crystalball_fitting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d1e3fab8",
   "metadata": {},
   "source": [
    "# Fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b38de567",
   "metadata": {},
   "outputs": [],
   "source": [
    "import uproot\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# fitting\n",
    "from scipy.optimize import curve_fit\n",
    "from scipy.stats import crystalball\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "form_title = {'family': 'helvetica', 'color': 'black', 'size': 15}\n",
    "form_label = {'family': 'helvetica', 'color': 'black', 'size': 20}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6de1b822",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>__experiment__</th>\n",
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      "text/plain": [
       "                __experiment__  __run__  __event__  __production__  \\\n",
       "charged 0                 1003        0    8640457           24816   \n",
       "        1                 1003        0    8640457           24816   \n",
       "        2                 1003        0    8640457           24816   \n",
       "        12                1003        0   12624230           24816   \n",
       "        13                1003        0   12624230           24816   \n",
       "...                        ...      ...        ...             ...   \n",
       "mixed   431043            1003        0     308753           25056   \n",
       "        431044            1003        0     308753           25056   \n",
       "        431045            1003        0    1175564           25056   \n",
       "        431046            1003        0    1175564           25056   \n",
       "        431048            1003        0    1175564           25056   \n",
       "\n",
       "                __candidate__  __ncandidates__  __weight__       Ecms  \\\n",
       "charged 0                   0                3         1.0  10.579557   \n",
       "        1                   1                3         1.0  10.579557   \n",
       "        2                   2                3         1.0  10.579557   \n",
       "        12                  0                9         1.0  10.579557   \n",
       "        13                  1                9         1.0  10.579557   \n",
       "...                       ...              ...         ...        ...   \n",
       "mixed   431043              7                9         1.0  10.579557   \n",
       "        431044              8                9         1.0  10.579557   \n",
       "        431045              0                9         1.0  10.579557   \n",
       "        431046              1                9         1.0  10.579557   \n",
       "        431048              3                9         1.0  10.579557   \n",
       "\n",
       "                aBminusMode  aBplusMode  ...  MCGenPDG_45  MCGenMothIndex_45  \\\n",
       "charged 0         -101002.0      1021.0  ...          NaN                NaN   \n",
       "        1         -101002.0      1021.0  ...          NaN                NaN   \n",
       "        2         -101002.0      1021.0  ...          NaN                NaN   \n",
       "        12        -101001.0      1022.0  ...          NaN                NaN   \n",
       "        13        -101001.0      1022.0  ...          NaN                NaN   \n",
       "...                     ...         ...  ...          ...                ...   \n",
       "mixed   431043        -99.0       -99.0  ...          NaN                NaN   \n",
       "        431044        -99.0       -99.0  ...          NaN                NaN   \n",
       "        431045        -99.0       -99.0  ...          NaN                NaN   \n",
       "        431046        -99.0       -99.0  ...          NaN                NaN   \n",
       "        431048        -99.0       -99.0  ...          NaN                NaN   \n",
       "\n",
       "                MCGenPDG_46  MCGenMothIndex_46  MCGenPDG_47  \\\n",
       "charged 0               NaN                NaN          NaN   \n",
       "        1               NaN                NaN          NaN   \n",
       "        2               NaN                NaN          NaN   \n",
       "        12              NaN                NaN          NaN   \n",
       "        13              NaN                NaN          NaN   \n",
       "...                     ...                ...          ...   \n",
       "mixed   431043          NaN                NaN          NaN   \n",
       "        431044          NaN                NaN          NaN   \n",
       "        431045          NaN                NaN          NaN   \n",
       "        431046          NaN                NaN          NaN   \n",
       "        431048          NaN                NaN          NaN   \n",
       "\n",
       "                MCGenMothIndex_47  MCGenPDG_48  MCGenMothIndex_48  \\\n",
       "charged 0                     NaN          NaN                NaN   \n",
       "        1                     NaN          NaN                NaN   \n",
       "        2                     NaN          NaN                NaN   \n",
       "        12                    NaN          NaN                NaN   \n",
       "        13                    NaN          NaN                NaN   \n",
       "...                           ...          ...                ...   \n",
       "mixed   431043                NaN          NaN                NaN   \n",
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       "        431045                NaN          NaN                NaN   \n",
       "        431046                NaN          NaN                NaN   \n",
       "        431048                NaN          NaN                NaN   \n",
       "\n",
       "                MCGenPDG_49  MCGenMothIndex_49  \n",
       "charged 0               NaN                NaN  \n",
       "        1               NaN                NaN  \n",
       "        2               NaN                NaN  \n",
       "        12              NaN                NaN  \n",
       "        13              NaN                NaN  \n",
       "...                     ...                ...  \n",
       "mixed   431043          NaN                NaN  \n",
       "        431044          NaN                NaN  \n",
       "        431045          NaN                NaN  \n",
       "        431046          NaN                NaN  \n",
       "        431048          NaN                NaN  \n",
       "\n",
       "[515952 rows x 907 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_pickle('semileptonic_Bdecay_data.pkl')\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2b9703c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([1601, 1701, 2601, 2701, 1600, 1700, 2600, 2700],\n",
       " [1401, 1501, 2401, 2501, 1400, 1500, 2400, 2500])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# reconstructed eta modes plus etaSB\n",
    "l_eta_Bp = [1600,1700,2600,2700]\n",
    "eta_Bp = list(i+1 for i in l_eta_Bp) + l_eta_Bp\n",
    "\n",
    "l_eta_B0 = [1400,1500,2400,2500]\n",
    "eta_B0 = list(i+1 for i in l_eta_B0) + l_eta_B0\n",
    "eta_Bp, eta_B0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "587097c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# eta and etaSB modes reconstruction\n",
    "df_eta_Bp = data.loc['charged'].query(\n",
    "    f'((B0_decayModeID=={eta_Bp} & B1_decayModeID<500) | (B1_decayModeID=={eta_Bp} & B0_decayModeID<500))'\n",
    ")\n",
    "\n",
    "df_eta_B0 = data.loc['mixed'].query(\n",
    "    f'((B0_decayModeID=={eta_B0} & B1_decayModeID<500) | (B1_decayModeID=={eta_B0} & B0_decayModeID<500))'\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "02eede5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# eta\n",
    "# splitting signal and background ****charged B****\n",
    "\n",
    "# background\n",
    "dfp_bkg = df_eta_Bp.drop(\n",
    "    df_eta_Bp[\n",
    "        ( ((df_eta_Bp['aBplusMode']%10000).isin([1019,1020,1039,1040])) | (abs(df_eta_Bp['aBminusMode'])%10000).isin([1019,1020,1039,1040]) )\n",
    "        &( (df_eta_Bp['pi4_B0_isSignal']==1) | (df_eta_Bp['pi4_B1_isSignal']==1) ) \n",
    "    ].index, inplace=False\n",
    ")\n",
    "\n",
    "# splitting peaking and combinatoprial background\n",
    "dfp_pkbkg = dfp_bkg[\n",
    "    ( (~(dfp_bkg['aBplusMode']%10000).isin([1019,1020,1039,1040])) & (~(abs(dfp_bkg['aBminusMode'])%10000).isin([1019,1020,1039,1040])) )\n",
    "    &( (dfp_bkg['pi4_B0_isSignal']==1) | (dfp_bkg['pi4_B1_isSignal']==1) ) \n",
    "]\n",
    "\n",
    "dfp_combkg = dfp_bkg.drop(\n",
    "    dfp_bkg[\n",
    "        ( (~(dfp_bkg['aBplusMode']%10000).isin([1019,1020,1039,1040])) & (~(abs(dfp_bkg['aBminusMode'])%10000).isin([1019,1020,1039,1040])) )\n",
    "        &( (dfp_bkg['pi4_B0_isSignal']==1) | (dfp_bkg['pi4_B1_isSignal']==1) )\n",
    "    ].index\n",
    ")\n",
    "\n",
    "# signal\n",
    "dfp_sig = df_eta_Bp[\n",
