{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4a89aebf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import json\n",
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ce41f624",
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = []\n",
    "values = []\n",
    "\n",
    "files = os.listdir('out')\n",
    "files.sort()\n",
    "\n",
    "for filename in files:\n",
    "    if filename.endswith(\".json\"):\n",
    "        with open('out/'+filename) as output:\n",
    "            output_json = json.load(output)\n",
    "            samples += output_json['x']\n",
    "            values += output_json['y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1e2edd6f",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(data={'samples': samples, 'avg': 0, 'std': 0, 'values': values})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "67cd6668",
   "metadata": {},
   "outputs": [],
   "source": [
    "df['avg'] = df.apply(lambda row: np.array(row['values']).sum() / len(row['values']), axis=1)\n",
    "df['std'] = df.apply(lambda row: np.sqrt(np.array(row['values']).var()), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3080eb16",
   "metadata": {
    "scrolled": false
   },
   "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>samples</th>\n",
       "      <th>avg</th>\n",
       "      <th>std</th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1.599000</td>\n",
       "      <td>2.799410</td>\n",
       "      <td>[0.0, 0.0, 0.0, 6.500000000000005, 0.0, 6.5000...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1.631500</td>\n",
       "      <td>2.070829</td>\n",
       "      <td>[0.0, 0.0, 3.2500000000000027, 6.5000000000000...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>1.664000</td>\n",
       "      <td>1.272142</td>\n",
       "      <td>[2.6000000000000023, 3.900000000000003, 0.0, 2...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10</td>\n",
       "      <td>1.654900</td>\n",
       "      <td>0.908579</td>\n",
       "      <td>[0.6500000000000006, 3.2500000000000027, 1.950...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20</td>\n",
       "      <td>1.133600</td>\n",
       "      <td>0.673453</td>\n",
       "      <td>[0.0, 1.3000000000000012, 0.6500000000000006, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>50</td>\n",
       "      <td>1.220960</td>\n",
       "      <td>0.431168</td>\n",
       "      <td>[1.1700000000000008, 1.1700000000000008, 1.040...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>100</td>\n",
       "      <td>1.106820</td>\n",
       "      <td>0.310923</td>\n",
       "      <td>[1.1700000000000008, 1.235000000000001, 1.4950...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>200</td>\n",
       "      <td>1.097460</td>\n",
       "      <td>0.212839</td>\n",
       "      <td>[0.9100000000000008, 1.4625000000000012, 0.975...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>500</td>\n",
       "      <td>1.102712</td>\n",
       "      <td>0.136280</td>\n",
       "      <td>[0.9880000000000008, 1.0790000000000008, 1.001...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1000</td>\n",
       "      <td>1.106060</td>\n",
       "      <td>0.100732</td>\n",
       "      <td>[1.0075000000000007, 1.209000000000001, 0.9555...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2000</td>\n",
       "      <td>1.112072</td>\n",
       "      <td>0.070502</td>\n",
       "      <td>[1.277250000000001, 1.098500000000001, 1.08875...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>5000</td>\n",
       "      <td>1.108662</td>\n",
       "      <td>0.043625</td>\n",
       "      <td>[1.090700000000001, 1.1089000000000009, 1.1232...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>10000</td>\n",
       "      <td>1.105114</td>\n",
       "      <td>0.032244</td>\n",
       "      <td>[1.1180000000000008, 1.0796500000000009, 1.122...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>20000</td>\n",
       "      <td>1.108188</td>\n",
       "      <td>0.022374</td>\n",
       "      <td>[1.0741250000000009, 1.123525000000001, 1.1371...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>50000</td>\n",
