{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Factorization test\n",
    "\n",
    "The [classic sWeights method](https://inspirehep.net/literature/1986730) is a powerful way to project out a component from a mixture of signal and background, but it is often not obvious whether it can be applied, because it requires that signal and background pdfs both factorize in the discriminatory variable $m$ and the control variable $t$.\n",
    "\n",
    "We show two kinds of tests, which can be applied. The first test can always be applied, but is slow to compute. The second test can only be applied under special conditions, but is fast.\n",
    "\n",
    "## Likelihood ratio test\n",
    "\n",
    "We show that a likelihood ratio test can be used to test the hypothesis that the sWeights are applicable. This technique is applicable to any problem and only requires prerequisites that are anyway needed to compute sWeights.\n",
    "\n",
    "While the test can only detect a factorization violation with a given confidence (there the usual type I and II errors), it should be safe to apply sWeights if the test passes. When it passes, a potential factorization violation is too small to be detected, which means that applying sWeights should give good results, too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm, expon, chi2\n",
    "import numpy as np\n",
    "from iminuit.cost import ExtendedUnbinnedNLL\n",
    "from iminuit import Minuit\n",
    "from iminuit.util import make_with_signature\n",
    "from iminuit.typing import PositiveFloat\n",
    "from typing import Annotated\n",
    "\n",
    "from sweights.testing import make_classic_toy\n",
    "from sweights.util import plot_binned\n",
    "from sweights.independence import plot_indep_scatter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We make a toy dataset to demonstrate the method. We then split the dataset into two subsets along an arbitrary value in the control variable. A good choice is the median, but any value will do. The splitting value is indicated in the plots with a dashed line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mrange = (0.0, 1.0)\n",
    "trange = (0.0, 1.5)\n",
    "tsplit = 0.2\n",
    "\n",
    "toy = make_classic_toy(1, mrange=mrange, trange=trange)\n",
    "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n",
    "plt.sca(ax[0])\n",
    "plot_binned(toy[0], bins=100, color=\"k\", label=\"total\")\n",
    "plot_binned(toy[0][toy[2]], bins=100, marker=\".\", color=\"C0\", label=\"signal\")\n",
    "plt.xlabel(\"m\")\n",
    "plt.sca(ax[1])\n",
    "plot_binned(toy[1], bins=100, color=\"k\", label=\"total\")\n",
    "plot_binned(toy[1][toy[2]], bins=100, marker=\".\", color=\"C0\", label=\"signal\")\n",
    "plt.axvline(tsplit, ls=\"--\", color=\"0.5\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"t\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use a mask to split our toy dataset and plot both parts along the $m$ variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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loFvhN+PHj8f48foNX7nTLQfltddeQ//+/RXN1y4qKkJERASSkpL0ag4REREFEdU9KBcuXMCxY8cc2yUlJSgqKkJiYiKuuuoqALYckXfeeQfPP/98i/vv2bMHX3zxBYYNG4b4+Hjs2bMHc+fOxZQpU9C2bVsfHgoRERGFCtUBypdffolhw4Y5tu35JFOnTsXatWsBAHl5eRAEwWWak11MTAzy8vKwaNEi1NXVIT09HXPnznXJSyGiwNJySm9jU/M0zMKScxjSrYOm04+JKDSp/tQZOnQoBEF+AfUZM2ZgxowZorf169cPe/fuVXtaIgpC+QfLkLvhkGN72pp9sFpikTsuA9mZ1gC2jIiMjmvxEJEuCoorMHPdAVRUuS71Xl5Zi5nrDiD/YJnEPb3HkvmklKcf2uQ9rZ5bBihEpIulmw/LLUiPxR8Wuwz/EPmDfZG8mpqaALckdNmfW7kFCZVgrWgi0oV7z4kzAUBZZS0+++/3GHotZ++R/0RGRiIhIQFnzpwBAMTFxcFkYk6UFgRBQE1NDc6cOYOEhARERvpWF4YBChEFzPfV0kEMkV7s68DZgxTSVkJCguK19uQwQCGigOkQzwrR5H8mkwlWqxVJSUm4dOlSoJsTUlq1auVzz4kdAxQi0kWyOQZnqupE81Ds+ndi7SMKnMjISM2+TEl7TJIlIl0sHNMDgGMBegfnbXs9FPdaKUyeJSIGKESki5EZyVg9pR+SzK7DOMlm18VD8w+WYcQLnzq2p63Zh8ErtukyDZmIggcDFCLSTXamFVtybnFsr33gehTk3OzYVlMrhb0sROGFOShEpJm46CicXD7W5TrnsvYD0xNdbpOrlWKCrVbKyIwUFBSXsyItUZhhDwoRBYySWil/2XbM7xVpiSjwGKAQkaGt2VXCirREYYgBChEZ2vmfpOtU2HtZCkvO+a9BROQXDFCIKGCSzTEtpiHbmQAktFa2lseZ6lrN2kRExsAAhYgCxlOtlAdu6qzoOEnxsZ53IqKgwgCFiFrw15ReqVopKZZYrJ7SD7OHd4PVEivby2K1xLaYHUREwY8BChG58HfhNLFaKZ/PG47sTCsiI0zIHZcBQLyXxZ6DUtfQqEvbiChwGKAQkUP+wbKATOl1r5XivJ2daVVUkRZgMTeiUMIAhYgA2L7cF39YrGpKb019AzrP34TO8zehpr5Bt7Z5qkgLsGQ+UahhgEJEAGw9DmWV0rNhtJrS620vh1wvi5qS+UQUHBigEBEA5VN173llr9e9JQXFFaK9HAXFFV4dz06uZD7AYm5EwYgBChEB8M9U3Tl5RaK9HHPyinw6rpKS+SzmRhRcGKAQEQDbsImnKb2+kuvl0BuLuREFFwYoRAQAHqf06skfQQqLuREFFwYoROQgNaU3xRKLlZP6BqZRCngqme9czM1fM4+IyDcMUIjIhVThtJEZyV4dLy46Cm89eINWzRPlqWR+7rgMl1k/RGR8DFCIqAW5Kb3e0Du/xVPJ/OxMq49nICJ/Y4BCRLrzR36LVM/Pzdd04JAOURBigEJEfuGP/Bate36IKHCiAt0AIgof2ZlW3HR1e/Ra9AkAWy/HkG4duNgfEbXAHhQi8iv2chCREgxQiMhwOBWYiFQHKDt37sS4ceOQmpoKk8mEDz74wOX2adOmwWQyuVyys7Nd9jl37hwmT54Ms9mMhIQETJ8+HRcuXPDpgRAREVHoUB2gXLx4EX369MGqVask98nOzkZZWZnj8tZbb7ncPnnyZBw6dAgFBQXYuHEjdu7ciRkzZqhvPRGFLW9XRSai4KA6SXb06NEYPXq07D4xMTFISUkRve3w4cPIz8/Hvn37MGDAAADAiy++iDFjxuCPf/wjUlNT1TaJiALEPUgY0q2DVzklcdFROLl8rGPb07BOQXEFlm4+7NietmYfrJZYzB/dXfW5iciYdMlB2bFjB5KSknDttddi5syZOHv2rOO2PXv2ICEhwRGcAMCIESMQERGBL774QvR4dXV1qKqqcrkQUWDlHyzDiBc+dWxPW7MPg1dsQ/7BMt3PrdeqyERkHJoHKNnZ2XjjjTewdetWrFixAp9++ilGjx6NxkbbNMLy8nIkJSW53CcqKgqJiYkoLy8XPeayZctgsVgcl7S0NK2bTUQeOPeWvLT9GGauOyAaJMxcd0CXICUuOgrHl46B1RIb0FWRicg/NK+DMmnSJMf/e/Xqhd69e6Nr167YsWMHbr31Vq+OuWDBAuTk5Di2q6qqGKQQ+VH+wTLkbjjk2P7L9uOi+wmwVYZd/GExRmakaD6FuLDkHMoqayVvZ5BCFDp0n2bcpUsXtG/fHseOHQMApKSk4MyZMy77NDQ04Ny5c5J5KzExMTCbzS4XIvKPguIK0d4SKQKAsspaFJac07wtZ6qlgxMiCi26Byj/+9//cPbsWVittsW6Bg0ahPPnz2P//v2OfbZt24ampiZkZWXp3RwiUmnp5sNe9UzoEUwkxcdqfkwiMibVAcqFCxdQVFSEoqIiAEBJSQmKiopw+vRpXLhwAb///e+xd+9enDx5Elu3bsXtt9+Oq6++GqNGjQIA9OjRA9nZ2XjwwQdRWFiIXbt2Yfbs2Zg0aRJn8BAZkNKeE3d6BBNarIrM6clEwUF1gPLll1/iuuuuw3XXXQcAyMnJwXXXXYennnoKkZGR+M9//oPx48fjmmuuwfTp09G/f3989tlniIlpXiBs/fr16N69O2699VaMGTMGgwcPxt/+9jftHhURBYwJgNUSi4HpiZof29dVkQuKKwI284iI1FGdJDt06FAIgvQvjo8//tjjMRITE/Hmm2+qPTUR+Ym9Lsme42dxzyt7Fd/PHiTkjsvQbY0d+6rIuRsOufTupFyug/IbmanGc/KKWgxX2WcerZ7SD9mZVl3aTETqcS0eIpLkaUjFXYol1i9f9NmZVmzJucWxvfaB6/H5vOEYmZHcYl/nIRy56cmLPyzmcA+RgWg+zZiIQod9SGXmugMwwfUL3n177QPXe11J1tu22dlXRXavSOs+PVqK88yjQV3b6dFcIlKJPShEJMs+pJJkjnG5PsUSiz9N6uvYtgcJRpF/sEzV9GiA05iJjIQ9KETkUXamFTdd3R69Fn0CoLm3pK6hUfWx3Hs59NDYJGDxh8Wqp0dzGjORcbAHhYgUERtS0YuvU4E9VZx1p+fMIyLyDgMUIjIULRYhVDNU44+ZR0SkHgMUIjIMqbwRtYsQqhmq8dfMIyJShzkoRGQIcnkjahchtE+PLq+slc1D+fvUAbjl2iT2nBAZEHtQiAg19Q3oPH8TOs/fhJr6hoC0QclKxUoXIVRacfaGru0YnBAZFAMUIjIEpXkjSveTmh6dbOZMHaJgwACFiAxBad6ImvwSsYqzBTk3q24bEfkfAxQiMgQlKxV7MxXYn9OjiUg7DFCIyBCU5I1wKjBR+GCAQhRmjJAQK0WurD6nAhOFF04zJiJDkSqrz54TovDCHhQiMhzmjRARe1CIKCj5Y9FBIgoc9qAQERGR4bAHhYi8xl4MItILAxQiUiSUg5Ga+gZkPPUxAKB4ySjERfOjkSjQOMRDREREhsMAhYiIiAyHAQoREREZDgdaiQiNTYLj/4Ul50K6MJq3uTTMUyHyL/agEIW5/INlGPHCp47taWv2YfCKbcg/WBbAVhFRuGOAQhTGCoorMHPdAVRU1blcX15Zi5nrDjBIIaKAYR8lURhbuvkwBJHrBdhWEF78YTFGZqQE9XBPKE+PJgpl7EEhCmPuPSfOBABllbUoLDnnvwYREV3GAIUozDgnxCpxprpWp5YQEUnjEA9RGMk/WIbcDYdU3ScpPlan1kjjsAwRMUAhChP5B8swc90B0ZwTMSYAKZZYDExP1LNZRESiOMRDFAYamwQs/rBYVXACALnjMoI6QZaIghd7UIhCnHOBMaVSLLHIHZeB7EyrTq0iIpKnugdl586dGDduHFJTU2EymfDBBx84brt06RLmzZuHXr16oU2bNkhNTcX999+P0tJSl2N07twZJpPJ5bJ8+XKfHwwR+W7tA9fj83nDwyo4ca+kqzaRmIi0pzpAuXjxIvr06YNVq1a1uK2mpgYHDhzAk08+iQMHDuC9997D0aNHMX78+Bb7LlmyBGVlZY7Lo48+6t0jICJNDUxPDKthHVbSJTIm1UM8o0ePxujRo0Vvs1gsKCgocLnuL3/5CwYOHIjTp0/jqquuclwfHx+PlJQUtacnIh+YANE8FKnrQ51U4rC9ku7qKf3CqieJyEh0T5KtrKyEyWRCQkKCy/XLly9Hu3btcN111+G5555DQ0OD5DHq6upQVVXlciEi77j3jYRPX4krucRh+3WLPyzmcA9RgOgaoNTW1mLevHm45557YDabHdf/+te/Rl5eHrZv346HHnoIS5cuxWOPPSZ5nGXLlsFisTguaWlpejabKGStnNQXSeYYl+tSLLFYOalvYBoUQIUl51BWKV2Ezr2SLvNUiPxLt1k8ly5dwt133w1BELB69WqX23Jychz/7927N6Kjo/HQQw9h2bJliImJcT8UFixY4HKfqqoqBilEXhiZkYzh3ZPQa9EnAGwJsUO6dUBdQ2OAW+Z/SivknqmubVHgbtqafbByphORrnTpQbEHJ6dOnUJBQYFL74mYrKwsNDQ04OTJk6K3x8TEwGw2u1yIyDvOCbDhlhDrTGmF3JM/1HDFZ6IA0DxAsQcn//3vf7Flyxa0a9fO432KiooQERGBpKQkrZtDRCRqYHoirJZYyRwcE4AUcwzeKjzNPBWiAFAdoFy4cAFFRUUoKioCAJSUlKCoqAinT5/GpUuXcOedd+LLL7/E+vXr0djYiPLycpSXl6O+vh4AsGfPHqxcuRL//ve/ceLECaxfvx5z587FlClT0LZtW00fHBGRlMgIE3LHZQCQThy+Z+BVKK9SnqdCRNpRnYPy5ZdfYtiwYY5te27I1KlTsWjRImzYsAEA0LdvX5f7bd++HUOHDkVMTAzy8vKwaNEi1NXVIT09HXPnznXJMSEi8ofsTCtWT+mH3A2HXIZw7JV06xqaFB2HKz4TaU91gDJ06FAIgnR3ptxtANCvXz/s3btX7WmJSAHnsvbFS0YhLpqrWXiSnWnFTVe3b5E4HBlhwp7jZxUdIxArPhOFOi4WSERhTypxWEmeipUrPhPpggEKEZEEJXkqXPGZSB8MUIhCHAuMqVdT34DO8zeh8/xNuPmaDlg9pZ9ogTuWwifSDweoiUKYWIGxZHPLYogkTy5PhYj0wQCFKIi5J8U6KyiuwJy8ohY1PM64FRwDgLjoKJxcPlavZoYEFrgj8i8O8RCFqKWbD8sWGAPA4R4iMiwGKEQhyr00u5j9p370Q0tCk3OeSk299GrsROQdBihEYez7as9BDBFRIDBAIQpjHeKZMEtExsQAhShEJZtjPBYYG9Ktgz+bRESkGAMUohC1cEwPACwwRkTBiQEKUYgamZHMAmNEFLRYB4UohLhXjR2ZkcICY0QUlBigEBmAklWIPe1TUFyBpZsPO7anrdkHqyUW80d3d1zHAmNEFCwYoBCFCLGqseWVtZiTVxSI5gQV90q6rGtCFHjMQSEKEZ6qxhIRBRMGKEQhjkGKelwBmijwOMQjQ0leAFEg8YtTe2IrQFstscgdl8FhICI/Yg8KUZDKP1iGES98GuhmhJT8g2WYue5Ai3WMyitrMXPdAeQfLAtQy4jCDwMUoiBUUFwh+kUqhnN2lGlsErD4w2LZXJ7FHxY7eq04DESkL45ZEAWhpZsPK8otYXCiXGHJOZRV1kreLgAoq6xFYck5VP5ULzkMxAJ4RNpgDwpREFLScwLYqsaunNRX38aEiDPV0sGJs4Licg4DEfkBe1CIQtTDN3fB77O7o66hMdBNCQpJ8bGK9vugqFRyGMgE4OF1BwAwsZ7IV+xBIQpRN3Rtx6qxKgxMT4TVEiu7AnRim1Y4d7Fe8hjMQiHSDgMUlWrqG9B5/iZ0nr+J0wwpYJLNMR7zS/p3auuXtoSKyAgTcsdlAJBeAfrnfTv6tU1E4YwBClEQWjimBwDpL1IAjt4Texn3k8vHcsjBg+xMq+wK0CMyUgLUMqLwwwCFyACUTFl1vs7SuhVW3dvyizTZrCyPgqRlZ1qxJecWx/baB67H5/OGIzvTqmgYiIi0wQCFKMDcC65NW7MPg1dsc5kNIrbP05uKMT+7eaXitQ9cj4Kcm/3T6BDnnLvjvAK0kmEgItIGAxSiAFJSuVRun5y3/+3Ydv4iJf3IDQNxSjeRdjggTRQgniqXmgAs2nAIgEl2H/K/7Ewrbrq6PXot+gSArfdqSLcOnNJNpCH2oMhgKWvSk5LKpeVVdSivkt+HAkNqGMgZZ/0ReY89KBKkVjSdP7q7zL2IlFNauZSIKBwxQBFhH/N3/3VaXlmLOXlFqo9XU9+AjKc+BsDqktRMaeVSIqJwpHqIZ+fOnRg3bhxSU1NhMpnwwQcfuNwuCAKeeuopWK1WtG7dGiNGjMB///tfl33OnTuHyZMnw2w2IyEhAdOnT8eFCxd8eiBaUbKiqRbY9UtqpqxyWisRhRvVAcrFixfRp08frFq1SvT2Z599Fn/+85/x8ssv44svvkCbNm0watQo1NY2d2dPnjwZhw4dQkFBATZu3IidO3dixowZ3j8KDSnJCyDSgtopq5zWSkThRHWAMnr0aDzzzDP4+c9/3uI2QRCwcuVKPPHEE7j99tvRu3dvvPHGGygtLXX0tBw+fBj5+fl49dVXkZWVhcGDB+PFF19EXl4eSktLRc9ZV1eHqqoql4temBfQjL08+lM6ZXXlpL6KprWyamxgMbGeSDuazuIpKSlBeXk5RowY4bjOYrEgKysLe/bsAQDs2bMHCQkJGDBggGOfESNGICIiAl988YXocZctWwaLxeK4pKWladlsF8wLIH+Tqlw6MiPZcd3IjGSP+1BgiRXTc94mInU0DVDKy8sBAMnJrh+aycnJjtvKy8uRlJTkcntUVBQSExMd+7hbsGABKisrHZdvv/1Wy2a78JQX4Iy/kEgrSqasKtmHAqOguEK0mN4Zt20iUi4o6qDExMTAbDa7XPQilxfgTqwkORGFn6WbD3tMrOePGSJ1NA1QUlJsK31WVFS4XF9RUeG4LSUlBWfOnHG5vaGhAefOnXPsE2hSeQFinEuSE1FoUJvL495zImb/qR+1aBpR2NA0QElPT0dKSgq2bt3quK6qqgpffPEFBg0aBAAYNGgQzp8/j/379zv22bZtG5qampCVlaVlc3zinhfQNq6V6H7230SLPyzmLyTyOybFBo/vqzncQ6SG6k+0Cxcu4NixY47tkpISFBUVITExEVdddRXmzJmDZ555Bt26dUN6ejqefPJJpKam4o477gAA9OjRA9nZ2XjwwQfx8ssv49KlS5g9ezYmTZqE1NRUzR6YFpzH+H+suSS5nwCgrLIWhSXnMKhrOz+0jIiCTYd4zz2yRNRMdYDy5ZdfYtiwYY7tnJwcAMDUqVOxdu1aPPbYY7h48SJmzJiB8+fPY/DgwcjPz0dsbPPsmPXr12P27Nm49dZbERERgYkTJ+LPf/6zBg8nsDhFmbTkPmW1f6e2AWwNubP3XjU2CRi8YhvKK2tl6yQ1NQlobBKY3EykkOoAZejQoRAE6behyWTCkiVLsGTJEsl9EhMT8eabb6o9te7cS9KrJTVF2f2LZki3Dt41kMKG2FpQyQpyosj/7In1M9cdgAnSxRx/+fqXsFpikTsuA9mZVn82kSgoBcUsHiNINsfIlhu3WmIxMD2xxW1itREGr9iGguKKFvsSAZyyGoyUJtYzqZ5IOQYoCi0c0wOAeLlxew5KXUOjy232RQfdv2jKK2vxG6dFB1lPhZxxympwck+sF8OkeiLlGKAoNDIjWfQXUrK55bCOvUT8wyIrIgMtu4Cl6qmw1Hx44pRVAPUXgUUW26X+YqBbo5iS/BLnpHoiksYARQWxkuQFOTdrcmwjdv1yXRHj4pTV4MekeiJ5DFBU0qvcuNG6fqVyZ4wUQIUzTllF0Pay2HHdLyJ5DFAMxChdv3K5M0br5QkV9imrx5eOkV0Lyp6QzZlgxudNUj0RNWOAojNv+lcC2fXb2CRg8YfFsrkzRunlCUVya0HZt3PHZbCWRpCQ+huWVdai68LNzC0jksEAxQ/UfpUEsuu3sOQcyiqlAySj9PKEMqkpqymWWKye0o81NILEykl9Rf+GKyf1DUyDiIIMF++QYe9298XKSX2xdPNhRTMzTLB9gAWy61dp7w0T/PSVnWnFTVe3R69FnwCwJWQP6dYhOHtO6i8CSy8vY7Gw1Pav83Z0m8C0S2cjM5IxvHtSi7+hezkCIhLHHhSdjcxIdpn5M3tYV5hg3O57pb03TPDTn14J2eQ//BsSeY8BihO9ptU6fyg9MuxqQ3ffD0xPVJSkyQQ/0lSQz8ghIu0xQLnMn9NqxeqpfD5veMCDE4BJmkREZAwMUODbtFpve1382fWrtiItkzRJMfZ8EJFOwj5J1tO0WhNs02pHZqS0CCIKiiuwdPNhx/a0NftgtcTisVHXOq4rLDmH/p3aet025+P4M0kypJI0Kfg0OSWSntoNdB0OREQGrj0KuSfWcxoxkffCvgfFl2m1c/KKWvS6lFXWYu7b/3ZsT1uzz2XoSCkjVHJlgh8FxJHNwKqBzdvr7wRWZgLFGwLXJiLyu7APUNROq42LjnJU+1SaQntGwRRjZ6zkSmHtvQeBarfXeFUZ8Pb9rkGKey9LU/BO33UfhuVCoUQMULyaVuup18WdcyDjKUeFlVyJZF79+fNtgUjxBvayEIW4sA9QvJlW60uRsv2nfpS9nZVciaQIQNV3wM4/2npTpHpZDJ60y1XCiZQJ+wDFm2m1vhQp+75afriHlVyJPPhiNWR7WQxMKresoLgigK0iMqawD1AA9dNqPfW6yOkQHyN7uxaVXDl+HThh/9yLTTt2zxVpqHfdVps78pNcL6Rxg5SC4grJ3LI5eUWBaRSRgYX9NGM7NdNq7b0uM9cdgAnqPhI9TTm2Bz/llbWixzXCej3kH1qsBRVwxRuAjx5r3l5/J2CKcN02pwK3LlJwMBPQOsFDgGIs9r9hY5OAwSu2yZYzICJX7EFxomZarVSvixj72jsvT+mH+NhWkvvV1Deg68LNjhwULtVOQe3IZvFcEaHJdbuqFHh/hoeDXX71B1Fw4kxJbhkRuWKA4gOxkvUv3dsPyRpUYNVyqXYm5ZFu5Kb6FjwJzb56zanAhFecrpBLazce5owRqcchHh+597rERUdhyDWeh4o8dd9rtVS7VLXb3HEZLFlPvhEbvol3ek2595x46563gW4jgAb3L3n3AVZjBicAV/8m8gZ7UHSgVQVWLY4jVu2WBd/IZ8UbxIdvqsu1P1dERMsy9xNeAeJTXK9r0ctiHErKGRCRKwYoIc6Xgm/2Xp6Ty8ciLpqdbWK8nbUT1LN9mhqB/Hnw21TfCyJTcLuPAWYVNm9PfheY87XtegNSUs6AiFwxQAlTLPjmP0EdjIg5tduW2OpJXDto8vV7RbL49c69Kp1u1HYxQR1WaZYrZ/DC3X0c24Ul51Df0OSyzbwxCkf8WRzmmLxHqon1aIjpOQHY9ypa5oqolJalfF+Dr4IsVs6gpq4Rizcecuwzbc0+OI/mMm+MwhV7UMLcb/KKNP9VH3I9BuRKqkfD3TWjgLvfaJkrYlLyseP0Da00wAiS9Xmcc8kqf7qEWW+2LN7m3mHCvDEKRwxQQpCS7mCOe+sjLKZ0d7rRlpDq6VXU1AR0H9syV+T3J1y373rddfYPAJhV9hRI1VwRWwXZQJZuPqyob4kLhVI4YoASYtzX+hDD4EQfBcUVob3Oij0vY0kiMGLJ5StlXk1v3W3rwfjm4+brOt0IREW7bve8o2UQ88gX6tomWXPFbRVkg3HvOZHDvDEKNwxQnAR61oqSX99y++QfLBNd68OdtwXfSJ7UlO6QXGel+xjx4Rt3VWXAew96Pp6ShFe5onCyNVcur4J8arfndgQB5o1RuNA8QOncuTNMJlOLy6xZswAAQ4cObXHbww8/rHUzgo7YKqfuPSFSK6HmHyxDY5OAxR8We+wu/vvUAfh83nCMzHDNIwiGvBGjtzE419f1QcZ4154PURo9A2L5Jc7bSihN7jU4Fn2jcKF5N8G+ffvQ2Nj8y+bgwYMYOXIk7rrrLsd1Dz74IJYsWeLYjouL07oZfqPFgm72ng/3j/IzTr/GC4orMCevqMU+9uS5OSO6ya71YRcRYfK6cBx5J6SDFEUJrD4+A0c2X+6FcTuO2qJwSpN7/SjZHIMzVXWKniEuFErhRvMelA4dOiAlJcVx2bhxI7p27YpbbmlesyYuLs5lH7PZrHUzgoZcz4fzdVLJdPbr1uw6qeh831crH/MOBoHuVfE2YdFwybQ61P3QjKf8EuBykq1MnVZzR9vQkcEsHNMDgOe8MPvtueMyZH9gBPr9QKQlXXNQ6uvrsW7dOvzyl7+EydT8plq/fj3at2+PzMxMLFiwADU1NbLHqaurQ1VVlcvFyNTksnha5dROLq9EAHD+p0uK2tYh3vPqy6SMkoRkJfdzHqqjy6LbAIsqgakbla3p03fy5f9I1GnNXm6oeih2IzOSRYu3uccg3iw4ShTsdA1QPvjgA5w/fx7Tpk1zXHfvvfdi3bp12L59OxYsWIB//OMfmDJliuxxli1bBovF4rikpaXp2Wy/0jLhLaF1K4+/xPp3auvTOfgLzUZpQrK7l7YfE72f4epceNWjosNKM0rzRpJ6iCftmlNt12eMb75OyWOTS8jVmNiq6AeeHOmy/fm84QxOKOzoOlXltddew+jRo5Gamuq4bsaMGY7/9+rVC1arFbfeeiuOHz+Orl27ih5nwYIFyMnJcWxXVVWFTJCiZcLbAzelY+WWb0TXeLVva51/UlPfgIynbNNIi5eMCos1e5QmJIv5y/bjotcLsP2dFn9YjJEZKUGcJ6TxCsNK80auSAbShwBdhgLLL382TH7Xu0qyYqs0m1OB7BWugY6G3BcGdebLgqNEwUy3HpRTp05hy5Yt+NWvfiW7X1aWrYz1sWPHJPeJiYmB2Wx2uYQKJaucpphjkGKW38dqicXs4VeLdhcnm1sGQXrmQBguv0JjSofl1Ar6Ohd6rDDssSicW36Jr+vzSK3SrGHBt0CXMyAKFroFKGvWrEFSUhLGjpWf4VJUVAQAsFrDs/tSySqni8b3xKLx8vvYk+fEuosLcm52uY+SKc3eCof8CqXDcm2ivct5CNo6F3qsMBwRaeu5AKB7fomSVZoNWvCNKBTpEqA0NTVhzZo1mDp1KqKimn8hHD9+HE8//TT279+PkydPYsOGDbj//vtx8803o3fv3no0JSjIrXJqT4xTso+de3ex83ZBcYVoDsQZlbkUYqSObbj8Ch8pHZa7WO/dF5lh61woycsQ68GwJ7wuqrT9333bk4zxyvNLfOFxlebQKvhGZHS69C9u2bIFp0+fxi9/+UuX66Ojo7FlyxasXLkSFy9eRFpaGiZOnIgnnnhCj2YEFbFVTod06+ASXCjZxxNP05UBYO/xs7jl2iTV495yx/aUX6Ekl8V96GhItw6q2qcV+7BceWWtpjVODF3nQiovY8QS6fuoYQ9apGSM1ya/RI7ShNwQKfhGZHS6BCi33XYbBKHlR3daWho+/VSboYRQJNfzoWYfOUpmnfzy9S+9Wt7d01Roe37FoK7tFB/TLv9gGXI3uC5Jb7XEYv7o7qqP5Sv7sNzMdQdkE5LVUFrnIiCkCqUpLWOvFV/zSzxRk5BLRLrjWjxBTsm0X3tS3p9UrL+j17CMN/kVUlN6yytr8RundW78mZArNeTmnJCcbI5RPIcl4HUu5IZvPBVKM3cEnjqnbLjGyNQm5BpQqCeoU3hhgBJG1OQ26LW8u9r8CqWVdgH/J+R6SkiWqhLqvh3wOhee1rkJl4X4/JmQq4NwSFCn8MIAJYx4mtLsTmzaq9wvNLkeA/tUaLX5FWqn9Po7IVduyE2qSmiKJdalNyugdS6kptUqqd7qLJjyMuR6i/yVkKsxuV7GUEpQp/DCSfhhRC53Qo59WEYsDyTZ6ct34ZgemJNXJFmqy5v8CrVDQkYreCaV2FzXYICpqrLTalUKlrwMJUXY/JGQ60Zs0VGli5B66mU00vuBSA32oIQZqdwJOUnxsZK/0Jy3La1bYdW9yqZCqzm3WkYreOZrYrMsXxb58zitVgnj52U4qCnCpiQh1yALLHrqZTTa+4FIKfaghCH3X/VS7NNe+3dqi1ue2+7xd7ZjZk12d8x9+98AvJsK7cyXKb1BW/DMX3weljFgXobUdGWPRdhMtiJs3cca57EopPR1zvcDBRsGKCFIrLvYnXPAYP+f1LDM/lM/Ks4DKa+sRc7l4ATwvcfA22EpIDAFz5Q89wFXfxFYmup5P0/MqbbgxDkvw1M9k0BRU4QtfYjfmqUFpa9zwxYAJJLAIR7Cykl9ZYdl1PzyUhpAuE+Plku+VTss5W1CbsiSG4qIt8KrBf3sZewNmjTagtLeotd/FtDhGm8oWc+L7wcKRgxQDETJImJ6LDQ2MiO5xXRZ52mvan95qR2KKSiu8Dg90n1K7+xhXWGC57WJyIORT1