{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tool for Statistical Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters for data import to be set\n",
    "data_folder = \"../results/perf_results_g0\"\n",
    "data_file = \"../results/all_results_g0.csv\"\n",
    "\n",
    "test_pairs = [\n",
    "    [\"0_comp\", \"alpha_beta\"],\n",
    "    [\"alpha_beta\", \"transposition_table\"],\n",
    "    [\"transposition_table\", \"transposition_table_opt_all\"],\n",
    "    [\"transposition_table\", \"transposition_table_opt_1\"],\n",
    "    [\"transposition_table\", \"transposition_table_opt_2\"],\n",
    "    [\"transposition_table\", \"transposition_table_opt_3\"],\n",
    "]\n",
    "\n",
    "test_value = [\"cycles\", \"time\"]\n",
    "\n",
    "# Parameters for the tests to be set\n",
    "alternative = \"greater\"\n",
    "alpha = 0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing the Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is assumed that the data are given in **csv-format**.\n",
    "Columns are separeted by a **semicolon** ```;``` and the first row contains the **names of the variables**. Furthermore it is assumed that for decimal numbers the **decimal point** ```.``` is used.\n",
    "\n",
    "The following example is based on ```Daten.csv``` (see TUWEL), where the results of **A** and **B** are given in the same file.\n",
    "It is assumed, that this file lies in the subfolder ```data``` of this notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing the data\n",
    "from data_processing import load_all_results\n",
    "import pandas as pd\n",
    "\n",
    "load_all_results(data_folder, data_file)\n",
    "all_data = pd.read_csv(data_file)\n",
    "all_data = all_data[[\"algorithm\", \"branch-misses\",\"branches\",\"cycles\",\"depth\",\"instance\",\"instructions\",\"time\"]]\n",
    "all_data[\"algorithm\"] = all_data[\"algorithm\"].replace({\"comp\": \"0_comp\"})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>algorithm</th>\n",
       "      <th>branch-misses</th>\n",
       "      <th>branches</th>\n",
       "      <th>cycles</th>\n",
       "      <th>depth</th>\n",
       "      <th>instance</th>\n",
       "      <th>instructions</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>transposition_table_opt_3</td>\n",
       "      <td>1.079039e+08</td>\n",
       "      <td>4.267404e+09</td>\n",
       "      <td>1.312706e+10</td>\n",
       "      <td>3</td>\n",
       "      <td>x5</td>\n",
       "      <td>2.466981e+10</td>\n",
       "      <td>4.095699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>transposition_table_opt_3</td>\n",
       "      <td>1.272508e+09</td>\n",
       "      <td>5.507174e+10</td>\n",
       "      <td>1.674238e+11</td>\n",
       "      <td>4</td>\n",
       "      <td>x4</td>\n",
       "      <td>3.202681e+11</td>\n",
       "      <td>51.422120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>transposition_table_opt_1</td>\n",
       "      <td>6.139813e+06</td>\n",
       "      <td>2.306997e+08</td>\n",
       "      <td>6.339644e+08</td>\n",
       "      <td>2</td>\n",
       "      <td>x9</td>\n",
       "      <td>1.252986e+09</td>\n",
       "      <td>0.208725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>transposition_table</td>\n",
       "      <td>1.010880e+08</td>\n",
       "      <td>4.536912e+09</td>\n",
       "      <td>1.213109e+10</td>\n",
       "      <td>3</td>\n",
       "      <td>x8</td>\n",
       "      <td>2.481745e+10</td>\n",
       "      <td>3.590559</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>alpha_beta</td>\n",
       "      <td>1.236493e+08</td>\n",
       "      <td>5.163768e+09</td>\n",
       "      <td>1.411102e+10</td>\n",
       "      <td>3</td>\n",
       "      <td>x5</td>\n",
       "      <td>2.844768e+10</td>\n",
       "      <td>4.183875</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   algorithm  branch-misses      branches        cycles  \\\n",
       "0  transposition_table_opt_3   1.079039e+08  4.267404e+09  1.312706e+10   \n",
       "1  transposition_table_opt_3   1.272508e+09  5.507174e+10  1.674238e+11   \n",
       "2  transposition_table_opt_1   6.139813e+06  2.306997e+08  6.339644e+08   \n",
       "3        transposition_table   1.010880e+08  4.536912e+09  1.213109e+10   \n",
       "4                 alpha_beta   1.236493e+08  5.163768e+09  1.411102e+10   \n",
       "\n",
       "   depth instance  instructions       time  \n",
       "0      3       x5  2.466981e+10   4.095699  \n",
       "1      4       x4  3.202681e+11  51.422120  \n",
       "2      2       x9  1.252986e+09   0.208725  \n",
       "3      3       x8  2.481745e+10   3.590559  \n",
       "4      3       x5  2.844768e+10   4.183875  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>branch-misses</th>\n",
       "      <th>branches</th>\n",
       "      <th>cycles</th>\n",
       "      <th>depth</th>\n",
       "      <th>instance</th>\n",
       "      <th>instructions</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>algorithm</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0_comp</th>\n",
       "      <td>18</td>\n",
       "      <td>18</td>\n",
       "      <td>18</td>\n",
       "      <td>18</td>\n",
       "      <td>18</td>\n",
       "      <td>18</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_beta</th>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>transposition_table</th>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>transposition_table_opt_1</th>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>transposition_table_opt_2</th>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>transposition_table_opt_3</th>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>transposition_table_opt_all</th>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             branch-misses  branches  cycles  depth  instance  \\\n",
