Module6_Lab2.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/harika136/IIIT_IHUB_HYD/blob/main/Module6_Lab2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H-Cp5UaReiof"
      },
      "source": [
        "#Regression Lab 2: Loss Functions\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "```\n",
        "Module Coordinator : Sajal Khandelwal\n",
        "```\n"
      ],
      "metadata": {
        "id": "TSBLUen_aWef"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rbxg8WQcetL2"
      },
      "source": [
        "## Motivation\n",
        "\n",
        "The main goal of machine learning tasks is to \"learn\" something about data we feed to our models. But how does the model actually learn anything? To understand this, we need to first understand what objective functions are.\n",
        "\n",
        "Mathematically, objective functions are a function whose values we desire to minimize/maximize. In the context of machine learning, the objective is commonly referred to as a **loss function**. Loss functions indicate how well the model is doing on the dataset. \n",
        "\n",
        "The value of the objective function is simply called **loss**. Our goal is to eventually find the best model parameters that has the least average loss on the data after training.\n",
        "\n",
        "\n",
        "We are familiar with the idea of **error** from the linear regression lab. RMSE is a common loss function used in machine learning. However, there are many other loss functions employed, depending on what the task is (classification, regression etc.). In this lab, we will take a look at some common loss functions, and understand why they are used where they are.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q_TjX0v1Upyt"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "plt.style.use('ggplot')\n",
        "\n",
        "# interactive visualization"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o9lGgMhd9hAX"
      },
      "source": [
        "# 1. Regression\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f9qiER5ef8Sh",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "17ba6dd4-cb6a-4f66-922d-c9d317ad5269"
      },
      "source": [
        "# initializing random data\n",
        "\n",
        "np.random.seed(0)\n",
        "x = np.linspace(0,100,100)\n",
        "y_actual = np.copy(x)\n",
        "y_pred = x + np.random.randint(-10,10,100)\n",
        "\n",
        "plt.plot(x,y_actual,color=\"red\")\n",
        "plt.scatter(x,y_pred,color=\"blue\")\n",
        "plt.show()"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JAOKu9cGhf7t"
      },
      "source": [
        "### Mean Squared Error\n",
        "\n",
        "As we have seen before, the formula for MSE is \n",
        "\n",
        "$MSE = \\frac{1}{m} \\sum_{i=1}^n (y-y_p)^2$\n",
        "\n",
        "The image below depicts a visualization of what the squared error is. \n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=12jmqRrrqknIWKhwRpgRIJAErBjkEcyx9\" width=\"350\" height=\"350\" align=\"middle\"/>\n",
        "\n",
        "MSE is also referred to as L2 loss.\n",
        "\n",
        "Typically, we would want the units of error to be the same as the data, so we use Root Mean Squared Error instead.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y0KIs1xP2AbG",
        "outputId": "20fd9917-db0a-44c4-c392-c16c121c1757"
      },
      "source": [
        "mse = np.mean((y_actual-y_pred)**2)\n",
        "print(\"MSE is: {}\".format(mse))\n",
        "print(\"RMSE is: {}\".format(np.sqrt(mse)))"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MSE is: 38.68\n",
            "RMSE is: 6.219324722186485\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "05Gx5pbfhk3P"
      },
      "source": [
        "### Mean Absolute Error\n",
        "\n",
        "$MAE = \\frac{1}{m} \\sum_{i=1}^n |y-y_p|$\n",
        "\n",
        "MAE is also commonly referred to as L1 loss."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PfqvIN2ThjWO",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "827fa91b-b6d4-4a4a-df3c-ad861b481c18"
      },
      "source": [
        "mae = np.mean(np.abs(y_actual-y_pred))\n",
        "print(\"MAE is: {}\".format(mae))"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MAE is: 5.5\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4j7VlwmH4WVU"
      },
      "source": [
        "MSE penalizes the model for making large errors by squaring the difference. However, this also means that MSE cannot handle outliers well, since they would throw the model off.\n",
        "\n",
        "On the other hand, MAE is robust to outliers. But, MAE is non-differentiable, making it difficult to perform mathematical operations on it.\n",
        "\n",
        "Hence, RMSE is most commonly used as a metric for evaluation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "buXwWqWjhT_9"
      },
      "source": [
        "# 2. Classification\n",
        "\n",
        "Classification tasks involve some data, along with labels assigned to that data. For example, we may have pictures of cats and dogs, and the corresponding labels assigned to those images. We then want to train a model that can predict a label for some input image belonging to either label class (cat or dog)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qiJUcm4vhthC"
      },
      "source": [
        "## The concept of maximum likelihood\n",
        "\n",
        "Ideally, we would want to obtain a model $\\hat{\\theta}$ which maximizes the probability of correctly predicting data. Mathematically, the likelihood is:\n",
        "\n",
        "$ \\prod_{i=1}^{N}  \\: \\hat{\\theta_i}^{\\theta_i}$\n",
        "\n",
        "This is because our actual data ($\\theta_i$) is either 0 or 1 depending on the label of the data, and our predicted data ($\\hat{\\theta_i}$) is a probability. \n",
        "\n",
        "We usually consider the negative log of the likelihood, since log is monotonic and easier to deal with as an optimization problem.\n",
        "\n",
        "Hence, we have\n",
        "\n",
        "$MLE = $ arg min $\\: - \\sum_{i=1}^{N} \\theta_i \\: log \\: \\hat{\\theta_i}$\n",
        "\n",
        "\\\n",
        "\n",
        "\n",
        "## Entropy and Cross-Entropy\n",
        "\n",
        "For some event $x$, we can obtain **information** based on its probability distribution. For example, for some event that occurs with $p=1$, we gain no information. Now, if we flip a coin and see that we obtained heads, we say that we got 1 bit of information. \n",
        "\n",
        "Thus, the information $I$ of some event $x$ is:\n",
        "\n",
        "$I = -log_2 \\: p(x)$\n",
        "\n",
        "We say that events with a low probability of occuring give high information, and those with a low probability give low information.\n",
        "\n",
        "Now, if we have some random variable $X$, its **entropy** is the expected value of the information obtained.\n",
        "\n",
        "$H(x) = - \\sum_{k} p_k \\: log \\: p_k$\n",
        "\n",
        "Now, suppose we are trying to correctly predict labels of some data. Let P be the true distribution of the labels, and Q be the predicted distribution of labels. \n",
        "\n",
        "Cross-Entropy is then defined as:\n",
        "\n",
        "$H(P,Q) = - \\sum_{x} P(x)\\: log \\: Q(x)$\n",
        "\n",
        "which is basically the entropy between two probability distributions over the same events.\n",
        "\n",
        "\\\n",
        "\n",
        "\n",
        "## MLE and Cross-Entropy\n",
        "\n",
        "So, in the case of classification, the equation for minimization of the cross-entropy between the actual data and the predicted data would be:\n",
        "\n",
        "arg min $\\: -\\sum_{i=1}^{N} P(x) \\: log \\: Q(x)$\n",
        "\n",
        "$= $ arg min $\\: -\\sum_{i=1}^{N} \\theta_i \\: log \\: \\hat{\\theta_i}$\n",
        "\n",
        "\n",
        "which is exactly the same as what we had obtained for minimizing the negative log likelihood. Hence, the two problems are equivalent."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "1/1+e^(-x)"
      ],
      "metadata": {
        "id": "UyJN_UiEbbch"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mLKuJyHth5-4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 441
        },
        "outputId": "7b124cd3-4cb4-4328-a2d1-fab00a027b6b"
      },
      "source": [
        "def sigmoid(z):\n",
        "  return 1/(1 + np.exp(-z))\n",
        "\n",
        "def cross_entropy_loss(y_,y):\n",
        "  if y==1:\n",
        "    return -np.log(y_)\n",
        "  \n",
        "  return -np.log(1-y_)\n",
        "\n",
        "z = np.arange(-10, 10, 0.1)\n",
        "h_z = sigmoid(z)\n",
        "\n",
        "cost_1 = cross_entropy_loss(h_z, 1)\n",
        "cost_0 = cross_entropy_loss(h_z, 0)\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(8,6))\n",
        "plt.plot(h_z, cost_1, label='y=1')\n",
        "plt.plot(h_z, cost_0, label='y=0')\n",
        "plt.xlabel('predicted probability')\n",
        "plt.ylabel('loss')\n",
        "plt.legend(loc='best')\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjgAAAGoCAYAAABL+58oAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAAsTAAALEwEAmpwYAABPBUlEQVR4nO3deXxU9b3/8deZmUwm62SZhBASQDaV1bKogAsKWrValVal1vZ6rVYr/m69Xaze3lvt7bXibbXVFq+7vba3rdZaa9VqxQ0FWkFwAUEQULZA9j2TzMz5/v44yUBYA0xyJpP38/HgkZnJyeQz34Tknc/3e77HMsYYRERERFKIx+0CRERERBJNAUdERERSjgKOiIiIpBwFHBEREUk5CjgiIiKSchRwREREJOX43C7gSOzYsaNXnjcUClFdXd0rzy0HpnF3j8beHRp3d2jc3dHb415aWrrfx9XBERERkZSjgCMiIiIpRwFHREREUk6/XIMjIsnFGEM4HMa2bSzLcruchDLG4PF4CAQCKffaRFKZAo6IHLVwOExaWho+X2r+SIlGo4TDYTIyMtwuRUR6SFNUInLUbNtO2XAD4PP5sG3b7TJE5DAo4IjIURsIUzcD4TWKpBIFHBEREUk5CjgiMqA99thjzJw5kyFDhlBbW+t2OSKSIAo4IjKgTZs2jd///veUlZW5XYqIJJACjoikhJ/85Cc89NBD8fsLFizg4YcfPuTHjR8/nvLy8t4sTURckLqnPYiIK+zfP4TZujmhz2mVH4Nn3jUHPWbevHlcffXVXHPNNdi2zbPPPsuTTz7JWWedtd/jFy5cyJgxYxJap4gkjz4JOPfddx8rV64kGAxy1113AdDc3MzPfvYzqqqqKCoq4l//9V/Jzs7ui3JEJAWVl5eTn5/P6tWrqaqqYty4cZSVlfHyyy+7XZqIuKBPAs6sWbM455xzWLhwYfyxZ555hgkTJnDRRRfxzDPP8Mwzz3DFFVf0RTki0osO1WnpTV/60pd48sknqaysZN68eTQ3N3PxxRfv91h1cERSW58EnLFjx1JZWdntseXLl3PbbbcBcPrpp3Pbbbe5GnBMfS0du7ZiCkqw0tJcq0NEjty5557LT3/6U6LRKAsXLsTr9aqDIzJAubbIuKGhgfz8fADy8vJoaGhwqxQAzAcrqPv3+dDkbh0icuT8fj8zZszgggsuwOv19uhjHnnkEaZMmUJFRQVz5szhO9/5Ti9XKSJ9ISkWGVuWddBdQhctWsSiRYsA58yIUCiU8Bpas7NpAgoK8vH2wvPLgfl8vl75msqhJWrsd+3alRSXarBtm1WrVvHwww/3uJ5rr72Wa6+99pDHpaenJ+z7VN/z7tC4u8OtcXftJ1IwGKSuro78/Hzq6urIzc094LFz5sxhzpw58fvV1dUJr8dubgagtrYWi5795SeJEQqFeuVrKoeWqLFvb2/vccekt6xfv55/+qd/4pxzzmHo0KFEo9GEPn97e3vCvk/1Pe8Ojbs7envcS0tL9/u4awFn6tSpvPHGG1x00UW88cYbTJs2za1SujNuFyAiR2LMmDEsW7bM7TJEZA8Pr9hFU6yKfz2pqM8/d58EnJ///Od8+OGHNDU1cd1113HppZdy0UUX8bOf/YxXX301fpq4q3QhPRERkYSqbIlQE3anc9AnAefGG2/c7+M/+MEP+uLTHya1cERERPo7Xaqhizo4IiIiKUMBZ29GHRwREZFEcPM3qgJOnDo4IgPRli1bOP/885k5cybXXXcdHR0dbpckklLcmiBRwNmbOjgiA8rtt9/ONddcw5IlSwgGg/zud79zuyQRSQAFnC5q4Ij0az/5yU946KGH4vcXLFjAww8/fNCPMcawZMkSPve5zwFwySWX8NJLL/VqnSLSN9zfejRpKOGIJMLDK3axuS6c0Oc8Jj/A1VMHHfSYefPmcfXVV3PNNddg2zbPPvssTz75JGedddZ+j1+4cCGhUIhgMBjf9Xjw4MHs3LkzobWLiDsUcPamKSqRfqm8vJz8/HxWr15NVVUV48aNo6ys7KAX26ytre3DCkUGHjd/pSrgdNFp4iIJcahOS2/60pe+xJNPPkllZSXz5s2jubmZiy++eL/HLly4kNGjR9PQ0EA0GsXn81FRUUFJSUkfVy2S2tz67aqAsw91cET6q3PPPZef/vSnRKNRFi5ciNfrPWgHB2DGjBk8//zzXHjhhfzhD3/g7LPP7qNqRaQ3aZFxFzVwRPo9v9/PjBkzuOCCC3p88c/vf//7PPjgg8ycOZO6ujq+9KUv9XKVItIX1MHZmxo4Iv2WbdusXLmSBx54oMcfM2zYMJ5//vlerEpE3KAOTpxaOCL92fr165k5cyannHIKI0aMcLscEQHc7Bqog7M3nUUl0i+NGTOGZcuWuV2GiOxFOxm7TWdRiRwxMwD+MBgIr1Ek0dz8b6OAsw/9EBM5XB6Ph2g06nYZvSYajeLx6MelyOFyfqO600DQFJWIHLVAIEA4HKa9vR0rxbqhxhg8Hg+BQMDtUkT6Je2DkyzUwBE5bJZlkZGR4XYZIiJx6rl2if/VqYQjIiKSKFpk7LYUa6uLiIi4TYuMk4nOlBAREUkIg3trcBRw4tTBERERSTiXZkgUcPamBo6IiEhCuPkrVQGnk5bgiIiIJJgxmqJKHmrhiIiIJIrOonKbWjgiIiIJpSmqZKKzqERERBJGU1SuUwdHREQkkdTBSSrq4IiIiCSEAculBoICThc1cERERBJPi4yThBo4IiIiCaEpqqTQGTG1yFhERCQhdKmGZKDTxEVERBJO++AkDXVwREREEsLFWREFnC5q4IiIiCScpqiShRo4IiIiCaFFxklBLRwREZFEMgbXFuEo4OxDLRwREZFE0RSV23QWlYiISMpQwNmb9sERERFJCO2DkxTUwREREUk07YOTLNTAERERSQg3J0UUcLqogSMiItILdBZVklALR0REJBG0D04y0FlUIiIiCWa0Bidp6CwqERGRhNFZVK7r/BIo4IiIiCSEFhknA81QiYiIJJSLV2pQwBEREZHeY+ksKrephSMiIpIqFHD2pjU4IiIi/Z4CThedJi4iIpJQWmScVNTBERERSQQtMk4GauCIiIgknPbBSRZq4IiIiCSIe79UFXDi1MIRERFJJGM0RZU8dBaViIhIAmkfHHfpLCoREZGE0tXEk4o6OCIiIomiKapkoXwjIiLS7yngdNEUlYiISEIZ494pPD6XPm/cc889x6uvvoplWZSXl3P99dfj9/tdrEgtHBERkUQZkFNUtbW1/PWvf2XBggXcdddd2LbN0qVL3SlGHRwREZGEGtCLjG3bpqOjg1gsRkdHB/n5+e4WpNPERUREEsOAW5NUrk5RFRQUcMEFF/CNb3wDv9/PpEmTmDRp0j7HLVq0iEWLFgGwYMECQqFQwmvp2JlHHRAMBvH3wvPLgfl8vl75msqhaezdoXF3h8a973l8W/B6LFfG3dWA09zczPLly1m4cCGZmZncfffdLF68mNNOO63bcXPmzGHOnDnx+9XV1QmvxTQ0ANBQX4/VC88vBxYKhXrlayqHprF3h8bdHRr3vheJRMGYXh330tLS/T7u6hTVBx98QHFxMbm5ufh8Pk466STWr1/vTjFagiMiIpJwlktrXF0NOKFQiA0bNtDe3o4xhg8++IAhQ4a4VE3nF0BrcERERBLCNuBxqYHg6hTV6NGjOfnkk/ne976H1+tl+PDh3aai+lT8K6CAIyIikggG41oHx/V9cC699FIuvfRSt8sAq7OZZSvgiIiIJIJxsYPj+mniScPSFJWIiEgi2WaArsFJKl0dHGO7W4eIiEiKMMa4FjQUcLp09dBsBRwREZFEsAGPOjgui3dwNEUlIiKSCMYM0GtRJZWuDo6mqERERBLCGKMOjuvUwREREUkoG3Vw3Nf5FTA6TVxERCQhnNPE1cFxl86iEhERSSjj4qyIAk4X7YMjIiKSUAZt9Oc+nSYuIiKSUEYb/SUBTVGJiIgklJsX21TA6eLRWVQiIiKJZNBp4u6zNEUlIiKSSLY2+ksC2gdHREQkoYwBD+rguEtnUYmIiCSUwaiD4zpdqkFERCShbG30lwS6pqi0BkdERCQhdLHNZKCzqERERBLGGKON/pKCpSkqERGRROlqF2ijP7fFp6jUwRERETlaXRMiLjVwFHDidBaViIhIwnT9NtUiY7fpUg0iIiIJ03UlcS0ydpsutikiIpIwXSs+1MFxm6aoREREEmb3ImN3Pr8CThePpqhEREQSxe6aonLp8yvgdNFZVCIiIgnTteLD59JGOAo4nSxNUYmIiCRMrPP3qUcBJwl4PJqiEhERSYBYZ7/Aq0XGScDjATvmdhUiIiL9XqxzyYdXHZwk4PFCTB0cERGRo9W1yFgBJwlYPp86OCIiIgnQdc6OFhknA48XYlG3qxAREen34lNUWoPjPsurKSoREZFEiC8yVgcnCWiKSkREJCG0yDiZaIpKREQkIbr2wdEUVRKwfD5NUYmIiCSArSmqJOLxaopKREQkATRFlUQsrxejKSoREZGjFp+icilpKODsyefbfXUwEREROWJdKz60BicZaJGxiIhIQmgn4yTiLDLWGhwREZGjFe/gKOAkAY9XU1QiIiIJEFMHJ3k4OxlrikpERORodQUcn9bgJAFNUYmIiCSEpqiSicergCMiIpIAWmScRCyvNvoTERFJhKg2+ksiXk1RiYiIJEKk83LiaS7t9KeAsyevpqhEREQSoauD4/eqg+M6Zx8cnUUlIiJytLo6OD6POjius3xpCjgiIiIJoA5OMknzQyTidhUiIiL9XsQ2WGiRcVKw/H6IKuCIiIgcrUjMkOa1sLTRn/ssXxpEOtwuQ0REpN+L2IY0l7o3oIDTnT8dbBujM6lERESOSiRm8Lm0/gYUcLqx0tKcG5qmEhEROSoR2+BTByc5WGl+54amqURERI5KVFNUScTfGXDUwRERETkqXYuM3aKAswfL19XBUcARERE5GlHbVgcnWVjq4IiIiCSE2x0cn2ufuVNLSwv3338/W7duxbIsvvGNbzBmzBh3iulaZKw1OCIiIkfF7dPEXQ84jz32GCeccALf/va3iUajtLe3u1aLlZbu3NAUlYiIyFGJxAyZfq9rn9/VKarW1lbWrl3LmWeeCYDP5yMrK8u1enSauIiISGI4HRz3Pr+rHZzKykpyc3O57777+PTTTxkxYgRXXnklgUCg23GLFi1i0aJFACxYsIBQKNQr9cTqKwHIzcggvZc+h+zL5/P12tdUDk5j7w6Nuzs07n3LWJ+SnRFwbdxdDTixWIzNmzdz1VVXMXr0aB577DGeeeYZ5s2b1+24OXPmMGfOnPj96urqXqknaDmttMbaaqxe+hyyr1Ao1GtfUzk4jb07NO7u0Lj3rZZwBMuOEI1Ge3XcS0tL9/u4q1NUhYWFFBYWMnr0aABOPvlkNm/e7Fo9XWdRGa3BEREROSrhmCHd617McDXg5OXlUVhYyI4dOwD44IMPKCsrc68g7WQsIiKSEO1Rm3SfezHD9bOorrrqKu69916i0SjFxcVcf/31rtVipXeu/elw70wuERGR/s42ho6YIeAbwKeJDx8+nAULFrhdBgBWIMO50R52txAREZF+rD1qAFzt4Ggn4z3EOzhhBRwREZEj1R61AQgo4CQHy+OB9AC0t7ldioiISL/VHnMCTroutplE0gPg4m7KIiIi/V24c4pKHZxkog6OiIjIUQl3TlFpDU4ySc/AaJGxiIjIEdManGQUCOgsKhERkaOw+ywqrcFJHv4AhDVFJSIicqQ0RZWM1MERERE5Kl1nUQUG6qUakpGVroAjIiJyNNoiTsDJSFPASR7pGQo4IiIiR6GlM+BkKuAkEXVwREREjkprR4yAz8Lr0SLj5BHIgEgHJhp1uxIREZF+qSVik5nmdbUGBZy9ZWY5b9ta3K1DRESkn2qN2K5OT4ECzr66Ak6rAo6IiMiRaO2IkeVXwEkqVma2c6O12d1CRERE+ilNUSWjrg5OiwKOiIjIkWjp0BRV8uns4BitwRERETkirRFNUSWfrikqdXBERESOSKumqJJQfJGxAo6IiMjh6ojZdMSMOjjJxvKngy9NZ1GJiIgcgcb2GADBdJ+rdSjg7E9mljo4IiIiR6Ax7ASc3IC7U1Q9jlerV6+muLiY4uJi6urq+L//+z88Hg+XX345eXl5vViiC7JyMFqDIyIicti6Oji56f1kDc4jjzyCx+Mc/vjjjxOLxbAsiwceeKDXinNNTi40N7hdhYiISL+ze4qqn3RwamtrCYVCxGIx3nvvPe677z58Ph/XXnttb9bnjpwgbP/U7SpERET6nYawcy3HftPBycjIoL6+ng8//JCysjICgQAA0RS8KKWVmweN6uCIiIgcrsb2GB4Lsvz9pINzzjnncMsttxCNRrnyyisBWLduHUOGDOmt2tyTkwetzZhoBMuX5nY1IiIi/UZje4xsvxevx3K1jh4HnIsuuogTTzwRj8dDSUkJAAUFBVx33XW9VpxrcvOct02NkF/oaikiIiL9SWN7zPXpKTiMgANQWloav7169Wo8Hg9jx45NeFFus3KCGIDGegUcERGRw5AsAafHa3BuvfVW1q1bB8AzzzzDPffcwz333MPTTz/da8W5pquD01jvZhUiIiL9Tn1blKDLe+DAYQScrVu3MmbMGABeeeUVbr31Vm6//XZefvnlXivONblBAExTvbt1iIiI9DO1bVEKMt1fv9rjKSpjDAA7d+4EoKysDICWlhS8pIE6OCIiIoetNRKjNWITynD3Mg1wGAHn2GOP5dFHH6Wuro5p06YBTtjJycnpteJck54Bfr8CjoiIyGGobXW2jinIdD/g9HiKav78+WRmZjJs2DAuvfRSAHbs2MF5553Xa8W5xbIsCBZAfa3bpYiIiPQbNW1OwAn1pymqnJwcLr/88m6PTZ48OeEFJY2CIkxtldtViIiI9Bs1nR2cwiTo4PS4gmg0ytNPP83ixYupq6sjPz+f0047jblz5+Lzuf9CEs3KD2HWr3a7DBERkX6jpjUCQEF/WoPzm9/8ho0bN3LNNddQVFREVVUVf/zjH2ltbY3vbJxS8guhvgZjx7A87p/uJiIikuxqWqPk+D2k+3q8AqbX9LiCv//979x0001MmjSJ0tJSJk2axHe+8x2WLVvWm/W5pyAEtg0N9W5XIiIi0i/UJMkp4nAYAafrNPGBwsovcm7UVbtbiIiISD9R0xollATrb+AwpqimT5/OnXfeyRe/+EVCoRDV1dX88Y9/5OSTT+7N+txTEHLe1lbBiGPdrUVERKQfqG6NMCI/3e0ygMMIOFdccQV//OMfeeSRR6irq6OgoIAZM2bwxS9+sTfrc0/RIABM1S7cvR6qiIhI8muL2DSEY5Rk+90uBThEwFm9uvtZROPGjWPcuHEYY5y9YoB169Yxfvz43qvQJVYgE3KCUFXhdikiIiJJb1dzBwAlOcmxBuegAed//ud/9vt4V7jpCjq//OUvE19ZMigqwVQq4IiIiBxKRbNzini/6OAsXLiwr+pISlbxYMz6NW6XISIikvQqmpKrg+P+ierJrKgE6qoxkYjblYiIiCS1nU0RctK9ZPuTY+84BZyDKRoMxkD1LrcrERERSWo7mzsoyU6O7g0o4ByUVTzYubFru7uFiIiIJLmKpg4G5yTH+htQwDm4wWUAmIqtLhciIiKSvNoiNpUtUcqDCjj9gpWZDXmFsEMBR0RE5EC2NbYDMDSYHJv8gQLOoZUOxezY4nYVIiIiSWtLvQJOv2OVlsPOrRjbdrsUERGRpLSloYM0j8UgLTLuR0qHQkeHzqQSERE5gK0N7ZQF/Xg9yXNxIwWcQ7BKhzo3NE0lIiKyX1sb2ilPoukpUMA5tCFDwbIw2za7XYmIiEjSaW6PUdkSZVieAk6/YgUyYdAQzCcfu12KiIhI0vm4NgzA6MKAy5V0p4DTA9bwUfCpAo6IiMjeugLOyHwFnP5n2Cior8XU17hdiYiISFL5uCbM4Jw0stOT4xpUXRRwesAaPsq58elGdwsRERFJMhtr2xhVkFzdG1DA6ZnyEWB5tA5HRERkDw3hKJUtUUYl2fobUMDpESs9AKXlmE/Wu12KiIhI0vi4xll/M6ogw+VK9qWA00PWyONg4zqMHXO7FBERkaTwYVUbXgt1cA7Etm1uuukmFixY4HYpBzZmPLS1wlbthyMiIgLwwa5WRhVmEPAlRZzoJikqeuGFFxgyZIjbZRyUdex4AMxHq12uRERExH3hqM3HNW1MGJTpdin75XrAqampYeXKlcyePdvtUg7KyiuE4lLMegUcERGRdVVtxAyMK06+9TcAPrcL+NWvfsUVV1xBW1vbAY9ZtGgRixYtAmDBggWEQqFeqcXn8x30uRsnTiG87HUK8/OxvMl1vn9/dqhxl96jsXeHxt0dGvfE2ri+Ga8FM48rI8t/4Djh1ri7GnDeeecdgsEgI0aMYM2aNQc8bs6cOcyZMyd+v7q6ulfqCYVCB31ue9hozKK/UP3eCqyhI3ulhoHoUOMuvUdj7w6Nuzs07om1/JMaRhYEaGus58Atit4f99LS0v0+7mrA+eijj1ixYgWrVq2io6ODtrY27r33Xv7lX/7FzbIOyBozHgOYde8r4IiIyIDVGomxoaaNzx9X4HYpB+RqwLn88su5/PLLAVizZg1/+ctfkjbcAFgFIRgyDPP+Cjj7YrfLERERccW7FS1EbZhSmu12KQfk+iLj/saadCJsWINpaXa7FBEREVcs395Mtt/D8UXJucAYkijgjBs3jptvvtntMg7JmjgNbBuz+h23SxEREelzMduwYnsLk0uz8Xost8s5oKQJOP3GMWMgJwjvve12JSIiIn1ufU0bje0xpg1J3ukpUMA5bJbHgzVxKmb1Skw06nY5IiIifWr5Nuf08MmlWW6XclAKOEfAmngitLXAxx+6XYqIiEifent7M+OKM8n2J/d+cAo4R2LsCeD3Y1YudbsSERGRPrOloZ2tDR2cWJbc01OggHNErEAG1oRpmBVLMDFdXVxERAaG1zc14LHg1GG5bpdySAo4R8g68TRoaoB177tdioiISK+L2YbXP2lk8uAs8jJcv9LTISngHKkJUyAjC/P3192uREREpNetrmylpjXKGSOCbpfSIwo4R8hK82NNOxWzcgmmrdXtckRERHrV65sbyEzzJP3p4V0UcI6Cdcoc6OjALF/sdikiIiK9Jhy1WbqliZlDc0j39Y/o0D+qTFbDR0PpUMxbi9yuREREpNcs29JEOGr6zfQUKOAcFcuysE77LGxej/lkg9vliIiI9Iq/bqijNCctqa89tTcFnKNkTT8T0gOYV593uxQREZGE21DTxkfVYc4bk4/HSt5rT+1NAecoWZlZWNPPxCx/E9PU4HY5IiIiCfXC+joCPosz+9H0FCjgJIR15ucgGsG89oLbpYiIiCRMTWuExZ80ccYxQbKS/NIMe1PASQBrcDlMOhHz2nOY9rDb5YiIiCTEX9bVYRvDRccXuF3KYVPASRDPOXOhuQnz1stulyIiInLUmjtivLihnplDcyjJ8btdzmFTwEkQa9RYGDUW89KfMJGI2+WIiIgclec/qqMtajN3bKHbpRwRBZwE8lwwD+qqMW++5HYpIiIiR6y5Pcaf19ZyUlk2IwoCbpdzRBRwEun4STBmPOaFP2Da292uRkRE5Ij8eV0tLRGbyyeG3C7liCngJJBlWXgu/DI01GFee87tckRERA5bfTjKs+vqmDk0h+H5/bN7Awo4CWeNGQcTpjpdHO2LIyIi/cxv36smErO5fFL/7d6AAk6v8Fzyz9Aexjz7O7dLERER6bFP69t5eWM9547Jpyw33e1yjooCTi+wBpdjnX4OZvGLmO1b3C5HRETkkIwxPLqyksw0D5dN6N/dG1DA6TXWBZdDIBP7t/+DMcbtckRERA5q6ZYm3q1oYd6EELnp/WvX4v1RwOklVk4u1hevhPVrMEtfcbscERGRA2rpiPHQil2MLEjnvDH5bpeTEAo4vciaOcfZ/O8Pj2nBsYiIJK3fvFdFQ3uMb5xYgtfTf64YfjAKOL3I8njwXHE9hNswv33A7XJERET2sXpXK39dX895Y/IZXZjhdjkJo4DTy6whQ7EumIdZ8Rb224vdLkdERCSuNRLjnmUVDMpO4ysnFLldTkIp4PQB65wvwIhjMf93P6a+xu1yREREAHj0nUqqWiLcOH0wAV9qRYLUejVJyvJ68fzzjRDtwH705xg75nZJIiIywC3b2sTLGxu4eGwBxxdnul1Owing9BGrZAjWvK/D2vcwLzzldjkiIjKA7Wru4BfLKhhVEOjX15s6GAWcPmSdchbWSadjnv0dZt37bpcjIiIDUCRm+MlbOwC46dRS0rypGQVS81UlKcuysK64HgYNxn74Lkyd1uOIiEjfenTlLjbUhPl/0wczKNvvdjm9RgGnj1mBDDzX3QzhMPbC2zEd7W6XJCIiA8SLG+p4YX09Fx1fwPTyHLfL6VUKOC6whgzDc/W3YMtGzK/u1aUcRESk132wq4UHl+9iSmkWX02xU8L3RwHHJdYJJ2Fd/BXM8jcxzz/hdjkiIpLCKpo6uHPxdgbn+Pn2zNKU2a34YHxuFzCQWed8AXZsxfz5t9jBAjynnu12SSIikmLq2qLc+upWsCz+fVYZWf7+fyHNnlDAcZFlWfBPN2Ca6jG/vg+TE8Q64SS3yxIRkRTR0hHjh69tpb4tyo/mDGVwTuouKt6bpqhcZvnSnEXHw0dhP/gTzPo1bpckIiIpoCNm8+PF29lS387Npw3h2FDqXGeqJxRwkoAVyMDz/34AhUXYv/hPzMZ1bpckIiL9WEfM5sdvbGfNrlb+ZfpgJpdmu11Sn1PASRJWTi6eb/8X5OZj//xWhRwRETkiHTGbO97YzqqKFm44uYRZxwTdLskVCjhJxMorxPOd2xVyRETkiHTEbBYs3s7KihZuOKmEOSPz3C7JNQo4ScbK7wo5edg/+wHmw1VulyQiIv1AayTGf762jXd2tDD/pBLOGpXndkmuUsBJQlZ+IZ7v3gFFJdj3/gh7+VtulyQiIkmsvi3K91/ewoeVrfzrjMGcPcDDDSjgJC0rrwDPd38MI8ZgHvoJ9msvuF2SiIgkoV3NHdz88qdsa+zg304vG7BrbvamgJPErMxsPDf+ECZOw/z2fuynHsPYMbfLEhGRJPFRdRs3vfQpTe0xfjR7KFOHDLyzpQ5EASfJWf50PN+4BWvWeZiX/oR93x2YcKvbZYmIiMve2NzA91/eQsDn4Y6zh3Fc0cDa5+ZQFHD6AcvrxfPl67AuvxY+WIG94HuY6l1ulyUiIi6wjeHX71Zx99IKjg0F+MlnhzE0mO52WUlHAacf8ZzxOTzfvBVqq7Fv/7bOsBIRGWCa22P8+I3tPLWmhrNGBrntzKHkBnTVpf1RwOlnrLGfwfNvP3FOI//5bdjP/k7rckREBoANNW38618/YVVFM9dMLWb+SSWkeVP/quBHSgGnH7JKyvD820+xTpqF+cvvsO/5Iaapwe2yRESkFxhjeGF9HTf/bQu2Mfz4rGGcf2yBc8FmOSAFnH7KSg9gXXUj1ldvgPVrsP/zm5gP33W7LBERSaCm9hg/eWsHDyzfxaSSTH523jED7qKZR0oTd/2YZVlYp56NGTYK++G7sH/2A6zZF2DN/SqWXwvORET6s1UVLdy7rIKGcJSvnFDE3LEFeNS16TEFnBRgDR2B59/vxjz9OOaVv2A+fBfP176FNWyk26WJiMhhao/a/O+qSp5fX0950M9/zBrOiIKA22X1Owo4KcLyp2PNuwYzcSr2Y/dg3/EdrPMuwTr3Eqy0NLfLExGRHviwspWF/9jJtsYOLjgun69MKiLdp9UkR0IBJ8VYYz+D57ZfYH77IOYvv8esWILnq/OxRo11uzQRETmAlo4Yj79bxYsb6inO8vHDM8s5YXCW22X1awo4KcjKysG65tuYk2dh/9//YN95M9asc7Eu/ipWpv7DiIgkk2Vbm3hw+S7qw1E+f1w+l08sIiNNXZujpYCTwqwJU/Dc9gvMn/8P88pzmHf/gXXJVVjTTtXphSIiLtvZ1MGjKyv5x7ZmjslP599OH8LoQp0hlSgKOCnOCmRgXXY15sTTsX+zEPPQTzGvv4Bn3jVYQ7UIWUSkr4WjNk+truGZtbV4PfDVE4q48PgCfB794ZlIrgac6upqFi5cSH19PZZlMWfOHM477zw3S0pZ1jGj8Xz/LsxbizB/+jX2f30L69TPYl10BVZOrtvliYikPGMMb37axK9WVlLTFuX04bn802eKKMzUiSC9wdWA4/V6+cpXvsKIESNoa2vj5ptvZuLEiZSVlblZVsqyPF6s0z6LmTrTWYD86nOYFW86Z1ud8TntnSMi0kvWVrbyq1VVrKtuY2RBgO+eWsrxRZlul5XSXA04+fn55OfnA5CRkcGQIUOora1VwOllVma2M2116tnYf3gM89SvMK88h3XBPKwZs7G8XrdLFBFJCZ/Wt/Prd6tYvr2Z/ICX+SeVMHtEEK+mo3qdZYwxbhcBUFlZya233spdd91FZmb3VLto0SIWLVoEwIIFC+jo6OiVGnw+H9FotFeeO5l1rF5F86/vI7J+Dd6y4WR/+VrSTzqtzxYiD9RxTwYae3do3N3Rl+O+szHMw3/fwotrK8nye/ny1DIuOaGUjLSB9wdkb4+73+/f7+NJEXDC4TC33norc+fO5aSTTjrk8Tt27OiVOkKhENXV1b3y3MnOGAOr/o79p1/Dzm1wzBg8F8yD8VN6PegM5HF3m8beHRp3d/TFuFe3Rnh6TQ0vfdyABXzu2Hy+MK6Q3PSBF2y69Pa4l5aW7vdx18+iikaj3HXXXZx66qk9CjfSOyzLgsnT8Uw6EbP0FczzT2Lf+58wbBSe8y+FSSfp1HIRkQPY1dzBH9fU8sqmBowxnDkiyGUTQhRlaQGxW1wNOMYY7r//foYMGcL555/vZinSyfJ6nQt4Tj8T84/XMS/8AXvhj6FsOJ7zL4PPTMfyaAMqERGAiqYOnlpTw2ubGrAsi7NGBpk7tpDibAUbt7kacD766CMWL17M0KFD+e53vwvAl770JSZPnuxmWQJYPh/WzDmYk8/ALF/sdHTuvxNKyrDOvgjr5FlYafuf9xQRSXUbatr489palmxpwuexOGdMPnPHFhDSKd9JIynW4BwurcHpe8aOYd5Zinnxj7BlE+QEnVPLZ5131PvoaNzdo7F3h8bdHUc77rYxrNjezJ/X1rK6so0Mn4fPjs7jwuMLKMhwfcVH0hqwa3Ckf7A8Xqxpp2KmngIffYD9t2cwz/4W8+JTWNPPxJpzIVbJELfLFBFJuPaozRufNPLM2lq2N3YQyvRx1eRizhoVJHMAnhXVXyjgyGGxLAuOm4j3uImYHVswL/8Zs2QR5o0XYfxkPLPOgwlTsDz6Ty8i/dvOpg5e3FDPok0NNLXHGFmQzrdnljJjaI4uq9APKODIEbNKh2L90//DXHQF5o2/Yhb/DfuX/wWFxVinn4N1yllYOUG3yxQR6bGYbVhV0cIL6+tYuaMFy4KTyrL53LH5jC/O1Nmk/YgCjhw1K5iP9fnLMeddCu/9A/u1FzBPP4559rdYU0/BOv1cGHmcfjCISNJqCEd5ZWMDL35cz67mCPkBL5dOKOTsUXlaONxPKeBIwlg+H0yZiXfKTGf66vW/Ypa9ivn7687ZV6fMwTr5DKxgvtuliogQsw0rd7SwaFM9y7c1EzMwvjiDfzqhiJPKNQ3V3yngSK+wSodiXX4tZu5XMMvfctbpPPUrzNOPw4SpeE6ZA+OnOqFIRKQPbWts55WNDby2qYG6cIxgupcLjitg9sggQ4O66HCq0G8X6VVWIBPr1LPh1LMxFducXZKXvYr93tvOqebTzyByzkWY7HxNYYlIr2luj7F09U6efX87a6va8FgwpTSbOSODTB2SrW5NCtI+OHvQ3hR9w8RisHol9pKX4f3lEIvB4HKsk07HOvE0rKISt0scMPQ97w6Ne99oj9qs2N7MG5808s6OFqK2YUiunzkjgswaEdTeNX1E++DIgGF5vTBpGt5J0zBNjWR99B5NrzyPeeY3mGd+4yxIPvE0Z4Fybp7b5YpIPxKzDe/vamXxJw0s29JMW9QmP8PHeWPy+PwJQwl5wuoWDxAKOOIqKyeXzHMupnXqqZiaSszbbzrXwPrdg5gnHobjJmFNnYl1wkk65VxE9itmG9ZUtrJ0SxPLtjZRH46RmeZhxtAcTj8ml/HFmXg9FqFQDtXV7W6XK31EAUeShlVYjHXuF+DcL2C2fYJ5+w3MiiWYx3+J+fV9cOx4rMkzsD5zMlZegdvlioiLorbhg12tLN3SyD+2NtPQHsPvtZhSms3pw3OZMiQLv1cXBh7IFHAkKVllw7HKhmMu/ips3excB2vlEsxv78f87gEYdbwTdiZPxyoocrtcEekDkZjNeztbWbKlibe3NdHcYRPweZg2JIvpQ3OYUppNwKdQIw4FHElqlmXB0BFYQ0dgLvoy7NiKWbkU884SzBMPO9NYQ0dgTToRa9KJMHSk5tdFUkhDOMo7O1p4e1sTqypaCUdtstI8TCvLZsbQHD4zWJ0a2T8FHOk3LMuCIUOxhgyFC+Zhdm7HrPo75v23Mc89ifnL7yGvAGviiViTpsFxE7H82tNCpD8xxrC1sYPl25p5e1szH1W3YYCCDB+zjsnlxCHZTCzJIs2rP2Tk4BRwpN+ySobsXrPT1ID5YAXmveWYf7yBWfwi+NNh7AlYE6ZijZuMVaipLJFk1B61+bCqjXe2N7N8ezM7myMAjCxI57IJhZxYlsOI/HR1Z+WwKOBISrByglgzZsOM2ZhIBD76wOnsvPc25t1/YMDZa2f8ZKxxk2HMOKw0v9tliwxIxhi2N3WwakcLK3e0sLqylY6YIc1jMbEkk4uOL2BaWbauASVHRQFHUo6VlgbjJ2ONn4z50rXOup01K51/rz2PefnP4PfDmAm7A8+gUv11KNKLWiMx3t/ZyqoKJ9RUtjhdmtIcP2ePymPy4CzGD8okXYuEJUEUcCSldVu3c/ZFmPYwrF+NWb0Ss2YV5vcPOd2dgiKs4yc6++4cN1GnoYscpUjM5qPqMO/tbOGDXa2sr24jZiDg8zCpJJO5YwuYXJrFoGx1UqV3KODIgGKlB2DCVKwJUwEwVTudzs7a9zCr/gFLXtk9nXXcRKzjJzn772Rmu1q3SLKL2YZNdWHe39nK+7ta+bBz2sljwciCABcdX8BnSrM4LpSpBcLSJxRwZECzikqwZp0Hs87D2DFnz5117zuBZ8kizGvPg+VxTkU/fhLWmPHOpSQys9wuXcRVtjF8Wt/OmspWPtjVyupdrTR