/+j8rnSo9CaZ6oLZHvLFiSeL2gZD0vvh8oGDFACXJaFWaSS+RUOz1ZrTl5RZLTI517WZzb9Mgw8ZWbA17wLNDUJm52HyM+rVZUkH7B1V+09YwAkC3CZnByRRnVrNVFFCwYoAQxfxVmkvuFpgUlRdjEiBVKC2jBs2CVMd51FWIAnsvLBbPQfGx8P1CoYYASpPxdmElNHohWH/dKghRvp/C6/xpVsmSA2D7eDrnpMVTnE+fhmgmvihcqm/CKf9ukhwmveP/YDDKt2E7s9ajrlHYiP2OAEoSUlH/XukQ90PIXGhCqv0WDiFxVVG91H+Pao2JPiO0+xvdjB5qWj02P556IHBigBKFAFmZy/kX2J4nZPyvdFiVU0jsRynTrLfG0ho4v9F45OJCUPDZPCblHNrd87ldmuhZ7IyKfMEAJQkYpzCQ1+2dkhroZE8GbthhAkmvolHu+L3/5++69B5VVpCUirxlg8JvU0qIwk3tBMW97NsTGvL05ttT6Pd6oqW9AxlMfAwCKl4zyutfC/TiG4bEqqtN+7o5sBgqebN62r0UzYonWrQxxoVeRlsho2IMShEKhMJNzfsysYV0VDRXRZUrX0Pn2C9u/zoHKe78S/+X/3oOej+dLHRKj06xXyakiLRH5hAFKEAr2wkzu06P/sv04BKE5YPF2qChsKK2KeqGiZZ6KKG2TqYOOWC6Pr/kkPq9zREQMUIKU1oWZ/DXttaC4QnR69PfV9Y7/24eK3IvQxURFGmtqbqAorYpa8ql4noqoEA5S5HpHjmxWvsKxGjpUrtWqKCNRsGCAEsSCsTDT0s2HPRZma2wSdC9C5/5hX9/Q5LIt9uFvmC+ITjfa8kY8Zer8522EdOChhKeZTgVPQjaXJ39+c0CjaNjHBJg72v5GGhJ7P9z6/A7HNgMWCkVh/DM0NARbYSb3nhMxf/30OFZtP97ia8NehM65h8ib1YPzD5Yhd8Mhx/a0Nfvg/LRNW7MPVkss5o/u7riuoLgCSzcfbrFP7rgM/weEEZFA9grbL3zVazx7MHWjLb/EAIXIfGaf6eT+/DjPdJLtXXLKJ/npR+Cjxzyc8PKLKHu5pgmy9qKM7n/lM069js6vR8Ovpk2kEHtQSBVvhoLU/rL7x97TuhWhk6rA63648spazMkrcmzLrRekddVeRTLGq1hDRwm3X/7BnhDrcaaTCWjdVtmxjkoMA7kzp9r+Jhqu8CxXlNFdQF+PRDpggEK6cu+aVqLyp0uSt/lShE7Nh737Pv6u2quI6Bo63tDnl39AeZzpJNh6RZRQMlR2z9u2irQaBieA56KMzgL+eiTSGAMU8olcj4pUb4UW5IrQSeWKqPmwB5QNnOhZtVcRLQIKHX75B5zSWTSt20K2VGBce6DmB8/HiYjQJbhTW2wx4K9HIg0xQCFdqOmtANQXZpMqQieXXKtnZV29q/bqxr4WTSgFJ4DyWTRZMy//R2LCfu+7lR1Hp2nFSosyugva1yOREwYopAu1vRXJ5lin/8d4VYTO0wrPJ3/QL/HT2y8SbSkM88ypzf8PtXV27DzOdLqcc3Pz78Rzeey9StcqXERQh2nFgOeijFKM8Xok8g1n8ZAu1PyCW/vA9RjSrYNjBpI90JAqfy9WhM7TCs8mAG8VnkaKORYVVbWazXsxwVZ7xjhVe8WeNaftye8CaVnA8jQ/t8vPZGc6ueXcZIwHugxtfk4mvwt0HW67ranRFqxUlUF20C8tS5eHYS/KKPZ+EGO81yOR99iDQrpQ8wvOfXq0N0XolKzwXF5Vh3sGXgVAm4UIDVe1d8Ir4j0BE15t3g7VHhMxUjOdxHJupFY4tgc6AKTrNkPX51Tq/eDOcK9HIh8xQAly/qoAq5aS9YLkqC1Cp7THpnP7ONEPe28+z72t2iuq/iKwyGK7eFuDpPsY11k99vyS7gqHKUKR+0wnb3JuJAMd/9W/cX8/zB7WFckaVZEmMioGKKQLJesFKTmGnacidGpWeBYLfg48OVJhq2zmZV9rzKq9Uj0B4UyL50Qs0HnkC9/bpoLz6/+RYVcHXRVpIrUYoJBu5IZqtF6pWO0Kz+7BT3RU81tBLknXbsoNndiNHm4MFvwFWxVpIrUYoJCupIZqtF6pWMsVnheO6SF7HPv5DCHYK74GMz73RLpigEK689cvPa1WeB6ZkSx6HOep0EREpC/NA5RFixbBZDK5XLp3b150rba2FrNmzUK7du1wxRVXYOLEiaio0KfIEYUfrVZ4FjtOQc7NmrUzoPjLn4iCgC7TPnr27IktW7Y0nySq+TRz587Fpk2b8M4778BisWD27NmYMGECdu3apUdTyKC8WYVYKa16bNyPE7TsAQlJ43NEZDi6BChRUVFISWm5ymplZSVee+01vPnmmxg+fDgAYM2aNejRowf27t2LG264QY/mUJirqW9AxlMfAwCKl4wy1HRsh6bG5v+f2t1cKIzIB0Hx2ieSoMur9b///S9SU1MRGxuLQYMGYdmyZbjqqquwf/9+XLp0CSNGjHDs2717d1x11VXYs2ePZIBSV1eHurrm8uVVVVV6NJsMRs9eFkMp3gB89Fjz9vo7bcXEsleoXyOHPQEthchz4v5+qKlvCGBriPSneQ5KVlYW1q5di/z8fKxevRolJSUYMmQIqqurUV5ejujoaCQkJLjcJzk5GeXl5ZLHXLZsGSwWi+OSlhbiZbopfBRvsJVjry5zvb6qzHZ98YbAtItCVk19AzrP34TO8zcxyCFD07wHZfTo0Y7/9+7dG1lZWejUqRPefvtttG7d2qtjLliwADk5OY7tqqoqBinkE7HeGU+9NZr36DQ1AvnzIL7CyuUVhPLnA93HcrjHCAzWExM2PYwUtnQfkExISMA111yDY8eOYeTIkaivr8f58+ddelEqKipEc1bsYmJiEBMjvw4FGRc/SCWc2g1UlcrsIABV39n2Sx/it2YRERmB7nVQLly4gOPHj8NqtaJ///5o1aoVtm7d6rj96NGjOH36NAYNGqR3U4iM5YLC6fVK9yMiCiGa96D87ne/w7hx49CpUyeUlpYiNzcXkZGRuOeee2CxWDB9+nTk5OQgMTERZrMZjz76KAYNGsQZPKQZrZIJde/5uUJhNd3/Nx24djRrlhBRWNE8QPnf//6He+65B2fPnkWHDh0wePBg7N27Fx06dAAA/N///R8iIiIwceJE1NXVYdSoUXjppZe0bgaRQ2NTc45HYck5DOnWwRil6jvdaJutU1UG8TwUk8T1RMqIvfaJgoVJEISg+wSsqqqCxWJBZWUlzGZzoJtDBpZ/sAy5Gw6hoqp5mrrVEovccRnGWPnVPosHgGswYnK9bmEpe1CCQf1FYGmq7f8LL+cXOW/78W8o9dqfP7o7fpNXBIC1Ucj/1Hx/cy0eCln5B8swc90Blw9oACivrMXMdQeQf7BM4p5+lDEeuPsNIN4tSdycCkx4JTBtoqAn99q3ByeArVfFuZeFyEgYoFBIamwSsPjDYskJvACw+MNiY3w4Z4wHZhU2b09+F5jzNdB9TODaRPqpvwgsstgu9Rc1P7yS177dtDX7MHjFNmME60RuGKBQSCosOYeyylrJ2wUAZZW1KCw5579GyXGuc9LpRtY9Ia95eu27M1SPIpETBigUks5UK/uAVrpfQLivz+O8TSRB7WvacD2KRJcxQKGQlBQfq+l+fle8AVg1sHl7/Z3AykyWviePvHlNG65HkQgMUChEDUxPhNUSC6nJxCbYZjQMTE/0Z7OUObKZ6/MEK/der4Z6120/9IJ5eu3LMXSPIoUdBigUkiIjTMgdlwEALT6o7du54zKMUQ/FXcGTkF6fB7b1eTjcYzxivV7PdXHdXplpC0B1JPfa98SwPYoUlhigUMjKzrRi9ZR+SDK7ruOUYonF6in9jFEHRYx7z4mLy+vzHN/mt+aQAlKrUgtNrttVZcB7v2re1qlXReq1L8XQPYoUthigUEjLzrRiS84tju21D1yPz+cNN15wYl8pd+Jryvbn+jzGIbsqtTu3fdTkFqmcnuz+2p89rCtMCMIeRQpbDFAo5Dl/6A5MTzT2h7DS9XmU7kf687gqtQc65hY5v9YfGXZ1cPYoUthigELkb3K/hO3r83jKHkjL0q15pJLPvVn+yy1S2qNYU9+AzvM3ofP8TV4vtknkKwYoREYSEQlkr7i8IdUZDxZyMxJNerMu5xad2q3BseQFVY8ihTUGKERGI7U+j/M2C7cZh9JeLyWYW0TkwACFyIjc1+cZ8jvX21m4zThke71UYm4RkQMDFCK9ebs4nPMwzmfPs3CbkUn1epmUfsSaAHNHW2+MFC59QGGGAQqFvLjoKJxcPhYnl49FXHRUoJvjJRZuMzyxVal/f6J5e8jvALmJvtnLpXOLvFz6IDRe+xSuGKDI0XlZdAoB7q8RJa8ZTX8J+y+5khRwX5U6Krp5e0iOeC+LOdV2fcZ48WNKFYHzsgdNSdDivGhgYck5LiJIAcEAhcifjmzWZxFAJlcGB7FeljlfSwcnskXg9OlByz9YhhEvfOrYnrZmHwav2Ib8g3IVjom0xwCFyJ/ee1CfXBImVwYP914WuSnjHovAaduDln+wDDPXHUBFVZ3L9eWVtZi57oBLkMJaKaQ3BihEenP5davil3B0G+Cpcx6msCpIrqTgpbRnTIMetMYmAYs/LJZ7hWLxh8Uc7iG/YYBCpCf35EZJEr+ElRRuk0uuJOOTy1vyw9IH9p6Qrgs3o6yyVnI/AUBZZS0KS855fS7n87HnhTxhgCKH0/rIE/fXSEN98/ZnL4gnN8oR+yUsNYXVU3Il+Z990cdFlbb/u2+r5bEInP970M5USwcxRFpigCLFy2l9FEI8zcgRe40816V5+7M/QtkKt06kfgmrTa6k0GDAHrSk+FjJ29x7R9hbQr5ggCJG42l9FIKkXiNCk5cHVPBLWE1yJRmX2l4VP/agJZtj5PpqYLXEYmB6IgBORSb9MUBxF4BpfRRkZF8j3mAuSVhTMpSsYw+ac2BxV/8rAUgvU5k7LgORESbJqcgFxZ6TdRnYkFIMUNz5eVofBSGPrxGVmEsSvtQMJevQg+YeaPxl+3FY4lrB0rqVy34pllisntIP2ZlW2anIc/KKVJ2PNVZIDmsfu/PjtD4yOPdftl2H274UtPzb3/M20G0Ee07CkX2Y0L0nzj6UrHPQag803PsvKmsuuVy39oHrMaRbB9Q1NKLz/E2Sx3M/TmHJOfRNS3Bsv7T9GFZtP95iv/LKWjy87gAAoHjJKMUl+WvqG5Dx1Meq70fBg39Rd36Y1kdBoHgD8NFjzdvr77T1dGSv0OBvb4Lj4zx9MIOTcORxKNlkG0ruPlaX14enmidOr1AMTE9EZIT6VZqnrdkH57v9Zftx0f2c28DhHnLGIR53Sqb1AcDrP+P6PKHKU5L0xbMeXiMemK3e3c/XKatkHAEeSi4sOeex5okW1MYb+0/9qNGZKRQwQHGnZFofhS4lSdKfLARGLbt8nafXhNvtk98FHvnCtzZS8PNmKFnDANWotUy+r67zvJNBcAq1/higiJGb1jfhlcC0ifxD6S/buHbirxGT21vKnApMeLV5m9ODCQj4ULJcLRMp/hh++eFCneLzcDZQ6GOA4sy5MNfVt4pP67tmVPN1rC4betT8shWb+vn7E67bc74Guo9xvS+HaijAFWIHpifCaon1WPPk+NIxiIuOajH7Ri8r8o8qmtXD2UDhgQGKHPdpfUc2sbpsqFP7y9b9NRIV7brN3hISE+AKsZERJuSOy5A7u0vNE7FpxXoRWznZmZoVlym4aR6gLFu2DNdffz3i4+ORlJSEO+64A0ePHnXZZ+jQoTCZTC6Xhx9+WOumaOvIZmNUl/VUft3fxwk0rR+HAdc+oRAV4DWWsjOtWD2lH5LMMS7XO9c8kZvt46xtXCvNMvTkVk420orLHGLSn+YByqeffopZs2Zh7969KCgowKVLl3Dbbbfh4kXXL48HH3wQZWVljsuzzz6rdVO0VfAkWF02DOjxy5ZDOiQlwGssZWdasSXnFsf22geux+fzhiM70zbTzNNsH7vJWVcBUJ0yLklq5WQls4+0WHHZEw4x+YfmAUp+fj6mTZuGnj17ok+fPli7di1Onz6N/fv3u+wXFxeHlJQUx8VsNkses66uDlVVVS4XXciVnJZdkdbDlMBQ6a0IF1w9mPwpwGssOdc4ca95onS2T6d2bUR7Y9zLp6RYYvGnSX0Vt839/ErbY99Pj5k2HGLyH91zUCorKwEAiYmJLtevX78e7du3R2ZmJhYsWICamhrJYyxbtgwWi8VxSUtL076hYiWnX8oC7v4HMPE1ZcfwR3VZJet2+PM4gabX41D6y9a9d4S9JRRClM726RAfI9obc+DJkS7bn88bjpEZymcmuZ9faXu8maWkhJGGmMKBrgFKU1MT5syZg5tuugmZmZmO6++9916sW7cO27dvx4IFC/CPf/wDU6ZMkTzOggULUFlZ6bh8++232jbUU2Gus+IVEFvQu7qsmnU7/HGcQNP7cXD1YApzSmf7DOnWAUDL3pjoqAiXbfeKtEpXTlbbHvf7acUoQ0zhQtcAZdasWTh48CDy8vJcrp8xYwZGjRqFXr16YfLkyXjjjTfw/vvv4/hx8UAgJiYGZrPZ5aIZJYW59q/1LXFSi1/5noIopV/KWh0n0ELlcRAZmJrZPt5Sc1y17dE6kVXtEBP5RrcAZfbs2di4cSO2b9+OK6+8UnbfrKwsAMCxY8f0ao40JYW5qkuBftMub6tMnJT6lf+fd5TnpXgMogTg7fuAWg+5OUqCsWBI9g2Vx0EEiA8LKslb02ifuOgonFw+FieXjxVdcE/JbB81nM+n9LjOuSQ3X9NB0f2UJrIqyVOx7/MbD6s128kNMbECrXKaLxYoCAIeffRRvP/++9ixYwfS09M93qeoqAgAYLV6uUaJL5TmjbTrakuQ/Ogx11/t5lRbcCKWOCm3Wul7Dypvo8cg6rJvvwC6jZS+Xc36H+lDlLfP3/z1OOxfHERhLjvTipuubo9eiz4B0LzCsXsPhz34cOa+7c1x1d5PaqVmeyKrN4GVXbI5Bmeq6kR/HplgC5T0GmIKN5oHKLNmzcKbb76Jf/3rX4iPj0d5eTkAwGKxoHXr1jh+/DjefPNNjBkzBu3atcN//vMfzJ07FzfffDN69+6tdXM8U1OYK30I0GUosPxyku7kd4Guw1v2nNRfBJamyhzMvl6oQmrX7XA+/8LS5l9l3qz/4YnUufSktH2v/0zbNgXisRIZhNxsn0AcV+x+NfUNyHjqY8n72D95F39YjJEZKZLncj5O8ZJRLrctHNMDc/KKXFZ8BrQb8vKWe5vFesOCjeZDPKtXr0ZlZSWGDh0Kq9XquPzzn/8EAERHR2PLli247bbb0L17d/z2t7/FxIkT8eGHH2rdFGXUFubSLHHS6aXtKS9FaRB18XttjqN3sq+vjN4+Il8pyVvTap8goGUuiXsiq5JjO19nad0Kq+71fsiLBd6U02WIR05aWho+/VT/NR0Usxfmevt+QComVluYS+2HwPo7Lw8VrXAdKnL+xR5vBarLIZ53cdmWRUDh34BbFzVfd2p3cy+PPRirKpM4jsl2u5oqqe4fgGI9Slrz+DicnNoNpGU193r50vMRiMdK4ad4g20o2U7s80GrfQDFPYNiwzdaEDuuc2/Anyb1xdLNhx23TVuzD1ZLLHLHZbS4n5ov+zPVtcg/WIbcDYdaHPuxUdc6rntp+zG8s/9/LfaZn90dc9/+NwDlQ1NS58sdl+H1kJOde+CjpD1GZxI8RRQGVFVVBYvFgsrKSu1m9NjfzC75JR1b5pd4ejOLHUeRyy8k50Jgzuea8KpT3orKP5nzh5IjL8b9OCLn90T0ORP5ANSD5OMQEW9tbqO3AUogHyuFD6m8Nef3J6DNPmKfMwYZunQOUNx/NtqvA9AiKTZ3wyHFawbNHXENVm75Ru2nqcv57fdVMqQilRcj9ljUEnvsWgU+WlPz/c0AxVltlef8EjmSHy5KXe7BmPO17bzu7am/aJud4mvwozQYE+OSXyPz0aH2A9CbD0lvgkH737WhVvn5lHxpMEghXzU12mb4SSaAm2zBtgm+7yP3OWOAnsHq2kuOBFgp9oTUz+cNR0FxueiXv9T9tPjScz6OPU9FKgeksUnA4BXbPC4b8PWi2xAf20pVPomegY8e1Hx/czVjZ77kl8hOfVXKafaJ2PTkjxcAIxZ7d1ygeeqtZut/BHiar/vjiGvn+T72ad5HNis7B6c0k78oLXmgxT5ynzMBLtroPj1Yij2XZO/xs4oWNARUTU1QdH6llK5ptP/Uj6raEOqVbRmgaEXpVGAlXv+ZdBGy9x/y8qBu6wW5B2MNtcrqsij6InY7l57JfM6Po+assvtUlQHv/UrZ+dRMaSbyhT+WynB21CArtDuRWudGzp4TPyj68gdsPS4v3N3H2+aJ+tOkvoiLjpJNflVauG3v8bNobBIUJ9LqVdnWKLVagn8ekpZ8qXuh+YeLVEzs428AX9rpnnSn5FxaJvNpxu25lTufHlOzicT4e3baf96G7OdM/nyg+1i/DffI9QbIU/aZ+PDNXdD7ygQs3njI884qJMXHekx+Vbo20Ms7TyDvy29d/ixyibShXtmWPShaUfrhEtcOvgUZYjPvVZBqp1gPhnMVyv+8I/5rS87/my7/C81+bCX71F/Ud1VoqV+NoTI1m4xPScmD+FRt9olrD9T8INOYyz2DSxL9tgK70mEQO/u6O4O6KhjaBRAVacKsN9X1zig5/48X6z2ubuxpDSFn52su4fxPlySP5UyvxRONMhWaAYpWPH64XDZq2eX/+NgTcsMjKo/jVs/Fubz2sa3i49CHNzZf53V+jUx5fjX7nNoNNNS7bjc1Nj+Op84pe/49tdM9n0RtnRwib9lLHgCQXFJj9Apt9ul9t/J2+al+ippf+c5F0W7o0k7Rl/87+/+nSXKs8/mfHNsDT2/ynANib6vzfdWQyifRY/FEpUsE+AMDFK14/HAxAXf/A+jzC9usj/gU38537RgVx5Gp5yK56F4p8P6M5m2l+R16WX8n8FwX123nZD7Z518pkXwSJV8aauvkEEnJGC/+vjanNs8Wk9tnwiu2dbnevs/2f6njXDtGeZv8lDir5le+c1E0TwsImgDMHdFNs54T5/O3bROjKAek68LNkmsIKWU/1mf//d5xndaLOUrlAEn14OiNAYqWlHy42PdTO/vEwekXu9hsnLtet00zlDu/nSYzj/xIaHLddh+WkXr+1XLPJ1H6dyXSgpJZdlL7XONUlr11AjBzj/hxlPb42vkhcVbpMMjfpw7A5/OGu+RjeFrQsHN7ZbVdHr65C166tx+S3Y6THN+8vfaB6x3nV9PrU1hyDiMzUrAl5xbF9xFjT6S102oxRyPOCGKAojWlU3i9mX0i9ovdfTZOzzuUTyHWcuYRAMRoWJNGEZFhGffnH4DqHhWxfBLNpmYTKaCk5IH7Pkc2tRyqXT1I/Diqexz1n1KvpDcAAG7o2k60RyA70+ry5e8cSCjtnbmhazuM6d3yOFt+27ztvF6Qml4f+1DJtiNnFN9HzMs7T7QYcpF77ErpNSPIFwxQ9KDkw8WeOzHxNeXHFfvFLrZUu9J6LlrPPKmr0vZ4ikgMy9hNeFVFj4qHfBLN1mEi8kDsfS23z7Gt4kO11eVwDC+7H0d1j6P+U+rlegNentIPJ5ePlS1aJrXwoNJcjSHdOogeJz62FU4uH9vi/GqSXwHbUMmcvCK8dO91qu4ndhz3IRdfF3M04owgBii+8nVmidLZHyMWef+LXaqNmsw8MchaD1LBVvcxrj0fQ36H5pFpZ8wnoSCltpig8+fB1beK9Dh64Lxqug6z6rToDXCnda6GkuOKsf+Fnt50GE+O9T1p9uF1BzSrVaLXjCBfMEDxldj0XCW/fuyUjgUPmK78i9P9/FJF0NSOQ4sxp9p+nU3d6HlfPTkHW+6P3/l5G5LjfT6Jmr8rkb+oLSbo/nmglv29puNKyd72BtgXHhTraVGTqyF3HHdSx5ViHypp2yZa9H4Jca2Q0LqVouPYFZacQ0xUpOI2i9FjRpCvuBaPL7RaQE7LBfzUtlHNonvunNftcKwj4mGF4dbtgJ/O+b6Pg9u6IkoZcP0RIq98/a6t5pAnE18DIqOlPw+6j/XwHnZ6rx3ZFLSLZzqv86N0FWK1x1XiT5P64va+HUXbU1PfoOpYgPjigGofq30WDyBecUuLdX24Fo8/SE7P9SLbXa9ZIkraqGoc2m1oRHHSndP2aF/2EWsPvBuWYT4JhQqlQ7Vnj8t/HhzZpGxK/ZFNhiuRr4avuRpKjquEfahErD3etMk9L8WbeiZazQjSCntQvKFk1dFA/6pX20YlKycrWfFYyUrJ3u5jinCdaqx0BWYl2KNCwcpj76VJ3QrHor0jl99rjl4WHz77Qvy9Zl+5uLyyVuqv4ViFWS4Q8XQcMfZjPzk2A7PeVLbCsaceHC17mQB1398MULxR8pltQT9Ppm4E0ofo3x4xWrTR2w8SJffzZp+OA4BnO6tvjydaDdURBYqnYeKhC4AdSz0fx/55IPX+9PVzJUzea1oNlUgdx5PENtE4d7Fe9DbnAKmguBy5Gw65FGaTWvdHKxzi0VswLCCnRRu9HQbxpoaDkn2ior1rjxwth+qIAsXTMHG7rsqOY/88kHp/Kv1cef1nwH8LgJofm2f6bH06bN5rWg2VqE3AtZMKToDmJN3fvl1kqKqxYtiD4o1w6UEJdXoN1REFil49H3ZKj2PnPiwrvWNIvte0SshVm4DrK6XDUN5gD4regmEBuWBoY6CpnZ5JZHRSPR++fh7UVtl6QV7/mboV2RUFJ4DH95r9/Isstp4ZpVOavb2fRlokwNZXe9Ue5+Mkm2NkpwIntvE8RdmTQFSNFcMAxRvBsIBcMLQx0IJhqI5IDalaPb58HhRvcC2hX3MWuq3fJfZecz+/0sULvb2fhlzqqRzb7HV7nI+zeHxPANLzIJ+5PdOnKrXO/Fk1VgwDFG8FwwJywdDGQFI6PVOTirtEAebN54FUjpZe3N9r3uaIGS23TMP2eMpvGdM7VVV1Wzn+rBorhjkovgqGKXPB0MZAUDI9MwTHxSnMKf088JijpSW391pToy3f5d1pwE8/Kr/Pqd22ICB/AVDzg7L7ibEf60KFLWjyJSlfp1w3T/kt+QfLWszQEROBJgyMOIIknMcZJODLpmswIOIbXBN3Ebn3Dkdk55s0/fzjNGMipfSs4ksUzJQmxI5aCny80IcTub3XxKYiy5m60RbEqLmP/X7+mAodwAkLnpJrR0UUIrfVG0g1NeeaNAomRJqcPgs1ngbOJFkipTgMRiROae5Vmw6+rekVb7XVaWmsB3asUD+kdHSzd8NQhzfYggfnRFXJoZhS4O37bD0z9vvYe3m+frflcZwpfR7F2mOn5Fwi+8THtsLxpWNEc1JGRRRidauVSIFrImyEya3PIoDTwNmDQgRo26VLFArU/PL/6UeFa3qZbLcPXWirzXL2OLB/jW85LnHtZYZzFGixFpGCIa3WbW3/Og8/SfU0qJ2a7X4cJT06HvZxL/gWgSZ8HvNrpOAclM0i1m64m0M8RETkG7U5WmqXp3AMr/rwFRRjBuqqvL+/rZG2f5RW2/V0HPeeV6ULqYodB5B4jpwCvdrzwN6XPLbHOSflhohi5EU/o/BxOdFgGIoBChER+U5tjpZ7T2RaFvDtFy17Jv2agKtQqzbApYu+H6d1W+Cu14HOg5t7G1SvGq9k/SSF4toD2cuAeCsaOw7EkX1b0PrYRnQpeVP9sSa+BvS606fmMEAhIiJtFG8A8ue5flH6ulCn2mGPYCQ2DOP+PPqb4sq+EvzcgxLl05mIiCi0ZYy35WdomaPlbfHD2ATbeWvOKr9PXHug5x3Avle9O6e3qspsibX2fJsrkoFf/9vWo3R4A1D4N/+2B/AhOLk8nOfnyuMMUIiISF5EpLZTYFUXP7w8pHTDIyryRC7f52f/Zxt28XeAYh/KcW6vvVelx/jABCheCVzlcU4zJiIi//K4NpAbtasyO98nY7z68+nFPmX34lljtEeMyS0sCGDJhYAGKKtWrULnzp0RGxuLrKwsFBYWBrI5RETkD0rWBhq60JaUOXWjbaZQxnjlPS+jljbfx+P5ZFw9Uv19ZF3uVflkITBqmcbH9tHAGbbn+vEK27/uz30ABCxA+ec//4mcnBzk5ubiwIED6NOnD0aNGoUzZ84EqklEROQv9iKJZqvr9eZU4O5/AEPn2WaMpA9Rvypz1sMthyOkzifnpt/Y2uJ+n9aJtotXLq/cHNdOfXv01GO87bmOirb96/7cB0DAZvFkZWXh+uuvx1/+8hcAQFNTE9LS0vDoo49i/vz5svflLB4iohChtkiir8tT+LLOj3MbAQXHkWGfstvUCGxfBnz2nOf7DJxhS/rdYe99Efn6znrYVk1W8arT/l1zzPCl7uvr67F//36MGDGiuSERERgxYgT27NnTYv+6ujpUVVW5XIiIKATYE3CV/mKX7XlRkCsREQl0HQqM+zNsQY3EEJNzUqhYGz0exwP7cFVEJNDlFmX36THe1rMk+vg72np7Rq+wJQY7PxZJgUuAVSIgs3h++OEHNDY2IjnZdTwxOTkZR44cabH/smXLsHjxYn81j4iIjEyLqc/2QKdFjZdUdTVepI4jSWTKrn3oylPVXvt9PD1+qTa1qOyr8rH6WVBMM16wYAFycnIc21VVVUhLSwtgi4iIKKC0mPqsVY0X9+OcPS4xDCPRY2FP4n37fjjK2Cu5j9zjF3tsUpV9DSogAUr79u0RGRmJigrXYj0VFRVISUlpsX9MTAxiYmL81TwiIgoXWtV4cT9OUg91vTNa9ejItQnQtp6NzgISoERHR6N///7YunUr7rjjDgC2JNmtW7di9uzZgWgSERGRdrzpndGjam8QC9gQT05ODqZOnYoBAwZg4MCBWLlyJS5evIgHHnggUE0iIiLSjje9M1pX7Q1iAQtQfvGLX+D777/HU089hfLycvTt2xf5+fktEmeJiIgo/HA1YyIiIvILw9dBISIiIpLDAIWIiIgMhwEKERERGQ4DFCIiIjIcBihERERkOAxQiIiIyHAYoBAREZHhMEAhIiIiw2GAQkRERIYTsFL3vrAXv62qqgpwS4iIiEgp+/e2kiL2QRmgVFdXAwDS0tIC3BIiIiJSq7q6GhaLRXafoFyLp6mpCaWlpYiPj4fJZPL5eFVVVUhLS8O3337LtX38gM+3//C59h8+1/7D59p/tH6uBUFAdXU1UlNTEREhn2USlD0oERERuPLKKzU/rtls5ovdj/h8+w+fa//hc+0/fK79R8vn2lPPiR2TZImIiMhwGKAQERGR4TBAARATE4Pc3FzExMQEuilhgc+3//C59h8+1/7D59p/AvlcB2WSLBEREYU29qAQERGR4TBAISIiIsNhgEJERESGwwCFiIiIDCdsApRVq1ahc+fOiI2NRVZWFgoLC2X3f+edd9C9e3fExsaiV69e2Lx5s59aGvzUPNevvPIKhgwZgrZt26Jt27YYMWKEx78NuVL72rbLy8uDyWTCHXfcoW8DQ4ja5/r8+fOYNWsWrFYrYmJicM011/CzRCG1z/XKlStx7bXXonXr1khLS8PcuXNRW1vrp9YGr507d2LcuHFITU2FyWTCBx984PE+O3bsQL9+/RATE4Orr74aa9eu1adxQhjIy8sToqOjhb///e/CoUOHhAcffFBISEgQKioqRPfftWuXEBkZKTz77LNCcXGx8MQTTwitWrUSvv76az+3PPiofa7vvfdeYdWqVcJXX30lHD58WJg2bZpgsViE//3vf35ueXBS+3zblZSUCB07dhSGDBki3H777f5pbJBT+1zX1dUJAwYMEMaMGSN8/vnnQklJibBjxw6hqKjIzy0PPmqf6/Xr1wsxMTHC+vXrhZKSEuHjjz8WrFarMHfuXD+3PPhs3rxZePzxx4X33ntPACC8//77svufOHFCiIuLE3JycoTi4mLhxRdfFCIjI4X8/HzN2xYWAcrAgQOFWbNmObYbGxuF1NRUYdmyZaL733333cLYsWNdrsvKyhIeeughXdsZCtQ+1+4aGhqE+Ph44fXXX9eriSHFm+e7oaFBuPHGG4VXX31VmDp1KgMUhdQ+16tXrxa6dOki1NfX+6uJIUPtcz1r1ixh+PDhLtfl5OQIN910k67tDDVKApTHHntM6Nmzp8t1v/jFL4RRo0Zp3p6QH+Kpr6/H/v37MWLECMd1ERERGDFiBPbs2SN6nz179rjsDwCjRo2S3J9svHmu3dXU1ODSpUtITEzUq5khw9vne8mSJUhKSsL06dP90cyQ4M1zvWHDBgwaNAizZs1CcnIyMjMzsXTpUjQ2Nvqr2UHJm+f6xhtvxP79+x3DQCdOnMDmzZsxZswYv7Q5nPjz+zEoFwtU44cffkBjYyOSk5Ndrk9OTsaRI0dE71NeXi66f3l5uW7tDAXePNfu5s2bh9TU1BZvAGrJm+f7888/x2uvvYaioiI/tDB0ePNcnzhxAtu2bcPkyZOxefNmHDt2DI888gguXbqE3NxcfzQ7KHnzXN9777344YcfMHjwYAiCgIaGBjz88MNYuHChP5ocVqS+H6uqqvDTTz+hdevWmp0r5HtQKHgsX74ceXl5eP/99xEbGxvo5oSc6upq3HfffXjllVfQvn37QDcn5DU1NSEpKQl/+9vf0L9/f/ziF7/A448/jpdffjnQTQs5O3bswNKlS/HSSy/hwIEDeO+997Bp0yY8/fTTgW4a+SDke1Dat2+PyMhIVFRUuFxfUVGBlJQU0fukpKSo2p9svHmu7f74xz9i+fLl2LJlC3r37q1nM0OG2uf7+PHjOHnyJMaNG+e4rqmpCQAQFRWFo0ePomvXrvo2Okh589q2Wq1o1aoVIiMjHdf16NED5eXlqK+vR3R0tK5tDlbePNdPPvkk7rvvPvzqV78CAPTq1QsXL17EjBkz8PjjjyMigr/FtSL1/Wg2mzXtPQHCoAclOjoa/fv3x9atWx3XNTU1YevWrRg0aJDofQYNGuSyPwAUFBRI7k823jzXAPDss8/i6aefRn5+PgYMGOCPpoYEtc939+7d8fXXX6OoqMhxGT9+PIYNG4aioiKkpaX5s/lBxZvX9k033YRjx445gkAA+Oabb2C1WhmcyPDmua6pqWkRhNgDQ4HLzWnKr9+PmqfdGlBeXp4QExMjrF27ViguLhZmzJghJCQkCOXl5YIgCMJ9990nzJ8/37H/rl27hKioKOGPf/yjcPjwYSE3N5fTjBVS+1wvX75ciI6OFt59912hrKzMcamurg7UQwgqap9vd5zFo5za5/r06dNCfHy8MHv2bOHo0aPCxo0bhaSkJOGZZ54J1EMIGmqf69zcXCE+Pl546623hBMnTgiffPKJ0LVrV+Huu+8O1EMIGtXV1cJXX30lfPXVVwIA4YUXXhC++uor4dSpU4IgCML8+fOF++67z7G/fZrx73//e+Hw4cPCqlWrOM3YVy+++KJw1VVXCdHR0cLAgQOFvXv3Om675ZZbhKlTp7rs//bbbwvXXHONEB0dLfTs2VPYtGmTn1scvNQ81506dRIAtLjk5ub6v+FBSu1r2xkDFHXUPte7d+8WsrKyhJiYGKFLly7CH/7wB6GhocHPrQ5Oap7rS5cuCYsWLRK6du0qxMbGCmlpacIjjzwi/Pjjj/5veJDZvn276Gew/fmdOnWqcMstt7S4T9++fYXo6GihS5cuwpo1a3Rpm0kQ2P9FRERExhLyOShEREQUfBigEBERkeEwQCEiIiLDYYBCREREhsMAhYiIiAyHAQoREREZDgMUIiIiMhwGKERERGQ4DFCIiIjIcBigEBERkeEwQCEiIiLDYYBCRAE1dOhQPProo5gzZw7atm2L5ORkvPLKK7h48SIeeOABxMfH4+qrr8ZHH30U6KYSkR8xQCGigHv99dfRvn17FBYW4tFHH8XMmTNx11134cYbb8SBAwdw22234b777kNNTU2gm0pEfsLVjIkooIYOHYrGxkZ89tlnAIDGxkZYLBZMmDABb7zxBgCgvLwcVqsVe/bswQ033BDI5hKRn7AHhYgCrnfv3o7/R0ZGol27dujVq5fjuuTkZADAmTNn/N42IgoMBihEFHCtWrVy2TaZTC7XmUwmAEBTU5Nf20VEgcMAhYiIiAyHAQoREREZDgMUIiIiMhzO4iEiIiLDYQ8KERERGQ4DFCIiIjIcBihERERkOAxQiIiIyHAYoBAREZHhMEAhIiIiw2GAQkRERIbDAIWIiIgMhwEKERERGQ4DFCIiIjIcBihERERkOP8fBBCMzQyCL8YAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mask = toy[1] < tsplit\n",
