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@Sagor0078
Created May 19, 2023 18:22
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howMatrices_transform.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": [],
"authorship_tag": "ABX9TyPRd5x6kJOf9E9HpMXJCznZ",
"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": [
"<a href=\"https://colab.research.google.com/gist/Sagor0078/7a5e434b8ed3cb052984562233d804db/howmatrices_transform.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"source": [
"#How Vector and Matrics Transform in Space\n"
],
"metadata": {
"id": "_PkcVJEdfLYv"
}
},
{
"cell_type": "markdown",
"source": [
"**The introduction of numbers as coordinates is an act of violence.\" - Hermann Weyl**\n",
"\n"
],
"metadata": {
"id": "OhrsLsMLgsSV"
}
},
{
"cell_type": "markdown",
"source": [
"Linear algebra is a surprisingly useful subject, at the heart of computer graphics, cryptography, and machine learning. It is applied in data compression, game theory, and understanding networks. Engineering applications of linear algebra are everywhere: electric circuits, statics and dynamics, digital signal processing, optimization, robotics, multi-body dynamics… you name it!\n",
"\n",
"Let's get started! We will be using our favorite libraries of the Python ecosystem: NumPy and Matplotlib. We also have a few helper functions in the plot_helper.py script, which will make it easy to visualize the ideas in these lessons. Go ahead and load these by executing the next two cells.\n"
],
"metadata": {
"id": "BG4mbaLnfo3c"
}
},
{
"cell_type": "code",
"source": [
"import numpy\n",
"%matplotlib inline\n",
"from matplotlib import pyplot\n",
"#\n",
"from urllib.request import urlretrieve\n",
"URL = 'https://go.gwu.edu/engcomp4plot'\n",
"urlretrieve(URL, 'plot_helper.py')\n",
"\n",
"import sys\n",
"sys.path.append('../scripts/')\n",
"\n",
"# Our helper, with the functions: \n",
"# plot_vector, plot_linear_transformation, plot_linear_transformations\n",
"from plot_helper import *"
],
"metadata": {
"id": "kQiLwYBBfsaL"
},
"execution_count": 7,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"#Vectors"
],
"metadata": {
"id": "AOqkeOZlgb84"
}
},
{
"cell_type": "markdown",
"source": [
"**What is vectors?**\n",
"\n",
"Vectors are everywhere: physics, engineering, mathematics, computer science, video games, and more. Each field's interpretation of what a vector is may be different, but vectors live a similar life in every space.\n",
"\n",
"\n",
"The first episode in the wonderful video series, **\"Essence of Linear Algebra, by Grant Sanderson**\" [link text] \n",
"(https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&pp=iAQB\n",
")tells you of three different ideas about vectors\n",
"\n",
"\n",
" For physicists, a vector is an \"arrow\" of a given length (magnitude) and direction. It can represent directional quantities like velocity, force, acceleration.\n",
" For computer scientists, a vector is an ordered list of numbers. It can represent a set of variables or features stored in order.\n",
" For mathematicians, vectors are generic objects that behave a certain way when they are added or scaled: u+v,αv.\n",
"\n",
"\n",
"\n",
"In physics, vectors are almost always two- or three-dimensional (although in some fancy branches of physics they do go to higher dimensions). Vectors help physicists describe things like motion and electro-magnetic fields on a plane or in physical 3D space.\n",
"\n",
"In computer science and in data science, vectors are often multi-dimensional, that is, they have many components. They contain a set of ordered variables in a data model, like for example: the age, weight, daily hours of sleep, weekly hours of exercise, and blood pressure of an individual (five dimensions).\n",
"\n",
"\n"
],
"metadata": {
"id": "Ubgjd_41hZaC"
}
},
{
"cell_type": "markdown",
"source": [
"\n",
"**Visualizing vectors**\n",
"\n",
"Let's start with the idea of a vector as an \"arrow\" (magnitude plus direction). We visualize a vector by placing this arrow with its tail at the origin of a coordinate system. But changing the position of the tail doesn't change the vector's magnitude or direction, so the vector is the same no matter where we draw it.\n",
"\n",
"In the code cell below, we define a list with a single vector of coordinates (2,2)\n",
", and we use our custom function plot_vector() to plot the vector with its tail at four different positions on a 2D coordinate system.\n"
],
"metadata": {
"id": "lOPRi-mMmFv8"
}
},
{
"cell_type": "code",
"source": [
"vectors = [(2,2)]\n",
"tails = [(-3,-2), (-3,1), (0,0), (1,-3)]\n",
"plot_vector(vectors, tails)\n",
"pyplot.title(\"The same vector, with its tail at four locations.\");\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 401
},
"id": "AU1zQ2MfhYNp",
"outputId": "bfe0e30d-487b-4c21-bde3-8e39fb16e06b"
},
"execution_count": 8,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 400x400 with 1 Axes>"
],
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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"In the 2D plane, we can see clearly the connection between the \"arrow\" idea of vector, and the \"list of numbers,\" which in this case represents the coordinates of the arrow head when the tail is at the origin of the coordinate system.\n",
"\n",
"The first coordinate designates the horizontal distance between head and tail, and the second coordinate designates the vertical distance between head and tail. We typically will denote horizontal and vertical axes as x\n",
"and y\n",
"\n",
".\n",
"\n",
"In three dimensions, x\n",
"and y are usually denoting the perpendicular axes on the horizontal plane, and the vertical axis is denoted by z. A 3D vector thus has three components: (x,y,z)."
],
"metadata": {
"id": "Hz9-_efYmyL9"
}
},
{
"cell_type": "markdown",
"source": [
"#Fundamental vector operations"
],
"metadata": {
"id": "NUBCm1SVnVbz"
}
},
{
"cell_type": "markdown",
"source": [
"Two operations are the foundation of everything: **vector addition, and multiplication by a scalar (i.e., scaling).**\n",
"\n",
"Let's first visualize vector addition. Suppose we have two vectors:\n",
"a=[−2,1],b=[1,−3]\n",
"\n",
"We can visualize vector addition as follows: draw vector a\n",
"with its tail at the origin; then draw vector b with its tail on the head of a. If you now draw a vector from the origin to the head of b, that vector is a+b\n",
"\n",
".\n",
"\n",
"With our helper function for plotting 2D vectors, it looks like this:\n"
],
"metadata": {
"id": "r-dVLmxBniYX"
}
},
{
"cell_type": "code",
"source": [
" #vector addition\n",
"a = numpy.array((-2,1))\n",
"b = numpy.array((1,-3))\n",
"origin = numpy.array((0,0))\n",
"\n",
"vectors = [a, b, a+b]\n",
"tails = [origin, a, origin]\n",
"plot_vector(vectors, tails)\n",
"pyplot.title(\"Adding vectors with coordinates $(-2, 1)$ and $(1,-3)$.\\n\");"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 421
},
"id": "A1nM9ug5mjbN",
"outputId": "e1ee811e-e6f8-48a6-d872-c3ecb28c9b66"
},
"execution_count": 9,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 400x400 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"source": [
"# vector scaling\n",
"c = numpy.array((2,1))\n",
"vectors = [c, 2*c]\n",
"plot_vector(vectors)\n",
"pyplot.title(\"Scaling of the vector $(2,1)$ by the scalar $2$.\");"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 394
},
"id": "X_PXhGAhoLYo",
"outputId": "f9ddb6ab-6485-416c-d359-434930fdc23d"
},
"execution_count": 10,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 400x400 with 1 Axes>"
],
"image/png": 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8HYELAJYQuABgCYELAJYQuABgCYELAJYQuABgCYELAJYQuABgCYELAJYQuABgCYELAJYQuABgCYELAJYQuABgCYELAJYQuABgCYELAJYQuABgCYELAJYQuABgCYELAJYQuABgCYELAJYQuABgCYELn1i9erU6dOigzMxMt0sB/AaBC8d99913WrJkidtlAH6HwIXj7r77bi1YsMDtMgC/E+R2AWhbMjIy1LFjRyUnJ5/R/vn5+c2uLywsPKN2AX/geOCWlJQ43aRXysrKVFtbq7KyMleO7wZ/63NZWZnmz5+vTZs2qbS0VJJUXl7eojERExPj9bYtbbu187fzbYPbfY6IiHC0PccDNzs72+kmvVJXV6eKigrt2bNHAQHt40qJv/V5zZo1GjdunAoKClRUVCRJ2rdvn0JDQ31yvNzcXBUXF/ukbX/kb+fbBrf7nJSU5Gh7jgfuwIEDnW7SK2VlZcrJyVGfPn0UFhbmSg22+VOfd+7cqUOHDik1NVUBAQE6cOCAJOmSSy5p0ZjYu3dvs+uLioo0evRoSVJ8fLzi4+PPvOhWxp/Oty1trc+OB67TU/CWCAwMVFhYmKs12OYvfc7MzFR1dbUmT54sSaqsrJQkLViwQOecc45SU1PVu3fv07aTkJDQ7Prw8HDP7dDQUNf7bZu/nG+b2lKf+dAMjli4cKEWLlzouZ+Xl6eLL75YK1eudPxtGdBatY8LQQDgBwhcOO7ee+/V1KlTT7kNtHdcUoDjVq5c6XYJgF9ihgsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGBJkNsFoG3ZsGGDUlNTVVtbq+LiYsXFxWnJkiWKi4tzuzTAdcxw4ajp06fr/vvv19atW/XZZ5+pc+fOmjBhgqqqqtwuDXAdM1w4avLkyUpOTpYkBQQE6J577tHgwYO1Y8cOXXnllafdPz8/v9n1hYWFjtQJuMHxwC0pKXG6Sa+UlZWptrZWZWVlrhzfDf7Y5xdffLHBGKitrZUkHTt2zKuxERMT4/WxysvLXRtvbvDH8+1rbvc5IiLC0fYcD9zs7Gynm/RKXV2dKioqtGfPHgUEtI8rJa2hz2+++aa6du2qTp06OT42cnNzVVxc7Gib/qw1nG8n1BmjwmOl2v/9v3SsrEKj4s93rc9JSUmOttfBGGOcbNDNGW5OTo769u2rsLAwV2qwzd/7XFVVpWHDhukPf/iDJk6c6NU+BQUFza4vKirS6NGjJf344h4fH3/WdbYW/n6+W8oYoyP/LFXOgULlHCjU3gNFyjlQqK8OHlZ5VbW6dz1Hf15wsyp/OOxan/1+hut0gS0RGBiosLAwV2uwzZ/7fPfdd+umm27StGnTvN4nISGh2fXh4eGe26GhoX7Zb1/y5/Ptrc/2/EPzUzdp1z8K9N//Km10m/ju5+n9pXN1bmgnZWf/d6vvc722+74Erpo3b55CQ0P16KOPul0K/MzQPj3162tGqqLqeKPrL+vZXR+vekg9zu9iuTLf41sKcNzixYt16NAhvfzyy5L+97r+wIED3SwLfuL7Y8Xa+e0h1Zm6U9YN69NTby++W+dGtP5LJo0hcOGo5557TuvXr1dqaqp27Ngh6ccPzuLi4gjcdu77Y8Va8vq7emZzpsorq09ZP/aKBP31sTsV3jnEhersIHDhmJKSEs2ZM0d1dXWnfOc2LS3NpargtsaCNjSkk+ZMTtKBwz9oQ2aWJo/orz//xyyFdOrocrW+ReDCMREREZ7v3QLNBe0DN47XeedGas7KVzX96qF68aGZ6hjU9uOo7fcQgFXeBG29X40bqmF9Lm7T3ys+EYELwBEtCdp6w/v1sl2mqwhcAGflTIK2vSJwAZwRgrblCFwALULQnjkCF4BXCNqzR+ACaBZB6xwCF0CjCFrnEbgAGiBofYfABSCJoLWBwAXaOYLWHgIXaKcIWvsIXKCdIWjdQ+AC7QRB6z4CF2jjCFr/QeACbRRB638IXKCNIWj9F4ELtBEErf8jcIFWjqBtPQhcoJUiaFsfAhdoZY78s0R/eOUdgrYVInCBVuLIP0v03Lt/V8aON1ReRdC2RgQu4Oc8lw7+mknQtnIELuCHjDHKyftOf/jTm9r8f3aquqZWkhTSMVC3//wqLZjxc4K2FSJwAZeVlFdq9/4C7d7/nXb9o0A7cg9ox76Dqqg+7tkmpGOQbv/5SCX2+onGjRqhiIgIFyvGmSJwAZeUV1bppkdT9V//98tmt/vVuCFafucv1Tmog7Kzsy1VB18IcLsAoL0KDQnWn//jt5o0vH/j64M76oNl92n9w7/h8kEbwQwXcEnO/gLd8lS6sr4+cMq6C7tG6cPlD+iSmPNdqAy+QuACljUXtJIU3/08vb90rnqc38VyZfA1LikAluTsL9Dg2Y+r322PNAjbwQlx2pAyS5J0Wc/u+njVQ4RtG8UMF/Cxpma0gxPilPbQTPW9+CL9v2/zNaxPT729+G6dGxHmUqXwNQIX8BFvgrZe927n6r2l9yq8c4jtMmERgQs4rCVBW+8nkcxq2wMCF3DImQQt2hcCFzhLBC28ReACZ4igRUsRuEALEbQ4UwQu4CWCFmeLwAVOg6CFUwhcoAkELZxG4AInIWjhKwQu8D8IWvgagYt2j6CFLQQu2i2CFrYRuGh3CFq4hcBFu0HQwm0ELto8ghb+gsBFm0XQwt8QuGhzCFr4KwIXjtu0aZOeeOIJhYSEKCAgQM8884z69u3r8+MStPB3BC4c9fnnn2vmzJnKzs5WfHy8XnrpJSUnJ2vv3r2KiIjwyTEJWrQW/NdeOGrx4sW69tprFR8fL0maPn26ampqlJ6e7vixcgu+b/K/4O5+MUWfP7uAsIVfcWyGW1NTo6KiIqeaa7HS0lIdOXJEBQUFCg8Pd60Om/yxz++9957uvfde5efne5b16dNHGRkZuv7660+7f2FhYbPrDx8+7Lk96cHlUnCo537/3jFadscvdGmPCySZBjW0Bf54vn3NH/ocHR2toCBnorKDMcY40VB+fr5iYmKcaAoA/MahQ4fUvXt3R9rikgIAWOLYDLf+kkJpaakTzbXIkSNH9Mtf/lKS9Kc//Uk9evSwXoNt/tjnY8eOafjw4Xrqqac0adIkz/KHH35Yu3fv1ubNm0/bxukuS+3bt0+33367JGn9+vUaOHDg2RXdSvjj+fY1f+hzeHi4o5cUHLuGGxQU5Ni0u6XCw8M9T9QePXooISHBlTps8tc+R0VFKTAwsEE9lZWV+ulPf+pVjafbJiwszHP7oosu8pt++5q/nm9faot95pICHDVmzBhlZ2d77htjtGPHDo0bN87FqgD/QODCUfPmzdNbb72lb775RpL0yiuvKDAwUDNnznS5MsB9/OIDHDVkyBClp6dr6tSp6ty5swICAvTOO+/47JcegNaEwIXjrr/+eq++cwu0N1xSAABLCFwAsITABQBL2sQ13O7du6u4uFjZ2dm66KL28cdK2mOfJemCCy7w3I6OjnaxErva4/lui31mhgsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlrTpwK2rq9PQoUMVFxfndik+98MPP2jRokUaOXKkkpKSNGDAAD3xxBOqqalxuzRHbdmyxXN7xowZysnJcbEaOzZs2KDx48dr4sSJmj17tm6++Wbl5eW5XZY1mzZtUmRkpDIzM90u5ay1iV/tbcqaNWu0b98+RUVFuV2Kz7399tvasGGDtm/frqioKBUUFOiKK65QdXW1Fi1a5HZ5jvj88881d+5cz/0bbrhBycnJ2rt3b5v+e7vTp09XRkaGhg8fri+++EIvvPCCJkyYoC+//FLBwcFul+dThYWFev31190uwzFtdoZbUFCgdevWadasWW6XYkWXLl30wAMPeF5cLrroIk2ZMkWvvfaay5U5Z/HixRo7dqzn/qRJk1RTU6P09HT3irJg8uTJSk5OliQFBARo9uzZ+vrrr7Vjxw6XK/O9Bx98UNOmTXO7DMe02cC95557tHjxYnXu3NntUqy45pprdNtttzVYFhISoqqqKpcqct7WrVt12WWXee4HBARo4MCBev/9912syvc2btzY4H5ISIgktalz25iMjAwFBQVpyJAhbpfimDYZuPUnasKECW6X4qrt27d7/s10a3f06FEVFxerW7duDZZHR0dr//79LlXljs8//1wXXnihRowY4XYpPlNWVqaHH35YixcvdrsUR7W5a7ilpaVasGCB3n33XbdLcdUHH3yg/Px8/f73v3e7FEeUl5dLkjp16tRgeXBwsGdde1BdXa1Vq1Zp9erV6tixo9vl+MzChQs1e/bsNvcnOFvNDHfevHnq0KFDkz+RkZE6ePCgHnvsMc2ePbvB301tzZrrd2RkpEaPHq19+/Y12KegoEB33nmnNm/erMjISJcqd1ZoaKikHwPnRFVVVZ517cHy5cv17//+7236f8bt2LFDn332mWbPnu12KY5rNTPcBQsW6K677mpyfWlpqQoKCvTRRx9p165dnuteeXl5KioqUlJSknr37q3U1FRbJTuiuX6XlpZq165d6tmzp2fZ0aNHdd1112nt2rW6/PLLLVXpe126dFFUVJSOHDnSYHlRUVGD/rdlKSkpCg4O1sKFC90uxafeeustVVRUaMyYMaqtrdXRo0clSffee6/OOeccpaamqnfv3i5XeYZMG1FcXGw+/PBDU1xc3GB5SkqKiY2NdacoHzu5z8XFxWb48OEmIyPDs83atWvdKs9x119/vZk8ebKRZCSZPXv2mOjoaPP000+7XZrPPfnkk2bKlClm69atpri42GRlZZmsrCy3y/K54uJi89prrxlJ5sMPP3S7nLPWai4poHmVlZWaNGmSrrzySkVHRysrK0tZWVlau3at26U5Zt68edq6davnfkZGhgIDAzVz5kwXq/K95557TuvXr9ftt9+u3Nxc7dixQxkZGdq1a5fbpaGl3E58p5w82yssLDSJiYkmNjbWBAcHm8TERJOWluZukQ47sc+rV6/2zPxO/mlLnn/+eU+/Bg0aZHbv3u12ST5VXFxsAgICGj2vbW08N+aOO+4wP/3pT40k079/f3PjjTe6XdJZ6WCMMW4EvdNKSkqUnZ2tgQMHtunfOjpRe+xzfn6+YmJiJEl79+5VQkKCyxXZ0x7Pd1vrM5cUAMASAhcALCFwAcASAhcALCFwAcASAhcALCFwAcASAhcALCFwAcASAhcALCFwAcASAhcALCFwAcASAhcALCFwAcASAhcALCFwAcASAhcALCFwAcASAhcALCFwAcASAhcALCFwAcASAhcALCFwAcCSILcLQNvwww8/6D//8z/1/vvvKygoSP/61780ZcoUPfTQQwoKYpgBEoELh7z99tvasGGDtm/frqioKBUUFOiKK65QdXW1Fi1a5HZ5gF/gkgIc0aVLFz3wwAOKioqSJF100UWaMmWKXnvtNZcrA/wHM1w44pprrjllWUhIiKqqqlrUTn5+frPrCwsLW9Qe4E8cD9ySkhKnm/RKWVmZamtrVVZW5srx3eDvff7kk0903XXXtWhMxMTEeL1teXm5a+PNDf5+vn3B7T5HREQ42p7jgZudne10k16pq6tTRUWF9uzZo4CA9nGlxJ/7vGPHDuXl5WnhwoU+GxO5ubkqLi72Sdv+yJ/Pt6+43eekpCRH2+tgjDFONujmDDcnJ0d9+/ZVWFiYKzXYZqPPKSkpWrFiRbPbZGVl6ZJLLvHc/+677zRx4kSlpaXpsssua9HxCgoKml1fVFSk0aNHS/rxxT0+Pr5F7bdmjHH7ffb7Ga7TBbZEYGCgwsLCXK3BNl/3edGiRbrvvvua3SY6Otrz1a+jR49q+vTpeuGFFzRixIgWHy8hIaHZ9eHh4Z7boaGh7epcS4zx1o4PzdCsyMhIRUZGerVtSUmJJk2apJSUFCUmJkqSnn/+ec2aNcuXJQKtRvu4EASfq6ys1KRJk3TllVcqOjpaWVlZysrK0tq1a90uDfAbzHDhiHXr1ikzM1OZmZlatmyZ2+UAfokZLhwxZ84cGWMa/QHwIwIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcAHAEgIXACwhcOG4uro6DR06VHFxcW6XAvgVAheOW7Nmjfbt2+d2GYDfIXDhqIKCAq1bt06zZs1yuxTA7wS5XQDalnvuuUeLFy/Wp59+ekb75+fnN7u+sLDwjNoF/IHjgVtSUuJ0k14pKytTbW2tysrKXDm+G/ytz1u2bJEkjRgxQtu2bZMxpsXjISYmxutty8vLXRtvbvC3822D232OiIhwtD3HAzc7O9vpJr1SV1eniooK7dmzRwEB7eNKiT/1uaKiQvPmzdOSJUuUnZ2twsJCVVVV+XQ85Obmqri42Gft+xt/Ot+2uN3npKQkR9tzPHAHDhzodJNeKSsrU05Ojvr06aOwsDBXarDNRp9TUlK0YsWKZrfJysrSxo0bNWfOHI0fP16S9M477yg4OLjF42Hv3r3Nri8qKtLo0aMlSfHx8YqPj29R+60ZY7z199nxwHV6Ct4SgYGBCgsLc7UG23zd50WLFum+++5rdpvo6Gh98skn2rVrlzIyMiRJeXl5Onz4sCZOnKjevXsrNTXVq+MlJCQ0uz48PNxzOzQ0tF2da4kx3trxoRmaFRkZqcjIyNNu9+WXXza4v2jRIqWnpyszM9NHlQGtT/u4EAQAfoDAhaOKioqUlJSk9PT0BrcBcEkBDouOjuYyAtAEZrgAYAmBCwCWELgAYAmBCwCWELgAYAmBCwCWELgAYAmBCwCWELgAYAmBCwCWELgAYAmBCwCWELgAYAmBCwCWELgAYAmBCwCWELgAYAmBCwCWELgAYAmBCwCWELgAYAmBCwCWELgAYAmBCwCWdDDGGLeLALyVn5+vmJgYSdKhQ4fUvXt3lysCvEfgolWpqalRUVGRJCk6OlpBQUEuVwR4j8AFAEu4hgsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlhC4AGAJgQsAlvx/SvX+k6q8+VwAAAAASUVORK5CYII=\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"**Basis vectors**\n",
"\n",
"With the ideas of vector addition and multiplication by a scalar fresh in your mind, now imagine this. Any horizontal vector (i.e., having zero as its second component) can be scaled to have length 1\n",
"\n",
"For example, the vector u=[u,0]\n",
"scaled by 1/u becomes [1,0]\n",
"\n",
"\n",
"Similarly, any vertical vector (having zero as its first component) can be scaled to have length 1\n",
"\n",
"Going the opposite way,\n",
"\n",
" scaling the vector **i=[1,0]**\n",
"\n",
"can give us all possible horizontal vectors, and\n",
"scaling the vector j=[0,1]\n",
"\n",
" can give us all possible vertical vectors.\n",
"\n",
"Since every vector is the sum of a horizontal and a vertical one, it means we can generate all vectors by adding scaled versions of **i**\n",
"and **j**. That's why they are called **basis vetors**.\n"
],
"metadata": {
"id": "PKgr5xkBpkMY"
}
},
{
"cell_type": "markdown",
"source": [
"For any vector, its components are the scalars we need to multiply the basis vectors by to generate it. For example:\n",
"[3,2]=3⋅[1,0]+2⋅[0,1]=**3i+2j**\n",
"\n",
"Let's visualize this using our helper function."