       "algorithm                                                                       \n",
       "0_comp                                  18        18      18     18        18   \n",
       "alpha_beta                              36        36      36     36        36   \n",
       "transposition_table                     36        36      36     36        36   \n",
       "transposition_table_opt_1               36        36      36     36        36   \n",
       "transposition_table_opt_2               36        36      36     36        36   \n",
       "transposition_table_opt_3               36        36      36     36        36   \n",
       "transposition_table_opt_all             36        36      36     36        36   \n",
       "\n",
       "                             instructions  time  \n",
       "algorithm                                        \n",
       "0_comp                                 18    18  \n",
       "alpha_beta                             36    36  \n",
       "transposition_table                    36    36  \n",
       "transposition_table_opt_1              36    36  \n",
       "transposition_table_opt_2              36    36  \n",
       "transposition_table_opt_3              36    36  \n",
       "transposition_table_opt_all            36    36  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_data.groupby([\"algorithm\"]).count()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preliminary Code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following packages need to be imported:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# scipy contains statistical tests and other useful content\n",
    "import scipy.stats\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_decision(pvalue, alpha):\n",
    "    print(\"Test Result:\")\n",
    "    print(\"p-value = %.4f\" % (pvalue))\n",
    "    if pvalue < alpha:\n",
    "        print(\"H0 can be rejected on a level of significance of \" + str(alpha) + \".\")\n",
    "    else:\n",
    "        print(\"H0 cannot be rejected on a level of significance of \" + str(alpha) + \".\")\n",
    "        \n",
    "def compute_pvalue(pvalue, diff, alternative):\n",
    "    if alternative == \"greater\":\n",
    "        if diff > 0:\n",
    "            pvalue = pvalue / 2\n",
    "        else:\n",
    "            pvalue = 1 - pvalue / 2\n",
    "    elif alternative == \"less\":\n",
    "        if diff < 0:\n",
    "            pvalue = pvalue / 2\n",
    "        else:\n",
    "            pvalue = 1 - pvalue / 2\n",
    "    return pvalue\n",
    "\n",
    "def plot_hist(data, group):\n",
    "    # Plot a histogram\n",
    "    plt.hist(data, density = True, alpha = 0.5)\n",
    "\n",
    "    # Fit a normal distribution to the data\n",
    "    mu, std = norm.fit(data)\n",
    "\n",
    "    # Plot the probability density function\n",
    "    xmin, xmax = plt.xlim()\n",
    "    x = np.linspace(xmin, xmax, 201)\n",
    "    y = norm.pdf(x, mu, std)\n",
    "    plt.plot(x, y, \"black\")\n",
    "    title = \"Fit results of \" + group + \": mu = %.2f,  std = %.2f\" % (mu, std)\n",
    "    plt.title(title, pad=20)\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization of the Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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l9erVGT9+/At6Xr9uz39qkkWttf9SVUcn+VJVHdJa++UmRV6Y5MJk8K6PfTo2AACwFaZOnZpVq1bFJMr2NX78+EydOvUFPWc4Qe3hJNOGrE/tbRvq95LMSZLW2o1VNT7J3kl++oKqAQAAdphx48Zlv/32G+ky2IzhXPq4OMn+VbVfVe2e5F1JrtikzUNJ3pgkVXVQkvFJxHIAAICtsMWg1lpbl+T9Sa5JsjyDd3e8q6o+XlUn9pp9MMkfVNVtSS5JcnpzoSsAAMBWGdZn1FprV2XwJiFDt31kyPKyJMf2tzQAAIDRaVhfeA0AAMCOI6gBAAB0jKAGAADQMYIaAABAxwhqAAAAHSOoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0jqAEAAHSMoAYAANAxghoAAEDHCGoAAAAdI6gBAAB0jKAGAADQMYIaAABAxwhqAAAAHSOoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0jqAEAAHSMoAYAANAxghoAAEDHCGoAAAAdI6gBAAB0jKAGAADQMYIaAABAxwhqAAAAHSOoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0jqAEAAHSMoAYAANAxghoAAEDHCGoAAAAdI6gBAAB0jKAGAADQMYIaAABAxwhqAAAAHSOoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0zrKBWVXOq6p6qur+qznmONv9XVS2rqruq6iv9LRMAAGD0GLulBlU1Jsn5Sd6UZFWSxVV1RWtt2ZA2+yf5D0mOba39S1X92vYqGAAAYFc3nBm1I5Pc31p7oLX2VJJLk5y0SZs/SHJ+a+1fkqS19tP+lgkAADB6DCeoTUmycsj6qt62oX4jyW9U1Q1VdVNVzelXgQAAAKPNFi99fAH97J9kdpKpSX5QVTNaaz8f2qiq5ieZnyQvf/nL+3RoAACAXctwZtQeTjJtyPrU3rahViW5orX2dGvtwST3ZjC4baS1dmFrbWZrbeY+++yztTUDAADs0oYT1BYn2b+q9quq3ZO8K8kVm7T5ZgZn01JVe2fwUsgH+lcmAADA6LHFoNZaW5fk/UmuSbI8yd+31u6qqo9X1Ym9ZtckWV1Vy5J8P8m/b62t3l5FAwAA7MqG9Rm11tpVSa7aZNtHhiy3JH/UewAAALANhvWF1wAAAOw4ghoAAEDHCGoAAAAdI6gBAAB0jKAGAADQMYIaAABAxwhqAAAAHSOoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0jqAEAAHSMoAYAANAxghoAAEDHCGoAAAAdI6gBAAB0jKAGAADQMYIaAABAxwhqAAAAHSOoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0jqAEAAHSMoAYAANAxghoAAEDHCGoAAAAdI6gBAAB0jKAGAADQMYIaAABAxwhqAAAAHSOoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0jqAEAAHSMoAYAANAxghoAAEDHCGoAAAAdI6gBAAB0jKAGAADQMYIaAABAxwhqAAAAHSOoAQAAdIygBgAA0DHDCmpVNaeq7qmq+6vqnOdp97tV1apqZv9KBAAAGF22GNSqakyS85O8OcnBSU6tqoM3025SkrOT/KjfRQIAAIwmw5lROzLJ/a21B1prTyW5NMlJm2n350nOTbK2j/UBAACMOsMJalOSrByyvqq3bYOqOjzJtNbat/tYGwAAwKi0zTcTqardknw2yQeH0XZ+VQ1U1cAjjzyyrYcGAADYJQ0nqD2cZNqQ9am9betNSnJIkuuqakWSo5JcsbkbirTWLmytzWytzdxnn322vmoAAIBd2HCC2uIk+1fVflW1e5J3Jbli/c7W2prW2t6ttemttelJbkpyYmttYLtUDAAAsIvbYlBrra1L8v4k1yRZnuTvW2t3VdXHq+rE7V0gAADAaDN2OI1aa1cluWqTbR95jrazt70sAACA0WubbyYCAABAfwlqAAAAHSOoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0jqAEAAHSMoAYAANAxghoAAEDHCGoAAAAdI6gBAAB0jKAGAADQMYIaAABAxwhqAAAAHSOoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0jqAEAAHSMoAYAANAxghoAAEDHCGoAAAAdI6gBAAB0jKAGAADQMYIaAABAxwhqAAAAHSOoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0jqAEAAHSMoAYAANAxghoAAEDHCGoAAAAdI6gBAAB0jKAGAADQMYIaAABAxwhqAAAAHSOoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0jqAEAAHSMoAYAANAxghoAAEDHCGoAAAAdM6ygVlVzquqeqrq/qs7ZzP4/qqplVXV7Vf33qtq3/6UCAACMDlsMalU1Jsn5Sd6c5OAkp1bVwZs0uzXJzNbaa5J8Ncl/7nehAAAAo8VwZtSOTHJ/a+2B1tpTSS5NctLQBq2177fWnuit3pRkan/LBAAAGD2GE9SmJFk5ZH1Vb9tz+b0kV29uR1XNr6qBqhp45JFHhl8lAADAKNLXm4lU1dwkM5N8enP7W2sXttZmttZm7rPPPv08NAAAwC5j7DDaPJxk2pD1qb1tG6mq30ry4SRvaK39a3/KAwAAGH2GM6O2OMn+VbVfVe2e5F1JrhjaoKoOS/I3SU5srf20/2UCAACMHlsMaq21dUnen+SaJMuT/H1r7a6q+nhVndhr9ukkL05yeVUtraornqM7AAAAtmA4lz6mtXZVkqs22faRIcu/1ee6AAAARq2+3kwEAACAbSeoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0jqAEAAHSMoAYAANAxghoAAEDHCGoAAAAdI6gBAAB0jKAGAADQMYIaAABAxwhqAAAAHSOoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0jqAEAAHSMoAYAANAxghoAAEDHCGoAAAAdI6gBAAB0jKAGAADQMYIaAABAxwhqAAAAHSOoAQAAdIygBgAA0DGCGgAAQMcIagAAAB0jqAEAAHSMoAYAANAxghoAAEDHCGoAAAAdI6gBAAB0jKAGAADQMYIaAABAx4wd6QIAdlkfnTzSFfTXR9eMdAUAMGqYUQMAAOgYM2oAALAr2tWu7EhG1dUdZtQAAAA6RlADAADoGJc+8tx2tenyUTRVDgDAzk1QAwC6aVd7wzDxpiEwbC59BAAA6BhBDQAAoGOGFdSqak5V3VNV91fVOZvZv0dVXdbb/6Oqmt73SgEAAEaJLQa1qhqT5Pwkb05ycJJTq+rgTZr9XpJ/aa29Ksnnkpzb70IBAABGi+HMqB2Z5P7W2gOttaeSXJrkpE3anJTk73rLX03yxqqq/pUJAAAwegwnqE1JsnLI+qrets22aa2tS7ImyV79KBAAAGC02aG356+q+Unm91Yfr6p7duTxeWEq2TvJz0a6jr75mEledixjCLbNLjeGEuOIHcoY2ins+1w7hhPUHk4ybcj61N62zbVZVVVjk0xOsnrTjlprFya5cBjHpAOqaqC1NnOk64CdlTEE28YYgm1jDO3chnPp4+Ik+1fVflW1e5J3JblikzZXJJnXWz4lyfdaa61/ZQIAAIweW5xRa62tq6r3J7kmyZgkC1trd1XVx5MMtNauSPLfknypqu5P8mgGwxwAAABbYVifUWutXZXkqk22fWTI8tok7+hvaXSAy1Rh2xhDsG2MIdg2xtBOrFyhCAAA0C3D+YwaAAAAO5Cg1iFVNb2q7tyBx7uuqvp2J6Cq+sd+9QU70s4+9mBXtqPHJ2xPW/taqapOrqqD+1jH6VX160PW/7af/dMfgtpOpqrGjHQNz6W1dsxI1wDbS5fHHgA7h214rXRyks0Gqd5XY71QpyfZENRaa7/fWlu2VZWx3Qhq3TO2qi6uquVV9dWqmlhVK6rq3Kq6Jck7quoPqmpxVd1WVV+rqolJUlWLqmpBVf1jVT1QVaes77Sq/t+quqP3nE8NOd47qurmqrq3ql63uYJ67/5/rqoGenXNqqqvV9V9VfWJIe0e7/18WVX9oKqWVtWdVfW6qhrTq+/OXh3/rtf2lVX1napaUlU/rKoDe9vf0Wt7W1X9oP9/ZniWER97vXHy6d4xbq+qP+xtf9aY2pF/GNhWVfXu3r/p26rqG1X1YFWN6+17yfr1qnpVVV3ba3dLVb1yk36MEXZqQ14rze69vvpqVd3dO/9Ub9+nqmpZ79/4Z6rqmCQnJvl079/4K3vP/cuqGkhydu88dMqmx+ktb3Qe6rWbmeTiXn8TasiVHlV1aq/9nVV17tA+q+o/9fq5qape2tvuNdv20lrz6MgjyfQkLcmxvfWFST6UZEWSPx7Sbq8hy59I8oHe8qIkl2cwgB+c5P7e9jcn+cckE3vrv9r7eV2S/9JbPiHJtc9R13VJzu0tn53kx0lelmSPJKvW15Pk8d7PDyb5cG95TJJJSY5I8t0hff5K7+d/T7J/b/nfZPA7+JLkjiRThrb18Nhej66MvSTzk/xpb3mPJANJ9tvcmBrpv5mHx3AfSV6d5N4ke/fWfzXJRUlO7q3PHzIefpTkbb3l8Ukm9sbnnUPaGiMeO+1jyGul2UnWJJnaO3fcmOQ3k+yV5J787xv+/Urv56Ikpwzp57okXxiyvun+9cd5vvPQzE36m5nBWbaHkuyTwbvDf2/IWG1J3tpb/s9DxqLXbNvpYUate1a21m7oLX85g4M2SS4b0uaQ3uzTHUlOy+BJcL1vttZ+2Qanr1/a2/ZbSS5qrT2RJK21R4e0/3rv55IMngyfy/ovOb8jyV2ttZ+01v41yQNJpm3SdnGS91TVR5PMaK091mv3iqr6fFXNSfKLqnpxkmOSXF5VS5P8TQYDYJLckGRRVf1BBk+6sL11Yez9dpJ398bDjzJ4wt4/mx9TsLP4P5Nc3lr7WbJhHPxtkvf09r8nyUVVNSmDL/a+0Wu3dv3YGcIYYVdyc2ttVWvtl0mWZvBcsCbJ2iT/rarenmTTMTDUZc+zb73nOw9tzqwk17XWHmmtrUtycZLX9/Y9leRbveWh5y6v2bYTQa17Nv2+hPXr//+QbYuSvL+1NiPJxzL4ruN6/zpkuYZxvPXtn0nve/Wq6qLeVPhVm2n3y02O8cts8n18rbUfZHBQP5zBgfvu1tq/JHltBt+xOTODJ+ndkvy8tXbokMdBvT7OTPKnGQyBS6pqr2H8LrAtRnzs9Z73gSHjYb/W2v+3uTE1jP6hs3pvikyvqtlJxrTWhnuzEGOEXcnQ88YzScb2wtGRSb6a5HeSfOd5nj/0/LQuvdf1VbVbkt37W2qS5OnW2vpz44Zzl9ds24+g1j0vr6qje8v/d5LrN9NmUpKf9K7vP20YfX43g+80rv88za8+X+PW2nt6J8ATXkDdG1TVvkn+Z2vtv2YwkB1eVXsn2a219rUMDubDW2u/SPJgVb2j97yqqtf2ll/ZWvtRG/xi9Ufy7Fk76LcRH3tJrkly1pDP7vxGVb1oc2NqGMeGrvheBj+TuVey0Tj4YpKvZPAyyPRmwVZV1cm9dnusHztDGCPs0npXG01urV2V5N9l8E3uJHksg+eg57Iigx8zSQY/zzaut/xc56Hn6u/mJG+oqr1r8CZapyb5H1uo2Wu27URQ6557kryvqpYn2TPJX2+mzZ9l8JKPG5LcvaUOW2vfyeCliwO9y0U+1LdqN292ktuq6tYk70zyV0mmJLmud/wvJ/kPvbanJfm9qrotyV1JTupt//T6D7Jm8Nrq27ZzzdCFsfe3SZYluaX3b/9vMviO5ew8e0zBTqG1dleS/5Tkf/T+r/9sb9fFGRxrlwxp/m+T/D9VdXsG/+//PzbpzhhhVzcpybd6Y+D6JH/U235pkn9fVbfWJjfZ6fmvGQxYtyU5Or3Ztuc5Dy1KcsH6m4ms76S19pMk5yT5fgZfey1prf3DFmr2mm07qf89gwkAsGP07jx3Umvt3450LQBdtDXfuwAAsNWq6vMZvBvdVl1iDzAamFEDAADoGJ9RAwAA6BhBDQAAoGMENQAAgI4R1AAAADpGUAMAAOgYQQ0AAKBj/hfkzg9SdgwyKAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6Pv30Ux544AGGDh3KW2+9RWlpKaNGjeKSSy5hwYIF2x2npKSEjRs3brd96NChTJs2jc2bN/Pee+/x9NNPM2jQoF38qWz9c/nzn/9My5YtadOmDe+88w6PPfbYVn23vA9u2rRpHH300Vu1HXTQQXTt2pXp06cDVe+hW7Ro0S7XUxNn1CRJkqR9pZbb6Rdbu3btGDJkCL169aJFixYccsgh1W3Dhg1j4sSJ9OjRg8MPP5zBgwfXur9LLrmEFStWkFLixBNPpG/fvixcuJBBgwZx1llnUVlZyahRoygrKwNgzJgx1UHq/PPP58gjj2TmzJlccsklNGnShJKSEn7zm99sd5yKigr69OlD//79mTp1avX2M844gzlz5tC3b18iguuvv54vfelLu3wDj4qKCoYNG8ahhx7KU089xZFHHkn37t3p3LkzQ4YM2arvhx9+SJ8+fWjWrBl/+MMfttvX1KlTGTt2LFdddRUbN27k3HPPpW/fvrtUT01iR3dD2dvKyspSLperl2NLkiRJ+8KyZcvo0aNHfZexV02ZMoVcLsctt9xS36VkWk2/CxExP6VUVlN/L32UJEmSpIypU1CLiGER8UpErIyIcTW0fzkinoqIFyPipYj4ZvFLlSRJkpQ1Y8aMyexs2hlnnEG/fv22esycObO+y6qTWt+jFhFNgVuBk4BKYF5EzEgpLS3odjlwT0rpNxHRE3gU6LIX6pUkSZKkOnnggQfqu4TdVpcZtUHAypTSaymlz4A/AsO36ZOAg/LLbYC3ileiJEmStP+qr3tCKDt253egLkGtI7C6YL0yv63QFcCoiKikajbt72raUURUREQuInLvvffeLhcrSZIk7U+aN2/OmjVrDGuNWEqJNWvW0Lx58116XrFuzz8CmJJS+ueIOBr4fUT0Sil9vk2Rk4BJUHXXxyIdW5IkScqkTp06UVlZiZMUjVvz5s3p1KnTLj2nLkHtTaBzwXqn/LZC3wWGAaSU5kREc6A98O4uVSNJkiQ1ICUlJXTt2rW+y9B+qC6XPs4DukVE14g4EDgXmLFNnzeAEwEiogfQHPDPBpIkSZK0G2oNaimlTcD3gZnAMqru7rgkIsZHxGn5bj8GvhcRi4A/AGOSF+JKkiRJ0m6p03vUUkqPUnWTkMJtPy9YXgoMKW5pkiRJktQ41ekDryVJkiRJ+45BTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLG1CmoRcSwiHglIlZGxLgd9PnfEbE0IpZExN3FLVOSJEmSGo8DausQEU2BW4GTgEpgXkTMSCktLejTDfhHYEhK6cOI+OLeKliSJEmSGrq6zKgNAlamlF5LKX0G/BEYvk2f7wG3ppQ+BEgpvVvcMiVJkiSp8ahLUOsIrC