{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4af79f60-faed-4bfe-bf2d-2dea82f32b22",
   "metadata": {},
   "source": [
    "# Lesson 12: linear algebra & statistics fundamentals\n",
    "\n",
    "1. Linear algebra with NumPy\n",
    "    - 1.1. Vectors\n",
    "    - 1.2. Matrices\n",
    "2. Statistics fundamentals (descriptive stats)\n",
    "    - 2.1. Measures of central tendency\n",
    "    - 2.2. Measures of dispersion\n",
    "    - 2.3. Measures of shape\n",
    "    - 2.4. Statistical data types\n",
    "    - 2.5. Correlation and covariance"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21ca14e2-5013-44ea-b691-551a57a15355",
   "metadata": {},
   "source": [
    "## 1. Linear algebra with NumPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e65d4644-eadc-4271-87af-29e387f465dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91f668e6-fb1d-4cec-9979-722c1c25bb3c",
   "metadata": {},
   "source": [
    "### 1.1. Vectors\n",
    "\n",
    "Ordered list of numbers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "666626f5-fcf7-4a55-8dff-a10ee16a0910",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u: [1 4 5]\n",
      "v: [ 2 -3  6]\n"
     ]
    }
   ],
   "source": [
    "u = np.array([1, 4, 5])\n",
    "v = np.array([2, -3, 6])\n",
    "\n",
    "print(f'u: {u}')\n",
    "print(f'v: {v}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efd2d815-3283-4887-94e5-59c789e5916b",
   "metadata": {},
   "source": [
    "Element-wise addition:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d4f06b87-89de-446e-a783-bfb49ba0219e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u + v = [ 3  1 11]\n"
     ]
    }
   ],
   "source": [
    "print(f'u + v = {u + v}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fad40edb-1418-4b13-91fc-6ec8e5f5dad2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 + u = [4 7 8]\n"
     ]
    }
   ],
   "source": [
    "print(f'3 + u = {3 + u}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "880bea24-c57e-438f-b229-799dff1cd196",
   "metadata": {},
   "source": [
    "#### 1.1.1 Dot product\n",
    "\n",
    "Multiply corresponding elements and sum the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cdbd1d7f-e716-4f34-b225-6d35f56a66a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u: [1 4 5]\n",
      "v: [ 2 -3  6]\n",
      "\n",
      "u dot v: 20\n"
     ]
    }
   ],
   "source": [
    "dot = np.dot(u, v)\n",
    "\n",
    "print(f'u: {u}')\n",
    "print(f'v: {v}')\n",
    "print(f'\\nu dot v: {dot}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3216b16c-479f-4751-8794-bf29985879dd",
   "metadata": {},
   "source": [
    "| u | v | u x v   | product |\n",
    "|---|---|---------|---------|\n",
    "| 1 | 2 | 1 x 2   |    2    |\n",
    "| 4 | -3| 4 x (-3)|   -12   |\n",
    "| 5 | 6 | 5 x 6   |    30   |\n",
    "\n",
    "2 + (-12) + 30 = 20"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5acc38a4-4da1-4b33-9111-e9a5f3aa3432",
   "metadata": {},
   "source": [
    "#### 1.1.2. Euclidean norm (magnitude)\n",
    "\n",
    "'Length' of the vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "040f652b-f782-4dac-ad18-2a3fc10c9cc0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm of u: 6.48\n"
     ]
    }
   ],
   "source": [
    "norm_u = np.linalg.norm(u)\n",
    "print(f'Norm of u: {norm_u:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cb4808d-ad62-4186-8112-103cc3049a22",
   "metadata": {},
   "source": [
    "### 1.2. Matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2390a603-060f-4142-bab9-ebd2be1cdfee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A:\n",
      "[[4 7]\n",
      " [2 6]]\n",
      "\n",
      "B:\n",
      "[[5 8]\n",
      " [3 4]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[4, 7],\n",
    "              [2, 6]])\n",
    "\n",
    "B = np.array([[5, 8],\n",
    "              [3, 4]])\n",
    "\n",
    "print(\"A:\")\n",
    "print(A)\n",
    "\n",
    "print(\"\\nB:\")\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aabdb16b-8e7a-4f92-b4cb-202c05db9de4",
   "metadata": {},
   "source": [
    "#### 1.2.1. Addition & subtraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0dc44faa-ffec-4835-b98a-1e23321ac639",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A:\n",
      "[[4 7]\n",
      " [2 6]]\n",
      "\n",
      "B:\n",
      "[[5 8]\n",
      " [3 4]]\n",
      "\n",
      "Sum:\n",
      "[[ 9 15]\n",
      " [ 5 10]]\n"
     ]
    }
   ],
   "source": [
    "print(\"A:\")\n",
    "print(A)\n",
    "\n",
    "print(\"\\nB:\")\n",
    "print(B)\n",
    "\n",
    "print(\"\\nSum:\")\n",
    "print(np.add(A, B))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d26659de-884e-4ff7-b54b-27f6b8e28a8f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A:\n",
      "[[4 7]\n",
      " [2 6]]\n",
      "\n",
      "B:\n",
      "[[5 8]\n",
      " [3 4]]\n",
      "\n",
      "Difference:\n",
      "[[-1 -1]\n",
      " [-1  2]]\n"
     ]
    }
   ],
   "source": [
    "print(\"A:\")\n",
    "print(A)\n",
    "\n",
    "print(\"\\nB:\")\n",
    "print(B)\n",
    "\n",
    "print(\"\\nDifference:\")\n",
    "print(np.subtract(A, B))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77056604-8f34-4d81-b224-b9a4d8c4c409",
   "metadata": {},
   "source": [
    "#### 1.2.2. Scalar multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ced6862f-128b-46b3-a5e7-7849d25b8933",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A:\n",
      "[[4 7]\n",
      " [2 6]]\n",
      "\n",
      "A * 3\n",
      "[[12 21]\n",
      " [ 6 18]]\n"
     ]
    }
   ],
   "source": [
    "print(\"A:\")\n",
    "print(A)\n",
    "\n",
    "print(\"\\nA * 3\")\n",
    "print(A * 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c18458d-3588-4ca2-a3c7-96947ec305ab",
   "metadata": {},
   "source": [
    "#### 1.2.3. Matrix multiplication\n",
    "\n",
    "Each output value is the dot product of a row in A with a colum from B."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5fa0633b-0f76-4968-9c50-cda2433d60dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A:\n",
      "[[4 7]\n",
      " [2 6]]\n",
      "\n",
      "B:\n",
      "[[5 8]\n",
      " [3 4]]\n",
      "\n",
      "A @ B:\n",
      "[[41 60]\n",
      " [28 40]]\n"
     ]
    }
   ],
   "source": [
    "print(\"A:\")\n",
    "print(A)\n",
    "\n",
    "print(\"\\nB:\")\n",
    "print(B)\n",
    "\n",
    "print(\"\\nA @ B:\")\n",
    "print(A @ B)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbda0e45-1054-4cf1-9654-3c87491af956",
   "metadata": {},
   "source": [
    "#### 1.2.4. Transpose\n",
    "\n",
    "Swaps rows and columns in matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9a02eef4-0db0-40dd-8538-1ca7ca059236",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A:\n",
      "[[4 7]\n",
      " [2 6]]\n",
      "\n",
      "Transpose A:\n",
      "[[4 2]\n",
      " [7 6]]\n"
     ]
    }
   ],
   "source": [
    "print(\"A:\")\n",
    "print(A)\n",
    "print()\n",
    "print(\"Transpose A:\")\n",
    "print(A.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4e794db-abf2-47d2-a30d-00399e2d3db9",
   "metadata": {},
   "source": [
    "#### 1.2.5. Rank\n",
    "\n",
    "The number of (linearly) independent rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ec59c28f-3c2a-445c-8ab5-ed3630207aa9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A:\n",
      "[[4 7]\n",
      " [2 6]]\n",
      "\n",
      "Rank of A 2\n"
     ]
    }
   ],
   "source": [
    "rank_A = np.linalg.matrix_rank(A)\n",
    "\n",
    "print(\"A:\")\n",
    "print(A)\n",
    "print()\n",
    "print(f'Rank of A {rank_A}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1247a176-e64b-4728-a5d2-96364046214b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C:\n",
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [2 4 6]]\n",
      "\n",
      "Rank of C 2\n"
     ]
    }
   ],
   "source": [
    "C = np.array([[1,2,3],\n",
    "             [4,5,6],\n",
    "             [2,4,6]]) # this row is 2 x row 0\n",
    "\n",
    "rank_C = np.linalg.matrix_rank(C)\n",
    "\n",
    "print(\"C:\")\n",
    "print(C)\n",
    "print()\n",
    "print(f'Rank of C {rank_C}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5c2760f-7877-4e56-96dd-e6208a84c681",
   "metadata": {},
   "source": [
    "## 2. Statistics fundamentals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7bc16f54-a6a7-4c7b-8b94-52f09154df23",
   "metadata": {},
   "outputs": [],
   "source": [
    "import statistics\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "33e28948-fed5-434c-af7f-add5bfe37e42",
   "metadata": {},
   "outputs": [],
   "source": [
    "scores = np.random.normal(65, 12, 200)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2704a05-6ccb-4646-a249-a988e9868931",
   "metadata": {},
   "source": [
    "### 2.1. Measures of central tendency\n",
    "\n",
    "Where the center of the the data tends to be.\n",
    "\n",
    "#### 2.1.1. Mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "503ada51-93fa-4faa-bc75-7cf6e3120ea8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 64.41\n"
     ]
    }
   ],
   "source": [
    "# Mean (average) add up observations and divide by\n",
    "# number of observations\n",
    "mean = statistics.mean(scores)\n",
    "print(f'Mean: {round(mean, 2)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "785c9216",
   "metadata": {},
   "source": [
    "#### 2.1.2. Median"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "fd2c9393-4295-4885-9d1a-34b71dbb5051",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median: 65.45\n"
     ]
    }
   ],
   "source": [
    "# Median middle number (or half way between the two middle numbers)\n",
    "median = statistics.median(scores)\n",
    "print(f'Median: {round(median, 2)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9258d59e",
   "metadata": {},
   "source": [
    "#### 2.1.3. Mode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9908de19-5cfa-4ff6-b650-64ab098d8085",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mode: A\n"
     ]
    }
   ],
   "source": [
    "brands = ['B', 'A', 'Z', 'A', 'C']\n",
    "\n",
    "mode = statistics.mode(brands)\n",
    "print(f'Mode: {mode}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d408429-6de7-4cfe-9567-5c543a3cea60",
   "metadata": {},
   "source": [
    "### 2.2. Measure of dispersion (spread)\n",
    "\n",
    "#### 2.2.1. Range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "03b26321-e348-42d4-86f7-5989702d771b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data range: 63.32\n"
     ]
    }
   ],
   "source": [
    "# Range: highest value - lowest value\n",
    "data_range = scores.max() - scores.min()\n",
    "print(f'Data range: {data_range:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49198a66",
   "metadata": {},
   "source": [
    "#### 2.2.2. Interquartile range (IQR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "40841c89-8231-4e1c-8fec-874b0a0f255a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q1: 55.34, Q3: 72.66\n",
      "IQR: 17.32\n"
     ]
    }
   ],
   "source": [
    "# IQR (interquartile range)\n",
    "q1 = np.percentile(scores, 25)\n",
    "q3 = np.percentile(scores, 75)\n",
    "\n",
    "iqr = q3 - q1\n",
    "\n",
    "print(f'Q1: {q1:.2f}, Q3: {q3:.2f}')\n",
    "print(f'IQR: {iqr:.2f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "33028bc4-9660-4370-8f0d-e5eedf2f2a94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))\n",
    "\n",
    "ax1.set_title('Histogram')\n",
    "ax1.hist(scores, color='black', bins=30)\n",
    "ax1.axvspan(q1, q3, color='green', alpha=0.5)\n",
    "ax1.set_xlabel('score')\n",
    "ax1.set_ylabel('count')\n",
    "\n",
    "ax2.set_title('Boxplot')\n",
    "ax2.boxplot(\n",
    "    scores,\n",
    "    patch_artist=True,\n",
    "    boxprops=dict(facecolor='green', alpha=0.4),\n",
    ")\n",
    "ax2.set_xlabel('Test')\n",
    "ax2.set_ylabel('Score')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "835bcc1c",
   "metadata": {},
   "source": [
    "#### 2.2.3. Variance & standard deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "31085b9b-84ee-4b92-a442-2b4148a233f3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance: 163.07866283689415\n",
      "Standard deviation: 12.770225637665693\n"
     ]
    }
   ],
   "source": [
    "# Standard deviation is square root of the variance\n",
    "# variance is the the average of the squared \n",
    "# differences from the mean\n",
    "\n",
    "std = statistics.stdev(scores)\n",
    "var = statistics.variance(scores)\n",
    "\n",
    "print(f'Variance: {var}')\n",
    "print(f'Standard deviation: {std}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "30cd4d64-9c4b-4e28-9b22-365f5caca7a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Standard deviation')\n",
    "plt.hist(scores, color='black', bins=30)\n",
    "plt.axvline(mean, color='red', label='mean')\n",
    "plt.axvspan(\n",
    "    mean - std, mean + std,\n",
    "    color='red',\n",
    "    alpha=0.5,\n",
    "    label='1 std'\n",
    ")\n",
    "plt.axvspan(\n",
    "    mean - (2 * std), mean + (2 * std),\n",
    "    color='red',\n",
    "    alpha=0.1,\n",
    "    label='2 std'\n",
    ")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad235843-9dee-4bba-96a3-00759e840d09",
   "metadata": {},
   "source": [
    "### 2.3. Shape\n",
    "\n",
    "#### 2.3.1. Skew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "2cd090ae-9535-48f4-81b2-c401bf246d0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x350 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "right_skew = np.random.beta(2, 7, 1000) * 100\n",
    "symmetric = np.random.normal(50, 10, 1000)\n",
    "left_skew = np.random.beta(7, 2, 1000) * 100\n",
    "\n",
    "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(12, 3.5))\n",
    "\n",
    "ax1.set_title('Skew left')\n",
    "ax1.hist(left_skew, color='black', bins=30)\n",
