{ "cells": [ { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "from TriangleFunctions import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# A Curious Algorithm\n", "\n", "During a lecture in a summer calculus class, I took to drawing random geometric patterns around the edges of my notes. As I was toying with different shapes and ideas for simple space filling curves, I came across an algorithm that happened to result in consistent patterns when drawn within triangles. Consider this simple algorithm below: \n", "\n", "1. Given any triangle, $P$, pick a point anywhere along one of $P$'s edges and call it `current_point`. \n", "2. From `current_point`, draw to the *farthest* edge of $P$, such that the line drawn is perpindicular to the chosen edge.\n", "3. Set `current_point` equal to the end of this drawn perpindicular line, and repeat this recursive process for some number of steps.\n", "\n", "Following this \"right angle algorithm\" in detail on paper, I noticed a couple curious properties. The most prominent property I noticed was that given any \"initial triangle\" and any starting point, the algorithm would quickly converge to some repeating shape, which I will call the \"ultimate shape\". \n", "\n", "Interested in finding the exact properties of this ultimate shape and putting my drawing skills to the test, I went home and wrote a program to generate a triangle and implement this right angle algorithm on it, graphing the result. This write up is a description of what I found when testing this algorithm, highlighting its more interesting features.\n", "\n", "If you would like to see the code I wrote for this, visit the GitHub repository linked [here](https://github.com/samgrassi01/A-Curious-Algorithm).\n", "\n", "\n", "## Putting the Algorithm to the Test\n", "\n", "The algorithm starts drawing from some point along the edge of the initial triangle, and draws a line to the farthest perpinducular edge, repeating the process from its new location in a recursive manner. When the algorithm is faced with two equal distances, it randomely picks one of the two edges to draw to. With this basic understanding of the algorithms' internals, we are equipt to begin the exploration into why it produces the ultimate shapes it does. \n", "\n", "Picking an equilateral triangle to begin, I started the algorithm at one of its vertices and let it run for 100 steps, resulting in the graph shown below. \n", "\n", "**NOTE:** The function `return_points` takes two angles and the right point of the triangle to build, returning the necessary points to make the triangle with the passed exact angles and right end point. The function `drawTriangle` takes `(number_of_iterations, starting_point, outer_triangle_points, steps_to_show)` where `number_of_iterations` is the number of steps the algorithm will execute, `starting_point` is where the algorithm will being drawing, `outer_triangle_points` is the set of three points generated by `return_points` to define the outer triangle, and finally `steps_to_show` is the index-range of steps to graph." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "eq_triangle = return_points(60, 60, [4, 0])\n", "visited_points = drawTriangle(100, [4, 0], eq_triangle, [0, 100])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, after just a few steps the algorithm converged to a different triangle within the outer one. It can be seen that the ultimate triangle has each edge perpindicular to one of the outer triangle's edges, with all three of its vertices touching the outer triangle's edges. \n", "\n", "One way I like to think of the outer triangle is an initial condition to this algorithm that will \"mold\" the lines into their \"natural resting points\" over time. You can see the result of this above. It seems that with every new step, the outer triangle is forcing the algorithm into its final repeating shape. \n", "\n", "To eak some more information out of this pattern, I wrote a function, `give_info` to return the inner angles of this ultimate triangle. Below those inner angles are printed along with the last steps the algorithm took for more clarity." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Outer Triangle Information: \n", " Inner angles: [60, 60, 60]\n", "\n", "\n", "Inner Triangle Information: \n", " Inner angles: [60, 60, 60]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "visited_points = drawTriangle(100, [4, 0], eq_triangle, [90, 100])\n", "give_info(visited_points, eq_triangle)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Right off the bat, we notice that not only does this algorithm converge to triangle, but this ultimate triangle is *similar* to the outer one, as all the interior angles are the same! This is a rather interesting result. \n", "\n", "As this initial equilateral outer triangles is scaled up and down, the convergence of the algorithm is not affected, however notice what happens when we change the starting point of the algorithm from $(4, 0)$ to $(3,0)$ and $(1, 0)$, where the final steps the algorithm took for each situation are graphed below." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "visited_points = drawTriangle(100, [3, 0], eq_triangle, [90, 100])" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "visited_points = drawTriangle(100, [1, 0], eq_triangle, [90, 100])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As the starting point of the algorithm shifted, the ultimate triangle flipped around the axis defined by $x=2$. Infact, when the starting point is to the left or right of $2$, the ultimate triangle will always be pointing in one direction or the other; unless the algorithm starts at the edge points of $(0,0)$ and $(4,0)$, where the ultimate triangles orientation will be determined randomely. When the starting point is at 2, the algorithm picks a random side to follow due to the symmetry of the triangle, and the ultimate triangle will be oriented to either the left or right. \n", "\n", "Curiousely enough, regardless of where the algorithm starts drawing from, the inner ultimate triangle is always the same size and has the same interior angles.\n", "\n", "What if we applied this algorithm to an isosceles triangle? Take the example shown below, with the interior angles of both the ultimate inner triangle and initial triangle printed with the resulting graph." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Outer Triangle Information: \n", " Inner angles: [65, 65, 50]\n", "\n", "\n", "Inner Triangle Information: \n", " Inner angles: [50, 65, 65]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "iso1 = return_points(50, 65, [4, 0])\n", "visited_points = drawTriangle(100, [3.6, 0], iso1, [0, 100])\n", "give_info(visited_points, iso1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the same thing happened for this particular isosceles triangle; the ultimate triangle the algorithm converged to is similar to the outer triangle!\n", "\n", "At this point, you are likely thinking that the ultimate shape may not always be a triangle, depending on the properties of the initial (outer) triangle! I will get to that, but first I am going to show that this property of convergence to similar triangles also holds for scalene triangles." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Outer Triangle Information: \n", " Inner angles: [50, 70, 60]\n", "\n", "\n", "Inner Triangle Information: \n", " Inner angles: [50, 60, 70]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scalene1 = return_points(60, 70, [4, 0])\n", "visited_points = drawTriangle(100, [3.6, 0], scalene1, [0, 100])\n", "give_info(visited_points, scalene1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once again, we can see the inner ultimate triangle is similar to the outer triangle. One natural question may be, \"If the computational resources are not available to find this ultimate triangle, how else might it be found exactly\"? \n", "\n", "The answer would be that this exact inner triangle could be found with relative ease using geometry. Take a look at the *general* diagram below for one of these cases.