    "m1 = toy[0][mask]\n",
    "m2 = toy[0][~mask]\n",
    "\n",
    "plot_binned(m1, bins=100, label=r\"$t$ < $t_0$\")\n",
    "plot_binned(m2, bins=100, label=r\"$t$ ≥ $t_0$\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"m\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For sWeights to be applicable, the pdfs in the $m$ variable must not depend on the $t$ variable. The respective yields are allowed to vary, but the shape parameters of the pdfs for signal and background must be identical. We can test this null hypothesis against the alternative (shape parameters are not the same) with a likelihood ratio test. This only requires parametric models for the signal and background densities in the $m$ variable, which are needed anyway to compute sWeights. Hence, this technique is easy to use in practice.\n",
    "\n",
    "Here, the $m$ distribution consists of a normal distribution for the signal and exponential background, which have the parameters $\\mu,\\sigma$ and $\\lambda$, respectively. In case of the null hypothesis, the two datasets share these parameters, but the signal and background yields $s,b$ are allowed to differ. In case of the alternative hypothesis, all parameters are determined separately for the two partial datasets. The $Q$ statistic\n",
    "$$\n",
    "Q = -2\\ln\\frac{\\sup L_{H_0}}{\\sup L_{H_1}} = -2\\ln\\frac{\\sup\\{ L_1(s_1, b_1, \\mu, \\sigma, \\lambda) L_2(s_2, b_2, \\mu, \\sigma, \\lambda) \\}}{\\sup \\{ L_1(s_1, b_1, \\mu_1, \\sigma_1, \\lambda_1) L_2(s_2, b_2, \\mu_2, \\sigma_2, \\lambda_2) \\}}\n",
    "$$\n",
    "is asymptotically chi-square distributed with 3 degrees of freedom, since that is the difference in dimensionality in the parameter space between $H_0$ and $H_1$. Note, that the likelihood ratio test requires $H_0$ to be nested in $H_1$, and that is the case here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first fit $H_0$ with iminuit. We use an extended unbinned maximum likelihood method, but one could also use a binned maximum likelihood method or the classic method instead of the extended method. Our choice is merely the most convenient.\n",
    "\n",
    "For the cost function `ExtendedUnbinnedNLL` from iminuit, we create `model`, a function that returns the integral of the density as the first argument and the density as the second argument (see the documentation of `ExtendedUnbinnedNLL`). We use type annotations to indicate that some parameters have lower bounds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(\n",
    "    x,\n",
    "    s: PositiveFloat,\n",
    "    b: PositiveFloat,\n",
    "    mu: Annotated[float, 0:1],\n",
    "    sigma: PositiveFloat,\n",
    "    slope: PositiveFloat,\n",
    "):\n",
    "    ds = norm(mu, sigma)\n",
    "    snorm = np.diff(ds.cdf(mrange))\n",
    "\n",
    "    db = expon(0, slope)\n",
    "    bnorm = np.diff(db.cdf(mrange))\n",
    "\n",
    "    integral = s + b\n",
    "    density = s / snorm * ds.pdf(x) + b / bnorm * db.pdf(x)\n",
    "    return integral, density"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we create the `ExtendedUnbinnedNLL`, one for each partial data set, add them (adding log-likelihoods is equivalent to multiplying the likelihoods) and fit the sum.\n",
    "\n",
    "iminuit detects the parameters from the function signature. Since the same function `model` is used in both instances of `ExtendedUnbinnedNLL`, all parameters would be shared. But we don't want that to happen for the yields, so we use the utility function `make_with_signature` to rename the yield parameters of our model, to make them distinct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = -1.567e+05 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 184 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 4.7e-06 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\"> time = 1.5 sec </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> s1 </td>\n",
       "        <td> 3.13e3 </td>\n",
       "        <td> 0.08e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> b1 </td>\n",
       "        <td> 4.07e3 </td>\n",
       "        <td> 0.09e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> mu </td>\n",
       "        <td> 0.4976 </td>\n",
       "        <td> 0.0018 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 1 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 0.0978 </td>\n",
       "        <td> 0.0018 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 4 </th>\n",
       "        <td> slope </td>\n",
       "        <td> 0.501 </td>\n",
       "        <td> 0.015 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 5 </th>\n",
       "        <td> s2 </td>\n",
       "        <td> 1.81e3 </td>\n",
       "        <td> 0.05e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 6 </th>\n",
       "        <td> b2 </td>\n",
       "        <td> 960 </td>\n",
       "        <td> 40 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
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       "        <td></td>\n",
       "        <th> s1 </th>\n",
       "        <th> b1 </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "        <th> slope </th>\n",
       "        <th> s2 </th>\n",
       "        <th> b2 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> s1 </th>\n",
       "        <td> 7.04e+03 </td>\n",
       "        <td style=\"background-color:rgb(184,184,250);color:black\"> -4e3 <strong>(-0.507)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -4.5580e-3 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,189,189);color:black\"> 62.6469e-3 <strong>(0.403)</strong> </td>\n",
       "        <td style=\"background-color:rgb(203,203,250);color:black\"> -459.58e-3 <strong>(-0.359)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.6e3 <strong>(0.143)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -0.6e3 <strong>(-0.165)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b1 </th>\n",
       "        <td style=\"background-color:rgb(184,184,250);color:black\"> -4e3 <strong>(-0.507)</strong> </td>\n",
       "        <td> 7.55e+03 </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 7.3652e-3 <strong>(0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(201,201,250);color:black\"> -60.6118e-3 <strong>(-0.377)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,207,207);color:black\"> 383.45e-3 <strong>(0.289)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -0.6e3 <strong>(-0.130)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,228,228);color:black\"> 0.5e3 <strong>(0.144)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -4.5580e-3 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 7.3652e-3 <strong>(0.046)</strong> </td>\n",
       "        <td> 3.43e-06 </td>\n",
       "        <td style=\"background-color:rgb(236,236,250);color:black\"> -0.4e-6 <strong>(-0.104)</strong> </td>\n",
       "        <td style=\"background-color:rgb(235,235,250);color:black\"> -3.2e-6 <strong>(-0.113)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -5.6570e-3 <strong>(-0.060)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,238,238);color:black\"> 6.4531e-3 <strong>(0.082)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,189,189);color:black\"> 62.6469e-3 <strong>(0.403)</strong> </td>\n",
       "        <td style=\"background-color:rgb(201,201,250);color:black\"> -60.6118e-3 <strong>(-0.377)</strong> </td>\n",
       "        <td style=\"background-color:rgb(236,236,250);color:black\"> -0.4e-6 <strong>(-0.104)</strong> </td>\n",
       "        <td> 3.43e-06 </td>\n",
       "        <td style=\"background-color:rgb(212,212,250);color:black\"> -8.2e-6 <strong>(-0.291)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 25.9113e-3 <strong>(0.273)</strong> </td>\n",
       "        <td style=\"background-color:rgb(207,207,250);color:black\"> -26.0566e-3 <strong>(-0.330)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> slope </th>\n",
       "        <td style=\"background-color:rgb(203,203,250);color:black\"> -459.58e-3 <strong>(-0.359)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,207,207);color:black\"> 383.45e-3 <strong>(0.289)</strong> </td>\n",
       "        <td style=\"background-color:rgb(235,235,250);color:black\"> -3.2e-6 <strong>(-0.113)</strong> </td>\n",
       "        <td style=\"background-color:rgb(212,212,250);color:black\"> -8.2e-6 <strong>(-0.291)</strong> </td>\n",
       "        <td> 0.000233 </td>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -139.88e-3 <strong>(-0.179)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,221,221);color:black\"> 127.41e-3 <strong>(0.196)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> s2 </th>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.6e3 <strong>(0.143)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -0.6e3 <strong>(-0.130)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -5.6570e-3 <strong>(-0.060)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 25.9113e-3 <strong>(0.273)</strong> </td>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -139.88e-3 <strong>(-0.179)</strong> </td>\n",
       "        <td> 2.62e+03 </td>\n",
       "        <td style=\"background-color:rgb(197,197,250);color:black\"> -0.9e3 <strong>(-0.406)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b2 </th>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -0.6e3 <strong>(-0.165)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,228,228);color:black\"> 0.5e3 <strong>(0.144)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,238,238);color:black\"> 6.4531e-3 <strong>(0.082)</strong> </td>\n",
       "        <td style=\"background-color:rgb(207,207,250);color:black\"> -26.0566e-3 <strong>(-0.330)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,221,221);color:black\"> 127.41e-3 <strong>(0.196)</strong> </td>\n",
       "        <td style=\"background-color:rgb(197,197,250);color:black\"> -0.9e3 <strong>(-0.406)</strong> </td>\n",
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      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = -1.567e+05                 │              Nfcn = 184              │\n",
       "│ EDM = 4.7e-06 (Goal: 0.0002)     │            time = 1.5 sec            │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬───────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name  │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼───────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ s1    │  3.13e3   │  0.08e3   │            │            │    0    │         │       │\n",
       "│ 1 │ b1    │  4.07e3   │  0.09e3   │            │            │    0    │         │       │\n",
       "│ 2 │ mu    │  0.4976   │  0.0018   │            │            │    0    │    1    │       │\n",
       "│ 3 │ sigma │  0.0978   │  0.0018   │            │            │    0    │         │       │\n",
       "│ 4 │ slope │   0.501   │   0.015   │            │            │    0    │         │       │\n",
       "│ 5 │ s2    │  1.81e3   │  0.05e3   │            │            │    0    │         │       │\n",
       "│ 6 │ b2    │    960    │    40     │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬─────────────────────────────────────────────────────────────────────────────────────┐\n",
       "│       │          s1          b1          mu       sigma       slope          s2          b2 │\n",
       "├───────┼─────────────────────────────────────────────────────────────────────────────────────┤\n",
       "│    s1 │    7.04e+03        -4e3  -4.5580e-3  62.6469e-3  -459.58e-3       0.6e3      -0.6e3 │\n",
       "│    b1 │        -4e3    7.55e+03   7.3652e-3 -60.6118e-3   383.45e-3      -0.6e3       0.5e3 │\n",
       "│    mu │  -4.5580e-3   7.3652e-3    3.43e-06     -0.4e-6     -3.2e-6  -5.6570e-3   6.4531e-3 │\n",
       "│ sigma │  62.6469e-3 -60.6118e-3     -0.4e-6    3.43e-06     -8.2e-6  25.9113e-3 -26.0566e-3 │\n",
       "│ slope │  -459.58e-3   383.45e-3     -3.2e-6     -8.2e-6    0.000233  -139.88e-3   127.41e-3 │\n",
       "│    s2 │       0.6e3      -0.6e3  -5.6570e-3  25.9113e-3  -139.88e-3    2.62e+03      -0.9e3 │\n",
       "│    b2 │      -0.6e3       0.5e3   6.4531e-3 -26.0566e-3   127.41e-3      -0.9e3    1.81e+03 │\n",
       "└───────┴─────────────────────────────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nll1 = ExtendedUnbinnedNLL(m1, make_with_signature(model, s=\"s1\", b=\"b1\"))\n",
    "nll2 = ExtendedUnbinnedNLL(m2, make_with_signature(model, s=\"s2\", b=\"b2\"))\n",
    "mi0 = Minuit(\n",
    "    nll1 + nll2,\n",
    "    s1=1000,\n",
    "    s2=1000,\n",
    "    b1=1000,\n",
    "    b2=1000,\n",
    "    mu=0.5,\n",
    "    sigma=0.1,\n",
    "    slope=0.5,\n",
    ")\n",
    "mi0.strategy = 0  # sufficient since we don't need accurate parameter errors\n",
    "mi0.migrad()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To fit $H_1$ with iminuit, we could follow the same strategy, but there is a better way. Since none of the parameters are shared now, it is equivalent to optimize the log-likelihood for each dataset separately and add the results. We avoid optimizing a combined likelihood and renaming model parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = -1.163e+05 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 132 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 3.75e-06 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\"> time = 0.6 sec </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
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       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
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       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </td>\n",
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       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
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       "        <th> 0 </th>\n",
       "        <td> s </td>\n",
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       "        <td> 0.09e3 </td>\n",
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       "        <th> 1 </th>\n",
       "        <td> b </td>\n",
       "        <td> 4.09e3 </td>\n",
       "        <td> 0.09e3 </td>\n",
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       "        <th> 2 </th>\n",
       "        <td> mu </td>\n",
       "        <td> 0.5014 </td>\n",
       "        <td> 0.0026 </td>\n",
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       "        <td> sigma </td>\n",
       "        <td> 0.0967 </td>\n",
       "        <td> 0.0025 </td>\n",
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       "        <th> 4 </th>\n",
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       "        <td> 0.500 </td>\n",
       "        <td> 0.018 </td>\n",
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       "        <td> 7.97e+03 </td>\n",
