Assignment_3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b6230cae",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c2f067ca",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Pressure</th>\n",
       "      <th>Property</th>\n",
       "      <th>Liq_Sat</th>\n",
       "      <th>Vap_Sat</th>\n",
       "      <th>75</th>\n",
       "      <th>100</th>\n",
       "      <th>125</th>\n",
       "      <th>150</th>\n",
       "      <th>175</th>\n",
       "      <th>200</th>\n",
       "      <th>...</th>\n",
       "      <th>425</th>\n",
       "      <th>450</th>\n",
       "      <th>475</th>\n",
       "      <th>500</th>\n",
       "      <th>525</th>\n",
       "      <th>550</th>\n",
       "      <th>575</th>\n",
       "      <th>600</th>\n",
       "      <th>625</th>\n",
       "      <th>650</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>V</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>129200.0000</td>\n",
       "      <td>160640.0000</td>\n",
       "      <td>172180.0000</td>\n",
       "      <td>183720.0000</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>333730.0000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>356810.0000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>379880.0000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>402960.0000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>426040.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>U</td>\n",
       "      <td>29.3340</td>\n",
       "      <td>2385.2000</td>\n",
       "      <td>2480.8000</td>\n",
       "      <td>2516.4000</td>\n",
       "      <td>2552.3000</td>\n",
       "      <td>2588.5000</td>\n",
       "      <td>2624.9000</td>\n",
       "      <td>2661.7000</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3049.9000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3132.4000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3216.7000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3302.6000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3390.3000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>H</td>\n",
       "      <td>29.3350</td>\n",
       "      <td>2514.4000</td>\n",
       "      <td>2641.5000</td>\n",
       "      <td>2688.6000</td>\n",
       "      <td>2736.0000</td>\n",
       "      <td>2783.7000</td>\n",
       "      <td>2831.7000</td>\n",
       "      <td>2880.1000</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3383.6000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3489.2000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3596.5000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3705.6000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3816.4000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>S</td>\n",
       "      <td>0.1060</td>\n",
       "      <td>8.9767</td>\n",
       "      <td>9.3828</td>\n",
       "      <td>9.5136</td>\n",
       "      <td>9.6365</td>\n",
       "      <td>9.7527</td>\n",
       "      <td>9.8629</td>\n",
       "      <td>9.9679</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10.8200</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10.9612</td>\n",
       "      <td>NaN</td>\n",
       "      <td>11.0957</td>\n",
       "      <td>NaN</td>\n",
       "      <td>11.2243</td>\n",
       "      <td>NaN</td>\n",
       "      <td>11.3476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10.0</td>\n",
       "      <td>V</td>\n",
       "      <td>1.0100</td>\n",
       "      <td>14670.0000</td>\n",
       "      <td>16030.0000</td>\n",
       "      <td>17190.0000</td>\n",
       "      <td>18350.0000</td>\n",
       "      <td>19510.0000</td>\n",
       "      <td>20660.0000</td>\n",
       "      <td>21820.0000</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>33370.0000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>35670.0000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>37980.0000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>40290.0000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>42600.0000</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>539</th>\n",
       "      <td>11200.0</td>\n",
       "      <td>S</td>\n",
       "      <td>3.4440</td>\n",
       "      <td>5.5476</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>6.2491</td>\n",
       "      <td>6.3515</td>\n",
       "      <td>6.4452</td>\n",
       "      <td>6.5324</td>\n",
       "      <td>6.6147</td>\n",
       "      <td>6.6929</td>\n",
       "      <td>6.7679</td>\n",
       "      <td>6.8401</td>\n",
       "      <td>6.9099</td>\n",
       "      <td>6.9777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>540</th>\n",
       "      <td>11400.0</td>\n",
       "      <td>V</td>\n",
       "      <td>1.5040</td>\n",
       "      <td>15.2840</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>24.1040</td>\n",
       "      <td>25.5990</td>\n",
       "      <td>27.0100</td>\n",
       "      <td>28.3590</td>\n",
       "      <td>29.6610</td>\n",
       "      <td>30.9250</td>\n",
       "      <td>32.1600</td>\n",
       "      <td>33.3700</td>\n",
       "      <td>34.5600</td>\n",
       "      <td>35.7330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>541</th>\n",
       "      <td>11400.0</td>\n",
       "      <td>U</td>\n",
       "      <td>1450.0000</td>\n",
       "      <td>2527.2000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>2873.1000</td>\n",
       "      <td>2929.4000</td>\n",
       "      <td>2982.6000</td>\n",
       "      <td>3033.9000</td>\n",
       "      <td>3083.9000</td>\n",
       "      <td>3133.1000</td>\n",
       "      <td>3181.9000</td>\n",
       "      <td>3230.4000</td>\n",
       "      <td>3278.8000</td>\n",
       "      <td>3327.2000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>542</th>\n",
       "      <td>11400.0</td>\n",
       "      <td>H</td>\n",
       "      <td>1467.2000</td>\n",
       "      <td>2701.5000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>3147.9000</td>\n",
       "      <td>3221.2000</td>\n",
       "      <td>3290.5000</td>\n",
       "      <td>3357.2000</td>\n",
       "      <td>3422.1000</td>\n",
       "      <td>3485.7000</td>\n",
       "      <td>3548.5000</td>\n",
       "      <td>3610.8000</td>\n",
       "      <td>3672.8000</td>\n",
       "      <td>3734.6000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>543</th>\n",
       "      <td>11400.0</td>\n",
       "      <td>S</td>\n",
       "      <td>3.4575</td>\n",
       "      <td>5.5357</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>6.2367</td>\n",
       "      <td>6.3399</td>\n",
       "      <td>6.4341</td>\n",
       "      <td>6.5218</td>\n",
       "      <td>6.6043</td>\n",
       "      <td>6.6828</td>\n",
       "      <td>6.7580</td>\n",
       "      <td>6.8304</td>\n",
       "      <td>6.9004</td>\n",
       "      <td>6.9683</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>544 rows × 37 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Pressure Property    Liq_Sat      Vap_Sat           75          100  \\\n",
       "0         1.0        V     1.0000  129200.0000  160640.0000  172180.0000   \n",
       "1         1.0        U    29.3340    2385.2000    2480.8000    2516.4000   \n",
       "2         1.0        H    29.3350    2514.4000    2641.5000    2688.6000   \n",
       "3         1.0        S     0.1060       8.9767       9.3828       9.5136   \n",
       "4        10.0        V     1.0100   14670.0000   16030.0000   17190.0000   \n",
       "..        ...      ...        ...          ...          ...          ...   \n",
       "539   11200.0        S     3.4440       5.5476          NaN          NaN   \n",
       "540   11400.0        V     1.5040      15.2840          NaN          NaN   \n",
       "541   11400.0        U  1450.0000    2527.2000          NaN          NaN   \n",
       "542   11400.0        H  1467.2000    2701.5000          NaN          NaN   \n",
       "543   11400.0        S     3.4575       5.5357          NaN          NaN   \n",
       "\n",
       "             125          150          175          200  ...        425  \\\n",
       "0    183720.0000  195270.0000  206810.0000  218350.0000  ...        NaN   \n",
       "1      2552.3000    2588.5000    2624.9000    2661.7000  ...        NaN   \n",
       "2      2736.0000    2783.7000    2831.7000    2880.1000  ...        NaN   \n",
       "3         9.6365       9.7527       9.8629       9.9679  ...        NaN   \n",
       "4     18350.0000   19510.0000   20660.0000   21820.0000  ...        NaN   \n",
       "..           ...          ...          ...          ...  ...        ...   \n",
       "539          NaN          NaN          NaN          NaN  ...     6.2491   \n",
       "540          NaN          NaN          NaN          NaN  ...    24.1040   \n",
       "541          NaN          NaN          NaN          NaN  ...  2873.1000   \n",
       "542          NaN          NaN          NaN          NaN  ...  3147.9000   \n",
       "543          NaN          NaN          NaN          NaN  ...     6.2367   \n",
       "\n",
       "             450        475          500        525          550        575  \\\n",
       "0    333730.0000        NaN  356810.0000        NaN  379880.0000        NaN   \n",
       "1      3049.9000        NaN    3132.4000        NaN    3216.7000        NaN   \n",
       "2      3383.6000        NaN    3489.2000        NaN    3596.5000        NaN   \n",
       "3        10.8200        NaN      10.9612        NaN      11.0957        NaN   \n",
       "4     33370.0000        NaN   35670.0000        NaN   37980.0000        NaN   \n",
       "..           ...        ...          ...        ...          ...        ...   \n",
       "539       6.3515     6.4452       6.5324     6.6147       6.6929     6.7679   \n",
       "540      25.5990    27.0100      28.3590    29.6610      30.9250    32.1600   \n",
       "541    2929.4000  2982.6000    3033.9000  3083.9000    3133.1000  3181.9000   \n",
       "542    3221.2000  3290.5000    3357.2000  3422.1000    3485.7000  3548.5000   \n",
       "543       6.3399     6.4341       6.5218     6.6043       6.6828     6.7580   \n",
       "\n",
       "             600        625          650  \n",
       "0    402960.0000        NaN  426040.0000  \n",
       "1      3302.6000        NaN    3390.3000  \n",
       "2      3705.6000        NaN    3816.4000  \n",
       "3        11.2243        NaN      11.3476  \n",
       "4     40290.0000        NaN   42600.0000  \n",
       "..           ...        ...          ...  \n",
       "539       6.8401     6.9099       6.9777  \n",
       "540      33.3700    34.5600      35.7330  \n",
       "541    3230.4000  3278.8000    3327.2000  \n",
       "542    3610.8000  3672.8000    3734.6000  \n",
       "543       6.8304     6.9004       6.9683  \n",
       "\n",
       "[544 rows x 37 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset = pd.read_csv('superheated_vapor_properties.csv')\n",
    "dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "206892c0",
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Pressure</th>\n",
       "      <th>Property</th>\n",
       "      <th>Liq_Sat</th>\n",
       "      <th>Vap_Sat</th>\n",
       "      <th>75</th>\n",
       "      <th>100</th>\n",
       "      <th>125</th>\n",
       "      <th>150</th>\n",
       "      <th>175</th>\n",
       "      <th>200</th>\n",
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       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>V</td>\n",
       "      <td>1.000</td>\n",
       "      <td>129200.000</td>\n",
       "      <td>160640.0</td>\n",
       "      <td>172180.0</td>\n",
       "      <td>183720.0</td>\n",
       "      <td>195270.0</td>\n",
       "      <td>206810.0</td>\n",
       "      <td>218350.0</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>333730.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>356810.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>379880.000</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10.0</td>\n",
       "      <td>V</td>\n",
       "      <td>1.010</td>\n",
       "      <td>14670.000</td>\n",
       "      <td>16030.0</td>\n",
       "      <td>17190.0</td>\n",
       "      <td>18350.0</td>\n",
       "      <td>19510.0</td>\n",
       "      <td>20660.0</td>\n",
       "      <td>21820.0</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>33370.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>35670.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>37980.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>40290.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>42600.000</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>20.0</td>\n",
       "      <td>V</td>\n",
       "      <td>1.017</td>\n",
       "      <td>7649.800</td>\n",
       "      <td>8000.0</td>\n",
       "      <td>8584.7</td>\n",
       "      <td>9167.1</td>\n",
       "      <td>9748.0</td>\n",
       "      <td>10320.0</td>\n",
       "      <td>10900.0</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16680.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17830.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18990.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20140.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>21300.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>30.0</td>\n",