       "      <td>1.106677</td>\n",
       "      <td>0.014118</td>\n",
       "      <td>[1.1052600000000008, 1.1278800000000009, 1.115...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>100000</td>\n",
       "      <td>1.107418</td>\n",
       "      <td>0.010126</td>\n",
       "      <td>[1.1035700000000008, 1.0917400000000008, 1.111...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>200000</td>\n",
       "      <td>1.106957</td>\n",
       "      <td>0.007035</td>\n",
       "      <td>[1.108770000000001, 1.1150425000000008, 1.1036...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>500000</td>\n",
       "      <td>1.106960</td>\n",
       "      <td>0.004477</td>\n",
       "      <td>[1.102660000000001, 1.099852000000001, 1.11181...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1000000</td>\n",
       "      <td>1.107122</td>\n",
       "      <td>0.003119</td>\n",
       "      <td>[1.1097190000000008, 1.106612000000001, 1.1135...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2000000</td>\n",
       "      <td>1.107152</td>\n",
       "      <td>0.002248</td>\n",
       "      <td>[1.1059262500000009, 1.1094655000000009, 1.107...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5000000</td>\n",
       "      <td>1.107034</td>\n",
       "      <td>0.001477</td>\n",
       "      <td>[1.105048100000001, 1.106229800000001, 1.11045...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>10000000</td>\n",
       "      <td>1.107038</td>\n",
       "      <td>0.000980</td>\n",
       "      <td>[1.107393300000001, 1.107971150000001, 1.10760...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>20000000</td>\n",
       "      <td>1.107093</td>\n",
       "      <td>0.000682</td>\n",
       "      <td>[1.107080650000001, 1.1058697000000008, 1.1065...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>50000000</td>\n",
       "      <td>1.107103</td>\n",
       "      <td>0.000438</td>\n",
       "      <td>[1.106985230000001, 1.106864330000001, 1.10673...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>100000000</td>\n",
       "      <td>1.107097</td>\n",
       "      <td>0.000300</td>\n",
       "      <td>[1.107135120000001, 1.106441765000001, 1.10693...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>200000000</td>\n",
       "      <td>1.107100</td>\n",
       "      <td>0.000229</td>\n",
       "      <td>[1.107198267500001, 1.1066414125000008, 1.1074...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>500000000</td>\n",
       "      <td>1.107083</td>\n",
       "      <td>0.000136</td>\n",
       "      <td>[1.107150577000001, 1.1068575310000008, 1.1071...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1000000000</td>\n",
       "      <td>1.107091</td>\n",
       "      <td>0.000095</td>\n",
       "      <td>[1.107090458500001, 1.107013505000001, 1.10705...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2000000000</td>\n",
       "      <td>1.107100</td>\n",
       "      <td>0.000067</td>\n",
       "      <td>[1.106987911250001, 1.1070893340000008, 1.1071...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>5000000000</td>\n",
       "      <td>1.107091</td>\n",
       "      <td>0.000044</td>\n",
       "      <td>[1.107101422700001, 1.107028651300001, 1.10703...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>10000000000</td>\n",
       "      <td>1.107071</td>\n",
       "      <td>0.000040</td>\n",
       "      <td>[1.1070528943500009, 1.107091172850001, 1.1070...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>20000000000</td>\n",
       "      <td>1.107083</td>\n",
       "      <td>0.000028</td>\n",
       "      <td>[1.107116142600001, 1.107052413675001, 1.10708...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>50000000000</td>\n",
       "      <td>1.107088</td>\n",
       "      <td>0.000010</td>\n",
       "      <td>[1.107083811470001, 1.107081873690001, 1.10711...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>100000000000</td>\n",