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       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -11.397e-3 <strong>(-0.050)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,177,177);color:black\"> 110.330e-3 <strong>(0.487)</strong> </td>\n",
       "        <td style=\"background-color:rgb(200,200,250);color:black\"> -638.33e-3 <strong>(-0.386)</strong> </td>\n",
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       "        <td> 8.26e+03 </td>\n",
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       "        <td style=\"background-color:rgb(186,186,250);color:black\"> -113.135e-3 <strong>(-0.490)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,197,197);color:black\"> 597.07e-3 <strong>(0.355)</strong> </td>\n",
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       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -11.397e-3 <strong>(-0.050)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 6.319e-3 <strong>(0.027)</strong> </td>\n",
       "        <td> 6.54e-06 </td>\n",
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       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -0e-6 <strong>(-0.070)</strong> </td>\n",
       "        <td> 6.45e-06 </td>\n",
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       "        <td style=\"background-color:rgb(212,212,250);color:black\"> -14e-6 <strong>(-0.295)</strong> </td>\n",
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       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = -1.163e+05                 │              Nfcn = 132              │\n",
       "│ EDM = 3.75e-06 (Goal: 0.0002)    │            time = 0.6 sec            │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬───────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name  │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼───────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ s     │  3.10e3   │  0.09e3   │            │            │    0    │         │       │\n",
       "│ 1 │ b     │  4.09e3   │  0.09e3   │            │            │    0    │         │       │\n",
       "│ 2 │ mu    │  0.5014   │  0.0026   │            │            │    0    │    1    │       │\n",
       "│ 3 │ sigma │  0.0967   │  0.0025   │            │            │    0    │         │       │\n",
       "│ 4 │ slope │   0.500   │   0.018   │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬─────────────────────────────────────────────────────────────┐\n",
       "│       │           s           b          mu       sigma       slope │\n",
       "├───────┼─────────────────────────────────────────────────────────────┤\n",
       "│     s │    7.97e+03        -5e3  -11.397e-3  110.330e-3  -638.33e-3 │\n",
       "│     b │        -5e3    8.26e+03    6.319e-3 -113.135e-3   597.07e-3 │\n",
       "│    mu │  -11.397e-3    6.319e-3    6.54e-06       -0e-6       -9e-6 │\n",
       "│ sigma │  110.330e-3 -113.135e-3       -0e-6    6.45e-06      -14e-6 │\n",
       "│ slope │  -638.33e-3   597.07e-3       -9e-6      -14e-6    0.000343 │\n",
       "└───────┴─────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nll = ExtendedUnbinnedNLL(m1, model)\n",
    "mi1 = Minuit(nll, s=1000, b=1000, mu=0.5, sigma=0.1, slope=0.5)\n",
    "mi1.strategy = 0\n",
    "mi1.migrad()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can safely ignore the remark that the covariance matrix is approximate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = -4.043e+04 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 102 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 6.17e-05 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\"> time = 0.3 sec </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> s </td>\n",
       "        <td> 1.83e3 </td>\n",
       "        <td> 0.06e3 </td>\n",
       "        <td>  </td>\n",
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       "        <td> 0 </td>\n",
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       "        <th> 1 </th>\n",
       "        <td> b </td>\n",
       "        <td> 940 </td>\n",
       "        <td> 50 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
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       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> mu </td>\n",
       "        <td> 0.4928 </td>\n",
       "        <td> 0.0032 </td>\n",
       "        <td>  </td>\n",
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       "        <th> 3 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 0.0990 </td>\n",
       "        <td> 0.0028 </td>\n",
       "        <td>  </td>\n",
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       "        <th> 4 </th>\n",
       "        <td> slope </td>\n",
       "        <td> 0.50 </td>\n",
       "        <td> 0.04 </td>\n",
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       "        <th> s </th>\n",
       "        <th> b </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "        <th> slope </th>\n",
       "    </tr>\n",
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       "        <th> s </th>\n",
       "        <td> 3.2e+03 </td>\n",
       "        <td style=\"background-color:rgb(185,185,250);color:black\"> -1.4e3 <strong>(-0.499)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 3.476e-3 <strong>(0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,191,191);color:black\"> 60.973e-3 <strong>(0.391)</strong> </td>\n",
       "        <td style=\"background-color:rgb(205,205,250);color:black\"> -0.7695 <strong>(-0.342)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(185,185,250);color:black\"> -1.4e3 <strong>(-0.499)</strong> </td>\n",
       "        <td> 2.31e+03 </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.055e-3 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(190,190,250);color:black\"> -61.111e-3 <strong>(-0.461)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,190,190);color:black\"> 0.7645 <strong>(0.400)</strong> </td>\n",
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       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 3.476e-3 <strong>(0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -1.055e-3 <strong>(-0.007)</strong> </td>\n",
       "        <td> 9.91e-06 </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -1e-6 <strong>(-0.059)</strong> </td>\n",
       "        <td style=\"background-color:rgb(219,219,250);color:black\"> -29e-6 <strong>(-0.235)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(190,190,250);color:black\"> -61.111e-3 <strong>(-0.461)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -1e-6 <strong>(-0.059)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -31e-6 <strong>(-0.284)</strong> </td>\n",
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       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = -4.043e+04                 │              Nfcn = 102              │\n",
       "│ EDM = 6.17e-05 (Goal: 0.0002)    │            time = 0.3 sec            │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬───────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name  │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼───────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ s     │  1.83e3   │  0.06e3   │            │            │    0    │         │       │\n",
       "│ 1 │ b     │    940    │    50     │            │            │    0    │         │       │\n",
       "│ 2 │ mu    │  0.4928   │  0.0032   │            │            │    0    │    1    │       │\n",
       "│ 3 │ sigma │  0.0990   │  0.0028   │            │            │    0    │         │       │\n",
       "│ 4 │ slope │   0.50    │   0.04    │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬────────────────────────────────────────────────────────┐\n",
       "│       │          s          b         mu      sigma      slope │\n",
       "├───────┼────────────────────────────────────────────────────────┤\n",
       "│     s │    3.2e+03     -1.4e3   3.476e-3  60.973e-3    -0.7695 │\n",
       "│     b │     -1.4e3   2.31e+03  -1.055e-3 -61.111e-3     0.7645 │\n",
       "│    mu │   3.476e-3  -1.055e-3   9.91e-06      -1e-6     -29e-6 │\n",
       "│ sigma │  60.973e-3 -61.111e-3      -1e-6   7.61e-06     -31e-6 │\n",
       "│ slope │    -0.7695     0.7645     -29e-6     -31e-6    0.00158 │\n",
       "└───────┴────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nll = ExtendedUnbinnedNLL(m2, model)\n",
    "mi2 = Minuit(nll, s=1000, b=1000, mu=0.5, sigma=0.1, slope=0.5)\n",
    "mi2.strategy = 0\n",
    "mi2.migrad()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The class `ExtendedUnbinnedNLL` computes the equivalent of $-2 \\ln L$. Thus, to compute the $Q$ statistic, we therefore can add the minimum values of the two cost functions for $H_1$ and subtract them from $H_0$. The degrees of freedom are obtained by subtracting the number parameters for $H_0$ from $H_1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.16428719440676362)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# difference in number of parameters for H1 and H0\n",
    "ndof = (mi1.nfit + mi2.nfit) - mi0.nfit\n",
    "# test statistic, which is asymptotically chi-square distributed\n",
    "q = mi0.fval - (mi1.fval + mi2.fval)\n",
    "pvalue = chi2(ndof).sf(q)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With a chance probability of 16 % we won't reject the null. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try this again for a toy dataset where the factorization requirement is not fulfilled. We artificially make the mean of the signal PDF in $m$ a function of the $t$ variable. This breaks factorization, because the parameter $\\mu$ is now a function of $t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5hib0WrITAFC8PBXhoTxEdxWmvRF5mF6vx+rVqwFYX+jMHH4i/6NW6VG0bds2N4+IiALdtGnTpEqY7vTUU0+hX79+Ln8dBj9EXoA5/ESBx1qlR9GCBQvMUuLq6+uh0+mg0+lQX1/vjmESUYBZvXo1NmzY4OlhuAyDHyInkh+k7Nu3z67y1Onp6SguLpauKy10JiL/YavSIwCUlZUhODjYq4KdpqYmbNy4ERs3bkRTU5Onh0NEThYVFYXo6GhPD8NlGPwQOUlubi569eolXU9LS0OXLl3salCqJYefiPyDr1ZwNJlM+Omnn/DTTz/BZDJ5ejhEfqeq5qJbXmfLli3o06cPWrdujZiYGKSkpKC+vr5Z2tu5c+cwceJEREREID4+HqtWrcKwYcMwd+5caZsuXbpgxYoV+NOf/oS2bduic+fOzfqkLViwAN27d0d4eDi6deuGv/zlL2hsbHTLe5Vj8EPkBGp5++Xl5cjMzLQrACKiwNDSCo4REREQBAGCIDilkAERec7WoiuzwCkv7sU7X5S69PUqKytx//33409/+hO+//577NmzB+np6YppuPPnz8f+/fvxwQcfYNeuXSgoKMBXX33VbLu//e1vuPnmm/H111/j4YcfxkMPPYRjx45J97dt2xYbNmxAcXExVq9ejXXr1mHVqlUufZ9KGPwQtZC1vH3xtrlz59qVAkdE/m/IkCFISEhoVuhEJFZ61EJtLVBLUnGJyD0qay5g6QdHpesmAXgi9ztU1lxw3WtWVqKpqQnp6eno0qUL+vTpg4cffliqDik6d+4c3njjDbzwwgsYMWIEevfujfXr1yvuS9LS0vDwww/j2muvxYIFC9C+fXvk5+dL9y9evBi33norunTpgrvuuguPPvoo3n33XZe9RzUMfohayFbeviAIOHHiBAoKCtw4KiLydloqPT733HNmt9sTzDgjFZeIXK/kdD1MFudPjYKA46fPu+w1b7zxRowYMQJ9+vTBPffcg3Xr1uH3339vtt2///1vNDY24pZbbpFui4qKQo8ePZpt27dvX+myTqeDwWDAyZMnpdveeecdJCcnw2AwoE2bNli8eDFKS107w6WEwQ9RC2nN2/fV/H4ich1blR7HjBkj3ZadnY3rr79eum4tmGEqLpHv6No+AkEWE8B6nQ5d2oe77DX1ej127dqFjz/+GL169cKaNWvQo0cPlJSUOPycls2PdTqdtC6wsLAQEydORFpaGrZv346vv/4aTz75JBoaGlr0PhzB4IeohbTm7bc0v58lbon8k1qlRwBmMzfPPvssKioqzB4rBjPyfkC1tbXIyMhgKi6Rj4iPao1lf7xBuh6kA1ak90Z8VGuXvq5Op0NycjKWLVuGr7/+GqGhoXjvvffMtunWrRtCQkLwxRdfSLfV1NTgxx9/tOu1Dhw4gKuvvhpPPvkkbr75Zlx33XX49ddfnfI+7MXgh6iFtOTtJyYmYsiQIdJtWlNXGPAQBQbLSo/btm2z2vxUJAYzCxYskG47ePCgzccwFZfIu2QMuLK+b/f823HvwM4ufb1Dhw5hxYoV+PLLL1FaWorc3FycOnXKbHYZuFykYOrUqXjssceQn5+Po0ePYvr06QgKClI97lFy3XXXobS0FJs2bcIvv/yCl156qVmg5S4MfohaSEvefk5OjnRwwzx8IrJGS/NTOUEQzNYdVldXa3qco6m4oaGhWLp0KZYuXYrQ0FCHnoOI1BmiWrn8NSIjI7Fv3z6kpaWhe/fuWLx4Mf72t79h1KhRzbZ98cUXkZSUhDFjxiAlJQXJycm4/vrr0aqV9nH+8Y9/xLx58zBr1iz069cPBw4cwF/+8hdnviXNdILWvasXqa2tRVRUFGpqahAZGenp4RABuBzUPPLII2ZnahMTE5GTkyM1KhXz8C3/7cQg6c0338TEiRMBAHV1dQAgVV6prq5GXFycdB9L25IncP+rriWfTX19vfS/npeXh7S0NIfHsXz5cixZssTmdvn5+Rg2bJjDr0NEwMWLF1FSUoKuXbvaFQxYOt/QhF5LdgIAipenIjw02FlDdLr6+np06tQJf/vb3zB9+nS3va61z9qe/a9dMz/Z2dkYOHAg2rZti9jYWIwbN86sfjcADBs2TErTEX8efPBBs21KS0sxevRohIeHIzY2Fo899hi7RJPPU8vbFwMfLSWx5akrRBSYqqqqWvR4W4GPUiouEZGar7/+Gm+//TZ++eUXfPXVV9JJ2rFjx3p4ZI6xK6zcu3cvsrKyMHDgQDQ1NeGJJ57AyJEjUVxcbHYWesaMGVi+fLl0PTz8SrUKo9GI0aNHw2Aw4MCBA6isrMSUKVMQEhKCFStWOOEtEXmOZd6+/LqWkthlZWVmZ2O5zocoMIgNSwFgz549LnsdpVRcezU1NUm5+nfffTeCg733DDWRrwgPDcbxlaM9PQxVL7zwAo4dO4bQ0FAMGDAABQUFaN++vaeH5RC79lg7duwwu75hwwbExsaiqKgIQ4cOlW4PDw+HwWBQfI5PPvkExcXF2L17N+Li4tCvXz88/fTTWLBgAZ566inmD5PfYklsItJCLKJSXl6ued2PVgkJCWapuI4wmUzSLLevnvklIu369++PoqIiTw/DaVpU8KCmpgYA0K5dO7Pb33rrLbRv3x69e/fGokWLcP78lSZNhYWF6NOnj7R2AQBSU1NRW1uLo0ePQsmlS5dQW1tr9kPka9xVEpuIfJu1Iiot8eSTT5ql4hIRBSKHgx+TyYS5c+ciOTkZvXv3lm6fMGEC3nzzTeTn52PRokX4v//7P0yaNEm6v6qqyizwASBdV8tzzs7ORlRUlPSTmJjo6LCJPMaRkthEFJjUmp926tRJuvz444/b9ZxvvPGGU8ZGROTLHA5+srKy8N1332HTpk1mt8+cOROpqano06cPJk6ciH/+859477338Msvvzg8yEWLFqGmpkb6OXHihMPPReQp9pbEJqLAplRERX7d3kptZWVl7O1D5CI+WDzZ5zjrM3Yo+Jk1axa2b9+O/Px8JCQkWN120KBBAICff/4ZAGAwGJr1IBCvq60TCgsLQ2RkpNkPkS9SO5ubkJCALVu2WE1H0doYlYj8h7UiKsnJyVZnk5WUlJSwcTKRE4WEhACA2RIPcg3xMxY/c0fZVfBAEATMnj0b7733Hvbs2YOuXbvafMzhw4cBXFnHkJSUhGeffRYnT55EbGwsAGDXrl2IjIw0a/xI5K/S09ORkpKCqKgoAJfP5o4cOVJxxkce4PTp00e6nJaWhoSEBKxevZr5+0QBSpxNzszM1PwYtZOMROQYvV6P6OhonDx5EsDlol/OXKtHl+OP8+fP4+TJk4iOjm5xhoxdwU9WVhY2btyIbdu2oW3bttIanaioKLRu3Rq//PILNm7ciLS0NMTExODbb7/FvHnzMHToUPTt2xcAMHLkSPTq1QuTJ0/G888/j6qqKixevBhZWVkICwtr0Zsh8hXWzuaKxKapot9++83s/vLycmRmZtqcMSIi/yXOJs+ePRsVFRWq2+l0OiQkJCA5OdmNoyMKDOJJBTEAIteIjo52ygkcnWBHAp1aJLt+/XpMmzYNJ06cwKRJk/Ddd9+hvr4eiYmJuPvuu7F48WKzVLVff/0VDz30EPbs2YOIiAhMnToVK1eu1NwrgB3GyVvJu7TX1dWZ9b+yZ7vc3FxkZmbazG8VD2hKSkq4Vojcgvtfda74bCz3FQAU9x3iaysRv7u3bNmC1NRU6fHV1dVSwSFr+ytLgiCgsbERwOX0E57lJrrMaDRK/xvkXCEhIVaPc+zZ/9qd9mZNYmIi9u7da/N5rr76auTl5dnz0kQ+Qd6o0FFGoxFz5szR9DyCIODEiRMoKCiwe/EzEfketX2M/KAgPj7erF+YvLePM9b56HQ69uQjUqDX63ki0gewLTORlykoKEBZWZldj2FjVCL/5MgJlaKiIqmoirU1hUREgYjBD5GXcSSQYWNUIhJZW1MoL6Kyf/9+h56/qakJ27dvBwCMGTNGc8o6EZE3cLjPDxHZp76+XlOJWXsCGTZGJSKtcnNzzaqqOlooxWQy4ZtvvsE333wDk8nkrOEREbkFgx8iLzNkyBBNvTvYGJWIRGJ6nCAIioULxCIq5eXlio/Pzs5m7zAiCggMfoi8jNi7A1CvsAhoa4xKRKSliMqzzz6LLl26IDc3140jIyJyPwY/RF5I7N0hLlq2lJeXh5KSEgY+RGST1iIqZWVlyMzMZABERH6NwQ+Rl0pPT0dxcbF0XX5AotYYlYjIMgXO3iIqc+fOZQocEfktBj9EHmArP18kD3DYmZ2IHGFPERV57zAiIn/E4IeIiHzaU089JVVSFH969uwp3X/x4kVkZWUhJiYGbdq0QUZGBqqrq82eo7S0FKNHj0Z4eDhiY2Px2GOPoampyd1vxSW0FlGRY+8wIvJXLM5PREQ+74YbbsDu3bul6/LeM/PmzcNHH32EzZs3IyoqCrNmzUJ6errU58ZoNGL06NEwGAw4cOAAKisrMWXKFISEhGDFihVufy/OJhZRyczM1PwYa7NFISEhePTRR6XLRES+hDM/RD5Oa/8gIn8WHBwMg8Eg/bRv3x4AUFNTg9dffx0vvvgihg8fjgEDBmD9+vU4cOAADh48CAD45JNPUFxcjDfffBP9+vXDqFGj8PTTT2Pt2rVoaGjw5NtyGltFVERaeofpdDpEREQgIiLCrtkkIiJvwOCHiIh83k8//YSOHTuiW7dumDhxIkpLSwEARUVFaGxsREpKirRtz5490blzZxQWFgIACgsL0adPH8TFxUnbpKamora2FkePHlV9zUuXLqG2ttbsx5ulp6fj+++/t7qNIAhYuXIlC6oQkd9i8EPkJvLqSfv27WM1JSInGTRoEDZs2IAdO3bg5ZdfRklJCYYMGYJz586hqqoKoaGhiI6ONntMXFwcqqqqAABVVVVmgY94v3ifmuzsbERFRUk/iYmJzn1jLiAPatRS28aOHWv1OZqamvDRRx/ho48+8pt1UUQUOBj8EGlgLbVMS9pZbm4uevXqJV1PS0tjQ0EiJxk1ahTuuece9O3bF6mpqcjLy8PZs2fx7rvvuvR1Fy1ahJqaGunnxIkTLn09ZysqKpIu27MvMplM+PLLL/Hll1/CZDK5YmhERC7D4IfIxXJzc5GZmYny8nKz28vLy9lQkMgFoqOj0b17d/z8888wGAxoaGjA2bNnzbaprq6GwWAAABgMhmbV38Tr4jZKwsLCEBkZafbjS1hKn4gCEYMfIgdoLTJgNBoxZ84cCILQ7D7xNq0NBbX2BiIKdHV1dfjll18QHx+PAQMGICQkBJ9++ql0/7Fjx1BaWoqkpCQAQFJSEo4cOYKTJ09K2+zatQuRkZFmM7ZEROT7GPwQuUh9fT2Cg4NRVlamuo2thoIMeIhse/TRR7F3714cP34cBw4cwN133w29Xo/7778fUVFRmD59OubPn4/8/HwUFRXhgQceQFJSEgYPHgwAGDlyJHr16oXJkyfjm2++wc6dO7F48WJkZWUhLCzMw+/OudT2KVyTSESBgsEPkRdgQ0Eix5WVleH+++9Hjx49MH78eMTExODgwYPo0KEDAGDVqlUYM2YMMjIyMHToUBgMBrN0U71ej+3bt0Ov1yMpKQmTJk3ClClTsHz5ck+9JbcbMGCAdJlrEonIn7HJKZEXsNZQkIis27Rpk9X7W7VqhbVr12Lt2rWq21x99dXIy8tz9tC8WkREBLZu3YrMzMxmJ2DENYlbtmxBenq6h0ZIROR8nPkhcgO1RoBaGgoqYWNTImopZ65JJCLyFQx+iNzEMgASr+fk5LSooSBz9YnIEQUFBQ6tSQwJCcGcOXMwZ84chISEuHqYREROxeCHyA3efPNNdOzY0ey2hIQEp6SUMFefiByhda2h5XY6nQ7R0dGIjo5WndUmIvJWDH6I3GDs2LEoLi6Wrufl5aGkpMQpufRqufoMgIjIGq1rDbkmkYj8CYMfIg2spZZpTTuTp7YNHTrUaalulpirT0RaDBkyBAkJCXavSTQajfjkk0/wySefcB9DRD6HwQ+RDbm5uWaNDtPS0syueyLtbP/+/Vbvt9U/iIhIr9dj9erVAOxbk2g0GlFYWIjCwkIGP0Tkcxj8EFmRm5uLzMxMlJeXm90uv66Wdvbee+9Jt1mbEXKkcltVVZWm7dg/iIisSU9Px5YtW5qtSRQboaampnpoZERErsHgh0iFtTKw1ogHDdOmTZNus5wtaimDwaBpO+bqE5Et6enpZmsSuV6QiPwZm5wSqbBVBtYWy5meioqKlg5JkpycbPV+nU6HhIQEu/sHEVFgkqe22dq/EBH5Ms78EKlwdsqYfAbJlXnyzuofRERERORvGPwQqXBlypitggXWWBZgsOSs/kFERERE/obBD5EKW2VgW0JrwQJLagUYRE8++aTT+gcRUWDSWr6fiMgXMfghUmGtDGxLde3a1e7HaCnA8MYbb7RkWEQUoCIiIiAIArZu3YqBAwdKtyuV7w8JCcFDDz2Ehx56CCEhIZ4YLhGRwxj8EFmhVgbWGmvrbNSaBmqhpQBDWVkZe/sQkUOslfbPzMyUAiCdTofY2FjExsa6ZGaciMiVGPwQ2WBZBhZQnwl68sknsWnTJqlvj9JjHC1EoLUAA3v7EJG9rM0si7fNnTuXKXBE5PMY/BBpIA9W3nrrLdWZoEWLFiEzM1NxtkitEIHW/HqtBRjY24eI7GVrZlkQBJw4cQIFBQUwGo3Ys2cP9uzZw2CIiHwOgx8iO40dO9ZmQ0DL2aK8vDzFQgSWlduU8utFWgowsLcPETnCnpllo9GIvXv3Yu/evQx+iMjnMPghcoCWhoDybYYOHdos1U1rfr38+WwVYHjuuefY24eI7MaZZSIKFAx+iDzA0fx6WwUYxo4d6/zBEpHfszWz3JJiLURE3sSu4Cc7OxsDBw5E27ZtERsbi3HjxuHYsWNm21y8eBFZWVmIiYlBmzZtkJGRgerqarNtSktLMXr0aISHhyM2NhaPPfYYmpqaWv5uiHyEPfn1lixT6pRS5IiI7GFtZrmlxVqIiLyJXcHP3r17kZWVhYMHD2LXrl1obGzEyJEjUV9fL20zb948fPjhh9i8eTP27t2LiooKs3UORqMRo0ePRkNDAw4cOIA33ngDGzZswJIlS5z3roi8XEsrt8kPQEaOHAlBEKQZI7HSnPz/kojIFrWZZbViLUREvijYno137Nhhdn3Dhg2IjY1FUVERhg4dipqaGrz++uvYuHEjhg8fDgBYv349rr/+ehw8eBCDBw/GJ598guLiYuzevRtxcXHo168fnn76aSxYsABPPfUUQkNDnffuiLwU8+uJyBulp6cjJSUFUVFRAC4Xaxk5ciRnfIjIb7RozU9NTQ0AoF27dgCAoqIiNDY2IiUlRdqmZ8+e6Ny5MwoLCwEAhYWF6NOnD+Li4qRtUlNTUVtbi6NHjyq+zqVLl1BbW2v2Q+TLmF9PRN7KVrEWIiJf5nDwYzKZMHfuXCQnJ6N3794AgKqqKoSGhiI6Otps27i4OFRVVUnbyAMf8X7xPiXZ2dmIioqSfhITEx0dNpFDIiIipNSyiIgIzfepYX49Efmq4OBg/PnPf8af//xnBAfblUBCRORxDgc/WVlZ+O6777Bp0yZnjkfRokWLUFNTI/2cOHHC5a9J5GrMryciXxQUFIROnTqhU6dOCApi0Vgi8i0OnbKZNWsWtm/fjn379iEhIUG63WAwoKGhAWfPnjWb/amurobBYJC2+fzzz82eT6wGJ25jKSwsDGFhYY4MlcglxNmelmJ+PREREZH72HXKRhAEzJo1C++99x4+++wzdO3a1ez+AQMGICQkBJ9++ql027Fjx1BaWoqkpCQAQFJSEo4cOYKTJ09K2+zatQuRkZFmne6JPK2+vr5FldO0psMxv56IvImtfZfRaMT+/fuxf//+Zr3IiIi8nV0zP1lZWdi4cSO2bduGtm3bSmt0oqKi0Lp1a0RFRWH69OmYP38+2rVrh8jISMyePRtJSUkYPHgwgMtleXv16oXJkyfj+eefR1VVFRYvXoysrCzO7hAREXk5o9GI3bt3AwAGDhzIEzZE5FPsmvl5+eWXUVNTg2HDhiE+Pl76eeedd6RtVq1ahTFjxiAjIwNDhw6FwWAwa8Ko1+uxfft26PV6JCUlYdKkSZgyZQqWL1/uvHdFFKDkZ2H37dvHs7JEREREMnbN/GhZ49CqVSusXbsWa9euVd3m6quvRl5enj0vTUQySmuOcnNz8cgjj0jX09LSkJCQgNWrV7N4AhERERFa2OeHiLxDbm4uMjMzUV5ebnZ7eXk5MjMzzWZfiYiIiAIVgx8iH2c0GjFnzhzFmVnxtrlz5zIFjoiIiAIegx8iH1dQUICysjLV+wVBwIkTJ/DJJ5+4cVRERERE3ofBD5GPq6ys1LSdWJ2RiIiIKFAx+CFS4a7KaVr7AamJj4/XtJ1aE2Eif7Ny5UrodDrMnTtXuu3ixYvIyspCTEwM2rRpg4yMDKnBtqi0tBSjR49GeHg4YmNj8dhjj6GpqcnNo/c+lj3PgoODMXXqVEydOhXBwQ71Sici8hgGP0QKcnNzzZrupqWloUuXLl5ZOGDIkCFISEiATqezul1ycrKbRkTkOV988QX+53/+B3379jW7fd68efjwww+xefNm7N27FxUVFWZVEI1GI0aPHo2GhgYcOHAAb7zxBjZs2IAlS5a4+y14vaCgIHTp0gVdunRBUBAPI4jIt3CvRWTB1yqn6fV6rF69GgCaBUDy62xESP6urq4OEydOxLp163DVVVdJt9fU1OD111/Hiy++iOHDh2PAgAFYv349Dhw4gIMHDwIAPvnkExQXF+PNN99Ev379MGrUKDz99NNYu3YtGhoaPPWWiIjIyRj8EMn4auW09PR0bNmyBR07djS7vVOnTh4aEZH7ZWVlYfTo0UhJSTG7vaioCI2NjWa39+zZE507d0ZhYSEAoLCwEH369EFcXJy0TWpqKmpra3H06FHF17t06RJqa2vNfgKB0WjE559/js8//9zr9oVERLYw+CGS0Vo5raCgwI2j0iY9PR3FxcXS9by8PLODNsu8fSJ/smnTJnz11VfIzs5udl9VVRVCQ0MRHR1tdntcXJxUCKSqqsos8BHvF+9Tkp2djaioKOknMTHRCe/E+1iuf2xoaMDHH3+Mjz/+mMEPEfkcBj9EMlorp2ndzhHnG5rQZeFH6LLwI5xvsG+xtTy1bejQoUx1o4Bw4sQJzJkzB2+99RZatWrlttddtGgRampqpJ8TJ0647bXdRWn943XXXWd2ooWIyJcw+CGS0Vo5Tet2niY/K7t//34PjoTIdYqKinDy5EncdNNNCA4ORnBwMPbu3YuXXnoJwcHBiIuLQ0NDA86ePWv2uOrqaqkKosFgaFb9TbyuVikxLCwMkZGRZj/+RG39Y0VFBd59910GQETkkxj8EMnYqpym0+mQmJiIIUOGuHlk9tu2bZvZGVt5ZSs5psORrxsxYgSOHDmCw4cPSz8333wzJk6cKF0OCQnBp59+Kj3m2LFjKC0tRVJSEgAgKSkJR44cwcmTJ6Vtdu3ahcjISLP/o0ChZf3jjh07mPZGRD6HwQ+RjJbKaTk5OS1OJ2tJaptWkyZNanbGVrRt2zaXvCaRJ7Rt2xa9e/c2+4mIiEBMTAx69+6NqKgoTJ8+HfPnz0d+fj6KiorwwAMPICkpCYMHDwYAjBw5Er169cLkyZPxzTffYOfOnVi8eDGysrIQFhbm4XfofrbWPwJAbW0t/vWvf7lpREREzsHgh8iCWuW0hIQEbNmyRXUGxdsonbEVLViwgGdsKaCsWrUKY8aMQUZGBoYOHQqDwWBWtl6v12P79u3Q6/VISkrCpEmTMGXKFCxfvtyDo/Ycresa1YpBEBF5K7ZmJlKQnp6OlJQUREVFAbhcOW3kyJF+U0CgrKwMBQUFGDZsmKeHQuQSe/bsMbveqlUrrF27FmvXrlV9zNVXX428vDwXj8w3aF3XqLYeiojIW3Hmh0hGvv7l4sWL0u3+WDnNlRXriMi3aVn/aDAYeAKFiHwOgx8iPxIREYH8/HxN28bGxrp4NETkq7Ssf1y7di1CQkLcPjYiopZg8EPkZ2ydsRVNmzbNbM0DEZGcv6x/JCKSY/BD5GesnbGVKy8vR2ZmZrPKbyx9TUSi9PR0s34+eXl5+Pnnn9GtWzccPnyYhVOIyOcw+CHyYlU1F21vpEA8Y2tt0bJYDe7xxx+Xbtu3bx8PZojIjHy949ChQwFcLpe/bds27i+IyOcw+CHyMluLrvTWSHlxL975otSh50lPT8err75qdRtBEMx6AaWlpQVkQ0ciIiIKDAx+iDxMPrtTWXMBSz84Kl03CcATud+hsuaCQ88t71avVUVFhUOvRUT+r76+Hm3atPH0MIiIHMbgh/yWI2tX5CkcRUVFaGpqgiAIiIiIcOrY1GZ3Sk7Xw2TRm9QoCDh++rxDr+NIDw55c1SmtBC5x/mGJnRZ+BG6LPwI5xuaPD0cMxERERAEwSX7QiIid2PwQ/Qfubm5ZilfaWlp6NKli9Mrolmb3enaPgJBFjUK9DodurQPd+i1kpOTWzJU7N+/v0WPJyIiIvImDH4oIFnOCuXm5iIzM9Ns/QtwpSKaMwMga7M78VGtseyPN0i3B+mAFem9ER/V2qHXki9UtlX6WklVVZVDr0tE/sloNMJkMuHIkSMoKSnh7DAR+RwGPxTwamtrkZGRYZbuJRJvmzt3rtO+5NVmd+Iiw9Bl4Uf4y7Yrs0K759+Oewd2dsrrOpICd/LkSR7cEBGAK7PjRqMRW7duxRtvvIHrrruO/cKIyKcw+KGAd/DgQav3C4KAEydOoKCgwCmvpza7Y4hq1Wxb8TZnrAcoKiqSLn/44YeaGqEuXLjQJal/RKTOG9f/qM2OV1RUOH12nIjIlRj8UMCrrq7WtF1lZaXTXjNjQIJ02ZmzO9bIU+DuuOMOTY1QAdek/hGRuupax/p7uYrRaMScOXPcNjtORORKDH4o4MXFxWnazlrD0JZQmvFxFmtVmsRGqB07drT6HDy4IXI9eQXIu9Z4V6GRgoIClJWVqd7v7NlxIiJXYvBDfkt+oL5v3z7VA/fBgwdbfR6dTofExEQMGTLEqePzBunp6SguLra5HQ9uiFxHqQKkN9E66+3M2XEiIldh8EN+yZ6y1dYqoonXc3JyzLbzJ/a8Lx7cEDmfUgVIb6J11ttVs+NERM7E4If8jpay1fJZIHkvG8uKaAkJCdiyZQvS09NdO2gfwYMbIudTqgApqqrx/PqfIUOGWC2Q4s+z40Tkfxj8kF/RsjB35syZuP7666Xb5YHNSy+9JF3Oy8tDSUmJXwY+ln2ORDy4IXI/ywqQ8v/ClBf34p0vSt0/KBm9Xq9aICUQZseJyL8w+CG/omVh7m+//YaKigrF+++55x7p8tChQx3+MvfGUrXWih/I8eCGyP3kFSDl0Y9JAJ7I/Q6VNRfcPygZtQIpnTp14uw4EfkUBj/kV5y5JmXbtm1Oey57ffbft+P4ytEIDw126+u++eabzQ5umPpH5F6WE9dGQcDx0+c9MxgZsUCKXq9HRkYGpk6dih9//JH7BiLyKQx+yK84c03KggUL7C7tLM749FqyU/U+tdkgealba6kurlwDMHbsWLPqb/6c+kfkrSzX/+h1OnRpH+6ZwVjQ6/UICgpCnz590LVrV84GE5HPYfBDfsXWwlx7lJWVua20s1KpW3mqi9bAyBGW6XDyg5mWpP4RkWOeSLuyJjFIB6xI7434qNYeHBERkf9g8EN+xdrCXEe4qrRzeGgwjq8cLaW2KZW6NQoCjlWdQ5eFH+Ev28wDowVbj3jVeiIicp5x/a+knu6efzvuHdjZg6Npzmg04v3338edd97JkyNE5HPsDn727duHu+66Cx07doROp8P7779vdv+0adOkKlLiz5133mm2zZkzZzBx4kRERkYiOjoa06dPR11dXYveCJFIbWFuQkICYmJi7AqK3FXaWanUrV6nQ+d23pHqQkSeYYhq5ekhmImIiIDRaMTXX3+NQYMGMfghIp9jd/BTX1+PG2+8EWvXrlXd5s4770RlZaX08/bbb5vdP3HiRBw9ehS7du3C9u3bsW/fPsycOdP+0ROpEBfmivLy8nD8+HG8+uqrmp8jISHBbaWdLUvdiqkurjrwka9l2rdvn+raJrWS2ETkXJazwURE5Bp2Bz+jRo3CM888g7vvvlt1m7CwMBgMBunnqquuku77/vvvsWPHDrz22msYNGgQbrvtNqxZswabNm1SLT9M5AiltSvirFCnTp1UHyce7K9evdqtZzXlpW6tpbqoNUPUKjc3F7169ZKup6WloUuXLsjNzW3ZExNRQDCZTPjxxx/x448/wmQyeXo4RER2ccmanz179iA2NhY9evTAQw89hN9++026r7CwENHR0bj55pul21JSUhAUFIRDhw4pPt+lS5dQW1tr9kPkKMtZoZiYGLP7vaG0s7UZnw9nJzv8vLm5ucjMzER5ebnZ7eXl5cjMzGQAREQ2NTU14e2338bbb7+NpiauOyQi3+L04OfOO+/EP//5T3z66ad47rnnsHfvXowaNUpKq6mqqkJsbKzZY4KDg9GuXTtUVVUpPmd2djaioqKkn8TERGcPm/ycZfqWfEbnyJEj0mVXlHYuOV2nWv7aEXGRzQMjLU1VjUYj5syZA8GyiQgg3TZ37ly7y3sTERER+QqnJxbfd9990uU+ffqgb9++uOaaa7Bnzx6MGDHCoedctGgR5s+fL12vra1lAERO4+rSznet2e/U53NUQUEBysrKVO8XBAEnTpzAV199JQVDXOdD5H7i+h8iInI+l5e67tatG9q3b4+ff/4ZAGAwGHDy5EmzbZqamnDmzBkYDAbF5wgLC0NkZKTZD5GvsCxhDbi2UakarWW7XVXem4iIiMjTXB78lJWV4bfffpNKBiclJeHs2bMoKiqStvnss89gMpkwaNAgVw+HyKXkzUitcXajUi20lu12V3lvIiIiInezO+2trq5OmsUBgJKSEhw+fBjt2rVDu3btsGzZMmRkZMBgMOCXX37B448/jmuvvRapqakAgOuvvx533nknZsyYgVdeeQWNjY2YNWsW7rvvvmZ9WYi80fmGJmn9TvHyy3/X4nWtldhMAvBE7ncY2r1Dizq3V9VcRLcObTRtO2TIECQkJKC8vFxx3Y9Op2tW3tuyJPbIkSPZ14OIiIh8lt0zP19++SX69++P/v37AwDmz5+P/v37Y8mSJdDr9fj222/xxz/+Ed27d8f06dMxYMAAFBQUICwsTHqOt956Cz179sSIESOQlpaG2267za7+K0RaREREQBAECIKAiIgIt7ymUoqbWkBkFAQcqzpntVCB0kzS+19fKQlvzwySXq/H6tWrAaBZo1fxek5OjhTcsCQ2EdnSpk0b9gEjIp9i98zPsGHDFM8ai3butF3Rql27dti4caO9L+109fX1aNPm8lnzuro6tx0gk+eJgRHg3EX9QbrmAdD6aTdj6vovm22r1+nQuV246nNV1lzA0g+ONrv92bzvpcviDNLALu00jU/sc/TII4+YlbtOSEhATk6OVOVOLIlt+b8ulsT2dClwIvIcvV6PUaNGoaGhAcuXL/f0cIiI7OLyNT9E3sAyfUt+3ZkzRE+kXd/sths6RTW7LUgHrEjvbdbPx7LDe8npesWZJMtzD0ZBQOmZ85rHaNnnyLK8N0tik695+eWX0bdvX6kgTlJSEj7++GPp/osXLyIrKwsxMTFo06YNMjIyUF1dbfYcpaWlGD16NMLDwxEbG4vHHnuMPWxU6PV63HLLLejbt6/U5NRyv0pE5K0Y/JDfc2f61rj+2tat7Z5/O+4d2NnqNl3bRzRLmQtC8zQ6WzNISqyV99ZaErugoMCu1yRylYSEBKxcuRJFRUX48ssvMXz4cIwdOxZHj16eOZ03bx4+/PBDbN68GXv37kVFRYXZzKXRaMTo0aPR0NCAAwcO4I033sCGDRuwZMkST70lr8e0WCLyVQx+yK+J6VvyFC/gSvqWp76o5TM+auKjWmPZH2+QrgfpgOyMPs1us5xBamkZbZbEJl9z1113IS0tDddddx26d++OZ599Fm3atMHBgwdRU1OD119/HS+++CKGDx+OAQMGYP369Thw4AAOHjwIAPjkk09QXFyMN998E/369cOoUaPw9NNPY+3atWhoaPDwu/M+W7Zs8cr9KhGRFgx+yK/U19dDp9NBp9OhtrbWK9K35AUK7JUxIEG6LM4WKd0mL4zQ0jLaWktdT5gwgQudyesYjUZs2rQJ9fX1SEpKQlFRERobG5GSkiJt07NnT3Tu3BmFhYUAgMLCQvTp0wdxcXHSNqmpqaitrZVmj+gyo9GIuXPneny/SkTkKAY/5Lf279/vFelbK2QFCkSOzM4ozRYZolo1K4wgFkGorLlg92sAV0piW1aEE4klsYm8yZEjR9CmTRuEhYXhwQcfxHvvvYdevXqhqqoKoaGhiI6ONts+Li4OVVVVAICqqiqzwEe8X7xPzaVLl1BbW2v242znG5qsVoR0t4KCgmYzPnJMiyUib8fgh/yWtYMWOVenbykVLbCnQIEtSoURjIKA46cdew0tJbGfe+45h56byFV69OiBw4cP49ChQ3jooYcwdepUs8IerpCdnY2oqCjpJzEx0aWv5w2YFktEvi6ggx9rFcDI9xkMBk3baU3zUmI5g1Nd23xGR6nPj70FCqxRKoyg1+nQpb3jryGWxLZsPJyQkIAtW7Zg7NixDj83kSuEhobi2muvxYABA5CdnY0bb7wRq1evhsFgQENDA86ePWu2fXV1tbSPMBgMzaq/idet7UcWLVqEmpoa6efEiRPOfVM2eGJWSOv+siX7VSIiVwrY4IeVavxfcnKyzfStxMREDBkyxK7ntVxf80TuEen6XWv2N9teqfy1Ugqbo4UKlAojrEjvjfio1qqP0VLe21ZJbCJvZjKZcOnSJQwYMAAhISH49NNPpfuOHTuG0tJSJCUlAQCSkpJw5MgRnDx5Utpm165diIyMNPuesBQWFiaV1xZ//N2QIUPQqVMn1fsd3a8SEblLQAY/3loBjJxLS/pWTk6OWZlnW5TW17x/uMLsuqh4eSqOrxyNCYPUS1o7q1CBUhEEZ7BWEpvIWyxatAj79u3D8ePHceTIESxatAh79uzBxIkTERUVhenTp2P+/PnIz89HUVERHnjgASQlJWHw4MEAgJEjR6JXr16YPHkyvvnmG+zcuROLFy9GVlYWwsLCPPzuvIter8eLL76oeJ+j+1UiIncKuOCHDRz9m2Uq49ixY62mb2mdxRDTS5KyP1Ncw+MIZxQq6LVkZ7OUFy1ltFuKKaPkTU6ePIkpU6agR48eGDFiBL744gvs3LkTf/jDHwAAq1atwpgxY5CRkYGhQ4fCYDCYneTS6/XYvn079Ho9kpKSMGnSJEyZMgXLly/31FtS1NIy9s4ybtw4jB8/vtlMl737VSIiTwi44IcNHP2XWiojAKembymt4ZHT63QoXDQc4aHBze4TZ4PCQ4OdXqjAXZgySt7m9ddfx/Hjx3Hp0iWcPHkSu3fvlgIfAGjVqhXWrl2LM2fOoL6+Hrm5uc3W8lx99dXIy8vD+fPncerUKbzwwgsIDm7+P+xulrPD/1d43OPV3/R6PR555BFs3boVQUGXDyOYFktEviLggh+tFWhKSkpcPBJyJlupjNu3b5dua2n6lnwNT5AOGNevo9l1W+ttRK4oVOBqTBklch+l2WH5dTl3zgrp9XokJycjKSkJJpMJANNiich3BFzwo7UCjdZKYeR5WlIZFyxY4LTXG9f/SrCze/7tWJHex+y61vU2WgoVhIcG4/jK0dJskfy24uWpLX0rdmHKKJF7Kc0Oy6/LGyi3tLkxEVGgCLjgx1YDR1FycrKbRkT2qq+vh06ng06nQ319vaZURmv3t4Tl+hp719u4qlCBs8irwn311VdMGSVyI6XZYfl1eQPlljY3tofJZEJ5eTnOnj0Lo9FotWokEZG3CbjgR0sFMHE78g3+0kzPHYUKWoLNDYncS2l2WH7dU2sGm5qa8Nprr+G1115DU5Nn1h0RETkq4IIfQL2Bo7XeBeS92EzPnFIFOFFLmiKyuSGR+1nODlvj7WsGiYi8QUAGP4ByA8dvv/1Wus7yvb7jpptusnq/2HSvqanJKekZ1bVXFhb3WrITvZbstLq90rodZ6u90OTydUC2UkbZ3JDI9dQKHthTbIWIKJAFbPADmKe2/f777+jT58rCdZbv9R3y36OzmplakpebvWvNfoefx5mc1SBVK1c0jSUi7X79rXkBBJGn1wxarsUkIvJWAR38yE2aNElT+V7u4D3PWoNNyyp9zmi6p1Ru1tPUGqTaW+7W3jQ4tZRRNjckcr2rY5oXQBB5+5pBIiJvweDnP1i+1zcoNdiUXy8qKpIuO6vpnlK5WU9Ta5Baesb1i52VUkbZ3JDINeRps906tGlWAMFbWDspRUTkTRj82MDyvd5DrcFmRcWVXhfylCtnNd1Ta0b62X9fWXxcvDzVpWt6tI6pczv3LHZ2xedMRLbJCyB8ONs7WjIonZRi2jgReSsGPxqple9lGpx7aGmwCcAlQapaM1JnpJk4WgzBlWMiIt8QF+mZ/3e9Xo/bb78dt99+Oz744APFk1Ll5eXIyMjgdyMReZ2AC37kwQoA5Ofna3ocy/d6lq1GpqLMzEyXvL43NiO1NSZx/Y/auh571wcRkXeRnzwB4HAZe3vp9XoMGzYMQ4YMwbx582yelGIKHBF5k4ALfizZW76Xec2e4UjjzG3btrlgJMoLiz0dSIhjsqwA12XhR2aluN//usLsfvn2RET20HpS6uWXX+Z3JRF5jYAPfuwp32trsT25jiMzbwsWLHDpF667S03boqUq3Yq8783uV+sZooQpnkQEXJ7VOXnyJH744QdN2y9cuJBrgIjIawR88ANoK9+rZbE9uY6tGTolZWVlLV4DJKaMWTYyVSs1XVlzoUWv1xJaqtJZ3i+/bs/sVUREBARBcErTWCLSzh1Nk21pbGzEyy+/jIMHD2p+jFLrCCIiT2Dw8x/WyvdqXWy/Z88et0ztB+IZeGszdNY4ki6nhVqp6eOnXV9qWo1SBThLlvfLr3rD7BURtZy70nCvvvpqdOrUSdM+ma0jiMhbBFzwY23Njlr5Xq15zWPGjOHUvgupzdBZ46pCFWqlpru0d0+paSVKFeAsPZF2vXTZ8m5vmL0iIsd4Ig03KCgIL774IgBtJ6XYOoKIvEFABT+O9iKwZ/aAU/uuZTlDp8ayUIWzqZWajo9q7ZLX08pWD5Bx/a8Eji/c0xeWc5menr0iIvt5Mg133Lhxdp+UctWMPBGRFgET/Kit2dESrERHR2t+HXFqf86cOQGXmuYu8hk6edly+W3AlUIVruKN5a/llHqAVNdeSYfp3/kqu2avWOmQyDt5Og1X60kpEVtHEJEnBUTwo2XNjrU85ORk+7poC4KgKU2OtFNb5/Tmm29aLVThTMXLU1UXGXuiuagjC5/vWrNfumyIaqV59ood3Im8l9p6v/vXHXR5zx+R5UkpJa6ekSci0iIggh9ba3bEPOT9+/cr3q9lp+5OPAN/xdixY1ULVQQ6eU8fkeXZYaXZK8umqC2ZNSUi19Oy3s/VxAqQW7duBWC7dQQRkacERPCjNb/47NmzNsv3GgwGZw7NbjwD35xaoQpn83QjU3vJe/pooTR75cisaSBWIyTyNFvr/ZxJr9cjKSkJSUlJzfa3WlpHEBF5UkAEP1rzi7VsV1RUZHMbnU6HhIQEm9vZKxDOwHvbgbO3NTK1h62eP1rs/9e/NM2asnoTkfdQWu/nTHq9HiNHjsTIkSMVTzZZax1BRORpARH82GqQqZSHLD8Ir62tlW6XN3Wzttg+Oztbus0ZqWktXbfkT9zVYNMbG5naQyn1xd50mKoqbbOmrN5E5J08NWPtrhl5IiJ7BUTwY61BppY85AEDBkiX5Weu1BbbP/roo1i4cKF0W1paGoKDg1s0m6F13ZK/noH3xDonT1dQail5Tx+RvekwBoPzZk2JyD3k6/1cMWMtCALOnj0rpYoTEfkSbSWi/ICYh/zII4+YpY0lJCQgJyfH6nS8tbPaxcXFiIqKAnB5ar++vh7jx49X/ULYtm0bJkyYYPf4tZ5Z98cz8Lm5uXjkkUek62lpaUhISMDq1atdkkZxvqEJvZbsBHB5pkQeAHm6kaktYgU44PL7eOYj83U/Xdu3ke4Xt5FfFt+3KPm225CQkIDy8nLFv2kxxZPVm4g8S/zfr6y5gOSVn0m3izPWQ7t3cFofssbGRumE4qJFixAaGtpsG3GGnojI2wTEzI/InjxkLTMLCxYsMLuenJyMefPmWd3hL1iwwKFZC2euW/IlWtY5uTINTj57YlkK2pFS077GkVlTViMk8hxfn7EmInI1u4Offfv24a677kLHjh2h0+nw/vvvm90vCAKWLFmC+Ph4tG7dGikpKfjpp5/Mtjlz5gwmTpyIyMhIREdHY/r06airq2vRG9FKax6yWtlrubKyMrPt9u/fb7O/T1lZmUOpaY6sW/JF8gPl/Px8j69zGtf/SlqjNzYydbWqmot2VW9iNUIiz1Lq+ePtM9ZERO5kd/BTX1+PG2+8EWvXrlW8//nnn8dLL72EV155BYcOHUJERARSU1Nx8eKVRZcTJ07E0aNHsWvXLmzfvh379u3DzJkzHX8XLqA1fayqqkrxstbn1lrdrKXrlnyB5YHzXXfd5VXrnDzRyNTVbM1eiesFtMyaBkI1QiJvp9TzR615sSd4W0VPIgo8dgc/o0aNwjPPPIO777672X2CICAnJweLFy/G2LFj0bdvX/zzn/9ERUWFNEP0/fffY8eOHXjttdcwaNAg3HbbbVizZg02bdqEiormTRk9ITc3t1lKmxp53x+tPYBiY2MVb7f1peCP/RPk71npwFkLf1zn5C3kFe6szZqyGiGR91BqXkxERJc5dc1PSUkJqqqqkJKSIt0WFRWFQYMGobCwEABQWFiI6Oho3HzzzdI2KSkpCAoKwqFDhxSf99KlS6itrTX7cRXx7PXp06etbiemmSUnX6melZycbDU1TTRt2jSbZ8HVAiFP9U9wx9k6RxfH+ts6J2+jZb1AoFcjJPJW3jZjzTWBRORpTg1+xLSvuLg4s9vj4uKk+6qqqprNfAQHB6Ndu3aqaWPZ2dmIioqSfhITEx0eo7XF8dbOXsvJ08wiIyOl54uMjFRNTZNraRoQ+ydc1pJ1TucbmtBl4UfosvAjs4pn/qp4earDhRm0rBcI5GqERN7Mm/Z1XBNIRN7AJ6q9LVq0CDU1NdLPiRMnXPI6ts5ei9q3b6+aZiamplmbjWAaUMu5a51Tda1nGgQ6gzOq0WldLxAdHa3p+ThLR+R61v73nREMBQUF4eabb8bNN9+MoCDbhxFi5kBGRgbXBBKRxzm1Pq+45qW6utrsIKe6uhr9+vWTtjl58qTZ45qamnDmzBnVNTNhYWEICwtz5lAVaT0rvWrVKqtpZunp6QgLC8OYMWNUtxHTgPbt2yfdpqXCHF2mpT+To7YWXQmA71oTOL8T+fsW7Z5/O7p1aAPAet8OefqnEvYDIvIfwcHBGD16tO0N/8PaST5BEKDT6TB37lyMHTs2YDMZiMh9nDrz07VrVxgMBnz66afSbbW1tTh06BCSkpIAAElJSTh79iyKioqkbT777DOYTCYMGjTImcOxm9az0p06dVK8Xb4uRuvs1JQpU6TL8gP5QAmEtMx86XQ6s8/cleucKmsuYOkHR6XrJuFy2lfhouF+28sHaP6+7SU/YPHXaoTkvbKzszFw4EC0bdsWsbGxGDduHI4dO2a2zcWLF5GVlYWYmBi0adMGGRkZqK6uNtumtLQUo0ePRnh4OGJjY/HYY4+hqcl/0mKrajwzk21rrR/XBBKRO9kd/NTV1eHw4cM4fPgwgMtFDg4fPozS0lLp7M0zzzyDDz74AEeOHMGUKVPQsWNHjBs3DgBw/fXX484778SMGTPw+eefY//+/Zg1axbuu+++ZlXM3M1WLx0Ams9eW657UvP7778r3i4/sLdcFOrKpp5qXLFI1TL/W4n4u3j++eel25y9zqnXkp1SCkigNghUet8AUHrG/vdtOYPry9UIyTfs3bsXWVlZOHjwIHbt2oXGxkaMHDnSrDjLvHnz8OGHH2Lz5s3Yu3cvKioqzP4mjUYjRo8ejYaGBhw4cABvvPEGNmzYgCVLlnjiLTmNfEY35cW9ZtcdDYYEQUB9fT3q6+ttrpHNzc3F5MmTNT0v1wQSkTvYHfx8+eWX6N+/P/r37w8AmD9/Pvr37y99QTz++OOYPXs2Zs6ciYEDB6Kurg47duxAq1ZXKs689dZb6NmzJ0aMGIG0tDTcdtttePXVV530lhxnrZeO6LnnntN04D148GCnjcvTi0JdsUhVrSeMJfHAeezYsQ6/llbnG5owYV3zioOB0CBQqTEiAHRuZ//7ls/quqsaIQW2HTt2YNq0abjhhhtw4403YsOGDSgtLZX+FmtqavD666/jxRdfxPDhwzFgwACsX78eBw4cwMGDBwEAn3zyCYqLi/Hmm2+iX79+GDVqFJ5++mmsXbsWDQ0Nnnx7DlOayV6y7cp1sY+XvRobG/HCCy/ghRdeQGNjo+p24n5e7SSfJa4JJCJ3sDv4GTZsmDTrIP/ZsGEDgMtBw/Lly1FVVYWLFy9i9+7d6N69u9lztGvXDhs3bsS5c+dQU1OD//3f/0WbNm2c8oZaSq2XjkjrQbi1NCBHlJWVISMjAxs3bmzxc9nDFY0rtVbV2759u8cPnL2tQaCrWDZGFGktkyufCRQPJoHArkZInlNTUwPg8ncNcDkgb2xsNGvD0LNnT3Tu3NmsDUOfPn3MZu1TU1NRW1uLo0cdTwn1JKUZXflVeR8vZ9O6nwdaVrmTiMhePlHtzd2Ueuk0NTXZTDOTHwAWFRWhqakJW7dubRZIiV/IjliwYIGmlDNn9OVxVeNKrVX1goKCPH7gHEgNAuWNEe1hOTPIWR7yJJPJhLlz5yI5ORm9e/cGcLnFQmhoaLOqhJZtGJTaNIj3KXFnDzpHqM3oyrkqrVfrfl7ENYFE5C4MflTY20tHLTUMgFkglZubizNnzjg8rrKyMrNFofIg5+TJk05tROqqxpVa87rlBxzOXuekVNlMibc1CPQ2ttIXt23b5uYRUaDLysrCd999h02bNrn8tZzZg84VLGd0df/5kXNVWq/W/XxMTAzXBBKRWzH4cQJbqWHbt2+XbpOXBHY0Hc5di0Jd1bhSa163WunzllKrbObLPX3sZavXh5amqFrSWrTOVBI5w6xZs7B9+3bk5+cjIeHKTKbBYEBDQwPOnj1rtn11dbW0nzEYDM2qv4nX1fZF7upB1xLyGd1P//t2LB97JRhyZVqv1v38O++8w8CHiNyKwU8LaUkNW7BggVNfMzY21qnPp8ZVjSu1VNUDgH79+jl1JkukVtns2xM1TnuNQKAlrcVyppLIFQRBwKxZs/Dee+/hs88