{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# An Optimal Algorithm for the Freeze-Tag Problem in 2D" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# allow to display plots in the notebook\n", "%matplotlib inline \n", "import matplotlib.pyplot as plt\n", "\n", "# Warning! Constants are imported as constant only.\n", "# So imports like 'from ... import *' will not work properly\n", "import freeze_tag_mini as ft\n", "from math import pi, cos, sin" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Optimal wake-up time for $n$ points regularly spaced on the unit circle (in $\\ell_2$ norm)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " n wake-up time \n", "─────┬─────────────\n", " 0 │ 0.0000\n", " 1 │ 1.0000\n", " 2 │ 3.0000\n", " 3 │ 2.7321\n", " 4 │ 3.8284\n", " 5 │ 3.3511\n", " 6 │ 3.7321\n", " 7 │ 3.4314\n", " 8 │ 3.6131\n", " 9 │ 3.4161\n", " 10 │ 3.5201\n", " 11 │ 3.3827\n", "─────┴─────────────\n" ] } ], "source": [ "ft.DIST = ft.dist_L2\n", "print(f\" n wake-up time \")\n", "print(f\"─────┬─────────────\")\n", "for n in range(0,12):\n", " P = ft.generate_regular_polygon(n) + [(0,0)] # a circle and its center\n", " x,T = ft.optimal_tree(n,P) # compute the optimal tree\n", " print(f\" {n:2} │ {x:.4f}\")\n", "print(f\"─────┴─────────────\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lower bound for $\\ell_p$ norm" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.LP_NORM = 1.66 # p for L_p\n", "ft.SEED = -1 # do not display seed\n", "\n", "P = [(0,0)] # the center of the circle\n", "if 1 <= ft.LP_NORM <= 2:\n", " P += [(1,0),(0,1),(-1,0),(0,-1)]\n", "else:\n", " u = 1/2**(1/ft.LP_NORM)\n", " P += [(u,u),(-u,u),(-u,-u),(u,-u)]\n", "\n", "x,T = ft.optimal_tree(0,P,ft.dist_Lp)\n", "u = 1 + 2**(1+max(1/ft.LP_NORM,1-1/ft.LP_NORM))\n", "ft.PROCESS_TIME = 0 # do not display elapsed time\n", "ft.draw_all(f'norm L_{ft.LP_NORM}\\nconjecture = {u:.3f}\\nlower bound',x,T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lower bound in $\\ell_1$ norm to wake-up a square of diameter $1$ from a corner, with $n = 6$ points. The wake-up time is $2+1/6$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.SEED = -1 # does not display seed\n", "\n", "eps = 1/12 # best value, if eps=1/6 => depth = 2.000\n", "P = [\n", " (0,0),(1/2,1/2),(1/2,-1/2),(1,0), # p0,p2,p5,p4 (the square)\n", " (1/2-eps, 1/2-eps), # p1\n", " (1-2*eps, -2*eps), # p3\n", " (1/2+2*eps, -1/2+2*eps), # p6\n", " ]\n", "\n", "x,T = ft.optimal_tree(0,P,ft.dist_L1)\n", "ft.PROCESS_TIME = 0 # do not display elapsed time\n", "ft.draw_disc(ft.dist_L1,r=0.5,C=(0.5,0))\n", "ft.draw_all('optimal dist_L1',x,T,clear=False,disc=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The complete binary tree is not always optimal even if $n = 2^k-1$, here in $\\ell_2$ norm" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.init_seed(2743) # set SEED\n", "n = 2**3 - 1 # number of points (asleep robots)\n", "P = ft.generate_von_mises(n,0.5) # uniformly random on the disc\n", "ft.normalize_bc(P, ft.dist_L2) # add ROOT = (0,0) at the end of the list POINTS\n", "x,T = ft.optimal_tree() # compute the optimal tree\n", "ft.PROCESS_TIME = 0 # do not display elapsed time\n", "ft.draw_all('optimal',x,T) # display results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $n=4$ points in convex position having a crossing (apart from the first edge)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#ft.init_seed(1548) # set SEED\n", "#P = ft.generate_convex(4) # points in convex position\n", "#ft.normalize_bc(P, ft.dist_L2) # add ROOT = (0,0) at the end of the list POINTS\n", "#ft.rounding_coordinates(P,2)\n", "P = [(-0.2, -0.8), (-0.98, 0.2), (0.6, 0.42), (0.6, 0.29), (0.0, 0.0)]\n", "x,T = ft.optimal_tree(4,P,ft.dist_L2) # compute the optimal tree\n", "ft.PROCESS_TIME = 0 # do not display elapsed time\n", "ft.draw_all('optimal',x,T) # display results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $n=11$ points in convex position with optimal tree solution. It may have several edge crossings." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.init_seed()\n", "P = ft.generate_convex(11) # n=11 points in convex position\n", "ft.normalize_bc(P, ft.dist_L2) # add ROOT = (0,0) at the end of the list POINTS\n", "x,T = ft.optimal_tree() # compute the optimal tree\n", "ft.draw_all('convex pts') # draw the points\n", "ft.draw_all('optimal',x,T,save='fig.svg') # draw the tree and save it the figure" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A tree with a 'controlled' shape in $\\ell_2$ norm" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.SEED = -1 # no seed to display\n", "h, eps = 20, 0.2\n", "P = [\n", " (0,-1), (0,h),\n", " (+eps,1), (+h-1,1),\n", " (-eps,3), (-h+3,3),\n", " (+eps,5), (+h-5,5),\n", " (-eps,7), (-h+7,7),\n", " (+eps,9), (+h-9,9),\n", " #(-eps,11), (-h+11,11) # works, but time consuming\n", " ]\n", "x,T = ft.optimal_tree(0,P,ft.dist_L2)\n", "ft.draw_all('optimal',x,T,disc=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lower bounds for $n = 2k+1$ points on a circle (in $\\ell_2$ norm). The worst-case on a circle is not the uniform case for odd $n$.