wordle.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "26798d70",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Wordle\n",
    "\n",
    "\n",
    "首先引入需要的库，定义文件存储位置和一些常量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "761344b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "import json\n",
    "import statsmodels.graphics.tsaplots as tsaplots\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "import seaborn as sns\n",
    "\n",
    "DATA_DIR = \"data\"\n",
    "IMG_DIR = \"img\"\n",
    "WORDLE_DATA_FILE = os.path.join(DATA_DIR, \"Problem_C_Data_Wordle.xlsx\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fac7c61",
   "metadata": {},
   "source": [
    "## 第一问\n",
    "\n",
    "### 题目概览\n",
    "\n",
    "**English**\n",
    "\n",
    "The number of reported results vary daily. Develop a model to explain this variation and use your model to create a prediction interval for the number of reported results on March 1, 2023. Do any attributes of the word affect the percentage of scores reported that were played in Hard Mode? If so, how? If not, why not?\n",
    "\n",
    "**中文**\n",
    "\n",
    "报告结果的数量每天都在变化。建立一个模型来解释这种变化，并使用你的模型为2023年3月1日的报告结果数量建立一个预测区间。词语的任何属性是否影响到报告的在困难模式下进行的分数的百分比？如果是，如何影响？如果没有，为什么没有？\n",
    "\n",
    "\n",
    "- 建立模型，解释变化原因、建立预测区间\n",
    "\n",
    "- 分析词语的属性是否影响了report number of hard/totol report number, 解释原因\n",
    "\n",
    "### 解题思路\n",
    "\n",
    "**模型选择**\n",
    "\n",
    "本题是与时间相关的预测问题，对随时间变化的数据进行建模和预测可以考虑使用时间序列预测模型。\n",
    "\n",
    "根据数据，报告数量随着时间有先增后减的变化，从wordle游戏的背景上来看，这显然是由于wordle这个游戏在社交网络上爆火所造成的。在突发事件导致时间序列数据先增后减的情况下，如果突发事件对后续数据产生了持续性影响，即使数据出现了变化，也不需要进行平稳化处理。这是因为平稳化处理的目的是消除时间序列数据的趋势和季节性变化，使数据更加稳定。但如果突发事件导致了持续性影响，这种稳定性就失去了意义。\n",
    "\n",
    "因此，在这种情况下，需要建立时间序列模型时，可以考虑使用带有趋势项的模型，如ARIMA模型。这样可以较好地捕捉数据的趋势变化，进而进行预测。当然，建立模型时，需要根据数据的特点进行具体选择，并结合模型的诊断结果进行优化调整，以提高预测的准确性。\n",
    "\n",
    "> 模型背景补充：\n",
    "> 自回归积分移动平均模型（ARIMA）是一种用于时间序列分析和预测的经典方法，它通过对时间序列数据的自相关性、差分运算和移动平均来捕捉时间序列的模式，并进行预测。在 ARIMA 模型中，自回归部分 AR 用于捕捉序列的自相关性，移动平均部分 MA 用于捕捉序列的滞后效应，积分部分 I 用于处理非平稳时间序列。\n",
    ">\n",
    "> ARIMA 模型在一定程度上可以用于预测时间序列的趋势。具体而言，ARIMA 模型中的 AR 部分和 I 部分可以用于捕捉时间序列的长期趋势，而 MA 部分可以用于捕捉时间序列的短期波动。因此，当时间序列的趋势较为平滑且没有明显的季节性波动时，ARIMA 模型可以通过调整其参数来预测时间序列的趋势。但是，在时间序列存在较为明显的季节性波动时，ARIMA 模型的预测效果可能会受到影响。\n",
    "> \n",
    "> 需要注意的是，ARIMA 模型的预测效果还受到很多因素的影响，例如时间序列的数据质量、模型参数的选择、模型的拟合效果等。在使用 ARIMA 模型进行趋势预测时，需要对时间序列数据进行适当的处理和模型参数的调整，以获得更准确的预测结果。\n",
    "\n",
    "\n",
    "\n",
    "题目数据中一共有359天的数据，考虑使用320天数据作为训练集，30天数据作为测试集。模型训练完成后直接预测3月1日。\n",
    "\n",
    "**模型测试**\n",
    "\n",
    "一共使用两种数据进行模型测试：\n",
    "\n",
    "- 使用预先分配出来的测试集的数据进行测试\n",
    "\n",
    "- 使用网络爬取的wordle单词搜索热度（搜索结果条数）进行测试，具体方法：归一化+距离度量\n",
    "\n",
    "**TODO LIST**\n",
    "\n",
    "- [ ] ARIMA时间序列预测，模型建立与训练\n",
    "- [ ] 爬取wordle每日热度，制作每日热度图\n",
    "- [x] 模型测试"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12f80242",
   "metadata": {},
   "source": [
    "首先先来看一下题目给出的数据，绘制日期和总报告数量的趋势图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "115da48c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = pd.read_excel(WORDLE_DATA_FILE)\n",
    "date = data[\"Date\"]\n",
    "total_num_repo = data[\"Total-num-repo\"]\n",
    "trend = [date, total_num_repo]\n",
    "# 绘制趋势图\n",
    "plt.plot(date, total_num_repo)\n",
    "plt.show()\n",
    "plt.savefig(os.path.join(IMG_DIR, \"arima.png\"))  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43dd7963",
   "metadata": {},
   "source": [
    "原始数据是时间序列相关数据，首先要对数据的随机性和平稳性进行检测，这两个检测是时间序列预测的重要部分。根据不同检测结果需要采取不同的分析方法。\n",
    "\n",
    ">  为什么时间序列要求平稳性呢？平稳性就是要求由样本拟合出的曲线在未来一段时间内仍然能够以现有的形态和趋势发展下去，这样预测结果才会有意义。\n",
    ">\n",
    "> 对于平稳序列， 它的均值和方差是常数， 现已有一套非常成熟的平稳序列的建模方法。 通常是建立一个线性模型来拟合该序列的发展 借此提取该序列的有用信息。\n",
    ">\n",
    "> 对于非平稳序列， 由于它的均值和方差不稳定， 处理方法一般是将其转变为平稳序列，这样就可以应用有关平稳时间序列的分析方法， 如建立ARIMA模型来进行相应的研究，或者分解趋势与季节性等并根据情况应用指数平滑模型等。\n",
    "> \n",
    "> 对于纯随机序列，又称为白噪声序列，序列的各项之间没有任何相关关系，序列在进行完全无序的随机波动，可以终止对该序列的分析。白噪声序列是没有信息可提取的平稳序列。\n",
    "\n",
    "\n",
    "前面从主观的数据趋势初步确定了需要使用ARIMA进行时间序列预测，为了确定是否真的可以使用这个模型，我们需要先对数据的平稳性和随机性进行检验。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da26d480",
   "metadata": {},
   "source": [
    "### 平稳时间序列的检验\n",
    "\n",
    "目前，对时间序列的平稳性检验主要有两种方法，一种是图检法，即根据时序图和自相关图进行直观判断，另一种是构造检验统计量的方法，有单位根检验法等方法。\n",
    "\n",
    "**图检法**\n",
    "\n",
    "我们可以通过自相关图来进行检验，对于平稳时间序列，其自相关图一般随着阶数的递增，自相关系统会迅速衰减至0附近，而非平稳时间序列则可能存在先减后增或者周期性波动等变动。\n",
    "\n",
    "参考文章：\n",
