machine_learning_exercises1_solutions.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "machine_learning_exercises1.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ko7Hm5QWCWqX",
        "colab_type": "text"
      },
      "source": [
        "# Exercises for Machine Learning with Python, Lecture 1: *Linear Least Squares Regression*\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AXY2tywnCawC",
        "colab_type": "text"
      },
      "source": [
        "## Before you begin the exercises:\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5WFgpPP6mrpa",
        "colab_type": "text"
      },
      "source": [
        "The datafiles are text files stored here (also try and download them to your own computer, open and see what they contain):\n",
        "\n",
        "Features: https://www.dropbox.com/s/pf2sfiy9l86xhww/boston_features.txt\n",
        "\n",
        "Prices: https://www.dropbox.com/s/j7flze0oe86pr6o/boston_prices.txt\n",
        "\n",
        "*   Start by downloading the dataset:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nFtEVyvxmrwJ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 772
        },
        "outputId": "7ff385cf-4342-4108-cc09-e7cd74682dc7"
      },
      "source": [
        "# Download the features and target (the prices) to Google Colab using !wget\n",
        "!wget -O boston_features.txt https://www.dropbox.com/s/pf2sfiy9l86xhww/boston_features.txt\n",
        "!wget -O boston_prices.txt https://www.dropbox.com/s/j7flze0oe86pr6o/boston_prices.txt"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "--2020-05-13 15:34:07--  https://www.dropbox.com/s/pf2sfiy9l86xhww/boston_features.txt\n",
            "Resolving www.dropbox.com (www.dropbox.com)... 162.125.82.1, 2620:100:6032:1::a27d:5201\n",
            "Connecting to www.dropbox.com (www.dropbox.com)|162.125.82.1|:443... connected.\n",
            "HTTP request sent, awaiting response... 301 Moved Permanently\n",
            "Location: /s/raw/pf2sfiy9l86xhww/boston_features.txt [following]\n",
            "--2020-05-13 15:34:08--  https://www.dropbox.com/s/raw/pf2sfiy9l86xhww/boston_features.txt\n",
            "Reusing existing connection to www.dropbox.com:443.\n",
            "HTTP request sent, awaiting response... 302 Found\n",
            "Location: https://ucfcce27fc0a2ecd38bd118e07c6.dl.dropboxusercontent.com/cd/0/inline/A3o5VSYBFQREn6bIHoMp8eCHzv-dlsHUxOhSzn0e-mGjJGXBIOBRccuEbsU007U_y6mY9lRWkNQOcGfZ-DeO-7KzLELA6md-IqkcjPs3uhHf7EpGEcnaMMu7NAhKw9gb2qs/file# [following]\n",
            "--2020-05-13 15:34:08--  https://ucfcce27fc0a2ecd38bd118e07c6.dl.dropboxusercontent.com/cd/0/inline/A3o5VSYBFQREn6bIHoMp8eCHzv-dlsHUxOhSzn0e-mGjJGXBIOBRccuEbsU007U_y6mY9lRWkNQOcGfZ-DeO-7KzLELA6md-IqkcjPs3uhHf7EpGEcnaMMu7NAhKw9gb2qs/file\n",
            "Resolving ucfcce27fc0a2ecd38bd118e07c6.dl.dropboxusercontent.com (ucfcce27fc0a2ecd38bd118e07c6.dl.dropboxusercontent.com)... 162.125.82.6, 2620:100:6032:6::a27d:5206\n",
            "Connecting to ucfcce27fc0a2ecd38bd118e07c6.dl.dropboxusercontent.com (ucfcce27fc0a2ecd38bd118e07c6.dl.dropboxusercontent.com)|162.125.82.6|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 164450 (161K) [text/plain]\n",
            "Saving to: ‘boston_features.txt’\n",
            "\n",
            "\rboston_features.txt   0%[                    ]       0  --.-KB/s               \rboston_features.txt 100%[===================>] 160.60K  --.-KB/s    in 0.05s   \n",
            "\n",
            "2020-05-13 15:34:09 (3.43 MB/s) - ‘boston_features.txt’ saved [164450/164450]\n",
            "\n",
            "--2020-05-13 15:34:11--  https://www.dropbox.com/s/j7flze0oe86pr6o/boston_prices.txt\n",
            "Resolving www.dropbox.com (www.dropbox.com)... 162.125.82.1, 2620:100:6032:1::a27d:5201\n",
            "Connecting to www.dropbox.com (www.dropbox.com)|162.125.82.1|:443... connected.\n",
            "HTTP request sent, awaiting response... 301 Moved Permanently\n",
            "Location: /s/raw/j7flze0oe86pr6o/boston_prices.txt [following]\n",
            "--2020-05-13 15:34:11--  https://www.dropbox.com/s/raw/j7flze0oe86pr6o/boston_prices.txt\n",
            "Reusing existing connection to www.dropbox.com:443.\n",
            "HTTP request sent, awaiting response... 302 Found\n",
            "Location: https://uc63c23951c29d2f4243330fd490.dl.dropboxusercontent.com/cd/0/inline/A3oMs8OaL6sBmtAZvWsZc5w7zgsOycuEFjBIN9ybJ7O0yGEQNTh2zDhrAo0bL1c1Y9SbS0o7vU4Fx8cVzgGAkkMNB_2ESIui9_YaJ6gaUNUiaScThF_-p8wGvq76PNYqpCU/file# [following]\n",
            "--2020-05-13 15:34:11--  https://uc63c23951c29d2f4243330fd490.dl.dropboxusercontent.com/cd/0/inline/A3oMs8OaL6sBmtAZvWsZc5w7zgsOycuEFjBIN9ybJ7O0yGEQNTh2zDhrAo0bL1c1Y9SbS0o7vU4Fx8cVzgGAkkMNB_2ESIui9_YaJ6gaUNUiaScThF_-p8wGvq76PNYqpCU/file\n",
            "Resolving uc63c23951c29d2f4243330fd490.dl.dropboxusercontent.com (uc63c23951c29d2f4243330fd490.dl.dropboxusercontent.com)... 162.125.82.6, 2620:100:6032:6::a27d:5206\n",
            "Connecting to uc63c23951c29d2f4243330fd490.dl.dropboxusercontent.com (uc63c23951c29d2f4243330fd490.dl.dropboxusercontent.com)|162.125.82.6|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 12650 (12K) [text/plain]\n",
            "Saving to: ‘boston_prices.txt’\n",
            "\n",
            "boston_prices.txt   100%[===================>]  12.35K  --.-KB/s    in 0s      \n",
            "\n",
            "2020-05-13 15:34:12 (105 MB/s) - ‘boston_prices.txt’ saved [12650/12650]\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oww6BHzPnN2K",
        "colab_type": "text"
      },
      "source": [
        "This time we will not be using a Pandas DataFrames, because we will code the Linear Least Squares Regression ourselves using Numpy.\n",
        "\n",
        "*   Now, load the txt files into NumPy arrays:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q8Eg67JbnMXs",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "features = np.loadtxt(\"boston_features.txt\")\n",
        "prices = np.loadtxt(\"boston_prices.txt\")"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W-A0JFizohhK",
        "colab_type": "text"
      },
      "source": [
        "As you can see below, the features is a matrix contatining 506 rows (one for each house), each with 13 entries (one for each feature). Additionally, there are 506 prices (again, one for each house)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1Ksqhh8DodXx",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "bc6cdc49-7352-4f4b-fe9e-15adc9d32ed8"
      },
      "source": [
        "print(features.shape)\n",
        "print(prices.shape)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(506, 13)\n",
            "(506,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8uLLxkixpUWP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 935
        },
        "outputId": "9deb02df-cfd6-477b-e5e5-6c4dec922036"
      },
      "source": [
        "print(features)\n",
        "print(prices)"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[1.58760e-01 0.00000e+00 1.08100e+01 ... 1.92000e+01 3.76940e+02\n",
            "  9.88000e+00]\n",
            " [4.54192e+00 0.00000e+00 1.81000e+01 ... 2.02000e+01 3.74560e+02\n",
            "  7.79000e+00]\n",
            " [7.52601e+00 0.00000e+00 1.81000e+01 ... 2.02000e+01 3.04210e+02\n",
            "  1.93100e+01]\n",
            " ...\n",
            " [2.68380e-01 0.00000e+00 9.69000e+00 ... 1.92000e+01 3.96900e+02\n",
            "  1.41000e+01]\n",
            " [1.09590e-01 0.00000e+00 1.19300e+01 ... 2.10000e+01 3.93450e+02\n",
            "  6.48000e+00]\n",
            " [1.54450e-01 2.50000e+01 5.13000e+00 ... 1.97000e+01 3.90680e+02\n",
            "  6.86000e+00]]\n",
            "[21.7 25.  13.  23.6 21.7 35.2 19.3 14.1 18.9 13.6 19.6 42.8 25.   9.7\n",
            " 20.7 19.3 37.6 13.1 21.7 16.5 29.4 18.3 15.6 48.3 36.2 21.4 15.2 18.2\n",
            " 17.8 19.6 25.  18.  32.4 50.  29.8 18.6 23.9 10.5 19.3 11.9  6.3 14.4\n",
            " 23.8 29.  22.   8.5 24.5 36.  43.5 16.5 20.4 22.5 23.1 37.  20.3  7.4\n",
            " 11.7 24.5 23.  25.  28.  21.4 20.3 13.8 20.  33.8 13.5 18.8 21.  23.2\n",
            " 26.4 20.1 14.6 17.1 17.8 27.5 15.  18.9 23.  20.5 19.1 12.  19.2 19.1\n",
            " 16.2 27.1 12.7 22.  19.3  7.2 21.7 17.4 20.2 35.1 50.  17.8 31.6 16.1\n",
            " 15.  21.9 13.9 19.4 23.1 24.3 22.8 10.4 13.4 25.2 15.6 21.7 20.6 20.1\n",
            " 18.7 12.7 11.7 19.8 24.7 23.7 20.9 46.  30.3 23.6 27.5 50.  10.2 22.\n",
            " 23.1 24.3 17.9 18.9 18.5 21.2 22.7 43.8 18.5 21.2 22.9 50.   5.  21.8\n",
            " 23.9 23.1 18.5 21.5 17.2 28.6 15.1 24.1 21.   8.7 21.7 31.5 14.4 21.7\n",
            " 10.4 19.5 15.7 16.4 20.9 19.6 17.8 17.3 50.  12.8 25.  30.1 10.8 15.6\n",
            " 14.6 19.4 28.7 23.2 18.7 23.5  7.2 22.6 10.9 23.9  9.5 16.1 24.3 23.7\n",
            " 21.1 21.2 21.9 22.  28.1 35.4  8.1 14.1 12.7 15.4 23.2 12.1 34.7  7.\n",
            " 24.  17.6 13.4 29.9 28.4 20.6 50.  44.  13.4 21.5 48.5 32.2 26.5 21.2\n",
            " 22.6 17.7 13.2 12.3 46.7 41.3 11.8 21.8 23.1 19.4 18.8 32.  17.8 22.6\n",
            " 43.1 22.5 17.2 16.6 14.8 27.1 22.  25.3 13.1 19.4 21.4 13.1  8.3 19.6\n",
            " 19.8 29.1 33.4 24.  37.2 22.8 38.7 29.1 19.7 24.4 23.2 22.5  8.5 34.9\n",
            " 15.  27.5 20.4 23.3 29.6  8.8 33.3 10.5 20.1 19.5 31.6 13.3 16.1 15.6\n",
            " 18.1 14.3 34.6 22.2 13.3 17.  15.6 33.1 23.8 22.7 25.1 35.4 13.1 22.6\n",
            " 23.7 12.5 20.  20.3 19.1 20.4 14.9 20.3 31.7 17.1 32.7 24.4 17.5 24.8\n",
            " 23.1 11.5 24.2 18.9  8.4 22.9 14.9 33.2 31.5 13.5 50.  19.  42.3 14.5\n",
            " 44.8 26.7 22.4 17.5 13.4 28.7 12.6 19.8 21.4 19.3 24.1 21.  23.3 23.8\n",
            " 21.1 50.  16.3 36.4 30.7 24.4 23.  23.1 16.7 14.5 26.4 36.2 20.6  8.4\n",
            " 16.2 20.1 10.2 17.1 19.4 33.4 32.  19.6 27.5 18.7 21.2 23.9 22.2 34.9\n",
            " 18.6 18.2 39.8 26.6 23.3 15.4 50.  11.  20.5 19.4 18.4 37.3 21.6 20.\n",
            " 11.3 50.  26.6 27.  18.4 11.9 33.  30.5 17.5 19.5 31.1 26.2 14.3 21.4\n",
            " 24.8 13.9 15.2 14.9 25.  13.8 10.2 33.1 48.8 20.6 17.2 11.8 17.4  5.\n",
            " 21.9 36.5 13.3 50.  23.7  8.3 24.8 23.9 25.  27.9 32.9 50.  19.1  8.8\n",
            " 50.  33.2 29.  50.  41.7 28.4 24.6 20.5 25.  22.9 22.2 17.4 20.8 16.8\n",
            " 19.9 21.6 19.7 22.3 24.1 24.7 19.2  7.2 50.  34.9 22.8 13.8 22.6 20.7\n",
            " 15.2 10.9 14.1 20.  20.1 19.   9.6 31.2 28.7 16.8 28.5 18.5 19.5 36.1\n",
            " 14.2 22.8 30.8  7.5 16.7 24.5 20.8 22.9  5.6 22.  45.4 20.4 19.9 22.2\n",
            " 16.   7.  28.2 24.8 19.9 23.4 22.1 23.8 13.6 22.2 26.6 29.6 23.4 24.4\n",
            " 50.  32.5 18.4 13.8 23.  30.1 31.  24.7 20.6 18.2 37.9 20.8 20.  20.2\n",
            " 15.3 14.5 14.  29.8 13.8 30.1 22.4 27.9 20.6 16.6 22.3 19.9 24.6 18.3\n",
            " 22.  23.3]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rUeXGXjbGjnG",
        "colab_type": "text"
      },
      "source": [
        "Beside the housing prices, the dataset contains and information about location, etc (see below), and the prices are units of in USD $1000.\n",
        "\n",
        "```\n",
        "Index   Description\n",
        "-----------------------------------------------------------------------\n",
        "   0    per capita crime rate by town\n",
        "   1    proportion of residential land zoned for lots over 25,000 sq.ft.\n",
        "   2    proportion of non-retail business acres per town\n",
        "   3    Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
        "   4    nitric oxides concentration (parts per 10 million)\n",
        "   5    average number of rooms per dwelling\n",
        "   6    proportion of owner-occupied units built prior to 1940\n",
        "   7    weighted distances to five Boston employment centres\n",
        "   8    index of accessibility to radial highways\n",
        "   9    full-value property-tax rate per $10,000\n",
        "  10    pupil-teacher ratio by town\n",
        "  11    1000(Bk - 0.63)^2 where Bk is the proportion of African Americans by town\n",
        "  12    % lower status of the population\n",
        "```\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gKW4IOjjpgpd",
        "colab_type": "text"
      },
      "source": [
        "## Exercise 1.1: Exploratory Data Analysis"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RLxdW_pPpg5U",
        "colab_type": "text"
      },
      "source": [
        "Before we begin the regression, lets have a look at the data. As in the lecture, we will plot the correlation between our features using Seaborn.\n",
        "\n",
        "Since we loaded in the data as a Numpy Array, we have to create a Pandas DataFrame for Seaborn. This can be done with the code below:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-wyVjM5UqK5y",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "a27d3b0e-a7aa-467a-9aee-911c2190762f"
      },
      "source": [
        "#Pandas DataFrames\n",
        "import pandas as pd\n",
        "\n",
        "# Make a Pandas dataframe from the features\n",
        "df = pd.DataFrame(features[:,:5]) \n",
        "\n",
        "# NOTE: ONLY TAKES THE FIRST 5 COLUMNS/FEATURES\n",
        "# features[:,:5] is Numpy slice notation for \"take all rows, and first five colums\"\n",
        "\n",
        "# Print the type of the dataframe, just to make sure we coverted correctly\n",
        "print(type(df))"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CrOYprZ5qLOe",
        "colab_type": "text"
      },
      "source": [
        "Note that since there are 13 features, the correlation plot would contain 169 plots. This would be quite slow in Google Colab. For speed reasons, we only loaded the first 5 featues into the pandas dataframe for plotting.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1Z-a3Etntajv",
        "colab_type": "text"
      },
      "source": [
        "### Question 1.1.1: "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dOPcP5g_tawa",
        "colab_type": "text"
      },
      "source": [
        "*   Just like in the lecture, make an `sns.pairplot()` using Seaborn of the dataframe we just made.\n",
        "*   (Optional) If you want, change the style of the plot as shown during the lecture. You can see some customization options in the documentation: https://seaborn.pydata.org/generated/seaborn.pairplot.html"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O3-7w7byp5AH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 945
        },
        "outputId": "033b11bb-b039-4802-dce9-7eadb39e9b71"
      },
      "source": [
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Plot the pairplot of the Pandas DataFrame\n",