    "    ( ((df_eta_Bp['aBplusMode']%10000).isin([1019,1020,1039,1040])) | (abs(df_eta_Bp['aBminusMode'])%10000).isin([1019,1020,1039,1040]) )\n",
    "    &( (df_eta_Bp['pi4_B0_isSignal']==1) | (df_eta_Bp['pi4_B1_isSignal']==1) ) \n",
    "]\n",
    "\n",
    "\n",
    "dfp = pd.concat([dfp_sig, dfp_pkbkg, dfp_combkg], keys=['signal', 'peaking background', 'combinatorial background'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4da6f7eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# eta\n",
    "# splitting signal and background ****mixed B****\n",
    "\n",
    "# background\n",
    "df0_bkg = df_eta_B0.drop(\n",
    "    df_eta_B0[\n",
    "        ( ((df_eta_B0['aB0Mode']%10000).isin([1017,1018,1035,1036])) | (abs(df_eta_B0['aBbar0Mode'])%10000).isin([1017,1018,1035,1036]) )\n",
    "        &( (df_eta_B0['pi4_B0_isSignal']==1) | (df_eta_B0['pi4_B1_isSignal']==1) ) \n",
    "    ].index, inplace=False\n",
    ")\n",
    "\n",
    "# solitting peaking and combinatoprial background\n",
    "df0_pkbkg = df0_bkg[\n",
    "    ( (~(df0_bkg['aB0Mode']%10000).isin([1017,1018,1035,1036])) & (~(abs(df0_bkg['aBbar0Mode'])%10000).isin([1017,1018,1035,1036])) )\n",
    "    &( (df0_bkg['pi4_B0_isSignal']==1) | (df0_bkg['pi4_B1_isSignal']==1) ) \n",
    "]\n",
    "\n",
    "df0_combkg = df0_bkg.drop(\n",
    "    df0_bkg[\n",
    "        ( (~(df0_bkg['aB0Mode']%10000).isin([1017,1018,1035,1036])) & (~(abs(df0_bkg['aBbar0Mode'])%10000).isin([1017,1018,1035,1036])) )\n",
    "        &( (df0_bkg['pi4_B0_isSignal']==1) | (df0_bkg['pi4_B1_isSignal']==1) )\n",
    "    ].index\n",
    ")\n",
    "\n",
    "# signal\n",
    "df0_sig = df_eta_B0[\n",
    "    ( ((df_eta_B0['aB0Mode']%10000).isin([1017,1018,1035,1036])) | (abs(df_eta_B0['aBbar0Mode'])%10000).isin([1017,1018,1035,1036]) )\n",
    "    &( (df_eta_B0['pi4_B0_isSignal']==1) | (df_eta_B0['pi4_B1_isSignal']==1) ) \n",
    "]\n",
    "\n",
    "df0 = pd.concat([df0_sig, df0_pkbkg, df0_combkg], keys=['signal', 'peaking background', 'combinatorial background'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "99be31ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "# combining the charged and mixed data set\n",
    "# eta\n",
    "df = pd.concat([dfp,df0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7922aaa4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# plotting the invariant mass of eta for both signal and background\n",
    "# Note: signal is the combination of signal and peaking background\n",
    "\n",
    "# Invariant mass of eta: signal + peaking background of both B0 and B1\n",
    "\n",
    "# eta\n",
    "eta_sig_InvM = pd.concat(\n",
    "    [\n",
    "        df.loc['signal']['pi4_B0_InvM'],df.loc['signal']['pi4_B1_InvM'],\n",
    "        df.loc['peaking background']['pi4_B0_InvM'],df.loc['peaking background']['pi4_B1_InvM']\n",
    "    ]\n",
    ")\n",
    "# Invariant mass of eta: combinatorial background of both B0 and B1\n",
    "eta_bkg_InvM = pd.concat([df.loc['combinatorial background']['pi4_B0_InvM'],df.loc['combinatorial background']['pi4_B1_InvM']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "33b17289",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x134404220>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 5))\n",
    "bin_value, bin_edge, _ = plt.hist([eta_bkg_InvM,eta_sig_InvM],label=['background','signal'], histtype='barstacked',density=True, bins=20)\n",
    "plt.xlabel('Invariant mass of $\\eta$', fontdict=form_label)\n",
    "plt.legend(fontsize='20')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62d21ebb",
   "metadata": {},
   "source": [
    "## Using curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "7809cd4a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# exponential distribution\n",
    "def exp_curve(x, a, b, c):\n",
    "    return ( a * np.exp(b * x) + c )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "c7a7ae92",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "157.0 1557.0 13.35185719564416\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x13d845d90>"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,5))\n",
    "data = eta_sig_InvM.dropna()\n",
    "\n",
    "# Create a histogram of the data\n",
    "counts, edges, _ = plt.hist(data, bins=20, density=True, label='Signal')\n",
    "\n",
    "# Define the Crystal Ball PDF function\n",
    "def crystalball_pdf(x, beta, m, norm):\n",
    "    return norm * crystalball.pdf(x, beta, m)\n",
    "\n",
    "# Find the optimal parameters for the PDF using curve_fit\n",
    "x_data = (edges[:-1] + edges[1:]) / 2\n",
    "y_data = counts\n",
    "popt, pcov = curve_fit(crystalball_pdf, x_data, y_data, p0=[157,1557, 13])\n",
    "beta_fit, m_fit, norm_fit = popt\n",
    "print(*popt)\n",
    "\n",
    "# Plot the histogram and fitted PDF\n",
    "x_vals = np.linspace(np.min(edges), np.max(edges), 20)\n",
    "plt.plot(x_vals, crystalball_pdf(x_vals, *popt), 'r-', label='Fitted PDF')\n",
    "plt.xlabel('Invariant mass of $\\eta$', fontdict=form_label)\n",
    "plt.legend(fontsize='20')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "079cd366",
   "metadata": {},
   "source": [
    "<font color='red'>beta:<font color='blue'> the value of the tail parameter longer tail on the left (negative skew), a smaller value of beta may be appropriate, longer tail on the right (positive skew), a larger value of beta may be appropriate.\n",
    "\n",
    "<font color='red'>m<font color='blue'> : the value of the shape parameter based on the kurtosis of the data. If the data has heavier tails and a more peaked distribution (higher kurtosis), a larger value of m may be appropriate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "a177f979",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal parameters:  [1.57430191e+02 1.55743743e+03 2.63385790e+03 5.40981176e-01\n",
      " 1.82348307e-02]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/sahargholipour/opt/anaconda3/lib/python3.9/site-packages/scipy/optimize/minpack.py:833: OptimizeWarning: Covariance of the parameters could not be estimated\n",
      "  warnings.warn('Covariance of the parameters could not be estimated',\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x13c2b17f0>"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HhKm81aI7ayvV8TuSiG+y6sk899xzCyZIAYuPjz/jsz/yyCM89thj3HfffWcUyem1B1i6dCk33ngj77zzDrt37+aTT9Kfj33o0KHEx8fnUfqc03ALEZGClpwMDzwAZ50Ft9/ud5pse/GS6zhUpBj3zB/vdxSRkJXemGQzY+zYsQDUrVv31LCB+Pj4U+3nzp17qu3JR9oe002bNnHnnXdSr149ihYtSoUKFejevTvfffddulm2bdvG4MGDqVKlCsWLF6dp06ancuSVO+64A4Bff/2VHTt2ZGubpk2b8sUXX1CpUiVmzpzJ5MmT8zRTXsmyJ9nM3gS6Adudc+cFlr0HnBNoUhbY65xrms62icABIBlIcs75P0O+iIjf3nkHVqyA99+HIkX8TpNte4uX5s2WPbj7m3dptO0XVlWp53ckkbDwyCOPMHnyZJYtW3baEIKyZctStmxZHnnkEcaMGcP69etPG8qRuhd1yZIldOrUid27d3PVVVfRu3dvdu7cyeTJk2nTpg2TJk2iS5cup9rv2rWLSy65hF9++YU2bdrQpk0btm7dyu23306nTp3y7LO5VHOo52RMdeXKlRkyZAgjRoxg/Pjx9OzZM88y5ZXsDLcYA7wEvH1ygXPuupOvzexZYF8m23dwzu3MbUARkUIlORlGjIAmTaBPH7/T5NgbF/Zk0OKPuWf+eG695mG/44j4Ir0hBPHx8RnOaDF8+HASExNZtmxZukMIhg8fzpw5c1i/fn26+05KSqJv374cPHiQ2bNn065du1PrtmzZwoUXXsjgwYNJTEykaNGiADz44IP88ssvDB06lOeee+5U+zvvvJOLL744x585Iy+//DIA9erVo2LFijnatn379owYMYJvv/023fXPP//8GWOSy5Yty9ChQ3MTNceyLJKdc/PMLD69deb9k6EvcHke5xIRKZzefRd++gk++ghC9Er2zOwvVorXWvXi/q/GccHWn/ih2tl+RxK/DR0KS5f6nSJzTZvC88/n2e4effTRM5a1a9cu36Z9mz59Oj///DP333//aQUyQPXq1XnggQcYOnQos2bNokuXLpw4cYLx48cTFxd3RtHdsmVLBgwYkKthF4mJiaf2d+jQIRYtWsRXX31FVFQUzzzzTI73V6NGDYAMh2m8kM7UmHXq1AmdIjkLbYFtzrm1Gax3wGdm5oBRzrnRQR5PRCR8JSfD44/D+ed7Nw8JU2+16M7NCVO596vxDOp7ZrEgUti5Ar5N+8kp1jLqaV671ivDVq9eTZcuXVizZg2HDx+mbdu26c6y0b59+1wVyevXrz/1D4SYmBgqVapE7969ue+++7jkkktyvL+TP8eMhmn8+uuvvl64F2yRfD0wIZP1lzrntphZZeBzM1vjnJuXXkMzuw24DaB2CM8XKiKSa++/Dz/+CB98AFHhe930oaIlGHVRbx6cM4Zmm9cAXf2OJH7Kwx5aSd+uXbsA+OCDDzJtd/DgQQD27fNGwVapUiXddlWrVs1Vjnbt2jFnzpxcbZueLVu2AFCpUqU822deyvW3tJnFAL2B9zJq45zbEnjeDkwCWmXSdrRzrqVzrmWo/rBERHLtZC/yeedB795+pwna/5p1ZW+xUty+6EO/o4gUeid7g6dMmYJzLsPHyYv+Trbftm1buvv77bffCiZ4FmbPng3ARRdd5HOS9AXTlXElsMY5tym9lWZW0sziTr4GOgErgjieiEj4mjgRVq/2bkMdxr3IJx0uUpyxzbtx1dqF3ucSkUxFR0cDkJycnOP1rVu3BuCrr77K1rHOPfdcSpQowdKlS0/1KqeWl73BubV9+3ZGjRoFwIABA3xOk74sv6nNbAKwADjHzDaZ2eDAqn6kGWphZtXNbEbgbRVgvpktA74FpjvnZuZddBGRMOEcPP20Ny9yGM5okZGxLa7mSExR77OJSKYqVKgAwIYNG3K8vkePHtSvX5+XX36ZGTNmnLEevHHLhw8fBiA2NpYBAwZw4MCBM8YwJyQkMH68v3OdL1u2jI4dO7Jz5066dOlC9+7dfc2TkezMbnF9BssHpbNsC9Al8PoXoEmQ+UREwt9XX8F338Grr0Kgt6gw2F2iDO9d0JFB48bBY49BzZp+RxIJWVdccQVPP/00t956K3369KFUqVKULVuWO++889T6Dz74gN69e9OlSxeKFy9OnTp1GDhwILGxsUycOJGrrrqKrl27cskll9C0aVNKlCjBxo0b+e677/jll1/YunUrJUqUAOBf//oXs2bN4vnnnychIeHUPMnvvfceXbp0YerUqfn+mVPPhnHixAl27tzJ4sWLWbx4MeD1IJ/sTQ5Fui21iEh+e/ppqFgRbrrJ7yR57vVWvRi07BN47jl49lm/44iErKuuuopnn32W1157jeeee47jx49Tp06dU0XyLbfcwvr163n33Xf5z3/+Q1JSEu3atWPgwIEAXHDBBSxbtoz//ve/TJs2jbfeeouoqCiqVatGs2bNePTRR0+bp7hixYp8/fXX/P3vf+fjjz8mISGBc845h1dffZX4+PgCKZJTz4ZRrFgxypYtS4MGDbj//vsZMGAATZs2zfcMwbCCnsYkO1q2bOkSEhL8jiEiErzVq6FRIxg+HFLdSSuvxQ+bnm/7zkripgkweTJs2ADly/uWQ/LP6tWradiwod8xRLItu+esmS3O6I7Q4X/1iIhIKHv2WShWDO64w+8k+eeBB+DQIXjtNb+TiIjkGRXJIiL5ZetW+N//4I9