PS1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "from math import floor\n",
    "import pprint\n",
    "import random\n",
    "#%matplotlib inline # Only use this if using iPython"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let there by $2^n+1$ uniformly spaced points in $[0,1-2^{-n}]$. Then \n",
    "$$x_i = i2^{-n}$$ where $i\\in \\{0,.....,2^{n}\\}$\n",
    "$$ y_i = 0 \\quad \\text{if i is even}$$\n",
    "$$ y_i = 1 \\quad \\text{if i is odd}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''2a'''\n",
    "\n",
    "n = 3\n",
    "points = np.linspace(0,1-2**(-n),2**n+1) #creating 2^n points\n",
    "\n",
    "\n",
    "Y=np.zeros(2**n+1)   #create y with 010101010\n",
    "for i in range(int(2**n/2)):\n",
    "    Y[2*i+1] = 1 \n",
    "\n",
    "plt.plot(points,Y);  #sawtooth graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input: [(0, 0), (0, 1), (1, 0), (1, 1)]\n",
      "Output after applying XOR: [0, 1, 1, 0]\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''2b'''\n",
    "\n",
    "input = []\n",
    "for i in [0,1]:\n",
    "    for j in [0,1]:\n",
    "        input.append((i,j))\n",
    "\n",
    "X_false = [0,1]\n",
    "Y_false = [0,1]\n",
    "\n",
    "X_true = [1,0]\n",
    "Y_true = [0,1]\n",
    "\n",
    "def XOR(vector):\n",
    "    if vector[0] == vector[1]:\n",
    "        return 0\n",
    "    else: \n",
    "        return 1\n",
    "    \n",
    "output = list(map(XOR,input))\n",
    "\n",
    "plt.plot(X_true,Y_true,'.',label = 'True = 1',markersize = 12)\n",
    "plt.plot(X_false,Y_false,'.',label = 'False = 0',markersize = 12)\n",
    "plt.legend(loc = 10)\n",
    "\n",
    "print('Input: {}'.format(input))\n",
    "print('Output after applying XOR: {}\\n'.format(output))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As seen in lectures, the `1-layer neural networks` cannot predict the function `XOR`. 1-layer neural nets can only classify linearly separable sets, however, as we have seen, the __Universal Approximation Theorem__ states that a `2-layer network` can approximate any function, given a complex enough architecture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''2ci'''\n",
    "(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()\n",
    "\n",
    "#function to visualize the images\n",
    "\n",
    "def plot_image(index):\n",
    "    '''plots the image when you give it an index and returns the correct output'''\n",
    "    print(y_train[index]) # The label is 8\n",
    "    plt.imshow(x_train[index], cmap='Greys')\n",
    "    \n",
    "index = 59000\n",
    "plot_image(index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0,   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,\n",
       "         0,   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,\n",
       "         0,   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,\n",
       "         0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "         0,   3,  18,  18,  18, 126, 136, 175,  26, 166, 255, 247, 127,\n",
       "         0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  30,\n",
       "        36,  94, 154, 170, 253, 253, 253, 253, 253, 225, 172, 253, 242,\n",
       "       195,  64,   0,   0,   0,   0,   0,   0,   0,   0], dtype=uint8)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''2cii'''\n",
    "'''Need to stretch matrix of image into a vector of dim 784 (28x28)'''\n",
    "\n",
    "def flatten(image):\n",
    "    return image.flatten()\n",
    "image = x_train[0]\n",
    "#print(image)\n",
    "flatten(image)[60:200]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2ciii and 2civ\n",
    "\n",
    "I have already done these steps in 2ci so please look above where my $N = 784$ and my $M = 60,000$ where $M$ is training data. The size of my whole data is $70,000$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        ...,\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0]],\n",
       "\n",