        "sns.pairplot(df)"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<seaborn.axisgrid.PairGrid at 0x7f3d95226828>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAA4oAAAOOCAYAAABGHOzuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAgAElEQVR4nOzde3hc1X3v/8/ac9PoApZlyQHLBJKCKaUmQQoxuL+Ehp4c2tCS1C5JgzEhqQ341/Q0JyXQnh9Pkoee54GQnpzkpPjWBHDgJKZ2KWnoL5cfCelpUpLIQFzixhCulkNsWcjGkkaay16/PzQz1pb2jG4z2ntm3q/nmceePTN71iyt+c5ee639XcZaKwAAAAAACpygCwAAAAAACBc6igAAAAAADzqKAAAAAAAPOooAAAAAAA86igAAAAAADzqKAAAAAACPmu4oXnnllVYSN27VvFUFbZfbItyqgrbLrcq3qqHtcqvyrSpot9wW4VZSTXcUjx07FnQRgHmh7aJW0XZRq2i7qEW0WwSppjuKAAAAAIDKo6MIAAAAAPCIBl0AABNc12pwJK10Nqd4NKKOlrgcxwRdLAAhQHyoPOoUaGzEgJnRUQRCwHWtDh45qU27+tQ/lFJ3e1I7N/Zq1fI2ghbQ4IgPlUedAo2NGDA7TD0FQmBwJF0MVpLUP5TSpl19GhxJB1wyAEEjPlQedQo0NmLA7NBRBEIgnc0Vg1VB/1BK6WwuoBIBCAviQ+VRp0BjIwbMTt1OPT37tkfn9bqX7nxPhUsCzCwejai7PekJWt3tScWjkQBLBSAMiA+VR50CjY0YMDuMKAIh0NES186NvepuT0pSca58R0s84JIBCBrxofKoU6CxEQNmp25HFIFa4jhGq5a36eEta8m+BcCD+FB51CnQ2IgBs0NHEQgJxzHqbEsEXQwAIUR8qDzqFGhsxICZMfUUAAAAAOBBRxEAAAAA4EFHEQAAAADgQUcRAAAAAOBBRxEAAAAA4EFHEQAAAADgQUcRAAAAAOARSEfRGPMxY8zPjDHPGGO+aoxpMsacY4z5kTHmF8aY3caYeBBlAwAAAIBGt+gdRWPMCkl/JqnXWnuhpIikD0i6S9LnrLW/JmlI0kcWu2wAAAAAgOCmnkYlJY0xUUnNkl6V9C5Je/KP3y/pvQGVDQAAAAAa2qJ3FK21hyV9VtIrmuggnpC0T9Jxa202/7R+SSv8Xm+M2WyM6TPG9A0MDCxGkYGKoO2iVtF2Uatou6hFtFuERRBTT9slXS3pHElnSmqRdOVsX2+t3WGt7bXW9nZ2dlaplEDl0XZRq2i7qFW0XdQi2i3CIoipp78j6UVr7YC1NiPpHyStlbQkPxVVkrolHQ6gbAAAAADQ8ILoKL4iaY0xptkYYyRdIemApO9JWp9/zvWSHgmgbAAAAADQ8IK4RvFHmkha86Skf8+XYYekWyX9V2PMLyR1SPrSYpcNAAAAADCRfXTRWWs/KemTUza/IOmSAIoDAAAAAJgkqOUxAAAAAAAhRUcRAAAAAOARyNRTANO5rtXgSFrpbE7xaEQdLXE5jgm6WABCgPhQedQpAIlYUA4dRSAEXNfq4JGT2rSrT/1DKXW3J7VzY69WLW8jWAENjvhQedQpAIlYMBOmngIhMDiSLgYpSeofSmnTrj4NjqQDLhmAoBEfKo86BSARC2ZCRxEIgXQ2VwxSBf1DKaWzuYBKBCAsiA+VR50CkIgFM6GjCIRAPBpRd3vSs627Pal4NBJQiQCEBfGh8qhTABKxYCZ0FIEQ6GiJa+fG3mKwKsyR72iJB1wyAEEjPlQedQpAIhbMhGQ2QAg4jtGq5W16eMtasm4B8CA+VB51CkAiFsyEjiIQEo5j1NmWCLoYAEKI+FB51CkAiVhQDlNPAQAAAAAedBQBAAAAAB5MPQVCwnWtBkfSzJEHMA3xofKoUwB+iA2n0FEEQsB1rQ4eOVlc9LWQdWvV8raGDU4AJhAfKo86BeCH2ODF1FMgBAZH0sWgJE0s9rppV58GR9IBlwxA0IgPlUedAvBDbPCiowiEQDqbKwalgv6hlNLZXEAlAhAWxIfKo04B+CE2eNFRBEIgHo0UF3st6G5PKh6NBFQiAGFBfKg86hSAH2KDFx1FIAQ6WuLaubG3GJwKc+I7WuIBlwxA0IgPlUedAvBDbPAimQ0QAo5jtGp5mx7espYsWwA8iA+VR50C8ENs8KKjCISE4xh1tiWCLgaAECI+VB51CsAPseEUpp4CAAAAADzoKAIAAAAAPOgoAgAAAAA86CgCAAAAADzoKAIAAAAAPALpKBpjlhhj9hhjfm6M+Q9jzKXGmKXGmO8YY57L/9seRNkAAAAAoNEFNaL4eUnftNaeL+kiSf8h6TZJj1lrz5X0WP4+AAAAAGCRLXpH0RhzuqR3SPqSJFlr09ba45KulnR//mn3S3rvYpcNAAAAABDMiOI5kgYk3WuMecoY83fGmBZJy621r+af8ytJy/1ebIzZbIzpM8b0DQwMLFKRgYWj7aJW0XZRq2i7qEW0W4RFEB3FqKSLJW211r5V0oimTDO11lpJ1u/F1tod1tpea21vZ2dn1QsLVAptF7WKtotaRdtFLaLdIiyC6Cj2S+q31v4of3+PJjqOR4wxZ0hS/t+jAZQNAAAAABreoncUrbW/knTIGLMqv+kKSQckfV3S9flt10t6ZLHLBgAAAACYmAYahI9KetAYE5f0gqQbNNFpfcgY8xFJL0u6JqCyAQAAAEBDC6SjaK19WlKvz0NXLHZZAAAAAABeQa2jCAAAAAAIKTqKAAAAAAAPOooAAAAAAA86igAAAAAADzqKAAAAAAAPOooAAAAAAI+g1lEEMIXrWg2OpJXO5hSPRtTREpfjmKCLBSAEiA+VR50CtYPvazDoKAIh4LpWB4+c1KZdfeofSqm7PamdG3u1ankbgRBocMSHyqNOgdrB9zU4TD0FQmBwJF0MgJLUP5TSpl19GhxJB1wyAEEjPlQedQrUDr6vwaGjCIRAOpsrBsCC/qGU0tlcQCUCEBbEh8qjToHawfc1OHQUgRCIRyPqbk96tnW3JxWPRgIqEYCwID5UHnUK1A6+r8GhowiEQEdLXDs39hYDYWH+fUdLPOCSAQga8aHyqFOgdvB9DQ7JbIAQcByjVcvb9PCWtWT0AuBBfKg86hSoHXxfg0NHEQgJxzHqbEsEXQwAIUR8qDzqFKgdfF+DwdRTAAAAAIAHI4pASLCYLIBSiA+VR50C8ENsOIWOIhACLCYLoBTiQ+VRpwD8EBu8mHoKhACLyQIohfhQedQpAD/EBi86ikAIsJgsgFKID5VHnQLwQ2zwmvfUU2PM+ZKulrQiv+mwpK9ba/+jEgUDGklhMdnJwYnFZAFIxIdqoE4B+CE2eM1rRNEYc6ukr0kykn6cvxlJXzXG3Fa54gGNgcVkAZRCfKg86hSAH2KD13xHFD8i6TestZnJG40x/0PSzyTdudCCAY2ExWQBlEJ8qDzqFIAfYoPXfK9RdCWd6bP9jPxjAAAAAIAaNd8RxT+X9Jgx5jlJh/LbzpL0a5L+tBIFAxoJ6ZgBlEJ8qDzqFIAfYoPXvEYUrbXflHSepE9L+lb+9ilJq/KPzcgYEzHGPGWM+Ub+/jnGmB8ZY35hjNltjGnMycBoSKRjBlAK8aHyqFMAfogNXvNeHsNa61prn7DW7s3fnrDWziV37H+RNDlD6l2SPmet/TVJQ5q4DhJoCKRjBlAK8aHyqFMAfogNXoGso2iM6Zb0Hkl/l79vJL1L0p78U+6X9N4gygYEoZCOebJGTscM4BTiQ+VRpwD8EBu8AukoSvqfkj6hU4lvOiQdt9Zm8/f7dWp9RqDukY4ZQCnEh8qjTgH4ITZ4zTeZzbwZY66SdNRau88Yc/k8Xr9Z0mZJOuussypcOqB6yrVdxzE6t7NVD914qTI5V7GIo67WRENeOI3wIe4Gi/gwf6XaLnWKMCPmBofY4LXoHUVJayX9gTHm9yQ1STpN0uclLTHGRPOjit2SDvu92Fq7Q9IOSert7bWLU2Rg4cq1Xde1emVoVC8Pjqo5HtFoOqexjpzO7mhp2OCE8CDuBov4MH+l2i51ijAj5i4u17UaHEkrnc0pFnU0PJbVxi//mKynCqCjaK39S0l/KUn5EcW/sNZea4z5e0nrJX1N0vWSHlnssgFBOZ5K68jrY7r9kWeKgenu9au1pDmmpS2JoIsHIEDEh8qjTgFI/sth3L1+tTpbE+ofShWznj68Za062xovNgR1jaKfWyX9V2PMLzRxzeKXAi4PsGhS6Zxu2bPfk475lj37lUo3ZpYtAKcQHyqPOgUg+S+Hccue/brp8jcXn9PIWU+DmHpaZK19XNLj+f+/IOmSIMsDBCVnrW865hwTToCGR3yoPOoUgFR6OYwlyVjxPllPAQSqKeafjrkpxlcUaHTEh8qjTgFIpZfDGM3PLmj0rKdERCAElrUkfNMxL+NaGaDhER8qjzoFIJVeDuOilafrB7f+th7esrZhE9lIAU89BTDBcYxWLW/Tw1vWKp3NKR6NqKMl3rCBCcApxIfKo04BSDPEgpagSxc8OopASDiOaciMWgBmRnyoPOoUgEQsKIeppwAAAAAADzqKAAAAAAAPOooAAAAAAA86igAAAAAADzqKAAAAAAAPOooAAAAAAA86igAAAAAAD9ZRBELCda0GR9Is/gxgGuJD5VGnQO3g+xoMOopACLiu1cEjJ7VpV5/6h1Lqbk9q58ZerVreRiAEGhzxofKoU6B28H0NDlNPgRAYHEkXA6Ak9Q+ltGlXnwZH0gGXDEDQiA+VR50CtYPva3DoKAIhkM7migGwoH8opXQ2F1CJAIQF8aHyqFOgdvB9DQ4dRSAE4tGIutuTnm3d7UnFo5GASgQgLIgPlUedArWD72tw6CgCIdDREtfOjb3FQFiYf9/REg+4ZACCRnyoPOoUqB3V/r66rtXAyXEdHhrVwMlxua6tyH7rAclsgJBY0hzVVzetUc5aRYwRJ8oAFBAfKo86BWqD4xitWt6mh7esrXjWU79EOV/d9HZFHEeZnKtYxFFXa0LRaGOOrdFRBELg9bG0jp1M6+YHnywGqq3XXqxkLKIlzYmgiwcgQMSHyqNOgdriOEadbZX/bk5NlHPZmzo0NJrRlsmxYUOPVrY36bSmxluSozG7x0DIjIznigcs0sRF2jc/+KRGxrlQG2h0xIfKo04BuK5VOpvT3/zRRdp+XY/eunKJNr3jTcVOopSPDQ/s07HhjA4eOdlw01IZUQRCIOta34xe2QYLSACmIz5UHnUKNDa/Kad3rVutqGN8Y4NjpE27+vTwlrVVGdkMK0YUgRCIOsY3o1e0waY4AJiO+FB51CnQ2PzWZrx1735FI45vbMjlTy412pIcdBSBEEhEHd1z7cWejF73XHuxEg168TSAU4gPlUedAo2t1NqMiZijbRt6psWGnf/ygrrbk4qViRH1mD2VqadACLhWSkSN7rvhEjlm4n7OzakOYgyABSI+VB51CjS2wtqMkzuL3e1JGRmdv7xNuzevUda1yuSsdnz/ef3whUHdvX51yVkHflNZd27s1arlbTWdAIdTZ0AI5KyrqccnVlLOctQCNDriQ+VRp0BjKoz6pbM5/e8/ebvefUGXJO/ajIWlMP78a0/r+YFhrevp1u1XXaDPfPOgUmn/qad+U1k37erT4Eh6cT5YlSz6iKIxZqWkXZKWayIu77DWft4Ys1TSbklnS3pJ0jXW2qHFLh8QBEdGuZzVq8dH1RyPaDSdU1dbnDM5AIgPVUCdAo3Hb9Rv+3U9uuPqC+U4jmdtxng0os62uOf1nW1xxUssuFpqKmutX9MYxNTTrKSPW2ufNMa0SdpnjPmOpA9Jesxae6cx5jZJt0m6NYDyAYvOGKPXx7K6/ZFnisHr7vWr1dnWFHTRAASM+FB51CnQePxG/W78yj7t3rxG8SlnidqTMf3ZFefppgf2FWPEtg09ak/GfPddaiprqY5lrVj0k2fW2lettU/m/39S0n9IWiHpakn35592v6T3LnbZgKBkcq5u2bPfE7xu2bNfmZwbcMkABI34UHnUKdB4So369Q+l9L57fuBZJ3EolSl2EgvPu+mBfRpKZXz33dES186NvZ4kOIWprLUs0GQ2xpizJb1V0o8kLbfWvpp/6FeamJoKNISsa9XZmtDtV12gJcmYjqcy2vb488qRWQFoeMSHyqNOgdriulaDI2mlsznFoxHPNNHZmjzq99aVS3TT5W9WR0tcpydj6mxNeNZJnOtUUscxWrW8TQ9vWbugMoZNYB1FY0yrpL2S/txa+7oxpyrSWmuNMb7R2hizWdJmSTrrrLMWo6hARZRru8lYRH/1e+frYw/9tDjF4XPXXKSmWG1PWUB9IO4Gi/gwf6XaLnWKMCPmelUqo2hh1O9z3zmo6y87R7fu3e+ZVhp1JkYdXdfOayqp4xh1tiUW9FnDJpDrto0xMU10Eh+01v5DfvMRY8wZ+cfPkHTU77XW2h3W2l5rbW9nZ+fiFBiogHJtN+fa4gGLNHHW6mMP/ZSz2wgF4m6wiA/zV6rtUqcIM2KuV6UyihZG/T71BxcWO4mF/d30wD69/FpK79/xhA4eOan2ZKwup5LOVRBZT42kL0n6D2vt/5j00NclXS/pzvy/jyx22YCgpHOu7xQHrpcBQHyoPOoUqB2VzCjqOEbWWt/9LUnGip3Qh7es1bmdrXroxkuVzbmKRhx1tSZqfirpXAUxorhW0nWS3mWMeTp/+z1NdBD/kzHmOUm/k78PNISIY4pnrQq625MNF5AATEd8qDzqFKgdhWmgky0ko2ip/R3PJ6opdEKfGxjWNdv/Te+4+3Fds/3f9NzAcDHZTaMIIuvpv1prjbV2tbX2LfnbP1trB621V1hrz7XW/o619rXFLhsQlJhjdPf61Z4pDnevX60YBy1AwyM+VB51CoSX61oNnBzX4aFRDZwcr/g00I6WuLZf1+PZ313rVmvb488X7xtjKjLdtdYFmvUUwISmuNGytoTuuPrC4uLPy9oSaopz0AI0OuJD5VGnQDiVSlxzbmfrtIyikjRwcnzOWUYdx+i8zlZ9ddMaZXKuIo7Rf3/0gJ46dLyY2CYeMXOe7lqJzKxhE0gyGwBeI2Ou9vzkFXW3J9XZllB3e1J7fvKKRsa4XgZodMSHyqNOgXAqlbjmtZR3JM91rV4aHNEzh0+ofyilZw6f0EuDI7OeGnoyndWvTqS08cs/1p9/7Wn98SVv1Hc//k7d+Ye/qS889qzGs67efUGXtl/Xo92b12j7dT169wVdJae7LrQ8YcWIIhACxkjvWLVcN9z3k+IZtLvWrZbhVA7Q8IgPlUedAuFUKnHN6HhOG770o+L39b4b3qahkbRuf+SZ4ra716/WkuaYlrbMvERFKp0rZj7uH0rphvt+ou72pG6/6gJ9+8BRffzdq/Sn7zpXWx580rOERiwiHR4anTZieDyV1uDwuKc8n7vmolmXJ6wIiUAIuFbTUjXfune/XE5uAw2P+FB51CkQTqUSzbx4bMTzfT30WmraEje37NmvsXTOc31jqRG9XJnMp93tSTnGFDuJhcduemCfnnrlhNbe9T29754f6OCRk8X9j03qeBae/7GHfqqx9Nwzs4YJHUUgBLKuf8BiTS8AxIfKo06BcGpPxrRtgzfRzNYNPfp///1Vz/Oa4xHf7/B4zup99/zAtzM3WVPMv0M6ms7prnWrNTye9d1/czxS/P/k5DaZEjElW+MxhamnQAhEHaN3X9CldT0rtSQZ0/FURnv3HVKkxi+CBrBwxIfKo06BcBpKZfSFx57V7VddUPxu/q/HntUfX/JGPbSvv/i80XTO9zv80pSRx8KaiJ1tE9M/CwlnMllX//tP3q6/fvSAvn3gqLrbk9q+oUfLWuO6/ZFntK5npbrbk57OX3d7Upmcq+3X9RTf081PQ4jml9yZ+vxajyl0FIEQaG1y9NErztPND+wrzm3fuqFHrU0M+gONjvhQedQpEE7pbE7fPnBU3z5w1LP9tt/99WJHrLs9qTOXJHy/w1/54Uue103OVOqXUXX7dT264+oL5TiOOlriGjg5pusvO0f3//BF3bVudXGKeuGaw1jU0W3/8O+e13e2NSkWcXT3+tW6Zc+p59+9frVikdqOKXQUgRAYHnOLwU6aCGw3P7BPuzev0enJGV4MoK4RHyqPOgXCqXCN4tSROccYz3I2zfGYPrLziWnf4TuuvtAz8tjdnixmKp2cUfWtK5fopsvfrFQ6J9NqZGX16omUjDH6l4NHtK5npU5riureD71No+mcTktGlYg6+tTXf+YZ7fz8//es/vv7Vssx0hlLmnTfDZfIMRPXQUcjUo0PKNJRBMKg1EXVrq3tue0AFo74UHnUKRBOHS1xbd/Qo88/9qzW9axUR0tcS1vi+qenD+sPe7olTXQmS2VHPWdZi2fkcefG3uKai4XXvHXlEv3Ff16lW/fuV2drQp+4cpVnJHDbhh594bFni1NS71q3Wp/6+s9057rf1PWXneMZZbxr3Wq5ritjjAZeHy8mtCmMQDZ31HZXq7ZLD9SJiPGf2+6YGj8VBWDBiA+VR50C4eQ4Rivam6YtTXH3+tVKxiPFpSaOnhzz/Q43xyN6eMta30XvC6OVN13+5mJn7/arLih2EqVT2U13b16jv3rPBXKM0SNP9uupQ8cVizi+2ZIfuvFSWdf1zXq6e/Oaxay+iqvtibNAnTBGumvdak+Wr7vWrRbHLACID5VHnWIuXNfOaskFVEY6Z6ctTXHLnv2eDKJRx+ju9d7v8N3rVyseLf0l7miJF0cYC/tekoz5jky+emJMH/va03r+6LCuesuZevTPfksm/9jU51pr5c5ilkIttiNGFIEQsFa6/4cveua93//DF/XJ3/+NoIsGIGDEh8qjTjFbrmv10uCIXh4cLV4f98aOZp3d0VIcqUJlZbKub6crkz210GkqndNnvnnQ8x1++MnDOu2ys3XjpAQ3Ozf2atXyNjmOkeMYrVrepl+9fmo08ngq4zsyOZbJFaen9g+ldO+H3lZ8bOpzC1Nhy81S8EukM7lsYcWIIhACTVFHf/GfVymez44Vj0zcb4ryFQUaHfGh8qhTzNbxVFpHXh/T7Y88o/fveEK3P/KMjrw+puOpdNBFq1uOmVi+Zvt1Pdq9eY22X9ejd1/Q5ZkaHo9GNDA8rhu/sk/v3/GEbvzKPv3ub55R7CRK3rUOC6N5r55IKREz2p5fq3Hb489PG5n8mz+6SCuXNnummTbHI/rCY89Nm4mwfUOPOlriM85SmJxIZ2rZwowRRSAEctYqnbW6/ZFnPBdT50isADQ84kPlUaeYrVQ6N+0atlv27J+49qwl4MLVqVjETLtG8Z5rL1YsYnR4aFTxaETtyZh2ffgSz0jvOZ0tviOR6Wxu2mjelz/Uq8/+0UUykuJRo10fvkSSFI86GhnP6PhoxrOv46mMBobH9chTh3Xvh96miGPkWmlJMirHMTPOUiiVfKewdEdYceoMCIGsa3XTlLNgNz2wzzMfH0BjIj5UHnWK2cpZq87WhGd0q7M1oRxNpWrGsu60axS3PPikTo5ntfau7+l99/xAzw0MS5JnpNeRiiN6Bd3tSRljpo3mffi+PnW1JfSlf31Bo2lXG7/8Y73rb76vD+x4Qq+NZNTWFPXsa9vjz+tvP/hWve/iFbrhvp/oXX/zfX3o3h/ryOsT1xp2tsT10SvO0x3fOKD373hCd3zjgD56xXnqzGdcLSTSmVq2wtIdYUVHEQiBTM7/Iugsv0RAwyM+VB51itlqSUT0iStXeToAn7hylVoSHELPZL7JW1zX//uZy7++MG3z5cFRT+fvrx89oG35KaWSijMFIsY/Cc2JVEa3/u6vT8tkesue/UrGI56ppAPD4+o6LaGxjKu/+aOLiicMbnxgnwZH0orHozpvWYt2b16j799yuXZvXqPzlrUoHp+YvFlIpDO5bJOX7ggrpp4CIRB1/FO1R0J8gTOAxUF8qDzqFLOVc6V7f+CdUnjvD17UX7/vN4MuWqgtJAlQLOr4fj+Pj2aK9/uHUmqOe0fjvn3gqD5x5fnFqaE512pP3yu6fu2bSu4vXSJxzuh4zjOV9KyOZg0Opz3T1e9at1qf/dZBpbM5ua7V4dfHPJ93fNLnLSTSKbV0R1hxOgQIgVjE0eeuuchzpulz11ykWISvKNDoiA+VF3OMf52G/KANi8+6Vh/5rTd5RhQ/8ltvkmWacllDqXHfJEBDqfEZX+tIvktfZHKnsp52tyfVmojqOx97h7778XfqOx97hz511fnK5UcjB06Oq38opd9dfabiEeM7mnfRytPV3Z70nRL66omUrr/snOLfPZubPl391r379WdXnKt4NFK3SY8YUQRCIOu6ikUd3XH1hcUzUbGoo5zrzvxiAHVtNvHBda0GR9I1daY6SFlr/euUZDaYwrXSl/71Bc+I4pf+9QV9+g8uDLpooZZKu75JgL42iyRAhbUHv/LhS5SzVr86MabPfPOgPvUHE4lhutuT+uqmt+t4Kqsb7vtJcYRv+4YejWVynlG/u9evlmtVcjTPTVrt3NjrSXRTGCmUVPy7l1on8exlLepoievVE6mySY9c1+qlYyN6+bVJI6xLm3X2suous7LQ3wZORwIhYK10z/d+oXT+bFk65+qe7/1CnLAEMFN8KKzP9b57flBM9HDwyMmaWMw5KMRczJqxnpGlO75xQNdfdo5kaCzl5EpcZzhTXHJdq9dGMrplz3799t98Xx+69ycyxqizLa5lrXH94Nbf1sNb1iriOLp5ygjfjQ/s02sjmWmdtckjkVNNnhL6g1t/Ww/deKnu/+GLeurQcT116Lhu/Mo+ffzvf6pIfrr6ZN3tScUjE52uXImOZOGy56HRcaUyWc/jqUxWQ6Mzj7DOVyV+GxhRnOLs2x6d1+teuvM9FS4JGoljpOsvO6d4QXXhjBYDAgBmig/HRsb1j08emnZdzkfe8WZ1tTUFW/iQIuZitlxX05Kd3Lo3P1KEkuIR/+sMZ5oyf2xkfNpaiLfu3a9dH75EjpGWn5bU4EhamZz/tYVTr1uc6KyVv17ScYw629DDxdAAACAASURBVBKSJjpXH/tPq3Tg1ZOe2BB1jO5ev7o4algYrYw6Rq+PpdUUi/h+3qbYxOfN5qxeH8tOG+1c1lq9Ew7HRsb1ue8c9IyGf+47B/XX7/vNWf820FEEQsC1/BABQQn7tM2Z44PVtZeerXR24oDDGKNrLz07mMLWCGIuZqvUyFiO4eeyknFH936oV/1DY8XO2cqlEwmjCmsh+sXasYz/eoMnx7JKROPF6ZtndzT7dsxG0951CQud08NDI9M6aUuaY1rakvA8vzDC+A9bLtPoeE4vHhvRZ791UH/93gvV0Rr3TFfvaI3LOEYj4zmdcXpy2hTWnRt7tSy//4xrS0/FrZKc6+r/ueoCGRnlrNWZS5L69asumFPbpaMIhEDpKQv8EAHVVJiaM/XHfdXyttB0FmeKDxFjdHw0M21x6hVLwr0+V5BK1alLzMUUpTLkRkMSH8JqPOPqRMo7grZ1Q48+881/17cPHC0ZayPGv77bmqJKRB298tqobn/kGXW2JqaN8G3b0KPmSSN7hfdwpLLXD07lOEZdbU1yW6xaElF98YNvzY8cZrRyabMcM3GyKevm9NrwuJLx6IxZTYM44dAUdTQ4PF5MwlOooxVLEjO/OI+OIhACUcd/ikbU4TJiYCHGxrIaTKWVda2ijlFHMq6mplM/fYMj6WkLMW/a1aeHt6wtTkUK2kwHqmMZV1/87nOe6UVf/O5z+uTv/0bJfWazro4OjyuTcxWLOOpqTSgabZx4Ey1xMBoxHPzDKxoxuu+Gt+nQaynPyFg0QlspJ2elP9/9tPqHUvrMH16oy87tVM61+uTv/4Y+vPZsfWDnj31jbTIe0dZrL9bNU058ZXI5jWWdYoevfyilz3zzoO64+kK9qbNFsYijRNRoPOsWZwYUOmv9x0dLnGwr/xkmT0kdODmuu791UOt6Vhbj7N59h/THl7xRq94Qn/b8qWLznIq7EKm0qy889qznt+ELjz2rT/3+b6h9hoRCBXQUgRBoiRtt29Az7axPS7x6P0QzHUADi20ubXI2zx0by+q5wZFiwoPCGe1zO1qKz01nc7rsTR3a9I43Fa/v2/kvLyidzfm9bSCijtHnP/AW/ZevPV38HJ//wFuKHcWS19uVOP7IZl2dGE/L5kfPrLU6MZ7W6Yo3TGcxGXd8Y24y3hifH7MXcYxSaW8mza3XXqz25ljQRQtcNutqKJXWeNZVzrWKOUYdzXElElHZ/Kj9Z/7wQv36iiX6wI4nPHH4x//tCn32mwenxdq2eFTL2hJ68E/ersIA/6snUvrkIwf1+T9+i6ej9dSh47rhvp/o/3ziciViRmNpt/ib0BR3dHoipnQ6p4gx+u7H31mM7w/t6/dcPzgbHS1xfex3VmnTV07NPrl7/Wp1tiXU1TrzScXOlrhvzOlsic+6DHNlSvw2mDmEOWNDNM3CGHOlpM9Likj6O2vtneWe39vba/v6+nwfm29SmvkimU3dqkpPbWrbPXIipXjMaHT8VJBrTjhKZ6yWn54ssyevcgfPrmt1bGRcY5mcTm+K6NDQ9OkIXW0JnRafeP7U/RTuJ6KOjKSxrDvtsahj1Bx3lHOl05tiisUiM5ZrLp2DTCano8PjyrpW8Ygjx5wqR1drovh+6XRWAyOn9tnZElc8PnMnePL+p+6z3GNTP8PpSUeDIznFIo6WNcd0bDTjO3IzPp7VsdFTr1uW/4Gd6TPM8pq6RWm7hfIcT6WVSufkWquIcWSMlWulppij8YyrjGvVFHWUs1ImN/E3a4o5GstMHGDEo46Gx7PTztova40plbZK51xFHKOYYxSLGv3yuLf93nfD29QciyhTOEjI7/v9+YOTgu72pHZvXlNsZyNj4zo2ktXAyXENjqT15EuD+uCas2U0cXY4HnG0pCmqeDzq+/eydvp3RZq+rakpWrYNlXP09TEdGxnXkRPjxbpZfnpCy1oS6jqtSYeHRkt+zhXtzdP293pqTBlX0w6qYo50WnLuyW/m8h0u1+bzqnZ2bHLbPfr6mJri0snUqTpoSzoaS0tdp5EACKccHhrVp//pZ9NGkj75+78x9fu16DF3LOMqk4+NbQlHYxmrrGvlWivHGBkzkeH3tKQj10rDY25xWy7/e55zrZTfNhG/J+LBWMYtPi+S/16P26yGx059Z1oSjp4fGNX27z+vjZeerTecnlQi6igRMcrJKudOVIpffPrqpjVyrdWylohamia+c5NjydTf+CMnRrX89Ga9f8cTnpN7rpWWJKMyzvSY1hSRXhgc95wsvOfai/XoTw/rvRevnPMlBq5rdWx44jiq8PuwtHn2J9jm+xswX3P4bShZCaEZPjDGRCT9raT/JKlf0k+MMV+31h4ItmRA9SUTRi9PCWZbN/TojR2zn/pWbvQkHo94rsP64W3vmrZw7E0P7NMdV1+olUuTGsu4noPwrRt6tO/FY/rUN35ePIv2mW8e1NUXvUE95yyb9p4dLVH98mROZ7Y1KZezJcslacYRn4JMJqefHx32PLdQjoHhcW3d0KPzu1plrdXBgen7XNXZUraz6Lf/wj4llXys1Oezbk5f/N7z+ugV53ke27ahR+cvb1Mu5+rZY9Nfd96yFhmjkp8hGo2E6po6153IJnfk9THPtSJ3rVut5351otg+OlsT+sSVqzzP2bqhR994ul/b/89L+vsbL1XWdT1n7bdvuFiHh9xiBrxilri2hP7p6f5i++1sTWjg5Pi0fS9tjvlON8q6E3+zczta9OLgmKet33Ptxfrvjx4oXkNTOGPcfVpy2t95+3U9ikcd3XDvTzx/36aYow9N2lZo037t5Pyu1hkPFJY2x/X6WMazrXCAIknZOV77YiX98vj0eHPW0rlPtZ3NqG3B+Hi2ZJuf0lmsuua49KJPzD1nDjEXjcFx5jZiX22FmDs0mi7OMnj3BV265crzdXwkrY899FNPOe//4Yv66BXnqaM1pk//08+Kn6UQk+/9wYvTPt+2DT0yRrrxK6e+Hw/dtEaDw5lpv2fffuZVfeS33qSP//1PPXE6GY/onu/9Qv/tPRf4xqdfHk/p43//U23b0KNf64jKmOnHA1N/45vjjv7u+h6ls9azfuK9N7xN4z7HLV2t8WlLaGx58Ent3rxGZ5yenPNvpuOYBZ1IisUivifvqmWuvw1+wjTH4hJJv7DWvmCtTUv6mqSrAy4TsChOptxpwezmB/bpZKr02j9TDabSvvsYTKWnXYdVLq30oddS0zqRNz+wT++64Izi/Vv27NdNl79Z77rgDN/3zLlGmazV0eHx8uUq89hUR4fHpz23UI7C644Oj2tgxH+fAyPT9znT/gv7LPdYqc/Q0dqkdT0rpz12U/51x0b9X3dsNF32M5S6pm5whs9XLYMjab08ODotUcCte/d72sdNl7952nNufmCf1veeJUla1hqf9vjRk+lpadJv2bNf/a+liq+TVHLfknzXvXKMKbazqW19y4NPal3PSs/7HXot5ft3vvEr+9T/Wmra3/fQlG2F9yrVhmYSjTo6e2mLVr2hTWec3qRVb2jT2UtbimexC9cwTv2ckRIHQcNj/vFmeGz28aZgLt/hcm1+sZ0oEXNPzCHmojGUWh7DDaipFGJuoZMoSet6Vqr/tVSxkzi5nIXfoVxu4nmFz1KIm5O3FV530wP7dPT1cc+2XE6+v2fre88qdhIL22/Zs19DIxmt61kpx/jHp+OpTHEfg6m0b3yY+hs/mnYVj0SKibsKz+svcdySKdFRyro2NMnKqmmuvw1+wtRRXCHp0KT7/fltHsaYzcaYPmNM38DAwKIVDliocm231Fmf7BzO+pTbRzrrTTddauHY46mMmuMR3/1MnqbeP5TSkmRMbpnMgY6ZKFO5cs3lc5d67pJkbN77nM3+F/IZliRLjGjl3Hnvc+rfsvBYNa+pK9d209lcyTYzuX2UqovCD5ZfFspS+22ORzw/dCXr2bW659qLi229MGL42sh48fFybWry+5V6rt+aXX7bFvodj0YdnbkkqbM6WnTmkqRnqlNHMq6tG3o8n3Prhp7iNNipKhFv5rOvSr7vbJVqu0GUBbWpEqMyczXXmLskGSsZLwvx0bXe36TC/0vFz6lxrFSm4IhjSr5+STKm10bGp8Xhu9at1rbHny8+t9zv3tTfeL/3K/kb5FrfY51GyVi7rNn/t2FZ8+yviwxTR3FWrLU7rLW91trezs7OoIsDzFq5tlvqrM9cglm5fcSjEc9jjlHJwD2azvnux0zKBljoVJY6U+iYiesGoo4pW665fO5Szz2eysx7n7PZ/0I+w/FUxv+xiDPvfU79WxYei0erd51DubYbj0ZKtpnJ7aNUXRQOtn51Ymza46X2O5rOFTPIlXueMUaP/vSwvrppjb778XfqvhsuUTxq9KmvHyjWZ7k2Nfn9Sj3Xb80uv22V+I6X0tQU1bkdLdq9eY2+f8vl2r15je/Uz4JKlqUS3+FqHrSVartBlAW1qRKjMnM115h7PJUpGQcLsdcx3t+kwv9LxeapcSxS4vc+HnVKvv54KqO//d4vdFoyql0fvkTfv+Vy3XH1hfrstw7qqUPHi88t97s39Tc+5vO8Up89FnHmdBKt3iQSUZ23zPvbMNep/mHqKB6WtHLS/e78NqDuzXVEYK776GiJa+fG3uJj9//gRZ3eHNODf/J2fffj7ywG7oHhca1cOnHdwdT9fPfAq8X7d6+f6FR+98Crvu8Zcaxi0YkLtcuWaw6fu6s1Me25hXKcuh4hoc4W/33OlFnMb/+FfZZ7rNRnGBwe0959h6Y9ti3/unJn+sp9hql/y+72iWsUO6qYOa2cjpa43tjRrLvXr5524mFy+9j2+PPTnrN1Q4/29L0iSdr1by9p65STF12nJaa1xYl9NOkfn+zXHVdfqO/9xeW6cMVpJdvsVRet0Mh4RsYYHXptVH+595ni9S6l/nZ79x3yvN/KpUnf526/rkfdS5PT/r4rp2wr916zyZY3G01NUa1ob9YbO1q0or25bAbjSsSb+eyrEme3K6WSdYD6Fra2Uoi5n//AW4pl2rvvkLqXJvW5ay6aFocLv0ORyMTz7lq32hOTJ28rvG7bhh51nZbwbItE5FsPybgzEQunxOn2lpj27jukG9aeM5EgJxZRMuaoqy2hgfyU+8l16Rcfpv7GdyTj6vB5XneJ45b2pticTqLVo0TC+9sw1+vBQ5P11BgTlfSspCs00UH8iaQPWmt/Vuo1Ycp6Ol9kSw29RctiVonlKmaX9dRVxExkQRsdn/j+Z1xbTG29tETWRrKezi3r6WsjOUUnZT3N5lxFGyLr6cSZ53JZT7P5LH2Ts546jlFT1CmmWY84Ro4zkbQlnbXK5Fw5+bPJjmMmRhUdo0TMUSrjaknS0YlJGSwL+45FJ66XndpOC+1s6t8uGXc0njmVZTUMWU+roZLL49Ri1tO5lhuNbZZtJZCsp9l8bJxz1lNrlYiUzno6nnHlzpD1NBl3FHWkdFbK5Lxx2s1nPY1HHJ0Wj+pkJqdYZOJ3ITUpO+nkupwcH6b+xpd6XrlYzPd51sKf9dRamzXG/Kmkb2lieYwvl+skAvWmqSmqFQsMauX24ThGXW3ebF1tZZJ3Td1PubLNVO5y5ZrL555txrB4PKoVs+gYzmX/5R7z+wytk+r2zBJlSSSiWlHi7F65z1BuUd8gOI7R0paENMsFfKuldYZkdH7tbC7tr9Tfy+/1ftsWO+NdOZWIN/PZV7k2v9gqWQeob2FrK8WYO8XpM7xuDqtt+WpSdN778HTaSvxWzDY+zCUWY2FCVaPW2n+W9M9BlwMAAAAAGlmYrlEEAAAAAIRAqEYUG1EtXEs53+soa+GzSVwnCgAAAEwVmmQ282GMGZD0comHl0k6tojF4b2Df/9qvPcxa+2VFd5nmNvuVGEpS1jKIdVOWRar7YapPhaKzxK8qrRbqWzcDVNdURZ/YSlLGGLuTMJSV9XEZ6yskm23pjuK5Rhj+qy1vbx347x/0J+9UsL0OcJSlrCUQ6IsYSxDpfBZGlOY6oqy+AtLWcJSjnJqoYwLxWdcPFyjCAAAAADwoKMIAAAAAPCo547iDt674d4/6M9eKWH6HGEpS1jKIVGWqcJQhkrhszSmMNUVZfEXlrKEpRzl1EIZF4rPuEjq9hpFAAAAAMD81POIIgAAAABgHugoAgAAAAA86CgCAAAAADzoKAIAAAAAPGq6o3jllVdaSdy4VfNWFbRdbotwqwraLrcq36qGtsutyreqoN1yW4RbSTXdUTx27FjQRQDmhbaLWkXbRa2i7aIW0W4RpJruKAIAAAAAKo+OIgAAAADAo2odRWPMl40xR40xz0zattQY8x1jzHP5f9vz240x5gvGmF8YY/YbYy6e7/u6rtXAyXEdHhrVwMlxuW7ZqbcAgAojDqMW0E5Rr2jbqJRoFfd9n6QvSto1adttkh6z1t5pjLktf/9WSb8r6dz87e2Stub/nRPXtTp45KQ27epT/1BK3e1J7dzYq1XL2+Q4ZoEfBwAwE+IwagHtFPWKto1KqtqIorX2XyS9NmXz1ZLuz///fknvnbR9l53whKQlxpgz5vqegyPp4hdDkvqHUtq0q0+DI+l5fQYAwNwQh1ELaKeoV7RtVNJiX6O43Fr7av7/v5K0PP//FZIOTXpef37bNMaYzcaYPmNM38DAgOexdDZX/GIUdzSUUjqbq0TZgQUp13aBMJtL2yUOI0xKtV3aKcJsIccLtG1UUjWnnpZlrbXGmDlPmrbW7pC0Q5J6e3s9r49HI+puT3q+IN3tScWjkYUWF1iwcm13srNve3Re+3/pzvfMr2DADGbbdiXiMMKlVNulnSLM5hJzp6Jto5IWe0TxSGFKaf7fo/nthyWtnPS87vy2OeloiWvnxl51tycndpKfl93REl9YqQEAs0IcRi2gnaJe0bZRSYs9ovh1SddLujP/7yOTtv+pMeZrmkhic2LSFNVZcxyjVcvb9PCWtUpnc4pHI+poiXPxLgAsEuIwagHtFPWKto1KqlpH0RjzVUmXS1pmjOmX9ElNdBAfMsZ8RNLLkq7JP/2fJf2epF9IGpV0w3zf13GMOtsSCyg5AGAhiMOoBbRT1CvaNiqlah1Fa+0fl3joCp/nWkn/dyXeN53OamAkraxrFXWMOlviiscDuxQTABpSNuvq6PC4MjlXsYijrtaEolGn5HZgsXG8gHoyNbYua47p2GiGWIsFqauImE5ndXBgRDc/sK+4dszWDT1a1dlC8AeARZLNuvr5kZO6aVIs3rahR+d1tujZgZFp289f3sYBDBYVxwuoJ34xd+uGHn3j6X5t/z8vEWsxb3XVWgZG0sWgL02kA775gX0aYO0YAFg0R4fHiwcs0kQsvikfi/22Hx0eD7K4aEAcL6Ce+MXcmx/Yp/W9ZxXvE2sxH3XVUcy61nftmKw751U4AADzlMm5JWOx7/acu5jFAzheQF0pFXMjkxLYEGsxH3XVUYw6ppgOuKC7PakomZ4AYNHEIk7JWOy7PVJXP0WoARwvoJ6Uirm5SSc+iLWYj7pqMZ0tcW3d0ONZO2brhh51snYMACyartaEtk2Jxdvysdhve1cr2fmwuDheQD3xi7lbN/RoT98rxfvEWsxHXV2xHY9HtaqzRbs3ryGLGQAEJBp1dP7yNj1046XK5lxFJ2XcK7UdWEwcL6Ce+MXWZc0xdax9k65dczaxFvNWdxHR2vL3AQDV47pWx0bGNZbJKWKMWpuiOi0R01AqU1z8uas1Ubw/lMqoPel9nMWhAYSJ61oNjqRDGaMKZTOystYqGjGy1uroSFqJaERvOK0pNGVF7amrjuL4eFbPHpue7vq8ZS1KJOrqowJA6Liu1cEjJ7VpV18xBv/tB9+qiONMWxLjC489q28fOOp7f+fGXq1a3sbBDaqG5TEwW35xLSwxqlC2f3zykN5z0Qp98bvP6frLztGte/eHrqyoTXU1Bn1s1D/d9bFR0l0DQLUNjqSLB1PSRAx+bSTjuyTGup6VJe9v2tWnQZYpQBWxPAZmyy+uhSVGFcq2vvcsbXnwSa3rWVnsJErhKitqU111FEl3DQDBSWdz02JwczziG5eXJGNl76ezueoWFg2N4wXMll9cC0uMKpQt4phiHA1rWVGb6qqjSLprAAhOPBqZFoNH0znfuHw8lSl7Px6NVLewaGgcL2C2/OJaWGJUoWw51xbjaFjLitpUVx3FZc3+6a6XNZPuGgCqraMlrp0bez0xeGlLzHdJjL37DpW8v3NjrzpYpgBVxPIYmC2/uBaWGFUo256+V3TPtRdr775Dumvd6lCWFbXJ2BpOC9rb22v7+vo828bHszo2mi6mu17WHCeRDRaiKqeX/dpuwdm3PTqvfb5053sWUiTUn0Vvu9LkrKeuIkZKxiPTsp5OzXJK1lNMUrU//NS2m05nNTCSZnkMzGiWWU8Di7mFrKfjWVfGTGT8t5ISxFPMTskGUncRMZGIagUdQwAIhOMYdbU1Tdve2ZaY032g2uLxqFbQMcQsOI4JbYwKc9lQ++ouQmazro4OjyuTcxVjgVEAWBSVWGcszGuVof5wvIB6VCqOEl8xH3XVUcxmXf38yMlp63Wdv7yN4A8AVVKJdcbCvFYZ6g/HC6hHpeLouZ2tem5gmPiKOauraHh0eNx3va6jw+MBlwwA6lcl1hkL81plqD8cL6AelYqjR4fHia+Yl7rqKGZyrv+6SDk3oBIBQP2rxDpjYV6rDPWH4wXUo1JxNFuivRNfMZO66ijGIo7/ukiRuvqYABAqM60zls26+uXxlF4eHNEvj6eUzU4/GA/zWmWoPxwvoB6ViqMRx+jG/+vsaduJr5hJXUXEZc2xEusoxgIuGQDUr3LrjBWuBbtm+7/pnXc/rmu2/5t+fuTktM5imNcqQ/3heAH1yC+O3rVutT79Tz/TVW/pLnYWia+YrbpKZnNsNKP/9dizuv2qC7QkGdPx1MT9T/3BhTqTFNgAUBWOY7RqeZse3rJ2Wka9X70+5nst2EM3XqozlyRntQ+g0jheQD0qxNHdm9fo1RNjGhxJ67PfOqinDh3XgVdPavfmNdp42TnEV8xaINHQGPMxSX+iifVA/13SDZLOkPQ1SR2S9km6zlo7p6tsMzlXf/rbb1ZHa5OyrlV3e1JnnPZmrjkAgCryS7uey7l69cS4YhGjez/0NkUco5xrtfNfXtBD+/qVzbnF5QkkK2ulnLWKOo6WtzUVM09mMjkdHR4vLore1ZpQLMZ0KSwMxwuoZYWYa2Q1nnWVs1YRY9QUczSWcdWacHTG6U3qbEvoix98q6ysDg+NyUp6Q1uThlIZvXoiRYcRM1r0jqIxZoWkP5N0gbU2ZYx5SNIHJP2epM9Za79mjNkm6SOSts5l3x0tEb0+FtH7dzxRTP+7dUOPlrZwUAEA1eCbjv26XkWjRnt+8oquuqhbNz94agmCe669WO3NUcWijn5+5KS+8Nizuv6yc3Tr3v3Tlimw1urnR4d186QlDLZu6NH5Xa10FrEgHC+gVhVi7j8+eUjvuWiFtjz4pKcNZzIZvRaLTYubr6fS+vjf/1TbNvToC489q28fOMoyGZhRUNcoRiUljTFRSc2SXpX0Lkl78o/fL+m9c93piZRb/GJIE1Ocbn5gn06kOEMIANXgm479K33qfy2l9b1nFTuJhce2PPikrrvsHDmSbnpgn9b1rCx2EgvPKSxTcHR43Dems4QBForjBdSqQsxd33tWsZMonWrDy09v9m3bF5x5ejG+rutZWXyMZTJQzqJ3FK21hyV9VtIrmuggntDEVNPj1tps/mn9klb4vd4Ys9kY02eM6RsYGPA8lnWtf1pg11b2QwDzUK7tAmFWru2WSsfeHI8o4hjfxzI5q7HsRLr2JclYyXTuxHQsVKm2S9tCmM0m5paKrzO17ULcnfwYy2SglEXvKBpj2iVdLekcSWdKapF05Wxfb63dYa3ttdb2dnZ2eh6LOsY/3TXD6QiBcm0XCLNybbdUOvbRdE65/LVfUx/L5a837G5P6ngqU3KZAmI6FqpU26VtIcxmE3NLxdeZ2nYh7k5+jGUyUEoQU09/R9KL1toBa21G0j9IWitpSX4qqiR1Szo81x13JOO+6a47kqT/BYBq8F3W4rpedS9Nak/fK7rn2ou9Mfnai5WITiSl2bahR3v3HdJd61Z7nrNtQ4+6WhPqak34xvSu1kQwHxZ1g+MF1KpCzPWNrxt6dOTEqG/bPvDLE8X4unffoeJjLJOBcoy1izvNwhjzdklflvQ2SSlJ90nqk/QOSXsnJbPZb629p9y+ent7bV9fn2fb2FhWg6l0MUNeRzKupiZSXWPeqnJ62a/tFpx926Pz2udLd75nIUVC/Vm0tlsq6+nR4Ymsp5mcLcbklkREpzVNZNkrZD01snInZT3tak2Q9bRxVW1Ib2rb5XgBFbboMbdc1tPhcbfYtk9LRvR6aiI+tydjGkplWIYIk5VsAIseEa21PzLG7JH0pKSspKck7ZD0qKSvGWP+Or/tS/PZf1NTVCsI9ACwaBzHqLMtMWVbRCvam8u+Lhp1PGsp+onFZt4PMB8cL6BW+cXcqU6fEjbbmk79f6bXAgWBREhr7SclfXLK5hckXbLQfXP2GQDCrTCSmMm5ikVOjSD6jUxyphvVwvEC6lGpOFoq7gLl1NWptEwmx5pbABBi2ayrnx85qZsmxeltG3q0qqtVvzg24l2PkfW9UCUcL6Ae+a5ru7FXv7asRQePDk+Lu+cvb6OziLLqqnWw5hYAhNvR4fHiwYrkXTdx2nqMrO+FKuF4AfXId13bXX1l4y5QTl11FFkXCQDCLZNz57T2F+t7oRo4XkA9KrWubcn2nnMXs3ioQXXVUWRdJAAIt1jEmdPaX6zvhWrgeAH1qNS6tiXbe6SuugGogrpqIay5BQDhVlg/0W/dxGnrMbK+F6qE4wXUI991bTf2RHBGhQAAIABJREFUlo27QDl1lcwmFovo/K5W7d68hixmABBC0aij85e36aEbL1U25yo6KfvequVtenjLWrKeouo4XkA9chxTMo6WirtAOXXVUQQAhNNsliKYzdpgAIDpZoqxs1m3FpiqrjqKpLsGgPAhNiNsaJOoJ7RnVEtdjTmT7hoAwofYjLChTaKe0J5RLXXVUSTdNQCED7EZYUObRD2hPaNa6qqjSLprAAgfYjPChjaJekJ7RrXUVUeRdNcAED7EZoQNbRL1hPaMaqmrZDakuwaA8CE2I2xok6gntGdUS111FKWJL8uK9uagiwEAmITYjLChTaKe0J5RDXU19RQAAAAAsHB0FAEAAAAAHnQUAQAAAAAedBQBAAAAAB50FAEAAAAAHnQUAQAAAAAedBQBAAAAAB6BrKNojFki6e8kXSjJSvqwpIOSdks6W9JLkq6x1g7Ndd/pdFYDI+nigqOdLXHF43W3XCQAhF426+ro8LgyOVexiKOu1oSiUafkdmAxcbyAejI5rsajjiLGKJXJEWOxIEFFxM9L+qa1dr0xJi6pWdJfSXrMWnunMeY2SbdJunUuO02nszo4MKKbH9in/qGUutuT2rqhR6s6Wwj+ALCIsllXPz9yUjdNisfbNvTovM4WPTswMm37+cvbOJDBouF4AfXEL97evX61PvPNgxoYHifGYt4WvcUYY06X9A5JX5Ika23aWntc0tWS7s8/7X5J753rvgdG0sWgL0n9Qynd/MA+DYykK1J2AMDsHB0eLx60SBPx+KZ8PPbbfnR4PMjiosFwvIB64hdvb9mzXzdd/mZiLBYkiFML50gakHSvMeYpY8zfGWNaJC231r6af86vJC33e7ExZrMxps8Y0zcwMOB5LOva4pekoH8opaxrK/4hgLkq13aBMJtP283k3JLx2Hd7zq1YeYGCUm2X4wWE2Vxjbql4uyQZK/6fGIv5CKKjGJV0saSt1tq3ShrRxDTTImut1cS1i9NYa3dYa3uttb2dnZ3eHTtG3e1Jz7bu9qSijqlg8YH5Kdd2gTCbT9uNRZyS8dh3e4QpUai8Um2X4wWE2Vxjbql4ezyVKf6fGIv5CKLV9Evqt9b+KH9/jyY6jkeMMWdIUv7fo3PdcWdLXFs39BS/LIVrDjpb4pUpOQBgVrpaE9o2JR5vy8djv+1drYkgi4sGw/EC6olfvL17/Wpte/x5YiwWZNGv2LbW/soYc8gYs8pae1DSFZIO5G/XS7oz/+8jc913PB7Vqs4W7d68hixmABCgaNTR+cvb9NCNlyqbcxWdlHmv1HZgsXC8gHoyNa7G8llPP/+BtxBjsSBBRcSPSnown/H0BUk3aGJ08yFjzEckvSzpmvnsOB6PagWBHgACF406OnNJctbbgcXE8QLqCXEV1RBIhLTWPi2p1+ehKxa670wmp6PD48UzhF2tCcVikYXuFgCwAK5rNTiSVjqbUzwaUUdLXM6k68FYWxGLjeMF1LKZYmqlEaMbU12dSstkcvr50eFp6yKd39VK8AeAgLiu1cEjJ7VpV18xNu/c2KtVy9vkOKbkmous+4Vq4XgBtWymmFppxOjGVVd/3aPD477rIrF2DAAEZ3AkXTygkSZi86ZdfRrMr1lXas1FYjeqheMF1LKZYmqlEaMbV111FFkXCQDCJ53N+cbmdDYnqcyai6z7hSrheAG1bKaYWmnE6MZVV1NPo47Ruy/o0rqelVqSjOl4KqO9+w6xLhIABCgejai7Pek50OhuTyoenZjiV1gDbOrjhXW/uJYMlcbxAmpZqZjaFHN0eGi04rFyphiN+lVXf+GOZFwfveI83fGNA3r/jid0xzcO6KNXnKeOJOsiAUBQOlri2rmx17PG186NverIr1lXas3FrtZE8Vqy9+94Qu+8+3G9f8cT+vnRYWUy1TlzjsbA8QJqmV9M3XXDJXr1xHhVYmW5GI36Zqyt3WkWvb29tq+vr3j/8NCo3r/jiWlnPHZvXqMV7c1BFBG1ryqnl6e23cnOvu3Ree3zpTvfs5Aiof4setstZ7ZZT6eurUhcbzhVG9Kb3HZpV6iCRY25U2NqJufqmu3/VrU2XSpGoy6UbLt1NfWUaw4AIJwcx6izrfTZ51JrgBHXUQ20K9S6qTH15cGRqrZp1mlsTHV1KiDqmOKweEF3e5JrDgCgRhHXUQ20K9Qb2jSqoa46il2tCW2dMod6K3OoAaBmEddRDbQr1BvaNKph3lNPjTE3WGvvrWRhFioWi+j8rlbt3ryG7HgAUAeI66gG2hXqDW0a1bCQaxQ/LSlUHUVp4ovChegAUD+I66gG2hXqDW0alVa2o2iM2V/qIUnLK18cAAAAAEDQZhpRXC7pP0samrLdSPphVUoEAAAAAAjUTB3Fb0hqtdY+PfUBY8zjVSkRAAAAACBQZTuK1tqPlHnsg5UvzsKNjWU1mEoXL+TtSMbV1FRXy0UCQN0gZiMotD00Ito95qKuWsbYWFbPDY7o5gf2qX8oVUwNfG5HC18CAAgZYjaCQttDI6LdY67qah3FwVS62PglqX8opZsf2KfBVDrgkgEApiJmIyi0PTQi2j3mqq46ilnXFht/Qf9QSlnXBlQiAEApxGwEhbaHRkS7x1zVVUcx6hh1tyc927rbk4o6JqASAQBKIWYjKLQ9NCLaPeaqrjqKHcm4tm7oKX4JCnOvO5LxgEsGAJiKmI2g0PbQiGj3+P/Zu/vwOMr7bvTfe2Z29k2yLa8kx0g2pqltAtQQS0mduE1JyJPSByhN7UAShBNOi7F5mqQ9KYGrfWjSk9NzIG6aJ6XFBjdvxCSY2OGiDXlScgg0bRLSSCS4xME4LwbLIZa0lkHSvszOzH3+0O56X2ZWu6t9mR19P9flCzS7O3Pv7G9+M/e8/O5a+erJ1VBIw/pYFAd3bmE1JyIij2POpnZh7NFSxLinWrUtMoQQKoBRAKeklFcLIS4A8BCAGIAxADdKKfl0LRFRhzFNGxOzaWQsGwFVQX9XEJrmfANLKKRhoM6DlHTaxFTiXJn33oiOYJAHPFQdRan8N1FOJmNhYjadzzX9XUEEAmq7m1WT0rw8sDwEy7Lnc+hcmjmUHLUzGj4E4CcAlmX/vhvAp6SUDwkh9gH4IwB7a5khy/4SEbWXadp4/vQMdhXk4X0jQ7hwVbdrZ7Ee6bSJF6bK8/2G3igPdGhBhmHi2GR5/Gzsi0LXGT90TiZj4fmJ2bJYubC/q2M6i055+fM3vQGpjF00jTmUSrXl/JkQYhDAVQD+Kfu3APA2AIeyb/kCgD+odb4s+0tE1F4Ts+n8gQcwn4d3HRjDxGy6ocuZSjjn+6kE8z0tbHLOOX4m5xg/VGxiNu0YK43Oac3klJdPnkmWTWMOpVLtutHifwH4CAA7+3cMwFkppZn9exzAgNMHhRA7hRCjQojRycnJotdY9pe8rFLsEnlZLbGbsWznPGzZLp+oD/M9VcMtdhk/VK12xEqjjxec8nJEV7kN0IJa3lEUQlwNYEJKOVbP56WU90sph6WUw319fUWvsewveVml2CXyslpiN6AqznlYbezuhvmequEWu4wfqlY7YqXRxwtOeTlhWNwGaEHtuKK4FcDvCyFOYL54zdsAfBrACiFE7qboQQCnap0xy/4SEbVXf1cQ+0ry8L6RIfR3BRu6nN6Ic77vjTDf08L6os7x0xdl/FCx/q6gY6w0Oqc1k1NeXrMyXDaNOZRKCSnbd4lZCHE5gD/PVj39CoDDBcVsjkgp7630+eHhYTk6Olo0LZUyEU8aLPtLjdKUU2tOsZuz7o7H6prnibuuWkyTyH9aHrs5uep6pmVDW6Dq6WKw6qkvNe1yRmnsGoaJyblz8dMX1VnIhhxVWfW0bTm3Gk55OV/1lDl0qXONXS9Fw+0AHhJC/N8AfgjgM/XMZDGl1omIaPE0TcF5K8ILv3GRgkENAzyooTrpuoYBdgypCoGAioGeSLubsShOeVnTFOZQqqit0SGlfArAU9n//zmANy52nn4Y64aIqNPZtkR8zoBhWtA1FbGoDqVBz77UMk4jkRseL9BSlMufgISUgAQQbHCOJv/w1WmETMbCL2dSyJgSigAylsQvZ1I4rzvE5E9E1CK2LXHs9AxufmA0Pz7X/h3D2Liqe9EHIqZp45evJmHk87yFX76axHnLwuwsUtV4vEBLUTptYjJhIGPZ0BQFB773C9z37ycamqPJX3zVUXwllcEriQxuffCZ/MHJvTdsRjSgopeJn4ioJeJzRr6TCMyXXL/5gVE8cutW9HUvrgDEKykDZ53yvK4i1hVqRPNpCeDxAi01mYyFF6bm8mNC5mJ+OmHi4bHxhuVo8hdfdRTTpo1nTsTxpZu3wJYSihD41tGXEbt4dbubRkS0ZBimVTQ+1yf+8BK8eX0fEoaJU9PWooqGpDJ2/uAemO+E3vrgMzi4c0tD2k5LA48XaKmZmE3nO4nAudz5ufe/AQ+PjWN8OgnDtPLvZ7EnAnzWUQwFFAxd0Iv37n86f7Zk78gQQgHejkRE1Cq6pmKwJ4zx6SQ+8YeX4HUDK/Du+4vz8sa+aF0HHRwonRqBxwu01LjlTjV7q+lgTxi6Nn813TBMHJssvvq4mLxNnctXGTGVscvOluw+MIZUxm5zy4iIlo5YVMf+HcMY7Anjzev7HPPy5JxR17w5UDo1Ao8XaKlxy52WLfPPKMay44hOzhkNzdvUuXzVUeSZZiKi9lMUgY2ruvHIrVthNTgv+2Hwa2o/Hi/QUuOWO1dEAnjk1q1FhWy4fVCOr64f586WFAY3zzQTEbWeogj0dQdxatqqOy+nUibiyXPPyMTCOkIhDRf2d+Hgzi0c1oDqxuMFWmosS6K/S8dDO7fAtiUCqoLeqO6YO7l9UI6vrijGwrrj2ZJYWG9zy4iIlqa+qHNe7otWzsuplInj8Tlcf//T+J09T+H6+5/G8fgcUikzP/j1+bEoBnoi7CRSzXi8QEtJLp9u2/c9/NbdT+K9//R9TM0ZsCznK4T15m3yH19dUYwnDYz9YgpfunkLpJQQ2SpmKyMBDIR89VWJiDqCrmvY2BctugJYTfW8eNL5GZmDO7cwn9Oi8XiBlpJa82m9eZv8x1e/uGlLPPrsr7C6J4oV4QDOJjN49Nlf4a2ve027m0ZEtGTpuoaBGg8w/PiMTCZjYWI2zVtmPYDHC7SU1JJPS/PUectCzFNLmK86iiFNwUeu3IjbDh3Jl/Pds30TQpqv7rAlIvI9vz0jk8lYeH5itqzc/IX9XTwIawMeL9BSUm0+ZZ6iUr7KiBLIJ31g/mzJbYeOoHPPPxMRLU1+e4bMabDr3QfGMDGbbnPLliYeL9BSUm0+ZZ6iUr66opg2bcdL62mT4yIREXWSUEjD+ljxMzK5qqedyI+30nYyHi/QUlJtPmWeolKducd14bdblYiIlrJQSPNNYRHun7yFvwctNdXkU24XVMofe+Cs/q4gvrJrC0wLsKSEKgQ0FeiNcCBmIqJOYxgmZjMmkobd8VcVc4Ndlz7709/F/VM78HiBlhLDMDE5Z7hWMC0cs/bgzi345o9fxse+9jzzFPmro2hZElOzmbIdcU9QRyDQ7tYREVG1DMPEVNJA3CGnr49FO66zGAiouLC/q+jWL1Y9bR8eL9BSYRgmjk3OlcX6xr4odF3Lj7FY+vrYnVcgZdjMU0ucr4rZuI0TE08abW4ZERHVYnLOgGXBVzk9EFAx0BPB+bEoBnoiPPhqIx4v0FIxOecc65Nz87Huti2kDJt5ivx1RZEP4RIR+YNpS0iAOZ2agscLtFQsFOvcFqgSX3UU+RAuEZE/aIqALeGa01+Mz3X0M4vUXjxeoKUiF+vXDw3i2s2DsLPP5HYFlaLXuS2QE1/deuo2TsyKsAKTJa+JiDpGX1SHqsIxp//1v/wYv7PnKVx//9M4Hp9DKmW2ubXUafw2TieRm76ojq/s2oLLX7cK793/NC7f8xTes/9pjJ9NI5UyuS1QRb46DRtPGrjniRdw59UXYUU4gLPJDO554gV89JqLIUQa560It7uJRERUBV3X0AsgpClFBWD++l9+jMePTgA49yzNwZ1bfDOMBrVGpeMFxhL5ia5rsF2eU3xo5xYIwFdj1lJjtTwKhBBrADwAYBUACeB+KeWnhRArARwEsA7ACQDXSSmna5m3aUs8fnQCkzMGdl3+WqwIB7BtaA0UAWQsXlEkIvKS0pLtsbCeL9Ge+3tlNARE59976tVUvpOYk3uWJp02MZU499neiI5gkAc65My0JSZnigvXTM4YsPhcFjnIZCxMzKY7tmKx23OIp6aT+PBXnsW+kSH8eraadD6XzqXbkktN08bEbBoZy0ZAVdDfFYSm1X8DZOHQH+wE164da8oE8GEp5TNCiG4AY0KIbwJ4P4AnpJR3CSHuAHAHgNtrmbGmCLzjon68780X4PbDR/Jlfu8bGcK6GMeAISLyitKS7e+4qB8fuGKD61AYk3MGTkwlXJ+leWGqvLz7ht4oO4vkKKQp+MiVG3HboXPHCnu2b0JwEQek5E+ZjIXnJ2bL8suF/V0d01l0ew7xbDKD8ekkdh0Yw4N//JtYBTgOldGqXGqaNp4/PYNdBcvfNzKEC1d119VZdBv6oxOHWGqXlmdEKeXLUspnsv8/A+AnAAYAXAvgC9m3fQHAH9Q6b0UAd/ze6/KdRGD+jMktB8ZwNskrikREXlFasn3b0JqKwxWYtsTfP3Ecd2/bVPQszb6RIYQCiuNnpxIc6oCcmbbMdxKB+Zi57dARVnqkMhOzacf8MjGbbnPLquf0HOLd2zZh31M/AzD/nSZn0q5DZbQql07MpvOdxNzydy1iXXMYnMVra3daCLEOwOsBfB/AKinly9mXfoX5W1OdPrMTwE4AWLt2bdFrlgRmUibL/JInVYpdIi9rROzatkR8zoBhWtA1texWqBXhQMXcrSkCk7Np/O2/Hss/V5YwLPR3BzGbtpj3yZFb7HJIAKpWO2Kl0ccLoZBW9Bzizyfn8Lf/egw/PHkWwHzHMT5noK872JTvWpr/Y1EdikNV1YxlOy+/zsfHuJ0vXtvusRBCdAE4DOBPpZSvFr4mpZSYf36xjJTyfinlsJRyuK+vr+i1gCLQHdLyZ0xyWOaXvKBS7BJ5Wa2xa9sSkzNpnJpOYHImDdO0cez0DN5573ew9e4n8c57vwM1eytUztlkpmLu7ovOnxGfnE3jli+O4cNfeRa93UGsCGn526rcPktLl1vsBlxiJsCYoRLtyC+NOF4ozcO6rmKgJ4LV3UH0dQcxmb1Kl7u6eHjsZFO+q23Lsvx/7PQMbIfOWkBVnJev1tdd4b5h8drSURRCBDDfSXxQSvnV7OTTQojV2ddXA5hw+7ybSFBAVQXuvWFz2a1JLPNLRNR8jgcFEzP41DePFd3+88Xv/qLoVqjDYycrlmjXdQ0b++bPiP/bbZfj4M4t2NgXna+OGnEu794bYd4nZ8vDCvaVxMy+kSEsD/MZRSrW3xV0zC/9Xd6tfVGpc6brGn49FsWDf/ybOLTrTbjz6ovwhe/+Ah+4YoPrUBmLyaXxOQM3PzBalP9vfmAU8bny2z/7u4KO22W965pDfyyemL9418IFCiEw/wziGSnlnxZM3wMgXlDMZqWU8iOV5jU8PCxHR0fzf5+aTuCB7/4C79t6AWw5v6FoqoKoLrA8EmrSNyKfa8ppp9LYLbTujsfqmueJu65aTJPIf1oeuwAwOZPGO+/9TlnRhDuvvgi3fHGs6L2jf3kF0qZdsepptQUHWPXUN5p2qr8wdk9NJ/CziVfx2v5l+ZjJ/T3QE2lWE6hDVVn1tC0514lbHn7k1q3o657vdJVWne6L6tB1reG59NR0AlvvfrJs+nduf6vjtparempaNjRWPW0V19htx5raCuBGAP8lhPhRdtpfALgLwMNCiD8C8CKA62qdsSUl7vv3E7jv308UTf/2R96K5cz7RERNZ5jOzwvGosVncAd7wpAQZQcK9Y5hFwxqGGDHkKpkSYkdnxsrm/7tj7y1Da0hrwsE1I46geCWhw3Tyv+t6xoG9PKc2ehcqmuqY8VVXXOuGKtpSkPHPQ+FNI6NugjtqHr6H1JKIaXcJKW8LPvv61LKuJTyCinleinl26WUZ2qddyigOt6LHArwVhIiolbIHRQUGuwJo787WHT7z/4dw2WdR6JW4fEC+ZlbHnbrnDVTLKpj/45h5v8O5asudm80iP07hvP3QueCsTfq3fvIiYj8JHdQUJqHz1s+f9vTQlXviFqBxwvkZ255uB2dM0UR2Liqm/m/Q/mqo8hgJCJqr0p5OPdsDFG78XiB/Mxr8c3837l81VEEGIxERO3GPEydgHFKfsb4pkbwXUeR1Y2IiPytmgqE3BfQQhgj5EdVVmhtKm5b/uGrXy2VMnE8PofdB8by92TvHRnC+liUAUpE5AOZjIXnJ2bL8vyF/V35gyHuC2ghjBHyo2ryY7Nx2/IXX5X3iieNfGAC86WAdx8YQzxZPqgnERF1nonZtGOen5hN59/DfQEthDFCflRNfmw2blv+4quOomlLx3FjTFu2qUVERNRI1eR57gtoIYwR8iMvxLUX2kCN46uOoqYIx3FjNFYxIyLyhWryPPcFtBDGCPmRF+LaC22gxvFVRzEW1rF3ZKhoUM+9I0OIhTmoJxGRH/R3BR3zfH/Xuep+3BfQQhgj5EfV5Mdm47blL756qjQU0rA+FsXBnVtYaYmIyIcCARUX9ncV5fnSqn7cF9BCGCPkR9Xkx2bjtuUvvvvVQiENAwxGIiLfCgRUDPREKr6H+wJaCGOE/Kia/Nhs3Lb8w1e3nhIREREREdHisbtPtMStu+Oxuj534q6rGtwSIiIiIvIKXlEkIiIiIiKiIuwoEhERERERURF2FImIiIiIiKgIO4pERERERERUhB1FIiIiIiIiKsKOIhERERERERVhR5GIiIiIiIiKsKNIRERERERERbR2N6CQEOJKAJ8GoAL4JynlXbXOI5UyEU8aMG0JTRHoDitIpiVCAYGEIWFYNlRFIKAIWFJCSiAUUJDK2LBsCVURiOgKEoYNIQApAUtKqEIgrCtIGjbM7PsCikAwIJDOSGRsCcuWCKgKAAlbArqmQNoSNiRUoUARQNq0820LagokBHrCAUwnMzBMC7qmIhbVoShiwe9q2xJTc2mkMla2fSpWhHUAQHzOKJufbUvH6aXzXOg9jeCFtrTquxItZbYt8UoqjUTaRndIwUzqXA7sCipIFeTPcECFaZ3LsbkcHAvrRXk9FtaRtk3Mpu2iaYXvyeX1sum6gpQxPz0U0pBKmTiTyiCT3TeENQUZWyJtzv+tqwpWhDTouoZ02sRU4ty8eiM6pERZ24DyaaHQ4na3pfu20nku9Hqt82tk2wo5rcNgsD2HIo1cB+RvnRYrhmFicu5ce/uiOnR9vr2F3yWXczPZ90V0BZYNGJadP/7VFAX9XUFomlK2HsJ69tg2I2Hasuj42IaEbQMRXYGuAmeT8/k6oAioikDKtBFQBFYWrMtcfsgdTysCSJl2UY7vDikwzPnj6YAqkLHmlxtQFWgCSFk2VHFu/5HLMZmMhYnZdP5YP7ePyH1WdVhW7nsqArCz+6LC/YWuCCwLBvLtb3SeboTFLtMzUS6EUAH8I4D/BmAcwA+EEP8spTxa7TxSKRPH43PYfWAM49NJDPaEsXdkCIM9QZycTmNXwfQ92zchrKv430d+iasvGyz7zNd+NI63bFyF2w8fKZp+zxMv4PGjExjsCeNT112K/uUh/HI6idsOnXvfJ991KT7zHz/HTVsvwPJIAIoABIC0KXHrg8+cm98NmzF2Io7hC3qL2rZ/xzA2ruqu2GmxbYljp2dw8wOjRd9p1bIQAGDHZ/+zaH7r+7pwfHK26P2ly3GaZzVtqVU1y2l2W1r1XYmWMtuWOHU2gelEBqZp4kwiUJZrI7qC9332B+jrCuIjV24syqV3b9uEbx87XZaj940MIRRQ8P7P/QDj00m846J+fOCKDWXznp5N4kxXuGz62C+mMHRBL9bHovhpfK4o/957w2b8w7eO5/P8nu2b0NcdxOCycNn+5b4bh6BrCm7KtsOpbbllro9FF9URc9q35ea50Ou1zq+RbSuUTpt4Yar8vRt6oy3vLDZyHZC/dVqsGIaJY5Pl7d3YF4VtI/9dnHLu3pEh9HYFEJ81sLvgeHXfyBB+PRYtWw/7RoawLKzh9Csp/NnDz5YdY9/75E/x19dejPGzmaLP7dm+CZ/4xjFMzqbz8xYCZfmh8H17R4awdmUQ00kLryQyeOzZU7jq0oGi4+rC99+9bRO+8N1f4ANXbMD6krbf8tvryvYruc/2detl+5PcvuiaywbL+hK93UGsQRgAGpqnG6ERy/TSradvBPBTKeXPpZQGgIcAXFvLDOJJI78yAGB8OondB8aQSNv5HzY3/bZDRzA9l8H24bWOn9k+vDbfSSycvm1oTf7vP3v4WWRMmd/IctM//JVnsW1oDW47dASnX0lDU1SoipoP5vz8HnwGb7todVnbbn5gFPE5o/J3nTPynZzC7/RiPIEX44my+U3MpsveX7ocp3lW05ZaVbOcZrelVd+VaCmLzxn5E2Srlkccc62UAuPTSey6/LVlufT2w0ccc/SuA2M4eSaZn7ZtaI3jvF/bv8xx+tsuWo3dB8YQTxpl+ffWB58pyvO3HTqCk2eSjvuXW744hvGCdji1LbfMeLL+3OK2b8vNc6HXa51fI9tWaCrh/N6pROvzbiPXAflbp8XK5JxzeyfnjKLv4pRzdx8Yg2kBU7NGWV5zWg+7DozBMGW+k5ibnjvG3ja0BqaFss/ddugIdl3+2qJ5O+WHwvftPjCG2ZSNTHafsn14bdlxdeH7bz98JL9vKG27034l91mn/UluX+TUlxjP7h8anacboRHL9NKpkAEAJwv+Hgfwm6VvEkLsBLATANauXVv0mmm50PtZAAAgAElEQVTL/MrIz2Q66To9oqtQFeH4mtv0FeFA0d+KgOv7csvIXaByep+Uzm0zTKv0qxcxTMv1O5Uan04iY9kLLsdtngu1pVbVLKfZbWnVdy1UKXbJH9bd8Vhdnztx11UNbklj1Ru7hmnlc6RbHs7lx1zOLH3dLRcX5jq3z7otM5d33V4vzfMRXa24H6lmmmlL1KvSvq2a12udXyPb1qzlVsstdtvRFupMXorbaizU3txrbnnTltI1h7nlcLfcGIEKy+U4N5dnndpW6X255S10nF54LF7a9mo+W/papX1RpfbXm6cboRHL9NIVxapIKe+XUg5LKYf7+vqKXtMUgcGecNG0wZ6w6/SEYcGypeNrbtPPJjNFf9sSru/LLcOWcH2fEM5t07XyDl8hXVNdv1PCsMqmB1RlweW4zXOhttSqmuU0uy2t+q6FKsVuJ1p3x2M1/6POVG/s6pqaz31ueTi3v8rlzNLX3XJxYZ5z+6zbMnN51+310jyfMKyK+5FqpmmLuKW90r6tmtdrnV8j29as5VbLLXbb0RbqTF6K22pUam/ha255UxHCNYe55XC33Hg2mYHqcpyby7NObav0vtzyFjpOLzwWL513pc/Wsy+q1P5683QjNGKZXuoongKwpuDvwey0qsXCevaZxPmVkn8GJqhgX8n0Pds3oScawKHRlxw/c2j0Jdy9bVPZ9MNjJ/N/f+q6SxHQBPZsL37fJ991KQ6PnZx/ZnB5EKZtwbIt3HvD5uL53bAZ3zr6clnb9u8YRiyqV/6uUR37dwyXfafzYxGcH4uUza+/K1j2/tLlOM2zmrbUqprlNLstrfquVKyeziU7mJ0rFtUR1ATuvWEzTr+ScMy1QszvfPc99bOyXHr3tk2OOXrfyBDWrAznpx0eO+k4759NvOo4/VtHX8bekSHEwnpZ/r33hs1FeX7P9k1YszLsuH+578YhDBa0w6ltuWXmitzUtR5d9m25eS70eq3za2TbCvVGnN/bG2l93m3kOiB/67RY6Ys6t7cvqhd9F6ecu3dkCJoK9HbpZXnNaT3sGxmCrgl86rpLHY+xD4+dhKai7HN7tm/Cvqd+VjRvp/xQ+L69I0PoCikIZPcph0ZfKjuuLnz/3ds25fcNpW132q/kPuu0P8nti5z6EoPZ/UOj83QjNGKZQkpv3GYhhNAAvADgCsx3EH8A4L1Syh+7fWZ4eFiOjo4WTVuo6mnGsqGUVj3NVsFzq3pqSwmloOqpZcv8PAqrntq2hKYqEJCwiqqeAqoQTax6akMVYNXTJrQB83WIGs4pdnPYMSrn9Vszczx262nLY9fJYqqeFlaaY9XTJVP1tGmn10tjt9MqWVL7VBkrnsi5QPuqnhYeHy+q6qmUCCguVU/DCoyMe9XTtGVDqVT1NDuSQTVVT3P9AkUBbPtc1VMz25fwUdVT19j1TEaUUppCiD8B8K+YHx7js5U6iW5CIQ0DJSsgWwgUyyMVPhgt/rMn6vy20vc1Sl93sObPKIpAf3eo6vkpilhwOdW8pxG80JZWfVeihXisg9lQiiLQEwmhJ5t/lxXfBYPlVc6nNK+HoJXl9NL3uE4vyOOhkIbzqtxRB4MaBhyqczot160t9XLat9Xy+mLf36h5ua3DdmjkOiB/67RY0XUNA7pzexfzXRbz2ajz4WqRhfJDftlVzKtUIKBioKdSR8BlWSUq7S8anacbYbHL9FTUSym/DuDr7W4HEXlLqztSvKpLRERES52nOopERI3EDh8RERFRfbxUzIaIiIiIiIg8wDPFbOohhJgE8KLLy70AplrYHC67/ctvxrKnpJRXNnieXo7dUl5pi1faAXROW1oVu15aH4vF79J+TYlboGLe9dK6YluceaUtXsi5C/HKumomfsfGco3dju4oViKEGJVSDnPZS2f57f7ujeKl7+GVtnilHQDb4sU2NAq/y9LkpXXFtjjzSlu80o5KOqGNi8Xv2Dq89ZSIiIiIiIiKsKNIRERERERERfzcUbyfy15yy2/3d28UL30Pr7TFK+0A2JZSXmhDo/C7LE1eWldsizOvtMUr7aikE9q4WPyOLeLbZxSJiIiIiIioPn6+okhERERERER1YEeRiIiIiIiIirCjSEREREREREXYUSQiIiIiIqIiHd1RvPLKKyUA/uO/Zv5rCsYu/7XgX1Mwdvmvyf+ahrHLf03+1xSMW/5rwT9XHd1RnJqaancTiOrC2KVOxdilTsXYpU7EuKV26uiOIhERERERETUeO4pERERERERURGt3AxotnTYxlTBg2hKaItAb0REM+u5rkg8xdomIWoc5l6gzcdttHV+t1XTaxAtTc9h9YAzj00kM9oSxd2QIG3qjDCDyNMYuEVHrMOcSdSZuu63lq1tPpxJGPnAAYHw6id0HxjCVMNrcMqLKGLtERK3DnEvUmbjttpavOoqmLfOBkzM+nYRpV6z8StR2jF0iotZhziXqTNx2W8tX12g1RWCwJ1wUQIM9YWiKaGOriBbG2CWiQuvueKyuz52466oGt8SfmHOJOhO33dby1RXF3oiOvSNDGOwJA0D+vuXeiN7mlhFVxtglImod5lyizsRtt7V8dUUxGNSwoTeKgzu3sBISdRTGLhFR6zDnEnUmbrut5bu1GgxqGGCwUAdi7BIRtQ5zLlFn4rbbOr669ZSIiIiIiIgWjx1FIiIiIiIiKsKOIhERERERERVhR5GIiIiIiIiK+O5J0FTKRDxp5CshdYcUdAWDUDi+CnlcaezGwjpCId9tokREnsCcS+RN3Da9w1drPZUycTw+h90HxjA+ncyPrbJqmURvNMTOInmWW+yuj0WZHImIGow5l8ibuG16i69uPY0njXxgAcD4dBK7D4zBMCXic0abW0fkzi1240nGLRFRozHnEnkTt01vaXlHUQixRgjxpBDiqBDix0KID2Wnf0wIcUoI8aPsv/9e67xNW+YDK2d8OgnLljBMq0HfgKjx3GLXtGWbWkRE5F/MuUTexG3TW9pxRdEE8GEp5UUAtgD4H0KIi7KvfUpKeVn239drnbGmCAz2hIumDfaEoSoCuqYuuuFEzeIWuxpvlyYiajjmXCJv4rbpLS3vKEopX5ZSPpP9/xkAPwEw0Ih5x8I69o4M5QMsd1+zrgnEonojFkHUFG6xGwszbomIGo05l8ibuG16S1ufChVCrAPwegDfB7AVwJ8IIXYAGMX8Vcdph8/sBLATANauXVv0WiikYX0sioM7t7DqKXlOrbHLKl/kFZVil8jL3GKXOZe8bCnnXG6b3iKkbM89v0KILgD/BuBvpJRfFUKsAjAFQAL4OIDVUsr/o9I8hoeH5ejoaPMbS0tZU84wMHapBRi7HWzdHY/V9bkTd13V4Ja0XNPO6jJ2qcmYc6lTucZuW6qeCiECAA4DeFBK+VUAkFKellJaUkobwH4Ab2xH24iIiIiIiJa6dlQ9FQA+A+AnUsq/K5i+uuBt7wTwXKvbRkRERERERO15RnErgBsB/JcQ4kfZaX8B4D1CiMswf+vpCQC3tKFtRERERERES17LO4pSyv+A872wNQ+HQURERERERI3XlmcUiYiIiIiIyLvYUSQiIiIiIqIi7CgSERERERFREXYUiYiIiIiIqAg7ikRERERERFSEHUUiIiIiIiIqwo4iERERERERFWFHkYiIiIiIiIpo7W5Ao2UyFqYSBgzThqoIBBSBkC5g2kBPOAhFEe1uIpGjVMpEPGnAtCU0RSAW1hEK+W4TJSLyBOZcIv/g9twcvlqDmYyFFyZnccsXxzA+ncRgTxh7tm9Cb3cQ3UEVJ+JzWBeLsrNInpNKmTgen8PuA+did+/IENbHokx0REQNxpxL5B/cnpvHV7eeTsym851EABifTuK2Q0cwfiYJ0wZejCcQnzPa3EqicvGkkU9wwHzs7j4whniS8UpE1GjMuUT+we25eXzVUTRtmQ+SnPHpJCK6CsuWiOgqDNNqU+uI3LnFrmnLNrWIiMi/mHOJ/IPbc/P4qqOoKQKDPeGiaYM9YSQMC6oikDAs6JraptYRuXOLXY23SRMRNRxzLpF/cHtuHl91FPu7grjvxqF8sOSeURxcGYamAOfHIohF9Ta3kqhcLKxj70hx7O4dGUIszHglImo05lwi/+D23Dy+esIzEFCxoa8LX9n1JmRMG0pJ1dN13WEWsiFPCoU0rI9FcXDnFlbsIiJqMuZcIv/g9tw8vluDgYCK1cvDC7+RyGNCIQ0DTGpERC3BnEvkH9yem8NXt54SERERERHR4rGjSEREREREREVa3lEUQqwRQjwphDgqhPixEOJD2ekrhRDfFEIcz/63p9VtIyIiIiIiovY8o2gC+LCU8hkhRDeAMSHENwG8H8ATUsq7hBB3ALgDwO1taB8REXncujseq+tzJ+66qsEtISIi8qeWX1GUUr4spXwm+/8zAH4CYADAtQC+kH3bFwD8QavbRkRERERERG2ueiqEWAfg9QC+D2CVlPLl7Eu/ArBqMfNOpUzEk0a+TK4iAFsCocB833h5SIem8RFN8o7SmGVpZyKi5mHOpWoxVryDv0VtFru+2rZmhRBdAA4D+FMp5atCnBvfUEophRDS5XM7AewEgLVr1zrOO5UycTw+h90HxjA+ncRgTxh3b9uEL3z3F/iTt63HikgAc0YS5y0Ls7NILVMpdp1idu/IENbHokyA1HbV5F0iL3KLXeZcqlY7YoU51xm329o0Yn21pZckhAhgvpP4oJTyq9nJp4UQq7OvrwYw4fRZKeX9UsphKeVwX1+f4/zjSSO/UgBgfDqJ2w8fwbahNbj1wWdgmBKGKTExm270VyNyVSl2nWJ294ExxJNGO5pKVKSavEvkRW6xy5xL1WpHrDDnOuN2W5tGrK+Wd7/F/KXDzwD4iZTy7wpe+mcA7wNwV/a/j9a7DNOW+ZWSMz6dxIpwAOPTSSjZi5emZde7CKKGcotZ03a8sE7kK/UWpiGqF3MuVYux4h38LWrTiPXVjiuKWwHcCOBtQogfZf/9d8x3EP+bEOI4gLdn/66LpggM9oSLpg32hHE2mcFgTxi2nH9eUVN52yl5g1vMaopw+QQREdWLOZeqxVjxDv4WtWnE+mpH1dP/kFIKKeUmKeVl2X9fl1LGpZRXSCnXSynfLqU8U+8yYmEde0eG8isn94zi4bGTuPeGzdA1AV0T6O8KNux7ES2GU8zuHRlCLKy3uWVERP7DnEvVYqx4B3+L2jRiffnyyc9QSMP6WBQHd26BZUuoioCiAB+95mJWPSVPKoxZVvIiImou5lyqFmPFO/hb1KYR68u3azYU0jDAwKEOwpglImod5lyqFmPFO/hb1Gax68v3a9o0bZxJGAAkLBswLBuqIhBQBCwpIbNjK6Yydv7qY0RXkDBsCAFICVhSQhUCYV1B0rBhZt8XUASCAYF0RiJjS1i2REBVAEjYEtA1BdKWsCGhCgWKANKmne/VBzUFEgI94QCmkxkYpgVdUxGL6lCquH/YtiWm5tJIZaxs+1SsyF5Ojs8ZZfOzbek4vXSeC72nEbzQllZ912pxbCAiotZhzqVqMVbqk06bmEqcW2+9ER3B4MLrzTBMnE2ZMKz5Y/OAIrAyrJf9BgDKpgkBx2VmMhYmZtP5Y/3csb+ZPXZXBZAy7fx8nMZij4V1nEllkMn2JXRFYFkwkI+FheKkE+PI261bJNO0ceLMHAzLRjpj4wNf/mF+HJE92zchrKv430d+iasvGywbY+RrPxrHWzauwu2HjxRNv+eJF/D40QkM9oTxqesuRf/yEH45ncRth86975PvuhSf+Y+f46atF2B5JABFAAJA2pS49cFnzs3vhs0YOxHH8AW92FWw/P07hrFxVXfFTottSxw7PYObHxgt+k6rloUAADs++59F81vf14Xjk7NF7y9djtM8q2lLrapZTrPb0qrvWi2ODURE1DrMuVQtxkp90mkTL0yVr7cNvdGKnUXDMPHS2SQmZ9JFx9b7RoZwZjaJHZ8bw2BPGF+99U04/apRNv9lYQ037P9+2W9V+Bve8tvryo7992zfhE984xj6unV84IoNZWOxf/vYaVxz2WDR8fqe7ZvQ2x3EGsw/A1gpTjo1jnz9kN7EbBonzyRx+pV0vpMIzJeGve3QEUzPZbB9eK3jGCPbh9fmO4mF07cNrcn//WcPP4uMKfOBnJv+4a88i21Da3DboSM4/UoamqJCVdR8JzE/vwefwdsuWp0Putz0mx8YRXyu8hgn8Tkj38kp/E4vxhN4MZ4om9/EbLrs/aXLcZpnNW2pVTXLaXZbWvVdq24PxwYiImoZ5lyqFmOlPlMJ5/U2lai83ibnDJw8kyw7tt51YAyv7V+W/9swpeP8M6Z0/K0K3+t07H/boSPYdflrsW1ojeNY7NuH15Ydr9926AjGzyQRTxoLxkmnxpF3u7ANkLFsRHQVABzHEYnoKlRFOL7mNn1FOFD0tyKc550bszGiq/lxG53eJ6XzGCeGaVX8boZpuX6nUuPTSWQse8HluM1zobbUqprlNLstrfqu1eLYQERErcOcS9VirNSn3vVm2hIRXV3ws5bL/EtvCst9rvC9Cx3j19IviOhqvl2V2typceTrK4oBVUHCsJAwLMdxRBKGBcuWjq+5TT+bzBT9bUtUHLMxYVj5cRud3ieE8xgnulbe4Suka6rrd0oYVtn0gKosuBy3eS7UllpVs5xmt6VV37VaHBuIiKh1mHOpWoyV+tS73jRFuB63F35WdZl/ab8r97nC91Y6xs8dv5e+5vaZhGFBU8SC37dT48jXHcX+riDWrAxj1fIg7nnP64vGEdmzfRN6ogEcGn3JcYyRQ6Mv4e5tm8qmHx47mf/7U9ddioAmsGd78fs++a5LcXjs5Pwzg8uDMG0Llm3h3hs2F8/vhs341tGXsa9k+ft3DCMWrTzGSSyqY/+O4bLvdH4sgvNjkbL59XcFy95fuhyneVbTllpVs5xmt6VV37Xq9nBsICKilmHOpWoxVurTG3Feb72RyuutL6pjzcpw2bH1vpEh/Gzi1fzfuiYc5x/QhONvVfhep2P/Pds3Yd9TP8PhsZOOY7EfGn2p7Hh9z/ZNGFwZRiysLxgnnRpHQkpvX/KsZHh4WI6OjlZ8T2nV04xlQymteqorSBnuVU9tKaEUVD21bJmfR2HVU9uW0FQFAhJWUdVTQBWiiVVPbagCrHrahDZgvg5RwznFbidWwyJPa1nsLta6Ox5r6PwqOXHXVS1b1mLUu0465ftV0LTT66Wxy5xL1aoyVjom57aKJ6ueZkcyqKbqaeFY7LZ9ruqpme1L+KjqqWvseqJ1zaRpCvqzlUArihb/2RN1flvp+xqlrztY82cURaC/2/m7Oc1PUcSCy6nmPY3ghba06rtWi2MDERG1DnMuVYuxUp9gUMNAFR3DUrquoV8v/5zTb+A4zWGZgYCKgZ5I1W1w+73PqxAHC8VJJ8aRr289JSIiIiIiotqxo0hERERERERF2FEkIiIiIiKiIuwoEhERERERURF2FImIiIiIiKgIO4pERERERERUhB1FIiIiIiIiKsKOIhERERERERVhR5GIiIiIiIiKaK1eoBDiswCuBjAhpbwkO+1jAG4GMJl9219IKb9ez/wzGQsTs2mYtoSmCPR3BREIqI1oOtGSxe2KiPyGeY2oHLcLKtTyjiKAzwP4BwAPlEz/lJTybxcz40zGwvMTs9h9YAzj00kM9oSxd2QIF/Z3MciJ6sTtioj8hnmNqBy3CyrV8ltPpZTfBnCmGfOemE3ngxsAxqeT2H1gDBOz6WYsjmhJ4HZFRH7DvEZUjtsFlfLSM4p/IoQ4IoT4rBCix+1NQoidQohRIcTo5ORk0WumLfPBnTM+nYRpy+a0mKgGlWLXy7hdUafGLpFb7DKvkZe1K+dyu6BSXuko7gXwWgCXAXgZwCfd3iilvF9KOSylHO7r6yt6TVMEBnvCRdMGe8LQFNH4FhPVqFLsehm3K+rU2CVyi13mNfKyduVcbhdUyhMdRSnlaSmlJaW0AewH8MZ65tPfFcTekaF8kOfure7vCjawtURLC7crIvIb5jWictwuqFQ7itmUEUKsllK+nP3znQCeq2c+gYCK9bEoDu7ckq/WFAvrfACXOkIqZSKeNIpiNxRq/yYaCKi4sL+raLtiFTQi6mQ8XqBa+KkSaDptYipx7lijN6IjGJw/1mjF/t4wTEzOnVt+X1SHrrf/WIec1f3LCCEuBDAA4PtSytmC6VdKKb9R4XNfBnA5gF4hxDiAjwK4XAhxGQAJ4ASAW+ppUypl4nh8rqxa0/pY1BMH3ERuvB67gYCKgZ5Iu5tBRNQQXs+55B1+qgSaTpt4Yao87jf0Ros6i83a3xuGiWOT5cvf2BdlZ9Gj6rr1VAjxQQCPAvgAgOeEENcWvPz/VPqslPI9UsrVUsqAlHJQSvkZKeWNUsrfkFJuklL+fsHVxZrEk4ZjtaZ40qhndkQtw9glImod5lyqlp8qgU4lnON+KtGauJ+cc17+5By3O6+qt/t+M4AhKeWsEGIdgENCiHVSyk8DaNsTr6zWRJ2KsUtE1DrMuVQtP8VKu79Lu5dPtau3mI2Su91USnkC87eS/p4Q4u/Qxo4iqzVRp2LsEhG1DnMuVctPsdLu79Lu5VPt6u0ons4+UwgAyHYarwbQC+A3GtGwesTCumO1plhYb1eTiKrC2CUiah3mXKqWnyqB9kac47430pq474s6L78vyu3Oq+q99XQHALNwgpTSBLBDCHHfoltVp1BIc6xixgfTyesYu0RErcOcS9XyU+XvYNA57nOFbJpN1zVs7CtePqueeltdv4yUcrzCa9+pvzmLwypm1KkYu0RErcOcS7XwS+VvL8S9rmsYYMewY9R766knsYoZdSrGLhFR6zDn0lLEuKda+aqjyGpK1KkYu0RErcOcS0sR455q5auOIqspUadi7BIRtQ5zLi1FjHuqla9uEo6FdXzupjdg/EwSEV1FwrAwuDLMKmbkeYxdIqLWYc6lpShX7bf0GUWvxH06bWIqYeQL3fRGWldoh5z5au0LARimjTsffS6/Adx34xAET5SQxzF2iYhahzmXliIvV/tNp028MFVeaGdDb5SdxTby1a2nUwkDt3yx+CHdW744hqkEH9Ilb2PsEhG1DnMuLVWhkIaBngjOj0Ux0BPxRCcRmN8mnQrtcJtsL191FPmQLnUqxi4RUesw5xJ5C7dJb/JVR5EP6VKnYuwSEbUOcy6Rt3Cb9CZfdRR7I/MP6eYCLXd/c2/EGw/pErlh7BIRtQ5zLpG3cJv0Jm/cmNwgwaDzQ7p8CJa8jrFLRNQ6zLnkZ4ZhYnLuXPXQvqgOXfd2bAeDGjb0Fm+TrHrafr5a+4Zh4ni8vGLSxr6o5zcQWtoYu+QH6+54rN1NIKoKcy75lWGYODbZmbEdDGoYYMfQU3z1a0zOGbjniRdw59UXYUU4gLPJDO554gV87JqLcZ7HNw5a2txi96PXXIwBxi4RUUNNzjlXWDy4cwtzLpXppPH9mhnbqZSJeNLw3NAa1Dy++nUVAbzvzRfg9sNH8mdR7t62CVIApmlD03z1SCb5iKI4x67CkCUiajjLpcKixQqLVKLTxvdrVvXQVMr5Kvz6WJSdRR9ry2GoEOKzQogJIcRzBdNWCiG+KYQ4nv1vT63ztSXyB9rA/IZx++EjsG1gYjbdwG9A1Fi27R67RETUWKpLhUWVFRapRKeN79es6qHxpPN6iCe9uR6oMdp1CuDzAP4BwAMF0+4A8ISU8i4hxB3Zv2+vZaZuZ1EsW8KWEpMzacSiOhTuCMhjKsUuERE1lhDAfTcOYeLVNCK6ioRhoX9ZEDw8oFKdNr5fX3S+emjplb++6OKqhzZiPaRSJs6kMshYNlRFIKAILA8GeEXSw9ryy0gpvy2EWFcy+VoAl2f//wsAnkKNHUVdVTDYEy4K5MGeMIQABIB33vsd7N8xjI2rutlZJE9xi92AyntPiYgaLaIrODMH3Pnoc/mD6X0jQwjrzLlULHeFrnT/7NXx/XRdw8a+4uqhjah6utj1kEqZ+Gl8DrsKOrB7tm9Cb3cQaxBmZ9GjvPSrrJJSvpz9/18BWFXrDBQBfPb9wzg1ncqfIeyJBvA3jx3Fx665GOPTSdz8wCgeuXUr+rqDjW090SIoAvjH974eZ+Yy+dhdGQ3w7DYRURPMpW38fUkBsb/PFhBbEWl368hLcuP7lV6h8/L4frquNbwoUyzsvB5i4erWQzxp5DuJwPzVyNsOHcHHr70EkYCKgZKOIgvneIMn17iUUgohHK9lCyF2AtgJAGvXri15DciYsugM4SffdSkmZwxkspfGx6eTMEyryd+AqFyl2LWkRCpjl8WuLb15awstLZVil8jL3GJXuBS/48k5KtWO8f28mHNDIeexR6vtvLnduhrR1bLbV1k4xzu8dI/FaSHEagDI/nfC6U1SyvullMNSyuG+vr6i1zKWxC0lZys+/JVn8cEr1ucvjQ/2hKFrajO/B5GjSrErJfDhrzxbFrsefQSClphKsUvkZW6xK92K3zHnkoNgUMNATwTnx6IY6Ik0vdqpV3NuKFS8HmrptLkV2UkYVtntqyyc4x1e6ij+M4D3Zf//fQAerXUGbmcr1vVGcfLMHAZ7wti/YxixRT7QS9RoLNVORNQ6zLlErRUL69g3MpTvLOaeURxcGS67fbXTCgj5WVuu3wohvoz5wjW9QohxAB8FcBeAh4UQfwTgRQDX1Tpftwdtg6rAmpVRPHLrVlY9JU9SXWKXpdqJiBqPOZeotUIhDb8ei+LhW94E07KhVKh62mkFhPysLVcUpZTvkVKullIGpJSDUsrPSCnjUsorpJTrpZRvl1KeqXW+uQdtC89W7B0ZwsqwjoGeCPq6g+wkkie5xW61D4kTEVH1mHOJWi8U0nDeijDWxqIY7Ilg1XLnaqfcPr3DV0+ELvZBW2F8EtwAACAASURBVKJ2YewSEbUOcy5RczSiWim3T+/w1RpnlSTqVIxdImqEdXc8VtfnTtx1VYNb4m3MuUSN18jtKhTSyobMoNbz1S+Qq5LU1xXEP7739VgZDcKyJeJJAytgIqzz1lPypnjSwNgvpvClm7fAlhKKEPjW0ZexMhJgoiRqIHakCGDOJWoGt2ql//KBNyM+zTERO5GvfiXTlujrCuL/3XYJDFPiPfufLjqjsS4GRNlZJA8K6QqGLujFe0tiNqR7qTAxEZE/MOcSNZ5TtdLrhwYxPp3m1fsO5auMqCkiO2aiilsffKbsjMarSRvxOY7BQt6TMmzHs3Apw65tPikTp6YTeDE+h1PTCaRSZjOaS0TU0RqVc4noHKexEv9g8yDHROxgvuooxsI61vVGoAi4jr9imFabWkfkrhFjBuWeDbj+/qfxO3uewvX3P43j8Tl2FomISnCcNqLGcxor0Zbc1jqZr675xpMGZlImeiK66/gruqa2sYVEzhoxZpDbswEHd27hMzdERAU4ThtRfSpVNQ2FNPR3B/Hxay9BRFdxNplxHbOU21pn8NUVRUUBDNPGge/9AvfesLls/JVlYQWxKMdgIe9pxJhBPENORFSd7rDimHO7w746LCJqqGruXEpmLNz0+R/g+vufxi1fHMN3j09yTMQO5qvLDLYN/OnBH2F8OonphInPvf8NUBWBgKogoissZEOeFU8a+NqPxvMxa9kSh0Zfwo43X1D11UCeISciqs5M0nbNuctC7W4dUXuZpo2J2TQylo2AqqC/KwhNU6q6c6n0WOQjX30O97x7E8dE7FC++pUsW+L6oUFcu3kwX+760WfG8cZfi2H18hBiXTxgJm8ybYmuYADBgApbSmiqgq5goKargbmrkqWVxdzO2qXTJqYS524f6Y3oCAZ9lRKIiBw1IufS0uHWcep0TreRAsDpuTQmZ9KIzxk4PHYSH7xiAy5c1V3VnUtOxyLr+paxc9ihfPWLdYdUXP66VWXlrsMBBZra+Rs0+Zdb7HaHqn+mNhTSsD4WreqsXTpt4oWp8kFxN/RG2VkkIt9rRM6lpcE0bTx/ega7CvaX+0aGcOGq7o7uLOZuIy09Dli1TMcN//T9/LS7t23C3z/xAj72+5dUdedSLcci5H2dG+EOEi7lrsMBFf1dwTa3jshd0iV2kzWWag+FNAz0RHB+LIqBnohrYp5KON8+MpVguWoi8r9G5Vzyv4nZdL6TCMzHyq4DY5iYTbe5ZYvjdhupYcqiabcfPoJtQ2tgWnbV9RSqPRYh7/PVL1fpkngnn/Uh/2t1IZpWL4+3uRKRl7D4F1UrY9nOsWJ19kkFt23AKtkGxqeTiEV1aKrCq4VLkK9+WbdL4gEW8yCPa1QhmkzGwsRsOp/A+7uCCATKb6VqdOGbSsvlba5E5DUs/kXVCmqKY6zoHr0AUWl/XPqa0/dSS7aBwZ4w+rqD+TvzQiEtX7gmlTLxqmFiKmnAsiUCisBKdhx9xZtRXqfusFI20Oee7ZuQyFgcdJw8rRHDY2QyFp6fmC0qW/38xCwyGavsvb0R5+X1RmovV+223HR6fpvjba5E5DUrXIbHWMHhMahEQBVlQ67de8NmBFTvnVSodBxQ+polpeM2oGuiaNq+kSGsipYX70mlTIy/msTPJmfx7uw8r7v/afy0ZLgM6my+6vJPz1lYtax4oM9PfOMYJmfTHHScPC2eNHDPEy/gzqsvwopwAGeTGdzzxAv46DUXVx23E7Np97LVPZGi9waDGjb0zt8+EtAEMqaEaUtMJQzEJGo6G+i23Id2bsFrVIW3eBGR55xN2q45N8rhMahAMmPjH751vChW/uFbx/FX11zc7qaVqXQcENEVrAgHcOCPfxOKEJDSxk9OncVDO7fAsiVUReC7xyfR29VXdGup06MihmHi9FwaJ88kceejz5U9v8ljbv/w1a/YHVLxStLETZ//QdlrPCglLzNticePTuDxoxNF0//yqotqmkctHbJgUENMAj+NzxVVc9s7MoT1sWjVnUW35RrZcuK8xYuIvMZyybn/8+rqcy4tDW6xUsv+uVXc9sfLwgpOxNNFj4DsGxnC1vV9SBgW9n/753h4bByDPWFsXd9XdnK51OScgcmZNCK6yhPBPuereyxSGYkTU4n8JfMcHpSS1+U6U4Vqjdta55E7I1hazW33gTHEk9XfFuq2XMuWMC27obe5EhE1guqSt1TBYwUqFnCJFS/Wv3DbH7+aLK/yu+vAGJ775au46fM/wMibzsctv72u6n2zaUvE5wwkDIvH3D7nqyuKGcvGc+Nn8eWbtyBj2bBsiUOjL+Gaywb53AF5WldQwedvegNOnkkioqtIGBbWrAyjK1h93PZ3BcsGud07MuQ6NEzujOBizwY6LffeGzbj0OhLeN/WXyu6zXWxVU+rLdZDRFSJEMA/vW8ImqJCEYAtAdO2wH4ilYpFdOwbGSobRzHmwZOdsbCOgzu3IGNLKELgW0dfxtAFva5XGleEAxifTuLWB5/BwZ1bqt43a4rA4bGT+NDbN2DP9k247dAR9HUF8cEr1mNdbwQC888wsqhN5/PcLyiEOAFgBoAFwJRSDlf72Yiu4nd/4zX46cRs/mB7+xvWIhYN4JWU5HMH5FlBRUMqk87f65/bEQWV6jfRQEDFhf1dRR2ySh2p3BlBp9tCQ5qCU9OJqspfBwIqNvRG8dDOLTDM4hM0uU5qMKhhYJEVTnMP4pd2hC/s72JnkYhqElAVqELg5JlE/nhhsCeEgMqTylQsGNSwvkEnO5spk7FwPF5eYXx9LIp40nlffzaZAQD0dQUhAfxqNg0tYSw45EVfVMcHrtiAT/9/L+BDb9+Ar+5+EyZmjEU9xkLe5NWM+FYp5WW1dBIBwLYl4rMG7nz0OVx//9O489HnMDWTRsaUrldViLwgnjQcB/St5RZQYL7TVjjIbaUOVO6M4N3bNhXdFvr5m96AyVmjqGra8YIqZqmUiVPTCbwYn8Op6QRSKRPBoIbXdIcQCqgIagret/XXcOGq7oaOX+r2kL4XBj3OZKyideJUaZaIvMO2JaZKjxdmDdh8toocBIPFA8h7rZMIuO8j40nDsbL63ds2Yd9TP8Pr16zAR67cmK9cWrrPd6LrGjb2RfHRay5GV1BDxpKLfoyFvMl7kb4IGVvitkNHigL1tkNH8NDOLQ09YCVqtHZUBs2dEcxV/otFdfR1B6GrCt7/ue85Vk2LAa5nLEMhDeetCFde6CJ4tXoqr3QSdZ5KxwtEnchtH/nyKymcSWQwPZvEl27eAkgJCeBvHjuKH548i8+9/w1l28LuKiqX6rqGAX3+9Rfjc57cP9PiebH3JAE8LoQYE0LsLH1RCLFTCDEqhBidnJwses1y2Uh4hpC8oFLsNqKYTa0Kzwhe+JpurF4ewuruIAzLdk348aTzmIitOGvYjnVUDS9f6WyUSrFL5GVuscvjBfKyenKu2z4yPje/3169Ioq3fOJJvGXPU3jyJ7/CX11zMf7ttsvxa33RRXfyvLp/psXzYkfxt6SUmwH8HoD/IYR4S+GLUsr7pZTDUsrhvr6+og8GVJdA9eCgqLT0VIpdp9tC9o4MIRZu7sPyul58O42uaxUTfjuv6uWK5pSuo3bfVu7VK52NVCl2ibzMLXZ5vEBeVk/OddpH5m4vHZ9OQi3otH3sa89jOpFBKHu33WI7ee06hqHm89ytp1LKU9n/TgghHgHwRgDfruazqhD49Lsvw4ce+lH+FrBPv/sylrsmzzuTyjgO/vyx378E57X4QfCwrjhWTw3rCpKG3bYxEWst1tMqC40TaWeLBhmmBV1TEYvqUHiWlaiteLxAflO4j3z5lRTicwb+9l+P4Ycnz+aHrMoZ7AljWUjD0Zdn8OX/fBF3b9uE2w8fKa7qWkMnLxTSsD5WXPBnoYI41Bk89QsKIaIAFCnlTPb/3wHg/6r28zYkokEVn7/pjfly16oCCC9eNyUqkLFsTM4U3745OWPAtOymLTOVMhFPGmVJvSugIdZl48s3b4Et50tsqyrQFdAQUeHYiWzVWcNcsZ52cOvwVRqWxLYljp2ewc0PjOZf279jGBtXdbOzSNRGNiSWhbSi4wUpbdjwz50AtPQEAir6ojrOJDL4+NeOFu2TDo2+BAD5juDfPHYUf/Rbv4bHj05gcsYoOlEd6wrU1MlzO56oh2namJhNI2PZCKgK+ruCi6oz0si2LUVeW1OrADwi5s/oaQC+JKX8RrUfViAwl7bwoYfOHbB96rpLYdk6lgU4ngt5V0hT8JErN+YfKB/sCWPP9k0INqkIUyplVixK04v5cRZtCSgC6A3r0LMPrXvlrGGjdyaVVOrwVbrSOTmTzn8GmL8l9eYHRvHIrVvR1x3k1UaiNtFVBamMjd0Pntum996wGSujPLNMnaVwPxLQFMymTIz9YgpfunkLpJzfJy0PK9jx5gvw3i3roCoCigAePzqBbUNrMNgTxg9PnsUtXxwDMN+RPOhQ1Mltn7vQ8UQtTNPG86dnysasrLeKeiPbtlR5KiNKKX8upbw0++9iKeXf1PJ5SyJ/Gwkwf1D2Zw8/i5NnkizRS55muVTgs5r0nNtCRWmcnl3MCYWKX2tXJ/H50zO47r7v4Xf2PIXr7vsenj89A9NszhXY+Jzh2OGLz82vLyEEsie4iv7fMC3H5xcN08p3Pt9573ew9e4n8c57v4Njp2dYTIOoBeY7ic8U58AHn0Eq07y7OIgaLZOxcDI7NNNzv3wV//OR/8LpV1N49Nlf4S2feDI/3MWZhIWtd8///Vt3P4m5tDXfCXvqZ2VDZO0dGUJftPguoUr73EYWuZuYTTsOFVZvcbh2FuDzC191pzMu1RojuuqrwhLkPxmXgiiZJsWtlwqw1HNbiNvO5OFb3tSUIToqdfhM08ax0zO4peCM5X0jQ9i4qhu6pjo+v6hrqmvnM3e1kYiax0s5kKgepmnj2MRs8SD3N2xGKmPjr655Hd557/cAzMe1Ks49S/+JP7wE0aCGL/7RG3FiKoFHf3gKH7/2EqzrjSKoKeiNBIpODgPn9rl9XcH8LaqTM2n0Lws2dFtyO46v9zEcbueL56kriovlVq0xYVgs0UueFnCJ3UCT4tYrpaxzt4VcX8NAv0DjdyYLyXX4CuU6fJNz6XwnMdeOWw6MYXIujVhUx/4dw0Vna/fvGEYsqlfsfBJRc3klB1JnsG2JyZk0Tk0nMDmT9sSdH04nTHc/+Axm0yYCqorrhgYBzMd1WFexf8cw7nn3JrxuYAWuu+97+D8PPgsA2P3W12Ljqi6s7gqiL6pjcs7Ai/E5nJpOIJOZ3x9lLBt9XUH8+e9uxMe/dhTX3/807nz0OUy8mnY9fqlnWwqoiks14vq6K9zOF89XHcWgpmDvDZuLDsr2bN+ENSvDLNFLnqapCvZs31QWu/Umx4V4pZR1vbeFNHpnspDKHT7nTmvGtKEoAhtXdeORW7fiO7e/FY/cujVfyEbXVLzjon7cd+MQDu7cgvtuHMI7LuqHrrW3iivRUpCr7lyaA8O6rw6LqAG8+phApbvodh0Yw67LX5vfV60I69i4qhubz49hd/bK4J//7kbc+ehzeOvf/huuu/9p/DQ+hxenE0Unbp+fmEUmYyGgKvjgFevzlVFzy9p1YAya6rwt1XM80d8VxL6See1bxDBYXjnW6WS+uvU0Zdq451vHcdcf/gZeszwEVQhMzRroCmp8aJU8LZmx8IlvHCuqOvaJbxzD/3r3ZU1ZXjxpOA7H8dFrLsZAC7eVem8Lye1MSh94z+1MGl3oRlEEfr03WlawRlEEVJfhMXJFaRRFON5K2hMO4INXbCj7Dj3hQN3tpOZZd8djdX3uxF1XNbgl1AgJw8bXfjSOz73/DVAVAcuWODT6Em588wVYGW1368hLvPqYQO6Eaem+57wVYXzu/W9ARFfxz3+yFSvC80XSTHO+pu8n33UpVkZ13PT5H5R1+j5+7SVlJ24P7tyCVd0hpHud74JJZqyGFbnTNAUXrurGw7e8CaZlQ1vk/pvDdiyer9aUbUs8fnQCjx+dKJr+7dsub0+DiKqkKgKTs+l81TFgPuGrTbo9wnTZVv7yqouasjw3C41B6Pq5CjuTRldNA5yfBcnNU89eDS6tWKsvcHVzOplxfM4yd/DRyqquREuNbUvc9/+zd//xcdz1ve/f39kf0uqHY1mW3WDZcUgdBzfXQCRCftzSQEqPITS559hAaESalNpxUuBcDg3JebSBXGgfl+BSbmmJHaeHQOJACDY9pCQF+gBSKGlaWwlxwWDyy4mVQCTLcmxJq/013/uHtOud3dnVrrS72tW+no+HHvHOzs58Z/Ldz8xnZ+bz/dER3fWjI57p11y0dkHag/pVr48J+P1gumPLRn34q09qZDw2/eNpZ4uOjk0qEgpo+NTpW1X3br+44NXI3GlJ1yoYdNRSIDENOma6yF2Fkq9g0KlorYFKtq0ZLao9F3CMbvjttdrSv8bzC2G1TraBSgk5Rl/+ozfJWpMZ08sYW/VnFMtN0CotfVvIXMZlLHQwqUahm2LLXNHRopOdLfrUVeerLRzQZDylns4WLWsrvg2zFcipdLIL4DTOF1CqYkXJFlL6B9Ovb79Y8aSr50Ym9JlvH9aTR09IUuYK4fVf2q97rnuTbvvmTzPbMDoR992mybg3+c0+L1jeHtZXtr5Z8aTNnKeEgyavQioWl0WVKLaGHL3rDb2Zy+npk87WECdWqG+tIaPhcTcvYVreXtmTlvR4S+Gg45ug1Trgz+e2kEJjEFaj0E2xZQaDjtYua1dbOFjWrTLFTj5qXdUVaDacL6BU6WfUc8fR7V7gBMl1rcaiCbmuVcAx+vz3ns4kiZL3CmFbOOA51qSHxUg/c9jbFdFn3/16dXeEM8el9Hci/UiH60qvRpN55w0r2ma//ZYxgxvXokoUpxKub2EMv4FDgXoyHivcd89oq8w6cgeNv+G31+qBbRcpNZOg9bSH80pilyIeT2pk4vTwFuUuZy63heRuS/rAvX5lZ8HnNkopdJNIpDQ8HvM8hxgKBWZd5lxulSl28nF0bLKmVV2BZsP5AkqVXZSsXhIdv2PgF/7gjTo1lVQo4OhENKF9g0d1IpqQJJ2IJjzHsCePntCXH3te91z3Jh2fiOtENKH/9a/P6VNXnZ85L1gaCWg85urlk1OZq4qFvjPFjuHFjtcki/VvUSWKjJeCRlWLvpv7QP5dPzqih3/6yrweyI/Hkzo8MpH3C+P6nvY5JZ2lKlZcYLZCN4UkEin9Yng8b1vOW9Ex6zJzE8zWkKPxWKros4WOY7Sup0MP3nCx5zlExzHzSnYBzI7zBZSjUFGyhZJ7DOzpaNFkPKVbv/Gf6ulo0V/8X+fr47//W0q6Vt/76O/okadeznuW/kOXn6sd3/mFvntoOHO8++K/Pqe7fnREf3v1Rq3tWeI5Ht7/x2+e9Tvjd+WwXosBoTSLKlEMFzi5mq2oBLDQavHMYDUeyB+Z8B/e4mvbLtKqKiaKxbYlGGyZU9W04fFY4W3paiu4TL8E885rLtCef3tBjz03WvDZQte1enpk3PdX1rkmuwBKw/kCGlnuMXD7Zefo5r0H1dPRov938/mKJ62u3v346R89r7lA3Z1hff2GixVPuUqkrCZjcX3i939Lf3bFBgUdo3sfez5T3OmNZ3VnPi/NDPmUskXPUwpdOVzSGqzLYkAozaKKiI6R71h0XNlGvets9R+HqLO1cl/RYoPGz1WxX+WrOcZUqdtSTgtmu8KQvr10TXe7XrM0kkn8/BLMm+5/Qlvf8trMs4XD47G89RX6lXV0Iu6p6vrDmy/TgzdcTCEboII4X0Cjcl2rlGs9x8ClkdD08eaycxR0Arrp/ie8P3re/4Sm4q5ca3XN3/+7fvev/0WfeOjn+unLJzVyKiYr6T+OnH6+MeVzPNz9L88WHZOw0DHNGP9B7xe6GBBKs6iuKE4l3ZqORQdUyqkpV4lEwlPU5ZVXJ3VqKqQlFapd0hUJ6St//GYNn4ppdCKufYNH9ZG3r5/XA/mFroQGHKPDr5yq2jMIxZ7vm2vF0Lle1S2UYKarJxZ6trDUK7zcCAdUHucLaFSjE3H9xcOHPMVoJuMp9XZFtDQSkmPke2xxjMkcr964eqn+9L+s9xSz2bFlY6Zqqt/4wI89N6qPbVpfsPhcoWNawKguiwGhNIsqUQwWGIuu1iX/gXK1tTgKBoN6b9atIndec4HaWipzBcnvNse73t+ndT0d80rketr9h7d47OkRff4Hz1ZtTMBixQV+fXJqThVDV3S0+G7LbLd7FkowUzNXIgs9W1is6ulsyS4V5ID54XwB5ainmBtPpvTdQ8MaORXP/NDR0RrUroE+jZyKybUq8Iy7Ucgx+v5Hf0fBgKO/+NbPPMfJm/cezAyn8eQLo77HwyUtQYU7/VOHQsc0x3HqrhgQSreoEsX2Fv+S/+0VOtkGquWM1haNt6X0pesvzIxP1BI0OqO1Ms+k+d0ScsN9g/N+mDwcDmp9z+nhLQKO0WNPj+hj3/ipJFV1TMBCxQXmOjxGKBTQeSs6PL+WpqueFv1cwOjOay7I3OqTTvLv/uFzRZ8tXNoa9I1XS1uDRYfH+I0lrVSQQ91Ye+vDc/rckU9fUeGWlCcS9j9fiIQ5X4BXvVXtTCdkTx49kfmh40cfu0zHJ+LqaAkqFFDeMWnnNRfovsee10Xn9Oj6L+1Xb1dEd2zeqJFT8cyQGkNjUZ3T065/ufmyzNXC7OPhbBXNi93pU2/FgFC6RZUojsdcDT5/TF/ZepGstTLG6PuHfqWutjO1tEJDDADV4DhGq5a2Ve0Xy2oUskkLh4MKx1J6750/9r06VusxAedTMTQUCmhVV3nBIpGyevipl3TPdW9SwDGykqbiKX3wbb+p//vt5xa8ejoyEdfffu+Xnlvf/vZ7v9TtV55fNNmlghwwf6emUnr05694zhe++cSQrnzjKi1rX+jWoZ7UW8z1S8iMMfqTrzyZua309is36KtbL5JrrZKu1V2PPqsHB4f0ttf9RmYbbtl3ULe9a0Mm2eztiigSDnq2qZyhq+pxGBHM36JKFFOu1Tef+rXO7GrPnHh986lfZ74YQD2r5i9uxW5zrIR6GhOw1hVDV3S0+A7cfeaSVoVCAbmu1cipWN6BM5Fy9d1Dw/ruoWHP8v78CrdoslvNpB9oFkHH6D9fflXnnrkkc77wny+/qv/W17vQTUOdqbeY65eQTcaTnjb++mRMUwlXr1ka0Z8++BM9efSEersimXEVpeltSD8nWKnnBrlyuPgsqkQxEgroY5vWe8aJ2bFlo1pnuXUMWOyKJXKVUOyXxFqPCZhdMbSc4THmKhQKeG6/Td+ik04SC92yVGy/FEt2x3IGTk5/jgpyQOnawo4+dPm5ebeetnHrKXJU+4fWuchNyH71qqveroh6OlryitTcsXmjvvzY87r+0rP1mW8fznymtyuiM89o1Y9veStX/1DQooqI1iqTJEqnH861lA1Ek8tO5H58y1v1DzddWvHnK9IHrlVdberpbMksO530ZJfUrvaYgIWGsqgG17V6dnRS7939uH5nx6N67+7H9ezoZKb4QaEhMIrtl2LDY6ST/uzPUUEOKE88Kd9xU+PJBW4Y6k4jxNye9hbdNdCnD1++LpMkSqdvMb31Ha9TJBzQyMxQTenjzcrO1rxjNpCtrq4oGmM2SfobSQFJf2+t/XQ5n4+l/G8PiFXpFjegkSzULSG1vsJXa8WeXyl2y1Iw2FJ0v6ST3Vw8BwLMH+cLKFUjxNxgcLqyaEeBwe1HTsX06X/6hW571wZ1t4d15hmtWtnZumiOw6ieukkUjTEBSV+Q9HZJQ5L2G2MestYeKnUZAVNgTLf6+S4DTalQ0rMYFEsGZ7tlaa77hedAgPnhfAHlaISYGww6agsHffv1iWjCUyX1x7e8lSQRJamnXnKhpGestc9Za+OSHpB0VTkLiIQD2rFlo+f2gB1bNioS5tkdANWRTgazpZPBRrhlCWhGnC9gMfI75uzYslG7Hn02M89CP1+JxlI3VxQlrZJ0NOv1kKQ3l7OApZGwVi5p1aeuOl9t4YAm4ymtXNKqpRFOygBUx2xjR9X7LUtAM+J8AYtR7jEnFHQ0PpX0PJvIj5UoRz0liiUxxmyTtE2S1qxZ43nPcYzWdrerszXESRnqTrG+i8Y1WzLYCLcszYa+i0ZVqO9yvoB6Np+Ym3vMWd5u+bESc1ZPieJLklZnve6dmeZhrd0tabck9ff359UzXQwnZVicZuu7aFyLPe7Qd+du7a0PL3QTmlqxvrvYv7doXJWMufRzzEc9PaO4X9I6Y8zZxpiwpKslPbTAbQIAAACAplM3VxSttUljzAclfUfTw2N80Vr7swVuFgAAAAA0nbpJFCXJWvuIpEcWuh0AAAAA0MyMtY37uIkxZkTSCwXeXi7pWA2bw7oXfv3VWPcxa+2mCi+znvturnppS720Q2qcttSq79bT/pgvtmXhVaXfSkXjbj3tK9rir17aUg8xdzb1sq+qiW2srIJ9t6ETxWKMMQestf2su3nWv9DbXin1tB310pZ6aYdEW+qxDZXCtjSnetpXtMVfvbSlXtpRTCO0cb7Yxtqpp2I2AAAAAIA6QKIIAAAAAPBYzInibtbddOtf6G2vlHrajnppS720Q6ItueqhDZXCtjSnetpXtMVfvbSlXtpRTCO0cb7YxhpZtM8oAgAAAADmZjFfUQQAAAAAzAGJIgAAAADAg0QRAAAAAOBBoggAAAAA8GjoRHHTpk1WEn/8VfOvKui7/NXgryrou/xV+a9q6Lv8VfmvKui3/NXgr6CGThSPHTu20E0A5oS+i0ZF30Wjou+iEdFvsZAaOlEEAAAAAFQeiSIAAAAAwCNYi5UYY74o6V2Shq215/u8byT9jaR3SpqUdJ219om5ZM6R9QAAIABJREFUrGtqKqnRaFxJ1yroGDmOZF2pJeQo5VolU1ZJ1yrgGBkjyUot4el8eSKWUsAYRcIBLY2E5ThmrpsMlC2373ZHwmptrd5XNJFIaXg8llnfio4WhUKBhl9XI3Fdq9GJuOLJlMLBgLrbGz/ulLNN89n+WCyp0cm4EjPxPBJylEhZxZKuQgFHKzpaFAyW/1toLJbUscnT38PlbWG1tJT3PaxGf58tPtQ6fgCoL+XGU9e1enUqpsmY64lVxhgNj8eUSOXHUr/4KKmsmDnf+Djb55NJt2D757O/5vs5SYrHkxqZOL2vetrDCoerG6fnu85aHUW+JOnvJN1b4P13SFo38/dmSTtn/luWqamknh6d0I17BjU0FlVvV0R3bN6oLz/2vD58+blqDTm67p79ee9t/e3XKhx0dPtDhzQyHtOOLRu1ckmr1na3N/xJGxqDX9/dOdCndd3tVTnZSyRS+sXweN76zlvRUfEErpbraiSua3X4lVPaeu+BzH65+9p+rV/Z2bBxp5xtms/2x2JJPX1sQttn+tTvbVihD75tnW66/4nMsnYN9Om8lZ1lJYuxWFK/PJb/PTx3eXvJyWI1+vts8aHW8QNAfSk3nrqu1UsnJjU2mfDEzXuuf5PiSVc33DeYF0tTKTcvPu4a6Ms7ty4WM+cbH2f7fDLp6hevnMocGwodC+Z6/JnPcSseT+rwSH6cXt/TXrVksRLrrMmtp9baH0o6XmSWqyTda6c9LmmpMebMctczGo1ndoYkDY1Fdcu+g9rct1rb9wzq6PGo73sfefApHZ9IaPtl52hoLKqb9x7UC6OTGp2Il7+xwBz49d0b9wxqNFqdPjg8HvNd3/B4rKHX1UhGJ+KZg400vV+23nugoeNOOds0n+0/NhnPnAhI0ua+1ZmTnfSyts+hjx2b9P8eHpss/f9JNfr7bPGh1vEDQH0pN56OTsQVS9q8uDl0PJpJEtPT0rHULz76nVsXi5nzjY+zfX54POY5NhQ6Fsz1+DOf49bIhH+cHqniMb8S66yXZxRXSTqa9XpoZloeY8w2Y8wBY8yBkZERz3tJ12Z2RmZBY1EtjYQ0NBZVWzhQ9L2lkVBmels4oHgyNe8NA9Lm0neTbtGqxXNWy/XVetsaRTyZ8t0v9Rh3ivXdbOVs03y2P7dPpeN47rKSKXfWZRVbbmY5ZfTVavT32ZbJd6ywUvsuUE/K7bflxtN4MiXHKO8zbeFAwVhaKM74nVsXij3zjVWzfT6Rcks6Fsz1+FPJ41Zu26uhEutsuHtSrLW7Je2WpP7+fs+WBh2j3q6IZ6f0dkV0IppQb1dEk3Hv/8jc9+IzHSn9Ohxs3tviUHlz6bvBKt2CWMv11XrbGkU4GPDdL/UYd4r13WzlbNN8tj+3T6XjeF4fC5T3W2gl+mo1+vtsy+Q7VlgpfXftrQ/PadlHPn3F3BsGFFFqzE0rN56GgwFFE27eZybjqYKx1Frr+57fuXWh2DPfWDXb50MBp6RjwVyPP5U8buW2vRoqsc56uaL4kqTVWa97Z6aVpTsS1s6BPvV2RaYXMvMc4r7Bo9o10KfVyyK+733uPa/XsvaQdj36rHq7ItqxZaPO6m5Td3u4ApsGzM6v7+4c6FN3pDp9cEVHi+/6VnS0NPS6Gkl3e1h3X9vv2S93X9vf0HGnnG2az/YvbwtrV1af2jd4VHdec4FnWbvm0MeWt/l/D9MFG0pRjf4+W3yodfwAUF/Kjafd7WG1BE1e3OxdFtFd7+/zjaV+8dHv3LpYzJxvfJzt8ys6WjzHhkLHgrkef+Zz3Opp94/TPVU85ldincba2tyaYoxZK+lbBaqeXiHpg5quevpmSZ+31l442zL7+/vtgQMHPNPSld9SM5XwfKueWquAMXKMZD1VT10FjKh6imxV6QTF+i5VT5tHlaue1qzvZlvoqqfxpKsgVU8buepp1Q68hfouVxRRIQsSc9MqXfU0mcqPpY1U9dSv/fPZX/P9nFTXVU8LbkCthsf4qqTLJC03xgxJ+oSkkCRZa3dJekTTSeIzmh4e4/q5rqu1NahVczw4drfPda3A/M2n785FKBTQqq62RbeuRuI4Rj2di+vKajnbNJ/tb2kJ6jVlJnClLnfVPJdbjf4+W3yodfwAUF/KjaeOY9TV1iq/UPWapRHfzxSKj+XEzPnGx9k+Hww6Bdufba7Hn/kct8LhoFZVOTGs9Dpr0lpr7ftmed9K+pNatAUAAAAAUFy9PKMIAAAAAKgTJIoAAAAAAA8SRQAAAACAB4kiAAAAAMCDRBEAAAAA4EGiCAAAAADwIFEEAAAAAHiQKAIAAAAAPEgUAQAAAAAeJIoAAAAAAA8SRQAAAACAB4kiAAAAAMCDRBEAAAAA4EGiCAAAAADwIFEEAAAAAHiQKAIAAAAAPEgUAQAAAAAeJIoAAAAAAA8SRQAAAACAB4kiAAAAAMCDRBEAAAAA4FGzRNEYs8kYc9gY84wx5laf99cYY35gjHnSGHPQGPPOWrUNAAAAAHBaTRJFY0xA0hckvUPSBknvM8ZsyJntzyU9aK19o6SrJd1Zi7YBAAAAALxqdUXxQknPWGufs9bGJT0g6aqceaykJTP/PkPSyzVqGwAAAAAgS60SxVWSjma9HpqZlu12SQPGmCFJj0j6kN+CjDHbjDEHjDEHRkZGqtFWoCrou2hU9F00KvouGhH9FvWinorZvE/Sl6y1vZLeKek+Y0xe+6y1u621/dba/p6enpo3Epgr+i4aFX0XjYq+i0ZEv0W9qFWi+JKk1Vmve2emZfuApAclyVr7b5JaJS2vSesAAAAAABm1ShT3S1pnjDnbGBPWdLGah3LmeVHS5ZJkjHmdphNFrrcDAAAAQI3VJFG01iYlfVDSdyT9XNPVTX9mjPmkMebKmdk+KmmrMeYpSV+VdJ211taifQAAAACA04K1WpG19hFNF6nJnvbxrH8fknRprdoDAAAAAPBXT8VsAAAAAAB1gEQRAAAAAOBBoggAAAAA8CBRBAAAAAB4kCgCAAAAADxIFAEAAAAAHiSKAAAAAAAPEkUAAAAAgAeJIgAAAADAg0QRAAAAAOBBoggAAAAA8CBRBAAAAAB4kCgCAAAAADxIFAEAAAAAHiSKAAAAAAAPEkUAAAAAgAeJIgAAAADAg0QRAAAAAOBBoggAAAAA8CBRBAAAAAB4kCgCAAAAADxqligaYzYZYw4bY54xxtxaYJ73GGMOGWN+Zoz5Sq3aBgAAAAA4LViLlRhjApK+IOntkoYk7TfGPGStPZQ1zzpJ/1PSpdbaMWPMilq0DQAAAADgVasrihdKesZa+5y1Ni7pAUlX5cyzVdIXrLVjkmStHa5R2wAAAAAAWWqVKK6SdDTr9dDMtGznSjrXGPNjY8zjxphNfgsyxmwzxhwwxhwYGRmpUnOByqPvolHRd9Go6LtoRPRb1It6KmYTlLRO0mWS3ifpbmPM0tyZrLW7rbX91tr+np6eGjcRmDv6LhoVfReNir6LRkS/Rb2oVaL4kqTVWa97Z6ZlG5L0kLU2Ya19XtIvNZ04AgAAAABqqFaJ4n5J64wxZxtjwpKulvRQzjz/W9NXE2WMWa7pW1Gfq1H7AAAAAAAzapIoWmuTkj4o6TuSfi7pQWvtz4wxnzTGXDkz23ckjRpjDkn6gaSbrbWjtWgfAAAAAOC0mgyPIUnW2kckPZIz7eNZ/7aS/sfMHwAAAABggdRTMRsAAAAAQB0gUQQAAAAAeJAoAgAAAAA8SBQBAAAAAB4kigAAAAAADxJFAAAAAIAHiSIAAAAAwINEEQAAAADgESxnZmPMhZKstXa/MWaDpE2SfmGtfaQqrQMAAAAA1FzJiaIx5hOS3iEpaIz5Z0lvlvQDSbcaY95orf3LKrURAAAAAFBD5VxR3CLpDZJaJP1aUq+19qQx5q8k/bskEkUAAAAAWATKeUYxaa1NWWsnJT1rrT0pSdbaqCS3Kq0DAAAAANRcOYli3BjTNvPvvvREY8wZIlEEAAAAgEWjnFtP32KtjUmStTY7MQxJ+sOKtgoAAAAAsGBKThTTSaLP9GOSjlWsRQAAAACABcU4igAAAAAADxJFAAAAAIAHiSIAAAAAwINEEQAAAADgQaIIAAAAAPAgUQQAAAAAeNQsUTTGbDLGHDbGPGOMubXIfJuNMdYY01+rtgEAAAAATqtJomiMCUj6gqR3SNog6X3GmA0+83VK+u+S/r0W7QIAAAAA5KvVFcULJT1jrX3OWhuX9ICkq3zm+5SkOyRN1ahdAAAAAIActUoUV0k6mvV6aGZahjHmAkmrrbUPF1uQMWabMeaAMebAyMhI5VsKVAl9F42KvotGRd9FI6Lfol7URTEbY4wj6a8lfXS2ea21u621/dba/p6enuo3DqgQ+i4aFX0XjYq+i0ZEv0W9qFWi+JKk1Vmve2empXVKOl/So8aYI5IukvQQBW0AAAAAoPZqlSjul7TOGHO2MSYs6WpJD6XftNa+aq1dbq1da61dK+lxSVdaaw/UqH0AAAAAgBk1SRSttUlJH5T0HUk/l/SgtfZnxphPGmOurEUbAAAAAAClCdZqRdbaRyQ9kjPt4wXmvawWbQIAAAAA5KuLYjYAAAAAgPpBoggAAAAA8CBRBAAAAAB4kCgCAAAAADxIFAEAAAAAHiSKAAAAAAAPEkUAAAAAgAeJIgAAAADAg0QRAAAAAOBBoggAAAAA8CBRBAAAAAB4kCgCAAAAADxIFAEAAAAAHiSKAAAAAAAPEkUAAAAAgAeJIgAAAADAg0QRAAAAAOBBoggAAAAA8CBRBAAAAAB4kCgCAAAAADxIFAEAAAAAHjVLFI0xm4wxh40xzxhjbvV5/38YYw4ZYw4aY75njDmrVm0DAAAAAJxWk0TRGBOQ9AVJ75C0QdL7jDEbcmZ7UlK/tXajpL2SPlOLtgEAAAAAvGp1RfFCSc9Ya5+z1sYlPSDpquwZrLU/sNZOzrx8XFJvjdoGAAAAAMhSq0RxlaSjWa+HZqYV8gFJ/+T3hjFmmzHmgDHmwMjISAWbCFQXfReNir6LRkXfRSOi36Je1F0xG2PMgKR+STv83rfW7rbW9ltr+3t6emrbOGAe6LtoVPRdNCr6LhoR/Rb1Ilij9bwkaXXW696ZaR7GmN+V9GeSfsdaG6tR2wAAAAAAWWp1RXG/pHXGmLONMWFJV0t6KHsGY8wbJd0l6Upr7XCN2gUAAAAAyFGTRNFam5T0QUnfkfRzSQ9aa39mjPmkMebKmdl2SOqQ9HVjzE+MMQ8VWBwAAAAAoIpqdeuprLWPSHokZ9rHs/79u7VqCwAAAACgsLorZgMAAAAAWFgkigAAAAAADxJFAAAAAIAHiSIAAAAAwINEEQAAAADgQaIIAAAAAPAgUQQAAAAAeJAoAgAAAAA8SBQBAAAAAB4kigAAAAAADxJFAAAAAIAHiSIAAAAAwINEEQAAAADgQaIIAAAAAPAgUQQAAAAAeJAoAgAAAAA8SBQBAAAAAB4kigAAAAAADxJFAAAAAIAHiSIAAAAAwCO40A0AAAAAamXtrQ/P6XNHPn1FhVsC1LeaJYrGmE2S/kZSQNLfW2s/nfN+i6R7JfVJGpX0XmvtkXLXMzWV1Gg0rqRrFXSMzog4moxLoYAUTVglUq4CjlHIMUpZK2ul1pCjqYSrlGsVcIzawo4m466MkayVUtYqYIwiYUfRuKvkzHwhx6glZBRLWCVcq5RrFQo4kqxcK4WDjqxr5coqYBw5Rool3UzbWoKOrIy6IiGNRROKJ1MKBwPqbg/Lccys2+q6VscmYppKpGbaF9DSSFiSNDoRz1ue61rf6bnLnG2eSqiHttRqW0uV23e7I2G1tpb3FS22jNz+sjTi6NXo6f5sjCQrLUv3oZzlpF+3BB0ZSVNJN++94Mz3J+VKZ7SGFAoFJEnxeFIjE6fn6WkPKxwOlr3diURKw+MxJV2rcGD6O5Vux4qOlpLWV0z28nOXWew9v7gzOpFSKOBoeVtIxyYTSqRchQKOVnS0KBh0Zm1nsffqre+6rtWJaFzReEopa9USCCjgTP+/CQeMkqnpGNkadJSyUiI1/f8sO/Y6M30nHWODjlEoaBQwRvGkVTwrdjuOUSLlTsfnmf67NOLoRPT0Z9PL7ow4OpU9PexoKu5m+tnUVFLHpxKZY0PYMWoJG52acjMxfXlbSOFwULFYUscmT/8/Wd4WlrX53xUpf1pra7BoH5rNbN+TcuNHJeLNXJbltw9bWvjNGihHOuZOJdxM7GoPO4onrZKulWutHGMy57FLIo5cK41PZZ3bzhzPU66VZqa5Wee7UwlXrpXnez3lJjUR857HBhxl1pt9fuzKKuVK4YCj9rA88TkUMIqnrEKO0RktoUy8SMeHdOzNPsanzzXS5xixpKtQwCiRml5vKOAoODN/+pzGWuWdo4SCRomkzRwj0p8N+Kwr/RnHSO7MsnKPF2e0hjIxbLZYONdzk/mYb6yvSXQ2xgQkfUHS2yUNSdpvjHnIWnsoa7YPSBqz1v6mMeZqSXdIem8565maSurp0QnduGdQQ2NR9XZFtHOgT2d1t+jF0Zi2Z03fsWWjIuGA/ungy3rXG3rzPvOtnwzpLetX6pZ9Bz3T//Z7v9R3Dw2rtyuiz73n9VpxRqteHovq5r2n5/vsu1+v//Wvz+n6S8/WGW0hOUYykmJJq5vuf+L08q65QINHRtV/9nJP2+6+tl/rV3YWPfFzXavDr5zS1nsPeLZp5ZJWSdK1X/wPz/LW9XTo6ZFxz/y56/FbZiltKVcp66l2W2q1raUq1HfXdbeX/IUutoxwOODZ3nuv79Oyjoin392xeaO+/Njz+tim8zSVcD3v7Rzo0+Dzx3T7t36R6Wuf+fZhXfX631Df2cvz1tndHtTLp1J6TWerrLU6PJLfrvU97XJdlbzdiURKvxge98ybbsfIeEw7B/p03oqOousrFpD9lp9epqSC76VS1ncbrJvS3/3gWX3o8nM97+0a6NN5Kzvlum7Bdkoq+F4wGKirvuu6VkdGJ/TKySlPHLzzmgv0xJFR9a3t1o33P6GejhZ9bNN6zzzpWHvXj47oht9emxeL77muX7GkzYvdyzvCSlmrP/7y9PTf27Aibz/vHOjT2HhUXR2RvOmDzx9T39nLta67Xc+MTuQvv7NFO779i0ys3zXQp9/sbs/7/3zX+/sUDjq6/p793v7fEdJ7dz+e16f9+sl5KzpmTRZniw/lxo9KxJu5LCsWS+qXx/LnPXd5O8kiUKJ0zB2bjOu/P/CTTAy8edN5OjER10cefCrvuP6hy89Vd0dI/88//kx/eMnZumXfwUxMvufHz2emZR+njJFuuO/0d/X+rW/WyWjS8/394nX9cozRWM560+fYd/7gGf35u16nV06lPJ+785oL9PBTL+my81ZqeWeLVisiY5QXH3KP8a9ZGtbJWEqvTib08FMv6YrXr/KcV2fPf8fmjfrh4Vfyjit3XnOBXjh2Smt7lviuq6cznHc8SS/r99/Q63u8WHNGRNYWP5+Jx5NzOjeZj0rE+lo9o3ihpGestc9Za+OSHpB0Vc48V0n68sy/90q63BhT1lnPaDSe2RmSNDQW1Y17BnUqevqkNz395r0HNTaR0Jb+Nb6f2dK/JvOlyZ6+uW915vVHHnxKiaTNnPikp3/0609pc99q3bz3oF55NaagE1DACWQ6c2Z59z+ht204M69tW+89oNGJePFtnYhnThSzt+mF0Um9MDqZt7zh8Vje/Lnr8VtmKW0pVynrqXZbarWtJbenQN8djZbenmLLyN3ec1Ysyet3t+w7qM19q3X0eDTvvRv3DOptG87MvL5570Ftv+wcvW3Dmb7rTLnTv9gNj8c0MuHfrpGJeFnbPTwey5s33Y7052ZbXzF+y08vs9h7hbahu6NVm/tW5723vYR2Ft1n9dZ3J+J6YXQyLw7eNBPfbpyJe9svOydvnnSsleQbi4fGpnxj99DYlIJOIDPdbz/fuGdQ56xY4js93W9Ho3H/5R+PemL99pl5c5d1w32DGjoeze//Kfn26UJ9aNZ9PMv3pNz4UYl4M5dlHZv0n/fY5ML0XaARpWNuOkmUpmPg0PFoJlmTvMf1dFza3Lc6c26bjsnZ09Kf275nUMMnY55piaTN+/6+NDaloz7rTZ9jb+5bLSMn73M33f+EtvSvycTb0WjcNz7kHuOn4laJmYsuW/rX5J1XZ89/y76DvseVm+5/Qm88q7vguvyOJ+llFTpeHJuc/Xxmrucm81GJWF+rn/BWSTqa9XpI0psLzWOtTRpjXpXULelY9kzGmG2StknSmjVrPAtIujazMzIrGosWnN4WDijgGN/3Ck1fGgl5XjtGBedLryP9I7/ffNb6ty2eTKmYeDJVcJtyDY1FlUi5s66n0DJna0u5SllPtdtSq23NNte+W6qiy8jZ3kLzpvt3ob6aO69boP9O3/aiTPuLbVup211Km8tdZinLn882pONA3nspV3aOy8z9f5l+b6H6bjyZUls4ULAfpKcX2heBmQDpF3MLLTc7rhZbdqH/p+m4W+zY0KZAScvKjbnp7S61LaV8x2f7bLnLrkS8mcuyKrneUhXru0C9KjfmFjt2p+Oja73HpPS/C8XP3Njmd76bnqdYHE0VOE9Ix/y2cKDocS/3GJ9ux2zn6cXmSc3hHKjQsmZr/1zjdCVUYp0NV/XUWrvbWttvre3v6enxvBd0jHq7Ip5pvV2RgtMn4ymlXOv7XqHpJ6IJz2vXquB86XW4VgXnM8a/beFg8VuRwsFAwW2ajKfypocCzqzrKbTM2dpSrlLWU+221Gpbs82175aq2DJyt7fQvCeiCU3GUwX7au68ToH+6xgj106vp1i7ytnuYm2e6zJLWf58tiEdB/LeCzhzXma99d1wMFCwz2T3j0L7IjVzwPKLuYWWm46raQX3c4H9mI67xY4NubG+2Lx+211qW0r5js/22XKXXYl4M5dlVXK9pSrWd4F6VW7MLXbsTsdHx3iPSel/F4qfubHN7zw2fc5ZLI4GCpwnpGP+ZDxV9LiXe4xPt2O28/Ri8wSKrKvYsarQdpZy7rEQ8a8S66xVoviSpNVZr3tnpvnOY4wJSjpD00VtStYdCWvnQF9mp/R2Td+L2xlxtCtn+o4tG9XVHtLeAy/6fmbvgRd1x+aNedP3DR7NvP7ce16vUNBoxxbvfJ999+u1b/Do9DODZ7Qo6aaUclO685oLvMu75gJ9/9Cv8tp297X96m4PF9/W9rDuvrY/b5vO6m7TWd1tectb0dGSN3/uevyWWUpbylXKeqrdllpta8ntKdB304Ux5ruM3O19dvhkXr+7Y/NG7Rs8qtXLInnv7Rzo0/cP/SrzeseWjdr16LP6/qFf+a4z4FiFgtPFOnra/dvV0x4ua7tXdLTkzZtuR/pzs62vGL/lp5dZ7L1C2zA6PqV9g0fz3ttVQjuL7rN667vtYZ3V3ZYXB++ciW87Z+LerkefzZsnHWsl+cbi3q5W39jd29WqpHv65MRvP+8c6NOzwyd9p6f7bXck7L/8ZRFPrN81M2/usu56f596l0Xy+39AedMK9ZMVHS2z7+NZviflxo9KxJu5LGt5m/+8y9sWpu8CjSgdc//m6jd4YmDvsunzUr/jejou7Rs8mjm3Tcfk7Gnpz+0a6NOKJS2eaaGgyfv+rupq1Wqf9abPsfcNHpWVm/e5O6+5QHsPvJiJt92RsG98yD3Gt4ani9GkP597Xp09/x2bN/oeV+685gI9+cJowXX5HU/Syyp0vFjeNvv5zFzPTeajErHeWFu9S56ZlUwnfr+UdLmmE8L9kv7AWvuzrHn+RNL/Ya3dPlPM5r9Za99TbLn9/f32wIEDnmmzVT1Nplw5TnlVT9PVo9JVT9MV+nKrnrquVTDgyMgq5al6KgWMqWLVU1cBI6qeVqENmq5DVHGl9N3qVT2d7i9UPS2+/PlWPT0+kVIwq+ppMuUqWNuqpzXru96qp1JLwCla9TQ5UzGunKqniazY7al6OlOlj6qni6bqadV+XvfruxJDJTSjKv0/r3nMnUq4mfPasqueWquWQJGqp0lXrnu6snQpVU+zz4/nVfXUWoWcOVY9TbkKmMpUPU1vu+NIrnu66ml6ny+iqqcF+25NEkVJMsa8U9L/p+nhMb5orf1LY8wnJR2w1j5kjGmVdJ+kN0o6Lulqa+1zxZZZKOgDFVSzwA9UGH0XjYhEEVXX6IkiUGEF+27N6lFbax+R9EjOtI9n/XtK0rtr1R4AAAAAgL+GK2YDAAAAAKguEkUAAAAAgEfNnlGsBmPMiKQXCry9XDljMNZQs657oddfjXUfs9ZuqvAy67nv5qqXttRLO6TGaUut+m497Y/5YlsWXlX6rVQ07tbTvqIt/uqlLfUQc2dTL/uqmtjGyirYdxs6USzGGHPAWtvPuptn/Qu97