07a. MLP Neural Networks with Bias.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MLP Neural Networks\n",
    "In this notebook we will build several different multi-layer perceptron models. Each time, we will add some common functionality to the model. We will start with building an easy to analyze system and build the overall complexity each time.  \n",
    "\n",
    "## Getting some data to test with:\n",
    "Let's start by grabbing some data for a (small) hand written digits dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1797, 64)\n",
      "(1797,)\n",
      "-0.5 0.5\n",
      "[0 1 2 3 4 5 6 7 8 9]\n"
     ]
    }
   ],
   "source": [
    "# lets load up the handwritten digit dataset\n",
    "from sklearn.datasets import load_digits\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import numpy as np\n",
    "\n",
    "ds = load_digits()\n",
    "X = ds.data/16.0-0.5 # normalize the input, very important\n",
    "y = ds.target\n",
    "\n",
    "print(X.shape)\n",
    "print(y.shape)\n",
    "print(np.min(X),np.max(X))\n",
    "print(np.unique(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "fig, ax = plt.subplots(nrows=2, ncols=5, sharex=True, sharey=True,)\n",
    "ax = ax.flatten()\n",
    "for i in range(10):\n",
    "    img = X[y == i][0].reshape(8, 8)\n",
    "    ax[i].imshow(img, cmap='Greys', interpolation='nearest')\n",
    "\n",
    "ax[0].set_xticks([])\n",
    "ax[0].set_yticks([])\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(nrows=5, ncols=5, sharex=True, sharey=True,)\n",
    "ax = ax.flatten()\n",
    "digit = 4\n",
    "x_digits = X[y == digit]\n",
    "for i in range(25):\n",
    "    img = x_digits[i].reshape(8, 8)\n",
    "    ax[i].imshow(img, cmap='Greys', interpolation='nearest')\n",
    "\n",
    "ax[0].set_xticks([])\n",
    "ax[0].set_yticks([])\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1437, 64)\n",
      "(1437,)\n",
      "(360, 64)\n",
      "(360,)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X,y,test_size = 0.2)\n",
    "print(X_train.shape)\n",
    "print(y_train.shape)\n",
    "print(X_test.shape)\n",
    "print(y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_____\n",
    "# Single Layer Neural Networks are just Linear and Logistic Regression\n",
    "The single layer network can be summarized with the notation given by previously covered topics (linear and logistic regression). When we calculated objective functions for linear regression and logistic regression we used the maximum likelihood priciple, showing that (under Gaussian noise) this led to minimizing the squared error of the output.\n",
    "\n",
    "This is identical to the objective function for generic, single layer neural networks:\n",
    "$$ \\sum_i^M (\\mathbf{y}^{(i)}-\\hat{\\mathbf{y}}^{(i)})^2 $$\n",
    "\n",
    "Here, the $\\mathbf{y}^{(i)}$ is a one-hot-encoded representation of the class for the $i^{th}$ instance.\n",
    "Adding in terms of single layer neural network explicitly:\n",
    "$$ J(\\mathbf{W}) = \\sum_i^M (\\mathbf{y}^{(i)}-\\phi(\\mathbf{W}\\cdot \\mathbf{x}^{(i)}))^2 $$\n",
    "\n",
    "Adaline network objective function:\n",
    "$$ J(\\mathbf{W}) = \\sum_i^M (\\mathbf{y}^{(i)}-\\mathbf{W}\\cdot \\mathbf{x}^{(i)})^2 $$\n",
    "\n",
    "To solve, we need the gradient:\n",
    "$$  \\nabla J(\\mathbf{W}) $$\n",
    "\n",
    "And then we can use the Widrow-Hoff learning Rule:\n",
    "$$ \\mathbf{W}\\leftarrow\\mathbf{W} +\\eta\\nabla J(\\mathbf{W}) $$\n",
    "\n",
    "Which can be separated for each row (they are independent):\n",
    "$$ \\mathbf{w}\\leftarrow\\mathbf{w} +\\eta[ \\mathbf{X}*(\\mathbf{y}-\\mathbf{\\hat{y}})] $$\n",
    "\n",
    "$$ \\mathbf{w}_{row}\\leftarrow\\mathbf{w}_{row} +\\eta[ \\mathbf{X}*(\\mathbf{y}_{row}-\\mathbf{\\hat{y}}_{row})] $$\n",
    "\n",
    "The same is true for the update equation of the perceptron with a sigmoid activation function:\n",
    "$$ \\mathbf{w}\\leftarrow\\mathbf{w} +\\eta[ \\mathbf{X}*(\\mathbf{y}-\\mathbf{g(x)})] $$\n",
    "\n",
    "$$ \\mathbf{w}_{row}\\leftarrow\\mathbf{w}_{row} +\\eta[ \\mathbf{X}*(\\mathbf{y}_{row}-\\mathbf{g(x)}_{row})] $$\n",
    "\n",
    "This means that the update equations are identical to the case of linear and logistic regression, using one-versus-all! So all of this we have already looked at and solved! Yay!! But, what about when we add more layers?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multi-layer Case\n",
    "In the multilayer perceptron, we need to adjust some notation:\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/eclarson/MachineLearningNotebooks/master/PDF_Slides/MultiLayerNetwork.png\" width=\"500\">\n",
    "\n",
    "\n",
    "## Formulation of multi-layer perceptron\n",
    "Our objective function becomes:\n",
    "$$ J(\\mathbf{W}) = \\sum_k^M (\\mathbf{y}^{(k)}-\\mathbf{a}^{(L)})^2 $$\n",
    "\n",
    "And the update equation becomes:\n",
    "$$  w_{i,j}^{(l)} \\leftarrow w_{i,j}^{(l)} - \\eta \\frac{\\partial J(\\mathbf{W})}{\\partial w_{i,j}^{(l)}}$$\n",
    "\n",
    "However, this is not tractable to compute by hand for each network architecture, so we expand the gradient calculation using the chain rule to get partial derivatives:\n",
    "$$  \\frac{\\partial J(\\mathbf{W})}{\\partial w_{i,j}^{(l)}} = \\frac{\\partial J(\\mathbf{W})}{\\partial\\mathbf{z}^{(l)}} \\frac{\\partial\\mathbf{z}^{(l)}}{\\partial w_{i,j}^{(l)}}   $$\n",
    "\n",
    "The second term in the partial derivatives is easy to calculate as $a_j^{(l)}$ (see lecture notes), such that:\n",
    "$$  \\frac{\\partial J(\\mathbf{W})}{\\partial w_{i,j}^{(l)}} = \\frac{\\partial J(\\mathbf{W})}{\\partial\\mathbf{z}^{(l)}} a_j^{(l)}   $$\n",
    "\n",
    "And our update equation would be:\n",
    "$$  w_{i,j}^{(l)} \\leftarrow w_{i,j}^{(l)} - \\eta \\frac{\\partial J(\\mathbf{W})}{\\partial\\mathbf{z}^{(l)}} a_j^{(l)}$$\n",
    "\n",
    "To calculate the other term, we need to continue to use the chain rule:\n",
    "$$ \\frac{\\partial J(\\mathbf{W})}{\\partial\\mathbf{z}^{(l)}} = \\left[\\frac{\\partial \\mathbf{z}^{(l+1)} }{\\partial\\mathbf{z}^{(l)}}\\right]^T \\frac{\\partial J(\\mathbf{W})}{\\partial\\mathbf{z}^{(l+1)}}  $$\n",
    "\n",
    "After some derivation, we can see that: \n",
    "$$ \\frac{\\partial \\mathbf{z}^{(l+1)} }{\\partial\\mathbf{z}^{(l)}} = \\text{diag}[\\mathbf{a}^{(l+1)}*(1-\\mathbf{a}^{(l+1)})] \\cdot\\mathbf{W}^{(l+1)}  $$\n",
    "\n",
    "and\n",
    "$$ \\frac{\\partial J(\\mathbf{W})}{\\partial\\mathbf{z}^{(l)}} = \\text{diag}[\\mathbf{a}^{(l+1)}*(1-\\mathbf{a}^{(l+1)})] \\cdot\\mathbf{W}^{(l+1)} \\frac{\\partial J(\\mathbf{W})}{\\partial\\mathbf{z}^{(l+1)}} $$\n",
    "\n",
    "This set up a recurrence relation such that if we know $\\frac{\\partial J(\\mathbf{W})}{\\partial\\mathbf{z}^{(l)}}$ for the final layer, we can use it to get the derivatives for the previous layers. For a two layer network, the final layer gradient can be formulated as:\n",
    "$$  \\frac{\\partial J(\\mathbf{W})}{\\partial\\mathbf{z}^{(2)}} = \\frac{\\partial}{\\partial\\mathbf{z}^{(2)}} (\\mathbf{y}^{(k)}-\\phi(\\mathbf{z}^{(2)}))^2 $$\n",
    "\n",
    "$$  \\frac{\\partial J(\\mathbf{W})}{\\partial\\mathbf{z}^{(2)}}  = -2(\\mathbf{y}^{(k)}-\\mathbf{a}^{(3)})*\\mathbf{a}^{(3)}*(1-\\mathbf{a}^{(3)}) $$\n",
    "\n",
    "where $\\mathbf{y}^{(k)}$ is the $k^{th}$ instance and $\\mathbf{a}^{(3)}$ is the feedforward result for the $k^{th}$ instance. We can make this more explicit by writing the $k^{th}$ instance of $\\mathbf{a}^{(3)}$ as $[\\mathbf{a}^{(3)}]^{(k)}$. Now the update becomes:\n",
    "\n",
    "$$  \\frac{\\partial J(\\mathbf{W})}{\\partial [\\mathbf{z}^{(2)}]^{(k)}}  = -2\\left(\\mathbf{y}^{(k)}-{[\\mathbf{a}^{(3)}]^{(k)}}\\right)*{[\\mathbf{a}^{(3)}]^{(k)}}*\\left(1-{[\\mathbf{a}^{(3)}]^{(k)}}\\right) $$\n",
    "\n",
    "Also recall that $\\cdot$ represent matrix multiplication and $*$ represents elementwise or row-wise multiplication. The update equation can be given by:\n",
    "\n",
    "$$ \\mathbf{W}^{(l)} \\leftarrow \\mathbf{W}^{(l)} -\\eta \\frac{\\partial J(\\mathbf{W}^{(l)})}{\\partial [\\mathbf{z}^{(l)}]^{(k)}} \\cdot {[\\mathbf{a}^{(l)}]^{(k)}} $$\n",
    "\n",
    "For single elements stochastic gradient descent. Or can be given by the following for batch gradient descent:\n",
    "\n",
    "$$ \\mathbf{W}^{(l)} \\leftarrow \\mathbf{W}^{(l)} -\\eta \\sum_k\\frac{\\partial J(\\mathbf{W}^{(l)})}{\\partial {[\\mathbf{z}^{(l)}]^{(k)}}} \\cdot {[\\mathbf{a}^{(l)}]^{(k)}} $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Programming a Two Layer Perceptron\n",
    "Example adapted from https://github.com/rasbt/python-machine-learning-book/blob/master/code/ch12/ch12.ipynb\n",
    "Original Author: Sebastian Raschka\n",
    "\n",
    "This is the optional book we use in the course, excellent intuitions and straightforward programming examples please note, however, that this code has been heavily manipulated to reflect our assumptions and notation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Example adapted from https://github.com/rasbt/python-machine-learning-book/blob/master/code/ch12/ch12.ipynb\n",
    "#Original Author: Sebastian Raschka\n",
    "\n",
    "import numpy as np\n",
    "from scipy.special import expit\n",
    "import sys\n",
    "import pandas as pd\n",
    "\n",
    "# start with a simple base classifier, which can't be fit or predicted\n",
    "# it only has internal classes to be used by classes that will subclass it\n",
    "# Start with the following functions:\n",
    "#    init\n",
    "#    encode_labels\n",
    "#    initialize weights\n",
    "#    sigmoid\n",
    "#    add bias (vector of ones)\n",
    "#    objective function (cost and regularizer)\n",
    "class TwoLayerPerceptronBase(object):\n",
    "    def __init__(self, n_hidden=30,\n",
    "                 C=0.0, epochs=500, eta=0.001, random_state=None):\n",
    "        np.random.seed(random_state)\n",
    "        self.n_hidden = n_hidden\n",
    "        self.l2_C = C\n",
    "        self.epochs = epochs\n",
    "        self.eta = eta\n",
    "        \n",
    "    @staticmethod\n",
    "    def _encode_labels(y):\n",
    "        \"\"\"Encode labels into one-hot representation\"\"\"\n",
    "        onehot = pd.get_dummies(y).values.T\n",
    "            \n",
    "        return onehot\n",
    "\n",
    "    def _initialize_weights(self):\n",
    "        \"\"\"Initialize weights with small random numbers.\"\"\"\n",
    "        W1_num_elems = (self.n_features_)*self.n_hidden\n",
    "        W1 = np.random.uniform(-1.0, 1.0, size=W1_num_elems)\n",
    "        W1 = W1.reshape(self.n_hidden, self.n_features_) # reshape to be W\n",
    "        b1 = np.zeros((self.n_hidden, 1))\n",
    "        \n",
    "        W2_num_elems = (self.n_hidden)*self.n_output_\n",
    "        W2 = np.random.uniform(-1.0, 1.0, size=W2_num_elems)\n",
    "        W2 = W2.reshape(self.n_output_, self.n_hidden)\n",
    "        b2 = np.zeros((self.n_output_, 1))\n",
    "        \n",
    "        return W1, W2, b1, b2\n",
    "    \n",
    "    @staticmethod\n",
    "    def _sigmoid(z):\n",
    "        \"\"\"Use scipy.special.expit to avoid overflow\"\"\"\n",
    "        # 1.0 / (1.0 + np.exp(-z))\n",
    "        return expit(z)\n",
    "    \n",
    "    \n",
    "    @staticmethod\n",
    "    def _L2_reg(lambda_, W1, W2):\n",
    "        \"\"\"Compute L2-regularization cost\"\"\"\n",