32AAMDTrTThMHZTJuUCbZfq/L1cpApIAj0snyeGHYKKxho+CzczHRCGxaj1n3nhN6Xv4z5sU/OoGn/BisMeOcwDNqLFZOrtvli/SqqG3YVBtmTWUrayrb+LCqlZbOQFOclcbJ5TlMKsliwqBM8nURS0kC+i4UOQDLl+acbTVmHHz+ckx7O2xah9mwBrN+DeaNFzGLnnUOLh3qHDfaOd7KK3S3eJGj1BGz2VATZs2uVtZUtrKuuo1w1ADOwuCZQ3MYV5zJ2KJMirN1tpMkHwUckR6y0tPh+EnOuhxwTkf/dIMTdjaswSx7HV7/q7OGp7AYa+RxznTWyOOhbLhzFXWRJFXTGuGj6jbWVbWxrrqNjbVhok6DhmF56cweEXQCTbE6NNI/6LtU5AhZaWnO9NSoscAlmFgMtm3GrF8DG9dh1q+Gtxc7gcefDseMwRp5PNao42DEsVhZOS6/AhmoYrazfmZtZ5hZV9UWP207zWMxujDA548r4LhQBmOLM8lJVziX/kcBRyRBLO8ea3jOuhBjDNRWYzaudQLPxnWYF5/C2J1/Fg8uxzpmDBwz2nk7ZDiWT/8lJfGqWyNsqA6zvqaN9TVhPq7ZPd1UkOHj+KIMLjgun2NDGYzID+gsJ0kJ+mkq0kssy4LCIucSESeeBuDsw/PJBszHa53A88EKWNp5arovDYaNxBo+2un2HDMGikq0AaEcltZIjA014Xig2VATprYtCoDPA8fkB5g9IshxRZkcX5RBKNOn7zFJSQo4In3ISg/AsROwjp0AOFvWU1OJ2bwBPlmP2bQe8+ZL8MpfnNCTleN0eIaPxho2EoaOgvxC/UISwLmG0+a6djbWhvm4to311WG2N3Y43zs4i4EnDspkdCjA6MIMRuSnk6Yrb8sAoYAj4iLLsiA0CCs0CKadAuCs5dmxBbN5vdPt2fQRZs27GNM5tZUT7JwKG+lMhw0bCfkhhZ4UF47abK4N83FtmI21YTbVtrO1sR27M80EA17GFAY4fXguo0MZjCoIaO2MDGgKOCJJxvJ6nX12yo+B0z4LdE5tbd2M2bIRPt2I+fRjzIerdq/nyQk6mxEOG4U1dCSUH+MEJ4/+Wu+PmjtifFrXzqa63YFme2NHPMzkBbyMLAhwUnk2owoCjCwMUJihqSaRPSngiPQDVnoARh2PNer4+GOmvd05a2vLRvj0Y8ynmzAv/nF36AlkQNkxWOXDoXyEE5hKh2L50915EbIPYwyVLRE217XzSWeg2VzXHj+jCSA/w8eognRmDs1hREGAUQUBChRmRA5JAUekn7LS0zv32Tku/pjpaHemt7Zuhq2bMFs/wSx7DV57wVmX4fHAoCFY5SNg6DG0j5uEyc6HYL5+Yfay9qjN1oYOPqkPs3NNA2t31LO5rp2WiBNILaA018+YUIDPjs7jmLx0jukMMyJy+PQ/RySFWP50GO4sSu5ibBuqdzlTXFs3YbZ9gvl4Dbz9BvVPdR6UneOcpj5kGAwZtvttIMOdF9KPxWzDruYIn9a382l9O590vt3ZvHuKKeDzMCzPz6nDczkmP51j8gMMy0sn4NOUokiiKOCIpDjL44HiwVA8GGvKjPjjprmRYFMd9R++D9s/dYLPkkXQHo6fhUNRyR6BZzhWaTkUlzqbHA5wxhhq26Jsa+yIh5lP69vZUt9Oe8wZQQsoyUljWF46pw7PYVheOsPy0pkwvJS62hp3X4BIilPAERmgrOxc/MNH4Bk8LP6YsW2oqYRtn2C2fwLbPsVs/xTz3nIw9u5prqLBzkaFg8uct6XlUFLmrBVKMbYxVDZH2NbYwZaGdrY1dLCt0XnbNb0EEEz3MiwvnbNH5cWDzNADdGW8Hk0HivQ2BRwRibM8HqdrU1SC9ZmT44+bSAdUbMVUbIMdWzE7t0LFNswHyyEW293xKSyGwWVYJeVQukcA6geXpYjEDBXNHWzrDDFbGzrY2tjO9sYOOmLxV0hewEtZMJ3ThudSHkynLOhnWDCdPK2VEUkq+h8pIodkpflh6EjnFPQ9mGgUqiqc8LOjM/Ts3Opch6tj94Zz5OZ1dnzKnQA0uBwGl7uyuLk9arN9r27M1oYOKpo62CPHUJzloyw3nYmDMikLplOe66csmK69ZUT6CQUcETlils/nBJXB5ViTdz8en+raua0z+GzF7NyG+ccb0NayO/hkZO0OPCVDsIpLYdAQKC5xQtUR6lofs72xg4qmCDuaOtja0M62xg4qmyPxz++xYHCOn7JcPyeX51Ae9FOW63RltOBXpH9TwBGRhOs21TVhavxxYww01HVOd3V2fCq2OtfkWrJod/CxLMgPwaBSrEGlzsLm4lIYNNjZwNCXhjGGhnCMHU0dzr/GDnY0Rahocrox7Xu0Y/xeiyG5fsYUOtdhKgv6Kc9NZ3COXxeWFElRCjgi0mcsy4K8AsgrwDp+Urf3mdYWqNyB2bUDKitg13ZMZQWN7yxnh5VJRUbI+ZcZYkfOYCrSC2jz7D6by2vBoOw0huT6mViSSWmOn8E5fobk+inM9OHRPj8iA4oCjoi4rqUjRkWblx0MYkdmPhUFo9mR1kFFsIOmYbvPVPJgKLI6KI00cGzTOkprtzK4qYLS1iqK2uvxejxQNMjp+HR1fjrfmvwCLI/Wz4gMFAo4ItLrYrahujXCzuYIu5oj7GzqiN/e1dxBU4fd7fhQpo/SHD8zhuZSmptGaY6f0hw/g7LTul0N2xgDjfVOt6ez82Mqd8CuHZi170Fkj4XOPh8UDoKiQVihEmeqq2gQhDqn0jIy+2w8RKT3KeCIyFEzxtDcYbOzucMJMJ3BpSvEVLVE4rv4gjOdVJydxqBsP6MKcxmUnUZJdlp8Wim9hwt8LcuCYOelJsaM716TbUN9jRN2du2A6l2Y6p1QtQuzaT20NmP2/IDsHAiVYBU54YeiEucq76FBUFDkXARVRPoNBRwR6ZFIzFDVEtknxOzqDDF7bnoHzsZ3g7LTOLYwg9OGOSHGCTLOmpje3uzO8nigoMgJJ3ut9wEwLc3OJSyqd2KqOoNP9U7MJxtg5dLu+/t4PM4eP6FBnQGoxOn+dIWhzGxdy0skySjgiAgA4ahNZUuEquaI87YlQlVLlMoW535dW7RbxyPNY8VDy/FFGQzK9sc7McXZaWSmJXfHw8rKhqxsGDaSvaOJicWc7k9VZ/ip3uXcrt6FWbkMmhu7d38CGU4AKijCChV33i7GKixybufmKQCJ9DEFHJEBoGsKqapld3ipbInQEKliW10zlS1Rmtpj3T7Ga0FRVhpFWWmcMDiL4ixftxCTn5G6ZyZZXq8TTAqLsY6buM/7Tbi1M/TswlRVQE0VpqbSebtxLbS2OMd1fYAvzekmFRZhhQbRXD4MO5C9OwDlFWoKTCTBFHBEUkDMNtSFo1S3RDs7L92DTGVLlHC0+xRSutdicDBAQbqPUQUZFGelUZTlc95mp5Ef6P1ppP7KCmRC2TFQdsw+3R8A09bqbHRYUxkPPtRUYmqrMO+9Tcubf3OO6/oAjwfyCp0A1Nn9IVSMVVAEBSHID+nK7iKHSQFHJMnZxlAfjlHTGqG6JUp1a4TqVifIVLc69+vaot0W8QJk+z0UZaUxOMfPxJIsirPSOkNMGsVZPnLSvRQVFVFdXe3OC0thVkYmlA2HsuH7DUCFOTlUb1gHtZWYzvDTFYbM+jVQvxhsu/s0WGaWs/lhQRFWfqgz+BR23i5ybvvT++YFivQDCjgiLjLG0Ngec4LKHoFlz/u1bRH2ar7g91qEMn2EMtOYVJJJKDONws77RZ2dmGRfAzOQWenpWCVDnMtT7Of98TVANZWYuhqorYa6KkxtNdRVYzavh+ZG59g9PzA7d3fHJx6CQlidb8kvxPKl7ecziqQeBRyRXhKJ2dS2RaltjVLTFqWmNRq/X9sWiT+255WqAXweJ7wUZvo4viiDUGYOoay0eKAJZTrdFy1aTV3d1gAd4BgT6YC6aqitjgcfaqsxddVOMNrwIbQ2O8fGn9hyLnyaV+jsJp1fCMECJ/h0viWvEDKz9P0l/Z4Cjshhso2hMRyjtjOg1LRF4rfr4o/tu2gXnM5LQYaPggwfowoCnFTWGVw6A0xRZhq5AW/KLt6VxLHS/FDcuVvzAY4x7eHd3Z94J6jauV1T6SyIbm5yjt3zA/1+J/jkFWDlFTrBZ58gVHBUF0QV6W0KOCJ7aI3EdnddOjsuNXt2XTpDzF5NFywgrzO4FGencVxRBoUZPgoynccKM9MozPCR5ffoL2PpM1Z6AAaXOVdsP8AxJtIB9bXQUIupq3Wmxuqdt6a+FvPpx/DeP6Cjwzl+zw/Oytl9bbE9gpDVGYDIK4ScoLMnkUgfU8CRlNd1inRd2Akn3f6FY9S17Z46att7sQuQmebpDCk+JgzKpDAzzenCZPriIUZnHEl/ZaX5d1/5/QDHGGOgrQXqdgefriBk6mugrgaz/VNoqAez1+Jorxdy853AE8zHCuY794P5WME8pzOUm+/sFZSm9UGSOAo40m9FbUN9t9AS6wwt+4aY6N6nGLF7uig/w8ewvHQmD87aHVwyfRRkOEEmI01/fcrAZlkWZGY7/4YMPXAQisWca4PV7xWE6mowDbXOZokb10FTg3P83k+QleOsEQrmY+XmQ15XGMpzpsY6b5OVo06oHJICjiQVu7PbUh+O0hB2QktXiKlti1LfFWTCURr3s8YFIDfdS36Gj/yAlyG5mc7tDB95AWe6KC/D6wQXn6aLRBLJ8nqdaar8QmD0gYNQNOqEnMY6qK/DNNZBg/Ov67bZtM55LLKfqTGvzwk68U7QHkGo87H4Ncq0TmjAUsCRXhe1DQ3hKA1hJ6zUd77tut8a20lVUxv14RiN4X3Xt4BzZlFBhpe8gI+SnDSOL87oDDE+8jO88RATTPeR5lVoEUlmls+3OwgN4+BTY+G2fcJPt/s1lZhNHzmnzRuzb1coMysehOqLBmEHMiEn6KwNys2H3GDn/TysdO0jlEoUcOSItEft/YaV+nCM+rYoDe2db8NRmjr2XdcCzhRRXsBLKDtAKNPHyIIAeQEfeQEvwc63eQEnuGRrca7IgGNZFmRkOv8OsGdQFxOLQVO9sw6osQ6zdxBqqCO64UNMfR20tzkfs/eTpGfsDjy5eVidwYfcve/nQVa2Fk8nOQUcAZyt/ps6YjSGYzS2x2g4QHhxHo8Sju6nzQJkpXni4aQ8mM6EQZnkBXwEA17yMnzkpTtvgwFvfIooFAppN10ROSqW19u5v0+hc38/x3T9rDHt7U4YamqAxgZMU72zdmjP+1U7nc5QUyMY54+0bj/1LA/k5O4RhvL2Ckd58WBETlC7TLtAASdFRWKGxnYnnHQFlsb2rtux7u9rj9HcHtv3rxmcHxK56U4nJZjhZUwowwkre3RYgnu89Xv1F42IJDcrPR3SB0FokHP/IMca24aWJmhsgKZ6TFODE4a67ncGI1P9kfNYT7pD2blYObnOztPZTkiy4rdzITsIGZnqWh8lBZx+Ihy14yFl79DSdX/P0NIa2f+0kMeCHL+X3ICXYLrTZRkf8JKb7iUY8JKb7gSVYGeoyUn36vRnERmwLI8nvmYHDnwGWZd9ukONdc7tzmBkmhqczRa3bILmBohGnY/b+4m8vs4AlLM7AOXsDkRk5+7xWBCyc3QZjr24HnDeffddHnvsMWzbZvbs2Vx00UVul9Tr2qM2je0xmtpj8a5KU3vMmSLqut0ZWBrDTodl7+38u/g8xENJbrqXQYX+eHjJ6QwtwXRf/LEsvwKLiEhvOazukDHQHnbCT3MTNDdgmhqd4NPcCE2NmOZGp0O0dbNzXOflN2A/oSgjKx6IunWJ4oEo2O39qd4lcjXg2LbNI488wr//+79TWFjILbfcwtSpUykrK3OzrB4zxtAasXeHk7DztmmP0LK/8HKgsALOGpacznCSF/AxNJhOMODbo8Pijd/PTfeSmabFtyIi/ZFlWRDIcP4VlTiPHeJjTCzmTJk1NTohqFsoanLCUHOj0yXqCkXRiPOxez/Znl2irJzOENR1Owey9rqfnetcp8zTPy7k62rA+fjjjykpKWHQICfpzpgxg+XLl7sScGK2oaEtwvbGDhrbo93DSdftvcJLU3tsv6c0g/NNmt0ZQnL8XkKZaYzID8TDS27XW7+XnIDzNjvdi0/dFREROQDL63UWLufm7X7sIMfHu0SdHSGaG51psubdocg0d4aliq2YliYnQMWcfcb2+RXXteljPATldIag3HgI2jskmdycBI9Cz7gacGprayksLIzfLywsZMOGDa7U8reP67l/+Uf7fZ/XIh5IctK9lOX6nduda1ly/F2hxRcPL1l+jy6YKCIirurWJerBtBnssf9Qc6PTFWppxDR3Bp/O+/Fg1FDrXKajpckJUuwbimrKj4Ef3JP4F3cIrq/B6YlFixaxaNEiABYsWEAoFEr455hJBhnZOeT4PQQDaQQDPoIZzttMv1fTQL3I5/P1ytdUDk1j7w6Nuzs07r3LRDqwmxqwmxoxjfXx276MTPwujLurAaegoICampr4/ZqaGgoKCvY5bs6cOcyZMyd+vzf2TMkFvjixpPO5Y86/SDttEWhL+GeTPWkfHPdo7N2hcXeHxr0vWJAVdP4Ndh7p7XEvLS3d7+OubloycuRIKioqqKysJBqNsnTpUqZOnepmSSIiIpICXO3geL1errrqKm6//XZs2+aMM86gvLzczZJEREQkBbi+Bmfy5MlMnjzZ7TJEREQkhWhffREREUk5CjgiIiKSchRwREREJOUo4IiIiEjKUcARERGRlKOAIyIiIilHAUdERERSjgKOiIiIpBwFHBEREUk5CjgiIiKSchRwREREJOUo4IiIiEjKsYwxxu0iRERERBJJHZw93HzzzW6XMCBp3N2jsXeHxt0dGnd3uDXuCjgiIiKSchRwREREJOUo4Oxhzpw5bpcwIGnc3aOxd4fG3R0ad3e4Ne5aZCwiIiIpRx0cERERSTkKOCIiIpJyfG4X4IZ3332Xxx57DNu2mT17NhdddFG390ciEX75y1+yadMmcnJyuPHGGykuLnan2BRyqHF/7rnneOWVV/B6veTm5vKNb3yDoqIid4pNIYca9y5///vfufvuu7njjjsYOXJk3xaZgnoy7kuXLuUPf/gDlmUxbNgwvvnNb/Z9oSnoUGNfXV3NwoULaWlpwbZtLr/8ciZPnuxOsSnivvvuY+XKlQSDQe6666593m+M4bHHHmPVqlWkp6dz/fXXM2LEiN4tygwwsVjM3HDDDWbnzp0mEomY73znO2br1q3djnnxxRfNAw88YIwx5q233jJ33323G6WmlJ6M+wcffGDC4bAxxpiXXnpJ454APRl3Y4xpbW01P/jBD8y//du/mY8//tiFSlNLT8Z9x44d5rvf/a5pamoyxhhTX1/vRqkppydjf//995uXXnrJGGPM1q1bzfXXX+9GqSllzZo1ZuPGjeZb3/rWft//zjvvmNtvv93Ytm0++ugjc8stt/R6TQNuiurjjz+mpKSEQYMG4fP5mDFjBsuXL+92zIoVK5g1axYAJ598MqtXr8ZoLfZR6cm4jx8/nvT0dABGjx5NbW2tG6WmlJ6MO8ATTzzBhRdeSFpamgtVpp6ejPsrr7zCZz/7WbKzswEIBoNulJpyejL2lmXR2toKQGtrK/n5+W6UmlLGjh0b/17enxUrVnDaaadhWRZjxoyhpaWFurq6Xq1pwAWc2tpaCgsL4/cLCwv3+UW65zFer5fMzEyampr6tM5U05Nx39Orr77KCSec0AeVpbaejPumTZuorq5Wiz6BejLuO3bsoKKigv/4j//g+9//Pu+++24fV5maejL2l1xyCW+++SbXXXcdd9xxB1dddVVflzng1NbWEgqF4vcP9TsgEQZcwJHkt3jxYjZt2sTnP/95t0tJebZt8/jjj/PVr37V7VIGHNu2qaio4NZbb+Wb3/wmDzzwAC0tLW6XNSAsWbKEWbNmcf/993PLLbfwi1/8Atu23S5LEmzABZyCggJqamri92tqaigoKDjgMbFYjNbWVnJycvq0zlTTk3EHeP/99/nTn/7ETTfdpOmSBDjUuIfDYbZu3coPf/hD5s+fz4YNG/jv//5vNm7c6Ea5KaOnP2emTp2Kz+ejuLiYwYMHU1FR0delppyejP2rr77K9OnTARgzZgyRSERd+l5WUFBAdXV1/P6Bfgck0oALOCNHjqSiooLKykqi0ShLly5l6tSp3Y6ZMmUKr7/+OuCcWTJu3Dgsy3Kh2tTRk3HfvHkzDz30EDfddJPWIyTIocY9MzOTRx55hIULF7Jw4UJGjx7NTTfdpLOojlJPvt9PPPFE1qxZA0BjYyMVFRUMGjTIjXJTSk/GPhQKsXr1agC2bdtGJBIhNzfXjXIHjKlTp7J48WKMMaxfv57MzMxeX/s0IHcyXrlyJf/7v/+LbducccYZzJ07lyeeeIKRI0cydepUOjo6+OUvf8nmzZvJzs7mxhtv1A+eBDjUuP/oRz9iy5Yt5OXlAc4Poe9973vuFp0CDjXue7rtttv4yle+ooCTAIcad2MMjz/+OO+++y4ej4e5c+cyc+ZMt8tOCYca+23btvHAAw8QDocBuOKKK5g0aZLLVfdvP//5z/nwww9pamoiGAxy6aWXEo1GATj77LMxxvDII4/w3nvv4ff7uf7663v958yADDgiIiKS2gbcFJWIiIikPgUcERERSTkKOCIiIpJyFHBEREQk5SjgiIiISMpRwBGRg5o/fz7vv/8+AE8//TT3339/r3/ONWvWcN111/X65wF4/fXX+Y//+I8j+thD1fnggw/y1FNP7ffYb33rW/F9cEQk8XxuFyAi/cfcuXN7dNzChQspLCxk3rx5vVxRcvv6179+wPfdfffd8dtPPvkkO3fu5F/+5V/6oiyRAUEdHJEBJBaLuV1CnxuIr1lE1MER6ffmz5/PnDlzWLx4MfX19UybNo2rr74av9/PmjVr+MUvfsE555zD888/z8SJE5k/fz7PPvssr7zyCi0tLYwfP56vf/3rZGdnA87FTn//+98TDoc5//zzu32uvTsN69at4ze/+Q3btm0jIyODyy67jGg0yltvvQXA888/z7hx47j55pupra3l0UcfZe3atQQCAT73uc9x3nnnAdDR0cFDDz3EihUryMvL44wzzjjoa7700ku58soreeGFF2hra2PWrFl8+ctfxuPx8Prrr/PKK68wcuRIFi9ezNlnn83nP/95Hn30UVatWkV6ejqzZ8/m4osvxuPZ/TfeI488wuLFi8nPz+drX/saEyZMAOC1117j2WefpaamhtzcXC688ELOOuusbvU8/fTTPP/88wQCAebNm8epp54KHLyTNX/+fK699lps2+ZPf/oTAMuXL6ekpIS5c+fyzDPPcOedd8aPf+655/jwww+56aabDvEdISKggCOSEt566y2+//3vEwgEuPPOO3n66afjv1Tr6+tpbm7mvvvuwxjDiy++yPLly7ntttvIzc3lscce4+GHH+bGG29k27ZtPPTQQ9xyyy2MHj2a3/72t90uXLinqqoqfvzjH/P1r3+dk08+mba2Nmpqahg+fDgfffRRt1/stm1z5513Mm3aNG688UZqamr40Y9+RGlpKSeccAJ/+MMf2LVrF7/4xS8Ih8Pccccdh3zNy5cvZ8GCBYTD4fhzzZ49G4ANGzYwY8YMHnroIWKxGA8++CCtra388pe/pKmpidtvv538/HzOPPPM+PEnnXQSjzzyCG+//TY//elPWbhwIdnZ2QSDQb73ve8xaNAg1q5dy49//GNGjhzJiBEj4uPb1NTE/fffz4YNG7jjjjsYOXIkpaWlPfranXDCCVx88cXdgmMkEuHBBx9k27ZtlJWVAU7w7OkUoYhoikokJXz2s58lFAqRnZ3NxRdfzJIlS+LvsyyLSy+9lLS0NPx+Py+//DLz5s2jsLCQtLQ0LrnkEv7xj38Qi8X4+9//zpQpUxg7dixpaWlcdtllB7zQ7FtvvcWECRM45ZRT8Pl85OTkMHz48P0eu3HjRhobG/niF7+Iz+dj0KBBzJ49m6VLlwKwbNky5s6dS3Z2NqFQiHPPPfeQr/nCCy+MH3/eeed1e835+fmce+65eL1efD4fS5Ys4fLLLycjI4Pi4mLOP/98Fi9eHD8+GAzyuc99Dp/Px4wZMygtLWXlypUATJ48mZKSEizLYuzYsUycOJF169Z1q+Wyyy4jLS2NsWPH8pnPfCb+uo5UWloaM2bM4M033wRg69atVFVVMWXKlKN6XpGBRB0ckRQQCoXit4uKiqitrY3fz83Nxe/3x+9XVVXx05/+tFtw8Xg8NDQ0UFtbS2FhYfzxQCBATk7Ofj9nTU1Njy9CW1VVRV1dHVdeeWX8Mdu2Of744wGoq6vr9nn3fD0HsufxRUVF1NXV7ffjGxsbicViBx2jgoKCbuOx5/tXrVrFU089xY4dOzDG0N7eztChQ+PHZmVlEQgEDljLkTr99NO55557mDdvHosXL2b69OmkpaUd9fOKDBQKOCIpoLq6utvtgoKC+P29OzCFhYV84xvf4LjjjtvnefLz89m+fXv8fnt7O01NTfv9nIWFhXz88cf7fd/enzMUClFcXMy999673+Pz8vKoqamhvLx8n9dzIHsfn5+fv9/jcnNz8Xq9VFdXx6d79h6j2tpajDHxuqurq5k6dSqRSIS77rqLG264galTp+Lz+fjv//7vbs/f0tJCOByOh5zq6up4XT21vy7ZmDFj8Pl8rF27lrfeeotvfvObh/WcIgOdpqhEUsBLL71ETU0Nzc3NPP3000yfPv2Ax5511ln8/ve/p6qqCnA6HMuXLwfg5JNP5p133mHdunVEo1GeeOIJjDH7fZ5TTz2VDz74gKVLlxKLxWhqauKTTz4BnCmfXbt2xY8dNWoUGRkZPPPMM3R0dGDbNlu2bIkHpOnTp/OnP/2J5uZmampqePHFFw/5mp999lmam5uprq7mhRdeYMaMGfs9zuPxMH36dH73u9/R1tZGVVUVzz33XHwhMEBDQwN//etfiUajLFu2jO3bt/OZz3yGaDRKJBKJh6RVq1bF9wTa05NPPkk0GmXt2rWsXLnyoOO/P8FgkKqqKmzb7vb46aefzqOPPorP59tvIBWRA1MHRyQFnHLKKfzXf/0XdXV1TJ06lS984QsHPLbrzKWu44PBINOnT2fatGmUl5fzta99jXvuuYf29nbOP//8blNBewqFQtxyyy38+te/5oEHHiAzM5PLLruM4cOHc+aZZ3L33Xdz5ZVXMnbsWG666Sa+973v8fjjjzN//nyi0SilpaVcdtllAFxyySU89NBD3HDDDeTn53PGGWfwwgsvHPQ1T506lZtvvpnW1lZmzZoVXzC8P1dddRWPPvooN9xwA36/n9mzZ3c7U2v06NFUVFTwta99jby8PL71rW/Fp+b++Z//mZ/97GdEIhGmTJnC1KlTuz13Xl4e2dnZXHvttfj9fq655hqGDBly0Nr3Nn36dN58802+9rWvUVxcHD976rTTTuOJJ5446NdTRPbPMgf680xE+oWu040nTpzodil95tJLL+Xee++lpKTE7VJ6VUdHB1dffTV33nkngwcPdrsckX5FU1QiIknqb3/7GyNHjlS4ETkCmqISEUlC8+fPxxjDd7/7XbdLEemXNEUlIiIiKUdTVCIiIpJyFHBEREQk5SjgiIiISMpRwBEREZGUo4AjIiIiKef/A0Ba6YRsF0IPAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## KNN-regression\n",
        "\n",
        "Till now, we have studied KNN as a classification algorithm, which uses feature similarity and voting to decide the class labels of unseen data. \n",
        "\n",
        "For regression, we use the same idea: We take the y-values of the k nearest neighbours, and compute their average, which is our predicted y-value. We do this for every x whose value we want to predict.\n",
        "\n",