    "\n",
    "ax2.set_title('Symmetric')\n",
    "ax2.hist(symmetric, color='black', bins=30)\n",
    "\n",
    "ax3.set_title('Skew right')\n",
    "ax3.hist(right_skew, color='black', bins=30)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1502f02c",
   "metadata": {},
   "source": [
    "#### 2.3.1. Kurtosis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "4c7ca372-6eb0-41c1-8701-7d681ae808a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ffvop8+fP5+mnnyYqKoqnnnqK2bNnAxAUFMTKlStZuHAhlZWVJCUl8fHHH9OrV6+Lrt+cto0ZPHgwgwcP5uWXX240wQoMDOSnn37i3nvvZdCgQYSFhTF//nybrjECoFFaM1HbToqLiwkMDKSoqKjJHwwhRPt224+3sT1nO/+89J9ck3hNnfdGfTKKc1XnWHHNClJCmv7LT9hfZWUlx48fJyEhocXbxQvn0tjPhLX3bxmmEULYlWWYxj/2ovcsdSNSxCqES5FkRAhhN5XVleSU5QB1p/WametIpIhVCNciyYgQwm5OlZ4CwM/dj2DPiyvzzT0jUsQqhGuRZEQIYTfmHo9Y/9h614iQtUaEcE2SjAgh7MacZNQ3RHP+cRmmEcK1SDIihLAb8/DLhdN6zczHc8tzqayutFtcQgjHkmRECGE35jVG6ptJAxDkGYS/u7o/iNSNCOE6JBkRQtiNOcGIC4ir932NRlM7VCN1I0K4DElGhBB2oTfqyS7LBhquGYHzZtTI7r1CuAxJRoQQdnGq9BQmxYS3mzehXqENtrOsNSI9I6INjRkzxrIXTXvXkWJtK5KMCCHs4vzi1ca2fpdVWEVHEh8fz+LFi9v0mitXruTpp59u02s2x+7duxk1ahReXl7Exsby/PPP2/wzZaM8IYRdmKfrNjZEc/77Mkwj2jO9Xo+Hh4dNrh0SEmKT61qjuLiY8ePHM27cOJYsWcKePXu49dZbCQoKsulmedIzIoSwi8b2pDmf+f3ssmz0Rr3N4xKtpCigL3PMoxX7vH733XcEBgaybNkyALKyspgxYwZBQUGEhIQwZcoUMjIyLO1nz57N1KlTeeaZZ4iOjiYlJYUxY8Zw4sQJHnzwQTQaTZ0ev88//5xevXrh6elJfHw8L730Up3Pf/3110lKSsLLy4uIiAimT59uee/CYZrG2ra1ZcuWodfreffdd+nVqxc33HAD999/Py+//LLNPhOkZ0QIYSeWBc8aWGPELNQrFB83H8qryzlZepKugV3tEZ5oKUM5/DPaMZ/92Gnw8G32aR999BF33XUXH330EZMnT8ZgMDBhwgSGDx/Oxo0bcXNz4x//+AcTJ05k9+7dlh6QNWvWEBAQwOrVqwGIioqiX79+3HHHHdx+++2W6+/cuZMZM2awcOFCZs6cyZYtW7jnnnsIDQ1l9uzZ/Pbbb9x///18+OGHjBgxgsLCQjZu3FhvrM1pC5CZmUnPnj0b/fofe+wxHnvssXrf27p1K6NHj67T6zNhwgSee+45zp49S3Dwxds4tAVJRoQQdmHtMI15eu/BwoNkFmdKMiLa1Guvvcbjjz/ON998w2WXXQbA8uXLMZlMvP3225bejffee4+goCDWr1/P+PHjAfD19eXtt9+uc6PW6XT4+/sTGRlpOfbyyy8zduxYnnjiCQCSk5PZv38/L7zwArNnzyYzMxNfX18mT56Mv78/cXFxDBgwoN54m9MWIDo6mrS0tEa/B40NA+Xk5JCQkFDnWEREhOU9SUaEEB2WwWTgdOlpoOmeEXMbczIi2jl3H7WHwlGf3QwrVqwgLy+PzZs3M2TIEMvxXbt2kZ6ejr+/f532lZWVHD161PLvPn36WFUncuDAAaZMmVLn2MiRI1m8eDFGo5Err7ySuLg4unbtysSJE5k4cSLTpk3Dx+fir6c5bQHc3Nzo1q1bkzG2N1IzIoSwuezSbIyKES+dF518OjXZXhY+60A0GnWoxBGPRmZl1WfAgAF06tSJd999F+W8epPS0lIGDRpEWlpancfhw4e56aabLO18fZs/JFQff39/UlNT+fjjj4mKimL+/Pn069ePc+fOtaotqD0pfn5+jT7++c9/NhhbZGQkubm5dY6Z/31+709bk54RIYTNmZOKzv6d0Wqa/hvIsvCZLAkv2lBiYiIvvfQSY8aMQafT8eqrrwIwcOBAli9fTnh4OAEBAc26poeHB0ajsc6xHj16sHnz5jrHNm/eTHJyMjqdDlB7MMaNG8e4ceNYsGABQUFBrF27luuuu+6iz2hO29YO0wwfPpzHH38cg8GAu7s7AKtXryYlJcVmQzQgyYgQwg4s9SJWDNFA7YwaGaYRbS05OZl169YxZswY3NzcWLx4MTfffDMvvPACU6ZM4amnnqJz586cOHGClStX8vDDD9O5c+cGrxcfH8+GDRu44YYb8PT0JCwsjL/+9a8MGTKEp59+mpkzZ7J161ZeffVVXn/9dQC+/fZbjh07xujRowkODub777/HZDKRkpJy0fWb0xZaP0xz00038eSTT3LbbbfxyCOPsHfvXv7973/zr3/9q8XXtIYkI0IIm7MseNZE8aqZud3pstMYjAbcde42i024npSUFNauXWvpIXnppZfYsGEDjzzyCNdddx0lJSXExMQwduzYJntKnnrqKe68804SExOpqqpCURQGDhzIp59+yvz583n66aeJioriqaeeYvbs2QAEBQWxcuVKFi5cSGVlJUlJSXz88cf06tXrous3p21bCAwM5KeffuLee+9l0KBBhIWFMX/+fJuuMQKgUZRWTNS2k+LiYgIDAykqKmp2F5oQwvHuXXMvG05u4IlLnmBGyowm2yuKwtBlQ6k0VvLttG8b3FhP2F9lZSXHjx8nISEBLy8vR4cj2oHGfiasvX9LAasQwuasndZrptFoaveokaEaIZyeJCNCCJuqNlVzsvQkYH3NyPltZUaNEM5PkhEhhE3llOVQbarGXetOhE+E1eeZk5ETxSdsFZoQop2QZEQIYVMZxRkAxAXEodPqrD4vPjAekGRECFcgyYgQwqaOFx0HICEwoYmWdZnbm88XQjgvSUaEEDZlTibiA+KbdV5CgJqMZJdlU24ob+uwhBDtiCQjQgibamnPSJBXEMGe6oqPMlQjhHOTZEQIYVPmZKQlu+/KUI0QrkGSESGEzRRVFXGm8gxQW5DaHJZkpFiSESGcmSQjQgibMc+kCfcJx9e9+TueSs+IaCtjxozhgQcecHQYVulIsbYVSUaEEDbT0noRM0lGRHsXHx/P4sWL2/SaK1eu5Omnn27TazbH7t27GTVqFF5eXsTGxvL888/b/DMlGRFC2IwlGQloYTJSc96J4hMYTcYmWgthP3q93mbXDgkJwd/fv0XnVlZWkp+f3+LPLi4uZvz48cTFxbFz505eeOEFFi5cyH//+98WX9MakowIIWymtT0j0X7RuGvdqTJWkV2W3ZahiTaiKArlhnKHPFqzz+t3331HYGAgy5YtAyArK4sZM2YQFBRESEgIU6ZMISMjw9J+9uzZTJ06lWeeeYbo6GhSUlIYM2YMJ06c4MEHH0Sj0aDRaCztP//8c3r16oWnpyfx8fG89NJLdT7/9ddfJykpCS8vLyIiIpg+fbrlvQuHaRpre6Hc3FxiYmKYOnUqX3zxBQaDoVnfl2XLlqHX63n33Xfp1asXN9xwA/fffz8vv/xys67TXG42vboQwqW1NhnRaXXEBcSRfi6d40XH6ezfuS3DE22gorqCYR8Nc8hnb7tpGz7uPs0+76OPPuKuu+7io48+YvLkyRgMBiZMmMDw4cPZuHEjbm5u/OMf/2DixIns3r0bDw8PANasWUNAQACrV68GICoqin79+nHHHXdw++23W66/c+dOZsyYwcKFC5k5cyZbtmzhnnvuITQ0lNmzZ/Pbb79x//338+GHHzJixAgKCwvZuHFjvbE2py1AXFwcW7du5YMPPuDOO+/EZDJx0003MWvWLAYNGtTk92br1q2MHj3a8jUDTJgwgeeee46zZ88SHBxs1fe4uSQZEULYhMFk4GSJukFeS5MR87nmZGRU51FtFZ5wUa+99hqPP/4433zzDZdddhkAy5cvx2Qy8fbbb1t6N9577z2CgoJYv34948ePB8DX15e33367zo1ap9Ph7+9PZGSk5djLL7/M2LFjeeKJJwBITk5m//79vPDCC8yePZvMzEx8fX2ZPHky/v7+xMXFMWDAgHrjbU5bs0GDBjFo0CBeeuklfvjhBz744ANGjhxJUlISs2bN4k9/+hMREfXvE5WTk0NCQt3/r+a2OTk5kowIITqWrJIsqpVqvN28m7VB3oVkem/75u3mzbabtjnss5tjxYoV5OXlsXnzZoYMGWI5vmvXLtLT0y+q06isrOTo0aOWf/fp06dOItKQAwcOMGXKlDrHRo4cyeLFizEajVx55ZXExcXRtWtXJk6cyMSJE5k2bRo+Phf38jSn7YXc3Ny45ppruOaaa8jOzuaWW27hb3/7GydPnmzzotvWkmRECGET5w/RnD+W3lwyo6Z902g0LRoqcYQBAwaQmprKu+++y+DBgy0/l6WlpQwaNMhSP3K+Tp06WV77+jZ/enp9/P39SU1NZf369fz000/Mnz+fhQsXsmPHDoKCglrc9kKKorBx40Y+/PBDPvvsM4KDg5k/fz633XZbg+dERkaSm5tb55j53+f3/rQ1KWAVQthEa+tFzCQZEW0lMTGRdevW8dVXX3HfffdZjg8cOJAjR44QHh5Ot27d6jwCAwMbvaaHhwdGY92ZXj169GDz5s11jm3evJnk5GR0OnXnajc3N8aNG8fzzz/P7t27ycjIYO3atfV+RnPaAhw+fJgnnniCrl27cvXVV1NdXc2XX37JsWPHePLJJ+nSpUuD5w4fPpwNGzbUKXxdvXo1KSkpNhuiAUlGhBA2klGUATR/g7wLmc8vrCykqKqodUEJl5ecnMy6dev4/PPPLTNWbr75ZsLCwpgyZQobN27k+PHjrF+/nvvvv5+TJ082er34+Hg2bNjAqVOnKCgoAOCvf/0ra9as4emnn+bw4cMsXbqUV199lYceegiAb7/9lv/85z+kpaVx4sQJPvjgA0wmEykpKRddvzltQa0x6dGjB1u2bOHJJ58kJyeH9957jzFjxljVQ3nTTTfh4eHBbbfdxr59+1i+fDn//ve/mTdvXpPntoYM0wghbMJc49HanhFfd1/CfcLJK88joziDfp36tUV4woWlpKSwdu1axowZg06n46WXXmLDhg088sgjXHfddZSUlBATE8PYsWMJCAho9FpPPfUUd955J4mJiVRVVaEoCgMHDuTTTz9l/vz5PP3000RFRfHUU08xe/ZsAIKCgli5ciULFy6ksrKSpKQkPv74Y3r16nXR9ZvTFiAsLIzjx4832vvRmMDAQH766SfuvfdeBg0aRFhYGPPnz+eOO+5o0fWspVFaMFH7tdde44UXXiAnJ4d+/frxyiuvMHTo0CbP++STT7jxxhuZMmUKX375pdWfV1xcTGBgIEVFRU3+YAghHE9RFEZ+MpISfQmfX/s5ycHJrbren3/6M9uyt/H0yKeZ2m1q2wQpWqSyspLjx4+TkJCAl5eXo8MR7UBjPxPW3r+bPUyzfPly5s2bx4IFC0hNTaVfv35MmDCBvLy8Rs/LyMjgoYceYtQomZonhLM7U3mGEn0JGjTEBcS1+nrmlVilbkQI59TsZOTll1/m9ttvZ86cOfTs2ZMlS5bg4+PDu+++2+A5RqORm2++mSeffJKuXZu/jbgQomMxJw0xfjF46jxbfT0pYhXCuTUrGdHr9ezcuZNx48bVXkCrZdy4cWzdurXB85566inCw8MbnU50vqqqKoqLi+s8hBAdR5MzaUwmKDgCOXvrPirrL1CVZEQI59asAtaCggKMRuNFK7dFRERw8ODBes/ZtGkT77zzDmlpaVZ/zqJFi3jyySebE5oQoh1pNBnJ3Qff/AVO7rj4PQ8/uOL/YOgdoNVZDpuvc7LkJAaTAXetu03iFkI4hk2n9paUlPCnP/2Jt956i7CwMKvPe/TRRykqKrI8srKybBilEKKt1TuTRl8OPy+EN0eriYjOE/wiah/ewaAvhVV/h7fHQvYuy6kRPhF4u3lTrVSTVSK/D9qD1mxSJ5xLW/wsNKtnJCwsDJ1OV+/qbPWtzHb06FEyMjK45pprLMdMJpP6wW5uHDp0iMTExIvO8/T0xNOz9ePMQgjHMK8xYklGjq6Dbx+As+pxuk+GSc9DYEztSSYT7HwPfn4STv8O/x0Dl9wDlz+OxsOHhMAE9p/Zz/Gi43QNlNozRzEv2qXX6/H2bt5y7MI5lZeXA+Du3vIey2YlIx4eHgwaNIg1a9YwdepUQE0u1qxZw9y5cy9q3717d/bs2VPn2P/93/9RUlLCv//9b2JjY1scuBCifaqoruB06WmgJhk5/BN8NANQICAGrnoBul998YlaLQy5TX1v1d9h3xew9VXIPwQ3La+TjAjHcXNzw8fHh/z8fNzd3dFqZe1MV6UoCuXl5eTl5REUFGRJVFui2YuezZs3j1mzZjF48GCGDh3K4sWLKSsrY86cOQDccsstxMTEsGjRIry8vOjdu3ed881r6V94XAjhHDKLM1FQCPQMJLjkDHz+Z0CB3tPhmsXg6d/4Bfwj4fr3oe8N8NksSF8Na58moZMUsbYHGo2GqKgojh8/zokTJxwdjmgHgoKCWr1vTbOTkZkzZ5Kfn8/8+fPJycmhf//+rFq1ylLUmpmZKZmyEC7MUrzq1wXN8pugqghiL4Gpb4Bb0zueWqRMhGtfhZV/hk3/ImHsX4HaISDhOB4eHiQlJaHX6x0dinAwd3f3VvWImLVoBVZ7kxVYheg43kh7g9d3vc40TRBPHdsN/tFwx3rwj2jy3Hr99ARs+Q9HvP24LjIEf3d/Nt+4uVU7AQsh7MNmK7AKIURjLD0jZ46rM2ZuWNbyRARg3EJIHEuXylK0CpQYSiioKGibYIUQ7YIkI0KINpWe+zsAXfUGuPY/EDOwdRfU6mD6O3gGdyW2Wt3W/OjZI60NUwjRjkgyIoRoM4bKIo6XZwOQ1PtG6HdD21zYOxhu+Jhu1eqocvq+5W1zXSFEuyDJiBCizWRueJZqjQYfBaLGP9u2Fw/vTreYSwBIP/4z6Mva9vpCCIeRZEQI0TZKcjmy92MAuvl1RuPe9tvLd+t5PQBHMMDW19r8+kIIx5BkRAjRNtb/kyNadYXlpOhhNvmIpNAeAKR7uGPatBhKchs/QQjRIUgyIoRovbwDkPoB6R7qctBJwUk2+ZguAV1w17pTrtWSrVTC+kU2+RwhhH1JMiKEaL3V80Exke4XBEC3oG42+Rh3rbtlv5t0d3dIXQp59e8YLoToOCQZEUK0zrH1cOQnKnTuZCnq1FtbJSPnX/tITF9QTPDzApt9lhDCPiQZEUK0nMmkrpAKHOv7BxQUQrxCCPUOtdlHmoeA0iOSQesGh1fB8Q02+zwhhO1JMiKEaLmD30LObvAM4Ei3UQAkBdmmXsTM0jNSkQOD1A06WfdPm36mEMK2JBkRQrTctjfV5yF/Jr08B4BuwbYbooHaZOR40XEMI/+i9o5kboXTaTb9XCGE7UgyIoRomZw9cGITaHRqMnIuHbBtvQhAtF80Pm4+GEwGsjBAz6nqG9v/a9PPFULYjiQjQoiWMfeK9LwWAmM4ck7dL8bWyYhWo60dqjl3BIbdpb6x5zMozbfpZwshbEOSESFE85WdUW/+AMPuoqiqiLzyPMD2yQjUDgWln0uHzoMheiAY9ZD6vs0/WwjR9iQZEUI0X+pSqK6EqH4QO8wyRBPtG42fh5/NP97SM3L2CGg0tb0jO94Bo8Hmny+EaFuSjAghmsdYDTveVl8Puws0GtLP1tSL2Lh41cycjJiTIHpNBd9wKMmGA1/bJQYhRNuRZEQI0TwHv4XiU+ATBr2uA7BbvYiZea2RzOJMKqsrwc0TBt+qvmmuZRFCdBiSjAghmsd8sx98K9TszGuvmTRmoV6hBHsGo6BwrOhYbTxad8jaBqdS7RKHEKJtSDIihLBe9i7I3KKu7VHTE6EoiiUZSQ5OtksYGo2mbhErgH8E9FZ7amSarxAdiyQjQgjrbau5yfecCgFRAORX5FNUVYROoyM+MN5uodQpYjUbdqf6vPdzKM2zWyxCiNaRZEQIYZ2qUti3Un099A7LYXPxapeALnjqPO0WTp21RsxiBqkPo7526rEQot2TZEQIYZ2D34GhHEK6QuxQy2F7F6+aWTbMq0mGLPrdqD7vXm7XeIQQLSfJiBDCOuabe9+Z6toeNcw1G7beIO9C5uQntzyXYn1x7Ru9rlNrWrJ3Qd5Bu8YkhGgZSUaEEE0ryYVj69TXfa6v85a5Z8LcU2Ev/h7+RPpGAnD03NHaN3xDoduV6us9n9o1JiFEy0gyIoRo2t4VoJig81AITbQcNikmjhapiYC9h2nO/8w6RawA/Waqz7s/A5PJzlEJIZpLkhEhRNMsQzQz6hw+VXKKiuoKPLQexPrH2j0s89DQRclI8kTwDICiTMj61e5xCSGaR5IRIUTj8g6q9RdaN8uKq2aHzx4GIDEoEZ1WZ/fQzEND5jgs3L3V3YRBClmF6AAkGRFCNM5cd9HtSrUe4zwHCg8A0D2ku72jAiAlJAWAQ2cPYVIuGI7pWzNUs+8LMFTaOTIhRHNIMiKEaJjJpNZdwEVDNAAHC9XZKo5KRhICE/DQelBmKONkycm6b8ZdCgExUFkER35ySHxCCOtIMiKEaFjmVrXuwsMfUiZd9La5Z6RHaA97RwaAu9bdMlRjjsVCq4U+09XXMlQjRLsmyYgQomHmm3jPKWodxnkKKwvJK89Dg8Zue9LUx9wrY+6lqcM8VHPkJygvtGNUQojmkGRECFE/QyXs+1J9Xd8QzRn15t8loAu+7r52DKwuczJyUc8IQEQviOitLg+//ys7RyaEsJYkI0KI+qWvhqoite4iftRFbx8869h6ETPz5x8qPFR/A3PvyG5ZAE2I9kqSESFE/fZ/rT73nKrWX1zA3DPi6GQkOTgZDRoKKgooqCi4uEHvmunImVtlJ18h2ilJRoQQF6vWw+Ef1dc9rqm3iaV4NcQxxatmPu4+xAfGA3DgTD1DNYGdIXoAoMCh7+0amxDCOpKMCCEulrFRHaLx7VRnh16zckM5J4pPAI7vGTk/hnqLWAG6T1afD3xrp4iEEM0hyYgQ4mIHa27a3a+GelZWPXz2MAoK4d7hhHqHXvS+vZl7Z+otYgXoUbMa67H16rojQoh2RZIRIURdJhMc/E593b3xIZruoY7vFQErekY6JUNYMpgMcGS1HSMTQlhDkhEhRF0nd0BprrrRXMLoeps4euXVC5l7RrJKsijRl9TfyDJU842dohJCWEuSESFEXQdrbtbJE8DNo94m5kJRRxevmgV5BRHpGwk0MsXXXIh7ZDUYKuwUmRDCGpKMCCFqKUptkae5J+ECBpOB9HPpapN20jMCVgzVRA+AgM5gKFNrR4QQ7YYkI0KIWrn74Oxx0HlCt3H1Njl27hgGkwF/d39i/GLsHGDDmixi1WjUglyQWTVCtDOSjAghapln0XQbC55+9Tep6XlICUlBo9HYK7ImpYSkAI0M00DtUM2h78FYbYeohBDWkGRECFGriSEaaH/Fq2bmnpGj546iN+rrb9RlOHiHQEUhZG6xY3RCiMZIMiKEUBUeh9w9oNFByqQGm1lWXg1tH8WrZlG+UQR4BFCtVFtqWi6ic4OUq9TXMlQjRLshyYgQQmUeookbAT4h9TYxKSbLMEh76xnRaDSW3pEGi1gBetT0+hz8Vi3YFUI4nCQjQgiVuafAvFppPU6VnKLUUIqH1oOEwAQ7BWY9c4JU7x41Zl0vB3dfKD4Fp1PtFJkQojGSjAghoOwMZG1TX3e/qsFm5iGapOAk3LXu9oisWcwrwjbaM+LuBUk1M4XMmwEKIRxKkhEhBBxdAygQ0Vvd5bYB7bV41cw8THPo7CGMJmPDDZMmqM+SjAjRLkgyIoSAIz+pz0njG21mKV5tJyuvXig+IB4vnRcV1RVklmQ23DDpSvU5Ow1Kcu0SmxCiYZKMCOHqTEZI/1l93UgyoigK+8/sB9rfTBoznVZHckgygCXWevmFqyuyAqTLxnlCOJokI0K4upO/QcVZ8AqCzkMabJZdlk1hZSFuWjfLAmPtUZ+wPgDsLdjbeEPzUI25V0gI4TCSjAjh6o7U1E10G6uuw9GAPQV7AEgJTsFT52mPyFqkd1hvoDbeBpl7gY6uA6PBxlEJIRojyYgQrs7KehFzT4P5Zt9emXtGDpw5gMHUSJIRPQB8wqCqGDJ/tVN0Qoj6SDIihCsrPg05ewBNgxvjme3O3w3U3uzbqy7+XQjwCEBv0nP47OGGG2q1tYWsMlQjhENJMiKEKztSU7wZMwh8wxpsVm2qtsykae/JiEajqa0byW+qbkSSESHaA0lGhHBl5ptw8oRGmx09d5SK6gp83X2JD4y3fVytZHXdSOIV6l48+Qfh7Ak7RCaEqI8kI0K4quoqOLZefW3uIWiApV4ktDdaTfv/tWH1jBrvYIgdpr6WKb5COEz7/60ihLCNE1tAXwq+4RDZr9Gm5h6GPp3a9xCNWa+wXgAcKzpGqb608cbmROywDNUI4SgtSkZee+014uPj8fLyYtiwYWzfvr3BtitXrmTw4MEEBQXh6+tL//79+fDDD1scsBCijZjrRZLGq8WcjegoM2nMwrzDiPaNRkFpfPEzqB2iOr4BDBW2D04IcZFmJyPLly9n3rx5LFiwgNTUVPr168eECRPIy8urt31ISAiPP/44W7duZffu3cyZM4c5c+bw44+yJ4QQDmWZ0tv4EE25oZz0c+lA+y9ePZ/VdSPhPSEgBqorIGOTHSITQlyo2cnIyy+/zO23386cOXPo2bMnS5YswcfHh3fffbfe9mPGjGHatGn06NGDxMRE/vKXv9C3b182bWr4P31VVRXFxcV1HkKINlR4DM4cAa0bJF7eaNODhQcxKkbCfcIJ9wm3U4CtZ3XdiEYjs2qEcLBmJSN6vZ6dO3cyblztegRarZZx48axdevWJs9XFIU1a9Zw6NAhRo8e3WC7RYsWERgYaHnExsY2J0whRFPMQzRdhoNXYKNNLfUiHahXBJrRMwJ1d/FVFBtGJYSoT7OSkYKCAoxGIxEREXWOR0REkJOT0+B5RUVF+Pn54eHhwdVXX80rr7zClVc23DX86KOPUlRUZHlkZWU1J0whRFPS16jP3cY22dR8M+8o9SJmPUN7otVoyS3PJa+8/mFki4TRoHWHcyfUXiMhhF3ZZTaNv78/aWlp7Nixg2eeeYZ58+axfv36Btt7enoSEBBQ5yGEaCPVVZCxUX2d2HQyYh7m6Gg9Iz7uPnQL6gZY0Tvi6QddLlFfH11r48iEEBdqVjISFhaGTqcjNze3zvHc3FwiIyMb/hCtlm7dutG/f3/++te/Mn36dBYtWtSyiIUQrZO1HQzl4NsJIhrv7ThTcYZTpafQoKFnaE87Bdh2rK4bgdramaPrbBiREKI+zUpGPDw8GDRoEGvWrLEcM5lMrFmzhuHDh1t9HZPJRFVVVXM+WgjRVsx/+Sde0eSU3n1n9gGQEJiAv4e/rSNrc82qGzH3Eh3fILv4CmFnDe8X3oB58+Yxa9YsBg8ezNChQ1m8eDFlZWXMmTMHgFtuuYWYmBhLz8eiRYsYPHgwiYmJVFVV8f333/Phhx/yxhtvtO1XIoSwztGaPyYSr2iyaUetFzEz94zsK9iHSTE1vnpsZF/wCYXyM3ByB8SNsFOUQohmJyMzZ84kPz+f+fPnk5OTQ//+/Vm1apWlqDUzMxPteX9tlZWVcc8993Dy5Em8vb3p3r07//vf/5g5c2bbfRVCCOuUFUD2LvV118an9EJtMtI3rK8to7KZxKBEvHRelBpKySjOoGtg14Yba7Xq92TvCrX3SJIRIexGoyjtfx5bcXExgYGBFBUVSTGrEK2xZwV8fhtE9IG7G1/gS1EURi0fRVFVEZ9M/oReob3sFGTbmvXDLFLzUnnm0me4NvHaxhv/vgy+ugeiB8IdUjsiRGtZe/+WvWmEcCWWepGme0VOlpykqKoID60HyUHJNg7MdsxDNXvyrakbqRm6Ov07lBfaMCohxPkkGRHCVShK3eLVJuwu2A1A95DuuOvcbRmZTfXupNa7mL+eRgVEqcvDo9TuaCyEsDlJRoRwFXkHoCQb3LzVlVeb8Hve7wD0C298R9/2rn+n/gAcKjxEuaG86RPMiZqsNyKE3UgyIoSrMN9c40eCu1eTzc3JyMDwgbaMyuYifSOJ8o3CqBitnOJrXm9krSwNL4SdSDIihKtoxhBNsb6YI2ePANA/vL8Ng7KPAeEDAEjNS226cdxI0HlC8SkoOGzjyIQQIMmIEK7BUAEnNquvrVgCflfeLhQU4gLiCPMOs3Fwtmfu3fk99/emG7t7107rlaEaIexCkhEhXEHmVqiuBP9o6JTSZHPzEI253qKjM/fu7MrfRbWpuukTzL1H6WsabyeEaBOSjAjhCs4fotFommxuHs4YGNGx60XMugV1w9/dn/Lqcg6ftWLoxbybccYmdWNBIYRNSTIihCswb/7Wrel6Eb1Rb9lYzlxr0dHptDrLrCBzr0+jwnuCXwRUV0DmrzaOTgghyYgQzq4kF3L3AhpIGNNk8/1n9lNlrCLYM5j4gHgbB2c/5rqR1Fwrilg1GpniK4QdSTIihLM7/ov6HNUPfEObbJ6WlwaovSIaK4Z0OgpzL09aXhpW7YJh3rtHFj8TwuYkGRHC2Zlvpl3HWNXc2epFzHqH9cZN60ZeRR6nSk81fULXy9Tn7F2yNLwQNibJiBDOTFGalYwoilI7k8YJ1hc5n5ebFz1DewJW1o34R0KnHoACxzfYNjghXJwkI0I4szPp6uJdOk/ockmTzY8XH+dc1Tk8dZ70DOlphwDty1I3Ys3iZ1CbwMlQjRA2JcmIEM7MPIumyyXqYl5NMC8K1iesT4feHK8h5roRqxY/g/OSkXW2CUgIAUgyIoRza2G9iLNM6b2QeejpaNFRzlWea/qE+JGgdYOzGVB43JahCeHSJBkRwlkZqyFjo/raymTEsjmekxWvmoV4hZAQmABAWn5a0yd4+kPnIepr86wkIUSbk2RECGd1+neoKgavIHVabxMKKgrIKslCg4Z+nZpu31FJ3YgQ7Y8kI0I4K/PNM2E0aHVNNjf3iiQFJ+Hv4W/DwBzLPFRjXk+lSZZk5BcwmWwRkhAuT5IRIZyVuegy8XKrmptXJnXWehEzc8/I3oK9VBmt2HcmZhB4+EFFIeTstnF0QrgmSUaEcEZVpZC1XX3d3HqRcOesFzGL9Y8l1CsUg8lg2YOnUTp3iL9UfS1DNULYhCQjQjijzK1gMkBQFwhOaLJ5ib6EA4UHAOctXjXTaDSWr/G3nN+sO0nqRoSwKUlGhHBG50/ptWJ/mZ25OzEpJuIC4oj0jbRpaO3B0MihAGzP2W7dCeZ9ajK3gqHSRlEJ4bokGRHCGTVzfZFt2duA2pu0sxsWNQxQi1grq61ILjqlgF8kVFdC1jYbRyeE65FkRAhnU5oHuTW1EAmXWXWKuYdgaJRrJCPxAfGEe4ejN+nZlb+r6RM0GhmqEcKGJBkRwtkcq1mcK7IP+IY12bywspDDZw8DMCRiiC0jazc0Go0l8TL3CjVJloYXwmYkGRHC2VjWF2ler0hScBKh3qE2Cqr9MQ9JbcuxNhmp+