    "[时间序列（二）：时间序列平稳性检测](https://smilecoc.vip/2021/01/15/time_series_part2_stability/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "017a7f77",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jxug3v/mNJKmkpERFRUX+/sOHD9f69eu1adMm/eAHP9BDDz2kJ554QjNmzPD3ycrK0quvvqoXX3xRo0ePVn5+vlavXq0JEyaE8lDaJK3Jvo3cS844qXAjha4yRMWpQaiCUygrQ3/ZXqyL/rBJz7//b725+6Cef//fuugPm/TXE6xiAYBZhbSCM2XKlBb/gEhSfn5+UNvkyZP18ccftzrutddeq2uvvfZkpxcWQlEZCtW44VZx8genFio4J71U18GVoabByT/2ka8L1+zWucMGnNTvj8oQADPpVntw0LyOrgyFatxwqzjNHJfaagWnuy3VhWovUuPYVIYAmEm3OosK4S+cKk6NwWlhY1VEDcHJkNExS3UdXBnqjCU1KkMAzIKAgw53bGUoPqZj/jMLxbjhtFQXbktqjWOHarM1ALSGJSr0eOGyVBduS2qchg+gKxFwgBC4blyq3rzrh/7nP/nhML13z5STqlqE29lv7BkC0JVYogJCpKcvqbFnCEBXooIDhJlwWVKjMgSgK1HBAUBlSFSGALOhggNAEpUhKkOAuVDBARAyVIaoDAFdhQoOgJCiMkRlCOgKVHAAhB0qQ1SGgOOhggMgLFEZojIEtIYKDgAcQWWIyhDMgwoOADRBZYjKEMyBgAMAIRaKW3dwbzKgdQQcAOgEVIZCVxmSuPkqgrEHBwDCFHuGGvxle7F+uWa3LBaLDMOQxWLRc5u/0tIZo0+qSobwRgUHAMJYT68MhXrpi8pQ+CLgAAAChNOeITZFoyUEHABAkHCpDLEpGi1hDw4AoFOEYs+Qf+mrmZDTIZuiWxh39fZiLbx0xAmNLXE9oM5AwAEAdJpjK0PxMSf3Z4hN0WgJS1QAgLDFpmi0hIADAAhrbIo+irO+jmKJCgAQ9jp66auxMrSw8b5caqgMGTK65aZoiaWvYxFwAABoRjhtiuYmqcFYogIAoAUdfbp8OC59hev1gAg4AAB0Eq4H1HkIOAAAdKJQbIoO15ukhhIBBwCAThYuS1+h3BQdagQcAADCXLhdD6gzEHAAADCBcLoeUGcg4AAAYBLhcpPUzsB1cAAAQItCcT2gztApFZynn35aw4cPV2xsrDIyMvTBBx+02Pfmm2+WxWIJeowaNcrfJz8/v9k+DoejMw4HAIAepaMrQ50h5AFn9erVWrBggX71q19p586dmjRpkqZNm6aioqJm+z/++OMqKSnxP4qLizVgwABdd911Af369u0b0K+kpESxsbGhPhwAABAGQh5wHn30Uc2dO1e33HKLzjrrLC1btkypqal65plnmu1vs9mUlJTkf2zfvl0VFRX6yU9+EtDPYrEE9EtKSgr1oQAAgDAR0oDjcrm0Y8cOZWdnB7RnZ2dry5YtbRpjxYoVuvjii5WWlhbQXlNTo7S0NA0ZMkRXXHGFdu7c2eIYTqdTdrs94AEAAMwrpAGnrKxMXq9XiYmJAe2JiYkqLS097vtLSkr01ltv6ZZbbgloHzFihPLz87Vu3TqtWrVKsbGxOu+887Rv375mx8nLy5PNZvM/UlO772ltAADg5HXKJuNjLxLUeBv348nPz1e/fv10zTXXBLRPnDhRN954o8455xxNmjRJf/nLX3TGGWfoySefbHacRYsWqaqqyv8oLu6+l5YGAAAnL6SniSckJCgyMjKoWnPo0KGgqs6xDMPQCy+8oJycHMXExLTaNyIiQueee26LFRyr1Sqr1dq+yQMAgLAV0gpOTEyMMjIyVFBQENBeUFCgrKysVt+7efNmffnll5o7d+5xv49hGNq1a5eSk5NPar4AAMAcQn6hv9zcXOXk5GjcuHHKzMzU888/r6KiIt12222SGpaPvv32W61cuTLgfStWrNCECROUnp4eNOaSJUs0ceJEnX766bLb7XriiSe0a9cuPfXUU6E+HAAAEAZCHnBmzZql8vJyPfjggyopKVF6errWr1/vPyuqpKQk6Jo4VVVVWrNmjR5//PFmx6ysrNStt96q0tJS2Ww2jRkzRu+//77Gjx8f6sMBAABhoFNu1TB//nzNnz+/2dfy8/OD2mw2m+rq6loc77HHHtNjjz3WUdMDAAAmw802AQCA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6UR19QQAAED4MwxDbq8hr8+QIUPxMV0bMQg4AABAUkNI8fgaQorb65PX1/C8ut7j7/PV4VrFREbI4/Md6dfQ3+sz/H16W6N09hBbVxyCHwEHAAATcri98hmSx+trNrQc+9zjDQwpx47VqKzaqdjoyM46jBNGwAEAIEw0hhKnxyeXxyeXt+Gr+8jXqnq3v+8nxVVhEURChYADAEA30BhSmgYX1zFtHm/zFZZGLo+vk2bb/RFwAAAIsWPDSmWdy//aruJKRVosamF1CCeIgAMAwEloWnk5unTkPfpvjy8ovDTd0+J0+3r0UlKoEHAAAGiBx3t0yeeQ3anICJc/uDg93mbDC7oHAg4AoMdqDCrOJhWYxuDi9PhU4zh6evT+sloqLWGEgAMAMCWfz5DL65PTfTTEUH3pOQg4AICw5PUZDcHF7VNl3dHTo784aJfFIrk8pJeejIADAOiWfD7Dv2Tk9ARWYhxur9xNTpluumm32uFhKQkEHABA1/D5DNW7vM0GmIYlJCowOHEEHABAyLg8PjmOLCM53F5V1h+9/su2ryuotCBkIjrjmzz99NMaPny4YmNjlZGRoQ8++KDFvps2bZLFYgl6/O///m9AvzVr1mjkyJGyWq0aOXKk1q5dG+rDAAAco7EKU1HrUmmVQ1+X1WpvabU+Ka7Uv/Z/rx3fVOjzb+368lCNDlTUq6zadfxBgQ4Q8grO6tWrtWDBAj399NM677zz9Nxzz2natGn64osvNHTo0Bbft3fvXvXt29f/fNCgQf5/FxYWatasWXrooYc0ffp0rV27VjNnztSHH36oCRMmhPR4AKCncXt9qna4/XtfGr863A33QDJYSUI3FPKA8+ijj2ru3Lm65ZZbJEnLli3T22+/rWeeeUZ5eXktvm/w4MHq169fs68tW7ZMl1xyiRYtWiRJWrRokTZv3qxly5Zp1apVHX4MAGB2jUtJDnfDctL3TW4l8PE3lSwlIeyENOC4XC7t2LFDv/zlLwPas7OztWXLllbfO2bMGDkcDo0cOVK//vWvdcEFF/hfKyws1N133x3Qf+rUqVq2bFmzYzmdTjmdTv9zu93eziMBgPDXNMQ4XE3+7fbJe8wFYZqelQSEo5AGnLKyMnm9XiUmJga0JyYmqrS0tNn3JCcn6/nnn1dGRoacTqf+9Kc/6aKLLtKmTZt0/vnnS5JKS0vbNWZeXp6WLFnSAUcEAN2bP8S4GoJLayEGMLNOOYvKYrEEPDcMI6it0ZlnnqkzzzzT/zwzM1PFxcX6/e9/7w847R1z0aJFys3N9T+32+1KTU1t93EAQHfg8fpUfyS0VNQeXUra/nWFoiM75dwRoNsLacBJSEhQZGRkUGXl0KFDQRWY1kycOFEvv/yy/3lSUlK7xrRarbJare2YOQB0LcMw5HA3Bhmv6t1e/zVjml4fpulSktdniK0yQIOQRv2YmBhlZGSooKAgoL2goEBZWVltHmfnzp1KTk72P8/MzAwa85///Ge7xgSA7sDl8amq3q3v7A59U16r/y21a2dRhbbu/167iiu1t7Ra35TX6ZDdqWqHh4vfAW0U8iWq3Nxc5eTkaNy4ccrMzNTzzz+voqIi3XbbbZIalo++/fZbrVy5UlLDGVLDhg3TqFGj5HK59PLLL2vNmjVas2aNf8yf//znOv/887V06VJdffXVev311/XOO+/oww8/DPXhAEC7+XyG6lxH70r91eEaybDI4fHK4yWwAKEQ8oAza9YslZeX68EHH1RJSYnS09O1fv16paWlSZJKSkpUVFTk7+9yuXTvvffq22+/VVxcnEaNGqU333xTl112mb9PVlaWXn31Vf3617/W/fffr9NOO02rV6/mGjgAulTj3pj6I2cp1bk9R5aVfKp3HV1KKqt2cdo1EGKdssl4/vz5mj9/frOv5efnBzz/xS9+oV/84hfHHfPaa6/Vtdde2xHTA4B2cXl8/j0xTb+6PL6unhqAI7gXFQC0oPGid/XuwCDDshLQ/RFwAPR4jiPhpc7t1fe1Ry8K+klxFUtJQJgi4ADoMZyeI0GmydJSncsbcAE8ruALmAMBB4DpuL2+hhDj8qrO5fEHGpaWgJ6DgAMg7B22O2XIeSTIcK0YAAQcAGHC4W5YTqp1NlRkmu6V+XdZLXtlAAQg4ADoVnw+Q3Vur+qcHtUeCTTNLS853JySDaBlBBwAXcbp8arO6Q0INA63VwYrTABOEgEHQKc5XO2UYTTslalzeeRm0y+AECHgAOhQjUtMtU6Pap0elde4/K/9+zB7ZQB0DgIOgBPWNMzUOD0Ny00uj5pcVobrygDoEgQcAG3i8xmqPXJNmZoj1Zk6F/tlAHRPBBwAQXw+Q9UOt2qdXtW6CDMAwg8BB+jhDMNQncursuqj15XZ/k2FrFHslQEQvgg4QA/j8vhU4/SoxuFRtbOhSuP1GQF7ZajUAAh3BBzAxHw+QzWuhjBT4/So2uGRy8MF8gCYHwEHMJF6l1fVTrdqHB7//hmqMQB6IgIOEMYqa90qr3E1LDk5PdwtGwCOIOAAYcLh9srucOtQk83Ae7+r5sJ5ANAMAg7QDTWe2VTt8MjucKva4ZbL01Cd4cJ5AHB8BBygG/D5DFU7Pap2uFXtYLkJAE4WAQfoAh6vT9UOj79CU+sMvL0BAODkEHCATuD0eP1LTtUON1cFBoAQI+AAIeDy+FRWffQu2ruKqtgMDACdiIADdACP1ye7w6Oqereq6t2qd3nZDAwAXYiAA5yAxk3B9iOBpsbJBfUAoDsh4ABtYBiGal3ehgpNXcNp22wKBoDui4ADtKD+SKCxOxqqNJy2DQDhg4ADNFFW7ZLL61BVvZubUgJAGCPgoMcyjIZ9NCUVDn/bV4drONsJAEyAgIMexeP1qbLerco6lyrr3HJ7Dc52AgATIuDA9OpdXlXUuVRR51K1g7OdAKAnIODAdAzDkL3e4w81Djd7aQCgpyHgwBTcXp8qjiw7ccYTAICAg7BV6/T4Qw0X2gMANBXRGd/k6aef1vDhwxUbG6uMjAx98MEHLfZ97bXXdMkll2jQoEHq27evMjMz9fbbbwf0yc/Pl8ViCXo4HI4WRoUZGE0SzM6iSu0+UKXi7+vZVwMACBLygLN69WotWLBAv/rVr7Rz505NmjRJ06ZNU1FRUbP933//fV1yySVav369duzYoQsuuEBXXnmldu7cGdCvb9++KikpCXjExsaG+nDQBewOt/59uEY7iyr9bVyjBgDQmpAvUT366KOaO3eubrnlFknSsmXL9Pbbb+uZZ55RXl5eUP9ly5YFPH/44Yf1+uuv64033tCYMWP87RaLRUlJSSGdO7pOjdOj8hqnympc/jDjZl8NAKCNQlrBcblc2rFjh7KzswPas7OztWXLljaN4fP5VF1drQEDBgS019TUKC0tTUOGDNEVV1wRVOFpyul0ym63BzzQ/dS5PCr+vk47iyr06YEqHax0UKkBAJyQkAacsrIyeb1eJSYmBrQnJiaqtLS0TWP84Q9/UG1trWbOnOlvGzFihPLz87Vu3TqtWrVKsbGxOu+887Rv375mx8jLy5PNZvM/UlNTT/yg0KEcbq8OVNTpk+JKfVJcpQMV9ZzWDQA4aZ1yFpXFYgl4bhhGUFtzVq1apcWLF+v111/X4MGD/e0TJ07UxIkT/c/PO+88jR07Vk8++aSeeOKJoHEWLVqk3Nxc/3O73U7I6UJOj1flNS6V17hU4/R09XQAACYU0oCTkJCgyMjIoGrNoUOHgqo6x1q9erXmzp2rv/71r7r44otb7RsREaFzzz23xQqO1WqV1Wpt3+TRodxen8prXCqrcaraQagBAIRWSJeoYmJilJGRoYKCgoD2goICZWVltfi+VatW6eabb9af//xnXX755cf9PoZhaNeuXUpOTj7pOaNjHa52ak+JXTu+qdD+slrCDQCgU4R8iSo3N1c5OTkaN26cMjMz9fzzz6uoqEi33XabpIblo2+//VYrV66U1BBubrrpJj3++OOaOHGiv/oTFxcnm80mSVqyZIkmTpyo008/XXa7XU888YR27dqlp556KtSHgzawO9z+f//7cC135wYAdLqQB5xZs2apvLxcDz74oEpKSpSenq7169crLS1NklRSUhJwTZznnntOHo9Hd9xxh+644w5/+5w5c5Sfny9Jqqys1K233qrS0lLZbDaNGTNG77//vsaPHx/qw0ELfD5DZbVOfVflVFmNs6unAwDo4Tplk/H8+fM1f/78Zl9rDC2NNm3adNzxHnvsMT322GMdMDOcLKfHq0N2pw5VO+TycJ0aAED3wL2ocELsDre+q3KovNbFbRIAAN0OAQdt1nQZitO7AQDdGQEHx+Xy+PSd3cEyFAAgbBBw0KJqh1ulLEMBAMIQAQcBfD5D5bUulVY5WIYCAIQtAg4kNSxDldfUsQwFADAFAg4kSbuKK2WN4oJ8AABzIOD0QF6fofIap74ur/W3sccGAGAmBJwexOH2qrTKocM1Tnm8hhxub1dPCQCAkCDgmJxhGKqoazgbqqreffw3AABgAgQck3J7fTpU7dR3doecbl9XTwcAgE5FwDEZu8OtQ3aHymtc8rGvBgDQQxFwTKBx03Cp3aFaJ/tqAAAg4ISxYzcNAwCABgScMGMYhr4/cqVhNg0DANA8Ak6Y+eRAlSyydPU0AADo1iK6egJond3h1leHa/zPOSMKAIDjo4LTDR27aZgL8gEA0D4EnG6ETcMAAHQMAk4X40rDAAB0PAJOF3J7ffr02yr21QAA0MHYZNyFfIZBuAEAIAQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQ6JeA8/fTTGj58uGJjY5WRkaEPPvig1f6bN29WRkaGYmNjdeqpp+rZZ58N6rNmzRqNHDlSVqtVI0eO1Nq1a0M1fQAAEGaiQv0NVq9erQULFujpp5/Weeedp+eee07Tpk3TF198oaFDhwb1379/vy677DLNmzdPL7/8sv7f//t/mj9/vgYNGqQZM2ZIkgoLCzVr1iw99NBDmj59utauXauZM2fqww8/1IQJE9o8tzqXR1EuT4cda12TseraMK7T45XD7T1+vyZ9nG3o31aMy7iMy7iMy7ihGDcqwtKmv4Pt1Z4xLYZhGB0+gyYmTJigsWPH6plnnvG3nXXWWbrmmmuUl5cX1H/hwoVat26d9uzZ42+77bbb9Mknn6iwsFCSNGvWLNntdr311lv+Ppdeeqn69++vVatWBY3pdDrldDr9z+12u1JTU5W64C+KsMZ3yHECAIDQ8jnrVLxspqqqqtS3b99W+4Z0icrlcmnHjh3Kzs4OaM/OztaWLVuafU9hYWFQ/6lTp2r79u1yu92t9mlpzLy8PNlsNv8jNTX1RA8JAACEgZAuUZWVlcnr9SoxMTGgPTExUaWlpc2+p7S0tNn+Ho9HZWVlSk5ObrFPS2MuWrRIubm5/ueNFZx//eqi4ybAUHJ6vNpVVNVl3x8AgFDobY3SqFM6/u+r3W5X8rK29Q35HhxJslgsAc8NwwhqO17/Y9vbM6bVapXVag1qj4+JUnxMp/wImhUZYVFsdGSXfX8AAEIhNjoyJH9fPe0YM6RLVAkJCYqMjAyqrBw6dCioAtMoKSmp2f5RUVEaOHBgq31aGhMAAPQsIQ04MTExysjIUEFBQUB7QUGBsrKymn1PZmZmUP9//vOfGjdunKKjo1vt09KYAACgZwn5+kxubq5ycnI0btw4ZWZm6vnnn1dRUZFuu+02SQ37Y7799lutXLlSUsMZU8uXL1dubq7mzZunwsJCrVixIuDsqJ///Oc6//zztXTpUl199dV6/fXX9c477+jDDz8M9eEAAIAwEPKAM2vWLJWXl+vBBx9USUmJ0tPTtX79eqWlpUmSSkpKVFRU5O8/fPhwrV+/XnfffbeeeuoppaSk6IknnvBfA0eSsrKy9Oqrr+rXv/617r//fp122mlavXp1u66BAwAAzCvk18Hpjux2u2w2W5vOow8lp8erj7+p7LLvDwBAKPS2RunsIbYOH7c9f7+5FxUAADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAk4XirRYFBcT2dXTAADAdEJ+N3G0LCoyQj9I7aeqOrdK7Q5V1LnU8259CgBAxyPgdAO2+GjZ4qPl9Hh1yO7UoWqHXB6SDgAAJ4qA041YoyKVOiBeQ/rHqbzWpdIqh6odnq6eFgAAYYeA0w1ZLBYl9LYqobdVtU6PvrM7VFbjktdHVQcAgLYg4HRzvaxROnVQbw0d4NPhGqe+sztV7/J29bQAAOjWCDhhIioyQsm2OCXb4tiUDADAcRBwwhCbkgEAaB0BJ4yxKRkAgOYRcEyATckAAAQi4JgMm5IBACDgmBabkgEAPRkBpwdgUzIAoKch4PQgbEoGAPQUBJwe6NhNyaV2h8qqnWJPMgDALAg4PVwva5ROG9RbQwfE61C1U9/ZHXK6fV09LQAATgoBB5Kk6MgIndIvTim2WH1f61Kp3SF7PctXAIDwRMBBAIvFooG9rRrY26o6l0clVSxfAQDCDwEHLYqPYfkKABCeCDg4LpavAADhhoCDNmu6fMXZVwCA7oyAgxPC2VcAgO6MgIOTwvIVAKA7IuCgQzS3fFXOHc0BAF0kIpSDV1RUKCcnRzabTTabTTk5OaqsrGyxv9vt1sKFC3X22WerV69eSklJ0U033aSDBw8G9JsyZYosFkvAY/bs2aE8FLRD4/LVuLT+OiOxtwb2jlGEpatnBQDoSUIacK6//nrt2rVLGzZs0IYNG7Rr1y7l5OS02L+urk4ff/yx7r//fn388cd67bXX9H//93+66qqrgvrOmzdPJSUl/sdzzz0XykPBCYiIaKjqnJHYRxlp/XXa4F7qFx8tC2EHABBiIVui2rNnjzZs2KCPPvpIEyZMkCT98Y9/VGZmpvbu3aszzzwz6D02m00FBQUBbU8++aTGjx+voqIiDR061N8eHx+vpKSkUE0fHSwqMkKD+8RqcJ9Yub0+fV/rUlmNU9UOjwxWsQAAHSxkFZzCwkLZbDZ/uJGkiRMnymazacuWLW0ep6qqShaLRf369Qtof+WVV5SQkKBRo0bp3nvvVXV1dYtjOJ1O2e32gAe6TnRkhBL7xmpUik1jh/bXsIR49YllOxgAoOOE7K9KaWmpBg8eHNQ+ePBglZaWtmkMh8OhX/7yl7r++uvVt29ff/sNN9yg4cOHKykpSZ999pkWLVqkTz75JKj60ygvL09Lliw5sQNBSMVERSjZFqdkW5wcbq/Ka10qr3Gq1unt6qkBAMJYuys4ixcvDtrge+xj+/btkhrOrDmWYRjNth/L7XZr9uzZ8vl8evrppwNemzdvni6++GKlp6dr9uzZ+tvf/qZ33nlHH3/8cbNjLVq0SFVVVf5HcXFxew8bnSA2OlKn9IvT6CH99IPUfhrSP05xMZFdPS0AQBhqdwXnzjvvPO4ZS8OGDdPu3bv13XffBb12+PBhJSYmtvp+t9utmTNnav/+/XrvvfcCqjfNGTt2rKKjo7Vv3z6NHTs26HWr1Sqr1drqGOhe4mIilTogXqkD4lXj9Ki8xqnyWhcXEwQAtEm7A05CQoISEhKO2y8zM1NVVVX617/+pfHjx0uStm7dqqqqKmVlZbX4vsZws2/fPm3cuFEDBw487vf6/PPP5Xa7lZyc3PYDQdjobY1Sb2uU0gb2kt3hVkWtSxV1btW7WMYCADTPYhihO4dl2rRpOnjwoP8U7ltvvVVpaWl64403/H1GjBihvLw8TZ8+XR6PRzNmzNDHH3+sf/zjHwGVngEDBigmJkZfffWVXnnlFV122WVKSEjQF198oXvuuUdxcXHatm2bIiOPv6Rht9tls9lUVVV13OoQui+H26uKOpcqat2qdri5JxYAdBO9rVE6e4itw8dtz9/vkJ668sorr+iuu+5Sdna2JOmqq67S8uXLA/rs3btXVVVVkqQDBw5o3bp1kqQf/OAHAf02btyoKVOmKCYmRu+++64ef/xx1dTUKDU1VZdffrkeeOCBNoUbmEdsdKR/g7LXZ6iyrqGyU1XvkstD2gGAniykFZzuigqO+VU73Kqsc6uizsUZWQDQyUxfwQG6Sp/YaPWJjVbqgHg5PV5/2KmqYykLAHoCAg5MzxoVqcS+kUrsGyufz1BVfUPYqax3c1YWAJgUAQc9SkSERf17xah/rxhJUq3T0xB26tyqcXLbCAAwCwIOerRe1ij1skZpSH/J4/XJ7vCoqt6tqnpOQweAcEbAAY6IiozQgF4xGnCkuuP0eGWvPxp4XB6WswAgXBBwgBZYoyI1qE+kBvVpuAp2vcvrDzt2h1seL+tZANBdEXCANoqLiVRcTKSSbLEyDEO1jYGnjgsNAkB3Q8ABToDFYvHfQuKUfnHy+QxVOzyyOxoqPGxYBoCuRcABOkBEhEW2+GjZ4qOVqsANy/Z6t+rYsAwAnYqAA4TAsRuWPV6fqh0ef5Wn1ulhSQsAQoiAA3SCqMiIgOvv+HyGqp0eVTvcqnZ4VOP0sGkZADoQAQfoAhERFtniomWLi5YkGYahOpdX9iOBp9rh5oahAHASCDhAN2CxWPwXHUw+cn86h/to4LHXu+XgthIA0GYEHKCbio2OVGx0pAb3aXju8vj8S1rVDo9qXZypBQAtIeAAYSImKkIDe1s1sHfDhQe9PkM1To9qnQ17eKodHq62DABHEHCAMBV5zD4eqeH2EjUOj2qdXlU73ap1euXldC0APRABBzARa1SkrL0jNbB3w/PGzcuNFZ5ap4dr8gDoEQg4gIk13byc2LehzeP1+Ss8jUtcnLEFwGwIOEAPExUZIVt8hGzxR5e2HO6GKk/NkWvy1LlY2gIQ3gg4APxnbCUc2cBsGIbq3V7VOr3+TcyEHgDhhIADIIjFYlF8TJTiY6I0qM/R0ONw+wLO3CL0AOiuCDgA2sRisSguJlJxMZEthp5al4cztwB0CwQcACesudAjSfVHztyqc3mOhB9CD4DORcAB0OEaQ490NPQ43F7/aep1Lq9qXR45uf0EgBAh4ADoFI0bmQc2afN4fap1eVV/JPDUOb2qc3lEsQfAySLgAOgyUZERssVFBFyNuXFfT2PgqXU1VH24DQWA9iDgAOhWmu7rUe+j7W6vr0ngObrUxQ1HATSHgAMgLEQ3c4FCn8+Qw9MQdOqPBJ46l0dOj4/gA/RwBBwAYSsi4uj1epry+houVFjn8jQJPixzAT0JAQeA6URGWNTbGqXe1sD/xXm8PtW5G6o9jcGn3s29uAAzIuAA6DGiIiPUNzJCfWOjA9rdXl+TZa6G/T0Ot1duL8EHCFcEHAA9XnQzZ3NJksvjU727Iewcrfiw1AWEAwIOALQgJipCMVHBwafpHh+HqyEENQYhNjcD3QMBBwDaqaU9Po1nddUfqfQ0/crFC4HORcABgA7S0lldhmHI6fH5A4+jScWHDc5AaESEcvCKigrl5OTIZrPJZrMpJydHlZWVrb7n5ptvlsViCXhMnDgxoI/T6dTPfvYzJSQkqFevXrrqqqt04MCBEB4JAJw4i8Wi2OhI9e8Vo5R+cTp1UG+NSrEpI22Axg8foLOH2PQfg3trSP84JfSOUS9rpCIjLF09bSCshbSCc/311+vAgQPasGGDJOnWW29VTk6O3njjjVbfd+mll+rFF1/0P4+JiQl4fcGCBXrjjTf06quvauDAgbrnnnt0xRVXaMeOHYqMjOz4AwGAEGlpuUuSnB6vHC5fwLKXw+3lQoZAG4Qs4OzZs0cbNmzQRx99pAkTJkiS/vjHPyozM1N79+7VmWee2eJ7rVarkpKSmn2tqqpKK1as0J/+9CddfPHFkqSXX35ZqampeueddzR16tSOPxgA6ALWqEhZoyJlU+Am58a9Pg63z7/HpyH4sOQFNApZwCksLJTNZvOHG0maOHGibDabtmzZ0mrA2bRpkwYPHqx+/fpp8uTJ+q//+i8NHjxYkrRjxw653W5lZ2f7+6ekpCg9PV1btmxpNuA4nU45nU7/c7vd3hGHCABd4uhen+DXvD4jYI+Pw+0j/KBHClnAKS0t9YeSpgYPHqzS0tIW3zdt2jRdd911SktL0/79+3X//ffrwgsv1I4dO2S1WlVaWqqYmBj1798/4H2JiYktjpuXl6clS5ac3AEBQBiIjLColzVKvZpZ8moMP0cDEOEH5tXugLN48eLjhoVt27ZJathYdyzDMJptbzRr1iz/v9PT0zVu3DilpaXpzTff1I9+9KMW39fauIsWLVJubq7/ud1uV2pqaqvHAABm09bw4zhyxlfjfh8ubIhw1O6Ac+edd2r27Nmt9hk2bJh2796t7777Lui1w4cPKzExsc3fLzk5WWlpadq3b58kKSkpSS6XSxUVFQFVnEOHDikrK6vZMaxWq6xWa5u/JwD0NK2Fn8Y9P063L+Crw+2T0801ftA9tTvgJCQkKCEh4bj9MjMzVVVVpX/9618aP368JGnr1q2qqqpqMYg0p7y8XMXFxUpOTpYkZWRkKDo6WgUFBZo5c6YkqaSkRJ999pkeeeSR9h4OAOA4WtvzIzWc7eX0HFnucvsazv468pWlL3QVi2GE7mTDadOm6eDBg3ruueckNZwmnpaWFnCa+IgRI5SXl6fp06erpqZGixcv1owZM5ScnKyvv/5a9913n4qKirRnzx716dNHknT77bfrH//4h/Lz8zVgwADde++9Ki8vb/Np4na7XTabTVVVVerbt29oDh4A4F/68gegJl+p/phXb2uUzh5i6/Bx2/P3O6TXwXnllVd01113+c94uuqqq7R8+fKAPnv37lVVVZUkKTIyUp9++qlWrlypyspKJScn64ILLtDq1av94UaSHnvsMUVFRWnmzJmqr6/XRRddpPz8fK6BAwDdzNGlr+Zfd3kCKz4Nwaex+uMjAOGEhbSC011RwQGA7s8wDLm8voDQc+y/e95fsPBg+goOAAAnymKx+C92qNjg1xvv8eU8UgVqCD4+f1WIClDPRsABAISlxnt8xUZHSsdc7blRY9g5Gnx8AW0eLwnIrAg4AADTiomKUExUhPq08LrXZ/irPy7vMUthHp/cXpbBwhUBBwDQY0Ue5xT4pstgLk9DCHIdswzmpgrULRFwAABoQeAyWPN8viaboY+EnqZhiKWwrkHAAQDgJEREWBQb0fpeIK/POFr58R5dEmtsc3upBHU0Ag4AACEWGWFRXEyk4mJaDkFNK0GNoefYShB7gtqOgAMAQDcQWAlqnmEYcnuNgOpPwN6gI1+9nB9PwAEAIFxYLBbFRFkUExUhtXIPaZ/PkMdnyOsz5Pb55PU2PPf4GvYDeX3NPW/4t1myEQEHAACTiYiwKCbCIkmKU/tuY+RrGn58RgvhqOG17hyOCDgAAMCvMRzFKKLd7/UdqRh1h31CBBwAANAhIiIsskZ0jxtftz+eAQAAdHMEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDohDTgVFRXKycmRzWaTzWZTTk6OKisrW32PxWJp9vHf//3f/j5TpkwJen327NmhPBQAABBGokI5+PXXX68DBw5ow4YNkqRbb71VOTk5euONN1p8T0lJScDzt956S3PnztWMGTMC2ufNm6cHH3zQ/zwuLq4DZw4AAMJZyALOnj17tGHDBn300UeaMGGCJOmPf/yjMjMztXfvXp155pnNvi8pKSng+euvv64LLrhAp556akB7fHx8UF8AAAAphEtUhYWFstls/nAjSRMnTpTNZtOWLVvaNMZ3332nN