diff --git a/Notebooks/Chap04/4_1_Composing_Networks.ipynb b/Notebooks/Chap04/4_1_Composing_Networks.ipynb new file mode 100644 index 0000000..b5c749c --- /dev/null +++ b/Notebooks/Chap04/4_1_Composing_Networks.ipynb @@ -0,0 +1,555 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Notebook 4.1 -- Composing networks\n", + "\n", + "The purpose of this notebook is to understand what happens when we feed one neural network into another. It works through an example similar to 4.1 and varies both networks\n", + "\n", + "Work through the cells below, running each cell in turn. In various places you will see the words \"TODO\". Follow the instructions at these places and make predictions about what is going to happen or write code to complete the functions.\n", + "\n", + "Contact me at udlbookmail@gmail.com if you find any mistakes or have any suggestions" + ], + "metadata": { + "id": "MaKn8CFlzN8E" + } + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "id": "8ClURpZQzI6L" + }, + "outputs": [], + "source": [ + "# Imports math library\n", + "import numpy as np\n", + "# Imports plotting library\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "# Define the Rectified Linear Unit (ReLU) function\n", + "def ReLU(preactivation):\n", + " activation = preactivation.clip(0.0)\n", + " return activation" + ], + "metadata": { + "id": "YdmveeAUz4YG" + }, + "execution_count": 2, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Define a shallow neural network with, one input, one output, and three hidden units\n", + "def shallow_1_1_3(x, activation_fn, phi_0,phi_1,phi_2,phi_3, theta_10, theta_11, theta_20, theta_21, theta_30, theta_31):\n", + " # Initial lines\n", + " pre_1 = theta_10 + theta_11 * x\n", + " pre_2 = theta_20 + theta_21 * x\n", + " pre_3 = theta_30 + theta_31 * x\n", + " # Activation functions\n", + " act_1 = activation_fn(pre_1)\n", + " act_2 = activation_fn(pre_2)\n", + " act_3 = activation_fn(pre_3)\n", + " # Weight activations\n", + " w_act_1 = phi_1 * act_1\n", + " w_act_2 = phi_2 * act_2\n", + " w_act_3 = phi_3 * act_3\n", + " # Combine weighted activation and add y offset\n", + " y = phi_0 + w_act_1 + w_act_2 + w_act_3\n", + " # Return everything we have calculated\n", + " return y" + ], + "metadata": { + "id": "ximCLwIfz8kj" + }, + "execution_count": 4, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# # Plot two shallow neural networks and the composition of the two\n", + "def plot_neural_two_components(x_in, net1_out, net2_out, net12_out=None):\n", + "\n", + " # Plot the two networks separately\n", + " fig, ax = plt.subplots(1,2)\n", + " fig.set_size_inches(8.5, 8.5)\n", + " fig.tight_layout(pad=3.0)\n", + " ax[0].plot(x_in, net1_out,'r-')\n", + " ax[0].set_xlabel('Net 1 input'); ax[0].set_ylabel('Net 1 output')\n", + " ax[0].set_xlim([-1,1]);ax[0].set_ylim([-1,1])\n", + " ax[0].set_aspect(1.0)\n", + " ax[1].plot(x_in, net2_out,'b-')\n", + " ax[1].set_xlabel('Net 2 input'); ax[1].set_ylabel('Net 2 output')\n", + " ax[1].set_xlim([-1,1]);ax[1].set_ylim([-1,1])\n", + " ax[1].set_aspect(1.0)\n", + " plt.show()\n", + "\n", + " if net12_out is not None:\n", + " # Plot their composition\n", + " fig, ax = plt.subplots()\n", + " ax.plot(x_in ,net12_out,'g-')\n", + " ax.set_xlabel('Net 1 Input'); ax.set_ylabel('Net 2 Output')\n", + " ax.set_xlim([-1,1]);ax.set_ylim([-1,1])\n", + " ax.set_aspect(1.0)\n", + " plt.show()" + ], + "metadata": { + "id": "ZB2HTalOE40X" + }, + "execution_count": 5, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "Let's define two networks. We'll put the prefixes n1_ and n2_ before all the variables to make it clear which network is which. We'll just consider the inputs and outputs over the range [-1,1]." + ], + "metadata": { + "id": "LxBJCObC-NTY" + } + }, + { + "cell_type": "code", + "source": [ + "# Now lets define some parameters and run the first neural network\n", + "n1_theta_10 = 0.0 ; n1_theta_11 = -1.0\n", + "n1_theta_20 = 0 ; n1_theta_21 = 1.0\n", + "n1_theta_30 = -0.67 ; n1_theta_31 = 1.0\n", + "n1_phi_0 = 1.0; n1_phi_1 = -2.0; n1_phi_2 = -3.0; n1_phi_3 = 9.3\n", + "\n", + "# Now lets define some parameters and run the second neural network\n", + "n2_theta_10 = -0.6 ; n2_theta_11 = -1.0\n", + "n2_theta_20 = 0.2 ; n2_theta_21 = 1.0\n", + "n2_theta_30 = -0.5 ; n2_theta_31 = 1.0\n", + "n2_phi_0 = 0.5; n2_phi_1 = -1.0; n2_phi_2 = -1.5; n2_phi_3 = 2.0\n", + "\n", + "# Display the two inputs\n", + "x = np.arange(-1,1,0.001)\n", + "# We run the first and second neural networks for each of these input values\n", + "net1_out = shallow_1_1_3(x, ReLU, n1_phi_0, n1_phi_1, n1_phi_2, n1_phi_3, n1_theta_10, n1_theta_11, n1_theta_20, n1_theta_21, n1_theta_30, n1_theta_31)\n", + "net2_out = shallow_1_1_3(x, ReLU, n2_phi_0, n2_phi_1, n2_phi_2, n2_phi_3, n2_theta_10, n2_theta_11, n2_theta_20, n2_theta_21, n2_theta_30, n2_theta_31)\n", + "# Plot both graphs\n", + "plot_neural_two_components(x, net1_out, net2_out)" + ], + "metadata": { + "id": "JRebvurv22pT", + "outputId": "5baa5b12-574e-4457-8b87-37f23a5310a9", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 405 + } + }, + "execution_count": 6, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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tkpOTtXfvXu9j165dPq8/9thjKioq0rx587R27Vq1adNGBQUFOnHiRKgPB3YRy9Ucifa1WBCDU0szngBA9HMYY4zVQfgrNzdX//Vf/6U//OEPkqTa2lplZmZqwoQJmjp1ap31FyxYoIkTJ+rw4cP17s8Yoy5dumjy5Mm69957JUlOp1Pp6elasGCBhg8f7ldcLpdLKSkpcjqdSk5ObtrBITJVVUnZ2e5Ep6hImjDB6oissWCBNGaM1LOntGmT1dEg2HJypM8+k1askPLz/d7Mzuc+xpPIdPiwVF5udRTWiYuTunaVWrSwOhIg/EJx/rPN/0pVVVVav369pk2b5l0WFxen/Px8FRcXN7jd0aNHdc4556i2tlYXX3yxHnnkEfXo0UOSVFpaqrKyMuWfMrCnpKQoNzdXxcXFDQ5MlZWVqqys9P7scrmae3iIVLFezfE4vX2NazmiR1WVtHOn+3mMVHQYTyLTyy9LP/2pdMrHEZOuuUZ6/XXJ4bA6EsD+bJPoHDhwQDU1NUpPT/dZnp6erm0NXDeQk5Oj5557ThdddJGcTqfmzJmjgQMHavPmzTrrrLNUVlbm3cfp+/S8Vp9Zs2Zp5syZzTwiRLxYvzbnVJ72tTffdLevPfCA1REhWHbskGpqpHbtpC5drI4mLBhPIs/LL0vDh3/3VYzViobTKb3xhvTcc9LYsVZHA9hfVJ9K8vLylJeX5/154MCBuuCCC/T000/roYceavJ+p02bpkmTJnl/drlcyszMbFasiEBUc3zddJM70XnxRRKdaHLqjGv8CblBjCehc2qSM3Kk+5f8+Hiro7LGnDnSlCnSpEnS4MFSjH0VgKCzzWQEHTt2VHx8vMpPa94tLy9XRkaGX/to2bKl+vbtqx07dkiSd7tA95mYmKjk5GSfB6IM1Zy6mH0tOsXgjGuMJ5GDJMfXPfdIeXnue/iOGyfZ5ypqIDLZJtFJSEhQv379tHLlSu+y2tparVy50uevbI2pqanRpk2b1LlzZ0lS165dlZGR4bNPl8ultWvX+r1PRCmqOXUx+1p0isF76DCeRAaSnLri493DT2Ki9Pbb7s8EQDMYG1m8eLFJTEw0CxYsMFu2bDHjx483qamppqyszBhjzM9+9jMzdepU7/ozZ840b7/9ttm5c6dZv369GT58uElKSjKbN2/2rjN79myTmppqXn31VbNx40Zz/fXXm65du5rjx4/7HZfT6TSSjNPpDN7BwjqVlcZkZhojGVNUZHU0kWX+fPfn0rOn1ZEgWPr1c/83XbYs4E3tfO5jPLHWSy8ZEx/v/uqNHGlMdbXVEUWWxx93fzbJycbs3m11NEB4hOL8Z6trdIYNG6b9+/dr+vTpKisrU58+fbR8+XLvxZ+7d+9WXNx3RapDhw5p3LhxKisrU/v27dWvXz+9//77uvDCC73r3HfffTp27JjGjx+vw4cP69JLL9Xy5cvr3AgOMYRqTsOYfS261NbGZOuaxHhiJSo5Z3bPPdLSpVJxsXsYeustLqEDmsJW99GJVLF+34Oown1zzuyaa9yTEjz4IJMS2N3u3dI557inuPr2W3cSGwDOfcEX7Z8pSY7/tm+Xevd2T7f9zDPMwoboF4rzn22u0QHCgmrOmd10k/vfF1+0Ng40n6eac+65ASc5QKBIcgKTkyP97/+6n0+a5B6aAASGRAfwYKY1/zD7WvTwTEQQY21rCD+SnKZhFjageUh0AA+qOf5h9rXoEYMzriH8SHKajlnYgOYh0QEkqjmBon0tOsToRAQIH5Kc5qOFDWg6Eh1AopoTKNrXogOtawghkpzgoYUNaBoSHYBqTuBoX7O/igpp3z7385wca2NB1CHJCS5a2ICmIdEBqOY0De1r9uapxGVmSm3bWhsLogpJTmjQwgYEjkQHsY1qTtPRvmZvTESAECDJCS1a2IDAkOggtlHNaTra1+yNiQgQZCQ5oUcLGxAYEh3ELqo5zUf7mn0xEQGCiCQnfGhhA/xHooPYRTWn+Whfsy9a1xAkJDnhRwsb4B8SHcQmqjnBQfuaPZ04IZWWup9T0UEzkORYgxY2wD8kOohNVHOCh/Y1+/nsM/efgNu3lzp1sjoa2BRJjrVoYQPOjEQHsYdqTnDRvmY/p7atORzWxgJbIsmJDLSwAY0j0UHsoZoTXLSv2Q8zrqEZSHIiBy1sQONIdBBbqOaEBu1r9sKMa2gikpzIQwsb0DASHcQWqjmhQfuavTDjGpqAJCdy0cIG1I9EB7GDak7o0L5mHzU17skIJCo68BtJTmSjhQ2oH4kOYgfVnNCifc0edu1yTy+dmChlZVkdDWyAJMceaGED6iLRQWygmhN6p7aveVqjEHk8rYXnncdvqzgjkhx7oYUN8EWig9hANSf0aF+zByYigJ9IcuyHFjbAF4kOoh/VnPDxtK+R6EQuJiKAH0hy7IsWNuA7JDqIflRzwof2tcjHPXRwBiQ59kcLG+BGooPoRjUnvGhfi2zG0LqGRpHkRAda2AA3Eh1EN6o54Uf7WuTav1+qqJAcDvdkBMApSHKiCy1sAIkOohnVHGvQvha5PG1rWVlSq1aWhoLIQpITnWhhQ6wj0UH0oppjDdrXIhdta6gHSU70ooUNsY5EB9GJao61aF+LTJ6KDjOu4T9IcqIfLWyIZSQ6iE5Uc6xF+1pkoqKDU5DkxA5a2BCrbJfozJ07V1lZWUpKSlJubq7WrVvX4Lp/+ctfdNlll6l9+/Zq37698vPz66w/evRoORwOn0dhYWGoDwOhRDXHerSvRSbuoeMjlscTkpzYQgsbYlXAic6DDz6ob7/9ts7y48eP68EHHwxKUA1ZsmSJJk2apBkzZujjjz9W7969VVBQoH379tW7/urVq3XLLbdo1apVKi4uVmZmpgYPHqyvv/7aZ73CwkLt3bvX+3jhhRdCehwIMao5kYH2tchy7Ji0e7f7eYRUdBYtWqTKyso6y6uqqrRo0aKQvncsjyckObGJFjbEJBOguLg4U15eXmf5gQMHTFxcXKC7C8iAAQPMHXfc4f25pqbGdOnSxcyaNcuv7aurq027du3MwoULvctGjRplrr/++mbF5XQ6jSTjdDqbtR8EQWWlMZmZxkjGFBVZHU1sq6gwpmVL93+LLVusjgbr17v/W6SlBW2XzT33MZ7UFerx5KWXjImPd38VRo40pro6JG+DCFVdbUxenvu/f0GBMbW1VkcEfCcU57+AKzrGGDkcjjrLP/nkE3Xo0KHZiVdDqqqqtH79euXn53uXxcXFKT8/X8XFxX7t49tvv9XJkyfrxLl69Wp16tRJOTk5uv3223Xw4MFG91NZWSmXy+XzQISgmhM5aF+LLBHYttbQePLVV18pJSUlZO8bq+MJlRzQwoZY08LfFdu3b+/tOT7vvPN8BqeamhodPXpUt912W0iClKQDBw6opqZG6enpPsvT09O1zTOT0Bncf//96tKli8/gVlhYqB/96Efq2rWrdu7cqV/96le6+uqrVVxcrPgGRoBZs2Zp5syZTT8YhAbX5kSem26S3nzTnehMn251NLHNc56MgLa1vn37eseTQYMGqUWL74aimpoalZaWhvTallgcT0hy4OFpYZsyxd3CNniwlJlpdVRAaPid6Dz55JMyxujnP/+5Zs6c6fPXtoSEBGVlZSkvLy8kQQbD7NmztXjxYq1evVpJp/wCPHz4cO/zXr166aKLLlL37t21evVqDRo0qN59TZs2TZMmTfL+7HK5lMlZwnpUcyLP6bOvRcAv2TErgmZcGzp0qCSppKREBQUFatu2rfc1z3hy4403WhTdmdltPCHJwenuuUdaulQqLnYPl2+9JdVTXAVsz+9EZ9SoUZKkrl27auDAgWrZsmXIgqpPx44dFR8fr/Lycp/l5eXlysjIaHTbOXPmaPbs2frXv/6liy66qNF1u3Xrpo4dO2rHjh0NDkyJiYlKTEwM7AAQWlRzIpOnfY2qjvUiqHVtxowZkqSsrCwNGzbMJ1kIh1gaT0hyUB9PC1vv3t+1sI0da3VUQPAFfI1O165dtXfvXu3evbveR6gkJCSoX79+WrlypXdZbW2tVq5c2Wgl6bHHHtNDDz2k5cuXq3///md8n6+++koHDx5U586dgxI3woRqTuRi9jXrVVdLn3/ufh4BFR2PUaNGhT3JkWJnPCHJQWOYhQ0xIdDZCxwOh4mLi2vwEUqLFy82iYmJZsGCBWbLli1m/PjxJjU11ZSVlRljjPnZz35mpk6d6l1/9uzZJiEhwbz88stm79693seRI0eMMcYcOXLE3Hvvvaa4uNiUlpaaf/3rX+biiy825557rjlx4oTfcTHrmsWYaS2yMfua9bZvd3/+rVsbU1MTtN0299zHeFJXsMYTZleDP5iFDZEkFL9P+9265rFhwwafn0+ePKkNGzboiSee0MOe1qEQGTZsmPbv36/p06errKxMffr00fLly70XlO7evVtxcd8Vqf70pz+pqqpKP/7xj332M2PGDP3mN79RfHy8Nm7cqIULF+rw4cPq0qWLBg8erIceeojWNDuhmhPZaF+znucC+5wcKS5y7hO9dOlSn4ltPOPJwoULQ36BfjSPJ1Ry4C9a2BDtHMYYE4wdvfHGG3r88ce1evXqYOzOVlwul1JSUuR0OpWcnGx1OLGlqkrKznYnOkVF0oQJVkeE+ixYII0ZI/XsKW3aZHU0sefRR6WpU6Wf/ET661+DtttQnfv+9re/acmSJXr11VeDtk+7aO5nSpKDppgzxz0LW3Kye+4Y5leCFUIxpgTtT3s5OTn68MMPg7U7wD9Uc+zh9NnXEF4RNBGBPy655BKf62fgH5IcNNU990h5eZLL5R5Kg/MncMB6ASc6p9/YzOl0atu2bfr1r3+tc889NxQxAvVjpjX74Oah1oqge+icyfHjx1VUVKTvf//7VodiKyQ5aA5uJIpoFfA1OqmpqXXuZG2MUWZmphYvXhy0wIAzoppjL9w81BrGRNQ9dE7luRG1hzFGR44cUevWrfX8889bGJm9kOQgGLiRKKJRwInOqlWrfH6Oi4tTWlqasrOzfe5uDYQU1Rz74eah1ti7192PEhfnvp4tgjz55JM+P3vGk9zcXLVv396aoGyGJAfBxI1EEW0CzkyuuOKKUMQBBIZqjv0w+5o1PG1r3bu7+1IiiOdG1GgakhwEG7OwIdo0aTKC7du3684779SgQYM0aNAg3XnnndrmGUyBUKOaY1/cPDT8IrRtzePQoUOaM2eOxo4dq7Fjx+q3v/2tKioqrA4r4pHkIFS4kSiiScCJzt///nf17NlT69evV+/evdW7d299/PHH6tWrl/7+97+HIkbAF9Uc+2L2tfCL4BnX1qxZo6ysLBUVFenQoUM6dOiQioqK1LVrV61Zs8bq8CIWSQ5CjVnYEC0CTnTuu+8+TZs2TcXFxXriiSf0xBNP6P3339evfvUr3XfffaGIEfgO1Rx7Y/a18IvgGdfuuOMODRs2TKWlpVq6dKmWLl2qL774QsOHD9cdd9xhdXgRiSQH4cAsbIgWASc6e/fu1ciRI+ss/+lPf6q9e/cGJSigQVRz7I/2tfCK4Na1HTt2aPLkyYo/5Tf1+Ph4TZo0STt27LAwsshEkoNwooUN0SDgROfKK6/U//t//6/O8nfffVeXXXZZUIIC6kU1JzrQvhY+Lpf0zTfu5xHYunbxxRdraz3fga1bt6p3794WRBS5SHJgBVrYYHcBz7p23XXX6f7779f69et1ySWXSJI++OADvfTSS5o5c6Zee+01n3WBoKGaEx2YfS18PG1rnTtLKSnWxlKPu+66S3fffbd27NjhM57MnTtXs2fP1saNG73rXnTRRVaFaTmSHFiFWdhgdw5jAsvP4+L8KwI5HA7V1NQ0KSi7cblcSklJkdPpVHJystXhRKeqKvc9QPbskYqKpAkTrI4IzbFggTRmjNSzp7Rpk9XRRK+FC6XRo6WrrpLeeSfou2/uue9M44nD4ZAxJqbHE5IcRII5c9w3Ek1OdhfjuZEoQiEUv08HXNGpra0NyhsDAaGaE124eWh4RPBEBJJUWlpqdQgRjSQHkYIbicKuAr5GZ9GiRaqsrKyzvKqqSosWLQpKUIAPrs2JPsy+Fh4RPBGBJO3atUvf//73dc455/g8vv/972vXrl0+y2LNK6+Q5CByMAsb7CrgRGfMmDFyOp11lh85ckRjxowJSlCAD6o50YnZ10Ivgu+hI0lXXXVVvTcHdTqduuqqqyyIKHKMGUOSg8jCLGywo4ATHU+/9Om++uorpUTgxa6wOao50YvZ10KrqkraudP9PEIrOg2NJwcPHlSbNm0siChy1NaS5CDyMAsb7Mbva3T69u0rh8Mhh8OhQYMGqUWL7zatqalRaWmpCgsLQxIkYhjVnOjF7GuhtWOHuyTQrp3UpYvV0fj40Y9+JMk92cDo0aOVmJjofa2mpkYbN27UwIEDrQovIgwfTpKDyMMsbLAbvxOdoUOHSpJKSkpUUFCgtm3bel9LSEhQVlaWbrzxxqAHiBhGNSf63XQTiU6onNq2FmFXDXuq/8YYtWvXTq1atfK+lpCQoEsuuUTjYvwPG3/8I0kOIpOnhW3KFHcL2+DBzMKGyOV3ojNjxgxJUlZWloYNG6YkfulEqFHNiX7MvhY6ETzj2vz58yW5x5N777035tvU6kOSg0jGLGywi4Cv0Rk1ahRJDkKPak5sYPa10InwGdck9x/QSHIA+2EWNthFwIlOXFyc4uPjG3wAQUE1J3Yw+1poeCo6ETrjmiR17dpV3bp1a/ABIHIxCxvsIOAbhi5dutRnlpyTJ09qw4YNWrhwoWbOnBnU4BCjqObEFtrXgq+2NqJb1zwmTpzo87NnPFm+fLmmTJliTVAA/EYLGyJdwImOZ1KCU/34xz9Wjx49tGTJEo1l+g00F9Wc2MLsa8H31VfSsWNSixZSBFdG7r777nqXz507Vx999FGYowEQKGZhQ6QLuHWtIZdccolWrlwZrN0hVlHNiU20rwWXp5pz7rnuapnNXH311fr73/9udRgA/EALGyJZUBKd48ePq6ioSN///veDsTvEMqo5sYmbhwaXDSYiaMzLL7+sDh06WB0GAD9xI1FEqoBb19q3b+9zjY4xRkeOHFHr1q31/PPPBzU4xBiqObGL9rXgOvUeOhHMcyNqD2OMysrKtH//fv3xj3+0MDIAgaCFDZEq4ETnySef9Pk5Li5OaWlpys3NVfv27YMVF2IR1ZzYxs1Dg8cGExFIda/59IwnV155pc6P8CQNgC9uJIpI5DCGAmNzuVwupaSkyOl0Kjk52epw7KmqSsrOdic6RUXShAlWR4RwO3RISk+XTp6UtmyJ+F/SI1p6urRvn/TRR1K/fiF7G859wcdnCjurqZEuu8w9C1tBAbOwITChOP8FXNGRpMOHD+vZZ5/V1v+0R/To0UM///nPlZKSEpSgEIOo5oD2teCoqHAnOZL7T6wRrqamRq+88orPeHLddddxXzbAhmhhQ6QJeDKCjz76SN27d9fvfvc7VVRUqKKiQk888YS6d++ujz/+OBQx+pg7d66ysrKUlJSk3NxcrVu3rtH1X3rpJZ1//vlKSkpSr1699Oabb/q8bozR9OnT1blzZ7Vq1Ur5+fn6/PPPQ3kIOB3X5sCD2deaz9O2lpkptW1rbSxnsGPHDl1wwQUaOXKkli5dqqVLl+qnP/2pevTooZ07d4b8/RlPgOBjFjZEFBOgSy+91IwePdqcPHnSu+zkyZNm1KhR5rLLLgt0dwFZvHixSUhIMM8995zZvHmzGTdunElNTTXl5eX1rv/ee++Z+Ph489hjj5ktW7aYX//616Zly5Zm06ZN3nVmz55tUlJSzCuvvGI++eQTc91115muXbua48eP+x2X0+k0kozT6Wz2McakefOMkYzp3NmYAD53RKGKCmNatnR/H7ZssToae3rmGffnN3hwyN+quee+q6++2hQWFpqDBw96lx04cMAUFhaaIUOGBCvMejGeAKFTXW1MXp77VFRQYExtrdURwQ5Ccf4LONFJSkoyW7durbN88+bNplWrVkEJqiEDBgwwd9xxh/fnmpoa06VLFzNr1qx617/55pvNNddc47MsNzfX/OIXvzDGGFNbW2syMjLM448/7n398OHDJjEx0bzwwgt+x8XA1AyVlcZkZrrPhkVFVkeDSDBkiPv7MHOm1ZHY0733uj+/u+4K+Vs199zXunVrs3HjxjrLS0pKTJs2bZobXqMYT4DQ2rbNmMRE9+nomWesjgZ2EIrzX8Cta8nJydq9e3ed5Xv27FG7du2aVV1qTFVVldavX6/8/Hzvsri4OOXn56u4uLjebYqLi33Wl6SCggLv+qWlpSorK/NZJyUlRbm5uQ3uU5IqKyvlcrl8Hmgirs3B6Whfax4b3UMnMTFRR44cqbP86NGjSkhICNn7Mp4AoUcLGyJBwInOsGHDNHbsWC1ZskR79uzRnj17tHjxYt1666265ZZbQhGjJOnAgQOqqalRenq6z/L09HSVlZXVu01ZWVmj63v+DWSfkjRr1iylpKR4H5nMn9g0XJuD+nDz0OaxyT10JOmHP/yhxo8fr7Vr18q4Owz0wQcf6LbbbtN1110XsvdlPAHCgxuJwmoBJzpz5szRj370I40cOVJZWVnKysrS6NGj9eMf/1iPPvpoKGKMONOmTZPT6fQ+9vBniqahmoP6eGZfk6jqBOrECam01P3cBhWdoqIide/eXXl5eUpKSlJSUpL++7//W9nZ2fr9739vdXhhwXiCaOaZhS0x8btZ2IBwCjjRSUhI0O9//3sdOnRIJSUlKikpUUVFhX73u98pMTExFDFKkjp27Kj4+HiVl5f7LC8vL1dGRka922RkZDS6vuffQPYpudstkpOTfR4IENUcNIb2tab57DP3n0zbt5c6dbI6mjNKTU3Vq6++qs8++0wvv/yyXn75ZW3fvl3Lli0L6e0KGE+A8KGFDVYKONHxaN26tXr16qVevXqpdevWwYypXgkJCerXr59WrlzpXVZbW6uVK1cqLy+v3m3y8vJ81pekFStWeNfv2rWrMjIyfNZxuVxau3Ztg/tEkFDNQWNoX2uaU9vWbHSXvuzsbF177bW69tprlZ2dHfL3YzwBwosWNlgmaNMahMHixYtNYmKiWbBggdmyZYsZP368SU1NNWVlZcYYY372s5+ZqVOnetd/7733TIsWLcycOXPM1q1bzYwZM+qdDjQ1NdW8+uqrZuPGjeb6669nOtBQY6Y1+IPZ1wL3m9+4P7Of/zwsb2fncx/jCRBezMKGM4mI6aWt9tRTT5mzzz7bJCQkmAEDBpgPPvjA+9oVV1xhRo0a5bP+iy++aM477zyTkJBgevToYd544w2f12tra80DDzxg0tPTTWJiohk0aJDZvn17QDExMAWI++bAH/Pnu78nPXtaHYl9DBvm/sxOmeI4lOx+7mM8AcLr8cfdp6jkZGN277Y6GkSaUJz/HMZQQGwul8ullJQUOZ1O+qvPpKpKys52t60VFUkTJlgdESLVoUNSerp08qS0ZYstLq63XO/e0saN0uuvSz/8YcjfjnNf8PGZIprV1EiXXSYVF0sFBdJbb9mqyxYhForzX5Ov0QGahGtz4C9mXwtMTY17MgKJpBBARGIWNoRb0BKdQ4cOadGiRcHaHaIRM60hUMy+5r9du9zTSycmSllZVkfjl9ra2gaX13djagD2xyxsCKegJTq7d+/WmDFjgrU7RCOqOQgUs6/5b9s297/nnef+s2kEc7lcuvnmm9WmTRulp6dr+vTpqqmp8b6+f/9+de3a1cIIAYQSs7AhXPxOdFwuV6OPI0eOhDJO2B3VHDQF7Wv+8ySCNmhbe+CBB/TJJ5/o//7v//Twww9r0aJFuv7661VVVeVdh8tHgehFCxvCxe9EJzU1Ve3bt2/wcfnll4cyTtgd1Rw0Fe1r/rFRovPKK6/o6aef1o9//GPdeuut+uijj7R//35de+21qqyslCQ5uEIZiGq0sCEcWvi7Yrt27fT//X//n3Jzc+t9/fPPP9cvfvGLoAWGKEI1B81xevuaDX6Rt4Snde38862Nww/79+/XOeec4/25Y8eO+te//qWCggINGTJEzzzzjIXRAQiXe+6Rli51z8I2bhyzsCH4/E50Lr74YknSFVdcUe/rqamptBqgflRz0Bye9rU333RXdaZPtzqiyGOMrSo6Z599trZu3epzHU67du30z3/+U4MHD9YNN9xgYXQAwsXTwta793ctbGPHWh0VoonfrWs/+clPlNTIX+IzMjI0Y8aMoASFKEI1B8FA+1rj9u+XKircfwo97zyrozmjwYMHa/78+XWWt23bVm+//XajYw2A6EILG0KJG4YGATd4a8TTT0u33eau5nzxBYkOmoabhzZuzRrpiiukrl3d/5+FSVPPfYcOHdI333yjHj161Pv6kSNH9PHHHzfYQRDNGE8Qi7iRKCRuGAq7oZqDYGH2tcbZqG1Nktq3b99gkiO529hiMckBYhWzsCFUSHQQOlybg2Cifa1hNpqIAADqQwsbQoFEB6FBNQfBxs1DG2azig4A1IcbiSLYSHQQGlRzEGy0rzWMRAdAFKCFDcFGooPgo5qDUKF9ra5jx6Tdu93PaV0DYHO0sCGYAk504uPjtW/fvjrLDx48qPj4+KAEBZujmoNQoX2tru3b3f+mpUnf+561sQSI8QRAfWhhQ7AEnOg0NBt1ZWWlEhISmh0QbI5qDkKJ9rW6bNy2xngCoD60sCFYWvi7YlFRkSTJ4XDomWeeUdu2bb2v1dTUaM2aNTqftglQzUGo3XST9Oab7kRn+nSro7GeDWdcYzwBcCaeFrYpU9wtbIMHS5mZVkcFu/E70fnd734nyf0XuHnz5vm0FSQkJCgrK0vz5s0LfoSwD6o5CIfT29dsWMkIKhtWdBhPAPjjnnukpUvdNxIdN44biSJwfic6paWlkqSrrrpKS5cuVfv27UMWFGyKag7CwdO+RlXHzZPo2KgCwngCwB+eFrbevb9rYRs71uqoYCcBX6OzatUqtW/fXlVVVdq+fbuqq6tDERfshmoOwonZ19yqq6XPP3c/t1FFx4PxBMCZMAsbmiPgROf48eMaO3asWrdurR49emj3f6Y1nTBhgmbPnh30AGETVHMQTsy+5vbFF9LJk1Lr1rZsXmc8AeAPZmFDUwWc6EydOlWffPKJVq9eraRT/mqfn5+vJUuWBDU42ATVHIQbs6+5eSYiyMmR4ux3WzTGEwD+YBY2NFXAI+Mrr7yiP/zhD7r00kvlOOWKsB49emjnzp1BDQ42QTUHVqB9zZYTEZyK8QSAv2hhQ1MEnOjs379fnTp1qrP82LFjPgMVYgTVHFiF9jXbJzqMJwACQQsbAhVwotO/f3+98cYb3p89g9EzzzyjvLy84EUGe6CaA6vQvmbLe+icivEEQCBoYUOg/J5e2uORRx7R1VdfrS1btqi6ulq///3vtWXLFr3//vv697//HYoYEamo5sBqsXzzUGNsX9FhPAEQKG4kikAEXNG59NJLVVJSourqavXq1Uv//Oc/1alTJxUXF6tfv36hiBGRimoOrBbL7Wt797r7N+Ljpexsq6NpEsYTAE1BCxv8FXBFR5K6d++uv/zlL8GOBXZCNQeRIJZvHuppW+vWzd3HYVOMJwACxY1E4S/7zUeKyEA1B5EiVmdfs3nbGgA0B7OwwR9+JzpxcXGKj49v9NGiRZMKRH6pqKjQiBEjlJycrNTUVI0dO1ZHjx5tdP0JEyYoJydHrVq10tlnn6277rpLTqfTZz2Hw1HnsXjx4pAdR1SgmoNIEqvta55jteFEBIwnAIKBFjacid8jybJlyxp8rbi4WEVFRaqtrQ1KUPUZMWKE9u7dqxUrVujkyZMaM2aMxo8fr7/97W/1rv/NN9/om2++0Zw5c3ThhRdq165duu222/TNN9/o5Zdf9ll3/vz5Kiws9P6cmpoasuOIClRzEElitX3N07pmw4oO4wmAYKCFDWdkmmHbtm1m6NChJj4+3owcOdJ8+eWXzdldg7Zs2WIkmQ8//NC77K233jIOh8N8/fXXfu/nxRdfNAkJCebkyZPeZZLMsmXLmhWf0+k0kozT6WzWfmyhstKYzExjJGOKiqyOBnCbP9/9nezZ0+pIwqdLF/cxf/CBZSEE89zHeOIWU+MJECSPP+4+HSYnG7N7t9XRoKlCcf5r0jU633zzjcaNG6devXqpurpaJSUlWrhwoc4555xg5V8+iouLlZqaqv79+3uX5efnKy4uTmvXrvV7P06nU8nJyXVaIu644w517NhRAwYM0HPPPSdzhtpnZWWlXC6XzyNmUM1BJIq19jWXS/rmG/dzG7aunYrxJIbHEyBIaGFDQwJKdJxOp+6//35lZ2dr8+bNWrlypV5//XX17NkzVPFJksrKyurcPbtFixbq0KGDysrK/NrHgQMH9NBDD2n8+PE+yx988EG9+OKLWrFihW688Ub98pe/1FNPPdXovmbNmqWUlBTvIzNWJnDn2hxEqli7eainba1zZyklxdpYmojxxC1mxxMgiLiRKBrkb+nn0UcfNR06dDAXXniheeWVV4JSTrr//vuNpEYfW7duNQ8//LA577zz6myflpZm/vjHP57xfZxOpxkwYIApLCw0VVVVja77wAMPmLPOOqvRdU6cOGGcTqf3sWfPnthoNZg3z10b7tzZmOPHrY4G8BVL7WsLFriP9Qc/