Homework_4/Homework_4.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.datasets import make_classification\n",
    "from sklearn.datasets import make_blobs\n",
    "from matplotlib.pylab import plt\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cross_validation import train_test_split\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from sklearn import datasets\n",
    "\n",
    "#kmean\n",
    "from scipy.spatial.distance import cdist, pdist\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.metrics import silhouette_samples, silhouette_score\n",
    "\n",
    "#Gaussian mixture\n",
    "from sklearn.mixture import GaussianMixture\n",
    "\n",
    "#logistics regression\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import confusion_matrix, accuracy_score, precision_score, classification_report\n",
    "\n",
    "\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 1.  (33 pts)\n",
    "\n",
    "Let's explore clustering models on an artificial data set with five features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        text-align: right;\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.624358</td>\n",
       "      <td>-0.007694</td>\n",
       "      <td>0.157510</td>\n",
       "      <td>0.440554</td>\n",
       "      <td>0.157423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.065098</td>\n",
       "      <td>-0.000790</td>\n",
       "      <td>0.271934</td>\n",
       "      <td>0.224854</td>\n",
       "      <td>0.158883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.086525</td>\n",
       "      <td>-0.280988</td>\n",
       "      <td>-0.025699</td>\n",
       "      <td>0.263920</td>\n",
       "      <td>0.421017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.581743</td>\n",
       "      <td>-0.275640</td>\n",
       "      <td>-0.290320</td>\n",
       "      <td>-0.213967</td>\n",
       "      <td>0.497857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.170606</td>\n",
       "      <td>1.020045</td>\n",
       "      <td>-0.583633</td>\n",
       "      <td>0.887644</td>\n",
       "      <td>0.105641</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          1         2         3         4         5\n",
       "0  0.624358 -0.007694  0.157510  0.440554  0.157423\n",
       "1 -0.065098 -0.000790  0.271934  0.224854  0.158883\n",
       "2 -0.086525 -0.280988 -0.025699  0.263920  0.421017\n",
       "3 -0.581743 -0.275640 -0.290320 -0.213967  0.497857\n",
       "4  0.170606  1.020045 -0.583633  0.887644  0.105641"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1 = pd.read_csv('hw4data1.csv')\n",
    "data1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### a) First, visualize the data after applying PCA in two dimensions. Based on the plot (with axes corresponding to the two leading PCs), guess the number of clusters we could have. (5 pts)\n",
    "\n",
    "#### b) Use K-means to cluster the original data based on your guess for the number of clusters. Report the resulting labels. (3 pts)\n",
    "\n",
    "#### c) Visualize the clustering result: reuse the plot from part a) and color the points according to the labels obtained in part b). (5 pts)\n",
    "\n",
    "#### d) Justify your guess for k (the optimal number of clusters for K-means clustering) by first using silhouette_score and then the Elbow method on the original data. Briefly explain your approach. Are your results consistent? (12 pts)\n",
    "\n",
    "#### e) Using a Gaussian Mixture model instead of K-means (but with the same value for k), repeat parts b) and c). (8 pts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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M/s2DDefExJ3kW03slGIAoEYcB2tUVZfNS71RiZunAFCj2aEcUiWp33TXgUVddyk3KpHY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\ndgDIGBI7AGTM/wPey1SUG6x1vwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2190a4738d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#a) \n",
    "n = data1.shape[1]\n",
    "pca = PCA(n)\n",
    "data1_ = pca.fit_transform(data1)\n",
    "plt.scatter(data1_[:,0], data1_[:,1]);\n",
    "\n",
    "#base on the plots we can see 4 clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0\n",
      " 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
      " 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2]\n"
     ]
    }
   ],
   "source": [
    "#b)\n",
    "KM = KMeans(n_clusters=4).fit(data1)\n",
    "print(KM.labels_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2190a3b4e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#c)\n",
    "plt.scatter(data1_[:,0], data1_[:,1], c = KM.labels_ );"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#d) \n",
    "def elbow(data,K):\n",
    "#data is your input as numpy form\n",
    "#K is a list of number of clusters you would like to show.\n",
    "    # Run the KMeans model and save all the results for each number of clusters\n",
    "    KM = [KMeans(n_clusters=k).fit(data) for k in K]\n",
    "    \n",
    "    # Save the centroids for each model with a increasing k\n",
    "    centroids = [k.cluster_centers_ for k in KM]\n",
    "\n",
    "    # For each k, get the distance between the data with each center. \n",
    "    D_k = [cdist(data, cent, 'euclidean') for cent in centroids]\n",
    "    \n",
    "    # But we only need the distance to the nearest centroid since we only calculate dist(x,ci) for its own cluster.\n",
    "    globals()['dist'] = [np.min(D,axis=1) for D in D_k]\n",
    "    \n",
    "    # Calculate the Average SSE.\n",
    "    avgWithinSS = [sum(d)/data.shape[0] for d in dist]\n",
    "    \n",
    "    \n",
    "    # elbow curve\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.plot(K, avgWithinSS, 'b*-')\n",
    "    plt.grid(True)\n",
    "    plt.xlabel('Number of clusters')\n",
    "    plt.ylabel('Average within-cluster sum of squares')\n",
    "    plt.title('Elbow for KMeans clustering')\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "    # Total with-in sum of square plot. Another way to show the result.\n",
    "    wcss = [sum(d**2) for d in dist]\n",
    "    tss = sum(pdist(data)**2)/data.shape[0]\n",
    "    bss = tss-wcss\n",
    "    \n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.plot(K, bss/tss*100, 'b*-')\n",
    "    plt.grid(True)\n",
    "    plt.xlabel('Number of clusters')\n",
    "    plt.ylabel('Percentage of variance explained')\n",
    "    plt.title('Elbow for KMeans clustering')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For n_clusters = 2 The average silhouette_score is : 0.57509003827\n",
      "For n_clusters = 3 The average silhouette_score is : 0.734781965186\n",
      "For n_clusters = 4 The average silhouette_score is : 0.850803605875\n",
      "For n_clusters = 5 The average silhouette_score is : 0.700651501101\n",
      "For n_clusters = 6 The average silhouette_score is : 0.553487179483\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2190a7a8e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dBzAEGJ091s+zThvbGg38Ons+Argxe/56s+Xmt7et4cOHR2dMmTKlU+u35itf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\n/wFsQ0KvvpNwAgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2190a368240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=np.asarray(data1.iloc[:,:-1])\n",
    "range_n_clusters = [2, 3, 4, 5, 6]\n",
    "\n",
    "for n_clusters in range_n_clusters:\n",
    "\n",
    "    clusterer = KMeans(n_clusters=n_clusters, random_state=324)\n",
    "    cluster_labels = clusterer.fit_predict(X)\n",
    "    silhouette_avg = silhouette_score(X, cluster_labels)\n",
    "    print(\"For n_clusters =\", n_clusters,\n",
    "          \"The average silhouette_score is :\", silhouette_avg)\n",
    "    sample_silhouette_values = silhouette_samples(X, cluster_labels)\n",
    "#elbow\n",
    "elbow(X,range(1,10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* from the average silluette score, we can see that 4 clusters is the best number of clusters \n",
    "* from the elbow plots, we can see the best number of clusters is 4\n",
    "* since when number of cluster is 4, \n",
    "    * average within-cluster sum of squares starts to converge \n",
    "    * Percentage of variance explained starts to converge to 100%\n",
    "* the result is consistent with previous prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3\n",
      " 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
      " 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "#e) Using a Gaussian Mixture model (with same k), repeat parts b) and c).\n",
    "n=4 # number of clusters.\n",
    "\n",
    "GM = GaussianMixture(n_components=n)\n",
    "GM.fit(data1.iloc[:,:-1])\n",
    "res_Mix=GM.predict(data1.iloc[:,:-1])\n",
    "print(res_Mix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2190e39a128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(data1_[:,0], data1_[:,1], c = res_Mix );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2. (14 pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following data comes from a larger set detailing every motor vehicle collision in NYC (available [here](https://data.cityofnewyork.us/Public-Safety/NYPD-Motor-Vehicle-Collisions/h9gi-nx95)). This particular subset only considers collisions that occurred on October 31, 2017.\n",
    "\n",
    "You have 680 collision records in the file ‘NYPD_Motor_Vehicle_Collisions_Duplicates.csv’, but you realize that some of these are actually duplicates resulting from a technical error. You know that there are approximately 620 unique records in the file, but you want to determine the exact number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>DATE</th>\n",
