{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cc570908-04b8-4ae6-a8ab-d277c303eb76",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Combinatorics\n",
    "using Distributions\n",
    "using StatsBase: countmap\n",
    "using StatsPlots\n",
    "default(fmt=:png)\n",
    "using SymPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "13cd988a-d45f-4a75-b84d-2606db7caedc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(21, 10)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n, k = 21, 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "322e3210-efb7-4053-9158-930320733a8d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xs = xmin:xmax = 55:165\n"
     ]
    },
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rank_sums = [sum(comb) for comb in combinations(1:n, k)]\n",
    "c = countmap(rank_sums)\n",
    "xmin, xmax = extrema(keys(c))\n",
    "@show xs = xmin:xmax\n",
    "ys = (k -> c[k]).(xs) / length(rank_sums)\n",
    "plot(xs, ys; label=\"dist. of rank sums\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7f8d685b-aa00-4142-bb00-8267cd4d88b7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Xs = Xmin:Xmax = 55:165\n"
     ]
    },
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@vars q x\n",
    "F = sympy.Poly(prod(1 + q^i*x for i in 1:n), x)\n",
    "f = F.coeffs()\n",
    "f_k = sympy.Poly(f[n+1 - k], q)\n",
    "Ys = float(f_k.coeffs())\n",
    "Ys ./= sum(Ys)\n",
    "Xmax = f_k.degree()\n",
    "Xmin = Xmax - length(Ys) + 1\n",
    "@show Xs = Xmin:Xmax\n",
    "plot(Xs, Ys; label=\"dist. of coeffs. of q-binom\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "173928a8-1581-4a5c-9826-8011f9aefc38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs == Xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "01fbab14-534e-4d2a-9c9c-5ac2408e6fa4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ys == Ys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6cecb147-0687-45dd-82ae-c3cdfb81a9e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "110.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu = mean(rank_sums)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9b6b9db4-fb20-4daf-a4f9-0f2ef24dbdfd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k*(n-k)/2 + k*(k+1)/2 == mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1bc56338-7d6a-4759-8775-cf6a89183db3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "201.66666666666666"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2 = var(rank_sums; corrected=false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e15aca7a-9ee2-4b62-92f5-dd05d0fb5ec2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k*(n-k)*(n+1)/12 == s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a9646c30-22cc-4736-b9b4-9976d52a9680",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(Xs, Ys; label=\"dist. of coeffs. of q-binom\")\n",
    "plot!(Normal(mu, √s2); label=\"normal approx.\", ls=:dash)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d6018aee-c53a-4c1f-b648-b301a05dcf11",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f_k = Poly(q^165 + q^164 + 2*q^163 + 3*q^162 + 5*q^161 + 7*q^160 + 11*q^159 + 15*q^158 + 22*q^157 + 30*q^156 + 42*q^155 + 55*q^154 + 74*q^153 + 95*q^152 + 124*q^151 + 157*q^150 + 200*q^149 + 248*q^148 + 310*q^147 + 378*q^146 + 463*q^145 + 556*q^144 + 669*q^143 + 792*q^142 + 939*q^141 + 1097*q^140 + 1281*q^139 + 1478*q^138 + 1703*q^137 + 1940*q^136 + 2208*q^135 + 2486*q^134 + 2795*q^133 + 3113*q^132 + 3460*q^131 + 3812*q^130 + 4191*q^129 + 4569*q^128 + 4970*q^127 + 5364*q^126 + 5776*q^125 + 6172*q^124 + 6580*q^123 + 6964*q^122 + 7352*q^121 + 7708*q^120 + 8060*q^119 + 8371*q^118 + 8672*q^117 + 8924*q^116 + 9160*q^115 + 9340*q^114 + 9499*q^113 + 9598*q^112 + 9673*q^111 + 9686*q^110 + 9673*q^109 + 9598*q^108 + 9499*q^107 + 9340*q^106 + 9160*q^105 + 8924*q^104 + 8672*q^103 + 8371*q^102 + 8060*q^101 + 7708*q^100 + 7352*q^99 + 6964*q^98 + 6580*q^97 + 6172*q^96 + 5776*q^95 + 5364*q^94 + 4970*q^93 + 4569*q^92 + 4191*q^91 + 3812*q^90 + 3460*q^89 + 3113*q^88 + 2795*q^87 + 2486*q^86 + 2208*q^85 + 1940*q^84 + 1703*q^83 + 1478*q^82 + 1281*q^81 + 1097*q^80 + 939*q^79 + 792*q^78 + 669*q^77 + 556*q^76 + 463*q^75 + 378*q^74 + 310*q^73 + 248*q^72 + 200*q^71 + 157*q^70 + 124*q^69 + 95*q^68 + 74*q^67 + 55*q^66 + 42*q^65 + 30*q^64 + 22*q^63 + 15*q^62 + 11*q^61 + 7*q^60 + 5*q^59 + 3*q^58 + 2*q^57 + q^56 + q^55, q, domain='ZZ')\n"
     ]
    }
   ],
   "source": [
    "@show f_k;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3871497d-8f26-4c00-99ad-eba136be4bd4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g_k = Poly(q^165 + q^164 + 2*q^163 + 3*q^162 + 5*q^161 + 7*q^160 + 11*q^159 + 15*q^158 + 22*q^157 + 30*q^156 + 42*q^155 + 55*q^154 + 74*q^153 + 95*q^152 + 124*q^151 + 157*q^150 + 200*q^149 + 248*q^148 + 310*q^147 + 378*q^146 + 463*q^145 + 556*q^144 + 669*q^143 + 792*q^142 + 939*q^141 + 1097*q^140 + 1281*q^139 + 1478*q^138 + 1703*q^137 + 1940*q^136 + 2208*q^135 + 2486*q^134 + 2795*q^133 + 3113*q^132 + 3460*q^131 + 3812*q^130 + 4191*q^129 + 4569*q^128 + 4970*q^127 + 5364*q^126 + 5776*q^125 + 6172*q^124 + 6580*q^123 + 6964*q^122 + 7352*q^121 + 7708*q^120 + 8060*q^119 + 8371*q^118 + 8672*q^117 + 8924*q^116 + 9160*q^115 + 9340*q^114 + 9499*q^113 + 9598*q^112 + 9673*q^111 + 9686*q^110 + 9673*q^109 + 9598*q^108 + 9499*q^107 + 9340*q^106 + 9160*q^105 + 8924*q^104 + 8672*q^103 + 8371*q^102 + 8060*q^101 + 7708*q^100 + 7352*q^99 + 6964*q^98 + 6580*q^97 + 6172*q^96 + 5776*q^95 + 5364*q^94 + 4970*q^93 + 4569*q^92 + 4191*q^91 + 3812*q^90 + 3460*q^89 + 3113*q^88 + 2795*q^87 + 2486*q^86 + 2208*q^85 + 1940*q^84 + 1703*q^83 + 1478*q^82 + 1281*q^81 + 1097*q^80 + 939*q^79 + 792*q^78 + 669*q^77 + 556*q^76 + 463*q^75 + 378*q^74 + 310*q^73 + 248*q^72 + 200*q^71 + 157*q^70 + 124*q^69 + 95*q^68 + 74*q^67 + 55*q^66 + 42*q^65 + 30*q^64 + 22*q^63 + 15*q^62 + 11*q^61 + 7*q^60 + 5*q^59 + 3*q^58 + 2*q^57 + q^56 + q^55, q, domain='ZZ')\n"
     ]
    }
   ],
   "source": [
    "# (x)_q = (1 - q^x)/(1 - q)\n",
    "# (n)_q! = (1)_q (2)_q … (n)_q\n",
    "# g_k = q^{k(k+1)/2} (n)_q!/((k)_q! (n-k)_q!), essentially a q-binomial coefficient\n",
    "g_k = sympy.Poly(q^(k*(k+1)÷2) * prod((1 - q^(n-k+j))/(1 - q^j) for j in 1:k; init=Sym(1)).factor(), q)\n",
    "@show g_k;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1f306692-6ee1-4155-bb5f-4ccc602b04b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_k == g_k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "955395d0-257a-4a85-93be-5f79df454532",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "02ad2505-9740-46a7-ba6f-a52596c2a8b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(31, 13)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n, k = 31, 13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e584406f-5d97-435e-bf82-a4d20d41375e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xs = xmin:xmax = 91:325\n"
     ]
    },
    {
     "data": {