\n", "\n", "\n", "We know $a, b, c$, and $A, B, C$. It is also known that each of the edges of the inner triangle will be perpindicular with its corresponding edge on the outer triangle, and that the inner ultimate triangle will be similar to the outer one (same interior angles). With this information, all the inner angles can be found, giving enough information to solve for $x, y$, and $z$ shown in the diagram above. After finding these values, the points of the inner ultimate triangle can be found. \n", "\n", "One interesting formula that can be used to *approximate* the side lengths of the inner ultimate triangle is given by\n", "\n", "$$\n", "a' \\approx \\frac{sin(\\gamma) \\cdot a}{\\varphi}\n", "$$\n", "\n", "where $\\gamma$ is the peak angle of the initial triangle, $a'$ is the inner side length to be approximated, $a$ is the corresponding outer side length, and $\\varphi=1.61803 \\cdots$, the Golden Ratio. The resulting error of the approximations when using this formula is highly dependent on the triangle being analyzed. In the example triangles I worked on, I saw side length approximations errors of the ultimate inner triangle between $0.1\\%$ and $7\\%$.\n", "\n", "The side length to be solved for, $a'$, can be found exactly with\n", "\n", "$$\n", "a' = \\frac{sin(\\gamma) \\cdot a}{c}\n", "$$\n", "\n", "where $c \\approx \\varphi$. I have a hunch $c$ is given by a function of the peak angle $\\gamma$, however I have yet to find this function exactly, assuming it exists.\n", "\n", "## Other Ultimate Shapes\n", "\n", "As alluded to earlier, when the angles of the outer triangle are adjusted, the algorithm can generate other interesting repeating shapes. One of the simpler repeating shapes is given below from an isosceles triangle. As a quick note, for most of the examples below I chose not to show the first steps the algorithm took as seeing them is usually not especially informative and they clutter the graph. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "iso2 = return_points(30, 75, [4, 0])\n", "visited_points = drawTriangle(100, [3.6, 0], iso2, [90, 100])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the first repeating ultimate shape we have seen that produces something other than a triangle. The above ultimate shape is nothing to get too excited about however, so lets start by slightly increasing and decreasing the interior angles of the isosceles triangle to see what else the algorithm comes up with." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "iso3 = return_points(40, 70, [4, 0])\n", "visited_points = drawTriangle(100, [1, 0], iso3, [90, 100])" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "iso4 = return_points(20, 80, [4, 0])\n", "visited_points = drawTriangle(100, [3, 0], iso4, [80, 100])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Those patterns are much more interesting! Recall that the algorithm will always draw the longest possible line it can while still obeying the right angle rule, as we can see the result of this taking form in the previous two examples. For this specific isosceles triangle, we can see that as the top angle decreases, the number of \"zig-zags\" formed within the ultimate shape increases, as the angles are much steeper. \n", "\n", "As shown below, scalene triangles succumb to a similar phenomena as well, producing different repeating shapes." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scalene2 = return_points(40, 80, [4, 0])\n", "visited_points = drawTriangle(110, [3, 0], scalene2, [90, 110])" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scalene3 = return_points(20, 86, [4, 0])\n", "visited_points = drawTriangle(110, [2, 0], scalene3, [80, 110])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lets take a look at what happens when we move the top angle in the other direction, starting with a $45-90-45$ triangle. In this case, it is interesting seeing all the steps the algorithm takes, so I plot them all below. The starting point is $(3.7, 0)$." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "iso6 = return_points(90, 45, [4, 0])\n", "visited_points = drawTriangle(130, [3.7, 0], iso6, [0, 130])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The final ultimate shape and its properties are shown below." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Outer Triangle Information: \n", " Inner angles: [45, 45, 90]\n", "\n", "\n", "Inner angles of each triangle are: [45, 90, 45]\n" ] }, { "data": { "image/png": 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r+oEDucIPrJS1d+NZ1yXnJe/9vcVNCnbiJSck11+94WF37wFmBD+wMta79eaGRD9jtknsz4h+IBH8wIrY6D77B7nvPzv4tehnjNaL/SPvddBL9+kHDiT4ge5t+aFav/La5IQzD94n+hmT9WL/2VckP3zw97KHcwEHEvxA17b9BN0zRT8jtVHs3/ketznVE3mBAwl+oFvbjv0Z0c/YbCP2Z0Q/MCP4gS7tOPZnRD9jsYPYnxH9QCL4gQ7tOvZnRD9D20Xsz4h+QPADXZlb7M+IfoYyh9ifEf2w2gQ/0I25x/6M6GfR5hj7M6IfVpfgB7qwZ7E/I/pZlD2I/RnRD6tJ8ANLb89jf0b0s9f2MPZnRD+sHsEPLLWFxf6M6GevLCD2Z0Q/rBbBDyythcf+jOhn3hYY+zOiH1aH4AeW0mCxPyP6mZcBYn9G9MNqEPzA0hk89mdEP7s1YOzPiH7on+AHlspoYn9G9LNTI4j9GdEPfRP8wNIYXezPiH62a0SxPyP6oV+CH1gKo439GdHPVo0w9mdEP/RJ8AOjN/rYnxH9bGbEsT8j+qE/gh8YtaWJ/RnRz0aWIPZnRD/0RfADo7V0sT8j+llriWJ/RvRDPwQ/MEpLG/szop+ZJYz9GdEPfRD8wOgsfezPiH6WOPZnRD8sP8EPjEo3sT8j+ldXB7E/I/phuQl+YDS6i/0Z0b96Oor9GdEPy0vwA6PQbezPiP7V0WHsz4h+WE6CHxhc97E/I/r713Hsz4h+WD6CHxjUysT+jOjv1wrE/ozoh+Ui+IHBrFzsz4j+/qxQ7M+Iflgegh8YxMrG/ozo78cKxv6M6IflIPiBhVv52J8R/ctvhWN/RvTD+Al+YKHE/hqif3mJ/VuIfhg3wQ8sjNjfgOhfPmL/NkQ/jJfgBxZC7G9C9C8Psb8h0Q/jJPiBPSf2t0j0j5/Y35Toh/EZRfBX1ZlV9fKquqSqvlFVraretMOx7lVVr6uqa6rqu1W1v6peWlV3nfe8gc2J/W0S/eMl9rdM9MO4HD70BKZ+J8mDknwryZeSHL+TQarq/kkuTXL3JO9K8pkkD0nyjCRnVNUprbVr5zJjYFNif4fOfO1k+8m33brvkvMm29Oev/j5IPZ3YBb9SfLmj1yVZBL9SXL+407MYftqsLnBqhnFFf4kz0pybJIjk/z6LsZ5VSaxf3Zr7dGttd9urZ2a5CVJjkvywl3PFNgSsb9LrvSPh9jfMVf6YRxGEfyttYtba59rre34//1VdUyS05PsT/LKNYdfkOSGJGdV1RE7niiwJWJ/TkT/8MT+rol+GN4ogn9OTp1uL2qt3XzggdbaN5N8KMmdkjxs0RODVSL250z0D0fsz43oh2H1FPzHTbdXbHD8c9PtsQuYC6wksb9HRP/iif25E/0wnLF8aHcejppur9/g+Gz/XbYyWFVdtsGhHX2gGHon9veYD/IujtjfMz7IC8Po6Qr/Zmb/FXEZAeZM7C+IK/17T+zvOVf6YfF6usI/u4J/1AbHj1xz3iG11k5eb//0yv9J25sa9EvsL5gr/XtH7C+MK/2wWD1d4f/sdLvRGv0HTLcbrfEHtknsD8SV/vkT+wvnSj8sTk/Bf/F0e3pVHfR1VdWdk5yS5MYkH170xKBHYn9gon9+xP5gRD8sxtIFf1XdrqqOnz5V9xattSuTXJTkvkmevuZt5yY5IskbWms3LGSi0DGxPxKif/fE/uBEP+y9Uazhr6pHJ3n09OXR0+3Dq+rC6e+/1lp7zvT390xyeZIvZhL3B3pakkuTXFBVp03Pe2iSR2WylOd5ezF/WCVif2Ss6d85sT8a1vTD3hpF8Cc5MckT1+w7ZvormcT9c7KJ1tqVVfXgJL+b5IwkP5/ky0kuSHJua+26uc0YVpDYHynRv31if3REP+ydUQR/a+2cJOds8dz9ufUWm+sdvzrJk+YxL+BWYn/kRP/Wif3REv2wN5ZuDT+weGJ/SVjTvzmxP3rW9MP8CX7gkMT+khH9GxP7S0P0w3wJfmBDYn9Jif7bEvtLR/TD/Ah+YF1if8mJ/luJ/aUl+mE+BD9wG2K/E6Jf7HdA9MPuCX7gIGK/M6sc/WK/G6IfdkfwA7cQ+51axegX+90R/bBzgh9IIva7t0rRL/a7JfphZwQ/IPZXxSpEv9jvnuiH7RP8sOLE/orpOfrF/soQ/bA9gh9WmNhfUT1Gv9hfOaIftk7ww4oS+yuup+gX+ytL9MPWCH5YQWKfJH1Ev9hfeaIfNif4YcWIfQ6yzNEv9pkS/XBogh9WiNhnXcsY/WKfNUQ/bEzww4oQ+xzSMkW/2GcDoh/WJ/hhBYh9tmQZol/sswnRD7cl+KFzYp9tGXP0i322SPTDwQQ/dEzssyNjjH6xzzaJfriV4IdOiX12ZUzRL/bZIdEPE4IfOiT2mYsxRL/YZ5dEPwh+6I7YZ66GjH6xz5yIflad4IeOiH32xBDRL/aZM9HPKhP80Amxz55aZPSLffaI6GdVCX7ogNhnIRYR/WKfPSb6WUWCH5ac2Geh9jL6xT4LIvpZNYIflpjYZxB7Ef1inwUT/awSwQ9LSuwzqHlGv9hnIKKfVSH4YQmJfUZhHtEv9hmY6GcVCH5YMmKfUdlN9It9RkL00zvBD0tE7DNKO4l+sc/IiH56JvhhSYh9Rm070S/2GSnRT68EPywBsc9S2Er0i31GTvTTo8OHngBwaGKfpXLmayfbT77t1n2XnDfZfuKtYp+lMIv+JHnzR65KMon+JDn/cSfmsH012NxgJwQ/jJjYZykdKvoPJPYZMdFPTyzpgZES+yy19Zb3HEjsswQs76EXgh9GSOzThdmV/rV+6iyxz9IQ/fRA8MPIiH268ZIT1t//sTfu7Im8MBDRz7IT/DAiYp9urHc3ngNt94m8MDDRzzIT/DASYp9ubHTrzZ0+kRdGQvSzrAQ/jIDYpxuHus/+Tp7ICyMj+llGgh8GJvbpxlYeqiX66YDoZ9kIfhiQ2Kcb23mCruinA6KfZSL4YSBin25sJ/ZnRD8dEP0sC8EPAxD7dGMnsT8j+umA6GcZCH5YMLFPN3YT+zOinw6IfsZO8MMCiX26MY/YnxH9dED0M2aCHxZE7NONecb+jOinA6KfsRL8sABin27sRezPiH46IPoZI8EPe0zs0429jP0Z0U8HRD9jI/hhD4l9urGI2J8R/XRA9DMmgh/2iNinG4uM/RnRTwdEP2MxquCvqntV1euq6pqq+m5V7a+ql1bVXbcxxl9VVTvErzvs5dcAidinI0PE/ozopwOinzE4fOgJzFTV/ZNcmuTuSd6V5DNJHpLkGUnOqKpTWmvXbmPIczfY/4NdTRQ2IfbpxpCxP3PmayfbT77t1n2XnDfZnvb8xc0DdmEW/Uny5o9clWQS/Uly/uNOzGH7arC5sRpGE/xJXpVJ7J/dWnv5bGdVvTjJs5K8MMlTtzpYa+2ceU8QNiP26cYYYn9G9NMB0c+QRrGkp6qOSXJ6kv1JXrnm8AuS3JDkrKo6YsFTgy0T+3RjTLE/Y3kPHbC8h6GM5Qr/qdPtRa21mw880Fr7ZlV9KJN/EDwsyXu3MmBV/U9J7pfke0kuT/K+1tp35zdluJXYpxtjjP0ZV/rpgCv9DGEswX/cdHvFBsc/l0nwH5stBn+St6x5/dWqenpr7W3rng07JPbpxphjf0b00wHRz6KNJfiPmm6v3+D4bP9dtjDWu5Kcl+RjSa5N8hNJnpjk2UneWlX/srX255sNUlWXbXDo+C3MgRUh9unGMsT+jOinA6KfRRpL8G9m9l2/6QK31tpL1uz6bJLnVtU1SV6e5N8n2TT4YTNin24sU+zPiH46IPpZlLEE/+wK/lEbHD9yzXk78ZokL0lyYlXdubX2zUOd3Fo7eb390yv/J+1iHnRA7NONZYz9GdFPB0Q/izCKu/RkchU+mazRX88DptuN1vhvqrX2nSSzyHe3H3ZM7NONZY79GXfvoQPu3sNeG0vwXzzdnl5VB82pqu6c5JQkNyb58E7/gKo6LsldM4n+r+10HFab2KcbPcT+jOinA6KfvTSK4G+tXZnkoiT3TfL0NYfPzeSK/BtaazfMdlbV8VV10Adoq+qYqrrn2vGr6keTvH768i2tNU/bZdvEPt3oKfZnRD8dEP3slbGs4U+SpyW5NMkFVXVaJvfOf2iSR2WylOd5a86/fLo9cHHbzyV5TVW9P8mVSa5Lcp8kP5/J5wP+Jsn/tldfAP0S+3Sjx9ifsaafDljTz14YTfC31q6sqgcn+d0kZ2QS6V9OckGSc1tr121hmMuSvCnJyUlOzOTDvt9M8ndJ/jjJH7TWvrcH06djYp9u9Bz7M6KfDoh+5m00wZ8krbWrkzxpi+fe5ru9tfZ3Sf71nKfFChP7dGMVYn9G9NMB0c88jWINP4yR2KcbqxT7M9b00wFr+pkXwQ/rEPt0YxVjf0b00wHRzzwIflhD7NONVY79GdFPB0Q/uyX44QBin26I/VuJfjog+tkNwQ9TYp9uiP3bEv10QPSzU4IfIvbpiNjfmOinA6KfnRD8rDyxTzfE/uZEPx0Q/WyX4GeliX26Ifa3TvTTAdHPdgh+VpbYpxtif/tEPx0Q/WyV4GcliX26IfZ3TvTTAdHPVgh+Vo7Ypxtif/dEPx0Q/WxG8LNSxD7dEPvzI/rpgOjnUAQ/K0Ps0w2xP3+inw6IfjYi+FkJYp9uiP29I/rpgOhnPYKf7ol9uiH2957opwOin7UEP10T+3RD7C+O6KcDop8DCX66JfbphthfPNFPB0Q/M4KfLol9uiH2hyP66YDoJxH8dEjs0w2xPzzRTwdEP4Kfroh9uiH2x0P00wHRv9oEP90Q+3RD7I+P6KcDon91CX66IPbphtgfL9FPB0T/ahL8LD2xTzfE/viJfjog+leP4GepiX26IfaXh+inA6J/tQh+lpbYpxtif/mIfjog+leH4GcpiX26IfaXl+inA6J/NQh+lo7Ypxtif/mJfjog+vsn+FkqYp9uiP1+iH46IPr7JvhZGmKfboj9/oh+OiD6+yX4WQpin26I/X6Jfjog+vsk+Bk9sU83xH7/RD8dEP39EfyMmtinG2J/dYh+OiD6+yL4GS2xTzfE/uoR/XRA9PdD8DNKYp9uiP3VJfrpgOjvg+BndMQ+3RD7iH46IPqXn+BnVMQ+3RD7zIh+OiD6l5vgZzTEPt0Q+6wl+umA6F9egp9REPt0Q+yzEdFPB0T/chL8DE7s0w2xz2ZEPx0Q/ctH8DMosU83xD5bJfrpgOhfLoKfwYh9uiH22S7RTwdE//IQ/AxC7NMNsc9OiX46IPqXg+Bn4cQ+3RD77JbopwOif/wEPwsl9umG2GdeRD8dEP3jJvhZGLFPN8Q+8yb66YDoHy/Bz0KIfboh9tkrop8OiP5xEvzsObFPN8Q+e0300wHRPz6Cnz0l9umG2GdRRD8dEP3jIvjZM2Kfboh9Fk300wHRPx6Cnz0h9umG2Gcoop8OiP5xEPzMndinG2KfoYl+OiD6hyf4mSuxTzfEPmMh+umA6B/WaIK/qu5VVa+rqmuq6rtVtb+qXlpVd93mOD8yfd/+6TjXTMe9117NnQmxTzfEPmMj+umA6B/O4UNPIEmq6v5JLk1y9yTvSvKZJA9J8owkZ1TVKa21a7cwzt2m4xyb5H1J3pLk+CRPSvILVfXw1trf781XsdrEPt0Q+4zVma+dbD/5tlv3XXLeMHOBHZpFf5K8+SNXJZlEf5Kc/7gTc9i+GmxuPRtF8Cd5VSaxf3Zr7eWznVX14iTPSvLCJE/dwjj/PpPYf0lr7TcPGOfsJC+b/jlnzHHeROzTkZeekNz0vYP3iX3GRPTTAdG/eIMv6amqY5KcnmR/kleuOfyCJDckOauqjthknCOSnDU9/wVrDr9iOv7/OP3zmBOxT1fEPstgveU9sGQs71mswYM/yanT7UWttZsPPNBa+2aSDyW5U5KHbTLOw5PcMcmHpu87cJybk1w0ffmoXc+YJGKfzol9xkz00wHRvzhjWNJz3HR7xQbHP5fJTwCOTfLeXY6T6Tjs0jl/8qlceOn+g/Z97wc35wV/8qkknxpkTrAT719n3y/f8fW57tWfTvLpRU8HtuEJef5h/5D/4aZLbnOvWJuvAAALwUlEQVTkEf/h4gHmAztzczs47t/58Wtyxx86PP/HY/77gWbUnzEE/1HT7fUbHJ/tv8uCxkmSVNVlGxw6fivv79n3b7r5NrE/88Vrv73YycBu3eHglz/9nVflH79z+yS+lxm/J+fX87Lb3ZRfOuzSg/Zfe+3X8q3caaBZwe699f+7Kr99xvE56k63G3oqXRjDkp7NzD65sduf7cxrnJV3u8P25fij7zz0NGDufvo7r8o/bu2aAIzGM77/G3nXTT9zy+vLb7632Gfp/ewDfixH3nEM16X7MIb/JWdX3o/a4PiRa87b63GSJK21k9fbP73yf9JWxujZf37Kw/L2j34ptztsXx5x7I8NPR3Ysf25Jofd8A+56Yh75L8MPRnYsUfmy9d8JLf/6idyxxOfkr8aejqwC7c7fF/ueZc7Dj2Nrowh+D873W60tv4B0+1Ga/PnPQ5bcNcjfihP/mdueEQnftT3Mh340VOTnJofGXoewOiMYUnP7JNFp1fVQfOpqjsnOSXJjUk+vMk4H56ed8r0fQeOsy+TD/4e+OcBAED3Bg/+1tqVmdwy875Jnr7m8LlJjkjyhtbaDbOdVXV8VR304dnW2reSvHF6/jlrxvmN6fh/4Um7AACskjEs6UmSpyW5NMkFVXVaksuTPDSTe+ZfkeR5a86/fLpd+yi25yZ5ZJLfrKoTk/x1kgcm+aUkX81t/0EBAABdG/wKf3LLVf4HJ7kwk9B/dpL7J7kgycNba9ducZxrM3kA1wVJ/sl0nIcmeX2Sk6d/DgAArIyxXOFPa+3qJE/a4rlrr+wfeOy6JM+Y/gIAgJU2iiv8AADA3hD8AADQMcEPAAAdE/wAANAxwQ8AAB0T/AAA0DHBDwAAHRP8AADQMcEPAAAdE/wAANAxwQ8AAB0T/AAA0DHBDwAAHRP8AADQMcEPAAAdE/wAANAxwQ8AAB0T/AAA0DHBDwAAHRP8AADQMcEPAAAdE/wAANAxwQ8AAB0T/AAA0DHBDwAAHRP8AADQMcEPAAAdE/wAANAxwQ8AAB0T/AAA0DHBDwAAHRP8AADQMcEPAAAdE/wAANAxwQ8AAB0T/AAA0DHBDwAAHRP8AADQMcEPAAAdE/wAANAxwQ8AAB0T/AAA0DHBDwAAHRP8AADQMcEPAAAdE/wAANAxwQ8AAB0T/AAA0DHBDwAAHRP8AADQMcEPAAAdE/wAANCx0QR/Vf1MVb27qq6rqm9X1Seq6plVddg2x2mH+PXhvZo/AACM0eFDTyBJquqXkrw9yXeSvDXJdUn+VZKXJDklyWO3OeQXk1y4zv4v7XyWAACwfAYP/qo6MskfJbkpySNba38z3f/8JO9LcmZVPb619pZtDLu/tXbO3CcLAABLZgxLes5M8mNJ3jKL/SRprX0nye9MX/76EBMDAIBlN/gV/iSnTrfvWefYB5J8O8nPVNXtW2vf3eKYd6mq/zXJ0UmuT3JZa836fQAAVs4Ygv+46faKtQdaaz+oqi8k+ckkxyS5fItjPijJaw/cUVV/m+Ss1trf7WKuAACwVMYQ/EdNt9dvcHy2/y5bHO/FmXwA+IpMPgR8fJLfymTp0Puq6sTW2n/dbJCqumyDQw+6/PLLc/LJJ29xOgAAsH2XX355ktx3t+PMJfiran+Sn9jGW/5Ta+0JWx1+um1bObm19uw1u/4myWOr6m1JfiXJc5I8a4t/9npuuvHGG6//6Ec/un8XY/Ti+On2M4POgrHxfcF6fF+wHt8XrMf3xa3um+Qbux1kXlf4r8zkavpWXXPA72dX8I9a78QkR645b6denUnw/9xWTm6tuYS/idlPQfxvxYF8X7Ae3xesx/cF6/F9MX9zCf7W2mm7ePtnkzw4ybFJDlpGU1WHJ7lfkh8k+ftd/BlJ8o/T7RG7HAcAAJbGGG7L+b7p9ox1jv1ckjsluXQbd+jZyMOm293+wwEAAJbGGIL/bUm+luTxVfXg2c6qukOSfzd9+fsHvqGq7lRVx1fVfdbsP6mqbnMFv6r+aZIXTl++aZ6TBwCAMRv8Lj2ttW9U1VMyCf+/qqq3JLkuyS9mcsvOtyV565q3PSTJxUnen+SRB+w/O8ljqup9Sa5O8t1MPvhxRpLDMnmi73/esy8GAABGZvDgT5LW2jur6hFJnpfJB2vvkOTzSX4zyQWttS3doSfJOzP5kO8/zeSBXndIcm2SP0/yR621P5n33AEAYMxq6y0NAAAsmzGs4QcAAPaI4AcAgI4JfgAA6JjgBwCAjgl+AADomOAHAICOCX4AAOiY4GfbqupeVfW6qrqmqr5bVfur6qVVddeh58YwqurMqnp5VV1SVd+oqlZVbxp6Xgynqu5WVU+uqndU1eer6saqur6qPlhVv1ZV/v5ZUVX1f1bVe6vq6un3xXVV9bGqekFV3W3o+TEOVXXW9O+SVlVPHno+y86Dt9iWqrp/kkuT3D3Ju5J8JslDkjwqyWeTnNJau3a4GTKEqvp4kgcl+VaSLyU5Psl/aq09YdCJMZiqemqS30/y5SQXJ7kqyT2SPCbJUUnenuSx23iSOp2oqu8l+WiSTyf5apIjkjwsyYOTXJPkYa21q4ebIUOrqnsn+bskhyX54SRPaa29ZthZLbfDh54AS+dVmcT+2a21l892VtWLkzwryQuTPHWguTGcZ2US+p9P8ohMAo/VdkWSX0zyZ621m2c7q+q5Sf46ya9kEv9vH2Z6DOjI1tp31u6sqhcmeW6S/z3J0xY+K0ahqirJ65Ncm+T/TvKcYWfUBz9SZcuq6pgkpyfZn+SVaw6/IMkNSc6qqiMWPDUG1lq7uLX2OVdrmWmtva+19qcHxv50/1eSvHr68pELnxiDWy/2p/54un3AoubCKJ2d5NQkT8qkK5gDwc92nDrdXrTOX+LfTPKhJHfK5EezABv5/nT7g0Fnwdj8q+n2E4POgsFU1QOTvCjJy1prHxh6Pj2xpIftOG66vWKD45/L5CcAxyZ570JmBCyVqjo8ya9OX75nyLkwrKp6Tibrs4/KZP3+z2YS+y8acl4MY/rfhjdm8nmf5w48ne4IfrbjqOn2+g2Oz/bfZQFzAZbTi5KckOTdrbW/GHoyDOo5mXyQe+Y9Sf51a+0fB5oPw/q3SX4qyc+21m4cejK9saSHearp1jpu4Daq6uwkz87k7l5nDTwdBtZaO7q1VkmOzuQD3Mck+VhVnTTszFi0qnpIJlf1z2+t/b9Dz6dHgp/tmF3BP2qD40euOQ8gSVJVT0/yskxuxfio1tp1A0+JkWit/UNr7R2ZLAm9W5I3DDwlFuiApTxXJHn+wNPpluBnOz473R67wfHZnRU2WuMPrKCqemaSVyT5ZCax/5WBp8QItda+mMk/CH+yqn506PmwMD+cSVc8MMl3DnjYVsvkDoBJ8kfTfS8dbJZLzhp+tmN2b/XTq2rfmntr3znJKUluTPLhISYHjE9V/VYm6/Y/nuSft9a+NvCUGLcfn25vGnQWLNJ3k7x2g2MnZbKu/4OZXHS03GeHBD9b1lq7sqouyuTHrk9P8vIDDp+bydMS/6C15r65QKrq+Ul+N8llSU63jIeqOj7J19f+lKeq9iX5vUwe7Hhpa+2/DTE/Fm/6Ad0nr3esqs7JJPj/oyft7o7gZ7ueluTSJBdU1WlJLk/y0CSPymQpz/MGnBsDqapHJ3n09OXR0+3Dq+rC6e+/1lrztMQVUlVPzCT2b0pySZKzJw/QPMj+1tqFC54awzojyX+oqg8kuTKTp6neI5MndB+T5CtJnjLc9KBPgp9tmV7lf3Amf5GfkeTnk3w5yQVJznUFb2WdmOSJa/YdM/2VJF+Mx6OvmvtNt4cleeYG57w/yYULmQ1j8ZdJ/jCTJaAPyuQ2zjdkcsHojUku8PcIzF+15g6KAADQK3fpAQCAjgl+AADomOAHAICOCX4AAOiY4AcAgI4JfgAA6JjgBwCAjgl+AADomOAHAICOCX4AAOiY4AcAgI4JfgAA6JjgBwCAjgl+AADomOAHAICOCX4AAOiY4AcAgI79/wPKwhWSVmVpAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "visited_points = drawTriangle(110, [3, 0], iso6, [100, 110])\n", "give_info(visited_points, iso6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the algorithm was implemented on the above right triangle, it produced some interesting results. The most immidiately noticeable of which being that the hourglass like ultimate shape, is built out of two $45-90-45$ triangles!\n", "\n", "In the current implementation of the algorithm I have prevented it from drawing along edges or meeting the triangles vertices, to force it into developing the hourglass ultimate shape seen above. It is for this reason that on what looks to be the fourth step above (shown on the first graph of the triangle), the algorithm chose to draw down instead of up to the top vertice of the triangle. If the algorithm had been allowed to do so, the resulting inner shape would have been the two ultimate triangles flipped around the y-axis and scaled up, as pictured below by a previous implementation of the algorithm.\n", "\n", "\n", "The algorithm is applied to a few more obtuse triangles to demonstrate this property of the algorithm converging to an \"hour-glass\" ultimate shape, composed to two similar triangles." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Outer Triangle Information: \n", " Inner angles: [40, 40, 100]\n", "\n", "\n", "Inner angles of each triangle are: [40, 100, 40]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "iso7 = return_points(100, 40, [4, 0])\n", "visited_points = drawTriangle(150, [3.4, 0], iso7, [100, 150])\n", "give_info(visited_points, iso7)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scalene4 = return_points(110, 30, [4, 0])\n", "visited_points = drawTriangle(150, [1, 0], scalene4, [100, 150])" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "iso8 = return_points(140, 20, [4, 0])\n", "visited_points = drawTriangle(150, [2.2, 0], iso8, [100, 150])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While this property is true for all obtuse triangles, note what happens as $\\gamma$, the peak angle, approaches 180 degrees. As $\\gamma \\rightarrow 180$, the range of starting points from which the algorithm will converge to this ultimate hour-glass shape decreases, approaching the center of the triangle. \n", "\n", "Notice what happens if the algorithm starts outside of this \"critical range\"." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "iso9 = return_points(140, 20, [4, 0])\n", "visited_points = drawTriangle(100, [2.3, 0], iso9, [0, 100])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The algorithm gets \"stuck\" in a corner and approaches the left/right endpoints as the number of steps approaches infinity! \n", "\n", "## Finding the Ultimate Triangle\n", "\n", "We have noticed that the ultimate shape may or may not be a triangle in different initial triangles. An important question is \"can we define a set of angles for each type of triangle, where the algorithm will always converge to an ultimate triangle?