        "In the visualization below, we have k=3, and the red dots are the new x-values whose output we want to predict.\n",
        "\n",
        "![image.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "f42L9ZmuWVIQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import neighbors\n",
        "from sklearn.metrics import mean_squared_error \n",
        "from math import sqrt\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import MinMaxScaler\n",
        "import numpy as np"
      ],
      "metadata": {
        "id": "cQIX2HoAbqqD"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "train_path = \"https://raw.githubusercontent.com/PranavTadimeti/Regression-lab2/main/BigMart-train.csv\"\n",
        "\n",
        "train = pd.read_csv(train_path)"
      ],
      "metadata": {
        "id": "VLMVfcylWlWB"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Preprocess Data\n",
        "\n",
        "def preprocess(df):\n",
        "  mean_weight = df['Item_Weight'].mean()\n",
        "  df['Item_Weight'].fillna(mean_weight,inplace=True)\n",
        "\n",
        "  mode_size = df['Outlet_Size'].mode()\n",
        "  df['Outlet_Size'].fillna(mode_size,inplace=True)\n",
        "\n",
        "  df.drop(['Item_Identifier','Outlet_Identifier'],axis=1,inplace=True)\n",
        "\n",
        "  return pd.get_dummies(df)\n",
        "\n",
        "train = preprocess(train)\n",
        "\n",
        "train.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        },
        "id": "bkMzDwYaYTlQ",
        "outputId": "5bec2207-e5f5-4762-b4cd-934d1e11fa50"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   Item_Weight  Item_Visibility  Item_MRP  Outlet_Establishment_Year  \\\n",
              "0         9.30         0.016047  249.8092                       1999   \n",
              "1         5.92         0.019278   48.2692                       2009   \n",
              "2        17.50         0.016760  141.6180                       1999   \n",
              "3        19.20         0.000000  182.0950                       1998   \n",
              "4         8.93         0.000000   53.8614                       1987   \n",
              "\n",
              "   Item_Outlet_Sales  Item_Fat_Content_LF  Item_Fat_Content_Low Fat  \\\n",
              "0          3735.1380                    0                         1   \n",
              "1           443.4228                    0                         0   \n",
              "2          2097.2700                    0                         1   \n",
              "3           732.3800                    0                         0   \n",
              "4           994.7052                    0                         1   \n",
              "\n",
              "   Item_Fat_Content_Regular  Item_Fat_Content_low fat  Item_Fat_Content_reg  \\\n",
              "0                         0                         0                     0   \n",
              "1                         1                         0                     0   \n",
              "2                         0                         0                     0   \n",
              "3                         1                         0                     0   \n",
              "4                         0                         0                     0   \n",
              "\n",
              "   ...  Outlet_Size_High  Outlet_Size_Medium  Outlet_Size_Small  \\\n",
              "0  ...                 0                   1                  0   \n",
              "1  ...                 0                   1                  0   \n",
              "2  ...                 0                   1                  0   \n",
              "3  ...                 0                   0                  0   \n",
              "4  ...                 1                   0                  0   \n",
              "\n",
              "   Outlet_Location_Type_Tier 1  Outlet_Location_Type_Tier 2  \\\n",
              "0                            1                            0   \n",
              "1                            0                            0   \n",
              "2                            1                            0   \n",
              "3                            0                            0   \n",
              "4                            0                            0   \n",
              "\n",
              "   Outlet_Location_Type_Tier 3  Outlet_Type_Grocery Store  \\\n",
              "0                            0                          0   \n",
              "1                            1                          0   \n",
              "2                            0                          0   \n",
              "3                            1                          1   \n",
              "4                            1                          0   \n",
              "\n",
              "   Outlet_Type_Supermarket Type1  Outlet_Type_Supermarket Type2  \\\n",
              "0                              1                              0   \n",
              "1                              0                              1   \n",
              "2                              1                              0   \n",
              "3                              0                              0   \n",
              "4                              1                              0   \n",
              "\n",
              "   Outlet_Type_Supermarket Type3  \n",
              "0                              0  \n",
              "1                              0  \n",
              "2                              0  \n",
              "3                              0  \n",
              "4                              0  \n",
              "\n",
              "[5 rows x 36 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-b717adb9-41b8-4ccf-b692-60d15c411a2b\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Item_Weight</th>\n",
              "      <th>Item_Visibility</th>\n",
              "      <th>Item_MRP</th>\n",
              "      <th>Outlet_Establishment_Year</th>\n",
              "      <th>Item_Outlet_Sales</th>\n",
              "      <th>Item_Fat_Content_LF</th>\n",
              "      <th>Item_Fat_Content_Low Fat</th>\n",
              "      <th>Item_Fat_Content_Regular</th>\n",
              "      <th>Item_Fat_Content_low fat</th>\n",
              "      <th>Item_Fat_Content_reg</th>\n",
              "      <th>...</th>\n",
              "      <th>Outlet_Size_High</th>\n",
              "      <th>Outlet_Size_Medium</th>\n",
              "      <th>Outlet_Size_Small</th>\n",
              "      <th>Outlet_Location_Type_Tier 1</th>\n",
              "      <th>Outlet_Location_Type_Tier 2</th>\n",
              "      <th>Outlet_Location_Type_Tier 3</th>\n",
              "      <th>Outlet_Type_Grocery Store</th>\n",
              "      <th>Outlet_Type_Supermarket Type1</th>\n",
              "      <th>Outlet_Type_Supermarket Type2</th>\n",
              "      <th>Outlet_Type_Supermarket Type3</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>9.30</td>\n",
              "      <td>0.016047</td>\n",
              "      <td>249.8092</td>\n",
              "      <td>1999</td>\n",
              "      <td>3735.1380</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>5.92</td>\n",
              "      <td>0.019278</td>\n",
              "      <td>48.2692</td>\n",
              "      <td>2009</td>\n",
              "      <td>443.4228</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>17.50</td>\n",
              "      <td>0.016760</td>\n",
              "      <td>141.6180</td>\n",
              "      <td>1999</td>\n",
              "      <td>2097.2700</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>19.20</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>182.0950</td>\n",
              "      <td>1998</td>\n",
              "      <td>732.3800</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>8.93</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>53.8614</td>\n",
              "      <td>1987</td>\n",
              "      <td>994.7052</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 36 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-b717adb9-41b8-4ccf-b692-60d15c411a2b')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-b717adb9-41b8-4ccf-b692-60d15c411a2b button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-b717adb9-41b8-4ccf-b692-60d15c411a2b');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "train , test = train_test_split(train, test_size = 0.3)\n",
        "\n",
        "x_train = train.drop('Item_Outlet_Sales', axis=1)\n",
        "y_train = train['Item_Outlet_Sales']\n",
        "\n",
        "x_test = test.drop('Item_Outlet_Sales', axis = 1)\n",
        "y_test = test['Item_Outlet_Sales']"
      ],
      "metadata": {
        "id": "JyYJSSj-Z3mT"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "scaler = MinMaxScaler(feature_range=(0, 1))\n",
        "\n",
        "x_train_scaled = scaler.fit_transform(x_train)\n",
        "x_train = pd.DataFrame(x_train_scaled)\n",
        "\n",
        "x_test_scaled = scaler.fit_transform(x_test)\n",
        "x_test = pd.DataFrame(x_test_scaled)"
      ],
      "metadata": {
        "id": "Pp38lIDgZsyn"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def knn_regression(k,x_train,y_train,x_test,y_test):\n",
        "    model = neighbors.KNeighborsRegressor(n_neighbors = k)\n",
        "\n",
        "    model.fit(x_train, y_train)  \n",
        "    pred=model.predict(x_test) \n",
        "    error = sqrt(mean_squared_error(y_test,pred)) \n",
        "    rmse_val.append(error) "
      ],
      "metadata": {
        "id": "XM_GDnVqbVKI"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "rmse_val = [] \n",
        "\n",
        "for k in range(1,21):\n",
        "  knn_regression(k,x_train,y_train,x_test,y_test)\n",
        "\n",
        "figure = plt.figure(figsize=(10,10))\n",
        "plt.plot(np.arange(1,21),rmse_val)\n",
        "plt.xlabel(\"K\")\n",
        "plt.ylabel(\"Loss\")\n",
        "plt.show()\n",
        "\n",
        "rmse_val = np.asarray(rmse_val)\n",
        "print(\"Minimum error {} is at k = {}\".format(np.min(rmse_val),np.argmin(rmse_val)))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 626
        },
        "id": "P0rIZOClcKI6",
        "outputId": "affd8075-7ebf-440c-fb95-261f167f814a"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Minimum error 1278.5816281094171 is at k = 6\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Exercises\n",
        "\n",
        "1. Try out these loss functions on regression tasks, and try to understand the model performance based on the loss function.\n",
        "2. Explore other loss functions and try to understand when and why they are used.\n",
        "3. Try out KNN-regression on other datasets see which values of K give the best results."
      ],
      "metadata": {
        "id": "0QNjfdMXk2AH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "->>Answer for Exercise-1"
      ],
      "metadata": {
        "id": "8rrmtSlkmdh5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "errors = {\n",
        "    \"mse\": [],\n",
        "    \"mae\": [],\n",
        "    \"rmse\": []\n",
        "}\n",
        "\n",
        "for k in range(1,21):\n",
        "  model = neighbors.KNeighborsRegressor(n_neighbors = k)\n",
        "  model.fit(x_train, y_train)  \n",
        "  pred = model.predict(x_test) \n",
        "  mse = mean_squared_error(y_test, pred)\n",
        "  errors[\"mse\"].append(mse)\n",
        "  errors[\"mae\"].append(mean_squared_error(y_test, pred))\n",
        "  errors[\"rmse\"].append(mse**0.5)"
      ],
      "metadata": {
        "id": "OWLSkRfqmmio"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "figure = plt.figure(figsize=(10,10))\n",
        "plt.subplot(2, 2, 1)\n",
        "plt.plot(np.arange(1,21),errors[\"mse\"], label=\"MSE\")\n",
        "plt.legend()\n",
        "plt.xlabel(\"K\")\n",
        "plt.ylabel(\"Loss\")\n",
        "\n",
        "plt.subplot(2, 2, 2)\n",
        "plt.plot(np.arange(1,21),errors[\"rmse\"], label=\"RMSE\")\n",
        "plt.legend()\n",
        "plt.xlabel(\"K\")\n",
