCAHqpuHw+Ai0pqkqgq8YigK20t09\n5TdKaBYY2l2kSpEbEv1kM4/IIrEmlqDy9DwaFWSYYTLa4GXcsJqwPJiAHzI8pMtMELzPVC65q/xs\nhyjbYDS+i02zWuVxV1P2CYwAyRRVJKOdU4TToUjk54QoiqfKwq1K8lw5DOyV55awGAbX5wNCjFLA\nhL7vooiQimG8GGeSn1dR3yWEIMCU3aIKw6o7hUjDNbqgbuYo7bD9Ok7uAdCU9YLZ4ggKR208N69d\nY3Ce3eaS+/fe4c03viAIaBzcYodeqGrB0w8986qRSbDesZjNaeqap+48hzEls6rk2vENSmNY73b5\ncHFOGDLLxR5Ka67feIpPG839b2Ph+zu2vBdp74uzE/YOjrh/7y77+/vUs5qz0xOOjq+xWC6xfUff\nhqzYNW1VGbouKyQbU7LbrmVjmSLzB7XWlGWNtf0ViF009SO9Siu013ilcv4mKL5D+TSBRwARkRKX\niajy4Cg3kELHiXezg5zKQSt0GFHNsjCZ86kmHjITjUN66uR1VH7udLv3o3YmXAVEstdUGuttLLdY\nikJk/tJh11sbASCfjTh5cACczx3g2cijZ8OBVxrvY40vdLjOApIDFqakqmbUCmzfyXBIa9FFyWy+\nh9GK7eUJq/UZ1lma2SFFvaCuatbBUscZEW63oWt3dH2br20YWmBfvK4OvPDcS+x2G5b7R+y2Ky7P\nHmK05vZTz3ByesLZ6UO5buT7/+pXX6eqSnwIvPjSp+nb7WPZ00+4wXk26w0hiKdZLPZw3nJ+csLT\nzz3HcrEgOEff7eLo4TQ5RgZXpHBGOJYyrshNJnuqmLinaTDTni6fwjnEKUlvl4tM8rHfTBuNtwKa\nZCAiBFwIwpKJdDA/8XzZC8V8LhBiyGpHnqcf75tZKbkOOBkkojVSMA9M9VGurqlYbARE8iEhRinc\n0CoXh3OtEQk7hQUixluWVQxFI7Wud3G8chrymML2SCZ3CrG+DrxFIbPCtZJ55127I4SNTE0t53mW\n++XlCW4YKOsZR9eeoigalClBaebzF7hz51leefUzvPX267z7zhvCl4yfadfu8DElODo8iJ6ukc+C\nwGa7YrWWibTPPvMCfddKfa+QKUPb7SXOWm7cfDpO0Wkfy55+og3OGNGeODo+pKxqZos9irKgKmva\nXcvKXDJrGunIKktqPEoH/C4QfC8hmRcde2MM/W4bk3gfQZLU4xVJw6aIwj4TUnMyDoTbWRRVhJdF\ndVghHs8PSRslgglK4b2Km8+jFdLNMCkVWCfcT5RsA+evGtgVdkp8biFYk0nYubSQCg2TnBKS8Qkb\n5FE7vFrXU1mF2XuPColBErL3TtSztt3Fyao2v0c79HGGwujlBBhyiE90BGchSBRRFnPKZo/BBrwT\nsvh8ecR8/zpOKbxTlM0hs2UDBPrB0u4eANJ8rEyBNhX7yxm/7ft/mE984vtFOPaNa3z5y59ju1nR\nxwbT2WyeSxxCdujYbtfcvvU0wzDQNHNefPGTvPHGl3Becjg3DNSzGd4F3nrji7z/3huPZU8/2QZX\nGPYP9nHeUSlYrc7xLlBWJfXqgu3+Ac8881zUOgn0VtrhvXWxpSZN5oRuu8mh5TB0WXSoKCo55Yti\nLOZGTcqgC7SeTNFUClOMDP0QZO5aEspJXiGzO7SWuXSW3HEwNbjkdYo4XHI6aFG070cgxOixkyD4\ngAte6FqIDLn0CF6VvhuNL9bgrryuz8/vvY+TUkU4x+Pp+kHC4+DjQSNF4aqq85zvqeiQjyTliLNm\nrysheQ94CgNaFeiiQZd7WC8yhNXigKpqKKsGR0VpSoypoiZmhVICxlDtI50MAiiVzT6mrNHaUM8V\niz3L8fVnefWTP8Rbb32Jd975CuvVOWdnDyPNq8S5gbOTeyyXexRlyXJvn81mzXK5z507z/Hm22/i\nbI82hv2Da5iy5guf/0U268vHsqefaINTQNfLNJW+7+njeOCmmXF88yZoRT/0VOUIUcuAw5T3xFaa\nro3SdeSQKY36TSJAJrYA+ci8sNZhJp+OThuXRAMzUZeDzGrRShPUmD9eGYQRrjJDpnokWut8MMir\nhxGtjIZqjMkDIFNR3QePUUJhE0LxVSJzYrBok2Tt4s1hnFqTAI+yrCkKyWlNYehtkv92ue4mudFA\nVdXsdpscYiYP6a0T4MePbJkQXAwzC7SqKKsZOs4NF05jRUDRD4OQoZ3FmorC9KgoKGS0oaya6EEL\ndFFQVfPc/CrhrSCSuijZNyWfObzBS6/+IA8fvMvdd9/g7r33KIuSsppzcXGBiVos3stQxhAC+/uH\naBWiTmng+o2nuTi9R9dtxqT5I64n2uCc91xeXhCCp27mLPb2OZovmS/3WCz3aGbz3Pwpo4eTh5AQ\nTWtF38uM7BCSBggkZkgCAEKIG1IbgouS5rHvLSCeIEmrJ9IxCTGM3EGU/Ky8ulIbwwvgwiPdAZln\nGT1mkmRIxOY0jHF639Q2lAY05sNCmwiH66yelXmScVRwhF3H5/Iu8kaLcRaDMbE4LwdQ0vtPY7hA\nCsIyqLJkGLr8WsLCseAFtSUofLDZKydlMO89OEehxOMOvfS1aVMIwKONSE8UBVoXmKKiaRZgRRRI\n6n1FRm1tahJ1XYxqVH6Ovb1DmnrO7dsvsF6d89ZXv8TDk/t471itLrh27cYVgoD3nqZq2KwuaWYL\nzk8fMNgWZyWaeBzriTY4YwzPvPgq8+WhNBcWaWaafIl1PaMsS7RRo56GNnHWgCghawWDs7gszgrG\nqNxlDIBWcQTx2B6jjYkisSMTY9pnVihRbyaFeS4an5ZBi8LftJlMrJW+Em5OgZdkcDByKpWSOeLy\nEmKAicNonaUyVb5dFTLMQwSHxvJBLhekijojoJLDvXhwC7G3lgA1HTCxny3gckkgBOlJTPUt+bzs\nVc/qfPRsAjqVZQUmEHCxHmjw3sphKO+