ZVST9tRL22pl3ZItKUe21ApbEtzqqd9RVv81Utb6qUdxTRCG+eLbawdbj0FAAAAAHiQKAIAAAAAPBZzoribdTfd+hd62yulnrajXtpSL+2QaEuuemhDpbAtzame9hVt8VcvbamXdhTTCG2cL7axRhbtM4oAAAAAgLlZzFcUAQAAAABzQKIIAAAAAPAgUQQAAAAAeJAoAgAAAAA8GjpR3LRpk5XEH3/V/KsK+i5/NfirCvouf1X+qxr6Ln9V/qsK+i1/NfgrqKETxWPHji10E4A5oe+iUdF30ajou2hE9FsspIZOFAEAAAAAlUeiCAAAAADwCC50A6olHk9qZCKupGsVdIwcI1krRcKOEilpWVtYwSB5MurH1FRSo9HTfbY7ElZr66L9igKoIOJH+dhnKFXuOWVPe1jhMH0Fi9+i7OXxeFKHRyZ0455BDY1F1dsV0R2bN+rLjz2vD19+rs6IBHXk+ITWLmsnWURdmJpK6ulRb5/dOdCndd3tnLgAKIr4UT72GUoujqqPAAAgAElEQVTld065c6BP63vaSRax6C3KLGlkIp75QkvS0FhUt+w7qM19q7V9z6Ako6PHoxoejy1sQ4EZo9H8PnvjnkGNRuML3DIA9Y74UT72GUrld055455BjUzQV7D4LcpEMenazBc6bWgsqqWRkIbGonKtVVs4oGTKXaAWAl6F+mzSLVq1GACIH3PAPkOp6CtoZovymnnQMertini+2L1dEZ2IJtTbFZFjjCbjKQUDizJPRgMq1GeDjlnAVgFoBMSP8rHPUCr6ymlrb314Tp878ukrKtwS1MqizJR62sPaOdCn3q6IJGWeUdw3eFS7BvokWa1eFtGKjpaFbSgwozuS32d3DvSpOxJe4JYBqHfEj/Kxz1Aqv3PKnQN96mmnr2DxW5RXFMPhoNb3tOtr2y5SyrUKOEaOI93++7+VqXp65pIIhWxQN1pbg1rXPd1nqcAHoBzEj/Kxz1Cq7HNKqp6i2SzaXh4OB7WKLzEaSGtrUKs4SQEwB8SP8rHPUCrOKdGsuKQGAAAAAPAgUQQAAAAAeJAoAgAAAAA8SBQBAAAAAB4kigAAAAAADxJFAAAAAIAHiSIAAAAAwINEEQAAAADgQaIIAAAAAPAgUQQAAAAAeJAoAgAAAAA8SBQBAAAAAB7BhW4AAAAAgNpYe+vDC90ENAiuKAIAAAAAPGqWKBpjNhljDhtjnjHG3Orz/hpjzA+MMU8aYw4aY95Zq7YBAAAAAE6rya2nxpiApC9IerukIUn7jTEPWWsPZc3255IetNbuNMZskPSIpLW1aB8AAACA+jHXW2SPfPqKCrekedXqiuKFkp6x1j5nrY1LekDSVTnzWElLZv59hqSXa9Q2AAAAAECWWiWKqyQdzXo9NDMt2+2SBowxQ5q+mvghvwUZY7YZYw4YYw6MjIxUo61AVdB30ajou2hU9F00Ivot6kU9FbN5n6QvWWt7Jb1T0n3GmLz2WWt3W2v7rbX9PT09NW8kMFf0XTQq+i4aFX0XjYh+i3pRq0TxJUmrs173zkzL9gFJD0qStfbfJLVKWl6T1gEAAAAAMmo1juJ+SeuMMWdrOkG8WtIf5MzzoqTLJX3JGPM6TSeKXG8HAAAAcjAeIqqtJlcUrbVJSR+U9B1JP9d0ddOfGWM+aYy5cma2j0raaox5StJXJV1nrbW1aB8AAAAA4LRaXVGUtfYRTRepyZ728ax/H5J0aa3aAwAAAADwV7NEcaElEimNTMSVSLkKOEYhxygYMOpqa5HjGLmu1ehEXPFkSuFgQN3tYTmOWehmo4lMTSU1Go0r6VoFHaPuSFitrU3zFQVQBPGh8uLxpEYmTu/TnvawwmH2KfLRV9CsmqKXJxIpHR4e1/Y9gxoai6q3K6IdWzZqSWtQr04mtWZZm54eGdfWew9k3r/72n6tX9lJsoiamJpK6unRCd2Y1Ud3DvRpXXc7J4NAkyM+VF48ntThkfx9ur6nnQQAHvQVNLN6Gh6jaobHY5kkUZKGxqK6ee9BDZ+K64Xjkxoej2WSxPT7W+89oNGJ+EI2G01kNBrPHISk6T54455BjUbpg0CzIz5U3siE/z4d4biPHPQVNLOm+Ckk6drMFzxtaCyqtnBg+v2U6/t+PJmqWRvR3Ar10aRLPSeg2REfKo99ilLRV9DMmuKKYtAx6u2KeKb1dkU0GU9pMp5SMOD4vh8OBmrZTDSxQn00yK3PQNMjPlQe+xSloq+gmTVForiio0W7BvoyX/T0M4orOsM6a1mbVnS06O5r+z3v331tv7rbwwvZbDSR7khYO3P66M6BPnVH6INAsyM+VF5Pu/8+7eG4jxz0FTSzprj1NBQKaP2KDj14w8UFq56uX9mpf7jpUqqeYkG0tga1rrtdX9t2EVUNAXgQHyovHA5qfY93n1LJEn7oK2hmTdPLQ6GAXrM0UvB9xzHq6WypYYsAr9bWoFZx4gfAB/Gh8sLhoFZxso8S0FfQrJri1lMAAAAAQOlIFAEAAAAAHk15Hd11rY5NxDSVSClgjCLhgJZGwnJdq1en4kqmrBKuVcq1CgcdtYUdjU+l5DiStUYp15WT9Tm/Zxld12p0Is4zjyjZ1FRSo9E4zyAByEN8qDz2KQAU13QR0XWtDr9ySlvvPaChsWimAurKzlZFWhyNTyV1bDyum/cezLy/a6BP//iTIb1l/Urdsu+g93NLWrW2u92TBPqt4+5r+7V+ZSfJInxNTSX19OhEZlDfdFW1dd3tnLgATY74UHnsUwCYXdPdejo6Ec8kcNL0oKk37z2oF45PKpmShsamMkli+v3tewa1pX9NJkn0fG50UqMT8VnXsfXeA3nzAWmj0XjmhEWa7jM37hnUaJQ+AzQ74kPlsU8BYHZNlyjGk6nMgSFtaCyqtnBAKWvVFg74vh9wTMHPxZOpktaROx+QlnStb59JunaBWgSgXhAfKo99CgCza7pEMRwMZAZNTevtimgyPv284mQ85ft+yrUFPxcOBkpaR+58QFrQMb59JsitykDTIz5UHvsUAGbXdIlid3tYd1/bnzlApJ81PGtZm4IBqberVTu2bPS8v2ugT3sPvKg7Nm/M/1x3m7rbw7Ou4+5r+/PmA9K6I2HtHOjz9JmdA33qjtBngGZHfKg89ikAzK7pnth2HKP1Kzv1jZsu0VTCVcDIU/U0HIhrSWtID2y7SK5rFZqpenrtJWfLcYwevOFipVwrJ+tzuQVq0uv4h5supeopStLaGtS67nZ9bdtFVOAD4EF8qDz2KQDMrikiYvZwGI4xCjlGoaCj1yxp1Vg0oWg8pZQbV3d7WN0drZ75Xdcq5UpnnhEpK9FzHKOezpYqbhUAAJgrY4q/BtIY8gzNatEniumhKj73z4d17cVrtaa7TaGgo6l4Sq9GEzpybFKf/97TGhmP6a6BPq1c0qJXTsZ0Q1bJ7PQwGEvbQorGCRKovKmppI6ejGro+HSBpMl4Sr3LIlqtCL9wA02O+FB5sVhSL77q3aeTyyJac0ZELS3sU5zGkGdoZov+GcXRibg+98+H9YH/87W699+OKOW6eulETO/Z/bje+lf/otu++VP96X9Zr56OFt2wZ1AnoslMkih5h8F46uiruvSOH+i/3vljHX7llFyqo6FCTsYSOnYqptu++VO9d/fjuu2bP9WxUzGdjCUWumkAFhjxofJenfLfp69OsU/hxZBnaGaLPlGMJ1Pa3LdaH/36U9rct1pBJ5A3dtIt+w5q+2XnaGgsKseo4DAYbeFA5jVBApUUd23e+J037z2oOD9GAE2P+FB57FOUiiHP0MxqligaYzYZYw4bY54xxtzq8/7njDE/mfn7pTHmRCXWm75NdGgsqqWRkFLWf+ykpZHQrMNgnIgmPJ8hSKBSUgXG9OKqNQDiQ+WxT1EqhjxDM6tJomiMCUj6gqR3SNog6X3GmA3Z81hrP2KtfYO19g2S/lbSNyqx7u72sFZ0tqi3K6IT0YQCxn/spMl4Sju2bNTdP3zOdxiM1yxtUXs4oK9tu0h3vb9PN/z2Whlj9NLYpEZOxeS6Vq5rNXIqlpmWTLqZ18cnYho+NeWZH0gLBRz/Mb0Ci/6iP4BZEB8qj32KUjHkGZpZrZ7YvlDSM9ba5yTJGPOApKskHSow//skfaISK3Yco9ecEdFd7+/TQ08O6fxVndo50Je5/TQ9TmJPR1i/Pjmlx54b1dPD4/rUVedr7fJ2BYw0lUwpnrS69Rv/mfnMzoE+3f7QT/XdQ8Pq7Yro3j+6ULGk63nYeddAnz7/vV9q5FRcH9u0PnObCw9CI9ey1pB2DfRpe06/XNYaWuimAVhgxIfKY5+iVAx5hmZWq0RxlaSjWa+HJL3Zb0ZjzFmSzpb0/UqtPBh09LrfWKKuS1+r2x/6qf7nO8/zjJ3UGnZ01d89pp6OFt32rg1aGglpMp5SIpXSWz/3I+35wIWZJFGavj3lxj2Duu1dG/TdQ8MaGovqhdFJ3fbNn3rm2T4zjyTdvPegLnltt7a+5bUKOEaulU5OxbW0bX5DaPiVbJbkW8a5nso711Nb6sFoNK5//MmQ7rnuTQo4RinXau+BF3XtJWdrFVUNgaZGfKg89inKwZBn87P21ocXugmYo3qMhldL2mut9X0A0BizTdI2SVqzZk3JC3UcI2utRk7F9fKJmG7ZN311b+/2izPPKgyNRXXDfYOZz/zgTy/TR393nVZ1RQo+15jWFg4UneeS13Zr4OKzdP2X9nuuSnaEQwoG53arS6GSzS1BR9d+8T8809b1dOjpkfG6KO/crKWmi/Vdx0hvWb/S0z/u2LxRDndBoQ7MNe6iMogPc1eo77JPUc+IuagXtQqJL0lanfW6d2aan6slfbXQgqy1u621/dba/p6enrIaEQ4G9OHL12WSRGn6yttkPOX7rMKRYxO66oJepVz5vp9d3KbQMk5EEzoRTWjb75yjm+5/Iu+q5PB4rKxtyFaoZPMLo5N504bHY3VT3rlZS00X67uuladfpqvxuu5CtBTwmk/cxfwRH+auUN9ln6KeEXNRL2qVKO6XtM4Yc7YxJqzpZPCh3JmMMedJ6pL0b9VoRHd7WGcvb/dc+dv16LPqag9pxxZvAZvPvvv1+vz3npa1VtF4Mq/AzZ3XXKB9g0czr8/qbst72HnXQJ/2DR7VrkefVTBgfK84JlNzPyoVKtmcHsYje1oi5dZNeWdKTedLFqjAl6LoEdD0iA+Vxz4FgNnV5NZTa23SGPNBSd+RFJD0RWvtz4wxn5R0wFqbThqvlvSAtbYqkdpxjNpapsscpw8QTx49oTt/8Iz+7IoNuu+PLpRrJWOkjz74lEbGYwo6RsfG4/rqf7yQeX7xRDShh596Sbdfeb4+8fvW82xg9sPOXZGQ/vK/bswkQL05t7DOt8JaumRz7jIn496Eq7crkqnwljvvQpR3LtTuZi41HXSM7z4JLOJbcQGUhvhQeexTAJhdzZ5RtNY+IumRnGkfz3l9e7Xbsby9RXdf25+59fH3NqzQre94nY5PxHViMqFl7SHd//iL+vDl67R2eZtCAUe/uaJd1196dqZq6e9tWKE/v2KDrLWKhANKula/ejXqW5Ql/fBzMunmVVjbOdCntrAj17VzejavKxLSV/74zRo+FdPoRFz7Bo/qI29fr5bg6aQw/fzfig7vdi9keed0qenZ2tJMBW+6I+HpYVfuO90/7np/n7ojlN8Gmh3xofLYpwByzbXozpFPX1HhltSPeixmU1XZZY5d19Wxibin8Ms91/Xr/Zes9Qyfcfe1/XrdmZ362raL5DhGxyfi+oO//3f1dLSUPOxFMOjovJWdevCGi5VIuUqkrHb/y7N67LnRORVycV2bV5zmrvf3aV1PhxzH+JZxrpfyzqW0pRkL3oSDjj511flqCwc0GU8pPMciRwAWH+JD5bFPAaC4pksUpdNljkdOxTK/JkqaqXw6lTfMxdZ7D+gfbrpUq7radHwipuGTMX323a/XsvZwpmJa9rxf23ZRwWEpjDH6y4cP6buHhjPtSS+/nNLLfgVhbrhvMLMcv2XVU3nn2dpSqOBNufupmHq6Yjkajev6e/bn3Qb1tW0XUaodaHLEh8pjnwLA7Jo6GvoVVSk0zEU8mZLrWv3qxOlEcu/2izU0FtUbVy/V9svOyTy/eGoqoT++9/GCw1LcsXmjRk7F9eTRE57lz7fti6kgTLW3r96uWCZd6xnH80Q0oV2PPqskhRWApkd8qDz2KcpRTz8sA7XU1ImiX1EVK/+iM6Ggo9GJuG7Yc/oK5OhEXL+3YYX+8JKzM2W209VOezpatPXeA3rwhovzrozdsu+gbnvXhsyYjXMp5LLYC8JUe/tqccWyHK1BJ+825h1bNqqVW6GApkd8qDz2KUpVbz8sA7XU1BGxu336YfbsIS1WLW3NGypjx5aNCjom7yrXrkef1a3veF3eWEzb9wxq+2XnFB2WIl24Za5FZdIFYbLbuVDFaaqh2ttXb1dkU1aZE5Z0W27ee1ApftwGmh7xofLYpyhVs479DEhNfkXRcYyWt4d127s26Jyedh09HtWx8bg+8+3DnttRPvPtw/qb971RHT5Da5yaSvomHOtWdOie696kSMj/ythrlkb041veOudbGOqpOE01VHv76u2KbKEfFBLzGGcTwOJAfKg89ilKVW8/LAO11BRXFF3XavjUlF48PqGXxiZ1fCImd+Y5hFDQUTjg6NRUUmd1tymWdDUyPl3k5r27H9cN9w1qZDymZ4fH9crJmO79ows9V7mWtoUyr9N6uyJ6enhct33zpxodj+d95u5r+/UbS1q1qqtNPZ0tc05+0gVh5rucelXN7au3K7KhmTG9svV2RRRaZP9PAZSP+FB5IccpsE+b4rQIZUj/sJxtMT3qAxSz6K8o+t1bvmPLRq1c0qo1XW165WQsU5ymtyuiL17Xr7sG+jLPIqaLz/zVdw5rZDymb9x0ib5x0yWaSrgKGKmjNZA3FlN6/qGxqLbed0DfuOmSRXvlr1HV2xXZSNjRzoE+z7AsOwf6FAlz0gI0O+JD5UXCpsA+5dgMr1LHfgYWo0WZKE5NJTUajSvpWgUdo//9xNG85xA+ddX5ag0F8u47/6MvHdA3P3iJvrbtIg2NRXUimtBffedwpkJpIulqVVebZ32dLWH9w02XKhpP6ue/PuWZf2gs6vsZLLx6Gi5kIu7qWz8Z0j3XvUkBxyjlWu098KLef8nZ6mqvzjpzvyfdkbBaKQuPBUSf9LcQ8WGxm4i7OjJyUg9su0gp1yrgGD35wqi62rrZp/Cotx+WgVpadEfgqamknh6d8PxKeOc1F2hsMqkHB4ckTSdvbeFAwWcUpuKuwsGAPvr1p0p6hu30uIzSp751qG6ee0PjSLlWd/3oiO760RHP9GsuWluV9fl9T3YO9Glddzsn5lgQ9MnCah0fmkE4YHTW8k5dvftxz7lCOMDJP/LV0w/LQC0tuvtWRqPxzImGNJ343XT/E9r6ltdm5untimgynlIo4P+MQvrXonKfYau3597QOMIF+mIoUJ2vqN/35MY9gxqNUsUNC4M+WVit40MzSKSsbrr/ibxzhQRlTwEgY9H9TJt0re9VwsDMLQLZzyiu6GgpeN/5XG414PYEzNXy9rB2DfRpe9bVlF0DfVpepR8ZCn1PGGwaC4U+WVit40MzoL8BwOwWXaIYnKkOl3v7Z0vQ0Q8/9lYFjBQJB7Q0MnsyOJdbDbg9AXMRCgW0fkWHvrbtoszzWSs6WhQKVee25ULfkyA/amCB0CcLq3V8aAb0NwCY3aK7b6U7EtbOgT7P7Z87B/rUHQlrzbI2nXlGZPqXxBOTGhqb1MipKQUcaWVnqyTpV69GNXLq9PAZ0nTl1JFTMb00Npn3HlApuf2qmv2s2PcEWAj0yeJqGR+aQXdk+iptdn/bRX9DAcmkq5dPRPXC6IRePhFVMsl4m2gOi+6KYmtrUOu62z2/vKYr5xUaKmNZe0gvn5jy3NZz97X9Wr+yU5LyPpN+j1tKUSmxWFK/PJZfyOPc5e1qaan817TY9wRYCPTJwmodH5pBIGDUGnL0qavOV1s4oMl4Sq0hRwGK2SBHMunqF6+cyrv1+7yVnQoGF931FsBjUfbw1tagVnW16azudq3qasucaIxOxPOGw7h570EFnEAmAKSnb733gEYn4r6fSb8HVMqxSf9CHscmq9fPCn1PgIVCn/S3EPFhsRsej+m6e/br+i/t13t3P67rv7Rf192zX8PjsYVuGurM8Hgs7xxx+55B+gqawryOwsaYe62111aqMZWQSKR0bDKueNJVwDEKOUatYaOkK8WT/sNhOEa+0+PJVObfhd4DKiHpWvV0tOi2d23Q0khIJ6IJ7Xr0WQorAKhK4ZVmH7OSmItSFRpKLZni9lMsfiUfFYwxD+VOkvRWY8xSSbLWXlnJhs1FIpHSL0fGdcN9g55bS5d3tqizJSDXyvfh9ULT0+MfFnsPqITWoKOPbVqvm/ce9PTdVm5rAZpepQuvMGalFCkQcyPEXORID6WW9/1jeBo0gXJ6ea+kk5L+WtJnZ/5OZf17wQ2PxzJJonT61tKh41ElXenXr07prvd7H17fsWWjUm4q76H29DAZjI2IWnD///buPE6uqk74/+d7a+8l6aaXAJ1AAmYx8ARJImRxnACKKAjDkyhLIpAREsy4PsriyxfKDD/nYdGZUccYwAEEERIDDjzgiIqAMyiQhE2IJCyiSYR0p0kn6a3W8/ujFqqq762u7q7ldvX3/Xrlla71nnvr3HPPueec7zFkKizwbt7Vm9tKqdY6+0A/rXWjuw7pmpUQcyhzY1rmqjztDQHbwEftDRrhXtW+kdw6XAh8AfgacIUx5nkRGTDGPFGepI2c0/CcOr+HeMIQ9Fk01/n5yaUnY1mC1xIsII7B77W4f90SorEEIoJHoCc1LGdS0MtP1y7GEhiMJfBZQs9AJLPEhlJjFYknbIdBRXRoi1ITXiBgH+hntIFsdA3B5HBCuzI3qmWuyuP1WsyZ0simtYuJxRN4PRbtDQENZKMmhKKvMsaYBPCvIvLT1P97R/L5SnAantMfiRNIndCfvPn3OcNM6vwern1wO129YW69aCEBr8VFtz1DW0PAdljKjb/YQVdvmJtWzGPKpCDTW+q1sajGTIdBKaWclHqoaDXXEAyHY+zrf3duZGvd6Bu8Y6FlrhoJr9fiyKZQtZOhVMWNuEQ0xuw2xnwC+C/gx6VP0ug5rcN1wrRJxBKGz9z97JBhJu/0Rbl82bGZaKZ/7u5PRrRadqztsJT0e6/Y/CJ/7u7X6KeqJHQYlFLKSTFDRQcHY+zZ38+fu/vYs7+fwcGY4/dVa83K9DIf593yFH970+Ocd8tT7NzXRzjsnNZy0TJXjUQ0Gs85v6JRDWioJoZR38YzxjwMPFzs+0XkDOA7gAf4oTHmepv3fBK4FjDAC8aYC0eSpu6BCN97dGfOUJLvPbqTK894L929YcdhqXV4ch4DNIV8tu9vCvly3qvRT1UpOEVV02FQSqnhhoqOtMexWmtWOi3zsXHNIjoq3KuoZa4qVjQa55XO3iHn15z2Bnw+DWyoaltFxliIiAf4PvBRYC5wgYjMzXvPTOCrwFJjzHHAF0e6nVjC8Mvtnay9axvn3fIUa+/axi+3d2IJ9AxEM3dP09LDUnsGojmPwfn9+e/V6KeqFNJDwbJVaiiYUsrdhisfRhOcphprVrppbqSWuapYnb1h2/NL11FUE0GlBuOfBLxmjHnDGBMB7gXOyXvPZcD3jTH7AYwxnSPdiFPBH08YNjz+Ojcsnzck4ml7o59JQS+bL1/MTy49mfe01ycjWj3+OjetGPr+DY+/ztTmEOtXzuc97fW01PtJJAxdh8Ls2d9P16EwiRFe9Mb6+VJyU1omkoDXYv3K+Tn5bf3K+Zm5tUqpiWu4oaJuaoAV4qbGmZa5qljj5fxSqhwqNdajA9iV9Xg3cHLee2YBiMiTJIenXmuM+cVINpIOIZ49PGD9yvnc+ts3eG5XD996ZAfXnXM8Rx1WR9BnEfRZ7O+PcsWPn828/9aLFvLgZ5cyEIkT8nsykVANYIzha2e+l+6+CP/+m1f50odmk0gYXu3q5bI7t+Z8x+wpjUUFuUkkDDv2Hhr150vJTWmZiCaFvNyx+iQsSS6XoZ3VSqm0KZP83LtmEfGEwWMJfu+7ZXI1g9OMhN01eizLfIyVlrmqGOPl/FKqHNwUtdQLzASWkVyz8bci8r+MMT3ZbxKRNcAagKOOOirnCwIBL7Na69m0ZhHRhCGeMETicX73RjcAXb1hgj4LAY6YHKK7L8Ilt2/JGU5w2Z1b+dm6pXQ012W+t+tQmJf2HOCaB17KKSi2v3WITWsXZxpW+d/R1jj8GjvdfZExfb6U3JSWWlQw7/qgLyokp+dm3k/AV8kUKmWvUN5V5dc9EOG8W54aUlHduGYRHUFvpscxvwFW7uA0I5W+RmfPjSx31FOnvOvzJMvY/DJXp5ypfO0NAdvzq5zrKGqZq9yiUg3FPcC0rMdTU89l2w08bYyJAn8SkZ0kG45bst9kjLkFuAVg4cKFQ/r9AwEvRwa8DA7G6B6IEPRZbFyziIQxiAghn0VzXQDLEiKxuO1wgvwANZFYnDq/x37ogcOE+GKD3BSbhkpwU1pqUaG8+05fnLd6+pl2WD2xhCFgCbve6QNTR2OwKslVKmO4cleV13BD36oVnGY0AgFvRQPXOOXdnoE4T7++jyUz24gnDH5L+N2rXZx8bCuT6xy/Tk1APp+HOe0NOedXe0OgrIFstMxVblGp0noLMFNEZpBsIJ4P5Ec0/U/gAuB2EWklORT1jZFuKN1ATJ/MhwX9HIrGicTi+DwW8bjhrwcG8KRGDDzwD0tJmASTU3deRcDnsdizvx+f18oMLeiPxO2HHngs2+eLDXLj93rG9PlSclNaJhqvJbQ35t79b2/069AWpcos/5rhxgaW1xLuXL2AY9snZdL5eufBnPIhGPTS4bJ0u5nXEhZObyJ9BAVYOL1Jy1xly+fz5Iw0U2qiqMhVxRgTE5HPAo+QnH94mzHmZRH5J2CrMebB1Guni8h2IA5cYYzpHsl2nEKER6NRrnt4B9cvPx6fx8OhwRiNQS/X/9cf6ToU4cozZvO5e57JWXT3xl/soKs3zL9+8gS8HmF6ax13/v1JbHzmz8yf3kJLvZ/2xgBt9X5uvWjhkHl9LfXFDflpGePnS8lNaZloWkJ+Xu2PctHtT+Xk3SMn6bFXqlxKvZB9ubSE/OxvCGWGn05tDrHBRUNLx0NjO5+WuUopNTwxZvz2aC9cuNBs3bo183jP/n7HeRx/eaef+oCXdXe/G7jmhuXzMMZw9f1/GPKZa86ay9q7tjG1OcR15xzP6ju2cPrcdj532qycSsWtFy1kZlsD+weiRGLJ5TJa6v0jCv6SSBi6+yKj/nwpuSktLlGWnR9J3tW7mGqUKpJ3x7PxcvfLWBkAACAASURBVN79dX8/n7RJ56Y1iziyyuksQ2O7bBec7Lw7Xn57Na5UvMydfnXRy5lPKG9ef+aoPjfa4zna7bmIY9519y2/EYolDG0NAa45ay5NIR89A1E2PP46sYTh8ElBPnXbMzmBWq6670XuWP1+27kfTSFf5u86f3Lo5fIF04aspVOKYC+WJa4JFuOmtEwkhfJu2bYZS9DZGyYaT+DzWLQ3BPBqaHhVRZXOkyMNex8Ox9jXH6lYIJa0qEM6oy4Iz++0hmM60I5bVaPMVUqp8ca9pfgoBL0WV54xmys2v5gzjDTotegN2wdq8Yh92OOegeiQv5tCPg32osqiUN4th1gswSt7D3F5Vi/AhlULmDOlURuLqiqqkSdHEvY+HI6xc9/QnrNZrfVlbyx6HNLpccFoj/G6xlyly1yllBqPaqpETBgyhT4kL1ZXbH6RhEkGqbFb6Pftg4PctGJezqK7N62Yx4bHX8/5G6BnIGr7HRrsRY1VobxbDp294UyFPL29y3+8jc7ecHk2qNQwqpEnh1vIPtu+fvues339kbKlL83vsWyvU35P9S/h6cZ2tvGwxlyly1yllBqPaqpHMeK0VEU8QdBn8YOV8/lM1hzFm1ct4LB6Hx7L4qdrFxOJJ/BZgtdj8e8XnojPY3FwMEpXqqJy37ZdbFi1IOeOtwZ7UaUQdci70USiotuLxcuzPaWGU408OZJlJarZc9YU9NLWGOC6c46nzu+hPxKnrTFAkwuGdo6XNRzzVbrMVUqp8aj6V5kSchpG5LEEQehITVSPGwj6LFrrA8MGamltCPCzdUszwV2aQ76cxxrsRZWC49AyKU/e8jks6+J1QQ+FmpiqlSeLXVZiJMNUS83v93JUU4iQz5Np0LbV+/H7q38JH09rOGardJmrlFLjUU3VClvr7IcR+b1CW0OAw+oDdDTXcdRhdbQ3Botq4KWDu3Q019HWmAyskP1YG4mqFJzybmtdee7KtzcE2JC3vQ2rFtDeoIGMVHW4PU9W+hzN5/d76Wiu4+iWejqa61zRSEwLBnPT5vZGIoxs2LFSSk1U7i/NRyAQ8DKrNffOZkPAot7v1wAdytXs8m45Iyp6vRZzpjSyae1iYvEEXo16qqrM7Xmy0ueoKq/x2hOqlFKVVHMlYv6okZDX65qKhlKF5Ofdco+A8notjmwKDf9GpSrE7XkyEPDSUUTDMBKJ0dUXcd0wUZXL7/fgj3ogNZXE79fAdMpeNBqnszecOafbGwL4fJpfVO2rqStXJBJjZ1ffkPDqs9rq9SKtXE3zrlLVMzgYo3sgUpKepUgkxo6uoctozNZz2VUSCcPeQwPE4hA3hkQ0zt5DA0xpDOmUEpUjGo3zSmfvkHN6TnuDNhZVzauprrbu/qhtePXu/ih79vfTdShMQmNfKxcqlHeVUuUzOBhj18EBdu7t5e0Dg+zc28uugwMMDsZG9X1dffbLaHT1lX8ZDVW8g4NhesNxXuvsZe+BQV7r7KU3HOfgoC4RpHJ19oZtz2ldTkpNBDV1e9NpeYzBWIK9B/r5yuY/cOtFC5k9pVHvGCpXcQzVrstVKFVWB8JR9h0Kc80DL+UsvD4p4B1Vr+J4XYB+oglHjePvrlQ2PafVRFZTJWJ2uOsTpzVx+bJjaan347WEmVMa2b1/gMvu3MrP1i2lrdEdkfSUgmTePX1uO8sXTKMp5KNnIMp923bhKfENjUTC0N0X0eVdVMVVK+8NN6w0mjC2C6/fu2bRqLZXzWU0VPGiCcPjr+zl9kvej8cS4gnD5q1/YdqSGdVOmnIZPafVRFZTDUWfJfxg5QK+95udXLxkBlfd92LOePLHv/JBln3rt0Ri8WonVakcQZ/F506bNWQORNBXutHhiYRhx95DXHbn1sw2tIddVUK18t7gYIxXu4fOF5zZUp9pLMYdegtGO02hrd5+Afq2el12wU38HuHMEzpYfceWzO+0fuV8/B4tC1Wu9oaA7TntlqV7lCqnmpqj6LGEtkY/15x1XKaRCO+OJ/d5PJw+tx2f12LP/n7+3N3Hnv39RKPacFTVNRhN2M6BGIyWbuhpd18kU1FPb+OyO7fSrXOnVJlVK+91D9jPF+weeHe7Po+VWUsvbWpzCK9ndJdHv9/L7LbksgtPXLGMjWsWlSSQTTgcy7luhcOjm0OpkqJxw7q7n83JG+vufpZoXIcTqlw+n4c57Q0557QGslETRU31KBrAGEPcOI8n//xpszg4EOWS27fk3BnSk15VUyXmQERicdttaA+7Krdq5b1izqvDgj42rFowJOLwYUHfqLfr93vpKGGE03A4xs59Q3tGZ7XW6zqOo6TzztRI+HweOprrqp0MpSqupnoUQTAIiYSxv0NsCZf/eBu73hnQ6FXKVdJzILKNZg7E4GBur0N25Ea/12O7Db9Xb5Co8qpG3hscjBV1XgWDXt7TktsD+J6soalusK/fvmd0X7+OBhitUpW5SilVy9xzJSyBRp+H3QMRwLB+5fzMsJL03ddd7/Sxe/8AdXmL6updRFVtTSHLdg5EU6j4eznDzcdqqfdz60ULh8wTa9G5U6rMKp330ufCm10Hbc+rllDudoNBLx0uahjm096v0itFmauUcqfpVz9c7STUDPdeGUeheyDCjb94hdVLZ3BMa/IOcTrS3a53+jj/1meY2hyiP5I73EnvIqpq6xlIMKMlkJNnJ4csegYS1AeL+w6n+Vgb1yyiI+jFsoTZUxr52bqlGvVUVUw62ulhdT42rV2MMabseS/7XLjxfx/PvWsWEU+dV0G/RfdAhBZwVa9hIRp1sfR6BhLs7x3IKXNf7zxIT52v6DJXKaVq3fi4ShbJEvjSh2fx9oEwb3b30x+Jc/jkAE0hX6aR+N3zT6Qx5M1cdDV6lXKDlpCf3QcH2PVOsse7PxJn2mEhpk4KDf/hlGJ6HSxLdGkYVTHO0U5DI2okDrfERb7sc+HK+1/ixGlNfOUjs4dEwp7psiGmTlrr7COpttbpaIDRsgTaJoXYubc3U+YePjmEpR2KSimV4f4r5Ah4LIue/uiQBXRb6gM8edUpiAgegaDfyrmL2N4Q0EA2qqoORWN02Sz+PDnkK7oiq70Oym2cop2OZC3bYpa4yJd/Lly+7FjbSNjp3na3CwS8zMobJdNa59dANmNQqL6glFIqqaauMpF4gtuf/BPXnDU3s2j57U/+ia9//Dim5kWrmlx8R41SZReOOefdYrWE7Hsd8udjKVUpI412atdzONyQajv550JLvX/cz/ELBLx0aMOwZArVF5RSSiXV1FXHErh4yYyc4UU3LJ+Hrp+r3M4p746kMzAY9DKzJbfXYbghekqVUzraaX4vt120U6eew5Z6n20jL54w7Nnfb5vX7c4F7W1X2UpR5qqJIxyOsa8/oj36asKp2Gh8ETlDRHaIyGsicrXN65eISJeIPJ/6d+lIt2EMQ4YXXXXfi8QNOcsEKOU2TnnXjLDDIxj00tFcx9Et9XQ012kjUVVVOtppehmCQtFOnXoOjcF2GQMDnHfLU/ztTY9z3i1P8Vp3X045n30upHsYs9Ohve0TW6nKXFX70uuYZpc3O/f1EQ5rvVLVvorUIkXEA3wf+DCwG9giIg8aY7bnvXWjMeazo91O3NgH8+jujWABR2qlWblU3CEQTVxrLWocG0mkXadgTAljhgyp3rBqAd98eHtOJf/yH29j05pFtuW89rarfFrmqmI5rWO6cc0iHQ6ual6lcvhJwGvGmDcARORe4Bwgv6E4Jh6xH1709sFBmup8pdyUUiVlOQyNs0THQanxrdhIu07DQy2RIY08y4Jfbu/M+fzu/QNEC8w5dPtaiaqytMxVxdJ1TNVEVqmhpx3ArqzHu1PP5VsuIi+KyGYRmTbSjQS8FjfnDS+6Yfk87tu2C49OPFAu5rOEm1bMy8m7N62Yh0/zrZogCg0PzR5GChCP2w9H9VjC4GCMPfv7+XN3H3v29+u0A2VLy1xVrPRNrGw6x1lNFG66vfr/gHuMMWERWQv8CDg1/00isgZYA3DUUUflvQaHNfi457JFROMJ4gnD5q1/4XOnziTk18WRVHUVyrsBn3Bkc4g7Vp+EJZAw4PMKAZ9eiFT1Fcq7YxWJxOjqSwaJmNIYYNOaRUQLDA+NJQy94Rg3rZjHFZvfDURy04p5NASsES+lkW+kazYqd3PKu36v0NoY4Lpzjs+so9jaGMDv1TJX5Wqt83PH6vcPWee4nOuYlrPMVWokKnX12wNk9xBOTT2XYYzpznr4Q+BGuy8yxtwC3AKwcOHCnH7/eNzw155BvnDv8+9WElbOxxIhHNUhAqq6CuXdcNTwTm+Ez93zXCbvfu+CEwl6glVJq1LZCuXdkbBrhNk17Ga31eP3O6+R+J1f7+QLH5qVU8lvawzQF06MeCmN/PSNtaGp3MUp7/ZHEjy5s5NT5x6BMQYR4Tfb3+LDxx1Bc33VkqtcajCayFlzc8OqBWXdXqnKXKXGqlLdbFuAmSIyQ0T8wPnAg9lvEJEjsh6eDfxxpBuJGZNpJEKqknD3szSGvETjidGnXqkyixuTaSRCMu9+7p7nNLBCAbFYgr