       "      <th>TIME</th>\n",
       "      <th>BOROUGH</th>\n",
       "      <th>ZIP CODE</th>\n",
       "      <th>LATITUDE</th>\n",
       "      <th>LONGITUDE</th>\n",
       "      <th>LOCATION</th>\n",
       "      <th>ON STREET NAME</th>\n",
       "      <th>CROSS STREET NAME</th>\n",
       "      <th>OFF STREET NAME</th>\n",
       "      <th>...</th>\n",
       "      <th>CONTRIBUTING FACTOR VEHICLE 2</th>\n",
       "      <th>CONTRIBUTING FACTOR VEHICLE 3</th>\n",
       "      <th>CONTRIBUTING FACTOR VEHICLE 4</th>\n",
       "      <th>CONTRIBUTING FACTOR VEHICLE 5</th>\n",
       "      <th>UNIQUE KEY</th>\n",
       "      <th>VEHICLE TYPE CODE 1</th>\n",
       "      <th>VEHICLE TYPE CODE 2</th>\n",
       "      <th>VEHICLE TYPE CODE 3</th>\n",
       "      <th>VEHICLE TYPE CODE 4</th>\n",
       "      <th>VEHICLE TYPE CODE 5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10/31/2017</td>\n",
       "      <td>0:00</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>40.7331</td>\n",
       "      <td>-73.9548</td>\n",
       "      <td>(40.733135, -73.954765)</td>\n",
       "      <td>MANHATTAN AVENUE</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>...</td>\n",
       "      <td>Unspecified</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>3781862</td>\n",
       "      <td>PICK-UP TRUCK</td>\n",
       "      <td>PICK-UP TRUCK</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10/31/2017</td>\n",
       "      <td>0:00</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>40.7535</td>\n",
       "      <td>-73.8979</td>\n",
       "      <td>(40.75351, -73.8979)</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>...</td>\n",
       "      <td>Unspecified</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>3781130</td>\n",
       "      <td>SPORT UTILITY / STATION WAGON</td>\n",
       "      <td>PASSENGER VEHICLE</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10/31/2017</td>\n",
       "      <td>0:00</td>\n",
       "      <td>MANHATTAN</td>\n",
       "      <td>10036</td>\n",
       "      <td>40.7597</td>\n",
       "      <td>-73.9917</td>\n",
       "      <td>(40.759727, -73.99169)</td>\n",
       "      <td>WEST 44 STREET</td>\n",
       "      <td>9 AVENUE</td>\n",
       "      <td></td>\n",
       "      <td>...</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>3781009</td>\n",
       "      <td>PASSENGER VEHICLE</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10/31/2017</td>\n",
       "      <td>0:00</td>\n",
       "      <td>BROOKLYN</td>\n",
       "      <td>11207</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>LINDEN BOULEVARD</td>\n",
       "      <td>WILLIAMS AVENUE</td>\n",
       "      <td></td>\n",
       "      <td>...</td>\n",
       "      <td>Unspecified</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>3780501</td>\n",
       "      <td>PASSENGER VEHICLE</td>\n",
       "      <td>DS</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10/31/2017</td>\n",
       "      <td>0:00</td>\n",
       "      <td>MANHATTAN</td>\n",
       "      <td>10030</td>\n",
       "      <td>40.8156</td>\n",
       "      <td>-73.9435</td>\n",
       "      <td>(40.81561, -73.943474)</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>2309      7 AVENUE</td>\n",
       "      <td>...</td>\n",
       "      <td>Unspecified</td>\n",
       "      <td>Unspecified</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>3780511</td>\n",
       "      <td>SPORT UTILITY / STATION WAGON</td>\n",
       "      <td>PASSENGER VEHICLE</td>\n",
       "      <td>PASSENGER VEHICLE</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         DATE  TIME    BOROUGH ZIP CODE LATITUDE LONGITUDE  \\\n",
       "0  10/31/2017  0:00                      40.7331  -73.9548   \n",
       "1  10/31/2017  0:00                      40.7535  -73.8979   \n",
       "2  10/31/2017  0:00  MANHATTAN    10036  40.7597  -73.9917   \n",
       "3  10/31/2017  0:00   BROOKLYN    11207                      \n",
       "4  10/31/2017  0:00  MANHATTAN    10030  40.8156  -73.9435   \n",
       "\n",
       "                  LOCATION    ON STREET NAME CROSS STREET NAME  \\\n",
       "0  (40.733135, -73.954765)  MANHATTAN AVENUE                     \n",
       "1     (40.75351, -73.8979)                                       \n",
       "2   (40.759727, -73.99169)    WEST 44 STREET          9 AVENUE   \n",
       "3                           LINDEN BOULEVARD   WILLIAMS AVENUE   \n",
       "4   (40.81561, -73.943474)                                       \n",
       "\n",
       "      OFF STREET NAME         ...          CONTRIBUTING FACTOR VEHICLE 2  \\\n",
       "0                             ...                            Unspecified   \n",
       "1                             ...                            Unspecified   \n",
       "2                             ...                                          \n",
       "3                             ...                            Unspecified   \n",
       "4  2309      7 AVENUE         ...                            Unspecified   \n",
       "\n",
       "   CONTRIBUTING FACTOR VEHICLE 3  CONTRIBUTING FACTOR VEHICLE 4  \\\n",
       "0                                                                 \n",
       "1                                                                 \n",
       "2                                                                 \n",
       "3                                                                 \n",
       "4                    Unspecified                                  \n",
       "\n",
       "   CONTRIBUTING FACTOR VEHICLE 5  UNIQUE KEY            VEHICLE TYPE CODE 1  \\\n",
       "0                                    3781862                  PICK-UP TRUCK   \n",
       "1                                    3781130  SPORT UTILITY / STATION WAGON   \n",
       "2                                    3781009              PASSENGER VEHICLE   \n",
       "3                                    3780501              PASSENGER VEHICLE   \n",
       "4                                    3780511  SPORT UTILITY / STATION WAGON   \n",
       "\n",
       "   VEHICLE TYPE CODE 2  VEHICLE TYPE CODE 3 VEHICLE TYPE CODE 4  \\\n",
       "0        PICK-UP TRUCK                                            \n",
       "1    PASSENGER VEHICLE                                            \n",
       "2                                                                 \n",
       "3                   DS                                            \n",
       "4    PASSENGER VEHICLE    PASSENGER VEHICLE                       \n",
       "\n",
       "  VEHICLE TYPE CODE 5  \n",
       "0                      \n",
       "1                      \n",
       "2                      \n",
       "3                      \n",
       "4                      \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 330,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2 = pd.read_csv('NYPD_Motor_Vehicle_Collisions_Duplicates.csv').fillna('')\n",
    "data2.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### a) Implement a clustering technique of your choice that will determine the exact number of unique records. (Hint: assigning each unique record to its own cluster would result in perfect clustering. Cluster the data\\* based on possible values for the number of unique records and observe the results.) Briefly explain your approach. (10 pts)\n",
    "\\* You may first have to factorize the data set, as it contains string variables.\n",
    "\n",
    "#### b) Confirm the number of unique records by using a more straightforward technique to identify duplicate rows. Pandas has a convenient function to drop duplicates for this purpose.  How well did your clustering technique perform?  (4 pts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "metadata": {},
   "outputs": [],
   "source": [
    "for col in data2.columns: \n",
    "    data2[col] = pd.factorize(data2[col])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GAicC7YuNZG8GfF3eC5vZWknnEK4q6gHjzGyOpKHx/FhgEmHBrPnAD2xY52R/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\nAN4qXolEewEFZvYfM1sL3E9Y16IsvYC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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2190beb29b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MAdYmjHBQrZiZSSqz552ktYEzgN0I53IXMAC4roTjDQGGAHTo0ME6d+5cqbjy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\n+3/YY+baceR3EgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2190beb69e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "elbow(data2,range(610, 620))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For n_clusters = 610 The average silhouette_score is : 0.196017730642\n",
      "For n_clusters = 611 The average silhouette_score is : 0.194547213626\n",
      "For n_clusters = 612 The average silhouette_score is : 0.193554746012\n",
      "For n_clusters = 613 The average silhouette_score is : 0.191604698624\n",
      "For n_clusters = 614 The average silhouette_score is : 0.190297697768\n",
      "For n_clusters = 615 The average silhouette_score is : 0.19068380951\n",
      "For n_clusters = 616 The average silhouette_score is : 0.187895298259\n",
      "For n_clusters = 617 The average silhouette_score is : 0.185294117647\n",
      "For n_clusters = 618 The average silhouette_score is : 0.185294117647\n",
      "For n_clusters = 619 The average silhouette_score is : 0.185294117647\n"
     ]
    }
   ],
   "source": [
    "X=np.asarray(data2.iloc[:,:-1])\n",
    "range_n_clusters = range(610, 620)\n",
    "\n",