\n", "\n", "The generic counter-example (see cell below) has $2k$ angles of value $x$ plus one of angle of value $y$, $0 < y < x$. So $2kx + y = 2\\pi = nx - \\varepsilon$, where $\\varepsilon = x - y$. If $\\varepsilon=0$ (or $x=y$), then this is the uniform case. To find the optimal $\\varepsilon$, we start by searching for it experimentally using binary search with optimal_tree(). Then, we observe the longest branches in the tree solutions (we sum the chords lengths) with some $\\varepsilon_1 < \\varepsilon$, then with some $\\varepsilon_2 > \\varepsilon$. This gives to us equations ($E_1$) and ($E_2$) respectively. The solution of $E_1 = E_2$ (approximated by Maple) confirms the value of optimal $\\varepsilon$. Here, $\\mathrm{chord}(x) = 2\\sin(x/2)$ denotes the length of the chord for an angle of $x$. Note that $\\mathrm{chord}(y) = \\mathrm{chord}(kx)$, and that we must have $x \\in [2\\pi/n,\\pi/k]$. The solutions around the optimal $\\varepsilon$ are without crossovers in general, except for $k=2$ with the $\\mathrm{chord}(y) + \\mathrm{chord}(y+x)$ branch. The same methodology can be applied for other norms, like $\\ell_1$.\n", "\n", "Here are the best values for $\\varepsilon = \\varepsilon(k)$ obtained so far:\n", "\n", "---\n", "- $n=3~(k=1)$\n", "- $\\varepsilon=0$ => depth = $2.732$ (uniform case)\n", "- $\\varepsilon=𝜋$ => depth = $3.000$ (worst-case)\n", "\n", "---\n", "- $n=5~(k=2)$\n", "- $\\varepsilon=0$ => depth = $3.351$ (uniform case)\n", "- $\\varepsilon=0.5827617039$ => depth = $3.535628694$ (worst-case)\n", "- $x$ is root of $2\\mathrm{chord}(x) = \\mathrm{chord}(y) + \\mathrm{chord}(y+x)$, where $y = 2\\pi - 2kx$, and $x\\in[2\\pi/5,\\pi/2]$\n", "- [ $x=1.373189402, y=0.7904276980$ ]\n", "- NB. $\\mathrm{chord}(y+x) = \\mathrm{chord}(3x)$, and the tree solution for $> \\varepsilon$ has a crossing.\n", "\n", "---\n", "- $n=7~(k=3)$\n", "- $\\varepsilon=0$ => depth = $3.431$ (uniform case)\n", "- $\\varepsilon=0.3784299788$ => depth = $3.544911380$ (worst-case)\n", "- $x$ is root of $\\mathrm{chord}(x) + \\mathrm{chord}(2x) = \\mathrm{chord}(y) + \\mathrm{chord}(3x)$, where $y = 2\\pi - 2kx$, and $x\\in[2\\pi/7,\\pi/3]$\n", "- [ $x=0.9516593267, y=0.5732293479$ ]\n", "\n", "---\n", "- $n=9~(k=4)$\n", "- $\\varepsilon=0$ => depth = $3.416$ (uniform case)\n", "- $\\varepsilon=0.2814874303$ => depth = $3.490388052$ (worst-case)\n", "- $x$ is root of $\\mathrm{chord}(x) + \\mathrm{chord}(3x) = \\mathrm{chord}(y) + \\mathrm{chord}(x) + \\mathrm{chord}(2x)$, where $y = 2\\pi - 2kx$, and $x\\in[2\\pi/9,\\pi/4]$\n", "- [ $x=0.7294080820, y=0.5732293479$ ]\n", "\n", "---\n", "- $n=11~(k=5)$\n", "- $\\varepsilon=0$ => depth = $3.383$ (uniform case)\n", "- $\\varepsilon=0.2991993005$ => depth = $3.451257847$ (worst-case)\n", "- $x$ is root of $\\mathrm{chord}(x) + \\mathrm{chord}(4x) = \\mathrm{chord}(y) + \\mathrm{chord}(x) + \\mathrm{chord}(3x)$, where $y = 2\\pi - 2kx$, and $x\\in[2\\pi/11,\\pi/5]$\n", "- [ $x=0.5983986008, y=0.2991993003$, NB. $y=\\varepsilon$, soit $x=2y$ ]\n", "\n", "---\n", "- $n=13~(k=6)$\n", "- $\\varepsilon=0$ => depth = $3.349$ (uniform case)\n", "- $\\varepsilon=0.2940862069$ => depth = $3.407695572$ (worst-case)\n", "- $x$ is root of $\\mathrm{chord}(x) + \\mathrm{chord}(5x) = \\mathrm{chord}(y) + \\mathrm{chord}(x) + \\mathrm{chord}(4x)$, where $y = 2\\pi - 2kx$, and $x\\in[2\\pi/13,\\pi/6]$\n", "- [ $x=0.5059439627, y=0.2118577558$ ]\n", "\n", "---\n", "- $n=15~(k=7)$\n", "- $\\varepsilon=0$ => depth = $3.318$ (uniform case)\n", "- $\\varepsilon=0.2453594624$ => depth = $3.392885535$ (worst-case)\n", "- $x$ is root of $2\\mathrm{chord}(x) + \\mathrm{chord}(4x) = \\mathrm{chord}(y) + \\mathrm{chord}(x) + \\mathrm{chord}(5x)$, where $y = 2\\pi - 2kx$, and $x\\in[2\\pi/15,\\pi/7]$\n", "- [ $x=0.4352363180, y=0.1898768556$ ]\n", "\n", "---\n", "- $n=17~(k=8)$\n", "- $\\varepsilon=0$ => depth = $3.331$ (uniform case)\n", "- $\\varepsilon=0.1920896074$ => depth = $3.386640398$ (worst-case)\n", "- $x$ is root of $2\\mathrm{chord}(x) + \\mathrm{chord}(5x) = \\mathrm{chord}(y) + \\mathrm{chord}(6x)$, where $y = 2\\pi - 2kx$, and $x\\in[2\\pi/17,\\pi/8]$\n", "- [ $x=0.3808985244, y=0.1888089170$ ]\n", "\n", "---" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x = 0.9516593265685123, but should be in [0.8976,1.0472]\n", "File /Users/gavoille/Freeze-Tag/fig.svg saved.