{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# CS-109A Introduction to Data Science\n",
"\n",
"\n",
"## Lab 11: Neural Network Basics - Introduction to `tf.keras`\n",
"\n",
"**Harvard University** \n",
"**Fall 2019** \n",
"**Instructors:** Pavlos Protopapas, Kevin Rader, Chris Tanner \n",
"**Lab Instructors:** Chris Tanner and Eleni Kaxiras. \n",
"**Authors:** Eleni Kaxiras, David Sondak, and Pavlos Protopapas. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"## RUN THIS CELL TO PROPERLY HIGHLIGHT THE EXERCISES\n",
"import requests\n",
"from IPython.core.display import HTML\n",
"styles = requests.get(\"https://raw.githubusercontent.com/Harvard-IACS/2018-CS109A/master/content/styles/cs109.css\").text\n",
"HTML(styles)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib.image as mpimg\n",
"import numpy as np\n",
"import pandas as pd\n",
"%matplotlib inline\n",
"\n",
"from PIL import Image"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2.0.0\n"
]
}
],
"source": [
"from __future__ import absolute_import, division, print_function, unicode_literals\n",
"\n",
"# TensorFlow and tf.keras\n",
"import tensorflow as tf\n",
"\n",
"tf.keras.backend.clear_session() # For easy reset of notebook state.\n",
"\n",
"print(tf.__version__) # You should see a 2.0.0 here!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Instructions for running `tf.keras` with Tensorflow 2.0: \n",
"\n",
"1. Create a `conda` virtual environment by cloning an existing one that you know works\n",
"```\n",
"conda create --name myclone --clone myenv\n",
"```\n",
"\n",
"2. Go to [https://www.tensorflow.org/install/pip](https://www.tensorflow.org/install/pip) and follow instructions for your machine.\n",
"\n",
"3. In a nutshell: \n",
"```\n",
"pip install --upgrade pip\n",
"pip install tensorflow==2.0.0 \n",
"```\n",
"All references to Keras should be written as `tf.keras`. For example: \n",
"\n",
"```\n",
"model = tf.keras.models.Sequential([\n",
" tf.keras.layers.Flatten(input_shape=(28, 28)),\n",
" tf.keras.layers.Dense(128, activation='relu'),\n",
" tf.keras.layers.Dropout(0.2),\n",
" tf.keras.layers.Dense(10, activation='softmax')\n",
"])\n",
"\n",
"model.compile(optimizer='adam',\n",
" loss='sparse_categorical_crossentropy',\n",
" metrics=['accuracy'])\n",
" \n",
"tf.keras.models.Sequential\n",
"tf.keras.layers.Dense, tf.keras.layers.Activation, \n",
"tf.keras.layers.Dropout, tf.keras.layers.Flatten, tf.keras.layers.Reshape\n",
"tf.keras.optimizers.SGD\n",
"tf.keras.preprocessing.image.ImageDataGenerator\n",
"tf.keras.regularizers\n",
"tf.keras.datasets.mnist \n",
"```\n",
"\n",
"You could avoid the long names by using\n",
"```\n",
"from tensorflow import keras\n",
"from tensorflow.keras import layers\n",
"```\n",
"These imports do not work on some systems, however, because they pick up previous versions of `keras` and `tensorflow`. That is why I avoid them in this lab."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Learning Goals\n",
"In this lab we will understand the basics of neural networks and how to start using a deep learning library called `keras`. By the end of this lab, you should:\n",
"\n",
"- Understand how a simple neural network works and code some of its functionality from scratch.\n",
"- Be able to think and do calculations in matrix notation. Also think of vectors and arrays as tensors.\n",
"- Know how to install and run `tf.keras`.\n",
"- Implement a simple real world example using a neural network."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Part 1: Neural Networks 101"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Suppose we have an input vector $X=${$x_1, x_2, ... x_L$} to a $k$-layered network.
\n",
"Each layer has its own number of nodes. For the first layer in our drawing that number is $J$. We can store the weights for each node in a vector $\\mathbf{W} \\in \\mathbb{R}^{JxL+1}$ (accounting for bias). Similarly, we can store the biases from each node in a vector $\\mathbf{b} \\in \\mathbb{R}^{I}$. The affine transformation is then written as $$\\mathbf{a} = \\mathbf{W^T}X + \\mathbf{b}$$ What we then do is \"absorb\" $\\mathbf{b}$ into $X$ by adding a column of ones to $X$. Our $X$ matrix than becomes $\\mathbf{X} \\in \\mathbb{R}^{JxL+1}$ and our equation:
$$\\mathbf{a} = \\mathbf{W^T}_{plusones}X$$ We have that $\\mathbf{a} \\in \\mathbb{R}^{J}$ as well. Next we evaluate the output from each node. We write $$\\mathbf{u} = \\sigma\\left(\\mathbf{a}\\right)$$ where $\\mathbf{u}\\in\\mathbb{R}^{J}$. We can think of $\\sigma$ operating on each individual element of $\\mathbf{a}$ separately or in matrix notation. If we denote each component of $\\mathbf{a}$ by $a_{j}$ then we can write $$u_{j} = \\sigma\\left(a_{j}\\right), \\quad j = 1, ... J.$$ In our code we will implement all these equations in matrix notation.\n",
"`tf.keras` (Tensorflow) and `numpy` perform the calculations in matrix format."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"
\n",
"*Image source: \"Modern Mathematical Methods for Computational Science and Engineering\" Efthimios Kaxiras and Athanassios Fokas.*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's assume that we have 3 input points (L = 3), two hidden layers ($k=2$), and 2 nodes in each layer ($J=2$) \n",
"\n",
"### Input Layer\n",
"\n",
"$𝑋$={$𝑥_1,𝑥_2,x_3$}\n",
"\n",
"### First Hidden Layer\n",
"\n",
"\\begin{equation}\n",
" \\begin{aligned}\n",
"a^{(1)}_1 = w^{(1)}_{10} + w^{(1)}_{11}x_1 + w^{(1)}_{12}x_2 + w^{(1)}_{13}x_3 \\\\\n",
"a^{(1)}_2 = w^{(1)}_{20} + w^{(1)}_{21}x_1 + w^{(1)}_{22}x_2 + w^{(1)}_{23}x_3 \\\\ \n",
"\\end{aligned}\n",
"\\end{equation}\n",
" All this in matrix notation: $$\\mathbf{a} = \\mathbf{W^T}X$$\n",
" NOTE: in $X$ we have added a column of ones to account for the bias
\n",
"**Then the sigmoid is applied**:\n",
"\\begin{equation}\n",
" \\begin{aligned}\n",
"u^{(1)}_1 = \\sigma(a^{(1)}_1) \\\\\n",
"u^{(1)}_2 = \\sigma(a^{(1)}_2) \\\\\n",
"\\end{aligned}\n",
"\\end{equation}\n",
" \n",
"or in matrix notation: $$\\mathbf{u} = \\sigma\\left(\\mathbf{a}\\right)$$\n",
"\n",
"### Second Hidden Layer\n",
"\n",
"\\begin{equation}\n",
" \\begin{aligned}\n",
"a^{(2)}_1 = w^{(2)}_{10} + w^{(2)}_{11}u^{(1)}_1 + w^{(2)}_{12}u^{(1)}_2 + w^{(2)}_{13}u^{(1)}_3 \\\\\n",
"a^{(2)}_2 = w^{(2)}_{20} + w^{(2)}_{21}u^{(1)}_1 + w^{(2)}_{22}u^{(1)}_2 + w^{(2)}_{23}u^{(1)}_3 \\\\ \n",
"\\end{aligned}\n",
"\\end{equation}\n",
" \n",
"\n",
"**Then the sigmoid is applied**:\n",
"\n",
"\\begin{equation}\n",
" \\begin{aligned}\n",
"u^{(2)}_1 = \\sigma(a^{(2)}_1) \\\\\n",
"u^{(2)}_2 = \\sigma(a^{(2)}_2) \\\\\n",
"\\end{aligned}\n",
"\\end{equation}\n",
"\n",
"### Output Layer\n",
"\n",
"#### If the output is categorical:\n",
"\n",
"For example with four classes ($M=4$): $Y$={$y_1, y_2, y_3, y_4$}, we have the affine and then the sigmoid is lastly applied: \n",
"\n",
"\\begin{equation}\n",
" \\begin{aligned}\n",
"a^{(3)}_1 = w^{(3)}_{10} + w^{(3)}_{11}u^{(2)}_1 + w^{(3)}_{12}u^{(2)}_2 \\\\\n",
"a^{(3)}_2 = w^{(3)}_{20} + w^{(3)}_{21}u^{(2)}_1 + w^{(3)}_{22}u^{(2)}_2 \\\\ \n",
"a^{(3)}_3 = w^{(3)}_{30} + w^{(3)}_{31}u^{(2)}_1 + w^{(3)}_{32}u^{(2)}_2 \\\\\n",
"a^{(3)}_4 = w^{(3)}_{40} + w^{(3)}_{41}u^{(2)}_1 + w^{(3)}_{42}u^{(2)}_2 \\\\\n",
"\\end{aligned}\n",
"\\end{equation}\n",
" \n",
"\\begin{equation}\n",
" \\begin{aligned}\n",
"y_1 = \\sigma(a^{(3)}_1) \\\\\n",
"y_2 = \\sigma(a^{(3)}_2) \\\\\n",
"y_3 = \\sigma(a^{(3)}_3) \\\\\n",
"y_3 = \\sigma(a^{(3)}_4) \\\\\n",
"\\end{aligned}\n",
"\\end{equation}\n",
"$\\sigma$ will be softmax in the case of multiple classes and sigmoid for binary.\n",
" \n",
" \n",
"#### If the output is a number (regression):\n",
"\n",
"We have a single y as output:\n",
"\n",
"\\begin{equation}\n",
" \\begin{aligned}\n",
"y = w^{(3)}_{10}+ w^{(3)}_{11}u^{(2)}_1 + w^{(3)}_{12}u^{(2)}_2 + w^{(3)}_{13}u^{(2)}_3 \\\\\n",
"\\end{aligned}\n",
"\\end{equation}\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Matrix Multiplication and constant addition"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"# make two arrays and multiply them using np.dot(a, b) or tf.matmul(a, b)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# both Tensorflow and numpy take care of transposing.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# how do we add the constant in the matrix\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
In class exercise : Plot the sigmoid
\n",
"\n",
"Define the `sigmoid` and the `tanh`. For `tanh` you may use `np.tanh` and for the `sigmoid` use the general equation:\n",
"\\begin{align}\n",
"\\sigma = \\dfrac{1}{1+e^{-2(x-c)/a}} \\qquad\\text{(1.1)}\n",
"\\textrm{}\n",
"\\end{align}\n",
"\n",
"Generate a list of 500 $x$ points from -5 to 5 and plot both functions. What do you observe? What do variables $c$ and $a$ do?"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"# your code here"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# %load solutions/sigmoid.py"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
2. In class exercise: Approximate a Gaussian function using a node and manually adjusting the weights. Start with one layer with one node and move to two nodes.
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The task is to approximate (learn) a function $f\\left(x\\right)$ given some input $x$. For demonstration purposes, the function we will try to learn is a Gaussian function: \n",
"\\begin{align}\n",
"f\\left(x\\right) = e^{-x^{2}}\n",
"\\textrm{}\n",
"\\end{align}\n",
"\n",
"Even though we represent the input $x$ as a vector on the computer, you should think of it as a single input. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 2.1 Start by plotting the above function using the $x$ dataset "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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p016XIklI4S5xL7iePFbWuAedmVTVuLt4QOEucS+47cCcyd5uOzDSgqm5mKEPM4knFO4S9+oa25kz2fttB0bKSk9l5qRsTaqKJxTuEvd2N3WwIEbWt48UnFQViTaFu8S1U919NMbQtgMjVZbkcvhkNx09/V6XIklG4S5xLdgrjt1wH6xrT5PG3SW6FO4S13bH6EqZIO3tLl5RuEtcq2tspygnncm5mV6XMqqS/EzyJ6RRp567RJnCXeLa4GRqbA7JAJiZLpgtnlC4S9zyDwTYc6yDyhgdkglaMDWPPU0dBALahkCiR+EucevAiS76YnDbgZEWluTR3TfAoZPdXpciSUThLnErOI4dy8My8PtJ1d0ampEoCinczWy1me0xs71m9pVztPmome0ys51m9lB4yxQ5W11jO2m+2Nt2YKS5U3JIMa2YkehKHauBmfmA+4HrgHpgo5k94ZzbNazNXOCvgSucc61mNjlSBYsE1TW2M7s4h/TU2P4FNDPNx6ziHHZpjxmJolB+KlYCe51z+51zfcDDwJoRbdYC9zvnWgGcc8fDW6bI2XY3dsT8eHtQZUmeeu4SVaGEeylwZNjt+qH7hpsHzDOz35nZa2a2erQDmdk6M9tkZpuam5vHV7EI0NrVR1N7T8yvlAmqLMml4dRp2rUNgURJKOE+2nXLRq7pSgXmAlcDtwI/MLOCs57k3APOuRrnXE1xcfGF1ipyRrAXHOuTqUHBq0Tt1tCMREko4V4PlA+7XQYcHaXN4865fufcAWAPg2EvEhHBlTLxNCwDmlSV6Akl3DcCc81sppmlA7cAT4xo8xjwHgAzK2JwmGZ/OAsVGW5w24EMinMzvC4lJFPyMpiYlcbuJoW7RMeY4e6c8wN3As8CdcAjzrmdZnavmd001OxZoMXMdgEvAF9yzrVEqmiRusb2uBlvh+A2BHlaMSNRM+ZSSADn3Hpg/Yj77h72tQP+YuiPSET1DwR4+1gnt19R4XUpF2TB1DweeuMQAwGHL2W0qSyR8IntBcIio9jf3EXfQCCueu4wuGKmpz/AwZYur0uRJKBwl7hTF+MX6DiX329DoKEZiTyFu8SduqZ20n0pzC6O7W0HRpozOQdfimnFjESFwl3iTl1jB3Mm55Dmi6//vplpPmYXZyvcJSri66dDhOBKmfgakgnSNgQSLQp3iSsnOntp7uiNu8nUoMqSPI629dDWrW0IJLIU7hJX4nUyNWjB1ME3pTp9mEkiTOEucSXew32htiGQKFG4S1zZ3djBlLwMCrPTvS5lXIpzM5iUna5wl4hTuEtc2RXHk6nw+20IdjdprbtElsJd4kafP8C+5s64DncYHHff09SBfyDgdSmSwBTuEjf2Hu+kf8DFfbhXluTR69c2BBJZCneJG8Fx6oVxugwy6Pd7u2toRiJH4S5xo66xnfTUFComZXtdykWZPTmbVG1DIBGmcJe4sbupg/lTckmNs20HRspI9TFnco7CXSIqvn9KJGk45+LuAh3nM7gNgYZlJHIU7hIXmjt6aenqi/vJ1KDKklya2nto7erzuhRJUAp3iQu74vyTqSMtmDo0qaptCCRCFO4SF4JDGJVTEyPctWJGIk3hLnGhrrGd0oIJ5GeleV1KWBTnZlCUk6FJVYkYhbvEhbrG9jM7KiaKypJcdmtYRiJE4S4xr7vPz77mTqpK870uJawqS/J461intiGQiFC4S8yra+wg4EjAcM+lzx9g/wltQyDhp3CXmLfzaBsAVaWJMZkaFJxU3XVUQzMSfgp3iXm1DW1Myk5nal6m16WE1eziHNJTU868eYmEk8JdYl5tQzuXlOZjZl6XElZpvhQqS/LY0aBwl/BTuEtM6/UP8NaxDqqmJdaQTFB1aR47G9oJBJzXpUiCUbhLTNvT1IE/4BJuMjWoujSfjl4/h052e12KJBiFu8S02obBycaqaYkZ7sE3LQ3NSLgp3CWm1R5tIzczlfLCCV6XEhFzJ+eS7kuhVuEuYRZSuJvZajPbY2Z7zewr52n3YTNzZlYTvhIlme1saKNqWuJNpgalp6awoCRX4S5hN2a4m5kPuB+4AVgI3GpmC0dplwv8OfB6uIuU5NQ/EKCuqSPh1rePVFWaT21DG85pUlXCJ5Se+0pgr3Nuv3OuD3gYWDNKu/uAbwE9YaxPktje4530+QMJO5kaVF2aT3uPn8OaVJUwCiXcS4Ejw27XD913hpktBcqdc0+GsTZJcsGhiksSdDI1qFqTqhIBoYT7aIOdZ35/NLMU4HvAF8c8kNk6M9tkZpuam5tDr1KS0s6j7WSl+5hZFN8XxB7LvCm5pPlM4S5hFUq41wPlw26XAUeH3c4FqoANZnYQeBfwxGiTqs65B5xzNc65muLi4vFXLUmhtqGNhSV5+FISczI1KD01hflTNakq4RVKuG8E5prZTDNLB24Bngg+6Jxrc84VOecqnHMVwGvATc65TRGpWJKCfyBA7dG2hB9vD6ouzae2oV2TqhI2Y4a7c84P3Ak8C9QBjzjndprZvWZ2U6QLlOT01rFOevoDLJ1e4HUpUVFVmk/b6X7qW097XYokiNRQGjnn1gPrR9x39znaXn3xZUmye/PIKQAWlyVHuA+fVC0vzPK4GkkE+oSqxKRtR05RkJXGjEnJEXTzpw5+UnXb0JuayMVSuEtM2lZ/isVlBQn7ydSRMlJ9LJyWx1aFu4SJwl1iTlevn7eOdbC4PDmGZIKWlBewo75N11SVsFC4S8zZ0dBGwMGS8uRYKRO0dHoBp/sH2HOsw+tSJAEo3CXmbEuyydSgpeUTAdh6WEMzcvEU7hJzttWforxwApNyMrwuJarKCydQmJ1+ZqWQyMVQuEvM2XakLel67QBmxtLyArYebvW6FEkACneJKcc7emg4dZolSTaZGrSkvIB9zV20ne73uhSJcwp3iSlvDo03J2u4L50+OO6+vV5DM3JxFO4SUzYfaiXdl5I0e8qMtKg8HzNNqsrFU7hLTNl0qJXqsnwy03xel+KJvMw0ZhfnaFJVLprCXWJGT/8AO+rbqJkx0etSPLVsegFbDrcSCGiHSBk/hbvEjB0NbfQNBFie5OFeU1HIqe5+9jZ3el2KxDGFu8SMjQdPAiR9uK+sKATgjQMnPa5E4pnCXWLG5oOtzCrOTroPL400Y1IWxbkZZ97sRMZD4S4xIRBwbDrUyooZhV6X4jkzY2VFIRvVc5eLoHCXmLCvuZO20/0sr0juIZmgFRUTOdrWQ31rt9elSJxSuEtM2Hhw8CP3KyrUcwdYMXPw+6ChGRkvhbvEhE2HTjIpO52KJLny0lgWTM0jNzOVNw5onxkZH4W7eM45x+v7T7KiojBprrw0Fl+KUTNjonruMm4Kd/Hc4ZPdNJw6zRVzJnldSkxZMbOQvcc7OdnV53UpEocU7uK53+1tAeCy2UUeVxJbfr/evcXjSiQeKdzFc6/sO8GUvAxmF2d7XUpMWVxeQHa6j5f3nvC6FIlDCnfxlHOOV/e1cPnsIo23j5DmS+Fdsyad+c1G5EIo3MVTe4510NLVx+WzNd4+mivmFHHgRJfWu8sFU7iLp14Z6pVePkfj7aO5cu7g9+V3GpqRC6RwF0+9su8EFZOyKC2Y4HUpMWnO5Bym5GXw0tsKd7kwCnfxjH8gwOv7T2qVzHmYGVfMKeKVfS3a310uiMJdPLOtvo2OXr/Wt4/h3XOKONnVx67Gdq9LkTiicBfPbNhznBSDK+cUe11KTLtijsbd5cIp3MUzL+w5zvIZE8nPSvO6lJg2JS+TeVNyNO4uFySkcDez1Wa2x8z2mtlXRnn8L8xsl5ltN7PnzWxG+EuVRHK8vYfahnaunj/Z61LiwnvmT+b1Ay109PR7XYrEiTHD3cx8wP3ADcBC4FYzWzii2Vagxjm3CHgU+Fa4C5XEsuGtZgDeu0DhHoprKqfQP+DUe5eQhdJzXwnsdc7td871AQ8Da4Y3cM694JwLfsriNaAsvGVKonlh93Gm5mWyYGqu16XEhWXTC8ifkMZzdce8LkXiRCjhXgocGXa7fui+c7kDeHq0B8xsnZltMrNNzc3NoVcpCaXPH+Dlt09w9fxibTkQolRfCu+ZX8yGPc0MaEmkhCCUcB/tp2/U/11m9gmgBvj2aI875x5wztU452qKi7VCIlm9su8EHb1+rls4xetS4so1lVM42dXH1sO6gIeMLZRwrwfKh90uA46ObGRm1wJfA25yzvWGpzxJRM/UNpGTkXpmiZ+E5qr5xaSmGL/R0IyEIJRw3wjMNbOZZpYO3AI8MbyBmS0F/p3BYD8e/jIlUQwEHL/edYz3LJhMZprP63LiSl5mGpfPKeLpHU04p6EZOb8xw9055wfuBJ4F6oBHnHM7zexeM7tpqNm3gRzgv83sTTN74hyHkyT3xoGTnOzq44aqqV6XEpc+UF3C4ZPd1Dbo06pyfqmhNHLOrQfWj7jv7mFfXxvmuiRBPVPbSEZqClfN05zLeLzvkil89ZfGUzsaqS7L97ociWH6hKpEzUDA8XRtE1fNKyY7I6R+hYxQkJXOFXOKeGrHUQ3NyHkp3CVqXtl3guMdvaxZcr6VtDKW9y8q4cjJ0+xoaPO6FIlhCneJml9uaSA3M5VrKvWp1Itx/cKppPtSeGzrWYvWRM5QuEtUdPf5eWZnE++vLtEqmYuUn5XGdQun8NibDfT5A16XIzFK4S5R8eudx+juG+APlmpIJhw+vLyMk119vLBHK49ldAp3iYpHN9dTWjCBlRWFXpeSEK6cW8Tk3Az+e1O916VIjFK4S8QdONHFy3tP8LEV5aSkaC+ZcEj1pfCHy0p5Yc9xmjv0gXA5m8JdIu7B1w6RmmLcsqJ87MYSso/WlDMQcPy/jYe9LkVikMJdIqqnf4BHt9TzvkumMDkv0+tyEsrs4hyunFvEz147TP+AJlblnRTuElFPbm/kVHc/n7hUF+eKhNsvr6CpvYdndzZ5XYrEGIW7RIxzju+/uJ+5k3O4bPYkr8tJSO+ZP5kZk7L4j1cOel2KxBiFu0TMC3uOs+dYB5+5arYuyhEhKSnGJy+rYOPBVjYf0j7v8nsKd4mYf92wj2n5mdy0ZJrXpSS0W1eWU5idzj/99m2vS5EYonCXiHjjwEk2Hmxl7apZpPn03yySstJT+ZMrZ7JhTzPbjpzyuhyJEfqpk7BzzvGtZ3ZTnJvBx7T8MSo+eVkF+RPS1HuXMxTuEnbP1R1n06FWvnDtXLLStbVvNORkpLJu1SyeqzvOa/tbvC5HYoDCXcLKPxDgW8/sZlZRNh+tUa89mu5490ym5Wfyt0/tIhDQXu/JTuEuYfXTVw/x9vFO/mr1fI21R1lmmo8v37CA2oZ2fr5Fe84kO/30SdgcPXWav//1Hq6eX8z1l+gaqV744KJpLJ1ewDef3k1Lp/acSWYKdwkL5xx3P76TAee4b02V1rV7JCXF+LsPLaKjp5+7n9jpdTniIYW7hMXDG4/wXN0xvnjdfMoLs7wuJ6nNn5rL56+Zy1PbG3lqe6PX5YhHFO5y0fY0dXDPEzu5cm4Rd7x7ptflCPCnV81mcVk+X/n5dg6c6PK6HPGAwl0uSlt3P3/24GZyM9P47keXaL/2GJHmS+H+jy/D5zP+7Geb6e7ze12SRJnCXcat1z/Auv/cRP3J09z/R0spzs3wuiQZpmxiFv9wy1L2HOvgroe2alvgJKNwl3Hp8wf4wsNv8vqBk3z7I4u4dJZ2fYxFV80r5r41VTy/+zhffnS71r8nEX18UC5YT/8An3twC8/vPs7ffGAha5bootex7BPvmsGp7j6+8+u36A84/v4ji0lPVb8u0Snc5YIca+/hMz/bzNbDp7jvD6q47V26CEc8uPO9c0nzpfDNp3dzsquXf751GROz070uSyJIb98SspfebuaD//Qye5o6+JePL1Owx5k/vWo23/nIYjYeaOXGf3yJjQdPel2SRJDCXcZ0orOXLz+6ndt++AY5man84rOXc2N1iddlyTh8eHkZv/js5aT5Uvjov7/K1x/bQVt3v9dlSQSYc95MsNTU1LhNmzZ5cm4JzfGOHn722mF++NJ+evwB1l45iy9cO5fMNJ/XpclF6uz1891fv8VPXjlATkYqf3LlLD51WQX5WWlelyZuBZtOAAAGfElEQVRjMLPNzrmaMduFEu5mthr4B8AH/MA593cjHs8AfgosB1qAjznnDp7vmAr32NTrH+CVfS08vrWBp3Y00j/gWH3JVL60ej6zi3O8Lk/CbNfRdr77m7d4ru4YGakp3FhdwkeWl7FiZqE2fotRYQt3M/MBbwHXAfXARuBW59yuYW0+Cyxyzn3GzG4B/tA597HzHVfhHht6+gfYebSdLYcGr8H5u70n6Oj1k5uRyodryrjtXTOYpVBPeLuOtvPQG4d4fOvRwX//zFRWzS2mpmIii8oKuGRann5jixHhDPfLgHucc9cP3f5rAOfcN4e1eXaozatmlgo0AcXuPAdXuIefc45ef2DwT/8Avf4AXX1+Wrv6ae3u42RXH61dfTS193CopZsDJ7o42naa4L9SeeEELp9VxPVVU7h8dpF+mJNQd5+fF99q5oXdzfzPW800tfcA4EsxyiZOYHphFuWFWZQWTKAwO52JWWlMzEqnICudrHQfGWkpZKb5yEz1keYzbSAXAaGGeyhLIUuBI8Nu1wOXnquNc85vZm3AJOBEaOWG7pGNR3jgpf0MnWvw7+EN3NlfDn+PGd42eLcbdu/wt6PR3ppGO9Y7njPKsUY75/BH3HhqHvF431Coh6IgK40Zk7JZUTGRGZPKqCzJY9mMAibnZob0fElcWemprK4qYXVVCc45jrX3sq3+FLUNbRw40cWR1tM8U9vEya6+MY9lBpmpPlJTDLPBN4gUGwz8lHfcHvb1hRZ8gU+40ONf6JtTqK3//Jq5fHBxZC8cH0q4j1bvyNgLpQ1mtg5YBzB9+vQQTn22idnpzJ+Se9aZhxcw/B/Eztw3erHBtu94Ae9oa2M8/53tzmp75utzPD7qfWOd8+xvd0ZaChmpPjJH/D0hzcfE7DQKs9MpHOph6QMsEgozY2p+JlPzp561P//pvgFau/to7e7jVPfgb4an+wboGfZbY0//AD39AwwEIODcmT8DgcHOyeBtCASG7r/AtR0XuhjkgpeOXGg9F/CE/AmRn7gOJdzrgeHXSysDjp6jTf3QsEw+cNYiWufcA8ADMDgsM56Cr1s4hesWThnPU0UkTCak+5iQPoFpBRO8LkXOIZQu3EZgrpnNNLN04BbgiRFtngA+NfT1h4Hfnm+8XUREImvMnvvQGPqdwLMMLoX8kXNup5ndC2xyzj0B/BD4TzPby2CP/ZZIFi0iIucX0t4yzrn1wPoR99097Ose4CPhLU1ERMZLM2siIglI4S4ikoAU7iIiCUjhLiKSgBTuIiIJyLMtf82sGTjkyckvThER2FYhxiXba0621wt6zfFkhnOueKxGnoV7vDKzTaFs2pNIku01J9vrBb3mRKRhGRGRBKRwFxFJQAr3C/eA1wV4INlec7K9XtBrTjgacxcRSUDquYuIJCCF+0Uws780M2dmRV7XEklm9m0z221m283sl2ZW4HVNkWJmq81sj5ntNbOveF1PpJlZuZm9YGZ1ZrbTzD7vdU3RYmY+M9tqZk96XUskKNzHyczKGbxo+GGva4mC3wBVzrlFDF4s/a89ricihi4Gfz9wA7AQuNXMFnpbVcT5gS865yqBdwGfS4LXHPR5oM7rIiJF4T5+3wP+inFcvSveOOd+7ZzzD918jcGrcSWilcBe59x+51wf8DCwxuOaIso51+ic2zL0dQeDYVfqbVWRZ2ZlwPuBH3hdS6Qo3MfBzG4CGpxz27yuxQN/DDztdRERMtrF4BM+6ILMrAJYCrzubSVR8X8Z7JyFdlX5OBTSxTqSkZk9B0wd5aGvAV8F3hfdiiLrfK/XOff4UJuvMfhr/IPRrC2KQrrQeyIysxzg58AXnHPtXtcTSWb2AeC4c26zmV3tdT2RonA/B+fctaPdb2bVwExgm5nB4BDFFjNb6ZxrimKJYXWu1xtkZp8CPgBck8DXxw3lYvAJx8zSGAz2B51zv/C6nii4ArjJzG4EMoE8M/uZc+4THtcVVlrnfpHM7CBQ45yLxw2IQmJmq4HvAlc555q9ridSzCyVwQnja4AGBi8O/0fOuZ2eFhZBNthD+Q/gpHPuC17XE21DPfe/dM59wOtawk1j7hKKfwZygd+Y2Ztm9m9eFxQJQ5PGwYvB1wGPJHKwD7kCuA1479C/7ZtDPVqJc+q5i4gkIPXcRUQSkMJdRCQBKdxFRBKQwl1EJAEp3EVEEpDCXUQkASncRUQSkMJdRCQB/X/ndaAkym0fmgAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(-5.0, 5.0, 500) # input points\n",
"def gaussian(x):\n",
" return np.exp(-x*x) \n",
"\n",
"f = gaussian(x)\n",
"plt.plot(x, f, label='gaussian')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(500,)"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 2.2 Now, let's code the single node as per the image above. \n",
"\n",
"Write a function named `affine` that does the transformation. The definition is provided below. Then create a simpler sigmoid with just one variable. We choose a **sigmoid** activation function and specifically the **logistic** function. Sigmoids are a family of functions and the logistic function is just one member in that family. $$\\sigma\\left(z\\right) = \\dfrac{1}{1 + e^{-z}}.$$ \n",
"\n",
"Define both functions in code. "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def affine(x, w, b):\n",
" \"\"\"Return affine transformation of x\n",
" \n",
" INPUTS\n",
" ======\n",
" x: A numpy array of points in x\n",
" w: An array representing the weight of the perceptron\n",
" b: An array representing the biases of the perceptron\n",
" \n",
" RETURN\n",
" ======\n",
" z: A numpy array of points after the affine transformation\n",
" z = wx + b\n",
" \"\"\"\n",
" \n",
" # Code goes here\n",
" return z"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"# your code here\n"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"# %load solutions/affine-sigmoid.py\n",
"def affine(x, w, b):\n",
" return w * x + b\n",
"\n",
"def sigmoid(z):\n",
" return 1.0 / (1.0 + np.exp(-z))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And now we plot the activation function and the true function. What do you think will happen if you change $w$ and $b$?"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"w = [.., .., ..] # Create a list of weights to try\n",
"b = [.., .., ..] # Create a list of biases\n",
"\n",
"fig, ax = plt.subplots(1,1, figsize=(9,5))\n",
"SIZE = 16\n",
"\n",
"# plot our true function, the gaussian\n",
"ax.plot(x, f, lw=4, ls='-.', label='True function')\n",
"\n",
"# plot 3 \"networks\"\n",
"for wi, bi in zip(w, b):\n",
" h = sigmoid(affine(x, wi, bi))\n",
" ax.plot(x, h, lw=4, label=r'$w = {0}$, $b = {1}$'.format(wi,bi))\n",
" \n",
"ax.set_title('Single neuron network', fontsize=SIZE)\n",
"\n",
"# Create labels (very important!)\n",
"ax.set_xlabel('$x$', fontsize=SIZE) # Notice we make the labels big enough to read\n",
"ax.set_ylabel('$y$', fontsize=SIZE)\n",
"\n",
"ax.tick_params(labelsize=SIZE) # Make the tick labels big enough to read\n",
"\n",
"ax.legend(fontsize=SIZE, loc='best') # Create a legend and make it big enough to read"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We didn't do an exhaustive search of the weights and biases, but it sure looks like this single perceptron is never going to match the actual function. Again, we shouldn't be suprised about this. The output layer of the network is simple the logistic function, which can only have so much flexibility.\n",
"\n",
"Let's try to make our network more flexible by using **more nodes**!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Multiple Perceptrons in a Single Layer\n",
"It appears that a single neuron is somewhat limited in what it can accomplish. What if we expand the number of nodes/neurons in our network? We have two obvious choices here. One option is to add depth to the network by putting layers next to each other. The other option is to stack neurons on top of each other in the same layer. Now the network has some width, but is still only one layer deep."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"x = np.linspace(-5.0, 5.0, 500) # input points\n",
"f = np.exp(-x*x) # data\n",
"\n",
"w = np.array([..., ...]) # ENTER TWO VALUES HERE\n",
"b = np.array([..., ...]) # HERE TOO\n",
"\n",
"# Affine transformations\n",
"z1 = w[0] * x + b[0]\n",
"z2 = w[1] * x + b[1]\n",
"\n",
"# Node outputs\n",
"h1 = sigmoid(z1)\n",
"h2 = sigmoid(z2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's plot things and see what they look like."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": false
},
"outputs": [],
"source": [
"fig, ax = plt.subplots(1,1, figsize=(9,5))\n",
"\n",
"ax.plot(x, f, lw=4, ls = '-.', label='True function')\n",
"ax.plot(x, h1, lw=4, label='First neuron')\n",
"ax.plot(x, h2, lw=4, label='Second neuron')\n",
"\n",
"# Set title\n",
"ax.set_title('Comparison of Neuron Outputs', fontsize=SIZE)\n",
"\n",
"# Create labels (very important!)\n",
"ax.set_xlabel('$x$', fontsize=SIZE) # Notice we make the labels big enough to read\n",
"ax.set_ylabel('$y$', fontsize=SIZE)\n",
"\n",
"ax.tick_params(labelsize=SIZE) # Make the tick labels big enough to read\n",
"\n",
"ax.legend(fontsize=SIZE, loc='best') # Create a legend and make it big enough to read"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Just as we expected. Some sigmoids. Of course, to get the network prediction we must combine these two sigmoid curves somehow. First we'll just add $h_{1}$ and $h_{2}$ without any weights to see what happens.\n",
"\n",
"#### Note\n",
"We are **not** doing classification here. We are trying to predict an actual function. The sigmoid activation is convenient when doing classification because you need to go from $0$ to $1$. However, when learning a function, we don't have as good of a reason to choose a sigmoid."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"# Network output\n",
"wout = np.ones(2) # Set the output weights to unity to begin\n",
"bout = -1 # bias\n",
"yout = wout[0] * h1 + wout[1] * h2 + bout"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And plot."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"fig, ax = plt.subplots(1,1, figsize=(9,5))\n",
"\n",
"ax.plot(x, f, ls='-.', lw=4, label=r'True function')\n",
"ax.plot(x, yout, lw=4, label=r'$y_{out} = h_{1} + h_{2}$')\n",
"\n",
"# Create labels (very important!)\n",
"ax.set_xlabel('$x$', fontsize=SIZE) # Notice we make the labels big enough to read\n",
"ax.set_ylabel('$y$', fontsize=SIZE)\n",
"\n",
"ax.tick_params(labelsize=SIZE) # Make the tick labels big enough to read\n",
"\n",
"ax.legend(fontsize=SIZE, loc='best') # Create a legend and make it big enough to read"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Very cool! The two nodes interact with each other to produce a pretty complicated-looking function. It still doesn't match the true function, but now we have some hope. In fact, it's starting to look a little bit like a Gaussian!\n",
"\n",
"We can do better. There are three obvious options at this point:\n",
"1. Change the number of nodes\n",
"2. Change the activation functions\n",
"3. Change the weights\n",
"\n",
"#### We will leave this simple example for some other time! Let's move on to fashion items!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Part 2: Tensors, Fashion, and Reese Witherspoon\n",
"\n",
"We can think of tensors as multidimensional arrays of real numerical values; their job is to generalize matrices to multiple dimensions. While tensors first emerged in the 20th century, they have since been applied to numerous other disciplines, including machine learning. Tensor decomposition/factorization can solve, among other, problems in unsupervised learning settings, temporal and multirelational data. For those of you that will get to handle images for Convolutional Neural Networks, it's a good idea to have the understanding of tensors of rank 3.\n",
"\n",
"We will use the following naming conventions:\n",
"\n",
"- scalar = just a number = rank 0 tensor ($a$ ∈ $F$,)\n",
"
\n",
"- $\\mathscr{N}$D array = rank $\\mathscr{N}$ tensor ( $\\mathscr{T} =[t_{i1},...,t_{i\\mathscr{N}}]∈F^{n_1×...×n_\\mathscr{N}}$ ) <-- Things start to get complicated here...\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Tensor indexing\n",
"We can create subarrays by fixing some of the given tensor’s indices. We can create a vector by fixing all but one index. A 2D matrix is created when fixing all but two indices. For example, for a third order tensor the vectors are\n",
"
\n",
"$\\mathscr{X}[:,j,k]$ = $\\mathscr{X}[j,k]$ (column), \n",
"$\\mathscr{X}[i,:,k]$ = $\\mathscr{X}[i,k]$ (row), and \n",
"$\\mathscr{X}[i,j,:]$ = $\\mathscr{X}[i,j]$ (tube) \n",
" \n",
"#### Tensor multiplication\n",
"We can multiply one matrix with another as long as the sizes are compatible ((n × m) × (m × p) = n × p), and also multiply an entire matrix by a constant. Numpy `numpy.dot` performs a matrix multiplication which is straightforward when we have 2D or 1D arrays. But what about > 3D arrays? The function will choose according to the matching dimentions but if we want to choose we should use `tensordot`, but, again, we **do not need tensordot** for this class. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Reese Witherspoon\n",
"\n",
"This image is from the dataset [Labeled Faces in the Wild](http://vis-www.cs.umass.edu/lfw/person/Reese_Witherspoon.html) used for machine learning training. Images are 24-bit RGB images (height, width, channels) with 8 bits for each of R, G, B channel. Explore and print the array."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
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gLaooiiwC0nE8HM+39xdIDg2e4MaNa1x5TUfvr1x5jTu3tMl+cHDA0ZF2EVpRi16vR7vdtWPOMr1T3759m96ZHfN8kX3mPM/JTDDP9XyioEFhAopSSltivbu1zdm9PTtPR/u6oGo+m1nU5Xg5ptPpIMxE14vDut0uvhea64549dWXAfjoMx+3fBJXr15la2cPhG/mpoHvm3oPKVBKL4tC5TWLdNWlFUKsdsv5EMk3rRSEEBeBnwP20Db0Tyul/q4QYhP4ReAycBX4caXU6OGHenrkfrX7QkEc66i+7+sFOZvpFF2WZRZRmMzn7N/SVYbjq1d54403AAijiGeeeQaA7/3+72M8HtNu63NGoxFN03SlHpPxPM+mHaMoQppin/l8wmB0kzt3dNXi7Vs3Kz6DRsS583pRfvq7XmD2Ea2gGo0Gw+HQjv/4eMZsqpXUYrGw66PZ7tDo6HHlec7RcGTHZQoWSedLOp0erqgavSQm3vH6669zYNyXzV7XugV5nluYtBu5HBr+B9CKoFysk8nEkqtsb2+TZ9rcf+2113j2Y58AoFApr7z6Et3+hnmewGZclBvVXImKjE6qkr6u3ATqzDbvJKvu5WmQhxlpDvxnSqlnge8F/gMhxMeAvwL8hlLqI8BvmJ/Xspa1nBL5pi0FpdQd4I75PBVCvIzuIfljwGfNYT8L/Cbwkw81yhMspavwbsw+SkAQGZbixQylFA1TYxB5HvOZrh1468obHBwak/nWDYJIm7jPfuyjdjeMooCiZnk0m03rctQDra1Wk8jUDiiliHO9G0spEcLl/NlzADz5+BP2QQLXIzdR+TRJGBpy1sPDQ+sujMdjHOGxs6PdhMFgSNkZptff5MZt3UZ0sVjY4GIQRIQGlBT6EUJhrRghFb2ehjzvbG+TmCzHwcEBM8MGDZCa7EHMnFarZc8fD4Z4pvCr3e6CgSzPp1OLkxCezxtXdKBx7/xlZJZz7S0dxH3qIyFeX9+/KDKUeRbhOtZFEYCj3ArboZStC9G/qO+v97MOTg+J7AcSUxBCXAa+C/gD4IxRGCil7ggh3j931imUunKwEed7eAEtJ6IQuChbteg7LlfNC1ukGa98/esA7HVdnn/+eUCbz5FJLwohKPLUKgKphPXdG42GTUPWYw2L+dz63kmS8PRTH7UVhHEcM51oM38+X3B4qNOI9SKqMGxYt2S5SBDCITO1EEmaV/TtwiUzvn+a5mxv6wj/4eGAuclWbG1tMRyO6TRb5tohsYmpKKWotxFM4goUlRkTX4qc0dGhVQqdTgfPAJaWy7n93Gg0SMwct9tt8kIv4uV8ynBwZJ9tZ+cMG5tGKUhBlUsQyJIHk5Li7v1ltiyD3vs669srD+3oCCHawC8D/4lS6vh9nPcTQogvCiG+WAaw1rKWtXz75aEsBSGEj1YIP6+U+sfm1/tCiLPGSjgLHNzvXKXUTwM/DZq49WHG8e0URzlV/4V7RDMUV9aCpQbzBFmeEhlI7eBgn2ypd8Tf+e3f4ns/8xkAzu40rIvQajVZGp6D4+Njey2A3b0ztoy5bh2MRiO7G7aaTWuiO47DaHBEIfUummUZyjxEq9VC5pqbYRFGNpOxv79v2ZgbjQa5lBwd6sBj0GgSmT2xEbXYM4HKxWJhzwnDkCTW95sfz2k3misVnCVt22Qy4eyudkt2d7et+e95DsNhbsa7wBWOtc6SZWyDg0EQgGeAWEVmf4/KuXBOYymuvHGVqNlmPtPz//I3/pCLFzWewfUbFjNTCLCkEUqiangaV1Rdux8stb+/17jkCZCHyT4I4H8GXlZK/e3an34V+IvA3zT//8pDjfBDJJb9WEAUhExNQdGNa2/wxquvAPCjn/+8TVkul0vbyj1XkjjRiuN4NufcuXN2wSyT2KbrPM+zL2673bZmr4NgPtdxiziOkXnFUdhsNWmadOV8PrU9I2ezmXULHMexRCSNRhMhod3rm58bzE3/x3qWIMsyplN9fhRFBCbtt1wmhGG4glwtn7PTaeGa2MNgMLAumJQSz/zeK1y80FkhiUmz2I6zlDTNaXf1GKezJdOZjk+cv3CO2XzJ0DxPv9/n1Zd1q9Onnvk0yqA4hePVHAkX3WSzpL1TVIb26YkXvBd5GEvh+4G/AHxNCPGi+d1/iVYGvySE+MvAdeDPPtwQT4fUezLcV4S0FXiB5zE7nnD3jk497t+9w0ef0v0NVJGwt60X+zQZMV1UcYBysX3qjzxPURQMRnqn3trcsQqnqBGSOi6khi59GSd2EbXbbWSueOstne4cDfRiBPA9hz2DE3jqicet1TEcDtnd1eGh8XjCcDSxcYx4mdpiKXAIg6pi8oUXngDg5s2bTI/1s+zs7HBwcES/owOXQRCQm/hEmqZsbGiLJgg9q4i0QjOIyEWBUA5uuWt7TtUdO0+q5/d8Fibu0m61ORpopbCx1QBZWJj13Vs3LX18sozxTX8JL8SyOLkCFMJWfcoaZ+ZpDSg+SB4m+/A7PJin5vPf7HXXspa1fHvlVCIa78fO9KAGMo9aChSu41JYai9VK8mt2Io0mk6PLVnOSZZT7hqQ0t72Bu2m3p1EUXBs0oCZX2gTGp1qe/7Tmhvgxo1beIFPr6stitlsVjVKSVO7u+ZZNZYoiuyuP5/PcXD5pKFMX87npCay/6/+4Hf52h9qw++tt97iscc0W1Kj0WA8NnFkx6HT6+EIPeZCCZuSBIc0q9Kjd0yswHVdOqYtfZ7nbG5ukpkU42I54/x57dPv7GzZa0VRZBmjiyKn1TWgqLTDcrlcqR+x5eJhYEFSDsLGZFw/oGvOn0wmdLt9FiYN3Gi0LHJyMj7i7Hn9zI4ryAy3BJ6PorC8Eeo91+qYWgmlR3Qa5FQqhftVSH67KiKFUChVoMqAlMD4npqYRFlzUiHzsvpQuwz9njbZi3iBQC8wpTKk0i/7nTsHfOQjmnswTjIbjGu1WqR5ZqHRvV7PKh/f960pn6ap9bWFOQ90B+jh0Yjf/33NNTA43Gf/7m1zvmvv+dkf/AEbh/B9n5u3NQLy619/iVdeepnAkLJmUlnkYLPdotWuOB5jV98/Cho27hH4ETJPbfcpIQRXrmhotZRPWPdhMNynbfpWbO/ucPWqxhXIPF+JScxmM/s5CAKrCPO8wDPkrHme4xs+BqEK8jy3adBGo8GxSckODg/om/s33Y49fx4vcIOQhsF9LBaLb3Hh3bdOTofqWsta1vItkxNnKbxbd6h3O+5+xz5ScQRFLTXlUGd+KiwQxkHZdvH7t24xnYxpmI2m3++ymOqdSiYJxwbF9/Qzz3D9umZb2jtzrip0Gt3l3NkLNvAnpbLFUp4nLO/BfD63JvvmZs8GKl955TW+9tUXLchpc7PPs888BUCWxGSGLPXq1Te5fk1Tr7uuy3gytce0GhGpGY+Q2tQGWMynLOZ6/L7vW7dmOplZBGe6jOl2+/huSQcnLJ/BeDRAFtqiuHz5ks2ejEcDNvo6MDhNE+bzuU0Fl6lNgPlyQRjo3by3sWlp1ubL2KIrO50Oo8mEbUPPFscJzZ4+5/atazz99FPmq5VkubFuAg+FshmgB1sJ9TT06Qw6njilAO+fkfkkMDjXq+ekqQaslePr4p+S1CTPaEchvqNf+MHhHUtsIvOUy5e1T3v34IAzZ3QXpDiO7Qt+/vx5Nje2LBvxcDK2L2mRFDQaerH3ej0bX7h69So3b97Uxw+HPP3009ZMd4ViZGIX1956ndu3NEx5PBzaFN9yubRKqdkKaciQiSmIygpJaDAXcZziB3osm5ubdoE2Gw2OJzrWsLu1Tb/ftynVW7dv2NhJq9lgs4QcZ4mFXKuiYGTo2zylXaESjjyfz+3YHNdfyZjs7Z2zY3QcQxgjJf1u17pfruta10ZORgxHGlpzvt2wCj8IW6SZtPcJA/9dcQqnCJqwImv3YS1rWcuKnEhL4TSJEhIlJMLsqILKcnGEwi2zIlnKDWOKjwcHuCojl3pHC0IPYdyMeLHk4FAH9Hq7j9l6gX6/T2CCXN1OH8/zuW0i5jvbZ5hOp2Y8FdJuNpszHOod+HgysQVMzz77LEW+sLve8XjEkaFNOxockGXVuOK53t2jwEWYwOL4eEYcJzRMM5em65FkZSepDp4piQ4dj62ePmY5j9nsaleGIqffadNp6uv94Pf9MRt03N+/y40bmuB1qXIyQyibZZltiJskqe5/aQrMms0m5aatqArFkmzBobFA+v0NC7ACHZCcTPXftrd37TlBlPPySxrItLG9RdQqMx4xOJ7ts5kkKY54H8tHyHuKpk6unEil8H5dgG9n0xcp7tOxquQzcBwKY77PxiNGZoG2ohDPCTjc1+ZwM3KZzTQceG93x/Is7N89tAsZx7XZAyklk8nEvpQ3btywbobruuTGfF4ulzYTce7cOevKxHFMv9+0imSxmNm/ndvbY2YaqMwmY0Svba9VFBVPQ6EEYdQy9/SJU/2cizimY5SH7wcU5ve9bpulUXCdTot0sSTzTRzh6NBmT1phxEVTvTlbTEgS890GASPTocpxHGbLBaHJPTabTXyDdsyyDN+gM9thyJ39AzNGj5ap8iwKxWw2Y8cUXi2WyxXCmWPDkj082mfboBvDVpekkCudqutSgtfeiY7vtMjpUF1rWctavmVy4iyF97rrn6SWcFJoMlAAJRVl1NkRrmUQPtw/sGAd6cLdwV0akWnYmsc0ze48GA9scO3xJ56xQbN2u21BOUWRkuSZbe6imYd0cG8+n1lLwfd9m2EQKMsN0Gq1iOOxvc+ZvR0b8e+c3+WrL35F37PTJDQ7ZZ63bSv3KGoShA1NeAq4XoBj8vmz2YLYBBSTJCEwZcwyyegad0EmGV5LIE0zGBGFHBtWp063RdMwU6sisgVJvu9SGLcmTnJCcy3QtRTC0WNrNpsIk9UoCmWzH6PRiP6GtgzSdEkQeHbXT9PUBmpFGtPuagvo1q0btEwwtN3fIJWqwloEEbWatA+VnDil8F7kJCEaS/BS1ZawqIpoBJYDYDwe0zNY++nkEMfBLnjXkczipTk/44knLwO6GnJ7t+Q7DG3tgOO4LBYL2jv6enledXIKgohGyf2IrPovOtV8SZkThj5FYY6TOWf2dHrz2htX2N01nad811K4Oeh4BUCSZKSZIohMZiLOmE9NtyYUDaOsHCFwjF0dNBqWrj5oBIShT9/0kgTYtMVdCwuY6ve7lmI+zWI2zQI/GB+zXC5tNqHZbFrAmJSS3Iw5CCIck67MspxvfEPHCj796e9mMpnY+e+2m2TGNUqzxC78g4MDPmq+1+VyiZSOVcRZVrxvboXTImv3YS1rWcuKnEpL4VHCnOvEp+/l/kJ5+I5DbkzhKPStmTufHHHjqmYT7kY5cqGzBYGc4arEAmHmcUxv05ip3Q0Wpu1a1Nql2dK79s2rb7C9pXfK+XTC5b1dJjOTt/dDS0EmXEFqdrBcCqKGNoXTorDjns/nuDKkbXbeo4NDC+e9eOnj+Ob5J4NDi61QWcpgoGsypsNjMlnVWCziWlQ/ChFC37PX7liWZsepSp09zyMMfVKZmEmsBfBciJoG5JRnOCUFXVAxP3U3HfrOpsU2ZFk1lk6ng2PaK6R5bH/vBw5PfeRxAH7/D36H7/mjP8BkPDXHSXvtdiCYjUzGYmuPoztH5rq7RH6rnA68Qtao2mr9HIS0zFsFDoXJxCgcvFPS9+FUKoVHKe9FudTdl8KU0JY+aZZleAayMp1ObRciRxTMTIPVRiRI09RG07u9Xq0tfIRjrtVohLz8ja8B8OTjl5ke6+Mb7RbTxdI2SM2ygtDEJJKisDUJoetZgI4uLtKLd3tzA5HOSU2xUTPwafj6nNFyiTC+0NH+Ab/3u/9S3yNJEYZOrtFo0Ot1aZi6hEarbbMcURTR6WiXx3VdC36qd+7Sc1cH/jhkhR5nnuc2E6KUslF9rUj0HPWbTWbzY554QpdlD4dDbt/WxWWTSVXSXf8ufd+1FPXnzp3jjTde5/Klp+w5jmmrlaYJ7f6WHX+ZoXEchyxP8Fyt5HJVIERpaNdQjMpBnnL7+0QohUcZB3ivsOlv9rqyAN8ViNJ3XaYUZquajAdIE43KZWUZCOlw89Z1zp3TqTetBPSbJKUTty0eAAAgAElEQVS0jEzTyYhtY0GMJyNSE3fY3d1lcjxCOBUZiDKRDN8PK0WkFF2zcBfzKcKMJZtPEfGUKDQcCL7DG6+8BMA/+/VfR5nddavfo9XS2IKwH9jWdN1ul06vSxQZtifPsxZBGIZ4XhnTwD7/ve38siyzlZlZlq0oDNetFElqgptZmltrYl5Itja3GdkGuy3OmjTm8fGxxV9EUWSZn9rdHscGl9DpdDk+GnJ3XxeB7Z05ZyHg5XgAZoMBYVtbU2EUks4ScoOnOM3dzN9NPrxPtpa1rOWbkhNhKQD3mJYf/HXvvfYHdT8hXKSs6AQ832VuynCT5RzH+JGL5ZQs0zv9bDLFcRybLvSDgNFEFxFtbmwxn5emtMO2sSZu3rzOc889B8Crr79G1GjR6WsrIGo07e5W38FEkRNPTeepRoOlaUgbuor2Zo8v/LZ2Df75P//nFnC13e9bluUg8Oi0dIaj0WjYyHvU1PyKyqRBXdfFNVkCzw1QBqkppbSgpJU6AVmY2E1lRUiprYtCZrVMUtWhqSgK5MLwTW5ucOvWLc6e1ZyLk8lkhX+ypJAbjsdsbWlXZv/wgI5pUjOdHmuafMOVIFVuS8wD368smMKxxWWL6Qw/iMjNc3heQG7QlvUChwdR/Z+cBPq7y4lRCqXcL9140qSuaFzhkOcZvuESDDyX24YkRRapXSCL2ZiRCdS1WyHdbtsGqsbDCWfN4l8uE7Ky8OnsFlff1DwDm9u7vHlVw6R3z5xlkSR4BhG4MLBfMPTvJujpey5tY/IfDw7YM2nH4eCQv/03/p6tstzstK2/fu7cOfomPVgiGEF3firdhShqIhzHYiNK5QC6YlPlc3N+UaOJy6xikOjFW8ZEosixyiyOsQtUKWXRiUJVimU6ndNudxkMtPLd2OixNJWd2n3RczGrEcdeunSJ69dumusKtnZ27fk3blyzrtxyfIzf0Oe32k1mJqbwta++yCe/69MIs2RKWHYpysYXanBmgW1CK8XpqZhcuw9rWctaVuTEWQoftDzI6ni/yMkHB0MFSGUDUJ4qmJiUliqWpEsdwFocj0kTvYPKhsve7jmu39QR87N7F230fnq8tGi9u7ev23RXv9tmaliWb926xflLj5OXYW4hKEybeYqUljlfZSkLU2680W0wH+omsv/bP/oHkGUUsbZitje3rCne2+jrFCcQNpo0Wto6SJIMYXZ2IVykEhV7uhTWTchziefcb66qbkuO42j3oyRbzbDPX7cuZC2FJ1G2QW0uBVmS0jLuwJ07+5w9q2s/lIgst8SFC4/ZjMPh4aEt1XZdl9v7d+h2tMuxWCwskMmPfNskxw2b5IYF68aNa3zsE5/E9bVV5LseibEC6y6DfMA+e98pOaHy0EpBaBvyi8AtpdSfEkI8DvwCsAl8GfgLSqn0na7xKOVhXJF3Orfejdh1XaQxeY8nQ5YzU7hDwtjQuMfLiWU5bjUjjo+PrY/u+77tiZBlGW1H+/E3b1/h+Re+G4DZdMLI8BdsnzmLF0TMjL/r+6FdcEWRMjrU9z9/ZpsGRsHcvMbf/x//HgCbmxvsbO/a7k1bu2fYMa5Ep9fDNYQnwvVtrwm/2UGpKg2rCmUzHiBwnBKDIFG5OU5iOywB1l0ASaGUdQfKeIg+36vRyVXZhzpLddhqaXZrgzPY2tYdpwBanaYllhlPj6u2ca5jK05936fX69k0cqfbZjDQCvPi2XNkMz3PMs8IoxL1mVHkKYEhinFdAdWwVxKsK3GFuttwShTDB+E+/MfAy7Wf/xbw35sGsyPgL38A91jLWtbyLZKH7RB1AfiTwH8N/KemQczngD9vDvlZ4K8BP/Vu16pnAx5VJuK9yIMCnQ9COsq8IApcMvO3+XRCbrIMroxZGMBRnsV2B4uikPl8TtTQPzcaDfbv6hLfixcfr3LrrQbTif6MF9gdtL+xwWB0TGgYlhwHlsZqaPseUbvED7jsX9W5+H/493+KnW0Nygn9gJ2z5y2D8sbmNm3De+BFIXPjpiiZ4xkOhyyXVQjd83Bdx4KcikLZGgkhBMIEQCGtsg6ug+uUAUmBzCvcged5ZFmViSilKIqVrEppWU1ncxzHsfORLNMaeKwgz7UF0ev1ODjSFsD29jaNhp6j0XCC6wrrJiRJZntADIdDwoap3XAhMxZgPoXhYJ8NwwG3iFM7/3WXYTX7IE9lKfXDug9/B/gvAMOewRYwVsqGZm+iO1G/o4haO65vtziOswKyeTdxPQdZZDRMlP/uzWuEBnyzf/cWgV8yOwc0TVXk8OiAze0zSKVf5MmkAs4IIbhxTfMy/sAPfg8HxhVQbsHWrvb7r169ytnzl5ibVnOucHDKlnSOR98Alr7xpS/xK7/8SwBsbWzSNwv//PnzbO09Sa+sANzo45UmuypwTAu6TBbkRclSLVZcJoeirEHCcYTln9SHmopDEVrKNJnltmhLKZ2SLBd1HMcWzuy5LrlbpTrLoqeiKFgu9SJuNJoslwsLZz6Oj21lo1KK8Vind70wsHwU0+l0pSFtkiTWz3fRDX8B3BLQBeR5aqtXheNx6/p19s5e1GNOar4D7951/DTJN70ShRB/CjhQSn2p/uv7HHrflbVuMLuWtZxMedi2cf+mEOJPABHQRVsOfSGEZ6yFC8Dt+518UhvMvtfaB+viOII0icmlNk3j5YLQRM2zJCZdavP/3N6uBb6EYch0OmVrU+/80+mUc3vaoLpx7WrVI3K5tCb2Il2waXbTTqfD8XRsmZiW02MaJipOFnP3pjaZf/X/+se0DUCq3Wxx/sIlAC5cuEBz6xyRySy4YUhhdLeUAlVmCVyHkudMSmndBYGOppemsRASaXgPHNQKNVopQghrNQgpQFTuoecKClPEJaW0VqMQYoUQ14pURGHI1LSEm8dLC55qNEJ7/uHhgK4BNSlkFcDMc0JC+/N8PrcZizyXFrLdbHcQJoSY5wnLxcwWvvV6GySlFYVjsQnaYpB2nuzzUxVKnXR5mLZxfxX4qwBCiM8C/7lS6t8RQvwfwJ9BZyA+9A1mAw/iNGY61DGBwBcc3tJ6MI/ntMpIvpK2GYwThDQbXesve45r03DTyYjnnvsEAMPRhIUhZtnc3bPHBH5EkmYUiWlm4rso4/v2Nnr8nZ/6HwCdkvSNK3HxsctcelI3eWm3OgSb23YhKarmt4VitYu2U/IpSHDMIpAKl9pLX2j3Rh+3CnoqF7N0hO2uBAqlqhSl67orcSRRO7euFEqlgixI8wzPuBmtqMFkpJVvUbTobeh6hcPhgP39ff3M7baNmzQakDmJTaNGMrCKYDgc2sKxZrNlqfHanQ3ixYyl4XrwwiYYAhkl7jWHKyCTOIU0748Cp/CTwC8IIf468BV0Z+oPldRf1ixLaDQD3nhZYw48RzI+0grCUwUbfd3WfT6f4weROUYzIg0GJbR5x6bEwtC3qcsb+xMabROcbDaJzS7VDEJcR1GYAqtGw7ddo/+/X/9VYtMOLQpCnn1GQ6O3987R6upAYxA1UY5A2oVYFWQpxwVVUQrZhexgtYVwJAoskapylN79y0OsRVB91pZFWegk32ZFlLtr3QqrizEu9GcpaQQhx4ZUNjcdo0BbV6V/3+v1GBhGp6OjI4YmaNtsNuk0W3ihfv2TJKEwmIOWSXfq7yIgNkVojZ0zFEVqfw7SJaFRCiinInlBW0u1STPPL20Z9UmXD0QpKKV+E/hN8/lN4DMfxHXXspa1fOvlQ49ofL9STz3eW0x1P/82ns8IHWnNyuXkkND0LHSKDJWXxIqVTxuEIcfHs8oPVcryN25ubFha9gLB5lYZPZ8TmBSY5zgslgvaDYMwzFJu3dQuy+/99m+yvaktgvMXLtHd0JbKxcefYnRs2JS7W8RZap/DcQwYB1DKqajlkDquABQFtluTkkKTiZTl40pQGFdgJQrvCIT5hTnSfJam/2YZx6jSkys1ElLCfczvTqfD0FgApZQxAU25b6YcZdPABWrluo7jEJjUaSOq2soP4oqmbTqd4Bt0Z5IsEU7E0Fh0OyYLUc3Uh0fWSuEhxXUUb129QvnaH4+HBGYhuY5ru0W5rms5ClGCPEnxDLGJlAW5qdjb2OhbmLTnNyjdc9evI/1ilMwpErPIXMX/809/DYDQhV5HxxEuPfYYuzsa/psXgt62DmwucwfPE4gyJ1ejpVcyR8kyaCgQpSugsEpMqlw/g13kpvM02osue13UKyOVUva6yqAZy6KiPM9rhVOFTV3Wpa6IF/MprVaDmQk0jhZTyx+ZFwWzoQ76bu5sszTxAcevSFpKgpuySlUpZfkWPc9jmpbQ5hs88YQmYkmWc7obFfLR910LaPwwpSNhXRC1lrWs5R5ZWwr3yDv1pay7FfY4ITk4OADDdlRkKbnZ6cLQs92SpFAW1FNkmaYI5+07qhDKIu3C9pbNPmxtb9uo/mI+JfQcFjMdqHzr+pvcuXEVgMcvXuCxCzq9eebMGSLDjeBFTWJZcgcKfEdaFKIqqjGIXCFkZQGUJb+OELZ3pZDCpDBNjYNS1uXQ/1epy8KWSyub3lRSczJWLkNhuQ3unf8yvVgvKFKyIE2Sqnah1WbflKUXStpCqfF4TKvdNgOr7qeUWkmJlpYLQK/XIV4YC2Q8IDUZnjxq0IgCmzGSUt6zpVYpSWncLFdV4z5NxsRaKdwj98Kc6y9OnfCj/LyYzeh229w60K3Osiwj9PTfQj+0CzwIIwJjrubSJU1TAsNPEMexxRwMh0PLC7h3oW1f/Pl8WTWRLQqkUCijfH79n/waZ3d0HGFra5OzpltUFEWWr3CZFhCUMGMfWeR2kVPomDmAcMAt3QQpK1fC9WuQ3TKeUCOtEdWisAu7NmdSyipbcU92oR5fWFEKjqophWqMoe8Rx7ElU3F8z0KgZ4u5vcbx8TG+STW6KOt+ua5LmqQrEOrSlYiT2H7nYRhacliES3c6xTetwheLBWE74r5yyv2JtfuwlrWsZUU+9JaCEmXQyqkQeMqrmaMOshaxVqKwATDhCZt/14XCZtfCxTe79nT4Mn46QqamRsEpiDZ1xmAex7h+WVzj4frGUohjyDNCY5ov04Su6WsYxylNQxaauT7KmOItV0KqLYgu4GcFv/v7vw1A04Eo1GZyb+ciXluXQUuvSZyZHdhN8A0CzykUQinbyqRAoYShTRMgnTJXIFEmmJiRWqSjklJbF2UjXalwVvwHnQkoigLXAISEkihTn1HkOXmWIE3gVRXgisCMJbU0bUI5eJ4J2ipFblCTMs8QQtE0VtAsXhIYluVOy9U88cDemfPcMU14t7e3WRjG6CAI2N4+w3hsvrNCkiy1+5fnLqGvQU6+N7eBSqlShJMS+Nq6uHv3TZ54Slt3WVHguHoshQRMJqcQygZjhQD3dDC8f/iVwqrUKLNWPteOcJya7ynsiw9Y891xXatU4jjm6OAQqaoqwXihX77Qc20Rjud5NlpepsQsmcg9XIalye87LlmqF5jXbDMb6+tubG1y98ZVXnzxRQB2t7Zte7R2u21Nac/zLKjmXllhVxZYIFO9Ya4+xjy756CMUrm3W9q9mQVV1J6rZHMuKvdBKhNfKSfRce35OLXUr+PY+S9QyBJWXMY/jGuhC6fK+xcV92OheOopnT2I49gyNjcaDUajEV3TBdtB2JRmkuZW2YR+wMggVVutJ3VXLgMAu3X9Bk89/SkAAuHZlGyhKkQmQmD53tW9s3ZyZe0+rGUta1mR7zBLoZIS338/miwbaJTVbuogLI5dKEhMLjteLBkMBngmnx/4rg1gNcPAmr9CVJRlZdmwZRxyHJtZSNPUUqANB4fs7Wh2pMV0ZnfqxWzGlVdfsxaB64fWUmi12tY60XX+ZncuqgqmrChQ1IKANWtope6hhl9AVhaEo7R9VQ8olsBlhbJsS6owQCdWGZhKIPB9i52EwDXjd5SqCrWyiuW5UKvt4F3XxXH1XAopyEtLBWmtswsXLlimqcFggONU1oEQgtx8F40oZGbg0KrImJmy9vlkDFJxaJZMe2PPEuQ6gU8hy/ekRrZUs8C+o+jYTr68szEk77Gu742M2+yDVHZRF1nKyCDqsiRGKIljou9RFNlKunpKTSlli26klLiuS2w4EhutKopdSKUXMBA2fDqGb/GNm1e5eEbHKsZHh3z5y1+mZRCOzWaTpqmR8IMATNflullfwIqLUghBtabl2567NiHmnNVmLnW3SjnCUrNJqWy3pcKtFQpJZT9LAVI4Nl7iuL5VGo4j7XfiOg5u3cUxxxdJjERRFFW6U9UUTDnOvCjI5lpBXL9+nccuXwZge3uLmzdv6lQyWmGUFPH7129bINnh/gEdQ1gzHo5oNto0DT1bOwqZGVr+9kZUoUNxKkXgiMpDEm+rmjqxsnYf1rKWtazId4CloOW90mIpVe10UmY4lDiFAsfo0ExmzKd6l8jzlHarYXs2+q6DU+7UMkcIU59AtVNrZmNBagKNHS+wDEee51nzXylJYczaQLgsDX7h2rW3SNPUPtPGxhatpmnvFjbs/YXrocrWclJVQUfHpZD12oN756dyk+y8rHQ8MRgFZf9YiRAWMiyokAzCERVIS0gc4ZKXDVo9QJUkDB4elXtgXYW8CkDiCIosJzHzlxVV05i6KyJlwU3TYzIIAmKDGXn8sUt0Oh02N8sK1ik3bmicSb/R4e5dbQUGvsvgQIOibt+8yYULFxgberdme4NJGYTs9HE9Yym4AWnJrC2x74+o1U6edDnxSuF+Zu0Hw91YEWSoFZdWrACW6tH7spzfdxyyVCuBLE3xHIHMS6SbawuHsEk/LWW2wTddomUN7TefaSBOq9VBmA7Q5BkTA54JA8/6ty9/4xWiqMmWKXZy/YDQgG/qHagRro3Q17FGSqoVf/ded6AsYtJrdtV/N0foUua6j2+i7AKFBUKJ+vQJ62IpIZBOWmYOcZS0aVDlqtq8SXLTGEfmhUVgSjSKMi97YxaFVR7SXL8cc5nJmUwm3DU8F62oQafTYTzWi38+n9t4w9VXXmdgqPCn45HVjK5QjIdDLl1+Ug+tyDk2Kc1zF3NKzeg5gqwkqcGxNSEnvL/Ripx4pfCwItS7eUirFfBKippT5VTpJVVD5OUJy4VeoMlywXK5xC2PFJLCvMh+q2nTY3leofOUI5BFZTkopSyxR6e/YZXH5tYmd2/qrka+K1Dm94PBgCKJuXTxMUCTrpS9GoTn28IlM6DyAVbnpa78qJSvqOKRhjOhishaxSAEnhDW9xfCqTAEUuIXvplZafkYJHIl1SuKYgX6W86Nh28HoI83vRXyAplXnQLqirwOU5a1x3Qcx7JYHRwc2MDs4eEhSimbYg7DkJde0g12l+OxrVg9d+4cjajqph36PlOT1nSCJs2uthaLPEEY69LxfRtpFMJDWEuTUyPrmMJa1rKWFTnRlsKjbFFv72E59aosAYZlWShs6TAK6yJkyYKF2THyNGY5n1rsvCscMlX1NcxN6jJJY8KgYe+RJAl5mcYSri2WCsMQYxWTzJcWqON4Dldv3NC/Xy7Z2tik0dCIuo2NTTzDAuQIV3OToyP8jk3bOZX/Q1HVPdw7HzU/Q6hadYOsfhCuWG0ZL7DIz8Jx8A1yTwqJQ2E/F6VbJRUFri0c0tyFBi3qYNO7BQWZ9ckrC0YiDPip2tPKcEUhC2vROY7DdKxTkmV2ATTT0v7+PmFYcTSWFsXwzh0uXdJcCc0opGHo9JrNJkmW0myaTJHMSGKd0szypf3+nCCsrAJHUD2ywDklfO8nQik8KA1Y/9sKWep9CpbeS5yhOrZGB1bm1B8QuyihuJHvIk3Q73gywjMIujgv8JyKK6FA2h4Ci8XCmqgSrK8vC8lgOGBrew/Q2ISy1j/LMnxPf87TmMw0TnWVx2gwrMbqCPobGl3nhUFVDei41MlbrIsiXJs/9xzdp6LmHFkl4SJwRRUTqGjZK/dHSkngeVXqEWXbqZFluCUKUji2+hEpiQypyTTLaLU6JKYCUaqcNNVjSZcL5rnJ/6NRnQCNMKLUlpPZdKVwTSIs5kO4Dp7pRJVJ/d2AdoMWcUnOmtPr9SwZTrvVst9T1GispI5L6ff7jEYjC43eO99mudSB39u3b/H40x/Tc6Fyokgr60US02zod2G2XBCcksDC2n1Yy1rWsiInwlJ4EG/Bez3nna2EqsbBWh0rQTdleA1K8IxX65moaJpdI11OaZrS48HhHZt9qHMCgGbksXe+p7GMBT+ZJqqlaRqnWUWHlhcEkR5zGqe0jQUwGRzZMt7Aj2g1O/hm5213Nqz7oBwfaWnWqvSoENVumqQprh9aO6He11GgbMbCoQLf6ESMua4yzyOrGgeb8VCSyPRbHB9Pql23UEyMy+X7HvP5nNFI77q3b99kOtGfx+OhrRPY3OiztaXNet9xrWWR59J+V/p6kjyrgFmluAhrgQkh8I0F4bseeZoxMDUqFx87z927unDq7NmzFiQ1PDri6rG2Bq5cucJTTz1Fq6OvkRcpieFd2D+4xXPf/QIAx9PENsIVQpAYl1O7F6eDtO1h28b1gX8IfBwdrP73gFeBXwQuA1eBH1dKjR5qlNX9Vv5/f1Ix675N6dQi6b7vkS5rMYGkrKzzbHHS9HhCHusUYsmtUL6MQeCtuDkl358+roYoLAqbLpvPl3hmgZeZBzB8AEZZHBwcsTTjarTb9Hp9WqZrchAEjM3L2+x6NIz5WkhFbCLpgMU/tBpN0rRq6SbyHCw0uILkqlpBEtjiPwozm/ZPUtm5pZCMjInd6XQsAzVCpwUBrt64ztHRoWVNzrLEdnJ69tnniELjluSZ/S6Oj48tZHnhaiVe8iOwkkauKlsdx6Nh4jitqGH7ViipCDyPnuFv7DQ73Mk1nmHjzAa3b+nPrWbbumwOkuVySWDa6A2PBjR7OiU8nQyYm2dutHosUq0IXDciM9+n6wVQfNv6LL8veVj34e8C/0wp9QzwKXSj2b8C/IZpMPsb5ue1rGUtp0S+aUtBCNEFfhD4SwCm3XwqhPgx4LPmsJ9FU7//5MMM0tzvm8tGlDl7sYrvtwAj8XaAUdluPEuWtMoA4GKJb3bDNJkjqEhH6+XWZcAKtEVS7vyO49TqIIqV4+r3VDInjcueiQ1yk5s/ODrkptnB0iRhMY/pb2uGpaDRptvXQcc0zUEszTMK3LK82HNQBkuQLBONP6jRo9nSZYWlibsX2+DUcBVF7ftIksQ+f5IkFFNtUX3ta19j/1Cj/kbjMZTPLAT7+/uc2dO8D5/93OdtJsARitj0c0jihcUWdDot6/68dOM6ea1Brev4NvsgpawKpajKvYVyrFuolEQWyrJdHR4e0uttmPMrS7Lf32Rm+lKCti5KREueplU5tJS8+OIXAfjM9/8QnnHZClVQLjFxSno+wMO5D08Ah8DPCCE+BXwJ3Zb+jFLqDoBS6o4QYvfhh6nlQd2g39O56kH1KHVuBe37FoZwpNFo2c5PmxsN3nzpVQC6rSYTwxic5xLfr3gTXNe3mbK6EvJ93yqFoijwPM+6FlJKu2Bd12ex1ItiPJpZivLlcmnpxvf2ztHv97l7R4/taDDGMczQYbNFo6njEM1mi57pilSPtkspbXrUjtNCkIUdi5SrHcDTMj5SZDh5pQiX84WtOJzNZuwb5OCdO3cYjXUcwQsD25EqiCL+2A/9a/jm50LA1HTNjuczm+pzhbJkNkrmFEbB9robzGYzq3CVUhak5uDiWESkQ6ul5y/LMquIfd9Hypx4bjpK5xmXLl0C4JWXvmFdjjROaDUM3+NowFZvi4VpBoMHmHhBkacMDJnL7ZvXuXDpaQCO5zmeIX/J0wz/lOiFhxmmBzwP/JRS6ruAOe/DVVg3mF3LWk6mPIylcBO4qZT6A/Pz/4lWCvtCiLPGSjgLHNzv5PfaYHalDuE+v383WUHsW1ivrOCnGMZiVe3ikQkAxnFsg1mzyYSDQ92XME9j2wcxz3PD/FOWDlcNUvO8KtRxXXfFxBZCUZgCHaEKG9zzhEOcaQvCC3zbC7HIFRtbOrDV7XZ54YXPcPbcBQBeeuV1Xnv9DX0tN6x25CCkY5iNt7c22N3S+P5Wq4HIK2hxBWrSwUUbgBTCulmiVgCVp6nu/2hM8zxNyUzQMFkurUfW7nbYM8zSOC6+ccWCKCRsRNZSOhwc2flUMre9Mubx0gLG6j0ZldJzWWYh6rLStEfpHRp0qz6/5EOTmvmpvH+/32c2NYHjtEA5+jtXmbTl6elijiccxkMdUOxtblhgWjybcn7nHABXr7zJufNP2vv7xoLM4+zUAAAepsHsXSHEDSHER5VSrwKfB14y//4i8Df5ABvMfjBFUO9+Lc/zbB1CIwiYzzThhi8Krl/VlXRb/QpI47qu4U0o05gFgTHTdWOTKmVZKog4XhC4gTVn69mLOrfBbDazhTqvvfYaw4Eey5mdPYqi4NhkHD72sY9x8bEnABiOjxmOTbPVLCcy9f+B61mzPM8SRNuxLo/w3KrTs6tKQKemlSndByrFnGUZRZajTIwhS2IKo8jIc1sH0dvsMRxpn9yPQmam89XdwSG7u7uW/j2KIgoTOxGyIDBp3cARVkHILLXpjnnurMQxtFL2ap8rkFX5Xbfbbfs5TWOiKLLNcGbTqWXQ7rc7VcVr2MA33+thWpDMlhwPtFK4ePG8VThFmtn4wnI+485NHfvZ2btki7g0iOp0kDQ+LE7hPwJ+XggRAG8C/y5aH/6SEOIvA9eBP/uQ91jLWtbyLZSHUgpKqReBF+7zp88/zHUfldSr/Eop4bKld+I4zgq2oATfzEcDu4Ms/ZxmrXpO707V9coduC51ayDLMjxR502o/lbkubXm+71NRgbUM5vN7Pgnx8ccHA6YL7TJPppMEY4BQiUZgSm9doLQ1ifUyWFDz9X0Y6VroxSq5AMQrq34q1dPSqWQ5vw0TZFFRp7oeThhLe4AACAASURBVFrOF2Tl5+XS0qm98uqrHI10nv/Jp57m0OT8Dw8POTg85Iap5ZBS2srCViPijHGT+r0OkXHfPFcQliXlQRsppZ0/3w9rfTGdFTyCaywIx62yP2EY6vZwxjr4nd/9HbYMm/bZzW0Cr7I6+ibQ+4dHA6IoYmyssDzPyc31GsLh7u07AOxd+gjXr13Vn88/wcIEM8OoteZTeBTyoPjCO4lyluXZVXpSVa3XkULrCIs8TOi0DKJwMabb0+b3l37vy/gG1J8uUzqmGMkNOrhuLUqPQlGmpDQWH1bjC47jUKDIpKkLcGFh2sp3N/ocHWkze7Pb4/COjik4MmRybMzyjZBX3xrR29T3+forX8ML9IL56LPPcN2UWweeQ5poX7kdRVy6qGMQF8+fJZrfZmNTuybLRFrCkSwvaBggVVbkSFO7IBxVcUYUSyaTiS0Cms6mNjMyi2NefktH4hudXT73fX8CgF/45V9hf6hdifEyxQ+bxI4ejxIKWQJ7jhNumEyEeGvAhmm48tTli3Ta+n6teEGz2SRy9T1917dZijxPycw4fSEoypiEcvFtTYfPfLYg9HTs6PKlpymD3cP8mK6vFYFyHIyHQKt7hkRETIWe86vDI3Z3tSI5nu2zp4eCGN2gu6PjKPHoLYKSrt9JcBJsEZssFImh3/e8wKZLZY22L8sTKhTk/dCQjyZIcaqUwoOUwds7DtWL6vV/FYvgqgghjEIoU3KKWUl4ErlgoLyHBwd4BtK3XM6ZHZtcuKFxlxbyW6zkzMu4ges6K0FH/XujMDJpCV6zOLGt5ibzGTfu6PTe8HiCNCbEy6+/hhs2mRzrce6eu8jEtE370te+SrunX2qKHM8oMlEUVvEcz6Y8sdsiMi9oEEQcDfUOuLm5SWr84DAMUCbAkOWJtaCEq5mjyjSklNJClvM8x/P0OX/qT/4b/LW//jcA+LE/8+d48pnnAPiffuZ/4b/5W/8d3/NHvw+A7/3ezzAc6vF3WgHDu9qCiLOU2UTvtKNhA1dpLEG/2yeKIoszCH2/6hUhVgvnSmsiSRL7+0YzYJnEdvyDwaAijCkKS8owm83Yu6gz6o7jMF8s7BykaWrTqGe2+tbqaDa7Nib1yksv8ZHv+m49RwgCL6pwK8JdiSmVxWUoZcflB6sYmm+VnJJ46FrWspZvlZwIS+FBZdHf7LXu+7Nw75+eVICoUpSe69gaeE8pDvf1Tj0aHrDdNcy+szHt0LgYiUbG2U5GrmOLm1yn2sE0Uq6igAvDmh8MuAZwU9/RCD3mZdoyclmM9C518+AuWztnyY1Kn2cJP/QjfxyAb7z8Ek888TgAV6+9ydKgA89sbVrq89euvslzj38foWk+m2UZTQPyCaKGHVeSJESGadpTyhYXjcdDlFK2FsFRjk3d3r59mx/67OcA+Pmf+zn+/b/0lwD4+PMv8PVXXtOPJeC//Rv/Fds90zFrOeUTH9VpvG4rovvpjwPw//6TX8Ex3booCjY3dK1Hu9mk023ZYjHfqWj1i6K4h6exylAEJf+D0k18yziQ77sVf2aB5WOIoshSzLd7bW7evGmb1xaq6k1ZFIo419bBbDZDutrqCTqCsbHgzj/xFCrD1q+4TmCL2OI0wzMxnbL3JdRQt/eVR7efnwilUJd7G7y+X7mXi6H0e7WbUJtIS3BSnmgCfVlC5JUFOTFf+aKGYfS7TY4OdDBJJktSUxCVmwBfeV/Pcy2Zhuu65HlFLZamVWflVquDKtNVnmeDYFmWWery2WxCZtySWbxkOtfowP5Wn9lywef+9R8F4PM/8qMcmzz7S2+8SquvUYxHXxkyPCppzM/ZZ/23/vSf5td+9h/wwz/8wwA89thlXBMTOJ5VfIWO59kX0/E9vKx6XebzufV9J8OJNdN/5Ed+hJ/5uf8dgEuPP8lzz2p0X7ac8eQl7WvvbXVRwPf8Ee1O7O3tceWKVhibT17mykv689NPXrZKYXujz5ZBZ57pbdJqtaySqr8zpele/r7ea6M8poRIlxDqS5cuWTxII3JwTdygEUb2HnvnzvLVl75Gq6cVaZIk9l6+K+i3u/b7K4OuiRrzxmsaBYvrce7spRrVXeVahqFv+37YXiCwCrKpFfS9Xd