       "      <td>V</td>\n",
       "      <td>1.022</td>\n",
       "      <td>5229.300</td>\n",
       "      <td>5322.0</td>\n",
       "      <td>5714.4</td>\n",
       "      <td>6104.6</td>\n",
       "      <td>6493.2</td>\n",
       "      <td>6880.8</td>\n",
       "      <td>7267.5</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>11120.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>11890.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>12660.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>13430.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>14190.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>40.0</td>\n",
       "      <td>V</td>\n",
       "      <td>1.027</td>\n",
       "      <td>3993.400</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4279.2</td>\n",
       "      <td>4573.3</td>\n",
       "      <td>4865.8</td>\n",
       "      <td>5157.2</td>\n",
       "      <td>5447.8</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8340.100</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8917.600</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9494.900</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10070.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10640.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>524</th>\n",
       "      <td>10600.0</td>\n",
       "      <td>V</td>\n",
       "      <td>1.474</td>\n",
       "      <td>16.778</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>26.276</td>\n",
       "      <td>27.834</td>\n",
       "      <td>29.313</td>\n",
       "      <td>30.732</td>\n",
       "      <td>32.106</td>\n",
       "      <td>33.444</td>\n",
       "      <td>34.753</td>\n",
       "      <td>36.039</td>\n",
       "      <td>37.304</td>\n",
       "      <td>38.552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>528</th>\n",
       "      <td>10800.0</td>\n",
       "      <td>V</td>\n",
       "      <td>1.481</td>\n",
       "      <td>16.385</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>25.703</td>\n",
       "      <td>27.245</td>\n",
       "      <td>28.706</td>\n",
       "      <td>30.106</td>\n",
       "      <td>31.461</td>\n",
       "      <td>32.779</td>\n",
       "      <td>34.069</td>\n",
       "      <td>35.335</td>\n",
       "      <td>36.580</td>\n",
       "      <td>37.808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>532</th>\n",
       "      <td>11000.0</td>\n",
       "      <td>V</td>\n",
       "      <td>1.489</td>\n",
       "      <td>16.006</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>25.151</td>\n",
       "      <td>26.676</td>\n",
       "      <td>28.120</td>\n",
       "      <td>29.503</td>\n",
       "      <td>30.839</td>\n",
       "      <td>32.139</td>\n",
       "      <td>33.410</td>\n",
       "      <td>34.656</td>\n",
       "      <td>35.882</td>\n",
       "      <td>37.091</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>536</th>\n",
       "      <td>11200.0</td>\n",
       "      <td>V</td>\n",
       "      <td>1.496</td>\n",
       "      <td>15.639</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>24.619</td>\n",
       "      <td>26.128</td>\n",
       "      <td>27.555</td>\n",
       "      <td>28.921</td>\n",
       "      <td>30.240</td>\n",
       "      <td>31.521</td>\n",
       "      <td>32.774</td>\n",
       "      <td>34.002</td>\n",
       "      <td>35.210</td>\n",
       "      <td>36.400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>540</th>\n",
       "      <td>11400.0</td>\n",
       "      <td>V</td>\n",
       "      <td>1.504</td>\n",
       "      <td>15.284</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>24.104</td>\n",
       "      <td>25.599</td>\n",
       "      <td>27.010</td>\n",
       "      <td>28.359</td>\n",
       "      <td>29.661</td>\n",
       "      <td>30.925</td>\n",
       "      <td>32.160</td>\n",
       "      <td>33.370</td>\n",
       "      <td>34.560</td>\n",
       "      <td>35.733</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>136 rows × 37 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Pressure Property  Liq_Sat     Vap_Sat        75       100       125  \\\n",
       "0         1.0        V    1.000  129200.000  160640.0  172180.0  183720.0   \n",
       "4        10.0        V    1.010   14670.000   16030.0   17190.0   18350.0   \n",
       "8        20.0        V    1.017    7649.800    8000.0    8584.7    9167.1   \n",
       "12       30.0        V    1.022    5229.300    5322.0    5714.4    6104.6   \n",
       "16       40.0        V    1.027    3993.400       NaN    4279.2    4573.3   \n",
       "..        ...      ...      ...         ...       ...       ...       ...   \n",
       "524   10600.0        V    1.474      16.778       NaN       NaN       NaN   \n",
       "528   10800.0        V    1.481      16.385       NaN       NaN       NaN   \n",
       "532   11000.0        V    1.489      16.006       NaN       NaN       NaN   \n",
       "536   11200.0        V    1.496      15.639       NaN       NaN       NaN   \n",
       "540   11400.0        V    1.504      15.284       NaN       NaN       NaN   \n",
       "\n",
       "          150       175       200  ...     425         450     475  \\\n",
       "0    195270.0  206810.0  218350.0  ...     NaN  333730.000     NaN   \n",
       "4     19510.0   20660.0   21820.0  ...     NaN   33370.000     NaN   \n",
       "8      9748.0   10320.0   10900.0  ...     NaN   16680.000     NaN   \n",
       "12     6493.2    6880.8    7267.5  ...     NaN   11120.000     NaN   \n",
       "16     4865.8    5157.2    5447.8  ...     NaN    8340.100     NaN   \n",
       "..        ...       ...       ...  ...     ...         ...     ...   \n",
       "524       NaN       NaN       NaN  ...  26.276      27.834  29.313   \n",
       "528       NaN       NaN       NaN  ...  25.703      27.245  28.706   \n",
       "532       NaN       NaN       NaN  ...  25.151      26.676  28.120   \n",
       "536       NaN       NaN       NaN  ...  24.619      26.128  27.555   \n",
       "540       NaN       NaN       NaN  ...  24.104      25.599  27.010   \n",
       "\n",
       "            500     525         550     575         600     625         650  \n",
       "0    356810.000     NaN  379880.000     NaN  402960.000     NaN  426040.000  \n",
       "4     35670.000     NaN   37980.000     NaN   40290.000     NaN   42600.000  \n",
       "8     17830.000     NaN   18990.000     NaN   20140.000     NaN   21300.000  \n",
       "12    11890.000     NaN   12660.000     NaN   13430.000     NaN   14190.000  \n",
       "16     8917.600     NaN    9494.900     NaN   10070.000     NaN   10640.000  \n",
       "..          ...     ...         ...     ...         ...     ...         ...  \n",
       "524      30.732  32.106      33.444  34.753      36.039  37.304      38.552  \n",
       "528      30.106  31.461      32.779  34.069      35.335  36.580      37.808  \n",
       "532      29.503  30.839      32.139  33.410      34.656  35.882      37.091  \n",
       "536      28.921  30.240      31.521  32.774      34.002  35.210      36.400  \n",
       "540      28.359  29.661      30.925  32.160      33.370  34.560      35.733  \n",
       "\n",
       "[136 rows x 37 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V_data = dataset.loc[(dataset[\"Property\"] == \"V\"),:]\n",
    "V_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6b3078eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd951f16100>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(V_data['Pressure'],V_data['Vap_Sat'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "70d79ce0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def r2_score(y, y_hat):\n",
    "    y_mean = np.mean(y)\n",
    "    ss_tot = np.sum((y - y_mean)**2)\n",
    "    ss_res = np.sum((y - y_hat)**2)\n",
    "    return 1 - ss_res / ss_tot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "005b5653",
   "metadata": {},
   "outputs": [],
   "source": [
    "V_data_1 = V_data.loc[(V_data[\"Pressure\"] < 300),:]\n",
    "V_data_2 = V_data.loc[(V_data[\"Pressure\"] >= 300) & (V_data[\"Pressure\"] < 1500),:]\n",
    "V_data_3 = V_data.loc[(V_data[\"Pressure\"] >= 1500),:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ae159641",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd9705422e0>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5QgAAxM3FXo62fft2I2nE4+677zbG9F9C/9hjjxmPx2OcTqe55ZZbzIEDByKO0d3dbVasWGHy8vJMZmamKS0tNY2NjRE1p06dMsuXLzfZ2dkmOzvbLF++3LS1tUXUHDlyxCxZssRkZmaavLw8s2LFiohL5Y0x5t133zU333yzcTqdxuPxmLVr14760nlj4nf5/D9u/9BMffh1s+bn9TF9HwAAxoLR/v22GZOEt1lOIh0dHXK73fL5fDGdL/TCzo/12GsH9SezPXpmeXHM3gcAgLFgtH+/WWssSbi4fB4AgLgjCCWJ8OXzZ5gsDQBA3BCEkkSWI9wjRBACACBeCEJJwrp8nvsIAQAQNwShJGGtNcYcIQAA4oYglCSyHP1zhBgaAwAgfghCSSLcI+TvC6kvGEpwawAAGBsIQkkiPEdIkroCDI8BABAPBKEk4Ui3KyOtf9kP1hsDACA+CEJJhIVXAQCIL4JQEnE5wpfQMzQGAEA8EISSyOAK9PQIAQAQDwShJDK43hhBCACAeCAIJRHrporcXRoAgLggCCWRwZsqMkcIAIB4IAglEa4aAwAgvghCSWRwvTGCEAAA8UAQSiJZjvBkaYbGAACIB4JQEhnP5fMAAMQVQSiJWHOEuGoMAIC4IAglEevO0vQIAQAQFwShJDJ41RhzhAAAiAeCUBKxlthgaAwAgLggCCUR7iMEAEB8EYSSiIvL5wEAiCuCUBJhrTEAAOKLIJREsgbmCJ0JBBUKmQS3BgCAyx9BKImEe4QkJkwDABAPBKEk4ky3K81uk9TfKwQAAGKLIJREbDabshz9w2OnuXIMAICYIwglmfFcQg8AQNwQhJIMd5cGACB+CEJJxuVgBXoAAOKFIJRkWIEeAID4IQglGYbGAACIH4JQkmFoDACA+CEIJZlwjxCXzwMAEHsEoSTDemMAAMQPQSjJZLECPQAAcUMQSjIuJ3OEAACIF4JQkmFoDACA+Il6EOrr69Pf/M3faNq0acrMzNTVV1+txx9/XKFQyKoxxmjt2rXyer3KzMzUwoULdfDgwYjj+P1+rVy5Uvn5+XK5XFq2bJmOHTsWUdPW1qby8nK53W653W6Vl5ervb09oqaxsVFLly6Vy+VSfn6+Vq1apUAgEO2PHTVZTJYGACBuoh6E/u7v/k6bNm3Sxo0b9dvf/lZPPvmknnrqKf3gBz+wap588klt2LBBGzdu1L59++TxeLRo0SJ1dnZaNZWVldqyZYuqqqpUW1ur06dPq7S0VMHg4NyZsrIy1dfXq7q6WtXV1aqvr1d5ebm1PxgMasmSJerq6lJtba2qqqr08ssva/Xq1dH+2FEz3hoaY44QAAAxZ6JsyZIl5hvf+EbEtq985SvmrrvuMsYYEwqFjMfjMU888YS1v6enx7jdbrNp0yZjjDHt7e0mIyPDVFVVWTVNTU3Gbreb6upqY4wxhw4dMpLM7t27rZpdu3YZSea9994zxhizdetWY7fbTVNTk1WzefNm43Q6jc/nG9Xn8fl8RtKo6y/V7t99YqY+/Lr5L09vj8v7AQBwORrt3++o9wjddNNNeuONN/TBBx9Ikv7jP/5DtbW1+pM/+RNJ0uHDh9XS0qKSkhLrNU6nUwsWLNDOnTslSXV1dert7Y2o8Xq9Kioqsmp27dolt9utOXPmWDVz586V2+2OqCkqKpLX67VqbrvtNvn9ftXV1Z21/X6/Xx0dHRGPeHKx+jwAAHGTHu0DPvzww/L5fPr85z+vtLQ0BYNBffe739XXvvY1SVJLS4skqbCwMOJ1hYWFOnLkiFXjcDiUm5s7oib8+paWFhUUFIx4/4KCgoia4e+Tm5srh8Nh1Qy3fv16fec737nYjx01LLEBAED8RL1H6KWXXtJPf/pT/exnP9M777yjF154QU8//bReeOGFiDqbzRbx3BgzYttww2vOVv9ZaoZ69NFH5fP5rMfRo0fP26Zosy6fD/TJGBPX9wYAYKyJeo/QX//1X+uRRx7RV7/6VUnS7NmzdeTIEa1fv1533323PB6PpP7emokTJ1qva21ttXpvPB6PAoGA2traInqFWltbNX/+fKvmxIkTI97/5MmTEcfZs2dPxP62tjb19vaO6CkKczqdcjqdn/XjXzLXwA0VjZG6e4PWDRYBAED0Rb1H6MyZM7LbIw+blpZmXT4/bdo0eTwe1dTUWPsDgYB27NhhhZzi4mJlZGRE1DQ3N6uhocGqmTdvnnw+n/bu3WvV7NmzRz6fL6KmoaFBzc3NVs22bdvkdDpVXFwc5U8eHVmONIU7q7iEHgCA2Ip6d8PSpUv13e9+V1deeaWuueYa7d+/Xxs2bNA3vvENSf1DVZWVlVq3bp2mT5+u6dOna926dcrKylJZWZkkye12695779Xq1as1YcIE5eXlac2aNZo9e7ZuvfVWSdLMmTO1ePFiVVRU6LnnnpMk3XfffSotLdWMGTMkSSUlJZo1a5bKy8v11FNP6dNPP9WaNWtUUVGhnJycaH/0qLDZbHI50nXa36cz/qCUnegWAQBwGYv25WodHR3mm9/8prnyyivNuHHjzNVXX22+/e1vG7/fb9WEQiHz2GOPGY/HY5xOp7nlllvMgQMHIo7T3d1tVqxYYfLy8kxmZqYpLS01jY2NETWnTp0yy5cvN9nZ2SY7O9ssX77ctLW1RdQcOXLELFmyxGRmZpq8vDyzYsUK09PTM+rPE+/L540x5ob/WWOmPvy6OXCsPW7vCQDA5WS0f79txjAj93w6Ojrkdrvl8/ni1ov0xad/rY8+6dJL983VnKsnxOU9AQC4nIz27zdrjSUhl7XeGJfQAwAQSwShJJTl6L+EnsnSAADEFkEoCY3n7tIAAMQFQSgJWXeXZmgMAICYIgglIevu0vQIAQAQUwShJBS+uzRBCACA2CIIJaHBoTGCEAAAsUQQSkKDQ2PMEQIAIJYIQkko3CPE5fMAAMQWQSgJjbduqEgQAgAglghCSSjLEe4RYmgMAIBYIgglIS6fBwAgPghCScgaGiMIAQAQUwShJDQ4NEYQAgAglghCSWj8kCU2jDEJbg0AAJcvglASCs8RCoaM/H2hBLcGAIDLF0EoCYWHxiQmTAMAEEsEoSSUZrcpM4O7SwMAEGsEoSTFemMAAMQeQShJcS8hAABijyCUpFxcQg8AQMwRhJLU4HpjzBECACBWCEJJKmtgaIweIQAAYocglKSsydIEIQAAYoYglKTGOxgaAwAg1ghCSYqhMQAAYo8glKTGMzQGAEDMEYSS1OAcIYbGAACIFYJQknI5uKEiAACxRhBKUiyxAQBA7BGEkhSXzwMAEHsEoSQVXmKDOUIAAMQOQShJubh8HgCAmCMIJanBtcYIQgAAxApBKEllcfk8AAAxRxBKUuElNgLBkAJ9oQS3BgCAyxNBKEmFl9iQGB4DACBWCEJJKiPNLkd6/z8PE6YBAIgNglASG888IQAAYooglMTCl9Bzd2kAAGKDIJTEBm+qSBACACAWYhKEmpqadNddd2nChAnKysrSH/3RH6murs7ab4zR2rVr5fV6lZmZqYULF+rgwYMRx/D7/Vq5cqXy8/Plcrm0bNkyHTt2LKKmra1N5eXlcrvdcrvdKi8vV3t7e0RNY2Ojli5dKpfLpfz8fK1atUqBQCAWHzvqWGYDAIDYinoQamtr04033qiMjAz9+7//uw4dOqTvfe97uuKKK6yaJ598Uhs2bNDGjRu1b98+eTweLVq0SJ2dnVZNZWWltmzZoqqqKtXW1ur06dMqLS1VMDg4X6asrEz19fWqrq5WdXW16uvrVV5ebu0PBoNasmSJurq6VFtbq6qqKr388stavXp1tD92TLiYIwQAQGyZKHv44YfNTTfddM79oVDIeDwe88QTT1jbenp6jNvtNps2bTLGGNPe3m4yMjJMVVWVVdPU1GTsdruprq42xhhz6NAhI8ns3r3bqtm1a5eRZN577z1jjDFbt241drvdNDU1WTWbN282TqfT+Hy+UX0en89nJI26Ppru/99vm6kPv25e2Hk47u8NAEAqG+3f76j3CL322mu6/vrr9ed//ucqKCjQF77wBf3whz+09h8+fFgtLS0qKSmxtjmdTi1YsEA7d+6UJNXV1am3tzeixuv1qqioyKrZtWuX3G635syZY9XMnTtXbrc7oqaoqEher9eque222+T3+yOG6oby+/3q6OiIeCRKuEeIy+cBAIiNqAehjz76SM8++6ymT5+uX/7yl7r//vu1atUq/eQnP5EktbS0SJIKCwsjXldYWGjta2lpkcPhUG5u7nlrCgoKRrx/QUFBRM3w98nNzZXD4bBqhlu/fr0158jtdmvKlCkXewqixlpvjKExAABiIupBKBQK6brrrtO6dev0hS98QX/xF3+hiooKPfvssxF1Npst4rkxZsS24YbXnK3+s9QM9eijj8rn81mPo0ePnrdNsZTlYAV6AABiKepBaOLEiZo1a1bEtpkzZ6qxsVGS5PF4JGlEj0xra6vVe+PxeBQIBNTW1nbemhMnTox4/5MnT0bUDH+ftrY29fb2jugpCnM6ncrJyYl4JApXjQEAEFtRD0I33nij3n///YhtH3zwgaZOnSpJmjZtmjwej2pqaqz9gUBAO3bs0Pz58yVJxcXFysjIiKhpbm5WQ0ODVTNv3jz5fD7t3bvXqtmzZ498Pl9ETUNDg5qbm62abdu2yel0qri4OMqfPPpcAz1CZwIMjQEAEAvp0T7gX/3VX2n+/Plat26d7rjjDu3du1fPP/+8nn/+eUn9Q1WVlZVat26dpk+frunTp2vdunXKyspSWVmZJMntduvee+/V6tWrNWHCBOXl5WnNmjWaPXu2br31Vkn9vUyLFy9WRUWFnnvuOUnSfffdp9LSUs2YMUOSVFJSolmzZqm8vFxPPfWUPv30U61Zs0YVFRUJ7ekZLSZLAwAQY7G4ZO3f/u3fTFFRkXE6nebzn/+8ef755yP2h0Ih89hjjxmPx2OcTqe55ZZbzIEDByJquru7zYoVK0xeXp7JzMw0paWlprGxMaLm1KlTZvny5SY7O9tkZ2eb5cuXm7a2toiaI0eOmCVLlpjMzEyTl5dnVqxYYXp6ekb9WRJ5+fzWd4+bqQ+/bv7bM/8v7u8NAEAqG+3fb5sxxiQ6jCWzjo4Oud1u+Xy+uPci7fjgpO7+l72aOTFH//7Nm+P63gAApLLR/v1mrbEkNj686CpDYwAAxARBKIlx1RgAALFFEEpi1urzAYIQAACxQBBKYuEeoZ7ekPqCoQS3BgCAyw9BKIm5BuYISVIX9xICACDqCEJJzJFmV7q9fymQMwyPAQAQdQShJGaz2ZgwDQBADBGEktx46+7SDI0BABBtBKEkF16B/gw9QgAARB1BKMmx3hgAALFDEEpy4aEx7iUEAED0EYSSXHhorIs5QgAARB1BKMmN56oxAABihiCU5Lh8HgCA2CEIJbms8Ar03FkaAICoIwglufEOeoQAAIgVglCS4/J5AABihyCU5MILr55haAwAgKgjCCU5eoQAAIgdglCS46oxAABihyCU5FwDk6UZGgMAIPoIQkkuPEeIoTEAAKKPIJTkuLM0AACxQxBKcllDhsZCIZPg1gAAcHkhCCW5cI+QJJ3pZZ4QAADRRBBKcuMy7LLb+n9neAwAgOgiCCU5m81mXTlGEAIAILoIQilg8F5CDI0BABBNBKEUwCX0AADEBkEoBYR7hM4ECEIAAEQTQSgFhOcI0SMEAEB0EYRSAHOEAACIDYJQCgjPEWJoDACA6CIIpYBwjxBDYwAARBdBKAWw3hgAALFBEEoBWY7+obGuAHOEAACIJoJQCqBHCACA2CAIpQAXQQgAgJggCKUAa2iMy+cBAIgqglAKsIbGuHweAICoIgilAC6fBwAgNmIehNavXy+bzabKykprmzFGa9euldfrVWZmphYuXKiDBw9GvM7v92vlypXKz8+Xy+XSsmXLdOzYsYiatrY2lZeXy+12y+12q7y8XO3t7RE1jY2NWrp0qVwul/Lz87Vq1SoFAoFYfdyYCC+xcYahMQAAoiqmQWjfvn16/vnn9Yd/+IcR25988klt2LBBGzdu1L59++TxeLRo0SJ1dnZaNZWVldqyZYuqqqpUW1ur06dPq7S0VMHgYBgoKytTfX29qqurVV1drfr6epWXl1v7g8GglixZoq6uLtXW1qqqqkovv/yyVq9eHcuPHXXhO0szWRoAgCgzMdLZ2WmmT59uampqzIIFC8w3v/lNY4wxoVDIeDwe88QTT1i1PT09xu12m02bNhljjGlvbzcZGRmmqqrKqmlqajJ2u91UV1cbY4w5dOiQkWR2795t1ezatctIMu+9954xxpitW7cau91umpqarJrNmzcbp9NpfD7fqD6Hz+czkkZdHwsnfN1m6sOvm2mPvG5CoVDC2gEAQKoY7d/vmPUIPfjgg1qyZIluvfXWiO2HDx9WS0uLSkpKrG1Op1MLFizQzp07JUl1dXXq7e2NqPF6vSoqKrJqdu3aJbfbrTlz5lg1c+fOldvtjqgpKiqS1+u1am677Tb5/X7V1dVF/0PHSNbAHKGQkXp6QwluDQAAl4/0WBy0qqpK77zzjvbt2zdiX0tLiySpsLAwYnthYaGOHDli1TgcDuXm5o6oCb++paVFBQUFI45fUFAQUTP8fXJzc+VwOKya4fx+v/x+v/W8o6PjvJ81HrIy0qzfT/v7lOlIO081AAAYraj3CB09elTf/OY39dOf/lTjxo07Z53NZot4bowZsW244TVnq/8sNUOtX7/emnztdrs1ZcqU87YpHux2m1wO5gkBABBtUQ9CdXV1am1tVXFxsdLT05Wenq4dO3boH/7hH5Senm710AzvkWltbbX2eTweBQIBtbW1nbfmxIkTI97/5MmTETXD36etrU29vb0jeorCHn30Ufl8Putx9OjRz3AWoi+LewkBABB1UQ9CX/rSl3TgwAHV19dbj+uvv17Lly9XfX29rr76ank8HtXU1FivCQQC2rFjh+bPny9JKi4uVkZGRkRNc3OzGhoarJp58+bJ5/Np7969Vs2ePXvk8/kiahoaGtTc3GzVbNu2TU6nU8XFxWdtv9PpVE5OTsQjGQyuN8Yl9AAAREvU5whlZ2erqKgoYpvL5dKECROs7ZWVlVq3bp2mT5+u6dOna926dcrKylJZWZkkye12695779Xq1as1YcIE5eXlac2aNZo9e7Y1+XrmzJlavHixKioq9Nxzz0mS7rvvPpWWlmrGjBmSpJKSEs2aNUvl5eV66qmn9Omnn2rNmjWqqKhImoAzWlxCDwBA9MVksvSFfOtb31J3d7ceeOABtbW1ac6cOdq2bZuys7Otmu9///tKT0/XHXfcoe7ubn3pS1/Sj3/8Y6WlDU4UfvHFF7Vq1Srr6rJly5Zp48aN1v60tDT94he/0AMPPKAbb7xRmZmZKisr09NPPx2/DxslWQ6GxgAAiDabMcYkuhHJrKOjQ263Wz6fL6G9SN/48T69+V6r/u6/zdadN1yZsHYAAJAKRvv3m7XGUoSLOUIAAEQdQShFcPk8AADRRxBKEdYK9MwRAgAgaghCKSIchFiBHgCA6CEIpQiGxgAAiD6CUIqwhsYIQgAARA1BKEWE7yx9JsDQGAAA0UIQShFZA0Nj9AgBABA9BKEUMbjWGEEIAIBoIQilCBdDYwAARB1BKEWEF11laAwAgOghCKUI15ChMZaHAwAgOghCKSIchPpCRoFgKMGtAQDg8kAQShFZGWnW7yy8CgBAdBCEUkR6ml3jMvr/ubhyDACA6CAIpRDrEnoWXgUAICoIQikky8G9hAAAiCaCUAoZXG+MOUIAAEQDQSiFjB+4l9AZeoQAAIgKglAKCQ+NcVNFAACigyCUQlhvDACA6CIIpZDwMhtdrDcGAEBUEIRSCFeNAQAQXQShFMLQGAAA0UUQSiHWwqsMjQEAEBUEoRRizRGiRwgAgKggCKUQF5fPAwAQVQShFBIeGjvD0BgAAFFBEEohDI0BABBdBKEUMrjWGEEIAIBoIAilkPEMjQEAEFUEoRSS5egfGqNHCACA6CAIpZBwj1CgL6TeYCjBrQEAIPURhFJIeIkNSTrjZ3gMAIBLRRBKIY50uxxp/f9kpwMMjwEAcKkIQimGS+gBAIgeglCKcbHwKgAAUUMQSjHhZTa6mCMEAMAlIwilmPDQGJfQAwBw6QhCKWZwvTGCEAAAl4oglGIGh8YIQgAAXCqCUIoZXG+MOUIAAFyqqAeh9evX64YbblB2drYKCgr05S9/We+//35EjTFGa9euldfrVWZmphYuXKiDBw9G1Pj9fq1cuVL5+flyuVxatmyZjh07FlHT1tam8vJyud1uud1ulZeXq729PaKmsbFRS5culcvlUn5+vlatWqVAIBDtjx034wfmCDE0BgDApYt6ENqxY4cefPBB7d69WzU1Nerr61NJSYm6urqsmieffFIbNmzQxo0btW/fPnk8Hi1atEidnZ1WTWVlpbZs2aKqqirV1tbq9OnTKi0tVTA42BNSVlam+vp6VVdXq7q6WvX19SovL7f2B4NBLVmyRF1dXaqtrVVVVZVefvllrV69OtofO26yWIEeAIDoMTHW2tpqJJkdO3YYY4wJhULG4/GYJ554wqrp6ekxbrfbbNq0yRhjTHt7u8nIyDBVVVVWTVNTk7Hb7aa6utoYY8yhQ4eMJLN7926rZteuXUaSee+994wxxmzdutXY7XbT1NRk1WzevNk4nU7j8/lG1X6fz2ckjbo+1ja++aGZ+vDr5q//T32imwIAQNIa7d/vmM8R8vl8kqS8vDxJ0uHDh9XS0qKSkhKrxul0asGCBdq5c6ckqa6uTr29vRE1Xq9XRUVFVs2uXbvkdrs1Z84cq2bu3Llyu90RNUVFRfJ6vVbNbbfdJr/fr7q6urO21+/3q6OjI+KRTFwDK9B3BZgjBADApYppEDLG6KGHHtJNN92koqIiSVJLS4skqbCwMKK2sLDQ2tfS0iKHw6Hc3Nzz1hQUFIx4z4KCgoia4e+Tm5srh8Nh1Qy3fv16a86R2+3WlClTLvZjx1QWd5YGACBqYhqEVqxYoXfffVebN28esc9ms0U8N8aM2Dbc8Jqz1X+WmqEeffRR+Xw+63H06NHztinexhOEAACImpgFoZUrV+q1117T9u3bNXnyZGu7x+ORpBE9Mq2trVbvjcfjUSAQUFtb23lrTpw4MeJ9T548GVEz/H3a2trU29s7oqcozOl0KicnJ+KRTAbXGmNoDACASxX1IGSM0YoVK/TKK6/ozTff1LRp0yL2T5s2TR6PRzU1Nda2QCCgHTt2aP78+ZKk4uJiZWRkRNQ0NzeroaHBqpk3b558Pp/27t1r1ezZs0c+ny+ipqGhQc3NzVbNtm3b5HQ6VVxcHO2PHheDc4ToEQIA4FKlR/uADz74oH72s5/pX//1X5WdnW31yLjdbmVmZspms6myslLr1q3T9OnTNX36dK1bt05ZWVkqKyuzau+9916tXr1aEyZMUF5entasWaPZs2fr1ltvlSTNnDlTixcvVkVFhZ577jlJ0n333afS0lLNmDFDklRSUqJZs2apvLxcTz31lD799FOtWbNGFRUVSdfTM1qsPg8AQPREPQg9++yzkqSFCxdGbP/Rj36ke+65R5L0rW99S93d3XrggQfU1tamOXPmaNu2bcrOzrbqv//97ys9PV133HGHuru79aUvfUk//vGPlZaWZtW8+OKLWrVqlXV12bJly7Rx40Zrf1pamn7xi1/ogQce0I033qjMzEyVlZXp6aefjvbHjpvxDI0BABA1NmOMSXQjkllHR4fcbrd8Pl9S9CKdOu1X8f/8lSTpd+v+RGn2808wBwBgLBrt32/WGksx4aExiXlCAABcKoJQinGm25U+0At0huExAAAuCUEoxdhsNmUNXDnGemMAAFwaglAK4qaKAABEB0EoBVmX0DNHCACAS0IQSkFZXEIPAEBUEIRSUPZAEDp0vCPBLQEAILURhFLQbdf0r5P29298oOqG5gtUAwCAcyEIpaC75k7V8jlXyhhpVVW99nx0KtFNAgAgJRGEUpDNZtPjf1qkklmFCvSF9N9/8rbeb+lMdLMAAEg5BKEUlWa36R++9gVdPzVXnT19uvtf9up4e3eimwUAQEohCKWwcRlp+qe7r9fvF4xXS0ePvv4ve9V+JpDoZgEAkDIIQinuiiyHXvjGH8uTM07/2Xpa//2Ft9XTy2X1AACMBkHoMjDpiky98I0/Vva4dL19pE2rNu9XMGQS3SwAAJIeQegyMcOTrX/6+vVypNu17dAJ/Y9/bZAxhCEAAM6HIHQZmXP1BP2vO/9INpv04p5GbXzzPxPdJAAAkhpB6DJz++yJ+s6yayRJ36v5QFV7GxPcIgAAkhdB6DL09XlX6cH/8nuSpG+/2qA3fnsiwS0CACA5EYQuU2tKZujPiicrGDJ68Gfv6J3GtkQ3CQCApEMQukzZbDat/8psLZzxOfX0hnTvj/fpdydPJ7pZAAAkFYLQZSwjza5nll+naye71XamV1//57060dGT6GYBAJA0CEKXuSxHuv7lnht01YQsNbV3654f7VNHT2+imwUAQFIgCI0BE8Y79ZNvzFH+eKd+29yhv/hJnfx93H0aAACC0Bhx5YQs/fj/u0EuR5p2fXRKq3/+Hwpx92kAwBhHEBpDiia5tam8WOl2m15/t1n3/e+39f/+8xMCEQBgzLIZ1mE4r46ODrndbvl8PuXk5CS6OVHx6v4m/dXP6xX+l5+cm6k/L56iP7t+siZdkZnYxgEAEAWj/ftNELqAyzEISVJDk0+b9zbqtfrj6vT3SZJsNumm38/XnTdM0aJZhXKmpyW4lQAAfDYEoSi5XINQWHcgqOqDzfr5vmPa9dEpa/sVWRn68h9N0h3XT9Es7+X3uQEAlzeCUJRc7kFoqCOnuvR/647p/7x9TC1D7jc0e5Jbd1w/WcuunSR3VkYCWwgAwOgQhKJkLAWhsGDI6DcfntTP3z6qmkMn1Bvs/4o40+1aXOTRHddP0byrJ8hutyW4pQAAnB1BKErGYhAa6tOugLbsb9LP9x3V+yc6re2TczP1X78wSdddmatrJuWoIHtcAlsJAEAkglCUjPUgFGaM0YEmn17adzRignVYYY5TRV63rpnkVpE3R7Mnu+XJGSebjV4jAED8EYSihCA0UniC9Y73T+rg8Q797uRpne1WRBNcDisYFU1ya/YktybnZhKOAAAxRxCKEoLQhZ0J9Om3zR1qaOpQQ5NPDcc79OGJTvWdJR3ljEtX0SS3iia5dY03R1fnj5f3inHKczkISACAqCEIRQlB6LPp6Q3q/ZZONRz3WQHp/ZZOBYKhs9ZnZqTJe8U4ea/I1OTcTE26IlPeK/p/TsrNlCdnnNLTuBE6AGB0Rvv3Oz2ObcIYMi4jTddOuULXTrnC2hboC+nD1k4dbOrQgSafDh736Vhbt1o7/eruDep3J7v0u5NdZz2e3SZ5cvqD0qQhQcmTM07urAy5MzOUM67/57gMO71LAIBRoUfoAugRij1/X1DN7T063t6tY+3damrr1vH2bjW19/883t5zzp6ks3Gk2ZWTma6czMiAlJOZLvewbf3bB39mO9O5LQAAXAboEULKcKan6ap8l67Kd511fyhk9Mlpv5qGhKOmtv7fWzv96ujula+7Vx09fQqGjALBkD45HdAnpwMX3RabTcp2psudNSRAhUNTVoZyxqVboSkcoIbWONIZvgOAVEIQQtKz220qyBmngpxx+sKVueesM8aoKxC0gpGvuzfy956+wdAUsb3/Z09vSMaov66nT1L3Rbc1MyPN6nkKh6Pscekal5GmcRlpcqbb5Rz4Oe4z/qTHCgCihyCEy4bNZtN4Z7rGO9PlvSLzol/v7wuqo7svIiCdNTgNq/F196qzp/++St29QXX3BnWiwx/tj2dxpNmHBSq7nOlp5/+ZkaZxQ14z9Hn4pyPNLke6Tel2uzLS7MpIsyk9za50u00ZaXalp9mUYbcrw6qxMRcLQMojCAEDnOlp+lx2mj6X7bzo1wZDRqd7+iLCUThAdfb0yd8XVE9vaBQ/Q/L3BuXvC6lnyM+htyIIBEMKBEMjbmqZCGl2W0RQSrfb5QgHqIHglD7wPGNooBoWsMLBavj+8OvSB4JZ+P3s4Z82m9LTBn7a7UqzS2lDf9r6XzP0MfJ1I2vSbDalpdkiXp9uJ/gBl6MxEYSeeeYZPfXUU2pubtY111yjv//7v9fNN9+c6GbhMpJmt/VfvRajRWn7ggMhaVhAGv4z/PvZwtT5f4bUGwwp0BdSXzCk3pBRXzCkvqBRb6j/59nuCxUMGQVDRv6+0U9mT2U2mwaD1JBANjRA2Qd+t9tsstsk+0CYstlsSrNrYHv/vsG6cE3ktoga+8Bz27BjDdlutw87lm3ka+3D2maz9femhp/breeRNf3HkWwa8jyifkjN8NdrSI39Au9h/d5fY1Pkfqn/GEO322z97RraFptsstl19tcPeW4b+Hcl5I5dl30Qeumll1RZWalnnnlGN954o5577jndfvvtOnTokK688spENw8Ylf4eFrtcF99ZFTXGGPUGjfpCof6fwZD6Qka9wXBQCinQd+79vecIWL3hur4h+4cdt3egLhy8rIcZ/L0vZBQK/zRGfcGBn0O2n+11Zzveuc+BBhYhNord4CcSZUSQGghZ9iGBTLazBylpSIALv1YDYW5IWBv6Og2pGfo6Dd0W0ZYhwW3Y68LHGh4Ohx5v+GuHt31wf+QxdJbXDH2uEZ858hjnPL4GA+itMwt10/T8WP7zntNlf/n8nDlzdN111+nZZ5+1ts2cOVNf/vKXtX79+gu+nsvngbHFGKOQkfpCIYVCkT/PF6DCwSsY6n99yPQHsKAxMkYD28M1g/tDRgM1Q147UBs0w56HBo41cJxQaMixhhzbDG/HWY4dMuHPamQkq9YYo5B1zMGawf1n/xlZP/L1I+vP/fpgqL9N4X0K12rwNf2bI98Tqetbi2fogYW/H9Vjcvm8pEAgoLq6Oj3yyCMR20tKSrRz586zvsbv98vvH/y/XkdHR0zbCCC52Gw2pdmkNHvawJa089YjeZhwSFJkyNKw50aSCY0MUkaDIcsKXqFzvN4KbpGvO+vvQ14vhY8z0F5d+HUasm3466SR7Qh/5pHHHXythr3P8PfV0LZFtLP/+YjjD3s+/N/jvMeX0XXnuSI41i7rIPTJJ58oGAyqsLAwYnthYaFaWlrO+pr169frO9/5TjyaBwCIovAwlCSliTk/GJ0xcfe34ZPgjDHnnBj36KOPyufzWY+jR4/Go4kAACABLuseofz8fKWlpY3o/WltbR3RSxTmdDrldCZwRioAAIiby7pHyOFwqLi4WDU1NRHba2pqNH/+/AS1CgAAJIvLukdIkh566CGVl5fr+uuv17x58/T888+rsbFR999/f6KbBgAAEuyyD0J33nmnTp06pccff1zNzc0qKirS1q1bNXXq1EQ3DQAAJNhlfx+hS8V9hAAASD2j/ft9Wc8RAgAAOB+CEAAAGLMIQgAAYMwiCAEAgDGLIAQAAMYsghAAABizCEIAAGDMuuxvqHipwrdZ6ujoSHBLAADAaIX/bl/odokEoQvo7OyUJE2ZMiXBLQEAABers7NTbrf7nPu5s/QFhEIhHT9+XNnZ2bLZbFE5ZkdHh6ZMmaKjR49yt+pLwHmMDs5j9HAuo4PzGB1j/TwaY9TZ2Smv1yu7/dwzgegRugC73a7JkyfH5Ng5OTlj8ssZbZzH6OA8Rg/nMjo4j9Exls/j+XqCwpgsDQAAxiyCEAAAGLMIQgngdDr12GOPyel0JropKY3zGB2cx+jhXEYH5zE6OI+jw2RpAAAwZtEjBAAAxiyCEAAAGLMIQgAAYMwiCAEAgDGLIBRnzzzzjKZNm6Zx48apuLhYv/nNbxLdpKS2du1a2Wy2iIfH47H2G2O0du1aeb1eZWZmauHChTp48GACW5w83nrrLS1dulRer1c2m02vvvpqxP7RnDu/36+VK1cqPz9fLpdLy5Yt07Fjx+L4KRLvQufxnnvuGfEdnTt3bkQN51Fav369brjhBmVnZ6ugoEBf/vKX9f7770fU8J28sNGcR76TF4cgFEcvvfSSKisr9e1vf1v79+/XzTffrNtvv12NjY2JblpSu+aaa9Tc3Gw9Dhw4YO178skntWHDBm3cuFH79u2Tx+PRokWLrDXixrKuri5de+212rhx41n3j+bcVVZWasuWLaqqqlJtba1Onz6t0tJSBYPBeH2MhLvQeZSkxYsXR3xHt27dGrGf8yjt2LFDDz74oHbv3q2amhr19fWppKREXV1dVg3fyQsbzXmU+E5eFIO4+eM//mNz//33R2z7/Oc/bx555JEEtSj5PfbYY+baa689675QKGQ8Ho954oknrG09PT3G7XabTZs2xamFqUGS2bJli/V8NOeuvb3dZGRkmKqqKqumqanJ2O12U11dHbe2J5Ph59EYY+6++27zp3/6p+d8Defx7FpbW40ks2PHDmMM38nPavh5NIbv5MWiRyhOAoGA6urqVFJSErG9pKREO3fuTFCrUsOHH34or9eradOm6atf/ao++ugjSdLhw4fV0tIScU6dTqcWLFjAOb2A0Zy7uro69fb2RtR4vV4VFRVxfof59a9/rYKCAv3BH/yBKioq1Nraau3jPJ6dz+eTJOXl5UniO/lZDT+PYXwnR48gFCeffPKJgsGgCgsLI7YXFhaqpaUlQa1KfnPmzNFPfvIT/fKXv9QPf/hDtbS0aP78+Tp16pR13jinF280566lpUUOh0O5ubnnrIF0++2368UXX9Sbb76p733ve9q3b5+++MUvyu/3S+I8no0xRg899JBuuukmFRUVSeI7+Vmc7TxKfCcvFqvPx5nNZot4bowZsQ2Dbr/9duv32bNna968efq93/s9vfDCC9bkP87pZ/dZzh3nN9Kdd95p/V5UVKTrr79eU6dO1S9+8Qt95StfOefrxvJ5XLFihd59913V1taO2Md3cvTOdR75Tl4ceoTiJD8/X2lpaSPSdmtr64j/AeHcXC6XZs+erQ8//NC6eoxzevFGc+48Ho8CgYDa2trOWYORJk6cqKlTp+rDDz+UxHkcbuXKlXrttde0fft2TZ482drOd/LinOs8ng3fyfMjCMWJw+FQcXGxampqIrbX1NRo/vz5CWpV6vH7/frtb3+riRMnatq0afJ4PBHnNBAIaMeOHZzTCxjNuSsuLlZGRkZETXNzsxoaGji/53Hq1CkdPXpUEydOlMR5DDPGaMWKFXrllVf05ptvatq0aRH7+U6OzoXO49nwnbyAxMzRHpuqqqpMRkaG+ed//mdz6NAhU1lZaVwul/n4448T3bSktXr1avPrX//afPTRR2b37t2mtLTUZGdnW+fsiSeeMG6327zyyivmwIED5mtf+5qZOHGi6ejoSHDLE6+zs9Ps37/f7N+/30gyGzZsMPv37zdHjhwxxozu3N1///1m8uTJ5le/+pV55513zBe/+EVz7bXXmr6+vkR9rLg733ns7Ow0q1evNjt37jSHDx8227dvN/PmzTOTJk3iPA7zl3/5l8btdptf//rXprm52XqcOXPGquE7eWEXOo98Jy8eQSjO/vEf/9FMnTrVOBwOc91110Vc8oiR7rzzTjNx4kSTkZFhvF6v+cpXvmIOHjxo7Q+FQuaxxx4zHo/HOJ1Oc8stt5gDBw4ksMXJY/v27UbSiMfdd99tjBnduevu7jYrVqwweXl5JjMz05SWlprGxsYEfJrEOd95PHPmjCkpKTGf+9znTEZGhrnyyivN3XffPeIccR7NWc+hJPOjH/3IquE7eWEXOo98Jy+ezRhj4tf/BAAAkDyYIwQAAMYsghAAABizCEIAAGDMIggBAIAxiyAEAADGLIIQAAAYswhCAABgzCIIAQCAMYsgBAAAxiyCEAAAGLMIQgAAYMwiCAEAgDHr/wezS7H89gFdHAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(V_data_1['Pressure'],V_data_1['Vap_Sat'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ace7bb31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd94158b790>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(V_data_2['Pressure'],V_data_2['Vap_Sat'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ab266c34",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd91009c1c0>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(V_data_3['Pressure'],V_data_3['Vap_Sat'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "be47e5f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "P_1 = V_data_1['Pressure'].values.reshape(-1,1)\n",
    "Vap_sat_1 = V_data_1['Vap_Sat'].values.reshape(-1,1)\n",
    "P_2 = V_data_2['Pressure'].values.reshape(-1,1)\n",
    "Vap_sat_2 = V_data_2['Vap_Sat'].values.reshape(-1,1)\n",
    "P_3 = V_data_3['Pressure'].values.reshape(-1,1)\n",
    "Vap_sat_3 = V_data_3['Vap_Sat'].values.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "626ed2db",
   "metadata": {},
   "source": [