/9IZbFFYXXACXXw4vvwxJSX6nERHJEyqSRUTyy6uvwokTcO+9fifJf3ffDRs3wqRJficREckTKpJFRPLDsWMwahR07epN/VbYde0K9erBCy/4nUREJE+oSBYRyQ8ffADbt8Ndd/mdpGBER3uf9euvITC9k4hIOFORLCKSH158Ec45B6680u8kBefmmyEuTr3JIlIoaJ5kEZE8FD9sOk22/MiUb7/lkSuHMPbvn/gdqeCULu1dpPjqq/DUU1Ctmt+JRERyTT3JIiJ57MYl0zhYpDgfnXeF31EK3l13eRcrvv6630kkj4XifRVE0pNX56qKZBGRPFTh0F66rfmKD8+7goNFS/gdp+CddRZ06gSjR2s6uEIkOjqaEydO+B1DJFtOnDhBdHR00PtRkSwikoeu++EziiYn8b/mXf2O4p/bb4dNm2DGDL+TSB6Ji4tj//79fscQyZb9+/cTFxcX9H5UJIuI5JXkZPovncnXdS7g5wq1/E7jn6uvhho1vLHJUiiUL1+ePXv2sHPnTo4fP66hFxJynHMcP36cnTt3smfPHsqXLx/0PnXhnohIXvnsM2ru386/2//R7yT+iomBW2+FRx+FX37x5k+WsFa0aFFq167N7t27SUxMJDk52e9IImeIjo4mLi6O2rVrU7Ro0aD3pyJZRCSvjBrFjhJl+ezs1n4n8d8tt8Djj3s3VHnqKb/TSB4oWrQo1apVo5pmLZEIoeEWIiJ5YfNmmDaND8+/khPRsX6n8V+NGtC9O7z5pnf3QRGRMKMiWUQkL7zxBiQnM6HJVX4nCR1/+hPs3AkTJ/qdREQkx1Qki4gEKznZmxe4Y0c2lNOfok+54gqIj/d6k0VEwoyKZBGRYH3yCWzcCEOG+J0ktERFeXfgmzULEhP9TiMikiMqkkVEgvXGG1ClijcGV053003e89ix/uYQEckhFckiIsHYvh2mTYOBAyFWF+ydoU4duPJKeOstSEnxO42ISLapSBYRCcb48d7tl/8Y4XMjZ+bmm2H9evjyS7+TiIhkW5ZFspm9aWbbzWxFqmXDzWyzmS0NPLpksG1nM/vRzNaZ2bC8DC4i4jvnvB7SVq2gUSO/04Sunj2hbFldwCciYSU7PcljgM7pLH/OOdc08JiRdqWZRQMvA38AGgHXm5l+i4hI4bFkCSxfrl7krBQrBgMGeFPB7dnjdxoRkWzJskh2zs0Ddudi362Adc65X5xzx4F3gR652I+ISGh66y2vAOzXz+8koe/mm72bikyY4HcSEZFsCWZM8p1m9kNgOEa5dNbXADamer8psExEJPwdPQrvvAO9enlDCSRzzZpBkyYaciEiYSO3RfKrQH2gKbAVeDadNpbOMpfRDs3sNjNLMLOEHTt25DKWiEgBmTrVGzowaJDfScKDGQweDIsXw7JlfqcREclSropk59w251yycy4FeA1vaEVam4Baqd7XBLZkss/RzrmWzrmWlSpVyk0sEZGC89ZbULOmd1c5yZ7+/aFIEe9nJyIS4mJys5GZVXPObQ287QWsSKfZd0ADM6sLbAb6Af1zlVJEJJRs3gyffQYPPgjR0X6n8V38sOnZbvtSvYu4ZPRbtI5pz/GY4OaVTnyya1Dbi4hkJjtTwE0AFgDnmNkmMxsM/MfMlpvZD0AH4J5A2+pmNgPAOZcE3Al8CqwG3nfOrcynzyEiUnDeftu7MYaGWuTY++dfSfkj+7li3SK/o4iIZCrLnmTn3PXpLH4jg7ZbgC6p3s8AzpgeTkQkbJ2cG7ltWzjrLL/ThJ358U3ZEleRvss/55Nz2/gdR0QkQ7rjnohITnzzDaxdq7mRcyklKpoPz7uCy379nqr7d/odR0QkQyqSRURy4q23oGRJuPZav5OErQ8u6Ei0S6H3St2mWkRCl4pkEZHsOnQI3nvPK5BLlfI7TdjaWLYqi2o2pveKL73hKyIiIUhFsohIdn30ERw8qKEWeWBy4w6ctXsT5/+2zu8oIiLpUpEsIpJdb78N9ep5F+1JUKaf24Zj0TEaciEiIUtFsohIdmzeDF9+CTfc4N09ToKyv1gpZtVvxdWr5xGTnOR3HBGRM6hIFhHJjgkTvPGzAwb4naTQmHTe5VQ8vI+2id/7HUVE5AwqkkVEsmPcOGjVCs4+2+8khcacei3YXby0dwGfiEiIUZEsIpKV5cth2TJvqIXkmRPRsUw7ty0d1y0i7tghv+OIiJxGRbKISFbGj4foaLjuOr+TFDqTGnegWNJxOv/4td9RREROoyJZRCQzKSlekXzVVVC5st9pCp3vq5/Dr+Wq0XvlbL+jiIicRkWyiEhm5s2DTZs01CK/mDG5UQcu3rCc6vu3+51GROQUFckiIpkZN867u16PHn4nKbQmNe4AQI9Vc31OIiLyOxXJIiIZOXoUPvgAeveGEiX8TlNobShXjYQaDem1YrZuUy0iIUNFsohIRqZNg/37NdSiAExq3IGzd22g8baf/Y4iIgKoSBYRydi4cVC1Klx+ud9JCr1p57YN3KZaF/CJSGhQkSwikp5du2DGDOjf35v+TfLVvuJxzK5/Id1XzyU6JdnvOCIiKpJFRNL1wQdw4oSGWhSgSY07UOnQXtr+qttUi4j/VCSLiKRn3Dho1AiaNvU7ScSYXe9C9hYrRS8NuRCREKAiWUQkrV9/ha+/9nqRzfxOEzGOx8Qy/dw2dFy3kBLHj/gdR0QinIpkEZG03nnHe+7f398cEWhyo/aUOHGMTmsX+h1FRCKcimQRkdSc84ZaXHYZ1Knjd5qIk1CzEZtKV9aQCxHxXZZFspm9aWbbzWxFqmVPm9kaM/vBzCaZWdkMtk00s+VmttTMEvIwt4hI/liyBNas0QV7PnEWxZRG7WiTuJSKh/b4HUdEIlh2epLHAJ3TLPscOM85dwHwE/BgJtt3cM41dc61zF1EEZECNG4cFCkCffr4nSRiTWrcgWiXwtWr5/kdRUQiWJZFsnNuHrA7zbLPnHNJgbcLgZr5kE1EpGAlJcGECdC1K5Qr53eaiLWuYm1WVq5Hj1Vz/I4iIhEsL8Yk3wx8ksE6B3xmZovN7LY8OJaISP6ZNQu2bdNQixAwqXF7mm5dS93dm/2OIiIRKqgi2cz+ASQB4zNocqlzrjnwB+AOM7ssk33dZmYJZpawY8eOYGKJiOTOuHFQtix06eJ3koj3ccPLSMHouXKO31FEJELlukg2s5uAbsAA55xLr41zbkvgeTswCWiV0f6cc6Odcy2dcy0rVaqU21giIrlz8CBMnAjXXgvFivmdJuJti6vIN3UuoOeq2d6MIyIiBSxXRbKZdQb+BnR3zh3OoE1JM4s7+RroBKxIr62IiO+mTIHDhzXUIoRMadSeOnt/o9mWH/2OIiIRKDtTwE0AFgDnmNkmMxsMvATEAZ8HpncbGWhb3cxmBDatAsw3s2XAt8B059zMfPkUIiLBGjcOateGNm38TiIBM8+5hKMxRbzeZBGRAhaTVQPn3PXpLH4jg7ZbgC6B178ATYJKJyKSS/HDpme7bcVDe1j06WeMuqg3//l7RtchS0E7ULQkX9RvRbfVX/H45beSFJ3lrywRkTyjO+6JSMS7evU8ol0KExtf7ncUSWNy4w5UOLKftonf+x1FRCKMimQRiXg9Vs1hRZX6rKtY2+8oksbces3ZUyxOs1yISIFTkSwiEa3erk003bqWSY3a+x1F0nEiOpbp57ah09qFlDyW7nXiIiL5QkWyiES0HqvmkGxRfNwww2ncxWeTG7eneNIxOq1d6HcUEYkgKpJFJHI5R6+Vs/m6ThO2x1XwO41kYHGNhmwsU4VeKzXLhYgUHBXJIhKxmm9eQ+1925iioRYhzVkUUxq149L1y6h0cI/fcUQkQqhIFpGI1WvVbI7EFOXTsy/2O4pkYXKj9kS7FK5ePc/vKCISIVQki0hEik0+QbfVX/F5g4s4WLSE33EkC+sq1mZFlfr0WDXH7ygiEiFUJItIRLrs1yWUO3qASY07+B1FsmlSo/Y0+W0t9XZt8juKiEQAFckiEpF6rZzDruKl+Sq+md9RJJs+bngZKZh6k0WkQKhIFpGIE3fsEFeuW8THDS/TrY7DyPa4Cnxdpwk9V80B5/yOIyKFnIpkEYk4nX/8hmJJx5msoRZhZ0rj9tTZ+xvNt6zxO4qIFHIqkkUk4vRcNZtfy1VjabWz/Y4iOTTz7Es4GlNEt6kWkXynIllEIkqVAzu5eP1yJjfqAGZ+x5EcOli0BF+cdRFd13wFJ074HUdECjEVySISUbqvmkcUjsmN2/sdRXJpUuP2VDiyHz77zO8oIlKIqUgWkYjSa9Vsvq92DuvLVfc7iuTSvLrN2VMsDsaN8zuKiBRiKpJFJGKcsyORRtt/ZZJ6kcPaiehYpjVsC1OmwIEDfscRkUJKRbKIRIyeK+eQZFFMa3iZ31EkSJMbtYcjR2DSJL+jiEghpSJZRCKCuRR6rJrD3Hot2F2ijN9xJEiLazSE+HgYP97vKCJSSKlIFpGIcNHGFVQ/sNPrgZTwZwYDBsAXX8Bvv/mdRkQKIRXJIhIReqycw8Eixfm8wUV+R5G8MmAApKTAu+/6nURECiEVySJS6BVNOk7XH7/2bkQRW8zvOJJXGjaE5s3hf//zO4mIFEJZFslm9qaZbTezFamWlTezz81sbeC5XAbbdjazH81snZkNy8vgIiLZ1eHn7yh97BCTdBvqwufGG2HJElixIuu2IiI5kJ2e5DFA5zTLhgGznHMNgFmB96cxs2jgZeAPQCPgejNrFFRaEZFc6LVyNttKlWdB7fP9jiJ5rX9/iImBsWP9TiIihUyWRbJzbh6wO83iHsDJb6SxQM90Nm0FrHPO/eKcOw68G9hORKTAlD2ynw4/JzC14WWkREX7HUfyWqVK0KWLd2ORpCS/04hIIZLbMclVnHNbAQLPldNpUwPYmOr9psCydJnZbWaWYGYJO3bsyGUsEZHTdV81lyIpSXx03hV+R5H8ctNN3gwXn3/udxIRKUTy88I9S2eZy6ixc260c66lc65lpUqV8jGWiESSPitmsbxKfdZUrut3FMkv3bpBhQowZozfSUSkEMltkbzNzKoBBJ63p9NmE1Ar1fuawJZcHk9EJMfO2ZHIBb+t48Pzr/Q7iuSnIkXg+uu921Tv2eN3GhEpJHJbJE8Fbgq8vgmYkk6b74AGZlbXzIoA/QLbiYgUiGuWz+J4VAxTdRvqwu+mm+DYMXj/fb+TiEghkZ0p4CYAC4BzzGyTmQ0GngQ6mtlaoGPgPWZW3cxmADjnkoA7gU+B1cD7zrmV+fMxREROF5OcRK+Vs5l1Viv26DbUhV+LFtC4sWa5EJE8E5NVA+fc9RmsOuMqGOfcFqBLqvczgBm5Ticikkvtfl1MpcN7+fB8XbAXEcy83uQHHoAff4RzzvE7kYiEOd1xT0QKpT7LZ7GjRFnm1m3hdxQpKDfcAFFR8PbbficRkUJARbKIFD47d3LFum+Z3Lg9SdFZ/sFMCotq1aBTJ69ITk72O42IhDkVySJS+EyYoLmRI9WgQbBpE8ye7XcSEQlzKpJFpPAZM0ZzI0eqHj2gTBldwCciQVORLCKFyw8/wJIlmhs5UhUrBtddBx99BPv3+51GRMKYimQRKVzGjoXYWM2NHMkGDYIjR+DDD/1OIiJhTEWyiBQeJ07AuHFw9dWaGzmStW4NDRpoyIWIBEVFsogUHjNnwvbtXk+iRC4z7xyYNw/WrvU7jYiEKRXJIlJ4jBkDlStD585+JxG/DRoE0dHw+ut+JxGRMKUiWUQKhx074OOPYcAAiI31O434rXp16NbN+4fT8eN+pxGRMKQiWUQKh7FjvTHJt9zidxIJFbfe6g2/+fhjv5OISBhSkSwi4c85GD0a2rSBRo38TiOhonNnqFkTXnvN7yQiEoZUJItI+Jszx7tA67bb/E4ioSQ6Gm6+GT77DBIT/U4jImFGRbKIhL/Ro6FcOejTx+8kEmoGD/ae33jD3xwiEnZUJItIeNuxw7u72o03QvHifqeRUFO7tjfs4s03ISnJ7zQiEkZUJItIeDt5wZ6GWkhGbr0VtmyBTz7xO4mIhBEVySISvnTBnmRHt25QpYou4BORHFGRLCLhSxfsSXbExnoX8E2fDps3+51GRMKEimQRCV+6YE+ya/BgSEmBt97yO4mIhAkVySISnnTBnuRE/fpwxRXeLBcpKX6nEZEwoCJZRMKTLtiTnLr1Vm++5C++8DuJiISBXBfJZnaOmS1N9dhvZkPTtGlvZvtStfln0IlFRHTBnuRGz55QoYJ37oiIZCEmtxs6534EmgKYWTSwGZiUTtOvnHPdcnscEZEznLxg7+GH/U4i4aRoURg0CF54AX77DapW9TuRiISwvBpucQXws3NufR7tT0QkY7pgT3JryBDvpiKaDk5EspBXRXI/YEIG6y42s2Vm9omZNc6j44lIpNqxAyZO1AV7kjsNGsBVV8GoUd6YdhGRDARdJJtZEaA78EE6q5cAdZxzTYAXgcmZ7Oc2M0sws4QdO3YEG0tECqvXX4fjx3XBnuTeHXd48yVPmeJ3EhEJYeacC24HZj2AO5xznbLRNhFo6ZzbmVm7li1buoSEhKByiYj/4odNz9P9RackM2/kLfxavjo39HsiT/ct4Sfxya652zA52ZsSrm5dmD07b0OJSFgxs8XOuZbprcuL4RbXk8FQCzOramYWeN0qcLxdeXBMEYlAHdcupMaBHYxtcbXfUSScRUfDn//sXQC6cqXfaUQkRAVVJJtZCaAjMDHVstvN7PbA2z7ACjNbBvwf0M8F23UtIhFr0OKP2VimCrPqX+h3FAl3N9/szXbx8st+JxGREBVUkeycO+ycq+Cc25dq2Ujn3MjA65ecc42dc02cc62dc98EG1hEItO523+l9cYV/K9ZF1Kiov2OI+GuYkXo1w/efhv27cu6vYhEHN1xT0TCwo1LpnEkpijvXZDl5Q8i2XPXXXDoELz5pt9JRCQEqUgWkZBX5sgBeq2cw+RG7dhXPM7vOFJYtGgBbdvC//2fdzGfiEgqKpJFJORdv+xTiicd0wV7kveGDoXERE0HJyJnUJEsIiEtNvkEgxZP5as6TVlTua7fcaSw6dED4uPhuef8TiIiIUZFsoiEtK5r5lP14G7euLCn31GkMIqOhr/8BebPB83PLyKpqEgWkdDlHLd8N5m1FWoxt15zv9NIYTV4MMTFwfPP+51EREKIimQRCVmtNy7nvG0/80bLHjjT15Xkk9KlvUL5vfe821WLiKAiWURC2ODvJrOzRBkmNe7gdxQp7P7yF0hJUW+yiJyiIllEQlK9XZvouO5bxjXrwrHYon7HkcKubl3o2xdGjYK9e/1OIyIhIMbvACIi6bnt24kcjSnCuGZd/I4iISp+2PQ83V/jYhcz/cC7PNnzHka27pNp28Qnu+bpsUUk9KgnWURCTpUDO+m94kveP78jO0uW8zuORIiVVeozL74ZNydMoWjScb/jiIjPVCSLSMi55bvJRLkURl/U2+8oEmFGXnQNlQ/toefK2X5HERGfqUgWkZBS5sgB+i+dydRG7dhUporfcSTCfFOnCcur1Oe2bycSlaJbVYtEMhXJIhJSbloyjZInjjLyomv8jiKRyIyRF/Wh/u7NXPXTAr/TiIiPVCSLSMgofvwogxZ/zOdnteKnSvF+x5EI9ck5l/Bz+ZrcteA9cM7vOCLiExXJIhIy+i+bSfkj+3m19bV+R5EIlhIVzUsX96XR9l+5ct23fscREZ+oSBaRkFDsxFFuX/Qh8+s0YUmNhn7HkQg3tVE7EstW4y/fTFBvskiEUpEsIiFhwNKZVDq0lxcuvd7vKCIkR0Xz8sXXcsFv62j/y2K/44iID1Qki4jvUvcif1frPL/jiAAwqfHlbCpdWb3JIhFKRbKI+E69yBKKkqJjeOXia2m+5UfaJn7vdxwRKWAqkkXEV+pFllD24XlXsql0Je776n/qTRaJMCqSRcRXN3w/Q73IErKOx8TywqX9abp1LZ3WLvQ7jogUoKCKZDNLNLPlZrbUzBLSWW9m9n9mts7MfjCz5sEcT0QKl7hjh7hjwQfMi2+mXmQJWRPPu5yfy9fk3q/G6S58IhEkL3qSOzjnmjrnWqaz7g9Ag8DjNuDVPDieiBQSty6aSLmjB3iq3U1+RxHJUHJUNM+16c+5O9dz9ep5fscRkQKS38MtegBvO89CoKyZVcvnY4pIGKh0cA+3JEzm43PbsrLqWX7HEcnU9HPbsKpyXe6dP56Y5CS/44hIAQi2SHbAZ2a22MxuS2d9DWBjqvebAstEJMLdueBdYpOTeOaygX5HEcmSsyieaTuQOnt/o98Pn/kdR0QKQLBF8qXOueZ4wyruMLPL0qy3dLZJ9/JgM7vNzBLMLGHHjh1BxhKRUFZ7z1b6L53Jexd0Yn256n7HEcmWL+tfyKKajRk6fzzs3+93HBHJZ0EVyc65LYHn7cAkoFWaJpuAWqne1wS2ZLCv0c65ls65lpUqVQomloiEuAfmvU1SVAz/d0k/v6OIZJ8ZIy6/hYqH98GTT/qdRkTyWa6LZDMraWZxJ18DnYAVaZpNBW4MzHLRGtjnnNua67QiEvZablpJtzVfMfKia9geV8HvOCI5srxaAyY1ag/PPQcbNvgdR0TyUTA9yVWA+Wa2DPgWmO6cm2lmt5vZ7YE2M4BfgHXAa8Cfg0orImHNXAr/nPUaW+IqMuqi3n7HEcmVp9vd6L34xz/8DSIi+Somtxs6534BmqSzfGSq1w64I7fHEJHCpfeK2Vzw2zru7nYfR2OL+R1HJFe2lK4M99wD//433H03tExvBlQRCXe6456IFIgSx4/wwLyxfF/tHKY2aud3HJHgDBsGVarAXXdBSorfaUQkH6hIFpEC8eeFH1Dl4G4eu+JWnOmrR8Jc6dLwn//AwoUwZozfaUQkH+g3lYjku/q7NnLbool81LgD39c41+84Inlj4EC49FL4299gzx6/04hIHlORLCL5yzke/+xVjsQW5V8dBvudRiTvmMHLL8Pu3fDQQ36nEZE8piJZRPJVz1VzuGTDD/yn3U3sKlnW7zgieatJE7jjDhg5EpYs8TuNiOQhFckikm9KHz3IP758g6XVzuadpp39jiOSPx57DCpVgltvhaQkv9OISB5RkSwi+eZvc8dQ/sh+/nHVHbpYTwqvsmXhpZe8nuTnnvM7jYjkEf3WEpH8MWsWA5bO5M2W3VlZpb7faUTy1zXXQM+e8M9/wtq1fqcRkTygIllE8t6BAzB4MD+Xr8EzbQf6nUYk/528iK9oUW/YheZOFgl7KpJFJO8NGwYbNvDAH+7mWGxRv9OIFIzq1eHZZ2HuXBg1yu80IhIkFckikrfmzIFXXoG772ZxzUZ+pxEpWDffDB07wv33w08/+Z1GRIKgIllE8s6ePXDTTXDWWfDEE36nESl4ZvDWW96wi4ED4cQJvxOJSC6pSBaRvOEc3H47bNkC48dDiRJ+JxLxR40a3nCLb7+FESP8TiMiuaQiWUTyxltvwfvvw+OPQ6tWfqcR8de113o9yU88AQsW+J1GRHJBRbKIBO/HH+Guu6BDB/jrX/1OIxIaXnwRatWC66/3bl0tImElxu8AIpL/4odNz7d9FztxlInj/kpVF8MfGt7Etn/MzLdjiYSVMmW8v65ceinceCNMnQpR6psSCRf6v1VEcs85nvj0Zc7dnsi9Xe9hW1xFvxOJhJYLL/Tuwjd9Ojz1lN9pRCQHVCSLSK4N/H4616yczfNt+jOn/oV+xxEJTX/+M/TrBw89BLNn+51GRLJJRbKI5ErzTav556zX+KL+hbx4yXV+xxEJXWYwejScfbZ3Qd8vv/idSESyQUWyiORYjX3bGTX5CTaXrsy93e7Dmb5KRDIVF+eNSU5Jgauvhv37/U4kIlnQbzYRyZG4Y4d488PhFE06wS3XPMz+YqX8jiQSHho0gI8+8u7E168fJCX5nUhEMqEiWUSyLSY5iVcm/Zt6uzczpNffWVextt+RRMJLhw7w0kvwySdwzz3eTXhEJCTlukg2s1pmNtvMVpvZSjO7O5027c1sn5ktDTz+GVxcEfFNYCaLtuuX8mDnu1hQp4nfiUTC05AhcO+9XrH8r3/5nUZEMhDMPMlJwH3OuSVmFgcsNrPPnXOr0rT7yjnXLYjjiIjfnOOhL1/nuuWf88Il/fjw/Cv9TiQS3p5+Gnbs8Ga8qFDBu6W7iISUXBfJzrmtwNbA6wNmthqoAaQtkkUkzA39+h1uSZjCWy2u5rk2A/yOIxL+oqLgjTe8O/H9+c9Qvjz07et3KhFJJU/GJJtZPNAMWJTO6ovNbJmZfWJmjfPieCJScG75diJDv57A++dfyWNX3OpNZyUiwYuN/f2OfP37wwcf+J1IRFIJukg2s1LAR8BQ51zaOW2WAHWcc02AF4HJmeznNjNLMLOEHTt2BBtLRPLAnxe8z0Oz32TauW0Z1vkuTfUmktdKlIAZM+Dii+H66+Hdd/1OJCIBQf3GM7NYvAJ5vHNuYtr1zrn9zrmDgdczgFgzS/e+tc650c65ls65lpUqVQomlogEyznun/c2D8x7m4mNO3D31feTEhXtdyqRwikuzpvt4tJLYcAAGDfO70QiQnCzWxjwBrDaOfffDNpUDbTDzFoFjrcrt8cUkfwXlZLMI7NGc+eC93mnSWfu63oPySqQRfJXqVJej3L79jBwIPw33V+rIlKAgpnd4lJgILDczJYGlv0dqA3gnBsJ9AH+ZGZJwBGgn3OaFFIkVBU/fpTnpz3DVWsX8tqFPXmiw2CNQRYpKCVLwvTpXpF8332wcSM8+6x3kZ+IFLhgZreYD2T629M59xLwUm6PISIFp9LBPbz+0WOc/9s6hl9xG2Nadvc7kkjkKVYM3nvPm0f5+ee9QnnMGK+nWUQKVDA9ySJSSFyw9SdenfRvyh3dz229H+KLBhf5HUkkckVFeQVynTpw//3ebawnTYL69f1OJhJRVCSLRDLnuGHpJzw8azQ7Spbj2v5PsbLqWX6nEgl58cOmF8BRzqZtn+G8OPU/WOMm/KX7A4x9XzeuFSkoFopDhFu2bOkSEhL8jiGSpwrml2r2lTp2mBGfvUzPVXOZXa8F93S7j73FS/sdS0TSqLX3N0ZPHEHDHYlez/KIEVC0qN+xRAoFM1vsnGuZ3jpdDSASgS5e/wMz37yDq1d/xTNtb+DmPo+oQBYJURvLVqXXwGcY1/QP8Mwz3pzKa9b4HUuk0FORLBJBih8/ysOzXmPCu3/neHQsfQb8h5cu6aebhIiEuKOxxXjoqjtgyhTvYr5mzeDJJ+HECb+jiRRa+s0oEgmco9NPC/ji9T8xOGEKbzfrStdB/8f3Nc71O5mI5ET37vDDD9ClCzz4ILRsCd9+63cqkUJJRbJIIVd/10be+OgxRk96ggNFS9BnwFP8s9OfOFKkmN/RRCQ3qlWDjz7yZrzYtQtat4Y//hE2b/Y7mUihotktJOKE2gV0+aXygV0M/fodrvvhc47EFuXxDoMZ2+JqkqL1v71IodCzJ1x+OTzxhDdl3Pvvw1//CvfcA2XK+J1OJOypJ1mkkKm6fycPz3qNuaNvo8/yWbzdvCuXDXmdN1r1UoEsUtiULg1PPeVdyNetGzz6KMTHw2OPwd69fqcTCWv6jSlSSDTYsZ6bE6ZwzYoviXIpTGncnucv7c/GslX9jiYi+a1uXe9OfX/7m1cgP/II/Pe/cOutcOed3o1JRCRHVCSLhLHY5BN0XLuIG5dMo/XGFRyNKcKEplfxWqvebCpTxe94IlLQmjeHyZNh6VL497/huee8YrlnTxgyBK64AqKjfQ4pEh5UJIuEG+douvUneq/4km5rvqL8kf1sLFOFf7cfxPvnd2RPCY1FFIl4TZt6PcsbN8Irr8Do0TBxItSsCTfdBNdfD40b+51SJKTpjnsSccLxwr3olGSab15N558WcNVPC6i5fztHY4rw+VkX8dF5lzOvbnNSotQ7JFLYJT7ZNXcbHjsGH38Mb74Jn34KKSnQsCFcey306OEV1VG6TEkiT2Z33FORLL4Ix0K1QDlH3T1buGjDctomfk+bxKWUOXaIY9ExzI9vxsyzL2bmOZdyoGhJv5OKSAHKdZGc2tatXq/yBx/AvHngHFStCp07Q4cO0KaNN8bZLPhjiYS4zIpkDbcQCQEljx2mydafaL5lDc22/EizLT9S/sh+ALaWqsDMsy9hbr0WzK3bnENFS/icVkTCWrVqcMcd3mP7dq9nefp0byzzmDFem6pV4dJLvYL50kvhggugaFE/U4sUOBXJIgWo2Imj1N+9mbN2buCsXZtosGsDDXZuJH7PFqJdCgBrK9Ti87MuYkmNc0mo0YifK9RUj46I5I/KlWHgQO+RkgIrV8L8+fD1197zRx957aKj4eyzvXHM5533+6NePYiN9fcziOQTFckRTsMe8k6RpBOUP7yPCkf2UfXATqrt30mN/TuonupR7cBOovCGOCVZFInlqrO2Yi0+btiWJdXPZWn1c9hfrJTPn0REIlJUFJx/vvf405+8ZZs3ewXzDz/AihXerBkffeQN0Ti5TY0a3tzM8fHeVHPx8d4FglWqeEV4pUoqpCUsqUhORQVjhHGOosknKJp0nKJJJyhy8nWy977k8SOUOnaYuOOHT3td6pj3Pu7YIcodOUCFw/sof3gfpY8fPuMQx6Ni2Fq6IltKV2JBnQvYULYqayvUYm3F2qwvV40T0frFISIhrEYN6NvXe5x0+DCsXu0VzT//DImJsH49zJ0LmzZ5PdJpVajgFcwVK3p3AyxTxrsRSnrPcXFQvDgUK/b7I/X72Fj9dU0KhIrkk556imenf/b7+zQXNKb3v6Od0SbN+3SuiTyzTdbHOTNL5vtIbz+5Oe6Z+83FcbPI7rVJu49sHMc5YlwyUSkpxKQkE+1SiE71HJOSQpQLPKeknN42JdkrhJOTzthvVo5Fx3KwSHEOFi3BoSLF2V28ND9Ua8CuEmXYVaIMu0uUYVfxMmyLq8Dm0pXYWbIsznTFuIgUIiVKQIsW3iOtEye8QnnLFti2zXts3/77886dXu/0qlWwfz/s2+dtkxNm3vjo2FiIifn9ER2d+fvUy6Kifi+0zTJ+ZLY+p9vmt/w+Rn7vv3dvb6aVEKIi+aRly2i1ceVpi84oEdM5QVyastBZ5uvT30+afaQTL+02WR03/TaZn+DZ+3z5k/XMn0HWP9ekqGiSo6I5Hh1LclQ0yVFR3rP9/pyUdllUFMkWzbGYIhyLieV4dGzgdRGORcdyLCaWY9HeukOBYvhgkRIcLFKcQ0VKcDxGPb8iIhmKjfVmxqhbN3vtnfOmpztZMO/f7z2OHj39ceTIma+TkyEp6fRHdpYdO/Z7b7dzGT+CWZ92XX7L72MUxGdI7x9dPtMUcKlouIWIiEj68mT6OZEQk9kUcPo7sIiIiIhIGkENtzCzzsALQDTwunPuyTTrLbC+C3AYGOScWxLMMUVERKTg+fXXVvVgi19yXSSbWTTwMtAR2AR8Z2ZTnXOrUjX7A9Ag8LgIeDXwLCIiIhKy/ByCqX8YhIZgepJbAeucc78AmNm7QA8gdZHcA3jbeQOfF5pZWTOr5pzbGsRxRUREJELoeiHxSzBFcg1gY6r3mzizlzi9NjUAFckiIiIi6YjEfxiEYu95MEVyehN5pZ0qIzttvIZmtwG3Bd4eNLMfg8gmp6sI7PQ7hIQFnSuSEzpfJCd0vkiG7KnT3hbkuVInoxXBFMmbgFqp3tcEtuSiDQDOudHA6CDySAbMLCGj6U1EUtO5Ijmh80VyQueLZFeonCvBTAH3HdDAzOqaWRGgHzA1TZupwI3maQ3s03hkEREREQl1ue5Jds4lmdmdwKd4U8C96ZxbaWa3B9aPBGbgTf+2Dm8KuD8GH1lEREREJH8FNU+yc24GXiGcetnIVK8dcEcwx5A8oWEskl06VyQndL5ITuh8kewKiXMlJG9LLSIiIiLiJ92WWkREREQkDRXJYczMOpvZj2a2zsyGZdLuQjNLNrM+qZYlmtlyM1tqZgkFk1j8lNX5YmbtzWxf4JxYamb/zO62UvgEeb7o+yWCZOf7IXC+LDWzlWY2NyfbSuES5PlSoN8tGm4RpgK3Bf+JVLcFB65Pc1vwk+0+B47iXVz5YWB5ItDSOac5KyNAds4XM2sP3O+c65bTbaVwCeZ8CaxLRN8vESGb50pZ4Bugs3Nug5lVds5t13dL5AnmfAmsS6QAv1vUkxy+Tt0W3Dl3HDh5W/C07gI+ArYXZDgJOdk9X/J6WwlP+m8u2ZWdc6U/MNE5twHgZMGTzW2lcAnmfClwKpLDV0a3/D7FzGoAvYCRnMkBn5nZ4sDdDqVwy/J8CbjYzJaZ2Sdm1jiH20rhEcz5Avp+iSTZOVfOBsqZ2ZzAOXFjDraVwiWY8wUK+LslqCngxFfZueX388DfnHPJZmc0v9Q5t8XMKgOfm9ka59y8fMgpoSE758sSoI5z7qCZdQEmAw2yua0ULsGcL6Dvl0iSnXMlBmgBXAEUBxaY2cJsbiuFS67PF+fcTxTwd4t6ksNXdm753RJ4NzCGpw/wipn1BHDObQk8bwcm4f0JRAqvLM8X59x+59zBwOsZQKyZVczOtlLoBHO+6PslsmTn+2ETMNM5dygwlnQe0CSb20rhEsz5UuDfLSqSw1eWtwV3ztV1zsU75+KBD4E/O+cmm1lJM4sDMLOSQCdgRcHGlwKW5fliZlUt8CcHM2uF9/2wKzvbSqGT6/NF3y8RJzvfD1OAtmYWY2YlgIuA1dncVgqXXJ8vfny3aLhFmMrmbcEzUgWYFPj9FgO845ybmd+ZxT/ZPF/6AH8ysyTgCNAvcNfMdLf15YNIgQjmfDEzfb9EkOycK8651WY2E/gBSAFed86tANB3S2QJ5nwxs3oU8HeLpoATEREREUlDwy1ERERERNJQkSwiIiIikoaKZBERERGRNFQki4iIiIikoSJZRERERCQNFckiIiIiImmoSBYRERERSUNFsoj4xsycmYXFZO1mNieQt6zfWeR0ZjbczDabWbKZXeZ3HhEpHFQki4hkz4fAC8Cx/D6QmQ0KFORD8/tY4c7MmgCPAMWB14At/iYSkcJCt6UWEckG59xLfmeQdNUOPL/tnBvqZxARKVzUkywikgkzK+53BslUdOB5n68pRKTQUZEsIiEjMO43ycxKmtmTZrbBzI6a2RozuzVVu5mB4Qg90tlH98C6UamWNTezd81sU2B/iWY21swuSLPtmMC2DczsFTPbDQxJle20McnZ3W8OP9sc4K3A2+cCx4zP4mfmzCzOzF40s21mtt/MpptZPTOrY2bvm9leMztgZp+YWb00+8jJ54gys8FmtjhwnH2BDJ1z0y6Tz1XRzJ4PZDkWGHM82sxqpPlZTQq8/Wfg59A+G/teaWaHzayEmT1oZqsCn3urmT1tZtFZ7UNECj8NtxCRUGPAZ8BZwCd431PXAKPNbLNzbgbwDnAV0BOYkmb7PoHn8QBm1hL4OrBsBrANOBcYCFxrZk2cc2vT7GM83p/xpwPL0g2Zu/1m57N9CBwHOgLzgO+B/ellSONzoHIgcxOgC1AHKAOkABOB+kBnvJ/Z+bn8HM8CQwM/l3eA8nj/LaabWXfn3PQctjuDmVUNZKoHfBnIVQ+4GehpZpc559YEflYHgG7AImAhsCmzH1LgLwPnAOuB2UCxwDHmA/2B+wP7eCGz/YhIBHDO6aGHHnr48gCc9zV06v2cwLIfgPKplg8MLB8feB8HHAZ2ANGp2sUCe/AKIAsseyWwbfs0x340sPz+VMvGBJatBaqkaX8yW9mc7jcnny2wbFBg2dBs/AxP7ncmUDzVz2F1YPlioGSq9p8FljfOxc+nBF4BvwyISrW8NnAQmJeTdpl8pncDxx6SZnkXIBlYmGpZz0Db4dk851qfPO+Av508TwLr+geWT/H7/w099NDD/4d6kkUkFP3VObc71fupgec6AM65A2Y2DbgWuBSvxxXgSqAsMNI5d3JquS+Adc65OWmOsTzwXCqd4z/lnNuWRcbc7Bey+GxBGO6cOwLgnDthZkvxeoSfdc4dStXuW7xe6lrASnL2OUriFeBl8P6hsi9wvA1m1jGwLiftzmBmFfD+GrAWGJ16nXNuhpl9AXQys7Odcz9l9gPJQLPA8yTn3FNp1i0JPGsoooioSBaRkHTaEAfn3D4zA6/4OukdvCK5B78XydcEnsel2nYigJlVxyuQ6uL96b4PGfshq4C53C9k77PlxvI0709OVfdzmuVJgedigeNn+3M453aY2WS83tsfzWwqMBf40jm3IKftMtAS72K8man+oZPaIqAT0BjITZHcPPA8Op11lQPPv+RivyJSyOhfyyISio5msNxSvZ4B7MUrkglcbNUDWOqcW3lqA7OGZvY1sBmYBgwHWvD7ONz0HM8qYC73C9n7bDmWprc4tUzndc7F57gW72LGn4A/4v2DZLOZfWNml+SiXVoVA88ZzXd8OPCc21lHmuEN2Zibzromgefvc7lvESlEVCSLSFhyzh0ncDGamZ0HtMcrsMafbGNmMXjDGVrgFWwVnXMVnXPtgPdze+z82m9By83ncM4lOedGO+cuA8oBf8Ab13whMMPM4nLSLh0ni+DyGaw/ObvF9hx8VADMLBY4D1h9cmhKGi0Cz4tzum8RKXxUJItIOHsn8NwTb3hACjAh1fpz8GaSmBgo2HalWnfaNGg5lF/7LWg5+hxm1trMJptZOwDn3EHn3Ezn3J14d7srAzTObrsMMp0cNtIug/Wd8YaM5KaQbQQUzWTbFsARvIseRSTCaUyyiISz2cBWoDdQHZjtnNucav3JYRO1zMxOjnENzP/71yCOm1/7PSkl8Jzf39E5/Rz78Ya0xJrZQufcsUD7WOACvJkhNuIVwdlpdwbn3DozWwi0NrNrnXMfnFxnZjfgFfXvOuf25OLznhyPvCTtisDUcA2B75xzSWnXi0jkUU+yiIQt51wK8B7eONMqpBpqEbAO+ApoA3xrZiMDsyMswZsyDaC/mQ3K4aHza78nnSwg7zKz/zOzjIYeBCtHn8M5twrv5h1dgFVm9j8zewP4EW+WkZHOuc3ZbZdJriF4M2K8Z96NY142s5nA23g/m/tz+XlPzmyRXk9yU7wLBjXUQkQAFckiEv5ODrk4CnyUekWgZ7Q3MBZvjt7+eN97VzvnBuEV1XUI3Fgju/Jrv6nMxZsruALenMn5cmvsXH6OG/FuFOKAvoFtDgD3AHfmol16uX7AG7v8Ht4QiFvxprMbCbTKosDOTDO8Xvql6aw72cusIllEgN8n2xcREYlYZvYm3iwcTQJFuohEOPUki4iIeD3WR4FVfgcRkdCgIllERCKamRXDm/limS7aE5GTVCSLiEika4I3k4jGI4vIKRqTLCIiIiKShnqSRURERETSUJEsIiIiIpKGimQRERERkTRUJIuIiIiIpKEiWUREREQkDRXJIiIiIiJpqEgWEREREUlDRbKIiIiISBr/DwuN3pNRu36HAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,5))\n",
    "# data invariant mass of eta signal (signal + peaking background)\n",
    "data = eta_sig_InvM.dropna()\n",
    "\n",
    "# plot the histogram\n",
    "counts, edges, _ = plt.hist(data, bins=20, density=True, label='Signal')\n",
    "# getting the middle of each bin to make length of counts and edges the same\n",
    "x_data = (edges[:-1] + edges[1:]) / 2\n",
    "y_data = counts\n",
    "\n",
    "# estimate the location and the scale of the distribution which are mean and standard deviation respectively\n",
    "loc = np.mean(data)\n",