    "        # only compute for non-bias terms\n",
    "        return (lambda_) * np.sqrt(np.mean(W1 ** 2) + np.mean(W2 ** 2))\n",
    "    \n",
    "    def _cost(self,A3,Y_enc,W1,W2):\n",
    "        '''Get the objective function value'''\n",
    "        cost = np.mean((Y_enc-A3)**2)\n",
    "        L2_term = self._L2_reg(self.l2_C, W1, W2)\n",
    "        return cost + L2_term\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# now let's add in the following functions:\n",
    "#    feedforward\n",
    "#    fit and predict\n",
    "class TwoLayerPerceptron(TwoLayerPerceptronBase):\n",
    "    def _feedforward(self, X, W1, W2, b1, b2):\n",
    "        \"\"\"Compute feedforward step\n",
    "        -----------\n",
    "        X : Input layer with original features.\n",
    "        W1: Weight matrix for input layer -> hidden layer.\n",
    "        W2: Weight matrix for hidden layer -> output layer.\n",
    "        ----------\n",
    "        a1-a3 : activations into layer (or output layer)\n",
    "        z1-z2 : layer inputs \n",
    "\n",
    "        \"\"\"\n",
    "        A1 = X.T\n",
    "        Z1 = W1 @ A1 + b1\n",
    "        A2 = self._sigmoid(Z1)\n",
    "        Z2 = W2 @ A2 + b2\n",
    "        A3 = self._sigmoid(Z2)\n",
    "        return A1, Z1, A2, Z2, A3\n",
    "    \n",
    "    def _get_gradient(self, A1, A2, A3, Z1, Z2, Y_enc, W1, W2):\n",
    "        \"\"\" Compute gradient step using backpropagation.\n",
    "        \"\"\"\n",
    "        # need to vectorize this computation!\n",
    "        # See additional code and derivation below!\n",
    "        pass\n",
    "    \n",
    "    def predict(self, X):\n",
    "        \"\"\"Predict class labels\"\"\"\n",
    "        _, _, _, _, A3 = self._feedforward(X, self.W1, self.W2, self.b1, self.b2)\n",
    "        y_pred = np.argmax(A3, axis=0)\n",
    "        return y_pred\n",
    "    \n",
    "    \n",
    "    def fit(self, X, y, print_progress=False):\n",
    "        \"\"\" Learn weights from training data.\"\"\"\n",
    "        \n",
    "        X_data, y_data = X.copy(), y.copy()\n",
    "        Y_enc = self._encode_labels(y)\n",
    "        \n",
    "        # init weights and setup matrices\n",
    "        self.n_features_ = X_data.shape[1]\n",
    "        self.n_output_ = Y_enc.shape[0]\n",
    "        self.W1, self.W2, self.b1, self.b2 = self._initialize_weights()\n",
    "\n",
    "        self.cost_ = []\n",
    "        for i in range(self.epochs):\n",
    "\n",
    "            if print_progress>0 and (i+1)%print_progress==0:\n",
    "                sys.stderr.write('\\rEpoch: %d/%d' % (i+1, self.epochs))\n",
    "                sys.stderr.flush()\n",
    "\n",
    "            # feedforward all instances\n",
    "            A1, Z1, A2, Z2, A3 = self._feedforward(X_data,self.W1,self.W2, self.b1, self.b2)\n",
    "            \n",
    "            cost = self._cost(A3,Y_enc,self.W1,self.W2)\n",
    "            self.cost_.append(cost)\n",
    "\n",
    "            # compute gradient via backpropagation\n",
    "            gradW1, gradW2, gradb1, gradb2 = self._get_gradient(A1=A1, A2=A2, A3=A3, Z1=Z1, Z2=Z2, Y_enc=Y_enc,\n",
    "                                              W1=self.W1, W2=self.W2)\n",
    "\n",
    "            self.W1 -= self.eta * gradW1\n",
    "            self.W2 -= self.eta * gradW2\n",
    "            self.b1 -= self.eta * gradb1\n",
    "            self.b2 -= self.eta * gradb2\n",
    "            \n",
    "\n",
    "        return self"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vectorized coding operations in gradient\n",
    "So we need to derive equations for vectorized operations. These can be derived by specifically writing out our current gradient calculations. If we plug in the equations for the final layer gradient, we have that:\n",
    "\n",
    "$$  \\nabla_k^{(2)} = -2\\left(\\mathbf{y}^{(k)}-{[\\mathbf{a}^{(3)}]^{(k)}}\\right){[\\mathbf{a}^{(3)}]^{(k)}}\\left(1-{[\\mathbf{a}^{(3)}]^{(k)}}\\right)\\cdot {[\\mathbf{a}^{(2)}]^{(k)} } $$\n",
    "\n",
    "where we use $\\nabla_k^{(2)}$ in place of $\\frac{\\partial J(\\mathbf{W}^{(l)})}{\\partial _k\\mathbf{z}^{(2)}} \\cdot {[\\mathbf{a}^{(2)}]^{(k)}}$ to simplify the notation. Therefore, the total batch gradient calculation is given by:\n",
    "\n",
    "$$ \\mathbf{\\nabla}^{(2)} = \\sum_k \\nabla_k^{(2)} $$\n",
    "\n",
    "This first operation is relatively easy to vectorize because each column in $\\mathbf{A}^{(2)}$ corresponds to the $k^{th}$ instance of $_k\\mathbf{a}^{(2)}$. Therefore we can simply transpose $\\mathbf{A}^{(2)}$ and multiply it by the elementwise multiplications of $\\mathbf{y}^{(k)}$ and $_k\\mathbf{a}^{(3)}$:\n",
    "\n",
    "$$ \\mathbf{\\nabla}^{(2)} = -2(\\mathbf{Y}-\\mathbf{A}^{(3)})*\\mathbf{A}^{(3)}*(1-\\mathbf{A}^{(3)})\\cdot [\\mathbf{A}^{(2)}]^T $$\n",
    "\n",
    "For convenience, we define another variable, $\\mathbf{V}^{(2)}$ (called the sensitivity):\n",
    "\n",
    "$$ \\mathbf{V}^{(2)} = -2(\\mathbf{Y}-\\mathbf{A}^{(3)})*\\mathbf{A}^{(3)}*(1-\\mathbf{A}^{(3)}) $$\n",
    "\n",
    "such that:\n",
    "\n",
    "$$ \\mathbf{\\nabla}^{(2)} = \\mathbf{V}^{(2)}\\cdot [\\mathbf{A}^{(2)}]^T $$\n",
    "\n",
    "Further details about this calculation can be found in the lecture notes or the video here: https://youtu.be/WRr2e7mKCUY\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "\n",
    "Similarly, the calculation of the gradient for the hidden layer, from our derivations was:\n",
    "\n",
    "$$  \\nabla_k^{(1)} = \\frac{\\partial J(\\mathbf{W})}{\\partial \\mathbf{z}^{(2)}}\\cdot \\mathbf{W}^{(2)} \\cdot \\text{diag}[{_k\\mathbf{a}^{(2)}}*(1-{_k\\mathbf{a}^{(2)}})] \\cdot \\mathbf{a}^{(1)}$$\n",
    "\n",
    "$$ \\mathbf{\\nabla}^{(1)} = \\sum_k \\nabla_k^{(1)} $$\n",
    "\n",
    "This can also be vectorized by recognizing that $\\frac{\\partial J(\\mathbf{W})}{\\partial \\mathbf{z}^{(2)}}$ is a matrix with columns equal to $\\frac{\\partial J(\\mathbf{W})}{\\partial {_k\\mathbf{z}^{(2)}}}$ for each instance $k$. We have already solved for this: $ \\mathbf{V}^{(2)} $. With some algebra, we can find that the computation is represented vectorized as:\n",
    "\n",
    "$$  \\mathbf{V}^{(1)} = \\mathbf{A}^{(2)} * (1-\\mathbf{A}^{(2)}) * [\\mathbf{W}^{(2)}]^T \\cdot \\mathbf{V}^{(2)} \\cdot \\mathbf{A}^{(1)}$$\n",
    "\n",
    "And we define an intermediate sensitivity variable $\\mathbf{V}^{(1)}$ as:\n",
    "\n",
    "$$ \\mathbf{V}^{(1)} =  \\mathbf{A}^{(2)} * (1-\\mathbf{A}^{(2)}) * [\\mathbf{W}^{(2)}]^T \\cdot \\mathbf{V}^{(2)}  $$\n",
    "\n",
    "such that: \n",
    "\n",
    "$$  \\mathbf{\\nabla}^{(1)} = \\mathbf{V}^{(1)}\\cdot [\\mathbf{A}^{(1)}]^{T} $$\n",
    "\n",
    "Now we can update the weight vectors according to:\n",
    "\n",
    "$$ \\mathbf{W}^{(l)} \\leftarrow \\mathbf{W}^{(l)} -\\eta \\mathbf{\\nabla}^{(l)} $$\n",
    "\n",
    "Let's get programming! All we really need to do is update the `_get_gradient` class method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = dict(n_hidden=50, \n",
    "              C=0.1, # tradeoff L2 regularizer\n",
    "              epochs=400, # iterations\n",
    "              eta=0.001,  # learning rate\n",
    "              random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "class TwoLayerPerceptronVectorized(TwoLayerPerceptron):\n",
    "    # just need a different gradient calculation\n",
    "    def _get_gradient(self, A1, A2, A3, Z1, Z2, Y_enc, W1, W2):\n",
    "        \"\"\" Compute gradient step using backpropagation.\n",
    "        \"\"\"\n",
    "        # vectorized backpropagation\n",
    "        V2 = -2*(Y_enc-A3)*A3*(1-A3)\n",
    "        V1 = A2*(1-A2)*(W2.T @ V2)\n",
    "        \n",
    "        gradW2 = V2 @ A2.T\n",
    "        gradW1 = V1 @ A1.T\n",
    "        \n",
    "        gradb2 = np.sum(V2, axis=1).reshape((-1,1))\n",
    "        gradb1 = np.sum(V1, axis=1).reshape((-1,1))\n",
    "        \n",
    "        \n",
    "        # regularize weights that are not bias terms\n",
    "        gradW1 += W1 * self.l2_C * 2\n",
    "        gradW2 += W2 * self.l2_C * 2 \n",
    "\n",
    "        return gradW1, gradW2, gradb1, gradb2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch: 400/400"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.9416666666666667\n",
      "CPU times: user 2.67 s, sys: 129 ms, total: 2.8 s\n",
      "Wall time: 780 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "nn = TwoLayerPerceptronVectorized(**params)\n",
    "\n",
    "nn.fit(X_train, y_train, print_progress=50)\n",
    "yhat = nn.predict(X_test)\n",
    "print('Accuracy:',accuracy_score(y_test,yhat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LlT9awtJXt+ZdkohI8BRQ3WTIUVXcdtXpDK+p4rIFS9STEhE5iEwDyszONbMXzGy1mV3XxvvvMbPHzWyvmX2+1XtrzewZM1tmZrVZ1tldhvev5o45ZzBqQDWX3bKYh/TghIhIuzILKDMrAPOA84DJwCVmNrnVYVuBa4D/aOdjznb3qe4+Las6u9vIAdX8/G/ipTrm/mSpluoQEWlHlj2o6cBqd1/j7g3AHcCs9AHuvtndlwCNGdYRnNZLdfz3wy/h7nmXJSISlCwDajSQnutnfdLWUQ48aGZLzWxOeweZ2RwzqzWz2rq6nvMYd/NSHRdOPZr/fOhFrv3ZMuobS3mXJSISjCwDytpo60w34Ux3P4V4iPAzZnZWWwe5+3x3n+bu04YNG3YodeamqljgG7On8oVz3s2vlm3g4vlPsHlHfd5liYgEIcuAWg+MTe2PATZ09GR335C8bgbuJh4y7HXMjM+cPZGbPn4KL7yxg/O//ShPrtETfiIiWQbUEmCSmU0ws0rgYmBhR040s35mVtO8DXwQeDazSgNw7gmjuOvTM+hXVeSS7z/Bd36/mnJZ96VE5MiVWUC5exNwNfAA8Bzwc3dfaWZzzWwugJmNNLP1wOeAfzCz9WbWHxgBPGpmy4HFwL3ufn9WtYbiuFH9WXj1mZx3wij+7f4X+Osf1/LW7oa8yxIRyYX1pqfHpk2b5rW1Pf8rU+7Ojx9/la/eu4rhNdXMu/QUpo4dmHdZIiKZMLOlbX2dSDNJBMjMuGzGeO6cOwOAj960iFsfX6tH0UXkiKKACtiUsQO595qZzJw4lC//aiXX/mwZu/Y25V2WiEi3UEAFbmDfSn5w2Wl8/oN/xK+Xb+DCeY+xevOOvMsSEcmcAqoHiCLj6vdP4tYrT2frrgYuuPEx7lnR4Sf2RUR6JAVUD3LmxKHcc81M3jOyhqtve5qv/eY5SnoUXUR6KQVUDzNqQB/umHMGl55+DN/7vzV88pbFehRdRHolBVQPVFmM+JeLTuRrHzmRJ9a8yQU3Psbzb2zPuywRkS6lgOrBLpl+DHfMOYP6xhIXzVvEvSs25l2SiEiXUUD1cKeOG8Q9n53JcaNq+MxtT/H1+5/XfSkR6RUUUL3A8P7V3D7nvVwy/Ri++/uXueKHS3h79xG1xJaI9EIKqF6iqljgax85kX+96EQWvbyFP7tRs6KLSM+mgOplPnZ6fF8KYPb8J7hh4Up2N2j2CRHpeRRQvdCp4wZx/7V/zCdnjOeHi9Zyzjcf4bfPb9JcfiLSoyigeqm+lUVuuOB4fv43Z1ARRVzxw1r+asFiXtykaZJEpGdQQPVy0ycM5v5rz+LL509m+bq3OO9bf+D6u1awbuvuvEsTETkgrQd1BNm6q4FvP/wStz35GmV3/uLUMXz6fRM5ZkjfvEsTkSNYe+tBKaCOQBvf3sNNv3+Z25eso6lU5pzjR3LFzAlMGzcIM8u7PBE5wiig5B02ba/nlsfWcvvi13h7TyMnjO7P5TMm8OGTRlFdUci7PBE5QiigpF27G5q4++nXueWxtazevJP+1UUuPHk0s08by/FHD8i7PBHp5RRQclDuzqKX3+RnS9Zx/8o3aGgqc8Lo/sw+7RgumHI0A/pU5F2iiPRCCijplLd2N/DLp1/nZ7XreW7jdqqKER84bgSzph7N+949nMqiHgAVka6hgJJD4u48+/p2frF0Hfes2MjWXQ0M7FvBh04cxYVTRzNt3CCiSA9WiMihU0DJYWsslXn0pS38ctnrPLhyE3saS4we2Ifzp4zinONHMnXMQIWViHSaAkq61K69TTy0ahN3P/06j63eQlPZGV5TxZ9OHsE5x4/kvccO0TCgiHSIAkoy8/aeRn73/GYeWPkGv3+hjj2NJWqqi5w1aRgzJw1l5sShjB2sLwOLSNsUUNIt6htLPPrSFh5Y+QaPvFTHpu17ARg/pC8zJw3ljGOHcsq4gYwa0CfnSkUkFAoo6XbuzurNO/nDS1t4dPUWnljzJrsbSgAcPaCak8cN4tRjBnHKuEEcN6qGqqK+HCxyJFJASe4aS2VWbdjOU69tY+mr23j6tbd4/a09ABQj413DjmLy0f05blQNk0cN4LhRNQw5qirnqkUkawooCdIbb9fz1GvbWLVhO6s2bue5jdvZ+HZ9y/uD+lZw7LCjOHZov/h1WD/eNawfxwzup4cwRHoJBZT0GNt2NfDcxjiwXq7bxZq6nazZsou6HXtbjokMRvavZvSgPowZ1Jcxg/okP30ZPbAPIwdUaz5BkR6ivYAq5lGMyIEM6lfJjIlDmTFx6H7t2+sbeaVuF2u27OSVLbt5fdse1m/bzeJXtrJweT2l8v7/2OpfXWRE/2qG969ieE3qtaaK4TVVDK2pYnDfSgb0qdD3t0QCpICSHqN/dQVTxg5kytiB73ivqVTmje31rN+2h/Xb9rBpez2bttezefteNu+oZ/ErW6nbsZeGUvkd50YGA/pUMKhfJYP7VjKwbyWD+1UwqG9lS1v/PkVqqiuoqY5fj6oqUlNdVC9NJEMKKOkVioUoGepr//tW7s7bexrZtH0vm7bXs3VXA1t3NfDW7ga27m5g265Gtu1uYP223Tz7eiNbdzfQ0PTOQEurLETUVBc5qjoOrJqqipb9vpUF+lbGIRZvF9rYLtInaetTWaBPRfyjHp2IAkqOIGbGwKSH