sDSMprYZMJ58J2bHEyAEaGGzt1C0rjmM8a/AFxcXp1atWik/P1/x8fENrrd06VK/k6z9+/fr4MGDja7TrVs3Pf/885o8ebIOHTrkXV5dXa2kpCS99NJLuuGGGxrc/siRIyooKFDr1q31j3/8Q0lnqEK88cYb+uEPf6gTJ04o0c97U7hcLqWkpHhbGaJSVZX7poR79khFRdKECVZHBPg6dEhKT5dOnpS2bLHlRfp+mzZNmj1b+uUvpblzLQujqec+xpOGxcR4AoRITY102WVScbFUUCC99ZbkcFgdFfwVivOf37OujRw5Uo4gf1vS0tKUlpZ2xvXy8vJ0+PBhrV+/3nu37HfeeUe1tbXKzc1tcDuXy6WCggIlJibqtddeO+OgJEklJSVq376934NSzODaHES6WJp9zeb30GE8ARAKzMKG0/ld0bHa1VdfrfLycs2bN887HWj//v2904F+/fXXGjRokBYtWqQBAwbI5XJp8ODB+vbbb7Vs2TK1adPGu6+0tDTFx8fr9ddfV3l5uS655BIlJSVpxYoVuvfee3Xvvfdq5syZfscW9X+Bo5oDu1iwQBozRurZU9q0yepoQicnR/rsM+lf/5IGDbIsDLue+xhPgOg2Z440ZYqUnOyeo4ZL3+whJOe/oDXBhdjBgwfNLbfcYtq2bWuSk5PNmDFjzJEjR7yvl5aWGklm1apVxhhjVq1a1WCfdmlpqTHGPaVonz59TNu2bU2bNm1M7969zbx580xNTU1AsUX9dKBcmwO7qKgwpmVL9/d1yxarowmNykpj4uPdx/jVV5aGYtdzH+MJEN2qq43Jy3OfJgsKjKmttToi+MPSa3TQsKj+CxzVHNjNNde429dmzozO9rUtW6QePaR27SSn09IG9Kg+91mEzxQIju3b3S1slZXSM8/QwhbpamulJUtc+slPgnv+a9J9dBBDuDYHdnPTTe5/o3Waac/1Oeefz1W2ANCAnBzpf//X/XzSJPevMog8tbXS0qVS377ST34S/P2T6KBh3DcHdhTtNw/13EPHphMRAEC4cCPRyHVqgnPjjdLGjVLbtsF/HxIdNIxqDuwo2m8eavMZ1wAgXLiRaOSpL8Fp10769a9DM4cQiQ7qRzUHdhbN7Wueis7551sbBwDYAC1skaGxBOfLL6WHHpI6dAj++5LooH5Uc2Bn0dq+VltL6xoABIgWNutYleB4kOigLqo5sLtobV/76ivp2DF3Etetm9XRAIAt0MIWflYnOB4kOqiLag6iQTS2r3mqOdnZ7mQHAOAXWtjCI1ISHA8SHfiimoNoEY3ta0xEAABNRgtb6ERaguNBogNfVHMQLaKxfY1EBwCajBa24IvUBMeDRAffoZqDaBNt7WvMuAYAzUILW3BEeoLjQaKD71DNQbSJtvY1KjoA0Gy0sDWdXRIcDxIduFHNQTSKpva1igpp3z7385wca2MBABujhS1wdktwPEh04EY1B9EqWtrXPG1rmZlS27bWxgIANkcLm3/smuB4kOiAag6iW7S0r9G2BgBBRQtbw+ye4HiQ6IBqDqJbtLSvMREBAAQVLWx1RUuC40GiE+uo5iAWREP7GhUdAAg6Wtjcoi3B8SDRiXVUcxALoqF9jUQHAEIillvYojXB8SDRiWVUcxAr7N6+duKEVFrqfk7rGgAEVSy2sEV7guNBohPLqOYglti5fe2zz9x/YmzfXurUyepoACDqxEoLW6wkOB4kOrGKag5ijZ3b105tW3M4rI0FAKJUNLewxVqC40GiE6uo5iDW2Ll9jRnXACDkorGFLVYTHA8SnVhENQexyq7ta0xEAABhES0tbLGe4HiQ6MQiqjmIVXZtX6OiAwBhY+cWNhIcXyQ6sYZqDmKZHdvXamqk7dvdz6noAEDI2bGFjQSnfiQ6sYZqDmKd3drXdu1yTy+dmChlZVkdDQDEBLu0sJHgNI5EJ5ZQzQHs177maVs77zz3nxkBAGERyS1sJDj+IdGJJVRzAPu1rzERAQBYIhJb2EhwAkOiEyuo5gDfsVP7GokOAFgmUlrYSHCahkQnVlDNAb5jp/Y1ZlwDAEtZ2cJGgtM8tkl0KioqNGLECCUnJys1NVVjx47V0aNHG93myiuvlMPh8HncdtttPuvs3r1b11xzjVq3bq1OnTppypQpqq6uDuWhhB/VHMCXXdrXjKGiEwKMJwACYUULGwlOcNgm0RkxYoQ2b96sFStW6B//+IfWrFmj8ePHn3G7cePGae/evd7HY4895n2tpqZG11xzjaqqqvT+++9r4cKFWrBggaZPnx7KQwk/qjlAXXZoX9u/X6qokBwO92QECArGEwCBClcLGwlOkBkb2LJli5FkPvzwQ++yt956yzgcDvP11183uN0VV1xh7r777gZff/PNN01cXJwpKyvzLvvTn/5kkpOTTWVlpd/xOZ1OI8k4nU6/twmbykpjMjONkYwpKrI6GiByVFQY07Kl+/+NLVusjqZ+//63O76uXa2OpF4Rfe5rAOMJgKaqrjYmL899Wi4oMKa2Nnj7rqkx5u9/N+aii9z7l4xp186YX//amIMHg/c+kSwU5z9bVHSKi4uVmpqq/v37e5fl5+crLi5Oa9eubXTbv/71r+rYsaN69uypadOm6dtvv/XZb69evZSenu5dVlBQIJfLpc2bNze4z8rKSrlcLp9HxKKaA9TPDu1rtK0FHeMJgKYKRQsbFZzQskWiU1ZWpk6dOvksa9GihTp06KCysrIGt/vJT36i559/XqtWrdK0adP0f//3f/rpT3/qs99TByVJ3p8b2++sWbOUkpLifWRmZjblsEKPa3OAxkV6+xoTEQQd4wmA5ghWCxsJTnhYmuhMnTq1zsWdpz+2eQb6Jhg/frwKCgrUq1cvjRgxQosWLdKyZcu0c+fOZsU9bdo0OZ1O72NPpN4ul2oO0LhIn32Nio7fGE8AhEtzZmEjwQmvFla++eTJkzV69OhG1+nWrZsyMjK0b98+n+XV1dWqqKhQRkaG3++Xm5srSdqxY4e6d++ujIwMrVu3zmed8vJySWp0v4mJiUpMTPT7fS1BNQc4M0/72ptvuqs6kXbhOImO3xhPAISLp4Wtd+/vWtjGjm18m9pa6ZVXpJkz3cmN5E5w7r7bnTiR3ISGpYlOWlqa0tLSzrheXl6eDh8+rPXr16tfv36SpHfeeUe1tbXewcYfJSUlkqTOnTt79/vwww9r37593laGFStWKDk5WRdeeGGARxNhqOYA/rnppshMdI4dk3bvdj+nde2MGE8AhJOnhW3KFHcL2+DBUn2dpyQ4FgvatAYhVlhYaPr27WvWrl1r3n33XXPuueeaW265xfv6V199ZXJycszatWuNMcbs2LHDPPjgg+ajjz4ypaWl5tVXXzXdunUzl19+uXeb6upq07NnTzN48GBTUlJili9fbtLS0sy0adMCii3iZslhpjXAf5E6+9r69e6Y0tKsjqRBEXfu8xPjCYBgaGwWNmZRC1wozn+2SXQOHjxobrnlFtO2bVuTnJxsxowZY44cOeJ9vbS01Egyq1atMsYYs3v3bnP55ZebDh06mMTERJOdnW2mTJlS58P78ssvzdVXX21atWplOnbsaCZPnmxOnjwZUGwRNzDNm+f+P6pzZ2OOH7c6GiDyDRni/n9m5kyrI/nO88+7Yzrll+lIE3HnPj8xngAIlm3bjElMdJ+un3mGBKc5QnH+cxgTyCVUqI/L5VJKSoqcTqeSk5OtDaaqSsrOdretFRVJEyZYGw9gBwsWSGPGSD17Sps2WR2N2wMPuPsixo+Xnn7a6mjqFVHnvijBZwrYz5w57ha25GQpK4sWtaYKxfnPFtNLIwBcmwMELhJnX2MiAgCwhVNnYWMWtchCohNNmGkNaJpIvHkoiQ4A2EJ8vPT889KQISQ4kYZEJ5pQzQGaLpJuHlpdLX3+ufs5M64BQMTr1k164w0SnEhDohMtqOYAzRNJ7WtffCGdPCm1bl3/fKUAAOCMSHSiBdUcoHkiqX1t2zb3v+efL8VxmgYAoCkYQaMB1RwgOCKlfc1TUaJtDQCAJiPRiQZUc4DgiJT2NSYiAACg2Uh07I5qDhA8kdK+dmrrGgAAaBISHbujmgMEl9Xta8ZQ0QEAIAhIdOyMag4QfFa3r+3d677rXHy8lJ0d/vcHACBKkOjYGdUcIPisbl/ztK116yYlJob//QEAiBIkOnZFNQcIHSvb12hbAwAgKEh07IpqDhA6VravkegAABAUJDp2RDUHCC0r29eYcQ0AgKAg0bEjqjlA6FnVvkZFBwCAoCDRsRuqOUB4WNG+5nJJ33zjfk5FBwCAZiHRsRuqOUB4WNG+5mlb69xZSkkJz3sCABClSHTshGoOEF7hbl+jbQ0AgKAh0bETqjlAeIW7fY2JCAAACBoSHbugmgOEX7jb16joAAAQNCQ6dkE1B7BGONvXSHQAAAgaEh07oJoDWCdc7WtVVdLOne7ntK4BANBsJDp2QDUHsE642td27JBqaqR27aQuXUL3PgAAxAgSnUhHNQewXjja105tW3M4Qvc+AADECBKdSEc1B7BeONrXmHENAICgItGJZFRzgMgQjvY1JiIAACCoSHQiGdUcIHKEun3NU9Eh0QEAIChIdCIV1RwgsoSyfa22ltY1AACCjEQnUlHNASJLKNvXvvpKOnbMnUh16xbcfQMAEKNsk+hUVFRoxIgRSk5OVmpqqsaOHaujR482uP6XX34ph8NR7+OlU35Jqe/1xYsXh+OQGkY1B4hMoWpf81RzsrPdyQ5CKqbGEwCIYS2sDsBfI0aM0N69e7VixQqdPHlSY8aM0fjx4/W3v/2t3vUzMzO1d+9en2V//vOf9fjjj+vqq6/2WT5//nwVFhZ6f05NTQ16/AGhmgNEptPb14J1PQ0TEYRVTI0nABDDbJHobN26VcuXL9eHH36o/v37S5KeeuopDRkyRHPmzFGXem6uFx8fr4yMDJ9ly5Yt080336y2bdv6LE9NTa2zrmWo5gCRy9O+9uab7qrO9OnB2S+JTtjE1HgCADHOFq1rxcXFSk1N9Q5KkpSfn6+4uDitXbvWr32sX79eJSUlGjt2bJ3X7rjjDnXs2FEDBgzQc889J2NMo/uqrKyUy+XyeQQN1RwgsoWifY2JCMImpsYTAIhxtqjolJWVqVOnTj7LWrRooQ4dOqisrMyvfTz77LO64IILNHDgQJ/lDz74oH7wgx+odevW+uc//6lf/vKXOnr0qO66664G9zVr1izNnDkz8AM5E6o5QOQLRfsaFZ2wiZnxBABgbUVn6tSpDV7g6Xls8/ylsxmOHz+uv/3tb/X+9e2BBx7Qf//3f6tv3766//77dd999+nxxx9vdH/Tpk2T0+n0Pvbs2dPsGCVRzQHsINizr1VUSPv2uZ/n5DR/fzGK8QQAcDpLKzqTJ0/W6NGjG12nW7duysjI0D7PLwL/UV1drYqKCr96oV9++WV9++23Gjly5BnXzc3N1UMPPaTKykolJibWu05iYmKDrzUZ1RzAPm66KXjX6Xh++c7MlE673gP+YzwBAJzO0kQnLS1NaWlpZ1wvLy9Phw8f1vr169WvXz9J0jvvvKPa2lrl5uaecftnn31W1113nV/vVVJSovbt24d/4KGaA9hHMNvXaFsLCsYTAMDpbDEZwQUXXKDCwkKNGzdO69at03vvvac777xTw4cP986Q8/XXX+v888/XunXrfLbdsWOH1qxZo1tvvbXOfl9//XU988wz+vTTT7Vjxw796U9/0iOPPKIJEyaE5bi8qOYA9hLM9jVPRYdEJyyifjwBAHjZItGRpL/+9a86//zzNWjQIA0ZMkSXXnqp/vznP3tfP3nypLZv365vv/3WZ7vnnntOZ511lgYPHlxnny1bttTcuXOVl5enPn366Omnn9YTTzyhGTNmhPx4fFDNAewnWLOveSo6zLgWNlE9ngAAvBzmTHNf4oxcLpdSUlLkdDqVnJwc2MZVVe67oe/ZIxUVSfz1D7CHQ4ek9HTp5Elpy5amV2S6d5e++EJavVq64oqghhhqzTr3oV58pgBiVSjOf7ap6EQtqjmAPQWjfe3ECam01P2cig4AAEFFomMlrs0B7K257WuffSYZ406aTru3CwAAaB4SHStRzQHs7fTZ1wJ16oxrDkdwYwMAIMaR6FiFag5gf81tX/PMuEbbGgAAQUeiYxWqOUB0aE77GvfQAQAgZEh0rEA1B4gezWlf4x46AACEDImOFajmANGjqe1rNTXS9u3u57SuAQAQdCQ64UY1B4g+TWlf27XLPb10YqKUlRWSsAAAiGUkOuFGNQeIPk1pX/O0reXkSPHxoYsNAIAYRaITTlRzgOjUlPY1T0JE2xoAACFBohNOVHOA6BVo+xozrgEAEFIkOuFCNQeIboG2r3EPHQAAQopEJ1yo5gDRLZD2NWOo6AAAEGIkOuFANQeIDf62r+3fL1VUSA6HdN55oY8LAIAYRKITDlRzgNjgb/uap20tK0tq1SosoQEAEGtIdEKNag4QO/xtX6NtDQCAkCPRCTWqOUBs8ad9zVPRIdEBACBkSHRCiWoOEHv8aV/jHjoAAIQciU4oUc0BYo8/7Wu0rgEAEHIkOqFCNQeIXY21rx07Ju3e7X5ORQcAgJAh0QkVqjlA7GqsfW37dve/aWnS974X/tgAAIgRJDqhQDUHiG2Nta/RtgYAQFiQ6IQC1RwADbWveWZco20NAICQItEJNqo5AKSG29eo6AAAEBYkOsFGNQeA1HD7GokOAABhQaITTFRzAJzq9Pa16mrp88/dz2ldAwAgpFpYHUBUef55qjkAvnN6+1p8vHTypNS6tZSZaXV0AABENSo6wTRnjvtfqjkApLrta6dORBDH6RcAgFBipA2mr7+mmgPA16nta57rc2hbAwAg5GyT6Dz88MMaOHCgWrdurdTUVL+2McZo+vTp6ty5s1q1aqX8/Hx97umP/4+KigqNGDFCycnJSk1N1dixY3X06NGmB0o1B8CpTm1fW7bMvYyJCCxlm/EEANAstkl0qqqqdNNNN+n222/3e5vHHntMRUVFmjdvntauXas2bdqooKBAJ06c8K4zYsQIbd68WStWrNA//vEPrVmzRuPHj29akOnpVHMA+Dq1fW3tWve/JDqWssV4AgBoPmMz8+fPNykpKWdcr7a21mRkZJjHH3/cu+zw4cMmMTHRvPDCC8YYY7Zs2WIkmQ8//NC7zltvvWUcDof5+uuv/Y7J6XQaScb56KP+HwiA2DF/vjHSd49PP7U6oqDwnvucTqtDaZKIHk9s+pkCQFOF4vwXtbOulZaWqqysTPn5+d5lKSkpys3NVXFxsYYPH67i4mKlpqaqf//+3nXy8/MVFxentWvX6oYbbqh335WVlaqsrPT+7HQ6JUmuG2+UXK4QHREA27rqKqlFC/f00nFxUqdOUXGucP3nGIwxFkcSWpaMJ1Hw/QCAQIRiTInaRKesrEySlJ6e7rM8PT3d+1pZWZk6derk83qLFi3UoUMH7zr1mTVrlmbOnFlneWZ2dnPDBhDtamvdiU4UOXjwoFJSUqwOI2QsGU+YfhxAjArmmGJpojN16lQ9+uijja6zdetWnR9hMxRNmzZNkyZN8v58+PBhnXPOOdq9e3dUD/ah4nK5lJmZqT179ig5OdnqcGyHz6/p+Oyax+l06uyzz1aHDh2sDoXxBJL4f7q5+Pyah8+veUIxplia6EyePFmjR49udJ1u3bo1ad8ZGRmSpPLycnXu3Nm7vLy8XH369PGus2/fPp/tqqurVVFR4d2+PomJiUpMTKyzPCUlhS92MyQnJ/P5NQOfX9Px2TVPXATcE4jxBKfi/+nm4fNrHj6/5gnmmGJpopOWlqa0tLSQ7Ltr167KyMjQypUrvQORy+XS2rVrvTPt5OXl6fDhw1q/fr369esnSXrnnXdUW1ur3NzckMQFAAg+xhMAwOms/zOcn3bv3q2SkhLt3r1bNTU1KikpUUlJic89Cs4//3wt+899KhwOhyZOnKj//d//1WuvvaZNmzZp5MiR6tKli4YOHSpJuuCCC1RYWKhx48Zp3bp1eu+993TnnXdq+PDh6tKlixWHCQAIMcYTAIgRQZu/LcRGjRplJNV5rFq1yruOJDN//nzvz7W1teaBBx4w6enpJjEx0QwaNMhs377dZ78HDx40t9xyi2nbtq1JTk42Y8aMMUeOHAkothMnTpgZM2aYEydONOcQYxafX/Pw+TUdn13z2PXzYzyJXnx+zcPn1zx8fs0Tis/PYUyUzwsKAAAAIObYpnUNAAAAAPxFogMAAAAg6pDoAAAAAIg6JDoAAAAAog6JThM8/PDDGjhwoFq3bq3U1FS/tjHGaPr06ercubNatWql/Px8ff7556ENNEJVVFRoxIgRSk5OVmpqqsaOHeszrWt9rrzySjkcDp/HbbfdFqaIrTV37lxlZWUpKSlJubm5WrduXaPrv/TSSzr//POVlJSkXr166c033wxTpJEpkM9vwYIFdb5nSUlJYYw2sqxZs0bXXnutunTpIofDoVdeeeWM26xevVoXX3yxEhMTlZ2drQULFoQ8TjtjPGkexpPAMaY0D2NK01g1npDoNEFVVZVuuukm743i/PHYY4+pqKhI8+bN09q1a9WmTRsVFBToxIkTIYw0Mo0YMUKbN2/WihUr9I9//ENr1qzR+PHjz7jduHHjtHfvXu/jscceC0O01lqyZIkmTZqkGTNm6OOPP1bv3r1VUFBQ5w7sHu+//75uueUWjR07Vhs2bNDQoUM1dOhQffrpp2GOPDIE+vlJ7jtan/o927VrVxgjjizHjh1T7969NXfuXL/WLy0t1TXXXKOrrrpKJSUlmjhxom699Va9/fbbIY7UvhhPmofxJDCMKc3DmNJ0lo0nQZuoOgbNnz/fpKSknHG92tpak5GRYR5//HHvssOHD5vExETzwgsvhDDCyLNlyxYjyXz44YfeZW+99ZZxOBzm66+/bnC7K664wtx9991hiDCyDBgwwNxxxx3en2tqakyXLl3MrFmz6l3/5ptvNtdcc43PstzcXPOLX/wipHFGqkA/P3//n45FksyyZcsaXee+++4zPXr08Fk2bNgwU1BQEMLIogPjSeAYTwLHmNI8jCnBEc7xhIpOGJSWlqqsrEz5+fneZSkpKcrNzVVxcbGFkYVfcXGxUlNT1b9/f++y/Px8xcXFae3atY1u+9e//lUdO3ZUz549NW3aNH377behDtdSVVVVWr9+vc/3Ji4uTvn5+Q1+b4qLi33Wl6SCgoKY+55JTfv8JOno0aM655xzlJmZqeuvv16bN28OR7hRge9f6DGefIfxJDCMKc3DmBJewfrutQhmUKhfWVmZJCk9Pd1neXp6uve1WFFWVqZOnTr5LGvRooU6dOjQ6Gfxk5/8ROecc466dOmijRs36v7779f27du1dOnSUIdsmQMHDqimpqbe7822bdvq3aasrIzv2X805fPLycnRc889p4suukhOp1Nz5szRwIEDtXnzZp111lnhCNvWGvr+uVwuHT9+XK1atbIosujBePIdxpPAMKY0D2NKeAVrPKGi8x9Tp06tc8HY6Y+GvsgI/ec3fvx4FRQUqFevXhoxYoQWLVqkZcuWaefOnUE8CsS6vLw8jRw5Un369NEVV1yhpUuXKi0tTU8//bTVocFGGE+ah/EE0YIxxXpUdP5j8uTJGj16dKPrdOvWrUn7zsjIkCSVl5erc+fO3uXl5eXq06dPk/YZafz9/DIyMupctFddXa2Kigrv5+SP3NxcSdKOHTvUvXv3gOO1g44dOyo+Pl7l5eU+y8vLyxv8rDIyMgJaP5o15fM7XcuWLdW3b1/t2LEjFCFGnYa+f8nJyTFVzWE8aR7Gk9BgTGkexpTwCtZ4QqLzH2lpaUpLSwvJvrt27aqMjAytXLnSOxC5XC6tXbs2oJl2Ipm/n19eXp4OHz6s9evXq1+/fpKkd955R7W1td7Bxh8lJSWS5DPQR5uEhAT169dPK1eu1NChQyVJtbW1Wrlype688856t8nLy9PKlSs1ceJE77IVK1YoLy8vDBFHlqZ8fqerqanRpk2bNGTIkBBGGj3y8vLqTD0bi98/xpPmYTwJDcaU5mFMCa+gjSeBzpQAY3bt2mU2bNhgZs6cadq2bWs2bNhgNmzYYI4cOeJdJycnxyxdutT78+zZs01qaqp59dVXzcaNG831119vunbtao4fP27FIViqsLDQ9O3b16xdu9a8++675txzzzW33HKL9/WvvvrK5OTkmLVr1xpjjNmxY4d58MEHzUcffWRKS0vNq6++arp162Yuv/xyqw4hbBYvXmwSExPNggULzJYtW8z48eNNamqqKSsrM8YY87Of/cxMnTrVu/57771nWrRoYebMmWO2bt1qZsyYYVq2bGk2bdpk1SFYKtDPb+bMmebtt982O3fuNOvXrzfDhw83SUlJZvPmzVYdgqWOHDniPb9JMk888YTZsGGD2bVrlzHGmKlTp5qf/exn3vW/+OIL07p1azNlyhSzdetWM3fuXBMfH2+WL19u1SFEPMaT5mE8CQxjSvMwpjSdVeMJiU4TjBo1ykiq81i1apV3HUlm/vz53p9ra2vNAw88YNLT001iYqIZNGiQ2b59e/iDjwAHDx40t9xyi2nbtq1JTk42Y8aM8RnUS0tLfT7P3bt3m8svv9x06NDBJCYmmuzsbDNlyhTjdDotOoLweuqpp8zZZ59tEhISzIABA8wHH3zgfe2KK64wo0aN8ln/xRdfNOedd55JSEgwPXr0MG+88UaYI44sgXx+EydO9K6bnp5uhgwZYj7++GMLoo4Mq1atqvdc5/nMRo0aZa644oo62/Tp08ckJCSYbt26+ZwHURfjSfMwngSOMaV5GFOaxqrxxGGMMQHXkwAAAAAggjHrGgAAAICoQ6IDAAAAIOqQ6AAAAACIOiQ6AAAAAKIOiQ4AAACAqEOiAwAAACDqkOgAAAAAiDokOgAAAACiDokOEIWuvPJKTZw40eowAAA2l5WVpSeffNLqMIAmIdEBAjB69Gg5HA7Nnj3bZ/krr7wih8MR0L78HTz+/Oc/68orr1RycrIcDocOHz58xm2WLl2qhx56KKB4guE3v/mN+vTpE/b3BQC7Cfd4UlFRoQkTJignJ0etWrXS2WefrbvuuktOp7PR7T788EONHz8+oHiCYfTo0Ro6dGjY3xfRhUQHCFBSUpIeffRRHTp0KCzv9+2336qwsFC/+tWv/N6mQ4cOateuXQijAgA0VzjHk2+++UbffPON5syZo08//VQLFizQ8uXLNXbs2Ea3S0tLU+vWrUMeHxAKJDpAgPLz85WRkaFZs2Y1ut67776ryy67TK1atVJmZqbuuusuHTt2TJK7tWzXrl2655575HA4Gv3r3cSJEzV16lRdcsklfsd4eutaVlaWHnnkEf385z9Xu3btdPbZZ+vPf/6z9/Uvv/xSDodDixcv1sCBA5WUlKSePXvq3//+t3edBQsWKDU11ed9Tv3L44IFCzRz5kx98skn3mNasGCB3zEDQKwJ53jSs2dP/f3vf9e1116r7t276wc/+IEefvhhvf7666qurm7wvU+vFjkcDj3zzDO64YYb1Lp1a5177rl67bXXvK+vXr1aDodDb7zxhi666CIlJSXpkksu0aeffupdp77q/5NPPqmsrCzv6wsXLtSrr77qPabVq1c3+hkB9SHRAQIUHx+vRx55RE899ZS++uqretfZuXOnCgsLdeONN2rjxo1asmSJ3n33Xd15552S3K1lZ511lh588EHt3btXe/fuDXncv/3tb9W/f39t2LBBv/zlL3X77bdr+/btPutMmTJFkydP1oYNG5SXl6drr71WBw8e9Gv/w4YN0+TJk9WjRw/vMQ0bNiwUhwIAUcHq8cTpdCo5OVktWrQIKO6ZM2fq5ptv1saNGzVkyBCNGDFCFRUVPutMmTJFv/3tb/Xhhx8qLS1N1157rU6ePOnX/u+9917dfPPNKiws9B7TwIEDA4oRkEh0gCa54YYb1KdPH82YMaPe12fNmqURI0Zo4sSJOvfcczVw4EAVFRVp0aJFOnHihDp06KD4+Hi1a9dOGRkZysjICHnMQ4YM0S9/+UtlZ2fr/vvvV8eOHbVq1Sqfde68807deOONuuCCC/SnP/1JKSkpevbZZ/3af6tWrdS2bVu1aNHCe0ytWrUKxaEAQNSwajw5cOCAHnrooSZdfzN69Gjdcsstys7O1iOPPKKjR49q3bp1PuvMmDFD//M//6NevXpp4cKFKi8v17Jly/zaf9u2bdWqVSslJiZ6jykhISHgOAESHaCJHn30US1cuFBbt26t89onn3yiBQsWqG3btt5HQUGBamtrVVpaakG00kUXXeR97nA4lJGRoX379vmsk5eX533eokUL9e/fv97jAwAET7jHE5fLpWuuuUYXXnihfvOb3wS8/anjSZs2bZScnNzoeNKhQwfl5OQwniDsAqtVAvC6/PLLVVBQoGnTpmn06NE+rx09elS/+MUvdNddd9XZ7uyzzw5ThL5atmzp87PD4VBtba3f28fFxckY47PM3zYEAEDDwjmeHDlyRIWFhWrXrp2WLVtWZ2zwB+MJ7IJEB2iG2bNnq0+fPsrJyfFZfvHFF2vLli3Kzs5ucNuEhATV1NSEOsSAfPDBB7r88sslSdXV1Vq/fr23DzwtLU1HjhzRsWPH1KZNG0lSSUmJz/aReEwAYAfhGE9cLpcKCgqUmJio1157TUlJSc2OuyEffPCBNxE7dOiQPvvsM11wwQWS3ONJWVmZjDHeyRMYTxAKtK4BzdCrVy+NGDFCRUVFPsvvv/9+vf/++7rzzjtVUlKizz//XK+++qo3aZDcM9msWbNGX3/9tQ4cONDge5SVlamkpEQ7duyQJG3atEklJSV1LvwMhrlz52rZsmXatm2b7rjjDh06dEg///nPJUm5ublq3bq1fvWrX2nnzp3629/+VmdWtaysLJWWlqqkpEQHDhxQZWVl0GMEgGgU6vHE5XJp8ODBOnbsmJ599lm5XC6VlZWprKwsJAnFgw8+qJUrV+rTTz/V6NGj1bFjR+99ca688krt379fjz32mHbu3Km5c+fqrbfe8tk+KytLGzdu1Pbt23XgwAEqPmgSEh2gmR588ME6JfuLLrpI//73v/XZZ5/psssuU9++fTV9+nR16dLFZ7svv/xS3bt3V1paWoP7nzdvnvr27atx48ZJcrc49O3b12c6z2CZPXu2Zs+erd69e+vdd9/Va6+9po4dO0py91g///zzevPNN9WrVy+98MILdXq7b7zxRhUWFuqqq65SWlqaXnjhhaDHCADRKpTjyccff6y1a9dq06ZNys7OVufOnb2PPXv2BP1YZs+erbvvvlv9+vVTWVmZXn/9de+EAhdccIH++Mc/au7cuerdu7fWrVune++912f7cePGKScnR/3791daWpree++9oMeI6OcwpzdJAog5X375pbp27aoNGzbUubcBAAD+Wr16ta666iodOnSozr3XgHCjogMAAAAg6pDoAAAAAIg6tK4BAAAAiDpUdAAAAABEHRIdAAAAAFGHRAcAAABA1CHRAQAAABB1SHQAAAAARB0SHQAAAABRh0QHAAAAQNQh0QEAAAAQdf5/LTAI9VrPmjQAAAAASUVORK5CYII=\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# TODO\n", + "# Take a piece of paper and draw what you think will happen when we feed the\n", + "# output of the first network into the second one. Draw the relationship between\n", + "# the input of the first network and the output of the second one." + ], + "metadata": { + "id": "NUQVop9-Xta1" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Now let's see if your predictions were right\n", + "\n", + "# TODO feed the output of first network into second network (replace this line)\n", + "net12_out = shallow_1_1_3(net1_out, ReLU, n2_phi_0, n2_phi_1, n2_phi_2, n2_phi_3, n2_theta_10, n2_theta_11, n2_theta_20, n2_theta_21, n2_theta_30, n2_theta_31)\n", + "\n", + "# Plot all three graphs\n", + "plot_neural_two_components(x, net1_out, net2_out, net12_out)" + ], + "metadata": { + "id": "Yq7GH-MCIyPI", + "outputId": "6f1424f4-48d2-4acd-de8e-c2d5e5a36258", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 843 + } + }, + "execution_count": 8, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Now we'll change things a up a bit. What happens if we change the second network? (note the *-1 change)\n", + "net1_out = shallow_1_1_3(x, ReLU, n1_phi_0, n1_phi_1, n1_phi_2, n1_phi_3, n1_theta_10, n1_theta_11, n1_theta_20, n1_theta_21, n1_theta_30, n1_theta_31)\n", + "net2_out = shallow_1_1_3(x, ReLU, n2_phi_0, n2_phi_1*-1, n2_phi_2, n2_phi_3, n2_theta_10, n2_theta_11, n2_theta_20, n2_theta_21, n2_theta_30, n2_theta_31)\n", + "plot_neural_two_components(x, net1_out, net2_out)" + ], + "metadata": { + "id": "BMlLkLbdEuPu", + "outputId": "9388cfa0-8ac9-4a3b-9f76-1f9633147f99", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 405 + } + }, + "execution_count": 9, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# TODO\n", + "# Take a piece of paper and draw what you think will happen when we feed the\n", + "# output of the first network into the modified second network. Draw the relationship between\n", + "# the input of the first network and the output of the second one." + ], + "metadata": { + "id": "Of6jVXLTJ688" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# When you have a prediction, run this code to see if you were right\n", + "net12_out = shallow_1_1_3(net1_out, ReLU, n2_phi_0, n2_phi_1*-1, n2_phi_2, n2_phi_3, n2_theta_10, n2_theta_11, n2_theta_20, n2_theta_21, n2_theta_30, n2_theta_31)\n", + "plot_neural_two_components(x, net1_out, net2_out, net12_out)" + ], + "metadata": { + "id": "PbbSCaSeK6SM", + "outputId": "e5e6b03b-955a-49b5-c338-396ad8a1a875", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 843 + } + }, + "execution_count": 10, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Let's change things again. What happens if we change the first network? (note the changes)\n", + "net1_out = shallow_1_1_3(x, ReLU, n1_phi_0, n1_phi_1*0.5, n1_phi_2, n1_phi_3, n1_theta_10, n1_theta_11, n1_theta_20, n1_theta_21, n1_theta_30, n1_theta_31)\n", + "net2_out = shallow_1_1_3(x, ReLU, n2_phi_0, n2_phi_1, n2_phi_2, n2_phi_3, n2_theta_10, n2_theta_11, n2_theta_20, n2_theta_21, n2_theta_30, n2_theta_31)\n", + "plot_neural_two_components(x, net1_out, net2_out)" + ], + "metadata": { + "id": "b39mcSGFK9Fd", + "outputId": "5c64d5cf-437d-4bdf-e5b0-f05ffe37672e", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 405 + } + }, + "execution_count": 11, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# TODO\n", + "# Take a piece of paper and draw what you think will happen when we feed the\n", + "# output of the modified first network into the original second network. Draw the relationship between\n", + "# the input of the first network and the output of the second one." + ], + "metadata": { + "id": "MhO40cC_LW9I" + }, + "execution_count": 12, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# When you have a prediction, run this code to see if you were right\n", + "net12_out = shallow_1_1_3(net1_out, ReLU, n2_phi_0, n2_phi_1, n2_phi_2, n2_phi_3, n2_theta_10, n2_theta_11, n2_theta_20, n2_theta_21, n2_theta_30, n2_theta_31)\n", + "plot_neural_two_components(x, net1_out, net2_out, net12_out)" + ], + "metadata": { + "id": "Akwo-hnPLkNr", + "outputId": "ceb51b90-1aea-4724-a358-2b4503ef41bb", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 843 + } + }, + "execution_count": 13, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Let's change things again. What happens if the first network and second networks are the same?