7pb+9f1u7DWtaylhU5cZbCNyMPsiyEECtovSrDUPX7+//Ze+9oS6/zvO+3v3Z6uWXuNEwDMCiDQSVBEgRYLKiRpkSLdNQc07Ll0F52omXZSWQlsS0XObSdJUdm4ixZViTLRZRCUpYoyqwmIREkQaIQfTC9z+33nnvK1/fOH3t/+ztnOCgCBiQAnXetAc6995zz9Xe/5Xmfx0EihLJv64/6NGe01z9y5Fm2NnT4l4ZDMlOoy8MhI11XYu6a66jX63ZwiVxZXUHXLQd1QI6NF7gEflUPLzGpXwllyOv4bsGsRqtZZ+dOPQAVjlLqDZfdOzVz0+b6Gvv2a83EHQvbOX70GKAx/rffrvUO52Znudbg+6Mw5J773oEygzvSKVOrerPBwBTQOp0OJmhiY2MNYVa2NE3xKwGx6WwkecKBAzpleeKJJ7jpxoMA/NRf/mmefe6YOdEuvkGKvufPvJMHv/41ZFP/XBUp+3fqSr4rEw6bVEKlMb4J+VvNOhUDalqYm8f3/QkwVcFj4fuuTd+yLLcpQhxHdjzeC3yCimejw/n5WTY2dMen6rnUKzqCGG9JC8fQ2ZkbZXV9jXrLDGs1yjmSURRRqevoZGNlmdygI88eP063s81GJzJ3bEHRdX2UKGY8BI73UvhBLn999ew14xSuVk3h8s8XhCN6xr5gLM7H5gC1Q3Ao++TDnu6nnzl1zHIMbqwvUyuQfvUATDvRUeU/0P3wwoKgasNCKaWeqQe8TJGmZb6opJhQb7KV6CShZh5EkSbMt3To2ifBrzVYPH0KgJlWG8e09N791rfxRw9+BYBudS+iQBdWa9x1+DYAnn7qCSr1Bo2WGZbqztiWWJIkeOZGFkKQmhQnCAI2NrQnrFarDAYDG/62223LUXn48CH6Q70vD3/zIT0dCcwtbLf1jX5vk1tvvM5e89XVVfpV/V2tVsPQxMNoKJnr6jpClsYszG+z1wjGQm1VdpZcx5m4B4pqv/BcHFVeCyklyly0PMuJDWmOmwl2zGnnWw0qnL+oOyHPnThOkmfMtfU1WN64ZIedJA6xoeOrjAkJz85sY2V5yWxT8cg3HuKmmzRt2/z8gl08YAxyDhbnMc6t8Z20afowtalNbcJeM5HC1bJv7z4UIiWlCTEmFouEXCGNvkA1cPnGo08AkIQDNle1p29WA9KRBt90m03CvtF9iGOzSprRXT+gKPoEjkNqUoRUpjiiYArKGQyGdM0qmBJPzEgUVfUgisGM6jbccr6i0W1z6PAdYCKP1fPnOGpW9FwI7rjhoD3WTTNvMN+d4clvflMfVxRz3U3X2p77em/Lks26ro9vZjdGYUjDaFkqSkRg0SEpFrdms2mjhs3NTWbMStvvD9i3V2tTxElCzwi3Vj1BjiI2Bbluq878TMvsW2TPX9XFpnwLCwt0TWRTzEmU8yJj8vNjku/jfBZBrWr/luYZaRrjG/DTxYsXbXQx252hYaIeqXKbSl1cvES1VcczHYf2TNeG/7VqQNMMTnmBb+c1WvUaq2ZWwpO5RjqaAve11yfML+ghqmrgoww2JU5zy0hVpEHanr+QKBQTOhiv1F7TTuFyYpUXSjGeD9hUcg+KScdQdCqVBDJ7w2ysrXH+7EkAttZWLGApDmNmzEO8ungJx4Tlc76PG/iW6Vlvs9iIY9WePMclTYdmXwWDYciOHbomEIYRwjzUaRrbSn7guziGzbmiJJlxEHv2XYOXJdxww436ffUm5y/ozohbKacPB4MBB41gTBKNqJkWZHfXTi5urFtikW63y4ZBG7ZaLZvyBEHFPlRxFJWQZylJkoSOeUijKOHo0SMAvOUtbyPN9Q2+sbFpb/DBoE/FoC5938fzPPtQZVliX8fhiMykQvMzszYHbzQaFjUpDduza5ykK8qUYdzhI6QFAOV5ao+lUqvieR6xObfnzp3luut0HeP2Q7fRN2nOybNnuPEW3SF5/MjT1FpN1o2wcKfTYW1FK0k1Gw17ztY3N9i5oLssG5vr3P+u+/SxbN/BkfNrnDmj05FvPfoI1x3U98PO3XttS9j1AsS43MCLOINXw6bpw9SmNrUJe01GCs+36j9fEfJK0UTxOjGhnCccyzyUJJHFIiAzqjWfo88+C8ATjz5Mv18KjG4a5qBmpRyp9jwPZTD1/dGQWrNR7ptyrC5kp9MhMHQ7URThmHC/3a3jAKOwWPF8BpHejuu6dnX1ohEV30Cr5digk0xp1Sq4poefhyP27d4JQJzntqvRbdZQBufQqAS4TlHAG9BoNGxxMIwjCxn2PM9GVNEoLFTtdXRgjj/Pc6pBxRb6GtWaDZ9PnTpFs6NxDrV6ncwUUD0/IDPj1ZGNOgp6uNBet/nZWSvcovv3k2S3AL4jyHNli7sIVUZ+QkyMTmdFJ8dxqJgCZRiGRFHIOSM+2+12mZ+ftcdfYBZm5+c4fvI4AM1uGzcoORj2z+21x7yxsW4Zsnbv2MWqSdnazQ5Hn9MRVLvV5JabD3LXm+4A4Pix05w7r6O7LJUs7NKphF+t2YE93/ctQEoIYYrQ5piZhM3n6urhFF4zTuGlU7Zf+bPP50iKllKepPY9jWoNYQZ9VtZXuXTuDJcunQZgs7dKATnftXM7B67RIf5zTz1G1bSqZJqwWtCVRxGtVossNTUBJenO6vZatVoly3UoKhV4vv58Ekc4joPrlkQtjiFG8R23PBZHERo26TRPqFaL9pgOiwteQxH4RCYUTmVJva6QCLeYfqTkaxQObrVqbzjPccukVEqyoj6RZzbpypO0FJbJNedDcX8KR1kBFs/TIixgZjyM8616HqpaAr0cyofXdcvX3lj34HJafNu2VYAsfxZSoSZIWEpa/eL6x3Fsh9PiOKLaqNvUZH5+1qZsvV6P2W3aqdW7bR7+oq4v1VpNhlHIwsK83Z8bD2pg1vHjx+13XVpasg4iyxJqVf29D/7xH3HbO76XbQu63rJv3x4Wtpv0Mc4YFRwetRqxqZlkeQJC13SCSgXfc7XWKejuVQHAc65uwD9NH6Y2talN2GsmUviT2JXEY64kNSeEsOGrcJSVHk9GQ1bNTEMaDRkNeiwu6lBu39697NmtJ+O6zRoPf/2rANxw482cMKHgMExY2K7D9bVej3anQxzryKPX6xOYiCKKE8uMLNwyLHdzpVd9E/IlWY6glGArRpRbrQauWWm8rELdrEC1VpPWTJt6x2D/gxp18+2JVBMhd2Gu41BgYoQQRLgEZhV3HLfkIMhlCcRSOUIVZK+ZpV8riF6LOr8Wg9GvPc9D2gjALaORMSi3i8AZiw5cUc5OQAlVlmk8ETUU6Ypvtqnykri1iHQmim/KsQVA13UtH4bn+YSjAc2mDv/r9foYTN0jjPTxb/Z6OEaDIpYJrVaLvtGumG137PfddNNNnDepyHA0tGlZQsxzz+m09Ife+2f5/ANf4vBtOn2448132zSx223SMZ2pXn9gRX78SoBvokGZK8IwtNiIaiWYiBouIyV/Rfa6dAovxKdwucMougdCKRpGHHTbbIdd23UOWfVdhAe9RY38S9MBualuP/3kY7zt7Xq89/Of+UOd7wFdx7cV7nQwNO04o76UJtTNtkdxYi+i4yl6hjBlttOl1ayzZUBSuVJWtSpPEjt6jOfT7OoOQZSu4dV09b3aalBrN8s2lO9awJMvsVRxQpbUbs6YCpYSkrpXsVVuIQDTEstVVjov4VgtRtdxKHCPoiCFkQXdeWoBT1IIPANE8jzvik4BDBlKoQWZS6vKNJ5W4JapVJ7nYx0jhRgbokOqMSUrZYFYgK0BVOs1XONEMqW7J8X2+/2+FZh1PJfAzDucOHvSLir1Zh0vcIlDk84kKesr+vpt37aNa6/VdHjHTp6wqMegVkFF+r44fuIY73//n+XUKU3p9/GP/Rb3/8B7AGhVAqQhg6kkPs226XKtr6FM+qDH7R2LwkzT1C4knue8MWsKhb2UesKVhqaeF+ps7pYszqgbmO2gt0G3WShA5yyfO8+2OU2G8cwzJ1hd0SQh1+zdzyf/8+8DEPa3mO/q97Q6s8RGcqzVcsjz3FJ/y1wZrAJ4bkC1mETMtBIUwO7dexCuYmQm5oQQOKbPnyQS3wzkxEnOnEHx9Qch1Yp2N92ZWZqtDrkdAHVxzEMtHYGnSkYn26pDMj4nqnUQxouyxZSgxDUPqOc6FunpCads9UnzUI5dj/GopLhxhcBiKxzPsY6rcAiFwK1yFco4mFRlpW6D61qOQ6GkJXcVqqB1L2sHxfbHdRuUUqXAr5TUDfX9+UvnqVar9Pva+YdhaIfA+sMRc7t0pLjy2DeITO0pDwfMzHWpFJoOeU7dLBJPPvE032OmVN9yz9v47d/+mL5+0ZBdpoZw5swJRm6V73vv+wC45dbbeeCPHtTH41e50XBNtGfnGJjBt9nZrlXYSpKIil/FNdtP4wRpULW1auP59Atelk1rClOb2tQm7DUTKfxJOw6XA5meL6UITXuwXquQGK/bajcsPbfvKObn5/nsZz4NwLXX7mXfvv0AfPlL/5WGGYntNFs2fG00O4zCMiwVY/x/wnNJTO4bxgmeEWnxfR8/0OlLs9mk19sgNB2DaiUAZfQHE9eG0mmcMWPae4v+Gu22jlRmu3PUqw2UCR8DNyAdk5IvuSixSbajHBvu6/OmUCbNQDl2jFvm6UTunxtMv6BkRvZcB9dxJrisxlf3AtiFyMDkykJNUGOa95vUxMOqYuVpaiMIocr6hsxTPErwFFLZnHo8UsiyrOySKFEK7yItO9JwOKRWq9I013ZtbcUec61e5+FHHgEgShJmDXfjam+NTqfDyLSoVS7ZMvUFz/f59Kf1/XPvu+7j+3/wBwB48IEvs2pG1xdmZ1hbXeF3f0dHET/ygR/lzXe/CYBmd5Znj+jW55mL57nn3ncAGghVICiDICDPUnueK5WKBcnpLsXVKyq8UoHZnwX+Kjp4eRLN5rwT+BgwCzwK/EUjKfdC3/Mn3e4L/n3cQRT95/W1VWqmJZYkCblp9Z0+f4aTJ47yjne+E4BHH/46J0/pC1St1aiYltbNB69npwkFP/eZz5Ka2D0xN20x5ZamKYOBEaLt95EmGOt2Z6iYAhTCJQxjy/XgOA5pYtp4gW8LaDIVVpnaUy4zTZ331v0aIlN2cIZMUTVov1wI61QmzoVUWt8C3cLLScp6gyodhJSSwC3rCFFSaiW4JkXxPE06W0C4ZZZPOOkiZXOFsqmIcMZqABSvi0KAO1FHcI1TUbmy3BSecFCuwTUUA01jaULhCLIsm1COcsbIegvS1TRNSdPEIkodx2E41IvHbK3DQw9rOPiBm2/ANSjMa665hjSNrQ6EjBIwhVe/7rNnu3bep06dsvfED773vXz1v35B73McE9QhMmnmF7/4ee6+R6MdN9bWueEGPeUapjlPP/2k/n1vi71msnV2dhakU9K5eY6ltTeX56rZy04fhBC7gZ8B3qyUOox2+z8O/DPgXxqB2Q3gp6/Gjk5talP7ztgrTR88oCaESIE6cAn4HuAnzd//HfALwP/zCrczYVdqPz4fqrGQPw+CgIsXdRtya32N3prGre9amGPPnj088YQGqYxGI1uJvvP229lzjWYcHvS2eOShbwCafquQfsfJSZLErjRbgz4dw8akhLBAoEqlYlez4XBIGIZjgrPKtqeq1YDcrNp1v0LV6BrWgipzphNRC2p4uOWsPx6ZWbVz4VjegHFQl5DKjlFLKRHOeMU+n4gaiuKc4zj2M1CK5/q+T5IkxNKAbLIML0jtd/uMRQ3jMwnmeB3HRTiO1XwcHxF2XRdRjJsrZVulMk9tS7KIEsZnMSZATlb3VeIXal15eVxxHFOpBLalWKvV2DJgtOc2Blx/vV61Y5WB0pFC0wyGtdu6WCmDzEYKYRgyV9VRpPTg9OnTAJw7c4L77tbErY9/85sEwB136JbkyVNn+cLnPg/ALbffSWAikGqjye7denZiz779DMx9tbS0RDWo2ZRHK2QVCNuSwu1q2CtRiLoghPg/0IIvIfA5tMjsplIFsR7ngd2veC8vMyGEbTU5jjOh6hTHMdu26Yr92toaJ08+Yz930003AfqhqtZ0z184Lk0/YN8BzQtY9R1MxEh/bZFNI+J65uSzHHlM8xTccPBaqobl+OSK5NwlrXgEcPbiIk3HtI3yBCfTD8XW1gapIWlZWlzEEy7S0TdaGCYI31Cs4zJK9fv2b2uzZkLemV27qXT1ceW1Dmm1BaZekWS5rcw7wkE4Ra1A2odaIO2oqO+CdCrkZvBI5XYYkUwp68g8zyOo6u5JtJngCF0T8UVG4GTESj9UeZqC4SNQsctKT6M49+7fZ1GUMk1ozeobfzgaaWHeAiGqclvTEJSDTjguaV6wLHvloBAxuYRcFk4iQ6rCKaRkRiA49xyiQsPC9/nM17RTbzYb1OoV9jf1PbC0vML27frcNrs+vqdTsdlWh60tfSxB6hJU6tTr+qEcpFvU6oaKvbfB1rK+T97znvfQMboVn//il/jM5zTO5S33vI21zR5PGzj9ve94F46Z0jx7/hLqnKbl73S30WjplqRQLp2GTktmmh5pXsoE4JS8C1rF6+qNSb6S9GEGeD9wANgFNID3XOGtV8x2pgKzU5vaa9NeSfrwvcAppdQKgBDik8Dbga4QwjPRwjXAxSt9+KUKzD6fWeCLlBNCK+Mhs+/7NhQcjUal/HrbsZwFDoJoNLCjuxE5vVWNbty7e4E/+L3PATDorTJnCo1hGFmJ9YMHb8N3y0hlfn7Wph9nzpxhz249uryxuWbx9WE4xFElsEYpBQaXH8aRpTZb27hAo6H30/MaJZVXccxCf971PcqMqQQVaVapYlBrnH9AkSNIcxtnW81Iz/fxTHET10EawZJaq2E7BFJWGcUjQjPgVAl8WoZU1fM8MOfigQce4C33vA2A7swMA5NyBbUqrpRWvSqOYzshLKXmtwBgrICpxlKEInUofk6SxKZfaV7iHDzftxMRW1t9O/TV6/VQNK1ClecKOxKdyyof+tBPAfArv/Ir7DIivv3eAEfBaCyNKPQ5atXttoj51a9/nbfdcy8AP/pjP0Hf4Fk+/olPcP1NN9m5iEuXljhwrZ6duPut99Df0vffZm9g0bGKDNekKI7wJgrInudc9ZkH+92v4LNngbcJIero9OF+4GHgS8CfR3cg/hJXSWB23Mal2QpK72CcGnvMKVQC81C5wcRNFZhWj5SSIAis0IpMcotI+9wXv2C/s1qtW6q11bU1rjuoiUyq3W1EY+i49fV1qzZUr9fJ84K2TVj4cuB6xHHM4qL2l9dddx0DA2R69NGHueYaPTHXrNUpxo7a7aZ1IhW3huNoWjnAQJHNAy/zSVpK83uZ52XuLiWb0VbJ2xAEE63drAAsOR6u6dhkYYYsBrjIEJ7LnBkcEgJiM4QVxakN5ZXKOX1Cd3KuPXi9be+O+gOq9RqDTV3vcRDlxKOUyLzotY3R3ClsWpPkmf5nVKeTJLNOIcsyi850XdeSl2z2eramECYxtbRiF4L5uRnLraBUjU984hMAvOlNd3P8uN7/Xm+DmXbLOoLA861gb6s+RjfvVXjuuFYAv7i8xh7j4H/iJ/8il5aXOHNWpwn1uuDUmbP6M9UW0qAw5xd2kNk6ikAUUHTrFMqpz/Ga1Dh27JXay3Y1RoL+4+i245Pmu/4N8HPA3xZCHAfmgF+7Cvs5talN7Ttkr1Rg9h8A/+CyX58E3vJKvvfFLM9zi6nXtGCTodQ4139uooagWrXhs+f5NhTL8xzhugRmSVrvj6woquP6ehYYaFQ6dFu6UHbw4I3MzRhY9InzHLjuOs6ZQtG2uTkSsyL3+32GQx0yb5vdxqBvOiGVKqdOn+Dt9+q5iv/8qd9nxbD4tNptHn/qcQDuufkGEhNKdro1K1Zab84aglKzjOZxmSag7KDV+LlIkmQC1DMzMzMB+JHmM4Hv2zTFdV0wYjSVWtVqQKSVACcJcVQBIc7tdwdBwPr6iv2uxx57DNB9/uIatdttknBEQMm6XIxoC6nIC1LbLNf/MBqRiT7+JEsM1kCfmzTPyIrOCqoMs5WyAjhbW1uM167COLadhHHA0/z8PIuLumj4/d9/I+fP6hTjhhtuIBmFDAZbZj9z9l2z256npkmfRmFKvaa/N8okX/maBkLt2LVIq9vh9rt0N6JRb3L6jB6iOnnqLLsMQ5aTSfxAFyBTR+EYyDuOgCLdYxKboZPBcqDsldprBtH4J7HLgSuXY++Lm0UIQW7EWATYXM3zHRsi5XlKHI1IQh0Krq6uWBTZzt277Dz8roVtpdJ04POoQb0duO4mVhaXbWg+HA7sDRrFIXt26RtnZWXJhqhC5txzz1v5t//23+hjcARLK/pG9Ko+J05oWvQ2wlK0C9cnx5CveA4yTcvWoetSyFrpNuBYq8481FmSkpsQ1XEcBlt961gdx7EoQs8p5x1UXtYn8iwppwyFQzbGubiwsIBrOinnzp2zvA/PHHmaXYY8xHG14K3el4gkTPAL1W0pKbjshVRg0qw8TS2iMk0iMiOmkwtJmmfEpqYRZyl5US8RAmXrTdhaTZKlDMw1brfbeJ5jhV6SNMUz53JxacU6xZWVlXLiMYw4ePAgjz/8MAB7bt0+xqXo2od6Zb2Ha7oX+687yJveqlOs3mjE9u3bLe+G8GrsP6DrXY1Ol9Onz5t9m6dnULiVoEbuFICzb+8uCNtTFtPZh6lNbWqvnr0uIwXP8yYKY+ORg+NM0lQ5XinU4ZvVJKh4SINwqbp1XFdgFgru2nMXS4vaa/c3Nti+TeMP8iyiaqYfjx97jgPXacyDAFELkgAAIABJREFUEIJOp2Ojg/6wz3BDpwkzc7M2Ldi9awfPPPkUANcfPswnPvk7tEz4ury6aucCBsO+DQtPnj3LPW/XlexiVQQzukyGU3QZxBjBp1NOLxZdCjBphIHFep5HsxrY8zQYDGz3JK9UkGaaVIix4mgQIEwovryyxGCrJGI9dfwEy8t6snTHjh2cu6i7N8vLS9x55536vPS27FRhGCc4CEYDHXkIqUjHrmexKqpcXsYNYfAfMifOUkIzyxIniR0dFkJYhiXlCDtePi5z5/k+9Xp5X9RqNTtiv7y8yt0GcHTi+CnuvFPPJzz6zW9w+sRJ/tz73w/Atx55mN0mCnIdh8jMwtx5x12cX9Yj8qMoZb6uMQfXzO4wKtgFh4YkMExcw2HM3KyOKOIsp9OeMe8Z15KUE2Awc+IAXajNr2Kk8Lp0CuMPvhAC1y0FRi//WyG6kmVZUZQmzxSRmX2oBB6O71H3dLvq0tIikWm9pVlOYEaf15ZHnDSV9G53Dmn4A6JBj2MnTxAY/se5uXn2GYHXCxcuIAyHw5EjR9izR6cS58+fpRr49kGXKqNj5OOTNLbha5bnPPa4xsHfdsttNiePoohapWpHZ2WW4pubOlUlOjBXEmnzUGEr557nIXLJqnFYp06dsojMXTt2smuXngnwfd+e17WlRZuTZ1nCs888w7PPamDYtm3bLPjn3MnTzJrj/KEbbrAtuLmZWYv7b7dajPoDMvNQIzU/AWjnVVKzuWN1j5TMdjgikiSxXAcTY9tjrReJsh2b5bVVO5FVOMric+12m9B0IkBw5IjWf7zrjjtte9lzNRFN4aS2bdtm25i7r9lrW5KjOGGHSRlnd+4hMCC5OJe0Wx2OHNHgpWuvvd4Sw0RpZusIuZIMTBtznHhG39KlY1RK2VF2pZQFQl0Ne106hTy/bABnHM479lrLfhUSYEPbF/cCHzcznIhBQBSmJCY/DJOYSkWvIlmWcez4KQBuvvEmtm/XK8Py8jJrK/oByaMIhWPbbdu2b+dhk3fedvutXDqvC1Xdbpt3mqGr3/j1X8PzHUJD2OGiCIzsWa1esSt6lkk+9ek/AODNb36LfXCSJMJzRDmg5GgkIkAus5JbADE2KCOsBJ3jODhK2Sio4nv2BgfYNK/TdFKP4tJFHUGtrKzQ621aWvSFuXkahp/immuuQRh17mq1aqHAw3BAzfBBDAYDAs+b4HyMzAOfRFHpFDzfbj+OY/swh3FEmpacmzoyGKsxmePIpLSovyRJbA3GdV2E69jr3O10rFNoNtoEJgI6f/48f+kvfgiA//L7f0Cn1bAtymv37aVnHMH6+jpz5t64eGmJO+7WhCsbGz3CFR01rvX6zHVn2LHdAHyd0uEiXFtTSaPU8mbkeT6hPK3vdbOyXa5vwtWzaU1halOb2oS9LiOFy3OrPM+/DcwEk7x+rutadp/hcGhrChsbPUbDHqORxrjXqxVC06Votma4+bDOiVcvXmJpSefKp06dZacZu13aWGXHrr3MzekwM4xC7n6r7sj2NjfYsVuvIMeOHqE/6JX7opQWOQXqjaodvd62bRs9M/ffrbapGQq29fVVOk2dn47iiMDzcU3KEkVROWdfDayWYY7CNbTw9Vrbria1oEKcDO3K2e52qBY5tijrM6PB0FLIHXv2mNVw3L5zO3v27WH7do3wzNPEVumDICDzCgGWfIImLUl13aJRq7OxuUHHzB6EWWbRhkFQDipJoXBNx0fliQUlEWvKNsdsJ/Aq9Ez64/oe0qiCqawEbIVRRGQ6GfW67rYUx3/06FEOXqc7Ab1B36ZcSpXvabfbuE4JjOv3h+zdp9PEXq9vz3miXL71hK4diaDOnuu0YM9t+w5MAIzCUWxbp0K4dj89v0JWTHQJ+5+Co6qMjnj17HXpFK5kzzclGZu81XHGCVkmodCdbqk14DsuTYNHSKKYlUWtAVCvt5hd0J/Zs+9amyLs2L2Hw4cPc9EIkeZbiu07tCNYW1tj3gy33HzLIb70pS8Bej+2zc1z4tRJs82AelM/FK5w2LNrDwAyymxO/q3HH+X+d99vDtBjMBoiVcV8xvKmsrGxYQtwo9GIG2+6GYAwjHFMHWQ46qNcG9mjhEIFlpkRx9ysjZkWdZMKdOa6Ze4uFZVKxSo5xWHplFzXhTFC1fGbuHDQi/0l2s0WS6u6pjEzM2NrGmma0+q2zT6H9M3vd+7ayeLionlPSmemS2hajGES25Qjy3ML3w5qNZvmBUFAPvYo1Wo1W28oCn4A/hjx7GgwZM3IvmGwMIVWxyhK6A20877pxkOs9/TrQVI61VsOHUIZngulFDIX1pF5gct4oF7AzMcnPouF7jtt0/RhalOb2oS9YSKFwi6PGDyvmOEvmXCFdHGFbk+5nsDzXFu0E44iKpSb3IB6UyMXFxcXbavs0cceskNLh27YTzgaIQ2Hwt4D11OtmZC90bIrwL1vfwf/9B/9Q0CLzARBYFt09ZrLTpNmhGGMb0A1QpRsyGfPnsc3xcg8zchlRpKUYKSikj9eaLzhxhvZ2NAr3czMHLHhXPA8h8hRZBSiMWODU0g7ROQ6Dp4J3wOkLXrFYQS+oGJWWOE4tvrebrdRprMDkGclatL1C7p4yTAc2e5Lr79V6jxWKviFgI+UrK5ptSU/CGz3IM0zqtVSM1PK0J6nOIopZJTm5uZ44MGvmWMOqJtUKo4jpJTMzGiqtYW5WbYMirXTnWHNbFOIsqu1vrbJNbt3Wlas9c2eZfVaXd+gZboUdx26g8ef1VIAWZ5SK8BPUQiiMtEdKQFnrj023R4vz1NpV3G44UXsDecULu9EFCpKUkqkLFB7ru1lCyGQubKhcJZltiXY2+zZm00qh8BMD77nfe+zeW+Ow9LaBgs79TTd6tqSDSt37tnLyWO6BXXjzTdz3XV6iKpRqyLznJVFHT67foU01jfbrbfebkPpjdVLhKaXv2vHAutGjqzi16g2miWvosot/bwjU7oGZ9Dr9SzPw/r6Oq5RcYpkRlr3LYEJYJWkXOHY1F3lktQgImv1ip1ynJmZwXdc26IUQM2csziKcI0j8KsVwtTUBxQM+zrvjqKIldGQpkmNLl66ZPezOzPDaGTUkhp1e53WNtbta8/zJlCsAsfmT1JKvAKP4HkWdSiEQJmaQjG8lMYlJ0fhPOfnF7j11lsBeO6551he1scYZzlr65tsM6zPlVrF4ggSKbn+oK4dKHJuvFG/3lhbZd50eJTjEmcl7ZzCmVDNLti41WUs2y9sr06gP00fpja1qU3Y6zJSeDHdh8nOhJlNz6UVCdG0YIUIqSLPJcow/AR+nUFfF7Acr8qaUZXasWs3iRlv3uz17WrTHw3IXZ/UVLyb3Vl+73d/B4Afef/7GIxMMW4Y2gJgxQ9Yvrhow9csy5id0yvK/r37OG0EQ6KKR7+nP7N7116ee06Dau6++y24rkdacCC4vk2T8kjZQtns/DzLppjXqNUtoi+KIrJhZH92PVHqEgqJaxmOFKogqI1GVA1+QsUpvcEmTcOclCWpRfQ5joNTwOuSjNDwBFRqVaTp6mxsbHBx8RLHT+gR4/f+0PtomwGzSr1GnBWFwrIAGIahXVkrlcqEpoMGqRnEp1N2pk6fPm27Ap1Oh2XDjuQ4HuTSKl4Nels2fTp79qxNH245dMjOKuy5Zh+uJ6gboZatjXXSmj5/0tni61//OgDzO3Zy651vBmD77g5RqLef5hIRtEvWb+Ha1FLvrw3PLB1fcXzmYnzH7HXpFC63F2J3tnwGwrPgJXDG4LPg4OKaB2Rra8t+X7PZoNvVeeNw2Lc0WVleVp6lEswt7LSKziqWvO+HPwDAxuaKBaJsbvXZvqCl5prVCudPn8E3uWO1Wmf/Hs3au33bdtYMTHbtUoznFj29jEUjdddoNBj0I/vwKMdlZFBw7WbdKhzFaUqjobefxiWPpBACz/UxHU28rOwMZFlKXlC7IazgipNntlXnez4bFy5y6cKiOTdDagUizyhSg6Yor5hW5/nFS7gmlTt59gwbgy3+uw9/GICFnTsIqubzmbIowiiKbJrWajQZjfT+FxOCxQOW57mtL/h+YGsKR44ctQ/4NXv22RQhS1K8VtO2QaMosunLmdPn6JoHf2lphaCqz1+z3WLnzp184xuG0q1RY++B/YBh7Ta3YBiGHHlGtyT9Wp19BzSQaX5hO2HqWX4HpdSYDJ9jxXiEEPa+kKhJGTxzVTB/fbVsmj5MbWpTm7A3RKTwQoWZMsTEFnMYK/IIpRCOa4tw7dYMnl9IuJWra6PRYhQN7XcW49XCCVDkLJrR50sXz3Ddfl10XN/o2a7C4uIia2s6FVmNE7bNb+fcWc28s3vXXouTmGnP2EJntRbg9/USNBoN8EzlenFxEb/SoPDpSZpalt9hOLQraMX3SiBSFNpC4dLSEjNBi2K1EWDBXEIqzeSKZjsqVrA8y6yE29ryCjLP2Wkin9nuvO5IoAVuw6FOGeqVKpEpGlY9n/OXdGTRqNX5cx/8AO223udms2k7I6BscXdpaclepzRNbTQgFBN8ClLKCZxEAfne3NzUeglMSsjNzszSbrdsx2NzdZXOfj36vH/vNRw5ehSAt97zdntew1jD2f/Wz/4dAD732f/C8oqOQubnZvAMNLpaCwhDfZ/UGg1WlvQxR1FErbO7TNl8f0LSzsKZlYsQ5b35vOu2KrtpV9tel07hhdKFyx1EwS2Q59ISrriuXwqiemaaMC3Dt4LYpF5vMDBIx2E4snlrpVKxFzQXLnku6RqdyUsXz9E2r4e9DgVLYD/JbRvz5JHnSNPUPvzLy8u8853vBjTgqbeukY/zs7OsreqQV+W5nf9/6qmnuPX2N1FvtMyxqZLrwPfscTqeS2bSp/HztmvnTlaOnbccElJKGibMr9frBQWB7m6YmQQVxbTMcJjT6lLxfRIjnro52LC5e5qmJEbeOo5jQiOMUm3U2XuNBmXt3LdHtx7HHv5C4ajb7VqatEFvy56j4XBoKfQQDrmUpZMQwn5XmmXkomxDF78Pw5BarVTrSuOEjmk3u65rgVGHDh1ieVU7b8/zOHJEtxc3t3q8813v0vsK/ND7f9iCvJaWL9kp0+XlZao1M1x36ZJ1Fr1nnsFtLDA/r9OUnTt32vskCCq2s6If9HG1p+LBv4JzUGO/u4oQx2n6MLWpTW3CXpeRwgvZt0URRszDHQONaDZjE64KDAdBQW0FyhQNB+EmaqzsW7GgonJarSkipIDUfP/1ew/gpmYC02kgpGE+kjm79+sJuce/9TV8z+HCsu4yzM/txDOFtosXVpFGX8HzWszM688sr60TmFD27MVFDt2uCE0606rWLbeCSBKC4hwkKYEpWvnNhpXNqzbq+EGNiydOA5D3+sRrOjqpjRLWTBHVq1ZIi1TCceiZ97iZZDOJSY0YSb3bRDR01DC/bY441itdFEVEBU7A8+nO6gLibLNNFZ9kS0c3aZpYOrM8jMsx5NFojEVLEZtoznFbJJlkEJtpUOUSF2Snjse6IYQNk5ymKQ6vr28yM6Nf1xpVVlcWcWsmomo4rPf1No+fWuSmm7Vgyw0Hr+d3P/lxAO55+92cPf40ww09/zLf/V46Mzo12btvH66vo4PrpUsq9b3RHyZ2dPro0eOsrC2TG9q0HB/XcH24XjCGWcAqkKsXkJdXVzEyuNzecE7h+exKbcyXYi/2mThN0d0MfQFrtZoddq3U6vgG6dhodfBdA55pd1hfWbTotvX19ZIAJPCtEGqWLJHlBXdi1QrULiws8NRTz3D7rbcBel4gN1RvrWbdDt5IOab2pDQDMWg6tUajwTYz0HSp1y8fyjTlsAHvRHlKUgjXuq5lX666PipNqDUNrt8TrPY1yGcYR4QmlE7T1NKhNVpNuia/b3XaZGjqOtD6mYXziJOEvvl9kozpXY61GpMsJo5jHJOm9LeGeGZwTLiOTQUcz+WsYU8WrmsHuLa2tlhY2IFjFoZqs2Vp34bDIZcu6Qc/CFzmFzRPxFcefJBbb7uFlaO6xbu0vsr936vl568/eDPNOf3wZ71S+Wt+2za2TH3l8OFDVOtvsmleHJdj6VLKifqC1Yt8lSjcX8xe1CkIIf5f4H3AstGMRAgxC/w2sB84DfyoUmpD6Kv2y8B7gRHwU0qpR1+dXf+T20tFil3JETwfDkK4Dq7rW/5AL6gwMNyFSZbRaJs8tlKlVTecCY0mowspkcmJu60Wm1u6dnDLm+/k8Se1hF2/P7ADOEkGjbYpZtWb/N7vfZr77n0XoHPvQtVIKpfYPJSZzKmbtpvrumVLVipcx2f7dtMi9QKWDN34en+LulmpD950IwumDoDnsmJITLvNFlE4IjFEqs8ef4a+wSmMk6hWWw3b9mu0W3YSM1WSTObkhfuULgPTbsyyzNYnojSZoDEvpgeV4yGFZKuIaCoVXFM7WFxZZVTwTmSSVePIup0ZLi0ZqcAdC3ieT8HU2e9t0TERRRx6XHeD5ok4cuRZKqbofP31N7C8tGqd3M5Kg89+5osA/PFXH+Xe+/S1uOue+yAuqOcT+4B32jWiOJ4YxCscQYHQLI6zcBbfLafwUrb6G8APXva7vwt80YjIftH8DFoh6qD592Gusobk1KY2tVffXjRSUEr9kRBi/2W/fj/wbvP63wFfRus9vB/4TaXd3teFEF0hxE6l1KWrtcPfSfs2TrwrmHIEqZI2FfB8n4qp0lerVVodA945d4qHv6Wp1XbtOcDFixd55LwOooIDdQZmiGjl0nmW13R7c++27Tz1jJ6d8Kq1MhXwfBAOy6bFWfUDlKEC3xpGuMWqIyQIvZq7gWtl3XMkjVqDYV/TlTe6M7RN+N6c7bK6pLf/5HNHSJ8uKdcGAx0K79u3D5ml9Lb09s9eWkaaVd/zHboLej6g2WxangXhOla8JY9ChOfaAakkHWNVSmLCMWGXMqwWJKZtGWYRwnWskpVyXda3dHQziCKE4dK8uLRCxWhhKuERmm5JnilkDpEJ5bM0ozajr9PBgzdYpGWtVrPh/uq6bm/e+aa7AHjiiSc4cK3mYJjfsYuvPaTl6x969Al+5IM/pj9fb9nR9/5wMMH74fu+vbfGWaQcp2SZzi2V3nfWXm5NYXvxoCulLgkhFszvdwPnxt5XCMy+pp3C+BBV8fNLNc+vEKeJ5SYI4wRMcS/Nc1bNPP6zR08gDN38bKfD295+n4VKHz96ggsXdO576PAtSPTN2+q0LZ9AHRdhsBSr65t83w+8h/NmoOrG6w9arYQwymg19A0uUQyH+qYOpGeh0K7rkjmZdi5oXsDt+zS2IhoMqRnMhMxyfNO63RqOEKY9uLi5yer6SqmQtLDAbPGZPMVplQXZcWo0VUgYOP5E7hxnqR1citOE1Ayn5bIUShNCWBr3WKYMhyEdAxMfxQmLBq24trHF6bP6dgtTSW7adlXHI6hoByHcACEFMx3dEqxV5ti3Vx//ME65915Nlnv27FnOnddp1c6dO1FYGQr+xv/wt236srq+xcq6fv2+H/4Ry+tZqddsq9XJJPV6fUIp22JlhLiibsl3y6520nKlp+mKifxUYHZqU3tt2suNFJaKtEAIsRNYNr8/D+wZe9+rJjB7te3ldCZAr2wyVzaUzVJJ4OrXFT/AETp8vvb6G3GlDuWHvTW279jNJz/5nwE4fMstXDLIt3PnzrK6oZ3kE0/08Q1zT61RJzIDVYPhiG8+8gQf//gn9ff1hzz7tAbZ+EqRFO2tOEaYqMP3haGCB6kkGal14anKcUwoT73CnOlExIOI2BQQRRxbxuHME9Tm5mmY75trNagZRqFwa8BAmPBfybGimYvnmzXIESRJTmIq/kmS2GNL09QK+OR6JEtvH1FSmHoeXrXC0qpGFC5tbnJxUb8+de4i6z2DqKy38Mx+ZTgIr6C4DxiNBgVwk2QkYbem11te3bBpzb4D+3n/n9dzLJsbWyilqJpZiAf+6Ku8+37NhHXDbXdz82HdxlxaWWNn3TBzJxmOmV2p1SqMRqG9zxzHmUBhjgsmF5HCa7b78Dz2+2jx2I8wKSL7+8B/L4T4GPBWoPd6rSe8VNNc/i7ChNm5yBgaivjAdfBNreHA/oOcPPo0ALt27cFVKfv27gfgM5//Aj/+4z8OaAm5AoW40YtYNRwKy5sbtGd1e+xbjz9Ne2aB2DxUnbl5ThvZuj27djI03Q+VprQbZjIyzagVdM5SkKrUXn2vWmFgOgkCkJb+3keYvGh+YQex6SrEKseTmVWSSrIM16QvXlAhN1yMrutaRN94KpHLlDTPkQVlexJbdGKaK/swuGO3Z5ZK0kRvYzMegevwzAnNtH3m3EU2De9EmObUTCdhNEqpGvzHsDdkvmP0FJKEa3YskIU65PedjK5xhH/vr/8M58/rc9lotu1w1v4DB6nWmvYYbn/z2+j3dWr33NPPMWN4Fvbs3WfTx2yMLzRK4ok6glLKpk/jtRPXdW172goCf4ftpbQkfwtdVJwXQpxHa0d+BPgdIcRPo9Wn/xvz9j9EtyOPo1uSf/lV2OepTW1qr6K9lO7DTzzPn+6/wnsV8Ddf6U69nkwoQZ5JVKajA98NcEyYXK1WiQwQp9XssmuXHrq5cOYE2+fb/PRP/zUAjh07ZgE39913H//hP/wmAO1Wh+sN4OfC0pJdQeuNBkpIvvW0xjPce++7+OIDXwbggx/4AMqsOr5TxTegns3VRTyj9+hWfcilpgEDpJBUaoU+RoojCzyDa2cPkjS37xEu5HFEUHADxDFeXsyYhNQM9l+BHdpRSln+gDzXA2mFUE+appa3QAmdagAIxyM335vmIWFkCpO54KsPPmTTh1RBnJlcyK0SJ4Z3odG248n1RoOe6bbMdupsbPXYs6ALjWdOPsvKip5pePCrX+X++zUoqd5s22ggqDYI49Smc2km8UwqsWvvfru6J3lGblb4CT4EJge3gDFuBTGBxxjXqPxu2J8aROOrZUJp9SBFeVEt8i6K7fRlkmS0W/omfGpji7lOG2FC+5tuOswzT+sZ/D179nDrrVpU9tK5s5y/qEsyUZYRFQrMKmM06vNHX3kAgHvf9T184QHNFH3k2FH+yS9oLsiNlUvkhqSlOzNLlulcO0oTmpUqwjivTElywz1Yr1QtTVvaj2gYPgg8H2VybUflutUmS2i4a/bNU5KoQEF65TRqmmU4ogTlSIm9+bNUEht5OtfzrdrR+kaPohaeScWiGVT69Fe+Rpwm9nxIx8cJCrHcAGVqOvnYtcjSnE5LO8V2t8Vcu8aJ01rY5bZbD4FriE2CChuGmVm4FWqmk5DlCoQPnv7uNI4s7ZtApz3mQ2MPs5yUs7usDj/uIMb5GL9bzqCw6UDU1KY2tQmbRgqv0BzTB7d+XmBXBDXRjXWomFV3x/ZdrK5u0Grqn99y99st1dqli8sWPhxGCb7RokxGIVsDHf5u9taZ2baDT33qUwB87/f9IFWjG5FKxd/+OQ0w/b//1S8RGoBRmEUkhp1pbrbLYDgkMHiGWquOKjAMjkto+u+dZguZ6mOoVCrkhtw1lwKEsLzPynFwCuYpz6WGAd9QcjP4XqltMEpDwjAkM2CmMIlR5pwNhjFbo0JOzSM0PA2Xllb4whf+qz4XtSa59C1uw/N8MNGFxAFZ0MkJXJOKVGouvZ6GPL/5zW/mqcceolo3+otC0DI4i8O33mm1IKMwZmSKxvVaG6lyUrPPbqVqj0eJ8bV1fIjJQbzAUNNr1aZO4RWaUJffFJTkF2OjbArsHMOtb307x771CBcu6k7u4Vvv4J3v0iWaX//1X+PDH/6rAJy/eImDB28A4LHHv2VbVbnKCAKPwNCvN9otLi7qJk/1QNNSoP2dn/u7/OI//PsArKwuc/0B3S1eunSRg/v2ceHCBQCk59gJwnA4sqAqRzl2zt/xXERRq8i1mrN9KBwHYVpvMnXsQJbvlYzRqVKWPERKnU7FBR+C47K8bDgMajW8QO9/LgWPPqkRnU8+/SyJCdGzXO+XY5wCroMqnLMow18h3JLN2XOJhtrBPP3sc9RbTWL031rdGavK9czTzzHT1Z2ERqtNZFCUUghyiZ3r8CseckzqeUyy09q3U6m9PmyaPkxtalObMPHSOeZfPbvrrrvUAw888N3ejZdl3mVBgcS54qy7K8Ez4fdoq0fY79Fq6tRgY3OV9XUdNXzu858hMUCea/fv5fOf/ywAO3YscPSELoxtbvWo1tu0DKlsKn02Ng1Gf23Tro6NSpXA1Tv4P/+tn2HGTGwOtnp4KmXnTj0l6SCpmHmBZrVmadfIITddAT+o4ZpiXi5NsdDgKZIwJDcMS9FoSFzQsTVrtoAWpZEtuvX6W5xfvMSm6Qb0hzG+mZFY2+xTNZqZX/ryH3Nxec1sszypsVPFcRyUU6Rppeq2wLXSbL4bYLIikiik29Lne6ZZ5W/8tZ/ioa/q4mzNhx/8ge8FoNq+gUOHb9G/r9WIxzQecR0LZ8/zHOGMBdpXoEbTkcJkOvHdtHa7/YhS6s0v9r5p+nAVTIny0ishr+gUcschNvRnjh+wc98BFi9oXP32XXtYMe21H/vJD/H00xrkdOnCGQ4ZpNz6+qrtZMzPLTC7bYFtRrNyeW3A9l26pvDlB75Kx9DFb6yu0azrh/0j/+f/xY998IcBuOn660FFLJptXrNjp+UTcKquVXUCLIcDjodjVLUcJEIJMstA7NjuSz42R5IluU0/XNcnNc5uGIYMRhEDUy+IckloQnvpBfyWQWrGuYPpLuJ6finQ6jooIcr0RSmrsCQchVOIsqqc3NREGrUam+sa1LW5usQ73/U9PP6YHkhznAxl2rVvfevbSQyxi25B+vZcZKmcSKcKEhTJ8z3u5XkUfEdZ2l+RTZ3CKzZHX+2iHy9039+ayXUdIam3NfzVkYrNrT6ulV0LrFZAr7/OO979PQD0N9d59GFNKf7m2bdTAAAgAElEQVTEE9+iYnLtd3/Pn+Hxp57kx3/sJwGoNDocOa7n0B74yjcZGWiyX2sQGW6BKE/5t7/xnwD4Cz/xo9x1x0FUZvgE+kO2tzVyLx6mlgsxyyWy0HpQOtoBUKkEqchMGzPNcmJT74ikomYcSZyk+IHhDPADstxwL45CRlFomZRGScbmUEcNX334UbYivf9u0EAZaHIvTi03g0zTCZiwEAKvgAw7ruXllFJaPYs0yS0/Yq3icuToSW48pElqbjh4LadPHTP7nJGYc+ZXK/gGvh7GMbmSuG6hAi0mrrNlUlSTtYRXUx361bJpTWFqU5vahE0jhVdoxaJQpgxy8m9FxV05jCKd90ejmPluB8zKJ4RidU0j6jqdGRIzO9DuzPKWt91nft/hbW99CwCLixf52Z/9O2w3+pW1zgIf/huaejzLld2ZKEppm7ZnGio8Az76zY99nKeOHOC//eCPApCkktBQsc+1OpYXUTkufcOh4PsVhDTcgWmGk5cMQXmuCsZLnduPreCyoKGPI9YMC1Kv32c4ilha1x2HzdGIb35Lg7dS4RCY7sfGVkhrRncCqpUaodHb9ESOlo8cL/UXMwUSYaIzgbAUdEpKKxxM7vPlLz3Iz/8v/yMAj3zzIQ4dvtNcNI+KqZ0ooazyFY5GqBZ1kTiLXxrI6FViXH41beoUroKN1cCQonQU0pFl+gC2pTc3N8doOMIVRU6cMzOruQHCaERgwm83V3Q6+hLddNMhakbNenVlme3bCgoLGPX7HDVaBc3ZHSQmLK/U6gzNg1Dzq1bCrNVsc+LMWf7x//4RAP75//b3rZBqM6hbko9hnJSw3jQjMEQurnK0IpaBSbu4djgK10OZ4pzv+7YY2NvoWSj31taAzf4WZ43uxfFz58mN80ilYGgGlertuTItiXOr1uRkOn1QxTbzUjxYOcoOp7mUylfVSoWKmfJMk4gHv/p1HKHfd/i2O5jp6NQuGpa8lhIs/sINfNIsITYOu9qof9cGll5tm6YPU5va1CbsDR8pvBiA5MWosl/s77kz2Ypy5ZiflVf2uXEc4njCovjAITZAGMevkxX77Pm2kh+7ilbbsCH72/Dabfu33/3kJ2jUdRtP5ClVs9JleYhfoBCVRJhVf32Y06q6OGal//l//i/5yC/8AgAXohE1k+bMN+skBt1YdxTCdE9cVyBRJQV5kiBNJ6HhODiGwkz4Hn3THl1d67G4riOVI6cv8PSpU5y8qCOHereDVEZcB2X3WSYpnjlHLUfgJno4SUqFI6WNQsCFYizcdZAFNwHKCtukIiM0iM6FuVmOnT7OBUM7d/C6A5Z2jbpDRsmyXJzj3Ay8BQVBbpzjXg5au4K9mlTsr5a94Z3C69mSJCmlzma7FtHY6XTY2Niw/IdHjhyZGK4psSdle1CIcirPdQVxFmEY0unFA/7hP/5FAP7Bz/1PRKYlOQpKFassTW0oHUUxUZqUebwjcI0CtRJY1emVjU0urGjKuJPnzvHYs5oI5omjx9hKUquQFOeS3E5Tls07JXXrEdBK2PYYL8cEOOUxX4a7KTQU8jy3k4xra2vU63U++tGPAvCvfvmXbco0iGKuhN0Z73QU/38tYHxeDZumD1Ob2tQmbBopvEbsSnRw1ao/IRhSsBMNwxEzMzOERgBmbW2tnMenjBR0ZFFKlwsKsV2J6wUEBsXoypxTRjTllz76r/krf+EvAFrhqW46FrPdDq7Zx1DFONWaDd+Hw9DuZ5ylDIz8+zCOOHZez1f88Te+yXGjG5F5AZV6i5HBIyjXK4u1LyHevnyFHgcvOWryKwp0ZxElADQaDVwHPv3pTwPwL/7ZP2M41GlSQbp6pe280D68kexPrVN4qbleUZP4buSGYRhO0H0XQJqqqyf+WoZC7ML5S/YBFaJE2o2bksIejKMgkw7ZSD+UjszxDK/g0VPn+Hv/5J8C8Ofe+15uv+UQAGeWlq3AbBiGBEFQircmsUUX9no9BkbO7qGHHuKhhx8GYHMwxKvpViOuRyYVrq/BWFk+/oAJ22p0xl6DmKgP5ZTIRSgfUv3/kvJsHJFYdCKatSpxFNm/rW9u0jZtUK7gnC/fRvH65fJ6vtZtmj5MbWpTm7A/lZHCy1n1hfrORwtBEFiJ80araUPhNNWYfN8Ac9YNCAjMaqYKxuBSjkwwLmyjC3OuSR9UnpoCHwi/QmDAO5/8zOf45B/oEPud993H/r17zfc69h/oWYZNA0w6fvw4Tx7Xsxuu6yJNBOLiEZlpIqE0qCmLDdtSEEziep4nMh+P2PWxFCnTFdIJY4X4ShzH1I0Ufb/fx3NdgkD/7VOf+hQf+tCHAE2weiWJwD9NhcY3vFO4mg/yd3o+XpJTqRnuvySiZjgSkySj19+y6Lo77riDz37hi+ZTOUX2IBElok4o++CDQjmOJTnRQrTaEaQyZ8ug+FqdGQZGeemzf/wg1eojevthhOM49oHLspJ7MI5jQrPJPElI8gLg4yAK+jLh4TgORZafZ+WJvYyyhtw8eC7lw68cF3FZkDv+sDpj6YPlUxCiBCWlIMaO/7d++2N8+MMf1sefvzAg6Y3qCMbt5QrM/gvgh4AEOAH8ZaXUpvnbzwM/DeTAzyilPvsq7fsbyq6cn4qS4zBNbbHM8VyazSaDvsYNfOlLXyqpw2UpYa7ALq+aNLTcllAOikJfwCNJiz58qSR1cWWN+W0aaenECUlBSe4FOI6DGUDUzElmO7VK1aIQMxQYvkTPC6xTTdMMpMR1Cvr38TxWIkz/XyisJ9b+zByAyeetI3gJ59X3fYtFcBxNn15EDisra1rZi28Xe73S68u/+41mL1dg9vPAYaXUbcBR4OcBhBCHgB8HbjGf+deioAye2tSm9rqwlyUwq5T63NiPXwf+vHn9fuBjSqkYOCWEOA68BfjaVdnb16BdnlK83HTlSp+TWSlIWqlUKIr0vu/R6/X44Ac/qH+u1hBmFZe5IjPjwkLKgnBZ/zwWYkdxTMNwNIZhaGccFNKONNfaTTaNLPxgMLA0bUG1ojUqzXaCWt2Kv/bjFMfQxLnCsRTrUl6W5yvHrkhqnHdAOBRFBeGUHZOJRTl/aSd5nDo9z3Mcq8KU47keoanXOI7DH/7hHwLwAz/wfZd1Mr79O9/odjVqCn8F+G3zejfaSRRWCMy+bu3FbozixiuGY9KkDPOF69g2WBAE9rXv+ziOQ2JozQGkCbmTJLGfDyploTEIAnzjID760Y/yG7/+m6TmiXdd3xKjKKUsZ6TeNwNzHlNkEkJQ8VxSQ0rqCQdlCFP05/U+ZbmyPIitdtc+YFIIqvU644FmxfAuuFlGKgruxZLcddx5ugZpaX8nXCtpN/5mKcbai2OOwxU+qLHCoyhRkONU6cXxFP8vzp+UEumBMgxTzWaTrzz4IAD33/9n7Gd9v8SJVKtV4rgsQmZZ9l2TdXu17RUdlRDifwUy4D8Wv7rC265YmZkKzE5taq9Ne9mRghDiL6ELkPercjl93QrMXsleSmFJKcVoNKJmila1Ws2u7nmeT7bEzKxCFEVkWTahs2jVn+p1+3o0