+Q9euXc3uHzBgAEJCQszaMBw7dgylpaVmbRiOHDli1odu165diIyMVK1KGRYWhsjISLMfb2aIamUWDLkyrdfWfl5c5zNs2DCXvD4RkRoGPy2kJTVM7f4333xTtWeQNdOmTbNZaMAZpam1NK50ZJGqtap6YrCzdetWlx1IqOXBP/H+dy55PX/lqplBIntlZWXhzTffxMaNG9G2bVtUVVWhqqoKFy5cXsgfFRWF6dOnY/78+cjPz0dRUREeeOABJCUlSZU5R44ciV69emHy5Mn45ptvsHPnTixevBhZWVluabLtCa5M67W1nwe4zoeIPIPBjwqta0zsPbCTByFXXXUVjhw5Il2PiYnR9BzySmuWQY6oT58+0mVHS1O7snGlWlU9d/SEUatspqEoUcCxlh6ndcaP5WvJ1V5++WXU1NRg2LBhiI+Pl37eeecdaZtVq1ZhzJgxyMjIwNChQ2EwGMz2iXq9Htu3b4der0dSUhImTZqEKVOmYPny5Z54S14tKCgIN954I2688UYEBakfRnhyP09EpEYnaKlD6WVqa2sRFRWFmpoaj6cZ7NmzB3fccYfN7fLz83HmzBk88sgjZmuDOnXqJF2vqKiQviTatWtntTCCTqdDu3btEBYWhoqKCpuvLwYr9nzh1NfXSyXI4+PjzQK9xMRE5OTktPjLS/xdAper6o0cOVIKpuSvX1dX59SGrucbmtBryU6r2+h1Ovxr4R1+WeZa/v6Ll6eqru2xtp3RaESXLl1QXl6umPap0+mQkJCAkpISnt31I960//U2vvDZyP+nv1w8Ajc/czkVUP7/rXX/oJW1/TwRkTPYs//lzE8Lac1rPn36tGJRBHngIv8ysNX0VRAE/Pbbb5oCH3F7oHlpamslseXbvfTSS9JlZzautFZVzxmpey3hqhKw/oJpLUS+Jzw0GMdXjrZZ0MSZIiMjpUyKUaNGcZ9ARB7F4KeFtBwA/u1vf8O8efOsFkUAzA/2T5065fSx2lOa2rJ09z333CNddkfjSrXS4Y40VXWUq0rAepuqGser3NmT1uKM3lNE5HmCIKChoQENDQ2ampgSEXkTBj9OYOsAsEOHDpqavR0+fFi6bNlsz5lsrVNyde8WWwfBtkqHuyoAemTEtdJlV5aA9QbyPkcpL+7FO1+UOvxcSk2BxZlBBjxEvqHkdJ3i+j6lkyONjY3Izs5GdnY2Ghsb3TlMIqIWY/DjJNYOALUWRTh79qyUGjBixAhXDdVsAbplallDQ4Nbe7dYFpbQUjrcMnVPia0+NkqmJF0tXXZlCVhPs+xzZBKAJ3K/Q2XNBauPszZDZG9TYCLyPPlJkLvW7Jcuv//1lXTqlp4csYYnR4jIExj8OJHaAaAjVbEiIyOxdetW6YvBmW666SYAyqllnTp18mjvFi2lw7Wm7rWEK0vAeppSnyO19U1KM0SOBJaA59dwEdEVSidBRCvyvje7XcvJEUdwn0BEnsDgxw20FkWw7JdjLZ0uJibGrqBIvu3Fixeh0+mQkZHRLLXs9OnTmp6vJb1brH3huat3jLjot3h5aouexxcp9TlSWt+kNkNkzxoh+e/WGeXXicg51Jo9A9B8cqQlvGFdJxEFJgY/btCSqlhK6XTHjx+XqsFpDYDkzVSdcXbN0d4ttr7w2DvG9Sz7HKmtb1KbISo90/wgSKkvluXv+rfffjN7jKvXcBGROrVmz0qcXfzFU+s6iYgABj9OZa0xakuavSml06k9n5K8vDx8++230vXXXntN61tqRm2WSgstX3iOzpKRfTIGJEiX1dY3qc0QdW5n+yDIVtEMwL41XETkXGrNni05u/iLs9Z1EhE5isGPG1kriuCM59u8ebN0WX7m7PfffzdLOVqyZIlDr2dv7xb5Ytba2lpNX3gAnN47Rq2KEeCZnhfeRm19k9LBkVEQENna+udk7eDGkrvWcBFRc/KTIGqcXfzFW9Z1ElHgYvDjZs6uimX5fKLk5GTp8qRJk6yegVcTExNjdl2cpUpNTVWs0GOtcs/+/fs1f+G1ZJZMpFbFyBoGQs3ZOjhSWv9j6+BGSUvXcBFRy6ilwCmdHAkKCkKvXr3Qq1cvBAXZdxjhrnWdRERqGPz4AGvpdFo42oQuNDRUutzSWaqqqipN24lfeC2ZJbNWxYhazlYZXEcOWriGi8iznki7Xrpsay1QcHAw7rnnHtxzzz0IDrbvRBHXdRKRp/H0tpuJgYyrnk9+OT8/H3fccYfDzy0PWByZpZLnbGudCZB/4Tk6S2atilGvJTsBAMXLUzm74yClMrhDu3eQ1gTYc9Ci0+mQkJDANVxEHiDOdgOXe6M989Hl/+3d829Htw5tXPKa4rrO8vJyq9+F9fX1MBqN7BlGRE7HmR8/1tK0AfkXkzyQUStVLb89Ozsb119/5UyirXVGzixkYE8Vo0DVkhQ/W2VwbRWtEDm6houIXMuVfc6sVT+VGzNmDEtfE5FLMPjxY85MG/jqq68AqJeqfvzxx81uf/bZZ1FRUdHseZSoHQQ7mu6nVMqZnMfyeMWyDK7Wgxt71nARkWtZOyFi2di4oaEBy5Ytw7Jly9DQ0GD3a2mtVsrS10TkCgx+/JjWM/BaVFZWqpYvLisrw1//+lfNRRUsF8i64iBYvlB/1vBrnfa8BEA286NWBtfWwU1L15ARkW+zXNephKWvicgVGPz4MfkZ+JaKjY3VXL7YFpPJJF12x0Hw3z/7udltSlXKqLnw0GAULhpuNnsm/wuwVgbX8uBGfvbWGZUOicj9nLnvjIyMRH5+vtVtWPqaiJyNwY+fE8/Ad+rUyaHHi2txAO1FC+zx+++/u/wgWKn4weETZ136mv7EWgGJ4X/bq9g/SST/3crLr1uyViadiDxL3jog5cW92Fxkf+sENSx9TUTuxuAnAFiegbfs3yNet9ZU9OTJky4Z24IFC1yezqC05ufRzd80K9FMylhAgihwKbUO+MsHxagXQpzy/Cx9TUTuxuAnQMjPwB85ckS6nJeXh+rqamzdutVqU1FXffGUlZW5PJ1B3r9CJJZorqy54NLX9gfOKiDR0n5VROR+SjO/JgGoNTmnIpyttanOrARKRAQw+AlISv1zbDUVdWbxBEuuTmcY11950b1liWZSJy8g8eFs9fQ1S1oDHrXy6UTkWUozv0E6IDLIOWt/rFWHZDl8InIFBj8ksdZUVGv5Yke4YlZJSx8byxLNpE1cpHN7gKiVT2d5WyLPU5r5fWbsDejXvQuuu+66ZtU7HaFWHZLl8InIFRj8BAhnpBypfUElJibisccea1ZUwVYPB1ekM1j2o1CjVqKZbBMDy+LlqdJtjlaAUiufzv4eRN5DPvO7e/7tmDC4CyZMmIAJEyYgONi+JslqbGUfEBE5C4OfANSSQEjtC+r5559vdvv3338vXfe2dAZrJZpJG8sKUPYWkDAajarl09nfg8g7RbYO1nSCyaHnjoyUvptGjRrFVDcicgkGPyTRGhSppcdZS5szGAxmz+HpdAZDlHNTtwKNUgUoewtIFBQUWC2fzv4eRERE5GzOma8mUiAGUwBQW1uLqKgoAJdnhUaOHOm2s3pimtb5hib0WrLTLa/pb8TPUHT4xNlmFaCMgoBjVeeQlP0ZAKB4earqeiuA/T2IfIX8//98QxP0MOKOkF/wzPPFeOrxOQgNDXX6a3ryO4OI/BtnfshuajNE1maOrM0KuYozO5GTOaUKUHqdDp3baS8gwf4eRL5na1EZjAjC7sbueLvueqc2PBWxCAoRuRKDH/IrLV2HQtooVYBakd7brnRC9vcg8i1X0l0v/88K0OHJbUeduv6HRVCIyNUY/JBbuKPBpa11KFrKX5N2lr1/Fmw9YldaIft7EPkWpYanYiDkDCyCQkTuwOCHWqS+vh46nQ46nQ719fUeHYvSFzMbmbqHUu8fW2mH9fX1yMjIgCAIXlcQg4iaU0p3BS7vdJ2RZswiKETkDgx+yG+orUNhI1PPsCftsKioSLrM/h5E3ulKuqt4lunK2SbL/3etPdfkWASFiNzB6cHPU089Jc0EiD89e/aU7r948SKysrIQExODNm3aICMjA9XV1c4eBrmJPP1g3759Hk1HUFuHwkamnmGr/LX8b+XgwYPSZXcVxCAi+2UMSIAeJgwL+eU/t1w+42QSgAVbj7Ro/Q+LoBCRO7hk5ueGG25AZWWl9POvf/1Lum/evHn48MMPsXnzZuzduxcVFRU8w+ujvKUij/wM46g+V9Kn2MjU89TSDi3/drgPIPIlOtQLIdC63kdrShyLoBCRO7gk+AkODobBYJB+2rdvDwCoqanB66+/jhdffBHDhw/HgAEDsH79ehw4cMDszC95P1+oyMNGpq4lLyDx8ZEqxW2U0g7V/nbEmeKdO68UTfCmNWVEdPn//peVd+Glx6YprP+5rKrmokOVN1kEhYjcwSXBz08//YSOHTuiW7dumDhxIkpLL+/0ioqK0NjYiJSUFGnbnj17onPnzigsLHTFUMgFWJGH5Cyr7ImU0g75t0PkHyzTjOWhyoi/7cWSbcqVN22tBUpPT8eWLVvQsWNHs9tZBIWInMXpwc+gQYOwYcMG7NixAy+//DJKSkowZMgQnDt3DlVVVQgNDUV0dLTZY+Li4lBVpXzmGAAuXbqE2tpasx/yHFbkITnl8rfAC/fc2CztUOvfTnBwMHQ6ndn/uqfXlJH32rdvH+666y507NgROp0O77//vtn9giBgyZIliI+PR+vWrZGSkoKffvrJbJszZ85g4sSJiIyMRHR0NKZPn466ujo3vgvfIy93L49+BMhLIVymlAKrlg6Xnp6OX3/9Ffn5+di4cSPy8/NZBIWInMbpwc+oUaNwzz33oG/fvkhNTUVeXh7Onj2Ld9991+HnzM7ORlRUlPSTmJjoxBGTvby5Ik/thSb28nEz5fK3QL/E6Ga32fs3MWDAAOkyu7yTmvr6etx4441Yu3at4v3PP/88XnrpJbzyyis4dOgQIiIikJqaiosXrxx8T5w4EUePHsWuXbuwfft27Nu3DzNnznTXW/ApDQ0N+Otf/4q1q1fhx+V/wMYZg6AwmWtGTIHVmg6n1+sxbNgw3H///bjpppukEyIff/wxT4IQUYu4vNR1dHQ0unfvjp9//hkGgwENDQ04e/as2TbV1dXN+nzILVq0CDU1NdLPiRMnXDxqssaTFXmUUiYcyS0n57FMfxEprbmy92/CMljypjVl5D1GjRqFZ555BnfffXez+wRBQE5ODhYvXoyxY8eib9+++Oc//4mKigpphuj777/Hjh078Nprr2HQoEG47bbbsGbNGmzatAkVFRVufje+4fz58zh//vJMjtIJEPlVMQUWgNVG1Eq8pbAOEfkPlwc/dXV1+OWXXxAfH48BAwYgJCQEn376qXT/sWPHUFpaiqSkJNXnCAsLQ2RkpNkPeY43VeSxXG+i5cuUnM8s/cUKW387ABAUpL5bUlsXxMIIpKakpARVVVVma02joqIwaNAgaa1pYWEhoqOjcfPNN0vbpKSkICgoCIcOHXL7mH2NUpuB5WOvXBcrb9pqRG15cssXCusQke9xevDz6KOPYu/evTh+/DgOHDiAu+++G3q9Hvfffz+ioqIwffp0zJ8/H/n5+SgqKsIDDzyApKQkDB482NlDIRfxpoo8tr5Myf2Kl6eqph1a+9sRmUwmq8/PNWVkD3E9aVxcnNnt8rWmVVVViI2NNbs/ODgY7dq143pUjeQnQHbPv93semTrYHRZ+BEmrDukuRE1i6MQkas4PfgpKyvD/fffjx49emD8+PGIiYnBwYMH0aFDBwDAqlWrMGbMGGRkZGDo0KEwGAw8e+ODvKUij1K6hdqXKXkHtb8de4PlkpISabaHhRHIE7geVZkhqpVZKXz5iZBZw6+VLltrRL19t7biKHv27HHq2InI/zk9+BFzpC9duoSysjJs2rQJ11xzjXR/q1atsHbtWpw5cwb19fXIzc21ut6HvFd6ejqKi4ul63l5eW6tyFNVc1Ex3ULty5S8h+XfzsqVK+0OWOT7DRZGIDXi30l1dbXZ7fK1pgaDASdPnjS7v6mpCWfOnOF6VI3Ugh3AfF3m3z/7Wbr84exkLNh6REpzk2/3xP6LaNP3DzZfd/z48fxfJyK7uHzND/k3+dn6oUOHujzVTam4gWW6hWV5ZXI9pQMfW/085H8rlilHtrRv3x4DBw6UrrMwAqnp2rUrDAaD2VrT2tpaHDp0SFprmpSUhLNnz6KoqEja5rPPPoPJZMKgQYNUn5vrUW1TWpcpiou8UhTlSFmN2XYCdGiXOgv6tjFWn//MmTP8XyciuzD4oRaJiIiAIAgQBAEREREufS2lL9EFW4+g15Kd0m1KFcbIO8n/drp27WrXY0+fPm01YBKfd86cOUyBCwB1dXU4fPgwDh8+DOBySuThw4dRWloKnU6HuXPn4plnnsEHH3yAI0eOYMqUKejYsSPGjRsHALj++utx5513YsaMGfj888+xf/9+zJo1C/fdd1+z9Ey6vF6vY8eOUl8la9T6gL09YzA+PnJlPdV9rx5stp0uSI+Qq2x//oIg4MEHH0RDQ4Om8RNRYGPwQz5D7UuUfJ+WKnCWlBZCWyorK+OagADw5Zdfon///ujfvz8AYP78+ejfvz+WLFkCAHj88ccxe/ZszJw5EwMHDkRdXR127NiBVq2unCx566230LNnT4wYMQJpaWm47bbb8Oqrr3rk/Xi7kJAQzJgxAzNmzEBISIjVbdXWZYaHBlnM9DSng4Cm37X1Bjt16hQSEhI4A0RENukELUcQXqa2thZRUVGoqalhmkEAqay5gOSVnykGQMXLU9nU1Mucb2iSZuU+++/b0a1DG7PbLH9nYllbQFtgo1W7du2wbt06dod3Eu5/1fGzUfZ/hcfxl22XA50gHZCd3geJ7cIxYZ16GfEg3eXZ/fPHDqBp7yv4/fczml5Lp9O5tegOEXkHe/a/nPkhn6FU3EBUVXNR4RHkSfY2n1WrAtdSXBNA5FlK6zKVZoTk1z+cnQwACO9xK9as32jX67EENhFZw+CHfIr8S1ReMlXLwTW5j1rzWVtBqmUVuMcff9xpY+IBEZFzNDY2IicnBzk5OWhsbLTrseK6TKWTWdnpfaTCKV/9ela67y8Hm5B4+3hNabHsA0ZEtjD4IZ8lL5kqHlxX1lzw4IhIpNZ8tvTMleazaoFQZGSkVLBg1KhRThmP0gFRbW2t1Cfo448/ZmBEpJEgCFJ5by0pqmplsNUqdSqdPNEPngx9G+uV3+QsK0ASEYkY/JDXkpdKPl13EV0WfmRW2U3p4Pr46fMgz1Nb5PxdeY10XctsnSOFEKwRD4hyc3PRq1cv6Xb2BiJyP3lQ1K1DG+l2pZMnAnR49qVX0b59e03PHR8f78yhEpEfYfBDPqd4eSoKFw1XPLju0j7cM4MiM0opLY/f2QMv7vpRuk3LbJ1er8fq1asBwCkBUHx8vFRYoby83Ow+9gYi8g5KJ08A4B8/hOKnkl/RoUMH6TZ92xiEde4j9QPS6XRITEzEkCFD3DVcIvIxDH7IJ1TXXkmRqqq5qHhwvSK9N+KjWntieKRAntJiEoDsj39waLZOrRCCZUNdaw12xQOiW2+9FXPmzFFM1RFv49ogIs+yVtymvLYBSJ4BAGjTdyQ6Pbgehvuz0enB9WjT9w8QBAEZGRkoKCjg/zERKWLwQ15LXi1szEv7pctiupRavjh5L0dn6ywLIeTl5eHUqVNm1zdt2iSt4ZETr+fk5ODAgQMoKyuDGmctluZ6IqKWUStuc9ea/QjvcSviJr2AdnfOgi7o8mGMLigI7VJnQd82Bjk5ObjjjjuYykpEihj8kFeQr+8539DUbMGr/Dy9UuUwsYIQeTf5QYw4WxfVOsTsd6/GshDCVVddZXY9MzNTcYZI3KZ169bNUt3U3HHHHQ4HLlxPRNRy4nqgwkXDmxW3AYBWnXpCpzM/hNEF6REcfeX/n6msRKSEwQ95JaUFr3JGQUB17SXFCkLkHcSDl6fHXklfkR/EuGK2Lj09Hb/++ivy8/Mxd+5cs8XRaWlpmDt3rl3PZ2/gwvVEFAh0Oh06dOiADh06OK0YiRpb3wVygsmIprMVV67/58THf/3Xf2HXrl14++23sWfPHs7EEgU4Bj/kdapqLqoueBWxuIFvUCpZK1KarXNGs1q9Xo8zZ85g9erVOH36tNl9lte10Bq4GI1Gu9YTMTWOfFVISAgefvhhPPzwwwgJCXHpa9n6LhAJJiPO7Pw7jOd+a3bf6dOnMXLkSEyYMIHpcETE4Ie8g3x9T8qLe5GU/ZnZgbL8u4/FDXyH2lnbt2cMlmbrLH/3LW1Way0IcYQ8cPn9998VA5ba2loEBwdrXk/E1DgibSyLH1gSBAGn3s9G+St/Qt23uzQ9J2diiQIbgx/yOGuzA6LtjyRLl1ncwHeo9fsRZ+2UfvctbVZbUFBgNQhxhBi4dO/eXbotLS0NBoMBd911F6655hrNz7Vt2zamxhHZQV784JER5usG/9QnDOeP7Vec8ZGTl8RmZUeiwMbghzxOS053XOSVFCkWN/AdtkqSK/3uW9qs1pWd3ZXS6LZv325XOt1bb73FUtvk0xobG/GPf/wD//jHP9DY2Ojy15M3Q33w9isnGnbPvx2L7x9usxFym75/UCyJ7YzKjkTkexj8kMdpzekm32StJLmtmSFHeGtnd3GRuLxEtyV7DsiMRiP27NnDRdzkdoIg4NSpUzh16pTT0ku1kgdC3Tq0MWuErETfNgbtUmcrlsQGXHuyhIi8E4Mf8jhbOd16nQ6NRoGV3fyAOGsnljZPyv4MT6RdL93vjPVcQ4YMsXkm2N3EsUycOFHT9rZKcufm5uLqq6/GHXfcYdcibgZM5I/ERsjt27c3S2/Tt41BeI/bpMBHJC+JHRMTw/8JogDDo0jyChkDEvCXbUcV7xPToFjgwD8lXdNOurx7/u3o1qENzjc0odeSnQCA4uWpdgW84pngzMxM6HQ6t5+ZVpKQkICcnBy0a9cOOTk5NrefN28eWrdujfT09Gb3ieW0Ld+XuGZoy5Ytqo975JFHzAKrhIQErF69WnF7Il+Snp6Omg598dSH30MXFATBZAJ0gE4XBEEQzE6GyEtip6WlmQU87du3x6RJkzB27FgMGTIEer3e7e+FiFyLMz/kdZydBkWeJU9TUarwdtea/dLl4X/b26zZqSPlr8UzwZYNTz1hxYoVWL9+PS5dugSj0ahpVurUqVPIyMjAvHnzzM5G21tOW8T+Q+TvKmsu4Om8Y2bpbWITVPlJEMuS2Jb/K6dPn0ZOTg5LYhP5MQY/5HJiipPlQa2c/ADZ2gJ58n1KFd70Oh0+++/bpdv+WfirdNnR8teWDU8BuDUVTqfTISYmBn//+9+RkpKCCRMmICUlBRcuXNA8G2V5EGarkp3SmiFHAyYiX2KrcI5Op8OZ3a+i/JU/4ULJV1JqHIBmqXLi5bKyMmRkZGD58uX8/yDyI0x7I7eqqrkIQ1QrqylN8hQ4MQ2K/Idahbf/O3gl4Hnp05+lyyYBWLD1CAZ2aWf334Jer8ewYcMwbNgwDBkypFnaV0xMDH777Tenp8eJz/fbb83L7545cwYA0LZtW5w7d07T84kHYZmZmZq2ly/itidgGjZsmKbnJ/I2YvEUtQBIMBlx/sf9aN31JqkAgmAyof7oZ4i4YXjzVDmTCWd2rkHdt7uwdOlSrFmzhulwRH6CMz/kcpZNLOXXbaU0say1/1Gq8BYE4I0Dx60+7vCJsy16XflM0MaNG5Gfn4/q6mps3bq1WXpchw4dWvRanTp1QkxMjOJ9LQmytmzZomk7ecU7rdWsWPWKtNLpdIiKikJUVJTXFBaxLJwjH5UOAs7s/DsANKv8FtF7hHKq3H+qwoX3SIa+bYxqOhyLiBD5Hp3gDauB7VRbW4uoqCjU1NQgMjLS08MhKyprLiB55WdmZ+N0AMSrQTogO70Pm5YGmP8rPC7N7gXpgD/f1hWvFpRYfYwr/1aMRiMKCgpQWVmJ+Ph43HrrrbjmmmtQXl6uGqwEBQXBZDJJ1zt06ICJEydi7NixMBqNSElJcfo4bdHpdEhISEBJSYl0ZvrTTz/VNJb8/HxNMz/c/6rjZ+N5lTUXcPz0eWmd6PHT51H50zfIGDUCYZ37wHB/tt3PKZhMOLt3PS5V/Yym3yuk9UJjxozBoUOHzMrXs4gIkWfYs/9l8EMudeCX05iw7pCmbe2t6kW+S17N7bP/vh2tQ/XNgmQlep0Ou+YPxfC/7QXg2r8ZsUgAYD5bI57pfuedd9ChQwcpYJKnwrz99tuYMGGCS8alRhyXvNpbbm4uZs+ejYqKCquPswyYrOH+Vx0/G+9kNBrRpUsXVNVcRMcH/9es9LVlJTg14nbydDiRvm0Mgq/qiKbfK2Cqu5zWqlZ1sSXvQX6Chql3RObs2f/ySJNcylYetlxVzUWu7wlAhqhWCA8NxrI/3mA2G6T0N2MUBJSeOS9dd+XfjFgxTqk8dE5OjtUDG080Wu3YsSNmzpyJS5cuYc+ePTh9+jTGjx9vNc1OPOjLycnhgRT5LXn5+zM7/452qVnQBekhmIyoP5qPiBvu+M/1K2t+LIn/K2I6XMPJEuhCWyPUcC2uuv0Bac3QmZ1rUH9kN+bMmYOoqCicPHnSarCiJajJzc3FnDlzzNbucYaJyHGc+SGXk6c4iefXlP7omAIX2OSzQR89kozRL+1vto1ep8O8P1yHFz75EYB7/mYcOeMqnmm2ljbnbO3bt8fp06el63q93ub6A0cOoLj/VRcon01jYyM2bNgAAJg2bRpCQkI8OyCNxCCisuYCgqM7Xu71c/4sEB595TqA0Pie6DB2QbPmqHKCYFLtIVT+yp+k1DhRp06dMHPmTFx33XXSfmTbtm02gxp5Xy93zDAR+SqmvZFXkR/U2qLX6fCvhXewtDUBaL42aMGdPfHcjh/MZoW89W9GrRmpmsWLF6Ourk5TE1Rn2b17N0aMGGHXY7j/VRcon01DQwOysy+vnVm0aBFCQ0M9PCLtlNb3HThwANu2bcObb74pnUBo0/cPaJc66/KMkGWAYyNVrmrjIlw6ccQsWLEMhuTVHpW2W7ZsGRYuXIhrrrkGZWVl/xnP7GYzTPakrBL5M3v2v6z2Ri4h7+1TVXMRx1eOxtNjb7D5OKMg4Pjp8za3o8CQMSBBurx7/u3okxClWCbbG/9mxLS59u3ba9p+xIgRWLVqFbZu3YpOnTq5eHSXnTx50i2vQ+QtxPL3999/P4YNG4bQ0FAMGzYMq1atQlVVFZYtWwYAqPt2F8pf+ROqNi7C73v+F4Lp8iyqYDJaDXwEkxFNZyvQpu8f0OnB9TDcn41OD65Hm75/MOshJAY+StsBwNKlS9GpUyeUlZVB3zamWZW6dqmzENSmHU6cOIE9e/a48BMj8j9c80MuYVneWjxjLxcEABZrO/Q6nVSlh0hsfitqHapvth5Ir9MhLjIMXRZ+BOByAQVvWTuWnp6OMWPGICEhwawilJxYcGDIkCHSY8aOHYtnn30WS5cuden4PLE2ichb6fV6LFmyBL1795bS0YznfsOlE0dw/vt9CI7uCKHxAgyTX1QsmiCYjDi7dwNCO/ZUCFZmS5fF6nGNNScVgxrTpfO4VPGDNAsVfFXHZil4uiA9gqM7wnjuN4wfPx7r1q1j+huRRgx+yOkqay5g6QdHpesmAXju4x9gstjOBOCBW7tg/f7jAC6nNa1I7+116UvkHc43NCEp+zOz28S/mf0/X1nrkvLiXq9aOxYaGopXXnnFauU4y4IDSgdhzmQZcBHRFeIJiIKCAmzbtg1vvfUWTp06JaWkndm55kpK3H8CnkuVPyM0/krxA0vy23RBQYge9ifFGSRdkB4dxi0yqyrX9HsFBJPJPOAyGaEPj4S+bQzOnPkNmZmZzSpQiil9rq4Qx0p05Gu45oecTq28tU4HCBZn7OVli73pjD15H/n6H5FamWxvXAekVLEpMTHRZuU48cBCfhAm6tChg+qMkjU6nc7hhdLc/6oLlM/Gl9f8OEL+P5iTkwOdToegNu2kIgnGc79B3zYGnR5cb7VIgr3kxRPM1iDJqtLJgyTLIieW17UUOLE3kGElOvIWXPNDHiWWt5bT63T47z90l66LZ+y7dWiD4ytH4/jK0Qx8SJXlbCJw+W+qdageJafrFdcBFf5ivsDY09LT03H8+HHk5+dj48aNyM/PR0lJic0DBHGNwqpVq1BZWWn2+LKyMiQkJGjqUyKKiYlhhSgiO8j/B8U1eWI6nDgbpJSaJhJMRgiCZe6DbbogPcK73wZ92xhpDdLJ9y4HnWI5bjFVTt82Bkaj0WxdkeX18vJyZGZmIjc3V/H1cnNz0aVLF9xxxx2YMGEC7rjjDnTp0sXq9pmZmdK6JK2vQ+RpTHsju1g2p+zWoY3ibZY9W1ak98a9AzsjY0CC1H3bm87Kk3dTC3COnz6v2kvq0c3foNFowl03dmz29+kp4kGUMx8v9i/R6p133rG7whuRpfDwwFybKU+Jq6ysRHV1NebNm6eamnb6g+dxqeIHtO56k3r1OJMRZz55Ge1GPtxsLVG7lBm4avh0aXbHdFWt6vqfy69xpSJc/dHPEHHDcKs9iGJjYwEA27dvlypNyqvPiYGMUkrdnDlzIAiCaiW6uXPnYuzYsUyBI6/DtDeyi1Lp4aqaC1h/4Fez2/okRCEiVI/zDSYGOtRilTUXVFPbAODVvb9If4NynugL5Am5ubnNmrFaEtf5tLQsLve/6vjZBB55T6+IPilma4HO7Pw76r7dJW2rbxuD4OiO/1kbNK3ZdlbLa/8nBQ5As/Q6a8GTlh5EckqBTN23uxAUFAST6crsVWRkJGpraxXT/eSvs2rVKsTFxTnU6FV+uxik2Woaq+V5yT+xzw+1WGXNBZScrkfX9hFS4PLNid8x7h8HoPUvxl8PNMkzLAPv7PQ+aGgyNVsHZElprZmj64GU/i+8hdFoVK0QJx4AOSPdjftfdfxsApOY/gWg2VogALj33nuxf/9+s3UxYiAk3068Pbz7bWiXMqPZ64j9g9TW/2ih1IMIuJy2JzQoVLKTBTJK/YjCOveB4f5s1deRa9++PSZNmoQxY8YAuBzI/PTTT1i3bp3ZZ9O+fXsMHjwYhw4dUl3TKG8aqxQYaWkgK3JmkKTWR4oBmOsx+CGbrB3EOXqQqcQbF56T76qsuSClTQJoNhtkKQhoVmUQAN6eMRhd2odL/wMAbAY1Sv8X3hjYO1pYQSvuf9Xxswlctv7vrBUuSUxMxH333Yf169fj9OnTNmdTgMtBUmh8T3QYu0B9rZHCzM/pD56HPipWqkpnWTxB6bnO7F4H6IPMHnN273pcqvrZoYBJidp2SkGaredSayBrqjsD4PJJIKVqfiIxSBs7dqxZ8CIPspQub9++vdlzWRadkD+3O6rvaZ0xU3uMtcc78hgtY3Y0SPSZ4Gft2rX461//iqqqKtx4441Ys2YNbrnlFpuP4xeM4yprLpilCMkP4iprLuDL42cwZ9NhswNKpX489nh7xmAkXRPT4rETyalVFRTX/+h1Ojx4ezf8Y+8vzWZ+5KlwOgCC7LFKQY21tDtvDOxdme7h7/tfR7+XAP//bESNjY146623AAATJ05ESEiIh0fkHbT+36lt19DQIPUEM5/duZwaV39kN9q1awdBEHDmzBnVWRfgcgBSfzQfETfc0bxCnEVQZPY4y4BJ7GGkdru0tugOmJX+rvoZoYZrFQMmy0DGcq2SuJ3l4y0r3F0o+cpqYKSWwtemTRu0atVK6qMEWAm+LIIXLSyfS+25lWbCLGeLbAVclo9RCubklAI7W49RevxVV13VbMbO1mPUgkmloNGRioE+Efy88847mDJlCl555RUMGjQIOTk52Lx5M44dOyZ9IGr84QvGGekz9j6HUqlg4HJwk3lzAt790rm9RADvPkAk36YWkOQ+nITzDSYU/XpGCnDk9ysFRJbbiGuJSk7XIyJUj8+Pn8GzH/3QbNu/398fA7pcJW1X32D0ypQ4Z/KH/a+alnwvAf792cgFWqlrd1JLoZPPWkRFRSElJUV1hkgssiAeeNuaIbIkzgBZC5LMtzei6v/+G7qQ1ma9jqwFTPJAxjJtTy3gshwjAMXASGwg2+GPC2zOngVf1dFqkGYZvACwetnyuSyLTlg+txKHAi7LMucaZsy0Pkbt8Y48xtp7U5ul0xoA+UTwM2jQIAwcOBB///vfAQAmkwmJiYmYPXs2Fi5caPWxvv4F884XpViUewQmoXmBAPHgCYDZAZXlff/7rxK8/q8Szc9ReuZ8sxmdlggC8PAd1+DlPf+GURAQBODPQ7sipk0Ynv/4GIyCAL1OJ1V5I3KFd74oxRO53zX7e1MKjMS/2bX5v8DWv8GEWzpj0xelNv9fxK9l+WbenBLnDL6+/7WmJd9LgH9/NnIMflxLSwqdliILYgBhbYbIkhjIhHW6QXHdkZqqjYvQdLbC6b2OHGEtaDr5XjZMF2vNgxSbs1rDFYMsxcsqz6X03GozYfYGXJaPsTZjphbYWXuM2uMtZ+y0PEbtvVm+vlgx0J4iPV4f/DQ0NCA8PBxbtmzBuHHjpNunTp2Ks2fPYtu2bVYf78tfMEoHZZaUDqjk92n5hVl7jpayPMi0LF2tdBuRqyj9vWlttOsq/jzj6cv7X2ta+r0E+O9nY4nBj+vZSqGzVWRh2bJlSEpKwsiRI5VniBRnYa4ET1Yfo1JFLviqjpqDLE8wmy3SOqulcTuHxqMyE2Z3wGX5GA1pjfY8xtaY7XmM6nuzUpkwPz9fU4sIe/a/Hunzc/r0aRiNRsTFxZndHhcXhx9+aJ5acunSJVy6dEm6Xltb6/IxuopSvxJL1u7WetzW0uM7tSDrL6OvR1rfeOmgLj6qdbMDPKXbiFxF6e9NqfdPEJTXrWk9oWAPsQcR/w98h73fS4B/fTeRd7HVEyw9PR1btmyRZojEoMdyhighIQHl5eU4s3ON2QzR2b0bcKnyZzSd/c/Zd4vgyXjuN9XHKJXqFh/XrNeR5hQ2QbnEt0qQBp1Oc4W7y69h/hitAU1LAx9r71u8Xf556YKCENF7hOp9apfNHmNlzPLn1foYW2O25zGq783i9cXeVcZzv6GyslLza2nlE01Os7OzsWzZMk8PwynUGjK6WxCA+wYlYtPnJ5qNRUyje27HD83WU8gDHyJvFR/VGtnpfcxS4h6/s0ezv+kgAO9l3YoTv1/ArI1f23xercU/9DqdVJGO/Jc/fTeR77FsuGo5Q6TX66UmyPVHdl8uEKBQXhuAWfB033334YUXXlB9zKUTR3D++30tCJiazzaJr2MZWKkFaWZNY23MIJz+4HkAQIdxi1Q/S1uFHexxJWCzKDqh8bkcCbjc9ZiW0vqagsko/c7j4+OdPg6PBD/t27eHXq9HdXW12e3V1dUwGAzNtl+0aBHmz58vXa+trUViYqLLx+kKlgdl7hYEYM2E/rjp6qsQH9UaNyZES2MR1+08kNwV8VGtER0e0mw9BQMf8hX3DuyMod07mKXEKf1N35h4FWIjW9k8KSFuD0B6Dh0AKPQR4v+K77H3ewnwr+8m8k2OzhB16NABEydObFZpTAyeBg8erPiYQYMGSf13WhIwAcqzTWqBlUi8XvftLrPXEZ9PaVbq/LH90LeNUZ+VsjKrpVoxT/WyecBmPPcbzhb8X/Ox