X6eToPyQtsEJYSLkmRECGeiKLXJiJXri2zPVpORYZHDbBRU+2SuG9lXsI9SfWnTJwREQ1gKoEDGJtsGJ4SLkWRECGdSeAyKT4LWHboMt+oUc8+I+ebsKqL9oon1j8WoGJuxNHxN74jUjQjRpiQZEcKZmG+SscPAw7fJ5jllOZwoPoFWo2VQxCDbxtYOWYZqmls3IpvmCdGmJBkRwplYpvQ2r16kV2gvp96PpiHm3iCr1xuJGwkaLZxJh6KTNoxMCNciyYgQzsJkhOMb1NfNXF/E1YZozIZEqrOHDhYe5FzluaZP8A6C6JoVao9J74gQbUWSESGcRc5uqDwHHv61N8xGKIricoudXSjMO4xuQd2A5qzGOkZ9lroRIdqMJCNCOAvzzTH+UtC5Ndk8syST3PJc3LXu9A/vb9PQ2rPmLw1fMwR2/Bd19pIQotUkGRHCWZiHDZo5RNOvUz+83bxtFFT7Zx6isrqItfNQcPOG0lzIP2jDyIRwHZKMCOEMDJXqJm7Q7OJVV60XMRscORitRktGcQa5ZblNn+DuBV0uUV9L3YgQbUKSESGcwcnt6iZufhHQqXuTzU2KiR05OwBJRgI8AugR0gOQuhEhHEWSESGcwflLwGs0TTY/cvYIhZWFeLt50zu0t21j6wCav09NTe9TxiYwVtsoKiFchyQjQjgDy/oiY6xqbr7pDowYiLvO3TYxdSDmpfC35WxDsaYoNbIveAeDvgROW7l6qxCiQZKMCNHRVZyD07+rr62sF9l8ejMAw6OsWzLe2Q2MGIiH1oOcshyOFR1r+gStDuJHqa+lbkSIVpNkRIiOLmMTKCYI7QaBnZtsXm4o57ec3wAY1XmUraPrELzdvC0LoG06ZeUmeFI3IkSbkWREiI7uePOm9O7I2YHepCfGL4aEgATbxdXBXBpzKQAbT2607gTz9/vkdtCX2SYoIVyEJCNCdHTnF69aYeMp9WZ7acylaKwodnUV5mRkZ95OygxWJBchXSEwFoz62mnVQogWkWREiI6s+DQUHAY0kND0kIuiKJZhCPPNV6jiAuLo7NeZalO1dbNqNJraGh0ZqhGiVSQZEaIjM98Eo/urszuakFGcwanSU7hr3V12P5qGaDQaSw2N9XUjl6vPkowI0SqSjAjRkVmm9F5uVXNzPcTgiMH4uPvYKKiOy1I3cmqjdVN8E0arzzl7oKzAhpEJ4dwkGRGio1KUZq8vIkM0jRsSOcQyxffouaNNn+AXDhE1i8Ydlym+QrSUJCNCdFT5B9XN2ty8IbbpJd3LDeX8lqtO6b20syQj9WnVFN+j62wTlBAuQJIRIToq880vbri6eVsTduTswGAyyJTeJrSqbsSaoR0hxEUkGRGio2puvYhM6bVKs6f4xg0HnQcUZUGhFau3CiEuIsmIEB2R0aCuvApW1YucP6V3VIysutqYuIA4Yv1jqTZV82v2r02f4OFbO0x2TIZqhGgJSUaE6IhO7gBDGfiE1RZQNuJ48XHLlF5zTYRomLl3xPqhGllvRIjWkGREiI7IMkRzGWib/m+86aR6Ux0SOUSm9FrB3Hu06dQm66b4mofKjm8Ak9GGkQnhnCQZEaIjauaU3vPrRUTThkQOwVPnSU5ZDunn0ps+IXoAeAZCZRGcTrN5fEI4G0lGhOhoKovgpDpF15ri1TJDGTtzdwKSjFjLy82LwZGDAdhwckPTJ2h1tcvxS92IEM0myYgQHU3GZlCMEJIIQbFNNt94aiMGk4G4gDjiA+JtH5+TGNN5DABrs9Zad4K5l0rqRoRoNklGhOhomjlEs/aEejO9ossVMqW3GS6PVXuddufvJq88r+kTEq9Qn7O2gd6KKcFCCAtJRoToaMzDAIlND9HojXo2nFKHGcZ2GWvLqJxOhG8EfcP6ArAu04qhl5CuEBgLRj1kbrVxdEI4F0lGhOhIik5BwWHQaCG+6fVCtmVvo8xQRifvTvQJ62OHAJ3LFV3U3o41mWuabqzR1E7xlaXhhWiWFiUjr732GvHx8Xh5eTFs2DC2b9/eYNu33nqLUaNGERwcTHBwMOPGjWu0vRCiEebN2KIHgndQk83NN9ErulyBViN/ezSXuTdpR84OiqqKmj7BsjS8bJonRHM0+7fT8uXLmTdvHgsWLCA1NZV+/foxYcIE8vLqH1Ndv349N954I+vWrWPr1q3ExsYyfvx4Tp061erghXA55r+4ragXMZqMrMtS25v/whfNEx8YT2JgItVKtXWzahJqekZy90CpFXUmQgigBcnIyy+/zO23386cOXPo2bMnS5YswcfHh3fffbfe9suWLeOee+6hf//+dO/enbfffhuTycSaNVZ0ewohaplMzaoX2ZW/i8LKQvw9/GXV1VYwJ3JrM62YVePXCSJrhsNkVo0QVmtWMqLX69m5cyfjxo2rvYBWy7hx49i61bqCrfLycgwGAyEhIQ22qaqqori4uM5DCJeXuxfK8sHDDzoPbbK5eYjmss6X4a51t3V0TmtcnPr7bvPpzVRWVzZ9QmJNofBRK6cECyGal4wUFBRgNBqJiIioczwiIoKcnByrrvHII48QHR1dJ6G50KJFiwgMDLQ8YmObXktBCKd3tKY3MX4UuHk02lRRFEsyIrNoWqdHSA+ifaOpqK5gy+ktTZ9gnuJ7dC1Ys5S8EMK+s2meffZZPvnkE7744gu8vLwabPfoo49SVFRkeWRlZdkxSiHaKfNf2olN138cPnuYU6Wn8NR5MiJ6hI0Dc24ajaZ5s2q6XALuPlCaC7n7bBydEM6hWclIWFgYOp2O3NzcOsdzc3OJjIxs9NwXX3yRZ599lp9++om+ffs22tbT05OAgIA6DyFcmr4MMmu2s+/WdE+H+aY5InqEbIzXBszJyC8nf6HaVN14YzdPiK9Zdv+o1MYJYY1mJSMeHh4MGjSoTvGpuRh1+PDhDZ73/PPP8/TTT7Nq1SoGDx7c8miFcFUZm9XFtIK6qItrNUGGaNrWwPCBBHsGU1RVZNnnp1HnD9UIIZrU7GGaefPm8dZbb7F06VIOHDjA3XffTVlZGXPmzAHglltu4dFHH7W0f+6553jiiSd49913iY+PJycnh5ycHEpLS9vuqxDC2Zn/wk4cqy6u1YiskiwOnz2MTqNjTOwY28fmAnTa2u+lVUM15iLWE1tBX267wIRwEs1ORmbOnMmLL77I/Pnz6d+/P2lpaaxatcpS1JqZmUl2dral/RtvvIFer2f69OlERUVZHi+++GLbfRVCOLtm1IuYp6AOjhhMoGegLaNyKeZepjWZazAppsYbhyVBQGcwVsEJK4pehXBxbi05ae7cucydO7fe99avX1/n3xkZGS35CCGE2bmsmiXgdZAwusnmq46vAmBsnAzRtKVLoi/B192XvPI8duXvYkD4gIYbazTQ7QpI/UBNJJManj0ohJC9aYRo/8y9Ip0HN7kE/IniE+w9sxedRsf4uPG2j82FeOo8Lb0j3x37rukTLHUjUsQqRFMkGRGivbPUizQ9RPP98e8BuCTqEkK9Q20ZlUu6KuEqAH7K+AmDydB444TL1A0N8w+qGxwKIRokyYgQ7ZnJWLuseGLjwy6KovD9MTUZuarrVTYOzDUNixpGiFcIZ6vOsi17W+ONfULUDQ1BZtUI0QRJRoRoz06lQmUReAVCdCM1CsDBwoNkFGfgqfPkiljZGM8W3LRuTIifAGBJ/BrVTZaGF8IakowI0Z6Zb2IJl4Gu8Xpz8xDN6M6j8fPws3VkLss8VLMmcw0V1RWNNzYPrR1bp/ZyCSHqJcmIEO2ZuV6kiVVXTYqJH47/AMDVCVfbOiqX1q9TP2L8YiivLmfDyQ2NN44ZDJ4BUHEWstPsEp8QHZEkI0K0VxXn4ORv6usmildTc1PJLc/F392fSztfavvYXJhGo2FSwiTAiqEanVvtdGwZqhGiQZKMCNFeHf8FFCOEdlOXgW+EuVdkbNxYPHWe9ojOpZmTkY2nNlKsL268sblX68jPNo5KiI5LkhEh2qsjP6nPSY2vF2IwGvjxxI9AbT2DsK3k4GS6BXXDYDKw5kQT64h0q1nw7OR2dbhGCHERSUaEaI8UBY6sVl8nXdlo063ZWymqKiLUK5ShkUPtEJwAuLqrWpvz3fEmFkAL6gKdeoBikqEaIRogyYgQ7VHObijNBXcfiBvZaFPzLJqJCRPRaXX2iE4AE+MnArAjZwf55fmNNzYnlOYEUwhRhyQjQrRH5ptW1zHg1nANSLmh3LIxngzR2Fdn/87069QPk2JiVcaqxhubh9rSfwZTE5vsCeGCJBkRoj0yJyPdGt9gbfWJ1VRUVxDrH0ufsD52CEyczzxU81X6VyiK0nDDLpeAhz+U5csUXyHqIcmIEO1NeaFa7AhN1ousPLISgGndpqHRaGwdmbjAVQlX4aH14NDZQ+wv3N9wQ507JI5RX8tQjRAXkWREiPbm6Fq12LFTj0an9GYUZZCal4pWo+XaxGvtGKAwC/QMZGycOnX3iyNfNN7YPFRjniUlhLBofH1pIdpIcaWB9YfyMVTLeHlTBv/+FXHAoYBL2LvzZIPtVucsBSDRbzCbDhqAhtsK2+mkjAJ+4Msj35CouwEPrVe97bwqe3M1oJzaybdbdqP3DLFrnB1RSqQ/vWMCHR2GsANJRoRdPPvDQT7alunoMNo9DSZ+81wHGlhwIIZf9+1qoKUR36RVaN1g94FkUrc31E7Yg29iCFUehTyx+mOqiwc22C7eI45e2hOs+fZjvjTJSrlN8dBp2fH4OAJ93B0dirAxSUaEXZw6q24o1j3Sn/CA+v9yFNC16iChuSVUaHzwThzJaE39/0XP8TvHdaW4KQEMjxqFJkr+KztSjmY02XxJp+hdJEVOaLDd0XMj6FV8gplBBygMm2bHCDuerUcL0BtN5JdWSTLiAuQ3mLCLCoO6Y+l9VyRxdd8oB0fTjq1bA7ng3X0c780c0WCz+9Z8yPGT8Kfef2De4IbbCfvIKevChM+/ppRD/GN6JF0CGqj1yTTBux8zXElj+OxBIOvCNOiSf64hp7iSSoPsduwKpIBV2IX5F4q3h/zINSrdvOpqw0vA55XnsfHURgCmJk21Q1CiKZG+kYyIVpPCL9IbKWSNGQxeQeqy8Kd22ie4DsrbQ03UKiQZcQlyZxB2UaFXf6F4uctfgg0qzYdTqerrRtYX+fro1xgVIwPCB9A1sKudghNNuS7pOkBdc6TaVF1/I51b7Q7MMqumUebfFebfHcK5STIi7ML81423JCMNO7oGUCCyDwTUP5SlKIplCum0blJz0J6M6TyGEK8Q8ivy2XRqU8MNZYqvVbzd1duT9Iy4BklGhF3UDtNIMtIgK3bp/S33NzJLMvFx82FCfMOFksL+3HXuTO46GahdjK5e5l6v7F1QkmOHyDom8+8KqRlxDZKMCLuoNKjri0jPSAOMBnXfEmg0GTHf5CYlTMLH3ccekYlmMA/VbDi5gbzyvPob+XWC6Jrpv4d/tFNkHY/5d4UkI65BkhFhc4qiyDBNU05shsoi8AmDzkPqbVJQUWDZkG168nR7RieslBiUyMDwgRgVI58d/qzhhik1mxoe+t4+gXVAUjPiWiQZETZnMCoYTeomYp6SjNTvYM1NKXlig9M9Pzv8GdWmavp26kvvsN52DE40x409bgTg00Ofojfq62/UvSYZObYe9GX2CayDsSQjBlm12RVIMiJs7vwCNOkZqYeiwKEf1Nfmm9QFDEYDnx1S/9K+ufvN9opMtMDYLmMJ9wmnsLKQHzMaGIYJ7wlBcVBdqe5FJC7i7S5Te12JJCPC5sxjvjqtBned7Cx7kdy9UJQJbl7Q9fJ6m6w+sZr8inw6eXfiyrjGd/IVjuWudeeGlBsAWHZgGYqiXNxIo4HuV6uvzYmoqEMKWF2LJCPC5sxjvt7uOtnmvj7mIZqul4NH/UWpyw4uA+D6lOtx18nS2O3dH5L/gIfWg31n9rG7YHf9jVImqc+HV4FJbrgXkpoR1yLJiLA5czerLHjWAHMRYwNDNHsL9rI7fzduWjeuT77ejoGJlgrxCmFSgppsLDuwrP5GXUaoq7GWn4GsbfYLroOQYRrXIsmIsLkKWQq+YUWnIDsN0KjFq/X46MBHAEyKn0SYd5j9YhOtclOPmwBYnbG6/mm+OjdIrlkr5uB3doysY5BFz1yL3B2EzVXqZVpvg8y9IrFDwS/8orcLKgr4IUOtKTDf3ETH0DO0JwPDB1KtVDc8zff8Kb711Za4MEvNiAzTuARJRoTNyRojjTAXL5rrBy4g03k7tian+XYbCzoPKDwGBYftHF375iXDNC5FkhFhc+bVV6Vm5AKVxXB8g/o65eqL3pbpvB1fk9N8Pf0hYbT6WoZq6pAVWF2LJCPC5ipkX5r6pf8MJgOEdoNOyRe9/UPGDzKdt4M7f5rv0n1L65/mK6ux1sv8+0IWPXMNkowIm7PMpnGTZKQOyxDNxbNoTIqJd/a8A8DNPW6W6bwd2IyUGXi7eXPo7KH6d/M1D9Gd/A1Kcu0bXDvmJT0jLkWSEWFzlgJW6RmpZTTAkZpu+3qSkXWZ6zhWdAx/d39mpsy0c3CiLQV6BlqmZL+95+2LGwREQ/QAQFHXHBHAeVN7pYDVJUgyImxO1hmpx4kttRvjxQ6t85aiKLy15y0Abuh+A34efo6IULShW3regrvWndS8VFJzUy9uYK4ZkqEaCylgdS2SjAibk9k09dj/lfqccvHGeL9m/8q+M/vw0nnxx55/dEBwoq1F+EZwbeK1QAO9Iz0mq89H16pJqjivZkSSEVcgyYiwOcty8LLomcpkhAPfqK97TrvobfPN6rqk6wjxCrFnZMKGbu19K1qNlo2nNnKo8FDdNzt1h7BkMOrhkAzVQO0fL/pqk2XXb+G85O4gbK5SekbqOrEFyvLUpcC7Xlbnrd35u9mesx03jRuze812SHjCNroEdGFCnLriqrk42UKjgZ5T1df7v7RrXO3V+b8vpIjV+UkyImxOakYuYL7ZdJ8MF8ySMfeKXN31aqL8ouwcmLC12/rcBsCPJ34ksziz7pu9pqrP6WvUNWhcnKdb7e1JhmqcnyQjwuYqZDZNLZMR9n+tvu5Vd4jmyNkjrMtahwYNt/a51QHBCVtLCUlhVMwoTIqJd/e+W/fN8J41QzVVMqsG0Go1eJn3p5EZNU5PkhFhc5XV6qJFMkxDo0M07+xVu+7HxY2ja2BXBwQn7OH2vrcD8PXRr8kpy6l94/yhmn1f2j2u9sj8O6OqWpIRZyfJiLA52SjvPA0M0aSfTef7Y+q0TnNXvnBOA8IHMDhiMAaTgf/u/m/dNy1DNT/LUA3nrzUiq7A6O0lGhM1JzUiNOkM0U+u89WraqygojOsyjl6hvewfm7CruQPmAvDFkS/q1o6E94TQJBmqqSFrjbgOSUaEzUkyUiNza80QTSAk1A7R7C3Yy5rMNWjQWG5SwrkNihjEpTGXUq1U8/qu12vf0GhqE1UZqpFkxIVIMiJsTgpYa5hvLt0ng5uH5fB/Uv8DwDWJ15AYlOiAwIQj3DfgPgC+P/Y9h88ern3DXDciQzW1C59JAavTk2RE2JysM0LNEE3Nqqvmmw2wPXs7W7O34qZ14+5+dzsmNuEQPUN7Mj5uPAoKr/z+Su0bEb3UnZyNVXD4R8cF2A54y2Z5LkOSEWFzshw8dYdouo4B1D1o/vO72isyPWk6nf07OzBA4QhzB8xFq9GyPms9u/J3qQc1mtpp3y6+AJoM07gOSUaETSmKUlsz4srLwdczRPPLyV/Ylb8LL50Xd/S9w3GxCYdJCExgSuIUAF5JPa93xNx7dmQ1VJXYP7B2QoZpXIcL3x2EPVRVm1BqtpVw2Z4RY/VFQzQmxWTpFbmpx0108unkoOCEo93V7y7cte5sy9nG1tNb1YPnD9Uc+sGxATqQt3nRM+kZcXqSjAibqjLUrg/gsrNpjq1Xh2i8QyxDNN8d+44jZ4/g7+7Prb1ltVVXFu0XzYyUGQAsTl2MSTGpQzW9p6sNdn3iwOgcy7LomSQjTk+SEWFT5r9o3HUa3HUu+uO2u+Zm0mc6uHlQbihn8c7FANza51YCPQMdF5toF27vczt+7n7sP7Ofr9JretH6zVSfj62DkpyGT3ZiXh5SM+IqXPTuIOzFUi/i5qK9IlUlcOBb9XXfGwB4a89b5FXk0dmvM3/q+ScHBifai1DvUO7qdxeg9o6U6kshpCvEDgPFBHs+c3CEjmH+vSHJiPOTZETYlLnwzMtV1xjZ/zVUV6irasYMJKski6X7lgLwtyF/w1Pn6eAARXtxU/ebiA+Ip7CykDd3v6ke7KcmsK46VFNbwCrLwTs7SUaETbn8tN5dH6vP/WaCRsOLO17EYDJwSdQlXB57uWNjE+2Ku86dvw35GwD/O/A/Mooy1Cm+Og/I3Qs5exwboAPIOiOuQ5IRYVMuveDZuSzI2KS+7juTrae3sjZrLTqNjr8P/Tsajcax8Yl2Z3Tn0YyKGUW1qZoXfnsBvIMheaL6pgv2jnjLOiMuQ5IRYVMuPUyz51NAgbhLqQ6I5rntzwFwQ/cbZNl30aCHhzyMm8aNDSc3sPHkxtqhmj2fqdPEXYiXrDPiMiQZETZVO0zjYj9qigK7lquv+93A8kPLOVp0lCDPIFn2XTQqPjCem3vcDMDzO57HkDBGnRZemgvH1zsyNLuTnhHX0aI7xGuvvUZ8fDxeXl4MGzaM7du3N9h23759/OEPfyA+Ph6NRsPixYtbGqvogFy2ZuT071BwCNy8yE8YyWu/vwaom6PJVF7RlDv73UmIVwgZxRksPfwx9P6D+oaLDdVIzYjraHYysnz5cubNm8eCBQtITU2lX79+TJgwgby8vHrbl5eX07VrV5599lkiIyNbHbDoWCw1I642TLO7plek+9Us2vUqJYYSeob25Lqk6xwbl+gQ/D38eWjwQwC8kfYGGUk1xc4HvnWp5eG9PWQFVlfR7GTk5Zdf5vbbb2fOnDn07NmTJUuW4OPjw7vvvltv+yFDhvDCCy9www034Okp0xhdjTkZcanVV40G2LMCgDUxvVh9YjU6jY6nRjyFm9bNwcGJjmJy18mMiB6B3qTnyWMrMIUmqtPE93/t6NDsxkt6RlxGs5IRvV7Pzp07GTduXO0FtFrGjRvH1q1b2yyoqqoqiouL6zxEx2ReH8ClhmnS10B5AcV+nXgmS13wbE7vOaSEpDg4MNGRaDQa5g+fj7ebN7/l/sbKhEHqG+bp4i7AUjMiBaxOr1nJSEFBAUajkYiIiDrHIyIiyMlpu+WKFy1aRGBgoOURGxvbZtcW9lXhij0jqeqiZv/qkkJ+RQHxAfGW1TWFaI4YvxjuG3AfAC8X7SFPp4OMjXDmqIMjs4/anhFZ9MzZtcspDo8++ihFRUWWR1ZWlqNDEi3kcuuMFJ2Ew6vY4eXJiopMAOYPny8rrYoWu6n7TfQO7U1JdRn/7FLTu7bzfYfGZC/m3xt6o4lqoyQkzqxZyUhYWBg6nY7c3Nw6x3Nzc9u0ONXT05OAgIA6D9ExmbtXXaaAdedSKlF4MjIGgOnJ0xkSOcTBQYmOTKfVsXDEQtw0bqyhlNU+3vD7/6C6ytGh2dz5vzcqqyUZcWbNSkY8PDwYNGgQa9assRwzmUysWbOG4cOHt3lwouNzqWEaowFSP+CV4EBOaKrp5N2JeYPmOToq4QRSQlK4tc+tAPyjUxhnqs65RCGrp1vtLUrqRpxbs4dp5s2bx1tvvcXSpUs5cOAAd999N2VlZcyZMweAW265hUcffdTSXq/Xk5aWRlpaGnq9nlOnTpGWlkZ6enrbfRWi3XKpdUYO/cDW6rN8EKj25M0fPh9/D38HByWcxR1976BbUDcKtRoWdApF+e0dR4dkcxqNRtYacRHNTkZmzpzJiy++yPz58+nfvz9paWmsWrXKUtSamZlJdna2pf3p06cZMGAAAwYMIDs7mxdffJEBAwbw5z//ue2+CtFu1a4z0i7Lk9rUuR1v8XinUABmJM9gTOwYxwYknIqnzpNnRz2Lu9adX3y8+fTsHsg74OiwbM6yc68kI06tRYsezJ07l7lz59b73vr16+v8Oz4+HkVRWvIxwglYakacvGdEKUhnYdl+8n19iPeL4aEhDzk6JOGEUkJSeHDQgzy/43leCAliyK//oeu1bzg6LJuS6b2uwfn/XBUO5So1Iys3PckaXx/cgOfGvIy3m7ejQxJO6uYeNzMiqDtVWi2P5K1HX3HW0SHZlJe7rMLqCiQZETblClN7MwoP89zZ3wG4P/Yqeob2dHBEwplpNVr+MfZVgkxw0N2NV9f+1dEh2ZR5mEZqRpybJCPCpsyLFTnr1F69Uc8jP8+lQqthqEFh1uinHR2ScAGd/CJ4MvpKAN4r2MGW01scHJHtSAGra5BkRNiUsw/TLNq+iP0V2QQYjTwTfx1aNw9HhyRcxBWXPsb0knIA/r7+IbJLs5s4o2My/+6QYRrnJsmIsClnLmD94sgXrDi8Ao2i8FzBWSKH3u3okIQr8Q3jkcgx9KjSc9ZQwoPrH6TK6HwLoVmSEb0seubMJBkRNqMoitP2jOwr2Mc/fv0HAPecK+LSxMkQEOXgqISr8Roxl3/l5RNoNLHvzD4WbVvk6JDanLf0jLgESUaEzVSdt3yzM9WMnK08y4PrH0Rv0jOmvII7zhXDyPsdHZZwRdEDiIkdyfP5BWiAz498zueHP3d0VG1KakZcgyQjwmbOXxfAy805ftSMJiMPb3iY7LJsuuh8eCa/AG3iWIjs4+jQhKsa8RdGVFRyX5FaP/LMtmfYk7/HwUG1HcuiZ7LOiFNzjjuEaJfM3aoeOi1uOuf4UVucuphfs3/FW+fFv06dJMCkSK+IcKxuYyG8F7cVFnC5TywGk4EH1z9IXnmeoyNrE1LA6hqc4w4h2qXaehHn+DFbfnA57+97H4AngweTXFEKUf0g4TLHBiZcm0YDI+9HCzxz4ggJAfHklucyd81cyg3ljo6u1aRmxDU4x11CtEuWmTROUC+y4eQG/rn9nwDM7XMnk/b9qL4x4n71ZiCEI/X+AwR0xr80j9cixxHiFcKBwgM89MtDVJuqHR1dq5j3taqUYRqnJsmIsJmqaueY1rvvzD4e+uUhTIqJad2mcUe1J5SfgaAu0HOqo8MTAnTucIk6tTz2tw959fL/4KXzYuOpjSzatqhD7w9mKWCtlmTEmUkyImzGvC5AR57Wm12azdw1c6mormB41HCeGPYYmq2vqW8Ovw90LdprUoi2N2gWeAbCmSP0KTzJs6OfRYOGTw9/ahle7Ig8ZaM8lyDJiLCZjr7GSFFVEfesuYeCigKSgpN4acxLuB9aBWePg3cwDLjZ0SEKUcvTH4bcqr7etJixsVfw8JCHAXh558t8f+x7BwbXclIz4hokGRE2U9GBN8kr0Zdwx+o7SD+XTifvTrw+9nX83Xzgl+fUBkPvAA9fxwYpxIWG3QU6Tzi5HY6u5Y89/8jNPdSk+bFNj7Emc42DA2y+2mREVmB1ZpKMCJup7KAFrOWGcu75+R72n9lPsGcwb41/i0jfSNizAvL2g1egZXxeiHbFPxKG3Ka+XvMUKAoPD3mYa7peg1Ex8tAvD7Hp1CbHxthMll17ZZjGqUkyImymI/aMVFZXct/a+0jLT8Pfw5//jv8viUGJUK2H9epsGkY+oA7TCNEejforePhBdhoc+BqtRstTI59ifNx4qk3VPLDuAbZnb3d0lFaTdUZcgyQjwmY6Ws2I3qjngfUPsD1nO77uvrw57k26h3RX3/z9AzibAb7hMOxOh8YpRKN8w+CSe9TXa/8BxmrctG48O+pZxnQeQ5Wxirlr55KWl+bQMK0lNSOuQZIRYTO164y0/x+zyupK5q2fx+ZTm/HSefHa2Nfo06lmiXd9Ofzygvr6soelVkS0fyPmqr13BYdh93IA3HXuvDjmRYZHDaeiuoK7f76b1NxUBwfaNBmmcQ3t/y4hOqzKDjJMU2Yo45419/DLyV/w1Hny7yv+zaCIQbUNtv8XSnPUdUUGznJcoEJYyysQLn1Qfb1+EVRXAVh+vgdHDKbUUMqdq+9k86nNDgy0adIz4hokGRE20xGSkXOV5/jzj39mR84OfN19WTJuCSOiR9Q2qCyCTf9SX495DNw8HBOoEM019A7wj4KiLNj5vuWwt5s3r497nUtjLqXSWMnctXNZfWK14+Jsgvn3R7VJwWCUGTXOSpIRYTOWmpF2OpsmrzyPOT/OYe+ZvQR5BvHO+HcYHDm4bqMtr0DlOejUHfrOcEicQrSIuzeM/pv6esMLUFVqecvbzZv/XP4fJsRPoNpUzUO/PMQXR75wUKCN8zpvmLdSekecliQjwmbM6wJ4ubW/ZCSjKINZP8wi/Vw64d7hvD/xfXqF9arbqCQHtr6uvr7i/0Db/r4OIRo18BYIjoeyfDCvHFzDXefOc6Oe4w9Jf8CkmJi/ZT7v732/3S0d76HTWrZ/kqEa5yXJiLCZ9rpR3o6cHdz8/c2cLD1JjF8MSyctVafvXujHx8FQBjGDoftk+wcqRGvp3OGKJ9TXm15WZ4Sd/7ZWx4LhC5jVU62FemnnSzz161MYTAY7B9owjUZTuz+NXoZpnJUkI8Jm2mPNyBdHvuCO1XdQrC+mb1hf/nfV/+js3/nihsfWw94VoNHC1S/Jzryi4+r9B4gfBdWV8P3DcEHPh0aj4a+D/8rDQx5Gg4YVh1dwz8/3UKwvdlDAF5MiVucnyYiwmfa0zohJMfHv1H8zf8t8qk3VTIifwDsT3iHMO+zixtVV8N1D6ushf4bo/naNVYg2pdGoCbXWHY78CIcu3qNGo9Hwp55/4j9X/AdvN29+zf6VP37/R7JKshwQ8MVk4TPnJ8mIsJn2MkxToi/hwXUP8vaetwG4o+8dPD/6ebzcvOo/YcsrcOaIusDZ5Y/bMVIhbKRTCoy4T339wyOgL6u32ZjYMXww6QPCfcI5XnScm7+7ma2nt9ox0PqZf4fIzr3OS5IRYTPtYZjmUOEhbvj2BtZmrcVd684zlz7DfQPuQ6tp4Ef/bIY68wBgwjPgHWSvUIWwrdF/g8Au6lRf8894PbqHdOfjqz+mZ2hPzlad5c7Vd/LmrjcxKY6r17DUjEjPiNOSZETYjKP3pvky/Utu/v5mMksyifKN4oNJH3Bt4rWNn/TD39Wx9fhR0Od6+wQqhD14+MCkZ9XXW16F/EMNNg33CWfpxKVcl3QdCgqvpr3KvWvu5VzlOfvEegGpGXF+kowIm7EkI3ZeDr6iuoIFWxbwxOYnqDJWcWnMpXw6+VN6h/Vu/MSD38HhH0DrJkWrwjmlXAXJE8FkgO/+elEx6/m83Lx4csSTPDXiKTx1nmw6tYkZ385gd/5uOwZcE4sM0zg9SUaEzVQ6oIB1b8FeZnwzg5VHVqJBw9z+c3lt7GsEeQU1fmJZAXxbs3z28LnqGLsQzkajgUnPgZsXZGyE7W81ecq0pGn876r/EesfS3ZZNrf8cAtvpL1h1+m/3u7qraqyWpIRZyXJiLAJk0mhsmbRM3sM0xhMBt5Ie4M/fv9HMooz6OTdiTevfJM7+93ZcH2ImaLAV3OhNBfCUuCyR2werxAOExwP455UX//0f5C7v8lTuod0Z/nk5UyMn4hRMfL6rteZ9cMsMooybBqqmWWYRnpGnJYkI8Imqqpri91s3TNyvOg4s36Yxeu7XseoGJkQP4EvpnzB8Ojh1l3gt3fU4RmdB0x/Rx1bF8KZDbsTul0Jxir4/DYwVDZ5ir+HP8+Pfp5nRz2Lv7s/ewr2cP031/PxwY9tXtzqJQWsTk+SEWET5xea2SoZMRgNvLnrTaZ/PZ09BXvwd/fn2VHP8sLoFwj0DLTuInkH1ZVWAcYthMg+NolViHZFo4Gpr4NvJ8jbDz8vsPI0DVd3vZqVU1YyLGoYlcZK/rntn8xZNYdj547ZLFxZZ8T5STIibML8S8PDTYtO2/aFoKm5qUz/Zjqvpr2K3qRnRPQIVk5ZydVdr0ZjbeFpdRV8/md19kziFTDs7jaPU4h2yy8cptTsvbRtCRyxfufeSN9I/nvlf3lkyCN4u3mTmpfKH775A6+lvUaVsarNQ61dZ0SWg3dWkowIm7AseNbGvSLnKs+xcMtCZq2axbGiY4R4hfDsqGdZMm4Jkb6RzbvYz09C7h7wCYWpb4BW/jsIF5M8Hobeqb7+8m4ozbf6VK1Gyx97/pEvp3zJ6M6jqTZVs2TXEqZ/PZ1t2dvaNEyZ2uv85LevsIm2XvDMYDTw4f4PueqLq/j8yOcAXJd0HV9P/bp5vSFm+7+GX2t2MZ3yOvg3M5ERwllc+RSE91R39v38VjA2b5ZMtF80r17xKi9e9iJh3mFkFGfw55/+zP1r7+dE8Yk2CVEWPXN+kowIm6hdY6R1yYiiKKzLXMe0r6fx/I7nKdGXkByczHsT3uPJEU9aXxtyvlOpsPIO9fWwuyFlYqtiFKJDc/eC6e+Chx8c3wDfzWt0/ZH6aDQaJsRP4OupX3Nj9xvRaXSsy1rH1K+m8vyO5ymqKmpViLLOiPOTZETYhPmXRmuKV9Py0tS/sNapf2GFeIWwYPgCPp38KYMjB7fsokUn4eMboLpCnU0w/h8tjk8IpxHeA/7wjrpLdeoH6v5MLeDv4c9jwx7j82s/59KYS6k2VfPh/g+Z/MVk3t/7PhXVFS26rgzTOD9JRoRN1C4F3/wfsX0F+7jr57v40w9/YnvOdjy0HtzW+za+m/Yd05Ono9O2MMGpKoGPblDXEwnvqf41qHNr2bWEcDYpE2HCP9XXq+fDgW9bfKnEoETeGPcGS8YtITEwkXNV53hp50tctfIqlh1Yht6ob9b1JBlxfvKbWNhEZQuGafad2cebu95kXdY6AHQaHVO6TeHOvncS7RfduoBMRlhxm1qw6hsONy0Hr4DWXVMIZzPsLig4oq69s/J2mPMDRPdv8eVGxoxkWNQwvjn6DUt2LeF02Wme3f4s7+19j9v73M7UpKl46jybvI55S4kqSUacliQjwiasLWBVFIWt2Vt5d++7lgp8rUbL1QlXc1e/u+gS0KX1wSgK/PAwHPlRXQb7xk8gqA2uK4Sz0Whg0vNw9jgcXasOac75HkK6tviSblo3piVNY3LXyXyR/gVv7n6T3PJc/rHtH7y+63X+2OOPzOw+kwCPhv84kHVGnJ8kI8ImzDUjng0kIwajgdUnVvP+vvc5UHgAUHtCJiZM5I4+d9A1qOW//OowmeD7h9S/9ACmLYHOg9rm2kI4I50bXP8+vDMB8g/Ae1fD7G8hNLFVl3XXuTMjZQZTuk1hxeEVLN23lOyybP7z+394e8/bXJ98PTf1uKneXlBJRpyfJCPCJioa2JcmtyyXzw5/xudHPqegokBt4+bNdUnXcUvPW1o/HHM+kwm+/YtakIcGrn0Fek1ru+sL4ay8AuGWL2HptVBwCN67CmZ9A52SW31pT50nN/e4mRkpM1h1fBXv7XuPI2ePsHT/Uj488CGjO4/mxpQbuST6Esu+UrV708iiZ85KkhFhExXnDdMYTUa25WxjxeEVrM1ci1FR3wvzDmNGygxuTLmx6V11m8tkVDe/2/WROkNg6hvQ74a2/QwhnJl/JMz+Dj64Vl0y/v2r4JavIaJnm1zeXevONYnXMLnrZDae2sgH+z9gW/Y21metZ33WeuID4rk++XomJ07G212tK5F1RpyXRlGaOaHcAYqLiwkMDKSoqIiAACk67Aj++f0B3tq6g2F9j3JGs4WcshzLewPDB3Jj9xsZ22Us7jr3tv9wo0FdTXLPZ6DRwXX/hT7T2/5zhHAFZWfgwymQU7Na8Z++hKi+NvmoY0XHWH5wOV8d/YoyQxmg1pxcEnEpP22Pg/IU0p+Z3PxFDoXDWHv/lmREtKnCykJ+PvEzr+/4jDPGg5bj/h7+XJVwFTNSZpAc3Pqu3gaVFcBnsyFjI2jd1LUTek213ecJ4QrKC+HDaZCdpi6ONm0J9LjGZh9XZijj26PfsjJ9JfvP7LccN1X788feU7i66yT6hPWRpKQDkGRE2E1RVRFrM9eyKmMV27K3WYZhFEVDF+9+3Df0Jq7ocoVVU/haJXsXfHIzFGWpvzD/8I6sripEW6k4B8v/qCb6AKMfhjGP2nxPp8NnD7Py8Bd8uPcLtG5lluMxfjGMjx/PxPiJ9AjpIYlJOyXJiLCpU6WnWJe5jrVZa0nNTbUkIAA9Q3tScbYPew4lsGDSCGaPTLB9QLs/g6/vU1dWDekKN3wM4d1t/7lCuBJjNax+An6t2e03eaI6DOrVgm0ZmkFRFLo9/g34HGLy8Fy25myos5prlG8Ul8dezuVdLmdQxCDctTYY/hUtYu39WwpYhVUMRgO/5/3O5tOb2XRqE4fPHq7zfnJwMhPiJzAxfiJdArpw2/s7UKrzWr03TZP05bDmSXULdFCXeP/D2+AdZNvPFcIV6dxg4iKI6gdf3w+HV8FbY+EPb0H0AJt9rEajwdvdk9LSnjzY7x6evUzLxpMbWZWxik2nNpFdls1HBz/io4Mf4e/hz8jokYyMGcmI6BGE+4TbLC7RdiQZEfVSFIX0c+lsz9nOr9m/sj17O+XV5Zb3dRodAyMGqn+NxF5OZ//Odc6vrG793jRNOr5R7Q05e1z996i/wuWPQ0uXixdCWKffDRCWrA7bnDmiJiQj7oMxfwd3b5t8pJe7jtKqaiqrjXi7+TI+fjzj48dTWV3Jr9m/si5rHeuz1lNYWciqjFWsylgFqH8ojYweyZDIIQyMGIivu69N4hOtI8mIAMBoMpJ+Lp3f835ne852dubupLCysE6bUK9QRkSPYETMCC6NvrTR6bhtsVFegyqL1b0zdr6n/jsgBiYvhuTxbf9ZQoj6xQyEOzeoqxvv/Rw2L4aD38K1r0Lc8Db/OK+afa4u3LnXy82LMbFjGBM7BqPJyJ6CPWw6tYktp7ewt2Avh88e5vDZw7y37z10Gh29wnoxJGIIgyMH07dT30ZXfhX2I8mIiyqqKmJfwT525e8iLT+N3fm7KTWU1mnj7eZN/079GRo1lJHRI0kJSbEsQtSUhhY9axWTEfasUIdlik+pxwbNgSufkn1mhHAE3zB1w8ne0+HbB+FMOrw3CQbeovaSBLTdIobWbJan0+roH96f/uH9mTtgLmcrz7L19Fa1dzdnO6dKT7E7fze783fzzt530KAhMShRPadTf/qE9SE+MN7q33Oi7Ugy4gKKqoo4VHiIA4UH2Fuwl70FezlZevKidj5uPvTp1IfBEYMZGjmUPmF9WrwOSEs2ymuQoqh/ca19Rl2eGiA4QV1RNWFU668vhGid7ldB3Aj46f/g9w8hdSnsXg5Db4eRD4JvaKs/wvy7pDkLnwV7BXNV16u4qutVAJwuPc32nO3syNnB73m/k1WSRfq5dNLPpbPi8AoAfN196Rnak96hvekZ2pOUkBS6+Hdp+W7hwiqSjDgRvVFPRnEGR88dJf1cOocLD3Pw7ME6C46dL9Y/lt5hvRkQPoAB4QPoFtQNN23b/EiYu1Jb1TNiMkH6z7B+EZxOVY95BcLIv8Cwu8HDpw0iFUK0Ce8gmPIq9L8J1jwFmVthyyvw2/sw/B4YemerkhKvNlgSPtovmqndpjK121QACioK2JWn9g7vyt/FgTMHKDOUsSNnBztydtR+aW7eJAUnkRKcQlJwEt2CupEYlEiIV0iLYxF1STLSARVVFXG86DgZxRlkFGWQUZzBsaJjZBZn1plie74YvxhSglPoFdaL3qG96RXWi0BP203HM3eltqhmpLwQ0pbBjndqi1PdfeGSu9UiOZkpI0T7FTcC5vyg/iGx5inI2Q2/PAebFqt7Qw29HWIGqTsEN4M1wzTNFeYdxti4sYyNGwtAtamao+eOsu/MPvYW7OVg4UGOnD1CRXWFZXjnfCFeIXQN7Ep8YDwJAQmW5yi/qDb7w85VyHerHdIb9eSU5XCq9BSnS09zqvQUWSVZZJZkklWSRYm+pMFz/dz9LFl7UnAS3UO6kxycjL+Hvx2/gvP2prF2mMZYDSc2w+5PYe8KqK5Uj3sGwIA/waUPgJ9M0ROiQ9BoIOlKSBwLB76CTf9SFyXc/Yn6iOoHA2epq7ha+f/aFsnIhdy0bqSEpJASksJ1SdcBanH/iZITHCo8xKHCQ5ae55OlJymsLKSwspDfcn+rex2NG9F+0cT6x9LZvzOx/rHE+MUQ7RdNjF8MAR4BskjbBSQZsbPK6kryK/LJL88nryKPvLI8cspzyCnLIbcsl5yyHPIr8lFofC26CJ8I4gPjiQ+IJyEwgfiAeBKDEonwiXD4D7nRpKCvtqKAtVoPx3+B/V/Bwe+g4rzZOxF9YOifoc/14CFT8YTokLRatTek51Q4tRN2vA17V6qJyXfz4PuHoMsI6Hmtmpg0UvBqqRnR2y4ZqY9Oq6NrYFe6BnZlUsIky/FyQznHi45zrOhYbU91cQaZxZlUGavILMkksySz3mv6uvsS6RNJpK/6iPCNINInknCfcDr5dCLcO5xAz0CH/y63J0lGWklRFEoMJZyrPEdhZSFnK89ytuoshZWFnKk4w5nKM5ypOENBRQEFFQUU64utuq63mzdRvlGWTDrWP9by6OzfGW8328zlbwvnF5jVSUaM1ereFhkbIWMTZP4K+vNm8HiHqIVwA26B2KHN7sYVQrRTGg10Hqw+xj+jDsPuWwmnf4cTm9THDw9Dpx5qUXr8pRB3aZ0aEy879Iw0h4+7D73CetErrFed4ybFRF55HlklWXUe2aXZnC47TUFFAWWGMo4WHeVo0dEGr++udSfMO4ww7zBCvUPVZ69Qgr2CCfEKIcQrhGCvYII9gwnyDLLNpqN2JMkIYDAZKNOXUWoopcxQRom+RH0Y1OdifTHFVcWW5yJ9EUVVRZyrOkdRVVGDdRoN8dR5qhmwdyfCfcIt2XGkj5ohR/tFE+wZ3GGz4kqDER1GEjWn8dz/qbrbZ/YuNRHR150+jF8EdJ+s/mUUd6m6wqMQwnn5hsLI+9XHuUw48A3s/xqyflVny+UfgO3/VduGpahDOlF96VERSACezZpN4whajdbyO31I5JCL3q+sriS7LJucMrVHPKe8bq94fnk+Z6vOYjAZyC7LJrss26rP9XX3JcgziEDPQAI9AgnwDLA8B3gE4O/hX/tw98fPww8/dz983X3xdvN2+P2mRXvTvPbaa7zwwgvk5OTQr18/XnnlFYYOHdpg+88++4wnnniCjIwMkpKSeO6557jqqqus/jxb7U3z5x//zK78XVQaK1t9LW83bzVT9Qyuk7lemNV28unkHOOFigJVxVCcra75cS4TCo/CmaMY8o9gOnMcT031xed5BapJh/mvn/BeNt9oSwjRAZSdUXtIMmoeefvrbVbiFop/dAqEJqqP4AQI7KwO8fhFOMUKzHqjnvyK/Dq96uZednMPvPm5SF+ESWn5DCNQV9T2dffltbGv0T+8f9t8ETVstjfN8uXLmTdvHkuWLGHYsGEsXryYCRMmcOjQIcLDLy5E2rJlCzfeeCOLFi1i8uTJfPTRR0ydOpXU1FR69+7d3I9vUwaToU4i4u3mjY+bD/4e/pZM0s/Dz/LvQM9AAjwCLK+DPIPUh1eQ7XektQWTCQzl6kNfVvNcriYZVcXqSqdVxVBxFsoKoPyM+igrgJLsi3s5argDaKAML3y7DIDIvjV/3fSD8B5O8ctCCNHGfEOh5xT1AervmVOpaq9qzi6KjqcSWHkK/+ozkLlFfVxIowP/SPDtBD6h6qJsPmHgE6L+IeQZoC6Q6BkAnn7qLD0PH3Cveejc28XwsIfOgxi/GGL8Yppsa1JMlOhLOFt51tJbX6wvtjybe/TNPf3mh3kkwKSYMCpGivXFeOg87PDV1a/ZPSPDhg1jyJAhvPrqqwCYTCZiY2O57777+Pvf/35R+5kzZ1JWVsa3335rOXbJJZfQv39/lixZUu9nVFVVUVVVZfl3cXExsbGxbd4z8s3/HkFbchovRYcXWtxo4C90K75F9f/4KjXvKXX/rVz43nmvldpj6r/VZw0mNErNMwoaxYQGE1rFhEYxokFBqxjVB0a0SjU6xYhOMaivTQZ0ihE3pQo3kx43RY9OqafnopkqdP4Ue4RT5B5OoVcshZ6xZBDFR+numPxj2PLYla3+DCGEeHvjMf793U5GhZxjbEQpoZVZhFRlEVx1igB9Af6GArS0bgjHhJZqrQfVGg+qtR4YNe4YNe6YNLqa126YNLo6DwUdJo0WBS2KRoup5llBU/uMFjTmO4F6zHzTUNBg/ked1xo4/86iWF7XvdtYfQOvJ8lSUKjCRKXGSAVG+k/4O/Fd+1h7RavYpGdEr9ezc+dOHn30UcsxrVbLuHHj2Lp1a73nbN26lXnz5tU5NmHCBL788ssGP2fRokU8+eSTzQmtRZIyfqF79QGbf05HUK54Uo4nlXhQovhQjA8lijcl+FCk+FKoBFCIP4WKP4UEkKsEk6MEU4EXlNV/zd7+Xvb9IoQQTivUz4MSfPi+0IfvCwGS67yvxUQoRURrzhCqKSZEU0II6nMwpfhryvGnvOa5Aj9NBd5U4UMVbhqT5Roepko8qKSVeU2HdLDwVujqmM9uVjJSUFCA0WgkIiKizvGIiAgOHjxY7zk5OTn1ts/JqX9VUIBHH320TgJj7hlpa0Up09l6Lqued5rupqs/G63nPM35GW9tG+WCNuaM2JwxK2ix9KloNJjQWY5bMm6NFhO6muxbi0njpmboNRm7msW7qZm9Vs3qjedn/VpPqrWeGLSeYMVeDIE1j4QmW4JWo2Fi70grWgohRNMm9Y6isMxAYVlV043PU1LzaIzWZMDdVIGbyYDOVIWbosfNVIXOZECrqL3KWpOhpqfZhKam91mrGNEopvOOmdAoJqjTm63U9F4D5l7vmuPUHDP3gkPdvhAzS9uLeukvvhNZN8hU/x0sIbyLVWfbQrucuuDp6Ymnp+1rMIZd/5DNP0MIIUTrebnruO1Sa/4UEh1Rs6YxhIWFodPpyM3NrXM8NzeXyMj6/wqOjIxsVnshhBBCuJZmJSMeHh4MGjSINWvWWI6ZTCbWrFnD8OHD6z1n+PDhddoDrF69usH2QgghhHAtzR6mmTdvHrNmzWLw4MEMHTqUxYsXU1ZWxpw5cwC45ZZbiImJYdGiRQD85S9/4bLLLuOll17i6quv5pNPPuG3337jv//9b9t+JUIIIYTokJqdjMycOZP8/Hzmz59PTk4O/fv3Z9WqVZYi1czMTLTnLWI1YsQIPvroI/7v//6Pxx57jKSkJL788kuHrzEihBBCiPahRSuw2putVmAVQgghhO1Ye/+WdbiFEEII4VCSjAghhBDCoSQZEUIIIYRDSTIihBBCCIeSZEQIIYQQDiXJiBBCCCEcSpIRIYQQQjiUJCNCCCGEcKh2uWvvhczrshUXFzs4EiGEEEJYy3zfbmp91Q6RjJSUlAAQGxvr4EiEEEII0VwlJSUEBgY2+H6HWA7eZDJx+vRp/P390Wg0jg7HoYqLi4mNjSUrK0uWxrcx+V7bh3yf7UO+z/Yh3+e6FEWhpKSE6OjoOvvWXahD9IxotVo6d+7s6DDalYCAAPlBtxP5XtuHfJ/tQ77P9iHf51qN9YiYSQGrEEIIIRxKkhEhhBBCOJQkIx2Mp6cnCxYswNPT09GhOD35XtuHfJ/tQ77P9iHf55bpEAWsQgghhHBe0jMihBBCCIeSZEQIIYQQDiXJiBBCCCEcSpIRIYQQQjiUJCNCCCGEcChJRpxEVVUV/fv3R6PRkJaW5uhwnEpGRga33XYbCQkJeHt7k5iYyIIFC9Dr9Y4OrcN77bXXiI+Px8vLi2HDhrF9+3ZHh+R0Fi1axJAhQ/D39yc8PJypU6dy6NAhR4fl1J599lk0Gg0PPPCAo0PpMCQZcRIPP/ww0dHRjg7DKR08eBCTycSbb77Jvn37+Ne//sWSJUt47LHHHB1ah7Z8+XLmzZvHggULSE1NpV+/fkyYMIG8vDxHh+ZUfvnlF+69915+/fVXVq9ejcFgYPz48ZSVlTk6NKe0Y8cO3nzzTfr27evoUDoWRXR433//vdK9e3dl3759CqD8/vvvjg7J6T3//PNKQkKCo8Po0IYOHarce++9ln8bjUYlOjpaWbRokQOjcn55eXkKoPzyyy+ODsXplJSUKElJScrq1auVyy67TPnLX/7i6JA6DOkZ6eByc3O5/fbb+fDDD/Hx8XF0OC6jqKiIkJAQR4fRYen1enbu3Mm4ceMsx7RaLePGjWPr1q0OjMz5FRUVAcjPrw3ce++9XH311XV+roV1OsSuvaJ+iqIwe/Zs7rrrLgYPHkxGRoajQ3IJ6enpvPLKK7z44ouODqXDKigowGg0EhERUed4REQEBw8edFBUzs9kMvHAAw8wcuRIevfu7ehwnMonn3xCamoqO3bscHQoHZL0jLRDf//739FoNI0+Dh48yCuvvEJJSQmPPvqoo0PukKz9Pp/v1KlTTJw4keuvv57bb7/dQZEL0TL33nsve/fu5ZNPPnF0KE4lKyuLv/zlLyxbtgwvLy9Hh9Mhyd407VB+fj5nzpxptE3Xrl2ZMWMG33zzDRqNxnLcaDSi0+m4+eabWbp0qa1D7dCs/T57eHgAcPr0acaMGcMll1zC+++/j1YruXxL6fV6fHx8WLFiBVOnTrUcnzVrFufOneOrr75yXHBOau7cuXz11Vds2LCBhIQER4fjVL788kumTZuGTqezHDMajWg0GrRaLVVVVXXeExeTZKQDy8zMpLi42PLv06dPM2HCBFasWMGwYcPo3LmzA6NzLqdOneLyyy9n0KBB/O9//5NfLG1g2LBhDB06lFdeeQVQhxC6dOnC3Llz+fvf/+7g6JyHoijcd999fPHFF6xfv56kpCRHh+R0SkpKOHHiRJ1jc+bMoXv37jzyyCMyJGYFqRnpwLp06VLn335+fgAkJiZKItKGTp06xZgxY4iLi+PFF18kPz/f8l5kZKQDI+vY5s2bx6xZsxg8eDBDhw5l8eLFlJWVMWfOHEeH5lTuvfdePvroI7766iv8/f3JyckBIDAwEG9vbwdH5xz8/f0vSjh8fX0JDQ2VRMRKkowI0YTVq1eTnp5Oenr6RUmedCy23MyZM8nPz2f+/Pnk5OTQv39/Vq1adVFRq2idN954A4AxY8bUOf7ee+8xe/Zs+wckRD1kmEYIIYQQDiUVeEIIIYRwKElGhBBCCOFQkowIIYQQwqEkGRFCCCGEQ0kyIoQQQgiHkmRECCGEEA4lyYgQQgghHEqSESGEEEI4lCQjQgghhHAoSUaEEEII4VCSjAghhBDCof4f8t/LL2QsgQoAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.stats as sp\n",
    "\n",
    "x = np.linspace(-5, 5, 100)\n",
    "\n",
    "plt.title('Kurtosis')\n",
    "plt.plot(x, sp.uniform.pdf(x, -3, 6), label='kertosis < 0')\n",
    "plt.plot(x, sp.norm.pdf(x), label='kertosis = 0')\n",
    "plt.plot(x, sp.laplace.pdf(x), label='kertosis > 0')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e442b624",
   "metadata": {},
   "source": [
    "### 2.4. Statical data types"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "9f95cadf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "5a6965c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>weather_condition</th>\n",
       "      <th>wind_strength</th>\n",
       "      <th>temperature_c</th>\n",
       "      <th>rainfall_inches</th>\n",
       "      <th>humidity_percent</th>\n",
       "      <th>pressure_hpa</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Sunny</td>\n",
       "      <td>Light Breeze</td>\n",
       "      <td>8.2</td>\n",
       "      <td>0.13</td>\n",
       "      <td>48.8</td>\n",
       "      <td>1016.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Snowy</td>\n",
       "      <td>Gale</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.29</td>\n",
       "      <td>89.6</td>\n",
       "      <td>1009.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Rainy</td>\n",
       "      <td>Strong Wind</td>\n",
       "      <td>7.3</td>\n",
       "      <td>0.01</td>\n",
       "      <td>100.0</td>\n",
       "      <td>1003.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Cloudy</td>\n",
       "      <td>Light Breeze</td>\n",
       "      <td>21.6</td>\n",
       "      <td>0.62</td>\n",
       "      <td>49.3</td>\n",
       "      <td>1006.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Sunny</td>\n",
       "      <td>Calm</td>\n",
       "      <td>12.0</td>\n",
       "      <td>1.09</td>\n",
       "      <td>38.6</td>\n",
       "      <td>1016.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  weather_condition wind_strength  temperature_c  rainfall_inches  \\\n",
       "0             Sunny  Light Breeze            8.2             0.13   \n",
       "1             Snowy          Gale            1.6             0.29   \n",
       "2             Rainy   Strong Wind            7.3             0.01   \n",
       "3            Cloudy  Light Breeze           21.6             0.62   \n",
       "4             Sunny          Calm           12.0             1.09   \n",
       "\n",
       "   humidity_percent  pressure_hpa  \n",
       "0              48.8        1016.5  \n",
       "1              89.6        1009.4  \n",
       "2             100.0        1003.3  \n",
       "3              49.3        1006.9  \n",
       "4              38.6        1016.0  "
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Simulated weather data from lesson 11 activity\n",
    "url = 'https://media.githubusercontent.com/media/gperdrizet/fullstack-2605/refs/heads/main/data/weather.csv'\n",
    "df = pd.read_csv(url)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "57b21b41",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.DataFrame'>\n",
      "RangeIndex: 365 entries, 0 to 364\n",
      "Data columns (total 6 columns):\n",
      " #   Column             Non-Null Count  Dtype  \n",
      "---  ------             --------------  -----  \n",
      " 0   weather_condition  365 non-null    str    \n",
      " 1   wind_strength      365 non-null    str    \n",
      " 2   temperature_c      365 non-null    float64\n",
      " 3   rainfall_inches    365 non-null    float64\n",
      " 4   humidity_percent   365 non-null    float64\n",
      " 5   pressure_hpa       365 non-null    float64\n",
      "dtypes: float64(4), str(2)\n",
      "memory usage: 17.2 KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "154ec2f1",
   "metadata": {},
   "source": [