       "      <td>1.107081</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>[1.107080884000001]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>200000000000</td>\n",
       "      <td>1.107081</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>[1.107080584805001]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>500000000000</td>\n",
       "      <td>1.107090</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>[1.107089721517001]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         samples       avg       std  \\\n",
       "0              1  1.599000  2.799410   \n",
       "1              2  1.631500  2.070829   \n",
       "2              5  1.664000  1.272142   \n",
       "3             10  1.654900  0.908579   \n",
       "4             20  1.133600  0.673453   \n",
       "5             50  1.220960  0.431168   \n",
       "6            100  1.106820  0.310923   \n",
       "7            200  1.097460  0.212839   \n",
       "8            500  1.102712  0.136280   \n",
       "9           1000  1.106060  0.100732   \n",
       "10          2000  1.112072  0.070502   \n",
       "11          5000  1.108662  0.043625   \n",
       "12         10000  1.105114  0.032244   \n",
       "13         20000  1.108188  0.022374   \n",
       "14         50000  1.106677  0.014118   \n",
       "15        100000  1.107418  0.010126   \n",
       "16        200000  1.106957  0.007035   \n",
       "17        500000  1.106960  0.004477   \n",
       "18       1000000  1.107122  0.003119   \n",
       "19       2000000  1.107152  0.002248   \n",
       "20       5000000  1.107034  0.001477   \n",
       "21      10000000  1.107038  0.000980   \n",
       "22      20000000  1.107093  0.000682   \n",
       "23      50000000  1.107103  0.000438   \n",
       "24     100000000  1.107097  0.000300   \n",
       "25     200000000  1.107100  0.000229   \n",
       "26     500000000  1.107083  0.000136   \n",
       "27    1000000000  1.107091  0.000095   \n",
       "28    2000000000  1.107100  0.000067   \n",
       "29    5000000000  1.107091  0.000044   \n",
       "30   10000000000  1.107071  0.000040   \n",
       "31   20000000000  1.107083  0.000028   \n",
       "32   50000000000  1.107088  0.000010   \n",
       "33  100000000000  1.107081  0.000000   \n",
       "34  200000000000  1.107081  0.000000   \n",
       "35  500000000000  1.107090  0.000000   \n",
       "\n",
       "                                               values  \n",
       "0   [0.0, 0.0, 0.0, 6.500000000000005, 0.0, 6.5000...  \n",
       "1   [0.0, 0.0, 3.2500000000000027, 6.5000000000000...  \n",
       "2   [2.6000000000000023, 3.900000000000003, 0.0, 2...  \n",
       "3   [0.6500000000000006, 3.2500000000000027, 1.950...  \n",
       "4   [0.0, 1.3000000000000012, 0.6500000000000006, ...  \n",
       "5   [1.1700000000000008, 1.1700000000000008, 1.040...  \n",
       "6   [1.1700000000000008, 1.235000000000001, 1.4950...  \n",
       "7   [0.9100000000000008, 1.4625000000000012, 0.975...  \n",
       "8   [0.9880000000000008, 1.0790000000000008, 1.001...  \n",
       "9   [1.0075000000000007, 1.209000000000001, 0.9555...  \n",
       "10  [1.277250000000001, 1.098500000000001, 1.08875...  \n",
       "11  [1.090700000000001, 1.1089000000000009, 1.1232...  \n",
       "12  [1.1180000000000008, 1.0796500000000009, 1.122...  \n",
       "13  [1.0741250000000009, 1.123525000000001, 1.1371...  \n",
       "14  [1.1052600000000008, 1.1278800000000009, 1.115...  \n",
       "15  [1.1035700000000008, 1.0917400000000008, 1.111...  \n",
       "16  [1.108770000000001, 1.1150425000000008, 1.1036...  \n",
       "17  [1.102660000000001, 1.099852000000001, 1.11181...  \n",
       "18  [1.1097190000000008, 1.106612000000001, 1.1135...  \n",
       "19  [1.1059262500000009, 1.1094655000000009, 1.107...  \n",
       "20  [1.105048100000001, 1.106229800000001, 1.11045...  \n",
       "21  [1.107393300000001, 1.107971150000001, 1.10760...  \n",
       "22  [1.107080650000001, 1.1058697000000008, 1.1065...  \n",
       "23  [1.106985230000001, 1.106864330000001, 1.10673...  \n",
       "24  [1.107135120000001, 1.106441765000001, 1.10693...  \n",