    "## Sklearn implementation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "46e7e3a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mTRu89957qFmzJnbv3l3utpbkk08+wZIlSzB//nx8//33yMrKsgt4Bb766ivVz9u2bcPJkyeVO63uu+8+1KxZE4cOHVJ6HYtu7u7u5W5jjx494OrqiuPHj5f4vOXVq1cv5OTklDqBZlRUFEQEaWlpxb5mq1atSn2Ngt/n8ePHy92+kuh0OrvP7o8//ugwE1127NgRer0e33zzjWr/9u3bVZdiy0Kv1yMiIkK56aDgDtCoqCgcP34c/v7+xf5eCoc3vV5fam/Un3/+CX9//zL1ppHjY48VURE9evRAnTp1EB0djebNm8NqtWLv3r149913UaNGDYwbNw6AbWyPr68vRo4cialTp8LNzQ1fffUV9u3bd8PXuJlji6pWrRpGjRqFSZMmwcvLq1wzVTdv3hzh4eGIjY1FamoqPv74Y9Xjq1evxoIFC/Dwww+jYcOGEBGsWLECWVlZZeoVs1qt2L59e7GP3X333dDr9Thw4ADGjh2LIUOGKGHq008/xYABAzB37lyMHz9eddyuXbvwzDPP4B//+AdSU1MxZcoU1K5dGy+88AIA22SM8+bNw5AhQ3Dx4kUMGDAAgYGBOHfuHPbt24dz587hww8/LPM5KlC/fn28+eabmDJlCv7880/07NkTvr6+OHPmDHbu3AkvLy+88cYb5XrOgQMH4vPPP8fIkSNx5MgRdOvWDVarFTt27ECLFi3wxBNP4L777sOzzz6Lp59+Grt27UKXLl3g5eWF9PR0bN26Fa1atcLzzz9f4msUBM7t27crY5FuVlRUFBYvXozmzZujdevWSExMxNtvv+0w8375+flhwoQJiI2Nha+vLx555BGcOnUKb7zxBoKDg2847cTrr7+OU6dOoXv37qhTpw6ysrLw/vvvq8ZBjh8/HsuXL0eXLl3w4osvonXr1rBarUhJScG6deswceJEdOzYEYCt13fTpk344YcfEBwcDG9vbzRr1kx5ve3btyMiIuK2mun/jla1Y+eJHM8333wjgwYNkiZNmkiNGjXEzc1N6tatKzExMXLo0CFV7bZt2yQ8PFw8PT2lVq1a8swzz8ju3btLvBOqIscOGTJEvLy8Sm3ziRMnBICMHDmy3O/3448/FgDi4eEhZrNZ9djvv/8uAwcOlEaNGomHh4cYDAbp0KGDLF68+IbPW9pdgQDk2LFjcvnyZWnevLm0bNlSrly5ojp+1KhR4ubmJjt27BCR63eprVu3TmJiYqRmzZri4eEhvXv3lmPHjtm9/ubNm6VPnz7i5+cnbm5uUrt2benTp4/qzreC38u5c+fsji/pTs5Vq1ZJt27dxMfHR/R6vdSrV08GDBggv/zyi+q9F/c7K+45r169Kq+//ro0adJE3N3dxd/fXx544AHZtm2bqu6zzz6Tjh07ipeXl3h4eEijRo3kqaeekl27dhV3+lU6d+5sdyddYaXdFVj0rjcRkczMTBk+fLgEBgaKp6en3H///fLbb79JRESE6o670u4KLHrOC16v8N2sJd0VWLidJb2O1WqV6dOnS506dcTd3V1at24tq1evljZt2tjdWVrU6tWrpVevXlK7dm1xd3eXwMBA6d27t/z222+qusuXL8urr74qzZo1E3d3dzEYDNKqVSt58cUXVXdh7t27V+677z7x9PS0uyvxjz/+EACyfPnyUttEzoNL2hDdBubNm4exY8ciKSkJd911V1U355ZYvHgxnn76aSQkJFTostudbPny5Xj88cdx8uRJ1K5du6qbU2WSk5PRvHlzTJ06Ff/617+qujkAgNdeew1ffvkljh8/XuykxOR8+FskcmJ79uxBcnIy3nzzTfTr1++2DVV0c/r374/27dsjNjYW8+fPr+rmVIp9+/Zh6dKl6NSpE3x8fHDkyBHMnj0bPj4+GD58eFU3D4DtZpUPPvgA8+bNY6i6jfA3SeTEHnnkEWRkZKBz586lzhhOdzadTodFixbh+++/L/UOxNuJl5cXdu3ahU8//RRZWVkwGAzo2rUr3nrrLYcZJJ6cnIzJkydj0KBBVd0U0hAvBRIRERFp5Pb/ZwsRERFRJWGwIiIiItIIgxURERGRRjh4vZJZrVacPn0a3t7enAyOiIjISYgILl26dMP1PRmsKtnp06cREhJS1c0gIiKiCkhNTS11lQEGq0rm7e0NwPaL8fHxqeLWEBERUVlkZ2cjJCRE+R4vCYNVJSu4/Ofj48NgRURE5GRuNIyHg9eJiIiINMJgRURERKQRBisiIiIijTBYEREREWmEwYqIiIhIIwxWRERERBphsCIiIiLSCIMVERERkUYYrIiIiIg0wpnXbwf5+cBvvwHp6UBwMNC5M1CtWlW3ioiI6I7DYOXsVqwAxo0DTp26vq9OHeD994H+/auuXURERHcgXgp0ZitWAAMGqEMVAKSl2favWFE17SIiIrpDMVg5q/x8W0+ViP1jBfvGj7fVERERUaVgsHJWv/1m31NVmAiQmmqrIyIiokrBYOWs0tO1rSMiIqKbxmDlrIKDta0jIiKim8Zg5aw6d7bd/afTFf+4TgeEhNjqiIiIqFIwWDmratVsUyoA9uGq4Oe5czmfFRERUSVisHJm/fsD330H1K6t3l+njm0/57EiIiKqVJwg1Nn17w/068eZ14mIiBwAg9XtoFo1oGvXqm4FERHRHY+XAomIiIg0wmBFREREpBEGKyIiIiKNMFgRERERaYTBioiIiEgjDFZEREREGmGwIiIiItIIgxURERGRRhisiIiIiDTCYEVERESkkSoNVlu2bEF0dDRMJhN0Oh1WrVqlPJaXl4dJkyahVatW8PLygslkwlNPPYXTp0+rnsNisWDMmDEICAiAl5cX+vbti1OnTqlqMjMzERMTA4PBAIPBgJiYGGRlZalqUlJSEB0dDS8vLwQEBGDs2LHIzc1V1Rw4cAARERHw8PBA7dq18eabb0JEND0nRERE5LyqNFhduXIFbdq0wfz58+0e++uvv7B792689tpr2L17N1asWIGjR4+ib9++qrrx48dj5cqViIuLw9atW3H58mVERUUhPz9fqRk0aBD27t2LtWvXYu3atdi7dy9iYmKUx/Pz89GnTx9cuXIFW7duRVxcHJYvX46JEycqNdnZ2XjooYdgMpmQkJCAefPm4Z133sGcOXNuwZkhIiIipyQOAoCsXLmy1JqdO3cKADl58qSIiGRlZYmbm5vExcUpNWlpaeLi4iJr164VEZFDhw4JANm+fbtSEx8fLwDk999/FxGRNWvWiIuLi6SlpSk1S5cuFb1eL2azWUREFixYIAaDQXJycpSa2NhYMZlMYrVay/w+zWazAFCel4iIiBxfWb+/nWqMldlshk6nQ82aNQEAiYmJyMvLQ2RkpFJjMpkQGhqKbdu2AQDi4+NhMBjQsWNHpebee++FwWBQ1YSGhsJkMik1PXr0gMViQWJiolITEREBvV6vqjl9+jROnDhxq94yERERORGnCVY5OTl45ZVXMGjQIPj4+AAAMjIy4O7uDl9fX1VtUFAQMjIylJrAwEC75wsMDFTVBAUFqR739fWFu7t7qTUFPxfUFMdisSA7O1u1ERER0e3JKYJVXl4ennjiCVitVixYsOCG9SICnU6n/Fz4/7Wskb8Hrhd3bIHY2Fhl0LzBYEBISMgN209ERETOyeGDVV5eHh577DEkJydj/fr1Sm8VABiNRuTm5iIzM1N1zNmzZ5XeJKPRiDNnztg977lz51Q1RXudMjMzkZeXV2rN2bNnAcCuJ6uwyZMnw2w2K1tqampZ3zoRERE5GYcOVgWh6tixY/jll1/g7++vejwsLAxubm5Yv369si89PR1JSUno1KkTACA8PBxmsxk7d+5Uanbs2AGz2ayqSUpKQnp6ulKzbt066PV6hIWFKTVbtmxRTcGwbt06mEwm1K9fv8T3oNfr4ePjo9qIiIjo9qQTqbqJmC5fvow//vgDAHD33Xdjzpw56NatG/z8/GAymfDoo49i9+7dWL16tapXyM/PD+7u7gCA559/HqtXr8bixYvh5+eHl156CRcuXEBiYiKqVasGAOjVqxdOnz6Njz76CADw7LPPol69evjhhx8A2KZbaNu2LYKCgvD222/j4sWLGDp0KB5++GHMmzcPgG3gfLNmzfDAAw/gX//6F44dO4ahQ4fi9ddfV03LcCPZ2dkwGAwwm80MWURERE6izN/ft/z+xFJs3LhRANhtQ4YMkeTk5GIfAyAbN25UnuPq1asyevRo8fPzEw8PD4mKipKUlBTV61y4cEEGDx4s3t7e4u3tLYMHD5bMzExVzcmTJ6VPnz7i4eEhfn5+Mnr0aNXUCiIi+/fvl86dO4terxej0SjTpk0r11QLIpxugYiIyBmV9fu7Snus7kTssSIiInI+Zf3+dugxVkRERETOhMGKiIiISCMMVkREREQaYbAiIiIi0giDFREREZFGGKyIiIiINMJgRURERKQRBisiIiIijTBYEREREWmEwYqIiIhIIwxWRERERBphsCIiIiLSCIMVERERkUYYrIiIiIg0wmBFREREpBEGKyIiIiKNMFgRERERaYTBioiIiEgjDFZEREREGmGwIiIiItIIgxURERGRRhisiIiIiDTCYEVERESkEQYrIiIiIo0wWBERERFphMGKiIiISCMMVkREREQaYbAiIiIi0giDFREREZFGGKyIiIiINMJgRURERKQRBisiIiIijTBYEREREWmEwYqIiIhIIwxWRERERBphsCIiIiLSCIMVERERkUaqNFht2bIF0dHRMJlM0Ol0WLVqlepxEcG0adNgMpng4eGBrl274uDBg6oai8WCMWPGICAgAF5eXujbty9OnTqlqsnMzERMTAwMBgMMBgNiYmKQlZWlqklJSUF0dDS8vLwQEBCAsWPHIjc3V1Vz4MABREREwMPDA7Vr18abb74JEdHsfBAREZFzq9JgdeXKFbRp0wbz588v9vHZs2djzpw5mD9/PhISEmA0GvHQQw/h0qVLSs348eOxcuVKxMXFYevWrbh8+TKioqKQn5+v1AwaNAh79+7F2rVrsXbtWuzduxcxMTHK4/n5+ejTpw+uXLmCrVu3Ii4uDsuXL8fEiROVmuzsbDz00EMwmUxISEjAvHnz8M4772DOnDm34MwQERGRUxIHAUBWrlyp/Gy1WsVoNMrMmTOVfTk5OWIwGGThwoUiIpKVlSVubm4SFxen1KSlpYmLi4usXbtWREQOHTokAGT79u1KTXx8vACQ33//XURE1qxZIy4uLpKWlqbULF26VPR6vZjNZhERWbBggRgMBsnJyVFqYmNjxWQyidVqLfP7NJvNAkB5XiIiInJ8Zf3+dtgxVsnJycjIyEBkZKSyT6/XIyIiAtu2bQMAJCYmIi8vT1VjMpkQGhqq1MTHx8NgMKBjx45Kzb333guDwaCqCQ0NhclkUmp69OgBi8WCxMREpSYiIgJ6vV5Vc/r0aZw4caLE92GxWJCdna3aiIiI6PbksMEqIyMDABAUFKTaHxQUpDyWkZEBd3d3+Pr6lloTGBho9/yBgYGqmqKv4+vrC3d391JrCn4uqClObGysMrbLYDAgJCSk9DdORERETsthg1UBnU6n+llE7PYVVbSmuHotauTvgeultWfy5Mkwm83KlpqaWmrbiYiIyHk5bLAyGo0A7HuDzp49q/QUGY1G5ObmIjMzs9SaM2fO2D3/uXPnVDVFXyczMxN5eXml1pw9exaAfa9aYXq9Hj4+PqqNiIiIbk8OG6waNGgAo9GI9evXK/tyc3OxefNmdOrUCQAQFhYGNzc3VU16ejqSkpKUmvDwcJjNZuzcuVOp2bFjB8xms6omKSkJ6enpSs26deug1+sRFham1GzZskU1BcO6detgMplQv3597U8AEREROZ0qDVaXL1/G3r17sXfvXgC2Aet79+5FSkoKdDodxo8fjxkzZmDlypVISkrC0KFD4enpiUGDBgEADAYDhg8fjokTJ2LDhg3Ys2cPnnzySbRq1QoPPvggAKBFixbo2bMnRowYge3bt2P79u0YMWIEoqKi0KxZMwBAZGQkWrZsiZiYGOzZswcbNmzASy+9hBEjRig9TIMGDYJer8fQoUORlJSElStXYsaMGZgwYcINL00SERHRHeLW36BYso0bNwoAu23IkCEiYptyYerUqWI0GkWv10uXLl3kwIEDque4evWqjB49Wvz8/MTDw0OioqIkJSVFVXPhwgUZPHiweHt7i7e3twwePFgyMzNVNSdPnpQ+ffqIh4eH+Pn5yejRo1VTK4iI7N+/Xzp37ix6vV6MRqNMmzatXFMtiHC6BSIiImdU1u9vnQinDq9M2dnZMBgMMJvNHG9FRETkJMr6/e2wY6yIiIiInA2DFREREZFGGKyIiIiINMJgRURERKQRBisiIiIijTBYEREREWmEwYqIiIhIIwxWRERERBphsCIiIiLSCIMVERERkUYYrIiIiIg0wmBFREREpBEGKyIiIiKNMFgRERERaYTBioiIiEgjDFZEREREGmGwIiIiItIIgxURERGRRhisiIiIiDTCYEVERESkEQYrIiIiIo0wWBERERFphMGKiIiISCMMVkREREQaYbAiIiIi0giDFREREZFGGKyIiIiINMJgRURERKQRBisiIiIijTBYEREREWmEwYqIiIhIIwxWRERERBphsCIiIiLSCIMVERERkUYYrIiIiIg0wmBFREREpBGHDlbXrl3Dq6++igYNGsDDwwMNGzbEm2++CavVqtSICKZNmwaTyQQPDw907doVBw8eVD2PxWLBmDFjEBAQAC8vL/Tt2xenTp1S1WRmZiImJgYGgwEGgwExMTHIyspS1aSkpCA6OhpeXl4ICAjA2LFjkZube8vePxERETkXhw5Ws2bNwsKFCzF//nwcPnwYs2fPxttvv4158+YpNbNnz8acOXMwf/58JCQkwGg04qGHHsKlS5eUmvHjx2PlypWIi4vD1q1bcfnyZURFRSE/P1+pGTRoEPbu3Yu1a9di7dq12Lt3L2JiYpTH8/Pz0adPH1y5cgVbt25FXFwcli9fjokTJ1bOySAiIiLHJw6sT58+MmzYMNW+/v37y5NPPikiIlarVYxGo8ycOVN5PCcnRwwGgyxcuFBERLKyssTNzU3i4uKUmrS0NHFxcZG1a9eKiMihQ4cEgGzfvl2piY+PFwDy+++/i4jImjVrxMXFRdLS0pSapUuXil6vF7PZXOb3ZDabBUC5jiEiIqKqVdbvb4fusbr//vuxYcMGHD16FACwb98+bN26Fb179wYAJCcnIyMjA5GRkcoxer0eERER2LZtGwAgMTEReXl5qhqTyYTQ0FClJj4+HgaDAR07dlRq7r33XhgMBlVNaGgoTCaTUtOjRw9YLBYkJibeojNAREREzsS1qhtQmkmTJsFsNqN58+aoVq0a8vPz8dZbb2HgwIEAgIyMDABAUFCQ6rigoCCcPHlSqXF3d4evr69dTcHxGRkZCAwMtHv9wMBAVU3R1/H19YW7u7tSUxyLxQKLxaL8nJ2dXab3TkRERM7HoXusvvnmGyxZsgRff/01du/ejS+++ALvvPMOvvjiC1WdTqdT/SwidvuKKlpTXH1FaoqKjY1VBsQbDAaEhISU2i4iIiJyXg4drF5++WW88soreOKJJ9CqVSvExMTgxRdfRGxsLADAaDQCgF2P0dmzZ5XeJaPRiNzcXGRmZpZac+bMGbvXP3funKqm6OtkZmYiLy/PriersMmTJ8NsNitbampqeU4BERERORGHDlZ//fUXXFzUTaxWrZoy3UKDBg1gNBqxfv165fHc3Fxs3rwZnTp1AgCEhYXBzc1NVZOeno6kpCSlJjw8HGazGTt37lRqduzYAbPZrKpJSkpCenq6UrNu3Tro9XqEhYWV+B70ej18fHxUGxEREd2eHHqMVXR0NN566y3UrVsXd911F/bs2YM5c+Zg2LBhAGyX5saPH48ZM2agSZMmaNKkCWbMmAFPT08MGjQIAGAwGDB8+HBMnDgR/v7+8PPzw0svvYRWrVrhwQcfBAC0aNECPXv2xIgRI/DRRx8BAJ599llERUWhWbNmAIDIyEi0bNkSMTExePvtt3Hx4kW89NJLGDFiBMMSERER2VTCHYoVlp2dLePGjZO6detK9erVpWHDhjJlyhSxWCxKjdVqlalTp4rRaBS9Xi9dunSRAwcOqJ7n6tWrMnr0aPHz8xMPDw+JioqSlJQUVc2FCxdk8ODB4u3tLd7e3jJ48GDJzMxU1Zw8eVL69OkjHh4e4ufnJ6NHj5acnJxyvSdOt0BEROR8yvr9rRMRqepwdyfJzs6GwWCA2WxmTxcREZGTKOv3t0OPsSIiIiJyJgxWRERERBphsCIiIiLSCIMVERERkUYYrIiIiIg0wmBFREREpBEGKyIiIiKNMFgRERERaYTBioiIiEgjDFZEREREGmGwIiIiItIIgxURERGRRhisiIiIiDTCYEVERESkEQYrIiIiIo0wWBERERFphMGKiIiISCMMVkREREQaYbAiIiIi0giDFREREZFGGKyIiIiINMJgRURERKQRBisiIiIijTBYEREREWmEwYqIiIhIIxUKVps2bdK4GURERETOr0LBqmfPnmjUqBGmT5+O1NRUrdtERERE5JQqFKxOnz6NcePGYcWKFWjQoAF69OiBZcuWITc3V+v2ERERETmNCgUrPz8/jB07Frt378auXbvQrFkzjBo1CsHBwRg7diz27dundTuJiIiIHN5ND15v27YtXnnlFYwaNQpXrlzBZ599hrCwMHTu3BkHDx7Uoo1ERERETqHCwSovLw/fffcdevfujXr16uHnn3/G/PnzcebMGSQnJyMkJAT/+Mc/tGwrERERkUNzrchBY8aMwdKlSwEATz75JGbPno3Q0FDlcS8vL8ycORP169fXpJFEREREzqBCwerQoUOYN28eHn30Ubi7uxdbYzKZsHHjxptqHBEREZEzKfelwLy8PNStWxcdO3YsMVQBgKurKyIiIm6qcURERETOpNzBys3NDStXrrwVbSEiIiJyahUavP7II49g1apVGjeFiIiIyLlVaIxV48aN8e9//xvbtm1DWFgYvLy8VI+PHTtWk8YREREROZMK9Vh98sknqFmzJhITE/Hxxx/jvffeU7a5c+dq2sC0tDQ8+eST8Pf3h6enJ9q2bYvExETlcRHBtGnTYDKZ4OHhga5du9rNn2WxWDBmzBgEBATAy8sLffv2xalTp1Q1mZmZiImJgcFggMFgQExMDLKyslQ1KSkpiI6OhpeXFwICAjB27FjONk9ERESKCvVYJScna92OYmVmZuK+++5Dt27d8NNPPyEwMBDHjx9HzZo1lZrZs2djzpw5WLx4MZo2bYrp06fjoYcewpEjR+Dt7Q0AGD9+PH744QfExcXB398fEydORFRUFBITE1GtWjUAwKBBg3Dq1CmsXbsWAPDss88iJiYGP/zwAwAgPz8fffr0Qa1atbB161ZcuHABQ4YMgYhg3rx5lXI+iIiIyMGJA5s0aZLcf//9JT5utVrFaDTKzJkzlX05OTliMBhk4cKFIiKSlZUlbm5uEhcXp9SkpaWJi4uLrF27VkREDh06JABk+/btSk18fLwAkN9//11ERNasWSMuLi6Slpam1CxdulT0er2YzeYyvyez2SwAynUMERERVa2yfn9XqMcKAE6dOoXvv/8eKSkpdpfD5syZc1Nhr8D333+PHj164B//+Ac2b96M2rVr44UXXsCIESMA2HrOMjIyEBkZqRyj1+sRERGBbdu24bnnnkNiYiLy8vJUNSaTCaGhodi2bRt69OiB+Ph4GAwGdOzYUam59957YTAYsG3bNjRr1gzx8fEIDQ2FyWRSanr06AGLxYLExER069at2PdgsVhgsViUn7OzszU5N0REROR4KhSsNmzYgL59+6JBgwY4cuQIQkNDceLECYgI7rnnHs0a9+eff+LDDz/EhAkT8K9//Qs7d+7E2LFjodfr8dRTTyEjIwMAEBQUpDouKCgIJ0+eBABkZGTA3d0dvr6+djUFx2dkZCAwMNDu9QMDA1U1RV/H19cX7u7uSk1xYmNj8cYbb5TznRMREZEzqtDg9cmTJ2PixIlISkpC9erVsXz5cqSmpiIiIkLT9QGtVivuuecezJgxA3fffTeee+45jBgxAh9++KGqTqfTqX4WEbt9RRWtKa6+IjVFTZ48GWazWdlSU1NLbRcRERE5rwoFq8OHD2PIkCEAbDOsX716FTVq1MCbb76JWbNmada44OBgtGzZUrWvRYsWSElJAQAYjUYAsOsxOnv2rNK7ZDQakZubi8zMzFJrzpw5Y/f6586dU9UUfZ3MzEzk5eXZ9WQVptfr4ePjo9qIiIjo9lShYOXl5aWMGzKZTDh+/Ljy2Pnz57VpGYD77rsPR44cUe07evQo6tWrBwBo0KABjEYj1q9frzyem5uLzZs3o1OnTgCAsLAwuLm5qWrS09ORlJSk1ISHh8NsNmPnzp1KzY4dO2A2m1U1SUlJSE9PV2rWrVsHvV6PsLAwzd4zERERObGKjIzv16+ffPzxxyIi8vLLL0vjxo1l+vTpcs8990j37t0r8pTF2rlzp7i6uspbb70lx44dk6+++ko8PT1lyZIlSs3MmTPFYDDIihUr5MCBAzJw4EAJDg6W7OxspWbkyJFSp04d+eWXX2T37t3ywAMPSJs2beTatWtKTc+ePaV169YSHx8v8fHx0qpVK4mKilIev3btmoSGhkr37t1l9+7d8ssvv0idOnVk9OjR5XpPvCuQiIjI+ZT1+7tCwer48eOyb98+ERG5cuWKPP/889KqVSt55JFH5MSJExV5yhL98MMPEhoaKnq9Xpo3b64EugJWq1WmTp0qRqNR9Hq9dOnSRQ4cOKCquXr1qowePVr8/PzEw8NDoqKiJCUlRVVz4cIFGTx4sHh7e4u3t7cMHjxYMjMzVTUnT56UPn36iIeHh/j5+cno0aMlJyenXO+HwYqIiMj5lPX7WyciUrV9ZneW7OxsGAwGmM1mjrciIiJyEmX9/q7QGCsiIiIislfmeax8fX1vOIVBgYsXL1a4QURERETOqszBSuvFlYmIiIhuN2UOVgXzVhERERFR8Sq8VmCBq1evIi8vT7WPg7KJiIjoTlShwetXrlzB6NGjERgYiBo1asDX11e1EREREd2JKhSs/vnPf+LXX3/FggULoNfr8cknn+CNN96AyWTCl19+qXUbiYiIiJxChS4F/vDDD/jyyy/RtWtXDBs2DJ07d0bjxo1Rr149fPXVVxg8eLDW7SQiIiJyeBXqsbp48SIaNGgAwDaeqmB6hfvvvx9btmzRrnVERERETqRCwaphw4Y4ceIEAKBly5ZYtmwZAFtPVs2aNbVqGxEREZFTqVCwevrpp7Fv3z4AwOTJk5WxVi+++CJefvllTRtIRERE5Cw0WSswJSUFu3btQqNGjdCmTRst2nXb4lqBREREzueWrBW4Y8cO/PTTT6p9X375JSIiIjBy5Eh88MEHsFgsFWsxERERkZMrV7CaNm0a9u/fr/x84MABDB8+HA8++CAmT56MH374AbGxsZo3koiIiMgZlCtY7d27F927d1d+jouLQ8eOHbFo0SK8+OKL+M9//qMMZCciIiK605QrWGVmZiIoKEj5efPmzejZs6fyc/v27ZGamqpd64iIiIicSLmCVVBQEJKTkwEAubm52L17N8LDw5XHL126BDc3N21bSEREROQkyhWsevbsiVdeeQW//fYbJk+eDE9PT3Tu3Fl5fP/+/WjUqJHmjSQiIiJyBuVa0mb69Ono378/IiIiUKNGDXzxxRdwd3dXHv/ss88QGRmpeSOJiIiInEGF5rEym82oUaMGqlWrptp/8eJF1KhRQxW2SI3zWBERETmfsn5/V2gRZoPBUOx+Pz+/ijwdERER0W2hQkvaEBEREZE9BisiIiIijTBYEREREWmEwYqIiIhIIwxWRERERBphsCIiIiLSCIMVERERkUYYrIiIiIg0wmBFREREpBEGKyIiIiKNMFgRERERaYTBioiIiEgjDFZEREREGmGwIiIiItIIgxURERGRRpwqWMXGxkKn02H8+PHKPhHBtGnTYDKZ4OHhga5du+LgwYOq4ywWC8aMGYOAgAB4eXmhb9++OHXqlKomMzMTMTExMBgMMBgMiImJQVZWlqomJSUF0dHR8PLyQkBAAMaOHYvc3Nxb9XaJiIjIyThNsEpISMDHH3+M1q1bq/bPnj0bc+bMwfz585GQkACj0YiHHnoIly5dUmrGjx+PlStXIi4uDlu3bsXly5cRFRWF/Px8pWbQoEHYu3cv1q5di7Vr12Lv3r2IiYlRHs/Pz0efPn1w5coVbN26FXFxcVi+fDkmTpx46988EREROQdxApcuXZImTZrI+vXrJSIiQsaNGyciIlarVYxGo8ycOVOpzcnJEYPBIAsXLhQRkaysLHFzc5O4uDilJi0tTVxcXGTt2rUiInLo0CEBINu3b1dq4uPjBYD8/vvvIiKyZs0acXFxkbS0NKVm6dKlotfrxWw2l/m9mM1mAVCuY4iIiKhqlfX72yl6rEaNGoU+ffrgwQcfVO1PTk5GRkYGIiMjlX16vR4RERHYtm0bACAxMRF5eXmqGpPJhNDQUKUmPj4eBoMBHTt2VGruvfdeGAwGVU1oaChMJpNS06NHD1gsFiQmJmr/pomIiMjpuFZ1A24kLi4Ou3fvRkJCgt1jGRkZAICgoCDV/qCgIJw8eVKpcXd3h6+vr11NwfEZGRkIDAy0e/7AwEBVTdHX8fX1hbu7u1JTHIvFAovFovycnZ1dYi0RERE5N4fusUpNTcW4ceOwZMkSVK9evcQ6nU6n+llE7PYVVbSmuPqK1BQVGxurDIg3GAwICQkptV1ERETkvBw6WCUmJuLs2bMICwuDq6srXF1dsXnzZvznP/+Bq6ur0oNUtMfo7NmzymNGoxG5ubnIzMwstebMmTN2r3/u3DlVTdHXyczMRF5enl1PVmGTJ0+G2WxWttTU1HKeBSIiInIWDh2sunfvjgMHDmDv3r3K1q5dOwwePBh79+5Fw4YNYTQasX79euWY3NxcbN68GZ06dQIAhIWFwc3NTVWTnp6OpKQkpSY8PBxmsxk7d+5Uanbs2AGz2ayqSUpKQnp6ulKzbt066PV6hIWFlfge9Ho9fHx8VBsRERHdnhx6jJW3tzdCQ0NV+7y8vODv76/sHz9+PGbMmIEmTZqgSZMmmDFjBjw9PTFo0CAAgMFgwPDhwzFx4kT4+/vDz88PL730Elq1aqUMhm/RogV69uyJESNG4KOPPgIAPPvss4iKikKzZs0AAJGRkWjZsiViYmLw9ttv4+LFi3jppZcwYsQIhiUiIiIC4ODBqiz++c9/4urVq3jhhReQmZmJjh07Yt26dfD29lZq3nvvPbi6uuKxxx7D1atX0b17dyxevBjVqlVTar766iuMHTtWuXuwb9++mD9/vvJ4tWrV8OOPP+KFF17AfffdBw8PDwwaNAjvvPNO5b1ZIiIicmg6EZGqbsSdJDs7GwaDAWazmT1dRERETqKs398OPcaKiIiIyJkwWBERERFphMGKiIiISCMMVkREREQaYbAiIiIi0giDFREREZFGGKyIiIiINMJgRURERKQRBisiIiIijTBYEREREWmEwYqIiIhIIwxWRERERBphsCIiIiLSCIMVERERkUYYrIiIiIg0wmBFREREpBEGKyIiIiKNMFgRERERaYTBioiIiEgjDFZEREREGmGwIiIiItIIgxURERGRRlyrugGkjaFDAR8foH17oEMHoEkTwIWxmYiIqFIxWN0Grl4FliwB8vOv7zMYgHbtbCGrIGzVrl11bSQiIroTMFjdJv77X2DnTiAhAUhMBMxmYMMG21bAZLoestq3twUvX9+qazMREdHtRiciUtWNuJNkZ2fDYDDAbDbDx8fnlrxGXh5w8KAtZO3caduSkgCr1b62adPrYatDB6BtW6B69VvSLCIiIqdV1u9vBqtKVhnBqjhXrgB79qjD1p9/2te5ugKtW6svIbZoAVSrVmlNJSIicjgMVg6qqoJVcc6fB3btun4JcedO4OxZ+zovLyAs7HqvVvv2QL16gE5X+W0mIiKqCgxWDsqRglVRIkBq6vUerZ07beO1Ll+2r61VS92r1b49EBBQ+W0mIiKqDAxWDsqRg1Vx8vOB339X92rt2wdcu2Zf26CBOmzdc4+tt4uIiMjZMVg5KGcLVsXJybGFq4JerYQE4MgR+zoXF+Cuu9SXEENDATe3ym8zERHRzWCwclC3Q7AqTlaWbbxWQa9WQgKQlmZfV726rSer8J2IjRpxvBYRETk2BisHdbsGq+KkpdkCVuGwZTbb1/