9O6RNQc93t3Z01hi664G3t7TyM76JnbUN7Fjb7y9vXm/vpGde/dtv7Z1Nzvqm9jTWGJPQ4k9jaVO11pRMKqKBSqLEZWFiKqK/V8ri9G+94sRVclPfEyBykJERSGiWDAqCkYhiqgoGMUoohgZxYJRLCTbkbUcW2jejpJjU+c3HxdFUDAjMiOKjMigECX7Zsk2WvxSDpsCSqQdZkbfyiJ9K4uMGXTon1MuO/VNcVjtTgJr33ZT/Jq0N283lMrsbSzTUCrR0FRmb1N5v9eGpjJv7W6I91uObT4mPqec8/NPZukgIw6vVqFmSVu8nQ66fdtmhiWfZwaGJa9xY8t7sP+xxI3p/ebPgH37vOO8/fdJ/b62Pqc9HXn+7GDHOAc+4ODnH34NzZ/SfFzz4c0P2E0bP5jPnD2xA7+p8xRQIhmLon1BN6Qbf2+p7DSWypTKTlPJaSyXW9qaSk5TuUxT83ul5vf2b28qJdvlcvxeySm54+6Uyk7Z4wAuuVN2p5y0xe/FP6UyLe/F58bvt/85JJ+z7z2Iz3PiP4zx6759WvaT49LbgJfBKe/3R7b157Dffvpz2vkdJCF5AB3pRNpBPuVwO6Id6cl29L8jHe7N+zvqmw6jugNTQIn0UoXIKER6iEN6Ln3TUUREgpRpQJnZuWb2gpmtNrPr2nj/PWb2uJntNbPPd+ZcERHp3TILKDMrAPOA84DJwCVmNrnVYVuBa4D/OIRzRUSkF8uyBzUdWO3ua9y9AbgDmJU+wN03u/sSoLGz54qISO+WZUCNBtal9tcnbV16rpnNMbNaM6utq6s7pEJFRCQ8WQZUW08udvSbGR0+193nu/s0d582bNiwDhcnIiJhyzKg1gNjU/tjgA3dcK6IiPQCWQbUEmCSmU0ws0rgYmBhN5wrIiK9QGZf1HX3JjO7GngAKAAL3H2lmc1N3r/JzEYCtUB/oGxm1wKT3X17W+dmVauIiISnVy1YaGZ1wKuH8RFDgS1dVE6WVGfXUp1dpyfUCKqzqx1unePc/R0PEfSqgDpcZlbb1qqOoVGdXUt1dp2eUCOozq6WVZ2a6khERIKkgBIRkSApoPY3P+8COkh1di3V2XV6Qo2gOrtaJnXqHpSIiARJPSgREQmSAkpERIKkgEqEvP6Uma01s2fMbJmZ1SZtg83sITN7KXkd1M01LTCzzWb2bKqt3ZrM7Prk2r5gZufkXOcNZvZ6cj2XmdmHAqhzrJn9zsyeM7OVZva3SXtQ1/QAdQZzTc2s2swWm9nypMZ/TNpDu5bt1RnMtWxVb8HMnjaze5L97K+nux/xP8SzVbwMHAtUAsuJZ7TIvbakvrXA0FZt/wZcl2xfB3y9m2s6CzgFePZgNRGv6bUcqAImJNe6kGOdNwCfb+PYPOscBZySbNcALyb1BHVND1BnMNeUeLLpo5LtCuBJ4L0BXsv26gzmWrb6/Z8DbgPuSfYzv57qQcV64vpTs4AfJds/Ai7szl/u7o8QLzjZkZpmAXe4+153fwVYTXzN86qzPXnWudHdn0q2dwDPES8xE9Q1PUCd7en2Oj22M9mtSH6c8K5le3W2J7f/fZrZGODDwM2t6sn0eiqgYoezdlV3cOBBM1tqZnOSthHuvhHiPxrA8Nyq26e9mkK8vleb2YpkCLB5aCKIOs1sPHAy8b+og72mreqEgK5pMhy1DNgMPOTuQV7LduqEgK5l4pvA3wPlVFvm11MBFTuctau6w5nufgpwHvAZMzsr74I6KbTr+13gXcBUYCPwn0l77nWa2VHA/wDXuvv2Ax3aRlu31dpGnUFdU3cvuftU4qV6ppvZCQc4PLdr2U6dQV1LMzsf2OzuSzt6Shtth1SnAioW9PpT7r4hed0M3E3cXd5kZqMAktfN+VXYor2agrq+7r4p+cNQBr7PvuGHXOs0swriP/o/dfe7kubgrmlbdYZ6Td39LeD3wLkEeC2bpesM8FqeCVxgZmuJb3+838x+QjdcTwVULNj1p8ysn5nVNG8DHwSeJa7vsuSwy4Bf5VPhftqraSFwsZlVmdkEYBKwOIf6gJb/MzW7iPh6Qo51mpkBPwCec/f/Sr0V1DVtr86QrqmZDTOzgcl2H+ADwPOEdy3brDOkawng7te7+xh3H0/8t/G37v5xuuN6dtcTIKH/AB8ifiLpZeBLedeTqutY4idilgMrm2sDhgAPAy8lr4O7ua7biYcfGon/xXTlgWoCvpRc2xeA83Ku81bgGWBF8n+mUQHUOZN4GGQFsCz5+VBo1/QAdQZzTYGTgKeTWp4FvpK0h3Yt26szmGvZRs3vY99TfJlfT011JCIiQdIQn4iIBEkBJSIiQVJAiYhIkBRQIiISJAWUiIgESQElkjEzK6Vmpl5mXThbvpmNt9RM7SK9STHvAkSOAHs8ns5GRDpBPSiRnFi8ztfXkzWBFpvZxKR9nJk9nEwW+rCZHZO0jzCzu5P1g5ab2Yzkowpm9v1kTaEHk1kJMLNrzGxV8jl35PSfKXLIFFAi2evTaohvduq97e4+HbiReMZoku0fu/tJwE+Bbyft3wb+z92nEK9xtTJpnwTMc/fjgbeAP0/arwNOTj5nbjb/aSLZ0UwSIhkzs53uflQb7WuB97v7mmQC1jfcfYiZbSGe3qYxad/o7kPNrA4Y4+57U58xnniZhknJ/heBCnf/qpndD+wEfgn80vetPSTSI6gHJZIvb2e7vWPasje1XWLfveUPA/OAU4GlZqZ7ztKjKKBE8jU79fp4sr2IeNZogEuBR5Pth4FPQctCd/3b+1Azi4Cx7v474oXmBgLv6MWJhEz/ohLJXp9k1dRm97t786PmVWb2JPE/Fi9J2q4BFpjZF4A64PKk/W+B+WZ2JXFP6VPEM7W3pQD8xMwGEC8g9w2P1xwS6TF0D0okJ8k9qGnuviXvWkRCpCE+EREJknpQIiISJPWgREQkSAooEREJkgJKRESCpIASEZEgKaBERCRI/x9iNvtaQgPn3gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(len(nn.cost_)), nn.cost_)\n",
    "plt.ylabel('Cost')\n",
    "plt.xlabel('Epochs')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Back to slides] \n",
    "\n",
    "## Adding complexity and functionality\n",
    "So now we can calculate the gradient quickly, but we need to account for more optimization methods in this new space because the optmiization surface can be highly non-convex. We need to steer clear of local optima as best as possible.\n",
    "\n",
    "To start, let's add: \n",
    "- some momentum to the calculation \n",
    "- $\\eta$ learning rate decay\n",
    "- perform mini-batching of the gradient updates \n",
    "- random reshuffling of the inputs\n",
    "\n",
    "For cooling the learning rate, at epoch $k$:\n",
    "$$ \\mathbf{W}_{k+1} = \\mathbf{W}_k - \\frac{\\eta}{1+\\epsilon\\cdot k} \\cdot \\rho_{k} $$\n",
    "\n",
    "For momentum:\n",
    "$$ \\rho_{k} = \\nabla J(\\mathbf{W}_k) + \\alpha\\rho_{k-1} $$\n",
    "\n",
    "For decaying the learning rate:\n",
    "$$ \\eta_k = \\max(\\eta_0^{(1+k\\cdot d)},\\frac{\\eta_0}{1000}) $$\n",
    "\n",
    "where $k$ is the epoch, $\\eta_0$ is the starting value of $\\eta$, $\\eta<1$, and $d<1$, the decreasing constant,. \n",
    "\n",
    "Now let's build in these vales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Example adapted from https://github.com/rasbt/python-machine-learning-book/blob/master/code/ch12/ch12.ipynb\n",
    "# Original Author: Sebastian Raschka\n",
    "# This is the optional book we use in the course, excellent intuitions and straightforward programming examples\n",
    "# please note, however, that this code has been manipulated to reflect our assumptions and notation.\n",
    "class TLPVectorizedMiniBatch(TwoLayerPerceptronVectorized):\n",
    "    def __init__(self, alpha=0.1, decrease_const=0.0, shuffle=True, minibatches=1, **kwds):        \n",
    "        # need to add to the original initializer \n",
    "        self.alpha = alpha\n",
    "        self.decrease_const = decrease_const\n",
    "        self.shuffle = shuffle\n",
    "        self.minibatches = minibatches\n",
    "        # but keep other keywords\n",
    "        super().__init__(**kwds)\n",
    "        \n",
    "    def fit(self, X, y, print_progress=0):\n",
    "        \"\"\" Learn weights from training data.\"\"\"\n",
    "        X_data, y_data = X.copy(), y.copy()\n",
    "        Y_enc = self._encode_labels(y)\n",
    "        \n",
    "        # init weights and setup matrices\n",
    "        self.n_features_ = X_data.shape[1]\n",
    "        self.n_output_ = Y_enc.shape[0]\n",
    "        self.W1, self.W2, self.b1, self.b2 = self._initialize_weights()\n",
    "        \n",
    "        # start momentum at zero for previous updates\n",
    "        rho_W1_prev = np.zeros(self.W1.shape) # for momentum\n",
    "        rho_W2_prev = np.zeros(self.W2.shape) # for momentum\n",
    "\n",
    "        self.cost_ = []\n",
    "        for k in range(self.epochs):\n",
    "\n",
    "            # adaptive learning rate\n",
    "            eta = self.eta**(1+self.decrease_const*k)# decreasing learning rate\n",
    "            eta = max(eta,self.eta/1000)\n",
    "            # there are many forms of adaptive learning rates out there!\n",
    "\n",
    "            if print_progress>0 and (k+1)%print_progress==0:\n",
    "                sys.stderr.write('\\rEpoch: %d/%d' % (k+1, self.epochs))\n",
    "                sys.stderr.flush()\n",
    "\n",
    "            if self.shuffle:\n",
    "                # shuffle the data so batches ar different\n",
    "                ridx = np.random.permutation(y_data.shape[0])\n",
    "                X_data, Y_enc = X_data[ridx], Y_enc[:, ridx]\n",
    "\n",
    "            # use numpy split to split into equal sized batches \n",
    "            # num batches == self.minibatches\n",
    "            mini = np.array_split(range(y_data.shape[0]), self.minibatches)\n",
    "            mini_cost = []\n",
    "            for idx in mini:\n",
    "\n",
    "                # feedforward\n",
    "                A1, Z1, A2, Z2, A3 = self._feedforward(X_data[idx],\n",
    "                                                       self.W1,\n",
    "                                                       self.W2,\n",
    "                                                       self.b1,\n",
    "                                                       self.b2\n",
    "                                                      )\n",
    "                \n",
    "                cost = self._cost(A3,Y_enc[:, idx],self.W1,self.W2)\n",
    "                mini_cost.append(cost) # this appends cost of mini-batch only\n",
    "\n",
    "                # compute gradient via backpropagation\n",
    "                gradW1, gradW2, gradb1, gradb2 = self._get_gradient(A1=A1, A2=A2, A3=A3, Z1=Z1, Z2=Z2,\n",
    "                                                  Y_enc=Y_enc[:, idx],\n",
    "                                                  W1=self.W1, W2=self.W2)\n",
    "\n",
    "                rho_W1, rho_W2 = eta * gradW1, eta * gradW2 \n",
    "                self.W1 -= (rho_W1 + (self.alpha * rho_W1_prev)) # update with momentum\n",
    "                self.W2 -= (rho_W2 + (self.alpha * rho_W2_prev)) # update with momentum\n",
    "                rho_W1_prev, rho_W2_prev = rho_W1, rho_W2\n",
    "                \n",
    "                self.b1 -= eta * gradb1 \n",
    "                self.b2 -= eta * gradb2 \n",
    "\n",
    "            self.cost_.append(mini_cost)\n",
    "            \n",
    "        return self"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch: 100/100"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.9694444444444444\n",
      "CPU times: user 2.77 s, sys: 28.6 ms, total: 2.8 s\n",
      "Wall time: 706 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "params['epochs'] = 100\n",
    "params['eta'] = 0.1\n",
    "nn_mini = TLPVectorizedMiniBatch(**params,\n",
    "                          alpha=0.1,# momentum calculation\n",
    "                          decrease_const=0.1, # decreasing eta\n",
    "                          minibatches=len(X_train)/32, # minibatch size\n",
    "                          shuffle=True)\n",
    "\n",
    "    \n",
    "nn_mini.fit(X_train, y_train, print_progress=50)\n",
    "yhat = nn.predict(X_test)\n",
    "print('Accuracy:',accuracy_score(y_test,yhat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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e1DJgT0TsjYg+YAuwIr9ARByIiB1A/9GuOyHcgzIzq0yZATUf2Jd73pNOG9d1Ja2S1C2pu7e395gKHdGsWcm9e1BmZhOuzIBSg2nN/sdr0+tGxKaI6IqIrs7OzqaLa0prK8ye7R6UmVkFygyoHmBh7vkCYP8ErDu+fMJYM7NKlBlQO4AlkhZLagdWAlsnYN3x5fPxmZlVoq2sDUfEgKQ1wN1AK7A5InZJWp3O3yhpHtANzAIGJa0HlkbEi43WLavWUfmM5mZmlSgtoAAiYhuwrTBtY+7xMySH75patxJz5sDPflZ1FWZmU47PJDEW96DMzCrhgBqLv4MyM6uEA2osc+fCK69AX1/VlZiZTSkOqLH4bBJmZpVwQI3F5+MzM6uEA2os7kGZmVXCATUW96DMzCrhgBqLe1BmZpVwQI3FPSgzs0o4oMbiHpSZWSUcUGOZPj25uQdlZjahHFDN8NkkzMwmnAOqGT4fn5nZhHNANWPuXBjvy8mbmdmoHFDNOO886O72+fjMzCaQA6oZl10GL78M27dXXYmZ2ZThgGrGpZdCayt897tVV2JmNmU4oJoxezYsWwb33lt1JWZmU4YDqlmXXQY7dng0n5nZBHFANevyy2FwEO6/v+pKzMymhFIDStJySU9I2iNpQ4P5kvT5dP4jks7PzVsn6TFJuyStL7POpvz+78PJJ/swn5nZBCktoCS1AjcBVwBLgWskLS0sdgWwJL2tAm5O130r8DFgGXAucJWkJWXV2pT2dnjnOz1QwsxsgpTZg1oG7ImIvRHRB2wBVhSWWQHcGokfAXMknQ78LvCjiHglIgaAfwHeV2Ktzbn8cvj5z+Gpp6quxMxs0iszoOYD+3LPe9JpzSzzGPAOSadKOgl4D7CwxFqbc9llyb17UWZmpSszoNRgWjSzTETsBv4OuBe4C3gYGGi4E2mVpG5J3b1ln45o6VI44wx/D2VmNgHKDKgehvd6FgD7m10mIm6JiPMj4h3AQeDnjXYSEZsioisiujo7O8et+IakpBd1333JiD4zMytNmQG1A1giabGkdmAlsLWwzFbgz9LRfBcBL0TE0wCSfiu9fxPwfuD2Emtt3pVXwrPPwle/WnUlZmaTWltZG46IAUlrgLuBVmBzROyStDqdvxHYRvL90h7gFeAjuU3cKelUoB/4eETU44JMH/gAnH8+XHst/OEfwsyZVVdkZjYpKaL4tdCJq6urK7q7u8vf0fbtcMklsGEDfOYz5e/PzGwSk7QzIrqK030miWNx8cXw4Q/DP/wD/OxnVVdjZjYpOaCO1Wc/C9Onw7p1MIl6oWZmdeGAOlbz5sGnPw133QXf/GbV1ZiZTToOqOOxZg2ccw6sXg0HDlRdjZnZpOKAOh7TpsFtt8ELL8DHPuZDfWZm48gBdbx+7/eSkXxbt8Itt1RdjZnZpOGAGg/r1sG73w3r18OePVVXY2Y2KTigxkNLC3zpS8khv/e9z0PPzczGgQNqvCxYAHfcAfv3w3nnwRe+4O+kzMyOgwNqPF1+OTzySPKPvKtWwfvfD7/8ZdVVmZmdkBxQ423+fLjnnuQsE9/5Dvz2b8N118Fz9TiVoJnZicIBVYaWFvjkJ5PvolauhBtugDPPhJtv9mE/M7MmOaDK9KY3JYMnHnoILrgA/uqvkjOg+596zczG5ICaCOeckxz2u/HG5HLx55wDW7bAr37lHpWZ2QhKux6UFbS0wNq1cOmlcM01yQ1g9mw4+2y48EK46KLk9uY3J1fvNTObwnw9qCocPgw//CE8/nhye+QR2LkTXn01mb94MXzwg8ntwgsdVmY2qY10PSgHVF0MDMCjjybB9e1vJ4cC+/vhjDOS76/OPTe5nX02vOUtyT8Fm5lNAg6oE81zz8E//