       "       [[0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        ...,\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0]],\n",
       "\n",
       "       [[0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        ...,\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0]],\n",
       "\n",
       "       ...,\n",
       "\n",
       "       [[0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        ...,\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0]],\n",
       "\n",
       "       [[0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        ...,\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0]],\n",
       "\n",
       "       [[0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        ...,\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0]]], dtype=uint8)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def mini_batch(batch_size = 20,batch_number = 1,data_set = x_train):\n",
    "    train_length = len(data_set)\n",
    "    \n",
    "    if batch_size>=train_length:\n",
    "        print('maximum size of mini_batch can be: {}'.format(train_length))\n",
    "    else:\n",
    "        index = (batch_number - 1)*batch_size\n",
    "        if index+batch_size-1>=train_length and train_length-1-index>0:\n",
    "            return data_set[index:]\n",
    "        elif train_length-1-index<=0:\n",
    "            return 'batch_number is too large for the size for mini-batch provided. Adjust your batch_number to <= {}'.format(floor((train_length-1)/batch_size)+1)\n",
    "        else:\n",
    "            return data_set[index:index+batch_size]\n",
    "\n",
    "# having a batch_size of 16-32 is always best\n",
    "mini_batch(batch_size = 30,batch_number = 60) #since there are only 60,000 training points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Task 4 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`https://mlfromscratch.com/neural-networks-explained/#cost-function`\n",
    "\n",
    "`http://neuralnetworksanddeeplearning.com/chap2.html`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''Different Activation functions'''\n",
    "\n",
    "class Tanh:\n",
    "    def activation(self,z):\n",
    "        return np.tanh(z)\n",
    "    \n",
    "    def derivative_activation(self,z):\n",
    "        return (np.cosh(z))**(-2)\n",
    "    \n",
    "class Sigmoid:\n",
    "    def activation(self,z):\n",
    "        return 1/(1+np.exp(-z))\n",
    "    \n",
    "    def derivative_activation(self,z):\n",
    "        return self.activation(z)*(1-self.activation(z))\n",
    "    \n",
    "class Relu:\n",
    "    def activation(self,z):\n",
    "        return np.maximum(0,z)\n",
    "    \n",
    "    def derivative_activation(self,z):\n",
    "        z[z<=0 ] = 0\n",
    "        z[z>0] = 1\n",
    "        return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "class NN(Tanh):\n",
    "    def __init__(self,X,Y, learning_rate = 0.1):\n",
    "        self.X = X\n",
    "        self.Y = Y\n",
    "        self.lr = learning_rate  \n",
    "        \n",
    "    def initialize_parameters(self):\n",
    "        '''Initializes all the parameters in NN and stores it in a dictionary'''\n",
    "\n",
    "        X,Y = self.X, self.Y\n",
    "        n_row = X.shape[0]   #gives me 2\n",
    "        n_col = X.shape[1] #give me 4\n",
    "        n_y = Y.shape[0]   #gives you 1, i.e. dimension of the output layer\n",
    "\n",
    "        W1 = np.random.randn(n_col, n_row)\n",
    "        b1 = np.zeros((n_col, 1))\n",
    "\n",
    "        W2 = np.random.randn(n_y, n_col)\n",
    "        b2 = np.random.randn(n_y, Y.shape[1])  #A1.shape[1] = 4\n",
    "\n",
    "        parameters = {\"W1\" : W1, \"b1\": b1,\n",
    "                      \"W2\" : W2, \"b2\": b2}\n",
    "        return parameters\n",
    "    \n",
    "    def forward_propagation(self,parameters):\n",
    "        X = self.X\n",
    "        \n",
    "        W1 = parameters[\"W1\"]\n",
    "        W2 = parameters[\"W2\"]\n",
