{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Moderne Methoden der Datenanalyse SS2024\n",
    "# Practical Exercise 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 4: Combination of correlated measurements\n",
    "\n",
    "A common problem in science is the combination of several measurements to one single result, e.g., the average value. Not only the uncertainties of the individual measurements have to be taken into account, but also the correlations between them. A wrong treatment of correlations or common systematic effects can lead to biased results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 4.1: Combination of *W* mass measurements (voluntary)\n",
    "\n",
    "At the LEP accelerator at CERN the mass of the *W* boson $m_W$ was\n",
    "  measured in two different channels:\n",
    "  \n",
    "  \\begin{eqnarray*}\n",
    "    e^+e^- &\\rightarrow \\ \\  W^+W^- \\  \\rightarrow& q_1 q_2 q_3 q_4 \\\\\n",
    "    e^+e^- &\\rightarrow \\ \\  W^+W^- \\  \\rightarrow& l \\nu q_1 q_2 \n",
    "  \\end{eqnarray*}\n",
    "  \n",
    "  The experimental signature in the detector for the first channel with four quarks are four reconstructed jets. The second channel is identified by a lepton (electron or muon) and two jets.\n",
    "  The neutrino is not detected. The measured *W* masses and the uncertainties are:\n",
    "  \n",
    "  \\begin{eqnarray*}\n",
    "    \\mbox{4 jets channel:} & \\,m_W = & \n",
    "    (80457 \\pm 30 \\pm 11 \\pm 47 \\pm 17 \\pm 17) \\mbox{ MeV} \\\\\n",
    "    \\mbox{lepton + 2 jets channel:} & \\,m_W = & \n",
    "    (80448 \\pm 33 \\pm 12 \\pm \\ 0 \\pm 19 \\pm 17) \\mbox{ MeV}\n",
    "  \\end{eqnarray*}\n",
    "  \n",
    "  To facilitate the interpretation of the results, different uncertainties are given, originating from different sources: The first two uncertainties are the statistical and systematic experimental\n",
    "  uncertainties, which are uncorrelated. The third uncertainty originates from the theory applied for the analysis and is only present in the first channel. The fourth uncertainty comes from a common theoretical model applied for both channels, and thus is 100\\% correlated. Also the last uncertainty is 100\\% correlated between both measurements, since it represents the uncertainty on the LEP accelerator beam energy.\n",
    "\n",
    "\n",
    "  - Construct a covariance matrix of the two *W* mass measurements taking into account all uncertainties and their correlations. Use this covariance matrix to define a $\\chi^2$ expression containing the average *W* mass $\\bar{m}_W$ as a free parameter. Determine $\\bar{m}_W$ and its uncertainty by minimizing the $\\chi^2$ expression using the IMinuit package.\n",
    "\n",
    "  For this exercise, you have to write your own $\\chi^2$-function to be minimized; see the previous exercise to learn how this can be done. There we have already used `iminuit`, however this time we'll be using the object-oriented interface. You can find some hints on how to use this in the documentation [here](https://iminuit.readthedocs.io/en/stable/notebooks/basic.html#Initialize-the-Minuit-object).\n",
    "  \n",
    "*Hint*: Make sure, that you are using a current version of `iminuit`, e.g. 2.11.2! Check this with the command in the next cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iminuit                      2.25.2\n"
     ]
    }
   ],
   "source": [
    "!pip list | grep iminuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from iminuit import Minuit\n",
    "from scipy.linalg import inv\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3687,  612],\n",
       "       [ 612, 1739]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u1 = np.array([30,11,47,17,17])\n",
    "u2 = np.array([33,12,0,19,17])\n",
    "mw = np.array([80457,80448])\n",
    "\n",
    "cov = np.array([[np.sum(u1[[0,2,3,4]]**2), np.sum(u1[[3,4]]*u2[[3,4]])],\n",
    "       [np.sum(u1[[3,4]]*u2[[3,4]]), np.sum(u2[[0,2,3,4]]**2)]])\n",
    "cov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def chi_square_creator(measurement_vector, inv_cov):\n",
    "    \n",
    "    # Using this outer function to pass the measured values (measurement_vector) and the inverse covariance matrix (inv_cov) to the function so we don't need to define them globally\n",
    "    \n",
    "    def chi_square_function(par):\n",
    "        #cnorm = np.sqrt(np.linalg.det(inv_cov)/4*np.pi**2)\n",
    "        #(measurement_vector - par)\n",
    "\n",
    "        #chi2_value = -(cnorm * np.exp(-1/2*np.sum((measurement_vector - par)*np.dot(inv_cov,measurement_vector - par))))**2\n",
    "        #print((measurement_vector - par), np.dot(inv_cov,measurement_vector - par))\n",
    "\n",
    "        chi2_value = np.sum((measurement_vector - par)*np.dot(inv_cov,measurement_vector - par))\n",
    "        \n",
    "        return chi2_value # return the chi2 value\n",
    "\n",
    "    return chi_square_function # return the function which calculates the value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "As this is using a different interface to IMinuit than in Exercise 3.2, here is a hint: These are the base two lines you'll need:\n",
    "\n",
    "```\n",
    "minuit_instance = Minuit(function, parametername=initial_parametervalue)\n",
    "res = minuit_instance.migrad()\n",
    "```\n",
    "\n",
    "The first line initializes the minuit object, gives the cost function and passes the initial parameter names and values.\n",
    "The second line performs the minimization using the `MIGRAD` algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = np.linspace(70000,90000,200)\n",
    "plt.plot(p, [chi_square_creator(mw, inv_cov)(pp) for pp in p])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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 = 4.587 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 15 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 6.12e-10 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </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> par </td>\n",
       "        <td> 8.23 </td>\n",
       "        <td> 0.12 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> par </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> par </th>\n",
       "        <td> 0.0136 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 4.587                      │              Nfcn = 15               │\n",
       "│ EDM = 6.12e-10 (Goal: 0.0002)    │                                      │\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 │ par  │   8.23    │   0.12    │            │            │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌─────┬────────┐\n",
       "│     │    par │\n",
       "├─────┼────────┤\n",
       "│ par │ 0.0136 │\n",
       "└─────┴────────┘"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO: Add code here to calculate the (inverse) covariance matrix\n",
    "# You can use scipy.linalg.inv to invert the matrix\n",
    "inv_cov = inv(cov)\n",
    "\n",
    "# Perform the minimization of the chi2 function\n",
    "minuit_instance = Minuit(chi_square_creator(mw, inv_cov), par=80400)\n",
    "\n",
    "# Get results of the minimization and plot or print them\n",
    "res = minuit_instance.migrad()\n",
    "res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "  - Because the minimization of the $\\chi^2$ expression in exercise 4.1 is a linear problem it can be solved analytically.  Determine\n",
    "  $\\bar{m}_W$ and its error analytically and compare them to the result from above.\n",
    "  \n",
    "**TODO:** Add your calculations here using the Latex syntax\n",
    "\n",
    "  - Estimate the contributions from statistical, systematic, theoretical, and accelerator based uncertainties to the error of the combined *W* mass measurement.  Use the quadratic difference between the total error and the error calculated with a covariance matrix where one component is removed.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: Add your code here to calculate the contribution of each uncertainty component"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 4.2: Normalisation uncertainty (obligatory)\n",
    "\n",
    "Two measurements $y_1=8.0$ and $y_2=8.5$ of the same physical\n",
    "  quantity with an uncorrelated relative statistical error of 2 %\n",
    "  and a common normalisation error of 10 % should be combined.\n",
    "  \n",
    "  -  Construct a covariance matrix and a $\\chi^2$ expression and\n",
    "  determine its minimum with `iminuit` or analytically. If you need hints on how to use `iminuit`, consult the exercises 3.2 and 4.1. \n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import ROOT # Only need for plotting... Feel free to replace the plot method with your own pure python implementation!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.6656, 0.68  ],\n",
       "       [0.68  , 0.7514]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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 = 4.386 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 11 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 8.64e-24 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </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> par </td>\n",
       "        <td> 7.9 </td>\n",
       "        <td> 0.8 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> par </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> par </th>\n",
       "        <td> 0.662 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 4.386                      │              Nfcn = 11               │\n",
       "│ EDM = 8.64e-24 (Goal: 0.0002)    │                                      │\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 │ par  │    7.9    │    0.8    │            │            │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌─────┬───────┐\n",
       "│     │   par │\n",
       "├─────┼───────┤\n",
       "│ par │ 0.662 │\n",
       "└─────┴───────┘"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import t\n",
    "\n",
    "cov = np.array([[(8*0.02)**2+(8*0.1)**2, (8*0.1)*(8.5*0.1)],\n",
    "               [(8*0.1)*(8.5*0.1), (8.5*0.02)**2+(8.5*0.1)**2]])\n",
    "\n",
    "display(cov)\n",
    "mw = np.array([8,8.5])\n",
    "\n",
    "def chi2_creator_4_2_1(measurement_vector, inv_cov):\n",
    "    \n",
    "    # We are using this outer function to pass the measured values (measurement_vector) and the inverted covariance matrix (inv_cov)\n",
    "    # to the function so we don't need to define them globally...\n",
    "\n",
    "    def chi2_function(par): \n",
    "        '''\n",
    "        calculate chi2 using 1 parameter for the mean\n",
    "        '''\n",
    "        #cnorm = np.sqrt(np.linalg.det(inv_cov)/4*np.pi**2)\n",
    "        #(measurement_vector - par)\n",
    "\n",
    "        #chi2_value = -(cnorm * np.exp(-1/2*np.sum((measurement_vector - par)*np.dot(inv_cov,measurement_vector - par))))**2\n",
    "        chi2_value = np.sum((measurement_vector - par)*np.dot(inv_cov,measurement_vector - par))\n",
    "        \n",
    "        return chi2_value # return the chi2 value\n",
    "    \n",
    "    return chi2_function\n",
    "\n",
    "# TODO: Add code here to calculate the (inverse) covariance matrix\n",
    "# You can use scipy.linalg.inv to invert the matrix\n",
    "inv_cov = inv(cov)\n",
    "\n",
    "# Perform the minimization of the chi2 function\n",
    "minuit_instance = Minuit(chi_square_creator(mw, inv_cov), par=8)\n",
    "\n",
    "# Get results of the minimization and plot or print them\n",
    "res = minuit_instance.migrad()\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "  message: Optimization terminated successfully.\n",
       "  success: True\n",
       "   status: 0\n",
       "      fun: 4.385964912280704\n",
       "        x: [ 7.874e+00]\n",
       "      nit: 1\n",
       "      jac: [ 0.000e+00]\n",
       " hess_inv: [[1]]\n",
       "     nfev: 6\n",
       "     njev: 3"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = np.linspace(5,10,200)\n",
    "plt.plot(p, [chi_square_creator(mw, inv_cov)(pp) for pp in p])\n",
    "plt.show()\n",
    "\n",
    "from scipy.optimize import minimize\n",
    "minimize(chi_square_creator(mw, inv_cov), x0=(8,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " - Is the result reasonable?  What could be the cause\n",
    "  for the unexpected value?  Make a plot of the covariance ellipse in\n",
    "  the $y_1^\\prime y_2^\\prime$ plane defined by\n",
    "  $$\n",
    "  \\Delta y^T V^{-1} \\Delta y = c^2, \\quad \\Delta y =\n",
    "  \\left( \\begin{array}{c} y_1-y_1^\\prime \\\\\n",
    "      y_2-y_2^\\prime \\end{array}\\right)\n",
    "  $$\n",
    "  for $c=1$ and $c=2$ together with the line $y_1^\\prime=y_2^\\prime$.\n",
    "  $V$ is the covariance matrix.  To draw the ellipse a TGraph\n",
    "  object can be used.  The points on the ellipse can be calculated as\n",
    "  a function of the angle $\\phi$ if $\\Delta y$ is expressed by $\\phi$\n",
    "  and the radius $r$.  You can use the function below to draw the ellipse.\n",
    "  Pay attention to where the bisector intersects with the ellipse."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Das Ergebnis ist nicht plausibel. Es sollte zwischen 8 und 8.5 liegen. Das Problem ist, dass die relative Unsicherheit relativ zum Messwert und nicht relativ zum tatsächlichen Wert betrachtet wird."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "\n",
    "def drawCovEllipse(CI: list, vec: list, mean: float):\n",
    "    '''\n",
    "    CI : inverse covariance matrix\n",
    "    vec: measured values i.e. [y1, y2]\n",
    "    mean: calculated mean value from chi2 minimization\n",
    "        \n",
    "    Draws and returns the covariance ellipses as well as the bisect line.\n",
    "    The outputs have to be stored in some variables or they will not be displayed.\n",
    "    '''\n",
    "    \n",
    "    npoints = 200\n",
    "    e1 = []\n",
    "    e2 = []\n",
    "    #ellipse1 = ROOT.TGraph(npoints + 1)\n",
    "    #ellipse2 = ROOT.TGraph(npoints + 1)\n",
    "    for i in range (npoints + 1):\n",
    "        phi = 2 * i * np.pi / npoints\n",
    "        V = [np.cos(phi), np.sin(phi)]\n",
    "        v = np.matrix(V)\n",
    "        sp = np.dot(v, np.dot(CI, v.getT()))\n",
    "        R = np.sqrt(1.0 / sp)\n",
    "        with warnings.catch_warnings():\n",
    "            warnings.simplefilter(\"ignore\")\n",
    "            e1.append( (float(vec[0] + R * V[0]), float(vec[1] + R * V[1])) )\n",
    "            e2.append( (float(vec[0] + 2 * R * V[0]), float(vec[1] + 2 * R * V[1])) )\n",
    "        #ellipse1.SetPoint(i, vec[0] + R * V[0], vec[1] + R * V[1])\n",
    "        #ellipse2.SetPoint(i, vec[0] + 2 * R * V[0], vec[1] + 2 * R * V[1])\n",
    "\n",
    "    #print(*zip(*e1))\n",
    "    plt.plot(*zip(*e1))\n",
    "    plt.plot(*zip(*e2))\n",