\".\n", "\n", "Lets begin with finding rules for when an isosceles triangle will or will not result in an ultimate triangle. Consider the two initial isosceles triangles below. Notice the minute difference in their interior angles, and the large difference in the ultimate shapes. " ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "iso2 = return_points(43.2, 68.4, [4, 0])\n", "visited_points = drawTriangle(100, [3.6, 0], iso2, [90, 100])" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "iso2 = return_points(43.3, 68.35, [4, 0])\n", "visited_points = drawTriangle(100, [4, 0], iso2, [90, 100])" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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VAPh6ayxNdr/Ehc40TetSkUEIZ2OPa0aNwHOXOZeEuo70MXACkCU8YSrjG/GCSbFEhfibOJqBc++MOH779nEaWywczq/iUF4lU+Jdq5OtcG/9DkbWZIVuy/1omvYUKhit1XX9//r7WkL0R0NzK5uy8tpvr3DjxIXOwoP8uGPKUF63Jm6sz8hhSvwUk0clhI0UShUe4+3DhVQ1qMSFxIggrh8dafKIBpZxqW7z/nxqrUkcQjgDCUbCY6w31Ge7PyUBLy/3TlzoLGXEYEYPCQagtqmVrdmSyCCch0ODka7rT+m6rskSnTDb6ZJq9p5XLbh9vDSWzXT/xIXOOicyrNsrxVOF85CZkfAIxooLt0yIITo0wMTRmGdJUjx+3urX/mBuBUetvZyEMJsEI+H2Gppbec2QuJBmqNfmaSKC/Vg4Obb9dnqGpHkL5yDBSLi97UeKuFSnqg7EhQcye+wQk0dkrhWGYPz6/nzqrW00hDCTBCPh9oxLdGkpCXh7WOJCZ9eNimREZBAA1Q0tbDtUaPKIhJBgJNzcudJaPjtbBoCXBstmeu4SXRtN00iTigzCyUgwEm7NeE1k3vgYYgd5ZuJCZ/clx+PrrWaImRcucbK42uQRCU8nwUi4raYWCxv3GSoueHDiQmdRIf7cOjGm/bbMjoTZJBgJt/Xu0WLKapsAGDoogJuu8ezEhc6Me442ZeXT0CyJDMI8EoyE2zIu0S2fmYCPt/y4G90wOoqEiEAAKuubeedwkckjEp5MfjuFW8opq2P3qVIANA2Wp8gSXWdeXlqHLrfrZKlOmEiCkXBLr+yzvbHOvWYIceGBJo7GeS1Ljm9Pdd97rpzTJTUmj0h4KglGwu00t1rYsM9YccFzWkVcreiwAG6ZEN1++xWpyCBMIsFIuJ2dx0q4WN0IQHSoP/PGR/fwCM9mDNYbM/NobJFEBjHwJBgJt9M5ccFXEheuaM5Y2zLmpbpmdhwpNnlEwhPJb6lwK3mX6vjw5MX22/dL4kKPvL00lhsqU8ieI2EGCUbCrWzIyEXX1d9nj40iISLI3AG5iOUp8bSV7Pv0TBnnS2vNHZDwOBKMhNto6ZS4sFISF3pt6KDADtfW0jOk8Z4YWBKMhNv44MRFiqoaAIgK8WP+hJgeHiGMjHuONmbm0tRiMXE0wtNIMBJuw5i4cF9yAn4+8uN9NeaOG0JsmCokW1rTxHvHJJFBDBz5bRVuobCynvePl7TfTpPEhavm4+3F8pnx7bclkUEMJAlGwi1syMjDYk1cuH50JCOigs0dkItanpKAZk1k2H2qlNzyOnMHJDyGBCPh8lotOhv22S64r5DEhT6LHxzUobr5K5LIIAaIBCPh8j46dZH8inoABgf5smCSJC70hzGRYcO+XJpbJZFBOJ4EI+Hy0vcaExfi8ffxNnE0rm/+hGiGhPoDUFLd2OFanBCOIsFIuLSSqgbeO2Z7s7w/RZbo+su3UyJDuiQyiAEgwUi4tFcz82i1Zi6kjoxgTHSIySNyD/fPtAX1D07alkGFcBQJRsJlWSx6h71FUnHBfhIjg5g9NgoAXVdlloRwJAlGwmV9cqaU3HL1iX1QoC+3TY41eUTupXMiQ4skMggHkmAkXJZxU+aSpDgCfCVxwZ5unRhDZLAfAIWVDR2qoQthbxKMhEu6WN3Yoe+O7C2yPz8fL+7rUJFBluqE40gwEi7ptaw8WqyJC8nDB3NNTKjJI3JPxqW6948XU1TZYOJohDuTYCRcjq7rHdKNZVbkOCOjgrluVCQAFp0OlS6EsCcJRsLlfHa2jPNlqmZaaIAPi6YMNXlE7m3FLFuwfyUjtz2VXgh7kmAkXI7x2sW9M+II9JPEBUdaOCmGwUG+AORX1LP7lCQyCPuTYCRcSnltE9sPF7XfTpOKCw7n7+PN0iRjRQZZqhP2J8FIuJRNWXk0Wfe7TEsIZ+KwMJNH5BnSUm39od47VkxJlSQyCPuSYCRchq7rHfYWrUyVBnoDZUx0KKkjIgBosei8mpln8oiEu5FgJFxGxvlLnLlYC0Cwnzd3Th1m8og8y4pZtuD/SkYuFklkEHYkwUi4DOOsaPGMOIL9fUwcjee5ffJQwgLUv3lOeR2fnikzeUTCnUgwEi6hoq6JbYcK229LUdSBF+DrzZIkY0UGaS0h7EeCkXAJr+/Pp6lFJS5Mjgtjctwgk0fkmYwbjHccLaK0ptHE0Qh3IsFIOD1VccGWTiwVF8wzLjaUpMRwAJpbdV6TRAZhJxKMhNPLyqngRHE1AIG+3tw9TRIXzGT8MJCekYuuSyKD6D8JRsLpGa9N3D1tGKEBviaORiyaOpRQa/LIudJaPj9bbvKIhDuQYCScWlVDM1uzC9pvG+ukCXME+flwz4y49tuSyCDsQYKRcGqb9+fT0KwSF8bHhjItXhIXnIFxqe6dw0Vcqm0ycTTCHUgwEk5L13XWGRIXVs5KRNM0E0ck2kwcFtb+waCp1cJrWZLIIPpHgpFwWtl5lRwrrAIgwNeLxdPjeniEGEiSyCDsSYKRcFrGaxGLpgxjUKAkLjiTu6YNI9javuN0SQ37LlwyeUTClUkwEk6pprGFLQdtiQsrZ0lRVGcT7O/D3YbZ6vo9ksgg+k6CkXBKWw4UUNfUCsDY6BCSEgebPCLRHWNZpm2HCqmsazZxNMKVSTASTsm4RLciVRIXnNWU+EFMsvaUamyx8Pp+SWQQfSPBSDidw/mVHMqvBMDPx4slSZK44MyMiQzr90oig+gbCUbC6RhnRXdMjiU8yM/E0YieLJ4+jEBflchworia/bkVJo9IuCIJRsKp1DW1sPmAoeKCFEV1eqEBvtw1bWj7bUlkEH0hwUg4la0HC6lpbAFg1JBgUkdGmDwi0RvGDw1bswupapBEBnF1JBgJp7LOmLiQIokLrmJ6QjjjY0MBqG9u7TC7FaI37BKMNE37naZpOzVNy9U0rV7TtHJN0/ZrmvZTTdMi7fEawv0dK6zigPV6g5+3F0uT43t4hHAWmqZ1TGTYkyOJDOKq2Gtm9BgQDLwLPAO8DLQATwHZmqbJjkXRo3TDrGjBpBgigiVxwZXcMyMOfx/1lnK0sKo9I1KI3rBXMArTdf1aXdf/S9f1H+i6/k1d11OAXwPDgB/a6XWEm6pvamXT/vz22yslccHlDAr0ZdFUQyKDtJYQV8EuwUjX9YbLnNpg/XOsPV5HuK+3DhVS3aASF0ZEBnHtKFnddUXGDxFbDhS0J6MI0RNHJzDcZf0z28GvI1yc8VP0/SmJeHlJ4oIrSh4+mDHRIQDUNrXy5kFJZBC9Y9dgpGnadzRNe0rTtD9pmrYb+AUqEP3Wnq8j3Mup4ur2is8+Xhr3SeKCy+qSyCBLdaKXfOz8fN8BYgy33wFW67p+sacHapqWeZlT4+0xMOG81hsa6N06MYYhof4mjkb015IZcfzuneM0tVjIzqvkcH4lk+OkQ6+4MrvOjHRdj9V1XQNigSXAKGC/pmlJ9nwd4T4amlvZZCiuKRUXXN/gYD9unxzbfjs9Q2ZHomcOuWak63qxruuvAwuASOCFXjwmubsDOO6IMQrnsP1IERXWtgPxgwO5cUyUySMS9mD8UPHG/gLqmiSRQVyZQxMYdF2/ABwFJmmaJu8yoot1hjpmaSkJkrjgJmaNjGBUVDCgGiVuzS40eUTC2Q1EOaBh1j9bB+C1hAs5V1jKlJwX+aL3W8R6VbBspuyNdheappGWavv/lEQG0ZN+ByNN08Zrmhbbzde9NE37FRANfKrr+qX+vpZwL2ff+jM/9n2ZJ31f4hO/bxDz1hfh1Ltgkc8t7mBpUjy+3mqmuz+nguNFVSaPSDgze8yMbgNyrbXp/lfTtN9omvYf4BTwBFAEfNkOryPcSGNLK2V5J9tve2OB41vh5fvgmWnwwe+gMv8KzyCcXWSIPwsmGRIZDFmTQnRmj2D0HvC/qESFJcB3gaVAOfAzYJKu60ft8DrCjbx7tJjG5svMgCpz4YNfw58nw7r74cTb0CoXwF2RsSLDpqw8Gi73fy48Xr/3Gem6fhj4uh3GIjzI+r053Gb8wnXfAE2DA+ugrkx9TbfAyXfUEToMZjwISQ9BuKR/u4rrRkUyPDKIC2V1VDW08NahQpYkyaZm0ZX0MxID7kJZLZ+cLuv4xcEjYMEv4fFjcN9/YORNHc9XF8BH/w/+PBVeug+OvQmt0sDN2Xl5adyfIokMomcSjMSAS8+4wrUDH3+YvBRWbYFvZsGNj0HwEMMddDj9LrzyIPxpErz3Myg/5/Axi767LzkeH2vKfsb5S5wuqTZ5RMIZSTASA6q51cKr+/J6viNA5Gi45Sl47CgsfwFGzwcM+5BqiuHjp+Ev0+GFe+DI69DS5IBRi/6IDg3glgm2KmHrJZFBdEOCkRhQO48VU1rTCECgn3fvHuTjBxMXw0Ob4FsHYc53IaTTboKzu+DV1fD0BNjxJJSdse/ARb+smGW7zveaJDKIbkgwEgNqneFT8ZghIVf/BIOHw7wfw2NHIG0djF0ImuHHuK4UPv0L/DUJ1twJhzZCS6MdRi76Y/aYKOLCAwGoqGtm+5Eik0cknI0EIzFgcsvr2H1KFXDXNNr73vSJtw+MXwQPbIBHD8HcH0JYXMf7nN8Nr30R/jge3nkCLp7ox+hFf3h5aaRJIoO4AglGYsBs2JeLrqu/zxk7hBB/O3UwGRQPc3+ggtLKDTBuEWiGJcD6cvj87/D3VPjP7XAwHZrr7fPaoteWzUzA25rI8PnZcs5erDF5RMKZSDASA6Kl1cKGfbYluhWpDqhD5+UN1yyEFevgscNw849hUKc9STmfwutfhT+Og7e+B8WyH3ugxA4K4OZx0e23X7lSVqXwOBKMxIDYdeIixVXq2k1UiD/zJ8T08Ih+ChsGN31XJTw8+BpMuBu8DDOxhkrY+yz88zr4v1th/0vQVOvYMQlWzrJ9CNmYmUdTi8XE0QhnIsFIDAjjNYJlM+Px9R6gHz0vLxhzC9z/okoRn/9TtcHWKG8vbP66ura09XEozB6YsXmgm66JZuigAADKapt492ixySMSzkKCkXC4gop6PjhR0n7beCF7QIXGwOzH4Zv74eHNMOle8PK1nW+sgn3PwbOz4X9vhsw10CgbNO3J20tj+UxJZBBdSTASDrdhXy4Wa+LCjWOiGB4ZbO6AvLxg1FxYtga+fRxu/QVEjO54n4IsePNbara05RHIz6I9+0L0y/KUBNp6KH58upQLZbI8KiQYCQdrtegdLlSnOSJxoT+Co+CGR+CbmbB6G0xZBt7+tvNNNZC1Fv59Mzw7BzL+T11vEn0WFx7IXElkEJ1IMBIO9eHJEgorGwCIDPZjwcQufRidg6bBiBth6f+p2dLC30DUuI73KcqGbd9Ws6XNX4fcDJkt9ZFxqXbDvjyaWyWRwdNJMBIOZaxDdl9yPH4+LvAjFxQB1/0PfH0P/Nd2mLYCfAJs55vrVPbdc7fAP2+APc9CvTQyvhrzxkcTHapmoKU1jew8VtLDI4S7c4F3BuGqiqsaeP+47U3mfrMSF/pK0yDxWrj3X2q2dPvvIXpSx/uUHIG3v6dmS69/DS58JrOlXvDx9pJEBtGBBCPhMK/uy6XVmrlw7agIRvWlFp2zCBwMs74C//0JfGmnavTnG2Q739IAB9fD87fB32fBZ/+AunLzxusC7k9JQLMmMnx06iK55XXmDkiYSoKRcAiLRe+wRLci1U26s2oaxM+ExX+Hb5+ARU9D7NSO9yk9Adt/qGZLr30Jzn8ss6VuJEQEMXus6lWl6+rDi/BcEoyEQ+w+XUp+har/Fh7ky8JJTpq40B8BYZDyRfjabvjKB5C8GvwMs7/WRjj0KqxZBH+bCZ/8BWpLTRqsc1phWLp9ZV8uLZLI4LEkGAmHSDdcA1iaFE+Aby97F7mqYTPgrmfUbOmuv8CwpI7ny07Du0+q2dKrq+HsB2CRN95bJsYQFaISGYqrGtl14qLJIxJmkWAk7O5idWOHMi8OKYrqrPxDIHkVfGUXfHU3pHwJ/MNs5y3NqiPtC4vhrzNg99NQ7bklcXy9vbgvOb79drokMngsCUbC7jZm5tFiTVxIGTGYMdGhJo/IJEOnwqI/qky8xX+H+NSO5y+dh50/gz9NhFcehNMEUdRpAAAgAElEQVTveeRsybjnaNeJEgorpb2HJ5JgJOzKYtFJz7B9uk1LcZPEhf7wC1bZd196F/77M5j1NQgYZDtvaYFjb8JLS+GZafDh76GqwLzxDrARUcHcMCYSAIsOGzLyTB6RMIMEI2FXn50t40KZStENC/Bh0dShJo/IycRMhNt/p64t3fssJF7f8XxlDuz6JfxpEqxfASe3g6XVnLEOIOOHllcyctq3BAjPIcFI2JVx8+IST0hc6CvfQJiWBv/1Nnx9L1z3DQiMsJ3XLXDiLVi3HP48BXb9BircN/V5waQYIoL9ACiobOCjk5LI4GkkGAm7KatpZPuRovbbTlcU1VkNGQcLfwWPH4Olz8GI2R3PV+XDh7+FZ6bCy8vg+DZobTFnrA7i7+PdIZFBKjJ4HglGwm5ey8qjuVUtr8xIDGd8bFgPjxAd+AbAlPtg9Vb4Zhbc8C0IirKd1y1wagekr1TLeDt/oZIg3ISxXNTO4yUUVzWYOBox0CQYCbvQdZ10d6y4YJbI0XDrz9VsadkaGHVzx/M1RbD7D/DMdHjxXji6GVqbTRmqvYweEsKskWqpstWiS0UGDyPBSNjFnnPlnC1VTdJC/X24UxIX7MPHT3WkffgNeOQAzP42hMQY7qDDmfdhw8Pw9AR496dQdsa04faX8UNMekYuFklk8BgSjIRdGDcrLp4xjCA/HxNH46YiRsL8n8BjR+D+l2DMrYBmO197ET75M/w1CdbeBYdfg5ZG04bbF7dNjmVQoGoFn3epno9PS/kkTyHBSPTbpdom3jpsSFyQvUWO5e0LE+6CBzfCo9kw53sQOqzjfc59BBv/S82Wtv8ISk+ZM9arFODrzdIkQ0WGDElk8BQSjES/bdqfT1OLqhwwNX4Qk+MG9fAIYTfhiTDvR/DoIViRDtfcBprh17quDD77myrU+vwdkL0Bmp07McBYPmrHkWIuVrvW7E70jQQj0S8qccH26VUSF0zi7QPjboeVr8Cjh2HuExAW3/E+Fz6BTV+GP46Dt38AJcfMGWsPxsaEMnP4YABaLDobM6UigyeQYCT6JfPCJU6V1AAQ5OfNXdOG9fAI4XCD4mDu99US3gMbYfydoBk2HzdUwJ5/wj+uhecWwIF10ORcje3SUjtWZJBEBvcnwUj0i7GB3uLpwwjxl8QFp+HlDWNvhbSX4fGjMO9JtaxnlLsH3vhv1dpi23eg6JA5Y+1k0ZShhAaon6XzZXV8frbM5BEJR5NgJPqssq6Zrdm2gp6SuODEQmNhznfgkYPw0OswcTF4GT44NFZCxr/hXzfCv+dB1gvQWGPacAP9vFk6fSjXeR3hUZ+NfPLRu6aNRQwM+Rgr+uyNA/k0WhMXJg4NY2q8JC44PS8vGD1PHTUlaokuay2Un7XdJz9THe88oSpCJK+GYdMHbow1JXDgZZ44uwY/v/MAVF94m7KKRUSGS1UPdyUzI9Enuq53qB+2YlYimqZd4RHC6YREw42PwjcyYdWbMHkpePvZzjdVQ+bz8L83wbNzYN9/oKHKMWOxWOD0Ttvm3feewq/qfPvpUK2edzKOOua1hVOQmZHokwO5FRwvqgYg0NebxdMlccFleXnByDnqqC2Dg+shcw2UGfYmFR6ErY/B9h/DlKWQtBrikqC/H0CqCuHAS5D1IlRcuOJdNx/IZ+UtunzocVMyMxJ9YpwV3Tl1KGEBviaORthNcCRc/w34RgZ84W2Yej94+9vON9eq60n/Nw/+NRv2/hvqK67uNSytcHIHpD+gCr6+/8uugSjhWrjnX+iGQrEXyurYe668H9+ccGYyMxJXrbqhmTcPFrbfXjFLEhfcjqbB8OvVcdtv1WbZzDVw0bA3qfgQvPUd2PEkTF4CSasgIfXys6XKPNhvnQVVdbN3KCAcpq9UzxM9Xg1j58863GX93hxmjYq00zcpnIkEI3HVNh8ooL5ZdR8dFxPKjIRwk0ckHCooAq79Gsz6KuRlqKB0eBO01KvzLfVw4GV1DJkAyavUjCooQvVdOrVDJUmc2qHaYHQ2/EaVJDHhLtVG4wreOlzEU3VNhAf5XfF+wvVIMBJXzVgvbEVqgqzhewpNUzOfhFRY+Gs49KoKTMWHbfe5eAze+YE6riQo0jYLihrb6yE0tVjYlJXPf904sm/fg3BaEozEVTmUV8nhfJVR5e/jxb0z4nt4hHBLgeGQ+mVI+RLkZ0HWGjiYDq1NV37cyJvULGj8IvDxv/J9LyM9I4cv3DBCPgS5GUlgEFdlnSFxYdGUoQwKksQFj6ZpajkuKKrjJtrLCY5SsyKvq/+5CfRTJY1OFteQlXPpqh8vnJvMjESv1Ta2sOVAfvttSVzwYC1NcHyruhZ09oPeP+7wa+qIGAVJD8P0B9R+p15YMDGG/z2gKo6v25NL8vCIPgxcOCuZGYlee/NgAbVNKnFhTHRIe2Vl4UFKT6vsuacnwMYvdA1EIbEw57vwrWx4qhJ+mA93/xXiZna8X/lZeO8p9TwbHlYbXi3dJDcYLJ4e1/73bYcKqKx37TbroiOZGYleW59hK4qaliKJCx6juUHNgjLXwPndXc9rXqrrbPJqGLtAtbNo4x+iZkBJD0PRYTWTOviKqoUHYGmBo5vVET4ckh6C6Q9CWNe29ROHhjJhaBjHCqtoaLaw+UA+D183whHfsTCBBCPRK0cKKjmYqzY3+nl7sSRJEhfc3sUTkLkWDq6D+m6u0YTFqSAz40EY1Iufh9jJcMfv4ZafwdE31HPnfm47X3FBbYDd9RvVmylpldoga6VpGitTE3hy8xEA1u3J4aFrh8uHIjchwUj0SrqhVcRtk2OJCJZ9Hm6puV7NUjLXQM5nXc9r3qqbbPJqGDNftam4Wn5BKq17+krV4C/rBVWwtcFayUFvVTOx41u7PHTxjDh+9dYxGpotHC+q5mBeJdNln5tbkGAkelTf1Mob+w2JC9LN1f0UH1Ezlex0aKjsen5QIiQ/fNkltD6LngC3/Qbm/xSObVFjuPBx9/dddz9hc3/I3VNi2JBVBMD6PTkSjNyEBCPRo63ZBVQ3tgAwMiqYa0dJFpNbaKqFI6+rWVBeRtfzXj4w7g41Cxp1syqo6ii+ATB1uTpKT6lrSwfWQZ2hqV5RNqSv4JdBMcT5XM+Glrm8me3Nj++cQKjURnR5EoxEj4xFUSVxwQ0UZqsAdOhVaOymJcTgkaqkz1WkXdtV1FhY8EvVmfaXXV/fr66Yb/m8zje93+Ajy1Te/zSExfNuHPhxCruSYCSu6ERRNVk5ai3f11tjabIkLrikxmq1vydzDRTs73rey1fVhkteDSNmO3YW1Fs+/hA6FKqtRXmnLIMjb4BFpXR7aTpzvQ+S8dlPYd5OEwcq7EGCkbgi46xowcRYokL6VsJFmEDXVeDJXKMCUVM3bcQjx6gANG2Fqo7gzAyByCi7fggBeZVMkU7DLk2CkbishoYG3syy9ZmRxAUX0VBpK2JadKjreW9/mLhYBaHh1/e/QZ4jWFrVRtjqQsPXOgais4FT+FvlDbxhuZG0jBymxE8Z4EEKe5JgJC7r0I41vKP/mg0+N/FhyO1cP1r6yDgtXYe8fSoAHdkEzXVd7zNkvApAbe0dnNFV9DwqrY1m07Mq/XzLgQJ+dMcEgv3lLc1V9ft/TtO0SOBeYBEwBYgDmoBDwPPA87reXRMT4eyCD73EEK2Sr/ts4esNW+ClV9RGxPF3go/sM3IK9Zdsje9KjnY97xMAk5aohISEWc45C2rreZS5Bk6/233PI4Bbfw6pX23veZSi64weEsyZi7XUNLawNbuA+1Nk9u6q7PExYhnwT6AQ2AXkADHAEuD/gNs1TVum67puh9cSA+Rsbj4RTXlgfO86+4E6gqIMvWjGmDRCD6brkPO5evM++ga0NHS9T/Qk6yxoGQQ6aQ3BSxdg/4tqJmRcjmsTFNkxtXvKsg7N9zRNY0VqIr/cprrPrtubK8HIhdkjGJ0E7ga2GWdAmqY9AewFlqIC02t2eC0xQNYdrOT5xr8wz2s/j4R/wpS6vYD180RdKXz6F3WMmK2CUi+6dIp+qiuHg+vVxtDSE13P+wbB5KUqCMUlO+ksqBlOvK0C6Zn3af+ZMjL2PHpmWveBympJUjz/750TNLVaOJhbwdGCKiYOC3PU6IUD9TsY6br+/mW+XqRp2r+AXwFzkWDkMhpbWnktK49WvHnXMpMHFv83xDSqT7D7X4QqWzUGzu9WR+BgmLZSLQcNGWfe4N2NrsP5j9Wb97Et3Tevi52q3rynLIMAJ30jLj+ryv7sfxlqS7qeD46GGQ+oWncRo3r9tBHBfiycHMubBwsA1Xjv54sn22vUYgA5+mpfW/pLi4NfR9jR9iPFXKpT/3Vx4YHMHjsEvDS4+Ydw0/fg9HvqzfHkdlVHDNS1i8//ro7E69RsadI94Bto3jfiymouqgKlWS9A2emu5/1CYMp9KggNmzHgw+uVtp5HmWvg3Ifd3EGD0fPU9zDudvDuWxWFFakJ7cHo9f35/PD2Ce2N+ITrcFgw0jTNB3jYevMdR72OsL/1e2x7i+5PScDby7Dc4+UN1yxUR1WB+qSb9QJU2h5DzmfqeOf7MDVNzZZiJg3gd+CiLBb1pp21Fo5t7XZPDXHJKtBPXqraMzij0tOqDfmB9WpJt7OQWNUqYsZDMHh4v1/uulGRjIgM4nxZHdUNLWw7VMh9sjnb5ThyZvRbYDLwlq7r23u6s6ZpmZc5Nd6uoxJXdK60ls/OqovGXhosn5lw+TuHDYObvguzH4ezu9Qn4BNvqx41oPa77H1WHfEp1jfRJeAX7PhvxJVUF8OBl1RQv3S+63n/MFWzLWkVDJ064MPrleYGOPam+hnortDplXoe9ZOmaaSlJvLbt48DaqO2BCPX45BgpGnaI8C3gePAQ454DeEY6Rm2Gc688dHEDupFUoKXN4y5RR3VxXDgZfXp3vjGmpehju1PqGsbyavsP3hXYmmFM7vUDMIYwI0SZtmWO501gJcctzbMW2+fnkd9dF9yPH/ccYLmVp3MC5c4WVzNNTGhDns9YX92D0aapn0deAY4CszXdb28N4/TdT35Ms+XCSTZb4TicppaLGzcZ9to2KeKC6ExaqZ0w6Nw/iPrhXfDklNjFex7Th2eqKrAtqnTuLTZJiAcpqWpIBQzceDH1xvN9ao0T+aajs3x2tij59FVigrx59aJMbx1yNpaYm8OP71LloZdiV2DkaZpjwJ/Ag6jAlE3aTPCWb13rJiyWpWtFRsWwE3XDOn7k3l5wai56qgtVe0AMtdA+Znu7//WdyAuCYYlOWdKcn9YWuHUu2oGcfKd7jd1Dr9BBaCJdztv0kfxEfV/mP3KwPY86qUVqYntwWhTVj7fv208Ab6SyOAq7BaMNE37Puo60QHgVl3Xu7lyKZyZsSjq8pQEfLztVLk5OApueASu/yZc+MS6WXMLtDZ2vN+/50HsFEOasosXvqzI7T4dvk1ghG3z8JBrBn58vdFUC4c3qUB6xZ5Hq2DUPFOrfd8wOoqEiEByy+uprG/mncNF3DMjzrTxiKtjl2CkadqTwM+BTGBBb5fmhPPILa9j9yn1+UHTVBad3WkajLhRHbeXw/8b2fU+RYdg27dhx5PWMjarIX6m68yWWptVynvWWjUb6nZT5xzbRmEfJ62CXnhQba69Us+jpIdVz6PQmIEfXze8vDTSUhL5/Xa1IXjd3hwJRi7EHrXpVqECUSuwG3ikm+Zr53VdX9Pf1xKOY0xcuOmaIcSFO3ipKCgCZn6x47UjnwBbaZvmOpVhduAliJ5oLW2z3IlL25xX14H2vwQ1RV3PBw+xzYIiRw/48HqlsRoObVSB9Io9j1bBiDnO0fOok2XJ8Tz97klaLTp7z5Vz5mINo4c4aQq86MAeM6O2j7fewKOXuc+HwBo7vJZwgOZWCxv6m7jQX3f8QW3izLa2Pig5YjtXchTe/h68+xOYeI8KTInXmj9bammCE2+pN+8zu+h2FjR6ngpA4+5wzuKyug4FWdZZ0EZoru16n8gx6nuYvtLpex5FhwUwf3w0O44WA5C+N4cfLXLSRBDRgT3KAT0FPNXvkQjTvH+8hIvV6vpNdKg/88ab0Goa1Kxn1lcg9cuQnwmZz6vrFW3tEFoaIDtdHVHj1Cf0aSsGvh1C2Rm1J+jAy1B7sev5kBiVyjzjIYjoZinSGfS659EqlVxhduC/CitmJbYHo42ZeXxn4Tj8fSSRwdlJ8w/RIXFh2cx4fO2VuNBXmqauE8XPhIW/MbxpZtvuU3pC7Vl67ymYcLe1XfaNjnvTbGlUmzqz1sK5j7obNIy9Vc0grlnY59I2DqXrKgkhc+2Vex4lrVLp5c7a86gHc8aqZeb8inou1TWz40gxd00bZvawRA8kGHm4/Ip6Pjxp+3Sf5mwl+APCIOWL6mhroX1oo62FdmsTHN6ojojR1tnSSgjpR1q6Uekp9ZoH1kF9N3k5ocOspW0ehHAn+7dr4w49j66Ct5fG8pkJ/Om9k4D6sCXByPlJMPJwr2Tk0tZpavbYKBIigswd0JUMm6GOBb+Cw6+pN9eCLNv58jPqutLOX6j2A8mrVTuCq73Q3tygKmRnrlGp6J1pXjB2oXVT5y12LW1jN7qu6gNmrnXtnkd9tDwlnmd2nsSiw6dnyjhfWsuIKCetYiEACUYeraXVwoaM3PbbpiQu9IV/iPoUn7wKCrPV0ln2BlsKsqVZvQEffQMGj7CmID/YcwpyyTH15n1wPTRUdD0/KMGWzjzISVOG23serYHSk13Pu0LPIzsYOiiQm8dFs/O42nefnpHLD26XMpfOTIKRB/vw5EWKqtQn5qgQP26Z4Bz7Ra7K0Kmw6I+qJXVbiZq8vbbzl87Dzp/Drl9bS9R8AUbfbCtR01SnglbmGsjd0/X5NW/V3qDz45yJrqueUplrXbvnkZ2tSE1sD0YbM3N5/NZr8PNxvnR0oUgw8mDGxIWlyfGu/YvqF6yas814AIqP2op3tpWtsbSo3jrHt6oZzrAZqizPud3Q2E1pm/DhauY1/QEIjR3Y76W32noeZa7tvsySK/Q8cqC544YQGxZAUVUDpTVN7DxWzO1TBr5MkegdCUYeqrCynveP20oHOl3iQn/ETITbfwe3PAVHN6s365xPbecrc9XRmZdv/641DQSLBc59oL6n49tct+fRAPDx9mL5zHj+8r5qTrhub44EIycmwchDvbovD4s1ceG6UZGMdMeLu76BKkV5yHiVBt5dMoJR0kNw4+MQ7oBSSP1VXaT2NWWuhYoLXc+7Qs8jEyxPSeCvu06j67D7VCm55XXOnaTjwSQYeaBWi84rxsSFWW40K2rTUKXSvTPXqDprvbHvP7DveZUhl7za/P1CllY4876taWFbi3cjV+h5ZKL4wUHMGTukffvCKxm5fGfhOJNHJbojwcgD7T51kfyKegAGB/mycJILJi50R9chP8tQuaGb0jZR11jTmdNUxlzWWtU6vb09tg6n31VHSKy6BpX0sMrKGyjtPY9e6H450RV6HjmRFamJ7cFow75cHr1lrP0q0gu7kWDkgTokLiTFu36plPoKW5WG4sNdz/sEdF/TLjhSZeHd/GM4sU0tgZ3dZXtcTRHs/qM6Rt2sHu+oGnOtLXD6PfU9nNruuj2PnND8CdEMCfXnYnUjJdWNvH+8hAWTnDQpxYNJMPIwJVUNvHfMkLjgKnuLOtN1yN2r3ryPvA4t9V3v09tq3z5+MOledZSfU/2H9r8ENcW2+5zdpQ57V9+uyFWvl/UiVBd0Pe8KPY+cnK+3F8uS4/nHByrjcP3eHAlGTkiCkYd5NTOPVmvmQurICMZEu1i2VV256jSauQYuHu963ifQtqmzL32QIkbC/J/A3B+qrqyZa9WMpa0id+1F+OQZdfS1L1Fbz6PMNR2f28gVeh65kLSUxPZg9MFJtUzt8DYp4qpIMPIgFoveoW/RilQnzBrrjq7DhU+tHWI3d+0QC/bvEOtt7d0z4S6oyLFew+k0ezn3kTraZi/JqyFq7OWf89J5dR1o/8uu2/PIRSVGBnHjmCg+Pl2KrsOGjFweu1Vmms5EgpEH+fRMGbnlajlrUKAvt0928j0XtWW2TZ1lp7qe9w3uuKnTUaVtwhPh5idgzvdUYkPm2o7XderL4bO/qaPzdZ22nkeZazpejzJy9p5HbmJFaiIfn1aJKhv25fLNeWMkkcGJSDDyIMbEhXtnxBHg64SJCxaLKm2TtVa1bOiutM2wGSoATV4K/qEDNzZvH1UaaNztUJmvZkv7X+yY8XbhE3W8/pUrP5cr9DxyM7dOjCEy2I+y2iYKKxv48ORF5rtiCSw3JcHIQ5TWNLLjqG1pyOmKotZehI//pJaxys92Pe8XqhIRklfB0GkDP77OBsXB3O/DnO/Y9gId39rz48YucO6eR27Mz8eL+5LjefYj9fO1fm+uBCMnIsHIQ7yWmUdzq7pQnjx8MONiB3BGcTnG9OUPf9f9feJT1Cxo0r3OuanTy1vVsevtPqTw4TB4uAQik9yfktAejN4/XkxRZQOxgwJMHpUACUYeQdf1Dkt0aSkmJy5UFcKBl9Tm1O4EDFKbUpNXQcykgR1bbzXXw1FrzyNj3bueZPxbHVI/zhSjhoRw3ahIPjtbhkWHV/fl8s35V0g6EQNGgpEH+OxsGefLVIvp0AAf7pxqQtdLSyuc3qmuBV2utE3idWoWNHGx827qbK8Int67nkc1JapLbNbajsuP+Znq2P6EygBMXuWRlbXNkJaawGdnywDV5+h/bh6Dt5d79nVyJRKMPED6XtsF9numxxHoN4CJC5V5trToqrzL3y/ly7DoDwM3rqvRVKc21nbuldTmSj2PQqLhxkfhhm9133OoqUbNEDOfV9fCklfD5Ps8pueQGRZOimVwkC+X6prJr6hn96mLzB0XbfawPJ4EIzdXXtvEO4cHOHGhtQVO7VCzgVM7ui9tM2I2FGXb+g0NccLilUWHVADKfrX7nkftXWR70fNI09RG1pFzrCnr69W/j7Eba+FB2PoYbP+RR3RjNUuArzdLkuJ57uNzgPqwJsHIfBKM3NymrDyaWlUwmJYQzsRhDvzEXZGjZkD7X4Tqwq7ngyLVG3fSKogaA1sfh33POW48fdFYA4dfU0GoIKvreXv0PAqOhOu/Add9HXI+U7OlI6/bNvM211lLEr0IMZNtm3kDw/vxjQmjFakJ7cHovWPFlFQ3EB0qiQxmkmDkxjonLqxwROJCa7O6BpS1Vl0T6q60zai51iKji5x3U2fBfhWADm1US2edRYxW13WmrYSQIfZ5TU2D4der47bfQPYG9e9YctR2n+LD8NZ3YMeTKqMweZVqGyGzpX4ZEx1K6ogI9p4vp8WiszEzj/+ZO8bsYXk0CUZuLOP8Jc5cVG0Ugv28uWuaHRMXys9ZS9u8BLUlXc8HR6tNnUkPQcQo+72uPTVUqWrfWWu773nk7QcT7laBdMSNjg0AQRFw7ddg1lchL0MFxsObbAVgW+pVNYqD61SzwOTVMPV+9TjRJ2mpCew9Xw6opbqvzRmNlyQymEaCkRtLN8yKFs+II9i/n//dLU1qY2fWWjj7QTd30GDMfGtpm9udcy+Nrqsstsw1ajmuua7rfYw9j4IjB3Z8mgYJqepY+Gtra4y1UHzIdp+Lx+GdH8C7P1WZh8mrVBkimS1dlTumDOWpLUeoamghp7yOT8+UcePYKLOH5bEkGLmpyrpmth2yXbdZkdKPxIXS0yoAHVhnaEJnEDrUVtpm8PC+v44j9bXnkZkCwyH1y5DyJXX9KnMNHHrN1jSwtREObVBH5FjbMuJAB1AX1ZbIsObT8wCsz8iRYGQiCUZu6vX9eTS2qMSFyXFhTIm/ykrWzQ1qFpS5RqUkd6Z52UrbjF2g6rY5G12H3D22BIH+9Dwyk6aprLq4ZOtsqa2d+gHbfcpOwY4fw86fw/g7rUuLs/uWYOFB0lIT2oPRjiNFlNY0EhUiLTvM4ITvIKK/VOKCbW9R2tXMii6eUG/eB9dB/aWu58Pi1XWgGQ/CoHg7jNYBHN3zyEz+oTDzC+ooOKBmrNmvQlO1Ot/aBEc2qWPwSDVbmv6A2u8kuhgfG0ZSYjhZORU0t+q8lpnHV2+S9h1mkGDkhrJyKjhRrN6cAn29WTy9h8SF5nrVJyhzjUo17kzzhmtuU2/eY+Z33NTpLHRdVcvOXDtwPY/MNmy6Om79hW1Tbv4+2/lL5+C9p+D9X6r2FMmrVft0mS11kJaaSFaOqqaRnpHLV+aMQnOlDyhuQoKRGzImLtw9bRihAZdJJCg+ot68s9Ntm0+NwhOtmzofhDAn7X1UW6o2kJrd88hM/iFqtpr0EBQdtpYresW2UdfSoqo+HNviGv+nA+zOqUP5xZtHqW5s4VxpLZ+fLee60XLdbaBJMHIzVQ3NvJlt60aa1rmba1OtobRNRtcn8PJx/k/RFguc/8haWudNsDR3vY9ZPY/MFjsZ7vg93PIz22w393Pb+YocNVPa9Rvnn+0OkCA/H+6ZEceLn18AID0jR4KRCSQYuZnNBwpoaFaJC+NjQ5meYN21X5htzcZ6FRqruj7QFa4v1JTAgZdVELp0rut5Z+t5ZCa/IJi+Qh0lx23ZkG3FXfVWOLFNHa5wHdDB0lIT2oPR24eKeOquJgYHO+kGbTclwciN6LrOuj22JbqHkiLRstZaS9vs7/oAL1+YcJdzZ15ZLHD2fRWATryllpw6c/aeR2aLHq8qPMz/qZpJZq6BCx/bzlflwQe/UT2lxtyq/i2dNUPSQSYNG8S0+EEczKukqdXCa1l5fGm2k27WdlOe89PmAbLzKjlWWMkU7RwP+r7P8o/3qGW5ztr3pKyAYCfdV9HW8yjrBbW01Jkr9DxyNr4BMHWZOkpPGfaOqXYK6BY4tV0drrB3zM7SUhM5mKc2F6dn5PLFG0dKIsMAkmDkRvbs2sxWv6eZ7FJ9PEIAACAASURBVHVefaHJcNLb37pbf7WqheaMv2SWVjj9npoFnXzHdXseuYKosbDglzDvSTi+Tc2Wzn1oO19dCB/9Hj76A4yeZ60t6KRVNezkrmnD+OXWo9Q2tXK6pIZ9Fy6RMkLKLQ0UCUZuoqahmXvP/IQhXp0avgUOhjnfg2lpzl3H7MPfwcd/7r7nUeBgVVkg6WG15CTsx8cfJi9RR/lZa73Blw31BnU4s1MdwdEw4wH1/+Cs9Qb7IcTfh7unx7UXF16/N0eC0QBywosEoi+2HCzkpCWu64n6S6qY6aGNqiSOs2htUdW+29Re7BqIRsyGpc/B48fhtl9LIHK0iFFwy1Pw+FFY/iKMng8YZtC1JfDxn+AvM2Dt3dZCrk2XeTLXtMKQfbotu5DKum4yNYVDyMzITaRn5HCy+Tsst3zAo+GfEFF72nay5Ai8/V14t60NwWrz2hBcumDt1fNS73oeiYHn7QsT71ZH2/9X1otQY2vSyLkP1REUpTL2kla7xf/XlLhBTBoWxpGCKhpbLLy+P4/VN4w0e1geQWZGbuBwfiXZeZU04E+6djte//MpfPE9tbHRN8h2x5YGtUH0Pwvh77Pgs3+o0jmO1toMR7fAi0vgmWnqWkR3gWjZGjULWvALt3hjcwuDh8O8H8NjRyBtPYxdqOoStqkrhU//Cn9LhucXqdJEzQ3mjbefNE0jzdANOT0jF13vpkeXsDuZGbmB9Axbttkdk2MJD/aH4BRISFHLW23VqosMbQhKT8D2H6pyMROtPXvs3Yag22sQl3HHH9SsTTgnbx8Yf4c6KvPUzDbrBajKt93nwsfqCBysMjWTVrnk0uri6cP49bZj1De3cryomv25FSQlOmkRXTciMyMXV9fUwhv7jRUXOhVFDRikWhB8dTd8eZd6g/ALsZ1vbVTBas0i+NtM+OQvqsROX7U0qWsJa+9W1xY+/lOnQKTBmFvg/pfUhXDhegbFw9wfwKOHYOWrqoOvZqjgUH8JPv8H/GMW/Oc2OLBe1T90EWEBvtw1zVYqaf2ebrYWCLuTmZGL23qwkJpGtRF0VFQws0ZeJvtH0yAuSR0Lf6Uay3XeDFt2Wl1X2vlzmNDWhmBO7zbDlp6GrDXqjeeyPY+su/zb9q2c2XU136pwNl7ecM0CdbTtC8t8ASoNb945n6njne+71L6wtNRENuxTCTVbswt58q6JhF2uxqOwCwlGLm69YYluRWpi7zbp+YeqQJO8WrXbzlzbsUyQpVnVrzvyOgweoWZT0x+A0JiOz9Pc0P2O/jZtPY+SV6ud/R60o9/jhA2FOd+FG78NZ3epnwljxYyGStj7rDriU9TP1OQlTlsxY0ZCOONjQzleVE19cyubDxTw0LWesfnXLPLu4MKOF1Wx31r63tdbY0lSN6ndPRk6De58WiUNdFdA9dJ52Pkz2PUrtekxeTWEDlMZVgfXX6Hn0cPWWmd9GJNwXV5eqvDqmPmXryWYl6GO7U+odh5OWEtQ0zRWpCby0y1HALVU9+CsXn7YE30iwciFpRsa6C2cFEtkfzpU+gVby7882H1rCUuLmgUde7P7x2veKlglrfL4KtDCKiQabnwMrv+W6hacuaZjlfXGKtj3nDqGzVA/O1Puc5oq6/dMj+PXbx2jscXC0cIqDuVXMjU+3OxhuS1JYHBR9U2tbMqybRJd0TlxoT9iJsEd/w++fQKuf6Tn+yfMUhez015W1w8kEAkjLy8YdRMsex6+fVw1A4zslLpfsB+2Pgp/GAdbHoH8TNUw0USDgnxZNNWQyLBXEhkcSYKRi3rrUCFVDWo9fnhkENeNsmP/laZatclxzZ3w6V96vn/uHnhugeqRU9lNOR8h2gRHwQ2PwDf2weptMGW5qpvYprlWFXD99zx4dnb3+9EGkPFD3pYDBe3JQsL+JBi5KOPeorSURLy87LCWXXgQtj5m/XT6jY4trEGVi5n7BCz8jSrVY1SVBx/+Fv48BV5eropvtsovrrgMTYMRN8LSf6vZ0sLfwJBOe5KM++IAcvcO+Gxp5vDBjIlWWyFqm1p582BBD48QfSXXjFzQqeJqMs6rxAEfL437kvvREK2xWtWty1wDhQe6nvf2Uz2PklZ17Hl03f9Y07nb2hBY07k7tyGYbi2s6SFtCEQfBEWon6dr/1vNsjPXwpFNqmKI0aurIHqiSqKZulxtrnWwtkSGX2w9CkD63hz7LomLdjIzckHrDYkLt06MYUjoVSYu6Lpak9/yTTUL2vpo10AUORYW/EqV57nvP2rNv/N+o6gxKgvv8WOqlM+ouR3PVxfC7j+oEkAvLlFtsFul8KS4DE2DxGvh3n+q2dLtv+96n5Kj8Pb34I/jYdNX4cKnDp8tLZkRh5+3+tk/mFfJ4fxKh76ep5KZkYtpaG5l037bdZkuFReu+OBKyN6gZjOdl0BArd1PukfNgq6m55GPnyrlM+leawkgayHUy7UhmL5Sqi+IKwscDLO+Arv/2LFAa5uWBpXtmZ0OUdeo2dK0FQ5pkzI42I/bp8Sy+YBaokvPyOGXcVPs/jqeToKRi9l+pIgKa1n7uPBAZo/poVOrrqs9HZlrrCX/uynLMmSCbemjv7/MEaPglp/CzU+oBnmZa+D0TsD66bW2BD75szqE6InxA9HX98L5j611FrNtXy89qfYsvfcUTLhb7VsaMduudRbTUhLbg9Hm/QU8cccEgvzk7dOe5F/TxRjTS1ekJlw+caH+Ehx8Rc2CSo52Pe8TqHbAJ62ChFT7t5Pw9lXXmibcZW1D8JLaKHu57KgdT6plvqix9h2HcB/+oZDyRXUU7FdB6dBGaKpR51ub4PBGdUSMVkFp2koIGdLvl752VAQjo4I5V1pLdWMLW7MLWT4zoecHil6Ta0Yu5OzFGj4/q1o+eHtpLOv8y6Drag1901fUmvo73+8aiGImqwrZ3z4O9/wDEgegr9Hg4TDvR/DoYViRDtfc1rENAagZ299mWtsQbHDpNgRiAAybAXc9o/bC3fUXiEvueL78DLz7E3h6AmxYBWfeB4ulzy+nEhlsv2+y58j+ZGbkQtIzbIkL88ZHExMWoG7UlqnSPFlr1ZJFZ77BahaU/AVVKNWskibePqpKw7jboTIf/jSx633a2xB8z1ZYM3rCwI9VuAb/EPUzkrwKCrPV70D2ho51Fo++oY7w4ep+0x+A0NirfqmlSfH8fvsJmlt19udUcLyoivGxYXb+hjyXzIxcRGNLKxszbYkLK1MS4NxHsPGL8PR42PGjroFo6HS4809qFrT4bxCfbF4g6mxQHMz8YsevdW5DsOef8I9r4bmFKn28qW5gxyhcy9CpsOiP1p/3f6jKIEYVF1RF+qcnQvoDcOo9sLT2+ukjQ/xZMMkWxIzluET/2WVmpGnafcBNwHRgGhAKvKzr+oP2eH4B7x4tpry2iUgq+ULwZ8x990m1FNGZX6iq75W8Si1luIo7/gDj71SFNbPWQoVhGST3c3W8/QOVZJG8GmInmzZU4eT8gmHGA+ooPqp+ng6mQ4MqKozeCse3qmNQgq2ob9iwHp96ZWoi27LVdc9NWXn/v73zDo+qzP74550ESGgBQoeE3nsCAaRJB0VUigIq4BbXta2o+7OtfV1Zd3XXtuq6KqAC9q6IgoqVklAiHZUaCAklJBACSe7vj3OHuUkm1MncyeR8nud9hpl7Z+YwmbnnPe97zvdwx+j2RFVS+atAEKhlur8gTigH2AmUv/aOIc6P3y7m6UpzGOFZQeWCAijeLbxJolykO42TpYvySM1GMPA26H+LtCFImS1KDt42BHlZsPwFGU16isMtz/9fpexp0BFG/x2G3Q/rPpDv1LbvfMezdogi/VePSEv1xOnS/LGUdid9W8YSX6cq2/cf4dDRfD5J3c24hHMoOldOEChnNANxQluQCEm7pgWQHTu3c0/6zVSJKFYwWiXGjhSmQcMwqnso0YZgrlxE9v/iO2fXChkL7oKuEyUrsHF392xWQptK0dDtchkZm3zKIbn2rM4qhE2fyqjRGBKukmaQtYomCXk8hklJcTy6YCMgiQzqjAJDQPaMLMv60rKszZblssxumPJ+yg4i8aPzVrma1AVFhbGsffX60P9muCEZpn4AnceLRJGXY9mw4iX47yB4fhCseFkkjhSlNOq1lW7Ht26A8S9Ci4FFj2enwdd/F53FVyfA+o+KKIdMSGxKpF1SsXzrAbbs1e9bINAEhhDneEEhs9bkcuXxu/i+oFj2mfNH89rEEj+asMLbhmDCSyJRNOJhkSxysnuVow3BjSHRhkAJYSKryP7qtA/hxhTo9yeo5qxJsmDL5/D6FfCvzpL8cGAr9WtEMayDr+vxPE1kCAjqjEKcRevTyczJ44fCTsyIfoj861bIj6aqU3nBgs0LHT+ah6RDa7hSLRbOuwFuWA7TP4Gul/tpQzBH2hA8NwCWveBrEqgo/ohtBcMfhBnrYOJsaDWk6PGcPSJN9EQ3mHMJNzZaSyV7teLtlJ0cPX76WXmKf0LGGRljkv0NKngyxFzHrOuynnFE1m8jP5oT4qSDiz4hZ48tTtodXrkU1r4H+ceCa3SwMAaa94Nx/5Ull1EzS7YhSE+FT26TaOm961xpQ6CUIyIriz7jVe/CTatgwK1QvUHRc375kk7f3sjSqBu5I3IetXK389laP/p5yhkRMs5IKcmO/Uf4ZnMGINfdIvIjXnHSqe+V8qOxpOr8zWlSXPr5fbDPTyp4uFC1jrQguO5H+M1CkYGJjPYdz8+VtPEXh8N/+sKPz8GR4imJiuKgTgsYei/MWAuXvwZtRgC+Or06ZHFt5Id8VeVWrC/ud83McCFknJFlWYn+BrDBbdvc4o0VO05M4ge0qUdcnar+Tyzyo3kVWg/H+aPhcIYIkz6VALMvEj2v/Lwyt98VjBGJI28bggv+KRJITjLWi1TSY+1FOikIbQiUckxEJegwBq54E6a+D1VLdlUemv0hv2giwzmhckAhSn5BIW+s8C3RTUk6DVFGpzjpwe2+Vg7Zju6Uvy6REV1HWjkkTg9fcdLoWpD0e+j1O9iVAskvi3L58cNyvCAP1rwuo25bSQ/vNln2pBTFS36eFMgmz5LfTjEKLcNLBaM5smInd16g0lVnizqjEOXLjRmkH5LopW71Kgzt0OAUzyhGrXgRJx10u2QEJc+SJAfLFovM3Q8/PC2jWT+5EHccK/UY4YYxIoXUNBFG/k1UnZNnF20omLlJJJUWPSDOPHF6wNsQKOWMzM3yu1k9D47sK3m8RmN+jb+UK5Pbsot6xCbv5NYR7agcGTILTuUKdUYhilMVeGLPplSKOMsveHFx0pWvSqbZIZ/OHdu+k/Hp/0lkEM7ipFE1oedvZKStFKeU+pbUK4HdhuBtGXVaipPufkVA2hAo5YDjR2H9B/K92PZtyePGI3tHidOh9XDiTQSFWxZD1lH2HT7G5+vSubBro6CbHQ4ESpvuEuAS+65XSbCvMWaW/e9My7JuC8R7VQTSDuby1ca9J+5P6hWgvikxTeD820Vy5+fFMuvb+KlodYFody19VkZcb/nBdbwEKpeyV1XeadxDxoi/wtp35PPYlew7vv8X+OI+WPwQtL9QPo8W55dsv66Uf/auFwe0Zr6I9BanZlOfhl1MkxMPRyCJRU8s2gzIJFKd0dkRqMioOzCt2GMt7QGwDVBndJq8sWIHhfZ+er/WsTSLrRbYN/BEQJvhMrL32NFScXHSpTJOiJOGmeSQkyrV5UKTMFXasSd72xDYtUmF+bDufRm1mvkuSmfRhkAJIY4dkdYSybNFiLc4JkJWFBKnS92Rx78g6mW94nhq8WYKLfh2Sybb9x0hPjZMJ3BlSKDkgO63LMucZDQPxPtUBAoKLd5w9C2anBRftm9Yo6FESjetltqKjheDxzFH8YqTPtdfikhT5kBeTtna5CYNu8CF3uaDz/pvQ7D4IUcbgs/PqA2BEgLs+Qk+vk2yKd/7Y0lHVCsehtwDt6yDSa/JpK0URwTQpFY0g9r6lnHnL9fGe2eD7hmFGEs2ZZCWJV1O61SrzPCOZ5i4cLZ4PDL7azXkJOKkyTIW3GW3qZgevuKklatKtmH3Kb4lnNXzSm9D0OOqEks4SgiRl2Mvxc4Wgd3ieCLPaSl2clI8X26UmsA3VuxkxvC2Z7/PW0FRZxRizHUkLkxIbEqVSBd6pXjFSc+7STZxk2fB+g9lcx9ksz/5ZRmNuskPuPMESQ4IR+p3gNEzpQ3B+g/k8yjehuCrv8HXM4tsbpfWhkAJImmr5O/lTFJxciJJZYp878+SIe3rU79GFfZm55GZk8ei9XsZ1VmXcc8E/bWEEOmHjrJ4QxkkLpwtHo8oGrcY6GttnjwL9m32nbN7NXw0Az77S2i0Ni9LKkXJ/lnXy3xtCJxpv1YhbFogo0YjiZYSrpJlHyV4HD3kP33fS0RlX/p+s/4BSUiJjPBwWc84nv5yCyCJDOqMzgx1RiHEmyt2UGBnLvRuUYeW9UKoaZxXnLTv9bD9B3FKa9+TwlGQQtKVr8ho0Fl+6F0mSuFpOOJtQzD0Xv8Fkdm7YcmjsOQf0pcpcTq0HSWFyUrgsSwpbE6ZBalv+wqbncS2kb9DGRU2X94rjme+2oJlwZLNGezYf6R01RSlBOqMQoTCQov5jsSFKb1DdDZtDDQ7T8aomZJ1ljxLJHa8pP8k4qQL7xH9vMTpEJcUntFSZBXpsdR5vGj/pcwRDbzDGfYJFmz5Qkb1BlKzlDBVJJyUcyf3IKS+KVFQemrJ4xFVRPg0cTrE9y3T72Bcnar0b12XbzZnYlkyubxlRLsye79wQ51RiPDtlkx2HsgFoFbVSozsVA5C/Kp1oM+10PsPsHO5OKWf3hFRUpDb1XNl1GsvF4Sul8vzwpHYVjD8ARh8t3QMTZ4l9VxectLh28dltBws6fLtLhTRW+X0sSxRX0+ZXfT75qReB/v7dllQv29TkuL5ZnMmAK+v2MFNQ9sQqYkMp4U6oxDBqbgwrkdToiq5kLhwthgjkU9cksjt+JupZmyABXeIenjHi+VCQZiKk0ZWlv9jx4ulr5RXIzDH0Wbgly9lVK3r0wiMbeWWxeWD3ANS65U8u2gk7iUy2t63nA5Ne7kSiQ/r2IC61auQmZNH+qE8vtqYwbBgZcSWc9QZhQAZ2Xl8vi79xP3JpyOKGqo4xUnTUuxMpreLipOmviGjIlC7OQy9B86/EzZ/ZmsEfs4JR3wkE75/UkbzAXIh7XCRLP8pRdXUnz3P/zkNukiUGQJ7lJUiPExIbMpzX0u7lnnLtqszOk3UGYUAbyXvJN9OXOjZrDZtGtRw2aIAYAw0SZQx8m+SWps8y392E8geU922ckEOR7mdCLuOpf2FcHCHREorX4FDu3znbP1GRnQdn0ZgvQq653B4nyzvOqNJJ5WqQZfxdq1baGVvTuoVd8IZfblxL7uzcmkUE4YCxAFGnZHLSOKCb4muzBUX3KBKDeh5tYy0VbLWv+bNknUfc8badR9TbXHSs6/7CGlqxcHgO2HgnyWxIWW2pIM7FdV/