    "#### 2.4.1. Discrete vs continuous variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "a1820311",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8eDEA1Yeb1qxZE/PmzYOXlxcePHgAFxcXlC9fHvfv38fevXsxbNgwTJo0CdbW1qhZsyYmTZqEqKgoGBoa4vfff8/13pDs1x47diycnJygqamJvn37Fmh/fH190bp1a9jY2GDo0KGoUaMGYmJiEBYWhn/++QeXLl0q6CECAAwcOBBbtmyBp6cnzp07hzZt2iA5ORlHjx7FyJEj4ezsjO7du6N9+/b47rvv8ODBA9ja2uLPP//EH3/8gfHjx6sMbpBfs2fPRmBgINq0aYORI0cqC5L69evj8uXL71zXzs4OmpqamD9/PhISEqCrq6t8zsN/DRs2DD///DM8PDwQEREBS0tL7N69G2fOnMGyZcty3MdERFTatG3bFsOHD4ePjw8uXryITp06QVtbG3fu3IG/vz+WL1+Onj17qu315HI5AgMD4e7uDnt7exw+fBgHDx7E9OnTld3Z1JGpU6dO0NHRQffu3TF8+HAkJSVh/fr1qFKlSo4vCps0aYI1a9Zg3rx5qFWrFqpUqYIOHTqgU6dOqFatGgYPHozJkydDU1MTGzZsQOXKlVW+nHuXyZMnY9++fejWrRs8PDzQpEkTJCcn48qVK9i9ezcePHiASpUqfdjBpNKt6AeYo9LOy8tLABAtW7bMsWzPnj0CgChfvnyuQ0L//vvvonXr1kJfX1/o6+sLa2trMWrUKHHr1i1lm+vXrwtHR0dhYGAgKlWqJIYOHaoc1nnjxo3KdhkZGWLMmDGicuXKQiaTKYfVzB5eeeHChTleH4Dw9vZWmXfv3j0xcOBAoVAohLa2tqhataro1q2b2L17t7JN9vCcf/31V76P06tXr8R3330nrKyshLa2tlAoFKJnz57i3r17yjYvX74UEyZMEObm5kJbW1vUrl1bLFy4UDkc9tu5R40aleM1/jtctRBCnDhxQjRp0kTo6OiIGjVqiLVr1+Y67Ghu665fv17UqFFDOTR29lCr/x3qWgghYmJixKBBg0SlSpWEjo6OsLGxUfn9CFHw3wURUXGV1+MV1q1bJ5o0aSL09PRE+fLlhY2NjZgyZYp48uSJsk316tVF165dc6yb23t7bu+b7u7uQl9fX9y7d0906tRJlCtXTpiamgpvb2+RmZmp1kxCCLFv3z7RsGFDIZfLhaWlpZg/f77yEQ5vD1MdHR0tunbtKsqXLy8AqJwnIiIihL29vdDR0RHVqlUTS5YsyXOo67xyvHz5Unh5eYlatWoJHR0dUalSJdGyZUuxaNEikZaWlus6RDIheEcxERERUUnl4eGB3bt3IykpSeooRMUe7/khIiIiIqIygcUPERERERGVCSx+iIiIiIioTOA9P0REREREVCbwyg8REREREZUJLH6IiIiIiKhMYPFDZcKCBQtgbW2NrKysPNs8ePAAMpkMmzZtUs6bNWsWZDJZESSUxrRp02Bvby91DCKiEi8/5xkptWvXDu3atZM6RqFo0aIFpkyZInUMKiFY/FCpl5iYiPnz52Pq1KnQ0Cg9/+SvX7+OWbNm4cGDBx+8jfHjx+PSpUvYt2+f+oIREZUxxeU8o47zQkk0depU+Pr6Ijo6WuooVAKUnk+CRHnYsGEDMjIy4ObmVuB1v//+e7x+/boQUn2869evY/bs2R91klMoFHB2dsaiRYvUF4yIqIz5mPOMOr3rvPDnn3/izz//LPpQRcDZ2RmGhoZYvXq11FGoBGDxQ6Xexo0b8eWXX0Iulxd4XS0trQ9a70NkZGQgLS2tSF7rbb1798bp06fx999/F/lrExGVBh9znikqOjo60NHRkTpGodDQ0EDPnj2xZcsWcBBjeh8WP1Sq3b9/H5cvX4ajo6PK/Pj4eHh4eMDIyAjGxsZwd3dHfHx8jvVzu+cnKCgIrVu3hrGxMQwMDFCnTh1Mnz5dpU1KSgpmzZqFTz/9FHK5HGZmZujRowfu3bsH4H/3Fy1atAjLli1DzZo1oauri+vXrwMAbt68iZ49e8LExARyuRxNmzZV6Zq2adMm9OrVCwDQvn17yGQyyGQyhISEKNscPnwYbdq0gb6+PsqXL4+uXbvi2rVrOfYx+9j88ccf+TyqRESULa/zTFZWFpYvXw4bGxvI5XJUrlwZnTt3xvnz55VtMjIyMHfuXOU5wNLSEtOnT0dqaqrKtiwtLdGtWzecPn0azZs3h1wuR40aNbBlyxZlm/edF/57z09ISAhkMhl27dqFH374AZ988gnkcjk6duyIu3fv5nh9Dw+PHPue231EsbGxGDx4MExNTSGXy2Fra4vNmzertMl+7bfPWUDu995GR0dj0KBB+OSTT6CrqwszMzM4OzvnuLr1+eef4+HDh7h48WKOnERv05I6AFFhCg0NBQA0btxYOU8IAWdnZ5w+fRrffvst6tati71798Ld3f2927t27Rq6deuGhg0bYs6cOdDV1cXdu3dx5swZZZvMzEx069YNwcHB6Nu3L8aNG4eXL18iKCgIV69eRc2aNZVtN27ciJSUFAwbNgy6urowMTHBtWvX0KpVK1StWhXTpk2Dvr4+du3aBRcXF/z+++/46quv8Nlnn2Hs2LFYsWIFpk+fjrp16wKA8r+//fYb3N3d4eTkhPnz5+PVq1dYs2YNWrdujcjISFhaWiozGBkZoWbNmjhz5gwmTJjwUcebiKisye08AwCDBw/Gpk2b8MUXX2DIkCHIyMjAqVOncPbsWTRt2hQAMGTIEGzevBk9e/bExIkTER4eDh8fH9y4cQN79+5V2d7du3fRs2dPDB48GO7u7tiwYQM8PDzQpEkT1K9f/73nhbz89NNP0NDQwKRJk5CQkIAFCxagf//+CA8PL/CxeP36Ndq1a4e7d+9i9OjRsLKygr+/Pzw8PBAfH49x48YVeJuurq64du0axowZA0tLS8TGxiIoKAiPHj1SOZc1adIEAHDmzBk0atSowK9DZYggKsW+//57AUC8fPlSOS8gIEAAEAsWLFDOy8jIEG3atBEAxMaNG5Xzvb29xdt/JkuXLhUAxLNnz/J8zQ0bNggAYsmSJTmWZWVlCSGEuH//vgAgDA0NRWxsrEqbjh07ChsbG5GSkqKyXsuWLUXt2rWV8/z9/QUAcfz4cZX1X758KYyNjcXQoUNV5kdHRwsjI6Mc84UQolOnTqJu3bp57hMREeUut/PMsWPHBAAxduzYHO2zzwMXL14UAMSQIUNUlk+aNEkAEMeOHVPOq169ugAgTp48qZwXGxsrdHV1xcSJE5Xz8jovCCFE27ZtRdu2bZU/Hz9+XAAQdevWFampqcr5y5cvFwDElStXVF7f3d39vdtctmyZACC2bt2qnJeWliYcHByEgYGBSExMVHnt/+bMPjdmn4f//fdfAUAsXLgwx2vnRkdHR4wYMSJfbansYrc3KtVevHgBLS0tGBgYKOcdOnQIWlpaGDFihHKepqYmxowZ897tGRsbA3jTRSyv4Ux///13VKpUKdft/bcLnaurKypXrqz8OS4uDseOHUPv3r3x8uVLPH/+HM+fP8eLFy/g5OSEO3fuICoq6p0Zg4KCEB8fDzc3N+X6z58/h6amJuzt7XH8+PEc61SoUAHPnz9/3+4TEdF/5Hae+f333yGTyeDt7Z2jffZ54NChQwAAT09PleUTJ04EABw8eFBlfr169dCmTRvlz5UrV0adOnU++n7NQYMGqdwLlP0aH7LdQ4cOQaFQqAz8oK2tjbFjxyIpKQknTpwo0Pb09PSgo6ODkJAQ/Pvvv+9tz3MZ5QeLHypzHj58CDMzM5UTFQDUqVPnvev26dMHrVq1wpAhQ2Bqaoq+ffti165dKoXQvXv3UKdOHWhpvb9XqZWVlcrPd+/ehRACM2bMQOXKlVWm7JNobGzsO7d5584dAECHDh1ybOPPP//MdX0hRKl+nhERUVG6d+8ezM3NYWJikmebhw8fQkNDA7Vq1VKZr1AoYGxsjIcPH6rMr1atWo5tVKhQIV9Fwbv8d7sVKlQAgA/a7sOHD1G7du0cw31nd7377z69j66uLubPn4/Dhw/D1NQUn332GRYsWJDnkNY8l1F+8J4fKtUqVqyIjIwMvHz5EuXLl//o7enp6eHkyZM4fvw4Dh48iMDAQOzcuRMdOnTAn3/+CU1NzQJv723ZRdSkSZPg5OSU6zr/PVH+V/Y2fvvtNygUihzLcyvK/v33X1SqVClfmYmI6H8+9jyT3w/reZ1fxEeObpaf7eaVMTMzs8Dnvfdt77/Gjx+P7t27IyAgAEeOHMGMGTPg4+ODY8eO5bi3Jz4+nucyei8WP1SqWVtbA3gzGk/Dhg0BANWrV0dwcDCSkpJUrv7cunUrX9vU0NBAx44d0bFjRyxZsgQ//vgjvvvuOxw/fhyOjo6oWbMmwsPDkZ6eDm1t7QLlrVGjBoA33QT+O3LQf+V18sgeUKFKlSrv3Ua2+/fvw9bWtgBJiYgIyP08U7NmTRw5cgRxcXF5Xv2pXr06srKycOfOHZVBCWJiYhAfH4/q1asXOEthXfWoUKFCriOiPnz4UHneAt7s0+XLl5GVlaVy9efmzZvK5dnbA5Bjm3ldGapZsyYmTpyIiRMn4s6dO7Czs8PixYuxdetWZZuoqCikpaW9d4AHInZ7o1LNwcEBAFSGFu3SpQsyMjKwZs0a5bzMzEysXLnyvduLi4vLMc/Ozg4AlEOTurq64vnz51i1alWOtu/7hq5KlSpo164dfv75Zzx9+jTH8mfPnin/X19fH0DOk4eTkxMMDQ3x448/Ij09/Z3bAICEhATcu3cPLVu2fGc2IiLKKbfzjKurK4QQmD17do722eeBLl26AACWLVumsnzJkiUAgK5duxY4S17nhY9Vs2ZNnD17VuVZdAcOHMDjx49V2nXp0gXR0dHYuXOncl5GRgZWrlwJAwMDtG3bFsCbIkhTUxMnT55UWf+/Dyl99eoVUlJScmQpX758juHAIyIiAIDnMnovXvmhUq1GjRpo0KABjh49im+++QYA0L17d7Rq1QrTpk3DgwcPUK9ePezZswcJCQnv3d6cOXNw8uRJdO3aFdWrV0dsbCxWr16NTz75BK1btwYADBw4EFu2bIGnpyfOnTuHNm3aIDk5GUePHsXIkSPh7Oz8ztfw9fVF69atYWNjg6FDh6JGjRqIiYlBWFgY/vnnH1y6dAnAm6JLU1MT8+fPR0JCAnR1ddGhQwdUqVIFa9aswYABA9C4cWP07dsXlStXxqNHj3Dw4EG0atVKpTA7evSocvhvIiIqmNzOM+3bt8eAAQOwYsUK3LlzB507d0ZWVhZOnTqF9u3bY/To0bC1tYW7uzvWrVuH+Ph4tG3bFufOncPmzZvh4uKC9u3bFzjLu84LH2PIkCHYvXs3OnfujN69e+PevXvYunWryqMbAGDYsGH4+eef4eHhgYiICFhaWmL37t04c+YMli1bpuwWaGRkhF69emHlypWQyWSoWbMmDhw4kOOe1Nu3b6Njx47o3bs36tWrBy0tLezduxcxMTHo27evStugoCBUq1aNw1zT+0k2zhxREVmyZIkwMDAQr169Us578eKFGDBggDA0NBRGRkZiwIABIjIy8r1DXQcHBwtnZ2dhbm4udHR0hLm5uXBzcxO3b99Wec1Xr16J7777TlhZWQltbW2hUChEz549xb1794QQ/xvOM6/hO+/duycGDhwoFAqF0NbWFlWrVhXdunUTu3fvVmm3fv16UaNGDaGpqZlj2NDjx48LJycnYWRkJORyuahZs6bw8PAQ58+fV9lGnz59ROvWrQt0TImI6H9yO89kZGSIhQsXCmtra6GjoyMqV64svvjiCxEREaFsk56eLmbPnq08V1hYWAgvLy+VRx0I8Wao6a5du+Z43f8ONS1E3ueFvIa69vf3V1n/v8NNZ1u8eLGoWrWq0NXVFa1atRLnz5/P9fVjYmLEoEGDRKVKlYSOjo6wsbHJsS0hhHj27JlwdXUV5cqVExUqVBDDhw8XV69eVXnt58+fi1GjRglra2uhr68vjIyMhL29vdi1a5fKtjIzM4WZmZn4/vvvc7wO0X/JhPjIO+WIirmEhATUqFEDCxYswODBg6WOU6xER0fDysoKO3bs4JUfIqIPxPOMtAICAtCvXz/cu3cPZmZmUsehYo73/FCpZ2RkhClTpmDhwoV5PpunrFq2bBlsbGxY+BARfQSeZ6Q1f/58jB49moUP5Quv/BARERERUZnAKz9ERERERFQmsPghIiIiIqIyocDFz8mTJ9G9e3eYm5tDJpMhICAgR5sbN27gyy+/hJGREfT19dGsWTM8evRIuTwlJQWjRo1CxYoVYWBgAFdXV8TExHzUjhAREREREb1LgYuf5ORk2NrawtfXN9fl9+7dQ+vWrWFtbY2QkBBcvnwZM2bMgFwuV7aZMGEC9u/fD39/f5w4cQJPnjxBjx49PnwviIiIiIiI3uOjBjyQyWTYu3cvXFxclPP69u0LbW1t/Pbbb7muk5CQgMqVK8PPzw89e/YEANy8eRN169ZFWFgYWrRo8d7XzcrKwpMnT1C+fHnIZLIPjU9ERAUkhMDLly9hbm4ODQ32nH4bz01ERNIoyLlJS50vnJWVhYMHD2LKlClwcnJCZGQkrKys4OXlpSyQIiIikJ6eDkdHR+V61tbWqFatWp7FT2pqKlJTU5U/R0VFoV69euqMTkREBfD48WN88sknUscoVp48eQILCwupYxARlVn5OTeptfiJjY1FUlISfvrpJ8ybNw/z589HYGAgevTogePHj6Nt27aIjo6Gjo4OjI2NVdY1NTVFdHR0rtv18fHB7Nmzc8x//PgxDA0N1bkLRET0DomJibCwsED58uWljlLsZB8TnpuIiIpWQc5Nar/yAwDOzs6YMGECAMDOzg6hoaFYu3Yt2rZt+0Hb9fLygqenp/Ln7B00NDTkCYaISALs1pVT9jHhuYmISBr5OTeptfipVKkStLS0cnRJq1u3Lk6fPg0AUCgUSEtLQ3x8vMrVn5iYGCgUily3q6urC11dXXVGJSIiIiKiMkatd6vq6OigWbNmuHXrlsr827dvo3r16gCAJk2aQFtbG8HBwcrlt27dwqNHj+Dg4KDOOEREREREREoFvvKTlJSEu3fvKn++f/8+Ll68CBMTE1SrVg2TJ09Gnz598Nlnn6F9+/YIDAzE/v37ERISAgAwMjLC4MGD4enpCRMTExgaGmLMmDFwcHDI10hvREREREREH6LAxc/58+fRvn175c/Z9+K4u7tj06ZN+Oqrr7B27Vr4+Phg7NixqFOnDn7//Xe0bt1auc7SpUuhoaEBV1dXpKamwsnJCatXr1bD7hAREREREeXuo57zI5XExEQYGRkhISGBN5USERUhvv/mjceGiEgaBXn/5RPqiIioxPH19YWlpSXkcjns7e1x7ty5d7b39/eHtbU15HI5bGxscOjQIZXlHh4ekMlkKlPnzp0LcxeIiEgCLH6IiKhE2blzJzw9PeHt7Y0LFy7A1tYWTk5OiI2NzbV9aGgo3NzcMHjwYERGRsLFxQUuLi64evWqSrvOnTvj6dOnymn79u1FsTtERFSE2O2NiIjyrTi8/9rb26NZs2ZYtWoVgDfPmLOwsMCYMWMwbdq0HO379OmD5ORkHDhwQDmvRYsWsLOzw9q1awG8ufITHx+PgICAD85VHI4NEVFZxG5vRERUKqWlpSEiIgKOjo7KeRoaGnB0dERYWFiu64SFham0BwAnJ6cc7UNCQlClShXUqVMHI0aMwIsXL9S/A0REJCm1PuSUiIioMD1//hyZmZkwNTVVmW9qaoqbN2/muk50dHSu7aOjo5U/d+7cGT169ICVlRXu3buH6dOn44svvkBYWBg0NTVz3W5qaipSU1OVPycmJn7obhERURFh8UNERGVe3759lf9vY2ODhg0bombNmggJCUHHjh1zXcfHxwezZ88uqohE+XL79m38+eefuHbtGhITE2FgYIDGjRujc+fOygfOE5VlLH6IqEzgh9T/8fb2ljrCB6tUqRI0NTURExOjMj8mJgYKhSLXdRQKRYHaA0CNGjVQqVIl3L17N8/ix8vLS/msO+DNlR8LC4v87gqR2mRmZsLf3x+LFi1CRERErm1kMhn69++POXPmwMrKqogTEhUfvOeHiIhKDB0dHTRp0gTBwcHKeVlZWQgODoaDg0Ou6zg4OKi0B4CgoKA82wPAP//8gxcvXsDMzCzPNrq6ujA0NFSZiIrayZMn0ahRI7i5uSEiIgJaWlr4/PPPMX36dCxevBjfffcdWrduDSEEtm7dCjs7O+zbt0/q2ESS4ZUfIiIqUTw9PeHu7o6mTZuiefPmWLZsGZKTkzFo0CAAwMCBA1G1alX4+PgAAMaNG4e2bdti8eLF6Nq1K3bs2IHz589j3bp1AICkpCTMnj0brq6uUCgUuHfvHqZMmYJatWrByclJsv0kepekpCRMmjQJP//8MwCgQoUKGD9+PEaOHIlKlSrlaH/hwgWMGTMGoaGhcHZ2xurVqzFixIiijk0kORY/RERUovTp0wfPnj3DzJkzER0dDTs7OwQGBioHNXj06BE0NP7XsaFly5bw8/PD999/j+nTp6N27doICAhAgwYNAACampq4fPkyNm/ejPj4eJibm6NTp06YO3cudHV1JdlHone5cuUKevTogbt37wIAhg8fjh9++AEVK1bMc53GjRsjJCQE48ePx+rVqzFq1CgYGxvDzc2tqGITFQt8zg8RlQm85+d/PuaeH77/5o3HhorC9u3bMWTIELx69QoWFhbYtGkTOnTokO/1hRAYO3YsVq1aBW1tbZw5cwbNmjUrxMREhY/P+SEiIiIqRTIyMuDp6Yl+/frh1atX+PzzzxEZGVmgwgd4M/DB8uXL0aNHD6Snp6Nv375ISEgopNRExQ+LHyIiIqJi7PXr13B1dcXSpUsBvBlp8PDhw+/s5vYuGhoa+PXXX1G9enX8/fffGDdunDrjEhVrLH6IiIiIiqm4uDg4Ojpi37590NXVhb+/P3788cc8H76bX8bGxvDz84NMJsPmzZtx4sQJNSUmKt5Y/BAREREVQ//88w9at26N0NBQGBsbIygoCD179lTb9lu2bIlhw4YBAEaNGoX09HS1bZuouGLxQ0RERFTMREdHo0OHDrhx4waqVq2KU6dOoU2bNmp/nR9//BGVKlXCtWvXlMO/E5VmLH6IiIiIipHnz5/D0dERd+7cQfXq1XHmzBnl0OzqZmJigjlz5gAA5s2bh1evXhXK6xAVFyx+iIiIiIqJ+Ph4dOrUCdeuXYO5uTmCg4NRvXr1Qn3NwYMHw9LSEtHR0fD19S3U1yKSGosfIiIiomIgLS0Nzs7OiIyMRJUqVRAcHIyaNWsW+uvq6Ogon4U2f/58JCcnF/prEkmFxQ8RERGRxIQQ+Pbbb3Hy5EkYGhoiKCgI1tbWRfb6/fv3R82aNfHixQts3LixyF6XqKix+CEiIiKS2OrVq7Fx40ZoaGhg586daNiwYZG+vqamJiZNmgQAWLx4MTIyMor09YmKCosfIiIiIglduHABnp6eAIAFCxagc+fOkuRwd3dH5cqV8eDBA+zevVuSDESFjcUPERERkURevXqFvn37Ku/3yS6CpKCnp4fRo0cDAFasWCFZDqLCxOKHiIiISCLTp0/HnTt38Mknn2Djxo2QyWSS5hk2bBi0tbURFhaGyMhISbMQFQYWP0REREQSOH36tPIKyy+//IIKFSpInAhQKBRwdXUF8OY+JKLShsUPERERURHLyMjAyJEjIYTAoEGD4OTkJHUkpVGjRgEAtm3bhvj4eGnDEKkZix8iIiKiIrZ27VpcuXIFJiYmWLhwodRxVLRq1QoNGjTA69evsWvXLqnjEKlVgYufkydPonv37jA3N4dMJkNAQECebb/99lvIZDIsW7ZMZX5cXBz69+8PQ0NDGBsbY/DgwUhKSipoFCIiIqIS58WLF5gxYwYAYN68eahYsaLEiVTJZDK4u7sDADZv3ixxGiL1KnDxk5ycDFtbW/j6+r6z3d69e3H27FmYm5vnWNa/f39cu3YNQUFBOHDgAE6ePIlhw4YVNAoRERFRibNw4ULEx8ejYcOGxfbzT//+/aGhoYHQ0FDcuXNH6jhEalPg4ueLL77AvHnz8NVXX+XZJioqCmPGjMG2bdugra2tsuzGjRsIDAzEL7/8Ant7e7Ru3RorV67Ejh078OTJk4LvAREREVEJER0drRzk4IcffoCmpqbEiXJnZmamvA9py5YtEqchUh+13/OTlZWFAQMGYPLkyahfv36O5WFhYTA2NkbTpk2V8xwdHaGhoYHw8PBct5mamorExESViYiIiKik8fHxwevXr2Fvb4+uXbtKHeedsru+bdmyBVlZWRKnIVIPtRc/8+fPh5aWFsaOHZvr8ujoaFSpUkVlnpaWFkxMTBAdHZ3rOj4+PjAyMlJOFhYW6o5NREREVKiePXuG9evXA3hzr4/Uz/R5H2dnZxgZGeHRo0cICQmROg6RWqi1+ImIiMDy5cuxadMmtf5Be3l5ISEhQTk9fvxYbdsmIiIiKgq+vr54/fo1mjZtio4dO0od573kcjn69OkDgAMfUOmh1uLn1KlTiI2NRbVq1aClpQUtLS08fPgQEydOhKWlJYA3D8+KjY1VWS8jIwNxcXFQKBS5bldXVxeGhoYqExEREVFJ8erVK6xatQoAMGXKlGJ/1Sdbdte333//nSPzUqmg1uJnwIABuHz5Mi5evKiczM3NMXnyZBw5cgQA4ODggPj4eERERCjXO3bsGLKysmBvb6/OOERERETFwpYtW/DixQvUqFEDPXr0kDpOvjk4OKB27dpITk7G3r17pY5D9NG0CrpCUlIS7t69q/z5/v37uHjxIkxMTFCtWrUcY9Vra2tDoVCgTp06AIC6deuic+fOGDp0KNauXYv09HSMHj0affv2zXVYbCIiIqKSTAiB1atXAwDGjBlTbEd4y41MJkO/fv0we/Zs7Nq1CwMGDJA6EtFHKfCVn/Pnz6NRo0Zo1KgRAMDT0xONGjXCzJkz872Nbdu2wdraGh07dkSXLl3QunVrrFu3rqBRiIiIiIq90NBQXLlyBXp6evDw8JA6ToH16tULAPDnn38iPj5e2jBEH6nAV37atWsHIUS+2z948CDHPBMTE/j5+RX0pYmIiIhKnDVr1gAA3NzcYGxsLG2YD1C/fn3Ur18f165dw759+zBw4ECpIxF9MLUPdU1EREREb8TFxcHf3x8AMGLECInTfLjevXsDAHbt2iVxEqKPw+KHiIiIqJDs3LkTaWlpaNiwocoD3kuat7u+/fvvvxKnIfpwLH6IiIiICsmWLVsA/G/I6JKqbt26aNCgAdLT0/HHH39IHYfog7H4ISIiIioEt27dwtmzZ6GpqYl+/fpJHeejsesblQYsfoiIiIgKwW+//QYAcHJyyvNB7iVJdte3oKAgdn2jEovFDxEREZGaCSGwc+dOAMDXX38tcRr1sLa2RsOGDZGRkcEHnlKJxeKHiIiISM0iIyNx9+5d6OnpoXv37lLHUZvsqz+///67xEmIPgyLHyIiIiI1y74vpmvXrjAwMJA4jfr06NEDAHD06FEkJiZKnIao4Fj8EBEREamREEJZ/GQPElBa1K1bF59++inS0tJw+PBhqeMQFRiLHyIiIiI1unDhAu7fv49y5cqhS5cuUsdRK5lMBhcXFwBAQECApFmIPgSLHyIiIiI12r9/P4A3o7zp6+tLnEb9vvrqKwDAwYMHkZqaKnEaooJh8UNERESkRgcOHACAUjXQwduaN28OMzMzvHz5EseOHZM6DlGBsPghIiIiUpMnT54gIiICMpms1HV5y6ahoaHs+sYhr6mkYfFDREREpCYHDx4E8ObqiKmpqcRpCk9217c//vgDmZmZEqchyj8WP0RERERqkn2/T7du3SROUrjatWsHIyMjxMbGIiwsTOo4RPnG4oeIiIhIDV6/fo2jR48CKL33+2TT1tZWFnjs+kYlCYsfIiIiIjU4duwYXr9+DQsLCzRs2FDqOIUuu+vb3r17IYSQOA1R/rD4ISIiIlKD7FHeunXrBplMJnGawte5c2fI5XLcv38fV65ckToOUb6w+CEiIiL6SEKIUj/E9X/p6+ujU6dOANj1jUoOFj9EREREH+nSpUv4559/UK5cObRv317qOEXm7a5vRCUBix8iIiKij3To0CEAgKOjI+RyucRpik737t2hoaGBS5cu4f79+1LHIXovFj9EREREHyl7lDcnJyeJkxStihUr4rPPPgPAqz9UMrD4ISKiEsfX1xeWlpaQy+Wwt7fHuXPn3tne398f1tbWkMvlsLGxUX5Ln5tvv/0WMpkMy5YtU3NqKq1evXqFM2fOAHhz5aesye76FhAQIG0Qonxg8UNERCXKzp074enpCW9vb1y4cAG2trZwcnJCbGxsru1DQ0Ph5uaGwYMHIzIyEi4uLnBxccHVq1dztN27dy/Onj0Lc3Pzwt4NKkVOnz6NtLQ0WFhYoHbt2lLHKXIuLi4A3hyHvP4OiYoLFj9ERFSiLFmyBEOHDsWgQYNQr149rF27FuXKlcOGDRtybb98+XJ07twZkydPRt26dTF37lw0btwYq1atUmkXFRWFMWPGYNu2bdDW1i6KXaFSIrvLm6OjY5kY4vq/qlWrhsaNG0MIgf3790sdh+idWPwQEVGJkZaWhoiICJWuRRoaGnB0dERYWFiu64SFheXoiuTk5KTSPisrCwMGDMDkyZNRv379fGVJTU1FYmKiykRl09vFT1nFUd+opGDxQ0REJcbz58+RmZkJU1NTlfmmpqaIjo7OdZ3o6Oj3tp8/fz60tLQwduzYfGfx8fGBkZGRcrKwsCjAnlBp8fz5c0RGRgIAOnbsKHEa6WQXP0ePHsXLly8lTkOUNxY/RERUpkVERGD58uXYtGlTgboseXl5ISEhQTk9fvy4EFNScXXs2DEAgI2NTY4iuyypV68eatWqhdTUVAQGBkodhyhPBS5+Tp48ie7du8Pc3BwymUxlZI/09HRMnToVNjY20NfXh7m5OQYOHIgnT56obCMuLg79+/eHoaEhjI2NMXjwYCQlJX30zhARUelWqVIlaGpqIiYmRmV+TEwMFApFrusoFIp3tj916hRiY2NRrVo1aGlpQUtLCw8fPsTEiRNhaWmZZxZdXV0YGhqqTFT2sMvbGzKZjF3fqEQocPGTnJwMW1tb+Pr65lj26tUrXLhwATNmzMCFCxewZ88e3Lp1C19++aVKu/79++PatWsICgrCgQMHcPLkSQwbNuzD94KIiMoEHR0dNGnSBMHBwcp5WVlZCA4OhoODQ67rODg4qLQHgKCgIGX7AQMG4PLly7h48aJyMjc3x+TJk3HkyJHC2xkqFVj8/E/2qG8HDx5EWlqatGGI8qBV0BW++OILfPHFF7kuMzIyQlBQkMq8VatWoXnz5nj06BGqVauGGzduIDAwEH/99ReaNm0KAFi5ciW6dOmCRYsWcXhRIiJ6J09PT7i7u6Np06Zo3rw5li1bhuTkZAwaNAgAMHDgQFStWhU+Pj4AgHHjxqFt27ZYvHgxunbtih07duD8+fNYt24dgDcPaaxYsaLKa2hra0OhUKBOnTpFu3NUovz999+4f/8+tLS0lA/6LMtatGgBU1NTxMTE4Pjx42Xuga9UMhT6PT8JCQmQyWQwNjYG8GbUHWNjY2XhA7z5tkRDQwPh4eG5boMj6hARUbY+ffpg0aJFmDlzJuzs7HDx4kUEBgYq77d49OgRnj59qmzfsmVL+Pn5Yd26dbC1tcXu3bsREBCABg0aSLULVEpkX/VxcHCAgYGBxGmkp6GhAWdnZwB84CkVXwW+8lMQKSkpmDp1Ktzc3JR9oaOjo1GlShXVEFpaMDExyXOkHh8fH8yePbswoxIRUQkyevRojB49OtdlISEhOeb16tULvXr1yvf2Hzx48IHJqCzJ7k5Zlkd5+6+vvvoK69atwx9//AFfX19oaHBsLSpeCu1fZHp6Onr37g0hBNasWfNR2+KIOkRERFScCCFw4sQJAECHDh0kTlN8dOjQAYaGhnj69GmePXqIpFQoxU924fPw4UMEBQWpjICjUCgQGxur0j4jIwNxcXF5jtTDEXWIiIioOLlz5w5iYmKgq6uLZs2aSR2n2NDR0UGXLl0AsOsbFU9qL36yC587d+7g6NGjOW4idXBwQHx8PCIiIpTzjh07hqysLNjb26s7DhEREZHaZV/1adGiBeRyucRpipe3h7wWQkichkhVge/5SUpKwt27d5U/379/HxcvXoSJiQnMzMzQs2dPXLhwAQcOHEBmZqbyPh4TExPo6Oigbt266Ny5M4YOHYq1a9ciPT0do0ePRt++fTnSGxEREZUI2cUPR3nLqXPnztDR0cGdO3dw48YN1KtXT+pIREoFvvJz/vx5NGrUCI0aNQLwZsjRRo0aYebMmYiKisK+ffvwzz//wM7ODmZmZsopNDRUuY1t27bB2toaHTt2RJcuXdC6dWvlkKNERERExdnb9/u0bdtW4jTFj6GhofK5R3zgKRU3Bb7y065du3dewszP5U0TExP4+fkV9KWJiIiIJPfgwQP8888/0NLSQosWLaSOUyy5uLjg0KFDCAgIwHfffSd1HCIljj9IREREVAAnT54EADRr1gz6+voSpymevvzyS8hkMpw/