      "image/png": 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PNAJI0Nrr3ChftqsLo/ctZAbAMuSfkezqi9oYBe6uB6nD3XsAQmriyEeXuX/2FqAlzunC3qwhJ0sxUwhShyAEENKmDC7ClUR5CDA+acWSF3qx71/CowpB6hCEAIKhhLx/iXs5UrA7gp4IZ0+UcOlV6BSCpCEIAQSzN486WJFRvoJdrmIvJ0si2E+uolMIkoYgBBDMx5e1y3sK3AaXRcgSM7lytbC1ABASLhgDEMbVKnqlkjzSWeAg9LIjEwPZb65zLwpxwY7ByeXy5ORk3SKc0A6U0gfe/2Z6jY2NxltWDEEIIIz/XuaWRLDWIkif53qyU5O1y3uychFUpoPi4+NbLH0CbVVfX//AlUsFcfca14aCIAQQQKWabM3i0qdbPbio8fV1ZwIdya4c7uEQs09CGxubu59+Cm2iVCr1vB3cYpj9cQ9gjjZlcGP9WS+7B5c0jaUR7FfpuGQGJApBCCCAdde5pyJE1PoeDmEvVdCMatxHAVIkoqYIIBHHiqmGkuE+IroewZol80LZ9TfQKQQpQhACmNpX6dxT3VgRxSAhhJAlEey3Nzg1HlMI0oMgBDCpCjXZncvNCxNd0+vizPR0Y37OQacQJEd0rRHAsv2QyY0LYN1thK5HaxaHs99cRxCC5CAIAUzq2xvcwq4ibXdTgtlzZTSvDpfMgLSItEECWKTLlbS0gYz2E9v84B22MjKjM/tdBoIQpAVBCGA6669zC7syMpHmICGEPBbGbsjgkIQgKQhCABNp4sgPmdwC8V0m09wgL8ZWRk6UIApBQkTdJgEsyZ48rpsL08VZxP1BQggh80LZDbihEKQEQQhgIt/fpCK8a+Juc0OZn7K5Bo3Q9QAwFTNolgAWoKaJpBRw04LNoMX52TN9OjH78tEpBKkwg2YJYAG2Z3Fj/NhOorx98G5zQ9nNNzFNCFKBIAQwhc03ubldxD47qDOjM3uokKtqFLoeACaBIAQwusJ6eqGcjgswm+bmbEXG+LE/ZWF0FCTBbFomgPnacotODWLtzOox2HNDmR8yEYQgCQhCAKNLzOTmhJpZWxsfwF4op4X1mCkEy2dmjRPA7GTV0qxaOlJMTx/Uh42MTAxkd2YjCMHyIQgBjGvrLTo9hJWbYVN7pDO75RZGR8HymWHrBDArW7O4mZ3NsqHFKZhrVbQAD6MAS2eW7RPAXGTW0KJ6OszcxkV5ViyZFMhuz0IQgoVDEAIY0ZZb9OFgVsyPm7g/jI6CFCAIAYxoexY3wzzHRXlj/JiMGpqP0VGwaGbcRAFELquWFtbTod5m2x8kxIolEwLZHbh2FCwaghDAWLZn0anmPC7KeziY3ZGN0VGwZAhCAGPZkW0ej5u4v1gFc6mCFjcIXQ8AozH7VgogTgV19EY1Helr5v1BQmxkJMGf/SUHnUKwWAhCAKPYkU0nBbHWFtHCpgUzGB0FC2YRzRRAfHZmc1ODzL47yBsbwJ4qpZVqoesBYBwIQgDDq1CTC+U0zt9C2peDnIzyZffmoVMIlslCGiqAqCTlctEK1lYmdD0MZ3IQsysHN1GAZUIQAhjerhw62VLGRXmTgtjkAk6lFboeAEaAIAQwsAYNOVTIjTef59Hrw92GRLozhwrRKQQLZFFtFUAMDhZw/T2YTjZC18PQJgexu3ATBVgiBCGAge3KoZODLLBlTQ1iduVwHPqEYHEssLkCCEhLyZ48bpJlTRDygp0YLzvm9G0kIVgaBCGAIZ0sob52TJCjBQYhIWRiIJOE0VGwOAhCAEPancdNtMTuIG9iIJuUix4hWBoEIYAhJeXQiYEW26wGejJlKppViywEi2KxLRbA9G7V0jI17e9hsT1CliFjA9jd6BSCZUEQAhgM3x1kLTYHCSFkQiCTlItpQrAoCEIAg9mdx00ItOgYJCROwZ4upbVNQtcDwHAQhACGUdNEzpTSGD8Lb1OOVuQhb+ZgPjqFYDksvNECmExyPjfEm3G0Eroexjc+gN2bh2lCsBwIQgDD2JtHx1nW+qL3MiGQ2ZuHFWbAckii3QIYGyVkfz4dG2DhE4S8ECfG1YY5X4YoBAuBIAQwgPNl1NmahDpLIggJIeMDmD0YHQVLgSAEMIA9eXS8NLqDvPGB7B7cRAGWAkEIYAB78ziJTBDyhnkzGTW0pEHoegAYgoSaLoCR3FaR61V0mI+EeoRWLBnjxx7ATRRgERCEAB21P58b48daS6wxjQ9gcBMFWAaJtV0AI9iXR8dJaYKQNzaATS7gNOgTgvlDEAJ0CEdJSgEX5y+5IPSxI4GOzBk8pxfMH4IQoEN+v0197JkAB8kFISFkrD+zD9OEYP4QhAAdsi+fGyu97iBvbAC7H9OEYP4QhAAdsi+PjpXSjRPNPeTFZNbiJgowexJtwAAGUaYiN6rpEG+J9gjlLBnjxx4swOgomDcEIUD7HSzgRvlK7saJ5sYFMPswOgpmTsItGKDDDuTTBOndONFcvIJJLuDwKAowawhCgHaihCQXcHEKSQehwoHxsWPO4UkUYM4QhADtlFZOXayZECdJByEhJMGf2Z+PIAQzhiAEaKcD+TReqjdONBfvj0VHwbwhCAHa6UA+F69ACyLDfZjLlbRCLXQ9ANoLzRigPeo05HwZHemLHiGxkZGh3syvhegUgrlCEAK0R0oBN9iLsZcLXQ9xiPdnDxRgmhDMFYIQoD0OFtA4fzSfOxL8mQO4XgbMFloyQHscxJUyzXR1YWQMSa9CFoJZQhACtFlWLVU20R5uCMI/xSqYgxgdBfOEIARos/35NCGARQw2F6tgkrHoKJgnBCFAmyUX0FhpLyhztxgFe7SIqrVC1wOg7RCEAG2j4cjhIi7GD23nL1ytSXc35mQpRkfB/KAxA7TN6du0sxPjZSd0PcQnTsEcxBIzYIYQhABtczBf6gtt30usgsX1MmCOEIQAbXOwgMZgZbXWDPZiMmvobZXQ9QBoI7RngDaoaiRXK+lQqT6S/v7kLBnhy6bi2lEwNwhCgDZILeCG+jA2MqHrIVaxCiYZo6NgbhCEAG2QXEBjMS56b3EKBouOgtlBkwZoA9xBeH9dXRgrFmutgZlBEALoK6uW1muwstoDxPhhrTUwMwhCAH0dyKdx/lhZ7QGw1hqYHQQhgL4wLqqPaAV7pIg2IgrBfCAIAfSipeRwEYc7CB/I3YaEuzCnsNYamA+0agC9nL1NFQ6MD1ZW00OMgsHdhGBGEIQAekkpxLiovmIULO4mBDOCIATQS0oBnjihr6HezOVKWtUodD0A9IOGDfBg9RpyrowO90GPUC+2MvKQF3OkCKOjYB4QhAAPdqSI9vNgHK2Erof5wOgomBEEIcCDpRRiXLRtYhRMCoIQzIS+bbuurm7ZsmVdu3YdNmzY4cOHWy3z9ddfR0ZG9uzZ84MPPtBt3Lx585IlS2JjYw8dOtS8cGJiYlRUVERExL/+9S+OwxAKiBruIGyrPu5MZSPNrkUWghmQ61nulVdeyczMTE5OPn78+JQpU27evOnh4dG8QGpq6muvvZaUlGRnZzd58uSAgICZM2cSQk6cOBEcHHzw4MHi4mJd4bS0tCVLluzYsUOhUMyYMcPT0/Ppp5824K8CMKCSBpJfR/t7IgjbgCFkjB97qIg+7oT9BmKnV49QpVJt3Lhx1apVQUFBc+bMGThw4Pfff9+izBdffLF06dJBgwb17t37hRde+PLLL/ntn3322csvv+zm5ta88FdffTV37twxY8aEh4evWLFCVxhAhFIKuFG+rAzn8zaK8WNSMToK5kCvIMzLy1MqlX369OH/GRUVdeXKlRZlrl69GhUVdZ8CLQr369dPVzg9PV2r1bat4gCmklpIY/wQg20Wq2BSCjkkIYifXkOjt2/fdnJyYtk7qeni4nL16tW7y7i4uPCvXV1dy8vLOY7TveX+hbVabUVFhaen590l09PTN23atH379jvVlcu3b9+uC1EDUiqVBv9MqbHUfZicb/tMqLrW+NNdKpVKLpfL5fpOWIicGyFOcpuTecperqZLQ0s9CE2prq6OUsv5A8be3l4me8CjtPVqcq6urvyuYRiGEFJbW+vu7n53Gd0hWFtb6+rqeq8UvLswy7Kurq6tlgwPD585c+bHH3+s29JilNWAnJycjPTJ0mF5+/B6NSWMtq+fowm+y8rKypKCkBAS5689WWU/JMCkF9xa3kFoYgzDODqa4oAXD70O0ICAAJZlMzMz+X9ev349JCSkRZkuXbqkp6fzr9PT0+8ucJ/CAQEBVlat36LFMIyNjY1bM/pUGMBQkgtoHK4Xba8YBZOCRUdB9PQKQicnp6lTp77//vuU0j/++OPAgQOPPvooISQ7O3v58uV8mfnz569du7aqqqq+vv6zzz6bP38+v12pVFZWVmo0mrq6Ov4FX/j7778vKipqamr66KOPdIUBxCa1gEYjCNtrjB97vISqcQEAiJu+QxYffvjhlStX3N3dR40a9Z///Ifv8JWVlSUmJvIFZs2aFRMTExQU5Ofn161btyVLlvDbH3/88S5duuTl5b300ktdunQ5ceIEISQ2Nvaxxx6LiIjw8vJycHB46aWXjPDTADpKS8nRYm4MbqVvL1drEuHKnMQjmUDcmDZNitbV1dnZ2d1n8q+pqYnjOBsbG30+TaPRaDQaW1vb+5RZt27d6dOn165dq38l26e2thZTCx1kefvwVCl96pj24jQTTdpZ2MUyvNfOagkhb/d/wNUKhmJ5B6HpKZVKzBHej4ODw31SkBBiZWWlZwoSQuRy+f1TEEBYKVhQpsOiFWxqIXqEIGoY8wG4p9RCLhrjoh0z1Ju5Wkkr1ULXA+De0MgBWodHLxmENUsGezFHinHtKIgXghCgdUeL8eglw4hWsFhrDcQMQQjQutQCjIsaRowfk4JpQhAxtHOA1qUU0hhcKWMIfdyZchXNr0MWgkghCAFaUaYiWbW0vweC0ABYhoz2w7WjIF4IQoBWpBZyI31ZK7QPA4nxwwPrQbzQ0AFakVKARy8ZUqyCSSnAI5lApBCEAK1IxQShQQU7MfZy5molohDECEEI0NLNGqrWkghXBKEhxSgwOgoihSAEaAkrqxlDtB+D62VAnBCEAC2lFuLRS4YXrWCPFnNNWGEGxAdBCPAXHCWHi7gxvghCA3O3IV2cmTO30SkE0UEQAvzF+XLqbccoHBCEhoebKECcEIQAf5FSgOtFjSVawaYWYmwURAdBCPAXqYVcNO4gNI4RPkxaOa1pEroeAH+FIAT4k0pLTpfSkb5oF0ZhKyMDPJnfijE6CuKCBg/wp2PFtHcnxhmPXjKaaD82tQCjoyAuCEKAP6UWcpggNKoYBR7JBKKDIAT4U0oBxTMIjSrKgymoo0X1QtcDoBm0eYA7KtXkRjUd5IUeoRHJGDLKlz2Ea0dBTBCEAHekFnLDfRhrtAkjw1prIDZo9AB3pBbSaAVahNHFKJhk3FYPYoJmD3BHMp5BaBJdXRg5S9KrkIUgFghCAEIIya6lyibasxOC0BSi/XDtKIgIghCAEEIOFtBYBYsYNI0YP4yOgoggCAEIwRKjphWjYI8U4ZFMIBYIQoA7j17CEqMm42FLOjsxv+ORTCAOCEIAcr6cetoy/nj0kgnh2lEQDwQhAMZFBRCrYJOx6CiIA4IQgKQUYIlRUxvmzVyqwCOZQBQQhCB1DRpy5jYevWRqdnIyyIs5jLXWQATQ+EHqjhbTPu549JIAYhUspglBDBCEIHXJBVwsVlYTQiyulwFxQPsHqUsuoLGYIBRCH3emspHmKpGFIDAEIUhaSQPJq6P9PRCEAmAIGePHYq01EByCECQtpYAb5cvK0Q4EgtFREAOcAEDSMC4qrDgFk1LAcYhCEBSCECQttRCPXhKSvwPjYctcrEASgpAQhCBdV6uonCVhLghCIcVhdBSEhiAE6TqYTxP8kYICw1prIDgEIUhXcgGHCULBjfZjTpfSOo3Q9QAJQxCCRDVy5HgJHY2V1YTmICf9PJjfijE6CoLBWQAk6lgx7eHGuNkIXQ/A6C7sFugAACAASURBVCgIDUEIEnUQ46KiEadgDuajRwiCQRCCRB3Mp3FYYlQcojyYkgaaX4csBGHgRABSVNpAspV0oCd6hKLAMmSMH5uCmyhAIAhCkKLkAm40VlYTkzh/5iCCEASCMwFI0YF8Go87CMUkXsEkY601EAiCECSHEpJSiCtlxEXhwHjbMefLkYQgAAQhSM7FcupsxYQ4IQjFJd6fOYBrR0EICEKQnIMFGBcVozgFezAfdxOCABCEIDkH8rk4fxz5ojPSl0krp9WNQtcDpAenA5CWOg35/TYd6YMeoejYyshgL+ZwETqFYGoIQpCWw0V0gCfjaCV0PaA18f7sfkwTgskhCEFa9udx8RgXFat4fwZBCKaHMwJIy348g1DEergxHCXXq5GFYFIIQpCQrFpap6G9OiEIxSven9mfhyAEk0IQgoTsyaNj/VnEoJjFK5gDeCQTmBaCECTkQD6HOwhFLtafPV5MG/DAejAhBCFIRSNHfiumMXj0krg5W5FId+YoHlgPJoSTAkjF0SLaw43phEfSi16CP7sfS8yACSEIQSr253MJuHHCHIwNYPbhehkwIZwXQCr25tFxAZggNAN93JnaJpJZgywEE0EQgiTk1dFyNe3rjiA0AwzurAfTQhCCJOzOpWP9Wdw5YS7GBjD78jBNCCaCIARJ2JdHx2Jc1HzEKdjfcBMFmAqCECxfI0eOFnO4ccKMuFjjJgowHZwawPIdKaI93Rh33DhhVsYGsPtwEwWYBIIQLN++PNw4YX7GBTB7cRMFmATODmD5dufRCYGYIDQzkZ0YtZbcwJMowPgQhGDhMmuosolG4sYJM5Tgz+xBpxCMD0EIFu6XXDohEPdNmKXxAcyeXEwTgtEhCMHC7cnlxuPGCfMUrWDP3KbVjULXAywdghAsmbKJ/H6bRvvhODdLDnIyxJtJLUSnEIwLJwiwZAcLuIe8GUcroesB7TU+gN2Ti2lCMC4EIViyvXl0XAAOcjM2PpDZm8chCcGocI4Ai8VRTBCavc5OjJsNc/Y2ohCMCEEIFuv329TdlunijCA0bxMDmSRcOwrGhCAEi7U7j8N99BZgQiC7G9OEYEwIQrBYSTl0YiCOcLM3xJvJq6M5SmQhGAtOE2CZ8upofh0d7IUeodmTMSTBn92HJWbAaBCEYJmScuj4QFaGHLQIEzBNCMaEIATLtCcP14tajgR/9lgxrcdzesE4EIRggeo05FgxTcAdhJbCxZoM8GSSC9ApBKPAmQIs0P487iFvxhkLyliQyUHsrhxME4JRIAjBAu3KoZODcGxblMlBTFIup0UUghHgZAGWRkvJ/nxuIu4gtCyBjoy/A3OyBEkIhocgBEvzWzENcmT8HRCElmZyELMrB9OEYHgIQrA0u3I4jItapMlB7M+YJgQjwPkCLE1SLp0UhO6gBerjzjRy5FoVshAMDEEIFuWPCspR0rsTgtACMYRMDmLQKQSDQxCCRdmRTacGIwUt1pQgdmc2pgnBwBCEYFF2ZnNTMUFouUb6Mtm1NK8OnUIwJJwywHJk19LiBvqQN3qEFkvGkPGBuLMeDAxBCJZjRzadHISFti3c1CAGo6NgWAhCsBw7c7ipwTikLVysgj1XRstUQtcDLIi+Zw1K6YoVK/z8/BQKxcqVK1sts3v37oiICHd39+nTp1dUVPAbGxoannjiCU9Pz86dO3/77bf8xuLi4v7NbNiwocM/BKSupIFcqaSjfdEftHB2chKjYHfjqUxgOHI9y23evHnbtm2nT5/WarWjR4/u0aPHtGnTmhcoLS2dM2dOYmLiyJEjFy9evHz58o0bNxJC3nnnnczMzIyMjIyMjNjY2P79+/fq1auxsfHatWtHjx7l36tQKAz7q0CCfs7hxvqzNjKh6wHGNy2Y+TGTe6wrev9gGPoeSevWrXvuuecCAgKCg4P/9re/rV+/vkWB77//fvDgwePGjXNwcHjzzTe3bt1aW1tLCFm/fv2KFStcXV0HDBgwY8aMb7755s4Xs2zU//j4+BjwJ4E0bc/iHg5Bd1ASJgayvxXT6kah6wGWQt8gTE9P7927N/+6d+/e6enpLQpcv349MjKSf921a1eGYbKzs6urq4uKinTbe/fuff36df51Q0NDr169oqKiXn75ZaVS2dHfAdJWria/36bx/ugiSIKTFRnhw+KZ9WAo+g6NVlRUODk58a+dnZ3LysruLuDn56f7p7Ozc3l5uYODAyFE90YXFxf+jS4uLlu3bu3du/ft27eff/75rKysLVu2tPq9165dW7du3bp163RbDh8+HBUVpWe19VdXV8cw6E90iID7MPGWLNqHpSrz/pNKpVLJ5XK5XN9WKWXjfdktGbIpPk0ttqMhd1xdXZ3QVTAke3t7ln3An8j6NrlOnTrV1NTwr6urqz09Pe8uwI+F8mpqajw8PNzd3fnXdnZ2hJCqqir+jS4uLvwUY2ho6Ndff92vXz+1Wm1jY3P390ZERCxatGjt2rV61rPdKKWOjo7G/hbLJuA+3F2oWdiVdXRs5RAyI/L/EboiZmBmOPnn+SbOxrHF45fRkA1CavtQ36Gkrl27XrlyhX995cqVsLCwuwtcvnyZf33z5k2O4wIDA11cXLy9vXXbr1y5Ehoa2uKNtra2HMdptdp2/gKQvKpGcqKEjg3AuKiEuFqToT7MXoyOgiHoe+54/PHH//vf/5aUlBQWFn7++eePP/44v33BggX8fOHcuXOPHz+empqqUqlWrlw5ffp0Z2dn/o2rV69WKpWXLl3atm0b/8ZTp06lpaWp1ers7Oy///3vMTEx9vb2xvmBYPl+yeGiFayT1YNLgiWZHsL+lI0lZsAA9A3C+fPnT5gwoWfPnn369Jk9e/b06dP57ZcuXeIvdfHx8fnuu++WLFni5eVVWVn50Ucf8QVee+01Hx+fgICA8ePHr169mr9wJj8//5FHHnF1dR06dKiXl9emTZuM8NNAKhJvcTM7Y1pIcqYFsykFnLLlLCFAmzGUivpPqnXr1p0+fdoEc4S1tbW6i3qgfQTZh5Vq0nlLU95sK0fz7xHiYpm2mnBA82goO6vLn3/QoyF3nFKpxBwhgDnZkc3FKlgLSEFoh0c6s1uzRP2nPJgFBCGYty0YF5WwKcHsr4Uc7qyHDkIQghkrU5Ezt2kCrheVKmcrMsIXd9ZDR+EMAmZsRzY3NoB1wJyahD0Swmy9hdFR6BAEIZixHzK52RgXlbYpweyxEq5cLXQ9wJwhCMFcFdbTyxVYX1TqHOQkVsH+lIXRUWg/nETAXG2+SaeF4LlLQGZ3YX7MRBBC+yEIwVz9mMnN7oIDGMi4APZyJc2vw0whtBPOI2CW0qtoSQMZ4YMJQiDWLJkSxG7BJTPQXghCMEv8smoy5CAQQgiZ3YXF6Ci0G4IQzA8lZPNNOjcURy/cMdKXKW4g16rQKYT2wKkEzM/JEmrFkigP9AfhDhlD5nRhvr+JTiG0B4IQzM93N7n5YTh04S8WhLHf36Qc+oTQdjibgJlp5MhPWdzcUHQH4S96uDFu1uTEbZzToM1w0ICZ2ZPL9XRjAhwQhNDSvDA2MQc3lkKbIQjBzHx3k87DuCi0Zk4XNimfbdAIXQ8wNzihgDm5rSK/FnIPh+C4hVb42pP+7tyObFwyA22DEwqYk803uUlBrDMewwv3MDdYuyEDQQhtgyAEc7LhBrewKw5auKcJ/tzFcnqrFhePQhvgnAJm41wZrWnCsmpwP9YsmdmZ/f4mghDaAEEIZuPbG9zCriyLHIT7WtiV/fYGhxsKQX8IQjAPKi3ZcoubH4YYhAfo58G4WpPDRUhC0BeCEMzDT1lcfw8myBFBCA/2RDi77joumQF9IQjBPKy9zi3uhsMV9DIvlN2fz91WCV0PMBM4s4AZuFFNr1fRiYE4XEEvLtZkYiCLNbhBTzizgBlYm8491pW1wtEKelsczn6djitmQC84tYDYNXLku5vcE+E4VqENhvkwDCHHixGF8GA4uYDY7cj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\" />"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rank_sums = [sum(comb) for comb in combinations(1:n, k)]\n",
    "c = countmap(rank_sums)\n",
    "xmin, xmax = extrema(keys(c))\n",
    "@show xs = xmin:xmax\n",
    "ys = (k -> c[k]).(xs) / length(rank_sums)\n",
    "plot(xs, ys; label=\"dist. of rank sums\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3bfeb520-9771-44b3-b70d-19fc3cac745c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Xs = Xmin:Xmax = 91:325\n"
     ]
    },
    {
     "data": {
      "image/png": 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zc3tUscDAwEGDBnl7e1++fHnr1q0tecJj2rRpx44d6969e1BQ0K1bt9avX29hYdG2KZtaQVumuro6Ojraw8PD3d19ypQpCoWC329lZXX69Gl+++uvv3Z0dAwICAgKCkpKSuJ3fvnll/W/7oMPPqCUrlq1ysbGxtfX18HBYcCAAXfu3HnU965Zs2bOnDktrGR7VFRU6OBbTBuOYZt9cVMVc1JZU1NTV1enm2/ckqJ6Yr8mv2v58uVvvfWWBj9QI7Kzsy9dulRbW1tRUcEnQVVVVWVlJf9f09LSzp8/n5aWVv9HFApFSUlJXV1dXV3dgwcPmvzYysrKq1ev5ubmqvfI5XKZTNZkYaVSmZSUdOnSpfoF8vPzr1y50uCSqa2tvX379pUrV8rLyxt/bF1dnXo/pTQlJeX8+fMZGRnqPYWFheo7c311dXW3b9++e/euUqnk96hUqtLS0kfVNj4+Pikp6cGDB2ZmZo0LVFVV1dTUlJSUXLx4sX59CgoK+A31oW58WLKysq5evVpVVaXeU1JSwnEcv11eXq4+//lvqf+9mZmZUqm0yTq3XxP9sM148OABwzCuro/svpHJZCUlJVKplJ9Q0gyFQpGfn893AjRTbO3atZcuXeKfNdKqyspKjG+1E45h28jqSKcddX+NE/tYKMRicZOD5RrHUdJjt/KHgSJNDeN9/fXXBQUFy5cv18ingd4VFhZKJBK+O9cQZGVlDRo0KDMzUxsf3rpLrpnGMs/W1tbW1rYlH2VhYdF4oBFAgNYkccM92UAHpt6zHVrHMuT/erFf3lJFSIQxux5aydraetGiRfquhY5g9h6APtVx5Pvb3P/11MOVGNOJTakgFx7grRTQBBsbm88//1zftdARBCGAPm1K5oIdSaiLHh5aMWPJwh7s8niDeWABQE8QhAB6QwlZHs+900tvM4JeCGLPF3CJZWgUgqAhCAH05nAWtTEjw/U3h8FaTOYFszpbCA3AMCEIAfTmh9uq+d31fA2+EizalsoVNzd7G8DE4YExAP24U0YTSsnTHfUchG5WJNqH/TWJW9S+B3bEYvHmzZv//PNPTVWsbSilj527Bc0zzGNYW1urvWXFEIQA+vGf29y8YNbcADpl3uzOTjqumt+dFbejMnPmzBkyZIjmKtVGzS/+CS1hsMew8RrXmoIgBNCDUgXZkc4lTjGIN3r3cWZ8bMm++9xT/m1PQltb28avHdU9rOrQfjKZrIXTwU2GAfw5CiA8m5K50d6sm5W+6/FfLwezqxLxyAwIFIIQQA/WJnFzgw3o6nvKn40vocnlmEcBQmRAlyKAQJzNp0pKhngY0PMI5iyZGcCuu4dGIQgRghBA11YlcnO7sAYUg4QQQuYFs+vvcQoTf00hQBMQhAA6VaIgBzO5mZ0N7tLrZM90d2L23kejEATH4K5GANP2eyo3Rso6W+i7Hk15MYj9NQlBCIKDIATQqfX3uNmBBnrdTfRjrxXRrCo8MgPCYqAXJIBJul1KH9SQJ70MbXzwIUsRmdqR3ZyMIARhQRAC6M66JG52ICMy0BwkhJDnOrMbkjkkIQgKghBAR+o48nsq96zhPSZTX383xlJEzhcgCkFADPqaBDAlh7K4Lg5MJ3sDbg8SQgiZGcBuwIRCEBIEIYCO/JZCDXDWRGMzApjdGVyNUt/1ANAVI7gsAUxARR2Jy+Em+xnBFedlzfTuwBzJRqMQhMIILksAE7ArnQv3YjsY5PTBxmYEsFtSMEwIQoEgBNCFLSncjE6GPjqoNrUjezKXK6vVdz0AdAJBCKB1udX0RjEdIzWay83ejIR7sbvT0TsKgmA0VyaA8dqeRif5slZG9RrsGQHM76kIQhAEBCGA1m1L5WICjOxaGytlbxTT3GqMFILpM7KLE8DopFfS9Eo6zJDePtgSFiIS7cP+kYEgBNOHIATQrh1pdIo/KzbCS+3pjuz2NPSOgukzwqsTwKjsSOemdTTKCy1Kwtwtozl4GQWYOqO8PgGMRWoFzaumg42tX5RnxpLxPuyudAQhmDgEIYAWbU+jT/mxhvy6ieahdxSEAEEIoEW70rmpxtkvygv3YpIraDZ6R8GkGfElCmDg0itpbjUd5G607UFCzFgyzofdg2dHwaQhCAG0ZVc6nWTM/aK8p/zYPRnoHQVThiAE0JY9GcbxuonmRUqY+BKaX6PvegBojdFfpQCGKaeK3iunwzyNvD1IiIWIjPJm999HoxBMFoIQQCv2ZNDxvqy5SVxhk/0Y9I6CCTOJyxTA8PyRwU3yNfrmIG+0lL34gJYq9F0PAO1AEAJoXomC3CimUd4mcn3ZiMlwT/ZwFhqFYJpM5EIFMCgHMrkREtZSpO96aM4EX2bffUyiANOEIATQvH336QRT6Rfljfdlj+dwcpW+6wGgBQhCAA2rUZKTudxY43kffUs4W5BezszJXDQKwQSZ1LUKYAhic7i+LkwHC33XQ9Mm+LL7MIkCTBGCEEDD9t2nE3xN8Mqa5Mvsu89xaBOCyTHByxVAj1SUHMrixpvWACHPz45xs2IuFSIJwdQgCAE06UIB9bRifG1NMAgJIdE+zAH0joLJQRACaNLBLC7aFJuDvGgf9kAmWoRgahCEAJp04D6N9jHZy6qfK1Mkp+mVyEIwKSZ7xQLoXlolLVLQvi4m2yJkGTJayh5EoxBMC4IQQGP45iBrsjlICCHjfJgDmRgmBJOCIATQmINZ3Dgfk45BQqIk7KUHtLJO3/UA0BwEIYBmVNSRyw9ohJeJX1O2ZmSgOxObjUYhmA4Tv2gBdOZ4NveEO2Nrpu96aN9YKXs4C8OEYDoQhACacTiLjjGt9UUfZZwPczgLK8yA6RDEdQugbZSQo9l0tNTEBwh5/naMowVzvQhRCCYCQQigAdeLqL05CbAXRBASQsZKmUPoHQVTgSAE0IBDWXSsMJqDvLE+7CFMogBTgSAE0IDDWZxABgh5g92Z5ApaUKPvegBogoAuXQAtKZSTpDI62ENALUIzloR7sccwiQJMAoIQoL2OZnPhXqy5wC6msVIGkyjANAjs2gXQgiNZdIyQBgh5o6Xs8RxOiTYhGD8EIUC7cJTE5XBR3oILQg8r4mPLXMZ7esH4IQgB2uVKIfWwZqQ2ggtCQshob+YIhgnB+CEIAdrlSDY3WnjNQd5oKXsUw4Rg/BCEAO1yJIuOFtLEifoGujGplZhEAUZPoBcwgEYUycm9cvqEu0BbhGKWhHuxsTnoHQXjhiAEaLvYHG64p+AmTtQ3RsocQe8oGDkBX8EA7XYsm44S3sSJ+kZKmOM5HF5FAUYNQQjQRpSQ4zlclETQQSixYTysmGt4EwUYMwQhQBvdLKYO5oy/naCDkBAyyps5mo0gBCOGIARoo2PZdKRQJ07UN9Ibi46CcUMQArTRsWxupARXEBniwdwupSUKfdcDoK1wGQO0RZWSXC+iwzzRIiQWIjLInfkzF41CMFYIQoC2iMvhBrgx1mJ918MwjPRmj+VgmBCMFYIQoC1ic2iUNy6fh0Z5M8fwvAwYLVzJAG0Riydl6gl0YEQMSSxDFoJRQhACtFp6JZXV0W5OCML/iZQwsegdBeOEIARotaPZdJSURQzWFylhjmPRUTBOCEKAVjueQyOFvaBMYxES9kweVaj0XQ+A1kMQArSOkiOn8rgIL1w7/+BoTro6MRceoHcUjA8uZoDWuVRIO9oxblb6rofhiZIwsVhiBowQghCgdWKzhb7Q9qNESlg8LwPGCEEI0DqxOTQCK6s1ZYAbk1pBC+X6rgdAK+F6BmiFslpyp5QOEuor6ZsnZslQT/YEnh0FY4MgBGiFEzncIA/GQqTvehiqSAlzHL2jYGwQhACtcDyHRqJf9NGiJAwWHQWjg0saoBUwg7B5gQ6MGYu11sDIIAgBWiq9klYrsbLaY0R4Ya01MDIIQoCWOpZNo7yxstpjYK01MDoIQoCWQr9oS4yQsKfzaC2iEIwHghCgRVSUnMrjMIPwsZwtSJADcxFrrYHxwFUN0CJXC6nEhvHAymotECFhMJsQjAiCEKBF4nLRL9pSERIWswnBiCAIAVokLgdvnGipQe7M7VJaVqvvegC0DC5sgMerVpJrRXSIB1qELWIpIgPdmNN56B0F44AgBHi803k0xIWxNdN3PYwHekfBiCAIAR4vLhf9oq0TIWHiEIRgJFp6bVdVVb3yyiuBgYGDBw8+depUk2VWr17dq1ev7t27f/311+qdW7ZsmTdvXmRk5MmTJ+sX3rZtW2hoaHBw8EcffcRx6EIBg4YZhK3V25kpraUZlchCMALiFpZ79913U1NTjx8/fu7cuYkTJ6akpLi4uNQvcOLEiffff//AgQNWVlYTJkyQSqXTpk0jhJw/f97Pzy82NjY/P19d+ObNm/PmzduzZ49EIpk6daqrq+trr72mwd8KQIMKakh2Fe3riiBsBYaQcC/2ZB593g7HDQxdi1qEcrl848aNS5cu9fX1jYmJ6dev32+//dagzC+//PLyyy/379+/Z8+eCxcuXLlyJb//559/fuedd5ycnOoXXrVq1YwZM8LDw4OCghYvXqwuDGCA4nK44Z6sCPfzVorwYk6gdxSMQYuCMCsrSyaT9e7dm/9naGhoQkJCgzJ37twJDQ1tpkCDwiEhIerCiYmJKpWqdRUH0JUTuTTCCzHYapESJi6XQxKC4WtR12hhYaGdnR3LPkxNBweHO3fuNC7j4ODAbzs6OhYXF3Mcp/6R5gurVKqSkhJXV9fGJRMTEzdt2rRr166H1RWLd+3apQ5RDZLJZBr/TKEx1WN4PNvy9QBFpfaHu+RyuVgsFotbOmBh4JwIsRNbXMiS9XDUXRqa6kmoS1VVVZSazh8w1tbWItFjXqXdokvO0dGRPzQMwxBCKisrnZ2dG5dRn4KVlZWOjo6PSsHGhVmWdXR0bLJkUFDQtGnTfvjhB/WeBr2sGmRnZ6elTxYO0zuGSeWUMKo+XrY6+C4zMzNTCkJCSJS36kKZ9RNSnT5wa3onoY4xDGNrq4sT3nC06ASVSqUsy6ampvL/TEpK8vf3b1CmU6dOiYmJ/HZiYmLjAs0UlkqlZmZNT9FiGMbCwsKpnpZUGEBTjufQKDwv2lYREiYOi46CwWtRENrZ2U2aNGn58uWU0r///vvYsWP/+te/CCEZGRnz58/ny8yaNWvNmjVlZWXV1dU///zzrFmz+P0ymay0tFSpVFZVVfEbfOHffvstLy+vrq7u+++/VxcGMDQncugIBGFbhXux5wqoAg8AgGFraZfFN998k5CQ4OzsPHz48G+//ZZv8BUVFW3bto0v8Mwzz0RERPj6+np5eXXp0mXevHn8/ueff75Tp05ZWVlvv/12p06dzp8/TwiJjIx87rnngoOD3dzcbGxs3n77bS38agDtpaLkTD4Xjqn0beVoToIdmQt4JRMYNqZVg6JVVVVWVlbNDP7V1dVxHGdhYdGST1MqlUql0tLSspkya9euvXTp0po1a1peybaprKzE0EI7md4xvPiAzj2rujVZR4N2JvawDO/9qypCyGd9H/O0gqaY3kmoezKZDGOEzbGxsWkmBQkhZmZmLUxBQohYLG4+BQH0Kw4LyrTbCAl7IhctQjBo6PMBeKQTudwI9Iu2zyB35k4pLVXoux4Aj4aLHKBpePWSRpizZIAbczofz46C4UIQAjTtTD5evaQZIyQs1loDQ4YgBGjaiRz0i2pGhBcTh2FCMGC4zgGaFpdLI/CkjCb0dmaK5TS7ClkIBgpBCNCEIjlJr6R9XRCEGsAy5EkvPDsKhgtBCNCEE7ncME/WDNeHhkR44YX1YLhwoQM0IS4Hr17SpEgJE5eDVzKBgUIQAjThBAYINcrPjrEWM3dKEYVgiBCEAA2lVFCFigQ7Igg1KUKC3lEwUAhCgIawspo2jPBi8LwMGCYEIUBDJ3Lx6iXNGyFhz+RzdVhhBgwPghDgHzhKTuVx4Z4IQg1ztiCd7JnLhWgUgsFBEAL8w/Vi6m7FSGwQhJqHSRRgmBCEAP8Ql4Hh2/oAACAASURBVIPnRbVlhIQ9kYu+UTA4CEKAfziRy43ADELtGOrB3CymFXX6rgfAPyEIAf5HriKXHtBhnrgutMJSRMJcmb/y0TsKhgUXPMD/nM2nPTsw9nj1ktaM8GJP5KB3FAwLghDgf07kchgg1KoICV7JBAYHQQjwP3E5FO8g1KpQFyaniuZV67seAPXgmgd4qFRB7pXT/m5oEWqRiCHDPdmTeHYUDAmCEOChE7ncEA/GHNeElmGtNTA0uOgBHjqRS0dIcEVoXYSEOY5p9WBIcNkDPHQc7yDUiUAHRsySxDJkIRgKBCEAIYRkVFJZHe3eAUGoCyO88OwoGBAEIQAhhMTm0EgJixjUjQgv9I6CAUEQAhCCJUZ1K0LCns7DK5nAUCAIAR6+eglLjOqMiyXpaMdcwSuZwDAgCAHI9WLqasl449VLOoRnR8FwIAgB0C+qB5ES9jgWHQXDgCAEIHE5WGJU1wa7M/EleCUTGAQEIQhdjZJcLsSrl3TNSkz6uzGnsNYaGABc/CB0Z/Jpb2e8ekkPIiUshgnBECAIQeiO53CRWFlNHyLxvAwYBlz/IHTHc2gkBgj1obczU1pLM2XIQtAzBCEIWkENyaqifV0QhHrAEBLuxWKtNdA7BCEIWlwON9yTFeM60BP0joIhwA0ABA39ovoVJWHicjgOUQh6hSAEQTuRi1cv6ZO3DeNiydwqQRKCPiEIQbjulFExSzo7IAj1KQq9o6BvCEIQrthsOsobKahnWGsN9A5BCMJ1PIfDAKHePenFXHpAq5T6rgcIGIIQBKqWI+cK6JNYWU3fbMQkxIX5Kx+9o6A3uAuAQJ3Np92cGCcLfdcD0DsK+oYgBIGKRb+owYiSMLHZaBGC3iAIQaBis2kUlhg1DKEuTEENza5CFoJ+4EYAQvSghmTIaD9XtAgNAsuQcC82DpMoQE8QhCBEx3O4J7GymiGJ8mZiEYSgJ7gTgBAdy6YjMYPQkIyUMMex1hroCYIQBIcSEpeLJ2UMi8SGcbdirhcjCUEPEIQgOLeKqb0Z42+HIDQsI72ZY3h2FPQBQQiCE5uDflFDFCVhY7MxmxD0AEEIgnMsm4vyxplvcIZ5MjeLaXmtvusBwoPbAQhLlZJcKaTDPNAiNDiWIjLAjTmVh0Yh6BqCEITlVB4Nc2VszfRdD2jKSG/2KIYJQecQhCAsR7O4kegXNVQjvRkEIege7gggLEfxDkID1s2J4ShJKkcWgk4hCEFA0itplZL26IAgNFwjvZmjWQhC0CkEIQjIoSw62ptFDBqykRLmGF7JBLqFIAQBOZbNYQahgYv0Zs/l0xq8sB50CEEIQlHLkb/yaQRevWTY7M1IL2fmDF5YDzqEmwIIxZk82s2J6YBX0hu8Ud7sUSwxAzqEIAShOJrNjcLECWMwWsocwfMyoEO4L4BQHM6iY6QYIDQCvZ2ZyjqSWoEsBB1BEIIgZFXRYgXt44wgNAIMZtaDbiEIQRAOZtLR3ixmThiL0VLmSBaGCUFHEIQgCEey6Gj0ixqPKAn7FyZRgK4gCMH01XLkTD6HiRNGxMEckyhAd3BrANN3Oo92d2KcMXHCqIyWskcwiQJ0AkEIpu9IFiZOGJ8xUuYwJlGATuDuAKbvYBYd54MBQiPTqwOjUJF7eBMFaB+CEExcagWV1dFemDhhhEZ5M4fQKATtQxCCidufScf5YN6EURorZQ5lYpgQtA5BCCbuUCY3FhMnjNMICXu5kJbX6rseYOoQhGDKZHXkSiEd4YXz3CjZiMkT7syJXDQKQbtwgwBTFpvDDXRnbM30XQ9oq7FS9lAmhglBuxCEYMoOZ9ExUpzkRmysD3M4i0MSglbhHgEmi6MYIDR6He0YJwvmaiGiELQIQQgm60ohdbZkOtkjCI1btA9zAM+OgjYhCMFkHcziMI/eBIzzYQ9imBC0CUEIJuvAfRrtgzPc6D3hzmRV0fsyZCFoC24TYJqyqmh2FR3ghhah0RMxZJQ3ewRLzIDWIAjBNB24T8f6sCLkoEkYh2FC0CYEIZimQ1l4XtR0jPJmz+bTarynF7QDQQgmqEpJzubTUZhBaCoczEmYK3M8B41C0ArcKcAEHc3iBroz9lhQxoRM8GX33ccwIWgFghBM0L77dIIvzm2TMsGXOZDJqRCFoAW4WYCpUVFyNJuLxgxC0+Jjy3jbMBcKkISgeQhCMDV/5VNfW8bbBkFoaib4MvvuY5gQNA9BCKZm330O/aImaYIvuxfDhKAFuF+AqTmQScf7ojlogno7M7UcuVuGLAQNQxCCSfm7hHKU9OyAIDRBDCETfBk0CkHjEIRgUvZk0El+SEGTNdGX/SMDw4SgYQhCMCl/ZHCTMEBouoZ5MhmVNKsKjULQJNwywHRkVNL8GjrQHS1CkyViyFgfzKwHDUMQgunYk0En+GKhbRM3yZdB7yhoFoIQTMcf97lJfjilTVykhL1WRIvk+q4HmJCW3jUopYsXL/by8pJIJEuWLGmyzMGDB4ODg52dnadMmVJSUsLvrKmpeeGFF1xdXTt27Lh+/Xp+Z35+ft96NmzY0O5fBISuoIYklNInPdEeNHFWYhIhYQ/irUygOeIWltuyZcvOnTsvXbqkUqmefPLJbt26TZ48uX6BBw8exMTEbNu2bdiwYS+++OL8+fM3btxICPniiy9SU1OTk5OTk5MjIyP79u3bo0eP2trau3fvnjlzhv9ZiUSi2d8KBGjvfW60N2sh0nc9QPsm+zFbU7nnAtH6B81o6Zm0du3aN998UyqV+vn5vfrqq+vWrWtQ4LfffhswYMCYMWNsbGw+/vjjHTt2VFZWEkLWrVu3ePFiR0fHsLCwqVOn/vrrrw+/mGVD/8vDw0ODvxII06507il/NAcFIdqH/Sufltfqux5gKloahImJiT179uS3e/bsmZiY2KBAUlJSr169+O3AwECGYTIyMsrLy/Py8tT7e/bsmZSUxG/X1NT06NEjNDT0nXfekclk7f09QNiKFeRKIR3pjSaCINiZkaEeLN5ZD5rS0q7RkpISOzs7ftve3r6oqKhxAS8vL/U/7e3ti4uLbWxsCCHqH3RwcOB/0MHBYceOHT179iwsLFywYEF6evr27dub/N67d++uXbt27dq16j2nTp0KDQ1tYbVbrqqqimHQnmgXPR7DbWmiER4slRv3n1RyuVwsFovFLb0qhWysJ7s9WTTRo67BflzI7VdVVaXvKmiStbU1yz7mT+SWXnIdOnSoqKjgt8vLy11dXRsX4PtCeRUVFS4uLs7Ozvy2lZUVIaSsrIz/QQcHB36IMSAgYPXq1SEhIQqFwsLCovH3BgcHz5kzZ82aNS2sZ5tRSm1tbbX9LaZNj8fwYK5ydiBra9vEKWRExP+l74oYgWlB5P+u13EWtg1ev4wLWSOEdgxb2pUUGBiYkJDAbyckJHTu3Llxgdu3b/PbKSkpHMf5+Pg4ODi4u7ur9yckJAQEBDT4QUtLS47jVCpVG38DELyyWnK+gI6Wol9UQBzNySAP5jB6R0ETWnrveP755//zn/8UFBTk5uauWLHi+eef5/c/++yz/HjhjBkzzp07d+LECblcvmTJkilTptjb2/M/+OWXX8pksvj4+J07d/I/ePHixZs3byoUioyMjH//+98RERHW1tba+QXB9O2/z42QsHZmjy8JpmSKP7s7A0vMgAa0NAhnzZo1bty47t279+7de/r06VOmTOH3x8fH84+6eHh4bN68ed68eW5ubqWlpd9//z1f4P333/fw8JBKpWPHjv3yyy/5B2eys7OffvppR0fHQYMGubm5bdq0SQu/GgjFtjRuWkcMCwnOZD82LoeTNRwlBGg1hlKD/pNq7dq1ly5d0sEYYWVlpfqhHmgbvRzDUgXpuL0ua7qZrfG3CPGwTGuNO6b8VwD7TKf//UGPC7n9ZDIZxggBjMmeDC5SwppACkIbPN2R3ZFu0H/Kg1FAEIJx245+UQGb6Mf+mcthZj20E4IQjFiRnFwupKP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7t+/v5navv7664cPHw4LC3N0dHRzc3tUscDAwEGDBnl7e1++fHnr1q0tecJj2rRpx44d6969e1BQ0K1bt9avX29hYdG2KZtaQVumuro6Ojraw8PD3d19ypQpCoWC329lZXX69Gl+++uvv3Z0dAwICAgKCkpKSuJ3fvnll/W/7oMPPqCUrlq1ysbGxtfX18HBYcCAAXfu3HnU965Zs2bOnDktrGR7VFRU6OBbTBuOYZt9cVMVc1JZU1NTV1enm2/ckqJ6Yr8mv2v58uVvvfWWBj9QI7Kzsy9dulRbW1tRUcEnQVVVVWVlJf9f09LSzp8/n5aWVv9HFApFSUlJXV1dXV3dgwcPmvzYysrKq1ev5ubmqvfI5XKZTNZkYaVSmZSUdOnSpfoF8vPzr1y50uCSqa2tvX379pUrV8rLyxt/bF1dnXo/pTQlJeX8+fMZGRnqPYWFheo7c311dXW3b9++e/euUqnk96hUqtLS0kfVNj4+Pikp6cGDB2ZmZo0LVFVV1dTUlJSUXLx4sX59CgoK+A31oW58WLKysq5evVpVVaXeU1JSwnEcv11eXq4+//lvqf+9mZmZUqm0yTq3XxP9sM148OABwzCuro/svpHJZCUlJVKplJ9Q0gyFQpGfn893AjRTbO3atZcuXeKfNdKqyspKjG+1E45h28jqSKcddX+NE/tYKMRicZOD5RrHUdJjt/KHgSJNDeN9/fXXBQUFy5cv18ingd4VFhZKJBK+O9cQZGVlDRo0KDMzUxsf3rpLrpnGMs/W1tbW1rYlH2VhYdF4oBFAgNYkccM92UAHpt6zHVrHMuT/erFf3lJFSIQxux5aydraetGiRfquhY5g9h6APtVx5Pvb3P/11MOVGNOJTakgFx7grRTQBBsbm88//1zftdARBCGAPm1K5oIdSaiLHh5aMWPJwh7s8niDeWABQE8QhAB6QwlZHs+900tvM4JeCGLPF3CJZWgUgqAhCAH05nAWtTEjw/U3h8FaTOYFszpbCA3AMCEIAfTmh9uq+d31fA2+EizalsoVNzd7G8DE4YExAP24U0YTSsnTHfUchG5WJNqH/TWJW9S+B3bEYvHmzZv//PNPTVWsbSilj527Bc0zzGNYW1urvWXFEIQA+vGf29y8YNbcADpl3uzOTjqumt+dFbejMnPmzBkyZIjmKtVGzS/+CS1hsMew8RrXmoIgBNCDUgXZkc4lTjGIN3r3cWZ8bMm++9xT/m1PQltb28avHdU9rOrQfjKZrIXTwU2GAfw5CiA8m5K50d6sm5W+6/FfLwezqxLxyAwIFIIQQA/WJnFzgw3o6nvKn40vocnlmEcBQmRAlyKAQJzNp0pKhngY0PMI5iyZGcCuu4dGIQgRghBA11YlcnO7sAYUg4QQQuYFs+vvcQoTf00hQBMQhAA6VaIgBzO5mZ0N7tLrZM90d2L23kejEATH4K5GANP2eyo3Rso6W+i7Hk15MYj9NQlBCIKDIATQqfX3uNmBBnrdTfRjrxXRrCo8MgPCYqAXJIBJul1KH9SQJ70MbXzwIUsRmdqR3ZyMIARhQRAC6M66JG52ICMy0BwkhJDnOrMbkjkkIQgKghBAR+o48nsq96zhPSZTX383xlJEzhcgCkFADPqaBDAlh7K4Lg5MJ3sDbg8SQgiZGcBuwIRCEBIEIYCO/JZCDXDWRGMzApjdGVyNUt/1ANAVI7gsAUxARR2Jy+Em+xnBFedlzfTuwBzJRqMQhMIILksAE7ArnQv3YjsY5PTBxmYEsFtSMEwIQoEgBNCFLSncjE6GPjqoNrUjezKXK6vVdz0AdAJBCKB1udX0RjEdIzWay83ejIR7sbvT0TsKgmA0VyaA8dqeRif5slZG9RrsGQHM76kIQhAEBCGA1m1L5WICjOxaGytlbxTT3GqMFILpM7KLE8DopFfS9Eo6zJDePtgSFiIS7cP+kYEgBNOHIATQrh1pdIo/KzbCS+3pjuz2NPSOgukzwqsTwKjsSOemdTTKCy1Kwtwtozl4GQWYOqO8PgGMRWoFzaumg42tX5RnxpLxPuyudAQhmDgEIYAWbU+jT/mxhvy6ieahdxSEAEEIoEW70rmpxtkvygv3YpIraDZ6R8GkGfElCmDg0itpbjUd5G607UFCzFgyzofdg2dHwaQhCAG0ZVc6nWTM/aK8p/zYPRnoHQVThiAE0JY9GcbxuonmRUqY+BKaX6PvegBojdFfpQCGKaeK3iunwzyNvD1IiIWIjPJm999HoxBMFoIQQCv2ZNDxvqy5SVxhk/0Y9I6CCTOJyxTA8PyRwU3yNfrmIG+0lL34gJYq9F0PAO1AEAJoXomC3CimUd4mcn3ZiMlwT/ZwFhqFYJpM5EIFMCgHMrkREtZSpO96aM4EX2bffUyiANOEIATQvH336QRT6Rfljfdlj+dwcpW+6wGgBQhCAA2rUZKTudxY43kffUs4W5BezszJXDQKwQSZ1LUKYAhic7i+LkwHC33XQ9Mm+LL7MIkCTBGCEEDD9t2nE3xN8Mqa5Mvsu89xaBOCyTHByxVAj1SUHMrixpvWACHPz45xs2IuFSIJwdQgCAE06UIB9bRifG1NMAgJIdE+zAH0joLJQRACaNLBLC7aFJuDvGgf9kAmWoRgahCEAJp04D6N9jHZy6qfK1Mkp+mVyEIwKSZ7xQLoXlolLVLQvi4m2yJkGTJayh5EoxBMC4IQQGP45iBrsjlICCHjfJgDmRgmBJOCIATQmINZ3Dgfk45BQqIk7KUHtLJO3/UA0BwEIYBmVNSRyw9ohJeJX1O2ZmSgOxObjUYhmA4Tv2gBdOZ4NveEO2Nrpu96aN9YKXs4C8OEYDoQhACacTiLjjGt9UUfZZwPczgLK8yA6RDEdQugbZSQo9l0tNTEBwh5/naMowVzvQhRCCYCQQigAdeLqL05CbAXRBASQsZKmUPoHQVTgSAE0IBDWXSsMJqDvLE+7CFMogBTgSAE0IDDWZxABgh5g92Z5ApaUKPvegBogoAuXQAtKZSTpDI62ENALUIzloR7sccwiQJMAoIQoL2OZnPhXqy5wC6msVIGkyjANAjs2gXQgiNZdIyQBgh5o6Xs8RxOiTYhGD8EIUC7cJTE5XBR3oILQg8r4mPLXMZ7esH4IQgB2uVKIfWwZqQ2ggtCQshob+YIhgnB+CEIAdrlSDY3WnjNQd5oKXsUw4Rg/BCEAO1yJIuOFtLEifoGujGplZhEAUZPoBcwgEYUycm9cvqEu0BbhGKWhHuxsTnoHQXjhiAEaLvYHG64p+AmTtQ3RsocQe8oGDkBX8EA7XYsm44S3sSJ+kZKmOM5HF5FAUYNQQjQRpSQ4zlclETQQSixYTysmGt4EwUYMwQhQBvdLKYO5oy/naCDkBAyyps5mo0gBCOGIARoo2PZdKRQJ07UN9Ibi46CcUMQArTRsWxupARXEBniwdwupSUKfdcDoK1wGQO0RZWSXC+iwzzRIiQWIjLInfkzF41CMFYIQoC2iMvhBrgx1mJ918MwjPRmj+VgmBCMFYIQoC1ic2iUNy6fh0Z5M8fwvAwYLVzJAG0Riydl6gl0YEQMSSxDFoJRQhACtFp6JZXV0W5OCML/iZQwsegdBeOEIARotaPZdJSURQzWFylhjmPRUTBOCEKAVjueQyOFvaBMYxES9kweVaj0XQ+A1kMQArSOkiOn8rgIL1w7/+BoTro6MRceoHcUjA8uZoDWuVRIO9oxblb6rofhiZIwsVhiBowQghCgdWKzhb7Q9qNESlg8LwPGCEEI0DqxOTQCK6s1ZYAbk1pBC+X6rgdAK+F6BmiFslpyp5QOEuor6ZsnZslQT/YEnh0FY4MgBGiFEzncIA/GQqTvehiqSAlzHL2jYGwQhACtcDyHRqJf9NGiJAwWHQWjg0saoBUwg7B5gQ6MGYu11sDIIAgBWiq9klYrsbLaY0R4Ya01MDIIQoCWOpZNo7yxstpjYK01MDoIQoCWQr9oS4yQsKfzaC2iEIwHghCgRVSUnMrjMIPwsZwtSJADcxFrrYHxwFUN0CJXC6nEhvHAymotECFhMJsQjAiCEKBF4nLRL9pSERIWswnBiCAIAVokLgdvnGipQe7M7VJaVqvvegC0DC5sgMerVpJrRXSIB1qELWIpIgPdmNN56B0F44AgBHi803k0xIWxNdN3PYwHekfBiCAIAR4vLhf9oq0TIWHiEIRgJFp6bVdVVb3yyiuBgYGDBw8+depUk2VWr17dq1ev7t27f/311+qdW7ZsmTdvXmRk5MmTJ+sX3rZtW2hoaHBw8EcffcRx6EIBg4YZhK3V25kpraUZlchCMALiFpZ79913U1NTjx8/fu7cuYkTJ6akpLi4uNQvcOLEiffff//AgQNWVlYTJkyQSqXTpk0jhJw/f97Pzy82NjY/P19d+ObNm/PmzduzZ49EIpk6daqrq+trr72mwd8KQIMKakh2Fe3riiBsBYaQcC/2ZB593g7HDQxdi1qEcrl848aNS5cu9fX1jYmJ6dev32+//dagzC+//PLyyy/379+/Z8+eCxcuXLlyJb//559/fuedd5ycnOoXXrVq1YwZM8LDw4OCghYvXqwuDGCA4nK44Z6sCPfzVorwYk6gdxSMQYuCMCsrSyaT9e7dm/9naGhoQkJCgzJ37twJDQ1tpkCDwiEhIerCiYmJKpWqdRUH0JUTuTTCCzHYapESJi6XQxKC4WtR12hhYaGdnR3LPkxNBweHO3fuNC7j4ODAbzs6OhYXF3Mcp/6R5gurVKqSkhJXV9fGJRMTEzdt2rRr166H1RWLd+3apQ5RDZLJZBr/TKEx1WN4PNvy9QBFpfaHu+RyuVgsFotbOmBh4JwIsRNbXMiS9XDUXRqa6kmoS1VVVZSazh8w1tbWItFjXqXdokvO0dGRPzQMwxBCKisrnZ2dG5dRn4KVlZWOjo6PSsHGhVmWdXR0bLJkUFDQtGnTfvjhB/WeBr2sGmRnZ6elTxYO0zuGSeWUMKo+XrY6+C4zMzNTCkJCSJS36kKZ9RNSnT5wa3onoY4xDGNrq4sT3nC06ASVSqUsy6ampvL/TEpK8vf3b1CmU6dOiYmJ/HZiYmLjAs0UlkqlZmZNT9FiGMbCwsKpnpZUGEBTjufQKDwv2lYREiYOi46CwWtRENrZ2U2aNGn58uWU0r///vvYsWP/+te/CCEZGRnz58/ny8yaNWvNmjVlZWXV1dU///zzrFmz+P0ymay0tFSpVFZVVfEbfOHffvstLy+vrq7u+++/VxcGMDQncugIBGFbhXux5wqoAg8AgGFraZfFN998k5CQ4OzsPHz48G+//ZZv8BUVFW3bto0v8Mwzz0RERPj6+np5eXXp0mXevHn8/ueff75Tp05ZWVlvv/12p06dzp8/TwiJjIx87rnngoOD3dzcbGxs3n77bS38agDtpaLkTD4Xjqn0beVoToIdmQt4JRMYNqZVg6JVVVVWVlbNDP7V1dVxHGdhYdGST1MqlUql0tLSspkya9euvXTp0po1a1peybaprKzE0EI7md4xvPiAzj2rujVZR4N2JvawDO/9qypCyGd9H/O0gqaY3kmoezKZDGOEzbGxsWkmBQkhZmZmLUxBQohYLG4+BQH0Kw4LyrTbCAl7IhctQjBo6PMBeKQTudwI9Iu2zyB35k4pLVXoux4Aj4aLHKBpePWSRpizZIAbczofz46C4UIQAjTtTD5evaQZIyQs1loDQ4YgBGjaiRz0i2pGhBcTh2FCMGC4zgGaFpdLI/CkjCb0dmaK5TS7ClkIBgpBCNCEIjlJr6R9XRCEGsAy5EkvPDsKhgtBCNCEE7ncME/WDNeHhkR44YX1YLhwoQM0IS4Hr17SpEgJE5eDVzKBgUIQAjThBAYINcrPjrEWM3dKEYVgiBCEAA2lVFCFigQ7Igg1KUKC3lEwUAhCgIawspo2jPBi8LwMGCYEIUBDJ3Lx6iXNGyFhz+RzdVhhBgwPghDgHzhKTuVx4Z4IQg1ztiCd7JnLhWgUgsFBEAL8w/Vi6m7FSGwQhJqHSRRgmBCEAP8Ql4Hh2/oAACAASURBVIPnRbVlhIQ9kYu+UTA4CEKAfziRy43ADELtGOrB3CymFXX6rgfAPyEIAf5HriKXHtBhnrgutMJSRMJcmb/y0TsKhgUXPMD/nM2nPTsw9nj1ktaM8GJP5KB3FAwLghDgf07kchgg1KoICV7JBAYHQQjwP3E5FO8g1KpQFyaniuZV67seAPXgmgd4qFRB7pXT/m5oEWqRiCHDPdmTeHYUDAmCEOChE7ncEA/GHNeElmGtNTA0uOgBHjqRS0dIcEVoXYSEOY5p9WBIcNkDPHQc7yDUiUAHRsySxDJkIRgKBCEAIYRkVFJZHe3eAUGoCyO88OwoGBAEIQAhhMTm0EgJixjUjQgv9I6CAUEQAhCCJUZ1K0LCns7DK5nAUCAIAR6+eglLjOqMiyXpaMdcwSuZwDAgCAHI9WLqasl449VLOoRnR8FwIAgB0C+qB5ES9jgWHQXDgCAEIHE5WGJU1wa7M/EleCUTGAQEIQhdjZJcLsSrl3TNSkz6uzGnsNYaGABc/CB0Z/Jpb2e8ekkPIiUshgnBECAIQeiO53CRWFlNHyLxvAwYBlz/IHTHc2gkBgj1obczU1pLM2XIQtAzBCEIWkENyaqifV0QhHrAEBLuxWKtNdA7BCEIWlwON9yTFeM60BP0joIhwA0ABA39ovoVJWHicjgOUQh6hSAEQTuRi1cv6ZO3DeNiydwqQRKCPiEIQbjulFExSzo7IAj1KQq9o6BvCEIQrthsOsobKahnWGsN9A5BCMJ1PIfDAKHePenFXHpAq5T6rgcIGIIQBKqWI+cK6JNYWU3fbMQkxIX5Kx+9o6A3uAuAQJ3Np92cGCcLfdcD0DsK+oYgBIGKRb+owYiSMLHZaBGC3iAIQaBis2kUlhg1DKEuTEENza5CFoJ+4EYAQvSghmTIaD9XtAgNAsuQcC82DpMoQE8QhCBEx3O4J7GymiGJ8mZiEYSgJ7gTgBAdy6YjMYPQkIyUMMex1hroCYIQBIcSEpeLJ2UMi8SGcbdirhcjCUEPEIQgOLeKqb0Z42+HIDQsI72ZY3h2FPQBQQiCE5uDflFDFCVhY7MxmxD0AEEIgnMsm4vyxplvcIZ5MjeLaXmtvusBwoPbAQhLlZJcKaTDPNAiNDiWIjLAjTmVh0Yh6BqCEITlVB4Nc2VszfRdD2jKSG/2KIYJQecQhCAsR7O4kegXNVQjvRkEIege7gggLEfxDkID1s2J4ShJKkcWgk4hCEFA0itplZL26IAgNFwjvZmjWQhC0CkEIQjIoSw62ptFDBqykRLmGF7JBLqFIAQBOZbNYQahgYv0Zs/l0xq8sB50CEEIQlHLkb/yaQRevWTY7M1IL2fmDF5YDzqEmwIIxZk82s2J6YBX0hu8Ud7sUSwxAzqEIAShOJrNjcLECWMwWsocwfMyoEO4L4BQHM6iY6QYIDQCvZ2ZyjqSWoEsBB1BEIIgZFXRYgXt44wgNAIMZtaDbiEIQRAOZtLR3ixmThiL0VLmSBaGCUFHEIQgCEey6Gj0ixqPKAn7FyZRgK4gCMH01XLkTD6HiRNGxMEckyhAd3BrANN3Oo92d2KcMXHCqIyWskcwiQJ0AkEIpu9IFiZOGJ8xUuYwJlGATuDuAKbvYBYd54MBQiPTqwOjUJF7eBMFaB+CEExcagWV1dFemDhhhEZ5M4fQKATtQxCCidufScf5YN6EURorZQ5lYpgQtA5BCCbuUCY3FhMnjNMICXu5kJbX6rseYOoQhGDKZHXkSiEd4YXz3CjZiMkT7syJXDQKQbtwgwBTFpvDDXRnbM30XQ9oq7FS9lAmhglBuxCEYMoOZ9ExUpzkRmysD3M4i0MSglbhHgEmi6MYIDR6He0YJwvmaiGiELQIQQgm60ohdbZkOtkjCI1btA9zAM+OgjYhCMFkHcziMI/eBIzzYQ9imBC0CUEIJuvAfRrtgzPc6D3hzmRV0fsyZCFoC24TYJqyqmh2FR3ghhah0RMxZJQ3ewRLzIDWIAjBNB24T8f6sCLkoEkYh2FC0CYEIZimQ1l4XtR0jPJmz+bTarynF7QDQQgmqEpJzubTUZhBaCoczEmYK3M8B41C0ArcKcAEHc3iBroz9lhQxoRM8GX33ccwIWgFghBM0L77dIIvzm2TMsGXOZDJqRCFoAW4WYCpUVFyNJuLxgxC0+Jjy3jbMBcKkISgeQhCMDV/5VNfW8bbBkFoaib4MvvuY5gQNA9BCKZm330O/aImaYIvuxfDhKAFuF+AqTmQScf7ojlogno7M7UcuVuGLAQNQxCCSfm7hHKU9OyAIDRBDCETfBk0CkHjEIRgUvZk0El+SEGTNdGX/SMDw4SgYQhCMCl/ZHCTMEBouoZ5MhmVNKsKjULQJNwywHRkVNL8GjrQHS1CkyViyFgfzKwHDUMQgunYk0En+GKhbRM3yZdB7yhoFoIQTMcf97lJfjilTVykhL1WRIvk+q4HmJCW3jUopYsXL/by8pJIJEuWLGmyzMGDB4ODg52dnadMmVJSUsLvrKmpeeGFF1xdXTt27Lh+/Xp+Z35+ft96NmzY0O5fBISuoIYklNInPdEeNHFWYhIhYQ/irUygOeIWltuyZcvOnTsvXbqkUqmefPLJbt26TZ48uX6BBw8exMTEbNu2bdiwYS+++OL8+fM3btxICPniiy9SU1OTk5OTk5MjIyP79u3bo0eP2trau3fvnjlzhv9ZiUSi2d8KBGjvfW60N2sh0nc9QPsm+zFbU7nnAtH6B81o6Zm0du3aN998UyqV+vn5vfrqq+vWrWtQ4LfffhswYMCYMWNsbGw+/vjjHTt2VFZWEkLWrVu3ePFiR0fHsLCwqVOn/vrrrw+/mGVD/8vDw0ODvxII06507il/NAcFIdqH/Sufltfqux5gKloahImJiT179uS3e/bsmZiY2KBAUlJSr169+O3AwECGYTIyMsrLy/Py8tT7e/bsmZSUxG/X1NT06NEjNDT0nXfekclk7f09QNiKFeRKIR3pjSaCINiZkaEeLN5ZD5rS0q7RkpISOzs7ftve3r6oqKhxAS8vL/U/7e3ti4uLbWxsCCHqH3RwcOB/0MHBYceOHT179iwsLFywYEF6evr27dub/N67d++uXbt27dq16j2nTp0KDQ1tYbVbrqqqimHQnmgXPR7DbWmiER4slRv3n1RyuVwsFovFLb0qhWysJ7s9WTTRo67BflzI7VdVVaXvKmiStbU1yz7mT+SWXnIdOnSoqKjgt8vLy11dXRsX4PtCeRUVFS4uLs7Ozvy2lZUVIaSsrIz/QQcHB36IMSAgYPXq1SEhIQqFwsLCovH3BgcHz5kzZ82aNS2sZ5tRSm1tbbX9LaZNj8fwYK5ydiBra9vEKWRExP+l74oYgWlB5P+u13EWtg1ev4wLWSOEdgxb2pUUGBiYkJDAbyckJHTu3Llxgdu3b/PbKSkpHMf5+Pg4ODi4u7ur9yckJAQEBDT4QUtLS47jVCpVG38DELyyWnK+gI6Wol9UQBzNySAP5jB6R0ETWnrveP755//zn/8UFBTk5uauWLHi+eef5/c/++yz/HjhjBkzzp07d+LECblcvmTJkilTptjb2/M/+OWXX8pksvj4+J07d/I/ePHixZs3byoUioyMjH//+98RERHW1tba+QXB9O2/z42QsHZmjy8JpmSKP7s7A0vMgAa0NAhnzZo1bty47t279+7de/r06VOmTOH3x8fH84+6eHh4bN68ed68eW5ubqWlpd9//z1f4P333/fw8JBKpWPHjv3yyy/5B2eys7OffvppR0fHQYMGubm5bdq0SQu/GgjFtjRuWkcMCwnOZD82LoeTNRwlBGg1hlKD/pNq7dq1ly5d0sEYYWVlpfqhHmgbvRzDUgXpuL0ua7qZrfG3CPGwTGuNO6b8VwD7TKf//UGPC7n9ZDIZxggBjMmeDC5SwppACkIbPN2R3ZFu0H/Kg1FAEIJx245+UQGb6Mf+mcthZj20E4IQjFiRnFwupKPwvKhQ2ZuRoZ6YWQ/thTsIGLE9GdxoKWuDMTUBe9qf2ZGG3lFoFwQhGLHfU7np6BcVtol+7NkCrlih73qAMUMQgrHKraa3S7C+qNDZiEmkhN2djt5RaDvcRMBYbUmhk/3x3iUg0zsxW1MRhNB2CEIwVltTuemdcAIDGSNlb5fS7CqMFEIb4T4CRimxjBbUkKEeGCAEYs6Sib7sdjwyA22FIASjxC+rJkIOAiGEkOmdWPSOQpshCMH4UEK2pNAZATh74aFhnkx+DblbhkYhtAVuJWB8LhRQM5aEuqA9CA+JGBLTifktBY1CaAsEIRifzSncrM44deEfnu3M/pZCObQJofVwNwEjU8uR3encjAA0B+EfujkxTubkfCHuadBqOGnAyBzK5Lo7MVIbBCE0NLMzu+0+JpZCqyEIwchsTqEz0S8KTYnpxB7IZmuU+q4HGBvcUMCYFMrJn7ncU/44b6EJntakrzO3JwOPzEDr4IYCxmRLCjfel7XHa3jhEWb4qTYkIwihdRCEYEw23ONmB+KkhUca583dKqZplXh4FFoB9xQwGteKaEUdllWD5pizZFpH9rcUBCG0AoIQjMb6e9zsQJZFDkKzZgey6+9xmFAILYcgBOMgV5HtadyszohBeIwQF8bRnJzKQxJCSyEIwTjsTuf6ujC+tghCeLwXgti1SXhkBloKQQjGYU0S92IXnK7QIjMD2KPZXKFc3/UAI4E7CxiBe+U0qYxG++B0hRZxMCfRPizW4IYWwp0FjMCaRO65QNYMZyu02ItB7OpEPDEDLYJbCxi6Wo5sTuFeCMK5Cq0w2INhCDmXjyiEx8PNBQzdnnSuRwcmwB6PyUDrvNSFXZmI3lF4PAQhGLqf73KvBONEhVZ7LpA9nMU9qNF3PcDg4f4CBu1OGU2rIOPwmAy0nqM5ecqP/fUeGoXwGLi/gEH7KYGbF4zHZKCNXu3K/nKXU2GgEJqFGwwYrso6sj2NeyEIo4PQRr2dGS9rciQLSQjNQRCC4dqYzEVKWC9rBCG03Std2Z/uqPRdCzBoCEIwUJSQnxK4N7vjFIV2mdaRjS+hd8vQKIRHwl0GDNThLGprRga6oTkI7WLOkrldRD8m4JEZeCQEIRioH26r5qM5CJrwcjC7PY0rUei7HmCocKMBQ3S3jN4upVM74vwEDXCzIuN8MI8CHgk3GjBE393mXg4WmeP0BA15sxv7YwJXhyiEpuBOAwbnQQ3Znc69jNVkQHNCXJgAe7IjDUkITcC9BgzOfxJUMZ1YF0t91wNMy6KeomXxeB8FNAFBCIalWknWJHH/xmMyoGmjvBmWISdyEIXQEG43YFjWJXHDPNhOeNcEaMG/u7PL4zG5HhpCEIIBqePIN39z/9cLpyVoxfRObGI5uVaERiH8A+44YEA2p3BdHElfFzQHQSvMWfJWD/aLm3hkBv4BQQiGQkXJslvce71F+q4ImLIXu7AXH9DbpWgUwv8gCMFQ7ErnOliQoR5oDoIWWYrIG93Yr26hUQj/gyAEg8BR8vlN7sMQNAdB617pyh7L5pLL0SiEhxCEYBB2pnMWLBnpjeYgaJ2dGXmjm2jJDTQK4SEEIegf3xz8PEyEGATd+Hd39ngOl4h3MwEhBEEIhmBrKmdnRqIkyEHQEVsz8kZ3NArhIQQh6JmSI5/e4JaEYnQQdOr1ruzJXA6PjwJBEILe/XqP87Im4V5oDoJO2ZqRt3uJFl9FoxAQhKBXNUry2Q3uyzA0B0EPXunK3i6h5wrQKBQ6BCHo0w8J3EB3pr8bmoOgB+Ys+SiEfecKVh8VOgQh6E2Jgnz7t2pJKE5C0JsZAWx5LTmQiQ5SQcM9CPTm4+uqZzqxgQ5oDoLeiBjy3QDRgotcLaJQwBCEoB+JZXR7GvdhH4wOgp6N8GICHcgvd5CEwoUgBP1YeEn1Xi8RXkMPhuCb/qIvbqmK5PquB+gJghD04HAWTakgr3TF6QcGoYsjM60j+9F1PDUjULgTga4pVGT+RdV3A0RmOPvAYHwSItqdzl0uxFQKIcKtCHTtq3iuRwdmjBTPyIABcbIgS8NEr55TcYhC4UEQgk6lV9IfE1Tf9seJBwbnuUDWXETWJeGpGcHB/Qh0at5Z1aKeIh9bNAfB4DCE/DJI9P41VX6NvqsCuoUgBN3ZlMwV1JD53XHWgYHq2YGZE8S+cR5PzQgLbkmgI0Vy8s4V1bqheEYGDNqHfUS3S+ne++ggFRDck0BHXj6nmhnAhrqgUxQMmoWIrBwsev08V6LQd1VAVxCEoAtbUrg7pfQTvHQQjMFQD2aKP/MqOkgFA0EIWpdbTRdcUm0cLrJEDoKR+DJM9HcJ3Z6GDlJBQBCCdnGUPHda9VpXUV90ioLxsBCR9UNFb15QZVdhXqHpQxCCdn0Vz8lV5L3eONPAyIS5Mm90E8X8qVIhCk0dbk+gRZcL6fe3VZuHi0RoDYIReqcXaykiS25gsNDEIQhBW4rkZNpJ1ZrBIl9MnwfjxDJk03DxmkQal4NWoSlDEIJWcJTMPKV8piMz3hfnGBgxDyuyY4ToX6eU6ZXIQpOFmxRoxQfXVHUc+awvnhMFozfInXmrp2jaSZUCXaQmCkEImrc1lfs9lW4NF2NoEEzDwh6svx0z5y88N2OaEISgYVeL6PyLqn2RIle8fR5MBUPIhqGilAr6+Q3MLDRBCELQpLRKOiFW9etQcc8OaAyCSbESkz8ixWuTuK2pyEJTI9Z3BcB0FMqZUadUH/Rh8dJdMEkeVuTgSFHEYaWrJRMhwUluOtAiBM2orCNPnTGL6cTMC8ZJBSaruxOza4R4xinltSIMF5oO3LNAA2R1ZMwxZT8X+nEIHhMFEzfYg1kzWDTumPJWCbLQRKBrFNqrWknGxSqDHZnlveoIwRMyYPrG+7K1HBl9VBk7WtzdCX2kRg8tQmiXijoy6qiykx2zchDmSoCATPFnvxsgijqivI4+UuOHIIS2K1WQqCPK7k7MmiEiFjEIAjOtI7t6sHjsMeW5AmShcUMQQhulVdKB+5URXsyKQUhBEKhxPsym4eJJx5V/ZGBOhRFDEEJbXHxABx9Q/rs7i0XUQOAiJczRUeI3LnDf3UYWGisEIbTahnvchOPKtUPEmCkBQAgJcWHORYs23ONeOIP1SI0SbmTQCgoVef286stb3KmxYsyaB1DzsWXOjxfLlGTYIWWmDEOGRgZBCC2VXE6fOKDMryGXJoiDHZGCAP9gIybbwkVT/dl++zBkaGQQhPB4lJBVidygA8o5QezOESIHc31XCMAgMYQs7MHujxIvusy9dFZVWafvCkHLIAjhMdIr6agjyvX3uDPjxC9jUBDgcfq5MjcmiRlCeu5RxuLV9sYA9zV4pFqOLL3F9dunHCFhz0WLu6A7FKBl7MzIqsGiVYNFL59VPXNSlVuNODRoCEJo2u50rusu5cUH9OpE8f/1ZLFsDEBrRUmY20+JOzuQnruVn97gqpX6rhA8AoIQGjqeQ5/Yr1xyg1s1WLQvUuRriwwEaCMrMVkSKro6UXynlAbuVP50h8P8CgOERbfhIUrIgfvcsniuREE+7MM+3ZHFejEAGuFnx2wLF90oph9eUy27xc3vwb4YxNqa6bta8F8IQiAVdWRTMvfzHc5WTP6vFzvZDx2hAJrXx5k5ECW+XkSXxXNf3Kx7tjM7L5gNsMfFpn8IQuHiKDmTTzfc4/ZnciO92dWDRUM8cE0CaFeIC7MtXJRRya5M5AYdUHZ3Yp4LZCf7sTa4GesPjr3gqCg5V0D/yOB2plNXS/JsZ3ZZPzM3K31XC0BI/OyYL8NEn4SIDmRyG+5xr59XjfRmp/gzI71Ze3SZ6lzrgrCurs7MrLn/SxzHUUpFooYLMT/qB5VKpViMMNaFrCoal0Njc2hcDudry0zwZU+MYYMc0AQE0BsLEZniz07xZ0sUZE8Gt+EeN+eMqp8bEylhIyVMrw4Mxul1o6VPjebn54eHhzs7O7u6um7cuLFxAUrpggULHB0dnZyc5syZo1Q+fFI4ISGhV69ezs7Ovr6+cXFx6vKffvqpo6Njhw4dpk2bVlNT0/7fBBpQqMjVIrriDvfsaVXH7cqwvcpj2TTCi7k5SXx1oviDPkhBAEPRwYLMCWIPjRTnzjB7vSubKaMz/lS5/FY3Plb1+U0uLoeWKvRdRZPW0tbYwoUL/fz8jh8/fuvWrWHDhg0fPtzX17d+gR07dhw4cCAtLc3S0nLYsGGrV69+5ZVXCCHPPvvsM88888477+zbt++ZZ57JysqysrI6efLkypUr//77b1dX17Fjxy5btuyjjz7S/C8nJHIVSamg98ppUjm5XUJvl9LkChpoz4S5MkM9mHd6sVgdFMDw2YjJeF92vC8hhDyoIWcLuAsFdMkN7mYx7WDJ9OzAdHMkwU5MkAMTYM90sNB3dU0FQ+njlzyQyWQuLi7x8fGBgYGEkMmTJ4eGhi5evLh+mdGjR4eHhy9atIgQsmHDhhUrVly+fPn27dv9+/cvKiqysrIihHTr1u3jjz+eOnXqrFmzPDw8li1bRgg5dOjQa6+9lp6e3uRXr1279tKlS2vWrGn/r9q8yspKOzs7bX9Le9RxpFhBiuW0SE5yq2lBDcmpotnVJEtG0ytJsYL62TJBjkwXB9LNienmxHR3Yix0+65Awz+GBk4ul4vFYgwWtIepnoSUkNQKGl9C75SSO2X0XjlNqaAMIf52jNSW8bUlntaMxJq4WjKe1sTZkjhbMNZtPY9kMpmtra1Gq2/oWnSoMjMzVSpV586d+X927do1JSWlQZmUlJTXXnutQYGUlBR/f38+Bfn9ycnJ/P7w8HD1zvv379fW1pqbN7GWM6VUoVCUlpaq9zg5OTVT1bJa0oJkb4KsllG2svOhWkkVzS4xX6Mk8nqTZ5UcUS/CK1eRGhUlhFTVkVqO1HFEVkdqOVKlpFV1RMGRMgWRKamsjlTUktJaUqqg1UribElcLBhXK+JpzbhbEW8bpo8L8bFhfe2IxBrDCQAmiyEkwJ4JsGcm+/1vZ7GCZFTSrCqaKSN51TSxjBTKudwqUqQgxXJKCHGyII7mjIM5sTUjTuaMjRmxYImjBTFniY2YsRARazFhCHG0IIQQMUPszBhCSE0N62RLreqFg4gh9s0utc8S4mCuuxuQnRkRa3QxmBYFYVlZmY2NDcM8/D3t7OxKSkoal1H/EWFnZ1dWVsZxHP+D6jJ2dnZ8pDUoTCktLy93dXVt/NWJiYnbt28/cOCAes/evXtDQ0ObrGdSBRMZZ9a2Rf0oNWOY2lb9iLWYMWea+zYrMbGs1yZjCVWfTBYstRIxhBBrMTVniRlLbMTUjCW2YsbFklqIiKMztRYRWzNib0YdzIijObFv5jejpLqqVXXXiqqqKvVJAm2AFmH7CeoktCAkyJIEWRLi3MR/rVGS0lpSoWQq6hhZHSmvI1VKRqEiFXWMQkkK5LSWY6qVhBJSXssQQpSUyJSEEKJSkVpaq+D+dxhVlFQ0e3fkCKnQ4as23uuuejmwpSv0WFtbs+xjYrNFl5yLi0tlZSXHcfzHlZaWuru7Ny5TXl7Ob5eVlbm6urIs6+LiUlFRoS5TWloaHBzcuLBIJOrQoUOTXx0cHDxr1qwWdo2G2pKSWS0p2ART7VHRJUqp0HpUNEv8X/quiBHDSahmS0gTbYsWkMlktrbWGq6NYWtR81IqlVpbW8fHx/P/vHnzZpcuXRqU6dq1640bNxoU6NKlS1pamjrzbt68yQdh165db968qd4ZFBTUeMYFAACADrQoCK2srGbOnPnBBx/k5+fv2bPnwoUL//rXvwghd+/eHTVqFF/mpZdeWrly5c2bN5OTk7/55puXXnqJEBIQEDBkyJDFixcXFRV9//33HMfx5V988cUtW7acO3cuMzPziy++ePHFF7X2CwIAADSnpZ0wX3311fz58/v16+fh4bF79243NzdCCMdxCsXDJ0xGjhy5ePHi6dOnK5XK559/PiYmht+/adOmV199NSQkJCAg4ODBg3y3T2ho6A8//PDyyy9XVlZOnz799ddf18KvBgAA8Hgtmj6hRzqbPvHZZ58tWrTIwgITc9qooKBgx44d+JumPfbu3SuRSMLCwvRdESP26aefvvvuu80vgAXNyM3N3bdv38svv6zviugU3kf40IoVK4qLi/VdCyN27969bdu26bsWxi02NvbChQv6roVx+/HHH8vKyvRdCyPGP6iv71roGoIQAAAEDUEIAACChiAEAABBM/SHZd57772ff/7ZxcVF21+UmZkpkUgwnbHNFApFSUmJp6envitixIqLi83NzbGwQ3tkZmZ6e3s/diUReBS5XF5aWmpKF3JMTMySJUuaL2PoQahUKlNTU3XwDJhCocAjo+2EY9hOSqWSYRj8NdYeOAnbz8SOoaenp3q960cx9CAEAADQKnQgAACAoCEIAQBA0BCEAAAgaAhCAAAQNAG9+ayysvL69evJycldu3Z94okn1PtlMtmaNWuysrIGDx48efJk9f7Lly/v3LnT1tZ29uzZPj4++qiywcnKyrp69WphYeH48eM9PDz4nTdu3Lhy5Yq6zIwZM/i3MXMct2nTpvj4+MDAwBdeeAHLPxJCZDLZ4cOHb9y4YWZmNnr06IEDB6r/06VLl3bt2mVnZzd79mypVMrvlMvl69atS01NDQ0NjYmJEc4rZ5uRkZFx8ODB9PR0T0/PmTNnqt+Nun79+rq6hy+H7dy585NPPslvp6Wlbdy4US6XP/PMM3369NFPpQ3Mvn37rl+/XllZ2blz55kzZ6rf4JiXl7d+/fri4uKJEycOGTJEXf7w4cNxcXGenp4vvviio6OjnmqtRQJqEc6bN++NN95YunRp/ZX0KKVRUVGnTp0KCAh45513li9fzu//888/o6KiPDw8ysrKwsLCCgoK9FRrA0Ip7d69+w8//PD666+npqaq9x86dGjlAPQV7AAAB/hJREFUypVp/6VSPXxz9BtvvPHTTz917tx569at/Hu74Jtvvlm7dq29vT3LsmPGjFm7di2//+TJkyNHjvTw8CgpKQkLC3vw4AG/f+rUqX/88Ufnzp2XLVv2zjvv6K/iBmTq1Kk3btyQSqXx8fFdu3a9f/8+v//NN9+8efMmfxKqD2B2dnZYWJhcLnd2dh4+fPjFixf1V3ED8ttvv5mbm/v7+//xxx8DBw7kXyJUUVHRv3//+/fvS6XSSZMm7d+/ny+8atWqefPmdezY8fr160OHDlUqlXqtu3ZQwVCpVJTSV1555Y033lDvPHHihJeXV21tLaX07Nmzbm5uCoWCUjpy5Mjly5fzZSZMmPDZZ5/po8oGhz+Gzs7OZ8+eVe9csmTJK6+80qBkQUGBpaVlRkYGpbS0tNTKyiopKUmXVTVMNTU16u0VK1aEhoby21FRUV9//TW/PX78+M8//5xSevPmTTs7O5lMRilNTEy0sbEpKyvTeZUNTv1jOGzYsK+++orftrOz48+3+t57773p06fz259++unkyZN1U0ljUVtba2Njc/nyZUrpTz/9NHToUH7/2rVrBwwYQClVqVR+fn4HDx7kt7t06bJ79249VlhLBNQibHKxidOnTz/55JN8r93AgQOrq6vv3r1LCDlz5kxUVBRfJjIy8vTp07qsqsF61IIdiYmJX3311ebNm2UyGb/n4sWLfn5+vr6+hBBHR8e+ffv+9ddfuquoobK0tFRvy+VydZfUmTNnIiMj+W31+Xb69OknnniC72cOCgpycXG5evWqzqtscBocw/oL8WzcuPH777+v/waP06dPNz6woHbt2jWRSOTn50cIOX36dP2b3qVLlxQKRWZm5v379yMiIgghLMuOGDHCJI+hgIKwSXl5ea6urvw2y7Kurq65ubllZWU1NTXq/W5ubnl5efqro6FzdXX19/evrKxct25dcHBwbm4uISQ/P199AAkh7u7u/H7g5ebmLl269O233yaElJaWyuXyxudbg2Po5uaGY1jfb7/9lpOTM2PGDP6fgwcPrq6uTktLGzdunLobuf4F7ubmVlJSon6XuMA9++yznp6eI0aM2LJlC3+IGhwrSmleXl5eXp6Dg4N6oRlTvZAF9LBMk8zMzNRjWoSQuro6c3Nzc3NzQoi6K1ypVPJ7oElz586dO3cuvz1u3Ljly5d/9913YrG48YHVUwUNTllZWXR09GuvvTZ69GhCCN8h0fh8wzFsRlxc3MKFCw8ePGhvb8/vOXz4ML8xd+7cnj17vv766xKJRCwW1z+wLMtiBTvezz//XFFRcfDgwWefffbq1av+/v5mZmb1jxUhxNzcvP5OQkhdXZ0prb6mJvQWoZeXV05ODr9dW1tbVFTk5eVlbW3t4OCg3p+Tk+Pl5aW/OhqTQYMGpaWlkX8eWIJjWE9ZWdmIESMiIyM//PBDfo+tra29vX39841f8lgikah3Ukpzc3NxDHmnT5+OiYnZtWtXWFhY4//arVs3e3v7jIwMQohEIlG3YHJyctzd3cViof/1z7O1tfXy8nrppZd69OjB/w1R/1hlZ2eLxWI3NzcvLy+ZTFZeXs7vV5+cJkboQRgdHX3ixImSkhJCyIEDB6RSaZcuXfj9O3fuJIRwHLdnz57o6Gg9V9SA1dTU8BtKpfLIkSPdu3cnhAwdOrS8vPzy5cuEkNTU1ISEhJEjR+qzloahoqJi1KhRQ4YM+fLLL+vvj46O3rVrF/nv+TZ+/HhCyJgxY65cuZKdnU0IOXPmDCGkf//++qi1YTl//vzTTz+9bdu2+s/3y+Vy9fZff/1VVVUVGBhI/ntgKaWEkJ07d+JCJoQoFAqO4/jt8vLy5ORkfiw/Ojp67969/BSUXbt2jR49WiwWe3l5hYaG8jdDmUx29OhR/uQ0NXp+WEeHVq9eHRoa6urq6ubmFhoaum7dOn7/7Nmzu3Tp8txzz7m6uu7Zs4ffeffuXTc3t2nTpg0dOrRv375VVVX6q7gBmTJlSmhoqFgsDgoKCg0NzczMpJT26tVr1KhR//rXvwICAkJDQ0tLS/nCP/74o4eHx/PPP+/j4/Pxxx/rteKG4u2332ZZNiQkJDQ0NDQ0NDw8nN9/584d9fkWFhamPt8WLVrk7+8/e/Zsd3d39RkrcH5+fs7OzqH/tXTpUkrpH3/8ERgY+Mwzz0RHR9va2v7444984fLy8h49eoSHh0+ZMsXLyys1NVWvdTcIFy5c8PHxmTJlyrRp09zd3adPn84/DV5bWzt06ND+/fvPmDHDxcXl2rVrfPnY2FhnZ+dZs2b17Nnzqaee0mvdtUVAb5/Iy8urP8zr5eWlbuOfPXs2KytrwIAB/v7+6gIlJSUnTpyws7MLDw/H2AwvISGh/p/e3bt3t7CwyM/Pv3r1amVlpb+/f79+/eo/WZqQkBAfHx8UFBQSEqKP+hqc7Ozs+nNSxWJxr169+O1HnW+XL19OTU3t06cP31cB8fHx6onzhBBXV1cfHx+lUnnr1q3k5GRra+u+ffvW70OWy+UnTpyQy+UREREODg76qLLBSU5Ovn37tkql6tq1a9euXdX7lUrln3/+WVpaOnz4cDc3N/X+7Ozss2fPenh4DBs2zCRXdRBQEAIAADQm9DFCAAAQOAQhAAAIGoIQAAAEDUEIAACChiAEAABBQxACAICgIQgBAEDQEIQAACBoCEIAABA0BCEAAAgaghAAAATt/wFguD/GVHPjRwAAAABJRU5ErkJggg==\" />"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### @vars q x\n",
    "F = sympy.Poly(prod(1 + q^i*x for i in 1:n), x)\n",
    "f = F.coeffs()\n",
    "f_k = sympy.Poly(f[n+1 - k], q)\n",
    "Ys = float(f_k.coeffs())\n",
    "Ys ./= sum(Ys)\n",
    "Xmax = f_k.degree()\n",
    "Xmin = Xmax - length(Ys) + 1\n",
    "@show Xs = Xmin:Xmax\n",
    "plot(Xs, Ys; label=\"dist. of coeffs. of q-binom\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a2db1257-7f0a-4b79-846a-1f6bb925af22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs == Xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "40b61bd8-df08-4520-a27d-ebe5b63840eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ys == Ys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9829112b-e9f2-4856-94bf-bb29e5836d21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "208.0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu = mean(rank_sums)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ff8a96ed-7edc-465e-a64c-559df99856c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k*(n-k)/2 + k*(k+1)/2 == mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f9c5c437-3838-4d7d-83fe-04b79dd3ec46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "624.0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2 = var(rank_sums; corrected=false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "cc875805-f39d-437b-863a-044e2efd52d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k*(n-k)*(n+1)/12 == s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "872e0bb2-79e7-467a-b80a-0d4619eb58f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(Xs, Ys; label=\"dist. of coeffs. of q-binom\")\n",