GpJRtijpG9oqibKjrGXqiwynGLFQxlM6lHjlEheanIrq8\nWZ9hTEndLJgv9rhx6xk2mxUnD95DAevNmqS4LSF2YDZboJSiqmes1heUZUkzm39vcCnrZsGd516V\nQnMkx6ZaUhFnBngUlS7lg1YSnm37NvOCvbMEl+aAQ98P8dSVTmaIzZV6HLAIIrdAGEnD0/pWGm+s\ntJEJMJkmpbFY6TcLkYXvQ6wNhShV14+QvB51LKeeLKGPacNOi+FJATkBHML0sJlPmNZoWD6yRxIt\nbKR1ifGTZeiKSmOAtusYhiEyeMaRvb21UcXMEUKXP49MR8uvKQac3qPRBqLCGfA19T6hZhnKQkLO\nsmooY4e4dzaOrzK03YbCyixxE1WqnRJKndQRB5TVQM96dc7e/jHGlPG7EBLyYrFH07zKzVvPcvLw\nfe6+9zr90EdJhcByeRDZJh37+0dst2u6NhKfH8N6og1OKUVR1nnDjrQmAUXafqAoDLPIDAm2x8d8\nI4V1xhiGaCS73TYzJCSfs3FeQSQle0eIpQGFzhsGyO07I40ogg+onA9+DecuekeFirIHBuXGgnvy\nbql1JxfCrY1tMwGdwjAlz6GceEU7WOqmFi/kbQZuvIvIqdGZrwkSWXrvwEy1SkbXp7WKqlYNhbX0\nXZs1PVyc/S3PL+0yIahstDrS3tLvzvkYlicQx0/+jUSDNLtBKx1FoFKnQg9D6hgf0E5KEloXhLLC\n6FIGMsYZ6so4Bh+o6gZnO1arUw4PbyIzALckQoOQFQJd36IU1KXh1u3no7c0XJw9YBg8Tz31LMPQ\nsVzuoYLn4YN3cr76UdcTb3DpRJ/WrxLyprSmqkpMVULvGbzPPUwSivnYxa3p+y1t27Jc7uG89MHN\nZiKZ5gHf96QJo0EJDK+8eD/RLySWF4o4Cktgc5TK4UY6tSX/EQ7fVJ9EJudcZXJMPVUOJRMfMhbM\nIwFNwkBrKasKF/OjKfXLOUehCsnn4uv6yUYP3qNM6nUzcRyUizS1cdSXmYTO6bb0/mSeucnOdGTr\npE3t6fueEOQw06aSPDiIvomPOWJMKfHe4gIol8YdG4yVGevayLwIGRYJZVFjh1JCx7KJ0hcOt9uw\n2D9Ga8P56V0Oj26ik7H5sWCf1MGMVqxWZ6KVUtV85Z0v832/7XdxfP0O997/Kv35Q0KQuXKbzSqi\nx98D1C5B4q9uUCCerjJ4oa4bmVjZg7NpCL3QroZOBgd6bzMw4ENgs17LZFTnKGOHtrODKG5BLoQX\nhSCRzg6CrDlB8yACIc7nzSrI3Di0QwqtPrPTE7qY2CMhb2af0ciUx01ZJclrwNh8WqrqiqE/er/J\nx4eaeN1ELyu0wfrRQ6cJOwTPMNjR+PV4ECSjLbQWvmlUT5uySzLTJ0hZxfjUVS4ez7kp+XqsMSbd\nFrkWSCULNfRoU8g/rbOXLqoG5XpCKCmKksVyH6MNl+f3ODi4Tlk2DN1WehYnc96CD3hE72Zv/ziW\nVRQvvfoD1HXN/sELXL/5DBcXJ7z39mu8/+5XeOfdN7ETuuBHXd/U4JRSDfCPgDre/2+FEP49pdT/\nGfivI7qTAP+9EMIvK7GKvwD8QWAbb/8n8bn+OPA/j/f/MyGEv/ZNXp0khPpoHgVQGkNZFgTGOWup\n4VFmQAORzNz3PXVdc3FxHkG7SnIfJ8XZYehl8o65SvIdhgGCdDCn4RoucSiViijldHOOxpbJyoxi\ntNOQKsH708MkeUKT0FBGgMOHgEqeCq54t0e+s/F5uUp0985TliInbowcIkLUdjGXC+y6Hc47uq6l\niIMtUke6sHZU9GIhPiYKNNmBEPMzYzQhjWSQb1KUpIsil2ESGpoYPnIAJPq3jrmdlA60MWhTikx9\nWUkZoG6oK1FmPn34HgdH1ynKkq5d4ayLcxHSHlJooyl1OWl30swWB8yXh/kzq6qGum44OrrJM89+\ngsX+DV778i+zvjj7xlv1Q64P4+GS1PlaKVUC/6VS6u/Gv/1PQgh/65H7/0uIIterwI8CfxH4UaXU\nMfDvAT+MfA2/qJT66RDCB16JUiq3yeQJnIyAgIl1FAVx4GKPsx3WtlGfUsKItm1Jo4i9k9FTbbtj\nvljiQ6DdbaXe5D11OSb3duglh3FuDG2QBk6pT8UcL0HfWlMo2Rxq0sSqlCL1fCulCLq44r2nJOpp\n+06CrL33uEnOlyb7ZIBlYpi5BhgpZYrAMKRcbVJiSFzQeKgVhcYFIQ47J8YWnGPXtTF/kU2b3ssw\niMH1vfhR7ywhUqukmdVglKY0BZUpKE1BYUbB3SRyO9VQgTQUUiQT0lx18YARoQ7EwS7SfLq6PGW3\nXXF07TZGF+y2l6KJYirqZpwH50MQ+p8yArgVFbP5noTIZpx7lz7Duq65fvMpfvTgX+Cz3/+jvPfu\nG/z8z/1/vpGdfKj1YUSEAvD1pM4/aP048Nfj435WKXWolHoK+D3Az4QQTgGUUj+DzBj4zz7oiRSj\norGEkaPWolKKqpTT0nYtbugJE6EXQf4gsU1S8TzVoKq6lpqTl6ks8/k8D7YIgSwyZK2VUNIUuXtZ\na0272+CdTLgZwuQQSBt9MqbXaBEUSsYhta+rY4jjZ52RyWnOaqPXq+N7dt7l2QrJaKcdElop8jit\nVJAnleJkkEeISVQqjxRVhXIxY4wo6DBpd0kjo5zzWG/pupaubcVj6bE0kBg8ScCHfC1ReAmwDCTB\nIlkFqX6RIxnv0MrgVcorfTwspVuj211yed6CMpKzaYkYqnKGLipEvPUCvNQIbexwUFph9KjMpjX0\n7ToqmclM9vG71MxmMlFnb+/gG2z5D79+U1LnIYR/HP/0Z5VSn1NK/XmlVJol9UGS5t+y1PnZmcxo\nHhsvJyeh1kIQju0uZVVSlFVO/kMI9F0rkO92g9JKmiBDYlkIe6Rtx40zAgQSglpnJbyL7TjWOgZr\n6fo+MlpkgwxDHwV0pJFRxTG8yYDk56vXGVIRPYIjU6rX1Hv5EOhjUd9FZTFrR8839XCjlxg/I7kd\n0mYGqUsG0hDHEk/IvX8AIaohSyhrs1H2Q0/bt2zWl+y2a7bbFbvdmt1uncWa5Dsav7Px/V1NBxI6\nmrQr5XVS+Ua69UVn1GP7nq7dkppku3bH6vIMU1QcHt4gdXWkIZm7zQUXp/dwcWqqoK1QFFLXI3pL\n54ZIeg8xOupxQxv/CfmZECiKkvl8/nVt41tdH8rgQgguhPCDiFryjyilPgv8JCJ5/l8DjoF/53G8\noRDCXw4h/HAI4YePjo7z7SoyRORn+W8/WNl8cYP64KPwi4Q83ju2223ufbN2wAdHEfMn5z3bzZoQ\nPF03olDeR+FYrbLknLA+PGVZCBMdskFY6/LAQ+KAC8n1psXsMRxOHlC693WWV/DR60wBkMGK8nNi\noKT3l/5Nc7gRJR0HJKbPbmqYRQzTpoCNyPKpmKdJHtz3HX3fMQw9XbfLZZVh6FGI0K3o/g/ZGMbv\nR115T/nwmXwe6X1N63HT60otQ0rLYJMQHF3fElAs96+xWB6hjTBPiqKi7zrW6wuGvqNu5tTVLPNT\n62aBKauIvEo+6pzPNcHxgBlwtkNYSbFeqxVD/3jac74l6CWEcI4oLv+BEML7QVYH/J8YNSo/SNL8\nW5c6ZzSuVPBOv3vvKYymKitUVJkKVmaQpVMxROKtR5pYh+QpYt3rcnXJdrOhqptEiY1qzzIn2rvk\nwYaMEHZdJ6Ou4v2dT/J24wZLhhNivUtyx6uTStM1pRDWpY0Hox6IUldkGMLE8BLCmT4LKawL7maM\nybMNUmNpkST/vJ+oP4+bPc1t8xEs2e02Obfd7bZ0nagWd+0aFZk+TdMwny8oyzJ7tnTYpH8jAnn1\n9vHv4+ehtaaqaim9xPctHEydgaOyrGhmy8hIUbHA3scoQwgCdTOL4W8MQcuSoMhGXVUye7zrdhLJ\nWIuJUUCaJy4RzUC7veTkwdvcf+/1b7ZVP9T6zUqdfzHmZURU8g8DvxYf8tPAH1Oyfgy4CCG8D/w9\n4PcrpY6UUkfA74+3fYMXR058nUYhXZ1/VhiBwdLg9tRQ6iNi6bwjhIi+TfiC1lrsMLDbbEApjCno\nWtGt6LqO3W6X75c2TToph15GL/mk1hwFf5jkYqQTXo19dUppAU60ynStdB1ZCToCGSruXjnlR2oX\nIamBiTefgiXe28ickTpbQvvG8gJZyn3wUZYi5j2pCD0MQ9y4DkJgu93QtjvaVv4LAjxMlcuqqoqT\nZWIRYkIhmxpdQibRGhkCrdBBodGT0kD6DGOaUDbZE+NDFPgJscdOpMutHeLQSxPnu4uhjl5Ti7gT\n5AMweB8l9KV8YQcRehVJRDmYhqGj3V5ycfY+F6fvcHbyzjfcqh92fRSp83+glLoRP+lfBv6H8f5/\nBykJvIaUBf5VudhwqpT608DPx/v9rxKA8sFrnExDCIQYtuVCr5dTyA02IpKSAwy9sBBsZ+m6juVy\nyWYl4dN2u8WYkr7v8AH2Dq+xWq+Zzxcimx7DydlsdkWyfKrOHIJ8OfVsRte2+ZROPMSss5I2kRpp\nVyGEfD9IG1OYGiGIepfRo65jCrlS2JbCXa2FhpXqjsScdCyfhMwvTUhvGkJinUepCFwgYavKeY1j\nu10zDANtu80UOOkoqEicR3md0bsno9E51558i4/k3wnMiR+I0N80+TMYwRYnmqNKCuGCSHusFWFZ\nUwpvUlqyBIFOh2QRdUqSwUovoZAohm6HRkJ5N4jCGkVJXdfyHdiB3faCdrdhtzmja7ePidj10aTO\nf+8H3D8Af/ID/vZXgb/6Yd+cUowhltZCvZqAD24SponOvovJts3hXwqXunhyi7eIGh1BPFZmzM9m\n7HZt7GgOdF0fQxxzZaMTZciHvqPdbeULruqrRpV4w+GqTAKAMhMlr3gdkYSSPVMyvpz3KBVzj9hJ\nUCeMSrznNAyVkBm0LnMoVhRlLCdoYKw7Oh/1XUKgH3pW6wvW6xXb7SaSBVLXAkxVzepa1Isl15FQ\nMDl6qf25SO9KWywO/iAZ3lT01iNd/VFjMq4M5KiAdT0FNQEp0k/boIahzftCRxVm5x0mhe9K+Jx9\n36KUwZQV3XZN225Epq9qAM1mfcrl5Qnt5kLmiysVOypKFsujD7ttv+F6spkmkEMrSQ9GGXBIELjO\n5QOlpKUkFbr7XqakJJqVtxYXRvrUbLHHanUROxEqLlcrttsdt5+6Qz/YPDVnGGx+TGqZUVrH2QEi\nn506pxNJWpSqHMMQJ/L4NMj+KvtjCv0rQvQ+Ooel6fnkPh7nxSN478GMBp3eq3xkIyqavKIxBYPd\nUFU1ylmpT3aitGVjaNV2LRcX5zHcspEdIwpdRVHQdbs84N65JoeMkmuNZYhpbTF7WyUdTWlKbcrp\n5IAZOao6EwiSonM6SOLUV4iUrxTGjoRskA77ae6YGTRxSo/Hsm3XKBTLvWN0UbBenXBxdh87dLTt\nFm8HiqLElFLLOzi6yfGNKfzwm19PuMEpgbhTzxlEWQQdJQBGkR6QEzE1XU4hc++deKK4GaQuJ+CA\ncx69UCLHvbrk4PAYUxguLy8zQ18hXQbTDmnvPW30mmXVkAd9ZF3EkIvj6dAuYpdB0iuZNpMm9or3\niWQoG0g2pZB0nfcM1pGmhqoqXb7K6GbOC7mKDDpnqaqaPgIRMgzFocwo6VCWFVUtnde77SZ7y0TU\nFqCmy4KqifuYmCazZhZd2KM5mUBSShGn1how0iMXUujLdFS0z+wTkacw5DHGesz5tBFeZaKWlbH7\nOzAadkozJFTs8wFpipKh37E+OWW7OZfUxFo0mmZ5RDNfslgec3h8m+X+NUzxPUBehrGQO81P3DDE\n0VPgvcliPAQilOxyV4B3jt12g7OWohhHWYUQWF9eUs1mhAAPH95l7+CQumnYbrfS2VxWtF3L3nIv\nlhlGzUfnPX3XiqhoZLEURQVIbQvI0PcITEhBum3bKwbiwlXmiHgdG/M48n3TkrqVTANKTZ1lnFl3\nNZdMeZ/DOrn+XS/hlzEG63yclSaWa+3AZrPi/v332G1WrNcXolzlRwNwbpzyOvXSqV3JFBVlKRzH\nqqwotJkcggK7K60xQYm2pkpEgZGCJh0EMY9jBJdMWVEYMRaVPRgkInZi9Es+n0JVH9lCAqSVZU0I\n0O42tNvLPJ64qmZU+0tm833mi/38XzkoAn33PaDapZSSQiVJianFO0l0BSKOULcbhL4TZeestXRt\ny2K+4PLynL5tBU5XMm8uMU4CQiV6cP8ue/v7gAgCnZycsFwuUcagTAFaambS4HlVfcsUJX2eO5fq\nOqlnTeaD+5hHZhGgEBsujSEMI+qXrhmI3MmrIrDZW6VyQCDC2aOXSyH4mHMm1eUAESSxXgy2LEWd\nq+9bQLHbbTk9fch2fYG1A13XT4rsMfS1luXegYShQTE4S2kMy+UeTSM6kGVRRgZKpGepUWTVewT0\nCAUmGExRx4PJoBXC9Egs2ITkakGSjSnE0CKbR2eoP7F6bDZOMTaXgRT5rgp8cLihiyWBjtlsj/3D\nm8zme9SzJaaoqJpZ5pAOXSwBPaYJOk+8wQ19l929teP4X4i6ICEWRwlst5fYXjqVtZJwre96vJP6\n1aCg74UV0rYt88WC1cU52hh2ux0Hxzc5PT2VL1BpimoGqhDphVhjCjHE67qegNSXxnqY5ELD0GUj\nGoZh0vx5dSBHCDBYd8VTKNSVLgAR/zEoF3X+lR9reqQCc6z7QRTyGTsO5G8SUrpApHmN9TuAqmrY\n7bZstxuqqmKx2GO327BYLNi1bfS0Qia4XK1Z7C0xpiYgdLOqqqN3SdY/sl2SYw4+EHSUgYilkqAU\nwQ0Ep6GMYWCkeKGQ4oGOkg1KgBgdO90F0bR5O0ge50cv7ydSEkpTlFIySHMo5vN9rt14lnq+pDAl\nKCjLWgAUJYXuvmuzoU0JBh9lPdEG572njyOHQxCmfNYUIbIUkLpb3+7wViQN7CCtNuLJxgKxc452\n14rSVkikZc9y/xClJEfabLYsFnuYoqaIevPDENFRIzUkpx0hNroO1ubRwqkzQR7TxxCXXDMLEaZL\n1zOWGVS+T1mV8jNqcnoLaCD6KiMoIs8dGMd+kK8zfT5JLEjg9oIwaSaVnDA24ZZpeGLB3t4+8/li\nAlyAit7i5nVLs9yjrOaUZSX6JpE3ml5ba4WLxe78/vP7kfeW6HI+TlEl8Ej9zESAbCwVS3mkpYxS\nEJaBolBZUj0Z2pRVU5Y1RWypcs5RlDV79Yy6mREwpMErs/k8GqRlt1uRJCKSQnVV1TyO9UQbHJPQ\nLbPoo5dwzjFrKvmi8tDFONAhKjb7kELMgRBJzMMwYMOAVtC3HVUzZ7O64PDaTc5OTyhMRVXPqKoa\nG/Oyoq5oN0DwoBXamxhmyq4f7DihNBmc8yLwmjrCfRjzpfT+dWztQYGzHmMi5csnwdYQ/yXlrgKl\nbQ7vXAgYJQSAKQMnGbIADQGjDA7xpEMc45VYLCAaKVqNfWl1XSOATXwfwTHYLYQKVM3ewXVB8YyI\n6KYQLwRwtgfvpMgfHDpI+1MVm1YzwhucFL9jqKm8mkydlXFacrA48FIW0UpIziE4GTqpFN5H4Sg9\nyqondLIoSkwRua1IIb2ICtt911IUpQwVqWf0Q4ezA0O3ifmozuBLYrs8jvVkGxyJ9T+hNk3AhXSy\n66jKVVYVw1mPKQxduxWINykve8/QdVGNd/zyAebLfdaXF3Rdz/Gtp6hnC2bLA4q6kTkERlM7R9/u\nJHkvKlSkjkkhW/h2qe7nosxBgrtl84N3Aascg3WxuJ1yI6FaJaBAKSVUJC06K9royGYhho4+brCx\ngTOxOaZwvNZpgyuUH9t9nLVQFCITHpHP0kgtra5r+gj2qFhUc0MHbmDv8OksayBAVix0a9nchalQ\nak8+czc2AycDUCp6NiXK0mgV2UDyPSgCmCKWVUaUOTWPyvkxSuwRNNYqikLwToUoYadyglyrMFGM\nKRj6lrZdM5/vyXy5ZkZR1bTbVezeGLISmXIaU9YQI6jHNQX1iTa4kGL9MI4XHnVGxi7koER5uT3d\n5dqbhJmpL07ADGH4j93X0l8V2G7WNN5T1jPqZs7htVvUewcURcFudcHQtxT1XLQqjcG12wh9T+eq\nSekg1ZFA8opRnEhqa4k0neQNUDqHVHLNkMrf6blVLEynvEhC08g/zJ3SYx44NtCq6GltDo1SOEl8\nHbmvdEAk/UipJ9pMxfJWgdIUZSXUtAT6RHRRp7wLYpNuhUeQTO/6+B5jmJiL/nK9PgI53ltUSIps\nJgs1jdqcAvwE7zJIIkYrQ0RMKvQxjknOyw10raOsavFyEdFUSrO+eBhRbof3w+TzcRRlFWcMjp37\nH3U90QaXcqJxM0W1X2BwSe8wFned9GhVVSUKTNZmwvLIMBnZCQmi7zrpqapnc4wpWO4fUi/25EQc\neukTiwMcdTp9A+iijgl/Gr6Ywl9FcNNTe0QdE89P63H2W85xtBiIqGwl3p+Jp71sUGslTPQ+8kJV\nBBUmtKlpch+ikcpnFaKeZIF1YlyaEeXbtpts1GVZMAxkhFE3S+ywZbc9Zbl3I9JEI3NERV8eAoqk\nOAZlLEB7V0XGiUeZgjR5VRglcl0ODz7ai48aLhHuTxNmjZHmU6XHvSB9gaOKtAqDhP3xEEplEUJg\nsTxEm5LEcCmLkt3mIhpSFKZyLpYhNGVVY4oKwtiq9DjWk21wYfqD0H7cYDPfcDmvRURUGy7PTuSE\nLgp2mxXtbiPoZmTAezc2gCYv2XVx3FLM73RR0cwWmLKkaRr6XmW1r2G3yWGtNqUgWd6hC0G4hqEV\nBr4GO5mz7aM3cJGWFlB5/LDUuE0+SBKAQg5HPc4lqb5kTCGf+MQ2Gx3Vyb6mLqZCfv4E76uIaKai\n8xC7IKwd6NsNUsUbeaAhBIqiZr44pO92kq+RQIrR0OXKQBHlJ5Bami40IZhY4pAG1MQGEU89pgYJ\nGJOf5Tnl80gjjyVszHXBeDLJ52HzZwYar4boIUua2V6MkqwoOBvDbrfBWmEgpUtQqqAsC4wuMGUJ\nSsaF+RDQEyWAj7KeaIMLpAEaSU7OZ7RLPqRA3+6y3kRRVqwuz3B2oO+7zPRwMYwb2fkjLJ6S4rqe\nM1vus9y/htaGYbAkYSBgnD0QQxGCfJlBGYZhl4Mq50bOpeRiBq+SCjKgPAGN80o4mUrAFRspXEnU\nRysdOZZJDWtk4ku3QJC8L3ZSjJ3x40mcZ8BNIgSjCrSO3iEIw8PZQbxyHvVlrnxOSmma5pBE3PZK\nDimpgYbY5Q3OdQL8BIf3PUrXklfplO+JlmTiRyY6lrxHIXwzkaNLh0wqb8jrqRwNaB2BNKLcvPJ4\nP9K9jCkpyzofunU9w5iS9foc8JRlk9+P91DXUQEuxPw55pemqESn9DGsJ9rgZMkpb3vZxDaie/sL\n8W7O9rTbFYvlHn27Y3V+KgBJ32VUEgQoMLGhNH2JCb0yRcVi/5DZfCE1tl2HifINySjxHnRBFeeK\nD30nxhGkoVFpHXkfiX4UJ/OYIGz8tJF8IOnUix2kuQPkkHMYLGVZXGlgTfmMkJWnU28CRW4iVZEQ\nIKdx0vgHJdN2jMF5S6E1bdcjWrc+ttwM+f2ksFfaXWLYqDWL5TF4R99fEmyX85uyrGjme7hujbn+\nAkqJerJ3onYWEPKwijKE6fqn4IZS060oA0rSZyJGCYkeliIeORwsBPGiqFHgyRQlWmsGKyF/on21\nu0u8d1RVPalVCmVQG5VHlBVJAlElNvb3AGgCAu8nTUYJGSQ0KwvpENitL1FKsbq8YHV5zubyQhJ3\nQty8qZNXhIBcPw6mEIMoqWYL9vaPqepZbLWJys6miKrGhi4y7pXSdO2KPo5sEph5yDWj4B0BjS5K\n2RYuFnuVQMzWB5HXU4qgoobK5IrTexskiQLIJQTv3djpEKFrZ3t0XZEI3DJso3okr0yorsaFgaSg\n5ZwXaQE3HeQojawhUppS0VlpMKrMn423HSFYvJU+Qje0ktN66RLQFKCcdHmEkAGnsUAeUBNUdvqd\n559i2Jo6EkjTgkLaBzKhVe4n4Xjy+EBGHMtqhlKK3W5NCI6qmstnaDuCKVAafFBSxw2CpA5e5lUI\nKl2SebsfcT3RBiehho9d1WNBFC8NpH0reVpVN1yen7BZXxAI7Npt1icZZcTHzSz1L0VAY8qK+Vxo\nXHsHx6A0zWxO3czouxiWDgPeOuxgOXt4l7pZsHd0IypVeYqqwbs+FtRLrHP4IGGnUhqMqAaDQhuZ\nCRcrdBGPjCgk0/xrfL+5o8COcuIJ9MHp/EypFSkBGj7VAmORfBj66OWizETf0fc9XddmFE6FkJki\nSlLJiScSDRlTGAo9l7yslPpnYQzD7kI0PE0BWhBR7SL5PCqCaYJMnw3JUB4lBU/QVpW0XkYUFK9l\nToH3+Ji3SaqQBGZVBNIkPK7rBmO0dAsQRMk7SBShdWLn6JiryoFihy7S8uKwztiN8TjWE21w5M0X\ni6DOcnlxxnw+wwcR+0z52nazYn1xRl3X7LYb6crOokCP5gMRnTOGqmqoZgsWe4fsHR6zWBxiTMF6\nsxJuZt+x26w4uf8eVVVz7fazEiaFwHxZsb48Zzbfp92ukC/fU9VzjC7p+x1GaeglWbdDDyiUMVkq\nIRGvlVZZ2UtrjbPS/Jq8WyJrw7QrQGeidCozpDDYxufyRLlwJaOF07WnQ8jage12LZ4yGTMKgmL8\nn0gDEv86yjQUKCUF8ECgmh8ydJu4qdNnblFBeJKuvcQpRTM/lCMiTGfZJQMcW5gI6ShhPIDw4DWS\nRnukP04aVGWJVLp3gaoR5Lnv2vx9e+9Fb7MoMEZI20mZzKYm39itkLohgJyafNT1RBuchO3SfLhd\nrVAomtlMGgyHQQrNBNrNJavTh9i+JYRA33exrhQ7xWNukk5/lJRJy7pmvjygWSw5OLpBM98TRatB\nJBQ2qwvuvfMGPniOrj1FPZ8DimaxZD5f0u7WLPaOWF+eSQjpPcFrirIRYwgifaBNJBETxzj5kdZl\nh0FqjGrsRAje4wabZxlc4VqGqyGYI1Bp0e3o11IWSe1HifhLLH7LVNY4ozsxYCIpwHuXR3AJaACC\n0QchcQNGp6GVRLSxiPUyF6+vwJQeZ3t5Pa+yd1IqSAMxgWEoCU4UlHW1JOVrV7/8FNWM3lWAlTR/\nQN6FpAAjI8nFXr+yalAKum5HapAFcHFkWQhFBmucDfGKxtzYmDivIhrfNNT9KOuJNjhCoN2uGWzH\nbL4ApfFRjs57R1nXnD58j836nMvzE9EucQNDDI/SaaVSO71zEtopTVE1zJeHLA+uceP2c9KxjZCl\nN5dnXJw+ZHN5wcG1G+wfXaNrdxhtOL51h8Vin6HvuDg7FTXfeiYjhZ0gm1VVg1JoU7DbrimKMuYb\nHhd8bFx12eBkmH2R23hkNJW/YmxaK4IfQ62qrHOIPXYq+Mi0GMNOFz+DoWspqxq8w7qoiBVD7njn\nSXFd2s+9i4XsxISJTH0Ba6OwT3CZ3QGBer4vAFMymCJqjeRpqdIyo7Siby8kbCvrnK+GGAYnC9Qg\nez3OnRtZ+yp7nxA8eMtgYxjZ7FGUddRm8ehCDhYFmEIMK+W1U5KAgKQyMotJnTERtx/H+tAGpyTY\n/gXg3RDCH1JKvQj8FHAN+EXgvxtC6JXoU/514LcDJ8C/EkJ4Mz7HTwJ/AnDAvxVC+IYiQt7LUI6m\nmefOaQmlJPNZX5wTnOP83ru42KXrrNC3grfYoQNlUGoiKacUypRUzYzDa7doFnvs7R8y2IHVxSmb\ni3NWl+ccHN9g//gWtt+x2645uv4Ut+48i/eezXpF