\n", + "net1_out = shallow_1_1_3(x, ReLU, n1_phi_0, n1_phi_1, n1_phi_2, n1_phi_3, n1_theta_10, n1_theta_11, n1_theta_20, n1_theta_21, n1_theta_30, n1_theta_31)\n", + "net2_out_new = shallow_1_1_3(x, ReLU, n1_phi_0, n1_phi_1, n1_phi_2, n1_phi_3, n1_theta_10, n1_theta_11, n1_theta_20, n1_theta_21, n1_theta_30, n1_theta_31)\n", + "plot_neural_two_components(x, net1_out, net2_out_new)" + ], + "metadata": { + "id": "TJ7wXKpRLl_E", + "outputId": "f26d9406-59a5-4019-9c2f-16378af9538e", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 405 + } + }, + "execution_count": 14, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# TODO\n", + "# Take a piece of paper and draw what you think will happen when we feed the\n", + "# output of the first network into the a copy of itself. Draw the relationship between\n", + "# the input of the first network and the output of the second one." + ], + "metadata": { + "id": "dJbbh6R7NG9k" + }, + "execution_count": 15, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# When you have a prediction, run this code to see if you were right\n", + "net12_out = shallow_1_1_3(net1_out, ReLU, n1_phi_0, n1_phi_1, n1_phi_2, n1_phi_3, n1_theta_10, n1_theta_11, n1_theta_20, n1_theta_21, n1_theta_30, n1_theta_31)\n", + "plot_neural_two_components(x, net1_out, net2_out_new, net12_out)" + ], + "metadata": { + "id": "BiZZl3yNM2Bq", + "outputId": "8fde9fd9-5143-4a6e-93f6-c7468cec065e", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 843 + } + }, + "execution_count": 16, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" 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Pz0dhYWGH923cuBHTpk1Dly5dPJ6vq6vD448/jk8//RRnzpzBvn37MHXqVPTr1w+5ubmKfCazI2U5mUNK5fDx5zIFGFM0FU6GC5BSORL4PHPEODpkmUpUUdTKcHXVw73rrrtw5coVLF68GGVlZRg+fDiKiooEIdW5c+dgtXpeQ5w4cQIfffQR9uzZ0+F8NpsNX3zxBbZs2YKqqipkZmZi8uTJWL58OWJilL3yMStyBFxSKocP36rhs6RswG1BoZheiCGBXvio7WZGoqkgKSgoQEFBgdfXiouLOzzXv39/MMa8Hh8XF4fdu3dLOTwiBKTu33JoIQyfQCplynDboJJy+Ph1M1NyWxCJpgizIHX/lkOeyuETqKQsdgHydSGrN0I1veCQp3L4+FPDK2p8YSXRFGES5CgnA6RUjgR/mQfQthgyMNS31Cs2LrkIx/SCQ0rl8PFXSSFrR4KQAbkCLimVw8PldqGysRKA7ww3LipOuGG3EZTK4ZhecEipHD7+LuyM3MOlgEuoglz9Ww4plUOnsrESDK1l4pS4FK/HWCwWQ/VxwzG9EENK5fDwV1Ima0eCkBi5+rccUiqHDs86kmOTEW2L9nmckewdwxVMcUigFx5qq5TJ+IIwFXKVkzm0EIZOIIUyx0j2juGYXoihknJ4+HM04/Or2dUslH6lRjC+oB4uYQZkD7ikVA6ZQD7KHCPZO0ac4ZJSOSz8qeET7AnCf8t1UUcZLmEa5O7fAqRUDodAPsocI9k7hmt6wSGlcnj4q6bYrDZ0im69hapcc4zuh0uYBrn7twAplcMhkI8yx0iiqUgzXFIqh06Ts0nIXH1tP5O7ikKiKcI0yF1O5pBSOTQCmV5wjGTvGK7phRhSKocGv7CzWWxIjE30eozcF3W0LYgwDUoFXFIqhwb3UQ5WNKX3DDcS0wsxJNALDR5wu8R3EfZ0t0fuizoyviBMgRL9Ww4thKERbA9XWAx13sONxPRCDJWUQyOQmxmgQIZLPVzCDCjRv+WQUjk0Qt0WVNOs7ww3UtMLDimVQyMYNbzc9o7UwyVMgVLlZICUyqESdA9XAa9bJYhUMMUhpXJoBHNhRz1cgpAAJQMuKZVDI5hSH2CcHm6kphccUiqHRjDzjHq4BBEhSvZvOaRUDo7Glkbh7j/BqpT1HnClynABUiqHghYyXDK+IAyPkv1bDimVg4MvgtHW6IACIqNYO0ZqeiGGBHrBE0wPV25zFcHakXq4hFFRspzMoYUwOMRZRyABkVGsHaXMcKmkHDzBZLhCFUUmYR5luIThUSXgklI5KIJVKAPGsXaUwvSCQ0rl4Alm+5nsGS6Jpggjo0b/FiClcrAEe+MCwLOk7GZuWcclF1KZXnBIqRw8wajhFbN2JNEUYUTU6N8CpFQOlmBNL4C2ch/QGrj0CC8nR2p6wSGlcnAwxjQhmiLjC8LQqFFO5pBSOTDB3rgAAGKjYhFljQKg3z4uD7iRml6IIaVyYGqba9HibgEQXA9XDmGey+0SKjMkmiIMiZoBl5TKgQnW9AJozeb0fgMDKQVTHBLoBYbPs/joeMRHx/s8Ts4Ml2e3AGW4hAFRq3/LoYUwMPzGBcGUlAH9m19IZXohhkrKgQlWnCd2M2OMSToGsaiNeriE4VCrf8shpXJgQlEpA/q3d5QlwyWlckBCdTNrcbd4ZKRSIP7bRFujJT13ICjgErKjZjkZIKVyMIRSUgYMlOFKYHrBIaVyYIJVwyfYE4T/lvqiTrwlSKr+fbBQwCVkR+2AS0rlwASbeXD0bu8oR4ZLSuXABFtJsVqsQtCVeo6pZXoBUMAlZEbt/i2HlMq+CXarhhi92ztKaXohhpTK/gnlwk6uOabWliCAAi4hM2r3bzmkVPZN1bUquJgLQAg9XB1nuFKbXoghgZ5/QmldyDXH1LoXLkABl5AZtcvJHFoIfcOzjs72zkGrNvVs7yi16YUYKin7h6vh1bQQVcvWEaCAS8iMZgIuKZV9Emo5GdC3aEoO0wsOKZX9E5KjmUz2jmrZOgIUcAkZ0Ur/FiClsj9C8VHmCNuCdNjDlUMwxSGlsn9CKSnLdVFHPVzCkGilfwuQUtkfoWQdHD1nuHKYXnBIqeyfUKopcrmZUQ+XMCRaKSdzSKnsnXBKynq2dpQzwwVIqewLp9spiNVCUSnTtiCCCAKtBVxSKnsnlBsXcAyR4UpoeiGGBHreqWysBABYYEFyXHLA44WLOplEU9TDDYL169ejV69eiI2NRVZWFg4cOODz2M2bN8NisXg8YmNjPY5hjGHx4sXo1q0b4uLikJOTg2+++Ubuj2F4tNS/5dBC6J2Ierg6VinLleFSSdk7vH+bHJcs3G3KH5Thqsyrr76K+fPnY8mSJTh06BCGDRuG3NxcXL582ed7HA4HLl26JDzOnj3r8fqzzz6LtWvXYsOGDdi/fz86deqE3NxcXLt2Te6PY2i01L/lkFLZO6br4cpkesEhpbJ3wvbrlsn4gnq4AVi9ejXmzp2L2bNnY+DAgdiwYQPi4+OxadMmn++xWCzIyMgQHunp6cJrjDGsWbMGTzzxBKZOnYqhQ4di69atuHjxInbt2qXAJzIuWisnA6RU9oWZerhyml5wSKnsnVDtQynDVZHm5mYcPHgQOTk5wnNWqxU5OTkoKSnx+b66ujr07NkT3bt3x9SpU3H0aFs58fTp0ygrK/M4Z2JiIrKysvyekwiMFgMuKZW9E+qNC4C2xbCuuQ4ut0uWccmBnKYXHFIqeyfU1oVs1o5kfBGYq1evwuVyeWSoAJCeno6ysjKv7+nfvz82bdqEN954A3/5y1/gdrsxbtw4XLjQ+o+Ovy+UcwJAU1MTampqPB5EG1rs33JIqdyRUDMPAB5tgrrmOsnHJBdyml6IIaVyR0IuKctt7UiiKWnJzs5Gfn4+hg8fjgkTJmDHjh1IS0vDn/70p4jOu2LFCiQmJgqP7t3l6QXpFS32bzmkVPakxdWC6qZqAKFluDG2GOFeonoqK8stmOKQQK8j4ZaUJVcpc+MLK2W4PklNTYXNZkN5ebnH8+Xl5cjIyAjqHNHR0RgxYgROnjwJAML7Qj1nYWEhqqurhcf58+dD+SiGR4vlZA4thJ7wRdBqsQa1VYNjsVh0KZyS0/RCDJWUOxJqSZmsHVXEbrdj1KhR2Ldvn/Cc2+3Gvn37kJ2dHdQ5XC4XvvzyS3Tr1g0A0Lt3b2RkZHics6amBvv37/d7zpiYGDgcDo8H0YamAy4plT3gAbdLXBdYLaEtB3rcGqRYhktK5Q6EewvImqYaMMYkGwf1cINk/vz5eOGFF7BlyxYcP34cDzzwAOrr6zF79mwAQH5+PgoLC4Xjly1bhj179uBf//oXDh06hHvuuQdnz57FfffdB6D1Kv2RRx7BU089hTfffBNffvkl8vPzkZmZiWnTpqnxEXWPlvu3ACmV2xOOQpmj6wxXJtMLDimVOxLq9jPew3UxF645pdumqaa1Y+DdxxrirrvuwpUrV7B48WKUlZVh+PDhKCoqEkRP586dg9Xadg3x3XffYe7cuSgrK0NycjJGjRqFTz75BAMHDhSOWbBgAerr6zFv3jxUVVVh/PjxKCoq6mCQQQSHlvu3QJuC9NMLn+Lo5aMY3HWw2kNSlXBMLzh63BqkVIYrnmfHrhwz/TwDQlfDd7J3ggUWMDDUNNUgLjpOknGouS1IVwEXAAoKClBQUOD1teLiYo+ff//73+P3v/+93/NZLBYsW7YMy5Ytk2qIpkbL5WTOoLRBwkJodsIxveDoMsOV2fRCDJ9nRy8fBQbJ/us0T6jVFKvFigR7Amqba1HbXIt0pAd+UxAIxhfUwyX0jh4CLimV2wjHR5mjtx6uEqYXYkig10ZDSwManY0AQtt+JsdFHRlfEIZA6/1bDi2EbYRjesFx2PWV4SpheiGGlMpt8Hlmt9mRYE8I+n1yXNTR/XAJQ6D1/i2HlMptXG0Mv6Sst5vQK2V6wSGlchvicnIo372cGS55KRO6Rg/lZICUymLMpFJWSjDFIaVyG+G4mQHy2DvStiDCEOgl4JKnchuRlJTlst6TC6VMLzjkqdxGuGp4OeYYGV8Qukcv/VsOeSq3Em7mAchnLi8XSme4AHkqc8KtpMhh70g9XEL36KV/yyGlcuvtKc1UUlbK9EIMCfRaCffCTtYMl3q4hF7RSzmZQwth611++NV+WCVlnW0LUiPDpZJyK5FmuLQtiCBE6C7gklJZWATjouLQyd4p5PfrLsNV0PSCQ0rlVsLu4cqghOeiKerhErpEb/1bgJTKQGQKZUBf1o5Km15wSKncSriOZpThEkQ79Na/BUipDEQecPWU4SptesEhpXIr4c41OS7qBGtH6uESekRv5WSO2ZXKkdy4AGgr9zW0NMDldkk2LjlQ2vRCDCmVw99+RhkuQbRDrwHX7ErlSG5cALRlH4D2y8pqCKY4ZhfouZkbFY0VACLo4Uq5LYiMLwi9osf+LcfsC2EkNy4AWkUnfNHSulJZadMLMWYvKVddq4KbuQFoK8Ml0RShO/TYv+WYXakcicsURy99XFUzXJMrlfk8c8Q4Qs4qpe7hMsbI+ILQL3otJwOkVI7kxgUcvdg7qmF6wTG7UlkqcxXGWMRjcbqdwn+TaIrQHXoOuGZXKkeqUgb0Y++oZoZrdqWyFPahbuYW7qcbCeIKA2W4hK7Qc/+WY2alsplKymqYXogxs1I5EjV8fHQ8rJbWMCXFHOPlZIB6uITO0HP/lmNmpXIkmQdHD/aOapleiDGzQC+SSorFYpG0bcEzXAsssFlsEZ8vVCjgEmGj53Iyx6wLocvtQmVjJQDjZ7hqmV6IoZJy+Bd2Ul7UiW0dld6PDVDAJSLAEAHXpErlysZKMLSKUFLiUsI+jx7sHdU0veCYWakcqcGKlBd1appeABRwiTAxQv8WMK9SmWcdybHJiLZFh30ePWW4apWTAXMrlbXk2a3mliCAAi4RJkbo3wLmVSpLoVAGRIuhhnu4appecMysVI7U0UyODFeNLUEABVwiTIxQTuaYUakcaZmPIyyGzZThBsKsSuVI1fBy9HApwyV0hZECrhmVypFmHRw9qJTVNL0QY1aBnpbuSqWmrSNAAZcIA6P0bzlmXAgj9VHmUA83eMxYUm5yNgm917BVytTDJcyMUfq3HDMqlaUwvQD0Ye2otukFx4xKZX6XIJvFhsTYxLDOQT1cwtQYqZwMmFOpLIWPMqB9a0ctmF5wzKhU5hd2XeK7CI5RoSLlHKNtQYTuMFrANaNSWSqVstZLylowveCYUaksiZuZhFUUsfGFGlDAJULCaP1bjtmUypJtC9K4aEoLphdizKZUlvIGGWR8QZgOo/VvOWZTKvNSXySZB9C2GDY6Gz1ufaYVtCKY4phNoCfF9jNJtwV9L5qiHi6hC4xWTuaYbSGU2vgC0GaWqwXTCzFmLSlThtsKBVwiJAwbcE2kVG5saUR9Sz2AyANutC0asVGxALTZx9VchmsypbKUPVxJtgWR8QWhF4zavwXMpVTmi2C0NVoSIZGWb2CgFdMLjtmUylKUlGlbEGFKjNq/BcylVBaX+aQQEmlZqay1DNdsSmUpSsriHi5jLKLxkPEFoRuMWk7mmEWpLFX/lqNlpbJWTC/EmEmpLIWFKL+gY2BCKyRcyNoxRNavX49evXohNjYWWVlZOHDggM9jX3jhBdx0001ITk5GcnIycnJyOhw/a9YsWCwWj0deXp7cH0OXGD3gmkWpLNWNCzhazXC1ZHohxkwCPSkczeKi4gTTjEgv6kg0FQKvvvoq5s+fjyVLluDQoUMYNmwYcnNzcfnyZa/HFxcX4+6778b777+PkpISdO/eHZMnT8a3337rcVxeXh4uXbokPLZt26bEx9EVRu7fcsyyEEp14wKOVu0dtWR6IcYsJWXGmCTVFIvFItlFnWB8QT3cwKxevRpz587F7NmzMXDgQGzYsAHx8fHYtGmT1+Nffvll/OIXv8Dw4cMxYMAAvPjii3C73di3b5/HcTExMcjIyBAeycnJSnwcXWHk/i3HLEplqW5cwNGqvaPWTC84ZlEq1zbXosXdAkA6R7NI5xhluEHS3NyMgwcPIicnR3jOarUiJycHJSUlQZ2joaEBLS0tSElJ8Xi+uLgYXbt2Rf/+/fHAAw+goqLC73mamppQU1Pj8TA6Ri8nA+ZRKkt14wKOVkvKWhNMccyiVObzLD46HvHR8RGdS6oqimB8QT1c/1y9ehUulwvp6ekez6enp6OsrCyocyxcuBCZmZkeQTsvLw9bt27Fvn378Mwzz+CDDz7AbbfdBpfL5fM8K1asQGJiovDo3l07ggy5MEPANYtSWaobF3CEbUEaE01pzfSCYxalspTiPKku6ijDVYiVK1di+/bt2LlzJ2JjY4XnZ8yYgR/96EcYMmQIpk2bhrfffhv//Oc/UVxc7PNchYWFqK6uFh7nz59X4BOohxn6txwzKJWlVilThhs6ZlAqS2F6wZFKCa+7bUG33norqqqqOjxfU1ODW2+9VYoxeSU1NRU2mw3l5eUez5eXlyMjI8Pve1etWoWVK1diz549GDp0qN9j+/Tpg9TUVJw8edLnMTExMXA4HB4PI2OG/i3HDEplqUvKwmKosR6u1kwvxJhBoCelGl7qDFc3oqni4mI0N3ds9F+7dg3/+Mc/JBmUN+x2O0aNGuUheOICqOzsbJ/ve/bZZ7F8+XIUFRVh9OjRAX/PhQsXUFFRgW7dukkybiNghnIyxwwLoZSZB0AZbjhQSTk0pHIzU9vaMSrYA7/44gvhv48dO+bRN3W5XCgqKsJ1110n7ejaMX/+fNx7770YPXo0xowZgzVr1qC+vh6zZ88GAOTn5+O6667DihUrAADPPPMMFi9ejFdeeQW9evUSxpyQkICEhATU1dVh6dKlmD59OjIyMnDq1CksWLAA/fr1Q25urqyfRU+YKuC2Uyqr9Q9TLqTaqiFGq9aOWjS94LRXKhttngHSXthJnuGqJJoKOuAOHz5cMIbwVjqOi4vDunXrJB1ce+666y5cuXIFixcvRllZGYYPH46ioiJBSHXu3DlYrW1J+/PPP4/m5mb813/9l8d5lixZgt/85jew2Wz44osvsGXLFlRVVSEzMxOTJ0/G8uXLEROjzh9Ea5ipfwu0KUhrmmrwdcXXGNx1sNpDkpSqa1VwsVZBoJF7uFo1