5Yr8xvK/Q14GsR8WxEzI2IYcUqUJIkSZIam1ovfdyF/XQDyoFOwNMR0Tul9FFhp4ioACoAvvzlLxfp0JIkSZLUsNRlRu1NoHPBeqf8tkKVwIyU0saU0uvAf1IV3LaSUpqUUipLKZV16NBhd2uWJEmSpAatLkFtHtAtIrpGxIHAucCMbfo8SNVsGhHRnqpLIV8rXpmSJEmS1HjUGtRSSpuA7wMzgWXAPSmlJRExPiJOy3ebCayJiKXAU8AlKaU1e6toSZIkSWrIIqVULwcuKytLuVyuXo4tSZIkSfUtIuanlMpqaqvTB15LkiRJkvYdg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZcwB9V2AJDVYV7Sp7wqK64q19V2BJGlXNLTzEDSqc5EzapIkSZKUMc6oSZKkbHI2QFIj5oyaJEmSJGWMQU2SJEmSMsZLH7VjDe2SEy83ybwu4x6p7xKKalXz+q5AkiTtr5xRkyRJkqSMMahJkiRJUsYY1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljLfnlyRJkvBjYpQtzqhJkiRJUsYY1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjLGoCZJkiRJGWNQkyRJkqSMMahJkiRJUsYY1CRJkiQpYwxqkiRJkpQxBjVJkiRJypgD6ruAhqLLuEfqu4SiW9W8viuQJO2KhnYu8jwkqTFzRk2SJEmSMqZOQS0ihkXEKxGxMiLG7aTfWRGRIqKseCVKkiRJUuNSa1CLiKbArcDJQE9gRET0rKFfa+CHwPPFLlKSJEmSGpO6zKgNAlamlF5LKX0G/BEYXkO/XwLXARuKWJ8kSZIkNTp1CWodgdUF65X5bdUioj/QOaXUsN7FLEmSJEn1YI9vJhIRTYAbgR/XoW9FROQiIvfee+/t6aElSZIkqUGqS1B7E+hcsN4pv22L1kAvYFZErAIGAzNquqFISmlSSqkspVTWoUOH3a9akiRJkhqwugS1eUC3iOgaEQcC5wIztjSmlNamlNqnlLqklLoAc4HTUkq5vVKxJEmSJDVwtQa1lNIm4PvATGAZcE9KaUlEjI+I0/Z2gZIkSZLU2BxQl04ppUeBR7fZ9vMd9C3f87IkSZIkqfHa45uJSJIkSZKKy6AmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMXUKahExLCJeiYiVETGuhvYfRcTSiHgpIv49Ir5S/FIlSZIkqXGoNahFRFPgVuBkoCcwIiJ6btPtRaAspdQHuBe4vtiFSpIkSVJjUZcZtUHAypTSaymlz4A/AsMLO6SUnkoprcuvzgU6FbdMSZIkSWo86hLUOgKrC9Yr89t25LvAYzU1RERFROQiIvfee+/VvUpJkiRJakSKejORiBgFlAG/qqk9pTQppVSWUirr0KFDMQ8tSZIkSQ3GAXXo8ybQuWC9U37bViLir4CfAsenlP6rOOVJkiRJUuNTlxm1eUC3iOgaEQcC5wIzCjtExJHAvwCnpZTeLX6ZkiRJktR41BrUUkqbgO8DM4FlwD0ppSURMT4iTst3+xXQCpgeEQsjYsYOdidJkiRJqkVdLn0kpfQo8Og2235esPxXRa5LkiRJkhqtot5MRJIkSZK05wxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjLGoCZJkiRJGWNQkyRJkqSMMahJkiRJUsYY1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjLGoCZJkiRJGWNQkyRJkqSMMahJkiRJUsYY1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjLGoCZJkiRJGWNQkyRJkqSMMahJkiRJUsYY1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjLGoCZJkiRJGWNQkyRJkqSMMahJkiRJUsYY1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjLGoCZJkiRJGWNQkyRJkqSMMahJkiRJUsYY1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjKmTkEtIoZFxCsRsTIixtXQ3iwipuXbn4+ILkWvVJIkSZIaiVqDWkQ0BW4FTgZ6AiMiouc23b4LfJhS+kvg18B1xS5UkiRJkhqLusyoDQJWppReSyl9BvwRGL5Nn+HA7/LL9wInRkQUr0xJkiRJajzqEtQ6AqsL1ivz22rsk1LaBKwF2hWjQEmSJElqbA7YlweLiAqgIr/6SUS8si+Pr10T0B54v77rKJorneTVvuUYkvZMgxtD4DjSPuUY2i98ZUcNdQlqbwKdC9Y75bfV1KcyIg4A2gBrtt1RSmkSMKkOx1QGREQupVRW33VI+yvHkLRnHEPSnnEM7d/qcunjPKBbRHSNiAOBc4EZ2/SZAYzOL58NPJlSSsUrU5IkSZIaj1pn1FJKmyLi+8BMoCkwOaW0JCLGA7mU0gzgX4HfR8RK4AOqwpwkSZIkaTfU6T1qKaVHgUe32fbzguUNwDnFLU0Z4GWq0p5xDEl7xjEk7RnH0H4svEJRkiRJkrKlLu9RkyRJkiTtQwa1DImILhGxeB8eb1ZEFO1OQBHxXLH2Je1L+/vYkxqyfT0+pb1pd18rRcTpEdGziHWMiYhDC9Z/W8z9qzgMavuZiGha3zXsSErpmPquQdpbsjz2JEn7hz14rXQ6UGOQyn801q4aA1QHtZTS+SmlpbtVmfYag1r2HBARUyNiWUTcGxGlEbEqIq6LiAXAORHxvYiYFxGLIuK+iCgFiIgpETEhIp6LiNci4uwtO42IyyLi5fxzri043jkR8UJE/GdEDK2poPxf/38dEbl8XQMj4v6IWBERVxX0+yT/9S8i4umIWBgRiyNiaEQ0zde3OF/HP+T7HhYR/xYR8yPimYjont9+Tr7vooh4uvg/Zmk79T728uPkV/ljvBQRF+S3bzem9uUPRtpTEXFe/nd6UUQ8EBGvR0RJvu2gLesR8ZcR8US+34KIOGyb/ThGtF8reK1Unn99dW9ELM+ffyLfdm1ELM3/jt8QEccApwG/yv+OH5Z/7k0RkQN+mD8Pnb3tcfLLW52H8v3KgKn5/bWIgis9ImJEvv/iiLiucJ8RcXV+P3Mj4pD8dl+z7S0pJR8ZeQBdgAQMya9PBi4GVgGXFvRrV7B8FfB3+eUpwHSqAnhPYGV++8nAc0Bpfv3g/NdZwD/nl78JPLGDumYB1+WXfwi8BfwF0Ayo3FIP8En+64+Bn+aXmwKtgQHA4wX7/EL+678D3fLLR1H1GXwALwMdC/v68LG3HlkZe0AFcHl+uRmQA7rWNKbq+2fmw0ddH8ARwH8C7fPrBwN3AKfn1ysKxsPzwBn55eZAaX58Li7o6xjxsd8+Cl4rlQNrgU75c8cc4FigHfAK/3PDvy/kv04Bzi7YzyzgtoL1bdu3HGdn56GybfZXRtUs2xtAB6ruDv9kwVhNwLfyy9cXjEVfs+2lhzNq2bM6pfRsfvkuqgYtwLSCPr3ys08vAyOpOglu8WBK6fNUNX19SH7bXwF3pJTWAaSUPijof3/+63yqToY7suVDzl8GlqSU3k4p/RfwGtB5m77zgO9ExBVA75TSx/l+X42ImyNiGPDniGgFHANMj4iFwL9QFQABngWmRMT3qDrpSntbFsbe14Hz8uPheapO2N2oeUxJ+4v/BUxPKb0P1ePgt8B38u3fAe6IiNZUvdh7IN9vw5axU8AxoobkhZRSZUrpc2AhVeeCtcAG4F8j4kxg2zFQaNpO2rbY2XmoJgOBWSml91JKm4CpwHH5ts+Ah/PLhecuX7PtJQa17Nn28xK2rH9asG0K8P2UUm/gSqr+6rjFfxUsRx2Ot6X/ZvKfqxcRd+Snwh+tod/n2xzjc7b5PL6U0tNUDeo3qRq456WUPgT6UvUXmwupOkk3AT5KKfUrePTI7+NC4HKqQuD8iGhXh+9F2hP1Pvbyz/u7gvHQNaX0/2saU3XYv5RZ+T+KdImIcqBpSqmuNwtxjKghKTxvbAYOyIejQcC9wKnAv+3k+YXnp03kX9dHRBPgwOKWCsDGlNKWc2P1ucvXbHuPQS17vhwRR+eX/w8wu4Y+rYG389f3j6zDPh+n6i+NW95Pc/DOOqeUvpM/AX5zF+quFhFfAd5JKd1OVSDrHxHtgSYppfuoGsz9U0p/Bl6PiHPyz4uI6JtfPiyl9Hyq+mD199h+1k4qtnofe8BMYGzBe3e+FhEtaxpTdTi2lBVPUvWezHaw1Ti4E7ibqssgyc+CVUbE6fl+zbaMnQKOETVo+auN2qSUHgX+gao/cgN8TNU5aEdWUfU2E6h6P1tJfnlH56Ed7e8F4PiIaB9VN9EaAfxHLTX7mm0vMahlzyvA30bEMqAt8Jsa+vyMqks+ngWW17bDlNK/UXXpYi5/ucjFRau2ZuXAooh4Efg28H+BjsCs/PHvAv4x33ck8N2IWAQsAYbnt/9qyxtZqbq2etFerlnKwtj7LbAUWJD/3f8Xqv5iWc72Y0raL6SUlgBXA/+R/7/+xnzTVKrG2h8Kuv818IOIeImq//u/tM3uHCNq6FoDD+fHwGzgR/ntfwQuiYgXY5ub7OTdTlXAWgQcTX62bSfnoSnAxC03E9myk5TS28A44CmqXnvNTyn9v1pq9jXbXhL/M4MpSZK0b+TvPDc8pfTX9V2LJGXR7nzugiRJ0m6LiJupuhvdbl1iL0mNgTNqkiRJkpQxvkdNkiRJkjLGoCZJkiRJGWNQkyRJkqSMMahJkiRJUsYY1CRJkiQpYwxqkiRJkpQx/w13XihN0W4uHQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KkpISzjjjDH784x/XaX/rrbfSt29fhgwZwurVq/fpb82aNYwaNYpBgwYxbNgwVq1atd9/j/Xr1/PXf/3X9OvXj5EjR/KnP/0JqP4uuiuvvJKSkhJOO+00Hn/8cT7++GNuuOEGZs+eTf/+/Wse697+4i/+gsGDB1NQULDf435anvooSZIkNYKbb76Z5cuXU1VVxfz58xk9ejTLly+nR48eAEyfPp1OnTqxfft2Bg8ezIUXXkjnzp3ZunUrQ4cOZcqUKXz/+9/nnnvu4frrr2fy5MnMmzePU045hc2bN9cc5+WXX2b58uUUFhYyePBgRo8eTUQwY8YMFi1aREqJM888k+HDh7N27Vq6du3KE088AcCWLVv2qfmuu+6iqqpqn8fzhz/8gaqqKpYtW8Y777zD4MGDawLjK6+8wooVK+jatSulpaW88MILfOELX9inj2uuuYbbb7+dZ599tuaUxilTptCpUyd2797NyJEjefXVV+nXrx8AHTp04LXXXuO+++7jO9/5Do8//nid/ioqKpg6dSo9e/Zk0aJFXH311TzzzDP1/nt861vf4rLLLuOyyy5j+vTpXHPNNTzyyCNAdYh7+eWXWbNmDSNGjGD16tVMnjyZyspK7rrrroP8SzcOZ9QkSZKkI2DIkCE1IQ2qZ5f2zJpt2LCBN954A4Djjz+ec889F4BBgwaxfv16