{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# An Optimal Algorithm for the Freeze-Tag Problem in 2D" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "plt.figure(figsize=(1,1))\n", "plt.plot([])" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "#import matplotlib.pyplot as plt\n", "#plt.plot([])\n", "\n", "# Warning! Constants are imported as constant only, so 'from ... import *' will not work properly\n", "import freeze_tag_mini as ft\n", "from math import pi, sin, cos" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Optimal wake-up times for $n$ points regularly spaced on the unit circle ($\\ell_2$ norm)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "regular(0) = 0.000\n", "regular(1) = 1.000\n", "regular(2) = 3.000\n", "regular(3) = 2.732\n", "regular(4) = 3.828\n", "regular(5) = 3.351\n", "regular(6) = 3.732\n", "regular(7) = 3.431\n", "regular(8) = 3.613\n", "regular(9) = 3.416\n", "regular(10) = 3.520\n", "regular(11) = 3.383\n" ] } ], "source": [ "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,ft.dist_L2) # compute the optimal tree\n", " print(f\"regular({n}) = {x:.3f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lower bound for $\\ell_p$ norm" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.LP_NORM = 1.5 # p for L_p\n", "ft.SEED = -1 # do not display seed\n", "ft.PROCESS_TIME = 0 # elapsed time in seconds in display draw_all()\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.draw_all(f'norm L_p, p = {ft.LP_NORM}\\nconjecture = {u:.3f}\\nlower bound',x,T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lower bound in $\\ell_1$ norm for a square of diameter $1$ with $6+1$ points with wake-up time $2+1/6$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.SEED = -1 # does not display seed\n", "ft.PROCESS_TIME = 0 # elapsed time in seconds for display draw_all()\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.draw_all('optimal',x,T)" ] }, { "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": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.init_seed(2074) # 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.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": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.init_seed(5687) # 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", "x,T = ft.optimal_tree() # compute the optimal tree\n", "ft.draw_all('optimal',x,T) # display results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $n=11$ points in convex position having $3$ crossings (apart from the first edge)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.init_seed(3906) # set SEED\n", "n = 11 # number of points (asleep robots)\n", "P = ft.generate_convex(n) # 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\n", "# T = [11, [5, [6, [7, [8, [9], [10]], [4]], [3, [2]]], [0, [1]]]]\n", "# T = [11, [5, [6, [7, [8, [9], [10]], [4]], [0, [1]]], [3, [2]]]]\n", "# ft.draw_all('???????',x,T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A tree with a 'controlled' shape in $\\ell_2$ norm" ] }, { "cell_type": "code", "execution_count": 21, "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 odd $n = 2k+1$ points on a circle (in $\\ell_2$ norm) showing that the worst-case on a circle is not the uniform case for $n$ odd\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": 22, "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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GV199VdseExPDqlWrGDVqFMXFxSxatIjbbrutud5mLQsLC+Lj4/nmm2/Iz8/Hw8ODfv36sXPnTrp06VJ7XFJSEvn5+bWPMzIymDt3LgUFBXh5eTF06FD27dt3xXV9/srKyoqPPvqIRx55BEVR6NSpE++88w533nlno77HK1H9OcNaCCGEENdg8eLFPPzwwxQXF5u7FPE3ZJ0eIYQQQrQLEnqEEEII0S7I5S0hhBBCtAsy0iOEEEKIdkFCjxBCCCHaBQk9QgghhGgXJPQIIYQQol2Q0COEEEKIdkFCjxBCCCHaBQk9QgghhGgXJPQIIYQQQF5eHtbW1lRUVKDT6XBwcCAtLe2q+khJSUGlUnHs2LGmKbIetm/fjkqluuTHwYMHr6nPHTt2MGnSJPz9/VGpVKxZs6Zxi24mEnqEEEIIYO/evfTo0QMHBweOHDmCu7s7gYGB5i7rqg0ePJisrCyTj3/961+EhITQt2/fS56zePFiRo4cedk+Kyoq6NGjBx999FETVd08JPQIIYQQwJ49exgyZAgAu3btqv38YiqVik8++YTx48djZ2dHaGgoK1asqG0PCQkBoFevXqhUqtogsX37dvr374+DgwOurq4MGTKE1NTUJnkf1tbW+Pr61n54eHiwdu1abr/9dlQq1TX1OX78eF555RWmTZvWyNU2L0tzFyCEEEKYS1paGt27dwegsrISCwsLFi9eTFVVFSqVCldXV2666SY+/vjj2nOee+45Xn/9dd5//32+++475syZw8mTJ4mKiuLAgQP079+fzZs306VLF6ytrdHr9UydOpU777yTJUuWoNVqOXDgwBUDSJcuXa4YioYNG8aGDRvq9R7XrVtHQUEBt99+ez2/Km2XhB4hhBDtlr+/P8eOHaO0tJS+ffuyf/9+HBwc6NmzJ7/++iuBgYE4OjqanDNz5kz+9a9/AfDyyy+zadMmPvjgAz7++GO8vLwA8PDwwNfXF4DCwkJKSkqYOHEiYWFhAERFRV2xrvXr16PT6S7bbmdnV+/3+NVXXzF27FgCAgLqfU5bJaFHCCFEu2VpaUlwcDDLli2jX79+dO/end27d+Pj48Pw4cMvec6gQYPqPL7SxGV3d3duu+02xo4dy/XXX8+YMWOYNWsWfn5+lz0nKCjomt7PX2VkZPDbb7+xbNkyk+fT0tKIjo6ufazX69HpdCYB7+mnn+bpp59ulDpaCgk9Qggh2q0Ll5F0Oh1GoxFHR0f0ej16vR5HR0eCgoI4ffp0g19n0aJFPPjgg2zcuJGffvqJZ599lk2bNjFw4MAr1nU59b28tWjRIjw8PJg8ebLJ8xdGuC5YtWoVK1eu5Icffqh9zt3d/W/7b20k9AghhGi3LlxGGj16NG+++SZ9+vRhzpw53HbbbYwbNw4rK6s65+zbt49bbrnF5HGvXr2AmknEAAaDoc55vXr1olevXjz11FMMGjSIH3/88bKhpzEubymKwqJFi7jlllvqvA9LS0s6depU+9jb2xs7OzuT59oiCT1CCCHaraCgILKzs8nJyWHKlCmoVCpOnz5NTEzMZS8/LV++nL59+zJ06FB++OEHDhw4wFdffQX8Lzxs3LiRgIAAbG1tKSws5PPPP2fy5Mn4+/uTkJBAYmKiSXC6VF0NtXXrVs6dO1c7/6ghysvLOXv2bO3jc+fOcezYsVZ3W7/csi6EEKJd2759O/369cPW1pYDBw4QEBBwxfk2L730EkuXLqV79+58++23LFmypHZ+jKWlJQsXLuSzzz7D39+fKVOmYG9vT3x8PDExMURERHDXXXdx3333cffddzfp+/rqq68YPHgwkZGRDe7r0KFDtSNVAI8++ii9evXi+eefb3DfzUmlKIpi7iKEEEKI1kClUrF69WqmTp1q7lLENZCRHiGEEEK0CxJ6hBBCCNEuyERmIYQQop5kRkjrJiM9QgghhGgXJPQIIYQQol2Q0COEEEKIdkFCjxBCCCHaBQk9QgghhGgXJPQIIYQQol2Q0COEEEJcZOTIkTz88MO1j4ODg3nvvffMVo9oPBJ6hGhj9Ho9VVVVlJaWUlhYSE5ODufPnyc9PZ2UlBSSk5M5e/YsiYmJnDlzxuQjMTGRpKQkzp07R2pqKhkZGWRlZZGXl0dRURHl5eVUV1djNBrN/TaFaDYHDx7krrvuMncZVy0rK4ubbrqJiIgI1Gq1SZC7ki1btjB48GCcnJzw9fXlySefRK/X17a/+OKLqFSqOh8ODg61x+h0OhYsWEBYWBi2trb06NGDjRs3NvZbvGqyOKEQrYTRaKSqqorKykqqqqqoqqpCo9HUfF5djUajobq6Gr3RiKKAQs1Cago1n4MCKhUWagtQqVCr1aC66AWUP49XFBTFiNFgAECFChU1ew4BqFU1p1lbWWNrY42trS12trbY2dnVfG5nh52dHfb29tjY2DTnl0iIJuHl5WXuEq5JdXU1Xl5ePPvss7z77rv1Ouf48eNMmDCBZ555hm+//ZbMzEzuueceDAYD//3vfwGYP38+99xzj8l5o0ePpl+/frWPn332Wb7//nu++OILIiMj+e2335g2bRp79uyp3bTUHGTDUSFaGI1GQ1lZGWVlZZSXl1NeXk5peTkVlZUYFTAqCkYUrGxssLaxxdrGBmtrmz//a42VtRVWVtZYWVlhaWmJhaVlzX8tLGqDS30ZjUb0ej16vR6DXo9Op0Ov06HVadFpdWi1WrTV1VRXa9BVV6OtrsZoMGChUqFWgZWFJU6Ojjg5OuDk5ISjoyOOjo44OTlhYWHRRF9BIeqvoqKCe++9l1WrVuHk5MT8+fP5+eef6dmzZ+0lreDgYB5++OHakZJ33nmHRYsWkZycjLu7O5MmTeLNN9/E0dERgMWLF/Pwww/z/fff89hjj5Gens6ECRP49ttvWb58OS+88AIlJSXcfPPNvPvuu83yb2HkyJEm7+lynn76aTZt2sTBgwdrn/v555+ZNWsWubm5ODk51Tnn+PHj9OzZkx07djBs2DAA/P39eeaZZ7jvvvtqj4uJicHOzo7vv/++cd7UNZCRHiHMRFEUysrKKCkpoaSkhKLiYopLSqnWaTEYFRS1Clt7B+wcHHDw8sHT3g47O3vs7O2xtbWtGalpYmq1Gmtra6ytret9jk6nQ1NVRdWfI1KVFRXkVlSQmpuLrlqLhUqFhQqcHR1xdXHB5c8PV1dXGRkSze7xxx/njz/+YO3atXh7e/P0009z5MgRevbsedlz1Go1CxcuJCQkhOTkZP7v//6PJ554go8//rj2mMrKShYuXMjSpUspKytj+vTpTJs2DVdXV9avX09ycjIxMTEMGTKE2bNnX/J1du7cyfjx469Y/2effca8efOu6b1fSnV1Nba2tibP2dnZodFoOHz4MCNHjqxzzpdffklERERt4LlSP7t27Wq0Wq+FhB4hmolGo6GoqIiioiIKCgspLCqiWm/AoBixtXfA3skJj46BODk54eDkhJ2d3VWPzLQEVlZWWFlZ4eTsXKdNr9dTUV5OeXkZ5aVl5JaXci4rG0Wvx0KtwtHeHg83N9zd3XFzc8PV1bVZwp1on8rLy/nqq6/4/vvvGT16NADffPMNAQEBVzzvr5OcX3nlFe655x6T0KPT6fjkk08ICwsDYMaMGXz33Xfk5OTg6OhIdHQ0o0aNYtu2bZcNPX379uXYsWNXrMXHx6ce77T+xo4dy3vvvceSJUuYNWsW2dnZLFiwAKiZI/RXGo2GH374gX//+991+nnnnXcYPnw4YWFhbNmyhVWrVmH487K5uUjoEeJvGHU6cleuRJuainVQEN4xMaitrP72vKqqKgoKCsjPzycvP5+S8nL0RgVLWxucXFzxDe2Es4sLTs7OWFq2j3+KlpaWuLi64uLqavJ8ZWUlpSXFlBSXkFNaTPL586iMCtYWajw9PPDy9MTDwwN3d3cJQaLRJCUlodVqGTBgQO1z7u7udO7c+Yrnbd68mddee434+HhKS0vR6/VoNBoqKyuxt7cHwN7evjbwQE04CQ4Orr0EduG53Nzcy76OnZ0dnTp1uta3d01uuOEG3nrrLe655x5uvvlmbGxseO6559i5c+cl/+2tXr2asrIybr31VpPn33//fe68804iIyNRqVSEhYVx++238/XXXzfXW7mk9vGTVohrlLFwIS7PP49vSUntc2UuLpQsWEDAgw+aHKvX62sCTl4e2Tm5lJSXoTMq2Dk64urmTqeQUFzd3OsM+YqaXxD29vb4+vkDNXOJykpLKS4qoqiwgKwziRh1sdhYWuDt6Ym3tzfe3t44X2I0SYimlJKSwsSJE7n33nv5z3/+g7u7O7t27eKOO+5Aq9XWhh6rv/xhpFKpLvncle6ENMflLYBHH32URx55hKysLNzc3EhJSeGpp54iNDS0zrFffvklEydOrDPi5OXlxZo1a9BoNBQUFODv78+///3vS/bRnCT0CHEZGQsX0uGhh+o871hSguNDD5EBuN1xBzk5OWRnZ5OTn49Wb8DS1hY3D0/CQ0Jx8/ConQ8jd3nXn1qtrh0RCgoJQVEUysvKKCwooCA/j/TTp1GdPIWTvR3+vr74+Pjg5eUlk6PFVQkLC8PKyor9+/cTGBgIQFFREWfOnGHEiBGXPOfw4cMYjUbefvvt2pGPZcuWNUl95ri8dYFKpcLfv+aPkCVLltCxY0d69+5tcsy5c+fYtm0b69atu2w/tra2dOjQAZ1Ox8qVK5k1a1aT1FtfEnqEuASjTofL888Dpnd1X3isAE7PP896f3/0FpaoLb0xKl3R6j0pTrfj0EHIPq8i+7yKzHQV2VkqCgvgk290TJom6edqqVQqnJydcXJ2JigkBKPRWBOA8vI4ez6L+KRkbCwt8Pf1xc/PD19f3zp/VQvxV46Ojtxxxx08/vjjeHh44O3tzTPPPHPFS6idOnVCp9PxwQcfMGnSJHbv3s2nn37aJPU1xuWtC6GpvLycvLw8jh07hrW1NdHR0UDN5amnnnqK+Pj42nPeeustxo0bh1qtZtWqVbz++ussW7aszh8VX3/9NX5+fpccjdq/fz+ZmZn07NmTzMxMXnzxRYxGI0888USD3k9DSegR4hJyV640uaT1VyrApaSE356u5tuUGHQ602hkYamgUoFBD4pS0+bgoODu3pRVtx9qtRpPLy88vbzoTHTNHWI5OWTnZJGUkYmNhRp/Hx86dOggAUhc0VtvvUV5eTmTJk3CycmJxx57jJIr/Nvv0aMH77zzDm+88QZPPfUUw4cP57XXXuOWW25pxqrr7+I1cQ4fPsyPP/5IUFAQKSkpAJSUlJCQkGByzoYNG/jPf/5DdXU1PXr0YO3atXWCjdFoZPHixdx2222XHGHVaDQ8++yzJCcn4+joyIQJE/juu+9w/ct8vuYm6/QIcQlpb7xB4F/uRriUJwJe562MJ694jIWFQoeOCj+s1tEpQv65NTWNRkNudjY52ecpLy7BztKCDn5+dOzYEW9vb5kILUQ7JiM9QlzEYDCQlZVFhtFIYD2OT9MFXbFdpVIwGFT0H2Rkx1Y16akKoZ1qQlA7uWGr2dna2hIYHExgcDAajYbs8+c5n3We5PQMHO1sCerYkcDAQJkELUQ7JCM9QgClpaWkpqaSkpZORXU1Dk6OjJg5E6eSkjpzeqBmTk+xoyveFTkYsKq9hFVfF0Z/IiIVQsJqgtCF//oHKMh83MZXXlZGZkYGuVmZoNPj5e5GSHAwHTp0aDdLBgjR3knoEe2W0WgkKyuL5HPnyM7LBytLfDt0pENAAPYODhR/8jGd5z8G1NmiCoATr7zNzzYP8NUnFqQkq7GwVDDo/xp+FJxdwMkJMjPqF4wsLRUCAmsCUWgnhZBOCqFhCiGdjPj5g1ydaRij0Uh+bi6ZGemUFBRgb2VFSFAgwcHBl1xiXwjRdkjoEe1OdXU1KSkpJJ07R2llFU7ubgR0DMLLx6fOfI/iTz6mw8sLcLpoYmOpqyvnn30O13v/DwBFgb071Sz+woL1a9UoChiN/ws4lpYKm/dqCemkkJ6q4lySiuSzNf89e0bF2TNqss/XLxBZWSsEBpkGopAwIyFhCr5+0AoXcDarqqoqMtPTycpIQ6XX4+ftTVhoKD4+Pq1yNWwhxJVJ6BHtRllZGWfPniUlPR2tUcHbvwOBwcE4XLRC6qUYdTrK167BmJ6OumNHHKdMveyKzHk58OO3Fiz+3JLs8yrUFgpGg4rorkY27tJyuZuIqqsh9VxNEDp3VkXyn4Eo6Yya3Jz6/fK1sVEIDFYI/zMQXRgdCg1T8PKRQHQlRqORnOws0lNTqCopxd3ZmfBOYXTs2FHW/hGiDZHQI9q8wsJCEhMTSc/KQrG0IiAomIDAwCa9jdlggG2b1Cz6zIJtm9QoiooPv9ISM+fq1+ipqoLUZBXnki8KRAkqkhLV5OfVL8nY2SsEmQQi45+jRAoenhKILlZcVERqyjmKcnNxsrUhPCyMkJAQue1diDZAQo9os/Lz84lPSOB8bh5W9vYEhoTg59+h2W9ZTk+DX9dY8M97DFzFZuX1UlkBKck1Qejcn5fMEhPUJJ9VUVhQvyRj76AQEvq/QHThcllImIK7R+PW25pUVlaSmpxMzvkM7C2tCA8LJTQ0VHaCF6IVk9Aj2py8vDziExLIysvHxsmRkNBOeLXDORrlZdRcLkv63yjRhUBUXFS/r4Wj08WByGhyp5mLa9PW31JUV1eTeu4cWelp2KpVhIeFERYWJuFHiFZIQo9oMwoLC4mNi+N8bh42To6EdYrA09vb3GW1SKUlmFwuO3dWTWJCzePS0voFImeXmgAU3vl/c4cuhCLHNngTlE6nIyU5mfNpqdiq1XQO71S7d5MQonWQ0CNavdLSUmJjY0nPysbKwYGw8Ai8mmgTvvaguIiL7jBT11wyi68ZLSovq18gcnOvCT+dIoz/u+X+zw+HK88bb/G0Wi0pyclkpadib2lFVOcIQkJCZMKzEK2AhB7RalVVVREXF0dyWhoqG1vCIiLw8fVrd5exmlNhgWkgSj5bE4hSklVUVtbv6+7uoRAWrhDe+c+5Q3+GoqBQBXv7Jn4Djai6uprkxERyz2fgYmdHl+hoAgIC5PtPNKnTp0/z/PPPc/jwYVJTU3n33Xd5+OGH//a8EydOcN9993Hw4EG8vLx44IEH6mz+uXz5cp577jlSUlIIDw/njTfeYMKECbXtiqLwwgsv8MUXX1BcXMyQIUP45JNPCA8Pb+y32WRkGVLR6uj1es6ePUv8mTNoVWpCOkfRoWNH2VOpGbh71ISWPv0V4H93oikKFORRe6nswsTqxAQVKedUaKr+FwQKC2omWR/cV/f/l5e3QliEkU4RF265r5lTFBSqYGvbHO+w/mxsbIjq2pWgkBASzySw5+AhvJOS6Na1K56enuYuT7RRlZWVhIaGMnPmTB555JF6nVNaWsoNN9zAmDFj+PTTTzl58iT//Oc/cXV15a677gJgz549zJ07l9dee42JEyfy448/MnXqVI4cOULXrl0BePPNN1m4cCHffPMNISEhPPfcc4wdO5bY2FhsW9o/0MuQkR7RqmRmZnLy1CmKq6roEBRCSFiYbCHQwilKzfpFFweiCyNEaSkqqqvrNzLi7VtzuaxThOnWHUEhSqPfFXctiouKOBMfS3VpGcEBHejSpQv2rWnoqp0yGo288cYbfP7552RnZxMREcFzzz3HjBkzao85ffo0Tz75JDt27EBRFHr27MnixYsJCwsD4Ouvv+btt9/m7NmzuLu7ExMTw4cfftjktQcHB/Pwww//7UjPJ598wjPPPEN2djbWf/5j+fe//82aNWuIj48HYPbs2VRUVPDLL7/Unjdw4EB69uzJp59+iqIo+Pv789hjjzF//nygZod2Hx8fFi9ezJw5c5rmTTYy+W0hWoXS0lKOnzjB+dw8XLy96d+nn/xCaSVUKvD2rQktA4cYTNoUBbKzMBkdSvozEKWnqtDp/heIcrNV5GZbsGdH3dfw6/CXQPTnKFHHIOWyC0I2Nlc3N/oPGkLW+UzOxseTmZVFdGQkYWFhMt+nBXvttdf4/vvv+fTTTwkPD2fHjh384x//wMvLixEjRpCZmcnw4cMZOXIkW7duxdnZmd27d6PX64GaQPHoo4/y+uuvM378eEpKSti9e/dlX++HH37g7rvvvmJNGzZsYNiwYY32Hvfu3cvw4cNrAw/A2LFjeeONNygqKsLNzY29e/fy6KOPmpw3duxY1qxZA8C5c+fIzs5mzJgxte0uLi4MGDCAvXv3SugRojHo9XoSEhKIP3sWlY0tXfr0xdPLy9xliUaiUoGfP/j5Gxk83LTNaITzmZCSdIlAlKYy2ecsK1NFVqYFO7f9tf+aDVw7RSi1gejCKFFAYNPsdO/n3wEvbx+Sz57laGwsKalp9OrZAy/5vm1xqqurefXVV9m8eTODBg0CIDQ0lF27dvHZZ58xYsQIPvroI1xcXFi6dGntnXoRERG1fbzyyis89thjPPTQQ7XP9evX77KvOXnyZAYMGHDFujp06NCQt1VHdnY2ISEhJs/5/HmzR3Z2Nm5ubmRnZ9c+d/Ex2dnZtcddfN6ljmkNJPSIFis7O5tjx49TotEQGNqJoJAQmbfTjqjVENARAjoaGTrStM1ggPMZ/9vDLPmiQJSZrqrd+0xRah5npsMfW/7af81O9+GRCmGdGnene0tLSyIiI+kQEEB87Cm27dpNWGBHunbtKuv7tCBnz56lsrKS66+/3uR5rVZLr169ADh27BjDhg275NIEubm5nD9/ntGjR9f7NZ2cnGRjWzOS0CNanOrqak6cOMG5jEwc3d3pJ5eyxF9YWEDHoJrLVyP+8vtGr4eMtJoglJL8ZyBKrJlUfT5DhaLUBCKjseYSWnoqbP3NtI8LO91fCETXutO9g6MjffoP5HxmBmfj48nKyaFHt2507Nix9hijTkfuypVoU1OxDgrCOybmsnu7icZVXl4OwK+//lpndOVCOLWzs7vs+VdquxxzXN7y9fUlJyfH5LkLj319fa94zMXtF57z8/MzOaZnz56NVmtTk9AjWpSMjAyOnThBpcFIeLdu+Pk37jCvaPssLSE4VCE4tO49GjodNTvdX1iU8aKd7rMy/3e5TK+vCUwpybDpL31YWSt0vEwgutxO9/4dAvD08iYhNpY9Bw8RmJFBz549KfjiC1yefx7fkpLaY8tcXChZsICABx9srC+JuIzo6GhsbGxIS0tjxIgRlzyme/fufPPNN+h0ujqjPU5OTgQHB7NlyxZGjRpVr9c0x+WtQYMG8cwzz5i8h02bNtG5c2fc3Nxqj9myZYvJpOhNmzbVXvYLCQnB19eXLVu21Iac0tJS9u/fz7333tuo9TYluXtLtAjV1dUcP36clMxMXL19iezSxWTSnRBNrboa0lJUF61DVDNCdPaMmpysxtvpPj83l7hTJ/H6/XdGfLAQgIt7v/ADOfP99yX4NINnn32WTz/9lLfffpuhQ4fWTkR2dnbm1ltvpaCggM6dOzNixAieeuopXFxc2LdvH/3796dz585888033HPPPbzxxhuMHz+esrIydu/ezQMPPNAk9Wq1WmJjYwGYMGEC8+bNY968eTg6OtKpUycAPvzwQ1avXs2WLTXXdEtKSujcuTM33HADTz75JKdOneKf//wn7777rskt6yNGjOD111/nxhtvZOnSpbz66qsmt6y/8cYbvP766ya3rJ84cUJuWRfiamRlZXHk2DEqDQY6R3fF+89hVCFaCo0GUs/9uY/ZhZ3uz6hIOqMmL7d+gcjWTiE4pCYQhQRXseDLAJxLS7jU2QpQ5uqKY26uXOpqYoqisHDhQj755BOSk5NxdXWld+/ePP300wwfXjO7/sSJEzz++OPs2rULCwuL2lvWQ0NDAfjss8949913SU5OxtPTkxkzZrBw4cImqTclJaXOpGSAESNGsH37dgBefPFFFi9eTEpKSm37xYsTenp68sADD/Dkk0+a9LF8+XKeffbZ2sUJ33zzzUsuTvj5559TXFzM0KFD+fjjj00mdrd0EnqE2ej1ek6ePEliSirOXl5Ed+0mozui1amshNRL7HSflHj5ne5n+yxlac7cv+07e8kSfFvJrcBCtAYyp0eYRVFREQcPHaaospJOXbrQIaDj358kRAtkbw9RXRWiutb9+7Gy4n873V+4ZHYmAcKq90LOJTr7C21qahNULET7JaFHNCtFUUhOTubYqVNYOjjQb/AQ7B0czF2WEE3C3gG6dFeI7mbkePZhCuOXkx67lKTTKjj+9+dbBwU1fZFCtCNyeUs0G61Wy5EjR0g5n4V/cAidIiJk3R3RpiXkx7I6bhkrY5eQUZpW+7