/2DPDn7j7+2jNALKbnuJulG2HZkQNf7e7joed3D2nYdfVFHH/Ptno/nzttFt/59U4i8QQeSzimrZ6pk0JjnkvkFHm1eyAyhj1XbuTzCPOnt3Dhrcn8eOGtTzF/egs+XU9L5dnXH+HyvHLh8h9vY1+/lguq9lWkoWiMiQGfBR4h2QDcZIx5WUT+SUTOTr3t8yLysoi8AHweuGSk24nG7SsJxqBjyZWrOeXdWFwbinZisQSv7D3EJ2/+PX970+N88ubf88reQ9pYdDGnRtiKhbnDqnbvH+CtA4OOv6ff72V2Wz3f+PhxzDm8kSMmBzmiMUAw6B3zXCINWjFxROOGdXc/m5Mf1939LFEtc1UeLRfURFaxiXvGmJ8bY2YZY441xnwz9dzXjTEPpv7+qjHmOGPMCcaYU4wxr4x0Gx6HSoLHEoI+naOo3Msp79otI6Cgszdse4e3szdc5ZQpJ06VrfxAY1ObQ3T3RQr+nn5/7nqh6WGqY10vUYNWTBxa+VfF0nJBTWQ11XoqFMVsclAXVlbuNZ4j8EUiuVEmI5HyR5mMxhMOPbDao+hGkUjMsbLl91pDIlVvePz1Uf2e2eslPnHFMjauWTSi+YVjbWiq8UMr/6pYrXX25UI5g9ko5RY1NTs/6LePYhb0C15vTbWJVY2ZHPDZ5t3JAXev/xmJxNjRNbJgJKXg81i2a6B5PXqeu006jzz0/G7Wr5yfGe6XqWyF/Gxcs4i3DgzS3RfhW4/s4LldPSP+PWOxBJ29YaLxBD6PRcfk4IjL/eyGpkY9rW0NQYsfrFowpOxqCGoZonIFAl5mteaWC611fgIBLRdU0vSrHx7xZ968/swypKT0aiqX9w4m2LzlL6xYeBQeS5LLY2z5CxctmcHk0PCfV6pavF6LgNdi2mF1meUx/F733+Do6rOfd7ZxzSI6ythQbG8IsGHVgszw03QUuvaG4Rd2V5WVnUf298e4/ZL347GEgNfKNMKmeC3290e57qHto/o903NW8/PDnCmNo2osFhMhVY1vvYMJHnp+dyY/ppfT0vqCshMIeOnQhqGagGoq18cShpv/+01u/u83c56/cNH0qqRHqWJ19oa58Nanh/SQbVq7mCObylNrCYdj7OuPFHWHNBqN09kbzry3vSGAz+ep2jwfr9dizpRGNq1dTCyewOuxaG8IuL5hPRFl55FN23azadtuAJ64Ylmmp26sv2dnb5jvPrqTa86aS1PIR89AlO8+upNrzz6+bOfPaDidR6rytL6gRiJ/xIJeb9REUVMNRV9qzkF+ZXs8zPNSE1ul59yFwzF27hs6ZHRWa/2QxmI0GueVzt4h753T3pCZ5zNkCGgFzjmv13JVI0DZK5RHStVwEjFcvGQGV933YiaP3rB8HiLuCUxS6DzSxmLlaX1BFauUIxaUGm9qKod7HQKC6OR05XbZAT3SpjaH8JXpIrSv337IqN26UJ29Ydv3dvaGaau3n+TfVq+T/FWSUx5pCfl5pbM3Z13FVzp7iUbjI95GIkGmkQjJPHrVfS+ScFFso0Lnkao8r8eyry/oPGeVR6Nsq4mspnoUB2IJdnX3ce+aRcQTBo8l/O7VLu11UK7nkeRNjis2v9sjctOKeXikPDc5hhsyOjgYo3vg3WGp5y2Yyrd//eqQ96bXtMue5N9W7y9rIBs1vogIUyb5c8plv1d4ZzDqPL+1uS7z+fy8aBdcxik/x1201IEux+AuA9G4bX2hQ+sLKo9G2VYTWU3V5hqDHt7b0cT5tzyVM7SnMajDepS7DUTj3PiLHTlzrG78xQ7+7fz3lWV7hYYDDg7GeLV76LBUINNYzB5e6vd7yxq4Ro1vnb1hzkuVyWlTm0PcfenJwzacnPJi/pIXTvk5f43GaqrmMG01lFN9oUHrCyqPRtlWE1lN5fKBSML2DvVARO/6KHfzWMI/nzuX44+cxOGTgxx/5CT++dy5ZavoFloXqnvAfljq382fmvPekUQYDYdz11oMh8u/1qJyB6eeNE+BdezSa3Puc8iL3QPJIdLpfGUJ3L9uMf9z1Sk8ccUy/ueqU7h/3WJXrXPW3hCwPec0Um91aH1BFau9IcDNn8o9d2/+lJ67amKoqW6AhLGvkCSMDu1R7tYcstjfb2V6XtKVyOZQee7lBAL268UFAl5ivWHH8+iJK5aNOOjISALnqNpj15O29m+m47OEO1a/n13vDGTWDp12WIiWkD+zNue3P3GCY69jdr76/CnH8t6OpiF5bFKLe9Yh9fk8zGlvyDnnNOpp9Wh9QRXLGIPfa+Wsc+z3WhjNK2oCqKlamiX2Q3usMs3zUqpUegbs725vXLOI+mDptxeJ2A/pm91WX3CIXPbcsXyJhKG7L0IkFsfv9dBS78eyxDFwzsY1i3RdqhqWzg8GuPvSk/nmw9v55fZO1v7NdM5631SueeAlPv2BY7jmgZdyIglmz13sGYg65sXsfLVkZltmCCHk5TEXrYno83kKnkOqcrS+oIrV2Rtm9e1bhuSV/PnUSlXC9KsfHtXn3rz+zFF9rqaGnorADctzo5glQ6RXOWFKDaPSgS7Si6C3pYbUfPsTJ7DvUJiewRgtIecolU4SCcOOtw9x7vonWXrDY5y7/kl2vH2IRMIUFTgne1jq4KAOSx3vEgnDjr3J/PCBGx5j5Q+f5gunzeJ3V5/CRUtm8Jkfb2P5gml8+acvDIkkGMsKHLHh8deHlOkbVi0gPSJ7yTEtAMSrGCjGLv/qUGv30/qCKpYGolITmXtutZaCgR/97k85AUF+9Ls/ce3Hj6t2ypQqqNJresUShraGAF/5yOyctec2rFpAU5v9sNT8SJPZDgyE8Xkt7vz7k4gnDLf+9g0uu2sr939myagC5+QHK3E7p97Uiaq7L8Jld27NaQSuTfXwpStdTSGfbeVLsnp6ntvVw7ce2cF15xzPsW31GMj0TE5tDrF+5XyAzHzHSgeKccq/rQ2+IcPIdai1y2h9QRVJA1GpiaymehS9HovVS2dw3UPbOe+Wp7juoe2sXjpDI1Mp16v0ml5eS/j8aTO56r4Xc3oVu1K9isGgl47mOo5uqaejua5goy0ajbO7J8wltz/Dqd9+gtV3bGHV4qNZckwLg9H4qALnpIOVjAfZvWeZ3tS9yd7UiSoSi9s2AnfvH8hUutLDSrNNbQ7x9oFBvn/h/MxrXb1h/F4LryWs/OHTdB2KZPJrd2+EL354Jr97tWvEveCl4JR/Y3GKWqNUVY/WF1Sx6gIW61fOzylf1q+cT11A84qqfTV1e3PQYYmB75z/PmKxBN4yLV6u1FhVenmMtno/kdY6x17FSX6vY+Mwf107S2RIZXnd3c9yx+qTsCwZVeAcNw7picUSdPaGicYT+DwW7Q0BvF7Ltvfssju38rN1S2lrDEzI3sag3+L2S95Pnd9Dz0CUDY+/TldvmJ6BKAcHItyx+v3s74uyYdWCzELW6aF///zzP/L/nXv8kJ6er5051zG/LnpPK5OCnhH1gpeC05C0/IAobs3TE1mh+oJS2SYHA/TWxZPXNIGEgYBXmBzUqKeq9tVUQ9FjCV29YdbetS3zXHotrc7eMEfqQrrKpbwOebdcQ1v8fi8Bj5XpVcyfJ7ZxzSLIagy21fvx+722Q+3u+vRJtpVln0fweyxisQSvdfflNAg2rFrAnCmN42ZITyyW4JW9h2z3wan3LBKLZ3ob0w3Jqc0hbr1oIbOnNNZsYzEWS/BWTzgnSM1NK+bREPDy9QdeZmZ7AxctqeNLm56nrSHAdeccz1EtdbzVM8C3HtlBV2+YhoCX6x7aTltDgM+fNpOvfuy9Ob3g+fn1J5ct4sBAnKNb6iu6r075Nz8gihvz9ERXqL6gVDbLEjqa6ibcDT+loMaGnloOk9MtgVhc10ZS7jWaADJj1VrvZ3prnWOP3nm3PMXf3vQ4593yFDu6+ohEYrZD7d7c1287hNBjCYfV+ensDWcaWOnPXP7jbXT2hquy36NRaB/8Xg+nz23n5k8tYOOaRdz8qQWcPrcdv9fj2NvY3VdbwxATCUPXoTB79vez99DgkGN1xeYXqQ94eW5XD5d98JjM68/t6mH1HVu4+LZn6IvE6eoN84NVC3irp5/7Ll/MdX93PNc88BKnfOsJfvXyW4751RhTlYaYU/71erAdaq3co1B9Qal8liW0NQboaK6jrTGgjUQ1YdRUj2LCYXL6Nz5+nM47UK4WDI48gMxYpXsVnXpE7JYasBtq991HXx0yhPAHqxbQVufH67WIZkWxTNu9f4BYPFGV/R6NQvvQ3hDg86fNGtLb2BzysffQoGNvY63I7zXdfPli231O81hi+/qcwxu5d80ifvdqF1fe/xL/c9UpOQ3Oax96hSePO8KxB7oai1875V8Rcp5rrfNrIBuXKVRfUEoplVRTV66A1+Kzp85k3d3PZips61fOJ+C1aHJZD4VS+YJBb1nXfLObK3dYqkckP2rjfz67O+ez6V5Gu6F2Xb1h2hr8jguJ+xwao+mbN+Xe71IotA/7B6K2vY33rlmEkFxc/ub/fjPnc37v8IusO82JdJv8XtPuvginz21n+YJpmQr4fdt2EfBaPHHFMscIv15LMpFCwX7Ji/u37bbNry0hf9UWrnfKv7pGqLsVqi8opZRKqqkrWcIYOpqDORXWoN8iHjeurGAplS0SidHVN3ReYCkUmiuX3yNS57fYuC23oZiuyLc4NCwnB3yOvYDtDYEhPY4bVi0oaw9QqRtZhfZh76FBvnHWe5l75OTMMdz+1wPs2T/Al3/6Aj9YtQCAm//7zcxxb6kvfOOq0JxIr9dyVYCc/Dmaj27fm1MBX/s30/n6x4/LBHMJx+PctGIeV2x+ccixvPWihZk8mr4pseSYFi774DF4LCFhoH2St+w90OU8F5U7FKovKKWUSqqpK1/IL7zZHR5SiZ3eopGplLtFIjF2dA1dj212W/2IKqjRaJzO3vCQnr3hInNm94hEIjHbxmC6sjzSoaJer8WcKY1sWruYWDyBt8y9Y8M1skbD67WY3d4wpNfU67WYFPJweFPdkHXzmuu87N4/wPce3ck3Pn4cFy6anmm0pht1Tg0+pzmRm9Yu5vBJQVcFyPF7PUxtDtHWEODyZcdybFs9u94ZoK0hwJJjWjjzhA7Ozzs2u7r7MkP++iNx2huT+XRmW0Mmn9T5LX5y2cn09EdZfceWIetspiPvdg9EaPdIyXoUS3UuKnfT+oJSSg2vpq56BwcSfO/RnTlzDtKVtMZgtVOnlLOuPvv12DauWURHkZXTaDTOK529Qyo+c9obCkbmzOf3e5ndltsYzO5RGc1QUa/XKknUYaeGcLZCjazRpiGRMLy2r8+2cXZwIO742504rYmLl8zIaUSmPwc4NvgKzYkcrtFfaS31fu78+5PYe3Awp5fwhuXzOHxykItve2bIsbnnskV8/p7neG5XDwC/vWIZiYTh1a7enOOxcc0i1t39LG0NgUy5vu9QmPYG/5CG+Zz2hpI0FktxLir30/qCUkoNr2JXPRE5A/gO4AF+aIy53uF9y4HNwPuNMVtHtg24eMmMnDW2blg+D9HgVMrlnNZjG8naa529YccKbrrXJ39emNNcOb/f67pKcaGGcHYDIRpP5DQs0uv4jSXycaHGWaHf7vJlxw5ZziH9OcDxO30ei7V/M50VC4/CYwnxhGHz1r/g9VgjavRXgmUJDUEvF92Wu59X3fcid196sm1ao/EEN66Yxzt9EfojcYIOvd7RhHFcO/G8BVP59q9fzW3INdeNeX9KcS4q99P6ghoJNw33V6qSKjJxT0Q8wPeBjwJzgQtEZK7N+xqBLwBPj2Y7xjCkUnbVfS9i9PquXC49HyvbSNdeK1TBban3c+tFC3NCwRczV85NnBrCnb3hnPeFfB6uPGM21z20nfNueYrrHtrOlWfMJlhEb1M0GmfP/n7+3N3Hnv39RKPJxlehxlmh366l3u/4uXCB72yt83HW+6ay+o4tnPrtJ1h9xxbOet9UWut8mUZ//vaKCZBTLtGYfQ+oJfbHJp4w9EfinHfLU1zzwEt0HgojGJYc05LzXkuc1048Z/7UnG2VqiFXinNRuZ/WF1Sx0nP8z13/JEtveIxz1z/Jjr2HSOjNIzUBVCrCy0nAa8aYN4wxEeBe4Byb910H3AAMjmYjCWNfUU5oya9crq3efj22thE05ApVcC1LmD2lkZ+tW8qTV53Cz9YtHXeLvhfb0xM3JjMEMv2eKza/SHyYciDdY5m9fuQrnb1Eo/GCjbOGgGX72zUELI6YHHT8nIDtawD7+qO2jeJ9/VFXNvqdjs87feEhx2b9yvls3voXGoNeTpzWlGn49QzEWLX4aD654N0G4G+2F147MXtbpWrIleJcGzKsbAAAEcVJREFUVO6n9QVVrImyHq5Sdio1tqwD2JX1eDdwcvYbRGQ+MM0Y87CIXDGajXjEPuy6R8eSKJcbbl5gMdobArZBaNLRRdMLBo9Xdktz2DUQIg69W9FY4aGnhYbuHjE5lBORM7tx9taBAaLRaM5vt/dAP71hX8HPvX1wgBuWzxsy9M0SiBSYo5jd6HfLMKh04zV7P29YPo9rH9zOqbPbuHfNIiKxRGYI7QdnT+H6//ojly87lrV3baOtIUDAa9HTn+ALH5rJtOYQG7ft5uRj2wg6DJu2UuV6fj4fq1Kci8r9tL6giuW24f5KVZIrrnwiYgH/AlxSxHvXAGsAjjrqqLwX4dufOIEv//SFTGXl2584QeccKFcomHcZ+7xAn8/DHJvInNVaX67U7BrCG1YtwGMJXYfCmcbScOs2OinUY1mocRb0Wfh8viHBVYI+q+DnnBb8/vrHjxt2Hyrd6B8u76b3c9Paxfy1Z4DuvgjfemQHz+3qoas3zDnzO3i1s5emkI/501syr336A8dw4rQmrjxjNhfcmnv8Llp6NI0BP/F4wvYGSH0guS5jOfK5G+foqtFxzLtaX1BFGukc/1IYrsxVqlLEVGCYhYgsBq41xnwk9firAMaY/5t6PBl4HehNfeRw4B3g7EIBbRYuXGi2bn335bd6BvjGgy8NWej5H88+niNKEHFRTUhlqTbk511VnHTU03jCYIBvPrydX27vzIkYmkiYUS2PsWd/f86C70Am8mahICmj/VznwUFe7+rNiRR604p5HNvWwGF1/lIs8VHxvGu3XucNy+dR7/fw2XueG3KMrv/f/4to3HDNAy8VPH7FRLtVNaNsTbXsvKv1BVWsQusQ543kqHiZO/3qh8uxSVUBb15/5qg+N9rffJjtOebdSt0y3QLMFJEZwB7gfODC9IvGmANAa/qxiDwOfGU0UU9XL50xpOKldwiVqg0+n4eO5jq6DoU5d/2TjktEjGbdxuGG7jqJO8x1Gm5OpDGGkN/DdeccT53fQ38kTsjvwRhT8bUnSyXds3j/uiWEo3EsEURARLhpxbwhZfOM1noGow7DbLPmnqZ/d6VKResLqlhuHO6vVKVUpKFojImJyGeBR0guj3GbMeZlEfknYKsx5sFSbCccS3DjL3bkDOW68Rc7+M757yvF1yulXGK4OSOjWbdxtEN3RzvXybIs1j/2GssXTKMOD5F4gvWPvcY3z5036n1wA8sS2huDOY35jWsWOZbNPk9xc0+VKiWtL6iRGO9z/JUarYpNwjDG/Bz4ed5zX3d477LRbMPvsejqDbP2rm2Z56Y2h/ANMzdJKTW+lGvOyGh6rgJei/Ur57Pu7mczPRPrV84nMEzvX0u9ny99eLZtoJtakN2Y7xmI2pbNIb+XpqB3VD25So2F1heUUmp4NTVbP+Cz+N4FJ/K51FyYqc0hvnfBiQR8WvArVUvsomxWq5FlEB5+YQ+3X/J+PJZkInte+sH3FPxcrQ9nym7Mb3j89SERXtO/l2VJTQdhUu6k9QWllBpeTTUUm0J+ekLRnDk/k0M+mkK1cYdeKZXkpkZWS72fv5s/jdV3bBlxo7WWhzNlN+af29XDj373J35y6cl4LBnye+kcRFVpWl9QSqnh1VRD0bKE6S31NAZ9Va88KqXKyy2NLDc1Wt1Ej4tyM60vKKXU8GqqoQjuqTwqpSYOLXfs6XFRbqb5UymlCtPB+EoppZRSSimlcmhDUSmllFJKKaVUDm0oKqWUUkoppZTKIcaYaqdh1ESkC/izw8utwL4KJke3Xf3tl2Pb+4wxZ5T4O92cd/O5JS1uSQeMn7RUKu+66XiMle5L9ZUl30LBctdNx0rTYs8taXFDmTsctxyrctJ9LC3HvDuuG4qFiMhWY8xC3fbE2X61971U3LQfbkmLW9IBmhY3pqFUdF8mJjcdK02LPbekxS3pKGQ8pHGsdB8rR4eeKqWUUkoppZTKoQ1FpZRSSimllFI5armheItue8Jtv9r7Xipu2g+3pMUt6QBNSz43pKFUdF8mJjcdK02LPbekxS3pKGQ8pHGsdB8rpGbnKCqllFJKKaWUGp1a7lFUSimllFJKKTUKNdlQFJEzRGSHiLwmIleXeVvTROQxEdkuIi+LyBdSzx8mIr8SkVdT/zeXMQ0eEXlORB5KPZ4hIk+n9n+jiPjLtN0mEdksIq+IyB9FZHGl9ltEvpQ63i+JyD0iEqzUfpdLJfOtzbad8vG1IrJHRJ5P/ftYhdLzpoj8IbXNrannKnZOpbY3O2u/nxeRgyLyxUodExG5TUQ6ReSlrOdsj4EkfTeVd14UkfnlSJNNGquWZ8dqJMfX7dxwHXKr4fKoiARS14vXUteP6VmvfTX1/A4R+UgF0vJ/Ur/hiyLyqIgcnfVaPKvMebDM6bhERLqytndp1msXp/LTqyJy8VjSUWRa/jUrHTtFpCfrtVIekyHlQd7rjmVsqY9JkektquwVkeUiYkSk6tEzR6qYfRSRT2aVez+pdBpLoYhz4KhU+f5cKu9VpB6WYYypqX+AB3gdOAbwAy8Ac8u4vSOA+am/G4GdwFzgRuDq1PNXAzeUMQ3/B/gJ8FDq8Sbg/NTfG4DPlGm7PwIuTf3tB5oqsd9AB/AnIJS1v5dUar/LdCwrmm9ttu+Uj68FvlKF4/Em0Jr3XMXOKYff523g6EodE+CDwHzgpeGOAfAx4L8AARYBT1fomFQtz1by+Lr9nxuuQ278V0weBdYBG1J/nw9sTP09N/X+ADAj9T2eMqflFKAu9fdn0mlJPe6t4DG5BPh3m88eBryR+r859XdzOdOS9/7PAbeV+pikvmtIeZD3um0ZW+pjUsrjlioLfgs8BSwsZ5qqsY/ATOC59PEG2qud7jLt5y2k6rOpcunNSqaxFnsUTwJeM8a8YYyJAPcC55RrY8aYt4wxz6b+PgT8kWRD5hySDSlS//9dObYvIlOBM4Efph4LcCqwuZzbFpHJJAvW/wAwxkSMMT1UaL8BLxASES9QB7xFBfa7jCqab/MVyMduUqm8Zec04HVjzEgWPR4TY8xvgXfynnY6BucAd5qkp4AmETmizEmsap4dqxEeX1er9nXIxYrJo9nHaDNwWuo6eg5wrzEmbIz5E/Ba6vvKlhZjzGPGmP7Uw6eAqWPY3qjTUcBHgF8ZY94xxuwHfgWMZYH5kablAuCeMWzPkUN5kM2pjC31MSlGscftOuAGYLDM6SmHYvbxMuD7qeOOMaazwmkshWL20wCTUn9PBv5awfTVZEOxA9iV9Xg3FarwpoasnAg8DUwxxryVeultYEqZNvtvwJVAIvW4BegxxsRSj8u1/zOALuD2VHf4D0WkngrstzFmD/At4C8kG4gHgG1UZr/LpWr5Nl9ePgb4bGq4w20VHLpmgF+KyDYRWZN6rlLnlJ3zya2gVOOYgPMxqEb+cU2eLaFq5rGSqNJ1yK2KyaOZ96SuHwdIXkdLnb9H+n2fJtmDlRYUka0i8pSIjKXBX2w6lqfKuM0iMm2Eny11WkgNw50B/Cbr6VIdk2I4pdWVZW9qaOw0Y8zDZU5LuRRzXGcBs0TkyVQeKHcDvRyK2c9rgVUishv4Ocme9YqpxYZiVYhIA3Af8EVjzMHs10yyv7jk4WVF5Cyg0xizrdTfXQQvyWEaPzDGnAj0kRzalFHG/W4mecdlBnAkUE/57+BNCDb5+AfAscD7SDbKv12hpHzAGDMf+CjwDyLywewXy5W37EhyruvZwE9TT1XrmOSo5DGYiMbj8a3GdUiVnoisAhYCN2U9fbQxZiFwIfBvInJsGZPw/4Dpxph5JHvIfjTM+yvhfGCzMSae9Vwlj8m4ISIW8C/Al6udljLzkhx+uoxkb/OtItJU1RSVxwXAHcaYqSSHQN+V+o0rohYbinuAaVmPp6aeKxsR8ZG8ON9tjLk/9fTe9NCv1P/l6BJfCpwtIm+S7K4+FfgOySER3tR7yrX/u4Hdxph0r9Nmkg3HSuz3h4A/GWO6jDFR4H6Sx6IS+10uFc+3+ezysTFmrzEmboxJALcytqFXRUv1GqeHkvwstd1K5C07HwWeNcbsTaWpKsckxekYVCP/VD3PlkG18tiYVfE65GbF5NHMe1LXj8lAd5GfLXVaEJEPAV8DzjbGhNPPZ5WJbwCPk+w1Lks6jDHdWdv+IbBgJPtQyrRkyR/VUcpjUgyntLqx7G0EjgceT9UPFwEPjrOANsUc193Ag8aYaGp4+E6SDcfxpJj9/DTJGBwYY34PBIHWiqSO2mwobgFmSjICpp9k4TKmaFiFpOYy/AfwR2PMv2S99CCQjn51MfBAqbdtjPmqMWaqMWY6yf38jTFmJfAYsKLM234b2CUis1NPnQZspwL7TXLI6SIRqUsd//S2y77fZVTRfJvPKR/nzXM7F7CNCFfitNSLSGP6b+D01HYrkbfs5MyLqcYxyeJ0DB4ELkpF5lsEHMgaclguVc2zZVKtPDYm1bwOuVwxeTT7GK0geR01qefPl2RU1BkkK6DPlDMtInIicDPJRmJn1vPNIhJI/d1K8sbo9jKmI7uMO5vknFeAR4DTU+lpJlk2PzLKdBSVllR65pAMFPP7rOdKeUyK4VTGlvqYFKPgcTPGHDDGtBpjpqfqh0+RzFNby5yuUiomb/wnyd7EdB6YRTKY0HhSzH7+hWQ9FxF5L8mGYlfFUmhcEPWn1P9Ids3uJBlJ6Gtl3tYHSA7neRF4PvXvYyTnODwKvAr8GjiszOlYxrtRT48heUF7jeRwuUCZtvk+YGtq3/+TZEFekf0G/hF4hWQl/S6Skekqst9l/A0rlm9ttu2Uj+8C/pB6/kHgiAqk5RiSkb9eAF5OH4tKn1OpbdaT7F2YnPVcRY4JycbpW0CU5J3TTzsdA5KR+L6fyjt/oEIR7qqZZyt5fN3+zy3XITf+s8ujwD+RrDhDstL109R14xngmKzPfi31uR3ARyuQll8De7N+wwdTzy9JndcvpP7/dJnT8X9TZe8LJG/Azsn67N+njtVrwOpyH5PU42uB6/M+V+pjYlceXA5cnnrdsYwt9TEp1XHLeu/jjLOop0XmUyE5xHZ76jc5v9ppLtN+zgWeTOX154HTK5k+SSVCKaWUUkoppZQCanPoqVJKKaWUUkqpMdCGolJKKaWUUkqpHNpQVEoppZRSSimVQxuKSimllFJKKaVyaENRKaWUUkoppVQObShOECJyhojsEJHXROTqaqdHqWKIyG0i0ikilVyrUKkxE5FpIvKYiGwXkZdF5AvVTpNSxRCRoIg8IyIvpPLuP1Y7TUoVS0Q8IvKciDxU7bTUAm0oTgAi4iG5/s9HSa7HcoGIzK1uqpQqyh3AGdVOhFKjEAO+bIyZCywC/kHLXTVOhIFTjTEnkFwv+YzUIvNKjQdfAP5Y7UTUCm0oTgwnAa8ZY94wxkSAe4FzqpwmpYZljPkt8E6106HUSBlj3jLGPJv6+xDJiktHdVOl1PBMUm/qoS/1TxfdVq4nIlOBM4EfVjsttUIbihNDB7Ar6/FutMKilFIVISLTgROBp6ubEqWKkxq+9zzQCfzKGKN5V40H/wZcCSSqnZBaoQ1FpZRSqkxEpAG4D/iiMeZgtdOjVDGMMXFjzPuAqcBJInJ8tdOkVCEichbQaYzZVu201BJtKE4Me4BpWY+npp5TSilVJiLiI9lIvNsYc3+106PUSBljeoDH0Lniyv2WAmeLyJskp1idKiI/rm6Sxj9tKE4MW4CZIjJDRPzA+cCDVU6TUkrVLBER4D+APxpj/qXa6VGqWCLSJiJNqb9DwIeBV6qbKqUKM8Z81Rgz1RgznWQ99zfGmFVVTta4pw3FCcAYEwM+CzxCMqDCJmPMy9VNlVLDE5F7gN8Ds0Vkt4h8utppUqpIS4FPkbyr/Xzq38eqnSilinAE8JiIvEjyRvOvjDG61IBSE5AYo4GslFJKKaWUUkq9S3sUlVJKKaWUUkrl0IaiUkoppZRSSqkc2lBUSimllFJKKZVDG4pKKaWUUkoppXJoQ1EppZRSSimlVA5tKCqllFJKKaWUyqENRaWUUkoppZRSObShqJRSSimllFIqx/8PnxAGDz2zc2wAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 900x900 with 30 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nLy2rXKUtwKo",
        "colab_type": "text"
      },
      "source": [
        "### Question 1.1.2:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gOuaxzWsuEzc",
        "colab_type": "text"
      },
      "source": [
        "One thing you might note from the pair-correlation plot is that some of the features look odd. However, these features still work well for linear regression. \n",
        "\n",
        "*    Can you explain why the correlations between Feature 3 and everything else look odd?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7BUPWp-WuT13",
        "colab_type": "text"
      },
      "source": [
        "**Give your answer:** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G_cWc1o-u-E7",
        "colab_type": "text"
      },
      "source": [
        "## Exercise 1.2: Training and Test sets"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mRjjCAMmvFdZ",
        "colab_type": "text"
      },
      "source": [
        "In order to train and evaluate our linear regression model, we first have to divide the dataset into two parts: A training set and a test set.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "742iy28bzVIN",
        "colab_type": "text"
      },
      "source": [
        "### Question 1.2.1:\n",
        "A common practice is to have the training set be 70% of the full set and test set 30%.\n",
        "\n",
        "There are 506 houses in our dataset, so divide your data into 354 in the training set and 152 in the test set.\n",
        "\n",
        "You can use Numpy's slice notation for this, as introducted in the first lectures. For example, to take the first five *rows* from an array you can use the following notation:\n",
        "```\n",
        "data_first_five_rows = data[:5]\n",
        "```\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "To complete this Question, do the following task:\n",
        "*    Divide both of the numpy arrays `features` and `prices` into two parts.\n",
        "*    Use, for example, the Numpy slice notation to achieve this.\n",
        "*    Make sure that the same house in never in both the test and training set at the same time! Other than that, you are free to choose which rows to the test set and which go to the training set."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f75qk7pww1K1",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Make the two sets of features below\n",
        "features_train = features[:354]\n",
        "features_test = features[354:]\n",
        "\n",
        "# Make the two sets of prices below\n",
        "prices_train = prices[:354]\n",
        "prices_test = prices[354:]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c0d3lJE_zc-4",
        "colab_type": "text"
      },
      "source": [
        "## Exercise 1.3: Regression Fit"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cad8uWOTzdB7",
        "colab_type": "text"
      },
      "source": [
        "In the linear least squares regression, we solve an equation that looks like this:\n",
        "\n",
        "$$ \\mathbf{y} = \\mathbf{X} \\mathbf{\\alpha}$$\n",
        "\n",
        "Where $\\mathbf{y}$ is a vector containing the target labels (for example housing prices), $\\mathbf{X}$ is a matrix where the each row contain features (in our case the features for a given house in Boston) for each house. Finally, $\\alpha is a vector containing the (unknown) regression coefficients.\n",
        "\n",
