{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Misure di Frequenze e Rappresentazione Grafica dei Dati\n",
    "In questa lezione, inizieremo a vedere dei primi strumenti per riassumere le caratteristiche fondamentali dei dati."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Frequenze Assolute e Relative\n",
    "\n",
    "### Frequenze Assolute\n",
    "Un primo modo di descrivere i dati consiste nel calcolare il numero di volte in cui ciascun valore appare. Queste sono chiamate \"frequenze assolute\". Le frequenze assolute sono in genere calcolate per variabili discrete in cui le osservazioni assumono un numero finito di valori. \n",
    "\n",
    "Siano \n",
    "\n",
    "$$a_1, a_2, \\ldots, a_3$$ \n",
    "\n",
    "i valori che la variabile in considerazione può assumere. \n",
    "\n",
    "Le frequenze assolute $n_i$ sono definite come il numero di volte che $a_i$ appare nel campione. Si noti che:\n",
    "\n",
    "$$\\sum_i n_i = n$$\n",
    "\n",
    "Dove $n$ è il numero totale di elementi nel campione."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Esempi\n",
    "\n",
    "Consideriamo un semplice campione di 10 pazienti per i quali sono stati rilevati dei dati. Consideriamo una variabile `gender` che indica il genere dei pazienti:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    M\n",
       "1    F\n",
       "2    M\n",
       "3    M\n",
       "4    M\n",
       "5    F\n",
       "6    F\n",
       "7    F\n",
       "8    F\n",
       "9    F\n",
       "dtype: object"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "data = pd.Series(['M','F','M','M','M','F','F','F','F','F'])\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I valori univoci in questo semplici esempi saranno due:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    M\n",
       "1    F\n",
       "dtype: object"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(data.unique())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le frequenze assolute del campione in oggetto sono riassunte nella tabella seguente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "F    6\n",
       "M    4\n",
       "dtype: int64"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consideriamo un dataset un po' più complesso, contenente pesi (in libbre), altezze (in pollici) e sesso di diversi soggetti. Il dataset avrà il seguente aspetto:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sex</th>\n",
       "      <th>height</th>\n",
       "      <th>weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>M</td>\n",
       "      <td>74</td>\n",
       "      <td>53.484771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>M</td>\n",
       "      <td>70</td>\n",
       "      <td>38.056472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>F</td>\n",
       "      <td>61</td>\n",
       "      <td>34.970812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>M</td>\n",
       "      <td>68</td>\n",
       "      <td>35.999365</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>F</td>\n",
       "      <td>66</td>\n",
       "      <td>34.559390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4226</th>\n",
       "      <td>F</td>\n",
       "      <td>69</td>\n",
       "      <td>23.862436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4227</th>\n",
       "      <td>M</td>\n",
       "      <td>69</td>\n",
       "      <td>38.262182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4228</th>\n",
       "      <td>F</td>\n",
       "      <td>64</td>\n",
       "      <td>34.970812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4229</th>\n",
       "      <td>F</td>\n",
       "      <td>64</td>\n",
       "      <td>28.388071</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4230</th>\n",
       "      <td>F</td>\n",
       "      <td>61</td>\n",
       "      <td>22.628172</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4231 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sex  height     weight\n",
       "0      M      74  53.484771\n",
       "1      M      70  38.056472\n",
       "2      F      61  34.970812\n",
       "3      M      68  35.999365\n",
       "4      F      66  34.559390\n",
       "...   ..     ...        ...\n",
       "4226   F      69  23.862436\n",
       "4227   M      69  38.262182\n",
       "4228   F      64  34.970812\n",
       "4229   F      64  28.388071\n",
       "4230   F      61  22.628172\n",
       "\n",
       "[4231 rows x 3 columns]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hw=pd.read_csv('http://antoninofurnari.it/downloads/height_weight.csv')\n",
    "hw['height'] = (hw['height']/2.54).astype(int)\n",
    "hw['weight'] = hw['weight']/2.205\n",
    "del hw['BMI']\n",
    "hw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notiamo che i valori delle altezze sono quantizzate. I valori univoci in questo caso saranno i seguenti:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([74, 70, 61, 68, 66, 65, 64, 67, 72, 71, 76, 69, 63, 75, 60, 59, 73])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hw['height'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le frequenze assolute in questo caso saranno le seguenti:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "59     52\n",
       "60    130\n",
       "61    411\n",
       "63    291\n",
       "64    435\n",
       "65    351\n",
       "66    391\n",
       "67    377\n",
       "68    355\n",
       "69    302\n",
       "70    272\n",
       "71    235\n",
       "72    260\n",
       "73    146\n",
       "74    104\n",
       "75     72\n",
       "76     47\n",
       "Name: height, dtype: int64"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hw['height'].value_counts().sort_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Diagramma a Barre delle Frequenze Assolute\n",
    "Le frequenze dei dati possono essere rappresentate graficamente mediante un diagramma a barre che pone sull'asse delle $x$ il valore univoco ($a_i$) e che rappresenta la frequenza assoluta $n_i$ come altezza della barra. \n",
    "\n",
    "##### Esempi\n",
    "Nel caso del campione `gender`:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.value_counts().plot.bar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il diagramma a barre delle frequenze assolute delle altezze nel nostro campione di pesi e altezze è il seguente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "hw['height'].value_counts().sort_index().plot.bar(figsize=(18,6))\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il grafico sopra ci dice qualcosa sul numero di occorrenze di un dato valore e ci da anche una idea di quali valori siano più o meno frequenti. Vediamo che i dati seguono una forma \"a campana\". Troveremo spesso questo tipo di forma e ne parleremo meglio in seguito."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Frequenze Relative (Probability Mass Function)\n",
    "Le frequenze assolute ci permettono di farci un'idea più precisa su come i dati sono distribuiti, indipendentemente dalla dimensione del nostro campione. Sappiamo ad esempio che il campione contiene più individui di altezza pari a $167.64\\ cm$ che individui di altezza pari a $193.04\\ cm$. Tuttavia, tale rappresentazione è legata al numero totale di elementi contenuti nel campione. Ad esempio, un campione distribuito in maniera simile, ma con più osservazioni, darà luogo a frequenze assolute più grandi. Possiamo ottenere una rappresentazione indipendente rispetto alla dimensione del campione mediante l'analisi delle frequenze relative, definite come seguono:\n",
    "\n",
    "$$f_j = f(a_j) = \\frac{n_j}{n}, j=1,2,\\ldots,k$$\n",
    "\n",
    "Si noti che, vista la definizione, si avrà:\n",
    "\n",
    "$$ n_j \\leq n \\Rightarrow f_j \\leq 1\\ \\forall j $$\n",
    "\n",
    "$$ \\sum_j f_j = \\sum_j \\frac{n_j}{n} = \\frac{1}{n}\\sum_j n_j = \\frac{n}{n} = 1$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Esempi\n",
    "Nel caso del nostro piccolo campione `gender` avremo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "F    0.6\n",
       "M    0.4\n",
       "dtype: float64"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nel caso del nostro dataset di altezze, avremo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "59    0.012290\n",
       "60    0.030726\n",
       "61    0.097140\n",
       "63    0.068778\n",
       "64    0.102813\n",
       "65    0.082959\n",
       "66    0.092413\n",
       "67    0.089104\n",
       "68    0.083905\n",
       "69    0.071378\n",
       "70    0.064287\n",
       "71    0.055542\n",
       "72    0.061451\n",
       "73    0.034507\n",
       "74    0.024580\n",
       "75    0.017017\n",
       "76    0.011108\n",
       "Name: height, dtype: float64"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hw['height'].value_counts(normalize=True).sort_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "È possibile verificare che tutti i numeri sono compresi tra zero e uno e che la somma dei valori è pari a 1. \n",
    "\n",
    "Come abbiamo visto, questa rappresentazione è nota anche come **probability mass function (PMF)** e associa ad **ogni valore discreto** presente nel campione una **probabilità**. Possiamo ad esempio dire che la probabilità di trovare un individuo di altezza $67 inches$ (circa $170.18 cm$) è pari a $0.089104$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Diagramma a Barre delle Frequenze Relative\n",
    "Plottando le frequenze relative con un diagramma a barre, otteniamo un grafico molto simile a quello delle frequenze relative, ma con una differente scala sull'asse delle $y$.\n",
    "\n",
    "##### Esempi\n",
    "\n",
    "Nel caso del campione `gender` avremo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD3CAYAAAANMK+RAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAMZklEQVR4nO3df6jd913H8efLm0VUHANzpZIfS9SMEqWDepc6UJxCMW3FbGxgWnH4Y4QIUfxDWP5xf7h/VvqPzmVewgi6fxaE1RnsrflD0AlzknTUsnRmXOJcrpk0rbLROszSvv0jp3B6eu8935uem9u8+3zAhfP9fj895/3H5cmH7z3fNFWFJOnO931bPYAkaTYMuiQ1YdAlqQmDLklNGHRJasKgS1IT27bqg3fs2FF79+7dqo+XpDvSU0899XxVza92bcuCvnfvXi5cuLBVHy9Jd6Qk/7HWNW+5SFITBl2SmjDoktSEQZekJgy6JDUxKOhJDiW5lGQ5yYk11rwvydNJLib5x9mOKUmaZurXFpPMASeB+4EV4HySs1X17NiadwCfBg5V1TeT/OgmzStJWsOQHfpBYLmqLlfVdeAMcHhizSPA41X1TYCqem62Y0qSphnyYNFO4MrY8Qpw38SadwFvS/IPwA8Df1pVn518oyRHgaMAe/bsuZV5b7u9J57Y6hFa+cYnHtrqEaS2huzQs8q5yf/N0TbgZ4CHgF8G/ijJu173H1WdqqqFqlqYn1/1yVVJ0i0askNfAXaPHe8Crq6y5vmqegl4KckXgXcDX5/JlJKkqYbs0M8D+5PsS7IdOAKcnVjzN8DPJ9mW5Ae5eUvma7MdVZK0nqk79Kq6keQ4cA6YA05X1cUkx0bXF6vqa0n+DngGeAX4TFV9dTMHlyS91qB/bbGqloCliXOLE8ePAY/NbjRJ0kb4pKgkNWHQJakJgy5JTRh0SWrCoEtSEwZdkpow6JLUhEGXpCYMuiQ1YdAlqQmDLklNGHRJasKgS1ITBl2SmjDoktSEQZekJgy6JDVh0CWpCYMuSU0YdElqwqBLUhMGXZKaMOiS1IRBl6QmDLokNTEo6EkOJbmUZDnJiVWuvy/Jt5M8Pfr52OxHlSStZ9u0BUnmgJPA/cAKcD7J2ap6dmLpP1XVr2zCjJKkAYbs0A8Cy1V1uaquA2eAw5s7liRpo4YEfSdwZex4ZXRu0nuT/GuSJ5P81EymkyQNNvWWC5BVztXE8VeAd1bVi0keBL4A7H/dGyVHgaMAe/bs2dikkqR1DdmhrwC7x453AVfHF1TVd6rqxdHrJeBtSXZMvlFVnaqqhapamJ+ffwNjS5ImDQn6eWB/kn1JtgNHgLPjC5LclSSj1wdH7/vCrIeVJK1t6i2XqrqR5DhwDpgDTlfVxSTHRtcXgQ8Bv5vkBvBd4EhVTd6WkSRtoiH30F+9jbI0cW5x7PWngE/NdjRJ0kb4pKgkNWHQJakJgy5JTRh0SWrCoEtSEwZdkpow6JLUhEGXpCYMuiQ1YdAlqQmDLklNGHRJasKgS1ITBl2SmjDoktSEQZekJgy6JDVh0CWpCYMuSU0YdElqwqBLUhMGXZKaMOiS1IRBl6QmDLokNWHQJamJQUFPcijJpSTLSU6ss+49SV5O8qHZjShJGmJq0JPMASeBB4ADwMNJDqyx7lHg3KyHlCRNN2SHfhBYrqrLVXUdOAMcXmXd7wGfB56b4XySpIG2DVizE7gydrwC3De+IMlO4APALwHvWeuNkhwFjgLs2bNno7NKGrP3xBNbPUIr3/jEQ1s9whs2ZIeeVc7VxPGfAB+tqpfXe6OqOlVVC1W1MD8/P3BESdIQQ3boK8DuseNdwNWJNQvAmSQAO4AHk9yoqi/MYkhJ0nRDgn4e2J9kH/CfwBHgkfEFVbXv1ddJ/gL4W2MuSbfX1KBX1Y0kx7n57ZU54HRVXUxybHR9cZNnlCQNMGSHTlUtAUsT51YNeVX95hsfS5K0UT4pKklNGHRJasKgS1ITBl2SmjDoktSEQZekJgy6JDVh0CWpCYMuSU0YdElqwqBLUhMGXZKaMOiS1IRBl6QmDLokNWHQJakJgy5JTRh0SWrCoEtSEwZdkpow6JLUhEGXpCYMuiQ1YdAlqQmDLklNDAp6kkNJLiVZTnJileuHkzyT5OkkF5L83OxHlSStZ9u0BUnmgJPA/cAKcD7J2ap6dmzZ3wNnq6qS3AP8FXD3ZgwsSVrdkB36QWC5qi5X1XXgDHB4fEFVvVhVNTr8IaCQJN1WQ4K+E7gydrwyOvcaST6Q5N+AJ4Dfns14kqShhgQ9q5x73Q68qv66qu4G3g98fNU3So6O7rFfuHbt2oYGlSStb0jQV4DdY8e7gKtrLa6qLwI/kWTHKtdOVdVCVS3Mz89veFhJ0tqGBP08sD/JviTbgSPA2fEFSX4ySUav7wW2Ay/MelhJ0tqmfsulqm4kOQ6cA+aA01V1Mcmx0fVF4IPAh5N8D/gu8GtjfySVJN0GU4MOUFVLwNLEucWx148Cj852NEnSRvikqCQ1YdAlqQmDLklNGHRJasKgS1ITBl2SmjDoktSEQZekJgy6JDVh0CWpCYMuSU0YdElqwqBLUhMGXZKaMOiS1IRBl6QmDLokNWHQJakJgy5JTRh0SWrCoEtSEwZdkpow6JLUhEGXpCYMuiQ1YdAlqYlBQU9yKMmlJMtJTqxy/deTPDP6+VKSd89+VEnSeqYGPckccBJ4ADgAPJzkwMSyfwd+oaruAT4OnJr1oJKk9Q3ZoR8ElqvqclVdB84Ah8cXVNWXqup/RodfBnbNdkxJ0jRDgr4TuDJ2vDI6t5bfAZ5c7UKSo0kuJLlw7dq14VNKkqYaEvSscq5WXZj8IjeD/tHVrlfVqapaqKqF+fn54VNKkqbaNmDNCrB77HgXcHVyUZJ7gM8AD1TVC7MZT5I01JAd+nlgf5J9SbYDR4Cz4wuS7AEeB36jqr4++zElSdNM3aFX1Y0kx4FzwBxwuqouJjk2ur4IfAz4EeDTSQBuVNXC5o0tSZo05JYLVbUELE2cWxx7/RHgI7MdTZK0ET4pKklNGHRJasKgS1ITBl2SmjDoktSEQZekJgy6JDVh0CWpCYMuSU0YdElqwqBLUhMGXZKaMOiS1IRBl6QmDLokNWHQJakJgy5JTRh0SWrCoEtSEwZdkpow6JLUhEGXpCYMuiQ1YdAlqQmDLklNDAp6kkNJLiVZTnJilet3J/nnJP+X5A9nP6YkaZpt0xYkmQNOAvcDK8D5JGer6tmxZf8N/D7w/s0YUpI03ZAd+kFguaouV9V14AxweHxBVT1XVeeB723CjJKkAYYEfSdwZex4ZXROkvQmMiToWeVc3cqHJTma5EKSC9euXbuVt5AkrWFI0FeA3WPHu4Crt/JhVXWqqhaqamF+fv5W3kKStIYhQT8P7E+yL8l24AhwdnPHkiRt1NRvuVTVjSTHgXPAHHC6qi4mOTa6vpjkLuAC8HbglSR/AByoqu9s3uiSpHFTgw5QVUvA0sS5xbHX/8XNWzGSpC3ik6KS1IRBl6QmDLokNWHQJakJgy5JTRh0SWrCoEtSEwZdkpow6JLUhEGXpCYMuiQ1YdAlqQmDLklNGHRJasKgS1ITBl2SmjDoktSEQZekJgy6JDVh0CWpCYMuSU0YdElqwqBLUhMGXZKaMOiS1IRBl6QmBgU9yaEkl5IsJzmxyvUk+eTo+jNJ7p39qJKk9UwNepI54CTwAHAAeDjJgYllDwD7Rz9HgT+f8ZySpCmG7NAPAstVdbmqrgNngMMTaw4Dn62bvgy8I8mPzXhWSdI6tg1YsxO4Mna8Atw3YM1O4Fvji5Ic5eYOHuDFJJc2NK3WswN4fquHmCaPbvUE2gL+bs7WO9e6MCToWeVc3cIaquoUcGrAZ2qDklyoqoWtnkOa5O/m7TPklssKsHvseBdw9RbWSJI20ZCgnwf2J9mXZDtwBDg7seYs8OHRt11+Fvh2VX1r8o0kSZtn6i2XqrqR5DhwDpgDTlfVxSTHRtcXgSXgQWAZ+F/gtzZvZK3BW1l6s/J38zZJ1etudUuS7kA+KSpJTRh0SWrCoEtSEwb9DpRkz1bPIOnNxz+K3oGSfKWq7h29/nxVfXCrZ5IAkkx+pfk1qupXb9csb0VDnhTVm8/4k7k/vmVTSK/3Xm7+MyCfA/6F1Z8i1yYx6HemWuO1tNXuAu4HHgYeAZ4APldVF7d0qrcIb7ncgZK8DLzEzd3PD3DzYS5Gx1VVb9+q2aRXJfl+bob9MeCPq+rPtnik9tyh34Gqam6rZ5DWMgr5Q9yM+V7gk8DjWznTW4U7dEkzk+QvgZ8GngTOVNVXt3iktxSDLmlmkrzCzduB8Nq/73g78DYw6JLUhA8WSVITBl2SmjDoktSEQZekJgy6JDXx/9SE9F0gz1jyAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "(data.value_counts(normalize=True).sort_index()).plot.bar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nel caso del campione pesi-altezze, avremo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "(hw['height'].value_counts(normalize=True).sort_index()).plot.bar(figsize=(18,6))\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I diagrammi a barre delle frequenze relative sono utili per confrontare tra di loro campioni diversi. Ad esempio, possiamo considerare le altezze di uomini e donne nel dataset pesi-altezze:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAGAwggcAAABgMIIHAAAAYDCCBwAAAGAwggcAAABgMIIHAAAAYDCCBwAAAGAwggcAAABgMIIHAAAAYDCCBwAAAGAwggcAAABgMIIHAAAAYDCCBwAAAGAwggcAAABgMBMFD1V1TlXtqKqdVXXVMutfVlV/VlW7q+qKSfatqhdV1a1V9Rej7y989uUAAAAAs+SAwUNVHZbkg0nOTfLyJG+pqpcv2eyvk1yeZOsK9r0qye3dfXqS20fzAAAAwByZ5I6HTUl2dveD3f1Ekm1JzhvfoLsf6e47kzy5gn3PS/Lh0fSHk7z54EoAAAAAZlV19zNvUPWPkpzT3e8YzV+U5DXdfdky216TZKG7tx5o36r6m+4+bmzfb3T304ZbVNUlSS5JkvXr179627ZtB1XovFpYWMi6deum3Y1Vcchrefj+wZpeOPKErHvikWT9mYMdY27N03lRy0TUMpvW+vXlC1/79r7p45+3N4/tHuaxVi878ZhB2h2nlpVTy8rMUy3j1vrn2Di1zKZ5qmU1bNmy5e7u3rjcusMn2L+WWfbMacXq7Lu4cfcNSW5Iko0bN/bmzZtXsvvc2759e+blz+SQ17L10sGa3r7h8mx+6Lrkgh2DHWNuzdN5UctE1DKb1vr15cprb9s3ffFLH8+NXzx6kOPcceHmQdodp5aVU8vKzFMt49b659g4tcymeaplaJPEmbuSbBibPyXJVyZs/5n2fbiqTkqS0fdHJmwTAAAAWCMmCR7uTHJ6VZ1WVUcmuTDJTRO2/0z73pTkbaPptyX5vcm7DQAAAKwFBxxq0d17quqyJJ9McliSG7v7/qp652j99VV1YpK7krwgyd6q+sUkL+/uby2376jp9yb5WFW9PclfJTl/lWsDAAAApmySZzyku29JcsuSZdePTX8ti8MoJtp3tPyxJK9bSWcBAACAtWWYR9YCAAAARPAAAAAADEjwAAAAAAxG8AAAAAAMRvAAAAAADGait1oAADNo6xnDtb3h8mTrpckVO4Y7BgDwnOCOBwAAAGAwggcAAABgMIIHAAAAYDCCBwAAAGAwggcAAABgMIIHAAAAYDCCBwAAAGAwggcAAABgMIIHAAAAYDCCBwAAAGAwggcAAABgMIIHAAAAYDCCBwAAAGAwggcAAABgMIIHAAAAYDCCBwAAAGAwh0+7AwDAbHh0Yfe+6T179+bRhd1507W3rfpx7rj67FVvEwCYXe54AAAAAAYjeAAAAAAGI3gAAAAABiN4AAAAAAYjeAAAAAAGI3gAAAAABiN4AAAAAAYjeAAAAAAGI3gAAAAABiN4AAAAAAYjeAAAAAAGM1HwUFXnVNWOqtpZVVcts76q6rrR+nur6lWj5WdU1T1jX9+qql8crbumqr48tu6Nq1oZAAAAMHWHH2iDqjosyQeTvD7JriR3VtVN3f35sc3OTXL66Os1SX4tyWu6e0eSs8ba+XKSj4/t94Hu3roKdQAAAAAzaJI7HjYl2dndD3b3E0m2JTlvyTbnJfmtXvTpJMdV1UlLtnldki92918+614DAAAAa8IB73hIcnKSh8bmd2XxroYDbXNykq+OLbswyUeX7HdZVb01yV1J3t3d35ik0wAAAEttuva2fdMXv/TxXDk2v5ruuPrsQdqFeVXd/cwbVJ2f5A3d/Y7R/EVJNnX3u8a2uTnJe7r7U6P525Nc2d13j+aPTPKVJGd298OjZeuTfD1JJ/mVJCd198XLHP+SJJckyfr161+9bdu2Z1fxnFlYWMi6deum3Y1Vcchrefj+wZpeOPKErHvikWT9mYMdY27N03lRy0TU8iysci179u7dN/3489bn6N0PZ2eduqrHSJKXnXjMqre51Be+9u1908c/b28e2z3M87TVsjJqWTm1rMw81TLOv/ln0zzVshq2bNlyd3dvXG7dJHc87EqyYWz+lCyGCCvZ5twkn3kqdEiS8emq+o0kf7Dcwbv7hiQ3JMnGjRt78+bNE3T5uWP79u2Zlz+TQ17L1ksHa3r7hsuz+aHrkgt2DHaMuTVP50UtE1HLs7DKtTy6sHvf9GfPeHdeseP9+eUjPrSqx0iSOy7cvOptLnXlkt963vjFowc5jlpWRi0rp5aVmadaxvk3/2yap1qGNkkEeGeS06vqtNGdCxcmuWnJNjcleevo7RavTfLN7h4fZvGWLBlmseQZED+b5L4V9x4AAACYaQe846G791TVZUk+meSwJDd29/1V9c7R+uuT3JLkjUl2Jvlukp97av+q+uEsvhFj6a9l3ldVZ2VxqMWXllkPAAAArHGTDLVId9+SxXBhfNn1Y9Od5Of3s+93kxy/zPKLVtRTAAAAYM0Z5mkrAAAAABE8AAAAAAMSPAAAAACDETwAAAAAgxE8AAAAAIMRPAAAAACDETwAAAAAgxE8AAAAAIMRPAAAAACDETwAAAAAgxE8AAAAAIMRPAAAAACDETwAAAAAgzl82h0AgLXs0YXd+6b37N2bRxd2503X3rbqx7nj6rNXvU0AgEPBHQ8AAADAYAQPAAAAwGAEDwAAAMBgBA8AAADAYAQPAAAAwGC81QIAmL6tZ6xqczc/+f23jXy2352bn3x/3nTEh1b1GADAZNzxAAAAAAxG8AAAAAAMRvAAAAAADEbwAAAAAAxG8AAAAAAMRvAAAAAADMbrNFmZVX7d2Q/YcHmy9dLkih3DHQMAAIBDyh0PAAAAwGAEDwAAAMBgBA8AAADAYAQPAAAAwGAEDwAAAMBgvNUCAABgxmy69rZ90xe/9PFcOTa/mu64+uxB2oVx7ngAAAAABjNR8FBV51TVjqraWVVXLbO+quq60fp7q+pVY+u+VFWfq6p7ququseUvqqpbq+ovRt9fuDolAQAAALPigMFDVR2W5INJzk3y8iRvqaqXL9ns3CSnj74uSfJrS9Zv6e6zunvj2LKrktze3acnuX00DwAAAMyRSe542JRkZ3c/2N1PJNmW5Lwl25yX5Ld60aeTHFdVJx2g3fOSfHg0/eEkb5682wAAAMBaMEnwcHKSh8bmd42WTbpNJ/nDqrq7qi4Z22Z9d381SUbfT1hJxwEAAIDZV939zBtUnZ/kDd39jtH8RUk2dfe7xra5Ocl7uvtTo/nbk1zZ3XdX1Y9091eq6oQktyZ5V3f/SVX9TXcfN9bGN7r7ac95GIUVlyTJ+vXrX71t27ZnWfJ8WVhYyLp16w7dAR++f7CmF448IeueeCRZf+Zgx/gB81TLPJmn86KWiaz1Wvbs3btv+vHnrc/Rux/Ozjp1VY+RJC878ZinL1TLfk21llX2ha99e9/08c/bm8d2D/NscLWsjFpWTi0rM0+1jDvk/38Z0DzVshq2bNly95LHK+wzyes0dyXZMDZ/SpKvTLpNdz/1/ZGq+ngWh278SZKHq+qk7v7qaFjGI8sdvLtvSHJDkmzcuLE3b948QZefO7Zv355D+mey9dLBmt6+4fJsfui65IIdgx3jB8xTLfNkns6LWiay1mt5dGH3vunPnvHuvGLH+/PLR3xoVY+RJHdcuPnpC9WyX1OtZZVdueSVejd+8ehBjqOWlVHLyqllZeaplnGH/P8vA5qnWoY2SWx2Z5LTq+q0qjoyyYVJblqyzU1J3jp6u8Vrk3xzFCg8v6qOSZKqen6Sn0py39g+bxtNvy3J7z3LWgAAAIAZc8A7Hrp7T1VdluSTSQ5LcmN3319V7xytvz7JLUnemGRnku8m+bnR7uuTfLyqnjrWR7r7E6N1703ysap6e5K/SnL+qlUFAAAAzIRJhlqku2/JYrgwvuz6selO8vPL7Pdgklfsp83HkrxuJZ0FAAAA1pZhnlACAAAAEMEDAAAAMCDBAwAAADAYwQMAAAAwGMEDAAAAMBjBAwAAADAYwQMAAAAwGMEDAAAAMBjBAwAAADAYwQMAAAAwGMEDAAAAMBjBAwAAADAYwQMAAAAwGMEDAAAAMBjBAwAAADAYwQMAAAAwGMEDAAAAMJjDp90BAAAA5tema2/bN33xSx/PlWPzq+mOq88epF2ePXc8AAAAAINxxwMAh9yjC7v3Te/ZuzePLuzOmwb47YfffDAVW89Y1eZufvL7Py+f7Xfn5iffnzcd8aFVPQYADMkdDwAAAMBgBA8AAADAYAQPAAAAwGAEDwAAAMBgBA8AAADAYAQPAAAAwGAEDwAAAMBgBA8AAADAYAQPAAAAwGAEDwAAAMBgBA8AAADAYAQPAAAAwGAEDwAAAMBgBA8AAADAYCYKHqrqnKraUVU7q+qqZdZXVV03Wn9vVb1qtHxDVf1RVT1QVfdX1S+M7XNNVX25qu4Zfb1x9coCAAAAZsHhB9qgqg5L8sEkr0+yK8mdVXVTd39+bLNzk5w++npNkl8bfd+T5N3d/ZmqOibJ3VV169i+H+juratXDgAAADBLJrnjYVOSnd39YHc/kWRbkvOWbHNekt/qRZ9OclxVndTdX+3uzyRJd387yQNJTl7F/gMAAAAzbJLg4eQkD43N78rTw4MDblNVpyZ5ZZI/H1t82Whoxo1V9cJJOw0AAACsDdXdz7xB1flJ3tDd7xjNX5RkU3e/a2ybm5O8p7s/NZq/PcmV3X33aH5dkj9Ocm13/85o2fokX0/SSX4lyUndffEyx78kySVJsn79+ldv27bt2VU8ZxYWFrJu3bpDd8CH7x+s6YUjT8i6Jx5J1p852DF+wDzVMk/m6byoZb/27N27b/rx563P0bsfzs46dVWPkSQvO/GYpy9Uy36pZeXmvpZV9oWvfXvf9PHP25vHdg/znHO1rIxaVk4tKzNPtYw75P8Xm3Fbtmy5u7s3LrdukuDhv0hyTXe/YTT/z5Kku98zts2vJ9ne3R8dze9Isrm7v1pVRyT5gySf7O5/s59jnJrkD7r77z5TXzZu3Nh33XXXM/b3uWb79u3ZvHnzoTvg1jMGa3r7hsuz+aHrkit2DHaMHzBPtcyTeTovatmvRxd275v+7Bnvzit2vD9vOuJDq3qMJLnj6rOfvlAt+6WWlZv7WlbZpmtv2zd98Usfz41fPHqQ46hlZdSycmpZGbWs3KGoZbVV1X6Dh0mipjuTnF5Vp1XVkUkuTHLTkm1uSvLW0dstXpvkm6PQoZL8ZpIHloYOVXXS2OzPJrlvwnoAAACANeKAb7Xo7j1VdVmSTyY5LMmN3X1/Vb1ztP76JLckeWOSnUm+m+TnRrv/V0kuSvK5qrpntOyXu/uWJO+rqrOyONTiS0kuXaWaAObS+G899+zdm0cXdudNY6n7almLCTsAALPrgMFDkoyCgluWLLt+bLqT/Pwy+30qSe2nzYtW1NO1bMDbrbPh8mTrpW7pBwAAYCYN81QPAAAAgAgeAAAAgAEJHgAAAIDBTPSMBwAAnoNW+TlVNz859mrQfndufnKYV4MCMFvc8QAAAAAMRvAAAAAADEbwAAAAAAxG8AAAAAAMRvAAAAAADEbwAAAAAAxG8AAAAAAMRvAAAAAADEbwAAAAAAxG8AAAAAAMRvAAAAAADEbwAAAAAAxG8AAAAAAMRvAAAAAADEbwAAAAAAxG8AAAAAAMRvAAAAAADEbwAAAAAAxG8AAAAAAM5vBpdwBgSI8u7N43vWfv3jy6sDtvuva2VT/OHVefveptAgDAPHDHAwAAADAYwQMAAAAwGMEDAAAAMBjBAwAAADAYwQMAAAAwGMEDAAAAMBjBAwAAADAYwQMAAAAwGMEDAAAAMBjBAwAAADCYiYKHqjqnqnZU1c6qumqZ9VVV143W31tVrzrQvlX1oqq6tar+YvT9hatTEgAAADArDhg8VNVhST6Y5NwkL0/ylqp6+ZLNzk1y+ujrkiS/NsG+VyW5vbtPT3L7aB4AAACYI5Pc8bApyc7ufrC7n0iyLcl5S7Y5L8lv9aJPJzmuqk46wL7nJfnwaPrDSd787EoBAAAAZs0kwcPJSR4am981WjbJNs+07/ru/mqSjL6fMHm3AQAAgLWguvuZN6g6P8kbuvsdo/mLkmzq7neNbXNzkvd096dG87cnuTLJ39nfvlX1N9193Fgb3+jupz3noaouyeLwjSQ5I8mOgy12Tr04yden3YlVohaGNk/nRS2zSS2zSS2zSS2zSS2zSS2zaZ5qWQ0/2t0vWW7F4RPsvCvJhrH5U5J8ZcJtjnyGfR+uqpO6+6ujYRmPLHfw7r4hyQ0T9PM5qaru6u6N0+7HalALQ5un86KW2aSW2aSW2aSW2aSW2aSW2TRPtQxtkqEWdyY5vapOq6ojk1yY5KYl29yU5K2jt1u8Nsk3R8Mnnmnfm5K8bTT9tiS/9yxrAQAAAGbMAe946O49VXVZkk8mOSzJjd19f1W9c7T++iS3JHljkp1Jvpvk555p31HT703ysap6e5K/SnL+qlYGAAAATN0kQy3S3bdkMVwYX3b92HQn+flJ9x0tfyzJ61bSWZY1T8NQ1MLQ5um8qGU2qWU2qWU2qWU2qWU2qWU2zVMtgzrgwyUBAAAADtYkz3gAAAAAOCiCBwAAAGAwggcAAABgMIIHgDWmqk6Ydh94uqo6ftp9AGA+ufbPJtf+yQke1oiqWldV/7Kq7q+qb1bVo1X16ar6J9Pu20pV1bFV9d6q+kJVPTb6emC07Lhp92+1VNX/Ne0+PFdV1YlV9WtV9cGqOr6qrqmqz1XVx6rqpGn3byWq6kVLvo5PckdVvbCqXjTt/q1EVZ0zNn1sVf1mVd1bVR+pqvXT7NtKjT6vXjya3lhVDyb586r6y6r6r6fcvRWpqs9U1T+vqpdOuy/P1uhc/FFV/R9VtaGqbh1dM++sqldOu38r4bq/9qzF635VvaCq3lNV/3tV/bdL1v3qtPp1MFz7Z5NrP08RPKwd/yHJg0nekORfJLkuyUVJtlTVv5pmxw7Cx5J8I8nm7j6+u49PsmW07D9OtWcrVFWv2s/Xq5OcNe3+PYf9+ySfT/JQkj9K8niSNyX50yTX73+3mfT1JHePfd2V5OQknxlNryXjn1XvT/LVJP8gyZ1Jfn0qPTp4b+rur4+m/+ckF3T3jyV5fRZrW0temOS4JH9UVXdU1X9XVT8y5T4drF9N8r4kNyf5f5L8encfm+Sq0bq1xHV/Bs3hdf/fJakkv53kwqr67ap63mjda6fXrYPy7+PaP4tc+0nidZprRlV9trtfMTZ/Z3f/51X1Q0k+390vm2L3VqSqdnT3GStdN4uq6m+T/HEWL9pLvba7jz7EXSJJVf2/3f3K0fRfdfd/Nrbunu4+a2qdW6GquiLJ2Un+h+7+3GjZf+ru06bbs5Wrqs9096tG0z9wHtbgeflCkr/b3Xuq6tPd/dqxdZ/r7p+YYvdWZMl5+ftJ3pLkHyZ5IMlHu3vNvKP8AD/7+9atBa77s2nervvLfBZfneSNSX4mya1PfTasBa79s8m1n6ccPu0OMLHvVNXf6+5PVdU/SPLXSdLde6tquYvfLPvLqroyyYe7++EkGd1q9U+ymFKvJQ8kubS7/2Lpiqpaa7XMk/G7uX7rGdbNvO7eWlXbknxg9Hfqf0yyVhPjE6rqv8/iP9hfUFXV30+/19R5SfLBJLdU1XuTfKKq/pckv5PkdUnumWK/Dsa+a0h3/2mSP62qd2XxNzgXJFkzwUOS71XVTyU5NklX1Zu7+3dHt8D+7ZT7tlKu+7Np3q77z6uqH+ruvUnS3ddW1a4kf5Jk3XS7tmKu/bPJtZ8kgoe15J8m+Y2q+vEk9yW5OEmq6iVZ/CFYSy7I4m2vfzz6h0cneTjJTUn+8TQ7dhCuyf4/NN91CPvBD/q9qlrX3Qvd/c+fWlhVP5bk/5tivw5Kd+9Kcv7oPx+3JvnhKXfpYP1GkmNG0x9O8uIkj1bViVljF+zu/rdV9bksfjb/eBavpz+e5HeT/E9T7NrB2LF0QXf/bZJPjL7WkndmcajF3iwOUfinVfXvknwlySXT7NhBeGeSD7nuz5xrMl/X/d9P8t8kue2pBd394ap6OMm/nVqvDo5r/2yat2v/fVn8fF7r1/5DTvCwRnT3Z5Nsemq+qv5eVf10kvu6+7rp9eyg/HiSf9Xdv1RVP5zFf4w8dSvfWvuN1ENZHKuWqjo6yT9L8sosjjFca2Nw58nNGf3DcHRenvo79vkkb59iv1asql6T5IHu/laS25P8/SQLVfWvs/hz9M2pdnBlPpHkC939zad+9mvxgX+fzxr7B/vovHymuy9Y8jn20iz+43AtnZcPVNULuvtby32OrbG/Y0cl+cejv2NHZ/E8/N9J7s/if97XkqOTvH7s5+WXquqpz7G1dn25KMn/1t2/NO2OrIIfSfLny63o7t89tF1ZFbuyfPj4iSSnH/ruPCtfz+IzaxbGF3b3ziT/aCo9OkhVdXmSj3f3Q939+1V1WxavL2vRNzKqZXxhd38tyVun06WDM3ZeLph2X9Yiz3hYI6rqju7eNJp+R5LLknw8yU8l+f3ufu80+7cSVXV/kleMxkfdkOQ7WXyo0etGy//hVDu4AsvU8t0k/2fWYC3zZJ7Oi5+X2eS8zCbnZTZV1TezeC6+mOQjSf5jf/8BbWvKklo+msVaHp1urw7ePNUz57V8zM/M9M3TZ9k0uONh7ThibPrSLP4W5NGq2prk00nWTPCQ5Ie6e89oeuPYg4s+VVX3TKlPB2ueapkn83Re1DKb1DKb1DKbHkzy6iw+LO+CJP+yqu7O4n9Cfqe7vz3Nzq3Q0lr+xRquJZmvetQym+a5lrX8WXbIrbUHejyX/VAtvrv3+CzeqfJoknT3d5LseeZdZ859VfVzo+nPVtXGJBmNY31yet06KPNUyzyZp/OiltmkltmkltnU3b23u/+wu9+exeEKv5rknCz+Q34tmadakvmqRy2zSS0kMdRizaiqL2XxYVmVxYcy/Zfd/bWqWpfkU722XkVzbJL/NYtj1b+exXHRD42+Lh89z2JNmKda5sk8nRe1zCa1zCa1zKZ6hleZVtXR3f34oe7TwZqnWpL5qkcts0ktPEXwsMaNHji1vrv/07T7slJVdUySv5PFIT+7evSKrbVonmqZJ/N0XtQym9Qym9QyW6rqx7t7zb1VYDnzVEsyX/WoZTaphacIHgAAAIDBeMYDAAAAMBjBAwAAADAYwQMAAAAwGMEDAAAAMBjBAwAAADCY/x8N0tp3/qdGdwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_height_m = hw[hw['sex']=='M']['height'].value_counts(normalize=True).sort_index()\n",