veAYfZ4BMmW4Oje+CDrgnj59Gowx9OnTBwcOHEBaWttVi91uR9euXWGz2WQZpJiCggIUFBR4fa290OnMmTN+zxUXF4fdu3dLNDJjYqb+LdCmIP30wqc4evmo4RZCvgh2tneW7Cpfi9aOWjW94Ijn2bErxww3zwCZerjNEm0LUqmHG3TA7dmzJ4DWvilhHsxUTuYMShskLIRGQ+pyMqDNDFerphdi+Dw7evkoMEjt0UiPlI5mUl3U6SbD5WzdutXv6/n5+WEPhtAeZgy4RlYqS+2jDGjT2pErlLVYTuYYXaCnxX24grWj1nu4nF/+8pceP7e0tKChoQF2ux3x8fEUcA2E2fq3HCMvhFL7KANti2GTq0kzAiBxhqtVjK5UlnL7mWmtHb/77juPR11dHU6cOIHx48eT6b/BMFv/lmNkT2U5SsriuaGVPq6WtwRxjOyp7HQ7BdGalKIpyawd9bIP1xs33HADVq5c2SH7JfSNGcvJgLE9laW+cQEARFmjEBcVB0A7W4O0bHrBMbKncmVjJQDAAgtS4lICHB0YsnZsR1RUFC5evCjV6QgNYNaAa2RPZd7DlbKkDGhPOKWHDNfInsq8nJwcl4woa8idyw5IZu2oF+MLzptvvunxM2MMly5dwh//+Ef88Ifm6fMZHbP2bzlGVSrLUVIGWhfE8vpyzZSUtWx6IcaoSmW5/Lprm2vhZm7hhvShohvjC860adM8frZYLEhLS8Ott96K3/3ud1KNi1AZs/ZvOUZVKssVcLWU4Wrd9EKMUQV6UtuH8h4u0Pr3DWdNcjO3cH9e3WS4tA/XHJi1nMwx6kLIS31SLYQcLdk7at30QoxhS8oSbz+LjYpFlDUKTrcTNU01YQXcFleL8N+6FE0xxsAYk2oshIYwfcA1qFLZDBmuHkwvOEZVKks9zywWS8QXdeLvV1eiqY0bN2Lw4MGIjY1FbGwsBg8ejBdffFHqsREqYfb+LWBMpXKLqwXVTdUA5OnhAtrYFqQH0wuOUZXKUpeUgcgv6viWIEBHAXfx4sX45S9/iTvuuAOvvfYaXnvtNdxxxx149NFHsXjxYjnGSCiM2fu3gDGVynwRtFqsSI5LlvTcDrs2M1ytY1SlsiyOZhFe1PEM12axwWaV3/ffGyH3cJ9//nm88MILuPvuu4XnfvSjH2Ho0KF46KGHsGzZMkkHSCiP2cvJHKMplXnA7RLXJWyVpy/4YqilgKuHDBcwplJZi57dats6AmFkuC0tLV5v5D5q1Cg4nU5JBkWoCwXcVoymVJarfwtIZ70nBXowvRBjRIGenBaikfZw1bQeDTng/uxnP8Pzzz/f4fk///nPmDlzpiSDItSD+rdtGG0hlKPMx9GiaEovGa4hS8oS+ihzIrV35D1cNQNuWBYgGzduxJ49ezB27FgAwP79+3Hu3Dnk5+dj/vz5wnGrV6+WZpSEYlD/to32SmUtmPJHghxZB0dL24L0YnrBaa9U1vs8A7RZUhZML1TaEgSEEXCPHDmCkSNHAgBOnToFAEhNTUVqaiqOHDkiHKd1OT7hHSont8EVpDVNNfi64mvd3yRcDh9ljlYyXD2ZXnCMNs8aWhrQ6GwEIK1KWbioC1M0pbatIxBGwH3//fflGAehESjgtsEVpFzQoveFUI4yH0cr24L0ZHrBEc+zY1eO6X6e8Qs7u82OBHuCZOeVLMPVk2jq5z//OWprO/6jqq+vx89//nNJBkWoA/VvO8L7uEbor11tlK+krJUMV0+mF2IEvYABtqCJL+yk/BsIF3VmEk1t2bIFjY2NHZ5vbGzE1q1bJRkUoQ7Uv+2IkZTKcqqUtdLD1ZPphRgjCfTkML0ApDO+0EUPt6amRrByrK2tRWxsrPCay+XCu+++i65du8oySEIZqJzcESMthHKWlLWY4eoJIymVZbsjlUTWjrro4SYlJcFiscBiseAHP/hBh9ctFguWLl0q6eAIZaGA2xEjKZXlyjyAtnJfs6sZTc4m1fpketsSxDGSUlmu7WdGML4IOuC+//77YIzh1ltvxf/93/8hJSVFeM1ut6Nnz57IzMyUZZCE/FD/1jtGUZAyxhQpKQOtGYhai5reTC84RplngHwXdlJZO+oiw50wYQIA4PTp0+jRo4euBAlEYKh/6x2jKJXrmuuEHpYcAddmtSE+Oh4NLQ2oaaqR5XcEg14zXCMplbV6Rypd9XA5Z8+exdmzZ32+fvPNN0c0IEIdqJzsGyN4KvNFMC4qDp3snWT5HY4YBxpaGlTdGqQ30wsxRvFUlrukbIoeLmfixIkdnhNnuy6XK6IBEepAAdc3RlAqy1lO5jhiHCirK1NNOKVH0wsxRhHoyS2aqmuug8vtCvmOP1owvgh5W9B3333n8bh8+TKKiorwb//2b9izZ48cYyRkhvq3/jHCQqhEwFV7a5AeTS/EGEWpLJeFqPhvWtdcF/L7dWntmJiY2OG5f//3f4fdbsf8+fNx8OBBSQZGKAf1b/1jBKUyL/PJYXrBUXtrkF5NLzhGUSrLtf0sJioG0dZotLhbUNtci8TYjrHIH1ooKUt2U8z09HScOHFCqtMRCkLlZP9wBamLufB1xddqDycsFMlwVbZ31KvpBYfPM6fbqdt55mZuVDRWANDefm9BNKWHbUGcL774wuNnxhguXbqElStXYvjw4VKNi1AQCrj+MYJSWc4bF3C0lOHqESMolauuVcHN3ADk8+yuaKwI66JOCxluyAF3+PDhsFgsYIx5PD927Fhs2rRJsoERykD92+DQu1KZl/nkLClrpYer1wwX0L9Smc8zR4xDlsAWUYbr1OG2oNOnT3v8bLVakZaW5mH1SOgH6t8Gh96VyvzGBXKrlAH1Mly9ml6I0btAT+7WRSQXdbrMcHv27CnHOAiVoHJycNBCGJhI71caKUbIcPWuVJbTPhTQfw83JNGU0+nEc889h5EjRyIhIQEJCQkYOXIkVq1ahZaWFrnGSMgIBdzgaK9U1htCSVmmhRAQLYbNKmW4Oja94LRXKusNuUwvOJEI87SQ4QYdcBsbGzFx4kQsWrQIaWlpuO+++3DfffchLS0NCxcuxKRJk3Dt2jU5x0pIDPVvg0fvSmWjq5T1bnrB0btSWe555rBHnuHqIuCuXLkS58+fx+HDh7F7926sWbMGa9aswe7du3Ho0CGcPXsWK1eulHOsAID169ejV69eiI2NRVZWFg4cOOD3+Ndeew0DBgxAbGwshgwZgnfffdfjdcYYFi9ejG7duiEuLg45OTn45ptv5PwImoH6t8HDFaSA/m4S7nK7UNlYCcC4PVy9m15wxPNMj2VlpUrKkfRw1RRNBR1wt2/fjtWrV2Po0KEdXhs2bBhWrVqFV155RdLBtefVV1/F/PnzsWTJEhw6dAjDhg1Dbm4uLl++7PX4Tz75BHfffTfmzJmDw4cPY9q0aZg2bRqOHDkiHPPss89i7dq12LBhA/bv349OnTohNzfXFNk6lZNDg/dx9bYQVjZWgqF1V0FKXEqAo8NHCwFXr6YXYgS9gM4u7AAFRFPfJwaRqJR1keGePXsWY8aM8fn62LFjce7cOUkG5YvVq1dj7ty5mD17NgYOHIgNGzYgPj7e53akP/zhD8jLy8Pjjz+OG2+8EcuXL8fIkSPxxz/+EUBrdrtmzRo88cQTmDp1KoYOHYqtW7fi4sWL2LVrl6yfRQtQwA0NvSqV+SKYHJuMaFu0bL9HzW1Beje9EKNngZ7cPdxILuqEDFcPoimHw+EzkwSAsrIydO4sX1myubkZBw8eRE5OjvCc1WpFTk4OSkpKvL6npKTE43gAyM3NFY4/ffo0ysrKPI5JTExEVlaWz3MCQFNTE2pqajweeoP6t6Gj14VQif4toJ0MV+/o9cIOkM9HmaP3bUFBB9xbbrkFTz/9tM/XV65ciVtuuUWSQXnj6tWrcLlcSE9P93g+PT0dZWVlXt9TVlbm93j+/6GcEwBWrFiBxMRE4dG9u/7+kVP/NnT0qlSWO+vgiEVT7Y1x5MYIW4I4ep1ngAKiKSm2Bemhh7tkyRLs2bMHY8eOxV//+ld88cUX+Pzzz7F9+3ZkZWVhz549WLJkiZxj1QyFhYWorq4WHufPn1d7SCFD5eTQ0atSWe6sg8MXwxZ3i7C4KYURTC84ep1ngHw3LuCYZlvQwIEDsXfvXtTW1mLGjBkYMWIERo4ciZ/+9Keora3Fnj17MGiQfF5kqampsNlsKC8v93i+vLwcGRkZXt+TkZHh93j+/6GcEwBiYmLgcDg8HnqDAm7o6FWprISPMtCqEOYovTXISBmuXudZk7NJKPVq0vjCqTPji7Fjx+Lo0aM4dOgQtm3bhm3btuHQoUM4duwYsrOz5RojAMBut2PUqFHYt2+f8Jzb7ca+fft8/u7s7GyP4wFg7969wvG9e/dGRkaGxzE1NTXYv3+/7J9HTah/Gz56VCrLnXVwrBarEHSV7uMawfRCjB7nGb9LkM1iC/nWecGi9x5uyNaOQOsNDNS4M9D8+fNx7733YvTo0RgzZgzWrFmD+vp6zJ49GwCQn5+P6667DitWrAAA/PKXv8SECRPwu9/9DlOmTMH27dvx2Wef4c9//jOA1ivJRx55BE899RRuuOEG9O7dG08++SQyMzMxbdo0xT+fUlD/Nnz0KJziPspyl5SB1gWxrrlOUaWyUUwvxOhxnvELuy7xXWC1SHbnVw/03sMNK+CqxV133YUrV65g8eLFKCsrw/Dhw1FUVCSIns6dOwerte0PPW7cOLzyyit44okn8Otf/xo33HADdu3ahcGD2257tWDBAtTX12PevHmoqqrC+PHjUVRUZOibMVA5OXz0qCBVSqUMtC6Il+ouKZrhGsX0QgzNM+/wBKGhpQEutws2qy3o9+o2w1WTgoICFBQUeH2tuLi4w3N33nkn7rzzTp/ns1gsWLZsGZYtWybVEDUPBdzwaa8gVfMfb7AoVVIG1LF3NJLpBUeP80xulymgraQMtJaVk2KTgn6vrowvCGNA/dvI0KOCVImFkKPGXlwjmV5w9DjPlNh+FhMVI5SEQ72o05XxBWEMqH8bGXpUkCpdUgaUDbhGMr3g0DzzTTj2ji63Cy7mAqCzDNftdvt8Xm5rRyJyqJwcOXpSkDa2NKK+pR6AQiVlFewdjbQlSIye5hmgXCUlnIs6sYGILowvampq8JOf/ASdOnVCeno6Fi9eDJfLJbx+5coV9O7dW5ZBEtJBATdy9KQg5YtgtDVaEUGRmiVlI5heiNHTPAMUdDQL46JOHHB1IZp68skn8fnnn+N///d/UVVVhaeeegqHDh3Cjh07YLe3fgCl7dyI0KD+rTToSUEqLvMpISgSFkMVRFNGy3D1NM8AbXt2i53PdFFS3rVrF/70pz/hv/7rv3Dffffhs88+w5UrV3DHHXegqan1wxhFIWhUqH8rDXryulWyfwuolOEazPSCo6d5BihnIRqOEp5/f9HWaFXjVNAB98qVK+jZs6fwc2pqKt577z3U1tbi9ttvR0NDgywDJKSDysnSoCcFKS/zKWF6AYgWQ4V6uEY0veDoaZ4Bym0/CyvD1YCtIxBCwO3RoweOHz/u8Vznzp2xZ88eNDY24sc//rHkgyOkhQKuNOhJQWr0DNeIphccPc0zxphyKuUIerhq72cOOuBOnjwZL730UofnExISsHv3bkM7MxkB6t9Ki14UpErduICjtErZiKYXYvQyz2qba9HibgGg0QzXpb7pBRCCaGrp0qW4ePGi19c6d+6MvXv34tChQ5INjJAW6t9Ki14UpLzMp1RJWekM14imF2L0Ms/4hV18dDzio+Nl/V3hCPME0wsVtwQBIQTc5ORkJCcn+3y9c+fOmDBhgiSDIqSHysnSohcFKb9xgVIlZaWtHY1oeiFGL/NMSftQ4aKuOfR9uGpnuOQ0ZRIo4EqLXhSkZunhGjbD1dk8U9I+NJSLOt2Jpgj9Qv1b6dGLglTJzAPwDLhK7Ms3qukFRy/zTMkLu3CsHSnDJRSD+rfSoxcFqZKZB9DWX3MxF645r8n++4ye4eplninlMgVEJppSu4dLAdcEUDlZHrSuIFVyqwank70TLGhVCytRVjaq6YUYrc8zQNkLO1NsC+LYbDZcvny5w/MVFRWw2YK/GTChHBRw5UHrCtKqa1XCHVKUCrhWixUJ9gQA8m8NMrLphRitzzNA+3ek0m0P11dfpqmpSfBUJrQD9W/lQ+sKUr4IdrZ3VnShUUo4ZWTTCzFan2eAsiXlSKwd1c5wg94WtHbtWgCtPYUXX3wRCQkJwmsulwsffvghBgwYIP0IiYig/q18tFeQqv2PuT1Kl5M5nWM6A7Xybw0yuukFR+vzDFAnw210NsLpdiLKGjiMaaWHG3TA/f3vfw+gNcPdsGGDR/nYbrejV69e2LBhg/QjJCKCysnywRWkNU01+LriawzuOljtIXmgZNYhRqkM1+imFxytzzNAuRsXAG09XKD1oi45zrc/BEd3Ge7p06cBALfccgt27Njh1wSD0A4UcOWDK0g/vfApjl4+qrmFUMlFUIxS9o5GN73gaH2eAcpuP4u2RSM2KhbXnNdQ01QTVMDlPVy1A27IPdz3338fycnJaG5uxokTJ+B0OuUYFyEB1L+VHy0rSNUqKSvdwzV6hgtoe5453U5BvKaYo1mIF3VasXYMOeA2NjZizpw5iI+Px6BBg3Du3DkAwEMPPYSVK1dKPkAifKh/Kz9aVpAKWYdCNy7gKGXvaHTTCzFanmeVjZUAAAssSIlLUeR3hnpRp5WScsgBd9GiRfj8889RXFzscYegnJwcvPrqq5IOjogMKifLj5YVpNxHWemSssNOGa7UaHme8Qu75LjkoARMUhCqvaMgmlJ5W1DI386uXbvw6quvYuzYsR7KwEGDBuHUqVOSDo6IDAq48qNlBanRS8pmML3g0DzzJFR7R91muFeuXEHXrl07PF9fX29oab7eoP6tMmjZ61bVbUGQVzRlFtMLjh7mmVL2oUDoF3WC8YXeerijR4/GO++8I/zMg+yLL76I7Oxs6UZGRAT1b5VBy163wr1wFVwIAWUyXLOYXnA0Pc9U2H4WrmhK7Qw35JLy008/jdtuuw3Hjh2D0+nEH/7wBxw7dgyffPIJPvjgAznGSIQBlZOVY1DaIHx64VPNKUhVy3AV2BZkFtMLMTTP2gg5w9VIDzfkDHf8+PEoLS2F0+nEkCFDsGfPHnTt2hUlJSUYNWqUHGMkwoACrnJoUUHa4mpBdVM1AGP2cM1ieiFGi/MMUKekLFzUBSma0m2GCwB9+/bFCy+8IPVYCImg/q2yaFFByhdBq8UalDGAlCixLcgsphditDjPAH1luGoHXLo9nwGh/q2ytFeQagG+CHaJ6wKrRdl/5opkuNUmzHA1OM8AlXq4IQrzdGd8YbVaYbPZ/D6iopTZg0X4h8rJyqJFBala/VtAoR5u7fcZrglMLzhanGeAOhaiejW+CDpC7ty50+drJSUlWLt2LdxutySDIiKDAq6yaNHrlmcdSpteAJ6LIWNMFlGTmUwvOFqcZ4BK+3BDvKjTyv1wgw64U6dO7fDciRMnsGjRIrz11luYOXMmli1bJungiNCh/q06aE1BqmqG+325z83caHQ2Ij46XvLfYSbTCzFam2eAsjcu4Og1ww2ruXPx4kXMnTsXQ4YMgdPpRGlpKbZs2YKePXtKPT4iRKh/qw5aU5AKAVdhH2UA6BTdCRa0ZrVy9HHNZnohRmvzrKGlAY3ORgDqGF+EbO2olx4uAFRXV2PhwoXo168fjh49in379uGtt97C4MHaKG0QVE5WC60pSAXTCxVKyhaLRVbhlNlML8RobZ7xCzu7zY4Ee4Jiv9fw1o7PPvss+vTpg7fffhvbtm3DJ598gptuuknOsXlQWVmJmTNnwuFwICkpCXPmzEFdXZ3f4x966CH0798fcXFx6NGjBx5++GFUV1d7HGexWDo8tm/fLvfHkQ0KuOqgNQUpv3GBGiVlQN6tQWY0veBobZ6Jy8lK/i3CtnbUSw930aJFiIuLQ79+/bBlyxZs2bLF63E7duyQbHBiZs6ciUuXLmHv3r1oaWnB7NmzMW/ePLzyyitej7948SIuXryIVatWYeDAgTh79izuv/9+XLx4Ea+//rrHsS+99BLy8vKEn5OSkmT5DHJD/Vv14ArSmqYafF3xteqCFjV7uIC8W4PMaHrB0eo8U9o+lIummlxNQd3MQSsZbtABNz8/X7WryePHj6OoqAj//Oc/MXr0aADAunXrcPvtt2PVqlXIzMzs8J7Bgwfj//7v/4Sf+/bti9/+9re455574HQ6PbYwJSUlISMjQ/4PIjPUv1UPrSlI1RCyiJFza5AZTS84Wptnat8gA2itonSJ7+L3eK30cIMOuJs3b5ZxGP4pKSlBUlKSEGyB1vvvWq1W7N+/Hz/+8Y+DOk91dTUcDkeH/cIPPvgg7rvvPvTp0wf3338/Zs+e7ffioqmpCU1NTcLPNTXy3oYsWKicrC5aUpCqlXlwZM1wTWh6IUZL80wN0wsAiLJGIS4qDo3ORtQ2Bw64ustw1aSsrKzDLQGjoqKQkpKCsrKyoM5x9epVLF++HPPmzfN4ftmyZbj11lsRHx+PPXv24Be/+AXq6urw8MMP+zzXihUrsHTp0tA/iMxQwFUXrShIGWOql5Rl7eGa0PRCjFbmGaBu68IR40CjszGoizqtBFxVrR0XLVrkVbQkfnz11VcR/56amhpMmTIFAwcOxG9+8xuP15588kn88Ic/xIgRI7Bw4UIsWLAAzz33nN/zFRYWorq6WnicP38+4jFGCvVv1UcrCtK65jqhhGbEHq4ZTS/EaGWeAepWUoK9qGOM6U80JQePPfYYZs2a5feYPn36ICMjA5cvX/Z43ul0orKyMmDvtba2Fnl5eejcuTN27tyJ6Ohov8dnZWVh+fLlaGpqQkyM9z9OTEyMz9fUgvq36tNeQarW1TRfBOOi4tDJ3kmVMcjZwzWr6QVHK/MMUK+kDAR/UediLjAwAOpnuKoG3LS0NKSlBb4yys7ORlVVFQ4ePCjcAvDvf/873G43srKyfL6vpqYGubm5iImJwZtvvonY2NiAv6u0tBTJycmaC6iBoHKy+mhFQap2ORmQL8M1s+kFRyvzDNCHZzfPbgH1RVO6uFvQjTfeiLy8PMydOxcHDhzAxx9/jIKCAsyYMUNQKH/77bcYMGAADhw4AKA12E6ePBn19fXYuHEjampqUFZWhrKyMrhcLgDAW2+9hRdffBFHjhzByZMn8fzzz+Ppp5/GQw89pNpnDRcKuOrDFaQAcPSyeuU+NbMOjlwZrplNLzhamWeAOjcu4AR7USfer2zqDDcUXn75ZRQUFGDSpEmwWq2YPn061q5dK7ze0tKCEydOoKGhAQBw6NAh7N+/HwDQr18/j3OdPn0avXr1QnR0NNavX49HH30UjDH069cPq1evxty5c5X7YBJA/VvtoAUFqZqLIEeuDNfMphditDDPAHW3nwVr78j1DBZYEGVVN+TpJuCmpKT4NLkAgF69eoExJvw8ceJEj5+9kZeX52F4oVeof6sdtKAgNXJJ2cymF2K0MM/czI2KxgoA6paUg81w7Ta76hdpuigpE/6hcrJ20IKCVM0bF3Dk2hZkZtMLMVqYZ1XXquBmrbdk1bJoSisKZYACriGggKsdtOB1q+aNCziyZbgmN73gaGGe8Qs7R4xDld6ocFEXQCeglT24AAVc3UP9W23BFaQu5sLXFV+rMga1b1wAyCiaMrnpBUcL80xt+9CgM9zve7gUcImIof6tttCCgtTIPVyzm15wtDTP1LIPDfaijme4am8JAijg6h4qJ2sPLmhRS0EqlJRVWggBzx5uIPFiKJjd9EKM2vNM7Qu7ULcFUYZLRAwFXO2htoJU7YUQaFsMGRjqW+olOSeZXnii9jxTe793sMI8Ek0RkkD9W22ipoLU5XahsrESgLoBNy4qDlZL6/IilVKZTC88UVuprHZJmTJcQlGof6tN1FSQVjZWCr6xgW5ZJicWi0XyPi6ZXniitlJZ7UpK0NaOGrkXLkABV9dQOVmbqKkg5Ytgcmyy6q46UiuVyfTCE7WVymqXlCnDJRSFAq42UVNBqnbWIUbODJdQX6mstoUon1/NrmaPGxS0h3q4RMRQ/1bbqKUg5VmHmqYXHKkDLpledERNpbLaF3cJ9gThv/1VUSjDJSKG+rfaRi0FqdqLoBip7R3J9KIjaiqV1Ta+sFlt6BTder9nfxd11MMlIobKydpGLQWpFnyUOXKVlCnDbUOtedbkbBKySlUdzYK4qKMMl4gYCrjaRi0FqRZ8lDmSi6bI9KIDas0zfpcgm8WGpNgkxX5ve4K5qKOAS0QE9W+1j1oKUi34KHOkzHDJ9MI7as0zfmHXJb6LsN9aDYK5qBNEU1RSJsKB+rfaRy0FqaZ6uHbperhkeuEds88zynAJ2aFysj5QQ0GqtpBFjLAYNkee4ZLphW/UmGdqu0xxgunhCqIp2hZEhAMFXH2ghoJUKwshIK1KmUwvfKPGPFPb9IJDGS4hK9S/1Q9qKEi1UuoDpO3hkumFb8w8z6iHS8gK9W/1g9IK0saWRuHOPGovhIC0KmUyvfCNGkplrVRSgspw3ZThEmFC5WT9oLSClC+C0dZoTQiLJM1wyfTCJ2oolbWS4fI55reHS9aORLhQwNUPSitIxYugFoRFwSyGwUKmF75RQ6mslR4ur6L4E+ZRD5cIC+rf6g8lFaRayTo4vOUhRYZLphf+UVqprPaNCzgkmiJkg/q3+kNJBamWblwAiDLc5lq4mTvs85DpRWCUVipr5eIupG1BJJoiQoHKyfpDSQWpVhZBDi/3Aa1BM1zI9CIwSs4zxphm9ntThkvIBgVc/aGkglRLNy4AgNioWERZowBEVlYm04vAKDnPaptr0eJuAaB+wA1pWxCJpohgof6tPlFSQaqlGxcArWIeKbYGkelFYJScZ/zCLj46HvHR8bL+rkBQhkvIAvVv9YmSClIt3biAI8XWIDK9CIyS80wr5WTAs4fLGPN6DPVwiZChcrJ+UUpBqrUeLiCNvSOZXgSH0vNMbdMLoO2CrsXdIgTW9lCGS4QMBVz9opSCVCgpa2Ah5EiS4ZLpRVAoNc+0dGGXYE8Q/tvXRR31cImQoP6tvlFKQaqlhZAjRQ+XTC+CQ6l5phXTCwCwWqxC0PV1UUcZLhES1L/VN0ooSBljmgy4UmS4ZHoRHEoplbVUUgY893t7g3q4REhQOVnfKKEgrbpWBRdzAdBmwA23h0umF8GjlFJZaxd2gr0jZbiEFFDA1TdKKEj5ItjZ3lkTvSpOoMUwEGR6ETxKKZW1VFIGAldRKOASQUP9W2Mgt4JUa1kHJ9KSMplehIYSSmWtzTV/SnjGmBBwtXAhqpuAW1lZiZkzZ8LhcCApKQlz5sxBXV2d3/dMnDgRFovF43H//fd7HHPu3DlMmTIF8fHx6Nq1Kx5//HE4nU45P0pIUP/WGMitINWajzJHWAzDFE2R6UVoKKFU1sqNCzj+Luq4IxagjQw3Su0BBMvMmTNx6dIl7N27Fy0tLZg9ezbmzZuHV155xe/75s6di2XLlgk/x8e3OaO4XC5MmTIFGRkZ+OSTT3Dp0iXk5+cjOjoaTz/9tGyfJRSonGwM5FaQai3r4EiZ4RKBUUKprCXjC8C/Ep5vCQJINBU0x48fR1FREV588UVkZWVh/PjxWLduHbZv346LFy/6fW98fDwyMjKEh8PR1gfas2cPjh07hr/85S8YPnw4brvtNixfvhzr169Hc7O8fqTBQgHXGMitINVqwI10WxCZXoSG3PPM6XYKIjatzDV/F3Xi70ALGa4uAm5JSQmSkpIwevRo4bmcnBxYrVbs37/f73tffvllpKamYvDgwSgsLERDQ4PHeYcMGYL09HThudzcXNTU1ODoUd9XiE1NTaipqfF4yAH1b42D3ApSIevQyI0LOBFnuGR6ERJyz7PKxkoAgAUWpMSlSH7+cBAu6rz0cPmWIJvFBpvVpui4vKGLgFtWVoauXbt6PBcVFYWUlBSUlZX5fN9Pf/pT/OUvf8H777+PwsJC/O///i/uuecej/OKgy0A4Wd/512xYgUSExOFR/fu8iwG1L81DnIrSLmPslb6apxIrR3J9CI0ZJ9n31dSkuOShTtBqU0wGa4WsltA5YC7aNGiDqKm9o+vvvoq7PPPmzcPubm5GDJkCGbOnImtW7di586dOHXqVETjLiwsRHV1tfA4f/58ROfzBZWTjYWcClKtlpQjzXDJ9CJ05JxnWuvfAv6FeVqydQRUFk099thjmDVrlt9j+vTpg4yMDFy+fNnjeafTicrKSmRkZAT9+7KysgAAJ0+eRN++fZGRkYEDBw54HFNeXg4Afs8bExODmBj5/4AUcI2FnApSrQbcSHq4ZHoRHkrMM624TAH6ynBVDbhpaWlISwv8h8vOzkZVVRUOHjyIUaNGAQD+/ve/w+12C0E0GEpLSwEA3bp1E87729/+FpcvXxZK1nv37oXD4cDAgQND/DTSQv1b4yGnglSLNy4A2hbDuuY6uJkbVkvwRTUyvQgPOeeZFi/s/Fk7ai3g6qKHe+ONNyIvLw9z587FgQMH8PHHH6OgoAAzZsxAZmYmAODbb7/FgAEDhIz11KlTWL58OQ4ePIgzZ87gzTffRH5+Pm6++WYMHToUADB58mQMHDgQP/vZz/D5559j9+7deOKJJ/Dggw8qksH6g/q3xkNOBakWF0IAHoGyrtn/vvn2kOlFeMg5z7TmMgX4dzPTko8yoJOAC7SqjQcMGIBJkybh9ttvx/jx4/HnP/9ZeL2lpQUnTpwQVMh2ux3vvfceJk+ejAEDBuCxxx7D9OnT8dZbbwnvsdlsePvtt2Gz2ZCdnY177rkH+fn5Hvt21YLKycZDLgVpi6sF1U3VALS1EAKtvbNoazSA0Pu4ZHoRHnIqlamkHBnakJkFQUpKil+Ti169eoExJvzcvXt3fPDBBwHP27NnT7z77ruSjFFKKOAaD64g/fTCpzh6+SgGdx0syXn5Imi1WJEclyzJOaXEEeNARWNFyAGXTC/CQ655BmizkuJPCa810ZRuMlwzQf1b4yKHgpQvgl3iuoTUI1WKcLcGkelF+MilVNZiSVmc4YqTLkB7Ga72/nUS1L81MHIoSLWYdYgJd2sQmV6Ej1xKZa35KANtPVwXc+Ga85rHa9TDJQJC5WTjIoeCVKs3LuCEuzWITC/CRy6lshYv7jrZO8GCVlFd+4s6ynCJgFDANS5yKEi1uAiKCTfDJdOL8JFLqaxF4wurxYoEewKAjhd11MMl/EL9W2Mjh4JUCLga81HmhNPDJdOLyJBjnjW0NKDR2QhAWyplwPdFHWW4hF+of2ts5PC6FUwvNFpSdthDz3DJ9CIy5Jhn/MLObrMLGaVW8HVRJ9x8nnq4hDeonGx8pFaQ8hsXaKnMJyacm9CT6UXkSD3PxOVkrf1NfGW4XDRFGS7hFQq4xkdqBakRe7hkehE5ZppnvuwdqaRM+IT6t+ZAagWpVn2UOf68bn1BpheRI/U806LLFMeXvaMgmqKSMtEe6t+aA6kVpFrOPAD/Xre+INOLyJF6nmnR9IJDoikiZKicbA6kVJAyxjQfcMMpKZPpReRIrVTW8jwT9nq3E00Jxhe0LYhoDwVccyClgrSuuU5YVLSqUg5nWxBluJEjtVJZyyVlynCJkKD+rbmQSkHKF8G4qDjER8dHPC45CCvDpR6uJEipVNZ0hutDCU89XMIr1L81F1IpSLW8CHJCtXYk0wvpkFKprMserpsyXMILVE42F1IpSLXuowyEnuGS6YV0SKlU1uKNCzi+LuoE4wvq4RJiKOCaC6kUpLrIcL+v2DS0NMDldgU8nkwvpENKpbKW55pP4wsnGV8Q7aD+rfmQSkGq5UWQw7MPILiyMpleSIdU88zN3KhoqACgzbkWyNqRAi4hQP1b8yGVglTrNy4AWst5fMELRqlMginpkGqeVV2rgou1Vie0GHADWTuSaIoQoHKyOZFCQar1GxdwQunj0pYgaZFinvELO0eMQzPZohiydiSChgKuOZFCQar1GxdwQrF3JNMLaZFinmnxPrhixG5mjDHhebofLuEB9W/NixQKUj30cIHQ7B0pw5UWKeeZFk0vgLYLOjdzo6GlQXieMlzCA+rfmhcpFKRav3EBJ5SSMvVwpUWKeab1C7v46HhYLa3hTFxFoR4u4QGVk82LFApSrS+EnGDtHcn0QnqkmGdaNr0AWsVh3qoolOESHlDANS+RKkhdbhcqGysBaHch5ASb4ZLphfRIoVTWekkZ8H5RRz1cQoD6t0QkCtLKxkowtApEusR3kXRcUhOsvSOZXshDpEplPVRSvF3UUYZLCFD/lohEQcoXweTYZERZoyQdl9QEm+GS6YU8RKpU1npJGfB+USdYO1IPl6ByMhGJglQPWQfH1/1K20OCKXmIVKmsh7nm7aKOi6YowyUo4BIRKUj1cOMCjrAYNgfIcGlLkCxEqlTW8o0LON56uFRSJgBQ/5ZoJRIFqR6yDk6wKmUyvZCHSJXKWje+ADpmuG7mhtPtBECiKdND/VsCiExBqgcfZU7QPVzKcGUhknnW5GwS+qKaDrh2TzczcSZPGa7JoXIywQlXQaoXH2UgeGtH6uHKR7jzrKKx9S5BNosNSbFJUg9LMnjiwi/q+JYggERTpocCLsEJV0GqFx9lIDhrRzK9kJew59n3lZQu8V0ENyct0r6KIs5wo23RqoypPdr99gwM9W8JMeEqSPXUww2mpEymF/IS7jzTQ/8W6LgtiCuUo63RmrlQ0MYoTAb1bwkx4SpI9eKjDAQnmiLTC3kJd57pwWUK8J3haqV/C1DAVQUqJxNiwlWQ6jHDbXQ2CsrR9pDphbwYfZ61v6gTTC80olAGdBRwKysrMXPmTDgcDiQlJWHOnDmoq6vzefyZM2dgsVi8Pl577TXhOG+vb9++XdbPQgGXEBOuglQvCyHQVu4DfGe5JJiSl3DnmR5cpoCOGS4XTVGGGwYzZ87E0aNHsXfvXrz99tv48MMPMW/ePJ/Hd+/eHZcuXfJ4LF26FAkJCbjttts8jn3ppZc8jps2bZpsn4P6t4Q3QlWQNrY0or6lHoA+VMrRtmjERsUC8N3HpS1B8hOOUlkvJeX2PVwtlpS1bcD6PcePH0dRURH++c9/YvTo0QCAdevW4fbbb8eqVauQmZnZ4T02mw0ZGRkez+3cuRM/+clPkJCQ4PF8UlJSh2Plgvq3hDdCVZDyRTDaGu2RPWqZzvbOuOa85nNrEJleyE84SmW9VFI6ZLgauxcuoJMMt6SkBElJSUKwBYCcnBxYrVbs378/qHMcPHgQpaWlmDNnTofXHnzwQaSmpmLMmDHYtGkTGGOSjb09VE4mvBGqglS8COpFYBRIqUwZrvyEo1TWS0lZ3MNljFGGGy5lZWXo2rWrx3NRUVFISUlBWVlZUOfYuHEjbrzxRowbN87j+WXLluHWW29FfHw89uzZg1/84heoq6vDww8/7PNcTU1NaGpq21RdU+PfPUcMBVzCG+0VpIEWCb1kHWICKZWphys/oc4zQB8+ykDbBR0DQ31LvebuhQuonOEuWrTIp7CJP7766quIf09jYyNeeeUVr9ntk08+iR/+8IcYMWIEFi5ciAULFuC5557ze74VK1YgMTFReHTvHtwCQf1bwhehKkj1dOMCjr8Ml0wvlCEcpbJeLu7iouKE/ba1TbWazHBVDbiPPfYYjh8/7vfRp08fZGRk4PLlyx7vdTqdqKysDKr3+vrrr6OhoQH5+fkBj83KysKFCxc8Mtj2FBYWorq6WnicP38+8IcF9W8J34SqINXLIijGn70jmV4oQ6jzjDGmG+MLi8XicVGnxR6uqiXltLQ0pKUFvkLPzs5GVVUVDh48iFGjRgEA/v73v8PtdiMrKyvg+zdu3Igf/ehHQf2u0tJSJCcnIybG9x8pJibG7+u+oHIy4Y9BaYPw6YVPg1KQ6unGBRx/9o5keqEcocyz2uZatLhbAGg/4AKtF3VV16pQ01SjyQxXFz3cG2+8EXl5eZg7dy42bNiAlpYWFBQUYMaMGYJC+dtvv8WkSZOwdetWjBkzRnjvyZMn8eGHH+Ldd9/tcN633noL5eXlGDt2LGJjY7F37148/fTT+NWvfiXL56CAS/gjFAWpnm5cwPFXUibTC+UIZZ7xC7v46HjER8fLOi4pEG8N0qLxhS4CLgC8/PLLKCgowKRJk2C1WjF9+nSsXbtWeL2lpQUnTpxAQ0ODx/s2bdqE66+/HpMnT+5wzujoaKxfvx6PPvooGGPo168fVq9ejblz50o+furfEoEIRUGqpxsXcITF0ItoigRTyhHKPNNLOZnjUVLWoPGFbgJuSkoKXnnlFZ+v9+rVy+t2nqeffhpPP/201/fk5eUhLy9PsjH6g/q3RCBCUZDquYfrNcOlLUGKEc4807rpBUeshBcyXA31cHWxD9cIUDmZCEQoClI93biAIyyG3kRTZHqhGKHMM71d2HkTTWkpw6WAqxAUcIlAhKIg1dtCCFCGqxVCmWd6Mb3geOvhUsA1GdS/JYIlGK9bxpguA257r1sx1MNVlmA9lfU2z7z1cKmkbDKof0sESzAK0qprVXAxFwD9LISA7wyXTC+UJ1ilsu56uPaOPVwtZbi6EU3pGSonE8ESjIKUL4Kd7Z01teUhEL6sHcn0QnmCVSrrNsNtroHNagOgrW1BlOEqAAVcIljaK0i9obdFkOMrwyXTC+UJZp4BOuzhelEpaynDpYArM9S/JUIhGAWpHn2UAd/WjmR6oTzBKpX1cuMCDvVwTQ71b4lQCEZBqtcMl/fXrjmveWRVJJhSnmCVynqba+KA2+ymDNd0UDmZCJVAClK9LYIc8QWnuI9LW4LUIdA8c7qdqGysBKCfuaZ1a0cKuDJDAZcIlUAKUj2aXgBAlDUKcVFxADzLymR6oQ6B5hkPthZYkBKXoti4IkHr1o4UcGWE+rdEOARSkOrRR5njTThFGa46BJxn31dSkuOSEWXVx4YWEk2ZGOrfEuEQSEGq15Iy4H1rEPVw1SHQPNPbjQsAT2HeNec1ACSaMg1UTibCIZCCVK8lZaBjhkumF+oRaJ7pzfQCaOvhAm0lccpwTQIFXCIcAilIdZ3htrN3JNML9TDiPIuNihXK33z8JJoyAdS/JSLBn4JUjwshp32GS6YX6uJvnunN9AJovYjgF3X83wlluCaA+rdEJPhSkLa4WlDdVA1AP2YEYtr3cMn0Ql38KZX1WFIG2i7q+O35qIdrAqicTESCLwUpXwStFiuSYpOUHlbEOOy+M1xCefwplfVaSWmf4FCGawIo4BKR4EtByhfBLnFdYLXo759ve3tH2hKkLv6UynosKQPooAWgHq7Bof4tESm+FKR6zTo4PPsQMlwyvVAVf0plvfkoc9oHXMpwDQ71b4lI8aUg1euNCziU4WoLf0plvV7cibcGAdTDNTxUTiakwJuCVK+LIIcvhtTD1Q6+lMp6NL4AKMM1HRRwCSnwpiAVAm6cvhZBjnhbEJleaANv86yhpQGNzkYA+gu47TNcCrgGhvq3hFR4U5AKLlM6LSmLtwWR6YU28DbPxHtY2wcwrUOiKRNB/VtCKrwpSPV84wLAM8Ml0wtt4HWeiVoXevvb0LYgE0HlZEIqvClIjdLDrW2uJdMLjeBtnum1fwt4yXBJNGVcKOASUuFNQarnGxcAvjNcQj28zTO9ukwBHXu4Wrq1IAVcCTlXdY76t4SktFeQ6j7D/b7c1+xqxqnvTgGgDFcLGGmeiTPcGFuMpkriFHAl5OPzHwOg/i0hHWIFKWNM1wsh4Jl98MWdTC/Up71SWa8uU4BnD1dL/VuAAq6k/OPcPwBQOZmQDrGCtK65TjBk16tK2Wa1oVN0JwDA8SvHAVCGqwXaK5X1XFL2yHA1pFAGKOBKykfnPgJAAZeQDrGC9GLtRQBAXFQc4qPj1RxWRAhbg753m6Iervq0VyrruZIiDriU4RqYs1VnqX9LSIpYQfrJ+U8A6HMRFNNeRUoZrvq0VyrruqQsaltoSTAFUMCVHOrfElIiVpDyPd56LSdzxAsimV5og/ZKZb3euADwvKBrfwcktaGAKzFUTiakhgtaeMDVY9YhRrwgkumFdhArlfVcUhb3bZucTSqOpCMUcCWGAi4hNXwhPFN1BoA+F0Ex4goQlZO1A59nX17+EhUNFQD0P9e4yFArUMCVEKvFSv1bQnJ4qY+jR+WomPYZLqEN+Dz75PwncDEXAAMEXMpwjcuIbiOof0tIDleQcvS+CIp7uJThagc+z8rrywG0XhhpTeUbKvzCQSvoJuD+9re/xbhx4xAfH4+kpKSg3sMYw+LFi9GtWzfExcUhJycH33zzjccxlZWVmDlzJhwOB5KSkjBnzhzU1dWFNcabetwU1vsIwh9cQcrRe8D1yHDJ9EIzGG2eaRHdBNzm5mbceeedeOCBB4J+z7PPPou1a9diw4YN2L9/Pzp16oTc3Fxcu3ZNOGbmzJk4evQo9u7di7fffhsffvgh5s2bF9YYx/cYH9b7CMIfYgUpoP+SMmW42sRo80yL6CbgLl26FI8++iiGDBkS1PGMMaxZswZPPPEEpk6diqFDh2Lr1q24ePEidu3aBQA4fvw4ioqK8OKLLyIrKwvjx4/HunXrsH37dly8eDHkMY69fmzI7yGIYOCCFkD/mQf1cLWLUeZZXFSc2kPwirZ2BUvI6dOnUVZWhpycHOG5xMREZGVloaSkBDNmzEBJSQmSkpIwevRo4ZicnBxYrVbs378fP/7xj72eu6mpCU1Nbc346upqAABrYqipqZHpExFmpm98X+D7wkysK1bX8yy6JVr4LA44dP1ZjIZ4nun5b/Pg0Aex6pNVeGjMQ0F9Bn4MY0zWcRk24JaVlQEA0tPTPZ5PT08XXisrK0PXrl09Xo+KikJKSopwjDdWrFiBpUuXdni+e3e6WifkZ+xK41RSeqzsofYQCB9s+/5/embd9/8LloqKCiQmJso2HlUD7qJFi/DMM8/4Peb48eMYMGCAQiMKjsLCQsyfP1/4uaqqCj179sS5c+dk/WNJTU1NDbp3747z58/D4dCP2w+NW1n0Om5Av2OncStLdXU1evTogZSUFFl/j6oB97HHHsOsWbP8HtOnT5+wzp2RkQEAKC8vR7du3YTny8vLMXz4cOGYy5cve7zP6XSisrJSeL83YmJiEBPT8S4UiYmJuppkHIfDQeNWEBq38uh17DRuZbFa5ZU1qRpw09LSkJYmjxKud+/eyMjIwL59+4QAW1NTg/379wtK5+zsbFRVVeHgwYMYNWoUAODvf/873G43srKyZBkXQRAEYU50o1I+d+4cSktLce7cObhcLpSWlqK0tNRjz+yAAQOwc+dOAK0S90ceeQRPPfUU3nzzTXz55ZfIz89HZmYmpk2bBgC48cYbkZeXh7lz5+LAgQP4+OOPUVBQgBkzZiAzM1ONj0kQBEEYFN2IphYvXowtW7YIP48YMQIA8P7772PixIkAgBMnTgiKYQBYsGAB6uvrMW/ePFRVVWH8+PEoKipCbGyscMzLL7+MgoICTJo0CVarFdOnT8fatWtDGltMTAyWLFnitcysZWjcykLjVh69jp3GrSxKjdvC5NZBEwRBEAShn5IyQRAEQegZCrgEQRAEoQAUcAmCIAhCASjgEgRBEIQCUMANAj3cGtAboZ7/zJkzsFgsXh+vvfaacJy317dv367auAFg4sSJHcZ0//33exxz7tw5TJkyBfHx8ejatSsef/xxOJ1OycYdztgrKyvx0EMPoX///oiLi0OPHj3w8MMPe6jtAem/8/Xr16NXr16IjY1FVlYWDhw44Pf41157DQMGDEBsbCyGDBmCd9991+P1YOa7FIQy7hdeeAE33XQTkpOTkZycjJycnA7Hz5o1q8P3mpeXp+q4N2/e3GFM4p0VgHLfd6hj9/bv0GKxYMqUKcIxcn/nH374Ie644w5kZmbCYrEIN6vxR3FxMUaOHImYmBj069cPmzdv7nBMqP9mvMKIgCxevJitXr2azZ8/nyUmJgb1npUrV7LExES2a9cu9vnnn7Mf/ehHrHfv3qyxsVE4Ji8vjw0bNox9+umn7B//+Afr168fu/vuuyUbd6jndzqd7NKlSx6PpUuXsoSEBFZbWyscB4C99NJLHseJP5fS42aMsQkTJrC5c+d6jKm6utrjsw0ePJjl5OSww4cPs3fffZelpqaywsJCycYdzti//PJL9p//+Z/szTffZCdPnmT79u1jN9xwA5s+fbrHcVJ+59u3b2d2u51t2rSJHT16lM2dO5clJSWx8vJyr8d//PHHzGazsWeffZYdO3aMPfHEEyw6Opp9+eWXwjHBzPdICXXcP/3pT9n69evZ4cOH2fHjx9msWbNYYmIiu3DhgnDMvffey/Ly8jy+18rKSsnGHM64X3rpJeZwODzGVFZW5nGMEt93OGOvqKjwGPeRI0eYzWZjL730knCM3N/5u+++y/7f//t/bMeOHQwA27lzp9/j//Wvf7H4+Hg2f/58duzYMbZu3Tpms9lYUVGRcEyo34MvKOCGwEsvvRRUwHW73SwjI4M999xzwnNVVVUsJiaGbdu2jTHG2LFjxxgA9s9//lM45m9/+xuzWCzs22+/jXisUp1/+PDh7Oc//7nHc8FM4nAJd9wTJkxgv/zlL32+/u677zKr1eqxcD3//PPM4XCwpqYmVcfenr/+9a/MbrezlpYW4Tkpv/MxY8awBx98UPjZ5XKxzMxMtmLFCq/H/+QnP2FTpkzxeC4rK4v993//N2MsuPmuxrjb43Q6WefOndmWLVuE5+699142depUycbojVDHHWidUer7Zizy7/z3v/8969y5M6urqxOeU+I75wTz72bBggVs0KBBHs/dddddLDc3V/g50u+BQyVlGQh0a0AAAW8NGClSnP/gwYMoLS3FnDlzOrz24IMPIjU1FWPGjMGmTZsku61VJON++eWXkZqaisGDB6OwsBANDQ0e5x0yZIjH3aNyc3NRU1ODo0ePqj52MdXV1XA4HIiK8vSlkeI7b25uxsGDBz3mptVqRU5OjjA321NSUuJxPND63fHjg5nvkRLOuNvT0NCAlpaWDgb1xcXF6Nq1K/r3748HHngAFRUVkow5knHX1dWhZ8+e6N69O6ZOneoxR5X4viMZu5iNGzdixowZ6NSpk8fzcn7noRJofkvxPXB04zSlJ+S8NWAoY4j0/Bs3bsSNN96IcePGeTy/bNky3HrrrYiPj8eePXvwi1/8AnV1dXj44YdVG/dPf/pT9OzZE5mZmfjiiy+wcOFCnDhxAjt27BDO6+3vwV+TAim+86tXr2L58uWYN2+ex/NSfedXr16Fy+Xy+l189dVXXt/j67sTz2X+nK9jIiWccbdn4cKFyMzM9Fg48/Ly8J//+Z/o3bs3Tp06hV//+te47bbbUFJSApvNpsq4+/fvj02bNmHo0KGorq7GqlWrMG7cOBw9ehTXX3+9It93uGMXc+DAARw5cgQbN270eF7u7zxUfM3vmpoaNDY24rvvvot47nFMG3D1emvAYMcdKY2NjXjllVfw5JNPdnhN/NyIESNQX1+P5557zu/iL/e4xQFqyJAh6NatGyZNmoRTp06hb9++YZ8XUO47r6mpwZQpUzBw4ED85je/8XgtnO+caGPlypXYvn07iouLPQRIM2bMEP57yJAhGDp0KPr27Yvi4mJMmjRJjaEiOzsb2dnZws/jxo3DjTfeiD/96U9Yvny5KmMKh40bN2LIkCEYM2aMx/Na/M6VwrQBV6+3Bgx23OGen/P666+joaEB+fn5AY/NysrC8uXL0dTU5NOLVKlxi8cEACdPnkTfvn2RkZHRQVVYXl4OAAHPq8TYa2trkZeXh86dO2Pnzp2Ijo72e3ww37k3UlNTYbPZhM/OKS8v9znGjIwMv8cHM98jJZxxc1atWoWVK1fivffew9ChQ/0e26dPH6SmpuLkyZOSLP6RjJsTHR2NESNG4OTJkwCU+b6ByMZeX1+P7du3Y9myZQF/j9Tfeaj4mt8OhwNxcXGw2WwR/w0FQur4mpxQRVOrVq0SnquurvYqmvrss8+EY3bv3i25aCrc80+YMKGDUtYXTz31FEtOTg57rGKk+l4++ugjBoB9/vnnjLE20ZRYVfinP/2JORwOdu3aNVXHXl1dzcaOHcsmTJjA6uvrg/pdkXznY8aMYQUFBcLPLpeLXXfddX5FU//xH//h8Vx2dnYH0ZS/+S4FoY6bMcaeeeYZ5nA4WElJSVC/4/z588xisbA33ngj4vFywhm3GKfTyfr3788effRRxphy33ckY3/ppZdYTEwMu3r1asDfIcd3zkGQoqnBgwd7PHf33Xd3EE1F8jcUxhPS0Sbl7Nmz7PDhw8IWmcOHD7PDhw97bJXp378/27Fjh/DzypUrWVJSEnvjjTfYF198waZOnep1W9CIESPY/v372UcffcRuuOEGybcF+Tv/hQsXWP/+/dn+/fs93vfNN98wi8XC/va3v3U455tvvsleeOEF9uWXX7JvvvmG/c///A+Lj49nixcvVm3cJ0+eZMuWLWOfffYZO336NHvjjTdYnz592M033yy8h28Lmjx5MistLWVFRUUsLS1Nlm1BoYy9urqaZWVlsSFDhrCTJ096bJVwOp2MMem/8+3bt7OYmBi2efNmduzYMTZv3jyWlJQkKLh/9rOfsUWLFgnHf/zxxywqKoqtWrWKHT9+nC1ZssTrtqBA8z1SQh33ypUrmd1uZ6+//rrH98r/3dbW1rJf/epXrKSkhJ0+fZq99957bOTIkeyGG26Q7CIsnHEvXbqU7d69m506dYodPHiQzZgxg8XGxrKjR496fDa5v+9wxs4ZP348u+uuuzo8r8R3XltbK6zRANjq1avZ4cOH2dmzZxljjC1atIj97Gc/E47n24Ief/xxdvz4cbZ+/Xqv24L8fQ/BQgE3CO69914GoMPj/fffF47B9/skOW63mz355JMsPT2dxcTEsEmTJrETJ054nLeiooLdfffdLCEhgTkcDjZ79myPIB4pgc5/+vTpDp+DMcYKCwtZ9+7dmcvl6nDOv/3tb2z48OEsISGBderUiQ0bNoxt2LDB67FKjfvcuXPs5ptvZikpKSwmJob169ePPf744x77cBlj7MyZM+y2225jcXFxLDU1lT322GMeW2/UGPv777/vdW4BYKdPn2aMyfOdr1u3jvXo0YPZ7XY2ZswY9umnnwqvTZgwgd17770ex//1r39lP/jBD5jdbmeDBg1i77zzjsfrwcx3KQhl3D179vT6vS5ZsoQxxlhDQwObPHkyS0tLY9HR0axnz55s7ty5IS+iUo/7kUceEY5NT09nt99+Ozt06JDH+ZT6vkMdO2OMffXVVwwA27NnT4dzKfGd+/o3xcd57733sgkTJnR4z/Dhw5ndbmd9+vTxWMs5/r6HYKHb8xEEQRCEAtA+XIIgCIJQAAq4BEEQBKEAFHAJgiAIQgEo4BIEQRCEAlDAJQiCIAgFoIBLEARBEApAAZcgCIIgFIACLkEQBEEoAAVcgtAYs2bNgsViwcqVKz2e37VrFywWS0jn6tWrF9asWRPwuD//+c+YOHEiHA4HLBYLqqqqghrntGnTQhqPFGzevBlJSUmK/16CiBQKuAShQWJjY/HMM8/gu+++U+T3NTQ0IC8vD7/+9a8V+X0EYUYo4BKEBsnJyUFGRgZWrFjh97iPPvoIN910E+Li4tC9e3c8/PDDqK+vBwBMnDgRZ8+exaOPPgqLxeI3O37kkUewaNEijB07NuwxT5w4EQ8//DAWLFiAlJQUZGRkdLivr8ViwfPPP4/bbrsNcXFx6NOnD15//XXh9eLi4g4ZdmlpKSwWC86cOYPi4mLMnj0b1dXVwmdq/zsIQqtQwCUIDWKz2fD0009j3bp1uHDhgtdjTp06hby8PEyfPh1ffPEFXn31VXz00UcoKCgAAOzYsQPXX389li1bhkuXLuHSpUuyj3vLli3o1KkT9u/fj2effRbLli3D3r17PY558sknMX36dHz++eeYOXMmZsyYgePHjwd1/nHjxmHNmjVwOBzCZ/rVr34lx0chCMmhgEsQGuXHP/4xhg8fjiVLlnh9fcWKFZg5cyYeeeQR3HDDDRg3bhzWrl2LrVu34tq1a0hJSYHNZkPnzp2RkZER+s2yw2Do0KFYsmQJbrjhBuTn52P06NHYt2+fxzF33nkn7rvvPvzgBz/A8uXLMXr0aKxbty6o89vtdiQmJsJisQifKSEhQY6PQhCSQwGXIDTMM888gy1btnjNAD///HNs3rwZCQkJwiM3NxdutxunT59WYbStAVdMt27dcPnyZY/nsrOzO/wcbIZLEHomSu0BEAThm5tvvhm5ubkoLCzErFmzPF6rq6vDf//3f+Phhx/u8L4ePXooNEJPoqOjPX62WCxwu91Bv99qbc0BxHcNbWlpkWZwBKEyFHAJQuOsXLkSw4cPR//+/T2eHzlyJI4dO4Z+/fr5fK/dbofL5ZJ7iCHx6aefIj8/3+PnESNGAADS0tIAAJcuXUJycjKAVtGUGC1+JoIIBiopE4TGGTJkCGbOnIm1a9d6PL9w4UJ88sknKCgoQGlpKb755hu88cYbgmgKaN2H++GHH+Lbb7/F1atXff6OsrIylJaW4uTJkwCAL7/8EqWlpaisrJT887z22mvYtGkTvv76ayxZsgQHDhwQxtyvXz90794dv/nNb/DNN9/gnXfewe9+9zuP9/fq1Qt1dXXYt28frl69ioaGBsnHSBByQAGXIHTAsmXLOpRmhw4dig8++ABff/01brrpJowYMQKLFy9GZmamx/vOnDmDvn37CtmjNzZs2IARI0Zg7ty5AFpL2SNGjMCbb74p+WdZunQptm/fjqFDh2Lr1q3Ytm0bBg4cCKC1JL1t2zZ89dVXGDp0KJ555hk89dRTHu8fN24c7r//ftx1111IS0vDs88+K/kYCUIOLEzcLCEIgpARi8WCnTt3quJQRRBqQxkuQRAEQSgABVyCIAiCUABSKRMEoRjUwSLMDGW4BEEQBKEAFHAJgiAIQgEo4BIEQRCEAlDAJQiCIAgFoIBLEARBEApAAZcgCIIgFIACLkEQBEEoAAVcgiAIglAACrgEQRAEoQD/HxVRlfun4BPcAAAAAElFTkSuQmCC\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# TODO\n", + "# Contemplate what you think will happen when we feed the\n", + "# output of the original first network into a second copy of the original first network, and then\n", + "# the output of that into the original second network (so now we have a three layer network)\n", + "# How many total linear regions will we have in the output?\n", + "net123_out = shallow_1_1_3(net12_out, ReLU, n2_phi_0, n2_phi_1, n2_phi_2, n2_phi_3, n2_theta_10, n2_theta_11, n2_theta_20, n2_theta_21, n2_theta_30, n2_theta_31)\n", + "plot_neural_two_components(x, net12_out, net2_out, net123_out)" + ], + "metadata": { + "id": "BSd51AkzNf7-", + "outputId": "a3934038-98f0-4cd8-9eed-2eb401f7268a", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 843 + } + }, + "execution_count": 17, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# TODO\n", + "# How many linear regions would there be if we ran N copies of the first network, feeding the result of the first\n", + "# into the second, the second into the third and so on, and then passed the result into the original second\n", + "# network (blue curve above)\n", + "\n", + "# Take away conclusion: with very few parameters, we can make A LOT of linear regions, but\n", + "# they depend on one another in complex ways that quickly become too difficult to understand intuitively." + ], + "metadata": { + "id": "HqzePCLOVQK7" + }, + "execution_count": null, + "outputs": [] + } + ] +} \ No newline at end of file diff --git a/README.md b/README.md index bc03301..a77b189 100644 --- a/README.md +++ b/README.md @@ -1 +1,3 @@ -# Algorithms \ No newline at end of file +# Algorithms + +This changes are made by prayush21