],
"metadata": {
"id": "OiEVbPearPg3"
}
},
{
"cell_type": "code",
"source": [
"# basis vector\n",
"i = numpy.array((1,0))\n",
"j = numpy.array((0,1))\n",
"\n",
"vec = 3*i + 2*j\n",
"vectors = [i, j, 3*i, 2*j, vec]\n",
"plot_vector(vectors)\n",
"pyplot.title(\"The vector $(3,2)$ as a linear combination of the basis vectors.\");"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 403
},
"id": "md88CJ1aoXt0",
"outputId": "c875d449-e6dd-4e33-99cc-a5b15056a84c"
},
"execution_count": 11,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 400x400 with 1 Axes>"
],
"image/png": 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KSQCnBooVsOCHH37Q1KlTnY4BwAUoVsCCUaNG6eGHH3Y6BgAXoFiBAC1dulQNGjTQwIEDnY4CwAX46zZAADwej8aPH68PP/xQJSUlNZpHdnZ2pdOPHDmiPXv2qHnz5oqNja3xHygHUDc4QoEATJgwQXfeeaeaN2+urKysGs3D3z8LKEm7du1Sq1atarQcAHWDYrVg2bJlioiI8PsPktcVr9eroqIi12Vzay6petm2b9+ujz76SFdddZXS0tKUl5cnSfrqq69qLd+//vUvNWvWrNbmXxNu3Z5uzSW5N5vX61Xfvn2djlHvUawWhIeHq23btoqMjHQ6Shkej0cZGRmuy+bWXFL1sq1YsUKhoaGaOHGiJKm4uFiS9OKLLyomJkYzZszQBRdcUOUyt27dWun0vLw89enTR5KUkJCghIQEf15KnXHr9nRrLsm92Twej9MRTgkUqwUhISGKjIxUdHS001HKcWs2t+aS/M/2+OOP6/HHH/fdzsrK0nnnnadnn31Wqampfi8vMTGx0ulRUVG+nyMiIur1Oqtrbs0luTsbAuOeaxAAAJwCKFbAgtGjR2vo0KHlfgZw+uFSMGDBtGnTnI4AwCUYsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWhTodAKjP3nnnHT3//PM6dOiQSkpKVFRUpIceekg33nij09EAOIRiBQIwe/Zs3XTTTbr11lslSUuXLtXgwYOVlJSkiy++2OF0AJzApWAgAJMnT9ZNN93ku52amipjjL799lsHUwFwEiNWIADJycm+nw8fPqwnn3xSbdu2Vf/+/f2eR3Z2dqXTc3Nza5wPQN2jWC0oLS2Vx+NxOkY5Ho/HldncmkuqebYHHnhAS5YsUWJiot58800ZY1RQUODXc+Pi4vxeTlFRkd/zrStu3Z5uzSW5N5vH41F0dLTTMeq9IGOMcTpEfbds2TJFREQoONhdV9a9Xq+Kiopcl82tuaTAspWWlmr+/PlasWKFZs2apSZNmvj1vD59+vi9jNdff13NmjWrVq7a5tbt6dZcknuzeb1e9e3b1+kY9R4jVgvCw8PVtm1bRUZGOh2lDI/Ho4yMDNdlc2suKfBsnTt3VlJSkj799FM9/vjjfj1n69atlU7Py8vzlW9CQoISEhKqnas2uXV7ujWX5N5sbhtB11cUqwUhISGKjIx05SUUt2Zzay6petkOHTqksLCwMvdddNFF2rFjh9+vLTExsdLpUVFRvp8jIiLq/TqrS27NJbk7GwLjnmsQQD3UqVOncvfl5uaqRYsWDqQB4AYUKxCALVu2aPny5b7bixYt0rZt23Tbbbc5mAqAk7gUDARg+vTpmjx5sp544gl5vV4FBQXp3XffVc+ePZ2OBsAhFCsQgFGjRmnUqFFOxwDgIlwKBgDAIooVAACLKFYAACyiWAEAsIhiBQDAIooVAACLKFYAACyiWAEAsIhiBQDAIooVAACLKFYAACyiWAEAsIhiBQDAIooVAACLKFYAACyiWAEAsIhiBQDAIooVAACLKFYAACyiWAEAsIhiBQDAIooVAACLKFYAACyiWAEAsIhiBQDAIooVAACLQp0OANR3ixcv1ty5c1VaWqr8/HzFx8dr6tSpio+PdzoaAAcwYgUCNGzYMD344INauXKlvvjiC4WHh2vQoEEqKSlxOhoAB1CsQIAGDx6sgQMHSpKCg4N17733atu2bVq/fr3DyQA4gWIFArRkyZIytxs1aiRJjFiB0xTvsQKWrVmzRi1atFCPHj38enx2dnal03Nzc23EAlBHKFYLSktL5fF4nI5RjsfjcWU2t+aSAs9WUlKiv//975o6daqKi4tVXFxc5XPi4uL8nn9RUZEKCgpqlK22uHV7ujXX7v352rbzBzVyYTaPx6Po6GinY9R7FKsFBw8e1JYtWxQc7K4r616v15XZ3JpLCjzblClTdOmll6pFixZat26d9XyZmZnKz8+3Pt9AuHV7uiWXMUZZe37Wv7fl6N/bs5W736OZw/vLhAU7nu1EXq9XsbGxTseo9yhWC8LDw9W2bVtFRkY6HaUMj8ejjIwM12Vzay4psGwTJ05Uq1at9Mwzz1TreVu3bq10el5envr06SNJij//fLVNTKzW/GubW7enk7mOlJZqzZbvtPyLDL33ZYay8vZKkhqEhmjpY3eqfXwz164zBI5itSAkJESRkZGuvITi1mxuzSXVLNuUKVO0e/duLVy4UMHBwb7RanJycpXPTayiKKOionw/Z3y/R5d06eJ3rrri1u1Zl7nyPQf1wZcZevffG/XeF5u0v6Co3GNmj75ZA7u1V0FBgWvXGQLnnmsQQD31/PPPa9GiRRo1apTWr1+v9PR0LV26VJs2bbK+rFUbM63PE3b8eKBAr678Qq+s+KLCUr3/2v76/ZU9HUiGusaIFQhAQUGBRo4cKa/Xq+7du5eZNn/+fCvLyMr9yfdz2lfbZIxRUFCQlXnDnjYtz9G8h25T9p7pWrd9Z5lpg7om6R93/s6hZKhrFCsQgOjoaJWWltbqMlas/+U92Ow9B7QlK1dJ57Wo1WWi+t7+fIPufPoV7d5f9sNliefG6vUJf1BoSIhDyVDXuBQMuNyKdWU/3LRs7X8dSoKK7P25UDc/PlfXTJit3fvzFdYgVA9eP0CSdGZ0hN6dPFIxUREOp0RdolgBF/u5sEhrt3xb5r6l/97oUBqc6O3PNyjpjkl6deWXkqQuifHa8MIj+vuI3ym8YQMtnjhCCa2aOZwSdY1LwYCLffifLSot9Za5b82Wb/XTzwU6O4ZPkzpl78+FunfG675CDWsQqr/ecbUevH6A75LvG38Zof7JbZ2MCYdQrICLLV1zwug0KEher9F7azfr1oHdK34SatWJ76V2SYzXgj/frrbxZd/3/s2l7Z2IBxegWAGXOlJaqqLiQ1o86Y+6ftBrkqQ7BnVTz84dlZH1g8PpTj/+jFIBiWIFXCskOFhv/vWuMr+kv0FwiIZf0VPGGAeTnX78HaUCEsUKuFZl31Xle6x1g1EqaoJiBYAKMEpFTVGsAHAcRqkIFMUKAP+HUSpsoFgBnPYYpcImihXAaY1RKmyjWAGclhilorZQrABOO4xSUZsoVgCnDUapqAsUK4DTAqNU1BWKFcApbW++R3dOf4NRKuoMxQrglPX517t0w/Sl+vFAgSRGqagbFCuAU87enwt11zOLtGT1BkmMUlG3KFYAp5QT30vtlBCnhQ//nlEq6gzFCuCUUO4Tv6Ehuj3l15pyz00684wznA2H0wrFCqDeq+gTv7PuuU6ePTlc+kWdo1gB1FuVfS/1YFGR1u3JcTghTkcUK4B6ie+lwq0oVgD1Cr89CW5HsQKoNxiloj6gWAG4HqNU1CfBTgcATgWHDh3S2LFjFRoaqqysLKfjnFLe/nyDku6Y5CvVLonx2vDCI/rzjYMoVbgSI1YgQFlZWbrxxht14YUXqrS01Ok4pwxGqaivKFYgQIWFhVq4cKGys7P18ssvOx3nlMB7qajPKFYgQO3atZMkZWdn1+j5VT0vNze3RvOtjxil4lRAsVpQWloqj8fjdIxyPB6PK7O5NZcUWLaioiJJR0ewBQUFfj8vLi7O78cePnK4WvOuC7a257K1mzT6uTd9f4mmU0Kcnr9vqBLPjdXB/1u3TuSqDW7N5vF4FB0d7XSMeo9iteDgwYPasmWLgoPd9Vkwr9frymxuzSUFlm379u2SpM2bN+unn36qjXjat2+f1q1bVyvzrqlAt+fPRSWa8UG6Vm7aKUlqEBKsO1Iv1vWXJsqzJ6fGvz3pVN3PapPX61VsbKzTMeo9itWC8PBwtW3bVpGRkU5HKcPj8SgjI8N12dyaSwos27ERa7t27dS6dWu/n7d169ZKp+fl5alPnz6SpLPOOkvJycnVylXbAllny9Zu0uj/t7TCUaqTuWqbW7O5bQRdX1GsFoSEhCgyMtKVl1Dcms2tuaSaZ4uIiJAkRUVFVeu5iYmJlU6Piory/Vx8uPSUWGd19V7qqbifwf0oVqAe2bl7n9MRAsYnfnGqo1gBlys+dNj38/c/7ncwSWD4xC9OFxQrEKBDhw7psssu04EDByRJQ4cOVVxcnJYsWWJl/msydvh+zvnpgAoPFisqvJGVedcVRqk4nVCsQIDCwsKUlpZWa/P/OP2XDzcZY/Rx+lZd06tjrS3PJkapOB1RrICLGWO0Yv3XZe5b+u+N9aJYGaXidEWxAi628Zts5f50oMx9y7/YJK/X66rvPx6PUSpOdxQr4GLL1vy33H0/7i/Qf77O0iVtz3cgUeUYpQIUK+BqS/+9Ud3anq+1a4/ebnZmY0WccZaWrvmvq4r156IS/f6pRVqyeoMkRqk4vVGsgEsdKS3VP/74O11wdqTiXpwsSWp+VmN9ueCvWrvlO4fT/WLZ2k0a+dxy7fcUS2KUClCsgEuFhoQopcNF5f76TYPQUPW6OMGhVL8o915qaIj+Onwwo1Sc9ihWANV24nupiS3O0ssP/15dkpwvfMBpFCsAv1X0id/xNw1Uj3OjrfzifOBUQLEC8MvJPvEb1yTadX/KDnASxQqgUlV9L9Vtf3gdcBrFCuCk+F4qUH0UK4By+O1JQM1RrADKYJQKBIZiBSCJUSpgC8UKgFEqYBHFCpzGGKUC9lGswGmKUSpQOyhW4DTDKBWoXRQrcBphlArUPooVOA0wSgXqDsUKnOIYpQJ1i2IFTlGMUgFnUKzAKYhRKuAcihU4hTBKBZxHsQKnCEapgDtQrEA9xygVcBeKFbDgrbfe0t/+9jc1atRIwcHBeu6555SUlFTry2WUCrgPxQoE6Msvv9Rtt92mdevWKSEhQS+//LIGDhyorVu3Kjo6ulaWySgVcK9gpwMA9d2UKVN05ZVXKiEhQZI0bNgwHTlyRAsWLKiV5b39+QYl3THJV6pdEuO14YVH9OcbB1kr1UUfr9Xv//GS3v58gzwHS6zM81THOsMxFCsQoJUrV6pz586+28HBwUpOTtaKFSusLytr915dM2G2du/PV1iDUE0Z8Vv9e+afrV/6vaZnRy1d819dM2G2mgy+X1eMfVbPvZ2mXT/us7qcUwnrDMdwKTgAR44cUV5envbs2aOcnBxFRUU5HamMwsJCV2Zzay6p+tn279+v/Px8NWjQQNnZ2b77o6OjtXHjxjL3nUxubm6l03fv3u37+cDevVLDCDUIDVFMowhNf/VdTX/13SqXURMFhUVS8SGVFEvvr16r91ev1UhJjSMbqdmZMWp2VmOdERmhI94j+vnAAcW8/S81CHHPKeVwad3naugtlooLy62zX8U314DkturfKVHt28SpqKjIlcdAYWGhoqKiFBsbq9BQ92zL+ibIGGOcDlFfZWdnKy4uzukYAGDVrl271KpVK6dj1FtcCg5AVSMNAKiPOLcFhrF+AJo2bSpJio2N1UsvvaRzzz3X4US/2LNnj66//npJclU2t+aSap6ta9euuuuuu3THHXf47vvjH/+o0NBQzZo1q8rn5+XlVTp9+/bt+uMf/yhJWrRokZKTk/3KFYiikkPq/6cZ2p/vUViDUHVre55SL05QavsENW8S43ucW7enE7lOlXWWl5fnO7ehZijWABx7DyIvL0/nnnuuEhMTHU70i6ioKN8J203Z3JpLqnm2/v37a9euXb7HG2O0fft2jR8/3q95VPWYyMhI388tW7ask3W26OO1+m3/XvpN94vVP/lXigxvWOHj3Lo9nch1Kq0z3l8NDGsPCNDYsWM1YMAA7dixQ23atNErr7yikJAQ3XbbbU5Hq7FhA7pp2IBuTseoV1hnOIZiBQLUtWtXLViwQEOHDlV4eLiCg4P14Ycf1tovhwDgbhQrYME111yja665xukYAFyATwUDAGARxQoAgEUUKwAAFlGsAABYxIeXAtCqVSsZY5SWlqaWLVs6HaeMVq1aKT8/X+vWrXNVNrfmktybrXnz5r6fY2NjHUxSnlvXmVtzSe7NdiwXn2YPHCNWAAAsolgBALCIYgUAwCKKFQAAiyhWAAAsolgBALCIYgUAwCKKFQAAiyjWWuL1enXJJZcoPj7e6SgqKSnRhAkT1LNnT/Xr108dO3bUkCFDtGPHDqejad++fZo0aZJ69uyp1NRUdezYUX/729905MgRp6NJkjIzM3XppZcqNTXV6SiSpJtvvlkpKSnKyMhwOook6dChQ5o4caL69eunnTt3Oh3HZ/HixRo8eLAeeOABpaSk6LrrrlNWVpajmd555x1dfvnl6tevny677DKNGDFCS5YscTRTRWbOnKmgoCClpaU5HaXe4jcv1ZJZs2Zp+/btiomJcTqKDhw4oHnz5mnDhg1q1qyZvF6vhg4dqqFDhyo9Pd3RbO+9954WL16sNWvWKCYmRjk5OerUqZMOHTqkSZMmOZpt4cKFeu655xQSEuJojg0bNvh+fuWVV/Tll19q4MCB2rp1q6O/JScrK0s33nijzjvvPHm9XsdyVGTYsGF64403dOaZZ6pjx44aNWqUBg0apI0bN6phw4aOZJo9e7Zuuukm3XrrrSooKNCMGTP0P//zP+rcubMuvvhiRzKdKDc3V1OnTnU6Rr3HiLUW5OTkaN68eRoxYoTTUSRJZ555ppYvX65mzZpJkoKDg9WrVy9XjFibNGmiMWPG+P4D0rJlS1133XV67bXXHE52NNvq1avVpk0bR3M899xzZW4PGzZMR44c0YIFC5wJ9H8KCwu1cOFCDRs2zNEcFRk8eLD69+8v6ej+fu+992rbtm1av369Y5kmT56sm266yXe7Q4cOMsbo22+/dSzTiR566CE9/PDDTseo9yjWWnDvvfdqypQpCg8PdzqKJCksLEwdO3b03c7JydFLL72k++67z8FUR11++eUaPnx4mfsaNWqkkpIShxL94oorrlBYWJjTMfT555+XuR0cHKzk5GStWLHCoURHtWvXzvH/dJzMiZdYGzVqJEmO7lfJyckKDT16kfDw4cN64403lJiY6PsPgNOWLl2q0NBQDRw40Oko9R7FatmxnXPQoEFORynn2GXWCy64QAMHDtSjjz7qdKQKrVmzRtdff73TMVxh7969KiwsLHd/bGysvvvuOwcS1U9r1qxRixYt1KNHD6ejaOTIkTr//PO1bt06vfXWW4qKinI6kjwej8aPH68pU6Y4HeWUQLFaVFhYqIcffljTpk1zOkqFWrZsqfXr1+ubb77RBx98oD/84Q9ORyrnk08+UXZ2th555BGno7hCUVFRhfc3bNjwpNNQVklJiaZOnaqZM2eqQYMGTsfRrFmz9N1336lDhw667LLLlJub63QkTZgwQXfeeafr/npSfUWx+mHs2LEKCgo66b8+ffpo+/btvp3z+D/z5WSuxo0b6/vvvy/3vJYtW2rKlCmaO3durX26tLJsjRs39q2z4+Xk5Ojuu+/WO++8o8aNG9d5rsrWmVMiIiIqvL+kpOSk01DWfffdpxtuuEHXXHON01F8QkNDNXz4cHm9Xj399NOOZlm/fr2++OIL3XnnnY7mOJXwqWA/PPzww7rnnntOOn3NmjU6//zz9cknn2jdunW+93eysrKUl5en1NRUtWnTRnPnzq3TXIWFhcrJyVFpaalKS0vLfLo1MTFRkrRlyxYlJSVZzVVVtsLCQm3atEnnn3++7769e/dqyJAhmjNnjjp06GA9jz+5jmXLycmpteVXV5MmTRQdHa2CgoIy9+fl5ZVZf6jYCy+8oIiICD322GNOR9GhQ4fKvGcfHBysNm3aaMuWLQ6mkpYvX66DBw+qb9++Ki0t1eHDhyVJo0eP1hlnnKG5c+e69r10t6JY/dC4ceNKR1BNmzZVaGioNm7cWOb+SZMmacGCBbX2fbCqchUUFCgvL0+vv/66CgsLNWbMGN+0Y5efWrRoUefZjuU69kGOgoICXX311Zo4caJSUlIkHT0h1sanqv1dZ27So0cPffDBB77bxhitX79e48ePdzCV+z399NP68ccf9eabb0qS1q1bJ+noh4ic0KlTJ23evLnMfXl5eerVq5cjeY6ZMGGCJkyYIOno/r93716dd955mjZtmmu+v13fcCn4NPHiiy/qp59+kiQVFxfrscceU7t27dSlSxdHcxUXF+vqq69W9+7dFRsbq/T0dKWnp2vOnDmO5nKTu+++u8ztV155RSEhIbrtttscSuR+zz//vN544w399re/1VdffaX09HQtXbpUmzZtcizTli1btHz5ct/tjz/+WJmZmWzHU5FBwFatWmXy8/N9t3Nzc01KSopp3bq1adiwoUlJSTHz58+v81z5+flm1apVZsuWLWbUqFGmQ4cOplevXqZjx45m2LBh5vvvv6/zTMfnys/PNzNnzjSSKvzndLZ33nnHpKSkmGbNmpmYmBiTkpJi5s6dW+eZdu3a5VsnnTp1Mr179zabN2+u8xwnKikpMSkpKebXv/61kWQ6d+5srr32Wqdjmfz8fBMcHFzhPuXEcXjMs88+a7p372569OhhunbtapKSkszixYsdy1ORu+66y1xyySVGkmnfvr254YYbnI5ULwUZY4wDfX5KSUtLU3JysqO/BaciBQUFWrduneuyuTWX5M5s2dnZiouLkyRt3brV9/64W7hxnUnuzSW5N1tBQYGr8tRXXAoGAMAiihUAAIsoViBAbvsLOACcRbECAVi4cKFuvfVWBQdzKAE4irMBEAC3/AUcAO7BL4gAAnDFFVcEPI/s7OxKp7vhd8kC8B/FakFpaak8Ho/TMcrxeDyuzObWXFLNsx0+fFilpaXlfvWgP459lcYfRUVFNVpGbXLr9nRrLsm92TweD1+3sYBiteDgwYPasmWL695n83q9rszm1lxSzbPt3bvX993E2pSZman8/PxaXUZ1uXV7ujWX5N5sXq+Xv3BjAcVqQXh4uNq2bavIyEino5Th8XiUkZHhumxuzSUdzTZ69Gi98cYblT4uPT1dF154oe92kyZN5PF4avR7aLdu3Vrp9Ly8PPXp00eSlJCQoISEhGovoza5dXu6NZfk3mxuG0HXVxSrBSEhIYqMjHTlJRS3ZnNrLkm65ZZbNGnSpEr/AHVsbKzvjwhIUoMGDRQSElKj11PVb1I6PkdERIQr15lbt6dbc0nuzobAUKzACSIjI9WyZUtOeABqxD0X9wEAOAVQrEAA3n33XaWmpuqDDz7QV199pdTUVM2bN8/pWAAcxKVgIABXX321rr76aqdjAHARRqwAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYFGo0wGA+mrfvn169tlntWLFCoWGhurnn3/Wddddpz/96U8KDeXQAk5XHP1ADb333ntavHix1qxZo5iYGOXk5KhTp046dOiQJk2a5HQ8AA7hUjBQQ02aNNGYMWMUExMjSWrZsqWuu+46vfbaaw4nA+AkRqxADV1++eXl7mvUqJFKSkocSAPALShWwKI1a9bo+uuvr9ZzsrOzK52em5sbSCQAdYxitaC0tFQej8fpGOV4PB5XZnNrLimwbKtXr9auXbt03333qaCgwO/nxcXF+f3YoqKias27Lrh1e7o1l+TebB6PR9HR0U7HqPcoVgsOHjyoLVu2KDjYXW9Ze71eV2Zzay7paLbZs2frzTffrPRxL730ks4991zf7T179ujBBx/UX/7yF2VmZtZavszMTOXn59fa/GvCrdvTrbkk92bzer2KjY11Oka9F2SMMU6HqO9WrlyppKQkRUZGOh2lDI/Ho4yMDNdlc2su6Wi2L7/8Uq1atVJERMRJH9esWTPfV2r27t2r3/72t5o8ebJ69uxZ7WXm5ORUOj0vL099+vSRJK1bt04JCQnVXkZtcuv2dGsuyb3ZPB4PxWoBI1YLQkJCFBkZ6cpLKG7N5tZcktS4cWMlJCT4la2goEA333yz/vrXv/o+zPTCCy9oxIgRfi8vMTGx0ulRUVG+nyMiIly5zty6Pd2aS3J3NgTGPdcggHqmuLhYV199tbp3767Y2Filp6crPT1dc+bMcToaAAcxYgVqaN68eUpLS1NaWpqeeuopp+MAcAlGrEANjRw5UsaYCv8BOH1RrAAAWESxAgBgEcUKAIBFFCsAABZRrAAAWESxAgBgEcUKAIBFFCsAABZRrAAAWESxAgBgEcUKAIBFFCsAABZRrAAAWESxAgBgEcUKAIBFFCsAABZRrAAAWESxAgBgEcUKAIBFFCsAABZRrAAAWESxAgBgEcUKAIBFFCsAABZRrAAAWESxAgBgEcUKAIBFoU4HAOqrkpISPf7441q1apUaNmyoffv2qXXr1nryySfVpk0bp+MBcAgjVqCG9u/fr3nz5unNN9/UypUrtW7dOoWFhWno0KFORwPgIIoVqKGzzjpLy5cvV7NmzSRJwcHB6tWrl3bs2OFwMgBO4lIwUENhYWHq2LGj73ZOTo5eeukl3XfffdWaT3Z2dqXTc3Nza5QPgDMoVgtKS0vl8XicjlGOx+NxZTa35pJqlu2HH37QDTfcoK+//lqjRo3SmDFjVFBQ4Pfz4+Li/H5sUVFRteZdF9y6Pd2aS3JvNo/Ho+joaKdj1HtBxhjjdIj6btmyZYqIiFBwsLuurHu9XhUVFbkum1tzSYFl27Nnj8aPH68LL7xQY8aM8ft5ffr08fuxr7/+uu/Ss1u4dXu6NZfk3mxer1d9+/Z1Oka9x4jVgvDwcLVt21aRkZFORynD4/EoIyPDddncmks6mm306NF64403Kn1cenq6LrzwwnL3h4WFaciQIfrLX/6iX/3qV34tc+vWrZVOz8vL85VvQkKCEhIS/JpvXXHr9nRrLsm92dw2gq6vKFYLQkJCFBkZ6cpLKG7N5tZcknTLLbdo0qRJioqKOuljYmNjFRQUJOnoazmmU6dOkqSdO3eqa9eufi0vMTGx0unH54iIiHDlOnPr9nRrLsnd2RAYihU4QWRkpFq2bFnlCW/BggX66aefylz2PfZBoxYtWtRqRgDu5Z6L+0A99OKLL+qnn36SJBUXF+uxxx5Tu3bt1KVLF4eTAXAKI1aghvr166f169drwIABio6OVmFhoZKSkvTee+8pLCzM6XgAHEKxAjUUFxenZ5991ukYAFyGS8EAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCgCARRQrAAAWUawAAFhEsQIAYBHFCljg9Xp1ySWXKD4+3ukoABxGsQIWzJo1S9u3b3c6BgAXoFiBAOXk5GjevHkaMWKE01EAuADFCgTo3nvv1ZQpUxQeHu50FAAuEOp0AKA+W7p0qUJDQzVo0CCtXbu2RvPIzs6udHpubm6N5gvAGRSrBaWlpfJ4PE7HKMfj8bgym1tzSdXLVlhYqLFjx+rtt99WQUGBSkpKZIxRQUFBtZYZFxfn92OLioqqPf/a5tbt6dZcknuzeTweRUdHOx2j3qNYLejXr5/TESoUHR2t2NhYp2OU49Zc0tFs06ZNU//+/St93NatWzVnzhzdfffdSkhIkCQ1bNhQQUFBtXpiOuecc1x34nPr9nRrLsm92dy2b9VXQcYY43QIwE3y8/OVn59f6WNiY2OVnJysmJgYBQcf/ahCVlaW8vLy1K1bN7Vp00Zz5871a3lVXQo+cuSI9uzZo+bNmys2Nlahofx/GHAzihWwZNKkSVqwYIGysrKcjgLAQXwqGAAAiyhWIEB5eXlKTU3VggULyvwM4PTEpWAAACxixAoAgEUUKwAAFlGsAABYRLECAGARxQoAgEUUKwAAFlGsAABYRLECAGARxQoAgEUUKwAAFlGsAABYRLECAGARxQoAgEUUKwAAFlGsAABYRLECAGARxQoAgEUUKwAAFlGsAABYRLECAGARxQoAgEUUKwAAFv1/wY7U+Ouv7KoAAAAASUVORK5CYII=\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"**Linear combination and span** "