    "        b1 = parameters[\"b1\"]\n",
    "        b2 = parameters[\"b2\"]\n",
    "        \n",
    "        Z1 = W1@X + b1\n",
    "        A1 = self.activation(Z1)\n",
    "        \n",
    "        Z2 = W2@A1 + b2\n",
    "        A2 = self.activation(Z2)\n",
    "        #print(A2)\n",
    "        \n",
    "        cache = (Z1, A1, W1, b1, Z2, A2, W2, b2)\n",
    "        return cache\n",
    "    \n",
    "    def backward_propagation(self,epochs = 10000):\n",
    "        X, Y = self.X, self.Y\n",
    "        parameters = self.initialize_parameters() #only needed at the start\n",
    "        \n",
    "        m = X.shape[1]\n",
    "        Cost = np.zeros(epochs)\n",
    "        \n",
    "        for i in range(epochs):\n",
    "            (Z1, A1, W1, b1, Z2, A2, W2, b2) = self.forward_propagation(parameters)\n",
    "            delta2 = np.multiply((A2-Y),self.derivative_activation(Z2))\n",
    "\n",
    "            Cost[i] = 0.5*np.sum((A2-Y)**2)   #cost function in each loop\n",
    "            \n",
    "            dW2 = delta2@A1\n",
    "            db2 = delta2 #np.sum(dZ2, axis = 1, keepdims=True)\n",
    "\n",
    "            delta1 = np.multiply(W2.T@delta2, self.derivative_activation(Z1))\n",
    "            dW1 = X@delta1\n",
    "            db1 = delta1\n",
    "\n",
    "            #adjusting the weights and biases (i.e. nudging them slightly)\n",
    "            W2 = W2 - delta2.dot(A1)*(self.lr/m)\n",
    "        \n",
    "            b2 = b2 - np.sum(db2, axis = 1, keepdims=True)*(self.lr/m)\n",
    "\n",
    "            W1 = W1 - delta1.dot(X.T)*(self.lr/m)\n",
    "            b1 = b1 - np.sum(db1, axis = 1, keepdims=True)*(self.lr/m)\n",
    "\n",
    "            # the nudged weights and biases become your new parameters\n",
    "            parameters = {\"W1\" : W1, \"b1\": b1,\n",
    "                          \"W2\" : W2, \"b2\": b2}\n",
    "\n",
    "        return parameters, A2, Cost\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Task 4a (n-ap) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 31 ms\n",
      "{'W1': array([[-0.30680778,  0.73565579, -0.71511536,  3.21842085, -0.74838698,\n",
      "        -0.13595865,  0.50595798,  0.51578523,  0.70163324]]),\n",
      " 'W2': array([[ 0.44603051],\n",
      "       [ 2.02041302],\n",
      "       [ 0.09667524],\n",
      "       [ 0.7370033 ],\n",
      "       [ 0.14812904],\n",
      "       [ 0.79022968],\n",
      "       [-1.44011787],\n",
      "       [-0.77967671],\n",
      "       [ 0.47036615]]),\n",
      " 'b1': array([[0.00523328]]),\n",
      " 'b2': array([[-0.42739296],\n",
      "       [ 0.04817085],\n",
      "       [-0.09263563],\n",
      "       [ 1.26829502],\n",
      "       [-0.14193942],\n",
      "       [ 2.17101551],\n",
      "       [ 1.37994201],\n",
      "       [ 2.72399947],\n",
      "       [-0.45071173]])}\n",
      "\n",
      "Activation Function: Tanh\n",
      "\n",
      "Desired Output: [0.] [1.] [0.] [1.] [0.] [1.] [0.] [1.] [0.]\n",
      "\n",
      "Output from neural network after 500 epochs:\n",
      " [2.84319814e-05] [0.96286096] [6.16251238e-06] [0.96214394] [9.44240835e-06] [0.99429388] [-9.17995602e-05] [0.96231634] [2.99832442e-05]\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 3\n",
    "X = np.array([[i] for i in np.linspace(0,1-2**(-n),2**n+1)])\n",
    "\n",
    "Y=np.zeros((2**n+1,1))   #create y with 010101010\n",
    "for i in range(int(2**n/2)):\n",
    "    Y[2*i+1] = 1 \n",
    "\n",
    "blah1 = NN(X,Y,learning_rate = 0.1)\n",
    "epochs = 500\n",
    "%time parameters, A2, Cost = blah1.backward_propagation(epochs = epochs)\n",
    "\n",
    "pprint.pprint(parameters)\n",
    "print('\\nActivation Function: {}'.format(blah1.__class__.__bases__[0].__name__))\n",
    "print('\\nDesired Output:',*blah1.Y)\n",
    "print(\"\\nOutput from neural network after {} epochs:\\n \".format(epochs),end='')\n",
    "print(*A2)\n",
    "print('')\n",
    "plt.plot(Cost);\n",