GtiKeaPe4h/9438EwP/3O59AOYLQjEX7nhpTGBIoUQqQFN2H8WPRv8+tB1dllM5YbW8iZr98tmI83RGKcjjJdXBkgS4UltNQqXGwkcIRomwlCjW2L5cDr0pGq8vtpaRqxXE7joMoVnbp6PNkhqj6o5BjJ08BOgKYNapcq6urWvQGfc2CIGA41MCscVDUG81ellMQQvwg8HPAu5RSo7E//T7wn4QQvwTsAg4C33jFe/kasMsdwnjlu9Vq2WGlfr9vH9AgCMAp8tgSpiylxPU9O2zU7/ft3zqdkuRkbnYbx45rmrBf+ZVf5fNf1ESjg3BEc0z8dDgY2TBXO4XxfTQOYjwmFBI1XmwYw2AIygdcMPbgKecKqVTxwJZfLoTAN7dVrpUf9DtVRiExq9WSsCrSE0hBlIU8C8SfwBmUDuf5zCo7K00QUzjcOI45ceIEAB/4wAf42Mc+BkC327VpYaVSIYoie55d17XX/I1mL1dg9ueBCvB5c6K/rpT660qpp4UQvwM8g04r/qYqktWpTW1qrwt7uQKzv/YC7/9F4BdfyU5dTbvSqvJSQUjfFh2Mf65Y3YRgMBjY99ZqJa15lmWW/TfLMptiuK5LlMR2FWo2m/bzzz33HP/+3/97AH73937PRhPDYWjD2nq9Sb/ftwCeSqVigThKKKtQNd7L17s82XOfOL6iO+AInPEZg7GR5G8bRLIfl+VC7Sg8wyPhOFgxGCkm6dDzy7/LvhinL1OWWm3iPWNDXi9qxUg2CinL7rhUyg54CcdhODJcESrjxhtvBODMmTM2/RuNRtTr9Wn34Y1q4zn05XZlXoLnf79Sim63y8C07uI4tkNMcRwjDVqvXq8zMjdet9sFR/DIIxoh+Ku/+qt85StfAcowFTSisJA663a7bG5qxmPXdakE1VIxKh97YL8tzZnwZEBZob/isUpVYoSEU9YaNCpKb+8yh3K543WsHoLENcpRWsWpcEoOKGm7IZfXpwunJOSVH8BxvohiO5cfo/2uKzzEFtkoC8Fbt+ysSMleA+f+8Ic/zK/9ml7/qtUqYRhahGTh4N+I9sbsqUxtalN72fanMlKAscLai6QSL/b3JIrwXdeuOp7n2UJhmqZUja5jgU0A+MhHPsJ//K3/ZIuLjUbDahrgOCizGuV5bqOB4bAco1ayoAor+AwGdjuT62IpU6IHeIpipNSVeGc8UiiO17EwY5RCybH0oSgUjvEX6D9dlgpY5SZBcYsJVQILlMpQUqCeB+w6URO9wvm/fADqeU1I4Nu34bouSimbvglRDncJIdi2bRsAJ06csBHc93//9yOlZH5es0uPRqM37BzEn1qn8Hz2Qhf6StNz9Xp9ovU4/h0L27ezsqrpyP75/9/etcfKUZ333zezj7u7vvfahIsNLg0kSlAjRcV2lKYKkIqqEaDiNKqUEKBFImnoI2pDFLVIRiX8hZymragaEjUlCZQ01DSNsFADoai0Ig8n4RUTqHkFEjC2g7kP38fe3Zn5+sd5fefszO5eY9/doPlJq52dPTPzzZkz3/le5/s++1ns2bMHgGIccbViXZRJkjg7hMgLmCSZzewcRRG6OmpwcXERMzOb0e0qlWV600bLYCSNMpAninx2kbJbZejSs/j3RkTWJpBSBJLnQ2SLoZC4Z1V41lj5yW6nwu6QUQyiyBac9QKZIBiBeBbSzsFRaEso0PPFSsZYMG7jAk5Td31TOHZpacWqgs1mEw8++CAA4H3vex/iOLb9vLKyYu09bzSU6kOJEiU8lJJCgJ6ApZxZSFr1F+bnMTMzY1UGRBGeeUbFFvzzDTfAFM5dbq9YaSKuqpV4xqAYx67MO6epnYE6nY6lp9vt2tLnU1NTWFhYsOfr6jJqBi5mIVxTkH+fRTb8GLFdZlABkFitgvVsa0rKZcjgQqjBrp2JVGAmq66o+IfU0ZQ6KYIYVrcjaLUDvhpBIPgFXYslBSn1JIkL5a7X69bgmHBmz1Cv123fVCoVK93de++9uOeee6xqMTMzg2O6fP0bDWPBFJjZi8s3MEEuIWSCCyO6y4UvBmmaIq6odQTdbtdajLMs8cRtIjnIIltLUS2i0S8rk116OzExgUZDV14iwncfecQOnvvuuw+pfnlbGzZgUScSyThCNarp8+oXRhc1TRmwJZYodnkPKIF5wxhApNMvr3YTMMHmUzA6srq3TDAFCF25EjA857HwXJekUqMD6sXNIidiu/ggRpp1LTeJZA6DjLGarYjzuuvZAEYi9bKb/JNB+jizDiJlxyyi2NWO5CzzksYwu7UbgLxn51UgEEwQIjPb5w8AceQWZ7WzzDLb+ZUVtHTG6cV2G5fs/CCuvvpqAMA111wDXZMX9XrV5ZNoty0t9XodaSrWt2TwAtvkGJSRrxU9ZtdmsxjCPTskxoIpAPn6OuA0XW+RXJrazp2YmEC327UdLAuP1mo1m/+v2Wxazl6tVu0sEYsU4Op6bPMNdpMMRLqEGpONIDx06AiuueZPAAAP/eC7OOOMMzA3p5KRrK6u2oQlx44dw/T0tKYrxsLCgj4X609xGHEehrF3RJEfeVi04k8y1jBXQIV6WbEnWQjGY64p2xVlJwq3TT8Xef6LYgLC+Av120gtjjmE9+X3MWAZLrsSeBkn9ph2u23vLaIKFhYWcMcddwAA9u7di2/prFSNRhUvvaSi+d90yik2H8XCwgImJtwL3mw27BiUtFgpE2psmr+UzWP9NfzSplCiRAkPYyMpBI6onn/Z+5eQ6DX/hAxpwlbkksE/ndXEZkCenZ21EYFpmmJlZcmeT3oPpKRRqVSsJHHLLV/E3XffDQA4cvhVuyCmWq3a4iKASpVmpZhGA7Ozs5quiR4R37jkwhkxTyLIS2suZ3o5W8vgHCdihwuiOFeKICJbgIXhhFIZgZjpWd7mQwiCmfKWFBdJDPaaBVJLngTVb8kyUVR4rvA8Nl5L9FOSJnbp+sSEe2ZdvczdzPSHDh2ykY8333wzLrnkIkvb7Gtq1W+r1RJBUYmXnVvm3wTcM2NmKzmoY0+cWjAsaBx8rdu2bWNjkAOKxUYD6f7LskznCjDRab7PWcYCGPG9VqthakqlR//5z1/E9PS0XbEYRRFefFHVJ7jpppvwg30qRfnWrVvtoplKpWYfbjdTD3B1VTxI8SIa5tHtJp7dg1mIwIJmKcqSFGvFwDXtrGgb3LOEtBtIpOKFkapAHMc96oChWfZ5eIxkPvKa8hp5jM1+Z5m3L6RZnjdvhaLsP6NCSBqLzmX+czaV1Ntfqzq3YyWOLfP3RP4oxrQuUHvXXXehtUHbrpLUU0+jKLI0yepfrVbLjtN2u22T2chrnAhMTU09zMzvGtSuVB9KlCjhYYzUB4VhFpysrKx47jjpXup2u87VlCQwfC9JMjvDrK6u4pXDqrjphqlpTE5tRFtXW/rYx/4Izz//PAAgrlZtUMvTzz2LCV0KvdVqWU+EWXdgVY5q1Rktma3brZ/RrSiJpZQa8mbgMMuQ+U9KEEUqAuXsy7t+HvIMfcMcdzzt89SHUCUKaWE2fZ6feDU8Tt5PrV636xsAJ5VmWYYkSez6FbPmBQAOvXzQtrvwwgtx6aWXAgD++obrrYpQiVTwlGmnDIpaZUkSO2aqYvyMCmPDFNay+qxWq9kX34jOUn2QNgGTN3ZhYcGqDBumJq0qsX//ftx0002Y078XFxdtFOHcL45iaqPyHqx2EqsWzM7N2es3Gg3Mz89bdaLdbnsrJld0NeZqtWrDatWgDFdgunBis50FTKToZZKieVHeh342iRBpToWpDO76GftJVjJh8VGrEXufRRFdFoaR9WFEoS2hyGMjX/48xhmeTzIFZkZVV5aWOROSJFGuVz2eqjX3PONa1UZBxjHZ0OgdO3Zg165dAIDLL78cqyttV90ajuF0Oh07fqSaq8aYUIFy70Tf8wkU+kv1oUSJEh7GwtC4fft2z9A4CEtLS5bLTk5PeYtTms2mTZkFABt0haK5uTn81wOqYMr999+Pxx57DICeJSpOgF9eXkZUcV6BhXk1A9SbDTubyBoM7aVlLwVbrVazMfXLy8t2oVOSJMGsXTyL5s10ef7/PPFfGiBDA6Bsm0FEPpJv0c+LQZD7+nkIjOEXgBdUhkwYUAOaelSbgtgKr03gschyDJUAvOCh0DCb1/9Zlub2WbVaRaVSRdLp6vOmVh2dmp60Vbo2NJpG6FExKzrg7JxzzsFtX/mqlTABuEVwgJU0VP+5ZL89957bI8NJCsMaGsdGfRhGaDGPaPOWLZif11WCqzV04sQ+oOWlZdx+mwow+c53vmNDjqvVqnUndbtdbNmyBQBwdG4WddSt9ZcR2bTo7e4qmpPKEpymqdUnJycnsdxWYmCzqSzHkc73t7LStgyr1WpZ/dRfkONbEYZlzEVBQeG5pE6ap5ZFUaRUABs85IvhRVb7QhUvEi9o0aiNCHZIcw4jyLs3oUrJ6+epQtJLI9ubnzKvhFEd8tSPOI4975bxABBFnpdrYmLCbs/PLbjFbVkGk5jS7ANUEeBtO7bj5ptvBgBcfPHFNps3sbu3NE1zmYGlU2wPr3CvDaX6UKJECQ9joT6ce+423rdP5Xdtt9teIEcq8hQcOHAAgAogMYaZAwcO4KGHHsKTTz4JAFhedTP17OwsTt2kApaWlpbErF1FpW7qGpLKWxCIxwCQhNZ/48oWM0yFe70KeWKx389+TEFo6Cry7Ydiuty/Fou/CVCSodESWc4y6p77iiiXnizL7OIlGT8h2zCzNzvKGIyi2AYiQsWcS5e8C4PBQjoBeOHsYcxTHv1Ecn9OOHVON3tqmqxPEfvGzHrVhbpfcMEFuPHGGwGorFpmPC8vL9vtTNQFMSqroTNNUy/Dlwmtj+PYSjeVSsXL89FsNn951Ic4dp01OTlpU5CdtnkG7bYS66+//no8+uijAIDDhw/bxU3dLO1x15mOqNfrIoOyE9s58hdUpZk/kMzKPjkomV1qD6nfZ1mvFT/vBZWLc8I2/XTi14s8BgUom7ZkCrlqQtQrXpv/KXjh/ZPne0LkuRh+joTC60hmYUTsbhL0H6wsHXopfA9Db4CT+y2jJfPdoMwMCNWPRTFaF/zEgpFGHvNeShJMTqv1M/t++DAuv1JVut6y5TT8sS5wu2PHDnfNuGI9HJPTU5h7bdZOeM1m00bLbtq0yab7l4wgyzKPQQyLgeoDEX2ZiI4Q0RM5/32aiJiITtW/iYj+gYieJaIfE9H2oSkpUaLEWGAY9vFVAP8I4Ha5k4jOBPA7AH4mdl8MVevhbQB+A8AX9HdfZJkzrqRpaoNCDh48ZHPwP/DAA1Y6aE1NemGhKh5BcedOp4PVrquvYPheCrZehiiKbG6CNM2QciZmfuH/ZycOhjOYkRvSjCF5qzpP/gxpDIB51nMDOWv3MxiGKsOg4KNctcYEzwTiu5UgOLKp1aSIbA11cf56C2Ohl/cSek8AZzSLxHqFMIQ6715MwQg5i5vM1hSxJx3k9ZfqCxIU+CpDHkxYuieR2pL3GSIW/RfL49w1K7WqHZsMxvwxJx3/+Sc/BUAZMLdt+3UAwK5du3CGNojPzx9Do9W0Y2Jh8Rg2b94MADh69CgaDeXJkGUH2+22yAbuPHKDcFwFZjX+HsBfArhb7PsAgNtZ9cT3iWgjEZ3OzK/0uwZRBNaZe9OE0U1UxzWbG7Bnz78DAOr1Bo4tr4hjzGCtIk0z+5IyIpjV8RFFPbq3ahTGwbsXOcucrgpmuNpFBMj0YYaJBMJWlBNkZBCmA5MDxuQjiIgQRy5evtDiLyDdkBJSlTLtwuNg7lwwiky+yPq5ZEnq2VQk8wCcHSLLMsTU68aUv3vogGOAal1If5tGReeGyOsbQgz5sve370jmUcSIXBlcSY+PyNXCJFhmy+IaDMZyu2OPr1CEql5i/cxzz9r1Diln+N739gEArrjiD7C0pDxmV111FT7y4Q/bHJGNRsMyleaGFkwFHZknolqt2mAps+x/GBxvhaidAF5m5seDTtoK4Ofitykw25cpgNnONBRHSPSNXXnlldY4KAdBp9OxOhJFEbJgQZQMM64Io6V9KcFWX2Yy6cb1gM3kTJ/6r7wInzXjLgsGSW+sooOlWRjYAIC1tBLSWdxdvcp4Xtr2foiKqi+xKOEm9nsLonISp0qaMuGLz3MjhvQTkahOnQmGH3t+fXtcunY3bh69/n/u5c+jNc+YK//zjw/o1dvNZgsLC8peVmk08Nr8nP0/ZTWTb5qaxtyK2s/kYhX27NmDO++800rRO3fuxPnnnw8AOHTwIM5/73kAlNHSMAJtXARwgiWFEETUBLALwPvz/s7Zl/v0iOjjAD4OAGeeeWZekxIlSowAxyMpvBXA2QCMlPArAB4honfjuAvM7mAzi9Ymqti9ezcA4ODBg5bTLa4so6W3q9WqFZOSNEWS+NZos4ipUqnY9QOqfqBpk4LYlyCM+uLpjYiBnoKn6h9bozEnGtEldusPK3EGbjg7u5J/fikKh/sHzZxhGyUR9HocpPQg7fBUcencImZ/vUNgLxgk6eTSF6gm4bakMU1S77fc9o6hfFdn0TeAwG0ZoWBO67HRSInISao+/a/NuZwei4uL2KDX4nQ6HdR18N0vXjuKLVvOAACsrizZgLljx1JsaDZs5OStt95qC9WkaYpNk+pct9xyi51kOx2nrki1YhDWzBSYeT+A08xvInoBwLuY+VUi2gvgE0R0J5SBcX6QPQFQA8+IN5//wm249957zbWsS6bb7dpQUGZG1yxG0SKmfZErMbjj9NMwYak5XiY1VWqB06/9F90wj/yVa2YwDyPOhi+LZAoyNsO2594cCkXfRdcfZr93vxnnqhVp+KIzF967NUBm+dfuq+IEjDDPJhIyxZCRuAMiaygepFa5e5CqQA7Tz3qfR3geR6fvEp3euNELh7dRtMxY1a7DRqOBI0eOAFAudXn8/LFFNBoqNmGi5tztjUbDbn/oQx/CO9/5TgDA5z73OeuSXEs6+mFckl8H8D0A5xDRS0T00T7N/xPA8wCeBfAlAH86NCUlSpQYC4xNROO/7fkGAOCyyy6z4tfWrVvxs58pj2etMWGNjlmWIdIza6WiEmpajthqeuXCTRy6dBXK6krMDM7ys0b7CDMH6ciyHEnEoB/HZeZc9cELZCI/2jB0UeaqHEM+T06z/NlVnENKDMxsg4esS7VISoocLcMU8w2zShnvRdGipWQ18YKUQjXDuw/Ketr0SGyeq9F5HHKlC1HwNs1cYJBMuyaNvnHs7qVLkQgicmnl/chNoFYx2bq6qFTNknKX0wEAqtUYzQmdDTxNAa1Sbdy40bbpdDrWpb9161a0Wq2hIhrHgins2PEubk0pV8uhI4dR06JOBvbEH6NfVV5iTJgAAAZuSURBVOOKyzmQpF6SCiZ4gzfOEUXz7jnXvVWgt8ttU2y1n+6ah5BhDPMcQvdcUaq2YSCTeYThxMPey6BreueVocDUPwdEHiJp/ziOMRsykX7tirwPIfMpemZhPEfeeUM63DG+fcL934d5M2NChzwnSWLDnzudjs0mvnv3bvzWeb9ZpmMrUaLE2jEWax9++tMX8PZfU9bTmZkZHDUZkBsTVhRqt9suYWeBAQvQ3LRIlOyD45WYQq4eGv3yZt0Tde3Xg26366kfRTQb9MvQPGyA1VpVnDcSzP3njRNfYji+8+elcKvX63j1VZVZ+tprrx36XGPBFLrdjrXKLs+t2BJqgHOlhAVcrausTy8qnbI4eMVgGJFw0H+yzVpellEhDEE2KBJx+7kZCz0ZA7CWtr3BRuuDorExLC1h8FOeOsbsIlLVkBU2mSGvY9TsOI5t8FK9XreRkqZY0TAo1YcSJUp4GAtJQQZCxnGMig7t9NKuTbpkqzFFhRIAEXnhJsMY/frNlIPaF9EwDNYqRg8ybK0FsvSeRJHRcS005hnQGOJZFAQEjQOG9t4c5zjJG4++WpFvEO+nfhKRVa2JyKrcq6ur9hlPTk4OpNdgLJhCkriqyY1GA22tMsjKTYuLi764O8CCDOgBLvYPwxjWqvua9nl6eBGzYR79ayG9F/28LEVuy2GYRb+BfDztLLMa2PLkYa2qoReMFniJityoeWpKyGzDNi5tHHmJZQyDWEuUaak+lChRwsNYSApRFNvApJQzlfwSypduOOLy8rJLhNlHrArVB4Nh1YfXa8waNy9DEWR+BIki+sN9w/ZZP/WhX03IcUc/I2DRTF/UZ/0M3aFkUjSGZB0UIx0kiStVKOtNDMJYBC8R0S8ALAF4ddS0CJyKkp5BGDeaSnr6483MPDOo0VgwBQAgoh8NE221XijpGYxxo6mk58Tgl1d+K1GixElByRRKlCjhYZyYwj+NmoAAJT2DMW40lfScAIyNTaFEiRLjgXGSFEqUKDEGGDlTIKKLiOgAqQIy142IhjOJ6L+J6Cki+gkR/YXe/xkiepmIHtOfS9aRpheIaL++7o/0vlOI6H4iekZ/D5+3+/XRco7og8eIaIGIPrne/UM5hYmK+oQUTmphogJ6/oaI/k9f85tEtFHvP4uIVkRfffFE03PCYIIqRvGBSoD4HIC3AKgBeBzAO0ZAx+kAtuvtSQBPA3gHgM8A+PSI+uYFAKcG+z4L4Dq9fR2A3SN6ZocAvHm9+wfABQC2A3hiUJ8AuATAt6Ciot8DYN860fN+ABW9vVvQc5ZsN86fUUsK7wbwLDM/z8wdAHdCFZRZVzDzK8z8iN4+BuApqHoV44YPALhNb98G4PdGQMNvA3iOmV9c7wsz8/8CeC3YXdQntjARM38fwEYiOv1k08PM32ZmU2Ty+1AZzX+pMGqmUFQ8ZmQgorMAbAOwT+/6hBYFv7xe4roGA/g2ET1MqkYGAGxmnR1bf59WePTJw2UAvi5+j6p/DIr6ZBzG1tVQ0orB2UT0KBH9DxGdv860DI1RM4W84PGRuUOIaAOAbwD4JDMvQNXCfCuAc6GqXP3tOpLzXmbeDlWf88+I6IJ1vHYuiKgGYCeAu/SuUfbPIIx0bBHRLgAJgK/pXa8A+FVm3gbgUwD+lYim1ouetWDUTGHo4jEnG0RUhWIIX2Pm/wAAZj7MzCmrIhFfglJ31gXMfFB/HwHwTX3tw0YE1t9H1osejYsBPMLMhzVtI+sfgaI+GdnYIqKrAPwugCtYGxSYeZWZj+rth6FsaW9fD3rWilEzhR8CeBsRna1nocsA7F1vIkgtQbsVwFPM/Hdiv9RBPwjgifDYk0RPi4gmzTaU8eoJqL65Sje7Cn5x3/XARyBUh1H1T4CiPtkL4A+1F+I9GLIw0esFEV0E4K8A7GTmZbF/hkjVoyait0BVZn/+ZNNzXBi1pRPKSvw0FOfcNSIazoMSLX8M4DH9uQTAvwDYr/fvBXD6OtHzFihPzOMAfmL6BcCbADwA4Bn9fco69lETwFEA02LfuvYPFEN6BUAXShL4aFGfQKkPn9fjaj9UFbP1oOdZKFuGGUdf1G1/Xz/LxwE8AuDSUYz1YT5lRGOJEiU8jFp9KFGixJihZAolSpTwUDKFEiVKeCiZQokSJTyUTKFEiRIeSqZQokQJDyVTKFGihIeSKZQoUcLD/wMaTTlaxLKRlgAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# load and show the image\n",
"FILE = '../fig/Reese_Witherspoon.jpg'\n",
"#img = np.array(Image.open(FILE)) # this works as well\n",
"img = mpimg.imread(FILE)\n",
"imgplot = plt.imshow(img)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The image is a: of shape (150, 150, 3)\n"
]
},
{
"data": {
"text/plain": [
"array([[[241, 241, 241],\n",
" [242, 242, 242]],\n",
"\n",
" [[241, 241, 241],\n",
" [242, 242, 242]]], dtype=uint8)"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"print(f'The image is a: {type(img)} of shape {img.shape}')\n",
"img[3:5, 3:5, :]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Slicing tensors: slice along each axis"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# we want to show each color channel\n",
"fig, axes = plt.subplots(1, 3, figsize=(10,10))\n",
"for i, subplot in zip(range(3), axes):\n",
" temp = np.zeros(img.shape, dtype='uint8')\n",
" temp[:,:,i] = img[:,:,i]\n",
" subplot.imshow(temp)\n",
" subplot.set_axis_off()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Multiplying Images with a scalar (just for fun, does not really help us in any way)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"temp = img\n",
"temp = temp * 2\n",
"plt.imshow(temp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For more on image manipulation by `matplotlib` see: [matplotlib-images](https://matplotlib.org/3.1.1/tutorials/introductory/images.html)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Anatomy of an Artificial Neural Network\n",
"\n",
"In Part 1 we hand-made a neural network by writing some simple python functions. We focused on a regression problem where we tried to learn a function. We practiced using the logistic activation function in a network with multiple nodes, but a single or two hidden layers. Some of the key observations were:\n",
"* Increasing the number of nodes allows us to represent more complicated functions \n",
"* The weights and biases have a very big impact on the solution\n",