n6qsdqdegAGI2V314iIqKSMFg5qDspWBVltQJ//KG+hLhnD2Cx2NeGhKh7tcLCbEv2EBERVQUGKwd1Jwer4uTmAgcOqAfHHzpku0OxMJ0OaN5c3avVujWg11dNu4mI6M7CYOWgGKxu7NIlYPduddg6edK+zt0daNNGHbaaNePi00REpD0GKwfFYFUxZ8+qZ41PSAAuXLCv8/Gxn8y0Th0OjicioptT1u9vh/63fWxsLNq3bw9vb28EBgbi4YcfxpEi9/WLCKZNmwaTyQQPDw907doVBw8eVNVYLBaMGTMGAQEB8PLyQt++fXHq1ClVTWZmJmJiYmAwGGAwGBATE4OsrCxVTUpKCqKjo+Hl5YWAgACMHTsWubm5t+S9k1pgINCnD/DGG8BPPwHnzgHHjwNxccCECcD99wMeHkB2NrBxIzBrFvDoo0DdurbFp/v1A6ZPB9atAy5erOp3Q0REtyuH7rHq2bMnnnjiCbRv3x7Xrl3DlClTcODAARw6dAhef888OWvWLLz11ltYvHgxmjZtiunTp2PLli04cuQIvL29AQDPP/88fvjhByxevBj+/v6YOHEiLl68iMTERFT7exG8Xr164dSpU/j4448BAM8++yzq16+PH374AQCQn5+Ptm3bolatWnj33Xdx4cIFDBkyBP3798e8efPK/J7YY3XrXLtmG59V+BLigQO2SU6LatxY3at19922YEZERFScMn9/ixM5e/asAJDNmzeLiIjVahWj0SgzZ85UanJycsRgMMjChQtFRCQrK0vc3NwkLi5OqUlLSxMXFxdZu3atiIgcOnRIAMj27duVmvj4eAEgv//+u4iIrFmzRlxcXCQtLU2pWbp0qej1ejGbzWV+D2azWQCU6xiquCtXRP7v/0Tee09k4ECRxo1FbEPj1Zurq0jbtiLPPivyySci+/eLXLtW1a0nIiJHUdbvb9dKiXkaMf89CZKfnx8AIDk5GRkZGYiMjFRq9Ho9IiIisG3bNjz33HNITExEXl6eqsZkMiE0NBTbtm1Djx49EB8fD4PBgI4dOyo19957LwwGA7Zt24ZmzZohPj4eoaGhMJlMSk2PHj1gsViQmJiIbt26Fdtmi8UCS6H5BLKzs7U5GVQmnp5Ap062rcCFC+rJTHfuBM6cAfbutW1/d1rC0/P6eK2CwfH163O8FhERlcxpgpWIYMKECbj//vsRGhoKAMjIyAAABAUFqWqDgoJw8u/byDIyMuDu7g5fX1+7moLjMzIyEBgYaPeagYGBqpqir+Pr6wt3d3elpjixsbF44403yvNW6Rbz9wd69LBtgK3P6tQpYMeO6xOa7tpluzvxt99sW4GAAPX8Wu3b2xakJiIiApwoWI0ePRr79+/H1q1b7R7TFelCEBG7fUUVrSmuviI1RU2ePBkTJkxQfs7OzkZISEipbaPKpdPZJiQNCQEGDLDty8+3rX9YuFdr3z7g/Hnb4Pmffrp+fP369otP16hRJW+FiIiqmFMEqzFjxuD777/Hli1bUKdOHWW/8e91TzIyMhAcHKzsP3v2rNK7ZDQakZubi8zMTFWv1dmzZ9Hp7+tDRqMRZ86csXvdc+fOqZ5nx44dqsczMzORl5dn15NVmF6vh56zWDqdatWAli1t25Ahtn0Wy/XFpwsC1++/AydO2LZly2x1Li624wr3arVqxcWniYjuBA493YKIYPTo0VixYgV+/fVXNGjQQPV4gwYNYDQasX79emVfbm4uNm/erISmsLAwuLm5qWrS09ORlJSk1ISHh8NsNmPnzp1KzY4dO2A2m1U1SUlJSE9PV2rWrVsHvV6PsLAw7d88ORy93haURo8GvvgCOHzYtvj0hg1AbCzwyCO2ObOsViApCfjsM2DkyOvL8XTqBIwbB3z1FXDsmP3s8kRE5PwcerqFF154AV9//TX+97//oVmzZsp+g8EAj7/vjZ81axZiY2Px+eefo0mTJpgxYwY2bdpkN93C6tWrsXjxYvj5+eGll17ChQsX7KZbOH36ND766CMAtukW6tWrZzfdQlBQEN5++21cvHgRQ4cOxcMPP8zpFkjl9Gn7xaeLTIkGAKhZ037x6UIdr0RE5EBui+kWABS7ff7550qN1WqVqVOnitFoFL1eL126dJEDBw6onufq1asyevRo8fPzEw8PD4mKipKUlBRVzYULF2Tw4MHi7e0t3t7eMnjwYMnMzFTVnDx5Uvr06SMeHh7i5+cno0ePlpycnHK9J063cOfJzxc5elRkyRKRsWNFwsNF9Prip32oU0fkkUdEYmNFNmwQycqq6tYTEZFI2b+/HbrH6nbEHisCgLw82+SlhQfHHzpku4xYVNHFp9u04eLTRESVjWsFOigGKyrJ5cv2i0+fOGFf5+Z2ffHpgsDVvDkXnyYiupUYrByUwwWr/HzbRE3p6bYBPp07226JI4dw9qxtTq2CXq2dO4tffNrbG2jXTj3HFhefJiLSDoOVg3KoYLVihe02tcILUtepA7z/PtC/f9W1i0okYuvFKtyrlZgI/PWXfW1QkLpXq3174O9FC4iIqJwYrByUwwSrFStss2EW/fUXdHF89x3DlZO4ds029UNBj1ZCArB/f8mLTxfu1eLi00REZcNg5aAcIljl59umCy/cU1WYTmfruUpO5mVBJ/XXX7Z1DwsPjv/jD/u6atVsk5cWHhzfsiXg6hRTBxMRVR4GKwflEMFq0yaghEWjVTZuBLp2vdWtoUpy8eL18VoJCba1EYtZcACenrZleQpfRmzQgOO1iOjOVtbvb/679E5UaPZ4TerIKfj5AZGRtg24vvh04V6tgsWnt261bQX8/dW9Wu3bA8WsW05EdMdjsLoTlXV6b04DflsrvPh0wXA6q9W2+HTh8Vp799ruRCy6+HS9euperbAwLj5NRMRLgZXMIS4FFoyxSksrfsE6jrGiQgoWny7cs/X77/Z1BYtPFx4cz8Wnieh2wTFWDsohghVw/a5AQB2ueFcglYHZbJvmofC0D8XdC6HX2+48LNyz1bgxJzMlIufDYOWgHCZYAcXPYxUSAsydy1BF5Zaerl54eufO0hefLtyzxavOROToGKwclEMFK4Azr9MtI2Kb4qHwJcQ9e4CcHPva2rXVvVrt2gEGQ+W3mYioJAxWDsrhghVRJcrLA5KS1L1aBw+WvPh04V4tLj5NRFWJwcpBMVgRqV2+bOvJKnwnYnKyfV3hxacLAlezZuxgJaLKwWDloBisiG7s3DlbwCp8GfH8efu6GjVslw0LX0YMCeFkpkSkPQYrB8VgRVR+IsDJk+perV27Sl98uvBkplx8mohuFoOVg2KwItJGweLThXu1Dhyw7S+qUSN1r9bdd9uW7iEiKisGKwd12wUr3lVIDuTqVdtM8YUHxx87Zl9XsPh04cHxXHyaiErDYOWgbqtgVdw8WHXqAO+/z3mwyGFkZl5ffLpgy8iwryu8+HRB4OLi00RUgMHKQd02wapg5vaiHx/O3E4OrvDi04UnNL10yb7W3189Vqt9e9sYLiK68zBYOajbIlgVrDVY3BomANcaJKdjtQJHj9ovPp2ba19br576EuI99wDe3pXeZCKqZAxWDuq2CFabNgHdut24buNGoGvXW90aolvCYgH277dffLq4TtqWLdWXEFu1Atzdq6bdRHRrlPX7m0M1qfzS07WtI3JAev31y38vvGDbl51tW3y6cNhKTbXNHn/wIPD559ePbdtWHbaaNOHi00R3AgYrKr+yrphb1jreWUhOwsfH1llbuMM2I8N+8enMTGDHDttWwGCwn8y0du3Kfw9EdGvxUmAluy0uBRaMsUpLs78uApRvjBXvLKTbjAhw/Li6V2v37uIXnzaZ1L1a7doBNWtWepOJqAw4xspB3RbBCrh+VyCgDlfluSuQdxbSHSIvz3apsHDYSkoqfvHppk3VYattW6B69UpvMhEVwWDloG6bYAUU39sUEgLMnXvjQKTlnYW8lEhO6MqV64tPFwSuP/+0r3N1BVq3Vl9CbNGCH3GiysZg5aBuq2AFVDzUaHVnIS8l0m3k/Hn7yUzPnbOv8/KyXTYsPO1D3bqczJToVuJdgVQ5qlWr2JQKWtxZWNKlxLQ02/7yXEpkrxc5gIAAoGdP2wbYPtopKeperV27bL1dmzfbtgK1aql7tdq3tz0fEVUu9lhVstuux6qibrbHSstLiez1IieSn2+bT6vwZKb79hW/+HTDhuperbvvtvV2EVH58VKgg2Kw+tvN3lmo5aVEZxlAz141KkFOjm2m+MKD448eta9zcQFCQ9WD40NDufg0UVnwUiA5tmrVbD1CAwbYQkxxdxbOnVtycNDiUmJ+vq2nqrhgJ2Jrx/jxQL9+VR9g2KtGpaheHbj3XttWICvr+nithATbnFrp6bbZ5PfvBz75xFbn4WFblqdwz1bDhhyvRVRR7LGqZOyxKqKidxZq0WPlLEvzOGOvWlqabdR1rVq2WTAdqXftDu75S0tT92rt2gWYzfZ1fn7qxac7dODi00S8FOigGKyKUZEvOi0mKV26FBg06Mbt+/prYODAG9fdCs604HVxIbmAo/SuOUvPXyWFP6sVOHZMPTh+z57iF5+uW1fdqxXWNh/ee50goN7BQZq0xWDloBisNHSzk5Q6Q4+VM7QRKLlXrTCdrmp715yl56+Kw19uLnDggHpw/KFDxZw2WNECh9EeCeiAnegQeBKt//MM3B9/5Ja3scwYpLXDNpb9+1uoUpnNZgEgZrO5qptye1i+XKROHRHb3/u2LSTEtv9Grl2zHavTqY8v2HQ623Ndu3br30dJvv66+LYV3b7+uuraWHAeb9TGqjyfN2qjI/yuRWyf2+I+jzqdbSvL5/oWyM4W2bhRZPZskQHhqVIXJ4o9je7IkQ5NLsjo0SJffCFy+LBIfn6VNNlhz6Wd4v4Oq1PHcdonwjb+razf3wxWFfDBBx9I/fr1Ra/Xyz333CNbtmwp87EMVrfAtWu2v/W//tr23/J8ORb85Vv0L2BH+ct348ayBauNGx2/jVXZVmc4j84Q/gq1MQOB8gP6yGt4Q3pijfjhfLHN9vEReeABkVdeEVmxQuTUqcptp8OeSxHnCH9so4LB6haJi4sTNzc3WbRokRw6dEjGjRsnXl5ecvLkyTIdz2DlgG6m1+tWu5161aqyd80Zev6cIfyV0kYrIH+goSzF4/LigBS57z4RD4/iy4ODRfr1E3nrLZF160QuXqy8djrMuXSG8Mc2qpT1+9tFs4uPd4g5c+Zg+PDheOaZZ9CiRQvMnTsXISEh+PDDD6u6aVRR/fsDJ07Yxil9/bXtv8nJjjEGo2BaCsD+/veyTEtRGYKDb229Fsr6mlXRtgJaTCFyq5Xy2joAjfAnnsA3mNN/K7ZuBbKzbfNrffwxMGIE0KaN7aOang7873/AlClAZKTtLsRmzYAnnwT+8x9g+3bb3Fy3op0VqrsVfvut5JtSAFssSE211VUVtrFCOI9VOeTm5iIxMRGvvPKKan9kZCS2bdtWRa0iTVR0aZ7K0L+/bWB1cYNwy7Lg9a3WubOtLaX95QZcv4Oxc+fKaVdhBW280V2kVdG2As4Q/srZRldXW5hq08YWrADgr7+uLz5dMDj++HHbhKZHjwJffQXl2Nat1XcilnnxaWc4l84Q/tjGCmGwKofz588jPz8fQUUmdAkKCkJGRkaxx1gsFlgsFuXn7OzsW9pGuk3172+bqNQR78opPNlrcaGlsKrqXbvZCWkrgzOEPw3a6OkJ3HefbStw4YItYBWeY+vsWWD3btv20Ue2Oi8vICxMPb9WvXrFTGbqDOfSGcIf21gxN33R8Q6SlpYmAGTbtm2q/dOnT5dmzZoVe8zUqVMFgN3GMVZ02ylurJqjjVlz5PF0Io5/M0UltdFqFTl5UuTbb0VeflkkIkKkRo3iP1q1aon07i0ybZrImjUi585VXjtvijOMn2QbVco6xorzWJVDbm4uPD098e233+KRR67P1TJu3Djs3bsXmwsvNf+34nqsQkJCOI8V3Z448/rNq+hqBJWpCtpYePHpgp6tkhafbtDg716t6vvRYc0buOfcWnjhr0ppZ7nc7Fx8lYFtVHCC0FukY8eOCAsLw4IFC5R9LVu2RL9+/RAbG3vD4zlBKBHdkKOHP8Ah2piTYwtXhcPWkSP2dS4ugrtqm9Gh1VV0iA5Ch3tdcNddgJtbpTa3eAzS2qiENjJY3SLffPMNYmJisHDhQoSHh+Pjjz/GokWLcPDgQdSrV++GxzNYERHdOllZQGKienB8Wpp9XfXq9otPN2pURYtPO0BIvSG2kcHqVlqwYAFmz56N9PR0hIaG4r333kOXLl3KdCyDFRFR5SpYfLqgVyshofjFp3197RefNhorv73kmBisHBSDFRFR1bJagT/+UPdq7dkDFBoOqwgJKbL4dBjAv7rvTAxWDorBiojI8RQsPl14yodiF5/WAc2bq3u1WrcG9PqqaTdVHgYrB8VgRUTkHC5dss2jVbhn6+RJ+zp3d9skqAW9Wh06AE2bAi5c2+S2wmDloBisiIic15kz9pOZXrxoX+fjA7Rrp+7Zql27igbHkyYYrBwUgxUR0e1DxLa0aOFercRE4OpV+9rgYPV4rXbtbAPmyTkwWDkoBisiotvbtWvAwYPqXq2kJNtsAEU1aaIOW23bAh4eld5kKgMGKwfFYEVEdOcpvPh0QeA6fty+ztUVaNVKfQmxZUvHmzLqTsRg5aAYrIiICLAtPr1r1/VerYLFp4vy8rJNZlrQq9W+PVC/PsdrVTYGKwfFYEVERMURAVJT1ZcQd+0CLl+2rw0IUPdqtW9vW5qTbh0GKwfFYEVERGWVn29b/7Do4tN5efa19eure7XuuQeoUaPSm3zbYrByUAxWRER0M3JygP371Xci/v67fZ2Li218VuGw1aqVgyw+7YQYrBwUgxUREWnNbLZdNiy8HuKpU/Z11asDd9+tvhOxcWOO1yoLBisHxWBFRESV4fRp+8Wns7Ls62rWtF98Oji4slvr+BisHBSDFRERVQUR+8Wnd+8ufvHp2rXVlxDbtQMMhspvsyNhsHJQDFZEROQo8vLUi08nJNgmN7Va7WubN1dfQmzT5s5afJrBykExWBERkSO7fNnWk1V42ocTJ+zr3NyuLz5dELiaNbt9JzNlsHJQDFZERORszp2zX3z6/Hn7Om9vICxMfRkxJOT2GBzPYOWgGKyIiMjZidh6sQoHrcRE29I9RQUF2U9m6udX6U2+aQxWDorBioiIbkfXrgGHD6snM92/v/jFpxs1Uvdq3X034OlZ+W0uDwYrB8VgRUREd4qrV4G9e9V3Ih47Zl9XrZpt8tLCg+NbtrQtSu0oGKwcFIMVERHdyS5eVE9munMnkJFhX+fpab/4dIMGVTdei8HKQTFYERERXScCpKWpe7USEoBLl+xr/f3tx2sFBlZOOxmsHBSDFRERUemsVtvi04V7tfbtA3Jz7Wvr1VP3aoWF3ZrFpxmsHBSDFRERUflZLNcXny4IXL//buvxKszFxXbHYkiItq9f1u9vBxoWRkRERFQ8vd7WI9W+/fV92dm2aR4KerV27rQNmK9Tp+rayWBFRERETsnHB+jWzbYVyMqq2glJXarupYmIiIi0VbNm1b4+gxURERGRRhisiIiIiDTCYEVERESkEQYrIiIiIo0wWBERERFphMGKiIiISCMMVkREREQaYbAiIiIi0giDFREREZFGGKyIiIiINMJgRURERKQRBisiIiIijTBYEREREWnEtaobcKcREQBAdnZ2FbeEiIiIyqrge7vge7wkDFaV7NKlSwCAkJCQKm4JERERldelS5dgMBhKfFwnN4pepCmr1YrTp0/D29sbOp3upp8vOzsbISEhSE1NhY+PjwYtvHPxXGqD51EbPI/a4bnUxp1+HkUEly5dgslkgotLySOp2GNVyVxcXFCnTh3Nn9fHx+eO/KDfCjyX2uB51AbPo3Z4LrVxJ5/H0nqqCnDwOhEREZFGGKyIiIiINMJg5eT0ej2mTp0KvV5f1U1xejyX2uB51AbPo3Z4LrXB81g2HLxOREREpBH2WBERERFphMGKiIiISCMMVkREREQaYbAiIiIi0giDlZNbsGABGjRogOrVqyMsLAy//fZbVTfJoU2bNg06nU61GY1G5XERwbRp02AymeDh4YGuXbvi4MGDVdhix7BlyxZER0fDZDJBp9Nh1apVqsfLct4sFgvGjBmDgIAAeHl5oW/fvjh16lQlvgvHcKNzOXToULvP6L333ququdPPZWxsLNq3bw9vb28EBgbi4YcfxpEjR1Q1/EyWTVnOJT+T5cNg5cS++eYbjB8/HlOmTMGePXvQuXNn9OrVCykpKVXdNId21113IT09XdkOHDigPDZ79mzMmTMH8+fPR0JCAoxGIx566CFljcc71ZUrV9CmTRvMnz+/2MfLct7Gjx+PlStXIi4uDlu3bsXly5cRFRWF/Pz8ynobDuFG5xIAevbsqfqMrlmzRvX4nX4uN2/ejFGjRmH79u1Yv349rl27hsjISFy5ckWp4WeybMpyLgF+JstFyGl16NBBRo4cqdrXvHlzeeWVV6qoRY5v6tSp0qZNm2Ifs1qtYjQaZebMmcq+nJwcMRgMsnDhwkpqoeMDICtXrlR+Lst5y8rKEjc3N4mLi1Nq0tLSxMXFRdauXVtpbXc0Rc+liMiQIUOkX79+JR7Dc2nv7NmzAkA2b94sIvxM3oyi51KEn8nyYo+Vk8rNzUViYiIiIyNV+yMjI7Ft27YqapVzOHbsGEwmExo0aIAnnngCf/75JwAgOTkZGRkZqnOq1+sRERHBc1qKspy3xMRE5OXlqWpMJhNCQ0N5bouxadMmBAYGomnTphgxYgTOnj2rPMZzac9sNgMA/Pz8APAzeTOKnssC/EyWHYOVkzp//jzy8/MRFBSk2h8UFISMjIwqapXj69ixI7788kv8/PPPWLRoETIyMtCpUydcuHBBOW88p+VTlvOWkZEBd3d3+Pr6llhDNr169cJXX32FX3/9Fe+++y4SEhLwwAMPwGKxAOC5LEpEMGHCBNx///0IDQ0FwM9kRRV3LgF+JsvLtaobQDdHp9OpfhYRu310Xa9evZT/b9WqFcLDw9GoUSN88cUXymBMntOKqch547m19/jjjyv/Hxoainbt2qFevXr48ccf0b9//xKPu1PP5ejRo7F//35s3brV7jF+JsunpHPJz2T5sMfKSQUEBKBatWp2/xo4e/as3b/SqGReXl5o1aoVjh07ptwdyHNaPmU5b0ajEbm5ucjMzCyxhooXHByMevXq4dixYwB4LgsbM2YMvv/+e2zcuBF16tRR9vMzWX4lncvi8DNZOgYrJ+Xu7o6wsDCsX79etX/9+vXo1KlTFbXK+VgsFhw+fBjBwcFo0KABjEaj6pzm5uZi8+bNPKelKMt5CwsLg5ubm6omPT0dSUlJPLc3cOHCBaSmpiI4OBgAzyVg6wkZPXo0VqxYgV9//RUNGjRQPc7PZNnd6FwWh5/JG6iaMfOkhbi4OHFzc5NPP/1UDh06JOPHjxcvLy85ceJEVTfNYU2cOFE2bdokf/75p2zfvl2ioqLE29tbOWczZ84Ug8EgK1askAMHDsjAgQMlODhYsrOzq7jlVevSpUuyZ88e2bNnjwCQOXPmyJ49e+TkyZMiUrbzNnLkSKlTp4788ssvsnv3bnnggQekTZs2cu3atap6W1WitHN56dIlmThxomzbtk2Sk5Nl48aNEh4eLrVr1+a5LOT5558Xg8EgmzZtkvT0dGX766+/lBp+JsvmRueSn8nyY7Bych988IHUq1dP3N3d5Z577lHdIkv2Hn/8cQkODhY3NzcxmUzSv39/OXjwoPK41WqVqVOnitFoFL1eL126dJEDBw5UYYsdw8aNGwWA3TZkyBARKdt5u3r1qowePVr8/PzEw8NDoqKiJCUlpQreTdUq7Vz+9ddfEhkZKbVq1RI3NzepW7euDBkyxO483ennsrjzB0A+//xzpYafybK50bnkZ7L8dCIildc/RkRERHT74hgrIiIiIo0wWBERERFphMGKiIiISCMMVkREREQaYbAiIiIi0giDFREREZFGGKyIiIiINMJgRUQEYNWqVWjcuDGqVauG8ePHV3VzKqR+/fqYO3duVTeD6I7GYEVEFSYiePDBB9GjRw+7xxYsWACDwYCUlJQqaFn5PffccxgwYABSU1Px73//u9ia+vXrQ6fT2W0zZ86s5NYWLyEhAc8++2xVN4PojsaZ14nopqSmpqJVq1aYNWsWnnvuOQBAcnIyWrdujXnz5mHo0KGavl5eXh7c3Nw0fc7Lly/D29sbv/76K7p161ZiXf369TF8+HCMGDFCtd/b2xteXl6atqk8cnNz4e7uXmWvT0TXsceKiG5KSEgI3n//fbz00ktITk6GiGD48OHo3r07OnTogN69e6NGjRoICgpCTEwMzp8/rxy7du1a3H///ahZsyb8/f0RFRWF48ePK4+fOHECOp0Oy5YtQ9euXVG9enUsWbIEJ0+eRHR0NHx9feHl5YW77roLa9asKbGNmZmZeOqpp+Dr6wtPT0/06tULx44dAwBs2rQJ3t7eAIAHHngAOp0OmzZtKvG5vL29YTQaVVtBqHrzzTdhMplw4cIFpb5v377o0qULrFYrAECn0+HDDz9Er1694OHhgQYNGuDbb79VvUZaWhoef/xx+Pr6wt/fH/369cOJEyeUx4cOHYqHH34YsbGxMJlMaNq0KQD7S4FmsxnPPvssAgMD4ePjgwceeAD79u1THp82bRratm2L//73v6hfvz4MBgOeeOIJXLp0SamxWq2YNWsWGjduDL1ej7p16+Ktt94qc1uJ7jQMVkR004YMGYLu3bvj6aefxvz585GUlIT3338fERERaNu2LXbt2oW1a9fizJkzeOyxx5Tjrly5ggkTJiAhIQEbNmyAi4sLHnnkESWEFJg0aRLGjh2Lw4cPo0ePHhg1ahQsFgu2bNmCAwcOYNasWahRo0aJ7Rs6dCh27dqF77//HvHx8RAR9O7dG3l5eejUqROOHDkCAFi+fDnS09PRqVOnCp2HKVOmoH79+njmmWcAAAsXLsSWLVvw3//+Fy4u1/+6fe211/Doo49i3759ePLJJzFw4EAcPnwYAPDXX3+hW7duqFGjBrZs2YKtW7eiRo0a6NmzJ3Jzc5Xn2LBhAw4fPoz169dj9erVdm0REfTp0wcZGRlYs2YNEhMTcc8996B79+64ePGiUnf8+HGsWrUKq1evxurVq7F582bVpc3Jkydj1qxZeO2113Do0CF8/fXXCAoKKldbie4oVbf+MxHdTs6cOSO1atUSFxcXWbFihbz22msSGRmpqklNTRUAcuTIkWKf4+zZswJADhw4ICIiycnJAkDmzp2rqmvVqpVMmzatTO06evSoAJD/+7//U/adP39ePDw8ZNmyZSIikpmZKQBk48aNpT5XvXr1xN3dXby8vFRb4eOOHz8u3t7eMmnSJPH09JQlS5aongOAjBw5UrWvY8eO8vzzz4uIyKeffirNmjUTq9WqPG6xWMTDw0N+/vlnEREZMmSIBAUFicVisWvfe++9JyIiGzZsEB8fH8nJyVHVNGrUSD766CMREZk6dap4enpKdna28vjLL78sHTt2FBGR7Oxs0ev1smjRomLPR1naSnSnca3KUEdEt4/AwEA8++yzWLVqFR555BF88skn2LhxY7E9ScePH0fTpk1x/PhxvPbaa9i+fTvOnz+v9FSlpKQgNDRUqW/Xrp3q+LFjx+L555/HunXr8OCDD+LRRx9F69ati23X4cOH4erqio4dOyr7/P390axZM6WXqDxefvllu3FjtWvXVv6/YcOGeOedd/Dcc8/h8ccfx+DBg+2eIzw83O7nvXv3AgASExPxxx9/KJcnC+Tk5Kguk7Zq1arUcVWJiYm4fPky/P39VfuvXr2qep769eurXis4OBhnz54FYDt3FosF3bt3L/E1ytJWojsJgxURacbV1RWurra/VqxWK6KjozFr1iy7uuDgYABAdHQ0QkJCsGjRIphMJlitVoSGhtpdRio6MPyZZ55Bjx498OOPP2LdunWIjY3Fu+++izFjxti9lpRwf46IQKfTlfs9BgQEoHHjxqXWbNmyBdWqVcOJEydw7do15ZyUpqAtVqsVYWFh+Oqrr+xqatWqpfz/jQbLW61WBAcHFzterGbNmsr/F70RQKfTKQHXw8Pjhq9RlrYS3Uk4xoqIbol77rkHBw8eRP369dG4cWPV5uXlhQsXLuDw4cN49dVX0b17d7Ro0QKZmZllfv6QkBCMHDkSK1aswMSJE7Fo0aJi61q2bIlr165hx44dyr4LFy7g6NGjaNGixU2/z6K++eYbrFixAps2bSpx6obt27fb/dy8eXMAtvN27NgxBAYG2p03g8FQ5nbcc889yMjIgKurq93zBAQElOk5mjRpAg8PD2zYsKHE19CirUS3EwYrIrolRo0ahYsXL2LgwIHYuXMn/vzzT6xbtw7Dhg1Dfn6+chfZxx9/jD/++AO//vorJkyYUKbnHj9+PH7++WckJydj9+7d+PXXX0sMSU2aNEG/fv0wYsQIbN26VRkwXrt2bfTr16/c7+vSpUvIyMhQbdnZ2QCAU6dO4fnnn8esWbNw//33Y/HixYiNjbULUt9++y0+++wzHD16FFOnTsXOnTsxevRoAMDgwYMREBCAfv364bfffkNycjI2b96McePG4dSpU2Vu54MPPojw8HA8/PDD+Pnnn3HixAls27YNr776Knbt2lWm56hevTomTZqEf/7zn/jyyy9x/PhxbN++HZ9++qmmbSW6nTBYEdEtYTKZ8H//93/Iz89Hjx49EBoainHjxsFgMMDFxQUuLi6Ii4tDYmIiQkND8eKLL+Ltt98u03Pn5+dj1KhRaNGiBXr27IlmzZphwYIFJdZ//vnnCAsLQ1RUFMLDwyEiWLNmTYXmw3r99dcRHBys2v75z39CRDB06FB06NBBCUkPPfQQRo8ejSeffBKXL19WnuONN95AXFwcWrdujS+++AJfffUVWrZsCQDw9PTEli1bULduXfTv3x8tWrTAsGHDcPXqVfj4+JS5nTqdDmvWrEGXLl0wbNgwNG3aFE888QROnDih3NVXFq+99homTpyI119/HS1atMDjjz+ujMHSqq1EtxNOEEpEVIl0Oh1WrlyJhx9+uKqbQkS3AHusiIiIiDTCYEVERESkEU63QERUiTj6guj2xh4rIiIiIo0wWBERERFphMGKiIiISCMMVkREREQaYbAiIiIi0giDFREREZFGGKyIiIiINMJgRURERKQRBisiIiIijfw/2Hb2namZgA0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "regressor_1 = LinearRegression()\n",
