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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Power-pairing vs random pairing\n",
"\n",
"_Chuan-Zheng Lee <czlee@stanford.edu>_\n",
"\n",
"This notebook shows a very basic simulation of debate tournaments using power-pairing and random pairing, comparing the variance in actual rank caused by randomness in the draw in both systems."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The functions below are run by the plotting code to simulate tournaments. Scroll down to see the plots."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"using PyPlot"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"function runpairings!(points, pairings, strengths)\n",
" for (t1, t2) in pairings\n",
" if strengths[t2] > strengths[t1]\n",
" points[t2] += 1\n",
" else\n",
" points[t1] += 1\n",
" end\n",
" end\n",
"end\n",
"\n",
"function groupbrackets(points)\n",
" maxpoints = maximum(points)\n",
" brackets = [[] for p in 0:maxpoints]\n",
" for (t, p) in enumerate(points)\n",
" push!(brackets[p+1], t)\n",
" end\n",
" return brackets\n",
"end\n",
"\n",
"function pairrandom(brackets)\n",
" teams = vcat(brackets...)\n",
" shuffled = shuffle(teams)\n",
" return collect(zip(shuffled[1:end÷2], shuffled[end÷2+1:end]))\n",
"end\n",
"\n",
"function pairpower(brackets)\n",
" pairings = []\n",
" odd = -1\n",
" for teams in brackets\n",
" if odd != -1 # pull-up team\n",
" push!(teams, odd)\n",
" odd = -1\n",
" end\n",
" shuffled = shuffle(teams)\n",
" if length(teams) % 2 == 1\n",
" odd = pop!(teams)\n",
" end\n",
" pairs = collect(zip(shuffled[1:end÷2], shuffled[end÷2+1:end]))\n",
" append!(pairings, pairs)\n",
" end\n",
" @assert odd == -1 # there should not be a pull-up left over at the end\n",
" return pairings\n",
"end\n",
"\n",
"function getrankedteams(brackets)\n",
" teams = vcat([sort(bracket) for bracket in reverse(brackets)]...)\n",
"end\n",
"\n",
"function simulatetournament(pairingfunction::Function, strengths, nrounds)\n",
" points = zeros(Int, length(strengths))\n",
" brackets = Vector{Vector{Int64}}(1)\n",
" brackets[1] = collect(1:length(strengths))\n",
" for i in 1:nrounds\n",
" pairings = pairingfunction(brackets)\n",
" runpairings!(points, pairings, strengths)\n",
" brackets = groupbrackets(points)\n",
" end\n",
" return brackets\n",
"end\n",
"\n",
"function simulatemanytournaments(pairingfunction::Function, ntournaments::Int, nteams::Int, nrounds::Int)\n",
" strengths = collect(nteams:-1:1)\n",
" positions = [[] for t in strengths]\n",
" for i in 1:ntournaments\n",
" brackets = simulatetournament(pairingfunction, strengths, nrounds)\n",
" rankedteams = getrankedteams(brackets)\n",
" for (pos, team) in enumerate(rankedteams)\n",
" push!(positions[team], pos)\n",
" end\n",
" end\n",
" return positions\n",
"end;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Simulation parameters\n",
"\n",
"If you're running this in Jupyter Notebook, you can change the parameters of the simulations below. It will run `ntournaments` tournaments with `nrounds` rounds in each tournament, each tournament having `nteams` teams.\n",
"\n",
"I haven't tried it myself, but I suspect the behavior of each system depends quite a bit on these parameters. The arguments we make are for typical debate tournaments, in which there are far fewer rounds than there are teams (thus preventing us from just running a round robin)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ntournaments = 100\n",
"nteams = 50\n",
"nrounds = 5;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Plots \n",
"\n",
"In the box-and-whisker plots below, each box (column) is a team, best team on the left, worst team on the right. The box shows the distribution of _actual_ ranks from each of the simulated tournaments. Some important assumptions and notes:\n",
"\n",
"* We model teams' \"true\" abilities as being ranked from first to last, and a \"better\" team _always_ beats a \"worse\" team (not just most of the time).\n",
"* For power-pairing, teams are randomly paired within brackets.\n",
"* When generating the final _actual_ rank from a tournament, however, teams are assumed to ranked \"correctly\" within brackets. So teams are ranked first by bracket, then by \"true ability\". This is advantageous to both systems, of course; you can think of it as modelling an assumption that within brackets, speaker scores will be a proxy for \"true ability\". (This doesn't work so well for draw strength/opp wins.)\n",
"* Other than that, there's no concept of speaker scores in the model. Perhaps it might be an interesting exercise to model this, but that would also reduce the ability of this simulation to capture the essence of the question at hand.\n",