    "\n",
    "    a,b = np.min([e1,e2]),np.max([e1,e2])\n",
    "    a = a\n",
    "    b = b\n",
    "    \n",
    "    plt.plot([a,b],[a,b])\n",
    "    plt.scatter([mean],[mean])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "drawCovEllipse(inv_cov, mw, res.params[\"par\"].value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "  - Use an additional normalisation parameter $N$ for the treatment of\n",
    "  the common normalisation uncertainty $\\sigma_{norm}$ instead of\n",
    "  taking it into account in the covariance matrix of $y_1$ and $y_2$.\n",
    "  Add a term to the $\\chi^2$ expression for the normalisation with an\n",
    "  expected value of 1 and an error of 10 %.  The normalisation\n",
    "  factor $N$ can be applied either to the measured values $y_i$ or to\n",
    "  the fit parameter $\\bar{y}$.  Try out both ways (using\n",
    "  `iminuit` for the $\\chi^2$ minimisation) and compare the\n",
    "  results.  Which one is the more meaningful result and why?\n",
    "  \n",
    "  Determine $\\bar{y}$ from the correct $\\chi^2$ expression in an analytical way.  How does the normalisation error affect\n",
    "  the averaged value and its error?\n",
    "  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{aligned}\n",
    "0 &= \\frac{\\partial\\chi^2}{\\partial p} = -\\frac{2 n (-n p + x1)}{\\sigma_x^2} - \\frac{2 n (-n p + x2)}{\\sigma_x^2}\\\\\n",
    "0 &= (-n p + x1) + (-n p + x2)\\\\\n",
    "p &=  \\frac{x1 + x2}{2 n}\\\\\n",
    "\\Rightarrow \\chi^2 &= \\frac{(n-1)^2}{\\sigma_n^2}+\\frac{(\\text{x1}-\\text{x2})^2}{2 \\sigma_x^2}\\\\\n",
    "0 &= \\frac{d\\chi^2}{d n} = \\frac{2 (n-1)}{\\sigma_n^2}\\\\\n",
    "\\Rightarrow n &= 1\\\\\n",
    "\\Rightarrow p &= \\frac{x1 + x2}{2}\n",
    "\\end{aligned}\n",
    "\n",
    "Nach Mathematica gilt folgt:\n",
    "\n",
    "\\begin{aligned}\n",
    "& \\chi^2(\\frac{x1 + x2}{2n}, n) =  \\chi^2(\\frac{x1 + x2}{2}, 1) + 1\\\\\n",
    "\\Rightarrow n &= 1 \\pm\\sigma_n\n",
    "\\end{aligned}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.0256, 0.    ],\n",
       "       [0.    , 0.0289]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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 = 4.386 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 34 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 4.2e-20 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </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> par </td>\n",
       "        <td> 7.9 </td>\n",
       "        <td> 0.8 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> N </td>\n",
       "        <td> 0.96 </td>\n",
       "        <td> 0.10 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> par </th>\n",
       "        <th> N </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> par </th>\n",
       "        <td> 0.662 </td>\n",
       "        <td style=\"background-color:rgb(250,102,102);color:black\"> 0.079 <strong>(0.990)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> N </th>\n",
       "        <td style=\"background-color:rgb(250,102,102);color:black\"> 0.079 <strong>(0.990)</strong> </td>\n",
       "        <td> 0.00956 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 4.386                      │              Nfcn = 34               │\n",
       "│ EDM = 4.2e-20 (Goal: 0.0002)     │                                      │\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 │ par  │    7.9    │    0.8    │            │            │         │         │       │\n",
       "│ 1 │ N    │   0.96    │   0.10    │            │            │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌─────┬─────────────────┐\n",
       "│     │     par       N │\n",
       "├─────┼─────────────────┤\n",
       "│ par │   0.662   0.079 │\n",
       "│   N │   0.079 0.00956 │\n",
       "└─────┴─────────────────┘"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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 = 4.587 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 45 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 2.1e-06 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </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> par </td>\n",
       "        <td> 8.2 </td>\n",
       "        <td> 0.8 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> N </td>\n",
       "        <td> 1.0 </td>\n",
       "        <td> 0.1 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> par </th>\n",
       "        <th> N </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> par </th>\n",
       "        <td> 0.693 </td>\n",
       "        <td style=\"background-color:rgb(121,121,250);color:black\"> -0.083 <strong>(-0.990)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> N </th>\n",
       "        <td style=\"background-color:rgb(121,121,250);color:black\"> -0.083 <strong>(-0.990)</strong> </td>\n",
       "        <td> 0.01 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 4.587                      │              Nfcn = 45               │\n",
       "│ EDM = 2.1e-06 (Goal: 0.0002)     │                                      │\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 │ par  │    8.2    │    0.8    │            │            │         │         │       │\n",
       "│ 1 │ N    │    1.0    │    0.1    │            │            │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌─────┬───────────────┐\n",
       "│     │    par      N │\n",
       "├─────┼───────────────┤\n",
       "│ par │  0.693 -0.083 │\n",
       "│   N │ -0.083   0.01 │\n",
       "└─────┴───────────────┘"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cov = np.array([[(8*0.02)**2, 0],\n",
    "               [0, (8.5*0.02)**2]])\n",
    "\n",
    "display(cov)\n",
    "mw = np.array([8,8.5])\n",
    "\n",
    "def chi2_creator_4_2_2(measurement_vector, inv_cov, sigma_norm):\n",
    "   \n",
    "    # Now we additionally have to set the normalisation uncertainty sigma_norm in the cost function.\n",
    "\n",
    "    def chi2_function(par, N):\n",
    "        '''\n",
    "        calculate the chi2 including an additional parameter for the normalization of the measured values (version 1)\n",
    "        '''\n",
    "        chi2_value = np.sum((measurement_vector*N - par)*np.dot(inv_cov,measurement_vector*N - par)) + (N-1)**2/sigma_norm**2\n",
    "        \n",
    "        return chi2_value # return the chi2 value\n",
    "    \n",
    "    return chi2_function\n",
    "\n",
    "def chi2_creator_4_2_3(measurement_vector, inv_cov, sigma_norm):\n",
    "    \n",
    "    def chi2_function(par, N):\n",
    "        '''\n",
    "        calculate the chi2 including an additional parameter for the normalization of the mean value (version 2)\n",
    "        '''\n",
    "        chi2_value = np.sum((measurement_vector - par*N)*np.dot(inv_cov,measurement_vector - par*N)) + (N-1)**2/sigma_norm**2\n",
    "        \n",
    "        return chi2_value # return the chi2 value\n",
    "    \n",
    "    return chi2_function\n",
    "\n",
    "inv_cov = inv(cov)\n",
    "\n",
    "minuit_instance1 = Minuit(chi2_creator_4_2_2(mw, inv_cov, 0.1), par=8, N=1)\n",
    "res1 = minuit_instance1.migrad()\n",
    "display(res1)\n",
    "\n",
    "\n",
    "minuit_instance2 = Minuit(chi2_creator_4_2_3(mw, inv_cov, 0.1), par=8, N=1)\n",
    "res2 = minuit_instance2.migrad()\n",