    "plot!(Normal(mu, √s2); label=\"normal approx.\", ls=:dash)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "265d048f-6836-4c36-94a1-413b8aa037b4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f_k = Poly(q^325 + q^324 + 2*q^323 + 3*q^322 + 5*q^321 + 7*q^320 + 11*q^319 + 15*q^318 + 22*q^317 + 30*q^316 + 42*q^315 + 56*q^314 + 77*q^313 + 101*q^312 + 134*q^311 + 174*q^310 + 227*q^309 + 290*q^308 + 373*q^307 + 470*q^306 + 595*q^305 + 743*q^304 + 928*q^303 + 1146*q^302 + 1417*q^301 + 1733*q^300 + 2119*q^299 + 2570*q^298 + 3113*q^297 + 3743*q^296 + 4496*q^295 + 5363*q^294 + 6389*q^293 + 7568*q^292 + 8947*q^291 + 10523*q^290 + 12356*q^289 + 14436*q^288 + 16835*q^287 + 19549*q^286 + 22654*q^285 + 26147*q^284 + 30121*q^283 + 34566*q^282 + 39590*q^281 + 45188*q^280 + 51471*q^279 + 58437*q^278 + 66218*q^277 + 74798*q^276 + 84326*q^275 + 94791*q^274 + 106345*q^273 + 118975*q^272 + 132853*q^271 + 147949*q^270 + 164452*q^269 + 182331*q^268 + 201772*q^267 + 222739*q^266 + 245438*q^265 + 269803*q^264 + 296052*q^263 + 324115*q^262 + 354200*q^261 + 386222*q^260 + 420402*q^259 + 456616*q^258 + 495094*q^257 + 535695*q^256 + 578628*q^255 + 623731*q^254 + 671222*q^253 + 720884*q^252 + 772935*q^251 + 827138*q^250 + 883681*q^249 + 942296*q^248 + 1003172*q^247 + 1065980*q^246 + 1130908*q^245 + 1197598*q^244 + 1266199*q^243 + 1336324*q^242 + 1408124*q^241 + 1481144*q^240 + 1555531*q^239 + 1630808*q^238 + 1707086*q^237 + 1783859*q^236 + 1861243*q^235 + 1938672*q^234 + 2016269*q^233 + 2093453*q^232 + 2170313*q^231 + 2246258*q^230 + 2321396*q^229 + 2395085*q^228 + 2467451*q^227 + 2537858*q^226 + 2606414*q^225 + 2672489*q^224 + 2736222*q^223 + 2796955*q^222 + 2854865*q^221 + 2909317*q^220 + 2960481*q^219 + 3007754*q^218 + 3051356*q^217 + 3090671*q^216 + 3125968*q^215 + 3156678*q^214 + 3183078*q^213 + 3204645*q^212 + 3221712*q^211 + 3233762*q^210 + 3241189*q^209 + 3243531*q^208 + 3241189*q^207 + 3233762*q^206 + 3221712*q^205 + 3204645*q^204 + 3183078*q^203 + 3156678*q^202 + 3125968*q^201 + 3090671*q^200 + 3051356*q^199 + 3007754*q^198 + 2960481*q^197 + 2909317*q^196 + 2854865*q^195 + 2796955*q^194 + 2736222*q^193 + 2672489*q^192 + 2606414*q^191 + 2537858*q^190 + 2467451*q^189 + 2395085*q^188 + 2321396*q^187 + 2246258*q^186 + 2170313*q^185 + 2093453*q^184 + 2016269*q^183 + 1938672*q^182 + 1861243*q^181 + 1783859*q^180 + 1707086*q^179 + 1630808*q^178 + 1555531*q^177 + 1481144*q^176 + 1408124*q^175 + 1336324*q^174 + 1266199*q^173 + 1197598*q^172 + 1130908*q^171 + 1065980*q^170 + 1003172*q^169 + 942296*q^168 + 883681*q^167 + 827138*q^166 + 772935*q^165 + 720884*q^164 + 671222*q^163 + 623731*q^162 + 578628*q^161 + 535695*q^160 + 495094*q^159 + 456616*q^158 + 420402*q^157 + 386222*q^156 + 354200*q^155 + 324115*q^154 + 296052*q^153 + 269803*q^152 + 245438*q^151 + 222739*q^150 + 201772*q^149 + 182331*q^148 + 164452*q^147 + 147949*q^146 + 132853*q^145 + 118975*q^144 + 106345*q^143 + 94791*q^142 + 84326*q^141 + 74798*q^140 + 66218*q^139 + 58437*q^138 + 51471*q^137 + 45188*q^136 + 39590*q^135 + 34566*q^134 + 30121*q^133 + 26147*q^132 + 22654*q^131 + 19549*q^130 + 16835*q^129 + 14436*q^128 + 12356*q^127 + 10523*q^126 + 8947*q^125 + 7568*q^124 + 6389*q^123 + 5363*q^122 + 4496*q^121 + 3743*q^120 + 3113*q^119 + 2570*q^118 + 2119*q^117 + 1733*q^116 + 1417*q^115 + 1146*q^114 + 928*q^113 + 743*q^112 + 595*q^111 + 470*q^110 + 373*q^109 + 290*q^108 + 227*q^107 + 174*q^106 + 134*q^105 + 101*q^104 + 77*q^103 + 56*q^102 + 42*q^101 + 30*q^100 + 22*q^99 + 15*q^98 + 11*q^97 + 7*q^96 + 5*q^95 + 3*q^94 + 2*q^93 + q^92 + q^91, q, domain='ZZ')\n"
     ]
    }
   ],
   "source": [
    "@show f_k;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b2872ff4-190b-43e7-82ee-12bafe47c014",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g_k = Poly(q^325 + q^324 + 2*q^323 + 3*q^322 + 5*q^321 + 7*q^320 + 11*q^319 + 15*q^318 + 22*q^317 + 30*q^316 + 42*q^315 + 56*q^314 + 77*q^313 + 101*q^312 + 134*q^311 + 174*q^310 + 227*q^309 + 290*q^308 + 373*q^307 + 470*q^306 + 595*q^305 + 743*q^304 + 928*q^303 + 1146*q^302 + 1417*q^301 + 1733*q^300 + 2119*q^299 + 2570*q^298 + 3113*q^297 + 3743*q^296 + 4496*q^295 + 5363*q^294 + 6389*q^293 + 7568*q^292 + 8947*q^291 + 10523*q^290 + 12356*q^289 + 14436*q^288 + 16835*q^287 + 19549*q^286 + 22654*q^285 + 26147*q^284 + 30121*q^283 + 34566*q^282 + 39590*q^281 + 45188*q^280 + 51471*q^279 + 58437*q^278 + 66218*q^277 + 74798*q^276 + 84326*q^275 + 94791*q^274 + 106345*q^273 + 118975*q^272 + 132853*q^271 + 147949*q^270 + 164452*q^269 + 182331*q^268 + 201772*q^267 + 222739*q^266 + 245438*q^265 + 269803*q^264 + 296052*q^263 + 324115*q^262 + 354200*q^261 + 386222*q^260 + 420402*q^259 + 456616*q^258 + 495094*q^257 + 535695*q^256 + 578628*q^255 + 623731*q^254 + 671222*q^253 + 720884*q^252 + 772935*q^251 + 827138*q^250 + 883681*q^249 + 942296*q^248 + 1003172*q^247 + 1065980*q^246 + 1130908*q^245 + 1197598*q^244 + 1266199*q^243 + 1336324*q^242 + 1408124*q^241 + 1481144*q^240 + 1555531*q^239 + 1630808*q^238 + 1707086*q^237 + 1783859*q^236 + 1861243*q^235 + 1938672*q^234 + 2016269*q^233 + 2093453*q^232 + 2170313*q^231 + 2246258*q^230 + 2321396*q^229 + 2395085*q^228 + 2467451*q^227 + 2537858*q^226 + 2606414*q^225 + 2672489*q^224 + 2736222*q^223 + 2796955*q^222 + 2854865*q^221 + 2909317*q^220 + 2960481*q^219 + 3007754*q^218 + 3051356*q^217 + 3090671*q^216 + 3125968*q^215 + 3156678*q^214 + 3183078*q^213 + 3204645*q^212 + 3221712*q^211 + 3233762*q^210 + 3241189*q^209 + 3243531*q^208 + 3241189*q^207 + 3233762*q^206 + 3221712*q^205 + 3204645*q^204 + 3183078*q^203 + 3156678*q^202 + 3125968*q^201 + 3090671*q^200 + 3051356*q^199 + 3007754*q^198 + 2960481*q^197 + 2909317*q^196 + 2854865*q^195 + 2796955*q^194 + 2736222*q^193 + 2672489*q^192 + 2606414*q^191 + 2537858*q^190 + 2467451*q^189 + 2395085*q^188 + 2321396*q^187 + 2246258*q^186 + 2170313*q^185 + 2093453*q^184 + 2016269*q^183 + 1938672*q^182 + 1861243*q^181 + 1783859*q^180 + 1707086*q^179 + 1630808*q^178 + 1555531*q^177 + 1481144*q^176 + 1408124*q^175 + 1336324*q^174 + 1266199*q^173 + 1197598*q^172 + 1130908*q^171 + 1065980*q^170 + 1003172*q^169 + 942296*q^168 + 883681*q^167 + 827138*q^166 + 772935*q^165 + 720884*q^164 + 671222*q^163 + 623731*q^162 + 578628*q^161 + 535695*q^160 + 495094*q^159 + 456616*q^158 + 420402*q^157 + 386222*q^156 + 354200*q^155 + 324115*q^154 + 296052*q^153 + 269803*q^152 + 245438*q^151 + 222739*q^150 + 201772*q^149 + 182331*q^148 + 164452*q^147 + 147949*q^146 + 132853*q^145 + 118975*q^144 + 106345*q^143 + 94791*q^142 + 84326*q^141 + 74798*q^140 + 66218*q^139 + 58437*q^138 + 51471*q^137 + 45188*q^136 + 39590*q^135 + 34566*q^134 + 30121*q^133 + 26147*q^132 + 22654*q^131 + 19549*q^130 + 16835*q^129 + 14436*q^128 + 12356*q^127 + 10523*q^126 + 8947*q^125 + 7568*q^124 + 6389*q^123 + 5363*q^122 + 4496*q^121 + 3743*q^120 + 3113*q^119 + 2570*q^118 + 2119*q^117 + 1733*q^116 + 1417*q^115 + 1146*q^114 + 928*q^113 + 743*q^112 + 595*q^111 + 470*q^110 + 373*q^109 + 290*q^108 + 227*q^107 + 174*q^106 + 134*q^105 + 101*q^104 + 77*q^103 + 56*q^102 + 42*q^101 + 30*q^100 + 22*q^99 + 15*q^98 + 11*q^97 + 7*q^96 + 5*q^95 + 3*q^94 + 2*q^93 + q^92 + q^91, q, domain='ZZ')\n"
     ]
    }
   ],
   "source": [
    "# (x)_q = (1 - q^x)/(1 - q)\n",
    "# (n)_q! = (1)_q (2)_q … (n)_q\n",
    "# g_k = q^{k(k+1)/2} (n)_q!/((k)_q! (n-k)_q!), essentially a q-binomial coefficient\n",
    "g_k = sympy.Poly(q^(k*(k+1)÷2) * prod((1 - q^(n-k+j))/(1 - q^j) for j in 1:k; init=Sym(1)).factor(), q)\n",
    "@show g_k;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c2e07f88-acbe-46a9-a5ae-5fd7e2f5b8ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_k == g_k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "76435a2c-38ea-4134-ab8c-4de41b29644c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "jupytext": {
   "encoding": "# -*- coding: utf-8 -*-",
   "formats": "ipynb,jl:hydrogen"
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   "language": "julia",
   "name": "julia-1.9"
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  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.9.0"
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 },
 "nbformat": 4,
 "nbformat_minor": 5
}