        "plt.ylabel(\"Loss\")\n",
        "\n",
        "plt.subplot(2, 2, 3)\n",
        "plt.plot(np.arange(1,21),errors[\"mae\"], label=\"MAE\")\n",
        "plt.legend()\n",
        "plt.xlabel(\"K\")\n",
        "plt.ylabel(\"Loss\")\n",
        "plt.show()\n",
        "\n",
        "errors[\"mse\"] = np.asarray(errors[\"mse\"])\n",
        "errors[\"rmse\"] = np.asarray(errors[\"rmse\"])\n",
        "errors[\"mae\"] = np.asarray(errors[\"mae\"])\n",
        "print(\"[MSE] Minimum error {} is at k = {}\".format(np.min(errors[\"mse\"]), np.argmin(errors[\"mse\"])))\n",
        "print(\"[RMSE] Minimum error {} is at k = {}\".format(np.min(errors[\"rmse\"]), np.argmin(errors[\"rmse\"])))\n",
        "print(\"[MAE] Minimum error {} is at k = {}\".format(np.min(errors[\"mae\"]), np.argmin(errors[\"mae\"])))"
      ],
      "metadata": {
        "id": "_j1bn--Rm5am",
        "outputId": "b68e99c0-398b-4495-b482-726c1deee0bf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 671
        }
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x720 with 3 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[MSE] Minimum error 1634770.9797389277 is at k = 6\n",
            "[RMSE] Minimum error 1278.5816281094171 is at k = 6\n",
            "[MAE] Minimum error 1634770.9797389277 is at k = 6\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "->>Answer for Exercise-2"
      ],
      "metadata": {
        "id": "H7MBFDtcnB9N"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Loss functions provide more than just a static representation of how your model is performing, they're how your algorithms fit data in the first place. Most machine learning algorithms use some sort of loss function in the process of optimization, or finding the best parameters (weights) for your data.\n",
        "\n",
        "Some of the loss functions used in machine learning algorithms are the cross-entropy loss, the mean-squared error, the huber loss, and the hinge loss."
      ],
      "metadata": {
        "id": "MOPSGc29nDH4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "->>Answer for Exercise-3"
      ],
      "metadata": {
        "id": "xcpPlvZrnMZ5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df=pd.read_csv(\"/content/california_housing_test.csv\")\n",
        "df.head()"
      ],
      "metadata": {
        "id": "3WEfWjIvnQbs",
        "outputId": "83983597-08b6-4e4d-8ec9-6ebfa034e6e6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        }
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
              "0    -122.05     37.37                27.0       3885.0           661.0   \n",
              "1    -118.30     34.26                43.0       1510.0           310.0   \n",
              "2    -117.81     33.78                27.0       3589.0           507.0   \n",
              "3    -118.36     33.82                28.0         67.0            15.0   \n",
              "4    -119.67     36.33                19.0       1241.0           244.0   \n",
              "\n",
              "   population  households  median_income  median_house_value  \n",
              "0      1537.0       606.0         6.6085            344700.0  \n",
              "1       809.0       277.0         3.5990            176500.0  \n",
              "2      1484.0       495.0         5.7934            270500.0  \n",
              "3        49.0        11.0         6.1359            330000.0  \n",
              "4       850.0       237.0         2.9375             81700.0  "
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-fc58076a-69a7-4251-a34d-55077b19eb2f\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>longitude</th>\n",
              "      <th>latitude</th>\n",
              "      <th>housing_median_age</th>\n",
              "      <th>total_rooms</th>\n",
              "      <th>total_bedrooms</th>\n",
              "      <th>population</th>\n",
              "      <th>households</th>\n",
              "      <th>median_income</th>\n",
              "      <th>median_house_value</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-122.05</td>\n",
              "      <td>37.37</td>\n",
              "      <td>27.0</td>\n",
              "      <td>3885.0</td>\n",
              "      <td>661.0</td>\n",
              "      <td>1537.0</td>\n",
              "      <td>606.0</td>\n",
              "      <td>6.6085</td>\n",
              "      <td>344700.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-118.30</td>\n",
              "      <td>34.26</td>\n",
              "      <td>43.0</td>\n",
              "      <td>1510.0</td>\n",
              "      <td>310.0</td>\n",
              "      <td>809.0</td>\n",
              "      <td>277.0</td>\n",
              "      <td>3.5990</td>\n",
              "      <td>176500.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-117.81</td>\n",
              "      <td>33.78</td>\n",
              "      <td>27.0</td>\n",
              "      <td>3589.0</td>\n",
              "      <td>507.0</td>\n",
              "      <td>1484.0</td>\n",
              "      <td>495.0</td>\n",
              "      <td>5.7934</td>\n",
              "      <td>270500.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-118.36</td>\n",
              "      <td>33.82</td>\n",
              "      <td>28.0</td>\n",
              "      <td>67.0</td>\n",
              "      <td>15.0</td>\n",
              "      <td>49.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>6.1359</td>\n",
              "      <td>330000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-119.67</td>\n",
              "      <td>36.33</td>\n",
              "      <td>19.0</td>\n",
              "      <td>1241.0</td>\n",
              "      <td>244.0</td>\n",
              "      <td>850.0</td>\n",
              "      <td>237.0</td>\n",
              "      <td>2.9375</td>\n",
              "      <td>81700.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-fc58076a-69a7-4251-a34d-55077b19eb2f')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-fc58076a-69a7-4251-a34d-55077b19eb2f button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-fc58076a-69a7-4251-a34d-55077b19eb2f');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(20, 5))\n",
        "features = ['longitude','latitude']\n",
        "target = df['housing_median_age']"
      ],
      "metadata": {
        "id": "4yX_tSDqoiw_",
        "outputId": "4f25c78d-0a2f-4080-95f4-c9ebfcbbe4a1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1440x360 with 0 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for i, col in enumerate(features):\n",
        "    plt.subplot(1, len(features) , i+1)\n",
        "    house_features = df[col]\n",
        "    target_price = target\n",
        "    plt.scatter(house_features, target_price, marker='o')\n",
        "    plt.title(col)\n",
        "    plt.xlabel(col)\n",
        "    plt.ylabel('housing_median_age')"
      ],
      "metadata": {
        "id": "JQpUYSlMooEJ",
        "outputId": "e72327bc-7e9f-4211-ab4a-20b859deb751",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        }
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X = pd.DataFrame(np.c_[df['longitude'], df['latitude']], columns = ['longitude','latitude'])\n",
        "y = df['housing_median_age']\n",
        "     \n",
        "\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state=42)\n",
        "errors = {\n",
        "    \"mse\": [],\n",
        "    \"mae\": [],\n",
        "    \"rmse\": []\n",
        "}\n",
        "\n",
        "for k in range(1,21):\n",
        "  model = neighbors.KNeighborsRegressor(n_neighbors = k)\n",
        "  model.fit(X_train, y_train)  \n",
        "  pred = model.predict(X_test) \n",
        "  mse = mean_squared_error(y_test, pred)\n",
        "  errors[\"mse\"].append(mse)\n",
        "  errors[\"mae\"].append(mean_squared_error(y_test, pred))\n",
        "  errors[\"rmse\"].append(mse**0.5)"
      ],
      "metadata": {
        "id": "shYYa00rosko"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "figure = plt.figure(figsize=(10,10))\n",
        "plt.subplot(2, 2, 1)\n",
        "plt.plot(np.arange(1,21),errors[\"mse\"], label=\"MSE\")\n",
        "plt.legend()\n",
        "plt.xlabel(\"K\")\n",
        "plt.ylabel(\"Loss\")\n",
        "\n",
        "plt.subplot(2, 2, 2)\n",
        "plt.plot(np.arange(1,21),errors[\"rmse\"], label=\"RMSE\")\n",
        "plt.legend()\n",
        "plt.xlabel(\"K\")\n",
        "plt.ylabel(\"Loss\")\n",
        "\n",
        "plt.subplot(2, 2, 3)\n",
        "plt.plot(np.arange(1,21),errors[\"mae\"], label=\"MAE\")\n",
        "plt.legend()\n",
        "plt.xlabel(\"K\")\n",
        "plt.ylabel(\"Loss\")\n",
        "plt.show()\n",
        "\n",
        "errors[\"mse\"] = np.asarray(errors[\"mse\"])\n",
        "errors[\"rmse\"] = np.asarray(errors[\"rmse\"])\n",
        "errors[\"mae\"] = np.asarray(errors[\"mae\"])\n",
        "print(\"[MSE] Minimum error {} is at k = {}\".format(np.min(errors[\"mse\"]), np.argmin(errors[\"mse\"])))\n",
        "print(\"[RMSE] Minimum error {} is at k = {}\".format(np.min(errors[\"rmse\"]), np.argmin(errors[\"rmse\"])))\n",
        "print(\"[MAE] Minimum error {} is at k = {}\".format(np.min(errors[\"mae\"]), np.argmin(errors[\"mae\"])))"
      ],
      "metadata": {
        "id": "c5goLipaouu6",
        "outputId": "08383ddc-3db6-477e-c734-8c32c2229215",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 661
        }
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x720 with 3 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmcAAAJQCAYAAADLzcMEAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAAsTAAALEwEAmpwYAAByjklEQVR4nO3deXyU1d3//9eZTMhCJpMMYQuLCAISlX1XVoO1apVy2yiK1q2UG75atVpFWuyvbumNFGpvqFpBq7RuVeC2i5ZAgVZEIgEVIiq4VNYQJoQESCCZ8/tjYEogQAJJrlnez8eDB5lrts8hyeE95zrXOcZaaxERERGRsOByugARERER+Q+FMxEREZEwonAmIiIiEkYUzkRERETCiMKZiIiISBhROBMREREJIwpnIiIiImHE7XQBDWn79u1Ol9BkMjIyKC4udrqMJqU2R7/6tjczM7MRq2l66sOiV6y1F9Tm0zlV/6WRMxEREZEwonAmIiIiEkYUzkRERETCSFTNOROJVdZaKioqCAQCGGOcLueM7dq1i8rKyhrHrLW4XC4SExMjum0isSxa+qjTOb4PO9P+S+FMJApUVFQQHx+P2x3Zv9Jut5u4uLgTjldVVVFRUUFSUpIDVYnI2YqWPup0auvDzqT/0mlNkSgQCASiutNzu90EAgGnyxCRMxTtfdSpnEn/FZv/UiJRJppPExzVGG2cO3cuBQUFeL1eZs6cCcBLL73E2rVrcbvdtG7dmsmTJ9O8efMTnrt+/Xqef/55AoEAl156KWPHjgWgqKiI2bNnU1ZWRufOnbnzzjtj9j8lkaNioY86lfq2XyNnItIg2rVrx5133hm6XVVVxUUXXcTNN98MwO7du7n55pvJzs5m5MiR3HTTTQB88803dOnShTFjxjB69GjGjBnD66+/3iQ1jxw5koceeqjGsZ49ezJz5kyefPJJ2rZty8KFC094XiAQYN68eTz00EPMmjWLd999l61btwKwYMECrrzySn7zm9/QvHlzli1b1iRtEZFT69ChQ6if+f73v09paSkQ7IPatWvHL3/5y9Bj/X4/55xzDtOmTQNg8+bNXHvttYwZM4YRI0bwk5/8BIBVq1Zx/vnnM2bMmNBrr1y58qxrjbmPc7aqCjashdaZmLYdnC5HJGokJyezadMmDh48SFJSEitXrqRNmzah+2fMmMHw4cO54447ACgsLAzdd84557BkyRLcbjdVVVVNVnNWVhZFRUU1jvXq1Sv0dbdu3Vi9evUJz9u8eTNt2rShdevWAAwdOpT8/HzatWvHxo0b+dGPfgQEw9/rr7/OZZdd1mA1268+h/IyzIV9G+w1RWJBYmIiS5YsAeBHP/oRL7zwQuh3tWPHjixdupQHHngAgLfeeotu3bqFnjt9+nR+8IMf8K1vfQuATz75JHTfwIEDefHFFwEarA+LvZEzawnMeQy79l2nKxGJOqNHj2bp0qUALFq0KHSqD4Kn+9q2bRu6nZWV1dTl1duyZcvo3bv3Ccf9fj8tWrQI3W7RogV+v5+ysjKSk5NDE4J9Ph9+v79Ba7J/X0Tg5Wcb9DVFYk2/fv3YuXNn6HZSUhJdu3blww8/BILh7Dvf+U7o/uP7rx49ejRqfTE3cmbi4yEpGcr2OV2KSNS55pprmDVrFtnZ2XzyySdcf/31vP/++wDccsst/Pd//zfPP/88w4YN47rrrguNrH399deMGTMGYwzWWh599FEGDRrkZFN48803iYuLY9iwYY32Hnl5eeTl5QGQm5tLRkbGaZ+zr1VrKjauq9Njw5nb7Y74NtRHrLUXarZ5165dYTH30u12U11dzapVq7jhhhtqXF353e9+l7feeos2bdoQFxdHZmYmu3fvxu1288Mf/pCcnBwGDBjAiBEjGD9+PF6vl7i4ONasWVNjdHz+/Pl06tSpxvsmJCTU6/vv/L+UE1JSoazU6SpEGkXgld9hv/myQV/TdDgX1/U/OO3jsrKy2Lp1K4sXL2b06NE17hs5ciSrVq1i+fLlLFu2jG9961uh+VhOndY8meXLl7N27VqmT59e60Ren8/Hnj17Qrf37NmDz+fD4/Fw4MABqquriYuLw+/34/P5Tvo+2dnZZGdnh27XZU++gDsBe6Cc3Tt2BD9sRqhY23cx1toLNdtcWVkZCkFO9VEVFRWMGjWKnTt30rVrVy6++GKqqqqorq4GYPjw4eTm5tKiRQu+853vUF1dTSAQoKqqiu9973sMGzaM5cuX88477/Diiy+yZMkSqquraz2teXw/VllZecL3X3trHs/jxZZr5EykMVx22WX84he/qHFK86j09HS++93v8pvf/IZevXrVOp/LaevXr2fx4sU88MADJCQk1PqYLl26sGPHDoqKiqiqqmLVqlX0798fYwwXXHBBqF3Lly+nf//+DVtgqjf4t/owkXo5OudszZo1WGt54YUXatzfrFkzevbsyTPPPMOVV155wvPbtGnD9ddfz/PPP4/b7ebTTz9ttFpjc+TM44U9Rad/nEgEqssIV2O67rrrSE1NpUePHqxatSp0/F//+hf9+vUjKSmJ8vJyvv76a9q1a+dgpTB79mwKCwspKytj0qRJ5OTksHDhQqqqqnjkkUcA6Nq1KxMnTsTv9/PMM88wdepU4uLiuO2223jssccIBAKMGjWKDh2CFxjdeOONzJ49m1deeYVzzz33hBHEs2