    "for n_clusters in range_n_clusters:\n",
    "\n",
    "    clusterer = KMeans(n_clusters=n_clusters, random_state= 356)\n",
    "    cluster_labels = clusterer.fit_predict(X)\n",
    "    silhouette_avg = silhouette_score(X, cluster_labels)\n",
    "    print(\"For n_clusters =\", n_clusters,\n",
    "          \"The average silhouette_score is :\", silhouette_avg)\n",
    "    sample_silhouette_values = silhouette_samples(X, cluster_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The average silhouette score stops improving at k = 617, and from the elbow plots, k = 617 is the inflection points, hence, there are 617 unique rows. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(617, 29)"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2.drop_duplicates().shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* above confirms my observation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 3. (8 pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which of the following is always true for the confusion matrix resulting from a binary classification task? (Select all that apply.)\n",
    "* a) it is a square matrix\n",
    "* b) it is symmetrical\n",
    "* c) it has dimensions $3\\times3$\n",
    "* d) it reports the size of each class in the test set\n",
    "* e) it reports the total size of the training set\n",
    "* f) it reports the number of observations the classifier assigned to each class\n",
    "* g) it reports the proportion of correct predictions across the test set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__ a) d) g)__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 4. (25 pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the following logistic regression task, use the first half of the data in 'hw4data4.csv' as the training set, and the second half as the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data4 = pd.read_csv('hw4data4.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>x3</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-1.057594</td>\n",
       "      <td>-0.143935</td>\n",
       "      <td>-1.245903</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.642280</td>\n",
       "      <td>1.382141</td>\n",
       "      <td>0.071458</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.842085</td>\n",
       "      <td>2.400458</td>\n",
       "      <td>-0.110854</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.003466</td>\n",
       "      <td>0.725551</td>\n",
       "      <td>-0.007954</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.607444</td>\n",
       "      <td>1.146293</td>\n",
       "      <td>-1.338008</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         x1        x2        x3  y\n",
       "0 -1.057594 -0.143935 -1.245903  1\n",
       "1 -0.642280  1.382141  0.071458  0\n",
       "2  0.842085  2.400458 -0.110854  0\n",
       "3 -0.003466  0.725551 -0.007954  0\n",
       "4 -0.607444  1.146293 -1.338008  0"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data4.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### a) Construct a logistic regression object for modeling, setting C = 10,000 to disable regularization. (2 pts)\n",
    "\n",
    "#### b) Fit your logistic regression model to the training data. Print out the fitted parameters (including the intercept). (5 pts)\n",
    "\n",
    "#### c) Use your trained model to predict labels for the test data. (3 pts)\n",
    "\n",
    "#### d) Draw two plots: one displaying your predicted labels and another with the actual labels. Include the decision boundary in both. (10 pts)\n",
    "\n",
    "#### e) Compute the confusion matrix. Print out accuracy, recall and precision. (5 pts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# a)\n",
    "logit = LogisticRegression(C = 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "# b) \n",
    "np.random.seed(3)\n",
    "x_train, x_test, y_train, y_test = train_test_split(data4[['x1', 'x2', 'x3']], data4.y, test_size=0.5)\n",
    "logit.fit(x_train, y_train);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coef: [[-36.17786301 -87.42016916 -37.62810052]]\n",
      "intercept: [-7.41295687]\n"
     ]
    }
   ],
   "source": [
    "print('coef:', logit.coef_) \n",
    "print('intercept:', logit.intercept_) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1,\n",
       "       0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0,\n",
       "       0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1,\n",
       "       0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1,\n",
       "       1, 1, 0, 0, 0, 0, 0, 1], dtype=int64)"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# c)\n",
    "pred_val = logit.predict(x_test)\n",
    "pred_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lWQR8geOfLCIiUmTxbBzPeAR9weOfvAwpERGRJccYw1hqjLAvrMpdRETK0lhqjIAdIOwP\nl7ooZUuJiIgsKTk3x4HEAepCdeoJERGRsuN6LoPxQWqCNYT8oVIXp6xpQ0MRWTISuQQT6QlWVq3U\nTrsiIlJ20k6akeQIK6tWak7IHKhHRESWhLHUWFGSEM/z6O7uxhizaK8hIiKnnsnMJMPJYVZVr1rU\nJMQYQ19fH7lcbtFeo1jUIyIiZc0YQ3+sn4AVYFX1qpO6juu6pNNpMpnMEbdsNstNN91ET08P1157\nLd/+9rcJhdSlLiIixzeUGCLn5lhTs+akruM4zqwxajpO3XbbbfT09PCXf/mX3H777bS1tS3QOygN\nJSIiUrZc47J3fC/1oXoaKxuPep4xhmw2O6PCHhsbI5vNMjIyguM4WJaFz+cjFAoVbpWVlTQ2NhIK\nhQgEAnz/+9/n4osv5v77759T+a688kp+/OMf09LSwrPPPgvA5z73Oe68806am5sB+MIXvsAb3/jG\nk/8wRESk7HjGo2u8i5pwDe017Uc9zxhDLpcjk8kUGsQmJyeJx+PEYjEcxwHAtm3C4XAhTlVUVFBf\nX08oFCIYDHLXXXdx8cUX88Mf/nDOZSznWKVERETKUjKXpC/Rx8bARiJWhPHx8VlbiDzPw7IsgsHg\njCSjoqKCyspK1q5di9/vX5ThXFdccQXXXHMNl19++YzHr732Wj7xiU8s+OuJiEj5yDgZeuO9vNx+\nObWBWiYmJmaNU67r5peaDwSOaAyzLIsNGzYQCAQWbdhxOccqJSIiUhKHtg4dfhuJjzA4OUiNV0P3\nru4ZFXc4HKa2trZw37Znn+o2ODiI4zgEAou3starX/1quru7F+36IiJSOsaYow6Viiai9E30UeVW\nMdA1QDQcnRGrqqurCz/7fLPPF4lGoziOQzC4uMvQl3OsUiIiIgvO87zCeNZsNkt/f/+MpMN1XYAZ\nrUPhcJjq6mpykRw1FTWc+5Jz2fG7HWzevLnE72b+br31Vu69917OPfdcvvjFL1JfX1/qIomIyCE8\nzysM6U2n0xw4cACgEKemh0od3otRVVWFF/GIRCK84Yw3sHfXXjZt2rSojV6LpRxilRKRwyQSCXbv\n3o1lWdi2jWVZR73Ztk06naa7u/uY587lOsc6fqzzRIrtWBPpMpkMxhhs2y4MlXJdF7/fT01NTaEi\n9/uPrHpcz6V7ohuTNZy18iyCgaW5UeFHPvIRPvvZz2JZFp/97Gf5+Mc/zte+9rVSF0tOIdlslh07\ndsw5fiQSCfr6+giFQosShxSnpNy4rluISdPzMbLZLOl0mmw2O2NIbzgcxnEcfD4fNTU1hfkZPp/v\niN9fz3j0TvaSzqY5Y8UZREKREr3Dk1cusUqJyGHC4TCdnZ1AvkvOGIPneYWfD79NT3499PyjPedY\n15k+DszpvKMtLRqPx3n88ceP+R4XOzmavk23MASDwUUJbgpyC2u2Cd/Tt1QqRTweZ9u2bfj9/iPm\nYhw6ke7woVLbt2+ntbX1mK1FqVyK7vFufDkfG1ZswO9bulVTa2tr4eerrrqKN73pTSUsjZyK/H4/\n69atw7KsOcWXkZGRwt/noeedSJyabzybLVYtVJxaiPgRj8cZGRkhkUio0XAJONaQ3kwmQyKRYNu2\nbUcsTBKJRKirqzvqkN6dO3fS3NxMVVXVUV8762bpGu/CTbtsbN24ZBvLppVLrFq60X6R+Hw+qqqq\n5lxx7Nu3j7a2tqOOUy8mYwxbtmzhoosuOuY5ixV0Zns8l8sdN/AtdDI2m0MD31wCyWIla/F4HNd1\nZzy2EMH2eA5tHcrlcvT09Bx1wvd0C1EoFCpU3JZlsWvXLl72spfN+TOfq/HUeH6crVXF2hVrjzqW\ndqkYHBwsLKd4//33s2nTphKXSE41tm1TVVU157gzMDBAS0sLFRUVi1yyuXn88cfnFadONg4d77zp\nXt5iJmOzSSQSbN26tVCnL1YcOt7xqakpPM9jZGRkQePi8UwP6Z2OU729vXOa8H1ob/szzzzDy1/+\n8jl93vMRy8ToGe8h6AY5bcVps/bqLzXlEquW/icp81LM1pmRkRFWr15dFnsxHBr4ipmMeZ6H4ziF\n+9lsthCUipGMTZ9r23ahojbGHFF5H+/LfzabXZTfm4HYACMTI9RF6ljTuGbJtRy+613v4tFHH2V0\ndJT29nY+//nP8+ijj/LMM89gWRYdHR3cfvvtpS6myJJSzDgVi8Voa2ujtra2KK93LFu3bmXz5s34\n/f6iJmOHx6l0Oo3neYyPjxclGZstTnmeRzAYnNOE70Mtxu/NcGKYA+MHqPRX0tHWsSR3Sy/nWKVE\nRJadUnaVG2Ooqqqa0SW6mHK5HLlcbkbrzeTkJCtWrCjK6x+N67n0jPcQi8dorm1mZd3KkpbnRH3r\nW9864rE///M/L0FJRORUUso4tX//flzXZe3atUV5PcdxyGazZRenjDHsn9xPdCpKXWUdaxqWXmPZ\ntHKOVUpERKSo0rk03ePdpJNp2hrbaK0uTlImIiIyFzk3R3e0m0QiQUt9Cytrl2Zj2VKgREREimYy\nNUlftA/XdVnTsoaGioZSF0lERKQgkU3QHe3GyTi0NbXRWqXGssWkREREiuLA1AGGJoawbZt1reuo\nCdWUukgiIiIFY4kx+qP9ALQ3t9NY0VjiEp36lIiIyKLyjEfXWBfpVBpf2Me6pnVUBipLXSwREREg\nPx+kf7KflJPC5/extmmtGsuKpPRrzorIKSvjZOiZ7GEqPoUv4mND0wYlISIiUjYc16F3spexiTH8\nQT+dzZ1KQopIPSIisiim0lP0RHvIZrOEK8Kc1nQaAf/RNzUUEREppmQ2SfdYN6l0iuYVzWxs2kgo\nUPotB5YTJSIisuCG48MMRgfxjEckFGFDwwYlISIiUjaiySj7o/vxXI9QOERnfaeSkBJQIiIiC8bz\nPHonepmMT+JZHnWROrxqb8nvli4iIqcGYwwDUwOMTo5ibENVpIo1NWsIBoKlLtqypDkiIrIgsk6W\n3aO7mYxN4tkejZFGOpo6sG1VMyIiUnqO67BvbF8+CbEMtcFaOps6l+Ru6acK9YiIyEmLZ+J0j3Xj\nOA74oS3SxoqG0u6KKyIiMi2VS9E12kUul8NYhoZwA6ubVi/Z3dJPFUpEROSkjCZGGRgfwDMeAO1V\n7TTVNpW4VCIiInnjqXH6on14xsOyLVojrbQ1tpW6WIISERE5QcYYesd7GY+PY9kWtmezpnENdVV1\npS6aiIgIxhgGpwYZmhwqxKmVtSvVWFZGlIiIyLzlnBxd0S6SqST4wXZsOpo7qK6oLnXRREREcF2X\n7vFu4sk4WGC7NqsbVlNfXV/qoskhlIiIyLzEM3F6oj3ksjnwgd/109naSUW4otRFExERIZ1Nsy+6\nLx+nbPA7fjpa1FhWjpSIiMicjSZG6Y/2gwHLsgiZEOva1mntdRERKQuTqUn6on1kc1l8Ph9+z8+6\ntnVUhNRYVo6UiIjIcRljGIoPwVg+AcGFSChCZ2snfp+qERERKb2x1BjdI91ggc/yESRIZ5s2Kixn\nWuBfRI7JcR32jexjPDUONhgnvwHU+hXrlYSIiEjJuZ5L12gXY7ExjGUwjiHsD7Nx5UYlIWVO3yJE\n5KiS2STdY90kMgmwwGQN9VX1rG1eq7XXRUSk5DJOhq7RLtLZNPiAHFRVVNHZ0qkNdZcAJSIiMqto\nIsr+8f35/UE8sLIWzXXNtDe0l7poIiIiTKWn6BnrwXEdIN9YVlddx9omNZYtFUpERGQGYwwDkwOM\nTI6ADbZnY2HRVNekJERERMrC0NQQQ5NDeMbD5/nwjEd9TT0dzR2lLprMgxIRESlwXIeeaA+xZAws\nsBwLYxvam9vxJ1RdiIhIaXmeR2+0l8nkJMYy4IFnPFY0riA3mit18WSeNHhORABIZVPsHt5NLPVi\nEmL5LdY2r6WhoqHUxRMRkWUu62TZNbyLicQEBgMO2LbN6pbVrKhZUeriyQlQIiIijCfH2T2ym4yT\nyc8HcSx8IR/rW9dTV1FX6uItGtd1yWQyJBIJJiYmePDBB0kkEnz5y1/GcZxSF09ERA6KpWO8MPQC\nmVwmn4TkwBfwsbZlLY2VjaUu3qLxPI9sNksikWBycpJHHnmEdDrNrbfeysTERKmLd9I01kJkGTPG\nMDg5yEhspNC6ZBkLf9jP+ub1hAPhUhfxuDzPw3EccrncjH+j0Si5XI5UKoXjOIVjnucVnmtZFoFA\nAL/fTyAQ4IUXXsDzPOrq6jDGlPBdiYjItJHYCAMTA2DAeAbLWPjCPjqbO6kMVpa6eMc1HacOj1WT\nk5PE43F2795deNxxHFzXLTzXsqxCjPL7/ezevRvP86iurj4lVgVTIiKyTLmeS89YD1OpqcJQLA+P\nSEWEdY3rCAaCRSvL0SrpbDZLV1fXjMenb5CvoA+vpKf/tW2bUChEc3PzjGO2bR91NZWPfexj/PCH\nP+T973//nMp95ZVX8uMf/5iWlhaeffZZAKLRKO985zvp7u6mo6OD7373u9TX1y/MByUisox4nkff\neB8TiQk8y8Ny83V+IBygs7GTcLB4jWXGmFkbvTKZDL29vUfEsdmSicNjlW3bBAIBmpqaZhzz+XxH\njVOnn3463/72t7niiivmXPZyjlVKRESWoXQuTddoF1kni7EMds7Gsz2qIlWsa1yH3z//quFEKmlj\nzIxk4vBKGqCysvKIJONYlfS0wcFBHMdZ1Ir1iiuu4JprruHyyy8vPHbjjTfyB3/wB1x33XXceOON\n3Hjjjdx0002LVgYRkVNR1snSNdZFKpsCO7+EvOWzCAaDrG9af0KNZdNx6vBYlUwmGRgYwLbtWRu9\nps3W6AVQUVFBKBSacWwucSoajRKNRhc9ASjnWKVE5DCxWIzf/va3cz4/kUjw61//+qjHp38Jp79s\nHfrzse4f67xj/ZxOp9m9e/cJX3s+r3W85ziOQyKRIJfLLcj1ZGHEs3F2j+zGcR1sbOycjfEZaiO1\nrG1ci+d5pFKpGZV0Op0mlUqxZ8+eIyrp6WQCjl5JRyIRwuHwvCvpoaEhWlpaFv0zOVGvfvWr6e7u\nnvHYAw88wKOPPgrA+9//fi6++GIlIrKgMpkMTzzxxJzPTyaTPP3000cdxnGydfN8zztanDqRa59s\nmbLZLMlkslAfnWyZZGGkcqlCnDLGQBbwQ0Wogs6mzvw5B4fdHhqrMpkMe/bsOSLZODxOHRqjpuNU\nKBSiurr6iGNzSSaampoKjWflqJxjlRKRw1RXV3PhhRfOuULZsmUL559//qwV/PQYc2PMET8f69iJ\nnmeM4cCBA9TW1s77ep7nzbh/rOfMtUzJZJKenh5s2z7p93iy4vE4jz/++IzHFiJJPNZzZvt5YmKC\nWCxGLBYrSpLoui7ZbBZjDLlcjsGJQXqjvUyZKXLpHE7OwbVcavw1tFS3MNYzVqh8D62MLcvCtm0a\nGhpOqJKeHh61HAwNDdHW1gbAihUrGBoaKnGJ5FQTCoW44IIL5jw+fPv27Zx++ulUVFQccWwh4s98\nnzM0NHTMOHW06y1GnIrFYriuSyAQOOlrn6xEIsHWrVtn1KnFThItyyIWixViRjGSxOnJ2NO95sNT\nw3RHu5kwE2RSGbych4NDhb+ClbUr2d63HZ/Pd0Sj1/SQ3Pr6+iOOHS9OJZNJGhsbqaqqmu//tiWr\nXGKVEpFFVOxWEmMMgUCgbFqQn3rqKc466yxCoVCpi8Ljjz/ORRddVLhfjMRwtvupVIpIJEJ1dfWc\nr3948J1PmabHqPr8PoYSQ6S9NJYvvzmhz+/DH/KzomoF7c3H3qgwm80yPj5OQ4OW8Z2PQ4OuSDkq\nRWu+3+8vmzi1Y8cO2tvbC4lRKW3dupXNmzcXWuiLlRgeft91XVzXLcSpY11v+nYyccrzPDzPIxAI\nMJoaJZ6Lgw0NNQ0EGgP4Aj6aKptY23r83dIHBwdpbDx1V9BaLKWMVUpEZFkqVVf61NQUVVVVtLa2\nFuX1crkc8WScvsk+KoOVVFLJYO8gVTX5Vp+VNStprmsuSlmWi9bWVgYHB2lra2NwcLBsvnCJyNJS\nqjiVyWRwXbdoccpxHJKpJH0TfQQDQZqsJg7sP0BVdRXGMrRWtbKycWVRyrKclEusWvrrfonIUU0m\nJ9kzvIf0wQsbAAAgAElEQVS0k8Z4L46ztYzFmvo1SkIWwZvf/GbuueceAO655x7+5E/+pMQlEhEp\nX4l0gl1Du0jmklhYmJzB83lYlkV7bbuSkEVSLrFKiYjIKWpoYoiesR4c44ADOGD8Btuz6WjuoL5a\nS8qerHe9611ceOGFvPDCC7S3t/Mv//IvXHfddTz00ENs3LiRhx9+mOuuu67UxRQRKUtjsTH2juwl\nZ3Lggska8IHP+FjdsFqNZQuknGOVhmaJnGI8z6N3pJeJTH7ddRywfBYmYPB7flbVr6KmoqbUxTwl\nfOtb35r18UceeaTIJRERWTqMMfRH+xmJj2Ask9/HyvKwgzaWa9FW00ZDteYkLpRyjlXqERE5hWSd\nLLsGdjGeHsdgCq1LxmcImiAbV24kEoiUupgiIrJMOa7DnsE9DMeHwQKTMXh4+Pw+fK6PDW0bqAyV\n/27psjDUIyJyioilYnSNdOHgYGFBDiy/hckYIsEIna2dBPzLYwldEREpP8lMkq7hLnLksC0bkzMY\nf37+YsAK0Lmqk1Cg9CttSvEoERE5BQxPDjMwMZDfJd21MZ7BClqQgqpwFRvaNuCzfaUupoiILFPR\neJT90f35xjJzsLEsYEEWKgIVbGjboMayZUiJiMgS5nkefaN9RFNRsMhPSMfke0KyhpqKGtrr25WE\niIhISUzPBxmNjWJ8LzaW4Qcv51EVrqK9vl1JyDKlRERkico6WfYN7SPlpLDsfOuSsUw+IclBU10T\nrTWtOI5T6qKKiMgy5LgO3cPdxHNxjG0gRz5G2WAcQ311Pe0N7eRyuVIXVUpEiYjIEhRPx+ke6cbB\nyU/2OzgpHQOWZ9Ha1EpbXZsqdxERKYlUNkXXcBdZk8VwMAk5GKdwoaWhhVX1q3Bdt8QllVJSIiKy\nxIxMjTAwPpBfDSuX3xfEBAyWa2EwtDe301TdVOpiiojIMjWRmKB3rBfHcrA9Oz8fJGiBBxhY0biC\ntrq2UhdTyoASEZElwhhD31gf0UT0xS5uwPN7WI4FPuho6qCusq60BRURkWWrP9rPcGwYbLBdG8/L\n7w/CwY6PVc2raK7WRoWSp0REZAnIOTm6RrpIZBMAWDkLYxss28r3igRsOls7qQpVlbikIiKyHLme\nS/dwN7F0LL9LXRbw5TfUJQf4oaO5g7oKNZbJi5SIiJS5ZCbJvuF9OMYBA8Y1EMjPBcGBUDjEuuZ1\nRILaqFBERIovk8uwb2gfGS+TXzTFIb8/iAEc8If8dDR3qLFMjqBERKSMjcXG2B/dj4cHHvmNCgNg\nuRae8aiprKGjqQO/T3/KIiJSfJPJSXpGe3CNi4WVbyTzk98rxINwZZjOpk6C/mCpiyplSN9eRMqQ\nMYb+8X5GpkYKFbuxDcZn8vNBLGipa2FV3Sosyyp1cUVEZBk6MHmAwfHB/F5VLvlVHH35HhEsqK+p\nZ03DGmzbLnVRpUwpEREpM47r0DXaRTwVx8bGc7387rOQr9xtWNO0hobKhpKWU0RElifP8+ge62Yy\nOYmFheu4+ZUcyTeWGZ9hVf0qWmpaSl1UKXNKRETKSDKbpHukm6yTxfIsHM/BDh3chdaDQDBAZ3Mn\nFcGKUhdVRESWoYyToWuki3Q2DS54eNh+G2MMlrGwAzbrmtdRHa4udVFlCVAiIlImxpPj9I715pMO\nN9+y5A/5MY4BGyojlaxrXqf5ICIiUhJT6Sm6R7vzmxC6gAE7cLCxDAiFQnQ2dRIKhEpbUFky9I1G\npMSMMfRP9jM8NZyf5Ofmlzu0fFZ+hSwfNFY10l7frvkgIiJSEkOxIQYnBjGuyc9btEx+2LADlm1R\nU1FDR2OH5oPIvCgRESkh13PpHutmKjmVT0I88quNWFZ+boht0V6vndJFRKQ0PM+jd7yXaDyKjZ2P\nU778MZPLN5a11bWxonZFScspS5MSEZESSeVSdI12kc3l54PAwV3SjYXneQSCAdY1raMyVFnikoqI\nyHKUdbLsG91HKpvC9g4OwfKT7w3xLOygzdrGtdRGaktdVFmilIiIlMBEaoLesd4Xx9lCvifEzSck\nFZEKOps7CfgCpSukiIgsW/FMnK7RLlzHxXgmv4+Vn/zPlkUgGGB983rCgXCpiypLmBIRkSIbig/h\nZb38OFtzcJytzypMSq+v0rrrIiJSOtFUlImRCYxnMK7JxyM731hmWRbVFdV0NHXk9w8ROQlKRESK\nxPVceiZ68GyPhvoGbOx8EmIdnJTuh1V1WnddRERKwxjD/qn9RGNR2iJt+d3RbfI3J79ZYWt1Kysb\nVpa6qHKKUCIiUgTpXJqusS4SmQQVoYr8iiM+k9+F1jEEAgHWNq2lOqJ110VEpPhybo59Y/uYSEzk\nN8/1wNj5ZXmNa/D5faxuXE19ZX1pCyqnFCUiIotsMjVJz3gPbs7NtyiFDMZn8j0ixhAJRVjXsk7r\nrh+HMQZjDJ7nFf6d7TZ9bGpqCsdxGBgYmPNzvvKVr9DX18drXvMafvrTnxIOa+yziJz6EtkEXWNd\n5LK5fJwiP1TY8iyMbQgFQqxrWUckGCl1UcveseLN4Y9PTU2RSCQYGBiY83PuvfdeBgYGuOSSS7jn\nnntYvXp1qd/ySVEicphsNks0Gj1iv4aj3Xcch7GxsRnj+Q89dy4/z+fY8c71PI9UKnXC1z+RY9rb\n4ugOTB3gwNQBPMfDNjZYgI9CElJbUUtHU/muuz5dAeZyucLv1ly/1E/fUqkU3d3d+SWJ53D+oRKJ\nBE888UThvmVZ2LZd+He22/SxbDZbuPZcn/PpT3+anTt38u///u+EQkoMpTy5rsvw8PAR9cbR6uhM\nJsP4+DipVGrWc+daty90nDrWecWIYZI3mhilf6I/P0/RBSyw/PnPyliG6lA1Hc0dZbuZ7mwxZ65f\n6qdv8Xic/fv34/f75/ScQyWTSbZv3z7j72Yu8ca2bdLpNK7r4nkelmXh9/uP+5yPfvSjbN26lfvu\nu4+amppSfOQLqjx/q0rIdV2mpqaOeNwYM+vPuVyO0dHRwi/goceO9by5njffY+l0mueee27Rrn+0\nY7NJJpM88cQTZfElOx6P8/jjj8/p3IUIcp7xGEwMEs/G85P7jAUWpDIp7HGb4QPDNFc0QzX8pv83\nC/rah94/tCKdrkynK83ZKtTZTP//SyaT7Nmz56gVrGVZ+Hy+wvHpCtXn81FTU0MgEJhTxXzoe3ni\niSc477zzjlvG2QwODuI4Du3t7XN+TkVFBbZtU1t7YktRdnR0UF1djc/nw+/38+STT57QdUSOxfM8\nYrHYEY8frb7OZrOMj4/j9/uPOHas+4sVK6bj1LGeV6w4lUqliEaj+Hyln3SdSCTYunXrnBOmk03i\njDEMp4aZSE8U9rGybZtMLoMxhsnxSWrDtXjVHr8b/N28rz/XY8YYXNc9apyafuxYn8uhX+yPFqdm\ne8zv9xcSgKqqqkIMON7zDi3L9u3b2bRpE4HA/Fe5jEajRKPReccpy7Koq6ub9+tB+cUpJSKHiUQi\nbNiwYc4VQTQa5fTTTy+LL9vGGLZs2cI555xT6qIA8NRTT7Fp06ayaFl+/PHHueiii455zkIF30wu\nQ9d4F22Ztny3tpefC4IFAwMDVEYq+f0Nv09NpOakAupcznUcB8dxZiQBv/3tb9m0adOMCvZ4stks\nO3fu5CUveclxzz3cwMAADQ0NJ1RJL0X/9V//RVOTNqCUxRMIBFi/fv2c404ymaSzs5OKiopFLtnc\nPP7442UTp3bs2EF7e/sJNz4spK1bt7J58+ZCwjibuSRuc4kVjuPQNd5FS7qFFrelcMz4DGPDY3ie\nx+bTN1NfVX/CrzXXc13XJZfLzRqnDk0C5uKJJ544oTgVjUapq6ujqqpq3s9disopTikRETloIYaa\nTaWm6JnswfEcQr5QPgEJ5MfbWpZFZaiSM1adQWtD6wKV+thyuRy5XG5GYLNte9kkBSIip5KFGGqW\nyCTonugm5+UI+oP5CelW/noGQzgQZlXdKlY2F2dlLMdxyGazilPLVOmb8UVOEUNTQ+wb24eTc/Ib\nExoKFTwWVIer6WjsIOQvfQ+RLA7Lsrj00kvZvHkzd9xxR6mLIyIyQzQRZc/IHrJuNt9j75rCnAaA\nymAl61vWa1L6Kazc4pR6REROkud59EZ7mUhN5JMPN78Drefz8jvRQmHd9b3xvSUurSymX/7yl6xa\ntYrh4WFe+9rXcsYZZ/DqV7+61MUSkWXOGEP/RD+j8VEwgJefy2jZBzfVNRYNVQ2sblxNf38/ruuW\nusiySMotTqlHROQkZJ0su4d3E01EC5W7bdtY/vwEdZ/lo6OpQ5s/LROrVq0CoKWlhbe85S1s27at\nxCUSkeXOcR32juxlJDZSaCzDAL58r72Nzar6VaxpWqOVxZaBcotTSkRETlA8E+f5A8+TzCaBfOVu\njMFY+X+D/iCnrTiNusoTW9lClpZEIlFYySiRSPAf//EfbNq0qcSlEpHlLJVNsWtoF7FMLN9T73j5\njXQP9oL4LT/rW9fTXNtc6qJKEZRjnNLQLJETMBIbYXByENd180vzGmak9dWhata1rMNnl35JSCmO\noaEh3vKWtwD5yZfvfve7ef3rX1/iUonIcjWeHKdvrA/Hc7CMhTEG27YxVr4XJBKI0NnSScCvSeHL\nRTnGKSUiIvNgjKF3rJdoIr/ppWXyy/Navvw4Wwy0VLWwsmGluriXmc7OTn7zm98c/0QRkUVkjGFg\ncoCRqREAbGPnl5H3Hdwx3YK6cB1rmtaUxdYDUjzlGKeUiIjMUc5J0nXgEVKZKfCvBa8qvw76wcrd\ntmzWNKwprLsuIiJSTK6bo3v4EWLJMYxvFTb1GHOwsezgMvIra1bSUtdS6qKKAEpEROYkkY7S3ftJ\nnNweLGNjmwim8n9i+VvBQNAfpKOxg4pweWwYJiIiy0s6m6R7/2fIprZjWxZ4ftzwRyDQgfEMwUCQ\ntY1rqY5Ul7qoIgXqkxM5jtH4KHv3fwPj7MayqjEmAlYKO/d9DIaqcBUbWzcqCRERkZKYSE6wa/8P\ncFLbwaoCU4nBwZ/7BgAV4Qo2tmxUEiJlRz0iIkdhjKFvvI/oVBTbjOF6+Y2ALJ8PTBBMlKaqJtrr\n2zUfRERESmJwcpChiSEsbxLXHNy/ygLLRPDMOLUVtXQ0dmg+iJQlJSIis3Bch30j+0hmkniWhzFr\n8WEAF4OFbadpb/wf1DesLnVRRURkGXI9l56xHqaSUwB4rMSPjbEcMDbYcdrqz6GlubPEJRU5OiUi\nIodJZpN0De/GSfw7tvcUlhfBhN6GF/hDyP0HEb+PNS0XEqn7X6Uuqpyinn32WbZs2cJFF13E2Wef\nzc6dO7nlllvIZDK8973v5XWve12piygiJZTJZdg3vId0/GfYzmNY+PCCb8IN/yl25gf4bVjb/BIq\nG/6/UhdVTlELFaeUiIgcIpqI0jfWh0neh895BM8LYvli2Jl/wq34ayK1l9HZ1E7AX1vqosop6ic/\n+QmXXXYZ1dXVJBIJ7r//fi6//HJe+tKX4nkeb3zjG3Fd91JjzMOlLquIFN9UaorusW685H/ic/49\nP1QYFzvzL5iKv8Jf/2XWN60iFGgADRuWRbCQcUoDBkXIzwfZP76f3tFejGuwnG35Sem+EJgInnFo\nCPdyWutZSkJkUV1//fV88pOfZGxsjLvvvpv3vOc9fOhDH+Khhx7ikUce4a//+q8BPlnqcopI8R2Y\nPMC+kX14OQ/b3QpeAGOFsK0KjGVRE3iO01ecTSjYqCREFs1CxiklIrKkua7HA1/5GZ96/Rf4/9/+\nJV7YtueIc3p27ueZn+zkse//mnQyc8Rxx3XYO7yX0clRjGfyGz7ZQbBdLAO27bKmNs26iofxpW4G\nb7IYb02WqR07dnDFFVcA8I53vINYLMbb3va2wvH3vOc9AL9XksKJyLwZY3jkG4/xmTfewN/9yT/w\n9MO/PeKcA13DPPPTnfziu1uIjyeOOO55Hl0jXQxODIKX37vKeCGM7WIZg2e5rKhKsaHmSQKpL4A3\nVIy3JsvUQsYpDc2Ssja6f4z/+taviE8kOPsVp3PeG142Y4WqB279KQ/e9jDBSICRfpcvXvnPvOFD\nf0CkMszZrzyDsYEoX/2rfyURT/LUD3bw0D2/4FPf+SjhihAAyUyS7rFuspksWIB1sIIPXoaV/Bq+\nQJb19UmqQhYGDyv3C3xuN27V/wErUKJPRU5106vb2LZNOBymtvbFXrjq6moAdcuJlInJ0Rj/+Y3H\nGB+aZOM567josvPw+X2F47/4zuN88/r7CIQCGOPxT//zX3n9B15DVX0lp527HoCbr/gqU5MxtoZ+\nw0/v/E8++72PUduUX2o3k8vQNdpFMp3Esqz8RrqAifwxvuSt2NYka+uy1EUMBh+WsxVffDdu9W1g\naVl5WRwLFaeUiEjZmhyZ4vaP30s6mSUUDrDryX2kExle/fYLC+f88gdbCVUGCYQC+D2Pvuf6+bfP\nfR9/wIfls2loq8cX8BGpDVNVVcXA3iGe/OkzvPJPz2c8MU7vWG++F8QzYMWwvBGwazC+lxKo/xs2\n1j5P2HsQY7WA5QdjwOsDbwB8a+f9ngL2EJX2Q1ipIPjPwQReupAfmZwCOjo62L17N52d+ZVutmzZ\nwpo1awrH+/r6AA6UpnQicqhUPM2df/11JkamCEeC7H5qH+PDk7z5L/6wcM5j39+KP+gnVBHEGMPI\nC4N88+/vJxDyY9kWKzeswHVdKmoiVFRWEB0c59Hv/Io/+cvXE0vH6BntIZfLgQFIgjuEscJgr8NX\n+7dsqN1HhfdtjNVaaCCzzCSW+wLG/7J5vyefFaUy8Kt8nPKdhQmcD5YG0MiLFjJO6TdL5iWdSDPS\nN0YyljrqOU7O4eGv/zc//fKj/OT2R0jF0yf0Ws9t3c348BS1jVVU1VdS31LDL+/fNuOcQDiA53oA\nxMcTuDkPzxiwLJysw8CeA/gDL+bbnmdIxFL0j/fTPdKNcQ0YsNmNL3UzVupr2Mkv0RB6ktNXXoy/\n4k1AFfBi65aFAU6gN8QbpiH8A/z0YXkjWNnvYeWeOoFPRk5lV199NdlstnB/06ZN+P0v/g4/+OCD\nAI8WvWAiS0Q2nWWkb4z4xJFDnKZ5nscvf7CVH33pYX70lYeYGoud0Gt1/baH4b6xQpxqbm9g24Pb\ncR23cE4wEizEqVQsRS6dwxiDZVl4jse+Z7pn9KBYlkU8mmB4aph9w/twHCcfp8wA/tQX8WX+BX/q\nK9TYD3F62ysIVl7GjDhlDg4xPqE4NUlt4DsE7S4sM4ad/RFW7hcn9NnIqWsh45R6RGTOep/bz/1f\n/im5TA7bZ/PGD13KGS/fMOMcYwxf/9z3ePLnvyHn5RjYOcKep7u59s4PzUgIjudA9zA/+up/MLB7\nkNH9Y7Sf3kZ1XSX2Ya0yf3rtm7jzr79OLBonMZnEYPD5bIzJ93J4nsdQ9zCBCj8+y4/th4rTAgxP\nDAP5Ct8zDlb6m4AfyxdgZY2hNfIdSPwXEMJYASwznu/yxuD5LwS7bd6fn+U8j4WLRz3YlWBsLOfX\nmMDmeV9LTl1/8Rd/cczjN9xwAzfccMMHilQckSVluHeU79/8I5KxFMbAJe95JZtfe+RQ9R/+0895\n6N7/xvVy9D4zwJ4nuvibf/srIlXhOb/W+NAk9335J+x/oZ/hnhFWdDTT1N6QnyN+yBDiy/7nG/ji\nlf/M1FiMVCzfMOfzH4xTxuB5htH9UfwVPnyWD2xoOq+WgehAIWHBBhLfwXg5PDvMihpYWfUwVnI7\nWJUYq+JgnPJjGQ/jPxPjO33en5/ldWOTImtawKrG2CGs3BZM8DXzvpacuhYyTqlHROYkl3X491t/\nRiAUoKm9kcq6Sh68/aEjJtXFxxM8/fDvqG+tI1Idpq6lhv3P99P3/MCcX8sYw3dvfICK6jCVdRV4\nrkvX7/oY7oty8bsuKpzneR7rX9rB1V96P3/w3ley9ux2bJ9NLp0jk8yQy+ZoW9fCmrNXk0nm8Hwu\nf/T3r6FqZUW+i9uAhwcmheVl8VkZNjbsZ0VlPxbD4MXBbgGrBs9/JibwWtzwh/Eq/uYEVyPxcbBv\n/eAb9TAET+A6cir51Kc+VeoiiJwSjDE88JWf4TguTe2N1LfW8si/PcZw7