2VFxTwtNM2Z2rEfStJ5JPmPn4Boopfcg/t5MdWeQmJiIIUOG2PVZaOHRgge33HIL1qxZA+DywtLOnTtj1qxZfl/wALiyTuHb8rNSgQCR0gGV0n1KRQasPYdaAQJra3S4fof8jdrftGXxhMfv7IG+CdEIDw3C+QaT6ro2ADh++rzidv7IH/a/alryvQT492cj19DQgBdeeAEA8Oijj3LNjw9wpPy92mPUblcq1GAZMClJSEjAjBkz8PvvvzcreawUpCk1RpVTayBrWT7cMkhRe7z8OgCbl21WVGsWpJkHT44EXOaPUZ4xsx7Yqc+yqT1ePmOn9THq78389f222ts777yDqVOn4n/+539wyy23ICcnB++++y5++OGHZjnXlvztC0Y8kJIfPAHmB1RK9ykdjFl7Dn8/KCNqKQb7tvnb/leuJd9LgH9/NkRaaAmYtDbOtLcpp1K/GPmsFKBcHAJQD9IcKTstBmy2eumoBVWOBlxqQZ+ctcDOWuNYtcdroTWYlD+fI425fSL4AYC///3vUjO5fv364aWXXsKgQYNsPo5fMEREnuHv+19Hv5cA//9siLydvbNSYpCiNqvlSMNRWwGbraaizujzYzljphQY2nqM/L2pNSKdMWMGrrvuOsXPQ8tryin9PuzhM8GPo/gFQ0TkGdz/quNnQ+S9HEn9c8dYLIMnRwIu+WPU3pu1wE7L5+GM1Em19+aM3weDHyIicgnuf9UFymfT1NSEd999FwAwfvx4BAf7ROFYIvJjXt/nh4iIiHyTyWTCTz/9JF0mIvIl2rsUERERERER+TAGP0REREREFBAY/BARERERUUBg8ENERERERAGBwQ8REREREQUEn6z2Jlbnrq2t9fBIiIgCi7jf9cEuCS4XKN9NDQ0NuHjxIoDL7zU0NNTDIyKiQGfPd5NP9vkpKytDYmKip4dBRBSwTpw4gYSEBE8Pw6vwu4mIyLO0fDf5ZPBjMplQUVGBtm3bQqfTaX5cbW0tEhMTceLECb9uQGcNPwN+BgA/A4CfgaPvXxAEnDt3Dh07dkRQEDOn5QLpu4ljdg+O2T18ccyAb47bVWO257vJJ9PegoKCWnTGMTIy0mf+SFyFnwE/A4CfAcDPwJH3HxUV5aLR+LZA/G7imN2DY3YPXxwz4JvjdsWYtX438bQdEREREREFBAY/REREREQUEAIq+AkLC8PSpUsRFhbm6aF4DD8DfgYAPwOAn0Ggv39v4ou/C47ZPThm9/DFMQO+OW5vGLNPFjwgIiIiIiKyV0DN/BARERERUeBi8ENERERERAGBwQ8REREREQUEvwt+1q5diy5duqBVq1YYNGgQPv/8c6vbb968GT179kSrVq3Qp08f5OXluWmkrmPPZ7Bu3ToMGTIEV111Fa666iqkpKTY/Mx8gb1/B6JNmzZBp9Nh3Lhxrh2gG9j7GZw9exZZWVmIj49HWFgYunfv7tP/D/a+/5ycHPTo0QOtW7dGYmIi5s2bh4sXL7pptM63b98+3HXXXejYsSN0Oh3ef/99m4/Zs2cPbrrpJoSFheHaa6/Fhg0bXD7OQOGL302++F3ii/t+X9xX+9r+1Rf3h/aOOTc3F3/4wx/QoUMHREZGIikpCTt37nTPYP/Dkc9ZtH//fgQHB6Nfv34uG59E8CObNm0SQkNDhf/93/8Vjh49KsyYMUOIjo4WqqurFbffv3+/oNfrheeff14oLi4WFi9eLISEhAhHjhxx88idx97PYMKECcLatWuFr7/+Wvj++++FadOmCVFRUUJZWZmbR+489n4GopKSEqFTp07CkCFDhLFjx7pnsC5i72dw6dIl4eabbxbS0tKEf/3rX0JJSYmwZ88e4fDhw24euXPY+/7feustISwsTHjrrbeEkpISYefOnUJ8fLwwb948N4/cefLy8oQnn3xSyM3NFQAI7733ntXt//3vfwvh4eHC/PnzheLiYmHNmjWCXq8XduzY4Z4B+zFf/G7yxe8SX9z3++K+2hf3r764P7R3zHPmzBGee+454fPPPxd+/PFHYdGiRUJISIjw1VdfuWfAgv1jFv3+++9Ct27dhJEjRwo33nijS8coCILgV8HPLbfcImRlZUnXjUaj0LFjRyE7O1tx+/HjxwujR482u23QoEHCf/3Xf7l0nK5k72dgqampSWjbtq3wxhtvuGqILufIZ9DU1CTceuutwmuvvSZMnTrV54Mfez+Dl19+WejWrZvQ0NDgriG6lL3vPysrSxg+fLjZbfPnzxeSk5NdOk530fIl9Pjjjws33HCD2W333nuvkJqa6sKRBQZf/G7yxe8SX9z3++K+2tf3r764P7QnkJDr1auXsGzZMucPSAN7xnzvvfcKixcvFpYuXeqW4Mdv0t4aGhpQVFSElJQU6bagoCCkpKSgsLBQ8TGFhYVm2wNAamqq6vbezpHPwNL58+fR2NiIdu3auWqYLuXoZ7B8+XLExsZi+vTp7himSznyGXzwwQdISkpCVlYW4uLi0Lt3b6xYsQJGo9Fdw3YaR97/rbfeiqKiIil149///jfy8vKQlpbmljF7A3/bH3oLX/xu8sXvEl/c9/vivjpQ9q+e/h90BpPJhHPnznn98dz69evx73//G0uXLnXbawa77ZVc7PTp0zAajYiLizO7PS4uDj/88IPiY6qqqhS3r6qqctk4XcmRz8DSggUL0LFjx2b/9L7Ckc/gX//6F15//XUcPnzYDSN0PUc+g3//+9/47LPPMHHiROTl5eHnn3/Gww8/jMbGRrfukJzBkfc/YcIEnD59GrfddhsEQUBTUxMefPBBPPHEE+4YsldQ2x/W1tbiwoULaN26tYdG5tt88bvJF79LfHHf74v76kDZv/rD/vCFF15AXV0dxo8f7+mhqPrpp5+wcOFCFBQUIDjYfSGJ38z8UMutXLkSmzZtwnvvvYdWrVp5ejhuce7cOUyePBnr1q1D+/btPT0cjzGZTIiNjcWrr76KAQMG4N5778WTTz6JV155xdNDc4s9e/ZgxYoV+Mc//oGvvvoKubm5+Oijj/D00097emhEPscXvkt8dd/vi/tq7l/db+PGjVi2bBneffddxMbGeno4ioxGIyZMmIBly5ahe/fubn1tv5n5ad++PfR6Paqrq81ur66uhsFgUHyMwWCwa3tv58hnIHrhhRewcuVK7N69G3379nXlMF3K3s/gl19+wfHjx3HXXXdJt5lMJgBAcHAwjh07hmuuuca1g3YyR/4O4uPjERISAr1eL912/fXXo6qqCg0NDQgNDXXpmJ3Jkff/l7/8BZMnT8af//xnAECfPn1QX1+PmTNn4sknn0RQkP+fJ1LbH0ZGRvrEWU5v5YvfTb74XeKL+35f3FcHyv7Vl/eHmzZtwp///Gds3rzZq7N4zp07hy+//BJff/01Zs2aBeDy/6AgCAgODsYnn3yC4cOHu+S1ve8vzkGhoaEYMGAAPv30U+k2k8mETz/9FElJSYqPSUpKMtseAHbt2qW6vbdz5DMAgOeffx5PP/00duzYgZtvvtkdQ3UZez+Dnj174siRIzh8+LD088c//hF33HEHDh8+jMTERHcO3ykc+TtITk7Gzz//LH35A8CPP/6I+Ph4nwp8AMfe//nz55t9AYsHF4IguG6wXsTf9ofewhe/m3zxu8QX9/2+uK8OlP2rp/8HHfX222/jgQcewNtvv43Ro0d7ejhWRUZGNvsffPDBB9GjRw8cPnwYgwYNct2Lu7ykghtt2rRJCAsLEzZs2CAUFxcLM2fOFKKjo4WqqipBEARh8uTJwsKFC6Xt9+/fLwQHBwsvvPCC8P333wtLly71i1LX9nwGK1euFEJDQ4UtW7YIlZWV0s+5c+c89RZazN7PwJI/VHuz9zMoLS0V2rZtK8yaNUs4duyYsH37diE2NlZ45plnPPUWWsTe97906VKhbdu2wttvvy38+9//Fj755BPhmmuuEcaPH++pt9Bi586dE77++mvh66+/FgAIL774ovD1118Lv/76qyAIgrBw4UJh8uTJ0vZiadfHHntM+P7774W1a9ey1LWT+OJ3ky9+l/jivt8X99W+uH/1xf2hvWN+6623hODgYGHt2rVm/4Nnz5712jFbcle1N78KfgRBENasWSN07txZCA0NFW655Rbh4MGD0n233367MHXqVLPt3333XaF79+5CaGiocMMNNwgfffSRm0fsfPZ8BldffbUAoNnP0qVL3T9wJ7L370DOH4IfQbD/Mzhw4IAwaNAgISwsTOjWrZvw7LPPCk1NTW4etfPY8/4bGxuFp556SrjmmmuEVq1aCYmJicLDDz8s/P777+4fuJPk5+cr/m+L73vq1KnC7bff3uwx/fr1E0JDQ4Vu3boJ69evd/u4/ZUvfjf54neJL+77fXFf7Wv7V1/cH9o75ttvv93q9t44ZkvuCn50guClc45ERERERERO5DdrfoiIiIiIiKxh8ENERERERAGBwQ8REREREQUEBj9ERERERBQQGPwQEREREVFAYPBDREREREQBgcEPEREREREFBAY/REREREQUEBj8EBERERFRQGDwQ0RERBTghg0bhrlz53p6GEQux+CHiIiIiIgCAoMfIhcbNmwYZs+ejblz5+Kqq65CXFwc1q1bh/r6ejzwwANo27Ytrr32Wnz88ceeHioREQWgadOmYe/evVi9ejV0Oh10Oh2OHz/u6WERuQSDHyI3eOONN9C+fXt8/vnnmD17Nh566CHcc889uPXWW/HVV19h5MiRmDx5Ms6fP+/poRIRUYBZvXo1kpKSMGPGDFRWVqKyshKJiYmeHhaRS+gEQRA8PQgifzZs2DAYjUYUFBQAAIxGI6KiopCeno5//vOfAICqqirEx8ejsLAQgwcP9uRwiYgoAA0bNgz9+vVDTk6Op4dC5FKc+SFyg759+0qX9Xo9YmJi0KdPH+m2uLg4AMDJkyfdPjYiIiKiQMHgh8gNQkJCzK7rdDqz23Q6HQDAZDK5dVxEREREgYTBDxEREVGACw0NhdFo9PQwiFyOwQ8RERFRgOvSpQsOHTqE48eP4/Tp08xEIL/F4IeIiIgowD366KPQ6/Xo1asXOnTogNLSUk8PicglWO2NiIiIiIgCAmd+iIiIiIgoIDD4ISIiIiKigMDgh4iIiIiIAgKDHyIiIiIiCggMfoiIiIiIKCAw+CEiIiIiooDA4IeIiIiIiAICgx8iIiIiIgoIDH6IiIiIiCggMPghIiIiIqKAwOCHiIiIiIgCAoMfIiIiIiIKCP8P+Hl9e8QBuQwAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# save the original toy for later\n",
    "toy_original = (toy[0].copy(), toy[1].copy(), toy[2].copy())\n",
    "\n",
    "# modify the toy to introduce non-factorization\n",
    "tm = toy[2]\n",
    "toy[0][tm] += 0.1 * toy[1][tm]\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n",
    "plt.sca(ax[0])\n",
    "plot_binned(toy[0], bins=100, color=\"k\", label=\"total\")\n",
    "plot_binned(toy[0][toy[2]], bins=100, marker=\".\", color=\"C0\", label=\"signal\")\n",
    "plt.xlabel(\"m\")\n",
    "plt.sca(ax[1])\n",
    "plot_binned(toy[1], bins=100, color=\"k\", label=\"total\")\n",
    "plot_binned(toy[1][toy[2]], bins=100, marker=\".\", color=\"C0\", label=\"signal\")\n",
    "plt.axvline(tsplit, ls=\"--\", color=\"0.5\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"t\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This change is hardly noticeable when we plot the full dataset. It becomes more apparent when we plot the distributions after splitting (we split in the same way as before)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mask = toy[1] < tsplit\n",
    "m1 = toy[0][mask]\n",
    "m2 = toy[0][~mask]\n",
    "\n",
    "plot_binned(m1, bins=100, label=r\"$t$ < $t_0$\")\n",
    "plot_binned(m2, bins=100, label=r\"$t$ ≥ $t_0$\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"m\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see now that the peaks are not at the same place. This becomes even more noticeable if we plot the 2D scatter plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_indep_scatter(toy[0], toy[1])\n",
    "plt.xlabel(\"m\")\n",
    "plt.ylabel(\"t\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Checks by eye are good, but not objective. The deviation could be more subtle. A change in the width of the peak or the slope of the background would be harder to detect by eye. Or there could be several changes in the shape variables at once, each individually too small to be noticeable.\n",
    "\n",
    "In any case, we need a p-value to quantify whether such a deviation is significant, which is provided by the likelihood-ratio test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = -1.565e+05 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 186 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 0.000109 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\"> time = 0.8 sec </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#FFF79A;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#FFF79A;color:black\"> Covariance APPROXIMATE </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> s1 </td>\n",
       "        <td> 3.14e3 </td>\n",
       "        <td> 0.08e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> b1 </td>\n",
       "        <td> 4.06e3 </td>\n",
       "        <td> 0.09e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> mu </td>\n",
       "        <td> 0.5199 </td>\n",
       "        <td> 0.0020 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 1 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 0.1002 </td>\n",
       "        <td> 0.0020 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 4 </th>\n",
       "        <td> slope </td>\n",
       "        <td> 0.489 </td>\n",
       "        <td> 0.016 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 5 </th>\n",
       "        <td> s2 </td>\n",
       "        <td> 1.84e3 </td>\n",
       "        <td> 0.05e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 6 </th>\n",
       "        <td> b2 </td>\n",
       "        <td> 930 </td>\n",
       "        <td> 40 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> s1 </th>\n",
       "        <th> b1 </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "        <th> slope </th>\n",
       "        <th> s2 </th>\n",
       "        <th> b2 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> s1 </th>\n",
       "        <td> 7.2e+03 </td>\n",
       "        <td style=\"background-color:rgb(180,180,250);color:black\"> -4e3 <strong>(-0.540)</strong> </td>\n",
       "        <td style=\"background-color:rgb(240,240,250);color:black\"> -12.489e-3 <strong>(-0.075)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,187,187);color:black\"> 69.131e-3 <strong>(0.418)</strong> </td>\n",
       "        <td style=\"background-color:rgb(200,200,250);color:black\"> -524.91e-3 <strong>(-0.386)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,225,225);color:black\"> 0.7e3 <strong>(0.165)</strong> </td>\n",
       "        <td style=\"background-color:rgb(225,225,250);color:black\"> -0.7e3 <strong>(-0.195)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b1 </th>\n",
       "        <td style=\"background-color:rgb(180,180,250);color:black\"> -4e3 <strong>(-0.540)</strong> </td>\n",
       "        <td> 7.5e+03 </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 12.903e-3 <strong>(0.076)</strong> </td>\n",
       "        <td style=\"background-color:rgb(195,195,250);color:black\"> -71.540e-3 <strong>(-0.424)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 537.44e-3 <strong>(0.388)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -0.6e3 <strong>(-0.133)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 0.6e3 <strong>(0.179)</strong> </td>\n",
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       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(240,240,250);color:black\"> -12.489e-3 <strong>(-0.075)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 12.903e-3 <strong>(0.076)</strong> </td>\n",
       "        <td> 3.84e-06 </td>\n",
       "        <td style=\"background-color:rgb(240,240,250);color:black\"> -0e-6 <strong>(-0.077)</strong> </td>\n",
       "        <td style=\"background-color:rgb(231,231,250);color:black\"> -5e-6 <strong>(-0.148)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -96e-6 </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 945e-6 <strong>(0.012)</strong> </td>\n",
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       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,187,187);color:black\"> 69.131e-3 <strong>(0.418)</strong> </td>\n",
       "        <td style=\"background-color:rgb(195,195,250);color:black\"> -71.540e-3 <strong>(-0.424)</strong> </td>\n",
       "        <td style=\"background-color:rgb(240,240,250);color:black\"> -0e-6 <strong>(-0.077)</strong> </td>\n",
       "        <td> 3.79e-06 </td>\n",
       "        <td style=\"background-color:rgb(202,202,250);color:black\"> -12e-6 <strong>(-0.371)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,206,206);color:black\"> 29.445e-3 <strong>(0.293)</strong> </td>\n",
       "        <td style=\"background-color:rgb(204,204,250);color:black\"> -28.462e-3 <strong>(-0.350)</strong> </td>\n",
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       "        <th> slope </th>\n",
       "        <td style=\"background-color:rgb(200,200,250);color:black\"> -524.91e-3 <strong>(-0.386)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 537.44e-3 <strong>(0.388)</strong> </td>\n",
       "        <td style=\"background-color:rgb(231,231,250);color:black\"> -5e-6 <strong>(-0.148)</strong> </td>\n",
       "        <td style=\"background-color:rgb(202,202,250);color:black\"> -12e-6 <strong>(-0.371)</strong> </td>\n",
       "        <td> 0.000256 </td>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -174.35e-3 <strong>(-0.211)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,202,202);color:black\"> 212.27e-3 <strong>(0.318)</strong> </td>\n",
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       "        <th> s2 </th>\n",
       "        <td style=\"background-color:rgb(250,225,225);color:black\"> 0.7e3 <strong>(0.165)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -0.6e3 <strong>(-0.133)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -96e-6 </td>\n",
       "        <td style=\"background-color:rgb(250,206,206);color:black\"> 29.445e-3 <strong>(0.293)</strong> </td>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -174.35e-3 <strong>(-0.211)</strong> </td>\n",
       "        <td> 2.67e+03 </td>\n",
       "        <td style=\"background-color:rgb(197,197,250);color:black\"> -0.9e3 <strong>(-0.407)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(225,225,250);color:black\"> -0.7e3 <strong>(-0.195)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 0.6e3 <strong>(0.179)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 945e-6 <strong>(0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(204,204,250);color:black\"> -28.462e-3 <strong>(-0.350)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,202,202);color:black\"> 212.27e-3 <strong>(0.318)</strong> </td>\n",
       "        <td style=\"background-color:rgb(197,197,250);color:black\"> -0.9e3 <strong>(-0.407)</strong> </td>\n",
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      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = -1.565e+05                 │              Nfcn = 186              │\n",
       "│ EDM = 0.000109 (Goal: 0.0002)    │            time = 0.8 sec            │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │        Covariance APPROXIMATE        │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬───────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name  │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼───────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ s1    │  3.14e3   │  0.08e3   │            │            │    0    │         │       │\n",
       "│ 1 │ b1    │  4.06e3   │  0.09e3   │            │            │    0    │         │       │\n",
       "│ 2 │ mu    │  0.5199   │  0.0020   │            │            │    0    │    1    │       │\n",
       "│ 3 │ sigma │  0.1002   │  0.0020   │            │            │    0    │         │       │\n",
       "│ 4 │ slope │   0.489   │   0.016   │            │            │    0    │         │       │\n",
       "│ 5 │ s2    │  1.84e3   │  0.05e3   │            │            │    0    │         │       │\n",
       "│ 6 │ b2    │    930    │    40     │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬──────────────────────────────────────────────────────────────────────────────┐\n",
       "│       │         s1         b1         mu      sigma      slope         s2         b2 │\n",
       "├───────┼──────────────────────────────────────────────────────────────────────────────┤\n",