AEpLSykvL+eee+5h9+7dNf188YtfpHPnzrRp04YLLriABQsWsGDBAsaOHUvbtm1p164dF1xwAc8//zx9+/blqaee4gc/+AHPP/88HTo0/HN7CxYsYNy4cbRs2ZKTTz6Z4cOHs3jx4prH1q1bN1q0aEH//v1ram6Ihx56iIEDBzJgwABWrFjBypUra/aNGzeu5ufChQvr3O+jjz7ixRdf5OKLL6Z///584xvf4M0339zvcRYuXMjf//3fA/C1r32NBQsW1Oz7u7/7O1q0aEHPnj353Oc+d8CZuSPFGTVJkiTpCGjbtm3N8vz583n66adZuHAhhYWFlJWVsWPHDgAKCgqICABatmxZ85m2qVOnsmjRIp544gkGDRrEkiVLAGra7rH3em2nnXYaS5cuZe7cuVx//fWMHDmSG2644bAfW6tWrWqWa9d8MOvWreO2225j8eLFdOzYkfLy8prnAeo+lr0f1yeffMKJJ55Y7+zfoTqU5/BIcUZNkiRJagTt27fnww8/rHffli1b6NixI4WFhaxatYqXXnrpoP2tWbOGM888k8mTJ9OlSxc2bNgAwFNPPcV7773H9u3beeSRRygtLWXYsGE88sgjbNu2ja1bt/Lwww8zbNgwNm3aRGFhIZdeeikTJkxg6dKl+xynoKCAnTt37rN92LBhzJ49m927d/P222/z3HPPMWTIkEN8Vuo+Lx988AFt27alQ4cOvPXWWzz55JN12u75bNjs2bM566yz6uw74YQT6NGjB3PmzAGqP0O3bNmy/R737LPP5sEHHwRg1qxZDBs2rGbfnDlz+OSTT1izZg1r167l9NNPP+C/35HgjJokSZKah4NcTj/fOnfuTGlpKUVFRbRp04aTTz65Zt+oUaOYOnUqvXv35vTTT2fo0KEH7W/ChAm88cYbpJQYOXIkxcXFVFVVMWTIEC688EI2btzIpZdeSklJCVB9kYw9QeqKK65gwIABzJs3jwkTJtCiRQsKCgq4++679zlORUUF/fr1Y+DAgcyaNatm+9ixY1m4cCHFxcVEBLfeeiuf+cxnDvk0wYqKCkaNGkXXrl159tlnGTBgAL169eLUU0+ltLS0Ttv333+ffv360apVKx544IF9+po1axZXXXUVP/nJT9i5cyeXXHIJxcXF9R73F7/4BZdffjk//elP6dKlCzNmzKjZ99nPfpYhQ4bwwQcfMHXqVFq3bs2IESO4+eab6d+/Pz/84Q/56le/uk+f//Zv/0ZJSQkffPABLVq04I477mDlypWccMIJh/Sc1Cf2d0WWxlZSUpIqKyub5NiSJEk69r3++uv07t27qctoVDNnzmzSC14cC8rLyzn33HO56KKLGvU49f0+RsSSlFJJfe099VGSJEmSMqZBpz5GxCjg50BL4N6U0s177f8s8GvgxFybiSmlA387nCRJkqTDUl5eTnl5eVOXUa+xY8eybt26OttuueUWvvSlLzXqcadMmVLzubU9Lr74Yq677rp628+cOfOgfc6YMYOf//zndbaVlpbyy1/+8lPXeTAHPfUxIloC/wp8EdgILAbGpZRW1mozDXglpXR3RPQB5qaUuh+oX099lCRJUmNqDqc+6ujRGKc+DgFWp5TWppQ+Bh4ExuzVJgF7PjHXAdh0SFVLkiRJjaCprscg1fZpfg8bEtROATbUWt+Y21bbJODSiNgIzAW+VV9HEVEREZURUfn2228fcrGSJElSQ7Vu3Zp3333XsKYmlVLi3XffpXXr1od0v3xdnn8cMDOl9N8j4izgNxFRlFL6ZK8ipwHToPrUxzwdW5IkSdpHt27d2LhxI04QqKm1bt2abt26HdJ9GhLU/gycWmu9W25bbf8AjAJIKS2MiNbAScC/H1I1kiRJUp4UFBTQo0ePpi5D+lQacurjYqBnRPSIiOOBS4BH92rzJ2AkQET0BloD/ulCkiRJkj6Fgwa1lNIu4JvAPOB14KGU0oqImBwR5+WafQ/4x4hYBjwAlCdPBpYkSZKkT6VBn1HLfSfa3L223VBreSVQmt/SJEmSJKl5asipj5IkSZKkI8igJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljGhTUImJURPwxIlZHxMT9tPm7iFgZESsi4v78lilJkiRJzcdxB2sQES2BXwJfBDYCiyPi0ZTSylptegI/BEpTSu9HxF80VsGSJEmSdKxryIzaEGB1SmltSulj4EFgzF5t/hH4ZUrpfYCU0r/nt0xJkiRJaj4aEtROATbUWt+Y21bbacBpEfFCRLwUEaPyVaAkSZIkNTcHPfXxEPrpCZQB3YDnIqJvSmlz7UYRUQFUAHz2s5/N06ElSZIk6djSkBm1PwOn1lrvlttW20bg0ZTSzpTSOuBfqQ5udaSUpqWUSlJKJV26dPm0NUuSJEnSMa0hQW0x0DMiekTE8cAlwKN7tXmE6tk0IuIkqk+FXJu/MiVJkiSp+ThoUEsp7QK+CcwDXgceSimtiIjJEXFertk84N2IWAk8C0xIKb3bWEVLkiRJ0rEsUkpNcuCSkpJUWVnZJMeWJEmSpKYWEUtSSiX17WvQF15LkiRJko4cg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZcxxTV2AJO3RfeITTV1CXq2/eXRTlyBJOgS+DilLnFGTJEmSpIxxRk2SpGOEswGSdOxwRk2SJEmSMsagJkmSJEkZ46mPeXKsnW4CnnIiSZIkNRVn1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjLGoCZJkiRJGWNQkyRJkqSMMahJkiRJUsYY1CRJkiQpY45r6gKUYZM6NHUF+TVpS1NXIEmSJDWIM2qSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGVMg4JaRIyKiD9GxOqImHiAdhdGRIqIkvyVKEmSJEnNy0GDWkS0BH4JfBnoA4yLiD71tGsPfBtYlO8iJUmSJKk5Oa4BbYYAq1NKawEi4kFgDLByr3b/BNwCTMhrhZJ0tJrUoakryK9JW5q6AkmSmo2GnPp4CrCh1vrG3LYaETEQODWl9EQea5MkSZKkZumwLyYSES2A24HvNaBtRURURkTl22+/fbiHliRJkqRjUkOC2p+BU2utd8tt26M9UATMj4j1wFDg0fouKJJSmpZSKkkplXTp0uXTVy1JkiRJx7CGBLXFQM+I6BERxwOXAI/u2ZlS2pJSOiml1D2l1B14CTgvpVTZKBVLkiRJ0jHuoBcTSSntiohvAvOAlsD0lNKKiJgMVKaUHj1wD5IkSZKOuGPtolbQrC5s1ZCrPpJSmgvM3WvbDftpW3b4ZUmSJElS83XYFxORJEmSJOWXQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDHHNXUBkiRJ9ZrUoakryL9JW5q6AklHCWfUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZ06CgFhGjIuKPEbE6IibWs/+7EbEyIl6NiP8dEX+V/1IlSZIkqXk4aFCLiJbAL4EvA32AcRHRZ69mrwAlKaV+wO+AW/NdqCRJkiQ1Fw2ZURsCrE4prU0pfQw8CIyp3SCl9GxKaVtu9SWgW37LlCRJkqTmoyFB7RRgQ631jblt+/MPwJP17YiIioiojIjKt99+u+FVSpIkSVIzkteLiUTEpUAJ8NP69qeUpqWUSlJKJV26dMnnoSVJkiTpmHFcA9r8GTi11nq33LY6IuJvgOuA4Sml/8hPeZIkSZLU/DRkRm0x0DMiekTE8cAlwKO1G0TEAOCfgfNSSv+e/zIlSZIkqfk4aFBLKe0CvgnMA14HHkoprYiIyRFxXq7ZT4F2wJyIqIqIR/fTnSRJkiTpIBpy6iMppbnA3L223VBr+W/yXJckSZIkNVt5vZiIJEmSJOnwGdQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZUyDglpEjIqIP0bE6oiYWM/+VhExO7d/UUR0z3ulkiRJktRMHDSoRURL4JfAl4E+wLiI6LNXs38A3k8p/SfgZ8At+S5UkiRJkpqLhsyoDQFWp5TWppQ+Bh4ExuzVZgzw69zy74CRERH5K1OSJEmSmo+GBLVTgA211jfmttXbJqW0C9gCdM5HgZIkSZLU3Bx3JA8WERVARW71o4j445E8vg5NwEnAO01dR97c6CSvjizHkHR4jrkxBI4jHVGOoaPCX+1vR0OC2p+BU2utd8ttq6/Nxog4DugAvLt3RymlacC0BhxTGRARlSmlkqauQzpaOYakw+MYkg6PY+jo1pBTHxcDPSOiR0QcD1wCPLpXm0eBy3LLFwHPpJRS/sqUJEmSpObjoDNqKaVdEfFNYB7QEpieUloREZOBypTSo8D/AH4TEauB96gOc5IkSZKkT6FBn1FLKc0F5u617YZayzuAi/NbmjLA01Slw+MYkg6PY0g6PI6ho1h4hqIkSZIkZUtDPqMmSZIkSTqCDGoZEhHdI2L5ETze/IjI25WAIuLFfPUlHUlH+9iTjmVHenxKjenTvleKiPMjok8e6yiPiK611u/NZ//KD4PaUSYiWjZ1DfuTUjq7qWuQGkuWx54k6ehwGO+VzgfqDVK5r8Y6VOVATVBLKV2RUlr5qSpTozGoZc9xETErIl6PiN9FRGFErI+IWyJiKXBxRPxjRCyOiGUR8fuIKASIiJkRcWdEvBgRayPioj2dRsQPIuK13H1urnW8iyPi5Yj414gYVl9Bub/+/ywiKnN1DY6IP0TEGxHxk1rtPsr9/MuIeC4iqiJieUQMi4iWufqW5+r4r7m2n4+If4mIJRHxfET0ym2/ONd2WUQ8l/+nWdpHk4+93Dj5ae4Yr0bEN3Lb9xlTR/KJkQ5XRHw99zu9LCIejoh1EVGQ23fCnvWI+E8R8XSu3dKI+Pxe/ThGdFSr9V6pLPf+6ncRsSr3+hO5fTdHxMrc7/htEXE2cB7w09zv+Odz970jIiqBb+dehy7a+zi55TqvQ7l2JcCsXH9totaZHhExLtd+eUTcUrvPiJiS6+eliDg5t933bI0lpeQtIzegO5CA0tz6dOBaYD3w/VrtOtda/gnwrdzyTGAO1QG8D7A6t/3LwItAYW69U+7nfOC/55a/Ajy9n7rmA7fklr8NbAL+EmgFbNxTD/BR7uf3gOtyyy2B9sAg4KlafZ6Y+/m/gZ655TOp/g4+gNeAU2q39eatsW5ZGXtABXB9brkVUAn0qG9MNfVz5s1bQ2/AGcC/Aifl1jsBM4Dzc+sVtcbDImBsbrk1UJgbn8trtXWMeDtqb7XeK5UBW4BuudeOhcAXgM7AH/n/F/w7MfdzJnBRrX7mA7+qtb73/j3HOdDrUMle/ZVQPcv2J6AL1VeHf6bWWE3A3+aWb601Fn3P1kg3Z9SyZ0NK6YXc8m+pHrQAs2u1KcrNPr0GjKf6RXCPR1JKn6Tq6euTc9v+BpiRUtoGkFJ6r1b7P+R+LqH6xXB/9nzJ+WvAipTSmyml/wDWAqfu1XYxcHlETAL6ppQ+zLX7XET8IiJGAR9ERDvgbGBORFQB/0x1AAR4AZgZEf9I9Yuu1NiyMPb+M/D13HhYRPULdk/qH1PS0eKvgTkppXegZhzcC1ye2385MCMi2lP9Zu/hXLsde8ZOLY4RHUteTiltTCl9AlRR/VqwBdgB/I+IuADYewzUNvsA+/Y40OtQfQYD81NKb6eUdgGzgHNy+z4GHs8t137t8j1bIzGoZc/e35ewZ31rrW0zgW+mlPoCN1L9V8c9/qPWcjTgeHva7yb3vXoRMSM3FT63nnaf7HWMT9jr+/hSSs9RPaj/TPXA/XpK6X2gmOq/2FxJ9Yt0C2BzSql/rVvvXB9XAtdTHQKXRETnBjwW6XA0+djL3e9btcZDj5TS/6pvTDWgfymzcn8U6R4RZUDLlFJDLxbiGNGxpPbrxm7guFw4GgL8DjgX+JcD3L/269Mucu/rI6IFcHx+SwVgZ0ppz2tjzWuX79kaj0Etez4bEWfllv8eWFBPm/bAm7nz+8c3oM+nqP5L457P03Q6UOOU0uW5F8CvHELdNSLir4C3Ukr3UB3IBkbESUCLlNLvqR7MA1NKHwDrIuLi3P0iIopzy59PKS1K1V+s/jb7ztpJ+dbkYw+YB1xV67M7p0VE2/rGVAOOLWXFM1R/JrMz1BkH9wH3U30aJLlZsI0RcX6uXas9Y6cWx4iOabmzjTqklOYC/5XqP3IDfEj1a9D+rKf6YyZQ/Xm2gtzy/l6H9tffy8DwiDgpqi+iNQ74Pwep2fdsjcSglj1/BP5LRLwOdATurqfNf6P6lI8XgFUH6zCl9C9Un7pYmTtd5Nq8VVu/MmBZRLwCfBX4OXAKMD93/N8CP8y1HQ/8Q0QsA1YAY3Lbf7rng6xUn1u9rJFrlrIw9u4FVgJLc7/7/0z1XyzL2HdMSUeFlNIKYArwf3L/19+e2zWL6rH2QK3mXwOuiYhXqf6//zN7decY0bGuPfB4bgwsAL6b2/4gMCEiXom9LrKTcw/VAWsZcBa52bYDvA7NBKbuuZjInk5SSm8CE4FnqX7vtSSl9D8PUrPv2RpJ/P8ZTEmSpCMjd+W5MSmlrzV1LZKURZ/mexckSZI+tYj4BdVXo/tUp9hLUnPgjJokSZIkZYyfUZMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZcz/A+AAo+/P6ue6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ge3LnnXeyceNGRowYwYgRIwC44oorKCsr47TTTuNHP/pRvfa33nor/fr1Y+jQoaxatWqv7a1evZpRo0YxePBghg8fzsqVK/f577Fu3Tr+7u/+jv79+zNy5Ej++Mc/ArXfRXf55ZdTVlbGKaecwmOPPcaHH37Iddddx8yZMxkwYED+te6pQ4cORET+vd09XQie+ihJkiQ1gZtvvplly5ZRU1PDvHnzGD16NMuWLaNnz54ATJ06leOPP55t27YxZMgQLrjgArp06cKWLVsYNmwYN954I9/97ne55557uPbaa5k0aRJz587lpJNOYtOmTfn9vPTSSyxbtozi4mKGDBnC6NGjiQimTZvGwoULSSlx+umnc/bZZ7NmzRq6devG448/DsDmzZv3qvmuu+6ipqZmr9fz+9//npqaGpYuXcrbb7/NkCFD8oHx5ZdfZvny5XTr1o3y8nKef/75Bk8BvOqqq7j99tt55pln8qc03njjjRx//PHs2rWLkSNH8sorr9C/f38AOnXqxKuvvsp9993Ht771LR577LF626uqqmLy5Mn06tWLhQsXcuWVV/L00083+O/xjW98g0svvZRLL72UqVOnctVVVzF79mygNsS99NJLrF69mhEjRrBq1SomTZpEdXU1d911137/nR9++GG+//3v8+c//zn/vhaCI2qSJEnSYTB06NB8SIPa0aXdo2br16/n9ddfB+DYY4/lnHPOAWDw4MGsW7cOgPLyciorK7nnnnvYtWtXfjuf+9zn6NKlC+3ateP8889n/vz5zJ8/n7Fjx9K+fXs6dOjA+eefz3PPPUe/fv148skn+d73vsdzzz1Hp06Nv25v/vz5jBs3jtatW3PiiSdy9tlns2jRovxr6969O61atWLAgAH5mhvjoYceYtCgQQwcOJDly5ezYsWK/Lpx48blfy5YsKDe8z744ANeeOEFLrroIgYMGMDXvvY13njjjX3uZ8GCBfzTP/0TAF/+8peZP39+ft0//uM/0qpVK3r16sWnP/3p/Y7M7Wns2LGsXLmS2bNn88Mf/rDRzzsQR9QkSZKkw6B9+/b56Xnz5vHUU0+xYMECiouLqaioYPv27QAUFRXlT6Fr3bp1/pq2yZMns3DhQh5//HEGDx7M4sWLAfY63W5/p9+dcsopLFmyhDlz5nDttdcycuRIrrvuukN+bW3atMlP1635QNauXcttt93GokWL6Ny5M5WVlfn3Aeq/lj1f10cffcRxxx3X4OjfwTqY93BfzjrrLNasWcPbb7+91w1QPg5H1CRJkqQm0LFjR95///0G123evJnOnTtTXFzMypUrefHFFw+4vdWrV3P66aczadIkunbtyvr16wF48skn+ctf/sK2bduYPXs25eXlDB8+nNmzZ7N161a2bNnCww8/zPDhw9m4cSPFxcVccsklTJgwgSVLluy1n6KiInbs2LHX8uHDhzNz5kx27drFW2+9xbPPPsvQoUMP8l2p/7689957tG/fnk6dOvHmm2/yxBNP1Gu7+9qwmTNncsYZZ9Rb94lPfIKePXsya9YsoPYauqVLl+5zv2eeeSYPPvggADNmzGD48OH5dbNmzeKjjz5i9erVrFmzhlNPPXW//367rVq1Kn893pIlS/jrX/9Kly5dGvM2HJAjapIkSWoZDnA7/ULr0qUL5eXllJSU0K5dO0488cT8ulGjRjF58mT69OnDqaeeyrBhww64vQkTJvD666+TUmLkyJGUlpZSU1PD0KFDueCCC9iwYQOXXHIJZWVlQO1NMnYHqcsuu4yBAwcyd+5cJkyYQKtWrSgqKuLuu+/eaz9VVVX079+fQYMGMWPGjPzysWPHsmDBAkpLS4kIbr31Vj75yU8e1GmCu7c/atQounXrxjPPPMPAgQPp3bs3J598MuXl5fXavvvuu/Tv3582bdrwwAMP7LWtGTNmcMUVV/DjH/+YHTt2cPHFF1NaWtrgfn/+85/z1a9+lZ/85Cd07dqVadOm5dd96lOfYujQobz33ntMnjyZtm3bMmLECG6++WYGDBjA97//fb70pS/ttc3f/e533HfffRQVFdGuXTtmzpxZsBuKxL7uyNLUysrKUnV1dbPsW5IkSUe/1157jT59+jR3GU1q+vTpjbrhhfatsrKSc845hwsvvLBJ99PQ72NELE4plTXU3lMfJUmSJCljGnXqY0SMAn4GtAbuTSndvMf6TwG/Ao7LtZmYUtr/t8NJkiRJOiSVlZVUVlY2dxkNGjt2LGvXrq237JZbbuHzn/98k+73xhtvzF+3tttFF13ENddc02D76dOnH3Cb06ZN42c/+1m9ZeXl5fziF7/42HUeyAFPfYyI1sB/Ap8DNgCLgHEppRV12kwBXk4p3R0RfYE5KaUe+9uupz5KkiSpKbWEUx915GiKUx+HAqtSSmtSSh8CDwJj9miTgE/kpjsBGw+qakmSJKkJNNf9GKS6Ps7vYWOC2knA+jrzG3LL6roeuCQiNgBzgG80tKGIqIqI6oiofuuttw66WEmSJKmx2rZtyzvvvGNYU7NKKfHOO+/Qtm3bg3peoW7PPw6YnlL6HxFxBvDriChJKX20R5FTgClQe+pjgfYtSZIk7aV79+5s2LABBwjU3Nq2bUv37t0P6jmNCWp/Ak6uM989t6yufwZGAaSUFkREW+AE4M8HVY0kSZJUIEVFRfTs2bO5y5A+lsac+rgI6BURPSPiWOBi4JE92vwRGAkQEX2AtoB/upAkSZKkj+GAQS2ltBP4OjAXeA14KKW0PCImRcS5uWbfAf4lIpYCDwCVyZOBJUmSJOljadQ1arnvRJuzx7Lr6kyvAMoLW5okSZIktUyNOfVRkiRJknQYGdQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZYxBTZIkSZIyxqAmSZIkSRljUJMkSZKkjDGoSZIkSVLGGNQkSZIkKWMMapIkSZKUMQY1SZIkScoYg5okSZIkZUyjglpEjIqIP0TEqoiYuI82/xgRKyJieUTcX9gyJUmSJKnlOOZADSKiNfAL4HPABmBRRDySUlpRp00v4PtAeUrp3Yj4/5qqYEmSJEk62jVmRG0osCqltCal9CHwIDBmjzb/AvwipfQuQErpz4UtU5IkSZJajsYEtZOA9XXmN+SW1XUKcEpEPB8RL0bEqEIVKEmSJEktzQFPfTyI7fQCKoDuwLMR0S+ltKluo4ioAqoAPvWpTxVo15IkSZJ0dGnMiNqfgJPrzHfPLatrA/BISmlHSmkt8J/UBrd6UkpTUkplKaWyrl27ftyaJUmSJOmo1pigtgjoFRE9I+JY4GLgkT3azKZ2NI2IOIHaUyHXFK5MSZIkSWo5DhjUUko7ga8Dc4HXgIdSSssjYlJEnJtrNhd4JyJWAM8AE1JK7zRV0ZIkSZJ0NIuUUrPsuKysLFVXVzfLviVJkiSpuUXE4pRSWUPrGvWF15IkSZKkw8egJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZc0xzFyBJu/WY+Hhzl1BQ624e3dwlSJIOgschZYkjapIkSZKUMY6oSZJ0lHA0QJKOHo6oSZIkSVLGGNQkSZIkKWM89bFAjrbTTcBTTiRJkqTm4oiaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxjQqqEXEqIj4Q0SsioiJ+2l3QUSkiCgrXImSJEmS1LIcMKhFRGvgF8AXgL7AuIjo20C7jsA3gYWFLlKSJEmSWpLGjKgNBVallNaklD4EHgTGNNDuX4FbgO0FrE+SJEmSWpzGBLWTgPV15jfkluVFxCDg5JTS4wWsTZIkSZJapEO+mUhEtAJuB77TiLZVEVEdEdVvvfXWoe5akiRJko5KjQlqfwJOrjPfPbdst45ACTAvItYBw4BHGrqhSEppSkqpLKVU1rVr149ftSRJkiQdxRoT1BYBvSKiZ0QcC1wMPLJ7ZUppc0rphJRSj5RSD+BF4NyUUnWTVCxJkiRJR7kDBrWU0k7g68Bc4DXgoZTS8oiYFBHnNnWBkiRJktTSHNOYRimlOcCcPZZdt4+2FYdeliRJkiS1XId8MxFJkiRJUmEZ1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjLGoCZJkiRJGWNQkyRJkqSMMahJkiRJUsYY1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjLGoCZJkiRJGWNQkyRJkqSMMahJkiRJUsYY1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjLGoCZJkiRJGWNQkyRJkqSMMahJkiRJUsYY1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjLGoCZJkiRJGWNQkyRJkqSMMahJkiRJUsYY1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjLGoCZJkiRJGWNQkyRJkqSMMahJkiRJUsYY1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjKmUUEtIkZFxB8iYlVETGxg/bcjYkVEvBIR/ysi/rbwpUqSJElSy3DAoBYRrYFfAF8A+gLjIqLvHs1eBspSSv2B3wK3FrpQSZIkSWopGjOiNhRYlVJak1L6EHgQGFO3QUrpmZTS1tzsi0D3wpYpSZIkSS1HY4LaScD6OvMbcsv25Z+BJxpaERFVEVEdEdVvvfVW46uUJEmSpBakoDcTiYhLgDLgJw2tTylNSSmVpZTKunbtWshdS5IkSdJR45hGtPkTcHKd+e65ZfVExN8D1wBnp5T+WpjyJEmSJKnlacyI2iKgV0T0jIhjgYuBR+o2iIiBwL8B56aU/lz4MiVJkiSp5ThgUEsp7QS+DswFXgMeSiktj4hJEXFurtlPgA7ArIioiYhH9rE5SZIkSdIBNObUR1JKc4A5eyy7rs703xe4LkmSJElqsQp6MxFJkiRJ0qEzqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGVMo27PL0mSdNhd36m5Kyi86zc3dwWSjhCOqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZc0xzFyBJkiSpCVzfqbkrKLzrNzd3BYeNI2qSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZ410fJampHG1322pBd9qSJKm5OaImSZIkSRljUJMkSZKkjDGoSZIkSVLGeI2a9s3rayRJkqRm4YiaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIwxqEmSJElSxhjUJEmSJCljDGqSJEmSlDEGNUmSJEnKGIOaJEmSJGWMQU2SJEmSMsagJkmSJEkZY1CTJEmSpIxpVFCLiFER8YeIWBURExtY3yYiZubWL4yIHgWvVJIkSZJaiAMGtYhoDfwC+ALQFxgXEX33aPbPwLsppf8C/BS4pdCFSpIkSVJL0ZgRtaHAqpTSmpTSh8CDwJg92owBfpWb/i0wMiKicGVKkiRJUsvRmKB2ErC+zvyG3LIG26SUdgKbgS6FKFCSJEmSWppjDufOIqIKqMrNfhARfzic+9fBCTgBeLu56yiYGxzk1eFlH5IOzVHXh8B+pMPKPnRE+Nt9rWhMUPsTcHKd+e65ZQ212RARxwCdgHf23FBKaQowpRH7VAZERHVKqay565COVPYh6dDYh6RDYx86sjXm1MdFQK+I6BkRxwIXA4/s0eYR4NLc9IXA0ymlVLgyJUmSJKnlOOCIWkppZ0R8HZgLtAamppSWR8QkoDql9AjwP4FfR8Qq4C/UhjlJkiRJ0sfQqGvUUkpzgDl7LLuuzvR24KLClqYM8DRV6dDYh6RDYx+SDo196AgWnqEoSZIkSdnSmGvUJEmSJEmHkUEtQyKiR0QsO4z7mxcRBbsTUES8UKhtSYfTkd73pKPZ4e6fUlP6uJ+VIuK8iOhbwDoqI6Jbnfl7C7l9FYZB7QgTEa2bu4Z9SSmd2dw1SE0ly31PknRkOITPSucBDQap3FdjHaxKIB/UUkqXpZRWfKzK1GQMatlzTETMiIjXIuK3EVEcEesi4paIWAJcFBH/EhGLImJpRPwuIooBImJ6RNwZES9ExJqIuHD3RiPiexHxau45N9fZ30UR8VJE/GdEDG+ooNxf/38aEdW5uoZExO8j4vWI+HGddh/kfv5NRDwbETURsSwihkdE61x9y3J1/Pdc289ExH9ExOKIeC4ieueWX5RruzQini382yztpdn7Xq6f/CS3j1ci4mu55Xv1qcP5xkiHKiK+kvudXhoRD0fE2ogoyq37xO75iPgvEfFUrt2SiPjMHtuxj+iIVuezUkXu89VvI2Jl7vgTuXU3R8SK3O/4bRFxJnAu8JPc7/hncs+9IyKqgW/mjkMX7rmf3HS941CuXRkwI7e9dlHnTI+IGJdrvywibqm7zYi4MbedFyPixNxyP7M1lZSSj4w8gB5AAspz81OBq4F1wHfrtOtSZ/rHwDdy09OBWdQG8L7AqtzyLwAvAMW5+eNzP+cB/yM3/UXgqX3UNQ+4JTf9TWAj8DdAG2DD7nqAD3I/vwNck5tuDXQEBgNP1tnmcbmf/wvolZs+ndrv4AN4FTipblsfPprqkZW+B1QB1+am2wDVQM+G+lRzv2c+fDT2AZwG/CdwQm7+eGAacF5uvqpOf1gIjM1NtwWKc/1zWZ229hEfR+yjzmelCmAz0D137FgAfBboAvyB/3fDv+NyP6cDF9bZzjzgl3Xm91y/ez/7Ow6V7bG9MmpH2f4IdKX27vBP1+mrCfiH3PStdfqin9ma6OGIWvasTyk9n5v+DbWdFmBmnTYludGnV4Hx1B4Ed5udUvoo1Q5fn5hb9vfAtJTSVoCU0l/qtP997udiag+G+7L7S85fBZanlN5IKf0VWAOcvEfbRcBXI+J6oF9K6f1cu09HxM8jYhTwXkR0AM4EZkVEDfBv1AZAgOeB6RHxL9QedKWmloW+91+Br+T6w0JqD9i9aLhPSUeKvwNmpZTehnw/uBf4am79V4FpEdGR2g97D+fabd/dd+qwj+ho8lJKaUNK6SOghtpjwWZgO/A/I+J8YM8+UNfM/azbbX/HoYYMAeallN5KKe0EZgBn5dZ9CDyWm6577PIzWxMxqGXPnt+XsHt+S51l04Gvp5T6ATdQ+1fH3f5aZzoasb/d7XeR+169iJiWGwqf00C7j/bYx0fs8X18KaVnqe3Uf6K2434lpfQuUErtX2wup/Yg3QrYlFIaUOfRJ7eNy4FrqQ2BiyOiSyNei3Qomr3v5Z73jTr9oWdK6f9vqE81YvtSZuX+KNIjIiqA1imlxt4sxD6io0nd48Yu4JhcOBoK/BY4B/iP/Ty/7vFpJ7nP9RHRCji2sKUCsCOltPvYmD92+Zmt6RjUsudTEXFGbvqfgPkNtOkIvJE7v398I7b5JLV/adx9Pc3x+2ucUvpq7gD4xYOoOy8i/hZ4M6V0D7WBbFBEnAC0Sin9jtrOPCil9B6wNiIuyj0vIqI0N/2ZlNLCVPvF6m+x96idVGjN3veAucAVda7dOSUi2jfUpxqxbykrnqb2mswuUK8f3AfcT+1pkORGwTZExHm5dm1295067CM6quXONuqUUpoD/Hdq/8gN8D61x6B9WUftZSZQez1bUW56X8ehfW3vJeDsiDgham+iNQ743weo2c9sTcSglj1/AP5bRLwGdAbubqDND6k95eN5YOWBNphS+g9qT12szp0ucnXBqm1YBbA0Il4GvgT8DDgJmJfb/2+A7+fajgf+OSKWAsuBMbnlP9l9ISu151YvbeKapSz0vXuBFcCS3O/+v1H7F8sK9u5T0hEhpbQcuBH437n/62/PrZpBbV97oE7zLwNXRcQr1P7f/8k9Nmcf0dGuI/BYrg/MB76dW/4gMCEiXo49brKTcw+1AWspcAa50bb9HIemA5N330xk90ZSSm8AE4FnqP3stTil9O8HqNnPbE0k/t8IpiRJ0uGRu/PcmJTSl5u7FknKoo/zvQuSJEkfW0T8nNq70X2sU+wlqSVwRE2SJEmSMsZr1CRJkiQpYwxqkiRJkpQxBjVJkiRJyhiDmiRJkiRljEFNkiRJkjLGoCZJkiRJGfN/AZWbxRne8S1hAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "all_values = [\"branch-misses\",\"branches\",\"cycles\",\"instructions\"]\n",
    "\n",
    "grouped = all_data.groupby([\"depth\", \"instance\"]).agg({value: ['min', 'max'] for value in all_values})\n",
    "\n",
    "for pair in test_pairs:\n",
    "    # normalize all results\n",
    "    all_depths = set(all_data[all_data[\"algorithm\"] == pair[0]][\"depth\"]).intersection(all_data[all_data[\"algorithm\"] == pair[1]][\"depth\"])    \n",
    "    normed_data = all_data[all_data[\"algorithm\"].isin(pair) & (all_data[\"depth\"].isin(all_depths))].copy()\n",
    "            \n",
    "    for value in all_values:\n",
    "        normed_data[value] = normed_data.apply(lambda row: (row[value] - grouped.loc[(row[\"depth\"], row[\"instance\"])][value][\"min\"]) / (grouped.loc[(row[\"depth\"], row[\"instance\"])][value][\"max\"] - grouped.loc[(row[\"depth\"], row[\"instance\"])][value][\"min\"]), axis=1)\n",
    "        \n",
    "    \n",
    "    normed_data.groupby(\"algorithm\").mean()[all_values].T.plot.bar(rot=0, figsize=(15,5), ylim=(0,1))\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tests for paired samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualisation of the distribution of the difference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We check, whether the difference ```data_A - data_B``` is (approximately) normally distributed.\n",
    "This can be done by plotting a **histogram**.\n",
    "Furthermore we plot the **density of an estimated normal distribution**.\n",
    "If the curve approximately follows the histogram, then normal distribution can be assumed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test for 0_comp against alpha_beta using cycles\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test for 0_comp against alpha_beta using time\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------\n",