    "scale = np.std(data)\n",
    "\n",
    "def crystalball_f(x, beta, m, norm, mu, sigma):\n",
    "    return norm * crystalball.pdf((x - mu) / sigma, beta, m) * sigma + mu\n",
    "\n",
    "# Initial parameter estimates\n",
    "beta0 = 2.0\n",
    "m0 = 3.0\n",
    "norm0 = 1.0\n",
    "mu0 = loc\n",
    "sigma0 = scale\n",
    "\n",
    "p0 = [beta0, m0, norm0, mu0, sigma0]\n",
    "\n",
    "# Fit Crystal Ball function to data\n",
    "params, pcov = curve_fit(crystalball_f, x_data, y_data, p0)\n",
    "beta_eta, m_eta , norm_eta, mu_eta, sigma_eta = params\n",
    "print('optimal parameters: ',params)\n",
    "\n",
    "\n",
    "# Plot the histogram and fitted PDF\n",
    "x_vals = np.linspace(np.min(edges), np.max(edges), 200)\n",
    "plt.plot(x_vals, crystalball_f(x_vals, *params), 'r-', label='Fitted PDF')\n",
    "plt.xlabel('Invariant mass of $\\eta$', fontdict=form_label)\n",
    "plt.legend(fontsize='20')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "c5e1bb78",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = lambda x : crystalball_f(x, beta=params[0],m=params[1],norm=params[2],mu=params[3],sigma=params[4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "9ee00c96",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eta: \n",
      "The area under the pdf function:  0.9937013382005413\n",
      "The area of the histogram:  1.0000000000000016\n"
     ]
    }
   ],
   "source": [
    "# checking if the number of enteries in pdf function and the histogram are the same\n",
    "import scipy.integrate as integrate\n",
    "\n",
    "print('eta: \\nThe area under the pdf function: ',integrate.quad(y,np.min(x_vals), np.max(x_vals))[0])\n",
    "# get the width of each bin\n",
    "bin_width = edges[1] - edges[0]\n",
    "# sum over number in each bin and mult by bin width, which can be factored out\n",
    "integral = bin_width * sum(counts[:])\n",
    "print('The area of the histogram: ', integral)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "e4436b8e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[inf inf inf]\n",
      " [inf inf inf]\n",
      " [inf inf inf]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# looking at the covariance matrix\n",
    "print(pcov)\n",
    "plt.imshow(np.log(np.abs(pcov)))\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "115aaaca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(nan)"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean, var, skew, kurt = crystalball.stats(2, 3, moments='mvsk')\n",
    "skew"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6583a50d",
   "metadata": {},
   "source": [
    "### Another way of fiding the best fit to the histogram (using the built_in function Fitter in Python)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "952edd24",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.01631044 0.01681985 0.01681985 ... 0.01633563 0.01709324 0.01709324]]\n"
     ]
    }
   ],
   "source": [
    "# normalizing the eta_sig_InM values\n",
    "from sklearn import preprocessing\n",
    "\n",
    "# removing nan\n",
    "cleanedList = [x for x in eta_sig_InvM if str(x) != 'nan']\n",
    "\n",
    "normalized_arr = preprocessing.normalize([cleanedList])\n",
    "print(normalized_arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "fa1594ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Fitting 1 distributions: 100%|████████████████████| 1/1 [00:00<00:00,  3.35it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best fit:  {'crystalball': {'beta': 6.874131935657582, 'm': 5.52359400467754, 'loc': 0.5354250673682897, 'scale': 0.026659854875006953}}\n",
      "Identifying the parameters:  (6.874131935657582, 5.52359400467754, 0.5354250673682897, 0.026659854875006953)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "from fitter import Fitter, get_common_distributions, get_distributions\n",
    "plt.figure(figsize=(12,5))\n",
    "\n",
    "f = Fitter(\n",
    "    cleanedList,\n",
    "    distributions=['crystalball']\n",
    ")\n",
    "\n",
    "f.fit()\n",
    "f.summary()\n",
    "print('best fit: ', f.get_best(method='bic'))\n",
    "print('Identifying the parameters: ', f.fitted_param[\"crystalball\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "ef83d590",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5.65427011e+02 -9.60739205e+00  4.86521523e-01]\n"
     ]
    }
   ],
   "source": [
    "# background\n",
    "# Fit the function a * np.exp(b * x) + c to x_data and y_data\n",
    "popt, pcov = curve_fit(lambda x,a,b,c: a * np.exp(b * x) + c, x_data, bin_value[0])\n",
    "a_eta, b_eta, c_eta = popt\n",
    "print(popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e024726",
   "metadata": {},
   "source": [
    "## Signal and Background to fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "63d3a843",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The area below the PDF function:  1.0025248501377284\n",
      "The area of the histogram:  0.990837633265723\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x13cb9d310>"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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///3vvPTSSxx++OE8/vjjXHHFFckuT6pR7DkDsjZP2LMdmkOfU+cy7tHDyMxOhzVZLB43izPOfIuvG24pt7qWlNuRJEmSivfTn/6Un/70p8kuQxL2nJXaWx2+5aJTZrM1LZ4Xo+Pq+jz08BG03JCZ5MokSZIkVUWGszJ4tfPXXDxiNtsSAa3zqgaMf/hwmm/MSHJlkiRJkqoaw1kZvbTfCn520hy2hzig7fdtQx585HCabqqd5MokSZIkVSWGs3LwfLevuOzEd8kO8Zxx3Vc24sFHDqfxdwY0SZIkSSVjOCsnT+//Jb844T1yiAPaAV835oH/9qbRZsdckSRJkrR7hrNyNPGAL/j1ce/nPT/oqybc99/eNNhiQJMkSZK0a4azcvboQcu44tj8gHbIl00Z9+hh1N+SnsSqJEmSJKU6w1kFeLjH51w55MO8572+aMY9jx1G3a0GNEmSJEnFM5xVkAcP/Yyxg+fmPT98WXPufrwXdbb5lkuSJEkqyqRQgcb1WsJ1g+blPT9yaQvueKIXmdt92yVJqmnGjRtHCIFx48Ylu5QSCSEwcODAZJch1SiOVFHB7uq9mNo5afz6tW4A9F/Skv880ZMLTn2HrbVyklydJEkVZGzjZFewa2PXlsthsrOzueeee3jwwQf54IMPWL9+PU2bNmXvvfemd+/eDB8+nOHDh5fLuSRVf4azSnDbEZ9SKzvwi2ldARi4eC9unXgoPznlHbalR0muTpIklUZ2djYnnngiL7zwAk2aNOGEE06gbdu2rFq1ik8//ZQJEyawYMGCvHB2yimncMQRR9C6deskVy4pVRnOKsktfT+hVk4a/+/NLgAc82krbnnqUC4ePpvtBjRJkqqchx56iBdeeIGDDz6Y1157jcaNC/cWbtq0ibfffjvveePGjYtsI0kFefNTJfpHv4+49YhP8p4P+2hvbn76ENJzQhKrkiRJpfHmm28CcN555xUbuurVq8egQYPynu/qnrMXX3yRvn37Ur9+fZo1a8bJJ5/MggULOO+88wghsGTJkrxtlyxZQgiB8847jyVLljBq1ChatGhBnTp16NWrF88880yR469du5Ybb7yRo48+mrZt25KRkUHLli0ZPnw4M2bMKPubIalcGM4qU4C/9F/IHYctyms6YWFr/vnUIdTKNqBJklSVNG/eHICPPvqoTMd55JFHOP7445kzZw7f//73ufDCC1m9ejV9+vQpFMp29Nlnn9G7d2+WLFnCOeecwxlnnMGHH37IiBEjePXVVwttO3/+fH73u9+RlpbGCSecwM9//nOGDBnClClTOOqoo3jhhRfK9BoklQ8va6xsAf40aD61cgLnv9MRiANa7ZzAxcPnOEiIJElVxKmnnsoNN9zA7bffzvr16znllFPo2bMnHTp0KPEx1q9fz0UXXUStWrV46623OPjgg/PWXXHFFdxwww073Xfq1KmMHTuWq6++Oq/trLPOYtiwYdx4442Feu26d+/O8uXLadGiRaFjLFu2jN69e3PZZZcxbNiwEtctqWLYc5YMAa4dPI97ei7Oaxr68d7cNvFQh9mXJKmKOOSQQ3jwwQdp1aoVDz74IKeddhpZWVk0b96cU045haeffnq3x5g0aRJr1qxh9OjRhYIZwJVXXkmTJk12um+HDh248sorC7Ude+yxtG/fnv/973+F2hs3blwkmAG0bduWkSNHsmDBApYuXbrbeiVVLJNAsiQC2n96f5rXNPjTVtz5eC8ynahakqQq4fTTT2fp0qW8+OKLXHXVVZx44onk5OQwceJEhg8fzrnnnksU7Xzgrzlz5gDQr1+/IusaNGhAjx49drpvjx49SE9PL9Lerl07Vq9eXaR9+vTpnH766bRr147MzExCCIQQuOWWWwD44osvdvdyJVUwL2tMpgDXD1zAtvSIi9/aF4jnQbvn8cP40amzklycJEkqidq1azN06FCGDh0KxEPsP/7445x//vncf//9nHLKKZx88snF7rt2bTzfWqtWrYpdv7N2YKe9arVq1SInp/BtEk8++SQjR46kTp06DBkyhM6dO1O/fn3S0tKYOnUqr732Glu2bNnNK5VU0QxnyRbgr0ctZGt6Nj9PzIPW97MWjHv0MLgGaJjc8iRJ0p5JT0/n9NNP54MPPuC6665jypQpOw1njRo1AmDFihXFrt9Z+5666qqryMjIYNasWXTv3r3QugsvvJDXXnutXM4jqWy8fi4VBPhn30/4S/8FeU2HL2sOxwJrk1eWJEkqvYYN47+w7uqyxkMOOQSAadOmFVm3YcMG3n333XKp5ZNPPmH//fcvEsxycnKKPbek5DCcpZBb+3zKdYPm5Te8BQwFil42LkmSkuyhhx7i5ZdfLnIJIcBXX33FnXfeCUD//v13eowRI0bQuHFjxo8fz3vvvVdo3XXXXceaNWvKpdasrCw+/vhjli9fntcWRRHXXHMN8+bN28WekiqTlzWmmLt6L2ZbesQ1rxwQN/wPOAZ4CWiexMIkSVIhb7/9NjfffDN77703/fr1o2PHeIqcxYsX8+yzz/Ldd98xYsQIRo4cudNjNGrUiFtvvZWzzz6bI488ktNPP53WrVvz5ptv8t577zFgwABee+010tLK9vf0yy67jIsuuohDDjmE0047jdq1azN9+nTmzZvHSSedVKKRJSVVPMNZCrqv5xK2p+Xwx5e+FzfMBo4GXgFaJrEwSZKU5xe/+AVdunThlVde4f333+fFF19k8+bNNG/enIEDB3LWWWdx1llnEULY5XHOOussmjZtyh/+8AceeeQRMjMz6d+/P2+99RaXX345kH9vWmldeOGFZGZmctNNN3HfffdRt25djjrqKO69914ef/xxw5mUIsKuroMub7169YpmzUq9UQizrng22SUUa8l+J8CPgNx/ov2BycDeyatJkiSA+fPnF7l/SeUrOzubTp06sWXLFr766qtklyNpN0r6vRhCeCeKol7FrfOes1R2PnAf+f9K84CBwPKd7SBJkqqaNWvWsGnTpkJtURRx3XXXsXTpUk499dQkVSapsnlZY6o7h/hf6RwgG1gIDACmAO2SWJckSSoXM2bM4IwzzmDo0KFkZWWxYcMGZsyYwbvvvku7du0YO3ZsskuUVEkMZ1XBmUAGMArYDnxCfkDLSl5ZkiSp7Lp27cqJJ57I9OnTee6559i+fTtt27blZz/7Gb/97W/Za6+9kl2ipEpiOKsqTgMeB0YC24DF5Ae0zkmsS5IklUnHjh0ZP358ssuQlAK856wqGQ5MBDITz5cC/YnvRZMkSZJUpRnOqprjgaeBOonny4kDWuoNgilJkiRpDxjOqqIhwPNAg8Tzb4nnQZuarIIkSZIklZXhrKoaSHy/WbPE8/XAMOCZZBUkSZIkqSwMZ1XZYcDrwD6J51uAU4AJSatIkiRJUikZzqq6A4BpQKfE8+3A2cBtSatIkiRJUikYzqqDjsQB7cDE8wj4KXB90iqSJEmStIcMZ9VFa+A14PACbb8Ffk0c1iRJkiSlNMNZddIMeIV45MZcfwEuArKTUpEkSZKkEjKcVTcNgGeBEQXa7gBGA1uTUpEkSapGxo4dSwiBqVOnlnifJUuWEELgvPPOq7C6pOrAcFYd1QEeA84p0PYIcDKwKRkFSZJUPYUQCi3p6em0aNGCo48+mvHjx+92+8zMTFq2bMmhhx7Kj370I55//nmys4u/3OW8884rsn/BZeDAgRX8anetMmtIhderijN16lRCCIwdOzbZpVS6WskuQBWkFjAOaAz8K9H2PPFcaE8n2iVJUrm4+uqrAdi2bRsLFy5k4sSJvPrqq7zzzjv8/e9/3+n22dnZrFmzhrlz5/LAAw9w991306tXL8aPH89+++1X7LlGjBhBjx49irRnZWWV2+vZlYsvvphRo0bRvn37SjmfVJMYzqqzNOCfQFPgD4m2N4BBwItAyyTVJUlSNbPjX/gnT57MkCFDuOmmm/jZz35WJDgV1yOwYsUKLrnkEh599FGOOeYYZs2axV577VVku5NPPjmplwe2aNGCFi1aJO38UnXmZY3VXQCuBf5WoG0O0B/4PCkVSZJU7Q0ePJhu3boRRREzZ84s0T6tWrXi4YcfZuDAgXz++ef86U9/Kve6+vTpQ2ZmJhs3bizU3r9/f0II/PCHPyzUPm/ePEIIjBkzJq9tx3vOxo0bRwgBgNdee63QpZbFhdAlS5YwatQoWrRoQZ06dejVqxfPPPNMierf3bk2bNhARkYGffv2LbTfd999R506dQgh8MADDxRad+uttxJC4J577inU/vHHHzNmzBjatGlDRkYG++yzD2PGjOHjjz8uUa25rzX3XrsFCxZw8skn06xZM+rXr0+/fv146aWXiuyzdu1abrzxRo4++mjatm1LRkYGLVu2ZPjw4cyYMaPY8+Re5vnVV1/xox/9iDZt2pCens64ceMA+Oijj7jiiivo1asXLVu2JDMzkw4dOnDBBRewbNmyIscreFnhrFmzGDZsGI0bN6Zp06acdtppfP55/EvkokWLGDVqFC1btqRu3boMGjSI9957r9gaN23axPXXX0+PHj2oX78+DRo0oE+fPjz00EOFtjvvvPMYNGgQANdcc02hf+Md73N86KGHGDRoEE2bNqVOnTp0796d6667ji1btuzxe7RixQouv/xyunbtSv369WnSpAldu3blvPPOY9GiRcW+popgz1lN8XOgCfBjIAdYAPQDXgaKv2pCkiSVQRTFc9nkhomSSEtL48orr2Tq1Kk89NBD/OMf/9ij/Xdn8ODBzJgxgzfeeINhw4YB8S/Nb7/9NhD3+BU0ZcqUvP12pkePHlx99dVcc801dOjQoVCv3o73hX322Wf07t2bTp06cc4557Bq1SoeeeQRRowYwSuvvJL3S3lpz9WgQQN69+7N22+/zfr162nYsCEA06dPz/uFffLkyZxzTv6N+cW9xpkzZ3LMMcewfv16hg8fzv7778+CBQsYP348kyZNYvLkyfTq1WuXtRa0ePFi+vTpw4EHHsiFF17Il19+ySOPPMJxxx3HhAkTOOOMM/K2nT9/Pr/73e/o378/J5xwAk2bNmXp0qU89dRTPP/88zz99NN5/3YFrVq1iiOOOIIGDRpw6qmnkpaWRqtWrQB44oknuP322xk0aBBHHnkkGRkZzJ07l7vuuounn36aWbNm0aZNmyLHnDlzJjfccAMDBgzgxz/+MR988AFPPPEEH3zwAU899RT9+vWjW7dujBkzhs8++4wnnniCIUOGsGjRIho0aJB3nDVr1nD00UczZ84cDj30UM4//3xycnJ48cUXOeuss5g7dy7XXXcdEPcMA9x3330MGDCg0GeoYA/0D3/4Q+655x7atm3LqaeeSpMmTZgxYwZXXXUVkydP5uWXX6ZWrcJRZ2fv0aZNm+jbty+ffvopQ4YM4aSTTiKKIj777DMmTZrEyJEj6dSpU4n/vcskiqJKW3r27Bmlog6/fiYllwrxaBRFtaP8f5UWURTNqJhTSZKqr3nz5iW7hJRAPJtokfaXX345CiFEIYRoyZIlu92+oM2bN0e1atWKgGjRokV57eeee24ERCNGjIiuvvrqIsvq1at3W+/kyZMjILr88svz2l544YUIiIYMGRIB0SeffJK37uSTT46AaOnSpXltV199dQREr776apH3YsCAAcWed/HixXmvfezYsYXW5Z7/uOOO2239JTnXVVddFQHRM8/k/y51xRVXROnp6dGgQYOitm3b5rVnZ2dHzZs3jzp16pTXlpOTE3Xr1i0CogcffLDQsR9++OEIiLp27RplZ2fvts6Cr7vgex5FUTRz5syoVq1aUZMmTaK1a9fmta9ZsyZauXJlkWN9/vnnUevWraNu3boVWZd7jnPOOSfatm1bkfXLli2LNm/eXKT9xRdfjNLS0qKLLrqoUPurr76ad8wd34Pzzz8/AqKmTZtG1113XaF11157bQREN910U6H23M/uDTfcUKj9u+++i4499tgohBDNmTOnyPmvvvrqIjVHURTde++9ERCdcsop0aZNmwqty/187ljDrt6jp556KgKiSy+9tMi5tmzZEq1bt67YOnZU0u9FYFa0k7zkZY01zUjiAUHqJZ5/Qzwv2rNJq0iSVN2EKrSUk7FjxzJ27Fh+97vfMXLkSIYNG0YURVx66aV06NBhj46VmZlJ8+bNAVi5cmWR9ZMmTeKaa64psqxZs2a3xz7yyCOpU6dOoR6yyZMnU6tWLa655pq85wA5OTlMnTqVLl260K5duz16DTvToUMHrrzyykJtxx57LO3bt+d///tfuZwjtwdsx9fYs2dPTjvtNJYtW8ZHH30EwLvvvsu3335bqNfszTffZMGCBfTp04fRo0cXOvYZZ5xBv379WLhwIdOmTStxTY0bN+b3v/99obZevXoxevRo1qxZw5NPPllo2+Lu6Wvbti0jR45kwYIFLF26tMj6jIwM/vrXvxbpLQJo06YNmZmZRdqHDh3KAQccwIsvvlhs3f369SvyHpx77rl5dV5xxRWF1uVe/vruu+/mtX377bc8+OCD9OrVi1/96leFtq9Tpw433HADURQxYcKEYmsozs0330ytWrW45557qFu3bqF1V111Fc2bNy92tNRdvUdAkWPl7pPbA1sZvKyxJjoWmAKcAHxLPLz+COL50M5PYl2SJFVRucEmhECTJk046qij+OEPf8jZZ59dquNFu7gk8t577y31gCB16tThyCOP5NVXX+Xbb7+lefPmTJkyhcMOO4w+ffrQqlUrJk+ezAUXXMDs2bNZs2ZNoUvuyqpHjx6kp6cXaW/Xrh1vvfVWuZyjT58+1K1bNy+crV27ltmzZ/OrX/2Ko48+GojD2n777Zd3SWNuO8Ds2bOLtBV09NFHM23aNObMmUP//v1LVNOhhx5a7C/4AwcO5L777mPOnDl5oQfiyzBvvvlm3nrrLb7++mu2bi08We0XX3xRZLTMrKysYgeQgfjzNH78eMaNG8d7773H6tWrC03ZkJGRUex+xV26uc8++wDF/1vmXhpZ8D62mTNnkp2dvdN7ELdt2wbEl3OWxKZNm3jvvfdo0aIFN910U7HbZGZmFnu8nb1HAwYMoE2bNvz5z39m9uzZHH/88fTt23enn9eKZDirqQ4H3iQOakuAbOCHwHLgd5TrXxMlSarucsNUedi8eTOrVq0CoGXL8h9aefDgwUyZMoVXX32VwYMHM2fOHH77298CcfB4+eWXiaIoL9zs6n6zPdWkSZNi22vVqkVOTk65nCMjI4N+/frxyiuv8PXXX/PWW2+RnZ3N4MGD6d69O/vssw+TJ0/mJz/5CZMnTyaEUCiIrV27FoDWrVsXe/zc9pL0VObKvfdrR3vvvXehcwI8+eSTjBw5kjp16jBkyBA6d+5M/fr1SUtLY+rUqbz22mvFDniRe6zi/PznP+emm26idevWHHvssbRp0yavl2jcuHF89tlnxe7XuHHRuZdye512tS43cEHccwZxSNvV4DgbNmzY6bqCVq9eTRRFrFy5Mu+PIiW1s/eoUaNGzJgxg6uvvpqnnnoqryexRYsW/PSnP+XKK6+kdu3ae3Su0jKc1WT7EQe044F3E21XEQe0W4DK/UOBJKm6KL+cUiNNmzaN7du306pVqwqZuyw3iLzyyiukpaWRk5OTF8COPvpoHnroId5777284LK7QTpSUW7InDJlCm+++SaZmZl5IzgOGjSI559/ni1btvDGG29wwAEHFOpNyQ0dX331VbHH/vLLLwttVxIrVqwotj33HAWPddVVV5GRkcGsWbPo3r17oe0vvPBCXnvttWKPtbOBY77++mv++c9/cuCBB/Lmm28W6cHbcbTE8pb72i677LJi5/wr7fEOOeSQvF7OktrV4Dpt27bl7rvvJooi5s2bx5QpU/j3v//NtddeS05ODn/4wx92um95KtM9ZyGEy0IIc0MIH4YQHgoh1CmvwlRJWgOvAQX/KHYb8H3gu6RUJElSjZWTk8Mf//hHAM4666wKOcdhhx1Go0aNmDx5MlOmTKFu3br06dMHyO8le+6555g+fToHHXRQiec0S0tLK3SpXEXa3bkK3nc2ZcoU+vbtS506dfLWrVq1ittuu42NGzcW6Rk85JBDAIoM254rt/3QQw8tcb2zZ89m/fr1Oz1W7jkBPvnkE/bff/8iwSwnJ2eP7nPLtWjRInJychg6dGiRYLZs2bIKHya+d+/epKWl8cYbb5R4n9xLCYv7N27QoAEHHHAAc+fOzethLk8hBA444AAuueQSXn75ZQAmTpxY7ufZmVKHsxBCG+BnQK8oig4k7mcZVV6FqRI1Ap4DzizQ9iQwFFidlIokSapxvv76a0aNGsXUqVNp37593qWG5S09PZ3+/fvzySef8Oijj9KvX7+8wSI6duxIVlYWN998M5s2bdrpfVfFad68ed78VxVtd+fq2bMnTZo0YdKkScydO7dQAMv9+frrrweK3lvWt29funbtyrRp03jssccKrXvsscd4/fXX2W+//ejXr1+J6127di3XXnttobZZs2Yxfvx4GjduzCmnnJLXnpWVxccff8zy5cvz2qIo4pprrmHevHklPmfB40HcI1sw7GzYsIEf//jHbN++fY+PuSf22msvRo8ezaxZs/jDH/5Q7Pk+/fRTFi9enPc8d0Cc4gY+gfgyza1bt3L++ecXe3np6tWr96hX7cMPP2TJkiVF2nN7POvVq1dkXUUp62WNtYC6IYRtxOP/Ld/N9kpVGcCDwD7kT1g9jXgutBeA8hmkSZIkQd7ACDk5OaxZs4a5c+cybdo0tm7dSu/evRk/fnyJe6xKY/DgwTzzzDN8/fXXRXqOBg8ezN133533854c8+GHH+akk06iZ8+e1KpVi/79+5d40Iw9sbtzpaWlMWDAACZNmlTkdbRv357OnTvz6aefkp6ezoABAwodO4TAfffdx5AhQzjjjDMYMWIE3bp1Y+HChUycOJGGDRty//33k5ZW8j6O/v37c9ddd/H222/Tt2/fvHnOcnJy+M9//kOjRo3ytr3sssu46KKLOOSQQzjttNOoXbs206dPZ968eZx00kk8/fTTe/Re7b333owaNYqHH36YHj16MHToUNauXcvLL79MnTp16NGjR6HRFSvCv/71Lz7++GN+//vf88ADD9CvXz9atWrF8uXLmT9/PjNnzuShhx6iY8eOAHTt2pU2bdrw8MMPk5GRQfv27QkhcM4559ChQwfOP/983nnnHW699VY6d+6cN+LnqlWrWLx4Ma+//jo/+MEPuP3220tU3yuvvMLPf/5zjjzySLp168Zee+3FsmXLmDRpEmlpafzyl7+syLenkFKHsyiKvggh/BVYSnwB3EtRFBWZ5jyEcAFwAVBkVBmlmDTgr8QB7ReJtnlAH+KAdmCS6pIkqZrJHcggd5juDh06MGbMGE477TSGDh26R7/4l0bBsLJjz1FuOMsNPCV18803E0Jg8uTJPPfcc+Tk5HD11VdXSDgrybkGDx7MpEmTaNSoUZFRBwcPHsynn35Kz549i7137PDDD2fmzJlcd911vPLKKzz99NO0aNGCM888k6uuuoquXbvuUb0dO3bk9ttv54orruD2229ny5YtHHroofz+97/n2GOPLbTthRdeSGZmJjfddBP33XcfdevW5aijjuLee+/l8ccf3+NwBnD33XfTqVMnHnnkEf7973/TsmVLhg8fzrXXXstpp522x8fbU40aNeK1117jjjvuYMKECTz++ONs3ryZVq1a0aVLF/7xj38wZMiQvO3T09N58sknueKKK/jvf//L+vXriaKIfv365U1N8e9//5vjjjuO22+/nVdeeYU1a9bQrFkz2rdvzy9/+cs9Gin12GOP5dJLL+X1119n0qRJrFu3jtatWzNkyJC80FZZQmlHFwohNAUeB84A1gCPAo9FUfTgzvbp1atXNGvWrFKdryJlXZGak3wtqVMx15qXyAenwcTbIScxtGqdNTDqTOjwJoxdu8tdJUnV3/z584vcEyOpsCVLltCxY0fOPfdcxo0bl+xyVMFK+r0YQngniqKi8xRQtgFBjgEWR1G0MoqibcATQOXFSlWs7z0Oo0dCxrr4+eYm8MCTMG94UsuSJEmSqquy3HO2FDgihFCP+LLGwUDqdYtVYVmbSz5TeoXYBw446z3GPXoYLTfWgew65Dx6P2n/Bv4vuaVJkiRJ1U2pe86iKHobeAyYDXyQONYd5VSXUsTcVus45ew3WdQ0nhgwjQAXE09U7Tw2kiRJUrkp02iNURRdDVxdTrUoRS1r8h2nnf0m9zx2GId82TRu/BPwBXEcz0hicZIkSSkqKyuL0o7voJqpYocCUrWxut42zhr1NlM6fZ3feB8wDOdCkyRJksqB4Uwl9l1GNj8+bRacX6DxVeJhYCp2cnlJkiSp2jOcaY9kp0VwF/DHAo0LgCOAt5JTkyRJklQdGM605wLwW+AhIDPRthIYBPw3WUVJkiqb99JIUqy8vg8NZyq9UcAUoEXi+RbiKcn/jCM5SlI1l56ezrZt25JdhiSlhG3btpGenl7m4xjOVDZHAjOArgXafgP8GPD/2ZJUbTVs2JB169YluwxJSgnr1q2jYcOGZT6O4Uxl1xl4ExhQoO1u4DhgTTIKkiRVtGbNmrF69Wq++eYbtm7d6iWOkmqcKIrYunUr33zzDatXr6ZZs2ZlPmaZ5jmT8jQDXiLuMbs/0TaZuGftWaBjkuqSJFWIzMxM2rdvz6pVq1iyZAnZ2dnJLkmSKl16ejoNGzakffv2ZGZm7n6H3TCcqfxkAOOALsBVibb5xCM5PgUcnpyyJEkVIzMzk9atW9O6detklyJJ1YKXNap8BeBKYDxxWAP4GhgIPJ6kmiRJkqQqwHCminEW8WWNzRPPNwMjgRtxJEdJkiSpGIYzVZx+xCM5dinQ9ivgQhzJUZIkSdqB4UwVa1/gLaB/gbY7gROAtUmpSJIkSUpJhjNVvObEIzmeXaDtZeIBQj5OSkWSJElSyjGcqXJkEg+xP7ZA20KgN3FQkyRJkmo4w5kqTwCuBh4C6iTa1gDDgJtxoBBJkiTVaIYzVb5RwBtAm8TzHOBS4gmstySpJkmSJCnJnIRae25s4/I5zhmt4JHx8MVh8fO7gZfegjPOhvrflKIuRxiRJElS1WXPmZKn4Qo47wQ4eEJ+2+d94I6p8NX3klaWJEmSlAz2nGmPZW2esPuN9sSx8KNm8/jN1O6kRwHWtWPTPVP5xfHv8Xy3r0p8mCXlW5UkSZJUqew5U/IFuKv3Yn542kzWZcSzU9fbVovbJvXk0mldCA4UIkmSpBrAcKaUMbXzSk4ZM51FTTfktV06fT9unXgo9bamJ7EySZIkqeIZzpRSPm2+kZPHTOf1rJV5bcd91JrHHzySNmvrJrEySZIkqWIZzpRy1tXZzg++P5O7ey3Ka+u+shGT7u/LYZ83TWJlkiRJUsUxnCklZadF/GHwfH553HtsTcsBoMWmTMY/fARnvNcuydVJkiRJ5c9wppT26EHLOPPMGaysF89OnZGTxg0vHMTYlw+gVnZIcnWSJElS+TGcKeW903Y1I86dxty98ieZPm92FhMePoKWGzKTWJkkSZJUfgxnqhKWN9rMyNFv8UzX5XltvZc145n7+nHoMu9DkyRJUtVnOFOV8V1GNhePmMOfB8wnOzH5WasNdXjkoSM4Z3YHcD40SZIkVWGGM1UtAW4/YhFjTn+bVXW3AlA7J40/vHwgnAtsSm55kiRJUmkZzlQlTc/6lpPOncb7e6/Jb3wAOBJYtJOdJEmSpBRmOFOV9UXj7/j+6Ld45Huf5ze+B/QCXkhWVZIkSVLpGM5UpW2plcOvj3uf3xz7PtRONK4GjgeuA3KSV5skSZK0JwxnqvoCPNTjc3gDaJNoi4CrgJOBtTvbUZIkSUodhjNVH4cD7wADCrQ9DRwGfJiUiiRJkqQSM5ypemkFvAL8vEDbx8TB7ZGkVCRJkiSViOFM1U8t4G/Aw0D9RNsmYBTwC2B7kuqSJEmSdsFwpurrDGAG0KVA29+BY4AVSalIkiRJ2inDmaq3A4GZwPACba8BPYCpSahHkiRJ2gnDmaq/xsCTwB+AkGj7ChiMw+1LkiQpZRjOVDOkAVcST07dItGWQzzc/nHAyiTVJUmSJCUYzlSzDAXeBY4q0PYS8WWObyShHkmSJCnBcKaapw0wBbiiQNtyYBBwPV7mKEmSpKQwnKlmqkUcxJ4DmifasoHfAicC3ySpLkmSJNVYhjPVbMcBc4AjC7Q9DxwCTE9KRZIkSaqhDGdSO+Jh9X9ZoG0ZMAD4C17mKEmSpEphOJMAahMHsaeBpom2bODXxHOkfZukuiRJklRjGM6kgk4kHs3xiAJtzxJf5jgjGQVJkiSppqiV7AKkcjO2cfkd65haEMbCW5fEzz8H+m6DY66GI/6dP5l1iepaW351SZIkqdqy50wqTvp2GHoljBoFddbEbTm14aU/wSMTYFOzpJYnSZKk6sdwJu1K1+fhwqOgzaz8toUnwO3TYXH/5NUlSZKkasfLGlVtZG2eUDEHrgO1z/yaK6Yu4oezOsVt6/ch5/6nuP2IT/l7v4/Ynh7tdPclFVOVJEmSqhl7zqQS2JYe8YfB8zn/tJl8W3cLAGkEfjpjXx4bfyQdVtdLcoWSJEmq6gxn0h6Ysu/XDDv/DV7PWpnX1uPLJjw77ihO+6AN7LwDTZIkSdolw5m0h1Y22MK5p/+P6wbNY2taPEN1g621+NtzPfjn0z1otNmrhSVJkrTnDGdSKUQB7uq9mFPOmc6nzTbktQ+f34bn7j2KQ5c13cXekiRJUlGGM6kM5u69jhPPncZDBy3Na2u7rh7/nXAEP5u+L+k5ezIhmiRJkmoyw5lURt9lZPOb4z7gJyPeYW3mNgBqRWn8fFpXHnroCFi6mwNIkiRJGM6kcvN8t68Ydv7rvN3