       "25  [1.107198267500001, 1.1066414125000008, 1.1074...  \n",
       "26  [1.107150577000001, 1.1068575310000008, 1.1071...  \n",
       "27  [1.107090458500001, 1.107013505000001, 1.10705...  \n",
       "28  [1.106987911250001, 1.1070893340000008, 1.1071...  \n",
       "29  [1.107101422700001, 1.107028651300001, 1.10703...  \n",
       "30  [1.1070528943500009, 1.107091172850001, 1.1070...  \n",
       "31  [1.107116142600001, 1.107052413675001, 1.10708...  \n",
       "32  [1.107083811470001, 1.107081873690001, 1.10711...  \n",
       "33                                [1.107080884000001]  \n",
       "34                                [1.107080584805001]  \n",
       "35                                [1.107089721517001]  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "91bacd93",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xffff7989b290>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9KYsAAIQjyiJqJTXVXBHtOLaTAACAQKIsolZSU81ai998YzsJAAAIJMoiauXUU6XYWKaiAQAIN5RF1Ep8vDRwIGURAIBwQ1lEraWmSosWSSUltpMAAIBAoSyi1lJTpfx8adky20kAAECguKYsTps2Tf369VNCQoJatWqlUaNGaf369bZjhZWTTpISE5mKBgAgnLimLC5atEjXX3+9Pv/8c82fP18lJSUaPny4CgsLbUcLG1FR0umnmyV0AABAeIiyHaC25s2bV+35rFmz1KpVK61YsUKnnXaapVThJzVVuuMOae9ec9ELAAAIba4ZWTxQXl6eJKlZs2Y+X1NcXCyv11ttQ/2kpkrFxdKnn9pOAgAAAsGVZdFxHE2aNEmDBg1S9+7dfb5u2rRpSkpKqthSUlICmDI0desmtWrFeYsAAIQLV5bFCRMm6Ouvv9arr756yNdNnjxZeXl5FVtOTk6AEoYuj0caNoyyCABAuHDNOYvlbrjhBr377rtavHixkpOTD/na2NhYxcbGBihZ+EhNlV5/XcrNlZo2tZ0GAAD4k2tGFh3H0YQJE/T2228rKytL7du3tx0pbKWmSmVl0sKFtpMAAAB/c01ZvP766/XKK6/ov//9rxISErR9+3Zt375de/futR0t7LRvbzamogEACH0ex3Gc2rxw0qRJtX7Txx9/vM6BfPF4PDXunzVrlq688spavYfX61VSUpLy8vKUmJjYgOnCz1/+Yq6IXrvWdhIAAFAXte1FtT5ncdWqVbV6na9SV1+17LQIkNRU6fnnpa1bpTZtbKcBAAD+UuuyuGDBAn/mgMsMG2a+ZmVJf/6z3SwAAMB/XHPOIoJLq1ZSjx6ctwgAQKir89I5y5Yt0xtvvKHs7Gzt27ev2vfefvvtegdD8EtNld56S3Ics/4iAAAIPXUaWZw9e7ZOPfVUrV27Vunp6dq/f7/Wrl2rrKwsJSUlNXRGBKnUVCknR9qwwXYSAADgL3Uqiw899JCeeOIJvf/++4qJidFTTz2ldevW6aKLLlLbtm0bOiOC1GmnSZGRTEUDABDK6lQWN27cqHPOOUeSuUtKYWGhPB6Pbr75Zs2YMaNBAyJ4JSZK/ftLL74obdtmOw0AAPCHOpXFZs2aKT8/X5J07LHH6ptvvpEk5ebmas+ePQ2XDkHvvvukjRulP/xBevxxaf9+24kAAEBDqlNZHDx4sObPny9Juuiii3TjjTfqL3/5iy655BKlpqY2aEAEt+HDpe+/l8aOlW67TerVS/r4Y9upAABAQ6n1HVyq2rVrl4qKitSmTRuVlZVp+vTp+uSTT9ShQwdNmTJFRx11lD+y1ht3cPGvr76SbrhBWrJEuvBC6bHHJE5hBQAgONW2Fx1xWSwpKdF//vMfnXXWWTr66KPrHTSQKIv+5zjSq6+aUcbdu6U775RuvVWKi7OdDAAAVFXbXnTE09BRUVEaP368iouL6xUQocnjkS69VPruOzPK+MADUrdu0nvvmSIJAADcpU7nLJ588sm1vlc0wlNCgvTII9LXX0sdOkh//KN07rnSDz/YTgYAAI5Ene7g8re//U233HKLfvrpJ/Xt21eNGzeu9v2ePXs2SDi4X+fO0rx50jvvSDfdJHXvLt1yi3TXXdIB/9oAAIAgVKcLXCIiDh6Q9Hg8chxHHo9HpaWlDRKuoXHOol1795rRxkcekVq0kKZPly66iFsFAgBgg98ucJGkLVu2HPL77dq1O9K3DIiQL4v790s//SRt2SKVlZmhuyZNKrfGjaXYWOvtbNMmadIkKSNDGjJEevppM+IIAAACp7a9qE7T0MFaBkPevn3mZsybN5tty5bKx5s3Sz//bErioURGVi+PVctkq1bS1KlScrJf/xjt20vp6dKHH0oTJ0q9e0sTJkj33y9xa3EAAIJLncriu+++W+N+j8ejuLg4dejQQe3bt69XsLC0b5+UnV29AFYthT//fPhLimNjpXbtpOhoqaDAbIWFUlGR+X5pqZSXZ7aaREVJM2c22B/pUM46S1qzRnrySXPV9EcfSUuXSk2bBuTjAQBALdT5nMXycxSrvVmV8xYHDRqkjIyMoFqgO2imoffuldavl9aurb5t2GDK3KHExUnHHVd9a9eu8nGrVlIN55SqpMSUxvLyWF4ky5+vXy9NmWIuY962LeBXn6xfLw0YIJ10kvTBB6azAgAA//HrOYuZmZm666679OCDD6p///6SpC+//FJ33323pkyZoqSkJP31r3/VySefrBdeeKHuf4oGFvCyWFBgFhw8sBT++KPvEcJGjQ4ugFW3li39c85hWZlZ42bTJunll6XLL2/4zziMrCwz2viXv0j/+pf1UysBAAhpfi2L3bt314wZMzRw4MBq+z/99FNdd911+vbbb/Xxxx/r6quvVnZ29pGn95OAlcUxY6QvvjDTx740a2ZWq+7atXLr0kVq08ZeS3rgAenee6WhQ01zs+D5501Z/Mc/zKLeAADAP/x6gcvGjRtrfNPExET9+OOPkqSOHTtq586ddXl79ys/z1Ay08JVC2F5QfTXCGF9jB0r3XeftGCBGWG0cN7ptdeawdibbjIDnWlpAY8AAACqqFNZ7Nu3r2677Ta9/PLLatmypSTp119/1e23365+/fpJkn744Qcl+/mq2qD18MPmpLsuXcyCgm7Rrp00bJiUmSm99JIpjhY88oj0/fdmgHbpUpbVAQDApjrd7u+FF17Qpk2blJycrA4dOqhjx45KTk7W5s2b9fzzz0uSCgoKNGXKlAYN6xpDh0qDB7urKJa7+mrz9cUXD78Mj59ERkr//a90/PHmFoE7dliJAQAAVMdzFiXJcRx9+OGH+v777+U4jjp37qwzzzyzxru7BIuguRo6mO3dKx1zjFlaJzPTjDRakpMj9e9vZsOzssyF4AAAoGH49QIXt6Is1tK4cdJzz0mXXSa98orVKF9+KZ1+unTBBSZKsJ3mCQCAW/m9LBYWFmrRokXKzs7Wvn37qn1v4sSJdXlLv6Ms1tIXX0innGKG8rZvt35blddfN+cvPvCAWQoSAADUn1+vhl61apVGjBihPXv2qLCwUM2aNdPOnTvVqFEjtWrVKmjLImqpf39zcc66ddJrr0nXXWc1zkUXmQtepkyROnUyxREAAARGnU4wvPnmm3Xeeedp165dio+P1+eff64tW7aob9++mj59ekNnRKB5PNJVV5nHs2bZzfK7u+4ys