3NyOY+HH4af/hQGB5N5bW1JSC1eDHPnwpw5cOqpyaCMxYuT27x5MGOGe19mVnsOqBPdq68OHRLcvTu59fQkQfbcc/D880MBlunogDe8AWbNSsJq+vTkfubM5HbKKXDyyXDSScn9jBlJz2zaNGhvH5o+c2aybltbcmttTW4tLUP32ePW1mT9trbkXhq6DQ7C668nvcWIoe3lt+lANZtyRgooD5I4UcyYkRzqu+CCxvP7+5PAevJJ+MUvoLcXDh5Mbi+8AK+9ltxefRX27YNDh+Cll+Dll5NbXf5QkZKwywdbxFB9LS1DgSYlYdffnwRfcV4mv372eHBwKNDz+8r23dIyfL1ijVmQT5uWLNPXl9RR/CMhH+LF8B2pRhgK7PwfAy0tQ6+3ry/ZV/aHQFvb0Pay1/f668kNhv8xkC0nJfP7+4e3YXG/WXtkt3x75X8+jdozmxcxfDvFbWR/uGQ159si/wdQ9sdTR0fyPKt9YGD4+yf/Mx4cPLK+/OsqvueyZbJ1svrztWc/h4GBpI6OjuSPuOz9UNxXS8uRP+d8W0ckrzvbX35fWZtkrzF7j2fbzG8339b5n2HxtWQ15JdrbR3+c8jae9q0od+p/B+b2Xvs4ovhU5868vdkHDigJotp04YO71166dGtG5EM3Hj11aFf+L4+eOWVJLwOHUrCLXvzDgwM/wDM/3Jl87Pt5H8hsgBpS9922fayD8d876r4y5b/xcj2ETH04dzaOryHVpT/8Mn/8mevv/gLPDg4fL95g4NDr6+/P5nf3j70i5xv1/wvcrHN84+LH+pZe2Ttmt1aW5N9tbcPfVBmbZiX//ArtnX+NRc/hPI/1/x+8x/yxQ+64gd8vi2LbVjcXnbLfoZtbUduK98eAwPJe7WvL3nc0ZH08LP3VLbvYqA2qq9YRxYq+fdrtm7x51l83732WlJXf/+R+8o+8PPhl7VF9rryQZHtK/vdytolmzcwkOwve48W3+PF91DWHvk/wrLliz/vfFgNDg794ZXVkn/fZO175plH/r6Nk1IDStJy4EagFfhiRHy2MF/p/PcArwD/MSIeTOd9AvgLIIBHgY9ExGtl1jtlSclff9OnV12JmdlvlPaPupJagZuAK4ClwDWSlhYWuwJYkt5WATen684H1gJdEfFWkoBbWVatZmZWP2WeSWIZsCci9kZEH7AFWFFYZgVwayR+BMyRdHo6rw2YIakNOAnYX2KtZmZWM2UG1HxgX+55TzptzGUi4lfADcAvgaeBFyLinkY7kbRKUrek7t7e3nEr3szMqlVmQDUaL1wcEtVwGUlzSXpXi4EzgJMlfajRTiJiU0R0RURXZ2fncRVsZmb1UWZA9QALc88XcORhupGWuQz4RUT0RkQ/8HXgkhJrNTOzmikzoHYASyQtltROMshha2GZrcCfKXERyaG8p0kO7V0k6aR0pN+7gd0l1mpmZjVT2jDziBiQtAa4m2QU3uaI2CVpdTp/I7CNZIj5HpJh5h9J5z0g6WvAg8AA8BNgU1m1mplZ/fhUR2ZmVqmRTnXkCxaamVktTaoelKRe4Knj2MRpwLPjVM5k4PYY4rYY4rYYzu0x5Fjb4s0RccQw7EkVUMdLUnejbuZU5fYY4rYY4rYYzu0xZLzbwof4zMyslhxQZmZWSw6o4TyUfTi3xxC3xRC3xXBujyHj2hb+DsrMzGrJPSgzM6slB5SZmdWSAyolabmkJyTtkbSh6nomkqSFku6XtFvSLknr0ulvkHSvpJ+n93OrrnWiSGqV9BNJ30qfT+W2mCPpa5J+mr5HLp6q7SHpE+nvyGOSbpc0fSq1haTNkg5Ieiw3bcTXL+n69DP1CUn//mj354Ci6av/TmYDwF9HxO8CFwEfT1//BuC+iFgC3Jc+nyrWMfwExVO5LW4E7oqIs4BzSdplyrXHKFf6nkpt8SVgeWFaw9effoasBM5O1/mf6Wdt0xxQiWau/jtpRcTTEfFg+vglkg+g+SRt8OV0sS8D762kwAkmaQFwJfDF3OSp2hazgHcAtwBERF9EPM8UbQ8aX+l7yrRFRPwrcLAweaTXvwLYEhGHI+IXJCcFX3Y0+3NAJZq5+u+UIGkRcB7wAPDG9PInpPe/VWFpE+lzwHXAYG7aVG2LM4Fe4H+lhzy/KOlkpmB7jHKl7ynXFgUjvf7j/lx1QCWaufrvpCdpJnAnsD4iXqy6nipIugo4EBE7q66lJtqA84GbI+I84GUm9yGsER3Nlb4NGIfPVQdUopmr/05qkqaRhNNXIuLr6eRfSzo9nX86cKCq+ibQ24E/kvQkyaHed0m6janZFpD8bvRExAPp86+RBNZUbI+RrvQ9Fdsib6TXf9yfqw6oRDNX/5200qsW3wLsjoh/zM3aCnw4ffxh4J8muraJFhHXR8SCiFhE8j74XkR8iCnYFgAR8QywT9LvpJPeDTzO1GyPka70PRXbIm+k178VWCmpQ9JiYAnw46PZsM8kkZL0HpLvHrKr//63aiuaOJL+APi/wKMMfe/yNyTfQ90BvInkl/OPI6L4BemkJemdwLURcZWkU5mibSHpbSQDRtqBvSRXvm5hCraHpE8DVzN0pe+/AGYyRdpC0u3AO0kuq/Fr4L8A32SE1y/pb4E/J2mv9RHxnaPanwPKzMzqyIf4zMyslhxQZmZWSw4oMzOrJQeUmZnVkgPKzMxqyQFlVjJJr0t6KHcbtzMxSFqUP7O02WTSVnUBZlPAqxHxtqqLMDvRuAdlVhFJT0r6O0k/Tm9vSae/WdJ9kh5J79+UTn+jpG9Ieji9XZJuqlXSF9LrFN0jaUa6/FpJj6fb2VLRyzQ7Zg4os/LNKBziuzo378WIWAb8D5IzmZA+vjUizgG+Anw+nf554F8i4lyS8+HtSqcvAW6KiLOB54EPpNM3AOel21ldzkszK4/PJGFWMkmHImJmg+lPAu+KiL3pyXqfiYhTJT0LnB4R/en0pyPiNEm9wIKIOJzbxiLg3vRicUj6T8C0iPivku4CDpGciuabEXGo5JdqNq7cgzKrVozweKRlGjmce/w6Q98tX0lypegLgJ3pRfbMThgOKLNqXZ27354+/iHJmdQB/hT4Qfr4PuAvASS1ple7bUhSC7AwIu4nufjiHJKTmpqdMPwXlVn5Zkh6KPf8rojIhpp3SHqA5I/Fa9Jpa4HNkj5FcjXbj6TT1wGbJH2UpKf0lyRXdm2kFbhN0mySC8f99/RS7WYnDH8HZVaR9Duoroh4tupazOrIh/jMzKyW3IMyM7Nacg/KzMxqyQFlZma15IAyM7NackCZmVktOaDMzKyW/j9OCNlG7Bf5kQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# take the mean of each minibatch epoch\n",
    "cost_avgs = [np.mean(x) for x in nn_mini.cost_]\n",
    "\n",
    "plt.plot(range(len(cost_avgs)), cost_avgs, color='red')\n",
    "plt.ylabel('Cost')\n",
    "plt.xlabel('Epochs')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using different optimization techniques\n",
    "While the above implementation is good for a number of applications, we have yet to use more advanced optimization algorithms. Why is that? Shouldn't we remedy this situation?\n",
    "\n",
    "### Self-test: Should we try quasi-Newton methods on the MLP?\n",
    "- A. Yes. Quasi-Newton methods converge much faster\n",
    "- B. Yes. Quasi-Newton methods are guaranteed to find the global optimum\n",
    "- C. No. There is no guarantee that Quasi-Newton methods will work better in a non-convex space.\n",
    "- D. No. With so many weights, the Hessian calculation is too complex. \n",
    "\n",
    "___\n",
    "\n",
    "## Quasi-Newton updates for the MLP\n",
    "Let's try to perform L-BFGS with on the previous models. The easy way of performing this is to add wrapper methods to the `_get_gradient` function in order to pack and unpack the data into the Weights matrices.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import fmin_bfgs\n",
    "from scipy.optimize import fmin_l_bfgs_b\n",
    "class TLPVectorizedBFGS(TwoLayerPerceptronVectorized):\n",
    "    \n",
    "    def __init__(self, gtol=1e-5, **kwds):        \n",
    "        # need to add to the original initializer \n",
    "        self.gtol = gtol\n",
    "        \n",
    "        # but keep other keywords\n",
    "        super().__init__(**kwds)\n",
    "        \n",
    "    @staticmethod\n",
    "    def _pack(in1, in2, in3, in4):\n",
    "        '''Pack and flatten input vectors '''\n",
    "        return np.hstack((in1.flatten(),in2.flatten(),in3.flatten(),in4.flatten()))\n",
    "    \n",
    "    def _unpack(self, in_tot):\n",
    "        '''Undo packing according to layer weight sizes'''\n",
    "        start = 0\n",
    "        end = self.W1.size\n",
    "        out1 = in_tot[start:end].reshape(self.W1.shape)\n",
    "        start = end\n",
    "        end += self.W2.size\n",
    "        out2 = in_tot[start:end].reshape(self.W2.shape)\n",
    "        start = end\n",
    "        end += self.b1.size\n",
    "        out3 = in_tot[start:end].reshape(self.b1.shape)\n",
    "        start = end\n",
    "        end += self.b2.size\n",
    "        out4 = in_tot[start:end].reshape(self.b2.shape)\n",
    "        return out1, out2, out3, out4\n",
    "    \n",
    "    def _calc_cost_gradient_packed(self,W,X_data,Y_enc):\n",
    "        '''Unpack and get cost, gradient for bfgs'''\n",
    "        W1, W2, b1, b2 = self._unpack(W) \n",
    "        # feedforward all instances\n",
    "        A1, Z1, A2, Z2, A3 = self._feedforward(X_data, W1, W2, b1, b2)\n",
    "        \n",
    "        cost = np.sum((Y_enc-A3)**2)\n",
    "        L2_term = self._L2_reg(self.l2_C, W1, W2)\n",
    "        cost = cost + L2_term\n",
    "        #perform back prop to get gradients\n",
    "        gradW1,gradW2,gradb1,gradb2 = self._get_gradient(A1=A1, A2=A2, A3=A3,Z1=Z1, Z2=Z2, Y_enc=Y_enc,\n",
    "                                         W1=W1, W2=W2)\n",
    "        return cost, self._pack(gradW1,gradW2,gradb1,gradb2)\n",
    "    \n",
    "    def _cost_packed(self,W,X_data,Y_enc):\n",
    "        '''Unpack and calculate MSE for bfgs'''\n",
    "        W1, W2, b1, b2 = self._unpack(W)\n",
    "        _, _, _, _, A3 = self._feedforward(X_data,W1,W2,b1,b2)\n",
    "        return np.sum((Y_enc-A3)**2)\n",
    "    \n",
    "    def fit(self,X,y,print_progress=0):\n",
    "        '''Learn weights from training data'''\n",
    "        X_data, y_data = X.copy(), y.copy()\n",
    "        Y_enc = self._encode_labels(y)\n",
    "        \n",
    "        # init weights and setup matrices\n",
    "        self.n_features_ = X_data.shape[1]\n",
    "        self.n_output_ = Y_enc.shape[0]\n",
    "        self.W1, self.W2, self.b1, self.b2 = self._initialize_weights()\n",
    "        \n",
    "        # make initial matrices into single row vector\n",
    "        W = self._pack(self.W1,self.W2, self.b1, self.b2)\n",
    "        \n",
    "        if print_progress>0:\n",
    "            def callback(xd):\n",
    "                callback.counter += 1\n",
    "                if callback.counter%print_progress==0:\n",
    "                    sys.stderr.write('\\rEpoch: %d/%d (max)' % (callback.counter,callback.epochs))\n",
    "                    sys.stderr.flush()\n",
    "\n",
    "            callback.counter = 0\n",
    "            callback.epochs = self.epochs\n",
    "            \n",
    "        else:\n",
    "            callback = None\n",
    "            \n",
    "        # compute gradient optimum with bfgs\n",
    "        W_best,_,props = fmin_l_bfgs_b(\n",
    "                        x0=W,\n",
    "                        func=self._calc_cost_gradient_packed,\n",
    "                        maxfun=self.epochs,\n",
    "                        callback=callback,\n",
    "                        pgtol=self.gtol,\n",
    "                        args=(X_data, Y_enc))\n",
    "        \n",
    "        self.W1, self.W2, self.b1, self.b2 = self._unpack(W_best)\n",
    "        if print_progress:\n",
    "            print(props)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch: 77/100 (max)"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'grad': array([-0.0314416 , -0.01663592, -0.08509574, ..., -0.08705802,\n",
      "       -0.14729867,  0.31486622]), 'task': 'STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT', 'funcalls': 102, 'nit': 77, 'warnflag': 1}\n",
      "Accuracy: 0.9833333333333333\n",
      "CPU times: user 1.27 s, sys: 142 ms, total: 1.41 s\n",
      "Wall time: 408 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "nn_bfgs = TLPVectorizedBFGS(**params, gtol=1e-3)\n",
    "\n",
    "nn_bfgs.fit(X_train, y_train, print_progress=1)\n",
    "yhat = nn_bfgs.predict(X_test)\n",
    "print('Accuracy:',accuracy_score(y_test,yhat))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wow! That was pretty fast compared to the other implementations we have seen. But don't let this fool you. The L-BFGS implementation is great for smaller datasets, but minibatch/stochastic methods are more optimal as the number of instances in our data gets larger. Eventually they over power the L-BFGS algorithm's ability to move along the curvature effectively and efficiently.  \n",
    "___\n",
    "# Using a bigger, more diverse dataset\n",
    "\n",
    "Now let's load in a more diverse, harder to classify dataset: Fashion MNIST\n",
    "https://www.kaggle.com/zalando-research/fashionmnist\n",
    "\n",
    "**Labels**\n",
    "\n",
    "Each training and test example is assigned to one of the following labels:\n",
    "\n",
    "- T-shirt/top\n",
    "- Trouser\n",
    "- Pullover\n",
    "- Dress\n",
    "- Coat\n",
    "- Sandal\n",
    "- Shirt\n",
    "- Sneaker\n",
    "- Bag\n",
    "- Ankle boot "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# more data \n",
    "# Let's use Raschka's implementation for using the fashion mnist dataset:\n",
    "# https://github.com/rasbt/python-machine-learning-book/blob/master/code/ch12/ch12.ipynb\n",
    "import os\n",
    "import struct\n",
    "import numpy as np\n",
    " \n",
    "def load_mnist(path, kind='fashion_train'):\n",
    "    \"\"\"Load Fashion MNIST data from `path`\"\"\"\n",
    "    labels_path = os.path.join(path, '%s-labels-idx1-ubyte' % kind)\n",
    "    images_path = os.path.join(path, '%s-images-idx3-ubyte' % kind)\n",
    "        \n",
    "    with open(labels_path, 'rb') as lbpath:\n",
    "        magic, n = struct.unpack('>II', lbpath.read(8))\n",
    "        labels = np.fromfile(lbpath, dtype=np.uint8)\n",
    "\n",
    "    with open(images_path, 'rb') as imgpath:\n",
    "        magic, num, rows, cols = struct.unpack(\">IIII\", imgpath.read(16))\n",