yFEfLfc8SltFzm9AjRjGSkRzSLoqIiDhw8SEm1lq69++Dp7W3ukoRoEilFyaxNWMGK0z9wtvCMSZu1hTUTwqcyPXo2mU5JuDz+BAqXvntr19yZ+J8+Tbdu3WQbCyEaiYQe0eRSUlI4euIEFn9ezrqWBb2EaMmyyjJZl7CSFad/5FRu3etWYztNJCZ6DqNDx2Nv9edCm/8HCSoLOry8AKeL1ukpdnbkpXFubIraxxPJoykuKaF/P1mgU4jGIJe3RJMxGo2cOHGCM+dS8OoQQOfoaLmcJdqM/Mo8fj2zhlWxSzmQuadO+4ig0UyPnsO48Ek427hcth+jTkf52jWcjzvAp1nLWRGUg0ENapWaUYE3cKfXfTio1Azo10/27xKigST0iCah0Wg4cPAg5wsKCI+Wu7NE21BaXcLGxJ9ZFbuUP1K31Gnv32Ew06PnMDFiGh72nlfVt0avIfx9L/RG/UXPqri9593EuMxBU1JMr27dateGEUJcPQk9otEVFxezb/9+ynR6uvfug4urq7lLEuKaVeoq2Zy0ntVxy/jt7C8omP7I7ObTk5jouUzuHIOfU8O2D5jw/TCOZh2q8/wLI19nlOMNZKemEBESTI8ePWTUVIhrIHN6RKPKysriwKFDqOzt6ddvQKtZmlyIi2kNWv5I2cyq2J9Yn7gGrUFr0h7u3pmYLjcxpfMMgt0ab+RlcMfhnMw59pfRHnhp+7/pMDmAPt0GkHD6FOUVFQzo318W8xTiKslIj2g0Z8+e5dipUzh7+dCle3e540S0KgajgT3pO1gTt4y1CSuo0JabtAc4BzKjy01MjZxJZ8/oJqnh97O/cuvqGZdss1JbsXz2BiLsozh59AhudnYMHjQQB1nnqtFt376dUaNGUVRUhKuMVLcpMj4qGkxRFI4fP87hEyfxCQqhW8+eEnhEq2BUjBzM3Mszmx+l20eBzFo2gR9PLq4NPJ723tzd90E23LyLA3fF8+TQF5os8AD07TDwsm0GxcA/Vk4jX8mj76DBlOn1bPvjDwoLC5usnvZg5MiRJjuLAwwePJisrCxcXC4/Ab2l0mg03HfffXh4eODo6EhMTAw5OVde/ltRFJ5//nn8/Pyws7NjzJgxJCYmmhxTWFjIvHnzcHZ2xtXVlTvuuIPyctM/DJYtW0bPnj2xt7cnKCiIt956q9HfX0NJ6BENYjAYOHjwIHHJ5wjr0oXwzp1Rqeq3AaMQ5qAoCidzjvHKH8/Q+5NOTP7xOr4++glFmprw4GLjyq097mTVnE0c/79zvDjqDXr69mmW72t3Ow9C3Dpdss2oGKnSVTJ72Y2UG0vpN2gw2NmxY9cusrOzm7y29sTa2hpfX99W+bPskUce4eeff2b58uX88ccfnD9/nunTp1/xnDfffJOFCxfy6aefsn//fhwcHBg7diwajab2mHnz5nH69Gk2bdrEL7/8wo4dO2p3aAfYsGED8+bN45577uHUqVN8/PHHvPvuu3z44YdN9l6vhVzeEtdMp9Oxb/9+zucX0KVnL1lwULRoZwvPsCZuGStifyS1+JxJm62lHZM7xzA1ahbDgkZhqTbfdMcnfn+AJScXozfqsVBbYrhofo8KFQoKXby6s+6mrdha2nHy+DHK8/Po27MnQbJtxVW57bbb+Oabb0yeO3fuHCkpKSaXtxYvXszDDz/M999/z2OPPUZ6ejoTJkzg22+/Zfny5bzwwguUlJRw88038+6779aOdFdXV/PMM8+wZMkSiouL6dq1K2+88QYjR45skvdTUlKCl5cXP/74IzNm1FwmjY+PJyoqir179zJwYN2RREVR8Pf357HHHmP+/Pm1/fj4+LB48WLmzJlDXFwc0dHRHDx4kL59+wKwceNGJkyYQEZGBv7+/tx0003odDqWL19e2/cHH3zAm2++SVpaGiqViuPHj/Pwww9z6NAhVCoV4eHhfPbZZ7V9NgeZyCyuiUajYffevRSUV9Cz/wC5Q0u0SOklqayNX87K2CXE58eatFmoLJkQMYVpUbMYFXIDtpYtY9J9/w6D+e74lwAmgeembrfhYe/F1nO/UaEtx0JtiVqtpnvPXiTExnLgyFG0Wi3h4eHmKr3Vef/99zlz5gxdu3ZlwYIFAHh5eZGSklLn2MrKShYuXMjSpUspKytj+vTpTJs2DVdXV9avX09ycjIxMTEMGTKE2bNnA3D//fcTGxvL0qVL8ff3Z/Xq1YwbN46TJ09e9v/T+PHj2blz52VrDgoK4vTp05dsO3z4MDqdjjFjxtQ+FxkZSWBg4GVDz7lz58jOzjY5x8XFhQEDBrB3717mzJnD3r17cXV1NQknY8aMQa1Ws3//fqZNm0Z1dXWdBTTt7OzIyMggNTWV4OBg5s2bR69evfjkk0+wsLDg2LFjWDXzNisSesRVq6ysZNfuPZRUV9NnwEAcHB3NXZIQtXLLs/n5zCpWnP6RY9mH67SPCR3H9Og53BB2Iw7WLe97d0DA4NrPbSxtCXIJ4UxBHNvObWLfXbE8PXwBBqMBC3XNaIJKpSKySxesrK05euoUOp2O6Oimm3fUlri4uGBtbY29vT2+vr5XPFan0/HJJ58QFhYGwIwZM/juu+/IycnB0dGR6OhoRo0axbZt25g9ezZpaWksWrSItLQ0/P39AZg/fz4bN25k0aJFvPrqq5d8nS+//JKqqqrL1nGlkJCdnY21tXWdydc+Pj6XvQR64XkfH5/LnpOdnY33X0byLS0tcXd3rz1m7NixPPLII9x2222MGjWKs2fP8vbbbwM1d/UGBweTlpbG448/TmRkJIBZArqEHnFVysvL2bV7NxVGhb6DBsuWEqJFKKoqZH3iWlaeXsLejLp/JQ/pOIKYLnMZHz4ZV1s3M1RYfwHOgXjae5NfmcvkzjFMiZzBP1ZOI6s8kyUnv+HWnnfWBp6LhYWHY2Vlxcn4OHQ6Hd27d2+Vc1JaKnt7+9rAAzWhIDg4GMeL/ujz8fEhNzcXgJMnT2IwGIiIiDDpp7q6Gg8Pj8u+TocODVvryVzuvPNOkpKSmDhxIjqdDmdnZx566CFefPHF2jWlHn30Uf71r3/x3XffMWbMGGbOnGnyNW0OEnpEvZWVlbFz926qVWr6DhyIjY2NuUsS7ViFtpyNZ39mdexPbDn3W5323n79iImey6TO0/Fy8LlEDy2TSqVicMfhrEtYwZyutzCo4zB6+vblWPYh/rv7ZWZ1+Qd2Vpf+YyMwOBi1hZq406cxGo307NlTgk8j+esIi0qluuRzRqMRqPkD0cLCgsOHD9e5m9XxCqPjDbm85evri1arpbi42GS0Jycn57IjWReez8nJwc/Pz+Scnj171h5zIcxdoNfrKSwsrD1fpVLxxhtv8Oqrr5KdnY2XlxdbttSsWn5hFfEXX3yRm266iV9//ZUNGzbwwgsvsHTpUqZNm3bZ99vYJPSIeiktLWXn7t3oLCzp03+ALIomzEKj17AleSNr4paxIXEdBsVg0h7l1ZUZ0XOZHDmDAOdAM1XZcPf2e4gevr0Z2HEoKpWKZ4a/zMxl48mvzOO7419yV98HLntuQMdALCwsSDh5EkVR6NWrlwSfK7C2tsZgMPz9gVepV69eGAwGcnNzGTZsWL3Pa8jlrT59+mBlZcWWLVuIiYkBICEhgbS0NAYNGnTJc0JCQvD19WXLli21Iae0tJT9+/dz7733AjBo0CCKi4s5fPgwffr0AWDr1q0YjUYGDBhg0p+FhUXtaNWSJUsYNGiQyZ5xERERRERE8MgjjzB37lwWLVokoUe0LLWBx9KKPv0HNPvEM9G+6Qw6dqZtY3XsT/xyZhUavcakPdg1lJld5jE5cgad3CMu00vr0tOvLz39/jdpdGjQSAYGDGVfxi7e2fMq87rffsX5SH7+HVCpVMSfOAEgwecKgoOD2b9/PykpKTg6OuLu7t4o/UZERDBv3jxuueUW3n77bXr16kVeXh5btmyhe/fu3HjjjZc8ryGXt1xcXLjjjjt49NFHcXd3x9nZmQceeIBBgwaZTGKOjIzktddeY9q0aahUKh5++GFeeeUVwsPDCQkJ4bnnnsPf35+pU6cCEBUVxbhx47jzzjv59NNP0el03H///cyZM6d2vlJ+fj4rVqxg5MiRaDQaFi1aVHvbPEBVVRWPP/44M2bMICQkhIyMDA4ePFgbzpqLhB5xRRcuaUngEc3JqBjZl7GbNXE/sSZuOWXaUpN2P8cOxHSZy9TImUR7dWsXv9CfGvYSU5aMpqS6mK+PfsIDAx6/4vG+fjW/jOJPnEClUsmlrsuYP38+t956K9HR0VRVVXHu3Lm/P6meFi1axCuvvMJjjz1GZmYmnp6eDBw4kIkTJzbaa/zVu+++i1qtJiYmhurqasaOHcvHH39sckxCQgIlJSW1j5944gkqKiq46667KC4uZujQoWzcuNFkG6EffviB+++/n9GjR9f2v3DhQpN+v/nmG+bPn4+iKAwaNIjt27fTv39/oGYEqKCggFtuuYWcnBw8PT2ZPn06L730UpN9LS5F1ukRl1VRUcEfO3eiVVvQWy5piSamKArHsg+xJm45q+KWkl+ZZ9LubufB9Kg5TI2aSW+//u3yF/icZRP5I3UL9lYOHL03CWebv18xOOt8JgknThAVFkqPHj2aoUohWi4JPeKSqqqq2LFzJxVGhT4DZNKyaDpxeadYE7+claeXkFmWbtLmaO3IlMiZTIuazcCAoZe8a6k9OZZ9mPHfDQXgscHPMH/Is/U6LyM9jaTTp+kW2VluZxftmoQeUYdWq2XHrl2UaKrpM3CQ7JQuGt25oqQ/g86PJBWZ7vFjbWHDxIhpTIuaxfDg0VhbyAjjxW5dNYPfk37F2sKao/cm4253+dufL5aWkkJKQhy9unaVBQxFuyWhR5jQ6/Xs2r2bvLIy+gwYhL3s4CwayfmyDNbFr2BF7BJO554waVOhZlz4JKZHzWJ06PjL3pItakbGrlvcD4D7+j/GsyNeqfe5SYmJnE9Oon/vXrJlhWiXJPSIWkajkf3795OWm0fvAQNxcnY2d0milcuvzOPXhNWsiF3CofP76rSPCrmeaVFzGNdpIk428v1WX3ev+wfrElaiUqk5fm/yVa1DFH/6NAXnMxgyYMDfrkIsRFsjoUfUOnLkCIlpaXTt3RcPT09zlyNaqRJNMRvP/szK00vYmbatTvuAgCHERM9lQvgUPOzl++xanC08w7CvaiYl39nnfhZc91a9z1UUhRPHjlJVkM/woUMb7RZtIVoDCT0CqNmJ91hsHJE9etTe6ipEfVVqK9iUvJ5VsT/xe9Kvddq7+/RiRpebmNR5Or6O8v3VGB5afyfLTn8PwOF7EvF3Cqj3uUajkcMH9qGurmbk8OE4yGVs0U5I6BGkpaWx7/ARAsMjCP5zuXAh/k61vprtKZtYHbeM9WfWoDPqTNojPCKJib6JqZEzCXQNNk+RbVhacQoDvogC4OYe/+LNGz64qvN1Oh0H9+7BydKSEcOHyZIUol2Q0NPO5efns2P3blx9/Ynu1s3c5YgWTm/UsydtB6vjfmJdwkoqdRUm7R2dg5jR5SamRM6ks2eUmapsP574/QG+O/4lAPvvjLvqcFlZWcmhvXvwc3NlyODBtRtDCtFWSehpxyoqKtj2xx+o7B3o1bef/MATl2RUjBzK3MfquGWsiV9GsabIpN3LwYcZ0XOZEjmT7j6y3UFzOl+WQZ9Pa24/n9XlH7w/4Yur7qOosJAThw4QERREr169GrtEIVoUCT3tlF6vZ/uOHZRUa+k/eIhsLyFMKIrCydxjrIlbxsrYpeRWZJu0u9i6MS1yFlOjZtKvwyDUKgnM5vL81sf54vCHAOy84/g17T92PjODxJMn6dezR+2O2EK0RRJ62iFFUThw4AAp2Tn0HTQYB8fLb1wo2pczBfGsjVvOitgfSStJMWmzs7RncmQM06JmMyRwBJZq2bqvJciryKHnJ6EYFSOTO8fw2eTvr6mfhLg48jPSGD54sMmu2EK0JRJ62qEzZ85w5NRpuvTqjZdP/df3EG1TWnEKaxNqtoFIKIgzabNUWzIhfCrTo2czMvh6bCxlO5KW6JU/nuWjA28DsOXWA0R7X/38PEVROHLwAEplBdeNHIm9vX1jlymE2UnoaWdyc3PZsWcP/qGdCO3UydzlCDPJKc9iXcJKVp5ewvGcI3Xabwi7kenRs7k+dAL21nI7c0tXWFVAr0/C0BqquSHsRr6ZvuKa+tHpdOzfvQtPB3uGDxsm8/xEmyOhpx2prKxk6/btWDg60bNPX5lw2s4UVhXw65k1rIpdyr6MXXXahwWOYnr0HMaHT8bF1rX5CxQN8t/dr/D2nv8AsOHmXfT07XNN/ZSVlnJ43x4ig4Pp2bNnI1YohPlJ6GknjEYjO3ftIq+8ggFDhsrE5XaiXFvGxsRfWBW3hG3nNtVp7+M/gBnRc5kYMQ1PB28zVCgaS2l1Cb0+CaNSV8GIoNEsnfXLNfeVkZ5Gcmwsg/v1JSCg/oseCtHSyUzEdiI2NpbswkJ6DRgkgaeNq9JVsSV5I6vjlrHx7DqMitGkPdqrGzO73MSkzjF0cO5opipFY3O2ceHhQU/y6o7n+SN1Cwcy9tA/YPA19RXQMZDiwiIOHz2Gq6srjnKzg2gjZKSnHcjOzmbn3n0EdY4kMDjY3OWIJqAz6NiRuoXVccv4JWEV1YZqk/ZQt07M6DKPKZEzCHWTuVxtVaW2gt6fdqKkupiBAUNZPbfu6F59GQwGDuzZjbO1FSOHD8fCwqIRKxXCPCT0tHEajYbNW7di6eRMzz59zV2OaEQGo4F9GbtYE7eMNfHLKdeWmbT7OwUQEz2XaVGziPTsInO42onPD33AC9ueAGD5rA0MDRp5zX2Vl5VxaO9uokND6d69eyNVKIT5SOhpwxRFYc/evZwvLGLAUNlbpy1QFIUjWQdYE7+c1bE/UVCVb9LuYefJ9Og5TI2cSS+/fhJ02iGNXkO/zyLIr8yjp29f1v9jR4O+D9JTU0mJj2P44EH4yBIXopWT0NOGJSUlcfD4Cbr17YeHp6e5yxHXSFEU4vJOsTp+GStPLyGrPNOk3cnamalRM5kaOYsBAUOwUMtliPbum2Nf8O9NDwLwfcxqRoeOa1B/Rw8dxFhRzpjrrsPGRtZqEq2XhJ42qrS0lC3bt+PeoSOdo2Tjx9Youegsa+KWsyL2B84VJZm02VjYMqnzdKZGzWJ40HVYWcjkdPE/WoOWgZ9Hk1WeSZRnV7bcdqBBoz3V1dUc2L2TQC8vBgwY0IiVCtG8JPS0QUajkT927KC4WsuAIUNlgbFWJLM0nXXxK1ge+yNxeadM2tQqNePDJzMtajbXhYzFzsrOTFWK1uCnU9/x8Ia7APhyyhJujJjaoP5ys7OJO3aUQX37EBgY2AgVCtH8JPS0QQkJCRyNjaX3wME4u7iYuxzxN/IqcvglYTUrY5dwOOtAnfbrQm5gevQcxnaaiKO1kxkqFK2R3qhn6JfdSS05R5hbBH/880iDL32eOn6cyoJ8rh99HXZ2ErpF6yOhp40pLS1l07Zt+ASF0Cni6ndbFs2jRFPM+sS1rIpdyq607XXaBwUMY3r0HG6MmIqbnXvzFyjahDVxy7j3l1sB+OjGRUyPntOg/nQ6Hft27qCjpwcDBw5sjBKFaFYSetoQo9HIjp07Ka7W0n/wELms1cJUaiv4PelXVsYuZXPyhjrtPX37EBM9l0mdp+Pj6GeGCkVbY1SMjPi6N2cLE+joHMSeO09hqW7YmrR5OTnEHj3C4H596dhRFrcUrYusyNyGJCcnk11YRK8BAyXwtBDV+mq2nfudVXE/sSFxLXqj3qQ90jOamOi5TImcSUeXIDNVKdoqtUrNU8Ne4o61c0gvTWX56R+Y2+3WBvXp5eODm48vx0+exNvbW+7mEq2KjPS0EZWVlWzasgVXvw50jo42dzntmt6oZ1fqdtbEL2Nd/Eqq9JUm7YEuwczsMo/JkTOI8Ig0U5WivVAUhTHfDCA27yS+jn7suzMOG8uGBRWtVsu+nTsI8/ejT59r29hUCHOQkZ424vjx4+jUFnTq3NncpbRLRsXIgcw9rIlbzpr4ZZRoik3avR18mRE9l6lRs+jq3UMWDRTNRqVS8fTwl/nHyqlkl2ex5ORibut1d4P6tLa2JqxzZ5JPnyYwMBAvL69GqlaIpiUjPW3A+fPn2bX/AFE9e+ElK6Y2G0VROJ5zhLVxy1kZt5S8ihyTdldbN6ZFzWZa1Cz6+A9ArZJLjsI8FEXhxh9GcDTrIB52nhy8+0yjLHlwaP9ebAxGRl83Si6pi1ZBQk8rp9fr2bxlC9g7yN5azSQhP441f66OnF6aatLmYOXA5MgZTI2cxeDA4Q2eNCpEY9md9gczfqpZmfnFUW9wd98HG9xnRXk5B3fvpE/XroSHhze4PyGamoSeVi4uLo7jCQn0Hzoce3t7c5fTZqUWn2NN/HJWnv6RxMIEkzYrtRU3RkxjWtQsRoZcj7WF7HEmWqbpS25gb8ZOnG1cOHLPWRysHRvcZ0JcHMXnM7hhzBhZu0e0eBJ6WrGKigp+37IF76AQwuSvrEaXXX6edfErWRH7IydzjtVpHxs2kenRsxkTOh57a4fmL1CIq3Qwcy+Tf7wOgKeGLeDBgY83uE+9Xs/enX8Q7O1Nv379GtyfEE1JQk8rduDAAdLy8hk0fAQWFrLJZGMoqMzn1zNrWBW3lP0Zu+u0Dwu6jhnRcxkXPglnG1ntWrQ+c5dPZnvKJuys7Dl6TxIutq4N7vN8ZgZJp05x3fBheHh4NLxIIZqIhJ5WKj8/n607dxHerRt+/h3MXU6rVlZdyobEn1kVt5Q/UjbXae/nP4iYLnO5MWIqnvZyl4po3Y5nH2Hcd0MAeHTQ0zw+9LkG96koCgf27sbFyooRw4fL3YmixZLQ0wopisL2P/6gzGCg/6Ah5i6nVarSVbE5eT2rY5ex8ezPKJj+M+jq3YOY6LlMjozB3ynATFUK0TRuXz2LjWd/xkptxdF7k/Gw92xwn0WFhZw4sJ8h/fsRECD/ZkTLJLeWtEKZmZnkFhbRY4DsfXM1tAYtO1K2sCruJ349swatodqkPcwtnBld5jElcgYhbmFmqlKIpvfk0BfYePZndEYdHx94l+dG/qfBfbq5u+Pi7c3p2Fj8/PzkkrtokWSkp5UxGo1s2rwZxd6Bnr1lJdS/YzAa2Ju+k9VxP7E2YQUV2nKT9g5OHZnR5SamRs4k0quLmaoUovnd+/OtrIlfhgoVx+5NxtvRt8F9VlZUcGDXDvp1705YmPzhIFoeGelpZVJSUiiqqKRfz97mLqXFUhSFw+f3syZ+OavjfqKwqsCk3dPem5joOUyNnEkP3z4y/0C0S/OHPMua+GUoKCzc/xavjH67wX3aOzjg7R9AXEICgYGBWFlZNUKlQjQeGelpRfR6Pb9t2oStmwddunc3dzktiqIonM49wdr45ayIXUJ2+XmTdmcbF6ZGzmRq1GwGBAyW1ZGFAB7ecBc/nfoOgEN3n6GDc8N3TddoNOzf+Qc9IyPpLNviiBZGQk8rkpiYyJHTp+k/bIQsAvanpMJE1sQtY0Xsj6QUJ5u02VraMqlzDNOiZjM0cCRWFvJXpxAXSy9Jpf/nNZvezuv+T/479qNG6TchLo6SrPOMu+F6rK1lsU7RckjoaSX0ej0bf/8dRy8fIru077kn6SWprItfwcrYJcTlnzZps1BZMD58CtOiZnFd6FhsLW3NVKUQrcO/f3+Qb45/AcC+O2MJcg1pcJ9arZZ9f2ynW0Q4UVFRDe5PiMYioaeVuDDKM2D4SGxt298v8ryKHNYlrGRl7FKOZh2s0z4mdBzTomYzttPERllaX4j2Iqssk96fdgJgZpd5LJzwZaP0m5iQQGFGOuPH3iCjPaLFkNDTClwY5XHw9Caqa1dzl9NsijVFrD+zlpWxS9iTvqNO++COw4mJnsv48Mm42bmboUIh2oYXtj7B54c/AGDHP48R7tHwuTharZa927fRI7IzkZGRDe5PiMYgoacVSEpK4uCJEwwYPrLNz+Wp0Jbz29lfWB33E5uTN9Zp7+XXjxnRc5kYMa1RbrEVQkB+RS49PwnFoBiY1Hk6n0/+oVH6vTC3Z/zYG+ROLtEiyC3rLZzRaOTM2bN4+vq32cCj0WvYmvwbq+OWsSFxLQbFYNIe5dnlz9WRZ9DRJchMVQrRdnk6ePN//R/lg/1v8XPCKmJzTxLt3a3B/QaFhLAvPZWUlBTCZVNk0QLISE8Ll5aWxp5Dh+k3dBgOjm1nrorOoGNn2jbWxC3j54RVaPRVJu1BriHMjJ7HlKiZdHKPMFOVQrQfRVWF9PokjGqDhuvDJvDt9JWN0m/syZNoigoYd8MNqNWyVIQwLxnpacEUReHM2bO4enm1icBjVIzsz9jDmrifWBO/nNLqEpN2X0d/ZkTPZUrkTLp4d5dFA4VoRm527jw48HHe2v0ym5LWcyzrED39+ja43+DQUPbvzCA9PZ2gIBmpFeYlIz0tWE5ODtt376F7/wG4ubfOibqKonA8+zBr4pezMnYp+ZW5Ju1utu5M/3N15D7+AyToCGFGZdWl9P60E+XaMoYFXceyWb82Sr/HDh/CUqdl9KhR8m9cmJWM9LRgZ5OSsHNxbpWBJz7v9J9B50cyStNN2hysHWtWR46cxaCOw7BQy8aEQrQETjbOPDzwSV7Z8Sw7U7eyL2MXAwOGNrjfoJBQTh7cT15eHt7e3o1QqRDXRkZ6WqjS0lJ+37qVsK7d8PPvYO5y6iWlKLk26JwtPGPSZm1hzY0R05geNZvhwaOxtpB1O4RoiSq1FfT9LIIiTSH9Ogxi7dwtjTI6s3/PLrwdHBg0aFAjVCnEtZGRnhbq3LlzKFZW+Pj6mbuUK8oqy2Ttn6sjn8o9btKmQsW4TpOYFj2L0aHjsbeyN1OVQoj6srd24NHBT/Pc1vkczNzLztRtDA++rsH9dgwKJvn0KcrLy3FsA3MUReskIz0tkE6nY/3GjXgGBhPWAm/zzK/M49eE1ayMXcrB83vrtI8IHsP0qDmMD5+Ek42zGSoUQjSERq+h/2edyavMpbtPbzbevKvBoz1Go5Fd27YSHRJM13a0yKpoWWSkpwVKT0+nSq+nQ8eG73jcWEqrS9iY+DMrY5ewI3VrnfYBAUOYHjWHGyOm4mHvaYYKhRCNxdbSlvlDnuPJTQ9wIucIW5I3MiZsfIP6VKvV+AV0JDkllaioKCwsZC6faH4y0tMCbdm2DZ2VNT179zFrHZW6SjYnrWdV3E/8dvaXOu3dfXoREz2XSZ2n4+fUOuYdCSHqR2vQMuiLLpwvyyDKsyubb9uPWtWwdXYqKyvZv+MPhvTtQ2BgYCNVKkT9yUhPC1NYWEhBcQnRZgo8WoOW7ec2sTpuGb8mrkFn0Jq0h7t3ZkaXeUyJnNEouzELIVomawtrnhz6Ag9tuJO4/FOsP7OWiZ2nNahPe3t7XDw8SElNldAjzEJGelqYo0ePkpyVzeARI5ttPQuD0cDutD9YE7+MdfErqNBVmLR3dA4ipstcpkbOpLNndLPUJIQwP71Rz9CvepBanEyoWzg7/nm0wUtM5GRlcebEccaNGY2Tk1MjVSpE/chITwui1+tJy8jELyi4yQOPUTFy+Px+VsctY3XcTxRrikzavRx8iImaw9SoWXT36SULignRDlmqLXlq2Ivc8/MtJBclsiZ+GTHRcxvUp5ePDwmWlqSlpdGlS5dGqlSI+pGRnhYkPT2dXQcPMXBE0+ymrigKp3KPsyZuGStjl5JTkWXS7mLjytSoWUyNmkn/DoMbfP1eCNH6GRUjI7/uQ2JhPB2dg9j9r5NYWTRsx/SE2Fgq8nNlPy7R7GSkpwVJTUvD2d2tXoEnuegsQS4h9RpqTixIYG38clbE/khq8TmTNjtLeyZHxjA1chZDg0ZiqZZvCSHE/6hVap4evoDb18wivTSV5ad/4KbutzWoT/+AAI6kpZKXl4ePj0/jFCpEPchvuBaiqqqK7Lw8QqKvPNyr0Wt4b+9rfLj/bW7teRf/GfPOJY9LL0mtCTqnfyShIM6kzUJlyYSIKUyPms2okBuwsbRptPchhGh7xnaaSFfvHpzKPc6buxcQEz23QT83nJydsXZwID09XUKPaFYSelqIzMxM9HDFFZgPZe7jwfX/4lxxEgC9/fuZtOeWZ7MuYSUrY5dwLPtwnfPHhI4nJnoO14dNwMFaVkQVQtSPSqXi6eEvc9OKyeSUZ/HjiUXc3vueBvXp69+BzJRkeur1WFrKryLRPGROTwuxdft2tJZWl1ybp1JbwWs7X+CrIx+jUqkxKgbc7Tw4em8yFdpyfj2zhlWxS9mbsbPOuUMDRxITPZdx4ZNwtXVrjrcihGiDFEVh0o+jOHx+P+52nhy8O6FBW8tUVVWx/4/tDBvQnw4dZJ0v0TwkXrcAFRUVFBYXE96tR522nanbeHjDXWSXn0dBQVEMqFVqwtzCuX31TLae+73OOX38BxATNYeJnafh5SBDx0KIhrsw2hOz9AYKq/L59tjn3NPv4Wvuz87ODnsXZzIyMiT0iGYjoacFOH/+PAZUeHp71z5Xoilmwfan+PHkYtQqNUbFWNtmVIwcPL/PpI9or27MiJ7LpMgYApxl0S8hROMb3HEYQzqOYHf6H7yz5zX+0eMOHK2vfa0dH19/ziclotPpsLJq2B1hQtSH3CtoRkadjuylS8n/8EO8Y2NRGWuCze9nf2XoV91Zeuq7muMuCjwXC3IJ4fEhz7PrjhNsue0A9/Z/RAKPEKJJPTX8JQDKtKV8efjjBvXl7etLtd5Abm5uY5QmxN+SOT1mkrFwIS7PP49TSUntc6UuLiye24eHfLeiRo2RS4cdABUqfBz9eHbEK0yLmi1r6gghms28FVPYeu537CztOHpvMi62rtfc1/49u/B3caFfv35/f7AQDSS/Kc0gY+FCOjz0EI4XBR4Ap5ISHvh0Kw/Edrhi4AFQUMguP8/9v/6TMYsHkF8hfykJIZrHk8NeBKBKX8VnhxY2qC8vb1/OZ+dgNF75Z54QjUFCTzMz6nS4PP88AH/d2OHC45c2lmBx0b9/C5Ullmor1KpLL0SYVZ6JvdyCLoRoJt19ejE+fDIAH+z/LwWV+dfcl7ePDxqdjvz8a+9DiPqSiczNLHflSnz/MsJzMRXgVlrObVlh7Olhi4+jP94OPng5eONp74WnvQ+e9l61jz3svWQVZSFEs3ty6AtsSFyH3qjjowPv8PzIV6+pH0cnJyxtbcnJycH7ops5hGgK8tuymWlTU+t13Pygf+J6+6NNXI0QQlybzp7RTIuazeq4n/j04Hvc3fcBfBwvv7jqlXh4eXM+K4tu3bo1cpVCmJLLW83MOiioXsepO3Zs4kqEEKJh5g95FqiZY7hw31vX3I+nlxelFZWUlZU1VmlCXJKEnmbmHRNDmYsLl7tlTgFKXV1xnDK1GasSQoirF+rWibndbgXg66OfkFGadk39uHl4YFBBXl5eY5YnRB0SepqZ2sqKkgULAOoEnwuPzz/7HGpZqEsI0Qo8Muip2s/f2/v6NfVhYWGBk6ubrNcjmpyEHjMIePBBTr/0EmXOzibPl7m6kvDft3G99//MVJkQQlydji5B3NbzbgB+OLGIc0VJ19SPu4cnOXn5cuu6aFKyOKGZHDhwgJySEjpnZWNMT0fdsSOOU6bKCI8QotXJLj9Pr0/CAIiJnsuHN3591X2UlpRwbN9exowYjru7e2OXKAQgIz1moSgKOXn5uHv74jxjJq6PPIrzjJkSeIQQrZKvoz93