\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.SEED = -1 # do not display SEED\n", "ft.PROCESS_TIME = 0 # elapsed time to display in draw_all()\n", "\n", "k = 3\n", "n = 2*k + 1\n", "eps = 0.3784299788 # x-y\n", "x = (2*pi+eps)/n # angle x\n", "# x = 0.37\n", "# eps = n*x - 2*pi\n", "print(f\"x = {x}, but should be in [{2*pi/n:.4f},{pi/k:.4f}]\")\n", "if x < 2*pi/n or x > pi/k: quit()\n", "P = [(0,0),(1,0)] # root and first point\n", "t = 0\n", "for i in range(k):\n", " t += x\n", " P += [(cos(t),sin(t)),(cos(t),-sin(t))] # add two points \n", "\n", "x,T = ft.optimal_tree(0,P,ft.dist_L2)\n", "ft.draw_all('optimal',x,T,save='fig.svg')\n", "\n", "# A more general construction, still for n = 2k+1 points. Chords are symmetric from (1,0) and are composed of k-1 chords of angle x1, followed by one of angle x2, and then the remaining. It happens that the worst-case is whenever there is only one chord of angle < 2𝜋/n and all the other greater and equal.\n", "\n", "# k=3 # Best: 3.544911380, eps1 = eps2 = 0.3784299788\n", "# k=4 # Best: 3.490388052, eps1 = eps2 = 0.2814874303\n", "# k=6 # Best: 3.407695572, eps1 = eps2 = 0.2940862069\n", "# k=7 # Best: 3.392885535, eps1 = eps2 = 0.2453594624\n", "# eps1, eps2 = 0.3, 0.1\n", "# n = 2*k + 1\n", "# x1 = (2*pi+eps1)/n\n", "# x2 = (2*pi+eps2)/n\n", "# P = [(0,0),(1,0)]\n", "# t = 0\n", "# for i in range(k):\n", "# if i" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.SEED = -1 # do not display SEED\n", "n = 4 # number of sides of each n-gons\n", "r1, r2 = 1.0, 0.5 # r2 = 0.5, 0.8 or 0.9 gives rather different shape trees\n", "P = [(0,0)]\n", "for i in range(n):\n", " P += [(r1*cos(i*2*pi/n),r1*sin(i*2*pi/n))]\n", " P += [(r2*cos(i*2*pi/n+pi/n),r2*sin(i*2*pi/n+pi/n))]\n", "x,T = ft.optimal_tree(0,P,ft.dist_L2)\n", "ft.draw_all('optimal',x,T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Search for a worst-case for $n = 8$ points (in $\\ell_2$ norm)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x = 2.7800411502247084\n", "T = [8, [3, [1, [5, [0]], [7]], [6, [2], [4]]]]\n", "ft.POINTS = [(0.4443, -0.8959), (0.7712, 0.4479), (-0.7286, -0.468), (0.4062, 0.7249), (-0.7068, -0.5116), (0.9306, 0.1187), (-0.8113, -0.1215), (-0.3056, 0.7055), (0, 0)]\n", "x = 2.7854761921664846\n", "T = [8, [4, [1, [7, [5]], [2]], [6, [0], [3]]]]\n", "ft.POINTS = [(0.8078, 0.2816), (-0.8189, -0.2544), (-0.0509, 0.7363), (0.8964, 0.0273), (-0.7317, 0.2698), (0.0864, -0.9963), (0.3983, 0.6644), (-0.5874, -0.7287), (0, 0)]\n", "x = 2.883044884921821\n", "T = [8, [1, [7, [0, [5]], [2]], [6, [3], [4]]]]\n", "ft.POINTS = [(0.9678, 0.2518), (-0.7474, 0.62), (0.6928, 0.7168), (-0.0533, -0.9763), (-0.7074, -0.6597), (0.9685, 0.249), (-0.4207, -0.8758), (-0.7003, 0.6742), (0, 0)]\n", "x = 3.2740680232370076\n", "T = [8, [5, [1, [2, [4]], [3]], [6, [0], [7]]]]\n", "ft.POINTS = [(0.9511, 0.2385), (-0.8528, -0.431), (-0.7759, 0.6107), (0.7388, 0.663), (-0.1754, 0.9845), (-0.7273, -0.6116), (0.0331, -0.9414), (0.8083, -0.5128), (0, 0)]\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 8 # number of points\n", "NB = 200 # number of tries\n", "ft.DIST = ft.dist_L2 # set the distance function\n", "\n", "xmax = 0\n", "for i in range(NB):\n", " # P = generate_von_mises(n,0.1,2,20) # close to the regular case\n", " P = ft.generate_von_mises(n,0) # random on the circle\n", " ft.normalize_bc(P)\n", " ft.rounding_coordinates(P,4) # round to 4 digits for display\n", " x,T = ft.optimal_tree()\n", " if x>xmax:\n", " xmax,Tmax,Pmax = x,T,ft.POINTS\n", " print(f\"x = {x}\")\n", " print(f\"T = {T}\")\n", " print(f\"ft.POINTS = {ft.POINTS}\")\n", "\n", "# Maximum for ft.generate_von_mises(8,0,8,10) with NB = 10,000\n", "# x = 3.5705\n", "# T = [0, [4, [3, [8, [2]], [7]], [5, [1], [6]]]]\n", "# ft.POINTS = [(0.0, 0.0), (-0.9985, 0.01182), (-0.0061, -0.9996), (0.9996, 0.0180), (0.7213, 0.6916), (-0.7102, 0.7017), (-0.0404, 0.9979), (-0.6851, -0.7272), (0.7196, -0.6943)]\n", "\n", "# Maximum for ft.generate_von_mises(8,0.1) with NB = 10,000\n", "# (many crossings ...)\n", "# x = 3.0498\n", "# T = [0, [3, [1, [8, [2]], [7]], [5, [4], [6]]]]\n", "# ft.POINTS = [(0.0, 0.0), (-0.3831, -0.8944), (0.2496, 0.9683), (-0.1987, -0.8715), (-0.9335, 0.2555), (-0.6785, -0.6434), (0.8959, -0.2604), (0.7954, 0.5057), (0.2528, 0.9403)]\n", "\n", "x,T,ft.POINTS = xmax,Tmax,Pmax\n", "ft.draw_all('optimal',x,T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Random points in the unit disk w.r.t. the hexagonal distance function " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P = ft.generate_von_mises(500,0.5) # 0.5 -> 0 for unit circle\n", "d = ft.dist_regular_polygon\n", "ft.NGON = 6\n", "ft.distortion(P,ft.dist_L2,d)\n", "plt.clf()\n", "plt.axis('equal')\n", "ft.draw_disc(d)\n", "ft.draw_points(P, s=2)\n", "ft.draw_points([(0,0)], 