998U3Pnzg167ZVXXlFCQoJGjRqle++9V9XV1S2O43Q6ZbfbAx4AAMC8QlbBKS0t1eDBg4PaBw8erNLS0jaN8dJLL6lPnz760Y9+FNB+ww03aPjw4UpKStJnn32mRYsW6ZNPPlFBQUGz4+Tl5WnJkiXtPwgAABCW2l3BWbx4cYsbgRsf27dvl9SwYfhYhmE0296cF154QTfccINiY2MD2ufNm6eLL75Y6enpmj17tv72t7/pnXfe0ccff9zsOIsWLVJVVZX/UVxc3M6jBgAA4aTdFZw777zzuGcsDRs2TLt379Z3330X9Nrhw4eVmJh43O/zwQcfaO/evVq9evVx+44dO1bR0dHat2+fxo4dG/S61WqV1Wo97jgAAMAc2h1wEhISlJCQcNx+mZmZqqqq0r/+9S+NHz9ekrR161ZVVVUpKyvruO9fsWKFMjIydM455xy37+effy63263k5OTjHwAAADC9kG0yPuuss3TppZdq3rx5+uijj/TRRx9p3rx5uuKKKwLOoBoxYoTWrl0b8F673a6//vWvuuWWW4LG/eqrr/Tggw9q+/bt+vrrr7V+/Xpdd911GjNmjM4777xQHQ4AAAgjIb3Q3yuvvKKzzz5b2dnZys7O1ujRo/WnP/0poM/evXtVVVUV0Pbqq6/KMAz9+Mc/DhozJiZG7777rqZOnaozzzxTd911l7Kzs/XOO+8oMjIylIcDAADChMUwDKOrJ9HZ7Ha7bDabqqqq1Ldv366eDgAAaIP2/P3mXlQAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0Qhpw/uu//ktZWVmKj49Xv3792vQewzC0ePFipaSkKC4uTlOmTNHnn38e0MfpdOpnP/uZEhIS1KtXL1111VU6cOBACI4AAACEo5AGHJfLpeuuu0633357m9/zyCOP6NFHH9Xy5cu1bds2JSUl6ZJLLlF1dbW/z4IFC7R27Vq9+uqr+vDDD1VTU6MrrrhCXq83FIcBAADCjMUwDCPU3yQ/P18LFixQZWVlq/0Mw1BKSooWLFighQsXSmqo1iQmJmrp0qX6z//8T1VVVWnQoEH605/+pFmzZkmSDh48qNTUVK1fv15Tp0497nzsdrtsNpuqqqrUt2/fkz4+AAAQeu35+x3VSXNqk/3796u0tFTZ2dn+NqvVqsmTJ2vLli36z//8T+3YsUNutzugT0pKitLT07Vly5ZmA47T6ZTT6fQ/r6qqktTwgwIAAOGh8e92W2oz3SrglJaWSpISExMD2hMTE/XNN9/4+8TExKh///5BfRrff6y8vDwtWbIkqD01NbUjpg0AADpRdXW1bDZbq33aHXAWL17cbFhoatu2bRo3blx7h/azWCwBzw3DCGo7Vmt9Fi1apNzcXP9zn8+n77//XgMHDjzuuO1lt9uVmpqq4uJilr/CCL+38MTvLTzxewtP3eH3ZhiGqqurlZKScty+7Q44d955p2bPnt1qn2HDhrV3WElSUlKSpIYqTXJysr/90KFD/qpOUlKSXC6XKioqAqo4hw4dUlZWVrPjWq1WWa3WgLa2ntV1ovr27csHNwzxewtP/N7CE7+38NTVv7fjVW4atTvgJCQkKCEhod0Taovhw4crKSlJBQUFGjNmjKSGM7E2b96spUuXSpIyMjIUHR2tgoICzZw5U5JUUlKizz77TI888khI5gUAAMJLSPfgFBUV6fvvv1dRUZG8Xq927dolSfqP//gP9e7dW5I0YsQI5eXlafr06bJYLFqwYIEefvhhnX766Tr99NP18MMPKz4+Xtdff72khuQ2d+5c3XPPPRo4cKAGDBige++9V2effbYuvvjiUB4OAAAIEyENOL/5zW/00ksv+Z83VmU2btyoKVOmSJL27t3rP6tJkn7xi1+ovr5e8+fPV0VFhSZMmKB//vOf6tOnj7/PY489pqioKM2cOVP19fW66KKLlJ+fr8jIyFAeTptYrVY98MADQUti6N74vYUnfm/hid9beAq331unXAcHAACgM3EvKgAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEnA709NNPa/jw4YqNjVVGRoY++OCDrp4SWrF48WJZLJaAR+PVtNG9vP/++7ryyiuVkpIii8Wiv//97wGvG4ahxYsXKyUlRXFxcZoyZYo+//zzrpks/I73e7v55puDPoMTJ07smslCUsO9G88991z16dNHgwcP1jXXXKO9e/cG9AmXzxsBp4OsXr1aCxYs0K9+9Svt3LlTkyZN0rRp01RUVNTVU0MrRo0apZKSEv/j008/7eopoRm1tbU655xztHz58mZff+SRR/Too49q+fLl2rZtm5KSknTJJZeourq6k2eKpo73e5OkSy+9NOAzuH79+k6cIY61efNm3XHHHfroo49UUFAgj8ej7Oxs1dbW+vuEzefNQIcYP368cdtttwW0jRgxwvjlL3/ZRTPC8TzwwAPGOeec09XTQDtJMtauXet/7vP5jKSkJON3v/udv83hcBg2m8149tlnu2CGaM6xvzfDMIw5c+YYV199dZfMB21z6NAhQ5KxefNmwzDC6/NGBacDuFwu7dixQ9nZ2QHt2dnZ2rJlSxfNCm2xb98+paSkaPjw4Zo9e7b+/e9/d/WU0E779+9XaWlpwOfParVq8uTJfP7CwKZNmzR48GCdccYZmjdvng4dOtTVU0ITjXcaGDBggKTw+rwRcDpAWVmZvF6v/47njRITE1VaWtpFs8LxTJgwQStXrtTbb7+tP/7xjyotLVVWVpbKy8u7empoh8bPGJ+/8DNt2jS98soreu+99/SHP/xB27Zt04UXXiin09nVU4Ma9trk5ubqhz/8odLT0yWF1+ctpPei6mksFkvAc8MwgtrQfUybNs3/77PPPluZmZk67bTT9NJLLyk3N7cLZ4YTwecv/MyaNcv/7/T0dI0bN05paWl688039aMf/agLZwZJuvPOO7V79259+OGHQa+Fw+eNCk4HSEhIUGRkZFB6PXToUFDKRffVq1cvnX322dq3b19XTwXt0HjmG5+/8JecnKy0tDQ+g93Az372M61bt04bN27UkCFD/O3h9Hkj4HSAmJgYZWRkqKCgIKC9oKBAWVlZXTQrtJfT6dSePXuUnJzc1VNBOwwfPlxJSUkBnz+Xy6XNmzfz+Qsz5eXlKi4u5jPYhQzD0J133qnXXntN7733noYPHx7wejh93lii6iC5ubnKycnRuHHjlJmZqeeff15FRUW67bbbunpqaMG9996rK6+8UkOHDtWhQ4f029/+Vna7XXPmzOnqqeEYNTU1+vLLL/3P9+/fr127dmnAgAEaOnSoFixYoIcfflinn366Tj/9dD388MOKj4/X9ddf34WzRmu/twEDBmjx4sWaMWOGkpOT9fXXX+u+++5TQkKCpk+f3oWz7tnuuOMO/fnPf9brr7+uPn36+Cs1NptNcXFxslgs4fN569JzuEzmqaeeMtLS0oyYmBhj7Nix/tPq0D3NmjXLSE5ONqKjo42UlBTjRz/6kfH555939bTQjI0bNxqSgh5z5swxDKPh1NUHHnjASEpKMqxWq3H++ecbn376addOGq3+3urq6ozs7Gxj0KBBRnR0tDF06FBjzpw5RlFRUVdPu0dr7vclyXjxxRf9fcLl82YxDMPo/FgFAAAQOuzBAQAApkPAAQAApkPAAQAApkPAAQAApkPAAQAApkPAAQAApkPAAQAApkPAAQAApkPAAQAApkPAAQAApkPAAQAApvP/AWj0KAbBOB6qAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制自相关图\n",
    "# total_log = np.log(total_num_repo)\n",
    "# total_log_diff = total_log.diff(1).dropna()\n",
    "tsaplots.plot_acf(total_num_repo, lags=20)  # lags为滞后阶数\n",
    "plt.show()\n",
    "plt.savefig(os.path.join(IMG_DIR, \"arima_acf.png\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b540cdf",
   "metadata": {},
   "source": [
    "如上图所示，该时间序列随着阶数的递增，自相关系数递减至零，因此可以判断该时间序列是平稳时间序列。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ead738a6",
   "metadata": {},
   "source": [
    "**统计检验方法**\n",
    "\n",
    "当然，图检验法具有一定的主观因素，我们使用单位根平稳检验作为定量验证。\n",
    "\n",
    "> 迪基-福勒（Dickey Fuller）检验是最流行的统计检验方法之一，可以用它来确定序列中单位根的存在，从而帮助判断序列是否是平稳。ADF检验是对DF检验的扩展。参考[ADF（增补迪基-福勒）检验](https://smilecoc.vip/2021/01/15/time_series_part2_stability/#ADF%EF%BC%88%E5%A2%9E%E8%A1%A5%E8%BF%AA%E5%9F%BA-%E7%A6%8F%E5%8B%92%EF%BC%89%E6%A3%80%E9%AA%8C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b54fc072",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF检验结果:\n",