    "display(res2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ par  │    7.9    │    0.8    │            │            │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ par  │    8.2    │    0.8    │            │            │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "drawCovEllipse(inv_cov, mw, res1.params[\"par\"].value)\n",
    "display(res1.params[\"par\"])\n",
    "drawCovEllipse(inv_cov, mw, res2.params[\"par\"].value)\n",
    "display(res2.params[\"par\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Construct a covariance matrix of $y_1$ and $y_2$ containing the\n",
    "  normalisation uncertainty of 10\\,\\% relative to the average value\n",
    "  $\\bar{y}$.  Solve the corresponding $\\chi^2$ minimisation with\n",
    "  `iminuit` and plot the covariance ellipse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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 = 4.587 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 12 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 7.85e-05 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </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> par </td>\n",
       "        <td> 8.2 </td>\n",
       "        <td> 0.8 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> par </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> par </th>\n",
       "        <td> 0.688 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 4.587                      │              Nfcn = 12               │\n",
       "│ EDM = 7.85e-05 (Goal: 0.0002)    │                                      │\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 │ par  │    8.2    │    0.8    │            │            │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌─────┬───────┐\n",
       "│     │   par │\n",
       "├─────┼───────┤\n",
       "│ par │ 0.688 │\n",
       "└─────┴───────┘"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.233675329754469 1.0001379297899027\n"
     ]
    },
    {
     "data": {
      "image/png": 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3RaQw5JGwBOc2w/yHIeEsuFWHIX9Bs75apxKi4Bzd4YVl8NA49f0dn8HyvpCVom0uITSUnJ3Me5vfY+bumeSYc3jI9yFWBK2gaeWmWkezOFJGtLb3O1j0DGQmQbXWMPRv8ArQOpUQhafTqWuP9F6gnmwvYj18+9jNM0gLYUWOXDvCs2ue5a/IvzDqjYx6YBSfPPQJbnZuWkezSFJGtGI2qScl++1dUEzqeWUGrAHnylonE+L+NHoGBq4FZy+IPQbfPAyXdmudSohSoSgKPxz7gZfWv0RUahQ+zj4s6raIFxu+iE4OQrgjKSNayM1Wd/jb+YX6/kPj4ZmvwcZe21xCFJdqLW+M8jWGtGuwMAhO/6V1KiFKVFJWEm///TYhe0PINefStUZXVgatpFGlRlpHs3hSRkpbTias6A/HV4PeRh3S7jRCDtsV5Y9bNRi8Huo8pp5LadnzcGKN1qmEKBEHYw/Se01vNl/ejI3ehnFtxvFRp49wsZW1dwpCykhpykqFpX3UuXSjPbywXB3SFqK8snOG5xZDw6fU0xmsGACHV2idSohiY1bMfHf0OwauH0hMWgzVXaqzpPsSnq//vEzLFIKswFpaMpNgSR+4tAtsnaHvj+DXXutUQpQ8oy30/g5+dYKDS9SVW3PSoeVArZMJcV8SMhMYFz6O8KhwALrV7MaktpNwsnHSOFnZI2WkNKQnwKKnIPoQ2LupK1dWa6V1KiFKj94AT3wGNg6wZz6sGQ45GfDga1onE6JI9l3dx8iwkcRmxGJnsGN069H0qtNLRkOKSMpISctKVUdEog+BYyV4aTVUaax1KiFKn14P3UPVRf22fwrrR6vXZbVWUYaYFTPzj8zn84OfY1bM+Ln6EdoplHru9bSOVqZJGSlJuVnw44sQtRccKsLA38CzgdaphNCOTgddP1DfbvsEfntH/dto+ITWyYS4p7iMOMZuHcuO6B0ABNUKYvyD43G0cdQ4WdknZaSkmE3wy6vqWU1tnKDfKikiQoBaRLpMgYzrsP8H+OllsF8FtTppnUyIO9oVvYvRW0cTlxGHg9GBsW3G8lTtp7SOVW7I0TQlQVHg9/fh2C/q4bvPL5Z9RIT4J50Oen4MDYLAlK0uHR+1X+tUQvyHyWzii4NfMPTPocRlxFG7Qm2W9VgmRaSYSRkpCZtmwL4FgA56fQP+D2udSAjLozdAr2+hZifIToXFvSDutNaphMh3Lf0ar2x4hXmH5qGg8EydZ1jaYyn+Ffy1jlbuSBkpbkdWwZbZ6vWe/4OAp7XNI4QlM9rB80vAuwVkJMCyF9TD4IXQ2Pao7fRe05vdMbtxMDows8NMpgROwcHooHW0cknKSHGKPgT/96Z6vf270GqQtnmEKAvsXKDvCnCtBvGn4aeh6j5XQmgg15zLp/s/Zdhfw0jITKBuxbr82PNHetbqqXW0ck3KSHFJvQbL+0FuBtTuCg9P0DqREGWHc2V13yqjPZz+AzZN1zqRsEIxaTG8/MfLfHPkGxQUnq37LEu6L6GmW02to5V7UkaKgykHVg6EpEvg7g+95qvz4UKIgvNuDk/MVa9v/UjdAVyIUrLl8hb6rOnD/tj9ONk4EdIxhAltJ2BvlBOYlgY5tLc4/DEWLoaDrQu8sAwcKmidSIiyqcmz6nTnjs9g9evgUQeqyBlPRcnJMecwd/9cFhxbAEAD9waEdgqlumt1jZNZFykj9+vEGtj9tXr9ma+hsqzCpzVFUUjPNpGQls319Gwyc8xk55rJNpnIzlXQ68DWqMfWqMfOqMfZzoaKTjZUdLTFxiCDhZrrMgWuHlPX6Fk1CF4JA1tZVEoUv+jUaEZsGcGha4cA6Fu/L++3eh9bg63GyayPlJH7kRIDv76tXm83HOp31zaPFcnONXM6NoVTMSlEJqQTmZDOpYR0Ll/PID4tm+xcc5E+r6u9EU9Xe6q7O1Ld3RFfd0dqVnKkYVU3vFzt5LwTpcFgVE+s90VbiIuAvyZB9xCtU4lyZlPkJsZvG09ydjIuNi580O4DutToonUsqyVlpKgURR1GzkhQzzXz0HitE5VbiqJwLi6NXecS2B95nWNXkjkTm0KOSbnrdnZGPe5OtjjYGLAxqCMhNgYdZoUbIyXqiElqVi7X07NRFEjOzCU5M5Uzsan/+XweTrY09HYlwNuNNjXdaelXEVd7m5L6tq2bozs89bm69sjur6HOo1Cnq9apRDmQY8phzr45LD6xGIBGHo0I6RRCNZdqGiezbjpFUe7+H90CJCcn4+bmRlJSEq6urlrHUe36GtaNUPf+fyUMPOtrnahciUvN4u+TsYSdusau8wnEpWb95z6u9kbqV3WlpocT1T1ujmRUcrbF3ckWR9uCd22TWSE5I4f4tGxikjLzR1siE9I4E5vK2WtpmMy3/qnoddDQ25VA/0o8XN+TVjUqYpRpnuK1bhTs+hKcveC17eBUSetEogy7nHKZEWEjOBp/FICXGr7EOy3ewcYgLypKSkGfv6WMFEXsSfi6E+RmQrcQaPOK1onKhcvX0/n10BX+On6VA5cS+edvpq1RT3PfCrSu6U5jHzcaerviU8Gh1KZNMnNMRFxN4diVZA5EXmfX+QQuxqffch83BxseqleZxxtV4aH6ntgZ5Yiq+5aTAV93hmsnoX5PeG6xupS8EIW04eIGJm2bREpOCq62rkxvP53Ovp21jlXuSRkpKWYzfNsFovZB7S7qCfDkn2ORJWfmsO5IND/tj2L3+YRbPtbIx5WH63vRzt+Dpr4VsLexrCf3mKRMdp2PJ+zUNTadiuV6ek7+x9wcbOjRpCq9WvjQonpF2dfkfkQfhm8eBnMOPDMfmvTROpEoQ7JMWYTuCWX5qeUANK3clJCOIVR1rqpxMusgZaSk7F2gnvbc1gXe3AOu8gtdFKevpvD99gv8vD+KjBx1tU2dDtrW8qB746o80sCTqm5lZ9llk1lhf+R1/jwWw5pD0cQkZ+Z/rK6XMwMC/Xi6uU+hpo7EP4SFwKZp6nTNm3vA3k3rRKIMiEyOJDgsmBMJJwAY1GgQbzV/Cxu9TMuUFikjJSEtDua2hMxEePxDePA17bKUQYqiEH4mjq/CzhF+Ji7/9tqezvRqUY0nm3njXaHsFJA7MZkVdp6L56f9l1l/NIb0bLVsudobeaF1dV7uUBNPF1lIqVBys2BeIMSfgTavQbcPtU4kLNy68+uYsmMKaTlpVLSryPT20+lQrYPWsayOlJGS8H9vwIHF4NUYXtmsHoIo7klRFLacjuOTvyLYH5kIqDt/dm3oxcDAmjxYy73cTmMkZeSwat9lFm6/QGSCuo+JnVHPiw/W4NVOtaSUFMbZv2HR06DTqzuNV22idSJhgTJzM5m1ZxarIlYB0MKzBbM7zsbLyUvjZNZJykhxi9wF3z2qXh/8J1Rvo02OMubgpUSm/nacfRevA+oTcd821Xm5fU2qVbSehazMZoVNp2L5bNMZDtwoZHZGPYPb1+SNh2rjbCfFtkBWDIDjq6Faaxj8B+jl6CVx0/mk8wSHBRNxPQIdOoY2GcprTV/DqJe/L61IGSlOZjN83RFijkCzF9X1D8RdxSRlMnv9SX4+EAWAvY2efm1kNEBRFLaejuPjf4wSVXK2Y+Rj9ejdshp6ffkcISo2SVHw2QOQkwZPfgHN+2mdSFiINWfXMHXnVDJyM3C3d2dmh5kEegdqHcvqSRkpTkdWwU8vg50bvL1f1jq4C5NZ4YcdFwj541T+vhK9W1ZjxGP18HK13hLyb4qisPFELNPXnuB8XBoATX0rENK7CXW9XDROZ+HCP1ZXZXXzhbf2gdFO60RCQxm5GczYNYPVZ1YD0LpKaz7s8CGVHStrG0wAUkaKjykXvmij7jj30DjoNLJ0v34ZciY2hVE/HcmfkmlZoyKTghrSpFoFbYNZsOxcMz/suMAnf50mJSsXG4OONx+qw2ud/bE1yhTEbeVkwKfNISUauodC66FaJxIaOXP9DMFhwZxNOotep2dY02G80vgVDHLWdIshZaS4HFwKq18DB3cYfgjsLWDRNQujKAqLdl5k2u8nyM4142xnZHS3+vRtXV2mHQooJimT8auP8NeJWAACvF35rG8LalZy0jiZhdr9DawNBucqMPwg2JT9o7BEwSmKwuozq5mxawaZpkwqOVRidsfZPFDlAa2jiX8p6PO3vPS6m9xs2HzjEML270gRuY2kjBxeW7yfif93jOxcM53qVubPdzvy4oM1pIgUQhU3e755qRWfvtCcio42HLuSTM9Pt/J/B6O0jmaZWrwEbtUhNQb2fKt1GlGK0nPSGRc+jonbJ5JpyiTQO5BVQaukiJRxUkbu5uBiSLwITp7wgAwF/9vJmGR6fLqV9cdisDHomNCzId8PeqBcrBWiBZ1OxxNNvVk3vCOta7qTlm1i+PKDjPvlCDmmop2FuNwy2t2cMg2fA1n/PbGhKH9OJZziud+eY825Neh1et5u/jbzuszDw8FD62jiPkkZuROzCbb+T73e4X2wtZ7DUAti44mr9PpiO5evZ+Dr7sCqYYG83L5muV0vpDRVcbNn6ZA2vP1IHXQ6WLIrkoELdpP0j+XmBdD0BXCvBenxsO97rdOIEqQoCisjVtL3975cSL6Ap6Mn3z32HUObDEWvk6ex8kB+indyah0kRYJDRWg5QOs0FmXBtvMM+WEvadkm2tbyYM2b7WnqW0HrWOWK0aDnva51+bp/KxxtDWw7E8/TX2wj8l8n57NqBiMEvq1e3/ON+gJClDup2amM2jKKD3Z8QLY5mw4+HVgVtIqWXi21jiaKUaHKiMlkYsKECdSsWRMHBwf8/f2ZOnUq99oHNisri3HjxlGjRg3s7Ozw8/Pju+++u6/gJW73V+rblgNl57gbFEXhk79OM2XNcRQFXmjtyw8vt6aCo63W0cqtrg29WDUsEG83e87FpdHnq+2ciZUpiXxNngX7CnD9ApzeoHUaUcxOxJ/gud+eY92FdRh1Rt5r+R6fPfIZFe0rah1NFLNCLUs3a9Ys5s2bx8KFCwkICGDv3r0MGjQINzc33n777Ttu9+yzz3L16lW+/fZbateuTXR0NGazBc+BXz0O57eoy063elnrNBZBURQ+XH+Sr8LOAfBe17q89XBtmZYpBQ29XVn9Rjv6zd/F6dhUnvtqBz+83JoAbzlZHLZO6s6s2z+FXV9Cvce1TiSKgaIoLD+1nJA9IeSYc6jqVJXZHWfTzLOZ1tFECSlUGdm+fTtPPvkkPXr0AMDPz49ly5axe/fuO26zfv16wsLCOHfuHO7u7vnbWbTdX6tv6/eECr7aZrEQoX+eyi8i43s0YEiHWhonsi6ervb8+GpbXvpuF0ejknlx/i5WDmtLbU9ZII0HhsCOz+DcJrh2CirX0zqRuA/J2clM3j6ZDRfVka7Ovp2Z1m4abnZSvsuzQk3TBAYGsnHjRiIiIgA4dOgQ4eHhdOvW7Y7b/Prrr7Rq1YrZs2fj4+ND3bp1CQ4OJiMj447bZGVlkZycfMul1GQkwuEf1ettXi29r2vB5