+iM8zzP4z+/8Utqm6qJ\n1ESobakhemCCXU/undfrPfCVn+J5hprGajzPo++FAfp3H+BVf3o+Pp9dKFPLmiauufVKXnfFxZx2\nbmc+TmVypJMZMuksda11nHbeepyUQ8bJcsl1F9JyRiPGyychBgOewfJGsG3orO+jvbof2xoCNwpW\ncz5O+ToxgT/EDX8At/LvT3Ae42FxCi8/LFmWtcWMU/rtkjlJTqXIJLPUrM5PngtFgsTGDJNjMarq\nKwvnGWOwOOxL+jy/tGfTOcaHJ2lZ00RlXSUH9g0zMTLJpe97Jef/0Tn58sRSfO1vv0n3s30A1K+o\nY2DPEMFwgGwqh+d6VNZEePU7LiQYChDp9FPTUUXHS1ZjGQtjHaxoPbCIEAlZdNYPEvJHAAewsMwo\nhjTYdVj4cStObgND49+Eax4kxBB4VYCDCb71pK4pS9+NN97IxMQEX/3qV0tdFJElzXVcxg9M0Lym\nCQB/0I9lWUyNxmg5+Bjkp/oVehqmWRQmgc/V4N4hGlprqWuuYXDvENHBCS74481c+v7/AeQb8P7t\n899jx69eAKCutZbuZ/sIVQTJJDN4nkcwHOS173sVkaowkbV+chUOZ71iYz422fnyWcYCC0LBOtbX\n7yISCBUKbRHDmEmwG7DMOG7FX53gp3fws/GtxzWNBOwh8LJgMpjQn57UNWXpW8w4pR4RmZOKmgjh\nyhDJqSQAmWQGy7apbayecV51QxVnv/IMJoYnScczTA5PsWJdC+2nzX0oUzAcoKaxmvGhSTLJLLXN\n1axY18Lm176UVCxFz8793HfLg3T9tpfa5hoSkym2/PBJYmMxfD4foYogDSvqaGirJxgKMOGMM5Ie\nIRwJYVv2i0mIyf+n3ncfpzU6hPwOEAdcIAzYYLJg4pgTGIp1BLuWsfTbSZmLMIHz8cJXgW/jyV9X\nlrTLL7+c2267jXe/+935seCz+NWvfsVFF1006zERyfP5fTS01RMbiwPgZB2MZ6htrpl5ns/mVW+7\ngInhqXycGpmipqGajed0zuv1WjtaGD8wSTqepqapmtaOZs57w8vIprL07NzPT+96hN/993PUtdSS\nTefY+uOnGR+aAMsiFAlR01hDXUsNkaowU+4UQ+mh/AR28okHvJgc1dj/wemNU0QCDpAAskCI/Ne4\nLJgYxlpxUp8fAFaEidw7iOVegQmcixe5AhM45+SvK0vaYsYp9YjInASCft7yv97Afbf8hNH9Y9g+\nmz/68KUzekMgP+fiyi/8GT+542F+/m//RVVNJee/6Rz8wbn/qnme4exXnsG3v3AfGHA9w+9ffBZd\nO/r4Px+6HSfrkE5mWLWxjeRUiqGekfwwK9eQmEriD/pxxhKs/b3VPNu1k4yXxjKGl7zqTDzLK/TY\neHi0VcdpD+4EVuSHYpEDwFhVWGYc3GfBqsOLXPtiAU0OK/ff4O4DuxETuATsurm9N1NDxlyECbbO\n+fOQU9vdd99NY2Mjt9xyC5OTk/zgBz8gHM6PU9+9ezd/8zd/wwMPPFDiUoqUP8uy+JNrXs/3v/gj\nRvePAfDa97+a5tWNR5z7p9f+EXUttfz4jp/j9/s5/03nEK4MHXHe0RhjOPOCjWx54AmcnIPnGta/\ndC2JySQf2vQJUok0mWSWxlX1ODmX/l2D+dUZgeRUEn/Ah5NzaD+jjee6nidpkuTSWc597e/n45Q5\nOCTLQFO1x9rAFrCbwU0A+cVijFWPZUawnBcwdiVe5H2HFNDBym0F97n8XI/ga/JDjefy3qgg5Z6H\nCc5/ZUg5NS1mnFIiInPWftpKrv7S5cSicSprK446qc/22Tz7yxeYODBFYizN1z/3PX732PMYzyOT\nyHDO636PS97zqsIY2kM5OYeb3vcVnvnPZ3FdFyfjEq4MseWBJ3jse7/G80yhC33/8wP4/Hb+sWkm\n3wqGz+PCv3gprnHxci6DkwPUNecwbhRDPbbPx/rW9dQFXsBK2hjbh7HWYrk9QBqMh2efAfZKwODL\nfBvX9ymwIljZB7Gc34HdAO5uLK8/37thzX2So8ihvvjFL9LY2MhnPvMZXve613HXXXfx5S9/mbvu\nuotcLse5557LDTfcUOpiipS95tWNfPCm9zA1FidSFaKiZvZ9NGyfze4n9zLWP4HPZ3PfLQ/yu8ee\no6ahmth4nLMvOp03fPAS/h97dx5fx1kf+v/zzMyZs+hoX21JlmQrdmI7IQUcSNjSEghbGwgtl1Io\nS3coBX7t5cWFe18vWuhtS1taLm1vS1toSRtyy5KmDYWwpSGQNHuIY5PYluVFm7VLZz8z8zy/P0bn\nRJKPZEmWJdn+vv06r7PNzHk8R+f5zrNHomePszDG8Fe/9QW+/y8P4nsBXtEnmnA5+P1nePJ7h/D9\nAGtuvY+xUxNMDc8Q6GDeAcAvBhjb55q376ZmWxIvHzA6O0JTh40yE0ATCkVncyeNiUlIO6BsjN2J\n0qfAZFGmgFY7wd4BWNjFfyVw9oJVj/LuQ3k/AKsJ9DQqfxs69stgyRJEYm0uVJySgohYlWjcJdre\nsOw2x544wfGnThJLRonF4nj5It/9p++TrKtCKcWxJ08A8Iq3XM9//ftjDB4dob61lpe86Toe/o/H\nOXT/M2hf4xU8jAav4OHGXLxiAduxsWwLywoH+wW+PuvzfccjX53lzv/zdX71079IxPFoGv0sVvoM\nCkUkdi3dHZ8lFq3G6J0Y5YDJAHGMagYawBzD0s+CPo6xrwIThCvVWttR/iGw2sOxLyoBwTDoEbC7\n1/18i8vHRz/6UWpra3n/+9/PVVddBcDu3bv55Cc/yZvfLH20hVipSDRC4/b6ZbcZOzXBY99+iljS\nxZRKzKYAACAASURBVHVddGB4+OuPE0/GsWzFscf7yWfy3Pqh1/Pot35E/49OUd2Q5IZbXsiJQwM8\n+G+PEgSaYtHDBIZirkiiNk4unceyLZRj4czFKd87uytL4PjkqjPc/Tf38Ft/+6tEozYNI/+Am+3D\nANFoL51df0VVvBFMPIw1ehZUEkMTYffhYSzTD/4pjL0LVAtKD2KsepT/eDi7o4rMxalB0INSEBHn\n5ULEKSmIiHXnFbxwkN3cQMDMbA4daHSgUZbF9OgM//rZb3LP5+9lamSGjj3baO1qZmxgktxslkwq\n3N7o0vF8rLnWk8AP4LlDYzkWCggCDQYKsTyFWA7ta6KRQxSHPoDbYKiKToOJUR2z6Wk6gtJfRvMe\nsJrQsd/Eyv8V6AmMvRcVHEcxTfjzKKCCH2HMlaDigDW3sJNPeY52pZGfkjgfxhhuu+02Pv3pT5ef\nb9u2jR/84Ac0Np7drUQIcX6KhSKWNdf9Ccilc/hegA4ClOWQmkzzzb//Hk/dd5ihvjO09bTQeeV2\nvvbno9S11pKZyeH7frgWFRD4Gi8fFjh0oFFKldcAtCyFsiyCIAADxWiBfCKL8Q22M0hh4IMkt7nU\nJSaACEk3ws6mYWz9d2g+BipBEP8Qdu7PQY+BswuCHEpPEo4R0ajgGYwphgsdAmF8mhengPnrYQmx\nWhcqTslgdbHudj6vi6raBPl0IZyiMJ3Hsiwc1wnnTscwdHSEsdMTOFGHk4cHGB+cJDUxy9TY7Fwh\nZOHsJYXscwvnBF6A7wVYtsIYjdbhXOzZZJpcNAsaGpoC3vDOYeJVY1h6DFsVaa322dWssJVGBU8D\noIrfwyrcDqoB7B0Y92aUGSYcBAjhiMEgLITMra5uIjeCHg5bSILTGKt3TeuKCAFw5513cvXVV/Pu\nd7+b4eFhPvKRj/Cnf/qnjIyMcNNNNzE6OrrZSRTiktPW00JLV/NcnPLJzubDFvNoJGzRUIqJ4WlO\nPzNIxHUY6jvD6cOD5LMFxgcmCbygXAgpyWcK5ceBH+AXA5QVLoGrjcZgyCUy5GIZCAzJuoA3/8ow\n1XWTGD2MrfI0JAJ2tyoitnkuTnmPYef/DlQS7C505I0o8yzgEsYoBWggACsccK8jN4EenxentoHd\nsxGnVlyCLmScUqucrm51c9tdhKampjh69GjF9yqdq4mJCRoaGhZMA7iSc7rcNiv9TiptNzU1RX19\n/XkdYzXpWGqbmTMpvv3X95Mez6IDzWjfRLitUhhtiMQixGuiOK6D0RpjYMc12wmCgEPfORquQlvh\n0HbEwolG8AteeWxIYAKyyTSB5aGMQin48F+cZHt3EdvSWErR1eRSF7cxc2XvgYlXMjj1KvZs+0eM\nUSRjg1jKIzAujp0GFMbYKKVRyuf0+Gs4NfHT5XQk3CFikXG8oIp0vhuzwpqmQqGAZVlEImuZ3331\nSgtmzf/7zGQyVFVVLbm9Uqq8femxMYZMJkNNTU3F9ys9L702Pj5OY2Mjtm2vaPv5j0+ePElPT8+K\nt5//3sTEBFprWltbV7S9UorZ2VluvfVW7rvvPqqrqxdO73mBWFbY1fAd73gHn/jEJ+jo6ADg9ttv\n593vfjc7duzg29/+Nt3d3fN3u/AJu3hd8nEqk8lw6NChJd9fnC9PTU1RU1ODbdtLbrOS46z2/aW2\n2SpxKjOd4zt/8wMmT09j2RbDR8YwgQ7jlDHYjk11YyJskVdQzHr0HOgkXh3lka8eDFvoKxzachRu\nPIJXCDBao024uG6uOkNgF1DawgC/8buDXPmCDJatsC3N9toILTURtAlb+sdS13Jk+N1c1f63GGNI\nxoawrQKBdrCtPJbSaBNBqQCFz+jsdRwdeWc5HfHIGWLuKIGOkc53oc3K1q0qrZjtuhuzztVScSqR\nCMf3LM6Hl4pTpTy8trZ2RXFq/uOpqSmqq6txXXfFMab02sDAAO3t7eWVxZeLc4ufp1IpZmdn6ezs\nXNH2AOl0mltvvZV7772X6upqLOvCtylcyDgl/UkWicVi7Ny5c8kLkMWvp9NprrjiigV/MOey3DYr\nvfCptJ0xhkcffZRrrjl7Fdn1TkPgB/zo3kOMnZpg264WrnnF3gU/BqUUje317Nu3j29//j7u+MO7\n8PIeWodN1s2djVTXJ5kYmiLQ4Dg2N7z6OlBw7IcnicQipMbTZwWQwNfUtVYxO56iub2OgcEhCtUp\nevdlSdYFpGdtGloKbO/KE7EVEcdiZ7NLPBIGEkXY32tH88O07ziAVYyjgkOUapMiZDDEUeQJm7UN\nEKez6yV07L5+jQsZPqevr49kMklr68bMmuV5Hp7nlTNIgEceeYQDBw4suU8pKJTOvTGGYrHIM888\nw969eyu+v9zz2dnZckFkJdsvfq61XtX2pceZTAatNUEQrHj/z3zmMwwMDHDLLbfwjW98ozwryIX0\nqle9ij/+4z8+63f7tre9jbq6On7u536Ol770pdxzzz3s27fvgqdHbH2O49DT07PsBcj8fPzw4cN0\nd3eX/543M05BmAdtRJzSWnPoh88yeGSEpo4GfuKV+3Eiz+WFSilaO5ppb2/n4Hee4W8//M/kM/mw\nVd5Ac0cD9dvqGDsVVqTZluHaF19N175OfvT1Z4jE4qQnM+hFLSPaN8SrEqBz1DRVMzxwhlxtiu6r\n0tQ1++QzFtGEofeaLI4NjmPoaYqRjIZxylJhnGqpfYbG1n4sLz7XOuITxqkAiAMeNpowTkVo2fYS\nmnteTLlP2BoNDAwQBAFdXRsza5bv+xSLxfOOU8YYnnjiiVXFqdLjXC5HfX19+Teyljjl+/6q41Q+\nnyefzzM0NLTi9P7DP/wDQ0NDvPGNb+S2224rFwoupAsZp6Qgsoht2ySTyRVntLZtk0gkNqREei7G\nGCzLuuC1GMYYvvInd/P093+ME3XwCj6Dz47w0+999YLzppTCsixOPzPEK/7b9TzyjSeZGZvFdmzy\n6QKxeJRETRy/6PPT7301N7/7J/E9n2994T5OPH0qLEsvrm0yMDEwibIUA2OD5JIZWtvzVDf4WBYY\nDdt2BPieRV3SoqcpgmOrCrVWGezcX2FUDWHmbhMWRhQKG6N2osypcPC63YFV/BLaqsa4r7iAZ3Zr\nmF/zUqK1XvPfluM41NXVrakVaGhoaM2Z7PDwML7v09nZueJ9vvCFL3DjjTdy7733rukzv/nNb/KB\nD3yAIAj45V/+ZT7ykY+cc5977rlnyfde97rXcc899/CGN7yBV7ziFYyPjy+5rbh8WJZFMplccdxx\nHId4PF6uYd5sGxGnAP7jb7/LD+98mEjUwSv6HHusn7f9z1vPqjSzLIv+g6d52Zuv44nvPs344CSW\nbVHIFcml8iTrEhRyRW5+z09yy2++Bsd12HOgl6d/8Ex5LONiUyPTKEsxNDpMriZDfVOB+pYwTmkN\nDU0+xljEo5qdzVFcp1KcKmLn/w5jtRLGKYtwivmwy7DhKhTPYlQjWJ1Y3j1hnIq+6UKczi2lUpwq\nvb6Wvy3XdampqSGZTK5639HRUbZv376mGDc5Ocnk5CS9vb0r3ufP/uzPeOKJJy6ZOLX5V8/iomKM\n4d//6lvc8/l7yWUL1LXU0ryjkUfv+RGpyXTFfWzH5onvPs3k8DQAxXwRNxahffc23vj+1/CRf/4t\nXvcrN2E7NtF4lN+967+HUy4uURY0GLLxFBknjdaGRFIzM2EzccYhGjO88CdTtLdU09sSDQshFflA\nKhzfAUApmthAEC69iwvOnvBexVDe2n704vIQBAHve9/7+MY3vsHhw4f50pe+xOHDh8/7uC996Uv5\nz//8zw3rzifEpeD7X/kvvvIn/0Z2JktNUzUtO5o48uhxRvor92V3YxEO3v8MoyfHQYXTwDuuQ1N7\nA2/4jVfzO59/L//tw7fgxlwsy+Kjd3yAxu31qCVijMGQi2ZIuym0r6lt9Jked5gadTBGcf1rptne\nHGN3ayIshFRUilOllonSFMClijOfME7NTaaikljF7635nIlL31aMU9IiIlblc79zG9/9p/vJpfNM\nnZlm7PQEP3HT1aCoOJUuQM81O/jP//fDuVlEFLFElELeQynFK9/+8or7aD1vQaf5r1uabFUarcK+\nuZZj8aKbMzi2T8Qx7L42z/7eKPXJLpQ5Rbj67FICUEWw2kDPUFpV3dAAjGIA5R8GNBgP49Qsc6x1\nEAxg5T+PMuMY5wXo6NvCqRfFReHhhx+mt7eXnTvDwaJvfetbueuuu9i7d+95H/vaa6/lBz/4wXkf\nR4jLwdf+/Ov8vz+6i+xsjsnhaUZOjHHd638CZakl41Tv87u5+6+/BXM17W7Mxct7FPMeN73j5WfV\nvjsRG7/gz1VaLWSUIVuVxrM9lAHbUVz9ogJ1TTkUFrv2Z7n6KpuW2k6UGaW0QGFlBqXPYKwdKD3K\nc3GqHhjBoFHes+HsjcbH2DvWetpWRo+HcUqfxth70bF3htMDi4vCVoxTUhARK5aaTPPdf74fy7Zw\nIg5BEDA7nuL04UH2vmQ3tc3VFfdrv2IbzZ3NjA9OEEtEcWMRMjNZmnc0lbd55qFjfObXP8fUmRk6\n92wnWZsgM51dcBzf8clWpcOMNxz3TkdvG9/7qsVv/u8jNDZa7N5eTTy+iyD5lyjvQaz8l1D6x2ij\nsVSwKGUOkETb14MawwqeDAedqziobSj9DMbkUfiAh/KfRhW/h3F/6twny2gwY0B0Zauu6ynszIfB\nZEG5WIWvgJ5CJz547n3FljA4OLigG1hHRwcPPfTQuh1/165d63YsIS5Vxhj+5VP/BkAk6uB7Abl0\nnv6Dp9n1vC5au5oq7tfc0URrdwvDx88QTbhEYy6ZmRyN2+rLhZDTzwzyJ+/5v5zpH6NtZwtuwi0v\nsluqMwvsIIxTSqO0wijDtl1t3P+NKO/93WfZ1qnp3ZakpqoZP/l3qOAQVv6fUMFBtPErxCkbrFYM\nNRgrh+U/NPdRVaDqUeYIhizKGKCICk6j8l8Nu2eda6yIMWAmCKelrz/3GEiTw878D9CjoKKo4CSW\nHkQnPnHe4yfFxtiKcUoKImLFinOtGEpBLOFSLHgYbdj9wp287WO3LtlfufPKdtqvaCXwfdJTGVKT\nBWpbanni20/xrS/cC0oxO57CGI1l2xx7oj+slbLDvrtBMaAQzVOI50AbzFw7ScSJcMObruNFr38+\n1XGXXU0FIk6UwN4bTrMbfQNB9A1Y2T9iZuJR6qqzKHOaMGIoIAaqDqWfxqhmjNUCKoJRTaA6wAyC\niWHIg9UJFFHFb2HsbrB3Ln2i9DRW9hMofQJlDNp9bbii7XIDL4ODYSFkbrEpQzTsCmZ+67wHHgoh\nxOVCB5rAC3DcsKuvZXkEfkB7byvv/v234sYqjx9o62mmc882inmP2fFZ0lMZ4tVxBo4M846e96G1\nIT2VQfsay1GcOHgKQzjeRdmKoBjguUVyiUzYiD43q6NtKfa95Cpe80s3EncjXNFSJBpx8O29oKIY\nu43AfSVW7u+ZnfgmtUmNMkd5Lk5FwrGM+iRKVWOsZsLuwtUY5yooDoGpwpAGazsQoLwHwO7FRJ63\n9IkyOazsH6GCg2GcilyPjn8I1NKXhSo4DnpiXuVaDMs/iDbTYUFGiDWQKxyxYvVttXTt7SDww7U7\nLNuivq2OX/zdnyNRHS9vNzM2y/DxM6QmMgDUNlXzrk++lRe94QXsf9lVvOpdN1LMFjhzapz0dIaZ\n8tohz60REvgB8aoYRmtyyQyFWLg+CCacMz1WFae+tYaa2gnaordxVe3f45pDGHv3WRmpjr0bP0gS\nLuzkAlFQLRhVjfLvg+AMqO3hWiJYqKAfFTwGJlzQMCwcOOFNVaGCM8ueJyv/uTDDpg6jalHFr6P8\nB89xdiOLhsRoZPGpi0t7ezunT58uPy9N6SiE2Di2Y/PC1zwPHZi5RXQVVbVV/NIf/gI1jc+12qcm\n0wwfP8PsWApjDLGqGO/6xFu54Y0v5OpX7OWn3v4ybMdiuH+E1GSG1EQqXDvEGAJPEwQaJ+JQVZsA\nbShU5ckl0mEhxITTnkTiERrbG0nWzdLo3M7++r8nxqMYuxdUdEG6dfRnKfhNGBThOlYu0IRRTSjv\nB6jgRDh5itUKKNAjKO9BwriWDdcYwUWhwGoAPbDsebIKd6D8JwnjVB2W90NU8evL7mNwKP8H514B\nli28iK1lK8Yp+esRK2ZZFv/zXz7E5377No4+3k/bzhZ+48/eGQ4sn3Py0GkO3v9jLNvm5IkTtNS2\nsfdFu2nrbuGdv/sWAB66+zHuu+MBMtPZcB72RYw22LbFp77/v7j981/mzNAYBJrTx0aYGp4ilogS\nT8Z53vUpXnvj3bTWJMB0gPd9LAJ0/JcWJbyFZ4bfxQ2th7G8/wIc0KdQZiL8POKo4AcY5wbQoygz\nhnGuxzitWMXbQQ+BasQ4Lwd8jLX8WBEVHA2DglKADUahguOYyA1L7mOca8MFp/QApZVydfTt0hpy\nETlw4ABHjx6lv7+f9vZ27rjjDm6//fbNTpYQl50P/M2v8vn/8SWe+s9D1LXW8qt/8g6a2hvK7w/3\nn+Hxbz2FsiwGBwax8hGuu/n51LfV8baP3grAs4/08cOvPRyuoF70z/oMow2+5/MH3/kod9/1TU71\nDYAFw8dGGR0YJ+o6VNVV0XNllrf87L101rtgtoH3GJZJoeP/fWEruVVL35m309ByGuXfDaoKghMo\nM0ZYMRUH/wGM8xKwEyj/KYx9NcbqxSp8CcwoUEA7L4FSYWQ5/pG5bshh5Z4xEVRwZPlFeOxdGPsq\nrODpcJ0tNDryalCVu2WLrWcrxikpiIhVqWms5nf+4b0V3/MKHocePEJDWz12xGYyNcaPvvc0+VSB\n5s5GOvdsByBRm2B2Ml2xEFLSelUzqcQMr/n1nywPWtda8+MHj/LsQ8fo6Mnxtrc8Tn3V3Iqy+jjG\n6kX5jwC/dNbxjLHARMNBf6qRsMYpglHdc9f9w6jg2XCaROdKjPN8LO9ulPLB+GEm79+LcQ6Atfxg\nQGN1ovwfhTVexqAwaGv78idWxQmSf4wq/DtKj4cFk8hLl99HbCmO4/AXf/EX3HzzzQRBwHve8x5Z\n90OITRBLRHnvZ95V8T1jDAfv+zG1zTVEohHSxVmOPn4cpS1adjTRta8DpRSJmjipyXQ4IH0J8XqX\noLXIT73rJRhtwsHwQcCJH53mR/cdor4pxzvf8SNaaue6WZlTGHpQwRHCAeoLB3kbbIxxUHoCo4pA\nEpjGWJ2gkqhgAIKDGLsXY/VgIjegvPtRKg8mADMJ/vcx9rXzZoRcgr0DgmfmpcHDnCO2oRx01ccx\nhbtRehBt78G4r1p+H7GlbMU4JQURsSZTZ2b4+l9/m+H+Ubb1tPD6X38V0YQLBuxI2KVo7PQUT339\nGf7r3x4DpXjlL7yMn3nfzey9YQ9KhZX9leZgL0YLbHtZI57noVDlVVRty2bfDXu47iefz86a7xLV\nR8NxFcYBZUCPhNMYLmYM3U13Y3vHMTgofRwwGNUKTidhgAgwqhYTeR3GTIE+Gi50aKKEUybmUWYc\n/Gexcn+ITnx8yRmtdPzXsDP/C/QUoNGR6zGRyrODLaCSmNjPX/rLQl/CXve61/G6171us5MhhADS\n0xn+43Pf4eThQRq21fHTv/5qGtvr8Yo+kWiYf0+fmeW//uUJHrrrCWzb4vmvuoZ3fPzn6Ni9jWgi\nSi6Tr7h6uh/xaHxxK/lCHgi7YmHAVja7fqKbq67bza7awyT0s6AdMDYoF6WHMVYPYZeqhdpq7yXi\nP47BRekBQGNUA9i7ABtDgCEaTphiiqAHsPwHwbhzs2ZlUWYKdD927pMEVf87bFmpQEd/ATt4FoIB\nUAbj7MVEbzn3SVVRTOzNEqcuYlstTkm/D7FqXtHn9k9+lVPPDpKojnH62SFu//2v4bg2NY1JZsZm\n8b2Ax+8+hBuPUNtSS01TNd+7/Qccf+okoyfH6LxyO/HqOMmGKpzo3IrbGPJVWeztile/80YwYe1V\nmL8btNHUJ+vp3daL61QBMaAaVB5MAYWPjv7C2Qk2E9QnD4WD/OwOjH0VhkawYkAeyIBKYGK/jIne\niIm++rnM23IIpwCOEM5eUo8K+iE4uvQJsloJkp8hqPokQfJP0PEPSx9aIYTYQMYYvvwn/86RR4+T\nqI4xMTDJbb/3ZQq5Ii07mpgcnkIHmkf/7UcoBfWttdQ21/DYt57i4P0/5szJMXpf0EOiOk51QxWR\n2HN5eDFRIGgp8uYPvgFLWWGFGQajwniVjCfZs30PMTcJRDFW/VycyoHy0NH/dnZFlvForX0gjE32\ndox9JUa1gJUkbD3JAg4m9k6Me1NYGLEamJvHPiyY4AJOOJhcj4Yt80uxagiq/pgg+QcEVZ9CJ34P\nVGy9vwYhzkmujsSqTY1MMz02S9P2sA9qQ1sd40OTzIymeMGrn8fT9/84XDRKG5raG7CssA+qDjT/\n9PEvo2yLWCKGbdvlaRLbeltI7o0SbYjysltfRCwRBRXWMhkdtoi0N7bTUtsCgI6+Ctt/AKMDIAJK\nEcQ/BJHnV0ixT7jQySjK9M+9ZgicX8TSZzDKxsR+ERO5JnxLVWGiP4vxvgEmNzeIPJjrTxsFk0Hh\nL18jpOJziyEKIYTYaLlUjsFnh2jqaEQpRW1zDeODk4yeGud5N+7l8A+fZfT0BPlMkbYdzVh2WC+r\nA82df/4NLFvh5T2cqEPEdXDjLg1tdTQeqMVOKm5443XUNoRjIwxzFWba0FLbwvaG7SilMJEXg/cN\nCBRGWaB8dPSXlpgCXgMG9AxKHy2/pq2fBZVDGR8duwUTeUX4loph3FswhX8DM4HCEMa6CBAnrGRb\nultZeIwI2Fec76kW4rxIQUSsWjQRxWhDEGhs2yLwA3SgiSZc4skYB177ExhjuO/OB8jO5qhtjlDI\nFpkem6W+tZa2Hc3lcSQHXnstnc/bTqTHQgdBuJDhXBN3qVuW4zh0N3dTHZ83IM7aRlD18XCaQgKM\n82KwOysnWLWQLzZQHX+KsBEw7K9re9/Fr/lXUBVmp7JqCar+EDv7qbnFDk24uq2ZBKshnPVECCHE\nlhSJuViOhe8FRFwHo8NxhtG4ixtzufaVVwPwX996lNG+CeLVcfyiT2oqQ1V9FV1XdWCMwbIUe196\nJbtf3IO708YPvAVdtUoxS9mKHY07qE/Om8bWqiNIfBzl3Q8mh4k8f+kLfxVlJttLMnYflOdQVFj+\nvfg1X4VKk6SoSBincn8EJg2miLF7wMyEFWr2/nU5l0JcSFIQEatW21TNDbcc4P6vPYSlFNoYXvbm\nFy2YGlEpxWs/eCP3//1jTI1M48Zcuva20zjXimLZFm7MJb49itMNQeCjjAoLIaWWEAwxN8bO1p1E\nI9GzE2K1YaK3njvBymJ09jqaa48QtmxEwlmtTHouw15idhG7l6D6c2CKqMJXwzEjVhs6+vOykqwQ\nQmxhEdfhVe+8kW/+3fcwhF21rr1xL209LQu2u/m9r+C7//cBzhwfw3Isdl7bRdXcdPRKKeLJOJFa\ni0ivwvOL5RhVaqlXlsK1XXpae4i78bMTYtVjoj+zojSPp15Ee8PDhOMS7bBbljFgRoAlZmu0txMk\nPwMmQBXvRvmPgqpDR9967pmzhNgCpCAi1uQn3/YSuvd3MjU6Q31LLT3XnD3bRl1bDR+5/TcJCppY\nVZSv/OndHHm0j6b2RnzfZ0ZNUUjmwoWfNGEBRKnyuJDaqlq6m7qXXChxNXLFtrnCgx22gJhi2M1K\n1Z57Z+XKIHIhhLjIHHjNtbR1NzM2MEmyLkHv83vKq6SXJOsTvPcv34lrubhxl+/cdj8P3f0Y8eo4\nxhimvEn8pu1oX4MGS1kYwhmyDIZkNElPSw+Off6XU3m/GaPiKKxwXKHxCbsHtJxzX5SNid6ysgHn\nQmwhUhARa6KUYufzula0XVVt2Hrw+l+9iZnxWYZPnGHKmmTvq3bTccW28nYllrJorW+lra5t3dKb\nLW5Dx96Flf/CXMJsgsQnKnfLEkIIcUnovLKdziuXX7AtnK43jFM3vvUGxk6P03/wBDPWNJ0v3s4V\nL9hZXildz5vqsam2iY6GjrMKN2vlB9V40f8Pt/DpcDpeDEH8w/NWMhfi0iMFEbFhkvVVvO33buXg\nsacxliZRFS/324WwO5Zt23Q1d1GbWEFLxSrp2DvQkVeGCxZaO8CqP/dOQgghLhuxRJSf+8hPc7Dv\naQp+gUQy/lyXYaPACu87mzpprG5c98/XkZvxowfmpvndDlbzun+GEFuJFETEhpnOTHNy8iTRZARL\nWeUB6RDWSLmOy87WncTcCziFoL0dwzkWFxRCCHFZSufT9I/34yRsHBJhnDIKbTSWsnAsh56WHqpi\nldfnWBdWC8ZaQXcsIS4BUhARG2J4epjhmWGsuaVrjHluxIVSimQsSU9rD7YlXaWEEEJsvLHUGIPT\ng6DDGKV4rsuVQhF34+xs3UnEqbyYrRBi9aQgIi6oQAf0jfaRyqWwzHOtIEqFU/RqNK21rWxvkFYK\nIYQQG88Yw6nxU0ykJ55rpTeqPDAdBQ3JBnY07Vi38SBCiJAURMQFU/ALHBk5AtZcC0hpbRAMSofz\nru9s2kldlQzEE0IIsfG8wOPY6DEs10KZMD6VpkjUaJRSbK/fXl5MVwixvs5/XlQhKpjJznBq6hR5\nLx82cZuwFqnU3O1GXXa37ZZCiBBCiE2RKWQ4OXWSrJctD0iHuTilFG7Epbe1VwohQlxA0iIi1t3I\nzAgjUyPlwX3MzXaorDCXT8bDeddlPIgQQojNMJ4aZ3BqEM/3wooyPW8aeQvisTg9TT24EXdzEyrE\nJU4KImLdaK05OX6S6dx0eQyICQzYhN2zMDTXNtNe3y79bIUQQmw4YwynJ08zmZkMYxSmPHmKIWwJ\naUg20NnQuS6L6QohlicFEbEuCl6B42PHKXiFMHM3YeZulMFgsCyLHY07aKhq2OykCiGEuAx5/xiE\noAAAIABJREFUvseJ8RNk8pnyIHSlVdgiosIWke0N22mpka5YQmwUKYiI8zabm+Xk+EkCHYSZO2GG\nrpRCoYhGo/Q095BwE5ucUiGEEJejbCFL/1g/nu+FLR8ojDblmOU4Dt3N3VTHqjc5pUJcXqQgIs7L\nmZkzDE8Pl2caUagFLSFV8Sr2tO3BseVPTQghxMabSE8wODmINhqjTHmBwtJU8rFYjN1tu4lGopud\nVCEuO3J1KNZEa82piVNMpafCudfmFUKUCu/rEnX0tvRKIUQIIcSGM8YwMDnARHqi3AqCIYxXcy32\n1Ylqept7pRAixCaRK0SxakW/yPGx4+QKuXC6w7lMHQMoMMqwo2kHelJfNoPSy4Md593PXz2+9DwI\nAjzPo1AoVNxn8b6VjrHUPpWO4fs+Wmtc18VxHGzbxhiD1loGYgohLll+4NM/1k+mkFkYowzlhQva\n6tqIZCKXTV64mrgRBMGK49RSr6/0vvR5ruti27bEqcuMFERW4Fw/RM/zsCzrvH6IK72QPdc+nucx\nMjJyXsdY7j6dTzMwPYAf+OXpecsD043BcRw6ajsYzY6SSqU4cuRIOSPZ6PMzXzqd5oEHHjjr9fVU\nKnQtd5/L5bBtmzNnzizYbyX7Lr6fX8ir9LpSCq01vu8vCC65XI7HHnvsrPNk23a5sLL4MUChUGBs\nbGzJbS6XQqcQW9FyeWUpH/A877xjzLnu1xKn1nKM5e5zxRynp05T8AsLT1IQLlJoWRbba7czlZ1i\namqKYrGI67pLpuNCnp/5MpkMDz300AXNS1cSW0oFkKmpqSVjy/zjnW/8KsUnY8LKOt/3yeVyPP74\n42edJ8uylo1VnucxNja25DYSp7YeKYgsMjs7y8GDByu+V+lHlMlkePLJJ8sX2+dzIbmWH/P8ewi7\nTGUymVXvOz/9S20zmZlkojhBPB4PV5y1wtlGlFIoSxGPxOlq7MJ1XJRSzMzM0Nraiuu663KhfT7n\n5YEHHuCGG25gs/X19ZFMJmltbd2Qz/M8D8/zcJznfuqPPPIIBw4cWLDd/IuVIAjKwaB0XywW0VqT\nSqXOer90m38spVQ5AKTTaY4ePUokElkyeJQel+4ty5KAIcQSCoUCDz/8cMXfSKV8MJ1Oc+jQoXI+\ncD6x5nzjVKmCJJPJrPqYleLU4uez+VnGCmO4MZeoioZTx2uDoxy00sQiMXY07CDuxgHI5XI0NzeT\nTCbX5f92PnHqoYce4gUveMGC/HozDAwMEAQBXV1dG/J5pRizOE698IUvXLBdKU4tjk/zY5IxhnQ6\nXTGWzY9TJaUYlMlkCIKAWCx2zvg0/yZx6vxJQWSRmpoarr/++hX/cT344IMcOHBgSzQfGmMYGxtj\n165d637cUxOnKNgFGuoaymuCoAErHBtSn6xnR8OOBectEolQW1tLNCp9b7e6+QWHSorFIpOTk+zc\nuXNFx5tfs/X000/T1tYGsCAw5PP5ioEkCAK0DlfBzGQyPPLIIwvStzgYVAoSjuNQLBaleV9ckqLR\nKNdff/2K/66feOIJ9uzZQyKxNWYuHB0dvSBxamh6iGwhS31dfVghMreIrtHhelbVsWp6mhYupjs8\nPEx1dTW1tbXrmh6x/ubHgVIL1mJDQ0P09PSs6HilOBUEAc8++yzNzc1Eo9EFMalQKJDNZivGKq01\nxphy683i1ppzVbzZtk2hUCgf83KtgJOCiFhWoAOOjx4nnU+Hg9HnBvxZxiJQAZay2F4n866LhZRS\nOI5TznCrq6uJRCKrPk6p9WZxLVilx8ViccHrpRqu8fHxs7pYWJZVMTB885vfJJ1O88UvfpGf//mf\nX1OahRAbyxjDifETTGenUVqhVdhiX2qdNZZhW+02ttVu2+ykii1kfpxyHIdkMkkymVz1cZ544gn2\n79+PbdsLeglUilelODW/C1qhUCCVSpUr4EqW6ob2/e9/n1wuxz/+4z/ypje9iZqamvU6JZtCCiJi\nSX7g0zfaR66YQ5kwMy81cxtlcG2XrqYumXddXHCWZWFZ1qoKBsPDw/i+T2dn54LX5zfvLw4WpZab\nycnJy7JmSoiLjdaa42PHSeVSYHiuEKINlrJQlmJn407qEnWbnVRxiVtLnJqcnGRycpLe3t6z3luq\nu3QpTk1PT1fsbnaxkf4KoqKiX+TomaNkC1nQhIWQedMext04u9t2SyFEXHRKzfuu6xKPx6murqau\nro7Gxkbe/OY3k0wm+eAHP3he/bQ//vGP097ezrXXXsu1117Lf/zHf6zj/0AIAWFl2bHRY+VCCCq8\nGDQ6bPWMOBF2t+6WQoi4KFmWVY5TyWSyHKde+9rXEo/H+cAHPkB9ff15fcZWiFXSIiLOki/m6Rvt\nw/O8cDpey4TT9BJexNXGa+lq7JJ+90Is40Mf+hC/8zu/s9nJEOKS5PkefaN95It5LCy0pcvTyVvK\nIhlN0t3ULetYCXEOmx2r5BcqFsgVchw7c4wgCMLxIHOD/Uqr0LbVtNFW17bJqRRCCHG5KngF+kb7\nKBQLYTcsFY4BK41jbKluYXv9duleKcRFQKq0RVk6l+bIyBH8wA9bQuzn5jx3lMOu5l1SCBFihT77\n2c9yzTXX8J73vIepqanNTo4Ql4R8Mc/RkaMUi8VwIPrcPx1oMLCjYQftDe1SCBFihTY7VklBRAAw\nk53h+NhxjA5nGcECy4RTyUXtKHu27aEmcXHPzCDEerrpppvYv3//Wbe77rqL3/iN3+D48eM8+eST\nbNu2jd/+7d/e7OQKcdHLFDIcGTmC53sYZTCWwcJCGUUsEmN3224aqxs3O5lCbClbPVZJ1yzBZHqS\nU+OnwITjQUo1ScYYamI1dDd3L5h3XQgB3/nOd1a03a/8yq/whje84QKnRohLWyqXon+sn8APwjhV\n6jaMpsqtYmfLThkPIkQFWz1WSYvIZW5sduy5QogdDkrXJpzLurWmlV2tu6QQIsQqDQ8Plx/feeed\n7N+/fxNTI8TFbTozzfHR4wR+ADYoS6FQoKGxqpEr2q6QQogQa7AVYpX8ci9jI9MjjEyNhE9KZQ0D\ntrLpauyirkqmPBRiLT784Q/z5JNPopSiu7ubv/mbv9nsJAlxUZpITXB6/HT4xA5nbixNI9/R0EFT\nTdPmJlCIi9hWiFVSELlMDUwOMD47DsxNzxuEtUwRO8Kull3E3Ngmp1CIi9dtt9222UkQ4qJ3ZvoM\ng1ODKBSWbYWLkRpNxIqws3knVbGqzU6iEBe1rRCrpCBymTHGcGr8FFPpKQwmbAnRgAXJaJKelh7p\niiWEEGJTDU0NcWbqDJaywAq7DFvKIubE2Nmyk4iz8tWrhRBblxRELiPGGE6MnmAmOxO+YBEWQoCW\nZAvbG2TedSGEEJvr9PhpJtIT5QV1FQplwsV0dzTtkMV0hbiESEHkMqG15vjocVLZ1HMLQM31s+1q\n7KI+Wb/ZSRRCCHEZM8Zwcuwk05npcHUQ67k4tb1+Oy21LZudRCHEOpOCyGUg0AF9I31k89lw7nUM\nlrZwHIddrbuIu/HNTqIQQojLmNaa/tF+ZrIz5al5rcDCcix6mnuojldvcgqFEBeCFEQucZ7vcWzk\nGAWvEM44MjflYSKaYGerzLsuhBBicwU64PjocTK5DLZthy32AcTcGDvbduI67mYnUQhxgchV6CWs\n6Bc5NnyMgl9AOSpcNV0rGpINdDZ1yngQIYQQm8r3ffrO9JEtZsEOu2epQFGTCBfTlfEgQlzapCBy\nicoX8xwbPoZvfJStMIHBwqKjqYPG6sbNTp4QQojLnOd7HB0+SjEoLpg8pa2ujbb6tk1NmxBiY0hB\n5BKULWTpO9NHYAKMCmuXXMelu7lb5l0XQgix6QpeIew2HBRQSqG0wrZtupq6qEnUbHbyhBAbRAoi\nl5hsIcvR4aNodDgo3VhUxavobuqWedeFEEJsuoJf4MjwEbzAQ1nh1LyxaIyeph6ibnSzkyeE2EDS\n+fISMp2ZZmh2iIAg7GdrFA3VDfS29kohRAghxKZL59IMTA0QmCAcp2igOlHNFa1XSCFEiMuQtIhc\nIibTk5waO0VAAAYsy6K9oZ3m6ubNTpoQQgjBbHaW/rF+AhVWlqGgtbaV7XXbNztpQohNIgWRS8Do\n9ChD00NorVFG4bou3U3dJKPJzU6aEEIIwVR6ihPjJwDCyVMsi66mLuoSdZubMCHEppKCyEVuZHqE\nkekRMOHzWDTG7tbdMu+6EEKILWEiNcHA1AAWFjrQuFGXPdv2EIvENjtpQohNJgWRi9jgxCBj6TFM\nYFBKUV9TT0dNhxRChBBCbAkj0yOMzIygtMIYQ3V1NTtqdkghRAgByGD1i5IxhpPjJxlLjWF8AzZs\na9pGd1M3lpKvVAghxOYbmhxieHoY7WkCE9Bc38yu5l3Ylr3ZSRNCbBHSInKRMcZwYvwE0+lpVKBw\nok4473q8Jhz8J9ZN6XwaY1Z1A9BaV9w3k8kQBOFsMedznJXuW9o/Go0SjUZxXRff98lkMriui+M4\n4cw1Qgixjk5PnGYsNYYKFFbEoqu5i/pE/WYn65JzPnFqqffS6TRBEDA6OnpB41Np3yAIAMoxSuLU\n5UUKIheRIAg4PnacdC4NBqJVUXY27SQaWdmUh+uZUa1k33w+z9DQEI7jrPkYa/38+fsDpNNpHnjg\ngTWdd6XUmm4Qzl42/xi5XK5cEFnJvpZlrfnzlVL4vk+xWCQIAorFItlsFt/36e/vL79eSl8kEikH\ngcW3+edSCCGWYsxcZVlqGmUUTsxhV/MuEm5ixfuv5WJ2rRfCmUyGM2fOMDs7u+Excn76S2l56KGH\n1nTRvR7xqXRLp9MYY5iZmVnRvmuNU6XjBEFAoVBAa02xWCSfz+P7PidOnKBYLOL7fvn/uVyccl1X\n4tRFSAoii3iex8TExIozmUKhQH9/f8VtYf1qDPzAZ2BmgEK+ABZUxapoq25jqn9qQfrPdcG9HpnU\nSm+lGnljzJoyq/VIQ2nfBx54gBtuuOE8/zrOX19fH8lkktbW1g35PM/z8DwPx3nupz42Nsb+/fsX\nbKe1xvM8isVi+ZbP55mdnaVYLFIoFEilUjzyyCPAuYNBJBKRGiwhLpBSbbVS525ZNSZsiT19+vSC\nSiFYv/hUugU6YGhmiEw+g0IRjUVpr27nyZNPLkj/esap86moKf0/SulfTZyC849Pi/8PDz30EC94\nwQsW5NebYWBggCAI6Orq2pDP832/3PJRMjo6yr59+xZsZ4w5K04Vi0XS6XT5cTab5eGHH0YpheM4\n54xTpe9QbB4piCzi+z6zs7PlP86lMpr5mVU8Hj8r81pu39VmUoEJOHbmGIl8AuUottVvo6227ay0\nG2N48MEHt8QFN8DExAQdHR1Eo7JI1VZnWVa5+1YlxWKRw4cPc+21164oGHieV943l8vx7LPPLmh2\nl2AgxNpprZmdncW2w7EWS8WPUlwq/b5jsdi6X8iXfrvaaPrH+onn4ihL0VTTREdDR8UKia1SMQSQ\nzWZpa2ujtrZ2s5MizkEptaCVvpJHHnmEAwcOLBmnMplMOUYVi8XyfoVCAc/zSCQSEqc2mBREFonH\n4/T29q64NvfUqVO0tbVdsD/Qgleg70wfXsErjwepjUuGKTbPSoJBiTGGxx9/nI6OjnKze6VgUKpl\nnd/SEolE8DyP8fHxBQFBgoG43EUiEXp7e1f8WxgdHaWlpYVEYmXdo1bLD3z6R/vJ5rLYjk1HYweN\nycYL8llCrMRq49ShQ4dobW3FcZwFrSvzK9dKLWeLW1oKhQITExMLCjESp1ZOCiJbWK6Yo2+kD8/z\ncBMuu5p2yZSH4qJSqo2tqqoiEoksu60xpjympXQr9VNeSTBYfCt1HRFCXDhFv8ix4WMUi0Ui0Qg9\nzT1URas2O1lCrFgpTsXjcZLJ5ReCNsaUx1zOj1OpVIrp6ekFrxljsG1b4tQ5SEFki8rkM/QN9xEQ\nUFNdQ3dTt0x5KC5pSoUD5iORCFVV4YXMqVOn2LVr11nbVgoGxWKxPKal1OqitWZ4ePicwcB13XI3\nFyHEyuSLeY4NH8PXPomqBD3NPUTs5SschLiYlcaeOI5TbmEcHByku7u7YmXb4sq1YrFIKpUq9wYo\ntbpMTk4uiFNLjcO0bfuSG38pBZEtKJVN0T/ST2AFtNS20F7fvtlJEmJLqRQMFhseHsb3fTo7O8vB\nYH6f4fljWkoziH3qU5/ixIkT3HrrrXzpS1+S8U1CLCGXz4WFEHwaaxvprO+85C6QhDhf54pTk5OT\nTE5O0tvbW7FyLZPJMDU1tSBOfe5zn+PkyZPccsst/PVf/zXbtm3b4P/V+pKCyBYznZ7m5OhJcKC7\nqVvmXRdiHZSCwbl85Stf4eUvfzmf/vSnV9S3WIjLUTqX5vjIcbSt6ajvoLm6ebOTJMRFz7Zt4vE4\n8Xh82e2uu+46Xv7yl/PZz36WpqamDUrdhSOjabaQiZkJToyewIk5XNF2hRRChNgElmXR3d296trd\nL3/5y+zbtw/Lsnj00UcXvPcHf/AH9Pb2smfPHu655571TK4QG2omPUPfSB9W1GJXyy4phAixCSzL\nYseOHecce7nYVoxT0iKyRYxOjzI0NURVsoqexh4cW74aIS4m+/fv52tf+xq/9mu/tuD1w4cPc8cd\nd3Do0CGGhoa46aabOHLkiIxJERedydQkp8ZPEU/E6WnswXWk1VCIi8lWjFPSIrIFDE8NMzg1SFNd\nE73NvVIIEeIidNVVV7Fnz56zXr/rrrt461vfSjQapaenh97eXh5++OFNSKEQazc+O87pidPU1tRy\nRfMVUggR4iK0FeOUFEQ22amxU4ymRulq7aKjvvLiT0KIi9fg4CCdnZ3l5x0dHQwODm5iioRYnZGp\nEQamBmhrbKOnsUfWSBDiErOZcUqq3jeJMYZTY6dI+2muaLuChHthFpoSQqyfm266iZGRkbNe//3f\n/31uueWWTUiREBfWwPgAU/kpdrbupCZWs9nJEUKcw8UWp6Qgsgm01pwYO4GvfPa07pGuWEJcJL7z\nne+sep/29nZOnz5dfj4wMEB7u0zJLbY2YwynJ06T8TPsbttN1JGprIW4GFxscUraVzdYoAP6Rvtw\nXIcrmq+QQogQl7if+Zmf4Y477qBQKNDf38/Ro0e57rrrNjtZQizJGMOJ8RN4eOxp2SOFECEucZsZ\np6QgsoH8wOfY6DHqq+vZUb9DxoMIcQm588476ejo4MEHH+T1r389N998MwD79u3jLW95C3v37uU1\nr3kNf/mXfykzZoktS2vN8fHjxKNxdjXtkvEgQlxCtmKckur4DVL0i5ycPEl7fTvJaHKzkyOEWGdv\netObeNOb3lTxvY997GN87GMf2+AUCbE6QRDQP9FPc3UztfHazU6OEGKdbcU4JQWRDVDwCwzNDNHd\n2E3EXt3iM0IIIcSF5gUep6dP01HfQSwS2+zkCCEuE1IQucByXo7J7CRd9V3SxC2EEGLLKfpFRtOj\ndNV3YVvSbVAIsXGkIHIBZYoZCn6B9lqZIUcIIcTWk/fypAopOuo6NjspQojLkFTRXyDZYhaAhkTD\nJqdECCGEOFvey+MFHs3J5s1OihDiMiUtIhdAwS8QsSMyHkQIIcSWVPSLWMqiOla92UkRQlzGpCCy\nzrTWuLYrU/MKIYTYkrTWOJYj4xaFEJtOCiLrTDJ2IYQQW5nEKSHEViG5kRBCCCGEEGLDSUFECCGE\nEEIIseGkICKEEEIIIYTYcFIQEUIIIYQQQmw4KYgIIYQQQgghNpwURIQQQgghhBAbTgoiQgghhBBC\niA0n64gIcZHSWp9zG2MMxhi01rJ2gBBCiA13rlhVilESpy5PUhARl42VXLhDmCmu5v1K2y91DN/3\nGRkZoVgskkgkiMViOI5T3n5+waH0eH4mvfi1+c8rvV5pP9/38X0fpRQASinJ/IUQYotYaSXTat5f\nTZwKgoCxsTEsyyIejxOLxYhEIuV9lotDK41Vi18LgmDB80KhgOd5KKXKN5DFOC9FUhARSzrfC3dj\nDPl8HsuyypnIUtuvNVM910V46T4IAh544AGi0Siu65ZvjuOglCpvV/p/nyujXW0mW0pvKS0TExML\ntilltJZlYdv2glvp/JXen58x27a94PnibW3bLv8fS9/Bnj17yv/nUrqCIFhwbucfRwghtrLzuXDX\nWi+46F1u+9XGqdJry1UYLY4VDz74INFolGg0SiQSwXVdIpHIquPUUrFq8b6LtymlOQgCZmdnF7wP\nYUGgdCvFl/mvLRWLzvXe4lh25ZVXYlnWgnSXYmXp8eI4JYWUi5MURNbRZte4l2oRTp06RVVVFfF4\nHNu2z9p+rbUYS9XAL7f9E088QRAE5YvmxRfYpfNW6RiVVLowXu5CvPS4tra2/H8sFotks9lyy4Ax\nBsdxcF23XFCJRqPEYrHyMZbLRBc/Xur95fi+Ty6XI5vNLrgvBcd4PF6+ldLmOE7F77NSgJv/uFgs\nMjo6etb3XiokVTpG6fX5wXr+/1EIcfHY7Bp33/c5efIkVVVVJBKJcpyav89yF9fnE6sWv1coFDh8\n+HC5MsZxnHPGqfnHqWQ1cWr+81IeX4pTpRgwP05FIpFyQWW5OLWSmFTp8XKCIKgYp4rFIkopYrHY\nWXHKdd2K5/5cj4MgWHWcKj0upUdaUy4OUhBZ5POf/zyDg4Ps27ePvXv3smPHjgUXxov/4JVSPPzw\nw+Uf4LmaMBcfYyWZ6GpqOpRSHDt2rPzDhYU1GJVqH5bKvBbXuC+XyVXK0Orq6sqPSxl+Pp+nUCiQ\ny+XI5/MYY4jFYlRVVS24ua67LrXxK7kwD4KgnOmX0jUzM4PneQDlQsri2qnFx19tgWC5QDaf1ppU\nKkUqlVqQKZf+/koBsxSkSreVBKHS97tcgar0dxWJRLBt+6y/OWlNEWJj/eu//iuPPfYY+/btY9++\nffT09ACVL+JL908++WT5IrF0gVjadi1xark4tFyNe+nW19e3IE7Nz5MWx6uVXESvpIJoJXGqWCyS\nz+cX3IwxRKPRcsEpmUxSVVVFNBpd9zi1XBxZHKdmZ2cpFosYYxbEp9Jtfn69mphU6fG5aK3JZDKk\n0+mKccqyLBzHWRCnSoW+c31vq4lTpc9YnHZjlm9NEZtHCiKLPO95z+NTn/pU+ccej8dxXZf3ve99\ndHV1lS+USxd6kUikfJGdyWQW9L8v1Vy4rluuwZ7f1WY1tRQrqX2v9IMyJuwelU6nyWQy5VsQBMRi\nsXKGWrpfTca1XKa11DaWZZXPSakQUGoNmJ2dLdf+zL/IXhxAVnLxXrKWc5pIJKiqqiq/Xkqj53mk\nUqlyGpVSC2ql5hdEV/Mdn09GWOpWkM1mF9RSZTIZjDHlv73ShcfiC5BK36HneSv+rufXTM3fdv42\nqVQK3/fL38fi70UIsTrXXXcdH/nIR/jiF79ILpcr/7bf/va3c/XVV59VoaOUwnXdcmtwKU8Dyhew\n87sDrSROrTY+LXfhNz+Gzo9Vvu8TiUTOilPzLzTP9wK70mtKqXJeWV1djdYaz/MoFAqkUikGBwfx\nPG/BRfbibrSl/9dKnOucVnotHo+TSCQqxqlMJkOxWCzHqfmt/PPj1EoKAesRp0rf7+I4NTMzUy5E\nleJULBYrXyOU4n2l76p0nbDS73TxbfH2mUyG9vZ2aU3ZBFIQWeT666/n+PHj5efGGKanp3nqqafK\nt6effppsNkt3dzf79u1j//797N+/n46ODnzfx3XdBbUDmUyG6elpisUijuMsqJUq1aic6wJ+NZno\nco/ny+VyZDKZ8ueWarZLBYBSwanShfVaCk7LjXeodFyt9YLan2w2S6FQACgXFkr3pULU+VgusC3V\ndFyqMcvlcqRSKQqFQrkr2vwaqlItzfzPWel3Of+1lZh/ga+1Jp1Ok0qlCIKAIAjKx1vcilIaN1Op\n9qnUCrTcd7ZUM3/pu69UwyatKUKsXldXF319feXnxhjS6TQHDx7kqaee4r777uPgwYPMzs7S0dHB\nvn37uPrqq9m/fz/d3d0EQVDOj+bHqdnZWQqFArZtL4hTsVisYpxaj0JApWPMV8r7F19EluJUKR+b\nX7t+Pl1pV1L7Pv9xqbKvFKuy2Sz5fB6gXFgoxahEIlHuMbFWqy2AleJoqTfC+Pg4hUKhXBCd34pS\nOo+WZa34e11LK39JKU6VCgKpVGrB9UgpJpTSNr9nQmnsY6UeHKuNU6XPcRxnwf9BWlM2hlrNHw2w\nqo0vZUEQ8JWvfIWPfvSj5cwnmUwSjUZ5//vfT2trK8lkkpqamnLJ3rKsckm+VHMxv+9nqUaq1Aqz\n0ubm1RQIzvXDKdVclAJT6b7UgjK/VqpUM1Xaby0X1mtpcQmCAM/zKBaL5XNYOo+lzGj++ZmfiZzL\nWs73UhfgnuctSGehUEBrjeP8/+3de3BU5f0G8GeTJSEhIZgLIYSQKMG4hABCQVAoYIW00eKFZsTB\ncaw6Ywv8oW21F9ppi4BMChYG6YwzpXW0VajTTiUJMmpQqRAuVXPBFJFrEpprQy5LSPZy3t8f/N7D\n2VtyNrs5u8k+n5kdyOZscnI2eZ/zfd/3vMfs0vujXT1rsB6pYDV8QtwY+XCf7yt7S6Ojoz16qORc\nZL3v22CfG+z/Qgj09vbirrvuAuA5miLfL1+amprgcDiQlZXl17FZtmwZPvvssyEeWcMwAX1jTv0/\nRVFw5MgRPP300+qJsuwVf/LJJ5Gbm+uSUzJzZE7JtlaOksqTQfc2IdBOqqHklM1mc8koq9WqdgS6\nj6Bop0sP5cR6KM/JEQptTsnj6K3o8Sen/DneAz0n91Puo81mg81m85oB8fHx6nWnekbLgsVXTjkc\nDkRFRan7J8+b5O8k4H2K4FCyS5tL2tW95HNWqxXz58/3uOBeT051dHSgo6MDubm5fh2X0ZRTLESC\nSIgb01BqampQXV2N2tpa1NbWwmq1IisrCzNnzkRBQQHy8/Mxbdo0dRqU7LHo6emB1Wq9xtB6AAAY\nX0lEQVSF1WrF9evXYTLdHH6Vf2jaij3QE3p/euG9/VF665nSjqAEciKv9zXujZ/D4fDonZI9fPHx\n8R69U8Ecbh2op0p7PN3n+fb19cFms6lFirceKgABNaR6/87lMXX/frKHSlFuTEVwH0nxdV2Kv++h\newEpf4+0P4+3n8VbL1VLSwsLkcjEnBqALPC//PJLVFVVoaamBrW1tbh69SoyMjLUEf6CggJMnz5d\nnX6sKAr6+vo8cgqAmk/uS5IHuxNqsPZtsJySJ/++RlACySx/2jhfOSUzX3u9pPvF/MF4//XkhiwA\ntDklO9Oio6M9rpuU+xjoyb8e2szXk1MyV+VIij/v+2Cf85ZT8jgMtu8A0NnZyUKEhcjwUxQFFy5c\nQGFhofqHLU+Mv/3tb+Pee+9VL4DTnsyZTCZ1Oo3sTdE2Atp5n76mPQXawz9Y74Y8sXYfQXE4HOrF\nfd56pnx9rUBPtn19Tvb6yIe2l899hRTtcLF8vV6BBJX8XZHvteyhkqM92us9ZPDHxsbqOvkPZi+V\nnJLm3kNls9kAwGWFL7mf8n339T75e1KivTbF1woq169fx6RJkzB58mQAngHgqwgdTQ18hGJODYGi\nKGhsbMTDDz+M5uZm9Pb2wmQyISEhAXfffTceeughxMXFISEhQR098ZZTciQlKirK5dqT2NhYj+k0\nwRqB1tO+aXNKZpXdbkdMTIxHTsnr6LwJZi65/6soNy5Il8sJy/ZfUW5cXymnTWlX89IWFnrP5wIt\nsrzllMxT9+s9ZE7pOfkPZk7Jwtn9uhQ5vVu7wpd2REW+Vu97Odi23opi7f9tNhuSkpKQnZ3tNa8j\nIadYiISIEDeG806fPo3q6mq1V6qrqwuZmZkuoyfTp09Xe8WBmw2q9uF0Ol16UuLj4xEbGwtg6D0U\ngTSysldChpK3nin58HUvjEB6KfR+DoDaO6XtobLb7TCbzS4jKHJJ5GCOogz2O6I9nn19fbh27ZrX\nZRO1gS+LVNmQDeWkf7BtBttn99fJ17iv8CV7qgYbQfP3PQZurvTlfizlx/L4yB4t+fXuvffeUdPA\nRyjmVJDIgr6urk7NqZqaGrS3t2PSpEmYOXOmev1JXl6ey4qCdrvdI6ccDoc6xVe2rfI6yWDmlD9f\nQxZQg+WUrzZqOPNJ2565X5MocyoqKsojp4I92j/Y74g2p+SiA+45JTvT3HNK2wk31JP/YOeULPr8\nzSl/sks7mqLNKXksvNGeJ42mnGIhEmYURUF9fT3279+PPXv2wGq1oq+vD0lJSYiNjcWzzz6L/Px8\nl/tIAK6/wNohSpPp5vCkdgrNUHvth/I5914ObyMo2p4p7fzeYFzYN9SGTVug9Pf3o7+/X+311zZQ\n2tVH/Gkw9dB7fLU9knJet7ZXUjt6JlfGCeQ99qfXShtQvb296pSO69evq8dUezxaW1tx9uxZpKWl\nISUlBSaTyaV3UDuiNdjz3j7WztnWFiPS1atXcfnyZd0/X4iwEPGNOTXMFEVBc3MzDh48iJdeekn9\nm05MTERcXBzWrFmDRYsWuSxnD7guL6w98Qegnvhpp9AM5cQvWO2aXH1Km1U2mw1jxozxOoISSE9+\nIL3uvnJKCKFOldYulStHNPRmox56jrP8OWVGyREVeZ6ivY+XHE2ROeXvCf5QcgqAmlNyqrxceEAe\nU/m7ajKZ0NXVhaqqKqSlpSE1NRXR0dEeeaQ3s7x9rH3eW061tLSgqanJr58vBFiIjGRyiFtO1fJ3\nTq/kdDrVRlTO7bXZbOoFfdqHt3mo2t6OYA5Be/vX/YRxoGV89fKn90pv77s8rrJxkvdHkSvRyLnS\n8iFHUbw1zP5QFGXQk2xvJ92y0df28smf4fDhw7hy5Qri4+ORnZ3t8j0G+7qy4dTD25xi93/HjRuH\n8ePHw+FwoKqqCs3NzbBYLLjzzjvVbdzvNhzIv8Gcdx0CLER8Y04ZRE4lkjlls9nU0RN5nWRbWxtS\nUlJcciovL8/lHhyKcnOVSZlV/f39MJvNSExMdMkpbQec5C2nAulJH2gb2fZr20WZU9oRftnjrbet\nDzSXfI2iyIySD4fDoa6Kps0pOYoS6Mm8zPLBTrK9ZYwsTLX74HQ6UVlZia+//hpxcXHIyspSf9f0\nnMxrp2EPRhZuA+VGXFwckpKSYDKZUFVVhStXrmDq1Km4++67XbaTj6Hmk/bam0CK3BBjITLaKcqN\nOb01NTU4fvw43nnnHXR0dMBkMiE9PR2JiYlYvHgxioqKXC441PZKaEdPANebH2ob1KE0hoGc9Lv3\n9msv6pMjKPLkVTuCMtDcXuBmT5x7Q6WnkRyocZUPp9OpNiLaFbEqKipw4sQJAEDO/y+fqf062l4P\nX0wmU9BOwuWjvb0d9fX1aG1txdq1a9W18/35eiO4kRzJeNB9Y06FESEEWlpaUF1djaqqKrz++uv4\n3//+B0VRMHHiREyYMAGzZs3Co48+qt5fSlsEaE9Q5fPepkwNNnoylFESf7ZVFMUlp+T1CGaz2WO1\nST03QnRfzUpPLvmTU9oV0GROnTp1ChUVFVAUxeWEX77On5wKRlbJjqeuri5cunQJra2tWLVqFVJS\nUvz6OrJQJsOxEIkk/f39qKysVFcruXTpEurr69HS0oLLly+jvb0dycnJyMvLwx133IGZM2ciLy/P\nZUhZCKFOndGuihIVFYVx48apPVMOhwOpqakBN4p6p9T4et5kMiExMRFJSUlITk7GhAkTsGfPHrS3\ntyMlJQXJyclej5We3nl/Tub1bCuEQFNTExoaGlBUVORxwj/Ce+fJeCxEfGNOhbGPPvpI7cC4fPky\n6uvr0dzcjMbGRjQ1NWH8+PHIy8uDxWLBjBkzYLFYEBcX55JT8ia9cpRfXlgvT/hlTqWlpXmc0Ovt\nnff1sa8M8/U8ACQkJGDChAmYMGECUlJS8MYbb+DSpUtISkpCWlqa1+Okp3fen5N5PdubTCa0tLSg\nsbER99xzD5KTkz1yih1P5AcWInSTnNMre6Vqa2vx1VdfoaenB/Hx8UhKSvLZO282mzFx4kT18Y9/\n/AONjY3IzMxERkZG0E7og9HomkwmdHZ2or+/H+np6SE84kTDimcDvjGnRighBNra2lBTU6NOQz5z\n5gy6urpgNptdOsDkDfkk+fn09HRMnDgRH374Ib766iukpaUhKyvL0BN6Pb3zVqsV3d3d6qp+RKMQ\nCxEamBACXV1d6OzsRHJyst+98w6Hw+t8XSIadixEfGNOjTJWqxUtLS1ITU31u3eeOUUUMixEiIhG\nKRYivjGniIhCT1dO8eodIiIiIiIyXMQVIk6nE3feeSceeOCBUO8KERGRB+YUEUWKiCtEdu3aBYvF\nEurdICIi8oo5RUSRIqIKkcbGRpSXl+OZZ54ZcLuGhgYsX74cM2bMQH5+Pnbt2mXQHhIRUSRjThFR\nJImopSSee+45lJSUoKenZ8DtzGYzduzYgblz56Knpwfz5s3DihUrMGPGDIP2lIiIIhFziogiScSM\niJSVlWHixImYN2/eoNtmZGRg7ty5AIDExERYLBZcuXJluHeRiIgiGHOKiCJNxBQiR48exYEDB5CT\nk4M1a9bg8OHDePzxxwd93aVLl/DFF1/grrvu8rnNoUOHkJeXh9zcXGzbti2Yu01ERBGCOUVEkSYi\n7yPy8ccfY/v27SgrKxtwO6vViqVLl2Ljxo145