fEZG/HnilDpeHJ6K6k4KC8UZp8wuWtfmpFF3O1NzgnyvQpDmdatxXqtYvv95H4UWvLF8J38aFqZtWgKIsUK8qZgxJjkhISEhOTn51CeXQ77fksmU/y0FoGZUJMvuHla+9ovOlrwceLSF/wsO+CriE6bJZn84RktODqXBytckGy/Lj5xMVAx0nSQX4gYdg25emZKzVzIQU+YUVfwozuT5ohVXDvhwdRo3zlsJQOOYKL65fQgRntCJ3gJFYmIiKSkpKXYj1HMizH/hoY9TceHSHk0qhiMCESftcZXvvvFAlRjffa846avj4MnuUq9zaHfw7QwWNRvDoD/Dn1bBFW/LvpFTI/BoFix7Hp7tC/8bLst8x/zU0pQXCgsl0/CNqfB4B/ji/pKOqEnPovcbdQuaeefKiE4NqFNNsiTTso6yZHPGKZ6hqDNykX05eSxc60hcCNXaomAw+lGHOGmfoscOboPFf4V/dRJx0k0Lw1ec1BMBbYZJ+/gZ62DofZIE4WTnMnj/ehH6/OgW2L3GFVPPiuw9sOSfMsF45VKZcBTm+45XiYGka+Da7+D3i0TJohxSJTKC8Qk+ncJ5S1U89VTonpGLvJOyi2MFsk/QPa4W7RuGqbbb6VJcnDRljgi2+hMnrdlUpHZ6XAkxTd21u6yo0QAG3AL9boZfv7b3Uj6CwuNyPO8QrHhRRuME2VvqPD709lIKC/z3z3IS18feGwuf/lmTkuJ54ZtfAVi0YS97Dx2lfs0ol60KXdQZuYRlWcxzJC5MCcfEhXOhfgcY9YhEBv46bx7aCV89Al//XcRJE6bJbTiKk3o80GqwjJwMn0bg/p9956SlyPjsbnFIidOlcaCbWWbezsIrXxEx2eJE1ZKJR8LUsOws3KpedZJa1GHZr/spKLR4M3kn1w9u7bZZIUsY/nLLB8t+3c8vGbLmX71KJGO6lc/liDLHKU6auVmig1VzK644afV60O8mOO9G2PqtfB7r3ncoqufIYymzoWFXX/1NVMzJXzdQFOTDls/teqqFvgxBJ836i10dxsrfN4yZkhTPsl/3A1Jz9MdBrfCEYSJDIFBn5BJOxYWLuzemamX9U5ySum2kRfiQe2xx0tmyfOWluDhpwjTJvgpHcVJjoMUAGaMfhdXzxQFkbvSds2cNfHyraAR2HgcJ06Fpz7KJlg5ut5UmXpG/Q3GqxtpR0DT5O1YQRnVuSMwHlcjKPc7OA7l8uyWTgY5GfIoPvQK6wMEjx/jkJ18xX1jWFpUlxcVJV9pyO/7ESavVl32lcBYnrVoH+l4Hff4I23+UqGjtu5AvTRo5fsReLnsV6neSqKTrZRBd+9zet+C4RKTJs2DLIvzKO7UYJO/XfkyFVJWIqhTBuIQmvPzdVkC6wKoz8o86Ixd4J2UXx/Jl+aJLkxg6NwnSEko4EttKmt6df5ctTjrbFie1L4yH9zrESc+XvZRwFSc1Bpr1lTHqEZ+i+t51vnP2roVP/w8+v1cU1ROmQXyfM4uW9v/qUyfPSS95vFo9mQD0uEr19pDJptcZLVybTkZ2HvVqVDzHfCrUGQUZy7KKLNFpVBQgioiTbpNoKeWVYuKkX8nwipMmTIO6YbqhHF1b1NSTroGdK+z+U+9IlAQSNa2eJ6NuO7vPz6TSFa7zj8HGj+V1fvnKzwlGWtYnToO2o8PT2Z8lbRvUoGez2qzYdoD8Qou3U3Zy7SB10sVRZxRkUrYfYPPeHACqVo5gbPfGLlsUhtRuBkP+AoPusMVJZ8umuncz3Z84afsx4bmZbgzE9ZIxyquoPgv2OBTVMzfCZ3dK4WnHsXYH1H7y3MwtjqSRzJKvX72hnWJ/lXzuil8mJcWzYtsBAOYv2841A1pqIkMx1BkFmblLfSmuY7s1pnoV/ROUGU5x0qydsmeSMqcUcdLa0G1KeIuTRsWImnrP30LaSrv/1NuSgQe2ovqbMk6G8UDr4fJZtRkZnun0AebCLo144MO1ZB/NZ+u+I/z4yz7Oa13XbbNCClVgCCJZucf5ODXtxH1dogsiMU3h/Dvg5lSY8ga0uwCMQ3op94AIkz6TBC+Nkuy0436atoUDxkCTBBj7pKheXPSE1CSdihqNpRXGzalwxRvi5NURnRbRlSO4tIdDkWG5n7qrCo46oyDy/qpdHD0uS0UdG9Wka1NNXAg6nghoOxImz4MZP8Hgv0BMsUnB9h/g3T/AY+3gk/+D9LXu2BoMPJEQGSXjVEREQkRl8IRhqnwQmNTL9z377Kc97D9cikhwBUWdUZCwLIu5S52JC3GYEOrBUiFxipNeeTJx0vPgf8PKvzipk/S14mgfayeOd/sPp37Owe2w6AH4V0d4/UpJnS/0U9Sq+KVj45p0j5Pmf8cKCnknZafLFoUWGmMHidU7s9iwR/r3RFXycLEjZFdcxhMBrYfJyE632xnMlpbhXnYul7HgTlE0SJwOjbq6ZfHZceyw1B8lz5L/S3E8kbJ8mTgNWg4RGaL0tZIAsma+OGcQYdP1H8qIiZcarh5XiHNXTsrkpDhW7RCtxbnLtvPb/i10UmqjkVGQcKr2junamJpRutQRknjFSW9cCVPfl1oc57KUV5z0+QHw3/Plwp6XXdqrhQa714i692PtRe27uCOq3UI0AGesg8tfEafs7R/VoBNc8CjcuhEufR7i+xZ9btZ2+NJWVJ83GTZ9Fr6K6gFgTFdf0tIvGYdPSAUpGhkFheyjx/lgtSYulCs8HimSbXk+HM6U1OYS4qQrZYSSOKmXvGzJlEueJTYWx1NJliUTp0HzgaduXlgpWuqQuk2CjI0SLa2eK4kfIGnzGz+RUbOJpHr3uFK62ionqFYlkrHdG59Ysp+/fAe9W8a6bFVooJFREPhgdRq5x2W22K5BDRLia7lskXJGVKsr4qQ3JsP0j2WZLsJRQe8VJ31hsERMy//nW9IKJpYFu1Lgg5skCvrwTyUdUWxrGP6QZNFNfFmc7Zl20a3XTmqWbtkA41+UWi0nh3bB1zPhia7w2kTY8LEIqCpAUYX+j1N3c/CIJjKARkZBwam4MEkTF8ovxkDz/jJG7y9FnDTVJ07aaZxES2UlTurlaJZdzDpbxFGLE1FFlCkSp/mKWQNBpSjoMkGGv+JYq1CUuzcvlOLYHldKgWzxZoEVjM5NYujSJIbUXVkcyy/knZRd/KZ/mOomngHqjMqY1J1Z/LTrEABVIj1Fag2UcoxTnHTHUltup5g46apXZQRSnNSLZYnMT8os+Mkh8+OkXnuRPDqZzE+gqNsaRjwkiur+ZINy9sA3/4RvHpO+TInTJVkiHBXVT4NJSXGkvivR8/zl27m6X/MKP0lVZ1TGOBvoXdClEbWqqmZXWGGMCI3G97HFSW25nb2O2qRAiJN6yT1gC6DOLvoeXiKj7IhsGsT1Dv7+VWRl+T92uhT2TDsOpAAAF3FJREFU/2K3lXhVBGsBsETI9ufFIqja/QrJxqtggqpjuzXm4Y/Xc+RYAZvSc0jZfoDEZmU8YQhx1BmVIYfz8nl/pU96RhMXwpzo2tD7Gkj6PexKhuSXi0YtJcRJp0G3yaeOWizLf2sIJ/U7SbTRdWLgoq9zpU5LGHYfDL7Lf6uJwxnw3b9ltBjo0wisAK0makRVYmy3xsy3lRjmLduhzshtA8KZj9akcfiYJC60qleNXs1D5CKhlC3GyD5R054w8hGHOKljPydzI3x2ly1OerFES837F41kjuy3W4zPLrov5aVSVV8WX5PE0Mji80eEnbnX4SJbUf3Vkk34fl0io2qsOOjE6WHfhG9SUvwJZ/TRmjTuGdORmOiKuWwJ6ozKlLnLfPpTk5PiK/yacIUkqib0+q0Mrzhp6lsOcdJjPnHS2NY+9esNHxdtJ+6kYVe5WHeZKK9fnqjdDIbcDYNu99+e/Mg++OFpGc36+e8aGyZ0axpDh0Y1Wb/7EEePF/L+ql1M7dvcbbNcQ51RGbEu7RCr7UrryhEexiU0ddkixXUa95Ax4mFHDVCK7/i+LfDFff6fW7m6ZK15a5nKOxGR0hK+3WjI2uVQVHdI5Gz7ruhz9q4PK5UHYwyTk+K4933Z+5u7dDtX9WlWYSetWmdURsx3JC6M6tyQOtU0cUGxqVJd9ot+twhG/PXU59duAX9Ycvrq2uWNmCZw/u1w8xqY8qbsGzkV1b28Og5eHCnp48f8ZA+WQy7u3oSoSnIZ3rAnm9U7XahPCxHUGZUBuccKeNeRuDApSavQFQfZ6ZLi/FQPWPiXU59/4FdpbfH6lbD5i/CV2/FEQNsRMOk1mLFW0sSLs+NHeO+PUtT78W2w56fg2xlAYqIrMaarL9qb76hJrGioMyoDPk7dTfZRqThvHluVvir3oRQWiCN5/UpRvV70YFEhVpBU7Iv/A79bDL2vlWZ4J55vi5O+Nh6e6A5fPwqH0ghbajaCgbdB9Qb+j+dlwfIX4Ll+8MJQWeLLywmujQFismOy+sHqNLKPHnfRGvfQPaMyoKjigiYuVGgOpdn7Ia+IqGhxomIkeyxhGjTo6Hu8aSIMu1+SGJJnw/bvfceytsOXD8NXj0DbUfLcNsMlsgg3jGO+fM3XUkibMltqmLzsWiFjwV2OfbXuwbb0rEmIr03bBtXZlJ7DkWMFfLA6jSt6V7wW7uqMAsym9GyS7V73lSIMExI1caHCUVgAmz+Xi+amBb5MMSfx58lFs+NYESH1R3Fx0pQ5sl+Says9VzRx0ur1of/NcN5N0io+ZbZEi96Mw2PZUtuV/DI06i77cp0nhHzGoTGGSb3iefCjdQDMX7ZDnZFy7jijohEdG1K3evgX8Ck2B3f4amgO7Sp5PLoOdJ8iigP12p3Za9drByMfln2UDR9JJt7Wb3zHveKkSx6VFhCJ06HNyPBsC+7xQMtBMg7vs2uxZsG+zb5zdq+Cj1bBZ3+BLuMhYbq0Wg/RVYpxCU2YuWADx/ILSd2VRerOLLpUsE7QYfhNdY+jxwt4J0UTFyoUBcelh0/KbImGvOoCTpoPEOfQ4aJzVxdwipPu+1ned+VrFVectFosnHcD9L0etn1vq1S8BwV5cvz4YYkoU+ZAgy4SLXWZCNGhpZxfq2plLuzS6ETi07zl2+nStIvLVgUXTWAIIJ/+tJusXNl8jKsTTb9WdV22SCkzDmyFRQ/BvzrD61fIxd/piKrWhX5/ghtTYPpH4jwCLXMT2wqGPwi3rIeJs6Dl4KLHveKkT3SHVy61i2jDdHPcGGjeD8b9V9pjjJopQrFO0lPhk9skE++962D7UpFaChEm9XIkMqxK43BexWq7oZFRAJnnUFyY1Csejyc0lwSUsyT/mOzPpMyGn7/EbxTU0qFIHRmk2rIi4qS/yjLhylchJ90+oYKJk1atI2rqva+FHcsciuq5cjw/V1rLr3oN6nWwFdUvL3tl81OQ1KIOLetV45eMw+Tk5fPRmjQu71Vx9Cw1MgoQW/bmnGghHOExTNTEhfBh38/w+X2Skv3mNLmoOx1R9QYw4Fa4aRVMfQ86XRI8R1ScOi1g6L1Sp3P5q9B6OOCYFHnFSZ9KgNkXiRJEfp47tpY1xkB8b7j0WYmWLvgnNOhc9JyM9bDgDomW3rkGtn7nWrRkjCnSeM85ua0IaGQUIF53KC4M61Cf+jWjXLRGOWfy83yJAr8u8XOC8SUKtB0Zen15nOKkB7f70suzHbVJFUmcNLqWqKn3+p10wz2hqH5YjhfkwZrXZcS2sRXVp8ieVBAZl9CURxds5FhBIat2HGRd2iE6Ng7tbMBAoZFRAMjLL+CtZJ+m1iRtFVF+ydwMn90Nj3eAt35T0hHVaCwinzevgSvfgg5jQs8RFadWvLRxuDkVJs+HtqOL1u94xUmf7gkvXyD9ko77aVMRDhgjNVwXPy3R0ph/SRq4k32bRRnj8fbyHfjlayj0k55fBtSpVpmRnRueuO+UFQt3NDIKAJ+tTefAEdkYblIrmoFt6rlskXJGHD8K6z+QKKi4OCfIhbvNSIkcWg8rv+nS/sRJV74CWY7loG3fyYj6sx0tTYP6HdyzuSyJqgk9fyMjbaUUF6e+JfVKIPVLP70to05L2WfrfoXUO5Uhk3vF8eFqiWDfXbmLO0d3ILpyGBY0F6Oc/qpCC6ee1OW94ojQxIXywd71cgFaPQ+OHix5PCbOdwGKCbN28V5x0oG3yR5Y8izY+ClYtu7d0YOw9FkZcb3tAt1LoHJVN60uO04oqv8V1r4jn8euZN/x/b9I76nFf4X2F4rqRcvBUvMUYPq0jKV5bFW27jtC9tF8Pk7dXSGK59UZnSNbMw/z/c/7APAYmNgz/L805ZpjR2Dde3Kx2bG05HETIZFD4tXQanB4Suw48USIlFCb4ZC9x9fK4eA23zk7lsr49A7oeplESw3DtAamSnWZgCRMhT2pMllZ84Zo4YFoBK57X0atZnJejyuhRsOTv+4Z4PEYJiXFM/PTDYAU0lcEZ6R7RueIt1MjwJD29WkUU4q0i+Iue1JF5fmx9qL6XNwR1WomWWi3rBPV6DbDwt8RFadGQ4mUbloFV70rHWg9jvnqCXHS/vDCkHItTnpaNOwCF/5T9pYusSNEJwe3weKH4PGOMP8KKXoOkKL6+ISmRNorLMnbDrApPTsgrxvKaGR0DhzLL+St5KK1RUoIkZfjf8nFi6eSLLkkTocWg8pkyaVc4vFAqyEycvaKHl4JcdJkGeVUnPSMqFxVZJy6T/G/tGsVSOblho9kaderEXgOS7v1alRhRKcGfJK6B5Do6L6LOgXifxOy6K/vHPhifTqZOSLS2LBmFOe308SFkCBtFXx4s0RBH9xY0hHVaelTLrhstr0cpz8Fv3jFSW9IhmkfQufxEOGoofKKk/53EDw/CFa8BEcPuWdvWVO/A4yeCbduhHEvSGt0J1k74Ku/wb87w9zLZR+u4OyUFJyT23dSdnH0eJj2sbLRyOgccIqiXtYrjsgIvaC5xtFD8NNbEgXtXl3yeERl6DBWZvDN+4esYGbI4vFAi4EywkSc9JyoFCX7Z10vg4xNEjmunidp8iAagZsWyKjRSKKlhKskzf406d+6Lk1rR7PzQC5ZucdZ8NMeLukRZok0DvTqeZbs2H+EbzaLOKUxcJkmLgQfy4KdyfD+DRIFfTSjpCOq2xZG/g1u2QATXoQWA8Lz4hhMvOKkNyyHqz8VKZ0Ih+6eV5z0f0PguQGw7AXI9ZOtGC7UayuK6reshwkvicN2kr1b1NT/3RVeHW+3vTi1RqDHY5jsqFmcG+ZdYDUyOkucxWiD2tajae0wTXkNRXIPQuqbMjNP99N2OjJK0pATp0N8H3U+ZYUx0Ow8GaNmStZZ8iyR2PHiFSddeA90Hicp0XFJ4fk3iawiy5idx9uK6nNE/+5whn2CBVu+kFG9gU8jsE6LUl9yYmJTHv98EwWFFst+3c/PGTm0qlc9OP+fIBOwyMgY09QY85IxJs0Yk2eM2WqM+bcxpnag3iNUOF5QyJsrHIoLmrhQ9liWqCy/+0eJgj65raQjqt8RRj8q2U/jnodmfcPzoheKVK0Dfa6F636A334uF9pIR2apV5z0pRHwn77w47NwZL979pY1sa1g+AMwYx1cNkeSQZzkpMO3j8OT3WHOxbaQ67ESL1O/ZhRD2/uKbOeHcXQUkMjIGNMK+B6oD7wPbACSgD8Bo4wx/SzL2heI9woFFm/Yy95sEZesV6MKQzuUbUV2hebIftELS54FGRtKHo+Mlplo4nRo2lOdj9sYI5FPXJIsj6a+Kdln6am+c7zipJ/fJ6KyCdMkugrHv11kZUmR73ixtB1J8Sqq7/Gd88tXMqrWtZsvToO6rU8cntw7noXrRIH97ZRd3DayHVUiw6/sIFDLdP9BHNFNlmU95X3QGPM4MAN4GLg2QO/lOs7ZyWU9m1JJExcCi2VJo7TkWXYPHj+q0g27iAPqMhGiKlZHzHKDU5w0LUX+nqlvh5w4adCo3RyG3gPn3wmbP5PPw9mQ8UgmfP+kDG9DxvZjGNimHk1qRbPrYC77Dx9j4dp0LurW2L3/Rxlxzs7IGNMSGAFsBZ4pdvg+4BrgKmPMrZZlHT7X93ObXQdz+WpTxon7l/fUJbqAcXgfrJ4rM2lnlpaXStUcNS09wnMmHY4YA00SZYz8m+i/Jc+S7DsvXnHSRQ+K0njCNLkghyMRkVLf1v7C0lvVb/1GRnRtIrpN4Q8dz+fe7+XQvGXb1RmVgncxdKFlWUWkbS3LyjbGfIc4qz7AogC8n6u8vnzHiXYnA9rUJT5WExcCwtLn4LO7RJyyOI17iAPqPB6q1Ai6aUoAqVIDel4tI22VpESvebN0cdLcA+7aW9bUioPBd8LAP0tiQ8psSQf3XkpzD8CPzzCVZ+hQuR1z84fwyc+92Zp5mOZ1q7lre4AJhDNqZ99uKuX4ZsQZtaWcO6NVOw7y5CLfjP2bzZn0/OvnLlpUvrm9YCcTvXf2bSlyLIdoPjUDec8zlI17W8KnwKc/BttEpcy5gGhrMMM933Np4Rd0wREROxUfgNFPLCHDhOkSHgARwG+o57mYsdaXXFy4iMb4VmF6eTbSq/JG7rdms/nNMTSf+ghUq+ueuQEmEM7Iu2CfVcpx7+O1TvYixhg/ei0AtC/l8aCzaH16ice8CgzKmXMo0lPiG5hS2Jp5BUP4qKAPuXgbFOpnHN5E8BIDeIkBtDfbmRSxmHER31LTHClyVvphi/0V4LuQSQ3WM5Z/MIYBnlQmRSxmmCeFSkYUGGLMETrt/QAiH3fZ0sASjDoj78K+O718A8iRY+EtxxFsPijoy/iIJRgs3ikYwPyCwWy0dA+uIrPBiuf+/OnMzJ/MBZ6lTI5cTC/PJj4s6MN+KkbHUy+FePi6sBtfF3ajHgeZELGESRGLaebZy/bGF9AuzJasA+GMvJFPaSlNNYud5xfLshL9PW5HTAlnZ1pguWN0e64Z2JKvN2bQtmENmtRShe5zYxjHC38PxsMYYxjjtjlKiHEh8CAZhQX0MR6WV/iElQlgFZKb9h3tYsNv0hYIZ7TRvm1byvE29m1pe0rlhkoRHhrUjOKyXnFum6IoSkWl5jC3LSgTAlEg86V9O8IYU+T1jDE1gH5ALqC7z4qiKIpfztkZWZb1M7AQaA5cX+zwA0A1YE441BgpiqIoZUOgEhiuQ+SAnjTGDAXWA72Bwcjy3N0Beh9FURQlDAmIjo0dHfUEZiFO6FagFfAk0DecdOkURVGUwBOw1G7LsnYAVwfq9RRFUZSKgyp8KoqiKK6jzkhRFEVxHXVGiqIoiuuoM1IURVFcR52RoiiK4jrqjBRFURTXUWekKIqiuI46I0VRFMV11BkpiqIorqPOSFEURXEddUaKoiiK66gzUhRFUVxHnZGiKIriOuqMFEVRFNdRZ6QoiqK4jjojRVEUxXXUGSmKoiiuo85IURRFcR11RoqiKIrrqDNSFEVRXEedkaIoiuI66owURVEU11FnpCiKoriOOiNFURTFddQZKYqiKK6jzkhRFEVxHXVGiqIoiusYy7LctuGkGGP2RUdH1+nQoYPbpiiKoigO1q9fT25u7n7LsmLP9bXKgzP6FagJbHXZFC/t7dsNrloRuujnc3L08zk5+vmcnFD7fJoDhyzLanGuLxTyzijUMMYkA1iWlei2LaGIfj4nRz+fk6Ofz8kJ589H94wURVEU11FnpCiKoriOOiNFURTFddQZKYqiKK6jzkhRFEVxHc2mUxRFUVxHIyNFURTFddQZKYqiKK6jzkhRFEVxHXVGiqIoiuuoM1IURVFcR52RoiiK4jrqjBRFURTXUWd0mhhjmhpjXjLGpBlj8owxW40x/zbG1HbbNrcxxkwwxjxljPnGGHPIGGMZY151265QwBgTa4z5nTHmXWPMFmNMrjEmyxjzrTHmt8YY/Q0Cxpi/G2MWGWN22J/RfmPMSmPMfcaYc+6VE24YY66yf2eWMeZ3btsTCLTo9TQwxrQCvgfqA+8jvUSSgMHARqCfZVn73LPQXYwxq4BuQA6wE+m58pplWVe6algIYIy5FngW2A18CWwHGgDjgBjgbWCiVcF/iMaYY0AKsA7YC1QD+gA9gTSgj2VZO9yzMHQwxsQBqUAEUB34vWVZ/3PXqnMn0m0Dygn/QRzRTZZlPeV90BjzODADeBi41iXbQoEZiBPaAgxCLrqKsAkYC3xsWVah90FjzF3AMmA84pjedse8kKGmZVlHiz9ojHkYuAu4E7gu6FaFGMYYA7wM7APeAW5z16LAoUsEp8AY0xIYgXSafabY4fuAw8BVxphqQTYtZLAs60vLsjZX9Nm9PyzLWmxZ1odOR2Q/vgd4zr57ftANCzH8OSKbN+zbNsGyJcS5CRgCXI1ce8IGdUanZoh9u9DPBSUb+A6oiiwpKMqZcNy+zXfVitDmIvt2jatWhADGmA7ATOAJy7KWuG1PoNFlulPTzr7dVMrxzUjk1BZYFBSLlHKPMSYSmGrfXeCmLaGEMeY2ZB8kBtkv6o84oplu2uU29vflFWTP8S6XzSkT1Bmdmhj7NquU497HawXBFiV8mAl0Bj6xLOszt40JIW5DEjy8LACmW5aV4ZI9ocK9QA+gv2VZuW4bUxboMt25Y+xb3S9RTgtjzE3ArUhW5lUumxNSWJbV0LIsAzREEjtaAiuNMQnuWuYexpgkJBp6zLKsH9y2p6xQZ3RqvJFPTCnHaxY7T1FKxRhzPfAEksI82LKs/S6bFJJYlpVuWda7yBJ4LDDHZZNcwbE8twm4x2VzyhR1Rqdmo33btpTj3iyf0vaUFAUAY8zNwNPAT4gj2uOySSGPZVnbEMfdyRhT1217XKA6cu3pABx1FLpaSDYvwAv2Y/92zcoAoHtGp8ZbMzPCGOMpVitSA+gH5AI/umGcUj4wxtyO7BOtAoZblpXpsknlicb2bYGrVrhDHvBiKccSkH2kb5FJc7lewlNndAosy/rZGLMQWS64HnjKcfgBpFL8ecuywirnXwkcxph7gAeBZGCELs0VxRjTHjhYPFK0pZIeQgrOv7cs64Ab9rmJnazgV+7HGHM/4oxmqwJDxeE6RA7oSWPMUGA90BuRA9oE3O2iba5jjLkEuMS+29C+7WuMmWX/O9OyrLCpFD8TjDHTEEdUAHwD3CRF9EXYalnWrCCbFkqMAv5hjFkC/IyoCzRA1DxaAnuA37tnnhIM1BmdBnZ01BO5qIwCLkC0xp4EHtCZLt2BacUea2kPgG2EkWzJGdLCvo0Abi7lnK+BWUGxJjT5AvgvsuTdDSmTOIxM9F4BntTfWPijQqmKoiiK62g2naIoiuI66owURVEU11FnpCiKoriOOiNFURTFddQZKYqiKK6jzkhRFEVxHXVGiqIoiuuoM1IURVFcR52RoiiK4jrqjBRFURTXUWekKIqiuI46I0VRFMV11BkpiqIorqPOSFEURXEddUaKoiiK66gzUhRFUVxHnZGiKIriOv8PCNITZuHMhFkAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "iso2 = return_points(43.3, 68.35, [4, 0])\n", "visited_points = drawTriangle(100, [4, 0], iso2, [0, 10])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see in the third graph, the algorithm (starting at $(4, 0)$) seemed to be converging to a triangle, until on the 6th step it went up again instead of down, as drawing up again was *just* longer than drawing down. What this means is that we have found a \"critical point\" for lack of a better term. We already know of the first critical point for isosceles triangles; it is the $45-90-45$ triangle, where when the angles are at that point the ultimate shape will not be a triangle. The graphs above show us that the inflection point on the other end is when the interior angles are about $68.35-43.3-68.35$. Now that we know the two critical points, we can begin to define a range on which the initial triangles will have triangular ultimate shapes.\n", "\n", "We will define each of the \"foot\" angles in an isosceles triangle as $x$, and the \"peak\" angle as $y$. From this we deduce the following rule for the interior angles of isosceles triangles\n", "$$\n", "2x+y = 180\n", "$$\n", "Treating $y$ as an unknown, we can solve for it and graph the equation\n", "$$\n", "y = -2x+180\n", "$$\n", "Using this function and the found critical points, we know that when $45 < x < 68.35$, and $x$ is passed through the function $y = -2x+180$ the returned triangle defined by $x$ and $y$ will always result in an isosceles triangle with a triangular ultimate shape. When $x \\leq 45$ and $x \\geq 68.35$, the triangle produced with the angles given by the function $y = -2x+180$ will have an ultimate shape equal to something *other than* a triangle!\n", "\n", "Visually, when the value of $x$ is shifted along this range of convergence towards $x=60$, the outer and ultimate triangle both approach the equilateral triangle, filling into it at $x=60$. \n", "\n", "A similar process can be used to find the subset of angles that define a scalene triangle with an ultimate shape equal to a triangle. For example, if we take the line perpindicular to $y = -2x+180$ that passes through $(60, 60)$ we get $y = \\frac{1}{2}x+30$. The points along this line give interior angles that can be used to construct scalene triangles, except when $x=60$.\n", "\n", "Now, a pair of critical points can be found for scalene triangles, and the range of points between the two critical points along the line defined by $y = \\frac{1}{2}x+30$ will define scalene triangles with triangular ultimate shapes!\n", "\n", "We now have an easy method for determining if a given initial triangle will have a triangular ultimate shape or not!\n", "\n", "Given these findings, we are in a position to make some simple conjectures and explore other questions.\n", "\n", "\n", "## Conjecture\n", "\n", "For any given triangle $P$, there *may* exists *a single* similar triangle $P'$, such that when $P'$ is placed within $P$, $P'$ can touch all three of $P$'s edges, and will form a right angle with each of $P$'s edges. Such a triangle $P'$ does not exist for triangles with an angle greater than or equal to $90$ degrees, and does not exist for specific accute triangles. A $P'$ does exist however for every equilateral triangle. \n", "\n", "In my belief, the best or perhaps only way of testing this conjecture is by using this \"right angle algorithm\" on a triangle $P$ to see if such a triangle $P'$ can be found.\n", "\n", "\n", "## Furthur Exploration\n", "\n", "This project was certainly a lot of fun, however I have many more ideas I would like to explore and questions I would like to have answered. I list some of these below.\n", "\n", "**Questions & Exploration**:\n", "1. Is it possible to create chosen shapes or patterns by passing the some unique engineered polygon to the algorithm?\n", "2. This leads into the question of how this algorithm would respond when applied to higher dimensional shapes. For example, given some 3D shape, and applying some form of this algorithm to it, will other repeating shapes emerge? Other repeating shapes similar to the \"outer\" 3D shape?\n", "3. In the cases when the algorithm does converge to a triangle, why does it do so? Specifically, what is special about the \"molding\" characteristics of certain initial triangles that force the ultimate shape into some specific repeating pattern?\n", "4. Do the ranges I defined along the lines describe all the isosceles/scalene triangles that have triangular ultimate shapes?\n", "5. Is there anything particularly special about the equilateral triangle and its predictable ultimate shape? Or is the equilateral triangle just a triangle that happens to have a triangular ultimate shape?\n", "6. Is there anything particularly special about the critical points that bound the ranges? \n", "7. One of the next things I would like to explore is what kind of repeating shapes, if any, this algorithm would produce on any polygon other than a triangle. For every polygon, does there exists at least one repeating shape that can be developed by applying this algorithm to it?\n", "8. I would like to continue searching for an exact formula that can be used to find the side lengths of any interior ultimate triangle given the initial triangle (assuming a formula of this kind exists). \n", "9. A fun project I am currently working on is a second program that can be used to recursively nest these \"ultimate triangles\" within eachother, to create some rather visually appealing patterns. \n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 2 }