'black', 4, '+')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Best parallelogram perimeter for a random 10-segment symmetric convex" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SEED = 4681\n", "half perimeter = 3.3594\n", "best parallelogram perimeter = 6.5834\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.init_seed()\n", "print(f\"SEED = {ft.SEED}\")\n", "ft.SEMI_CONVEX = ft.generate_semi_convex(5)\n", "ft.SEMI_ARC = False\n", "ft.DIST = ft.dist_convex\n", "print(f\"half perimeter = {ft.half_perimeter():.4f}\")\n", "\n", "P = ft.SEMI_CONVEX + [(-x,-y) for (x,y) in ft.SEMI_CONVEX]\n", "pmax, Pmax = ft.best_quadrilateral(P, quadri=False)\n", "print(f\"best parallelogram perimeter = {pmax:.4f}\")\n", "\n", "plt.axis('equal')\n", "ft.draw_points(Pmax, 'red', 4)\n", "ft.draw_points([(0,0)], 'black', 4, '+')\n", "ft.draw_disc()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Segment-arc mixed symmetric convex" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SEED = 9388\n", "half perimeter = 3.1987\n" ] }, { "data": { "image/png": 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urILV5cKBQ4cQjUbljkOUESwvVLDOnDmDE/1nsaq5BVabTe44RHmraU0zIuk0Dh48KHcUooxgeaGCNDk5iQPd3XAvXYbKqmq54xDlNY1Gg6Y1LTg7MoqBgQG54xAtGssLFZxEIoG977wLlcmEFY2NcschKgjlFRVwVlXjYPdhRCIRueMQLQrLCxWc7u5uBKJRtLSv4yHRRAuwavVqxCUJ+w8cgBBC7jhEV42/+amgDA8P49TAIFasXs0JukQLpFKp0NTSiiHvGM6cOSN3HKKrxvJCBSMWi+HAoUOwulyc50J0lcqcTrhrlqL7yBGEQiG54xBdFZYXKhiHDx9GJJVG05pmuaMQFbQVjY1IqTXcfUQFi+WFCoLX68XpwSGsaGqCRqOROw5RQVMqlVjT2oYR3wROnjwpdxyiBWN5obyXSqVwqPswjHY7dxcRZYjNbkfVsloc6elBMBiUOw7RgrC8UN47deoUJsMh7i4iyrCGlSsBrQ779u9HOp2WOw7RvLG8UF6LRqPo6euDu2YZDEaj3HGIiopCocCa1jZ4Jydx/PhxueMQzRvLC+W1np4exCChrqFB7ihERclitaKmrgFH+/owNTUldxyieclJeXn66adRW1sLnU6Hzs5O7N27d173e/HFFyFJEj75yU9mNyDlpenpaZweGEBtfQOvFk2URcvr66EyGvHu/v1IpVJyxyG6oqyXl5deegkPPPAAHn30Uezfvx9tbW246aabMDY2dtn79ff34ytf+Qquv/76bEekPNXb2wuhUmPJ0qVyRyEqagqFAmta2uALBtHb2yt3HKIrynp5+fu//3vcc889uOuuu7B69Wo888wzMBgMeP755y95n1Qqha1bt+Kxxx5DXV1dtiNSHgoGgzg7PIzahgZeAoAoB0xmM2obVqLnxAn4/X654xBdVlY/FeLxOPbt24fNmze//4QKBTZv3oyurq5L3u9b3/oWXC4X7r777is+RywWQzAYnHOjwnf8+HFAo0VV9RK5oxCVjGXLl0NrsWDf/gNIJpNyxyG6pKyWF5/Ph1QqhYqKijnLKyoq4PF4LnqfN998E8899xyeffbZeT3Hjh07YLVaZ281NTWLzk3yCofD6B8awrK6Oo66EOWQJElY09IGfziEY8eOyR2H6JLy6pNhenoan/3sZ/Hss8/C6XTO6z7bt29HIBCYvQ0ODmY5JWXbqVOnIFQqVC9hESXKNYPRiOUrVqHv1GmMj4/LHYfoolTZfHCn0wmlUgmv1ztnudfrhdvtvmD9U6dOob+/H3/2Z382u+z8iZNUKhX6+vpQX18/5z5arRZarTYL6UkO8Xgcp/v7UV3LURciudQsW4bxMQ/2HziAj330ozzaj/JOVj8dNBoNOjo6sHv37tll6XQau3fvxsaNGy9Yv7GxEYcPH8bBgwdnb3/+53+Oj370ozh48CB3CZWAgYEBRNNpHmFEJCNJkrC6pQ1TM1EcPXpU7jhEF8jqyAsAPPDAA9i2bRvWr1+PDRs24KmnnkI4HMZdd90FALjjjjtQXV2NHTt2QKfTobl57ingbTYbAFywnIqPEAKnTp+Gs6KSF18kkpler0d9YyNOHDuGysrKC+YuEskp6+Xltttuw/j4OB555BF4PB60t7dj165ds/8jDAwMcPcAAQDGx8cRCIfRuqZF7ihEBGBJzVKMeTzYf/AgNn/sY9x9RHlDEkIIuUNkUjAYhNVqRSAQgMVikTsOLcA777yD4ckpXHsdT0xIlC+i0Sj2vvl71FdXoaOjQ+44VMQW8vnNIQ/KC/F4HEOjo6jkeV2I8opOp0NDUxNODQxidHRU7jhEAFheKE+MjIwglkrBXVUldxQi+iNV1UtgcTqx/+BBxGIxueMQsbxQfhgcGoLFUcbD3onyVFNzC8LJFLq7u+WOQsTyQvKbmZmB1+fjqAtRHtNqtVi1eg3ODA1jeHhY7jhU4lheSHajo6NIAnBVXHjiQiLKHxWVlbC6XDhw6BCi0ajccaiEsbyQ7IZHRmB1lEGlyvqR+0S0SE1rmhFJp3Ho0CG5o1AJY3khWcXjcYxNTKCcJ8AiKggajQaNq5txdmSE15Ij2bC8kKzGxsYQT6VR7mJ5ISoULrcb9opKHDjUjZmZGbnjUAlieSFZeb1eGMxmHmVEVGAa16xBDMDBgwfljkIliOWFZCOEwKjXC4ezXO4oRLRAarUaTc0tGBj14OzZs3LHoRLD8kKyCQaDiMTiKHM65Y5CRFfB6XLBWVWNg92HEYlE5I5DJYTlhWTj8/kgFBJsdrvcUYjoKq1avRoJhQL7DxxAkV0qj/IYywvJxufzwWS18ariRAVMpVKhqaUVQ94x9Pf3yx2HSgQ/NUgWQgiM+SZgszvkjkJEi1TmdKJiSQ26jxxBOByWOw6VAJYXkkUoFMJMPM5dRkRFYmVTE5IqNXcfUU6wvJAsJicnkYaA1WaTOwoRZYBSqcTqllYMj43j9OnTcsehIsfyQrKYnJyEzmjiJQGIiojd4UDl0mU4fPQoQqGQ3HGoiLG8kCwmJidhtljljkFEGdawahVSag327d/P3UeUNSwvlHPpdBpTgQAsVpYXomKjVCqxprUNoxN+nDx5Uu44VKRYXijnpqenkUwLmC0WuaMQURbY7HZULavFkZ4eBINBueNQEWJ5oZwLBoNIiTRMZrPcUYgoSxpWrgS0Ouw/cADpdFruOFRkWF4o56anp6HR6zlZl6iIKRQKrGltg8c/yd1HlHEsL5RzwWAQBqNJ7hhElGUWqxVLltdx9xFlHMsL5VxgeprlhahE1DU0QKE34N39+7n7iDKG5YVyKp1OIxQOw2gyyh2FiHLg/O6jsclJHD9+XO44VCRYXiinIpEI0gIwGFheiEqF2WJBTV0Djvb1YWpqSu44VARYXiinwuEwUkJAbzDIHYWIcmh5fT2UBiP28egjygCWF8qpmZkZQCFBp9PJHYWIckihUKC5tQ2+QAB9fX1yx6ECx/JCORWJRKDWaiFJktxRiCjHTGYzauoacOz4cUxOTsodhwoYywvl1MzMDLQcdSEqWcvr66EyGvHu/v1IpVJyx6ECxfJCORWZmYFGw/JCVKokSUJzazsmpqfR29srdxwqUCwvlFORmRno9Hq5YxCRjIwmE2obVqLnxAn4/X6541ABYnmhnIpGY9BqtXLHICKZLVu+HFqLBfv2H+DuI1owlhfKmWQyiUQqCY1WI3cUIpKZJElY09IGfziEnp4eueNQgWF5oZyJx+MQAlCrWV6ICDAYjahtWInekycxMTEhdxwqICwvlDPxeBwCgEbD8kJE5yytrYXOasW+/QeQTCbljkMFguWFciaRSEAIATXLCxG9R5IkrG5uxWQ4jKNHj8odhwoEywvlTCKRQBqASqWSOwoR5RGD0Yi6VY04fvoMxsfH5Y5DBYDlhXLm3JCwYHkhogssWboUBrsN+w9w9xFdGcsL5UwikYBSqeKlAYjoApIkoam5FVMzURw5ckTuOJTnWF4oZ1KpFBQqpdwxiChPGQwG1K1ahRNn+jE2NiZ3HMpjLC+UM6lUCgolywsRXVrN0mUw2O3Yf+AAEomE3HEoT7G8UM6kUilIEt9yRHR5q1taEYjGuPuILiknnyRPP/00amtrodPp0NnZib