       "│    s1 │    7.2e+03       -4e3 -12.489e-3  69.131e-3 -524.91e-3      0.7e3     -0.7e3 │\n",
       "│    b1 │       -4e3    7.5e+03  12.903e-3 -71.540e-3  537.44e-3     -0.6e3      0.6e3 │\n",
       "│    mu │ -12.489e-3  12.903e-3   3.84e-06      -0e-6      -5e-6     -96e-6     945e-6 │\n",
       "│ sigma │  69.131e-3 -71.540e-3      -0e-6   3.79e-06     -12e-6  29.445e-3 -28.462e-3 │\n",
       "│ slope │ -524.91e-3  537.44e-3      -5e-6     -12e-6   0.000256 -174.35e-3  212.27e-3 │\n",
       "│    s2 │      0.7e3     -0.6e3     -96e-6  29.445e-3 -174.35e-3   2.67e+03     -0.9e3 │\n",
       "│    b2 │     -0.7e3      0.6e3     945e-6 -28.462e-3  212.27e-3     -0.9e3   1.74e+03 │\n",
       "└───────┴──────────────────────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nll1 = ExtendedUnbinnedNLL(m1, make_with_signature(model, s=\"s1\", b=\"b1\"))\n",
    "nll2 = ExtendedUnbinnedNLL(m2, make_with_signature(model, s=\"s2\", b=\"b2\"))\n",
    "mi0 = Minuit(\n",
    "    nll1 + nll2,\n",
    "    s1=1000,\n",
    "    s2=1000,\n",
    "    b1=1000,\n",
    "    b2=1000,\n",
    "    mu=0.5,\n",
    "    sigma=0.1,\n",
    "    slope=0.5,\n",
    ")\n",
    "mi0.strategy = 0  # sufficient since we don't need accurate parameter errors\n",
    "mi0.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = -1.163e+05 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 119 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.83e-05 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\"> time = 0.3 sec </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </td>\n",
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       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
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       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
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       "        <th> 0 </th>\n",
       "        <td> s </td>\n",
       "        <td> 3.12e3 </td>\n",
       "        <td> 0.09e3 </td>\n",
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       "        <th> 1 </th>\n",
       "        <td> b </td>\n",
       "        <td> 4.08e3 </td>\n",
       "        <td> 0.09e3 </td>\n",
       "        <td>  </td>\n",
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       "        <td> mu </td>\n",
       "        <td> 0.5095 </td>\n",
       "        <td> 0.0026 </td>\n",
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       "        <td> 0.0973 </td>\n",
       "        <td> 0.0026 </td>\n",
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       "        <td> 0.018 </td>\n",
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       "        <th> slope </th>\n",
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       "        <th> s </th>\n",
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       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -5.887e-3 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,173,173);color:black\"> 118.847e-3 <strong>(0.512)</strong> </td>\n",
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       "        <td> 8.88e+03 </td>\n",
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       "        <td style=\"background-color:rgb(187,187,250);color:black\"> -117.562e-3 <strong>(-0.487)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,189,189);color:black\"> 676.61e-3 <strong>(0.404)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 6.899e-3 <strong>(0.028)</strong> </td>\n",
       "        <td> 6.64e-06 </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0e-6 <strong>(-0.024)</strong> </td>\n",
       "        <td style=\"background-color:rgb(224,224,250);color:black\"> -9e-6 <strong>(-0.201)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0e-6 <strong>(-0.024)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(250,189,189);color:black\"> 676.61e-3 <strong>(0.404)</strong> </td>\n",
       "        <td style=\"background-color:rgb(224,224,250);color:black\"> -9e-6 <strong>(-0.201)</strong> </td>\n",
       "        <td style=\"background-color:rgb(205,205,250);color:black\"> -16e-6 <strong>(-0.348)</strong> </td>\n",
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       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = -1.163e+05                 │              Nfcn = 119              │\n",
       "│ EDM = 1.83e-05 (Goal: 0.0002)    │            time = 0.3 sec            │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬───────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name  │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼───────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ s     │  3.12e3   │  0.09e3   │            │            │    0    │         │       │\n",
       "│ 1 │ b     │  4.08e3   │  0.09e3   │            │            │    0    │         │       │\n",
       "│ 2 │ mu    │  0.5095   │  0.0026   │            │            │    0    │    1    │       │\n",
       "│ 3 │ sigma │  0.0973   │  0.0026   │            │            │    0    │         │       │\n",
       "│ 4 │ slope │   0.499   │   0.018   │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬─────────────────────────────────────────────────────────────┐\n",
       "│       │           s           b          mu       sigma       slope │\n",
       "├───────┼─────────────────────────────────────────────────────────────┤\n",
       "│     s │    8.22e+03        -5e3   -5.887e-3  118.847e-3  -669.93e-3 │\n",
       "│     b │        -5e3    8.88e+03    6.899e-3 -117.562e-3   676.61e-3 │\n",
       "│    mu │   -5.887e-3    6.899e-3    6.64e-06       -0e-6       -9e-6 │\n",
       "│ sigma │  118.847e-3 -117.562e-3       -0e-6    6.56e-06      -16e-6 │\n",
       "│ slope │  -669.93e-3   676.61e-3       -9e-6      -16e-6    0.000316 │\n",
       "└───────┴─────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nll = ExtendedUnbinnedNLL(m1, model)\n",
    "mi1 = Minuit(nll, s=1000, b=1000, mu=0.5, sigma=0.1, slope=0.5)\n",
    "mi1.strategy = 0\n",
    "mi1.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = -4.029e+04 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 103 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 8.02e-05 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\"> time = 0.3 sec </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
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       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </td>\n",
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       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
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       "        <th> 0 </th>\n",
       "        <td> s </td>\n",
       "        <td> 1.83e3 </td>\n",
       "        <td> 0.06e3 </td>\n",
       "        <td>  </td>\n",
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       "        <th> 1 </th>\n",
       "        <td> b </td>\n",
       "        <td> 950 </td>\n",
       "        <td> 50 </td>\n",
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       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
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       "        <th> 2 </th>\n",
       "        <td> mu </td>\n",
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       "        <td> 0.0030 </td>\n",
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       "        <th> 3 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 0.1007 </td>\n",
       "        <td> 0.0028 </td>\n",
       "        <td>  </td>\n",
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       "        <th> 4 </th>\n",
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       "        <th> s </th>\n",
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       "        <th> slope </th>\n",
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       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -4.467e-3 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 61.232e-3 <strong>(0.378)</strong> </td>\n",
       "        <td style=\"background-color:rgb(194,194,250);color:black\"> -1.1100 <strong>(-0.434)</strong> </td>\n",
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       "        <td> 2.46e+03 </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 5.158e-3 <strong>(0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(191,191,250);color:black\"> -62.497e-3 <strong>(-0.451)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,175,175);color:black\"> 1.0962 <strong>(0.501)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 5.158e-3 <strong>(0.034)</strong> </td>\n",
       "        <td> 9.29e-06 </td>\n",
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       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -18e-6 <strong>(-0.131)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -18e-6 <strong>(-0.131)</strong> </td>\n",
       "        <td style=\"background-color:rgb(208,208,250);color:black\"> -40e-6 <strong>(-0.323)</strong> </td>\n",
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      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = -4.029e+04                 │              Nfcn = 103              │\n",
       "│ EDM = 8.02e-05 (Goal: 0.0002)    │            time = 0.3 sec            │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬───────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name  │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼───────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ s     │  1.83e3   │  0.06e3   │            │            │    0    │         │       │\n",
       "│ 1 │ b     │    950    │    50     │            │            │    0    │         │       │\n",
       "│ 2 │ mu    │  0.5331   │  0.0030   │            │            │    0    │    1    │       │\n",
       "│ 3 │ sigma │  0.1007   │  0.0028   │            │            │    0    │         │       │\n",
       "│ 4 │ slope │   0.50    │   0.04    │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬────────────────────────────────────────────────────────┐\n",
       "│       │          s          b         mu      sigma      slope │\n",
       "├───────┼────────────────────────────────────────────────────────┤\n",
       "│     s │   3.35e+03     -1.5e3  -4.467e-3  61.232e-3    -1.1100 │\n",
       "│     b │     -1.5e3   2.46e+03   5.158e-3 -62.497e-3     1.0962 │\n",
       "│    mu │  -4.467e-3   5.158e-3   9.29e-06      -1e-6     -18e-6 │\n",
       "│ sigma │  61.232e-3 -62.497e-3      -1e-6   7.81e-06     -40e-6 │\n",
       "│ slope │    -1.1100     1.0962     -18e-6     -40e-6    0.00195 │\n",
       "└───────┴────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nll = ExtendedUnbinnedNLL(m2, model)\n",
    "mi2 = Minuit(nll, s=1000, b=1000, mu=0.5, sigma=0.1, slope=0.5)\n",
    "mi2.strategy = 0\n",
    "mi2.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.2536969037517682e-08)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# difference in number of parameters for H1 and H0\n",
    "ndof = (mi1.nfit + mi2.nfit) - mi0.nfit\n",
    "# test statistic, which is asymptotically chi-square distributed\n",
    "q = mi0.fval - (mi1.fval + mi2.fval)\n",
    "pvalue = chi2(ndof).sf(q)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(5.57275687575988)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm.isf(pvalue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the p-value is $1.2\\times 10^{-8}$, equivalent to a $5.5\\,\\sigma$ deviation from a normal distribution. In this case, we should reject the null hypothesis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Alternative: Kendall's tau test\n",
    "\n",
    "The Kendall's tau test is a simple test you can apply if you have pure samples from the signal and background components available. In general, you won't have these, because if you did, you would not need sWeights in the first place.\n",
    "\n",
    "A pure background sample can be obtained from data, by selecting samples from the side-bands around the signal peak. For the signal, you can usually only get it from Monte-Carlo simulation of the experiment. You need to trust the simulation then.\n",
    "\n",
    "The Kendall's tau test checks whether two variables are independent and returns a p-value for that null hypothesis. You should apply this test to each component. If the p-values for a component is very small, you cannot compute classic sWeights, although you can still use COWs after expanding the component into many sub-components. To apply the classic sWeights, all components must pass the test."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first apply the test to the signal and background samples in the original toy, where these components factorize, to see that it passes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sweights.independence import kendall_tau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.09029195168931155)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "m, t, truth_mask = toy_original\n",
    "\n",
    "m_sig = m[truth_mask]\n",
    "t_sig = t[truth_mask]\n",
    "\n",
    "# p-value for true signal\n",
    "val, err, pvalue = kendall_tau(m_sig, t_sig)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.7015075243963227)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_bkg = m[~truth_mask]\n",
    "t_bkg = t[~truth_mask]\n",
    "\n",
    "# p-value for true background\n",
    "val, err, pvalue = kendall_tau(m_bkg, t_bkg)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both components pass the test, neither p-value is very small ($\\ll 0.01$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Warning**: As already said, you cannot apply the test to the mixed sample. The mixed sample does not factorize, even if the components separately factorize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.00588671692380863)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this p-value is meaningless and likely going to be small\n",
    "val, err, pvalue = kendall_tau(m, t)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we apply the test to the modified toy which violates the factorization requirement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.9412926161716674e-24)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m, t, truth_mask = toy\n",
    "\n",
    "m_sig = m[truth_mask]\n",
    "t_sig = t[truth_mask]\n",
    "\n",
    "# p-value for true signal\n",
    "val, err, pvalue = kendall_tau(m_sig, t_sig)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.7015075243963227)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_bkg = m[~truth_mask]\n",
    "t_bkg = t[~truth_mask]\n",
    "\n",
    "# p-value for true background\n",
    "val, err, pvalue = kendall_tau(m_bkg, t_bkg)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that the signal component does not pass the factorization test, but the background does. That is exactly what we expect, since we only modified the signal component.\n",
    "\n",
    "As mentioned, a pure background sample can also be obtained by selecting events from the side bands without knowing true labels. We see that a sample from the side band passes our test, even though the signal region would fail it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.3855929053284022)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ma = (m < 0.2) | (m > 0.8)\n",
    "m_bkg = m[ma]\n",
    "t_bkg = t[ma]\n",
    "\n",
    "# p-value for background from side-bands\n",
    "val, err, pvalue = kendall_tau(m_bkg, t_bkg)\n",
    "pvalue"
   ]
  }
 ],
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