930IgJWxS0jIj7vqPpycncHCQtbrEU1KQo8ZlJWVUaXV4iZ/zQgh2oj7BzxWu2bYW7tfvurzVSoVTq6uEnpEk5LQYwYFBQUYVeDi6mruUoQQolF42nvxf/1r1hb79cxqTueeuOo+XN3cySsolHk9oslI6DGDgoIC7J2csLC49LYSQgjRGt3b72FsLW0BeH3ni1d9vqubG9V6PaWlpY1cmRA1JPSYQX5hIS6ucmlLCNG2uNq68cCAJwDYnLyBo1kHr+p8F1dXjCooKipqivKEkNDT3DQaDeWVlbjKpS0hRBt0Z5/7cLR2AuC1HS9c1blqtRp7JycKCwubojQhJPQ0t+LiYvRGBRc3N3OXIoQQjc7JxplHBv0bgJ1p29ibvuuqzndxcaNAQo9oIhJ6mllxcTGWNtbY2tqauxQhhGgSt/W6Bzfbmkv4r+54jqtZDs7Z1YXSigq0Wm1TlSfaMQk9zayoqAgHJ+e/P1AIIVopeyt7HhvyDACHzu9jR+rWep/r4uKKwahQUlLSVOWJdkxCTzMrLC7GydnF3GUIIUST+kf3O/B28AHgP1cx2mNnbw8WFhJ6RJOQ0NOMNBoNVdXVODvLSI8Qom2zsbTh8SHPA3Ay5yibktbX6zyVSoW9k6Pcti6ahISeZlRaWorBqOAooUcI0Q7M7nozHZw6AvDqjucxKvVbdNDR0ZnCouImrEy0VxJ6mlFpaSkqCwvs7OzMXYoQQjQ5Kwsrnhz2IgAJBbH8emZ1vc5zdHaitLxMVmYWjU5CTzMqKyvD1tEBlUpl7lKEEKJZTI+aTYhrzQ7sr+54AYPR8LfnODo6oTcqlJeXN3V5op2R0NOMSsrKsLd3NHcZQgjRbCzUFjw1/CUAUoqTWBX309+e4+jkhEFRKCsra+ryRDsjoacZlZaW4eAooUcI0b7cGDGNCI8oAN7c9RI6g+6Kx1tZWWFpbSUjPaLRSehpJhqNBq1eh4ODg7lLEUKIZqVWqXl6+AIAMkrTWHb6+789x9benoqKiqYuTbQzEnqaSUVFBQajIiM9Qoh26YawG+nm3ROAt3YtoFpffcXj7e0dKZHLW6KRSehpJhUVFRhRahbeEkKIdkalUvH08JcByKnI5ocTX1/xeHsHB8rLZaRHNC4JPc2ksrISKxsb1Gr5kgsh2qcRwaPp6z8QgP/u+Q+VusrLHmtnb0e1TotOd+X5P0JcDfkN3EwqKyuxkfV5hBDt2MWjPUVVBXxz9LPLHmtnZ49RqfnZKURjkdDTTCoqK7G1lUtbQoj2bVDHoQwNHAnAO3tfo1x76Xk7tnZ2GBWFqqqqZqxOtHUSeppJRWUltjLSI4QQPDWsZt2ecm0ZXxz+6JLH2NjYgFoloUc0Kgk9zUBRFCqrqrC1tTV3KUIIYXa9/fszOnQcAAv3vUGxpuiSx1nb2kroEY1KQk8z0Gq1GBWl5i8XIYQQ/HvoiwBo9Bo+Pfj+JY+xsrZGo9E0Y1WirZPQ0ww0Gg1GBWxkpEcIIQDo6tODGyOmAfDRgbfJr8yrc4y1ja2EHtGoJPQ0A61Wi6IoWMtIjxBC1Hpi6PMA6I16Ptz/dp12G2sbqjRXXsRQiKshoacZVFdXY0TB2tra3KUIIUSLEeERSUz0XAA+O/Q+OeVZJu3WNjZoqiX0iMYjoacZaLVa1GoLLCwszF2KEEK0KI8Nfqb28/f3vWnSZmVtRbW2GkVRmrss0UZJ6GkGWq0WS2src5chhBAtTohbGDd1uw2ARUc/Jb0ktbbNysoKo6Kg1+vNVJ1oayT0NAOdToeFpYQeIYS4lEcGP1X7+Xt7X6/93NLSCkVBtqIQjUZCTzPQ6XRYWlmauwwhhGiRApwDub3XPQD8eHIx54qSgJqRHgUJPaLxSOhpBjqdDgsLCT1CCHE5Dw18ovbz/+5+Bfgz9MjlLdGIJPQ0A51eL6FHCCGuwMfRj3v6PgzAqrilJOTHobawQAEJPaLRSOhpBnqDQe7cEkKIv3HfgEexVNfMf3xz10tYWlqiAAaDwbyFiTZDQk8zMOgl9AghxN/xtPfi/gGPAbA+cS2xeScARUKPaDQSepqB0WhApZYvtWhhjDqs01bgsGoILkvDcVg1BOu0FWCUSaOicVkV7EZdnVuvY+/p+xB2lnYAvLXjJZwPHaL0s8/IXroUo0xoFg2kUmTVpya38fffcfDyIbxzZ3OXIgQA6qrzuPwyGBurHDAAFtT+t1rnQ8nEPRjt/M1cpWj1FAWH+FdwSniVKr/JlHV7E1RWWBfuQeN7I1jYXfK09/a+QeXnX7BgYwmupeW1z5e5uFCyYAEBDz7YXO9AtDEyu7YZKIqCWkZ6REth1OHyy2Cs1Tk1jy9cef3zv9bqHFx+GUxRTCKoZX0p0QAqFSpFj4Iau6x12GWtw2DtiVpbAD3eR+tzA9YFezHaeKL1HlN72rzDNnRdllmnO8eSEhwfeogMkOAjromM9DSDXzdsxK1DAKGdOpm7FCGwTluB+5Gb//a4wt7fow2MaYaKRJumGFBXZuJy7F5s8rbWaTaqbTHYB1IR8Tg6l27Ynf0SZdJyHEtKUF2qO6DM1RXH3FzUVhLKxdWRkZ5mILlStCRWh96t+c1xpbn1BrDZ+zzuR/5Befjj6Nz7Y527Gftzn1M8YBkAjvH/QVHbUBExH4zVuB38BxVhD6L1HIZ1/k4ckhZS1O97UNvgcOa/qIzVlEfW7LPkun8WlSF3ofUeg1XhARwT36K491coVs7YJ32AujqP8ugFNcce/AdVAXOp9rsRy5LjOMW/QnHPj1FsvLA/9zkWFUmUdX0DAJfD/6LadzyaDjFYlMXjHPscJd3fxWgXgF3qt1gVH6G0x3sAOB+7D63HEDQdb8Ki4hzOp56gtMvrGBzDsM1Yik3edkp6fVpz7IlH0bl0oyrodtSaLFyOP0hZ1EvonaOxOb8G26x1lPT5GgCnU09hsA+iMvQeVNoCXI/eQ1nnp9G79sImewN2ad9R3P/Hmq9h3IsYrdyo7PQQKn0Frodvo7zTo+g8BmGduxWHc59Q1P8nUKlxSHgNVBZURDwBRj1uB+dSEXo/Wq8RWBXsxvHsexT1/RYs7HBIfAeVvpzyqJpdzF0PzKEy6Ha0PmOxKjqM45nXKe79BYqVK/bJH2NRdZ6yLjVr47gcuhVNhxiq/SZjWXISp/gFlPT4EKOtD3YpX2JZFk9Zt//WHHvkLqq9r0cTMBOL8kScTz9NSbe3MdoHYpf2PVaF+ynt+UHN913xMRSVNSpFa/KtpjZqUJefwfXInQBkHfXHr6Tkst+aKsC5uJjslSvxnTPnit/rQvyVhB4h2hlLbS7Y/s1BFmBRmQs2YJO1FsvSU1iWn0GFgt25L0GlxrLkBAB2KV+DYgTAJvtXLMoTsahI/l+b2garkmOojNU1jwEVCjbZG7CoTMOiMq3m2NRvUCwdsCo6jNpQ8b9jjdXY5P6OujoHddX5mmPTvkexcsGq8ABqfUntsWp9Cda5W1HpSmonztqlL8Fo7YFV0QEstAW1x1pU52KT9wcqgwaVtggA24xlGG19sCo+gvriY6vSUemKQVFQ6cpq3mvmSqwK92FZchK1vqz2WMuKs6g1mdiprcFQVdPv+dUYio9iWRaHStHVHmtVehpFZYWS8nXtBHKbrJ+xLIvDsjzxz6/hV6CywKrkBCiGP7/eyv++3hVJWFSc+/PYRWBhi1XxUVRGzf++hooBm5zfsKjKxKIq/c+v97colo5YFR5EbSj/39fQUIlNzmbU1fmoNTW7ntum/4Bi5Yp14X7UuuL/HasrwjpvKyp9Gerq/D+/3ksx2nhiVXQIC23eRccWoqj+/leOrqh+UwG0qal/f5AQfyGhR4h2Rm/tDYaMvx3p0TlEUN3zn2g9R2JwDMOiPBHr/B1UBd0GKgusczeDYkTrcwMoCnapX6P1GIrBqTMWFeewzttKVcd/gIUN1nnbUekrqPa7EQC7lMXo3Puhd+6CujIdm9zf0QTMqQk9+btQawuo9p8CgG3a9+idu6F37YFak4VN9no0/jEo1q5YFe5DXZVJdYeay3C26UvRO4ajd+uDqjoP26x1aPymoNh4Yll0CMuKJDQBs2uOzVyBwS4AnftAVNpibM+vpNr3Roy2vlgWH8OyNBZN4E0A2Jxfg9HaE53nUFT6cmwzfqLaZyxGuwAsS05hVXyYqqBba47N+hXF0hGt1wgwaLBL/wGt12gMDsFYlMVjXbCbquA7ALDO+Q1Ulmi9R4NRj13aN2g9R2Bw7IRFeRLW+dupCrwV1JZY524Bow6t77g/v4ZfofUYgsEpEouKVKzzNlPVcR5Y2GKd9wcqfRnVfhNrjk39Fp1rL/Qu3VBXZWCT8xuaDrNQrJz+/HrnU+0/9c+v94/onaPQu/ZCrcnGJvtXNP7TUazdsCrcj0VlGpqAmTXHZvyEwSEUnVs/VNoCbM+vQeM3GcXGC8uiw1iWn0HTcS4ATsfuxyHlq0t+uylYoHPvj86lB1buP9fr+9g6KKhexwlxMZnT0wzWb9yIi18HwsLDzV2KEDKnRzQr69yt2Cd/jE32elTU/LpRUKFz64/WayRWRQfRO4ZT9udlR2N1BU4hYTKnRzQJGelpBiqVSub1iBZDGzCF6v0+WKtzUF1itEcxgNbogzZgSvMXJ9oc69zfsc3+Fb19KJqAmRhs/bA9v5qSvosw2vrVOV5t48C+B29hzMsfoIBJ8LnwU7T0pZdwlsAjroGEnmagVqsxGo3mLkOIGmorSibuqVmnx6LuOj1aY806Pajlx4NoIEVB02EGKoMGrecIqjtMA6Aq9O4rnKLwmN9ORs7qUHedHldXSl96SW5XF9dMfqo1Awu1GkVCj2hBjHb+FMUkYp2xDqtD72KpyUFv7YOu9yM1IzwSeERjUKnQu/WlzK1vvU/5PelXTuYe42Q0BN6/kKj15wmxtMS9Sxe8Y2JkhEc0iPxkawYWlpayd4xoedRWaANjZN6OaDGMipFXd9TcZh/gHMiMbjezN28bLgP649uhg5mrE22BLBPcDCwtLCT0CCHE3/glYRVnCuIAeHLoi6hRowLZsFk0Ggk9zcDK0hKDQW/uMoQQosXSG/W8tvMFAELcOjEtahZ6vV5Cj2hUEnqagZWVlYz0CCHEFayK/YmU4ppFLZ8e9hIWagsMej0qlQpLS5mJIRqHhJ5mYGlpiUEvIz1CCHEpOoOON3a9CECkZxcmREyteV5Xs0q1lUxeFo1EQk8zsLKyQv/nP14hhBCmlp76lvNlGQA8PXwBalXNrya9TodaJaFHNB4JPc3A2tpaRnqEEOISNHoN/939MgDdfXozJnR8bZtOr0OFhB7ReCT0NANra2v0Oq2syiyEEH/xw4mvya3IAWpGeVSq/63BrNPqsLK0Qq2WX1Wicch3UjOwtrZGhar2+rQQQgio1FXy9u7/ANCvwyCGB11n0q7VarGxsTZHaaKNktDTDKytrVGrQFtdbe5ShBCixVh89FOKNIUAPDXMdJQHan5m2tnamqM00UZJ6GkGtra2qFCh0WjMXYoQQrQIZdWlvLv3dQCGBY5iUMehdY6prtZga2PT3KWJNkxCTzOwsbFBpar5ByyEEAK+OPwR5doyAJ4a/tIlj9FptdjZ2TVnWaKNk9DTDCwsLLCxsqZaI5e3hBCiqKqQhfveBGBM6Hh6+fW75HFajQZbubwlGpGEnmbiYG+PpqrK3GUIIYTZfXrofaoNNSPf/x724iWPMRgMGPR6GekRjUpCTzNxsLdDo5HQI4Ro3/Ircvlo/9sATIyYThfv7pc8TlNVhRok9IhGJaGnmTg4OFAtIz1CiHbuw/1vY1Bq9iJ8fOhzlz2uqrIStUqFvb19c5Um2gEJPc3E3t4erUxkFkK0Y1llmXx2eCEAM6JvIsIj8rLHVlVVYWWhljk9olFJ6Gkm9vb2KAaj3LYuhGi33v9z8jLAY4OfueKxlRUVONjb11m7R4iGkNDTTBwdHVGrVFRWVJi7FCGEaHbpJal8c+xzAOZ1/yfBbqFXPL6ysgInR8fmKE20IxJ6mom9vT2WahWVlRJ6hBDtzzt7Xqv9/JFB//7b46sqKnBycmrKkkQ7JKGnmajVapwcHKgoKzd3KUII0aySi86y9NQ3ANzR+//o4NzxiscbjUa0miocHByaozzRjkjoaUbOTk5UVEjoEUK0L//d/QoAKlQ8OODxvz2+sqIClYKM9IhGJ6GnGTk7O1MloUcI0Y4k5MeyOu4nAO7p9zDejr5/e055eRkWapWEHtHoJPQ0I2dnZ7SaanQ6nblLEUKIZvHGrpp9tazUVtzX/9F6nVNeVo69rS3W1tZNWZpohyT0NCMnJycsVCrKy8rMXYoQQjS5EzlH2ZC4DoD7B8zHw96zXueVl5Xi5uLSlKWJdkpCTzNydHTE2kJNWWmpuUsRQogm9/rOFwGws7Tn7r4P1vu88rJSXCT0iCYgoacZqdVqXFxcKC0pMXcpQgjRpA5l7mPbud8BeGjQk7jYutbrPJ1Oh05TLaFHNAkJPc3M3dWV8jIZ6RFCtG2v7XwBAGcbF/7V+//qfV5JcTGWKhWurq5NVJlozyT0NDM3Nzc0FeUYDAZzlyKEEE1id9of7EnfAcAjg57Cwbr+KyuXlpRgY2UlG42KJiGhp5m5urqiRiWXuIQQbZKiKLy643kA3O08ubXnXVd1fmlJMZ7ubrLnlmgSEnqamZOTEzaWlpQUF5u7FCGEaHTbUjZxJOsAAI8PeRY7K7urOr+spBh3d/emKE0ICT3NTaVS4eHuRnFRoblLEUKIRnXxKI+vox9zu912VedXVlZi1Opwc3NrguqEkNBjFp4eHpSVFJu7DCGEaFS/nf2F07nHAXhi6AvYWNpc1fnFRYVYqFUy0iOajIQeM/Dw8MCo1VFRLltSCCHaBqNirB3l6egcxMwu8666j6KCQtycXbCysmrs8oQAJPSYhZubG1YWagoLC8xdihBCNIqfE1aSWBgPwJPDXsBSbXnVfZQUFeLtVb9Vm4W4FhJ6zMDS0hIPNzeKCmRejxCi9dMb9bz25+rLoW7hTI2cddV9aDQatFVVeHh4NHJ1QvyPhB4z8fbyoqRIRnqEEK3fqtilpBYnA/DUsJewUFtcdR9FhQVYqlUSekSTuvrxR9EoPD09MZ48Rd7332OVl4u6Y0ccp0xFLdeyhRCtiNagrd1JPcqzKxMiplxTPwV5+bi7umJjc3WTn4W4GhJ6zKTqhx8Y/8ILOF+0+WiZiwuZzz2P6731X7JdCCHMaenJbzlflgHA08MXoFZd2wWE4sJ8okNCGrM0IeqQ0GMGGQsX0vGRR+o871hSQuf5j5EAEnyEEC2eRq/hv7tfBqCHbx9Gh467pn7Ky8owVGvx8vJqzPKEqEPm9DQzo06Hy/M1t3X+dZH1C4/9X3kZo07XrHUJIcTV+u74l+RV5gLwzPCXr3nriPy8PGytLGU+j2hyMtLTzHJXrsT3CvtuqQDn4mKWvnc/xdf3w8vBG097LzztvfFy8MbBylH2pBFCmF2ltoJ39rwKwICAIQwNHHnNfeXn5eDr7Y1aLX+Hi6YloaeZaVNT63Vc8qntvMG3dZ63UlvjbueBp4MXfo7+eDn44OXgw5NDX7jma+lCCHG1vj76CcWaIqDmjq1r/WNMp9NRXlxMV5nPI5qBhJ5mZh0UVK/jUhyqL/m8zqglpyKLnIosTueeqH3+H93/SUeX+vUthBANUVpdwnt73wBgeNBoBgQMuea+8vNysVSp8PX1bazyhLgsGRpoZt4xMZS5uKBcpl0BipwdWRGUc8V+Lozq9OswiPX/2CGBRwjRbL449CEVupptdJ4a/lKD+srNycHTzQ1bW9vGKE2IK5LQ08zUVlaULFgAUCf4XHj81eyeGNSgqjPVuYal2hKjYmRk8PV8Nuk7evn1a7qChRDiIkVVhXyw/78A3BB2Iz19+1xzX0ajkZL8fDr4+zdWeUJckYQeMwh48EEy33+fchcXk+fLXF1J+O/bzHv3dz66cRFONs5YqOqubKo36gHYnrKJ3p92YsqPo/n22JcUVOY3S/1CiPbrk4PvUW3QAPDvYS82qK/83FxURiN+fn6NUJkQf0+lKMrlrrSIJmbU6chduZLShATOaqoJ+7/7cLnols38ilye2fIo6xJWokKFctHYkJutB0WauttYjAgew/SoOYwPn4STjXOzvA8hRPuQX5FLz09CMSgGJnWezueTf2hQfyeOHsVCq2H0qFGNVKEQVyahpwUwGo2s37gRZ19/IiIj67T/dvYXHtt4L8WaIgyKAbVKTW+//nw2+Tt+TljFitM/cir3uMk5KlSM6zSJadGzGB06Hnsr++Z6O0KINuqFrU/w+eEPANjxz2OEe3S+5r4MBgO7tm6hV1QkERERjVWiEFckoaeFOHHiBIkZmQwZeem/eEo0xby47d8sPfVN7XObbtlHV58eAKQUJbM2YQUrTv/A2cIzJudaW9hwY8RUpkXNYkTwGKwtrJvujQgh2qSsskx6f9oJgJld5rFwwpcN6i8nK4vEk8cZf/31ODg4NEaJQvwtCT0tREFBAVt27KRbv/64ubtf9ridqdt4eMNdnC/L4KZut/H2uE/qHBOfd5o18ctZGbuEjNI0kzYHa0emdJ7B1KhZDO44/Jp2QxZCtD///v1Bvjn+BQD77owlyLVh6+ocO3wIW6OBkSNGNEZ5QtSLhJ4WQlEUft+0CSsXN6K7dbvisZXaCt7f9wZTo2YR5dX1in0ezz78ZwBaSv6fy8Vf4GbrzrSo2UyLmkUf/wGy0rMQ4pLSilMY8EUUAP/ocQdv3fBhg/rT6XTs2baFft27Exoa2hglClEvEnpakLi4OE4mnmXodaMbfTl2o2Jkf8Ye1sYtY3X8MkqrTbfC8HX0Z0b0XKZEzqSLd3cJQEKIWg+vv4ufTn8HwOF7EvF3CmhQf+lpqaQlxDNx3DhsbGwao0Qh6kVCTwtSXl7Oxs2b6dStO75+Tbduhd6oZ2fqNtbELWNdwko0+iqT9mDXUGZE38SUqJl0cpcJhkK0Z0mFiQz9qjsA/+p9Hy+P/m+D+9y/Zxe+Tk4MGDCgwX0JcTUk9LQwO3bupNyo0Ltf/2Z5PY1ew7Zzv7Mq9ic2JK7FoBhM2qM8uxATPZfJkTNk1Wch2qF7fr6FtfHLUaHm2L1JeDs2bLuI8rIyDu/exfBBA2V9HtHsJPS0MGlpaew+dJiBI0ZiZ2fXrK9doS3nt7O/sDruJzYnb6zT3suvHzHRc5gUMb3BP/iEEC1fXN4prltcs+L7ff0f49kRrzS4z4TYWMrzchg/dqzsqi6anYSeFkav17N+42+4B3SkkxnXrijWFLH+zFpWxS5ld/ofddoHdxzO9Og53BgxFVdbNzNUKIRoaretnslvZ3/B2sKao/cm427n8fcnXYHRaGTn1i106xRGdHR0I1UpRP1J6GmBTpw4QUJ6OkNGjGoRfwnlVeTwc8IqVsYu4UjWwTrto0PGMj16DmM7TcTB2tEMFQohGtvx7COM+65m9/THBj/D/CHPNrjP85kZJJ8+JWvzCLOR0NMClZaW8tuWrUR074FPC7vmnV6Sys8JK1lx+kfi8k+btFmoLBgfPplpUbO5LnQstpaya7IQrdXc5ZPZnrIJeysHjt6bhLONy9+f9DcO7tuDu60tQwYPboQKhbh6EnpaqJ27dlGq19On/0Bzl3JZZwvPsC5+BctP/0BKcbJJm62lHZM6T2dq1CyGBY7CysLKTFUKIa7Wwcy9TP7xOgCeHr6ABwY83uA+S0tKOLp3j0xgFmYloaeFyszMZOf+A/QdMhRHJydzl3NFiqIQm3eyZhHE00vIKs80aXe2cWFq5EymRM1iYMAQ1CrzX7ITQlze9CU3sDdjJy42rhy+J7FRLlufOn4cQ1kJN1x/vawDJsxGQk8LZTQaa1do7tK9u7nLqTdFUTiSdYDVcctYHfcThVWmO8F72nsz/c9VoHv49pEffkK0MLtStzNz2XgAXhz1Bnf3fbDBfVZXV7P3j2307dqVTp06Nbg/Ia6VhJ4WLDExkcOnTzN45HVYW7e+TUINRgN703eyJn4Za+KXU6EtN2nv4NSRmC5zmRY5i0ivLmaqUghxgaIo3PjDCI5mHcTDzpODd5/BzqrhS2ecPXOGgvRUJowbh5WVXOoW5iOhpwXTarVs+O03PDoGmfX29cagNWjZkbKF1XHL+OXMarSGapP2MLdwZnSZx5TIGYS4hZmpSiHaty3Jv/GPlVMBeH3M+9za664G92kwGNi9fRtRwUF0+5t9BYVoahJ6WrhTp04Rey6FISNHYWHRNnZEr9RVsjV5I6vilrExcR0Kpt+CXb17/LkKdEyD9/gRQtSPoiiM+WYAsXkn8XX0Z/9dcVhbNHyEOT01lbQz8YwbM0ZuUxdmJ6GnhausrGTDpk10DO9MYHCwuctpdGXVpWw8+wsrY5fwR8rmOu39/AcREz2HGztPw9PeywwVCtE+rD+zljvWzgHg3XGfMafbLQ3uU1EUdv+xnWBvL/r27dvg/oRoKAk9rcDhw4c5l53D4BEjW8RihU2loDKfX8+sYVXcUvZn7K7TPjzoOqZHz2F8+ORGWTNECFHDYDQw4uveJBWdIdAlmN3/Ooml2rLB/Wadz+TsyZPccN0oXFzk36wwPwk9rUBZWRm/bdlCcFQ0AR0DzV1Os8guP8+6+JWsjF3CiZyjddrHhk1kevRsxoRNwN7K3gwVCtF2rI77if/75TYAPp64mGlRsxvcp6Io7Nu1Ez8XZwYObLnrjYn2RUJPK3HgwAHSCwoZPHxEu7vNO7X4HGvjV7Ay9kfOFMSbtFmprZgQMZXpUbMZETwGG0sbM1UpROukN+oZ8mU30kpS6OTemT/+eaRR1tLKycrizInjjB4xHHd390aoVIiGk9DTSpSWlvL71q2ERHehQ0BHc5djNgn5cayNX86K0z+SXppq0uZg5cCkzjFMi5rN4MDhjTI8L0Rbt/Tktzyy8W4AvpqylAkRUxrcp6Io7N+9Cx8nRwYNGtTg/oRoLBJ6WpEDBw6Qll/A4OEj2vTcnvpQFIUTOUdrAlDsEvIqckzaXW3dmBY1m6mRM+nbYaCsAi3EJWgNWgZ8HkV2+Xmivbqx+db9jTKSnJ11nsQTJ2SUR7Q4EnpakQujPUGRUXQMDDJ3OS2GUTFyMHMvq+NqFkEs0RSZtPs4+BETPYcpUTPp5t2z3V0eFOJyvjn6Of/e/BAA38esYXTo2Ab3qSgKe3fuwM/FWUZ5RIsjoaeVOXz4MMlZ2QweMbLNrNvTmPRGPbtSt7Mmfhnr4ldSpa80aQ90CWZG9E1MjZpFuEdnM1UphPlV6aro/3ln8ivz6OXXj1/n/dEofxBkZqRzLvY0Y0aOxNXVteGFCtGIJPS0MhUVFWzcvBn/0E6EhMnKxVdSra9m27nfWR23jPWJa9Ab9SbtnT2iiOkyl6mRs+joIiNnon35/NAHvLDtCQCWz9rA0KCRDe7TaDSy54/tBHl70a9fvwb3J0Rjk9DTCp08eZK4cykMGjFS9rGpp0ptBb8n/cqquJ/YlLS+TnsP3z7MiJ7LpM7T8XH0M0OFQjSfCm05fT4Np6S6mIEBQ1k9d1Oj9JuSnExmUiJjR4/G0bHhO7ML0dgk9LRC1dXV/LZpMy6+fnSOjjZ3Oa1OiaaYDYnrWBm7hF1p2+u0DwoYxvToOUyImIK7nUfzFyhEE/tg/1u8uuN5ANbO3UL/gMEN7lOr1bJvxx90DgqkR48eDe5PiKYgoaeVSkxM5Mjp0/QbMgx72c/mmuVX5PLLmdWsiF3C4fP767RfF3ID06LmMC58Io7WTmaoUIjGVVpdQq9PwqjUVTAieAxLZ/7cKP3Gnz5NaU42Y68fg42NrJclWiYJPa2UwWBg85YtKHb29Owje9o0hszSdNbFr2BF7BJi806atKlVasZ1msy0qFmMDh2HnZWdmaoUomH+u/sV3t7zHwA23rybHr69G9xnRXk5B3fvpE/XroSHhze4PyGaioSeViwzM5Nd+w/QtW8/PDw9zV1Om5JcdJY1cctZEfsD54qSTNpsLGyZ2Hka06JmMzzoOqwsZF6VaB0Kqwro9UkoWoOWsZ0msnja8kbp98jBA1hqtYwZfV27X0NMtGwSelq5nbt2kV9RyYAhQ+WHTRNQFIW4vFOsiV/OytglnC/LMGl3snZmSuQMpkXNZkDAECzUsoyAaLle+eNZPjrwNgBbbztIlFfXBveZl5ND3LGjDB80EF9f3wb3J0RTktDTypWWlrJp2zY6hIUTHBpq7nLaNEVROJp1kDXxy1kVu5SCqnyTdg87T6ZHz2Fq5Ex6+fWTRRBFi5Jbnk3PT8JQMDIlciafTvq2wX0aDAb27txBBzdXWYhQtAoSetqAU6dOcTopmQHDhmNra2vuctoFg9HA/ozdrI77iTXxyynXlpm0+zsFEBM9l6mRM4ny6ioBSJjdc1vm8+WRjwDYdccJwtwbPvfm7Jkz5KWlcMPo0TjIDRWiFZDQ0wbodDo2bdmC2tGJnr37mLucdkdn0LEjdSur437il4TVVBs0Ju0hbmHMiJ7H1KiZhLp1MlOVoj3LLE2n72cRAMzucjPvTfi8wX1WlJdzaM8uekRGEhkZ2eD+hGgOEnraiMzMTHYfOEBUz954+fiYu5x2q0pXxZbkjayOW8aGxHUoGE3ao726MSN6LpMjZ9DBuaOZqhTtzeO/38/3x78C4MBd8Y2yAvmh/XuxMRi5bpRsiSNaDwk9bci+fftIzy9g0PARWFpamrucdq+supTfzv7K6rilbD33e532Pv4DmBE9l4kR0/B08DZDhaI9SC0+x8AvahYxvbXHnbx+w8IG95mRnsa52FhGDh2Cl5dXg/sTorlI6GlDKisr2bRlK84+vkR1bfhdGaLxFFYVsP7MWlbFLmVvxs467UMDRxITPZfx4ZNxsXVt/gJFm/XQ+jtZdvp7AI7ccxY/pw4N6k+j0XBg1046BXSgd++Gr/EjRHOS0NPGnDt3jv1Hj9G9X3/cPWQLhZYopzyLnxNWseL0jxzPOVKn/fqwCUyPms0NYTdiby2TQ8W1O1t4hmFf1WwJcWef+1lw3VsN7vPY4UMYK8oZc911WFtbN7g/IZqThJ42RlEUdu3eTW5ZOQOHDpNr7S1cWnEKaxOWs/L0EhIK4kzaLNWW3Bg+lalRsxgVcgM2lrK0v7g6d6/7B+sSVqJWqTl2bzJeDg2b75d1PpPEkycZNnAAfn6yMa9ofST0tEEVFRVs3roVZx8/uczVipwpiGdt3HKWx/5AekmqSZu9lQOTOk9nauQshgaNxFItc7bElcXmnmT0N/0BuL//fJ4Z8XKD+rtwWSusgz99+shdoqJ1ktDTRp07d44DR4/RpU9fPGWiYauiKAqnco+zJm4ZK2KXkFuRbdLuYuvG1MiZTIuaRb8Og1CrZCVuUdetq2bwe9KvWFvYcOzeZNzs3BvU35GDB6CqUi5riVZNQk8bpSgK+/btI6OgkAFDh8kPqVbKqBg5lLmPNfHLWR33E8WaIpN2LwcfYqLmMDVqFt19eskiiAKAY9mHGf/dUADmD36Wx4Y806D+0lNTSYmPY8SQwXh7y52GovWS0NOGaTQaNm/diqWziyxa2AbojXr2pO1gddxPrEtYSaWuwqS9o0sQM6JvYkrkTDp7RpmpStESzF42kR2pW3CwcuTIvWdxtnG55r7Ky8o4tHc30aGhdO/evRGrFKL5Sehp47Kysti5bz8hUVF0DGz4gmSiZajWV/NHymZWxf3E+jNr0Bl1Ju0RHpHERN/ElMgZBLmGmKlKYQ77M3YzdckYAJ4Z/jL3D5h/zX0ZjUYO7NmNo6UFo0aMkBsjRKsnoacdOH78OPEpKfQZOBhHJydzlyMaWaW2gs3JG1gV+xO/Jf1Sp727Ty9ioucyOTIGX0d/M1QomouiKExdMoYDmXtwtXXj8N2JDVr2IO7UKYqzzzN65EicnZ0bsVIhzENCTztgMBjYvmMHpVod/QcPkb/W2rDS6hI2JK5jZexSdqZurdM+IGAI06PmMLHzNNztZB2ntmZn6jZmLZsAwILr3uLOPvdfc185WVnEHz/GgN69CA4ObqQKhTAvCT3tRHl5OVu2bcfB04uuPXqYuxzRDPIrcvn1zBpWxC7h0Pl9ddpHBI8hJnou4zpNxMlG/opv7RRFYfz3wziefRgve28O3J2AraXtNfVVWVHBwT27CevgT9++fRu5UiHMR0JPO5KRkcGeg4cIjY4moGOgucsRzeh8WQbr4leyIvZHTueeMGlToWZcp4lMj57N6NDx2FnZmalK0RCbkzZw86rpALxx/Qfc0vNf19SPwWDg4N49OKjVjBop+/iJtkVCTztz/Phx4s6do1f/gbi4upq7HGEG54qSWBu/ghWnfyCpKNGkzdrChokR05gWNYvhwaOxtpClDloDRVEYvbg/cfmn8HcKYO+dp6/5/92p48epyM9l1IgRMo9HtDkSetoZo9HIzl27yCsrp/+QobJ+TzsXn3ea1fHLWHl6CZll6SZtjtZOTImcwdTIWQzqOAwLtcwFa6l+PbOGf62dC8D7479gVtd/XFM/6ampnIuPY3C/vgQEBDRmiUK0CBJ62iGNRsPW7dsx2tjQu98A1GpZ0be9UxSF49mHWR23jFVxS8mvzDNpd7fzYFrUbKZGzqSP/wBZBLEFMRgNjPi6N0lFZwhyCWHXv05c0zYlRYWFHD+4n67h4XSV7WtEGyWhp50qLCxk+86duPl1kP25hAmjYmRfxm7Wxi1jTfxySqtLTNp9Hf2ZET2XqVGziPbqJgHIzFbFLuW+X28H4JOJ3zA1atZV91FVVcXBPbvxd3dj8KBB8oeQaLMk9LRjaWlp7Dt8hJDIKDoGycKFoi6dQcfOtG2siVvGzwkr0eg1Ju3BrqHM7DKPKZEzCXMPN1OV7ZfeqGfwF11JL02lk3tn/vjnkavei02v13No317sVSpGjhgul7xFmyahp507deoUpxLP0rV3H9mYVFyRRq9ha/JvrI77iQ2J6zAoBpP2KM8uzOhyE5MjZxDgLHcHNoclJ7/h0Y33APD11J8YHz75qs5XFIVjhw+hKy1l1IjhOMnipaKNk9DTzimKwv79+0nNyaXPwEGyYrOol3JtGb+f/ZVVsUvZcu63Ou29/PoxI3oukzpPx8vBxwwVtn3V+moGfBFFTnkWXby6s+nWfVd9qTEhNpb8zHSGDRokG4mKdkFCj0Cv17Nj1y4KKyrpO2gwtrbXtqCZaJ+KqgpZn7iWVbFL2ZO+o077kI4jmB49hwkRU/6/vfsOjvu87zz+/u0Ciw4syEUh0XthL6YkqsSWrWZbEiWq0L6ZJHeaOJdcYjvJae48d1EsOTP2JHdnS+eRoty56O4kWiwSJctxiQspq7AXkQTRuOgdWABbgMW23/2xYAGLCIog2n5eMzsozy722RkC/Ozze57vF3ti5hzMcHH68bGX+cavvw7Aq4+9xd0l917X49tbW2ltqGfTurWquCwxQ6FHgOiJrr379uE3LGy89TYVJJNPpN/by08b32B33XaO9Ry+bPxzpffzSM2T3Ff+RVJsqXMww8VhPDjOxpcrcY0Psn7ZJt75N3uva5Wnr6eHMyeOs7q6itra2ps4U5H5RaFHzvN4POx99/dYUpJZt3GTTnDIDekYbePt+l3sqttO/eDpKWNWI44HKh7i0don+UzJvZ+4XUKs+qdDz/Ps3v8MwO4nf8nmwrum/VjX0BAfHTlERUEB69ev1+k7iSkKPTLF0NAQv3//fZKWOli9dp3+IMqMaBpq4O36Xeyse5W2kZYpY4lxSTxY9SiP1DzJHYWfJt4aP0ezXBh8AS/rXirDE3CzueAudm+7fE/V1Xjcbo4e2E9BloNbb71Vb2wk5ij0yGV6e3t5/8AB7DnLWLF69VxPRxYR0zQ53f8Re+p3sOv0dvp8PVPGMxLsbKl+nIdrnuCW/M3Xffw6Fjy//x/4zu//DoCffvl3bMy7dVqPG/P5OHLgQ7LT07l982ZdwpaYpNAjV9TR0cGBI0fIKiiiqqZmrqcji5BpmhzpPsCbZ3bw5pnXGfa7poxnJWfzaO02tlQ/zprcDVp1BEb9I6x7qZTx0Dh3l9zLq4+9Na3HjY+Pc2T/h9iTErnrDrWfkdil0CNX1dLSwqHjJ1heUkp5ZeVcT0cWsXAkzAcd77LnzA7eatiFL+CdMp6fXsjW2i+xpfpxqrNWzNEs594/vPcc3/3w2wD88g8/YHXOums+xu/3c+TAftLi4rjrzjt0OlNimkKPfKzm5maOnjxFflk5peXlcz0diQGBcIB9rb/mzTM7+FnjmwTCgSnj5Usq2Vr7ZbZUP05xZukczXL2DY0Nsu6lUoKRIA9UPMQPt7x+zcdMTExw5MB+kg246847SU5OnoWZisxfCj1yTY2NjRw/XafgI7NuLDjGb5w/54261/ll8zuYTP1ztTJ7TbQKdNVWlqXlzdEsZ8e39v4XXjz0PwDY+2+PUOX4+KPmFweeO++4g5SUlNmYpsi8ptAj06LgI3PNPTHKL5re4Y267exr+81l45vyNvNo7Ta+ULkFR/LCbqkSMSP4Al7SEtKBaP2jtS+VYmKypfoJXnrwlY99vN/v5+jBAwo8IpdQ6JFpOxd8tMdH5trQ2CDvNL7JG3U/4WDXB5eN/0HRZ3m0dhv3VzxIekLGHMzwxvztb/8jPzjyIof+tIG89AL+62/+hh8cfRGA95766GObu46Pj3P04AFSLIYCj8glFHrkupzb45NTUEiVKrnKPNDj6eLtht3srtvOyb7jU8YMDO4t/wKP1jzJ58o+T3L8wtjT8tkfb6Ju4CTfuPM5ttZuY+PL0TcZ21b+Id994OWrPm5sbIyjBw+QFmfljttvV+ARuYRCj1y3lpYWjpw4QWbucmpXrdJRYpk3WoedvNWwi92nX6PJ1TBlzGa18fmKLTxS8wSfLrkHm3V+Htv2BjxUPp+DiUlhRjF3Fn2GVz/6EQAHv1JPQUbRlR/n8XDs8EHsCYnccftmkpKSZnPaIguCQo98Ih0dHRw8epSUycrNquwq803DYB176ney6/RrdLrbp4ylxKfwUPVjPFLzJJsL7sJqsc7RLC/3butveXLnFy77/h+t/Qr/YdNfs6/1N3gDbv79p75+fmxkeJgTRw6TnZ7G5ttuIyEhYRZnLLJwKPTIJ9bb28v+gweJT09nzfqNqvAq85JpmpzoO8pbZ3ayq247g2P9U8YzE5ewpeYJHql5gg3Lb5nzKtD/7f2/53sffoewGcZqxBE2Q0C0WvXoxAgACdYEjv2Zk8ykJQz293P6xDGWL13KrbfcQny82niIXI1Cj9wQl8vF+x/uJxwfz9qNn1LhM5nXImaEg10fsKduB3vqd54PEefkpCzjsRVf4uHqx1mZvWZOLt1u/cl9fNDx7vmvDQysFiuhSOj81//r4df4QuUWOjvaaa6rozRvORs2bMBqnT8rViLzkUKP3DCPx8P7H3yANxRm7cZPkZqWNtdTErmmUCTE79t+x54zO3i7YTf+0PiU8SJ7CY/VfpmHqx+nYmnVrMwpGA5S8XwWE+GJq97nubv/kT/Z8Bc0NzbS5TxLdVkpq1ev1t46kWlQ6JEZ4ff7+XD/fvpH3axYuw5H1sKukyKxxR/y87uWX/HmmR38S+Nb5y8pnVPtqGVrbXQF6GobiWfC8Z7DPPD/7rzq+Fc2/CV/9+nvcOrECdwDfaxZsYKKiqsfXxeRqRR6ZMaEQiEOHz5Ma08vZdU1FBTdvP8cRG4WX8DLr87+jDfqXufXzp9fNr42dwNba7/EQ1VbyU7NndHnfvnwCzy39xtEzMiU71sMC/eXP8j37/8Rp44fI+z1smnjRpYvXz6jzy+y2Cn0yIwyTZO6ujpONzbhWJ5H9YoVOtklC9aIf5ifN73N7tPbeb9j32Xjt+XfydYVX+LzFQ+TmbTkhp/v3+15kl82vzMl9FgNK2tyN/DK53dSf+IUyVYLt91yC5mZmTf8fCKxRqFHbor29naOHD9OfFoaq9au1xFaWfAGfH280/Amu+pe42jPocvG7y65j0drn+S+8i+Sarv+fW2maVL7/TxG/MPnv2c1rORnFPHje3bQ19hJTqadWzZtUg0ekU9IoUduGpfLxf6DB/GFwqxev4EMu32upyQyIzrd7fy0fjc7617jzMCpKWNWw8oDFQ+xpeYJPlt6P4lx0zvR6Bxu5vb/ver81xbDSnpCBi9tfgVjIEh5USFr167VCS2RG6DQIzeV3+/n4KFD9AwNUVpdQ0Gh9vnI4nLW1cRb9TvZefpVWkecU8YS4xL5YuWjbKl5gruK7ibeenkNnUgwiPetPTQc/1dedf2KXUV9RCwGNquNb6/+HoXmMtauXElZWdlsvSSRRUuhR266SCTCqVOnqD/rJDMnl9pVq/RuVRYd0zSpGzjJnvqd7D69nR5v15TxNFs6W2oeZ0v1E9ySfztWi5WRl14k71vPkTY6ev5+I+mpPHN/BskPPsVdjtvYtHEjDodjtl+OyKKk0COzpquri8NHjxGOj2f1uvWq5yOLlmmaHO05yJ76nbxR9xNc40NTxh3JWXy741ae+p8/BeDiCjvn/iDvf/pp1j33nAp+iswghR6ZVV6vlwOHDjEwOho91q7LXbLIhSNh9ne+x54z0SrQ3oAHawQGv5dKhtvLlUoKmoDHbie1vx+L2kqIzBiFHpl14XCYU6dO0ehsIc3hoHbVamy2+dnxWmQmmCa4hqCxKcgv6n5LwqGXeeH/Xl4D6FK927eTu23bLMxQJDaoQ6TMOqvVypo1a8jJyeHw0aPsf+9daleuxpGdPddTE7khwy5oOWtM3iw4mw2a6g1anAY+rwEkAg/zdH49cO3QE2hru9lTFokpCj0yZ3Jzc/nc3Xdz7NgxTh89QlZePpU1NerWLvOaexScZw1amqPhxtlsoakh+rnHPb3+VwNxhdO6n01VzUVmlC5vybzQ2trKiZOnCFqt1KxcxVKdVpE55PVcWLGJBpxosHE2G4yOTC/YpKWblJSZVFSZlJZHKCkzKSk3KSwK0d9dx/p7P0ea2609PSKzSKFH5g2fz8ex48fp6uvXqo/cdGO+i4LN5KpNc6OFs00Gw67pBZvkFJOSUpOKapPScpOSssjkR5PMK3SlcA0NcebUSSzBAOXHjrHym98Ernx6q+v558n/6ldv6DWKyFQKPTKvmKZJW1sbH506zQRQVbuC7NyZbeoosWN8HNqcxvnLUc6zBs0N0WAzNDi9YJOUbFJccuVgs2QpGNP4McFgkKb6evq7OsnLzmLd2rWkpqbS+cILZDzzzJQ6PW67HfezzyrwiNwECj0yL42Pj3PixAnae3pJdzioql2hfkNyRRMT0Oo0aHVeFGwao6s2A33TCzaJiSaFxReCTWmZSUl5hNIyE0f29ILN1fR0d9FUf4ZEDFatqKW4uBjjoh8YCQbp372bQFsbtqIisrdu1SUtkZtEoUfmte7ubk6cPIl73E9hWTlFJSXq2h6DAgFob730UlQ02PT1TC+RxNtMiiaDTVl5dH9NcWl01SYn98aCzZX4vF4azpzG6xqmJD+PVatWqdCgyBxT6JF5LxQK0dDQQH1zM0ZCIpU1tTiysuZ6WjLDQiHoaLsQas4HmwYL3V3TSyRxcSYFRSaV5y5FXbRqk7sMZiMvh0IhnM3N9LS3kpmSyprVq8jJybn5Tywi16TQIwuG2+3mo5Mn6e7vJ22pg6qaWpJTUuZ6WnIdwmHobL8QbJzN0VtTg0FXp4EZuXa4sVpN8gvPnYoyz++vKSmPkJc/O8HmSkzTpKuzg5amRmymSU1VFeXl5VqZFJlHFHpkwenu7ubkqVMM+3zk5hdSWlGhis7zSCQCXZ3Q0myZEmwa6w26OgzC4WsHG8NikpcfDTZlFReCTWm5SV6ByXzrVzs0OEhT/RlCYz5KCgqora3VHjSReUihRxakcDhMS0sLdfUN+CMR8otLKCopUff2WRKJQE83tJ61XDgZNRlsOtoMQqHpXY7Kyzcpq4xQXjm5WjMZbPILTRbCXl6P201TQz1e1xC5DgerVq4kMzNzrqclIleh0CMLWiAQoLGxkSank5DVSnFpOXkFBbqkMANME/p6mbwUZZkSbNrbDIKB6QWb3GUm5VUXgs25VZuCIpOFukA35vPR3NiIq6+XpenprFxRy7Jly+Z6WiJyDQo9siiMjY1RX1+Ps70d4m0Ul5ezPC9f4ecaTBMG+zlfddg5eTmqqd6grdVgwj+9YJOdc2HFpnSy8nBJmUlRiUlCwk1+EbNobGwMZ1MTg7092JOTqKmupkAhW2TBUOiRRcXj8VBfX09bVxeGLYHC0lLy8mP7PyXThKHByerDzQbOyUaYzQ0GrS0G42PTCzaOLJOyigjlVRcFm1KTolKTxb59Zcznw9nczGBvN+lJSVRXVlJcXBzT/65EFiKFHlmU3G43jY2NtHZ2YsbFU1hSSl5BwZy1tRh2ccW2BDP9HBfq2Ezt8D3mm16wyVwarWFTUXWhV1RpmUlxqUlyDB6U87jdtJw9i6u/j/SkRKorKykqKtLeMZEFSqFHFjWv10tTUxPO9nZChoXlBYUUFheTMAvXXEIh+PUvLPzoZSvv7bXwk7eD3PmZyA39zNERaHFe0uG7frLDt2d6wcaeGd