"* Finding the \"correct\" weights and biases is really hard to do manually\n",
"* There must be a better method for determining the weights and biases automatically\n",
"\n",
"We also didn't assess the effects of different activation functions or different network depths. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### \n",
"https://www.tensorflow.org/guide/keras\n",
"\n",
"`tf.keras` is TensorFlow's high-level API for building and training deep learning models. It's used for fast prototyping, state-of-the-art research, and production. `Keras` is a library created by François Chollet. After Google released Tensorflow 2.0, the creators of `keras` recommend that \"Keras users who use multi-backend Keras with the TensorFlow backend switch to `tf.keras` in TensorFlow 2.0. `tf.keras` is better maintained and has better integration with TensorFlow features\".\n",
"\n",
"#### IMPORTANT: In `Keras` everything starts with a Tensor of N samples as input and ends with a Tensor of N samples as output."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The 3 parts of an ANN\n",
"\n",
"- **Part 1: the input layer** (our dataset)\n",
"- **Part 2: the internal architecture or hidden layers** (the number of layers, the activation functions, the learnable parameters and other hyperparameters)\n",
"- **Part 3: the output layer** (what we want from the network)\n",
"\n",
"In the rest of the lab we will practice with end-to-end neural network training\n",
"\n",
"1. Load the data \n",
"2. Define the layers of the model.\n",
"3. Compile the model.\n",
"4. Fit the model to the train set (also using a validation set).\n",
"5. Evaluate the model on the test set.\n",
"6. Plot metrics such as accuracy.\n",
"7. Predict on random images from test set.\n",
"8. Predict on a random image from the web!"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"seed = 7\n",
"np.random.seed(seed)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Fashion MNIST \n",
"\n",
"\n",
"\n",
"MNIST, the set of handwritten digits is considered the Drosophila of Machine Learning. It has been overused, though, so we will try a slight modification to it.\n",
"\n",
"**Fashion-MNIST** is a dataset of clothing article images (created by [Zalando](https://github.com/zalandoresearch/fashion-mnist)), consisting of a training set of 60,000 examples and a test set of 10,000 examples. Each example is a **28 x 28** grayscale image, associated with a label from **10 classes**. The creators intend Fashion-MNIST to serve as a direct drop-in replacement for the original MNIST dataset for benchmarking machine learning algorithms. It shares the same image size and structure of training and testing splits. Each pixel is 8 bits so its value ranges from 0 to 255.\n",
"\n",
"Let's load and look at it!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 1. Load the data"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"%%time\n",
"# get the data from keras\n",
"\n",
"\n",
"# load the data splitted in train and test! how nice!\n",
"\n",
"\n",
"# normalize the data by dividing with pixel intensity\n",
"# (each pixel is 8 bits so its value ranges from 0 to 255)\n",
"\n",
"\n",
"# classes are named 0-9 so define names for plotting clarity\n",
"class_names = ['T-shirt/top', 'Trouser', 'Pullover', 'Dress', 'Coat',\n",
" 'Sandal', 'Shirt', 'Sneaker', 'Bag', 'Ankle boot']\n",
"\n",
"# plot\n",
"plt.figure(figsize=(10,10))\n",
"for i in range(25):\n",
" plt.subplot(5,5,i+1)\n",
" plt.xticks([])\n",
" plt.yticks([])\n",
" plt.grid(False)\n",
" plt.imshow(x_train[i], cmap=plt.cm.binary)\n",
" plt.xlabel(class_names[y_train[i]])\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.imshow(x_train[3], cmap=plt.cm.binary)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"x_train.shape, x_test.shape"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"y_train.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 2. Define the layers of the model."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 3. Compile the model"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Model: \"sequential\"\n",
"_________________________________________________________________\n",
"Layer (type) Output Shape Param # \n",
"=================================================================\n",
"flatten (Flatten) (None, 784) 0 \n",
"_________________________________________________________________\n",
"dense (Dense) (None, 154) 120890 \n",
"_________________________________________________________________\n",
"dense_1 (Dense) (None, 64) 9920 \n",
"_________________________________________________________________\n",
"dropout (Dropout) (None, 64) 0 \n",
"_________________________________________________________________\n",
"dense_2 (Dense) (None, 10) 650 \n",
"=================================================================\n",
"Total params: 131,460\n",
"Trainable params: 131,460\n",
"Non-trainable params: 0\n",
"_________________________________________________________________\n"
]
}
],
"source": [
"model.summary()"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tf.keras.utils.plot_model(\n",
" model,\n",
" #to_file='model.png', # if you want to save the image\n",
" show_shapes=True, # True for more details than you need\n",
" show_layer_names=True,\n",
" rankdir='TB',\n",
" expand_nested=False,\n",
" dpi=96\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Everything you wanted to know about a Keras Model and were afraid to ask](https://www.tensorflow.org/api_docs/python/tf/keras/Model)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 4. Fit the model to the train set (also using a validation set)\n",
"\n",
"This is the part that takes the longest.\n",
"\n",
"-----------------------------------------------------------\n",
"**ep·och** \n",
"noun: epoch; plural noun: epochs. A period of time in history or a person's life, typically one marked by notable events or particular characteristics. Examples: \"the Victorian epoch\", \"my Neural Netwok's epochs\". \n",
" \n",
"-----------------------------------------------------------"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"%%time\n",
"\n",
"# the core of the network training\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Save the model\n",
"\n",
"You can save the model so you do not have `.fit` everytime you reset the kernel in the notebook. Network training is expensive!\n",
"\n",
"For more details on this see [https://www.tensorflow.org/guide/keras/save_and_serialize](https://www.tensorflow.org/guide/keras/save_and_serialize)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [],
"source": [
"# save the model so you do not have to run the code everytime\n",
"model.save('fashion_model.h5')\n",
"\n",
"# Recreate the exact same model purely from the file\n",
"#model = tf.keras.models.load_model('fashion_model.h5')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 5. Evaluate the model on the test set."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Test accuracy=0.8866999745368958\n"
]
}
],
"source": [
"test_loss, test_accuracy = model.evaluate(x_test, y_test, verbose=0)\n",
"print(f'Test accuracy={test_accuracy}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 6. We learn a lot by studying History! Plot metrics such as accuracy. \n",
"\n",
"You can learn a lot about neural networks by observing how they perform while training. You can issue `kallbacks` in `keras`. The networks's performance is stored in a `keras` callback aptly named `history` which can be plotted. "
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"dict_keys(['loss', 'accuracy', 'val_loss', 'val_accuracy'])\n"
]
}
],
"source": [
"print(history.history.keys())"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# plot accuracy and loss for the test set\n",
"fig, ax = plt.subplots(1,2, figsize=(20,6))\n",
"\n",
"ax[0].plot(history.history['accuracy'])\n",
"ax[0].plot(history.history['val_accuracy'])\n",
"ax[0].set_title('Model accuracy')\n",
"ax[0].set_ylabel('accuracy')\n",
"ax[0].set_xlabel('epoch')\n",
"ax[0].legend(['train', 'val'], loc='best')\n",
"\n",
"ax[1].plot(history.history['loss'])\n",
"ax[1].plot(history.history['val_loss'])\n",
"ax[1].set_title('Model loss')\n",
"ax[1].set_ylabel('loss')\n",
"ax[1].set_xlabel('epoch')\n",
"ax[1].legend(['train', 'val'], loc='best')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 7. Now let's use the Network for what it was meant to do: Predict!"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [],
"source": [
"predictions = model.predict(x_test)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"predictions[0]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"np.argmax(predictions[0]), class_names[np.argmax(predictions[0])]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's see if our network predicted right! Is the first item what was predicted?"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.figure()\n",
"plt.imshow(x_test[0], cmap=plt.cm.binary)\n",
"plt.xlabel(class_names[y_test[0]])\n",
"plt.colorbar()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Correct!!** Now let's see how confident our model is by plotting the probability values:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# code source: https://www.tensorflow.org/tutorials/keras/classification\n",
"def plot_image(i, predictions_array, true_label, img):\n",
" predictions_array, true_label, img = predictions_array, true_label[i], img[i]\n",
" plt.grid(False)\n",
" plt.xticks([])\n",
" plt.yticks([])\n",
"\n",
" plt.imshow(img, cmap=plt.cm.binary)\n",
"\n",
" predicted_label = np.argmax(predictions_array)\n",
" if predicted_label == true_label:\n",
" color = 'blue'\n",
" else:\n",
" color = 'red'\n",
"\n",
" plt.xlabel(\"{} {:2.0f}% ({})\".format(class_names[predicted_label],\n",
" 100*np.max(predictions_array),\n",
" class_names[true_label]),\n",
" color=color)\n",
"\n",
"def plot_value_array(i, predictions_array, true_label):\n",
" predictions_array, true_label = predictions_array, true_label[i]\n",
" plt.grid(False)\n",
" plt.xticks(range(10))\n",
" plt.yticks([])\n",
" thisplot = plt.bar(range(10), predictions_array, color=\"#777777\")\n",
" plt.ylim([0, 1])\n",
" predicted_label = np.argmax(predictions_array)\n",
"\n",
" thisplot[predicted_label].set_color('red')\n",
" thisplot[true_label].set_color('blue')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"i = 406\n",
"plt.figure(figsize=(6,3))\n",
"plt.subplot(1,2,1)\n",
"plot_image(i, predictions[i], y_test, x_test)\n",
"plt.subplot(1,2,2)\n",
"plot_value_array(i, predictions[i], y_test)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 8. Predicting in the real world\n",
"\n",
"Let's see if our network can generalize beyond the MNIST fashion dataset. Let's give it an random googled image of a boot. Does it have to be a clothing item resembling the MNIST fashion dataset? Can it be a puppy?\n",
"\n",
"**Download an image from the internet and resize it to 28x28.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# your code here. \n",
"# Resize it to 28 x 28 and one channel (you could do this outside the notebook)\n",
"# make into one channel and see .shape\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`tf.keras` models are optimized to make predictions on a batch, or collection, of examples at once. Accordingly, even though you're using a single image, you need to add it to a list:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# your code here\n",
"# Add the image to a batch where it's the only member.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# your code here\n",
"# print the prediction\n"
]
}
],
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