        "Fortunately, Numpy has built-in capabilites for solving linear least squares regression. This is done using the function which performs the \"least squares\" fit:\n",
        "\n",
        "```\n",
        "alpha, residual, rank, singular_values = np.linalg.lstsq(X, y)\n",
        "```\n",
        "\n",
        "As you can see, the function actually returns four items, the first one being the regression coefficients, and the next three are the residuals of the fit, the rank of the matrix problem, and finally the singular values of the matrix.\n",
        "\n",
        "For this exercise we only need to use the first one, but feel free to print and look at the three other items as well.\n",
        "\n",
        "You can see the documentation for `np.linalg.lstsq()` here: https://numpy.org/doc/stable/reference/generated/numpy.linalg.lstsq.html\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A2ORY5BZ2PPz",
        "colab_type": "text"
      },
      "source": [
        "### Question 1.3.1:\n",
        "\n",
        "*    Just like in the code above, use `np.linalg.lstsq()` to fit the alpha regression-coefficients. \n",
        "\n",
        "**Hint:** Use the `features_train` instead of `X` and `prices_train` instead of `y`.\n",
        "\n",
        "**Note:** *Google Colab uses a version of Numpy which might give you a warning abour \"rcond\", which is not a problem.*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DSxMpIjz15kA",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 147
        },
        "outputId": "8eb621cf-3139-48be-839b-d15290756c19"
      },
      "source": [
        "# Get the alpha coefficients \n",
        "alpha, residual, rank, singular_values = np.linalg.lstsq(features_train, prices_train)\n",
        "\n",
        "print(alpha)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[-0.07637644  0.04115234 -0.02369435  2.54631417  0.04041712  6.10926255\n",
            " -0.01919318 -0.87295404  0.11448186 -0.01157476 -0.35137899  0.00886255\n",
            " -0.35929319]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:2: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
            "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
            "  \n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gJylexpu9dTD",
        "colab_type": "text"
      },
      "source": [
        "## Exercise 1.4: Making predictions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gOLtQqUK9dee",
        "colab_type": "text"
      },
      "source": [
        "Now that you have obtained the alpha coefficients in the previous question, it is time to use them to make predictions.\n",
        "\n",
        "Remember how we are approximating the price as a linear sum of the weighted features for a given house:\n",
        "\n",
        "\\begin{equation}\n",
        "f(\\mathbf{x}) = x_1 \\alpha_1 + x_2 \\alpha_2 + \\dots + x_n \\alpha_n\n",
        "\\end{equation}\n",
        "or written in vector notation:\n",
        "\\begin{equation}\n",
        "f(\\mathbf{x}) = \\mathbf{x} \\cdot \\mathbf{\\alpha}\n",
        "\\end{equation}\n",
        "\n",
        "where $\\mathbf{x}$ is the vector containing all the features for the house and $\\mathbf{\\alpha}$ is the vector of regression coefficient you obtained by fitting the features to the prices of the training set."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7j9iFs8DEZcL",
        "colab_type": "text"
      },
      "source": [
        "### Question 1.4.1:\n",
        "\n",
        "With the alpha regression coefficients you found in the previous exercise, you can use your linear least squares \"machine\" to predict the price of house that are not in your training set.\n",
        "\n",
        "As in the equation above, this is done by taking the dot product between the feature vector for a given house and the regression coefficients.\n",
        "\n",
        "Remember, that the features for each house are stored in the rows of the \"features\" numpy arrays you created in Question 1.2.1.\n",
        "\n",
        "*    Calculate the price of all the houses in the test set. That is, take the dot product between the regression coefficients and every row-vector of the `features_test` array.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HirrxfiqGEzI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 495
        },
        "outputId": "d715122c-5899-4ef8-b893-6a1fe46ecec4"
      },
      "source": [
        "# Calculate the prices of the houses in the test set\n",
        "#, i.e. the dot product between \"features_test\" and \"alpha\"\n",
        "prices_test_predicted = np.matmul(features_test, alpha)\n",
        "\n",
        "print(features_test_predicted)"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[27.08891037 19.40768589 40.73604442 14.74809218 20.47140433 22.12963816\n",
            " 17.05747905 34.9702988  24.73185704 15.56529702 12.39884119 39.47063809\n",
            " 26.34010844 28.61534347 22.11361184  3.18403021 26.81028117 29.09876667\n",
            " 18.02380111 21.17361141 31.58247512 26.04626572 17.78535658 19.79125809\n",
            " 25.79350711 18.89456458 20.62019168 17.26913808 22.17780792 15.96777779\n",
            "  5.25537392 31.83600946 42.52094819 18.79530044 16.28459705 14.39752525\n",
            " 17.50229859  9.0630825  23.69766619 34.76964504 14.92175461 29.42299817\n",
            " 12.68160434 11.4095486  25.7283809  29.78209888 27.53029616 16.43034755\n",
            " 32.05528062 44.44065123 15.40174248  1.21258613 35.17710926 35.93682876\n",
            " 30.56069276 21.6886704  39.78606429 29.72725493 26.13632751 20.21009359\n",
            " 25.8010759  21.61063321 24.40576075 19.57518593 16.05095174 20.67048149\n",
            " 16.76494214 24.63346547 20.76028385 24.28298716 24.66337165 25.75692176\n",
            " 21.80124907 11.74836368 41.98719941 33.14918355 24.39680145  4.74327622\n",
            " 23.36998542 24.57347741 18.3432605  14.36578646 18.5252126  19.8870277\n",
            " 16.3526096  22.28521677 16.13198458 29.8903321  31.30195767 19.71691996\n",
            " 33.29908759 20.45076518 17.35093391 33.99351059 17.42632737 26.18499206\n",
            " 31.13949275 15.73894941 19.74703888 21.12887375 21.90239835 27.44500634\n",
            " 12.79628345 26.46402109 38.11585401 22.75966775 20.39941232 24.555675\n",
            " 18.4844471   8.61226014 31.6148623  29.58540095 18.2835844  23.97817612\n",
            " 25.6524885  25.41707772 13.87415922 24.39300916 29.18818841 27.79792975\n",
            " 23.25900244 25.36008706 16.60072053 29.060445   18.97941877 -1.63033123\n",
            " 27.78769895 27.72044381 34.21961564 24.84762105 20.09799795 17.55782539\n",
            " 33.15523117 15.25499585 21.50440107 22.50788458 18.98674393 19.43606724\n",
            " 16.70870136 25.44730446 12.73039663 27.88586237 21.97523425 31.48189927\n",
            " 23.32963543 18.15092789 25.61402465 19.69604668 26.75515522 19.15657774\n",
            " 28.17345794 22.77691171]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jZ5ZhTqQMab6",
        "colab_type": "text"
      },
      "source": [
        "*Hint:* Save the predicted prices for the test set in a list or numpy array, which you can use in question 1.4.2."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-Qa_7aIKFVeF",
        "colab_type": "text"
      },
      "source": [
        "### Question 1.4.2:\n",
        "Since we already know the true price of the houses in ou dataset, we can now compare the true prices of the house \n",
        "\n",
        "Use for example `plt.scatter()` as we did in the introductory lectures.\n",
        "\n",
        "*    Plot the correlation between the true prices stored in the `prices_test` and the predicted prices.\n",
        "\n",
        "Does it look like there is some correlation?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QYU4QANnMurZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "d87f7cc3-31a4-4a74-8fad-a65909a753bc"
      },
      "source": [
        "# Write the code to plot the correlation between \"prices_test\" and the prices  \n",
        "# you predicted in Question 1.4.1.\n",
        "\n",
        "plt.scatter(prices_test, prices_test_predicted)\n",
        "plt.show()"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NDJsRFCxN3rx",
        "colab_type": "text"
      },
      "source": [
        "### Question 1.4.3:\n",
        "\n",
        "One common measure of the prediction error is the \"root mean squared error\" (RMSE) between the true values and the predicted values. The RMSE is calculated as follows:\n",
        "\n",
        "\\begin{equation}\n",
        "\\mathrm{RMSE} = \\sqrt{\\frac{1}{N}\\sum_{i=0}^{N} \\left( y_i^\\mathrm{true} - y_i^\\mathrm{predicted}\\right)^2}\n",
        "\\end{equation}\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7Ni70RBhZKyg",
        "colab_type": "text"
      },
      "source": [
        "*    In this question, calculate the RMSE for your test set, i.e. the RMSE between the true prices and the prices you predicted in Question 1.4.1."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eYO9U5-pZajH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "3bb35eed-0b10-4107-f6ec-7442dc94518f"
      },
      "source": [
        "# Calculate the RMSE \n",
        "error = prices_test - prices_test_predicted\n",
        "rmse = np.sqrt(np.mean(error**2))\n",
        "\n",
        "print(\"RMSE [x $1,000] = \", rmse)"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "RMSE [x $1,000] =  5.662741307904864\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ml0aWTqdFOO4",
        "colab_type": "text"
      },
      "source": [
        "## Exercise 1.5: Linear Regression with Scikit-learn"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EeSKRpzUaxT9",
        "colab_type": "text"
      },
      "source": [
        "As we saw in the lecture, the Python library Scikit-learn has capabilities for almost any type of macine learning you can think of.\n",
        "\n",
        "It also does Linear Regression. Below is the a code example to use linear regression with sklearn.\n",
        "\n",
        "```\n",
        "# Import the machine\n",
        "from sklearn.linear_model import LinearRegression\n",
        "\n",
        "# Make a linear regression machine identically to our fitting in Numpy\n",
        "machine = LinearRegression(fit_intercept=False)\n",
        "\n",
        "# Fit the machine using the training features and training labels\n",
        "machine.fit(x_train, y_train)\n",
        "```\n",
        "\n",
        "After the machine has been fitted, you can use the built-in `predict()` method to make predictions on new feature maps:\n",
        "\n",
        "```\n",
        "# Predict y-values using x_test features\n",
        "y_test_predicted = machine.predict(x_test)\n",
        "```\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7yyahz3HhZVy",
        "colab_type": "text"
      },
      "source": [
        "### Question 1.5.1:\n",
        "\n",
        "*    In this question, use Scikit-learn to train a `LinearRegression` machine on the housing dataset. Use the same training and test data which you used in the previous example.\n",
        "\n",
        "**Hint:** You use the above code snippets to solve this question."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hE-cVxkIf9r1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 495
        },
        "outputId": "0d8f0a82-79e6-4715-b67a-d5995bc6d850"
      },
      "source": [
        "# Implement the linear regression with Scikit-learn\n",
        "\n",
        "from sklearn.linear_model import LinearRegression\n",
        " \n",
        "machine = LinearRegression(fit_intercept=False)\n",
        " \n",
        "machine.fit(features_train, prices_train)\n",
        "\n",
        "prices_test_sklearn = machine.predict(features_test)\n",
        "\n",
        "print(prices_test_sklearn)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[27.08891037 19.40768589 40.73604442 14.74809218 20.47140433 22.12963816\n",
            " 17.05747905 34.9702988  24.73185704 15.56529702 12.39884119 39.47063809\n",
            " 26.34010844 28.61534347 22.11361184  3.18403021 26.81028117 29.09876667\n",
            " 18.02380111 21.17361141 31.58247512 26.04626572 17.78535658 19.79125809\n",
            " 25.79350711 18.89456458 20.62019168 17.26913808 22.17780792 15.96777779\n",
            "  5.25537392 31.83600946 42.52094819 18.79530044 16.28459705 14.39752525\n",
            " 17.50229859  9.0630825  23.69766619 34.76964504 14.92175461 29.42299817\n",
            " 12.68160434 11.4095486  25.7283809  29.78209888 27.53029616 16.43034755\n",
            " 32.05528062 44.44065123 15.40174248  1.21258613 35.17710926 35.93682876\n",
            " 30.56069276 21.6886704  39.78606429 29.72725493 26.13632751 20.21009359\n",
            " 25.8010759  21.61063321 24.40576075 19.57518593 16.05095174 20.67048149\n",
            " 16.76494214 24.63346547 20.76028385 24.28298716 24.66337165 25.75692176\n",
            " 21.80124907 11.74836368 41.98719941 33.14918355 24.39680145  4.74327622\n",
            " 23.36998542 24.57347741 18.3432605  14.36578646 18.5252126  19.8870277\n",
            " 16.3526096  22.28521677 16.13198458 29.8903321  31.30195767 19.71691996\n",
            " 33.29908759 20.45076518 17.35093391 33.99351059 17.42632737 26.18499206\n",
            " 31.13949275 15.73894941 19.74703888 21.12887375 21.90239835 27.44500634\n",
            " 12.79628345 26.46402109 38.11585401 22.75966775 20.39941232 24.555675\n",
            " 18.4844471   8.61226014 31.6148623  29.58540095 18.2835844  23.97817612\n",
            " 25.6524885  25.41707772 13.87415922 24.39300916 29.18818841 27.79792975\n",
            " 23.25900244 25.36008706 16.60072053 29.060445   18.97941877 -1.63033123\n",
            " 27.78769895 27.72044381 34.21961564 24.84762105 20.09799795 17.55782539\n",
            " 33.15523117 15.25499585 21.50440107 22.50788458 18.98674393 19.43606724\n",
            " 16.70870136 25.44730446 12.73039663 27.88586237 21.97523425 31.48189927\n",
            " 23.32963543 18.15092789 25.61402465 19.69604668 26.75515522 19.15657774\n",
            " 28.17345794 22.77691171]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tL9FTkdbiD4l",
        "colab_type": "text"
      },
      "source": [
        "### Question 1.5.2:\n",
        "\n",
        "*    In this question, make a scatter plot between the between housing prices you predicted with Scikit-learn and the true prices.\n",
        "*    Additionally, calculate the RMSE for prices you predicted with Scikit-learn.\n",
        "\n",
        "**Hint:** If everything went well, you should have gotten the exact same plot and RMSE as you found in Questions 1.4.2 and 1.4.3."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sX5YekdUPSXd",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "f0087830-2488-43b5-994f-dd6edb8c8276"
      },
      "source": [
        "# Make a scatter plot for  the housing prices you predicted with \n",
        "# Scikit-learn and the true prices for the test set\n",
        "\n",
        "plt.scatter(prices_test, prices_test_sklearn)\n",
        "plt.show()"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2X662vC8iEAT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "7f38d2dd-efed-4547-9b86-dd5e11d9232a"
      },
      "source": [
        "# Calculate the RMSE for the housing prices you predicted with \n",
        "# Scikit-learn and the true prices for the test set\n",
        "\n",
        "# Calculate the RMSE \n",
        "error = prices_test - prices_test_sklearn\n",
        "rmse = np.sqrt(np.mean(error**2))\n",
        "\n",
        "print(\"RMSE [x $1,000] = \", rmse)"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "RMSE [x $1,000] =  5.662741307904864\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}