+JXXmkGPgEAQGDUqSyuXr1at9xyiyIjIxUZGani4mKlpKTo73//u+68886GzggbLr/cXJb8+edmhNEyj8cs2N2njzRypLmFNgAA8L86lcXo6Gh5fr/SoHXr1hV3aUlKSgqqO7agHo4+Whoxwjx+8UWrUcrFxUnp6VJ8vHTeeVJ+vu1EAACEvjqVxRNPPFHLly+XJA0dOlT33HOP/vOf/+imm25Sjx49GjQgLCqfin75ZamkxG6W37VqJb3/vrnBzCWXSKWlthMBABDa6lQWH3roIR1zzDGSpKlTp6p58+YaP368duzYoeeee65BA8Kic84xC4tv3y7Nm2c7TYVu3cwV0nPnSrfdZjsNAAChjXUWcWg33yw9+aRZ6PCtt2ynqeaf/5RuuMFc+PLgg+ZuhQAAoHZq24vqNLI4bNgw5ebm1vihwyze8QN+UD4V/d570s6ddrMcYMIEaeZM6eOPzZI6t9wi7dplOxUAAKGlTmVx4cKFBy3ELUlFRUVasmRJvUMhiPTsaS5B3r9f+s9/bKc5yLXXShs2mKV1Zsww95N+5BFz10IAAFB/R1QWv/76a3399deSpLVr11Y8//rrr7Vq1Sq98MILOvbYY/0SFBZdfbX5GiRrLh6oSRPpnntMafzzn6W77zYjjbNmcQEMAAD1dUTnLEZERFQsmVPTj8XHx+vpp5/W1eXlIshwzmId7dolHXOMtG+ftHKldOKJthMd0g8/mJHGN96Qunc3I41padxXGgCAqvxyzuKmTZu0ceNGOY6jL7/8Ups2barYfv75Z3m93qAtiqiHZs2kUaPM4yAdXayqY0dztfQXX0jNm5uLuocNk5Yts50MAAD34Wpo1M68eWZ4rlkzaetWKTbWdqJacRzpgw+kO+6Qvv3W3Gf6wQelDh1sJwMAwK7a9qI6l8Xvv/9eCxcu1I4dO1RWVlbte/fcc09d3tLvKIv1UFpq1qb5+WczbDd6tO1ER6S01Kwtfs89ZtnIK680g6Wnn27OeQQAINz4tSzOnDlT48ePV4sWLXT00UdXnMcoSR6PRytXrqxbaj+jLNbTnXdK06aZEcYPPrCdpk727pX+8Q/pmWfM/aWjo6VTT5WGD5fOPNNc+B1RpzUCAABwF7+WxXbt2ulvf/ub7rjjjnqFDDTKYj398IO5zDgiwjQtF1/57jjmj/PRR2ZbsEAqKDDnOJ5xRmV5TEmxnRQAAP/w66Lcu3fv1miXTUOiAXTsKA0aJJWVSf/+t+009eLxmN47YYL07rvSb79JixdL48eb+05fe63Utq3UpYt0443SnDmmTAIAEG7qVBZHjx6tjz76qKGzwA3K7+gya5YZngsRMTHS4MHS1KnmKuqdO82pmYMHSxkZ0rnnmmt7hgyRHnpIWr6cNRwBAOGhTtPQ06ZN0+OPP65zzjlHPXr0UHR0dLXvT5w4scECNiSmoRtAfr509NHSnj3Sp59KAwfaTuR3h5qyPv10s5Zjly5S165mtDIuznZiAAAOz6/nLLZv3973G3o8+vHHH4/0LQOCsthArrxSeukl6ZprpOefr997FRRI778vpadL8fHmIppOnRokpr/s3y99/rkpjp98Iq1bJ/3yi/leRIS55WDXrmYrL5GdO3PVNQAguPh96Rw3oiw2kEWLzHxskyZmHZrGjY/s5wsKzEmAr79urqouKqr8XnS0NHGiNGWKlJTUoLH9adcuUxrXrq3+NTu78jVt21YWyI4dzUpE5RtFEgAQaA1eFidNmqSpU6eqcePGmjRpku839Hj02GOPHXniAKAsNhDHMW1n40YzwnjFFYf/mcLC6gVx797K73XoIF14obRmjXmNJLVsaVbPvvpqKTLSP3+OAMjPl7777uAiuXmzVFJS+brmzU1pPO64ygJZ9XHTptyuEADQsGrbi6Jq+4arVq3S/v37Kx774uE3WujzeMxU9JQp5kIXX2WxvCC+8Yb5WrUgnnCCuZ3K6NFS796VTWjuXOnmm6X166XrrjMLIj71lHTaaf7+U/lFQoLUr5/ZqiotNTfC2bLFFMctWyofz5ljHhcXV74+MdGUxrZtzZaSUvm4bVupTRszKAsAQENjGhp1k5Nj2ovjmBHG4483+wsLzcjhG2+YcxEPLIijR5vtxBN9D5Xt3y/961/SffdJeXlm3+jR0qOPms8MA2Vl0o4dBxfJnBwztZ2TI+3eXfn6iAjpmGMOLpJVHzdvzugkAKAS5yzWgLLYwIYPl+bPl267Terf30wxz5ljrpQud/zxlSOIhyqINfn1V3N/vhkzTHuKizOfdccdR36eZAjKzzelsbxAlpfIqo/37at8fXy8KY8pKWaWv3nzyq1Fi4MfN2lCuQSAUEZZrAFlsYG9+qp06aUH72/fvrIg9ulT/8bx9dfSTTeZNWskc+eYRx4xn02b8amszPTtqiWyvFzu3GkWIv/tN/O46pR3uejo6uUxKckUzqpbXNzB+w7c36hRzV+ZNgcAuyiLNaAsNrC9e83FKVu3moI4erQpiQ1REA/kOGZ5nVtvNbdYkaQBA8z5jAeeEOg2paWmrRUVVX4t36o+Ly42F/uUb1FRdXscFVW5RUfLiYrWnr2eauWxpsd5eeYfeVGR+Vp1K9/3+2nNtRIV5ahRI4/PQnngvpiY6tF/j3/YfeXPD/X1wH1RUWZqPzLy0F/5fxUAbkZZrAFl0Q+2bjVNonv3wPzmLCqSnnjCXCldWGj2tWpl5kzLt4SE6s9r2h8XZ5rN/v1mrrb8cdWtpv017SspMduRPC4uriyCR9Kw/CUi4uDWdGCDioio/HP42Er2OyoqidJexWmv4qtte9TIx9fG5rGnkfZ4GmmvGtXwmnjtV7RKnEiVKOr3x1EqkXlesU9RKlMgr54vU8Tvm0eOIlUmT5XnHjmKkPkrtvy5p4bnVfeVO/B1B+6v6Xnlz0g66LFHkmP+M3XMvsr/Yqs+rnyv8r0HfuahXuNUfK/ync3rqu+v+r2qCQ58n/KfOfB5VVXfx03qkvngf1K1/CyP+45POGusQq3KyjXL1PkRZbEGlMUQsnWrWcD7pZdsJ2lYERGmyMbFSbGxlY/j4szQWlmZKWalpWY70scBukdhiSKVq6bKVVPtVbyKFat9ilGxYn0+PtS+ql9rs5W/trxAlv5eKgNbJOui5vJ4YCH0XR59VQnfFaO8yPmuIFVL5+Ed/v2qvq/nECWz6nvW5p2O/HsIDDf+M7BdjOJVpB2Z30jDhvn1cyiLNaAshqBffjGXDRcUmC0/v/LxobaiIjNaFhNTOYpWdTvS/TXNgfp6HBVVWQQPLIRRtV7Nqm4cp7I0Vh0Z/f1rWfF+7S0o1Z78UhUWONqTX6o9BWXas0fKL/Bo99447S6M0e7CGOUWRmt3QZR250cpNz9Ku72R2u2N0O68CBUUHtlt56OiHMVEO4qNkWJjHMXEOIqNdszj6LLfv+coJlrmezFSTLSjmBjzvHx/zO//iMq36GgpKtJRVKSjyEhHkRH6/bEUGfH7/vKvv+8rfx4RYZ5XTjubnz94/wHPPc5B09UREWZ/RIQUEemp9twT4amY0q4YnPfXKH1t/rqv668E5uSPjOOEzzGrT82wdYyCIXOrVn6/f2yDr7MIBKXWrc2GCvv3m/78yy+VW+Vzj379NUqFhVHasydWhYXm4vXyrerNdHyJjZWOOsosFH7UUWZLPlrqXuV5+febNjXnHMbGmvIWG3vw4+hoKTLSI/eNPQBAeKAsAi7gONLPP0vbtlUvgTVtu3Yd/PNNm5r/SW3d2nw95hhT4ho3rryY5MDtwO81aWJKYHx8wP/4AACLXFUWFy9erEcffVQrVqzQtm3blJ6erlGjRtmOBTSoPXukb76Rvvqqcvv6a8nrrf665s0rB1aPPlrq1avyedWtVSszggcAQF24qiwWFhaqV69euuqqq/SnP/3JdhygXspHC6uWwq++kn74wVzHEhEhdepkSuCIEVKPHmaJydatzaLarFMIAAgEV5XFtLQ0paWl1fr1xcXFKq6y2rD3wKEZIEBKS83trleuNNvq1aYYlk8ZJyWZUjh8uLlJTa9eUrduTPkCAOxzVVk8UtOmTdP9999vOwbCzP790rp1phSuWFFZDsvvgnjCCVLv3uamNL16ma1t2/C5MBIA4C