VSvFiAsr2Q3uI0jxYJP073UUlJSTzyyCPcdtttfP/7369x3w9/+EMGDx5Menp6jeP/+Mc/uOSSS4iPj6eoqIiSkhLatGnD5s2bG6XGmAxnxuPFftU4/6AisS4zM5Pbb7/9hOMff/wxP/3pT0MLMo4fP57evXvzzTffnDDn7Prrr6/1NRra3XfffcKxk4Upn8/H1KlTQ7f79u1L374nXjHZunVrnnjiiQar8QRHR872aWqGyJm68MIL6dGjB4sWLaoxv7V79+507979hMevWLGC6dOnh0bTf/rTn9KqVSs2b97MmjVrGDNmDBBcz+yuu+7iqquuOqv6jLXWntUrhJHt27fX6XGBN3+P/fsiXL99M2IXxov1+Quxoq5tPnDgAMnJyU1QUeM61Zyz2tp4qjkbkagufZjdtZ3ATydhbrsH15BRTVBV44i13+dYay/UbHO09FGnc7I+rL79V2zOOUvxQnU1HNjvdCUiIvXjOTJyVrbX0TJEpPHEZjgLdW46LSAiESYpGdxundYUiWIxGc6MJzX4Rbk6NxGJLMYY8KTpw6VIFIvJcIYnLfi3FqKVKBFFU0dPKhbaWGceL1bhTCJIrP/+1rf9MRrOgiNn6twkWrhcrrBYvLWxVFVV4XLFZndVK48W0pbIEu191KmcSf8Vk0tpaM6ZRJvExEQqKiqorKyM2CuQIbjFSWVlZY1j1lpcLheJiYkOVRV+jCcNu3Ob02WI1Fm09FGnc3wfdqb9V0yGMxPfDBKStMK2RA1jDElJSU6XcdZicbmBM5LqhbK9WGuj+j86iR7R0kedTkP1YbF7nsCTqqudRCQyebxw6BBUVjhdiYg0ghgOZ16srtYUkUgUuqhJfZhINIrdcJaiCbUiEplMaAunvY7WISKNo0nC2dy5c7njjjv48Y9/fMJ9b731Fjk5OezbF5z/Za1l/vz53Hnnndx333188cUXjVKTSfVqKQ0RiUy6qEkkqjVJOBs5ciQPPfTQCceLi4v56KOPyMjICB1bt24dO3fu5KmnnmLixIk899xzjVNUihfKS2N+7RURiUBHTmtqOSCR6NQk4SwrK4uUlJQTjv/+97/nxhtvrHG10QcffMDw4cMxxtCtWzf2799PSUlJwxfl8UJVFVQcbPjXFhFpTEd3OVE4E4lKjs05y8/Px+fz0alTpxrH/X5/jZG0Fi1a4Pf7G76AUOe2t+FfW0SkEZlmCcHlgBTORKKSI+ucVVZWsnDhQn7605+e1evk5eWRl5cHQG5ubo1Qd9oa2nVgL+B1GZrV43nhwu1216u90UBtjn6x1t6zkurVckAiUcqRcLZr1y6Kioq4//77AdizZw8PPPAATzzxBD6fr8YCbnv27MHn89X6OtnZ2WRnZ4du12fhNxsInkot3fpvTEbbM2mGo2JxsU61OfrVt72ZmZmNWE2Y83ixGvkXiUqOhLOOHTvWmOg/ZcoUnnjiCVJTU+nfvz9vv/02F198MZ9//jnJycmkp6c3fBFHLkW3ZaVofW0RiTgeL+wpcroKEWkETRLOZs+eTWFhIWVlZUyaNImcnBxGjx5d62P79OlDQUEBd911F82aNWPy5MmNU1TKkUvRtYWTiEQgk5qG/epzp8sQkUbQJOHs7rvvPuX9c+bMCX1tjOGOO+5o5IrAJCRAswRNqBWJYXPnzqWgoACv18vMmTMBeO+993j99dfZtm0bjz/+OF26dDnhedu3b2fWrFmh20VFReTk5HDllVfy2muvsXTpUlJTgxcdjR8/nr59+zZ88R4vlO/DBgIYV+yuJy4SjWJy4/MQjxaiFYllI0eO5PLLL6/xAbFDhw7cd999PPvssyd9XmZmJjNmzAAgEAjwwx/+kIEDB4buv/LKK7n66qsbr3AIXnFeXQ0H90NzT+O+l4g0qdgOZympmlArEsOysrIoKqo5b6t9+/b1eo2PP/6YNm3a0LJly4Ys7fSO7q+5r1ThTCTKxHY483i1N52InJV3332Xiy++uMaxd955h5UrV9K5c2duvvnmWhfhPlvG48VCcK3GtvULlCIS3mI6nBlPKnb7106XISIRqqqqirVr13LDDTeEjl122WVce+21ALz66qu8+OKLJ72w6WzWajzcsRN+wEOAxAhcGy7W1rSLtfaC2nxWr9MAtUQuTxqU7cNaW2MLKRGRuli3bh3nnnsuaWlpoWPHfn3ppZfyy1/+8qTPP6u1GquD+wLv27aV8ghcC09r+EU/tfnUTrVOY2xf4uNJhcOHoLLC6UpEJALVdkrz2L2A16xZQ4cOHRrnzVO0BZ1ItIrxkbMja52VlUJikrO1iEiTq20NxpSUFObPn8++ffvIzc2lU6dOTJs2Db/fzzPPPMPUqVMBqKio4KOPPmLixIk1XnPBggV89dVXGGNo2bLlCfc3FBMXBykeLQckEoViOpyZlKMTakuhZRunyxGRJnayNRiPXRbjKJ/PFwpmAImJicyfP/+Ex915550NVt9pedKwCmciUUenNUFrnYlIZPKkauRMJArFeDg7sr9muTo3EYlAHm9wnTMRiSoKZ6BPniISkYwnTf2XSBSK7XCWkAjxzXRaU0Qik8cL+8uwVVVOVyIiDSimw5kxRnM2RCRypR4Z/S/XB0yRaBLT4QyAFC9WHZuIRCBzdH9NfcAUiSoKZ55U7a8pIpFJ82ZFolLMhzPj8eqUgIhEpiOnNbXWmUh0iflwRopXnzpFJDKFRs72OlqGiDQshbNULxyqxFZWOl2JiEj9JDWHuDitdSYSZRTOjm4erIVoRSTCGJdLo/8iUSjmw5nRhFoRiWQer+aciUSZmA9n/5mzoYsCRCQCpXp1xblIlFE4O7L5udWEWhGJQMaj05oi0UbhLEUjZyISwTxp6r9EoozCWVIyuN365CkikcmTCpUHdcW5SBSJ+XBmjAmOnulqTRGJREfnzaoPE4kaMR/OAPCkYnVaQEQikElNC36htc5Eoobb6QLCgibUisSkuXPnUlBQgNfrZebMmQC89957vP7662zbto3HH3+cLl261PrcKVOmkJiYiMvlIi4ujtzcXADKy8uZNWsWu3fvpmXLltxzzz2kpKQ0XiO0S4BI1FE4A0yKF1u0w+kyRKSJjRw5kssvv5w5c+aEjnXo0IH77ruPZ5999rTPf/jhh0lNTa1xbNGiRVx00UWMHTuWRYsWsWjRIiZMmNDgtYd4/rO/pmm8dxGRJqTTmhCcUKvTmiIxJysr64RRrfbt25OZmXnGr5mfn8+IESMAGDFiBPn5+WdV42nptKZI1NHIGQQ/eVYexB4+hIlv5nQ1IhIhHnvsMQDGjBlDdnY2AKWlpaSnpwOQlpZGaWnjhiaTkAjNEnRBgEgUUTiDY+ZslIKvpbO1iEhEeOSRR/D5fJSWlvLoo4+SmZlJVlZWjccYY4JXhJ9EXl4eeXl5AOTm5pKRkXFGtexO89HsUAXeM3y+E9xu9xm3NxLFWntBbT6r12mAWiKe8XixEDy1qXAmInXg8/kA8Hq9DBgwgM2bN5OVlYXX66WkpIT09HRKSkpOmJN2rOzs7NCIG0BxcfEZ1RJITqFi9y4On+HznZCRkXHG7Y1EsdZeUJtP51TTJzTnDEJbOOmKTRGpi4qKCg4ePBj6+qOPPqJjx44A9O/fnxUrVgCwYsUKBgwY0PgF6YpzkaiikTMIbeFky3W1k0gsmT17NoWFhZSVlTFp0iRycnJISUlh/vz57Nu3j9zcXDp16sS0adPw+/0888wzTJ06ldLSUp588kkAqqurueSSS+jduzcAY8eOZdasWSxbtiy0lEZjM6le7DdfNvr7iEjTUDiD/8w509VOIjHl7rvvrvX4wIEDTzjm8/mYOnUqAK1bt2bGjBm1Ptfj8TB9+vQGq7FOPGlQVoq19pRz3EQkMui0JkByc4iL09VOIhKZPF6oroKD+52uREQagMIZR/fX1FpnIhKhUjX6LxJNFM6O8nixmlArIhHIeNKCX2j0XyQqKJwd5fFCuUbORCQCHb3iXCNnIlFB4ewIk5KqS9FFJDIdGTnT6L9IdFA4O0rrBIlIpAqt1bjX0TJEpGEonB3lSYWDB7CHDztdiYhIvRh3fPCqc53WFIkKTbLO2dy5cykoKMDr9TJz5kwAXnnlFT744AOMMXi9XiZPnozP58Nay/PPP8+6detISEhg8uTJdO7cufGLPLIQLeX7IL1F47+fiEhDOrLWmYhEviYZORs5ciQPPfRQjWNXX301Tz75JDNmzKBv37786U9/AmDdunXs3LmTp556iokTJ/Lcc881RYmY1GM2PxcRiTS64lwkajRJOMvKyiIlJaXGseTk5NDXlZWVoVWtP/jgA4YPH44xhm7durF//35KSkoav8jQyJk6NxGJQKmaNysSLRzdvunll19m5cqVJCcn8/DDDwPg9/vJyMgIPaZFixb4/X7S09Mbt5gjWzjZsn3aX1NEIo7xeLGfFzpdhog0AEfD2fjx4xk/fjwLFy7k7bffJicnp17Pz8vLIy8vD4Dc3Nwaoa6+As3i2Q2kBKpIPovXaSput/us2huJ1OboF2vtbVBH1mq0gWqMK87pakTkLITFxufDhg3jiSeeICcnB5/PR3Fxcei+PXv24PP5an1ednY22dnZodvHPq++bCAALhflO7dz4Cxep6lkZGScVXsjkdoc/erb3szMzEasJsJ4vGAtlJdBaprT1YjIWXBsKY0dO3aEvs7Pzw91sv3792flypVYa/nss89ITk5u/FOagHG5oLlHczZEJDId3cJJfZhIxGuSkbPZs2dTWFhIWVkZkyZNIicnh4KCAnbs2IExhoyMDCZOnAhAnz59KCgo4K677qJZs2ZMnjy5KUoM8nix2vxcRCKQSfViAfbthXbnOFyNiJyNJglnd9999wnHRo8eXetjjTHccccdjVzRSXi8ulpTRCJT6KKmUl3UJBLhtEPAMYzHCxo5E5FIpNOaIlFD4exYHm1+LiIRqnkKGJf6MJEooHB2rBQvHCjHVlU5XYmISL0YlwtSdFGTSDQIi6U0wobnmP0102pfvkNEokdt+/6+9957vP7662zbto3HH3+cLl26nPC84uJi5syZw969ezHGkJ2dzRVXXAHAa6+9xtKlS0lNTQWC6zn27du3aRqUmobV5uciEU/h7BjGkxq82qm8VOFMJAaMHDmSyy+/nDlz5oSOdejQgfvuu49nn332pM+Li4vjpptuonPnzhw8eJAHH3yQnj170r59ewCuvPJKrr766kav/wQeL5Ttbfr3FZEGpdOaxwpNqNVFASKxoLZ9f9u3b3/axW3T09Pp3LkzAElJSbRr1w6/399oddZV8KImjZyJRDqNnB3LEzwNoUvRRaSuioqK+PLLLznvvPNCx9555x1WrlxJ586dufnmm08IgI0mNU3hTCQKKJwd6+icM42ciUgdVFRUMHPmTG655RaSk5MBuOyyy7j22msBePXVV3nxxRdPuph2Q+4PDFDeui37Dx6ghTcVE9/srF6rscXaPqqx1l5Qm8/qdRqglujRPAWM0UK0InJaVVVVzJw5k2HDhjFo0KDQ8bS0tNDXl156Kb/85S9P+hoNuT8wQCAuPvg6X36B8YX3f4raNzb6qc2ndqrpE5pzdgzjigvur6mrnUTkFKy1PP3007Rr146rrrqqxn0lJSWhr9esWUOHDh2arC6TenT0X32YSCTTyNnxPF6sRs5EYkJt+/6mpKQwf/589u3bR25uLp06dWLatGn4/X6eeeYZpk6dyqeffsrKlSvp2LEj999/P/CfJTMWLFjAV199hTGGli1bhvYNbhIpR8PZ3qZ7TxFpcApnx9MuASIxo7Z9fwEGDhx4wjGfz8fUqVMBOP/883nttddqfe6dd97ZYPXV25GRM7tPFzWJRDKd1jye9tcUkUil/TVFooLC2XGMx6sLAkQkMiUmgTtepzVFIpzC2fFSvLC/HBuodroSEZF6McYET23qoiaRiKZwdjxPKlgL5WVOVyIiUn+eNKxOa4pENIWz43l0KbqIRDBt4SQS8RTOjmNSgls4qXMTkUhkdMW5SMRTODteahoAVldsikgk8qRBWSnWWqcrEZEzpHB2vCObn+uKTRGJSKleOHwIKg86XYmInCGFs+M112lNEYlgR+fN6opNkYilcHYcE3dkf02d1hSRCGS0EK1IxFM4q40nFatFHEUkEqVqf02RSKdwVpsUbeEkIhHqyGlNXdQkErkUzmqjS9FFJFKF5pztdbQMETlzCme1MJ40KNenThGJPCa+WXCPTX3AFIlY7ro+cMOGDbRq1YpWrVpRUlLCH/7wB1wuFzfccANpaWmNWKIDPKlQXoYNBDAu5VeRcBZTfVNdaZcAkYhW5+Qxb948XEeCyosvvkh1dTXGGJ555plGK84xHi/YAOwvd7oSETmNmOqb6ipV+2uKRLI6j5z5/X4yMjKorq7mww8/ZO7cubjdbn74wx82Zn3OSDlmIdqji9KKSFiKqb6prjxe2L3T6SpE5AzVeeQsKSmJvXv3UlhYSPv27UlMTASgqqqq0YpzitEijiIRI5b6proyOq0pEtHqPHJ2+eWXM3XqVKqqqrjlllsA2LRpE+3atWus2pxzNJxpCyeRsBdTfVNdHbmoSfNmRSJTncPZ2LFjGThwIC6XizZt2gDg8/mYNGlSoxXnmNA6QaUYh0sRkVM7m75p7ty5FBQU4PV6mTlzJgDvvfcer7/+Otu2bePxxx+nS5cutT53/fr1PP/88wQCAS699FLGjh0LQFFREbNnz6asrIzOnTtz55134nbXuattGKleCATgQPl/pmmISMSo10eqzMzMUOe3YcMG9u7dS8eOHRulMEcd7cy0iKNIRDjTvmnkyJE89NBDNY516NCB++67jx49epz0eYFAgHnz5vHQQw8xa9Ys3n33XbZu3QrAggULuPLKK/nNb35D8+bNWbZs2Vm07AwdHf3XqU2RiFTncPbwww+zadMmABYtWsSvf/1rfv3rX/Pmm282WnFOMW43JDdXxyYSAc6mb8rKyiIlJaXGsfbt25OZmXnK523evJk2bdrQunVr3G43Q4cOJT8/H2stGzduZPDgwUAw/OXn559hy86c5s2KRLY6h7NvvvmGbt26AbB06VIefvhhHnvsMZYsWdJoxTkqxauFaEUigBN9k9/vp0WLFqHbLVq0wO/3U1ZWRnJyMnFxcUDw9Krf72+0Ok7Ko/01RSJZnSdCWGsB2LkzeHl2+/btAdi/f38jlBUGPKlaJ0gkAkRy35SXl0deXh4Aubm5ZGRkNMjrVrtdFAPNA9UkN9BrNjS3291g7Y0EsdZeUJvP6nXq+sDu3bszf/58SkpKGDBgABDsDD0ez1kXEZa0TpBIRHCib/L5fOzZsyd0e8+ePfh8PjweDwcOHKC6upq4uDj8fj8+n++kr5OdnU12dnbodnFxcYPUZ6urwRjKd2zjQAO9ZkPLyMhosPZGglhrL6jNp3Oq6RN1Pq05ZcoUkpOTOeecc8jJyQFg+/btXHHFFXV9iYiidYJEIoMTfVOXLl3YsWMHRUVFVFVVsWrVKvr3748xhgsuuIDVq1cDsHz5cvr3799odZyMiYuD5h6d1hSJUHUeOfN4PNxwww01jvXt27fBCwobHq/WCRKJAGfTN82ePZvCwkLKysqYNGkSOTk5pKSkMH/+fPbt20dubi6dOnVi2rRp+P1+nnnmGaZOnUpcXBy33XYbjz32GIFAgFGjRtGhQwcAbrzxRmbPns0rr7zCueeey+jRoxu8zXXi8WJ1xblIRKpzOKuqquLNN99k5cqVlJSUkJ6ezvDhwxk3blzTr+HTFDypwXWCDu4PfgIVkbB0Nn3T3XffXevxgQMHnnDM5/MxderU0O2+ffvWGgJbt27NE088Ub9GNIbUNI2ciUSoOqeqBQsWsGXLFn7wgx/QsmVLdu/ezRtvvMGBAwdCq3JHlZRj1glSOBMJWzHXN9WRSUnFbvvK6TJE5AzUOZytXr2aGTNmhCbZZmZmcu6553L//feftgOsbRXul156ibVr1+J2u2ndujWTJ0+mefPmACxcuJBly5bhcrm49dZb6d2795m17iwYjxcLwYVo2zT524tIHZ1N3xTVUr3wiebNikSiOk+mOnq5+pmobRXunj17MnPmTJ588knatm3LwoULAdi6dSurVq3iV7/6FdOmTWPevHkEAoEzfu8z5jm6S8Depn9vEamzs+mboponDQ6UY6sOO12JiNRTncPZkCFD+OUvf8n69evZunUr69evZ8aMGQwZMuS0z61tFe5evXqFFmrs1q1baKHG/Px8hg4dSnx8PK1ataJNmzZs3ry5Pm1qGClH99fUhFqRcHY2fVNUO7oQrRbTFok4dT6tOWHCBN544w3mzZtHSUkJPp+PoUOHUlVVddZFLFu2jKFDhwLBlbe7du0aus/5FbZ1WkAknDVm3xTJTOqRqRn7SiGtxekeLiJhpM7hzO12c91113HdddeFjh06dIibbrqJCRMmnHEBb775JnFxcQwbNqzez22s1bWPKkpuTmLVIVLDcIVjrbwcG2KtzWfS3sbqmyKeJy34tz5gikScs1oDwxhzVm++fPly1q5dy/Tp00OvdfzK26daYbuxVtc+yjb3ULF7F4fCcIVjrbwcG2KtzfVt78lW2D7bvikqeI5OzShF/xoikcWx1VXXr1/P4sWLeeCBB0hISAgd79+/P6tWreLw4cMUFRWxY8cOzjvvPGeK9Hi1v6aIRKZUTc0QiVSnHTnbsGHDSe+r65yO2lbhXrhwIVVVVTzyyCMAdO3alYkTJ9KhQweGDBnCvffei8vl4vbbb8fl1Ar9Hi/s2e3Me4vIKX322WcnnY8a6/PNAEhqDnFuXXEuEoFOG85++9vfnvL+uswPqW0V7lNtaTJu3DjGjRt32tdtbCYlFfuVA1eKishpvfLKK6ErvmsTS3P1amOMCS4JtE8jZyKR5rThbM6cOU1RR3g6ur+mtZrDIhJmpk+fftI5Z3KEpmaIRCTt6H0qHi9UVwX31xQRiTSeNM05E4lACmenElrrTIs4ikjkMale2LfX6TJEpJ4Uzk7BhLZw0idPEYlAR6ZmiEhkUTg7ldD2JwpnIhKBPGlQWYGtrHC6EhGpB4WzUzm6v6audhKRSKTRf5GIpHB2KurYRCSCGW3hJBKRFM5OwTRLgIREzdkQkch0dJcAjf6LRJSz2lszJni8+tQpEqXmzp1LQUEBXq+XmTNnAlBeXs6sWbPYvXs3LVu25J577iElJaXG8zZs2MDvf//70O3t27fzox/9iIEDBzJnzhwKCwtJTk4GYMqUKXTq1KnJ2lRDaH/NvdpfUySCKJydjseL1VIaIlFp5MiRXH755TUW2160aBEXXXQRY8eOZdGiRSxatIgJEybUeN6FF17IjBkzgGCYu/POO+nVq1fo/ptuuonBgwc3TSNOxaP9NUUikU5rnk5Kqq7WFIlSWVlZJ4yK5efnM2LECABGjBhBfn7+KV9j9erV9OnTh4SEhEar80yZhMTg1Ayd1hSJKApnp2E8Xi1CKxJDSktLSU9PByAtLY3S0lMHm3fffZeLL764xrGXX36Z++67jxdeeIHDhw83Wq114vHqA6ZIhNFpzdPxpELZXu2vKRKDjDGn/L0vKSnh3//+d41TmjfccANpaWlUVVXxzDPPsHjxYq699tpan5+Xl0deXh4Aubm5jbJZu9+Xgak4QHqYbQTvdrtjanP6WGsvqM1n9ToNUEt083ihqgoqDkJSstPViEgj83q9lJSUkJ6eTklJCampqSd97HvvvcfAgQNxu//TlR4ddYuPj2fUqFG89dZbJ31+dnY22dnZodvFxcUN0IKaqhOTYc/uRnnts5GRkRF2NTWmWGsvqM2nk5mZedL7dFrzdDShViSm9O/fnxUrVgCwYsUKBgwYcNLH1nZKs6SkBABrLfn5+XTo0KHxiq0DoyvORSKORs5Ow3i8WAh2bq3aOl2OiDSg2bNnU1hYSFlZGZMmTSInJ4exY8cya9Ysli1bFlpKA2DLli0sWbKESZMmAVBUVERxcTFZWVk1XvOpp55i377gPNVzzjmHiRMnNm2jjpfmg317sRUHMYlJztYiInWicHY6KUf319RFASLR5u677671+PTp00841qVLF7p06RK63apVK5555pkTHvfwww83WH0NwfTojf3La7BxHfQb6nQ5IlIHOq15Oke2cLI6LSAikei8HtDcg12/2ulKRKSOFM5OJzTnTCNnIhJ5TFwcpucA7EcfYKuqnC5HROpA4ew0TEIiNGsGZXudLkVE5IyY3oPgQDl8vtHpUkSkDhTO6sLXCrvjG6erEBE5Mxf0gfhm2A/XOF2JiNSBwlkdmJ794ZOPsAfKnS5FRKTeTEIiZPXGrluNtdbpckTkNBTO6sD0HQrVVdiPPnC6FBGRM2J6DwL/bvjmS6dLEZHTUDiri3O7QZoPW7DK6UpERM6I6TkAjNFVmyIRQOGsDozLhekzBDYWYCsrnC5HRKTeTGoadOmBXf++06WIyGkonNWR6TcUDh2CDWudLkVE5IyY3oPgmy+xxbucLkVETkHhrK66ZoHHi12rU5siEplM70EAumpTJMwpnNWRccVheg8KLuR4+JDT5YiI1JtpnQltO2DXad6ZSDhTOKsH03cIVB6EwvVOlyIickZMn8Hw+Ubs/jKnSxGRk1A4q4/ze0JSc2zBe05XIiJyRkzvQRAIaGkgkTCmcFYPxh2P6TUQu/597VEnIpHpnPOCSwPpqk2RsKVwVk+m35DgHnWffex0KSIi9WZcLkyvgcGlgTR/ViQsKZzVV1YfSEjErtWpTRGJTKb3YKisgE8+dLoUEamFwlk9mWYJmAv7Yde9hw1UO12OiEj9db8IEpN0alMkTCmcnYl+Q6GsFDZ/4nQlIiL1ZuLjMRf1x364BhsIOF2OiBxH4ewMmIv6gTteV22KSOTqNRD27YUvP3O6EhE5jtvpAiKRSUyGC/oET21edwfGGKdLEpEzMHfuXAoKCvB6vcycOROA8vJyZs2axe7du2nZsiX33HMPKSkpJzz3uuuuo2PHjgBkZGTwwAMPAFBUVMTs2bMpKyujc+fO3Hnnnbjd4dfVmov6YePisOtWY7qc73Q5InIMjZydIdN3KPiL4avPnS5FRM7QyJEjeeihh2ocW7RoERdddBFPPfUUF110EYsWLar1uc2aNWPGjBnMmDEjFMwAFixYwJVXXslvfvMbmjdvzrJlyxqzCWfMJKdA94uwH2remUi4UTg7Q6bXQIiL016bIhEsKyvrhFGx/Px8RowYAcCIESPIz8+v8+tZa9m4cSODBw8GguGvPs9vaqb3INi5Dbtjq9OliMgxFM7OkGmeAt17YgtWYa11uhwRaSClpaWkp6cDkJaWRmlpaa2PO3z4MA8++CDTpk1jzZrgRuJlZWUkJycTFxcHgM/nw+/3N03hZ8D0GgigqzZFwkz4TYSIIKbfEOxLc2HrV9DhXKfLEZEGZow56ZzSuXPn4vP52LVrF7/4xS/o2LEjycnJ9Xr9vLw88vLyAMjNzSUjI+Osa66XjAz2dDkfs+EDfDf9sEnf2u12N317HRRr7QW1+axepwFqOa3aJt2+9957vP7662zbto3HH3+cLl26hB6/cOFCli1bhsvl4tZbb6V3795NUWa9md6DsQuexhaswiiciUQFr9dLSUkJ6enplJSUkJqaWuvjfD4fAK1btyYrK4uvvvqKQYMGceDAAaqrq4mLi8Pv94ceV5vs7Gyys7NDt4uLixu2MXUQuLAf9v/+yO7Nn2HSTl5rQ8vIyHCkvU6JtfaC2nw6mZmZJ72vSU5r1jbptkOHDtx333306NGjxvGtW7eyatUqfvWrXzFt2jTmzZtHIEzX4TGpadA1S0tqiESR/v37s2LFCgBWrFjBgAEDTnhMeXk5hw8fBmDfvn18+umntG/fHmMMF1xwAatXrwZg+fLl9O/fv+mKPwOm9yCwFvvRGqdLEZEjmmTkLCsri6KiohrH2rdvX+tj8/PzGTp0KPHx8bRq1Yo2bdqwefNmunXr1hSl1pvpOxT7yrPYnVsxbWpvk4iEp9mzZ1NYWEhZWRmTJk0iJyeHsWPHMmvWLJYtWxZaSgNgy5YtLFmyhEmTJrFt2zaeffZZXC4XgUCAsWPHhvq0G2+8kdmzZ/PKK69w7rnnMnr0aCebeHrtzoGWbbDr18Dwy52uRkQIwzlnfr+frl27hm6H/YTaPoOD4WztKsyVOU6XIyL1cPfdd9d6fPr06Scc69KlS2j6Rffu3UNTNI7XunVrnnjiiQarsbEZYzC9BmGX/wVbcSC4jqOIOCrswll9OD6ZFiAjA3+3C7Af5dPi+5Ob7G010TI2xFqbY6294cL0GYTNWwwb10G/i50uRyTmhV048/l87NmzJ3T7VBNqw2EyLUCg5wDsn15g9ycbMC3bNMl7aqJlbIi1Nte3vaeaUCv10KUHpHiCuwUonIk4LuzWOevfvz+rVq3i8OHDFBUVsWPHDs477zynyzol03coAHadLgwQkchj4uIwPQdiP/4AW1XldDkiMa9JRs5qm3SbkpLC/Pnz2bdvH7m5uXTq1Ilp06bRoUMHhgwZwr333ovL5eL222/H5Qq7DFmDadkGOpwbvGrzsu86XY6ISL2Z3oOwq5bC5xuhRy+nyxGJaU0Szk426XbgwIG1Hh83bhzjxo1rxIoanuk7FLv4D9i9ezBpLZwuR0SkfrL6QLNm2PXvYxTORBwV3kNSEcT0HQKAXbfa4UpEROrPJCRAj97Y9au1JZ2IwxTOGojJ7Aht2msjdBGJWKbPYPAXwzdfOF2KSExTOGtApu9Q+Gwjtqz2jZJFRMKZ6TkAjAu7ThuhizhJ4awBmX5DwAaw69WxiUjkMR4vnHe++jARhymcNaQOnSGjNbZApzZFJDKZvkNg65cEnv4ldtd2p8sRiUlhtwhtJDPGYPoOwS79M/ZAOSY5xemSRETqxYy8Avbvxy5ZhF2/GjPsMsxV12O86U6XJhIzNHLWwEzfoVBdhf0o3+lSRETqzbjjcV1zA67HnsEM+xb2n38n8NBEAov/gD14wOnyRGKCwllDO7cbpPmwf3kd+8mHuiRdRCKS8abjunESrl/MwfQaiP3zq8GQtvQt7OHDTpcnEtUUzhqYcblwTZgMFQcJ/OpnBJ58CPvpBqfLEhE5I6ZVJq6J9+OaNhPad8K+8jsC0ycTWL0cGwg4XZ5IVFI4awSm10Bcjz+DuX4i7NpB4MmHqH5yGvbzQqdLExE5I6ZTV1z3PoLr7v8PkpKx835F4NF7sBsKdIZApIHpgoBGYuKbYS69CjtsDHbl29i/vUHgfx6ErN64rr4B0+V8p0sUEakXYwxc0AdXj17Y/H9iFy0g8OufQ/eLcF2ZA+f3DD5GRM6KwlkjM80SMNnXYIddjl3xV+zbbxLI/Qlc2DcY0s7t5nSJIiL1YlwuzKAR2H5DsSvewf7lVQK/+hm074TJvgYzcDgmPt7pMkUilk5rNhGTkIDrsu/ievxZzLjvw5efE3j8Pqp/8wj26y1OlyciUm/GHY/r0qtw/XIe5pa7wFrsC78m8ODtBP78KrZsn9MlikQkjZw1MZOYhPn2f2FHfTu4HtrfFxF49B64qD+u0VdBVm+MS5lZRCKHiW+GuTgbO/RS+GQ9gSWLsYv/gP3r65ghozDZV2PadnC6TJGIoXDmEJOYjLkyBzvqSuyyt7DL/hKcu9GqLWbEtzEXZ2OaaxFbkcY0d+5cCgoK8Hq9zJw5E4Dy8nJmzZrF7t27admyJffccw8pKTV/F7/66it+97vfcfDgQVwuF+PGjWPo0KEAzJkzh8LCQpKTkwGYMmUKnTp1atJ2OcUYA1l9iMvqg93+b2ze/2FXLcOufCf4AXTMNZqXJlIHxkbRZTbbt0fuViP28GFswSrsP/4CWzZBs2aYgSMwI6/AnNPlhMdnZGRQXFzc9IU6SG2OfvVtb2Zm5lm9X2FhIYmJicyZMycUzhYsWEBKSgpjx45l0aJFlJeXM2HChBrP2759O8YY2rZti9/v58EHH2TWrFk0b96cOXPm0K9fPwYPHlzveiK5DzsZu28vdsXbwb6trDQ0L63lVf/FnpK9TpfXZGLtdxnU5tM5Vf+l82dhwsTH4xo0grgH/wfXz2ZjBo/CrllJ4NF7qH7ifgLv/QN7+JDTZYpElaysrBNGxfLz8xkxYgQAI0aMID//xN0+MjMzadu2LQA+nw+v18u+fZpfVRuTmobrO9efMC9t7yM/xu4vd7o8kbCkcBaGTMfOuG6agmvG85jr7oD95dj5swj85DYCb/weW7zL6RJFolZpaSnp6cF9JNPS0igtLT3l4zdv3kxVVRWtW7cOHXv55Ze57777eOGFFzis1fSB4Lw018XZuB5+CvP9Ozm0cR2Bx+/D7tzqdGkiYUdzzsKYSU7BZF+NvfQ78MmHBJb/FfvOQuw7b7J30Ajs927FpGozYpHGYow55fyokpISfvOb3zBlyhRcRy7kueGGG0hLS6OqqopnnnmGxYsXc+2119b6/Ly8PPLy8gDIzc0lIyOj4RsRjsaOpzqrJ3seux/7xE9Ivf8REnoPcrqqRuV2u2Pn+3uE2nwWr9MAtUgjC06y7U1cVm+sfzd2xTtU5i2CTR/h+uFPMOdlOV2iSNTwer2UlJSQnp5OSUkJqamptT7uwIED5ObmMn78eLp1+896hUdH3eLj4xk1ahRvvfXWSd8rOzub7Ozs0O1Ymp+T0e0CzNQZBP73UfY+8mNMzh2Y0VdG7cUCmn8VGzTnLEYZX0tc352AL/dZiG9G4MlpBPIWa/sUkQbSv39/VqxYAcCKFSsYMGDACY+pqqriySefZPjw4SdM/C8pKQHAWkt+fj4dOmgJiZMxGa1xPfg/0HMA9pVnsQvmYquqnC5LxHEaOYtQ8ed2w/XTXxF4/tfYV+fB5k1wy52YxGSnSxOJGLNnz6awsJCysjImTZpETk4OY8eOZdasWSxbtiy0lAbAli1bWLJkCZMmTWLVqlV88sknlJWVsXz5cuA/S2Y89dRToYsDzjnnHCZOnOhU8yKCSUzC9d9TsYsWYP/2J+yu7bgmPYBJqX3EUiQWaCmNCHV06NRai33nTeybL0HrtrgmTcW06+h0eY1CQ+TRr6mX0gg3sdiHHSuwejn297+B9Ba4/t9PMZnR05fF2u8yqM2no9OaUcwYg+vy/8L140fgwH4Cj/+YwOrlTpclIlJvrsEjcd33GFRWEHjifuzHHzhdkogjFM6ihOl+Ea6fzYZzumDn/YrAH5/G6hJ+EYkwpsv5uKbNhFZtCfzmEQJ/X6g5tRJzFM6iiEnz4br3Ucxl38X+468EZkzF7tntdFkiIvVifC1x/SQX+gzBvv489vdPaRFuiSkKZ1HGuN24vncrrv9+EHZ8Q+DRu7Eb1zldlohIvZiExOBSQVddj313KYEff5/A/NnYj9fqik6JerpaM0qZvkNxtetE4LdPEPj1zzFX5mBGfwfj0RVQIhIZjMuFueYG7Pk9sauWYtetxr63DJp7MH2HYAYMg24XYuLinC5VpEEpnEUx0zoT19QnsX/4LfbPr2L/8jp0zcL0GYzpPQiT0fr0LyIi4jDT/UJM9wuxEyZD4Trsmn8G//zz7+DxYvpdjBlwCZyXhXHphJBEPoWzKGcSEjC33Y299DvY9auDnzxffQ776nPQ4VxMnyGYPoOgXaeoXZlbRKKDiY+HXgMxvQZiD1XCx2ux+f/ErsrDLv8rpPmOBLVhcG43BTWJWApnMcKc0wVzThe45kZs0XbsuveDYe2tl7H/90fIaI3pPRjTZzCcdz7GpdMEIhK+TLME6DcU028otuIg9qN8bP6/sCvexi59CxISoU17TJt20LYDpk17aNseWrXFuOOdLl/klBTOYpBplYn51nfhW9/F7ivBrl+DXf8+dvlfsHmLg6cJLuoPHTtjWmVC60xo0UrzOkQkLJnEJMzA4TBwOPbgAeyHa+Crz7E7t2I/L4T3VxBajMPlgpZtoW37UGAzbdpD+07BwCdyhmx1dYMtYaVwFuNMajpm+Ldg+LewFQewHxfA+tXY9e/DqqX/6dDi3NCyNbTKDAU20/pIcEtrodMHIhIWTFIyZvBIGDwydMxWHIRd27E7voEdW7E7t8KOb7Afr4XqqmA/503HNf6HmH5DHapcIpE9UI7dUAAf5mM3rKXiB/fAhSfux1tfCmcSYhKTg5NqB1wSXPSxbC/s2oHdtQ2KtmN3bQ92cJs+hEOH/hPc4psFw9qwyzAjvq0RNqkXay1s/zd2YwF7t36FveVHCvvSoExiEhyd2nEMW1UFxbtg+9cE/vIagadzoc9gXDf8EJPWwqFqJdzZXduDp9E/XAObC6G6GlJSMb0GENemfYO8h8KZ1MoYA6npkJqO6ZpV4z4bCMDePcGgtmt7MLh98Sn25WexK98JfvrsfqFDlUsksGX7sIXroHB98O+9fgCqOpwL+/ZCms/ZAiUmGLcb2rSDNu1w9RyIzVuM/b+XCUz/f5hrb8FcMkYfFARbXQ1bPsF+mI/9aA3s3Ba8I7Mj5rKxmJ4DoXM3jCuOZhkZ0AD7iSqcSb0Zlwt8LcHXEtOjF3Bk9GPdewRem0/gyYcwA4Zhrr0V48twuFoJB7aqCr7YhN24Lrgo8r+3gLWQnILJ6g1ZvTEX9CGjW4+Y2yhZwoNxuzGX/xe2zxACL83BvjQH+/4KXDf/v+AUDolotrQEvt4MgcDRI8fceewD/3PDVhwMLt3y8Vo4UB6c3tP9QszIKzE9+2Natmm0ehXOpEEYY6DvUFwX9MO+8wb27TexH67BXPG94CeL+GZOlyhnwQYCsP3fUHKS4HSSvQ/tnt3YjQWw6WOoPBicjN35fMzV4zEX9A2eatKVwRJGTOtMXD9+FPuvJdjXnyfw8zuDP69jxgZH2iQi2MpK+Hwj9pP1wQ+E274+sxdKScX0GojpNQCy+mCSkhu20JPQT5o0KJOQgLn6BuzQSwm8Ph+7aAH23Txc190BPQdoLbUIYQMB2PY19rMN2E8/hs83QnnZmb1YRmvM4BGYrD5wfk9McvOGLVakgRljMMMuw17Un8DLz2LffBGb/09c378Tc855jf7+trICPlkPXXpgPN5Gf79oYAMB2PoltnA9tnA9fF4IVYfB7Q4uTjzu+5iuPeCEK3KP+z/p2P+j4uKgTTtHPkAqnEmjMBmtifvvqdjCdQReeY7A/z4KF/bDdd0dwXWHGpktXIfdtT24yK7mL51WsGP7CvvZx9hPNwbD2P4jYSyjNabXwOA2Oa3bBUe/alVL8E7xBJ+vUC4RyKT5iPvvB7EF7xH44zMEHrsPM+YazNU3YBIaZ9kNW7SDwNzHgyM9bjem71DM8Muh2wX6PTqOLdkTDGKF67CffAhlpcE72p2DGXVFcMpE1wsb7XvVmBTOpFGZrD64pv8a+4+/YN96OXiKIPtqzFU5mMSGHx62hw9hX38e+4+/BG+//Du4oDdmyOjgllVaxyj4qbzUD3tLsF9vPjIyVhicUwHQsg2m9yDofhGm24WYFi2dLVjEYabvEFznX4T90wvYvy/ErnsP101TQnNuG4rdUEDgd08G3/PWu+HfW7DvLcOuWRlcUHf4tzBDR2Oaexr0fcONra4OXhi0dw/s9WP37oGSY77e6w/+Obg/+ITUNMwFfaBHb0xWr6i40tZYe5LJIhFo+/btTpfQZDIyMiJu4rQtLQmeHli1NLjNyrjvYwaNqPPVUKdrs93xDYFnZ8DWr4Kfbi/ODu6/t/of4N8NScnBrV2GjIqYPfjq8322B8qhuAhKS7D7SqD0P3/+c3tvcO7XsVq1xXS7MDjRtduFGJ9zYay+P9eZmdE1UVt9WPizn35M4MU5ULQdM2QU5nu3Yzypp33eqdprrcW+8yb2zZcgswOuKdNCk81tZSV27b+wK9+BLZvAHY/pf3FwNO28HmE9mlbX77Hd9nVwjt/nhcHQtW8v2EDNB7lc4PUFr+RO8wUDWMs2mB49w2r7wfr8XJ+q/2qScDZ37lwKCgrwer3MnDkTgPLycmbNmsXu3btp2bIl99xzDykpKVhref7551m3bh0JCQlMnjyZzp071+l91LFFBrtlE4GXnw1eOXNut+Cpzi7nn/Z5J2uztTb4i/3K7yAhEdetPwrucHD0/kAgODH0vWXYD1YFw0mLVsGOdfCosL4S67SBtOJAcCuuNSugcP0xVyIdkdQcvGnBJVG86eANLo+CNx2Tmha8FDyMrqht6nBWn77peMuXL+fNN98EYNy4cYwcORKAL774gjlz5nDo0CH69OnDrbfeWuf/ONSHRQZ7qBL7l9ex77wR/ND3vduCo/On+D6ftP+qrMC+8BT2g39h+l+CueUuTEJi7e+79Svsyrexq5fDwQPBbalGXB7sx5qf+DPqtFMG0oMHsPkrsf/Kgy8/C14J2e2C4IfD9Bbg9WHSWxwJYy3AkxoRFw9FVDgrLCwkMTGROXPmhDrABQsWkJKSwtixY1m0aBHl5eVMmDCBgoIC3n77baZOncrnn3/OCy+8wOOPP16n91HHFjlsIIBd/Y/gJ8VSP2bgCMx/3XzKUZva2mwP7McumIvN/yf06IXrtntOOcfMVlYG9xRdtQw++TD46azL+cHObcAlYXe6oNY2Vx2GDQXYNSuxH74Phw4Fw+bAYZhOXYOfLlPTgoEswuZaNHU4q0/fdKzy8nIefPBBcnNzAUJfp6SkMHXqVG699Va6du3KE088wbe//W369OlTp3rUh0UWu+1rAi/NCY5ond8T14TJJ/2wV+vv8u6dBOY8Btu/wYy7CfOtcXUK8rayIrjh+8p3gsEmvlkw2PUZHJyOECYX3RzfZmstfF4Y/DC99l04VBmcH3ZJNmbQqDqNQIa7hgpnTTLnLCsri6KiohrH8vPz+fnPfw7AiBEj+PnPf86ECRP44IMPGD58OMYYunXrxv79+ykpKSE9Pb0pSpUmYlwuzNBLsX2HYv/2RnAex/r3MN/6r2AHVYdQYb/4NDg/w78b892bMJePO+0nK5OQgBk0AgaNCE4mXbMCu2oZ9g+/xf7xGehwbvDUXvcLoOsFYRPWgqN/hcF6P3g3OD8sJRUzNBszaHjwqq4wGdaPJPXpm461fv16evbsGRpR69mzJ+vXr+eCCy7g4MGDdOvWDYDhw4eTn59f53AmkcW0OwfXT3KxK9/BvvlicE7tlTnBvug0m6vbwnUEnpkBgOtHDwfnTNX1fRMSMZeMgUvGYP/9RXA07f0V2PeWBU//ndsNk9UnOCH+3G6O79piS0uC/ey7ebBrGyQmYQaPDLahU1f1XbVw7IKA0tLSUOBKS0ujtDR4lYXf7ycj4z+nWVq0aIHf71c4i1ImMQnz3QnY4ZcFJ9u+9TL2X0sw424Ozker5ZfWBgLYdxZiFy+AtBa4fpJbp9OiJ7x3egvMt8ZhL/su/PsL7IfvYz/biF3+1+AG8MYE5zJ0vxDT7YLgVT9N+MnOWsvhLz8j8Pbi4MhgSTEkJAYvbBg0Enr00rpLjeBkfdOx/H4/LVr8Z9Kxz+fD7/efcPxo/yXRy7hcmJHfxvYehH3ld9jFf8CuWRm8YOC43VXgyDSMvy/EvvFicH7Z5Icwrdqe+ft37IyZMBl7/Q9gy6dHlpJYh/3zK9i3XoakZOjeE5PVG3NBb2jZtknCkK2qojL/X1T/9Q34KD845aJrFuaKa4Nzf09y6laCwqJnN8ac0Q9LXl4eeXl5AOTm5tYIddHO7XZHV3szMmDa/3Co8EPK5v+aqnm/wv3Pd/Dcfjfx3S4Agm1OjzPs+9/HOPRhPglDR5M6+QFcDTG61bIl9BsEBK/4PPx5IYc2ruPwxvUc+uffsUvfAiCuw7k0u6APzS7sQ3y34MiaSUjAxNX/V8kePkSgZA/V/mICJcUE/MVHvt5DwL+b6p3b8O/aDnFxNOszmKThd5Iw4JLgPoFRKtx+rs+0b6or9WFR1N6MDPjpDCo/eJd9zz5J4H8eJOmya0i56b9xpaTidrtpkdKc0jlPUPmvPBKGjsZ757SG/X1u0xYuHglAYF8phz5ey6EP11C5fg2B9auxgKtVW5r1GkCzXgOJa9Um+AE5IfHI30nQrNlpf+ZtVRWBkmKq9+wmULyL6j1FBPbsprq4iMCeouDtkj3sDQRwpflIvGY8SZdehbvdOQ3X1jDVUD/XjoUzr9cbOl1ZUlJCampwRMLn89U4X7tnzx58vtrnEGVnZ5OdnR26HenzF+ojGuZr1KpVO+xPcjHvLePwwpfwP/CD4PD3uO+TWl7C3ln/H1QexNw0hcPDLsN/sBIOVjZCHe2Df0Z9B1fVYfhqM/azDVR/toGD//gbB99+s+bj49zBxQ0TEoJ/H/fHJCRCXBx2X2lwGYtSf+2LusbFBSfte32Q2RHP2BvZf34vqlNSKQfKy/dD+f6Gb2+YCIerNU/WNx3L5/NRWFgYuu33+8nKysLn87Fnz57Q8VP1X6A+LCrb26k7TH8K839/5OCStzi4egXm+h/Qou8gih+9D7Z9jRn3fQ5fPo49jf373L1n8M/3bsdVtANbuJ5A4ToO/iuPg0v+r/bnGFewH0tIPNKnJf7n64qD4C+GfSUn7gqSkAjpGZDeAtO9Jya9Bak9+1HWsSuVbjeV0CB7Toa7iJpzVpv+/fuzYsUKxo4dy4oVKxgwYEDo+Ntvv83FF1/M559/TnJysk5pxhjjcgWXweh3dD7aIuzaVew9fAjanYNr4mOYzI5NV487PnjJ+nk94IrvBdfg+fcW7L+/gMoKOFQRnNh66FDw78pK7KHKI8cq4EB58HZVFXi8wdMKXS8IhrA0H+aYy8Np7qmxxEdyRgYHYqBDCycn65uO1bt3b15++WXKy4Nrw3344YfccMMNpKSkkJSUxGeffUbXrl1ZuXIll19+eVM3QRxmEpMwObdjB40M7tP57AyK3fHQrBmuux7GXNi3aesxBlpnBi9WGHVFqA+jrDS4zdGhCqg40pdVVsAxx+zRY4cqIak55sKO4MuA9Izg1ZRHAhlJzU8YcUvMyKBc/dcZaZKrNWfPnk1hYSFlZWV4vV5ycnIYMGAAs2bNori4+ISlNObNm8eHH35Is2bNmDx5Ml26dKnT++hKp+hkd+/E/t8fSWrZmorLr42phWRj6fsMTT9yVp++acuWLSxZsoRJkyYBsGzZMhYuXAgEl9IYNWoUAFu2bGHu3LkcOnSI3r17c9ttt2kpjVrEys+2ra7G/uPPxG/+hKpx3z+r+WWRJla+x8eKqKU0moo6tuimNke/cDit6ST1YdEr1toLavPpnKr/Cv8l0kVERERiiMKZiIiISBhROBMREREJIwpnIiIiImFE4UxEREQkjCiciYiIiIQRhTMRERGRMKJwJiIiIhJGFM5EREREwkhU7RAgIiIiEuk0chahHnzwQadLaHJqc/SLtfbGslj7Xsdae0FtPhsKZyIiIiJhROFMREREJIwonEWo7Oxsp0tocmpz9Iu19sayWPtex1p7QW0+G7ogQERERCSMaORMREREJIy4nS5A6m/KlCkkJibicrmIi4sjNzfX6ZIa3Ny5cykoKMDr9TJz5kwAysvLmTVrFrt376Zly5bcc889pKSkOFxpw6itva+99hpLly4lNTUVgPHjx9O3b18ny2xQxcXFzJkzh71792KMITs7myuuuCKqv8+i/itaf65jrQ9r9P7LSsSZPHmyLS0tdbqMRrVx40a7ZcsWe++994aOvfTSS3bhwoXWWmsXLlxoX3rpJYeqa3i1tffVV1+1ixcvdrCqxuX3++2WLVustdYeOHDA3nXXXfabb76J6u+zqP+yNjp/rmOtD2vs/kunNSUsZWVlnfBpIz8/nxEjRgAwYsQI8vPznSitUdTW3miXnp5O586dAUhKSqJdu3b4/f6o/j5LbIi1/gtirw9r7P5LpzUj1GOPPQbAmDFjYuaKmNLSUtLT0wFIS0ujtLTU4Yoa3zvvvMPKlSvp3LkzN998c9R2fkVFRXz55Zecd955Mfl9jjXqv2Ln5zoW+rDG6L8UziLQI488gs/no7S0lEcffZTMzEyysrKcLqtJGWMwxjhdRqO67LLLuPbaawF49dVXefHFF5k8ebLDVTW8iooKZs6cyS233EJycnKN+2Lh+xxr1H/Fzs91LPRhjdV/6bRmBPL5fAB4vV4GDBjA5s2bHa6oaXi9XkpKSgAoKSkJTTKNVmlpabhcLlwuF5deeilbtmxxuqQGV1VVxcyZMxk2bBiDBg0CYu/7HGvUf8XOz3W092GN2X8pnEWYiooKDh48GPr6o48+omPHjg5X1TT69+/PihUrAFixYgUDBgxwuKLGdfQXHGDNmjV06NDBwWoanrWWp59+mnbt2nHVVVeFjsfa9zmWqP+KrZ/raO7DGrv/0iK0EWbXrl08+eSTAFRXV3PJJZcwbtw4h6tqeLNnz6awsJCysjK8Xi85OTkMGDCAWbNmUVxcHHWXotfW3o0bN/LVV19hjKFly5ZMnDgxNJchGmzatInp06fTsWPH0ND/+PHj6dq1a9R+n2Od+q/o/bmOtT6ssfsvhTMRERGRMKLTmiIiIiJhROFMREREJIwonImIiIiEEYUzERERkTCicCYiIiISRhTORERERMKIwplEpClTpvDRRx+Fbr/77rvceuutFBYWOliViEjdqA+TU9HemhLxli9fzosvvsiDDz5I9+7dnS5HRKRe1IfJ8RTOJKItWbKEV155hWnTptGlSxenyxERqRf1YVIbhTOJWH//+9/59NNP+dnPfkanTp2cLkdEpF7Uh8nJaM6ZRKyPP/6Yrl27xszGySISXdSHyckonEnEuuOOO9ixYwdPP/002iJWRCKN+jA5GYUziVher5ef/exnbNq0ieeee87pckRE6kV9mJyMwplENJ/Px/Tp01m/fj0vvPCC0+WIiNSL+jCpjcKZRLyMjAwefvhh3n//ff74xz86XY6ISL2oD5PjGasT3SIiIiJhQyNnIiIiImFE4UxEREQkjCiciYiIiIQRhTMRERGRMKJwJiIiIhJGFM5EREREwojCmYiIiEgYUTgTERERCSMKZyIiIiJhROFMREREJIwonImIiIiEEYUzERERkTCicCYiIiISRhTORERERMKIwpmIiIhIGFE4ExEREQkjCmciIiIiYUThTERERCSMKJyJiIiIhBG30wU0pO3btztdQpPJyMiguLjY6TKalNoc/erb3szMzEasRkTEGRo5ExEREQkjCmciIiIiYUThTERERCSMRNWcM5FYZK2loqKCQCCAMcbpcs7Krl27qKysrHHMWovL5SIxMTHi2yciUhcKZyIRrqKigvj4eNzuyP91drvdxMXFnXC8qqqKiooKkpKSHKhKRKRp6bSmSIQLBAJREcxOxe12EwgEnC5DRKRJKJyJRLhYOdUXK+0UEVE4E5Gz1q5dO+68887Q7aqqKi666CJuvvnmGo+77bbbuOqqq2ocmzlzJv369WPMmDGMHj2aMWPGUFpa2iR1i4iEo+g+F1ILW1lBYMZDmBGX4xp2mdPliESF5ORkNm3axMGDB0lKSmLlypW0adOmxmNKS0v56KOPaN68OV9//TXnnHNO6L4f/OAHTJo0CbfbTVVVVVOXLyISVmJv5KxZAmz9EnbvcLoSkagyevRoli5dCsCiRYsYO3Zsjfv/9re/MWbMGK655hoWL17sQIUiIpEh5kbOjDGQ4oWyfU6XItLgAq/8DvvNlw36mqbDubiu/8FpH3fNNdcwa9YssrOz+eSTT7j++ut5//33Q/cvWrSIe+65h4yMDCZOnMhdd90Vuu93v/sdb7zxBsYYUlNT+dOf/tSgbRARiSQxF84A8KRiyzSnRaQhZWVlsXXrVhYvXszo0aNr3Ld7926+/PJLBg4ciDEGt9vNpk2bOP/88wGd1hQROVaMhjMvlGvkTKJPXUa4GtNll13GL37xC/70pz9RUlISOv7WW29RWlrK4MGDASgvL2fRokU8+OCDTpUqIhK2Ym/OGWBSUkEjZyIN7rrrruPee++lR48eNY4vWrSIBQsW8P777/P+++/zt7/9jf/7v/9zqEoRkfAWuyNnCmciDS4zM5Pbb7+9xrFvvvmGbdu20a9fv9Cxjh074vF4KCgoAGrOObPWMn/+fDp06NCktYuIhAtjrbVOF9FQtm/fXqfHBf78CnbxH3HNfQMTH9/IVTWOjIwMiouLnS6jSanNtTtw4ADJyclNVFHjOtWcs9ramZmZ2RRliYg0qZg8rYknLfi35p2JiIhImInJcGY8qcEvdGpTREREwkxMhjNSvMG/yxXOREREJLzEZjjzBMOZ1UK0EgWiaNroKcVKO0VEYjScHT2tudfRMkQagsvlivqFW6uqqnC5YrO7EpHYE5tLaSSngMulLZwkKiQmJlJRUUFlZWVwe7IIlpCQQGVlZY1j1lpcLheJiYkOVSUi0rRiMpwZlwuae3RBgEQFYwxJSUlOl9EgYnG5FBGR48XueYLUNM05ExERkbATu+EsJVVXa4qIiEjYidlwZjxezTkTERGRsNMk4Wzu3Lnccccd/PjHPz7hvrfeeoucnBz27QsGpaP76t15553cd999fPHFF41TlEebn4uIiEj4aZJwNnLkSB566KETjhcXF/PRRx+RkZEROrZu3Tp27tzJU089xcSJE3nuuecap6gULxwox0b5EgQiIiISWZoknGVlZZGSknLC8d///vfceOONNS7//+CDDxg+fDjGGLp168b+/fspKSlp+KI8R3cJ0KlNERERCR+OzTnLz8/H5/PRqVOnGsf9fn+NkbQWLVrg9/sb/P1D+2vqogAREREJI46sc1ZZWcnChQv56U9/elavk5eXR15eHgC5ubk1Qt3pHGp/DiVAqsuQUI/nhQu3212v9kYDtTn6xVp7RURq40g427VrF0VFRdx///0A7NmzhwceeIAnnngCn89XYxHKPXv24PP5an2d7OxssrOzQ7frs3ilDQT36Svd+m9cmZ3OoBXOisXFOtXm6Fff9mZmZjZiNSIiznAknHXs2LHGRP8pU6bwxBNPkJqaSv/+/Xn77be5+OKL+fzzz0lOTiY9Pb3hizg650zLaYiIiEgYaZJwNnv2bAoLCykrK2PSpEnk5OQwevToWh/bp08fCgoKuOuuu2jWrBmTJ09unKKap4AxmnMmIiIiYaVJwtndd999yvvnzJkT+toYwx133NHIFYFxxQX319yncCYiIiLhI2Z3CADA48Vq5ExERETCSMyHM+0SICIiIuEkxsNZqi4IEBERkbAS0+HMeLy6IEBERETCSkyHM1K8sL8cW13tdCUiIiIiQKyHM08qWAv7dWpTREREwkOMhzMtRCsiIiLhJabDmUk5svm5rtgUERGRMBHT4YzUNACsRs5EREQkTMR2OPMcGTnTFZsiIiISJmI7nDXXaU0REREJLzEdzkzckf01dVpTREREwkRMhzMAPKnYsr1OVyEiIiICKJwFF6LVyJmIiIiECYWzVG1+LiIiIuEj5sOZSfFCuUbOREREJDzEfDjDkwrlZdhAwOlKRERERBTO8HjBBmB/udOViIiIiCicEdrCaa+jZYiIiIiAwhlGm5+LiIhIGIn5cMbRcKYtnERERCQMKJwdCWdWy2mIiIhIGFA4C80502lNERERcV7MhzPjdkNycy1EKyIiImEh5sMZENzCSQvRioiISBhQOIPg5uf79jpdhYiIiIjCGRC8KEAjZyIiIhIGFM44staZ5pyJiIhIGFA4g9DImfbXFBEREacpnEFw8/NAAA7ud7oSERERiXEKZxC8WhN0alNEREQcp3CG9tcUERGR8KFwBsHTmgBlex0tQ0REREThDEKnNa1GzkRERMRhCmcQ2vxcc85ERETEaQpngImPh6RkLUQrIiIijlM4OyolVSNnIiIi4jiFs6M8XqzCmYiIiDhM4ewobeEkIiIiYUDh7AiTkqp1zkRERMRxCmdHpR7ZX9NapysRERGRGOZuijeZO3cuBQUFeL1eZs6cCcArr7zCBx98gDEGr9fL5MmT8fl8WGt5/vnnWbduHQkJCUyePJnOnTs3fpEpXqiuCu6vmZzS+O8nIiIiUosmGTkbOXIkDz30UI1jV199NU8++SQzZsygb9++/OlPfwJg3bp17Ny5k6eeeoqJEyfy3HPPNUWJx6x1plObIiIi4pwmCWdZWVmkpNQcjUpOTg59XVlZiTEGgA8++IDhw4djjKFbt27s37+fkpKSRq/RhLZw0kUBIiIi4pwmOa15Mi+//DIrV64kOTmZhx9+GAC/309GRkboMS1atMDv95Oent64xRwdOStXOBMRERHnOBrOxo8fz/jx41m4cCFvv/02OTk59Xp+Xl4eeXl5AOTm5tYIdfVVbasoBpoHqkk+i9dpKm63+6zaG4nU5ugXa+0VEamNo+HsqGHDhvHEE0+Qk5ODz+ejuLg4dN+ePXvw+Xy1Pi87O5vs7OzQ7WOfV1/2cDUA5Tu2ceAsXqepZGRknFV7I5HaHP3q297MzMxGrEZExBmOLaWxY8eO0Nf5+fmhTrZ///6sXLkSay2fffYZycnJjX9KEzDNEiAhSftrioiIiKOaZORs9uzZFBYWUlZWxqRJk8jJyaGgoIAdO3ZgjCEjI4OJEycC0KdPHwoKCrjrrrto1qwZkydPbooSgzzaX1NERESc1STh7O677z7h2OjRo2t9rDGGO+64o5ErOgmPF6ulNERERMRB2iHgWCmpulpTREREHKVwdgzj8cI+hTMRERFxjsLZsTzBkTPtrykiIiJOUTg7lscLVVVQcdDpSkRERCRGKZwdK7S/pk5tioiIiDMUzo5hFM5ERETEYQpnx0o5ur+mltMQERERZyicHcuTCoDVyJmIiIg4ROHsWDqtKSIiIg5TODuGSUiEZs0UzkRERMQxCmfH86SBtnASERERhyicHS8lFastnERERMQhCmfH83g1ciYiIiKOUTg7jvGkas6ZiIiIOEbh7Hger/bXFBEREcconB0vxQuHDkFlhdOViIiISAxSODvekYVodWpTREREnKBwdhzjSQt+oS2cRERExAEKZ8fTyJmIiIg4SOHseEe2cLJaTkNEREQcoHB2vKMjZ1qIVkRERBygcHa8hCRwx8M+hTMRERFpegpnxzHGHNklQOFMREREmp7CWW08Xqyu1hQREREHKJzVRls4iYiIiEMUzmphdFpTREREHOKu6wM3bNhAq1ataNWqFSUlJfzhD3/A5XJxww03kJaW1oglOiDFq0VoRURExBF1HjmbN28eLlfw4S+++CLV1dUYY3jmmWcarTjHeFKhsgJbWel0JSIiIhJj6jxy5vf7ycjIoLq6mg8//JC5c+fidrv54Q9/2Jj1OePIQrSUl0JCK2drERERkZhS55GzpKQk9u7dS2FhIe3btycxMRGAqqqqRivOKUZbOImIiIhD6jxydvnllzN16lSqqqq45ZZbANi0aRPt2rVrrNqcc3Tzc23hJCIiIk2szuFs7NixDBw4EJfLRZs2bQDw+XxMmjSp0YpzzJGRM1tWinG4FBEREYktdQ5nAJmZmaGvN2zYgMvlIisrq8GLclzKMXPORERERJpQneecPfzww2zatAmARYsW8etf/5pf//rXvPnmm41WnGOSkiHOrdOaIiIi0uTqHM6++eYbunXrBsDSpUt5+OGHeeyxx1iyZEmjFeeU4P6aqVC21+lSREREJMbU+bSmtRaAnTt3AtC+fXsA9u/f3whlhYEUL1YjZyIiItLE6hzOunfvzvz58ykpKWHAgAFAMKh5PJ5GK85RqdrCSURERJpenU9rTpkyheTkZM455xxycnIA2L59O1dccUWjFeckoy2cRERExAF1HjnzeDzccMMNNY717du3wQsKG55UjZyJiIhIk6tzOKuqquLNN99k5cqVlJSUkJ6ezvDhwxk3bhxud71W5IgMHi9UHMQePoyJj3e6GhEREYkRdU5VCxYsYMuWLfzgBz+gZcuW7N69mzfeeIMDBw6EdgyIKsdu4eTLcLYWERERiRl1DmerV69mxowZoQsAMjMzOffcc7n//vtPG87mzp1LQUEBXq+XmTNnAvDSSy+xdu1a3G43rVu3ZvLkyTRv3hyAhQsXsmzZMlwuF7feeiu9e/c+s9adBZPixYLCmYiIiDSpOl8QcHQpjTMxcuRIHnrooRrHevbsycyZM3nyySdp27YtCxcuBGDr1q2sWrWKX/3qV0ybNo158+YRCATO+L3PmOfILgGadyYiIiJNqM7hbMiQIfzyl79k/fr1bN26lfXr1zNjxgyGDBly2udmZWWRkpJS41ivXr2Ii4sDoFu3bvj9fgDy8/MZOnQo8fHxtGrVijZt2rB58+b6tKlhHAlnVls4iYiISBOq82nNCRMm8MYbbzBv3jxKSkrw+XwMHTqUqqqqsy5i2bJlDB06FAC/30/Xrl1D9/l8vlBwa1KhkTMtpyEiIiJNp87hzO12c91113HdddeFjh06dIibbrqJCRMmnHEBb775JnFxcQwbNqzez83LyyMvLw+A3NxcMjIabm6YbdGCorg4kqoP42nA120obre7QdsbCdTm6Bdr7RURqc1ZrYFhjDmrN1++fDlr165l+vTpodfy+Xzs2bMn9Bi/34/P56v1+dnZ2WRnZ4duFxcXn1U9J0hJ5WDRTiob+nUbQEZGRsO3N8ypzdGvvu3NzMxsxGpERJxR5zlnDW39+vUsXryYBx54gISEhNDx/v37s2rVKg4fPkxRURE7duzgvPPOc6bIlFSsLggQERGRJnTakbMNGzac9L66zjebPXs2hYWFlJWVMWnSJHJycli4cCFVVVU88sgjAHTt2pWJEyfSoUMHhgwZwr333ovL5eL222/H5XIoQ3q0v6aIiIg0rdOGs9/+9renvL8u80PuvvvuE46NHj36pI8fN24c48aNO+3rNjbj8WK/duBKUREREYlZpw1nc+bMaYo6wpPHq6s1RUREpEk5NucsInhS4eB+bNVhpysRERGRGKFwdiopR9Y6K9fomYiIiDQNhbNTMFqIVkRERJqYwtmpeFKDf5ftdbQMERERiR0KZ6dydH9NjZyJiIhIE1E4O5XQaU2tdSYiIiJNQ+HsVJJTwOXSnDMRERFpMgpnp2BcLmjugXKNnImIiEjTUDg7HY9X+2uKiIhIk1E4Ox3tEiAiIiJNSOHsNExKqi4IEBERkSajcHY6qV6FMxEREWkyCmenk+KFA+XYqiqnKxEREZEYoHB2OkfXOttf5mwdIiIiEhMUzk7DhLZw0qlNERERaXwKZ6ejXQJERESkCSmcnU7K0f01Fc5ERESk8SmcnU7otKbWOhMREZHGp3B2OikeMEZbOImIiEiTUDg7DeOKC+6vWVridCkiIiISAxTO6qJTV+wnH2KtdboSERERiXIKZ3Vg+g6B4l3wzRdOlyIiIiJRTuGsDkzvweByYde+53QpIiIiEuUUzurAeFKh24XYglVOlyIiIiJRTuGsjkzfIbBzK3b7v50uRURERKKYwlkdmT6DAbAFOrUpIiIijUfhrI5MWgvocr5ObYqIiEijUjirB9N3KHzzJXb3TqdLERERkSilcFYPpu8QAI2eiYiISKNROKsHk9EazjkPu1bhTERERBqHwlk9mT6D4cvPsP5ip0sRERGRKKRwVk+m31AA7DpdtSkiIiINT+Gsnkyb9pDZUUtqiIiISKNQODsDpu9Q+LwQu2+v06WIiIhIlFE4OwOm3xCwAez61U6XIiIiIlFG4exMtOsErdpqI3QRERFpcApnZ8AYg+kzBD79CLu/3OlyREREJIoonJ0h028oVFdjP3zf6VJEREQkiiicnalOXcGXoas2RUREpEEpnJ2h0KnNjeuwFQecLkdERESihMLZWTB9h0LVYezHa50uRURERKKEuyneZO7cuRQUFOD1epk5cyYA7733Hq+//jrbtm3j8ccfp0uXLqHHL1y4kGXLluFyubj11lvp3bt3U5RZf+edD6lpsHYVDBjmdDUiIiISBZpk5GzkyJE89NBDNY516NCB++67jx49etQ4vnXrVlatWsWvfvUrpk2bxrx58wgEAk1RZr0ZVxym92DshrXYQ5VOlyMiIiJRoEnCWVZWFikpKTWOtW/fnszMzBMem5+fz9ChQ4mPj6dVq1a0adOGzZs3N0WZZ8T0GwKVFbBxndOliIiISBQIuzlnfr+fFi1ahG77fD78fr+DFZ1Gt4sgOQVbsMrpSkRERCQKNMmcs8aSl5dHXl4eALm5uWRkZDhSR+ng4VSuXkkLrxcTH98k7+l2ux1rr1PU5ugXa+0VEalN2IUzn8/Hnj17Qrf9fj8+n6/Wx2ZnZ5OdnR26XVxc3Oj11cZm9cMu+yvF7y7DXNivSd4zIyPDsfY6RW2OfvVtb21TI0REIl3Yndbs378/q1at4vDhwxQVFbFjxw7OO+88p8s6taxekJikBWlFRETkrDXJyNns2bMpLCykrKyMSZMmkZOTQ0pKCvPnz2ffvn3k5ubSqVMnpk2bRocOHRgyZAj33nsvLpeL22+/HZcr7DJkDSa+Geai/th1q7E3/jcmLs7pkkRERCRCGWutdbqIhrJ9+3bH3tuufZfA07/E9eNHMef3bPT3i7XTXaA2xwKd1hQRCcPTmhHrwn7QrJmu2hQREZGzonDWQExCIlzQN3hqM0wXzRUREZHwp3DWgEzfobDXD19+5nQpIiIiEqEUzhqQ6TkA4tw6tSkiIiJnTOGsAZnk5tCjF3btKqLoOgsRERFpQgpnDcz0HQJ7iuDfXzhdioiIiEQghbMGZnoPBpcL+/5yp0sRERGRCBR22zdFOuNJhZ4DsEsWU/31FlxX34DpfqHTZYmIiEiE0MhZI3BNvB9z/UTYtZ3Akw9RPfOn2M2FTpclIiIiEUAjZ43AxDfDXHoVdtgY7Mq3sX/9E4FfPghZfXBdPR7T5XynSxQREZEwpXDWiEyzBEz2Ndhh38Iu/xv2nTcJ5P4ELuwXPN15blenSxQREZEwo3DWBExCIuZb38WOuBz7j78GQ9rjP4aeA4Ih7ZwuTpcoIiIiYULhrAmZxCTMt/8LO+rb2KV/xv59EYFH74Heg3Bddb1CmoiIiCicOcEkJmOuzMGOuhK79C3sksUE1t8D5/XAjLwC03coJj7e6TJFRETEAQpnDjLJzTHfuR576VXYd5dil/8V+9xMrOc5zLDLMMMvx7Ro6XSZIiIi0oQUzsKASU7BjLkGe+l3oHA9geV/xf7tDezf3oBeA3CNugLO74VxaeUTERGRaKdwFkaMywUX9iXuwr7YPUXYFW9j/7WEwPr3oVUmZtS3MUMuxTRPcbpUERERaSTGRtEO3du3b3e6hAZnDx/Grn0Xu/yvsGUTNGuGGTSS9O/eSKkn3enymlRGRgbFxcVOl9GkYq3N9W1vZmZmI1YjIuIMjZyFORMfjxk8EgaPxP57S3C9tPeX4383D3PNjZjL/0unO0VERKKI/lePIKZjF1w3/z9c//MCCUNHYRe+RGDOY9j95U6XJiIiIg1E4SwCmeYpeO/9RXD/zo0FBB69B/vvLU6XJSIiIg1A4SxCGWNwXXoVrvufgKoqAk/8hMA//+50WSIiInKWFM4inOlyPq7ps6FrFvbF/yXwwq+xhyqdLktERETOkMJZFDAeL667fx7cdeDdpQRyf4It2uF0WSIiInIGFM6ihHHF4Ro7AdedP4M9uwk8ei92/WqnyxIREZF6UjiLMqbnAFw/mwWt2hKY8ziBN3+Pra52uiwRERGpI4WzKGQyWuN6IBcz/HLs394gMGs6dl+J02WJiIhIHSicRSkT3wzXTZMxt94NX35K4Od3EXh1HvazDdiARtJERETClXYIiHKuoaOxHc8l8OZL2OV/weYthpRUTK+BmD6DoUcvTLMEp8sUERGRIxTOYoBpfy5xd03HVhyADQXYde9jC1Zh382DhES4oC+mzyDMRQO0qbqIiIjDFM5iiElMhv6XYPpfgq06DJ9uwK5f/Z+wFhcH3S7E9BkcHFnztXS6ZBERkZhjrLXW6SIayvbt250uoclkZGRQXFzcIK9lAwH46vMjQW017NwWvCPFA60yMa0zoVUmtG6Had02eCwxqUHeuz4ass2RItbaXN/2ZmZmNmI1IiLO0MiZYFwu6Nwd07k7jPs+dsdW7Ia1sHMrdtd27CcfwXv/ACCU5L0+aN0W07odtGqLadMOevTBJGj+mpwZG6im6ust0NzrdCkiIo5SOJMTmLbtMW3b1zhmKyugaAcUbcfu2g67tmOLtmPXvw9lpcHQ5muJK+d26DsEY4wjtUtksf7d2I3rYOM67CcfsqfiAK5fLdDcRxGJaQpnUicmIRE6nAsdzuX42GUPlMMXnxJ44/cEns6FHr1wXfcDTLuOjtQq4ctWVsBnG7EbC4KhbOfW4B1pPkyfQaQOHkGZO97ZIkVEHKZwJmfNJKfAhf1w9eiNXfk2dtEfCPziLszoqzDfGY9Jbu50ieIQay1s/QpbuC4Yxj7fCFVVEN8Mul2AGXYZ5oK+kNkBYwyJGRmUx9AcOxGR2iicSYMxcXGYUVdi+w/DLlqAXfoW9v0VmP/6PmbI6ODcNokoNhCAHd9gP/0Y+9kGKNlz3ANOcz2RfzeUHtmdot05wcCe1Qe6Zml9PRGRk1A4kwZnPKmYmyZjh3+LwMvPYF94CrvibVzjJ2LO7eZ0eXIKNhCA7f/GfroB+9nH8NlGKN8XvNOXAa3bgTkuZB9/nvuY+YamVVvo0RtzQW9MWovGLV5EJEoonEmjMed0wfXAL7Grl2PfeIHA4/dhLs7GjLsJk5reaO9rd+8k8Pxs2LkN0/8SzNDRcM55ukihFjYQgG1fB7f1+vTj4GnH8rLgnS1aYS7qD90vxHS7EDJa699QRKQJKJxJozLGYIaMwvYZhP3zq9i8t7AFqzBXj8eMvBLjbtgfwUD+v7Av/S9goPtF2H/+HfuPv0DbDpghozCDRsTM4rrWWji4H0r3wr4S7F4/7NsbPM1YWoIt9cO/v4D9R8JYRmtMz4GhMGYyWjtZvohIzNIitBEqUhcntTu3Enjld7BxHbTtgCvnNsyF/er03FO12VZWYF99DvvPv0Pn7rh+cB8mozX2QDn2g3ex7/0DNhcGT7md3xMzeBSm7xBHFtOtj7p8n6218NVm7Np/YYt2hMIX+/bC4UMnPsHtDq5Tl5qGyewA3XsGw1gL50OrFqEVEWmicDZ37lwKCgrwer3MnDkTgPLycmbNmsXu3btp2bIl99xzDykpKVhref7551m3bh0JCQlMnjyZzp071+l9FM4ig7UWPlxD4PX5wbXTLuqP63u3nbC22vFO1ma79UsCz8yAXdswl/8X5uobah2Rs0U7gqdYV/8Ddu+EZgmYvkMxQ0bB+RdhXHEN1saGcspAunMbds0K7PsroWh7MHS1ygRvOsabDqnp4A3+MalpkOYLHktuHranJxXORESaKJwVFhaSmJjInDlzQuFswYIFpKSkMHbsWBYtWkR5eTkTJkygoKCAt99+m6lTp/L555/zwgsv8Pjjj9fpfRTOIos9fBj7jz9j//wqHKrEjLwiuPTGSRYgPb7N1lrs8r9iX5sPzVNw3X4vpkev07+vtbDlE+x7/8Dm/yt46i+tBWbAJZjze8J5WWGz/McJbd67B5v/L+z7K+DrzcGRwO4XYQYOx/QbGlzWJIIpnImINNGcs6ysLIqKimocy8/P5+c//zkAI0aM4Oc//zkTJkzggw8+YPjw4Rhj6NatG/v376ekpIT09MabQC7OMPHxmMu+ix08Crv4j9hlf8GuXo655gbM8MsxcScfybL7ywi88BtYvzq4xtqtPwqODtXlfY0JBrDzsrDX/yA4irdqWfD9lywOXo3Y4dzgqb7uF0LXCxxdsd4eKMcWvBcMZJ9+HFy+4pzzMN+7DTNwmK6CFBGJMo5dEFBaWhoKXGlpaZSWlgLg9/vJyMgIPa5Fixb4/X6FsyhmUtOCS2+M+jaBV57D/vEZ7D/+iuu6OzAX9Dnh8fazjQSemwn79gYDSvbVZ7yGmolvBv0vIa7/JdhDlfDFp8ErFz/bGByVy1scHJ1q1wnT/UJMtwug64UYT+rZNrtWtqoK9pXAXj929072blhL4IN3oeowtGyDufK64CjZaU4Bi4hI5AqLqzWNMWc0ByYvL4+8vDwAcnNza4S6aOd2u6OvvRkZ2F79qVyzkvIX/pfq2Q/TrP/FeG75f7jbnUOcMSQuXcz+154nrnUm3oeeIf68Hg1bQ2Y7uGQ0APZQJYc/L+TQxvUc3riOQ//8O3bpWwDEdTiX+O4X4mqegmmWiElIwCQkBi8wSEg4cuzonwRMQhLG7SZQWkK1v5hASTEBfzHVJXsIHLld7S/G7ttbo5zDaT6SL/8uicMuw921R9jOFWsoUflzLSJST46FM6/XGzpdWVJSQmpqcCTC5/PVmHOyZ88efD5fra+RnZ1NdnZ26Hakz8Gqj2iYc3ZSXS7ATn8Ks+wtDv35Vfb8aAJm5BW4d3zD4cL1mMEjsTdOojQxGRr736B1h+Cf0d/BVXUYvvoc++kGqj/bSPX7K6GyAg5VntlrGxd404JXTqb5MB3PC07kT/NhvD5I95HRqx97SvZSCbBnz2leMPJpzpmIiIPhrH///qxYsYKxY8eyYsUKBgwYEDr+9ttvc/HFF/P555+TnJysU5oxyMTHY741DjtkFHbRH7DL/kxVQiLm1rtxDR3tTE3u+NBcNa78z3FrbXDJikOVwT+Vlf/5+lAlVFYET5lWV2FSvMGrJr3pkOo97RWiJi4sBrdFRKQJNcnVmrNnz6awsJCysjK8Xi85OTkMGDCAWbNmUVxcfMJSGvPmzePDDz+kWbNmTJ48mS5dutTpfXS1ZvSyO7bia92aEle806U0qVj7PmvkTEREi9BGrFj7TxvU5ligcCYiAmd2iZuIiIiINAqFMxEREZEwonAmIiIiEkYUzkRERETCiMKZiIiISBhROBMREREJIwpnIiIiImFE4UxEREQkjCiciYiIiISRqNohQERERCTSaeQsQj344INOl9Dk1OboF2vtFRGpjcKZiIiISBhROBMREREJIwpnESo7O9vpEpqc2hz9Yq29IiK10QUBIiIiImFEI2ciIiIiYcTtdAFSf1OmTCExMRGXy0VcXBy5ublOl9Tg5s6dS0FBAV6vl5kzZwJQXl7OrFmz2L17Ny1btuSee+4hJSXF4UobRm3tfe2111i6dCmpqakAjB8/nr59+zpZZoMqLi5mzpw57N27F2MM2dnZXHHFFVH9fRYRqQud1oxAU6ZM4Yknngj9px2NCgsLSUxMZM6cOaGwsmDBAlJSUhg7diyLFi2ivLycCRMmOFxpw6itva+99hqJiYlcffXVDlfXOEpKSigpKaFz584cPHiQBx98kPvvv5/ly5dH7fdZRKQudFpTwlJWVtYJoyX5+fmMGDECgBEjRpCfn+9EaY2itvZGu/T0dDp37gxAUlIS7dq1w+/3R/X3WUSkLnRaM0I99thjAIwZMyZmrnArLS0lPT0dgLS0NEpLSx2uqPG98847rFy5ks6dO3PzzTdHbYArKiriyy+/5LzzzovJ77OIyLEUziLQI488gs/no7S0lEcffZTMzEyysrKcLqtJGWMwxjhdRqO67LLLuPbaawF49dVXefHFF5k8ebLDVTW8iooKZs6cyS233EJycnKN+2Lh+ywicjyd1oxAPp8PAK/Xy4ABA9i8ebPDFTUNr9dLSUkJEJyvFM1z7iA4auRyuXC5XFx66aVs2bLF6ZIaXFVVFTNnzmTYsGEMGjQIiL3vs4jI8RTOIkxFRQUHDx4Mff3RRx/RsWNHh6tqGv3792fFihUArFixggEDBjhcUeM6GlAA1qxZQ4cOHRyspuFZa3n66adp164dV111Veh4rH2fRUSOp6s1I8yuXbt48sknAaiuruaSSy5h3LhxDlfV8GbPnk1hYSFlZWV4vV5ycnIYMGAAs2bNori4OOqWWKitvRs3buSrr77CGEPLli2ZOHFiaC5WNNi0aRPTp0+nY8eOoVOX48ePp2vXrlH7fRYRqQuFMxEREZEwotOaIiIiImFE4UxEREQkjCiciYiIiIQRhTMRERGRMKJwJiIiIhJGFM5EREREwojCmUSkKVOm8NFHH4Vuv/vuu9x6660UFhY6WJWIiMjZ096aEvGWL1/Oiy++yIMPPkj37t2dLkdEROSsKJxJRFuyZAmvvPIK06ZNo0uXLk6XIyIictYUziRi/f3vf+fTTz/lZz/7GZ06dXK6HBERkQahOWcSsT7++GO6du0aMxu/i4hIbFA4k4h1xx13sGPHDp5++mm0RayIiEQLhTOJWF6vl5/97Gds2rSJ5557zulyREREGoTCmUQ0n8/H9OnTWb9+PS+88ILT5YiIiJw1hTOJeBkZGTz88MO8//77/PGPf3S6HBERkbNirCbriIiIiIQNjZyJiIiIhBGFMxEREZEwonAmIiIiEkYUzkRERETCiMKZiIiISBhROBMREREJIwpnIiIiImFE4UxEREQkjCiciYiIiISR/x9wNh1YQzdnDAAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[MSE] Minimum error 99.4734 is at k = 9\n",
            "[RMSE] Minimum error 9.97363524498465 is at k = 9\n",
            "[MAE] Minimum error 99.4734 is at k = 9\n"
          ]
        }
      ]
    }
  ]
}