],
"metadata": {
"id": "SgtovxditAcV"
}
},
{
"cell_type": "markdown",
"source": [
"Adding two vectors that were each multiplied by a scalar is called a linear combination of those two vectors. Thus, we say that every vector is some linear combination of the basis vectors.\n",
"\n",
"This brings us to the idea of the span of two vectors: the set of all possible linear combinations of the two. The second episode of the series **\"Essence of Linear Algebra\"** uses rich visuals to bring these ideas to life [2]. Recommended!\n",
"\n",
"In the code cells below, we will use the NumPy function randint to get random integers in an interval (in this case, from 10 to 10). We then create a list of 30 random vectors on the plane via a linear combination of the basis vectors **i** and **j** , and we draw them all.\n"
],
"metadata": {
"id": "-vDtFjaMtiSe"
}
},
{
"cell_type": "code",
"source": [
"from numpy.random import randint\n",
"# span\n",
"vectors = []\n",
"i = numpy.array((1,0))\n",
"j = numpy.array((0,1))\n",
"\n",
"for _ in range(30):\n",
" m = randint(-10,10)\n",
" n = randint(-10,10)\n",
" vectors.append(m*i + n*j)\n",
" \n",
"plot_vector(vectors)\n",
"pyplot.title(\"Thirty random vectors, created from the basis vectors\");\n",
"\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 392
},
"id": "p-b140xisEGR",
"outputId": "a96882b4-4ebe-46b7-acf2-9ca410f72942"
},
"execution_count": 13,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 400x400 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"**Matrices**"
],
"metadata": {
"id": "p_hxeTdByMof"
}
},
{
"cell_type": "markdown",
"source": [
"What's a matrix?\n",
"\n",
"In many books, they'll tell you that a matrix is a \"table\" of numbers, ordered in rows and columns. Maybe that's enough for some people, but you will get a kick out of seeing what a matrix does!\n",
"\n",
"Let's remember our friendly vectors from above:\n",
"a = $\\begin{bmatrix} \n",
"-2 & 1\n",
"\\end{bmatrix}$\n",
"b = $\\begin{bmatrix} 1 & 3\\end{bmatrix}$\n",
"\n",
"Our little experiment with 30 random linear combinations of and helped us visualize that they can span the 2D space, and nothing is stopping us from using them as a basis if we so desire.\n"
],
"metadata": {
"id": "RJq3zseayX1y"
}
},
{
"cell_type": "markdown",
"source": [
"**Matrices with NumPy**"
],
"metadata": {
"id": "bIO5P9ml-Jgi"
}
},
{
"cell_type": "markdown",
"source": [
"\n",
"Let's play around with this a bit more.\n",
"\n",
"We can define a NumPy array to represent the matrix\n",
",A as follows:"
],
"metadata": {
"id": "cx22lNCF-WjM"
}
},
{
"cell_type": "code",
"source": [
"A = [[-2,1], [1,-3]]\n",
"A = numpy.array(A)\n",
"print(A)\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "CEj7J5QVu0-k",
"outputId": "2a0fb630-d825-4734-de24-301ab378d5f2"
},
"execution_count": 14,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[[-2 1]\n",
" [ 1 -3]]\n"
]
}
]
},
{
"cell_type": "code",
"source": [
"A.dot(c)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "1uuhl_04-hLV",
"outputId": "ec0fe92d-2f66-42e1-c09e-b622c8a49d46"
},
"execution_count": 15,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([-3, -1])"
]
},
"metadata": {},
"execution_count": 15
}
]
},
{
"cell_type": "code",
"source": [
"A.dot(i)\n",
"#A.dot(j)\n",
"\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "RAHF0Ppq-lPe",
"outputId": "5b462ef7-4c37-4b05-8df6-d327dd8ff232"
},
"execution_count": 18,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([-2, 1])"
]
},
"metadata": {},
"execution_count": 18
}
]
},
{
"cell_type": "code",
"source": [
"A.dot(j)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "DjkLW42j-vQb",
"outputId": "06044282-a64c-419e-be19-9e461894150a"
},
"execution_count": 19,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([ 1, -3])"
]
},
"metadata": {},
"execution_count": 19
}
]
},
{
"cell_type": "markdown",
"source": [
" The matrix A when multiplied by the vector **i** gives the vector and when multiplied by the vector **j** gives the vector **b**.\n",
"\n",
"Remember that we used the components of **c**\n",
"in a linear combination of **a** and **b** to get **c'**: 2**a**+1**b**. What we find is that the linear transformation represented by the matrix , transforms the vector to the linear combination of the transformed **i** and **j**.\n",
"\n",
"Since all vectors are a linear combination of the basis vectors,**i** and **j** , scaled by the vector components, they are all transformed to a linear combination of **a** and **b** with the same scalars.\n",
"\n",
"Let's try to visualize that. Our helpful custom function **plot_linear_transformation()** draws a grid of points on the plane, then applies the linear transformation described by the matrix argument, and plots the transformed grid. This is what **A** does to the grid:"
],
"metadata": {
"id": "Q7cw3WId_B-A"
}
},
{
"cell_type": "code",
"source": [
"plot_linear_transformation(A)\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 401
},
"id": "ThiduAvP-2F1",
"outputId": "21e4bd12-7bdc-4846-e542-d51a1e6266fb"
},
"execution_count": 20,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 800x400 with 2 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"**Some special transformations**"
],
"metadata": {
"id": "Wjjq2lrcFEm7"
}
},
{
"cell_type": "markdown",
"source": [
"Rotation,Shear,Scaling here : [link text](https://people.math.harvard.edu/~knill/teaching/math19b_2011/handouts/lecture08.pdf)"
],
"metadata": {
"id": "tQylgurBF3wC"
}
},
{
"cell_type": "code",
"source": [
"rotation = numpy.array([[0,-1], [1,0]])\n",
"print(rotation)\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "o0_Y74fbEubd",
"outputId": "44f2527a-960a-4152-c37c-8899c2cdc833"
},
"execution_count": 22,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[[ 0 -1]\n",
" [ 1 0]]\n"
]
}
]
},
{
"cell_type": "code",
"source": [
"shear = numpy.array([[1,1], [0,1]])\n",
"print(shear)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "UUPMMWSrGJoR",
"outputId": "c934cf0e-65e0-4a1b-83fd-fda73f27a416"
},
"execution_count": 23,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[[1 1]\n",
" [0 1]]\n"
]
}
]
},
{
"cell_type": "code",
"source": [
"plot_linear_transformation(rotation)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 401
},
"id": "S4qgCWStGO5G",
"outputId": "fa5d96fa-bde4-4651-ecff-27f23e9ba3dc"
},
"execution_count": 24,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 800x400 with 2 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"source": [
"plot_linear_transformation(shear)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 401
},
"id": "Rbo9e55gGRd9",
"outputId": "06636fbf-ee7f-4519-ab36-78f8cecc91ec"
},
"execution_count": 25,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 800x400 with 2 Axes>"
],
"image/png": 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pvbS0FCUlJQ6rnSDuZz777DN8+OGH2L9/f8X/Dh8+DA8Pjzs6Mqv7fYyKirplDD59+jTmzZv3r2qrfIyysrI7Nj/nz59HYWEhBg0aVPFztR0rAeDLL7+Ev78/3nnnHRw5cgTPPfccduzYcdvn2/8OaLXaiscuX74MZ2dndOjQodbHvxs1eZ+Vz5vVaoVGo7lt7dWN823btr1lBpAQBtSICgij0YgPPvgArVq1Qtu2bQEA06dPxwcffIArV64AAORyOebOnYuoqKjbvs6IESOgUqnw+eefA7BNN2zduhVTpkyp8stcHYMHD0aTJk2wePHiisfWrFlToTipjpCQEAC25ujrr7/GrFmz7niMDh064OTJk5DL5QBsVy8KCgru+DM3c+jQISxYsKBiEDeZTHB3d0ezZs1u+zP2c2n3Cf7xxx84d+6cw9RONXmfISEhKC0tBQAMHDgQ58+fv+V1WrRogVdeeQWrV6+uaFRXrlyJ9u3b18kVDYJ4kLBYLDhw4AAefvjhKo/7+/vjqaeewueff37b5q+638fJkycjKysLv/32GwDbWDNz5sy7hvrbUfkYPXv2RFlZ2W2fGxkZCU9PT+zbt6/ivX333Xe1PubkyZNx+vTpiq9NJtMdp+YHDx6Mxo0bY926dRXPX7t2Ld58880q0/J1RU3eZ1BQUMXypszMzIolbTczefJkZGRk4ODBgwBsG4T8myUZRD3CaW1qg+bw4cMVug77zUoJCQmsQ4cO7LnnnmPZ2dlVnr9y5UrWvn17lpCQwJKSktivv/7KGLtV39S/f/8qx6isb5o5c2aVG5Xatm3L3N3dWVJSUpUF5Iz9o+2Iiopiffr0YW+//TYrKyu743saPHgw69q1K4uPj2fnz59nixcvrqJHsd9ZzphtYfhLL73EmjVrxp588kk2ZswYJpFIWNu2bdmHH35Ypb5HH32UMcZY//79K97nhx9+yC5cuMAGDhzIYmNjWXJyMuvZs2fFXao365vWrFlTcezly5ezqKioCrXHvn37Kr730ksvVWhMKt+cUFBQUPHv1aVLF7Zv374qqpeJEyfeorEqKCi46/tkjLFz586xqKgolpCQwF599dUq+qa2bdtWaEdu1jc98cQTFYv2q6tvzZo1Fed/8ODBd/y3I4gHBYVCwWJjY1lQUBAbMWJEle9t376dtWzZkgFgcXFxTCQSVYxP9ru3b/59tPPLL7+w6OjoCoXTqlWrKr43evToKton+53rtyMlJYW1bduW9erVi02ZMuWW39/p06dXef7XX3/N2rRpw2JjY9mzzz7LXn/9debu7s4eeughxhirMl588skn7PPPP68YP+3PWbNmDevRowdLSkpisbGx7PXXX6+o82Z9k0KhYIzZ/g7069evQt/03nvvVWj8fv755yrjXeWbJiuP/a+++uot6qUzZ85U0VjZtXx3e5+MMTZp0iTWsWNH1rNnT5aamlqhb7L/LbO/p59++on16NGDxcbGsqioqCr6ppvrUygUVc7/b7/9dsd/P6LuETFGiyIIgiAIgiCI+oem5gmCIAiCIAguUCNKEARBEARBcIEaUYIgCIIgCIIL1IgSBEEQBEEQXKBGlCAIgiAIguACNaIEQRAEQRAEF6gRJQiCIAiCILhAjShBEARBEATBBWpECYIgCIIgCC5QI0oQBEEQBEFwgRpRos7YsGEDRCIR9u/fz7sUgiCI+xIaR4mGBjWiRJ1w48YNLF++nHcZBEEQ9y00jhINEWpEiTph5MiRmDZtGu8yCIIg7ltoHCUaItSIEvfM3r174erqin79+vEuhSAI4r6ExlGioeLCuwDi/kaj0WD69On49ddfYTAY/tVrXLt2rUbPa9Kkyb96fYIgCCFD4yjRkKFGlLgnZs6ciXfffRdhYWHIy8v7V6/RtGnTGj2PMfavXp8gCELI0DhKNGREjNOn8stvd6C5nys8nPmuDtBbrMhVmQRRi9DquVstWq0WV65cQbt2bQGIYDQacOrUKbRp0xa+vr41Ps7Ro5l3f5KLOxZt+gqfbJwl+PPSkOsRUi05Bnc89dggrjU4mgO/foAgD2euNWjNVlwpM8HH1QlNvF251mK2MuSpTRCJgEhfVziLRNxqYQCulpmgM1sR4Xv734d6G0d9GgE+gVixcB0+e392zd+IA1CbrLhWZkKguzMkXnyvhxnLPzNuTiI083GBE8fPjJUx5JeZYbYyRPi6ws2JXy0AUKA1Q2GwYOCzbzr0ONw+AbvMMVjWNhQt/PgOXDkqE3alFwqiFqHVc7daNm3ahN//SIWP93EAgNFowIkTJ9CuXTv4+vphwYL5aNas2V2P4x3e/a7PyddYcH3Zl/Bo+5jgz0tDrkdItZiUZq7Hrw9iej3J9fj5ahOWHZGjha8rpkeHwJVj9igzWTErQw6NkxWLeoZybdAZA9acLMFhgw4zooPRoZH7bZ9bH+Po71Iz9lw1YWBTV5gsG9Ci+4Bav6e64mypAUsyi9AjxBPjujQCx74PJXoLpmfI4eEmwvzYEPhw/ACbrMDiLDkumo2YFxOK5pzHz08vKvG1vAwjOwU6/FjcGlEZfOHsFQhP39v/gtYHzmYDZNAJohah1XO3WsZNmoFxk2ZUfJ2Xl4fmzZtj98dfIDk5ucbHifQNuutz9KUGmOF0X5yXhlyPkGrxMP+7tXb3E541+N1xFDc0JozOKkCwdyPMSgyDN8c/4nqzFVMypcg1eGNH3zA08XPjVgtjDMuPl+BbmQuW9GyJmCbed3y+o8fRn/PLsEUqx9CO/ni7cyOscXLm9rnJVhgwLqsMHYJCMKmXBG7O/LpQldGCsekF0MAXu/o0RgjHK7NWxjD/sBz7Sz2wITECHUI8udUCAJ9mK7EpR4SxnSPQv42/w49Ha0QJgiCIWlGit+C9A1J4uYiwPkHCtQk1WxmmHCrEBYURm/tI0JxjEwoAO84p8MVlFaZ1D8JDd2lCHc1BqRZzMuV4OtKnXq5s3YnrZSaMSJGhma8LVvYSc21C9WYrxqTJUKy3YEdyGEI5NqG24FKMP65rsKRnKKI5N6E/5Zdh1ckSvNbWH/+phyYUIH0TUUeMGTMGL7/88i3/TRDEg0WZyYoRKVLoLQwbEyVoxHEK3MoY5mcW4ZBMh+XxoYgK8uBWCwB8eVmFzWcVeK9jIJ5v4Vfrn6/LcfRksR4T0wvRW+KF6d2DIeI4B16sN+O9FCl8XJ2wtrcEXpyDy+RDhbioMGJdggSRnIPLtnMK7LmsxtRu/INLWoEWc8uDy/Co+gsudEWUqBPWrFnDuwSCIByM0cIw/qAMBVoztiWHoTHHm5MYY1h7sgQ/XSnDgtgQxEu8uNUCAH9c02DpsWK80soPr7f7d1eS6moczVEZMSZVhg6B7lgcFwJnjje9lJmsGJkig9HCsKMv/+AyL7MIh2U6rE2QoOMd1u7WB3suq7D1rALDowLx3L8ILnXJyWI9Jh0qREJY/QcXakQJgiCIu2JlDNMPF+JUsQHv95GglT/fK0kfZSvxyUUVJnYNQr9mPlxryZDpMONwIfo19cbYLo24Xn0s0JgwIkUKsZcLVvUKhTtHe4XRwjAuzRZctgsguKw5WYKfr5RhUc8Q9BTznQL//WoZlh0rxuDWfnitbf1Mgd+Oy0ojRqfK0DHQHYt61n9woUaUIAiCuCOMMSzKKsbfBVqsiBejazDfKfDvc9VYd6oU/20fgJda8b2SdLbEgAnpMsSKPTG7RwhX/U+pwYLhKTK4iERYnyCGrxu/q48WK8O0w4U4U2rA+4kStOQcXD64oMSnF1WY3C0IjzblG1wOy3SYmSFH/2beGNNZGMElzMsFq3qLuQQXakQJgiCIO7LpTCm+zVVjTo9g9GnMdwr87xsaLMgqwvPNffFOhwCuteSrTRiVKkVLPzcsjQuFK8cbcLQmK0anylBmsmJH3zAEe/K9AWdRVhEOFGixqpcYXTgHl29z1dhwuhRvdwjAoJYCCC4HhRVc3JxFWJ8o5qavokaUIAiCuC2fZiux87wSYzo3wpORNResO4IsuQ5TD8nRt7E3pnQP4nolqVBrxvAUKRp5OGNtghieLnynwCeky5CvNmFrkgRNffg6KDeeLsV3eWWYFxOChDC+wWX/dQ0WZRVhUEtfvNU+gGsteSojRqZK0TrAFlxcOK7d1ZqsGJUqRZnJip19wxDkwa8dpEaUIAiCqJafy1UuQ9v4Y0g9qVxuR7bCgLFphegS5I75sXyvJKmMFoxIlYIxhg0JYfDjOAVuZQyzjshxvMiA9YlitA3kewPOJ9lK7L6gxLjOjfB4BN8p8Cy5DtMOy/FwuDcmduUfXEakyhDk4Yw1vYURXK6ozdiWLEETzsGFGlGCIAjiFshBWT1CdFD+eV2DpXHCcFCuLndQDuYcXC6U2oJL12B3zI3hG1yUBltwAYANCRLuwWVmhi24bEgUo00A/01ZqBElCIIgqkAOyuoxWxkmlTsoNyeFCcZBOSM6GH3D+TooUwtsweWZenZQVsfVMhNGpsoQ4euKFfF8g4uuPLiU6C3Y0bcx9+Cy9Fgx/rqhwfL4UHTnHFzsUCNKEARBVEAOyuqxOygzBOKg/OKSzUE5IioQzzbnu3b3RJEekw8Vok+YF6ZxDi5FOjNGpEjh6+qEtQli7sFl8qFCXFYZsblPGCJ8+U6Bbz2rwFc5asyKDkZSY77BpTLUiBIEQRAAyEF5O4TmoPztahmWH7c5KIcJwEE5Js3uoAzlGlzURgtGpcpgsjJsTpYg0J1vcJmbKUeGTId1CRJ0EEBw2XZOgZFRgXiac3C5GWpECYIgCHJQ3gGhOShnZcgxoJkPdwfljZsclDynwA0WK8YdLIRUa8b2vmEI4xxcVp8owS9XNFjUMwSxAgku/2nth6Gcg0t1UCNKEATRwCEH5e0RooOyp9gTs3oEc70Bp0RvwYgUGdw5OygBW3CZekiOs6UGbOojQQvOa3d3nVfis0sqTBFAcDkktQWXx5v5YDTn4HI7qBElCIJowJCD8vb8RQ7KatGarBidJoXGbMXOZL4OSsYYFmYVIU2qxereYnQO4htcvslR4f0zpXinQwAGcg4up4v1mJguQ5zYEzM5B5c7QY0oQRBEA4UclLfnqFyH6QJyUA5PkVY4KD04OyjHH/zHQRnOObhsOF2K7/PKMD8mBL0kfIPLn9c0WHysGC+29MN/OQeXXJURo9NkaB3ghiWcg8vdoEaUIAiiAcIYw7Jj5KCsDpuDUiYYB+XwFClEIpFgHJQnioXhoPw4W4kPLigxvksjDOAcXDILdZieIccj4d6Y0JXvFLhMazMHBAsguNQEakQJgiAaINvOKfBlDjkob8buoIz0dROMg7LUYMFOATgol2QJx0H5Q54aa06W4I12/nilNd/gcr7UgHEHZege7CGI4DIiRQonkQgbEvkGl5pCjShBEEQDgxyU1VOkM2P4AWE4KE2Wqg7KZpwdlFvOKvB1rjAclCk3tJh3tAjPNvfF/3XkG1yuqG3BpbmvG5bHh8KVY3Cxrd2VQWG0YkdyGEI43nRYG+6PKgmCIIg6gRyU1aM2WjAyVQYzY9iSKAwH5ZFCPdb2FnN3UP7vkgrbzykwqhN/B+Xx8uCSFOaFqd34rt2Vl8vz/QQUXHJURmxJ4h9cagM1ogRBEA0Eu8qFHJRVsTsoZQJxUK46UYJfr2qwOC6Uu4Py1yu24DKktT9e5bx295LSiLFpMnQKcsdCzsFFVSm4bO0ThgDOwWVOphyZcj3WJYjRnvNNh7WFGlGCIIgGwJkSAyamk4PyZuwOynOlBrwvEAfl55dUmNotCI804TsFni7VYtYROZ5o5oNRnQMFEVwae7tgVS++wUVvtmJsmgyF5cFFwnnt7srjJfjtqgZL4kIREyqM/eNrAzWiBEEQDzh5KiNGkYPyFoTmoPy63EH5bocAvCAIB2Uhekm8uDsoS/Q2c4CHswjrEyTw5rx//NTDclxQGAUhz995Xon/XVZhWvcgPMw5uPxbqBElCIJ4gJGRg/K2rD8lLAflknIH5ZsCcFCOSpWhbYAbFvcM4RpcNCYrRqVKoTUz7EwOQyMPflPgjDEsOFqEg+XBpZMAgsumM6X4v46BeL4F3+ByL1AjShAE8YBiV7mQg/JWPrqgxIfZ5KC8GXtwCfF0xmqBBJdrGjO2JYVxDy7rTpXih/wyLIjlH1z2XdNgcVYxXmrphzfaCW//+NpAjShBEMQDiM5sU7mQg/JWfshTY+0pYTkoo0OE4aAcniKFiwAclFbGMCOjECeLDdiYKEHrAL5T4B9eUOCjbCUmdGmE/s34BpcjhTrMyJDjsabeGM85uNQF1IgSBEE8YJgsDJPSbSoXITgotwrQQfmcwByUy+KE4aBUCsBBaQ8u+29osSJejG4hfKfAv89VY92pUrzZLgAvcw4u50oNGH9Qhh4hHpjTg29wqSuoESUIgniAqKxyEYqDcpvAHJTJjb0wtbswHJT+bsJwUE4qd1BuFYCDctOZUnydq8bsHsHo05jvFPiBG1osyCrC88198W7HAK61XFGbMCpVhhZ+bljGWZ5fl1AjShAE8YBQWeVCDsqqXFTY5PmdgtyxIDaU65UkldG2dtfMGLYm8ndQzj4ix9FyB2U7zg7Kzy4qsfO8EqM6BeKpSL7BJUuuw5Ty4DJFAMFleIoUAW5OWNtbDE+B7x9fG6gRJQiCeEDYVa5ymUIOyirc0JgwMlWKcAE5KOU6iyAclCuOl+D3axosFYCD8uf8Mqw8UYJX2/hjaNsArrVkKwwYd7AQnQUUXKyMYUNiGPw5BhdHQI0ocU9899132Lx5M4xGIwwGA7RaLSZOnIhXXnmFd2kE0aCwOyjf6RCAgQJwUE5KL0S82FMwDkpPF+E6KHmNozvPK/FFuYPyIc7B5aBUizmZcjwV4YNRnfiu3b1eZlu728TbBSsFElyK9BbsSA6DmGNwcRQP3jsi6pVNmzZh8ODBGDp0KABg7969eOaZZ9CxY0d07tyZc3UE0TCo7KD8r0AclG0C3LCEszxfY7JiZLmDcldfvg5KayUH5ZqbHJQ8xtGvLtsclO8JwEF5sjy49JJ4YUZ0MNer58V62xS4l4sI6wQQXKYcKkS2wojNSWGI5CzPdxQPziIDggsLFy7E4MGDK75OTk4GYww5OTkcqyKIhsMRclBWi91BeV1jxoYECRpz3D8esMnzf8gvw7yYEMTf5KCs73F0X3lwebmVH17n7KDMURkxJlWGduXyfJ77x5eZrBiZIoPewrAxUcI9uMzLLMIhmQ7L48XoyPmmQ0dCV0SJeyI6Orriv00mE1asWIEOHTrgkUceqfFrXLt27a7Pkaot/6o+gniQsatchOSgdCYH5S1UdlD2q8ZBWV/jKADozKzCQTmuC9/gItXazAGhXi5YJYDgMi5NhgKtGduSw7gGF8YY1p4swc9XbPL8OMn9t398beDWiIqhhkVbCp0L35Rq0ZoEU4vQ6qlNLfPnz8fevXvRqlUr/PjdHjgzA3RqQ42OkxDX/e5PCm4CF1jvu/PS0OrRa8ywWszQaxTQufDNuXqNGQgUc63B0cxPuYhu3i6YE+UDs7YEZk516M0Mc48Wwc1gxrLYEPiYldCp+dTCmM1beu6GBku7BqGdhwY6tYZPMQD+uq7F/06XYngLXzwjMUOnLr7tcx0/jjZFic6IwY0MmNLOF4aykpq+jTpHbbRiZoYcYjAs6BYCV4MCupq91TrHyoCVx4tRWKLHqh4hCHdSc/v8AsB3uWr8cVGFae0D0Cew5p8BR3Cq2IDYyMYOPYaIMcYceoTb8OW3O9DczxUeznxXB+gtVuSqTIKoRWj11LYWxhhu3LiBkpJitGvXHq6uNWuKjh7NvPuTXNwxbflH+O6DJffdeWlI9eQY3DHlenMsCc9FC3d+g6e9lqceG8S1Bkfz/d6diPR1hTPHq1oMwNUyE3RmKyJ8+X8G5TozivQWNPZ2gT/Hq7KAbar3apkJge7ONb473mHjqLMrEBSOGdOW4ccPl3K9em5lDPllZpitDBG+rnDjOB0PAAVaMxQGC5r6uMKH45pQAFAYLSjQmBHs6YwQD85h3mJFvtqE559506HH4fYud5ljsKxtKFr48b2Ck6MyYVd6oSBqEVo9/6aWFt0ZHnroITz+uBMmTpxYo5/xDr97ks/XWKBc9iU82j52X56XhlKPSWmGe6kKTTv0QQt/voOoScnr+mD90S3uSQRzXMfGGLDmZAkOG3SYER3MXZ7/Y34Zdp1XYmgbf3RrzncbxrOlBizOLEJ0iAfGdwlCbfq+uh5HS41WLD9vgKuTCJ6em9Aq+vGaF1PHmKzA4iw5LpqNmBvDf8z69KISX8vLMLJTIDpzludnFOqw4ngJHmnijcfbB9TqM1PX3NCYsSCjEBJvVzzv4GNx+0shgy+cvQLh6ct34HI2GyCDThC1CK2emtRiNBrh5lZ1/ZW3fwgOHz0FT9+gGh0nsgbP05caYIbTfXNeGmo9HmYDnJy18PAOEEQtDzpNQ0K5HZsxhuXHS/CN1AVL41oihrP+5+f8Miw5r8LQNk3wUudGXGvJVhgw/lgZ2geFYHIvyV31P44cR1VGCybtL4DG3YqdfRuj7zTnGr9mXWNlDPMPy7G/1APrEyLQkbO39NNsJTbliDCmcwT6c95wIUuuw9QTaiQ2lmBkLN/13oVaM0ZnFcDLIxBz+4Q5/Hj85xWJ+5ru3W9N4QUFBWjc2LFrSgiC4IvdQTlVYA7KkQJyUK6ooYPSUeOo3mzFmDQZivUWbEyUcHVQ2uX5f1zXYGFsCHpwbkJ/yi/DqpMlGNrGH0M4N6HZCgPGphWia7A75nNuQlVGC0akSgEAGxLq56ZDakSJe+Ls2bP48ccfK77++OOPceHCBQwbNoxjVQRBOBIhOShPlTsoewvAQWmX53u7ONXKQemIcdTuoLyoMGJdgoS7g3L7OYUtuHTjH1zSCrSYmynH05H8g8u1MhNGpMjQzNcFK+L5y/PHpMlQUh5cQuspuJC+ibgn1q5di4ULF2Lx4sWwWq0QiUT4/vvvkZCQwLs0giAcgNAclKPtDso4/g7KESlS6C0MO/vWzkFZ1+NoZQfl2gQJdwfll5dV2HJWgfc6BuI5IcjzD9mCy/TuwpDn+7jagosXZ3n+pPLgsiUpDBG+9bd2lxpR4p4YOXIkRo4cybsMgiDqgQyZTpAOytW9xXDneLf+vToo63IcZYxhTbmDcmHPEPQU850C//1qGZYeK8YrAggul5W24NIh0F0QwWVkigxGC8OOvhIEctw/3h5cMsqDS33fdEiNKEEQBHFXzpUaMCFdhh4hHpjTg+86NoXBguEHpHARibAhQQxfjpomi5Vh2uFCnCk14P1ECVr585bnK/HpRRUmdQ3CY035mgMyZDrMzJCjfzNvjOUcXAo0JoxIkSLMywWreoUKIrhIBSLPtweXRZyCCzWiBEEQxB25ojZhVKoMLfzcsCw+FK4c17FpTVaMSpVBbbJiR98wBHvyvQFn8bFiHCjQYlUvMboEe9z9hxzId7lqrD9dirc7BODFVnynwM+W2Hb9ihV7Yjbn4FJqsGB4igxuziKsT+QfXKaWB5dNfSRoyTm4fFAeXKZ0C8KjnIILNaIEQRDEbSks3z8+wM0Ja3uL4cl5G8aJ6YXIUxuxLSkMTX34OijfP1OKb3PVmBsTjIQwvg7K/dc1WJhVhIEtfPFW+wCuteSpjBiVKkUrfzcsjQuFC8cpcK3JitGpMpSZrNjZNwxBHCXxjDEszCpCSoEWq3uJ0TmIb3D5NleNDeXBZWBLfsGFGlGCIAiiWuwqFytj2JAYBn/O69jmHJEjq0iPDYlitA3kewPOp9lK7DqvxNjOjfBEhC/XWrLkOkw7LMdD4d6Y1C2I6xR4odaMEakyNPJwxtoE/sFlQroM+WoTtiZJ0IRzcNl4uhTf55VhXkwIenMOLn9d12BRVhEGteQfXKgRJQiCIG6hsoNyR3KYYByUS+NCER0iDAflsLb++I+AHJTzYhqeg/J2WBnDzAw5jhcZBBFcPslWYvcFJcZ1boTHI/iu3T0q12H6YTkeCffGxK58gwtAjShBEARxE2Yrw+RylcvmpDDBOChnRAejb7hwHJQjooThoIzwdeXuoNRVclDu6Nu43hyU1cEYw9JjxfjrhgbL4kLRnXNw+TFfjdUnS/B6O38M5hxcLpQaMDZNhm7BHpjLObjYoUaUIAiCqMCucjksMAfl8KhAPNuc7xS43UGZEMbfQVmk+8dBuTZBzN1BOZmTg7I6tp5V4KscNWZGByOZc3BJLdBibmYRnon0wXsd+QaXq+W7fkX6umE555sOK0ONKEEQBAFAuA7Kwa398FpbYTgoOwa6Y1FPvg5KtdGCUak2B+VOATgo52bKkSHTYR0HB+XNfHFJhW3nFBgRFYhnOAeXE0V6TD5UiD5hXpgmhOByQApfAQSXm6FGlCAIggAgXAflmM4CclBylucbLFaMP1gIqdaM7X3DEMbZQbn6RAl+uaLBop4hiOUcXH67Woblx23BZZgAgsuYNHtwCeUeXEamymBmDFv7hHENLtVBjShBEARR4aB8qz05KCtzs4PSh+OVJJs8X17hoGzBee3u7gtKfHaJr4PSziGpDrMy5BjQzId7cLlxU3DhuXbXYLFi3MFCyMqDi4Tj2t3bIbyKCIIgiHqlsoPy7Q4BXGuxOyhbB5CDsjJ2B2VqgRare/N3UH6To8JGATgoAeB0sR4T02XoKfbErB7BXINLid6CESkyuDuLsCFRwj24TD0kx7lSA94XQHC5HdSIEgRBNGCE6qBcIwB5vt1BuS2Zv4NyQyUHZS8JXwfln9c0WHysGC+29OPuoMxVGTE6TSaI4KIxWTEqVQqN2YqdyWFo5MFvCpwxhgVHi5AmFUZwuRPUiBIEQTRQbCoXclDezM0OyjYBfG/A+ThbiQ8E4qDMLNRheobNQTmhK98pcJnWjBEpUgSVBxcP3sHloAxXy8zYlixBOOfgsv5UKfbml2G+AILL3aBGlCAIogFiV7mQg7IqQnRQrhGQg3LcQRm6C8BBqTRYMCJFCieRSBDBZUZGIU4UCyO4fHRBiQ+zlRjfpREGcA4uNYEaUYIgiAZGkc52JUlIDspLSiM29+HvoNx2zuagnCUgB+WzzX3JQVkJndmK0WkylBos2CmA4LIkqxj7b2ixIl7MPbj8kKfG2lMleKOdP15pzTe41BRqRAmCIBoQ5KC8PV9cUmHrWQVGRgXiaYE4KJPCvDCV89rdyg7KdZyDi8nCMCm9EDkqW3Bpxjm4bDmrwNe5tuDSpzHfKfADN7SYd7QIzzX3xf9xDi61gRpRgiCIBoJd5UIOyluxOyj/09oPQzk7KC9VclAuFICDckQlB2UA5+AyJ1OOTLkea3uLuQeXzy8qsf2cAqM68Q8ux4v0mHKoEMmNvTC1O//942sDNaIEQRANALvK5Sw5KG+hsoNyNDkoKzBYrBibJkOhAByUjDGsPF6C365qsCQulHtw+eVKGVacKMGQ1v54lfPa3YsKW3DpHOSOBbGhgtg/vjZQI0oQBPGAY3dQCkXl8m2uGhtPl+IdATgoz5QYMDFdhjgBOSg9BOSgPK8wCsJBueu8Ev+7rMLUbkF4uAnftbsHpVrMPiLHkxE+GNU5kHtwGZkqRbi3C1b24htc/i3UiBIEQTzgCM1BuSirCC+29MN/BeCgtMvzl5CDsgKhOSi/zlHh/TOleLdDAF4QgDx/Unohekm8MCOaf3AZniKFp4sI6xMk8BbQ/vG1gRpRgiCIBxhyUFaP3UEZLBAH5fiDMlzTmLEtKUwwDsoFsfyDy75rGizOssnz3+QcXHJURoxKlaFtgBsW9wzhHlxGpkqhNTPs6ss3uNwr1IgSBEE8oPyQRw7K6qjsoFwvEAflyWIDNiZK0DqA7xT4hxcU+DBbiQldGqF/M77B5UihDjMy5Hi0Cf/gIi0PLiGezlgtkOByvTy4NOZ402FdQI0oQRDEA0hKucqFHJRVsTsoFUYrdiSHCcpB2S2E7xT43jw11p0qxRvt/PEyZwfluVIDxh+UITqEf3BRlAcXF5Ft7a5Qgsv7ffgHl7qAGlGCIIgHjOPkoKyWyg7KLUn8HZSbz9gclLN7CMNBOf9oEZ4XgIPyitqEUakyNPd1w7I4vsFFa7JidKoMyvLgEuLJN7gsrhRcugYLd//42kCNKEEQxAPEJaURY9NkiGpEDsrKVHZQrksQo30gfwfljvM2B+VTkXwdlMfk/zgop3B2UMp1ZgxPkcLfjf+uXyYLw6RDhchVG7FVAMFl05lSfJOrxhwBBJe6hBpRgiCIBwRyUFbPzQ7KmFBhOChfbeOPoW0DuNZyUWHE2IPCcFCqjLYpcAtj2JDIP7jMPiLH0fLg0o5zcPnsohI7zysxulMjPMk5uNQ11IgS98wXX3yB7du3w2KxQKVSITIyEsuXL0dkZCTv0giiwWBXuQjNQSkEeb7dQTmtu8AclJ3+mQLnMY7e0JgwIlWKJgJwUOrNtuAi11mwQwDBZcXxEvxxXYMlPfkHl5/zy7DyRAmGtvHHq5x3/XIE96d0ihAUQ4YMwfjx47Fv3z4cPnwYnp6e6N+/PwwGA+/SCKJBYHdQas0MGxMlgnFQLosPRSeBOCj/r2Mgnm8hHAflzOjgKlPg9T2O2oOLl4sI6zg7KM1WhimHCnFBYcS6BDGacw4uO84p8MVl265fDwkguMzJlOPpSB+M7HT/7B9fG6gRJe6ZZ555Bv369QMAODk5YdSoUbhw4QKysrI4V0YQDz6VHZQbEiSCcVDOFYg8f8mxYrzU0g9vtON7JcnuoGxX7qC8ee1ufY6jZeUOSp0AgouVMczPLEK6TIfl8aGI4hxcvryswuazCrwngOBysjy49JZ4YXr34Ptq//jaQFPzxD2zZ8+eKl97eNgGEroiShCOhRyUt+dIuTz/0SbeGC8QB2Vo+drd6hyU9TWOMgDjD8pwQ2PGtmS+DkrGGNaeLMGPV8qwMDYE8ZyDyx/XNFh6rBgvt/LD6wIILmPswSXu1uDyIEGNKFHnpKeno3Hjxujdu3eNnn/t2rW7PkeqttxrWQTxwEEOyuqxOyh7hHhgTg/hOCjXJ4hr7KB0xDhqZQyFOjNOlTsoW/nzDS4fZSvxyUUVJnYNQj/OwSVDpsOMw4Xo19Qb47oII7iIvVywurcY7s585fmOXjvMrREVQw2LthQ6F77TSBatSTC1CK2ef1OL0WjCx7u3YfOGVTDrVTDr7/4zCXHd7/6k4CZwgfW+PS+ORK8xw2oxQ69RQOfCN1sKrRYEirnW4GjScm9gdsdAxPjqoFPruNWRWajH1uPFGNLEG681Y9Cpi7nVUqAxY36GHN28XTAnygdmbQnMnGrRmxnmZBbBzWDGstgQ+JiV0Knv/nMOG0cTX4LRbMGyLq5o666BTq25+884iD+vafG/M6UY3sIXT4tNXD8zl5UmLMssxCPB7pjczg+GshJutaiNVszMkEMMhoXdQuBiUEDHaXLRYmWYeUyD1ckRDj2OiDHGHHqE2/DltzvQ3M8VHhw7fQDQW6zIVZkEUYvQ6vk3teTl5cLNzQ2NG4fX+DhHj2be/Uku7pi2/CN898GS+/K8OJIcgzumXG+OJeG5aOHOdzmE0Gp56rFBXGtwNAd+/QBBnPeY1pqtuFJmgo+rE5pw3mrQbGXIU5vgJAIifF3hzPGqFoNtRymd2YoI39qNFQ4ZR30aAT6BmD11CX74cGmNX9cRqE1WXCszIdDdmevd8QBgLP/MuDmJ0MzHhevVcytjyC8zw2xliPB1hRvH6XjGgC1FEuxXB+DU6z0ceixun4Bd5hgsaxuKFn58B64clQm70gsFUYvQ6qltLatWrUJZWRlmzZpVq+N4h989yedrLFAu+xIebR+7786LozEpzXAvVaFphz5o4c93UBdaLQ86Mb2e5Hr8fLUJy47I0cLXFdOjQ8DxxmuUmayYlSGHxsmKRT1DuTbojAFrTpbgsEGHGdHB6NCo5g5KR4yjv0vN2HPVhIFNXeHhuQEtug+o1WvXJWdLDViSWYToEA+M7xIEnvfflOgtmJYhh4erCAtiQ+DjxlGebwUWZ8lx0WzEvJhQNOf8t2XzBS3SZHrMjXO8NYDbXwoZfOHsFQhPX76SWGezATLoBFGL0OqpTS1LlizB2ew8fPTRR3BycsLRo0cBANHR0Xc9TqRv0F2foy81wAyn++681AceZgOcnLXw8A7gXo/QannQ8azB746juKExYXRWAUK8G2FWYhhX/Y/ebMWUTCnyjN7YnhyGJhz1P4wxLD9egm9lLljSsyViaqH/ccQ4+nN+GbZI5Rja0R9vd26ENU7O3D432QoDxmWVoUNQCCb3knD1lqqMFoxNL4AGvtiZ1BghHK/MWhnD/MNy/F3qgfWJEegQwtdb+mm2Ep/kmTG+Wyieb+P49d50sxJxz2zevBkff/wxtm/fXqEa+eGHHxAZGVmjAZQgiPsLIToosxVGbE4KE4yDcnr32jkoHTGOCslBeb3MhBEpMjTzFYY8f0yaDMV6C3Ykh0EsEHn+0rhQRHNuQn/KL8OqkyV4ra0//lMPTShAjShxj6jVagwfPhxWqxXx8fFVvrdr1y5OVREE4SgqOyh39g0ThIPykEyHNb0l6FiLKXBHUNlB+VwtHJSOGEdPFusxUSAOymK9Ge+lSOHj6oS1vSVc9483W237x18sDy6RnIPLtvLgMiM6GH3D+crz0wq0mFseXIZH1V9woUaUuCd8fX1hsZBaiSAaAnZ5vpAclD9dKcOC2BDESfheSbI7KF/5Fw7Kuh5H7Q7KDoHu3B2UZSYrRqbIYLAw7OzLX54/L7MIGTId1ibwDy57Lquw9awCw6MC8WxzvvvHnyzWY9KhQiSE1X9woUaUIAiCuCtWxjD9cCE5KKuhsoNyLGcHZYHGVOGgXNUrlLuDclyaDAVaM7YLILisOVmCn6+UYWHPEPQU8w0uv18tw7JjxRjc2g+vcd4//rLSiNGpMnQMdMeianb9cjTUiBIEQRB3hDGGRVnF+LtAi5XxYnQN5ivP/z7XJs//b/sAvNSK7zaMZ0sMmJAuQ6zYE7M5y/NLDRYMT5HB1ckmz/etoTzfEVisDNMOF+JMqQHvJ0rQknNw+eCCEp9eVGFS1yA81pRvcDks02FmhhwDmvlgTGdhBJew8l2/eAQXakQJgiCIO7LpTCm+zVVjbkwwEhvz3Ybx7xsaLMgqwgstfPFOhwCuteSrTRiVKkVLPzcsjQuFK8cbcLQmK0anylBmsmJn3zAEe/K9AWdRVhEOFGixqpcYXTgHl29z1dhwuhRvdwjAi0IILgdtwWVWj2BBBBc3ZxHWJ4rhw2ntLjWiBEEQxG35NFuJneeVGNO5EZ6I4LuOLUuuw9RDcvRt7I3J3YK4Xkkq1JoxPEWKRh7OWJsghmc1+8fXF0YLw4R0GfLVJmxNkqCJD18H5cbTpfgurwxzY4KREMY3uPx1XYNFWUUY2MIXb7UP4FpLnsqIkalStA6wBRcXjmt3tSYrRqVKK4JLkAe/dpAaUYIgCKJafi5XuQxt448h9aRyuR3ZCgPGphWiS5A75sfynQJXGS0YkSoFYwwbEsJqvH+8I7AyhllH5DheZMD6RDHaBvK9AeeTbCV2X1BirACCy1G5DtMPy/FQuDcmCSC4jEiVIcjDGWt6CyO4XFGbsS2Zf3ChRpQgCIK4BXJQVs/NDspQzg7K5ceL8ed1DZYJxEG5up4dlLfjQqkBY9Nk6BrsjnkxfIOL0mALLgCwIUHCPbjMzLAFlw2JYrQJ4L8pCzWiBEEQRBWE5qAcXu6gXJfA30E5udxBuUUgDso9l9WYGR2MZM4OytSCf4JLfTooq+NqmQkjU2WI9HXDini+wUVXHlxK9Bbs6NuYe3BZeqwYf93QYHl8KLpzDi52qBElCIIgKhCqg3JHXwkC3fk7KA+XOyhrs3+8I7A7KEdEBeIZzg7KE0V6TD5UiEQODsqbKdKZMfxAuTw/QSyI4HJZZcTmPmGI8OU7Bb71rAJf5agxKzoYSY35BpfKUCNKEARBACAH5e2o7KBcJAAH5W+VHJTDBOCgHJPGz0FZGbXRgpGpMpisDFuS+AeXuZlyZMh0WCeA4PLFJRW2nVNgZFQgnuYcXG6GGlGCIAhCsA7KTX2E46Cc3C0IjwrAQTlLIA7KGwJwUNoxWKwYd7AQMq0Z2/uGIYxzcFl9ogS/XNFgcVwoYgUQXJYfL8Z/WvthKOfgUh3UiBIEQTRwhOqgXN1LjM5BwnFQDmopDAdlTwE4KEv0FowQgIMSsAWXqYfkOFseXFpwXru767wSn11SYUq3IDzShO8U+CGpLbg83swHozkHl9tBjShBEEQDRqgOynkxIegtEAfloJbkoKyM1mTF6DRhOCgZY1iYVYQ0qRare/MPLt/kqPD+mVK80yEAAzkHl9PFekxMlyFO7ImZnIPLnaBGlCAIooEiVAfluM6N8HgE3ylwu4Py4XBvTOzK30E5PEVa4aD04OygHH9QOA7K9adK8X15cOkl4Rtc/rymweJjxXixpR/+yzm45KqMGJ0mQ+sANyzhHFzuBjWiBEEQDRDGGJYdszkolwrMQTlYQA7KuQJwUA5PkUIkEgnGQXmiWBgOyo8uKPFhtjCCS2ahDtMz5Hgk3BsTuvKdApdpzRiRIkWwAIJLTaBGlCAIogGy7ZwCX+aoMSM6GH0F4qB8hhyUVbA7KEsNFuwUgINySZZwHJQ/5Kmx9lQJXm/HP7icLzVg3EEZugd7CCK4jEiRwkkkwoZEvsGlplAjShAE0cD44tI/DspnBeKg7BPmhWkCcVD6CsBBabJUdVA24+yg3HJWga9zheGgPHBDi3lHi/Bsc1+815FvcLmitgWX5r5uWB4fCleOwcW2dlcGhdGKHclhCOF402FtuD+qJAiCIOoEu8pFeA7KUEE4KM2MYUuiMByURwr1WNtbzN1B+b9LKmw/p8CoTvwdlMeL9JhyqBBJYV6Yynn/eLnONgXuJ6DgkqOy7frFO7jUBmpECYIgGgh2lYsQHZQ8p8CF5qBcdaIEv14VhoPy1yu24DKktT9e5TwFflFhCy5RjdyxkHNwUVUKLlv7hCGAc3CZkylHplyPdQlitOd802FtoUaUIAiiAXCmxICJ6cJyULoLyEF5rtSA9wXioPz8kgpTBeCgTJdqMeuIHE8088GozoHcg8vIVCkaCyC46M1WjE2TobA8uEg4r91debwEv13VYElcKGJChbF/fG2gRpQgCOIBJ09lxCiBOSg1Zit2JpODsjJ2B+W7HQLwggAclJPSCxEvAAdlid5mDvBwtt2AwzO4mK0MUw/LcUFhFIw8/3+XVZjWPQgPcw4u/xZqRAmCIB5ghOygDBeIg3K+wByUbwrAQTkqVYY2AnBQakxWjEyVQmtm2JkchkYe/KbAGWNYcLQIB8uDSyfOweXr8uDyfx0D8XwLvsHlXqBGlCAI4gGFHJS3x+6gHN+lEQaQg7ICWXlwCfF0xmqBBJfrGjO2JYVxDy7rTpXih/wyLIjlH1z2XdNgcVYxXmrphzfaCW//+NpAjShBEMQDiM5sU7mQg/JW7A7KN9r545XWwnBQRocIw0E5PEUKZwE4KK2MYUZGIU4WG7AxUYLWAXynwD+8oMBH2UpM6NII/ZvxDS5HCnWYkSHHY029MZ5zcKkLqBElCIJ4wDBZGCal21QuQnBQbhWQgzKl3EH5XHNf/J+AHJTL4oThoFQKwEFpDy77b2ixIl6MbiF8p8C/z1Vj3alSvNkuAC9zDi7nSg0Yf1CGHiEemNODb3CpK6gRJQiCeICorHIRioNym4AclJMPFSK5sRemdheGg9LfTRgOyknlDsqtAnBQbjpTiq9z1ZjdIxh9GvOdAj9wQ4sFWUV4vrkv3u0YwLWWK2oTRqXK0MLPDcs4y/PrEmpECYIgHhAqq1zIQVkVu4OyU5A7FsSGcr2SpDLatmE0M4atifwdlLOPyHG03EHZjrOD8rOLSuw8r8SoToF4KpJvcMmS6zClPLhMEUBwGZ4iRYCbE9b2FsNT4PvH1wZqRAmCIB4Q7CoXclBWxe6gDPd2wapewnBQynUW7BCAg3LF8RL8fk2DpQJwUP6cX4aVJ0rwaht/DG0bwLWWbIUB4w4WorOAgouVMWxIDIM/x+DiCB6clprgitFoxJQpU+Di4oK8vDze5RBEg+NrATooe0m8BOOg9HQRYX2CBN4CcVCuSxCj+U0OyvoeR3eeV+KLyypM7R6EhzgHl4NSLeZkyvFUhA9GdeK7dvd6mW3tbhNvF6wUSHAp0luwMVECMcfg4iioESXumby8PCQlJaGgoAAWi4V3OQTR4PjzmgZLBOigXNwzRDAOyo2JEq4OSmslB+Xy+FBE3eSgrO9x9KvLKmw6U4r3BOCgPFkpuMyIDuZ69bxYb5sC93IRYZ0AgsuUQ4XIVhixLkGCSM7yfEdBjShxz5SVleGjjz7C66+/zrsUgmhwHCEHZbVUdlBuSJCgMcf94wGbPP+H/DLMiwlBfDUOyvocR/eVB5eXW/nhdc4OyhyVEWNSZWhXHlx47h9fZrJiZIoMeoswgsu8zCIckumwPF6MjpxvOnQkD941XqLeiYqKAgBcu3btX/18TX5OqqYrrQRxM3aVCzkoqyJkB2W/2zgo62McBQCdmVU4KMd14RtcpFqbOSC0fP943sFlXJoMBVoztiWHcQ0ujDGsPVmCn6/Y5Plxkvtv//jawK0RFUMNi7YUOhe+KdWiNQmmFqHVU9taRBY9IsJDYNaroFMX1/g4CXHd7/6k4CZwgVUQ50WvMcNqMUOvUUDnwj/LCakeodWCQDHXGhzN/JSL6ObtgjlRPjBrS2DmVIfezDD3aBHcDGYsiw2Bj1kJnZpPLYzZvKXnbmiwtGsQ2nlooFNr+BQD4K/rWvzvdCmGt/DFMxLzXcdGx46jTVGiM2JwIwOmtPOFoaykxq9f16iNVszMkEMMhgXdQuBqUEBn4FOLxcow85gGJ+VGrIn1RbiTmtvnFwA+ydHho/M6jOvohT6BBujUnE4MgCNFJvRpLnHoMUSMMebQI9yGL7/dgeZ+rvBw5rs6QG+xIldlEkQtQquntrWo1WpkZ19Ap06d4OZW82mEo0cz7/ockYs7pi7/CN99sIT7eckxuGPK9eZYEp6LFu78Bggh1iO0Wp56bBDXGhzN93t3ItLXFc4cr2oxAFfLTNCZrYjw5T9uyXVmFOktaOztAn+OV2UB21Tv1TITAt2da3x3vMPGUWdXICgcM6Ytw48fLuV69dzKGPKLtTA5OSEywANuHKfjGQO2FEmwXx2AieJriPYu41YLAPyl9scmeRheCCjCS42KuNZy2eCBeQXNkDks1qHH4XbJYpc5BsvahqKFH9+rWzkqE3alFwqiFqHVU9taMjKOYNaq2fjjjz8QHh5e4+N4h989yecfuQCF+XN4tH2M+3kxKc1wL1WhaYc+aOHP/4qokOoRWi0POt3inkQwx3VsjAFrTpbgsEGHGdHB3OX5P+aXYdd5JYa28Ue35ny3YTxbasDizCJEh3hgfJcg1LTvc8Q4Wmq0Yvl5A1ydRPD03IRW0Y/X+HXrGu2FPCz48Sxy3CVY9J8YtAjg+5nZfEGLNJkec+O8MaBJc661HJAasftYGV5q544JHSO5Lpu4UmbBmkMqtJc4fnzh9pdCBl84ewXC05fvh9DZbIAMOkHUIrR6alsLc/ZA/nU5XDz84OkbVOPjRNbgubLdf8FsBpw8/OHpy3e9jIfZACdnLTy8A7j/GwmtHqHV8qDTNCSU27EZY1h+vATfSF2wNK4lYjjrf37OL8OS8yoMbdMEL3VuxLWWbIUB44+VoX1QCCb3ktRK/1PX46jKaMGk/QXQuFuxs29j9J3mXKvXrSusChVKl23F7CtAekRbrGnrhY5NG9d7HZX5NFuJT/LMGNctFM9z3nAhS67D3FNqPNzUHzPi+K73LtSaMf5YAYK9PbAxOczhx+M/F00Qd4ExBsPBowAYTBdyeJdDEASE66AcKSAH5QoBOCjHpMlQzNFByaxWaD7bi4LEl7Dqggapke0x5ewBJAxMqvdaKvNTfhlWnSzB0Db+GMK5Cc1WGDA2rRBdg90xP5ZvE6oyWjAiVQoA2JBQPzcdUiNKCB7TqQuwym2L6g0HszhXQxCEkByUp8odlL0F4KC0y/O9XZwE46C8yNFBaTx5HvJn3kbp+IX4pFkn7O0Qg+FpP2LAwN4QcbyZMa1Ai7mZcjwdyT+4XCszYUSKDM18XbAiXhjBpaQ8uITWU3Dhv8CNuO8xGo147LHHoFAoAAAvv/wymjZtij179tTJ6+v/SKv4b0PaUWDCq3XyugRB1B6hOShH2x2UcfwdlCNSpNBbGHb2rb2Dsi7H0coOyrUJknp3UFpLlVAu3QzNR98CjOHH9j3wcfdkDM38C0+qrsF7IL81qieL9Zh0yBZcpncXhjzfx9UWXLw4B5dJ5cFlS1IYInzr714MakSJe8bNzQ379+932Ovrfk+t+G/zpTyYr8vgEv5ga3kIQohkyHSCdFCu7i2GO8e79evCQVlX4yhjDGvKHZQLe4agp7j+1tTbpuG/h2rRJlhLlQCAA8074P1ej+OZM4fx0okU+MwbC5E7H6/rZaUtuHQIdBdEcBmZIoPRwrCjrwSBHPePtweXjPLgUt83HdLUPCFoLFI5TCfOVXlM/0fqbZ5NEISjOFdqwIR0GXqEeGBOD77r2BQGC4YfkMJFJMKGBDF8OWqaLFaGaYcLcabUgDW9xWjlz1uer8SnF1WY2DUIjzWtP3OA8dgZFD75XygmLqloQo81bo4Vyc8j+fIpvHXoNzgHB8J78DP1VlNlCjQmjEiRIszLBat6hQoiuEi1ZmxI5LvrV+XgMj+2foOLHWpECUGj25d2y2OVp+oJgnA8V9QmjEqVoYWfG5bFh8KV4zo2rcmKUakyqE1WbOwjQbAnv4k9xhgWHyvGgQItlsaFokuwx91/yIF8l6vG+tOleLtDAF5sVT9rdy3FCpROWITCJ/8L0/GzFY9nBzfG/EdfRtcbORj793dwAoPP26/Ayav+z1GpwYLhKTK4OYuwPpF/cJlqDy4JYrTkHFw+KA8uk7sF4dF6DC6VoUaUEDT63269+qlPzYRVq+NQDUE0PArL948PcHPC2t5ieHLehnFieiHy1EasTxCjqQ9fp/D7Z0rxba4as3sEIyHs1v3j65P91zVYmFWEgS188Vb7gHo9tlt8N3g++yicAm1rhq/6B2F2v8GILJFh6r49cGFWiAL84DPshXqtC7AFl9GpMpSZrNiYKEGQB9/gsjCrCCkFWiyLC0XnIL7B5dtcNTaUB5eBLfnddEiNKCFYmE4PQ8qRW79hMMJwoJrHCYKoU+wqFytj2JAogT/ndWxzjsiRVaTH6t5itA3k66n9NFuJXeeVGNu5EZ6I8OVaS5Zch2mH5Xgo3BuTugXV69pd56AAeL8wAEEb5yFg/jgUefliZv8hCNBrMPfXT+FpNgEAfN4YBCff+tV8GS0ME9JlyFebsD5BjCacg8vG06X4Pq8Mc3qEoDfn4PLXdQ0WZRVhUMv6Dy43Q40oIVj0aUfB9NVLyXW/p9RzNQTRsBCCg9IOYwwrjpfgj+saLOoZgugQvpta2B2Uw9r64z8CclDOi+G3dle//xDyJy3DzAFDAADzf/4YvkY9AEDk7QXfN1+s13qsjGFmhhzHiwxY3TuUe3D5JFuJ3ReUGNe5ER6P4Lvr11G5DtMPy/FIuDcmdq3f4FId1IgSgkX/++1vStLvOwhmtdZjNQTRcDBbGSZzdlBWZvs5Bb64rMK07sHoG85Xnl/ZQTkiShgOyghfV64OSkPWaVx7dxbmPPwSFB7eWPDLxwjv1qbi+97Dnq+Ytq8PGGNYeqwYf92wBZfunIPLj/lqrD5Zgtfb+WMw5+ByodSAsWkydAv2wFyOwaUy1IgSgoQxdse7462FxTCdPF+PFRFEw8Cucjks02FFL3G9Oyhv5svLKmw5q8DwqEA825zvFLjdQZkQxt9BWaT7x0G5NkHMzUFpupgL2dCJWBT/JHIbiTH310/R/o1nEbR9CeDhDni4w/edV+q1pq1nFfgqR43p3YORzDm4pBZoMTezCM9E+uC9jnyDy9XyXb8ifd2wnPNNh5UhjyghSEynLsBSIL/jc3S/pcKta4d6qoggHnx4Oiir4/erZVh6rBiDW/vhtbZ8ryTZHZQdA92xqCdfB6XaaMGoVJuDcidHB6X5ugyFr4zFys7JON64Beb++gm6Pd4TfhP+C5FIBM8BSXBuFADnkPrb2/6LSypsO6fAiKhAPMM5uJwo0mPyoUL0CfPCNCEElwNS+HIOLtUhnEoIohL2aXmPR3rD47HEisedQhrB593/QOThfsepe4Igag8vB2V1ZMh0mJkhR/9m3hjTma88v4qDkrM832CxYvzBQki1ZmzsI0EYJwelpUQJ+eDR2NysC/a37IQJ+79Gr+7NEbBwQsW/lc+rz8Hn3f/UW02/XS3D8uO24DJMAMFlTJo9uIRyDy4jU2UwM4aNffjK86uDGlFCkDArQ+hPOxH84Uq4to6seFzk4Y6AWSMhOfw13BNjYClWcKuRIB4k7A7Kt9rXn4PydpwtMWD8QRlixZ6YzVmef7OD0ofjlSSbPF9e4aBswWntrlWjRfHQcfjUqwm+69gT7x38CY+Ge6HR+jkQOf/T5LjHdau3XfAOSXWYlSHHgGY+3IPLjZuCC8/94w0WK8YdLISsXJ4v4XjT4e0QXkUEAcB/4lt3/L5zSBACZo2sp2oI4sGmsoPy7Q4BXGvJUxkxKlWK1gFuWBoXCheOV5IqOyh39g0ThIMytUCL1b3F3ByUzGhC8VvT8J3GHR8kPIT/ZP2NZ13LELRzI7etO08X6zExXYaeYk/M6hHMNbiU6C0YkSKDu7MIGxIl3IPL1ENynCs14P0+Em7B5W5QI0oQBNGA4emgvJlCrRkjUmVo5OGMNQKQ59sdlNuSJdwdlBvKHZTzYkLQS8LHQcmsVpSMmY8/85TY+NBAPHX2CIYqcxH83RY4+fC5KShXZcToNJkggovGZMWoVCk0Zit2JoehkQe/KXDGGBYcLUKalG9wqQnUiBIEQTRQbCoX/g5K4B95PgBsSJDAj+M2jJUdlBsSxWgTwNcc8HG2Eh9wdlAyxqCctRqHDmdjWf//ICH3LP4v9yhCvtsM5yA+d4PLtGaMSJEiqDy4ePAOLgdluFpmxrZkCcI5B5f1p0qxN78M8zkGl5pCjShBEEQDxK5y4e2gBABduTy/RG/Bjr6NEcpZnm93UC6LCxWEg3KNAByU6rW7cOK7FMx74jVEFeRjwvE/IP7qfbg0bcylHqXBghEpUjiJRIIILjMyCnGiWBjB5aMLSnyYrcT4Lo0wgLM8vyZQI0oQBNHAKNLZriTxdlAC/8jzLymN2NwnDBG+fK8kbTtnc1DOihaOg/LZ5r5cHZRlH32D85u/xMwnX0dTZRFmpn6LsE9WwbVdSy716MxWjE6TodRgwU4BBJclWcXYf0OLFfFi7sHlhzw11p4qwRvt/PFKa77mgJpCd80TBEE0ICo7KDcmirmqXKyMYW6mHBkyHVbEi9GBszz/i0sqbD2rwMioQDwtEAdlUpgXpnJcu6v94U/kzH0f0wcMgY9Rj7m/f47wTfPgHtOZSz0mC8Ok9ELkqGy7fjXjHFy2nFXg61w1ZnQPRp/GfKfAD9zQYt7RIjzX3Bf/x1meXxvoiihBEEQDwa5ykWrN2N43jJuDErBdSVp9ogS/XLFtwxjLWZ5vd1D+p7UfhnJ2UF6q5KBcyNFBqU/NxJVxizCj/xBYRM5Y+vNuRC4ZD8+He3Gpx8oY5mTKkSnXY21v/sHl84tKbD+nwKhO/IPL8SI9phwqRHJjL0ztzn//+NpAjShBEEQDwK5yOVtqwCYBqFx2X1Dis0sqTOkWhEc5y/MrOyhHk4MSAGA8eR43/jsNc5MHodjLD8t+2IXWE1+H98ABXOphjGHl8RL8dlWDJXGh3IPLL1fKsOJECYa09sernPePv6iwBZfOQe5YEBsqiP3jawNNzRMEQTzg2B2UaVItlseHcle5fJurxsbTpXinQwAGtuQrzz9TYsDEdBniBOSg9ODsoDRdvgLZkHFY3PNxXA6SYM5vnyJqyAD4vl2/e8ZXZtd5Jf532RZcHm7Cd+3uQakWs4/I8WSED0Z1DuQeXEamShHu7YKVvfjedPhvoUaUIAjiAcfuoJzdg7/K5c9rGizKKsKLLf3w3/YBXGvJrSTPXyIgB+XGRAk3B6VFKof8lVFY0yERmU1bYdq+PYh+uBv8pv4fl3oA4OscFd4/U4p3OwTgBc7B5XSxHpPSC9FL4oUZ0fyDy/AUKTxdRFifIIG3gPaPrw00NU8QBPEAIwQHpZ3MQh2mZ8jxSLg3JnTlOwVud1AGC8RBOf6gDNc0ZmxLCuPmoLQqVJAPHoPtYVH4vXUXTNz/NRKiwhG4dDK3f6t91zRYnFWMF1v64U3OwSVHZcSoVBnaBrhhcc8Q7sFlZKoUWjPDrr585fn3CjWiBEEQDyg/5AnDQQnY5PnjDsrQPdgDcznL8ys7KNcLxEF5stiAjYkStA7gtH+8Vo+iYRPwuZsYX3buhXcO/YJ+oa4Ien8eRC58WoUjhTrMyJDj0Sb8g4u0PLiEeDpjtUCCy/Xy4NKY402HdQE1ogRBEA8gKeUqF94OSuAfeX6krxuWx4fClbM8f3SaDAqjFTuSwwTloOwWwmn/eJMZJe9Ox48KEXb2eQQvHU/BQFaK4F2bIPLgc2f6uVIDxh+UITqEf3BRlAcXF5Ft7a5Qgsv7ffgFl7qEGlGCIIgHjOMCcVACNnn+8ANS+Lo6YR1neX5lB+WWpDDuDsrNZ2wOytk9+DkomdWK0vELsT9bjrWPvIQB54/i9eKLCP52C5z8+CzluKI2YVSqDM193bAsjm9w0ZqsGJ0qg7I8uIR48g0uiysFl67Bwt0/vjZQI0oQBPEAcUlpxNg0GaIa8XVQAjZ5/ohUGcyMYWufMARwlufbHZTrEsRoH8jfQbnjvM1B+VQkHwclYwzK+euRkXoGS/q/ivj88xh58TBCv9sC59AgLjXJdWYMT5HC343/rl8mC8OkQ4XIVRuxVQDBZdOZUnyTq8YcjsHFEVAjShAE8YAgFAclYJPnj02TobBcni/hPAVe2UEZEyoMB+WrbfwxtG0AtzrK3v8Yp/b8iblPvIb2hVcxKfNXhH65ES4R4VzqURltU+AWxrAhkX9wmX1EjqPlwaUd5+Dy2UUldp5XYnSnRniSU3BxFPfnvf6E4Pjmm28QExODxMREJCUl4cyZM7xLui0nZdfwe85ZGC1m3qUQRJ1hV7nwdlAC/8jzzyuMWJsg5i7Ptzsop3YXmIOyU9W1u/U5jmo+24sLaz/BjP5DEKYuxcwDX6PxrqVw69i6Rj9foFbiq3NZUBv0dVKP3mwLLnKdBRsTJdyDy4rjJfjjugYLY0O4B5ef88uw8kQJhrbxx6ucd/1yBHRFlLhnMjIyMGzYMBw9ehStW7fGhx9+iH79+uHcuXPw9RVecovwD0LSR6tgsVrRr2UHPNmqEx5vFYUQb+HVShA1we6g1JoZdibzVbkwxrDgqE2ev7q3GJ04y/PtDsr/6xiI51sIx0E5Mzq4ytrd+hxHdT//jZyZ6zDjiWHwNBkw97fP0HTDLLjHdavxa0h8/LAw7WcM/nYnkiPa4MnWnfBU606IDAiudT1mK8OUQ4W4oDBicx8JmnMOLjvOKfDFZRWmdQ/CQwIILnMy5Xg60gcjO90/+8fXBroiStwzS5YswRNPPIHWrW1JesiQITCbzdi9ezffwm6Dv4cnxvV8GGqjHl+ey8Jrez+AePUk9N69DEvSfsHpwutgjPEukyBqRGUH5YYECTcHpZ31p0qxN78Mc2OEIc9fcqwYL7X0wxvt+F5Jsjso25U7KG9eu1tf4yjT6XFl9ALMeuwV6F3csODnj9FiwWh49u9Tq9cRiUSY0+dJGC1m/JZzFqN+/R+ab5iBTlvmYdqf3yL9Wg4sVutdX8fKGOZnFiFdpsPy+FBEcQ4uX15WYfNZBd4TQHA5WR5ceku8ML178H21f3xtoCuixD2zb98+zJo1q+JrJycnREdH448//sDIkSPr9FhGswXHpFfu+XUSm7aCm7NLxfQ8A8PBazk4eC0HU//6Fs0DgisSflJEG7g5068KITyE4qC08+EFBT7MVmJCl0bo34yvPP9IuTz/0SbeGC8QB2Vo+drd6hyU9TGOGs9chOlGIea/OhEy3wAs/WE3fN54AtnJnYF/Ma428Q1EM79GuKIqqXjstPwGTstvYPHBXxDi5YvHW3XEU60747EWHeDrXrXJZIxh7ckS/HilDAtjQxDPObj8cU2DpceK8XIrP7wugOAyxh5c4m4NLg8S9NeVuCeKi4uhUqkgFourPC6RSHDkyJEavca1a9fu/AS1uuI/b5Qp8Mj2RbWus7bkKoqw/shfWH/kL/i6eVSZwgfuf28b8WAgBAelnb15aqw7VYo32vnj5dZ8/4jbHZQ9Qjwwp4dwHJTrE8TVOijrZRwFYF2zA8WePjgf2gQLf/4QvzVjWGA6DWx3zFpUuVaND04ewgcnD8HN2QXJEW3wVOtOeLJ8Cv+jbCU+uajCxK5B6Mc5uGTIdJhxuBD9mnpjXBdhBBexlwtW9xbD3ZmvPN/RNz1ya0TFUMOiLYXOhe80kkVrEkwtQqunJrWoSqSICA+Bj4cTdOriisdDG/kgwMetymO3IyGu+x2/H+3qA0loa1icnPBHtzBEuN99uqduseBIzikcyTmF+b8748kOyTCbO0CvUUDHaceRyug1ZlgtZkHUI7RaECi++xPvY9Jyb2B2x0DE+OqgU+u41ZFZqMfW48UY0sQbrzVjNfq9dxQFGjPmZ8jRzdsFc6J8YNaWgNdtiXozw5zMIrgZzFgWGwIfsxI69a3Pq49xlAEo6/0qtO7umHTsB+Q2t+LjuAhE1GPDdeH6RVy4fhEr9n+NqKbJuMKi8GYbLzwtNnH9zJxTmDEuQ43ugS6Y1M4JhrKSu/+Qg1AYrfi/dDVEVoZlXT3hYlBAZ+BTi8XKMPOYBquTIxx6HBGr58Vw165dQ9OmTdGqdXOYDXquSRUAGAOMVgY3JxF4L79gjMFgMALOLnBzcbo/zg0D9AY9XF1d4ez8T9I3mUywWq1wd7+78kKvv/tdl2Y4obBIiVBxI7iI6rsRBZxFtn8PZycnmJgIMpMbxK5GuIr4riVljEFjMKFU5A2xqwlunFd9C+Xc2M9LoawIV69eRZMmTbjV4ggqxtEWTWExm7levWEMMFkZnETguve2HaOFwWq1ABYz3N3duZ4bk5WBMcD1bn9f6mEc1cAdWpEbLEXXEB4aCAuH8+IkcoKzSAQjXFBidoWXkwWBLnztJWYmQqHZFSKLGQHQwoPjZ4YBkJtcYYEIIS4muHD++1JqdkGZRQSTNN+h4yi3Sxam/yzAB892QmyLxrxKAADkqEyYlF6IZfGhaOHH9wqkTCZD8sAhwHMTsPs+OjexsbH4v/97D6+//lrFY++++y5cXFywYcOGux5HJpPd8ftyuRzPvjsesMiw8PPP0b3JvU/7qQ0G/PfHj2GyVj8INvENRN+INugb2RY9GkfA1emfPw4XlGa8kabCzt5+aOvP96qfTCZD7xeGQvTMdOx+oS16teB7BVAo58Z+XiAr4lZDfWAy6LF///5bpnTri3y1CTOPyNHC1xXTo0PA0RiFMpMVszLkKNHocHjaK4BGgT/3/cHl3DAGrDlZgsOFOsyIDkZUo7s3ko4cR78rADZfNkP++VKo/tqD7d99heCgRjV6L3eCMWDEr5+joExZ7fcbeXgjKaI1+ka2Ra/wlvB2c8OxYhPGHVHj5VA3zO/mzfWCS6HeinfTVehoMuD0pCfgZHDm9pkxWhgmHi3DWYUZG3v6og3nvy2bL2ix67wa0u1TIJfmO/RY3N5pvs4VzM0Pnr58dm+w42w2QAYdnL0C4enLV1jrotQhX6oA7rNz07p9F6QeOor3Ro0HYLsa9dufqZg+fXqN3kPkXZ7j4nENN2QlAGNoFdwE3Zvf+zTB/JQfcUn3z1Smk0iE+PAWeKpNZzzZuhM6BIfdNhV7mA1wctbCwztAEJ+ZG7ISwGiGs5s398+MUM5NxXl5wMm/LoeLB5+x4obGhNFZBQjxboRZiWHw5tiF6s1WTMmUIs/ojfmdfNA7+yIAcDk3jDEsP16Cb2UuWNKzJWJqqP9x1Dj6c34ZPpLJ8UoLhtm/fgoA6CBpUSdXt77PPoFDxVXDXqfQcDzVuhOeat0ZMY0j4ez0z+ciW2HA1ONSdAv1wZIECdcNF1RGCyamF8DJ2RULOrqie04eAD6fGStjmH9YjtNKYH2fcHQJ4est/TRbiU/yzHirlSdG/b3X4cfjv8CNuO+ZMmUKHn30UVy6dAmtWrXCJ598AmdnZwwbNox3adWi1Ouw6vA++Lp5oH/LDniydWc83ioKwV58F8sTxP2CXZ7v5SLCugQJ1ybU7qDMVhixOSkM/lo5t1qAfxyU02vpoHTEOFrZQfm6WI/Z//qVboUxhjkHfoCbswv6lntEn7yDR/R6mQkjUmRo5uuClb347vqlN1sxJk2GYr0FO5LD4KIq5FZLZXn+0rhQRHNuQn/KL8OqkyV4ra0/ng3UYlQ9HJMaUeKeiY2Nxe7du/Hyyy/D09MTTk5O+PXXXwUpsweAfGUx9jz/FvpEtCYtE0HUkjKTFSNTpdCZGXb25SvPtzsoD8l0WNNbgo6N3HFNy62cKg7K52rpoKzrcfRksR4TKzkoC25c/1evczukZSrMSHgcjzZvf4uW6WaK9Wa8lyKFj6sT1vaWcN0/3my17R9/sTy4RPq54ZqKWznYVh5cZkQHo284X3l+WoEWc8uDy/CoQFy/Xj+/TPRXmKgTnnvuOTz33HO8y6gRncUP1o0rBFFf2OX5NzRmbEsOQ2Nvfuvq7Q7Kn66UYUFsCOIkfK8k2R2Ur9yDg7KuxlG7g7JDoLvDHJRhvv54vt3dd2IqM1kxMkUGg4VhZ18J9+AyL7MIGTId1ibYggtP9lxWYetZBYZHBeLZ5nwv3Jws1mPSoUIkhNW/PJ8aUYIgCOKuWBnD9MOFOFVswPt9JGjlz9enK1QH5VjODsoCjanCQbmqVyh3B+W4NBkKtGZsF0BwWXOyBD9fKcPCniHoKeYbXH6/WoZlx4oxuLUfXuO8f/xlpRGjU2XoGOiORdXs+uVoqBElCIIg7ghjDIuyivF3gRYr48XoGsxXnv99rk2e/9/2AXipFd9tGM+WGDAhXYZYsSdmc5bnlxosGJ4ig6uTTZ7vW408v76wWBmmHS7EmVID3k+UoCXn4PLBBSU+vajCpK5BeKwp3+ByWKbDzAw5BjTzwZjOwgguYeW7fvEILtSIEgRBEHdk05lSfJurxtyYYCQ25rsN4983NFiQVYQXWvjinQ4BXGvJV5swKlWKln5uWBoXCleON+BoTVaMTpWhzGTFzr5hCPbk9+fdFlyKcKBAi1W9xOjCObh8m6vGhtOleLtDAF4UQnA5aAsus3oECyK4uDmLsD5RDB9Oa3epESUIgiBuy6fZSuw8r8SYzo3wRATfdWxZch2mHpKjb2NvTO4WxPVKUqHWjOEpUjTycMbaBDE8q9k/vr4wWhgmpMuQrzZha5IETXz4OrE3ni7Fd3llmBsTjIQwvsHlr+saLMoqwsAWvnirfQDXWvJURoxMlaJ1gC248NwAQmuyYlSqtCK4BHnwawfr/chNmjQBYww9vsyFRCKp78MLmiZNmuDcuXMYsu8GnZtK2M9Lt05RdF5ugj4z1WM/L+0C+d6M4Cjs46ij+blc5TK0jT+GtOG7ji1bYcDYtEJ0CXLH/NjbT4HXx7lRGS0YkSoFYwwbEsKq3T++vrAyhllH5DheZMD6RDHa3uYzbz8vHTp0cOhOY59kK7H7ghJjBRBcjsp1mH5YjofCvTHpDsGlPj4zhVozRqTKEOThjDW9hRFcrqjN2JZ8++BSX+MMXRElCIIgbqGyg3Jkp0CutQjZQRnqxXcKfPnxYvx5XYNlAnFQri53UP6Hc3C5UGrA2DQZuga7Y14M37W7SoMtuADAhgQJ9+AyM8MWXDYkitEmgH9Yp0aUIAiCqMLNDkqeU+DFetsUuI+rE9Yl8HdQTi53UG4pd1DyZNs5BfZcVmNmdDCSOTsoUwv+CS7Do/gGl6tlJoxMlSHS1w0r4vkGF115cCnRW7Cjb2PuwWXpsWL8dUOD5fGh6M45uNihRpQgCIKooD4clDWlsoNyR18JAt35OygPlzsoOwjEQTkiKhDPcHZQnijSY/KhQiRycFDeTJHOjOEHyuX5CWJBBJfLKiM29wlDhC/ftbtbzyrwVY4as6KDkdSYb3CpDDWiBEEQBAByUN6Oyg7KRQJwUP5WyUE5TAAOyjFp/ByUlVEbLRiZKoPJyrAliX9wmZspR4ZMh3UCCC5fXFJh2zkFRkYF4mnOweVmqBElCIIgBOug3NRHOA7Kyd2C8KgAHJSzBOKgvCEAB6Udg8WKcQcLIdOasb1vGMI4B5fVJ0rwyxUNFseFIlYAwWX58WL8p7UfhnIOLtVBjShBEEQDR6gOytW9xOgcJBwH5aCWwnBQ9hSAg7JEb8EIATgoAVtwmXpIjrPlwaUF57W7u84r8dklFaZ0C8IjTfhOgR+S2oLL4818MJpzcLkd1IgSBEE0YITqoJwXE4LeAnFQDmpJDsrKaE1WjE4ThoOSMYaFWUVIk2qxujf/4PJNjgrvnynFOx0CMJBzcDldrMfEdBnixJ6YyTm43AlqRAmCIBooNXVQ1hd2B+W4zo3weATfKXC7g/LhcG9M7CoMeb7dQenB2UE5/uDdHZT1xfpTpfi+PLj0kvANLn9e02DxsWK82NIP/+UcXHJVRoxOk6F1gBuWcA4ud4Pfp/kmrFYrevbsicjISN6lCAKFUok5c+YgISEBycnJ6NatGxYtWgSz2cy7NC78/scfMBgN+M+QIUhKSsKZM2d4l8SdL774Ao899hhee/11nDt3DqPHjEFeXh7vsgTFhg0bIBKJsH//ft6l1Bs1HUsZY1h2zOagXNgzRFAOysF15KAsKSn5V+NoZQflXAE4KIenSCESie7ZQfnNN98gNzcXiYmJ/2octTsoTxQbsLp3KHcH5UcXlPgw+96Ci30cffjhhxETE4NBgwb9q3E0s1CH6RlyPBLujQld+U6By7RmjEiRIriOgoujx1HBXBHduHEjsrOz4e8vvIW0PDjw99/44osvkJ6eDn9/f1y/fh3du3eH0WjEnDlzeJdXr2RkZGDKlClwc3XFJx9/jIy9/0O/fv1w7tw5+PoK6+6/+mTIkCHYu3cvImKTMeSP6/C4+hv69++PEydOwN2dv6SYN4WFhVi+fDnvMuqdmo6l284p8GWOGjOig9FXIA7KZ+rYQfnTTz/VehwVooOy1GDBznt0UGZkZGDYsGEIDw9HSkoKPvzww1qNo4wxLMkSjoPyhzw11p4qwevt7i242MfRfv36wWq14rXXXqv1OHq+1IBxB2XoHuwhiOAyIkUKJ5EIGxLvXZ5/48YNh4+jgrgiev36dezYsQNvv/0271IEQ0BAICZMmFDxxyQ8PByDBg3CZ599xrmy+mfJkiVITkqCSGT7uA4ZMgRmsxm7d+/mWxhnnnnmGfTr18/2hUiEV199FRcuXEBWVhbfwgTCggULMG3aNN5l1Cs1HUu/uPSPg/JZgTgo+4R5YVodOyiDgoJqNY7aHZS+AnBQmiz/OCjXJUjQ7B4dlEuWLMETTzwBNzfbjTy1HUe3nFXg61w1ZnTn76A8cEOLeUeL8GxzX7zX8d6CS+Vx1MnJCaNGjarVOHpFbQsuzX3dsDw+FK4cg4tt7a4MCqMVGxMlCKmDmw5Hjhzp8HFUEI3oqFGjsGTJEnh6CsPyLwT69EnEG2+8UeUxDw8PGAwGThXxY9++fYiKiqr42snJCdHR0fjjjz84VsWfPXv2VPnarTy9N8TPyM3s3bsXLi4u/zTqDYSajKV2lYvwHJShde6gHDBgQI3HUbuD0swYNiSKBeGgPFKox4p4cZ04KPft24cePXpUfF2bcfR/l1TYfk6BUZ34OyiPF+kx5VAhksK8MPUO+8fXlJvHUQ8P281ONRlH5TrbFLifgIJLjsqIdQniew4ugG0cdXV1dfg4yr0Rtf/B6N+/P+9SBE96ejpefPFF3mXUK8XFxVCpVAgKCqryuEQiQW5uLqeqhMnx48fRuHFj9O7dm3cpXNFoNJg+fTqmTJ3Ku5R6pSZjqV3lIkQHZX1NgVc3jlZ2UG5IlHB3UK46UYJfr2owPzakThyU9nFULBZXebwm4+ivV2zBZUhrf7zKef/4iwpbcIlq5I6FDggugO3zUZNxVFUpuGzsI0EA5+AyJ1OOTLkeK3uJ0b4Objq0j6OrV6+ugwrvDNc1ohqtFtOmTcNvv/3Gs4z7gj///BPXrl3DjBkzeJdSr2i1WgComE6y4+7uXvE9AmBWK3bu2IENGzbA1ZXvXay8mTlzJt59912EhoQAygLe5dQLZWVldx1Lz5QYMDFdWA5K93p2UFY3jtodlOdKDXhfIA7Kzy+pMLUOHZT2sfLmNY93G0fTpVrMOiLHE818MKpzIPfgMjJVisYODC4GgwHLly+/6ziqN1sxNk2GwnJ5voTz/vErj5fgt6saLIkLRUxo3cws28fRsLAwh98E65Df/ilTpkAkEt3xf3q9HuvWrq14ow2Fu52b9u3bQ6/XV/mZ69ev47333sN3330HPz++XrL6xsvLpuMwGo1VHjcYDBXfI4D8/HwMePxxPPfcc7xL4UpWVhYOHz6Md999l3cpdUJNxtLz589X+aNRHXkqI0YJzEGpMdvWsf0bB2VNz0tlqhtHKzsol8WHCsZB+W6HALxQhw5K+1h583TzncbR08V6TEovRLwAHJQleps5wMPZdgOOo4LLO++8g5deeumO46jZyjD1sBwXFEasTRALIrj877IKU7sH4eE6Ci71PY46pI2fNm0aRowYccfnPJNuxKHDh5F7SFOxRiMvLw9SqRTJyclo1aoVtm/f7ojyuHK3c3NJbcH405aKr4uLi/Hss89iy5Yt6Nq1az1UKCyCgoLg7++P4uLiKo9LpVK0aNGCU1XCYuXKlXAK7IXRo0bxLoU7P/74I3Q6HR566CFofcVwkucDAMaMGYOAgABs374drVq14lxlzanJWCqRSPDnn3/i6NGj1Y6l4e06QfHUREE6KMP/pYOypufFzu3GUbuDcr7AHJRv1rGD0j6OymSyKo/fbhzNVRkxKlWGNgJwUGpMVoxMlUJrZtiZHIZGHo6ZAp8yZQq8vLwwf/782z6HMYYFR4twsFye34lzcPm6PLj8X8dAPN+i7oJL5XEUQMXFMYeNo4wT0Xty2LkSfZXHZs+ezSIiIuq1jnMl+mpr4UXlelQqFevVqxfbu3dvxfe3bNnCpRaePPfcc+yJN0Ywj/BW7FyJnlmtViaRSNj69eu51COU88IYY4sXL2ZPvDmSRX9xmZ0r0bPMzEyWmZnJrR4hnZtzJXqWm5vLALC//vqLdzn1in0sVejNbOAvV9kTP15hMo2Ja00Wq5VNOihj8V/lsqOF2no77u3G0Q/PK1j0nhz2abai3mq5HUdkWhb3VS6bmi5jFqvVIcd47rnn2CuvvMLat2/PGGO3HUelGhMb8EM+e/HXq0xpMDuklppiMFvZO/tvsKRv81h2qcFhx1m8eDEbPHgws1gsjDF223F0zYliFr0nh/2cr3ZYLTXlj6tlrMeeHLYsq4hZHfSZsePocZT7zUpE9RgMBjz99NOIj4+HRCJBZmYmMjMzsWXLFt6l1TtTpkzB/r//BmMMAPDJJ5/A2dkZw4YN41wZXzZv3oyPP/4YQ4YMgVarxenTp7F3716cOnWKd2mEALC6uGF0uYPy/UTJPTko7xVWyUG5OC6k3hyUer2+2nF02U+HsfZUCd5o549XWvO9AcfuoIwOcayDcsqUKfjxxx8rljlVN47a5fnOdeSgvBesjGFGRiFOFhuwupcYrQMcMwVuH0dHjhyJrKwsZGZmVjuOfnhBgY+ylZjQpRH6N+O769eRQh1mZMjxWFNvjOcsz68THNLe1oDKV00KCgpYUlISi4iIYO7u7iwpKYnt2rWrXuoQ0hUcxv6pZ8aGnQxAtf+r71qEcG7WffEDE4U0Zd0fH8j69OnDTp8+za0WIZwXlUrFnJycbJ8JcXOGyV/Y/h+ot9+d6hDCubHz6sTZrGfPngwA69KlC3vppZd4l+Rw7GNps+YtmNMrs5j/nO/Ygh2f8y6LbT5dwqL35LDvclT1etwNGzbcOoa2jGaY9DlbkCl3+JWku5GvMrJHvs9nQ/+4zjRGi8OP9/XXXzMPDw+WkJBwyziqMVrYsH3X2SPf57N8ldHhtdwJq9XKFmbKWcyXOezv6xqHHafKOHrT/yqPo9/lqFj0nhz2/qkSh9VSU86W6FniN7lsxIECZjQ7/vM7evRoh4+jgmhEeSKkP5yMCaseodVin5rnjZDOC2PCqkdotTRELFYrm3ZIxuK+ymWHpfU3BX47Pr+oZNF7ctgH50t5l8KOyXUs/qtcNvGg1GFT4DWlUGtiT/14hb3wy1VWqq+/KXD71HxljGYrG36ggCV+kyuI35uNp2xT4N/n1m9wqY6/r2tYzJc5bKGAgsuwfdeZ1uT44FJfCGaLT4IgCOLeYJVULovjQuvEQXkvCNFB2SnIHQtiQ7neBa4y2rZhNDOGrYlh3B2Us4/IcVSux7oEMdrVgYPyXvjsohI7zysxqlMgnorkK8/Pkusw5VAhkht7YUr3e5fn3wtynRnDU6QIcHPC2t5ieHK86bCuoUaUIAjiAaFC5VKHDsp/ixAdlOHeLljVi+/+8XYHpVxnwQ4BOChXHC/B79c0WFqHDsp/y8/5ZVh5ogSvtvHH0LYBXGvJVhgw7mAhOgsouFgZw4bEMPhzDC6O4MFpqQluXLx4Eb169UJycjLvUgiiwfK1gxyU/wa7g7KXxEswDkpPFxHWJ0jgzXEbxsoOynUJYjSv5KDkMY7uPK/EF+UOyoc4B5eDUi3mZMrxVIQPRnW6t/3j75XrZbb945t4u2ClQIJLkd6CjYkSiDkGF0dBjShxT3z00UcYOnQonJzoo0QQvPjzmgZLHOSgrC2VHZSLe4YIxkG5MVHiMAdlTbBWclAujw9FVCUHJY9x9KvLKmw6U4r36thB+W84WSm4zIgO5nr1vFhvmwL3chFhnQCCy5RDhchWGLEuQYJIzvJ8R0HdA3FPBAUF4e+//76vJOEE8SBxpFCH6RlyPBLujQmcVS4yre2PeIinM1YLRJ5/XWPGhgQJGnPcPx6wyfN/yC/DvJgQxN8kz6/vcXRfeXB5uZUfXm/Hd+1ujsqIMakytCsPLo7YP76mlJmsGJkig94ijOAyL7MIh2Q6LI8Xo2Mjvmt3HcmDd42XqFcef/zxe36Na9eu3fU5UrXlrs8hiIbGuVIDxteDg7ImCNVBuTFR4jAHZU2p7KDsV42Dsr7GUQDQmVmFg3JcF77BRao1Y0SKFKHl+8fzDi7j0mQo0JqxLTmMa3BhjGHtyRL8fKUMC2JDECfhu3bX0XBrRMVQw6Ithc6Fb0q1aE2CqUVo9eg1ZlgtZug1Cuhc7vxRCfBxR0igD3Tq4js+rzoS4rrf9TmmoGYAWI1qcTS1OS8NrR6h1YJAMdcaHM38lIvo5u2COVE+MGtLYOZUh97MMPdoEdwMZiyLDYGPWQmdmk8tjDEsP6PFn1cNWNzdB+08NNCpNXyKAfDjNQPWnNRgWCsPPCMx33GMdPw4GoFSnQn9A4DJ7ZxgKCup9XHqCoXRiv9LV0NkZVjW1ROuBgV0Bj61WKwMM49pcFJuxJpYX4Q7qbl9fgHgkxwdPjqvw7iOXugTaIBOzenEADhSZEKf5pK7P/Ee4PaX4nWXI9BfcEWOM9