    "pmf_height_f = hw[hw['sex']=='F']['height'].value_counts(normalize=True).sort_index()\n",
    "\n",
    "plt.figure(figsize=(18,6))\n",
    "#sommiamo e sottraiamo 0.2 agli indici per \"spostare\" le barre e renderle\n",
    "#visibili quando sovrappose. Inoltre impostiamo alpha=0.9 per rendere le barre\n",
    "#parzialmente trasparenti\n",
    "plt.bar(pmf_height_m.index+0.2, pmf_height_m.values, width=0.5, alpha=0.9)\n",
    "plt.bar(pmf_height_f.index-0.2, pmf_height_f.values, width=0.5, alpha=0.9)\n",
    "plt.xticks(hw['height'].unique(), rotation='vertical')\n",
    "plt.legend(['M','F']) #mostriamo una legenda\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dal confronto sopra, possiamo già fare delle considerazioni qualitative sui due campioni. In particolare notiamo (poco sorprendentemente) che gli uomini sono generalmente più alti delle donne. Ciò non vuol dire che non esistano uomini più bassi di alcune donne o viceversa, ma ragionevolmente si tratta di casi meno frequenti."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Grafici a Torta\n",
    "In alternativa ai grafici a barre, le frequenze relative possono essere visualizzate anche mediante dei grafici a torta.\n",
    "\n",
    "##### Esempi\n",
    "Nel caso del campione `gender`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='None'>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.value_counts(normalize=True).plot.pie()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nel caso del campione pesi-altezze:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(hw['height'].value_counts(normalize=True).sort_index()).plot.pie(figsize=(18,6))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Empirical Cumulative Distribution Function (ECDF)\n",
    "\n",
    "Le frequenze relative funzionano particolarmente bene quando i valori unici sono pochi. Quando invece il numero di valori univoci cresce, le frequenze discrete calcolate per i valori diventano molto piccole e dunque soggette a rumore (ad esempio dovuto ad errori di misura). \n",
    "\n",
    "Torniamo al nostro esempio di dataset di pesi e altezze:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sex</th>\n",
       "      <th>height</th>\n",
       "      <th>weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>M</td>\n",
       "      <td>74</td>\n",
       "      <td>53.484771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>M</td>\n",
       "      <td>70</td>\n",
       "      <td>38.056472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>F</td>\n",
       "      <td>61</td>\n",
       "      <td>34.970812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>M</td>\n",
       "      <td>68</td>\n",
       "      <td>35.999365</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>F</td>\n",
       "      <td>66</td>\n",
       "      <td>34.559390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4226</th>\n",
       "      <td>F</td>\n",
       "      <td>69</td>\n",
       "      <td>23.862436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4227</th>\n",
       "      <td>M</td>\n",
       "      <td>69</td>\n",
       "      <td>38.262182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4228</th>\n",
       "      <td>F</td>\n",
       "      <td>64</td>\n",
       "      <td>34.970812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4229</th>\n",
       "      <td>F</td>\n",
       "      <td>64</td>\n",
       "      <td>28.388071</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4230</th>\n",
       "      <td>F</td>\n",
       "      <td>61</td>\n",
       "      <td>22.628172</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4231 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sex  height     weight\n",
       "0      M      74  53.484771\n",
       "1      M      70  38.056472\n",
       "2      F      61  34.970812\n",
       "3      M      68  35.999365\n",
       "4      F      66  34.559390\n",
       "...   ..     ...        ...\n",
       "4226   F      69  23.862436\n",
       "4227   M      69  38.262182\n",
       "4228   F      64  34.970812\n",
       "4229   F      64  28.388071\n",
       "4230   F      61  22.628172\n",
       "\n",
       "[4231 rows x 3 columns]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I valori dei pesi, a differenza di quelli delle altezze, non sono quantizzati. Un grafico a barre delle frequenze relative (o Probability Mass Function) avrebbe questo aspetto:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist=hw['weight'].value_counts(normalize=True).sort_index()\n",
    "plt.figure(figsize=(18,6))\n",
    "plt.bar(hist.index,hist.values, width=.1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Come possiamo notare, abbiamo ottenuto una rappresentazione grafica più \"rumorosa\". Supponiamo adesso di voler confrontare le distribuzioni dei pesi di donne e uomini:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_weight_m = hw[hw['sex']=='M']['weight'].value_counts(normalize=True).sort_index()\n",
    "pmf_weight_f = hw[hw['sex']=='F']['weight'].value_counts(normalize=True).sort_index()\n",
    "\n",
    "plt.figure(figsize=(18,6))\n",
    "plt.bar(pmf_weight_m.index-0.5, pmf_weight_m.values, width=.1)\n",
    "plt.bar(pmf_weight_f.index+0.5, pmf_weight_f.values, width=.1)\n",
    "plt.legend(['M','F'])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le due rappresentazioni sono affette da rumore dovuto alla natura discreta dei dati per cui due valori molto vicini vengono trattati come due casi distinti nel calcolo delle probabilità. Vedremo alcuni modi per ovviare a questo problema. Uno di essi consiste nel calcolare una **Empirical Cumulative Distribution Function (ECDF)**. Una **ECDF** calcola per un valore $x$ la somma delle frequenze relative di tutti i valori $y$ minori o uguali a $x$:\n",
    "\n",
    "$$ECDF(x) = \\sum_{a_j: a_j\\leq x} f(a_j)$$\n",
    "\n",
    "Dove $a_j$ sono i valori univoci all'interno del campione, mentre in generale $x\\in \\mathbb{R}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consideriamo un semplice dataset di valori numerici:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     1\n",
       "1     5\n",
       "2     2\n",
       "3     6\n",
       "4     5\n",
       "5     4\n",
       "6     3\n",
       "7     5\n",
       "8     4\n",
       "9     2\n",
       "10    4\n",
       "11    5\n",
       "12    6\n",
       "13    4\n",
       "14    4\n",
       "15    3\n",
       "dtype: int64"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=pd.Series([1,5,2,6,5,4,3,5,4,2,4,5,6,4,4,3])\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le frequenze relative saranno le seguenti:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    0.0625\n",
       "2    0.1250\n",
       "3    0.1250\n",
       "4    0.3125\n",
       "5    0.2500\n",
       "6    0.1250\n",
       "dtype: float64"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.value_counts(normalize=True).sort_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La ECDF calcolata sui valori univoci sarà la seguente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    0.0625\n",
       "2    0.1875\n",
       "3    0.3125\n",
       "4    0.6250\n",
       "5    0.8750\n",
       "6    1.0000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.value_counts(normalize=True).sort_index().cumsum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Da notare che i valori della ECDF sono sempre crescenti e l'ultimo valore è pari a 1 (la somma di tutte le frequenze relative).\n",
    "\n",
    "Una ECDF può essere rappresentata graficamente mettendo i valori di $x$ sulle ascisse e i valori di $ECDF(x)$ sulle ordinate. Ad esempio, la ECDF dei pesi nel nostro dataset di pesi-altezze sarà la seguente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6hiRJXo/R4vI8LSzL07qFpSrLz9K1S8pY+QFAwiEIAwAcG4tEdetXf6PuQOj0vpwMr65aVKoPrp+vdQtLtaQiX9kZXherBABnCMIAAMdeP9Gn7kBIf37LMl2zuEwF2T7VlOQoy0fwBZB8CMIAAMeeaTilTK9HH7p6gfKy+BUCILmxagQAwLFnDnbqqsWzCMEAUgJBGADgyNGugI53D+nGFRVulwIAcUEQBgA48kzDKUnSDcsJwgBSA0EYAODI0w2dWj67QDUluW6XAgBxQRAGAJxT/3BIO0726aaVlW6XAgBxQxAGAJxT/aEuRaJWW1YQhAGkDoIwAOCcnm44pfKCLK2uLnK7FACIG9a/AQC8zUgoojea+7WzqU+vn+jVS409evfl1fJ4jNulAUDcOArCxphbJH1VklfSI9baByc9XyTp3yXNi73m31trvxPnWgEAcRaNWh065dfJnmG19o+oqWdIu5r7daBtUOGolSTVVuTrPVdU6zM3LXW5WgCIr3MGYWOMV9LXJd0kqUXSdmPM49baAxMO+yNJB6y1txtjyiUdMsb8wFobmuIlAQAue6O5X7/Y3aYn97arfWD09P7cTK8urS7Sx69fpLr5pbp8XrGKczNdrBQApo+TM8LrJDVaa49JkjFmq6Q7JE0MwlZSgTHGSMqX1CspHOdaAQBx8B/bm/TZn+5VptejjUvL9T/fsUzLKgtUXZKjktwMjb+VA0DqcxKEqyU1T9hukbR+0jH/IulxSW2SCiS931objUuFAIC4aekb1t/94oCuWTxLD927VoXZGW6XBACuMdbasx9gzF2SbrbWfjS2fa+kddbaP55wzJ2SrpX0GUmLJf1a0hpr7eCk17pf0v2SVFlZuXbr1q1x/FHGBQIB5efnx/11UxG9co5eOUOfnHOjV9Za/f3rozraH9X/2ZCjspzkWDiIceUMfXKOXjmXKr3avHnzDmtt3eT9Ts4It0iaO2G7RuNnfie6T9KDdjxVNxpjjktaLum1iQdZax+W9LAk1dXV2U2bNjn+AZyqr6/XdLxuKqJXztErZ+iTc2706gevntT+nn36v+9epTvXz5/R730xGFfO0Cfn6JVzqd4rJ0F4u6RaY8xCSa2S7pZ0z6RjmiRtkfSCMaZS0jJJx+JZKADg/ESiVi19wzrWNaSjXQH9068Pa8OSMt2zbp7bpQFAQjhnELbWho0xD0h6SuPLp33bWrvfGPOJ2PMPSfqCpO8aY/ZKMpI+a63tnsa6AQAT9A+HtLtlQG809etA+4COdQ3pZM+wQpHfXq4xrzRXD773Ui6GA4AYR+sIW2uflPTkpH0PTXjcJukd8S0NAHAmLzV260evNam1f0QtfSPq8gclScZIC2flaXFFvm5YUaHFZflaVJ6nReX5Ks1jGTQAmIg7ywFAEvrq00d0oH1Qq2uKtGlpuRaU5enyucVaVVPEShAA4BBBGACSTDRqtb9tQHeurdHf3rHK7XIAIGklx9o5AIDTTvQMaSgU0SXVRW6XAgBJjSAMAElmX9v4Eu2r5hCEAeBiEIQBIMnsbx1Qptej2srkX+QeANxEEAaAJLOvbUDLqwqU4eUtHAAuBu+iAJBErLXa1zqoS5gWAQAXjSAMAEmkpW9EAyNjWlVd6HYpAJD0CMIAkET2tw1I4kI5AIgHgjAAJJF9rYPyeoyWzS5wuxQASHoEYQBIIvvaBlRbka/sDK/bpQBA0iMIA0CSGL9QbkCruJEGAMQFQRgAkkSnP6juQEir5nChHADEA0EYAJLEvtbYhXKcEQaAuCAIA0CS2Nc6KGOkFVWcEQaAePC5XQAAYGrWWm0/0aftJ3p1rGtILxzp0qKyPOVl8dYNAPHAuykAJBhrrZ4/3KWvPduoHSf7JEmzC7O1uDxfd6+b63J1AJA6CMIA4LI3z/zubOpTQ/ug9rYM6Fj3kOYUZevv7rhE7768WgXZGW6XCQAphyAMAC4ZCob16M4WfW/bSTV2BiRJc4qytbyqUB/buEjvvaJGmT4u5QCA6UIQBgAXDI9ZbfmH59UxOKpLq4v093et0Y0rKlScm+l2aQCQNgjCAOCCl1rD6hgM6ZHfr9OWFRUyxrhdEgCkHYIwAMywaNTqmaYxXTa3WDeurHS7HABIW0w+A4AZ9tLRbnUMW33omvlulwIAaY0gDAAz7PvbTqogU3rnpVVulwIAaY0gDAAzqLl3WM80nNL1NRnK8nndLgcA0hpBGABm0A9ebZIkbZ7LJRoA4DbeiQFgBjT1DOs3R7q0dXuT3rFytmbl+N0uCQDSHkEYAOIsGrXa2zqgXU19eqO5Xzub+tXUOyxJmluao09uqVXn4Z0uVwkAIAgDQBz4R8fU0O7Xk3vb9ct97To1GJQkVRRk6bK5xfrItQu0cWm5FpblyRijzsMuFwwAIAgDwIXa09Kvzz+2V009wxocDUuSMn0ebV5WrltXVWndwlJVFWVzswwASFAEYQC4QE/sadehDr/uvnKeqktytGBWrjbUlis/i7dWAEgGvFsDwAXa2zKgFVWF+sLvrnK7FADABWD5NAC4ANZa7Wsb0KrqIrdLAQBcIIIwAFyAkz3D8o+GdSlBGACSFkEYAC7A3tYBSSIIA0ASIwgDwAXY1zagTK9HSysL3C4FAHCBCMIAcAH2tQ5o2ewCZfp4GwWAZMU7OACcJ2ut9rUOcqEcACQ5gjAAnKfm3hENjIwxPxgAkhxBGADO05sXyq2qLnS5EgDAxSAIA8B52ts6oAyv0bLZXCgHAMmMIAwA52lf64CWVhYoy+d1uxQAwEUgCAPAeXjzjnLMDwaA5EcQBoDz0NI3ov7hMVaMAIAUQBAGgPOwu6VfEneUA4BU4HO7AABIdJGo1YuN3frRq016uuGUinMzuFAOAFIAQRgApnD4lF/PHuzUq8d69PqJPvmDYZXmZeojGxbq99bPU3YGF8oBQLIjCANATE8gqMd2teqxXa3a3zYoSVpSka/bL5ujDUvKtGVFBStFAEAKIQgDSHvDobC+9cJxPfT8UQ2FIlpTU6S/uX2l3rm6ShUF2W6XBwCYJgRhAGnt6QOn9Jc/26tTg0Hdcsls/clNS5n/CwBpgiAMIG1Za/X5x/aqMCdDX7/nCtUtKHW7JADADGL5NABp6/CpgDr9Qd1/3SJCMACkIYIwgLT1wpEuSdKG2jKXKwEAuIEgDCBt/eZIt5ZU5GtOcY7bpQAAXEAQBpCWRscievVYjzYs4WwwAKQrgjCAtPT6iT4Fw1FtXEoQBoB0RRAGkJZeONKlDK/R+oWz3C4FAOASgjCAtPSbI91aO79EeVmsIgkA6YogDCDtdPmDamgf1HW15W6XAgBwEUEYQNp5qbFbkrSRIAwAaY0gDCCtRKJWTzecUkluhi6ZU+h2OQAAFzE5DkDKGwlF9Kv97XqmoVMvNXarb3hMd62tkcdj3C4NAOAigjCAlGSt1f62Qf349WY9tqtV/tGwKguztGVFpa6rLdPNl8x2u0QAgMsIwgCSXiRq1TsUUncgqLb+Eb1wpFu/PnBKrf0jyvR5dNulVfrAunm6ckGJjOEsMABgHEEYQFLr8ge15R/qNTgaPr0vO8OjDUvK9cktS3TzJbNVnJvpYoUAgERFEAaQ1Pa09GtwNKz/sWmxVlUXqbwgS6vmFCkn0+t2aQCABEcQBpDUGjsDkqSPb1ysotwMl6sBACQTlk8DkNQaOwMqL8giBAMAzhtBGEBSa+wKaEl5vttlAACSEEEYQNKy1qqxM6AlFQRhAMD5IwgDSFpd/qD8o2GCMADggjgKwsaYW4wxh4wxjcaYz53hmE3GmDeMMfuNMc/Ht0wAeLsjsQvlCMIAgAtxzlUjjDFeSV+XdJOkFknbjTGPW2sPTDimWNI3JN1irW0yxlRMU70AcFojQRgAcBGcnBFeJ6nRWnvMWhuStFXSHZOOuUfSo9baJkmy1nbGt0wAeLvGzoAKsnyqKMhyuxQAQBIy1tqzH2DMnRo/0/vR2Pa9ktZbax+YcMxXJGVIukRSgaSvWmu/P8Vr3S/pfkmqrKxcu3Xr1jj9GL8VCASUn8/ZISfolXP0ypmZ7tMXXxtRMCL91dU5M/Y944Ux5Ry9coY+OUevnEuVXm3evHmHtbZu8n4nN9QwU+ybnJ59ktZK2iIpR9I2Y8wr1trDb/kiax+W9LAk1dXV2U2bNjn49uenvr5e0/G6qYheOUevnJnpPv3ZS09r09Jybdq0Zsa+Z7wwppyjV87QJ+folXOp3isnQbhF0twJ2zWS2qY4pttaOyRpyBjzG0lrJB0WAEyDgeExdfmDzA8GAFwwJ3OEt0uqNcYsNMZkSrpb0uOTjvm5pOuMMT5jTK6k9ZIa4lsqAPxWY5dfEhfKAQAu3DnPCFtrw8aYByQ9Jckr6dvW2v3GmE/Enn/IWttgjPmVpD2SopIesdbum87CAaQ3VowAAFwsJ1MjZK19UtKTk/Y9NGn7y5K+HL/SAODMGjsDyvR5VFOS63YpAIAkxZ3lACSlxs6AFpXlyeuZ6npeAADOjSAMICk1dgWYFgEAuCgEYQBJZyQUUUvfiGorCtwuBQCQxBzNEQYAtwWCYT22s0WHTwV0qMMva7lQDgBwcQjCABLevtYBPfDDnTrRM6yCLJ8WlefpfXU12lBb5nZpAIAkRhAGkLDGIlF9f9tJPfjLBs3Ky9KPPnaVrlpUKmO4QA4AcPEIwgASSvvAiH66o0WvHu/VjpN9Gg5FdNPKSn3pvatVkpfpdnkAgBRCEAaQEEbHInr4N8f0zfqjGhmLaPnsAt21tkYbast144oKzgIDAOKOIAzAdftaB/Txf9uh1v4R3XZplT5363LNLeVGGQCA6UUQBuC6h54/qqFQWD/62FW6evEst8sBAKQJ1hEG4CprrV451qtNS8sJwQCAGUUQBuCqxs6AugNBXbOYpdAAADOLIAzAVS8f7ZEkzgYDAGYcQRiAq7Yd7VF1cQ4XxwEAZhxBGIBrolGrV473cDYYAOAKgjAA1xzs8Kt/eExXLyIIAwBmHkEYgGu2HWN+MADAPQRhAK7ZdrRH82flak5xjtulAADSEEEYgCsiUatXj/cwLQIA4BqCMABXHGgblH80zLQIAIBrCMIAZpx/dEw/2dEsSZwRBgC4xud2AQBSXzgS1eFTAb3R3K/nDnXq+cNdCoWj2ri0XBWF2W6XBwBIUwRhANMmGI7or362X4/vbtPIWESSNLswWx9cP1+3ra7S5XOL3S0QAJDWCMIApsVQMKyP/9sOvdjYrffXzdU1S2bpsrnFmleaK2OM2+UBAEAQBhB/vUMh3fed17SvbVBfunO13lc31+2SAAB4G4IwgLj405/s1rP7hxV67ikFgmFl+Tx66INrddPKSrdLAwBgSgRhABdtOBTWT3e2aFGhR9evmquCbJ9uWlmpVdVFbpcGAMAZEYQBXLSDHX5ZK922KEOfuX2l2+UAAOAI6wgDuGgH2gYlSfMKeUsBACQPfmsBuGgH2gdVmO3TrGxWgwAAJA+CMICL1tA+qBVVhSyLBgBIKgRhABclErU62O7XyjmFbpcCAMB5IQgDuCgneoY0MhbRyiqCMAAguRCEAVyUNy+UW0EQBgAkGYIwgIvS0D4on8eotjLf7VIAADgvBGEAF+VA+6CWVOQry+d1uxQAAM4LQRjARTnQNsj8YABAUiIIA7hg3YGgOv1BVowAACQlgjCAC9bQPn6hHGeEAQDJiCAM4IKxYgQAIJkRhAFcsAPtg6oqylZJXqbbpQAAcN4IwgAuSKd/VHtaBpgWAQBIWj63CwCQPDoGRvXlpw7plWM9au0fkSTdubbG5aoAALgwBGEA52St1U93tupvf7Ff4YjVlhUVuu/aBbpsbrEun1fidnkAAFwQgjCAMwpHonqxsVvfffmE6g916coFJfrynWu0oCzP7dIAALhoBGEAb2Gt1c6mPv38jTb915529QyFVJjt0/+6bYU+cu1CeTzG7RIBAIgLgjAASdJYJKqvPXNEj+5qVUvfiLJ8Ht24slJ3rJmj65eVcwtlAEDKIQgDkCQ9/kab/vnZRl1XW6bP3LRU77hktvKzeIsAAKQufssBkCS9cKRLZfmZ+t5965j+AABIC6wjDEDRqNWLjT26dkkZIRgAkDYIwgB0sMOv7kBQG5aUuV0KAAAzhiAMQC82dkmSrqstd7kSAABmDkEYgF440q3ainzNLsp2uxQAAGYMQRhIc6NjEb12vFcbapkWAQBILwRhIM29fqJPwXBUG5kWAQBIMwRhIM290NilDK/R+kWlbpcCAMCMIggDae6Fw926Yl6JcjNZVhwAkF4IwkAa6w4EdaB9UBuXMi0CAJB+OAUEpKFAMKyf7WrVv207KUnMDwYApCWCMJBGDnX49e+vnNRju1oVCIZ1yZxC/dP71+jSmiK3SwMAYMYRhIE0sO1oj/7x14e0/USfMn0evWt1le69ar4um1ssY7ilMgAgPRGEgRQ2HArri788qO9tO6nq4hz95TtX6M61NSrJy3S7NAAAXEcQBlLIsa6Anm44peBYVMFwVI/vblNz37A+cu1C/dnNy5ST6XW7RAAAEgZBGEghX/zVQT21/5QkyRhpUVmetn7sKq1fNMvlygAASDwEYSCFHOsa0pblFXro3rXyeQzzfwEAOAvWEQZSRDRqdbJ3WIvK85Th9RCCAQA4B4IwkCLaB0cVCke1oCzP7VIAAEgKBGEgRZzsHpIkLZxFEAYAwAmCMJAijveMB+H5nBEGAMARgjCQIk72DCvT51FVYbbbpQAAkBQcBWFjzC3GmEPGmEZjzOfOctyVxpiIMebO+JUIwInj3UOaX5orj4eL5AAAcOKcQdgY45X0dUm3Slop6QPGmJVnOO6Lkp6Kd5EAzu1kzxAXygEAcB6cnBFeJ6nRWnvMWhuStFXSHVMc98eSfiqpM471AXAgGrU62TOsBbNy3S4FAICk4SQIV0tqnrDdEtt3mjGmWtK7JT0Uv9IAONUxOKogS6cBAHBenNxZbqoJh3bS9lckfdZaGznbIv7GmPsl3S9JlZWVqq+vd1bleQgEAtPyuqmIXjmX6L060BORJA20NKp+5LhrdSR6nxIJvXKOXjlDn5yjV86leq+cBOEWSXMnbNdIapt0TJ2krbEQXCbpncaYsLX2ZxMPstY+LOlhSaqrq7ObNm26sKrPor6+XtPxuqmIXjmX6L1qe7VJ2r5Xd2y5RtXFOa7Vkeh9SiT0yjl65Qx9co5eOZfqvXIShLdLqjXGLJTUKuluSfdMPMBau/DNx8aY70p6YnIIBjB9TvQMsXQaAADn6ZxB2FobNsY8oPHVILySvm2t3W+M+UTseeYFAy47wdJpAACcNydnhGWtfVLSk5P2TRmArbUfvviyAJyPEz1Dms+tlQEAOC/cWQ5Icm8unbawjKXTAAA4HwRhIMmxdBoAABeGIAwkuRM9Q5KkBUyNAADgvBCEgSR3ontYkjgjDADAeSIIA0nuJEunAQBwQRytGgEg8YTCUT3dcEpP7e/QPJZOAwDgvBGEgSQTiVo99PxRfeel4+oOhDSnKFufu3W522UBAJB0CMJAEunyB/Xp/9illxp7dMPyCt179XxtrC2Xl7PBAACcN4IwkCReOdajT/5olwZGxvSl967W+66c63ZJAAAkNYIwkOBOdA/pS08d1JN7O7SwLE/fvW+dVs4pdLssAACSHkEYSEDRqNXOpj49uqtVP3m9WT6PR5/aUqv7Ny5SXhb/bAEAiAd+owIJxFqrrz3bqB++2qSOwVFl+jy6c22N/uTGpapgeTQAAOKKIAwkkF3N/frHXx/WtUtm6S/euVxbVlQqnzPAAABMC37DAgnkh682KS/Tq3+9t44ADADANOPOckCCGBgZ0xN72nTH5dWEYAAAZgBBGEgQP3+jVaNjUd2zbp7bpQAAkBYIwkACsNbqh6826dLqIq2qLnK7HAAA0gJBGEgAu5r7dbDDr3vWczYYAICZQhAGEsCbF8ndvmaO26UAAJA2uCIHcNGhDr8e3dWix3e36b1X1HCRHAAAM4jfusAMOtkzpJ1NfdrdPKBXj/eqoX1QXo/RpqXl+tSWWrfLAwAgrRCEgWk2FAzrF7vb9KPtzdrd3C9JysnwanVNkf769pW6fc0cleVnuVskAABpiCAMxNng6Jh++GqTjpwK6Hh3QAc7/BoORVRbka//ddsKXbukTLUV+fJ5maIPAICbCMJAnP3n6y168JcHVVGQpUXlebpzbY3uuGyOrphXImOM2+UBAIAYgjAQZwc7BlWWn6nX/vJGt0sBAABnwd9mgTg7dCqgpZUFbpcBAADOgSAMxFE0anXklJ8gDABAEiAIA3HU2j+i4VBEy2YThAEASHQEYSCODnX4JYkgDABAEiAIA3F06NR4EK6tyHe5EgAAcC4EYSCODnX4VV2co4LsDLdLAQAA50AQBuLo8Ck/0yIAAEgSBGEgTsYiUR3tYuk0AACSBUEYiJMT3UMai1gt54wwAABJgSAMxMmbF8pxRhgAgORAEAbi5FCHX16P0aLyPLdLAQAADhCEgTg51OHXglm5ys7wul0KAABwgCAMxAkrRgAAkFwIwkAcjIQiOtk7rGWVhW6XAgAAHCIIA3HQ2BmQtdKy2dxRDgCAZOFzuwAgmQ2Ojmlvy4Ae3dkqiRUjAABIJgRh4AKMhCL668f36Sc7WmTt+L6180s0fxYrRgAAkCwIwsB5OtoV0P/495063OnXh69ZoM3LKrSmplhFuRlulwYAAM4DQRhwKBiO6Mfbm/XgLw8qK8Or7923ThuXlrtdFgAAuEAEYeAcRkIR/frEmD73cr06Bke1fmGpvnL3ZaoqynG7NAAAcBEIwsAZHOrw60evNenRnS0aHA1r3YJSffmu1dqwpEzGGLfLAwAAF4kgDEzhC08c0LdePK5Mr0c3r5qtVVm9+vh7rna7LAAAEEcEYWCSUDiqH73WpJtWVuqL712t0rxM1dfXu10WAACIM26oAUyys6lPw6GI7lpbo9K8TLfLAQAA04QgDEzywpEueT1GVy+e5XYpAABgGhGEgUleONKtK+YVqyCbdYEBAEhlBGFggt6hkPa2Dui6WtYHBgAg1RGEgQleauyWtdJ1tWVulwIAAKYZQRiY4IUjXSrM9ml1TbHbpQAAgGlGEAZirLV64Ui3NtSWyevhhhkAAKQ6gjAQ09gZUPvAKPODAQBIEwRhIOY3R7olSRuWMD8YAIB0wJ3lkPaGgmFtO9qjn7zerEVleZpbmut2SQAAYAYQhJGWguGIntp/Sj95vVmvHOvRWMQqJ8Orv7p9pdulAQCAGUIQRloZHB3TN547qv/Y3qS+4TFVF+foIxsW6vracq1dUKIsn9ftEgEAwAwhCCMtWGv1+O42/Z//alB3IKibV87WPevnacOSMnlYIQIAgLREEEZKstbqpztbdawroC5/UIc7A9rd3K9Lq4v0yO/Xac3cYrdLBAAALiMIIyUd7PDrT3+yWz6PUVl+lioKs/SFOy7RPevns0YwAACQRBBGijrQNihJ+tWnN2pJRb7L1QAAgETEOsJISQc7BpXl82hhWZ7bpQAAgARFEEZKamj3a9nsAqZBAACAMyIIIyUd7BjU8tkFbpcBAAASGEEYKafTP6ruQEgrqgrdLgUAACQwgjBSzsF2vyRp+WyCMAAAODOCMFLOwY7xFSNWVDE1AgAAnJmjIGyMucUYc8gY02iM+dwUz/+eMWZP7ONlY8ya+JcKONPQ7ldVUbaKczPdLgUAACSwcwZhY4xX0tcl3SpppaQPGGNWTjrsuKTrrbWrJX1B0sPxLhRwqqGdC+UAAMC5OTkjvE5So7X2mLU2JGmrpDsmHmCtfdla2xfbfEVSTXzLBJwJhaM62hXgQjkAAHBOToJwtaTmCdstsX1n8geSfnkxRQEX6mhXQGMRq+UEYQAAcA7GWnv2A4y5S9LN1tqPxrbvlbTOWvvHUxy7WdI3JG2w1vZM8fz9ku6XpMrKyrVbt269+J9gkkAgoPx8bqnrRCr26uW2sB7eE9T/3ZCj6vz4XQuair2aDvTJOXrlHL1yhj45R6+cS5Vebd68eYe1tm7yfp+Dr22RNHfCdo2ktskHGWNWS3pE0q1ThWBJstY+rNj84bq6Ortp0yYH3/781NfXazpeNxWlYq9efrJBmb4Tev+tm+Tzxi8Ip2KvpgN9co5eOUevnKFPztEr51K9V06SwnZJtcaYhcaYTEl3S3p84gHGmHmSHpV0r7X2cPzLBJxpaB/U0sr8uIZgAACQms55RthaGzbGPCDpKUleSd+21u43xnwi9vxDkv5K0ixJ3zDGSFJ4qtPPwHRraPdr07Jyt8sAAABJwMnUCFlrn5T05KR9D014/FFJH41vaYBzo2MRvXq8V92BICtGAAAARxwFYSARRaJWv9zXrn9/5aR2NvUrFI7K5zFat6DU7dIAAEASIAgj6USiVo/vbtW/PNuoo11DWliWp9+/ar7WLSzVuoWl3FEOAAA4QhBGUnnlWI/+9hcHTt897l/uuVy3rqqS12PcLg0AACQZgjASmrVWrf0jamj362e7WvVfe9tVXZyjr33gct12aZU8BGAAAHCBCMJIWL/c267P/nSPBkfDkqTsDI/+5Malun/jIuVkel2uDgAAJDuCMBLWD19rUl6WT392y3KtrCrQ8tmFystiyAIAgPggVSAhDYfCevVYr37/6vm696r5bpcDAABSELffQkLadrRHoUhUm5ZVuF0KAABIUQRhJKTnDnUqN9OrKxeWuF0KAABIUQRhJBxrreoPdenaJWXK8nFRHAAAmB4EYSSco10BtfSNaNOycrdLAQAAKYwgjITz3MEuSWJ+MAAAmFYEYSSc+sOdWlZZoOriHLdLAQAAKYwgjIQSCIb12vFepkUAAIBpRxBGQnnxSLfGIpZpEQAAYNpxQw24JhyJ6nj3kA60D+qN5n69drxXB9oHVZyboboFLJsGAACmF0EYM25f64C+8vQRvXCkS8FwVJKUneHRFfNK9KkttXrX6iplePljBQAAmF4EYUy7SNTq1OCoTvYM699eOaEn93aoKCdD96yfp1VzirSiqlBLKvKV6SP8AgCAmUMQxrT6ox/s1FP7OxSOWklSXqZXn7xhif7gukUqyslwuToAAJDOCMKYNoFgWE/ua9d1teW6+ZJK1ZTkak1NkYpzM90uDQAAgCCM6bO3ZUDWSvddu0CbWQUCAAAkGCZlYtrsbumXJK2pKXa1DgAAgKkQhDFt9rT0a15prkrzmAoBAAASD0EY02Z384BW1xS5XQYAAMCUCMKYFp3+UbX2j+iyucVulwIAADAlgjCmxZ7mAUnSGoIwAABIUARhTIs9Lf3yeowumVPodikAAABTIghjWrzRMqCllQXKzWSFPgAAkJgIwog7a612N/frsrlcKAcAABIXQRhxd7JnWAMjY1rN+sEAACCBEYQRd9xIAwAAJAOCMOJud/OAsjM8WlqZ73YpAAAAZ0QQRlxFolY7m/p0aXWRfF6GFwAASFxc0o+LNhaJ6vlDXXpqf4eePdipnqGQPrml1u2yAAAAzoogjAvW1DOsrdub9JMdLeryB1WQ7dPmZRW6cWWlbl012+3yAAAAzoogjPMSCkf13wc6tPW1Zr3Y2C2PkTYvq9Dd6+Zp07JyZTAdAgAAJAmCMM4pErV69XiP/mtPu365r0O9QyFVF+foMzct1V11NaoqynG7RAAAgPNGEMZZnege0t0Pv6KOwVHlZHh1w4oK3bW2RtfVlsvrMW6XBwAAcMEIwjirf/3NMfUNh/T1e67QDcsrlJPpdbskAACAuCAI44z6hkJ6dGeL3nNFtW5bXeV2OQAAAHHFlU04ox++1qRgOKr7rl3odikAAABxRxDGlMYiUX1/2wltWFKmpZUFbpcDAAAQdwRhTOnJve06NRjURzYscLsUAACAaUEQxpS+/dIJLSzL06alFW6XAgAAMC24WA6nRaNWu5r79OjOVu1u7tff3XGJPCyRBgAAUhRBOM1Za7W/bVC/2NOmJ3a3q7V/RJk+j+64bI7uWjvX7fIAAACmDUE4TR3tCuixIyH93Y7ndaxrSD6P0YbaMv3PdyzVTSsrVZCd4XaJAAAA04ognAZ2NvXp57taFQxHFQxHdajDrwPtgzKS1i8q0B9sWKhbV1WpNC/T7VIBAABmDEE4xVlr9flH9+pY95BKcjOU5fOqoiBL//tdK1UaOK5333K12yUCAAC4giCc4l473quDHX598b2X6v1XznvLc/X1J12qCgAAwH0sn5bivr/tpIpyMvQ7a6rdLgUAACChEIRTWMfAqJ7a36H31dUoJ9PrdjkAAAAJhSCcwn74WpMi1uqDV813uxQAAICEQxBOUaFwVD96rUmbl1Vo/qw8t8sBAABIOFwsl0ICwbBa+oYVHIvqlWM96vIHde/VnA0GAACYCkE4BbT0DevbL57Q1u1NGg5FTu9fWJan62vLXawMAAAgcRGEk1RL37BeONKt+kOderqhU0bS7WvmaMuKCuVkeJXl86q2Ml8ej3G7VAAAgIREEE4C0ajVvzzXqN3N/eoOBNXpD6p9YFSSNLswW/dds0Af2bBQc4pzXK4UAAAgeRCEk8AjLx7TP/76sJZW5mt2UY4WV+RrZVWhrl9ariUV+TKGs74AAADniyCc4HY39+tLvzqkmy+p1EMfXEvoBQAAiBOWT0tg/tExfXLrLlUUZOmL711NCAYAAIgjzggnoNGxiA51+PXN+qNq7h3W1vuvVnFupttlAQAApBSCsMsGRsa0s6lPB9oG1dA+/nG8e0hRO/78n928TOsWlrpbJAAAQAoiCM+QcCSqpxtOqcsf1OBoWJ2Do9p+ok8NHYOysdBbU5KjFVWFum31HK2sKtDKqiLNm5XrbuEAAAApiiA8Q77834f0r88fO72dm+nVZXOL9ektS7VuYakuqS5UYXaGixUCAACkF4LwDGjqGdZ3Xjyh371sjv7ytpUqyPYpO8PrdlkAAABpjSA8Ax78VYO8HqO/eOcKlRdkuV0OAAAAxPJp0+614716cm+HPnH9YlUWZrtdDgAAAGIIwtMoGrX6whMHVFWUrfs3LnK7HAAAAEzA1IiLMBwKq3MwqE5/UJ3+UZ0aHP/cNRjUKf+o2vtHdax7SP/0/jXKyWROMAAAQCIhCDt0rCug/9jerD0tAzoVC7v+YPhtx2V6PSovyFJFYZaWVhbovWtrdMeaahcqBgAAwNk4CsLGmFskfVWSV9Ij1toHJz1vYs+/U9KwpA9ba3fGudZpMxaJyj8a1uDI2Pjn0TH5R8c0OBJW/0hIzzR06tXjvfJ5jC6tKdLy2QXaWFuu8oIsVRZmq2LC5+LcDG6FDAAAkATOGYSNMV5JX5d0k6QWSduNMY9baw9MOOxWSbWxj/WSvhn7nFA6/aP6s5/sGQ+5E4LvyFjkrF83f1au/vyWZbpzbY0qCrjgDQAAIBU4OSO8TlKjtfaYJBljtkq6Q9LEIHyHpO9ba62kV4wxxcaYKmtte9wrvgg+j0d9wyEVZmeosjBbhdkZKszxqSA7Q4XZPhXmZEx6/NvnOMsLAACQWox98/6+ZzrAmDsl3WKt/Whs+15J6621D0w45glJD1prX4xtPyPps9ba1ye91v2S7pekysrKtVu3bo3nzyJJCgQCys/Pj/vrpiJ65Ry9coY+OUevnKNXztAn5+iVc6nSq82bN++w1tZN3u/kjPBUp0Inp2cnx8ha+7CkhyWprq7Obtq0ycG3Pz/19fWajtdNRfTKOXrlDH1yjl45R6+coU/O0SvnUr1XTtYRbpE0d8J2jaS2CzgGAAAASBhOgvB2SbXGmIXGmExJd0t6fNIxj0v6fTPuKkkDiTY/GAAAAJjonFMjrLVhY8wDkp7S+PJp37bW7jfGfCL2/EOSntT40mmNGl8+7b7pKxkAAAC4eI7WEbbWPqnxsDtx30MTHltJfxTf0gAAAIDp42RqBAAAAJByCMIAAABISwRhAAAApCWCMAAAANISQRgAAABpiSAMAACAtEQQBgAAQFoiCAMAACAtEYQBAACQlgjCAAAASEsEYQAAAKQlgjAAAADSEkEYAAAAaclYa935xsZ0STo5DS9dJql7Gl43FdEr5+iVM/TJOXrlHL1yhj45R6+cS5VezbfWlk/e6VoQni7GmNettXVu15EM6JVz9MoZ+uQcvXKOXjlDn5yjV86leq+YGgEAAIC0RBAGAABAWkrFIPyw2wUkEXrlHL1yhj45R6+co1fO0Cfn6JVzKd2rlJsjDAAAADiRimeEAQAAgHNK2iBsjJlrjHnOGNNgjNlvjPlUbH+pMebXxpgjsc8lbtfqtrP06m+MMa3GmDdiH+90u1a3GWOyjTGvGWN2x3r1t7H9jKtJztIrxtUUjDFeY8wuY8wTsW3G1BlM0SvG1BSMMSeMMXtjPXk9to9xNYUz9IpxNYkxptgY85/GmIOxzHB1qo+ppJ0aYYypklRlrd1pjCmQtEPS70r6sKRea+2DxpjPSSqx1n7WvUrdd5ZevU9SwFr7927Wl0iMMUZSnrU2YIzJkPSipE9Jeo8YV29xll7dIsbV2xhjPiOpTlKhtfZdxpgviTE1pSl69TdiTL2NMeaEpDprbfeEfYyrKZyhV38jxtVbGGO+J+kFa+0jxphMSbmSPq8UHlNJe0bYWtturd0Ze+yX1CCpWtIdkr4XO+x7Gg98ae0svcIkdlwgtpkR+7BiXL3NWXqFSYwxNZJuk/TIhN2MqSmcoVdwjnGFC2KMKZS0UdK3JMlaG7LW9ivFx1TSBuGJjDELJF0u6VVJldbadmk8AEqqcLG0hDOpV5L0gDFmjzHm26n2544LFfuz7BuSOiX92lrLuDqDM/RKYlxN9hVJfy4pOmEfY2pqX9HbeyUxpqZiJf23MWaHMeb+2D7G1dSm6pXEuJpokaQuSd+JTU16xBiTpxQfU0kfhI0x+ZJ+KunT1tpBt+tJZFP06puSFku6TFK7pH9wr7rEYa2NWGsvk1QjaZ0xZpXLJSWsM/SKcTWBMeZdkjqttTvcriXRnaVXjKmpXWutvULSrZL+yBiz0e2CEthUvWJcvZVP0hWSvmmtvVzSkKTPuVvS9EvqIBybl/hTST+w1j4a230qNif2zbmxnW7Vl0im6pW19lQsyEQl/X+S1rlZY6KJ/UmoXuNzXhlXZzGxV4yrt7lW0u/E5ihulXSDMebfxZiaypS9YkxNzVrbFvvcKekxjfeFcTWFqXrFuHqbFkktE/6y958aD8YpPaaSNgjHLtT5lqQGa+0/TnjqcUkfij3+kKSfz3RtieZMvXpzYMe8W9K+ma4t0Rhjyo0xxbHHOZJulHRQjKu3OVOvGFdvZa39C2ttjbV2gaS7JT1rrf2gGFNvc6ZeMabezhiTF7v4WbE/X79D431hXE1ypl4xrt7KWtshqdkYsyy2a4ukA0rxMeVzu4CLcK2keyXtjc1RlMavbHxQ0o+NMX8gqUnSXe6Ul1DO1KsPGGMu0/jcqROSPu5GcQmmStL3jDFejf+P4o+ttU8YY7aJcTXZmXr1b4wrR3ivcu5LjKm3qZT02Ph5Dvkk/dBa+ytjzHYxriY7U694r3q7P5b0g9iKEcck3afY+3uqjqmkXT4NAAAAuBhJOzUCAAAAuBgEYQAAAKQlgjAAAADSEkEYAAAAaYkgDAAAgLREEAYAAEBaIggDAAAgLRGEAQAAkJb+f2HaVTamU+V5AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hw['weight'].value_counts(normalize=True).sort_index().cumsum().plot(figsize=(12,8))\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La definizione della ECDF ci dice che, dato un punto di coordinate $(x,y)$, la somma delle frequenze degli elementi minori o uguali a $x$ è pari a $y$. Alternativamente, possiamo dire che l'$y\\%$ degli elementi ha un valore inferiore a $x$.\n",
    "\n",
    "Osservando il grafico sopra, possiamo dire che:\n",
    "* Circa il $40\\%$ dei soggetti ha un peso inferiore alle $\\approx 33$ libre (circa $66kg$);\n",
    "* Circa l'$80\\%$ dei soggetti ha un peso inferiore $\\approx 42$ libre (circa $84Kg$);\n",
    "\n",
    "Le ECDF tornano utili per verificare graficamente se due fenomeni hanno distribuzioni simili. Possiamo ad esempio usarle per confrontare le distribuzioni dei pesi di uomini e donne:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ecdf_weight_m = hw[hw['sex']=='M']['weight'].value_counts(normalize=True).sort_index().cumsum()\n",
    "ecdf_weight_f = hw[hw['sex']=='F']['weight'].value_counts(normalize=True).sort_index().cumsum()\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(ecdf_weight_m.index, ecdf_weight_m.values)\n",
    "plt.plot(ecdf_weight_f.index, ecdf_weight_f.values)\n",
    "plt.legend(['M','F'])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Osservando il grafico sopra, possiamo dire che:\n",
    "* Circa il $40\\%$ degli uomini ha un peso inferiore agli $80Kg$;\n",
    "* Circa il $40\\%$ delle donne ha un peso inferiore ai $60Kg$;\n",
    "* Il $100\\%$ degli uomini ha un peso inferiore ai $140Kg$;\n",
    "* Il $100\\%$ delle donne ha un peso inferiore ai $130Kg$.\n",
    "\n",
    "In generale, il grafico sopra ci dice che gli uomini tendono a essere più pesanti delle donne."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Istogrammi\n",
    "\n",
    "Abbiamo visto che i diagrammi a barre delle frequenze diventano poco chiari quando le variabili sono continue (es. nel caso dei pesi). In questi casi, per ridurre l'influenza del rumore, è possibile utilizzare gli istogrammi. Un istogramma divide il range dei dati in un certo numero di \"bin\" e riporta per ogni bin il numero di valori che ricadono in quell'intervallo. Di seguito l'istogramma dei pesi nel dataset pesi-altezze:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "_,edges,_=plt.hist(hw['weight'], width=10.8)\n",
    "plt.xticks(edges)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ogni \"bin\" dell'istogramma copre un determinato range. Pratica comune è quella di suddividere il range dei dati, dal minimo al massimo, in un determinato numero di bin della stessa larghezza."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Scegliere il numero di bin: Struges e Rice\n",
    "\n",
    "Il numero di bin può essere specificato arbitrariamente o determinato a seconda del risultato grafico che si vuole ottenere. Esistono due criteri euristici per trovare dei valori di partenza:\n",
    "\n",
    "* Struges: $\\#bins=3.3\\log(n)$ \n",
    "* Rice: $\\#bins=2\\cdot n^{1/3}$ \n",
    "\n",
    "Dove $n$ è il numero di elementi.\n",
    "\n",
    "Va notato che il numero di bin, può cambiare il risultato grafico. Di seguito due esempi ottenuti calcolando il numero di bin con i due criteri considerati:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "bins_struges=int(3.3*np.log(len(data['weight'])))\n",
    "bins_rice=int(2*len(data['weight'])**(1/3))\n",
    "\n",
    "plt.figure(figsize=(12,4))\n",
    "plt.subplot(1,2,1)\n",
    "plt.title('Struges ({} bins)'.format(bins_struges))\n",
    "plt.hist(data['weight'], bins=bins_struges)\n",
    "plt.grid()\n",
    "plt.subplot(1,2,2)\n",
    "plt.title('Rice ({} bins)'.format(bins_rice))\n",
    "plt.grid()\n",
    "plt.hist(data['weight'], bins=bins_rice)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternativamente, possiamo definire dei range arbitrari per i nostri bin. Ad esempio, considerando i seguenti limiti per i bin `[20,25,30,35,40,45,50,55,60,65]`, otterremmo il seguente istogramma:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "_,edges,_=plt.hist(hw['weight'], bins=[20,25,30,35,40,45,50,55,60,65]) #costruiamo un istogramma con i bin definiti\n",
    "plt.xticks(edges)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'istogramma mostrato sopra riporta le frequenze assolute per ogni bin e ci permette di rispondere a domande del genere \"quanti soggetti hanno un peso compreso tra $30$ e $35$ libbre\"?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In casi particolari, è possibile anche definire istogrammi con bin di dimensioni variabili. Ad esempio:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "_,edges,_=plt.hist(hw['weight'], bins=[20,30,35,40,45,50,51,52,55,60,65]) #costruiamo un istogramma con i bin definiti\n",
    "plt.xticks(edges)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Istogrammi di densità\n",
    "Un istogramma può essere utilizzato anche per approssimare una Probability Density Function. L'istogramma delle frequenze assolute mostrato sopra, tuttavia, non ci permette di ragionare in termini probabilistici. \n",
    "\n",
    "Ad esempio, non ci permette di dire qual è la probabilità che un soggetto abbia un peso contenuto tra $30$ e $40$ libbre. Se avessimo la PDF della popolazione dalla quale è stata estratto il campione, potremmo rispondere a questa domanda calcolando l'integrale:\n",
    "\n",
    "$$\n",
    "\\int_{30}^{40} pdf(x) dx\n",
    "$$\n",
    "\n",
    "Possiamo costruire un **istogramma di densità**, che approssimi in maniera discreta la PDF che cerchiamo. In pratica, vogliamo che l'area sottesa dal bin di \"bordi\" $[30, 40[$ contenga un valore che approssimi l'integrale della PDF:  \n",
    "\n",
    "$$\n",
    "\\int_{30}^{40} pdf(x) dx \\approx b_j \\cdot w_j\n",
    "$$\n",
    "\n",
    "dove $j$ indica il bin di bordi $[30, 40[$, $w_j$ rappresenta la sua larghezza ($40-30=10$) e $b_j$ rappresenta la sua altezza (il valore del bin). Sotto queste condizioni, vale dunque la seguente proprietà:\n",
    "\n",
    "$$\n",
    "\\sum_{i=0}^{n} b_i \\cdot w_i = \\int pdf(x) dx = 1\n",
    "$$\n",
    "\n",
    "dove $n$ è il numero totale di bin.\n",
    "\n",
    "Il risultato è graficamente molto simile a quello ottenuto in precedenza, ma cambia la scala sull'asse delle y:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "_,edges,_=plt.hist(hw['weight'], bins=[20,25,30,35,40,45,50,55,60,65], density=True) #costruiamo un istogramma con i bin definiti\n",
    "plt.xticks(edges)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stima della densità\n",
    "Uno svantaggio degli istogrammi è che categorizzano dei dati continui in maniera arbitraria mediante dei bin. La scelta degli intervalli dei bin cambia l'aspetto finale dell'istogramma. \n",
    "\n",
    "La stima della densità cerca di risolvere questo problema ottenendo una versione \"continua\" dell'istogramma. Invece di suddividere l'asse delle $x$ in bin, la stima della densità calcola un valore per ciascun punto dell'asse delle $x$, ottenendo così una rappresentazione continua. \n",
    "\n",
    "Vedremo meglio come si effettua la stima di densità più in là nel corso. Nel caso uni-dimensionale, può essere calcolata come mostrato nell'approfondimento di seguito (opzionale). Per adesso, sappiamo che si può calcolare la stima della densità con una funzione apposita (lo vedremo a laboratorio) che dipende da un unico parametro di **bandwith** che determina la \"sensibilità ai dettagli\" della stima della densità."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Confrontiamo la stima di densità dei pesi nel nostro dataset di pesi-altezze con il relativo istogramma:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hw['weight'].plot.density(figsize=(12,6))\n",
    "plt.hist(hw['weight'], density=True)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se nel caso degli istogrammi cambiare il numero di bin cambiava il risultato grafico, qui è cambiare la bandwidth a cambiare il risultato grafico. Il grafico seguente mostra diversi esempi di stima di densità con diversi valori di bandwidth:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "hw['weight'].plot.density(figsize=(12,6), bw_method=0.05)\n",
    "hw['weight'].plot.density(figsize=(12,6), bw_method=0.1)\n",
    "hw['weight'].plot.density(figsize=(12,6), bw_method=0.2)\n",
    "hw['weight'].plot.density(figsize=(12,6), bw_method=0.5)\n",
    "hw['weight'].plot.density(figsize=(12,6), bw_method=0.8)\n",
    "plt.hist(hw['weight'], density=True)\n",
    "ax.legend(['h=0.05','h=0.1','h=0.2','h=0.3','h=0.4','histogram'])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calcolo della stima di densità con Kernel di Epanechnikov (Opzionale)\n",
    "Il calcolo avviene mediante la seguente formula:\n",
    "\n",
    "$$\\hat f_n(x)=\\frac{1}{nh}\\sum_{i=1}^n K(\\frac{x-x_i}{h}), h>0$$\n",
    "\n",
    "Dove $n$ è la dimensione del campione, $h$ è un parametro detto \"bandwidth\" e $K$ è una funzione \"kernel\" che determina quanto gli elementi del campione devono contribuire alla stima nel punto $x$, dipendentemente dalla loro distanza da $x$. Una scelta comune di kernel è quello di Epanechnikov:\n",
    "\n",
    "$$\n",
    "K(x) = \\begin{cases}\n",
    "\\frac{3}{4}(1-x^2) & \\text{if } |x| \\leq 1 \\\\\n",
    "    0 & \\text{otherwise.}\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In pratica il Kernel di Epanechnikov ha la seguente forma:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-4.0, 4.0)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "x = np.linspace(-4,4,1000)\n",
    "y = 3/4*(1-x**2)\n",
    "y[abs(x)>1] = 0\n",
    "plt.plot(x, y)\n",
    "plt.xlim([-4,4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Facendo \"scorrere\" questo kernel su diversi punti dell'asse delle x e sommando i contributi, si ottiene la stima di densità finale:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VxyxatIi7776bCy64gMsuu4xHH32UpUuXTnsfP//5zwG47LLLZr3Ozs5OZFlm2bJls57DwWG2ODF2Dg7zyEUXXcSvfvUr9uzZw+WXX048HkdRFN70pjdx2223lW01NDg4OK9reMtb3oJpmnz5y1+e8J5hGESj0XnbVyaT4d3vfjcjIyP867/+a0kMHI01DA8Pj/s9EAiwZMkScrlcxe38fv+k+6utreWKK67gF7/4BbfccguXX375vFpZymVRFosQF9ddFD3zeV0mo2gpG2sZy+fzfOc735kw1u/3T8s129TUxPr16/nZz3427hi2bt3KPffcw+te97q5L7zAWWedxejo6LjYy3KsWbOGO+64g2QyySWXXDIuxrASDzzwAF/+8pdZuHAh73znO2e9zueff57Vq1ePi4N0cDhWOBY7B4d55pprrilVun/961/PXXfdxf/9v/+XBx98kDPOOIMPfOADrFq1ipGRETZv3sx9991XVgDMlgsuuIAPfehDfPWrX2XLli1ceumlaJrG7t27+e1vf8t//ud/zqqobnd3d6m2VzKZZPv27fz2t7+lr6+PT3ziE+NKSxyNNaxatYoLL7yQjRs3Ul1dzXPPPcfvfvc7PvKRj1TcbuPGjdx333184xvfoLm5mYULF5aSDcB2xxbXUk6IVuLRRx8lm81OeH3t2rWlEiePPPIIV155Je3t7QwMDPCd73yH1tZWzj33XMC2bkYiEb73ve8RDAbx+/2cccYZc04AKMfZZ59NVVUV1113HR/96EeRJImf//znZV2gGzdu5NZbb+XjH/84p512GoFAgKuvvrrsvF/72te44oorOOuss3jf+95XKncSDof54he/OG/rv/LKK1FVlfvuu69UvmYyzjrrLH7/+99z9dVXlyzoNTU1pffvvPNOdu7ciWEY9Pf388ADD3DvvffS3t7On/70p7JFmH/3u9+VLftyySWX0NDQANj1Fh9++GH+4R/+YY5H6+AwS45bPq6Dw0lApdIJ//Ef/yEAcdVVVwld10V/f7/4X//rf4m2tjahaZpobGwUF110kfjBD35Q2qZYtuG3v/3thPmuu+464ff7J7xersSHEEL84Ac/EBs3bhRer1cEg0GxZs0a8clPflL09PSUxsyk3AmF8g6SJIlQKCRWr14tPvCBD1Qs6TCdNUxWSuXItf2f//N/xOmnny4ikYjwer1ixYoV4t/+7d9EPp+veC527twpzj//fOH1egUwofRJLpcTVVVVIhwOi0wmM+W5EGLqcifFcin333+/eMMb3iCam5uFy+USzc3N4u1vf7t4+eWXx813++23i1WrVglVVceVEpms3MnXvva1sus58nNT7vP5+OOPizPPPFN4vV7R3NwsPvnJT4q7775bAOLBBx8sjUsmk+Id73iHiEQipVIiY9dwZHmW++67T5xzzjnC6/WKUCgkrr76arF9+/ZxY4rX58jyL8V1dnZ2VjjrNq9//evFRRddNK3jF0KIW2+9VciyLE477TQRj8dL+yr+uFwu0djYKC655BLxn//5nyIej0+Yo1K5kyPP25133ikAsXv37imPxcHhaCAJMUW0qoODg8NJjGEYNDc3c/XVV/PjH//4eC/HYQoeffRRLrzwQnbu3Dmj2LljxRvf+MZJu5o4OBwLHGHn4ODwquZ3v/sdb37zm3nooYe44IILjvdyHKbBFVdcQWtrKz/84Q+P91LGsWPHDtasWcOWLVs45ZRTjvdyHF6lOMLOwcHhVcnTTz/Niy++yJe//GVqa2snFIl2cHBwOBFxsmIdHBxelXz3u9/l7//+76mvr+d//ud/jvdyHBwcHOYFx2Ln4ODg4ODg4HCS4FjsHBwcHBwcHBxOEhxh5+Dg4ODg4OBwkvCqK1BsWRY9PT0Eg0GnQbODg4ODg4PDKx4hBIlEgubmZmS5sk3uVSfsenp6Ss3ZHRwcHBwcHBxOFA4dOkRra2vFMa86YRcMBgH75IRCoeO8GgcHBwcHBweHysTjcdra2koaphKvOmFXdL+GQiFH2Dk4ODg4ODicMEwnhMxJnnBwcHBwcHBwOElwhJ2Dg4ODg4ODw0mCI+wcHBwcHBwcHE4SHGHn4ODg4ODg4HCScFyF3SOPPMLVV19Nc3MzkiTxxz/+ccptHnroIU499VTcbjdLlizh5ptvPurrdHBwcHBwcHA4ETiuwi6VSrFu3Tq+/e1vT2t8Z2cnV155Ja95zWvYsmULH/vYx3j/+9/P3XfffZRX6uDg4ODg4ODwyue4lju54ooruOKKK6Y9/nvf+x4LFy7k61//OgArV67kscce46abbuKyyy47Wst0cHBwcHBwcDghOKHq2D355JNcfPHF41677LLL+NjHPjbpNrlcjlwuV/o9Ho8freU5OJxQ5DNphg4dIB2LIckSgaoaatraUTVt3DhLCPZlchzI5MlaFhFVYZnfQ51Lm2TmEwfLshgaGiIajWKaJl6vl3A4TDweJ51O09raWioImk53kkrtxe1pJOBfhiy7Zr6/VIrc7t0oNTW4Ch1wMnmTzqEUyxoCqEplJ4pl5Uml9pKM7yc22IuRUXBrCwjVLKCmpQ1VkUCxr4tlWjy0dT9Vho+wrOAJaFQ3+/H45/+65c08u6O7GUgNUOWpYn39+hnPYeVMsntHGcmM0McgsXAGr89HR6iDJn/TK7IFpOj6G3pUxpQaAQk54EJr9CG7535rzeRNdvUnGIhnkSSJhpCbZQ1BPJpyeP9C0LsnRjapI6sSwRoPVY1+ZPnYnqvMtm1YiSTuJYtRa2uP6b4dJnJCCbu+vj4aGhrGvdbQ0EA8HieTyeD1eids89WvfpUvfelLx2qJDg4nBN27dnBo69+wLLP0Wj97OPDSFhZt2ETtgg4ATCH4Ve8Ivbn8uO2fiCZZFfByUXUIzxRi5JXMnj176O7uBuybZDQaJR6PEwgEiEQiNDc3l8bqeoxEYhuJxDZGRx6npuY1BALLprUfIQSZF7aQeuopDg4mqD/njFJrw97RFI/d/xyPt3dw0cp6FtUFJp0nldzHnh0/Jz40AEIUXpXo29+McTdUrVjN+gvfas+7f4QXH9kBqpvqUB2LggG6do3SuDBE64oq5Hm6brtGdvFY92PkTPsBennV8lnNkybD1h3Pk0onALBkwcH6LrbUbqEl2MJrF7yWoGvqqvtHDVOHoZehYbW9vrRO6uG9WOkMqC9D7VLwhMntieJeGMLVEUaahcASQrDlUJTH9wyhm6L0+tZueGzPEOcvreOUljBgF6uNDqRJjmQBGNgfx+3XWLS+jmC1Zx4OujxmMokSOPw5NUejZF54gfSzz+JevozABRcgu91Hbf8OlTlx/yJPk09/+tPEYrHSz6FDh473khwcjjtunw/LMglU17Jg9TpaV56CJxDEyOfY/cyTZBK2ZVuRJNYFvXhkmQ0hP+dXBVnq8yAhsT2Z4dd9I1hCTLG3Vy4tLS243W6am5sRQpDP5wv/5khndpDL7SmN7evX0Y0ONC2MaWYZGLiT0dFnptyHsCwS995L/LHH2NE1yj7h5fm0hiicN3nri7S/+DiuF5/n9he6eeHg6KRzubQFZIddyPoCAr5TqW1cQzAcJG++wH51L48c7CFrGACEI2kaAmlEJMmg6yDbRJKsadK3L8aup/sxdWtO504IwVO9T3H/wfvJmTki7ggbGzayvPqwsBvNjvJI1yNYYuK+hBDo/anSeXCrbgZakow0ZgjX1bDA38aKWAct3RG649081fvUnNY7J/QsbPkl7PgzxHsBkLwqSkM1skfGHezHoz+OKg8hLEF2b4zsrpFZ764/nkU3BXVBN2cuquGMRdXUBFzkdIun9w6TNw6fz6bFYVpXVtO4KIzqVsildHY+2ctwd3LOh12O/P79jP7iF2S3by+95l7YgXvxIpAkcrteJnrbbZjJ1FHZv8PUnFAWu8bGRvr7+8e91t/fTygUKmutA3C73bidJwcHh3HUtrXjDYbwhSMlF1frqlM4tPUlPIEA3uDhdntrgj6W+z245MPPgT3ZPH8ejHJ62I/8CnSRVcI0TRTFdmf5/X5OP/10duzYgSzLNDc309TUxL59j6KqWVKpZzDNU0gkMvR0J4EQK1ZswufvJBZ9ntHRJ5FljXB4Q9l9CSFIPvww2V272D2YYvfidWQXLuPS1Y2l814f9uBti3BgcC/bVI2HJAm3qrCq2b4G6fQBPJ4WZFnF7fWx9uz/TSo6Sl37QqRsjIPPfosdtU0oAYvatrMxsecN1Czg7W8LMvDin/hj2kVM7mSnfzVrByQyyTzZtI4/PPu/jS8MvMDm/s0AbGrYxKbGTcjS4c+IJSzu7LyTaC6KJSwuaL1gnDs1fyBOdncU96IwnsURNEXjwlMvQQhByBVC706S3TlCk97E/mQPG9aeM+u1zgnTgK2/g3gPaB6wbOEsSRLe15wPZh5p910wsAO3dC/55jeQGw7hWjC7lpWSJHHJqkYW1QVYWh8onbMzF9bw/P4R2J+if3eU1hVVSJJEVaOfqsK2Lcuq6HxxiJGeJHtfGETRZCL1vvk4CwDoPT3E77wTYZjk9nXiXrkSSZLQWlrQWlrQ+/qI//VOzOER4n/+E+E3vQnZNfOQBYe5cUJZ7M466yzuv//+ca/de++9nHXWWcdpRQ4OJw7Rvl70XLb0uz9SNe5GK8sK7WvXE1iwkD/2jxI3Drtpx4o6gGaPi/e21LEqUP6B6pVKJpPh6aefpq+vr/RaV1cXQ0NDyLLM2rVraWjIsmBBjPYONw0Nl6MobsLhcMl1+vLLe3C71lNVfTYAwyOPksl0l91fbtcuslu30RPLsWPZaaQ7lvGGDS0sbTjsUvRt2kTo/PPoqPWztn8X3sFe7tvRz0AiSy43SH//n+jt/QOWpQP2davvWIQkBPltt3OPuYQh17m4F/4jS7rq6XlhCEM3yWfS4K2ifuPbeEcgR9jKEMvu5sBiD6vObZ6TqBvKDJUsaOe0nMPpTaePE3UAsiRzZtOZtnV3eDs7RnaU3jNGs+T2RBHCYlg/bNkKuUKE3WEkScLVGsS7tg6v5mGVtAzVPE63q86HIXoIVDfmoreQ7fcjCi5SSZGRXB5Y9QZoWgtC4Br6K4ENXpQZxjLGs3rJeqnIEssagkd8PyXqMyBSBoMHE+SzJqY13lquaDKLT62jtjWIL6jhDcxfPKWVzRK/+x6EYeLq6CB0xeUT4h61xkYib/o7ZJ8PY2iY5P33l47J4dhxXIVdMplky5YtbNmyBbDLmWzZsoWDBw8Cthv1Pe95T2n8hz/8Yfbt28cnP/lJdu7cyXe+8x1+85vf8E//9E/HY/kODicMmUScnU88wt/u+SvZZGUXzX0jcXans9ze1c/LTz2Goetlx2lj4ocypkVPNl923CsFIQS7du0il8vR3d2NZdnurIaGBqqqqli+fDk+n8nw8MO43TK1NWfj8y0suWgXL15MTU0NlmWxfft2QsFTCQRXEPAvx+Wqnrg/yyL97HMkcwYv1iwm1djGa1bU01o10YLiXb8e7ymn0FbtY9W+FxDZLHe/1EVf/53ks2kO/O0lhg4eGn+TPPgkDyYMRiUv7ubzWT5UA6Ygn82y++nHeOmBezENA1Q3gbVv4hp1BFVPcjC5n86C1Wm21HhqeO2C17K+bj3r6tZNOm5RZBFnNJ0BwGPdjxHPxxG6RWbrMELAfl8vt2fv4tm+Z8tur9X78K6rI3BmE7JbxRIWz/c/P+n4eWdkHxyy3e1i2VWkOyF3MEFuX3T8OEmCZZdDuBWMPFL34fWZ8TxWuvx3qEgyZ3DLUwe546VesrpZdky0P03/vhgAi9bXsS+a5uYn9pPJjx8vSRId62pZeXYzbt/8CDshBMkHH8RKJlEiEUKXXYqkKGXHKuEwoauuBFnCTCYRk/z9cDh6HFdh99xzz7FhwwY2bLDdGB//+MfZsGEDn//85wHo7e0tiTyAhQsXcscdd3Dvvfeybt06vv71r/OjH/3IKXXi4FABIQT7Nj+LZRp4Q2Hcfv+kY/ems7ycyiIDbbtfYujQAbp2bK04/2Be56fdQ/xhIErGnFvc1tGkv7+f0dFRZFlm5cqVyAUrpNfrZd26ddTX1zM8/DBCmHi9CwiHN6LrOtu3b2fz5s1YlsWKFSvQNI1UKkV3dzd1tZdQX38ZijLRcinJMuG/u4aXahYxvGglyxqCrG6e3D0XOPdc1KpqlgRk2rt3saJmP7o+QrR3GJFayOCBzsOD0yMc6HyeFwkh1SzmbCNAPpZH0WSaV+SIJR4lm07QvbMQB+UOUrfyUi5hgNfl97DCa8f4DXUl2PlUL5Y1M6uKJEmsqF7B2S1nTzl2Q/0GmgPNGJbB492Pk90bxcoaZLU8T/leBKDaM1EYF9HqfEiafa26k9083fs0z/U/x2h28ljEecE04OVCjdSWU8kl6rHSBrJHxd1R5jrKCqy8GhaeB0vs6g35niSpZ3rJbBuuaLl6cOcAWd0kltHRyiS1WKbFga3DADQsDBOq8/Lc/hHiGZ3H9wxNXIosoWjyuO3nQr5zP7k9e0GRCV56KdIU7lWtoYHINdcQcVyxx4XjKuwuvPBChBATfordJG6++WYeeuihCdu88MIL5HI59u7dy/XXX3/M1+3gcCIx2ttDbKAPWVZYvOmMSctGGJbg/mE7aWJTOMDa1acA0Lt7ZymZohxVqopHlkibJk/Hjk7A9lwxDIO9e/cC0NHRgc/nwzQPWzokSSKT6SSTOYQkKdTWvhZJkpBlmVgsRjabpaurC5fLxeLFiwHYv38/+fx4a4Q4Ikkgq7qJr1yHy6XymhV1FUt2SJpG4ILz0RSZM42D1EgvkU3E0aNNKIqPJaedeXh7bxVbWl4DwSbW1LShd9rnvXmpj1jqPgJNFkIZoGfXdjJJO8uU2qWcsuo1rD797UiKimlYHNw2Qnwww+CBxLTOY0pPoZszs8BIksT5recjSRJ7B/ewb/9OAP4WeRlLtlgYXsjiyOIp5xFC0JCoYikdCCF4sufJGa1jxgxsg0wU3AGspvPIH7C/A57lVUhaeWsV3gh0nGuLPECt8oAiYURzGAPpspt0RzPsGUgiSxKXrW5EKZNJ29cZJ5fW0TyqndEsS7xmRT0AW3ti9MWyE7YBMA2LQ9tHeOmhbkxjduJOmCapxx8HwLd+PVpD/bS205qbkeQTKtrrpME56w4OJzHCsjjwoh3g3rR0BR7/5KU0XkpmiBkmAUXhrIifqqZmIo3NCMvi4Na/TbqdKku8ptq2YLwQT5MwyruSjifd3d3k83l8Ph9tbW2YpskzzzzDzp070QuuomzWjpMLhzegaXY5CUVRWLRoEQAHDhwgl8vR2NhIKBTCsiyi0SgAuj5KX/+fGRy813bddtlz+d0q7zh9AW/Z1IbPNXWumqutDd+mjYiLWxAKJPpzSGYdzctW4PaNsbRKElcuOYXXLt3AolETU7fwhd00LqwjHN6ENxTCVT2IaeU5tO3Fw9s1rAalsA5Fpmapfd26Xx7FmMQFOJZHuh7hlh23cCg+s+oC1Z5q1tWuwxzJsi33MvFAmj0cQJZkzmqaXox0/mCCzLZh1sWXISGxP76frkTXjNYxIxrXwsqrYMklZPenEZZArfag1k0zrtSykM2RUhJFbk8UcYRlVAjBY7sHAVjdHKI2MDHuUc+Z9OyOAtC2sgpFtW/brVU+VjYFEQKe2DvRage2h3ikN0UurdO3Nza9dZfBu+YUlKoqvJs2zXhbkc+TeuppzNjs9+8wMxxh5+BwEjPUdZBMIo7qctOyYtWk4wxL8HTUtvqcEfHjkmU7VmetHSYx3HWIdHzyP8wdXhetHheGEDwZfWVZ7QzDKJU5am9vR5Zlenp6yGazJdcsQE3N+bS2votIZPzNq6GhgWAwiGmadHd3I0kSy5cv54wzzijV1bSsPOnUPpKpXaR2PU/sD38gftddgO0WqwtOP1HBtWkVGa2fVDTKYF8d2/pzhNqXHh5QiA1UZYm1Hg+xg/b5bl1ehSRLhMMbUNUAofowQuln6OCBw1a7AnuTGX748k5e8oMn4MLImwxMYbUbSA/QGeskY2TwuyZ350/GhvoNXLDwQi5tuJgtgV0AnFJ7ChFPZFrbu5oDSKqMO6exXrFryT3f//yM1zFtJAka12AFFmP026U7PEurKlpdS2Rj8Mz34YWf4252IbtkzLSB3ju+BEjnUIqeaBZNkThzcU3ZqVLRHAjwhd3UtIx/MDtrUS2yJHFgOE1vLDNhW1mRaV1p58z2dcZmVeJGUhS869dT9Y63z8qtmnjwIdLPPkv6hRdmvK3D7HCEnYPDSYoQgp5ddoxV89IVqBX+KG9NZkiYJkFFYW3gcHC/LxyhurkVEHTv3Dbp9pIkcW5VsDRX6hVktRseHkbXdXw+H/X19ViWRVeXbelpb28vlT4BcLlqkOXxIkySJNrb2wHb8mcYBoFAYFyJJbe7Ab9/CcKyGHniLwghOKCr4+qNTRdL6LjdTaSHoX9EJRlu5cWiIIj3kHzy+1gH7eD8fMbA5VHwR9yE6+31FMuvuDxe3DVxBObhWDsAy8K/9VaSvVvZOTJAoMMWC/374hVjsbYMbAFgWdWyijFxk+HVvKxffhqZUxQOmT3Iksz6uvXT3l7SZFxt9lqXJRYgIdGd7KY/1T/FljPENGBM4e7c/jhCgFbrRQlNU9i4QyCrdiLFwN9wddgW4Pz+2LhYu+cP2HGCa1sjBCbpVhFp8LHu4jYWrZ/oyg/7NFY22d+7ZzrL182rbvLjCbgwdYuBg9NzuZdjtm5Vz2pbhOd27MBKObXtjgWOsHNwOEmxTANfOIKiuWhYsrTi2OV+D6+pDnF+dRD1iBiflpX2H+ahgwfIpSf/w9zmcdHidmEKwQuJ8vFEx4OGhgZOP/10VqxYgSzLDA4Oks1mcblcNDQ0kMsPoeuV3US1tbX4fD4Mw6Cnp2fce+l0GsMwCEc2wkCSbPdeBtNZHpTq+PWzB2dc7sHtqiWoXUDmJY2W7r1ovjAvdcfI6ibi4NPcng/wk4Ekvbk8/oibNRe0snRTw7ibfih4CrLiIVDjRShDRPt6sIoxhbJMY1UjC0kjYl3s9oPLq6LnDIa6yltb4/k4e6N2jOK6+smzYKdDxsjgVbwsCi0i4Jo8NKAcrgUhJFlCTUmsVu2uHy8MzLMlqOcFeOq70PeSvc/2EK6WAK6FM6hLJ0mw4Ez7/13P4Gr0IKm21c4YtuPhMnmTaFpHliQ2LIhUnE5zKfgmEZWnL6xGkmDfYIpoemJmuiRJNC22hWXfvti0EymEEMTvupvc7t0Ia/bJF1pLM1pTI8Iwyfxt8pAOh/nDEXYODicpiqqx9PSz2XTVG9FclV2BXkVmU9hfti5dsLqWuvaFtK1agzxJiYMip4Z9SEikX2HZsX6/n3A4jBCi5JZtaWlBURRGRx7nUNf/kEjunHR7SZJYsGABwLgi6S+//HKpLp7H3YiyNwdCsMvnxnR7WX5ELbLpEqqrZ0XrEhbX1rFgtIe8YbGts5uewQP04CERWkCocC0kWcLlHW/tkWU3oeAa3D4/jauCnHrF68dfu7bTOY1RyIyyMx6lusO2+vR3xssK0ZcGX0IgaA22UuudeS/Q3IE4uQNxrLyJpmioikrOyk294RHILgWt4I5ckV3EiuoVs+pLOylCQPdzkEvYLcQAxa/hXVWDGplhi676VeAJQT6NNPoyrpYAkiYjCuVJvC6F9567kDdtbCHomViWRAhBKjb1OYr4XFy4vJ53nLGAiK+8+KtpDaB5VPSswWjf9B669IMHye3eTeKBBxHG7MvjSJKE99RTAchu3z6nuRymhyPsHBxOchR17rWslp5+Nq2rTkFzV765LfN5+EBrLZfWhue8z/kgnx9vwUgkEiQSiVKXCV2Pk84cAGHhcTdWnKu+vp4VK1aUyjMB+Hy227qnpwcjmUQb1MjoMrtCPmRJsKZ1+udBCEEstgXDsK2i1aedQbU/xOJYD5JpsnXXy7woguCJsDxSTW4wW9H6EgqtweNpoqHlrIluNF81C6oaqSZHPt7HUJVGdXOAtlUTXayGZbBzxBa9lWrWTXpcpiC/P0b25VHMWA6v6iWRT9CV7CKlz9w152q1hZ0nKnNhw/k0+itftxkxut/OhFXd0LhmbnPJCjQVzlfvFtwLQwTPa8HVfNhKqchS2bqGALHBDNse6WbnU71TWn3Xt0VoCE3+3ZRlifoFtnifKpaySLFlmGflijmXLHF1dCAHAliZLLm9++Y0l8PUOMLOweEkZLSvh3QsOuW4hGHyy55hticnBl7PBlmSCGuvjE6FqVSKJ598ku3bt5dujMWOE3V1dbhcLhKJrSAEXm8bmhapOJ+iKDQ1NaGqh4+vsbERRVFIpVIMP/ccmlpFv7eOjM9NWzg9rUzYIpnMQYaHH6ar6+cIYeLqaEcOBKhRLSKDXQwO9vNsNgSBBpZZKnue6+fFB7smrUGnqkGam99CMLgaSZLs3qxjOo9ILRtYTxwSfbyUTrP41Doi9b4JFsbuZDc5M0dAC9AWbJv28RQxBtNYeQvcMj2uAao91TT5mxBCsH14+9QTHIEScKFG3ChhNyI/z5bh3i32vw2rMUYNMluHMKZhNZuUpnUgyRA9hJQfRSrUqEuM6TIxGYOFeDhvwDUjq+9k89YuCNK8rIpF66e2uFqpFLl9tgDzrJo86Wq6SLJcmie7tXJdTIe54wg7B4eTDGFZ7H3uabbccwejveVbXRXZkczQncuzZRoxcZZlMtx1sGLpk7HEdIOUefySKPr7+7EsC9M0SzfGjo4OlixZQktLC0JYJJK2sAgGT5nR3EIILMtCVdVSZuzI1q1YAg7Wb8Tn62BDR8eM5kwktyGEoH9XlD3PPYOh5/GsXoUqyyzr386QCT0JjZpIA8qALdCCNR7kMnXPjiQ20M8Ld/6Jvc89ffjFmqWsclmoVp6B2ACD+fIusvZQO29Z/hYubLtwQtuw6ZAvNKMfCSe5o/Ov3Lb7NlbV2Df5XSO7ZtVyyndqPf7TGlGCLoYyQzx06CEOxg9OuV3lhaZgaLf9/6b15LsS5HtTGP1ziBd1B6GmUKNv0LZ6WpbFnU8c5MeP7pu0/lw+axAt7LduQbDsmCOJZXTu2dbHH7eU/867vSqty6um1Y0iu3MnWAK1sQG1duau93J4Vq9CUhVkvw9xHP8uvBpwhJ2Dw0lGbKCffCaN6nITrp/cTSWEYFvKvrGsnkbP11wqxa4nH6V753b0bPkbUpGHRxL8oGuQLfHjk0QhhCjFwhWFF4DL5aKtrY1wOEw224VppJAVD37/1AVyiwwMDPDss8/S3d09bv6hNWsYOf18ki3rqIu00lEbmfacppkjndpLNpnASEQY7elG0TQ8K1cC0DS8G1UxqKqrZk3Az2ivfV5rW6dOPjDNNFljN+lMF6N9Pej5ggVKlvE2rOAyBniP2k+dSyWTyHNoxwgjR5TlqPXWsiC0YNrHU8TKGhgjWSQJdrsPANASaGFReBGarBHPx+lPzzyrVRrTnWHXyK4JvWhnxcBOOxs22IjlrsUYsq3YWvPMS7uMY+EFsPF6aD/H/lw+2k14dww5licyicga6UkhLEGgyjNp0sSRKLLE9t44+4fSxKZoYVYJIYQt7Jgfa10RJRCg+r3vJXT55ZO2I3OYHxxh5+BwkjHUZVsualoXVEx2GMgbDOV1VEliuW/qwHBvMESgugYhLIa6DlQcW19wQW5PZo9LE/BoNEo2m0VVVWpqytcHSybtWmoB/1Ikafo3mnw+TyqVYmBgAIBwOIzH48GwLDoVH2gaKxpnljSRTu9BCItcQiCJIHULOpBlBSUYRGtuRo000uEW1LS00JwSGHkTzaMSqplakEejz5HKPo8WitrlWLrGFBdu3cSqTW+mYbndaWO0L03vniiDhS4Lc712esHqJEIKnTn7M7OsahmaorEwvBCAl0dfnvX8Vt5kidQBwIH4gRl3xRjHQKGcT8MpGANphAAl6EIJzLElVqAOQk0gSUiSRFcheWC5rOKZpIPFSE8hzrJl+qIy4FZZUG3H6+3om7xTzGhfit3P9RMfLh9+YQ4PY46MgiLjXrJk2vufDrJ7+vUcHWaPI+wcHE4iiu5SgNq29opjd6TsP+yLfR48ZfpTlqM459DBysJuic+DJklEDYP+SVx8R5Oita6+vh5FUdB1nRdffJGenp5C60KLdGY/AH7/8hnNXVdn1xOLx+NkMpnSfgDavTned+5C1jR7icdfZHj44WnNmUy+jGVZZEfsG1/NmGvnXbuGqgsu5pLXXsGFjY2kC1mNNS1+pGm4Yf0BuyyIJ5JHYIzvOesJQ7DBLs8BVBesU7GhLPmswe17b+feA/cSy82ua4DeZwuUfv8opjCp8lRR47GF9rIqe117onswrZm75sx4juQjXXh3W4RdYQzLoDPeOfWGk7HoQmg5FepXoBfOsdZYPrFhtgjLYqdlfx+aLQlRJvklm9JJjmZBkqhumpm1cEWjXZJlV19iUlEe7U8z2ptiuLt84oowDLSWFtwdHUdNiJnRKGZi9jX1HCrjCDsHh5OIaF8fpp7H5fESqq2bdJwQgt0p2yW3wj/9Mg62sJNIDA+STU7eYUKTJRYVrIAvpyq7becby7IYGrJbLNXV2edgaGiI4eFhurq6kCQJSZJpbXkP9fWX4/E0z2h+t9tNJBIBbLes3tWF/4EHWKrrrFixgqBHw+eyGBp6sJDlWvkGZpppMtkusskEIl+N2+cnWHM4rsm9dCmBM8+kvamBxbLKtl3DGJagpnl6NeDcrgY0LYw3FEAow8SHBsilx7vIB/M6fx0Y5YlsBn/EDUJw6OAAPcke9kT3oMkzz6wWpkD2qEiqxG5lPwBLIktKlszWYCun1J7CJe2XzCp2Tw64kDQFkbdYIdmWpd2ju2c8T4nIAlh2GZbwYkbtz6zWMEc3bBE9CzvvIP7QfzFs5bFcMhG3WqppN5bRghs8VOvB5ZlZItLiej+aIjGSyjOYLJ/0UV343Iz2psom3miNjUT+7hqCl18+o31Pl9STTzLy81+Q2eLUtDtaOMLOweEkYviQbUmraV1QsVL8QN4gahhoksRC7wzaXXl9hOps69RIT+V+ocv89ry7UsfWHRuPx9F1HU3TSgJscNDux1m0rAEoiptAYPms6swV5xkYGCC3ezdKNkdAUUsZs6oaxONpAiCV2ltxrmzWztTNJyUk4bOvXXFNRg523wexLhCCPz11iINDKeKmiS88PRehJEn4/ctQNRfuiC0kRnvG9Fg1DdK77mHbjofZHo9TVbDavbzP/iy1BlrxaTO3XEmKhG9dHdrZtRzM2ftbGjlcKFuWZM5vPZ+2YNusroEkS6gN9rracnac46HEIXLmHLJYAWMwgxCgRtzI3nnK8FbdMLKP0ZFBwrlegi0BZEkquarH0rAozLLTG2leEpnxbtyqwoIa+/rtGSj/4BWq8aC5VYy8SXxo8mz42XaamAq1EJOa27vnuIRpvBpwhJ2Dw0mCEIL4kB33VdNaOdDdQtDhdbPY50GbhjtvLDUtdsmLke7KDdgXed0ld+zAMXTHer1elixZQltbG7Iso+s6o6N266aiBW+u1NbWIkkSyWSSxN59mJbgtmEXv3u+i6xuuxX9ftuKlErtqTiX37+Ittb3kR9qBY64dsN7eKlrF/f/7RG6t+9kVbITc3GATN3MSmAU1+IK5hCYDHePEeWKSlu6B4+VI5McJltlC8a+viGELrEosmja+ylHd9p2f1d7qqfdF3a6aHV2jKE3rhJxRbCENfPs2FzCFs+j++3fZQnFr6HWTR2/OG0kCVGzlJFUnurMfpqW2PUCjaEMwhwvbmRZItLgI1Q7u/0vqbMtcnsHy7taJVmiquBijh4hLI3BQaz00U14crW1IWkqViKJUXjgcphfHGHn4HCSIEkSGy6/mlXnvXacK68cTW4Xb26s5qq6mRcSrmpuAex4PqtCbJRLlukoWAN3p4+dO9btdtPW1lbq7zo6OoplWfh8Pvx+P9lsD93dvyYW2zLrfbhcLsLhMFYqxXAiQcyEWKiK/d39bHtxC6Zp4vfb1qlsrgfTrHyzlNBoWbqRSGMzgeoxyR7De9lKkL/JjQzfeSd1e7ehiBzduo4+g+4eLledbUUM+qntCNOyYvW49+W6ZSwmBekRDggDJQBpPYMUc7MwtHD6J6aA0C2sQmbm4shirl12Lee0nFN2bF+qjye6n2AwPfObvFJlt+qyciZLlA6CriCWmGFtu+E90PUs7LPjIV0tAQJnN+NaMIMWYtOhdimL6wKs8QzS1hZC9igIw8IYmZ8akkUW1fmpDbpZVOuftMZhpOGwsBtrNUvcfz/DP/kpuc45xCpOgaRpaG32w2G+c/9R28+rmVdGJVEHB4d5QVYUIo1N0x4/GxeYxx9g01XX4PJO7Z7bGPaz3O+hfQbu3vlmeHgYoJQdm0rtJZfrR3NVzWnehoYGOHAQnyzT46tFUlT8VpJ43GJ0dJTa2lpc7jryuUHS6QMEgysnzCGEhSTJqJpG2+q149+0LDLDnfTQjFXTTG3rIOrgAPXRfno9Czk0kmZR3fTi7CRJwudbiGGmqG5qJRI+ogxO7TKWHPgb2zKj7EmlWemPgWpRpVXNyg2rD6TJbB9Ga/ThW1NHva9+0rEvDb1kx8ZJUOebmUVVkiXUWg96X5rV0jJOW3nWzD/TwwVXec34DNDpJKbMBCnSTjjoJ2zkId2PtLwaSZNRwoe/G/tfGkJRZeo7Qrhn6Qb2aArvPrNy4lSo1oOsyuQzBumY3XPYTCYxBodAktDGlAg6GrgXLiS/r5N8Zyf+M04/qvt6NeJY7BwcXmUM5Q2SxtwKhE5H1AG0eVysDHjxTTPrdq709/fT09NTaiUmhGBkZAQ4LOzSabuivs87c0vUWJqbm+nIZgkqMgf9tYDEqlbbUloUkz5vh73PTHkLyNDwg3R3/5p0ev/EN+Pd7DdkLFmlNlBN2tfBoViYplH7ePZN4mqbjEjkNNoXfJBIeOPEN4ONdLhVVGEQTYzQFeqG9SMsWd46o30UKdaAk6dRDLcj1AHY5Upmg1ZnfxbFUH7mos7UYbRwbWqWYCbyE1yj84aiQnXBrT28G63eh1rlKQlI07AYOpSgd08UUz+6vZZlRSZc57UFXcHyW7SeaY0NyL75zQY+EldHB0gSxuCgkx17FHCEnYPDSUA2mWTznX/mwItbpgxIfmQ0wXcPDfDiNLpNTIVpGAjr6N6EZkJXVxe7du0qCStd1/H5fGiaRjgcJp8fQdejSJKMz1fZqjEVtoVjkFTeZDjcgEuVWbGgkFgyMoIQAp+vw24pVcY9KIQgnd5HKnmIaF8vhn5EDbaRvezFD54qFvu9JOUw8ZybcCqGZJp0DqVmFHyuqgEUxY2wLGIDfRzc+uLhaydJuGoWsoAMZKJYrmrq/XW0h2Z+joQpSu7F7WI39x+8n/7U5EWI24JtSEiMZkdJ5Gd+k1drvXhX1+A71T73lrCmP8/oATAN8IQQvjrSm/tJPHIIM5mfetsZkMmbPLhrgB61IJSHJybUxIcyWKbA7dPwBufe3zlvWHQOpcgb5b+fS06tZ/V5LaVaiPn9+4GC6DrKyD4fWlNjYb+zE/QOk+O4Yh0cTgJGerrIJuMkR4crWi0MS3AwY2cNNrnndvN4+anHGO4+xOoLLiJUO7mrLWmYbE1mMITg3KrptUeaDfl8nkTh6b+62g5Od7lcbNiwAdM0kWW5ZDnzeFqR5Tm6h4XAs+YUdu7pIW/prKzxU1NdhSzLZLNZMpkMXm8jHe0fLLuvXL4f00iTSaQZ7NxNtDvLqvNeU3rfGtpDJ0HwVdGGwoBwIbs06r0GgdgQGa2ReNYg7J35ddzxxMNYukFVczPB6kI8ZtVCOnr2k8wNcErdpawNnm33l82baK7pF3A2R7MIQyC5ZXbkXyaWjFWM0/OoHup99fSn+zmUOFRqNzZdJFXGVSjh0Zfq4y/7/oJf8/P2FW+feuPhQmJLwVpn5S0kTZ6WpXEm7B9OseVglD5vgLcHG2zLnRCY8Tz53hRK0MXooC2GI40T+/XOhl8/e5DhZJ43rG8u67If62oWuo5eKFx9LIQdgG/jRsQ6oxRv5zB/OBY7B4eTgGhfDwBVTZVrsnXl8uhCEFAUarW5P9cJyyLa11dxTNK0eHQ0wfOxNOZRLG8QjUYRQuD3+3EfUVhVKXTgyKTtjEmfr2PO+1OCQfS1a3nB48MY6aajxoeqqoTDdkLKyMgIkiRPKiAzadtSoSfcSChEGsbERupZevImWRQ8/hp8cQMJCDaF0RS4vNrkwxcunrGoy2Z76en9Da4a2x0d7es9/GZVO6eG/FzXXM1av4fkaJYt9x1i15O9k8xWHr3Q0UAPC2L5GJIk0Rqs7NJtC9o390OJyiV0piLsDqObOqPZUZL5yessAiAEjByOryvWlFNrPPMeX7d/yHabL2isg03vtYshS5It7A4lyPckiRWFXf38ZOO2ROx5DgxXtsybukVy70GEYaKEgiiTdGqZb1wdHbiXLHG6URwFHGHn4HCCY5km8UG7zEmksbKw60zb1rqFXvecrQLhghCJ9le+8Te4VLyyTF5Y9OXm0PJpCoqxdEVrnWma6GPcm5ZlkM3ZAtjrnR8rQTgcpj7kJeKBep80bv/F9Rze//j6apnMISzLJBuzBfY4Ua55yKx/D6EFG+kIBEgUREfVQju5IKSn0WYRt6goHnK5flRfDoEx/tppXqSN7+FQzUJyQsft19BzJul4nnx2+uVqzBF7rQOeKACNvkZcSuWae8U+tF2JrplntQLCtMgdiCO2Jaj12hbIrmTlcjzoadtFLisQWVBat1o9j2VOsF3u+wviqqN2fMFjtcYu4p0byqCndWRFIlA9/YLhlWgv1LM7MDx5LGZfZ4zN9xzg0Ga777HWNruagg6vLBxXrIPDCU5ieAjLMtE8XrzByiUaOgtu2A7fHPtfQsnClBwZRs/n0Fzln7wlSaLN6+LlVJYDmTwtnrnv+0iEEKVadVVVdrbr0NAQO3bsoL6+nlWrVmFZWXzedvL6KJo2N6uEmUhgJRKoDQ2sWNDA6OgouVQcqkJUVVWhqiqaZlvTLEunp/e35PPDtC/4AIriwbJ0crle8uk0ktGA2+fHExjvpl4a8LLE34FuCra+YFuyak5ZiP/0hSjB2bm0VTWCqoXw+PPE5RjJYRdGPo/qsq9JMp/kz/v+DMi8acV1+EIu0rEc8aEsta1TZ+BaORMzaYvpQ7ItGqey1gHU++pxKS5kSSaRTxB2z7AMjySR64whdIuO9lYGGaQr0cWK6hWTb+Pyw1kfgWwMIRTMmP3dUOdJWBUZTOTI6iYuVaYpVJjbyEPsEFLVQmSPSq4vhSLAX+9DmadEo9YqL7IkMZrWiaV1wmXcyx6/hrAE2UgzgQ11qFVzyxSfKcbICLnde1DCITwrKlwrhxnhWOwcHE5wYgN2YHq4vqHi03bCMBnWDSQk2j1zd3+4fT68oTAgiA9MHhwPsKCwv4PZuXUFmIx0Ok02m0WW5VK3iaJrtiiwVDVAQ8NVtLa8a85WidyuXURv+z2Je+8rCcmisAwEApxzzjmsXGmXN5FlDSEMEBbZrG0ZyWZ7EMJCzwgQXkJjr50Q9g+2KM4ndIy8iaLJBOsCJVH3TOcIP3/qAIdGpp8EI0kSXu8CVJcLzZ9FCIvY4OFr153sJprL8bdojjuHkoQLRXrjg9OrtSapEr61tbgXh+nK2cfaGpha2MmSzFuWv4XrV18/c1FHoexJQZA15QsWu0TX1MklkgTeCMZoFiFA9qrz122iwKFR+9y1RLzIsgSWBU/+N7z4G6T0MGq1GyEELksQqp0/UenRFJrC9nwHRspb7YIFt7NhytC2GK2xsey4o4Xe3UP6mWfIbtt+TPd7suMIOweHE5zYgB3jFq6rXHvqUNbO9Gtwq3jnySoQmaY7tt1rW4R6cjr6JEVT50IymUSSJMLhcCmeLhqNAocteEXmw9WU77LdfN3uEKonUNqfZVlIkoR8RDsmr8d2/WYydoyfLLvwB5ahJwNISOOvXXqY/BPfxtrxV8DufRuo9hCq9Y6L/RpJZhlK5Dg4A2EH4PXabk932LasjY2z60504+/fgj+dYTAxilroQhEbykwrA1dSZLQGP8kmg6yRRZO1ijXsxhJyheZ0bYrCLpTxo8oqaSPNcHa4/OAx4hkY44adX2sdQNeofX3aii5eWYaQXeSb0f0oVR4CVR4WLgzRuGjmorYS7TV22ZLJ4uwURSZYOOb44LHt6QzgWmB/L/S+Xqz8/GYiv5pxhJ2DwwmMEAJfOILbFyDcUPlpu93r4qq6CKeHp1fUdjpECvuM9VdOoKhSFYKKgikEPbn5/wPe0NDA2WefzdKlhW4P2SzpdLok9ixLR9ej89KbUhgGRm8vOcPk/lGV37w4hCQrGIZRysoF+9rkcraFshjTl8nagtDjaaImchH5EVvQhevHXLvRAzyZd/HtmMrmeIpQjZdV5zSzZKMtkMxkktif/0zbw3eAEDMXdp42kCRUn4kgRyo6WnqvJ9WD5g7SrvogF2fYKyMrEnrWIJOYfnxkzsxR7ammKdCEIk8/oxbs8zab61QSZTGdFq8dr9iVmCTOLjkAj/8n7LwDAK0lgGdZFVqTv/z4WSKEIFrowNFWNaY2XFWH/e9oZ2ndViKPNM+Vg9qq7X12RycX5u54L3pvH6OHRsq+fzRRwmGUcBgsgd7Vfcz3f7LixNg5OJzASJLE4o2nI4SY0trhVxRWBuY3MDxYW09Vcyuh2nqEZU3aOFySJBZ4XexO5YjPsTjyZLhcLlyFWLGitS4QCKBpGqnUPvr7/4zH20Jz07Vz2o/e14cwTOKSCz0QojHspdZXzeDgIKOjo4V6eXmee+45dF3n3HPPxeNpBUlCz49gGEm7ppymseGKq0mODOMeWxA2eoCD+Mi6I3jGnM/i9ZXdbvKHDhHWdbR0kn5ZImeYuNXpCShF8eBy1WL5DRrOXUNt4yYA4vk48XwcyRthpaHxt2yMHl2nvdpDbDBDYjiLLzR5fKSVNdB7kijVXloiLbxtxdswK7ScK8dj3Y+xN7qXi9svpiXQMqNtZZ+G7FGxsgYrtKXUNzZMHt8XPQB6BvK2i1IJuFAC8x/7KUkS7zmrndG0TmRsBnNVoT5g7BCWJJB9Kgj7HCra/K2jIeThtSvqaama/HuvHdpB/pBKPOBFiPZjnjyhtbZgxmLoPT24F82taLiDjWOxc3A4CThemWyqprHynAtoWb5yUlFX5MLqEB9pr2dN8OhWtYeJbthstlCjS6ue89x6wQ07GKgBSaKtyseCBQtYv349ra22kDicOGERj8dLYgogmdxJPm+7CL2BIHULOg5PLgSZ0UP04wZPmGZFndCFQNI0tPp63KpCTXoUIaAvNjM3mt+3mGBoBYFIU+mz052wLSYNkUUslHTIxunK5KhuCdC4OIw/Ujku0xjOkt0bI7f7sAVwpta6jJEhpafoSfbMaLsiapW9xhazgdMaTytlyE5gdL/9b2RuRaqngyRJVPtddnxdEX89qC4w8ux/cjt74gbmsiqU4PyKS0WWWNcWoTZQPgveTCRwpUeRZYHwBWZklZ0vtGbbuqr3zu6aO0zEEXYODicwmUR8Wp0fDmZyPB1NMnAUy41MhU+RUY6CAO3t7eWFF16gt/dwrFgxkaGYSJHN2jcNj2dmVqByFIVdn9cWja1VXkKhw9mwYN/MxyZxwOE4u5GRx+jq+gUjo49PnDw5QJchISSF6kCEdHeK5+8+wMHt42PFijfD5qw9d/fozBrJV1WdQUP96/B6D1u0imKquWYlLYoJwmA4Fcff7GfBqhoCVZWFnTlaEJdhdcaWuiLN/uZxa5kpSsRtxyFWagtmWRAr1MurakfvS5HvSWLl5t+SPKlLWZYh1GoXgB48gG6YuDzH3oGmd3cjSdDY4qZjfQOae2ZCfD4ofpaNgQGEE2c3LzjCzsHhBMU0dLbcfQfP3P479Fxli83OVJZHRhNsTc5MAEyXbCrJcPf0i8vOR6xbkdHRUaLRKNlstjR3R0cHDQ0Nhfi6PLn8EAAeT+U6f1MhDAN9YIC8aTHor0KSoClSPuC+WKg4FosBdlHkQGCFXZjWNOjdcZCel3eOPxexQ3TjBXeINq+H5EgWhJhw01eb7KSVmpQdF9Udnd11zSaT7H76CXY8/jCbGjdxQdsFLKleii/cTC15yMXpzk7vZmtE7XjCfdIhfvTSj3iy58kZr6cpYB9Xf7p/VuJQa/ITvLANz7IqMkaGfdF99CaPSOxJDdrlRlQX+OvJ7Y+T2TaMGZ3f5AHTEvzk8f385cUesnqZY4m02V090j0omow3oNnxhfOcXJQ3LF7qivHAzv4J3zu98DDUsqqeho7QcRF2cjCIHAggqRpm4bviMDecGDsHhxOU5MgwQlioLi+au3I2XzEjtu0o1JDTc1k2//V2AE57/ZsqruXFRJpnYylW+D2cMw/txYQQJYtY0UImSRJNTU00FcRPJnMIhIWqBlHVOe5Tlolccw37dnSiG0HqAu5SbFs0GmVwcNAuWlxfX1pPLBbDNE283jbc7gaSqZfJZ9LEejPk47tpXjamflesix484AnR7NJIjNiWx+AR2ZpaczNIEqF8hgh5Ir6ZZ1MKITDMGAOHtiMJH0uls1hds9p+M9LGqSMvYFi91LvWYhoWydEsqkvBH55oubNyBlbGQJKgR+7HFOaURYnLUeWuwqN6yBpZBjODNPpnVn5DGpPtvXVoK8/2PcvSqqUlwQhAvJBQEWpBWGAV+sIqU7iaZ8pQMkc8oxfiH8vYUGqXEa8xiKd9BKo8ZHeOoA+k8Z1Si1o7f7GwkgQP7hrAtASnLqgiMqaGZVHYFfu2Hg8kSSLypr+zxd0U4RwO08M5iw4OJyjxoUEAgjWTxBEVSJkmI4X6da1HQdhpbk+pMHJieKjiWFPAiG7QM08u4Ww2Sy6XQ5IkQqHyxZkPu2HnZq0DkGQZramJ3pYlIEmltk1gC7uuri4GB+3r4vP5cLlcWJZVypbN5fpBWBhZQLgJ1o6/doavlj5XDXhCVOt2uydZlSckLchuN2ptDR5N5h0dbi5ZVbnUTTmGRx5mYPh3qIFRQJAYHjz8Zu1y1i0/h43LzyKsqfS8HGXXU30M7I+XncssWOvkgEZvxs6QbvI3lR1bCUmS5uyOLdLkayzNM94qeljYmbHc4fp17vm1c/QUrKjNYW/5GFh/LVF5BYZWTbDaDZZA6FbJ8jlfaIpMY6EwctcYl72Vy2EWHhy0xkYyyTwDB+Iz6jIyXyihkCPq5hHnTDo4nKAURVSwpq7iuJ6sLaJqXPNXv+5IQnV2KY5ia7PJaHHbSQW9OR1rHtyxRTdnMBgs1a/r7+8nkUhgFWIP51PYFTljYQ1Xr2tmdfNhMTnW9VrMUj7SHZvJdmOYabJxW2iHjrh2xoKzOX3VeSytbkCO29ctWOUu27vUtWABrrY2JG12DevdLvuauYImQ5lh/rbnGeL5gnDz10DzevDZySaBatualRgpLzrMmG31yvlN0kYaWZKp81X+XE5G0brWk5qdsDOGMySf7CG0R0WSJFJ6ioR+uAwNgQYINUOkrSSi1Hm21gH0FhJaikWCy5EsxCUGqjwli2GxA8Z8UsyKHeuyN0dGQJZQwmFkv5/OLUPsf3GI+NDRCddwOHY4rlgHhxMQIQSJosWutvINtLdgHWt2z04ATIdQbT39+/YQH6os7GpdKm5ZJmdZDOUN6ue4pqIbtiigDMNgx44dCCE466yz8Hg8hMPrcblq7JIjc0AIQeqxx1Hr6/AsXsyS+vH1AEOhELIsk8vlyGQy+Hw+6uvrcbvdhwVe9DnisReJD0bwq8smWFs9isy5BRf1nuftcxmsKS8M/GefPW5tiZxByDP981lMJFG9OQbSMfbv66X5lNWEXIfFakw3OJTNUxOwRXM2mUfPmRNiscy4LUaGXXHIQJ23Dk2e3bVtCbRQ76unzjs7YShpMmZSR8rJ1DXVMZAZoDfZS6i6cFwLzrR/AHOf3XVjvt2wMMZiFynvVs1lDIxkDH/+IP5MFKpOsdcUyyEsUVbMz5biGsZmT2tNTdR+8INYySRgu/uTo1kSw1lqW+ceJjFTko8+Rr6zk+CllxzzDhgnG8fdYvftb3+bjo4OPB4PZ5xxBs8880zF8d/85jdZvnw5Xq+XtrY2/umf/qkUNO3g8GohHYtiGjqKquEPRyqOLRYEbjqKwq5oNUxFR7HMyYPeZUkqraNrHgoVx+O2hakonBKJBEIIPB4PHo8tiHy+hdTUnI/LNbdSJ2Y0SmbLFpIPPFD2fUVRCBbafRUtdPX19SxdupRIJIIQAsvKY+ZN8mkLRVMLLdkKZEbBPOyiHmvNqUQ0ned7D+/jlqcOzigpRVVDKKofxeMizwgimaPeO6ZLRDbGY3v/xp2dL9OpG3gLpTgSIxP/3vpObSBwRiO9LvthYzZu2CK13lquXXYtZzSdMavt5YALSZEQukWrbK+jNzWxM4qwREmQzrewS2R1Elk75rAhVP76SUBLU55m60mUnmeR/RqSJiNMUYr7my+KrtiRVH5cIoekqiiFWNCprLJHGzMWs+vZ9U68Vg4z47gKu1tvvZWPf/zjfOELX2Dz5s2sW7eOyy67jIGB8k/9v/zlL/mXf/kXvvCFL7Bjxw5+/OMfc+utt/KZz3zmGK/cweH4UnTDBqprKsamCCEYytsxM0dT2Ln9flSXG2FZ4zoZlKNoOSy6iGeLZVl4PB40TSvF1xUF1WTxdnPB6LNjxwbdQZ48EGUgMVHgFAVmUXCOR9DY+EbQG8B04Qm5xsVeia1/ZN8j3yM9uAdhCZoWR6htDU5ZP84vDKxMhqxulrocTAdJkvC4G8nLBponh4aKkh4jyhP9NPU+DfEeenN5AoUEjlSZGDBJllBCbnpz9jmaadLDfGKvxRahDWYNAAPpwj0lPQKGvX4rpSMMgaTJyP75/W4U3bB1QTeucokTgMur0rRhJVUNfkiPIBlZ1EJiynzH2XldChGffYyT1TwsPkBkk3mMclm8Rxmt0Y4TNforW/0dpua4CrtvfOMbfOADH+CGG25g1apVfO9738Pn8/GTn/yk7PgnnniCc845h3e84x10dHRw6aWX8va3v31KK5+Dw8lGsKaWtlVrqGuvXKldkiQ+3FbPO5tqqNWOXuSFJEklt+JUCRTFBI65thaTZZm1a9dyzjnn4HbbN8QjLXip1D4ymYNY1twtIEVLwkElyNP7RugpUx6jaLEb21rMMAxGR0dJpzP4/YtwS6uQJAl3YEz9QSNPNDnKbTTy/ZiKJUHDwhCLNtShTCIMABIPPUT0Jz9hwbDdg7YvPjPvhdvdSEpPoQVMIjX1WMaYwPlQE01kQU/Tm8niD9vXrZywA/shYnn1cjpCHfMi7HRLJ5abXfkLpSCQIrp9PYazw+iWDttvh8duguG9KEEXwfNb8a2vm/cC34os0Rzx0Dq2jVg5XD4o1EMk3lNatznPwg7sWD9JgtF0Hr1/gNFf/YrUk4dL0mhuBXdB/KWix76enNpQEHYD/cd83ycbxy3GLp/P8/zzz/PpT3+69Josy1x88cU8OebDNpazzz6bX/ziFzzzzDOcfvrp7Nu3j7/+9a+8+93vPlbLdnB4ReCPVOGPVE09EFBlieajkA17JE1LV1DfsWjKmL9Gt0adS6PBpWIKMeeixcWbshCiJOyKFruRkUfQ9RiNjW/E55tblwG9rw+BoM9ti8ZyQfHF/eq6jmVZyLJMZ2cnXV1dtLa2snTpUtrXbiLQlMXnG2MlSvTSgwsUNw2+wLTPiVJw5dZm4+zBFnYrm6ZvrXS7G0jmk7haNFYtvphw/ZjsWneQOrcbJWeRycQxGiIAJKPjY8Cyu0YQhsC1IMiG+g1sqN8w7f1PxsH4Qe7ovIMaTw1vWf6WGW9ftNhpKZlLl19Kna8OVWD3iBUCfLYlT3YryEehdtviugCL6ybvyWyaFsmRHP6ICzXUbLvhE70o1a2oo56SwJtPzllSy2tW2B1LMi++iDE0jBwYv0Z/xE0urZOK5gjXzW/7walQ6wu9kGNxrHQa2TeFKHaYlOMm7IaGhjBNk4aG8Wn6DQ0N7Ny5s+w273jHOxgaGuLcc8+1azAZBh/+8IcrumJzuVypETdM5iJxcHCYK5GG6Vlp3LLM9S2VS7RMB13XS627ANLpNLquoygKgUAA08yi67bFx+2eeTmQsYh8HnNklJxuEfNHUGSJ2sDEm6/b7eass87C7T7cwumwyNxMOq3i0mqQFRnDGtNNIt5DLx5wB2lyu4j2p3F5VbwBrWIQvdZg3wyr0lFg5q3FXK46hqUq0q4GGnwTz5EabqZ+IElvLkFUg461tbZruLAkIQR6fxorZ6K1TC5kZkqVpwohRMnSNtNEjKIwspJ5FocW2fXtYt0gLNtK5pl53b/5JB3Ls+upXjSPyoaVzdC/DeK9qB1u1I1z+6xORnBMYo3eb1vF1Lr6cWMCVW5GepKTWmWPJrLbjVJVhTk6it7fj3uh0zd2thz35ImZ8NBDD/GVr3yF73znO2zevJnf//733HHHHXz5y1+edJuvfvWrhMPh0k9bW9sxXLGDw/yTScQZ7j5EPpOecuwf+0e5ZyhGwjj2MTNHEyEEzzzzDE888QSplN3Ivej+DAQChexU++alaWEUpXICwlQYg4MgBCnVjenxURd0o5QRXJIk4fF4xrn2gsEgQhik00/T0/tHVC1iz6nHMc1CaYlEr90f1h2kQVPZs3mArQ93kUlWjplT6+pAlvAbOZRMmsFEDsOcusVckYxpEJOb0dVa6nx1WKaJNbbjQ7DZdsfmEvTqBvXtIfzhw6JV5EysnIkkwaA8Qjwfn5euIgEtgF/z2zGi6cqu/XJIbgW1yo3W6EcYhfUkekvHJAxB6oUBsnuj89oFBexOD3mj8jUoCid/xAXBQqJJvNu2Jh4DjEIcu9owXthVNfpYdkYjC9fN/cFrNjhxdvPDcRN2tbW1KIpCf/94f3p/fz+Nk6Q6f+5zn+Pd734373//+1mzZg3XXHMNX/nKV/jqV79aqll1JJ/+9KeJxWKln0OHpt/2yMHhlchw10F2PfEI+/+2ueK4jGmxO53lb4n0UenRWo740CBd27eSHBmecqwpBFF9dsVQc7kc+XyefD5fyn6tqalh3bp1dHR0FMbYf1vc7rnHexkjduuuqC8CQENo+q4yr9eLpqWwhEW0b5RdjzwD6WU0Nr4BSbKtKGa8jwHc4PJTZYBl2IWJvYHKlirJ5UKtqcGtyUTSUUxLMDSDjMqAK8D71ryPNy19E3uffoqn//gb4mOT10LNNJGDXIK+Mq3FzLj9mhzQuOfQPfxi+y/KZqDOFEmSShbE/vTMY64kScK/qRHvKbXoqsELAy+wtfM++81gI2Y8hzGUQe9NzXt83Y7eON95aA/375h83SVhF3bbdfVkBfQM5GyPkpU3sWaQCDNd/nYoym+f2MtAV+Ghp368sHP7NCL1PlTXsW8tBqA2NKLW1iB75t8V/WriuAk7l8vFxo0buf/++0uvWZbF/fffz1lnnVV2m3Q6jXxEBmCxKOlkT11ut5tQKDTux8HhRCY5aosMf1VNxXH9efvGUKWp+I5SYeIJ+9y3m4Pb/sZIT3fFcUN5g28d6OcXPcOzspgUQyr8fn/pb4CmaVRXV1NdbZc1yeWLwq6+/CQzwLtmDTXvvYHuJWuAyUtYAGQyGV566SU2b7aFtyRJ+Hy2AEpFBcnRYbyeRfh8HciyCvk0Q7ksBhIeTwglaYtdf7h8YeIjUesbkJBYoWQ4Y2E1Xm1mN2VVggApdHEQYVkkRsZYyIKNtJPlGusgb6zSMPImAwfidO2yM5+L5UIMH6T0FBLSrOvPHUm9z75ufem+Oc/1VM9TjAxutRMogk2YiUIbsdD8x572x7MIYWeiTkYqVrTYuUFRYf074dx/Ak+YfHeSxMNdZF+unF0+G6IZneGDPSTSOnIwgOz3z/s+5oJ3zSlUvf3teNevP95LOaE5rgWKP/7xj3PdddexadMmTj/9dL75zW+SSqW44YYbAHjPe95DS0sLX/3qVwG4+uqr+cY3vsGGDRs444wz2LNnD5/73Oe4+uqrS3/cHRxOdorWsGB1ZWHXVyhM3OA6emVOjiRQXcPggU6So5UtdhFVQQAZyyJmmERmmLF7ZJJEOebTYgcg+XwMyx7ArCjsVFVlaMgWR/l8HpfLhdttu1xToxYRNwSqamy3229/Cz/8ATXPPcdHdYPEipVIl16LtOn1BAr1xaZCa2wgu20by5QskSUzd6Hpeoy+vj9huWIIFo23tioa/o3vYImvFlQXuYzB/heHkGSJpiXhksUu6kpA1o6N05T5+bw1+G2L3UBq9m45YQnUjES15seTT5PSU0RCTZjddhjD0UhS6E/Yom2yz4ihm2QLLvZSKZtwS+l9uWClNWP5UgeT+aIx5GFfbIRkzphgrSuSiuUY6Unh9qnUtzuGkBOR4yrs3vrWtzI4OMjnP/95+vr6WL9+PXfddVcpoeLgwYPjLHSf/exnkSSJz372s3R3d1NXV8fVV1/Nv/3bvx2vQ3BwOKbks5lCbJ2Eb4qs2KLFrsF17L7mwWpbWCRHhivelFRZos6l0pfT6cvrMxZ2xXi6orBLp9P09vYSCoWoq6vDMBKYRgokCZdrfuKFJEni/ecuYiSdp9o3uaVH0zR8Ph/pdJpEIkFNTQ2qmkKYJpk4VNXLeDJpzAuvRnnkKcD+Q6wC7uefg+efw9f2I/L/80tYNXVRZa25Gc+aU9CaZlYUWAjBX/b9hYg7TBOgeVSQ0qQKFuESocOt2FweBc2toucM251YEHZDShRg1m3EylHrLXyW9CQZI4NXnVmWpjAFiUe6EIZFfXs9BxuWE/a1EnH5MeO2NUwJzq/FTjcthpOVhV2xlIjbp6GVseopAQ1Jst2xImcieebv+9sQciMkmZjqQa4rL+zSsTy9e6IEa7zHTdgJ00SYJrLr6Gfzn4wc95ZiH/nIR/jIRz5S9r2HHnpo3O+qqvKFL3yBL3zhC8dgZQ4OrzyK1hRvKIQ6RY/QgZzt0ms4ioWJj8QXjiBJMkY+Rz6Txu2b3NXT4NLoy+n05wxWzMAjJIQgWWyDNKbTw8GDB4lEItTV1aEoflpa3oauR5Hlud0c9J4e0s8/j2vBArzr1pXNhj2SYDBYEnaRiB9FyRL0+ZBDCwjnddQLXoO0b9/hDRobweuFzk4AvIf24HnjJXD33XBG5Q4MSiRC8MILAUjnDQbiOZoj3kkL4xaJ5+McShyiO9nNwtoGsHoQcpJ81k8+m8HlOSykhvIGO1MZfIpMoMpFtM8gOZQlpMlYpqAX26pWLrN2trgVN+vq1uHX/EjM3GolKRKyW8E0LBqkJnZUtbE7tIClOQMrayd8zLcrdjCRQwgIuFUC7vK318OJE2M+R0Ye9j8KqSGkNW9GDrgwE3nMWA55HoVd2KuRWbqSzoXLSS9fQLk85uK6UrHcvFsMp0N682bSTz+N55Q1BM4795ju+2ThhMqKdXB4tZMsBPEHpnDDZkyLaKHYbP0xdMXKioKvUBw4eaTl5wgaC4Kzd4aFijOZDIZhIMsyvkKtq6IFryj0JEnG7W4gEFg+o7nLoff0kN9/AL13+rFeYwsV53L9KIqCRw3hsxQWf/7GkqgzGsJkf3oj7H4J9u4l89CTpBauso8hFoOrroI9e6a9318+fZA/vNBN/zQKFRe7MdR6a/G4G5BlBS1gZ8SOs9rpGUb2PMKTu55hayKDv5A4ks0YBM5pIXB+C4M5u5XYfMXXFTmn5RzW16/Ho84uq1kuWOSqDNvyNJQeOpzw4deQphC/M6V43usrJNdUN/npWFtLbdsYWSWr0LMZRvZBZqQkOItrnS8kSaI+aK9tMFm+pIk3oCErEpZhkUvNLrlpLsheL8Iw7Ux0h1nhCDsHhxOIVCF2LVBV2UWXNE0iqkqVpuI9RokTRYou4tRo5eDvYouzgbwxowQKSZJoaWmhoaGhFKpxpLCbT4qlIZ5Nyty1tZfR1NQ320Ch8GsymcTrbaO19Z1I2aUs+un/4N67FwCzvYnu3/4DPQuibH72t/Rn0rjOPh39vgfJn32+PdHQELz1rZCvvE+h6+h9fTTl7djDyW7aYxlM2zfOel99KcHE5SsKuzHXTtao738BMiMMZVK4Q/Z1SxcSAJIiRdbIIksyNd7KDxzHGiVorzU0cBBfNklaT5JOp5BUad7dsAD98cpuWABPQKO+PUSkfkwBXlm2s2MBkv1HTdgJ0ywJu4FE+c+IJEulvsDFJI9jiVpru+CNoaF5L0XzasERdg4OJxAdGzax9PSzqWpsqTiuzqXxgbY6rm8+9vWoAhFbdKZilYVdjaaiSRI5y2J0BnX2vF4vy5YtY8WKFYCdTX+ka3Z4+BHi8RfnpZWYMTiIEIJ9lpcdvYmpN+CwsMtmsxiGictVS/UTu6l/6FEKCyXzh+9jVmnsxc392gIei+dQNJnIonpcf/0TLC9YGzdvhs9/vuL+srteJvrb39GwdysAA/Gpb8gDGVuw1nnrcLlsS5vmN6luacM7NilFUQn7w3iwMHNJcl47LiydyGOZFh7FwyXtl3BW81mo8vxG91jCYiQ7wr7ovqkHl0EJusDMoh64i42HtqAKi1SNTvDCNjwrpo5fnCkdtT5WNoVorZpF14aisEv0oRQsfmYiP6/iJrNlC/V/uZXm/dtRK2Rc+wtJJel5FpbTQamuBkVG5HJYTkOBWXHcY+wcHBymjzcQxBuYvlWq0h/vo0VN2wJCdfXjxUEZZEni1JAfTZZwzSGOJ5VKYVkWqqri9XoxjBSx2AsgSQQCK2c9L4CVzWLGE2R0k3QggkuVS83UK6FpGoFAAEVR7A4Z+TxN//lfhwd861uoKzfC9gfpww+u4PhYyHAYfv1rO74un4evfQ2uuWbSeDu1zhZmoXQMhJjSYieEYChjZ+7W+epwuaqQJBlfOEDbKevQtPGdGaRgI/WpEQ7mkgzLFqpLJrUnxvDjPdSc0cjSqqVTnpPZkDNz/HrnrwF435r34VZmlsUqB11I+jBCt1jSsYmV6//hsPhU5/+7saIxxIrGyT/3mWSexHCWQJUH35HxfSWL3QDyQg1XWxAloIGAWYQYlsUYHKLGBVef2oZv6eRuc1+hL3D6OFjsJEVBranFGBjAGBxECR/fLiEnIo7FzsHhJOR4ujBcHi/+SBWyPHUJovOrg5wVCRBQp1euSAhBLBbDGNOsvmitCwQCSJJEPm+7GDUtgjzDVlRHYgzZru+0y4uluagNuKYdTL5p0ybWr19NMvUo2X/7BEqhGPvQWWdhvutddraunmYQD0JzU6uqdO0aZaQ3hWUJWL8eiolilgXXXw/Z8rFzak01yBI+YaBm04wk8xU7UMTzcfJmHlmSqXJXIUkK9fVX0tL6TlS1zINDsJEGcpBPMaCbLNtQz+rFIdy6hTTDunkzwat6CWi29bMoRGeC7FJQpCgALlfTvFsUZ0q0P8P+F4foLlejLlgoy5PsQ5LBu6IaV2twWrUMp4sxNISEVHJ3ToavYDHMZY59jB2AWldwxzpxdrPCEXYODicIIz3d9Ly8g3QsWnFc1rT474MD3No7gmGdXDEquVyOzZs38/jjj2Oatvs2nbZrkhXdn7mCsHO75l6Y2Byy54r7bKtBXXD6FiNbZA6T2fcMrv+8GQBLUdjz4Q+TSqeRZRdKzmQUP4YqE9YFPS+Psm/L4GEDzSc/CZs22f/fuRP+8R/Ltp2SVBW1uhqXKhPKxLCEYLhCLGBaT+NTfVR7qlEKAtzvX4TbVQtIZJNJ9LEiMtBAPTnIJxnI6bglUBQZ2a+xbWQbh+KHMKyjIwKKJVSKMYEzxRVMolZ5kCKNGKNZko93k91VObFnNkTTeYaTOVuUT0I6Xuw4USa+z1db6ECRhWxs3tcn8nnMaBQ4HMdmTrJWX9jF2te2sebC1nlfx3QoWqCNoZmLeQdH2Dk4nDAMHexk/982M9JbuavDQF4na1nEDOO4uGIBRvt62P3sk/R37q04ThTaiu1NT695fdE65/V6S0XJFy1axJlnnlnqA1202M1H/Tqh60guF6Nu24pVH5xZdmYuP0joxw8ip+0bet9VV5Jpa7OPw8ihGq0EaMDna0RL20LVF3IdttKoKtx8MxTref3oR7ZbtgxqXR0SEvU5+xxVirNrCjRx/SnXc82Saya8t+fZJ9l85+0MHOg8/GJR2Jk5RrPpUscJ0wePdD3Cn/f9GVMcnX7ExUzb2VjsADRfArXKAzVNPLfnKV469CK5aX7eZsLzB0b5nycP8OS+yYtzp2O22PaVy5pVVPDVgOaFXAJhCoyY3fpsPjBGRkAIZJ+PraM6P3xkH4/vKX9OZVnC49eOeamTIlpjI+7Fi3C1tx+X/Z/oOMLOweEEIRW13Tf+KQoTD+Vty0ndMSxzciTpaJTB/fuI9vVUHJcXgh91DfH7/lFS5tTC4MgkCbAtY16vt9QzNp8rCru5l97wnXYa1R94P/ub7RiymVjsDMNgx1P3Efzl4wBYmkb0Qx8GClm8yQHiUjWy6qfe6ysFqk+IvVq9Gn7608O/f+Yz8OijE/ZXtHIsVrNcsqqBBTW+CWOOZGyXCMvKEYu9gKm9DBzOwLYnd1HtDfJe1xB/X6Ogx/L09KXZvncAISDkCs04/m26lCx2mVlY7CwT0vZxyIFGRoeHSespEq70fC4RsGvYAZPWObRMi2zKLho+4RoXWf9OOOd/Q6