1+2oZzOctcwWS7Y+0DRpHLGJQJrCu8vMmkhG\nL2CFlZDVDhktm458glT+SHmMjnLqsVWlkFpeonQ5ayPtauxg0EbLQMgoSTDYgcIUhDAQpt3UWqPy\nPo6SfnHOXMifubxOymVChFaN1kwbTo0x4wQiNQpApZ7GVBIYhh2maDJNLED8zjYyYDIalEejQ5yp\nrmQOH0qhIm9WiutRzkFJX5tSATf0EdVV2fMZFMFHmhw+HnBRokLLNepCwuOx90m863eCvPxvA18A\n9uPvfw748yGEn1JK/SXEkP5i/O9ZCOEVpdRPxPv9K0qpTwM/AXwGuAP8faXUJ0II7tEXSivpdCSO\nYpI4qIxiszpndXHC6vwh5xeniNJSy3p1CYRR/syAj3UzIkSuTcFseUCz2GOxf0Tb7fDOcbFeUVYN\n1249DQHa9QXzvX2efuEVmsU+u/Ulu+0GG1ntZVUj4jsJTYzamNbh3BAVk11EBCOReoiqW1OpdMih\nZLAuTwBKAqlp1HDqik4GICf0GAqNtTOVO9C1Unit8UNAKUcfa3hCXwpiQDlXkgGNChWJ0ib3tKFG\nSQsp6CdFZjJjJUH4xujYVhQbR1OJJELsLnqbslpmFDIEHylwojmjkud2HapcAGBdRFhNiY7hYCDI\nqGOtKYpawmTnZHSwivU6RWS5OLwDRbxm5SHINKQUvoo6dAJg5FpHdPWjrw+rvPwM8C8D/0n8XQG/\nF0hzBf4aIpUHInX+1+LPfwv45+P9fxz4qRBCF0J4A1H1SlqWX3clOJ8Qss6/DNewnJ/cExmz0weA\nJLVp2HtSAZYE2ubTb8r0mC33WSwPKMuS7WbNbrtluX9EUZRsV4J2PvfK9/HKZ34IU9Rcnp2wXa8Y\nIvm5bhZUjaCZ0oEshuedkKT7tr2ilpz6+nyWXHfZ6FKzqAqSY1xt33GxDORzLpZJyn6a3411OKVS\nV3ikmIWrE27SZwHIXLZMFkmMnjgnIXaRi7qRyqQDIHY25A1CSu4yawMVPdsowZ4I2FoVlNUCldk1\nqSG3wJg5RbmkLBcCnERPmkLWNDM8vQ9vLaBic6knBBtLBmPYTvAQPy9nB4H/Ix1wsF2OMvq+lSGU\nUYYwyy86GwGvj74+rIf7D4H/KbAXf78GnIcQ0szYqWx5ljQPIVil1EW8/9PAz06e8wOlzoF/HeDG\nzZv00YiItbj5Yk/Uf/uO87MT+m4XTyDY7bosryA1q6gdGYycakqAA6UMKGGDi9esKIqa1eUZZVFx\n54WXufPsS3gfWF+cxVnXAz4E6tmcsqzlVI7S3oLaafrBiiamHaKil4xkaNudDL/wNjbTpn8juOGG\n4QqcncIgCAStBDMA8NIDmGhjBpELnArGSigu3dh1VRFsyHSyaFPkuQeTonL6Jx4tyR9EL5bLAsII\nGT2sxmidc7RseEh9O806l9w78iij8BMKdKHzY67+JxCCtFh511KoJhbyzdiG5YRap3WcDmvGnM7j\n0arM71vI0XFssnNZTEpCWTG+oqhFC8YneftxZt20cfijrA8zruoPAfdDCL+olPo9j+VVv8EKIfxl\n4C8DvPLKqyEV+9Np3tSSp203KxKBVeS3h0zlElpWQrJkJphSCoyMq9VFJeyM4JnPl5yfPEABt555\nnude/j6qesZ2u2a3XqEQ71lWNc1sGZPpIPLjQSaztLsNQ5QAt33HYDv6bsfQ76T/ruvp+pZhaHFR\n/Xk6DSgdKM47qbWR6nFp3LGPNawx/Bz6Husdxhuc9/lwUWqc3CpGAT7sACeGGQLehcnr9mjjwQ1o\nJZtcqejZ6FGqkG6GGC1IiKWluK+lBUjpOLZZwdhFkFgy5NAy+DH0DD6W/HVSKAvRK461R6UshfEE\nt2HwLaaYUZQNILosZVkIZzJ0sUTh8mep0Cg1oCgJPh4CWmOtcDmJt8l8B4MvCpxr8T51jMf8lTij\nIXz7+uF+J/DfVEr9QaBBcri/ABwqpYro5aay5UnS/B0lfJ0DBDz5lqXOX3/9tfUf/kP/8pe+hev5\nblnXgYff6TfxT2H9Vr+u5z/yM6XT5MP8A34P8Lfjz/834Cfiz38J+Dfiz38S+Evx559AlJpBwJJf\nQQY7vgh8BTDf5PV+4Vt5f98t/z6+ru+uf4/zuj5KHe7fAX5KKfVngF8C/kq8/a8A/6lS6jXgNBod\nIYRfV0r9TeDzSC/FnwzfAKH8eH28fisuFS34iVxKqV8IIfzwd/p9PO718XV9d63HeV2PJxP8p7f+\n8nf6DfxTWh9f13fXemzX9UR7uI/Xx+u32nrSPdzH6+P1W2p9bHAfr4/Xt3E9sQanlPoDSqkvKaVe\nU0r9qe/0+/lmSyn1V5VS95VSvza57Vgp9TNKqS/H/x7F25VS6n8fr+1zSqkfmjzmj8f7f1kp9ce/\nE9cyXUqpZ5VS/1Ap9Xml1K8rpf7tePt37bUppRql1M8ppX4lXtO/H29/USn1j+N7/xtKyXwipVQd\nf38t/v2FyXP9ZLz9S0qpf/Gbvvh3usbxAXUPA7wOvARUSP3u09/p9/VN3vPvBn4I+LXJbf8b4E/F\nn/8U8Ofiz38Q+LsIkeHHgH8cbz9G6pPHwFH8+eg7fF1PAT8Uf94DfgP49HfztcX3tow/l8A/ju/1\nb3K1tvw/ij//G1ytLf+N+POnuVpbfp1vVlv+Tm/UD/hAfgfw9ya//yTwk9/p9/Uh3vcLjxjcl4Cn\nJhv3S/Hn/xj4o4/eD/ijwH88uf3K/Z6Ef8B/jsx5/y1xbcAc+CfAjyJskuLRPYjMov8d8eci3k89\nui+n9/ugf09qSJkJ0HF9XaLzd8G6FUJ4P/58F7gVf/6g63uirzuGUv8M4hG+q69NKWWUUr8M3Ad+\nBvFO5+FDEPKBKSH/W7qmJ9XgfsutIEfgd20NRim1BP7vwP84hHA5/dt347WFEFwI4QcRTu+PAJ/6\ndrzuk2pw3zLR+Qld95RSTwHE/96Pt3/Q9T2R162UKhFj+7+EEP4f8ebfEtcWQjgH/iESQh6qUSDz\n6xHy+aiE/CfV4H4eeDWiRhWSqP70d/g9/WbWTwMJjfvjSP6Tbv9jEdH7MeAihmd/D/j9SqmjiPr9\n/njbd2zF5uG/AnwhhPAfTP70XXttSqkbSqnD+PMMyUm/gBjeH4l3e/Sa0rX+EeAfRK/+08BPRBTz\nReBV4Oe+4Yt/p5PWb5DM/kEEEXsd+He/0+/nQ7zf/wx4HxiQWP5PIHH+/xv4MvD3geN4XwX8R/Ha\nfhX44cnz/GtIN/xrwL/6BFzXP4eEi58Dfjn++4PfzdcG/DaEcP854NeA/0W8/aVoMK8h3TB1vL2J\nv78W//7S5Ln+3XitXwL+pW/22h9Tuz5eH69v43pSQ8qP18frt+T62OA+Xh+vb+P62OA+Xh+vb+P6\n2OA+Xh+vb+P62OA+Xh+vb+P62OA+Xh+vb+P62OA+Xh+vb+P6/wMryY53xw4R3gAAAABJRU5ErkJg\ngg==\n"
}
}
],
"source": [
"plt.imshow(np.concatenate([hani_left,hani_right],axis=1))"
],
"id": "2d50224c-6eca-4c29-8193-592bbccdbc34"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 7. Naive Bayes classifier (120점)\n",
"\n",
"> ref:\n",
"> \n",
"\n",
"아래의 데이터프레임은 날씨, 도로 상태, 교통 상황, 엔진 문제 및 사고\n",
"여부와 같은 여러 가지 변수를 포함하는 10개의 행과 5개의 열로\n",
"구성되어있다."
],
"id": "28124790-9105-4e2e-afce-e5df1c0f7ecc"
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [],
"source": [
"df = pd.DataFrame({\n",
" 'WeatherCondition': ['rain', 'snow', 'clear', 'clear', 'snow', 'rain', 'rain', 'snow', 'clear', 'clear'],\n",
" 'RoadCondition': ['bad','average','bad','good','good','average','good','bad','good','bad'],\n",
" 'TrafficCondition': ['high','normal','light','light','normal','light','normal','high','high','high'],\n",
" 'EngineProblem': ['no','yes','no','yes','no','no','no','no','yes','yes'],\n",
" 'Accident': ['yes','yes','no','yes','no','no','no','yes','no','yes']\n",
"})"
],
"id": "7889f90f-0b74-470b-82f4-746993568907"
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {},
"outputs": [],
"source": [
"df"
],
"id": "f2d8135b-4a6a-4552-b308-81297500ed1e"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"각 열에 대한 설명은 아래와 같다.\n",
"\n",
"- ‘WeatherCondition’: 각 행에서 기록된 날씨 조건을 설명하며, ’rain’은\n",
" 비, ’snow’는 눈, ’clear’는 맑은 날씨를 나타낸다.\n",
"- ‘RoadCondition’:각 행에서 기록된 도로 상태를 설명하며, ’bad’는 안\n",
" 좋은, ’average’는 보통, ’good’은 좋은 도로 상태를 나타낸다.\n",
"- ‘TrafficCondition’:각 행에서 기록된 교통 상황을 설명하며, ’light’는\n",
" 움직이기 쉬운, ’normal’은 평균, ’high’는 교통이 많은 상황을\n",
" 나타낸다.\n",
"- ‘EngineProblem’: 각 행에서 기록된 엔진 문제 여부를 설명하며, ’yes’는\n",
" 문제가 있음을 나타내고, ’no’는 문제가 없음을 나타낸다.\n",
"- ‘Accident’: 각 행에서 기록된 사고 여부를 설명하며, ’yes’는 사고가\n",
" 있음을 나타내고, ’no’는 사고가 없음을 나타낸다.\n",
"\n",
"우리는 ‘WeatherCondition’, ‘RoadCondition’, ‘TrafficCondition’,\n",
"‘EngineProblem’ 를 이용하여 ‘Accident’ 행의 값이 yes일지 no일지를\n",
"판단하는 일에 관심이 있다고 하자. 아래의 (1)-(4) 이러한 분류를 수행하는\n",
"방법을 구체화 한 것이다. (1)-(4)의 물음에 답하라.\n",
"\n",
"`(1)` 주어진 자료에서 $P({\\tt Accident == no})$를 계산하여라.\n",
"\n",
"**hint**: `Accident=='no'인 데이터수 / 전체데이터수`를 계산하면 되며\n",
"답은 0.5이다.\n",
"\n",
"`(풀이)`"
],
"id": "82ac41f8-c28b-44a8-9b9e-55fc4ca61083"
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [],
"source": [
"len(df.query('Accident==\"no\"')) / 10"
],
"id": "c3f6e11d-dd3b-4f53-b9c7-f86dcd4b8ce4"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(2)` 아래와 같은 조건부 확률은\n",
"\n",
"$$P({\\tt WeatherCondition == rain} ~|~ {\\tt Accident==no})$$\n",
"\n",
"아래와 같이 계산한다고 하자."