/VAXqLFa+7mARRi9DquWpwh0HbHFfPHoer+51/ER6NaQJD51DkZP1c6+PMGzf4rs+5IQrA7OUf4urZA3etxdHU5rw0tHqEVkvXJoO41uBoXhZlINLVFTdO8ruqxQBcLTOhj9mKCF9X6C44IYdbNcDnJSH4WhGE90IK0Pi6EjnX+dWSqfHBClkTPOSrwMNqKXKy7vx8R46jxSIf7HBNgmrxW/ivKA1Xj7NaH6Ou0FlFmFcQgSKzK+Y1zoP6rAm8+j7GgC1FEuxXB2Ci+Bp888qQk8epGAB/qf2xSR6GFwKK0K24CDm1zyR1xmWDB+YVNEPmg9qI7jLHYFnbULTw43vVL0dlwq70QkHUIpR6Vq1ahW3btsEU1AxFz0zHu2uWwrX4SpXn/PjTT2jRvHnF19v2TMP169fx4Stjan087/C7J/nLGsBp5cdo2qEPWvjzvdJmUprhXqoSRC1Cq0dotTzodIt7EsEc17ExBqw5WYLDBh1mRAejA+d1bF/k6vGjVItx3T0xuEXzu/+AA5mwbjd2aN3hfvV7fPvnFnyHWxu/+hpHi4zA5DNAMyfA6OOODj361/r16wqjhWHi0TKUuJvxfh9ftPXne3/B5gtapMn0mBvnjQFN+H5mDkiN2H2sDC+1c8eEjpFcl01cKbNgzSEV2kscP75w+0shgy+cvQLh6ct34HI2GyCDThC1CKWekWMnY9ib/4dLagtGHdNj3StfoZVv1Q+jRCKBS6WpV0WZAfLSMnj6BtX6eJE1+Bl9qQGACB7eAdz/nTzMBjg5awVRi9DqEVotDzpNQ0K5HZsxhuXHS/CN1AVL41oihrP+5+f8MqzPVuG19kF4s3MjrrVkKww42e5ZDPJkmBsVBzent6t9Xn2MoyqjBZP2F8DDy4qdfRuj70znf/X6dYGVMcw/LMcpJbA+MRxdOXtLP81W4pM8M8Z1C8XznDdcyJLrMPeUGg839ceMOL7rvQu1Zow/VoBgbw9sTA5z+PH4X84hBIefnx/8/PxQVmqAm9sNSCQSNOG82wZBEMLC7qCcJjAH5UiBOCgj/D2wOSmMq/5Hb7ZiTJoMxXoLdiSHcXVQ2uX5f1zXYEnPUPTg3IT+lF+GVSdLMLSNP4ZwbkKzFQaMTStE12B3zI/l24SqjBaMSJUCADYk1M9Nh9SIEgRBELVCSA7KU+UOyt4CcFDa5fneLk6CcVBeVBixOSmMu4Ny+zkFvriswnQBBJe0Ai3mZsrxdCT/4HKtzIQRKTI083XBinj+8vwxaTKU6C3Y0bcxQuspuPC/O4e4r/n++++RnJyMX375BcePH0dycjJ27NjBuyyCIByE0ByUo+0Oyjj+DsoRKVLoLQwbEsW1clDW9Tha2UG5ohd/B+WXl1XYclaB9zoG4jkhyPMP2YLL9O7CkOf7uNqCixfn4DKpPLisS5Agwrf+7lGhK6LEPfH000/j6aef5l0GQRD1QIZMJ0gH5ereYrhztIzcq4OyLsdRxhjWlDsoF/YMQU8x3ynw36+WYemxYrwigOByWWkLLh0C3QURXEamyGC0MOzoK0Egx/3j7cElQ6bD2gRJvd90SI0oQRAEcVfOlRowIV2GHiEemNOD7zo2hcGC4QekcBGJsCFBDF+O8nyLlWHa4UKcKTXg/UQJWvnzlucr8elFFSZ1DcJjTW+V59cnGTIdZmbI0b+ZN8ZyDi4FGhNGpEgR5uWCVb1CBRFcpAKR59uDyyJOwYUaUYIgCOKOXFGbMCpVhhZ+blgWHwpXjuvYtCYrRqXKoDZZsaNvGII9+d6As/hYMQ4UaLGqlxhdgj3u/kMO5LtcNdafLsXbHQLwYiu+U+BnS2y7fsWKPTGbc3ApNVgwPEUGN2cR1ifyDy5Ty4PLpj4StOQcXD4oDy5TugXhUU7BhRpRgiAI4rYUlu8fH+DmhLW9xfDkvA3jxPRC5KmN2JYUhqY+fN3P758pxbe5asyNCUZCmNfdf8CB7L+uwcKsIgxs4Yu32gdwrSVPZcSoVCla+bthaVwoXDhOgWtNVoxOlaHMZMXOvmEI8uAbXBZmFSGlQIvVvcToHMQ3uHybq8aG8uAysCW/4EKNKEEQBFEtdpWLlTFsSAyDP+d1bHOOyJFVpMeGRDHaclbKfZqtxK7zSozt3AhPRPhyrSVLrsO0w3I8FO6NSd2CuE6BF2rNGJEqQyMPZ6xN4B9cJqTLkK82YWuSBE04B5eNp0vxfV4Z5sWEoDfn4PLXdQ0WZRVhUEv+wYUaUYIgCOIWhOqgXBoXiugQYTgoh7X1x38E5KCcF9PwHJS3w8oYZmbIcbzIIIjg8km2ErsvKDGucyM8HsF37e5RuQ7TD8vxSLg3JnblG1wAakQJgiCImzBbGSYL0EE5IzoYfcOF46AcESUMB2WEryt3B6WOk4OyOhhjWHqsGH/d0GBZXCi6cw4uP+arsfpkCV5v54/BnIPLhVIDxqbJ0C3YA3M5Bxc71IgSBEEQFdhVLofLVS5CcVAOjwrEs835ToHbHZQJYfwdlEW6fxyUaxPE3B2U9uCyJSmsXh2U1bH1rAJf5agxMzoYyZyDS2qBFnMzi/BMpA/e68g3uFwt3/Ur0tcNyznfdFgZakQJgiAIAMJ1UA5u7YfX2grDQdkx0B2LevJ1UKqNFoxKtTkodwrAQTk3U44MmQ7rODgob+aLSypsO6fAiKhAPMM5uJwo0mPyoUL0CfPCNCEElwNS+AoguNwMNaIEQRAEAOE6KMd0FpCDkrM832CxYvzBQki1ZmzvG4Ywzg7K1SdK8MsVDRb1DEEs5+Dy29UyLD9uCy7DBBBcxqTZg0so9+AyMlUGM2PY2ieMa3CpDmpECYIgiAoH5VvtyUFZmZsdlD4cryTZ5PnyCgdlC85rd3dfUOKzS3wdlHYOSXWYlSHHgGY+3IPLjZuCC8+1uwaLFeMOFkJWHlwkHNfu3g7hVUQQBEHUK5UdlG93COBai91B2TqAHJSVsTsoUwu0WN2bv4PymxwVNgrAQQkAp4v1mJguQ0+xJ2b1COYaXEr0FoxIkcHdWYQNiRLuwWXqITnOlRrwvgCCy+2gRpQgCKIBI1QH5RoByPPtDsptyfwdlBsqOSh7Sfg6KP+8psHiY8V4saUfdwdlrsqI0WkyQQQXjcmKUalSaMxW7EwOQyMPflPgjDEsOFqENKkwgsudoEaUIAiigWJTuZCD8mZudlC2CeB7A87H2Up8IBAHZWahDtMzbA7KCV35ToHLtGaMSJEiqDy4ePAOLgdluFpmxrZkCcI5B5f1p0qxN78M8wUQXO4GNaIEQRANELvKhRyUVRGig3KNgByU4w7K0F0ADkqlwYIRKVI4iUSCCC4zMgpxolgYweWjC0p8mK3E+C6NMIBzcKkJ1IgSBEE0MIp0titJQnJQXlIasbkPfwfltnM2B+UsATkon23uSw7KSujMVoxOk6HUYMFOAQSXJVnF2H9DixXxYu7B5Yc8NdaeKsEb7fzxSmu+waWmUCNKEATRgCAH5e354pIKW88qMDIqEE8LxEGZFOaFqZzX7lZ2UK7jHFxMFoZJ6YXIUdmCSzPOwWXLWQW+zrUFlz6N+U6BH7ihxbyjRXiuuS/+j3NwqQ3UiBIEQTQQ7CoXclDeit1B+Z/WfhjK2UF5qZKDcqEAHJQjKjkoAzgHlzmZcmTK9VjbW8w9uHx+UYnt5xQY1Yl/cDlepMeUQ4VIbuyFqd357x9fG6gRJQiCaADYVS5nyUF5C5UdlKPJQVmBwWLF2DQZCgXgoGSMYeXxEvx2VYMlcaHcg8svV8qw4kQJhrT2x6uc1+5eVNiCS+cgdyyIDRXE/vG1gRpRgiCIBxy7g1IoKpdvc9XYeLoU7wjAQXmmxICJ6TLECchB6SEgB+V5hVEQDspd55X432UVpnYLwsNN+K7dPSjVYvYROZ6M8MGozoHcg8vIVCnCvV2wshff4PJvoUaUIAjiAUdoDspFWUV4saUf/isAB6Vdnr+EHJQVCM1B+XWOCu+fKcW7HQLwggDk+ZPSC9FL4oUZ0fyDy/AUKTxdRFifIIG3gPaPrw3UiBIEQTzAkIOyeuwOymCBOCjHH5ThmsaMbUlhgnFQLojlH1z2XdNgcZZNnv8m5+CSozJiVKoMbQPcsLhnCPfgMjJVCq2ZYVdfvsHlXqFGlCAI4gHlhzxyUFZHZQfleoE4KE8WG7AxUYLWAXynwD+8oMCH2UpM6NII/ZvxDS5HCnWYkSHHo034BxdpeXAJ8XTGaoEEl+vlwaUxx5sO6wJqRAmCIB5AUspVLuSgrIrdQakwWrEjOUxQDspuIXynwPfmqbHuVCneaOePlzk7KM+VGjD+oAzRIfyDi6I8uLiIbGt3hRJc3u/DP7jUBdSIEgRBPGAcJwdltVR2UG5J4u+g3HzG5qCc3UMYDsr5R4vwvAAclFfUJoxKlaG5rxuWxfENLlqTFaNTZVCWB5cQT77BZXGl4NI1WLj7x9cGakQJgiAeIC4pjRibJkNUI3JQVqayg3JdghjtA/k7KHectzkon4rk66A8Jv/HQTmFs4NSrjNjeIoU/m78d/0yWRgmHSpErtqIrQIILpvOlOKbXDXmCCC41CXUiBIEQTwgkIOyem52UMaECsNB+WobfwxtG8C1losKI8YeFIaDUmW0TYFbGMOGRP7BZfYROY6WB5d2nIPLZxeV2HleidGdGuFJzsGlrqFGlPjXlJSUYN26dfjjjz/g4uICpVKJQYMGYdKkSXBxoY8WQdQndpWL0ByUQpDn2x2U07oLzEHZKZDrOHpDY8KIVCmaCMBBqTfbgotcZ8EOAQSXFcdL8Md1DZb05B9cfs4vw8oTJRjaxh+vct71yxFQt0D8a3766Sd88cUXSE9Ph7+/P65fv47u3bvDaDRizpw5vMsjiAaD3UGpNTPBOSg7CcRB+X8dA/F8C+E4KGdGB0MkEnEbR+3BxctFhHWcHZRmK8OUQ4W4oDBicx8JmnMOLjvOKfBFeXB5SADBZU6mHE9H+mBkp/tn//jacH/aTwlBEBQUhAkTJsDf35bQwsPDMWjQIHz22WecKyOIhkNlB+WGBIlgHJRzBSLPX3KsGC+19MMb7fheSbI7KNuVOyjta3d5jKNl5Q5KnZlhY6KEa3CxMob5mUVIl+mwPD4UUZyDy5eXVdh8VoH3BBBcTpYHl94SL0zvHnxf7R9fG+iKKPGvGTBgwC2PeXh4wGAwcKiGIBoe5KC8PUfK5fmPNvHGeIE4KEPL1+5WdlDW9zjKAIw/KMMNjRnbkvk6KBljWHuyBD9eKcPC2BDEcw4uf1zTYOmxYrzcyg+vCyC4jLEHl7gQrjcdOhpqRIk6JT09HS+++GKtfubatWt3fY5Ubfm3JRHEAws5KKvH7qDsEeKBOT2E46BcnyCukYPSUeOolTEU6sw4Ve6gbOXPN7h8lK3EJxdVmNg1CP04B5cMmQ4zDheiX1NvjOsijOAi9nLB6t5iuDvzlec7eu0wt0ZUDDUs2lLoXPhOI1m0JsHUAgB6jRlWixl6jQI6zjf81LaWw4cPw2rSYOLYEdCpi2t8nIS47nd9jimoGQB2X56XhlSP0GpBoJhrDY7my0ulmNrJGzG+OujUOm51pMqMmJtVhqeauuO1ZtZa/f7XNVc1FoxIV6GZlzPmRLnArC2BmVMtWjPD6Aw1FDoL3o/zg49ZCZ36zj/jqHGUAVD1HgK9yYp5XdzR1l0DnVpT49eva364asCaUxoMa+WBp8Umrp+ZcwozxmWo0T3QBZPaOcFQVsKtFoXRiv9LV0NkZVjW1RMuBgV0nCYZLVaGmcc0WJ0c4dDjcPtL8brLEegvuCKHY6cPAHqLFa+7mARRCwBcNbjDoG2Oq2ePw9Wdz6fv+vVrkEqluCEKQKnbQ/hlzyc4yRRVntOxYxQ8PP65AmMyGSHLzsb6ee+hMPsACmtxvHnjBt/1OTdEAZi9/ENcPXuA23mxI4R/I6HWI7RaujYZxLUGRzPQ4yI6yEuQI+dXwzmdJxZIm6G7VxmeN1xH7jF+tZSYXTDrRgTcRAwj/PMgPWnlVkv+tetYVdICV0VBeN10AIdyFDh003Pqcxzd59wBB1zaQZ++B2HX9iHn7hdQHcYRjQ9WyprgIV8FHlZLkZPFr5YbRjfMKoiA2MWIN0VXcPU441aLzirCvIIIFJldMa9xHlRnTVBxqoUxYEuRBPvVAcCD2ojuMsdgWdtQtPDjexUyR2XCrvRCQdQCACalGe6lKjTt0Act/Pn884S20UCjKcNlDfDpKSCm04toedONg8HBwXB2tk0xKRQKvPXWW5g0aRI6xsTU+nje4Xe/InpZAzit/JjrebEjhH8jodYjtFoedMY+1JPr8S+pzFh3SI0eTZyxskdzuDl35laLymjF7MNquPkxbIn3g9izLbdarIxhm1mBEpERy9sCnf2rn2avr3H0uwLgWD4wKgLY6uWFFt1vXZdaXxwrNmHzETUebeGG+d0iuS6bKNRbsSpdhbAgEd6P84W/WwdutRgtDBOPlqHE3YxNfXzRxr8Vt1oAYPMFLdJkesyNc7w1gNtfChl84ewVCE9fvpJYZ7MBMugEUQsAeJgNcHLWwsM7gFs9nr5BCAGgLzXA7eINhDdrjMjbyHzVajUGvjwUU6dORZ+H+gMAtm7dirfffrvGx4v0Dbrrc/SlBgAirufFjhD+jYRaj9BqedDxrMHvjqO4oTFhwrECNPP3xNqkMK76H73ZimmZUpSanbG9bxgiOep/GGNYfrwEBxXOWNEnokb6H0eOoz/nl+EjmRz/7eyPUZ0bYZuTM7fPTbbCgKnHpegW6oMlCRKu3lKV0YKJ6QVwcnbFpr6NIeboLbUyhvmH5TitBNb3CUeXEL7e0k+zlfgkz4zx3ULxfBvHr/fmPxdN3Lfo9Xo8/fTTiI+Ph0QiQWZmJjIzM7FlyxbepREE4UCE6KDMVhixLkE4Dsqp3WrmoHTkOCokB+X1MhNGpMjQzFcY8vwxaTIU6y3YmCjh2oRWlucv7BmCaM5N6E/5ZVh1sgSvtfXHf+qhCQXornniHtixYwf279+P/fv3Y+XKlbzLIQiiHqjsoNzZl6883+6gPCTTYU1vCTo24nsVvrKD8rkaOigdNY6eLNZjokAclMV6M95LkcLH1Qlre0u47h9vttr2j7+oMGJzEt+r5wCwrTy4zIgORt9wvvL8tAIt5pYHl+FR9Rdc6Ioo8a8ZPnw4GGPV/o8giAcPuzz/hsaMDYkSQTgof7pik+fHSfheSbI7KF+ppYPSEeOo3UHZIdCdu4OyzGTFyBQZDBaGDYli7sFlXmYRMmQ6rOgl5h5c9lxWYetZBYZHBeLZ5nz3jz9ZrMekQ4VICKv/4EJXRAmCIIi7YmUM0w8XkoOyGio7KMdydlAWaEwVDspVvUK5OyjHpclQoDVjuwDk+WtOluDnK2VY2DMEPcV8g8vvV8uw7FgxBrf2w2uc94+/rDRidKoMHQPdsahn/QcXakQJgiCIO8IYw6KsYvxdoMXKeDG6BvOV53+fa5Pn/7d9AF5qxXcbxrMlBkxIlyFW7InZnOX5pQYLhqfI4Opkk+f71kCe7ygsVoZphwtxptSA9xMlaMk5uHxwQYlPL6owqWsQHmvKN7gclukwM0OOAc18MKazMIJLWPmuXzyCCzWiBEEQxB3ZdKYU3+aqMTcmGImN+W7D+PcNDRZkFeGFFr54p0MA11ry1SaMSpWipZ8blsaFwpXjDThakxWjU2UoM1mxs28Ygj353oCzKKsIBwq0WNVLjC6cg8u3uWpsOF2KtzsE4EUhBJeDtuAyq0ewIIKLm7MI6xPF8OG0dpcaUYIgCOK2fJqtxM7zSozp3AhPRPBdx5Yl12HqITn6NvbG5G5BXK8kFWrNGJ4iRSMPZ6xNEMPThe8U+IR0GfLVJmxNkqCJD18n9sbTpfgurwxzY4KREMY3uPx1XYNFWUUY2MIXb7UP4FpLnsqIkalStA6wBRcXjmt3tSYrRqVKK4JLkAe/dpAaUYIgCKJafi5XuQxt448h9aRyuR3ZCgPGphWiS5A75sfynQJXGS0YkSoFYwwbEsJqtH+8o7AyhllH5DheZMD6RDHa3sb5XF98kq3E7gtKjBVAcDkq12H6YTkeCvfGJAEElxGpMgR5OGNNb2EElytqM7Yl8w8u1IgSBEEQt0AOyuqp7KDckRyGUM4OyuXHi/HndQ2WxYUKwkG5up4dlLfjQqkBY9Nk6BrsjnkxfIOL0mALLgCwIUHCPbjMzLAFlw2JYrQJ4L8pCzWiBEEQRBWE5qAcXu6gXJfA30E5udxBuUUgDso9l9WYGR2MZM4OytSCf4JLfTooq+NqmQkjU2WI9HXDini+wUVXHlxK9Bbs6NuYe3BZeqwYf93QYHl8KLpzDi52qBElCIIgKhCqg3JHXwkC3fk7KA/LdFibIEEHgTgoR0QF4hnODsoTRXpMPlSIRA4Oypsp0pkx/EC5PD9BLIjgclllxOY+YYjw5TsFvvWsAl/lqDErOhhJjfkGl8pQI0oQBEEAIAfl7ajsoFwkAAflb5UclMME4KAck8bPQVkZtdGCkakymKwMW5L4B5e5mXJkyHRYJ4Dg8sUlFbadU2BkVCCe5hxcboYaUYIgCEKwDspNfYTjoJzcLQiPCsBBOUsgDsobAnBQ2jFYrBh3sBAyrRnb+4YhjHNwWX2iBL9c0WBxXChiBRBclh8vxn9a+2Eo5+BSHdSIEgRBNHCE6qBc3UuMzkHCcVAOaikMB2VPATgoS/QWjBCAgxKwBZeph+Q4Wx5cWnBeu7vrvBKfXVJhSrcgPNKE7xT4IaktuDzezAejOQeX20GNKEEQRANGqA7KeTEh6C0QB+WgluSgrIzWZMXoNGE4KBljWJhVhDSpFqt78w8u3+So8P6ZUrzTIQADOQeX08V6TEyXIU7siZmcg8udoEaUIAiigSJUB+W4zo3weATfKXC7g/LhcG9M7MrfQTk8RVrhoPTg7KAcf1A4Dsr1p0rxfXlw6SXhG1z+vKbB4mPFeLGlH/7LObjkqowYnSZD6wA3LOEcXO4GNaIEQRANEMYYlh2zOSiXCsxBOVhADsq5AnBQDk+RQiQSCcZBeaJYGA7Kjy4o8WG2MIJLZqEO0zPkeCTcGxO68p0Cl2nNGJEiRbAAgktNoEaUIAiiAbLtnAJf5qgxIzoYfQXioHyGHJRVsDsoSw0W7BSAg3JJlnAclD/kqbH2VAleb8c/uJwvNWDcQRm6B3sIIriMSJHCSSTChkS+waWmUCNKEATRwPji0j8OymcF4qDsE+aFaQJxUPoKwEFpslR1UDbj7KDcclaBr3OF4aA8cEOLeUeL8GxzX7zXkW9wuaK2BZfmvm5YHh8KV47BxbZ2VwaF0YodyWEI4XjTYW24P6okCIIg6gS7ykV4DspQQTgozYxhS6IwHJRHCvVY21vM3UH5v0sqbD+nwKhO/B2Ux4v0mHKoEElhXpjKef94uc42Be4noOCSo7Lt+sU7uNQGakQJgiAaCHaVixAdlDynwIXmoPz/9u40vKk6bQP43YXuK6VtWnYoUtl3CrRQ9HUG3xl1xtnUcRllxlcEyo6gqGzKKksBEbCIOs7iNTrOIDqbyyUtOwVBtlKg0BaSpmvSJE2b5LwfkjBlUVqgff629++TYkge2np47pyT+6z6uhz/LFSjg/KfF9zB5dEekXhM+BT46Up3cOnTNhCvCAcXU73gsnl0AqKEg8v8A0YcMNYgMzUedwp/6LCxuIgSEbUCx8rtmLVbrQ7KQIU6KE9U2PG6Ih2Uf8o3Ya4CHZS79Va8tN+IH3UKQ0a/aPHgMjlbj0QFgkuNw4VpOQaUeIKLTvja3dcOl+NfhRYsTYnD0Dg17h/fGFxEiYhauAJTLTIU66C0OFzYms4Oyvq8HZTP9IrCzxTooJy9uwQjFOigLK9xNwcE+bk/gCMZXBwuDXP3GnGqslaZ8vw/nzHh+UExuFs4uNwsLqJERC2Yyh2U7RXpoFykWAfleAU6KDOyDbhDgQ5KS50Lk7P1sDo0bE1PQNsguVPgmqZh8cFS7PIEl77CweVDT3CZ0DsaD3aTDS63gosoEVELxQ7Kb+ftoJzRvy3uZQflZQZPcIkN9sNqRYJLscWBLWMSxINL5tEKfHy+GouHyQeXz4osWJJbhl91j8BTyerdP74xuIgSEbVANoe7yoUdlNfydlA+lRyJh3uo0UE5OFaNDsqJO/XwU6CD0qVpmLevBEfK7NiQpkOPKNlT4O+cqsS7eVWY2b8txnWSDS77S2yYt8+IH3QMxQzh4HI7cBElImph6pwaZu92V7mo0EG5WaEOyp2eDsqfdg3HBIU6KJenqNFBWaVAB6U3uHx50YqVI+IxMFb2FPjfz5mRebQC45Oj8JBwcDlRYceMXQYMiQ3C/CGyweV24SJKRNSC1K9yUaWDcotCHZTP7SlBemII5g5So4MyMkCNDsrZng7KzQp0UG48VoEPz5nx8pB2GJ0oewr8q4tWLM4txYNdw/FM7yjRWS6Y65CRbUC3iAAsFy7Pv524iBIRtRD1q1zYQXklbwdl35hALB4WJ/pOkqnWfRtGh6Zhc5p8B+XL+4046OmgTBbuoPzj6SpsPVmFjL7RuK+LbHDJNdowxxNc5igQXCbu1CMqwBdrR8UjWPH7xzcGF1EiohbCW+XCDsoreTso24f6Y9VINToojTYnshTooFx5uBz/LrJgmQIdlJ+er8ZrX5fjsTsi8XjPKNFZ8irtmL6rBP0UCi4uTcP6tARECgaXpsBFlG6a3W7H4sWL8cUXXyAwMBDl5eXo3LkzVq5ciaSkJOnxiFqVDxXsoBypC1GmgzLY3wfrUnUIVaSD8o3ROnSNCBA9jm49WYX3PR2UdwkHl116K+YfMOK+zmHI6Ct77W5xtfva3Q6h/nhNkeBSWuNEVnoC4gWDS1NpOe/tUrOrqKhAVlYWPvjgA3z22Wc4ePAgAgIC8NBDD0mPRtSqfF5kwVIFOyiXDI9VpoNyQ5pOtIPSVa+DcsWIOPTxdFBKHUc/OGPCxmMVeFaBDsoj9YLLvMHtRN89L6txnwIP8fdBpgLBZc6eEuRV1iIzVYcuwuX5TYWLKN20tm3bYseOHYiPjwcA+Pr6Ii0tDfn5+