      "Test Statistic                  -3.811621\n",
      "p-value                          0.002791\n",
      "Number of Lags Used             17.000000\n",
      "Number of Observations Used    341.000000\n",
      "Critical Value (1%)             -3.449673\n",
      "Critical Value (5%)             -2.870053\n",
      "Critical Value (10%)            -2.571306\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "#定义ADF输出格式化函数\n",
    "def adf_test(timeseries):\n",
    "    print ('ADF检验结果:')\n",
    "    dftest = adfuller(timeseries, autolag='AIC')\n",
    "    dfoutput = pd.Series(dftest[0:4], index=['Test Statistic','p-value','Number of Lags Used','Number of Observations Used'])\n",
    "    for key,value in dftest[4].items():\n",
    "       dfoutput['Critical Value (%s)'%key] = value\n",
    "    print (dfoutput)\n",
    " \n",
    "#对数据集使用ADF检验\n",
    "adf_test(total_num_repo)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4443a3cc",
   "metadata": {},
   "source": [
    "ADF的结果主要看以下两个方面：\n",
    "\n",
    "> - Test Statistic的值如果比Critical Value (5%)小则满足稳定性需求.\n",
    "> - p-value越低（理论上需要低于0.05）证明序列越稳定。\n",
    "\n",
    "在上面的检测结果中，test statistic < Critical Value (5%) ，这意味着序列是平稳的。同时p值为0.002791,这证实了我们最初在目视检测中观察的结果。\n",
    "\n",
    "**至此，我们确定了原始数据是一个平稳的时间序列**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e300e74",
   "metadata": {},
   "source": [
    "### 随机性检验\n",
    "\n",
    "对于纯随机序列，又称白噪声序列，序列的各项数值之间没有任何相关关系，序列在进行完全无序的随机波动，可以终止对该序列的分析。白噪声序列是没有信息可提取的平稳序列。**白噪声检验原假设：时间序列是白噪声。**\n",
    "下面进行原始数据集的白噪音检测，输出检验结果中会返回两个值：\n",
    "lbvalue: 测试的统计量 和 pvalue: 基于卡方分布的p统计量。如果p-value>0.05则可判断为白噪声序列"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "763b6ab8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lb_stat</th>\n",
       "      <th>lb_pvalue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>353.842651</td>\n",
       "      <td>6.171075e-79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>706.017645</td>\n",
       "      <td>4.900229e-154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1054.337382</td>\n",
       "      <td>2.933510e-228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1400.934409</td>\n",
       "      <td>4.334766e-302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1744.670829</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2084.277647</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2418.404212</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2747.532237</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3069.353583</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>3384.289511</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        lb_stat      lb_pvalue\n",
       "1    353.842651   6.171075e-79\n",
       "2    706.017645  4.900229e-154\n",
       "3   1054.337382  2.933510e-228\n",
       "4   1400.934409  4.334766e-302\n",
       "5   1744.670829   0.000000e+00\n",
       "6   2084.277647   0.000000e+00\n",
       "7   2418.404212   0.000000e+00\n",
       "8   2747.532237   0.000000e+00\n",
       "9   3069.353583   0.000000e+00\n",
       "10  3384.289511   0.000000e+00"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#白噪声检验\n",
    "from statsmodels.stats.diagnostic import acorr_ljungbox\n",
    "acorr_ljungbox(total_num_repo)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f98eeafe",
   "metadata": {},
   "source": [
    "可以发现白噪音检测得到的卡方检验p-value值远小于0.05，因此拒绝原假设，即时间序列不是白噪声。\n",
    "至此，我们证明了原始数据序列是平稳的非白噪声序列。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ef35528",
   "metadata": {},
   "source": [
    "### 平稳时间序列建模\n",
    "\n",
    "**模型定阶**\n",
    "\n",
    "对于复杂的ARMA(p,q)模型，难以用自相关函数和偏自相关函数确定阶数，可以网格搜索法：对于给定的时间序列数据，可以通过构建所有可能的ARIMA模型，并通过交叉验证选择最佳的模型参数。可以使用Python中的pmdarima库中的auto_arima函数来进行网格搜索。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "17afbc51",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performing stepwise search to minimize aic\n",
      " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=7781.609, Time=0.12 sec\n",
      " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=9206.616, Time=0.01 sec\n",
      " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=7822.357, Time=0.04 sec\n",
      " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=8971.189, Time=0.05 sec\n",
      " ARIMA(0,0,0)(0,0,0)[0]             : AIC=9460.578, Time=0.01 sec\n",
      " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=7776.957, Time=0.18 sec\n",
      " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=inf, Time=0.12 sec\n",
      " ARIMA(3,0,1)(0,0,0)[0] intercept   : AIC=7777.809, Time=0.40 sec\n",
      " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=7777.269, Time=0.27 sec\n",
      " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=7780.452, Time=0.18 sec\n",
      " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=inf, Time=0.18 sec\n",
      " ARIMA(3,0,2)(0,0,0)[0] intercept   : AIC=7779.244, Time=0.41 sec\n",
      " ARIMA(2,0,1)(0,0,0)[0]             : AIC=7776.002, Time=0.11 sec\n",
      " ARIMA(1,0,1)(0,0,0)[0]             : AIC=7779.345, Time=0.07 sec\n",
      " ARIMA(2,0,0)(0,0,0)[0]             : AIC=inf, Time=0.07 sec\n",
      " ARIMA(3,0,1)(0,0,0)[0]             : AIC=7778.166, Time=0.08 sec\n",
      " ARIMA(2,0,2)(0,0,0)[0]             : AIC=7776.309, Time=0.15 sec\n",
      " ARIMA(1,0,0)(0,0,0)[0]             : AIC=inf, Time=0.02 sec\n",
      " ARIMA(1,0,2)(0,0,0)[0]             : AIC=7778.521, Time=0.20 sec\n",
      " ARIMA(3,0,0)(0,0,0)[0]             : AIC=inf, Time=0.17 sec\n",
      " ARIMA(3,0,2)(0,0,0)[0]             : AIC=7778.193, Time=0.29 sec\n",
      "\n",
      "Best model:  ARIMA(2,0,1)(0,0,0)[0]          \n",
      "Total fit time: 3.150 seconds\n",
      "(2, 0, 1)\n",
      "(0, 0, 0, 0)\n"
     ]
    }
   ],
   "source": [
    "from pmdarima.arima import auto_arima\n",
    "\n",
    "# 使用auto_arima选择最佳模型参数\n",
    "model = auto_arima(total_num_repo, start_p=1, start_q=1, max_p=3, max_q=3, \n",
    "                   start_P=0, seasonal=True, d=0, D=0, trace=True, error_action='ignore', \n",
    "                   suppress_warnings=True, stepwise=True)\n",
    "\n",
    "# 输出选择的最佳模型参数\n",
    "print(model.order)\n",
    "print(model.seasonal_order)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d43428a",
   "metadata": {},
   "source": [
    "这里的 ARIMA(2,0,1)(0,0,0)[0] 表示使用 ARIMA 模型进行拟合时，得到的最佳模型的参数是 (2,0,1) 和 (0,0,0,0)。\n",
    "\n",
    "(2,0,1) 表示 ARIMA 模型中的三个参数：p, d, q。其中，p 是自回归项数，d 是差分次数，q 是移动平均项数。这里的 (2,0,1) 意味着 ARIMA 模型选择了 2 个自回归项，0 次差分和 1 个移动平均项。\n",
    "(0,0,0,0) 表示季节性 ARIMA 模型（SARIMA）的四个参数：P, D, Q, m。其中，P 是季节性自回归项数，D 是季节性差分次数，Q 是季节性移动平均项数，m 是季节长度。这里的 (0,0,0,0) 表示该模型不考虑季节性。\n",
    "在 ARIMA 模型中，[0] 表示使用不使用常数项（也叫截距项）进行建模。在这个例子中，[0] 表示不使用常数项。\n",
    "\n",
    "因此，我们得到的 Best model: ARIMA(2,0,1)(0,0,0)[0] 的意思是，最佳模型的参数是 (2,0,1) 和 (0,0,0,0)，它不考虑季节性，且不使用常数项。\n",
    "\n",
    "接下来，我们使用这个模型参数拟合模型并完成预测和评估，我们采用前80%数据作为训练集，后20%作为测试集。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6801f4ff",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/huangrui/miniconda3/envs/d2l/lib/python3.9/site-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.\n",
      "  warn('Non-stationary starting autoregressive parameters'\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                               SARIMAX Results                                \n",
      "==============================================================================\n",
      "Dep. Variable:         Total-num-repo   No. Observations:                  287\n",
      "Model:                 ARIMA(2, 0, 1)   Log Likelihood               -2891.492\n",
      "Date:                Fri, 17 Feb 2023   AIC                           5792.984\n",
      "Time:                        21:39:13   BIC                           5811.281\n",
      "Sample:                             0   HQIC                          5800.317\n",
      "                                - 287                                         \n",
      "Covariance Type:                  opg                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const       5.193e+04   2.52e-09   2.06e+13      0.000    5.19e+04    5.19e+04\n",
      "ar.L1          0.9466      0.068     13.883      0.000       0.813       1.080\n",
      "ar.L2          0.0529      0.068      0.778      0.436      -0.080       0.186\n",
      "ma.L1         -0.5577      0.051    -10.964      0.000      -0.657      -0.458\n",
      "sigma2      3.292e+07   9.92e-10   3.32e+16      0.000    3.29e+07    3.29e+07\n",
      "===================================================================================\n",
      "Ljung-Box (L1) (Q):                   0.63   Jarque-Bera (JB):               945.27\n",
      "Prob(Q):                              0.43   Prob(JB):                         0.00\n",
      "Heteroskedasticity (H):               9.01   Skew:                             1.72\n",
      "Prob(H) (two-sided):                  0.00   Kurtosis:                        11.20\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