m89x+ebzgIw9alGUkQ04u5ky9KhD9K0mhvX03Po/+1uohLv/HdkNSrWgHrd1et5LyREmXQ07ijPrnmWDRc3YNQbGfXAKD596FMpIlagUGVk9OjRPP/889SvXx8bGxuaN2/OO++8Q79+dz4/xLlz5wgPD+fo0aP88ssvfPzxx6xatYrXX3/9jtvMnDkTNze3/IuvbymOThz/P8hJh8oNoEa70vu6Fmr1gSim/X4CgBGP1aP/gzU0TmTdXO1tWDCoNf6VnYhOyqT/t7vkKBtQR0dAPXVDbra2WUShKYrCouOL6L+uP1GpUfg4+7Co2yJebPiiTAVbiUKVkRUrVrBkyRKWLl3K/v37WbhwIaGhoSxcuPCO25jNZnQ6HUuWLKF169Z0796dOXPmsHDhwjuOjowZM4akpKT8y6VLlwr3Xd2Po+ppp2nyLFj5H8GhS4mM/OkwAC+3r8nrnf01TiRAHSFZ9HIbdafWa2m8uWw/JrPFL6Rcsmp2VFdjzUyEs39rnUYUQlJWEm9vepvZe2aTa86la42urAhaQaNKjbSOJkpRocrIiBEj8kdHGjduTP/+/Xn33XeZOXPmHbepWrUqPj4+uLndHGZr0KABiqJw+fLl225jZ2eHq6vrLZdSkRID57eq1xs9Uzpf00LFpmTy6qJ9ZOea6dLAk3HdG8grFAviXcGBbwa0wt5Gz9bTccxef1LrSNrSGyDgafX60Z+0zSIK7GDsQfqs6cPmS5ux0dswts1YPur0Ea62stq1tSlUGUlPT0evv3UTg8Fw1yNj2rVrx5UrV0hNvXk4YkREBHq9nmrVqhUybgk7thpQwKcVVPTTOIx2zGaFd388SExyJv6Vnfjfc81kaXcLFODtRkjvpgB8teUcG45f1TiRxhr1Ut+e/B2yZT0WS2ZWzCw4uoBB6wcRnRZNdZfqLOm+hBfqvyAveqxUocpIUFAQ06dP5/fff+fChQv88ssvzJkzh6effjr/PmPGjOGll17Kf79v3754eHgwaNAgjh8/zpYtWxgxYgSDBw/GwcHC1u/Ie0XVuLe2OTT23bbzbDsTj4ONga/6t8LF3kbrSOIOgpp6M6R9TQBG/3SYaylZGifSULVWUKE65KTB6T+0TiPu4Hrmdd7c+CZz9s0hV8mlm183fuz5Iw08GmgdTWioUGVk7ty59O7dm9dff50GDRoQHBzMq6++ytSpU/PvEx0dTWRkZP77zs7ObNiwgcTERFq1akW/fv0ICgri008/Lb7vojgkXYbLuwEdNHxK6zSaORmTzOz1pwCY0LMhtT2dNU4k7mXE4/WoX8WF+LRsRv10+J6LEJZbOt3N0ZGjP2ubRdzWvqv76L2mN1ujtmJnsGNi24nM6jgLZ1v5P2PtdEoZ+M9V0FMQ35f9P8Cvb0G11jDEOldyNJsVen+5nf2RiXRp4Mk3L7WSIdMy4lRMCkGfhZOda+azvs3p2cRb60jauLwX5j8Cdm4w6ry6L4nQnFkx8+2Rb/n84OeYFBN+rn6EdgqlnrusCVPeFfT5W85Nk+fcZvWt/0OaxtDSyn2X2B+ZiJOtgWlPNZYiUobUq+LCG51rAzD1t+OkZuVqnEgj3s3VIpKVBFcOap1GAPEZ8QzbMIxPD3yKSTERVCuIH3v+KEVE3ELKCIDZDOfC1Ou1OmsaRStJGTl8uE49IuPdrnWp4mavcSJRWK92qkUND0euJmfx6cbTWsfRht4ANTuo189t0jaLYHf0bnqv6c2O6B3YG+z5IPADprefjqONnAVd3ErKCEDsMUiPAxsn9UgaK/Tt1nNcT8+htqczAwL9tI4jisDexsDkoAAAFm6/wNXkTI0TaSTvBUXeaKcodSaziXkH5zF0w1DiMuLwd/Nnec/lPF3naRlxFbclZQRu/tPyawdG6zsDbUJaNt9tuwDA+13rYmOQX4uyqnO9yrSqUZGsXDOfbzqjdRxt1Lox1Xpplxziq4Fr6dd4dcOrfHHoC8yKmadrP82ynsvwryCLJoo7k2cdgAvh6tuanbTNoZHvws+TmpVLgLcrjwVU0TqOuA86nY73H1Xn4pftjrTO0REPf3D1AVM2XN6jdRqrsv3Kdnqv6c2umF04GB2Y0X4GH7T7AAejhS3jICyOlBGAaHXJc6pZ3xRNZo6JJbsuAvDmQ7VlcbNyoK2/B61qVCTHpLBk50Wt45Q+nQ58WqrXYw5rm8VK5Jpz+XT/pwzbMIyEzATqVqzL8p7LCfIP0jqaKCOkjKTFQcoV9bpXgLZZNPDroStcT8/Bp4IDXRt6aR1HFJNB7dSF0JbujiQr16RxGg1UaaK+jTmibQ4rEJMWw8t/vMw3R75BQaFP3T4s6b6EWm5ydm9RcEatA2gu75+Vey2wc9E2iwaW7VYXqHvxwRoYZV+RcuPRAC+qutkTnZTJn8euEtTUytYdqdJYfStlpERtvbyVseFjScxKxMnGiUltJ9GtZjetY4kySJ598oZx8/55WZFLCekciExEr4NeLX20jiOKkY1Bz9PN1Z/pmkNXNE6jgby/52unIOf2ZwcXRZdjzmHOvjm8vvF1ErMSaeDegBU9V0gREUUmZSTvlVPesK4VWXNYfZJ6sJYHni6yrkh5kzcasvnUNZIycjROU8pcvcHRAxQTxJ7QOk25Ep0azaD1g1hwdAEAL9R/gUXdF1HdtbrGyURZJmXk2o1Tr1vh/iJ5Z3m12qXDy7n6VVyo7elMtslMWMQ1reOULp0OPBuq16+d0jZLObIpchO91/Tm0LVDuNi4MKfzHMa2GYudwU7raKKMkzKSFKW+dfPVNkcpS8rI4dClREBdm0KUPzqdjs511Z/t9jNxGqfRQIUbr9STL2uboxzIMeUwe89s3t70NsnZyTTyaMSPQT/StUZXraOJcsK6y0h2OmQkqNfdrGufiZ3n4jErUKuyE94VZA2A8qpdnUoAbD0dZ31n83W98Ted94JDFMnllMsMWD+ARccXAdC/YX9+6PYDvi7W9QJOlCzrPpomJVp9a+ME9hU0jVLa9l+8DkDbWh4aJxElqbWfO3odRCVmEJuShZerFe0blPcCI9kKd+AtJn9d/IuJ2yaSkpOCq60r09pN46Hq1nsyUVFyrLuMJN0YvnXzUeeYrcixK8kANPZx0ziJKElOdkb8KztzOjaV41eSrauMuFZT3ybLyEhhZZuyCd0byrKTywBoWrkpszvOxttZ9i8TJcO6p2ny/km5WtcfmKIoHI9Wy0hDb1eN04iSFnDjZ3zsSpLGSUpZ3t91kuwzUhiRyZG8uPbF/CIyqNEgFjy+QIqIKFHWPTKSHq++dfLUNkcpS8rIISEtG4A6nta30Ju1qeOl/ozPxaVpnKSUOd/4u85MBLMJ9AZN45QF68+vZ/KOyaTlpFHBrgLT20+nY7WOWscSVsC6y0jOjZOI2Tpqm6OURSep37e7ky0OtvIPurzzubGDckySlZ00z+YfO2bnZoKtk3ZZLFxmbiaz98xmZcRKAFp4tmBWx1lUcZITZ4rSYeVl5Mbpxa3sjJLRSeqKlFXdrGj/AStW5cbPOdraysg//65zMqSM3MH5pPMEhwUTcT0CHTqGNB7C681ex6i37qcHUbqs+7ct98Y/ZxvrKiPX09TVON2dbDVOIkpDJWf153w9PVvjJKVMrwejvfp3nvfCQ9xizdk1TN05lYzcDNzt3ZnZYSaB3oFaxxJWyLrLSN4/KCsrI5k3zuLqYCNTNNbAzqj+nBPTc1AUBZ01HTmW94IjK1XbHBYmIzeDmbtm8suZXwBoXaU1H3b4kMqOsgCi0IaVl5Eb/6iM1jVdkZGtlhF7KSNWwWS+udhZZo7ZOvcTuhAOXg21TmERziaeJTgsmDOJZ9Ch47Wmr/FKk1cwyA6+QkPWXUaslFW9MhYCrG4doTtZfWY103dOJ9OUSSWHSszqMIvWVVtrHUsIKy8jedMzuda1Y5+9jbq8TGaOSeMkojQY9OoTsb2N3vpGRWycICcNanXWOomm0nPSmb5rOr+e/RWAtlXbMqPDDCo5VNI4mRAqKSNgdTu35e0rkiFlxCrklU6rnJYz56pvrWwq9p8irkcQHBbM+aTz6HV63mz2Ji83fhm9zrrXvBSWRcoIqIf9WZGKN46iiUu1sqMrrNS11CzACo+eMpvApH7v2FjXWkKgrrT80+mf+HD3h2SZsvB09GR2x9m09GqpdTQh/sO6y4jROsuIt5v6feetNyLKt+hEdRoy7+duNf45/WpjXSMjqdmpfLDjA9ZdWAdAe5/2zGg/g4r2FTVOJsTtWXcZsdJpmqoV1H/Miek5pGXl4mRn3b8G5d2VRCtd5C77H3/XVrSw4Yn4EwSHBROZEolBZ2B4i+EMCBgg0zLColn3b6fTjWPqU69qm6OUudrbUNnFDoBTV1M0TiNKWt7P2N/TWeMkpSzv79rRQ10ArZxTFIXlJ5fTb20/IlMiqeJUhe8f/55BjQZJEREWz7p/Q/PP6ml9pxhvWFU9k+vxK8kaJxElLe9nnPcztxpWdFbulOwU3g97n+m7ppNjzqGzb2dWBa2imWczraMJUSDWPT7v5qO+Tb4CimJVaxE09HYlLOIaRy5b2WnlrUxyZg7n49Wz9Tb0ttYyUk3bHCXsaNxRgsOCiUqNwqg38l7L93ixwYuynpAoU6x7ZMTlxium3AzIuK5tllLW2s8dgB3n4jVOIkrSrnMJKArUrOREJWc7reOUrrwRz7wXHeWMoigsPr6Y/uv6E5UahY+zD4u6LaJ/w/5SRESZY90jIzb24FgJ0uMg6TI4umudqNS0rumOUa8jMiGdyPh0qntY36GP1mDbmTgA2tX20DiJBsrxNE1SVhITtk1g06VNAHSp3oUp7abgamtlo1+i3LDukREAtxtDuImR2uYoZU52RlpUVw/z23QqVuM0oiQoipL/s23nb4Urbeb9TZezaZpD1w7RZ00fNl3ahI3ehrFtxjKn8xwpIqJMkzLi2UB9e/WYtjk08GiAFwBrDl3ROIkoCYcvJ3ExPh17Gz0d61rZ2VgVBa4eVa/n/Y2XcWbFzPdHv2fguoFEp0Xj6+LL4u6LeaH+CzItI8o8KSNVGqtvYw5rm0MDPZt4o9PB3ovXiUqUBdDKm7yS2aWBl/WtJZN0CTKTQG8Dletrnea+Xc+8zlt/v8VH+z4iV8nlcb/HWdFzBQ095EzEonyQMmLFZaSKm33+jqwr917SOI0oTlm5Jn45oO4z8UTT8rfPxD1F3/h7rlwfjGV7Gfz9V/fTe01vtlzegq3eloltJzK742ycba1s3RhRrkkZySsjiZGQkahpFC30e7AGAIt3RpKda9Y4jSguvx2KJj4tm6pu9jxc31PrOKUv5oj6tmoTbXPcB7NiZv6R+Qz+YzCx6bH4ufqxtMdS+tTtI9MyotyRMuJQEdyqq9fz5pitSLdGVfBytSMuNYvfj8i+I+WBoigs2H4egBcfrIHRYIV/5nllJO/FRhkTnxHPa3+9xif7P8GkmOhZqyc/9vyReu71tI4mRImwwv9St5H36unSbm1zaMDGoKf/jdGRz/4+g8msaJxI3K9Np2I5GpWMvY2e5x/w1TpO6VMUiNqrXq9S9kZG9sTsoc+aPmy/sh17gz0fBH7AjPYzcLTCMw8L6yFlBMCvg/r2fJi2OTTyUqAfFRxtOHstjf87aH1L45cniqLw0Z8RAAxo64eHtS10BhB7Qj0vjdEBfFpqnabATGYT8w7NY8ifQ7iWcQ1/N3+W9VjG03WelmkZUe5JGQGo1Vl9e3EH5FjfUSWu9ja82tEfgP/9FUFmjknjRKKofj8SzbEryTjZGni1k7/WcbRxbrP6tkZbdWHDMiAuI45XN7zKFwe/wKyYear2UyztsZTaFWtrHU2IUiFlBKByPXCuAqYsuLRL6zSaGBBYAy9XOy4lZPBl2Fmt44giSM3KZdpvJwAY2rEW7k5l+yiSIssrI3kvMizcjis76PVrL3bF7MLB6MCM9jOY2m6qTMsIqyJlBNQT5OX948r7R2ZlHG2NjO+hrlnwxeazRMana5xIFNbcjaeJSc7E192BYdY6KmLKgQvh6nULLyO55lzmHpjLqxteJSEzgToV67C853KC/IO0jiZEqZMykifvH9fZTZrG0FLPJlVpX7sS2blmRv50CLPszFpmHLyUyPxw9QiaD55ohL2NQeNEGrm8B3LSwMEdvCz3SJqraVcZ8ucQvj78NQoKvev2Zmn3pdRyq6V1NCE0IWUkj/9DgA6iD1rdeWry6HQ6pj/dCEdbAzvPJfDN1nNaRxIFkJaVyzvLD2AyKwQ19eYha1xXJM+J39S3/g+D3jL/vYVHhdNnTR/2Xd2Ho9GR2R1nM6ntJOyNZWP/FiFKgmX+tWrBpQr4tVevH/1Z2ywaquHhxMSe6nRN6J+nOHI5SeNE4l4+WHOcC/HpVHWzZ9qTjbSOox2zCY7d+Ntt1EvbLLeRY87hf/v+x2t/vcb1rOs0cG/AiqAVdKvZTetoQmiuUGXEZDIxYcIEatasiYODA/7+/kydOhVFKdhw/rZt2zAajTRr1qwoWUteo2fUt0d/0jaHxp57wJdHG3qRY1IYtngfcalZWkcSd7Bk10V+3HsJnQ4+6tMUN0cbrSNpJ3IHpESDvRvUfkTrNLeITo1m8PrBfHf0OwCer/c8i7ovooZrDY2TCWEZClVGZs2axbx58/jss884ceIEs2bNYvbs2cydO/ee2yYmJvLSSy/xyCOW9U/iFg2eBL1RPU9N3Gmt02hGp9MR0qcpNSs5EZWYwRtL9pNjkqXiLc2eCwlM/lU923Two/UIrF1J40Qay3sR0SAIjJazvsrmS5vp81sfDl47iLONMx91+ohxD47DzmA5GYXQWqHKyPbt23nyySfp0aMHfn5+9O7dm0cffZTdu++9cumwYcPo27cvbdu2LXLYEufkAbUeUq9b+eiIm4MNX/dviZOtgV3nExjz85ECj4CJknf2WiqvLtpHjkmhR+OqvN7ZSo+eyWPKgeP/p163kCmaHFMOIXtCeOvvt0jKSiLAI4AVQSt41O9RraMJYXEKVUYCAwPZuHEjERHqCo+HDh0iPDycbt3uPue5YMECzp07x6RJkwr0dbKyskhOTr7lUmoa91bfHv4RzNY9GlDHy4VPX2iOXger9l1mxtoTUkgsQHRSBi99u5uEtGwa+bgS0qeJrNB5ZiOkx4NTZfDrqHUaLqdcZsD6Afxw/AcAXmzwIou6LcLXxQqX5xeiAIyFufPo0aNJTk6mfv36GAwGTCYT06dPp1+/fnfc5vTp04wePZqtW7diNBbsy82cOZMpU6YUJlrxqd8T7Fwh4Ryc/RvqdNEmh4V4pIEXs3o1YcSqw3yz9Tyu9ja89UgdrWNZrWspWfT/djdRiRnUquTE94Na42hbqD/j8mn31+rbJs+BQdvHY+PFjUzYNoGUnBRcbF2Y1m4aD1d/WNNMQli6Qo2MrFixgiVLlrB06VL279/PwoULCQ0NZeHChbe9v8lkom/fvkyZMoW6desW+OuMGTOGpKSk/MulS5cKE/P+2DlDsxvlavdXpfd1LVifVr6M79EAgI82RBDyx0kZIdHAlcQMnv1qB2diU6nqZs+iIW2oZI3nnvm3uNNwdiOggweGaBYj25TNzF0zeWfzO6TkpNCkchNWBa2SIiJEAeiUQjyr+Pr6Mnr0aN54443826ZNm8bixYs5efLkf+6fmJhIxYoVMRhuLsBkNptRFAWDwcCff/7Jww/f+w81OTkZNzc3kpKScHV1LWjcoos/C3NbAgq8tR88rHw+/oavws4yc536cx4Y6MfEng3R6618eqCUXIhLo9/8XUQlZuBTwYGlQ9tQw8NJ61iWYe0IdWSkXnd4YZkmES4lXyJ4SzDH448DMChgEG+1eAsbvRUf3SQEBX/+LtR4Znp6Ovp/LSRkMBgw32HfCldXV44cOXLLbV988QV///03q1atombNmoX58qXHwx/qdIXTf8Lub6Dbh1onsgivdvLH0dbAhP87xvfbLxCTlMmc55rKNEEJ230+gVcX7eV6eg41KzmxeEgbfCo4aB3LMmQmw8Gl6vXWr2gSYf2F9UzePpm0nDQq2FVgevvpdKym/X4rQpQlhXoWCQoKYvr06VSvXp2AgAAOHDjAnDlzGDx4cP59xowZQ1RUFD/88AN6vZ5GjW5dhMnT0xN7e/v/3G5x2ryqlpGDS+DhcWDnonUii9C/rR8u9jaMXHWY9cdiuPxVOvNfeoAqbrJ6ZElYufcSY385Qo5JobGPG98ObIWnizzW+Q4uhexUqFSv1M9Fk5mbScieEFZErACghWcLZnWcRRWnKqWaQ4jyoFD7jMydO5fevXvz+uuv06BBA4KDg3n11VeZOnVq/n2io6OJjCwHy6nXehg86kBWsjo6IvI91dyHJUPb4O5ky9GoZHrO3crW09e0jlWuZOaYGL/6CCNWHSbHpNC9cRVWvNpWisg/5WTC9k/V621eUU94WUrOJ52n39p+rIhYgQ4dQxsP5dvHvpUiIkQRFWqfEa2U+j4jeQ79CL+8AvYV4J3D6sqOIt+lhHSG/rCXkzEp6HTwemd/3u1SF6NBzjJwP85eS+WNJfs5GZMCwNsP1+adLnVl/5x/2/UVrBsJLt7w9gGwKZ2i9tu53/hgxwdk5Gbgbu/OzPYzCfQJLJWvLURZU9Dnb3nWuJvGvdXh38xE2DlP6zQWx9fdkdVvtKNvm+ooCny+6Sy9v9xBxNUUraOVSWazwvfbzhM0N5yTMSl4ONmycHBr3nu0nhSRf8tOh60fqdc7BpdKEcnIzWDS9kmM2TqGjNwMHqjyACuDVkoREaIYSBm5G70BHhqjXt/xOaQnaJvHAtnbGJjxdGPmvtAcFzsjBy8l0vPTcD7deFqWkC+Es9dSefarHUxec5z0bBNta3mwdngHOtWtrHU0y7RnPqRehQrVoXn/Ev9yZxPP0vf3vvx8+md06Hit6Wt80/UbPB2t+AzJQhQjKSP30uBJ8Gqs7juSNz8t/iOoqTd/vteRR+p7km0yM2dDBN0+2UpYhOxLcjcpmTnMWn+Sbh9vZe/F6zjZGpj6VCOWDGmDl6vsH3JbWSkQ/j/1eqfRYLQt0S+3+sxqXvj9Bc4knqGSQyW+efQbXm/2Oga94d4bCyEKRPYZKYhT62DZ82DjCG/uBTef0s9QRiiKwq+HrjBlzXES0rIBeKheZcb1aEBtTzkiKY/JrLBq3yVC/ojIPyty53qVmf50Yzls9142zYCwWeBRG17fVWIrrqbnpDN913R+PfsrAA9WfZCZHWZSycHKT0goRCEU9PlbykhBKAp89zhc2gkNn4Jnb7/irLgpKSOHuRtP8/32C+SaFfQ6eLKZD28+XBv/ys5ax9NMrsnMmsNXmPv3Gc5dSwOgZiUnxnVvwCMNPOUcM/eScA4+fxBMWdBnIQQ8VSJfJuJ6BMFhwZxPOo9ep+eNZm8wpPEQ9DoZTBaiMKSMFLeYI/BVR1DM8OLPUPsRbXKUMeeupTJz3Uk2HL8KgF6nTukM7VCLRj7Wc3RSZo6JXw9d4cvNZzkXp5aQCo42vPlQbV5q64etUZ7k7klRYEkfOLNBPbt2/1+K/XBeRVH4+fTPzNw9kyxTFp4OnszqOItWVVoV69cRwlpIGSkJ60bDrnng7g+v7wCjnBekoI5cTuKTjaf568TV/Nse8KvIwMCaPBrghU05PRw4OimDxTsvsmz3pfxpq4qONgzpUIsBgX4428nqtQV2Yg38+CIYbOG1HVCpdrF++rScNKbsmMK68+sAaOfTjhntZ+Bu716sX0cIayJlpCRkJsFnD6h78T88HjqO0C5LGXU0Komvt5xj7ZFocs3qr15lFzuebOrN0y18aFjVtcxPVWRkm/jzeAy/HIhi6+k4TDe+T58KDvRvW4MXH6whJaSwstPgs9aQfBk6BMMjE4r1059MOElwWDAXky9i0Bl4u8XbDAwYKNMyQtwnKSMl5fBK+HkIGB3U0RF3Cz2/joW7mpzJkp0XWbo7krjU7Pzb61dxoVujqnRp6FmmiklaVi5bT1/jz+NX+fPYVVKzcvM/9mAtdwYG+tGlgZcsCFdUGybBto/BrTq8sQtsHYvl0yqKwo+nfiRkTwjZ5myqOFUhpGMIzTybFcvnF8LaSRkpKYoCC4PgwlbwfRAGrVXXIxFFkp1rJiziGj/vv8zGE7Fk/2NtEm83ex5u4Ek7/0q0rumOh7PlTIuZzQonY1LYdT6ezaeuseNs/C3Zq1V04JnmPjzV3IdaVrzDbrGI3AkLuqn7az2/DOp3L5ZPm5KdwqTtk9hwcQMAnat1Zmq7qVSwr1Asn18IIWWkZF2/APPaQ3YKPDxBXQFS3Lek9BzWH4tmw/FYws9cIzPn1kXT6ng607qmO4193Gjo7UpdLxfsbUq+CCqKwrWULI5FJ3P8SjIHIq+z+3wCyZm5t9yvursjXRp48XijKrSqUVFWTS0OmcnwZXtIvAhNX4CnvyyWT3ss7hjBYcFcTr2MUWfk3Zbv0r9h/zIzEidEWSFlpKQdXAarh4HeCC9vAJ8WWicqVzJzTGw7E8fmU9fYdT6eiKup/7mPQa+jViUnang4Ud3dkeruDvi6O1LJ2Q53J1vcnWxxtDXc8wnGZFZITM/meno28anZxCRncikhncgblzOxqbdMJeVxsjXQ0s+dtrU86NLAk9qezvJkVtxWv66eObtCdRi2Dezv7+9fURSWnFjCR/s+Iteci4+zDyEdQ2hcuXExBRZC/JOUkZKmKLByIBxfrS6+9OoWsHXSOlW5lZCWze7zCeyPvM7xK8kcu5LE9fSce25na9TjYGPAxqDHzqjH1qjHZFbIzjWTbTKTk2smNTuXe/0V6HVQq7IzDau60tjHjdY13QnwdpV9QErSsdWwcgDo9DDwd6hxf+eAScpKYuK2ifx96W8AulTvwpR2U3C1tZD/KUKUQ1JGSkN6AswLhJRoaDkIgj7WOpHVUBSFq8lZnIxJvmUU4/L1DBLSsolPyyY7t3DnxnG1N+LhbEdlZzuqezjeGG1xxK+SE/W8XHCwlX2DSk3yFfiirXqSyg7vwyMT7+vTHb52mBFhI7iSdgUbvQ3BrYJ5of4LMpIlRAkr6PO3HF94Pxzd4al5sOgp2LcAfNtAsxe0TmUVdDodVdzsqeJ2+/O3KIpCeraJ6+nZZOaYyc41k2NSR0P0Oh12Rj02BnWkxNnOSAVHm3K71kmZk5sFK15Si0jVZur5Z4rIrJhZdHwRH+/7mFwlF18XX0I6hRDgEVBscYUQ90/KyP3yf0hdb2RLCKwZDpXrgk9LrVNZPZ1Oh5OdESdZz6NsURT4/T24vAfs3aD3d0U+EV5iZiLjto1jy+UtADzm9xiT207G2VaObhLC0shLweLQeSzUfVw9X8byFyE1VutEQpRNe+bDgcXqfiK9vwMP/yJ9mgOxB+i9pjdbLm/BVm/LhAcnENIxRIqIEBZKykhx0Ovhma/Bow6kXIEf+0Puf4++EELcxYVwWH9jSqbLZKjdpdCfwqyYmX9kPoPWD+Jq+lX8XP1Y2mMpz9Z7VvYPEcKCSRkpLvZu8MIysHNVz+67bgT3PERDCKFKjFT3EzHnQqPeEPh2oT9FfEY8r//1Op/s/wSTYqJHrR4s77mceu71SiCwEKI4SRkpTpXqQK9vAR3s+x7C52idSAjLlxYPi3tBejxUaQJPzC302Xj3xOyhz5o+bLuyDXuDPR8EfsDM9jNxspHD7YUoC6SMFLe6j8JjM9TrGz+AvQu0zSOEJctKgSW9IS4CXH3U0cVCnHfGZDYx79A8hvw5hGsZ16jlVoulPZbydJ2nZVpGiDJEDjUoCW1fh/Q42PoR/PYuOFSEgKe0TiWEZcnNguX94Mp+cHCH/r+AW7UCbx6XEcforaPZFb0LgKdqP8WY1mNwtCmek+gJIUqPlJGS8vAEddh53/fw0xB1GWv/h7VOJYRlMJvUv4vzYWDjBC+ugsoF37djZ/RORm8ZTXxmPA5GByY8OIEg/6ASDCyEKEkyTVNSdDroMQcaPgnmHPWQ30t7tE4lhPbMZnXE8MSvYLCF55cUeG2eXHMunx34jFf+fIX4zHjqVKzD8p7LpYgIUcZJGSlJegM88w3U6gw5abDoabi4XetUQmjHbII1b8H+hepaIr3mqwsHFkBseixD/hzCV4e/QkGhV51eLO2+lFputUo4tBCipEkZKWlGO3huCfh1gOwUWPQMnNmodSohSp8pR52ayVvU7Mkv1JHDAgiPCqf3r73Zd3UfjkZHZnWYxeTAydgbb386ACFE2SJlpDTYOUO/lVC7K+RmwLLn4eTvWqcSovTkZKqLAR77GfQ20HtBgc7jlGvO5eN9H/PaX69xPes69d3rsyJoBd1rdS+F0EKI0iJlpLTYOMDzS6HBE2DKVv8xH1mldSohSl52Gix7DiLWgcFO/TsowNFlMWkxDP5jMN8e/RaA5+o9x+Lui6nhWqOEAwshSpuUkdJktFVfETZ5HpQbRxPs/kbrVEKUnLR4dWry3OabR83UffSem4VdCqP3mt4ciD2As40zH3X6iPEPjsfOYFfymYUQpU4O7S1tBiM8NU9d2Gnvd7A2GOLPwKPT1Y8JUV5cOwVLn4XrF8DOTS0ivq3vukmOKYeP93/MD8d/ACDAI4CQTiH4uviWQmAhhFbk2U8Ler162K+rD/w9FXZ9qRaS3t+p57gRoqw7sxFWDoKsJKhQA/quAM/6d90kKjWKkWEjORx3GIAXG7zIuy3fxdZgWxqJhRAakmkareh00DEY+iwEowOc+Qu+fUx9FSlEWbb7G1jSRy0ivg/C0L/vWUQ2Rm6kz5o+HI47jIutCx8/9DGjWo+SIiKElZCREa0FPAUVqsOyF+DaCfjmYXUHv+oPap1MiMIx5cIfY2H3V+r7TV+AoE/Uw9vvINuUzZx9c1hyYgkATSo3IaRjCN7O3qWRWAhhIWRkxBL4tFBfPVZpoi4h/30P2PapulKlEGVB0mX19zaviDwyUd036i5F5FLyJfqv659fRAYGDOT7x7+XIiKEFZIyYincfGDwegh4Gsy5sGGCejhkWrzWyYS4u1Pr4Mv2cGkn2LnCc4uhw/vqVOQd/HHhD5797VmOxx+ngl0FPn/kc95v9T42eptSDC6EsBRSRiyJrZN66G/P/6nrMZz+E75sBxe2aZ1MiP/KzYb1Y9VF/DKuQ9Vm8GoYNLjzeWKyTFlM2zmN4LBgUnNSae7ZnJVBK+lYrWPp5RZCWBzZZ8TS6HTQajBUaw2rBkFcBCzsCZ3HqK829QatEwoBCefV388rB9T3H3wdukzOn5YxmRV2n08gNiUTTxd7Wtd051LKRYLDgjl1/RQAQxoP4Y1mb2DUy78hIaydTlEUResQ95KcnIybmxtJSUm4urpqHaf0ZKXC2hFwaKn6fvW28MRcqFRH21zCepnNsP97+HOieq4l+wrqviH1by7Pvv5oNFPWHCc6KTP/tkpVjoHHKrLMGbjbuzOj/Qza+bQr/fxCiFJV0OdvKSNlwcFl6uJo2anq9M1DY6DtW7JImihd8WdhzXC4sFV9v3pb9azUFW4uSLb+aDSvLd5P/j8VXTZ2XmuwrbgHAH/npnzdbQ6ejp6lm10IoYmCPn/LPiNlQbMX4PUd4P8wmLLgr8kw/xGIOap1MmENzCbYPhfmtVOLiI0jPP4hDPz9liJiMitMWXM8v4jobWNx9Psc24p7UBQd2dceISZiAB72lbX5PoQQFkvKSFlRoTq8+LN62nV7N4g+CF93gr+nQ26W1ulEeRV7Ar7tCn+OV884XbMjvLYdHnztP/sv7T6fkD81Y3Tbh2PNuRjsr2LOdSYj8mWy4roSk5TN7vMJWnwnQggLJuP8ZYlOB837Qe1H4Pf34eRvsGW2elr2R6dD3cfuejilEAWWkQhbQmDXV2DOUQ/ZfXQatHjpjr9jsSmZoMvGvspqbCrsByA3tTaZV55DMbncej8hhPgHKSNlkUsVdS2H46vVHVzjz6hrktR6CB6fCZ4NtE4oyipTLuxfCJumqwvwAdR9XD2XkpvPXTfN0V9RR0Psrt2YlulCdvxD/HsA1tPFvoTCCyHKKikjZZVOpy6Q5v8IbA2FnfPg3CaYF6geGtx5LDh5aJ1SlCXnNsP6MRB7XH2/Ul14bAbU6XrXzRRF4efTP/Ph4ZkY7LIw57iSeeV5TOm1brmfDqjiph7mK4QQ/yRH05QXCedgw0Q4sUZ9394NOo2CVi+DjbwSFXdxLQL+mgSn1qrv21eAh8aqpdZw9xVR03LS+GDHB6w9r25bz7UV+/Y+DiZn/vmPJW9iZ96LLXi8UdVi/xaEEJZJDu21Vue3qKtiXj2ivu9SFdq/Cy0GSCkRt7p2St0v5MgqQAGdAVoPVUus471HL04mnGRE2AguJF/AoDPwVvO3GNRoEH8eu/qfdUaqutkzKaihFBEhrIyUEWtmNsGBxRA2G5Ivq7c5V1FLScsBYOOgbT6hrdiT6o7PR3+GvPGLet3VFVQr17vn5oqisOLUCmbvmU22ORsvRy9COoXQ3LN5/n1utwKrQS87VwthbUpknRGTycSECROoWbMmDg4O+Pv7M3XqVO7WZ37++We6du1K5cqVcXV1pW3btvzxxx+F+bKisPQGtXS8vV/d8dC1GqTGwPpR8ElTdf+SnAytU4rSFnsCVg6CLx6Eoz8BCtTvCa9ugReWFaiIpGSnMGLLCKbtmka2OZtO1TqxKmjVLUUEwKDX0dbfgyeb+dDW30OKiBDirgq1A+usWbOYN28eCxcuJCAggL179zJo0CDc3Nx4++23b7vNli1b6Nq1KzNmzKBChQosWLCAoKAgdu3aRfPmzW+7jSgmRjt44GVo/iIcXAJb50DSJVg/GraEQqtB6j4lrjJ0Xm4pirpj866vIOIP8kdC6vdUp2OqNinwpzoWd4zgsGAup17GqDPyTst3eKnhS+jkcHIhxH0q1DRNz5498fLy4ttvv82/rVevXjg4OLB48eICf9GAgACee+45Jk6cWKD7yzRNMcnNVs9zs+UjSIpUb9MboeGT0PpV8G0t65SUF1mpcGgZ7P5aPdlingZBagmp0rjAn0pRFJaeXEro3lByzbl4O3kT0imEJpULXmSEENapoM/fhRoZCQwM5OuvvyYiIoK6dety6NAhwsPDmTNnToE/h9lsJiUlBXf3O+8gl5WVRVbWzVVFk5OTCxNT3InRFloOhGYvqgum7foKIrerQ/ZHf1JPAd9mGDR6Jv/sq6KMiT8Le+ar+wxl3fi7sXVRF8t7YChUql2oT5eUlcSk7ZPYGLkRgEeqP8KUwCm42bkVd3IhhBUrVBkZPXo0ycnJ1K9fH4PBgMlkYvr06fTr16/AnyM0NJTU1FSeffbZO95n5syZTJkypTDRRGEYjBDwlHqJPgy7v1KPqIg+CKuHwR9joXFvaPI8+LSQ0RJLl5WiHtJ9aLl6NFXeVIxHbWj9CjR9AewLP6J4+NphRoSN4EraFWz0Nrzf6n361u8r0zJCiGJXqGma5cuXM2LECEJCQggICODgwYO88847zJkzhwEDBtxz+6VLlzJ06FD+7//+jy5dutzxfrcbGfH19ZVpmpKUFq+uvLlnPiRH3bzdo7ZaSpo8CxVraJdP3MqUqy5Sdng5nPhNPW9Mntpd1REu/4dBX/jTTymKwg/Hf+DjfR+Tq+RSzbkaoZ1DCfAIKL78QgirUCKH9vr6+jJ69GjeeOON/NumTZvG4sWLOXny5F23Xb58OYMHD2blypX06NGjoF8SkH1GStXdnuRqtIMmz6k7P8rqrqVPUdTRqyOr4MhKSL1682P5pbEPVPQr8pdIzExk/LbxhF0OA+Axv8eY1HYSLrYu99hSCCH+q0T2GUlPT0f/r1daBoMBs9l81+2WLVvG4MGDWb58eaGLiChlBiPU6aJe8of/l8H5rXBxm3r57R3wbQP1ukHdblCpjkzllJScTHXq5dRa9WiYlCs3P+bgDo16QdPnwaflff8MDsQeYOSWkcSkxWCrt2VU61H0qdtHpmWEECWuUGUkKCiI6dOnU716dQICAjhw4ABz5sxh8ODB+fcZM2YMUVFR/PDDD4A6NTNgwAA++eQT2rRpQ0xMDAAODg64uclOcBbNzgWa9VUvSVFwZAUc+Uld3TVyh3rZMBHc/dViUq8b+D6oFhpRdKmxavGIWA9n/4ac9Jsfs3FSi2KT56F2F3Wn5PtkVsx8d/Q7PjvwGSbFRA3XGoR2CqW+e/37/txCCFEQhZqmSUlJYcKECfzyyy/Exsbi7e3NCy+8wMSJE7G1Vf8pDhw4kAsXLrB582YAOnfuTFhY2H8+14ABA/j+++8L9HVlmsbCJEaqT5an1qojJuacmx+zc4PqD4JfO3Vap2rTe57fxOqlxcHF7TdHnmKOwj/P7OLifbPs+XUo1mX9EzITGBs+lm1R2wDoXrM7E9tOxMnGqdi+hhDCesly8KJ0ZCarr94j1qsFJSPh1o/bOKnrl+SVE5+WcthwcvTN4nFxO1y7zf5WVZuqS7TX6wZVmpTINNiemD2M3jKa2IxY7Ax2jG0zlqdrPy3TMkKIYiNlRJQ+swliDsOFbTdf6Wcm3nofvREq11cX3frnxaGiJpFLlNmsnk055jDEHLl5SY357309G0KNQLWw1QgElyolFstkNvHNkW+Yd2geZsVMLbdahHYKpU7FOiX2NYUQ1knKiNCe2QzXTtwoJzcuadduf1+36mop8WygHg3iXlN961JVPdeOJctOg+sX4foF9RJ/Bq4eVadbctL+e3+dXv1ea9wYLarettSOTorLiGP01tHsit4FwBP+TzCuzTgcbRxL5esLIayLlBFheRRFXcMkb4Qg+pD6NvHinbcx2EKF6moxqegHbr7gVAkcPcCxknqqe0cPsHcr/qkMUw6kx9+8pMWpb1Ov3lo+0mLv/DmMDuAV8I9RoCbg1RBsS3+fjJ3ROxm9ZTTxmfE4GB0Y12YcT9Z+stRzCCGsR4kc2ivEfdHpwK2aeqnX7ebtGYlw9Zg6nRF3+uaTfGIkmLLVkYb4M3f/3HqjWkoc3NUdPA226sVoBwY79aiTvNsUM+RmqZ/blH3zet7b7FR1EbispIJ/bw4Vbxamin7g1UgtH+7+mh9dZDKb+PLwl3x16CsUFGpXqM1HnT6iVoVamuYSQog8UkaE9hwqqDu4+rW79XazSR1JySsn1y9A0uV/jVbEq1Mh5lx1xOKfC4EVC92N0Ze80Rh3cKp8a/Go6Kd+DxYoNj2WUVtGsffqXgB61enF6NajsTcW3xE5Qghxv6SMCMulN6hTNBWqQ82Od75fTgakJ0B6HGRcV0c4bjfykXddb1BHSww2N0dO/nnd1lEtH06V1OkfS99n5Q62RW1jbPhYEjITcDQ6MrHtRHrUkkUHhRCWR8qIKPtsHMDNR70Ics25fHbgM749+i0A9SrWI7RTKH5uftoGE0KIO5AyIkQ5EpMWw8gtIzkQewCA5+o9x4gHRmBnsPK1XYQQFk3KiBDlxJbLWxgbPpakrCScbZyZHDiZx/we0zqWEELck5QRIcq4HHMOn+z7hIXHFwLQ0KMhoR1D8XX11TiZEEIUjJQRIcqwqNQoRoaN5HDcYQD6NejHey3fw9Zw/yfQE0KI0iJlRIgyamPkRiZsm0BKdgouti5MbTeVR6o/onUsIYQoNCkjQpQx2aZs/rfvfyw+sRiAJpWaMLvTbHyc5WgiIUTZJGVEiDLkUsolgsOCOR5/HIABDQcwvMVwbAw2GicTQoiikzIiRBnx54U/mbR9Eqk5qbjZuTG93XQ6+XbSOpYQQtw3KSNCWLgsUxYhe0L48dSPADT3bM7sjrOp4lRF42RCCFE8pIwIYcEuJl8kOCyYkwknARjSeAivN3sdG71Mywghyg8pI0JYqLXn1jJlxxTSc9OpaFeRmR1m0s6n3b03FEKIMkbKiBAWJjM3kw93f8hPp38CoJVXK2Z1nIWno6fGyYQQomRIGRHCgpxLPMf7Ye9zJvEMOnS80uQVhjUdhlEvf6pCiPJL/sMJYSF+Pfsr03ZOIyM3Aw97D2Z2mElb77ZaxxJCiBInZUQIjaXnpDNj1wz+7+z/AdCmahs+7PAhlRwqaZxMCCFKh5QRITR0+vppgsOCOZd0Dr1Oz2tNX2No46EY9AatowkhRKmRMiKEBhRF4ZczvzBz10wyTZl4OnjyYccPeaDKA1pHE0KIUidlRIhSlpaTxtSdU/n93O8AtPNux4wOM3C3d9c4mRBCaEPKiBCl6FTCKYLDgrmQfAGDzsCbzd9kcKPB6HV6raMJIYRmpIwIUQoURWFlxEpm7Z5FtjkbL0cvQjqF0NyzudbRhBBCc1JGhChhqdmpTN4xmT8u/AFAp2qdmNZuGhXsK2gbTAghLISUESFK0LH4Y4wIG8GllEsYdUbeafkOLzV8CZ1Op3U0IYSwGFJGhCgBiqKw9ORSPtr7ETnmHLydvJndaTZNKzfVOpoQQlgcKSNCFLOkrCQmbZ/ExsiNADzs+zAftPsANzs3jZMJIYRlkjIiRDE6cu0II7aMICo1CqPeSHCrYPrW7yvTMkIIcRdSRoQoBoqi8MPxH/h438fkKrlUc65GaKdQAioFaB1NCCEsnpQRIe5TUlYS48PHs/nyZgAerfEokwMn42Lrom0wIYQoI6SMCHEfDsYeZMSWEcSkxWCrt2XkAyN5tt6zMi0jhBCFIGVEiCIwK2YWHF3A3ANzMSkmarjWILRTKPXd62sdTQghyhwpI0IUUkJmAuPCxxEeFQ5A95rdmdh2Ik42ThonE0KIsknKiBCFsDdmL6O2jCI2IxY7gx1jWo/hmTrPyLSMEELcBykjQhSAyWxi/pH5fHHoC8yKmZpuNQntFErdinW1jiaEEGWelBEh7iEuI44xW8ewM3onAE/4P8G4NuNwtHHUOJkQQpQPUkaEuItd0bsYtWUU8ZnxOBgdGNdmHE/WflLrWEIIUa5IGRHiNkxmE18e/pKvDn2FgkLtCrUJ7RSKfwV/raMJIUS5I2VEiH+JTY9l9NbR7InZA0CvOr0Y1XoUDkYHjZMJIUT5JGVEiH/YHrWdMeFjSMhMwNHoyMS2E+lRq4fWsYQQolyTMiIEkGvO5fODnzP/yHwA6lWsR2inUPzc/LQNJoQQVkDKiLB6MWkxjNoyiv2x+wF4rt5zjHhgBHYGO42TCSGEdZAyIqzalstbGBc+jsSsRJxsnJgcOJnH/R7XOpYQQlgVfWHubDKZmDBhAjVr1sTBwQF/f3+mTp2Koih33W7z5s20aNECOzs7ateuzffff38/mYW4bznmHObsncMbG98gMSuRhh4NWdlzpRQRIYTQQKFGRmbNmsW8efNYuHAhAQEB7N27l0GDBuHm5sbbb799223Onz9Pjx49GDZsGEuWLGHjxo0MGTKEqlWr8thjjxXLNyFEYVxJvcKILSM4fO0wAH3r9+X9Vu9ja7DVOJkQQlgnnXKvYY1/6NmzJ15eXnz77bf5t/Xq1QsHBwcWL158221GjRrF77//ztGjR/Nve/7550lMTGT9+vUF+rrJycm4ubmRlJSEq6trQeMK8R9/R/7N+G3jSclOwcXWhamBU3mkxiNaxxJCiHKpoM/fhZqmCQwMZOPGjURERABw6NAhwsPD6dat2x232bFjB126dLnltscee4wdO3bccZusrCySk5NvuQhxP3JMOczaPYvhm4aTkp1C40qNWRm0UoqIEEJYgEJN04wePZrk5GTq16+PwWDAZDIxffp0+vXrd8dtYmJi8PLyuuU2Ly8vkpOTycjIwMHhvwtJzZw5kylTphQmmhB3dCnlEiPCRnAs/hgAAxoOYHiL4dgYbDROJoQQAgo5MrJixQqWLFnC0qVL2b9/PwsXLiQ0NJSFCxcWa6gxY8aQlJSUf7l06VKxfn5hPf688CfPrnmWY/HHcLNzY+7Dcwl+IFiKiBBCWJBCjYyMGDGC0aNH8/zzzwPQuHFjLl68yMyZMxkwYMBtt6lSpQpXr1695barV6/i6up621ERADs7O+zsZI0HUXRZpixC9oTw46kfAWhWuRkhnUKo4lRF42RCCCH+rVBlJD09Hb3+1sEUg8GA2Wy+4zZt27Zl7dq1t9y2YcMG2rZtW5gvLUSBXUy+yIiwEZxIOAHAy41e5o3mb2Cjl9EQIYSwRIUqI0FBQUyfPp3q1asTEBDAgQMHmDNnDoMHD86/z5gxY4iKiuKHH34AYNiwYXz22WeMHDmSwYMH8/fff7NixQp+//334v1OhADWnV/H5O2TSc9Np6JdRWZ0mEF7n/ZaxxJCCHEXhSojc+fOZcKECbz++uvExsbi7e3Nq6++ysSJE/PvEx0dTWRkZP77NWvW5Pfff+fdd9/lk08+oVq1asyfP1/WGBHFKjM3k1l7ZrEqYhUALb1aMqvDLLycvO6xpRBCCK0Vap0Rrcg6I+JuziWdIzgsmNPXT6NDx9AmQ3mt6WsY9XK2AyGE0FJBn7/lv7Uo09acXcPUnVPJyM3Aw96DmR1m0tZb9kcSQoiyRMqIKJPSc9KZsWsG/3f2/wBoU6UNH3b8kEoOlTROJoQQorCkjIgy58z1MwSHBXM26Sx6nZ5hTYfxSuNXMOgNWkcTQghRBFJGRJmhKAqrz6xmxq4ZZJoyqexQmVkdZ/FAlQe0jiaEEOI+SBkRZUJ6Tjof7PyA38+ph4QHegcyo/0MPBw8NE4mhBDifkkZERbvVMIpgsOCuZB8AYPOwJvN32Rwo8HodYU6m4EQQggLJWVEWCxFUVgZsZJZu2eRbc7Gy9GL2R1n08KrhdbRhBBCFCMpI8IipWanMmXHFNZfWA9Ax2odmdZuGhXtK2qcTAghRHGTMiIszvH44wSHBXMp5RJGnZHhLYbzUsBLMi0jhBDllJQRYTEURWHZyWWE7g0lx5yDt5M3szvNpmnlplpHE0IIUYKkjAiLkJydzKRtk/gr8i8AHvJ9iKntpuJm56ZxMiGEECVNyojQ3JFrRxixZQRRqVEY9Ubeb/k+/Rr0Q6fTaR1NCCFEKZAyIjSjKAqLji/if/v/R645l2rO1QjtFEpApQCtowkhhChFUkaEJpKykhgfPp7NlzcD0LVGV6YETsHF1kXbYEIIIUqdlBFR6g7GHmTElhHEpMVgq7dl5AMjebbeszItI4QQVkrKiCg1ZsXM98e+59P9n2JSTNRwrUFop1Dqu9fXOpoQQggNSRkRpSIhM4Fx4eMIjwoHoFvNbkxqOwknGyeNkwkhhNCalBFR4vZd3cfIsJHEZsRiZ7BjdOvR9KrTS6ZlhBBCAFJGRAkyK2bmH5nP5wc/x6yYqelWk9BOodStWFfraEIIISyIlBFRIuIy4hi7dSw7oncA8IT/E4xrMw5HG0eNkwkhhLA0UkZEsdsVvYvRW0cTlxGHg9GBsW3G8lTtp7SOJYQQwkJJGRHFxmQ28dXhr/jy0JcoKNSuUJvQTqH4V/DXOpoQQggLJmVEFItr6dcYtXUUe2L2APBMnWcY3Xo0DkYHjZMJIYSwdFJGxH3bHrWdMeFjSMhMwMHowMS2E+lZq6fWsYQQQpQRUkZEkeWac/ni4BfMPzIfBYV6FesR2ikUPzc/raMJIYQoQ6SMiCKJSYth1JZR7I/dD8CzdZ9lxAMjsDfaa5xMCCFEWSNlRBTalstbGBc+jsSsRJxsnJgcOJnH/R7XOpYQQogySsqIKLAccw5z989lwbEFADRwb0Bop1Cqu1bXOJkQQoiyTMqIKJDo1GhGbBnBoWuHAOhbvy/vt3ofW4OtxsmEEEKUdVJGxD1titzE+G3jSc5OxsXGhQ/afUCXGl20jiWEEKKckDIi7ijHlMOcfXNYfGIxAI08GhHSKYRqLtU0TiaEEKI8kTIibutyymVGhI3gaPxRAF5q+BLvtHgHG4ONxsmEEEKUN1JGxH9suLiBSdsmkZKTgqutK9PbT6ezb2etYwkhhCinpIyIfFmmLEL3hLL81HIAmlVuxuyOs6nqXFXjZEIIIcozKSMCgMjkSILDgjmRcAKAwY0G82bzN7HRy7SMEEKIkiVlRLDu/Dqm7JhCWk4aFe0qMr39dDpU66B1LCGEEFZCyogVy8zNZNaeWayKWAVAC88WzO44Gy8nL42TCSGEsCZSRqzU+aTzBIcFE3E9Ah06hjYZymtNX8Ool18JIYQQpUueeazQmrNrmLpzKhm5GbjbuzOzw0wCvQO1jiWEEMJKSRmxIhm5GczYNYPVZ1YD0LpKaz7s8CGVHStrG0wIIYRVkzJiJc5cP0NwWDBnk86i1+kZ1nQYrzR+BYPeoHU0IYQQVk7KSDmnKAqrz6xmxq4ZZJoyqexQmVkdZ/FAlQe0jiaEEEIAUkbKtfScdKbunMpv534DINA7kBntZ+Dh4KFxMiGEEOImKSPl1KmEUwSHBXMh+QIGnYE3m7/J4EaD0ev0WkcTQgghbiFlpJxRFIVVp1fx4a4PyTZn4+noSUjHEFp4tdA6mhBCCHFbUkbKkdTsVD7Y8QHrLqwDoINPB6a3n05F+4oaJxNCCCHuTMpIOXEi/gTBYcFEpkRi1BkZ3mI4LwW8JNMyQgghLF6hnqn8/PzQ6XT/ubzxxht33Objjz+mXr16ODg44Ovry7vvvktmZuZ9BxcqRVFYdnIZ/db2IzIlkqpOVVnw+AIGNhooRUQIIUSZUKiRkT179mAymfLfP3r0KF27dqVPnz63vf/SpUsZPXo03333HYGBgURERDBw4EB0Oh1z5sy5v+SC5OxkJm+fzIaLGwDo7NuZae2m4WbnpnEyIYQQouAKVUYqV751pc4PP/wQf39/OnXqdNv7b9++nXbt2tG3b19AHVl54YUX2LVrVxHjijxH444SHBZMVGoURr2R91u+T78G/dDpdFpHE0IIIQqlyOP42dnZLF68mMGDB9/xCTAwMJB9+/axe/duAM6dO8fatWvp3r37XT93VlYWycnJt1yESlEUFh1fRP91/YlKjcLH2YdF3RbxYsMXpYgIIYQok4q8A+vq1atJTExk4MCBd7xP3759iYuLo3379iiKQm5uLsOGDWPs2LF3/dwzZ85kypQpRY1WbiVlJTF+23g2X9oMQNcaXZkcOBlXW1dNcwkhhBD3Q6coilKUDR977DFsbW1Zs2bNHe+zefNmnn/+eaZNm0abNm04c+YMw4cPZ+jQoUyYMOGO22VlZZGVlZX/fnJyMr6+viQlJeHqap1PvAdjDzJyy0ii06Kx0dsw8oGRPFfvORkNEUIIYbGSk5Nxc3O75/N3kcrIxYsXqVWrFj///DNPPvnkHe/XoUMHHnzwQUJCQvJvW7x4Ma+88gqpqano9QWbJSroN1MemRUzC48t5NP9n5Kr5FLdpTqhnUJp4NFA62hCCCHEXRX0+btI0zQLFizA09OTHj163PV+6enp/ykcBoN6ltgiDshYleuZ1xkXPo6tUVsB6ObXjYltJ+Js66xxMiGEEKL4FLqMmM1mFixYwIABAzAab938pZdewsfHh5kzZwIQFBTEnDlzaN68ef40zYQJEwgKCsovJeL29l3dx8gtI4lNj8XOYMfo1qPpVaeXTMsIIYQodwpdRv766y8iIyMZPHjwfz4WGRl5y0jI+PHj0el0jB8/nqioKCpXrkxQUBDTp0+/v9TlmFkx8+2Rb/n84OeYFBN+rn6Edgqlnns9raMJIYQQJaLIO7CWJmvZZyQ+I54xW8ewI3oHAEG1ghj/4HgcbRw1TiaEEEIUXonuMyKK3+7o3YzaOoq4jDjsDfaMbTOWp2o/JdMyQgghyj0pIxozmU18ffhrvjz8JWbFjL+bPx91/gj/Cv5aRxNCCCFKhZQRDV1Lv8aYrWPYFaMuj/907acZ02YMDkYHjZMJIYQQpUfKiEa2X9nOmK1jSMhMwMHowIQHJxDkH6R1LCGEEKLUSRkpZbnmXL44+AXzj8xHQaFuxbqEdgqlpltNraMJIYQQmpAyUopi0mIYtWUU+2P3A9Cnbh9GPjASe6O9xsmEEEII7UgZKSVbL29lbPhYErMScbJxYnLbyTxe83GtYwkhhBCakzJSwnLMOcw9MJcFRxcA0MC9AaGdQqnuWl3jZEIIIYRlkDJSgqJToxmxZQSHrh0C4IX6LxDcKhhbg63GyYQQQgjLIWWkhGyK3MT4beNJzk7GxcaFKe2m0LVGV61jCSGEEBZHykgxyzHl8L/9/2PR8UUANPJoREinEKq5VNM4mRBCCGGZpIwUo8splxm5ZSRH4o4A0L9hf95t8S42BhuNkwkhhBCWS8pIMfnr4l9M3DaRlJwUXG1dmdZuGg9Vf0jrWEIIIYTFkzJyn7JN2YTuDWXZyWUANK3clNkdZ+Pt7K1xMiGEEKJskDJyHyKTIwkOC+ZEwgkABjUaxFvN38JGL9MyQgghREFJGSmi9efXM3nHZNJy0qhgV4Hp7afTsVpHrWMJIYQQZY6UkULKzM1k9p7ZrIxYCUALzxbM6jiLKk5VNE4mhBBClE1SRgrhfNJ5gsOCibgegQ4dQxoP4fVmr2PUy8MohBBCFJU8ixbQmrNrmLpzKhm5GbjbuzOzw0wCvQO1jiWEEEKUeVJG7iEjN4OZu2byy5lfAGhdpTUfdviQyo6VNU4mhBBClA9SRu7ibOJZgsOCOZN4Bh06Xmv6Gq80eQWD3qB1NCGEEKLckDJyB6vPrGb6zulkmjKp5FCJWR1m0bpqa61jCSGEEOWOlJF/Sc9JZ/qu6fx69lcA2lZty4wOM6jkUEnjZEIIIUT5JGXkH04lnGLElhGcTzqPXqfnzWZv8nLjl9Hr9FpHE0IIIcotKSOAoiisOr2KWbtnkWXKwtPRk9kdZ9PSq6XW0YQQQohyz+rLSGp2Kh/s+IB1F9YB0N6nPTPaz6CifUWNkwkhhBDWwarLyIn4EwSHBROZEolBZ2B4i+EMCBgg0zJCCCFEKbLaMmJWzIzfNp7IlEiqOlVldsfZNPNspnUsIYQQwupY7RCAXqdnRvsZPFrjUVYGrZQiIoQQQmhEpyiKonWIe0lOTsbNzY2kpCRcXV21jiOEEEKIAijo87fVjowIIYQQwjJIGRFCCCGEpqSMCCGEEEJTUkaEEEIIoSkpI0IIIYTQlJQRIYQQQmhKyogQQgghNCVlRAghhBCakjIihBBCCE1JGRFCCCGEpqSMCCGEEEJTUkaEEEIIoSkpI0IIIYTQlFHrAAWRd2Lh5ORkjZMIIYQQoqDynrfznsfvpEyUkZSUFAB8fX01TiKEEEKIwkpJScHNze2OH9cp96orFsBsNnPlyhVcXFzQ6XRax7EIycnJ+Pr6cunSJVxdXbWOU2bI41Y08rgVnjxmRSOPW9FY6uOmKAopKSl4e3uj1995z5AyMTKi1+upVq2a1jEskqurq0X94pUV8rgVjTxuhSePWdHI41Y0lvi43W1EJI/swCqEEEIITUkZEUIIIYSmpIyUUXZ2dkyaNAk7Ozuto5Qp8rgVjTxuhSePWdHI41Y0Zf1xKxM7sAohhBCi/JKRESGEEEJoSsqIEEIIITQlZUQIIYQQmpIyIoQQQghNSRmxQH5+fuh0uv9c3njjjTtu8/HHH1OvXj0cHBzw9fXl3XffJTMzsxRTa89kMjFhwgRq1qyJg4MD/v7+TJ069Z7nRNi8eTMtWrTAzs6O2rVr8/3335dOYAtRlMft559/pmvXrlSuXBlXV1fatm3LH3/8UYqptVXU37U827Ztw2g00qxZs5INamGK+rhlZWUxbtw4atSogZ2dHX5+fnz33XellFp7RX3clixZQtOmTXF0dKRq1aoMHjyY+Pj4UkpdSIqwOLGxsUp0dHT+ZcOGDQqgbNq06bb3X7JkiWJnZ6csWbJEOX/+vPLHH38oVatWVd59993SDa6x6dOnKx4eHspvv/2mnD9/Xlm5cqXi7OysfPLJJ3fc5ty5c4qjo6Py3nvvKcePH1fmzp2rGAwGZf369aWYXFtFedyGDx+uzJo1S9m9e7cSERGhjBkzRrGxsVH2799fism1U5THLM/169eVWrVqKY8++qjStGnTkg9rQYr6uD3xxBNKmzZtlA0bNijnz59Xtm/froSHh5dSau0V5XELDw9X9Hq98sknnyjnzp1Ttm7dqgQEBChPP/10KSYvOCkjZcDw4cMVf39/xWw23/bjb7zxhvLwww/fctt7772ntGvXrjTiWYwePXoogwcPvuW2Z555RunXr98dtxk5cqQSEBBwy23PPfec8thjj5VIRktUlMftdho2bKhMmTKlOKNZrPt5zJ577jll/PjxyqRJk6yujBTlcVu3bp3i5uamxMfHl3Q8i1WUxy0kJESpVavWLbd9+umnio+PT4lkvF8yTWPhsrOzWbx4MYMHD77jSQIDAwPZt28fu3fvBuDcuXOsXbuW7t27l2ZUzQUGBrJx40YiIiIAOHToEOHh4XTr1u2O2+zYsYMuXbrccttjjz3Gjh07SjSrJSnK4/ZvZrOZlJQU3N3dSyqmRSnqY7ZgwQLOnTvHpEmTSiOmxSnK4/brr7/SqlUrZs+ejY+PD3Xr1iU4OJiMjIzSiq25ojxubdu25dKlS6xduxZFUbh69SqrVq2y3OcFrduQuLsff/xRMRgMSlRU1F3v98knnyg2NjaK0WhUAGXYsGGllNBymEwmZdSoUYpOp1OMRqOi0+mUGTNm3HWbOnXq/Oc+v//+uwIo6enpJRnXYhTlcfu3WbNmKRUrVlSuXr1aQiktS1Ees4iICMXT01M5deqUoiiKVY6MFOVxe+yxxxQ7OzulR48eyq5du5Tff/9dqVGjhjJw4MBSSq29ov6NrlixQnF2ds5/XggKClKys7NLIXHhSRmxcI8++qjSs2fPu95n06ZNipeXl/LNN98ohw8fVn7++WfF19dX+eCDD0oppWVYtmyZUq1aNWXZsmXK4cOHlR9++EFxd3dXvv/++ztuI2WkaI/bPy1ZskRxdHRUNmzYUMJJLUdhH7Pc3FylVatWyrx58/Jvs8YyUpTfta5duyr29vZKYmJi/m0//fSTotPp5G/0Lo/bsWPHlKpVqyqzZ89WDh06pKxfv15p3Ljxf6Z7LIWUEQt24cIFRa/XK6tXr77r/dq3b68EBwffctuiRYsUBwcHxWQylWREi1KtWjXls88+u+W2qVOnKvXq1bvjNh06dFCGDx9+y23fffed4urqWhIRLVJRHrc8y5YtUxwcHJTffvutpOJZpMI+ZtevX1cAxWAw5F90Ol3+bRs3biyN2Joryu/aSy+9pPj7+99y2/HjxxVAiYiIKJGclqYoj9uLL76o9O7d+5bbtm7dqgDKlStXSiTn/TBqN0Ek7mXBggV4enrSo0ePu94vPT0dvf7W3X8MBgNAgQ81LA/u9DiYzeY7btO2bVvWrl17y20bNmygbdu2JZLREhXlcQNYtmwZgwcPZvny5ff8HS1vCvuYubq6cuTIkVtu++KLL/j7779ZtWoVNWvWLLGslqQov2vt2rVj5cqVpKam4uzsDEBERAR6vZ5q1aqVaF5LUZTHLT09HaPx1qd4i35e0LoNidszmUxK9erVlVGjRv3nY/3791dGjx6d//6kSZMUFxcXZdmyZcq5c+eUP//8U/H391eeffbZ0oysuQEDBig+Pj75h7/9/PPPSqVKlZSRI0fm32f06NFK//7989/PO7R3xIgRyokTJ5TPP//c6g7tLcrjtmTJEsVoNCqff/75LYeh/3MovTwrymP2b9Y4TVOUxy0lJUWpVq2a0rt3b+XYsWNKWFiYUqdOHWXIkCFafAuaKMrjtmDBAsVoNCpffPGFcvbsWSU8PFxp1aqV0rp1ay2+hXuSMmKh/vjjDwXI39ntnzp16qQMGDAg//2cnBxl8uTJir+/v2Jvb6/4+voqr7/+unL9+vXSC2wBkpOTleHDhyvVq1dX7O3tlVq1ainjxo1TsrKy8u8zYMAApVOnTrdst2nTJqVZs2aKra2tUqtWLWXBggWlG1xjRXncOnXqpAD/ufzz97I8K+rv2j9ZYxkp6uN24sQJpUuXLoqDg4NSrVo15b333rOa/UUUpeiP26effqo0bNhQcXBwUKpWrar069dPuXz5cimnLxidoljieI0QQgghrIWsMyKEEEIITUkZEUIIIYSmpIwIIYQQQlNSRoQQQgihKSkjQgghhNCUlBEhhBBCaErKiBBCCCE0JWVECCGEEJqSMiKEEEIITUkZEUIIIYSmpIwIIYQQQlNSRoQQQgihqf8Hqd+qVKBOCigAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#cov = np.array([[(8.25*0.02)**2, 0],\n",
    "#               [0, (8.25*0.02)**2]])\n",
    "#cov\n",
    "\n",
    "def chi2_creator_4_2_4(measurement_vector, cov, sigma_norm):\n",
    "\n",
    "    # Here we pass only the non-inverted covariance matrix as the inverted matrix should depend on the normalisation. This means we have to do the matrix inversion inside chi2_function(par).\n",
    "    def chi2_function(par):\n",
    "        #print(par, N)\n",
    "\n",
    "        # Hier ist wieder die Normalisierung mit N gemacht und die einzelnen Unsicherheiten sind jetzt auch relativ zum Fit-Parameter.\n",
    "        cov = np.array([[(8*0.02)**2+(par*0.1)**2, (par*0.1)**2],\n",
    "                        [(par*0.1)**2, (8.5*0.02)**2+(par*0.1)**2]])\n",
    "        inv_cov = np.linalg.inv(cov)\n",
    "\n",
    "        \n",
    "        '''\n",
    "        calculate the chi2 including an additional parameter for the normalization of the mean value (version 2)\n",
    "        '''\n",
    "        chi2_value = np.sum((measurement_vector - par)*np.dot(inv_cov,measurement_vector - par))\n",
    "        \n",
    "        return chi2_value # return the chi2 value\n",
    "    \n",
    "    return chi2_function\n",
    "\n",
    "minuit_instance = Minuit(chi2_creator_4_2_4(mw, inv_cov, 0.1), par=8)\n",
    "res = minuit_instance.migrad()\n",
    "display(res)\n",
    "print(res2.params[\"par\"].value, res2.params[\"N\"].value)\n",
    "drawCovEllipse(inv_cov, mw, res2.params[\"par\"].value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 7, 14],\n",
       "       [ 8, 16]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[1,2]])\n",
    "b = np.array([[7,8]])\n",
    "\n",
    "a*b.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}