"* This model uses two-team formats (like most North American, Oceanian and Asian styles), not British Parliamentary.\n",
"\n",
"The ideal would be a series of zero-height boxes (which would just look like red dashes) along the $y=x$ line, _i.e._ the team with true rank $x$ should always have actual rank $x$ (with no variance). Note that the first and last teams will always come first and last with both tournament structures, because they will win and lose respectively all their debates. It's the teams in the middle where variance comes into play."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Power-pairing** results in some variance. There's an interesting, but unsurprising, effect with outliers at the bracket boundaries. If a team draws a lucky or unlucky opponent within their bracket, they might end up in the \"wrong bracket\" at the end, which catapults them up or down the tab. This can happen, but not too often. In most cases, going into a lower bracket the next round \"saves\" an unlucky team. By and large, the variance isn't totally unbearable."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f34ce20e090>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"powerpositions = simulatemanytournaments(pairpower, ntournaments, nteams, nrounds)\n",
"powerplot = boxplot(powerpositions)\n",
"xlabel(\"true rank\")\n",
"ylabel(\"actual rank\")\n",
"title(\"Rank distributions with power pairing\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Random pairing**, on the other hand, is all over the place. Again, the first and last teams come first and last. But teams in the middle have both bigger quartile spreads and bigger whisker ranges (excluding outliers). This means there's a much weaker relationship between one's actual rank in any one given tournament and their true rank (and the sole other variable in this model is randomness in the draw).\n",
"\n",
"This, again, isn't surprising. There's a lot more randomness in the system now, so luck of the draw factors in every round. If you have very many rounds—as many as there are teams—each team will converge individually to their true rank. But because there are so few rounds, drawing multiple weak or strong opponents doesn't take that much luck."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f34ccfa3110>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"randompositions = simulatemanytournaments(pairrandom, ntournaments, nteams, nrounds)\n",
"randomplot = boxplot(randompositions)\n",
"xlabel(\"true rank\")\n",
"ylabel(\"actual rank\")\n",
"title(\"Rank distributions with random pairing\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How unlucky do you have to be to draw, say, three strong opponents in an eight-round tournament? Contrary to what you might think, it's not a rare scenario. We can compute the probability of any _given_ team at some percentile rank drawing such opponents using the binomial distribution. Because it's hard to pick a team that should be our \"example\" rank, we just plot every team's probability of not breaking as a function of their percentile rank. The below plot only plots within the range of the expected break cut-off.\n",
"\n",
"Now, teams close to the break cut-off wouldn't have much cause to complain. In any system, you'd always expect the borderline team to have a half-chance of breaking. The salient group is that in the middle two quartiles of the break: not safe, but also not borderline.\n",
"\n",
"But also, remember this is the probability for any _one_ team of some percentile rank. The probability that any _one_ (or say, three, because one upset doesn't really break a tournament) team in the \"true break\" being affected would be much higher."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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e3lYnQk6Z3tO7cuVKeXl5ZXqvQIECKl26tBo1aqRKlSrlOBwAAEBu++svYxZvkSLS5s1S0aJWJ4IzmC69oaGht3yNl5eX+vTpo2XLlsnHh2flAABA3nD5stS5s/Tbb8ZRw+XLW50IzmJ6e8PevXvl5+enIUOGaOfOnfruu++0Y8cODR48WH5+foqJiVF4eLiioqI0c+ZMV2QGAABwOodDGjRI2r1bevddqU4dqxPBmUwvw77yyit6/PHHNX/+/PRrderUUcuWLTVmzBgtX75c69at03/+8x+tWbNG06ZNc2ZeAAAAl5g+XVq1SlqzRmre3Oo0cDbTK71bt25VYGBgpvfatWunDz74QJLUqlUrnThxImfpAAAAcsHKlUbpnT1bCgmxOg1cwXTpTUtL07FjxzK9d/z4cTkcDklSwYIFVbhw4ZylAwAAcLGPPpIGDjQ+JkywOg1cxXTpfeyxxzRlyhTFxcVluB4bG6vJkyfrsccekyQdPXpUfn5+TgkJAADgCocOScHB0qOPGiev3WBAFTyA6T29Cxcu1COPPKKAgACVLFlSFSpU0MmTJ3XmzBnVrFlTCxcuTH/t6NGjnRoWAADAWX77TWrfXqpeXVq/XipY0OpEcCXTpbdKlSo6ePCgVq5cqV27dik5OVn33HOPWrZsqSeffFJF/zvM7umnn3Z6WAAAAGc4e9Y4fCItzThquEQJqxPB1bI1RLdYsWIaPny4hg8f7uw8AAAALnX1qtSjh/Tjj8Z4sipVrE6E3MDJEQAAIN9wOKQRI6TYWCkmRmrQwOpEyC2mH2S7fPmywsPD5e/vr6JFi6pAgQIZPrw5nBoAALipefOkJUukpUul/z57j3zC9Erv888/rwULFqhdu3Z6/PHHrxtL5sVjjwAAwA2tXy+NGydNmmSMJ0P+Yrr0rlu3TlOmTOGkNQAAkGd89pnUp4/Us6cUHm51GljB9PaG//znP2rRooUrsgAAADjdsWNSx45SkybS8uXM4s2vTJfehx9+WAcPHnRFFgAAAKc6dUpq104qV07atEnisNj8y/T2hldffVUdOnRQtWrV1KFDBxUqVMgVuQAAAHLk4kWpUyfp9Glpzx6pbFmrE8FKpkvvPffcoytXrqhr167y8vJSsWLF5HA45OXllf6fqamprsgKAACQJXa79OST0ldfSTt3SnfdZXUiWM106e3cufNN7zO9AQAAWG3iRGNaw8aN0v33W50G7sB06Y2IiHBBDAAAAOdYulR68UVpwQLpiSesTgN3YfpBNgAAAHcVEyM99ZRx6tqoUVangTvJ0kpvfHy8GjZsqBIlSig+Pv6Wr2/evHmOgwEAAJjx1VdSt25SUJA0f77VaeBuslR6W7ZsqT179uj+++9Xy5Ytb/paLy8vpaWlmQpx9uxZTZ48WevXr1dKSorq1KmjCRMmqHv37qbeZ/LkyZo9e7bq1q2rb7/91tTnAgCAvOvnn6X27SV/f2nNGsnb2+pEcDdZKr07duyQv79/+q+dLTg4WPv27dPcuXNVq1YtRUZGKiQkRHa7XSEhIVl6j4MHD2revHmqUKECD9MBAJCPnD4tBQYaM3i3bJGKFbM6EdxRlld6M/u1M8TExGj79u2y2WzpK7stWrTQiRMnNG7cOHXv3l0FCtx86/HVq1cVGhqqoUOH6uDBg0pOTnZqRgAA4J6uXJG6dJF++cU4arhCBasTwV2ZfpAtJibmpvenT59u6v02bdqkEiVKqGvXrhmuh4aGKikpSXv37r3le8yZM0d//fWXZs6cKYfDYerrAwCAvMnhkIYOlXbtMk5b++8PpYFMmS693bt311dffZXpvXnz5pkuvYcOHZK/v/91q7n169eXJB0+fPimn//dd99p1qxZWrJkiYrx8wwAAPKNWbOk5cuNDyf/IBoeyHTpDQ4OVlBQkH7++ecM15cuXapx48bppZdeMvV+ycnJKpvJuYDXrt1sq0JaWpr69++vzp07KyAgwNTXBQAAedfq1dKUKdKMGVLv3lanQV5guvQuW7ZMtWvXVmBgYPpxw++8846eeuophYWF6dlnn3V6yBtZsGCBjh8/roULF+ba1wQAANbatUvq318KDZUmT7Y6DfIK06W3YMGCio6Olt1uV3BwsGw2m/r376/Ro0dr2rRppgP4+vpmupqbkpKSfj8ziYmJCgsL09SpU+Xj46O//vpLf/31l65evaq0tDSdPn1aFy9eNJ0HAAC4ryNHpMcfl1q0kN54Q2JgE7LK9DHEklS6dGlt3bpVTZs2Va9evTRo0CC9/PLL2QrQoEED2Ww22e32DPt6r83ZrVevXqafl5CQoIsXL2rEiBEaMWLEdffLlCmjUaNGaf5NplOPHj1apUqVynAtJCQky2PSAABA7vn9d2M0WZUq0oYNUsGCVieCs9hsNtlstgzXTp8+7dSv4eXIwriDefPmZTr7dv/+/frwww/13HPPZSisY8aMyXKA2NhYBQYGKioqSt26dUu/HhAQoMOHDysxMTHTr3369Gl9/fXXGa45HA6NGjVKqampWrFihSpXrqwaNWpc97kHDhxQ48aNtX//fjVq1CjLWQEAgDXOnZMeecQYTbZnj1StmtWJ4GrO7mtZWukdN27cTe8/99xzGX5vpvQGBASoTZs2GjZsmFJTU1WjRg3ZbDbFxcUpMjIyvfAOGDBAq1atUkJCgqpWrapSpUpletxxqVKldPXqVY5CBgDAQ6SlST17St99J8XHU3iRPVkqvQkJCS4NER0drUmTJiksLEwpKSny9/e/buXXbrfLbrffcg6vl5cXJ7IBAOBBxoyRtm6V3n9f4ge0yK4sbW/wNGxvAAAgb1i4UBo9Wlq6VBoyxOo0yE3O7mumpzcAAADkhuhoY5X3uecovMi5bE1v2LVrlxYtWqSjR4/qwoUL6dcdDoe8vLxcvh0CAAB4tj17pF69pG7dpBdesDoNPIHpld7du3fr0UcfVWpqqo4cOaI6deqoUqVKOnHihHx8fNSiRQtX5AQAAPnE8eNShw7SvfdKERFSAX4uDScw/T+jqVOnKjQ0VNu2bZMkhYeHa/fu3frqq6907tw5BQcHOz0kAADIH5KTjVm8ZcpI774r3Xab1YngKUyX3kOHDik4ODh9QoLdbpdkHDIxZcoUzZgxw7kJAQBAvnDxonHaWkqKtG2bdINDWYFsMb2n9/z58ypWrJi8vb1VuHBhnTp1Kv1e7dq1dfjwYacGBAAAns9ul/r1k/btkz7+WMrkbCkgR0yv9FarVk1JSUmSJH9/f23ZsiX9Xnx8vHz5axkAADDp+eeldeukyEipaVOr08ATmV7pbdGiheLj49WjRw8NHjxYw4cP19GjR1WoUCHFxcXp2WefdUVOAADgod54Q5o7V5o/X+LRILiK6dI7Y8YMpaSkSJKGDh2q8+fPa/Xq1SpQoICmTJmiSZMmOT0kAADwTDEx0vDh0tNPS6NGWZ0Gnsx06S1XrpzKlSuX/vsxY8ZozJgxTg0FAAA831dfGXN4g4KMk9f++4w84BLZnnzncDh09OhRffrppzp79qwzMwEAAA+XmCi1by/5+0tr1kje3lYngqfLVuldtWqVqlSporvvvlvNmzfXDz/8IEnq1q2b3nrrLacGBAAAnuX0aaPwFi4sbdkiFStmdSLkB6ZL7/r169WvXz81btxYr7/+uhwOR/q9hg0bat26dU4NCAAAPMfly1LnztIvvxj7eStUsDoR8gvTpfeFF15Qv3799P7772vQoEEZ7vn7+zOnFwAAZMrhkIYMkeLjjdPW/P2tToT8xHTpPXLkiEJCQjK9V7ZsWSUnJ+c4FAAA8Dzh4VJEhLRihdSihdVpkN+YLr1FixbV6dOnM72XlJSkMmXK5DgUAADwLKtWSVOnSjNnSr16WZ0G+ZHp0vvggw/qtddek91uv+5eRESEWrZs6YxcAADAQ+zYIQ0cKA0YYJy8BljB9JzesLAwPfjgg2rSpEn6Nofo6GiFhYVp165d+uKLL5weEgAA5E2HDhmnrLVsKS1ZwixeWMf0Su+9996r2NhYnT17VmPHjpUkzZ49Wz/++KO2bdum+vXrOz0kAADIe5KSpMBA6c47pQ0bpIIFrU6E/MzUSu/ly5e1c+dO1a5dW0eOHNGxY8f0+++/q1y5cqpdu7arMgIAgDzmzBljFq/DYYwmK1nS6kTI70yVXm9vb7Vv316xsbG68847VbNmTdWsWdNV2QAAQB505YrUtauUkCDt3i1Vrmx1IiAbpbdKlSpKTU11VR4AAJCHORzS8OHSRx9JsbESux7hLkzv6R0wYIBef/11paWluSIPAADIw2bPlpYtk95+W3r0UavTAP9jenpD4cKF9f3338vf318dO3ZUxYoV5fWPRzHHjBnjtIAAACBvWL1amjxZmjFD6tvX6jRARqZL7/jx49N/PX/+/ExfQ+kFACB/2bFD6t/f+Jg82eo0wPVMl96EhARX5AAAAHnUtVm8jzwiLV3KLF64J9Ol18/PzwUxAABAXnRtFq+fn7R+PbN44b5Ml95rfv75Z33yySdKTk6Wr6+vmjdvripVqjgzGwAAcGN/n8W7dSuzeOHeTJdeu92ukSNHasmSJbLb7enXvb29NWTIEC1atEgFCpgeCgEAAPIQZvEirzFdeqdNm6bXX39dgwYNUs+ePVWhQgWdPHlSa9as0eLFi1WmTBmFh4e7IisAAHADzOJFXmS69C5fvlwjRozQwoUL06/VqVNHLVu2VNGiRbVixQpKLwAAHuzaLN6VK5nFi7zD9D6ElJQUBQUFZXovMDBQycnJOQ4FAADcE7N4kVeZLr0NGjTQDz/8kOm9H3/8UfX5GQcAAB6JWbzIy0xvb3jppZcUEhKiatWqZVjx3bx5s2bPnq2oqCinBgQAANZjFi/yuiyV3vr166cfNexwOHTp0iV17NhRJUuWTH+Q7cyZM/L19dVTTz2lb775xqWhAQBA7mEWLzxBlkqvr6/vTX9fsWLF9F978Vc/AAA8BrN44SmyVHp37tzp4hgAAMDdXLkidevGLF54hmyfyAYAADyXwyENGyZt384sXngGSi8AALjOjBnS229Lq1YxixeegfOCAQBABsuXS9OmGYdQ9OljdRrAOSi9AAAgXWysNHiwNHSoNGGC1WkA56H0AgAASdKBA1KXLsZ4sldfZRYvPIvp0puYmKjLly9neu/KlStKTEzMcSgAAJC7fvrJKLt160o2m+TDUz/wMKZLr5+fnw4ePJjpva+//lrVq1fPcSgAAJB7UlKkgACpeHFp82apWDGrEwHO59S/x6WlpTnz7QAAgItduCB17CglJ0uffy6VL291IsA1nFZ6L168qNjYWJUrV85ZbwkAAFwoLU3q3dvYy/vxx1LNmlYnAlwnS6V3+vTpmj59evoRw02bNr3hawcOHOicZAAAwGUcDmnMGOndd6VNm6QmTaxOBLhWlkrvfffdp+HDh0uSFi9erC5duqj8P37+UbhwYTVo0EA9e/Z0fkoAAOBUCxZIixZJS5YY2xsAT5el0hsYGKjAwEBJ0tmzZxUWFqa77rrLpcEAAIBrrF0rPfusNHGiMY8XyA9M7+mNiIhwQQwAAJAb4uOlvn2NvbyzZlmdBsg92Tqc4tixY+rdu7cqVqyoQoUKqXLlyurbt6+OHz/u7HwAAMBJDh+WOnWSHn5YevttDp9A/mJ6pffo0aNq1qyZLl68qFatWqlixYpKSkrSunXrtGXLFn322WeqU6eOK7ICAIBsSkqS2rWTqlWTNm6UChWyOhGQu0yX3ueff16+vr7auXOnqlSpkn79l19+0SOPPKLnn39e0dHRTg0JAACyLzXVOG3N4ZBiYqRSpaxOBOQ+09sbdu3apWnTpmUovJJUpUoVTZ06VR9//LHTwgEAgJy5fFnq3Nk4ZnjbNqlyZasTAdYwvdJ7/vz5Gx5A4evrqwsXLuQ4FAAAyDmHQxo0yHh47YMPpHr1rE4EWMf0Sm+tWrW0evXqTO9FRUWxnxcAADcRFiatWiVFREgtW1qdBrCW6ZXekSNHauBLdntxAAAgAElEQVTAgTp9+rT69euX/iDb6tWr9f7772vZsmWuyAkAAEx4801p5kzpxRelkBCr0wDWM116+/fvr99//13h4eHaunVr+vUiRYpo9uzZ6t+/v1MDAgAAc95/Xxo2THr6aWnsWKvTAO7BdOmVpIkTJ2rYsGH6/PPPlZycLF9fXzVr1kylS5d2dj4AAGDC559LPXpITzwhLVzILF7gmmyVXkkqXbq02rVr58wsAAAgB44elYKCpHvvlVavlry9rU4EuI9slV673a4vv/xSiYmJmU5r6Nu3b46DAQCArEtKktq2lSpWlN57T7rtNqsTAe7FdOn94Ycf1KFDB/344483fA2lFwCA3HP6tHHamt0uxcZKZcpYnQhwP6ZL71NPPaVLly5p3bp1ql+/vgoXLuyKXAAAIAsuXTL27yYmSrt3S/84OwrAf5kuvV988YXefPNNdenSxRV5AABAFtnt0pNPSp99Jn34oVS3rtWJAPdluvQWL15cpTi0GwAAy40dK61bJ23YID38sNVpAPdm+kS2fv36ac2aNa7IAgAAsmjePGnBAunVV6XgYKvTAO7P9Epv/fr1ZbPZ1KFDB3Xs2FG+vr7XvSaY//cBAOAya9YYq7zPPy899ZTVaYC8wXTp7dmzpyTpp59+ynAi2zVeXl5KS0sz9Z5nz57V5MmTtX79eqWkpKhOnTqaMGGCunfvftPP2759u+bOnavvvvtOycnJKlWqlOrVq6exY8cyQxgA4JG2b5f69TM+Zs60Og2Qd5guvTt27HB6iODgYO3bt09z585VrVq1FBkZqZCQENntdoXc5MDwlJQU1a9fX4MHD9Ydd9yh5ORkLV26VO3bt9c777yjXr16OT0rAABW+eorY1JD69bSm29y2hpghpfD4XBYGSAmJkZBQUGy2WwZVnbbtm2rw4cPKzExUQUKZH3r8dWrV1W9enXddddd2rVrV6avOXDggBo3bqz9+/erUaNGOf4zAADgav/+t9SsmVS1qvTxx1Lx4lYnAlzL2X3N9INszrZp0yaVKFFCXbt2zXA9NDRUSUlJ2rt3r6n38/HxUalSpeTjk+0TlgEAcCunThmnrZUoIW3dSuEFssPy0nvo0CH5+/tft5pbv359SdLhw4dv+R52u11Xr15VUlKSpk6dqh9++EGjR492SV4AAHLTuXNSUJBx6lpsrFS+vNWJgLzJ8uXQ5ORk1axZ87rrZcuWTb9/K4GBgYqLi5MkFS1aVJGRkQoKCnJuUAAActnVq1L37tKhQ9KuXVKNGlYnAvIuy0uvM7z22ms6ffq0fvvtt/QH2C5fvsyDbACAPMvhkIYMkT74wNjS0Lix1YmAvC1L2xvef/99/fXXXy4J4Ovrm+lqbkpKSvr9W6lZs6YaN26soKAgrV27Vq1bt9Yzzzzj9KwAAOSWqVOl5cuNj8ceszoNkPdlaaX38ccf1549e3T//ferevXqevfdd/Wvf/3LKQEaNGggm80mu92eYV/vt99+K0mqV6+e6fe87777FBsbqz/++EPlb7L5afTo0dcdqRwSEnLTMWkAALjaG29I4eHSnDlSnz5WpwFcz2azyWazZbh2+vRpp36NLJXeokWL6ty5c5KkEydO6NKlS04L8MQTT+itt97Shg0b1K1bt/TrERERqly5spo0aWLq/RwOh3bt2qUyZcqoXLlyN33tggULGFkGAHAr774rDR8uPfOM9NxzVqcBckdmi47XRpY5S5ZKb506dTR58mQ98cQTkqQ1a9Zo9+7dN3z9mDFjshwgICBAbdq00bBhw5SamqoaNWrIZrMpLi5OkZGR8vrv5O0BAwZo1apVSkhIUNWqVSVJnTp10j333KN//etf8vX1VVJSkiIiIhQfH6/Fixebmu8LAIDV4uOlHj2kzp2lBQs4fAJwpiyV3rlz56pbt2567r9/5Vy0aNFNX2+m9EpSdHS0Jk2apLCwMKWkpMjf319RUVEZVn7tdrvsdrv+fpbGQw89pA0bNui1115TamqqSpcurfvuu09bt27lGGIAQJ7yzTdSx47Sgw9K77wjeXtbnQjwLFk+kc3hcCgpKUlVq1ZVdHS07rnnnhu+1s/Pz1n5XIIT2QAA7uTf/5YeeECqVMk4ba1kSasTAdZzdl/L8sgyLy8vVa5cWWFhYbrvvvtUuXLlHH9xAADyuz/+MKYzFC8ubdtG4QVcxfSc3mnTpqX/+ocfflBycrLKlSun//u//3NmLgAAPF5qqtSunXT2rPTZZ5y2BrhStp70WrdunapVq6Y6derowQcfVO3atXXnnXdq/fr1zs4HAIBHunRJeuIJ6dgx43jh6tWtTgR4NtMrvTExMQoJCVHdunX1zDPPqGLFikpKStLq1asVEhKiYsWKKTAw0BVZAQDwCGlpUu/e0qefSnFxkpNG3wO4CdOld9asWWrTpo1iYmIyjAQbO3asAgMDNWvWLEovAAA34HAYM3ijo42P5s2tTgTkD6a3Nxw8eFDDhw+/bgZugQIFNHz4cB08eNBp4QAA8DQzZkhLlhinrnXqZHUaIP8wXXq9vb11+fLlTO9duXKFAyEAALiBpUuladOk2bOlgQOtTgPkL6Yb6n333acXX3xR58+fz3D94sWLevnll00fGwwAQH6wYYNxvPDIkdKECVanAfIf03t6p0+frlatWqlGjRrq0qVL+oNs0dHRSk5O1o4dO1yREwCAPGvHDqlXLykkRJo/n+OFASuYLr0PPfSQPvzwQ02YMEGLFy+Ww+FQgQIF1KRJE0VFRenBBx90RU4AAPKkAweMvbuPPCKtWCGxCxCwhunSK0ktWrTQ559/rnPnzuk///mPypQpo2LFijk7GwAAedqxY8bhE3ffbWxvKFTI6kRA/pWt0ntNsWLFKLsAAGTit9+M44XLlJG2bjWOGQZgnRyVXgAAcL2//pICAqTLl6WdO6Vy5axOBIDSCwCAE124YOzh/fln6ZNPpGrVrE4EQKL0AgDgNFevSj17Sl9+KW3fLtWta3UiANdQegEAcAKHQxo2TNq8WXrvPemBB6xOBODvTA9OOXnypCtyAACQpz3/vLRsmbR8udS+vdVpAPyT6dJbrVo19ejRQ7t373ZFHgAA8pwXX5TmzDEOnujb1+o0ADJjuvROnjxZn3zyiZo3b66GDRtq2bJlunDhgiuyAQDg9t56Sxo/XpoyRRo92uo0AG7EdOkNCwvTiRMnFBUVpRIlSmjw4MGqUqWKnn32WSUkJLgiIwAAbmn9emnIEOmpp6Tp061OA+BmsnUYoo+Pj7p166b4+HgdPHhQnTt31htvvKFatWqpffv2io2NdXZOAADcygcfSL16GdMaFi2SvLysTgTgZnJ8Ani9evXUrl071atXT3a7XR999JECAwPVuHFj/fDDD87ICACAW/nsMyk4WGrbVlqxQiqQ43+bAnC1bP/f9M8//9Ts2bNVvXp1de7cWd7e3rLZbEpNTdV7772nM2fO6Mknn3RmVgAALPfNN8Z0hnvvldatkwoWtDoRgKwwPad3z549ev3117V+/XpJUrdu3TRixAjde++96a/p0KGDfHx81KlTJ+clBQDAYseOSY89Jt11lzGPt0gRqxMByCrTpfeBBx5QhQoVNHHiRA0dOlQVKlTI9HV33nmnHnzwwRwHBADAHfz6q9S6tVS6tBQbK5UsaXUiAGaYLr0rV65Ujx49VPAWP8+5++679fHHH2c7GAAA7uLUKalNG+PUtQ8/lG6/3epEAMwyvac3ISFBf/75Z6b3fvvtN82YMSPHoQAAcBdnzkiBgUbx/fBDqWpVqxMByA7TpXf69On65ZdfMr3366+/atq0aTnNBACAW7h4UerUSfr+e2NEWa1aVicCkF2mtzfczLlz52657QEAgLzg6lWpRw/p88+luDipYUOrEwHIiSyV3q+//lpff/21HA6HJGnr1q06evRohtdcuHBBq1evVo0aNZyfEgCAXGS3SwMGSFu3Su+9Jz38sNWJAORUlkrvpk2bMuzVDQ8Pz/R1RYoU0fLly52TDAAACzgc0ujR0jvvSGvWGPt5AeR9WSq9gwcPVlBQkCTp/vvv14oVK1S3bt0MrylcuLBq1KihokWLOj8lAAC5JDzcOFZ4yRJjewMAz5Cl0lupUiVVqlRJkrRjxw41btxYJUqUcGkwAABy26JF0tSp0uzZ0tChVqcB4EymH2Rr2bKlC2IAAGCtd96RRo6Uxo6VJkywOg0AZ8tS6e3fv7+mTJmi6tWrKzQ0VF5eXjd9Pft6AQB5yfvvS6GhxsNrL74o3eJfcwDyoCyV3h07dmjkyJGSpI8//viGpdfhcNyyEAMA4E4++kjq1k164gnpjTcovICnylLp/emnnzL9NQAAednu3VLHjtIjj0irV0ve3lYnAuAqpk9kAwDAE+zbJ7VvL91/vxQdLRUubHUiAK5E6QUA5Dvffiu1bSvdfbexn7dIEasTAXC1LG1vqF69ury8vNJPZMvMtfteXl5KSEhwWkAAAJzphx+kNm2kO++Utm2TmMAJ5A9ZKr0tWrTI8hvyIBsAwF399JP06KOSr68UFyeVLm11IgC5JUulNyIiwsUxAABwrV9/lVq1km67Tdq+XSpXzupEAHKT6cMpAADIa/74Q2rdWkpLk3bulCpWtDoRgNyWpdKbmJioO+64Q4UKFVJiYuItX1+tWrUcBwMAwBlSUow9vKdPS/HxEv+KAvKnLJVePz8/7dmzR/fff7/8/Pxu+lovLy+lpaU5IxsAADmSmioFBEhJSdKuXVLNmlYnAmCVLJXe5cuX66677kr/NQAA7u7cOSkoSPrxR2nHDmM8GYD8K0ult1+/fpn+GgAAd3TxonGs8IEDxkNrDRtanQiA1XJ0OIXD4dCZM2duOr8XAIDcdOWK1K2b9Mkn0pYtUtOmVicC4A6yVXr37Nmjxx57TEWKFFGpUqVUtGhRPfbYY/r888+dnQ8AgCxLS5P69JFiY6VNm6SWLa1OBMBdmB5ZtmPHDrVr104lSpRQjx49dMcdd+jkyZPavHmzWrZsqa1bt6p169auyAoAwA3Z7dLAgdKGDdL69cYDbABwjenSO378eN1zzz366KOPVLx48fTrZ86c0aOPPqoJEyZo3759Tg0JAMDNOBzSiBHSypXS6tXGfl4A+DvT2xsOHTqk5557LkPhlaQSJUpo/PjxOnTokNPCAQBwKw6HNGGC9Prr0ptvSj17Wp0IgDsyXXpvv/12eXt7Z3rP29tb5cuXz3EoAACyKjxcevFF6ZVXjO0NAJAZ06V3yJAhWrBggS5fvpzh+qVLlzR//nwNGjTIaeEAALiZl1+Wpk6VZs82tjcAwI1kaU/vvHnz5OXlJUkqVKiQfvrpJ9WoUUPBwcG644479Ntvvyk6Olre3t4qUqSISwMDACBJCxdK48ZJkyZJEydanQaAu/NyZGHIboEC5haE7XZ7tgPlhgMHDqhx48bav3+/GjVqZHUcAIBJr75qrOyOHy+98IL033UZAB7E2X0tSyu9CQkJOf5CAAA4w+LFRuEdO5bCCyDrslR6/fz8XBwDAIBbe+MN6amnpNGjjYfXKLwAsipHxxADAJBb3npLGjpUGjlSmjePwgvAHNOHU0jSrl27tGjRIh09elQXLlxIv+5wOOTl5cV2CACAUy1fLg0eLD39tLRgAYUXgHmmV3p3796tRx99VKmpqTpy5Ijq1KmjSpUq6cSJE/Lx8VGLFi1ckRMAkE+tXGnM3x02TFq0iMILIHtMl96pU6cqNDRU27ZtkySFh4dr9+7d+uqrr3Tu3DkFBwc7PSQAIH9avVoKDTVK72uvUXgBZF+2jiEODg5On9t7bTxZgwYNNGXKFM2YMcO5CQEA+dKaNdKTT0r9+0tLl0omp2cCQAam/xFy/vx5FStWTN7e3ipcuLBOnTqVfq927do6fPiwUwMCAPKftWulPn2kvn2lN9+k8ALIOdP/GKlWrZqSkpIkSf7+/tqyZUv6vfj4ePn6+jovHQAg31m/XurVy/hYtozCC8A5TE9vaNGiheLj49WjRw8NHjxYw4cP19GjR1WoUCHFxcXp2WefdUVOAEA+EB0thYRIPXpIK1ZI3t5WJwLgKUyX3hkzZiglJUWSNHToUJ0/f16rV69WgQIFNGXKFE2aNMnpIQEAnu/dd6Xu3aWuXaWICAovAOcy/UOjcuXKqVatWum/HzNmjA4cOKB9+/Zp2rRpKliwYLaCnD17VqNGjVLlypVVpEgRNWzYUGvXrr3l523cuFHdunVT9erVVbRoUVWvXl29e/fWsWPHspUDAJD7Nm+WunWTgoOld96RfLI1RR4AbixH/1hJSkpScnKyfH19ValSpRwFCQ4O1r59+zR37lzVqlVLkZGRCgkJkd1uV0hIyA0/76WXXlL58uUVFhammjVrKjExUbNnz1ajRo20Z88e3X333TnKBQBwra1bpc6dpY4djRFlFF4ArpCtf7Rs3LhREydOzLCaWrNmTc2aNUtdu3Y1/X4xMTHavn27bDabunfvLsnYO3zixAmNGzdO3bt3V4EbPMmwefNm3X777RmutWrVSn5+flqwYIHeeust03kAALkjNtZY3Q0Kkmw2KZs/LASAWzK9vWHt2rXq2rWrfHx8FBYWpsWLFyssLEze3t7q0aOHoqKiTIfYtGmTSpQocV1hDg0NVVJSkvbu3XvDz/1n4ZWkihUrqnLlyvrll19MZwEA5I64OOnxx6WAACkqisILwLWy9SBbQECAtmzZkmH1dcqUKQoKClJ4eLh69Ohh6j0PHTokf3//61Zz69evL0k6fPiwmjVrluX3S0hIUGJiIqfDAYCb2r5d6tRJat1aWrdOKlTI6kQAPJ3pld7jx49r+PDh1xVUb29vDR8+PFsPkCUnJ6ts2bLXXb92LTk5OcvvdfXqVfXv318lSpTQ6NGjTWcBALjWtm3GdoZWraSNG6XCha1OBCA/ML3SW61aNZ0/fz7Te+fPn1e1atVyHCq77Ha7BgwYoM8++0wbN25U5cqVLcsCALje++8bI8natTNOXaPwAsgtpld6n332WYWHh+vPP//McP2PP/5QeHh4tg6n8PX1zXQ199o84Kyc8uZwODRo0CBFRkYqIiJCHTp0MJ0DAOA6Gzf+b0rD+vUUXgC5K0srvc8884y8vLwkGeUyNTVV1atX16OPPqo77rhDJ0+e1EcffSRfX1999913pkM0aNBANptNdrs9w7aJb7/9VpJUr169m36+w+HQwIEDFRERoeXLl6tnz55Z+rqjR49WqVKlMlwLCQm56Yg0AIB5NpvUp49x+MTKlYwlA5CRzWaTzWbLcO306dNO/RpeDofDcasX3Whc2I3Y7XZTr4+NjVVgYKCioqLUrVu39OsBAQE6fPiwEhMT00v3P11b4V2xYoXefPNNDRgw4JZf78CBA2rcuLH279+vRo0amcoKADBn1SopNNQovW+/zUlrALLG2X0tS3/XNltizQoICFCbNm00bNgwpaamqkaNGrLZbIqLi1NkZGR64R0wYIBWrVqlhIQEVa1aVZI0YsQILV++XP3791e9evW0Z8+e9PctXLiwGjZs6NLsAIAbe/ttadAgacAA6Y03JJNrKADgNG7zA6bo6GhNmjRJYWFhSklJkb+//3Urv3a7XXa7XX9fnN6yZYu8vLy0fPlyLV++PMN7+vn5KSEhIdf+DACA/1myRBo+3Ph49VUKLwBrZWl7Q2a2b9+uHTt2KDk5WeXKldOjjz6qVq1aOTufS7C9AQBc65VXpFGjjI/586Ub7FADgBuyZHvD312+fFnBwcGKiYkx3sDHR1evXtULL7yg9u3bKzo6WgU5VgcA8q2XXpKee04aP1564QUKLwD3YPqHTTNmzFBcXJzmzp2r33//XZcvX9bJkyf14osvKi4uTtOnT3dFTgBAHjBzplF4p0yh8AJwL6ZXem02myZOnKhx48alXytfvrzGjh2rs2fPatWqVZo5c6ZTQwIA3JvDIU2dKoWHGx+TJ1udCAAyMr3S+8svv6h58+aZ3nvooYf0yy+/5DgUACDvcDikiRONsvviixReAO7JdOktV66cvvnmm0zvHTp0SLfffnuOQwEA8gaHQxozRpo7V1q4UPrbDwEBwK2YLr2dOnVSWFiYNm7cmOH6u+++q6lTp6pTp05OCwcAcF92u/T000bZXbxYGjnS6kQAcGOm9/TOnDlTn376qbp27arixYunH0N89uxZNWjQQLNmzXJFTgCAG7HbpSFDjMMnli0zDp8AAHdmuvSWLVtWe/fu1cqVK9Pn9DZs2FCtW7dW3759VbhwYVfkBAC4ibQ0o+S+844UESH17Wt1IgC4NVOl9/z582rdurVmzJihIUOGaMiQIa7KBQBwQ1evSk8+Ka1dK61eLYWEWJ0IALLGVOktWrSoDh06JB8ftzm9GACQSy5elHr0kLZulaKipC5drE4EAFln+kG2pk2b6osvvnBFFgCAmzpzRmrfXoqLk95/n8ILIO8xvWQ7f/58dezYURUqVFDnzp1VvHhxV+QCALiJ5GSpXTvp+++lDz6QHn7Y6kQAYJ7pld5mzZrp119/VWhoqEqWLKkSJUqoRIkS6b8uWbKkK3ICACzw669S8+bSTz9JO3dSeAHkXaZXejt37nzT+14ctA4AHuH4calNG+PhtU8+kWrXtjoRAGSf6dIbERHhghgAAHdy6JBReEuWNFZ4q1WzOhEA5EyWS++FCxf07rvv6sSJE7r99tvVsWNHjhwGAA+0Z48UGCjdeaexh7d8easTAUDOZan0JiUl6eGHH9a///3v9GtjxoxRbGysmjVr5rJwAIDctX279PjjUsOG0ubNUunSVicCAOfI0oNskydPVlJSkqZMmaItW7Zo4cKFKly4sIYNG+bqfACAXLJpkzGW7OGHjRVeCi8AT5Klld4PP/xQEydOVFhYWPq1GjVqqEOHDvr9999VoUIFlwUEALheRIRxtHDXrtKqVVKhQlYnAgDnytJK78mTJ9WiRYsM1679/vfff3d+KgBArnnlFSk0VBo4UIqMpPAC8ExZKr1paWkqUqRIhmu33XabJOnq1avOTwUAcDmHQ5o2TRo1Sho/Xlq6VPL2tjoVALhGlqc3HD16VD4+/3v5tbJ75MiR617bqFEjJ0QDALiK3W6U3VdflV54QZowwepEAOBaWS69/fr1y/R6nz59Mvzey8tLaWlpOQoFAHCdq1eN/bvvvCMtWSINHWp1IgBwvSyV3uXLl7s6BwAgF1y8KIWESFu2SGvWSD16WJ0IAHJHlkrvjVZ5AQB5x5kzxgzezz6T3nvPOIACAPIL08cQAwDynj//lIKCpKNHpbg4YxYvAOQnlF4A8HDHj0sBAcZK78cfSzxrDCA/ytLIMgBA3vTll1KzZlKBAtLnn1N4AeRflF4A8FBbt0otW0o1a0qffipVr251IgCwDqUXADzQ229LnTpJbdpI27dL5cpZnQgArEXpBQAPcu2UtYEDpcGDpY0bpaJFrU4FANbjQTYA8BBXrxoHTbz9tjR7tnHKmpeX1akAwD1QegHAA5w9K3XvbowjW7lS6tvX6kQA4F4ovQCQx/3xh9S+vTGDd+tW6bHHrE4EAO6H0gsAediPPxozeM+fl+LjpYYNrU4EAO6JB9kAII/au1d64AGpYEFjBi+FFwBujNILAHnQli3SI49ItWoZM3j9/KxOBADujdILAHnMm28aM3gDAowZvL6+VicCAPdH6QWAPMLhkMLCpCFDpGHDpPXrpSJFrE4FAHkDD7IBQB5w5Ypx2EREhDRnjvTcc8zgBQAzKL0A4ObOnpW6dJF27JBWr5Z69bI6EQDkPZReAHBjP/8sdewoHT8uxcRIrVtbnQgA8iZKLwC4qS++MB5YK1RI2r1batDA6kQAkHfxIBsAuKGoKKlFC6l6daP8UngBIGcovQDgRhwOado0KSRE6tzZ2MdboYLVqQAg72N7AwC4iQsXpH79pHXrpFmzpIkTmdAAAM5C6QUAN/Dbb8b+3UOHpA0bjFVeAIDzUHoBwGJffWVMaLDbjQfWGjWyOhEAeB729AKAhTZtkh56yNi3++WXFF4AcBVKLwBYwOEwTlYLDpYCA6X4eKlSJatTAYDnovQCQC67dMl4YG3iRGnKFGntWqloUatTAYBnY08vAOSiP/+UnnhC2rdPioyUeva0OhEA5A+UXgDIJYcOSR06GKPJdu6Umja1OhEA5B9sbwCAXBATIz3wgFSypHHCGoUXAHIXpRcAXMjhkBYsMFZ4H3lE+vRTqVo1q1MBQP5D6QUAF7lyRRoyRBozRnr2WSk6Wipe3OpUAJA/sacXAFzgt9+krl2NrQzLl0uhoVYnAoD8jdILAE62e7dReAsUkHbtkpo1szoRAIDtDQDgJA6HtGiRsXe3Vi1p/34KLwC4C0ovADjBuXNS797SyJHSiBHS9u3SHXdYnQoAcA3bGwAgh44dM44TTkiQoqKk7t2tTgQA+CdWegEgB7Zske69V7p4Udq7l8ILAO6K0gsA2WC3S1OnGvN3W7aUvvxSqlvX6lQAgBthewMAmJSSYuzfjY2VZs2SJkwwJjUAANwXpff/27v3uCqrfI/jnw3KNUVBFI8XMMwkAwSPYTaGaIpp1qipB6+RjaUeU2fy0uQldJz0lFlOMpWWl1K8pTOmYoaXLE1NfXnt8jKvmaYiphB4g+f88Qw7t4AgbNiw+b5fr/2S/ezn2fv3LFf2dbn2WiIid2HfPnP+7uXLkJwMsbGOrkhERIpCYxMiIkX00UfmEmQ1apjLkSnwiohUHAq9IiKFuH4d/vd/YcAA+J//gW3bICjI0VWJiMjdKDehNyMjg5EjR1KvXj08PT2JiIhg6dKlhV53+vRpRo4cSXR0NDVq1MDFxYUFCxaUQcUiUhmcOWNuNvH++/DPf5pbCnt6OroqERG5W+Um9Hbv3p2FCxfy6quvsn79eodrJMQAACAASURBVFq2bElcXBxJSUl3vO7HH39k8eLFeHh40KVLFwAsFktZlCwiTm7rVoiMhJMn4csv4YUXQH+8iIhUTOXii2zr1q0jJSWFpKQkev9nkcvo6GhOnjzJ6NGj6d27Ny4FfDU6Ojqa8+fPA7Bnz55CQ7KISGEMA95+G156Cdq0gaVLoXZtR1clIiIlUS5GeletWkW1atXo2bOnzfH4+HjOnDnDzp07C7z21lFdwzBKrUYRqRwuXoQ//hFGjYKRI+HzzxV4RUScQbkIvYcOHSIkJCTPaG5oaCgAhw8fdkRZIlLJfPEFhIebX1RbvRreeAOqlIt/DxMRkZIqF6H34sWL+Pr65jmee+zixYtlXZKIVCI3b8LEieYX1u67D/bvN3daExER56ExDBGp1E6dgj59YMcOmDwZXn4ZXF0dXZWIiNhbuQi9fn5++Y7mpqWlWV8XEbG3Tz6B556D6tXNqQ2PPOLoikREpLSUi9AbFhZGUlISOTk5NvN6Dx48CMCDDz5YKp87atQofHx8bI7FxcURFxdXKp8nIuVDVpb5RbX33oMePWDOHKhZ09FViYhUXklJSXlW4Lp8+bJdP6NchN5u3boxZ84cVqxYQa9evazH58+fT7169YiKiiqVz505cyaRkZGl8t4iUj4dOmTuqnb0qBl6//Qnrb0rIuJo+Q067t27lxYtWtjtM8pF6O3UqRMdOnRgyJAhXLlyheDgYJKSktiwYQOLFi2yLks2aNAgFi5cyLFjx2jQoIH1+hUrVgBw7NgxAL755hu8vLwAePrpp8v4bkSkPDIMM+SOGgWNG8Pu3dCsmaOrEhGRslIuQi/AypUreeWVV5g4cSJpaWmEhISwZMkSm5HfnJwccnJy8qzHe+s5FouF2bNnM3v2bCwWC9nZ2WV2DyJSPqWlmSO6K1fC0KHmUmTaSlhEpHKxGJVwR4fc4fI9e/ZoeoOIk/vyS+jbFzIy4IMPoFs3R1ckIiJFYe+8Vi7W6RURsbfsbHMJsrZtITAQ9u1T4BURqczKzfQGERF7OX3aHN396iuYMAHGj9fOaiIilZ3+NyAiTmXVKnPtXU9P2LQJoqMdXZGIiJQHmt4gIk4hLQ369YPu3aFNG3MrYQVeERHJpZFeEanwVq+G55+Hq1dhwQLo319r74qIiC2N9IpIhXXpEgwYAE89BZGR5sYTAwYo8IqISF4a6RWRCmnNGhg8GDIzYd48GDhQYVdERAqmkV4RqVB+/RWeeQa6doXwcHN095lnFHhFROTONNIrIhVGcrK5s1p6urnRRHy8wq6IiBSNRnpFpNy7fBmefRY6d4ZmzczR3WefVeAVEZGi00iviJRrn31mrrt7+TLMmQODBinsiojI3dNIr4iUS5cvm2G3Uydo2tQc3X3uOQVeEREpHo30iki58/nn5ojupUvw3nvmPF6FXRERKQmN9IpIuXHlirnJRMeO0KQJHDxoLkumwCsiIiWlkV4RKRfWrzcD78WL8M9/mj8r7IqIiL1opFdEHOqnn+Dpp+Hxx6FxY3N094UXFHhFRMS+FHpFxCFu3IDXX4eQENi2DRYvhpQUaNTI0ZWJiIgz0vQGESlzW7fC0KHw3XcwfDgkJICPj6OrEhERZ6aRXhEpM+fOwYABEB0N1arBnj3w1lsKvCIiUvoUekWk1GVnQ2Ii3H8/rF0Lc+eaUxqaN3d0ZSIiUlko9IpIqdq1C6KiYNgw6NkTfvjBXIPXRX/6iIhIGdL/dkSkVKSlwZAh0KqVOdK7fbu5jXCtWo6uTEREKiN9kU1E7ConBxYuhNGj4fp1ePttM/xW0Z82IiLiQBrpFRG7OXjQ/JJafDzExsL335urMyjwioiIoyn0ikiJpafDX/4CERGQmgqbNsHHH0Pduo6uTERExKTQKyLFlp0N8+ZB06bw7rswdSrs3w8xMY6uTERExJZCr4jcNcOAdevMJceefRYeeQS+/RbGjgU3N0dXJyIikpdCr4jcld27oX176NIF/Pxg505YtgwCAx1dmYiISMEUekWkSI4dg7g4aNkSzp+HNWtg82Z46CFHVyYiIlI4hV4RuaPUVBgxwpy3u3UrfPCBOW+3SxewWBxdnYiISNFoISERyVdmJrz1Fkyfbj5PSDDDr5eXY+sSEREpDoVeEbGRnQ3z58PEiXDhAgwdCuPHayc1ERGp2DS9QUQAc0WGNWsgPByeew4efdTcXOKttxR4RUSk4lPoFRF27YK2baFrV/D3h2++gaQkuPdeR1cmIiJiHwq9IpXYjz9Cr14QFQVpabB2rbmb2n//t6MrExERsS+FXpFK6NtvoX9/c0WG7dvhww9h3z7o3FkrMoiIiHNS6BWpRPbsgR49oFkz2LIF3nwTjhyB+HhwdXV0dSIiIqVHoVekEvjyS3j8cXPawoEDMHcuHD0KL74Inp6Ork5ERKT0KfSKOCnDgA0bIDraXInh9GlYvBi++w4GDQI3N0dXKCIiUnYUekWcTE4O/Otf5vbAsbGQlWU+37/f3Ea4ilbnFhGRSkihV8RJ3LxpjuSGhUG3buDtbY707twJTz0FLvqvXUREKjH9b1Ckgrt+3Zyj27Qp9O0LDRvCV1+ZX1Tr0EGrMYiIiIC2IRapsDIzzbD7+uvw88/QvTssWwaRkY6uTEREpPxR6BWpYM6ehTlz4J13zA0l+vSBl1+GkBBHVyYiIlJ+KfSKVACGYS47Nns2rFxprrwwYACMHq2tgkVERIpCoVekHEtPh48/hsREOHQImjSBN96AgQOhRg1HVyciIlJxKPSKlEOHD8M//wkLF8Jvv5mrL8ycCe3b64tpIiIixaHQK1JO3LhhrqebmGiuvFCnDowYAYMHQ4MGjq5ORESkYlPoFXGwM2fg/ffNx9mz0KYNJCWZqzFo1zQRERH7UOgVcQDDMEdzExNh1Srw8ID+/WHIEHNzCREREbEvhV6RMpSWZu6alpgI331nLjP21lvmSgzVqzu6OhEREeel0CtSyjIz4dNPzbCbnAw5OeY2wbNnQ9u2+mKaiIhIWVDoFSkFN25ASooZdFetMldgiIoylxvr1QsCAhxdoYiISOWi0CtiJzk58PXXZtBdtgxSU6FpUxg3DuLiIDjY0RWKiIhUXgq9IiV08KAZdJOS4ORJqF8f4uPN7YHDwzV9QUREpDxQ6BUphhMnzJC7eLG5U5qvL/TsaQbdP/wBXFwcXaGIiIjcSqFXpIjOn4fly82gu307eHmZO6W99hp07Kg1dUVERMozhV6RAuTkwL59sG6d+di50xzBjY2FRYvgySfhnnscXaWIiIgUhUKvyC0uX4bPPzdDbnIy/PILVKtmjuS+/745slurlqOrFBERkbul0CuVmmHA4cO/j+Zu2wY3b0KzZuYOaZ07Q+vWmrogIiJS0Sn0SqXz22+waROsXWsG3Z9+Ak9PaN8eZs0yg25goKOrFBEREXtS6JVK4ciR30dzt2yB69ehcWNzZ7TOnSE6Gjw8HF2liIiIlBaFXnE62dnm2rnbt5vTFbZtM9fPdXMzt/39v/8zg+599zm6UhERESkrCr1S4aWnw44dZrjdvt38OT0dqlaFyEjo3t0Mu+3bg7e3o6sVERERR1DolQrFMMxR21tHcQ8eNJcX8/U1v3T28svwyCPQsqU5V1dEREREoVfKtRs3zLVyc0dxt22DM2fM15o0McPt8OFm2L3/fu2EJiIiIvlT6JVy4/x5c9T20CHzcfAgHDgAWVng7m6O3PbrZwbd1q21Xq6IiIgUXbkIvRkZGYwfP57ly5eTlpZG06ZNGTduHL179y702vPnzzNmzBjWrl1LZmYm4eHh/O1vf6Ndu3ZlULkUR3r678E2N9weOgQXLpivu7vDAw/Agw9Cz55mwI2MNI+LiIiIFEe5CL3du3dn9+7dTJ8+nSZNmrBo0SLi4uLIyckhLi6uwOuuXbtG+/btuXLlCrNmzaJ27dq88847dOrUiZSUFB599NEyvAu53bVr8P33ecPtyZPm6y4u5goKoaEwbJgZckNDITgYXF0dW7uIiIg4F4eH3nXr1pGSkkJSUpJ1ZDc6OpqTJ08yevRoevfujUsBEzU/+OADDh8+zNdff01UVBQAbdu2JTw8nDFjxrBjx44yu4/KKCcHzp0zQ+yJE+avuT8fPw4//JCEYZh/aWnY0Ay1vXubwfbBB6FpU62NWxJJSUl3/EuhlJzauHSpfUuf2rh0qX0rFod/7WfVqlVUq1aNnj172hyPj4/nzJkz7Ny5847XNm3a1Bp4AVxdXenXrx+7du3i7NmzpVZ3ZXDzphlit26Fjz6CKVPgueegQwdzhNbTE/7rv+DhhyEuDqZNM79sVrUqdOwIoaFJbNsGv/5qvs/atTB9ujkvt3lzBd6SSkpKcnQJTk9tXLrUvqVPbVy61L4Vi8NHeg8dOkRISEie0dzQ0FAADh8+zMMPP1zgtdHR0XmO33pt3bp17VxxxXbjBly8CKmp+T8uXIDTp82Qevq0udFDLn9/CAoyt+h96inz19zngYHg42P7WU8+ac7HFREREXE0h4feixcv0rhx4zzHfX19ra8XJC0tzXre3V5bUeXkmKsZ/Pab+cjM/P3ny5cLDrO5j8uX876nqyv4+ZmrIdSqBfXqmWE1N9AGBZnTE7y8yvpuRUREROzD4aHXkb791gyRhmE+wPbXgn6+9Vh2tjkN4MYN89fbH/kdv/3Y9eu24TW/QJv7yMoq/L58fX8PsLVqQbNmts9vf/j4aH1bERERcW4OD71+fn75jsimpaVZX7/Ttbnn3c21Wf9Jjv37f3fX9RaHxWKOplapYv6a+8h9XqWKOb/V0/P3h4cH1Kxp+/zWX29/eHiYW+xWr26+X1Gkp5uP0nL58mX27t1beh9Qyal9S5/auHSpfUuf2rh0qX1L13ffmTktqygjfkXg8NAbFhZGUlISOTk5NvN6Dx48CMCDDz5Y4LWhoaEcOHAgz/HCrj1x4sR/fupXvKLvkmH8Pqpb2bRo0cLRJTg1tW/pUxuXLrVv6VMbly61b+k7ceIEjzzySInfx2IYuf9g7xjr16+nc+fOLFmyhF69elmPd+rUicOHD3Pq1CksFku+17777rsMHTqUHTt28NBDDwFw8+ZNmjdvTvXq1dm+fXu+16WmpvLZZ58RFBSEp6en/W9KREREREokKyuLEydOEBsbSy07bMPq8NALEBsba92cIjg4mKSkJObOnWvdpAJg0KBBLFy4kGPHjtGgQQMArl+/TosWLbhy5QrTpk3D39+fxMRE1q5dS0pKCm3atHHkbYmIiIhIOeHw6Q0AK1eu5JVXXmHixImkpaUREhKSZ+Q3JyeHnJwcbs3obm5ubNy4kTFjxjB8+HAyMzOJiIggOTlZgVdERERErMrFSK+IiIiISGmqVAtVZWRkMHLkSOrVq4enpycREREsXbrU0WU5jS1btuDi4pLvY9euXY4ur0LJyMhgzJgxdOzYEX9/f1xcXEhISMj33L179/LYY49RrVo1atasSY8ePTh+/HgZV1zxFLWNn3nmmXz79AMPPOCAqiuOjRs3MnDgQJo0aYK3tzf169fnj3/8Y77fdFcfLp6itrH6cPHs27ePLl26EBgYiJeXF35+frRu3ZpFixblOVd9uHiK2sb26sPlYnpDWenevbt17nCTJk2sc4ZzcnK0d7Ydvfbaa8TExNgca9asmYOqqZhSU1OZM2cOzZs3p1u3bsydOzffL3R+//33tG3blsjISJYvX05WVhYTJ06kTZs27Nu3zy4T/51VUdsYwNPTk82bN+c5JgV77733uHDhAqNGjaJZs2ZcuHCBGTNm0KpVKz777DPrnxHqw8VX1DYG9eHiuHz5Mg0bNqRv377Uq1ePjIwMFi1aRP/+/Tlx4gSvvPIKoD5cEkVtY7BTHzYqibVr1xoWi8VYsmSJzfGOHTsa9erVM7Kzsx1UmfPYvHmzYbFYjE8++cTRpTiV1NRUw2KxGAkJCXle69mzp1G7dm0jPT3deuzkyZOGm5ubMXbs2LIss0K7UxsPHDjQqFatmgOqqtjOnTuX51hGRoYREBBgPPbYY9Zj6sPFV9Q2Vh+2r1atWhkNGza0Plcftr/b29hefbjSTG9YtWoV1apVo2fPnjbH4+PjOXPmDDt37nRQZc7H0DRxuyqoPW/evMmaNWvo0aMH99xzj/V4w4YNiYmJYdWqVWVVYoVXWJ9Vn757tWvXznPM29ubkJAQTp8+DagPl1RR2jiX+rD9+Pn5UeU/u0CpD5eOW9s4lz36cKUJvYcOHSIkJMRmAwwwN7gAOHz4sCPKckrDhg2jatWq+Pj40KlTJ7Zt2+bokpzS0aNHuXr1KmFhYXleCw0N5ccff+T69esOqMz5ZGVlUbduXapUqUKDBg0YPnw4ly5dcnRZFU7u7lW5053Uh+3v9jbOpT5cfIZhcPPmTS5cuEBiYiKfffYZL730EqA+bC93auNc9ujDlWZO78WLF2ncuHGe476+vtbXpWRq1KjByJEjadu2LX5+fhw5coTXX3+dtm3bsnbtWjp27OjoEp1Kbp/N7cO38vX1xTAMLl26RJ06dcq6NKfSvHlzIiIirDs8btmyhZkzZ7Jx40a++eYbvL29HVxhxTFs2DCysrKs8/TUh+3v9jYG9eGSGjJkCO+//z4Arq6uvPHGGwwZMgRQH7aXO7Ux2K8PV5rQK6WvefPmNG/e3Pr8kUceoVu3boSGhjJ27FiFXqmQRo4cafO8ffv2RERE8PTTTzN37lxGjBjhoMoqlgkTJrB48WLeeecdIiIiHF2OUyqojdWHS+aVV15h8ODBnD9/ntWrV/PnP/+Zq1evMnbsWEeX5jQKa2N79eFKE3r9/PzyHc1NS0uzvi725+PjQ5cuXXjvvfe4du0a7u7uji7JaeT22dw+fKu0tDQsFgs1a9Ys67IqhW7duuHt7a3vAhRRQkICU6dO5e9//ztDhw61Hlcftp+C2rgg6sNF16BBA+tOsJ06dQLMv2AMGjRIfdhOCmrjZ599Fn9//3yvKU4frjRzesPCwvjuu+/IycmxOX7w4EEA65C5lJ6CloOS4gkODsbT05MDBw7kee3gwYPcd999uLm5OaAy52cYRp4/SyR/CQkJ1se4ceNsXlMfto87tXFB1IeLr2XLlty8eZNjx46pD5eS3Da+01rHxenDlSb0duvWjYyMDFasWGFzfP78+dSrV4+oqCgHVebcLl26xKeffkpERIT+w7ezKlWq0LVrV1auXElGRob1+KlTp9i8eTPdu3d3YHXObcWKFWRlZfHwww87upRybcqUKSQkJDBhwgQmTJiQ53X14ZIrrI0Loj5cfJs3b8bV1ZXg4GD14VJyaxsXpDh9uFJtQxwbG2vdnCI4OJikpCTmzp1r3aRCSqZv3740atSIyMhIfH19OXLkCDNmzOD48eMkJyfTrl07R5dYoSQnJ/Pbb7+Rnp7OoEGD6Nmzp3XJvS5duuDp6ckPP/xAy5YtiYyMZNy4cdZF0X/99Vf27dunaTuFKKyNz58/T79+/ejTpw/33nsvhmHwxRdf8Pbbb9O4cWN27typBf4LMGPGDEaPHk2nTp2YNGlSnuWGWrVqBaA+XAJFaeOTJ0+qDxfT4MGD8fHxoWXLltSpU4fU1FSWL1/OsmXLGDNmDNOmTQPUh0uiKG1s1z5c4pV+K5CMjAxjxIgRRt26dQ13d3ejefPmxtKlSx1dltOYNm2aERERYdSoUcOoUqWKUbt2baNHjx7G7t27HV1ahRQUFGRYLBbDYrEYLi4uNj+fPHnSet6ePXuMxx57zPD29jZ8fHyM7t27G8eOHXNg5RVHYW186dIlo3v37kajRo0MLy8vw93d3bj//vuNcePGGVeuXHF0+eVa27Ztbdr01oeLi4vNuerDxVOUNlYfLr558+YZjz76qOHv729UrVrVqFmzphETE2MsWrQoz7nqw8VTlDa2Zx+uVCO9IiIiIlI5VZo5vSIiIiJSeSn0ioiIiIjTU+gVEREREaen0CsiIiIiTk+hV0REREScnkKviIiIiDg9hV4RERERcXoKvSIiIiLi9BR6RURERMTpKfSKiEO5uLgU6bF161ZHl+r01q1bR0JCQr6vBQUF8eyzz1qfnzhxAhcXFxYsWFBW5dnV/PnzcXFxYe/evY4uRUTKSBVHFyAilduOHTusPxuGwZQpU9iyZQubNm2yOS8kJKSsS6t01q1bR2JiIpMmTcrz2r///W+qV6+e57jFYimL0kRESkyhV0Qc6qGHHrJ5XqtWLSwWS57jt8vKysLT07M0SytzhmFw7do1PDw8HFZDQSE2PDy8jCspH+0hIs5D0xtEpNxr27YtoaGhbN26ldatW+Pt7c2gQYMAc3pEfv8kHxQURHx8vM2xX375heeff54GDRrg7u7Ovffey+TJk8nOzi60hqCgILp27cqqVasICwvD09OT4OBg/vGPf+Q598qVK7z00ks0atQId3d36tevz6hRo8jMzLQ5z8XFheHDh/Puu+8SEhKCh4cHCxcuBOD7778nLi6OgIAAPDw8CAwMZODAgVy/fv2u7id3GsKMGTN48803adSoEdWqVaN169bs3LnTet4zzzxDYmIihmHYTCs5depUge2ZnyNHjtCnTx/q1KmDh4cHDzzwAImJiYVeV1h7JCQkEBUVhZ+fHz4+PrRo0YIPP/wwz3vk/j6tX7+eyMhIvLy8CAkJYd68eYV+/tmzZ2nRogVNmjTh6NGjRapZRCoOjfSKSLlnsVg4e/Ys/fv3Z+zYsUybNg0XFxeb1/O75tbjv/zyCw899BBVqlRh0qRJBAcHs337dv72t79x4sSJfAPU7e+3b98+Ro0aRUJCAgEBAXz88ceMGDGC69ev85e//AWAzMxMoqOjOXPmDH/9618JCwvj0KFDTJw4kYMHD5KSkmLzvv/617/46quvePXVVwkICMDf35/9+/fzhz/8gdq1azNlyhTuu+8+zpw5w6effsr169dxc3O76/uZPXs2ISEhzJo1C8MwmDBhAp07d+b48eNUr16diRMnkpmZyYoVK2ymnAQEBOTbnvn59ttvad26NUFBQbz55psEBASwfv16XnzxRVJTU5k4ceIdr8+vPWrXrg2Y4X3w4MEEBgbi4uLC119/zYsvvsjPP//MhAkTbH6f9u/fz0svvcTLL79MnTp1mDNnDoMGDaJx48a0adMm3889dOgQnTt3JjAwkM8//xxfX99CaxWRCsYQESlHBg4caNxzzz02x6Kjow2LxWJs2bIlz/kWi8VISEjIczwoKMiIj4+3Pn/++eeN6tWrGz/99JPNeTNmzDAsFovx7bff3rGuwMBAw9XV1Thw4IDN8Y4dOxo+Pj5GVlaWYRiG8dprrxmurq7Gnj17bM775JNPDIvFYiQnJ9vUXrNmTePXX3+1Obddu3aGr6+vkZqaWmA9Rb2f48ePGxaLxQgPDzdycnKs533zzTeGxWIxlixZYj02bNgww2Kx5Pt5t7dn7vsuWLDAeiw2NtZo2LChkZ6ebnPt8OHDDU9PT+PSpUsF3o9hFNwet8vOzjZu3LhhTJ482ahVq5bNa4GBgYaXl5dNu1y9etXw8/MzXnjhBeuxefPmGRaLxdi9e7exYcMGo3r16kavXr2Ma9eu3fGzRaTi0vQGEakQfH19iY6OLvb1a9asISYmhrp163Lz5k3ro1OnTgB88cUXhb5Hs2bNCA0NtTkWFxfHlStXrKsArFmzhtDQUMLDw20+p2PHjlgsFrZs2WJzfbt27fDx8bE+z8zM5IsvvqBXr174+fnZ7X66dOliM1Kbex+50xdK6urVq2zcuJFu3brh4eFhU9Pjjz/O1atXbUaQC3J7e+TatGkTjz32GDVq1KBKlSq4ubkxadIk0tLSuHDhgs25zZs3p379+tbn7u7uNGnSJN97nTdvHl26dOH5559n6dKluLm5FePuRaQi0PQGEakQ6tate1fnG4Zh8/zcuXOsXr2aqlWr5jnXYrFw8eLFQt8z95/68zuWe/25c+c4evRokT/n9vu6dOkSOTk5NqEtP3d7P7cHaHd3d8D8QqA9XLx4kezsbGbNmsWsWbOKVFN+8vt93rVrF7GxscTExDB37lzq16+Pm5sbq1atYurUqXnuIb+/LLi5ueV7r8uWLcPb29tmOTYRcU4KvSJSIRQ0n9Td3Z1r167lOZ6Wlmbz3N/fn/DwcKZOnZrv+xQlVJ89ezbPsV9++QX4PWj5+/vj7e1d4BzhWrVq2Ty//b58fX1xdXXlp59+umMt9rgfe6pZsyaurq4MGDCAYcOG5XtOUFBQoe+T3+/zkiVLcHNzY82aNTYjsStXrix2vbkWL17M+PHjiY6OZsOGDQ5ZpUJEyoZCr4iUO3ez9mtQUBD79++3ObZp0yYyMjJsjj3xxBOsW7eOe++9lxo1ahSrrsOHD3PgwAHCwsKsxxYvXkz16tWJjIy0fs7f//53fH19ixTybufp6Ul0dDTLly9n6tSpBU5xsMf93C539Pfq1at3vUyYl5cXMTEx7N27l9DQ0HxHoIvLYrHg6upq8+XFrKwsPvrooxKvE+zr60tKSgpPPPEEMTExJCcnExUVVdKSRaQc0pxeESl3bp+aUNAxgP79+5OcnMykSZPYuHEj//jHPxg6dCg+Pj4210yePJmqVavSunVr3n33XTZt2mTdjKFr1678/PPPhdZVt25dnnzySebPn8/69evp168fKSkpjB8/3hoSR44cyf3338+jjz7KzJkzSUlJYcOGDcydO5fevXuza9euQj/nzTff5MaNG0RFRTF37lw2b97MkiVL6Nu3rzXM2+N+bpcb5qdPn87OnTvZvXs3N27cAApu/1u9/fbbnDp1ijZt2rBgwQK2bNnCp59+ysyZM2nXrt1d15PriSeeICMjgz59+vD555+zZMkS2rRpg4eHR5HqylXQuffccw/r16+nVatWdOjQr2BLtAAAAa5JREFUoUjzu0Wk4tFIr4iUK/ktjXWn5bJGjx7NlStXmD9/Pm+88QZRUVEsW7aMp556yuaagIAAdu/ezZQpU3j99dc5ffo01apVIzg4mNjYWGrWrFlobZGRkcTHxzNx4kSOHDlCvXr1eOutt3jxxRet53h5efHll18ybdo05syZw/Hjx/Hw8KBhw4Z06NChSKO/YWFh7Nq1i0mTJvHyyy+Tnp5OQEAA7du3t/7zvj3u53Z9+vRh27ZtJCYmMnnyZACOHz9Ow4YNizSiGhISwt69e5kyZQrjx4/n/Pnz1KhRgyZNmtC5c+e7ridXTEwMH374IdOnT+fJJ5+kfv36/OlPf8Lf35/nnnvO5tyC6iyoX+Xy8PDg3//+N3369OHxxx9n5cqV1i8FiohzsBh389dkEZFKKigoiLCwMFavXu3oUkREpBg0vUFEREREnJ5Cr4hIEZT0C1MiIuJYmt4gIiIiIk5PI70iIiIi4vQUekVERETE6Sn0ioiIiIjTU+gVEREREaen0CsiIiIiTk+hV0REREScnkKviIiIiDg9hV4RERERcXoKvSIiIiLi9P4fD3fEZN+Deh8AAAAASUVORK5CYII=",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f34cc802390>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"rounds = 8\n",
"wins_to_break = 6\n",
"\n",
"ranks = 0:0.01:(rounds+1-wins_to_break)/(rounds+1) # plot up to the expected break cut-off\n",
"probnotbreak(rank) = sum([(1-rank)^i*rank^(rounds-i)*binomial(rounds,i) for i in 0:wins_to_break-1])\n",
"probs = map(probnotbreak, ranks)\n",
"plot(ranks*100, probs)\n",
"xlabel(\"True percentile rank\")\n",
"ylabel(\"Probability of not breaking\");"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.4.2",
"language": "julia",
"name": "julia-0.4"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "0.4.2"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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