f56j9FKxwuKHiIiIqAB4v8/7mZqaolWrVgA46hsVLyx+iIiIiAog+8oP7/d5NxcXFwC874eKFxY/RERERPkUFRWFe/fuQUNDQ3llg3KXPeT1yZMn8ezZM4nTEL3B4oeIiIgon7Kv+jRq1IgPXX+PGjVqoHHjxsjMzMQff/whdRwiACx+iIiIiPKN9/sUTM+ePQEAu3fvljgJ0RssfoiIiIjyiff7FIyrqysAIDg4GHFxcRKnIWLxQ0RERJQvsbGxuHHjBgCgdevWEqcpGT799FM0bNgQGRkZ7PpGxQKLHyIiIqJ8OHXqFADAxsYGFStWlDhNycGub1ScsPghIiIiygfe7/NhsoufoKAgxMfHSxuGyjwWP0RERET5wPt9PkzdunVRv359pKenY//+/VLHoTKOxQ8RERHRe/z777+4fPkyAKBNmzYSpyl52PWNigsWP0RERETvcfr0aQghUKdOHSgUCqnjlDjZxc+RI0eQmJgocRoqy1j8EBEREb0H7/f5OPXr10edOnWQmpqKgwcPSh2HyjAWP0RERETvwft9Po5MJmPXNyoWWPwQERERvcPLly9x4cIFALzy8zGyi59Dhw4hKSlJ4jRUVrH4ISIiInqH0NBQZGZmwsrKChYWFlLHKbFsbW1Rq1YtpKSk4NChQ1LHoTKKxQ8RERHRO/B+H/V4u+ubv7+/xGmorNKSOgAR5W727NlSRyg2vL29pY5ARGUY7/dRn969e+Onn37CgQMH8PLlS5QvX17qSFTG8MoPERERUR5ev36Nc+fOAeCVH3Wws7PDp59+ipSUFOzbt0/qOFQGsfghIiIiykNYWBjS09NRtWpV1KhRQ+o4JZ5MJkPfvn0BADt27JA4DZVFLH6IiIiI8pB9v0/btm0hk8kkTlM6ZBc/R44cQVxcnMRpqKxh8UNERESUh7eLH1KPunXrwtbWFunp6dizZ4/UcaiMYfFDRERElIuUlBScPXsWAIsfdWPXN5IKix8iIiKiXJw7dw6pqakwNTXFp59+KnWcUiW7+Dl+/Diio6MlTkNlCYsfIiIiolzwfp/CY2lpiRYtWiArK4vP/KEixeKHiIiIKBchISEA2OWtsLDrG0mhwMXPyZMn0b17d5ibm0MmkyEgIEBluRACM2fOhJmZGfT09ODo6Ig7d+6otImLi0P//v1haGgIY2NjDB48GElJSR+1I0RERETqkpaWhrCwMAAsfgpL7969IZPJEBoaiocPH0odh8qIAhc/ycnJsLW1ha+vb67LFyxYgBUrVmDt2rUIDw+Hvr4+nJyckJKSomzTv39/XLt2DUFBQThw4ABOnjyJYcOGffheEBEREanRX3/9hdevX6NSpUqoV6+e1HFKJTMzM7Rr1w4AsHPnTmnDUJlR4OLniy++wLx58/DVV1/lWCaEwLJly/D999/D2dkZDRs2xJYtW/DkyRPlFaIbN24gMDAQv/zyC+zt7dG6dWusXLkSO3bswJMnTz56h4iIiIg+Fu/3KRrs+kZFTa33/Ny/fx/R0dFwdHRUzjMyMoK9vb3y0nFYWBiMjY3RtGlTZRtHR0doaGggPDw81+2mpqYiMTFRZSIiIiIqLHy+T9FwdXWFlpYWIiMjcevWLanjUBmg1uIne6hCU1NTlfmmpqbKZdHR0ahSpYrKci0tLZiYmOQ51KGPjw+MjIyUk4WFhTpjExERESmlp6fjzJkzAFj8FLaKFSuiU6dOAHj1h4pGiRjtzcvLCwkJCcrp8ePHUkciIiKiUurChQtITk6GiYkJGjRoIHWcUu/trm9CCInTUGmn1uJHoVAAAGJiYlTmx8TEKJcpFArExsaqLM/IyEBcXJyyzX/p6urC0NBQZSIiIiIqDNld3tq0aQMNjRLxPXGJ5uzsDLlcjps3b+Ly5ctSx6FSTq1/0VZWVlAoFAgODlbOS0xMRHh4OBwcHAAADg4OiI+PR0REhLLNsWPHkJWVBXt7e3XGISIiIiowPt+naBkaGqJr164AgO3bt0uchkq7Ahc/SUlJuHjxIi5evAjgzSAHFy9exKNHjyCTyTB+/HjMmzcP+/btw5UrVzBw4ECYm5vDxcUFAFC3bl107twZQ4cOxblz53DmzBmMHj0affv2hbm5uTr3jYiIiKhAMjIycPr0aQAsfooSu75RUdEq6Arnz59H+/btlT97enoCANzd3bFp0yZMmTIFycnJGDZsGOLj49G6dWsEBgZCLpcr19m2bRtGjx6Njh07QkNDA66urlixYoUadoeIiIjow128eBEvX76EkZERbG1tpY5TZnTt2hUGBgZ4+PAhwsLC0LJlS6kjUSlV4OKnXbt276zIZTIZ5syZgzlz5uTZxsTEBH5+fgV9aSIiIqJC9fb9PpqamhKnKTv09PTw1Vdf4bfffoOfnx+LHyo0vIuPiIiI6P/x+T7S6d+/PwBg586dSE9PlzgNlVYsfoiIiIgAZGZm4tSpUwBY/EihY8eOqFKlCp4/f46goCCp41ApxeKHiIiICEBERATi4+NhZGSExo0bSx2nzNHS0kKfPn0AgLdHUKFh8UNEREQEKB/V0b59e97vI5Hsrm8BAQFITk6WOA2VRix+iIioxPH19YWlpSXkcjns7e1x7ty5d7b39/eHtbU15HI5bGxscOjQIZXls2bNgrW1NfT19VGhQgU4OjoiPDy8MHeBiqGjR48CABwdHSVOUnY1b94cNWvWRHJyMvbt2yd1HCqFWPwQEVGJsnPnTnh6esLb2xsXLlyAra0tnJycEBsbm2v70NBQuLm5YfDgwYiMjISLiwtcXFxw9epVZZtPP/0Uq1atwpUrV3D69GlYWlqiU6dOePbsWVHtFkns9evXOHPmDIA3956QNGQyGfr16wfgzaNRiNSNxQ8REZUoS5YswdChQzFo0CDUq1cPa9euRbly5bBhw4Zc2y9fvhydO3fG5MmTUbduXcydOxeNGzfGqlWrlG369esHR0dH1KhRA/Xr18eSJUuQmJiIy5cvF9VukcTOnDmD1NRUVK1aFXXq1JE6TpmWXfwcOXIEz58/lzgNlTYsfoiIqMRIS0tDRESESrckDQ0NODo6IiwsLNd1wsLCcnRjcnJyyrN9Wloa1q1b996HXKampiIxMVFlopIr+34fR0dHyGQyidOUbdbW1mjcuDEyMjLg7+8vdRwqZVj8EBFRkfj7778/ehvPnz9HZmYmTE1NVeabmpoiOjo613Wio6Pz1f7AgQMwMDCAXC7H0qVLERQUhEqVKuWZxcfHB0ZGRsrJwsLiA/eKioPs+33Y5a14yB74gF3fSN1Y/BARUZGoVasW2rdvj61btyIlJUXqODm0b98eFy9eRGhoKDp37ozevXvneR8RAHh5eSEhIUE5PX78uAjTkjrFxcUhIiICAIuf4qJv376QyWQ4c+YMHjx4IHUcKkVY/BARUZG4cOECGjZsCE9PTygUCgwfPvy9o7T9V6VKlaCpqYmYmBiV+TExMVAoFLmuo1Ao8tVeX18ftWrVQosWLfDrr79CS0sLv/76a55ZdHV1YWhoqDJRyRQSEgIhBOrWrQtzc3Op4xAAc3NztG/fHgCwfft2idNQacLih4iIioSdnR2WL1+OJ0+eYMOGDXj69Clat26NBg0aYMmSJfkaWU1HRwdNmjRR3p8BAFlZWQgODoaDg0Ou6zg4OKi0B4CgoKA827+93dTU1HzsGZV0HOK6eHq765sQQuI0VFqw+CEioiKlpaWFHj16wN/fH/Pnz8fdu3cxadIkWFhYYODAgXj69Ok71/f09MT69euxefNm3LhxAyNGjEBycjIGDRoEABg4cCC8vLyU7ceNG4fAwEAsXrwYN2/exKxZs3D+/HmMHj0aAJCcnIzp06fj7NmzePjwISIiIvDNN98gKioKvXr1KrwDQcXG24MdUPHRo0cP6Ojo4Nq1a7hy5YrUcaiUYPFDRERF6vz58xg5ciTMzMywZMkSTJo0Cffu3UNQUBCePHkCZ2fnd67fp08fLFq0CDNnzoSdnR0uXryIwMBA5aAGjx49UimgWrZsCT8/P6xbtw62trbYvXs3AgIC0KBBAwCApqYmbt68CVdXV3z66afo3r07Xrx4gVOnTqF+/fqFdyCoWHj06BFu374NDQ0NtG3bVuo49BZjY2N069YNAAc+IPXRkjoAERGVDUuWLMHGjRtx69YtdOnSBVu2bEGXLl2gofHmezgrKyts2rQJlpaW793W6NGjlVdu/iskJCTHvF69euV5FUcul2PPnj353g8qXQ4fPgzgTfdIIyMjidPQf/Xv3x979uzB9u3b4ePjo3y/IPpQ/BdERERFYs2aNejXrx8ePnyIgIAAdOvWLccHmSpVqrxzkAEidcsufr744guJk1BuunTpAiMjIzx+/BinT5+WOg6VAix+iIioSAQFBWHq1KkwMzNTmS+EwKNHjwC8GdDA3d1dinhUBqWmpioHO+jSpYvEaSg3crkcrq6uANj1jdSDxQ8RERWJmjVr4vnz5znmx8XFwcrKSoJEVNadPn0aycnJMDMzg52dndRxKA/9+vUDAPj7+yMtLU3iNFTSsfghIqIikddQtUlJSZDL5UWchgg4dOgQAKBz586QyWQSp6G8tGvXDmZmZvj3338RGBgodRwq4TjgARERFSpPT08AgEwmw8yZM1GuXDnlsszMTISHh/Nbd5JE9v0+7PJWvGlqasLNzQ1LlizBtm3b8OWXX0odiUowFj9ERFSoIiMjAby58nPlyhXo6Ogol+no6MDW1haTJk2SKh6VUffv38eNGzegqanJ5/uUAP369cOSJUuwb98+vHz5EuXLl5c6EpVQLH6IiKhQHT9+HAAwaNAgLF++HIaGhhInIvrfVZ9WrVrB2NhY2jD0Xo0bN0adOnVw69Yt7N27FwMHDpQ6EpVQvOeHiIiKxMaNG1n4ULHBIa5LFplMhv79+wPgqG/0cXjlh4iICk2PHj2wadMmGBoaokePHu9syweNUlFJSUlBcHAwAN7vU5K4ublh5syZOHr0KGJiYmBqaip1JCqBeOWHiIgKjZGRkXIULSMjo3dOREXlxIkTeP36NapWrQobGxup41A+1apVC/b29sjKysLOnTuljkMlFK/8EBFRodm4cWOu/08kpYCAAABA165dOcR1CdOvXz+Eh4fDz88PY8eOlToOlUC88kNEREXi9evXePXqlfLnhw8fYtmyZfjzzz8lTEVlTVZWFv744w8AwFdffSVxGiqoPn36QFNTE+Hh4bh7967UcagEUnvxk5mZiRkzZsDKygp6enqoWbMm5s6dq/JwOyEEZs6cCTMzM+jp6cHR0RF37txRdxQiIipGnJ2dsWXLFgBAfHw8mjdvjsWLF8PZ2Rlr1qyROB2VFeHh4Xj69CkMDQ3RoUMHqeNQAZmamiqHJvfz85M4DZVEai9+5s+fjzVr1mDVqlW4ceMG5s+fjwULFmDlypXKNgsWLMCKFSuwdu1ahIeHQ19fH05OTkhJSVF3HCIiKiYuXLiANm3aAAB2794NhUKBhw8fYsuWLVixYoXE6ais2Lt3L4A3Xd7efuYUlRz9+vUD8Kb4efvLdaL8UHvxExoaCmdnZ3Tt2hWWlpbo2bMnOnXqhHPnzgF4c9Vn2bJl+P777+Hs7IyGDRtiy5YtePLkibIPLhERlT6vXr1SPpjwzz//RI8ePaChoYEWLVrg4cOHEqejskAIoSx+2OWt5Prqq68gl8tx69YtXLhwQeo4VMKovfhp2bIlgoODcfv2bQDApUuXcPr0aeU4+vfv30d0dLTK05SNjIxgb2+PsLCwXLeZmpqKxMRElYmIiEqWWrVqISAgAI8fP8aRI0fQqVMnAEBsbCyf/0NF4tq1a7h79y50dXX5fJ8SrHz58vjyyy8BsOsbFZzai59p06ahb9++sLa2hra2Nho1aoTx48crH0wVHR0NADnGZjc1NVUu+y8fHx+V4VAtLCzUHZuIiArZzJkzMWnSJFhaWsLe3h4ODg4A3lwFatSokcTpqCzIvurz+eefw8DAQOI09DGyP1du374dmZmZEqehkkTtxc+uXbuwbds2+Pn54cKFC9i8eTMWLVqEzZs3f/A2vby8kJCQoJweP36sxsRERFQUevbsiUePHuH8+fMIDAxUzu/YsSOWLl0qYTIqK7IfpMsubyVf586dUaFCBTx9+hQhISFSx6ESRO3Fz+TJk5VXf2xsbDBgwABMmDABPj4+AACFQgEAiImJUVkvJiZGuey/dHV1YWhoqDIREVHJo1Ao0KhRI2ho/O/007x5c1hbW0uYisqC+/fv4+LFi9DQ0ED37t2ljkMfSUdHB7169QLArm9UMGovfl69eqVyUgMATU1NZGVlAQCsrKygUCgQHBysXJ6YmIjw8HBlFwgiIip9kpOTMWPGDLRs2RK1atVCjRo1VCaiwpQ9qNJnn32GypUrSxuG1CK769vu3bs5YjDlm5a6N9i9e3f88MMPqFatGurXr4/IyEgsWbIE33zzDQBAJpNh/PjxmDdvHmrXrg0rKyvMmDED5ubmcHFxUXccIiIqJoYMGYITJ05gwIABMDMzg0wmkzoSlSE7d+4EAPTo0UPiJKQurVu3hoWFBR4/foyDBw/C1dVV6khUAqi9+Fm5ciVmzJiBkSNHIjY2Fubm5hg+fDhmzpypbDNlyhQkJydj2LBhiI+PR+vWrREYGAi5XK7uOEREVEwcPnwYBw8eRKtWraSOQmXMvXv3EB4eDg0NDfTu3VvqOKQmGhoacHNzw4IFC+Dn58fih/JF7d3eypcvj2XLluHhw4d4/fo17t27h3nz5qk8SEwmk2HOnDmIjo5GSkoKjh49ik8//VTdUYiIqBipUKECTExMpI5BZdD27dsBAI6OjjlGm6WSLbvr24EDBxAfHy9tGCoR1F78EBER5Wbu3LmYOXMmXr16JXUUKkOEENi2bRsAwM3NTeI0pG42NjaoX78+0tLSlKP5Eb0Lix8iIioSixcvxpEjR2BqagobGxs0btxYZSIqDJcuXcLNmzehq6vLIa5LIZlMprz6k13kEr2L2u/5ISIiyg0HtSEpZHd569atG4yMjCROQ4XBzc0N06dPx/HjxxEVFYWqVatKHYmKMRY/RERUJLy9vaWOQGVMVlaWsvjp16+fxGmosFhaWqJVq1Y4c+YMdu7cCU9PT6kjUTHGbm9ERFRk4uPj8csvv8DLywtxcXEAgAsXLiAqKkriZFQanTlzBo8fP4ahoSG6dOkidRwqROz6RvnF4oeIiIrE5cuX8emnn2L+/PlYtGiRcmSmPXv2wMvLS9pwVCr5+fkBAFxdXfk4jVKuV69e0NLSwoULF3Dz5k2p41AxxuKHiIiKhKenJzw8PHDnzh2VD6JdunTByZMnJUxGpdHr16+xY8cOAOzyVhZUqlQJTk5OAP5X9BLlhsUPEREVib/++gvDhw/PMb9q1aqIjo6WIBGVZnv37kV8fDyqVauGDh06SB2HisDbXd+EEBKnoeKKxQ8RERUJXV1dJCYm5ph/+/ZtVK5cWYJEVJpt2LABADBo0CBoaPDjTlnw5ZdfQl9fH3///TfOnTsndRwqpvhuQEREReLLL7/EnDlzkJ6eDuDN8zkePXqEqVOnwtXVVeJ0VJrcv38fwcHBkMlkGDRokNRxqIjo6+srh9TnwAeUFxY/RERUJBYvXoykpCRUrlwZr1+/Rtu2bVGrVi2UL18eP/zwg9TxqBTZuHEjAMDR0RHVq1eXOA0Vpeyub9u3b0daWprEaag44nN+SG1mz54tdYRig88zIcrJyMgIQUFBOHPmDC5duoSkpCQ0btwYjo6OUkejUiQzM1NZ/AwePFjiNFTUPv/8cygUCkRHR+Pw4cNwdnaWOhIVMyx+iIio0GVlZWHTpk3Ys2cPHjx4AJlMBisrKygUCgghIJPJpI5IpURQUBD++ecfmJiYKLtAUdmhpaWFAQMGYOHChdi4cSOLH8qB3d6IiKhQCSHw5ZdfYsiQIYiKioKNjQ3q16+Phw8fwsPDA1999ZXUEakU+fXXXwEAX3/9NXR1dSVOQ1Jwd3cHABw8eBCxsbESp6HihsUPEREVqk2bNuHkyZMIDg5GZGQktm/fjh07duDSpUs4evQojh07hi1btkgdk0qBmJgY/PHHHwCAb775RuI0JJX69eujWbNmyMjI4DN/KAcWP0REVKi2b9+O6dOno3379jmWdejQAdOmTePITKQW69evR3p6Olq0aAFbW1up45CEskf527Rpk7RBqNhh8UNERIXq8uXL6Ny5c57Lv/jiC1y6dKkIE1FplJGRgbVr1wIARo0aJXEaklrfvn2ho6ODS5cu4eLFi1LHoWKExQ8RERWquLg4mJqa5rnc1NQU//77bxEmotLojz/+QFRUFCpXroxevXpJHYckVqFCBeWAF9mj/xEBLH6IiKiQZWZmQksr78FFNTU1kZGRUYSJqDTy9fUFAAwdOpQDHRAAwMPDA8CbB57ymT+UjUNdExFRoRJCwMPDI88PpKmpqUWciEqb69ev4/jx49DQ0MDw4cOljkPFRKdOnWBubo4nT57g4MGDHFmSAPDKDxERFTJ3d3dUqVIFRkZGuU5VqlTBwIEDpY5JJVj2VR9nZ2dUq1ZN4jRUXGhqamLAgAEAOPAB/Q+v/BARUaFif3sqTImJicqh0jnQAf2Xu7s75s+fj4MHDyImJuad9x9S2cArP0RERFRibdiwAUlJSbC2tkaHDh2kjkPFTN26dWFvb4/MzExs3bpV6jhUDLD4ISIiohIpIyMDy5cvBwCMHz8eMplM4kRUHGU/8+fXX3+FEELiNCQ1Fj9ERERUIgUEBODBgweoWLEi7xujPLm5uUFfXx83btzA6dOnpY5DEmPxQ0REJY6vry8sLS0hl8thb2+Pc+fOvbO9v78/rK2tIZfLYWNjg0OHDimXpaenY+rUqbCxsYG+vj7Mzc0xcOBAPHnypLB3gz7SkiVLAAAjR46Enp6exGmouDI0NISbmxsAYN26dRKnIamx+CEiohJl586d8PT0hLe3Ny5cuABbW1s4OTkhNjY21/ahoaFwc3PD4MGDERkZCRcXF7i4uODq1asAgFevXuHChQuYMWMGLly4gD179uDWrVv48ssvi3K3qIDCwsIQFhYGHR0djBw5Uuo4VMwNGzYMwJsvQuLi4iROQ1Ji8UNERCXKkiVLMHToUAwaNAj16tXD2rVrUa5cOWzYsCHX9suXL0fnzp0xefJk1K1bF3PnzkXjxo2xatUqAICRkRGCgoLQu3dv1KlTBy1atMCqVasQERGBR48eFeWuUQEsXboUANC/f38oFAqJ01Bx17RpU9jZ2SE1NVU5OiCVTYVS/ERFReHrr79GxYoVoaenBxsbG5w/f165XAiBmTNnwszMDHp6enB0dMSdO3cKIwoREZUiaWlpiIiIgKOjo3KehoYGHB0dERYWlus6YWFhKu0BwMnJKc/2AJCQkACZTAZjY+M826SmpiIxMVFloqLx4MED/P777wCACRMmSJyGSgKZTKZ8AO66des48EEZpvbi599//0WrVq2gra2Nw4cP4/r161i8eDEqVKigbLNgwQKsWLECa9euRXh4OPT19eHk5ISUlBR1xyEiolLk+fPnyMzMzPGsDlNTU0RHR+e6TnR0dIHap6SkYOrUqXBzc4OhoWGeWXx8fFQe1mphYVHAvaEPtXTpUmRlZeHzzz+HjY2N1HGohOjXrx/KlSvHgQ/KOLUXP/Pnz4eFhQU2btyI5s2bw8rKCp06dULNmjUBvLnqs2zZMnz//fdwdnZGw4YNsWXLFjx58gQBAQHqjkNERJRv6enp6N27N4QQWLNmzTvbenl5ISEhQTk9fvy4iFKWbc+fP8f69esBAFOmTJE4DZUkbw988PPPP0uchqSi9uJn3759aNq0KXr16oUqVaqgUaNGyjcpALh//z6io6NVuiAYGRnB3t4+zy4I7FpAREQAUKlSJWhqaiImJkZlfkxMTJ73fSgUiny1zy58Hj58iKCgoHde9QEAXV1dGBoaqkxU+FatWoXXr1+jcePG6Nixo9RxqITJ7vrm7++PZ8+eSZyGpKD24ufvv//GmjVrULt2bRw5cgQjRozA2LFjsXnzZgBQdjMoSBcEdi0gIiIA0NHRQZMmTRAcHKycl5WVheDgYDg4OOS6joODg0p7AAgKClJpn1343LlzB0ePHkXFihULZwfooyQlJWHlypUAgGnTpvGhplRgzZo1Q7NmzZCWloZffvlF6jgkAbUXP1lZWWjcuDF+/PFHNGrUCMOGDcPQoUOxdu3aD94muxYQEVE2T09PrF+/Hps3b8aNGzcwYsQIJCcnK5/iPnDgQHh5eSnbjxs3DoGBgVi8eDFu3ryJWbNm4fz58xg9ejSAN4VPz549cf78eWzbtg2ZmZmIjo5GdHQ00tLSJNlHyt0vv/yCuLg41KpVCz169JA6DpVQ2X/7a9asQUZGhsRpqKipvfgxMzNDvXr1VObVrVtXOVxodjeDgnRZYNcCIiLK1qdPHyxatAgzZ86EnZ0dLl68iMDAQGWPgkePHuHp06fK9i1btoSfnx/WrVsHW1tb7N69GwEBAWjQoAGANyOU7tu3D//88w/s7OxgZmamnEJDQyXZR8opLS1N+VDTyZMnQ1NTU+JEVFL17t0blSpVwuPHj7Fv3z6p41ARU3vx06pVK9y6dUtl3u3bt1G9enUAgJWVFRQKhUoXhMTERISHh+fZZYGIiOhto0ePxsOHD5Gamorw8HDY29srl4WEhGDTpk0q7Xv16oVbt24hNTUVV69eRZcuXZTLLC0tIYTIdWrXrl0R7RG9z/bt2/H48WOYmppi4MCBUsehEkwulysfepr9vC8qO9Re/EyYMAFnz57Fjz/+iLt37yq/bRs1ahSAN+Osjx8/HvPmzcO+fftw5coVDBw4EObm5nBxcVF3HCIiIirhsrKysGDBAgBvPmfI5XKJE1FJ9+2330JDQwPHjx/HtWvXpI5DRUjtxU+zZs2wd+9ebN++HQ0aNMDcuXOxbNky9O/fX9lmypQpGDNmDIYNG4ZmzZohKSkJgYGBfDMjIiKiHA4cOIDr16/D0NAQ3377rdRxqBSwsLBQfunu6+srbRgqUmovfgCgW7duuHLlClJSUnDjxg0MHTpUZblMJsOcOXMQHR2NlJQUHD16FJ9++mlhRCEiIqISTAiBn376CQAwYsQIGBkZSZyISovsgQ+2bNmC+Ph4acNQkSmU4oeIiIhIHU6dOoWwsDDo6upi3LhxUsehUqRdu3Zo0KABkpOTsW7dOqnjUBFh8UNERETFlo+PDwDA3d0dZmZmEqeh0kQmk8HT0xMAsGLFCg5tX0aw+CEiIqJiKTIyEoGBgdDQ0MCUKVOkjkOlUL9+/aBQKBAVFYVdu3ZJHYeKAIsfIiIiKpay7/Xp06cPatasKXEaKo10dXWV9/4sWbIEQgiJE1FhY/FDRERExc7t27fh7+8PAJg2bZrEaag0+/bbb6Gnp4fIyEiEhIRIHYcKGYsfIiIiKnYWLFgAIQS6deuGhg0bSh2HSrGKFSti0KBBAIDFixdLnIYKG4sfIiIiKlb++ecfbNmyBQAwffp0idNQWTBhwgTIZDIcPHgQN27ckDoOFSIWP0RERFSsLF68GOnp6Wjbti0cHBykjkNlQK1ateDs7AwAWLp0qcRpqDCx+CEiIqJi4/nz58pnrnh5eUmchsqSiRMnAnjz0NNnz55JnIYKC4sfIiIiKjZWrFiBV69eoXHjxujUqZPUcagMadWqFZo3b47U1FSsXr1a6jhUSFj8EBERUbHw8uVLrFy5EsCbqz4ymUziRFSWyGQy5dWfVatW4dWrVxInosLA4oeIiIiKhZ9//hnx8fH49NNP8dVXX0kdh8qgHj16oEaNGnj+/Dk2bNggdRwqBCx+iIiISHIpKSnKYYanTZsGTU1NiRNRWaSlpYXJkycDABYuXIj09HSJE5G6sfghIiIiyW3evBnR0dH45JNP0L9/f6njUBnm4eEBU1NTPHr0CDt27JA6DqkZix8iIiKSVEZGBhYsWAAAmDx5MnR0dCRORGWZXC7HhAkTAAA//fQTsrKyJE5E6sTih4iIiCS1a9cu/P3336hUqRKGDBkidRwifPvttzA0NMT169exf/9+qeOQGrH4ISIiIskIIfDTTz8BAMaNG4dy5cpJnIgIMDIywqhRowAAPj4+EEJInIjUhcUPERERSebgwYO4cuUKypcvr/ywSVQcjBs3DnK5HOHh4Thx4oTUcUhNWPwQERGRJIQQ+PHHHwEAI0aMQIUKFSRORPQ/pqam+OabbwBAeXWSSj4WP0RERCSJkydPIiwsDLq6usobzImKk0mTJkFTUxNHjhzBhQsXpI5DasDih4iIiCTh4+MDAPjmm2+gUCgkTkOUk5WVFfr27QuAV39KCxY/REREVOQuXbqEI0eOQFNTU/lQSaLiaOrUqQCA3bt3486dOxKnoY/F4oeIiIiK3KJFiwAAvXr1gpWVlcRpiPJmY2ODbt26QQihfB4VlVwsfoiIiKhIPX78GDt27ADw5p4KouJu2rRpAIDNmzcjKipK4jT0MVj8EBERUZFatmwZMjIy0L59ezRp0kTqOETv1apVK7Rp0wbp6elYvHix1HHoI7D4ISIioiITHx+PdevWAQDv9aES5bvvvgMArF27Fs+ePZM4DX0oFj9ERERUZNatW4ekpCQ0aNAAnTt3ljoOUb516tQJTZs2xevXr7F06VKp49AHKvTi56effoJMJsP48eOV81JSUjBq1ChUrFgRBgYGcHV1RUxMTGFHISIiIgmlpaVh+fLlAICJEydCJpNJnIgo/2QyGb7//nsAwKpVq/Dvv/9KnIg+RKEWP3/99Rd+/vlnNGzYUGX+hAkTsH//fvj7++PEiRN48uQJevToUZhRiIiISGJ+fn548uQJzM3N0a9fP6njEBVY9+7dYWNjg5cvX2LlypVSx6EPUGjFT1JSEvr374/169ejQoUKyvkJCQn49ddfsWTJEnTo0AFNmjTBxo0bERoairNnzxZWHCIiIpKQEEI5vPW4ceOgo6MjcSKigtPQ0MD06dMBAMuXL8fLly8lTkQFVWjFz6hRo9C1a1c4OjqqzI+IiEB6errKfGtra1SrVg1hYWG5bis1NRWJiYkqExEREZUcgYGBuHbtGsqXL4/hw4dLHYfog/Xq1Qu1a9dGXFwc1q5dK3UcKqBCKX527NiBCxcuwMfHJ8ey6Oho6OjowNjYWGW+qakpoqOjc92ej48PjIyMlJOFhUVhxCYiIqJCsnDhQgDA0KFDYWRkJHEaog+nqampvPqzaNEivH79WuJEVBBqL34eP36McePGYdu2bZDL5WrZppeXFxISEpTT48eP1bJdIiIiKnwRERE4fvw4tLS0VAZAIiqp+vfvj+rVqyM2Nha//PKL1HGoANRe/ERERCA2NhaNGzeGlpYWtLS0cOLECaxYsQJaWlowNTVFWloa4uPjVdaLiYmBQqHIdZu6urowNDRUmYiIiKhkyL7q07dvX/beoFJBW1sb06ZNAwAsWLAAqampEiei/FJ78dOxY0dcuXIFFy9eVE5NmzZF//79lf+vra2N4OBg5Tq3bt3Co0eP4ODgoO44REREJKEHDx7A398fADBp0iSJ0xCpj4eHB8zNzfHPP/9gy5YtUsehfNJS9wbLly+PBg0aqMzT19dHxYoVlfMHDx4MT09PmJiYwNDQEGPGjIGDgwNatGih7jhEREQkoZUrVyIrKwuff/45bG1tpY5DpDZyuRyTJ0/GhAkT4OPjg0GDBkFLS+0frUnNCv0hp7lZunQpunXrBldXV3z22WdQKBTYs2ePFFGIiIiokCQlJeHXX38FAN7rQ6XS0KFDUblyZdy/fx/bt2+XOg7lQ5EUPyEhIVi2bJnyZ7lcDl9fX8TFxSE5ORl79uzJ834fIiIiKpm2bNmChIQE1K5dG507d5Y6DpHa6evrw9PTEwDw448/IjMzU+JE9D6SXPkhIiKi0i0rKwsrVqwAAIwZMwYaGvzIQaXTyJEjYWxsjJs3b7InUwnAdyIiIiJSu6CgINy6dQvly5eHh4eH1HGICo2hoSHGjh0LAPjhhx8ghJA4Eb0Lix8iIiJSu+yrPt988w3Kly8vcRqiwjV27FgYGBjg0qVL2L9/v9Rx6B1Y/BAREZFa3b59G4cOHYJMJsPo0aOljkNU6CpWrIhRo0YBALy9vZGVlSVxIsoLix8iIiJSq1WrVgEAunbtilq1akmchqhoTJo0CQYGBrh48SICAgKkjkN5KLODkc+ePVvqCMWKt7e31BGIiKgUSEhIwMaNGwEA48aNkzgNUdGpVKkSxo8fj3nz5sHb2xsuLi4c6KMY4m+EiIiI1GbTpk1ISkpCvXr10LFjR6njEBUpT09PGBkZ4erVq9i1a5fUcSgXLH6IiKjE8fX1haWlJeRyOezt7XHu3Ll3tvf394e1tTXkcjlsbGxw6NAhleV79uxBp06dULFiRchkMly8eLEQ05demZmZWLlyJYA3N4DLZDKJExEVrQoVKiif+zNr1iw+96cYYvFDREQlys6dO+Hp6Qlvb29cuHABtra2cHJyQmxsbK7tQ0ND4ebmhsGDByMyMhIuLi5wcXHB1atXlW2Sk5PRunVrzJ8/v6h2o1Q6fPgw7t27B2NjY3z99ddSxyGSxPjx42FiYoJbt25h27ZtUseh/2DxQ0REJcqSJUswdOhQDBo0CPXq1cPatWtRrlw5bNiwIdf2y5cvR+fOnTF58mTUrVsXc+fORePGjZU35QPAgAEDMHPmTDg6OhbVbpRKy5cvBwAMHToU+vr6EqchkoahoSEmT54MAJg5cyZSU1MlTkRvY/FDREQlRlpaGiIiIlSKFA0NDTg6OiIsLCzXdcLCwnIUNU5OTnm2z6/U1FQkJiaqTGXZ9evXcfToUWhoaCiH/CUqq8aOHQtzc3M8fPhQ5YsWkh6LHyIiKjGeP3+OzMxMmJqaqsw3NTVFdHR0rutER0cXqH1++fj4wMjISDlZWFh81PZKuuyHmrq4uKB69eoSpyGSVrly5TB37lwAwLx58xAXFydxIsrG4oeIiOgDeHl5ISEhQTk9fvxY6kiS+ffff7FlyxYAb77xJiLA3d0d9evXR3x8PHx8fKSOQ/+PxQ8REZUYlSpVgqamJmJiYlTmx8TEQKFQ5LqOQqEoUPv80tXVhaGhocpUVv3yyy94/fo1GjZsiM8++0zqOETFgqamJhYsWADgzZXRBw8eSBuIALD4ISKiEkRHRwdNmjRBcHCwcl5WVhaCg4Ph4OCQ6zoODg4q7QEgKCgoz/ZUMBkZGcp7GsaNG8fhrYne8sUXX6B9+/ZIS0vDd999J3UcAosfIiIqYTw9PbF+/Xps3rwZN27cwIgRI5CcnIxBgwYBAAYOHAgvLy9l+3HjxiEwMBCLFy/GzZs3MWvWLJw/fx6jR49WtomLi8PFixdx/fp1AMCtW7dw8eLFj74vqCzYt28fHj16hIoVK8LNzU3qOETFikwmw8KFCyGTyeDn54eTJ09KHanMY/FDREQlSp8+fbBo0SLMnDkTdnZ2uHjxIgIDA5WDGjx69AhPnz5Vtm/ZsiX8/Pywbt062NraYvfu3QgICECDBg2Ubfbt24dGjRqha9euAIC+ffuiUaNGWLt2bdHuXAmUPdDB8OHDoaenJ3EaouKnSZMmGDp0KABg5MiRSE9PlzhR2aYldQAiIqKCGj16tMqVm7eFhITkmNerVy/06tUrz+15eHjAw8NDTenKjosXL+LEiRPQ1NTEiBEjpI5DVGz9+OOP+P3333Ht2jWsWLECEydOlDpSmcUrP0RERPRBVq5cCQDo2bMnPvnkE4nTEBVfFStWVA5+MGvWLERFRUmcqOxi8UNEREQF9uzZM2zbtg0Ah7cmyg8PDw84ODggKSkJnp6eUscps1j8EBERUYGtX78eqampaNq0KUfOI8oHDQ0NrF69GhoaGti1axd+//13qSOVSSx+iIiIqEDS09OxevVqAG+u+nB4a6L8sbOzw9SpUwG8GSTk7cFZqGiw+CEiIqIC2bNnD6KiomBqaorevXtLHYeoRJk1axbs7Ozw4sULDBkyBEIIqSOVKSx+iIiIqECWLVsGAPj222+hq6srbRiiEkZHRwdbt26Frq4uDh06hHXr1kkdqUxh8UNERET5dvbsWZw9exY6Ojoc3proA9WvXx8+Pj4A3jy4+caNGxInKjtY/BAREVG+ZV/16devn/LBskRUcOPGjUPHjh3x6tUrODs7499//5U6UpnA4oeIiIjy5fHjx9i9ezcAYPz48dKGISrhNDQ0sH37dlSrVg137tyBm5sbMjMzpY5V6qm9+PHx8UGzZs1Qvnx5VKlSBS4uLrh165ZKm5SUFIwaNQoVK1aEgYEBXF1dERMTo+4oREREpEarVq1CZmYm2rdvD1tbW6njEJV4lStXxh9//AE9PT0cOXIEXl5eUkcq9dRe/Jw4cQKjRo3C2bNnERQUhPT0dHTq1AnJycnKNhMmTMD+/fvh7++PEydO4MmTJ+jRo4e6oxAREZGaJCcnK2/M5lUfIvWxs7PDxo0bAQALFy7Er7/+KnGi0k1L3RsMDAxU+XnTpk2oUqUKIiIi8NlnnyEhIQG//vor/Pz80KFDBwDAxo0bUbduXZw9exYtWrRQdyQiIiL6SJs3b0Z8fDxq1aqFbt26SR2HqFTp06cPLl++jB9//BFDhw6Fvr4++vbtK3WsUqnQ7/lJSEgAAJiYmAAAIiIikJ6eDkdHR2Uba2trVKtWDWFhYbluIzU1FYmJiSoTERERFY2srCwsX74cwJubtDU0eMswkbrNmzcPw4YNgxACAwYMwL59+6SOVCoV6rtXVlYWxo8fj1atWqFBgwYAgOjoaOjo6MDY2FilrampKaKjo3Pdjo+PD4yMjJSThYVFYcYmIiKitxw+fBi3b9+GkZERPDw8pI5DVCrJZDKsWbMGX3/9NTIyMtCrVy8cOXJE6lilTqEWP6NGjcLVq1exY8eOj9qOl5cXEhISlNPjx4/VlJCIiIjeZ+nSpQCAoUOHwsDAQOI0RKWXhoYGNm7ciB49eiAtLQ3du3fHzp07pY5VqhRa8TN69GgcOHAAx48fxyeffKKcr1AokJaWhvj4eJX2MTExUCgUuW5LV1cXhoaGKhMREREVvitXriA4OBgaGhoYPXq01HGISj0tLS1s374dvXv3Rnp6Otzc3LBq1SqpY5Uaai9+hBAYPXo09u7di2PHjsHKykpleZMmTaCtrY3g4GDlvFu3buHRo0dwcHBQdxwiIiL6CAsXLgQAuLq6onr16hKnISobdHR04Ofnh1GjRkEIgTFjxmDGjBkQQkgdrcRT+2hvo0aNgp+fH/744w+UL19eeR+PkZER9PT0YGRkhMGDB8PT0xMmJiYwNDTEmDFj4ODgwJHeiIiIipGHDx/Cz88PADBlyhSJ0xCVLZqamli5ciWqVKkCb29vzJs3D/fv38evv/4KXV1dqeOVWGq/8rNmzRokJCSgXbt2MDMzU05v91dcunQpunXrBldXV3z22WdQKBTYs2ePuqMQERHRR1i0aBEyMzPh6OiIpk2bSh2HqMyRyWSYOXMm1q9fD01NTWzbtg2ff/45Xrx4IXW0EkvtV37yczlOLpfD19cXvr6+6n55IiIiUoPY2Fj88ssvAMCnzhNJbMiQIbC0tISrqytOnToFBwcHHDx4ELVr15Y6WonDgfqJiIgoh+XLlyMlJQXNmzdH+/btpY5DVOY5OjoiNDQU1atXx507d9CiRQucOnVK6lglDosfIiIiUpGYmKjsnTFt2jTIZDKJExERANSvXx/h4eFo3rw54uLi4OjoiG3btkkdq0Rh8UNEREQqsu/frVu3LpydnaWOQ0RvMTU1xfHjx5XPAvr6668xZ84cjgSXTyx+iIiISCkxMVE5vPXUqVOhocGPCkTFTbly5eDv74/JkycDALy9veHu7o7U1FSJkxV/fEcjIiIipaVLl+LFixeoU6cO+vfvL3UcIsqDhoYGFixYgJ9//hmampr47bff0KlTJ8TFxUkdrVhj8UNEREQAgBcvXmDx4sUAgDlz5kBLS+2DwhKRmg0bNgyHDh1C+fLlcfLkSTg4OODu3btSxyq2WPwQERERAGD+/Pl4+fIl7Ozs0LNnT6njEFE+derUCaGhoahWrRpu376NFi1a4MyZM1LHKpZY/BARERGePn2KVatWAQDmzZvHe32ISpgGDRrg7NmzaNq0KV68eIEOHTpg165dUscqdvjORkRERPjhhx/w+vVrODg4oEuXLlLHIaIPYGZmhpCQEHz11VdIS0tD3759sXnzZqljFSssfoiIiMq4a9euYe3atQDeFEF8rg9RyaWvrw9/f38MGzYMQggMGjQI69evlzpWscHih4iIqAwTQmD06NHIzMyEi4sL2rdvL3UkIvpImpqaWLt2LUaPHg0hBIYNG6Z8cHFZx+KHiIioDNu1axdCQkIgl8uxdOlSqeMQkZrIZDKsWLECEydOBACMHj2af+Ng8UNERFRmJSUlKT8YTZ8+HZaWltIGIiK1kslkWLhwIby8vAAAnp6e+OmnnyROJS0WP0RERGXU3LlzERUVhRo1aiifFE9EpYtMJsMPP/yAWbNmAQC8vLwwe/ZsCCGkDSYRFj9ERERl0OXLl5VdYJYvXw65XC5xIiIqLDKZDN7e3vjxxx8BALNmzcL06dPLZAHE4oeIiKiMSUtLw8CBA5Geng4XFxd069ZN6khEVAS8vLywePFiAMBPP/2E8ePHIysrS+JURYvFDxERURkzZ84cXLp0CRUrVlQOcU1EZYOnpydWr14NAFixYgWGDx+OzMxMiVMVHRY/REREZcjRo0eVXV/WrFkDU1NTiRMRUVEbMWIENm3aBA0NDfzyyy8YOHAgMjIypI5VJFj8EBERlRFPnjxB//79lc/96NWrl9SRiEgi7u7u2L59O7S0tODn54fevXvj9evXUscqdCx+iIiIyoBXr17B2dkZsbGxaNiwIZYtWyZ1JCKSWO/evbFnzx7o6Ohg7969cHR0xPPnz6WOVahY/BAREZVymZmZ8PDwwPnz51GxYkXs3bsXenp6UsciomKge/fuOHLkCIyNjREaGgoHBwfcuXNH6liFhsUPERFRKSaEwMiRI+Hv7w9tbW38/vvvqFGjhtSxiKgYadeuHc6cOYPq1avj7t27cHBwQFBQkNSxCgWLHyIiolIqKysLY8aMwbp166ChoYGtW7eibdu2UsciomKoXr16OHv2LJo2bYoXL17AyckJs2bNKnUjwbH4ISIiKoVSU1MxcOBA+Pr6QiaTYf369ejdu7fUsYioGFMoFDh58iSGDRsGIQRmz54NJycnPHnyROpoasPih4iIqJR58uQJ2rVrh23btkFLSwvbtm3DN998I3UsIioB9PT08PPPP+O3335DuXLlEBwcjLp162L16tWl4oGoLH6IiIhKkT179qBhw4Y4e/YsjI2NcfDgQbi5uUkdi4hKmK+//hp//fUXmjdvjsTERIwaNQqtWrXC+fPnpY72UVj8EBERlQL37t2Ds7MzXF1d8eLFC9ja2uKvv/5Cp06dpI5GRCVUvXr1EBoaipUrV6J8+fI4e/YsmjVrhu7du5fYIojFDxERUQl2/fp1DB48GNbW1ti3bx80NTUxbdo0hIeHo1atWlLHI6ISTlNTE6NHj8aNGzcwYMAAaGho4MCBA2jWrBkcHR2xdetWvHr1SuqY+SZp8ePr6wtLS0vI5XLY29vj3LlzUsYhIqISoqDnD39/f1hbW0Mul8PGxgaHDh1SWS6EwMyZM2FmZgY9PT04OjoW6+dcPHr0CKtXr0abNm1Qv359bNiwARkZGXBycsLly5fh4+MDXV1dqWMSUSlStWpVbNmyBTdu3MDAgQOhqamJ4OBgDBgwAKamphg4cCC2bduGmJgYqaO+k2TFz86dO+Hp6Qlvb29cuHABtra2cHJyQmxsrFSRiIioBCjo+SM0NBRubm4YPHgwIiMj4eLiAhcXF1y9elXZZsGCBVixYgXWrl2L8PBw6Ovrw8nJCSkpKUW1W7kSQiAqKgrHjh3D6tWr4e7uDktLS1SvXh2jRo3C6dOnoampCRcXF4SGhiIwMBD16tWTNDMRlW6ffvopNm/ejLt372L27NmwsrJCUlISfvvtN3z99ddQKBRo0KABBg4ciMWLFyMoKAj37t1Damqq1NEBADIhhJDihe3t7dGsWTOsWrUKwJtnEVhYWGDMmDGYNm3aO9dNTEyEkZEREhISYGho+EGvP3v27A9ar7Ty9vb+6G3wmP4Pj6d68Xiq18ccT3W8/36sgp4/+vTpg+TkZBw4cEA5r0WLFrCzs8PatWshhIC5uTkmTpyISZMmAQASEhJgamqKTZs2oW/fvvnK9THH5sWLF/jhhx/w7NmzHFNuBZimpiaaN28OV1dX9OnTB5988kmBXo+ISF2ysrJw+vRpHDx4EEFBQYiMjMy1nUwmg6mpKapUqQJjY2NUqFABFSpUgLGxMQwMDFCuXDm4ubnB0tKywBkK8v6rVeCtq0FaWhoiIiLg5eWlnKehoQFHR0eEhYXlaJ+amqpSLSYkJAB4s6MfSupv84qbjzmW2XhM/4fHU714PNXrY45n9roSfW9W4PMHAISFhcHT01NlnpOTEwICAgAA9+/fR3R0NBwdHZXLjYyMYG9vj7CwsDyLH3WemxISErB06dJcl2loaMDS0hK1a9dGgwYN0KpVK9jb28PAwEDZRh1/I0REH8rOzg52dnb47rvv8Pz5c5w7dw5Xr17F1atXcf36dTx+/BgpKSmIjo5GdHR0ntuxsbGBiYlJgV+/QOcmIYGoqCgBQISGhqrMnzx5smjevHmO9t7e3gIAJ06cOHEqJtPjx4+L6pShoqDnDyGE0NbWFn5+firzfH19RZUqVYQQQpw5c0YAEE+ePFFp06tXL9G7d+88s/DcxIkTJ07Fa8rPuUmSKz8F5eXlpfKtXVZWFuLi4lCxYkXIZDIJk32cxMREWFhY4PHjx5J1HylNeDzVi8dT/UrDMRVC4OXLlzA3N5c6iuRK67mpoErDv+uPxWPAYwDwGADSHYOCnJskKX4qVaoETU3NHKNBxMTEQKFQ5Givq6ubY9QaY2PjwoxYpAwNDcvsH0lh4PFULx5P9Svpx9TIyEiy1y7o+QMAFArFO9tn/zcmJgZmZmYqbezs7PLMUtrPTQVV0v9dqwOPAY8BwGMASHMM8ntukmS0Nx0dHTRp0gTBwcHKeVlZWQgODoaDg4MUkYiIqAT4kPOHg4ODSnsACAoKUra3srKCQqFQaZOYmIjw8HCek4iIShnJur15enrC3d0dTZs2RfPmzbFs2TIkJydj0KBBUkUiIqIS4H3nj4EDB6Jq1arw8fEBAIwbNw5t27bF4sWL0bVrV+zYsQPnz5/HunXrALwZgWj8+PGYN28eateuDSsrK8yYMQPm5uZwcXGRajeJiKgQSFb89OnTB8+ePcPMmTMRHR0NOzs7BAYGwtTUVKpIRU5XVxfe3t58EJ2a8HiqF4+n+vGYqsf7zh+PHj2Chsb/Oja0bNkSfn5++P777zF9+nTUrl0bAQEBaNCggbLNlClTkJycjGHDhiE+Ph6tW7dGYGAg5HJ5ke9fScN/1zwGAI8BwGMAlIxjINlzfoiIiIiIiIqSJPf8EBERERERFTUWP0REREREVCaw+CEiIiIiojKBxQ+VGu3atcP48eOljlFsyWQyBAQEFPrrWFpaYtmyZYX+OkREREQFxeKnAJ49e4YRI0agWrVq0NXVhUKhgJOTE86cOSN1tBLPw8MDMpkMMpkM2trasLKywpQpU5CSkpLvbezZswdz584txJTFW3R0NMaMGYMaNWpAV1cXFhYW6N69e47nm1DB8O+eKG8//PADWrZsiXLlyuX5gNdHjx6ha9euKFeuHKpUqYLJkycjIyOjaIMWMl9fX1haWkIul8Pe3h7nzp2TOlKhOXnyJLp37w5zc/Ncv1QTQmDmzJkwMzODnp4eHB0dcefOHWnCFhIfHx80a9YM5cuXR5UqVeDi4oJbt26ptElJScGoUaNQsWJFGBgYwNXVNcfDlkuyNWvWoGHDhsqHmTo4OODw4cPK5cV5/1n8FICrqysiIyOxefNm3L59G/v27UO7du3w4sULqaOVCp07d8bTp0/x999/Y+nSpfj555/h7e2d7/VNTExQvnz5QkxYfD148ABNmjTBsWPHsHDhQly5cgWBgYFo3749Ro0aJXW8Eo1/90R5S0tLQ69evTBixIhcl2dmZqJr165IS0tDaGgoNm/ejE2bNmHmzJlFnLTw7Ny5E56envD29saFCxdga2sLJycnxMbGSh2tUCQnJ8PW1ha+vr65Ll+wYAFWrFiBtWvXIjw8HPr6+nBycirQl5nF3YkTJzBq1CicPXsWQUFBSE9PR6dOnZCcnKxsM2HCBOzfvx/+/v44ceIEnjx5gh49ekiYWr0++eQT/PTTT4iIiMD58+fRoUMHODs749q1awCK+f4Lypd///1XABAhISF5tgEg1q9fL1xcXISenp6oVauW+OOPP1TahISEiGbNmgkdHR2hUCjE1KlTRXp6uhBCiP379wsjIyORkZEhhBAiMjJSABBTp05Vrj948GDRv39/kZSUJMqXLy/8/f1Vtr93715Rrlw5kZiYqK5dLxLu7u7C2dlZZV6PHj1Eo0aNhBBCPH/+XPTt21eYm5sLPT090aBBA+Hn56fSvm3btmLcuHHKn6tXry5++OEHMWjQIGFgYCAsLCzEzz//rFzevn17MWrUKJVtxMbGCm1tbXH06FH17mAh++KLL0TVqlVFUlJSjmX//vuvEOLNv8+9e/cq51++fFm0b99eyOVyYWJiIoYOHSpevnypXP7f4ymEEM7OzsLd3V35c0xMjOjWrZuQy+XC0tJSbN26VVSvXl0sXbpUCCHEoEGDRNeuXVW2kZaWJipXrix++eWXj9rnovC+v/v79+8LACIyMjLHOsePHxdCCHH8+HEBQBw9elQ0adJE6OnpCQcHB3Hz5k3lOt7e3sLW1lZs2bJFVK9eXRgaGoo+ffoo/443b94sTExMREpKisrrOzs7i6+//lq9O030ATZu3CiMjIxyzD906JDQ0NAQ0dHRynlr1qwRhoaGIjU1tQgTFp7mzZurnEsyMzOFubm58PHxkTBV0fjveSUrK0soFAqxcOFC5bz4+Hihq6srtm/fLkHCohEbGysAiBMnTggh3uyztra2yme0GzduCAAiLCxMqpiFrkKFCuKXX34p9vvPKz/5ZGBgAAMDAwQEBCA1NTXPdrNnz0bv3r1x+fJldOnSBf3790dcXBwAICoqCl26dEGzZs1w6dIlrFmzBr/++ivmzZsHAGjTpg1evnyJyMhIAG++WahUqRJCQkKU2z9x4gTatWsHfX199O3bFxs3blR5/Y0bN6Jnz54l/grI1atXERoaCh0dHQBvLp82adIEBw8exNWrVzFs2DAMGDDgvV0LFi9ejKZNmyIyMhIjR47EiBEjlJemhwwZAj8/P5Xf59atW1G1alV06NCh8HZOzeLi4hAYGIhRo0ZBX18/x/LcuqIkJyfDyckJFSpUwF9//QV/f38cPXoUo0ePLtBre3h44PHjxzh+/Dh2796N1atXq3zbOWTIEAQGBuLp06fKeQcOHMCrV6/Qp0+fAr2WFPL7d58f3333HRYvXozz589DS0sL33zzjcrye/fuISAgAAcOHMCBAwdw4sQJ/PTTTwCAXr16ITMzE/v27VO2j42NxcGDB3Nsh6g4CQsLg42NjcoDzJ2cnJCYmKj8hrgkS0tLQ0REBBwdHZXzNDQ04OjoiLCwMAmTSeP+/fuIjo5WOR5GRkawt7cv1ccjISEBwJseKAAQERGB9PR0leNgbW2NatWqlcrjkJmZiR07diA5ORkODg7Ffv9Z/OSTlpYWNm3ahM2bN8PY2BitWrXC9OnTcfnyZZV2Hh4ecHNzQ61atfDjjz8iKSlJ+QF99erVsLCwwKpVq2BtbQ0XFxfMnj0bixcvRlZWFoyMjGBnZ6csdkJCQjBhwgRERkYiKSkJUVFRuHv3Ltq2bQvgzQfLI0eOKD9YxsbG4tChQyX2w9CBAwdgYGAAuVwOGxsbxMbGYvLkyQCAqlWrYtKkSbCzs0ONGjUwZswYdO7cGbt27XrnNrt06YKRI0eiVq1amDp1KipVqoTjx48DgPLy6x9//KFsv2nTJuX9RyXF3bt3IYSAtbV1vtfx8/NDSkoKtmzZggYNGqBDhw5YtWoVfvvtt3z3yb19+zYOHz6M9evXo0WLFmjSpAl+/fVXvH79WtmmZcuWqFOnDn777TflvI0bN6JXr14wMDDI/05KJL9/9/nxww8/oG3btqhXrx6mTZuG0NBQlW4gWVlZ2LRpExo0aIA2bdpgwIAByvu19PT00K9fP5UvO7Zu3Ypq1aqhXbt2H72fRIUlOjpapfABoPw5Ojpaikhq9fz5c2RmZua6j6Vh/woqe5/L0vHIysrC+PHj0apVKzRo0ADAm+Ogo6OT48vH0nYcrly5AgMDA+jq6uLbb7/F3r17Ua9evWK//yx+CsDV1RVPnjzBvn370LlzZ4SEhKBx48bYtGmTsk3Dhg2V/6+vrw9DQ0PlN+E3btyAg4ODygfrVq1aISkpCf/88w8AoG3btggJCYEQAqdOnUKPHj1Qt25dnD59GidOnIC5uTlq164NAGjevDnq16+PzZs3A3jzYah69er47LPPCvtQFIr27dvj4sWLCA8Ph7u7OwYNGgRXV1cAb75VmDt3LmxsbGBiYgIDAwMcOXIEjx49euc23/59yGQyKBQK5e9DLpdjwIAB2LBhAwDgwoULuHr1Kjw8PApnBwuJEKLA69y4cQO2trYqV4patWqFrKysHDdtvmsbWlpaaNKkiXKetbV1jje7IUOGKD+0x8TE4PDhwyWqQM/P331+vP1v0czMDABUrpJZWlqqXLE1MzNTWT506FD8+eefiIqKAlAyC3UqGaZNm6YcgCav6ebNm1LHJCoWRo0ahatXr2LHjh1SRylyderUUX5uGzFiBNzd3XH9+nWpY70Xi58Cksvl+PzzzzFjxgyEhobCw8ND5aZ8bW1tlfYymQxZWVn53n67du1w+vRpXLp0Cdra2rC2tka7du0QEhKCEydOKK/6ZBsyZIjyQ9jGjRsxaNCgEvthSF9fH7Vq1YKtrS02bNiA8PBw/PrrrwCAhQsXYvny5Zg6dSqOHz+OixcvwsnJCWlpae/c5vt+H0OGDEFQUBD++ecfbNy4ER06dED16tXVv3OFqHbt2oXyYURDQyNHYZWenl7g7QwcOBB///03wsLCsHXrVlhZWaFNmzbqilkk8vq719B48xb69nHK6xi9/W8x+2/07X+L7/u32qhRI9ja2mLLli2IiIjAtWvXSlyhTiXDxIkTcePGjXdONWrUyNe2FApFjqvJ2T8rFAq1Zy9qlSpVgqamZq77WBr2r6Cy97msHI/Ro0fjwIEDOH78OD755BPlfIVCgbS0NMTHx6u0L23HQUdHB7Vq/V979x4UVfnGAfy7oLvtyk1lRSPBNfOC6QLrOGwjKlmIlZfGKbPEa95RYbQJCzKzBszMAadyYiYgp0LHRp1yNBsRJkFNlIu4DNjGJXXLwXAUQQH3+f3hcHKFn3hBV+T7mdmZ3XPec97nPZzdPQ/nnGcHwGQyISEhAUajEUlJSY/8+Jn83KeAgACH6h63M2TIEBw+fNjhQCknJwfu7u7Km6b5vp9NmzYpiU5z8pOVldXiEpcZM2agsrISycnJsFgsmDVrVvsMzMlcXFzw3nvvIS4uDvX19cjJycHkyZMxY8YMGI1G9O/fH2VlZffdz7BhwzBixAikpKTg+++/71BnJJr16NED48ePxxdffNHqvnjrhw9wY18sLCx0aJ+TkwMXFxcMGjQIAKDX6x3u1bl+/TqKi4uV14MHD0ZTUxOOHz+uTCstLW3RX8+ePTFlyhSkpqYiLS0Nc+bMudehPjKa3/d6vR4AHLZTQUHBA+u3+Z8dqampeOGFF9C3b98H1hd1Xnq9HoMHD77to/l+zLaYzWacPHnS4Szmr7/+Cg8PDwQEBDyoITw0arUaJpPJ4ScF7HY7Dhw4ALPZ7MTInMNgMKB3794O2+PSpUs4evToY7U9RARRUVHYuXMnMjMzYTAYHOabTCZ07drVYTuUlpaiqqrqsdoOt7Lb7bh27dqjP34nFlvoUKqrqyUsLEy2bt0qhYWF8ueff8r27dvFx8dH5s6dKyItq56IiHh6ekpqaqqIiJw5c0Z0Op0sXbpUSkpKZNeuXeLt7S1r1qxxWCYwMFBcXV3lq6++EhGRCxcuSNeuXQWAQ4WoZm+++aao1WqJiIho93E/LK1Ve2tsbBRfX1/ZsGGDxMTESN++fSUnJ0csFou8/fbb4uHh4bBMa9XemquONTMajS2299dffy1qtVq6d+8u9fX17Tuwh8RqtUrv3r0lICBAduzYIWVlZWKxWCQpKUkGDx4sIo7755UrV6RPnz4ydepUOXnypGRmZkr//v0dKrlt2bJFdDqd/Pzzz1JSUiLz588XDw8PhzYRERESFBQkR44ckby8PBk1apRotdoW233//v2iVqvF1dVVzp49+4C3Rvu5k/d9SEiIhIaGisVikaysLBk5cmSr1d6aq+6J/FfJsby8XET+q/Z2s02bNom/v7/DtIsXL4pOpxO1Wi0ZGRkPaNREd66yslLy8/Nl7dq14ubmJvn5+ZKfn69UjmxqapJnn31WwsPDpaCgQPbt2yd6vV5Wr17t5MjbT0ZGhmg0GklLSxOLxSILFiwQLy8vhwp3j5PLly8rf2cA8vnnn0t+fr5UVlaKiEhiYqJ4eXnJ7t27paioSCZPniwGg6HDfr+2ZvHixeLp6SlZWVlis9mUR11dndJm0aJF4ufnJ5mZmZKXlydms1nMZrMTo25fsbGxkp2dLeXl5VJUVCSxsbGiUqlk//79IvJoj5/Jzx26evWqxMbGSnBwsHh6eopOp5NBgwZJXFycsrO3lfyI3L7UdbMVK1YIACkpKVGmGY1G6d27d6uxHThwQADI9u3b22ewTtBa8iMikpCQIHq9Xs6cOSOTJ08WNzc36dWrl8TFxcnMmTPbJfm5fPmy6HQ6WbJkSfsNyAnOnTsnS5cuFX9/f1Gr1eLr6yuTJk1SDsJv3T/bKnXd0NAgixcvlh49ekivXr0kISGhRalrm80mL7/8smg0GvHz81NKNd+63e12u/j7+8tLL730ALdA+7uT973FYhGz2SxarVYCAwNl//79Dyz5ERGJjIxstew1kTPMmjVLALR4NO//IiIVFRUyYcIE0Wq14u3tLStXrmzxvdfRbd68Wfz8/EStVsvIkSPlyJEjzg7pgWn+TLv10fzdYLfbJT4+Xnx8fESj0ci4ceOktLTUuUG3s9bGD8DheK++vl6WLFki3bt3F51OJ6+++qrYbDbnBd3O5s6dqxxv6PV6GTdunJL4iDza41eJ3MPd0vRI2bp1K2JiYnDu3Lk7vhSB/lNRUYGnn34ax44dQ3BwsLPDeSzV1tbC19cXqampj86PnHVQ48aNw9ChQ5GcnOzsUIiIiDqcLs4OgO5dXV0dbDYbEhMTsXDhQiY+d6mxsREXLlxAXFwcQkJCmPg8AHa7HdXV1di4cSO8vLwwadIkZ4fUYdXU1Cj3/n355ZfODoeIiKhDYvLTgX366af45JNPMHr0aKxevdrZ4XQ4OTk5CAsLw8CBA7Fjxw5nh/NYqqqqgsFgwFNPPYW0tDR06cKPnHsVFBSEmpoarF+/XilKQURERHeHl70REREREVGnwFLXRERERETUKTD5ISIiIiKiToHJDxERERERdQpMfoiIiIiIqFNg8kNERERERJ0Ckx8iIiKi+zB27FhER0c7O4wH7sMPP0RgYKCzwyC6L0x+iIiIiDqxhoaGh9qfiKCpqemh9knUjMkPERER0T2aPXs2srOzkZSUBJVKBZVKhYqKChQXF2PChAlwc3ODj48PIiMjUV1drSw3duxYLFu2DNHR0ejevTt8fHyQkpKCK1euYM6cOXB3d8eAAQOwd+9eZZmsrCyoVCrs2bMHw4cPxxNPPIGQkBAUFxc7xHTo0CGEhoZCq9Wib9++WL58Oa5cuaLM79evH9atW4eZM2fCw8MDCxYsAAC8++67GDhwIHQ6Hfr374/4+Hg0NjYCANLS0rB27VoUFhYq40xLS0NFRQVUKhUKCgqU9V+8eBEqlQpZWVkOce/duxcmkwkajQaHDh2C3W5HQkICDAYDtFotjEbjXf3o+KlTp/DKK6/Aw8MD7u7uCA0NhdVqvePlqXNi8kNERER0j5KSkmA2mzF//nzYbDbYbDa4u7vj+eefR1BQEPLy8rBv3z78888/eP311x2WTU9Ph7e3N37//XcsW7YMixcvxmuvvYbnnnsOJ06cQHh4OCIjI1FXV+ew3DvvvIONGzfi2LFj0Ov1mDhxopKkWK1WREREYOrUqSgqKsK2bdtw6NAhREVFOazjs88+g9FoRH5+PuLj4wEA7u7uSEtLg8ViQVJSElJSUrBp0yYAwLRp07By5UoMHTpUGee0adPualvFxsYiMTERJSUlGD58OBISEvDtt99iy5YtOHXqFGJiYjBjxgxkZ2e3ua6zZ89i9OjR0Gg0yMzMxPHjxzF37lyeUaK2CRERERHdszFjxsiKFSuU1+vWrZPw8HCHNn/99ZcAkNLSUmWZUaNGKfObmpqkW7duEhkZqUyz2WwCQA4fPiwiIgcPHhQAkpGRobS5cOGCaLVa2bZtm4iIzJs3TxYsWODQ92+//SYuLi5SX18vIiL+/v4yZcqUNse1YcMGMZlMyus1a9aI0Wh0aFNeXi4AJD8/X5lWU1MjAOTgwYMOce/atUtpc/XqVdHpdJKbm+uwvnnz5sn06dPbjG316tViMBikoaGhzbZEN+vizMSLiIiI6HFTWFiIgwcPws3NrcU8q9WKgQMHAgCGDx+uTHd1dUXPnj0xbNgwZZqPjw8A4Pz58w7rMJvNyvMePXpg0KBBKCkpUfouKirCd999p7QREdjtdpSXl2PIkCEAgBEjRrSIbdu2bUhOTobVakVtbS2amprg4eFx1+P/f27u848//kBdXR1efPFFhzYNDQ0ICgpqc10FBQUIDQ1F165d2y0+6hyY/BARERG1o9raWkycOBHr169vMa9Pnz7K81sP3FUqlcM0lUoFALDb7XfV98KFC7F8+fIW8/z8/JTn3bp1c5h3+PBhvPXWW1i7di3Gjx8PT09PZGRkYOPGjbftz8Xlxh0UIqJMa74E71Y391lbWwsA2LNnD3x9fR3aaTSa2/YJAFqtts02RK1h8kNERER0H9RqNa5fv668Dg4Oxo8//oh+/fqhS5f2P9Q6cuSIksjU1NSgrKxMOaMTHBwMi8WCAQMG3NU6c3Nz4e/vj/fff1+ZVllZ6dDm1nECgF6vBwDYbDbljM3NxQ/+n4CAAGg0GlRVVWHMmDF3FStw46xZeno6GhsbefaH7goLHhARERHdh379+uHo0aOoqKhAdXU1li5din///RfTp0/HsWPHYLVa8csvv2DOnDktkod78dFHH+HAgQMoLi7G7Nmz4e3tjSlTpgC4UbEtNzcXUVFRKCgowOnTp7F79+4WBQ9u9cwzz6CqqgoZGRmwWq1ITk7Gzp07W4yzvLwcBQUFqK6uxrVr16DVahESEqIUMsjOzkZcXFybY3B3d8eqVasQExOD9PR0WK1WnDhxAps3b0Z6enqby0dFReHSpUt44403kJeXh9OnT2Pr1q0oLS1tc1nq3Jj8EBEREd2HVatWwdXVFQEBAdDr9WhoaEBOTg6uX7+O8PBwDBs2DNHR0fDy8lIuE7sfiYmJWLFiBUwmE/7++2/89NNPUKvVAG6cEcnOzkZZWRlCQ0MRFBSEDz74AE8++eRt1zlp0iTExMQgKioKgYGByM3NVarANZs6dSoiIiIQFhYGvV6PH374AQDwzTffoKmpCSaTCdHR0fj444/vaBzr1q1DfHw8EhISMGTIEERERGDPnj0wGAxtLtuzZ09kZmaitrYWY8aMgclkQkpKCs8CUZtUcvNFmkRERET0SMrKykJYWBhqamrg5eXl7HCIOiSe+SEiIiIiok6ByQ8RERERPVIWLVoENze3Vh+LFi1ydnjUgfGyNyIiIiJ6pJw/fx6XLl1qdZ6Hhwd69er1kCOixwWTHyIiIiIi6hR42RsREREREXUKTH6IiIiIiKhTYPJDRERERESdApMfIiIiIiLqFJj8EBERERFRp8Dkh4iIiIiIOgUmP0RERERE1Ckw+SEiIiIiok7hf71hd8nsbZaSAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(10, 4))\n",
    "\n",
    "weather_counts = df['weather_condition'].value_counts().sort_values()\n",
    "\n",
    "axes[0].set_title('Weather condition\\n(discrete)')\n",
    "axes[0].bar(weather_counts.index, weather_counts.values, color='grey')\n",
    "\n",
    "axes[1].set_title('Temperature\\n(continuous)')\n",
    "sns.kdeplot(x='temperature_c', data=df, ax=axes[1], color='black')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45c30838",
   "metadata": {},
   "source": [
    "#### 2.4.2. Measurement scales\n",
    "\n",
    "**Nominal data**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "64486f65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "weather_condition\n",
       "Sunny     153\n",
       "Cloudy    107\n",
       "Rainy      71\n",
       "Snowy      34\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['weather_condition'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bc77495",
   "metadata": {},
   "source": [
    "**Ordinal data**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "ece92c8d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "wind_strength\n",
       "Light Breeze     121\n",
       "Moderate Wind     98\n",
       "Calm              66\n",
       "Strong Wind       55\n",
       "Gale              25\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['wind_strength'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a544a129",
   "metadata": {},
   "source": [
    "**Interval data**: numerical, but has no 'true' zero point, ratios don't really mean anything"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "afdd07eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    365.000000\n",
       "mean       5.753425\n",
       "std        7.720141\n",
       "min      -10.000000\n",
       "25%        0.700000\n",
       "50%        5.700000\n",
       "75%       10.700000\n",
       "max       25.000000\n",
       "Name: temperature_c, dtype: float64"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['temperature_c'].describe()    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6b92e7a",
   "metadata": {},
   "source": [
    "**Ratio data**: numerical (continuous) has true zero, ratios are meaning full. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "a51f74c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>weather_condition</th>\n",
       "      <th>wind_strength</th>\n",
       "      <th>temperature_c</th>\n",
       "      <th>rainfall_inches</th>\n",
       "      <th>humidity_percent</th>\n",
       "      <th>pressure_hpa</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Sunny</td>\n",
       "      <td>Light Breeze</td>\n",
       "      <td>8.2</td>\n",
       "      <td>0.13</td>\n",
       "      <td>48.8</td>\n",
       "      <td>1016.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Snowy</td>\n",
       "      <td>Gale</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.29</td>\n",
       "      <td>89.6</td>\n",
       "      <td>1009.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Rainy</td>\n",
       "      <td>Strong Wind</td>\n",
       "      <td>7.3</td>\n",
       "      <td>0.01</td>\n",
       "      <td>100.0</td>\n",
       "      <td>1003.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Cloudy</td>\n",
       "      <td>Light Breeze</td>\n",
       "      <td>21.6</td>\n",
       "      <td>0.62</td>\n",
       "      <td>49.3</td>\n",
       "      <td>1006.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Sunny</td>\n",
       "      <td>Calm</td>\n",
       "      <td>12.0</td>\n",
       "      <td>1.09</td>\n",
       "      <td>38.6</td>\n",
       "      <td>1016.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  weather_condition wind_strength  temperature_c  rainfall_inches  \\\n",
       "0             Sunny  Light Breeze            8.2             0.13   \n",
       "1             Snowy          Gale            1.6             0.29   \n",
       "2             Rainy   Strong Wind            7.3             0.01   \n",
       "3            Cloudy  Light Breeze           21.6             0.62   \n",
       "4             Sunny          Calm           12.0             1.09   \n",
       "\n",
       "   humidity_percent  pressure_hpa  \n",
       "0              48.8        1016.5  \n",
       "1              89.6        1009.4  \n",
       "2             100.0        1003.3  \n",
       "3              49.3        1006.9  \n",
       "4              38.6        1016.0  "
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "2ba076cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    365.000000\n",
       "mean       0.303699\n",
       "std        0.311469\n",
       "min        0.000000\n",
       "25%        0.080000\n",
       "50%        0.210000\n",
       "75%        0.400000\n",
       "max        2.230000\n",
       "Name: rainfall_inches, dtype: float64"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['rainfall_inches'].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f8863e1",
   "metadata": {},
   "source": [
    "### 2.5. Correlation and covariance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "d1fc31c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>study_hours</th>\n",
       "      <th>exam_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.986028</td>\n",
       "      <td>-14.756865</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.443228</td>\n",
       "      <td>-2.971443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.695879</td>\n",
       "      <td>-11.054895</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6.423281</td>\n",
       "      <td>-7.185086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.589365</td>\n",
       "      <td>-15.329768</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   study_hours  exam_score\n",
       "0     5.986028  -14.756865\n",
       "1     5.443228   -2.971443\n",
       "2     8.695879  -11.054895\n",
       "3     6.423281   -7.185086\n",
       "4     5.589365  -15.329768"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Simulated: study hours and exam score, positively correlated\n",
    "study_hours = np.random.normal(loc=6, scale=1.5, size=80).clip(0.5, 12)\n",
    "exam_score  = 30 + - 6 * study_hours + np.random.normal(0, 7, size=80)\n",
    "\n",
    "df = pd.DataFrame({'study_hours': study_hours, 'exam_score': exam_score})\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "4fcda1bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Grades vs study time')\n",
    "plt.scatter(df['study_hours'], df['exam_score'], color='black')\n",
    "plt.xlabel('Study hours')\n",
    "plt.ylabel('Exam score')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "506fadb5",
   "metadata": {},
   "source": [
    "- **Covariance**: How likely two variables are to change together.\n",
    "- **Correlation (Pearson)**: Covariance, but standardized by the standard deviations (-1: perfect inverse, 0: no relationship, +1: perfect direct relationship)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "35b54b2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>study_hours</th>\n",
       "      <th>exam_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>study_hours</th>\n",
       "      <td>1.815801</td>\n",
       "      <td>-11.306065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>exam_score</th>\n",
       "      <td>-11.306065</td>\n",
       "      <td>123.605797</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             study_hours  exam_score\n",
       "study_hours     1.815801  -11.306065\n",
       "exam_score    -11.306065  123.605797"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Covariance matrix\n",
    "cov = df.cov()\n",
    "cov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "7b1f78f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>study_hours</th>\n",
       "      <th>exam_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>study_hours</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.754672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>exam_score</th>\n",
       "      <td>-0.754672</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             study_hours  exam_score\n",
       "study_hours     1.000000   -0.754672\n",
       "exam_score     -0.754672    1.000000"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Correlation matrix\n",
    "corr = df.corr()\n",
    "corr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "1c4ced52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['replicas', 'temperature_ladder', 'elapsed_time', 'hyperparameters', 'is_dataframe', 'column_names', 'bounds', 'exchange_interval', 'verbose', 'n_workers'])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "url = 'https://github.com/gperdrizet/fullstack-2605/raw/refs/heads/main/data/pearson_spearman_results.pkl'\n",
    "pearson_spearman_df = pd.read_pickle(url)\n",
    "pearson_spearman_df.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "d6a657da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18.732420</td>\n",
       "      <td>-26.637757</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12.915538</td>\n",
       "      <td>-17.591157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>17.195900</td>\n",
       "      <td>-22.663048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>15.028460</td>\n",
       "      <td>-19.811119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18.016394</td>\n",
       "      <td>-22.699903</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           0          1\n",
       "0  18.732420 -26.637757\n",
       "1  12.915538 -17.591157\n",
       "2  17.195900 -22.663048\n",
       "3  15.028460 -19.811119\n",
       "4  18.016394 -22.699903"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(pearson_spearman_df['replicas'][1]['best_data'])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "c28aedd5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.DataFrame'>\n",
      "RangeIndex: 1000 entries, 0 to 999\n",
      "Data columns (total 2 columns):\n",
      " #   Column  Non-Null Count  Dtype  \n",
      "---  ------  --------------  -----  \n",
      " 0   0       1000 non-null   float64\n",
      " 1   1       1000 non-null   float64\n",
      "dtypes: float64(2)\n",
      "memory usage: 15.8 KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "af9804a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Perdrizet's Falcon\")\n",
    "plt.scatter(df[0], df[1], color='black', s=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e9b7525",
   "metadata": {},
   "source": [
    "Generated with hill climbing optimization. See `hill-climber` [Example climb: creating non-linear monotonic relationships](https://github.com/gperdrizet/hill_climber/blob/dev/notebooks/05-pearson_spearman.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "079be8ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>4.879232e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.879232e-07</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              0             1\n",
       "0  1.000000e+00  4.879232e-07\n",
       "1  4.879232e-07  1.000000e+00"
      ]
     },
     "execution_count": 82,
     "metadata": {},
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   "source": [
    "pearson_corr = df.corr()\n",
    "pearson_corr"
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  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "57187ae7",
   "metadata": {},
   "outputs": [
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