    "plt.title('Cost Function after {} epochs: '.format(epochs))\n",
    "plt.show()\n",
    "\n",
    "plt.plot(X, A2);\n",
    "plt.title('Plot sawtooth function with n = {} using {}\\\n",
    " activation'.format(n,blah1.__class__.__bases__[0].__name__));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Task 4b (XOR Problem)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'W1': array([[-1.08123715, -0.54309983],\n",
      "       [-1.73742514,  0.78424109],\n",
      "       [ 2.63573396, -0.86199578],\n",
      "       [ 0.75092963,  0.8948772 ]]),\n",
      " 'W2': array([[-0.83346333,  0.12195009, -0.05632569,  1.73915782]]),\n",
      " 'b1': array([[ 0.47513212],\n",
      "       [-0.17486064],\n",
      "       [-0.16123176],\n",
      "       [ 0.02902263]]),\n",
      " 'b2': array([[0.33460824, 0.43406655, 0.57980925, 2.72347241]])}\n",
      "\n",
      "Activation Function: Tanh\n",
      "\n",
      "Desired Output: [0 1 1 0]\n",
      "\n",
      "Output from neural network after 2000 epochs: [0.00429593 0.9532083  0.96357586 0.9998834 ]\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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e8dSzcD8ZETFc5YRCSZzz6cE5nx7mY84elpGkAhnuklSghRru23rdQA8459ODcz49zPmcF+Qxd0nSzBbqnrskaQandLhHxNqI2BMReyPimL80GRGLIuLezvpHI2LV/HdZrwpz/mxEPBMRT0bEjyPigl70Waduc55Ud31EZEQs+Csrqsw5Ij7Uea2fjojvzHePdavwtf2WiHgkIh7vfH1f14s+6xIRd0XEgYj49XHWR0R8tfP/8WREXFZrA5l5Sn4A/cD/Am8FBoEngDVTaj4J/Fvn8Qbg3l73PQ9zfi9wZufxJ06HOXfqlgA/A3YBzV73PQ+v82rgceDczvKyXvc9D3PeBnyi83gN8Fyv+z7JOf8lcBnw6+Osvw54iPY72V0JPFrn+KfynntP35i7R7rOOTMfyczXOou7aL8z1kJW5XUG+CLwZeD1+WxujlSZ88eBrZn5MkBmHpjnHutWZc4JnNV5fDbHvuPbgpKZP2Oad6SbZD2wPdt2AedExJvrGv9UDveevjF3j1SZ82Q30v7Jv5B1nXNEXAqszMwH57OxOVTldb4IuCgifh4RuyJi7bx1NzeqzPkLwEciYhTYCdw6P631zGy/32dloK4NzYHa3ph7Aak8n4j4CNAE3j2nHc29GeccEX3AncDH5quheVDldR6gfWjmPbR/O/uviHh7Zr4yx73NlSpz3gh8MzPviIi/AHZ05tztPeoWqjnNr1N5z722N+ZeQKrMmYi4Gvg8sC4zD81Tb3Ol25yXAG8HfhoRz9E+Njm0wE+qVv3afiAzD2fmb4A9tMN+oaoy5xuB+wAy8xfAYtp/g6VUlb7fT9SpHO49fWPuHuk6584hiq/TDvaFfhwWusw5Mw9m5tLMXJWZq2ifZ1iXmQv5nV6qfG3/gPbJcyJiKe3DNPvmtct6VZnzb4GrACLibbTDvTWvXc6vIWBT56qZK4GDmfn72rbe6zPKXc42Xwf8D+2z7J/vPLeF9jc3tF/87wJ7gf8G3trrnudhzv8J7Ad+1fkY6nXPcz3nKbU/ZYFfLVPxdQ7gn4BngKeADb3ueR7mvAb4Oe0raX4FXNPrnk9yvncDvwcO095LvxG4Gbh50mu8tfP/8VTdX9feoSpJBTqVD8tIkk6Q4S5JBTLcJalAhrskFchwl6QCGe6SVCDDXZIKZLhLUoH+D1PkjOqxGr6fAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.array([[0,0,1,1],[0,1,0,1]])\n",
    "Y = np.array([[0,1,1,0]])\n",
    "\n",
    "blah = NN(X,Y)\n",
    "epochs = 2000\n",
    "parameters, A2, Cost = blah.backward_propagation(epochs = epochs)\n",
    "\n",
    "pprint.pprint(parameters)\n",
    "print('\\nActivation Function: {}'.format(blah.__class__.__bases__[0].__name__))\n",
    "print('\\nDesired Output:',*blah.Y)\n",
    "print(\"\\nOutput from neural network after {} epochs: \\\n",
    "\".format(epochs),end='')\n",
    "print(*A2)\n",
    "print('')\n",
    "plt.plot(Cost);\n",
    "plt.title('Cost Function after {} epochs: '.format(epochs))\n",
    "plt.show()\n",
    "plt.plot(X,'.', markersize=18);\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "batch_size = 50\n",
    "train_length = x_train.shape[0]\n",
    "\n",
    "np.random.shuffle(x_train) #randomly shuffles the trainig data\n",
    "np.random.shuffle(x_train) #randomly shuffles the trainig data\n",
    "np.random.shuffle(x_train) #randomly shuffles the trainig data\n",
    "np.random.shuffle(x_train) #randomly shuffles the trainig data\n",
    "np.random.shuffle(x_train) #randomly shuffles the trainig data\n",
    "#print(x_train)\n",
    "\n",
    "no_of_batches = floor((train_length-1)/batch_size)+1\n",
    "epochs = 10000\n",
    "\n",
    "\n",
    "for number in range(1,no_of_batches+1):\n",
    "    x_train_batch = mini_batch(batch_size,batch_number = number, data_set = x_train)\n",
    "    y_batch = mini_batch(batch_size,batch_number = number, data_set = y_train)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    },
    {
     "data": {