17915y3WeffRbXX3897HY77HY7Nm/efNn1qXCkUikoOfJCRFeg1+tR39iIk/1n4fV65Y5DeSjr5eWll17CAw88gEcffRT79+9HW1sbbrrppkvuz3zjjTfw6U9/Gr/97W/R1dWFmpoafPzjH8fw8HC2o1KWCSEgKThZl4iubEnNUhgdDhw4eJC7j+gCkhBCZPMJOjs7cc011+B73/seACCdTqOmpgb3338/Hn744SveP5VKwW6343vf+x7uuOOOK64fDAZhtVoRCARgsVgWnZ8yZ//+/RgJBLC+c6PcUYioAESjUez5/e+wcmkN1q5dK3ccyrKFfH5ndeQlHo9j37592Lx58/tPqFBg8+bN6OrqmtdjRCIRJBIJOByOi34/FoshGAzOuVF+OteTOfJCRPOj0+lmdx/x6CP6oKyWF5/Ph1QqhYqKijnLKyoq4PF45vUYDz30EKqqquYUoA/asWMHrFbr7K2mpmbRuSk7hBA8xwsRLcj53Uc8+og+KK8P/XjiiSfw4osv4uc//zl0Ot1F19m+fTsCgcDsbXBwMMcpiYgom5qaWxCIxnjtI5qV1fO0O51OKJXKC2aLe71euN3uy953586deOKJJ/Cb3/wGra2tl1xPq9VCq9VmJC8REeUfvV6PulWrcLK3B8uWLYPdbpc7EsksqyMvGo0GHR0d2L179+yydDqN3bt3Y+PGS0/a/Lu/+zs8/vjj2LVrF9avX5/NiEREVACW1CyFpNXh9OnTckehPJD1K+Q98MAD2LZtG9avX48NGzbgqaeeQjgcxl133QUAuOOOO1BdXY0dO3YAAL797W/jkUcewQsvvIDa2trZuTEmkwkmkynbcSmLzs13yerBbURUpCRJQkVlFUaGh7CO8+dKXtbLy2233Ybx8XE88sgj8Hg8aG9vx65du2Yn8Q4MDECheH8A6J//+Z8Rj8fxn//zf57zOI8++ii++c1vZjsuZZEkScjykflEVMTKXS6MnDkNv9+PsrIyueOQjLJeXgDgvvvuw3333XfR773xxhtzvu7v789+IJKFQqFAOp2WOwYRFSiL1QpJrcLY2BjLS4nL66ONqLgoFAqINEdeiOjqSJIEe1k5RuZ5qg0qXiwvlDPnygtHXojo6pW7XJgMBDAzMyN3FJIRywvljFKpRCqdkjsGERUwh9OJpBC8YGOJY3mhnFEqlRx5IaJFUavVMNlsLC8ljuWFckapVCKV5MgLES1OmdMFz9g4DwAoYSwvlDMqlQpp7jYiokVylpcjmkjA7/fLHYVkwvJCOaNSqQABpFIsMER09cwWC5RaDa80XcJYXihnVCoVJIBXhiWiRbM5nBjlvJeSxfJCOXO+vKSSSbmjEFGBc7rKMRkIIBqNyh2FZMDyQjmjVqshSRJHXoho0RxlTiTSAuPj43JHIRmwvFDOaDQaKCQgyfJCRIuk0WhgtFg476VEsbxQzqjVagBAPBGXOQkRFQN7mROesTFe8LUEsbxQziiVSqiVSiTiHHkhosUrczoRjsYQDAbljkI5xvJCOaXVahGPc+SFiBbPZrdDKCTOeylBLC+UU1qtFvFYTO4YRFQEFAoFzDY7y0sJYnmhnNJrtUhwzgsRZYijzIkxn4+XCigxLC+UUzqdDgnuNiKiDHGUlSGWTGJyclLuKJRDLC+UUzqdDvEYTypFRJlhtlgApQo+n0/uKJRDLC+UU1qtliMvRJQxkiTB4nBgjPNeSgrLC+WUTqcD0oJHHBFRxpSVOTE+McGLvpYQlhfKKZ1OB4UkIcbrkRBRhtgdDiRSafj9frmjUI6wvFBO6fV6KCQgOjMjdxQiKhImsxkKjRoTExNyR6EcYXmhnNJqtVBIEqKctEtEGWSxc95LKWF5oZySJAkGvR7RGZYXIsoch6MMPr+f815KBMsL5ZzRYMBMJCJ3DCIqIufnvfB8L6WB5YVyzmQ0IhbjnBciyhyjyQSFmvNeSgXLC+WcXq9HjBN2iSiDJEmC2WaDj+WlJLC8UM4ZjUYkYjFei4SIMspmd8A3McHfLSWA5YVyzmAwQAGJ816IKKNsdjtiyRQCgYDcUSjLWF4o54xGI5QKCZFwWO4oRFRELFYrhELipN0SwPJCOafVaqFSKBDhyAsRZZBCoYDRYuGk3RLA8kI5J0kSzCYzR16IKOOsNgfGWV6KHssLycJsMiISYXkhosyy2WyIRKMc2S1yLC8kC7PZjCjLCxFlmNVuRyItOO+lyLG8kCyMRiPi0ShP5U1EGaXRaKDV61leihzLC8nCZDJBKSk474WIMs5stWHC75c7BmURywvJwmw2QyEBodC03FGIqMjY7HZMTE7yZHVFjOWFZKFWq2HQ6RAOceSFiDLLYrUimRY8WV0RY3kh2dgsFo68EFHGmS0WpCVgampK7iiUJSwvJBuLxYKZUEjuGERUZBQKBQxmM8tLEWN5IdmYzWbEZiLcL01EGWc2Wzlpt4ixvJBszGYzFJAQ5ugLEWWYxWbF1PQ0ksmk3FEoC3JSXp5++mnU1tZCp9Ohs7MTe/fuvez6P/3pT9HY2AidToeWlha88soruYhJOXb+iKPp6aDcUYioyFitNqQ4abdoZb28vPTSS3jggQfw6KOPYv/+/Whra8NNN92EsbGxi67/hz/8AZ/+9Kdx991348CBA/jkJz+JT37ykzhy5Ei2o1KOqdVqmAwGTAc5aZfmxzs6ip1/+zfwjo7KHYXynNFkApQKlpcilfXy8vd///e45557cNddd2H16tV45plnYDAY8Pzzz190/X/8x3/Eli1b8NWvfhVNTU14/PHHsW7dOnzve9/LdlSSgd1qRYgjLzRPXo8H3/n//hZej0fuKJTnJEmC3mTipN0ildXyEo/HsW/fPmzevPn9J1QosHnzZnR1dV30Pl1dXXPWB4CbbrrpkuvHYjEEg8E5NyocNpsNER4uTVfgHR1F94EDOHzoIADg8KGD6D5wgCMwdFlmsxX+ySm5Y1AWZLW8+Hw+pFIpVFRUzFleUVEBzyX+cvJ4PAtaf8eOHbBarbO3mpqazISnnLBYLEjFE4hGo3JHoTz2v59/Djddtwlf+cLnAQBf+cLncdN1m/C/n39O5mSUz8xWC4KhaV5DrQgV/NFG27dvRyAQmL0NDg7KHYkWwGq1QilJCHHEjC7js5+7G6+++QfsfPqfAAA7n/4nvPrmH/DZz90tczLKZ2azBcm0wPQ0R3eLjSqbD+50OqFUKuH1eucs93q9cLvdF72P2+1e0PparRZarTYzgSnnDAYDdBoNgsEgnC6X3HEoT1VUVqKisnL265a2drSuXStjIioEJrMZaQgEg0HYbDa541AGZXXkRaPRoKOjA7t3755dlk6nsXv3bmzcuPGi99m4ceOc9QHgtddeu+T6VPjsNiuCQR4RQFdW4Xbjwa99HRWX+GOG6IOUSiW0egOPOCpCWR15AYAHHngA27Ztw/r167FhwwY89dRTCIfDuOuuuwAAd9xxB6qrq7Fjxw4AwJe+9CXccMMN+M53voNbb70VL774It5991384Ac/yHZUkonDboenv1/uGFQAKior8ZWvf0PuGFRADGYzAtwtXXSyXl5uu+02jI+P45FHHoHH40F7ezt27do1Oyl3YGAACsX7A0CbNm3CCy+8gG984xv42te+hhUrVuAXv/gFmpubsx2VZGK1WpGIxhCPx6HRaOSOQ0RFxGy2YGJwQO4YlGGSEELIHSKTgsEgrFYrAoEALBaL3HFoHsLhMF759WtoWtcBZ3m53HGIqIiMeTw43n0Qf7plC3Q6ndxx6DIW8vld8EcbUeEzGo3nJu1yvzQRZZjJbEaKRxwVHZYXygtOhx2BqUm5YxBRkdEbDIBSwfJSZFheKC/Y7XaEeMQREWWYJEnQGYwsL0WG5YXygs1mQyqewMzMjNxRiKjI6A1GBFleigrLC+UFu90OlULiriMiyjiT2YypAA+XLiYsL5QXtFotLEYjAryIGhFlmMFoQCwRRzwelzsKZQjLC+WNMocDgQBHXogos4xGE9JCIBQKyR2FMoTlhfKGw+FAZHoa6XRa7ihEVEQMRiNSLC9FheWF8obdbodCAIGpKbmjEFERUSqV0Oh0CIfDckehDGF5obxhsVigValYXogo47R6A0deigjLC+UNhUIBZ5kDU5N+uaMQUZExGIyY5shL0WB5obxS5nAgyJEXIsowg9GIUIjlpViwvFBeKSsrg0gkEObwLhFlkF6vRzyZ4OHSRYLlhfKK3W6HWqnAJHcdEVEG6Q0GpAUQiUTkjkIZwPJCeUWlUsFus2FyguWFiDJHbzAgJQTLS5FgeaG843I6EZhieSGizFGr1VAolbx+WpFgeaG8U1ZWhmQ0xl8yRJRRGp2OIy9FguWF8o7D4YBKIWHSPyF3FCIqIlqWl6LB8kJ5R6PRwGGzwe9jeSGizNHp9AhzRLcosLxQXnI5nQjwiCMiyiCdXo9IhOWlGLC8UF5yOp1IRKOc90JEGaPVaRGLx3jx1yLA8kJ5qaysDCqFBP+ET+4oRFQktFod0gKIxWJyR6FFYnmhvKRWq1Fmt3PeCxFljFarhQAQjUbljkKLxPJCeauivByBSZYXIsoMrU6HtBAceSkCLC+Ut5xOJ1KxOK9zREQZoVarISTuNioGLC+Ut8rKyqBRKTHh47wXIlo8SZKgUqtZXooAywvlLaVSifKyMk7aJaKMUWu0LC9FgOWF8pqrvBwBvx9CCLmjEFERUGvUiMfjcsegRWJ5obxWXl4OKZ3G1OSk3FGIqAio1BqWlyLA8kJ5zWazQa/RwD/Bo46IaPHUKjWiLC8Fj+WF8pokSXC7yuGfGJc7ChEVAbWGIy/FgOWF8p7L5UI4EEAikZA7ChEVOJVKhXicv0sKHcsL5T2XywWVJMHPQ6aJaJFUahXiCY68FDqWF8p7er0eNrMFvnHuOiKixVGpVBAAksmk3FFoEVheqCBUuis474WIFk2lVAFgeSl0LC9UEFwuF9KxOELT03JHIaICplSpIASQSqXkjkKLwPJCBaGsrAw6tYq7johoUZRKJXcbFQGWFyoICoUCbpcLvnGv3FGIqIAplUoAgiMvBY7lhQpGRUUFQlNTPGSaiK6aQqmEEEA6nZY7Ci0CywsVDB4yTUSLpVAoIMDyUuhYXqhgGAwG2K1WjI+NyR2FiAqUQnHuY4/lpbCxvFBBqXK7MTkxzqtME9FVkSSJIy9FgOWFCkpFRQVEIolgICB3FCIqQOdHXvgHUGHLannx+/3YunUrLBYLbDYb7r77boRCocuuf//992PVqlXQ6/VYunQpvvjFLyLADyp6j91uh1GnxejwsNxRiKgASZIEQLC8FLislpetW7fi6NGjeO211/Dv//7v+N3vfod77733kuuPjIxgZGQEO3fuxJEjR/CjH/0Iu3btwt13353NmFRAJEnCivp6eIcHEb5MESYiouIliSzVz56eHqxevRrvvPMO1q9fDwDYtWsXbrnlFgwNDaGqqmpej/PTn/4U//W//leEw2GoVKorrh8MBmG1WhEIBGCxWBb1Gig/pVIpvP7GG4hKEtZ3bnzvLykioitLp9P4j1/vwvUbNmDJkiVyx6EPWMjnd9ZGXrq6umCz2WaLCwBs3rwZCoUCe/bsmffjnH8RlyousVgMwWBwzo2Km1KpRMfatYgFgxjo75c7DhER5VjWyovH44HL5ZqzTKVSweFwwOPxzOsxfD4fHn/88cvuatqxYwesVuvsraamZlG5qTA4HA40NjSg/+RxRMJhueMQUYE4t7NB4ohtgVtweXn44YchSdJlb729vYsOFgwGceutt2L16tX45je/ecn1tm/fjkAgMHsbHBxc9HNTYWhqaoLdYMTRw4c4+Y6I5uX87wqWl8J25Ukkf+TBBx/EnXfeedl16urq4Ha7MfZHJxNLJpPw+/1wu92Xvf/09DS2bNkCs9mMn//851Cr1ZdcV6vVQqvVzjs/FQ+lUomOdWvx29//HgP9/Vi2fLnckYgoz6XTaUh4/5BpKkwLLi/l5eUoLy+/4nobN27E1NQU9u3bh46ODgDA66+/jnQ6jc7OzkveLxgM4qabboJWq8Uvf/lL6HS6hUakElJWVobGhgYcOdGHcpcLBqNR7khElMfOn5yOIy+FLWvVs6mpCVu2bME999yDvXv34q233sJ9992H22+/ffZIo+HhYTQ2NmLv3r0AzhWXj3/84wiHw3juuecQDAbh8Xjg8Xh4BVC6pKamJpSZzNx9RERXdH7k5dzVpalQZXXc7Mc//jEaGxtx44034pZbbsF1112HH/zgB7PfTyQS6OvrQyQSAQDs378fe/bsweHDh9HQ0IDKysrZG+ey0KWc330UCwZx9swZueMQUR5Lp1KQJJaXQrfg3UYL4XA48MILL1zy+7W1tXP+Uv7IRz7Cv5zpqjgcDjStWIHDJ46j3OWC0WSSOxIR5aFzo/gSy0uB44wlKhqNjY0oM3P3ERFdWjKZ5G6jIsDyQkVDqVRi/bp1SIRC6D99Wu44RJSHUskkJAnzOmM75S+WFyoqdrsdTStWYODUCYSmp+WOQ0R5JplKAsBlT8FB+Y/lhYpOY2MjyiwW7j4iogsk4gmolUqe56XA8adHRUehUGD9unVIhsM4c+qU3HGIKI8kEgloNBq5Y9AisbxQUbLZbFizahUGT5/ENC/WSUTvScTj0Gp4VvZCx/JCRWvlypVwWq042n1o9qyaRFTa4ok4dFqOvBQ6lhcqWud3H6VmIjh98qTccYgoDyTiMV52pgiwvFBRs1qtaG5sxNCZUwgGAnLHISKZxaMxXsy3CLC8UNFbsWIFKux27j4iIiTjcY68FAGWFyp6CoUCHevWAbEoTp04IXccIpJJIpFAKpVieSkCLC9UEiwWC5qbmjDcfwaBqSm54xCRDKIzM1BKgF6vlzsKLRLLC5WMhoYGVJY5uPuIqERFZ2agkCQYDAa5o9AisbxQyZAkCevWroUUj+FEX5/ccYgox2ZmZqBSKDhhtwiwvFBJMZvNaFm9GqNn+zE1OSl3HCLKoZlIBCajEZIkyR2FFonlhUpOfX09qsqdONp9CKlUSu44RJQj4XAIZpNJ7hiUASwvVHLO7z5SJuI4yd1HRCUjGonAxPJSFFheqCSZTCa0NjdjdOAs/BMTcschoixLp9OIR2dgNpvljkIZwPJCJWv58uWodpXj2OFuJJNJueMQURaFQyEoAI68FAmWFypZ53cfqVNJnOjtlTsOEWVRKDQNhSRx5KVIsLxQSTMajWhtbsbY0CAmfD654xBRlgQDQZgMBqjVarmjUAawvFDJq62tRXWFCz3cfURUtELTQThsNrljUIawvFDJO7/7SCME+o4dkzsOEWVBOBiEjeWlaLC8EAEwGAxoa2mGb2QYvvFxueMQUQZFIhGIZJLlpYiwvBC9Z9myZVha6UbP4W4kEgm54xBRhgSmJqFUSCwvRYTlhegD2tvboQW4+4ioiAQmp2A1maDRaOSOQhnC8kL0AXq9HmvbWjExOoIxj0fuOESUAYGpSZQ7nXLHoAxieSH6IzU1NaitrkLvsSOIx+NyxyGiRUgkEpgJTcPhcMgdhTKI5YXoItra2mBQKNB79KjcUYhoEab8fqgkCU6OvBQVlheii9DpdFjb1oapMS+8o6NyxyGiq+SfmIDZYIDBYJA7CmUQywvRJVRXV6O2ugp9x44iFovJHYeIrsKEbxzuigq5Y1CGsbwQXUZbWxuMKiV6jh6ROwoRLdDMzAzikQjKy8vljkIZxvJCdBlarRbr2tsRHB/H6Miw3HGIaAF8Y2PQKBUsL0WI5YXoCiorK1FXswTHjx1DNBqVOw4RzdP4mBcup5MXYyxCLC9E89Da2gqzRo2eI4fljkJE85BMJhGc9KOqslLuKJQFLC9E86DRaLCuvR3TExMYHhqUOw4RXcH4mBcqnBs5peLD8kI0T263Gytql+FkTw9mZmbkjkNEl+EdHUW5wwG9Xi93FMoClheiBWhuboZVp8Wxw91yRyGiS0gkEpia8KFmyRK5o1CWsLwQLYBarUbHunWITE5icOCs3HGI6CK8nlGoAFRVVckdhbKE5YVogcrLy7GybjlO9/YiEonIHYeI/sjo8BCqKyqg0+nkjkJZwvJCdBXWrFkDu9GIY4cPQQghdxwiek8kHEZ4KoClS5fKHYWyiOWF6CqoVCp0rFuLaCCAgf5+ueMQ0XsGBwZg0ml5lFGRY3khukplZWVobGjAmRN9CIdCcschKnnpdBrekWEsX7YMCgU/3opZVn+6fr8fW7duhcVigc1mw913343QPH/JCyFw8803Q5Ik/OIXv8hmTKKr1tTUhDKTGUe5+4hIdqMjw1CkkqitrZU7CmVZVsvL1q1bcfToUbz22mv493//d/zud7/DvffeO6/7PvXUU5AkKZvxiBZNqVSiY91aJEIh9J8+LXccopI22N+PJW43jEaj3FEoy7JWXnp6erBr1y78r//1v9DZ2YnrrrsO3/3ud/Hiiy9iZGTksvc9ePAgvvOd7+D555/PVjyijHE4HGhasQIDp05gOhiUOw5RSfKNjyMeDqO+vl7uKJQDWSsvXV1dsNlsWL9+/eyyzZs3Q6FQYM+ePZe8XyQSwWc+8xk8/fTTcLvdV3yeWCyGYDA450aUa42NjXBarTh6uBvpdFruOEQl5+yZU3A57LyCdInIWnnxeDxwuVxzlqlUKjgcDng8nkve78tf/jI2bdqET3ziE/N6nh07dsBqtc7eampqFpWb6GooFAqsX7cOqUgYp0+elDsOUUmZmpxEyD+JlStWyB2FcmTB5eXhhx+GJEmXvfX29l5VmF/+8pd4/fXX8dRTT837Ptu3b0cgEJi9DQ7yonkkD6vViubGRgydOY1gICB3HKKScfrkCZTZrDw8uoSoFnqHBx98EHfeeedl16mrq4Pb7cbY2Nic5clkEn6//5K7g15//XWcOnUKNpttzvJPfepTuP766/HGG29ccB+tVgutVruQl0CUNStWrMCox4Oj3YfQ+aHreLgmUZZN+v2YnpjA9dd28iCPErLg8lJeXj6vfYobN27E1NQU9u3bh46ODgDnykk6nUZnZ+dF7/Pwww/jv/23/zZnWUtLC/7hH/4Bf/Znf7bQqEQ5p1AosG7tWux+4w2cPH4cKxsb5Y5EVNROnehDucPOUZcSk7U/C5uamrBlyxbcc8892Lt3L9566y3cd999uP3222cvljU8PIzGxkbs3bsXAOB2u9Hc3DznBgBLly7F8uXLsxWVKKMsFgtaVq/GyNl+TPr9cschKlpjHg8iUwE0r17NUZcSk9Ux7R//+MdobGzEjTfeiFtuuQXXXXcdfvCDH8x+P5FIoK+vjxe3o6JTX1+PKmcZjh3uRiqVkjsOUdFJp9M40deLGnfFBQeHUPGTRJGdFjQYDMJqtSIQCMBiscgdh0pYOBzGb15/HVZ3FRrXrJE7DlFR6T99GsOnTuDjH/sYzGaz3HEoAxby+c3ZhERZYjQa0drcDM/gACZ8PrnjEBWNmZkZnD15Aqvq61lcShTLC1EW1dbWYkmFCz2Hu5FMJuWOQ1QU+o4dhUWvw6pVq+SOQjJheSHKIkmSsG7tWmiEQN+xY3LHISp43tFRBH0+tLe2Qq1Wyx2HZMLyQpRlBoMB7a0t8I0MY9zrlTsOUcGKxWLoO3YUy5dU89DoEsfyQpQDS5cuxbKqSvQeO4J4PC53HKKC1HPkMIwqJVpbW+WOQjJjeSHKkfb2duglCb1Hj8odhajgDA6cRdDnQ8fatTyrOrG8EOWKTqfD2rY2TI154RkdkTsOUcGYDgZxqrcHq+qWX/LyMlRaWF6Icqi6uhrLl1Tj+LFjiMVicschynvJZBLdB/bDZbPNnnWdiOWFKMfa2tpgUqtw7HC33FGI8poQAkcOHYQ6lULnNddAqVTKHYnyBMsLUY5pNBqsa2/H9MQEhgYH5I5DlLdOHj+O0IQPndesh9FolDsO5RGWFyIZuN1urKhdhlO9vZiZmZE7DlHeGRkewsiZ02hvbkZFRYXccSjPsLwQyaS5uRk2vQ7HDh9CkV1ijGhRfOPjOHH0CFbVLUdDQ4PccSgPsbwQyUStVqNj3TrMTE1hoL9f7jhEeSEwNYWjBw9gmdvN87nQJbG8EMnI6XSisaEBZ070IRwKyR2HSFbTwSAOvvsOKh12XHPNNVAo+BFFF8d3BpHMmpqaUGY240j3Qe4+opIVmp7GwXf3wmUxY+O11/LIIroslhcimSmVSqxftw7JcBinT56UOw5Rzk0Hg9i/dw/KTCZ8aNMmXnCRrojlhSgP2O12rFm1CoOnTyIYCMgdhyhnAlNT2L93D1wWM67btAkajUbuSFQAWF6I8sTKlStRYbfjaPchpNNpueMQZZ1vfBwH9+5BlcOOD7G40AKwvBDlCYVCgY5164BYFCf6+uSOQ5RVw0ODOLL/XdRWurFp40buKqIFYXkhyiMWiwWta9Zg9Gw//BMTcschyjghBE709eHkkSNoXL4cGzZs4ORcWjCWF6I8U1dXh2pXOXoOdyOZTModhyhjkskkDu3fB+/ZM+hobUF7ezskSZI7FhUglheiPCNJEjrWrYM6nUbfsWNyxyHKiHAohL1/eAvxQADXXXstz5xLi8LyQpSHDAYD2ltb4BsZxpjHI3ccokUZHRnGu11/gEWjxsc+cgPcbrfckajAqeQOQEQXt3TpUoyOjqLv2BFY7XZotVq5IxEtSCqVQu/Ro5gYHUbD0qVoa2uDSsWPHVo8jrwQ5bH29nYYlEr0HDksdxSiBQlMTeHtN3+P0LgX13Z0oKOjg8WFMoblhSiPabVadKxdi6DPh6HBAbnjEF1ROp3Gib4+HNjzNsoMetz40Y9i6dKlcseiIsMaTJTn3G43VtQuw/HeXjjKnDAYDHJHIrqowNQUjh3uhojOYN2a1WhoaODFFSkr+K4iKgAtLS2wGww4yos3Uh5KJBLoPXoUB97ugl2nxeaPfhQrV65kcaGs4TuLqACoVCqs71iHWDCI/tOn5Y5DNGtkeAhdv/8PBDyj2NDehhs+/GFYLBa5Y1GR424jogLhcDiwZtUqdPf1oczphMVqlTsSlbDA1BSO9x5DNBBEXc0SrFmzBnq9Xu5YVCJYXogKyKpVq+AdG8ORQwfR+aHreFp1yrlIJIKTfX3wez1wOezYeP11cDqdcseiEsPdRkQFRKFQYH1HBxTxGI739Mgdh0pILBZD79GjeOfN3yEVCmLT+g589IYbWFxIFhx5ISowJpMJ7a2t2LP/AJzl5SivqJA7EhWxWCyG/tOn4RkagEGlxro1a1BXV8dRP5IVywtRAaqtrYXX60XPkcOw2Gw8+y5lXDQaxdnTp+EZHoReqULbqlWor6+HWq2WOxoRywtRoWpvb8fEb3+LI4cOYt01G3h1XsqI0PQ0+k+fxoR3FAa1Bu2Njairq2NpobzC8kJUoLRaLa7p6MB/vPUWzp45g9q6OrkjUYESQmBifBxn+89g2u+HzWjA+pYWLFu2jKf0p7zEdyVRASsvL8fqlStx+Phx2B0OWG02uSNRAUkkEhgZGsLQwFmkolG4HHa0bbgGVVVVPMEc5TWWF6IC19jYCN/EBA4f2I8NH7oOGo1G7kiU5/wTExgeHMTEmAdahQK11dVYvnw5HA6H3NGI5oXlhajAKRQKXLN+PV5/4w28+3YX6lasQJmznHMUaI5IJILR4WF4RoaRikZhN5uxvrkZNTU1nPBNBYflhagI6PV63HD99Xh33z6cPNyNXiFgtFpR5nSh3OWCmadrL0nxeBze0VF4RocRngpAr1ajbkk1li5dirKyMrnjEV01SRTZVd6CwSCsVisCgQCvr0ElaWZmBmNjY/B6vRj1jiGaSECp1cBeVg5neTnKyss5CbOIxeNxjHk98I6OYnrSD41CgUqXCzU1NXC73fzZU95ayOc3ywtREUun05iYmMDY2BhGPV5MTQeRFAImmw3O8go4y8thMpvljkmLFAmHMT42hvExD0JTAagVEtzl5VhSXY3KykrOg6KCkBflxe/34/7778f//b//FwqFAp/61Kfwj//4jzCZTJe9X1dXF77+9a9jz549UCqVaG9vx6uvvjrvC36xvBBdWiQSmR2V8YyNIZpIQqnTwvHeqIzD6eRf5gUgnU5j0u+Hb3wcE+NjiEci0KmUcLtcqKqqgtvtZmGhgrOQz++s/ZbaunUrRkdH8dprryGRSOCuu+7CvffeixdeeOGS9+nq6sKWLVuwfft2fPe734VKpcKhQ4d4yB5RhhgMBtTW1qK2tnbOqMzIqAfHR4eRAuaMyhiv8McG5U5oehr+iQlM+MYR9PshCQGTXof6ykq4XC6Uc3cglZCsjLz09PRg9erVeOedd7B+/XoAwK5du3DLLbdgaGgIVVVVF73ftddeiz/5kz/B448/ftXPzZEXoqsTDofnjMrEkimodDo4nO+PyvB6NrkTDoXg909gcsKPwOQE0vEEtColyp1OVLxXViwWC8+sTEVD9pGXrq4u2Gy22eICAJs3b4ZCocCePXvwn/7Tf7rgPmNjY9izZw+2bt2KTZs24dSpU2hsbMTf/u3f4rrrrstGTCL6AKPRiOXLl2P58uVIpVKYmJg4N+nX40Hv8BBSEmC22eEsP3cEk8FolDty0UilUggGApianERgahLBqSmIRAJqpQJOhwM19fVwOp1wOBwskETIUnnxeDxwuVxzn0ilgsPhgMfjueh9Tp8+DQD45je/iZ07d6K9vR3/+q//ihtvvBFHjhzBihUrLnq/WCyGWCw2+3UwGMzQqyAqXUqlEi6XCy6XCy0tLQiFQrOjMiOnTqC/rxdqvX52VMZeVsYP1XlKp9MIh0IIBKYQnApgOhjATGgaCkjQqlRwljmwfOUKOBwO2O127goiuogF/V/x8MMP49vf/vZl1+np6bmqIOl0GgDwl3/5l7jrrrsAAGvXrsXu3bvx/PPPY8eOHRe9344dO/DYY49d1XMS0fyYTCaYTCbU1dUhmUzC5/O9dwSTBz1Dg0grJJhtdpS7KlBWXg6DwSB35LyQSCQQmp5GaHoawUAA4dA0IqFpKISASqGA1WzBsnIn7CtXwGazcTcQ0TwtqLw8+OCDuPPOOy+7Tl1dHdxuN8bGxuYsTyaT8Pv9cLvdF71fZWUlAGD16tVzljc1NWFgYOCSz7d9+3Y88MADs18Hg0HU1NRcNiMRXT2VSgW32w23243W1lZMT09jbGwMHq8Xg8d7carnGDQGA8qc584p4ygrK/pJ9/F4HOFQCOFwCOHpEEKhacyEQ0jE4lBKEjRKBSwWC5Y6y2Ctr4PVaoXFYuGoCtFVWtD/OeXl5SgvL7/iehs3bsTU1BT27duHjo4OAMDrr7+OdDqNzs7Oi96ntrYWVVVV6Ovrm7P8+PHjuPnmmy/5XFqtlqe2JpKR2WyG2WxGfX397KiM1+vFiMeDscEBpCUJFocDTpcLznLXvE97kG9isRhmIhFEImHMRGYQCYcRnYlgJhxGOpmEQpKgUkgwG41wms2wuitmt43JZCr6AkeUS1k7z8vNN98Mr9eLZ555ZvZQ6fXr188eKj08PIwbb7wR//qv/4oNGzYAAJ566ik8+uijeO6559De3o5/+Zd/wc6dO3HkyBHU19fP63l5tBFR/ggGg7OjMmM+H+KpNLRG4/tzZRyOvPhQTyQSiEWjiEajiMWiiM5EEZ2ZQTQ6g3g0ingsCpFKQyFJUEiAQaeD2WSC2WSC0WiE6QP/5sPrISpEsh9tBAA//vGPcd999+HGG2+cPUnd//yf/3P2+4lEAn19fYhEIrPL/uqv/grRaBRf/vKX4ff70dbWhtdee23exYWI8ovFYoHFYkFDQwMSiQTGx8fPnVfG44F34CyEQgHrB0ZldDpdRp43lUohkUggEY8jHo8jkYgjEU8gHo8jHoshFo8hEY8hEY8jEYshnUpDAcyWE61GC6PRgHKDHsZyJ/R6PQwGw+yNu3uI5MXLAxBRzgkh5o7KTEwgkUpDZzLB4Tw3T0aSJIh0GqlUCql0CqlkCqlUCslkEqlkEslkEsnU+f9OIJVIIpVKIplIQKQFJJwrIxIASQKUkgSdTgetRgu9Tnvuv7Xn/v3jG0dPiHIvL0ZeiIguRZIkWK1WWK1WrFixAolE4gMXkxyF92z/e+u9tz7OFRGVSg2VSgm1SgWVWg29SgW1QQ+12gK1Wn3BTaPRzN7UarVsr5eIMovlhYhkp1arUV1djerqagghZncnK5XK2RtHQ4joPJYXIsorkiTByLP3EtFl8E8ZIiIiKigsL0RERFRQWF6IiIiooLC8EBERUUFheSEiIqKCwvJCREREBYXlhYiIiAoKywsREREVFJYXIiIiKigsL0RERFRQWF6IiIiooLC8EBERUUFheSEiIqKCUnRXlRZCAACCwaDMSYiIiGi+zn9un/8cv5yiKy/T09MAgJqaGpmTEBER0UJNT0/DarVedh1JzKfiFJB0Oo2RkRGYzWZIkiR3nAUJBoOoqanB4OAgLBaL3HFkxW3xPm6L93FbvI/bYi5uj/cV6rYQQmB6ehpVVVVQKC4/q6XoRl4UCgWWLFkid4xFsVgsBfWGyyZui/dxW7yP2+J93BZzcXu8rxC3xZVGXM7jhF0iIiIqKCwvREREVFBYXvKIVqvFo48+Cq1WK3cU2XFbvI/b4n3cFu/jtpiL2+N9pbAtim7CLhERERU3jrwQERFRQWF5ISIiooLC8kJEREQFheWFiIiICgrLSw75/X5s3boVFosFNpsNd999N0Kh0CXX7+/vhyRJF7399Kc/nV3vYt9/8cUXc/GSrtpCtwUAfOQjH7ngdf73//7f56wzMDCAW2+9FQaDAS6XC1/96leRTCaz+VIyYqHbw+/34/7778eqVaug1+uxdOlSfPGLX0QgEJizXiG8N55++mnU1tZCp9Ohs7MTe/fuvez6P/3pT9HY2AidToeWlha88sorc74vhMAjjzyCyspK6PV6bN68GSdOnMjmS8iYhWyLZ599Ftdffz3sdjvsdjs2b958wfp33nnnBT//LVu2ZPtlZMRCtsWPfvSjC16nTqebs06pvC8u9ntSkiTceuuts+sU8vtilqCc2bJli2hraxNvv/22+P3vfy8aGhrEpz/96Uuun0wmxejo6JzbY489Jkwmk5ienp5dD4D44Q9/OGe9mZmZXLykq7bQbSGEEDfccIO455575rzOQCAw+/1kMimam5vF5s2bxYEDB8Qrr7winE6n2L59e7ZfzqItdHscPnxY/MVf/IX45S9/KU6ePCl2794tVqxYIT71qU/NWS/f3xsvvvii0Gg04vnnnxdHjx4V99xzj7DZbMLr9V50/bfeeksolUrxd3/3d+LYsWPiG9/4hlCr1eLw4cOz6zzxxBPCarWKX/ziF+LQoUPiz//8z8Xy5cvz6nVfzEK3xWc+8xnx9NNPiwMHDoienh5x5513CqvVKoaGhmbX2bZtm9iyZcucn7/f78/VS7pqC90WP/zhD4XFYpnzOj0ez5x1SuV9MTExMWc7HDlyRCiVSvHDH/5wdp1CfV98EMtLjhw7dkwAEO+8887ssl/96ldCkiQxPDw878dpb28Xn/vc5+YsAyB+/vOfZypq1l3ttrjhhhvEl770pUt+/5VXXhEKhWLOL61//ud/FhaLRcRisYxkz4ZMvTd+8pOfCI1GIxKJxOyyfH9vbNiwQXzhC1+Y/TqVSomqqiqxY8eOi67/X/7LfxG33nrrnGWdnZ3iL//yL4UQQqTTaeF2u8WTTz45+/2pqSmh1WrF//k//ycLryBzFrot/lgymRRms1n8y7/8y+yybdu2iU984hOZjpp1C90WP/zhD4XVar3k45Xy++If/uEfhNlsFqFQaHZZob4vPoi7jXKkq6sLNpsN69evn122efNmKBQK7NmzZ16PsW/fPhw8eBB33333Bd/7whe+AKfTiQ0bNuD555+f1yXF5bKYbfHjH/8YTqcTzc3N2L59OyKRyJzHbWlpQUVFxeyym266CcFgEEePHs38C8mQTLw3ACAQCMBisUClmnvJsnx9b8Tjcezbtw+bN2+eXaZQKLB582Z0dXVd9D5dXV1z1gfO/YzPr3/mzBl4PJ4561itVnR2dl7yMfPB1WyLPxaJRJBIJOBwOOYsf+ONN+ByubBq1Sr8j//xPzAxMZHR7Jl2tdsiFAph2bJlqKmpwSc+8Yk5/8+X8vviueeew+233w6j0ThneaG9L/5Y0V2YMV95PB64XK45y1QqFRwOBzwez7we47nnnkNTUxM2bdo0Z/m3vvUtfOxjH4PBYMCvf/1rfP7zn0coFMIXv/jFjOXPpKvdFp/5zGewbNkyVFVVobu7Gw899BD6+vrwb//2b7OP+8HiAmD26/luYzlk4r3h8/nw+OOP4957752zPJ/fGz6fD6lU6qI/s97e3ove51I/4/Pb6fy/l1snH13NtvhjDz30EKqqquZ80G3ZsgV/8Rd/geXLl+PUqVP42te+hptvvhldXV1QKpUZfQ2ZcjXbYtWqVXj++efR2tqKQCCAnTt3YtOmTTh69CiWLFlSsu+LvXv34siRI3juuefmLC/E98UfY3lZpIcffhjf/va3L7tOT0/Pop9nZmYGL7zwAv76r//6gu99cNnatWsRDofx5JNP5vwDKtvb4oMfzC0tLaisrMSNN96IU6dOob6+/qofN1ty9d4IBoO49dZbsXr1anzzm9+c8718eW9Qdj3xxBN48cUX8cYbb8yZqHr77bfP/ndLSwtaW1tRX1+PN954AzfeeKMcUbNi48aN2Lhx4+zXmzZtQlNTE77//e/j8ccflzGZvJ577jm0tLRgw4YNc5YXw/uC5WWRHnzwQdx5552XXaeurg5utxtjY2NzlieTSfj9frjd7is+z89+9jNEIhHccccdV1y3s7MTjz/+OGKxWE6vbZGrbXFeZ2cnAODkyZOor6+H2+2+YBa+1+sFgAU9bqbkYntMT09jy5YtMJvN+PnPfw61Wn3Z9eV6b1yM0+mEUqmc/Rmd5/V6L/m63W73Zdc//6/X60VlZeWcddrb2zOYPrOuZluct3PnTjzxxBP4zW9+g9bW1suuW1dXB6fTiZMnT+bth9RitsV5arUaa9euxcmTJwGU5vsiHA7jxRdfxLe+9a0rPk8hvC8uIPekm1JxflLmu+++O7vs1VdfnfekzBtuuOGCI0ku5W/+5m+E3W6/6qzZtthtcd6bb74pAIhDhw4JId6fsPvBWfjf//73hcViEdFoNHMvIMOudnsEAgFx7bXXihtuuEGEw+F5PVe+vTc2bNgg7rvvvtmvU6mUqK6uvuyE3T/90z+ds2zjxo0XTNjduXPn7PcDgUDBTMxcyLYQQohvf/vbwmKxiK6urnk9x+DgoJAkSbz88suLzptNV7MtPiiZTIpVq1aJL3/5y0KI0ntfCHFuErNWqxU+n++Kz1Eo74sPYnnJoS1btoi1a9eKPXv2iDfffFOsWLFizuGwQ0NDYtWqVWLPnj1z7nfixAkhSZL41a9+dcFj/vKXvxTPPvusOHz4sDhx4oT4p3/6J2EwGMQjjzyS9dezGAvdFidPnhTf+ta3xLvvvivOnDkjXn75ZVFXVyc+/OEPz97n/KHSH//4x8XBgwfFrl27RHl5ecEcKr2Q7REIBERnZ6doaWkRJ0+enHPIYzKZFEIUxnvjxRdfFFqtVvzoRz8Sx44dE/fee6+w2WyzR4x99rOfFQ8//PDs+m+99ZZQqVRi586doqenRzz66KMXPVTaZrOJl19+WXR3d4tPfOITBXNI7EK2xRNPPCE0Go342c9+Nufnf/40CtPT0+IrX/mK6OrqEmfOnBG/+c1vxLp168SKFSvyuswLsfBt8dhjj4lXX31VnDp1Suzbt0/cfvvtQqfTiaNHj86uUyrvi/Ouu+46cdttt12wvJDfFx/E8pJDExMT4tOf/rQwmUzCYrGIu+66a875Ws6cOSMAiN/+9rdz7rd9+3ZRU1MjUqnUBY/5q1/9SrS3twuTySSMRqNoa2sTzzzzzEXXzScL3RYDAwPiwx/+sHA4HEKr1YqGhgbx1a9+dc55XoQQor+/X9x8881Cr9cLp9MpHnzwwTmHDuerhW6P3/72twLARW9nzpwRQhTOe+O73/2uWLp0qdBoNGLDhg3i7bffnv3eDTfcILZt2zZn/Z/85Cdi5cqVQqPRiDVr1oj/9//+35zvp9Np8dd//deioqJCaLVaceONN4q+vr5cvJRFW8i2WLZs2UV//o8++qgQQohIJCI+/vGPi/LycqFWq8WyZcvEPffcc8H5T/LVQrbFX/3VX82uW1FRIW655Raxf//+OY9XKu8LIYTo7e0VAMSvf/3rCx6r0N8X50lC5Mlxk0RERETzwPO8EBERUUFheSEiIqKCwvJCREREBYXlhYiIiAoKywsREREVFJYXIiIiKigsL0RERFRQWF6IiIiooLC8EBERUUFheSEiIqKCwvJCREREBYXlhYiIiArK/w+o9+Qw9GSDsAAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from random import choice\n", "\n", "ft.init_seed()\n", "print(f\"SEED = {ft.SEED}\")\n", "\n", "ft.SEMI_CONVEX = ft.generate_semi_convex(5)\n", "ft.SEMI_ARC = [ choice([True,False]) for _ in range(len(ft.SEMI_CONVEX))]\n", "ft.DIST = ft.dist_convex\n", "print(f\"half perimeter = {ft.half_perimeter():.4f}\")\n", "\n", "plt.axis('equal')\n", "ft.draw_points([(0,0)], 'black', 4, '+')\n", "ft.draw_disc()" ] } ], "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": "3.9.6" }, "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 2 }