u27y23suawUHAf5NXlyRJkqoGw5lUjr5stJkzR83gr0ctZHuIBwthLXAG8ENgwy52liRJUo1mOJPKWU4a/OvITzh99Ft83nhT/op7gEOBmcmqTJIkSanMcCZVkNlt1nD8D96Aswo0fgz0Aa4GtiWnLkmSJKUmw5lUgdZnbofxwANAg0RjNnAtcAQwL1mVSZIkKdUYzqTKcDbwPnBUgbbZxJc5/o04sEmSJKlGM5xJlaUj8CrwVyAz0bYFuBw4GlicpLokSZKUEgxnUmVKB34BvEPca5brdeIh9+8CoiTUJUmSpKQznEnJcAAwA/g9cWCDeJj9HwMnAV8mqS5JkiQljeFMSpbawDXAW0DXAu3PAgfixNWSJEk1jOFMSrbDgDnA/yvQtop44uozEz9LkiSp2jOcSamgLnATMAVoX6D9YeJetBeSUJMkSZIqleFMSiWDiIfc/0GBti+B44CLiO9LkyRJUrVkOJNSTWPgHmASsFeB9v8Qj+g4JRlFSZIkqaIZzqRUNRz4EDi1QNtiYDDxqI5rklCTJEmSKozhTEplLYHHgAeAJgXa7wL2J+5dkyRJUrVgOJNSXQDOBuZTuBftS+BkYBTwdeWXJUmSpPJVK9kFSNXe2Mbld6zvAenD4bm/wsZWcdsjwFOrYNiv4Xv/jcNciepaW351SZIkqczsOZOqmv2fgv87HHo8mN/2XTN48k6Y8CisbZu82iRJklRqZQpnIYQmIYTHQggLQgjzQwh9yqswSbtQdzWM+D84+xRo/Fl++ydD4dYZMPNHEJW0C02SJEmpoKw9ZzcDL0RR1A04mPiuGEmVpfMU+Gkf6H0bkBO3bW0Iz/0Nxj0L3+yb1PIkSZJUcqW+5yyE0AjoD5wHEEXRVmBr+ZQlVR9ZmydU/EkGQc8uM7jh+YPYd1WDuG1pX7bc/j9u6vcxd/ReRHZaVGiXJRVflSRJkvZAWXrOOgErgXtDCHNCCHeFEOrvuFEI4YIQwqwQwqyVK1eW4XSSduWdtqs54QdvcEufj9mWFveiZWan8+vXujHx/r7sv6JRkiuUJEnSrpQlnNUCDgVui6LoEGAjcMWOG0VRdEcURb2iKOrVsmXLMpxO0u5sqZXD3/p/xIgx0/mgVf5ojN9b0Zin7uvLFVO7UW9rehIrlCRJ0s6UJZwtA5ZFUfR24vljxGFNUpLNa7WOk8dM588D5rMlPRuAWlEaF73dmZfvGsCxC/eGaDcHkSRJUqUqdTiLougr4PMQQtdE02BgXrlUJanMstMibj9iEcPOf4O3232b195mfV3+M7EnnAB8mrz6JEmSVFhZR2u8BBgfQngf6AH8qcwVSSpXi5tt5IwzZ/CL49/lm3pb8lc8DxwAjAU2J6c2SZIk5Sv1aI0AURS9C/Qqn1IkVZgAj3/vC17usoJfvt6N0XPak0aALcA1wD8XwXG/hC6vJLtSGLt299tIkiRVQ2XtOZNUhayrs52rhn7IyWOmwz6z81es7gQTHof/PgBr2ySvQEmSpBrMcCbVQO+3Xgs/HAwnXAZ11uSvmD8c/j0Tpv8/yK6dtPokSZJqIsOZVFOl5UCve+DintDjwfz2bfXhlWvh9mmwpF/y6pMkSaphDGdSTVf/Gxjxf/CDY2Gvufnt33SD+56FJ+6ADXslrz5JkqQaokwDgkiqurI2TyjcsBfUGvMZ574TuGz6fjTYmvh6+OAM1i08lb8f9REPHvIZ29MrdoK0JRV6dEmSpNRlz5mkPNvTI+7uvZjBP5rKM92W57U32lqbsZMP4MV7+nPMx3s5gbUkSVIFMJxJKmJFwy1cPGIOZ5/+Nouabshr77yqAXc9cRgPPXwEB37VKIkVSpIkVT+GM0k7Na3jNww7/w2uHzifdRnb8tr7LG3OM/cdxd+eOZjW6+oksUJJkqTqw3AmaZe21srhP4cvYuCFUxl36BK2h5y8dafNbcurdw7k8te7Un9LehKrlCRJqvoMZ5JKZFW9rYwdMpehP3ydl/f9Kq+9zvZ0Ln5rX6beMYjRc9qTnhOSWKUkSVLVZTiTtEcWNd/Ij097h1FnvsUHrdbmtbfclMkfX/oeL9xzFIM+ddAQSZKkPWU4k1QqM9qvYvi507j0xHf5ouF3ee1dvm3IvY8dxoOPHM7+Kxw0RJIkqaQMZ5JKLQow8YAvOPrHU/lL/wWsLzBoSL/PWvDMuH7c+OxBtFqfmcQqJUmSqgbDmaQy21I7h1v7fMrAC6bywCGf5Q0akkbg+x+2Y+odg/j11K4025SR5EolSZJSl+FMUrn5tv5Wrhr6IcPOf4NXOq/Ia6+7PZ2fvL0v024fxG9e7UaLjYY0SZKkHRnOJJW7T1ps4EcjZ3HWGTOYu1f+oCH1ttXiwv915o3bj+bKyd1pucHLHSVJknIZziRVmDezvuXE86Zx4cnvMK9ASKu7PZ0fzerEtNsHcfUr+3tPmiRJEoYzSRUsCvBi16844bxp/PjUWXxYYPj9zOx0fvBOR17/zyCufekAWq+rk8RKJUmSkqtWsguQVDNEAV7usoKX913B0Z/uxf+b3oWDv2oCxCFtzJwsRr3XHnKA3wAdklmtJElS5bPnTFLlCjBl368ZMWY65438H3Nar85blZGTBv8B9gV+DCxOVpGSJEmVz3AmKTkCTO28klPOeZNzTn+bWW1W5a/bDtwFdAHOBz5JTomSJEmVyXAmKbkCvNHxG0aOfouzzpgBRxVYlw3cC+wHnAg8l2iTJEmqhgxnklJDiEd35HXgVWBQgXUR8CxwAnFv2l+Abyq/REmSpIpkOJOUegYCU4iD2rAd1i0Gfg20BcYAM4jDmyRJUhVnOJOUuo4Cngc+Bi4HmhVYtwV4AOgD9CS+R21jZRcoSZJUfgxnklLfvsCNwDJgHNB7h/VziEd3bANcCiysxNokSZLKieFMUtVRFzgXeBuYSTySY8F5q9cCNwPdgGOAJ4hHfpQkSaoCnIRaUmoZ27jk27YDftYU3j0TZv0IVnXOXzc5sTT8Ag58HLo/BW1nQSjlDWpj15ZuP0mSpBIynEmq2uquhj63whG3waJBMPOH8NFxEKXH69e3gbd+Fi8NvoRuz0K3ZyDrDUi3W02SJKUOw5mk6iFE0HlKvKxtC++cB7PPhY175W+zoXXcwzbrR1BnDez3PHR/Ot6n9nfJqlySJAkwnEmqjhovg6OvgwE3wKKBMH84LDweNrXI32ZzE3j/zHiptQm6vALdnob9XoQ6XsIoSZIqn+FMUvWVvg26vBwvOZfC0iNgwYkw/yRY1y5/u+314gA3fzikbYOOr8eXPnZ9FhquSFr5kiSpZjGcSaoZ0rIha3q8HPsb+LJHHNIWnAjfdMvfLqc2fDo4Xp79G+zzLrSZCZ2Bw4D9cJxbSZJUIQxnkmqeQBy69nkXBv8BvumSCGonwfJDC2yYFj9ffiiMSTQ1Ig5phxHPt3YY8fxqoRLrlyRJ1ZLhTJJafAxH/T1e1raFBSfEPWqf9c0f9THXOvKH6c/V4EtoMxv2mQ1t3oF95kDdNZVTu0P8S5JUbRjOJKmgxsvg8P/Ey3dNYVnPuOfsi57xsqll0X02tIaFJ8RLrmafxCGt6RJo8BU0LLA0WBHfD1cVRcBmYGNi2VDMz5uAdCBzhyWjmLYd19fGXkhJUo1lOJOUUrI2T0h2CfkC8UTX7WBJnTPiYLK2XRzSlh8KXxwa37u2tWHRfVftGy87U++bwqGtwQpo+GX+Y8MV8XD/ISeeJiDkxAsFfg5RXNPOwkwOcWAquKzfyc/FPS8ueG1MHLfC5EDmOmjxCbRYCC0+gpYL45+bLoG0Mp7cnkZJUgoznElSSQWgyefxcsDEuC0nDb7Zr0Bg6wkrDoCcjF0fa1OLePn6wLLVdG2irrQCj7kDlmwu26GTIw22NIEvesVLQelboPkncWBrsRBaJh6bfwK1q+SLlSSpEMOZJJVFWg7stSBeDhkft23PhK8OhBXfg/V7x8uG3MdW8bLjvWxlEQHZ5Xe43coA6gMNEo87/lwPmPNw/D5k14bszMTPGfmP2RmwPaPoumgX/1vKzoSvD4iXQnKg6Wf5PW0d3oTOk6HW1op49ZIkVRjDmSSVt1pboO078VKcnLS412x9a1jfKn7c0KpwiFu/N2xtAFGAKC1eKPBzlBav2924/g12WBru5Ocdn9ff4eeCS+0SvAdjLyzBRsXISYONe8W9kSv3g2+6xsvK/eJ7+4qVBqs7xsvHw+Ctn0HmWuj6POz/JHSeYlCTJFUJhjNJqmxpOdDg63jZWd4oqQjyQ9sOQa7W5vi+tJLYkli+KWM9ZZWWk38fXsfXC6/b3Die9mBlIrB9s1/885oORXsitzSG90fFS+Za6Poc7D8xfo2ZlfViJEnaM4YzSarKAsSDhFTmdY1JUmcttJ0VLwVtz4RvO8eBbXkPmD8cVnfKX7+lMbx/Zrw8B4wAvg8MxaAmSUophjNJUtVWawu0mhcvBzwJx1wNXx0Mc0+GeafElzvmWgc8kFgaEQe104EhGNQkSUlnOJMkVS8BaP1evAy+JhHUToF5J+88qDUmP6gdx25v5ZMkqSL4vx9JUvWVG9SOGQuX9IBZwK+BTjtstxa4HzgROBh4ksT9fJIkVR7DmSSpZghAT+DPwCfkB7WOO2z3IXAqcBjwPIY0SVKlMZxJkmqegkHtU2Am8HPiqQNyvQMcDxwFTK3k+iRJNZLhTJJUswWgF/A3YBFwOVCnwPrpwCDgGGBGpVcnSapBDGeSJOVqCdxI3Jv2fxSecHsy0Ac4CZhT+aVJkqo/w5kkSTvaB/gX8BFwPlBwjutngEOJ50qbX/mlSZKqL8OZJEk7kwXcDcwDziQx6XfCY8CBwBjinjZJksrIcCZJ0u7sB0wA3gNOKdCeQzxPWlfgAuDzyi9NklR9GM4kSSqp7wFPEI/uOKxAezZwJ9AduI04tEmStIdqJbsASZIqzdjG5Xesw4HWR8CUK+Gzo+K2jcBPgRunwvCLoUkJu9LGri2/uiRJVZY9Z5IklVb7GXDuiXD2ydBiQX774oFw25swe4yTWEuSSsyeM0kqgazNE5JdQrGW1Dkr2SUoAJ1fhQv7w6u/hbcugSgdtjaCp2+BeSNg+CXQaHmyK5UkpTh7ziRJKg+1tsCQq+EHx0KzT/LbPz0Gbn0L3j3TXjRJ0i4ZziRJKk/tZsJF/eDwf5M3MsiWJjDpdnj4YVjfKpnVSZJSmOFMkqTyVvs7GPZbOO8EaLo4v/2j4+DWt+GDkfaiSZKKMJxJklRROrwJFx0Jh/0nv21zU3jibvjvg7ChZfJqkySlHMOZJEkVKWMTHP8rGHMSNP4sv33BSXEv2txTdr6vJKlGMZxJklQZOr4OPzkSet6T3/Zdc3hsHJwBfJOswiRJqcJwJklSZcncACdeBmefAo2W5bf/FzgAeD5ZhUmSUoHhTJKkytZ5CvykD/R4IL/ta+AE4GogO0l1SZKSynAmSVIy1FkHIy6Gs0ZC60RbBFxLHNK+TV5pkqTkMJxJkpRMXV6Gd4GjC7S9CPQEZiWlIklSkhjOJElKtr2Al4DfFGj7DOgL3IFzoklSDWE4kyQpFaQDfwImAo0SbVuBC4Hzge+SU5YkqfIYziRJSiUjgHeAgwq0jQOOBBYloyBJUmUxnEmSlGr2Bd4CzinQ9i7xfWjPJKMgSVJlMJxJkpSK6gH3AbcBGYm2NcBJwJU43L4kVUO1kl2AJKn0sjZPSHYJxVpS56xkl1A9BOAi4FBgJPB5ov2PwP+ACUCL5JQmSSp/hjNJkpJtbOPdbzOqGTx+NyxKjLn/MtD5czh9DLSZXYG1ra24Y0uSCvGyRkmSqoJ6q2D0aXDUX/Lb1rWDe16EmT90uH1JqgYMZ5IkVRVpOXD0H+HM70OdNXFbTgY893eYeDtsq5PU8iRJZWM4kySpqtnvJbhgAOz9fn7b+2fCvS/Aun2SV5ckqUwMZ5IkVUVNl8D5Q6DHA/ltXx4Cd0yFz3snqypJUhmUOZyFENJDCHNCCM68IklSZaq9GYZfDMf/AtK2xW0bW8G4Z2H2ObveV5KUcsqj5+z/AfPL4TiSJGlPBeCwu+Cck6HeN3FbTgY8/S947i+Q7cDMklRVlCmchRDaAicAd5VPOZIkqVSypsGPB0GrD/LbZl4IDz4Jm5olry5JUomVtefsJuBXQE7ZS5EkSWXSZCmcPxT2n5jftqQ/3DkVVhyQrKokSSVU6msdQggnAl9HUfROCGHgLra7ALgAoH379qU9nSSpCsnaPCHZJRRrSZ2zkl1CxcvYBCPPhTcuh1evitvWdIC7X4aTL4L9n0pufZKknSpLz1lfYHgIYQnwMHB0COHBHTeKouiOKIp6RVHUq2XLlmU4nSRJKpEA9P8rjBoFGevitm314dEH4NXfQhSSWp4kqXilDmdRFP0miqK2URRlAaOAKVEUnV1ulUmSpLLp+jz86Bhouii/7fVfwyPjYUvD5NUlSSqW85xJklSdtVwIPz4aOk3Jb1t4QnyZ46qOyatLklREuYSzKIqmRlF0YnkcS5IklbO6q2H0SOhzS37byu5w56vw6aDk1SVJKsSeM0mSaoK0bBh6JZx8IaRvjts2N4Xxj8NbP4UoueVJkgxnkiTVLAc/DD84Dhouj59H6fDS9TDxdthWN7m1SVINZziTJKmmaTMbfjwQ2v4vv+39M+Gel2B1h6SVJUk1neFMkqSaqOEKOPcE6PFAfttXB8Edr8Eng5NXlyTVYIYzSZJqqlpbYfjFcMKlkLY1btvcFMY/Bq9f7nxoklTJDGeSJNVkAeh1b+H70EiDV6+CRx6EtcksTpJqFsOZJEmCtrPggv7QYVp+28IToTcwL2lVSVKNYjiTJEmxBivhnBFwxL/y2z4iDmiPJasoSao5DGeSJClf+nY49ndw6vlQa1PcthH4PvBrYHsSa5Okas5wJkmSivre4/CjY6Bzgba/AMOAlUmqSZKqOcOZJEkqXqu5MBM4vkDbZKAnMCs5JUlSdWY4kyRJO9cUeBq4ukDb50A/4J6kVCRJ1ZbhTJIk7VoaMJY4pDVOtG0BfghclPhZklRmhjNJklQyJxJfznhggbb/AAOAxUmpSJKqFcOZJEkquX2BGcCoAm1vAz2ACckoSJKqD8OZJEnaM/WJg9jfgVqJtnXAaOCcxM+SpD1mOJMkSXsuAJcB0yk83P6DxL1oM5JQkyRVcYYzSZJUer2BOcC5BdoWE4/meB2QnYyiJKlqMpxJkqSyaQiMAx4CGiXasoGrgKOBpckpS5KqGsOZJEkqH6OA94C+BdpeBw4GHk1KRZJUpRjOJElS+ckCphLPi5b7W8Ya4HTiedE2JKEmSaoiDGeSJKl81QKuJu4161Cg/R7gUOK50iRJRdTa/SaSJFUPWZtTcyKuJXXOSnYJFaMv8WWOPyG+Hw3gY6AP8EfgcvwzsSQV4FeiJEmqOI2B8cD9QINE23bg18AQ4Isk1SVJKcieM0mStHNjG5ffsX7QEZ64E744LH4+BeiyCo7/BRzwRDx3WonrWlt+dUlSirDnTJIkVY5mi+EHw+CoG4GcuO27ZvD4vTDhMVidlczqJCnp7DmTJCnJUvVeOKiA++HSt8PR10GnV+HJO2Bd27j9kyFw6wzofyMc+U9I31a+55WkKsCeM0mSVPmypsNP+sBhd5DXi7a9Lkz5PfznDVh6RFLLk6RkMJxJkqTkqLMOjv8l/Ggw7P1+fvvK7nDvi/DULfBd0+TVJ0mVzHAmSZKSq81s+PFAGPobqF1gluo5Y+Bfs+C9URAlrTpJqjSGM0mSlHxp2dDnVvi/3tDt6fz2TS1g4n/ggafgm32TV58kVQLDmSRJSh2Nv4AzzoZRo6DR5/ntiwfA7W/C1Ctge2by6pOkCmQ4kyRJqafr8/B/h0OfWyBsj9uyM+G138Btb8ZzpElSNWM4kyRJqSljIwy9Ei4YCG1m5bev2hcGA+cAXyepNkmqAIYzSZKU2vb+AM4fAsf/AjLX5rc/COwH/BHYsJN9JakKMZxJkqTUl5YDh90F/3cYHPB4fvta4EqgE3ATsDkp1UlSuTCcSZKkqqPhChh5PjwPdCnQvhK4LNF2J7AtGcVJUtkYziRJUtUzDJgH3AW0K9C+DLgA6A6MB7IrvzRJKi3DmSRJqppqAT8EPgZuBvYqsO5T4GzgYOBJnMRaUpVgOJMkSVVbJvAzYBFwPdC0wLq5wKnA4cBLGNIkpTTDmSRJqh7qA1cQh7QrgQYF1s0EjgUGAdMrvzRJKolayS5AkiSlrqzNE5JdQrGW7GplE+APxL1pfwb+DWxJrHsN6AccB1wHHFpRFUrSnrPnTJIkVU8tgb8R3392EYX/JP080BM4AXgRyKn06iSpCMOZJEmq3toAtwELgXOAUGDdc8QjP+5P3MO2vtKrk6Q8hjNJklQzdALuBz4ETqNwSFsIXAy0JZ4v7ZNKr06SDGeSJKmG2R94DPgIuBRoVGDdOuAmYD/gJOBlHOFRUqUxnEmSpJppX+AfxBNX/wvoWmBdBDwDDAUOIL4sckNlFyippjGcSZKkmq0h8H/APOAF4Pgd1s8Hfkp8yeMviIfql6QKYDiTJEmC+LeiY4FniS95/BlxcMu1Fvg7cY/bcOJJrbMruUZJ1ZrznEmSpKpnbOOKP0dT4P8awrtnwv8uhFX7xu0R8HRiafAlHPgYHPQo7P0eXLO24uuSVG0ZziRJknYmcz0cfgf0vhM+GQz/uwg+GZK/fkNrmHFJvLRYCLWBs4hHhpSkPeRljZIkSbsTIujyCoweCf/XEw6/FeqtLLzNN13hKqAz0Be4Ffim8kuVVHUZziRJkvZEi09g2G/gF11h9Klw0MNQe4ehHN8kHmSkNXAi8BCwqdIrlVTFeFmjJElSaaRlw76T4+WEerDwONhyTzziY+5AIduJBxh5FqgPnAKMBo7B38IkFeHXgiRJqnKyNk9IdglFdYElfwZWAv8FxgNvFVi/EXgwsewFnEw80fVgoG6lViopRXlZoyRJUnlqSXxJ45vAp8AfgG47bPM1cAdxOGtOPDT/ncCXlVempNRjOJMkSaoonYAriSe4fgf4OfF9aAV9Rzws/wXAPsBhwDXAbOJh+yXVGIYzSZKkihaAQ4G/AZ8DrwO/pGiPGsAsYCzQE2gHXER8z9p3lVGopGQynEmSJFWmdOAo4C/AfOBj4O/AIIqOBvAF8B/iER9bACOAu/DyR6maMpxJkiQl077AZcAU4sFEHiKeyLrpDtttAp4Cfkx8+eMBwM+AScDayipWUkVytEZJkqRU0QQYlVi2A9OJ70d7Gvhoh23nJZZbiP/c3ot45MfBxJNg16mUiiWVI3vOJEmSUlEtYADwV2BhYvkbMBCovcO2OcD/gOuJ51BrQhzS/gS8TRz0JKU8e84kSZLKy9jGFX+OAUCferC0DyweAIv7w5cHU+hv7luIL5OcAvwOaEQc6nJ71vYnHqREUkoxnEmSJJWTSp0cu21iOWo5jb9byRFLm9P3s+b0/awFnVc1KLztOuL71Z5KPG9BfOljv8RyKJBRWYVL2hnDmSRJUhW3tu42Xuz6FS92/QqAvdfV4cilcVA7cklzWm+oW3iHb4gHEpmUeF4HOJz8sNYHqIROQEmFGc4kSZKqma8abeaJA7/giQO/gAiW/PAEmEy8TAW+3WGHzcBriQXiSx4PIh7yvx9xL1vbSildqtEMZ5IkSdVZAPZLLD8hHjxkITCtwLJoh30i4L3E8q9EWwfyg9oRwPfwN0mpnPmflCRJUk2SBnRPLD9OtC0nHrZ/GvAGcSjL2WG/zxLL+MTzusTD9x+eWI7A3jWpjAxnkiRJNd0+wPcTC8QDiMwgv2dtBvDdDvt8Rxzk3tjhOAXDWk9gh7FJJO2c4UySJEmFNQKGJhaAbcAc4iA2g3jutM+L2W858GRigbiX7kDyw9rhQDcgvaIKl6o2w5kkSZJ2rTbQO7HkWk4c0nKXmcDGHfbLAd5PLHcm2hoAhxBfEpm77EuhadqkmspwJkmSpD23D3BKYgHIBuZSOLDNJR5cpKANFL0cshHxXGu5Ya0n0BknylaNYziTJElS2aUTD79/EPkDjawDZlE4sH1VzL7riIf4n1qgrQlxSOtV4DELA5uqNcOZJEmSKkYj4OjEkms5cWCbBbxDfDnkymL2XUP+3Gy5mgE9iC+LzF264j1sqjYMZ5IkSao8+wDDEwvElz0uIz+s5Qa3HSfKBlgFTEksueoS99YVDGzfA+pUQO1SBTOcSZIkVXdjGye7guKNXRtfptguseTevxYRz6lWMKy9A6wu5hjfkX/JZK504nncCga2HsSXSkopzHAmSZJUzWVtnpDsEoq1ZGcrAvH9ZVnAaYm2KLHDnB2W5cXsnw18mFgeKNCeBRxM3NN2cGLphCNFKmWUOpyFENoB9wN7Ew+UekcURTeXV2GSJEmq3rKueLb0Ox8YL803ZnDAikYc8HVjDljRiP1XNKLT6p3MfL0ksUzKb9pYezsLW65n/l7r4qXleh6/7UhoWPrSpNIqS8/ZduAXURTNDiE0BN4JIbwcRdG8cqpNkiRJ2qVv62/l9U7f8Hqnb/La6m9Jp/vKRhywIg5sB6xoRJdvGpKRU7SLrP62Why6vCmHLm+a3zieuEdtx162LOxlU4UqdTiLouhL4MvEz+tDCPOBNoDhTJIkSUmzMTObWW1XM6tt/k1qtbMDnb9tQPevGyWWhnRf2YgWmzKLP8iixPJkgbb6wAHEA44cWOCxVcW8DtU85XLPWQghi/hWy7d3s6kkSZJU6balRyzYaz0L9lrPk3yR195yQybdv25It5X5oa3bqrqQU7voQTYC/0ssBdVbCa3mQct58eNe86DlAsjcUL4vYuza8j2eUk6Zw1kIoQHwOHBpFEXrill/AXABQPv27ct6OkmSJKncrGywhZUNthS6LDJjexr7ftsg7l37uhHdVzai68qGO+9l29QSFg+IlwKWNt7EwpbrWdhyPR+1WM/HLdazqNlGttTKKVWtS0q1l6qSMoWzEEJt4mA2PoqiJ4rbJoqiO4A7AHr16hWV5XySJElSRdtaK4d5rdYxr9U6KNDL1nxjBl1XNqTbyobs90382OWbhtTfVvyv1O3X1qP92noM+ST/usfsEPFZk4183GJDIrBtKHNoU/VRltEaA3A3MD+Kor+XX0mSJElS6vm2/lberP8tb2blz5AdImi7ti7dVjZivwLBrdOq+tQuZgCS9CjQaXUDOq1uwLEf753XbmgTlK3nrC9wDvBBCOHdRNtvoyh6rsxVSZIkSVVAFODzJt/xeZPveLnLirz2jO1pdFpVv0APWwO6fNOQ9mvqkUYocpzdhbZPmyfuX+sOdEs8NqrY16bKV5bRGqdBMZ8sSZIkqYbbWisnbwCSpwq019mWRudVcVDb75sGexTauGGHlfsQh7SCSzfiWYj9Lb1KKpfRGiVJkiTt3ubaOcxttY65rQqPo7enoQ2A5Yll8g7tTcjvXcsNbF2J527zt/+U5j+PJEmSlGS7C22dv23AP3scAvOJl4+AbTs52BpgRmIpqBawL3FQ23FpUV6vRGVhOJMkSZJSVMHQ9tTW5dAZ6AzpOYH2a+qx77cN2PfbBnT+tn7isQENtxYzRxvAdmBBYtnBqrpbWdRsA4uabcx7/LTZRpY23ci29F0PuL7kzyeU9WUqwXAmSZIkVTHZaRGLm21kcbONhQYiIYJWGzIToa0h+37bgE6r6tPp2/q03lB3p8dr9l0Gzb5oRq8vmhVq3x5yWNb4OxY328iSphtZlHhc3Gwjyxt+RzEDUqoMDGeSJElSdRFgRcMtrGi4hekFhvwHqLc1nY6r6tN5VRzYOieCW8fV9am3k7naakVpZK2pT9aa+kXWbUnP5rMmm+KeuP2ALgUeW+OgJKVgOJMkSZJqgE0Z2czdex1z9y58X1uIYO/1deIeth2CW9t19XZ6vMzsdPb7tiFMKmZlfeKQ1oX4PreCi8FtpwxnkiRJUg0WBfiy0Wa+bLS5SG9b5rY0OqypR8dVDei0uj5ZiZ62jqvr0XJjnZ0fdCPwbmLZUT3ie+f2LfCYu7QF0sv+mqoqw5kkSZKkYm2pncNHLTfwUcsNRdY12FKLrNX1eObYo+Bj4hEkcx/X7OKgm4APEsuOMoiH/M8Nbp0TzzsDWcAu8mB1YDiTJEmStMc2ZG7nw73XkfXes3FD28QyEJp+V5uOqxqQtaYeHVbXJ2t1PTokfm66OWPnB93KTkeUzCHiq4ab+bzJJpY23sRnTTextEn+sqru1kKXS1bFUSQNZ5IkSZLKT4DV9baxut5qZrddXWR14+9q02FNPbJW16fD6npkrYkfO6yuT8tNmTs9bBqBfdbXZZ/1dTn88+ZF1q/P2BYHtybfsbTxJrgN6Ad8rxxfWwUznEmSJEmqNGvrbuP9umt5v/XaIusabKlFhzX1aJ8Ibe3WxD1u7dfUY591dUmPdj6SSMOttdn/68bs/3XjuGEmcC2GM0mSJEnaUxsyt+dNur2j2tmBfdbVpX0isLVLhLY4vNWnwdZiok3nSii6HBnOJEmSJKW8bekRnzWN7zV7Y8eVUXyfW4c19WmfCG2X79sVDk5GpaVnOJMkSZJUteXd57aGd/dZA8Dlf+6a3JpKIS3ZBUiSJEmSDGeSJEmSlBIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAgxnkiRJkpQCDGeSJEmSlAIMZ5IkSZKUAsoUzkIIw0IIC0MIn4QQriivoiRJkiSppil1OAshpAP/Bo4D9gfODCHsX16FSZIkSVJNUpaes97AJ1EULYqiaCvwMDCifMqSJEmSpJqlLOGsDfB5gefLEm2SJEmSpD1Uqwz7hmLaoiIbhXABcEHi6YYQwsIynFOVpwXwTbKLkPaAn1lVNX5mVdX4mVWVEm5I2c9sh52tKEs4Wwa0K/C8LbB8x42iKLoDuKMM51EShBBmRVHUK9l1SCXlZ1ZVjZ9ZVTV+ZlXVVMXPbFkua5wJdAkhdAwhZACjgKfKpyxJkiRJqllK3XMWRdH2EMLFwItAOnBPFEVzy60ySZIkSapBynJZI1EUPQc8V061KLV4KaqqGj+zqmr8zKqq8TOrqqbKfWZDFBUZw0OSJEmSVMnKcs+ZJEmSJKmcGM5qoBDCsBDCwhDCJyGEK3ax3WEhhOwQwsgCbUtCCB+EEN4NIcyqnIpV0+3uMxtCGBhCWJv4XL4bQvh9SfeVylsZP69+x6rSleR7MvG5fTeEMDeE8Nqe7CuVtzJ+ZlP6e9bLGmuYEEI68BEwhHg6hJnAmVEUzStmu5eBzcSDvTyWaF8C9IqiKBXnjFA1VJLPbAhhIHB5FEUn7um+Unkqy+c1sW4JfseqEpXwM9sEeBMYFkXR0hDCXlEUfe13rJKhLJ/ZxLolpPD3rD1nNU9v4JMoihZFUbQVeBgYUcx2lwCPA19XZnFSMUr6mS3vfaXS8DOnqqYkn9mzgCeiKFoKkPtLbgn3lcpbWT6zKc9wVvO0AT4v8HxZoi1PCKENcApwezH7R8BLIYR3QggXVFiVUr7dfmYT+oQQ3gshPB9COGAP95XKS1k+r+B3rCpfST6z+wFNQwhTE5/NMXuwr1TeyvKZhRT/ni3TUPqqkkIxbTte23oT8OsoirJDKLJ53yiKlocQ9gJeDiEsiKLo9QqoU8pVks/sbKBDFEUbQgjHAxOBLiXcVypPZfm8gt+xqnwl+czWAnoCg4G6wFshhBkl3Fcqb6X+zEZR9BEp/j1rz1nNswxoV+B5W2D5Dtv0Ah5OXJM7Erg1hHAyQBRFyxOPXwNPEnctSxVpt5/ZKIrWRVG0IfHzc0DtEEKLkuwrlbOyfF79jlUylOR7chnwQhRFGxP36bwOHFzCfaXyVpbPbMp/zxrOap6ZQJcQQscQQgYwCniq4AZRFHWMoigriqIs4DHgp1EUTQwh1A8hNAQIIdQHhgIfVm75qoF2+5kNIewdEt28IYTexN9t35ZkX6mclfrz6neskqQk35OTgKNCCLVCCPWAw4H5JdxXKm+l/sxWhe9ZL2usYaIo2h5CuBh4EUgnHolxbgjhosT64u4zy9UKeDLxO0UtYEIURS9UdM2q2Ur4mR0J/CSEsB34DhgVxUPRFrtvUl6IaoSyfF5DCH7HqtKV5DMbRdH8EMILwPtADnBXFEUfAvgdq8pWls9sCKETKf4961D6kiRJkpQCvKxRkiRJklKA4UySJEmSUoDhTJIkSZJSgOFMkiRJklKA4UySJEmSUoDhTJIkSZJSgOFMkiRJklKA4UySqoAQQhRCqBITU4YQpibqbZLsWlRYCGFsCOGLEEJ2CKF/suuRJBVmOJMklbfHgJuBLRV9ohDCeYkgeGlFn6uqCyEcDFwN1AXuBJYntyJJ0o5qJbsASVL1EkXRv5Jdg4rVPvF4fxRFlyazEElS8ew5kySVixBC3WTXoF1KTzyuTWoVkqSdMpxJUhWUuK9rewihfgjhzyGEpSGEzSGEBSGEHxfY7oXEZX8jijnG8MS6/xRoOzSE8HAIYVnieEtCCPeFEA7aYd9xiX27hBBuDSGsAi4sUFuhe85Ketw9fG1TgXsTT/+ROGfWbt6zKITQMIRwSwhhRQhhXQjh2RBCpxBChxDCf0MIa0II60MIz4cQOu1wjD15HWkhhB+GEN5JnGdtooZhpdluF6+rRQjhpkQtWxL3lN0RQmizw3v1ZOLp7xPvw8ASHHtuCGFTCKFeCOE3IYR5idf9ZQjhxhBC+u6OIUkqOS9rlKSqKwAvAfsCzxN/p58G3BFC+CKKoueACcCxwMnApB32H5l4HA8QQugFTE+0PQesALoB5wDfDyEcHEXRxzscYzzx5XLPAu8VW2TpjluS1/YYsBUYArwOzAHWFVfDDl4G9krUfDBwPNABaAzkAE8AnYFhxO/Z90r5Ov4GXJp4XyYAzYj/LZ4NIQyPoujZPdyuiBDC3omaOgFTEnV1As4HTg4h9I+iaEHivVoPnAi8DcwAlu3qTUr0hHYFPgNeBeokzjENOAu4PHGMm3d1HEnSHoiiyMXFxcUlxRcgir+y855PTbS9DzQr0H5Oon184nlDYBOwEkgvsF1tYDXxL94h0XZrYt+BO5z7mkT75QXaxiXaPgZa7bB9bm1N9vS4e/LaEm3nJdouLcF7mHvcF4C6Bd6H+Yn2d4D6BbZ/KdF+QCnen3rEwfE9IK1Ae3tgA/D6nmy3i9f0cOLcF+7QfjyQDcwo0HZyYtuxJfzMHZH7uQN+nfs5Saw7K9E+Kdn/bbi4uLhUp8WeM0mq2n4ZRdGqAs+fSjx2AIiiaH0I4Rng+0Bf4h4mgGOAJsDtURTlDtH/CvBJFEVTdzjHB4nHBsWc/4YoilbspsbSHBd289rKYGwURd8BRFG0LYTwLnEP2N+iKNpYYLv/EffKtQPmsmevoz5x8GtMHJDXJs63NIQwJLFuT7YrIoTQnLj382PgjoLroih6LoTwCjA0hLBfFEUf7eoN2YlDEo9PRlF0ww7rZicevT1CksqR4UySqrZClxJGUbQ2hADxL/25JhCHsxHkh7PTEo8PFtj3CYAQwj7Ev5h3JL5EbiQ79/7uCizlcaFkr600Ptjhee6Q/5/u0L498Vgncf4Sv44oilaGECYS91YtDCE8BbwGTImi6K093W4nehEP8vFCgYBd0NvAUOAAoDTh7NDE4x3FrNsr8bioFMeVJO2Ef/GSpKpt807aQ4GfnwPWEIczEoM4jADejaJobt4OIXQPIUwHvgCeAcYCPcm/z6o4W3dXYCmPCyV7bXtsh96xgnY5L1spXsf3iQdJ+Qj4AXEQ/iKE8GYI4chSbLejFonHnc1XtinxWNpRNA8hvjTytWLWHZx4nFPKY0uSimE4k6RqLoqirSQGuQghHAgMJP7FfnzuNiGEWsSXDfYkDgotoihqEUXRAOC/pT13RR23spXmdURRtD2KojuiKOoPNAWOI75v7TDguRBCwz3Zrhi54avZTtbnjtb49R68VABCCLWBA4H5uZeA7qBn4vGdPT22JGnnDGeSVDNMSDyeTHwZXg7wUIH1XYlHRnwiERS+LbCu0HDye6iijlvZ9uh1hBCOCCFMDCEMAIiiaEMURS9EUXQxcCfxPWYHlHS7ndSUe3nmgJ2sH0Z8aWZpAtT+QOYu9u0JfEc8mIokqZx4z5kk1QyvAl8CpwL7AK9GUfRFgfW5lye2CyGE3HuYEvN3/bIM562o4+bKSTxW9P/P9vR1rCO+dLR2CGFGFEVbEtvXBg4iHunwc+LwVZLtioii6JMQwgzgiBDC96MoejR3XQjhbOIw+XAURatL8Xpz7zebveOKxBD73YGZURRt33G9JKn07DmTpBogiqIc4BHi+4haUeCSxoRPgDeAfsD/Qgi3J0b7m0089DzAWSGE8/bw1BV13Fy5weWSEMI/Qwg7u8SvrPbodURRNI940ufjgXkhhAdCCHcDC4lHzbw9iqIvSrrdLuq6kHiEx0dCPOH4v0MILwD3E783l5fy9eaO1Fhcz1kP4oFIvKRRksqZ4UySao7cSxs3A48XXJHoCToVuI94jq2ziP8fcVIURecRh7kOJCZkLqmKOm4BrxHP9dWceM6z0g5+sUulfB1jiCeYjoDTE/usBy4DLi7FdsXV9T7xvWmPEF9q+GPiaQFuB3rvJtjtyiHEvZLvFrMut1fNcCZJ5Sx34lFJkqTdCiHcQzyq5MGJcChJKif2nEmSpD3Rk7j3dV6yC5Gk6sZwJkmSSiSEUId4JMf3HAxEksqf4UySJJXUwcQjY3q/mSRVAO85kyRJkqQUYM+ZJEmSJKUAw5kkSZIkpQDDmSRJkiSlAMOZJEmSJKUAw5kkSZIkpQDDmSRJkiSlAMOZJEmSJKUAw5kkSZIkpYD/D5SAHvNWmyHeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_data = bin_value[0]+(bin_value[1]-bin_value[0])\n",
    "x_data = x_data\n",
    "\n",
    "# with two parameters\n",
    "popt, pcov = curve_fit(lambda x,p1,p2: p1*crystalball_f(x,beta_eta,m_eta,norm_eta,mu_eta,sigma_eta) + p2*exp_curve(x,a_eta,b_eta,c_eta), x_data, y_data)\n",
    "p1 = popt[0]\n",
    "p2 = popt[1]\n",
    "\n",
    "x_fitted = np.linspace(np.min(bin_edge), np.max(bin_edge))\n",
    "y_fitted = lambda x: p1*crystalball_f(x,beta_eta,m_eta,norm_eta,mu_eta,sigma_eta) + p2*exp_curve(x,a_eta,b_eta,c_eta)\n",
    "\n",
    "print('The area below the PDF function: ', integrate.quad(y_fitted,np.min(x_fitted),np.max(x_fitted))[0])\n",
    "print('The area of the histogram: ', bin_width*sum(y_data[:]))\n",
    "\n",
    "plt.figure(figsize=(15,8))\n",
    "plt.hist([eta_bkg_InvM, eta_sig_InvM], bins=20, histtype='barstacked', density=True, label=['Background', 'Signal'])\n",
    "plt.plot(x_fitted,y_fitted(x_fitted), color='fuchsia', linewidth=3, label='PDF with two parameters')\n",
    "plt.xlabel('Invariant mass of $\\eta$', fontdict=form_label)\n",
    "plt.legend(fontsize='20')"
   ]
  }
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