      "image/png": 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4F0mjJW1x938qvIlhmNksDR7tpcFJTLeX2ZuZPSvpBg3+6uuwpNWSXpD0C0mXSTog6VZ3L/yLtwq93aDBt65/nrn51Gfsgnv7G0lvSvpA0lfZ4gc0+Pm6tNcu0ddSlfC6cYYfEBRn+AFBEX4gKMIPBEX4gaAIPxAU4QeCIvxAUIQfCOr/Ae8qDtDMbWTlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
    {
     "data": {
      "image/png": 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q6FtfByT9VNK/S/qVpG5Jv5f0fXdv+QdvFXrr1dBL17/M3HzyPXaLe/tHSW9Iek/SiWzxEg29vy7s2CX6mqcCjhtX+AFBcYUfEBThB4Ii/EBQhB8IivADQRF+ICjCDwRF+IGg/h8hx/A0McgqvQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "data": {
      "image/png": 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Xqv/1dWnHLtHXQpVw3LjCDwiKK/yAoAg/EBThB4Ii/EBQhB8IivADQRF+ICjCDwT1dwMY978HU1UDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
    {
     "data": {
      "image/png": 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mAvr4DjMbmn0RIzMbKukHar3VhzdJmpvdnitpY4G9/I1WWbk5b2VpFfzatdqK14Wc5JNNZfy7pIGS1rj7E01vog9mdrV6jvZSzyKmvy2yNzN7WdI09Vz1tV/SYkn/KWmdpAmS9ki6w92b/sVbTm/T1PPW9duVm898xm5yb/8k6S1J2yWdzjYvUs/n68Jeu0Rfs1TA68YZfkBQnOEHBEX4gaAIPxAU4QeCIvxAUIQfCIrwA0ERfiCo/wfUfDMOeJJjxgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    },
    {
     "data": {
      "image/png": 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0V0X2ZmbPSrpFY7/6Oirpp5J2SfqtpEsl/UXS99294R+8lejtFo29dP37zM1n3mM3uLd/kvSfkt6WdGYK5A0ae39d2LFL9LVCBRw3vuEHBMU3/ICgCD8QFOEHgiL8QFCEHwiK8ANBEX4gKMIPBPV/CpUUSBfKN94AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "data": {
      "image/png": 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vFXq7SiNPXf8xc/PJ19gt7u1rkn4n6U1Jw9ni+zTy+rqwxy7R1woV8LjxCT8gKD7hBwRF+IGgCD8QFOEHgiL8QFCEHwiK8ANBEX4gqP8HFZMLT8TZ0M0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    },
    {
     "data": {
      "image/png": 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M0ir42LXbjNeFfMknG8r4d0mXS+p1939teRPDMLO/0+DZXhqcxPQ3RfZmZi9Kmq/BX30dlfQzSX+QtEnSVEkHJf3A3Vv+wVuF3uZr8KXr32ZuPvceu8W9/aOk/5HUJ+lstvgRDb6/LuzYJfpaqgKOG9/wA4LiG35AUIQfCIrwA0ERfiAowg8ERfiBoAg/EBThB4L6f0+xH5ExCyitAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n"
     ]
    },
    {
     "data": {
      "image/png": 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fCIrwA0ERfiAowg8ERfiBoAg/EBThB4L6f4HX95M+4mqBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    },
    {
     "data": {
      "image/png": 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CIvxAUP8P+HHkrwmTo1QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    },
    {
     "data": {
      "image/png": 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Leqs1s/TbKvG1K3LG60L64Rd+QEz8wg8IivADQRF+ICjCDwRF+IGgCD8QFOEHgiL8QFD/B5SxFCGj3+rXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n"
     ]
    },
    {
     "data": {
      "image/png": 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78EZJ87L78yRtKLCXv9EuMzdXmllaBb927TbjdSEn+WRDGf8pqUPSand/ouVNjMDMrtDQ0V4amsT050X2ZmZrJd2ioau+DkhaJum/Jf1S0kRJf5I0091b/sVbhd5u0dBb17/O3HziM3aLe5si6TeStkkazBY/oqHP14W9dom+ZquA140z/ICgOMMPCIrwA0ERfiAowg8ERfiBoAg/EBThB4Ii/EBQ/w8rdTKAA7e+QwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    },
    {
     "data": {
      "image/png": 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AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    },
    {
     "data": {
      "image/png": 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dlvQjSS9I2iHpSkm/l/Rtd+/6B285vd2q8Zeuf165+dx77C739reS/lPSkKSxbPM6jb+/ru25S/S1UjU8b3zDDwiKb/gBQRF+ICjCDwRF+IGgCD8QFOEHgiL8QFCEHwjq/wBgxyKPV9fQtQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    },
    {
     "data": {