      "[2] Covariance matrix is singular or near-singular, with condition number 1.82e+33. Standard errors may be unstable.\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "statsmodels.tsa.statespace.mlemodel.MLEResults.predict() got multiple values for keyword argument 'start'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[7], line 16\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[38;5;28mprint\u001b[39m(model_fit\u001b[38;5;241m.\u001b[39msummary())\n\u001b[1;32m     12\u001b[0m \u001b[38;5;66;03m# 对测试集中的数据进行预测\u001b[39;00m\n\u001b[1;32m     13\u001b[0m \u001b[38;5;66;03m# start=0 表示从测试集的第一个时间点开始预测\u001b[39;00m\n\u001b[1;32m     14\u001b[0m \u001b[38;5;66;03m# end=len(test_data)-1 表示预测到测试集的最后一个时间点\u001b[39;00m\n\u001b[1;32m     15\u001b[0m \u001b[38;5;66;03m# typ='levels' 表示返回预测值本身而不是差分值\u001b[39;00m\n\u001b[0;32m---> 16\u001b[0m forecast_values \u001b[38;5;241m=\u001b[39m \u001b[43mmodel_fit\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mforecast\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mlen\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mtest_data\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mstart\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mend\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mlen\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mtest_data\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtyp\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mlevels\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m     18\u001b[0m \u001b[38;5;66;03m# 打印预测结果\u001b[39;00m\n\u001b[1;32m     19\u001b[0m \u001b[38;5;28mprint\u001b[39m(forecast_values)\n",
      "File \u001b[0;32m~/miniconda3/envs/d2l/lib/python3.9/site-packages/statsmodels/base/wrapper.py:113\u001b[0m, in \u001b[0;36mmake_wrapper.<locals>.wrapper\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    111\u001b[0m     obj \u001b[38;5;241m=\u001b[39m data\u001b[38;5;241m.\u001b[39mwrap_output(func(results, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs), how[\u001b[38;5;241m0\u001b[39m], how[\u001b[38;5;241m1\u001b[39m:])\n\u001b[1;32m    112\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m how:\n\u001b[0;32m--> 113\u001b[0m     obj \u001b[38;5;241m=\u001b[39m data\u001b[38;5;241m.\u001b[39mwrap_output(\u001b[43mfunc\u001b[49m\u001b[43m(\u001b[49m\u001b[43mresults\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m, how)\n\u001b[1;32m    114\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m obj\n",
      "File \u001b[0;32m~/miniconda3/envs/d2l/lib/python3.9/site-packages/statsmodels/tsa/statespace/mlemodel.py:3442\u001b[0m, in \u001b[0;36mMLEResults.forecast\u001b[0;34m(self, steps, **kwargs)\u001b[0m\n\u001b[1;32m   3440\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m   3441\u001b[0m     end \u001b[38;5;241m=\u001b[39m steps\n\u001b[0;32m-> 3442\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpredict(start\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mnobs, end\u001b[38;5;241m=\u001b[39mend, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n",
      "\u001b[0;31mTypeError\u001b[0m: statsmodels.tsa.statespace.mlemodel.MLEResults.predict() got multiple values for keyword argument 'start'"
     ]
    }
   ],
   "source": [
    "from statsmodels.tsa.arima.model import ARIMA\n",
    "# 将数据分成了训练集和测试集\n",
    "train_data = total_num_repo[:int(len(total_num_repo)*0.8)]\n",
    "test_data = total_num_repo[int(len(total_num_repo)*0.8):]\n",
    "# 创建 ARIMA 模型对象\n",
    "# p=2, d=1, q=1 表示 ARIMA(2, 1, 1) 模型\n",
    "model = ARIMA(train_data, order=(2, 0, 1))\n",
    "# 使用训练集拟合 ARIMA 模型\n",
    "model_fit = model.fit()\n",
    "# 查看模型拟合结果\n",
    "print(model_fit.summary())\n",
    "# 对测试集中的数据进行预测\n",
    "# start=0 表示从测试集的第一个时间点开始预测\n",
    "# end=len(test_data)-1 表示预测到测试集的最后一个时间点\n",
    "# typ='levels' 表示返回预测值本身而不是差分值\n",
    "forecast_values = model_fit.forecast(len(test_data), start=0, end=len(test_data)-1, typ='levels')\n",
    "\n",
    "# 打印预测结果\n",
    "print(forecast_values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e635d67",
   "metadata": {},
   "source": [
    "\n",
    "## 第二问：\n",
    "\n",
    "- [ ] 计算单词的信息熵\n",
    "- [ ] 提取单词的特征\n",
    "    - [ ] 元音字母个数\n",
    "    - [ ] 重音\n",
    "    - [ ] 词性\n",
    "    - [ ] ngram出现频率高的字母在单词里面出现过吗\n",
    "    - [ ] 词根、前缀、后缀\n",
    "    - [ ] 词频特征：单词在语料库的出现频率\n",
    "- [ ] 确定模型？XGBOOST？决策树？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4bce3300",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9358679",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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