4hXRYnT56sSZMmVTz3er1KSUmxmAihprjYnF9YPmK4cqUZMSwuNuWvUyepb1/pggvMjW1OPNFcbAIAgFuEdFmMjY1VLGf2o4Hl5EjvvCNlZEiLF5uRxIgIqWtXUwgvvdQUxF69zE1jAABws5Aui0BDcBxp7Vpza+qMDDO1HBVlFtafPl3q31/q2dMsLwMAQKihLAI1KC2VPv/clMOMDGnDBrPO4IgR0i23SGlpTCcDAMKDq8piQUGBNmzYUPF806ZNWr16tZo1a6a2bdtaTIZQUFQkZWaacvjuu+auJ61bSyNHSv/4hxlJ5KwGAEC4cVVZXL58uYYOHVrxvPzilbFjx+rFF1+0lApulpsrzZljCuLcuVJhodSxo3TlldKoUdLJJ5vzEQEACFeuKotDhgyRU5+bewOSfvtNeu01UxAXLJBKSqR+/aQ775TOP1/q3JllbAAAKOeqsgjUxw8/SE88Ib34ormCeehQ6amnpD/+UUpOtp0OAIDgRFlESHMcackS6bHHpPfeM7fJ+5//kcaPN48BAMChURYRkkpKpDffNCVx+XKzBuLMmdJll0lxcbbTAQDgHpRFhBSvV3r+eTO9nJ0tpaZKH3wgnXUWF6oAAFAXlEWEhOxsUxBnzpT27pUuuUSaNMncgxkAANQdZRGuUFJi1kE8cPv1V2nGDOmNN8yt9a6/XpowQTr2WNuJAQAIDZRFBIV//EN66aWaC2FRkVRW5vtn27c3VzlfdZW5ywoAAGg4lEVYl5Eh3XijWQT7uOPMBSg1bbGxB+9r1Ejq1k2KjLT8hwAAIERRFmHVd99JV1wh/elPZiqZxbABAAguXB8KSdLGjdLFF0vbtwfuM71eM5qYkiLNmkVRBAAgGDGyCEnmyuF335UKCszi1f4ubmVl0tix0rZt0rJl5uIUAAAQfBhZhBYuNEXxqqukOXOkF17w/2dOm2bOVfz3v6VOnfz/eQAAoG4YWQxzZWXSLbdI/fubkhgRId18szRsmHT88f75zLlzpSlTpHvuMfdlBgAAwYuRxTD3n/9IK1ea2+J5PGYJmpYtzUUnpaUN/3kbN0qXXiqNGCHde2/Dvz8AAGhYlMUwtmePdOed0gUXSIMGmX0JCWa9w6VLpenTG/bzCgul88+XWrSQXnmF2+8BAOAG/LoOY088If3yi/TII9X3Dx4s3XabmSr+6quG+SzHka69VvrxRyk9XWratGHeFwAA+BdlMUxt3y49/LC5PV6HDgd//4EHpC5dpMsvl4qL6/95jz8uzZ4t/d//Sd271//9AABAYFAWw9S990rR0Wb0sCaxseZK5fXrfb+mtrKypNtvN6OVF11Uv/cCAACBRVkMQ998Iz3/vCmBzZr5fl3PntLUqebcxcWL6/ZZ2dnSmDHS0KHSQw/V7T0AAIA9HsdxHNshAsXr9SopKUl5eXlKTEy0HceaESOk77+X1q6VYmIO/drSUlP0cnLM+YtHctj27jXnP+7cKS1fbi5sAQAAwaG2vYiRxTAzf75Z5/CRRw5fFCUpMtJcHb1zp1l/sbYcR/rb36RvvzUXtFAUAQBwJ8piGCktNQtwn3qqWS6nttq3l5580lyc8s47tfuZZ5+VXnxRmjFDOvHEuqQFAADBgLIYRl58UVqzpnIB7iNx9dXSeedJf/mLtGPHoV/76afSjTdKN9xgrqYGAADuRVkMEwUF0t13SxdfLJ188pH/vMcjzZxpHl93nZlmrsnWrdKFF0oDBphSCgAA3I2yGCYefVTavVuaNq3u79G6tZlWfucdM0p5oH37pNGjzZ1ZXn/dLM0DAADcjbIYBn7+2ZTFG2+Ujjuufu81apR05ZXmvTZvrv69m26Sli2T3npLOvro+n0OAAAIDpTFMDBlitS4sbkPdEN46imzPuPYseaiGUmaNctc1PLPf0qnnNIwnwMAAOyLsh0A/rV6tZkyfvppKSmpYd4zMdEspzN0qLlK+vTTpfHjzb2fr7uuYT4DAAAEBxblDmGOI515pvTTT+Yq6IY+h/DWW00JbdFCSk42d3mJjW3YzwAAAP7BotzQBx9ImZnmfEV/XGzyv/8rdeoklZSY8xQpigAAhB6moUNUSYl0223SkCHSuef65zPi4qRFi6SiIqlNG/98BgAAsIuyGKJmzpS++0565ZUjX4D7SDRr5r/3BgAA9jENHYK8Xunee83dU/r0sZ0GAAC4GWUxBD38sLljy4MP2k4CAADcjrIYYvbtk555xtyXOTnZdhoAAOB2lMUQs2CBlJcnXXaZ7SQAACAUUBZDTEaGdPzxUo8etpMAAIBQQFkMIWVl0jvvmPs3+/MKaAAAED4oiyHkyy+lbduk88+3nQQAAIQKymIISU+XWraUBgywnQQAAIQKymKIcBxTFkeOlCIjbacBAAChgrIYItatk374wZyvCAAA0FAoiyEiI0Nq0kRKTbWdBAAAhBLKYohIT5fS0qS4ONtJAABAKKEshoCcHGn5cq6CBgAADY+yGALeeUeKjpZGjLCdBAAAhBrKYghIT5eGDZOSkmwnAQAAoYay6HK7dkmLFnEVNAAA8A/Kosu9/765zd/IkbaTAACAUERZdLmMDOmUU6RjjrGdBAAAhCLKoovt2SPNm8cUNAAA8B/KoovNny/t3cuSOQAAwH8oiy6Wni517Sp17Gg7CQAACFWURZcqKZHee49RRQAA4F+URZdassQsm8P5igAAwJ8oiy6Vni4lJ0t9+9pOAgAAQhll0YUcxyyZM2qU5PHYTgMAAEKZ68riM888o/bt2ysuLk59+/bVkiVLbEcKuJUrpZwczlcEAAD+56qy+Nprr+mmm27SXXfdpVWrVmnw4MFKS0tTdna27WgBlZEhHXWUNHiw7SQAACDUeRzHcWyHqK2TTz5Zffr00bPPPluxr0uXLho1apSmTZt22J/3er1KSkpSXl6eEhMT/RnVr7p3N+cqvvSS7SQAAMCtatuLXDOyuG/fPq1YsULDhw+vtn/48OFaunRpjT9TXFwsr9dbbXO7H36Qvv2Wq6ABAEBguKYs7ty5U6WlpWrdunW1/a1bt9b27dtr/Jlp06YpKSmpYktJSQlEVL/KyJDi46WzzrKdBAAAhAPXlMVyngMu/3Uc56B95SZPnqy8vLyKLScnJxAR/SojQxo+XGrUyHYSAAAQDqJsB6itFi1aKDIy8qBRxB07dhw02lguNjZWsbGxgYgXENu3S599Js2aZTsJAAAIF64ZWYyJiVHfvn01f/78avvnz5+vgQMHWkoVWO++K0VESOeeazsJAAAIF64ZWZSkSZMm6fLLL9dJJ52kAQMGaMaMGcrOzta4ceNsRwuI9HTptNOk5s1tJwEAAOHCVWVxzJgx+u233/TAAw9o27Zt6t69uz744AO1a9fOdjS/y8uTMjOlxx6znQQAAIQTV62zWF9uXmdx9mzpkkukLVuktm1tpwEAAG4Xcusshrv0dLMQN0URAAAEEmXRBYqLpQ8+YCFuAAAQeJRFF8jMlAoKpPPPt50EAACEG8qiC2RkSB06SF272k4CAADCDWUxyJWWSu+8Y0YVfdyoBgAAwG8oi0Hu88+lHTs4XxEAANhBWQxy6elS69bSKafYTgIAAMIRZTGIOY45X3HkSHObPwAAgECjggSxb76RNm7kKmgAAGAPZTGIpadLCQnS0KG2kwAAgHBFWQxiGRnSOedIsbG2kwAAgHBFWQxSmzdLq1ZxFTQAALCLshik3nlHiomR0tJsJwEAAOGMshik0tOl1FQpMdF2EgAAEM4oi0Fo505pyRKuggYAAPZRFoPQe++ZNRb/+EfbSQAAQLijLAahjAxp4EBz5xYAAACbKItBprBQ+ugjpqABAEBwoCwGmQ8/lIqKWDIHAAAEB8pikElPl3r0kE44wXYSAAAAymJQ2b9fev99RhUBAEDwoCwGkUWLpNxczlcEAADBg7IYRNLTpXbtpN69bScBAAAwKItBwnHM+oojR0oej+00AAAABmUxSGzYIOXkSMOH204CAABQibIYJLKypMhIafBg20kAAAAqURaDRGam1L+/lJhoOwkAAEAlymIQKCuTFiyQhg2znQQAAKA6ymIQWLNG2rlTSk21nQQAAKA6ymIQyMyU4uKkAQNsJwEAAKiOshgEsrKkU081hREAACCYUBYt27/f3LmFKWgAABCMKIuWLV8uFRRwcQsAAAhOlEXLMjPNcjl9+9pOAgAAcDDKomVZWdLpp0tRUbaTAAAAHIyyaNHevdLSpZyvCAAAghdl0aKlS6XiYs5XBAAAwYuyaFFmptSypdS9u+0kAAAANaMsWpSZaUYVPR7bSQAAAGpGWbQkL88sm8P5igAAIJhRFi1ZtEgqK+N8RQAAENwoi5ZkZUnt2knHH287CQAAgG+URUs4XxEAALgBZdGCX36RvvmG8xUBAEDwoyxasGCB+Tp0qN0cAAAAh0NZtCArS+rSRWrTxnYSAACAQ6MsWpCZyRQ0AABwB8pigG3eLP34I0vmAAAAd6AsBlhWlrkCesgQ20kAAAAOj7IYYJmZUp8+0lFH2U4CAABweJTFAHIcM7LI+YoAAMAtKIsBtG6dtH075ysCAAD3oCwGUFaWFB0tDRpkOwkAAEDtUBYDKDNTOuUUqXFj20kAAABqh7IYIKWl0sKFnK8IAADchbIYIKtWSbm5nK8IAADchbIYIFlZUqNG0skn204CAABQe5TFAMnMlAYPlmJibCcBAACoPdeUxQcffFADBw5Uo0aN1LRpU9txjkhxsbRkCecrAgAA93FNWdy3b59Gjx6t8ePH245yxL74Qtq7l/MVAQCA+0TZDlBb999/vyTpxRdftBukDjIzze39eve2nQQAAODIuKYs1kVxcbGKi4srnnu9Xis5srKkIUOkyEgrHw8AAFBnrpmGrotp06YpKSmpYktJSQl4hoIC6fPPOV8RAAC4k9WyeN9998nj8RxyW758eZ3ff/LkycrLy6vYcnJyGjB97XzyiVRSQlkEAADuZHUaesKECbr44osP+Zrjjjuuzu8fGxur2NjYOv98Q8jMlI45RvrDH6zGAAAAqBOrZbFFixZq0aKFzQh+l5VlRhU9HttJAAAAjpxrLnDJzs7Wrl27lJ2drdLSUq1evVqS1KFDBzVp0sRuOB927TK3+ZswwXYSAACAunFNWbznnnv00ksvVTw/8cQTJUkLFizQkCFDLKU6tIULJcdhfUUAAOBerrka+sUXX5TjOAdtwVoUJXO+4gknSO3a2U4CAABQN64pi26UmclV0AAAwN0oi37y88/S+vVMQQMAAHejLPpJVpb5OnSo3RwAAAD1QVn0k6wsqUcPqVUr20kAAADqjrLoB47D+YoAACA0UBb9YONGKSeH8xUBAID7URb9IDNTioyUTj/ddhIAAID6oSz6QceO0uTJUmKi7SQAAAD145o7uLjJsGFMQQMAgNDAyCIAAAB8oiwCAADAJ8oiAAAAfKIsAgAAwCfKIgAAAHyiLAIAAMAnyiIAAAB8oiwCAADAJ8oiAAAAfKIsAgAAwCfKIgAAAHyiLAIAAMAnyiIAAAB8oiwCAADAJ8oiAAAAfKIsAgAAwKco2wECyXEcSZLX67WcBAAAwK7yPlTej3wJq7KYn58vSUpJSbGcBAAAIDjk5+crKSnJ5/c9zuHqZAgpKyvT1q1blZCQII/HYztOUPF6vUpJSVFOTo4SExNtxwlpHOvA4DgHDsc6MDjOgRMux9pxHOXn56tNmzaKiPB9ZmJYjSxGREQoOTnZdoyglpiYGNL/YQQTjnVgcJwDh2MdGBznwAmHY32oEcVyXOACAAAAnyiLAAAA8ImyCElSbGys7r33XsXGxtqOEvI41oHBcQ4cjnVgcJwDh2NdXVhd4AIAAIAjw8giAAAAfKIsAgAAwCfKIgAAAHyiLAIAAMAnyiIAAAB8oiyiVs4//3wdddRRuvDCC21HCVn5+fnq16+fevfurR49emjmzJm2I4W0qKgo9e7dW71799a1115rO05IWr9+fcUx7t27t+Lj45WRkWE7VsiaPn26unXrpu7du+uVV16xHSek+PodGC6/G1k6B7WyYMECFRQU6KWXXtKbb75pO05IKi0tVXFxsRo1aqQ9e/aoe/fuWrZsmZo3b247Wkhq0aKFdu7caTtG2CgoKNBxxx2nLVu2qHHjxrbjhJw1a9Zo7NixWrp0qSQpNTVVc+bMUdOmTe0GCxG+fgeGy+9GRhZRK0OHDlVCQoLtGCEtMjJSjRo1kiQVFRWptLRU/L8cQsW7776r1NRUiqKfrFu3TgMHDlRcXJzi4uLUu3dvzZs3z3askOHrd2C4/G6kLIaBxYsX67zzzlObNm3k8XhqnAZ65pln1L59e8XFxalv375asmRJ4IO6XEMc59zcXPXq1UvJycm6/fbb1aJFiwCld5eGONZer1d9+/bVoEGDtGjRogAld5eG/Lvj9ddf15gxY/yc2L3qe6y7d++uBQsWKDc3V7m5ucrKytLPP/8cwD9B8OJ3YP1RFsNAYWGhevXqpX/+8581fv+1117TTTfdpLvuukurVq3S4MGDlZaWpuzs7AAndbeGOM5NmzbVV199pU2bNum///2vfvnll0DFd5WGONabN2/WihUr9P/+3//TFVdcIa/XG6j4rtFQf3d4vV59+umnGjFiRCBiu1J9j3XXrl01ceJEDRs2TOeff7769eunqKioQP4Rgha/AxuAg7AiyUlPT6+2r3///s64ceOq7evcubPzP//zP9X2LViwwPnTn/7k74ghoT7Hudy4ceOc119/3V8RQ0ZDHOuzzz7bWbZsmb8ihoT6HOeXX37Zueyyy/wdMWQ0xL/T11xzjfP+++/7K6Jr+eN3YDj8bmRkMczt27dPK1as0PDhw6vtHz58eMWJ0qi/2hznX375pWJ0y+v1avHixfrDH/4Q8KxuV5tjvXv3bhUXF0uSfvrpJ61du1bHH398wLO62ZH83cEUdP3U9ljv2LFDkrkK/csvv9RZZ50V0JxuxO/A2mGMOszt3LlTpaWlat26dbX9rVu31vbt2yuen3XWWVq5cqUKCwuVnJys9PR09evXL9BxXas2x/mnn37SNddcI8dx5DiOJkyYoJ49e9qI62q1Odbr1q3TX//6V0VERMjj8eipp55Ss2bNbMR1rdr+3ZGXl6cvv/xSb731VqAjhozaHutRo0YpNzdXjRs31qxZs5iGroX6/g4Ml9+N/JsESZLH46n23HGcavs+/PDDQEcKSYc6zn379tXq1astpApNhzrWAwcO1Jo1a2zECjmH+7sjKSmJc28byOGONSNhdVfX34Hh8ruRaegw16JFC0VGRlb7PyjJTGcc+H9aqDuOc+BwrAOD4xw4HGv/4djWDmUxzMXExKhv376aP39+tf3z58/XwIEDLaUKPRznwOFYBwbHOXA41v7Dsa0dpqHDQEFBgTZs2FDxfNOmTVq9erWaNWumtm3batKkSbr88st10kknacCAAZoxY4ays7M1btw4i6ndh+McOBzrwOA4Bw7H2n84tg3A3oXYCJQFCxY4kg7axo4dW/Gaf/3rX067du2cmJgYp0+fPs6iRYvsBXYpjnPgcKwDg+McOBxr/+HY1h/3hgYAAIBPnLMIAAAAnyiLAAAA8ImyCAAAAJ8oiwAAAPCJsggAAACfKIsAAADwibIIAAAAnyiLAAAA8ImyCAAAAJ8oiwAQxK688kqNGjXKdgwAYYyyCAAAAJ8oiwAAAPCJsggAv3vzzTfVo0cPxcfHq3nz5jrjjDNUWFioZcuW6cwzz1SLFi2UlJSk008/XStXrqz2sx6PR88995zOPfdcNWrUSF26dNFnn32mDRs2aMiQIWrcuLEGDBigjRs3VvzMfffdp969e+u5555TSkqKGjVqpNGjRys3N9dnRsdx9Pe//13HH3+84uPj1atXL7355psV39+9e7cuu+wytWzZUvHx8erYsaNmzZrV4McKQPigLAKApG3btumSSy7R1VdfrXXr1mnhwoW64IIL5DiO8vPzNXbsWC1ZskSff/65OnbsqBEjRig/P7/ae0ydOlVXXHGFVq9erc6dO+vSSy/VX//6V02ePFnLly+XJE2YMKHaz2zYsEGvv/663nvvPc2bN0+rV6/W9ddf7zPn3XffrVmzZunZZ5/Vt99+q5tvvll//vOftWjRIknSlClTtHbtWs2dO1fr1q3Ts88+qxYtWjTw0QIQVhwAgLNixQpHkrN58+bDvrakpMRJSEhw3nvvvYp9kpy777674vlnn33mSHJeeOGFin2vvvqqExcXV/H83nvvdSIjI52cnJyKfXPnznUiIiKcbdu2OY7jOGPHjnVGjhzpOI7jFBQUOHFxcc7SpUur5bnmmmucSy65xHEcxznvvPOcq6666gj+5ABwaIwsAoCkXr16KTU1VT169NDo0aM1c+ZM7d69W5K0Y8cOjRs3Tp06dVJSUpKSkpJUUFCg7Ozsau/Rs2fPisetW7eWJPXo0aPavqKiInm93op9bdu2VXJycsXzAQMGqKysTOvXrz8o49q1a1VUVKQzzzxTTZo0qdhefvnliunt8ePHa/bs2erdu7duv/12LV26tAGODoBwFmU7AAAEg8jISM2fP19Lly7VRx99pKefflp33XWXvvjiC11//fX69ddf9eSTT6pdu3aKjY3VgAEDtG/fvmrvER0dXfHY4/H43FdWVuYzR/lryr9WVf5zc+bM0bHHHlvte7GxsZKktLQ0bdmyRXPmzNHHH3+s1NRUXX/99Zo+fXqtjwUAVMXIIgD8zuPx6NRTT9X999+vVatWKSYmRunp6VqyZIkmTpyoESNGqFu3boqNjdXOnTsb5DOzs7O1devWiuefffaZIiIi1KlTp4Ne27VrV8XGxio7O1sdOnSotqWkpFS8rmXLlrryyiv1yiuv6Mknn9SMGTMaJCuA8MTIIgBI+uKLL5SZmanhw4erVatW+uKLL/Trr7+qS5cu6tChg/7973/rpJNOktfr1W233ab4+PgG+dy4uDiNHTtW06dPl9fr1cSJE3XRRRfp6KOPPui1CQkJuvXWW3XzzTerrKxMgwYNktfr1dKlS9WkSRONHTtW99xzj/r27atu3bqpuLhY77//vrp06dIgWQGEJ8oiAEhKTEzU4sWL9eSTT8rr9apdu3Z67LHHlJaWpqOPPlrXXXedTjzxRLVt21YPPfSQbr311gb53A4dOuiCCy7QiBEjtGvXLo0YMULPPPOMz9dPnTpVrVq10rRp0/Tjjz+qadOm6tOnj+68805JUkxMjCZPnqzNmzcrPj5egwcP1uzZsxskK4Dw5HEcx7EdAgDC0X333aeMjAytXr3adhQA8IlzFgEAAOATZREAAAA+MQ0NAAAAnxhZBAAAgE+URQAAAPhEWQQAAIBPlEUAAAD4RFkEAACAT5RFAAAA+ERZBAAAgE+URQAAAPj0/wHx6XquqPzY2wAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplot_mosaic([['log-linear']], layout='constrained')\n",
    "ax = axs['log-linear']\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlabel('samples')\n",
    "ax.set_ylabel('intagral')\n",
    "ax.plot(df['samples'], df['avg'], color=\"red\", linewidth=1.5)\n",
    "ax.plot(df['samples'], df['avg'] + df['std'], color=\"blue\", linewidth=1)\n",
    "ax.plot(df['samples'], df['avg'] - df['std'], color=\"blue\", linewidth=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e4a992a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplot_mosaic([['log-linear']], layout='constrained')\n",
    "ax = axs['log-linear']\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlabel('samples')\n",
    "ax.set_ylabel('intagral')\n",
    "\n",
    "ax.plot(df['samples'][18:36], df['avg'][18:36], color=\"red\", linewidth=1.5)\n",
    "ax.plot(df['samples'][18:33], df['avg'][18:33] + df['std'][18:33], color=\"blue\", linewidth=1)\n",
    "ax.plot(df['samples'][18:33], df['avg'][18:33] - df['std'][18:33], color=\"blue\", linewidth=1)\n",
    "\n",
    "for i in range(18, 33):\n",
    "    ax.plot(df['samples'][i], np.array(df['values'][i]).max(), \"go\", linewidth=1)\n",
    "    ax.plot(df['samples'][i], np.array(df['values'][i]).min(), \"go\", linewidth=1)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3ed7523e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplot_mosaic([['log-linear']], layout='constrained')\n",
    "ax = axs['log-linear']\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlabel('samples')\n",
    "ax.set_ylabel('intagral')\n",
    "\n",
    "ax.plot(df['samples'][24:36], df['avg'][24:36], color=\"red\", linewidth=1.5)\n",
    "ax.plot(df['samples'][24:33], df['avg'][24:33] + df['std'][24:33], color=\"blue\", linewidth=1)\n",
    "ax.plot(df['samples'][24:33], df['avg'][24:33] - df['std'][24:33], color=\"blue\", linewidth=1)\n",
    "\n",
    "for i in range(24, 33):\n",
    "    ax.plot(df['samples'][i], np.array(df['values'][i]).max(), \"go\", linewidth=1)\n",
    "    ax.plot(df['samples'][i], np.array(df['values'][i]).min(), \"go\", linewidth=1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4b52e2ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xffff774ecd90>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplot_mosaic([['log-log']], layout='constrained')\n",
    "ax = axs['log-log']\n",
    "ax.set_xscale('log')\n",
    "ax.set_yscale('log')\n",
    "ax.set_xlabel('samples')\n",
    "ax.set_ylabel('standart deviation')\n",
    "ax.plot(df['samples'], np.abs(df['std']), color=\"orange\", linewidth=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cf83bc8d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax.plot(10**np.linspace(0, 12, 12), np.pi/np.sqrt(10**np.linspace(0, 12, 12)), color=\"blue\", linewidth=1)\n",
    "\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9d95ac22",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}