      "image/png": 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gqP8HpnwBwyK/3d8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAADTdJREFUeJzt3WGoXPWZx/Hfb7UxYPLCkKsNNppsEFkNbrJMworr4rKkMVqMQSoJUrNQmqIVN9gXK3kTUVZkia0iSyE1l0ZMbAtp1ryQ3QZZcQNLyRg0ppt1K3K3vZtr7g0RaokQkjz74p6Ua7xz5jpzZs7cPN8PhJk5zznzfxj93TMzZ875OyIEIJ8/qbsBAPUg/EBShB9IivADSRF+ICnCDyRF+IGkCD+QFOEHkrqyn4MtXLgwlixZ0s8hgVRGRkZ06tQpz2TdrsJv+25JL0q6QtLLEfFc2fpLlixRs9nsZkgAJRqNxozX7fhtv+0rJP2zpHWSbpG0yfYtnT4fgP7q5jP/akkfRsRHEXFW0k8lra+mLQC91k34r5f0uymPR4tln2N7i+2m7ebExEQXwwGoUjfhn+5LhS+cHxwROyOiERGNoaGhLoYDUKVuwj8qafGUx1+TdKK7dgD0SzfhPyzpJttLbc+RtFHSgWraAtBrHR/qi4hzth+T9G+aPNQ3HBG/rqwzAD3V1XH+iHhD0hsV9QKgj/h5L5AU4QeSIvxAUoQfSIrwA0kRfiApwg8kRfiBpAg/kBThB5Ii/EBShB9IivADSRF+ICnCDyRF+IGkCD+QFOEHkiL8QFKEH0iK8ANJEX4gKcIPJEX4gaQIP5AU4QeSIvxAUoQfSIrwA0l1NUuv7RFJn0o6L+lcRDSqaApA73UV/sLfRMSpCp4HQB/xth9Iqtvwh6Rf2n7H9pYqGgLQH92+7b8jIk7YvlbSQdv/HRFvT12h+KOwRZJuuOGGLocDUJWu9vwRcaK4HZe0X9LqadbZGRGNiGgMDQ11MxyACnUcfttX255/8b6kr0s6VlVjAHqrm7f910nab/vi8+yNiH+tpCsAPddx+CPiI0l/XmEvAPqIQ31AUoQfSIrwA0kRfiApwg8kRfiBpKo4q69vtm/f3rL29NNPl267cePG0vojjzzSUU/ZLV26tLR+9uzZlrW5c+eWbvvJJ5+U1pcvX15aRzn2/EBShB9IivADSRF+ICnCDyRF+IGkCD+QlCOib4M1Go1oNpsdbz9//vyWtTNnznT8vOjczTffXFr/7LPPWtbmzZtXuu34+Hhpfe3ataX1l19+uWVtzpw5pdvOVo1GQ81m0zNZlz0/kBThB5Ii/EBShB9IivADSRF+ICnCDyQ1q87nP3as9Zwgu3fv7uq5d+3aVVofHR3t6vkvVx988EFtY+/Zs6e0XnaNhttvv73qdmYd9vxAUoQfSIrwA0kRfiApwg8kRfiBpAg/kFTb8/ltD0v6hqTxiFheLFsg6WeSlkgakfRgRJRfZF3dn8/fSx9//HFpvey89EG2Y8eO0nq7c+ofeuih0nq7+RDKTExMlNZPnz7d8XNL0gMPPNCy9uqrr5ZuO1vP96/6fP6fSLr7kmVPSnozIm6S9GbxGMAs0jb8EfG2pEv/BK+XdPEndbsl3V9xXwB6rNPP/NdFxJgkFbfXVtcSgH7o+Rd+trfYbtputvuMB6B/Og3/SduLJKm4bXmlxYjYGRGNiGgMDQ11OByAqnUa/gOSNhf3N0t6vZp2APRL2/Dbfk3Sf0q62fao7W9Lek7SGtu/kbSmeAxgFplV1+3H5eWll14qrW/durVnY7/11lul9TvvvLNnY/cS1+0H0BbhB5Ii/EBShB9IivADSRF+IKlZdeluzD7Hjx9vWXv22Wd7OvYTTzzRsrZ69eqejj0bsOcHkiL8QFKEH0iK8ANJEX4gKcIPJEX4gaQ4zo+utJuie82aNS1r4+MtLwBViWeeeaZl7aqrrurp2LMBe34gKcIPJEX4gaQIP5AU4QeSIvxAUoQfSIrj/Ch17ty50nq7qa7HxsaqbOdzhoeHS+scyy/Hnh9IivADSRF+ICnCDyRF+IGkCD+QFOEHkmp7nN/2sKRvSBqPiOXFsqckfUfSRLHatoh4o1dNoj7tpnA/ffp0z8a+9dZbS+vr1q0rrdszmqk6rZns+X8i6e5plv8wIlYU/wg+MMu0DX9EvC2pd3/eAdSim8/8j9k+anvY9jWVdQSgLzoN/48kLZO0QtKYpOdbrWh7i+2m7ebExESr1QD0WUfhj4iTEXE+Ii5I+rGklrMeRsTOiGhERGNoaKjTPgFUrKPw21405eEGSceqaQdAv8zkUN9rku6StND2qKTtku6yvUJSSBqR9N0e9gigB9qGPyI2TbN4Vw96wSw0d+7cjrddtWpVaf3gwYOl9fnz53c8NviFH5AW4QeSIvxAUoQfSIrwA0kRfiApLt2NUmfOnCmtv/DCC6X1stNqH3300dJtOZTXW+z5gaQIP5AU4QeSIvxAUoQfSIrwA0kRfiApjvMn1+7SamvXru3q+VeuXNmy9vDDD3f13OgOe34gKcIPJEX4gaQIP5AU4QeSIvxAUoQfSIrj/MkdOXKktP7ee+919fzPP99yJjfUjD0/kBThB5Ii/EBShB9IivADSRF+ICnCDyTV9ji/7cWSXpH0VUkXJO2MiBdtL5D0M0lLJI1IejAiPuldq5iNli1bVncLaGEme/5zkr4fEX8m6S8lfc/2LZKelPRmRNwk6c3iMYBZom34I2IsIo4U9z+VdFzS9ZLWS9pdrLZb0v29ahJA9b7UZ37bSyStlPQrSddFxJg0+QdC0rVVNwegd2YcftvzJO2TtDUifv8ltttiu2m72e56cQD6Z0bht/0VTQZ/T0T8olh80vaior5I0vh020bEzohoRERjaGioip4BVKBt+D05zeouSccj4gdTSgckbS7ub5b0evXtAeiVmZzSe4ekb0l63/a7xbJtkp6T9HPb35b0W0nf7E2LAHqhbfgj4pCkVpOs/2217QDoF37hByRF+IGkCD+QFOEHkiL8QFKEH0iKS3df5s6fP19a37t3b586waBhzw8kRfiBpAg/kBThB5Ii/EBShB9IivADSXGc/zIXEaX1dlN0d+vxxx9vWdu3b19Px0Y59vxAUoQfSIrwA0kRfiApwg8kRfiBpAg/kBTH+S9zV15Z/p94x44dpfV77rmnq/EPHTrUsnb06NHSbW+77bauxkY59vxAUoQfSIrwA0kRfiApwg8kRfiBpAg/kFTb4/y2F0t6RdJXJV2QtDMiXrT9lKTvSJooVt0WEW/0qlHMTqdOnWpZO3z4cOm2HOfvrZn8yOecpO9HxBHb8yW9Y/tgUfthRJT/SgTAQGob/ogYkzRW3P/U9nFJ1/e6MQC99aU+89teImmlpF8Vix6zfdT2sO1rWmyzxXbTdnNiYmK6VQDUYMbhtz1P0j5JWyPi95J+JGmZpBWafGfw/HTbRcTOiGhERGNoaKiClgFUYUbht/0VTQZ/T0T8QpIi4mREnI+IC5J+LGl179oEULW24bdtSbskHY+IH0xZvmjKahskHau+PQC9MpNv+++Q9C1J79t+t1i2TdIm2yskhaQRSd/tSYfoqVWrVpXW9+/fX1rfsGFDaf3GG29sWbv33ntLt0VvzeTb/kOSPE2JY/rALMYv/ICkCD+QFOEHkiL8QFKEH0iK8ANJcenu5BYsWFBav++++0rr58+fr7Id9BF7fiApwg8kRfiBpAg/kBThB5Ii/EBShB9IyhHRv8HsCUn/O2XRQkmtr+1cr0HtbVD7kuitU1X2dmNEzOh6eX0N/xcGt5sR0aitgRKD2tug9iXRW6fq6o23/UBShB9Iqu7w76x5/DKD2tug9iXRW6dq6a3Wz/wA6lP3nh9ATWoJv+27bX9g+0PbT9bRQyu2R2y/b/td282aexm2PW772JRlC2wftP2b4nbaadJq6u0p2/9XvHbv2r6npt4W2/5328dt/9r23xfLa33tSvqq5XXr+9t+21dI+h9JaySNSjosaVNE/FdfG2nB9oikRkTUfkzY9l9L+oOkVyJiebHsnySdjojnij+c10TEPwxIb09J+kPdMzcXE8osmjqztKT7Jf2danztSvp6UDW8bnXs+VdL+jAiPoqIs5J+Kml9DX0MvIh4W9LpSxavl7S7uL9bk//z9F2L3gZCRIxFxJHi/qeSLs4sXetrV9JXLeoI//WSfjfl8agGa8rvkPRL2+/Y3lJ3M9O4rpg2/eL06dfW3M+l2s7c3E+XzCw9MK9dJzNeV62O8E83+88gHXK4IyL+QtI6Sd8r3t5iZmY0c3O/TDOz9EDodMbrqtUR/lFJi6c8/pqkEzX0Ma2IOFHcjkvar8GbffjkxUlSi9vxmvv5o0GauXm6maU1AK/dIM14XUf4D0u6yfZS23MkbZR0oIY+vsD21cUXMbJ9taSva/BmHz4gaXNxf7Ok12vs5XMGZebmVjNLq+bXbtBmvK7lRz7FoYwXJF0haTgi/rHvTUzD9p9qcm8vTV7ZeG+dvdl+TdJdmjzr66Sk7ZL+RdLPJd0g6beSvhkRff/irUVvd2nyresfZ26++Bm7z739laT/kPS+pAvF4m2a/Hxd22tX0tcm1fC68Qs/ICl+4QckRfiBpAg/kBThB5Ii/EBShB9IivADSRF+IKn/B/GoyrVSjyPRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "data": {
      "image/png": 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Lq+DXrt1WvC7kJJ9sKuNfJQ2T1OXu/9zyJgZgZn+uvqO91LeI6bYiezOzJyTNVt+vvk5KWi1ph6TfSpoi6YikH7l7y794q9DbbPW9df165eYLn7Fb3NtfS/pPSfsknc82r1Lf5+vCXrtEX4tUwOvGGX5AUJzhBwRF+IGgCD8QFOEHgiL8QFCEHwiK8ANBEX4gqP8D8SUu1H3ItFkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    },
    {
     "data": {
      "image/png": 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dd2c/90l6Va23+vDeE4ukZj/3Nbmfv2mllZv7WllaLfDctdKK180I/0eSrjSzEWbWX9IPJa1sQh+nMbMLsg9iZGYXSPqeWm/14ZWSZmS3Z0h6rYm9nKRVVm4utbK0mvzctdqK1005ySebyvgXSedLWuTu8xveRB/M7O/Uc7SXehYx/UMzezOzJZImqudbX3sldUr6N0nLJF0uaYekH7h7wz94K9HbRPW8dP3bys0n3mM3uLebJf2HpE8kHc82z1XP++umPXeJvqapCc8bZ/gBQXGGHxAU4QeCIvxAUIQfCIrwA0ERfiAowg8ERfiBoP4Pkt1KiiraQAoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    },
    {
     "data": {
      "image/png": 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z85n32G3u7Z8lvSnpQ0mns8XrNfL+urRjl+hrqUo4bnzDDwiKb/gBQRF+ICjCDwRF+IGgCD8QFOEHgiL8QFCEHwjq/wHuNBQoT9Jq9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    },
    {
     "data": {
      "image/png": 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CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
    {
     "data": {
      "image/png": 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mgyXNkrSphD6+w8yGZF/EyMyGSPqBWm/24U2S5mX350l6scRevqVVZm6uNLO0Sn7tWm3G61JO8smGMv5N0tmSVrn7vzS9iX6Y2RXqPdpLvZOYPldmb2a2VtIN6v3V135JD0v6T0nrJF0u6Y+SfuzuTf/irUJvN6j3retfZ24+9Rm7yb39g6T/lvSBpJPZ4iXq/Xxd2muX6Gu2SnjdOMMPCIoz/ICgCD8QFOEHgiL8QFCEHwiK8ANBEX4gKMIPBPV/t+EqBRxN++MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAADNZJREFUeJzt3WGIXPW5x/HfT9u+MC2iZEwWu3ZjCeVKwFSG5IJFU0qK1UKsUEmQkgtNt0KFFvqimjeNL9RQbpubF6Ww1aURUtNAa80LuTdBSmyhREeRmN54b0T2NjExmagQ+6ponvtiT8o22TkzmTkzZ+Lz/UCYmfOcs+dhNr89M/M/Z/6OCAHI56q6GwBQD8IPJEX4gaQIP5AU4QeSIvxAUoQfSIrwA0kRfiCpT4xyZ0uXLo2pqalR7hJIZW5uTmfPnnUv6w4Uftt3Sdop6WpJT0bE9rL1p6am1Gq1BtklgBLNZrPndft+2W/7akk/l/Q1SbdI2mT7ln5/HoDRGuQ9/xpJb0bEWxHxd0l7JG2opi0AwzZI+G+UdHzB4xPFsn9ie9p2y3ar3W4PsDsAVRok/It9qHDJ9cERMRMRzYhoNhqNAXYHoEqDhP+EpMkFjz8r6eRg7QAYlUHC/7KklbZX2P6UpI2S9lXTFoBh63uoLyI+tP2QpP/S/FDfbET8pbLOAAzVQOP8EfG8pOcr6gXACHF6L5AU4QeSIvxAUoQfSIrwA0kRfiApwg8kRfiBpAg/kBThB5Ii/EBShB9IivADSRF+ICnCDyRF+IGkCD+QFOEHkiL8QFKEH0iK8ANJEX4gKcIPJEX4gaQIP5AU4QeSIvxAUoQfSIrwA0kNNEuv7TlJH0j6SNKHEdGsoikAwzdQ+AtfjoizFfwcACPEy34gqUHDH5L2237F9nQVDQEYjUFf9t8eESdt3yDpgO03IuLFhSsUfxSmJemmm24acHcAqjLQkT8iTha3ZyQ9K2nNIuvMREQzIpqNRmOQ3QGoUN/ht73E9mcu3Jf0VUlHqmoMwHAN8rJ/maRnbV/4Ob+OiP+spCsAQ9d3+CPiLUm3VtjLFevgwYOl9QMHDpTW169fX1q/+eabS+uTk5OldWAxDPUBSRF+ICnCDyRF+IGkCD+QFOEHkqriqr70ug3lbd++vbT+xBNPlNaLcyk6uuOOOzrWbr21fDR248aNpfW1a9eW1nHl4sgPJEX4gaQIP5AU4QeSIvxAUoQfSIrwA0k5Ika2s2azGa1Wa2T7GxdPPvlkaX16uvzrD7uN85f9DgfZVpJuu+220vrbb79dWn/ppZc61rgUuXrNZlOtVqv8l17gyA8kRfiBpAg/kBThB5Ii/EBShB9IivADSTHOPwaOHz8+0PYzMzMda7Ozs6XbvvPOO6X1Qc8TWL58ecfao48+Wrrtli1bSuu4FOP8ALoi/EBShB9IivADSRF+ICnCDyRF+IGkuo7z256V9HVJZyJiVbHsekm/kTQlaU7S/RHxfredMc4/fo4dOzZQff/+/aX1svMMlixZUrrtG2+8UVq/9tprS+sZVT3O/ytJd1207GFJL0TESkkvFI8BXEG6hj8iXpT03kWLN0jaVdzfJeneivsCMGT9vudfFhGnJKm4vaG6lgCMwtA/8LM9bbtlu9Vut4e9OwA96jf8p21PSFJxe6bTihExExHNiGg2Go0+dwegav2Gf5+kzcX9zZKeq6YdAKPSNfy2n5H0Z0lfsH3C9rclbZe03vYxSeuLxwCuIJ/otkJEbOpQ+krFvaAGK1euHKh+9913l9YPHz7csXbw4MHSbc+dO1daZ5x/MJzhByRF+IGkCD+QFOEHkiL8QFKEH0iq61AfUKbb146XDeeN8mvjcSmO/EBShB9IivADSRF+ICnCDyRF+IGkCD+QFOP8GKpuU3yjPhz5gaQIP5AU4QeSIvxAUoQfSIrwA0kRfiApxvkxkPffL5+Zveya/TvvvLN028nJyb56Qm848gNJEX4gKcIPJEX4gaQIP5AU4QeSIvxAUl3H+W3PSvq6pDMRsapYtk3SdyS1i9W2RsTzw2oS42vv3r2l9bLr+R944IGq28Fl6OXI/ytJdy2yfEdErC7+EXzgCtM1/BHxoqT3RtALgBEa5D3/Q7YP2561fV1lHQEYiX7D/wtJn5e0WtIpST/ttKLtadst2612u91pNQAj1lf4I+J0RHwUEecl/VLSmpJ1ZyKiGRHNRqPRb58AKtZX+G1PLHj4DUlHqmkHwKj0MtT3jKR1kpbaPiHpx5LW2V4tKSTNSfruEHsEMARdwx8RmxZZ/NQQesEV6PHHHy+tl43zT0xMdKxh+DjDD0iK8ANJEX4gKcIPJEX4gaQIP5AUX92NUocOHSqtd5uCu6y+bt26flpCRTjyA0kRfiApwg8kRfiBpAg/kBThB5Ii/EBSjPOj1LvvvltaL5uCW5KWLVvWsXbNNdf01ROqwZEfSIrwA0kRfiApwg8kRfiBpAg/kBThB5JinB+ldu/eXVrvdj3/zp07q2wHFeLIDyRF+IGkCD+QFOEHkiL8QFKEH0iK8ANJdR3ntz0p6WlJyyWdlzQTETttXy/pN5KmJM1Juj8i3h9eqxiGPXv2DFRfsWJFaf2ee+657J4wGr0c+T+U9MOI+BdJ/yrpe7ZvkfSwpBciYqWkF4rHAK4QXcMfEaci4tXi/geSjkq6UdIGSbuK1XZJundYTQKo3mW957c9JemLkg5JWhYRp6T5PxCSbqi6OQDD03P4bX9a0m8l/SAizl3GdtO2W7Zb7Xa7nx4BDEFP4bf9Sc0Hf3dE/K5YfNr2RFGfkHRmsW0jYiYimhHRbDQaVfQMoAJdw+/5y7aeknQ0In62oLRP0ubi/mZJz1XfHoBh6eWS3tslfUvS67ZfK5ZtlbRd0l7b35b0V0nfHE6LGKYjR46U1rtdsvvII4+U1vl67vHVNfwR8SdJnf4HfKXadgCMCmf4AUkRfiApwg8kRfiBpAg/kBThB5Liq7s/5o4dO1Zaf+yxx0rrV11VfnxYtWrVZfeE8cCRH0iK8ANJEX4gKcIPJEX4gaQIP5AU4QeSYpz/Y27btm2l9W7j+Fu2bCmtr1279nJbwpjgyA8kRfiBpAg/kBThB5Ii/EBShB9IivADSTHO/zF38uTJ0vr58+dL61yv//HFkR9IivADSRF+ICnCDyRF+IGkCD+QFOEHkuo6zm97UtLTkpZLOi9pJiJ22t4m6TuS2sWqWyPi+WE1iv6sXr26tH7fffeV1h988MEq28EY6eUknw8l/TAiXrX9GUmv2D5Q1HZExL8Prz0Aw9I1/BFxStKp4v4Hto9KunHYjQEYrst6z297StIXJR0qFj1k+7DtWdvXddhm2nbLdqvdbi+2CoAa9Bx+25+W9FtJP4iIc5J+IenzklZr/pXBTxfbLiJmIqIZEc1Go1FBywCq0FP4bX9S88HfHRG/k6SIOB0RH0XEeUm/lLRmeG0CqFrX8Nu2pKckHY2Iny1YPrFgtW9IOlJ9ewCGpZdP+2+X9C1Jr9t+rVi2VdIm26slhaQ5Sd8dSocYyI4dO+puAWOql0/7/yTJi5QY0weuYJzhByRF+IGkCD+QFOEHkiL8QFKEH0iK8ANJEX4gKcIPJEX4gaQIP5AU4QeSIvxAUoQfSMoRMbqd2W1J/7dg0VJJZ0fWwOUZ197GtS+J3vpVZW+fi4ievi9vpOG/ZOd2KyKatTVQYlx7G9e+JHrrV1298bIfSIrwA0nVHf6ZmvdfZlx7G9e+JHrrVy291fqeH0B96j7yA6hJLeG3fZft/7H9pu2H6+ihE9tztl+3/ZrtVs29zNo+Y/vIgmXX2z5g+1hxu+g0aTX1ts3228Vz95rtu2vqbdL2H2wftf0X298vltf63JX0VcvzNvKX/bavlvS/ktZLOiHpZUmbIuK/R9pIB7bnJDUjovYxYdt3SPqbpKcjYlWx7CeS3ouI7cUfzusi4kdj0ts2SX+re+bmYkKZiYUzS0u6V9K/qcbnrqSv+1XD81bHkX+NpDcj4q2I+LukPZI21NDH2IuIFyW9d9HiDZJ2Ffd3af4/z8h16G0sRMSpiHi1uP+BpAszS9f63JX0VYs6wn+jpOMLHp/QeE35HZL2237F9nTdzSxiWTFt+oXp02+ouZ+LdZ25eZQumll6bJ67fma8rlod4V9s9p9xGnK4PSJuk/Q1Sd8rXt6iNz3N3Dwqi8wsPRb6nfG6anWE/4SkyQWPPyvpZA19LCoiTha3ZyQ9q/Gbffj0hUlSi9szNffzD+M0c/NiM0trDJ67cZrxuo7wvyxppe0Vtj8laaOkfTX0cQnbS4oPYmR7iaSvavxmH94naXNxf7Ok52rs5Z+My8zNnWaWVs3P3bjNeF3LST7FUMZ/SLpa0mxEPDbyJhZh+2bNH+2l+UlMf11nb7afkbRO81d9nZb0Y0m/l7RX0k2S/irpmxEx8g/eOvS2TvMvXf8xc/OF99gj7u1Lkv4o6XVJ54vFWzX//rq2566kr02q4XnjDD8gKc7wA5Ii/EBShB9IivADSRF+ICnCDyRF+IGkCD+Q1P8D3ii1kn50oPkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    },
    {
     "data": {
      "image/png": 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9z91b/sZbhd5u1tBT17+u3Hz6NXaLe/sHSf8t6QNJp7LNqzT0+rqwxy7R12IV8LjxCT8gKD7hBwRF+IGgCD8QFOEHgiL8QFCEHwiK8ANBEX4gqP8HUyEU5W8XwNEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n"
     ]
    },
    {
     "data": {
      "image/png": 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n77pp5ubRZpZWF7x23TTjdRXh3yFpmpl918xOkrRI0tYK+vgaMzs5+yJGZnaypMvUfbMPb5W0JLu9RNKLFfbyJd0yc3PezNKq+LXrthmvKznIJxvKeFzSGEn97v5wx5sYhZn9g4b39tLwJKbPVtmbmT0nabaGz/o6KGmlpC2Snpd0lqS9kn7o7h3/4i2nt9kafuv695mbv/iM3eHeLpb0uqTdko5mi+/W8Ofryl67RF+LVcHrxhF+QFAc4QcERfiBoAg/EBThB4Ii/EBQhB8IivADQRF+IKj/Bz9cNclJ3G5xAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    },
    {
     "data": {
      "image/png": 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1S/qZpM2SfitpmqQ/S/qBu7f8i7cKvV2vobeuf5+5+fRn7Bb3Nk/S7yW9K+lUtvgBDX2+LmzfJfpapAL2G2f4AUFxhh8QFOEHgiL8QFCEHwiK8ANBEX4gKMIPBEX4gaD+H3q3GJZY189cAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
    {
     "data": {
      "image/png": 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nrn9eufnsa+wm9/Z3kv5D0geSzmSb12jw9XVpj12irxUq4XHjE35AUHzCDwiK8ANBEX4gKMIPBEX4gaAIPxAU4QeCIvxAUP8Hw3bwvMoPF28AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_image(index):\n",
    "    'plots the image when you give it an index and returns the correct output'\n",
    "    print(y_batch[index]) # The label is 8\n",
    "    plt.imshow(x_train_batch[index], cmap='Greys')\n",
    "    \n",
    "for index in range(len(y_batch)):\n",
    "    plot_image(index)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}