cKTEbUe+9lBeV31OyjXp+qQKHj/eMBdnv/x+WosHBqLEfU6KCWOo595gstDSRF4UriD8qypFlOzDUj2BBfJ+8dX17kweacBNU41gsvCA6XYY7BhxYh49Bb+0GFTannv8VKzCQgIwMCBAy//e3FxMd5++21MmTKlUc9TVFR0w8fozc5Gz0fU0nmrXNhBeSWVOyh/eFUHZXMeRwHA5tAud1BO7y8bXPRWd3NAnOf+8dLBZXqOAZesDmxJTxANLpqmYe2Rcnx6wV2en6L7/t0/vjHEFtF4mOG0VsDmL5tSaywOuJwO1FgqYfOX38tVmqehsxhKSjBhwgScyc/Hk08+ialTM2AzlzX4dVJTBt3wMXUxnQBo36uvS2ucR7VZEB0vOkNTm/RlITqF+GFBH384rOVwCM1hdWiYus+MCqsTG0dEIMxRBZtZZhZN07DimBWfF9qxZFAYkoMssJktMsMA2FFkx5ojFjyRFIQHdI5vPTY2z3G0MypsdRgXBTyX7At7dXmDn/92q6x1YcJuM3xcGpYPCEYbeyVsdplZnC4NLx6y4IixFmuGhaO9r1ns5xcA3jtrw7snbZjeOwSjo+2wmYW+MAD2l9ZhdFddk76G2N8UT/rvR82pNjjrJ3t1QKE9EHZrVxQeP4w2gXLfbBXnacwsK1/4LerqapGfn48v/roRnTt3afDrLJz+yA0fc9EnCi+veAeFx7/6Xn1dWts8qs0yoMMvRGdoan6WEkyMPA/9EbkzBnUasFzfEXn2YLyUcAF1p2pwVmwa4E/lsfiwMgbPxl5CYnEVzhbLzXLAEoaVhg64K7wSd5v1OJv73Y9vyuNomU8YstqMgWnJ7/BbnxwUHtYa/Ny3m83lg4WXOqPU0QYLEwtgPl4Hqb1P04BNpTp8aY7CrPgihBdU42yB0DAAvjBHYqMxAT+LKsXAslKcbXgWue3O2IOw8FInHGipi+hbjqFY3jMO3SJk3xGtq3IgsMKEjr1Go1uk/LtbKsyzatUqbNmyBXUxnVD6wAt4Zs0ytCm7cMVjdnzyCbp17XrN7y1z7sL48eOxffv2Bn/iM7T9jZP8GQvg+9rvlfg+qfA9UnUe1WZp6Tb9IAm64J5ir+/SNMw/bMEZv1qsHh2OIe26i80CAO+fq8EOvRXTBwXjkW7XHp+a08zMbciyBiKw8O/46PNN+BuuXfya6zhaWgs8dwzo5AvUhgWi15BxDf+D3Ga1Tg2zDlajPNCB10eHo2ekbMPKG6esyDHUYEFKKO7tIPsz85W+FtsOVeNXyYGY2buL6GUTF6qdWLPHhDt1TX+JjdjfFAaEwy8kGsHhshfgBjns8PWzIig0SnwWVeaZPO05PDF+AvLNTmQcqkHmwx8gKfzKH0adTnf5fxI/v//+tzt6DcD5YiNO5l9A34HDG/R6XcJjbviYmgo7AB8lvk8qfI9UnUe1WVq6rnFxYq+taRpWHC7HlyUuLBuRiDTh+p9Pz1djXZ4Jv7kzBuP7tRWdJa/SjiPJP8EvgjUs6JOCAN+nr/u45jiOmmqdmP3lJQSFuLB1bCLGvuiH4AYcc5uCS9OwaK8RR6uAdWntMUC4t/QPeVV4r8CB6QPj8KDwDRdyjTYsOGrG3R0jMS9F9nrvEqsDMw5dQrvQIGxIT2jy15N/O4eUExERgYiICFRX2BEQcBE6nQ4drnO3jW3btqG0tBQzZ868/GuXLl0CACQmJjbbvETU/FTtoJysSAdl58ggvDEm4Yb1P015HK1xuDA1x4AyBTooveX5/ym2YOnwOAwRXkI/OV+NVUfK8fgdkXhUeAnNq7RjWk4JBrQLxKJhskuoqdaJSdl6AMD61Ob50CHrm+iWbN26FaWlpQCAmpoaLFq0CH369MHQoUOFJyOipqJSB+VRTwflKAU6KL3l+aH+vo3qoGyK46i3g/K0Ih2Ub56oxPueu35JB5ecS1YsOGDE/V3kg0tRdR0m7TSgU7g/Vo6QL8+fmmNAeY0TG9J0iGum4MJ3ROmm3X333cjNzcU999yD8PBwVFdXo3fv3vjkk08QENAyi3eJWjvVOiineDsoU+Q7KCft1KPGqWHr2IZ3UDbFcbR+B+XaVJ14B+Vfzpiw6Xglnu0djZ+qUJ6/xx1cXhikRnl+WBt3cAkRLs+f7Qkum8YkoHN4831+h4so3bSOHTsiMzNTegwiaib7DDYlOyhXj4pHoGADy610UN7u46imaVjj6aB8ZXgshsfLngL/d2E1lh0qw8MKBJczVe7g0is6UIngMnmnAbVODVljdYgWvH+8N7js8wSXXs0cXLiIEhHRDZ2osGPmbgOGxAZh/hDZ69gq7U5M/EoPfx8frE+NR7hgeb7TpeH5vSU4VmHH62k6JEVKl+dX4Q+nTZg9IAY/6Bh249/QhPYZbHhxnxHjOoVimnBwuWSpw6SdeiSE+GPVyDglgotekfJ8b3B5VSi4cBElIqLvdMFch4xsA7pFBGD5iDi0EbyOzVrnQka2AeY6F7LGJqBdsOwHcJYcKsNXl6xYNTIe/dsFic0CAH87Z8a6byrwdK8o/DJJ9hT48XL3Xb+GxQfjZeHgUmF3YuJOAwL8fLAuTT64zPUEl42jdeguHFze9gSXOQNjcI9QcOEiSkRE36rEc//4qABfrB0Vj2Dh2zDO2l2CAnMttoxJQMcw2R7q149V4KNzZiwY2g6pCSE3/g1N6MtiC17JLcXPu4Xjd3dGic5SYKpFRrYeSZEBWJYSB3/BU+DWOhemZBtQXefC1rEJiAmSDS6v5JZi5yUrVo+MR78Y2eDy0Tkz1nuCy8+7ywUXLqJERHRd3ioXl6ZhfVoCIoWvY5u/34jc0hqsT4tHz+tUyjWnP+RV4a2TVZjWry1+1DlcdJZcow3P7zXirvahmD0wRvQUeInVgUnZBrQN8sPaVPngMnO3AefNddg8RocOwsFlwzcV+HtBNRYOjcUo4eDyRbEFr+aW4hfd5YMLF1EiIrqGqh2Uy1LiMDhWjQ7KJ3pG4tcKdVAuHNr6Oii/jUvT8OI+Iw6X2pUILu/lVWHbqSpM79cW/9tZ9trdg0YbXthrxP+0D8WsAbLBBeAiSkREV3G4NDznqXJ5Y0yCMh2U8wa3w9j26nRQTuqjRgdl5/A24h2UtnodlFljE5utg/J6NE3DskNl+OKiBctT4jBIOLjsOG/G6iPleDI5Eo8IB5dTFXZMyzFgYLsgLBAOLl5cRImI6DJvlctexTooJ/aJxk+6yp4C93ZQpibId1CW2v7bQbk2NV68g/I5oQ7K69l8vBIfnDXjxcHtkC4cXLIvWbHgQCke6BKGZ3vLBpdCz12/uoQHYIXwhw7r4yJKREQA1O2gfKRHBH7TU40Oyt7RgXh1uGwHpbnWiYxsdwflVgU6KBccMGKfwYZMgQ7Kq72fb8KWE5WY1CcaDwgHl69La/DcnhKMTgjB8yoEl6/0CFcguFyNiygREQFQt4Nyaj+FOiiFy/PtThdm7CqB3urAm2MTkCDcQbn663L844IFrw6PxTDh4PKvwmqsOOwOLk8oEFym5niDS5x4cJmcbYBD07B5dIJocLkeLqJERHS5g/J3d7KDsr6rOyjDBN9JcpfnGy93UHYTvnZ326kq/DFftoPSa4/ehpf2GXFvpzDx4HLxquAiee2u3enC9F0lMHiCi07w2t1vo95ERETUrOp3UD7dK0p0Fm8HZY8odlDW5+2gzL5kxepR8h2Ufz1rwgYFOigB4JuyGszabcDw+GC8NKSdaHApr3Fi0k4DAv18sD5NJx5c5u4x4kSFHa8rEFy+DRdRIqJWTNUOyjUKlOd7Oyi3pMt3UK6v10E5UifbQfl5kQVLDpXhl90jxDsoz5lqMSXHoERwsdS5kJGth8Xhwtb0BLQNkjsFrmkaFh8sRY5ejeDyXbiIEhG1Uu4qF3ZQXu3qDso7omQ/gPP7vCq8rUgH5YESG17Y5+6gnDlA9hS4werApJ16xHiCS5B0cNllQGG1A1vSdWgvHFzWHa3A9vPVWKRAcLkRLqJERK2Qt8qFHZRXUrGDco1CHZTTdxkwSIEOyiq7E5N26uHr46NEcJm3rwRfl6kRXN49VYV38qowo39b3CscXBqCiygRUStTanO/k6RSB2V+VS3eGC3fQbnlhLuD8iWFOih/0jWcHZT12BwuTMkxoMLuxFYFgsvS3DJ8edGKlSPixYPLxwVmrD1ajqeSI/FwD9ng0lBcRImIWhF2UH679/NN2Hy8EpP7RON+RTooxySEYK7wtbv1OygzhYNLnVPD7N0lOGtyB5dOwsFl0/FKfHjOHVxGJ8qeAv/qohULD5bip13DMUE4uDQGF1EiolbCW+XCDspreTsof90jAo8Ld1Dm1+ugfEWBDspJ9Tooo4SDy/wDRhww1mDtqHjx4PKn01V480QlMvrKB5fDpTWYs6cE6YkhmDtI/v7xjcFFlIioFfBWuRxnB+U16ndQTmEH5WV2pwvTcgwoUaCDUtM0vHa4HP8qtGBpSpx4cPnHhWqs/Locj/aIxGPC1+6ernQHl34xgVg8LE6J+8c3BhdRIqIWzttBqUqVy0fnzNjwTQX+T4EOymPldszabUCKQh2UQQp1UJ6srFWig/Ktk1X48xkT5g6Mwd0dZK/d3aW34uX9Rvy4cxgy+kWLB5fJ2Xq0D/XHayNlg8vN4iJKRNTCqdZB+WpuKX7ZPQK/VaCD0luev5QdlJep1kH54VkTXj9WgWd6ReFnCpTnz95dgpG6EMwbLB9cJu7UI9jfB+tSdQhV6P7xjcFFlIioBWMH5fV5OyjbKdJBOWOXAUUWB7aMSVCmg3LxMPng8lmRBUty3eX544WDy1lTLTKyDegZFYAlw2PFg8vkbD2sDg1vjZUNLreKiygRUQv1cQE7KK+nfgflOkU6KI+U2bEhTYceUbKnwN85VYl38qows39bjOskG1z2l9gwb58R93SQDy56T3CJDfbDakWCS7EnuCQKfujwduAiSkTUAu30VLmwg/JK3g7KyloXstITlOqgHBgrewp8e4EZmUcr8FRyJB4S7qA8UWHHjF0GDI6VDy6VnuDi7+O+dleV4PL6aPngcjtwESUiamEOs4Pyuup3UG4aI99B+cYxdwfly0PU6KBcdLAUDyrQQXnBXIeMbAO6hgdgeYpscLHWuTAl24AqT3CJDZYNLkvqBZcB7dS9f3xjcBElImpB8qtqMS3HgD5t2UFZX/0OyszUeNwZLd9BmXXS3UF5XxfZDspDxv92UM4R7qA02hyYuFOPyAD5u37VOTXM3lOCc+ZabFYguGw8VoG/njNjvgLB5XbiIkpE1EKwg/L6ru6gHBqnRgflY3dE4vGeUaKznK6sxbRdanRQmmrdp8Cdmob1afLB5eX9Rhz0BJdk4eDyx9NV2HqyClP6tsWPhYPL7fb9/Kw/KcflcmH48OHo0qWL9ChErZK3ykW1Dsq1qfHqdFAOUqyDsu+Vp8Cb+zh60VKHSdl6dFCgg7LG4Q4uRpsTG9J04sFl5eFy/KfYgleGxYoHl0/PV+O1r8vx+B2ReEz4rl9NgYso3RYbNmxAXl6e9BhErZK3g9Lq0LAhTadMB+XyEXHoq0gH5YTe0XiwmzodlC8ObnfNKfDmPI56g0uIvw8yhTsoHS4Nc/aU4FRlLTJT49FVOLhknajE+2fcd/26S4HgMv+AEfd3CcPkvt+f+8c3BhdRumXFxcXIysrC008/LT0KUatTv4NyfapOmQ7KBYqU5y89VIZfdY/AU8my7yR5OyiTPR2UV1+725zH0WpPB6VNgeDi0jQsOlCK3QYbVoyIQx/h4PKXMya8cbwSzyoQXI54gssoXQheGHRtcGkpuIjSLcvIyMDSpUsRHCx7+oKotalf5bJ6ZLx4lYtqHZQveDooZyjSQRnnuXb3eh2UzXUc1QDM2GXARYsD69N0oh2UmqZh7ZFy7LjgvuvXCOHg8p8iC5YdKsNDSRF4UoHgMtUbXFKuDS4tCT+sRLdk+/bt8Pf3x7hx47Bnz56beo6ioqIbPkZvdt7UcxO1ZOygvD5vB+WQ2CDMH6JOB+W61PjrdlA213HUpWkosTlw1NNBmRQpG1zezavCe6dNmDUgBj8UDi77DDbM21uCH3YMxfT+agSX+BB/rB4Vj0A/2fL8pr52WGwRdTkdqLFUwuYvuwvXWBzKzKLaPDeaxWq1InPVMmRlvQmbuQyhgb5IjIuGzVzWqNdJTRl0w8fUxXQCoH0vvi6teR7VZkF0vOgMTe0v+RWY2zcUQ8NtsJltYnNkG2qxILca93UMxG86uRp9DLidCi1OTNptQqcQP8zv4w+HtRwOoVmsDg1T9plRYXVi44gIhDmqYDNf9ZhmOo5qAEyjHkVNnQsL+weiZ6AFNrOlkX+i2+fjQjvWHLXgiaQg3B9fJ/ozc7LKgel7zRgU7Y/Zyb6wV5eLzVJZ68KE3Wb4uDQsHxAMf3slbHaZWZwuDS8esmB1eucmfR0fTdO0Jn0F+t6ZM2cOli1b9p2POXHiBDZt2oSkpCRMnDgRADB//nxs27YNBQUFjXq9hibPkSNHIicnp1HPTUQkgcdRoobhIkrXMJlMMJlM3/kYnU6HwYMHIzIyEr6+7tMGBQUF0Ov1SElJQVJSEt58880GvV5DTikBQIcOHRr0OCIiaTyOEjUMF1G6bW42yRMRkRuPo9Ta8FPzRERERCSCiyjdMr1ej/T0dGzbtu2KfyYioobhcZRaK56aJyIiIiIRfEeUiIiIiERwESUiIiIiEVxEiYiIiEgEF1EiIiIiEsFFlIiIiIhEcBElIiIiIhFcRImIiIhIBBdRIiIiIhLBRZSIiIiIRHARJSIiIiIRXESJiIiISAQXUSIiIiISwUWUiIiIiERwESUiIiIiEVxEiYiIiEgEF1EiIiIiEsFFlIiIiIhEcBElIiIiIhFcRImIiIhIBBdRIiIiIhLBRZSIiIiIRHARJSIiIiIR/w+oxtxSYAtBmAAAAABJRU5ErkJggg==\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"source": [
"scale = numpy.array([[2,0], [0,0.5]])\n",
"print(scale)\n",
"plot_linear_transformation(scale)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 436
},
"id": "4Rmu1D2kGUMB",
"outputId": "8793a528-56a6-463a-94d7-9df7c850f466"
},
"execution_count": 26,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[[2. 0. ]\n",
" [0. 0.5]]\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 800x400 with 2 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"**Inverse of a matrix**"
],
"metadata": {
"id": "zhoqzywtIFs4"
}
},
{
"cell_type": "markdown",
"source": [
"Thinking of matrices as linear transformations also helps demistify the idea of an inverse. \n",
"\n",
"NumPy has great built-in Linear Algebra capabilities in the numpy.linalg module. Among its many functions, we get inv(), to compute the inverse of a matrix. So we can try right away to visualize a sequence of transformations: first with the matrix M, then the inverse of M. Check it out."
],
"metadata": {
"id": "jBJ6s7SXININ"
}
},
{
"cell_type": "code",
"source": [
"from numpy.linalg import inv\n",
"M = numpy.array([[1,2], [2,1]])\n",
"M_inv = inv(M)\n",
"plot_linear_transformations(M, M_inv)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 709
},
"id": "Zk41DGMDGXqo",
"outputId": "bd885299-40f2-4f40-9ed0-4f2af91ea904"
},
"execution_count": 27,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 800x800 with 4 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"**\"The Matrix is everywhere, it is all around us, even now in this very room.\" (Morpheus)**"
],
"metadata": {
"id": "8h__TZLzI0QF"
}
},
{
"cell_type": "markdown",
"source": [
"**A matrix is a linear transformation**\n",
"\n",
"In the first lesson of this module, we saw that a matrix corresponds to a linear transformation. For example, the matrix \n",
"A = $\\begin{bmatrix}\n",
"1 & 1 \\\\\n",
"-1 & 1 \\\\\n",
"\\end{bmatrix}$\n",
"\n",
"Let's use our helper function plot_linear_transformation() to visualize what this matrix does to the unit vectors and a grid on the 2D plane:"
],
"metadata": {
"id": "sWJZP7eTJOKw"
}
},
{
"cell_type": "code",
"source": [
"A = numpy.array([[1,1], [-1,1]])\n",
"plot_linear_transformation(A)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 401
},
"id": "adOaDWERIk9f",
"outputId": "abe17c2d-a6f2-4a62-c9c3-cbb422f9aac5"
},
"execution_count": 28,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 800x400 with 2 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"## **Applications in Image Processing**\n",
"\n",
"So where can we use this concept of matrix vector multiplication other than in thinking about abstract spaces ? One very important application of this concept can be see in image processing applications. We can consider an image to be a collection of vectors. Let’s consider grayscale images for simplicity, then a grayscale image basically is just a collection of vectors in 2-D space (location of grayscale pixels can be considered a 2-D vector). And we can multiply each pixel vector with a given matrix to transform the entire image!\n",
"\n",
"Let’s import necessary libraries for image manipulation and downloading sample images from the web."
],
"metadata": {
"id": "-zXaIES5LBWV"
}
},
{
"cell_type": "code",
"source": [
"from PIL import Image \n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"import requests\n",
"\n",
"url = 'https://images.pexels.com/photos/2850833/pexels-photo-2850833.jpeg?auto=compress&cs=tinysrgb&dpr=2&h=650&w=940'"
],
"metadata": {
"id": "aJWgWLvNK3vE"
},
"execution_count": 42,
"outputs": []
},
{
"cell_type": "code",
"source": [
"im = Image.open(requests.get(url, stream=True).raw)\n",
"plt.imshow(im)\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 851
},
"id": "oEMBrraZLubm",
"outputId": "3fbbc68f-006b-4aed-deb1-ffa107502fcf"
},
"execution_count": 43,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x7ff76b5637f0>"
]
},
"metadata": {},
"execution_count": 43
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 1280x960 with 1 Axes>"
],
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