1XU1EVOb9ac24TcWraDU1v0RgcGKCtxYnX5SIzLZXKigoKCwu1siOywCn0SEwYHx/H6XTS7GzBHw6xNGcZRSUlpKWnz/hz9fXAq69YeeWf4+ifbIOQmGiy93CAopJr/7p5PVyoY3NJh2/36PQ7fJeWRasPn2uncC7gpGfc0MtbtCKRCD3dXXS0thLw+cjKtFNZUcHy5cuntI0QkYVLoUdiSjAYpK2tjbNOJyNeH8n2DAqKisnOyb3qu/hIMIj3rT1EOjqwFBSQ+vCWy3ojmSa8t9fCj/7Zyq9+ZsE0IXJRob3vfC/IH/1J+PzXV+rw3dQQvSQ13Q7fKalX7/Bt16npaRsfH6ezvZ2ezg4s4RAFy5ZRVlaGw+GY66mJyAxT6JGYZJomvb29nHU66R0YwIyLIzevgLyCApKTk8/fb+SlF8n71nNTumB7MjLo+ttnsP/ZnzPsgh2vWvnhP1lpb7VgtZpTiu9ZrSaZS+BP/zJEi/P6O3wnJ0f301wp2GQumfl+UbHCNE0G+/vp7GhnZHCQFJuN0uIiSkpKSFGVb5FFS6FHYp7H46G1tZWWtnbGAgHSly5hWV4+iXvepPrppwG4OFuc+4V58Z7v8lf7vkYoGF3pmXqv6UtMjB7trqye2iuqtMxkaZaCzUwa8/no6uykt7sTAkGylmRSUlxMXl7enG1yF5HZo9AjMikcDtPd3U1rWxu9vb3c99RTpLndV4wyJjCSaifL20+Ya5cOtiVc6PBdelGwKSk1yb4JHb7lgkAgQF9vDz1dnYyNuklJSKC4sIDCwkIyMrTBSSSWKPSIXEHbK69Q9Md/fM37bcvZzut92z7mHiZg8Bd/E+Ib3wzNWTPMWBMKhejv66Wvp4fRoUHiLRbycnIoKCggNzdXR85FYpTWc0WuwOjtndb9CuPbgOjeHYslekzdNC9etol+/v3/HkfDGYMXfxjUsfCbJBAIMNDfR39vL6OuIeKAHIeD6rVrWb58+ayUKRCR+U2hR+QKbEVF07pf9T0R/lPBWfz+TDzuVPp7rXR2GPR0GwwOQPiixpv/+i9W/s8PIvz518Mf8xPlevi8Xgb6+xkc6MM7MkKcYZDjcFC1ejXLli1Tp3MRmUKXt0SuIBIM4svKInV09Kp7ejx2Ox379tEzMMiIx00YSLXbWbI0i6UOB6lp6Qy7DPp6DHp7oh/veSCMI3uWX8wiEgwGGR4aYmhwENfgACG/n4Q4K8tycsjNzSU3N1crOiJyVQo9IlfR+cIL5H3ta8CVT291Pf88+V/9KhBtRNnX1xe9DQwyEQpixMWTlpnJ0qUOMpcsISU1VUXurlMoFGLE5cLlcjHsGmTc4yHOMMhITSU3J4fs7GwcDof26IjItCj0iHyMzhdeIOOZZ6bU6XHb7bifffZ84LlUJBJheHiYgYEBBgYHGRgaIhiOYMTFkWa3k2HPJMNuJ8Nu1zHpS4z5fIyMDDM6PIJ7dIRxrwcrBilJieRkZZGVlYXD4ZhSS0lEZLoUekSuIRIM0r97N4G2NmxFRWRv3XpZReaPEw6HGR4exuVyMTQ0xMCQi4lgkJAZITE5hZS0dNIzMkhLTyctPR2bzXYTX838YJomYz4fbvcoHrcHj3sUn9uNGQphtURXcrIcDpYsWcKSJUtITU2d6ymLyCKg0CMyy0zTxOv1MjIywsjICMOTt0AoTMg0ibPFk5SSSmpqGimpqSQlJ5OckkJSUtKCuzwWCoUYHxvD5/Pi8/rweb2M+bz4x3wYEROrxSAlKYmlmZnY7XbsdjuZmZnEX0eoFBGZLoUekXnANE18Ph9utxuPx4Pb7WbU7cHr8xIMR4iYJqbFwJaQSEJSEomJSSQkJpKYlEiCLYGExERsCQnYbLZZ6wQeDAYJBgJMTEwwMeFnwj+Bf3wc/4SfifFxJsbHCQWDWA0DiwGJtgQy0tNIT0sjPT2dtMmPsbCyJSLzg0KPyDxmmiZjY2P4fD7GxsbO37yTH8f9fkwgYhINRphYrXFY4+OwxsUTFx+H1RqHxWrFarFitVqxWCwYFguGYVy2cmSaJpFIBEyTcDgcvUXChEMhIuEwoWCQcChEMBgAEyyAMRlq4q1WkpOSSElOJvmiW0pKCikpKQo3IjLnFHpEFrBIJEIgEMDv9xOYXHUJBALRVZjJWzgcjn4eDhMOhYlEwoQjEUzT5NJff8MwsFosWCxWLFYLcVYrcVYr8fHxxMfHExcXh81mIz4+HpvNhs1mIzExkYSEBF2SEpF5T6FHREREYoI6AYmIiEhMUOgRERGRmKDQIyIiIjFBoUdERERigkKPiIiIxASFHhEREYkJCj0iIiISExR6REREJCYo9IiIiEhMUOgRERGRmKDQIyIiIjFBoUdERERigkKPiIiIxASFHhEREYkJCj0iIiISExR6REREJCYo9IiIiEhMUOgRERGRmKDQIyIiIjFBoUdERERigkKPiIiIxASFHhEREYkJCj0iIiISExR6REREJCYo9IiIiEhM+P9rfqD/YmhjtAAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ft.SEED = -1 # do not display SEED\n", "ft.PROCESS_TIME = 0 # elapsed time temps 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 ($\\ell_2$ norm)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x = 2.34352457302443\n", "T = [8, [6, [4, [2, [5], [7]], [1, [3]]], [0]]]\n", "ft.POINTS = [(-0.8517104894840652, 0.4053985820237106), (0.21077865455389472, 0.9591255647552167), (0.378988753049117, -0.5489884178113221), (-0.0027347253259811435, 0.9999962606317043), (0.6297350510976314, -0.3162636551124339), (-0.42988109024091553, -0.5780038610508595), (0.5725444102412329, -0.38824037692073743), (-0.507720563890914, -0.5330240965152787), (0.0, 0.0)]\n", "x = 2.7515595204571954\n", "T = [8, [5, [2, [3, [6]], [4]], [1, [0], [7]]]]\n", "ft.POINTS = [(-0.4235229146932943, 0.8764402629204343), (-0.6404856719998917, -0.5086687438838305), (-0.3419906782827621, -0.7255026276489608), (0.33292739516034064, -0.7510016720840152), (0.49069035784055026, 0.8686856290304633), (-0.4705433199756285, -0.6546779158034347), (0.9073911439414452, -0.09462822921209373), (0.14553368800924057, 0.9893532966814377), (0.0, 0.0)]\n", "x = 2.870396973754615\n", "T = [8, [6, [3, [2, [4]], [0, [5]]], [1, [7]]]]\n", "ft.POINTS = [(0.49679068934950255, 0.6640095945454308), (-0.5755906454150279, 0.7100377010541793), (-0.12241827175653007, -0.9619285933141067), (0.6397875880604852, -0.623177745951648), (-0.8203344080670892, -0.5718841306953868), (0.40534958569412577, 0.7279588147298061), (0.7111139639326483, -0.5210797199770333), (-0.7346985017981146, 0.5760640796087589), (0.0, 0.0)]\n", "x = 2.9509254249789634\n", "T = [8, [5, [6, [4, [0], [3]], [1]], [2, [7]]]]\n", "ft.POINTS = [(-0.750934840231266, -0.6603763061519113), (-0.22210650572090465, 0.8521940595382698), (-0.9413745317944747, 0.1787047880475292), (0.518322514027024, 0.6796757184220886), (0.646179325346649, -0.6794135771979117), (0.8841246227690432, -0.06792906179190121), (0.8288645528599697, -0.3744020828594511), (-0.9630751372560408, 0.07154646199328771), (0.0, 0.0)]\n", "x = 2.976828259566534\n", "T = [8, [4, [5, [7, [6]], [1]], [2, [0], [3]]]]\n", "ft.POINTS = [(0.6282676746640667, -0.6046676082554339), (-0.9445128248549869, -0.3284745403900476), (0.7107217006106927, -0.49080673593709606), (-0.4779147189695988, -0.8404785646149209), (0.7563824035300738, 0.3933106916169937), (0.6704071451873866, 0.5373012194082324), (-0.8362995375634513, 0.5217065222483047), (-0.507051842604183, 0.8121090159239673), (0.0, 0.0)]\n", "x = 3.219912584786834\n", "T = [8, [2, [5, [1, [0]], [4]], [7, [3], [6]]]]\n", "ft.POINTS = [(0.2803304971021551, 0.9432524620940111), (0.4545182848983478, 0.8778586068453944), (0.09718850029394882, -0.9712246730289411), (-0.6036908972745423, 0.7463106092933968), (0.918596842737996, 0.39519595204377495), (0.35021917913888706, -0.9184111289905204), (-0.8901800640623485, -0.33260228009982296), (-0.6069823428344441, -0.7403795481572923), (0.0, 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", " 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 = 3.570593145854709\n", "# T = [0, [4, [3, [8, [2]], [7]], [5, [1], [6]]]]\n", "# ft.POINTS = [(0.0, 0.0), (-0.9985549564600698, 0.011827106584179929), (-0.006175724711713601, -0.9996790979426582), (0.9996797961518151, 0.018006435511381674), (0.7213105266396888, 0.6916888441126671), (-0.7102685631588145, 0.7017728500934621), (-0.040494833692801824, 0.9979330572465028), (-0.6851648746614944, -0.7272314994841055), (0.7196686298933903, -0.69431769612143)]\n", "\n", "# Maximum for ft.generate_von_mises(8,0.1) with NB = 10,000\n", "# (many crossings ...)\n", "# x = 3.0498501436246337\n", "# T = [0, [3, [1, [8, [2]], [7]], [5, [4], [6]]]]\n", "# ft.POINTS = [(0.0, 0.0), (-0.38313149525860823, -0.8944996655519788), (0.24967021557384517, 0.9683309266233882), (-0.1987667780636083, -0.8715771404052549), (-0.9335487858180874, 0.25552358830278954), (-0.6785219343019202, -0.6434257547307705), (0.8959422895728233, -0.26045916474825553), (0.7954899585093611, 0.5057387380199572), (0.2528665297861946, 0.9403684724901246)]\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_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)\n", "plt.show()" ] } ], "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": "3.7.3" }, "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 2 }