QNM5Yj9UwfmZ3zY100Bm0Rp9bVIksSyZwxaWbs8UatqyP0utfhXbv2eC/lhMQRdg4OJwCmoZMplPSYUtjpRWF3/OKJ/IVyLBO6GByBW5aJFGK0ioK0EsWyJkW365FYVh7dsN1Ybvf81FTLmwK/14UqS1T7p18iQ1VV6v54L2rBJTpw/rmET1kN2Akf+OsY6LgEqjqoc6kla46/XJurd7wDPvc5+/+mCW9+Mzz++Pj9FYRdTTbBKS1hwt6ZCnuJ4ZFHMZUuBDlSR7j85U3XUXPO3yOHmxEpneFojqF4ErJKqUvE0aDGY5dQieaiM3f3poYQloGFhh7XqM7biQ2jyvxmW4oxru/aQPnPSCah2y3OXAqaZ5K4RM0DBStZsVSLlTEQ+uTxktPFKIQVqLW1pQeUoWRu0njc5GiO3c/1s/8lxx16ouEIOweHE4B0LAYINI93XEeAcgwWBFLt8RR2hT6n2VQSQ9crji0K0IFpCLtUKgUcFnbRaJStW7fS3W27p/O67W5SVD+KMrXFajp4NIV3n9XBP7xmCdoMagIKQ6f190/a/5ckBq/9O8IFwZtMJhGqm9PblvC6hjzNuadIxWyXm69c/BXYiRSveY39//5+eO1r4S9/Kb2t1tbiP/ccgpdcXDF5Jmfm+Nm2n/GXfX/BtA5bSWXZhaZF0NwehJwkm0hgjbWiqrYYELqFyJp43QppKQtp9ajWr/NrftyKGyEEo9nKJXQm4K2CtW8lk95Aassg4azd4mRInuE8UxBN6+QNC1WWqJqk3VzJIhueXgKOpCmlrhNmcu5lR9TaWlztC1Abm6j2u5AkyORNUvnylnLLtBjtTREbmB9X8EwRQmDG46W4QIfp45Q7cXA4ASgmTExlrRNClCxftVO0HDuaaG4PmseLns2QiccI1kxu0al3abycyjKQrywADcMgk7FvMn6/fYOOxWIMDg6WihZ73I20t38Iw0zO+Riyu3aRfuZZ3MuX4T/9dJQZxisaf70Nd79tGepfsxr1lFPw+XysW7eulMHrURQCmc3k0jli2SZUNYg3MMl1UxT4zW/g2mvh4YftMihvepP9/zPPRHK58G3YAEBPNMNgIsfi+sCE1lbDmWFSegoJqZQ4UcTlqiWfH0Fx5RFZi3Q8Nq4Ydn9O55nBOHJYYlG1m1QiDZmja7GTJIlzW87FpbgIuWfYu1R1IdUshsYAojeF13JjqhbD1uRxcLNhqFBepjboRp7kc1Is9jupGxbs7Odtv4fkAGy6ASWoYWUNzETejhOcA941a/CuWVP6vcrnYiSVZyiRK9v+rLjOXFrH0E3Uo5j9XI7MC1tIPf447qVLCV1+2THd94nOjC12HR0d3HjjjRw8ePBorMfBwaEMxfg6XzhScVzUMMkLC1WSqD7Gf4iPxF9Y61RZvPXTtNgVrXUulwtXIZngSAsegKJ4Ctmdc8MYGMSMRrEys7NYSD++ufT/PeeeUygBI1NdXY1LVWH/Y0hDu3FpteTSKqaRxuPXkCtZBWtr4b774O1vt38virtCd4wiD+0a5IGdA/RGJ669mIRQToy5tBokJLSAbfEbd+2MHPq2P7Gz8wm6Gt2ET60jY2YgrR5VYQewvHo5C8MLZx3HpwQ0RN7EbbnIeQxGc6NYYu7uzSJTxdcBtCyvYvmZTdS1VahDKcuQ7LezYlODpZZoVrLyQ89sKK51aJKah6pLweW1v5uZxPzvfyrUavsh1hh2XMEzZcbC7mMf+xi///3vWbRoEZdccgm//vWvyeVemQGYDg4nC9NNnDCEoMPrps3jQj5OGW1FfNMWdraFaiRvoFcoFeF2u1myZEkp+xUOJ1MULXjzSbHUwj19Br965iDD02jTVaK/H/Wv9wOQiYQ4uGIF3tCYQquZEXo7n+GB7Y/TLerxRfIsOj3NovXTEEiqCj/7GZxfaDvW0wPvfz8IgZlMkd21i8ZoLwBDZVx4wxnbWlXOfVrMJFa9tsged+0UF7XJg2BkiWeSpLQ0CFBz7lKtuVcUQkDnozCwE9ln3+pcqobuF5jCJJqLztuuigWhKyXXaC6FcJ231K5rUvyF2NDUYKntmZmYmyvWSqcnPKAUYwHLfUaKFNeameP+Z4NSY38+zWgUYRyfenonKrMSdlu2bOGZZ55h5cqV/OM//iNNTU185CMfYfPmzUdjjQ4Or3pWnf9a1lx0GZGGxorj6lwab26s5trG+W+XNFNsYSeh5ysLooAi45FlLAQj+uR/wD0eD21tbSxYsAAA0zTH1bATQtDX9yeGhx/Bsub2sCmEwBwewhSCftVPXyyLZyYW0F/+Ego3o64LX4MaCqP5bfGTSqXYu/Mlnk14eF5tYp8RQZJAUkcITNfdpmlw661QSJjgz3+G//t/0bu7SNxzL9WdOwEYTk08D0PZChY7l30zdfmhedlKqpqaD78pSXgCtQQtA/Ip5GCYlTUrWehdgmnMn/WrHIZlsC+2jxcGXpj+RrkE7H8Mtt+OEtBQgi60xgCiw0PIFSJnzJ9BYkNbFWctrqFtNq3EjqQo7JKDducJbIudmENNysyLLzL8ox+TfPSx0msNIQ8tVV5qJkn2APAWEjiOR2sxORBAcrvBEphT9J12GM+sY+xOPfVUTj31VL7+9a/zne98h0996lN897vfZc2aNXz0ox/lhhtuOG41cBwcTjYUVSVYfez7vs6FmtYF1LS2oaiVY/0kSeL86iAuSSI0zQ4UYBcmFkKgaRputxvDSJBOdyJJMtXV58xp7SKdxspkyeoWeX8Ij6bgc81A2P3614fnuuG9rFm6FLfPtirmcjkOHtjPPssFLj+N3jAkIa8PI4SY/t/Nxkb4yU/g6qvt3z/zGVwHD8LKVQTScRCCoSPKWVjCYiRjZyoXs03HoqphJFnF4/fR0rYQTRtvIRa+OgK7dYbzaWJNFtWhMJYpyGeObgyWEIK7Ou8CYHnVcnzaNBJj0gUXnrcKOehFksDKmbx+wdVonulnN0+HBTW+iuVlUtEcI70pgtUeIg1TrH2MxU7yqHiWV6H459hBZdi20iqhw27gjlo/HbWVLd3FOLvjYbGTJAm1phq9pxdjZKSU9e0wNbPOitV1nd/85je8/vWv5xOf+ASbNm3iRz/6EW9605v4zGc+wzvf+c75XKeDg8M0yFZoI3WsUVR1SlFXZF3Qx8qAF2+F+LL+/n4SiQSWZR/jWDesJEnoun3z0jS7RdZcMAoWgozbh1BUambQSox9++CZZ+x5TlnC0quvYuXKlXi93tJ60dMMCRdC81HvjtC3O8TQAZl8foZJH1ddBV/6UulX+Xvfw3f3XXhlgZpJEc3o6GM+E/FcHFOYKJJSNhFBkiRamt9KR8ffTxB1AEKrpUY3EbrOkBCcckELGy5dUDkhYB7QFI2Qy17vSHaadd1SBWHnrwVZgkKJESl97L8j8aEMvXuiDHVN4/oGCh1TUoNIErgXhFBrvHNqLWYO2+dMqZ6ZJd8bdCEr0nEz0pTcscPzm+xysjNji93mzZv56U9/yq9+9StkWeY973kPN910EytWrCiNueaaazjttNPmdaEODq9Whg7uJz40SHVzK5HGpknH6Zbgvw8O4FdkbmipxTOD0hyvdPL5PNu3b7czJM89F1mW0XUdWZZLiRP5fEHYueZeeqN4I0l4bQvHZLXJyvKb35T+G7t8NaF8Hs192MXqcrlQzQxxrQYPGmGhcmgoQpIs1qY4UCG4vhyf/zy0tNhxdoD/r39Fb24m1LSWEV+AkVSehpC9f0MYNPmbkCUZWSr/+SjG2enZLKlYFG8wWLI2mlI1NeZ+JLI8PfQyTXhYVr3sqBUnHkuNt4Z4Ps5wdpjW4DRaXaUKBY39dZixHOZQFiXsRi64N2dkHa3AQDxLImdQH3QT9JR/kMkUkh+Krs2K+GpAksHIQS4OnvDU21RA6Dpm3M7OVssIu7xhYQlRNtTAF3Kx8fKOee1XOxPUgrAzHGE3I2Ys7E477TQuueQSvvvd7/LGN74RrUxJhYULF/K2t71tXhbo4PBqZ7Svh8EDnbg83orCbkjXEQgseMWIuv7OvQzu30ftgg4aFy+ddJxhCQ5l88RNk3XBia6qYvarx+NBVe0/WwsWLKC1tbVkwcsXLHYube7CTtI01Lo6opYtsmr8MxAut95a+m/facvY9afbaF97KtULOvB6vUiWAYqFKUlYqLjSJsHASvwRH15fy+wW/L73wego/H//HwChn/+CjiWnMlLdzFAyVxJ2td5arlk6sY1YOfY+/zQjPV10rNtI8zL7wd2ygtSYBhJZDkb38WhumCVVS2a35hlS46mhM9ZZSv6YkjEWOyupI/s11Ihd7uT23X9iNDfKu1e+e1z3jdmwrTfOloNRTm2v4oJl5d2FRVfmlIkTYPeLDTYCAowcVs7AGMkhSaA1zjxJyBgdtVuJeT1IvvHfrSf2DPHM/hFO66jmnCUTQz0kSYLjGFGlNTfj23gqaoW/ew4TmbGw27dvH+1T9G/z+/38dGwLHAcHh1mTKTxtj8uqLMPhVmKvnPKU+Uya+NAAbr+/orDLCYvf9dvuopV+Dy55vDCdLPtVlmXkwtiixc7lmnviiGfVKjyrVnHosU7I6NPvOHHgAGzZAkB2TRupqgaMYZOXdu/B2zfAeeedh5weJudygSTjFZBN6siyC394joH3n/gEPPcc3Horci7LeV/6Z0751ncIvOZdM5rGMJJEo89iul8GAqTjhxvSW1mJGsXNu5Vh/qwO47VqObQ5Rj47wurzmo+qy66YxTucnYawE2K8xW7EtpjJAQ1N1ojmomSNLCPZERr8DXNa10ghq7Rmks+IEKJULsQ3HWEHsPG60n/NwTSZrUMoQW1Wws4cKbhhq6onXB+/W0WIyUueHG/UmhrUs88+3ss44ZjxY/1rXvMahsuYRaPRKIsWLZqXRTk4ONgIIUo3Vl+4srArdpyo0145ws4XigDFzhmT41cUfIrtChoukxlbrl7dWISw0PP2Dcw1D65YAMsS1AXdhL1axfpk47jjjtJ/Uxefgp4CRZZxebxYlmUXWPbXkV9+Mfhr8Rn50k1/WtacSkgS/PjHWIWwGDmTpuYD1+O+6RulIWM7TUw+jUw8/iJC7UdgkI4dzkg0UzpS86mkl24EzUtVIEJsMEM6lkPPTj33XKj22IJ9NDtasbMGYNeBM3Xb+uWtsuvACYEwLHIH46XEkWmJxCkoZh5Pll2aSxtYpoWsSLh9M/9uKoV5rZQxq8zYkrCrmfjAUzONkiejfSm2PtJN54tOPbkThRkLu/3792OWadady+VKbX0cHBzmh2wqiWUayLKCx1+5VtgroZXYkfgKrcUy8RjCqhy0XlsQpMNlChUXhd3YjhPPPfcce/bsAcA0U0iyhiQpqOocY5IsC2FZyLLE69c1895zF+KdbkbsmBZfiXOXgulFUTXCVVWHj0NWOLu5lStVWGHmyCTyWMIgoz9Db+9tU4uWSvj98MADmG984+HXPvlJ+MlPsITFj7f+mFt23EJaT086haL4UBQvmtsNcppMPI4QAmGJUqHcEdkW6jW+aty+QkmMo5w5GXaHkSUZwzJI6InKg90hOONDsOZahCRjFfq45jpjZHeNUivZ12PaiRiTkNVNUjn7fjiZVbfohvUEXDOPVbMsJI+CpEr2+U/PvFCw1tKCd+0aXIUyQWMphhjEM3ZLtMlIx3KkosfHqmdlMuQPHcIYHDwu+z8RmfYd4E9/+lPp/3fffTfhMdYD0zS5//776ejomNfFOTi82skUrHXeUAhJrvwcVrR0vZKEncfnR5YVLMskm07hDUyeGFDjUjmYzTF0hMVOCDFB2KVSKRKJRCnGV1WDtC/4IJaVRZokKWC66F1dxO+4A23BAsJXXjn9DVMpeOABAIzGMMmF1bDHj68qjMvvJx6Pk0wmqa+vJxgM8tqzzkJTNTbffRAJGZ2XIWNgmklUdYYJFGOQm5rg979HfPnLSF/4AgDigx8k3ViN0WyQ0lN41cpuX5erBsNIgZzBNHTymQwulwetJYCV1nlJT7A5W49bj3BByEU2aVseI/WzXvbUxyXJvG7h6wi4AlMXRJZl8FWDrxqRM7HyFpIsIUc8WCmdaisCzF3YFV2YQY+Ke5JSPTNKnCiST8ELt0AujnTux5H9GmYsj5XSSxa86eJqb8c1SfiU16XgdSlk8ibRdJ760MQ6ikVLcjaZR1jimCdSpDdvJrP5Bbxr1xC44IJjuu8TlWnfAd5YeAKUJInrrrtu3HuaptHR0cHXv/71eV2cg8OrnWLl/6ni67KmRapgSa9+BbliJVnGGwqRio6SiccrCrvJLHbZbBbTNJFluVQypFiY2DcmGFySJBRl7gVijeFhhGFiWjPMnHzgASh04clctA7LUJFQ8YbDeAqCNJ1Ow577UVx+lKZ1ZAruS82t4fWHMPQR8vnhOQk7ACQJ6XOf46VtB1jzm58gmSa+v3srZ779Ajo/9p4pj0nTqpGkLjSfjhG3HzDcjT68K6ohPUL04UeIy+1kG04t9bY9FrXOFoQmWp2mwiq4GWWvihzUsFI6YdMWhqPZuRW+HSlYAiu56psWh6lp9jMjQ6zqtd3JlgHZKEpB2JlJHW1uIYETqPa76M5nGE6VF3Zur4qsSFimIJcx8Myxpt5MUQvWbmPEKVI8XaZ9Byhmni1cuJBnn32W2toTq1iqg8OJSL7QBsg3hbAzhWB90EfasnBPYdk71niDRWEXg+bJsz6LlsYjLXaaprFmzRry+XwpUeJIC958Uqxy/2xMsO/hfVy6uoHFddNomTXGDRt86z/j0oNAN75gGE9BgKaTCaKDL/AgtTR6l3BWXS0bL28nnzWJJasx9BF0fQTomNMx6P395Pcf4MA7rsd/oJNFTz+InMtz6s33surOzXDRnbB+PVx//eHuFWPQCgkoqs/CiEM6HitlZOdlFSk3AO4WcpaC229ft2zq2PcTnZR9D4OiQeMaUF1oDT4kt4KsyeiAX7cfAFJ6iryZx6XMLr5xuCDsKiXXSJJUcldPm6LFMTkA6WHkQAOQwprhObbSacx4HKW6GtlVfo01fhfdo5mSSJ2wflnC49dIx/Nkk/oxF3bF2ntO94npM+NH+87OzqOxDgcHhzIsOvU02k5ZO+U4v6pwSe3cYsuOFt5QGJdnaktaTcFiFzdMcmMEqqqqEx4kj7TY9fXdDkhUV58756zYYs2sYdVHVjfxTqejghCHEyc8HrjoIupGhnB5/YTq6lEL68zEh+lXNfYoEfpGkwT7+wiHw7S1tZHJ15BK7Sll984FvauL9DPPUOOv5y+f+xZvvP0HtPzseyh5HU//sN3y7Je/hC98Ab72NfiHf7CTLwq4NPsc+qvdtLScQai+ASutI7kUXJ4Q/1Czhv/IVWHms1hVBWGX1OetNtxkpPQUL4++jGmZbGrcVH6QEND1DJgG1K1ADQdR19riVe+3HwiUDNRF6nArbnJmbtbCbkNbhOawl6qZCrfp4KuxhV1qCNlv1+2bqbDL799P4v4H0FpbiVzzxrJj2qp9mJYolcQphyfgIh3Pk0nqRObZYjgVSsFiZ6VSWLkcsvvo10w80ZmWsPvWt77FBz/4QTweD9/61rcqjv3oRz86LwtzcHCw0Vwn9h+y1pWn0LZqzZTjvIrMVXURIpqCWkEcGIZBNpsFbIudECaZzEGEsKipuXBOaxVCYI6MYlgWoy7bSjetUic7d0IxeezCC8Hno8a3gJrWBaV5Gxoa8Gb66I66QfMRsEwGBwcRQtDW1lYqrDwfwk6psoVZMJfEdLnY/PefYvtVC1j/2W/T+NL+wwMzGfjIR2DbNvjv/7YtRVDqOuEJ+qlvW4QkySSf6sFM6PhPrccfbKDVsBjRMyRdoGgybp+KZQoU9egJu4yR4cmeJ3EpLjY2bCwvIjOjtqiTVfBExr0lF6xNZkrn2tOunbMIjfhcRHyTfz6yKZ1DO0bwR9w0L4lMOq4s/sLDTHoYtdmFb33djOPriu5LtUxGbJFlDUGWNVR2/R9Ld/uRyG43st+PlUphjo4iN1bul+0wTWF300038c53vhOPx8NNN9006ThJkhxh5+BwHBjVDfyKPKH+2yuBmdw8VwYmWvZ6e3tRFIWqqio0TStZ61wuF5qmkc8PI4SFLGtzjk2zkklEPk/GEOT9QYIetWxF/gkUkiYAopuqyfT+nrq6S0rrkSSJVatWwd4+tsbd4PLR7PcR7xLkBmMsW6yXrGS6PjJny5dSFQHAm06CZTGczGK0B9n3P/8f7+z4O8IH+uG734Xvf9/e4LvfhUAA/v3f7e0VP+3tH0JRbCuOsARWynaRy14V/LXUjHYzoqeJmhanXtZ+TNpORdwRJCTyZp6MkSnfM7ZYmNhXjZAkRNZAcitIkoTs1ZAkEIaFyJtI7qMbj5qO5RntTZHPGDMXdr5C2Z70EJKmoNVNoz/uEZgjhR6xVXOzYnuDLjwBF5rn6PUDroRSVVUSdpoj7KZkWp/qse5XxxXr4HBsiPb1/v/svXe8XHWd//88dc70ub2l91CSQAKRErqCiqIu9oIorv3ryroK63f5rvtdxbLr4ve3rij2sisrVkRBYakiVWogIRDSbsqt02dO//1x5sxtM3NnbkkgmdfjkUdm5rTPOTP3fF7nXV4v9j/3LInu3rLyfzXcdHCUpGXx9p42FsyxwfmRhOu6PP/881iWxSmnnIKiKNi2TSgUQtM80mGaXlTCK/ifHbnwNb/yWgREqX5h4nHELntqL/n0TkJKjnBcQx7vzpMbZggVlBA94RBPp0B3DWzHIagkEAQJUQriOMVZNYJI8ThIIkHJQS7mGRVVTlywjJyVIRbvgvXdcP31sGULXHYZ2LaXkt24Ed761lIjind900MDZA8OEzAUFE3loeQjWPl+VDsLZoEh0zpsXqKyKBMLxEjpKUaKI5WJXd53nOjANWwy9/YjKCLRsxYgSALBE9sRNBmhRNgtx0IWGyd4IzmDF4dydMUCLGipTLoK2QYcJyYjNBaxw3UnpMrrhVXyiK0VsQOwbIdkwSQSqPwg09obprV37utZ64Xc2oK5bx/WyOy6mI8VzPpxxbZtnnrqKRYvXkxLy1TT6CaaaGJmyI4Mkzx0YILPaCWYjkvK8rorW6pILhxpPP/wAyQP7mfl5tOJd1Z/4s5YNjvyRQQEToqFMAwDy/KIg98R29LSwubNm8t6b4ZP7NTZ338ERSGwYjmZtNcsVhexcxy4804A3JY4xtpeiiN5tj55B51LlrPilFd4y1yXfHKAYaMFlBBtgoogiLiCg+0aCEKAxYs/iCjOvl5LEEWkRAJ3eJhoMYsV6uak9i10Rif9lt75Tkil4KMf9d5/6ENw5pme92wJOx78M/nBUZbG1hFo7WH76HPk8vs50ZVpsdIEx0WJ57vGDqAl0EJKTzFaHK3sGZsvpbJDbeUoo6CIZZkOpcsjKIP5QX734u+QRZl3rn1nw+PYN5rnnucGWdoerkrsiiWpEy0yg+802ALRLi9y51jYWQdzqIAUUcrnUAuuYeCUHFukCh6x43HTo/s4kCpy8boeVk6Tlj0SCKxcidTejtLTtBarBw3nbf7mb/6G73znO4BH6s466yxOPvlkFi5cyF133TXX42uiiWMWhWzJSiwaq7neqGnh4qKJIqGXiEfsZJiGjlEsTLCnqoSkZXPHcJqHU96E5KddNU1DkiaSVp9AeF2koMizJ3ZKby+xV7+agdUbAGipUT9VxhNPeD6tgHXmJhBFLN17Zh4vUzN46AB3v5DCGM6gBMIoRQdVUZDVsfOcC1LnQ25tRUDggj6VD5y1jI5qkhwf+Qj43t7JpGdNBhQKezlw4JeIkd24pkOxmMUNiuTMHKghNiVauKJNYUtLhNRggSfv3MdzDx2as/FXQ4vmfc+jepUuyQnEziNWUoVOzqAcJGfmSBvpuhw5JqOejli/U3hGnaSSDJveB8ddApKCNVpE35nCHKguLj0eVjIJgBjUELXaD4ctpXMYrtIZ68N1XZwZuF/MFkpvL8Hjj0eehqA24aHhWeCmm25i/fr1ANx8883s2rWLbdu28clPfpLPfvazcz7AJpo4VlHI+B6xtYmdL0zcpsiHLSXWKEJRj+D4vrfV0FqKOKYtB9NxK+rVTXZmMM0kMDcROx898SBL2kN0ROtoXBmXhtXP9JpE7KJ3HsHoWPQjFIlh9G5E1LqIqwH0nImiKEiBMWI3l5AS3vWIG3lE0cBxazh/fP3r4Hce33gj/PnPuK5FobAHMZDDNWyKxSx52Wta0QIxgqd8ANZeDIKAKAklkeL5L64vE7tKGnSu6zVPgEfsSk4N4riuVUe3MPZmUA44qJKK67qkjNoPHJUwOg2xc113TJx4JhG7SfAbP/wo5HSwR5PAWFdpLfg+t9UkTwD2bB3mL7ftZmjvNK4fTRxxNEzshoaG6C4VL/7ud7/jzW9+M6tWreJ973sfTz311JwPsIkmjkV4xuHeDVSrIeoL44jdS8hxYjJ8cuqT1WoISSKaKOLikrSsKcTOtm3uu+8+Hn30USyrVMwvKIiigqrMntjZ2Syu63Lq0lbeeNICehN11LmNI3aFV6zAxcXIewR7fLQ1GAySCATY3BLnjW1RClkTRVVRgmLZprFY3M/+/TdxaOB3sz4X7YTjaXnXO4mcfTa/e/F3fOupb7Envafyyq2t8E//NPb+k59EkRMAiKqJY3rELi17ciEtgbFr7bpuWcvOKFjYZm3ruNnCP3ZST05dKAhw2sfhlCsg1IqdL/1Gxnm0ukWbwrYRjN1pEoEEMDOhYp8EtVQhdqZu41ie40VgNtpvjgNmoUxOnbxZl+2c3NlBZMuZaCecMO26LXUQOwSwTafsbXy4YR48SOGpp7FL6eUmqqPhmaCrq4tnnnmGnp4ebr31Vr7xjW8A3hPn5FRJE000MTOYehHbNABh2lTsiPnSc5yYDJ/YTZeKFQSBFkXmgG4wYtoUJxG7fD6PZVkUCoXy/aan502z81ctwdF1Rr73fQRFpu1970OoIug6AZYF99zjve7uprgkhF0YwrWCiIJIYJyAsiRJBINB8vk8TrFAMWcSjUZZcfJy2hf45F2gWOxHkmdfqC5FPLmWTNHkif39FC2D8Koa+/3AB7zI3dat8OCDyP/zAMJqCVmVkeIOpmOSUrxJNR7wIrB3DiV5Op3lrI5W5ICEpdsUcybhxPxJ9LQF23jzqjeTmCRlUoYkQ8TTrfNTseI4YlWOfOk2rVILAww0TOxM2yFT9EhjNQ07o2B5pC4kI87UhmvwOXjm1xDvQ1z3dq+j13ZxdRtBq/33Lre0lF0bpoMfsRvNGTiOW3G8wciYtdiRQPbee7EOHiKmXYi0cuURGcPLBQ1H7C6//HLe8pa3cMIJJyAIAhdccAEADz74IGvW1O7cq4Svf/3rLFmyBE3T2Lx5Mw899FDN9ZPJJB/96Efp6ekhEAiwatUqfve72T/dNtHESwlFP1oXDiNO88A0PhX7UkWwlIo1iwUso/bE0Frqyhsxp0bsxr8fn3YWBGH2HbGlmiRbVtCFOh9Sn3gCShEE9+yzkZQojiUiOCG0SARRHLef3fcTSu4APeORO9tFFARCsTES5OvH2VYOx5kb0/WskWfXcJqBjE5UqfGQIMvwuc+V3wpf/gqK0oIcCCDGTNwYDNlex2mL1gIHnsR96ucUB59jxLDKE39hnid+WZTpCHWgTFOP6NoObol8jSd2giwilmQ7Wl3vd1m1Xq8KkqUUr6ZIVQWsIy0am169hDWnzaLgPxDxbMVyQ57XbdD7G29UqHg6xDQFWRSwHJd0sfK+/QYQP718uOHX11lNB4pp0fBM8I//+I+ccMIJ7N27lze/+c0ESirQkiRx1VVXNbSvG2+8kSuvvJLrr7+ezZs3c91113HhhReyfft2OjunukkbhsErX/lKOjs7uemmm+jr62P37t0kEolGT6OJJl7SMA0dWQ2gTROtA1gfCTJgKHS8hFOxsqKgBkMYhTz5dIpY+1QbKx8tJYI6alqcvW4d+XyeSCn6VPAt1kKNa3pNB9+yaL+j8p93vcCJfXEuOG4amf377y+/FM48k96eSxFy2xnhkanf3eB2HsrqmKi0ZrKsP2sNtuVMiI5IkoYkBbHtAqaZJBCYncx/4emt6DufJpbJo8c7yBsuNX8mb3gDrFoFzz0Hd95JcOslGCtlJM3GzUMmNQKSpyeH5dBGEcwCw6bF0ohCZrhwxCZ+APY9CtmD0HU8RBahLo7hFC0EZWIMQwwpOEV7xp6xo/lSGjak1HygEEQBdZrIWk34WnZGDswiYljBzls4eQvaqm/mui76jh1IiQRyezvCNPqWoijQElYZzOgM54yKost+naCfbpeUw9uo5dcK2k3P2Gkxo1/cpZdeOuWzyy67rOH9fPWrX+UDH/gAl19+OQDXX389t9xyC9/97ncrksTvfve7jIyMcP/996OUtKGWLFnS8HGbaOKljra+hbT1LcSxp+/WOzl+5PSlGkGsvaPkfVs7beqnlEdMm3A4McEP1o/Y+dInIyN/IpffSSJ+MtHo8bManx+xSwe8yT5Sz4T8pz+NvT79dADind0sWb+RQGjc9+K66PlRBtV2bF3GKHoEVZJFdu7cycjICEuXLqWtrQ1FaZkzYmfs2kV+21baIzpDLdGqk3YZkgR/93deWhaI3nALyc9fRMeCTtq7zuPUtjYMLBRJASNPKwaYBUYMEy3idV4WDwOx25fZx/PJ5+kIdXB827jvfWQnDD8P0R6EliVoKyunIsWIAiNFYlaEnnAPnaGpgYRaWNIW5u2nLsKZgxKAmpADEIiCnoH8EGIoDBSw87WvsZPNkrntDyAKtH/oQ3Ud6sS+OLrlVO0El1UJJSBj6ta8p9srwW8GspNNYjcdZkTs7rjjDu644w4GBgZwnImFst/97nfr2odhGDz66KNcffXV5c9EUeSCCy7gz3/+c8VtfvOb33Daaafx0Y9+lF//+td0dHTwjne8g8985jPN+r4mjkpMl4Z9OWHVK86sa72Fmsrbe9oq1gxOjtgZxhCmMYLrNi5XMRl+xC4le6SxLg07P2IXDuOeeCICEIrFCY2TOfEGmmPEBjGgorUtYsmCMf21QqFAJuOlZ31iVyzuxzBnL8YqtSQoWjrxoklGjHqdnNWDpR7e/W64+moYGkK5+S6ED5+N7EgEtAByt4pM6boEYrQKDrgu6WIeJRElFA+gzYdv6iSMFkd5ZvgZllpLJxK7stRJbVkMqTTGoKnyxuPf2PDxVVmkO15bQuS5hw8iSSIL1rYSCM4yaqdnID+MuqgbpS9STslWg/+QIsUTCHXeQ9YvTEy7jhZRMHWLQtY47MRObi0Ru9FRXMeZNgp5LKPhK/O5z32OV73qVdxxxx0MDQ0xOjo64V+9GBoawrZturomPpF2dXVx8ODBitvs3LmTm266Cdu2+d3vfsc//MM/8K//+q/88z//c9Xj6LpOOp2e8K+JJo4WjJoWg4aJeQS0peYLIUlkgaaSGxlm9+7dZEr1hq7rTonY+eRHUWavb2Unk7i4jMgeaUxMR1D27vX+AWzezFDybvbs/R6Z7Lap6+aHGUVFCIbpXroUY0Tm2fv3M7I/Vz4X/9wUJQGMOWrMBlIiQdEqEjVMNDFau+vRRyAA73kPAIJhsuD3NglOL5OhMgSBUDCGhoNrFnASCiec1cfC4+Zfa8zvZp3QGWtbUCy9D7VhZw0c3arYWON3yc51rVp5KLZD8lCB4f7szBsnfJStxUYQNRkprJTFlqsevzQXS3NcphRr10h0hZDrsdmbY4ixGEgirmWXhZebqIyGHyOuv/56vv/97/Pud797PsZTE47j0NnZybe+9S0kSWLjxo309/fzla98hf/zf/5PxW2uvfZaPjeuILiJJl7qcBybJ/7wO7RIlFWvOANJrk4wHk7leCKT57REhDNbXnqK8ZXgOPbEpoIqGBgYYGBgAEEQiEajOI5DPB6nUCgQDAZxHAvL8kifMkupE9d1sZNJLNslGwgjCHWIE4+rr+P00zHNEUwjSfLAAYT2TsKJlrH6q8IIIyggB2lVZLLJApnhIm19kXL00Y9GqmobshxBEmtHhOqBFE8QD8RZYBc4JLWWi/6nxRVXwFe/CoD88x9jnfc2ntz9ALtf2Mfx605jTavXKCeEW2nJ5zlgFRk1bTrU+Y/WAcQCXv1iSk/huA6iIHqkznVBVkGNUHj8IHbaILS+A6VzYk2mFA8QPqULMeiN13RMbMdGk6e/5q7rcs+OIWKazPG9cVR5anxEz1ngukiKiKzOMrIULP22C/VHcMvEruQZXA8cxyVZMEkXTJa0Vy7v6Ft15NylBFFEisWxR0exUymkafQ9j2U0TOwMw+D0Ui3JbNDe3o4kSRw6NFGp/NChQ2WdvMno6enxBD3HhZbXrl3LwYMHMQwDtYI8wdVXX82VV15Zfp9Op1m4cOGsx99EE/OFYjZLIZPGKBQQpdp/oqMlqZOWl3BHrA+jWOCpO27D1HU2v/EtNYvOd+Z17ksXiCFyYon4SJLEunXrxvZnDIHrIooqkjTLZgrLIrh+Pdn+AcxgmJimoEzn4jGe2J1xBoa5G1PXOfjMdvbLQ5x6ybha5PwIIyWP2JjrMDw4jGMJaBEFV54YsQuFlrJo0ftndz4lSIkEnaFOwobNNiFBRq9P3Ja1az0f2XvvRdy1A2HrI+yI7WLAHqJ75aqx9YKt9DFCwM2ilqJIruPiui7iPLqgRNUooiDiuA5ZM0tMjY2lYYOtuDBOnHjq34Ygi8gJj8Q9fPBhHj74MCe2n8iWBVumPXbBtPnL7lEEAU7oi1dcp1gWJlZnLxoe7YbONRBfBIC+J42TNlCXxis6asC4VGwDETvDdvjB/bsA+Oi5KyoS1iONyJYzQZKRO6erJzi20fA3d8UVV/Cf//mfsz6wqqps3LiRO+64o/yZ4zjccccdnHbaaRW3OeOMM3j++ecn1PU999xz9PT0VCR1AIFAgFgsNuFfE028lOGL+GqR6LSTQrIk0pt4iXrEjoeiBjCKBRzbQs/naq77Yr7IU7rNIcSqHbBlj1ilZdaTp6AohE8/nezp54IoVtUmmwC/cUIQsE9Zj2MXPSkXN0QwGps4JiNXInYa+X172dn/HJlCkmBELZ+frutloeK5ghgOISgKQUXkvevaeN8ZS+rfuNTUBiDdcR2OeghshxjjojnxBZzb1cmbu1tZEgywe+swj966i4Hd8+tOIApiWUsvVSxpI+ZLEa1QG65u41ougjDRdaISQop3/et1n/DT2dEa5L9YWmdGHrGTkVgIx78RFmwEwDqYxziQw6khK+NLgtSrYwcl6RbVu48kC9X37boupmHPiXZko1AXL0Zd0IdYj8bkMYyGH/OLxSLf+ta3uP3221m3bl25O9XHV0vh+3pw5ZVXctlll7Fp0yZOPfVUrrvuOnK5XLlL9j3veQ99fX1ce+21AHz4wx/m3//93/nEJz7Bxz/+cXbs2MEXvvAF/tf/+l+NnkYTTbxk4WvYTWclZjouaevlE7ETRBEtHKGQSVPMZtHCkarrRnBwXYcsIlrJ59JxHMRxBdPzYSXWElZZvzBOW3iawvBcDh5/3Ht9/PGYYRdS4JgSAtIEKzEAd+3rkKOHkE2bRC7LflxsTGRVRBAkFEXBNE0KhUJZ2gW8SXQ2pLVgFTDCKrJlEjaLje3rr/4K9xN/g5BJE/vjI0TOW8RQcAFBc9xvrX2l968EURRwbLfskTqfSAQSjBZHSepJFrIQzNLDQqjVkwMBhKBctR7NGi5gDReJB0rETq+P2Pnp7Frk35d8mZFH7DQQwzKk9KrWYq5p4mS8GrRGa+xaQgoFwyaVN+mMTk1Lu47LY3/cg2XYbHjlotlJuTQxb2j4W3nyySfZsGEDAE8//fSEZY3egN761rcyODjINddcw8GDB9mwYQO33npruaFiz549E27kCxcu5LbbbuOTn/wk69ato6+vj0984hN85jOfafQ0mmjiJYuyR+w0VmJ+tE4TRYKzLdA+TNCiMY/YZdLQVbnkAiBkeRNjUVHL94CtW7eSSqVYtWoVnZ2dSGIANdCBqrbPelzW6CiCotIbD9FXj43Yn/8MfnTtjDPKTRyOUeq2jEwk5YIg8K6F3TiuywvP7gbAFa3yPTMcDmMYRtkmbWTkfjLZZ0gkTiEeWz/j83pu9DkeXJFiWdcaXrloUWMbx2LYH/4k8pc/h+C4nPzTB9h1+aWoZuXfmu44ZSKjHwZiF1e9iF3OKhG6FRfAkrPAdXAOesevlqoEsEaK6LvThHu86E/aSGM7NtI09Z9lDbsaXdN+KnZOInbg1Q7qaZDUCdZiFSEIxF77Wpx0CiFYx295HOJBlf3JIqNV9i2IApIsYhk2xax52Imdo+vozz+Pq+uETj75sB775YSGv5U777xzTgfwsY99jI997GMVl911111TPjvttNN44IEH5nQMTTTxUkIhWyJ204gTj6+vm3Udz2FCMBxhFChka6fqNMubPA1ZxXZdJEGgUChgmma5xjYWW0cstq7WbupG9q67MfftI3rB+Whr106/gW8jBnDWWeXooVn0xlYt2ioKAqLjEQJHGJs8N2zYMOE7dHGwrRymMTvJk6SexA6qxIOtPD+QYfvBLIvbQlVrwyZDuPKTOD/6JuKBgyx8rJ8lZ/bjnD0xTWdaNt/avZc8MpfHvI7YYp1G9bPBSV0nsal7E6o0jmDJpWtbqleslYb1l6mGjCzLWI5FxshUtyoroewRW6O5xnU9EhScK2L39M9haAesuhAx7DWu2FXIsyDLBJYtndFh/CikT14rQYso6HkTPT//3/FkuIZB9n/uBFEguGFDU/KkCmZ8VZ5//nluu+22cifXkci3N9HE0YhCSZJnOteJ0ZKVWMsRkB6YKfxzKk5D7IRiERmQZJlR08ZxnPl1nUgmcV2XUTmIbtVR53bvvWOvt2xBlsIEAt2YOe9ZWRsfbR15ER7/L9jjPZAGVA1JFkFyMU1vcp5MzNVSl69PGGcK31EhHogzkjN57lCGfaOFureXuuI4n/+H8vszfnUvxdTEMSlP/Ng7t0KSouqdh16wcOyJGqdzjaAcnEjqxsEplKzEKjRO+ChLnuStcvSvnjo7PxXbWoPYnXBWHxtfvWTuInY+2SyMThj3XM+7fhQyWYPYBUrHPxxC1JMhRiIIsgSOi9OULquKhond8PAw559/PqtWreI1r3kNBw4cAOD9738/f/u3fzvnA2yiiWMJjm2jhSNIijqlTmsyFgcDnNUSZXV49rIYhwv+ORUytYndkiVLOH7xQqKxKEnLQtf1co1dIBDAdd05m9Rc08TJZtEth/9+LsO37t5Ze9+6Dn7WYMkSWLiQePwkOtsuAb0dECYSu+wh7hnN8MOBLM9mCyxY1critZ3E2rRyJ+xkyHICANNKzurcUnoKqWAQfmArsQfu8j6rURhfCeK7309urZc2b997iOgPfjRxhWCCFkywiqRFF1EWS04bhzGikzkEj/0EXvAySkpPmMDiGFK8eq2kT5Dc4hixm6CLVwGO45aJXWKa+jlRnL1/cRllyZNRxKCCIIBrObjmVPKsv/gi+o4d2NnaDUqVkChH7KqTNp+sFuuVzplDCIKAGPe+KztVX03ksYiGid0nP/lJFEVhz549E56c3/rWt3LrrbfO6eCaaOJYgyhJrLvgIk695NKa+nUA3QGFzYkIK0IvH2KnRWJE2zqIdXTWJE+yLNMdiaAoCinTLkfrgsEgoihiGAPs2v0fHDjw81mPyS49+euijKOoxKfx/+Thh6FY9F6fdVb5Y1GWWXPG2SzfeCqSPC5SlB9hgACHxChG6Zx9UWL/vAqFAo888ki5zERRvMnLsjIzdtUwbIO8lccVBaTn96Dt34NgWzUn7fFwbQdzII9bFMj838twS9ek90c/gaeeGlsx2EJLyVosZY/V2R2OBor799/Pb174DanRFyG5B9L7AVC6wmirWpCi1aNqgiohyAKuC4uVBaxpXUNroLa4sigK/PVZy3jrKQuJBg5jfVmoROzyIwiSgBCQPXJXmEqeC3/5C+lbb8Pc39/wYRJBldOWt3Hu6up/n+Xv9wh5AsulhhBf0qWJqWj4l/mHP/yB2267jQXjLHEAVq5cye7du+dsYE00cSzj5VIz1ygCoRAnnvequtY9pzXK+a1RQpJIf7+XUvQJkWkmcR0L1519us9/8i9oYRAE4sFp0mfja3/PPrs0BhdJlmntXTB1/WKSJAooWlmWZsGCBXR3dxMvRR8URSk7bJimiSyHEUQZ17GwrPSMBJj9Ls9AKIqi2QhuESWfpSDJFE0bbZoUvpO3yD8xiKCICGeeSfavtxL95m8RDAP++q89HT9BgGCrF7EzC4yaFgs6ggRCMrI6/yUC+zL7GCoMMaIYxGEsslUHBEFADCnYaYMV2jLWdpxQ13ZBVSKoVm9KOPB8ktGDeToWRelYNEei4cES4SwmwXEIn9KFoEgI0tT7hJ30vncpnmj4MKos8oplbTXXKTfI5M1Zd23PBOWIXZPYVUXDEbtcLlexxmVkZIRA4PB6xzXRxLEK03HZkSsyZBz+Aub5hmEYbN++ndSB/YRlCaHUOAFj9XWm6U1efmRrNvAnwlzA02dLTOc4cffdY6/PPpticT8v7qoePXTyo6RQQNYIFh0ev30PyV0OPT09ZaIqy3L5/lkoFBAEAcVPx5ozSzn5xC6uJZAScSRRIG56qd96HCjG16l1dV1M9LqfwRqvcJ8HHoCf/tR7HSoRO6vAqGmzcG0rKzd1EW2d/0hyWcsu65UEEWzB0S2spI5jTB/p9D1XnTlMG+fTBtnRIlYdx68bgRiIEjg26ClETa5I6lzDKDeOSInZ/21UHEpQJt4ZomNRDOcIWBn6Ei7NVGx1NEzstmzZwg9/+MPye0EQcByHL3/5y5x77rlzOrgmmjjW8MKjD/HYrTcztGdXzfVGTItfDYxy48HZG8UfCTiO7Yn5VkAul2P//v3094+lkkKhEK2trURLNXpWqfbMr0WbDey0N0GkFY9kJWpF7ExzzHFiwQJYtgzLSoHrkB1NMrR3N0ZhXN2cbZHWCziArIaQiw5GwUKvkEKb7Bkb0LrRtD4EYWY9bgktwcaujaxqWVWO3iQsjyDX6nr04ctpuJrAjdtu5PcH7iT9D58dW+HTn4Z8fiwVaxuM6vqMxjpT+J6xqfyg90GwBWuwQO7hgxSfGZ52e21lC9Gz+lAXRbEci+HCMLZTnZA93Z/iru0D9CerN6D4KejAXGrYieKEOrtq8MmOGNQQZxhoyekWLw7lOJCqfI6CKLB6czeLT2hDmkd3kWrwf8vNiF11NJyK/fKXv8z555/PI488gmEYfPrTn2br1q2MjIzwJ1+JvYkmmpgR8ulkWceuFkb8jtiXgePEZOzbtpU9Tz1B94qVLDvplCnLy56pmsZdI2mSps3renvp6+srrzOXETt18WIEWWFkxLuWiVpOBY884pEZgLPPBkEod64mD4wyuPU+Vp92Fm0LSlkNPw0rSMQDWrmhQA1JjI6OUigU6OnpQRAEQqEQyWSyfP4d7efP6rzag+20Bz2Nv1zCG3PcLCCJAkVz+miSH8UqyAbDxWEyZoahtRuwT1pPy2NPwL59cMMN8IlPkJBlFlkFWmUD23URAVO3513nzCd2yeIwaAu8iF2yFGkMTn9sfx3Xdfn+1u9j2AZvW/M2WrXKtXYvDGbZOZijJaRW1Tv0v+M5FyfuOgGsAgRi2DkTY1fKk/1YO5Y6LRO7+Mz/LrYdTHPPc0Os7o7Sc2JjOniHA3JnB/E3XNKw+PKxhIbp9gknnMBzzz3HmWeeySWXXEIul+NNb3oTjz32GMuXL5+PMTbRxDEDPespxmvTihP7GnYvP2KnBDTALTtsTIZPbCKhEI+l8+zIF8sOGz78blFFScx6PIGlSwmfcTqDYW+CTARrpGIn1dd5Y/EmUyvvpca0cc4RmAWSUgRkjRZFLgv3aiGJxx9/nO3bt5clTyZH7OYS/iS4NuzwsXNXcNKi6WvR/FRsTi4guAad5lZy7m3sesdbxlb68pehWETt28BbFy/mle0JXNPh0d/v5vE/7sGeZ8mTeCAOtkXSKP2Wggmcgu8RWz+xEgTB85uldmdsqrTvauTfMuxyCjZQQ2plRlh8Giw/D8Lt4LgY+3NYAxN/Kz6xk2ZB7PxShOmiupZhV4w8zzdEVUVduBBpGtWAYxkz+uXF43E++9nPTr9iE000UTdsy8QoeqQmMJ4cVICvYZd4GViJTYbvqFFN8mR8PV1CkBksGgwV9bJtmuMY2JY3ocny3NQR2Y7L6SvaSOZNorWiTJPq68Br5HBsG9uQEZlE7BILEU96O62jGdoUmWLe66YNRjW0lEaxWKRQKKCqapnYFf2O2xJc10YQGifwB7IHCKthokq0XG8lOQ5inS4lPrHLSDlcZIKCjSRDenE3yVdsJvHAg7B/P3zve/DhD5e3k1wXQQRs0HMWodj8+XrGA3FwTHKigKkEUeRAOdJYT8TOdVz0F5I4eYtEJMEQQ6T1yhFz13VJ+VInVci/L8ysaLKnVThPKNcGGp7kiaB4x7JT3thn0jjhwy9FSNZojhjYnWbXk0MkukOsOqW6g0wTRwYNzwo7duzg17/+Nbt27UIQBJYtW8Yb3vAGli6dmdJ1E0004aFYitbJagBFrV0fkzRfvhE7rfSkredzOLaNKE08h/HSJi2WyF69yF2PPE8mHuHkk0/GcUzC4eXYdhFJml2BvqPr2MPDSIkEGxfXlrrAssAvN+nuhpUrcV0Xy0xhGTqC24aiBafI1KyLhlgX9VKzj2e9+igtrBAMBikWi+TzeeLxOMFgkFAoVPbGtawc+/ffiG3nWbLkIw3V2lmOxa+e/xUuLu89/r0EOzpo/9AHEZT6oliu7eIWPZKSJAOCiKa0Icsqrphnzxte5xE7gK9+FT74QRBFDMfBdF20sEIuqVPMmfNK7DRJQ9XiiEvPJr/sDcRcty5x4jIEMPqzuKZDS7h2xC6rW1iOiygIVcm/nvc9Yufhgct1wchCMY0Q70MMSDi6jVMwkRTvfhE6+STUJYtnFbGLlYidYTkUTYdghe7mMZHiI9O8Zezrx9y3F7mri0CTe0xBQ7++a6+9lmuuuQbHcejs9HRuBgcH+cxnPsMXvvAFPvWpT83XOJto4qhHsZyGrR2tAxj1U7Hyyy9ipwQ0JFnBtkz0fG6CdZrruhOIXbxgYZkWOQTk0rnKcpiurovnZCzWgQOkbv4tcnsbLW9/e+2VH3wQSt+RX1/n2Hkcx8AyTXC1mt+dYzsYRe9784mdX2cHEIlE2Lx5c3l9SQpi2zlc18GysihKbSeS8UgbaVxcVEklKAe9qIso4routz59kNG8yRtP6qs4afsIntiOU7BIllLN4UAHkmAgSDrZZUuwzzkH6a674Pnn4Xe/49FTN/E/IxmOa+tgTYnYzbdnrCAIXHbcZShSyT+1aOHaLoIAQh31fZ7kiYydMoi73gOH3008GX4ncSwoV416ui4EQsrc19cB6Bn489dBEOGsv0MMyh6xy1tIMY/YSYnErGvPFEkkEpDJ6hapglnxNzJB8sRxEQ6zV7W5dw/5Rx5FO+H4JrGrgLofAe+8807+9//+33z2s59laGiIAwcOcPDgQQYHB7nqqqu46qqruGe8f2ITTTTREHybrenq63THIV8yoI+/DJsnBEEgEPYI0GRrMcMwsG0bQRDQNI2EImNaJlmEcqpyLuHXJOUCYQYyRQyrRk3YeAH2Cy8EvDRpJLIa0WlHQEILTyR27uM/hSduhPwIlukQaQkQCCvIqjhFpHgyBEFELgsVJxs6Lz+dGFNjE1JpgiDQnyxwKF0kWcOBQpAElK4wgSXxss1WROtCEATkUpC0+N7Lxjb42r8S2fozGHiWlGmXO0KLh8F9wid1MNbwIQTlusmGn9aMOl5UNW1UTsVOV18H0L4gwvrzF7JkXXtdx24IgagneeI6nuTJOGuxuUa8dI7+OU+GqnnX13VcjOLhj9r5EcmmrVhl1E3srr/+eq644gr+8R//kZaWscLb1tZW/umf/on3ve99fOMb35iXQTbRxLEAWVUJJ1oJTVMfIyJwcUeCc1pjaEdAbmAuoIU9zbhiLjvh80AgwJYtW9i0aROiKNKiSFiWRY4xIuQ4+pzZifmuE9vz8JMH9vD0/hraWL///djriy4CQJajdHZehGqf7J3XeFLuOGST/fx/I/CTwTxKQOK4M3pZf95CBEGoWlMHY97bSqmGsFEtO5+MxQJjUb7CU0+T/MUv6Ty4y1unyqQ9eRwBKYAsysSDPd45Bz3ymz39NM9SDeD2u2jbtx9sg6RhllN1+uGwndr6K8+LN70fMSQTXNNKYHH90U2f2AUtj7FmjWxFyZN0sXZ93XjMi2ivIIzzjE2O1dmVvkc7myX/l7+gv/jirA/li3RX+40IojDuOz4CDRQx31asSewqoe48zkMPPcSPfvSjqsvf/e538573vGdOBtVEE8ciupatoGvZimnXU0SBtZGXngxBI4h3dSPJSsXopCzLREopzYQsYZkWFpQFfA8euhldP0Rnx6sJh5fNahy+OHFKmkbDbv9+ePRR7/X69dDTM2Fx39rjaentm5BWRk+TdEWKyBQEdcpkXyli9+KLL9Lf38/ChQtZvHhxOWLnd97Wi7I4sTpWa+VkM5j9/cTjQGJBuRGgEqyRIq7tIMVU3rL6LbiuSy73PDmgdUE7PRsvIRAKwUc+4unZAYk/PAzvO5mcnkds9a6Dnpv/Sf/A0LM8knmRWDDA2avfhLqwsW5JsfSdK7rIcR3HEVEiOK6DxMRo+GnL2tiwMMER0OQdQzAB+WEoJhFDnQC4ljcga2CQ3J/uR+7omHV68vjeGItaQ/TEq9ewBkIKxax5RIidFPd+X3Y2g+s4COLL8wF3vlA3sTt06BBL/KezCli6dCkHDx6cizE10UQTRzl6VqyG6TksUUnkIjuHgl12nbDMFK5jIUmzJ7d2KoWLy6hP7Kq5TowTZef1rx/b3i4gigGCkWi527eMwihJVJA14qo8pcMwGAyyevVqgsHghGWmaZajeL77hFXSyqsXfjrRd2YAEGPeZBgxPCJZK2Kn705jDRUIHteG2hdBEARUtYVAoBM10DlWS/ie98DVV4NtI//hUYKXWRSsIrom0tITnp9as/GwTSwjy14zQ8Ks3GU9HcpadgWLcxaeU3U9QRAIqdWnTNt0eOLOvWhhhTWv6Eacj2j6uIidvCRE7LyFCJLfEZsE5sZxYkHLVHepyTisUdlJEMNhkESwHZxcril9Mgl1E7tisYiqVg9BK4qCUUVJvokmmqgNP/VWTwpnT0HHdF26VYXwy7DGrhZ2796Nrut0d3cTi8WwLQvVGau5cxwTy/LSt7PVsHMdBzudwrRd8oEQggCxSgX3rgvf+c7Y+/e+t/zy4KHfoOsDdHddTCg0KUpSGJ3gEbvj4UMUMiaLT2gj0RVCkiR6e3snbOJ3xPpRPF+AueFUbCli52uzwVhdUkj3pGJqETu3NFmPlwxR1Xb6+iY1mHR1wWteAzffDANJ1vzlcR67cDU5EVZu6mpozDNCIUlMVEGUydhFjIE8YkBCiqgVLbcqYYJ0yCy8T4t5E0u3KbrMD6kDL2IHUEyWzm9srHOhYdcIYu3ew1CkZf6t4yZDEEWkaAw7mcROpZvEbhIaaqn79re/XU6RTEamiiZVE000MT0KmTRP/vH3hBItrDv/wprrPpTK8WJB58L2eFlG4+UIx7HR83m0cKQ8mQ4NDZFOp8t1vK7r0tvbi2VZSJKEYXhyIaIYQBRnKXWSzYLtoDtgaSFimoJcaUK+5x6v8xPg/PNh2Vj61zKTWIbOwIv9xFpUWnvH3DEojDKKAnKQFkWmmDPR8yZiDcIxue5OUVrQtF5UtbFi/E1dmxjVRyc4KEiliF1Az4PjVCV2rjMmGfJI6i/sHtjLhs4NrG5d7Z2zYbD/uW2YeoHlGzfD5Zd7xA5Yc+tdPHb+JaSsOfRJrYXCKFFBQVCC2I5N+on9KChETu9FqjNaKAQkolv6EAIStmuT0b25rEUbqyUvmja3bT1IS0hly8r2iuTPTzvPa5RyXMRuMpw5JHau67J7OE+yYHJCb6zi30VrT5jWnvCsjzVTSHGP2DnpFNA37frHEuomdosWLeKGG26Ydp0mmmiicRSzWRzHxq3hU+nDd514OXbE+nAcmwd/+d+4jsMpr/srlEmRKj9yFQgEkBYuZlu2gJ7KsVr2UoyyEpt1gbqgqkTOPouB/aMgitXr67773bHX739/+aVt69h2EaOYZ/C5F0i3ZCcSu2KSVCliF5dFkqVapPGOBNlslkwmQzAYJJFITCB2juOgKAl6e9/c8Ln5JGw8xEgERIGACKpRRI4EcBx3inSHW7RwXa9AfsgZYbg4jOWOq6MSYO+zjyMgsfjEk5Bf+1poa4PhYXr//DgnFQ7Srm7EdV1M3futzpu1WGG0pCvXQs4WKBpF1ICC2MDxBFEoS6M8M/QM9/Xfx7L4Mi5aelF5ndG8wc7BHFFN56xVHRX3U8z7HrHzKEEU6YRFmyHsjUF/MYU1XCSwNFZuJPAbC2aLW546gGE5LGoN0RqePy3CmSK8ZQuRs0XEZrRuCur+Be7atWseh9FEE8c29Fx9VmKO65bttRIvY2InihKqFkTP5yjmsiiahmVZU+y1AFKmzXO5Iq4Ly7WSR+wcOE6ImkZw3TpS4SHYOVLuBJyAfB5+8QvvdTwOb3xjeZEvQeKYIgJyWcLFhyvIJMUgyBoRS2C0pPc1nuQMDAywe/du+vr6SCQSqKqKKIo4jkOxWCzXFc4F/PSVkkpyxYZ2AgsXVFxvvMBvuVav1IQxPHwP6fQTiCETN99FMZcl0tIKb3oT3HADYtHgguf2wpkBdm8d5tDOFD0rEixcO43480xR8CK48WA7hiGh20WEQKLuNOxk+KnryZInvoZdxd9ICWWP2AaszBpGMOHZipVgZ02s0SJSq4pd8pieixo7QRCIBRWGMjqpglmV2FmmjZ63CEaU+Us/V4E8Tp2jiYlotpI00cRLAL6e22RyMBlZ2ymZrAtEX8bEDsbO1Zc8GUs/KmUx4mKxSKQ0R6ctu9wd6neLzgWWtUfYsrKdlV0Vrv1vfzsmSnzppaCNpX9Ny5tIXdObyCeLE1trX0/P6nNpjXUQMLwaSl//y8fkmrpqMiiua+M49dUwjxZH6c/2kzenes5KiThSOAJm9fo6n9gJmkSm5MEaVaOl8cm4roMS9M6nrEP45nFRxdvuByAQPAxyGKIMaphYuAPFkNBtvS4rsckwB/LknxwkPOR9l2kjPUFSZ0zDrnrkym8iUOfaI7YG/HO1R7LguAiy5DUWzAGmkzwBePJ/9rH1nn4K2cPfQNFEdbz8ZOubaOIoRDGfA5gicDsZyZJHbFyREOdDK+swQgtHSA8eQi8Rp/GOEz6eeeYZ9qTS5DoWkBKjqGo7ofAyAmrnrI9v7t8PgkBnWxvd8SoRpZ/8ZOz1O94xYZFVamiwdO/5eHK0VREFLu329ju41yfuE2+5lUhcPB4nEAggliQchkfuI5X6Cy2JU2lpecW05/Xs8LM8Pvg46zrWcWbfmROWxS6+eFppCJ/YmaqNbXqNKz6x85s55ICDwTgdwnPPLadj3d/+lqFkCjXoPXjMa9fkygtg5QXEDv2F0OA2gIbSsD6cvIl5KI/W5UnqGLaBbutoJTXmRiJ2gfkmdkYO8iMQiI6RWEGh5W1vxSkU5kxDL1EHsQuEZCzDi9qF47VtEOcajq5TeOxxnHye6HnnHtZjv9TRjNg10cRLAD65CUzztJ06CurrfGhVInbauKhYsVgkjIssyxQdBzV0HN1dryMSWTXr42fvu4/kTT/H3Lev8gojI2OixL29no3YOFiWR9asYonY1fjujPKkP5EY+Ofq19QBrF69mvXr15MoWUOJYgBcF8uqT4w1bXrr+WRsPHxS98z+NP/10B4e2Dk8ZR2lN0LoxHbyLd5vLaJEEEs+tXIpBS4q3vn4JQTIspeOBYR8nvt/9J9YAZ/Yzb/O2frODbym50L6IgsQZhCx8wmSWISw4n2P49Ox6UJtYueW/HEDIWXKdzzneP4OeOzHMLhtTKpFd5A7OlDnsM69noidf65G4Qh4xgoC+Ycfprh1K05TkWMCmsSuiSaOMFzXRS9F7AKhY4fYBSITiZ2u68AY2bFtG13XkYF4SZw4PYfdlk46jeO67NFFBjLFqW4WN900lrJ829tAmnjNA4EuwuGVWAVvcpuQRh/YhvPAN+GF/wFA0SQirRqhmDppHwEEQcBxnKpyUYrs1X2ZZp3EbpydWDXols3BVJHBjD5lmRRWULrDZLT8lP34ETtBMXFxyv7GwIR07OpbfkVB9SJHlmFjmfPbJSsK4lht4EyIXYmgOAVrrM5OH0fsirWJnSAIrN7czfrzF5ZT0PMGX/KkkETUvN+kU7DmzI3FR5nY5auTJj8CXZxnT+BKEFUVMejdK/yO4CY8NFOxTTRxhOHYNvGubvRcdtpU7HGRIG2KTOwoIHb+ufpRnxUrVrB48eLycj81K8syLQGVA0WdESNLh5qYdbrJNQycQhHdcvjdi1nkg/v4yDnLJ650441jryelYQGi0eMIyEsQrFEEQSQQHNfoUBjh9oLE9hGJMzvynLQ4RmcFmytRFNE0jUKhQKFQmBCttG0bSZKQZS/yVm/EbnJd3HjY2SyZP95OZDgNi19RMxojCAItWssE2Q9JCpc8bGUQ9PIDCeClYxMxSKZZet997NCLyAEJS/dSdXJ8jn+zqX3w7M0QXwBrX0dgaRy5I4icaDwl6KdvHcMmLsU4wIFyxM5xXPSSh3BsvklbPfAlT4pJBE1GEMAcGCD/0CCBVcvmrKlgfMSumr6f3yhyJNwnwBPddgpF7HQauaNyt/KxiLp+pekGjHZjsfo9+ppoogmQZJk1p59V17qtikyr8hKYXOYAWiRCx6KlaJFIeeJQlLGIyPiau5gsccDJ82L/7wmHZRYuvKzabuuC7xGrizKOohLT5IkT18gI3H2393rZMjj55Ir7kQMB1r/yNRjFwsTatWKKNApFSWO6Bs1gMEihUCinoguFAo8++iiu63LmmWeW05+WncV1bQShOkHya8OgcsROUFXMfftQDQvBNEkVxAmTtms7GP1ZxKDMyvaVrGqZmPIWBBFZjqFoFsedeybxlpXjLoYM550Ov7iVQC6Pe++9aO0byerzVINVGPX03DTv+tyVuY+B/AAXdlxIG20N7UpQRERVxDEclmiLiIZi9EY88WhRFPjIOcspmDZBpfK1n42wccMYF7HzpVrs4QFyh/Ygt8bmjNjFggoXHt9NvEZq+Uj6xQJIsTjWoYGmZ+wk1DVDJBLTPyH7P2zbPkzClE000cTLGkpAY+Xm06suH19zd1F7jHODBxkczCJJvVW3qRd22otqFQNelC02OcX229+Cfy974xs9A/ZxcBwL284jyxHCiRbCTJpMC0lSyCAHiEliRb04H4sXL2bRokWESzV6qqqWZV9M00RRQgiijOtYWFampuOGH2XSZA1VmtrB6aevAm4BpZDFUBSKpkNQLaX08hbF7aMIikjsnIUVjxEMLUZV2wlGEojiJKLzqgvgF7cCEL71VkKfPotIS2B+GgqKpfRbidgl9SRJPUlKT9EWbIzYAV5tnmGwUO5jWefKicumsRPb/1ySgd0ZupbF6F2RaPjYDaEcsUuB4xA5vRdj+204eWvONOwAJFHguN7agZrxtmKHldyWUPaMTTdTseNR11/bnXfeOd/jaKKJYxaObSOI4rQ3RdNxeSqTJ65ILAsGDvtNdD6h6zrbt28nGAyyYsUKBEEoE7tgMIgqiuRtL2Ury7PPCjiliSBfjdj96ldjr9/whinbG8YA+/f/DEWJs3Dhe6csdwsp0rSCrKHpLo/euYtgROGEs6dqx/lNEj4kSSIQCKDrOoVCAVVVkeUYpjGCZaXrInaV0rA+xFgMqVAkbhUYpIVUwRwjdsXp69Ta286puoxXvxZX/DSC49D+h1uJXf/16uvOFr77gpbAKVh0ZOKkjJEpGnT1QgzKOBkT13Qa3lbPW5i6BXNb5lYZgagn8+JYoKdBDuPkvXpIKXZ4xXpVTaZzSYxASMF13BnrB84UvsuG00BW8VhAXcTu7EndYE000cTc4cXHH2Vw94ssOmE9vavWVF0vaVncMZImKIp8bPFh8OE8DHAdBz2fJ53NMjw8jKZprFzpRUvi8TiO4xAv3bzHNOxmT+zskgViVvHkRiYUxefzcKsXdaKzE047bcr2voZdPlmkP/cMLb19hPxoieOQ03NYtCEoGorh4DqNzfiapqHrOsVikXg8Tii0FFvt9Dpka6A92M7ZC89GEaunz/z0VcIqMohXQ9UdLxWh+92NAZHvPPUdomqUS1ZcQkCaetzBPbtIHthP64KFtPWVons9izFPWIL65E5iL+6EHTtg5cop284JxkXsrJEiHXtCpIiQXjizST64tg1O8IhJspgkbaRZEF3Ak/vS7BnJc1xPlBWdlYlT2XXicGjYCYIXpcwPQzGJXWKTgqoiaHPr2zqY0dmfLNASUlnUNlUsWxAFlpzYmN3dXMKPUPoR+CY8zOhXeO+99/LNb36TnTt38rOf/Yy+vj5+9KMfsXTpUs4888zpd9BEE02UoedzOLaFpNSWSUiWOgsTR0mNHcDupx5n/3PPonV66dXxGnadnZ10dnp6dQXb4XfDNim9m/e2zz4qEVi1CikeZ2Sf1/EX08Zd+z/+EUr1fbz+9VO6YQGsUodqdjjH8OBjKJo2RuyMDClXBARigSBW3vveqslgWJbF4OAghmGUm0c0TSOVSpWjlm2t9d1XY2qM49uOr7mOn76K20XiQQV3XJjJLRE7XTHRTR2raKGKU1O6ruuSHupncM8u1GBojNjJGuJpa+HJnQA4v/0t1oc/jqnbc19j5xO7YAJnyEKVVEzJLjePNApB9mokXdflxu03Yrs271z7TvYnC7wwkKUvUZ00+XIfh4XYASw8FVwbgi2Yzw9i51qQ5NCcR/F3Dma5/4Vhju+NVSR2RxpKVyet73m3Z5fXRBkNy538/Oc/58ILLyQYDPKXv/ylLFGQSqX4whe+MOcDbKKJox2+ZEQtHTQYkzo5Gjpiffi6fdmSHZJWJeKgCAIvFG0OWgFMcfZ1REpXF8F16xgKebVxEyJ2voUYVEzDAlil6KFV4n8TXCdsk1So23NEUGT0Qu1ojuu6bNu2jZ07d2JZJVuq0nXw769zCbHU4HZiQuR9Zy5lTfdYBNRPxeYlj1BG1egUsmAYw+za9XXyrifloufHSZ4IAvKl7xp7/9tbePyPe3jmvv0NRy1rwrG9NCSAFsctWATEAKY6c2LnQxAEYoExyZPpNOwc28Eo1ibvc47eDdC3EbQ4djaHa6sgzj258UsU0sXqzRG25ZBL6RQyh19LTlAUpHgcocLD17GMhondP//zP3P99ddzww03TOhgO+OMM/jLX/4yp4NroomjHZ6GXUmcOFT7xnw0adj58M8555PbcRp22Wy2THQkwUVzPRaVE+ZmAnNdl/PXdnLmyvaxSTuV8vTrAGIxOP/8ittalmc55YsTT/juwu1oJ76JJcs30xdQxzkSVJ70FUUp30snizRPthXzRZGrYWdqJ/3ZfkynuoyJFIshhkKIgakk2k/F5mTvWleq1ZOkiNedK7m4WBRzuYkrnP9WWLIEAOG+e5H0PK7jYuhz2FhnFSHaDVoM1AhOwUKVxojdTDTdXNMm/+QguYcPElW8806b6bKG3YSo7jgYBRtcF1ESkdXDLw3rFrzfhKBoc0ueGUfsasjiHNqVZus9/ex/Pjmnx25i5mg4brx9+3bOOmuqNEM8HieZTM7FmJpo4piBWSzgOo6ngzaN4XvmaIzYlc45n8+jMZaKzefzPPLII6iqyhlnnIHr2nSEu9GLJjlndik91zDQX9yFFI+xqrt74sKf/MSrsQN417smeMOOh2mlsS0T1wkhiiLquBQywLJQgGUhb5xPP50unWv1262maZim6XnjRiKEw2FaW1uJRj2CoRtD9Pf/J5IUZPGiD1Q+L9flf/b8D4Zt8LY1b6NVq2yTpi5cSNv731dxe6fg/cbSgke044Gp0VFJCiCKKrKiTNWyAxAE7IsuQrr+egTDoHXbQwyuPwc9b86deK8aho3vLb/1iJ2KGJSJB4JYjoUiNRg9k0SsgTyuC/E2L2KXLKbJ6d5+pjTYlDC+vu6wNTRZBuQGwDYInX4KVmYngiDi6vaMnDeqIVrS98sUraqd3YfFE7gGis8+i7F3L9qaNXPqvPFyRsOPF93d3Tz//PNTPr/vvvtYtmzZnAyqiSaOFfiuC2owNK2H51EZsfNFinUdx3GmRKr896Ko0Jc4jkhkFSm78a7F8bBGk2T+8AfSt/xu4gLXhW98Y+z9Bz9YcXvXdbCsLJZhILgagVCk6oTuRWSnL6yffN7xeJz169ezdOlSAGQpAq6LbeVxqkTjdFvHsL10WK2uWB8Fw+anD+3h2/fuLEe4Qid3EjqxnZSYrbkfWY4hqSquUMQsFnDGy1yZBbZu3FB+m3jsHqAU2ZoHuLaLo9uIgsjbN7yLt6x+S+OkDq8RQCjZoMVcr0RgIJsEQJVFAnLlv09RFIi1B4m0zm3jQk3kh+AvP4JttyAFAihtMQRNG2t+mSNEVBlREHBcl5xRed/+7/qI2IrheT7r25/DPHjwiBz/pYiGid0HPvABPvGJT/Dggw8iCAL79+/nJz/5CZ/61Kf48Ic/PKNBfP3rX2fJkiVomsbmzZt56KGH6trupz/9KYIg8IYqdTBNNPFSh15KY2l1FP/6dlrRKhPMyxGyoiApKq7rYptGVWIHY5HK2dqKOaV6vpyi8fxAdsx94a674Omnvdennw7r1lXc3nUtEvGTkYU+cANTayOfuBHzgRtgdBeu45LoDBFp1VBrELtAyTJtfOp1PETRi5JBdQcKX+YjJIdqdsWWjymLHErrZIoWOcNGEATkeAClO1z2m61mSybLUURJGvOMHR+1G92N3ZPHlr3zjTx4J7guRo103mzg1wUKsoCgzO5vw3egCNteBHYw79VSxoNKVfIeaw+y5rQelq47jN2hmt+okwPbKkfp5prYiaJQjtpVq7NTS8c2ijbOHKeC64FYimo74+3tjnE0HLO96qqrcByH888/n3w+z1lnnUUgEOBTn/oUH//4xxsewI033siVV17J9ddfz+bNm7nuuuu48MIL2b59e7kjrhJ27drFpz71KbZs2dLwMZto4qUCJaDR2ruAcKK2Wrzrurypq4W0ZZOQj56uWPCsxZZ2tLLiuONQVY+8TCZ2lpUlKno6YalZEjtfGmGfrfDgE/vZtKSFLSva4UtfGlupxr1MFFVaW88guz+KwFPlBhAfTm6Y/6d3EBgwuDzmsvzk6vcxH9WaJSzLQhAEz1pMiWPog1hWGlWdKsBby0psMrJ3342xezft2iIGWnpJF0wigbHfVSKQwHCMiqlY8CRnBARkDSxdwCgUCEZLJFCLEw5J7Fu3lsV/eQqlfw/a/l3oFSzVZoxnf+tZii09C7FtDaENHbjW7AVyBU0GdMKOR+xSepqgJFRNwx4xKCGQZFxDJ3fnrVjFLoRAx5wTO/BS0KmCSbpg0pcITlmuBCREScCxXYyChRY+vNdKKhE7u6llV0bDM4QgCHz2s5/l7/7u73j++efJZrMcd9xxRGbYbvzVr36VD3zgA1x++eUAXH/99dxyyy1897vf5aqrrqq4jW3bvPOd7+Rzn/sc9957b7O2r4mXLRLdPSS6e6ZdTxAE+jSVvsMwpsONjsVLaenpJRKPlyfmycRuZPRPZEdfxHROgdDSWR3PV6nPyt6+Y5oCv/kN3Habt8KCBfCmN027n97Va2lbsBBxfEeeY5PR8ziAIQUITZNe91GpWeLJJ59keHiY448/ns7OTmQ5iqEPljX0JsMndn5HZy04hSJ2Kk1cLjKAZ3LfOSJgZw3khMb5iys3jfjw/Wv7jltOT+/FEx0otDhxLJ7dtJ7Ff3kKgPijd1HccNy046obhRHPUkwQEGQRpcOr1Xx2+FkeG3iMJfElnN5b3dWkGsSgdx5hO8gp3acQU2OsalmBaVePRNVyFZk3CAJoCdzMbvQdf8GWlhNc3wPzMIzTl7fhLm+jLTxV9sYbioAalClmzSNC7MTSA4XT1LIrY8aP/qqqctxxs/tDNQyDRx99lKuvvrr8mSiKXHDBBfz5z3+uut0//dM/0dnZyfvf/37uvffeWY2hiSaaOLKoJMo8JWJnZuiSdD7eEyYardwUUC+ckjhxRi6JE0sufOpTYyt89augVp7EAEwz7UXR5PDUSKue9qzEEIkFgji2iyh69Vu14NfUjdfxk0uRWf9aKL5nrFk7FVtPxM53KIhY3r4zRQszaWHszRBYGkOKVT9/gIDaSTi8Ak3rm2orpgSJifDi5g2c860fA9C57c/kFnxm2nHVjXGuE+PhuI5nLVZMzmi3fipWNkVO6T6l/LkqV//+Hr99D4IgsPb0nsNLagIxHN1AdG2EToXoWVNdTeYCvRWidFOGUiJ2+hGos/N/y3Y2c0RszV6KaJjY5XI5vvjFL3LHHXcwMDCA40wsZN65c2fd+xoaGsK2bbq6Jqrod3V1sW3btorb3HfffXznO9/h8ccfr+sYuq5PSG+km+HaJl5CMPUisjq9Pdi+osGAYdIbUOkOvMTSQrNEf38/w8PDdHZ20l3qUp2aik0jCqAos9ews1NpXFySkrfvzh/eAH5D2Nlnw6WX1tx+dPTPZLPbaG09g0Ri08SFxRQpFJA14opM//ZRDu1K07syQd+q6ul2VVVpbZ1IWCdH8XwrNV9DbzIaIXZ+lCNseLIm6YKJW/R+g4I2/bQQDC4kGKzsJYsgoGlRMkuiZLq6iB46RPCRPxFsm6OmH9v0assAtDjmYB5sFykRKJ/7TLXsRE32SHidpWK26WCVZFwOu9SJFsfViwiuXBadPlJoXxgl1hGaexHqOiBGIiAKYDs4uTxSpLYe6LGAhondFVdcwd1338273/1uenp6Dis7zmQyvPvd7+aGG26gvb2+QtVrr72Wz33uc/M8siaaaByu4/DIzb9EEEU2vuYSlBp2QM/nizycyrEpFj7qiF06leLQwQMogtd17zgOixYtolgsEggEvC7Usk/s7FwnXNfFyaSxbJeCGkRLjRD8YklYXRDg3/7N+78GPA07h4M79pCLhelZuWosalVIehE7OUBcltALRVzHRZpBUf9kYhcIdBKJrEHTKqfuN3VtYml8KX3h6RP2fpQjZJaIXdHEKXhjfKG4k/ufepjVLavZsqB2DXM+laR/+zNIisKyk8YiXEIwTixvsvOM01n/i19CsQh33w0XXTTt2KaF7zghq6AEMV48hJXSCa3vIFo6r4w5s+iN1KoRPW8hgiCQMTL858PPENdivO6ElYQDU6dLP0IlKSKycpi71bU4rm4gOGa5gWA+UDRtnjuUwbAcNi2pHC1v6ztyzg+CKCKGwzjZHE4u1yR2zIDY/f73v+eWW27hjDPOmPXB29vbkSSJQ4cOTfj80KFD5Sf38XjhhRfYtWsXr3vd68qf+RFDWZbZvn07y5cvn7DN1VdfzZVXXll+n06nWbiwypNmE00cRuiFPK7rgAtyoPaT7tEodeIjNTrKgR3bEUcGWXviOkRRLFtrAZ4or+siCCIPpl12FofYHI+wKjwDeQnXJXrhRQwdGsZMhzjjh19DSJWIwuWXw0knTbsLy8pgmSbDew6SFMyJqeRiijQKKBpxWRqzmqpDW2xwcJBsNktHRweRSKRCh3AvmtZbdfvucDfd4an3zUrwiYCm54lrMiFVxhn1pFIyYq4sm1ILrutiGGkGdj9PIBidQOzQ4qzjBbQtJ8EvfgmA8cubEc57JYo6y9+wT+wCMRCEclesqElEVI9gGLaBbutocmO/kfEp8wf2P8x9B/9ET+B43rh+VcX1x6zEjsDDVusyjOBxWHIaNRYj//gAdtYkfHIn4hyOR7cc7nh2AEkU2Li45SWZ6kxc+mbEoNZ0oCih4cfIlpaWKSmDmUJVVTZu3Mgdd9xR/sxxHO644w5Oq2C8vWbNGp566ikef/zx8r/Xv/71nHvuuTz++OMVCVsgECAWi03410QTLwUYJSHcQCg87c3Sl/iIHe6owGGA7bsE2Ba2NbVGx3dbkOUoadvmoG4ybM6slkcQRQLLllJYvgYtk+KEX/7IW6CqUEdk348e2qYJjkYgPOm7U0KktVZQQsRkqRzRUesgdgcOHGDXrl3lcpHxxG4mTgq14HcSxiR47ym9vHJlB26pQSAteGnO6VK6/fv/i8HRn+GKKYxCAccZ163cuZaTV5/G6kvfVvbadW6+hfRAfvaDH28lVtKwAy+FrIgKIdlrpJi1tZjr1Za5YoFAlQcqo+h/v0fg7zLahel24UgJxIjnvuH/m9PDBDwtO9txyRmVO9IdxyWX0knOxfc7A0iRcJPUjUPDEbv/+3//L9dccw0/+MEPCE2jlF8PrrzySi677DI2bdrEqaeeynXXXUculyt3yb7nPe+hr6+Pa6+9Fk3TOOGEEyZsn0gkAKZ83kQTL3X42l+B0PSpg5RZInZH2c3LdV1My0IURWRJRM/nEBQV27bRNA1ZlstdoLIcJVqaYDOzlDzpjmu85Z6bUAqliegDH/C6YaeBZWU9oWDTAtSp393CU1gQWYOkmyREkUyJdNQTsZuaevWiuLZtY5omqqqWbMWySFKwrGsHkDWy9Gf7iQfidUXtBEVBbm8DWcY1DPxnfDEgkbW8tHdEqZ1ek6UwoiwhyCYYLno+TzBSIoOJRd4/gC1b4K670A7sJvPoY7BgqnNRQ5ACEOuBSCeuXtKwk8Y07KJqlLyVJ2Nk6Ah1NLz74vNJrJECquxdf0mu7tdbJu511CXOB5ysR16laBQr6UDWxCnOrRC0KApENJl0SfIkUiElbeo2W+/pRxAFNr16ybTNQk3MLxr+Nf7rv/4rL7zwAl1dXSxZsmSCXyzQsF/sW9/6VgYHB7nmmms4ePAgGzZs4NZbby03VOzZswexTsmAJpp4OcEnduo0D0iG41AolRwcTXZi4DU3ua6LrAaQRY/YDWUG2LdvH4sWLWL58uUocpxYfD2KnCAuzk6k2Dw0gJ1KokkSke990/tQVaGKtNJk+NFD11YQECrawJ3Z4pGbQtZgLyDKYl01dpOJnSRJJZkTuRyx699/I4Y+SHf3JYRCS8rbHsof4o49d9Ad7uZNK6eXagFoefvby6/NUqRF0KRypMtPa1aDLHtadormYhme2HaZ2OFFYkdNG+mvLqXlrrsAUH/533DJLIld13HeP8AZ8a6VqI3ZebUF27Bde8YpQ6dgYqcMxGCJOIuFqus2kmqfD7S87lzskf1I4QBiwEufO1WEhGeDmE/siia9TO2SVQMSgijgOi6mbtcVoZ5LmIcGKDzxOGI4TGQOysRe7mj46s+Hy8PHPvYxPvaxj1VcdlfphlAN3//+9+d8PE00cTig+6nYYO2IXdrySJ0mimjS0fWQ43esa8EggiCg53JTOmI1rafcMBAreOvPlNjpz22n8PgTxJ58AtlXqr/iirqidQCW7ZEex/RunRO+Oz9dWiIU4yf9ekhGJS27448/fsI6shTBYLBMMH2Uydg0UbZKuP2ZQ7wwkOGspS0sbwuR211fKtZvZJE0FysNem6c8r/rMjC4mx8fStF25rlcLssIlkXod78A6zqYI5HtsuuENvbAc87Cc2a1T1/yRCyUUshCAcd1EIWpf3vBiEqsPUgwWlseZr4gvvhHxMIodC9CLEm/uPNB7IIKjBZIV0nzCqKAqsnoeU/y5HATO9fQ0bc/h9TaAk1i1xix81XQ3/e+97GgzhthE000URlGORVbO2JXrq87yqJ14N1TZFn2yjrMgkfsdM96SqvQJTyWinVm1PXoZDJgmkg//wUArigi/N3f1b29qrSSSGwivceTY5oQbdUzWA9+C0dLoJ76fiRZorU3Unf91XS2YjBGpibbimXNUvp0mihbJRi2Q950yCsCxbCJi4soiOVatenGIqneg4f/oOIj9uzPwVnEcN9GzPMvRL3tFpTBA/Db38JsAgSuWybPbrlxYu6IhL8vtyB64ruSQN7MV7y2vSsT9K5MzNmxG4YW94Sa9TRC0FOKmOtULJREvPFkcapBDZaIXd5illKTDcOvGXUyTS07aLB5QpZlvvKVr2BVKHBuookmGkO0o5PW3gWE4oma6/VpCu/oaePc1vmTNDhSaGtrY8uWLaxdvRoAPZ+dUmNmGEPYdgHXdcs1hobrUJyBL6WdyRL4y1+QR0e8473uEliypO7tA4FOWlvPwCl4NmETauz0NM87Ab6md/HzQ6NEWgKs2NjJouOm2n9Vgk9kDcOYoA9qWVY5sjlG7Cb6YmYN731Uqf83ou/cycgPf0j7I/cBkC5YuK7LwuhC+iJ9006Ovq6e5xcrYJnjatEEgVAgioILlk72ig+UF7n/8R91j3EKXBfu+yo8cD0YOZSeCKENHagV5DZm2nDi+65KposmhgnI4qwbMeYDxp49FF7YhzU6AsUUYilqOS+p2KDvF1ud2AVKXsjGERApFkvOV65p4Raqp86PFTT8mHPeeedx9913s6SBm2ETTTQxFQvWHD/9SkBAFOnTjkyq53Ah0dWFa5+AFk/Q/7wncq5pGq7rsn//f+M4JgsWvBtVbSUmS0iCQNFxCDaYmnYyaSJ3/s/YB1d+ckbjPfH8V2Hk82jjrRSLaTIlDbvADOqCVVVFFEUcx0HXdYLBIAcOHGDbtm20tbWxbt26ccRuUirWrK8ubgIEATuVJqTY2CmdUTFDdGkrr1v+uum3ZYxkhluCHH/SpUjSxN+oEIwTK5gMWzqpV72SUPcitIN7EP74R3juOVhVWUKkJowsWAbYFshBRFVEnJT2yxgZbn7hZkzH5LLjL2v4ED5BOq4tzCdPvAjXpaJnruu4uK6LeITKI8z9BzB3H0RsySAXU4hdMmJAQgxIcx61WtIW5s2bFpAIVb8P+XWGR8J9QpBlT8sul8POZBHnoLHz5YyGid2rX/1qrrrqKp566ik2btxIeJIB9utf//o5G1wTTTRxbCDa2k60tZ1cLgfsRJZlZFnGtos4jhcl8InEXy/omNGk5Zom0hNPouzfD8DBtevp2nJmQ/vQ9UNIUghZCaNUsBNLl4hdTJYwdRtZEevuEBQEgfXr16OqajlaqZaszcbcJ0rEzp5I7HJGfXVx4yGVpJ8CxTx2Umc4Y+LqNlToeqy4vRQmHFmJLEUqazprcWIcYtgqkhGg5d3vR/vK//GWXX+9Z93WKIqlFHQgAlXIsyZpJPUkALqtE5Aac0Mop2JNhzWx1eVu28nIJnWevf8AkUSA486sri84AQMDcM898Mwz3mtVhY4OOPlkOP10aEBo2M6kcQTNa5oophCD8rzZioUDckWB5vHw6+qMfPWo3nxCikVxcjmcTBq6Oo/IGF4qaJjYfeQjHwHgqxX+KAVBwLbnPr/fRBNHG2zLwrGtuuzE/pLKIQgCK0MBIkdZnd1TTz2F67osX76ccDhcwUqsJOcgBRFFr85nppEIO5tFu/9P5ffb3/Z+uhvYl+u6HDjw8wnRwwkopj1x4hKxe+a+/RhFi7Wn9xJpqY9c+PJNPvzrUCkV67oOgiBiORZ5y6tva6R5whcpVi0TQdfJqAFctf7rIQgCXZ2vqb6CFiPGPrB00pZN4jMfhf/3BdB1+N734AtfgBpuKxXha9gFYp5A8p4MYkBC7gghSN7YFUlBkzWKVpGMkSEQbIzYCbKIGJBAEnBNuyqxMwqWJ5w9HXF3Xfj1r+HrX4fbb6++nqbBJZd4vsWbNlVfrwQnk8UVNARVHyO8RxCR1gAL17YSnMZneL4gRmNw4CB2+qWXNj/caDiG7DhO1X9NUtdEE/UhNXCIh3/zc56+84/TrvtAKsftwymytjPtui8nuK7L6Ogow8PDABRzWcxclkULF9LT43XBjhcnni2c3bsJPPEEAPl4KyMXvrax7R0DxzHR8zn2Pr2dwd0vTlzBj9hJAaKiiFG0cB0XVZs5Gfcjd5ZlYVkWkhQmEl1DIr4R1y0J8yJw8bKLOWfhOQ1Fp0RVRdACqAIoeh7Ddbl59x/4zlPfYWeyfs9vgOcfeZCn77p9YgNFIEYcC2zDawBqa4M3v9lblkzCzTc3dAxgjMBocVzTofjcKIWnh2ASt/IJbs7MNX4MILuujZtlmz/uOsje9F52p3dPWUevR+rkkUfgtNPgjW+sTerAs1278UY45RTPr7gUWa4GJ5vBFYIIquoRXmd+7w/PHkjzp+eHSOYru5IEIyo9KxIkOo9MGlSKRkAQcPXqzUfHCmbVSlQsFit2rjXRRBO14XfEKtNYiVmOS670wBSVjy6pE9M0yw+Dmqbx5B9/RyGT5vizzyfe6Yns+inH8cTuhXyR+5NZulSFV7VPrX2qBvn3v0coHW/rhW8iEm3MU9Ifi6U7jO7ciaXbdCxeOrZCMUWaCMgBNNvFdbxojhKon9hlMhmGhoYIBAL09vaWU9KWZVEsFolEInR2XDhhG0mUWBRb1NC5lLeNRrFHc3TJJk5MI6Vn0R0dRazPksp1XWw7T2pgF3rOQs9nx7q8tRiLyHOmM0BPJIhl2phvejvBH//YW/7DH44RvXpRdp2IlTtiBVWaEjWLKBGGCkPlppJGkSqaHEoXydopXjAeJh6Iszi2eMI6RtlVpML36zheRPJzn4PxzYbLlnmk7RWvgN5eb9muXXDvvXDTTVB6yOHnP4c77vCEs23bc+/o7vakPDZuxJUk7GwWBBXWXASt3oOQvjOFsT+LuihKYNHcuiw9sTfJgVSRrligZq3dkUJo0yZCmzc3HSiYAbGzbZsvfOELXH/99Rw6dIjnnnuOZcuW8Q//8A8sWbKE97///fMxziaaOKqgj7MTq4VsiYjIgkDoKBPq9tOLqqoiSRJqMEQhk54Q9bHMMdcJH7YLB3UTYXKYphZcF/F73yu/ffrVb2ZtgxIZtjVJw25SgbYR7qJoSCBraKbXkalqckMq/Llcjl27dtHS0kJvr1e3pWka2WwWXdeJRBpojqgDYjiCazm8sk0htLKT/+QBoP4mjGTyIUZHH8DVTMj1TIzYhdrpWX0uPVocggEOvZhmt7CSkzp7UQb2w+9/79WZdTZQDzXOJ9aX9agkdeKP328qaRSZEmlsD8U5iBf5m9yQYFSziysW4bLL4L//e+yz44+HL34RXvOaqbWBZ5wB73wnfO1r8N3vwj/+o3ddkkn4ylemDq67G/eDH0IIhXBDIcQVZ5b36drOvNiKAUQ0GVKQrtF1m08b6HmTcCJw2N04BPWlRzaPFBqeKT7/+c/z/e9/ny9/+cvlwl7wLL2+/e1vz+ngmmjiaIVeKGnYhacTJ/ajddJRp800uZ4uEApTNC1SIyPlSF6liJ2v59eQSPHdd8OOHQCYZ5/D6RedxorOxkiSb202Ruwmfnf26tewfvXprEy04Ba9tFijQq2VtOz8z3wi7Lo2ppkqp6n3Z/ezfWQ7o8XRho4FIHe0IyXaEWQFS3UwS40q9RI7WfbWk0tadsZ4YqeGoPckaF3mvQ1KIEkkX/lGb7ltw3/+Z2MDDrV6dmKhVo+82BbS1ofg2mvhIx+BD30IrrmGvrseQ84XZxyxKx7KsbQ/z6IR77dmORZFe2KKryKxS6fhla8cI3WiCP/wD/DYY3DxxVUbPgAIBODDH/YaK8a5gkzBwYOIn/tHWr7wBQLP70AYt89y48c8SJ5ES1p22Rr73vXkEDsePkR2tLoNWxPzj4Yp9Q9/+EO+9a1vcf755/OhD32o/Pn69evZtm3bnA6uiSaOVui5+nxi/bq66FGYXphK7EIcSmdJbttGx7IVJBIJwqHlSFKIQGDM/9QndjnbxnJc5HoiYj/8Yfml9N7LWN3deM2eT6RswzveZCu4oCSWU8P7dyRL59TYLXZ8s4QfIWptbUVVVYJBz8ppdPRBksmHicXW0d5+LttGtrFtZBundp/Kpu7pi+7HI/yKVyDGVmL0Z9FlA9eCkBKsOxXrE25B9Ui2/8AyHkOGRcayaQl4BGTwnDfS8ZOvewt/8AP4m7+pf8DLz/P+T6cRr/sy0e9dj5ganroasDgYYOjtr4fPranbWcRHvmAR1B2ilkhQDlKwCmSNLEF5zE6rXGPnf8eFArzudXCfpwtIKOTVzF18cUPHpq0NfvIT+Nu/hRde8FKwrutJxNxyi1eb6DhIqSSxr30NFAGufB+E2xBK7hPzIVIcLZHGTA1ip5TqSY+Elp1r22TuuAMnmyP+uosRlPp+w0cjGo7Y9ff3s2LFiimfO46DaR6ZNucmmni5oV6f2LGI3dGVhoWxCJQfkVK0ILbjYJlm+bNIZDXtbeegaWNyEkFRQClFLzP1NGwVCl79EuAENOwzG5M48eETO7PoHXsCKXecMUsxaqTppoGfBRl/P12wYAFr1qyhpcWTV5nsPjEb1wmAwIoEexaF+e7OQ+zoDza0H38souQ5Vkx2nyBzkJ/t2MpNe/vJyt51y3Ytxd10irf88cfh6acbG/Ctt8Jxx6Fc9/mKpK48toJO93d/BmvXwr//+4TvZzqkSo0Imjt2Xf3rDOA4Li3dYWLtQS/laJpeveA993grtLV5rxsldT4EATZuhLe8Bc46C84+26u3+9WvYNs2uHBcneW/XOelcvufKkfs5iMVGysTuxoixb7kyTxEDKeFKGLsfBGzv9+rPzyG0fBscdxxx3HvvfdO+fymm25iw4YNczGmJpo4quE4NkZJHX26iF3mKLYTA8/NxidxkhrAcV2cccSuEgRBKFuL1ZWO/e1vIeORsuL6dWw1A7ww2PiNPxJeSSx2Ek5xLMJYxsEnyN/zVYxtvwcgnAjQ2hshkmhMakOSpDK584nvZEwWKZ6NTyyAqEooMZWUpaMbYkPuFZLkHVOUBcCamIoF2H0/sYEnoTBKThgT87Xe+o6xdX70o/oOZttwzTXw6ldDfz/gWcI5r73Ei/w9+CA8+qhH4q+4AkoRTrJZ+PjH4W1vg8njq4Kk4/2uArZLpJRuHp/WFUWBZRs6WHNaD5Iswqc/7UXTACIRr35w48b6zqtRrFzp7f+668ZSu3c+BX/7z4gluRrXdHCtue2SjQRKqVi9Omkra9kVDr9ChiAIiFHvu3KOcWLXcCr2mmuu4bLLLqO/vx/HcfjFL37B9u3b+eEPf8hvf/vb+RhjE00cVXAdh54Vq9ALeZRA7a7y01siHBcJEjpC6vbziRUrVrBixYqy9ZPjp5ttu+TAYGCao8hyDEkKTtg2JkuMmFaZ+NaE34UJpE/axJ17skQGTZZ3NEaEwuEViG4XgrMXSVaQ1XGkrZjmLqeFrdko56ZybFoUpWPRzCRaNE3DMAyKxSLRqE/iLAzDIBQKla28LMvzxSzbiTUgTuzDyeVI/vznqKMZlKUbCYqtdIbqb2YQRQVJ0pCUAggG7mTJDS1GhBTYOjnbQQ1KFLMOxYvfhHL133ldoT/5iddBWqvcwLbhXW+Bn/6i/JF7/gVYn/9XpJOOB3XctiefDH/1V3DttbhXX43g137/93/Dnj1w220Qq94xatmO1/RS8omNMjViNwH/9V8eyQJQFPjNbzzJknlE/tFHcTZsIPijHyFd/l4wTPj9fQj/++8RXvu/cE0Hp2ghReauocBPxWZ1C9txkSqUQPgNE0ckYgdIkQj2yKjnCX0Mo+HZ4pJLLuHmm2/m9ttvJxwOc8011/Dss89y8803c9ppp83HGJto4qiCJCssPWkTa04/a9qGiLAk0aeptCiHt8PscMK/Bq4oEWvvpGvxElzXRdcH6O//Kfv3//eUbVoUmRZFnr6hZHgYfvc7AOx4nNTa40GUypNUo9DCEU655FJOPP/Ciccep2EXniUJn9wsUSgUuPfee3n44YdxXbfcsOA4BjkjhV3Sswsrjcm3ACAp6C8OICXztIsaS6JrOKnzpMZ2IUdRAhrrLzqPDZO1AQNxYlieSLFtlyM6eqQFLrrIW6e/H+66q/oBHAc++MExUicI8C//gvDHP6BsXoeoViaEv07+iRs+fgrJG3/gRdEAHnjAi/jViOjIksh7z1zGaWs7kESR5cElnLfoPFbTCdu3w5492LqFUyjCN74B45UgvvY1OPfcWpdrTqA//zyFJ5/CPv10+OENY5G7f/kXAnf9AjkegJlZ5VZFSJV486YFXH7GUqqVtfrSL0eixg7GRLeP9VRs3Xe3f/u3f+OTn/R8Fbds2cIf/zhRWDWTyXDhhRfypz/9qdLmTTTRRBM1YVkW8c4uOjo8y7AxceKp0ZUL2urU6PrZz8o6YvrGjRQ1b4L3O/zqhePoGMYwshxFUaMo6qQU6zif2IgoYhQslMBUfbV6sGzZMpYtW1YmeIGA507iOA6GYRAIBJAkDdsukioeAiAkh5DFxsmqa7g4BRHRKqAUCxQDIXKGTaROWzGASHgVQW0BipqYujAQHSN2lsOJC6MkOkOEEwF497u9NDnA//t/cP75lQ/wuc/Bd77jvZZE+Le/h4//7bTjsl0by7EYftUZJO69Fy64wCP699/v1aT98pdjhOjFF+Hhh2H3bi86uGABkrwAV2mh83u30/OzH3v1gCUIWhCxOMls/rLLvK7cwwC7FJESo1F446Xw8V/A134DQOBLVxF4yysh2l1rFw1DEAQWtNSuCS6nYot2WcfxcEIMN1Ox0ACx+/u//3va2tp4z3veM2VZLpfjoosuKivIN9FEE9VhFAsIgjCtnZjpuNyfzBKVRU6Kho4quZNisciTTz5JMBjkhBNOQBCECnZiUzXsGsa4NGxx0ykUVC+l22jETteHOHDgJhQlzsKF752y3CmmydAGcgC16PD4n/pRNJmTXtm4cHBoUkONKIqoqoqu6+i67hE7OYptF0nmPWI308YJp2gjBEOIBZ2wVaCIJ2fRCLFLJGp04moxIiX3iYxl09aXGFt2ySXQ1+dF7H7zG6/B4WMfm7j9zTfDP/2T91oQ4O/fAq9/DXbWwBoqIEVU5PaJaXoffs1hxsjAhg3wxz960bRUyjve3/+9py/37/8ODz00ZftaFGYKqXvLW7zo3WH4G3UNA7foRXPFaNRL/77xTNh5EG5+yNPRe8c7vJrDaQTQ5xpKQGLh2lbUoIzLFEOQeYfUrLEDGkjF/uhHP+KDH/wgv/nNbyZ8ns1mufDCCxkcHOTOO++c8wE20cTRhr1bn+Lh3/ycfc88VXO9tGXzUCrLfaPZo4rUgZdmzOVyZLNj59be3s7Cvl4U16WQSc/eTqy/H0oZBHvJEuy+PnKKN9E1Sux8Pb3scI6djz1MemhwbKHrktfz2AgIcgDF8OrMGnGcmA6T07PRyFoSiU0siC/j4mUXs7l784z26xQtRC0MssALBx/ksYHHGMrNbFLs3/YMT991O8P79o4beIwYpkfsJqsmBALwpS+Nvf/EJ8YaECzLc19417vGln/8rXDuOtDi2CmD4o4kxt7qtVQ+sSvXxp10kldn50fpvvQleM97KpK6SiisPx733e+C178eq6UdAPOMs73tb7xxrFljnuGnGYVAAFFVPTIZiMJHXgtrVnkrPfEE/PM/z/mx9wznuW/HUNXmI0EQ6FmRoK0vgniYo3VQIrqCgNuIxuVRiLrvbpdeeinJZJK3v/3t3HLLLZxzzjnkcjle/epXc+jQIe6+++6yv2MTTTRRHb6dmBqsndbwpTwiR2HjxGSpE4BEIsHIzh30v/AcwtoTUNqqE7ucZfOLgVGKtssVC9orE99f/rL8UnjrW4ldfDEjL3hRwEZTsT7JLCSLjA4+R6SljVh7h7fQyJJ2RUAgGghi6d73VtFqqg4YhkF/fz+2bZelpTRNI51Ol6Oa8fhYHVz9pmpT4ZYidlbOIeEWiIYMwkpjNpG+rVg23U96cIB4ZxdtLPQWqmESgsOZ7hDxsIhtOxTSBrblEO8IeSnRp5/2XBkcB976VvjUpzzh4pKgNODZcL1ti+c8ocVwhkp2YjV8eCvJlPCqV8G//iuUyorK2LDBiyCuXctj+zNkt25j3fZHiY8M4L7ylfz3lijDy3u47PjLCCthnv7DLsxsgbXnLkNpObxRMb8xwI9OAZ6+nyDCjy/CfcUZCJaF+8UvIbzznbBmzZwde99onod3jbB+Ybzh5qPDAaW3l/YPf+iYtxVr6LH1iiuuYGRkhEsuuYRf//rXXHPNNezfv5+77767bH/TRBNN1Ea9dmJHs9RJJWIHoJaiHno+h5CoTuwCoshB3YsAFR2XoFSB2P1irINSfMc7CCxbysjeF8Cwy5pc9cK3E7N0X8NuHCl3HdKJ5aCHiSoyRqqkYTfDBg3Hcdi1axeCILBs2TJEUZwSsZsr+BE7S7RYEMzSuUZkaYMTtq4fYP/+n6ELeWDRRC07QSC49tWcJmsQT5DPWTxz334kRWTjRUu8dT7/eU+I92c/g1zOq6kbjzPOgG9/Gx7/pvc+EMMtekb0lezEfJSJ3WT3iU98Ag4e9AjeunXwL/8yoeFhxyN76T/hLDpP7CHeHUUA9K0/BDNLxsgQlEIYhgtKYMbkfTawM975iJFxfxcdpUhdO7gf/yTCv30FwTK9mr8775yzFHGkDpHiYs6kkDFQgzLh+OElvcc6ofPRcCjg05/+NB/+8Ic5//zz6e/v56677mJBg6reTTRxrMJ13RmIEx99N6vJ9XSO4zA8PIwtiKVrlMe2vAnM7wIdD1kUCJZSatlKIsVDQ56NGMCKFXDiiQC8fkMvrzmxp2ETc8vK4OJillyl1PGkXIsTXXsR61dsYnkwgFH0I3YzI3aqqiIIAq7rYhgegalmK/bEwT+zfWQ7ebM+fbbJcIoWYiSO2R7HjGgzkkzxtewEycDFLUeky+g6HtqWg6yWBWxt08H2ddZE0dOhe8UrJm63ZYsnTXLPPRDWoG0FxHpBjZSdFYQaxM7X45tC7ATBixBms57u3aQuVp+0RIDsQwfIPnCgTBJzZg6zaIHrNQbMZbq9Xvj1Y2K0CgH/+8/idJcipnff7cnJzBH8SHctYje4J8OOhw8xuOfYlhw5kqj7zvOmN71pwntFUWhvb+cTn/jEhM9/Me4puYkmmpgI2zSxLS/SdCzbiU2O2Om6zpNPPolZKBAG9EKWBYlTse1cmThMRlSWKBgOGcuhYzJP+/WvvdQe4L7hDRQeewwxEqF75Up64o1HLywrg2PbuJaKAAQmpdH7NJU+zRvEtoI3oc00YudH6IrFIrquo2ka0WiU3t5eYiX9tWLxIAcO3MRdB3aghI/j0lWXElJqPyhUglu0kTt6KWw+nWTmYbqUMI7jNlQfJcthEAQkRQYM9MJUkpk0LUZNm4QiISkitulgFCyC0dIXFwx6jhJf+Qrs2wevfz288Y1jkSYxACeMzUFuKd0t1iBWETVCe7CdqBot27NNQIXGAsdxy16o0ZCCnfKIdaRzrBHDKIkX+1p3hxuhzacS3LC+/PsGQM9Acg8IEkLbavIf+yfC//tyb9lnP+ulsrXGUuyVUI+tmP9AY86DrVk9yD3wIOb+/YROPRV1Qd8RGcORRt13nnh8YiXH22uZFDfRRBMV4UfrZDWAJNf+88scQ3Zi/vtgOIyQG8XMF4nHN9acOKOyxIBhVrYVG/eAab/qVeT+dD+CohBYuXJG47WsLLZpIrhRFC2IOJ5s2yaIcpmE+OKsao36r+kwntiBV3+YSCTKy2U5gu06ZM0sCdedsetE+NRuHN0mk9xNvihy55MiL+5+kSu2LKt7H4IgIUkhJKUIgo6Rz08kUoVR/rR3L8+YMmf1LSKkyRRMA6M4jtgBxON1Ffy7rotTcj8QahC7oBzkLavfUvd5AOQMC8d1EQWBcFglJwq4jkvU9R7CcmYOSRNpXxBFUo/M36UgCAiTSVp2AJ75DUQ6EDrX4Jx5Aeams1AeuccTZf761z3v2VnCJ3ZF08awHNQK9yb/d68fIS07a2jIsxUbHYUmsauN733ve/M5jiaaOCZgFPz6uumjK+mjuMZOkqQJdmI+gQlHoxQHBBzHxtJ1lBpRBr+pZIr7RCoFt9/uvV6wAGf1ati2nZwSYN++FB3RAH2J+jsYXdeltfV0Royd4KamfnfP/JrUyF6Cqy5A7TmR1t4Ies4kEJ65Cfl0NXWSFKZgmeA6SAITzOkbgajJiJpMdjiLLDo4plTTWaAaZDmKJGdwRR3bMrFMY0zrb+RFYv2PQHA5GXsBiaBMIWM0ZjtlWyBKHnm2XFzLLY1/bv82ymlYTUaSRERNws5bZWKXMTOEYirLTuqY0+POGoGSrqPuRYsFTaL4/quQH70XwXW9Osb3vQ9KfsMzPowsocoihuWQKZq0RaZGPdUj6RcLiBHvu3Kyx24q+OgLBTTRxEsYajBEz4rVtPVNr2/25u5W3tHTRpc6c4LwUsWGDRvYsmVL2TLLr7kLBoOomoYrFMmkdmPbhar78GsPs5M9MX/7WyjVpvHGN+KUfHlHXYU7tw3w1L5kQ2MVBIFYbB2aeBwC8tRuZj3DT5wevjYickg3WbC6heUnd5bryWYCv/bQvy7gCTjncjls20YUZYqud/sOSrNPCfbevY1Nf9hOe6GI69b2A60EWYogiiKS6qBqQazxhFSLE8UESydjjXOfaCSi8+LdcM9XYNefQBKIvKKH0EmdCHV0jLuui+PW55tqOy4tIYWWkPc359fwhW2POE+p1zvMcF2X9K23kr37bpzx1zhQqo00i2AZiAEJZ/lxOH/1Nu/z0VHPK3cOmm9i46zFKsH/fi3dxrHn1q+2HkhN94nGvWKbaKKJmSOcaGHpSTUEXcchKktHZePEePiEZHxqtmXtCeSNrQynbsYW19HR8aqK2yZkiRZFJjh+cndduOGGsfeXXlouNs/LXnTBNzNvFF3LV9K2aDHupNSvrWfJEwFJJTJHafNKEbtHHnmEQqHASSedRCKRQBe823dwhjWYVkrHGsgjxVSWxJZgZlX2SgoHgUzRJB6s/zr5ncsrX7GR9vazJ51MjCgW2DppyyYwE9spPQOODZKCIApIURWpjj6PP+//M08NPcXGro1s7No47foLW0O894yl5fd+RLBFTHDeovNIBBKYuo0kC4hHQIbI1XX0Hc8DED799LEFigayCpYBegYxoiIbDs5nrkH6wy2QTsMf/uDJyfzsZ56o8Qzx6hN7UGWRiFqZPsiKiCiJOLaDUbTRwof3Ovndwk6mSeyaaKKJJo4YxhO77r5lDA31k04rVRsnANZGgqyNTEpBfutbY92wK1fCli0499wDQF72omCRBpsaTDONbWeR5RjKZIcHxyZn6LiAJAdQbRfDmLmdmI/Ozk5aW1snyMFomkahUChH8XTHIx3aDKN1dlJH35VG6Q6VOyxjts5BGo/YBYMLJ/w/AVrMsxVzLDKGQbyjDVESPVuxelFKMZYjU3VCEiQsx5pxpM2P2AUsmTWtnh7cM/ftJztaZOUpXbR0z8CfdxZwcrnSuAIIk8lZIAbWEOgptBV+jWS355X8qldBPu81FX30o/DNb85YAqW9Qvp1PARBQA3KFLMGRsFCm0VJwkwgNVOxTWLXRBOHE8VsFkmWkQO17cQGdJNnc0W6AjJrwodH0f5wYXBwkF27dtHa2sry5cuBqfInll1d6qQq7rrL0yjz8aUvgSCUUzLZcsSusdteNruN0dE/E40eR0fHKycuNLJkkACRiKoxeiDPrieHSHSHWHXKzL06VVVFVdUpnwFlCRS9lIqdaZmZ31mKKuKWfmNhy/seanU9VkIotJRQaGnlhXKAqCSCDQWjiBpT6W6E1MEEYmcOFXCyBnKLhjSNTlpY9Sb5CSLFDUAMyohBGWFcJNavHTuSUidSpMLfRSAGuSEopid+fsYZnoXaa1/rpWJvuAEGBz2v3le/el4cM/pWJ8BlYnPMYYI4LhVbsRv6GECzxq6JJg4jtv3pbh6++eekDh2sud4Bw+ShVJZnssWa670cUSgUyGazE9KMixcvZtmyZYTDYUxDJzt6AD2fQ5LqiIjs3evJOZx77lgN0cc/7sllAE7Wi3JkxZnZidm2t/3Azn52PvZwubMZAD1DBtlLwyrSmIbdDKVOamFyenZjzxZet+JNnNAxczsxgKSb5jcHb2fr8FbCJaG+7AwL30f27+Ppu25n15OPTRy7GkbFAVuv3MVcC64LfsQtEMUayFPckcQarl5/6cPvFs6ZuWnW9PCbJ/bzkwd305/09q32Roie2Ye2soUD2QNsHdxKNuc1QM3Hdzwd/IcUsRKx0yY2UIBXkwfA+efDd74ztu6vfgV/9VewaJHXiTw6WvcYhrM69+0Y4pFdI1XXaeuN0NYXOSLkVwyHQRQQtSDuHAt6v1zQjNg10cRhhK/xpU7zlFyWOjlG7MQ6OzvLr4f27qZ/x+OoYZllK2tH7B78/77ByVd9CmW828F553l6aCVELzgfK5lidJs3KTYasfPFiZMHR0gZz9GzcpxFk54hiwyySlSSMAqeRuFcTPq7d++mUCiwdOlSAoHAFGLX3bKO7pZ1M96/H7HLS0WsoIokiEQdgwUtQeKhxtJnnq1YjmLhAKnBA1OiJIIW5ezCEErIJCiKZEd19IJJojOENF1dopHz6usEwRMn1oe9fdbxPYaVMZmSejCY0UkXzIrm9Q8efJD+kYMsMzbSFmw/QhE77zzEcIW/i54N0LYSwu04RYvcI4fAdoictcD7Pt75Tu/B51OfGiNyQ0PwD/8A113nOXBcdtm0KdqsbvHwrhHaIyqblrTO7QnOAQRJov1Dx7at2NE3azTRxEsUtmVim14abTqf2KPZdaKanZgPRdNAMLBNs3rEzrbhox9l8//6yBip6+yEf/93T+h23L7ltjbMvoVYqoYoCITUxq6pZWdL4sTedqo2jpQrQTKxxV7npyyOadjNgdXUgQMHOHDgAIVSV+9c24r57g15sYAdVFEllQ7R4s2bFnLyosZlMfbs/R7J/B9AMMqyPmUsPp0N6y7i+J5lBCWR5x4+yAuPDlDMmdPv2I9AKSEQJdzSNa5H6sQndgWrgOXUjkK6rktOH5M7mYyIEgFDxLANVG12NZQzhZPzI3YV/i5iPdC+AoIJBEXEKVg4hgMlaRjAkzw5eBB+/3uvS7bk3sLwMFx+OVxwgbe8BsIlQp2pUYdp6jajB3MkD83MEWW2OJZJHTSJXRNNHDYYpQlakhWkabrSMiUJj6NRw66SOPHw8DC5UmG4FABwcSwLUawQ2TQMePvb4T/+o/zRyLveDdu3e4XhFa5tUJF46ykLuXh9T8M1N7aVxbEsBDcwVVi6ZQm9a85j/aK19AXUsjbbXETsJhO58e8d1+Hhgw/z9MAj5PJ7x1JudcJ1XNzSxJwRc17Errsbpa+34X2BVzAvS2Hvdy3oGIXCxP20LPZsxQJepMm/PnW5E4gydKyGVq8hwClFGmuJE/vQJA1J8NbLW7VJRsG0sR0XQYDwuI7P3COHyNyzj4gdAlPEsM0jkoYFcPKle0ilVOw4CJKIoHjTuzOZgKkqXHQR/Nd/wY4dXqesj//5Hzj5ZLjvvqr79iPeuulgVpEzySV1djx8iH3b60/xNjF3aKZim2jiMMEYl4adjlz4dUiRYyAVm0wmeeaZZ0gkEpx00kkEghFEcwVgYRvmxMiMacKb3gS33AKAoyjc9s9fIv6BD3B6YupkZ6dS6C+8gJRooXdZleL+GnAcC9suYJkmuIGKkdbVYY3VYQ3XdXm07Dox98RO0zR6e3u97lirwEMHHiCVfIS3LDqJpUs+jCTV35Dgmjau62XdMuRwNAX1knOJdXipXdtxEQUaIsGSHEaSk7iCUYpOm8jjGkCyls2AYREQBVRNIp+qU8Q20lG2E3MtB9f0yIRYxzUWBIFFsUW4rjstYfXrCkOqNEGc2dUtHN0m4obAEDEdE2WOhZHrRey1r8HVdQSxwn3BNmHoOTDysPAUT1zZdHCLtmd8WwnLlsFPfwrvfS+8//2wfz8cOOCVM/z4x/CWqc4dAVksixRnixYt4akNEv71aUjSZg5RfPZZis9uQ126hNBJJx2RMRxJNIldE00cJuh5n9jVTsO6rluusTvaInaO45S7Ov0O2MlET1HCaNIqTL2IUSyMuU+4LnzgA2VSRzDIth/8hKc3vYJ1VQryrYEBcn+6H6W3h8AMiJ3fOOFYDqAQmFwbaekgqV73reWU1gNlDlKxk4mdqqqsXr0agEO5QwiCREgJIgoCtp1piNgJqkR0Sx+uYZM7+AjgpRpd1+U7971Ipmjx/i1LiWkNaNlJEURRQlQssMEoFsaInZHjuf4XuCPjsLJrMesbidiNQzlaJ4sTOlVr4dVLX13Xen5qcbLOoRCQIW95IsWajdtWINZ+ZDrVK9qJ+XAsz1YMoHcDYkDGzpjla1YTF10Ejz3mpWfvvNN7gHrb27xavA9+cMoYwqrkETu9MrErixQbnkjx4db8c3I5zP7+sozPsYajLxzQRBMvUZQjdtPYiRUdF6sUXYgcZbUilmURCoVQVRWllDL1id54eQ+f/PpkmB07vPTrD37gvQ8E4Pe/x77oQqCCrVgJfhfhkCPz+N4kg5nG6tNEUaWt/RwCwmoEhCnfnfvwdxm++2sYyf3gQs/yBB2LokhzMJFNljcZD78ZIKJ4nZCW1ZichyAIiJqMFAuUpUD8ejSh5NLQaGesJHvby4GSZ+74hpZimuiuuyC5m6ztlP1E64rYWYZH6mGsvm4eGhf88w1P2rcfMdYcFSFuYi0epWtJbM6PP2vIGkilWI2eKaeqnXq/x85OT8T4/e/33rsufOhD8O1vT1k1UiL81fQOPZFi3zu5wS7oOYDfNezr/h1reEkQu69//essWbIETdPYvHkzDz30UNV1b7jhBrZs2UJLSwstLS1ccMEFNddvoomXCiItbfSsWE2iq6fmepoo8MGFnbyrtw35CBRozydUVeXUU0/ljDPOqOg6AWAYI0hBHRcT7r8fzjkHVq2CG2/0diII8JOfwNlnl5tLMlVqffwuwr26wJ3bBtgz0lgxtyQFicfWIzletG9CtNV1yet5vuv28f8GDQRFZOFxrSxdPzc+opWaJXxbsdG8V7sULXmE+rp/M8HS+FIWxRYhPfA4Q9/4Bh39OwHKjQT1Qi6JScsBz1bMccZN6IEoESywTbLmWI1aXZP+0zd5dmKD25ESASKv6EE7vq2hsbmuO23zhCQKtIZVWkITI1A+QdJs7/vIW/m6LcrmEnY6TeqWW8j+6U+VVxCECZ6xPiF164nY+ZBlT+fu058e++yDH4Sbbpqwml9nV43YCYKAUlrHbOT4cwQx7IsUH5vE7oinYm+88UauvPJKrr/+ejZv3sx1113HhRdeyPbt2ydIIPi46667ePvb387pp5+Opml86Utf4lWvehVbt26lr6/vCJxBE03Uh0R3D4nu2qQOSt6ksnTUpWGrYXLELpV6BFF+lBN+9iDxn/1x4sqSBF/7mqfBBUQlz1aspcq18p/Ys5KXvmpUw87HspNPYdGJ6xHGC2GYeTKuAAiEVQ1pjoVQKxG7bdu2MTg4SLatJN2iJgAbu8GInXkwh50xkNuCnLXgLACy/fdSsB0itne8Wl2PlSCVxKS7Vy6lE16oYwAAYs5JREFUt/dNExeqYaI4gEvOKCLHPBFZs55okm8nJmsIkojUoOjts8PPcm//vSyOLebCJRdWXe+Evjgn9MWnfO4TO9WSObvzXKKhI5Pes9NpjJ0vIrW0eKLDlaBGID8CRhYx3I4cD9RVizgBggBf/CJYFnz1q+A48I53QHc3nHkmAKevaOO05W01pYMUTULPm0ekzu5Yj9gdcWL31a9+lQ984ANcfvnlAFx//fXccsstfPe73+Wqq66asv5PfvKTCe+//e1v8/Of/5w77riD97znPYdlzE000cTcYXLEztm9m+Xv/Q6B7QfGVlq1Cv76rz0h4sWLyx+3qTJXLKgeIfPlITKiRwYa1bDT9QFc10JRWlDUSXVVvjixqBBVFIyChQuos7QT8xGJRNi8efMEWRj/daqQggBE1QQw3HAq1hoqYBzIISgicqtHen1ttGBJpLjRiF1AbScePwlVbZ+6UBAIBYKIOjiWAWGZRSe0oU2nl+e6oJecFBq0E/OhiAqWY9WtZTcZftrX1W0Kj2vkbJOu820CocNcN1YWJ64h2u1fIz2DsiiM0jVDyzNB8HTtRkfhe98ba1p65BFYtKiu2sty5/MRjNi5hoFjGIhqYw8DL3ccUWJnGAaPPvooV199dfkzURS54IIL+POf/1zXPvL5PKZp0tpaWShR1/UJT7zpdLriek00Md/IJUdRteC0dmLP54vsL5osDqosDjZovTRTDAzAo4/CCy94nXGZknaYpkFPj0emTjoJli6dscckwM6dOxkaGmLhwoX09PTguu7EiN1zz9F2yVXI+0uq9sGgJzb8wQ96aaIG4WSzuLhkpBKxazB6kUw+TC73PG3t5xCPrZ+4UM+WxYkjkkj/c6MM7snQt7qFvlWN68BNhiRJhCbV9PlRzbSehgDEtDYwhhtOxfoF9baCp8smqeXJMGjNzH1CVdtpazur6nJRixLWLTK2TlER6Fk6NTo2BZYOdmkcgSjGvgyu5SB3hJDq9CCNqI25T0wZd1BGDMm4iohje7V+yhGQO6lpJ+ajJCeDPvPUfBmC4Hkv790Lt9/u2ZC94Q2eFMo0dcIAnYujtHSHGvMEniOIqoqgqh6xy+WaxO5wYmhoCNu26erqmvB5V1cX27Ztq2sfn/nMZ+jt7eWCCy6ouPzaa6/lc5/73KzH2kQTs4Hj2Dzxx98DLqe87q/GOj0rYFfB4LF0DlGIzB+xcxy491745S/ht7/1CF09aG/3OuguuQQuvtgjfg0gn8+Ty+WwS12sruuyatUqdF0nMDgIF1xQJnX2koVkvvd9Euec19AxfLiui53LYdouhhqcok9WDyw7i+M47HniGcIRgyXrT0YUS2lfPe0ROylARJYwiqXu1eD83Vb9iN2JoRNZsmwJEcnF1eOVo2Q14Dch7Cy+yD1P3c+qllWcHVnrHcMoEbsGI3Y+cslRXnzsEWRVZc0ZZ48tUCNEyJGxTTKWQ089P+2yOLEGkoLRP4SdNgiFlbqJ3Xj3iVreod/704uossglG/omRHalWIDoGX3kUjq5FwfRxQKDhTBd4a6K+5kv1LQT81GusRsLYPgyLzPyTJVlr7b11FO9e8Rjj8Hf/i35r/1//GV3EtN2OHfN1JIp4Ih1DvsQoxHcoo5bofnoaMcRT8XOBl/84hf56U9/yl133VWWTpiMq6++miuvvLL8Pp1Os3DhwsM1xCaaAHxxYhdBFJGrOC74yJY6PMPz0RGby8E3vwnXX+91mjaKoSFP3+rHP4a2Ns+C6G/+Bur8m5qcdhVFke7ubkin4fTTvegAUFzdzZN/+7eQGuHUafb5x6EUO/I6Z7dGOT4ycTJJXHopQ4dGsfa7RFR5gj5ZPbCtLLZlkh5IkhvcydINm8adTCkVK6tEJbFcSzSX4rX9/f1kMhl6enqIx+Pl66baKgtjpWseXtTQPl3XLUfssoIXxdJkbSxiZ+osbAnSFW+MtANYVg7DGCA11I86OXUaiHEq+zDVDN0BhVxKR89ZRFoC1cnwpDSsW2q2aKRuLCSHEBBwXIeCVSCkTI026ZZNMl+yg6vS0WwWbYYKgwwIB0ik7cNO7MbsxGqkV9uWg5aAkJfByj5wACdnEn5FT91EeApaW+HXv4ZTToFCAa6/HuGc83i4dT2iIHD2qg7El2CTV8vb3z4zMnsU4IgSu/b2diRJ4tChQxM+P3TokHezr4F/+Zd/4Ytf/CK3334769ZV90sc77HYRBNHCr7rRCAYmvZmky11eM6pOHGx6JG5a6/10q7jIctw2mnejfuEE6CvD1pavFRMNuulZrdv9+pr7r13LE07POwVV//7v8MVV8A110BX7cmukrQJruvVz23dCoC5qI2DP/gY5p42BEPHtqyJbg+TYLuQs+2yDZsPQRBQOjvJCyE4uL/hNKzrOlh2Hts0wQmgRiZ9d6E2MpEiqBGiskRhDu3EfAwPDzM8PEw0Gp1A7HRdrxl9qgnLwS2lFDOC1yUcUSJlwhCW4E0ndCA2GI0FOHjwlxTyh3BFFVNXcBx7LMLZs45VrUsh1AayxLNbB8gMF1h+cidtfVWiUH7ELhDDtV0co37XCR+SKBGUg+StPDkzV5HY+WnngOKJ71aCUbRQJBUke8Zp3dnAbwSo6BPrI9ji/fPhup7LSNGCmRI7gOOP95qW/vqvAdA+9NfE/uM3pNu7yJt2xdpV23JIDxWwLYf2BTOrj5wNjlVSB0eY2KmqysaNG7njjjt4wxveAHgCpnfccQcf+9jHqm735S9/mc9//vPcdtttbNq0qep6TTTxUoGvYaf8/+3deXgb5bX48e/MaJe8x44dx4mzAEnIBgECoRTCUgItJFCW0hYCBArclgvNpbfQXwv00t7SBQotFGgpSbllpyxd2NJAAoUCYQt7IKuz2HESr9qlmfn9MRp5ibzLVuycz/PkAUkj6dXIto7O+77ndC5wm4GdsQv0sgBrj1autNaodZ5uPf54q2bVqadCYWHvHiseh1Wr4P77rRIIsZh13e9+Bw8+aAWO3/pWWw/KdkzT3CtjFw6HMe65h0CqlImZn0ftfZejjhmLY4cLPZkgHo3gDXT9wWCfp65q2Y0t8nLu4VX0tVGWrofANDCSOuDE3XldUfl0DvRNpCieoEhRCaY6Irj6uEGjO20lYOLpyxEjwvbodsp2lzGldAqJRAvJZCsu16heFSm2e8SqLpVgsq2GneJ04ho/DsXlsnrx9oOm+VEdGooWB8P6QuOxA5FAmfUvpa2WXTfP5c6z2onlVaRboCmqkm6X1Vt+l59wMkwwEaSUvTfb2NPOeV28d5EPdxP/tIFA3AEFRk4COzNqfTnsdvNEJ4pbg2AvixT35JJLYMUKeOwxlKYmTrrjRv5yw+8IRpMZA7tkXOfzNTtRNYWSysB+HWgNtZzXsVu6dCl/+MMf+NOf/sQnn3zCFVdcQSgUSu+SveCCCzpsrvj5z3/Oj370I+677z6qq6upq6ujrq6OYDALi0WFGCR2YOfuRdeJUDpjN8DMT0uL1fT7xBM7BnXnngsff2wFfF//eu+DOrD6TH7pS9ZU7NatcN11YK/5aWqCK66wSjFs3LjXXROJRDrLlC5t8vzzeNvtftfvuYP8w86goGA2To8VBHcodJuBXcsu2KmWXWLHDsLvvIO6s44xhV4qC/u25idpd53QHSiouDIE5Yfk+/jSqAIKDetDS3OqaH0MOrrTueSJpmn4S/3s8u7i3V3vAlC382lqax8nHt/Z5eO019Zr1dGu0LH1Hhacfjr5Cxag+v3oholu9C0cdjgCKChtRYpTmWpbRDfYGI6xIRxt1y+2m7V8JZOsdmLjj2obt0frc5BQ6a+kOr8adxeBrx3Y+bsI7EzdQI8kcZsOcOUmsCu64AJKLr0ER0kPNfx2fgw1r0Miipp6PWY2igQrirWMIzWbNu61Fzlw1TMEY4mMh9sbTAzdJJkY+rp/8Zoamv7yBK2rVg35c+dazgO7c889l1/96ldcf/31zJ49m/fee4/nnnsuvaGipqaG2tq2sgd33XUX8Xics846i4qKivS/X/3qV7l6CUL0KN7LdmJh3cDAREHBP5Cp2Pffh8MOs0oV2I45Bt57z+oNOXVq/x/bVloK//u/VtC4eHHb9a+/bu2gfeyxDofbwYnT6USNROC66yg/5xw0e3Hzf/wHjq9dQGHBHAryZ6UzZHZQ3JW8VADcOWMX37KF0KuvEVu/vl8vz64NZyZTdcw8nd67eDjdEcHOOmW7OXymWnallaUUFhaS77EWytuFgZPJ1l49pqPYQ94xlXiml6QDFL+rYxbosbe28puVn7O1rwWdU7XsNHfqvLR/7/Qk9ds+4C/r3uelPS1t/UR7GXTYhXbVfmRE51XO49SJpzImMCbj7fZUbFflcBS3A5fPQUmJD3z9L50yEFa3EA9KT1/4NqyEDS9BpBEldY6Nfm6E2UtREdx5Z/ri/N/dRHhH5i8UqqrgcOeuZ6yZTJLYsYNk56Un+4GcB3YA3/nOd9iyZQuxWIw33niDuXPnpm9btWoVy5cvT1/evHlzuqFz+3833njj0A9ciF6KpTIXPQV2dtbJr6mo/Z26+L//gyOPbNsckZ9vra9btQpmzer2rv1SVgbLl1uPP2mSdV1Li9VA/OqrrUKnWMss/H4/JTt2wKGHws03o6Rui8+YAbfc0uFhXXbGrlPWp7O81FRs54ydvYtwUxjerWmkJZo5s9AVl6uUUaPmoybHWpd97TJ2yRjxV3/D7tW3E0vEcHk0KiYVUjI2u8Vr7cxm+8AuHYyldns6HHZg17tgQ1GtdmIJj45upjbqONoCO9M0cdptxfrcfcJ6HM1l3b9zUJ63cQU0bSaUiLcL7Lp5jkQkHTzbrbHsjgrZZL/OrtZhqm4NX76bqvFFKAUJ4nqchN63n6chkyrvQjzYoQZf1px5ZrpAuK+5kfIb/1/XQ+lnT+BssNci7o/dJ4b1rlghhoviyrG4vF4Cxd1Po5S6HFxWVUbM6MfUhWnCTTfBDTe0XXfooVbmbOLEvj9eXx17LLzzjtVf8qGHrOtuvx2eego8HgricY4Ih6HdZinD6aTmnHMI3HQTozweYjHrNqezMB0E95Sxs3cPh3Ud3TTTHSDsP+gfN+vsWLeLUQF3n5raO50FOJ0zIVEH7OoYlMeCbMfL44yjtL6VCytHUTUtcy3Ngei8xg6gOdpMPB7HaVivRUsFU7retw8w0zSZVjKNhJFAS21wCL/7LqF//5sSfwWbxhzc98DOYa2FVJ1GKjBv9+VEcxBwOCEJ8UQUM98KyLv90H/jbtATcNgSXGOLcJR4oZ87MO22Yk5t758Br1Oj2O+iwJv558PerKEmFFxOF3E9TjARpEgbeL3C3ohv3Upk7fu4xlbinT27+4PdedBaB7EWFLfVjSkra+zau+MOkiv+iaOlmbKnH4XXrrJ2tXfi8miEm3vZEzjL0m3FwmFMw0DJsO53pJLAToghUDqumtJx1T0ep6baiUEfsxLJJHz721ZBUdull8JvftPnWnMDkp9v9XE97jhrPMkkbNmS+djZs3nv+9+nefRo5qTWDe3Zs5potJay0adSXDkWTyCAv7D7D0+vqjDK5cSnqsQNE69mB3YdixP3t53Y9ONOIpmIt+3uBIi1dCh1MljswC6RSKDrOpqmUVNXw/ba7RzkOAjGt8vY9bJIcWxTM2bCwD3Gz3FVx3W4TXG6QDf6XaTYDjILK4oZP/fMvW53eQJ4ggbRZJx4ai1iPJrMvMNXT0CqCwYuP4qj7+3EbLXBWv628W/kufI4b8p5e90+b/Io5k3uphagSyOZ0FEjSY6fdDwu1ZVelzgUkrt3E9+0CcXppMeVounuE0HUAgeOQjfqQHbEZlJejvGTn8J/pjY5XnUVvPHGXpumnLnM2PlSXwIMEyMc7r6w8wgjgZ0Qw10yCeefb62ds/3yl/Bf/zWgLhH9pijWztgDD4Qrr7Q2Urhc4HRahZETCTj/fIyf/5yWNWvANNNTjnZrLIfmx1MyirySngvvKorCRZUdjzNNEyMURDdMok7ro7CrhfFdiURqUBQHLlcJTlenRfex1nRx4jyHRjSYQNEUnG4tqzW9HA5Huq2YlspMJhRrCtChW6+nLWPXu/VwiboQejCBo8QDnT7rtNSOS0+qSHEo3teMXT4FBYekM3d7cecRCCaI6nFiDhg3vcSarjPpkNwD2kqdaE5wDKxklcfhGVBbsYRuUL+pBcWpMuXorstrDZZ0Dbve7Iht11ZMC7jwH9596bD+cl1xGfz+bvjwQ6sU0v33w4UXdjymN9Ptg0RRVVSfHyMYxAgGJbATQmSPnkwSaW3B7fV123EC4IPWMA0JnQN8bsZ4epGd0HW46KK2oM7ptNa7ff3rAx/4QB13HHzwQfrixx9/TDAYZNLEiZSMGkWiXS02l8tldYpITSd2GRj0khmPYyaSxJMGSY8Xj1PD2cfM2q7dK0kmWqioOAuvt7LjjXZg53AR0DQ2rt1FsCHK5DmjKR7Tz/6cGSiKsldbsTjWtKyatF6Pllofp/dyjZ09LRd3JDFS7cRsdlcDdypT1trnjJ2n27ZiuPMIUM/uZIyQYTChu7Zi6eLE+aAoRDc0WcHzmACqq28ZbXs9or02LtN0bHcSBhgOFYfPiWmYWekF3Bd2z2Otu+LEtnZr7AaVwwG33Wbtuge49lpr/V1+fvqQonI/noATbyA3Lb3UQCqwC+1f6+z2n0lnIXIk0tLM+/98lrUrnunx2M9CUd5sDrI70YsPVNO0plv//GfrstMJTzyxbwR1GYRCIUKhUDqLqGkaU6dOZdKkSaiqimFEMFOL9jXNh2kYNNfXsWvLJsxerjm02yfZfTUTDiem5iDQh4K29uPoyRDxaISNb6+l5sP3Ox4QD1pTsZqbgENNTzU5B2Fhf2cLJy3kcP/hOJLW93Kno4DCoiMoLOqpR4dVtsNMlZ54c89b3PvBvby98+307fa6JGcihqLrhPq5mzIRi/LhSyt497m/pd8TwCrmTBL0OK16D++p3e/UHbB6Cm9uIfp5E/SxBAuAS3OlA9hgomPA0xxJcM/qDTyypqbL+yd1g9CYAObkQpriTXy05yO2tHSxxGAQtBUn7lvGzmamChVnk2ma/GvcLOpOOMW6YudO+MlPOhzjy3dRMiaALz83gZ2Wl4fq92P2sy7jcCUZOyEGWTzaux2x0L7rRC8ChB/+sK2cicNhbZL4ylf6Pc7B1rnrhMPh6NBhxp6G1TQviqJhmgYfrX4RMCkoG93t+XujKcjbLWFm5nn5QlEeWkEBRV87l11b98Cevk/DGkYM09RJxuM01+7GiDuAdlNwsVaCaOBw4VdVGuyuE4MQ2NXX17Nnzx5KSkooKyujPL+cUmcpRtJIrbvzUlx0VK8ey94dqWgKQdMKFryOtlVbiseD4tBwGwbjfOAr9ve5w4Wuh0kajTTvqUExPSTjMZzuVKbancfBtFCl7aHc5yESjBNpSeAJOPf+8I+nsiyuAGbCSAcmSh+zdTafw9e26cHTtm4zGEsSjutddpyAduVs3A62tW7jle2vMLFgIuPzx/drLH3Vp8AurxxmnA0eKxsafq+e5J4o3hmjcJb1/DeotxRF4YPtzXx2wX9x0b9eRInFrAzekiVw0EFZe56ByDv55P2yMLJk7IQYZImoNa3Vq64TvW0n9vvfWzXkwMqAPfQQLFw4oHEOJsMwOnRPyMSehrVroSmqiis1dd1TyROw2orZtewUhwNHaSmhYqvTQV8DO3sspq6goO1dnLhgLEF/BTh9eA3SQYezj5nB3mhtbaWuro7m5mbrOZxO1NQi9XgfG5y3FSfWCCetNXn2NCWkaqX5/ThUldMmF7BgenmfPxh371lFbe3jqB5rvB3eu+KJVM08nYOnfJESl4OdG1tY//ZOGmozTJXF7XZigbYadi6139OggdQUZTjRcS2ivUGku5+R9hlZu+Zf58zfYLHWi/YhsHN6YdRkCKQ6bCjWz2dWS56kBDwOmiuqaP72VdYViYS1vjb1npumSUNtiJ2bWjB6ytAOgv0xqAPJ2Akx6OxyHXZdtq7opklYt9uJdRMgPPus1eHB9pvfwFlnDXicg8kOQFRVxem01je1trYSj8fx+/14PJ52GyfaFjm7fD7i0QixSJgAXZeKCXTRfWL6mALGFnn7vL5Ob9d1AvZ+78yquRySFyKo63hSs5UOl4Y6CDtk2xcprg/XU9NSQ5PSRD75xGIxvF4vyWQriUQLTmdBepdsJmbcLvKrpQOc9oEdgHPcOBzRqJUF7gf7/XO4rTJ0sXC4bWezJ9/6Zz+Xvbg+UwHbwGgom5JqJ9b3HrGd2a+zc0CWrmHXTWAXjyZxNcXQ1jXgUKzjhqpIsZlIpJcvqJ3b2vWCknpdWS95AgTcGrtbYfsVV1P42ENWN5qXX4ZTToG//Q0CATa+W4+hmxSUefH4JZc0FCSwE2KQpadie9g4YbcS0xQFb1dZifXr4bzzrN2lANdcA930Vd5X2AV2XS5X+lv09u3bqa2tZcKECVRXV+P2VFBc8gUcWtvGCTugSvSQsbMznHZgF9uwAb25GefYsVSUlXV314zsYr9GqutE52yroijMK7ICmKZ6u6vI4Pw5taeu4/E4O4I7eLPuTYp8RcwaNSsd9O3e/RLh8CZGjTqe/PwZXT6W/eFuOhUiSeuc+hwdg4W8445L/79umBim2afA2N7MobkNEkAi2vG9SxgmW6NxIoZBmV0OI1PQUT7D+gcY261gTBlAH95yXzlxPU6+K7/D9eF4LzJ2MR0wUQ0Tj269H+FkGMM0UJXBDVZUl4uSyy7DjMdRnL3c9LF7PYR2wagDUV2ptmKDEtilvqSpLmsD14IF0NoKq1fDSSehPPccTo+DWChBPJrEk+2yKz1INjQQfGkVikOjYB+e0cg2CeyEGGTx3nadSE0jBjQ18xRCKARnnAGpKTnOOAN+/vOsjnWw2IFd+2nYzlOzbtco3K6OZUtcqQxFrJdFiu1zGPvsM2LrNxD44jE4+xHYpadi49aHdoeMnaGDHgeHBxSlbZpuEKZhoWPGzkxYU77jK8ZTXVmdPia9M7aHIsWusXk4y3yE4iHMjdbaufZr7Npb8fFOPtzezBcPLGXO+N4X4rUzdqozFWR36vUb3/kRf6mLoOSN5uI8KwvbU8updKaxn+vrAA4edTAHjzp4r+vtDSL+bh67uMJPJJrEEUniTFi9ak3TJJKM7JXxHAyKoqB0sYQho21vQuMWcAdQ3BMAMOKDEdilspexpFWgeOVKK7hraLDq2n35y7j/535iKDmpZYeikNixA8Xp7PNa0eFM8qJCDDI7sHP2MBXb7cYJ04RLLrFqRgFMmQJ/+tNeBUH3VYqiEAgEOpTuaJ/F60q6+0S0dxm7qGGQNNrWJH3UlOTdmkYiffxQ8/qqGTVqPmbMCjQ7BHbBesL/+g17/v0HYoaBN89FxeRCiisG5wO+fWBnTyP6nB2/JNitvJI9BHZ2O7GwZq379Dv8GT/sTNPEZVoBT193xmp2YOdIlVXp9N75Nr+C1rQJMxEh4bSee6+MnWlamyfsXc7pqdjs/7wHU4/dXcaufGIBY2eMwunWMONGOssZHOySIv3Vvkhxuq1Y9mvJ+VOPne5QcvjhVmvB0tT6vtdeY9z130JJxHvdEzib7Np1ZiKB2cf1qMOZZOyEGGSjJ04m0tqCNz+/2+Mm+9xcXlVGwsxQluDee9tq1eXlwZNPWv8dJkpLSym1/9indM7iRSJbUVUXTmcxqmpN2aT7xYa7z9i5VQWnopAwTYK6brURwuTtXTHC8V1MLA3g7UM3Dzt7aCY2AOGOmyfiIdaRxz/NKg7Y1cyi0UUEigZWQLc79vS1aZq0RqwNBR7VQygUwjRNAoFAW5HiXtayc2kuppVMw6nuPTUW27iJlmefocCZDxPm9qOtmB3YJXF6vWid1uop7gCBqE6zHifusAK7ZFxH1w00e8pXj8OrvwFFhWOW4plUgKsygOIcWGBnmiZxI45ba3u/8j0Oiv2uHjuTpAOkqI6/0E8oESLUy/M9ENFPPyW2fgPuSRPxTJ3auzu1K3miFA9Cv9gUfzpj1+6xZ8yA55+36li2tOB77UUmOv6b0B1/zPrz90RxOlHcbsxYDCMUQu1L1nMYk8BOiEFWPumAXh2nKgp5mTZNrFsHV1/ddnn5citjN4zpuk4iYXVQsDN29fXPoOtRKsd+Iz0lmz+qjElz5uIJdB/EKopCpceFYVqbUMxQiKRuEnda6xq7m2brzpwvL0JPJDoGJ/FWQmigufAPYjsxm73hJB6PE4wEQYVYa4w3P3iToqIiZs+e3eu2YtHPGgEoGJe3Vzux9PN53GCY6e4TfQ3s7CDTV5DP1Jmnommd1pa6AwQI0pyME1ZB1VQM3SAR1dHsxfV2DTvNCZoTRQPNObCp7lAixJ8//jMmJpfNvCydqfzSwd13ZtCTBomYjpbKLppxnSMrjgRglLfnzigDlayvJ75pE47iPvSldaV+X+KtKG4NR6Ebxa1lfTqyqsjHkmMm4Hd1CiUOOcTaPHHyyRCNUvLy3+COX8I9v8jac/eWGvCjx2JWbcvi7Pdz3hdJYCfEviweh298A+yM1WWXWdXdh7nOu2QNI4muW4GEPa0I4AkE8AQm9+oxzy63/mgb0Sh7kjoJ3UB3e/G6NBx9DMBCoY2oqhu3uwxH56niWJAQDtBcBBwa4ZY4mlPF5dYGrSPBnDlzcDqdLPt4GehQ4CuggYZ01rOtrVj3GaT4jiBmwsBZ2fXOWbukhisRBdPsc79YVXVQWHg4mubJHES4AvhoAj1OyDConlmCqqk42wffdqkTV9fj7CuP5kE3rcxSJBnZazq7K8HGKOter8MbcDJesWaHx7gq0hm8wWakfvd7VerE5k6dt1gQ1aUNXlsxh9p1/b8vfhEeeQRz0SIU06Tk97+EEw+Hs88elLF0RfP70fc0pM/j/mB4LNARYphKxuMEGxvStey680ZTkNUNrexu35/zhhvg7VRngIMOgltuGaSRDq63336bN998k9ZW6wO7/cYJRVHSAYmiaKhq97uHe2Kvr7O6Tmh9ztaZpkl9/TPU1j6euf9qPJjqE+sioKl89mYda/9ZQ7hl8NbweDweDAziuvUcBV6r+Kx9HtsCu7buHZ217zoRVWPpx+rMLqnhNA3UZIJQLNmxe0QvFBfPo6DgUFQ1w9SXK0AAawNKKGkwamwexRV+tPbTrJ26TkTXNRDb3Iw5gFpomqqlN4rYNfx6w17/5/I60ArcOIo8/ep+0V/pGnZ9KXWSbiuW41Zap5+O/pOftV1evNjqKzuE7IB4f2orJhk7IQZRy+5dfPrqKgJFJcw8cUG3x34UjLAnkaTa62IUDnjttbZdr04nPPgg9OVb+z4kHA6TTCbThXU9Hg9T260XaitOvPdi/ub6ncQjYQorxuB09bxGRk/9AY+5UtOw/ew6EQ0F+fyNtykYVU7llGltB8RDVtcJzYVPUWmIDU07MU3V+NqUrxFKhMjzWlNtyWSSZDKJpnkpLDoCh+bHNA2UDCU42nedeGnHKmpaazh+3PFMKe44rW+vS3KZUbRohITTRTRh4O1HgPzR6pXEI2GmH3di265wdwB/qq1YqKtAzd6UkOo6EauxvhC4xnW/TrUnPoePSDJi1fDzwo6mCH9bu4PyAg8LZ1dmvE88vevZgf8Qa51oMB5ky54taIq21/nLtj4VJ7bZGbt40EoxptZoYpL1rPIbG/fQGI4zd0IJRf69N0I5rvtv+OwTa7NXJAJf/jL89KdWl5zywckktqcG8qweyPvJjliQwE6IQWXX8OpN1wn7Q86vaRCLWbtg7UzJT34Chx46aOMcTHbwAe1Km7jdGduJta9hZ1u/5nVi4SDT538J56jSvW63fdgaZnVjkGqnn5O/di6bNzdAU/+7TugJk9baWlS10/1jrYTwgsPV1nVCUTpOJWZZQ0MDO3fuJC8vj6qxVZimiaZp6LpOPB7H5/P12FYsU9eJzjXsbKrfhxmLMSlPRanIx+hjxk7XIySSzYRba0lGVeKRSFtg5wowmRAFyk5G5fuIhhKEmmO4PA7yilPZ2ni7jF0Wuk7YfE4fe6J70sWF7XZisUTXmcBMfYCbYk2s3rqaIk/RoAZ2fe46YXPlwcxz0pm7yMd7SNSG8BxYhKsqu5uu1u8KUt8S46Dy/IyBHYoC99wDGzfCK69Afb3V4xrgyCPh/POt2pxFfVhD2Af+I+fiP3LuoDz2vkqmYoUYRL3tOpEwTKJGu3ZiP/0pfPKJdeMRR8B//degjnMw2dOFDocDRxfdDPTUon+7Hlt79o7UzoVuO1MVhbCuE0TBUVpKMM/6oOiuo0DmsaRq2CUdHZ4/fXvxJMK+MnB4cCat98w5iOvrACKRCHV1dTQ2WpsfFEXpULi4N9IBkltLBzZdrTNTfdb7MH9cgAXTy/scHDc3v8OO7Y+geHdaY2z/3uWVUzrrDKbNWECZ20ljbYgNb9dTv6Wl7ZhYu4xdFrpO2Oyac3Zga28M6e71xVNrDNsHdnZAPNjdJ8xYDDNVm7FPgZ2qQskkyBttBVaagmmYGINR8sTVrpZdF5qadepvvx/j8CM63vD66/Dtb0NFhRXc/fvfWR/f/kgydkIMot52nQimWok5FQX3Rx/Cz1LrUhwOq9RJptp2w0SmenWNjY0YhkEgEMDtdqc7PbTfOGGzA6ue+sX6090nrHN5xIRiplTk4XP27c+cPRY9maE4MWBUH8O8ohAhXccRN1PHDO7743a7aYm30LCrgaLWIsbmjcXtdhOJRNLn12or1ozDEcDpLNzrMewCtd11nbC5xlaiej19Cybasfv9ai6TBJ3eO6cXiie2XbS7T7Svc1YwFjDBX4oRsQO7gX9c2YGdHZClixN3EzSm19i5HcS3tRLb2IyzxCoTE9fjJPQETm1wOioYkQiK0wGahtLPFm/QrlTLIJY86W739LZPGwk3G7ieXknhtk/g6aetf3ZdzljMKuf08MNw9NHwve/BaacNmzqd+xoJ7IQYRL3uOpGahs1TQPnWtyA1dcm111p1oYaxTF0ntmzZQmNjI9OmTWP06NH4/ZNwOPy4XHt3iXCmguKeixRbH15NtXWEd9bgnjiRin5M7+zVdaLTe+dU29qJ2VmmwV5f53K5aI41U99aT3lLOWPzxjJ69GiKiorwp4Kvpqa3aGl5n8KiIzJOy9of6nFHEhKgKmqXXSd8hx+e/v+kbqCbJu7u+hd3YgfoqtN6zs7ZVsM02RSJEdQNxrms89yhSPHYw6x/gLnR6rQykK4TtlHeUUwomECJ1+p4Yddf6y6r22EqNmxgxHScCRcuzUVcjxNMBCnSBmca0VFURMlll0GqNFCfNGyC1jooHIfisjbbDEa/WDso7i5j5/JohJshHjesIsaHH24tL1m7FpYtgz//GfbssQ5+9VXr3+zZ1hfck08e0Po4Ixql5R/PYEQiFH3j6/tF9wkJh4UYRL3uOpGabpn58J+tVjxg7YL9f/9vUMc3FOypwvYZu85ZPI9nDAUFh+L1jt3r/ukixT0FdqmyC+Fdu2j69+vo9gdFH9mBXTKRIWOnJyAeTq99tD/0XVnIJnXH5XKRMBKYSTOdZRszZgzV1dUEUtX1eypS7J5USN4XK4mNsT7YfA5fjx9yazY38NsX1/Ovz3f3abz2WFQtc/cJpf5TnvrsfV6orUt3n4h3UVbFzjRmYyp2UuEkTplwCgeXWK3F7GDE17kOWzujqgKMqsrD7XOkx2DE9CGbjlUUBaWb7ixdqv8YNq6Cxs2Dm7Gzp2K76e7iypSVBZg1C267DbZvh/vug2ntNim99x6ccgrMn99WGaAfFKeTxI4d6I2NmL2oTjASSGAnxCCyMxWd12l1FtIN3M1NzPpFu9IAv/899DCFOxxomtZlOzF3LyrB2xmzRA9TsW5VxaWomPEEQVXl7foY79Q0kuhjiQx/4CBGjZqPEbF2YDrbvweNW2h99U52v/VnYoZBXomHismFFJT1vDlmINKBnWniNDNP+zl66BerqAqq20FESbUT66HHqWmaeAwr8Olv9wnFkcTE3GsaXdm+Bn/jBoiHiKcCOz1hoOsGGIa1xi4VPLdfG5htoVRpoe4ydpUHFjFxdikuj6MtQIrre03r7nNcbTtj2wek2eZ397zGzs5odxW843bDRRfBBx/A3//ecaPY6tVWhu/b34bUGtO+UDQN1Wf9fu4vJU8ksBNiEFUcOJWKA6bg7qEG1aH5Pi6/725cDQ3WFeedZxX4HAEqKys5/PDDqa6uBqxdsnpqHZzL5cI0TUKhDURjdRlrsLVNxfb8bduvKZiJOC2mytu7Yqxet4u+Trx43OUEAgej6FZg17GdWCtryWeZPoaXG1rJH+WlamoxReWDW4ZGVVWSivWh6MLK3ui6TjAYTNcG1HrZL9bv9HNwycFUF1R3eUyitpbdv/sdnuf/BvSn+4T18646VFxe595Fnl0BAiRBTxDGRNVSPWOjOkQa4bXfwqu3A+CdVkzgyAocZX2o49YN0zSJJqOYpkmRz0VJwEWgh3ZiNqVd5iuQCl4HM7ALv/suzX//B7GNG/t+53