    "        images = np.fromfile(imgpath, dtype=np.uint8).reshape(len(labels), 784)\n",
    " \n",
    "    return images, labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rows: 60000, columns: 784\n",
      "Rows: 10000, columns: 784\n",
      "-0.5 0.5\n"
     ]
    }
   ],
   "source": [
    "X_train, y_train = load_mnist('data/', kind='fashion_train')\n",
    "print('Rows: %d, columns: %d' % (X_train.shape[0], X_train.shape[1]))\n",
    "\n",
    "X_test, y_test = load_mnist('data/', kind='fashion_t10k')\n",
    "print('Rows: %d, columns: %d' % (X_test.shape[0], X_test.shape[1]))\n",
    "\n",
    "# don't forget to normalize\n",
    "X_train = X_train/255.0 - 0.5\n",
    "X_test = X_test/255.0 - 0.5\n",
    "\n",
    "print(np.min(X_train),np.max(X_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "fig, ax = plt.subplots(nrows=2, ncols=5, sharex=True, sharey=True,)\n",
    "ax = ax.flatten()\n",
    "for i in range(10):\n",
    "    img = X_train[y_train == i][0].reshape(28, 28)\n",
    "    ax[i].imshow(img, cmap='Greys', interpolation='nearest')\n",
    "\n",
    "ax[0].set_xticks([])\n",
    "ax[0].set_yticks([])\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qV78aAPDggw9i/fr1AJzdSXv3Eg6V0hTiSXk8Hnrz1113HXPN58+fj5tuugmA45VUO+TedbuE0q6jco3f7yeF4Xa7KU+Px2N49lq2cn1LSwsLSLSXl0ql2E3wG9/4xvjf4AmGUBM9PT08MNu9ezf77QwPD2PlypUAnAFAv/vd7wA4dKNcv2/fPnppDQ0NzL6IxWJ45plnADjerei4zkJJpVLHPRhjIkLrXT6fp3eey+Xo5R84cICFb4VCgWtUdz6tq6ujnmazWdIXbrebetfa2kovVkdTuVyu6iMoiV7y+TzvfevWrbRhDQ0NZDMymQx1TK9jbR9DoRCj0M7OTmY4Pvfcc2RLvF4vi+8qxbgY/q1bt/KH27p1K0+g6+rqaMQaGhooHK/Xa/Tq0Vkookg+n48n1qFQiAt83759VCQdJlUrdI8SXbwhylMoFIwsCs3rjwTNr+pFKmF5c3Oz8VnyfDVC0gOBIxvegQMH2FI4kUiwuFBPf0qlUtwUpTgGcH4PoSNCoRBD6VwuZ6TgCaLRaFUb/nw+z+8fCARokPS0srq6OsoKOLLxud1uo9JUrtEZKW6326gA1sZNqNzRjrecSNBnk7pFuvSDKhaLhoHXvfl1Rp6k0zY2NhozS8SR+cY3vkGqx+v1sqNBpbBUj4WFhcUkw7h4/IVCwdjB5LFuC6wPGnVGii4+crvdxjW6aERw6NAhHgQdPny46j3+j33sYwAc71wfjkmYV5o3fTyQ630+H+WfSCTo/Tc1NTGyikQiHMryP//zP1XXtkHuyeVykfqTzB35u+jj1KlTmany7LPPGl1PRdfmzJlDSmfx4sU8GN6/fz9pEC3Xao6WAPPeXS4X6S/JqAOAKVOmMPIJh8Ncj7lcjpFpKpWiTDT1mMlkjLbi4v27XC5DdtWevy/3mMvleBDb0tLCWgjgSHTf09PDXmXZbNYovhRd1YOoDh48SKrH7/ez7sLn86Grq2tU33dcDL9u1uR2u3mDyWSybIUaACMjRVMTupeHKE9zczPf0+v1UlGF66pmSB+ZYDBoNLCSSr3h4eFRT8jS2UHRaNQwkiLDYrHI5nnVZvSBIzrQ1NRkbJxyf5FIhIb82Wef5TVLlizh9KNHHnmE/Xn6+/sN6kd+nzlz5nB619SpU2vG8KdSKaPitlxhn56r4fP5jCl5mr7Vlef6zEnTuvo9Rd90ll+53l7VAC0H0b2+vj6ejWSzWd5joVAwnAiBlpueXtjT08M1evbZZxvFdHYCl4WFhYXFcWHcmt7obBwJY8RLEOioQPezkN1StyQozQDSp+bitVVKgUw0DA8P0wtoa2vj40AgYERK8lhPOdIDbEpb5mp6TbxdXUwSDocNj2Ms7V1faQgl5vP5jDBZDr06OjrYSXP58uW8PhqN8mC4sbGRlGF9fT2v6e3tpS4fOnTIoETks6rd408mkwatI4919Nfb28s+W+Fw2Fjrol/Dw8PUr3w+z2tKe3HJ47a2NlJGOqKoVsj95vN5HspOmTIFs2bNAuDIUPTH7/cbstLRo17fQvUkk0lGU6eddhoP4Ovq6ijPdDpd0SH5uBj+0gIiXX0mf9Ncvg4RS1sNa6Ou08OEv9UKIsKoVujWvh6Ph/cTCARoWA4dOmSkxpWbunU0ikYULBKJGJXBooThcNgIy6sVWjZer5eGas+ePWwUuH//fhar6ZTZfD6P559/HoBTXSqGP5VKGcZet8/VNEU1Q/hiwFlbkvmkdSqfzxv94wU6/Vr3nNGtmzOZDF+bzWYp9/b2dq513aOrWiF6EgwGybuHw2HqYaFQMKgeTeloZ1fkEI1GWS0diUQot5NOOgn33XcfALMqPZlMVmT4q1vaFhYWFhYV44T2N9Yn/TqTR1MT2rPQJeN+v9/IDJDS5yeffJLh5bEGkUx06IOdYDDI+y0UCqQqCoVC2bBQU2S6D4/8Ta7XOdTyuKenxxguXs3QMhRPvVAo4PrrrwcA3HrrrUaWmbRjiEQijCKfeOIJvjYYDDLzZ+bMmZT9k08+WVZW1a6DehCSzhgBzCEr5Yaq67YCOiPP6/XyGt1KXKOjo4PRl+4cW62QyK+urs4oghNd2rNnD+8xlUrRhmlqVidj6PcMBAJsO97U1ESdLBaLRuvmSjAuq765uZm8kzZAuieFy+V6yRg2wGwdrBXJ5/MZVa3SivSxxx5jylm1UxTSpApw5CGLpTRbQgx2LpejfHQanh4ErjfP0s1AFEkvxmoPsXXGk9CAxWKRvfaj0SjPMFpbW2m8n3/+eYbeZ599NjN5Nm3aRP06+eSTuVGUpiXK5+rCpmpEKBQy6CrtiMmGoLlnracAymacla5LMUp6kwyHw0Yv+Wp3QDTVIzpx+PBh9nfSFHVDQwPPhjTVEwwGjfeR1wQCAfahWrRoEUfSJhIJo89PJajuVW9hYWFhUTHGtM3KLqMPduQwA3A8htKOkoC5y2kvQJfF61YO+XyeJfjpdJregc78qUbofPFQKMToqLu7m31SNI2jPX6v18vrdY2EnoTkcrnotelsjNLsoGqGtO/QetbY2Mi6j4GBAaMgS3fzFJn19vYyomxoaMCLL74IwDl8l8jhvPPOM8rv5f315K9qRCQS4TpKp9NGHr1OnpAIUUc+esC6Xou5XM6YmCcecDQa5fvn83ljalQ1t70AYBzWiiz00JlsNmvQOHKInsvl+NpEIsG1G4lEKJNischD3Llz5xptxkXvK408xy2rR4yK9DkBXprVI9D0ju4fr2kKrVTJZJILM5PJGOcG1QxpLw04Bl5+6KGhIfziF78A4IyokwXY2NhIgx0IBIwMqHJy1pOoBgYG8Fd/9VcAnMpWoTA04vG4MWC7GiBGqL29nQvtoosuMiYZCZe/b98+pnCeeuqp5Jjb2tqot0NDQ7jssssAOPKT61etWkWjtW7dOi44XSVcjfB6vbyXXC5nbKByzqRTC3O5HNddOp0um1Ks+89EIhHSFPF4vOzGonW5WiF62NTUxCHoLpeLToceyajtlpa3zurRZ6K6sKs0PXa0hYTV7e5ZWFhYWFSMcfP4ZUfSg1G0J5rNZrmDaUoHMA+IylFAw8PD9Pjz+bwxhaqakU6nGfINDg4a3rq0Ev7sZz+Lb37zmwAcb1S8iVmzZhnhnc7v10OsxZO69NJLccsttwAAfvnLXxp9VQSrV6/G5ZdfPv43egKhez6JbE455RTDg5S5xtlsFitWrADgyF7K6V988UV6bM3Nzcxsqa+vZ4+aSCRC3X7uuef4u9XCJC65d529AxyhsVpaWowDWn2QqKdBCUKhED1Q3YlSH3Dqgew6s6VaIfqWyWSoP5rqDgQChi0UJJNJ40BXt6OR1/r9fupZacKGFBhWWk8y7oZfDDTgKIAUITQ0NBiLUVematpHZ0uIYYvH47xBPeKt2nt4u1wu8nXlqBfAaeImjdw09JD60gWr6aCRIHLO5XLkWu+9996qM/yyILThmT9/PtPopk+fTqrH4/HQ+ORyOerjokWLmOFTLBaNdGGR4Wte8xrOligUCnyfau8X5XK5jElYWg+FOquvrzfuU2fblUvD1FRPPB6njmvO2+v1cn1rWqNaoQ2zlo/YqIGBAdJcui29x+MhjabPVPTZSLFYZNZkLpdji3pdVGizeiwsLCwsjopx8fg15aJbKCeTSe5aPp+PGRher9cYJq7fR3b+xsZGDmrYv38/r9cHStXesuHrX/86/vu//xuA4xlpL+BY0DKsFCeddBLpj9bWVoblMjmtmiD6sn//fmaUzZ49m3/v7u5mm9xcLme0YBD90b130uk0Iym/38/unNOnT2dklEqlSPvIgIxqhV5/LpfLoK42b94MwKFv9fO6TkTXngi0LuvDS50B5fP5SJel0+mq9/hFH0KhEPXqrW99K6PH7u5ug5YsVxAn/wcc2ymPU6kUbWFLSwvOOOMMACZDonX+eDAmw6+rbHU1meBd73oXv3B7e3vZalGdJaBPqX0+HzcR4WXltbXSpC0YDFI+y5Yt4+MbbrhhxNeUo8U0Snv4lGuQ9ba3vQ233XYbAOcc4J3vfCcA4D3vec/YbugVwLx58wCYE4v0pK3u7m6mXpb2lCqH0kpy4WunTJmCdevW8RpZrDIStFqhU6vl/4Apn2g0amT+CHRVuW6vDhxxyrxeL2ki/dpsNkunMBgMVv15nRj4fD7Ps6bbb7+d9mzdunU499xzAZi9enRasabI8vm8cT4gfb3cbjfe9ra3AXDmZwilqRvtHQ8s1WNhYWExyTAmj1+3VpYdTA4eAOB973vfWN6+LPRhlFBH1Qwd7soh2L59+/j3TCZTtgiu0qEp2uN/1atexfeMRqP4+Mc/PvobeIUh9E40GqU+SrEfAB7sjha6sEi8+8HBQeb3V+ppTTTE43Fs3LgRgONZnnbaaQAc/frMZz7Dx2PxyPVhp0Bnv+h6k2rHrFmz2A12xowZvPfLLruMlKOmwnTHUn3om81mSTl6vV686U1v4meIfi9btmzUdTdjMvwS3ixZsoQckw59S/nD8cANN9yA7du3AwCnJlUzREY/+MEPSG3p6ucTUdgydepU8tXV3hJXmvdde+21NNLaWOuU4tLsp+OBLqKRDLUbbriB9JH0YqlWzJ07l9RifX29YUiOt/X3sVCuuHDp0qWUZz6fr3o5Cq677rqyz996663j9hmShjyW96zeFW9hYWFhMSq4KgnhXC5XL4A9J+7rjAtmF4vFCTu408pwbKgS+QFWhuMBK8OxYUT5VWT4LSwsLCyqH5bqsbCwsJhksIbfwsLCYpLBGn4LCwuLSQZr+C0sLCwmGazht7CwsJhksIbfwsLCYpLBGn4LCwuLSQZr+C0sLCwmGazht7CwsJhksIbfwsLCYpLBGn4LCwuLSQZr+C0sLCwmGSpq9j5lypSiDBM4GhKJBABg165dHK8GHOnHXSgUOO6toaEBAwMDAEYejTdjxgxMnz79uL7j7t270dfXNz7N/08AjleGGnrwjAwbqaur4/PFYpEDHHK5HB9nMhnOTGhtbTUGuhwNE1mGxyO/RCLBoTaxWIwDLUKhEPUxm81S33w+H3U2GAxSZtlslrNmQ6EQh+bILIOjYe3atX0TtbNkpTpYql8iTz3DOBQK8ZpDhw5h6lTn1ltaWsqOXD0eVLsMi8UiR1DKSEvAme0ga7e/v59/c7vdlGFdXR2am5sBOPMKxB76fD5j3OXRcLR1XNEvMWfOHKxZs+aY161fvx4AcM011+DFF1/k87JgYrEYh45cfPHF+MlPfuJ8Ga+XN5PJZLg53HjjjfiHf/iH4/qOej7vRMTxylBDZsnedddd6O3tBQCsXLmSU4symQwN3eHDh3n9vn37OLThPe95jzGQWRSpnPJMZBkej/yeffZZ/O53vwMAPP744+jq6gLgDG3ZsmULAKC3t5f6NWPGDDz99NN8f5lC1d3dzWEhy5Ytw5VXXgkAnLB0NLhcrgnbsrdSHSzVL5k+dujQITptp5xyCvXuP/7jPziQ5Oqrr+Ys6cbGRmO+77FQ7TJMpVLYtWsXAKCnp4drrrGxkXOIf/CDH6C7uxuAMwhH5Lxy5Uq85S1vAeDMxZYNpKOjA7NmzQKAYzpyR1vH4z7e6bbbbsMtt9zC/4v3pAcqt7e303vas2cPJ0653W56E36/nzd7880342c/+xkA4C9/+UtVT4waDXbs2AEAmD59OlpaWgAAv/71rynPpqYmeg0zZszAOeecA8CcqDQwMGAY/lqE6N2jjz6KmTNnAnBkI+MXE4kELrvsMgDO+DvxqKZMmYKzzz4bgON8RKNRAI4Oime2adMm/PnPfwYAXHnllZxaVatIJpM4cOAAAMfwy8Sx9vZ2evDBYJCG7S1veQsuuOACAMCnPvUpXHjhhQAcmYunH4vFaPjD4XDNrmOJHv/0pz9xvU6ZMoW2MJPJ0OZ94QtfoI7lcjlOj3O5XNwEwuEwZT4wMIAnnngCAHDuuecedxRfinEz/GKkP/3pT9PY6BmSmUyG3uXg4CDn5ebzeQpEXgM44ZAIob6+nh7Z3/7t3+J73/veeH3tCYnSkZUin1AoxMUVDAbpbZ166qncSJuamri4UqkUZyDrcYS1iO7ubqxduxaAM5pOz3nVVI/MM45EIvRcd+zYYeigpjUCgQAARy/F03rqqafw7ne/G4BDVVY7ykV/u3fv5lrs6OigDPP5PBYsWAAA6Orqwo033ggA+PjHP06983g8nKfr8XgMSk0eDw8PU2drDRs2bADg0KsSMaZSKTpnHo+HHn8ikSCdqOWmaUb5G+DMkBa57d27l79FpajNLdfCwsLCYkSMm8cvvH4mkyGXn81mDe9VQrtAIEBvwu12M9QpFAoMbwAwvEylUowifvOb39Ajq4QvrCaU8u4vvPACAOCb3/wm/uqv/gqA471efPHFAJwDNAkvM5kMoy/t7YrnMdJnVDvuvPNOY1C4nH8AJhcqXpT25n0+H0Npn89H+dXX1xuerjx2uVz41a9+BQB417vedaJu6RWB8PR6APrw8DDXdCqVogxnzJiBQ4cOAQCam5u5HvP5vPFYdK1QKHDtAkdYAvkdagHZbBb9/f0AHFpM9NDr9dIW5nI52kKXy8XHHo+Hcs7n83yttqH5fJ62s7+/f9S2cNwM/+rVq/lYfuhSykL+r398LYREIkFj1t/fj40bNwKAEYYPDAwwTKqFMHskiIy6u7vJRd944438gefOnUsuOhqNcjHm83mGi+FwGJs3bwbgGLGOjg6+/9EOd6sRa9asIW+aTqd5X5pHdrvdNDKFQoEyyGQyDMMjkQg3UTFMgLORaGflwQcfBFAbhl/rgNz7E088gYULFwJwDL/Iyuv1MjPK5/NRN7PZLB04nb1TLBYNoyTGLBgMciOtJcMfj8eZgFFXV8fzJW3z3G43ZRIIBJjo0tfXh6eeegqAw9/LNYlEgq/3er10jrPZLH8L7fQcDyzVY2FhYTHJMG4e/7Zt28o+fyyP0uVycWcrFotMlWtvb8cnPvEJAE6oLqF4oVDA7t27AYBpd7UISRULBAKYN28eAGfnFy9/165d3OXdbrchZ/GgWltbccUVVwAA9u/fz+yg+fPn14ynL9REd3c3M3n6+voYAXm9XoNiFM9eH5wFAgHDI5PDuba2Nspe154EAgEeEpcewlU7xLPPZrNMfZ0zZw6jbL0WxWMHzBx07dHqiCufzzMq0NcXi8Wa0cdoNEqd2blzJynWTCZDyjEYDJLGTqfT1Mmf//zntHlXXHEFvvnNbwJwonWJ4nO5HFPkTz31VOp/pR7/uBl+yZAATBrhWJRCsVg0ikC+9rWvAXCURPiuXC5HhQGOnCfUquE/cOAAeUIJtwFnMUohW0dHh1EQp7k+yeDJZDJcsO3t7VzITU1NaG1tfXlu5gRD0gm1jni9Xi4yTTfqxacNvc54crvdTO3U18diMcOwibHfv38/5s6de0Lu7ZVAT08PAOCcc84hZREKhVBfXw/A0TWRl167uigpl8tRPtopKRaLvEbbhloy/IODg5RVOBwmLaPpar/fj/vvvx8A8Hd/93c46aSTADg09n/9138BAO655x78y7/8CwDgjjvuoB4eOnSIWT065b1SWKrHwsLCYpJh3Dx+CUUAjLiTy2OPx2N4T/wyXi8PhkoPhvUBkVAWtYpEIsFQcHBwkIc/hUKBh2P5fN4o3dZ0gzz2+XwMBVOpFOU/MDBQMx6/1DKEQiF6VX19fUaxjI6ARN/S6bSRfSbQmVDAkcigUCjQW00mk/wddBZatSOTyRieusgwGo1SDq2trYZ8hGIYHh7m8/X19azWDYVCXNPZbNbIOJPfIp/P10wxVzwe57psamoyIiWR7QMPPIC//du/BQC8853vxN133w3AoXeli8Hdd9/NSPJf/uVfeIheV1cHaRWRTCaNSKISjLvhd7lcRjgnKBaLRlbPSBSQTgMbiQOsVcMvC2f37t2ssj1w4AAVqb6+3shW0WGeKFVzczOeffZZAI5inH/++XwfqSKUzI1agLRj0HqXTCZ5zuF2u3m/zc3NRkGhziYRw6NpnFKHQ+i32bNn87eSM5dagO5f1NjYyFTNGTNmMDvsa1/7Gt72trcBcIzQ3r17+VrR2eHhYcpq5syZWLlyJQCn3YNe0/o8oZbOScShePTRR7l2Ozs7eb+33347PvjBDwIATj75ZLz2ta8F4BQeimzvvPNOnlkJnQY4OinOXCQSMZyWSlAb26yFhYWFxXFj3Dx+HfLqg9hKMRJNpKkf8TJqDevWrQPgeJFSo/D000/TG2pqajKyVcRjTSQSRnGRZATt2LGDLR5isRjfU4fu1V4EJx5VIBCg3qXTacpJF3Lp/P5gMMh714WGOlpwuVx8vd/vJ33R3t5Oj7aWqJ50Ok29CAaDBu0qxVwrVqxg64pkMolly5bxsW5JINHl9OnT+T6RSATbt28H4FBGEmVpj7ba4Xa7SS02NTUx6WXBggU8LN+wYQPuvPNOAE5ygmQyfuELX8Ab3/hGAI6NE32ORCIvSVIAzMP1SjFuhl++mNvtLkvjuFyuskU1epPQN+f1eg0qQ17rcrmwadOm8fraEwqLFi3iY/lBt23bRr6/paWlbFW0rv7bt28f3vve9wJwFq8oWyqVIt+YyWSM/jXVDK1TYqQXLlxII5RIJHie4fV6jcUkFJCmdHRlZDwe5/XNzc2kMuLxODeH0TbJmohIp9PUB7fbzeIgj8fDTW///v3MpNJnSP39/ZTh2972Nso/mUwaKZzSO2r27NnUZb3uawFy71OnTqUDojl+AFyj27dvx1lnnQXAcSJEhn6/n/YgEolQhplMxnDaRut4WKrHwsLCYpJh3Dx+KaryeDz0PkfayfWJvu7VU+rxa49MdjmXy8XOnrUGffAlHv/w8DA9rBkzZtBT10Uy2pPN5/M4ePAgrxGPeOvWrSwm0fm/1e7x61BXPP45c+bwYLJQKPAaPUREUzq6d1Q8HjfaE+g6CJGfDsOrnSrTSKVSxroUffT7/Yw6t2/fzrYq06dPNw63pSWI1+ulXILBoPE+InMdsdYS1ZPP57m2Ghsb6f1nMhnm39fV1eG8884DAHzyk59kssp5552HO+64A4AT3f/4xz8G4ERi8rtEo1HqpGS0jQbjYvgzmcyIRVs6zBOMlLqlrwfMDB/N/dcqxCjpatPBwUGmdekFUl9fX1amgUDA4LElFN+yZQuVLZfLjTobYCJDqInm5mYOt4jFYuyXovudezwe6pJeWFqmuVyOhs3r9RqTt2Tx1ZI+6kynXC7He9RFW16vl9O1fvnLXzJj59lnnyXtsGHDBnR2dgIAfvWrX+Hzn/88ACfbRTbYVCrFM6exnAlONPj9fiPDUacVi2y//OUv49vf/jYARz4i2ze/+c0444wzADg9oCSNe2hoiOmcPT09/F3S6TSLvyrNjLJUj4WFhcUkw7h4/Jp60cVZgUDAKOnWwzFG8vrLRQg6w8fn8xkFJLUECRH1FKgzzjiDHkEsFmMHymw2S29C50Rr6Ba6r3/963mwFg6HjVnItQKRX2ltiPw/kUgYUaT28iVsrq+vpw7W1dXRQ9VdZH0+HwuXaslbTafTpHQymQw98kgkwky61atXUx/Xr1/PkaiS9QM4+egyIKS7u5uTvE4++WTSHQMDA6SGakEXtd3S07J0R1yJvt/whjdwXd57773s9HrOOefgrW99KwCH0pHri8UiI/S5c+eyTbs+MM7n8xV5/ONi+AcGBozsBt1DRi9C3bhJ9+AXlBqwkbJ/BGOpXJuI0Py9pAu+7nWvY3pmNBpl+AccyR7QFIbm/nUFcEtLC88KWlpajF41tQLRHd2uO5VKkaLR7YL9fj/lXVdXZ3DVOmtCZJnL5ZgVlc1m6ezUkhOizyui0SgpMo/HQ117/etfT3rhQx/6EGmHSCRibJJizGfMmGH06pEMqy1bthhnWtUOvXnJ5rZx40ZjDoboSjqdZtrmeeedx/NR4AhvH4vFKE/dIHBgYICU2syZM8u2uj8eWKrHwsLCYpJhXDz+RCLBgwt9UKYpGu3llx7iloPOp87lcmUPd1OpVE15/FomsqvPmTOHh2k9PT30GnQPGp/PR49MH8QBR7y4UChEryCfz9dUJgVg9tgJh8M8YAsGg9TH3t5eUjRapzKZDGWsM3/04JZAIEC56nx3HUVUO1KplBEtSqGWHkx//fXXMxLQ+eUul8so+NKRvvwWyWSS0VhfX5+hs+XaZVcT9HoS3fD5fGzfPX36dMpKD1apr6/H0qVLATjy0bVLmiYX2e7cuZO2QUfulUZN46K1u3fv5uLKZrMGd6rHrmkerFzxkTZ8enybTv0qV8FWa9C0WUNDA3/0oaEhprhGIhEuKD202u/3l90MfT6fEQ7Wiuw0HaiL0iT0DoVCDJ/D4TBlm81madTr6uoo12KxyGt0PySPx8OwvXQIe7VDr0VZc8lkkhRZb28vDXNrayvpncOHD1M+DQ0Nht7K9doJcblc1NV8Pk+ZB4PBqqd7dIGp6ITP56Me6kw9nZ6uC7BKW1iXS4svFotc34FAwKhMrwSW6rGwsLCYZBgXd6W7u5s7ly7gKm3TcLSCrlLoHW+kNhC14rUKdK8Z8aT8fr9RLCSepm4xnMlk6AUUCgV6GfF4nB6XnnGqBz9XO8RzyuVylJnP56Pn6vP5jBoH3VpEkEql6KHqaVy60E0fXrpcrpppaw0c0TtdOOj3++nBp1Ip3nsikSAd4/F4jNbg5ZIx9DqOxWKkjJqbm5nAIJlq1Qw9BEjbKLlfXRCnD9FLsx1FzrooEzhC+wjNJu852vqmcTH8dXV1zB6Jx+PGQGW5Sb0JjAT9d53yqYdh6/F5ow1zJirEyNTV1RmNmERhWlpajN4fukFZOaUqNWKSHqazLqodummdpl1ElvpsSWf4aI4/nU4bU+CEgvD7/ZRnfX192Srh0U5AmkgQXdDFl36/n/LUFKEuFNLrTxe3adnqQi19fS6Xozx1X6Bq7X2knTOxY/l8noZfb4AjvVZD/xZut5s2LxKJGOnzeqZBJbBUj4WFhcUkw7h4/LFYzBiYLqfU27dv566ud7BCocDHelanXCfvI15vW1sbdzYZvAE4PVMkp7gWILJKJpP0tpLJJO95wYIF3Nm9Xi/lE4vFjFbC5Q7U9W+kva1qh9xHPp83sim056gnkukiLz08XWSWy+X4fCqV4vXDw8OMagOBQNVmn5SD3LuubdAtPfSAFk0TllITOgtF1qv2+DUd0dbWRtn29vYaEUM1olz2Yn19PWdk53I54wBYy6Jc0kvp4a5ERG1tbZyLnM/njbVeCcbF8G/evNkogHn/+98PAPjc5z7HDIDjhRagZK2sWLGC02i+973v8dp169bhkksuGdN3n0jQVIUevSjPh0IhykSHdpoW09SDpif27t1rFH9Va0hdCu1wCJVQKBSMClGtUzo01uG5yEMbM5/Px6Itn89n0Jk6lbbaIfIJh8OUp3bOstms0RBQoOce5HI5QyfFEenr6zN68uhNQxvIWsiOAhxZyhqcMmUKqZ7e3t6yVPdIFHjpLBLZkKdMmcIzEV1NXinHb6keCwsLi0mGcdlm9+7dyzA7kUiwY18ikTAyLcqdQJdSDuX+1tTUhCVLlvB52Q2lB0itQO43Eomw0OjAgQNl58TqcFp7sn6/36A2BHPmzGExif6saofowtSpU5lZ5na76SENDQ3R+0+n04xA9RBwDa/Xy740M2fOJAXR09PDqMDr9fJxLUROskb12qurqzMKrHTSgOiOzqrTB7TZbJZeqcfj4WG51rm6ujquX919slohstIHsboGR9eNaJR66iNRN7qPl+ikjk5fkaye0lGIMo4tn88b3F25sYojZfpoRWtubuZ76r898cQT4/DtJw40LSbGPh6P49xzzwXgyK3cVDKddlgsFo0pPrr4S+iJbDZbM6mwuqe7yEzTMrppltvt5vM6k0dXjgaDQaMKXU8+kt9HFyXVwgYq07VcLhdTLFtaWnhviUSChlmvS13sVigUKLeDBw+SIgsEAmWdv9bWVvziF78AACxfvpyV05qOrCbosZOyAeomfzrddaQMH93bTKd/6ow1n89XdgOpVA8t1WNhYWExyTAuHv/8+fPZKrS+vp60T1NTEz2m0l3qWJ03tWdx8OBBDhHRebJnn332eHz9CQOhd4LBIGmLadOm4Uc/+hEA4LLLLuMBps66GIn2Ke2MKr9BLRxICnRxlniNXq+XBVb6UE13mfR6vfTcXS4XZVIsFlkkow+Mzz77bHpdv/3tb/n+teDxi1709/czEmxoaOAarKurMyhG3WVX5K9bEnR0dFB/GxoaGEV4vV7KPxwOc1iLpnGrFdpTF49/6tSplGc0GjWmj4kMdR8eHbXqbEc91Uvrai6XM/S2EoyL4V+wYAG/5Lve9S4+39PTY9AOOrTWX7Qc3aP77j/wwAOkjGbOnMk2ph/96EfH4+tPGMhiefHFFzl1q66uDp/61KcAAKeffrqxSer+SKIAWjH8fj8X3cknn0yFfP755zF//vyX4Y5OPGSz1OmEDQ0NTIHt7+83qiq13gn3rKskdVvrbDZLmW3cuBHnnHMOAMdQyvUtLS0n9P5ebuj+7mKku7u7KZNwOEzjlEqlSH+Fw2Gj8E2/nxi8gYEBZue5XC5s2bIFgDNzotoroculoedyOVJX0WjUWK/loGlanRbq8/m4jk866STqeSqVov5XOgLUUj0WFhYWkwzjRvVIuHb66afz+Ww2y7zzQqFAT2FwcJAhdGknSfE4gsEgPQd94q9zY2uJsgBg0BOSFdHU1ITzzz8fgBPtSL1EaetbTWeInN1uNz3SlpYW9Pb2AnCKufQBZTVD6J18Pm8chsn9NTQ0YPbs2QDMcFvnT+vukLlczkhIkKHtS5Ys4fWltRXVDlmj8XicEc7Q0BCnagUCAaNdc7kpZrFYjHSE7jipM6B0V9Pe3l5G7v39/ZS//FbVBl1PIohGo6SzLrroorJdiEspmnJ5+brgKxQKGddI9HCsdjilGBfD/4EPfAAf+MAHXvrmXm/ZU3pZrKPBM888M+rXVgs8Hg/76ixevBirV68el/eVhVZLlaeysBYvXsznWltb8Y1vfGPcP2vnzp0AgHPPPZfZQXrCUrVizpw5AJyqUD2/QQzMZZddNi6fM2/ePD6ePXs2Pve5zwFwetVXe+WufP9UKsUzIu1cjaeDoNuwix5W+v6W6rGwsLCYZHBVchrscrl6Aew5cV9nXDC7WCyOPqQ4wbAyHBuqRH6AleF4wMpwbBhRfhUZfgsLCwuL6oeleiwsLCwmGazht7CwsJhksIbfwsLCYpLBGn4LCwuLSQZr+C0sLCwmGazht7CwsJhksIbfwsLCYpLBGn4LCwuLSQZr+C0sLCwmGazht7CwsJhksIbfwsLCYpLBGn4LCwuLSYaK+vFPmTKlKL27jwYZNDA0NITDhw8DADKZDAdlyGiyUvh8Pg4UaG1t5cCVSnpN7969G319fZVNJXgZcTwy1LNeS8exCdxuN0ewbd26laMUXS6XMX9XrikWi8ZIxqNhIsvweOW3Y8cOAEAymeTwj87Ozor6vsfjcezfvx+AM1RIhtp0dHQc87Vr167tm6idJY93HQsGBgawd+9eAOaMYT0gxOPxUK9SqZQxSESG1nR0dFQ0i6OWZBiLxTgIqVAoGMNq9AxdPSZU1n1jYyOHNFWiv0dbxxUZ/jlz5mDNmjUveb50GpQYrd/+9rf43//9XwBAV1cXBgYGAAB79pTvZjp16lQqyXvf+1789V//NQDg1FNPfcnnAeWnzqxYsaKSW3rZcTwyTKfT2LRpEwBnEcngBb0B1tXVcQ7npZdeirvuuguAswBlOENdXR033mw2i/b2dgBHhpeMhIksw+ORXy6Xw5vf/GYAwIYNG3DSSScBAG677TaceeaZx/1ZzzzzDD72sY8BAA4cOIB3vvOdAIDPfOYzZT9Xw+VyTdiWvSPJcCT87Gc/w4c+9CEARyaSAS+dcyyG8IUXXjCcOxnG9MlPfhLXX3/9cX9uNcpwJH1YvXo1vv3tbwNw7ONvfvMbAM56FUfi0KFDnIDW2trKdX/55Zdzlvny5cuP+zsebR2PaQKXHlAtu9kNN9yArVu3AnA8fvG2gsEgd/tZs2ZxZFgwGKSxj0ajHNh811130ZhNnTqV4wf/4z/+wxhsXOnIsYkK7T1t2rSJk51CoRA9qVJvXhbUiy++SE/A5XJxMSaTSQ5jLhaL3Hj37dvHode1IkN9D7fccgueffZZAM5YUNHNK664ggbpve99L8477zwAjtESrFmzBnfffTcAZ8yg6OyMGTPwzW9+E4CzoX7iE594yefWGj796U8DAG699VaOAp01axbXdKFQoK5ls1k6GdOnT6dcXC4XHcEPf/jDuOGGGwCMHPVXO7Q+DA0N4d3vfjcAYPPmzbRz06ZNo+51d3dzrU+ZMoVjMKdPn05b+OCDD+K3v/0tAEf+t99+OwBzzG2lGLXhLxaLBvVw3XXXAXB2exk9FggEuINlMhn+2Pl8nuGNKIs8L5tJY2OjMTleFmMmk+ECrLVFNzg4CMDZDEeiE2SuabFY5IZQOkZR/l/6vBi4rq4u/hbHon2qEWvXrqW3JDOKAWfcn4y0/OlPf4of/OAHABy9E10Kh8PcRNvb2ynveDzOBbp69Woa/lqCdgKGhoZwxx13AACdBMDRv1K6B3jprGdNMYqOzZo1C7t27QLgeP+33nrrCb6jVxbXXXcdx3XOnj2b8snlcpTJSSedRJ1saGigoxGPxzm6MRwO0xZGo1F6/88888yoZ2fbw10LCwuLSYYxefyy2//xj3/E5s2bATghsexg+oAnmUwydIlGo4wEtKfQ2NjIHc/tdvP1+XyeUYQctunvAdSG9y9UzJw5c3j4c9VVV2H9+vUAQE7/aHC5XJRVW1sblixZAgB43/veh0suuQQA0NzczN+iljx+0aPu7m5DHySKTCQSpL7q6+uNiFWQy+X4vHj7AvG6enp6xv/LTzD85Cc/QTweB+CsS5GF1+ulnMvJuPSx2+3m/5PJJA8pH3nkkRN7A68g5CB848aNjNxTqRT1R8tQbCXg6JvIuVS2IsNwOMxzlm9961u46aabRvUdR2349aJ5+umnSR2k02n+raenh/xqIBDAueeeC8Dhst7znvcAAB544AEsWLAAAHDffffhgQceAOBQOhLGLFy4kBtFd3d3zdIU+tzjlFNOAeAokWyGpdypbHqFQoHPFwoFvs/+/fuxb98+AMA999yDL3/5ywCAj370o1ROOSeoBXR3dwNwaArJwMnn81xwLpeLCy6bzVJPi8UiqQmPx1NWxvl8nhRQT08PjaJsJLUAbWzuvvturq9CoUC5BQIBPtYoHeFaziErFAqkH7dt20aaVzaDWoGsrXQ6bTi4+mxSy0d0T1OObrfboLoF6XSaz69du3bU39FSPRYWFhaTDGPK6hHs2LGDO1UqlWIqYltbG73MUCiEefPmAXDSjO677z4AwKpVq3hoNjg4yEyCBx98kDvavffei4ULF/IayRLw+/01QfEI5B7T6TQPhRYtWsTwL5/Pl/WkNO3mdrv52Ov1MpMgEolQth/96EeZ2llL+OMf/wjAoWvEK9X1CzohQVMQLpeL1xQKBXpU+rGOFlKpFCnHk08++WW4s5cfjz/+OOtofD4fqcFS+QhK16HoqdZHHX2lUin86U9/AuDQmbUEsX+FQoFrt7GxkZG4rEnAkZPIUUcFwBHq0uPxvIQ+A0A2ZTQYF8MvSgE4CvDxj38cAHDTTTfh4MGDAIAlS5Zg48aNAByO/4UXXgDg0D7CmYZCIcyYMQMAcNlll2H69OkAnDz+O++8k9eUCzWrHel0Gtdeey0AZzMUZLNZI0Qsx6/qIi9NYejQMZPJMFUMAJ5//nkAleUFT3TIPemsEr3gNA3p8XgoM52lAhyh3DR9kU6nUV9fD8CR6+OPPw6g9gy/UBNNTU1M20wmk5SVNt5Hg95gBdrIud3umjX8UjxYLBZpG+vr6w0ZljtfktcApqOh5Z3P50mBHzhwYNTf0VI9FhYWFpMM4+Lx9/X18cA1kUgY+blf+tKXAAAHDx5kdsrw8DAPjnK5HA93hoaG8Lvf/Q4A8NnPfpYHnH/zN3+D733vewAcj0Q8VznAqwUEAgH86Ec/AgA8+uijjHY8Hg9DQ7/fz8f5fH7EfGodIWiqYtasWQCcQ2LJDCg9lKtmPPfccwAcGYiO7NixgxWlLperrLdaKBRekoEGOPIWPd21axfl53a7SUO+733vOzE38wpBvNVYLMaDa32gWCgUDKqiUohuBgIBPPbYY2P8thMTu3fvBuDoidjFAwcOYPbs2QBM+wegLIOho9ZwOMzEBa/Xy99FPmc0GBfD393dbYSFQlXceuutNPwAeOP19fUMgaZNm8bME5fLxayeBx54gIvr85//vFHcJGmPshBrAQMDAzwD8fv9vMfDhw8bRW6VQjbHuro6GkO3211zGVEAGALrLJSHH36YrRZ8Ph/1tDSTRygIfSZQX1/PgqMvfOEL+Na3vgXA0VOpDK41PPzwwwBemootbUAAk9sXHC2rR4zf8PAws8i8Xi+2bNkyrt99okCcKk3n9PT0sHVIPB43jH05Z0T/PRwO0x54vV7S4aXpxpXAUj0WFhYWkwzj4vG3tbXRI49EIti2bRsA4KKLLsKDDz4IwCwaampq4ol0sVjkKfiSJUu409XV1eG1r30tAIfekVz2RCIxptPsiYrNmzfTI49EIpg7dy4AR26S9bRq1SqWz7e3t9N7CgQCLATp7e3lwfmGDRuMvjNyOOnxeNjSIJfLjSl0n0iQArdsNsvHF110ET2krVu38r4zmYxR+1AOXq+XntbHPvYx0o29vb01GTEBYCGmy+WiXHK5HFtfiA4dC+VqTHRLFo/HYySF1BL6+voAOPoj0U4p7aohkcFIegjAyIaSSHWkA+Ljwbg0aYvFYvwSuVyOC21wcJAKkEqlmK7Y0tJCo/WFL3yB1We5XI7nABdeeCG5rHA4zM/K5/NjOs2eqIjFYpRJV1cXU+l+//vfH9frpVp3wYIFOOecc/j81772NQCOUZTnda+e7du3Y9GiReNyD680xDilUilunMCRHkWJROK4FossMl1o43a78ZrXvAYA8L3vfQ9dXV0AnLC9loq4hF4NhUK8x49//OM0+J/+9KfZAlwygMpBVz+LfFwuFwvfdGO8VCo16p4zExGSpdjS0sJ1pjsRaFpMb7AahUKBMsxkMqQfh4eHjfTu0cJSPRYWFhaTDGPy+HV+tC5z11k3t912GwBnCMPKlSsBOF7FsmXLADiho3TbTCQSOO200wAAd9xxB+mLcDhsdJqsRarn0ksvJeXV29tL2Zbm3+uhLOIR6NYC8jeB/C4tLS247LLLADg9RKTNrva8qhn9/f2UUzqdZj9+ALzX1tZWyhUw5aSLuXRbBw2ZD3HnnXfy+m3bto2pPe5Eg2SK6PX2kY98hK2AARiea7kCSl0o53K5SOm86lWvIg2pEY1Ga8rjFy/f6/UyQyyZTBqtqIVeLa1tkMc+n89gOWQWR6FQMOgjef9KhlUBYzT85fqe6PAjEAiwqObPf/4zvv/977/kPXSTtlIDplMa9cKsRcM/ODjIXjBC2wBmBkAgEDAM/7GqlnVGhcfjwde//vUT8dUnBPr6+iinQqGAN7zhDfybVEGX2xDleo1y/DQAphdrnZUzgFqB0BS6snvv3r34+c9/DsA5e9OtwY+VDuxyubiB7tu3j/SQniTV39/Pc6xqRzweNzKaRFa6946eq6HtZenzurW1UL+bNm3iexYKBWZESsbQ8cJSPRYWFhaTDOPi8WuqpxQSZk+dOpU7lS6XT6fTxsxJHQKJd6AHFwBHTs1rCalUiveezWb5WOfq6tC69ICoHEpDcaHO9JCHQCBQcZg4EdHT02OUuOvhIZIv3tLScswoqbS3jJazyMzj8dAb07NTawk6OnrooYcYCdTX1x81+0Sgo1RNWZTDoUOHaibB4NChQ4Z8RH+ampoMvdJUmL62XP+ofD7PA/JgMGhk9cgY20o9/jEZfjHMuieMfqxDHS0Mbcx8Ph+5Wc0N6sHrHo+HAtQpdrUEXcThdruNpmGCfD5vbIxazuVaCevX6x4fQ0NDxu9VC9i+fbvRmE0P9Rbj3NHRwUUz0gagm5CVprlK8Zfb7eZnlc6HqGYMDQ3RUfN4PMwye+655ygLnZ1yNGi6TGTe2dnJzCutd0fLDqo26P76eo02NTUZE8p0U8WRzuf02hVqzO/3G32QRpsSa6keCwsLi0mGMXn82pvXuc8a5XJXR2rVqnNXdThUegBSS16WQN+jfuz1esc0LEXTOHrgw/F0WKwmlEaB0mJAT8vy+/3HNeS7XNbKnj172HIkkUjQAyvt7FnNGBoaIo1aX19POWzcuNHoWDpSa3BNX8jfcrkcI6XNmzcz+tK1D7USdQKmHPL5PD3ycDhsZImVi9wBs5hLR/1yjc720W1HKsW4FHAdrc2ooJSCqOR53bCoVhGJRGik9cI544wz2Puovb3dGNgsyGQyVKpcLmdM8pLQc9myZfjkJz8JwAlHJUugluYZlEvD/P73v29U6B4tmwd46cKVx3fddRfnGch1tYZNmzaxRfLf/d3f4dJLLwUAvP/978e//uu/AjDTiMtx2XKN/M3v97N3zdVXX80CMWnXDqBmK3i1TDR1fbQzknIzDrSjrGlvXQ1cKSzVY2FhYTHJMC4e//F6P+UyUo4GfUCkP1OH67UybF3v3sPDwyyR3717N7tz6t2+lK4pd1hULBZJxz388MP0+Ds6OmqmcEugM200nnjiCYbMI0WOpYfhItdAIECa7cEHHzQ8fn2QXCtIJpP4+7//ewBOpClYtWoVe3HpyN7r9Rp6J9A9eeR9AeDyyy+nPuqWwtJXqRagI6JsNsvD8pkzZzLy8fv9FR2Qa2QyGdJEI7V7OB6Me3cubXh0yAeMvEjKhTH6ea/Xyz4zDzzwADMDagnvfve78ctf/pL/FznU19dzXoHP5zN+dEE2m6Vx8/l8xuD7ctTQqlWr8MY3vhEA8I53vIPV0tWMkRrNPf/88zTepZW45RwL4IhRTyaT5KJffPFF/v1YdFG1Ytu2bUaqoJxpLF++HCtWrADg8PTSq2doaKjstDKv18sMMmnYCDgt2MUQFgoF6nUtrWddqJXNZinDSCRipKGLjnm9XuN8VG+gIltdwHr22Wdj3bp1fH60joeleiwsLCwmGcbk8WvqRh4PDw/zFD8cDh8zb7rc+8l76nB66dKlAID777+fE5VqCQ0NDSxb11kOfr/faNcsOc+lQ5l1JKCpMLle5xdv2rSJfYGKxWJNePzTpk0z5CaUwvDwML3PkVoMjJSYkMvl+FrpVAk4UVUlel0tWLx4MXXnjDPO4JrzeDx45plnyr5GJ3joWpKRDh2lhctIQ9urHbrHUT6fZxKFHrxe6uVrnZTHHo+H76XbjF9zzTUcVtXQ0DBqj39Mhl83CxKcfvrprJQsnRp/LJTSPPL/dDrNBmNf/epX2dpVrqsF1NfX0wDp9E2/30/jfbQsCkHpItLVwIKLLroITz75JIAj/WeqHXV1dcZ5jyysaDTKnk/HC81bl0s1rKurozz1ZKpqx8DAAGmcHTt2GI3uRkK5oepHgzRq1I5drcyDAMwJWQcPHsR5550HwOkXJTrp9/uPeUZUKBSMKl6hic4888yyY0IrhaV6LCwsLCYZxqUtczab5WSja665BjfeeCMAxzPSLUePB7rfingCmUyG82h9Pl9NlXgLAoEAByp3dnbyebfbzWIhLUPdxlYXvgEwcvp16Cloa2sjVaHzqasZPp/P6A8jupNKpehpjVQoVNoDSVMQ5TLXfD7fqNvhTmR0dXWRRrjqqquMbJtynmnpc+Wy9nSCh9vt5oFuMBg8rrz2aobL5cLFF18MwGntIZlRU6dONWSluxOXG74SCATYkbi+vp6zxvv6+l4ZqkdSsrSBeec734lrr70WgMn7AUcUQqcijjSGzOVy0bjt27ePG0s0GmWqY6nBq2ZMnz6d91VK3YhxbmpqeklmCvBSGeowslylanNzM685nkrWaoA2wKXy0Bz/8TS5O9ZiikQiFY8irAZcf/31pFETiQSNFnBEJiO1ttY4Gv0qPZR09lmtjbHUVbmy0Xk8HqZQ62wczeVr/dSpsoFAgHIPBoNs257L5Yyzu0pQG1bTwsLCwuK4MSaPXw4c0uk0J2rpgxrdp6NQKBi7XLlukqWP9eB1iRAaGhqMOZa1BAl5RWYAsH79evzbv/0bAIfCEfmEw2HKWs+SzefzPBwOh8OkJDTlo3+jWvH4A4EAdUq3+C0UCgyxj7e8vZw+ajoiGAxS3rV0MPmRj3yEFGA6ncZ//ud/jvtn6C6f8nvVUrddHS3qbLtnnnmGhZgNDQ0jtgvRkZXuEivFX6FQiFFZPp8fNVU7aq3t7u7Gz372MwDOSDtd6SehW39/P41YLpcru4hGCgu9Xi+VUGfxvPWtb8VPf/pTAE4PETGKug1vNWL37t2Uj55+NG3aNHz1q18d189qaGgoW3FZzSgdzynQ2RS6X4rGSBy/rozU5wNz585leqfepKsdb3/72/H6178eADBr1qwTsqbkvKq1tZW95M8888xx/5xXCsVi0ZguJuvr2WefZbZjIBCgjcxkMnS+dJpwOp02nAqxgVOmTOHjQqHAzaRS1Maqt7CwsLA4boza49+zZw+efvppAE7mREdHB/8mBUfd3d3c8Y5nPqeGbv2gQ3TdcfJHP/oRPvaxjwGofo9/eHiYO39pL6JyB2vyN+Doh5M6yhIPIh6P05PduHHjeN7GKwZduKaH08+dO3fcP6uvr486eODAgXF//1cK+oB8wYIFxt/GUi9T7rXTp0+n7tVSQWZ/fz9pmXg8brAVJ5988rh8hlCXyWRy1O0uRm34ly9fjv/+7/8GABw+fJgFVsARPlmPvxsv3HTTTaSVwuHwCfmMVwJ33XUXPvOZzwCAUXCkWzSX4nie12cpgve85z0MEa+77roxfe+Jgo6ODpx//vl8rHGsdMGRCgdLJ5sJ3vzmN7Pw7dxzzx37l58g6OjoYCaPFFqdKCxbtoznT2OZNzHRsGjRIvzN3/wNAMcB0ZuaTtss1/VgJJT28Ln55psBOJPRpI12pbBUj4WFhcUkg6sS+sXlcvUC2HPivs64YHaxWJywvI+V4dhQJfIDrAzHA1aGY8OI8qvI8FtYWFhYVD8s1WNhYWExyWANv4WFhcUkgzX8FhYWFpMM1vBbWFhYTDJYw29hYWExyWANv4WFhcUkgzX8FhYWFpMM1vBbWFhYTDJYw29hYWExyWANv4WFhcUkgzX8FhYWFpMM1vBbWFhYTDJYw29hYWExyVDRIJYpU6YUZR5sMpk0BnzrOaXyuHTAheBogy/0tCmZPyn/l9fK8x6Ph8/X1dUBcGbX9vX1jX5c0AnGlClTisczcUim+HR3dxvPy5CbfD7PuZ2AM4hdnpeBD263m4+bm5vR2dkJAMbrymEiy/B45JdIJNDT0wPAmd0sk8cOHz5Meej5vHrKWTab5SSqpqYmpNNpAM7kN5nydjzTqNauXds3UVsKH48M0+k0h6D39fWhtbUVgDPUJpFIAHDkEAwG+VhkOzQ0RHl6vV4OWunr6+M67ejoMCZ+lUO1y/BoEPls3LiR9tLj8VCG06dPR0tLy5i+49HWcUWGf86cOfjxj3/MLyyDpgcHB/klfT4fIpEIAHNAtd/vNxaXGGxt7D0eDxdaJBLhlKhCoYD6+noAzoYjCtnY2EjlWblyJVwuF1asWFHJLb3smDNnDtasWcP/jzQ+UQas33bbbcbfxPjE43HMmDGDz8sGMTw8jKGhIQDOUGcZ0/aa17wGX/7ylwEAs2fPNj6/9LMnsgxHkh9wRIbr16/HHXfcAcAZTt3c3AwA+MEPfoD+/n4A5pSuXC6HVCoFAOjt7eV0rTe96U3Yvn07AGDJkiX4P//n/wBwdHyk3019lwnbq13LsPT3l2llO3bswC9+8QsAwHe+8x1cc801AJyxoGvXrgXg6NfChQsBOOtb1uXvf/97OiJtbW248sorAThT5pYvXw4A+PznP4/FixcDeOlIUUG1yHAkjOT4AqCdW7JkCRoaGgAA9fX1HOn5iU98Au94xzuO+r7HckCOto4rHr0ok+LlywKOsoiBmTt3LjcEAPS29AzdXC5HxdAIh8NUAr/fj2nTpgEA1qxZg2XLlvF5ueH6+nps2LABADBr1ixINFJN0D/eU089BcAZh7h7924AQGtrK6/x+/18fubMmRybGI1G8fnPfx6AEynIOEqfz8cN86GHHsLpp58OALjqqqvwrW99i9fUAlwuF7q6ugAAP/zhD3HSSScBcO5PNsvbb78d9913HwBg165dePHFFwE4jojo11VXXYWzzz4bgLOZimHr6enBP/7jPwIAvvzlL1c0Oq9a8NRTT+E///M/AZjR0axZs/Dss88CAC6++GJ88IMfBADs3buXjlcymcSUKVMAAO9+97u5sQ4PD3M29/z58zmj+Oqrr8bSpUsBAJ/61KewaNGil+MWX1ZovUgkEvjTn/4EALjnnnvw/PPPA3AicYmCisUibdgXv/hF/P3f/z0A4Mwzz8TrXvc6AMCNN944Lmu2IsNfKBRIQaxcuZKDhAOBAHbt2gUAOOWUU2jUU6kUDY94VIBJ4xQKBe5+4XCYYU9XVxfmz58PADh48CC91La2NipkPB7HrFmzAABbt26tOsOvjcbmzZvpGYXDYdIyqVSKMkmlUnw+mUziU5/6FABnSLZssLNnz+ZjPbS9tbWVm+q9997L3+uRRx45ofd4oqEX1/3338/nRAY+nw+9vb0AHCN04YUXAgAuvfRSOiuAI3PA2QT27dsHwJGx6GkkEqG+b968md5qtRt+l8vFNf2Vr3yFTltjY6OxjkWX7r33Xq6/k08+mTROMBikY5dMJvHcc88BcNaxGDav10tnzuv1Uv6f+9zn8D//8z8AjvwOtQKJ3L/73e/Sznk8HjIkgUCA6zuRSFDmra2taGxsBOAwKj/4wQ8AAD/5yU/w6U9/GgBw+eWXH7f3Xwp7uGthYWExyVAx1SM7tvYCZsyYQW8ok8lwF6qrq+Nu73K56D1ls1l6ZIFAgB6HvAZwdkXZxaLRKA/r5syZQw9u6tSpDDX7+/vR19dnHAhPdOhd+ktf+pJxUC0RUj6fN85A5GANOML1JRIJHrK53W56DW63m5+Ry+X4eN68eVi/fj0A4PHHH8d55513om7xZcXBgwcBmJy92+02vMi9e/cCcGQvuuPxeMhPa77Z7XbTGxNvDXBkdix+uprw6KOPAnDWpehRLpczIkZBS0sLPf59+/ZRnplMhms6l8sxctCH65FIxKB45Zq+vj5Stq961avG/f5eKdx///342te+BgA47bTTKM9cLmecf8rjXC5HWXV3d5PK3bZtGymyZDJJWvfCCy8cdYRUkeFPp9M0rKFQiB+aSCRIy3R2djLMA46cCWzfvp3Xn3rqqUgmkwCAPXv2UNlmzJjB64vFIlatWgUAWL58OQ8yfT4fzxeam5tpCJPJJLLZLKp1hvBjjz3GTU8baX2QCLzUMAnkmnw+z9fqjcXlcvH/iUSCBu2//uu/asbw9/X1AXAMeTQaBeDoqRgbn89n8KNizHO5nJFhIgecWpY6g0yMXa3gmWeeAeCcIcl6CoVCNMzpdNpI5BA5T5s2jTJsaWmh8zc0NEQjd/7552PHjh0AzGSPQCBgODdbt24FUFuG/6c//Smp6Hw+b9Db5c6IvF4v5dnc3Iy77roLgLMhi8NdX19POf/0pz/Fu9/97lF9t+p3VywsLCwsKkJFHn8wGGS2xK9//Wt6+X6/n2lvX/ziF3HOOecAcMI/8ZLcbjdTDvfs2WN4YRIJ7Ny5kxkYPp8PDz74IABgw4YNjBBWrVpF7+Ppp59mBssb3/hGtLS0VF2WyubNmwE43qrcey6XY669zssvRSXRTbFYNCIEkfkf/vCHUX3viYZsNksvv6GhgQeHU6dOpRfr8XjozWuvS9MaOkrK5/PU0+7ubuqdpITWCoRGCAQC9Obj8Tj1ETgSHQ0NDTFVdubMmfRiZ86cSflHIhHK85FHHmHaY2NjI/UunU7zPd1uNzOyagmawtYJB+l0mo8BMPrW6z6bzTJLCjiyXjOZDO3Bzp07R/3dKjL8LpeLp/iJRILG/tlnn2XY9utf/5rUzTXXXMOFpo2O1+vl/wuFgpHmqfP4xdgXi0VyZYlEgqlfF154IT+3WrMBfvOb3wAw5VNq+MtB1z+U+1vpNaV8tRgxvbirGalUirpZLBYpt1QqRVlqnh4wF5z8TRciBYNBGvmuri4sWLAAgLNJa8el2iH36/f7acgPHjyI6dOnA3DWq5yrXXTRRbjooosAmBtmOBzmWvd6vaQtf/nLX/L9vV4vdXNoaIjGz+Px8HymljAwMGAUnupzTVmX2v7J3wAzS0rbhng8Tp2TOqfRwFI9FhYWFpMMFWf1yO69fPlyegEvvvgiHnroIQDAr371K/z85z8H4Ozk4m11dXWx7Fsf7Oj8fgBGRoqEoB/84Adx8803AwA++clP8nBtaGiInlp3dzfGUkL9SkGyGfx+v5Gvr0vhBXrn17RFsVjk41KUUhelkCrMakdvby8jRJ/PR70qFovM2Mnn85SrRqFQoN5lMhl6q9lslvSk9uynTp3KAzaJMmoBLpeLkXMsFuPz8XicBVmrV68mBXvJJZcwkaOtrY0V40uXLmXR1pYtW3DyyScDcGQrOh6NRg17UNqapBbQ1tZmtL0Q2ba2tlLfdB5/Pp83WrJI9OX3+0kbDQ8PMyoYS5JBxYZfeLxUKsXFFYvFjAV1xRVXAHAyVWQx1tfX88bz+Ty/vM/nM1IwdY8PKWDQRu2yyy7Dbbfdxv+LYSvdQKoFYkBKoYvadGqioNTQa+qsHNxuN99H91OqhXREwOHd9UYo2WFnnXUWdVZnNunzJ4/HwzBcbwKRSIRUz+HDh5lZlkqluOhqwfBrnZGMuUwmQ30pFArUl/r6enzzm98E4BTByXneu971Ltx5550AnDUtGSkNDQ2GronzoZ0Qj8dTU+cmYs+Gh4epV/39/UxJDwaDBgUuxl47xLlczjiPko33xRdfNNJjR4vaWPUWFhYWFseNij1+8VAjkQhPladMmWL07hGvvbu7m/mnun+PzokuFApGl0/Z5RKJBE+1pe0DAJx++ukMn4aGhngANTw8XJU5/JK/rA++PB4PQ+2GhgajoV255nb6gOgoDa8oW92dU7fM0L9RtaGrq4v3l8lkSDskk0nDu9KJBAKdw5/P5ynDWCzGViEdHR2kNoPBIHsmnXbaaSfwrl4eaFmIbni9XjYMA45EoLNmzWI09aEPfQif/exnAQD/9//+X2ZPvfOd72RE1NHRQe++WCwaSQvlmphpmrNaITZSH36vXLkSF1xwAQCn8eIZZ5wBwLFzIh+dWKCzfg4fPoyPfexjAEDKGzjCvowGo+b4w+Ewf1xdIQocCR110zVNxdTX1/OaXC5nLEYJCwHQwGcyGSqDDpMGBwexZMkSAI6w0+l01Rl/MSb6pD8YDHLR6ZbXGqX3qQtCykGH2T6f7yWZAvIdqhUHDhzgvcdiMRrzoaEhUjehUMgoztJy1WG1vE80GsXcuXMBAAsXLsTtt98OwOGwpcHbG9/4xhN9ayccmnYRPWpoaGDWSGtrK9dfNpulTDZu3IhLLrkEALBs2TK88MILAJzKc3HIXC6X4WjI+yeTSUPfdPVqtUPsFgBuhosWLcJZZ50FwFnzOttHU5R6/YosUqkU5bl7926emUSj0VFnl1mqx8LCwmKSoWKPXx8EiUdQSi/onOjSTBR5D32IKzubLnLQfUO0x+/z+Yx+Irrtc2lObDVAQkEd3nq9Xh6K53I5gxYb6fBWUDrwRmcM6NdqOUmx01gHP7yS2L17N++9p6cHV199NQCzXXNprYRuc6E9TfGi0uk0M08uuugi3HLLLfx7rbRtKO0bo1uFSKaNtB0oxbx58yi3np4ezJs3D4BDFwlV6ff7DapNy1brqj7UrHborq+aNiwd/lMOIittCw8fPmy0bBCbUSgUyAxUunYrNvzaSMuXl8UhEMOvb043XSu9aRGOLuzyer1Uhr6+Pp4huFwuZlfo9Dypsqw2wy8GvjQ7RDKgRnM/IkNdqFUqK42xcIUTBf39/byvQqHA/uV33323USikaUW9oYpu5vN5Xu/3+7FnjzMLpLW1Fdu2bQPg8LWat67mtsyl50OydpPJJM9JgsGg0WdGt18WGTY3NxtnLOWmvGlKOJvN8rP8fj8fl2sMV20Q6lTTOPX19caUwnLtlPXzxWKRa/fw4cMstLz44ovx5JNPAnBshNBKlRp+S/VYWFhYTDJU7PELfD4fdzA9AhA40qMiHA7TeyodsajDv9IQXK6RQppt27bxQMnlctFDTafTBpVRjR6/ztHXnrh4/DqHWuisY0GHi+JBNTQ0MFdaZ1UB1d17Ro/zlPvetWsXh/LoQiGPx8MIS/dL0fKIxWJ8z1AohL/85S/8HJnGpXP9dYRQjdDtKjweD+9Le/a6jXopymWW6bWezWaNtg7yWPdB0lFTtdbjaIiOaTmceeaZPOg9mo3SEUA5arylpcWgw3TmVSWoSGN1DxS/309lkBsFHEWSCUYNDQ1GiqLGSAVHwoNpRYvH49i/fz8ApxmUnHDr1LuRetpMZOiw1ufzcSHoocu6mm+kWcXyf8Dk9T0eD5UkHA6Te8xkMtxYPB4PM4uqEWK0UqkUdcbr9TKrR/c90shms8YCksea7giHw8aAdd3bR1KNSxtuVRtKOX49dUvri9y7zjwppSZEB7UTo3V08eLFHC+ay+X4/roQSc+bqFbI2adOz5w/f77xfGnfqFKU2kWRVVNTk/F7CR1XKSzVY2FhYTHJMOqsnnQ6TU9KPHDAoXnEm9QZO8BLy7QB0zvQXpW8HnBCbtktZ86cyelHe/fuNQ70dBFUNUAfqrpcLh4KnX766byvRCJBOWvvqTRc1CG3pjDEg4vFYnjDG94AAPjOd76D5uZmAI63NZYuf680dPgsuunxeIwccdHB0iEsco2WpR5Gks1mDW9UR5ci10QiQUqyGhGLxQxvXqL3oaEhJgPMnj2b9K32+P1+P+VQuu7k/36/n3qtDzi1DPVBey1QPdLa2u12s+16IBBgppOmuvP5fNmIVLMrwJHagMWLFxvZaKP1+Ctuy6ypBvkRpY8EYCpSqTJoekeHgprvl+f1BuD3+w0eWrjWPXv2GE2Nqg0DAwNGoYv8iGeffTZT6fr7+9mz6Hg2NU1VeL1eLt54PM6UsFwux8Xo8XjYQ6QaoakB0QF9FqLpsWw2a0whk0wxzf3rfj564hxwpIK82nl9jZEK2bLZLL7+9a8DcCZ0leunVVp9q8+W9DoWA3/gwAHO8JgyZYpRSa4zgqod+ixN4PP5jMwlTeXojDItW+3IyKYxc+ZM47WjPZ+zVI+FhYXFJEPFboumaMTrkcEogHPKrA8XdWinPTJ9KKQjBF2QJV6Gzu8HwDYNDzzwAJ+rxi6TAwMDxoGueJ3nnXcefvnLXwIwexkdL/QhpNAZsViMkUMqlTLaN1RzVo+OHEWnGhoa6Dnqg2wdHfT29jLbR+uapojcbjd/k2w2y0KmRCLBiOx4sqwmMtLpdNlhSYVCAStXrgQAfPvb32bLc50w4PV6jXWsW6rLOs7n84yUtm/fjre97W0AgK9+9asGRSyfPVK32mqCTpYQ/QyFQrw3HVWWFg+Wy3Z0u9083F2yZInR0llP+aoEozb82khLxR7g8NY6nVOPt5NQR764QPOBcrO6dw1gKoQoYSgUOmZzsokMTbHo79/Z2WlQMSI3bWR0MVIpyqWBJZNJpt16vV6jP0g5jrEaIXo1d+5chsalToNQgz09PZyoVTrzQC842UD27dtH+W3bto2fVe2GKhaLGSmcQjc2NTVh9erVAJyNTta6rngu7S0j0LZBD6wfHh7GunXrAADXXXcdfv3rXwMwqQ89B6BaUS7Fsrm5mRXkpRW8OoVdUz26L5o0c7zgggs4p2TmzJmjllf1WUsLCwsLizGhYo9f54tLrrQO2RYtWmQMrNDevc7AEZTm/wr047q6OtIUwJFsn76+Pu54Pp+v6nr1HD582KDCBPX19Uavk3IeVrlDtXL/l8fRaBRLly4F4JTgi8wLhUJNzI1taGgg/VJfX88siNJBP3KvI+mK2+2mXmvZHDx4kAflejDGsfKxJzoGBgaMth6SaTZ79mzKTdOxw8PDZdsm60hAd8nV2Slut5ut3D/4wQ/S49fe7WgLkiYSdASlW35Ly48FCxYYrW9K+2vJ87r4ctOmTbxGZ2GNNguqYsOvm6hJGptWBJ3hc6LR2dlJhamrq6s6vrWnp8egwgTNzc1GD45yBTM6hNYoNfr6esmo0PRRacVwtUE4eI/Hw0Xm9/u5CWi+uVAocDHlcrkRQ2xZWMlkkjRYIpGggayrq+OGUO2Gf3h4mDJJpVK8n6VLlxpGRWSlz0w0SvtyacdNV/GKk/i1r33NkL8eM1jtkPWUTqcNGnz9+vUAzPbg+nrgyPrVqfAzZszgiFYApChLs84qgaV6LCwsLCYZKvb4daiswxiB7nQIHHtAyGgg79nZ2Wnkulabx9/f32/MgBV5hkIhels6c6J02I38vzT3XLKs5s2bh0ceeYSvEW9u9uzZPFiur6+vqqK3Ukh7kHg8Tpqgr6+Pk7F0vr2OknRvn9LhF9q7FXR3dzNUj8fj9P737NmD008//UTc2suCRCJh5JtLhteMGTOMdiuaihHaVXucun2KrtMBjmRK6UPcxsZG6qN+bS20ZRZ5JhIJY0KbTG1bunSpQW/r9SeyKn1epp4BYLbVk08+OeoWFxUbfr1IyhWxaCNUrpfMWKHfc/78+eTCW1paqo7j16mv+Xye1FnpxlmOAyxNiZXHPp+PrYR7e3uNRa2Nnn7Pau6PctFFFwFwFpPcazgcxpe+9CUAZqqm5qr7+/uNBnk6BVacm7q6Oma59PT04Nvf/jYAR15itKQCulqhN0NdNLRgwQIaqoaGBmaS6CpbTdHooeF6o/D7/XyczWZZJX7mmWfinnvu4WsF1ayLArGL6XQaq1at4vNCP06ZMoXXHO2sTuD3+435D1KBv3r16rLT+Y4HluqxsLCwmGQYdVZPoVA45kHMWLx8ne1TuivKLheJRIwy8Wry9gG8pFWC9PgAjgwA1yHf8ezuLpeLXlg6neZBXEdHB7MNFixYwGEOxWKxKmsgBOJlShtmgXjqnZ2dbM0AgI/nzZtHbz0cDvOxph3q6+up4319fYzIqrk3TymGh4d577q9xZw5c7Bx40YApifq9/sZKemMvWw2a2Sb6MEt8nq9Xs8991xjeIg8rrY1fDS43W4sW7aM/5f1ffDgQYPSkvWt657cbjeTZkKhkFFYOHv2bL5utMkFY6J6TqTBKHdOUPq4sbHRGHNW2jtkouOqq67C448/DsDJIPnOd77Dv0m2SldXFysfARiVzYLS5m3lKJ3BwUEqyde//nWsWLECgCPP888/f9zv7eWCNkpaJqIXevD1oUOHaPg7OztZUNPf38/zgebmZm6WuudPaeaTdjiq+YwEMO9NNrWZM2fiqquuAgDcc8893FgzmQwpC7/fz41XnxV4PB7qaTgcppEbHh7Gm970JgDO2tXjRUX+1VxFLhB98Hq9xmQ9qRQvnVhYKeSMJRAIjNrwV6+rZ2FhYWExKlTs8euDmhN9Al8um0V7t5FIBLt27QLghIqZTKaqPP6VK1fS08nlcobnLWH2d77zHR5gv/DCCyywOVqbAQkLTznlFHpe73jHOxhOx2IxeqwHDhyo6sHhct+lv7tk4KTTacycOROAE0WJ/uZyOWbt6ClRAwMDHPozbdo0Pj711FON99cZVdWM3bt3GwPQhX7s7Oxkdtgtt9zCw/KpU6eyTUUulytbIwHAoCwk6rr66qtx2223AQB27tyJgwcPAgDOOussowV7tUPWlo42gbF1ENby1O8vMqwUFRt+mTxUelMvF3Q439zczIZtLS0taGhoGPUp9yuBefPm4eGHHwbgKIu0mwYcow0At99++7h/7qxZs/i5vb29OO+888b9M14JaEfh3//93wE4enrSSScBcEJv4ezD4bCROqfPReR8IBqNcvSiDtlrCf/8z/+M7du3A3CoG3EO9ByCm266CR/+8IcBODMwhOo5fPgwDU86nebabGxsJA/d2dnJ5nYa8+bN42t1W2axL9UMsUkNDQ10OjRGY6M0pSmFmP/0T/9ks3osLCwsLI4PrkqoEZfL1Qtgz4n7OuOC2cViceor/SVGgpXh2FAl8gOsDMcDVoZjw4jyq8jwW1hYWFhUPyzVY2FhYTHJYA2/hYWFxSSDNfwWFhYWkwzW8FtYWFhMMljDb2FhYTHJYA2/hYWFxSSDNfwWFhYWkwzW8FtYWFhMMljDb2FhYTHJYA2/hYWFxSSDNfwWFhYWkwzW8FtYWFhMMlTUj3/KlCnFOXPmHPWaTCbDYSGpVIp9pH0+H3v465mcuVzO6JEuo9yAIz2ovV4vBzU0NjYedVjD7t270dfXN2GnYxyPDDUSiQR2794NwOkbL8Mc9FCHfD5PWbndbvbo9vv9vG7WrFnGCMejYSLLsFL5xeNxHDp0CIAziEVko/ubF4tFykn0DACCwSD7w0cikYpGja5du7ZvonaWrFSGGoVCgeMR8/m8MX9YBrokk0mOuKyrqxv1sJpakmEymaT90+s1mUxyhnE+n6esmpqaOAI0k8nQRjY3Nxvzd4+Go63jigz/nDlzsGbNGv6/3ISs3bt348EHHwTgTEGSCVMzZszAz3/+cwCmEA4dOsR5nmeccQamT58OwBlWIK+dNm0aF+CVV17JISXlILNkJypKZahRTp5r167FtddeC8AZ/i2b6tDQEI3V0NAQpyKFQiEuulmzZvH5b3zjG7jwwgvLfmbpwpzIMhxJB4Hy07CeeeYZfPGLXwTgTDAT2SQSCRr5ZDJJObW0tPB9FixYgOuuuw4AcP7553Mh6s8dyai5XK4J27L3aDp4LAwPD+Pee+8F4ExyW758Of8mA1o2btyIyy67DACwfPny4zZUpahWGZbTjQ0bNtD+DQwMGFP1Nm3aBMCRpzi+l112GU4//XQAwJ49ezB37lwAwFve8hbMmzfvuL7j0dZxxRO4NPSNibF/+OGHuaACgQAXWigUwo033ggA2Lx5sxEVyPDgxsZGemSDg4N8PpfLUam+8IUv4PrrrwcArFq1aixff8JB5Llv3z58/OMfB+BspG1tbQAcecoiWr58OTo7OwE4i/HJJ58E4HgE4pm2trZSwW666SZOQnr1q1+Nm266iZ95LCNWDdD3cfvtt+PRRx8F4HjtspjOOeccXjM8PMypWsPDw/RWp02bxmg0Go3ijjvuAADceeedaG5uBgDcddddlFW5jbOaoXVBPNEtW7ZwPGcikaDhiUajvD4cDlM+F198Mccw/va3v6X8Z82axXGOwWCwJvSuHOR+/vznP+NXv/oVAOd+ZbrZ3LlzKav3ve99uP/++wE4G8IVV1wBwHGU9+xx9r0lS5agt7cXAPD973+f8rz66qshUUelejgmw68hI+rC4bAxj1S+ZCwW4+KaOXOmQVXI89FoFIODgwDM2ZuFQoEGr6GhAffddx+A2jP869evBwB85jOfQTAYBAC0t7dThqlUisqzceNGzuWdOnUqIyXt8YdCIRw+fBgAMHv2bKTTaQDA3Xffzef/9V//taoXnv7usplt2bIF06ZNA2DSXfl8nsYmm80yfHa5XGhtbeXzslkGg0GOICwUCqTcVq9ejQsuuODE3tgrBL2hPfDAAwAcZ0IMjF63HR0dpCyKxSJlpSnJlpYWyry3txfPPPMMACeCqma9OxrEnv3pT3/irOZIJGJQOkI/9vf3MxL3+/20f+vXr6fN83q9mDFjBgBnHQsTcs899+Dmm28GUPnmaQ93LSwsLCYZxsXjP3DgAL3JUCjEUNntdnOX8/v9xs4vz3u9Xnq0mUyGnr72LHTYWSwWuVum0+lR84cTEbfeeisA574kFIzH4xz+7fP5KIfFixdTRv39/fS8otEoqZ7+/n6epTQ1NfH6jo4OhpdXXHEFzjnnnJfj9k4o9u/fT72YNWsW6cZEIkFPNJFI8Prm5mbs3LmTj4WaED0GTPoom82ScvvZz35Gj79WvdadO3dSB2fPns0zEJfLRT1KpVJcux6PhzpYKBSog263m9fMmzePlEUymTxqkkY1Q4bXe71e2sKuri6DuhaZ+Hw+6uXAwADlNmXKFEOeyWSS7y90+Jw5c3DgwAEAYERwvBgXw9/T02OEfEJTuN1uPq8XSDAY5MLUShIKhbgA/X4/BeLxeHjjHo+H79Xb20ueu9qxc+dO/og65Mtms5TP1KlTmVHR1dXFBag3CpfLxWuy2Sxmz54NwKHaxDAuXLgQCxcuBOAoaS0Y/u3bt9No60wxrYORSIRnS5qS9Pv9xkKU64PBIK/XetfT00NDqLNaagm7du2iTPbt28fNMx6PG1ljQmvIvwKRYT6fp/FLJpP8jXp6eqibtQahs1KpFB2vuro62jafz0f9DAQChjzF5nm9XiOLTDbJWCxG2fb19XGtV2r4LdVjYWFhMckwLh7/4OAgQ+JCocAd3uv10hPQ+fmZTIbeqtvtNl4rXlUul+P7uFwuhk9Lly7lrtjV1VUzHv+Pf/xjPs5mswbFIHIIhUJYtmwZACcNVqKmWCzGw1qdh57L5Zi7P2vWLB4AZ7NZeg3PPfcc3vWud53IW3tZ8Pzzz9ND0rRMOp0mPXb48GHKcnh4mDop3jvgePmig42NjTwoDwQCjMgKhQI2b94MAEY6Yy1A1mswGKQXOTQ0RDnoega3212W6tIUmcfj4XrVmXri/dYi5PAVcCIbwMnM0WxGuZoQnQyjZRgKhQzmRNZ4Q0PDSyKt48W4GP59+/ZRAXRo5/f7jZBG00Fi+F0uF68pFApG6ChCOHDgALnBpqYmhjfyby3gz3/+MzexHTt28MdtbW2lTPbv30/Kq7Ozk9knXq+XWSxDQ0PMN29paTGKvyQjaMuWLVRCfZZSzdiyZQuNyv79+0nR5PN5Uo8rV67EwYMHAThG6PLLLwcAHDx40DhTEfrmscceYxgei8X4vNvtxrZt2wDUnuGXtM0nnniC5xher5fp1LIOAcd4y5oWOQEvNU4i23A4zA3k+eefZ266dlZqAULTer1eOgjLli0jzRWLxUidlW6AYjs9Hg/PL9PpNOWWzWbpyNTV1RnnVpXAUj0WFhYWkwzjstUeOnSIoUuhUOAuVl9fT48gnU7zee0pyN8AJxKQa2KxGN9z8+bN9Ao6OzvplUjoXQs4cOAA6YlMJsNoZu7cufQC0uk07zkWi/HgKJPJ0Bv1eDz0JlpbW3nNgQMHmB3kdrspTznwrXYMDAwwogmFQnjiiScAOFGnyOaqq66i9+/1elkgM3v2bEZMXV1djDRffPFFTJ3qdAzo7u5mJWSxWMSOHTtepjt7edHV1QXA0a9nn30WgHMoqyNxKXwrFotco7qASNO3ek17vV56/7t27WJEId5srUDsWX19PatyN2/ejAULFgAAo07A0U9Zi7qVQy6X4+NUKkUZ/f73v2ekdNpppxk0ZSUYt6weWVDZbJbhh+b/ksmkwWuVctECoR50KX46nWbLhnQ6zc+qJcNfX19PPj6fz3OxHDx4kJtAW1ubQT2IoVu4cCGv7+rqIsfY1dWFjo4OvqcopE6DrXa6TBZHNps1ioY0JaGv1TqoK0e1vsnjD3zgA3yut7cXN9xwAwCH/xYDWWuQe+/o6CjbK0ZXoGpKR8sPOLKmM5kMKclDhw7xN/L5fHREasnwF4tFIw2z9G/yr5aXbKoul4v66XK5uF79fj/X/bZt2/j4lFNOGfVZiaV6LCwsLCYZxsXj1wdf8XicHn9dXR1DEe3V62yAQqFg7IziQXg8HnoZyWSS14fDYV5fCzSFLkwTz6ehoYERzqmnnor9+/cDcPJ2dW2DeE8bN27E0qVLATjZA+I1DA4O8rWxWIyy9fl8vEYyfaoVEt3oAhc52C1FaSaFjkhHeiyoq6tj2L5y5coRP6PaIffe2dlp1Cjo4iN5XmeUeL1eeqJut9vwXCXqzGQybMiYSqUq6nZaLdCRJ3BEnhdffDEpar/fb+iYeP8jyUNf+6Y3vYnN4fL5vKH3lWBcDH80GmUDMMBp1AY4HJR8sXQ6bYSF5dI/y4U/gLOohd6Jx+PkYHXaVLVCDPm2bdto+Lu7u7lY9EYaCoXYUyaXyzFUjkQi2Lp1KwCnD5KEf8PDw6R0gsEgn+/u7uZC3rRpk5FmVm0QGRQKBRqeZDLJDa++vp5ZFvl8njqo79Xj8fC1etH6fD7q2saNG/mbuN1u9PX1ncC7euUgFNbhw4epj+vWrWPBn3byABjGXkPknMvlqGs7d+40CpGEjqu0+GgiI5PJUBbJZJI2rb29nb21Smkxgc6M0mcm+j1XrVqFxx57DICZ6l0pam/LtbCwsLA4Ksbk8QtNkclk+DgWixn9ebQ3KTua7vHh9Xp5iKEpoHA4TE9Xe2eZTIY7ZjqdNgaQVCPk4CsQCJB2cblc9Fj14At9IJ7JZCg3r9drFLUJvRYOh+kRz549m4d1zc3N9BRmzJjB66vR45f7Lo0i3//+9wNw2izrnHLdW0ZeGw6HGVEODAxQNo2Njdi3bx8AJ3oSz7RYLDLazOVyNZWHLpG2vsempiZjLYqsXC4X17TP5zMoCd2yQaKjhQsXMjLVsyVqCbFYjPLp7+9nhD5nzhyyH7pdiD6cdblcZWlGfU1dXR1lm8lkXpkCLt3TROD3+5mm1dnZycKPRYsWsZhIFydkMhkapGAwaKSHySJta2vjDWruv7m52WgOV42Q76+zH3QaZjabxZlnngnAWVwiQ5/PZ2ykkmJXKBSYHXTqqafSqG/fvp2Pp0yZgpNPPhmAYzhlgUuqXTVBjH0+n6deNDY2kppYtmwZdu3aBcAx6mKk58+fT/kFg0E+7unp4e8wb948zJw5E4BDU8hmrHUtk8nUlOEXDl5SggHg9NNPxwsvvADAyZjS613Wq67M19kpegPp6OigbCuZJFVNyGazRoNAmZPh9/vpUGhZAcfX6E/sn3amxcEGKu/HX51usoWFhYXFqDEuVI8uQgiHw/QmA4EAw7lAIMCQr62tjbtWLpcz+tLIbpjNZumhzps3jx5IX18fvbCNGzfyO1Srxy87eUdHB+9lx44dlEkgEMDzzz8PADjppJM4dlKPC+zr66NXFQgEGJZv2LCBE48uvPBC9jv605/+RPmvX7+eh5/6gL5aoGlCPd9Z2k5v3rwZ8+fPB+B4sXKvw8PD2LBhAwDgzDPPpPwymQy9/8cee4y1Ij09PdQ7AEbPHz2SsdohtKJ45oATuUu0o7NxtIepD8h1h1NN5ba3t5elaWsJhw8fZuSpa45cLhfX5ZQpU0Y84NXQA610UZgcrsdiMUZN8XjciNKOhTEZflksLpfLaCIkPWcGBwf5fCKRoLEJBAI0WsFg0OjbI4LK5XK8JhAI4KyzzgLg9GGR63O5XNU3exJKp6+vj21q0+k0F9GiRYtYQbljxw5upNFolDRac3MzFam1tZUGauvWrdw0NL/a0NBAGerWutUI0RE99cnlctGor127ljN3L7jgAjz00EMAnNnNMlZx2bJl3ByCwSCpsmuvvZY00dSpUzmFSnOxo62cnKgQg9/X10ejotsLC6UImK2DdVq2pjuSySQ3k0WLFrFqtaGhoSYzo4aGhmj4i8Ui5+YCKNtTX2fllM6Plv97vV7qmc/nY3bQmWeeSacjGo1WZPgt1WNhYWExyTAmj1+XX8vOf+jQIVx66aUAnOnw4j0lEgnucpqW0Z069UxUr9dLjyORSODss88GAHzrW99iXnCxWDQOOKoResiKPPb7/fTsn3vuOUY1LS0tRtfJM844A4BDTwiNc/DgQbZoDofDlO3evXvZd2Z4eJhy1ofK1QiJOnV/mHQ6jbe+9a0AHFpRop6nn36aVOLNN99MnfrjH//I8DmVStGLevWrX41rrrkGgJMtJV7vtGnTqMt6YlctQDx6PSwkEolQd2bMmGFkRml6R/TX6/Ua3XolMm1oaGCWS2NjY1UmExwPdGtlSTIAYFCRmiE5Fu3jcrmMAUKa8RCGpNIuu+Ni+PP5PI35/v37WXW6bt06KlJ3dzev0aPE9E3rUWV6GHZ/fz8Vr1AoGNOSqpmmAI6kUNbX1zOjor+/nz/o3Llz2QI4FotxoXk8HhqdadOmsX/K8PAwZauvd7lcRstXeX7x4sXkvasRupJZG2NdLCiOgqYpgCObbktLC3W5ra3N0EHdSrxcC9xao3pkjRaLRa6tRCJBnRoaGjJ0SmSYz+eNFG2BXqNut5uvjUQiL8luqRWI41AoFGgLARhyE4yUwqnhdrvp4Hg8Hr5nJpMxph1WAkv1WFhYWEwyjMnjL3ew1tvby0KkXC7Hsu+uri4WwCQSCe72uq+Hnj/pcrmMDpLyPm63mx5EoVCoeo9Lvr/QEfKcbrMs4XE+n6es0uk0p/sUi0V6s83NzUZutXhqXq+X0VUqlWLo6HK5qlqGmurR3qfQY9lslo/1AaQuFgwGg0YSguhgoVAgDaYjSx1Wj7ZXykSF0Fm65mH69OmkVPXM3dJupwJda6ML5dxuN/trud3umpmeVwp9sD1SrYKW2/H0jNKUorQQH0vx4JgMvw7h5IsFAgF+scHBQaPVsM4S0K1Lda8eudlkMskFG41GGT6VDiEeba+KiQIxxm1tbXjVq14FwOkDLyf3wBHjNn/+fG6YfX19pHe6urpYoZvP57l4XS4Xe4C73W4u3lNPPZW/3fbt23l9NUIbZO0QiB7pil5daaoXTT6fNzhp3X9GNtSDBw8ai090uZrPR8pBzof6+vooh46ODmbmNDQ08PlSmlafz+nGY2L48/m8kTU02ulRExmFQoGbnp60BcDIpNPZiCIrrZPa6Jc2dZOeUel0etR0maV6LCwsLCYZxqVlQyQSoec9d+5cY3cSTyEUCtFTj0aj3P28Xi/DZbfbzd1Se156d/T7/fSA8/l81XsN4m0PDg7S21q8eDGnQ7W1tTEXeOvWrUYravHym5qaKPNYLMZJUcFgkDUAup9PR0cHC8HC4XBVH7Lpw1eB7lqoDyk9Ho/RQ0ag24Nor0u32E0mkzwE15lo1V5HUgqJarR8AoEAo8VEImG0Y9BD1XWrdd0FVbx8/dpsNltz0ZJA7jEejxtDZnS0WW7wD3BE7rpTJ2AOdZE6nf3795MJeVmzeuTLhEIhLjRt9L1eL41ZW1sbuWTdSx44Iih9c+VCeMBpUiT/nz59elU2FtOQU/nW1lY2BItGo1yA3d3dNErLli2j3KLRKNvaxmIxysHn8zELaOHChTjvvPMAOLKVoqbnn3+en7tmzRoWjlUztAHWGU8jTdfSRYelfxcZ6xTRfD5vFNHIwqz2rLJSSIVuf38/1+WsWbPYS16nbQLmmtV0mcgtHA7zPGnHjh3U8VAoVJWV4seCHms6PDxsVHvLmqurqzPS0PVGKo+14ff7/YZzNm/ePACOIzjatGJL9VhYWFhMMozJ49eeutAI+qR+aGiIhxvBYJCFHJFIhGGe9iDy+TwjB53Bog9wGxsbGUVUGt5MRAhdo+sWotEoPcmpU6fSSwKOeFUHDx40MqDEy5gzZw5efPFFAMDu3btJJbndbso8HA6TMurs7KQHUY2QQ1bdvsPtdpfVI43SqW/lMii0l9XU1ESKUSch1JrHLzrocrmYWTZ9+nRSg3PnzjUyScploeiMKZ/PR4ps2rRpLNrSc3xrCVo30uk0M/IKhQLl0NfXZ7S/luu1l6+z1LxeL9dxsVjke+q+UpUmuYzJ8MsPp39oadAmX1jCGzFwgNmMTd+gbrSlhxbrlKjp06fTaOmp9NUO3bQqlUpxU0skErz/np4eo1paMk4GBgZ4TtLV1WUsTEn5bGhooOHX4/MOHz5cE1yr2+0m39nf30/dzOVyXGSlBkvrmub19aLUmWsCbbRqzfAL/dLQ0EAd2b9/P55++mkATiW5psJEbqXZdnpDEB1sb2/n+2cyGY4LrTXoGSRikJPJJDP1Zs2axed1Smxpaqa2bXJWVygUmM3n8XjKOsfHA0v1WFhYWEwyjMnj16Gw7Djasy/NYdWHGPpQQrd+0B0WxZvSvX06Ozuxbt06AI7HUe1TfGSwypIlSxgdFYtFLF68GICZq6s9CK/XS89Ch3z9/f18rGej+nw+esTJZJIRQn9/v/GbVRuE9jt8+DDnxQYCAdIyusW1zrH2eDxGto/OvpCDt1wuRwpzcHCQXmxfXx/1Ttdb1AKkDfXevXvZQsTtdvN53TfG5/MZh+UC3YbA4/FQTzdu3MiOnPF4vCao2lLkcjnSMg0NDdSluro6/OhHP+LzAp1YUEpJyt+KxSKuvfZaAI48pUA2GAxSzyvNzBuT4ZeeEbqPiTRoA5xe6HKq7XK5yoaIOgNAP06n0zRIYhwBpye9oFAoVH1GyrnnngsAuPPOO3HaaacBcDh4WSCDg4NGZoDmtEWpwuFw2UyLXC7HBZhKpWgkdZ+UbDbLZmXViLe85S0AgNWrV1Meb37zm7n4HnjgAS4UHUrncjnKUhsql8vFDTIQCHCjXblypdH7X/C+973vhN3bKwHhof/4xz+y+O8rX/kK5xuEQiEsWbIEwMiVu8ARQ7R//35mQ11wwQX4x3/8RwDORv2e97znhN3HKwW/329QNNo+iR6OBtqJE46/rq7OmGhWCSzVY2FhYTHJMCaPXygFfbg4d+5c/v2f//mfsXr1al4robgO8Twej1EDIHRHQ0MDW5q+7nWv4/U6SyCZTL6k42K1QbyqmTNnUg5dXV3493//dwDA61//euzcuRMAmFkBONGUwOv1GoVJEhW5XC5eFwqFGC4+/PDD9F6nTJnykmKRaoJEmgcPHqT32dfXxyhxzZo1LHEvLYnXCQbyvJ773NLSQtkvWLDAoDNloIj2xGoBQs92d3cz+l6xYoXRS2q0SKfTuPrqqwE49KQc+tYShoaGWLSaTqdJlwFHIvFKZuOWQndEbW1tJe1WaR7/mAy/KIlQFIDJxy9btgzLli0by0e8BHV1dSxKGh4eZsvdaoXwfW1tbcb4PxlYPzw8zHBOp3kmk0lSG7qhndfrNaqiRUn0htzd3c2NOhqNVnWzLDkL+dKXvsTnLrjgAsry7W9/O42zbkg3PDxsZFbIAtKV4MViEZdccgkA4IYbbsCVV14JAPj2t7/NiV3Vrn+luP766wE49GElE52OB4FAAA8//DAA52xJZFtLOOuss0jpNDU1GRSMphMrRbme/eeeey7b1Ut/tOOFpXosLCwsJhlcxzP0lxe7XL0A9py4rzMumF0sFqe+0l9iJFgZjg1VIj/AynA8YGU4Nowov4oMv4WFhYVF9cNSPRYWFhaTDNbwW1hYWEwyWMNvYWFhMclgDb+FhYXFJIM1/BYWFhaTDNbwW1hYWEwyWMNvYWFhMclgDb+FhYXFJIM1/BYWFhaTDP8PkrU/nKM81EQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 0,T-shirt/top\n",
    "# 1,Trouser\n",
    "# 2,Pullover\n",
    "# 3 Dress\n",
    "# 4 Coat\n",
    "# 5 Sandal\n",
    "# 6 Shirt\n",
    "# 7 Sneaker\n",
    "# 8 Bag\n",
    "# 9 Ankle boot\n",
    "\n",
    "fig, ax = plt.subplots(nrows=5, ncols=5, sharex=True, sharey=True,)\n",
    "ax = ax.flatten()\n",
    "imgs_of_one_class = X_train[y_train == 2]\n",
    "for i in range(25):\n",
    "    img = imgs_of_one_class[i].reshape(28, 28)\n",
    "    ax[i].imshow(img, cmap='Greys', interpolation='nearest')\n",
    "\n",
    "ax[0].set_xticks([])\n",
    "ax[0].set_yticks([])\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### L-BFGS Optimization for Fashion MNIST\n",
    "This is a nice test to show that mini-batching has better conversion properties for some datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch: 91/100 (max)"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'grad': array([ -0.21986078,  -0.10453559,  -0.36817325, ...,  13.13373878,\n",
      "        24.55882285, -12.95431239]), 'task': 'STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT', 'funcalls': 101, 'nit': 91, 'warnflag': 1}\n",
      "Validation acc: 0.8603\n",
      "CPU times: user 50.4 s, sys: 1.69 s, total: 52.1 s\n",
      "Wall time: 13.3 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "nn_bfgs = TLPVectorizedBFGS( \n",
    "                      n_hidden=50, \n",
    "                      C=0.1, \n",
    "                      epochs=100, # max iterations\n",
    "                      gtol=1e-9,\n",
    "                      random_state=1)\n",
    "\n",
    "nn_bfgs.fit(X_train, y_train, print_progress=1)\n",
    "yhat = nn_bfgs.predict(X_test)\n",
    "print('Validation acc:',accuracy_score(y_test,yhat))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MiniBatch Gradient Descent for Fashion MNIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch: 40/40"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation acc: 0.8258\n",
      "CPU times: user 4min 13s, sys: 19.6 s, total: 4min 33s\n",
      "Wall time: 1min 10s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "nn_mini = TLPVectorizedMiniBatch( \n",
    "                          n_hidden=50, \n",
    "                          C=0.01,  \n",
    "                          epochs=40, \n",
    "                          eta=0.01,\n",
    "                          alpha=0.05,\n",
    "                          decrease_const=0.01,\n",
    "                          minibatches=len(X_train)/16, \n",
    "                          shuffle=True,\n",
    "                          random_state=1)\n",
    "\n",
    "nn_mini.fit(X_train, y_train, print_progress=1)\n",
    "yhat = nn_mini.predict(X_test)\n",
    "print('Validation acc:',accuracy_score(y_test,yhat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "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": [
    "# take the mean of each minibatch epoch\n",
    "cost_avgs = [np.mean(x) for x in nn_mini.cost_]\n",
    "\n",
    "plt.plot(range(len(cost_avgs)), cost_avgs, color='red')\n",
    "plt.ylabel('Cost')\n",
    "plt.xlabel('Epochs')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "label_names=[\n",
    "    'T-shirt/top',\n",
    "    'Trouser',\n",
    "    'Pullover',\n",
    "    'Dress',\n",
    "    'Coat',\n",
    "    'Sandal',\n",
    "    'Shirt',\n",
    "    'Sneaker',\n",
    "    'Bag',\n",
    "    'Ankle boot']\n",
    "\n",
    "# get first 25 confusions\n",
    "miscl_img = X_test[y_test != yhat][:25]\n",
    "correct_lab = y_test[y_test != yhat][:25]\n",
    "miscl_lab = yhat[y_test != yhat][:25]\n",
    "\n",
    "fig, ax = plt.subplots(nrows=5, ncols=5, sharex=True, sharey=True, figsize=(10,10))\n",
    "ax = ax.flatten()\n",
    "for i in range(25):\n",
    "    img = miscl_img[i].reshape(28, 28)\n",
    "    ax[i].imshow(img, cmap='Greys', interpolation='nearest')\n",
    "    ax[i].set_title('%s, (p:%s)' % (label_names[correct_lab[i]],label_names[miscl_lab[i]]))\n",
    "\n",
    "ax[0].set_xticks([])\n",
    "ax[0].set_yticks([])\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While these misclassifications are looking mostly okay, we can do better. Is 85% good for Fashion MNIST?  We can check out the leaderboard here: https://paperswithcode.com/sota/image-classification-on-fashion-mnist\n",
    "\n",
    "But we have some additional implementation details that are needed for practical implementation of neural networks, in order to get them training more efficiently and more meaningfully. These are visited in the next notebook, `08. Practical Implementation of Neural Networks`\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## In this notebook you learned:\n",
    "- an introduction to neural networks notation and programming\n",
    "- using a two-layer perceptron architecture with sigmoid activations\n",
    "- optimizing this network with mini-batch descent and Quasi-newton methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}