    "regressor_1.fit(P_1, Vap_sat_1)\n",
    "plt.scatter(P_1, Vap_sat_1, color = 'red')\n",
    "plt.plot(P_1, regressor_1.predict(P_1), color = 'blue')\n",
    "plt.title('Salary vs Experience (Training set)')\n",
    "plt.xlabel('Years of Experience')\n",
    "plt.ylabel('Salary')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e6173ddb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-145.33343846] [27608.03471493]\n"
     ]
    }
   ],
   "source": [
    "print(regressor_1.coef_[0],regressor_1.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "280583ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "regressor_2 = LinearRegression()\n",
    "regressor_2.fit(P_2, Vap_sat_2)\n",
    "plt.scatter(P_2, Vap_sat_2, color = 'red')\n",
    "plt.plot(P_2, regressor_2.predict(P_2), color = 'blue')\n",
    "plt.title('Salary vs Experience (Training set)')\n",
    "plt.xlabel('Years of Experience')\n",
    "plt.ylabel('Salary')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "52ee7c22",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.35253625] [565.92897361]\n"
     ]
    }
   ],
   "source": [
    "print(regressor_2.coef_[0],regressor_2.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "07a97b7a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "regressor_3 = LinearRegression()\n",
    "regressor_3.fit(P_3, Vap_sat_3)\n",
    "plt.scatter(P_3, Vap_sat_3, color = 'red')\n",
    "plt.plot(P_3, regressor_3.predict(P_3), color = 'blue')\n",
    "plt.title('Salary vs Experience (Training set)')\n",
    "plt.xlabel('Years of Experience')\n",
    "plt.ylabel('Salary')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "8533acad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.00983263] [103.50437059]\n"
     ]
    }
   ],
   "source": [
    "print(regressor_3.coef_[0],regressor_3.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "9253246d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "784942852.3769547 2420.0128505933712 238.3643458021637\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "p_1 = regressor_1.predict(P_1)\n",
    "e_1 = mean_squared_error(Vap_sat_1, p_1)\n",
    "p_2 = regressor_2.predict(P_2)\n",
    "e_2 = mean_squared_error(Vap_sat_2, p_2)\n",
    "p_3 = regressor_3.predict(P_3)\n",
    "e_3 = mean_squared_error(Vap_sat_3, p_3)\n",
    "print(e_1,e_2,e_3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fb948f1",
   "metadata": {},
   "source": [
    "## Gradient descent approach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "2c64beae",
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss(y_hat, y):\n",
    "    l = (y_hat - y) ** 2 / 2\n",
    "    return l.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "3db592a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "L_1=[]\n",
    "L_2=[]\n",
    "L_3=[]\n",
    "N_1=P_1.shape[0]\n",
    "N_2=P_2.shape[0]\n",
    "N_3=P_3.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "041984ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "def forward_pass(x,m,c):\n",
    "    return m*x+c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "54891e41",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 5000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 10000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 15000\n"
     ]
    },
    {
     "data": {
      "image/png": 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AwCYEKwAAAJsQrAAAAGxCsAIAALAJwQoAAMAmBCsAAACbEKwAAABsQrACAACwCcEKAADAJgQrAAAAmxCsAAAAbEKwAgAAsAnBCgAAwCYEKwAAAJsEdLC6cOGC/vVf/1WDBg1SRESEbrzxRj377LNqamqyaowxWrhwoTwejyIiIjR27Fjt27fP53Xq6uo0e/ZsxcbGKjIyUlOnTtXRo0d9aqqqqpSRkSGXyyWXy6WMjAxVV1f71JSUlGjKlCmKjIxUbGys5syZo/r6+iu2/QAAILgEdLD6+c9/rpUrV2r58uU6cOCAlixZoueee04vvviiVbNkyRItXbpUy5cv165du+R2uzV+/HjV1tZaNVlZWVq7dq1ycnKUn5+v06dPKy0tTY2NjVbN9OnTVVRUpLy8POXl5amoqEgZGRnW+sbGRk2ePFlnzpxRfn6+cnJy9M4772jevHm9MxgAACDwmQA2efJk8/DDD/ssmzZtmvnOd75jjDGmqanJuN1us3jxYmv9+fPnjcvlMitXrjTGGFNdXW3CwsJMTk6OVVNWVmZCQkJMXl6eMcaY/fv3G0lm+/btVk1BQYGRZA4ePGiMMWbdunUmJCTElJWVWTVr1qwxTqfTeL3eLm+T1+s1krr1HAAA4F9d/f4O6Bmru+++Wx988IH+8pe/SJI++ugj5efn6x//8R8lSYcOHVJFRYVSU1Ot5zidTo0ZM0bbtm2TJBUWFqqhocGnxuPxKDk52aopKCiQy+XS8OHDrZoRI0bI5XL51CQnJ8vj8Vg1EyZMUF1dnQoLCzvchrq6OtXU1PjcAADA1amPvxvozE9+8hN5vV7dfPPNCg0NVWNjo372s5/poYcekiRVVFRIkuLj432eFx8fryNHjlg14eHh6tevX5ualudXVFQoLi6uzfvHxcX51LR+n379+ik8PNyqaU92draeeeaZ7mw2AAAIUgE9Y/Xmm2/q9ddf1xtvvKHdu3fr1Vdf1fPPP69XX33Vp87hcPg8Nsa0WdZa65r26ntS09pTTz0lr9dr3UpLSzvtCwAABK+AnrF64okn9OSTT+rb3/62JGno0KE6cuSIsrOzNWPGDLndbknNs0kJCQnW8yorK63ZJbfbrfr6elVVVfnMWlVWVmrUqFFWzfHjx9u8/4kTJ3xeZ8eOHT7rq6qq1NDQ0GYm62JOp1NOp7Mnmw8AAIJMQM9YnT17ViEhvi2GhoZap1sYNGiQ3G63NmzYYK2vr6/X5s2brdCUkpKisLAwn5ry8nIVFxdbNSNHjpTX69XOnTutmh07dsjr9frUFBcXq7y83KpZv369nE6nUlJSbN5yAAAQjAJ6xmrKlCn62c9+pv79++vLX/6y9uzZo6VLl+rhhx+W1LxrLisrS4sWLdLgwYM1ePBgLVq0SH379tX06dMlSS6XS4888ojmzZun66+/XjExMZo/f76GDh2qr3/965KkIUOGaOLEiZo1a5ZeeuklSdKjjz6qtLQ03XTTTZKk1NRU3XLLLcrIyNBzzz2nU6dOaf78+Zo1a5aio6P9MDoAACDg9MIvFHuspqbGzJ071/Tv399cd9115sYbbzRPP/20qaurs2qamprMggULjNvtNk6n09xzzz1m7969Pq9z7tw5k5mZaWJiYkxERIRJS0szJSUlPjUnT5406enpJioqykRFRZn09HRTVVXlU3PkyBEzefJkExERYWJiYkxmZqY5f/58t7aJ0y0AABB8uvr97TDGGH+Hu2tJTU2NXC6XvF4vM10AAASJrn5/B/QxVgAAAMGEYAUAAGATghUAAIBNCFYAAAA2IVgBAADYhGAFAABgE4IVAACATQhWAAAANiFYAQAA2IRgBQAAYBOCFQAAgE0IVgAAADYhWAEAANiEYAUAAGATghUAAIBNCFYAAAA2IVgBAADYhGAFAABgE4IVAACATQhWAAAANiFYAQAA2IRgBQAAYJM+l/Pks2fPqqSkRPX19T7Lb7311stqCgAAIBj1KFidOHFC//zP/6w//vGP7a5vbGy8rKYAAACCUY92BWZlZamqqkrbt29XRESE8vLy9Oqrr2rw4MF699137e4RAAAgKPRoxmrjxo363e9+p7vuukshISEaMGCAxo8fr+joaGVnZ2vy5Ml29wkAABDwejRjdebMGcXFxUmSYmJidOLECUnS0KFDtXv3bvu6AwAACCI9ClY33XSTPvnkE0nS7bffrpdeekllZWVauXKlEhISbG0QAAAgWPRoV2BWVpbKy8slSQsWLNCECRO0evVqhYeHa9WqVXb2BwAAEDQcxhhzuS9y9uxZHTx4UP3791dsbKwdfV21ampq5HK55PV6FR0d7e92AABAF3T1+7tHuwKfffZZnT171nrct29fDRs2TJGRkXr22Wd78pIAAABBr0czVqGhoSovL7cOYG9x8uRJxcXFcR6rTjBjBQBA8LmiM1bGGDkcjjbLP/roI8XExPTkJQEAAIJetw5e79evnxwOhxwOh770pS/5hKvGxkadPn1ajz32mO1NAgAABINuBasXXnhBxhg9/PDDeuaZZ+Ryuax14eHhGjhwoEaOHGl7kwAAAMGgW8FqxowZkqRBgwZp1KhRCgsLuyJNAQAABKMencdqzJgx1p/PnTunhoYGn/UclA0AAK5FPTp4/ezZs8rMzFRcXJz+7u/+Tv369fO5AQAAXIt6FKyeeOIJbdy4UStWrJDT6dR//dd/6ZlnnpHH49Frr71md48AAABBoUe7At977z299tprGjt2rB5++GGNHj1a//AP/6ABAwZo9erVSk9Pt7tPAACAgNejGatTp05p0KBBkpqPpzp16pQk6e6779aWLVvs605SWVmZvvOd7+j6669X3759dfvtt6uwsNBab4zRwoUL5fF4FBERobFjx2rfvn0+r1FXV6fZs2crNjZWkZGRmjp1qo4ePepTU1VVpYyMDLlcLrlcLmVkZKi6utqnpqSkRFOmTFFkZKRiY2M1Z84c1dfX27q9AAAgePUoWN144406fPiwJOmWW27RW2+9Jal5JusLX/iCXb2pqqpKX/3qVxUWFqY//vGP2r9/v37xi1/4vMeSJUu0dOlSLV++XLt27ZLb7db48eNVW1tr1WRlZWnt2rXKyclRfn6+Tp8+rbS0NJ8zxE+fPl1FRUXKy8tTXl6eioqKlJGRYa1vbGzU5MmTdebMGeXn5ysnJ0fvvPOO5s2bZ9v2AgCAIGd6YOnSpWbZsmXGGGM2btxoIiIiTHh4uAkJCTEvvPBCT16yXT/5yU/M3Xff3eH6pqYm43a7zeLFi61l58+fNy6Xy6xcudIYY0x1dbUJCwszOTk5Vk1ZWZkJCQkxeXl5xhhj9u/fbySZ7du3WzUFBQVGkjl48KAxxph169aZkJAQU1ZWZtWsWbPGOJ1O4/V6u7xNXq/XSOrWcwAAgH919fu7RzNW//Iv/6I5c+ZIku69914dPHhQa9as0e7duzV37lzbQt+7776rO++8U//0T/+kuLg43XHHHfr1r39trT906JAqKiqUmppqLXM6nRozZoy2bdsmSSosLFRDQ4NPjcfjUXJyslVTUFAgl8ul4cOHWzUjRoyQy+XyqUlOTpbH47FqJkyYoLq6Op9dkwAA4NrV7WDV1NSk//7v/1ZaWpqSk5M1dOhQZWZm6vTp07r11lttbe6vf/2rfvWrX2nw4MH605/+pMcee0xz5syxfnlYUVEhSYqPj/d5Xnx8vLWuoqJC4eHhbU4D0bqm9QWlJSkuLs6npvX79OvXT+Hh4VZNe+rq6lRTU+NzAwAAV6duBStjjKZOnarvfe97Kisr09ChQ/XlL39ZR44c0cyZM/WNb3zD1uaampo0bNgwLVq0SHfccYe+//3va9asWfrVr37lU9f6gtCmg4tEd1bTXn1PalrLzs62Doh3uVxKSkrqtC8AABC8uhWsVq1apS1btuiDDz7Qnj17tGbNGuXk5Oijjz7S+++/r40bN9p6HquEhATdcsstPsuGDBmikpISSZLb7ZakNjNGlZWV1uyS2+1WfX29qqqqOq05fvx4m/c/ceKET03r96mqqlJDQ0ObmayLPfXUU/J6vdattLT0ktsNAACCU7eC1Zo1a/TTn/5U9957b5t148aN05NPPqnVq1fb1txXv/pVffLJJz7L/vKXv2jAgAGSmq9Z6Ha7tWHDBmt9fX29Nm/erFGjRkmSUlJSFBYW5lNTXl6u4uJiq2bkyJHyer3auXOnVbNjxw55vV6fmuLiYpWXl1s169evl9PpVEpKSofb4HQ6FR0d7XMDAABXqe4cER8fH2/27NnT4frdu3eb+Pj47rxkp3bu3Gn69Oljfvazn5lPP/3UrF692vTt29e8/vrrVs3ixYuNy+Uyubm5Zu/eveahhx4yCQkJpqamxqp57LHHTGJionn//ffN7t27zbhx48xtt91mLly4YNVMnDjR3HrrraagoMAUFBSYoUOHmrS0NGv9hQsXTHJysvna175mdu/ebd5//32TmJhoMjMzu7VN/CoQAIDg09Xv724Fq7CwMHPs2LEO15eVlZnw8PDuvOQlvffeeyY5Odk4nU5z8803m5dfftlnfVNTk1mwYIFxu93G6XSae+65x+zdu9en5ty5cyYzM9PExMSYiIgIk5aWZkpKSnxqTp48adLT001UVJSJiooy6enppqqqyqfmyJEjZvLkySYiIsLExMSYzMxMc/78+W5tD8EKAIDg09Xvb4cxxnR1dis0NFQVFRX64he/2O7648ePy+Px+Jx4E75qamrkcrnk9XrZLQgAQJDo6vd3t64VaIzRzJkz5XQ6211fV1fXvS4BAACuIt0KVjNmzLhkzXe/+90eNwMAABDMuhWsXnnllSvVBwAAQNDr0SVtAAAA0BbBCgAAwCYEKwAAAJsQrAAAAGxCsAIAALAJwQoAAMAmBCsAAACbEKwAAABsQrACAACwCcEKAADAJgQrAAAAmxCsAAAAbEKwAgAAsAnBCgAAwCYEKwAAAJsQrAAAAGxCsAIAALAJwQoAAMAmBCsAAACbEKwAAABsQrACAACwCcEKAADAJgQrAAAAmxCsAAAAbEKwAgAAsAnBCgAAwCYEKwAAAJsQrAAAAGxCsAIAALAJwQoAAMAmBCsAAACbEKwAAABsQrACAACwCcEKAADAJgQrAAAAmxCsAAAAbEKwAgAAsAnBCgAAwCZBFayys7PlcDiUlZVlLTPGaOHChfJ4PIqIiNDYsWO1b98+n+fV1dVp9uzZio2NVWRkpKZOnaqjR4/61FRVVSkjI0Mul0sul0sZGRmqrq72qSkpKdGUKVMUGRmp2NhYzZkzR/X19VdqcwEAQJAJmmC1a9cuvfzyy7r11lt9li9ZskRLly7V8uXLtWvXLrndbo0fP161tbVWTVZWltauXaucnBzl5+fr9OnTSktLU2Njo1Uzffp0FRUVKS8vT3l5eSoqKlJGRoa1vrGxUZMnT9aZM2eUn5+vnJwcvfPOO5o3b96V33gAABAcTBCora01gwcPNhs2bDBjxowxc+fONcYY09TUZNxut1m8eLFVe/78eeNyuczKlSuNMcZUV1ebsLAwk5OTY9WUlZWZkJAQk5eXZ4wxZv/+/UaS2b59u1VTUFBgJJmDBw8aY4xZt26dCQkJMWVlZVbNmjVrjNPpNF6vt8vb4vV6jaRuPQcAAPhXV7+/g2LG6kc/+pEmT56sr3/96z7LDx06pIqKCqWmplrLnE6nxowZo23btkmSCgsL1dDQ4FPj8XiUnJxs1RQUFMjlcmn48OFWzYgRI+RyuXxqkpOT5fF4rJoJEyaorq5OhYWFHfZeV1enmpoanxsAALg69fF3A5eSk5Oj3bt3a9euXW3WVVRUSJLi4+N9lsfHx+vIkSNWTXh4uPr169empuX5FRUViouLa/P6cXFxPjWt36dfv34KDw+3atqTnZ2tZ5555lKbCQAArgIBPWNVWlqquXPn6vXXX9d1113XYZ3D4fB5bIxps6y11jXt1fekprWnnnpKXq/XupWWlnbaFwAACF4BHawKCwtVWVmplJQU9enTR3369NHmzZv1H//xH+rTp481g9R6xqiystJa53a7VV9fr6qqqk5rjh8/3ub9T5w44VPT+n2qqqrU0NDQZibrYk6nU9HR0T43AABwdQroYPW1r31Ne/fuVVFRkXW78847lZ6erqKiIt14441yu93asGGD9Zz6+npt3rxZo0aNkiSlpKQoLCzMp6a8vFzFxcVWzciRI+X1erVz506rZseOHfJ6vT41xcXFKi8vt2rWr18vp9OplJSUKzoOAAAgOAT0MVZRUVFKTk72WRYZGanrr7/eWp6VlaVFixZp8ODBGjx4sBYtWqS+fftq+vTpkiSXy6VHHnlE8+bN0/XXX6+YmBjNnz9fQ4cOtQ6GHzJkiCZOnKhZs2bppZdekiQ9+uijSktL00033SRJSk1N1S233KKMjAw999xzOnXqlObPn69Zs2YxCwUAACQFeLDqih//+Mc6d+6cfvjDH6qqqkrDhw/X+vXrFRUVZdX88pe/VJ8+ffTggw/q3Llz+trXvqZVq1YpNDTUqlm9erXmzJlj/Xpw6tSpWr58ubU+NDRUf/jDH/TDH/5QX/3qVxUREaHp06fr+eef772NBQAAAc1hjDH+buJaUlNTI5fLJa/Xy0wXAABBoqvf3wF9jBUAAEAwIVgBAADYhGAFAABgE4IVAACATQhWAAAANiFYAQAA2IRgBQAAYBOCFQAAgE0IVgAAADYhWAEAANiEYAUAAGATghUAAIBNCFYAAAA2IVgBAADYhGAFAABgE4IVAACATQhWAAAANiFYAQAA2IRgBQAAYBOCFQAAgE0IVgAAADYhWAEAANiEYAUAAGATghUAAIBNCFYAAAA2IVgBAADYhGAFAABgE4IVAACATQhWAAAANiFYAQAA2IRgBQAAYBOCFQAAgE0IVgAAADYhWAEAANiEYAUAAGATghUAAIBNCFYAAAA2IVgBAADYhGAFAABgE4IVAACATQhWAAAANgnoYJWdna277rpLUVFRiouL0/33369PPvnEp8YYo4ULF8rj8SgiIkJjx47Vvn37fGrq6uo0e/ZsxcbGKjIyUlOnTtXRo0d9aqqqqpSRkSGXyyWXy6WMjAxVV1f71JSUlGjKlCmKjIxUbGys5syZo/r6+iuy7QAAIPgEdLDavHmzfvSjH2n79u3asGGDLly4oNTUVJ05c8aqWbJkiZYuXarly5dr165dcrvdGj9+vGpra62arKwsrV27Vjk5OcrPz9fp06eVlpamxsZGq2b69OkqKipSXl6e8vLyVFRUpIyMDGt9Y2OjJk+erDNnzig/P185OTl65513NG/evN4ZDAAAEPhMEKmsrDSSzObNm40xxjQ1NRm3220WL15s1Zw/f964XC6zcuVKY4wx1dXVJiwszOTk5Fg1ZWVlJiQkxOTl5RljjNm/f7+RZLZv327VFBQUGEnm4MGDxhhj1q1bZ0JCQkxZWZlVs2bNGuN0Oo3X6+3yNni9XiOpW88BAAD+1dXv74CesWrN6/VKkmJiYiRJhw4dUkVFhVJTU60ap9OpMWPGaNu2bZKkwsJCNTQ0+NR4PB4lJydbNQUFBXK5XBo+fLhVM2LECLlcLp+a5ORkeTweq2bChAmqq6tTYWFhhz3X1dWppqbG5wYAAK5OQROsjDF6/PHHdffddys5OVmSVFFRIUmKj4/3qY2Pj7fWVVRUKDw8XP369eu0Ji4urs17xsXF+dS0fp9+/fopPDzcqmlPdna2ddyWy+VSUlJSdzYbAAAEkaAJVpmZmfr444+1Zs2aNuscDofPY2NMm2Wtta5pr74nNa099dRT8nq91q20tLTTvgAAQPAKimA1e/Zsvfvuu9q0aZMSExOt5W63W5LazBhVVlZas0tut1v19fWqqqrqtOb48eNt3vfEiRM+Na3fp6qqSg0NDW1msi7mdDoVHR3tcwMAAFengA5WxhhlZmYqNzdXGzdu1KBBg3zWDxo0SG63Wxs2bLCW1dfXa/PmzRo1apQkKSUlRWFhYT415eXlKi4utmpGjhwpr9ernTt3WjU7duyQ1+v1qSkuLlZ5eblVs379ejmdTqWkpNi/8QAAIOg4jDHG30105Ic//KHeeOMN/e53v9NNN91kLXe5XIqIiJAk/fznP1d2drZeeeUVDR48WIsWLdKHH36oTz75RFFRUZKkH/zgB/r973+vVatWKSYmRvPnz9fJkydVWFio0NBQSdKkSZN07NgxvfTSS5KkRx99VAMGDNB7770nqfl0C7fffrvi4+P13HPP6dSpU5o5c6buv/9+vfjii13eppqaGrlcLnm9XmavAAAIEl3+/r7Cv068LJLavb3yyitWTVNTk1mwYIFxu93G6XSae+65x+zdu9fndc6dO2cyMzNNTEyMiYiIMGlpaaakpMSn5uTJkyY9Pd1ERUWZqKgok56ebqqqqnxqjhw5YiZPnmwiIiJMTEyMyczMNOfPn+/WNnG6BQAAgk9Xv78DesbqasSMFQAAwaer398BfYwVAABAMOnj7wbgX41NjdpaslXlteVKiErQ6P6jFRoS6u+2AAAISgSra1jugVzNzZurozWfX5A6MTpRyyYu07Qh0/zYGQAAwYldgdeo3AO5euCtB3xClSSV1ZTpgbceUO6BXD91BgBA8CJYXYMamxo1N2+ujNr+bqFlWVZelhqbGnu7NQAAghrB6hq0tWRrm5mqixkZldaUamvJ1l7sCgCA4EewugaV15ZfuqgbdQAAoBnB6hqUEJVgax0AAGhGsLoGje4/WonRiXLI0e56hxxKik7S6P6je7kzAACCG8HqGhQaEqplE5dJUptw1fL4hYkvcD4rAAC6iWB1jZo2ZJrefvBt3RB9g8/yxOhEvf3g25zHCgCAHuBagb0s0K4VyJnXAQC4tK5+f3Pm9WtcaEioxg4c6+82AAC4KrArEAAAwCYEKwAAAJsQrAAAAGxCsAIAALAJwQoAAMAmBCsAAACbcLoFXBbOgwUAwOcIVuix3AO5mps3V0drjlrLEqMTtWziMs7cDgC4JrErED2SeyBXD7z1gE+okqSymjI98NYDyj2Q66fOAADwH4IVuq2xqVFz8+bKqO3VkFqWZeVlqbGpsbdbAwDArwhWV4s//1kaN675/grbWrK1zUzVxYyMSmtKtbVk6xXvBQCAQEKwulq89pq0aZP0P//T/ed2M5SV15bbWgcAwNWCYBXMjhyRCgul3bulN99sXpaT0/y4sLB5fVd0M5QlRCX4PE4pkz5Y1XzfWV2nenHGDQCAK4VgFcwGDpTuvFNKSZFOnGheduJE8+M772xe35HLCGWj+49WYnSiHHJIkr77kTTusJTxcfN6hxxKik7S6P6ju7QZjU2NOrp8kbRpk47+Z3bPjs0imAEAAgDBKpi9/rrU57MzZhjje9+nT/P6jlxGKAsNCdXLQ5/WsGNGw45J39rXvPzbxdKwY9KwY0YvDf3ppc9ndeSINr79nNKe8Cjs7bWSpLD/zVXaEx5tfPu5rs+4SZe3K7QF4QwAcJkcxpi2P+3CFVNTUyOXyyWv16vo6OjLf8Hdu5vDUGuFhdKwYR0/b/VqaeZM6cKFtuv69JFWrZLS0zt+vsNh/bFJzQm95d5yqY/W5b7GkSPS3/7W/DqTJkmVlVJcnPTHPzY/LzZWGjCg8x4uNmeO9OKLzffLlnX9eQCAq15Xv7+ZsbpahIT43l9Kerq0Y0f763bs6DxUST6zZS3vaL3zpWbL1Lz7b3Z6jBpa2m71Gg0h0pz0mM53C14062ZOVEpS831XdoW2sOs4td7CrBoABDSCVbCLi5Pc7uYwsXJl873b3by8q7obyqTLDmZbS7Zq+eBTGv699tcP/5704uBTnZ+y4fXX1RTavLvR8dnEVst9U2joJcOdpMs7Ts0f7NjlCQC4YghWwS4xUTp8uDnMfP/7zfeHDzcvvxQ7QpnUo2DW+lQMja3uO6q7WO6wCN31SPszWnc90qjcYRGXbuRyjlPrLcE6q/baa8yuAbjmcK3Aq4HT+fmfHQ7fx51pCWXh4c3Pe/RRqb6+689vCWZJSdIjj0i/+Y1UWtqlYNZyKobKSKn876TSaOk3w6RHdktJNc3LL65rreXs719seSwp9KJ7qfns7/fddF/nB9Gnp2vjdeUa98ATbVZtzMnWuG9eYpdob7h41qzluLSWWbUWgXSoZMus2qlT0kcfNc+u3Xmnv7vy9ec/Sz/+sbRkSeD1BiCoEayudT0NZdJlBbOWUzaUqUwDs4zqQyU5pJdTpPBGqaGPQ0nRiR2esqHl7O+mg2B2PFIq++zs72MHju2wj9wDufrZ+idUqLbh7In1T+jpW270/wWlX3/98x8atDertmqVvzr7XMsPCSoqPp/l+/iz82/8z/9IqanNIby7Pyi4Ui7epUqwAmAjghUuTw+DWWhIqJZNXKYH3npADX0cUst1Bx367LH0wsQXOpxtatlFWOaSBmapTTCr7+Nb1x7rmoedzJp1adbrSgu2WbUWLeGvqkpKS2u7vLdd/CvSi3epzpjRs1+RXmnMqgFBiWOs4DfThkzT2w++rRuib/BZnhidqLcffLvTmaKLdxHW95HUcuYGx+ehqnVday2zXi3hbPgs6eU7m+8HZklHXQqIax7mHsjVE+ubQ1XrY9GeWP+Ecg/k+qUvHxcfq9YRfx+zxg8VAPQCghX8atqQaTo897A2zdikN6a9oU0zNunQ3EOX3P3W+uzvrXXl7O8Xz2Z1Fs78ec3Dllm145/NqhV6pO+nNd+X/93ns2o9Olu9ndLTtTEnu9OSjTnZlz6Nx5UURD9UaPzzLtW/0Ryo6le/psY/7wrsHyrwAwXAwq5A+F1oSGinx0F19JyWXYkOOWT0+e6llrDV2a5EqevXMuzWNQ9t1jKrps52eXbhWLIrrb1j1Uxzq9ZJX/1+zFoQ7VL97K9ZktTnZLVC7vrK5zUB8kOFxqZGlS9fpMTPLkWV8Ju3/LvLvAONTY3aWrJV5bXlSohK0Oj+owOuT3q0R6D0yIwVgtbl7EqU7Jn1utKCcVbt43jJ65TOhDXffxwfGLNrwbBLddfP53Z60txdP5/rj7Z82Xkpqiss90CuBi4bqPmL7lX81Omav+heDVw2MCD+rlu09Hjvq/dqeu503fsqPfZEIPXIJW16me2XtMFl/Ssl90CuHnjrAUlqd9arKwHtSvrw8Ie699V7L1m3acYmv81YXdxj+IXmWbXwRqk+RApvuuhxH//12tjUqIHLBsqUHtWuX7f9ocJXZkmOpCQdmnvIb/8Kb+nxiwePavfLbdenPCqduNm/PUqy53JWvaDlv20jo2XrpDk7pWXDpX+ZFBj/bbfu8WKB8v8fiR4vxiVtrqAVK1Zo0KBBuu6665SSkqKtW/17cPO1rmVX4kNDH9LYgWO79aVzubNeV1qwzqrV95EU0upxO/W9JRh+qGDt9v1M61k1I//3aMulqHpBY1OjlrzxI91xzOiOVheKv/2Y0bBjRs+9kenXPq1fJX8WBlLKpA9WNd+3LPP38ZOte7wYPXaMYNVNb775prKysvT0009rz549Gj16tCZNmqSSkhJ/t4Ye6ukB9L2h5VgySW3CVVePJbvSunsMmj+OWQuGXaot713ZyQ8V/N2jLZei6gVbS7Zq+79XqPBlaffL0hfPNC//4pnmx39+WSr49/KACtLf/Ugad1jK+Oz0b0bG70G6dY+t0WP7CFbdtHTpUj3yyCP63ve+pyFDhuiFF15QUlKSfvWrX/m7NVyGy5n1utKCZVbtUvw5uxYMP1Roee+OZtXKXP7v0Y5LUfWG8tpypU9TpzNr6dP8H6T7V0vDjqnNrNodx5qX96/2f48Xu3hWrbO63tTV9+7NHvlVYDfU19ersLBQTz75pM/y1NRUbdu2rd3n1NXVqa6uznpcU1NzRXvE1WnakGm676b7AuIXL61d/AvN9qbjL+av2TXrTP81Ze326JBDiZ2c6b83XNxjfZ+LevxsVi0QerzcS1H1loSoBL1xq3QgVu0erzb8e9IejzTLz0H6yAufP2767L5lVq3Fh3P9H/ZbXDyrVnhDx3W9qfV7p5RJSzZIPx7vvx6ZseqGv/3tb2psbFR8fLzP8vj4eFVUVLT7nOzsbLlcLuuWlJTUG63iKhQMs2odzVwlRSf5dXYtGHapBkOPLeHvmMvR7qzaMZf/j/m7uM+WUWw9s+aQ/N7n6P6ju3S8mr97HH7BrZQOZtVSjkkjLiT4vceLj0NtvUvVHzPlBKsecDh8/6dnjGmzrMVTTz0lr9dr3UpLS3ujRaDXXXys2uvfeF2/nPBLvf6N1wPmmLVA36UqBX6PF4e/hj4On2PVunIpqt7S0mdnx6v5u8/QkFDd+/SvNaKD49VGfE8a+/Sv/d7j9n+v0J8vcayav3t8eejTGnbMaFir8DfsmDTsmNFLQ3/aqz1yuoVuqK+vV9++ffW///u/+sY3vmEtnzt3roqKirR58+ZLvganWwD8K1BOItiZQO8x90Cu5ubN9TloOCk6SS9MfMHv4e9iuQdy9cTv5+ivZ8qaQ6CR/j4yUUvSlgVMnxvfeV7jHniizUXgN779nMZ9c75/m5Ok1avVNGOGQhrb/qquKTRUIa++6t8rKki9dgqQrn5/E6y6afjw4UpJSdGKFSusZbfccovuu+8+ZWd3fkkPiWAF4OoQ6OGvRcD3efSozJ13qjb+Czp43926+Xf5ijpeLcef/ywlXvpHIb1i9+7ma2q2VlgoDRvW+/20tnq1NHOmdOFC23V9+kirVtkS/rr6/c3B6930+OOPKyMjQ3feeadGjhypl19+WSUlJXrsscf83RoA9JqeXIrKHwK+z8REOY4cUXR4uL7icEjPGKm+XnI6/d1ZWyEhUlPT5/eBIj1dGjKk/fC3Y0evhz+CVTd961vf0smTJ/Xss8+qvLxcycnJWrdunQYMGODv1gAAwejiEOVwBF6oiouT3G4pKUl65BHpN7+RSkublweaAAh/7ArsZewKBAAEnbo6KTy8OfiZAJxVO3pUuuuutuFv1y7bdqmyKxAAANgj0GfVEhOlw4c/D3+PPuq38EewAgAAwS9Awh/nsQIAALAJwQoAAMAmBCsAAACbEKwAAABsQrACAACwCcEKAADAJgQrAAAAmxCsAAAAbEKwAgAAsAnBCgAAwCZc0qaXtVzzuqamxs+dAACArmr53m75Hu8IwaqX1dbWSpKSkpL83AkAAOiu2tpauVyuDtc7zKWiF2zV1NSkY8eOKSoqSg6H47Jfr6amRklJSSotLVV0dLQNHV67GEt7MI72YBztw1ja41ofR2OMamtr5fF4FBLS8ZFUzFj1spCQECUmJtr+utHR0dfkB/1KYCztwTjag3G0D2Npj2t5HDubqWrBwesAAAA2IVgBAADYhGAV5JxOpxYsWCCn0+nvVoIeY2kPxtEejKN9GEt7MI5dw8HrAAAANmHGCgAAwCYEKwAAAJsQrAAAAGxCsAIAALAJwSrIrVixQoMGDdJ1112nlJQUbd261d8tBbSFCxfK4XD43Nxut7XeGKOFCxfK4/EoIiJCY8eO1b59+/zYcWDYsmWLpkyZIo/HI4fDod/+9rc+67sybnV1dZo9e7ZiY2MVGRmpqVOn6ujRo724FYHhUmM5c+bMNp/RESNG+NRc62OZnZ2tu+66S1FRUYqLi9P999+vTz75xKeGz2TXdGUs+Ux2D8EqiL355pvKysrS008/rT179mj06NGaNGmSSkpK/N1aQPvyl7+s8vJy67Z3715r3ZIlS7R06VItX75cu3btktvt1vjx461rPF6rzpw5o9tuu03Lly9vd31Xxi0rK0tr165VTk6O8vPzdfr0aaWlpamxsbG3NiMgXGosJWnixIk+n9F169b5rL/Wx3Lz5s360Y9+pO3bt2vDhg26cOGCUlNTdebMGauGz2TXdGUsJT6T3WIQtL7yla+Yxx57zGfZzTffbJ588kk/dRT4FixYYG677bZ21zU1NRm3220WL15sLTt//rxxuVxm5cqVvdRh4JNk1q5daz3uyrhVV1ebsLAwk5OTY9WUlZWZkJAQk5eX12u9B5rWY2mMMTNmzDD33Xdfh89hLNuqrKw0kszmzZuNMXwmL0frsTSGz2R3MWMVpOrr61VYWKjU1FSf5ampqdq2bZufugoOn376qTwejwYNGqRvf/vb+utf/ypJOnTokCoqKnzG1Ol0asyYMYxpJ7oyboWFhWpoaPCp8Xg8Sk5OZmzb8eGHHyouLk5f+tKXNGvWLFVWVlrrGMu2vF6vJCkmJkYSn8nL0XosW/CZ7DqCVZD629/+psbGRsXHx/ssj4+PV0VFhZ+6CnzDhw/Xa6+9pj/96U/69a9/rYqKCo0aNUonT560xo0x7Z6ujFtFRYXCw8PVr1+/DmvQbNKkSVq9erU2btyoX/ziF9q1a5fGjRunuro6SYxla8YYPf7447r77ruVnJwsic9kT7U3lhKfye7q4+8GcHkcDofPY2NMm2X43KRJk6w/Dx06VCNHjtTf//3f69VXX7UOxmRMe6Yn48bYtvWtb33L+nNycrLuvPNODRgwQH/4wx80bdq0Dp93rY5lZmamPv74Y+Xn57dZx2eyezoaSz6T3cOMVZCKjY1VaGhom38NVFZWtvlXGjoWGRmpoUOH6tNPP7V+HciYdk9Xxs3tdqu+vl5VVVUd1qB9CQkJGjBggD799FNJjOXFZs+erXfffVebNm1SYmKitZzPZPd1NJbt4TPZOYJVkAoPD1dKSoo2bNjgs3zDhg0aNWqUn7oKPnV1dTpw4IASEhI0aNAgud1unzGtr6/X5s2bGdNOdGXcUlJSFBYW5lNTXl6u4uJixvYSTp48qdLSUiUkJEhiLKXmmZDMzEzl5uZq48aNGjRokM96PpNdd6mxbA+fyUvwzzHzsENOTo4JCwszv/nNb8z+/ftNVlaWiYyMNIcPH/Z3awFr3rx55sMPPzR//etfzfbt201aWpqJioqyxmzx4sXG5XKZ3Nxcs3fvXvPQQw+ZhIQEU1NT4+fO/au2ttbs2bPH7Nmzx0gyS5cuNXv27DFHjhwxxnRt3B577DGTmJho3n//fbN7924zbtw4c9ttt5kLFy74a7P8orOxrK2tNfPmzTPbtm0zhw4dMps2bTIjR440N9xwA2N5kR/84AfG5XKZDz/80JSXl1u3s2fPWjV8JrvmUmPJZ7L7CFZB7j//8z/NgAEDTHh4uBk2bJjPT2TR1re+9S2TkJBgwsLCjMfjMdOmTTP79u2z1jc1NZkFCxYYt9ttnE6nueeee8zevXv92HFg2LRpk5HU5jZjxgxjTNfG7dy5cyYzM9PExMSYiIgIk5aWZkpKSvywNf7V2ViePXvWpKammi9+8YsmLCzM9O/f38yYMaPNOF3rY9ne+Ekyr7zyilXDZ7JrLjWWfCa7z2GMMb03PwYAAHD14hgrAAAAmxCsAAAAbEKwAgAAsAnBCgAAwCYEKwAAAJsQrAAAAGxCsAIAALAJwQoAAMAmBCsAAACbEKwAAABsQrACAACwCcEKAADAJv8ftQ7T++moy6QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 20000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 25000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 30000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 35000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 40000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 45000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Random Initialisation\n",
    "m1 = np.random.randn(1)\n",
    "c1 = np.random.randn(1)\n",
    "\n",
    "# Hyperparameters\n",
    "learningrate = 0.25*1e-4\n",
    "numiter = 50000\n",
    "\n",
    "for i in range(numiter):\n",
    "    # forward pass\n",
    "    y_hat=forward_pass(P_1,m1,c1)\n",
    "    # Loss\n",
    "   \n",
    "    # Gradient\n",
    "    dm = (2.0/N_1) *  -np.sum(np.multiply(P_1,(Vap_sat_1 - (m1*P_1 +c1))))\n",
    "   \n",
    "    dc = (2.0/N_1) * -np.sum(Vap_sat_1 - (m1*P_1 + c1))\n",
    "    \n",
    "    m1 = m1 -learningrate * dm\n",
    "    c1 = c1 - learningrate * dc\n",
    "    if i%5000==0:\n",
    "        L_1.append(loss(y_hat,Vap_sat_1))\n",
    "        print (\"no of iterations:\",i )\n",
    "        plt.plot(P_1,Vap_sat_1,'go')\n",
    "        plt.plot(P_1,y_hat,'r*')\n",
    "        plt.ylabel('Data')\n",
    "        plt.show()\n",
    "\n",
    "R_1 = r2_score(P_1, y_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "11d5cdee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 5000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 10000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 15000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 20000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 25000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 30000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 35000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 40000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 45000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Random Initialisation\n",
    "m2 = np.random.randn(1)\n",
    "c2 = np.random.randn(1)\n",
    "\n",
    "# Hyperparameters\n",
    "learningrate = 0.1*1e-6\n",
    "numiter = 50000\n",
    "\n",
    "for i in range(numiter):\n",
    "    # forward pass\n",
    "    y_hat=forward_pass(P_2,m2,c2)\n",
    "    # Loss\n",
    "   \n",
    "    # Gradient\n",
    "    dm = (1.0/N_2) *  -np.sum(np.multiply(P_2,(Vap_sat_2 - (m2*P_2 +c2))))\n",
    "   \n",
    "    dc = (1.0/N_2) * -np.sum(Vap_sat_2 - (m2*P_2 + c2))\n",
    "    \n",
    "    m2 = m2 -learningrate * dm\n",
    "    c2 = c2 - learningrate * dc\n",
    "    if i%5000==0:\n",
    "        L_2.append(loss(y_hat,Vap_sat_2))\n",
    "        print (\"no of iterations:\",i )\n",
    "        plt.plot(P_2,Vap_sat_2,'go')\n",
    "        plt.plot(P_2,y_hat,'r*')\n",
    "        plt.ylabel('Data')\n",
    "        plt.show()\n",
    "        \n",
    "R_2 = r2_score(P_2, y_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "3610d76b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 5000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 10000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 15000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 20000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 25000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 30000\n"
     ]
    },
    {
     "data": {
      "image/png": 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NNN5ConhPsc7+29l0VAYA2B5lrAhER2UAQCQh7EQYOioDACINYSfC0FEZABBpCDsRho7KAIBIQ9iJMHRUBgBEGsJOhKGjMgAg0hB2IgwdlQEAkcbSYefUqVN64IEH1K9fP8XFxal///566KGH1NDQ4LnGMAzNnDlTTqdTcXFxysnJ0e7du0N419bXVkfl5/OeV3JcspZ/uFwb925kVRYAIOxZuqng3Llz9cQTT2jJkiU6//zztWPHDt1yyy1KSkpSfn6+JGnevHmaP3++Fi9erO9973uaPXu2rrzySn3yySdKSEgI8U9gXblZuRp7zlivjspfffOVCtcW0mgQAGArlt4uYsyYMUpNTdU//vEPz7Gf//znio+P17PPPivDMOR0OlVQUKDp06dLkurq6pSamqq5c+fq9ttv9+n7RMp2EW1xNxps2n/HXdpiDy0AgNX4+vvb0mWsyy67TBs2bNCnn34qSXr//fe1ZcsW/eQnP5EklZWVqaKiQqNHj/Z8TWxsrEaMGKGtW7e2+r51dXWqrq72ekUyGg0CAOzM0mFn+vTpGj9+vM4991x16dJFgwYNUkFBgcaPHy9JqqiokCSlpqZ6fV1qaqrnXEuKioqUlJTkeWVkZATuhwgDNBoEANiZpcPO888/r6VLl2rZsmUqLS3VkiVL9F//9V9asmSJ13UOh/eqIsMwmh1rbMaMGaqqqvK8Dhw4EJD7Dxc0GgQA2JmlJyhPnTpV9913n2644QZJ0sCBA7Vv3z4VFRVp0qRJSktLk+Qa4end+3QTvMOHDzcb7WksNjZWsbGxgb35MEKjQQCAnVl6ZOf48eOKivK+xejoaM/S8379+iktLU3r1q3znD9x4oQ2bdqkYcOGBfVewxmNBgEAdmbpsHPttdfq4Ycf1v/93/9p7969Wr16tebPn6+f/exnklzlq4KCAs2ZM0erV6/Wrl27NHnyZMXHx2vChAkhvvvw0V6jQUOGfnXxr7Ry90p67wAAwo6ll57X1NToD3/4g1avXq3Dhw/L6XRq/Pjx+uMf/6iuXbtKcs3PmTVrlv7+97+rsrJSQ4cO1aOPPqrs7Gyfvw9Lz12K9xQrf02+12TlHnE9JElf137tOUbvHQCAFfj6+9vSYSdYCDun1TfUexoNfnb0M83cOJPeOwAAS/L197elJygj+KKjopWTmaP6hnplLsxstfeOQw4VrCnQ2HPGso8WAMDSLD1nB6FD7x0AgF0QdtAieu8AAOyCsIMW0XsHAGAXhB20qL3eO5KUHJes+oZ6lqIDACyNsIMWtdV7x+1o7VFd8ewVylyYqeI9xcG8PQAAfEbYQatys3K1atwq9Uns0+Z15dXlyluZR+ABAFgSYQdtys3K1d78vVp/03olxyW3eI17eXrBmgJKWgAAyyHsoF3RUdGKjorW0dqjrV7DUnQAgFV1qqng8ePHtX//fp04ccLr+AUXXNCpm4L1sBQdABCuOhR2jhw5oltuuUX//Oc/WzxfX08pw25Yig4ACFcdKmMVFBSosrJSb7/9tuLi4rRmzRotWbJEAwYM0Msvv2z2PcIC2luK7pBDGYkZGt53eJDvDACAtnUo7Lzxxht65JFHdMkllygqKkpnnXWWbrzxRs2bN09FRUVm3yMsoK2l6A45ZMjQry7+lVbuXqmNezcyURkAYBkdCjvffPONUlJSJEnJyck6cuSIJGngwIEqLS017+5gKa0tRU+OS1aPuB56cOODmlA8QSOXjKT3DgDAMjoUds455xx98sknkqSLLrpIf//731VeXq4nnnhCvXszZ8PO3EvRSyaVaFnuMs3KmaWjtUf1de3XXtfRewcAYBUOwzAMf7/oueee08mTJzV58mS9++67uuqqq/T111+ra9euWrx4sa6//vpA3GvAVFdXKykpSVVVVUpMTAz17YSN+oZ6ZS7MbHV3dIccSk9MV1l+maKjooN8dwAAu/P193eHVmNNnDjR8++DBg3S3r179fHHH6tv377q2bNnR94SYWjz/s2tBh3Ju/dOTmZO8G4MAIBGOlTGeuihh3T8+HHP5/Hx8br44ovVrVs3PfTQQ6bdHKyN3jsAgHDQobAza9YsHTt2rNnx48ePa9asWZ2+KYQHX3vq/Oubf7E6CwAQMh0KO4ZhyOFo3m/l/fffV3Jyy/snwX7a673jVvh6IauzAAAh41fY6d69u5KTk+VwOPS9731PycnJnldSUpKuvPJKjRs3LlD3Cotpq/dOU6zOAgCEil+rsZYsWSLDMPTLX/5SCxYsUFJSkudc165dlZmZqR/+8IcBudFAYjVW5xTvKVb+mvw2JytLrM4CAJjL19/fHVp6vmnTJg0bNkxdunTp1E1aBWGn8+ob6vW3d/6mwtcL2722ZFIJq7MAAJ0W0KXnI0aM8Px7bW2tTp486XWewBB5oqOildot1adrWZ0FAAimDk1QPn78uKZMmaKUlBR95zvfUffu3b1eiEzsjA4AsKIOhZ2pU6fqjTfe0GOPPabY2Fj993//t2bNmiWn06lnnnnG7HtEmPBldVav+F4qry5ns1AAQNB0aM5O37599cwzzygnJ0eJiYkqLS3Vd7/7XT377LNavny5XnvttUDca8AwZ8c8xXuKlbcyT5Krg3Jb0hPTtfDqhcrNyg3GrQEAbMbX398dGtk5evSo+vXrJ8k1P+fo0aOSpMsuu0xvvvlmR94SNtHazugtYTk6ACAYOhR2+vfvr71790qSzjvvPK1cuVKS9Morr+jMM880694QphrvjL70Z0vVK75Xi9e5R34K1hRQ0gIABEyHws4tt9yi999/X5I0Y8YMz9ydwsJCTZ061dQbRHiKjopWTmaO+iT20ZHjR1q9rvFmoQAABEKHlp4XFp7upTJy5Eh9/PHH2rFjh84++2xdeOGFpt0cwp+vy8w3fLFBw/sOp9kgAMB0fo/sNDQ06H/+5380ZswYZWdna+DAgZoyZYqOHTumCy64IBD3iDDm6zLz2Ztns38WACAg/Ao7hmHouuuu069+9SuVl5dr4MCBOv/887Vv3z5NnjxZP/vZzwJ1nwhTvm4WKjFhGQAQGH6FncWLF+vNN9/Uhg0b9O6772r58uVasWKF3n//fa1fv15vvPEGfXbgxZ/NQpmwDAAIBL/CzvLly/X73/9eI0eObHbu8ssv13333afnnnvOtJuDPfizHJ0JywAAs/kVdj744ANdffXVrZ7/8Y9/7FmlBTTmXo7+wPAHfLqe/bMAAGbxK+wcPXpUqamtb/aYmpqqysrKTt8U7Ck6Klqj+o/y6dqPjnzElhIAAFP4FXbq6+sVE9P6avXo6GidOnWq0zcF+/J1wvLszbM1cslIVmgBADrNrz47hmFo8uTJio2NbfF8XV2dKTcF+3JPWM5bmSeHHO3un+VeobVq3Cr20AIAdIhfG4HecsstPl339NNPd/iGQoGNQIOveE+x8tfk62D1wXavdcih9MR0leWX0XQQAODh6+/vDu16bjeEndCob6jX5v2bteGLDZq9eXa715dMKlFOZk7gbwwAEBYCuus5YAb3/lnn9TrPp+s3fLGBCcsAAL8RdhBybCkBAAgky4ed8vJy3XjjjerRo4fi4+N10UUXaefOnZ7zhmFo5syZcjqdiouLU05Ojnbv3h3CO4a/2FICABBIlg47lZWVuvTSS9WlSxf985//1EcffaS//OUvOvPMMz3XzJs3T/Pnz9eiRYu0fft2paWl6corr1RNTU3obhx+YUsJAEAgWTrszJ07VxkZGXr66af1/e9/X5mZmRo1apTOPvtsSa5RnQULFuj+++9Xbm6usrOztWTJEh0/flzLli0L8d3DH2wpAQA2tWOHdPnlro8hYumw8/LLL2vIkCH6xS9+oZSUFA0aNEhPPfWU53xZWZkqKio0evRoz7HY2FiNGDFCW7dubfV96+rqVF1d7fVC6Pm7pcQLH71Al2UAsLpnnpFKSqRnnw3ZLVg67HzxxRd6/PHHNWDAAL3++uu64447dM8993h2Vq+oqJCkZltYpKames61pKioSElJSZ5XRkZG4H4I+MWfLSUWbV9El2UAsKJ9+6SdO6XSUun5513HVqxwfb5zp+t8EFk67DQ0NOjiiy/WnDlzNGjQIN1+++369a9/rccff9zrOofDe56HYRjNjjU2Y8YMVVVVeV4HDhwIyP2jY/yZsCwxaRkAQqa1ElVmpjRkiDR4sHTkiOvYkSOuz4cMcZ0PIkuHnd69e+u887x7sGRlZWn//v2SpLS0NElqNopz+PDhNjcsjY2NVWJiotcL1uHPhGWJScsAEDKtlaiWLpXce2m6exe7P8bEuM4HkaXDzqWXXqpPPvnE69inn36qs846S5LUr18/paWlad26dZ7zJ06c0KZNmzRs2LCg3ivM5c+EZYlJywAQNL6UqCZOlLZta/nrt21znQ8iS4edwsJCvf3225ozZ44+//xzLVu2TE8++aTuuusuSa7yVUFBgebMmaPVq1dr165dmjx5suLj4zVhwoQQ3z06yz1huWRSiaZcMsWnr2HSMgCYxKwSVVSU98cQsHTYueSSS7R69WotX75c2dnZ+tOf/qQFCxZoYqNEOG3aNBUUFOjOO+/UkCFDVF5errVr1yohISGEdw6zuLeU+Pl5P/fpeiYtA4BJOluiSkmR0tJcIeiJJ1wf09Jcx4OMjUDFRqDhoL6hXpkLM1VeXe6Zo9MW91yfVeNWKTcrN9C3BwD2sG+f9NVXksMh/fjH0uHDrnDyz3+6Ak3PntJZZ7lKVoMHN//6nTuliy8+/XldndS1q+v9DEM6cUKKjTXtdtkIFLbCpGUAMFGwSlSxsa6gI7k+mhh0/EHYQdjo6KTlv73zNwIPADRmoxKVLyhjiTJWuKlvqNfm/Zv1wkcvaNH2RT59TXpiuhZevZCSFoDIFWYlKl9QxoJt+TtpWaLxIIAIEmElKl8QdhC2/Om0zBweABEjwkpUvqCMJcpY4ax4T7HyVuZJkk+rtCTpgeEPaFT/URred7iio6IDeXsAEBw2LFH5gjIWIoK/k5Ylafbm2fTiARCeKFF1CGEHYc/dafmRqx7x6+uYxwMg7FCi6hDKWKKMZRf+Nh6UXD170hPTVZZfRkkLQGjt2CFNmybNm+cajXGL0BKVLyhjIeL423hQohcPAAtpbdSGElWnEXZgKx2ZwyNJha8XMocHQPD5soM4JapOo4wlylh25G48uOGLDZq9ebZPX8N+WgACprUSlcPh/e+Gcfqjm2FEZInKF5SxENHcjQdn5sykFw+A0OvsxGI3SlQdQtiBrXVkA9ED1Qc0c+NMbdy7kdADoON8KVFNnCht29by12/b5jovUaLqJMpYoowVCYr3FCt/Tb4OVh/06+vYUwtAm1orT0n+l6iioqSGhtMfI7xE5QvKWEAj9OIBEBCtlack8ycWU6LqMEZ2xMhOJOlILx5JSo5L1sq8lcrJzKEfDxDpfO17IzGxOMAY2QFa0JFePJJ0tPaornj2CpanA5HErK0ZJCYWhxhhBxGno714JMpaQEQxYwUVE4stgTKWKGNFqo704pHYYgKwNbO3ZpAoUQUQZSygHR3pxSOxPB2whWDtHi5RorIAwg4iXkfn8czePFsjl4xkHg8Qjtg9PKJQxhJlLLh0tBcP20wAYYLdw22HMhbgJ3cvnvU3rVdyXLLPX2f8559fv/JrbfhiA2UtINSCVaKiPBU2CDtAI9FR0RrVf5SeuvYpOf7zj69Yng5YBCUqNEEZS5Sx0DLKWoAFtbY9AyWqiOTr7++YIN4TEFZys3I19pyxfi9Pd3dmvuPVO1R7slZ9EvtoeN/hLFMHzNB41KZx2GlcgnKXltwlKrfG/2/fdB+qphoHG0pUYY+RHTGyg/Z1dJsJNzYUBTrBl1GbLVukyZOlU6eaf31MjLR4sWsH8YMHpUsukTIypFtvlf7xD+nAAWn7dik9Pdg/GTrJ19/fhB0RduCb4j3FyluZJ0l+Bx5KW4APWitR+bt7eFOUqGyL1ViAyTqzzYR7xdYdr96h5z54jmaEQEvM2J5BYhUVmmFkR4zswD/1DfXauHejxq0ap6O1Rzv8PpS2AJk7sZgSVcShjOUHwg46ojNlLYnSFiKMWSWqphOLKVFFNMpYQIB1pqwl0YwQESZYvW8oUaEFjOyIkR10jnv39PLqchW+Xqivjn/Fii1AovcNAo4+O0CQuHdPl6S4LnHKW5knhxx+B57y6nL9fOXPNStnlgYkD1DvhN7050F4aK1ERe8bWARlLMBEnV2xJUkPbnxQE4onsKM6wgfbM8DiKGOJMhbMZ1Zpi0nMsCxKVLAAylhACJlV2nJf/+tXfq2k2CTlZOZQ1kJwUaKCDVDGAgKss6u2JHZURwhRooINUMYSZSwEhxnNCN2jQ0xiRkBRokKYoKmgHwg7CKbONiNsiiXr6JDWylOS+Y3+gAChqSBgUWaUtRorry5X3so8ylvwT2vlKYkSFWyHkR0xsoPQcK/YOlRzSJ8d/UwzN86U1PHRnuS4ZK3MW8kkZrQ+auNreUqiRIWwYMuRnaKiIjkcDhUUFHiOGYahmTNnyul0Ki4uTjk5Odq9e3fobhLwkXvF1viB4/XHEX9kEjPM09qoTWamK/wMHuxaOSWdXkE1ZIj3Cis3dhCHDYRN2Nm+fbuefPJJXXDBBV7H582bp/nz52vRokXavn270tLSdOWVV6qmpiZEdwp0TG5Wrvbm79X6m9YrOS65w+/j7sT80KaHtPzD5dq4dyP7bkWCfftcoy6lpdLzz7uOrVjh+nznTtd5X8tTEiUq2EpYlLGOHTumiy++WI899phmz56tiy66SAsWLJBhGHI6nSooKND06dMlSXV1dUpNTdXcuXN1++23+/T+lLFgNUxiRqvM2j28qZYmFVOigsXZqox111136ZprrtEVV1zhdbysrEwVFRUaPXq051hsbKxGjBihrVu3Bvs2AdOYPYn5YPVB/Xzlz1X4eiEjPeGus31v3NorT0mUqGAblu+gvGLFCpWWlmr79u3NzlVUVEiSUlNTvY6npqZq3759rb5nXV2d6urqPJ9XV1ebdLeAeXKzcjX2nLGmTmJe8PYCLXh7ASM94abxxOLGJapJk05PLJ44UcrKannUZtu206M27vJURoZ0663SP/4hHThAeQq2Zumwc+DAAeXn52vt2rU644wzWr3O0Xj4Vq5Jy02PNVZUVKRZs2aZdp9AoDTedkKSslOylb8mXwerD3bqfdlh3aKCsTVDerq0d+/p8tRtt1Gegu1Zuoy1c+dOHT58WIMHD1ZMTIxiYmK0adMm/fWvf1VMTIxnRMc9wuN2+PDhZqM9jc2YMUNVVVWe14EDBwL6cwBmMWsSMzusW1SwtmagPIUIY+kJyjU1Nc3KUbfccovOPfdcTZ8+Xeeff76cTqcKCws1bdo0SdKJEyeUkpLCBGXYntmTmNlhPUTYmgHoMFvsep6QkKDs7GyvY926dVOPHj08xwsKCjRnzhwNGDBAAwYM0Jw5cxQfH68JEyaE4paBoHFPYjajrCWdDkx3vHqHak/Wqk9iH0pbZmL3cCBkLB12fDFt2jTV1tbqzjvvVGVlpYYOHaq1a9cqISEh1LcGBFwgJjEfOX5EN66+URJL1k3VuETVOOwsXSpNniydOtVyiWrxYte/M7EY6DBLl7GChTIW7KR4T7Fpoz1uBT8o0NhzxjLS4y9KVEBAseu5Hwg7sBv3vlsvffySFmxbIIccpjUnnD96vnp166VDNYdYxeVmVqM/dg8H/GKLOTsAOsa9ZD0nM0fDzxpu2kjPweqDGrdqnNcxSl2iRAVYHCM7YmQH9mf2DustibhSFyUqIOQoY/mBsINIE4h5PW62G+mhRAVYlq32xgJgLndzwpJJJVr6s6XqFd/L02ens8J61/UdO6TLL3d9dAtWoz8AAcPIjhjZAcxuUNiUZUd7mo7a3HOP9Le/uebZTJlCiQqwOEZ2APjM7F3Wm7LsruvuUZu//MUVXNybbC5e7Ao/gwe7GvxJpxv9DRni3QhQan8HcbZnAEKKkR0xsgO4BWrJelMhWcLuHsUpLJScTu9RG3+4V1FNnCgdPChdcknzVVTbt7s23AQQUExQ9gNhB2gukJOYW2J6qau1ElVjTScU+4ISFWAZhB0/EHaAljVest47obe++uYrFa4tDGgAMm0Juzvc3HCDNHXq6VGcxETpm2+keh9LaayiAiyLsOMHwg7gu2CWunwe6fGnRNXWaI77nDvY9Ogh9e9PiQqwKMKOHwg7QMcEstTlDlGzcmZpQPIA73k9ZpWomvbHOe8813u5g82WLa6wQ4kKsCTCjh8IO0DHBbo78+Byad46adqV0r+yXBObf/j/lit9yWr9a8xI9XxwrqKvGeN/iarpqM3+/a5Rm4wMgg0QJgg7fiDsAOYxe7Rn4WvSPe9I/3OR9Oj3JUPSP5+TUr85fY0huVoi+lOieustaehQRm2AMEbY8QNhBzBXR+f1uEdx5v9AOpTYcrCRpAa5moR5Qk5L2itRMfcGCHuEHT8QdoDAaWukp3GJamef06M4jbmDjfujL+rO/I7q+vbRx2Mv07kvbVFCRaUcO3ZQogJshrDjB8IOEFitLWGfuuKg7nlHWp4t/b9hp0dxqmKlbiekGB//6+QOQvWSoiUNvVV6J12uYR9D6hfv1OShtzef6AwgrBF2/EDYAYKgyfLweqNB9VePVtev/+25xF2Wam8Uxx1q3B939ZL+NlS6tVTKqJYu+bVUntT611t2ry4AfiHs+IGwAwSAH8vD25p703TU5qs46Yvu0j8u/k+4qfpPuDlTkiF1rZdOxLR9a20uawcQNgg7fiDsAJ3UNNhIpnQwbhZsqqVLb5HKkuUpUfkSbnzRJ6GPbht8G+EHCCOEHT8QdoBOcgebyZOlKVNM62B83T299Er3I6YHG1+EZLNSAH4h7PiBsAP4accOV8D5zW+k889vOdiY0MG4ftvb2txQFtS9udrCXB/AWgg7fiDsAG1oq0Tl1pHdwzvYwThYe3O1xPGfmUWrxq0i8AAWQNjxA2EHaIM/Jaq2BKCDcSD35mqNQw6lJ6arLL9M0VHRzZbVU+oCgoew4wfCDtCIWSUqd6gJcAfj1nr4BDoAlUwq0dHao83CFqUuIHgIO34g7CBimV2icgecEG+y2XRz0qd2PqWDNeaGn4KhBVq4bWGzElpLpS5Gf4DAIOz4gbCDiGVWiarpqM2WLa6wY5FNNgOxM3uv+F46cvxIi+cal7pe+uQlRn+AACHs+IGwg4jQpINxq8HGnxKV++OOHdLgwZYINr7ozFwfhxzqGd+z1aDT2KycWZq5cSajP0CAEHb8QNiBLfnRwdgnrZWownQH8Y6UutwhJf8H+Vrw9oJ2v0dyXLKO1h5t9b0Y/QE6h7DjB8IOwl6AOhhLsnyJyiy+THTOSMzQgqsXKDkuWSOXjDTl+zL6A3QcYccPhB2EPbM6GEthX6IyU2vhor6hXpkLM1VeXd7ivB+HHOoe173VUZ3GGP0BOo6w4wfCDsKO2R2MbVaiCobiPcXKW5knyXuis3tEZmbOTD248UFTvhejP0DLCDt+IOzA0oLVwdjGJapAaWmis7vUNfacsYz+AAFG2PEDYQeWZuEOxmh7JIXRHyCwCDt+IOzAUsKsgzHaxugPEDiEHT8QdhAyNu1gDG/hOPrT3n0DVkDY8QNhB0HTWu8bm3cwRtusNvoTHRXd4j0xAgSrIez4gbCDoGmt901jEdDBGM1ZZfTHvcFp3so85v/A8gg7fiDsICB83Z7BVywPj2jBGv1Z+rOlum/Dfa1updGR+T8EIgQKYccPhB10mi9zb6SOLRGnRIX/CMbozyNXPaLC1wvbvc7X+T+UwxBIhB0/EHbQaW3NvfF3ewZKVOigzo7+pCemq2hUkW5cfWO738uX+T/zR8/XuFXjKIchYAg7fiDswG/+LA9vazSHDsYwWWdGf1aNW2Xqvl+94nu1ujs85TCYgbDjB8IO2mTm8vCmAYgSFYKsrdGf3KxcU/f98gXlMHQGYccPhB20yazl4fS+gUW0N0ISzNVflMPQGbYIO0VFRSouLtbHH3+suLg4DRs2THPnztU555zjucYwDM2aNUtPPvmkKisrNXToUD366KM6//zzff4+hB14MbuDMdszIAx1dv5Pz/ierZaw/EU5DK3x9fd3VBDvyW+bNm3SXXfdpbffflvr1q3TqVOnNHr0aH3zzTeea+bNm6f58+dr0aJF2r59u9LS0nTllVeqpqYmhHeOsLFjh3T55a6Pbs884womN9/smhh8pIX/yLYWdKL+81eqRw/X1z7xhOtjWppr3o3D9X+icjgIOrC03Kxc7c3fq5JJJVqWu0wlk0pUll+m3KxcRUdFa+HVCyWdHl1xc3/+6E8eVXpierPzja9Ljkv26V7aCk2GDB2oPqCHNz+svJV5zZbMl1eXK29lnor3FEtyhbjMhZkauWSkJhRP0MglI5W5MNNzHvZk6ZGdpo4cOaKUlBRt2rRJP/rRj2QYhpxOpwoKCjR9+nRJUl1dnVJTUzV37lzdfvvtPr0vIzsRhA7GgGnam/9DOQyBZosyVlOff/65BgwYoA8//FDZ2dn64osvdPbZZ6u0tFSDBg3yXDd27FideeaZWrJkSYvvU1dXp7q6Os/n1dXVysjIIOxEAjoYA6byZf4P5TAEiu3CjmEYGjt2rCorK7V582ZJ0tatW3XppZeqvLxcTqfTc+1tt92mffv26fXXX2/xvWbOnKlZs2Y1O07YsRk6GAOW0Jnl8M/nPa97194b1qvDCEWB42vYiQniPXXKlClT9MEHH2jLli3Nzjkc3jVhwzCaHWtsxowZuvfeez2fu0d2EOaalqieeUYqKXG93Nr4c9GqtkpUt93GSA7QjuioaOVk5rR4LjcrV6vGrWoxOLjLYdFR0cpbmSeHHC0Govyh+aaVwxZuW9hiqDJkyCGHCtYUqKGhocVymHt+UONymK+hiEAUWGExsnP33XfrxRdf1Jtvvql+/fp5jne0jNUUc3ZsorUSFR2MAcuzaznMlw1VCUQdZ4sylmEYuvvuu7V69Wpt3LhRAwYMaHbe6XSqsLBQ06ZNkySdOHFCKSkpTFC2O39KVHQwBmwhnMph629ar8kvTW53Q1VfJ00TiFpmizLWXXfdpWXLlumll15SQkKCKioqJElJSUmKi4uTw+FQQUGB5syZowEDBmjAgAGaM2eO4uPjNWHChBDfPUzTUgdjf0pUjYNO0w7GWVmUqIAwEU7lsI17N7YadKTTS+bvfO1O08pmdJlunaVHdlqbd/P0009r8uTJkk43Ffz73//u1VQwOzvb5+/DyI7F+LM83J8SFR2MAduzSjnsgeEPaPbm2ab8TL6UzSJ1Wb0tyljBQtixGH+Wh/tToqKDMQAFvhyWnpiup8c+rSuevSIIP41LpC6rJ+z4gbATQmYuD29vk03m3gDwQWebJa4atyrok6Z9YfayeisEIsKOHwg7QdRaiaoxX3cQb4wSFQATdaYc1njZeWdHicwMRGZ2mbZKICLs+IGwE0SBWh5OiQpAkPnyi7yzo0TBDkRmzg8KxoRpwo4fCDsBwvJwAOj0KJHVltWbPWG6Mwg7fiDsmMSsElV7c2/YZBOAzQQ6EJm56aovfJ0w3dmSFmHHD4Qdk5hRomLuDQC0yCrL6s1SMqmk1b5JviLs+IGw0wGBKlEx9wYAOizQy+rNDETLcpdp/MDxnXoPX39/R3XquyBy7NghXX6566N0uoPxdde5SlaDB0tHWvkL0LSDceOPWVnSE0+4vj4tzTXvpvE1BB0A8Jm7y/T4geOVk5njNfLj7jLdJ7GP19ekJ6Zr1bhV+sX5v9DCqxdKOh2A3NyfP/qTR5WemN7sfOPresX38uleeyf09vnn6izCDpprGmyk0+HmL3+RSkul5593HU9MlKL/85epvUHCHj1cweiJJ1wfU1OlNWuk22+Xtm2T9u5lkjEABFBuVq725u9VyaQSLctdppJJJSrLL/NMFg5WIMpIzNDwvsPN/vFaRRlLlLGaaWt7hqYoUQGA7QR6wjSrsUIgosOOr3NvzFhFxfJwALANMxovdhZhxw8RFXboYAwACBKrdFCOMe07Ijw0nnszdar33Bv38nBfgk7TEtWrr54uUd12m3e4YaIxAEQk94TpUGOCsp25Jxq/8oq0c6f3xOIVK1wroNzlqpqatvvgRP3njwqrqAAAYYaRHTtpWqJyj+KUlJy+xtHy7Phmy8Pb2p5h/37XKqqMjOajOAAAWAwjO+EqGMvD3aM227a5Xu4l4vv2uYKOxCgOAMDymKCsMJug7B69SUlxhRmWhwMAIhQTlO1mxw7XyqnvfMc1ehMX5zq+eLHrJflXonJ/zMryXh7O3BsAgM0QdqzIPXozebIryBQWSs895xp1cautbf51vpSomHsDAIgwhB0raVyiKimRKiqkPXu8Jxj7g+XhAAAQdkKm8copybtE5Q4de/b4957uUEOJCgAAD8JOsDUdvXn0UVdJqnGJqq7O9/dzBxtKVAAAtIjVWArgaqzWRm/WrXMFD39CTWvOO086elTassUVdlhFBQCIEKzGsgJ335vOjt60JCtLqqx0jd6kpHgHG0pUAAB4EHbMtm+f9NVXrsCxbJnrmHtpeGdNmya98YZ08KD0+uvNQw4AAGiGMpZMLmO11uumI844Q+raVTrrLFezwB07pD59KFEBACDff3+zXYTZli6VYjo5YJaVJaWmSp984go577/vGjFyr6Yi6AAA4DPCjtkmTnTtH+Wr6GhXOPrTn1x7UqWluUpU+/ZJffu6gg0BBwCADmPOTiC5+960xD3BePNm14jNGWdI999PiQoAAJMxshMIKSmuEZrBg6WiIqlLl5ZHb/bulb77XVfQkRjBAQAgAJigrAD12amrc00udjikb791HTvjDHrgAABgEvrshFrjMOMeuZEYvQEAIMgoYwEAAFsj7AAAAFsj7AAAAFsj7AAAAFsj7AAAAFsj7AAAAFsj7AAAAFsj7AAAAFsj7AAAAFsj7AAAAFtjuwhJ7u3BqqurQ3wnAADAV+7f2+1t80nYkVRTUyNJysjICPGdAAAAf9XU1CgpKanV8+x6LqmhoUFffvmlEhIS5HA4Qn07PqmurlZGRoYOHDhg3k7taBHPOnh41sHDsw4unndgGIahmpoaOZ1ORUW1PjOHkR1JUVFRSk9PD/VtdEhiYiJ/cYKEZx08POvg4VkHF8/bfG2N6LgxQRkAANgaYQcAANgaYSdMxcbG6sEHH1RsbGyob8X2eNbBw7MOHp51cPG8Q4sJygAAwNYY2QEAALZG2AEAALZG2AEAALZG2AEAALZG2AmRoqIiXXLJJUpISFBKSop++tOf6pNPPvG6xjAMzZw5U06nU3FxccrJydHu3bu9rqmrq9Pdd9+tnj17qlu3brruuut08OBBr2sqKyt10003KSkpSUlJSbrpppv073//O9A/omUVFRXJ4XCooKDAc4xnba7y8nLdeOON6tGjh+Lj43XRRRdp586dnvM8b3OcOnVKDzzwgPr166e4uDj1799fDz30kBoaGjzX8Kw75s0339S1114rp9Mph8OhF1980et8MJ/r/v37de2116pbt27q2bOn7rnnHp04cSIQP7Z9GQiJq666ynj66aeNXbt2Ge+9955xzTXXGH379jWOHTvmuebPf/6zkZCQYLzwwgvGhx9+aFx//fVG7969jerqas81d9xxh9GnTx9j3bp1RmlpqTFy5EjjwgsvNE6dOuW55uqrrzays7ONrVu3Glu3bjWys7ONMWPGBPXntYp33nnHyMzMNC644AIjPz/fc5xnbZ6jR48aZ511ljF58mRj27ZtRllZmbF+/Xrj888/91zD8zbH7NmzjR49ehivvvqqUVZWZvzv//6v8Z3vfMdYsGCB5xqedce89tprxv3332+88MILhiRj9erVXueD9VxPnTplZGdnGyNHjjRKS0uNdevWGU6n05gyZUrAn4GdEHYs4vDhw4YkY9OmTYZhGEZDQ4ORlpZm/PnPf/Zc8+233xpJSUnGE088YRiGYfz73/82unTpYqxYscJzTXl5uREVFWWsWbPGMAzD+OijjwxJxttvv+255q233jIkGR9//HEwfjTLqKmpMQYMGGCsW7fOGDFihCfs8KzNNX36dOOyyy5r9TzP2zzXXHON8ctf/tLrWG5urnHjjTcahsGzNkvTsBPM5/raa68ZUVFRRnl5ueea5cuXG7GxsUZVVVVAfl47ooxlEVVVVZKk5ORkSVJZWZkqKio0evRozzWxsbEaMWKEtm7dKknauXOnTp486XWN0+lUdna255q33npLSUlJGjp0qOeaH/zgB0pKSvJcEynuuusuXXPNNbriiiu8jvOszfXyyy9ryJAh+sUvfqGUlBQNGjRITz31lOc8z9s8l112mTZs2KBPP/1UkvT+++9ry5Yt+slPfiKJZx0owXyub731lrKzs+V0Oj3XXHXVVaqrq/MqDaNtbARqAYZh6N5779Vll12m7OxsSVJFRYUkKTU11eva1NRU7du3z3NN165d1b1792bXuL++oqJCKSkpzb5nSkqK55pIsGLFCpWWlmr79u3NzvGszfXFF1/o8ccf17333qvf//73euedd3TPPfcoNjZWN998M8/bRNOnT1dVVZXOPfdcRUdHq76+Xg8//LDGjx8viT/bgRLM51pRUdHs+3Tv3l1du3aNyGffUYQdC5gyZYo++OADbdmypdk5h8Ph9blhGM2ONdX0mpau9+V97OLAgQPKz8/X2rVrdcYZZ7R6Hc/aHA0NDRoyZIjmzJkjSRo0aJB2796txx9/XDfffLPnOp535z3//PNaunSpli1bpvPPP1/vvfeeCgoK5HQ6NWnSJM91POvACNZz5dl3HmWsELv77rv18ssvq6SkROnp6Z7jaWlpktQsuR8+fNiT8tPS0nTixAlVVla2ec2//vWvZt/3yJEjzf5vwa527typw4cPa/DgwYqJiVFMTIw2bdqkv/71r4qJifE8B561OXr37q3zzjvP61hWVpb2798viT/bZpo6daruu+8+3XDDDRo4cKBuuukmFRYWqqioSBLPOlCC+VzT0tKafZ/KykqdPHkyIp99RxF2QsQwDE2ZMkXFxcV644031K9fP6/z/fr1U1pamtatW+c5duLECW3atEnDhg2TJA0ePFhdunTxuubQoUPatWuX55of/vCHqqqq0jvvvOO5Ztu2baqqqvJcY3ejRo3Shx9+qPfee8/zGjJkiCZOnKj33ntP/fv351mb6NJLL23WRuHTTz/VWWedJYk/22Y6fvy4oqK8/zMeHR3tWXrOsw6MYD7XH/7wh9q1a5cOHTrkuWbt2rWKjY3V4MGDA/pz2kqwZ0TD5Te/+Y2RlJRkbNy40Th06JDndfz4cc81f/7zn42kpCSjuLjY+PDDD43x48e3uLQxPT3dWL9+vVFaWmpcfvnlLS5tvOCCC4y33nrLeOutt4yBAwfaesmoLxqvxjIMnrWZ3nnnHSMmJsZ4+OGHjc8++8x47rnnjPj4eGPp0qWea3je5pg0aZLRp08fz9Lz4uJio2fPnsa0adM81/CsO6ampsZ49913jXfffdeQZMyfP9949913jX379hmGEbzn6l56PmrUKKO0tNRYv369kZ6eztJzPxF2QkRSi6+nn37ac01DQ4Px4IMPGmlpaUZsbKzxox/9yPjwww+93qe2ttaYMmWKkZycbMTFxRljxowx9u/f73XN119/bUycONFISEgwEhISjIkTJxqVlZVB+Cmtq2nY4Vmb65VXXjGys7ON2NhY49xzzzWefPJJr/M8b3NUV1cb+fn5Rt++fY0zzjjD6N+/v3H//fcbdXV1nmt41h1TUlLS4n+jJ02aZBhGcJ/rvn37jGuuucaIi4szkpOTjSlTphjffvttIH9823EYhmGEZkwJAAAg8JizAwAAbI2wAwAAbI2wAwAAbI2wAwAAbI2wAwAAbI2wAwAAbI2wAwAAbI2wAwAAbI2wAwAAbI2wAwAAbI2wAwAAbI2wAwAAbO3/A60xOhoWWYOjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 35000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 40000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "no of iterations: 45000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Random Initialisation\n",
    "m3 = np.random.randn(1)\n",
    "c3 = np.random.randn(1)\n",
    "\n",
    "# Hyperparameters\n",
    "learningrate = 1e-8\n",
    "numiter = 50000\n",
    "\n",
    "for i in range(numiter):\n",
    "    # forward pass\n",
    "    y_hat=forward_pass(P_3,m3,c3)\n",
    "    # Loss\n",
    "   \n",
    "    # Gradient\n",
    "    dm = (1.0/N_3) *  -np.sum(np.multiply(P_3,(Vap_sat_3 - (m3*P_3 +c3))))\n",
    "   \n",
    "    dc = (1.0/N_3) * -np.sum(Vap_sat_3 - (m3*P_3 + c3))\n",
    "    \n",
    "    m3 = m3 -learningrate * dm\n",
    "    c3 = c3 - learningrate * dc\n",
    "    if i%5000==0:\n",
    "        L_3.append(loss(y_hat,Vap_sat_3))\n",
    "        print (\"no of iterations:\",i )\n",
    "        plt.plot(P_3,Vap_sat_3,'go')\n",
    "        plt.plot(P_3,y_hat,'r*')\n",
    "        plt.ylabel('Data')\n",
    "        plt.show()\n",
    "\n",
    "R_3 = r2_score(P_3, y_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "16f503cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-83.81642215] [16536.03531202]\n",
      "[0.2618115] [-0.12297254]\n",
      "[0.00522492] [-0.29444303]\n",
      "-13437.320660242458 -2.8850476929582656 -3.6304132253592973\n"
     ]
    }
   ],
   "source": [
    "print(m1,c1)\n",
    "print(m2,c2)\n",
    "print(m3,c3)\n",
    "print(R_1,R_2,R_3)"
   ]
  }
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