SR4ta2gDRhDKgWYCaBXgR2dsaux36xqmqVQ1mzBh59FA5Ide0xTfjd76xZjIceaqsW0Ev7Wy07WWMnxCCqPKh3vR3VTz7B9bs7rQteb1v9uhHIztbZu2R1PcrOnX8HoLr6P/aqweYvLGLSnLm4/T13IajQFJRoBH0AXScAVFXjiEVnW+3EnO0yZPFQh64TQymppnZnpjJ2zc3NrF27Fr/fzxFHHJHesKAnM7cVi3y0G8WpUTZhFKOrju32uRSPVYTXmbSC6e4+tDPeX9HQNC/eAEz+0gnpFnFprgABWlLdJ0ycbgexcIJETMejpLpOpHbsKk5twO3EbLqh88cP/0jSSHLR9Is4bdaYbo9PJnSScQOnR0PTVBSnhpLqPjGzaAZTRk2hyD046+sAknV1xDdtwlW19xKFHqXbigXBoeIo8qC4VKu4chZ/dEcFXFxyzIRup7PtjF2it11MVNXqULFoEdx+O9x4I4RCsGsXfP3r8MQTcNddMKp3Ld1Uvx927d5vAjvJ2AmRa6YJ3/0upLJYXHcdVFXldkyDqPOaO7u/qap5UDM0pXd5vIyeOJnC0T0XMz3ZrXJ6Uz3FhmF1nejj2jfTNAkG1xGJbAcMHC5Xx3VosbauE35NJdgYIxZOWLXsBlFCT+CsdOI/yM+YMisYsaex04FyKktmdZ/omBkxkwbxHSFiW1p6tRBds9uKmTpKMkE4rqP38TUWFh5GSckX0dQM09TuAD6SkIwT0nWqphUz+bDReALODl0nsk1TNRypuoS9ybQ11oV5/8WtrF9jlW1RVAUltYmjWCmkMlDZ69Zk/dGvdmK2dm3FFEXBf9hofDNLUbIUJNscmkqex4nWTbmfXmfsOnM64Zpr4NNP4atfbbv+8cfh4IPhH//o1cPsbxk7CeyEGCTxaKR37cT+/nd44QUAjPHjrT9kI4Rpmrz22mu8+eab6QCk8/o6PV2ceOAf5PYf7rjbmr4N9HFdlmHEqK9/jtraxzO30YoH010n/IrKx6/uYO3KrSS7KXCbDeFkGMWh4HQ4calWQJwOjFNT26rqTWc7O7dCM+0NCJpCUA8R02PdtglTXC4UpxOHpuCORzHNtvVovVVQcCgFBYek1/510L6tmG5QXOGnuMJvFXnu0HVCJ/Jpqp1YH6ffuuJPjSeS6H7NJrTfEdv2BUErcOMo9tDnOf5+6FdxYlv7tmJZOnf95fY7mDxnNAccPrp/DzB2rBXMPfIIFFs9oamvt7pXXHddWxWBLth1GfVg5mz2SCOBnRCDpHHHdt7/57Osf/uNrg+KRjGXLk1fDN/8c2sqdoRIJpPEYjFCoVC6OHFBQQFTp05l7Fhreql9O7GutOyup37zRmI9NPK2MxxRp3UOu5seysQeSzQYZd2/X6Vuw+cdD4gHralYhwuPboJpoqgKDtfg/ikNOAN8bcrXOG3iaekMosPhQEuVeInH4yiKQlHxPEaNmo+idMx8tu868cymZ/jjB39ka+vWbp9T9ftRUAgYVoa1r9Oxtk9fXc07zzxNqKndwne3vcYuQ1uxdhk7I6oT39pKfEtr1spU2Bm2T3bWc8/qDTz/UV2XxyYytIvzzSrFP2c0SZ/JR7s/4t36d7Myrs46dJ3oS59YmyvVRss00j1jTdPE1LMf5L1T08izH9RS15z5S6ymqRSP8bd1Fumvc86Bjz6yAjrbzTfDiSdCbW2Xd1PzAqiBAIqzH7uLhyFZYyfEIGnrOtHFH7O6OjjzTJT16wGomXsUFWefPVTDGxL2tKvT6UwHIV6vF2+74LWtnVjXgd3mte8SbNjNQfO+2O1GlO0VY3nmhFNpaAiTH+l/14lk1CS4Y9tez2VEg4Txg+bEmbA+IJ1ubdBrY2mqhhbTaNrRRNQTZcKECenuE3aRYq/XS2HBnIz379B1Itl91wmb6vejNzVR7VcorcjH2ce1iroeJZFoJBKuIxpKEguH8Rem1qO5AlQR4cvmdooK/cQiSYINURwulYJ4ao2dKy+rXSds9utuiLQSjud1u2va3sWZqZxNQk+wettqFEVhVuks1Az9eQei310nbKoKM8+11io6vUQ3NBHf1IxrfD6eA7K7LnDLnhCbd4epKvZRXjDIO/nLy+Gvf4Vf/xq+/30rW7d6NRxyCDz5JBy1dw1H78EH4z344MEd1z5EMnZCDJK2rhMZMnDvvmtt4U+10Il7vfzrx//b5w/PfV2mrhOdtWXsup6KtYPjnkqeuNwuol4vjU7r+L6usbO7ThhJLfW8Hd+7UOlUTN8oVIcHLW6kjhma78fxeJy6ujoa7J3T0Ou2Yu27TkSTvSt3YmeJ5pS6WTC9nFGBnkvTtBcKfcaOHY9iujYDnYoUe4somnUm0w5ZRIXbRcvuCBveqaduQ3M6u4Q70CHTmC32626KWl8ouvsZyZSxS78EhxcFJb3LNtvsbJ3icfe/60TxBKutmKqhaAqmOci17LrJ6rbsibBzUwvhlt61wOuWosDSpbBqFVRWWtft3GnVvHvkkYE//jAnGTshBkmXXSf+9jc491xI3Z6srOShu/6IPgK/UdoBR/t6dbt27UJRFAoKCnA6nb3K2NnnsOfuE1ZgXDnKx9emFJHn6VurJzvINFLFiTsXltYmzefoljBJ0yTZnOoTO8hdJwA2Nm1kW/M2gokgnnhbRsQ+r/Z5TiZDJBKNqJqnw07UTF0nPFr3mRXnmArARCso7NeY7fIritM6Tx3eO83Zoa2YK13nTIeKidY0orcYM5jKWGWh64TNLizcHAvhonddJ9q3jEvsDBFd14hW4MLn9BFKhAgmglnfRGHGYihOR7/bunVmt2QbjFp26ZIn3azDrN/cSsOOIOMOLsGXn6Up0aOPtr4kn3OOFeTFYvC1r8Hnn1vF3feDLhOZSGAnxCDJ2HVi2TK49NK2HbBHHcWG/3uAetVD9RCXzxgKmTJ269evJxqNcuihh1JQUEBBwWy83rF4PF2XnuhtLTv1ww9JhA0cJcUU57lx97HXpL1DNxm3PhA6F5b2aWq6ndjWnVbmbCgydhubN/Jp46eUxEvIj+djmiaKolBaWorf7yc/36q519r6EY2N/yYvbxqlpSel728HdjEtDgkra9XT9LF35ky8M2cCVluxhG7i7UOAZa+ZVB3Wh32mXr8bwzFadZ1xznZtxcbPS99ubLfOcTYzdiXeEiYWTGRdq4ZBW7apM9M001OxzvbPryoYMR0lquMrsgK7wahl5xwzxmon1sPGgG41b4OmrRAoQ3VZv19mNx0i+suXrmXXTfcJbyp4jwzg9WRSWgrPPw9XXGF1rwD40Y9gwwb4wx/A4cA0TZqffAoj2ErhV7+atWB5XzWy5n2E2Id06Dphmlbfw4svbgvqvvY1eOklmkpKgbZs00jSubSJaZp7ZfG83nEUFByKq3Ots3bsKdFEpPvNE/oH76PU1GDGE3svyu8Fux2XHu34vAAkYx12GHboITrIQomQtStWdWIYBolU79CysjKqq6vTgZ29A7VzkWLPtBLyvlhJpMQ6J3bWqjfW1bXy2xfX848Pul6cnomdgVU0HRNj72zr7vU8//l7vLB9B6HUKUzGdYx275uZmtrLZteJykAlCyYsoNhhFb/1d/HYpgkVkwoYVZXXIbDr0H3CMbjdJxRFQXH2LevcQcMmq63Y7s8HtftEoFf9YvtZ8qQ3XC64915rI4Vt+XKrFl40iqIo6E1N6M0t6PtByZOR90kixD7ANIx0dsnldsN//Rf84AdtB1x1FTzwALjdtKY+yOwm9iOJ0+kkEAikN0skEgkMI7U2rQ/9L+3MWXdTsfYuQreeZFswwRs1jX0ukVFQcAjFxcdixPwdnheA+k9oevV37F77JHHDoKjCR8XkwoHv9OuFcDKMoih43anz0MWaOi1dy65jAGy3EwthXd/T+jqbaRh4+7krVtP8oCioDhVIdFxjB1C3Fn/D5xBrIapau4sxDRItLVZbMRiUNXa2YOqxu1pjp6oKY6cUM3F2KWq7L10duk84B7/7xIC4Uu9zPDio3Sfsc9hdh5Ie24oNlKJYmykee8wK9ACeesraQRsM7le17PaJwO7OO++kuroaj8fD3LlzefPNN7s9/rHHHmPKlCl4PB5mzJjBM888M0QjFaJ3TNNk/MxDGDP5IJz//X1rB5ft5puty6lpwuOL87i8qoxDCwav0GmuVFdXc/jhhzNmjDUN1H5qVlVVDCNGKLSBWGxnt49jT2d3NxVr7yJ0JZLsCOms2drY592qHs8YfO4D0dRCFFXF4Wq3YSAe5A2KWZYo5a3mMEXlfqqmFg9JYGcHDn6v9eFkn0fDMAgGgzQ3NwOgad13nyj2FnNwycFU5fVcADvZ2Mjuu+5CeeJRoO9txRRFRdO8OBxOXD7HXusV29qKWd0nXB4HRFuIv/ZHeOuP1us9pMxqJ1aU3XOs6wZFfij2O/q8c7p99wm/ab2mwQjsQq+9RvPf/k5827b+P4g71X0i1goO1Qqeyf4GCrusUCSud/llys7YJQYjY9feWWdZhYvtHe0rV8JJJ6GmxmWEus/6jwQ5X2P3yCOPsHTpUu6++27mzp3Lbbfdxsknn8y6desoKyvb6/jXXnuN8847j5/97Gd85Stf4cEHH2TRokW88847TJ8+PQevQIi9qZpG5YFT4Mor4c5UqzBFsaYLLr6447GKQt4IXF+XSeep2Xi8gZ07/47Dkce4cRd3eT9PII9Jc+bi6qbUiZEqPpqn6xQqGsV93Dhhc3l9zD3jHPRksmNgGA+lu04EHEP3nThhJIjr1nnL9+XTEm9JT8VGIhHWrFmDpmkcc8wxOOy2YnoEw0igqk7MhEHko92oASdjJo2hMlDZq+dVfT6rrZiRRNGTxHEQS+q4+/Czqml+XN4wB88/Bp9vQscb2xUpDiZ1ir0OYskosbhGXiogyWY7sfb+/On/EXKGOHf6uXi6ePx4NImhm7g8WseMXar7hBnTmeibQHnxGApcBVkfY7xmK8ldu/AcPK3/D5IuUmx1n9CKPahOFbrpEtEfeW4HlxwzAb/L0eWXKXsDSiKWTK8RHTQnngj//Ceceio0NcHrrxPY8yMaL16yX2Tsch7Y3XrrrVx66aVcdNFFANx999384x//4L777uPaa6/d6/jbb7+dBQsW8L3vfQ+Am266iRUrVnDHHXdw9913D+nYu9TUBKk/vGI/petwww3w+99blxUF/vQnOP/83I4rx/bqOtGL4sQADqeT0RMnd3tMcs8eAGYbBg2mgwm+vmV5kskQkcgWXK4S3O7RODqvbYq10oATNCcBRaW1IYrLo+H2DWANVC+EE1aGwaE6OPiggzsUJvZ6vaiqiq7rRKNRvF4vmuZJ1ZBrwO0ejR6Kk9gVQW1N4Jnc+/plVvcJB1oiiTcZJ6w5CMX6FtgV5M/CMOI4nRme11NgtRWLhwnpBgdPLqBci+BvjoGvdz1A+yvgDBBKhNgT3UOJtyTjMTs3tVC7vomy6nyqZ3Qcj+LWIKYTwE9RIPtjNU0TvakJAK1oADXn7LZi8RAYBv5D9k6WZIOqKj3uQLfXKRq6STJhWF1GBtNRR1k7Zb/0JaivR/v8cwruuIPY2LEwcUKPd++X0tLBedw+Usxs9Wnph3g8js/n4/HHH2fRokXp6xcvXkxTUxNPP/30XvcZN24cS5cu5eqrr05fd8MNN/DUU0+xdu3avY6PxWLpDxOAlpYWqqqqaG5uTi84zrpTToHnnhucxxbDj6rCn/7EdcFNxNyd//gp7HHnU91Sx//71g24UtOzf/7ZEhyuzFNfpqFw3veWpy//+X8vweHO/EXCNOG8a/6Uvvx/P70Up6frOlILLvo1hamWPf/3k2/h9Ma6PPaQk67ioJmHAnD/Ty7D5d17mjSpgmbChNlnceTxp7F161Ze+eNN5Gccg/UNPm/KqRy7yCrU/PCPv0PA3fU37LB7MgcfeiQAn/7tIbzFSZKaSsKhsttdwCZ/W3/ZpDqKyvFWcLjl8/eYHtvIqFQx3N2uPNbnlaM4Y5i6h7g+lqpqa7py82ebmbw7zqhIDF1VaHK72RrwoxhOUEzUwjCl46sB2LlxPdW766iIWmNucrr5pLDtj73i9VJWbZX5qN+8kapdtVRGrExjq8PFh0XtPnjdbkZPnExYj7Kldj1TdjZxym7ru/geh8azpdYHvq4aBDUFpSAPBQU1UcvsPUHmNiUh4aHZCX+ryMPAtDYxuAz0PCtjqsSSTNsZYV6z9XMXUk2eKm/LihrhMIaSpAkvhqkyPRzjpNSO4ahi8mhh27ExM0k49VmtGiZTIglOiqam/oAHJ4ax280m0EmgY2Cio1EVhtPq8nApMTQS/H6CDyOV0UmYSZKkfhdMcIdizN1zIE7V+nKwquIz9PYxQrtEkDMSZ+7OybhTpV1eLl9HwqFgoINidjjYGYvz1ehM8lNZruWON4nbmdlOySVnPMml8amMLQugegxurH2HaPtApd3xWlJniaOcicXWcoQf73ibSPvp33bHqobJ+UYRU0eNI7F9OzcrtYR8Xa9FvWjakcw98mQAvve762nNsJHHkeob/OXSSk45/TIAfnLHj2nwd12XcK7Lx7nf+E8A/ve3P2Z3NzUMZxgaFy2xEi033/Fj6rt53HFNCZYs/h7+Qje//O3/sDO/62PHNoZYuvQmAG75zf+wPa/r81C+u4X//t7/AvDr3/6ErYG281u2o57/+OW95De3dnn/rFCU9NrQwdDS0kJBQUGvYpecZux2796NruuMHt2xf9zo0aP59NNPM96nrq4u4/F1dZnbwvzsZz/jxz/+cXYGLEQfmaqKcv/98I1vEPzzrwh59v7jpJGgtrAIrd3UhNMbx5EhUIK24rk2hyeB05953YhpdPxEcroTOAO9W2Oiubo/NhxsaxHlcCQzHusEVFMhkpomraysxK3peAJdB5fRUEvb4ypxPIGug8s9u5torrd+93W/iis/jkNVcCmwx51HU6At8AhFNOIhawF/k8eHoup4Neuy4vLR5AsAAUw9QGtcJxkMg6Kwx+nhQNwEdCfoEHW6aPKmpt6UJHEiBFOP26o4qNR8aKYViBiqlz3ewvQYkiQI2ceiUubwo5lWUG4q7g7H6maccOpYUy/EB/jM1PjRqEstBjcxiSgG8dR77VAKmYyGL279/IQMqPXkp4+NazESphVPqJqTKoeCK269dzENdnraphWTDjeGESduODBNlbDuwJV6L3XFpN7fNt6EkSCaei0KCq16AldLa+o2k/pAWwFqA51kKuAwUQiSxBU3URUXJi4aA270VExlmi6SZtuXnDwMwuvCOBXrutYDPCS7mBr3qxBqDKGnnqt1soe4U8MKNTvyOKI0bg1hpn69wgd6iLozBxPueIzY9g3ou4rQgXC+h7A3c5DiTCZo3VJHImR96EcCboL+zG0DVcOgeWM9iZg1iIjXQzDQ9fKD5pam9P+HXQ6CgUyZb+u1NgbbNq+E3U6a8rp+3Nbdbb+DYaej22NDO/ak/z+iqd0eW75rW3pNaszR/bGjdrYV4o6qdHtsSV3bGKKm0eHYpoOqufnHV/LfP76DwsaWTHcfcXI+FTvYrrvuOpa268VpZ+wG1dy5bK/bTjjW9UJvj8tF1Tjrm3vt9hqC3ZRxcDudjBs/CYCdddtpCXb9zcOlORg/wcpK7Kqvo6ndL35nTk2jeoK15X/37p00tu/l2IlDVZkw8UAAmhr3sGvPrm6OVZgw8SAAWlubqdvZdZkETVGYOMk6NhqNsHXbli6PVRWYNGlK+vLn6zMH/xmP3fBppr/lgPVFa3JvjwUmT247dv2GT7vsrx33uJj26zvh2GMBGF/fTKKLg/MSsQ6BXSRcitnaRUDTaW1KLFZCJNRF14bOxyZGEanv3Y7IpFlKrL6bP6bl49L/rzvKaKnPPPWpmXDICbMAUFWVZGAM9Y0NHQ8yHNipi8O+MDt9tVoykfrdbV/aTNOg/Zsz+bB5HDDzEAC2b99MXeMukm4XqqKgRh1MDrU9z5hJVYw/wPo9+uD1Gmj202BaY1YiTiaHGwAFPRpn9MRxHHCQ9Xv0Uevb4N5Jq9vAVN14iTAjbH1AqFqCsqpJVEy0HnerEYPQblSP9X7kKyqHRNp+V0rGTWDsgdaxO7QkyeBu1FHWsX5F6XBs8ZgqqlLHNrhdOFtC7K6ygockJkeHm1PnxMQoKSCv0vrCG2ncTWFjA7urCgErk3ZkqA5dtQILrcCPv9Q6NhGKUNwSI3mwNTWlGkmOju1Mn2PF78Xt8ZDUdZpb4pRpkfSxGDqH79qS/vk3PC6UQuu1mIkEo0Lh9LGmaTJ7+3vpUjGGQwO/G0ydRDJOoMVEnzYbQ1UxVC8H7vgA3bACt4Sqo6V68ZqYKGGTKV+agdNhZb9r1j9PXE8FlKraYYrPjCSZdvx0XC7rfd66/gViqfWKuqqjOdS2jFlcZ+YJM/B6rJ/5ie+sI6wHreVoCijtdq2rySTjTjidvDwruz1hxYOEGtv9XW5XP1HVdSYffzp5hdaU7cR/PkRL8+6Mx2IYTD1+AXlFFaDA5NVP0FDX6XelnQMPPzX9/wdoPnZnOFYxDDQSTD/hzPR1kxQn+dvqu3zcGUcc23as002gm2Onzzos/f8TPAE8W7s+dsrU2en/r/YW4Kjp+tgDJrT9na0uKEWp2d7lsePHTWob76gxmDWbOx2h8MAV53PkS/+mLBylKnV87bYagtGuP3tdTifj7c/e2m20hDJvSnKoChPafYbk2oifiu2sL+lMIYQQQohc60vsktNyJy6Xizlz5rBy5cr0dYZhsHLlSo7K0MgX4KijjupwPMCKFSu6PF4IIYQQYn+R86nYpUuXsnjxYg477DCOOOIIbrvtNkKhUHqX7AUXXEBlZSU/+9nPALjqqqs49thjueWWW/jyl7/Mww8/zFtvvcXv7d2HQgghhBD7qZwHdueeey67du3i+uuvp66ujtmzZ/Pcc8+lN0jU1NSgtluDMG/ePB588EF++MMf8oMf/IADDjiAp556SmrYCSGEEGK/l9M1drkga+yEEEIIMZwMmzV2QgghhBAieySwE0IIIYQYISSwE0IIIYQYIXK+eWKo2UsKW1r2jwrUQgghhBje7JilN9si9rvArrXVqg4+6N0nhBBCCCGyqLW1lYKCgm6P2e92xRqGwY4dO8jLy0Pp1G4pm+zWZVu3bpXdt1kg5zP75Jxmn5zT7JLzmX1yTrNvKM6paZq0trYyZsyYDiXgMtnvMnaqqjJ27Nghe778/Hz55ckiOZ/ZJ+c0++ScZpecz+yTc5p9g31Oe8rU2WTzhBBCCCHECCGBnRBCCCHECCGB3SBxu93ccMMNuN3uXA9lRJDzmX1yTrNPzml2yfnMPjmn2bevndP9bvOEEEIIIcRIJRk7IYQQQogRQgI7IYQQQogRQgI7IYQQQogRQgI7IYQQQogRQgI7IYQQQogRQgI7IYQQQogRQgI7IYQQQogRQgI7IYQQQogRQgI7IYQQQogRQgI7IYQQQogRQgI7IYQQQogRQgI7IYQQQogRwpHrAQw1wzDYsWMHeXl5KIqS6+EIIYQQQnTLNE1aW1sZM2YMqtp9Tm6/C+x27NhBVVVVrochhBBCCNEnW7duZezYsd0es98Fdnl5eYB1cvLz83M8GiGEEEKI7rW0tFBVVZWOYbqz3wV29vRrfn6+BHZCCCGEGDZ6s4RMNk8IIYQQQowQEtgJIYQQQowQEtgJIYQQQowQ+90aOyGEGAluvHFkPpfonq7rJBKJXA9DZJnT6UTTtKw8lgR2QgghxD7ONE3q6upoamrK9VDEICksLKS8vHzANXYlsBNCCCH2cXZQV1ZWhs/nkwL7I4hpmoTDYerr6wGoqKgY0ONJYCeEEELsw3RdTwd1JSUluR6OGARerxeA+vp6ysrKBjQtK5snhBBCiH2YvabO5/PleCRiMNnv70DXUEpgJ4QQQgwDMv06smXr/ZXATgghhBBihJDATgghhBA5s3z5cgoLC3M9jBFDNk8IIYQQw9BQ1xfsz/NdeOGFNDU18dRTT3W4ftWqVcyfP5/GxkbOPfdcTj311F493vLly7n66qul7Es3JLATQgghRM54vd70rtB9STwex+Vy5XoYfSZTsUIIIYTImc5TsWvXrmX+/Pnk5eWRn5/PnDlzeOutt1i1ahUXXXQRzc3NKIqCoijcmEojNjY2csEFF1BUVITP5+OUU07h888/7/A8f/jDH6iqqsLn83HGGWdw6623dnjeG2+8kdmzZ3PvvfcyYcIEPB4PAM899xxf+MIXKCwspKSkhK985Sts2LAhfb/NmzejKAqPPvooxxxzDF6vl8MPP5zPPvuMNWvWcNhhhxEIBDjllFPYtWvXoJ1HmwR2QgghhNhnfOMb32Ds2LGsWbOGt99+m2uvvRan08m8efO47bbbyM/Pp7a2ltraWq655hrAmvJ96623+Otf/8q///1vTNPk1FNPTZcOefXVV7n88su56qqreO+99zjppJP46U9/utdzr1+/nr/85S888cQTvPfeewCEQiGWLl3KW2+9xcqVK1FVlTPOOAPDMDrc94YbbuCHP/wh77zzDg6Hg69//ev893//N7fffjuvvPIK69ev5/rrrx/ck4dMxQohhBBiEP39738nEAh0uE7X9S6Pr6mp4Xvf+x5TpkwB4IADDkjfVlBQgKIolJeXp6/7/PPP+etf/8qrr77KvHnzAHjggQeoqqriqaee4uyzz+a3v/0tp5xySjoQPPDAA3nttdf4+9//3uG54/E4999/P6WlpenrvvrVr3Y45r777qO0tJSPP/6Y6dOnp6+/5pprOPnkkwG46qqrOO+881i5ciVHH300AEuWLGH58uXdn6wskIydEEIIIQbN/Pnzee+99zr8u/fee7s8funSpVxyySWceOKJ3HzzzR2mPTP55JNPcDgczJ07N31dSUkJBx10EJ988gkA69at44gjjuhwv86XAcaPH98hqAMrcDzvvPOYOHEi+fn5VFdXA1YA2t7MmTPT/z969GgAZsyY0eE6u23YYJLATgghhBCDxu/3M3ny5A7/Kisruzz+xhtv5KOPPuLLX/4yL774ItOmTePJJ58csrF2dtppp9HQ0MAf/vAH3njjDd544w3Ayu6153Q60/9vFxvufF3n6dvBIIGdEEIIIfYpBx54IN/97nd54YUXOPPMM1m2bBkALpdrr2ncqVOnkkwm0wEXwJ49e1i3bh3Tpk0D4KCDDmLNmjUd7tf5cib24/zwhz/khBNOYOrUqTQ2Ng705Q0qCeyEEEIIsU+IRCJ85zvfYdWqVWzZsoVXX32VNWvWMHXqVACqq6sJBoOsXLmS3bt3Ew6HOeCAA1i4cCGXXnop//rXv1i7di3f/OY3qaysZOHChQBceeWVPPPMM9x66618/vnn3HPPPTz77LM9tvEqKiqipKSE3//+96xfv54XX3yRpUuXDvp5GAgJ7IQQQgixT9A0jT179nDBBRdw4IEHcs4553DKKafw4x//GIB58+Zx+eWXc+6551JaWsovfvELAJYtW8acOXP4yle+wlFHHYVpmjzzzDPpqdCjjz6au+++m1tvvZVZs2bx3HPP8d3vfjdd0qQrqqry8MMP8/bbbzN9+nS++93v8stf/nJwT8IAKaZpmrkexFBqaWmhoKCA5uZm8vPzcz0cIYTol6HsOjDUHQ5ER9FolE2bNnWorSYG7tJLL+XTTz/llVdeyfVQgO7f577ELlLuRAghhBAj3q9+9StOOukk/H4/zz77LH/605/43e9+l+thZZ0EdkIIIYQY8d58801+8Ytf0NraysSJE/nNb37DJZdckuthZZ0EdkIIIYQY8R599NFcD2FIyOYJIYQQQogRQgI7IYQQYhjYz/Y67ney9f5KYCeEEELsw+ySHeFwOMcjEYPJfn/bd6voD1ljJ4QQQuzDNE2jsLAw3WfU5/P1WFhXDB+maRIOh6mvr6ewsBBN0wb0eBLYCSGEEPu48vJygCFpIi9yo7CwMP0+D4QEdkIIIcQ+TlEUKioqKCsrI5FI5Ho4IsucTueAM3U2CeyEEEKIYULTtKwFAGJkks0TQgghhBAjhAR2QgghhBAjxLAM7DZu3JjrIQghhBBC7HOGZWA3efJk5s+fz5///Gei0WiuhyOEEEIIsU8YloHdO++8w8yZM1m6dCnl5eVcdtllvPnmm7kelhBCCCFETg3LwG727Nncfvvt7Nixg/vuu4/a2lq+8IUvMH36dG699VZ27dqV6yEKIYQQQgy5YRnY2RwOB2eeeSaPPfYYP//5z1m/fj3XXHMNVVVVXHDBBdTW1uZ6iEIIIYQQQ2ZYB3ZvvfUW//Ef/0FFRQW33nor11xzDRs2bGDFihXs2LGDhQsX5nqIQgghhBBDZlgWKL711ltZtmwZ69at49RTT+X+++/n1FNPRVWtOHXChAksX76c6urq3A5UCCGEEGIIDcvA7q677uLiiy/mwgsvpKKiIuMxZWVl/PGPfxzikQkhhBBC5M6wDOxWrFjBuHHj0hk6m2mabN26lXHjxuFyuVi8eHGORiiEEEIIMfSG5Rq7SZMmsXv37r2ub2hoYMKECTkYkRBCCCFE7g3LwM40zYzXB4NBPB7PEI9GCCGEEGLfMKymYpcuXQqAoihcf/31+Hy+9G26rvPGG28we/bsHI1OCCGEECK3hlVg9+677wJWxu6DDz7A5XKlb3O5XMyaNYtrrrkmV8MTQgghhMipYRXYvfTSSwBcdNFF3H777eTn5+d4REIIIYQQ+45hFdjZli1blushCCGEEELsc4ZNYHfmmWeyfPly8vPzOfPMM7s99oknnhiiUQkh9mU33jiyn08IITobNoFdQUEBiqKk/18IIYQQQnQ0bAK79tOvMhUrhBBCCLG3YVnHLhKJEA6H05e3bNnCbbfdxgsvvJDDUQkhhBBC5NawDOwWLlzI/fffD0BTUxNHHHEEt9xyCwsXLuSuu+7K8eiEEEIIIXJjWAZ277zzDscccwwAjz/+OOXl5WzZsoX777+f3/zmNzkenRBCCCFEbgzLwC4cDpOXlwfACy+8wJlnnomqqhx55JFs2bIlx6MTQgghhMiNYRnYTZ48maeeeoqtW7fy/PPP86UvfQmA+vp6KVoshBBCiP3WsAzsrr/+eq655hqqq6uZO3cuRx11FGBl7w455JAcj04IIYQQIjeGTbmT9s466yy+8IUvUFtby6xZs9LXn3DCCZxxxhk5HJkQQgghRO4My8AOoLy8nPLy8g7XHXHEETkajRBCCCFE7g3LwC4UCnHzzTezcuVK6uvrMQyjw+0bN27M0ciEEEIIIXJnWAZ2l1xyCatXr+b888+noqIi3WpMCCGEEGJ/NiwDu2effZZ//OMfHH300bkeihBCCCHEPmNY7ootKiqiuLg418MQQgghhNinDMvA7qabbuL666/v0C9WCCGEEGJ/NyynYm+55RY2bNjA6NGjqa6uxul0drj9nXfeydHIhBBCCCFyZ1gGdosWLcr1EIQQQggh9jnDMrC74YYbcj0EIYQQQoh9zrBcYwfQ1NTEvffey3XXXUdDQwNgTcFu3749xyMTQgghhMiNYZmxe//99znxxBMpKChg8+bNXHrppRQXF/PEE09QU1PD/fffn+shCiGEEEIMuWGZsVu6dCkXXnghn3/+OR6PJ339qaeeyssvv5zDkQkhhBBC5M6wDOzWrFnDZZddttf1lZWV1NXV5WBEQgghhBC5NyynYt1uNy0tLXtd/9lnn1FaWpqDEQkxvN1448h8rqE2Ul/bSP75kPdMjDTDMmN3+umn8z//8z8kEgkAFEWhpqaG73//+3z1q1/N8eiEEEIIIXJjWAZ2t9xyC8FgkNLSUiKRCMceeyyTJ08mLy+Pn/70p7kenhBCCCFETgzLqdiCggJWrFjBq6++ytq1awkGgxx66KGceOKJuR6aEEIIIUTODLvAzjAMli9fzhNPPMHmzZtRFIUJEyZQXl6OaZooipLrIQohhBBC5MSwmoo1TZPTTz+dSy65hO3btzNjxgwOPvhgtmzZwoUXXsgZZ5yR6yEKIYQQQuTMsMrYLV++nJdffpmVK1cyf/78Dre9+OKLLFq0iPvvv58LLrggRyMUQgghhMidYZWxe+ihh/jBD36wV1AHcPzxx3PttdfywAMP5GBkQgghhBC5N6wCu/fff58FCxZ0efspp5zC2rVrh3BEQgghhBD7jmEV2DU0NDB69Ogubx89ejSNjY1DOCIhhBBCiH3HsArsdF3H4eh6WaCmaSSTySEckRBCCCHEvmNYbZ4wTZMLL7wQt9ud8fZYLDbEIxJCCCGE2HcMq8Bu8eLFPR4jO2KFEEIIsb8aVoHdsmXLcj0EIYQQQoh91rBaYyeEEEIIIbomgZ0QQgghxAghgZ0QQgghxAghgZ0QQgghxAghgZ0QQgghxAghgZ0QQgghxAghgZ0QQgghxAghgZ0QQgghxAghgZ0QQgghxAghgZ0QQgghxAgxrFqKCSGEGNluvDHXIxgZhvI8ynu2b5GMnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECCGBnRBCCCHECOHI9QCEELmjGzqv1LzCB9SSRwXjOAYVba/jDHRqeIXWHo4bjjK9NqDDdWOZxzZey8rrt5+vhe2E2YWPUvKp7PVj9nT/JHHe4nc0sIEiJlDGDMLsHvT3baA/IwM9L0Op/Wv1UwZAiPqsn+PenNNc/m7az/3QB7VU5FVwzLhj0NR9673aH0lgJ8R+6olPnuCq565iW8s2UKzr8s2xLOB2pnJm+rhPeILnuIoWZVv6ukzHDUeZXpvXLAEgouxJX6eYGqaipy/39/Vner6+PGZP969gDp/x9w5j7etz9MdAf0YGel6GUndjheyNtzfnNJe/m+2f+09PWNeNzR/L7Qtu58yp+8Z7tb9STNM0cz2IodTS0kJBQQHNzc3k5+fnejhC5MQTnzzBWY+ehUmnX3/TivDO4XGmciaf8ASPchZgpoO/TMf1xY039n/cfdXdc3X92lL/7XzdAF9/l8/X4XmVLh+zd/fPMPYOx/T/fevKQH9GBnpehlKPY4WsnOPenFMg67+bAx2fkrrw+DmPS3CXZX2JXWSNnRD7Gd3Queq5q/YO6gAU67rnuJokcZ7jKjJ+iLU7ziBzdmhfZqB389rIfF2Hy317/d0+X4fnMDM+Zu/vn2GsAxh3T7o/jz0/10DPy1Dq1VhhwOe4N+f0Wa7i2Rz9bnY3PvtvytXPXY1uDL+/CyPFfjcVaycoW1pacjwSIXLjlS2vsK0+8zSSxaSFrbzOrbTQ83HreY7xqXVpvTGUv3qxWObrt/BKD6+tN3r/+vvyfJkeMzvjtfXvfcuk53F1/1wDPS9DqW/vQf/PcW/OaWuP48jee9xZT+MzMdka3cpzHz3HMeNz816NRHbM0ptJ1v1uKnbbtm1UVVXlehhCCCGEEH2ydetWxo4d2+0x+11gZxgGO3bsIC8vD0XpLp8+MC0tLVRVVbF161ZZy5cFcj6zT85p9sk5zS45n9kn5zT7huKcmqZJa2srY8aMQVW7X0W3303FqqraY7SbTfn5+fLLk0VyPrNPzmn2yTnNLjmf2SfnNPsG+5wWFBT06jjZPCGEEEIIMUJIYCeEEEIIMUJIYDdI3G43N9xwA263O9dDGRHkfGafnNPsk3OaXXI+s0/Oafbta+d0v9s8IYQQQggxUknGTgghhBBihJDATgghhBBihJDATgghhBBihJDAbgicfvrpjBs3Do/HQ0VFBeeffz47duzI9bCGrc2bN7NkyRImTJiA1+tl0qRJ3HDDDcTj8VwPbdj66U9/yrx58/D5fBQWFuZ6OMPSnXfeSXV1NR6Ph7lz5/Lmm2/mekjD1ssvv8xpp53GmDFjUBSFp556KtdDGvZ+9rOfcfjhh5OXl0dZWRmLFi1i3bp1uR7WsHXXXXcxc+bMdO26o446imeffTbXwwIksBsS8+fP59FHH2XdunX85S9/YcOGDZx11lm5Htaw9emnn2IYBvfccw8fffQRv/71r7n77rv5wQ9+kOuhDVvxeJyzzz6bK664ItdDGZYeeeQRli5dyg033MA777zDrFmzOPnkk6mvr8/10IalUCjErFmzuPPOO3M9lBFj9erVfPvb3+b1119nxYoVJBIJvvSlLxEKhXI9tGFp7Nix3Hzzzbz99tu89dZbHH/88SxcuJCPPvoo10OTXbG58Ne//pVFixYRi8VwOp25Hs6I8Mtf/pK77rqLjRs35noow9ry5cu5+uqraWpqyvVQhpW5c+dy+OGHc8cddwBW68KqqiquvPJKrr322hyPbnhTFIUnn3ySRYsW5XooI8quXbsoKytj9erVfPGLX8z1cEaE4uJifvnLX7JkyZKcjkMydkOsoaGBBx54gHnz5klQl0XNzc0UFxfnehhiPxSPx3n77bc58cQT09epqsqJJ57Iv//97xyOTIiuNTc3A8jfzSzQdZ2HH36YUCjEUUcdlevhSGA3VL7//e/j9/spKSmhpqaGp59+OtdDGjHWr1/Pb3/7Wy677LJcD0Xsh3bv3o2u64wePbrD9aNHj6auri5HoxKia4ZhcPXVV3P00Uczffr0XA9n2Prggw8IBAK43W4uv/xynnzySaZNm5brYUlg11/XXnstiqJ0++/TTz9NH/+9732Pd999lxdeeAFN07jggguQWfCO+npOAbZv386CBQs4++yzufTSS3M08n1Tf86nEGLk+/a3v82HH37Iww8/nOuhDGsHHXQQ7733Hm+88QZXXHEFixcv5uOPP871sGSNXX/t2rWLPXv2dHvMxIkTcblce12/bds2qqqqeO211/aJtO2+oq/ndMeOHRx33HEceeSRLF++HFWV7ynt9ednVNbY9V08Hsfn8/H44493WAe2ePFimpqaJDs/QLLGLru+853v8PTTT/Pyyy8zYcKEXA9nRDnxxBOZNGkS99xzT07H4cjpsw9jpaWllJaW9uu+hmEAEIvFsjmkYa8v53T79u3Mnz+fOXPmsGzZMgnqMhjIz6joPZfLxZw5c1i5cmU6+DAMg5UrV/Kd73wnt4MTIsU0Ta688kqefPJJVq1aJUHdIDAMY5/4XJfAbpC98cYbrFmzhi984QsUFRWxYcMGfvSjHzFp0iTJ1vXT9u3bOe644xg/fjy/+tWv2LVrV/q28vLyHI5s+KqpqaGhoYGamhp0Xee9994DYPLkyQQCgdwObhhYunQpixcv5rDDDuOII47gtttuIxQKcdFFF+V6aMNSMBhk/fr16cubNm3ivffeo7i4mHHjxuVwZMPXt7/9bR588EGefvpp8vLy0us/CwoK8Hq9OR7d8HPddddxyimnMG7cOFpbW3nwwQdZtWoVzz//fK6HBqYYVO+//745f/58s7i42HS73WZ1dbV5+eWXm9u2bcv10IatZcuWmUDGf6J/Fi9enPF8vvTSS7ke2rDx29/+1hw3bpzpcrnMI444wnz99ddzPaRh66WXXsr487h48eJcD23Y6upv5rJly3I9tGHp4osvNsePH2+6XC6ztLTUPOGEE8wXXngh18MyTdM0ZY2dEEIIIcQIIQuThBBCCCFGCAnshBBCCCFGCAnshBBCCCFGCAnshBBCCCFGCAnshBBCCCFGCAnshBBCCCFGCAnshBBCCCFGCAnshBBCCCFGCAnshBAiC4477jiuvvrqXA9DCLGfk8BOCLHfO+2001iwYEHG21555RUUReH9998f4lEJIUTfSWAnhNjvLVmyhBUrVrBt27a9blu2bBmHHXYYM2fOzMHIhBCibySwE0Ls977yla9QWlrK8uXLO1wfDAZ57LHHWLRoEeeddx6VlZX4fD5mzJjBQw891O1jKorCU0891eG6wsLCDs+xdetWzjnnHAoLCykuLmbhwoVs3rw5Oy9KCLFfksBOCLHfczgcXHDBBSxfvhzTNNPXP/bYY+i6zje/+U3mzJnDP/7xDz788EO+9a1vcf755/Pmm2/2+zkTiQQnn3wyeXl5vPLKK7z66qsEAgEWLFhAPB7PxssSQuyHJLATQgjg4osvZsOGDaxevTp93bJly/jqV7/K+PHjueaaa5g9ezYTJ07kyiuvZMGCBTz66KP9fr5HHnkEwzC49957mTFjBlOnTmXZsmXU1NSwatWqLLwiIcT+SAI7IYQApkyZwrx587jvvvsAWL9+Pa+88gpLlixB13VuuukmZsyYQXFxMYFAgOeff56ampp+P9/atWtZv349eXl5BAIBAoEAxcXFRKNRNmzYkK2XJYTYzzhyPQAhhNhXLFmyhCuvvJI777yTZcuWMWnSJI499lh+/vOfc/vtt3PbbbcxY8YM/H4/V199dbdTpoqidJjWBWv61RYMBpkzZw4PPPDAXvctLS3N3osSQuxXJLATQoiUc845h6uuuooHH3yQ+++/nyuuuAJFUXj11VdZuHAh3/zmNwEwDIPPPvuMadOmdflYpaWl1NbWpi9//vnnhMPh9OVDDz2URx55hLKyMvLz8wfvRQkh9isyFSuEECmBQIBzzz2X6667jtraWi688EIADjjgAFasWMFrr73GJ598wmWXXcbOnTu7fazjjz+eO+64g3fffZe33nqLyy+/HKfTmb79G9/4BqNGjWLhwoW88sorbNq0iVWrVvGf//mfGcuuCCFEb0hgJ4QQ7SxZsoTGxkZOPvlkxowZA8APf/hDDj30UE4++WSOO+44ysvLWbRoUbePc8stt1BVVcUxxxzD17/+da655hp8Pl/6dp/Px8svv8y4ceM488wzmTp1KkuWLCEajUoGTwjRb4rZeRGIEEIIIYQYliRjJ4QQQggxQkhgJ4QQQggxQkhgJ4QQQggxQkhgJ4QQQggxQkhgJ4QQQggxQkhgJ4QQQggxQkhgJ4QQQggxQkhgJ4QQQggxQkhgJ4QQQggxQkhgJ4QQQggxQkhgJ4QQQggxQkhgJ4QQQggxQvx/1ueYvNq4QY4AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Generate fewer random data points\n",
    "np.random.seed(0)\n",
    "data = np.random.normal(0, 1, 20)\n",
    "\n",
    "# Create a range of x values for plotting\n",
    "x = np.linspace(-3, 3, 1000)\n",
    "\n",
    "# Bandwidth for the Epanechnikov kernel\n",
    "bandwidth = 0.5\n",
    "\n",
    "# Initialize arrays to store the kernel contributions and the kernel density estimate\n",
    "kernel_contributions = np.zeros_like(x)\n",
    "kernel_density_estimate = np.zeros_like(x)\n",
    "\n",
    "# Create subplots with separate y-axes\n",
    "fig, (ax1, ax2) = plt.subplots(2, 1, gridspec_kw={'height_ratios': [2, 1]}, sharex=True)\n",
    "\n",
    "# Plot individual kernels centered at data points\n",
    "for xi in data:\n",
    "    # Calculate the Epanechnikov kernel at xi\n",
    "    kernel_values = (1 / (2 * bandwidth)) * (1 - ((x - xi) / bandwidth) ** 2) * (np.abs(x - xi) <= bandwidth)\n",
    "    \n",
    "    # Add the kernel contribution to the array\n",
    "    kernel_contributions += kernel_values\n",
    "    \n",
    "    # Plot the individual kernel on the upper subplot\n",
    "    ax1.plot(x, kernel_values, linestyle='--', label=f'Kernel at Data Point {xi:.2f}', alpha=0.5)\n",
    "\n",
    "# Calculate the kernel density estimate\n",
    "kernel_density_estimate = kernel_contributions / (len(data) * bandwidth)\n",
    "\n",
    "# Plot the kernel density estimate on the upper subplot\n",
    "ax1.plot(x, kernel_density_estimate, color='red', linewidth=2, label='Kernel Density Estimate')\n",
    "\n",
    "# Add labels and a legend to the upper subplot\n",
    "ax1.set_ylabel('Kernel Density')\n",
    "ax1.set_title('Kernel Density Estimation (KDE)')\n",
    "#ax1.legend()\n",
    "\n",
    "# Plot the histogram of the data in the lower subplot\n",
    "hist_values, bins, _ = ax2.hist(data, bins=10, density=True, alpha=0.5, color='blue', label='Histogram')\n",
    "ax2.set_xlabel('Value')\n",
    "ax2.set_ylabel('Density')\n",
    "ax2.legend()\n",
    "\n",
    "# Create a subplot for data points (shared x-axis with the lower subplot)\n",
    "ax2.scatter(data, np.zeros_like(data), marker='o', color='green', label='Data Points')\n",
    "ax2.set_yticks([])\n",
    "\n",
    "# Adjust layout\n",
    "plt.tight_layout()\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confrontare campioni mediante istogrammi\n",
    "\n",
    "Gli istogrammi possono essere utili per comparare campioni. In grafico che segue confronta i pesi di uomini e donne nel nostro campione pesi-altezze:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "plt.hist(hw[hw['sex']=='F']['weight'], alpha=0.9)\n",
    "plt.hist(hw[hw['sex']=='M']['weight'], alpha=0.9)\n",
    "plt.legend(['F','M'])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Referenze\n",
    "\n",
    "* Capitolo 2 di: Heumann, Christian, and Michael Schomaker Shalabh. Introduction to statistics and data analysis. Springer International Publishing Switzerland, 2016."
   ]
  }
 ],
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