JFHvG7jdDpx++2344MPPsCUKVMwf/58vP322xwe\nJ6LhxPuI+MaccsOcIqIQ4H1EAmG327F69WqsXbvWZ+MOACdPnkRubi5uu+02xMTEYM2aNXj33Xd1\nfY8XXngBd9xxB2bNmoWHH34YnZ2dwdp9IiIa5ZhTRDTSRWQhsmzZsgF7mYQQePrpp2GxWPCjH/1o\nwK915coVZGVlqR9PmTJF9zzdFStW4PTp06ipqcHtt9+Ol19+Wd8PQBThduzYAZPJhPb29lDvCtGw\nYE4RjXzMqsFFZCEymKNHj+LNN9/E4cOHMWfOHMyZMwcHDx4M+vdZuXIlzOYbC5ctXLgQjY2NQf8e\nREMVrj2hDQ0NeP/99zF16tRQ7wpRyDCniMI3pwBmlV4sRLxYvHgxhBCoqalBVVUVqqqqUFRU5HXb\nzMxMNDQ0qB83NjYiMzPT7+/5pz/9Cd/5znd0bcsKe+QbCReOhmtP6PPPP4+SkhKYTLxMgiIXc4qM\nEO5ZFa45BTCr9GIhAqCrq2vIr50/fz6+/vprXLx4ETabDfv27cOqVavUz993332YOXOmx0M7P3fL\nli0wm81Yu3btoN+PFbZ+4XrDL6fTifXr1+O9995DXV0d3n77bdTV1YV6tzyEY0/ou+++i8zMTMye\nPTvUu0JkKObU6BSuOQWMjKwKx5wCmFV+EUL48xiVvvvd74px48aJI0eODOn15eXlYvr06eK2224T\nmzdv9uu1f/7zn8XChQvFtWvXdG2/evVqUVVVJbKzs0VbW9tQdjfoHA6HmDNnjrj//vtDvSsu/vvf\n/4rPPvtMCCFEd3e3mD59uvjyyy9DvFdCHDt2TKxcuVL9eOvWrWLr1q0h3KPBPfDAA+LNN9805Ht9\n61vfEvn5+R6Pf/7zn2LBggWis7NTCCHC6m8gBPxtuyPpMSoxpwLDnPLfSMsqI3NKCGaVDrra7Ii6\ns7ovP/vZz1BWVoa9e/diyZIlEELAZDLBbrfjV7/6Faqrq/GDH/wADz74oNfXFxUV+RwSH8ihQ4dQ\nUlKCTz75BPHx8YNuH64V9q5du2CxWNDd3R3qXXGRkZGBjIwMAK43/Ar1kpXeLhw9ceJESPblvvvu\nQ3Nzs8fzW7ZsUX/f/ekJDYYPP/zQ6/O1tbW4ePGi+vvf2NiIuXPn4uTJk5g0aZIh+0YUKsypwDCn\n/BcuWRWOOQUwq4KFhQiAyZMn49Zbb0V1dTVsNhtiYmLwn//8Bz/96U9RVlaGpUuXIjU1Nejfd8OG\nDejv78eKFSsA3BhWPHfunM8/uK1bt+L9998P+n4EorGxEeXl5di4cSNeeeWVUO+OT3pu+BWJfDWk\n0uuvv46ysjJUVFSEfJ5rQUEBWltb1Y9zcnLw73//e1j+NonCDXNq6JhTI9tIyimAWeWviC9EFEVB\nTk4OioqKsGfPHpSWliIxMREbNmxAY2MjNm3ahI0bN8JkMsHpdCI6Ojpo3/vcuXO6tw3XCvu5555D\nSUkJenp6QrYPg7FarVi9ejV27tyJ8ePHh3p3gnbh6HDztyeUiIYHcyowzKmhGQlZxZwaBfTO4RKj\ndO6t0+kUQgjx17/+VSQlJYl58+aJyZMni6lTp4pDhw6p2zkcDpfX2e12j+eMFA5zDktLS8UPf/hD\nIYQQH330UdjNvRVCCJvNJlauXCl27NgR6l1R2e12ceutt4oLFy6I/v5+MWvWLHH69OlQ75aHadOm\niSlTpojZs2eL2bNni2effTbUu0Q3hfo6jHB+jDrMqaFjTg3dSMgq5lRY4zUiekRF3Vg4LDExEfHx\n8fj8889RXFyMnTt3qvM2hRCIjo6G3W6HEAIxMTHqKg2R7OjRozhw4AAOHjyIvr4+dHd34/HHH8df\n/vKXUO8aAP9u+GUks9mMV199FYWFhXA6nXjqqaeQn58f6t3y4E9PKBENH+bU0DGnhm4kZBVzauQz\nCSH82d6vjUcCm82Gt956Cz/5yU/Q0dEBADh58iS+8Y1veGx77Ngx7N69G2fOnEFiYiJ+85vfYNmy\nZWpIRLKPP/4Y27dvH/BOwEb79NNPsWTJEhQUFKjv0datW4d0wSZRmAn9ROjwxZxiTnnFnCIylK6c\niuiWqampCS+++CKeeuopWCwW7N27FwCwe/dur9vb7XZYLBY8+eST+PTTT3HmzBk27mHMnxt+hRtF\nUdDV1QWr1erxOSEEzpw5gxMnTvBmYUSjHHNqdGNOUcTTO4dLjLK5t6dOnRKLFi0SJpNJrF+/Xtjt\ndtHW1iZycnJEfn6+sFqtPl9bXV0tkpKSREVFhYF7TJFAURQhhBCVlZUiLi5O5ObmqmvKy3niZWVl\nYuzYsSI7O1tUVla6vI4iRqivwwjnx6jBnKJwxJwinXS12RHXTSKEwC9+8QssWLAAdXV1eOutt/Dq\nq6/CbDYjNTUVDz74IOrq6vDee+8BuFHxSw6HAwBQVVWF8ePHIz09PSQ/A41ecunBhQsXoqSkBOfP\nn8drr70G4MY88aNHj2LdunXIzs5GaWkpFi5cCKfTCZPJBEVR1Ifwb8olEYUR5hSFM+YUBVPEFSIA\n8M1vfhMvvvgiKisrsWbNGgA3G3K5fvepU6cAwOuQ9vHjx5GTk4Pk5GSD9pgiiWyci4qKMG/ePLzz\nzjs4fvw4Lly4gHXr1qG3txd/+MMfUFBQALvdri7VGRUVpT7CYS11Iho65hSFM+YUBUvEX6zu7urV\nqyguLsbFixdx7Ngxl94kuT77PffcA4vFgp07dyIhISGEe0uj3d///ncUFxdj+fLlmDRpEvbt24d9\n+/ahuLgYdrsdY8aMgcPhwPnz53H27Fm0t7cjJiYGc+bMCbvVTSiomOC+MaeYU2Qg5hT5oCunInJt\nPzkk6O2mT7fccovPu3jK7c+dO4eHHnoIcXFxw7qfREuWLMGjjz6K/fv3Y+zYsdi9ezeKi4vhcDgw\nZswYAMD58+exfv16XLt2DcCN3++YmBg8//zzeOSRRyCEYM8T0QjDnKKRgjlFgYjIqVlRUVE+7zwr\nhIDT6fT52vb2dvT09CA3Nzeod68l8kY793vWrFn4/ve/DwAu9weIjo7GokWL8Le//Q2VlZU4ePAg\nsrKy8MILL6C3t5eNO9EIxJyikYI5RYGIyEJkICaTyaPhVhQFR48exSeffIJDhw4hISEBkydPDtEe\nUqTo7u7Gb3/7W+zfvx8FBQX4/PPP8fLLLwNwbfhzc3Px0ksvISsrC4qiICUlBT/+8Y/R0tKCy5cv\nh2r3iWiYMKcoXDCnKFAsRHSw2+0oLS3F8uXL8cQTT6C9vR3PPPMMfv3rX+PChQuh3j0ahWw2G155\n5RW89tpr+PnPf44PPvgA48aNwxtvvIH6+nqPi1PlKiTy+dLSUqSnpyMvLy8Uu09EBmNOkdGYUxQM\nLER0iI2NxbZt26AoCtra2lBRUYFVq1ahoaFBvcstUbAIIbB3715s2rQJjz32GLZs2YJbbrkFv/vd\n71BfX49NmzYBcO1tkquQAMCBAwfwxz/+Eb/85S8RFRXFJRKJIgBziozEnKJg4apZOsmVSIiG2/79\n+/HYY4+hsLAQZWVlMJlMiIqKQkdHBxYvXoyzZ8+ivLwchYWFHq89fPgw1q1bh+9973vYvHmzS+8T\njSqcUO0bc4pomDGnSAddOcV3Xidt464oChwOh0ulTxQM//rXv/DEE09gwYIF2LdvH6Kjo9UGOjk5\nGb///e+Rk5Oj3shM25Fw5MgRrFu3DoWFhdi8eTOcTicbd6IIwpwiIzCnKJg4IkI0CnzxxRfYsGED\nFi1ahO3bt4d6d2j4cUTEN+YUURhiTkUcXTnFQoRohHE6neowOAB0dXUhLy8Pra2t2LZtG6xWK/r6\n+gAA999/P5YuXRrK3aXhwULEN+YUUYgxpwi8oSHR6OQ+BzwqKgrTpk3D4sWLUV5ejrFjx2LMmDFI\nTExEb29viPaSiIgiFXOK9OKICBHRyMMREd+YU0REoccREaJI4XA4vD4fHR3NO9YSEVHIMafIG46I\nEBGNPExt35hTREShx+V7iYiIiIgoPLEQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIi\nw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQ\nISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIi\nIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIi\nw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQ\nISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIi\nIiIiw7EQISIiIiIiw7EQISIiIiIiw7EQISIiIiIiw5n93N40LHtBREQUHMwpIqIRgiMiRERERERk\nOBYiRERERERkOBYiRERERERkOBYiRERERERkOBYiRERERERkOBYiRERERERkOBYiRERERERkOBYi\nRERERERkOBYiRERERERkOBYiRERERERkuP8DuoHewWf3yvAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2190a778b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (14,7))\n",
    "ax, ax1 = fig.add_subplot(121, projection='3d'), fig.add_subplot(122, projection='3d')\n",
    "ax.scatter(x_test.x1, x_test.x2, x_test.x3, c = list(pred_val))\n",
    "z = lambda x,y: (-logit.intercept_[0] - logit.coef_[0][0]*x - logit.coef_[0][1]*y) / logit.coef_[0][2]\n",
    "\n",
    "\n",
    "xx, yy = np.meshgrid(range(-5, 5), range(-5, 5))\n",
    "ax.plot_surface(xx, yy, z(xx, yy),  color='g', alpha = 0.2)\n",
    "ax.set_xlabel('$x_1$', fontsize = 20)\n",
    "ax.set_ylabel('$x_2$', fontsize = 20)\n",
    "ax.set_zlabel('$x_3$', fontsize = 20)\n",
    "ax.set_title('actual')\n",
    "ax.view_init(elev = 0, azim = 160)   \n",
    "\n",
    "ax1.scatter(x_test.x1, x_test.x2, x_test.x3, c = list(pred_val))\n",
    "ax1.plot_surface(xx, yy, z(xx, yy),  color='g', alpha = 0.2)\n",
    "ax1.set_xlabel('$x_1$', fontsize = 20)\n",
    "ax1.set_ylabel('$x_2$', fontsize = 20)\n",
    "ax1.set_zlabel('$x_3$', fontsize = 20)\n",
    "ax1.set_title('predicted')\n",
    "ax1.view_init(elev = 0, azim = 160)   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[57,  0],\n",
       "       [ 1, 42]])"
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix(y_test, pred_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precision_score(y_test, pred_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.98999999999999999"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y_test, pred_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 5. (20 pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's revisit the Iris data set, which consists of three different classes of irises (labeled 0, 1, and 2).\n",
    "<br>We'll use all four features (sepal length, sepal width, petal length and petal width) to train a logistic regression multi-class classifier.\n",
    "\n",
    "#### a) Load Iris data from sklearn.datasets and set up X and y accordingly (retain all the features for X). (2 pts)\n",
    "\n",
    "#### b) Fit a logistic regression model to the entire data set (no need to split into training and test sets). (5 pts)\n",
    "\n",
    "#### c) Use the model to predict class labels for the same data on which it was trained. (2 pts)\n",
    "\n",
    "#### d) Calculate and print out the multi-class (3$\\times$3) confusion matrix. (5 pts)\n",
    "\n",
    "#### e) Based on the confusion matrix you've obtained, calculate: (2 pts)\n",
    "    i) the precision with respect to the class labeled 0\n",
    "    ii) the model's overall accuracy\n",
    "    \n",
    "#### f) Create a scatter plot of the data after applying PCA in two dimensions. Use the labels obtained in part c) to visualize the classification.  (4 pts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#a) \n",
    "iris = datasets.load_iris()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris.data\n",
    "Y = iris.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [],
   "source": [
    "# b)\n",
    "logit1 = LogisticRegression(C = 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=10000, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 278,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit1.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [],
   "source": [
    "# c)\n",
    "pred_val1 = logit1.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[50,  0,  0],\n",
       "       [ 0, 48,  2],\n",
       "       [ 0,  1, 49]])"
      ]
     },
     "execution_count": 280,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# d) \n",
    "confusion_matrix(Y, pred_val1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             precision    recall  f1-score   support\n",
      "\n",
      "          0       1.00      1.00      1.00        50\n",
      "          1       0.98      0.96      0.97        50\n",
      "          2       0.96      0.98      0.97        50\n",
      "\n",
      "avg / total       0.98      0.98      0.98       150\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# e.i) Find precision for class 0\n",
    "print(classification_report(Y, pred_val1, digits=2))\n",
    "\n",
    "\n",
    "# Precision for class 0 is 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97999999999999998"
      ]
     },
     "execution_count": 284,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# e.ii) Overall accuracy\n",
    "accuracy_score(Y, pred_val1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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l7Fn49UhFnxtrvvzvDPzeyH8wfq/BAyOfDokMVihqCgHTZMzUz3n7rz/Zm5fH7rxcXv/z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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2190af69400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# f)\n",
    "n= X.shape[1]# how many eigenvectors we choose\n",
    "pca = PCA(n)\n",
    "X_ = pca.fit_transform(X)\n",
    "plt.scatter(X_[:,0], X_[:,1], c = pred_val1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}