      "Test for alpha_beta against transposition_table using cycles\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test for alpha_beta against transposition_table using time\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------\n",
      "Test for transposition_table against transposition_table_opt_all using cycles\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test for transposition_table against transposition_table_opt_all using time\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------\n",
      "Test for transposition_table against transposition_table_opt_1 using cycles\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test for transposition_table against transposition_table_opt_1 using time\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------\n",
      "Test for transposition_table against transposition_table_opt_2 using cycles\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test for transposition_table against transposition_table_opt_2 using time\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------\n",
      "Test for transposition_table against transposition_table_opt_3 using cycles\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test for transposition_table against transposition_table_opt_3 using time\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------\n"
     ]
    }
   ],
   "source": [
    "for test_pair in test_pairs:\n",
    "    data_X = all_data[all_data[\"algorithm\"] == test_pair[0]]\n",
    "    data_Y = all_data[all_data[\"algorithm\"] == test_pair[1]]\n",
    "\n",
    "    matched_df = pd.merge(data_X, data_Y,  how='inner', left_on=['depth','instance'], right_on = ['depth','instance'])\n",
    "    for value in test_value:\n",
    "        print(\"Test for {} against {} using {}\".format(test_pair[0], test_pair[1], value))\n",
    "        values_x = matched_df[value+\"_x\"]\n",
    "        values_y = matched_df[value+\"_y\"]\n",
    "        plot_hist(values_x - values_y, \"difference\")\n",
    "    print(\"---------------------------------\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wilcoxon Test for two paired samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.wilcoxon.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test for 0_comp against alpha_beta using cycles\n",
      "Test Result:\n",
      "p-value = 0.0000\n",
      "H0 can be rejected on a level of significance of 0.05.\n",
      "\n",
      "Test for 0_comp against alpha_beta using time\n",
      "Test Result:\n",
      "p-value = 0.0000\n",
      "H0 can be rejected on a level of significance of 0.05.\n",
      "\n",
      "Test for alpha_beta against transposition_table using cycles\n",
      "Test Result:\n",
      "p-value = 0.9861\n",
      "H0 cannot be rejected on a level of significance of 0.05.\n",
      "\n",
      "Test for alpha_beta against transposition_table using time\n",
      "Test Result:\n",
      "p-value = 0.9997\n",
      "H0 cannot be rejected on a level of significance of 0.05.\n",
      "\n",
      "Test for transposition_table against transposition_table_opt_all using cycles\n",
      "Test Result:\n",
      "p-value = 0.0000\n",
      "H0 can be rejected on a level of significance of 0.05.\n",
      "\n",
      "Test for transposition_table against transposition_table_opt_all using time\n",
      "Test Result:\n",
      "p-value = 0.6585\n",
      "H0 cannot be rejected on a level of significance of 0.05.\n",
      "\n",
      "Test for transposition_table against transposition_table_opt_1 using cycles\n",
      "Test Result:\n",
      "p-value = 0.0000\n",
      "H0 can be rejected on a level of significance of 0.05.\n",
      "\n",
      "Test for transposition_table against transposition_table_opt_1 using time\n",
      "Test Result:\n",
      "p-value = 0.0000\n",
      "H0 can be rejected on a level of significance of 0.05.\n",
      "\n",
      "Test for transposition_table against transposition_table_opt_2 using cycles\n",
      "Test Result:\n",
      "p-value = 0.8677\n",
      "H0 cannot be rejected on a level of significance of 0.05.\n",
      "\n",
      "Test for transposition_table against transposition_table_opt_2 using time\n",
      "Test Result:\n",
      "p-value = 0.0114\n",
      "H0 can be rejected on a level of significance of 0.05.\n",
      "\n",
      "Test for transposition_table against transposition_table_opt_3 using cycles\n",
      "Test Result:\n",
      "p-value = 0.0000\n",
      "H0 can be rejected on a level of significance of 0.05.\n",
      "\n",
      "Test for transposition_table against transposition_table_opt_3 using time\n",
      "Test Result:\n",
      "p-value = 0.6700\n",
      "H0 cannot be rejected on a level of significance of 0.05.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for test_pair in test_pairs:\n",
    "    data_X = all_data[all_data[\"algorithm\"] == test_pair[0]]\n",
    "    data_Y = all_data[all_data[\"algorithm\"] == test_pair[1]]\n",
    "\n",
    "    matched_df = pd.merge(data_X, data_Y,  how='inner', left_on=['depth','instance'], right_on = ['depth','instance'])\n",
    "    for value in test_value:\n",
    "        print(\"Test for {} against {} using {}\".format(test_pair[0], test_pair[1], value))\n",
    "        values_x = matched_df[value+\"_x\"]\n",
    "        values_y = matched_df[value+\"_y\"]\n",
    "        # Apply the statistical test\n",
    "        res = scipy.stats.wilcoxon(values_x, values_y, alternative = alternative)\n",
    "\n",
    "        # Print results\n",
    "        print_decision(res.pvalue, alpha)\n",
    "        print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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