],
"id": "6850cd95-6242-4805-a761-75d2096e2176"
},
{
"cell_type": "code",
"execution_count": 508,
"metadata": {},
"outputs": [],
"source": [
"# 방법1\n",
"len(df.query('WeatherCondition == \"rain\" and Accident == \"no\"'))/len(df.query('Accident==\"no\"'))"
],
"id": "6f93a7c6-93e0-4592-a253-a3dade3bb9bf"
},
{
"cell_type": "code",
"execution_count": 509,
"metadata": {},
"outputs": [],
"source": [
"# 방법2\n",
"((df['WeatherCondition'] == 'rain') & (df['Accident']== 'no')).sum() / (df['Accident']== 'no').sum()"
],
"id": "ece6d9bf-df12-4314-9148-3bdd4a896d64"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"이와 유사한 방식으로 아래를 계산하라.\n",
"\n",
"- $P({\\tt WeatherCondition == rain} ~|~ {\\tt Accident==no})$\n",
"- $P({\\tt WeatherCondition == snow} ~|~ {\\tt Accident==no})$\n",
"- $\\dots$\n",
"- $P({\\tt EngineProblem == no} ~|~ {\\tt Accident==yes})$\n",
"- $P({\\tt EngineProblem == yes} ~|~ {\\tt Accident==yes})$\n",
"\n",
"`(풀이1)`"
],
"id": "faf24af8-efe2-4e15-bb09-dc044057e99a"
},
{
"cell_type": "code",
"execution_count": 316,
"metadata": {},
"outputs": [],
"source": [
"*cond, _ = df.columns\n",
"{'P({}={}|Accident={})'.format(i,j,k): ((df[i]==j)&(df['Accident']==k)).sum()/(df['Accident']==k).sum() for i in cond for j in set(df[i]) for k in ['no','yes']}"
],
"id": "e7843644-3a79-43b4-864a-3efb8e3a3f0c"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(풀이2)`"
],
"id": "c6b0edad-4417-4cc8-a46c-b6162fed36f5"
},
{
"cell_type": "code",
"execution_count": 386,
"metadata": {},
"outputs": [],
"source": [
"dct = {(j,k):((df[i]==j)&(df['Accident']==k)).sum()/(df['Accident']==k).sum() for i in cond for j in set(df[i]) for k in ['no','yes']}\n",
"dct"
],
"id": "62908351-57bd-466f-8424-1aaac9554a8a"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(3)` 아래와 같은 새로운 상황이 발생하였다고 가정하자.\n",
"\n",
"- ${\\tt WeatherCondition==rain}$\n",
"- ${\\tt RoadCondition==good}$\n",
"- ${\\tt TraffictCondition==normal}$\n",
"- ${\\tt EngineProblem==no}$\n",
"\n",
"아래를 각각 계산하라.\n",
"\n",
"$\\begin{align} A&=P({\\tt Accident == yes})\\\\ &\\times P({\\tt WeatherCondition==rain~ |~ Accident == yes}) \\\\ &\\times P({\\tt RoadCondition==good~|~ Accident == yes}) \\\\ &\\times P({\\tt TrafficCondition==normal~ |~ Accident == yes}) \\\\ &\\times P({\\tt EngineProblem=no~ |~ Accident == yes}) \\end{align}$\n",
"\n",
"$\\begin{align} B&=P({\\tt Accident ==no})\\\\ &\\times P({\\tt WeatherCondition==rain~ |~ Accident == no}) \\\\ &\\times P({\\tt RoadCondition==good~|~ Accident == no}) \\\\ &\\times P({\\tt TrafficCondition==normal~ |~ Accident == no}) \\\\ &\\times P({\\tt EngineProblem=no~ |~ Accident == no}) \\end{align}$\n",
"\n",
"여기에서 $\\frac{A}{A+B}$와 $\\frac{B}{A+B}$를 각각 주어진 상황에 대하여\n",
"사고가 날 확률, 사고가 나지 않을 확률을 의미한다고 하자. 주어진 상황에서\n",
"사고가 날 확률은 얼마인가?\n",
"\n",
"**hint:** 답은 1/25\n",
"\n",
"`(풀이)`"
],
"id": "9a8906c8-d3f0-455f-a9e3-c0eda60ef894"
},
{
"cell_type": "code",
"execution_count": 388,
"metadata": {},
"outputs": [],
"source": [
"dct = {(j,k):((df[i]==j)&(df['Accident']==k)).sum()/(df['Accident']==k).sum() for i in cond for j in set(df[i]) for k in ['no','yes']}\n",
"dct"
],
"id": "4b7a2b7b-4da1-46df-82d0-14bc88e9be02"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- dct의 키는\n",
" `(WeatherCondition~EngineProblem의 라벨, Accident의 라벨)`로\n",
" 이루어짐"
],
"id": "272bc539-acc1-48e6-bd94-e34ce192ddb4"
},
{
"cell_type": "code",
"execution_count": 389,
"metadata": {},
"outputs": [],
"source": [
"A = dct['rain','yes']*dct['good','yes']*dct['normal','yes']*dct['no','yes']\n",
"B = dct['rain','no']*dct['good','no']*dct['normal','no']*dct['no','no']"
],
"id": "4d27a64f-fb0c-4f8e-a1bc-2f11641935de"
},
{
"cell_type": "code",
"execution_count": 390,
"metadata": {},
"outputs": [],
"source": [
"A/(A+B) # 실제정답은 0.04, 0.000000000000000015는 에러"
],
"id": "ad6651c0-67fd-4afa-8ae4-cd5cd7be18b2"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(4)` 모든 상황에 대하여 사고가 날 확률을 구하여라.\n",
"\n",
"`(풀이1)`"
],
"id": "90b077f1-1fb3-4839-a74b-e7dcaf22a85f"
},
{
"cell_type": "code",
"execution_count": 405,
"metadata": {},
"outputs": [],
"source": [
"W = set(df.WeatherCondition)\n",
"R = set(df.RoadCondition)\n",
"T = set(df.TrafficCondition)\n",
"E = set(df.EngineProblem)"
],
"id": "574fead6-76a4-4e23-b6a7-42a2985e225f"
},
{
"cell_type": "code",
"execution_count": 406,
"metadata": {},
"outputs": [],
"source": [
"df2 = pd.DataFrame([[w,r,t,e,dct[w,'yes']*dct[r,'yes']*dct[t,'yes']*dct[e,'yes'],dct[w,'no']*dct[r,'no']*dct[t,'no']*dct[e,'no']] for w in W for r in R for t in T for e in E])\n",
"df2.columns = pd.Index(['WeatherCondition','RoadCondition','TrafficCondition','EngineProblem','A','B'])\n",
"df2.eval('Prob = A/(A+B)')"
],
"id": "8adab597-37cb-44d1-8a8a-476df277d125"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(풀이2)` – 좀 더 일반적인 풀이"
],
"id": "17bb3379-fe14-481d-b999-df6a6d766074"
},
{
"cell_type": "code",
"execution_count": 410,
"metadata": {},
"outputs": [],
"source": [
"import itertools\n",
"lst = []\n",
"for cond_details in itertools.product(*[set(df[col_name]) for col_name in cond]):\n",
" A=1;\n",
" B=1;\n",
" for c in cond_details:\n",
" A = A* dct[c,'yes']\n",
" B = B*dct[c,'no']\n",
" lst.append([*cond_details,A,B,A/(A+B)])"
],
"id": "df91c516-3622-4b84-8e1b-64918227b931"
},
{
"cell_type": "code",
"execution_count": 411,
"metadata": {},
"outputs": [],
"source": [
"df2 = pd.DataFrame(lst)\n",
"df2.columns = pd.Index(['WeatherCondition','RoadCondition','TrafficCondition','EngineProblem','A','B','Prob'])\n",
"df2"
],
"id": "1b48a439-dcd9-4f7a-911d-fdd067ffe778"
}
],
"nbformat": 4,
"nbformat_minor": 5,
"metadata": {
"kernelspec": {
"name": "python3",
"display_name": "Python 3",
"language": "python"
},
"language_info": {
"name": "python",
"codemirror_mode": {
"name": "ipython",
"version": "3"
},
"file_extension": ".py",
"mimetype": "text/x-python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.16"
}
}
}